Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(74,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.74");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3253342510\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 75 x^{18} + 3638 x^{16} - 105775 x^{14} + 2246038 x^{12} - 30934571 x^{10} + 307864753 x^{8} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 74.10 | ||
Root | \(4.50647 + 2.60181i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.74 |
Dual form | 175.4.k.d.149.10 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.50647 | − | 2.60181i | 1.59328 | − | 0.919879i | 0.600538 | − | 0.799596i | \(-0.294953\pi\) |
0.992740 | − | 0.120283i | \(-0.0383803\pi\) | |||||||
\(3\) | 4.24917 | + | 2.45326i | 0.817753 | + | 0.472130i | 0.849641 | − | 0.527362i | \(-0.176819\pi\) |
−0.0318881 | + | 0.999491i | \(0.510152\pi\) | |||||||
\(4\) | 9.53885 | − | 16.5218i | 1.19236 | − | 2.06522i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 25.5317 | 1.73721 | ||||||||
\(7\) | 4.23212 | − | 18.0302i | 0.228513 | − | 0.973541i | ||||
\(8\) | − | 57.6442i | − | 2.54754i | ||||||
\(9\) | −1.46305 | − | 2.53407i | −0.0541869 | − | 0.0938545i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −28.3386 | + | 49.0839i | −0.776764 | + | 1.34539i | 0.157034 | + | 0.987593i | \(0.449807\pi\) |
−0.933798 | + | 0.357802i | \(0.883526\pi\) | |||||||
\(12\) | 81.0644 | − | 46.8025i | 1.95011 | − | 1.12589i | ||||
\(13\) | 43.4297i | 0.926556i | 0.886213 | + | 0.463278i | \(0.153327\pi\) | ||||
−0.886213 | + | 0.463278i | \(0.846673\pi\) | |||||||
\(14\) | −27.8393 | − | 92.2639i | −0.531455 | − | 1.76133i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −73.6685 | − | 127.598i | −1.15107 | − | 1.99371i | ||||
\(17\) | 34.5013 | + | 19.9193i | 0.492223 | + | 0.284185i | 0.725496 | − | 0.688226i | \(-0.241610\pi\) |
−0.233273 | + | 0.972411i | \(0.574944\pi\) | |||||||
\(18\) | −13.1864 | − | 7.61315i | −0.172670 | − | 0.0996909i | ||||
\(19\) | 26.1940 | + | 45.3693i | 0.316280 | + | 0.547813i | 0.979709 | − | 0.200427i | \(-0.0642328\pi\) |
−0.663429 | + | 0.748239i | \(0.730899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 62.2158 | − | 66.2310i | 0.646505 | − | 0.688228i | ||||
\(22\) | 294.927i | 2.85812i | ||||||||
\(23\) | 46.3460 | − | 26.7579i | 0.420166 | − | 0.242583i | −0.274982 | − | 0.961449i | \(-0.588672\pi\) |
0.695148 | + | 0.718866i | \(0.255339\pi\) | |||||||
\(24\) | 141.416 | − | 244.940i | 1.20277 | − | 2.08326i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 112.996 | + | 195.715i | 0.852320 | + | 1.47626i | ||||
\(27\) | − | 146.833i | − | 1.04659i | ||||||
\(28\) | −257.522 | − | 241.910i | −1.73811 | − | 1.63274i | ||||
\(29\) | −49.6376 | −0.317844 | −0.158922 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158922 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.8930 | − | 63.9006i | 0.213748 | − | 0.370222i | −0.739137 | − | 0.673555i | \(-0.764766\pi\) |
0.952884 | + | 0.303333i | \(0.0980996\pi\) | |||||||
\(32\) | −264.599 | − | 152.767i | −1.46172 | − | 0.843924i | ||||
\(33\) | −240.831 | + | 139.044i | −1.27040 | + | 0.733467i | ||||
\(34\) | 207.305 | 1.04566 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −55.8231 | −0.258440 | ||||||||
\(37\) | −265.938 | + | 153.540i | −1.18162 | + | 0.682210i | −0.956389 | − | 0.292096i | \(-0.905647\pi\) |
−0.225232 | + | 0.974305i | \(0.572314\pi\) | |||||||
\(38\) | 236.085 | + | 136.304i | 1.00784 | + | 0.581879i | ||||
\(39\) | −106.544 | + | 184.540i | −0.437455 | + | 0.757694i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 292.064 | 1.11251 | 0.556254 | − | 0.831012i | \(-0.312238\pi\) | ||||
0.556254 | + | 0.831012i | \(0.312238\pi\) | |||||||
\(42\) | 108.053 | − | 460.342i | 0.396975 | − | 1.69124i | ||||
\(43\) | 365.956i | 1.29786i | 0.760850 | + | 0.648928i | \(0.224783\pi\) | ||||
−0.760850 | + | 0.648928i | \(0.775217\pi\) | |||||||
\(44\) | 540.635 | + | 936.407i | 1.85236 | + | 3.20838i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 139.238 | − | 241.167i | 0.446294 | − | 0.773004i | ||||
\(47\) | −383.175 | + | 221.226i | −1.18919 | + | 0.686577i | −0.958122 | − | 0.286361i | \(-0.907554\pi\) |
−0.231065 | + | 0.972938i | \(0.574221\pi\) | |||||||
\(48\) | − | 722.912i | − | 2.17382i | ||||||
\(49\) | −307.178 | − | 152.612i | −0.895563 | − | 0.444934i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 97.7346 | + | 169.281i | 0.268345 | + | 0.464787i | ||||
\(52\) | 717.536 | + | 414.269i | 1.91354 | + | 1.10479i | ||||
\(53\) | 22.3185 | + | 12.8856i | 0.0578430 | + | 0.0333957i | 0.528643 | − | 0.848845i | \(-0.322701\pi\) |
−0.470800 | + | 0.882240i | \(0.656035\pi\) | |||||||
\(54\) | −382.032 | − | 661.698i | −0.962739 | − | 1.66751i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1039.34 | − | 243.957i | −2.48013 | − | 0.582146i | ||||
\(57\) | 257.043i | 0.597300i | ||||||||
\(58\) | −223.690 | + | 129.148i | −0.506413 | + | 0.292378i | ||||
\(59\) | 188.300 | − | 326.146i | 0.415502 | − | 0.719670i | −0.579979 | − | 0.814631i | \(-0.696939\pi\) |
0.995481 | + | 0.0949609i | \(0.0302726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −316.287 | − | 547.826i | −0.663876 | − | 1.14987i | −0.979589 | − | 0.201012i | \(-0.935577\pi\) |
0.315713 | − | 0.948855i | \(-0.397756\pi\) | |||||||
\(62\) | − | 383.955i | − | 0.786489i | ||||||
\(63\) | −51.8817 | + | 15.6546i | −0.103754 | + | 0.0313062i | ||||
\(64\) | −411.183 | −0.803092 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −723.531 | + | 1253.19i | −1.34940 | + | 2.33723i | ||||
\(67\) | −442.624 | − | 255.549i | −0.807091 | − | 0.465974i | 0.0388534 | − | 0.999245i | \(-0.487629\pi\) |
−0.845945 | + | 0.533271i | \(0.820963\pi\) | |||||||
\(68\) | 658.206 | − | 380.015i | 1.17381 | − | 0.677700i | ||||
\(69\) | 262.576 | 0.458123 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 134.881 | 0.225457 | 0.112728 | − | 0.993626i | \(-0.464041\pi\) | ||||
0.112728 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(72\) | −146.075 | + | 84.3362i | −0.239098 | + | 0.138043i | ||||
\(73\) | 354.564 | + | 204.708i | 0.568474 | + | 0.328208i | 0.756540 | − | 0.653948i | \(-0.226888\pi\) |
−0.188066 | + | 0.982156i | \(0.560222\pi\) | |||||||
\(74\) | −798.962 | + | 1383.84i | −1.25510 | + | 2.17390i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 999.443 | 1.50847 | ||||||||
\(77\) | 765.061 | + | 718.680i | 1.13230 | + | 1.06365i | ||||
\(78\) | 1108.83i | 1.60962i | ||||||||
\(79\) | −463.424 | − | 802.674i | −0.659991 | − | 1.14314i | −0.980618 | − | 0.195932i | \(-0.937227\pi\) |
0.320627 | − | 0.947206i | \(-0.396106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 320.717 | − | 555.498i | 0.439941 | − | 0.762000i | ||||
\(82\) | 1316.18 | − | 759.897i | 1.77253 | − | 1.02337i | ||||
\(83\) | − | 296.372i | − | 0.391940i | −0.980610 | − | 0.195970i | \(-0.937214\pi\) | ||
0.980610 | − | 0.195970i | \(-0.0627856\pi\) | |||||||
\(84\) | −500.786 | − | 1659.68i | −0.650479 | − | 2.15579i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 952.150 | + | 1649.17i | 1.19387 | + | 2.06785i | ||||
\(87\) | −210.918 | − | 121.774i | −0.259918 | − | 0.150063i | ||||
\(88\) | 2829.40 | + | 1633.55i | 3.42744 | + | 1.97884i | ||||
\(89\) | 244.391 | + | 423.297i | 0.291071 | + | 0.504150i | 0.974063 | − | 0.226275i | \(-0.0726550\pi\) |
−0.682992 | + | 0.730426i | \(0.739322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 783.047 | + | 183.800i | 0.902040 | + | 0.211730i | ||||
\(92\) | − | 1020.96i | − | 1.15698i | ||||||
\(93\) | 313.529 | − | 181.016i | 0.349586 | − | 0.201833i | ||||
\(94\) | −1151.18 | + | 1993.90i | −1.26314 | + | 2.18782i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −749.552 | − | 1298.26i | −0.796883 | − | 1.38024i | ||||
\(97\) | − | 475.907i | − | 0.498155i | −0.968484 | − | 0.249077i | \(-0.919873\pi\) | ||
0.968484 | − | 0.249077i | \(-0.0801274\pi\) | |||||||
