Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,5,Mod(3,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.65391940934\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 11.4 | ||
Root | \(-2.15805 + 1.82834i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.11 |
Dual form | 16.5.f.a.3.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.329715 | + | 3.98639i | 0.0824289 | + | 0.996597i | ||||
\(3\) | 3.91498 | + | 3.91498i | 0.434998 | + | 0.434998i | 0.890324 | − | 0.455327i | \(-0.150477\pi\) |
−0.455327 | + | 0.890324i | \(0.650477\pi\) | |||||||
\(4\) | −15.7826 | + | 2.62875i | −0.986411 | + | 0.164297i | ||||
\(5\) | 4.72348 | + | 4.72348i | 0.188939 | + | 0.188939i | 0.795237 | − | 0.606298i | \(-0.207346\pi\) |
−0.606298 | + | 0.795237i | \(0.707346\pi\) | |||||||
\(6\) | −14.3158 | + | 16.8975i | −0.397661 | + | 0.469374i | ||||
\(7\) | 45.3712 | 0.925943 | 0.462971 | − | 0.886373i | \(-0.346783\pi\) | ||||
0.462971 | + | 0.886373i | \(0.346783\pi\) | |||||||
\(8\) | −15.6830 | − | 62.0487i | −0.245046 | − | 0.969511i | ||||
\(9\) | − | 50.3458i | − | 0.621554i | ||||||
\(10\) | −17.2722 | + | 20.3870i | −0.172722 | + | 0.203870i | ||||
\(11\) | 110.228 | − | 110.228i | 0.910974 | − | 0.910974i | −0.0853752 | − | 0.996349i | \(-0.527209\pi\) |
0.996349 | + | 0.0853752i | \(0.0272089\pi\) | |||||||
\(12\) | −72.0800 | − | 51.4970i | −0.500555 | − | 0.357618i | ||||
\(13\) | −157.128 | + | 157.128i | −0.929754 | + | 0.929754i | −0.997690 | − | 0.0679357i | \(-0.978359\pi\) |
0.0679357 | + | 0.997690i | \(0.478359\pi\) | |||||||
\(14\) | 14.9596 | + | 180.867i | 0.0763244 | + | 0.922792i | ||||
\(15\) | 36.9847i | 0.164376i | ||||||||
\(16\) | 242.179 | − | 82.9768i | 0.946013 | − | 0.324128i | ||||
\(17\) | −378.592 | −1.31001 | −0.655003 | − | 0.755626i | \(-0.727333\pi\) | ||||
−0.655003 | + | 0.755626i | \(0.727333\pi\) | |||||||
\(18\) | 200.698 | − | 16.5998i | 0.619438 | − | 0.0512340i | ||||
\(19\) | 203.127 | + | 203.127i | 0.562680 | + | 0.562680i | 0.930068 | − | 0.367388i | \(-0.119748\pi\) |
−0.367388 | + | 0.930068i | \(0.619748\pi\) | |||||||
\(20\) | −86.9656 | − | 62.1319i | −0.217414 | − | 0.155330i | ||||
\(21\) | 177.627 | + | 177.627i | 0.402783 | + | 0.402783i | ||||
\(22\) | 475.755 | + | 403.067i | 0.982964 | + | 0.832783i | ||||
\(23\) | −740.444 | −1.39971 | −0.699853 | − | 0.714287i | \(-0.746751\pi\) | ||||
−0.699853 | + | 0.714287i | \(0.746751\pi\) | |||||||
\(24\) | 181.521 | − | 304.318i | 0.315141 | − | 0.528330i | ||||
\(25\) | − | 580.377i | − | 0.928604i | ||||||
\(26\) | −678.183 | − | 574.567i | −1.00323 | − | 0.849951i | ||||
\(27\) | 514.217 | − | 514.217i | 0.705372 | − | 0.705372i | ||||
\(28\) | −716.074 | + | 119.269i | −0.913360 | + | 0.152129i | ||||
\(29\) | 82.6244 | − | 82.6244i | 0.0982455 | − | 0.0982455i | −0.656276 | − | 0.754521i | \(-0.727869\pi\) |
0.754521 | + | 0.656276i | \(0.227869\pi\) | |||||||
\(30\) | −147.435 | + | 12.1944i | −0.163817 | + | 0.0135494i | ||||
\(31\) | 286.217i | 0.297833i | 0.988850 | + | 0.148916i | \(0.0475785\pi\) | ||||
−0.988850 | + | 0.148916i | \(0.952421\pi\) | |||||||
\(32\) | 410.628 | + | 938.062i | 0.401004 | + | 0.916076i | ||||
\(33\) | 863.080 | 0.792543 | ||||||||
\(34\) | −124.828 | − | 1509.21i | −0.107982 | − | 1.30555i | ||||
\(35\) | 214.310 | + | 214.310i | 0.174947 | + | 0.174947i | ||||
\(36\) | 132.346 | + | 794.587i | 0.102119 | + | 0.613107i | ||||
\(37\) | 1470.39 | + | 1470.39i | 1.07406 | + | 1.07406i | 0.997028 | + | 0.0770352i | \(0.0245454\pi\) |
0.0770352 | + | 0.997028i | \(0.475455\pi\) | |||||||
\(38\) | −742.770 | + | 876.719i | −0.514384 | + | 0.607146i | ||||
\(39\) | −1230.31 | −0.808882 | ||||||||
\(40\) | 219.008 | − | 367.164i | 0.136880 | − | 0.229478i | ||||
\(41\) | − | 1301.21i | − | 0.774070i | −0.922065 | − | 0.387035i | \(-0.873499\pi\) | ||
0.922065 | − | 0.387035i | \(-0.126501\pi\) | |||||||
\(42\) | −649.525 | + | 766.658i | −0.368212 | + | 0.434613i | ||||
\(43\) | −366.979 | + | 366.979i | −0.198474 | + | 0.198474i | −0.799346 | − | 0.600871i | \(-0.794820\pi\) |
0.600871 | + | 0.799346i | \(0.294820\pi\) | |||||||
\(44\) | −1449.92 | + | 2029.44i | −0.748924 | + | 1.04826i | ||||
\(45\) | 237.808 | − | 237.808i | 0.117436 | − | 0.117436i | ||||
\(46\) | −244.136 | − | 2951.70i | −0.115376 | − | 1.39494i | ||||
\(47\) | 751.307i | 0.340112i | 0.985434 | + | 0.170056i | \(0.0543948\pi\) | ||||
−0.985434 | + | 0.170056i | \(0.945605\pi\) | |||||||
\(48\) | 1272.98 | + | 623.275i | 0.552509 | + | 0.270519i | ||||
\(49\) | −342.455 | −0.142630 | ||||||||
\(50\) | 2313.61 | − | 191.359i | 0.925444 | − | 0.0765437i | ||||
\(51\) | −1482.18 | − | 1482.18i | −0.569850 | − | 0.569850i | ||||
\(52\) | 2066.84 | − | 2892.94i | 0.764364 | − | 1.06988i | ||||
\(53\) | −1929.33 | − | 1929.33i | −0.686838 | − | 0.686838i | 0.274693 | − | 0.961532i | \(-0.411424\pi\) |
−0.961532 | + | 0.274693i | \(0.911424\pi\) | |||||||
\(54\) | 2219.41 | + | 1880.32i | 0.761115 | + | 0.644829i | ||||
\(55\) | 1041.32 | 0.344238 | ||||||||
\(56\) | −711.555 | − | 2815.22i | −0.226899 | − | 0.897712i | ||||
\(57\) | 1590.48i | 0.489529i | ||||||||
\(58\) | 356.616 | + | 302.130i | 0.106009 | + | 0.0898129i | ||||
\(59\) | −1357.57 | + | 1357.57i | −0.389994 | + | 0.389994i | −0.874685 | − | 0.484691i | \(-0.838932\pi\) |
0.484691 | + | 0.874685i | \(0.338932\pi\) | |||||||
\(60\) | −97.2234 | − | 583.714i | −0.0270065 | − | 0.162143i | ||||
\(61\) | −1835.78 | + | 1835.78i | −0.493356 | + | 0.493356i | −0.909362 | − | 0.416006i | \(-0.863430\pi\) |
0.416006 | + | 0.909362i | \(0.363430\pi\) | |||||||
\(62\) | −1140.97 | + | 94.3702i | −0.296819 | + | 0.0245500i | ||||
\(63\) | − | 2284.25i | − | 0.575523i | ||||||
\(64\) | −3604.09 | + | 1946.22i | −0.879905 | + | 0.475150i | ||||
\(65\) | −1484.39 | −0.351334 | ||||||||
\(66\) | 284.571 | + | 3440.57i | 0.0653284 | + | 0.789846i | ||||
\(67\) | 2205.02 | + | 2205.02i | 0.491204 | + | 0.491204i | 0.908686 | − | 0.417481i | \(-0.137087\pi\) |
−0.417481 | + | 0.908686i | \(0.637087\pi\) | |||||||
\(68\) | 5975.15 | − | 995.222i | 1.29220 | − | 0.215230i | ||||
\(69\) | −2898.83 | − | 2898.83i | −0.608869 | − | 0.608869i | ||||
\(70\) | −783.662 | + | 924.984i | −0.159931 | + | 0.188772i | ||||
\(71\) | 8970.40 | 1.77949 | 0.889744 | − | 0.456460i | \(-0.150883\pi\) | ||||
0.889744 | + | 0.456460i | \(0.150883\pi\) | |||||||
\(72\) | −3123.90 | + | 789.572i | −0.602603 | + | 0.152309i | ||||
\(73\) | 9350.46i | 1.75464i | 0.479909 | + | 0.877318i | \(0.340670\pi\) | ||||
−0.479909 | + | 0.877318i | \(0.659330\pi\) | |||||||
\(74\) | −5376.75 | + | 6346.37i | −0.981875 | + | 1.15894i | ||||
\(75\) | 2272.17 | − | 2272.17i | 0.403941 | − | 0.403941i | ||||
\(76\) | −3739.84 | − | 2671.90i | −0.647480 | − | 0.462587i | ||||
\(77\) | 5001.17 | − | 5001.17i | 0.843509 | − | 0.843509i | ||||
\(78\) | −405.652 | − | 4904.49i | −0.0666752 | − | 0.806129i | ||||
\(79\) | − | 2860.08i | − | 0.458273i | −0.973394 | − | 0.229137i | \(-0.926410\pi\) | ||
0.973394 | − | 0.229137i | \(-0.0735903\pi\) | |||||||
\(80\) | 1535.87 | + | 751.991i | 0.239980 | + | 0.117499i | ||||
\(81\) | −51.7173 | −0.00788253 | ||||||||
\(82\) | 5187.13 | − | 429.029i | 0.771436 | − | 0.0638057i | ||||
\(83\) | −1036.63 | − | 1036.63i | −0.150477 | − | 0.150477i | 0.627854 | − | 0.778331i | \(-0.283933\pi\) |
−0.778331 | + | 0.627854i | \(0.783933\pi\) | |||||||
\(84\) | −3270.35 | − | 2336.48i | −0.463486 | − | 0.331134i | ||||
\(85\) | −1788.27 | − | 1788.27i | −0.247512 | − | 0.247512i | ||||
\(86\) | −1583.92 | − | 1341.92i | −0.214159 | − | 0.181439i | ||||
\(87\) | 646.946 | 0.0854731 | ||||||||
\(88\) | −8568.19 | − | 5110.80i | −1.10643 | − | 0.659969i | ||||
\(89\) | − | 5171.06i | − | 0.652830i | −0.945227 | − | 0.326415i | \(-0.894159\pi\) | ||
0.945227 | − | 0.326415i | \(-0.105841\pi\) | |||||||
\(90\) | 1026.40 | + | 869.585i | 0.126716 | + | 0.107356i | ||||
\(91\) | −7129.10 | + | 7129.10i | −0.860899 | + | 0.860899i | ||||
\(92\) | 11686.1 | − | 1946.44i | 1.38068 | − | 0.229967i | ||||
\(93\) | −1120.54 | + | 1120.54i | −0.129557 | + | 0.129557i | ||||
\(94\) | −2995.00 | + | 247.717i | −0.338954 | + | 0.0280350i | ||||
\(95\) | 1918.94i | 0.212625i | ||||||||
\(96\) | −2064.90 | + | 5280.10i | −0.224055 | + | 0.572927i | ||||
\(97\) | 8539.92 | 0.907633 | 0.453817 | − | 0.891095i | \(-0.350062\pi\) | ||||
0.453817 | + | 0.891095i | \(0.350062\pi\) | |||||||
\(98\) | −112.913 | − | 1365.16i | −0.0117568 | − | 0.142145i | ||||
\(99\) | −5549.51 | − | 5549.51i | −0.566219 | − | 0.566219i | ||||
\(100\) | 1525.67 | + | 9159.85i | 0.152567 | + | 0.915985i | ||||
\(101\) | 537.642 | + | 537.642i | 0.0527049 | + | 0.0527049i | 0.732968 | − | 0.680263i | \(-0.238134\pi\) |
−0.680263 | + | 0.732968i | \(0.738134\pi\) | |||||||
\(102\) | 5419.85 | − | 6397.24i | 0.520939 | − | 0.614883i | ||||
\(103\) | −5543.86 | −0.522562 | −0.261281 | − | 0.965263i | \(-0.584145\pi\) | ||||
−0.261281 | + | 0.965263i | \(0.584145\pi\) | |||||||
\(104\) | 12213.9 | + | 7285.38i | 1.12924 | + | 0.673574i | ||||
\(105\) | 1678.04i | 0.152203i | ||||||||
\(106\) | 7054.92 | − | 8327.18i | 0.627886 | − | 0.741116i | ||||
\(107\) | −2989.60 | + | 2989.60i | −0.261123 | + | 0.261123i | −0.825510 | − | 0.564387i | \(-0.809113\pi\) |
0.564387 | + | 0.825510i | \(0.309113\pi\) | |||||||
\(108\) | −6763.92 | + | 9467.41i | −0.579897 | + | 0.811677i | ||||
\(109\) | −3353.83 | + | 3353.83i | −0.282285 | + | 0.282285i | −0.834020 | − | 0.551734i | \(-0.813966\pi\) |
0.551734 | + | 0.834020i | \(0.313966\pi\) | |||||||
\(110\) | 343.339 | + | 4151.10i | 0.0283751 | + | 0.343066i | ||||
\(111\) | 11513.1i | 0.934431i | ||||||||
\(112\) | 10988.0 | − | 3764.76i | 0.875954 | − | 0.300124i | ||||
\(113\) | −3193.81 | −0.250122 | −0.125061 | − | 0.992149i | \(-0.539913\pi\) | ||||
