Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(11,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.i (of order \(6\), 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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.8 | ||
Root | \(-3.09125i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.41 |
Dual form | 45.3.i.a.11.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67710 | − | 1.54563i | 1.33855 | − | 0.772813i | 0.351959 | − | 0.936015i | \(-0.385515\pi\) |
0.986593 | + | 0.163202i | \(0.0521822\pi\) | |||||||
\(3\) | −2.82138 | − | 1.01971i | −0.940461 | − | 0.339902i | ||||
\(4\) | 2.77793 | − | 4.81151i | 0.694481 | − | 1.20288i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.387298 | + | 0.223607i | ||||
\(6\) | −9.12922 | + | 1.63094i | −1.52154 | + | 0.271824i | ||||
\(7\) | 1.10296 | + | 1.91037i | 0.157565 | + | 0.272911i | 0.933990 | − | 0.357299i | \(-0.116302\pi\) |
−0.776425 | + | 0.630210i | \(0.782969\pi\) | |||||||
\(8\) | − | 4.80953i | − | 0.601191i | ||||||
\(9\) | 6.92040 | + | 5.75396i | 0.768933 | + | 0.639329i | ||||
\(10\) | 6.91225 | 0.691225 | ||||||||
\(11\) | −15.4454 | + | 8.91740i | −1.40413 | + | 0.810673i | −0.994813 | − | 0.101721i | \(-0.967565\pi\) |
−0.409313 | + | 0.912394i | \(0.634232\pi\) | |||||||
\(12\) | −12.7439 | + | 10.7424i | −1.06199 | + | 0.895203i | ||||
\(13\) | 1.25688 | − | 2.17697i | 0.0966828 | − | 0.167459i | −0.813627 | − | 0.581387i | \(-0.802510\pi\) |
0.910310 | + | 0.413928i | \(0.135843\pi\) | |||||||
\(14\) | 5.90545 | + | 3.40951i | 0.421818 | + | 0.243537i | ||||
\(15\) | −4.32352 | − | 5.12905i | −0.288234 | − | 0.341937i | ||||
\(16\) | 3.67796 | + | 6.37042i | 0.229873 | + | 0.398151i | ||||
\(17\) | − | 32.6026i | − | 1.91780i | −0.283746 | − | 0.958899i | \(-0.591577\pi\) | ||
0.283746 | − | 0.958899i | \(-0.408423\pi\) | |||||||
\(18\) | 27.4201 | + | 4.70761i | 1.52334 | + | 0.261534i | ||||
\(19\) | 7.93398 | 0.417578 | 0.208789 | − | 0.977961i | \(-0.433048\pi\) | ||||
0.208789 | + | 0.977961i | \(0.433048\pi\) | |||||||
\(20\) | 10.7589 | − | 6.21163i | 0.537943 | − | 0.310581i | ||||
\(21\) | −1.16384 | − | 6.51459i | −0.0554208 | − | 0.310218i | ||||
\(22\) | −27.5659 | + | 47.7456i | −1.25300 | + | 2.17026i | ||||
\(23\) | −18.4415 | − | 10.6472i | −0.801803 | − | 0.462921i | 0.0422985 | − | 0.999105i | \(-0.486532\pi\) |
−0.844101 | + | 0.536184i | \(0.819865\pi\) | |||||||
\(24\) | −4.90431 | + | 13.5695i | −0.204346 | + | 0.565397i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | − | 7.77065i | − | 0.298871i | ||||||
\(27\) | −13.6577 | − | 23.2909i | −0.505842 | − | 0.862626i | ||||
\(28\) | 12.2557 | 0.437704 | ||||||||
\(29\) | −30.7730 | + | 17.7668i | −1.06114 | + | 0.612647i | −0.925746 | − | 0.378145i | \(-0.876562\pi\) |
−0.135390 | + | 0.990792i | \(0.543229\pi\) | |||||||
\(30\) | −19.5021 | − | 7.04847i | −0.650070 | − | 0.234949i | ||||
\(31\) | −1.01221 | + | 1.75321i | −0.0326521 | + | 0.0565550i | −0.881890 | − | 0.471456i | \(-0.843729\pi\) |
0.849238 | + | 0.528011i | \(0.177062\pi\) | |||||||
\(32\) | 36.3533 | + | 20.9886i | 1.13604 | + | 0.655893i | ||||
\(33\) | 52.6705 | − | 9.40963i | 1.59608 | − | 0.285140i | ||||
\(34\) | −50.3914 | − | 87.2805i | −1.48210 | − | 2.56707i | ||||
\(35\) | 4.93257i | 0.140930i | ||||||||
\(36\) | 46.9096 | − | 17.3135i | 1.30304 | − | 0.480929i | ||||
\(37\) | 50.6833 | 1.36982 | 0.684909 | − | 0.728628i | \(-0.259842\pi\) | ||||
0.684909 | + | 0.728628i | \(0.259842\pi\) | |||||||
\(38\) | 21.2401 | − | 12.2630i | 0.558950 | − | 0.322710i | ||||
\(39\) | −5.76600 | + | 4.86043i | −0.147846 | + | 0.124626i | ||||
\(40\) | 5.37722 | − | 9.31361i | 0.134430 | − | 0.232840i | ||||
\(41\) | 4.65056 | + | 2.68500i | 0.113428 | + | 0.0654879i | 0.555641 | − | 0.831422i | \(-0.312473\pi\) |
−0.442213 | + | 0.896910i | \(0.645806\pi\) | |||||||
\(42\) | −13.1848 | − | 15.6414i | −0.313925 | − | 0.372414i | ||||
\(43\) | −7.76798 | − | 13.4545i | −0.180651 | − | 0.312896i | 0.761452 | − | 0.648222i | \(-0.224487\pi\) |
−0.942102 | + | 0.335326i | \(0.891154\pi\) | |||||||
\(44\) | 99.0875i | 2.25199i | ||||||||
\(45\) | 6.96816 | + | 18.8797i | 0.154848 | + | 0.419550i | ||||
\(46\) | −65.8263 | −1.43101 | ||||||||
\(47\) | −1.63440 | + | 0.943620i | −0.0347744 | + | 0.0200770i | −0.517286 | − | 0.855812i | \(-0.673058\pi\) |
0.482512 | + | 0.875889i | \(0.339724\pi\) | |||||||
\(48\) | −3.88098 | − | 21.7238i | −0.0808538 | − | 0.452580i | ||||
\(49\) | 22.0670 | − | 38.2211i | 0.450347 | − | 0.780023i | ||||
\(50\) | 13.3855 | + | 7.72813i | 0.267710 | + | 0.154563i | ||||
\(51\) | −33.2451 | + | 91.9843i | −0.651864 | + | 1.80361i | ||||
\(52\) | −6.98302 | − | 12.0949i | −0.134289 | − | 0.232595i | ||||
\(53\) | 62.0293i | 1.17036i | 0.810902 | + | 0.585182i | \(0.198977\pi\) | ||||
−0.810902 | + | 0.585182i | \(0.801023\pi\) | |||||||
\(54\) | −72.5622 | − | 41.2424i | −1.34374 | − | 0.763749i | ||||
\(55\) | −39.8798 | −0.725088 | ||||||||
\(56\) | 9.18800 | − | 5.30469i | 0.164071 | − | 0.0947267i | ||||
\(57\) | −22.3848 | − | 8.09033i | −0.392716 | − | 0.141936i | ||||
\(58\) | −54.9216 | + | 95.1270i | −0.946924 | + | 1.64012i | ||||
\(59\) | 31.3202 | + | 18.0827i | 0.530850 | + | 0.306487i | 0.741363 | − | 0.671105i | \(-0.234180\pi\) |
−0.210512 | + | 0.977591i | \(0.567513\pi\) | |||||||
\(60\) | −36.6889 | + | 6.55450i | −0.611482 | + | 0.109242i | ||||
\(61\) | 21.1242 | + | 36.5883i | 0.346299 | + | 0.599808i | 0.985589 | − | 0.169158i | \(-0.0541049\pi\) |
−0.639290 | + | 0.768966i | \(0.720772\pi\) | |||||||
\(62\) | 6.25802i | 0.100936i | ||||||||
\(63\) | −3.35934 | + | 19.5669i | −0.0533228 | + | 0.310586i | ||||
\(64\) | 100.338 | 1.56779 | ||||||||
\(65\) | 4.86786 | − | 2.81046i | 0.0748902 | − | 0.0432379i | ||||
\(66\) | 126.461 | − | 106.599i | 1.91607 | − | 1.61514i | ||||
\(67\) | 7.38738 | − | 12.7953i | 0.110259 | − | 0.190975i | −0.805615 | − | 0.592439i | \(-0.798165\pi\) |
0.915875 | + | 0.401464i | \(0.131498\pi\) | |||||||
\(68\) | −156.868 | − | 90.5675i | −2.30688 | − | 1.33188i | ||||
\(69\) | 41.1734 | + | 48.8446i | 0.596716 | + | 0.707893i | ||||
\(70\) | 7.62391 | + | 13.2050i | 0.108913 | + | 0.188643i | ||||
\(71\) | − | 105.070i | − | 1.47985i | −0.672687 | − | 0.739927i | \(-0.734860\pi\) | ||
0.672687 | − | 0.739927i | \(-0.265140\pi\) | |||||||
\(72\) | 27.6738 | − | 33.2838i | 0.384359 | − | 0.462276i | ||||
\(73\) | −66.9435 | −0.917034 | −0.458517 | − | 0.888686i | \(-0.651619\pi\) | ||||
−0.458517 | + | 0.888686i | \(0.651619\pi\) | |||||||
\(74\) | 135.684 | − | 78.3375i | 1.83357 | − | 1.05861i | ||||
\(75\) | −2.63800 | − | 14.7662i | −0.0351733 | − | 0.196883i | ||||
\(76\) | 22.0400 | − | 38.1744i | 0.290000 | − | 0.502295i | ||||
\(77\) | −34.0711 | − | 19.6710i | −0.442482 | − | 0.255467i | ||||
\(78\) | −7.92378 | + | 21.9240i | −0.101587 | + | 0.281076i | ||||
\(79\) | 34.5753 | + | 59.8862i | 0.437662 | + | 0.758053i | 0.997509 | − | 0.0705432i | \(-0.0224733\pi\) |
−0.559847 | + | 0.828596i | \(0.689140\pi\) | |||||||
\(80\) | 16.4484i | 0.205604i | ||||||||
\(81\) | 14.7838 | + | 79.6394i | 0.182516 | + | 0.983203i | ||||
\(82\) | 16.6001 | 0.202440 | ||||||||
\(83\) | −18.3844 | + | 10.6143i | −0.221499 | + | 0.127883i | −0.606644 | − | 0.794973i | \(-0.707485\pi\) |
0.385145 | + | 0.922856i | \(0.374151\pi\) | |||||||
\(84\) | −34.5780 | − | 12.4972i | −0.411643 | − | 0.148777i | ||||
\(85\) | 36.4508 | − | 63.1346i | 0.428833 | − | 0.742760i | ||||
\(86\) | −41.5914 | − | 24.0128i | −0.483621 | − | 0.279218i | ||||
\(87\) | 104.939 | − | 18.7475i | 1.20620 | − | 0.215488i | ||||
\(88\) | 42.8885 | + | 74.2850i | 0.487369 | + | 0.844148i | ||||
\(89\) | − | 7.16304i | − | 0.0804836i | −0.999190 | − | 0.0402418i | \(-0.987187\pi\) | ||
0.999190 | − | 0.0402418i | \(-0.0128128\pi\) | |||||||
\(90\) | 47.8355 | + | 39.7729i | 0.531506 | + | 0.441921i | ||||
\(91\) | 5.54511 | 0.0609353 | ||||||||
\(92\) | −102.458 | + | 59.1541i | −1.11367 | + | 0.642980i | ||||
\(93\) | 4.64360 | − | 3.91430i | 0.0499312 | − | 0.0420893i | ||||
\(94\) | −2.91697 | + | 5.05234i | −0.0310316 | + | 0.0537483i | ||||
\(95\) | 15.3641 | + | 8.87046i | 0.161727 | + | 0.0933733i | ||||
\(96\) | −81.1643 | − | 96.2865i | −0.845462 | − | 1.00298i | ||||
\(97\) | −55.6703 | − | 96.4238i | −0.573921 | − | 0.994060i | −0.996158 | − | 0.0875744i | \(-0.972088\pi\) |
0.422237 | − | 0.906485i | \(-0.361245\pi\) | |||||||
\(98\) | − | 136.429i | − | 1.39214i | ||||||
\(99\) | −158.199 | − | 27.1603i | −1.59797 | − | 0.274346i | ||||
\(100\) | 27.7793 | 0.277793 | ||||||||
\(101\) | 53.8621 | − | 31.0973i | 0.533288 | − | 0.307894i | −0.209066 | − | 0.977901i | \(-0.567042\pi\) |
0.742354 | + | 0.670008i | \(0.233709\pi\) | |||||||
\(102\) | 53.1730 | + | 297.636i | 0.521304 | + | 2.91800i | ||||
\(103\) | −27.5473 | + | 47.7133i | −0.267449 | + | 0.463236i | −0.968202 | − | 0.250168i | \(-0.919514\pi\) |
0.700753 | + | 0.713404i | \(0.252847\pi\) | |||||||
\(104\) | −10.4702 | − | 6.04498i | −0.100675 | − | 0.0581248i | ||||
\(105\) | 5.02977 | − | 13.9167i | 0.0479026 | − | 0.132540i | ||||
\(106\) | 95.8741 | + | 166.059i | 0.904473 | + | 1.56659i | ||||
\(107\) | − | 85.2584i | − | 0.796807i | −0.917210 | − | 0.398404i | \(-0.869564\pi\) | ||
0.917210 | − | 0.398404i | \(-0.130436\pi\) | |||||||
\(108\) | −150.005 | + | 1.01389i | −1.38893 | + | 0.00938785i | ||||
\(109\) | −64.0279 | −0.587412 | −0.293706 | − | 0.955896i | \(-0.594889\pi\) | ||||
−0.293706 | + | 0.955896i | \(0.594889\pi\) | |||||||
\(110\) | −106.762 | + | 61.6393i | −0.970568 | + | 0.560358i | ||||
\(111\) | −142.997 | − | 51.6821i | −1.28826 | − | 0.465604i | ||||
\(112\) | −8.11326 | + | 14.0526i | −0.0724398 | + | 0.125469i | ||||
\(113\) | 131.196 | + | 75.7460i | 1.16103 | + | 0.670319i | 0.951550 | − | 0.307495i | \(-0.0994908\pi\) |
0.209476 | + | 0.977814i | \(0.432824\pi\) | |||||||
\(114\) | −72.4311 | + | 12.9399i | −0.635360 | + | 0.113508i | ||||
\(115\) | −23.8078 | − | 41.2364i | −0.207025 | − | 0.358577i | ||||