\(98\) | −1781.36 | + | 111.477i | −1.83617 | + | 0.114907i | ||||
\(99\) | 165.843 | 0.168362 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −38.7904 | + | 67.1870i | −0.0382158 | + | 0.0661917i | −0.884501 | − | 0.466539i | \(-0.845501\pi\) |
0.846285 | + | 0.532731i | \(0.178834\pi\) | |||||||
\(102\) | 880.876 | + | 508.574i | 0.855095 | + | 0.493689i | ||||
\(103\) | −985.340 | + | 568.886i | −0.942606 | + | 0.544214i | −0.890776 | − | 0.454442i | \(-0.849839\pi\) |
−0.0518297 | + | 0.998656i | \(0.516505\pi\) | |||||||
\(104\) | 2503.47 | 2.36044 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 134.103 | 0.122880 | ||||||||
\(107\) | 65.0735 | − | 37.5702i | 0.0587934 | − | 0.0339444i | −0.470315 | − | 0.882499i | \(-0.655860\pi\) |
0.529109 | + | 0.848554i | \(0.322526\pi\) | |||||||
\(108\) | −2425.94 | − | 1400.62i | −2.16145 | − | 1.24791i | ||||
\(109\) | 41.4673 | − | 71.8235i | 0.0364390 | − | 0.0631142i | −0.847231 | − | 0.531225i | \(-0.821732\pi\) |
0.883670 | + | 0.468111i | \(0.155065\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1506.69 | −1.28837 | ||||||||
\(112\) | −2612.39 | + | 788.251i | −2.20400 | + | 0.665024i | ||||
\(113\) | − | 714.602i | − | 0.594903i | −0.954737 | − | 0.297452i | \(-0.903863\pi\) | ||
0.954737 | − | 0.297452i | \(-0.0961367\pi\) | |||||||
\(114\) | 668.777 | + | 1158.35i | 0.549444 | + | 0.951666i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −473.485 | + | 820.101i | −0.378983 | + | 0.656418i | ||||
\(117\) | 110.054 | − | 63.5397i | 0.0869615 | − | 0.0502072i | ||||
\(118\) | − | 1959.69i | − | 1.52885i | ||||||
\(119\) | 505.164 | − | 537.765i | 0.389145 | − | 0.414259i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −940.651 | − | 1629.26i | −0.706725 | − | 1.22408i | ||||
\(122\) | −2850.68 | − | 1645.84i | −2.11548 | − | 1.22137i | ||||
\(123\) | 1241.03 | + | 716.510i | 0.909756 | + | 0.525248i | ||||
\(124\) | −703.834 | − | 1219.08i | −0.509727 | − | 0.882873i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −193.073 | + | 205.533i | −0.136510 | + | 0.145320i | ||||
\(127\) | 1881.66i | 1.31473i | 0.753574 | + | 0.657363i | \(0.228328\pi\) | ||||
−0.753574 | + | 0.657363i | \(0.771672\pi\) | |||||||
\(128\) | 263.812 | − | 152.312i | 0.182171 | − | 0.105177i | ||||
\(129\) | −897.786 | + | 1555.01i | −0.612757 | + | 1.06133i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −91.9544 | − | 159.270i | −0.0613289 | − | 0.106225i | 0.833731 | − | 0.552171i | \(-0.186201\pi\) |
−0.895060 | + | 0.445946i | \(0.852867\pi\) | |||||||
\(132\) | 5305.27i | 3.49822i | ||||||||
\(133\) | 928.876 | − | 280.275i | 0.605592 | − | 0.182729i | ||||
\(134\) | −2659.56 | −1.71456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1148.23 | − | 1988.80i | 0.723972 | − | 1.25396i | ||||
\(137\) | −768.812 | − | 443.874i | −0.479445 | − | 0.276808i | 0.240740 | − | 0.970590i | \(-0.422610\pi\) |
−0.720185 | + | 0.693782i | \(0.755943\pi\) | |||||||
\(138\) | 1183.29 | − | 683.174i | 0.729917 | − | 0.421417i | ||||
\(139\) | 2335.25 | 1.42499 | 0.712495 | − | 0.701678i | \(-0.247565\pi\) | ||||
0.712495 | + | 0.701678i | \(0.247565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2170.90 | −1.29661 | ||||||||
\(142\) | 607.837 | − | 350.935i | 0.359215 | − | 0.207393i | ||||
\(143\) | −2131.70 | − | 1230.74i | −1.24658 | − | 0.719716i | ||||
\(144\) | −215.561 | + | 373.363i | −0.124746 | + | 0.216066i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2130.44 | 1.20765 | ||||||||
\(147\) | −930.854 | − | 1402.06i | −0.522283 | − | 0.786668i | ||||
\(148\) | 5858.36i | 3.25375i | ||||||||
\(149\) | −1201.54 | − | 2081.12i | −0.660629 | − | 1.14424i | −0.980451 | − | 0.196766i | \(-0.936956\pi\) |
0.319821 | − | 0.947478i | \(-0.396377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −617.188 | + | 1069.00i | −0.332623 | + | 0.576120i | −0.983025 | − | 0.183470i | \(-0.941267\pi\) |
0.650402 | + | 0.759590i | \(0.274600\pi\) | |||||||
\(152\) | 2615.28 | − | 1509.93i | 1.39557 | − | 0.805735i | ||||
\(153\) | − | 116.572i | − | 0.0615965i | ||||||
\(154\) | 5317.60 | + | 1248.17i | 2.78249 | + | 0.653118i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2032.62 | + | 3520.60i | 1.04320 | + | 1.80688i | ||||
\(157\) | −1240.57 | − | 716.244i | −0.630627 | − | 0.364092i | 0.150368 | − | 0.988630i | \(-0.451954\pi\) |
−0.780995 | + | 0.624538i | \(0.785287\pi\) | |||||||
\(158\) | −4176.81 | − | 2411.48i | −2.10310 | − | 1.21422i | ||||
\(159\) | 63.2233 | + | 109.506i | 0.0315342 | + | 0.0546188i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −286.309 | − | 948.872i | −0.140151 | − | 0.464482i | ||||
\(162\) | − | 3337.78i | − | 1.61877i | ||||||
\(163\) | 745.500 | − | 430.415i | 0.358234 | − | 0.206826i | −0.310072 | − | 0.950713i | \(-0.600353\pi\) |
0.668306 | + | 0.743887i | \(0.267020\pi\) | |||||||
\(164\) | 2785.96 | − | 4825.42i | 1.32651 | − | 2.29757i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −771.104 | − | 1335.59i | −0.360538 | − | 0.624470i | ||||
\(167\) | − | 1346.77i | − | 0.624049i | −0.950074 | − | 0.312024i | \(-0.898993\pi\) | ||
0.950074 | − | 0.312024i | \(-0.101007\pi\) | |||||||
\(168\) | −3817.83 | − | 3586.38i | −1.75329 | − | 1.64700i | ||||
\(169\) | 310.861 | 0.141493 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 76.6461 | − | 132.755i | 0.0342765 | − | 0.0593686i | ||||
\(172\) | 6046.25 | + | 3490.80i | 2.68036 | + | 1.54751i | ||||
\(173\) | 2260.75 | − | 1305.25i | 0.993536 | − | 0.573618i | 0.0872067 | − | 0.996190i | \(-0.472206\pi\) |
0.906329 | + | 0.422572i | \(0.138873\pi\) | |||||||
\(174\) | −1267.33 | −0.552161 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8350.65 | 3.57644 | ||||||||
\(177\) | 1600.24 | − | 923.899i | 0.679556 | − | 0.392342i | ||||
\(178\) | 2202.68 | + | 1271.72i | 0.927515 | + | 0.535501i | ||||
\(179\) | 675.224 | − | 1169.52i | 0.281947 | − | 0.488347i | −0.689917 | − | 0.723889i | \(-0.742353\pi\) |
0.971864 | + | 0.235541i | \(0.0756863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2846.61 | 1.16899 | 0.584493 | − | 0.811399i | \(-0.301293\pi\) | ||||
0.584493 | + | 0.811399i | \(0.301293\pi\) | |||||||
\(182\) | 4006.99 | − | 1209.05i | 1.63197 | − | 0.492423i | ||||
\(183\) | − | 3103.74i | − | 1.25374i | ||||||
\(184\) | −1542.44 | − | 2671.58i | −0.617989 | − | 1.07039i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 941.940 | − | 1631.49i | 0.371325 | − | 0.643154i | ||||
\(187\) | −1955.44 | + | 1128.97i | −0.764683 | + | 0.441490i | ||||
\(188\) | 8440.97i | 3.27458i | ||||||||
\(189\) | −2647.43 | − | 621.415i | −1.01890 | − | 0.239160i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2101.75 | − | 3640.33i | −0.796215 | − | 1.37909i | −0.922065 | − | 0.387036i | \(-0.873499\pi\) |
0.125849 | − | 0.992049i | \(-0.459834\pi\) | |||||||
\(192\) | −1747.19 | − | 1008.74i | −0.656730 | − | 0.379163i | ||||
\(193\) | 120.018 | + | 69.2923i | 0.0447620 | + | 0.0258434i | 0.522214 | − | 0.852814i | \(-0.325106\pi\) |
−0.477452 | + | 0.878658i | \(0.658440\pi\) | |||||||
\(194\) | −1238.22 | − | 2144.66i | −0.458242 | − | 0.793699i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5451.55 | + | 3619.38i | −1.98672 | + | 1.31902i | ||||
\(197\) | 1473.76i | 0.532998i | 0.963835 | + | 0.266499i | \(0.0858670\pi\) | ||||
−0.963835 | + | 0.266499i | \(0.914133\pi\) | |||||||
\(198\) | 747.365 | − | 431.492i | 0.268247 | − | 0.154873i | ||||
\(199\) | −1804.80 | + | 3126.00i | −0.642909 | + | 1.11355i | 0.341872 | + | 0.939747i | \(0.388939\pi\) |
−0.984780 | + | 0.173804i | \(0.944394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1253.86 | − | 2171.74i | −0.440001 | − | 0.762104i | ||||
\(202\) | 403.702i | 0.140616i | ||||||||
\(203\) | −210.072 | + | 894.977i | −0.0726315 | + | 0.309434i | ||||
\(204\) | 3729.10 | 1.27985 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2960.27 | + | 5127.34i | −1.00122 | + | 1.73417i | ||||