−0.125061 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(114\) | −6340.27 | + | 524.406i | −0.487863 | + | 0.0403513i | ||||
\(115\) | −3497.48 | − | 3497.48i | −0.264459 | − | 0.264459i | ||||
\(116\) | −1086.83 | + | 1521.22i | −0.0807690 | + | 0.113052i | ||||
\(117\) | 7910.76 | + | 7910.76i | 0.577892 | + | 0.577892i | ||||
\(118\) | −5859.41 | − | 4964.18i | −0.420813 | − | 0.356520i | ||||
\(119\) | −17177.2 | −1.21299 | ||||||||
\(120\) | 2294.85 | − | 580.030i | 0.159365 | − | 0.0402798i | ||||
\(121\) | − | 9659.34i | − | 0.659746i | ||||||
\(122\) | −7923.41 | − | 6712.84i | −0.532344 | − | 0.451010i | ||||
\(123\) | 5094.22 | − | 5094.22i | 0.336719 | − | 0.336719i | ||||
\(124\) | −752.393 | − | 4517.24i | −0.0489329 | − | 0.293785i | ||||
\(125\) | 5693.58 | − | 5693.58i | 0.364389 | − | 0.364389i | ||||
\(126\) | 9105.91 | − | 753.153i | 0.573565 | − | 0.0474397i | ||||
\(127\) | − | 22900.5i | − | 1.41983i | −0.704287 | − | 0.709915i | \(-0.748733\pi\) | ||
0.704287 | − | 0.709915i | \(-0.251267\pi\) | |||||||
\(128\) | −8946.69 | − | 13725.6i | −0.546063 | − | 0.837744i | ||||
\(129\) | −2873.43 | −0.172672 | ||||||||
\(130\) | −489.425 | − | 5917.34i | −0.0289601 | − | 0.350139i | ||||
\(131\) | 19255.9 | + | 19255.9i | 1.12207 | + | 1.12207i | 0.991429 | + | 0.130644i | \(0.0417045\pi\) |
0.130644 | + | 0.991429i | \(0.458296\pi\) | |||||||
\(132\) | −13621.6 | + | 2268.82i | −0.781773 | + | 0.130212i | ||||
\(133\) | 9216.13 | + | 9216.13i | 0.521009 | + | 0.521009i | ||||
\(134\) | −8063.02 | + | 9517.08i | −0.449043 | + | 0.530022i | ||||
\(135\) | 4857.79 | 0.266545 | ||||||||
\(136\) | 5937.44 | + | 23491.1i | 0.321012 | + | 1.27007i | ||||
\(137\) | − | 19938.2i | − | 1.06229i | −0.847280 | − | 0.531147i | \(-0.821761\pi\) | ||
0.847280 | − | 0.531147i | \(-0.178239\pi\) | |||||||
\(138\) | 10600.1 | − | 12511.6i | 0.556609 | − | 0.656985i | ||||
\(139\) | 25175.4 | − | 25175.4i | 1.30301 | − | 1.30301i | 0.376649 | − | 0.926356i | \(-0.377076\pi\) |
0.926356 | − | 0.376649i | \(-0.122924\pi\) | |||||||
\(140\) | −3945.73 | − | 2819.00i | −0.201313 | − | 0.143826i | ||||
\(141\) | −2941.35 | + | 2941.35i | −0.147948 | + | 0.147948i | ||||
\(142\) | 2957.68 | + | 35759.5i | 0.146681 | + | 1.77343i | ||||
\(143\) | 34639.8i | 1.69396i | ||||||||
\(144\) | −4177.54 | − | 12192.7i | −0.201463 | − | 0.587998i | ||||
\(145\) | 780.550 | 0.0371249 | ||||||||
\(146\) | −37274.5 | + | 3082.99i | −1.74867 | + | 0.144633i | ||||
\(147\) | −1340.70 | − | 1340.70i | −0.0620438 | − | 0.0620438i | ||||
\(148\) | −27071.9 | − | 19341.3i | −1.23593 | − | 0.883003i | ||||
\(149\) | −3216.99 | − | 3216.99i | −0.144903 | − | 0.144903i | 0.630934 | − | 0.775837i | \(-0.282672\pi\) |
−0.775837 | + | 0.630934i | \(0.782672\pi\) | |||||||
\(150\) | 9806.91 | + | 8308.57i | 0.435862 | + | 0.369270i | ||||
\(151\) | −14770.5 | −0.647802 | −0.323901 | − | 0.946091i | \(-0.604994\pi\) | ||||
−0.323901 | + | 0.946091i | \(0.604994\pi\) | |||||||
\(152\) | 9418.15 | − | 15789.4i | 0.407642 | − | 0.683407i | ||||
\(153\) | 19060.5i | 0.814239i | ||||||||
\(154\) | 21585.6 | + | 18287.6i | 0.910168 | + | 0.771109i | ||||
\(155\) | −1351.94 | + | 1351.94i | −0.0562723 | + | 0.0562723i | ||||
\(156\) | 19417.5 | − | 3234.17i | 0.797890 | − | 0.132897i | ||||
\(157\) | −18014.6 | + | 18014.6i | −0.730845 | + | 0.730845i | −0.970787 | − | 0.239942i | \(-0.922872\pi\) |
0.239942 | + | 0.970787i | \(0.422872\pi\) | |||||||
\(158\) | 11401.4 | − | 943.014i | 0.456714 | − | 0.0377749i | ||||
\(159\) | − | 15106.6i | − | 0.597547i | ||||||
\(160\) | −2491.33 | + | 6370.52i | −0.0973175 | + | 0.248848i | ||||
\(161\) | −33594.8 | −1.29605 | ||||||||
\(162\) | −17.0520 | − | 206.165i | −0.000649748 | − | 0.00785571i | ||||
\(163\) | 15083.2 | + | 15083.2i | 0.567700 | + | 0.567700i | 0.931483 | − | 0.363784i | \(-0.118515\pi\) |
−0.363784 | + | 0.931483i | \(0.618515\pi\) | |||||||
\(164\) | 3420.55 | + | 20536.5i | 0.127177 | + | 0.763551i | ||||
\(165\) | 4076.74 | + | 4076.74i | 0.149743 | + | 0.149743i | ||||
\(166\) | 3790.63 | − | 4474.22i | 0.137561 | − | 0.162368i | ||||
\(167\) | 23733.6 | 0.851001 | 0.425501 | − | 0.904958i | \(-0.360098\pi\) | ||||
0.425501 | + | 0.904958i | \(0.360098\pi\) | |||||||
\(168\) | 8235.83 | − | 13807.3i | 0.291802 | − | 0.489203i | ||||
\(169\) | − | 20817.7i | − | 0.728885i | ||||||
\(170\) | 6539.13 | − | 7718.37i | 0.226267 | − | 0.267072i | ||||
\(171\) | 10226.6 | − | 10226.6i | 0.349736 | − | 0.349736i | ||||
\(172\) | 4827.18 | − | 6756.57i | 0.163169 | − | 0.228386i | ||||
\(173\) | −12072.3 | + | 12072.3i | −0.403363 | + | 0.403363i | −0.879416 | − | 0.476053i | \(-0.842067\pi\) |
0.476053 | + | 0.879416i | \(0.342067\pi\) | |||||||
\(174\) | 213.308 | + | 2578.98i | 0.00704545 | + | 0.0851823i | ||||
\(175\) | − | 26332.4i | − | 0.859834i | ||||||
\(176\) | 17548.6 | − | 35841.3i | 0.566521 | − | 1.15707i | ||||
\(177\) | −10629.7 | −0.339293 | ||||||||
\(178\) | 20613.9 | − | 1704.98i | 0.650608 | − | 0.0538120i | ||||
\(179\) | −28111.5 | − | 28111.5i | −0.877361 | − | 0.877361i | 0.115900 | − | 0.993261i | \(-0.463025\pi\) |
−0.993261 | + | 0.115900i | \(0.963025\pi\) | |||||||
\(180\) | −3128.08 | + | 4378.36i | −0.0965458 | + | 0.135134i | ||||
\(181\) | −15906.7 | − | 15906.7i | −0.485539 | − | 0.485539i | 0.421356 | − | 0.906895i | \(-0.361554\pi\) |
−0.906895 | + | 0.421356i | \(0.861554\pi\) | |||||||
\(182\) | −30770.0 | − | 26068.8i | −0.928932 | − | 0.787006i | ||||
\(183\) | −14374.1 | −0.429218 | ||||||||
\(184\) | 11612.4 | + | 45943.6i | 0.342993 | + | 1.35703i | ||||
\(185\) | 13890.8i | 0.405866i | ||||||||
\(186\) | −4836.34 | − | 4097.43i | −0.139795 | − | 0.118437i | ||||
\(187\) | −41731.4 | + | 41731.4i | −1.19338 | + | 1.19338i | ||||
\(188\) | −1975.00 | − | 11857.6i | −0.0558792 | − | 0.335490i | ||||
\(189\) | 23330.6 | − | 23330.6i | 0.653134 | − | 0.653134i | ||||
\(190\) | −7649.63 | + | 632.703i | −0.211901 | + | 0.0175264i | ||||
\(191\) | 28038.6i | 0.768581i | 0.923212 | + | 0.384290i | \(0.125554\pi\) | ||||
−0.923212 | + | 0.384290i | \(0.874446\pi\) | |||||||
\(192\) | −21729.3 | − | 6490.54i | −0.589446 | − | 0.176067i | ||||
\(193\) | 56713.1 | 1.52254 | 0.761270 | − | 0.648436i | \(-0.224576\pi\) | ||||
0.761270 | + | 0.648436i | \(0.224576\pi\) | |||||||
\(194\) | 2815.74 | + | 34043.4i | 0.0748152 | + | 0.904544i | ||||
\(195\) | −5811.35 | − | 5811.35i | −0.152830 | − | 0.152830i | ||||
\(196\) | 5404.82 | − | 900.227i | 0.140692 | − | 0.0234337i | ||||
\(197\) | −10179.3 | − | 10179.3i | −0.262292 | − | 0.262292i | 0.563692 | − | 0.825985i | \(-0.309380\pi\) |
−0.825985 | + | 0.563692i | \(0.809380\pi\) | |||||||
\(198\) | 20292.7 | − | 23952.3i | 0.517619 | − | 0.610965i | ||||
\(199\) | 31787.3 | 0.802689 | 0.401344 | − | 0.915927i | \(-0.368543\pi\) | ||||
0.401344 | + | 0.915927i | \(0.368543\pi\) | |||||||
\(200\) | −36011.7 | + | 9102.04i | −0.900292 | + | 0.227551i | ||||
\(201\) | 17265.2i | 0.427346i | ||||||||
\(202\) | −1965.98 | + | 2320.52i | −0.0481811 | + | 0.0568699i | ||||
\(203\) | 3748.77 | − | 3748.77i | 0.0909697 | − | 0.0909697i | ||||
\(204\) | 27288.9 | + | 19496.3i | 0.655731 | + | 0.468482i | ||||
\(205\) | 6146.25 | − | 6146.25i | 0.146252 | − | 0.146252i | ||||
\(206\) | −1827.89 | − | 22100.0i | −0.0430742 | − | 0.520783i | ||||
\(207\) | 37278.3i | 0.869992i | ||||||||
\(208\) | −25015.3 | + | 51091.3i | −0.578200 | + | 1.18092i | ||||
\(209\) | 44780.6 | 1.02517 | ||||||||
\(210\) | −6689.32 | + | 553.276i | −0.151685 | + | 0.0125459i | ||||
\(211\) | −10699.8 | − | 10699.8i | −0.240332 | − | 0.240332i | 0.576655 | − | 0.816988i | \(-0.304358\pi\) |
−0.816988 | + | 0.576655i | \(0.804358\pi\) | |||||||
\(212\) | 35521.5 | + | 25378.1i | 0.790350 | + | 0.564660i | ||||
\(213\) | 35118.9 | + | 35118.9i | 0.774073 | + | 0.774073i | ||||
\(214\) | −12903.4 | − | 10932.0i | −0.281759 | − | 0.238711i | ||||
\(215\) | −3466.84 | −0.0749992 | ||||||||
\(216\) | −39970.9 | − | 23842.0i | −0.856716 | − | 0.511018i | ||||
\(217\) | 12986.0i | 0.275776i | ||||||||
\(218\) | −14475.5 | − | 12263.9i | −0.304593 | − | 0.258056i | ||||
\(219\) | −36606.9 | + | 36606.9i | −0.763263 | + | 0.763263i | ||||
\(220\) | −16434.7 | + | 2737.36i | −0.339560 | + | 0.0565571i | ||||
\(221\) | 59487.5 | − | 59487.5i | 1.21798 | − | 1.21798i | ||||
\(222\) | −45895.8 | + | 3796.05i | −0.931251 | + | 0.0770241i | ||||
\(223\) | − | 91700.4i | − | 1.84400i | −0.387187 | − | 0.922001i | \(-0.626553\pi\) | ||
0.387187 | − | 0.922001i | \(-0.373447\pi\) | |||||||
\(224\) | 18630.7 | + | 42561.0i | 0.371307 | + | 0.848234i | ||||
\(225\) | −29219.6 | −0.577177 | ||||||||
\(226\) | −1053.05 | − | 12731.8i | −0.0206173 | − | 0.249271i | ||||
\(227\) | 17499.5 | + | 17499.5i | 0.339605 | + | 0.339605i | 0.856218 | − | 0.516614i | \(-0.172808\pi\) |
−0.516614 | + | 0.856218i | \(0.672808\pi\) | |||||||
\(228\) | −4180.97 | − | 25101.9i | −0.0804280 | − | 0.482877i | ||||
\(229\) | −63859.8 | − | 63859.8i | −1.21775 | − | 1.21775i | −0.968420 | − | 0.249326i | \(-0.919791\pi\) |
−0.249326 | − | 0.968420i | \(-0.580209\pi\) | |||||||
\(230\) | 12789.1 | − | 15095.5i | 0.241760 | − | 0.285359i | ||||
\(231\) | 39159.0 | 0.733850 | ||||||||
\(232\) | −6422.54 | − | 3830.94i | −0.119325 | − | 0.0711754i | ||||
\(233\) | 63891.7i | 1.17688i | 0.808540 | + | 0.588441i | \(0.200258\pi\) | ||||
−0.808540 | + | 0.588441i | \(0.799742\pi\) | |||||||
\(234\) | −28927.1 | + | 34143.7i | −0.528290 | + | 0.623560i | ||||
\(235\) | −3548.79 | + | 3548.79i | −0.0642605 | + | 0.0642605i | ||||
\(236\) | 17857.2 | − | 24994.6i | 0.320620 | − | 0.448769i | ||||
\(237\) | 11197.2 | − | 11197.2i | 0.199348 | − | 0.199348i | ||||
\(238\) | −5663.58 | − | 68474.8i | −0.0999855 | − | 1.20886i | ||||
\(239\) | 12096.4i | 0.211768i | 0.994378 | + | 0.105884i | \(0.0337672\pi\) | ||||