\(116\) | 197.419i | 1.70189i | ||||||||
\(117\) | 21.2243 | − | 7.83350i | 0.181404 | − | 0.0669530i | ||||
\(118\) | 111.796 | 0.947428 | ||||||||
\(119\) | 62.2831 | − | 35.9592i | 0.523388 | − | 0.302178i | ||||
\(120\) | −24.6683 | + | 20.7941i | −0.205569 | + | 0.173284i | ||||
\(121\) | 98.5400 | − | 170.676i | 0.814380 | − | 1.41055i | ||||
\(122\) | 113.104 | + | 65.3004i | 0.927079 | + | 0.535249i | ||||
\(123\) | −10.3831 | − | 12.3176i | −0.0844155 | − | 0.100143i | ||||
\(124\) | 5.62371 | + | 9.74055i | 0.0453525 | + | 0.0785528i | ||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 21.2499 | + | 57.5750i | 0.168650 | + | 0.456944i | ||||
\(127\) | 42.9132 | 0.337899 | 0.168950 | − | 0.985625i | \(-0.445963\pi\) | ||||
0.168950 | + | 0.985625i | \(0.445963\pi\) | |||||||
\(128\) | 123.203 | − | 71.1313i | 0.962524 | − | 0.555713i | ||||
\(129\) | 8.19676 | + | 45.8814i | 0.0635408 | + | 0.355670i | ||||
\(130\) | 8.68785 | − | 15.0478i | 0.0668296 | − | 0.115752i | ||||
\(131\) | 52.6936 | + | 30.4227i | 0.402241 | + | 0.232234i | 0.687451 | − | 0.726231i | \(-0.258730\pi\) |
−0.285209 | + | 0.958465i | \(0.592063\pi\) | |||||||
\(132\) | 101.040 | − | 279.564i | 0.765456 | − | 2.11791i | ||||
\(133\) | 8.75083 | + | 15.1569i | 0.0657957 | + | 0.113961i | ||||
\(134\) | − | 45.6726i | − | 0.340840i | ||||||
\(135\) | −0.408060 | − | 60.3725i | −0.00302267 | − | 0.447203i | ||||
\(136\) | −156.803 | −1.15296 | ||||||||
\(137\) | −180.500 | + | 104.212i | −1.31752 | + | 0.760670i | −0.983329 | − | 0.181835i | \(-0.941796\pi\) |
−0.334191 | + | 0.942505i | \(0.608463\pi\) | |||||||
\(138\) | 185.721 | + | 67.1235i | 1.34581 | + | 0.486402i | ||||
\(139\) | −67.2445 | + | 116.471i | −0.483773 | + | 0.837919i | −0.999826 | − | 0.0186370i | \(-0.994067\pi\) |
0.516053 | + | 0.856556i | \(0.327401\pi\) | |||||||
\(140\) | 23.7331 | + | 13.7023i | 0.169522 | + | 0.0978736i | ||||
\(141\) | 5.57348 | − | 0.995707i | 0.0395282 | − | 0.00706175i | ||||
\(142\) | −162.398 | − | 281.282i | −1.14365 | − | 1.98086i | ||||
\(143\) | 44.8323i | 0.313512i | ||||||||
\(144\) | −11.2022 | + | 65.2487i | −0.0777931 | + | 0.453116i | ||||
\(145\) | −79.4554 | −0.547968 | ||||||||
\(146\) | −179.215 | + | 103.470i | −1.22750 | + | 0.708696i | ||||
\(147\) | −101.234 | + | 85.3346i | −0.688665 | + | 0.580507i | ||||
\(148\) | 140.794 | − | 243.863i | 0.951313 | − | 1.64772i | ||||
\(149\) | −105.245 | − | 60.7633i | −0.706343 | − | 0.407807i | 0.103363 | − | 0.994644i | \(-0.467040\pi\) |
−0.809705 | + | 0.586836i | \(0.800373\pi\) | |||||||
\(150\) | −29.8852 | − | 35.4533i | −0.199235 | − | 0.236356i | ||||
\(151\) | 21.0246 | + | 36.4156i | 0.139236 | + | 0.241163i | 0.927208 | − | 0.374548i | \(-0.122202\pi\) |
−0.787972 | + | 0.615711i | \(0.788869\pi\) | |||||||
\(152\) | − | 38.1587i | − | 0.251044i | ||||||
\(153\) | 187.594 | − | 225.623i | 1.22611 | − | 1.47466i | ||||
\(154\) | −121.616 | −0.789714 | ||||||||
\(155\) | −3.92029 | + | 2.26338i | −0.0252922 | + | 0.0146024i | ||||
\(156\) | 7.36847 | + | 41.2451i | 0.0472338 | + | 0.264391i | ||||
\(157\) | −46.7940 | + | 81.0497i | −0.298051 | + | 0.516240i | −0.975690 | − | 0.219155i | \(-0.929670\pi\) |
0.677639 | + | 0.735395i | \(0.263003\pi\) | |||||||
\(158\) | 185.123 | + | 106.881i | 1.17167 | + | 0.676462i | ||||
\(159\) | 63.2517 | − | 175.008i | 0.397809 | − | 1.10068i | ||||
\(160\) | 46.9319 | + | 81.2884i | 0.293324 | + | 0.508053i | ||||
\(161\) | − | 46.9735i | − | 0.291761i | ||||||
\(162\) | 162.671 | + | 190.353i | 1.00414 | + | 1.17502i | ||||
\(163\) | −115.792 | −0.710377 | −0.355189 | − | 0.934795i | \(-0.615583\pi\) | ||||
−0.355189 | + | 0.934795i | \(0.615583\pi\) | |||||||
\(164\) | 25.8378 | − | 14.9175i | 0.157548 | − | 0.0909602i | ||||
\(165\) | 112.516 | + | 40.6657i | 0.681917 | + | 0.246459i | ||||
\(166\) | −32.8114 | + | 56.8310i | −0.197659 | + | 0.342355i | ||||
\(167\) | −1.40886 | − | 0.813403i | −0.00843626 | − | 0.00487068i | 0.495776 | − | 0.868450i | \(-0.334884\pi\) |
−0.504212 | + | 0.863580i | \(0.668217\pi\) | |||||||
\(168\) | −31.3321 | + | 5.59751i | −0.186501 | + | 0.0333185i | ||||
\(169\) | 81.3405 | + | 140.886i | 0.481305 | + | 0.833645i | ||||
\(170\) | − | 225.357i | − | 1.32563i | ||||||
\(171\) | 54.9063 | + | 45.6518i | 0.321090 | + | 0.266970i | ||||
\(172\) | −86.3154 | −0.501834 | ||||||||
\(173\) | −104.098 | + | 60.1013i | −0.601725 | + | 0.347406i | −0.769720 | − | 0.638382i | \(-0.779604\pi\) |
0.167995 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(174\) | 251.956 | − | 212.386i | 1.44803 | − | 1.22061i | ||||
\(175\) | −5.51478 | + | 9.55187i | −0.0315130 | + | 0.0545821i | ||||
\(176\) | −113.615 | − | 65.5958i | −0.645541 | − | 0.372703i | ||||
\(177\) | −69.9271 | − | 82.9556i | −0.395068 | − | 0.468676i | ||||
\(178\) | −11.0714 | − | 19.1762i | −0.0621988 | − | 0.107732i | ||||
\(179\) | 157.742i | 0.881238i | 0.897694 | + | 0.440619i | \(0.145241\pi\) | ||||
−0.897694 | + | 0.440619i | \(0.854759\pi\) | |||||||
\(180\) | 110.197 | + | 18.9191i | 0.612206 | + | 0.105106i | ||||
\(181\) | −219.069 | −1.21033 | −0.605164 | − | 0.796101i | \(-0.706892\pi\) | ||||
−0.605164 | + | 0.796101i | \(0.706892\pi\) | |||||||
\(182\) | 14.8448 | − | 8.57068i | 0.0815651 | − | 0.0470916i | ||||
\(183\) | −22.2903 | − | 124.770i | −0.121805 | − | 0.681803i | ||||
\(184\) | −51.2079 | + | 88.6947i | −0.278304 | + | 0.482036i | ||||
\(185\) | 98.1478 | + | 56.6656i | 0.530528 | + | 0.306301i | ||||
\(186\) | 6.38134 | − | 17.6563i | 0.0343083 | − | 0.0949262i | ||||
\(187\) | 290.730 | + | 503.560i | 1.55471 | + | 2.69283i | ||||
\(188\) | 10.4852i | 0.0557725i | ||||||||
\(189\) | 29.4305 | − | 51.7802i | 0.155717 | − | 0.273969i | ||||
\(190\) | 54.8417 | 0.288641 | ||||||||
\(191\) | 321.773 | − | 185.776i | 1.68468 | − | 0.972648i | 0.726196 | − | 0.687488i | \(-0.241286\pi\) |
0.958480 | − | 0.285160i | \(-0.0920468\pi\) | |||||||
\(192\) | −283.093 | − | 102.316i | −1.47444 | − | 0.532894i | ||||
\(193\) | 19.7796 | − | 34.2593i | 0.102485 | − | 0.177509i | −0.810223 | − | 0.586122i | \(-0.800654\pi\) |
0.912708 | + | 0.408613i | \(0.133987\pi\) | |||||||
\(194\) | −298.070 | − | 172.091i | −1.53645 | − | 0.887067i | ||||
\(195\) | −16.5999 | + | 2.96559i | −0.0851279 | + | 0.0152082i | ||||
\(196\) | −122.601 | − | 212.351i | −0.625514 | − | 1.08342i | ||||
\(197\) | 104.454i | 0.530224i | 0.964218 | + | 0.265112i | \(0.0854089\pi\) | ||||
−0.964218 | + | 0.265112i | \(0.914591\pi\) | |||||||
\(198\) | −465.494 | + | 171.805i | −2.35098 | + | 0.867703i | ||||
\(199\) | 118.036 | 0.593147 | 0.296573 | − | 0.955010i | \(-0.404156\pi\) | ||||
0.296573 | + | 0.955010i | \(0.404156\pi\) | |||||||
\(200\) | 20.8259 | − | 12.0238i | 0.104129 | − | 0.0601191i | ||||
\(201\) | −33.8901 | + | 28.5675i | −0.168608 | + | 0.142127i | ||||
\(202\) | 96.1296 | − | 166.501i | 0.475889 | − | 0.824264i | ||||
\(203\) | −67.8824 | − | 39.1919i | −0.334396 | − | 0.193064i | ||||
\(204\) | 350.231 | + | 415.484i | 1.71682 | + | 2.03669i | ||||
\(205\) | 6.00385 | + | 10.3990i | 0.0292871 | + | 0.0507267i | ||||
\(206\) | 170.311i | 0.826754i | ||||||||
\(207\) | −66.3587 | − | 179.794i | −0.320574 | − | 0.868571i | ||||
\(208\) | 18.4910 | 0.0888990 | ||||||||
\(209\) | −122.543 | + | 70.7505i | −0.586332 | + | 0.338519i | ||||
\(210\) | −8.04474 | − | 45.0305i | −0.0383083 | − | 0.214431i | ||||
\(211\) | −68.1995 | + | 118.125i | −0.323220 | + | 0.559834i | −0.981151 | − | 0.193245i | \(-0.938099\pi\) |
0.657930 | + | 0.753079i | \(0.271432\pi\) | |||||||
\(212\) | 298.454 | + | 172.313i | 1.40780 | + | 0.812796i | ||||
\(213\) | −107.140 | + | 296.442i | −0.503005 | + | 1.39174i | ||||
\(214\) | −131.778 | − | 228.246i | −0.615783 | − | 1.06657i | ||||
\(215\) | − | 34.7395i | − | 0.161579i | ||||||
\(216\) | −112.018 | + | 65.6872i | −0.518603 | + | 0.304108i | ||||
\(217\) | −4.46571 | −0.0205793 | ||||||||
\(218\) | −171.409 | + | 98.9632i | −0.786282 | + | 0.453960i | ||||
\(219\) | 188.873 | + | 68.2627i | 0.862434 | + | 0.311702i | ||||
\(220\) | −110.783 | + | 191.882i | −0.503560 | + | 0.872191i | ||||
\(221\) | −70.9749 | − | 40.9774i | −0.321154 | − | 0.185418i | ||||
\(222\) | −462.699 | + | 82.6616i | −2.08423 | + | 0.372350i | ||||
\(223\) | −169.164 | − | 293.000i | −0.758581 | − | 1.31390i | −0.943574 | − | 0.331162i | \(-0.892559\pi\) |
0.184993 | − | 0.982740i | \(-0.440774\pi\) | |||||||
\(224\) | 92.5979i | 0.413383i | ||||||||
\(225\) | −7.61440 | + | 44.3511i | −0.0338418 | + | 0.197116i | ||||
\(226\) | 468.300 | 2.07212 | ||||||||
\(227\) | 132.851 | − | 76.7018i | 0.585248 | − | 0.337893i | −0.177968 | − | 0.984036i | \(-0.556952\pi\) |
0.763216 | + | 0.646143i | \(0.223619\pi\) | |||||||
\(228\) | −101.110 | + | 85.2303i | −0.443465 | + | 0.373817i | ||||
\(229\) | 126.688 | − | 219.430i | 0.553223 | − | 0.958210i | −0.444816 | − | 0.895622i | \(-0.646731\pi\) |
0.998039 | − | 0.0625886i | \(-0.0199356\pi\) | |||||||
\(230\) | −127.472 | − | 73.5960i | −0.554226 | − | 0.319983i | ||||
\(231\) | 76.0691 | + | 90.2419i | 0.329303 | + | 0.390658i | ||||
\(232\) | 85.4498 | + | 148.003i | 0.368318 | + | 0.637946i | ||||
\(233\) | 309.268i | 1.32733i | 0.748030 | + | 0.663664i | \(0.231000\pi\) | ||||
−0.748030 | + | 0.663664i | \(0.769000\pi\) | |||||||
\(234\) | 44.7120 | − | 53.7760i | 0.191077 | − | 0.229812i | ||||
\(235\) | −4.22000 | −0.0179574 | ||||||||
\(236\) | 174.010 | − | 100.465i | 0.737331 | − | 0.425698i | ||||
\(237\) | −36.4838 | − | 204.219i | −0.153940 | − | 0.861682i | ||||
\(238\) | 111.159 | − | 192.533i | 0.467055 | − | 0.808962i | ||||
\(239\) | −62.2034 | − | 35.9131i | −0.260265 | − | 0.150264i | 0.364190 | − | 0.931325i | \(-0.381346\pi\) |
−0.624456 | + | 0.781060i | \(0.714679\pi\) | |||||||
\(240\) | 16.7725 | − | 46.4071i | 0.0698854 | − | 0.193363i | ||||
\(241\) | −151.480 | − | 262.370i | −0.628546 | − | 1.08867i | −0.987844 | − | 0.155451i | \(-0.950317\pi\) |
0.359297 | − | 0.933223i | \(-0.383016\pi\) | |||||||