\(207\) | −135.613 | − | 78.2961i | −0.0455350 | − | 0.0262896i | ||||
\(208\) | 5541.53 | − | 3199.40i | 1.84729 | − | 1.06653i | ||||
\(209\) | −2969.20 | −0.982699 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1782.00 | 0.581412 | 0.290706 | − | 0.956812i | \(-0.406110\pi\) | ||||
0.290706 | + | 0.956812i | \(0.406110\pi\) | |||||||
\(212\) | 425.785 | − | 245.827i | 0.137939 | − | 0.0796390i | ||||
\(213\) | 573.132 | + | 330.898i | 0.184368 | + | 0.106445i | ||||
\(214\) | 195.501 | − | 338.618i | 0.0624495 | − | 0.108166i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8464.06 | −2.66623 | ||||||||
\(217\) | −996.006 | − | 935.625i | −0.311582 | − | 0.292693i | ||||
\(218\) | − | 431.561i | − | 0.134078i | ||||||
\(219\) | 1004.40 | + | 1739.67i | 0.309914 | + | 0.536787i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −865.091 | + | 1498.38i | −0.263314 | + | 0.456073i | ||||
\(222\) | −6789.85 | + | 3920.12i | −2.05272 | + | 1.18514i | ||||
\(223\) | − | 5258.44i | − | 1.57906i | −0.613709 | − | 0.789532i | \(-0.710323\pi\) | ||
0.613709 | − | 0.789532i | \(-0.289677\pi\) | |||||||
\(224\) | −3874.23 | + | 4124.26i | −1.15562 | + | 1.23020i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1859.26 | − | 3220.33i | −0.547239 | − | 0.947846i | ||||
\(227\) | 5809.18 | + | 3353.93i | 1.69854 | + | 0.980652i | 0.947149 | + | 0.320795i | \(0.103950\pi\) |
0.751391 | + | 0.659857i | \(0.229383\pi\) | |||||||
\(228\) | 4246.80 | + | 2451.89i | 1.23356 | + | 0.712195i | ||||
\(229\) | 600.126 | + | 1039.45i | 0.173177 | + | 0.299951i | 0.939529 | − | 0.342470i | \(-0.111264\pi\) |
−0.766352 | + | 0.642421i | \(0.777930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1487.76 | + | 4930.69i | 0.423756 | + | 1.40440i | ||||
\(232\) | 2861.32i | 0.809719i | ||||||||
\(233\) | −5500.49 | + | 3175.71i | −1.54656 | + | 0.892909i | −0.548163 | + | 0.836372i | \(0.684673\pi\) |
−0.998400 | + | 0.0565373i | \(0.981994\pi\) | |||||||
\(234\) | 330.637 | − | 572.680i | 0.0923692 | − | 0.159988i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3592.34 | − | 6222.11i | −0.990853 | − | 1.71621i | ||||
\(237\) | − | 4547.59i | − | 1.24640i | ||||||
\(238\) | 877.343 | − | 3737.76i | 0.238948 | − | 1.01800i | ||||
\(239\) | 3003.73 | 0.812951 | 0.406475 | − | 0.913662i | \(-0.366758\pi\) | ||||
0.406475 | + | 0.913662i | \(0.366758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2846.16 | + | 4929.70i | −0.760736 | + | 1.31763i | 0.181736 | + | 0.983347i | \(0.441828\pi\) |
−0.942472 | + | 0.334286i | \(0.891505\pi\) | |||||||
\(242\) | −8478.03 | − | 4894.79i | −2.25202 | − | 1.30020i | ||||
\(243\) | −707.789 | + | 408.642i | −0.186850 | + | 0.107878i | ||||
\(244\) | −12068.1 | −3.16631 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7456.89 | 1.93266 | ||||||||
\(247\) | −1970.38 | + | 1137.60i | −0.507579 | + | 0.293051i | ||||
\(248\) | −3683.50 | − | 2126.67i | −0.943155 | − | 0.544531i | ||||
\(249\) | 727.077 | − | 1259.33i | 0.185047 | − | 0.320510i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6973.37 | 1.75361 | 0.876803 | − | 0.480850i | \(-0.159672\pi\) | ||||
0.876803 | + | 0.480850i | \(0.159672\pi\) | |||||||
\(252\) | −236.251 | + | 1006.50i | −0.0590571 | + | 0.251602i | ||||
\(253\) | 3033.12i | 0.753719i | ||||||||
\(254\) | 4895.72 | + | 8479.64i | 1.20939 | + | 2.09472i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2437.31 | − | 4221.54i | 0.595045 | − | 1.03065i | ||||
\(257\) | 2677.59 | − | 1545.90i | 0.649896 | − | 0.375217i | −0.138521 | − | 0.990360i | \(-0.544235\pi\) |
0.788416 | + | 0.615142i | \(0.210901\pi\) | |||||||
\(258\) | 9343.48i | 2.25465i | ||||||||
\(259\) | 1642.87 | + | 5444.73i | 0.394143 | + | 1.30625i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 72.6221 | + | 125.785i | 0.0172230 | + | 0.0298311i | ||||
\(262\) | −828.779 | − | 478.496i | −0.195428 | − | 0.112830i | ||||
\(263\) | 1718.91 | + | 992.413i | 0.403013 | + | 0.232680i | 0.687783 | − | 0.725916i | \(-0.258584\pi\) |
−0.284770 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(264\) | 8015.06 | + | 13882.5i | 1.86853 | + | 3.23640i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3456.73 | − | 3679.81i | 0.796788 | − | 0.848210i | ||||
\(267\) | 2398.21i | 0.549694i | ||||||||
\(268\) | −8444.25 | + | 4875.29i | −1.92468 | + | 1.11121i | ||||
\(269\) | 3090.37 | − | 5352.68i | 0.700458 | − | 1.21323i | −0.267848 | − | 0.963461i | \(-0.586313\pi\) |
0.968306 | − | 0.249767i | \(-0.0803540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3059.49 | + | 5299.20i | 0.685797 | + | 1.18784i | 0.973186 | + | 0.230022i | \(0.0738797\pi\) |
−0.287388 | + | 0.957814i | \(0.592787\pi\) | |||||||
\(272\) | − | 5869.71i | − | 1.30847i | ||||||
\(273\) | 2876.39 | + | 2702.01i | 0.637682 | + | 0.599023i | ||||
\(274\) | −4619.50 | −1.01852 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2504.67 | − | 4338.22i | 0.546245 | − | 0.946125i | ||||
\(277\) | −2853.41 | − | 1647.42i | −0.618935 | − | 0.357342i | 0.157519 | − | 0.987516i | \(-0.449650\pi\) |
−0.776454 | + | 0.630174i | \(0.782984\pi\) | |||||||
\(278\) | 10523.7 | − | 6075.89i | 2.27040 | − | 1.31082i | ||||
\(279\) | −215.905 | −0.0463294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4604.53 | −0.977521 | −0.488760 | − | 0.872418i | \(-0.662551\pi\) | ||||
−0.488760 | + | 0.872418i | \(0.662551\pi\) | |||||||
\(282\) | −9783.09 | + | 5648.27i | −2.06587 | + | 1.19273i | ||||
\(283\) | −1056.16 | − | 609.776i | −0.221846 | − | 0.128083i | 0.384959 | − | 0.922934i | \(-0.374216\pi\) |
−0.606805 | + | 0.794851i | \(0.707549\pi\) | |||||||
\(284\) | 1286.61 | − | 2228.47i | 0.268825 | − | 0.465618i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12808.6 | −2.64821 | ||||||||
\(287\) | 1236.05 | − | 5265.99i | 0.254223 | − | 1.08307i | ||||
\(288\) | 894.019i | 0.182919i | ||||||||
\(289\) | −1662.94 | − | 2880.30i | −0.338478 | − | 0.586260i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1167.52 | − | 2022.21i | 0.235194 | − | 0.407368i | ||||
\(292\) | 6764.27 | − | 3905.35i | 1.35565 | − | 0.782683i | ||||
\(293\) | 8434.81i | 1.68180i | 0.541192 | + | 0.840899i | \(0.317973\pi\) | ||||
−0.541192 | + | 0.840899i | \(0.682027\pi\) | |||||||
\(294\) | −7842.77 | − | 3896.45i | −1.55578 | − | 0.772944i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8850.66 | + | 15329.8i | 1.73795 | + | 3.01022i | ||||
\(297\) | 7207.13 | + | 4161.04i | 1.40808 | + | 0.812956i | ||||
\(298\) | −10829.4 | − | 6252.35i | −2.10513 | − | 1.21540i | ||||
\(299\) | 1162.09 | + | 2012.79i | 0.224767 | + | 0.389307i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6598.28 | + | 1548.77i | 1.26352 | + | 0.296577i | ||||
\(302\) | 6423.23i | 1.22389i | ||||||||
\(303\) | −329.654 | + | 190.326i | −0.0625021 | + | 0.0360856i | ||||
\(304\) | 3859.35 | − | 6684.58i | 0.728121 | − | 1.26114i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −303.298 | − | 525.327i | −0.0566613 | − | 0.0981403i | ||||
\(307\) | 846.546i | 0.157378i | 0.996899 | + | 0.0786888i | \(0.0250734\pi\) | ||||
−0.996899 | + | 0.0786888i | \(0.974927\pi\) | |||||||
\(308\) | 19171.7 | − | 5784.78i | 3.54678 | − | 1.07019i | ||||
\(309\) | −5582.50 | −1.02776 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −980.793 | + | 1698.78i | −0.178829 | + | 0.309740i | −0.941480 | − | 0.337070i | \(-0.890564\pi\) |
0.762651 | + | 0.646810i | \(0.223897\pi\) | |||||||
\(312\) | 10637.7 | + | 6141.66i | 1.93025 | + | 1.11443i | ||||
\(313\) | −5655.11 | + | 3264.98i | −1.02123 | + | 0.589609i | −0.914461 | − | 0.404674i | \(-0.867385\pi\) |
−0.106772 | + | 0.994284i | \(0.534052\pi\) | |||||||
\(314\) | −7454.13 | −1.33968 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17682.1 | −3.14778 | ||||||||
\(317\) | −6660.19 | + | 3845.26i | −1.18004 | + | 0.681298i | −0.956025 | − | 0.293287i | \(-0.905251\pi\) |
−0.224019 | + | 0.974585i | \(0.571918\pi\) | |||||||