−0.994378 | + | 0.105884i | \(0.966233\pi\) | |||||||
\(240\) | 3068.87 | + | 8956.93i | 0.0532790 | + | 0.155502i | ||||
\(241\) | 27978.6 | 0.481717 | 0.240859 | − | 0.970560i | \(-0.422571\pi\) | ||||
0.240859 | + | 0.970560i | \(0.422571\pi\) | |||||||
\(242\) | 38505.9 | − | 3184.83i | 0.657501 | − | 0.0543821i | ||||
\(243\) | −41854.0 | − | 41854.0i | −0.708801 | − | 0.708801i | ||||
\(244\) | 24147.5 | − | 33799.1i | 0.405595 | − | 0.567709i | ||||
\(245\) | −1617.58 | − | 1617.58i | −0.0269484 | − | 0.0269484i | ||||
\(246\) | 21987.2 | + | 18627.9i | 0.363328 | + | 0.307818i | ||||
\(247\) | −63834.2 | −1.04631 | ||||||||
\(248\) | 17759.4 | − | 4488.73i | 0.288752 | − | 0.0729828i | ||||
\(249\) | − | 8116.80i | − | 0.130914i | ||||||
\(250\) | 24574.1 | + | 20819.6i | 0.393185 | + | 0.333113i | ||||
\(251\) | 1996.06 | − | 1996.06i | 0.0316830 | − | 0.0316830i | −0.691088 | − | 0.722771i | \(-0.742868\pi\) |
0.722771 | + | 0.691088i | \(0.242868\pi\) | |||||||
\(252\) | 6004.72 | + | 36051.4i | 0.0945565 | + | 0.567702i | ||||
\(253\) | −81617.5 | + | 81617.5i | −1.27509 | + | 1.27509i | ||||
\(254\) | 91290.1 | − | 7550.63i | 1.41500 | − | 0.117035i | ||||
\(255\) | − | 14002.1i | − | 0.215334i | ||||||
\(256\) | 51765.7 | − | 40190.5i | 0.789882 | − | 0.613259i | ||||
\(257\) | −73510.4 | −1.11297 | −0.556484 | − | 0.830859i | \(-0.687850\pi\) | ||||
−0.556484 | + | 0.830859i | \(0.687850\pi\) | |||||||
\(258\) | −947.415 | − | 11454.6i | −0.0142331 | − | 0.172084i | ||||
\(259\) | 66713.5 | + | 66713.5i | 0.994521 | + | 0.994521i | ||||
\(260\) | 23427.5 | − | 3902.08i | 0.346560 | − | 0.0577231i | ||||
\(261\) | −4159.80 | − | 4159.80i | −0.0610648 | − | 0.0610648i | ||||
\(262\) | −70412.5 | + | 83110.5i | −1.02576 | + | 1.21075i | ||||
\(263\) | 68109.3 | 0.984680 | 0.492340 | − | 0.870403i | \(-0.336142\pi\) | ||||
0.492340 | + | 0.870403i | \(0.336142\pi\) | |||||||
\(264\) | −13535.6 | − | 53553.0i | −0.194210 | − | 0.768380i | ||||
\(265\) | − | 18226.3i | − | 0.259542i | ||||||
\(266\) | −33700.4 | + | 39777.8i | −0.476290 | + | 0.562182i | ||||
\(267\) | 20244.6 | − | 20244.6i | 0.283980 | − | 0.283980i | ||||
\(268\) | −40597.3 | − | 29004.4i | −0.565232 | − | 0.403826i | ||||
\(269\) | −15056.1 | + | 15056.1i | −0.208069 | + | 0.208069i | −0.803446 | − | 0.595377i | \(-0.797003\pi\) |
0.595377 | + | 0.803446i | \(0.297003\pi\) | |||||||
\(270\) | 1601.69 | + | 19365.0i | 0.0219710 | + | 0.265638i | ||||
\(271\) | 104320.i | 1.42046i | 0.703968 | + | 0.710232i | \(0.251410\pi\) | ||||
−0.703968 | + | 0.710232i | \(0.748590\pi\) | |||||||
\(272\) | −91687.1 | + | 31414.3i | −1.23928 | + | 0.424610i | ||||
\(273\) | −55820.6 | −0.748979 | ||||||||
\(274\) | 79481.4 | − | 6573.93i | 1.05868 | − | 0.0875637i | ||||
\(275\) | −63973.7 | − | 63973.7i | −0.845934 | − | 0.845934i | ||||
\(276\) | 53371.2 | + | 38130.6i | 0.700630 | + | 0.500560i | ||||
\(277\) | 2136.36 | + | 2136.36i | 0.0278430 | + | 0.0278430i | 0.720891 | − | 0.693048i | \(-0.243733\pi\) |
−0.693048 | + | 0.720891i | \(0.743733\pi\) | |||||||
\(278\) | 108659. | + | 92058.1i | 1.40598 | + | 1.19117i | ||||
\(279\) | 14409.8 | 0.185119 | ||||||||
\(280\) | 9936.65 | − | 16658.7i | 0.126743 | − | 0.212483i | ||||
\(281\) | − | 36783.7i | − | 0.465846i | −0.972495 | − | 0.232923i | \(-0.925171\pi\) | ||
0.972495 | − | 0.232923i | \(-0.0748290\pi\) | |||||||
\(282\) | −12695.2 | − | 10755.6i | −0.159640 | − | 0.135249i | ||||
\(283\) | 14172.0 | − | 14172.0i | 0.176953 | − | 0.176953i | −0.613073 | − | 0.790026i | \(-0.710067\pi\) |
0.790026 | + | 0.613073i | \(0.210067\pi\) | |||||||
\(284\) | −141576. | + | 23580.9i | −1.75531 | + | 0.292364i | ||||
\(285\) | −7512.60 | + | 7512.60i | −0.0924913 | + | 0.0924913i | ||||
\(286\) | −138088. | + | 11421.3i | −1.68820 | + | 0.139631i | ||||
\(287\) | − | 59037.5i | − | 0.716744i | ||||||
\(288\) | 47227.5 | − | 20673.4i | 0.569391 | − | 0.249245i | ||||
\(289\) | 59810.8 | 0.716117 | ||||||||
\(290\) | 257.359 | + | 3111.58i | 0.00306016 | + | 0.0369985i | ||||
\(291\) | 33433.6 | + | 33433.6i | 0.394819 | + | 0.394819i | ||||
\(292\) | −24580.0 | − | 147574.i | −0.288281 | − | 1.73079i | ||||
\(293\) | 80721.8 | + | 80721.8i | 0.940276 | + | 0.940276i | 0.998314 | − | 0.0580384i | \(-0.0184846\pi\) |
−0.0580384 | + | 0.998314i | \(0.518485\pi\) | |||||||
\(294\) | 4902.52 | − | 5786.62i | 0.0567185 | − | 0.0669469i | ||||
\(295\) | −12824.9 | −0.147370 | ||||||||
\(296\) | 68175.9 | − | 114296.i | 0.778122 | − | 1.30451i | ||||
\(297\) | − | 113362.i | − | 1.28515i | ||||||
\(298\) | 11763.5 | − | 13884.9i | 0.132466 | − | 0.156354i | ||||
\(299\) | 116345. | − | 116345.i | 1.30138 | − | 1.30138i | ||||
\(300\) | −29887.7 | + | 41833.6i | −0.332085 | + | 0.464818i | ||||
\(301\) | −16650.3 | + | 16650.3i | −0.183776 | + | 0.183776i | ||||
\(302\) | −4870.07 | − | 58881.1i | −0.0533976 | − | 0.645598i | ||||
\(303\) | 4209.72i | 0.0458530i | ||||||||
\(304\) | 66048.1 | + | 32338.4i | 0.714683 | + | 0.349922i | ||||
\(305\) | −17342.5 | −0.186429 | ||||||||
\(306\) | −75982.7 | + | 6284.55i | −0.811468 | + | 0.0671168i | ||||
\(307\) | 113714. | + | 113714.i | 1.20653 | + | 1.20653i | 0.972143 | + | 0.234389i | \(0.0753090\pi\) |
0.234389 | + | 0.972143i | \(0.424691\pi\) | |||||||
\(308\) | −65784.5 | + | 92078.1i | −0.693461 | + | 0.970633i | ||||
\(309\) | −21704.1 | − | 21704.1i | −0.227313 | − | 0.227313i | ||||
\(310\) | −5835.12 | − | 4943.61i | −0.0607193 | − | 0.0514424i | ||||
\(311\) | −93801.8 | −0.969819 | −0.484909 | − | 0.874564i | \(-0.661147\pi\) | ||||
−0.484909 | + | 0.874564i | \(0.661147\pi\) | |||||||
\(312\) | 19294.9 | + | 76339.2i | 0.198214 | + | 0.784220i | ||||
\(313\) | − | 9229.52i | − | 0.0942086i | −0.998890 | − | 0.0471043i | \(-0.985001\pi\) | ||
0.998890 | − | 0.0471043i | \(-0.0149993\pi\) | |||||||
\(314\) | −77752.9 | − | 65873.5i | −0.788601 | − | 0.668115i | ||||
\(315\) | 10789.6 | − | 10789.6i | 0.108739 | − | 0.108739i | ||||
\(316\) | 7518.44 | + | 45139.5i | 0.0752928 | + | 0.452046i | ||||
\(317\) | −8447.44 | + | 8447.44i | −0.0840634 | + | 0.0840634i | −0.747888 | − | 0.663825i | \(-0.768932\pi\) |
0.663825 | + | 0.747888i | \(0.268932\pi\) | |||||||
\(318\) | 60220.7 | − | 4980.87i | 0.595513 | − | 0.0492551i | ||||
\(319\) | − | 18215.0i | − | 0.178998i | ||||||
\(320\) | −26216.8 | − | 7830.94i | −0.256023 | − | 0.0764740i | ||||
\(321\) | −23408.5 | −0.227176 | ||||||||
\(322\) | −11076.7 | − | 133922.i | −0.106832 | − | 1.29164i | ||||
\(323\) | −76902.4 | − | 76902.4i | −0.737114 | − | 0.737114i | ||||
\(324\) | 816.232 | − | 135.952i | 0.00777542 | − | 0.00129507i | ||||
\(325\) | 91193.8 | + | 91193.8i | 0.863373 | + | 0.863373i | ||||
\(326\) | −55154.4 | + | 65100.7i | −0.518973 | + | 0.612562i | ||||
\(327\) | −26260.4 | −0.245587 | ||||||||
\(328\) | −80738.5 | + | 20406.8i | −0.750469 | + | 0.189683i | ||||
\(329\) | 34087.7i | 0.314924i | ||||||||
\(330\) | −14907.3 | + | 17595.6i | −0.136890 | + | 0.161576i | ||||
\(331\) | −46092.1 | + | 46092.1i | −0.420698 | + | 0.420698i | −0.885444 | − | 0.464746i | \(-0.846146\pi\) |
0.464746 | + | 0.885444i | \(0.346146\pi\) | |||||||
\(332\) | 19085.8 | + | 13635.7i | 0.173155 | + | 0.123709i | ||||
\(333\) | 74028.2 | − | 74028.2i | 0.667588 | − | 0.667588i | ||||
\(334\) | 7825.33 | + | 94611.2i | 0.0701471 | + | 0.848105i | ||||
\(335\) | 20830.7i | 0.185616i | ||||||||
\(336\) | 57756.6 | + | 28278.7i | 0.511592 | + | 0.250485i | ||||
\(337\) | 39317.8 | 0.346201 | 0.173101 | − | 0.984904i | \(-0.444621\pi\) | ||||
0.173101 | + | 0.984904i | \(0.444621\pi\) | |||||||
\(338\) | 82987.4 | − | 6863.91i | 0.726405 | − | 0.0600812i | ||||
\(339\) | −12503.7 | − | 12503.7i | −0.108803 | − | 0.108803i | ||||
\(340\) | 32924.5 | + | 23522.6i | 0.284814 | + | 0.203483i | ||||
\(341\) | 31549.1 | + | 31549.1i | 0.271318 | + | 0.271318i | ||||
\(342\) | 44139.1 | + | 37395.4i | 0.377374 | + | 0.319717i | ||||
\(343\) | −124474. | −1.05801 | ||||||||
\(344\) | 28525.9 | + | 17015.3i | 0.241059 | + | 0.143788i | ||||
\(345\) | − | 27385.1i | − | 0.230079i | ||||||
\(346\) | −52105.1 | − | 44144.3i | −0.435239 | − | 0.368742i | ||||
\(347\) | −67694.0 | + | 67694.0i | −0.562201 | + | 0.562201i | −0.929932 | − | 0.367731i | \(-0.880135\pi\) |
0.367731 | + | 0.929932i | \(0.380135\pi\) | |||||||
\(348\) | −10210.5 | + | 1700.66i | −0.0843116 | + | 0.0140430i | ||||
\(349\) | −7662.83 | + | 7662.83i | −0.0629127 | + | 0.0629127i | −0.737863 | − | 0.674950i | \(-0.764165\pi\) |
0.674950 | + | 0.737863i | \(0.264165\pi\) | |||||||
\(350\) | 104971. | − | 8682.20i | 0.856908 | − | 0.0708751i | ||||
\(351\) | 161596.i | 1.31165i | ||||||||
\(352\) | 148663. | + | 58137.9i | 1.19983 | + | 0.469217i | ||||
\(353\) | 70618.0 | 0.566716 | 0.283358 | − | 0.959014i | \(-0.408551\pi\) | ||||
0.283358 | + | 0.959014i | \(0.408551\pi\) | |||||||
\(354\) | −3504.78 | − | 42374.2i | −0.0279675 | − | 0.338138i | ||||
\(355\) | 42371.5 | + | 42371.5i | 0.336215 | + | 0.336215i | ||||
\(356\) | 13593.4 | + | 81612.7i | 0.107258 | + | 0.643958i | ||||
\(357\) | −67248.3 | − | 67248.3i | −0.527649 | − | 0.527649i | ||||
\(358\) | 102795. | − | 121332.i | 0.802055 | − | 0.946695i | ||||
\(359\) | −168144. | −1.30465 | −0.652323 | − | 0.757941i | \(-0.726206\pi\) | ||||
−0.652323 | + | 0.757941i | \(0.726206\pi\) | |||||||
\(360\) | −18485.2 | − | 11026.1i | −0.142633 | − | 0.0850782i | ||||
\(361\) | − | 47799.6i | − | 0.366783i | ||||||
\(362\) | 58165.8 | − | 68655.2i | 0.443864 | − | 0.523909i | ||||
\(363\) | 37816.1 | − | 37816.1i | 0.286988 | − | 0.286988i | ||||
\(364\) | 93775.0 | − | 131256.i | 0.707757 | − | 0.990643i | ||||
\(365\) | −44166.7 | + | 44166.7i | −0.331520 | + | 0.331520i | ||||
\(366\) | −4739.35 | − | 57300.6i | −0.0353799 | − | 0.427757i | ||||
\(367\) | − | 82596.4i | − | 0.613238i | −0.951832 | − | 0.306619i | \(-0.900802\pi\) | ||