\(242\) | − | 609.224i | − | 2.51746i | ||||||
\(243\) | 39.4981 | − | 239.768i | 0.162544 | − | 0.986701i | ||||
\(244\) | 234.726 | 0.961993 | ||||||||
\(245\) | 85.4650 | − | 49.3433i | 0.348837 | − | 0.201401i | ||||
\(246\) | −46.8351 | − | 16.9272i | −0.190387 | − | 0.0688097i | ||||
\(247\) | 9.97203 | − | 17.2721i | 0.0403726 | − | 0.0699274i | ||||
\(248\) | 8.43209 | + | 4.86827i | 0.0340004 | + | 0.0196301i | ||||
\(249\) | 62.6930 | − | 11.2002i | 0.251779 | − | 0.0449806i | ||||
\(250\) | 17.2806 | + | 29.9309i | 0.0691225 | + | 0.119724i | ||||
\(251\) | 108.551i | 0.432476i | 0.976341 | + | 0.216238i | \(0.0693787\pi\) | ||||
−0.976341 | + | 0.216238i | \(0.930621\pi\) | |||||||
\(252\) | 84.8144 | + | 70.5189i | 0.336565 | + | 0.279837i | ||||
\(253\) | 379.781 | 1.50111 | ||||||||
\(254\) | 114.883 | − | 66.3278i | 0.452296 | − | 0.261133i | ||||
\(255\) | −167.220 | + | 140.958i | −0.655766 | + | 0.552776i | ||||
\(256\) | 19.2083 | − | 33.2697i | 0.0750323 | − | 0.129960i | ||||
\(257\) | −86.8847 | − | 50.1629i | −0.338073 | − | 0.195186i | 0.321347 | − | 0.946962i | \(-0.395865\pi\) |
−0.659419 | + | 0.751775i | \(0.729198\pi\) | |||||||
\(258\) | 92.8592 | + | 110.160i | 0.359919 | + | 0.426978i | ||||
\(259\) | 55.9014 | + | 96.8241i | 0.215836 | + | 0.373838i | ||||
\(260\) | − | 31.2290i | − | 0.120112i | ||||||
\(261\) | −315.190 | − | 54.1133i | −1.20763 | − | 0.207331i | ||||
\(262\) | 188.088 | 0.717895 | ||||||||
\(263\) | 373.654 | − | 215.729i | 1.42074 | − | 0.820264i | 0.424377 | − | 0.905486i | \(-0.360493\pi\) |
0.996362 | + | 0.0852214i | \(0.0271598\pi\) | |||||||
\(264\) | −45.2559 | − | 253.320i | −0.171424 | − | 0.959546i | ||||
\(265\) | −69.3508 | + | 120.119i | −0.261701 | + | 0.453280i | ||||
\(266\) | 46.8538 | + | 27.0510i | 0.176142 | + | 0.101696i | ||||
\(267\) | −7.30420 | + | 20.2097i | −0.0273566 | + | 0.0756917i | ||||
\(268\) | −41.0432 | − | 71.0889i | −0.153146 | − | 0.265257i | ||||
\(269\) | − | 233.075i | − | 0.866448i | −0.901286 | − | 0.433224i | \(-0.857376\pi\) | ||
0.901286 | − | 0.433224i | \(-0.142624\pi\) | |||||||
\(270\) | −94.4057 | − | 160.993i | −0.349651 | − | 0.596269i | ||||
\(271\) | 388.155 | 1.43230 | 0.716152 | − | 0.697944i | \(-0.245902\pi\) | ||||
0.716152 | + | 0.697944i | \(0.245902\pi\) | |||||||
\(272\) | 207.692 | − | 119.911i | 0.763574 | − | 0.440850i | ||||
\(273\) | −15.6449 | − | 5.65439i | −0.0573073 | − | 0.0207120i | ||||
\(274\) | −322.145 | + | 557.972i | −1.17571 | + | 2.03639i | ||||
\(275\) | −77.2269 | − | 44.5870i | −0.280825 | − | 0.162135i | ||||
\(276\) | 349.393 | − | 62.4194i | 1.26592 | − | 0.226157i | ||||
\(277\) | −17.9546 | − | 31.0983i | −0.0648182 | − | 0.112268i | 0.831795 | − | 0.555083i | \(-0.187313\pi\) |
−0.896613 | + | 0.442814i | \(0.853980\pi\) | |||||||
\(278\) | 415.739i | 1.49547i | ||||||||
\(279\) | −17.0928 | + | 6.30864i | −0.0612645 | + | 0.0226116i | ||||
\(280\) | 23.7233 | 0.0847261 | ||||||||
\(281\) | −261.015 | + | 150.697i | −0.928879 | + | 0.536289i | −0.886457 | − | 0.462811i | \(-0.846841\pi\) |
−0.0424222 | + | 0.999100i | \(0.513507\pi\) | |||||||
\(282\) | 13.3818 | − | 11.2801i | 0.0474531 | − | 0.0400005i | ||||
\(283\) | −212.734 | + | 368.467i | −0.751712 | + | 1.30200i | 0.195281 | + | 0.980747i | \(0.437438\pi\) |
−0.946993 | + | 0.321255i | \(0.895895\pi\) | |||||||
\(284\) | −505.543 | − | 291.875i | −1.78008 | − | 1.02773i | ||||
\(285\) | −34.3027 | − | 40.6938i | −0.120360 | − | 0.142785i | ||||
\(286\) | 69.2940 | + | 120.021i | 0.242287 | + | 0.419653i | ||||
\(287\) | 11.8458i | 0.0412744i | ||||||||
\(288\) | 130.812 | + | 354.425i | 0.454207 | + | 1.23064i | ||||
\(289\) | −773.928 | −2.67795 | ||||||||
\(290\) | −212.710 | + | 122.808i | −0.733484 | + | 0.423477i | ||||
\(291\) | 58.7432 | + | 328.816i | 0.201867 | + | 1.12995i | ||||
\(292\) | −185.964 | + | 322.099i | −0.636863 | + | 1.10308i | ||||
\(293\) | −332.917 | − | 192.210i | −1.13624 | − | 0.656006i | −0.190740 | − | 0.981641i | \(-0.561089\pi\) |
−0.945496 | + | 0.325635i | \(0.894422\pi\) | |||||||
\(294\) | −139.118 | + | 384.919i | −0.473190 | + | 1.30925i | ||||
\(295\) | 40.4342 | + | 70.0340i | 0.137065 | + | 0.237403i | ||||
\(296\) | − | 243.763i | − | 0.823523i | ||||||
\(297\) | 418.643 | + | 237.946i | 1.40957 | + | 0.801164i | ||||
\(298\) | −375.669 | −1.26064 | ||||||||
\(299\) | −46.3573 | + | 26.7644i | −0.155041 | + | 0.0895130i | ||||
\(300\) | −78.3759 | − | 28.3267i | −0.261253 | − | 0.0944223i | ||||
\(301\) | 17.1355 | − | 29.6795i | 0.0569285 | − | 0.0986030i | ||||
\(302\) | 112.570 | + | 64.9923i | 0.372748 | + | 0.215206i | ||||
\(303\) | −183.676 | + | 32.8138i | −0.606190 | + | 0.108296i | ||||
\(304\) | 29.1809 | + | 50.5428i | 0.0959898 | + | 0.166259i | ||||
\(305\) | 94.4705i | 0.309739i | ||||||||
\(306\) | 153.480 | − | 893.966i | 0.501569 | − | 2.92146i | ||||
\(307\) | −130.907 | −0.426407 | −0.213204 | − | 0.977008i | \(-0.568390\pi\) | ||||
−0.213204 | + | 0.977008i | \(0.568390\pi\) | |||||||
\(308\) | −189.294 | + | 109.289i | −0.614592 | + | 0.354835i | ||||
\(309\) | 126.375 | − | 106.527i | 0.408981 | − | 0.344749i | ||||
\(310\) | −6.99668 | + | 12.1186i | −0.0225699 | + | 0.0390923i | ||||
\(311\) | 486.453 | + | 280.854i | 1.56416 | + | 0.903066i | 0.996829 | + | 0.0795736i | \(0.0253559\pi\) |
0.567327 | + | 0.823492i | \(0.307977\pi\) | |||||||
\(312\) | 23.3764 | + | 27.7317i | 0.0749243 | + | 0.0888838i | ||||
\(313\) | −20.2397 | − | 35.0562i | −0.0646636 | − | 0.112001i | 0.831881 | − | 0.554954i | \(-0.187264\pi\) |
−0.896545 | + | 0.442953i | \(0.853931\pi\) | |||||||
\(314\) | 289.305i | 0.921352i | ||||||||
\(315\) | −28.3818 | + | 34.1353i | −0.0901010 | + | 0.108366i | ||||
\(316\) | 384.190 | 1.21579 | ||||||||
\(317\) | −113.107 | + | 65.3025i | −0.356805 | + | 0.206001i | −0.667678 | − | 0.744450i | \(-0.732712\pi\) |
0.310873 | + | 0.950451i | \(0.399379\pi\) | |||||||
\(318\) | −101.166 | − | 566.279i | −0.318133 | − | 1.78075i | ||||
\(319\) | 316.867 | − | 548.829i | 0.993313 | − | 1.72047i | ||||
\(320\) | 194.304 | + | 112.182i | 0.607201 | + | 0.350568i | ||||
\(321\) | −86.9385 | + | 240.546i | −0.270836 | + | 0.749366i | ||||
\(322\) | −72.6034 | − | 125.753i | −0.225477 | − | 0.390537i | ||||
\(323\) | − | 258.668i | − | 0.800831i | ||||||
\(324\) | 424.254 | + | 150.100i | 1.30943 | + | 0.463272i | ||||
\(325\) | 12.5688 | 0.0386731 | ||||||||
\(326\) | −309.986 | + | 178.971i | −0.950877 | + | 0.548989i | ||||
\(327\) | 180.647 | + | 65.2897i | 0.552438 | + | 0.199663i | ||||
\(328\) | 12.9136 | − | 22.3670i | 0.0393707 | − | 0.0681921i | ||||
\(329\) | −3.60534 | − | 2.08154i | −0.0109585 | − | 0.00632687i | ||||
\(330\) | 364.072 | − | 65.0418i | 1.10325 | − | 0.197096i | ||||
\(331\) | −245.341 | − | 424.944i | −0.741213 | − | 1.28382i | −0.951943 | − | 0.306274i | \(-0.900918\pi\) |
0.210730 | − | 0.977544i | \(-0.432416\pi\) | |||||||
\(332\) | 117.943i | 0.355249i | ||||||||
\(333\) | 350.748 | + | 291.630i | 1.05330 | + | 0.875765i | ||||
\(334\) | −5.02887 | −0.0150565 | ||||||||
\(335\) | 28.6112 | − | 16.5187i | 0.0854066 | − | 0.0493095i | ||||
\(336\) | 37.2201 | − | 31.3746i | 0.110774 | − | 0.0933767i | ||||
\(337\) | 55.9933 | − | 96.9833i | 0.166152 | − | 0.287784i | −0.770912 | − | 0.636942i | \(-0.780199\pi\) |
0.937064 | + | 0.349158i | \(0.113532\pi\) | |||||||
\(338\) | 435.514 | + | 251.444i | 1.28850 | + | 0.743918i | ||||
\(339\) | −292.915 | − | 347.490i | −0.864056 | − | 1.02504i | ||||
\(340\) | −202.515 | − | 350.767i | −0.595633 | − | 1.03167i | ||||
\(341\) | − | 36.1053i | − | 0.105881i | ||||||
\(342\) | 217.551 | + | 37.3501i | 0.636113 | + | 0.109211i | ||||
\(343\) | 205.445 | 0.598966 | ||||||||
\(344\) | −64.7099 | + | 37.3603i | −0.188110 | + | 0.108606i | ||||
\(345\) | 25.1220 | + | 140.621i | 0.0728174 | + | 0.407596i | ||||
\(346\) | −185.788 | + | 321.795i | −0.536960 | + | 0.930042i | ||||
\(347\) | 170.190 | + | 98.2592i | 0.490461 | + | 0.283168i | 0.724766 | − | 0.688995i | \(-0.241948\pi\) |
−0.234305 | + | 0.972163i | \(0.575281\pi\) | |||||||
\(348\) | 201.309 | − | 556.995i | 0.578476 | − | 1.60056i | ||||
\(349\) | 109.579 | + | 189.797i | 0.313981 | + | 0.543832i | 0.979220 | − | 0.202799i | \(-0.0650037\pi\) |
−0.665239 | + | 0.746630i | \(0.731670\pi\) | |||||||
\(350\) | 34.0951i | 0.0974147i | ||||||||
\(351\) | −67.8698 | + | 0.458735i | −0.193361 | + | 0.00130694i | ||||
\(352\) | −748.654 | −2.12686 | ||||||||
\(353\) | 219.479 | − | 126.717i | 0.621755 | − | 0.358970i | −0.155797 | − | 0.987789i | \(-0.549795\pi\) |
0.777552 | + | 0.628819i | \(0.216461\pi\) | |||||||
\(354\) | −315.421 | − | 114.000i | −0.891019 | − | 0.322033i | ||||
\(355\) | 117.471 | − | 203.466i | 0.330905 | − | 0.573145i | ||||
\(356\) | −34.4650 | − | 19.8984i | −0.0968119 | − | 0.0558944i | ||||
\(357\) | −212.392 | + | 37.9441i | −0.594937 | + | 0.106286i | ||||
\(358\) | 243.810 | + | 422.290i | 0.681032 | + | 1.17958i | ||||
\(359\) | − | 152.604i | − | 0.425081i | −0.977152 | − | 0.212540i | \(-0.931826\pi\) | ||
0.977152 | − | 0.212540i | \(-0.0681737\pi\) | |||||||
\(360\) | 90.8026 | − | 33.5136i | 0.252230 | − | 0.0930933i | ||||
\(361\) | −298.052 | −0.825629 | ||||||||
\(362\) | −586.471 | + | 338.599i | −1.62009 | + | 0.935357i | ||||
\(363\) | −452.059 | + | 381.061i | −1.24534 | + | 1.04976i | ||||
\(364\) | 15.4039 | − | 26.6804i | 0.0423184 | − | 0.0732977i | ||||
\(365\) | −129.635 | − | 74.8451i | −0.355166 | − | 0.205055i | ||||
\(366\) | −252.521 | − | 299.570i | −0.689949 | − | 0.818497i | ||||
\(367\) | −174.997 | − | 303.104i | −0.476832 | − | 0.825897i | 0.522816 | − | 0.852446i | \(-0.324882\pi\) |
−0.999648 | + | 0.0265489i | \(0.991548\pi\) | |||||||
\(368\) | − | 156.640i | − | 0.425652i | ||||||
\(369\) | 16.7343 | + | 45.3405i | 0.0453505 | + | 0.122874i | ||||
\(370\) | 350.336 | 0.946853 | ||||||||
\(371\) | −118.499 | + | 68.4155i | −0.319405 | + | 0.184408i | ||||
\(372\) | −5.93413 | − | 33.2163i | −0.0159520 | − | 0.0892913i | ||||