\(318\) | 569.828 | + | 328.990i | 0.100485 | + | 0.0580153i | ||||
\(319\) | 1406.66 | − | 2436.40i | 0.246890 | − | 0.427625i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 368.678 | 0.0641047 | ||||||||
\(322\) | −3759.03 | − | 3531.14i | −0.650567 | − | 0.611127i | ||||
\(323\) | 2087.07i | 0.359528i | ||||||||
\(324\) | −6118.54 | − | 10597.6i | −1.04913 | − | 1.81715i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2239.72 | − | 3879.30i | 0.380511 | − | 0.659064i | ||||
\(327\) | 352.403 | − | 203.460i | 0.0595962 | − | 0.0344079i | ||||
\(328\) | − | 16835.8i | − | 2.83415i | ||||||
\(329\) | 2367.11 | + | 7844.98i | 0.396666 | + | 1.31461i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3263.13 | − | 5651.92i | −0.541867 | − | 0.938542i | −0.998797 | − | 0.0490389i | \(-0.984384\pi\) |
0.456929 | − | 0.889503i | \(-0.348949\pi\) | |||||||
\(332\) | −4896.59 | − | 2827.05i | −0.809444 | − | 0.467332i | ||||
\(333\) | 778.161 | + | 449.271i | 0.128057 | + | 0.0739337i | ||||
\(334\) | −3504.04 | − | 6069.18i | −0.574050 | − | 0.994283i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13034.3 | − | 3059.45i | −2.11630 | − | 0.496746i | ||||
\(337\) | 1217.56i | 0.196809i | 0.995146 | + | 0.0984047i | \(0.0313740\pi\) | ||||
−0.995146 | + | 0.0984047i | \(0.968626\pi\) | |||||||
\(338\) | 1400.89 | − | 808.802i | 0.225438 | − | 0.130157i | ||||
\(339\) | 1753.10 | − | 3036.46i | 0.280872 | − | 0.486484i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2090.99 | + | 3621.70i | 0.332063 | + | 0.575150i | ||||
\(342\) | − | 797.675i | − | 0.126121i | ||||||
\(343\) | −4051.65 | + | 4892.62i | −0.637809 | + | 0.770194i | ||||
\(344\) | 21095.3 | 3.30634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6792.01 | − | 11764.1i | 1.05532 | − | 1.82787i | ||||
\(347\) | 7299.98 | + | 4214.64i | 1.12935 | + | 0.652029i | 0.943771 | − | 0.330601i | \(-0.107251\pi\) |
0.185576 | + | 0.982630i | \(0.440585\pi\) | |||||||
\(348\) | −4023.84 | + | 2323.16i | −0.619829 | + | 0.357858i | ||||
\(349\) | 135.644 | 0.0208047 | 0.0104023 | − | 0.999946i | \(-0.496689\pi\) | ||||
0.0104023 | + | 0.999946i | \(0.496689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6376.91 | 0.969727 | ||||||||
\(352\) | 14996.7 | − | 8658.38i | 2.27082 | − | 1.31106i | ||||
\(353\) | 2012.77 | + | 1162.07i | 0.303481 | + | 0.175215i | 0.644005 | − | 0.765021i | \(-0.277271\pi\) |
−0.340525 | + | 0.940236i | \(0.610605\pi\) | |||||||
\(354\) | 4807.62 | − | 8327.04i | 0.721814 | − | 1.25022i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9324.82 | 1.38824 | ||||||||
\(357\) | 3465.80 | − | 1045.76i | 0.513809 | − | 0.155035i | ||||
\(358\) | − | 7027.22i | − | 1.03743i | ||||||
\(359\) | −2663.65 | − | 4613.58i | −0.391594 | − | 0.678260i | 0.601066 | − | 0.799199i | \(-0.294743\pi\) |
−0.992660 | + | 0.120939i | \(0.961409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2057.25 | − | 3563.26i | 0.299934 | − | 0.519501i | ||||
\(362\) | 12828.1 | − | 7406.33i | 1.86252 | − | 1.07533i | ||||
\(363\) | − | 9230.64i | − | 1.33466i | ||||||
\(364\) | 10506.1 | − | 11184.1i | 1.51282 | − | 1.61046i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8075.34 | − | 13986.9i | −1.15329 | − | 1.99756i | ||||
\(367\) | 6314.73 | + | 3645.81i | 0.898164 | + | 0.518555i | 0.876604 | − | 0.481212i | \(-0.159803\pi\) |
0.0215599 | + | 0.999768i | \(0.493137\pi\) | |||||||
\(368\) | −6828.49 | − | 3942.43i | −0.967282 | − | 0.558460i | ||||
\(369\) | −427.304 | − | 740.112i | −0.0602834 | − | 0.104414i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 326.784 | − | 347.874i | 0.0457299 | − | 0.0486811i | ||||
\(372\) | − | 6906.75i | − | 0.962629i | ||||||
\(373\) | 1438.90 | − | 830.751i | 0.199742 | − | 0.115321i | −0.396793 | − | 0.917908i | \(-0.629877\pi\) |
0.596535 | + | 0.802587i | \(0.296544\pi\) | |||||||
\(374\) | −5874.74 | + | 10175.4i | −0.812235 | + | 1.40683i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12752.4 | + | 22087.8i | 1.74908 | + | 3.02950i | ||||
\(377\) | − | 2155.75i | − | 0.294500i | ||||||
\(378\) | −13547.4 | + | 4087.73i | −1.84339 | + | 0.556217i | ||||
\(379\) | −409.820 | −0.0555436 | −0.0277718 | − | 0.999614i | \(-0.508841\pi\) | ||||
−0.0277718 | + | 0.999614i | \(0.508841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4616.19 | + | 7995.48i | −0.620721 | + | 1.07512i | ||||
\(382\) | −18942.9 | − | 10936.7i | −2.53718 | − | 1.46484i | ||||
\(383\) | 9475.33 | − | 5470.58i | 1.26414 | − | 0.729853i | 0.290269 | − | 0.956945i | \(-0.406255\pi\) |
0.973873 | + | 0.227092i | \(0.0729217\pi\) | |||||||
\(384\) | 1494.64 | 0.198628 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 721.142 | 0.0950911 | ||||||||
\(387\) | 927.360 | − | 535.411i | 0.121810 | − | 0.0703269i | ||||
\(388\) | −7862.83 | − | 4539.60i | −1.02880 | − | 0.593978i | ||||
\(389\) | −3118.40 | + | 5401.23i | −0.406450 | + | 0.703992i | −0.994489 | − | 0.104840i | \(-0.966567\pi\) |
0.588039 | + | 0.808833i | \(0.299900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2132.00 | 0.275754 | ||||||||
\(392\) | −8797.21 | + | 17707.0i | −1.13349 | + | 2.28148i | ||||
\(393\) | − | 902.351i | − | 0.115821i | ||||||
\(394\) | 3834.43 | + | 6641.43i | 0.490294 | + | 0.849215i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1581.95 | − | 2740.02i | 0.200747 | − | 0.347705i | ||||
\(397\) | −9914.10 | + | 5723.91i | −1.25334 | + | 0.723614i | −0.971771 | − | 0.235928i | \(-0.924187\pi\) |
−0.281565 | + | 0.959542i | \(0.590854\pi\) | |||||||
\(398\) | 18783.0i | 2.36559i | ||||||||
\(399\) | 4634.54 | + | 1087.84i | 0.581496 | + | 0.136491i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4616.74 | + | 7996.42i | 0.574935 | + | 0.995816i | 0.996049 | + | 0.0888085i | \(0.0283059\pi\) |
−0.421114 | + | 0.907008i | \(0.638361\pi\) | |||||||
\(402\) | −11300.9 | − | 6524.59i | −1.40209 | − | 0.809495i | ||||
\(403\) | 2775.18 | + | 1602.25i | 0.343032 | + | 0.198049i | ||||
\(404\) | 740.032 | + | 1281.77i | 0.0911336 | + | 0.157848i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1381.88 | + | 4579.76i | 0.168920 | + | 0.559826i | ||||
\(407\) | − | 17404.4i | − | 2.11966i | ||||||
\(408\) | 9758.08 | − | 5633.83i | 1.18406 | − | 0.683618i | ||||
\(409\) | −2217.57 | + | 3840.95i | −0.268097 | + | 0.464358i | −0.968370 | − | 0.249517i | \(-0.919728\pi\) |
0.700273 | + | 0.713875i | \(0.253062\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2177.87 | − | 3772.19i | −0.261379 | − | 0.452721i | ||||
\(412\) | 21706.1i | 2.59559i | ||||||||
\(413\) | −5083.57 | − | 4775.39i | −0.605681 | − | 0.568962i | ||||
\(414\) | −814.847 | −0.0967332 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6634.61 | − | 11491.5i | 0.781943 | − | 1.35437i | ||||
\(417\) | 9922.88 | + | 5728.98i | 1.16529 | + | 0.672780i | ||||
\(418\) | −13380.6 | + | 7725.31i | −1.56571 | + | 0.903965i | ||||
\(419\) | 6434.23 | 0.750197 | 0.375099 | − | 0.926985i | \(-0.377609\pi\) | ||||
0.375099 | + | 0.926985i | \(0.377609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9442.51 | −1.09311 | −0.546556 | − | 0.837423i | \(-0.684061\pi\) | ||||
−0.546556 | + | 0.837423i | \(0.684061\pi\) | |||||||
\(422\) | 8030.53 | − | 4636.43i | 0.926351 | − | 0.534829i | ||||
\(423\) | 1121.21 | + | 647.328i | 0.128877 | + | 0.0744070i | ||||
\(424\) | 742.778 | − | 1286.53i | 0.0850767 | − | 0.147357i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3443.74 | 0.391666 | ||||||||
\(427\) | −11216.0 | + | 3384.27i | −1.27115 | + | 0.383551i | ||||
\(428\) | − | 1433.51i | − | 0.161895i | ||||||
\(429\) | −6038.63 | − | 10459.2i | −0.679598 | − | 1.17710i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1120.60 | − | 1940.94i | 0.125238 | − | 0.216918i | −0.796588 | − | 0.604522i | \(-0.793364\pi\) |
0.921826 | + | 0.387604i | \(0.126697\pi\) | |||||||
\(432\) | −18735.5 | + | 10817.0i | −2.08661 | + | 1.20470i | ||||