0.951832 | − | 0.306619i | \(-0.0991977\pi\) | |||||||
\(368\) | −179320. | + | 61439.7i | −1.32414 | + | 0.453684i | ||||
\(369\) | −65510.6 | −0.481126 | ||||||||
\(370\) | −55373.9 | + | 4580.00i | −0.404485 | + | 0.0334550i | ||||
\(371\) | −87536.0 | − | 87536.0i | −0.635973 | − | 0.635973i | ||||
\(372\) | 14739.3 | − | 20630.5i | 0.106510 | − | 0.149082i | ||||
\(373\) | −76631.0 | − | 76631.0i | −0.550791 | − | 0.550791i | 0.375878 | − | 0.926669i | \(-0.377341\pi\) |
−0.926669 | + | 0.375878i | \(0.877341\pi\) | |||||||
\(374\) | −180117. | − | 152598.i | −1.28769 | − | 1.09095i | ||||
\(375\) | 44580.5 | 0.317017 | ||||||||
\(376\) | 46617.6 | − | 11782.7i | 0.329742 | − | 0.0833431i | ||||
\(377\) | 25965.3i | 0.182688i | ||||||||
\(378\) | 100697. | + | 85312.4i | 0.704749 | + | 0.597075i | ||||
\(379\) | −95935.8 | + | 95935.8i | −0.667886 | + | 0.667886i | −0.957226 | − | 0.289340i | \(-0.906564\pi\) |
0.289340 | + | 0.957226i | \(0.406564\pi\) | |||||||
\(380\) | −5044.40 | − | 30285.8i | −0.0349335 | − | 0.209735i | ||||
\(381\) | 89654.8 | − | 89654.8i | 0.617623 | − | 0.617623i | ||||
\(382\) | −111773. | + | 9244.76i | −0.765965 | + | 0.0633532i | ||||
\(383\) | − | 168708.i | − | 1.15011i | −0.818116 | − | 0.575054i | \(-0.804981\pi\) | ||
0.818116 | − | 0.575054i | \(-0.195019\pi\) | |||||||
\(384\) | 18709.3 | − | 88761.6i | 0.126881 | − | 0.601953i | ||||
\(385\) | 47245.9 | 0.318744 | ||||||||
\(386\) | 18699.2 | + | 226080.i | 0.125501 | + | 1.51736i | ||||
\(387\) | 18475.9 | + | 18475.9i | 0.123362 | + | 0.123362i | ||||
\(388\) | −134782. | + | 22449.3i | −0.895299 | + | 0.149121i | ||||
\(389\) | 66490.0 | + | 66490.0i | 0.439397 | + | 0.439397i | 0.891809 | − | 0.452412i | \(-0.149436\pi\) |
−0.452412 | + | 0.891809i | \(0.649436\pi\) | |||||||
\(390\) | 21250.2 | − | 25082.4i | 0.139712 | − | 0.164907i | ||||
\(391\) | 280326. | 1.83362 | ||||||||
\(392\) | 5370.71 | + | 21248.9i | 0.0349510 | + | 0.138282i | ||||
\(393\) | 150773.i | 0.976199i | ||||||||
\(394\) | 37222.4 | − | 43934.9i | 0.239779 | − | 0.283020i | ||||
\(395\) | 13509.6 | − | 13509.6i | 0.0865859 | − | 0.0865859i | ||||
\(396\) | 102174. | + | 72997.3i | 0.651552 | + | 0.465497i | ||||
\(397\) | 18578.8 | − | 18578.8i | 0.117879 | − | 0.117879i | −0.645706 | − | 0.763586i | \(-0.723437\pi\) |
0.763586 | + | 0.645706i | \(0.223437\pi\) | |||||||
\(398\) | 10480.8 | + | 126716.i | 0.0661647 | + | 0.799957i | ||||
\(399\) | 72162.0i | 0.453276i | ||||||||
\(400\) | −48157.9 | − | 140555.i | −0.300987 | − | 0.878471i | ||||
\(401\) | −129108. | −0.802908 | −0.401454 | − | 0.915879i | \(-0.631495\pi\) | ||||
−0.401454 | + | 0.915879i | \(0.631495\pi\) | |||||||
\(402\) | −68825.7 | + | 5692.60i | −0.425891 | + | 0.0352256i | ||||
\(403\) | −44972.9 | − | 44972.9i | −0.276911 | − | 0.276911i | ||||
\(404\) | −9898.70 | − | 7072.05i | −0.0606479 | − | 0.0433294i | ||||
\(405\) | −244.286 | − | 244.286i | −0.00148932 | − | 0.00148932i | ||||
\(406\) | 16180.1 | + | 13708.0i | 0.0981586 | + | 0.0831616i | ||||
\(407\) | 324156. | 1.95689 | ||||||||
\(408\) | −68722.4 | + | 115212.i | −0.412836 | + | 0.692116i | ||||
\(409\) | − | 17952.4i | − | 0.107319i | −0.998559 | − | 0.0536594i | \(-0.982911\pi\) | ||
0.998559 | − | 0.0536594i | \(-0.0170885\pi\) | |||||||
\(410\) | 26527.8 | + | 22474.8i | 0.157810 | + | 0.133699i | ||||
\(411\) | 78057.7 | − | 78057.7i | 0.462096 | − | 0.462096i | ||||
\(412\) | 87496.3 | − | 14573.4i | 0.515461 | − | 0.0858551i | ||||
\(413\) | −61594.5 | + | 61594.5i | −0.361112 | + | 0.361112i | ||||
\(414\) | −148606. | + | 12291.2i | −0.867031 | + | 0.0717124i | ||||
\(415\) | − | 9793.04i | − | 0.0568619i | ||||||
\(416\) | −211918. | − | 82874.9i | −1.22456 | − | 0.478891i | ||||
\(417\) | 197122. | 1.13361 | ||||||||
\(418\) | 14764.8 | + | 178513.i | 0.0845038 | + | 1.02168i | ||||
\(419\) | 56887.3 | + | 56887.3i | 0.324031 | + | 0.324031i | 0.850311 | − | 0.526280i | \(-0.176414\pi\) |
−0.526280 | + | 0.850311i | \(0.676414\pi\) | |||||||
\(420\) | −4411.14 | − | 26483.8i | −0.0250065 | − | 0.150135i | ||||
\(421\) | −144162. | − | 144162.i | −0.813365 | − | 0.813365i | 0.171772 | − | 0.985137i | \(-0.445051\pi\) |
−0.985137 | + | 0.171772i | \(0.945051\pi\) | |||||||
\(422\) | 39125.8 | − | 46181.6i | 0.219704 | − | 0.259325i | ||||
\(423\) | 37825.2 | 0.211398 | ||||||||
\(424\) | −89454.8 | + | 149970.i | −0.497590 | + | 0.834205i | ||||
\(425\) | 219726.i | 1.21648i | ||||||||
\(426\) | −128418. | + | 151577.i | −0.707633 | + | 0.835245i | ||||
\(427\) | −83291.4 | + | 83291.4i | −0.456819 | + | 0.456819i | ||||
\(428\) | 39324.7 | − | 55042.5i | 0.214673 | − | 0.300477i | ||||
\(429\) | −135614. | + | 135614.i | −0.736870 | + | 0.736870i | ||||
\(430\) | −1143.07 | − | 13820.2i | −0.00618210 | − | 0.0747440i | ||||
\(431\) | 18641.5i | 0.100352i | 0.998740 | + | 0.0501760i | \(0.0159782\pi\) | ||||
−0.998740 | + | 0.0501760i | \(0.984022\pi\) | |||||||
\(432\) | 81864.6 | − | 167201.i | 0.438661 | − | 0.895923i | ||||
\(433\) | 2193.97 | 0.0117019 | 0.00585094 | − | 0.999983i | \(-0.498138\pi\) | ||||
0.00585094 | + | 0.999983i | \(0.498138\pi\) | |||||||
\(434\) | −51767.3 | + | 4281.69i | −0.274838 | + | 0.0227319i | ||||
\(435\) | 3055.84 | + | 3055.84i | 0.0161492 | + | 0.0161492i | ||||
\(436\) | 44115.7 | − | 61748.5i | 0.232071 | − | 0.324828i | ||||
\(437\) | −150404. | − | 150404.i | −0.787586 | − | 0.787586i | ||||
\(438\) | −157999. | − | 133859.i | −0.823581 | − | 0.697751i | ||||
\(439\) | 118115. | 0.612880 | 0.306440 | − | 0.951890i | \(-0.400862\pi\) | ||||
0.306440 | + | 0.951890i | \(0.400862\pi\) | |||||||
\(440\) | −16331.0 | − | 64612.5i | −0.0843541 | − | 0.333742i | ||||
\(441\) | 17241.2i | 0.0886523i | ||||||||
\(442\) | 256754. | + | 217526.i | 1.31424 | + | 1.11344i | ||||
\(443\) | 37885.8 | − | 37885.8i | 0.193050 | − | 0.193050i | −0.603963 | − | 0.797013i | \(-0.706412\pi\) |
0.797013 | + | 0.603963i | \(0.206412\pi\) | |||||||
\(444\) | −30265.1 | − | 181707.i | −0.153524 | − | 0.921733i | ||||
\(445\) | 24425.4 | − | 24425.4i | 0.123345 | − | 0.123345i | ||||
\(446\) | 365553. | − | 30235.0i | 1.83773 | − | 0.151999i | ||||
\(447\) | − | 25188.9i | − | 0.126065i | ||||||
\(448\) | −163522. | + | 88302.1i | −0.814741 | + | 0.439962i | ||||
\(449\) | −85186.6 | −0.422550 | −0.211275 | − | 0.977427i | \(-0.567762\pi\) | ||||
−0.211275 | + | 0.977427i | \(0.567762\pi\) | |||||||
\(450\) | −9634.15 | − | 116481.i | −0.0475760 | − | 0.575213i | ||||
\(451\) | −143430. | − | 143430.i | −0.705157 | − | 0.705157i | ||||
\(452\) | 50406.5 | − | 8395.71i | 0.246723 | − | 0.0410942i | ||||
\(453\) | −57826.4 | − | 57826.4i | −0.281793 | − | 0.281793i | ||||
\(454\) | −63989.9 | + | 75529.6i | −0.310456 | + | 0.366442i | ||||
\(455\) | −67348.4 | −0.325315 | ||||||||
\(456\) | 98687.2 | − | 24943.4i | 0.474604 | − | 0.119957i | ||||
\(457\) | − | 96935.7i | − | 0.464142i | −0.972699 | − | 0.232071i | \(-0.925450\pi\) | ||
0.972699 | − | 0.232071i | \(-0.0745502\pi\) | |||||||
\(458\) | 233514. | − | 275625.i | 1.11322 | − | 1.31398i | ||||
\(459\) | −194678. | + | 194678.i | −0.924042 | + | 0.924042i | ||||
\(460\) | 64393.2 | + | 46005.2i | 0.304315 | + | 0.217416i | ||||
\(461\) | 295014. | − | 295014.i | 1.38816 | − | 1.38816i | 0.558988 | − | 0.829176i | \(-0.311190\pi\) |
0.829176 | − | 0.558988i | \(-0.188810\pi\) | |||||||
\(462\) | 12911.3 | + | 156103.i | 0.0604904 | + | 0.731352i | ||||
\(463\) | − | 224348.i | − | 1.04655i | −0.852164 | − | 0.523275i | \(-0.824710\pi\) | ||
0.852164 | − | 0.523275i | \(-0.175290\pi\) | |||||||
\(464\) | 13154.0 | − | 26865.8i | 0.0610974 | − | 0.124786i | ||||
\(465\) | −10585.7 | −0.0489567 | ||||||||
\(466\) | −254697. | + | 21066.1i | −1.17288 | + | 0.0970090i | ||||
\(467\) | 189556. | + | 189556.i | 0.869168 | + | 0.869168i | 0.992380 | − | 0.123212i | \(-0.0393196\pi\) |
−0.123212 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(468\) | −145648. | − | 104057.i | −0.664985 | − | 0.475093i | ||||
\(469\) | 100044. | + | 100044.i | 0.454827 | + | 0.454827i | ||||
\(470\) | −15316.9 | − | 12976.7i | −0.0693387 | − | 0.0587449i | ||||
\(471\) | −141054. | −0.635832 | ||||||||
\(472\) | 105526. | + | 62944.7i | 0.473670 | + | 0.282537i | ||||
\(473\) | 80902.6i | 0.361610i | ||||||||
\(474\) | 48328.2 | + | 40944.4i | 0.215102 | + | 0.182238i | ||||
\(475\) | 117891. | − | 117891.i | 0.522506 | − | 0.522506i | ||||
\(476\) | 271100. | − | 45154.4i | 1.19651 | − | 0.199290i | ||||
\(477\) | −97133.7 | + | 97133.7i | −0.426907 | + | 0.426907i | ||||
\(478\) | −48221.0 | + | 3988.37i | −0.211047 | + | 0.0174558i | ||||
\(479\) | 132796.i | 0.578781i | 0.957211 | + | 0.289390i | \(0.0934526\pi\) | ||||
−0.957211 | + | 0.289390i | \(0.906547\pi\) | |||||||
\(480\) | −34693.9 | + | 15187.0i | −0.150581 | + | 0.0659156i | ||||
\(481\) | −462081. | −1.99723 | ||||||||
\(482\) | 9224.98 | + | 111534.i | 0.0397074 | + | 0.480078i | ||||
\(483\) | −131523. | − | 131523.i | −0.563778 | − | 0.563778i | ||||
\(484\) | 25392.0 | + | 152449.i | 0.108394 | + | 0.650781i | ||||
\(485\) | 40338.2 | + | 40338.2i | 0.171488 | + | 0.171488i | ||||
\(486\) | 153046. | − | 180646.i | 0.647964 | − | 0.764815i | ||||
\(487\) | −283936. | −1.19719 | −0.598595 | − | 0.801052i | \(-0.704274\pi\) | ||||
−0.598595 | + | 0.801052i | \(0.704274\pi\) | |||||||
\(488\) | 142698. | + | 85117.3i | 0.599209 | + | 0.357419i | ||||
\(489\) | 118101.i | 0.493896i | ||||||||
\(490\) | 5914.96 | − | 6981.64i | 0.0246354 | − | 0.0290781i | ||||
\(491\) | −111725. | + | 111725.i | −0.463435 | + | 0.463435i | −0.899780 | − | 0.436345i | \(-0.856273\pi\) |
0.436345 | + | 0.899780i | \(0.356273\pi\) | |||||||
\(492\) | −67008.5 | + | 93791.3i | −0.276821 | + | 0.387465i | ||||
\(493\) | −31280.9 | + | 31280.9i | −0.128702 | + | 0.128702i | ||||