\(373\) | 202.998 | − | 351.603i | 0.544231 | − | 0.942636i | −0.454424 | − | 0.890786i | \(-0.650155\pi\) |
0.998655 | − | 0.0518506i | \(-0.0165119\pi\) | |||||||
\(374\) | 1556.63 | + | 898.721i | 4.16211 | + | 2.40300i | ||||
\(375\) | 11.4007 | − | 31.5440i | 0.0304018 | − | 0.0841174i | ||||
\(376\) | 4.53837 | + | 7.86068i | 0.0120701 | + | 0.0209061i | ||||
\(377\) | 89.3225i | 0.236930i | ||||||||
\(378\) | −1.24441 | − | 184.110i | −0.00329208 | − | 0.487062i | ||||
\(379\) | 410.698 | 1.08364 | 0.541818 | − | 0.840496i | \(-0.317736\pi\) | ||||
0.541818 | + | 0.840496i | \(0.317736\pi\) | |||||||
\(380\) | 85.3606 | − | 49.2830i | 0.224633 | − | 0.129692i | ||||
\(381\) | −121.074 | − | 43.7588i | −0.317781 | − | 0.114853i | ||||
\(382\) | 574.280 | − | 994.682i | 1.50335 | − | 2.60388i | ||||
\(383\) | −421.457 | − | 243.328i | −1.10041 | − | 0.635322i | −0.164081 | − | 0.986447i | \(-0.552466\pi\) |
−0.936329 | + | 0.351125i | \(0.885799\pi\) | |||||||
\(384\) | −420.136 | + | 75.0577i | −1.09410 | + | 0.195463i | ||||
\(385\) | −43.9857 | − | 76.1854i | −0.114248 | − | 0.197884i | ||||
\(386\) | − | 122.288i | − | 0.316807i | ||||||
\(387\) | 23.6594 | − | 137.807i | 0.0611354 | − | 0.356091i | ||||
\(388\) | −618.592 | −1.59431 | ||||||||
\(389\) | 553.846 | − | 319.763i | 1.42377 | − | 0.822013i | 0.427150 | − | 0.904181i | \(-0.359518\pi\) |
0.996619 | + | 0.0821675i | \(0.0261842\pi\) | |||||||
\(390\) | −39.8561 | + | 33.5965i | −0.102195 | + | 0.0861449i | ||||
\(391\) | −347.126 | + | 601.239i | −0.887789 | + | 1.53770i | ||||
\(392\) | −183.826 | − | 106.132i | −0.468943 | − | 0.270744i | ||||
\(393\) | −117.647 | − | 139.566i | −0.299355 | − | 0.355130i | ||||
\(394\) | 161.447 | + | 279.634i | 0.409764 | + | 0.709732i | ||||
\(395\) | 154.625i | 0.391457i | ||||||||
\(396\) | −570.146 | + | 685.725i | −1.43976 | + | 1.73163i | ||||
\(397\) | 295.328 | 0.743899 | 0.371950 | − | 0.928253i | \(-0.378689\pi\) | ||||
0.371950 | + | 0.928253i | \(0.378689\pi\) | |||||||
\(398\) | 315.995 | − | 182.440i | 0.793958 | − | 0.458392i | ||||
\(399\) | −9.23386 | − | 51.6866i | −0.0231425 | − | 0.129540i | ||||
\(400\) | −18.3898 | + | 31.8521i | −0.0459746 | + | 0.0796303i | ||||
\(401\) | 35.9199 | + | 20.7384i | 0.0895758 | + | 0.0517166i | 0.544119 | − | 0.839008i | \(-0.316864\pi\) |
−0.454543 | + | 0.890725i | \(0.650197\pi\) | |||||||
\(402\) | −46.5726 | + | 128.860i | −0.115852 | + | 0.320547i | ||||
\(403\) | 2.54446 | + | 4.40713i | 0.00631378 | + | 0.0109358i | ||||
\(404\) | − | 345.544i | − | 0.855306i | ||||||
\(405\) | −60.4109 | + | 170.750i | −0.149163 | + | 0.421605i | ||||
\(406\) | −242.304 | −0.596809 | ||||||||
\(407\) | −782.823 | + | 451.963i | −1.92340 | + | 1.11047i | ||||
\(408\) | 442.401 | + | 159.893i | 1.08432 | + | 0.391895i | ||||
\(409\) | −10.4599 | + | 18.1170i | −0.0255742 | + | 0.0442959i | −0.878529 | − | 0.477689i | \(-0.841475\pi\) |
0.852955 | + | 0.521984i | \(0.174808\pi\) | |||||||
\(410\) | 32.1459 | + | 18.5594i | 0.0784046 | + | 0.0452669i | ||||
\(411\) | 615.526 | − | 109.964i | 1.49763 | − | 0.267553i | ||||
\(412\) | 153.049 | + | 265.088i | 0.371477 | + | 0.643417i | ||||
\(413\) | 79.7777i | 0.193166i | ||||||||
\(414\) | −455.544 | − | 378.762i | −1.10035 | − | 0.914884i | ||||
\(415\) | −47.4684 | −0.114382 | ||||||||
\(416\) | 91.3832 | − | 52.7601i | 0.219671 | − | 0.126827i | ||||
\(417\) | 308.488 | − | 260.039i | 0.739780 | − | 0.623595i | ||||
\(418\) | −218.708 | + | 378.813i | −0.523224 | + | 0.906251i | ||||
\(419\) | −360.820 | − | 208.319i | −0.861145 | − | 0.497182i | 0.00325066 | − | 0.999995i | \(-0.498965\pi\) |
−0.864395 | + | 0.502813i | \(0.832299\pi\) | |||||||
\(420\) | −52.9878 | − | 62.8602i | −0.126161 | − | 0.149667i | ||||
\(421\) | −167.096 | − | 289.420i | −0.396904 | − | 0.687457i | 0.596438 | − | 0.802659i | \(-0.296582\pi\) |
−0.993342 | + | 0.115201i | \(0.963249\pi\) | |||||||
\(422\) | 421.644i | 0.999156i | ||||||||
\(423\) | −16.7402 | − | 2.87404i | −0.0395750 | − | 0.00679442i | ||||
\(424\) | 298.332 | 0.703612 | ||||||||
\(425\) | 141.173 | − | 81.5064i | 0.332172 | − | 0.191780i | ||||
\(426\) | 171.363 | + | 959.204i | 0.402260 | + | 2.25165i | ||||
\(427\) | −46.5982 | + | 80.7104i | −0.109129 | + | 0.189017i | ||||
\(428\) | −410.221 | − | 236.841i | −0.958461 | − | 0.553368i | ||||
\(429\) | 45.7158 | − | 126.489i | 0.106564 | − | 0.294846i | ||||
\(430\) | −53.6942 | − | 93.0011i | −0.124870 | − | 0.216282i | ||||
\(431\) | − | 389.685i | − | 0.904142i | −0.891982 | − | 0.452071i | \(-0.850685\pi\) | ||
0.891982 | − | 0.452071i | \(-0.149315\pi\) | |||||||
\(432\) | 98.1402 | − | 172.669i | 0.227176 | − | 0.399696i | ||||
\(433\) | 742.678 | 1.71519 | 0.857596 | − | 0.514324i | \(-0.171957\pi\) | ||||
0.857596 | + | 0.514324i | \(0.171957\pi\) | |||||||
\(434\) | −11.9552 | + | 6.90232i | −0.0275465 | + | 0.0159040i | ||||
\(435\) | 224.174 | + | 81.0212i | 0.515343 | + | 0.186256i | ||||
\(436\) | −177.865 | + | 308.071i | −0.407947 | + | 0.706584i | ||||
\(437\) | −146.314 | − | 84.4745i | −0.334815 | − | 0.193306i | ||||
\(438\) | 611.142 | − | 109.181i | 1.39530 | − | 0.249272i | ||||
\(439\) | 110.831 | + | 191.965i | 0.252462 | + | 0.437277i | 0.964203 | − | 0.265165i | \(-0.0854264\pi\) |
−0.711741 | + | 0.702442i | \(0.752093\pi\) | |||||||
\(440\) | 191.803i | 0.435916i | ||||||||
\(441\) | 372.635 | − | 137.533i | 0.844978 | − | 0.311866i | ||||
\(442\) | −253.343 | −0.573174 | ||||||||
\(443\) | −151.065 | + | 87.2171i | −0.341003 | + | 0.196878i | −0.660716 | − | 0.750636i | \(-0.729747\pi\) |
0.319712 | + | 0.947515i | \(0.396414\pi\) | |||||||
\(444\) | −645.903 | + | 544.462i | −1.45474 | + | 1.22627i | ||||
\(445\) | 8.00853 | − | 13.8712i | 0.0179967 | − | 0.0311712i | ||||
\(446\) | −905.737 | − | 522.928i | −2.03080 | − | 1.17248i | ||||
\(447\) | 234.976 | + | 278.756i | 0.525673 | + | 0.623614i | ||||
\(448\) | 110.669 | + | 191.684i | 0.247028 | + | 0.427866i | ||||
\(449\) | 317.066i | 0.706161i | 0.935593 | + | 0.353080i | \(0.114866\pi\) | ||||
−0.935593 | + | 0.353080i | \(0.885134\pi\) | |||||||
\(450\) | 48.1657 | + | 130.502i | 0.107035 | + | 0.290003i | ||||
\(451\) | −95.7730 | −0.212357 | ||||||||
\(452\) | 728.905 | − | 420.833i | 1.61262 | − | 0.931047i | ||||
\(453\) | −22.1851 | − | 124.181i | −0.0489738 | − | 0.274131i | ||||
\(454\) | 237.105 | − | 410.677i | 0.522257 | − | 0.904575i | ||||
\(455\) | 10.7381 | + | 6.19962i | 0.0236001 | + | 0.0136255i | ||||
\(456\) | −38.9107 | + | 107.660i | −0.0853304 | + | 0.236097i | ||||
\(457\) | 247.622 | + | 428.893i | 0.541842 | + | 0.938497i | 0.998798 | + | 0.0490082i | \(0.0156060\pi\) |
−0.456957 | + | 0.889489i | \(0.651061\pi\) | |||||||
\(458\) | − | 783.250i | − | 1.71015i | ||||||
\(459\) | −759.344 | + | 445.277i | −1.65434 | + | 0.970103i | ||||
\(460\) | −264.545 | −0.575099 | ||||||||
\(461\) | −185.857 | + | 107.304i | −0.403160 | + | 0.232764i | −0.687846 | − | 0.725856i | \(-0.741444\pi\) |
0.284687 | + | 0.958621i | \(0.408110\pi\) | |||||||
\(462\) | 343.125 | + | 124.013i | 0.742695 | + | 0.268426i | ||||
\(463\) | −210.893 | + | 365.277i | −0.455492 | + | 0.788935i | −0.998716 | − | 0.0506528i | \(-0.983870\pi\) |
0.543225 | + | 0.839587i | \(0.317203\pi\) | |||||||
\(464\) | −226.364 | − | 130.691i | −0.487853 | − | 0.281662i | ||||
\(465\) | 13.3686 | − | 2.38832i | 0.0287497 | − | 0.00513616i | ||||
\(466\) | 478.012 | + | 827.942i | 1.02578 | + | 1.77670i | ||||
\(467\) | 123.800i | 0.265097i | 0.991177 | + | 0.132549i | \(0.0423160\pi\) | ||||
−0.991177 | + | 0.132549i | \(0.957684\pi\) | |||||||
\(468\) | 21.2686 | − | 123.882i | 0.0454457 | − | 0.264705i | ||||
\(469\) | 32.5918 | 0.0694922 | ||||||||
\(470\) | −11.2974 | + | 6.52254i | −0.0240370 | + | 0.0138777i | ||||
\(471\) | 214.671 | − | 180.956i | 0.455777 | − | 0.384195i | ||||
\(472\) | 86.9693 | − | 150.635i | 0.184257 | − | 0.319142i | ||||
\(473\) | 239.959 | + | 138.540i | 0.507313 | + | 0.292897i | ||||
\(474\) | −413.317 | − | 490.324i | −0.871976 | − | 1.03444i | ||||
\(475\) | 19.8350 | + | 34.3552i | 0.0417578 | + | 0.0723266i | ||||
\(476\) | − | 399.568i | − | 0.839428i | ||||||
\(477\) | −356.914 | + | 429.267i | −0.748248 | + | 0.899931i | ||||
\(478\) | −222.033 | −0.464505 | ||||||||
\(479\) | −581.609 | + | 335.792i | −1.21421 | + | 0.701027i | −0.963675 | − | 0.267079i | \(-0.913941\pi\) |
−0.250540 | + | 0.968106i | \(0.580608\pi\) | |||||||
\(480\) | −49.5225 | − | 277.202i | −0.103172 | − | 0.577505i | ||||
\(481\) | 63.7026 | − | 110.336i | 0.132438 | − | 0.229389i | ||||
\(482\) | −811.054 | − | 468.262i | −1.68268 | − | 0.971498i | ||||
\(483\) | −47.8991 | + | 132.530i | −0.0991701 | + | 0.274389i | ||||
\(484\) | −547.474 | − | 948.252i | −1.13114 | − | 1.95920i | ||||
\(485\) | − | 248.965i | − | 0.513330i | ||||||
\(486\) | −264.852 | − | 702.934i | −0.544963 | − | 1.44637i | ||||
\(487\) | 134.773 | 0.276742 | 0.138371 | − | 0.990380i | \(-0.455813\pi\) | ||||
0.138371 | + | 0.990380i | \(0.455813\pi\) | |||||||
\(488\) | 175.972 | − | 101.598i | 0.360599 | − | 0.208192i | ||||
\(489\) | 326.692 | + | 118.073i | 0.668082 | + | 0.241459i | ||||
\(490\) | 152.533 | − | 264.194i | 0.311291 | − | 0.539172i | ||||
\(491\) | 411.108 | + | 237.353i | 0.837288 | + | 0.483408i | 0.856341 | − | 0.516410i | \(-0.172732\pi\) |
−0.0190536 | + | 0.999818i | \(0.506065\pi\) | |||||||
\(492\) | −88.1099 | + | 15.7409i | −0.179085 | + | 0.0319937i | ||||
\(493\) | 579.243 | + | 1003.28i | 1.17493 | + | 2.03505i | ||||
\(494\) | − | 61.6522i | − | 0.124802i | ||||||
\(495\) | −275.984 | − | 229.467i | −0.557544 | − | 0.463570i | ||||
\(496\) | −14.8915 | −0.0300233 | ||||||||
\(497\) | 200.722 | − | 115.887i | 0.403868 | − | 0.233173i | ||||
\(498\) | 150.524 | − | 126.884i | 0.302258 | − | 0.254787i | ||||
\(499\) | −279.196 | + | 483.582i | −0.559511 | + | 0.969102i | 0.438026 | + | 0.898962i | \(0.355678\pi\) |
−0.997537 | + | 0.0701394i | \(0.977656\pi\) | |||||||