\(433\) | 14181.1i | 1.57391i | 0.617012 | + | 0.786954i | \(0.288343\pi\) | ||||
−0.617012 | + | 0.786954i | \(0.711657\pi\) | |||||||
\(434\) | −6922.79 | − | 1624.94i | −0.765679 | − | 0.179723i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −791.101 | − | 1370.23i | −0.0868965 | − | 0.150509i | ||||
\(437\) | 2427.98 | + | 1401.79i | 0.265780 | + | 0.153448i | ||||
\(438\) | 9052.61 | + | 5226.53i | 0.987558 | + | 0.570167i | ||||
\(439\) | 4346.32 | + | 7528.05i | 0.472525 | + | 0.818438i | 0.999506 | − | 0.0314396i | \(-0.0100092\pi\) |
−0.526980 | + | 0.849878i | \(0.676676\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62.6856 | + | 1001.69i | 0.00676877 | + | 0.108162i | ||||
\(442\) | 9003.22i | 0.968867i | ||||||||
\(443\) | 8135.18 | − | 4696.85i | 0.872492 | − | 0.503734i | 0.00431671 | − | 0.999991i | \(-0.498626\pi\) |
0.868176 | + | 0.496257i | \(0.165293\pi\) | |||||||
\(444\) | −14372.1 | + | 24893.2i | −1.53619 | + | 2.66076i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13681.5 | − | 23697.0i | −1.45255 | − | 2.51589i | ||||
\(447\) | − | 11790.7i | − | 1.24761i | ||||||
\(448\) | −1740.18 | + | 7413.72i | −0.183517 | + | 0.781842i | ||||
\(449\) | −9511.86 | −0.999761 | −0.499880 | − | 0.866094i | \(-0.666623\pi\) | ||||
−0.499880 | + | 0.866094i | \(0.666623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8276.69 | + | 14335.7i | −0.864156 | + | 1.49676i | ||||
\(452\) | −11806.5 | − | 6816.48i | −1.22861 | − | 0.709337i | ||||
\(453\) | −5245.08 | + | 3028.25i | −0.544007 | + | 0.314083i | ||||
\(454\) | 34905.2 | 3.60833 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14817.0 | 1.52165 | ||||||||
\(457\) | −1184.04 | + | 683.607i | −0.121197 | + | 0.0699732i | −0.559373 | − | 0.828916i | \(-0.688958\pi\) |
0.438176 | + | 0.898889i | \(0.355625\pi\) | |||||||
\(458\) | 5408.90 | + | 3122.83i | 0.551837 | + | 0.318603i | ||||
\(459\) | 2924.81 | − | 5065.93i | 0.297426 | − | 0.515157i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8760.60 | 0.885080 | 0.442540 | − | 0.896749i | \(-0.354078\pi\) | ||||
0.442540 | + | 0.896749i | \(0.354078\pi\) | |||||||
\(462\) | 19533.3 | + | 18349.1i | 1.96704 | + | 1.84779i | ||||
\(463\) | − | 10357.4i | − | 1.03963i | −0.854278 | − | 0.519817i | \(-0.826000\pi\) | ||
0.854278 | − | 0.519817i | \(-0.174000\pi\) | |||||||
\(464\) | 3656.73 | + | 6333.64i | 0.365861 | + | 0.633689i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16525.2 | + | 28622.5i | −1.64274 | + | 2.84530i | ||||
\(467\) | −7360.99 | + | 4249.87i | −0.729392 | + | 0.421115i | −0.818200 | − | 0.574934i | \(-0.805028\pi\) |
0.0888078 | + | 0.996049i | \(0.471694\pi\) | |||||||
\(468\) | − | 2424.38i | − | 0.239460i | ||||||
\(469\) | −6480.85 | + | 6899.09i | −0.638076 | + | 0.679255i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3514.26 | − | 6086.88i | −0.343798 | − | 0.595475i | ||||
\(472\) | −18800.4 | − | 10854.4i | −1.83339 | − | 1.05851i | ||||
\(473\) | −17962.6 | − | 10370.7i | −1.74613 | − | 1.00813i | ||||
\(474\) | −11832.0 | − | 20493.6i | −1.14654 | − | 1.98587i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4066.15 | − | 13475.9i | −0.391537 | − | 1.29762i | ||||
\(477\) | − | 75.4088i | − | 0.00723843i | ||||||
\(478\) | 13536.2 | − | 7815.15i | 1.29526 | − | 0.747817i | ||||
\(479\) | −361.486 | + | 626.113i | −0.0344817 | + | 0.0597240i | −0.882751 | − | 0.469841i | \(-0.844311\pi\) |
0.848270 | + | 0.529565i | \(0.177645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6668.18 | − | 11549.6i | −0.632106 | − | 1.09484i | ||||
\(482\) | 29620.7i | 2.79914i | ||||||||
\(483\) | 1111.26 | − | 4734.31i | 0.104687 | − | 0.446001i | ||||
\(484\) | −35890.9 | −3.37067 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2126.42 | + | 3683.07i | −0.198470 | + | 0.343760i | ||||
\(487\) | −1998.19 | − | 1153.66i | −0.185927 | − | 0.107345i | 0.404147 | − | 0.914694i | \(-0.367568\pi\) |
−0.590075 | + | 0.807349i | \(0.700902\pi\) | |||||||
\(488\) | −31579.0 | + | 18232.1i | −2.92933 | + | 1.69125i | ||||
\(489\) | 4223.67 | 0.390595 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8668.77 | −0.796774 | −0.398387 | − | 0.917217i | \(-0.630430\pi\) | ||||
−0.398387 | + | 0.917217i | \(0.630430\pi\) | |||||||
\(492\) | 23676.0 | − | 13669.4i | 2.16951 | − | 1.25257i | ||||
\(493\) | −1712.56 | − | 988.748i | −0.156450 | − | 0.0903265i | ||||
\(494\) | −5919.63 | + | 10253.1i | −0.539143 | + | 0.933823i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10871.4 | −0.984155 | ||||||||
\(497\) | 570.833 | − | 2431.93i | 0.0515198 | − | 0.219491i | ||||
\(498\) | − | 7566.87i | − | 0.680883i | ||||||
\(499\) | 9960.86 | + | 17252.7i | 0.893606 | + | 1.54777i | 0.835520 | + | 0.549460i | \(0.185166\pi\) |
0.0580860 | + | 0.998312i | \(0.481500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3303.97 | − | 5722.65i | 0.294632 | − | 0.510318i | ||||
\(502\) | 31425.3 | − | 18143.4i | 2.79398 | − | 1.61311i | ||||
\(503\) | − | 17007.8i | − | 1.50763i | −0.657084 | − | 0.753817i | \(-0.728210\pi\) | ||
0.657084 | − | 0.753817i | \(-0.271790\pi\) | |||||||
\(504\) | 902.395 | + | 2990.68i | 0.0797537 | + | 0.264316i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7891.62 | + | 13668.7i | 0.693330 | + | 1.20088i | ||||
\(507\) | 1320.90 | + | 762.622i | 0.115707 | + | 0.0668032i | ||||
\(508\) | 31088.3 | + | 17948.9i | 2.71520 | + | 1.56762i | ||||
\(509\) | −9232.52 | − | 15991.2i | −0.803977 | − | 1.39253i | −0.916980 | − | 0.398934i | \(-0.869380\pi\) |
0.113003 | − | 0.993595i | \(-0.463953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5191.48 | − | 5526.52i | 0.449428 | − | 0.478432i | ||||
\(512\) | − | 22928.6i | − | 1.97913i | ||||||
\(513\) | 6661.71 | − | 3846.14i | 0.573337 | − | 0.331016i | ||||
\(514\) | 8044.31 | − | 13933.1i | 0.690310 | − | 1.19565i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17127.7 | + | 29666.0i | 1.46125 | + | 2.53096i | ||||
\(517\) | − | 25076.9i | − | 2.13323i | ||||||
\(518\) | 21569.7 | + | 20262.1i | 1.82957 | + | 1.71866i | ||||
\(519\) | 12808.4 | 1.08329 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2167.92 | − | 3754.95i | 0.182300 | − | 0.315753i | −0.760363 | − | 0.649498i | \(-0.774979\pi\) |
0.942663 | + | 0.333745i | \(0.108312\pi\) | |||||||
\(522\) | 654.539 | + | 377.898i | 0.0548820 | + | 0.0316861i | ||||
\(523\) | 7251.40 | − | 4186.60i | 0.606275 | − | 0.350033i | −0.165231 | − | 0.986255i | \(-0.552837\pi\) |
0.771506 | + | 0.636222i | \(0.219504\pi\) | |||||||
\(524\) | −3508.56 | −0.292504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10328.3 | 0.856150 | ||||||||
\(527\) | 2545.71 | − | 1469.77i | 0.210423 | − | 0.121488i | ||||
\(528\) | 35483.3 | + | 20486.3i | 2.92465 | + | 1.68854i | ||||
\(529\) | −4651.53 | + | 8056.69i | −0.382307 | + | 0.662175i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1101.97 | −0.0900591 | ||||||||
\(532\) | 4229.77 | − | 18020.2i | 0.344706 | − | 1.46856i | ||||
\(533\) | 12684.3i | 1.03080i | ||||||||
\(534\) | 6239.70 | + | 10807.5i | 0.505652 | + | 0.875815i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14730.9 | + | 25514.7i | −1.18709 | + | 2.05610i | ||||
\(537\) | 5738.28 | − | 3313.00i | 0.461126 | − | 0.266231i | ||||
\(538\) | − | 32162.2i | − | 2.57735i | ||||||
\(539\) | 16195.8 | − | 10752.7i | 1.29425 | − | 0.859278i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5937.49 | − | 10284.0i | −0.471853 | − | 0.817274i | 0.527628 | − | 0.849475i | \(-0.323081\pi\) |
−0.999481 | + | 0.0322016i | \(0.989748\pi\) | |||||||
\(542\) | 27575.0 | + | 15920.5i | 2.18533 | + | 1.26170i | ||||
\(543\) | 12095.7 | + | 6983.46i | 0.955942 | + | 0.551913i | ||||
\(544\) | −6086.02 | − | 10541.3i | −0.479661 | − | 0.830798i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19992.5 | + | 4692.72i | 1.56703 | + | 0.367820i | ||||
\(547\) | 25018.5i | 1.95560i | 0.209532 | + | 0.977802i | \(0.432806\pi\) | ||||
−0.209532 | + | 0.977802i | \(0.567194\pi\) | |||||||