\(494\) | −21047.1 | − | 254468.i | −0.0862459 | − | 1.04275i | ||||
\(495\) | − | 52426.1i | − | 0.213962i | ||||||
\(496\) | 23749.4 | + | 69315.9i | 0.0965359 | + | 0.281754i | ||||
\(497\) | 406998. | 1.64770 | ||||||||
\(498\) | 32356.7 | − | 2676.23i | 0.130468 | − | 0.0107911i | ||||
\(499\) | 61595.1 | + | 61595.1i | 0.247369 | + | 0.247369i | 0.819890 | − | 0.572521i | \(-0.194035\pi\) |
−0.572521 | + | 0.819890i | \(0.694035\pi\) | |||||||
\(500\) | −74892.4 | + | 104826.i | −0.299570 | + | 0.419305i | ||||
\(501\) | 92916.5 | + | 92916.5i | 0.370184 | + | 0.370184i | ||||
\(502\) | 8615.21 | + | 7298.95i | 0.0341868 | + | 0.0289636i | ||||
\(503\) | −70874.1 | −0.280125 | −0.140062 | − | 0.990143i | \(-0.544730\pi\) | ||||
−0.140062 | + | 0.990143i | \(0.544730\pi\) | |||||||
\(504\) | −141735. | + | 35823.8i | −0.557976 | + | 0.141030i | ||||
\(505\) | 5079.09i | 0.0199160i | ||||||||
\(506\) | −352270. | − | 298449.i | −1.37586 | − | 1.16565i | ||||
\(507\) | 81500.9 | − | 81500.9i | 0.317064 | − | 0.317064i | ||||
\(508\) | 60199.5 | + | 361428.i | 0.233274 | + | 1.40054i | ||||
\(509\) | −128181. | + | 128181.i | −0.494754 | + | 0.494754i | −0.909800 | − | 0.415046i | \(-0.863765\pi\) |
0.415046 | + | 0.909800i | \(0.363765\pi\) | |||||||
\(510\) | 55817.8 | − | 4616.71i | 0.214601 | − | 0.0177498i | ||||
\(511\) | 424241.i | 1.62469i | ||||||||
\(512\) | 177283. | + | 193107.i | 0.676281 | + | 0.736644i | ||||
\(513\) | 208903. | 0.793797 | ||||||||
\(514\) | −24237.5 | − | 293041.i | −0.0917406 | − | 1.10918i | ||||
\(515\) | −26186.3 | − | 26186.3i | −0.0987324 | − | 0.0987324i | ||||
\(516\) | 45350.2 | − | 7553.53i | 0.170325 | − | 0.0283694i | ||||
\(517\) | 82814.9 | + | 82814.9i | 0.309833 | + | 0.309833i | ||||
\(518\) | −243949. | + | 287942.i | −0.909160 | + | 1.07311i | ||||
\(519\) | −94525.3 | −0.350924 | ||||||||
\(520\) | 23279.6 | + | 92104.3i | 0.0860932 | + | 0.340623i | ||||
\(521\) | − | 494250.i | − | 1.82084i | −0.413688 | − | 0.910419i | \(-0.635759\pi\) | ||
0.413688 | − | 0.910419i | \(-0.364241\pi\) | |||||||
\(522\) | 15211.0 | − | 17954.1i | 0.0558235 | − | 0.0658905i | ||||
\(523\) | 179670. | − | 179670.i | 0.656859 | − | 0.656859i | −0.297776 | − | 0.954636i | \(-0.596245\pi\) |
0.954636 | + | 0.297776i | \(0.0962450\pi\) | |||||||
\(524\) | −354527. | − | 253289.i | −1.29118 | − | 0.922473i | ||||
\(525\) | 103091. | − | 103091.i | 0.374026 | − | 0.374026i | ||||
\(526\) | 22456.7 | + | 271510.i | 0.0811660 | + | 0.981329i | ||||
\(527\) | − | 108360.i | − | 0.390163i | ||||||
\(528\) | 209020. | − | 71615.6i | 0.749756 | − | 0.256886i | ||||
\(529\) | 268417. | 0.959175 | ||||||||
\(530\) | 72657.1 | − | 6009.50i | 0.258658 | − | 0.0213937i | ||||
\(531\) | 68347.9 | + | 68347.9i | 0.242402 | + | 0.242402i | ||||
\(532\) | −169681. | − | 121227.i | −0.599529 | − | 0.428329i | ||||
\(533\) | 204457. | + | 204457.i | 0.719694 | + | 0.719694i | ||||
\(534\) | 87377.9 | + | 74027.9i | 0.306421 | + | 0.259605i | ||||
\(535\) | −28242.7 | −0.0986729 | ||||||||
\(536\) | 102237. | − | 171400.i | 0.355860 | − | 0.596596i | ||||
\(537\) | − | 220112.i | − | 0.763300i | ||||||
\(538\) | −64983.7 | − | 55055.2i | −0.224512 | − | 0.190210i | ||||
\(539\) | −37748.1 | + | 37748.1i | −0.129932 | + | 0.129932i | ||||
\(540\) | −76668.4 | + | 12769.9i | −0.262923 | + | 0.0437925i | ||||
\(541\) | 300961. | − | 300961.i | 1.02829 | − | 1.02829i | 0.0287034 | − | 0.999588i | \(-0.490862\pi\) |
0.999588 | − | 0.0287034i | \(-0.00913784\pi\) | |||||||
\(542\) | −415861. | + | 34396.0i | −1.41563 | + | 0.117087i | ||||
\(543\) | − | 124549.i | − | 0.422417i | ||||||
\(544\) | −155460. | − | 355143.i | −0.525318 | − | 1.20007i | ||||
\(545\) | −31683.6 | −0.106670 | ||||||||
\(546\) | −18404.9 | − | 222523.i | −0.0617374 | − | 0.746430i | ||||
\(547\) | −159057. | − | 159057.i | −0.531591 | − | 0.531591i | 0.389455 | − | 0.921046i | \(-0.372663\pi\) |
−0.921046 | + | 0.389455i | \(0.872663\pi\) | |||||||
\(548\) | 52412.5 | + | 314676.i | 0.174531 | + | 1.04786i | ||||
\(549\) | 92423.8 | + | 92423.8i | 0.306647 | + | 0.306647i | ||||
\(550\) | 233931. | − | 276117.i | 0.773326 | − | 0.912784i | ||||
\(551\) | 33566.6 | 0.110561 | ||||||||
\(552\) | −134406. | + | 225331.i | −0.441104 | + | 0.739506i | ||||
\(553\) | − | 129765.i | − | 0.424335i | ||||||
\(554\) | −7811.98 | + | 9220.76i | −0.0254532 | + | 0.0300433i | ||||
\(555\) | −54382.0 | + | 54382.0i | −0.176551 | + | 0.176551i | ||||
\(556\) | −331152. | + | 463512.i | −1.07122 | + | 1.49938i | ||||
\(557\) | −394524. | + | 394524.i | −1.27164 | + | 1.27164i | −0.326409 | + | 0.945229i | \(0.605839\pi\) |
−0.945229 | + | 0.326409i | \(0.894161\pi\) | |||||||
\(558\) | 4751.15 | + | 57443.2i | 0.0152591 | + | 0.184489i | ||||
\(559\) | − | 115326.i | − | 0.369065i | ||||||
\(560\) | 69684.2 | + | 34118.7i | 0.222207 | + | 0.108797i | ||||
\(561\) | −326755. | −1.03824 | ||||||||
\(562\) | 146634. | − | 12128.1i | 0.464261 | − | 0.0383992i | ||||
\(563\) | 169317. | + | 169317.i | 0.534177 | + | 0.534177i | 0.921813 | − | 0.387636i | \(-0.126708\pi\) |
−0.387636 | + | 0.921813i | \(0.626708\pi\) | |||||||
\(564\) | 38690.0 | − | 54154.2i | 0.121630 | − | 0.170245i | ||||
\(565\) | −15085.9 | − | 15085.9i | −0.0472579 | − | 0.0472579i | ||||
\(566\) | 61167.9 | + | 51822.4i | 0.190937 | + | 0.161765i | ||||
\(567\) | −2346.48 | −0.00729877 | ||||||||
\(568\) | −140682. | − | 556602.i | −0.436057 | − | 1.72523i | ||||
\(569\) | − | 165645.i | − | 0.511626i | −0.966726 | − | 0.255813i | \(-0.917657\pi\) | ||
0.966726 | − | 0.255813i | \(-0.0823432\pi\) | |||||||
\(570\) | −32425.2 | − | 27471.1i | −0.0998005 | − | 0.0845526i | ||||
\(571\) | 335641. | − | 335641.i | 1.02945 | − | 1.02945i | 0.0298925 | − | 0.999553i | \(-0.490483\pi\) |
0.999553 | − | 0.0298925i | \(-0.00951651\pi\) | |||||||
\(572\) | −91059.4 | − | 546706.i | −0.278312 | − | 1.67094i | ||||
\(573\) | −109771. | + | 109771.i | −0.334331 | + | 0.334331i | ||||
\(574\) | 235346. | − | 19465.6i | 0.714305 | − | 0.0590804i | ||||
\(575\) | 429737.i | 1.29977i | ||||||||
\(576\) | 97983.9 | + | 181451.i | 0.295331 | + | 0.546908i | ||||
\(577\) | −99615.9 | −0.299211 | −0.149605 | − | 0.988746i | \(-0.547800\pi\) | ||||
−0.149605 | + | 0.988746i | \(0.547800\pi\) | |||||||
\(578\) | 19720.5 | + | 238429.i | 0.0590287 | + | 0.713680i | ||||
\(579\) | 222031. | + | 222031.i | 0.662301 | + | 0.662301i | ||||
\(580\) | −12319.1 | + | 2051.87i | −0.0366204 | + | 0.00609949i | ||||
\(581\) | −47033.3 | − | 47033.3i | −0.139333 | − | 0.139333i | ||||
\(582\) | −122256. | + | 144303.i | −0.360930 | + | 0.426019i | ||||
\(583\) | −425331. | −1.25138 | ||||||||
\(584\) | 580184. | − | 146643.i | 1.70114 | − | 0.429967i | ||||
\(585\) | 74732.7i | 0.218373i | ||||||||
\(586\) | −295173. | + | 348403.i | −0.859570 | + | 1.01458i | ||||
\(587\) | −45023.9 | + | 45023.9i | −0.130667 | + | 0.130667i | −0.769416 | − | 0.638748i | \(-0.779452\pi\) |
0.638748 | + | 0.769416i | \(0.279452\pi\) | |||||||
\(588\) | 24684.1 | + | 17635.4i | 0.0713943 | + | 0.0510071i | ||||
\(589\) | −58138.5 | + | 58138.5i | −0.167584 | + | 0.167584i | ||||
\(590\) | −4228.57 | − | 51125.1i | −0.0121476 | − | 0.146869i | ||||
\(591\) | − | 79703.6i | − | 0.228193i | ||||||
\(592\) | 478107. | + | 234090.i | 1.36421 | + | 0.667944i | ||||
\(593\) | −385101. | −1.09513 | −0.547564 | − | 0.836764i | \(-0.684445\pi\) | ||||
−0.547564 | + | 0.836764i | \(0.684445\pi\) | |||||||
\(594\) | 451905. | − | 37377.2i | 1.28078 | − | 0.105934i | ||||
\(595\) | −81136.1 | − | 81136.1i | −0.229182 | − | 0.229182i | ||||
\(596\) | 59229.0 | + | 42315.7i | 0.166741 | + | 0.119127i | ||||
\(597\) | 124447. | + | 124447.i | 0.349168 | + | 0.349168i | ||||
\(598\) | 502156. | + | 425435.i | 1.40422 | + | 1.18968i | ||||
\(599\) | 209331. | 0.583417 | 0.291709 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291709 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(600\) | −176619. | − | 105351.i | −0.490609 | − | 0.292641i | ||||
\(601\) | 515555.i | 1.42734i | 0.700484 | + | 0.713668i | \(0.252967\pi\) | ||||
−0.700484 | + | 0.713668i | \(0.747033\pi\) | |||||||
\(602\) | −71864.3 | − | 60884.6i | −0.198299 | − | 0.168002i | ||||
\(603\) | 111013. | − | 111013.i | 0.305310 | − | 0.305310i | ||||
\(604\) | 233117. | − | 38828.0i | 0.638999 | − | 0.106432i | ||||
\(605\) | 45625.7 | − | 45625.7i | 0.124652 | − | 0.124652i | ||||
\(606\) | −16781.6 | + | 1388.01i | −0.0456970 | + | 0.00377961i | ||||
\(607\) | 30292.7i | 0.0822167i | 0.999155 | + | 0.0411084i | \(0.0130889\pi\) | ||||
−0.999155 | + | 0.0411084i | \(0.986911\pi\) | |||||||
\(608\) | −107136. | + | 273956.i | −0.289821 | + | 0.741094i | ||||
\(609\) | 29352.7 | 0.0791432 | ||||||||
\(610\) | −5718.10 | − | 69134.1i | −0.0153671 | − | 0.185794i | ||||
\(611\) | −118052. | − | 118052.i | −0.316220 | − | 0.316220i | ||||
\(612\) | −50105.3 | − | 300824.i | −0.133777 | − | 0.803175i | ||||
\(613\) | −99803.4 | − | 99803.4i | −0.265598 | − | 0.265598i | 0.561726 | − | 0.827324i | \(-0.310138\pi\) |
−0.827324 | + | 0.561726i | \(0.810138\pi\) | |||||||
\(614\) | −415816. | + | 490803.i | −1.10297 | + | 1.30188i | ||||
\(615\) | 48124.9 | 0.127239 | ||||||||
\(616\) | −388749. | − | 231883.i | −1.02449 | − | 0.611093i | ||||
\(617\) | − | 102196.i | − | 0.268451i | −0.990951 | − | 0.134226i | \(-0.957145\pi\) | ||
0.990951 | − | 0.134226i | \(-0.0428547\pi\) | |||||||
\(618\) | 79364.8 | − | 93677.1i | 0.207802 | − | 0.245277i | ||||
\(619\) | −105904. | + | 105904.i | −0.276395 | + | 0.276395i | −0.831668 | − | 0.555273i | \(-0.812614\pi\) |
0.555273 | + | 0.831668i | \(0.312614\pi\) | |||||||
\(620\) | 17783.2 | − | 24891.0i | 0.0462623 | − | 0.0647530i | ||||
\(621\) | −380749. | + | 380749.i | −0.987314 | + | 0.987314i | ||||
\(622\) | −30927.9 | − | 373930.i | −0.0799410 | − | 0.966518i | ||||