\(500\) | 53.7943 | + | 31.0581i | 0.107589 | + | 0.0621163i | ||||
\(501\) | 3.14549 | + | 3.73154i | 0.00627842 | + | 0.00744819i | ||||
\(502\) | 167.780 | + | 290.603i | 0.334223 | + | 0.578891i | ||||
\(503\) | − | 681.680i | − | 1.35523i | −0.735417 | − | 0.677614i | \(-0.763014\pi\) | ||
0.735417 | − | 0.677614i | \(-0.236986\pi\) | |||||||
\(504\) | 94.1076 | + | 16.1568i | 0.186721 | + | 0.0320572i | ||||
\(505\) | 139.071 | 0.275389 | ||||||||
\(506\) | 1016.71 | − | 586.999i | 2.00931 | − | 1.16008i | ||||
\(507\) | −85.8304 | − | 480.437i | −0.169291 | − | 0.947607i | ||||
\(508\) | 119.210 | − | 206.477i | 0.234665 | − | 0.406451i | ||||
\(509\) | 462.890 | + | 267.250i | 0.909412 | + | 0.525049i | 0.880242 | − | 0.474525i | \(-0.157380\pi\) |
0.0291697 | + | 0.999574i | \(0.490714\pi\) | |||||||
\(510\) | −229.798 | + | 635.819i | −0.450585 | + | 1.24670i | ||||
\(511\) | −73.8357 | − | 127.887i | −0.144492 | − | 0.250268i | ||||
\(512\) | 450.295i | 0.879483i | ||||||||
\(513\) | −108.360 | − | 184.790i | −0.211228 | − | 0.360214i | ||||
\(514\) | −310.133 | −0.603371 | ||||||||
\(515\) | −106.690 | + | 61.5976i | −0.207165 | + | 0.119607i | ||||
\(516\) | 243.529 | + | 88.0164i | 0.471955 | + | 0.170574i | ||||
\(517\) | 16.8293 | − | 29.1492i | 0.0325518 | − | 0.0563813i | ||||
\(518\) | 299.308 | + | 172.805i | 0.577814 | + | 0.333601i | ||||
\(519\) | 354.987 | − | 63.4188i | 0.683983 | − | 0.122194i | ||||
\(520\) | −13.5170 | − | 23.4121i | −0.0259942 | − | 0.0450233i | ||||
\(521\) | 352.483i | 0.676552i | 0.941047 | + | 0.338276i | \(0.109844\pi\) | ||||
−0.941047 | + | 0.338276i | \(0.890156\pi\) | |||||||
\(522\) | −927.437 | + | 342.300i | −1.77670 | + | 0.655747i | ||||
\(523\) | −260.994 | −0.499033 | −0.249516 | − | 0.968371i | \(-0.580272\pi\) | ||||
−0.249516 | + | 0.968371i | \(0.580272\pi\) | |||||||
\(524\) | 292.758 | − | 169.024i | 0.558698 | − | 0.322564i | ||||
\(525\) | 25.2994 | − | 21.3260i | 0.0481893 | − | 0.0406210i | ||||
\(526\) | 666.875 | − | 1155.06i | 1.26782 | − | 2.19593i | ||||
\(527\) | 57.1590 | + | 33.0008i | 0.108461 | + | 0.0626201i | ||||
\(528\) | 253.663 | + | 300.925i | 0.480423 | + | 0.569933i | ||||
\(529\) | −37.7751 | − | 65.4283i | −0.0714084 | − | 0.123683i | ||||
\(530\) | 428.762i | 0.808985i | ||||||||
\(531\) | 112.701 | + | 305.355i | 0.212242 | + | 0.575056i | ||||
\(532\) | 97.2366 | 0.182776 | ||||||||
\(533\) | 11.6904 | − | 6.74943i | 0.0219331 | − | 0.0126631i | ||||
\(534\) | 11.6825 | + | 65.3930i | 0.0218774 | + | 0.122459i | ||||
\(535\) | 95.3217 | − | 165.102i | 0.178171 | − | 0.308602i | ||||
\(536\) | −61.5395 | − | 35.5298i | −0.114812 | − | 0.0662870i | ||||
\(537\) | 160.850 | − | 445.049i | 0.299535 | − | 0.828769i | ||||
\(538\) | −360.246 | − | 623.965i | −0.669603 | − | 1.15979i | ||||
\(539\) | 787.120i | 1.46033i | ||||||||
\(540\) | −291.616 | − | 165.747i | −0.540030 | − | 0.306938i | ||||
\(541\) | 492.273 | 0.909932 | 0.454966 | − | 0.890509i | \(-0.349651\pi\) | ||||
0.454966 | + | 0.890509i | \(0.349651\pi\) | |||||||
\(542\) | 1039.13 | − | 599.942i | 1.91721 | − | 1.10690i | ||||
\(543\) | 618.078 | + | 223.386i | 1.13827 | + | 0.411393i | ||||
\(544\) | 684.282 | − | 1185.21i | 1.25787 | − | 2.17870i | ||||
\(545\) | −123.989 | − | 71.5854i | −0.227504 | − | 0.131349i | ||||
\(546\) | −50.6226 | + | 9.04377i | −0.0927153 | + | 0.0165637i | ||||
\(547\) | −429.066 | − | 743.164i | −0.784399 | − | 1.35862i | −0.929358 | − | 0.369181i | \(-0.879638\pi\) |
0.144959 | − | 0.989438i | \(-0.453695\pi\) | |||||||
\(548\) | 1157.97i | 2.11309i | ||||||||
\(549\) | −64.3394 | + | 374.753i | −0.117194 | + | 0.682611i | ||||
\(550\) | −275.659 | −0.501199 | ||||||||
\(551\) | −244.152 | + | 140.961i | −0.443107 | + | 0.255828i | ||||
\(552\) | 234.920 | − | 198.025i | 0.425579 | − | 0.358740i | ||||
\(553\) | −76.2700 | + | 132.104i | −0.137921 | + | 0.238885i | ||||
\(554\) | −96.1328 | − | 55.5023i | −0.173525 | − | 0.100185i | ||||
\(555\) | −219.130 | − | 259.957i | −0.394829 | − | 0.468392i | ||||
\(556\) | 373.600 | + | 647.094i | 0.671943 | + | 1.16384i | ||||
\(557\) | − | 474.887i | − | 0.852581i | −0.904586 | − | 0.426290i | \(-0.859820\pi\) | ||
0.904586 | − | 0.426290i | \(-0.140180\pi\) | |||||||
\(558\) | −36.0084 | + | 43.3080i | −0.0645312 | + | 0.0776129i | ||||
\(559\) | −39.0535 | −0.0698632 | ||||||||
\(560\) | −31.4225 | + | 18.1418i | −0.0561117 | + | 0.0323961i | ||||
\(561\) | −306.778 | − | 1717.19i | −0.546842 | − | 3.06095i | ||||
\(562\) | −465.843 | + | 806.864i | −0.828902 | + | 1.43570i | ||||
\(563\) | −649.150 | − | 374.787i | −1.15302 | − | 0.665696i | −0.203398 | − | 0.979096i | \(-0.565199\pi\) |
−0.949621 | + | 0.313400i | \(0.898532\pi\) | |||||||
\(564\) | 10.6919 | − | 29.5828i | 0.0189572 | − | 0.0524518i | ||||
\(565\) | 169.373 | + | 293.363i | 0.299776 | + | 0.519226i | ||||
\(566\) | 1315.23i | 2.32373i | ||||||||
\(567\) | −135.835 | + | 116.081i | −0.239568 | + | 0.204729i | ||||
\(568\) | −505.335 | −0.889675 | ||||||||
\(569\) | −431.712 | + | 249.249i | −0.758720 | + | 0.438047i | −0.828836 | − | 0.559492i | \(-0.810996\pi\) |
0.0701161 | + | 0.997539i | \(0.477663\pi\) | |||||||
\(570\) | −154.729 | − | 55.9224i | −0.271455 | − | 0.0981095i | ||||
\(571\) | 302.743 | − | 524.365i | 0.530197 | − | 0.918328i | −0.469182 | − | 0.883101i | \(-0.655451\pi\) |
0.999379 | − | 0.0352270i | \(-0.0112154\pi\) | |||||||
\(572\) | 215.711 | + | 124.541i | 0.377117 | + | 0.217728i | ||||
\(573\) | −1097.28 | + | 196.030i | −1.91498 | + | 0.342112i | ||||
\(574\) | 18.3091 | + | 31.7123i | 0.0318974 | + | 0.0552480i | ||||
\(575\) | − | 106.472i | − | 0.185168i | ||||||
\(576\) | 694.381 | + | 577.343i | 1.20552 | + | 1.00233i | ||||
\(577\) | −898.993 | −1.55805 | −0.779023 | − | 0.626995i | \(-0.784285\pi\) | ||||
−0.779023 | + | 0.626995i | \(0.784285\pi\) | |||||||
\(578\) | −2071.89 | + | 1196.20i | −3.58458 | + | 2.06956i | ||||
\(579\) | −90.7403 | + | 76.4892i | −0.156719 | + | 0.132106i | ||||
\(580\) | −220.721 | + | 382.300i | −0.380554 | + | 0.659139i | ||||
\(581\) | −40.5544 | − | 23.4141i | −0.0698011 | − | 0.0402997i | ||||
\(582\) | 665.488 | + | 789.479i | 1.14345 | + | 1.35649i | ||||
\(583\) | −553.140 | − | 958.066i | −0.948782 | − | 1.64334i | ||||
\(584\) | 321.966i | 0.551312i | ||||||||
\(585\) | 49.8588 | + | 8.55999i | 0.0852287 | + | 0.0146325i | ||||
\(586\) | −1188.34 | −2.02788 | ||||||||
\(587\) | 730.025 | − | 421.480i | 1.24365 | − | 0.718024i | 0.273817 | − | 0.961782i | \(-0.411714\pi\) |
0.969836 | + | 0.243758i | \(0.0783803\pi\) | |||||||
\(588\) | 129.368 | + | 724.140i | 0.220014 | + | 1.23153i | ||||
\(589\) | −8.03089 | + | 13.9099i | −0.0136348 | + | 0.0236161i | ||||
\(590\) | 216.493 | + | 124.992i | 0.366937 | + | 0.211851i | ||||
\(591\) | 106.512 | − | 294.705i | 0.180224 | − | 0.498654i | ||||
\(592\) | 186.411 | + | 322.874i | 0.314884 | + | 0.545395i | ||||
\(593\) | 238.158i | 0.401615i | 0.979631 | + | 0.200808i | \(0.0643566\pi\) | ||||
−0.979631 | + | 0.200808i | \(0.935643\pi\) | |||||||
\(594\) | 1488.53 | − | 10.0610i | 2.50594 | − | 0.0169377i | ||||
\(595\) | 160.814 | 0.270276 | ||||||||
\(596\) | −584.726 | + | 337.592i | −0.981084 | + | 0.566429i | ||||
\(597\) | −333.025 | − | 120.362i | −0.557831 | − | 0.201612i | ||||
\(598\) | −82.7355 | + | 143.302i | −0.138354 | + | 0.239636i | ||||
\(599\) | 777.853 | + | 449.093i | 1.29859 | + | 0.749739i | 0.980160 | − | 0.198209i | \(-0.0635126\pi\) |
0.318426 | + | 0.947948i | \(0.396846\pi\) | |||||||
\(600\) | −71.0185 | + | 12.6875i | −0.118364 | + | 0.0211459i | ||||
\(601\) | 51.9420 | + | 89.9663i | 0.0864260 | + | 0.149694i | 0.905998 | − | 0.423282i | \(-0.139122\pi\) |
−0.819572 | + | 0.572976i | \(0.805789\pi\) | |||||||
\(602\) | − | 105.940i | − | 0.175980i | ||||||
\(603\) | 124.747 | − | 46.0420i | 0.206878 | − | 0.0763549i | ||||
\(604\) | 233.619 | 0.386786 | ||||||||
\(605\) | 381.644 | − | 220.342i | 0.630816 | − | 0.364202i | ||||
\(606\) | −441.001 | + | 371.740i | −0.727724 | + | 0.613432i | ||||
\(607\) | −539.314 | + | 934.118i | −0.888490 | + | 1.53891i | −0.0468297 | + | 0.998903i | \(0.514912\pi\) |
−0.841660 | + | 0.540007i | \(0.818422\pi\) | |||||||
\(608\) | 288.426 | + | 166.523i | 0.474385 | + | 0.273887i | ||||
\(609\) | 151.558 | + | 179.795i | 0.248864 | + | 0.295231i | ||||
\(610\) | 146.016 | + | 252.907i | 0.239371 | + | 0.414602i | ||||
\(611\) | 4.74405i | 0.00776441i | ||||||||
\(612\) | −564.464 | − | 1529.37i | −0.922326 | − | 2.49898i | ||||
\(613\) | −387.302 | −0.631814 | −0.315907 | − | 0.948790i | \(-0.602309\pi\) | ||||
−0.315907 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(614\) | −350.452 | + | 202.333i | −0.570768 | + | 0.329533i | ||||
\(615\) | −6.33526 | − | 35.4617i | −0.0103012 | − | 0.0576612i | ||||
\(616\) | −94.6082 | + | 163.866i | −0.153585 | + | 0.266016i | ||||
\(617\) | 459.415 | + | 265.244i | 0.744596 | + | 0.429892i | 0.823738 | − | 0.566971i | \(-0.191885\pi\) |
−0.0791422 | + | 0.996863i | \(0.525218\pi\) | |||||||
\(618\) | 173.668 | − | 480.513i | 0.281015 | − | 0.777530i | ||||
\(619\) | −321.146 | − | 556.241i | −0.518814 | − | 0.898613i | −0.999761 | − | 0.0218628i | \(-0.993040\pi\) |
0.480947 | − | 0.876750i | \(-0.340293\pi\) | |||||||
\(620\) | 25.1500i | 0.0405645i | ||||||||
\(621\) | 3.88601 | + | 574.935i | 0.00625766 | + | 0.925821i | ||||
\(622\) | 1736.38 | 2.79161 | ||||||||
\(623\) | 13.6841 | − | 7.90052i | 0.0219648 | − | 0.0126814i | ||||
\(624\) | −52.1701 | − | 18.8554i | −0.0836060 | − | 0.0302170i | ||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −108.368 | − | 62.5661i | −0.173111 | − | 0.0999459i | ||||
\(627\) | 417.887 | − | 74.6558i | 0.666486 | − | 0.119068i | ||||
\(628\) | 259.981 | + | 450.300i | 0.413982 | + | 0.717038i | ||||
\(629\) | − | 1652.41i | − | 2.62704i | ||||||
\(630\) | −23.2206 | + | 135.251i | −0.0368581 | + | 0.214685i | ||||
\(631\) | −88.5117 | −0.140272 | −0.0701361 | − | 0.997537i | \(-0.522343\pi\) | ||||