\(548\) | −14667.2 | + | 8468.09i | −1.14334 | + | 0.660107i | ||||
\(549\) | −925.486 | + | 1602.99i | −0.0719468 | + | 0.124616i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1300.21 | − | 2252.02i | −0.100528 | − | 0.174119i | ||||
\(552\) | − | 15136.0i | − | 1.16708i | ||||||
\(553\) | −16433.7 | + | 4958.62i | −1.26371 | + | 0.381306i | ||||
\(554\) | −17145.1 | −1.31485 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22275.6 | − | 38582.5i | 1.69909 | − | 2.94292i | ||||
\(557\) | 3422.69 | + | 1976.09i | 0.260366 | + | 0.150323i | 0.624502 | − | 0.781023i | \(-0.285302\pi\) |
−0.364135 | + | 0.931346i | \(0.618635\pi\) | |||||||
\(558\) | −972.969 | + | 561.744i | −0.0738155 | + | 0.0426174i | ||||
\(559\) | −15893.4 | −1.20254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11078.6 | −0.833762 | ||||||||
\(562\) | −20750.2 | + | 11980.1i | −1.55746 | + | 0.899201i | ||||
\(563\) | 276.666 | + | 159.733i | 0.0207106 | + | 0.0119573i | 0.510320 | − | 0.859985i | \(-0.329527\pi\) |
−0.489609 | + | 0.871942i | \(0.662860\pi\) | |||||||
\(564\) | −20707.9 | + | 35867.1i | −1.54603 | + | 2.67780i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6346.09 | −0.471283 | ||||||||
\(567\) | −8658.44 | − | 8133.53i | −0.641305 | − | 0.602427i | ||||
\(568\) | − | 7775.10i | − | 0.574359i | ||||||
\(569\) | −12125.5 | − | 21001.9i | −0.893366 | − | 1.54736i | −0.835813 | − | 0.549014i | \(-0.815004\pi\) |
−0.0575529 | − | 0.998342i | \(-0.518330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1413.73 | − | 2448.66i | 0.103613 | − | 0.179463i | −0.809558 | − | 0.587040i | \(-0.800293\pi\) |
0.913171 | + | 0.407578i | \(0.133626\pi\) | |||||||
\(572\) | −40667.9 | + | 23479.6i | −2.97274 | + | 1.71632i | ||||
\(573\) | − | 20624.5i | − | 1.50367i | ||||||
\(574\) | −8130.88 | − | 26947.0i | −0.591248 | − | 1.95949i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 601.580 | + | 1041.97i | 0.0435171 | + | 0.0753738i | ||||
\(577\) | −15813.8 | − | 9130.11i | −1.14097 | − | 0.658738i | −0.194297 | − | 0.980943i | \(-0.562243\pi\) |
−0.946670 | + | 0.322205i | \(0.895576\pi\) | |||||||
\(578\) | −14988.0 | − | 8653.31i | −1.07858 | − | 0.622717i | ||||
\(579\) | 339.984 | + | 588.869i | 0.0244028 | + | 0.0422669i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5343.65 | − | 1254.28i | −0.381570 | − | 0.0895636i | ||||
\(582\) | − | 12150.7i | − | 0.865400i | ||||||
\(583\) | −1264.95 | + | 730.318i | −0.0898607 | + | 0.0518811i | ||||
\(584\) | 11800.2 | − | 20438.6i | 0.836123 | − | 1.44821i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21945.8 | + | 38011.2i | 1.54705 | + | 2.67957i | ||||
\(587\) | 7749.13i | 0.544873i | 0.962174 | + | 0.272437i | \(0.0878295\pi\) | ||||
−0.962174 | + | 0.272437i | \(0.912170\pi\) | |||||||
\(588\) | −32043.8 | + | 2005.30i | −2.24739 | + | 0.140641i | ||||
\(589\) | 3865.50 | 0.270416 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3615.50 | + | 6262.23i | −0.251644 | + | 0.435861i | ||||
\(592\) | 39182.6 | + | 22622.1i | 2.72026 | + | 1.57054i | ||||
\(593\) | 549.634 | − | 317.332i | 0.0380620 | − | 0.0219751i | −0.480848 | − | 0.876804i | \(-0.659671\pi\) |
0.518910 | + | 0.854829i | \(0.326338\pi\) | |||||||
\(594\) | 43304.9 | 2.99128 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −45845.1 | −3.15082 | ||||||||
\(597\) | −15337.8 | + | 8855.28i | −1.05148 | + | 0.607073i | ||||
\(598\) | 10473.8 | + | 6047.07i | 0.716232 | + | 0.413517i | ||||
\(599\) | 4318.74 | − | 7480.27i | 0.294589 | − | 0.510243i | −0.680300 | − | 0.732934i | \(-0.738151\pi\) |
0.974889 | + | 0.222690i | \(0.0714839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19947.7 | −1.35388 | −0.676941 | − | 0.736037i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736037i | \(0.736695\pi\) | |||||||
\(602\) | 33764.6 | − | 10188.0i | 2.28595 | − | 0.689752i | ||||
\(603\) | 1495.52i | 0.100999i | ||||||||
\(604\) | 11774.5 | + | 20394.1i | 0.793210 | + | 1.37388i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −990.385 | + | 1715.40i | −0.0663888 | + | 0.114989i | ||||
\(607\) | 1071.42 | − | 618.585i | 0.0716435 | − | 0.0413634i | −0.463750 | − | 0.885966i | \(-0.653497\pi\) |
0.535394 | + | 0.844603i | \(0.320163\pi\) | |||||||
\(608\) | − | 16006.3i | − | 1.06766i | ||||||
\(609\) | −3088.24 | + | 3287.55i | −0.205488 | + | 0.218749i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9607.78 | − | 16641.2i | −0.636152 | − | 1.10185i | ||||
\(612\) | −1925.97 | − | 1111.96i | −0.127210 | − | 0.0734450i | ||||
\(613\) | 15179.4 | + | 8763.81i | 1.00014 | + | 0.577434i | 0.908291 | − | 0.418339i | \(-0.137388\pi\) |
0.0918535 | + | 0.995773i | \(0.470721\pi\) | |||||||
\(614\) | 2202.55 | + | 3814.94i | 0.144768 | + | 0.250746i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 41427.7 | − | 44101.3i | 2.70969 | − | 2.88457i | ||||
\(617\) | 18508.3i | 1.20764i | 0.797120 | + | 0.603821i | \(0.206356\pi\) | ||||
−0.797120 | + | 0.603821i | \(0.793644\pi\) | |||||||
\(618\) | −25157.4 | + | 14524.6i | −1.63750 | + | 0.945414i | ||||
\(619\) | −3014.92 | + | 5221.99i | −0.195767 | + | 0.339079i | −0.947152 | − | 0.320786i | \(-0.896053\pi\) |
0.751385 | + | 0.659865i | \(0.229386\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3928.94 | − | 6805.12i | −0.253886 | − | 0.439743i | ||||
\(622\) | 10207.4i | 0.658003i | ||||||||
\(623\) | 8666.43 | − | 2614.97i | 0.557325 | − | 0.168165i | ||||
\(624\) | 31395.8 | 2.01417 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16989.7 | + | 29427.1i | −1.08474 | + | 1.87882i | ||||
\(627\) | −12616.6 | − | 7284.22i | −0.803605 | − | 0.463962i | ||||
\(628\) | −23667.2 | + | 13664.3i | −1.50386 | + | 0.868256i | ||||
\(629\) | −12233.6 | −0.775495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5728.80 | 0.361426 | 0.180713 | − | 0.983536i | \(-0.442160\pi\) | ||||
0.180713 | + | 0.983536i | \(0.442160\pi\) | |||||||
\(632\) | −46269.5 | + | 26713.7i | −2.91218 | + | 1.68135i | ||||
\(633\) | 7572.02 | + | 4371.71i | 0.475451 | + | 0.274502i | ||||
\(634\) | −20009.3 | + | 34657.1i | −1.25342 | + | 2.17099i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2412.31 | 0.150400 | ||||||||
\(637\) | 6627.91 | − | 13340.7i | 0.412256 | − | 0.829790i | ||||
\(638\) | − | 14639.4i | − | 0.908434i | ||||||
\(639\) | −197.337 | − | 341.798i | −0.0122168 | − | 0.0211601i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 937.912 | − | 1624.51i | 0.0577930 | − | 0.100100i | −0.835681 | − | 0.549214i | \(-0.814927\pi\) |
0.893474 | + | 0.449114i | \(0.148260\pi\) | |||||||
\(642\) | 1661.44 | − | 959.231i | 0.102137 | − | 0.0589686i | ||||
\(643\) | 20619.9i | 1.26465i | 0.774703 | + | 0.632325i | \(0.217899\pi\) | ||||
−0.774703 | + | 0.632325i | \(0.782101\pi\) | |||||||
\(644\) | −18408.1 | − | 4320.82i | −1.12637 | − | 0.264386i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5430.16 | + | 9405.31i | 0.330723 | + | 0.572828i | ||||
\(647\) | 9982.80 | + | 5763.57i | 0.606591 | + | 0.350216i | 0.771630 | − | 0.636072i | \(-0.219442\pi\) |
−0.165039 | + | 0.986287i | \(0.552775\pi\) | |||||||
\(648\) | −32021.2 | − | 18487.5i | −1.94122 | − | 1.12077i | ||||
\(649\) | 10672.3 | + | 18485.0i | 0.645494 | + | 1.11803i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1936.87 | − | 6419.09i | −0.116608 | − | 0.386458i | ||||
\(652\) | − | 16422.6i | − | 0.986443i | ||||||
\(653\) | 3911.15 | − | 2258.11i | 0.234388 | − | 0.135324i | −0.378207 | − | 0.925721i | \(-0.623459\pi\) |
0.612595 | + | 0.790397i | \(0.290126\pi\) | |||||||
\(654\) | 1058.73 | − | 1833.77i | 0.0633022 | − | 0.109643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21516.0 | − | 37266.7i | −1.28057 | − | 2.21802i | ||||
\(657\) | − | 1197.99i | − | 0.0711384i | ||||||
\(658\) | 31078.5 | + | 29194.4i | 1.84129 | + | 1.72966i | ||||
\(659\) | 27663.5 | 1.63523 | 0.817615 | − | 0.575766i | \(-0.195296\pi\) | ||||