\(623\) | − | 234617.i | − | 0.604483i | ||||||
\(624\) | −297956. | + | 102087.i | −0.765213 | + | 0.262181i | ||||
\(625\) | −308949. | −0.790909 | ||||||||
\(626\) | 36792.5 | − | 3043.12i | 0.0938880 | − | 0.00776551i | ||||
\(627\) | 175315. | + | 175315.i | 0.445948 | + | 0.445948i | ||||
\(628\) | 236961. | − | 331673.i | 0.600838 | − | 0.840989i | ||||
\(629\) | −556679. | − | 556679.i | −1.40703 | − | 1.40703i | ||||
\(630\) | 46569.1 | + | 39454.1i | 0.117332 | + | 0.0994057i | ||||
\(631\) | 692480. | 1.73920 | 0.869598 | − | 0.493760i | \(-0.164378\pi\) | ||||
0.869598 | + | 0.493760i | \(0.164378\pi\) | |||||||
\(632\) | −177465. | + | 44854.6i | −0.444301 | + | 0.112298i | ||||
\(633\) | − | 83779.3i | − | 0.209088i | ||||||
\(634\) | −36460.0 | − | 30889.5i | −0.0907065 | − | 0.0768481i | ||||
\(635\) | 108170. | − | 108170.i | 0.268262 | − | 0.268262i | ||||
\(636\) | 39711.4 | + | 238421.i | 0.0981749 | + | 0.589427i | ||||
\(637\) | 53809.4 | − | 53809.4i | 0.132611 | − | 0.132611i | ||||
\(638\) | 72612.1 | − | 6005.77i | 0.178389 | − | 0.0147546i | ||||
\(639\) | − | 451622.i | − | 1.10605i | ||||||
\(640\) | 22573.1 | − | 107092.i | 0.0551101 | − | 0.261456i | ||||
\(641\) | 49519.0 | 0.120519 | 0.0602595 | − | 0.998183i | \(-0.480807\pi\) | ||||
0.0602595 | + | 0.998183i | \(0.480807\pi\) | |||||||
\(642\) | −7718.13 | − | 93315.2i | −0.0187259 | − | 0.226403i | ||||
\(643\) | −165494. | − | 165494.i | −0.400276 | − | 0.400276i | 0.478054 | − | 0.878330i | \(-0.341342\pi\) |
−0.878330 | + | 0.478054i | \(0.841342\pi\) | |||||||
\(644\) | 530213. | − | 88312.3i | 1.27844 | − | 0.212936i | ||||
\(645\) | −13572.6 | − | 13572.6i | −0.0326245 | − | 0.0326245i | ||||
\(646\) | 281207. | − | 331919.i | 0.673846 | − | 0.795365i | ||||
\(647\) | −666565. | −1.59233 | −0.796166 | − | 0.605078i | \(-0.793142\pi\) | ||||
−0.796166 | + | 0.605078i | \(0.793142\pi\) | |||||||
\(648\) | 811.080 | + | 3208.99i | 0.00193159 | + | 0.00764221i | ||||
\(649\) | 299284.i | 0.710548i | ||||||||
\(650\) | −333466. | + | 393602.i | −0.789268 | + | 0.931602i | ||||
\(651\) | −50840.0 | + | 50840.0i | −0.119962 | + | 0.119962i | ||||
\(652\) | −277702. | − | 198402.i | −0.653256 | − | 0.466714i | ||||
\(653\) | 461118. | − | 461118.i | 1.08140 | − | 1.08140i | 0.0850198 | − | 0.996379i | \(-0.472905\pi\) |
0.996379 | − | 0.0850198i | \(-0.0270954\pi\) | |||||||
\(654\) | −8658.45 | − | 104684.i | −0.0202435 | − | 0.244751i | ||||
\(655\) | 181910.i | 0.424008i | ||||||||
\(656\) | −107970. | − | 315127.i | −0.250898 | − | 0.732280i | ||||
\(657\) | 470757. | 1.09060 | ||||||||
\(658\) | −135887. | + | 11239.2i | −0.313852 | + | 0.0259588i | ||||
\(659\) | 326883. | + | 326883.i | 0.752698 | + | 0.752698i | 0.974982 | − | 0.222284i | \(-0.0713511\pi\) |
−0.222284 | + | 0.974982i | \(0.571351\pi\) | |||||||
\(660\) | −75058.2 | − | 53624.8i | −0.172310 | − | 0.123106i | ||||
\(661\) | 549615. | + | 549615.i | 1.25793 | + | 1.25793i | 0.952080 | + | 0.305848i | \(0.0989401\pi\) |
0.305848 | + | 0.952080i | \(0.401060\pi\) | |||||||
\(662\) | −198938. | − | 168544.i | −0.453944 | − | 0.384589i | ||||
\(663\) | 465785. | 1.05964 | ||||||||
\(664\) | −48064.3 | + | 80579.2i | −0.109015 | + | 0.182762i | ||||
\(665\) | 87064.5i | 0.196878i | ||||||||
\(666\) | 319513. | + | 270697.i | 0.720345 | + | 0.610288i | ||||
\(667\) | −61178.8 | + | 61178.8i | −0.137515 | + | 0.137515i | ||||
\(668\) | −374577. | + | 62389.6i | −0.839437 | + | 0.139817i | ||||
\(669\) | 359005. | − | 359005.i | 0.802137 | − | 0.802137i | ||||
\(670\) | −83039.3 | + | 6868.21i | −0.184984 | + | 0.0153001i | ||||
\(671\) | 404708.i | 0.898869i | ||||||||
\(672\) | −93686.8 | + | 239564.i | −0.207463 | + | 0.530498i | ||||
\(673\) | 191664. | 0.423166 | 0.211583 | − | 0.977360i | \(-0.432138\pi\) | ||||
0.211583 | + | 0.977360i | \(0.432138\pi\) | |||||||
\(674\) | 12963.7 | + | 156736.i | 0.0285370 | + | 0.345023i | ||||
\(675\) | −298440. | − | 298440.i | −0.655012 | − | 0.655012i | ||||
\(676\) | 54724.4 | + | 328557.i | 0.119753 | + | 0.718980i | ||||
\(677\) | −544201. | − | 544201.i | −1.18736 | − | 1.18736i | −0.977795 | − | 0.209564i | \(-0.932796\pi\) |
−0.209564 | − | 0.977795i | \(-0.567204\pi\) | |||||||
\(678\) | 45721.9 | − | 53967.3i | 0.0994638 | − | 0.117401i | ||||
\(679\) | 387466. | 0.840416 | ||||||||
\(680\) | −82914.6 | + | 139005.i | −0.179314 | + | 0.300617i | ||||
\(681\) | 137020.i | 0.295455i | ||||||||
\(682\) | −115365. | + | 136169.i | −0.248030 | + | 0.292759i | ||||
\(683\) | −570769. | + | 570769.i | −1.22354 | + | 1.22354i | −0.257179 | + | 0.966364i | \(0.582793\pi\) |
−0.966364 | + | 0.257179i | \(0.917207\pi\) | |||||||
\(684\) | −134519. | + | 188286.i | −0.287523 | + | 0.402443i | ||||
\(685\) | 94177.8 | − | 94177.8i | 0.200709 | − | 0.200709i | ||||
\(686\) | −41040.9 | − | 496201.i | −0.0872106 | − | 1.05441i | ||||
\(687\) | − | 500020.i | − | 1.05943i | ||||||
\(688\) | −58424.0 | + | 119325.i | −0.123428 | + | 0.252090i | ||||
\(689\) | 606305. | 1.27718 | ||||||||
\(690\) | 109168. | − | 9029.29i | 0.229296 | − | 0.0189651i | ||||
\(691\) | −333477. | − | 333477.i | −0.698409 | − | 0.698409i | 0.265658 | − | 0.964067i | \(-0.414411\pi\) |
−0.964067 | + | 0.265658i | \(0.914411\pi\) | |||||||
\(692\) | 158796. | − | 222266.i | 0.331611 | − | 0.464153i | ||||
\(693\) | −251788. | − | 251788.i | −0.524286 | − | 0.524286i | ||||
\(694\) | −292174. | − | 247535.i | −0.606629 | − | 0.513946i | ||||
\(695\) | 237831. | 0.492378 | ||||||||
\(696\) | −10146.0 | − | 40142.2i | −0.0209449 | − | 0.0828672i | ||||
\(697\) | 492628.i | 1.01404i | ||||||||
\(698\) | −33073.6 | − | 28020.5i | −0.0678845 | − | 0.0575128i | ||||
\(699\) | −250135. | + | 250135.i | −0.511941 | + | 0.511941i | ||||
\(700\) | 69221.3 | + | 415593.i | 0.141268 | + | 0.848150i | ||||
\(701\) | 31503.2 | − | 31503.2i | 0.0641089 | − | 0.0641089i | −0.674325 | − | 0.738434i | \(-0.735565\pi\) |
0.738434 | + | 0.674325i | \(0.235565\pi\) | |||||||
\(702\) | −644185. | + | 53280.7i | −1.30718 | + | 0.108117i | ||||
\(703\) | 597354.i | 1.20871i | ||||||||
\(704\) | −182744. | + | 611798.i | −0.368720 | + | 1.23442i | ||||
\(705\) | −27786.9 | −0.0559064 | ||||||||
\(706\) | 23283.8 | + | 281511.i | 0.0467138 | + | 0.564788i | ||||
\(707\) | 24393.5 | + | 24393.5i | 0.0488017 | + | 0.0488017i | ||||
\(708\) | 167764. | − | 27942.8i | 0.334682 | − | 0.0557447i | ||||
\(709\) | 609708. | + | 609708.i | 1.21291 | + | 1.21291i | 0.970064 | + | 0.242847i | \(0.0780815\pi\) |
0.242847 | + | 0.970064i | \(0.421919\pi\) | |||||||
\(710\) | −154939. | + | 182880.i | −0.307357 | + | 0.362785i | ||||
\(711\) | −143993. | −0.284841 | ||||||||
\(712\) | −320858. | + | 81097.6i | −0.632926 | + | 0.159973i | ||||
\(713\) | − | 211928.i | − | 0.416878i | ||||||
\(714\) | 245905. | − | 290251.i | 0.482359 | − | 0.569346i | ||||
\(715\) | −163621. | + | 163621.i | −0.320056 | + | 0.320056i | ||||
\(716\) | 517570. | + | 369774.i | 1.00959 | + | 0.721291i | ||||
\(717\) | −47357.2 | + | 47357.2i | −0.0921187 | + | 0.0921187i | ||||
\(718\) | −55439.7 | − | 670288.i | −0.107541 | − | 1.30021i | ||||
\(719\) | − | 720908.i | − | 1.39451i | −0.716823 | − | 0.697256i | \(-0.754404\pi\) | ||
0.716823 | − | 0.697256i | \(-0.245596\pi\) | |||||||
\(720\) | 37859.6 | − | 77324.7i | 0.0730317 | − | 0.149160i | ||||
\(721\) | −251531. | −0.483862 | ||||||||
\(722\) | 190548. | − | 15760.3i | 0.365535 | − | 0.0302335i | ||||
\(723\) | 109536. | + | 109536.i | 0.209546 | + | 0.209546i | ||||
\(724\) | 292864. | + | 209235.i | 0.558714 | + | 0.399169i | ||||
\(725\) | −47953.4 | − | 47953.4i | −0.0912311 | − | 0.0912311i | ||||
\(726\) | 163218. | + | 138281.i | 0.309668 | + | 0.262355i | ||||
\(727\) | −279904. | −0.529591 | −0.264796 | − | 0.964305i | \(-0.585304\pi\) | ||||
−0.264796 | + | 0.964305i | \(0.585304\pi\) | |||||||
\(728\) | 554157. | + | 330546.i | 1.04561 | + | 0.623691i | ||||
\(729\) | − | 323526.i | − | 0.608772i | ||||||
\(730\) | −190628. | − | 161503.i | −0.357718 | − | 0.303065i | ||||
\(731\) | 138935. | − | 138935.i | 0.260003 | − | 0.260003i | ||||
\(732\) | 226860. | − | 37785.8i | 0.423385 | − | 0.0705191i | ||||
\(733\) | −266306. | + | 266306.i | −0.495648 | + | 0.495648i | −0.910080 | − | 0.414432i | \(-0.863980\pi\) |
0.414432 | + | 0.910080i | \(0.363980\pi\) | |||||||
\(734\) | 329261. | − | 27233.3i | 0.611151 | − | 0.0505485i | ||||
\(735\) | − | 12665.6i | − | 0.0234450i | ||||||
\(736\) | −304047. | − | 694583.i | −0.561287 | − | 1.28224i | ||||
\(737\) | 486108. | 0.894948 | ||||||||
\(738\) | −21599.8 | − | 261151.i | −0.0396587 | − | 0.479489i | ||||
\(739\) | −594958. | − | 594958.i | −1.08943 | − | 1.08943i | −0.995587 | − | 0.0938378i | \(-0.970086\pi\) |
−0.0938378 | − | 0.995587i | \(-0.529914\pi\) | |||||||
\(740\) | −36515.3 | − | 219232.i | −0.0666824 | − | 0.400350i | ||||
\(741\) | −249910. | − | 249910.i | −0.455142 | − | 0.455142i | ||||
\(742\) | 320090. | − | 377814.i | 0.581386 | − | 0.686231i | ||||
\(743\) | 289367. | 0.524170 | 0.262085 | − | 0.965045i | \(-0.415590\pi\) | ||||
0.262085 | + | 0.965045i | \(0.415590\pi\) | |||||||
\(744\) | 87101.1 | + | 51954.5i | 0.157354 | + | 0.0938592i | ||||
\(745\) | − | 30390.8i | − | 0.0547557i | ||||||
\(746\) | 280214. | − | 330747.i | 0.503515 | − | 0.594317i | ||||
\(747\) | −52190.2 | + | 52190.2i | −0.0935293 | + | 0.0935293i | ||||
\(748\) | 548927. | − | 768329.i | 0.981096 | − | 1.37323i | ||||
\(749\) | −135642. | + | 135642.i | −0.241785 | + | 0.241785i | ||||
\(750\) | 14698.9 | + | 177715.i | 0.0261314 | + | 0.315938i | ||||
\(751\) | 935795.i | 1.65921i | 0.558352 | + | 0.829604i | \(0.311434\pi\) | ||||
−0.558352 | + | 0.829604i | \(0.688566\pi\) | |||||||
\(752\) | 62341.0 | + | 181951.i | 0.110240 | + | 0.321750i | ||||
\(753\) | 15629.1 | 0.0275641 | ||||||||