−0.0701361 | + | 0.997537i | \(0.522343\pi\) | |||||||
\(632\) | 288.024 | − | 166.291i | 0.455735 | − | 0.263119i | ||||
\(633\) | 312.870 | − | 263.732i | 0.494265 | − | 0.416639i | ||||
\(634\) | −201.867 | + | 349.643i | −0.318401 | + | 0.551487i | ||||
\(635\) | 83.1010 | + | 47.9784i | 0.130868 | + | 0.0755565i | ||||
\(636\) | −666.346 | − | 790.496i | −1.04771 | − | 1.24292i | ||||
\(637\) | −55.4709 | − | 96.0785i | −0.0870815 | − | 0.150830i | ||||
\(638\) | − | 1959.03i | − | 3.07058i | ||||||
\(639\) | 604.567 | − | 727.123i | 0.946114 | − | 1.13791i | ||||
\(640\) | 318.109 | 0.497045 | ||||||||
\(641\) | 285.641 | − | 164.915i | 0.445618 | − | 0.257278i | −0.260360 | − | 0.965512i | \(-0.583841\pi\) |
0.705978 | + | 0.708234i | \(0.250508\pi\) | |||||||
\(642\) | 139.052 | + | 778.342i | 0.216591 | + | 1.21237i | ||||
\(643\) | 39.2339 | − | 67.9551i | 0.0610170 | − | 0.105684i | −0.833903 | − | 0.551911i | \(-0.813899\pi\) |
0.894920 | + | 0.446226i | \(0.147232\pi\) | |||||||
\(644\) | −226.013 | − | 130.489i | −0.350952 | − | 0.202622i | ||||
\(645\) | −35.4240 | + | 98.0133i | −0.0549210 | + | 0.151959i | ||||
\(646\) | −399.805 | − | 692.482i | −0.618893 | − | 1.07195i | ||||
\(647\) | − | 68.7558i | − | 0.106269i | −0.998587 | − | 0.0531343i | \(-0.983079\pi\) | ||
0.998587 | − | 0.0531343i | \(-0.0169212\pi\) | |||||||
\(648\) | 383.028 | − | 71.1031i | 0.591093 | − | 0.109727i | ||||
\(649\) | −645.003 | −0.993841 | ||||||||
\(650\) | 33.6479 | − | 19.4266i | 0.0517660 | − | 0.0298871i | ||||
\(651\) | 12.5995 | + | 4.55371i | 0.0193540 | + | 0.00699495i | ||||
\(652\) | −321.660 | + | 557.132i | −0.493344 | + | 0.854497i | ||||
\(653\) | 832.196 | + | 480.468i | 1.27442 | + | 0.735786i | 0.975816 | − | 0.218591i | \(-0.0701462\pi\) |
0.298603 | + | 0.954378i | \(0.403479\pi\) | |||||||
\(654\) | 584.525 | − | 104.426i | 0.893769 | − | 0.159673i | ||||
\(655\) | 68.0272 | + | 117.826i | 0.103858 | + | 0.179888i | ||||
\(656\) | 39.5014i | 0.0602155i | ||||||||
\(657\) | −463.275 | − | 385.190i | −0.705138 | − | 0.586287i | ||||
\(658\) | −12.8691 | −0.0195580 | ||||||||
\(659\) | −105.512 | + | 60.9172i | −0.160109 | + | 0.0924389i | −0.577914 | − | 0.816098i | \(-0.696133\pi\) |
0.417805 | + | 0.908537i | \(0.362800\pi\) | |||||||
\(660\) | 508.225 | − | 428.406i | 0.770038 | − | 0.649101i | ||||
\(661\) | −418.001 | + | 723.999i | −0.632377 | + | 1.09531i | 0.354688 | + | 0.934985i | \(0.384587\pi\) |
−0.987064 | + | 0.160324i | \(0.948746\pi\) | |||||||
\(662\) | −1313.61 | − | 758.413i | −1.98430 | − | 1.14564i | ||||
\(663\) | 158.463 | + | 187.987i | 0.239008 | + | 0.283539i | ||||
\(664\) | 51.0496 | + | 88.4205i | 0.0768819 | + | 0.133163i | ||||
\(665\) | 39.1349i | 0.0588495i | ||||||||
\(666\) | 1389.74 | + | 238.597i | 2.08670 | + | 0.358254i | ||||
\(667\) | 756.664 | 1.13443 | ||||||||
\(668\) | −7.82739 | + | 4.51915i | −0.0117177 | + | 0.00676519i | ||||
\(669\) | 178.501 | + | 999.162i | 0.266818 | + | 1.49352i | ||||
\(670\) | 51.0635 | − | 88.4445i | 0.0762141 | − | 0.132007i | ||||
\(671\) | −652.544 | − | 376.747i | −0.972495 | − | 0.561470i | ||||
\(672\) | 94.4226 | − | 261.254i | 0.140510 | − | 0.388771i | ||||
\(673\) | −171.808 | − | 297.580i | −0.255287 | − | 0.442169i | 0.709687 | − | 0.704517i | \(-0.248837\pi\) |
−0.964973 | + | 0.262348i | \(0.915503\pi\) | |||||||
\(674\) | − | 346.179i | − | 0.513619i | ||||||
\(675\) | 66.7083 | − | 117.367i | 0.0988270 | − | 0.173877i | ||||
\(676\) | 903.832 | 1.33703 | ||||||||
\(677\) | 334.217 | − | 192.960i | 0.493674 | − | 0.285023i | −0.232424 | − | 0.972615i | \(-0.574666\pi\) |
0.726097 | + | 0.687592i | \(0.241332\pi\) | |||||||
\(678\) | −1321.25 | − | 477.529i | −1.94875 | − | 0.704320i | ||||
\(679\) | 122.804 | − | 212.702i | 0.180860 | − | 0.313258i | ||||
\(680\) | −303.648 | − | 175.311i | −0.446541 | − | 0.257810i | ||||
\(681\) | −453.038 | + | 80.9356i | −0.665254 | + | 0.118848i | ||||
\(682\) | −55.8053 | − | 96.6576i | −0.0818259 | − | 0.141727i | ||||
\(683\) | 699.925i | 1.02478i | 0.858753 | + | 0.512390i | \(0.171240\pi\) | ||||
−0.858753 | + | 0.512390i | \(0.828760\pi\) | |||||||
\(684\) | 372.180 | − | 137.365i | 0.544123 | − | 0.200826i | ||||
\(685\) | −466.050 | −0.680364 | ||||||||
\(686\) | 549.998 | − | 317.542i | 0.801747 | − | 0.462889i | ||||
\(687\) | −581.190 | + | 489.912i | −0.845982 | + | 0.713118i | ||||
\(688\) | 57.1407 | − | 98.9706i | 0.0830533 | − | 0.143853i | ||||
\(689\) | 135.036 | + | 77.9631i | 0.195989 | + | 0.113154i | ||||
\(690\) | 284.601 | + | 337.627i | 0.412465 | + | 0.489314i | ||||
\(691\) | 257.065 | + | 445.249i | 0.372019 | + | 0.644355i | 0.989876 | − | 0.141935i | \(-0.0453324\pi\) |
−0.617857 | + | 0.786290i | \(0.711999\pi\) | |||||||
\(692\) | 667.827i | 0.965068i | ||||||||
\(693\) | −122.600 | − | 332.175i | −0.176912 | − | 0.479329i | ||||
\(694\) | 607.488 | 0.875344 | ||||||||
\(695\) | −260.437 | + | 150.363i | −0.374729 | + | 0.216350i | ||||
\(696\) | −90.1665 | − | 504.708i | −0.129550 | − | 0.725155i | ||||
\(697\) | 87.5380 | − | 151.620i | 0.125593 | − | 0.217533i | ||||
\(698\) | 586.712 | + | 338.738i | 0.840561 | + | 0.485298i | ||||
\(699\) | 315.362 | − | 872.562i | 0.451162 | − | 1.24830i | ||||
\(700\) | 30.6393 | + | 53.0688i | 0.0437704 | + | 0.0758125i | ||||
\(701\) | − | 842.009i | − | 1.20115i | −0.799567 | − | 0.600577i | \(-0.794938\pi\) | ||
0.799567 | − | 0.600577i | \(-0.205062\pi\) | |||||||
\(702\) | −180.985 | + | 106.129i | −0.257814 | + | 0.151181i | ||||
\(703\) | 402.120 | 0.572006 | ||||||||
\(704\) | −1549.76 | + | 894.757i | −2.20137 | + | 1.27096i | ||||
\(705\) | 11.9062 | + | 4.30316i | 0.0168883 | + | 0.00610377i | ||||
\(706\) | 391.713 | − | 678.467i | 0.554834 | − | 0.961001i | ||||
\(707\) | 118.815 | + | 68.5978i | 0.168055 | + | 0.0970267i | ||||
\(708\) | −593.394 | + | 106.010i | −0.838127 | + | 0.149732i | ||||
\(709\) | 84.2898 | + | 145.994i | 0.118885 | + | 0.205916i | 0.919326 | − | 0.393496i | \(-0.128735\pi\) |
−0.800441 | + | 0.599412i | \(0.795401\pi\) | |||||||
\(710\) | − | 726.268i | − | 1.02291i | ||||||
\(711\) | −105.308 | + | 613.381i | −0.148113 | + | 0.862702i | ||||
\(712\) | −34.4509 | −0.0483860 | ||||||||
\(713\) | 37.3334 | − | 21.5545i | 0.0523610 | − | 0.0302306i | ||||
\(714\) | −509.949 | + | 429.860i | −0.714215 | + | 0.602044i | ||||
\(715\) | −50.1240 | + | 86.8173i | −0.0701035 | + | 0.121423i | ||||
\(716\) | 758.974 | + | 438.194i | 1.06002 | + | 0.612003i | ||||
\(717\) | 138.879 | + | 164.754i | 0.193694 | + | 0.229782i | ||||
\(718\) | −235.869 | − | 408.537i | −0.328508 | − | 0.568993i | ||||
\(719\) | 1132.23i | 1.57472i | 0.616490 | + | 0.787362i | \(0.288554\pi\) | ||||
−0.616490 | + | 0.787362i | \(0.711446\pi\) | |||||||
\(720\) | −94.6433 | + | 113.829i | −0.131449 | + | 0.158096i | ||||
\(721\) | −121.534 | −0.168563 | ||||||||
\(722\) | −797.916 | + | 460.677i | −1.10515 | + | 0.638057i | ||||
\(723\) | 159.841 | + | 894.712i | 0.221080 | + | 1.23750i | ||||
\(724\) | −608.558 | + | 1054.05i | −0.840550 | + | 1.45587i | ||||
\(725\) | −153.865 | − | 88.8339i | −0.212227 | − | 0.122529i | ||||
\(726\) | −621.230 | + | 1718.86i | −0.855689 | + | 2.36757i | ||||
\(727\) | −476.178 | − | 824.764i | −0.654990 | − | 1.13448i | −0.981896 | − | 0.189420i | \(-0.939339\pi\) |
0.326906 | − | 0.945057i | \(-0.393994\pi\) | |||||||
\(728\) | − | 26.6694i | − | 0.0366338i | ||||||
\(729\) | −355.933 | + | 636.202i | −0.488248 | + | 0.872705i | ||||
\(730\) | −462.730 | −0.633877 | ||||||||
\(731\) | −438.652 | + | 253.256i | −0.600072 | + | 0.346452i | ||||
\(732\) | −662.253 | − | 239.352i | −0.904717 | − | 0.326984i | ||||
\(733\) | −69.0917 | + | 119.670i | −0.0942588 | + | 0.163261i | −0.909299 | − | 0.416143i | \(-0.863381\pi\) |
0.815040 | + | 0.579404i | \(0.196715\pi\) | |||||||
\(734\) | −936.972 | − | 540.961i | −1.27653 | − | 0.737004i | ||||
\(735\) | −291.445 | + | 52.0670i | −0.396524 | + | 0.0708394i | ||||
\(736\) | −446.938 | − | 774.120i | −0.607253 | − | 1.05179i | ||||
\(737\) | 263.505i | 0.357537i | ||||||||
\(738\) | 114.879 | + | 95.5161i | 0.155663 | + | 0.129426i | ||||
\(739\) | 529.373 | 0.716337 | 0.358168 | − | 0.933657i | \(-0.383401\pi\) | ||||
0.358168 | + | 0.933657i | \(0.383401\pi\) | |||||||
\(740\) | 545.294 | − | 314.826i | 0.736884 | − | 0.425440i | ||||
\(741\) | −45.7474 | + | 38.5626i | −0.0617373 | + | 0.0520412i | ||||
\(742\) | −211.490 | + | 366.311i | −0.285027 | + | 0.493681i | ||||
\(743\) | 537.511 | + | 310.332i | 0.723434 | + | 0.417675i | 0.816015 | − | 0.578030i | \(-0.196178\pi\) |
−0.0925813 | + | 0.995705i | \(0.529512\pi\) | |||||||
\(744\) | −18.8260 | − | 22.3335i | −0.0253037 | − | 0.0300182i | ||||
\(745\) | −135.871 | − | 235.335i | −0.182377 | − | 0.315886i | ||||
\(746\) | − | 1255.04i | − | 1.68236i | ||||||
\(747\) | −188.302 | − | 32.3285i | −0.252077 | − | 0.0432778i | ||||
\(748\) | 3230.51 | 4.31886 | ||||||||
\(749\) | 162.875 | − | 94.0362i | 0.217457 | − | 0.125549i | ||||
\(750\) | −18.2345 | − | 102.068i | −0.0243127 | − | 0.136090i | ||||
\(751\) | 49.6464 | − | 85.9901i | 0.0661070 | − | 0.114501i | −0.831077 | − | 0.556157i | \(-0.812275\pi\) |
0.897185 | + | 0.441656i | \(0.145609\pi\) | |||||||
\(752\) | −12.0225 | − | 6.94120i | −0.0159874 | − | 0.00923032i | ||||
\(753\) | 110.691 | − | 306.265i | 0.146999 | − | 0.406726i | ||||
\(754\) | 138.059 | + | 239.126i | 0.183103 | + | 0.317143i | ||||
\(755\) | 94.0248i | 0.124536i | ||||||||
\(756\) | −167.385 | − | 285.447i | −0.221409 | − | 0.377575i | ||||
\(757\) | 395.640 | 0.522642 | 0.261321 | − | 0.965252i | \(-0.415842\pi\) | ||||
0.261321 | + | 0.965252i | \(0.415842\pi\) | |||||||
\(758\) | 1099.48 | − | 634.786i | 1.45050 | − | 0.837449i | ||||
\(759\) | −1071.51 | − | 387.265i | −1.41173 | − | 0.510230i | ||||
\(760\) | 42.6627 | − | 73.8940i | 0.0561352 | − | 0.0972290i | ||||
\(761\) | 1219.62 | + | 704.146i | 1.60265 | + | 0.925291i | 0.990955 | + | 0.134198i | \(0.0428458\pi\) |