0.817615 | + | 0.575766i | \(0.195296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15755.4 | − | 27289.2i | 0.927103 | − | 1.60579i | 0.138959 | − | 0.990298i | \(-0.455624\pi\) |
0.788144 | − | 0.615491i | \(-0.211042\pi\) | |||||||
\(662\) | −29410.4 | − | 16980.1i | −1.72669 | − | 0.996905i | ||||
\(663\) | −7351.83 | + | 4244.58i | −0.430651 | + | 0.248636i | ||||
\(664\) | −17084.1 | −0.998482 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4675.68 | 0.272040 | ||||||||
\(667\) | −2300.51 | + | 1328.20i | −0.133547 | + | 0.0771035i | ||||
\(668\) | −22251.0 | − | 12846.6i | −1.28880 | − | 0.744089i | ||||
\(669\) | 12900.3 | − | 22344.0i | 0.745523 | − | 1.29128i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35852.5 | 2.06270 | ||||||||
\(672\) | −26580.1 | + | 8020.18i | −1.52582 | + | 0.460395i | ||||
\(673\) | 9072.58i | 0.519647i | 0.965656 | + | 0.259823i | \(0.0836643\pi\) | ||||
−0.965656 | + | 0.259823i | \(0.916336\pi\) | |||||||
\(674\) | 3167.86 | + | 5486.90i | 0.181041 | + | 0.313572i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2965.26 | − | 5135.97i | 0.168710 | − | 0.292215i | ||||
\(677\) | −21648.6 | + | 12498.9i | −1.22899 | + | 0.709557i | −0.966818 | − | 0.255465i | \(-0.917771\pi\) |
−0.262170 | + | 0.965022i | \(0.584438\pi\) | |||||||
\(678\) | − | 18245.0i | − | 1.03347i | ||||||
\(679\) | −8580.71 | − | 2014.10i | −0.484974 | − | 0.113835i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16456.1 | + | 28502.8i | 0.925990 | + | 1.60386i | ||||
\(682\) | 18846.0 | + | 10880.7i | 1.05814 | + | 0.610916i | ||||
\(683\) | −11485.0 | − | 6630.90i | −0.643431 | − | 0.371485i | 0.142504 | − | 0.989794i | \(-0.454485\pi\) |
−0.785935 | + | 0.618309i | \(0.787818\pi\) | |||||||
\(684\) | −1462.23 | − | 2532.66i | −0.0817395 | − | 0.141577i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5528.98 | + | 32590.1i | −0.307722 | + | 1.81384i | ||||
\(687\) | 5889.06i | 0.327047i | ||||||||
\(688\) | 46695.2 | − | 26959.5i | 2.58755 | − | 1.49392i | ||||
\(689\) | −559.617 | + | 969.284i | −0.0309430 | + | 0.0535948i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12321.8 | + | 21341.9i | 0.678353 | + | 1.17494i | 0.975477 | + | 0.220103i | \(0.0706395\pi\) |
−0.297123 | + | 0.954839i | \(0.596027\pi\) | |||||||
\(692\) | − | 49802.2i | − | 2.73583i | ||||||
\(693\) | 701.867 | − | 2990.18i | 0.0384729 | − | 0.163907i | ||||
\(694\) | 43862.8 | 2.39915 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7019.55 | + | 12158.2i | −0.382292 | + | 0.662150i | ||||
\(697\) | 10076.6 | + | 5817.73i | 0.547602 | + | 0.316158i | ||||
\(698\) | 611.274 | − | 352.919i | 0.0331476 | − | 0.0191378i | ||||
\(699\) | −31163.4 | −1.68628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20723.2 | 1.11656 | 0.558278 | − | 0.829654i | \(-0.311462\pi\) | ||||
0.558278 | + | 0.829654i | \(0.311462\pi\) | |||||||
\(702\) | 28737.3 | − | 16591.5i | 1.54504 | − | 0.892032i | ||||
\(703\) | −13932.0 | − | 8043.63i | −0.747446 | − | 0.431538i | ||||
\(704\) | 11652.3 | − | 20182.4i | 0.623813 | − | 1.08048i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12094.0 | 0.644705 | ||||||||
\(707\) | 1047.23 | + | 983.744i | 0.0557075 | + | 0.0523303i | ||||
\(708\) | − | 35251.7i | − | 1.87124i | ||||||
\(709\) | 12967.9 | + | 22461.0i | 0.686910 | + | 1.18976i | 0.972833 | + | 0.231510i | \(0.0743665\pi\) |
−0.285923 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1356.02 | + | 2348.70i | −0.0715257 | + | 0.123886i | ||||
\(712\) | 24400.6 | − | 14087.7i | 1.28434 | − | 0.741515i | ||||
\(713\) | − | 3948.72i | − | 0.207406i | ||||||
\(714\) | 12897.7 | − | 13730.0i | 0.676027 | − | 0.719655i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12881.7 | − | 22311.8i | −0.672363 | − | 1.16457i | ||||
\(717\) | 12763.4 | + | 7368.93i | 0.664793 | + | 0.383818i | ||||
\(718\) | −24007.3 | − | 13860.6i | −1.24784 | − | 0.720438i | ||||
\(719\) | −6826.85 | − | 11824.4i | −0.354101 | − | 0.613320i | 0.632863 | − | 0.774264i | \(-0.281880\pi\) |
−0.986964 | + | 0.160943i | \(0.948546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6087.07 | + | 20173.5i | 0.314416 | + | 1.04203i | ||||
\(722\) | − | 21410.3i | − | 1.10361i | ||||||
\(723\) | −24187.6 | + | 13964.7i | −1.24419 | + | 0.718332i | ||||
\(724\) | 27153.3 | − | 47031.0i | 1.39385 | − | 2.41422i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24016.4 | − | 41597.6i | −1.22773 | − | 2.12649i | ||||
\(727\) | 17709.4i | 0.903448i | 0.892158 | + | 0.451724i | \(0.149191\pi\) | ||||
−0.892158 | + | 0.451724i | \(0.850809\pi\) | |||||||
\(728\) | 10595.0 | − | 45138.1i | 0.539391 | − | 2.29798i | ||||
\(729\) | −21328.7 | −1.08361 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7289.61 | + | 12626.0i | −0.368832 | + | 0.638835i | ||||
\(732\) | −51279.3 | − | 29606.1i | −2.58926 | − | 1.49491i | ||||
\(733\) | −10282.7 | + | 5936.73i | −0.518146 | + | 0.299152i | −0.736176 | − | 0.676790i | \(-0.763370\pi\) |
0.218030 | + | 0.975942i | \(0.430037\pi\) | |||||||
\(734\) | 37942.9 | 1.90803 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16350.8 | −0.818886 | ||||||||
\(737\) | 25086.7 | − | 14483.8i | 1.25384 | − | 0.723904i | ||||
\(738\) | −3851.27 | − | 2223.53i | −0.192096 | − | 0.110907i | ||||
\(739\) | 15651.4 | − | 27109.0i | 0.779087 | − | 1.34942i | −0.153382 | − | 0.988167i | \(-0.549017\pi\) |
0.932469 | − | 0.361250i | \(-0.117650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11163.3 | −0.553433 | ||||||||
\(742\) | 567.542 | − | 2417.91i | 0.0280797 | − | 0.119629i | ||||
\(743\) | 10385.8i | 0.512808i | 0.966570 | + | 0.256404i | \(0.0825378\pi\) | ||||
−0.966570 | + | 0.256404i | \(0.917462\pi\) | |||||||
\(744\) | −10434.5 | − | 18073.1i | −0.514178 | − | 0.890583i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4322.92 | − | 7487.51i | 0.212163 | − | 0.367476i | ||||
\(747\) | −751.028 | + | 433.606i | −0.0367854 | + | 0.0212380i | ||||
\(748\) | 43076.4i | 2.10565i | ||||||||
\(749\) | −402.000 | − | 1332.29i | −0.0196112 | − | 0.0649946i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8285.63 | − | 14351.1i | −0.402593 | − | 0.697311i | 0.591445 | − | 0.806345i | \(-0.298558\pi\) |
−0.994038 | + | 0.109034i | \(0.965224\pi\) | |||||||
\(752\) | 56455.8 | + | 32594.8i | 2.73768 | + | 1.58060i | ||||
\(753\) | 29631.0 | + | 17107.5i | 1.43402 | + | 0.827929i | ||||
\(754\) | −5608.84 | − | 9714.80i | −0.270905 | − | 0.469220i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −35520.3 | + | 37812.7i | −1.70881 | + | 1.81909i | ||||
\(757\) | 16463.8i | 0.790473i | 0.918579 | + | 0.395236i | \(0.129337\pi\) | ||||
−0.918579 | + | 0.395236i | \(0.870663\pi\) | |||||||
\(758\) | −1846.84 | + | 1066.27i | −0.0884964 | + | 0.0510934i | ||||
\(759\) | −7441.04 | + | 12888.3i | −0.355853 | + | 0.616356i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8210.95 | − | 14221.8i | −0.391126 | − | 0.677449i | 0.601473 | − | 0.798893i | \(-0.294581\pi\) |
−0.992598 | + | 0.121444i | \(0.961248\pi\) | |||||||
\(762\) | 48041.9i | 2.28395i | ||||||||
\(763\) | −1119.50 | − | 1051.63i | −0.0531174 | − | 0.0498973i | ||||
\(764\) | −80193.0 | −3.79749 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28466.9 | − | 49306.0i | 1.34275 | − | 2.32572i | ||||
\(767\) | 14164.4 | + | 8177.83i | 0.666815 | + | 0.384986i | ||||
\(768\) | 20713.0 | − | 11958.7i | 0.973200 | − | 0.561877i | ||||
\(769\) | −17603.4 | −0.825479 | −0.412739 | − | 0.910849i | \(-0.635428\pi\) | ||||
−0.412739 | + | 0.910849i | \(0.635428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15170.0 | 0.708605 | ||||||||
\(772\) | 2289.66 | − | 1321.94i | 0.106744 | − | 0.0616290i | ||||
\(773\) | 13777.0 | + | 7954.16i | 0.641041 | + | 0.370105i | 0.785015 | − | 0.619476i | \(-0.212655\pi\) |
−0.143975 | + | 0.989581i | \(0.545988\pi\) | |||||||
\(774\) | 2786.08 | − | 4825.63i | 0.129384 | − | 0.224100i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −27433.3 | −1.26907 | ||||||||