\(754\) | −103508. | + | 8561.16i | −0.182067 | + | 0.0150588i | ||||
\(755\) | −69768.4 | − | 69768.4i | −0.122395 | − | 0.122395i | ||||
\(756\) | −306887. | + | 429547.i | −0.536951 | + | 0.751567i | ||||
\(757\) | −626956. | − | 626956.i | −1.09407 | − | 1.09407i | −0.995089 | − | 0.0989818i | \(-0.968441\pi\) |
−0.0989818 | − | 0.995089i | \(-0.531559\pi\) | |||||||
\(758\) | −414069. | − | 350806.i | −0.720666 | − | 0.610560i | ||||
\(759\) | −639062. | −1.10933 | ||||||||
\(760\) | 119068. | − | 30094.6i | 0.206142 | − | 0.0521029i | ||||
\(761\) | 253505.i | 0.437741i | 0.975754 | + | 0.218871i | \(0.0702372\pi\) | ||||
−0.975754 | + | 0.218871i | \(0.929763\pi\) | |||||||
\(762\) | 386960. | + | 327838.i | 0.666432 | + | 0.564612i | ||||
\(763\) | −152167. | + | 152167.i | −0.261380 | + | 0.261380i | ||||
\(764\) | −73706.4 | − | 442521.i | −0.126275 | − | 0.758137i | ||||
\(765\) | −90032.1 | + | 90032.1i | −0.153842 | + | 0.153842i | ||||
\(766\) | 672536. | − | 55625.7i | 1.14619 | − | 0.0948021i | ||||
\(767\) | − | 426625.i | − | 0.725197i | ||||||
\(768\) | 360007. | + | 45316.6i | 0.610363 | + | 0.0768306i | ||||
\(769\) | −740462. | −1.25213 | −0.626066 | − | 0.779770i | \(-0.715336\pi\) | ||||
−0.626066 | + | 0.779770i | \(0.715336\pi\) | |||||||
\(770\) | 15577.7 | + | 188340.i | 0.0262737 | + | 0.317660i | ||||
\(771\) | −287792. | − | 287792.i | −0.484138 | − | 0.484138i | ||||
\(772\) | −895078. | + | 149084.i | −1.50185 | + | 0.250148i | ||||
\(773\) | 422057. | + | 422057.i | 0.706337 | + | 0.706337i | 0.965763 | − | 0.259426i | \(-0.0835334\pi\) |
−0.259426 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(774\) | −67560.2 | + | 79743.8i | −0.112774 | + | 0.133111i | ||||
\(775\) | 166114. | 0.276569 | ||||||||
\(776\) | −133931. | − | 529891.i | −0.222412 | − | 0.879961i | ||||
\(777\) | 522364.i | 0.865229i | ||||||||
\(778\) | −243132. | + | 286978.i | −0.401683 | + | 0.474121i | ||||
\(779\) | 264312. | − | 264312.i | 0.435553 | − | 0.435553i | ||||
\(780\) | 106995. | + | 76441.5i | 0.175862 | + | 0.125643i | ||||
\(781\) | 988787. | − | 988787.i | 1.62107 | − | 1.62107i | ||||
\(782\) | 92427.9 | + | 1.11749e6i | 0.151143 | + | 1.82738i | ||||
\(783\) | − | 84973.7i | − | 0.138599i | ||||||
\(784\) | −82935.5 | + | 28415.8i | −0.134930 | + | 0.0462304i | ||||
\(785\) | −170183. | −0.276171 | ||||||||
\(786\) | −601040. | + | 49712.2i | −0.972877 | + | 0.0804670i | ||||
\(787\) | 658152. | + | 658152.i | 1.06262 | + | 1.06262i | 0.997904 | + | 0.0647134i | \(0.0206133\pi\) |
0.0647134 | + | 0.997904i | \(0.479387\pi\) | |||||||
\(788\) | 187414. | + | 133897.i | 0.301822 | + | 0.215634i | ||||
\(789\) | 266647. | + | 266647.i | 0.428334 | + | 0.428334i | ||||
\(790\) | 58308.7 | + | 49400.0i | 0.0934284 | + | 0.0791540i | ||||
\(791\) | −144907. | −0.231599 | ||||||||
\(792\) | −257307. | + | 431373.i | −0.410206 | + | 0.687706i | ||||
\(793\) | − | 576906.i | − | 0.917400i | ||||||
\(794\) | 80188.2 | + | 67936.7i | 0.127195 | + | 0.107761i | ||||
\(795\) | 71355.7 | − | 71355.7i | 0.112900 | − | 0.112900i | ||||
\(796\) | −501685. | + | 83560.7i | −0.791781 | + | 0.131879i | ||||
\(797\) | −573702. | + | 573702.i | −0.903171 | + | 0.903171i | −0.995709 | − | 0.0925382i | \(-0.970502\pi\) |
0.0925382 | + | 0.995709i | \(0.470502\pi\) | |||||||
\(798\) | −287666. | + | 23792.9i | −0.451733 | + | 0.0373630i | ||||
\(799\) | − | 284439.i | − | 0.445549i | ||||||
\(800\) | 544430. | − | 238319.i | 0.850672 | − | 0.372374i | ||||
\(801\) | −260342. | −0.405769 | ||||||||
\(802\) | −42569.0 | − | 514676.i | −0.0661828 | − | 0.800175i | ||||
\(803\) | 1.03068e6 | + | 1.03068e6i | 1.59843 | + | 1.59843i | ||||
\(804\) | −45385.8 | − | 272489.i | −0.0702115 | − | 0.421538i | ||||
\(805\) | −158685. | − | 158685.i | −0.244874 | − | 0.244874i | ||||
\(806\) | 164451. | − | 194108.i | 0.253143 | − | 0.298794i | ||||
\(807\) | −117889. | −0.181019 | ||||||||
\(808\) | 24928.2 | − | 41791.8i | 0.0381828 | − | 0.0640131i | ||||
\(809\) | − | 297398.i | − | 0.454402i | −0.973848 | − | 0.227201i | \(-0.927043\pi\) | ||
0.973848 | − | 0.227201i | \(-0.0729575\pi\) | |||||||
\(810\) | 893.273 | − | 1054.36i | 0.00136149 | − | 0.00160702i | ||||
\(811\) | 481203. | − | 481203.i | 0.731621 | − | 0.731621i | −0.239320 | − | 0.970941i | \(-0.576924\pi\) |
0.970941 | + | 0.239320i | \(0.0769243\pi\) | |||||||
\(812\) | −49310.7 | + | 69019.8i | −0.0747875 | + | 0.104679i | ||||
\(813\) | −408412. | + | 408412.i | −0.617899 | + | 0.617899i | ||||
\(814\) | 106879. | + | 1.29221e6i | 0.161304 | + | 1.95023i | ||||
\(815\) | 142491.i | 0.214522i | ||||||||
\(816\) | −481940. | − | 235967.i | −0.723790 | − | 0.354381i | ||||
\(817\) | −149087. | −0.223355 | ||||||||
\(818\) | 71565.2 | − | 5919.18i | 0.106954 | − | 0.00884616i | ||||
\(819\) | 358921. | + | 358921.i | 0.535095 | + | 0.535095i | ||||
\(820\) | −80846.7 | + | 113161.i | −0.120236 | + | 0.168294i | ||||
\(821\) | 506859. | + | 506859.i | 0.751971 | + | 0.751971i | 0.974847 | − | 0.222876i | \(-0.0715444\pi\) |
−0.222876 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(822\) | 336905. | + | 285431.i | 0.498613 | + | 0.422433i | ||||
\(823\) | 401221. | 0.592357 | 0.296179 | − | 0.955133i | \(-0.404288\pi\) | ||||
0.296179 | + | 0.955133i | \(0.404288\pi\) | |||||||
\(824\) | 86944.1 | + | 343989.i | 0.128052 | + | 0.506629i | ||||
\(825\) | − | 500912.i | − | 0.735959i | ||||||
\(826\) | −265848. | − | 225231.i | −0.389649 | − | 0.330117i | ||||
\(827\) | 410169. | − | 410169.i | 0.599725 | − | 0.599725i | −0.340515 | − | 0.940239i | \(-0.610601\pi\) |
0.940239 | + | 0.340515i | \(0.110601\pi\) | |||||||
\(828\) | −97995.2 | − | 588347.i | −0.142937 | − | 0.858170i | ||||
\(829\) | −328989. | + | 328989.i | −0.478710 | + | 0.478710i | −0.904719 | − | 0.426009i | \(-0.859919\pi\) |
0.426009 | + | 0.904719i | \(0.359919\pi\) | |||||||
\(830\) | 39038.9 | − | 3228.92i | 0.0566684 | − | 0.00468706i | ||||
\(831\) | 16727.6i | 0.0242233i | ||||||||
\(832\) | 260499. | − | 872111.i | 0.376322 | − | 1.25987i | ||||
\(833\) | 129651. | 0.186846 | ||||||||
\(834\) | 64994.2 | + | 785805.i | 0.0934421 | + | 1.12975i | ||||
\(835\) | 112105. | + | 112105.i | 0.160788 | + | 0.160788i | ||||
\(836\) | −706753. | + | 117717.i | −1.01124 | + | 0.168432i | ||||
\(837\) | 147178. | + | 147178.i | 0.210083 | + | 0.210083i | ||||
\(838\) | −208018. | + | 245531.i | −0.296219 | + | 0.349638i | ||||
\(839\) | −114596. | −0.162797 | −0.0813985 | − | 0.996682i | \(-0.525939\pi\) | ||||
−0.0813985 | + | 0.996682i | \(0.525939\pi\) | |||||||
\(840\) | 104120. | − | 26316.6i | 0.147563 | − | 0.0372968i | ||||
\(841\) | 693627.i | 0.980696i | ||||||||
\(842\) | 527152. | − | 622216.i | 0.743552 | − | 0.877642i | ||||
\(843\) | 144007. | − | 144007.i | 0.202642 | − | 0.202642i | ||||
\(844\) | 196998. | + | 140744.i | 0.276552 | + | 0.197581i | ||||
\(845\) | 98332.0 | − | 98332.0i | 0.137715 | − | 0.137715i | ||||
\(846\) | 12471.5 | + | 150786.i | 0.0174253 | + | 0.210678i | ||||
\(847\) | − | 438256.i | − | 0.610887i | ||||||
\(848\) | −627333. | − | 307154.i | −0.872382 | − | 0.427135i | ||||
\(849\) | 110966. | 0.153949 | ||||||||
\(850\) | −875914. | + | 72447.1i | −1.21234 | + | 0.100273i | ||||
\(851\) | −1.08874e6 | − | 1.08874e6i | −1.50337 | − | 1.50337i | ||||
\(852\) | −646586. | − | 461948.i | −0.890732 | − | 0.636377i | ||||
\(853\) | 79602.6 | + | 79602.6i | 0.109403 | + | 0.109403i | 0.759689 | − | 0.650286i | \(-0.225351\pi\) |
−0.650286 | + | 0.759689i | \(0.725351\pi\) | |||||||
\(854\) | −359494. | − | 304570.i | −0.492920 | − | 0.417610i | ||||
\(855\) | 96610.5 | 0.132158 | ||||||||
\(856\) | 232387. | + | 138615.i | 0.317149 | + | 0.189175i | ||||
\(857\) | − | 556304.i | − | 0.757444i | −0.925510 | − | 0.378722i | \(-0.876364\pi\) | ||
0.925510 | − | 0.378722i | \(-0.123636\pi\) | |||||||
\(858\) | −585326. | − | 495897.i | −0.795102 | − | 0.673623i | ||||
\(859\) | 825505. | − | 825505.i | 1.11875 | − | 1.11875i | 0.126825 | − | 0.991925i | \(-0.459521\pi\) |
0.991925 | − | 0.126825i | \(-0.0404788\pi\) | |||||||
\(860\) | 54715.6 | − | 9113.44i | 0.0739800 | − | 0.0123221i | ||||
\(861\) | 231131. | − | 231131.i | 0.311782 | − | 0.311782i | ||||
\(862\) | −74312.2 | + | 6146.38i | −0.100010 | + | 0.00827190i | ||||
\(863\) | 800580.i | 1.07494i | 0.843284 | + | 0.537469i | \(0.180619\pi\) | ||||
−0.843284 | + | 0.537469i | \(0.819381\pi\) | |||||||
\(864\) | 693519. | + | 271215.i | 0.929032 | + | 0.363318i | ||||
\(865\) | −114046. | −0.152422 | ||||||||
\(866\) | 723.387 | + | 8746.03i | 0.000964572 | + | 0.0116621i | ||||
\(867\) | 234158. | + | 234158.i | 0.311509 | + | 0.311509i | ||||
\(868\) | −34137.0 | − | 204953.i | −0.0453091 | − | 0.272028i | ||||
\(869\) | −315261. | − | 315261.i | −0.417475 | − | 0.417475i | ||||
\(870\) | −11174.2 | + | 13189.3i | −0.0147631 | + | 0.0174254i | ||||
\(871\) | −692941. | −0.913398 | ||||||||
\(872\) | 260699. | + | 155503.i | 0.342852 | + | 0.204506i | ||||
\(873\) | − | 429949.i | − | 0.564143i | ||||||
\(874\) | 549980. | − | 649161.i | 0.719986 | − | 0.849825i | ||||
\(875\) | 258325. | − | 258325.i | 0.337403 | − | 0.337403i | ||||
\(876\) | 481520. | − | 673981.i | 0.627490 | − | 0.878293i | ||||
\(877\) | −684224. | + | 684224.i | −0.889609 | + | 0.889609i | −0.994485 | − | 0.104876i | \(-0.966555\pi\) |
0.104876 | + | 0.994485i | \(0.466555\pi\) | |||||||
\(878\) | 38944.3 | + | 470851.i | 0.0505190 | + | 0.610794i | ||||
\(879\) | 632048.i | 0.818036i | ||||||||
\(880\) | 252186. | − | 86405.3i | 0.325653 | − | 0.111577i | ||||
\(881\) | −995272. | −1.28230 | −0.641150 | − | 0.767415i | \(-0.721542\pi\) | ||||
−0.641150 | + | 0.767415i | \(0.721542\pi\) | |||||||
\(882\) | −68730.0 | + | 5684.68i | −0.0883506 | + | 0.00730750i | ||||
\(883\) | 67491.2 | + | 67491.2i | 0.0865617 | + | 0.0865617i | 0.749062 | − | 0.662500i | \(-0.230505\pi\) |