0.611696 | + | 0.791093i | \(0.290487\pi\) | |||||||
\(762\) | −391.764 | + | 69.9890i | −0.514126 | + | 0.0918491i | ||||
\(763\) | −70.6199 | − | 122.317i | −0.0925556 | − | 0.160311i | ||||
\(764\) | − | 2064.28i | − | 2.70194i | ||||||
\(765\) | 615.528 | − | 227.180i | 0.804612 | − | 0.296968i | ||||
\(766\) | −1504.38 | −1.96394 | ||||||||
\(767\) | 78.7311 | − | 45.4554i | 0.102648 | − | 0.0592639i | ||||
\(768\) | −88.1192 | + | 74.2797i | −0.114739 | + | 0.0967184i | ||||
\(769\) | −382.059 | + | 661.746i | −0.496826 | + | 0.860528i | −0.999993 | − | 0.00366110i | \(-0.998835\pi\) |
0.503167 | + | 0.864189i | \(0.332168\pi\) | |||||||
\(770\) | −235.508 | − | 135.971i | −0.305855 | − | 0.176586i | ||||
\(771\) | 193.984 | + | 230.126i | 0.251600 | + | 0.298477i | ||||
\(772\) | −109.893 | − | 190.340i | −0.142348 | − | 0.246554i | ||||
\(773\) | 477.095i | 0.617199i | 0.951192 | + | 0.308600i | \(0.0998603\pi\) | ||||
−0.951192 | + | 0.308600i | \(0.900140\pi\) | |||||||
\(774\) | −149.660 | − | 405.493i | −0.193359 | − | 0.523893i | ||||
\(775\) | −10.1221 | −0.0130608 | ||||||||
\(776\) | −463.753 | + | 267.748i | −0.597620 | + | 0.345036i | ||||
\(777\) | −58.9871 | − | 330.181i | −0.0759165 | − | 0.424943i | ||||
\(778\) | 988.469 | − | 1712.08i | 1.27053 | − | 2.20062i | ||||
\(779\) | 36.8975 | + | 21.3028i | 0.0473652 | + | 0.0273463i | ||||
\(780\) | −31.8444 | + | 88.1089i | −0.0408262 | + | 0.112960i | ||||
\(781\) | 936.948 | + | 1622.84i | 1.19968 | + | 2.07790i | ||||
\(782\) | 2146.11i | 2.74438i | ||||||||
\(783\) | 834.093 | + | 474.076i | 1.06525 | + | 0.605461i | ||||
\(784\) | 324.646 | 0.414090 | ||||||||
\(785\) | −181.233 | + | 104.635i | −0.230870 | + | 0.133293i | ||||
\(786\) | −530.669 | − | 191.795i | −0.675152 | − | 0.244014i | ||||
\(787\) | 615.120 | − | 1065.42i | 0.781600 | − | 1.35377i | −0.149409 | − | 0.988776i | \(-0.547737\pi\) |
0.931009 | − | 0.364996i | \(-0.118930\pi\) | |||||||
\(788\) | 502.581 | + | 290.165i | 0.637794 | + | 0.368230i | ||||
\(789\) | −1274.20 | + | 227.638i | −1.61496 | + | 0.288514i | ||||
\(790\) | 238.993 | + | 413.949i | 0.302523 | + | 0.523986i | ||||
\(791\) | 334.178i | 0.422475i | ||||||||
\(792\) | −130.628 | + | 760.861i | −0.164934 | + | 0.960683i | ||||
\(793\) | 106.202 | 0.133925 | ||||||||
\(794\) | 790.624 | − | 456.467i | 0.995748 | − | 0.574895i | ||||
\(795\) | 318.152 | − | 268.185i | 0.400191 | − | 0.337339i | ||||
\(796\) | 327.896 | − | 567.932i | 0.411929 | − | 0.713483i | ||||
\(797\) | 82.5422 | + | 47.6557i | 0.103566 | + | 0.0597939i | 0.550888 | − | 0.834579i | \(-0.314289\pi\) |
−0.447322 | + | 0.894373i | \(0.647622\pi\) | |||||||
\(798\) | −104.608 | − | 124.098i | −0.131088 | − | 0.155512i | ||||
\(799\) | 30.7644 | + | 53.2856i | 0.0385037 | + | 0.0666903i | ||||
\(800\) | 209.886i | 0.262357i | ||||||||
\(801\) | 41.2159 | − | 49.5711i | 0.0514556 | − | 0.0618865i | ||||
\(802\) | 128.215 | 0.159869 | ||||||||
\(803\) | 1033.97 | − | 596.962i | 1.28763 | − | 0.743414i | ||||
\(804\) | 43.3087 | + | 242.421i | 0.0538666 | + | 0.301519i | ||||
\(805\) | 52.5179 | − | 90.9637i | 0.0652397 | − | 0.112998i | ||||
\(806\) | 13.6235 | + | 7.86556i | 0.0169027 | + | 0.00975876i | ||||
\(807\) | −237.668 | + | 657.593i | −0.294508 | + | 0.814861i | ||||
\(808\) | −149.563 | − | 259.051i | −0.185103 | − | 0.320608i | ||||
\(809\) | − | 1184.24i | − | 1.46383i | −0.681395 | − | 0.731916i | \(-0.738626\pi\) | ||
0.681395 | − | 0.731916i | \(-0.261374\pi\) | |||||||
\(810\) | 102.189 | + | 550.488i | 0.126160 | + | 0.679615i | ||||
\(811\) | −991.880 | −1.22303 | −0.611517 | − | 0.791232i | \(-0.709440\pi\) | ||||
−0.611517 | + | 0.791232i | \(0.709440\pi\) | |||||||
\(812\) | −377.144 | + | 217.744i | −0.464464 | + | 0.268158i | ||||
\(813\) | −1095.13 | − | 395.804i | −1.34703 | − | 0.486844i | ||||
\(814\) | −1397.13 | + | 2419.90i | −1.71638 | + | 2.97286i | ||||
\(815\) | −224.229 | − | 129.459i | −0.275128 | − | 0.158845i | ||||
\(816\) | −708.253 | + | 126.530i | −0.867957 | + | 0.155061i | ||||
\(817\) | −61.6310 | − | 106.748i | −0.0754357 | − | 0.130659i | ||||
\(818\) | 64.6682i | 0.0790565i | ||||||||
\(819\) | 38.3744 | + | 31.9064i | 0.0468552 | + | 0.0389577i | ||||
\(820\) | 66.7130 | 0.0813573 | ||||||||
\(821\) | −986.241 | + | 569.407i | −1.20127 | + | 0.693553i | −0.960837 | − | 0.277114i | \(-0.910622\pi\) |
−0.240431 | + | 0.970666i | \(0.577289\pi\) | |||||||
\(822\) | 1477.86 | − | 1245.76i | 1.79789 | − | 1.51552i | ||||
\(823\) | −381.236 | + | 660.320i | −0.463227 | + | 0.802333i | −0.999120 | − | 0.0419536i | \(-0.986642\pi\) |
0.535893 | + | 0.844286i | \(0.319975\pi\) | |||||||
\(824\) | 229.478 | + | 132.489i | 0.278493 | + | 0.160788i | ||||
\(825\) | 172.421 | + | 204.546i | 0.208995 | + | 0.247934i | ||||
\(826\) | 123.307 | + | 213.573i | 0.149282 | + | 0.258563i | ||||
\(827\) | − | 1111.94i | − | 1.34455i | −0.740301 | − | 0.672275i | \(-0.765317\pi\) | ||
0.740301 | − | 0.672275i | \(-0.234683\pi\) | |||||||
\(828\) | −1049.42 | − | 180.169i | −1.26742 | − | 0.217596i | ||||
\(829\) | −128.075 | −0.154493 | −0.0772465 | − | 0.997012i | \(-0.524613\pi\) | ||||
−0.0772465 | + | 0.997012i | \(0.524613\pi\) | |||||||
\(830\) | −127.078 | + | 73.3685i | −0.153106 | + | 0.0883958i | ||||
\(831\) | 18.9457 | + | 106.049i | 0.0227987 | + | 0.127616i | ||||
\(832\) | 126.113 | − | 218.434i | 0.151578 | − | 0.262541i | ||||
\(833\) | −1246.11 | − | 719.440i | −1.49593 | − | 0.863674i | ||||
\(834\) | 423.932 | − | 1172.96i | 0.508312 | − | 1.40643i | ||||
\(835\) | −1.81883 | − | 3.15030i | −0.00217823 | − | 0.00377281i | ||||
\(836\) | 786.158i | 0.940381i | ||||||||
\(837\) | 54.6583 | − | 0.369438i | 0.0653026 | − | 0.000441383i | ||||
\(838\) | −1287.94 | −1.53692 | ||||||||
\(839\) | 597.707 | − | 345.086i | 0.712404 | − | 0.411307i | −0.0995467 | − | 0.995033i | \(-0.531739\pi\) |
0.811950 | + | 0.583726i | \(0.198406\pi\) | |||||||
\(840\) | −66.9325 | − | 24.1908i | −0.0796816 | − | 0.0287986i | ||||
\(841\) | 210.816 | − | 365.145i | 0.250674 | − | 0.434179i | ||||
\(842\) | −894.669 | − | 516.538i | −1.06255 | − | 0.613465i | ||||
\(843\) | 890.090 | − | 159.015i | 1.05586 | − | 0.188630i | ||||
\(844\) | 378.906 | + | 656.285i | 0.448941 | + | 0.777589i | ||||
\(845\) | 363.766i | 0.430492i | ||||||||
\(846\) | −49.2576 | + | 18.1801i | −0.0582241 | + | 0.0214894i | ||||
\(847\) | 434.741 | 0.513272 | ||||||||
\(848\) | −395.153 | + | 228.142i | −0.465982 | + | 0.269035i | ||||
\(849\) | 975.933 | − | 822.659i | 1.14951 | − | 0.968974i | ||||
\(850\) | 251.957 | − | 436.403i | 0.296420 | − | 0.513415i | ||||
\(851\) | −934.674 | − | 539.634i | −1.09832 | − | 0.634118i | ||||
\(852\) | 1128.70 | + | 1339.00i | 1.32477 | + | 1.57159i | ||||
\(853\) | 21.2098 | + | 36.7364i | 0.0248649 | + | 0.0430673i | 0.878190 | − | 0.478312i | \(-0.158751\pi\) |
−0.853325 | + | 0.521379i | \(0.825418\pi\) | |||||||
\(854\) | 288.094i | 0.337346i | ||||||||
\(855\) | 55.2853 | + | 149.792i | 0.0646612 | + | 0.175195i | ||||
\(856\) | −410.052 | −0.479033 | ||||||||
\(857\) | −129.055 | + | 74.5099i | −0.150589 | + | 0.0869427i | −0.573401 | − | 0.819275i | \(-0.694376\pi\) |
0.422812 | + | 0.906217i | \(0.361043\pi\) | |||||||
\(858\) | −73.1189 | − | 409.284i | −0.0852202 | − | 0.477021i | ||||
\(859\) | 101.735 | − | 176.211i | 0.118435 | − | 0.205135i | −0.800713 | − | 0.599048i | \(-0.795546\pi\) |
0.919148 | + | 0.393913i | \(0.128879\pi\) | |||||||
\(860\) | −167.149 | − | 96.5036i | −0.194359 | − | 0.112213i | ||||
\(861\) | 12.0792 | − | 33.4214i | 0.0140293 | − | 0.0388170i | ||||
\(862\) | −602.308 | − | 1043.23i | −0.698733 | − | 1.21024i | ||||
\(863\) | 923.552i | 1.07016i | 0.844800 | + | 0.535082i | \(0.179719\pi\) | ||||
−0.844800 | + | 0.535082i | \(0.820281\pi\) | |||||||
\(864\) | −7.66041 | − | 1133.36i | −0.00886622 | − | 1.31176i | ||||
\(865\) | −268.781 | −0.310729 | ||||||||
\(866\) | 1988.23 | − | 1147.90i | 2.29587 | − | 1.32552i | ||||
\(867\) | 2183.55 | + | 789.180i | 2.51851 | + | 0.910242i | ||||
\(868\) | −12.4054 | + | 21.4868i | −0.0142919 | + | 0.0247544i | ||||
\(869\) | −1068.06 | − | 616.644i | −1.22907 | − | 0.709601i | ||||
\(870\) | 725.366 | − | 129.587i | 0.833754 | − | 0.148951i | ||||
\(871\) | −18.5701 | − | 32.1643i | −0.0213204 | − | 0.0369280i | ||||
\(872\) | 307.944i | 0.353147i | ||||||||
\(873\) | 169.558 | − | 987.616i | 0.194225 | − | 1.13129i | ||||
\(874\) | −522.265 | −0.597557 | ||||||||
\(875\) | −21.3586 | + | 12.3314i | −0.0244099 | + | 0.0140930i | ||||
\(876\) | 853.122 | − | 719.136i | 0.973883 | − | 0.820931i | ||||
\(877\) | 333.571 | − | 577.762i | 0.380355 | − | 0.658794i | −0.610758 | − | 0.791817i | \(-0.709135\pi\) |
0.991113 | + | 0.133023i | \(0.0424686\pi\) | |||||||
\(878\) | 593.412 | + | 342.606i | 0.675867 | + | 0.390212i | ||||
\(879\) | 743.289 | + | 881.775i | 0.845607 | + | 1.00316i | ||||
\(880\) | −146.677 | − | 254.051i | −0.166678 | − | 0.288695i | ||||
\(881\) | 837.220i | 0.950307i | 0.879903 | + | 0.475153i | \(0.157607\pi\) | ||||
−0.879903 | + | 0.475153i | \(0.842393\pi\) | |||||||
\(882\) | 785.009 | − | 944.145i | 0.890033 | − | 1.07046i | ||||
\(883\) | −790.539 | −0.895287 | −0.447644 | − | 0.894212i | \(-0.647737\pi\) | ||||
−0.447644 | + | 0.894212i | \(0.647737\pi\) | |||||||
\(884\) | −394.326 | + | 227.664i | −0.446070 | + | 0.257539i | ||||
\(885\) | −42.6661 | − | 238.824i | −0.0482103 | − | 0.269857i | ||||
\(886\) | −269.610 | + | 466.979i | −0.304301 | + | 0.527064i | ||||
\(887\) | −336.825 | − | 194.466i | −0.379735 | − | 0.219240i | 0.297968 | − | 0.954576i | \(-0.403691\pi\) |
−0.677703 | + | 0.735336i | \(0.737025\pi\) | |||||||
\(888\) | −248.566 | + | 687.748i | −0.279917 | + | 0.774491i | ||||
\(889\) | 47.3313 | + | 81.9803i | 0.0532411 | + | 0.0922163i | ||||
\(890\) | − | 49.5128i | − | 0.0556323i | ||||||
\(891\) | −938.518 | − | 1098.23i | −1.05333 | − | 1.23258i | ||||
\(892\) | −1879.70 | −2.10728 | ||||||||
\(893\) | −12.9673 | + | 7.48666i | −0.0145210 | + | 0.00838372i | ||||