−0.662500 | + | 0.749062i | \(0.730505\pi\) | |||||||
\(884\) | −782489. | + | 1.09524e6i | −1.00132 | + | 1.40154i | ||||
\(885\) | −50209.3 | − | 50209.3i | −0.0641058 | − | 0.0641058i | ||||
\(886\) | 163519. | + | 138536.i | 0.208306 | + | 0.176480i | ||||
\(887\) | 180136. | 0.228957 | 0.114479 | − | 0.993426i | \(-0.463480\pi\) | ||||
0.114479 | + | 0.993426i | \(0.463480\pi\) | |||||||
\(888\) | 714375. | − | 180560.i | 0.905941 | − | 0.228979i | ||||
\(889\) | − | 1.03902e6i | − | 1.31468i | ||||||
\(890\) | 105423. | + | 89315.8i | 0.133093 | + | 0.112758i | ||||
\(891\) | −5700.68 | + | 5700.68i | −0.00718078 | + | 0.00718078i | ||||
\(892\) | 241057. | + | 1.44727e6i | 0.302963 | + | 1.81894i | ||||
\(893\) | −152611. | + | 152611.i | −0.191374 | + | 0.191374i | ||||
\(894\) | 100413. | − | 8305.17i | 0.125636 | − | 0.0103914i | ||||
\(895\) | − | 265569.i | − | 0.331536i | ||||||
\(896\) | −405922. | − | 622747.i | −0.505623 | − | 0.775703i | ||||
\(897\) | 910976. | 1.13220 | ||||||||
\(898\) | −28087.3 | − | 339587.i | −0.0348303 | − | 0.421112i | ||||
\(899\) | 23648.5 | + | 23648.5i | 0.0292607 | + | 0.0292607i | ||||
\(900\) | 461160. | − | 76810.9i | 0.569334 | − | 0.0948283i | ||||
\(901\) | 730428. | + | 730428.i | 0.899763 | + | 0.899763i | ||||
\(902\) | 524475. | − | 619057.i | 0.644632 | − | 0.760883i | ||||
\(903\) | −130371. | −0.159884 | ||||||||
\(904\) | 50088.4 | + | 198172.i | 0.0612915 | + | 0.242496i | ||||
\(905\) | − | 150271.i | − | 0.183475i | ||||||
\(906\) | 211452. | − | 249585.i | 0.257606 | − | 0.304061i | ||||
\(907\) | −893550. | + | 893550.i | −1.08619 | + | 1.08619i | −0.0902686 | + | 0.995917i | \(0.528773\pi\) |
−0.995917 | + | 0.0902686i | \(0.971227\pi\) | |||||||
\(908\) | −322189. | − | 230185.i | −0.390786 | − | 0.279194i | ||||
\(909\) | 27068.1 | − | 27068.1i | 0.0327589 | − | 0.0327589i | ||||
\(910\) | −22205.8 | − | 268477.i | −0.0268154 | − | 0.324208i | ||||
\(911\) | − | 638798.i | − | 0.769709i | −0.922977 | − | 0.384855i | \(-0.874252\pi\) | ||
0.922977 | − | 0.384855i | \(-0.125748\pi\) | |||||||
\(912\) | 131973. | + | 385181.i | 0.158670 | + | 0.463101i | ||||
\(913\) | −228532. | −0.274160 | ||||||||
\(914\) | 386423. | − | 31961.2i | 0.462563 | − | 0.0382587i | ||||
\(915\) | −67895.7 | − | 67895.7i | −0.0810961 | − | 0.0810961i | ||||
\(916\) | 1.17574e6 | + | 840001.i | 1.40127 | + | 1.00113i | ||||
\(917\) | 873663. | + | 873663.i | 1.03898 | + | 1.03898i | ||||
\(918\) | −840251. | − | 711874.i | −0.997066 | − | 0.844730i | ||||
\(919\) | −1.28409e6 | −1.52043 | −0.760213 | − | 0.649674i | \(-0.774905\pi\) | ||||
−0.760213 | + | 0.649674i | \(0.774905\pi\) | |||||||
\(920\) | −162163. | + | 271865.i | −0.191592 | + | 0.321201i | ||||
\(921\) | 890380.i | 1.04968i | ||||||||
\(922\) | 1.27331e6 | + | 1.07877e6i | 1.49786 | + | 1.26901i | ||||
\(923\) | −1.40950e6 | + | 1.40950e6i | −1.65449 | + | 1.65449i | ||||
\(924\) | −618029. | + | 102939.i | −0.723877 | + | 0.120569i | ||||
\(925\) | 853383. | − | 853383.i | 0.997380 | − | 0.997380i | ||||
\(926\) | 894338. | − | 73971.0i | 1.04299 | − | 0.0862660i | ||||
\(927\) | 279110.i | 0.324800i | ||||||||
\(928\) | 111435. | + | 43579.0i | 0.129397 | + | 0.0506035i | ||||
\(929\) | 198494. | 0.229994 | 0.114997 | − | 0.993366i | \(-0.463314\pi\) | ||||
0.114997 | + | 0.993366i | \(0.463314\pi\) | |||||||
\(930\) | −3490.25 | − | 42198.5i | −0.00403544 | − | 0.0487901i | ||||
\(931\) | −69562.0 | − | 69562.0i | −0.0802551 | − | 0.0802551i | ||||
\(932\) | −167955. | − | 1.00838e6i | −0.193358 | − | 1.16089i | ||||
\(933\) | −367232. | − | 367232.i | −0.421869 | − | 0.421869i | ||||
\(934\) | −693144. | + | 818143.i | −0.794566 | + | 0.937855i | ||||
\(935\) | −394235. | −0.450953 | ||||||||
\(936\) | 366789. | − | 614917.i | 0.418663 | − | 0.701883i | ||||
\(937\) | − | 389175.i | − | 0.443267i | −0.975130 | − | 0.221634i | \(-0.928861\pi\) | ||
0.975130 | − | 0.221634i | \(-0.0711389\pi\) | |||||||
\(938\) | −365829. | + | 431801.i | −0.415788 | + | 0.490770i | ||||
\(939\) | 36133.4 | − | 36133.4i | 0.0409805 | − | 0.0409805i | ||||
\(940\) | 46680.1 | − | 65337.8i | 0.0528295 | − | 0.0739450i | ||||
\(941\) | −481044. | + | 481044.i | −0.543257 | + | 0.543257i | −0.924482 | − | 0.381225i | \(-0.875502\pi\) |
0.381225 | + | 0.924482i | \(0.375502\pi\) | |||||||
\(942\) | −46507.6 | − | 562295.i | −0.0524109 | − | 0.633669i | ||||
\(943\) | 963474.i | 1.08347i | ||||||||
\(944\) | −216128. | + | 441422.i | −0.242531 | + | 0.495347i | ||||
\(945\) | 220404. | 0.246806 | ||||||||
\(946\) | −322509. | + | 26674.8i | −0.360379 | + | 0.0298071i | ||||
\(947\) | −399574. | − | 399574.i | −0.445551 | − | 0.445551i | 0.448321 | − | 0.893872i | \(-0.352022\pi\) |
−0.893872 | + | 0.448321i | \(0.852022\pi\) | |||||||
\(948\) | −147286. | + | 206155.i | −0.163887 | + | 0.229391i | ||||
\(949\) | −1.46922e6 | − | 1.46922e6i | −1.63138 | − | 1.63138i | ||||
\(950\) | 508828. | + | 431087.i | 0.563798 | + | 0.477659i | ||||
\(951\) | −66143.2 | −0.0731348 | ||||||||
\(952\) | 269389. | + | 1.06582e6i | 0.297239 | + | 1.17601i | ||||
\(953\) | 1.26137e6i | 1.38885i | 0.719564 | + | 0.694427i | \(0.244342\pi\) | ||||
−0.719564 | + | 0.694427i | \(0.755658\pi\) | |||||||
\(954\) | −419239. | − | 355186.i | −0.460644 | − | 0.390265i | ||||
\(955\) | −132440. | + | 132440.i | −0.145215 | + | 0.145215i | ||||
\(956\) | −31798.4 | − | 190912.i | −0.0347928 | − | 0.208890i | ||||
\(957\) | 71311.5 | − | 71311.5i | 0.0778638 | − | 0.0778638i | ||||
\(958\) | −529376. | + | 43784.9i | −0.576811 | + | 0.0477082i | ||||
\(959\) | − | 904620.i | − | 0.983624i | ||||||
\(960\) | −71980.2 | − | 133296.i | −0.0781035 | − | 0.144636i | ||||
\(961\) | 841601. | 0.911296 | ||||||||
\(962\) | −152355. | − | 1.84203e6i | −0.164629 | − | 1.99043i | ||||
\(963\) | 150514. | + | 150514.i | 0.162302 | + | 0.162302i | ||||
\(964\) | −441574. | + | 73548.7i | −0.475171 | + | 0.0791445i | ||||
\(965\) | 267883. | + | 267883.i | 0.287668 | + | 0.287668i | ||||
\(966\) | 480937. | − | 567667.i | 0.515388 | − | 0.608331i | ||||
\(967\) | 1.50478e6 | 1.60924 | 0.804619 | − | 0.593791i | \(-0.202370\pi\) | ||||
0.804619 | + | 0.593791i | \(0.202370\pi\) | |||||||
\(968\) | −599350. | + | 151487.i | −0.639631 | + | 0.161668i | ||||
\(969\) | − | 602143.i | − | 0.641286i | ||||||
\(970\) | −147503. | + | 174104.i | −0.156768 | + | 0.185040i | ||||
\(971\) | 818605. | − | 818605.i | 0.868233 | − | 0.868233i | −0.124044 | − | 0.992277i | \(-0.539586\pi\) |
0.992277 | + | 0.124044i | \(0.0395864\pi\) | |||||||
\(972\) | 770588. | + | 550540.i | 0.815623 | + | 0.582716i | ||||
\(973\) | 1.14224e6 | − | 1.14224e6i | 1.20651 | − | 1.20651i | ||||
\(974\) | −93618.2 | − | 1.13188e6i | −0.0986830 | − | 1.19312i | ||||
\(975\) | 714044.i | 0.751131i | ||||||||
\(976\) | −292261. | + | 596915.i | −0.306811 | + | 0.626632i | ||||
\(977\) | 753210. | 0.789091 | 0.394545 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394545 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(978\) | −470796. | + | 38939.7i | −0.492215 | + | 0.0407113i | ||||
\(979\) | −569995. | − | 569995.i | −0.594711 | − | 0.594711i | ||||
\(980\) | 29781.8 | + | 21277.4i | 0.0310098 | + | 0.0221547i | ||||
\(981\) | 168852. | + | 168852.i | 0.175456 | + | 0.175456i | ||||
\(982\) | −482218. | − | 408543.i | −0.500058 | − | 0.423658i | ||||
\(983\) | −460098. | −0.476149 | −0.238075 | − | 0.971247i | \(-0.576516\pi\) | ||||
−0.238075 | + | 0.971247i | \(0.576516\pi\) | |||||||
\(984\) | −395982. | − | 236197.i | −0.408964 | − | 0.243941i | ||||
\(985\) | − | 96163.6i | − | 0.0991147i | ||||||
\(986\) | −135012. | − | 114384.i | −0.138873 | − | 0.117655i | ||||
\(987\) | −133453. | + | 133453.i | −0.136991 | + | 0.136991i | ||||
\(988\) | 1.00747e6 | − | 167804.i | 1.03209 | − | 0.171905i | ||||
\(989\) | 271727. | − | 271727.i | 0.277806 | − | 0.277806i | ||||
\(990\) | 208991. | − | 17285.7i | 0.213234 | − | 0.0176366i | ||||
\(991\) | − | 1.16135e6i | − | 1.18254i | −0.806472 | − | 0.591272i | \(-0.798626\pi\) | ||
0.806472 | − | 0.591272i | \(-0.201374\pi\) | |||||||
\(992\) | −268490. | + | 117529.i | −0.272837 | + | 0.119432i | ||||
\(993\) | −360899. | −0.366005 | ||||||||
\(994\) | 134193. | + | 1.62245e6i | 0.135818 | + | 1.64210i | ||||
\(995\) | 150147. | + | 150147.i | 0.151659 | + | 0.151659i | ||||
\(996\) | 21337.0 | + | 128104.i | 0.0215087 | + | 0.129135i | ||||
\(997\) | 271712. | + | 271712.i | 0.273349 | + | 0.273349i | 0.830447 | − | 0.557098i | \(-0.188085\pi\) |
−0.557098 | + | 0.830447i | \(0.688085\pi\) | |||||||
\(998\) | −225233. | + | 265851.i | −0.226137 | + | 0.266918i | ||||
\(999\) | 1.51220e6 | 1.51523 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 16.5.f.a.11.4 | yes | 14 | |
3.2 | odd | 2 | 144.5.m.a.91.4 | 14 | |||
4.3 | odd | 2 | 64.5.f.a.15.3 | 14 | |||
8.3 | odd | 2 | 128.5.f.a.31.5 | 14 | |||
8.5 | even | 2 | 128.5.f.b.31.3 | 14 | |||
12.11 | even | 2 | 576.5.m.a.271.3 | 14 | |||
16.3 | odd | 4 | inner | 16.5.f.a.3.4 | ✓ | 14 | |
16.5 | even | 4 | 128.5.f.a.95.5 | 14 | |||
16.11 | odd | 4 | 128.5.f.b.95.3 | 14 | |||
16.13 | even | 4 | 64.5.f.a.47.3 | 14 | |||
48.29 | odd | 4 | 576.5.m.a.559.3 | 14 | |||
48.35 | even | 4 | 144.5.m.a.19.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.4 | ✓ | 14 | 16.3 | odd | 4 | inner | |
16.5.f.a.11.4 | yes | 14 | 1.1 | even | 1 | trivial | |
64.5.f.a.15.3 | 14 | 4.3 | odd | 2 | |||
64.5.f.a.47.3 | 14 | 16.13 | even | 4 | |||
128.5.f.a.31.5 | 14 | 8.3 | odd | 2 | |||
128.5.f.a.95.5 | 14 | 16.5 | even | 4 | |||
128.5.f.b.31.3 | 14 | 8.5 | even | 2 | |||
128.5.f.b.95.3 | 14 | 16.11 | odd | 4 | |||
144.5.m.a.19.4 | 14 | 48.35 | even | 4 | |||
144.5.m.a.91.4 | 14 | 3.2 | odd | 2 | |||
576.5.m.a.271.3 | 14 | 12.11 | even | 2 | |||
576.5.m.a.559.3 | 14 | 48.29 | odd | 4 |