\(894\) | 1059.91 | + | 383.073i | 1.18558 | + | 0.428493i | ||||
\(895\) | −176.360 | + | 305.465i | −0.197051 | + | 0.341302i | ||||
\(896\) | 271.775 | + | 156.909i | 0.303320 | + | 0.175122i | ||||
\(897\) | 158.083 | − | 28.2417i | 0.176236 | − | 0.0314847i | ||||
\(898\) | 490.066 | + | 848.819i | 0.545730 | + | 0.945233i | ||||
\(899\) | − | 71.9351i | − | 0.0800168i | ||||||
\(900\) | 192.243 | + | 159.841i | 0.213604 | + | 0.177601i | ||||
\(901\) | 2022.31 | 2.24452 | ||||||||
\(902\) | −256.394 | + | 148.029i | −0.284251 | + | 0.164112i | ||||
\(903\) | −78.6101 | + | 66.2641i | −0.0870543 | + | 0.0733821i | ||||
\(904\) | 364.302 | − | 630.990i | 0.402989 | − | 0.697998i | ||||
\(905\) | −424.226 | − | 244.927i | −0.468758 | − | 0.270637i | ||||
\(906\) | −251.330 | − | 298.156i | −0.277406 | − | 0.329091i | ||||
\(907\) | −36.6233 | − | 63.4335i | −0.0403785 | − | 0.0699377i | 0.845130 | − | 0.534561i | \(-0.179523\pi\) |
−0.885508 | + | 0.464623i | \(0.846190\pi\) | |||||||
\(908\) | − | 852.287i | − | 0.938642i | ||||||
\(909\) | 551.680 | + | 94.7149i | 0.606908 | + | 0.104197i | ||||
\(910\) | 38.3292 | 0.0421200 | ||||||||
\(911\) | −830.528 | + | 479.506i | −0.911667 | + | 0.526351i | −0.880967 | − | 0.473178i | \(-0.843107\pi\) |
−0.0306997 | + | 0.999529i | \(0.509774\pi\) | |||||||
\(912\) | −30.7917 | − | 172.357i | −0.0337628 | − | 0.188987i | ||||
\(913\) | 189.303 | − | 327.883i | 0.207342 | − | 0.359127i | ||||
\(914\) | 1325.82 | + | 765.461i | 1.45057 | + | 0.837485i | ||||
\(915\) | 96.3322 | − | 266.537i | 0.105281 | − | 0.291298i | ||||
\(916\) | −703.860 | − | 1219.12i | −0.768406 | − | 1.33092i | ||||
\(917\) | 134.219i | 0.146368i | ||||||||
\(918\) | −1344.61 | + | 2365.72i | −1.46472 | + | 2.57703i | ||||
\(919\) | 1280.94 | 1.39384 | 0.696919 | − | 0.717149i | \(-0.254554\pi\) | ||||
0.696919 | + | 0.717149i | \(0.254554\pi\) | |||||||
\(920\) | −198.327 | + | 114.504i | −0.215573 | + | 0.124461i | ||||
\(921\) | 369.339 | + | 133.487i | 0.401019 | + | 0.144937i | ||||
\(922\) | −331.705 | + | 574.530i | −0.359767 | + | 0.623135i | ||||
\(923\) | −228.734 | − | 132.059i | −0.247816 | − | 0.143076i | ||||
\(924\) | 645.514 | − | 115.322i | 0.698608 | − | 0.124807i | ||||
\(925\) | 126.708 | + | 219.465i | 0.136982 | + | 0.237260i | ||||
\(926\) | 1303.85i | 1.40804i | ||||||||
\(927\) | −465.179 | + | 171.689i | −0.501811 | + | 0.185209i | ||||
\(928\) | −1491.60 | −1.60732 | ||||||||
\(929\) | 1468.25 | − | 847.697i | 1.58047 | − | 0.912483i | 0.585676 | − | 0.810545i | \(-0.300829\pi\) |
0.994791 | − | 0.101938i | \(-0.0325042\pi\) | |||||||
\(930\) | 32.0977 | − | 27.0567i | 0.0345137 | − | 0.0290932i | ||||
\(931\) | 175.079 | − | 303.246i | 0.188055 | − | 0.325720i | ||||
\(932\) | 1488.04 | + | 859.122i | 1.59661 | + | 0.921805i | ||||
\(933\) | −1086.08 | − | 1288.43i | −1.16407 | − | 1.38096i | ||||
\(934\) | 191.349 | + | 331.426i | 0.204871 | + | 0.354846i | ||||
\(935\) | 1300.19i | 1.39057i | ||||||||
\(936\) | −37.6754 | − | 102.079i | −0.0402515 | − | 0.109059i | ||||
\(937\) | −1690.96 | −1.80465 | −0.902326 | − | 0.431054i | \(-0.858142\pi\) | ||||
−0.902326 | + | 0.431054i | \(0.858142\pi\) | |||||||
\(938\) | 87.2517 | − | 50.3748i | 0.0930189 | − | 0.0537045i | ||||
\(939\) | 21.3569 | + | 119.546i | 0.0227443 | + | 0.127312i | ||||
\(940\) | −11.7228 | + | 20.3045i | −0.0124711 | + | 0.0216006i | ||||
\(941\) | −1049.49 | − | 605.926i | −1.11530 | − | 0.643917i | −0.175100 | − | 0.984551i | \(-0.556025\pi\) |
−0.940196 | + | 0.340634i | \(0.889358\pi\) | |||||||
\(942\) | 295.006 | − | 816.239i | 0.313170 | − | 0.866496i | ||||
\(943\) | −57.1754 | − | 99.0308i | −0.0606314 | − | 0.105017i | ||||
\(944\) | 266.030i | 0.281812i | ||||||||
\(945\) | 114.884 | − | 67.3677i | 0.121570 | − | 0.0712885i | ||||
\(946\) | 856.527 | 0.905419 | ||||||||
\(947\) | −510.822 | + | 294.923i | −0.539411 | + | 0.311429i | −0.744840 | − | 0.667243i | \(-0.767474\pi\) |
0.205429 | + | 0.978672i | \(0.434141\pi\) | |||||||
\(948\) | −1083.95 | − | 391.762i | −1.14341 | − | 0.413251i | ||||
\(949\) | −84.1397 | + | 145.734i | −0.0886614 | + | 0.153566i | ||||
\(950\) | 106.200 | + | 61.3149i | 0.111790 | + | 0.0645420i | ||||
\(951\) | 385.708 | − | 68.9071i | 0.405582 | − | 0.0724575i | ||||
\(952\) | −172.947 | − | 299.553i | −0.181667 | − | 0.314656i | ||||
\(953\) | 1597.56i | 1.67635i | 0.545402 | + | 0.838174i | \(0.316377\pi\) | ||||
−0.545402 | + | 0.838174i | \(0.683623\pi\) | |||||||
\(954\) | −292.010 | + | 1700.85i | −0.306090 | + | 1.78286i | ||||
\(955\) | 830.815 | 0.869963 | ||||||||
\(956\) | −345.593 | + | 199.528i | −0.361499 | + | 0.208711i | ||||
\(957\) | −1453.65 | + | 1225.35i | −1.51896 | + | 1.28040i | ||||
\(958\) | −1038.02 | + | 1797.90i | −1.08353 | + | 1.87672i | ||||
\(959\) | −398.167 | − | 229.882i | −0.415190 | − | 0.239710i | ||||
\(960\) | −433.814 | − | 514.641i | −0.451890 | − | 0.536084i | ||||
\(961\) | 478.451 | + | 828.701i | 0.497868 | + | 0.862332i | ||||
\(962\) | − | 393.842i | − | 0.409399i | ||||||
\(963\) | 490.574 | − | 590.022i | 0.509422 | − | 0.612691i | ||||
\(964\) | −1683.20 | −1.74605 | ||||||||
\(965\) | 76.6061 | − | 44.2286i | 0.0793846 | − | 0.0458327i | ||||
\(966\) | 76.6111 | + | 428.831i | 0.0793075 | + | 0.443925i | ||||
\(967\) | −313.476 | + | 542.957i | −0.324174 | + | 0.561486i | −0.981345 | − | 0.192256i | \(-0.938420\pi\) |
0.657171 | + | 0.753742i | \(0.271753\pi\) | |||||||
\(968\) | −820.873 | − | 473.931i | −0.848009 | − | 0.489598i | ||||
\(969\) | −263.766 | + | 729.802i | −0.272204 | + | 0.753150i | ||||
\(970\) | −384.807 | − | 666.506i | −0.396708 | − | 0.687119i | ||||
\(971\) | − | 1907.25i | − | 1.96421i | −0.188328 | − | 0.982106i | \(-0.560307\pi\) | ||
0.188328 | − | 0.982106i | \(-0.439693\pi\) | |||||||
\(972\) | −1043.92 | − | 856.104i | −1.07400 | − | 0.880766i | ||||
\(973\) | −296.671 | −0.304903 | ||||||||
\(974\) | 360.802 | − | 208.309i | 0.370434 | − | 0.213870i | ||||
\(975\) | −35.4613 | − | 12.8164i | −0.0363705 | − | 0.0131451i | ||||
\(976\) | −155.388 | + | 269.141i | −0.159209 | + | 0.275759i | ||||
\(977\) | −764.149 | − | 441.181i | −0.782138 | − | 0.451568i | 0.0550495 | − | 0.998484i | \(-0.482468\pi\) |
−0.837187 | + | 0.546916i | \(0.815802\pi\) | |||||||
\(978\) | 1057.09 | − | 188.849i | 1.08087 | − | 0.193098i | ||||
\(979\) | 63.8757 | + | 110.636i | 0.0652459 | + | 0.113009i | ||||
\(980\) | − | 548.288i | − | 0.559477i | ||||||
\(981\) | −443.099 | − | 368.414i | −0.451680 | − | 0.375550i | ||||
\(982\) | 1467.44 | 1.49434 | ||||||||
\(983\) | 838.049 | − | 483.848i | 0.852543 | − | 0.492216i | −0.00896527 | − | 0.999960i | \(-0.502854\pi\) |
0.861508 | + | 0.507744i | \(0.169520\pi\) | |||||||
\(984\) | −59.2420 | + | 49.9378i | −0.0602053 | + | 0.0507498i | ||||
\(985\) | −116.783 | + | 202.274i | −0.118562 | + | 0.205355i | ||||
\(986\) | 3101.39 | + | 1790.59i | 3.14542 | + | 1.81601i | ||||
\(987\) | 8.04947 | + | 9.54921i | 0.00815549 | + | 0.00967498i | ||||
\(988\) | −55.4031 | − | 95.9610i | −0.0560760 | − | 0.0971265i | ||||
\(989\) | 330.828i | 0.334508i | ||||||||
\(990\) | −1093.51 | − | 187.739i | −1.10455 | − | 0.189635i | ||||
\(991\) | 416.462 | 0.420245 | 0.210122 | − | 0.977675i | \(-0.432614\pi\) | ||||
0.210122 | + | 0.977675i | \(0.432614\pi\) | |||||||
\(992\) | −73.5946 | + | 42.4899i | −0.0741881 | + | 0.0428325i | ||||
\(993\) | 258.884 | + | 1449.11i | 0.260709 | + | 1.45932i | ||||
\(994\) | 358.236 | − | 620.484i | 0.360399 | − | 0.624229i | ||||
\(995\) | 228.576 | + | 131.969i | 0.229725 | + | 0.132632i | ||||
\(996\) | 120.267 | − | 332.761i | 0.120750 | − | 0.334097i | ||||
\(997\) | 438.591 | + | 759.663i | 0.439911 | + | 0.761948i | 0.997682 | − | 0.0680464i | \(-0.0216766\pi\) |
−0.557771 | + | 0.829995i | \(0.688343\pi\) | |||||||
\(998\) | 1726.13i | 1.72959i | ||||||||
\(999\) | −692.219 | − | 1180.46i | −0.692912 | − | 1.18164i |
(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 | 45.3.i.a.41.8 | yes | 16 | |
3.2 | odd | 2 | 135.3.i.a.71.1 | 16 | |||
4.3 | odd | 2 | 720.3.bs.c.401.8 | 16 | |||
5.2 | odd | 4 | 225.3.i.b.149.14 | 32 | |||
5.3 | odd | 4 | 225.3.i.b.149.3 | 32 | |||
5.4 | even | 2 | 225.3.j.b.176.1 | 16 | |||
9.2 | odd | 6 | inner | 45.3.i.a.11.8 | ✓ | 16 | |
9.4 | even | 3 | 405.3.c.a.161.14 | 16 | |||
9.5 | odd | 6 | 405.3.c.a.161.3 | 16 | |||
9.7 | even | 3 | 135.3.i.a.116.1 | 16 | |||
12.11 | even | 2 | 2160.3.bs.c.881.3 | 16 | |||
15.2 | even | 4 | 675.3.i.c.449.3 | 32 | |||
15.8 | even | 4 | 675.3.i.c.449.14 | 32 | |||
15.14 | odd | 2 | 675.3.j.b.476.8 | 16 | |||
36.7 | odd | 6 | 2160.3.bs.c.1601.3 | 16 | |||
36.11 | even | 6 | 720.3.bs.c.641.8 | 16 | |||
45.2 | even | 12 | 225.3.i.b.74.3 | 32 | |||
45.7 | odd | 12 | 675.3.i.c.224.14 | 32 | |||
45.29 | odd | 6 | 225.3.j.b.101.1 | 16 | |||
45.34 | even | 6 | 675.3.j.b.251.8 | 16 | |||
45.38 | even | 12 | 225.3.i.b.74.14 | 32 | |||
45.43 | odd | 12 | 675.3.i.c.224.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.i.a.11.8 | ✓ | 16 | 9.2 | odd | 6 | inner | |
45.3.i.a.41.8 | yes | 16 | 1.1 | even | 1 | trivial | |
135.3.i.a.71.1 | 16 | 3.2 | odd | 2 | |||
135.3.i.a.116.1 | 16 | 9.7 | even | 3 | |||
225.3.i.b.74.3 | 32 | 45.2 | even | 12 | |||
225.3.i.b.74.14 | 32 | 45.38 | even | 12 | |||
225.3.i.b.149.3 | 32 | 5.3 | odd | 4 | |||
225.3.i.b.149.14 | 32 | 5.2 | odd | 4 | |||
225.3.j.b.101.1 | 16 | 45.29 | odd | 6 | |||
225.3.j.b.176.1 | 16 | 5.4 | even | 2 | |||
405.3.c.a.161.3 | 16 | 9.5 | odd | 6 | |||
405.3.c.a.161.14 | 16 | 9.4 | even | 3 | |||
675.3.i.c.224.3 | 32 | 45.43 | odd | 12 | |||
675.3.i.c.224.14 | 32 | 45.7 | odd | 12 | |||
675.3.i.c.449.3 | 32 | 15.2 | even | 4 | |||
675.3.i.c.449.14 | 32 | 15.8 | even | 4 | |||
675.3.j.b.251.8 | 16 | 45.34 | even | 6 | |||
675.3.j.b.476.8 | 16 | 15.14 | odd | 2 | |||
720.3.bs.c.401.8 | 16 | 4.3 | odd | 2 | |||
720.3.bs.c.641.8 | 16 | 36.11 | even | 6 | |||
2160.3.bs.c.881.3 | 16 | 12.11 | even | 2 | |||
2160.3.bs.c.1601.3 | 16 | 36.7 | odd | 6 |