\(777\) | −6376.50 | + | 27165.9i | −0.294409 | + | 1.25428i | ||||
\(778\) | 32454.0i | 1.49554i | ||||||||
\(779\) | 7650.34 | + | 13250.8i | 0.351864 | + | 0.609446i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3822.34 | + | 6620.48i | −0.175127 | + | 0.303328i | ||||
\(782\) | 9607.79 | − | 5547.06i | 0.439353 | − | 0.253660i | ||||
\(783\) | 7288.43i | 0.332653i | ||||||||
\(784\) | 3156.39 | + | 50437.9i | 0.143786 | + | 2.29765i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2347.75 | − | 4066.42i | −0.106541 | − | 0.184535i | ||||
\(787\) | −16444.8 | − | 9494.43i | −0.744847 | − | 0.430038i | 0.0789818 | − | 0.996876i | \(-0.474833\pi\) |
−0.823829 | + | 0.566838i | \(0.808166\pi\) | |||||||
\(788\) | 24349.0 | + | 14057.9i | 1.10076 | + | 0.635524i | ||||
\(789\) | 4869.29 | + | 8433.86i | 0.219710 | + | 0.380549i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12884.4 | − | 3024.28i | −0.579163 | − | 0.135943i | ||||
\(792\) | − | 9559.87i | − | 0.428908i | ||||||
\(793\) | 23791.9 | − | 13736.3i | 1.06542 | − | 0.615119i | ||||
\(794\) | −29785.1 | + | 51589.2i | −1.33128 | + | 2.30584i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34431.4 | + | 59637.0i | 1.53315 | + | 2.65550i | ||||
\(797\) | − | 33731.8i | − | 1.49917i | −0.661906 | − | 0.749586i | \(-0.730252\pi\) | ||
0.661906 | − | 0.749586i | \(-0.269748\pi\) | |||||||
\(798\) | 23715.7 | − | 7155.89i | 1.05204 | − | 0.317438i | ||||
\(799\) | −17626.7 | −0.780460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 715.110 | − | 1238.61i | 0.0315445 | − | 0.0546367i | ||||
\(802\) | 41610.4 | + | 24023.8i | 1.83206 | + | 1.05774i | ||||
\(803\) | −20095.7 | + | 11602.2i | −0.883140 | + | 0.509881i | ||||
\(804\) | −47841.4 | −2.09855 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16675.0 | 0.728726 | ||||||||
\(807\) | 26263.0 | − | 15162.9i | 1.14560 | − | 0.661414i | ||||
\(808\) | 3872.94 | + | 2236.04i | 0.168626 | + | 0.0973561i | ||||
\(809\) | 13321.8 | − | 23074.1i | 0.578950 | − | 1.00277i | −0.416650 | − | 0.909067i | \(-0.636796\pi\) |
0.995600 | − | 0.0937039i | \(-0.0298707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15678.2 | 0.678835 | 0.339418 | − | 0.940636i | \(-0.389770\pi\) | ||||
0.339418 | + | 0.940636i | \(0.389770\pi\) | |||||||
\(812\) | 12782.8 | + | 12007.8i | 0.552447 | + | 0.518955i | ||||
\(813\) | 30022.9i | 1.29514i | ||||||||
\(814\) | −45282.9 | − | 78432.3i | −1.94983 | − | 3.37721i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14399.9 | − | 24941.4i | 0.617767 | − | 1.07000i | ||||
\(817\) | −16603.2 | + | 9585.86i | −0.710982 | + | 0.410486i | ||||
\(818\) | 23078.8i | 0.986469i | ||||||||
\(819\) | −679.873 | − | 2253.21i | −0.0290069 | − | 0.0961336i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5066.92 | + | 8776.17i | 0.215392 | + | 0.373070i | 0.953394 | − | 0.301729i | \(-0.0975637\pi\) |
−0.738002 | + | 0.674799i | \(0.764230\pi\) | |||||||
\(822\) | −19629.0 | − | 11332.8i | −0.832897 | − | 0.480873i | ||||
\(823\) | −12178.6 | − | 7031.33i | −0.515820 | − | 0.297809i | 0.219403 | − | 0.975634i | \(-0.429589\pi\) |
−0.735223 | + | 0.677826i | \(0.762922\pi\) | |||||||
\(824\) | 32793.0 | + | 56799.1i | 1.38640 | + | 2.40132i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35333.6 | − | 8293.64i | −1.48839 | − | 0.349362i | ||||
\(827\) | − | 13697.4i | − | 0.575942i | −0.957639 | − | 0.287971i | \(-0.907019\pi\) | ||
0.957639 | − | 0.287971i | \(-0.0929807\pi\) | |||||||
\(828\) | −2587.18 | + | 1493.71i | −0.108588 | + | 0.0626933i | ||||
\(829\) | 8777.47 | − | 15203.0i | 0.367737 | − | 0.636940i | −0.621474 | − | 0.783435i | \(-0.713466\pi\) |
0.989211 | + | 0.146495i | \(0.0467992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8083.09 | − | 14000.3i | −0.337424 | − | 0.584436i | ||||
\(832\) | − | 17857.6i | − | 0.744110i | ||||||
\(833\) | −7558.11 | − | 11384.1i | −0.314373 | − | 0.473513i | ||||
\(834\) | 59622.9 | 2.47551 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28322.8 | + | 49056.5i | −1.17173 | + | 2.02949i | ||||
\(837\) | −9382.71 | − | 5417.11i | −0.387472 | − | 0.223707i | ||||
\(838\) | 28995.7 | − | 16740.7i | 1.19527 | − | 0.690091i | ||||
\(839\) | −1415.03 | −0.0582268 | −0.0291134 | − | 0.999576i | \(-0.509268\pi\) | ||||
−0.0291134 | + | 0.999576i | \(0.509268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21925.1 | −0.898975 | ||||||||
\(842\) | −42552.4 | + | 24567.6i | −1.74163 | + | 1.00553i | ||||
\(843\) | −19565.4 | − | 11296.1i | −0.799370 | − | 0.461517i | ||||
\(844\) | 16998.2 | − | 29441.8i | 0.693250 | − | 1.20074i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6736.90 | 0.273782 | ||||||||
\(847\) | −33356.8 | + | 10064.9i | −1.35319 | + | 0.408306i | ||||
\(848\) | − | 3797.05i | − | 0.153763i | ||||||
\(849\) | −2991.88 | − | 5182.08i | −0.120943 | − | 0.209480i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8216.79 | + | 14231.9i | −0.330985 | + | 0.573282i | ||||
\(852\) | 10934.0 | − | 6312.77i | 0.439664 | − | 0.253840i | ||||
\(853\) | 16014.1i | 0.642804i | 0.946943 | + | 0.321402i | \(0.104154\pi\) | ||||
−0.946943 | + | 0.321402i | \(0.895846\pi\) | |||||||
\(854\) | −41739.3 | + | 44433.0i | −1.67247 | + | 1.78040i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2165.71 | − | 3751.11i | −0.0864746 | − | 0.149778i | ||||
\(857\) | −37669.9 | − | 21748.7i | −1.50149 | − | 0.866886i | −0.999999 | − | 0.00172420i | \(-0.999451\pi\) |
−0.501492 | − | 0.865162i | \(-0.667215\pi\) | |||||||
\(858\) | −54425.8 | − | 31422.8i | −2.16558 | − | 1.25030i | ||||
\(859\) | 12639.3 | + | 21891.9i | 0.502034 | + | 0.869548i | 0.999997 | + | 0.00235021i | \(0.000748096\pi\) |
−0.497963 | + | 0.867198i | \(0.665919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18171.0 | − | 19343.7i | 0.719242 | − | 0.765659i | ||||
\(862\) | − | 11662.4i | − | 0.460814i | ||||||
\(863\) | 13343.5 | − | 7703.88i | 0.526325 | − | 0.303874i | −0.213194 | − | 0.977010i | \(-0.568387\pi\) |
0.739519 | + | 0.673136i | \(0.235053\pi\) | |||||||
\(864\) | −22431.2 | + | 38851.9i | −0.883245 | + | 1.52982i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36896.7 | + | 63906.9i | 1.44781 | + | 2.50767i | ||||
\(867\) | − | 16318.5i | − | 0.639221i | ||||||
\(868\) | −24958.9 | + | 7531.01i | −0.975993 | + | 0.294492i | ||||
\(869\) | 52531.1 | 2.05063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11098.4 | − | 19223.0i | 0.431752 | − | 0.747816i | ||||
\(872\) | −4140.21 | − | 2390.35i | −0.160786 | − | 0.0928297i | ||||
\(873\) | −1205.98 | + | 696.274i | −0.0467541 | + | 0.0269935i | ||||
\(874\) | 14588.8 | 0.564615 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 38323.3 | 1.47811 | ||||||||
\(877\) | 28395.7 | − | 16394.3i | 1.09334 | − | 0.631238i | 0.158874 | − | 0.987299i | \(-0.449214\pi\) |
0.934463 | + | 0.356061i | \(0.115880\pi\) | |||||||
\(878\) | 39173.1 | + | 22616.6i | 1.50573 | + | 0.869333i | ||||
\(879\) | −20692.8 | + | 35840.9i | −0.794027 | + | 1.37530i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30457.9 | −1.16476 | −0.582379 | − | 0.812918i | \(-0.697878\pi\) | ||||
−0.582379 | + | 0.812918i | \(0.697878\pi\) | |||||||
\(882\) | 2888.70 | + | 4350.99i | 0.110281 | + | 0.166106i | ||||
\(883\) | − | 37997.3i | − | 1.44814i | −0.689725 | − | 0.724071i | \(-0.742269\pi\) | ||
0.689725 | − | 0.724071i | \(-0.257731\pi\) | |||||||
\(884\) | 16503.9 | + | 28585.7i | 0.627927 | + | 1.08760i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24440.6 | − | 42332.4i | 0.926749 | − | 1.60518i | ||||
\(887\) | 4.84633 | − | 2.79803i | 0.000183454 | − | 0.000105917i | −0.499908 | − | 0.866078i | \(-0.666633\pi\) |
0.500092 | + | 0.865972i | \(0.333300\pi\) | |||||||
\(888\) | 86851.9i | 3.28216i | ||||||||
\(889\) | 33926.7 | + | 7963.41i | 1.27994 | + | 0.300432i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18177.3 | + | 31484.0i | 0.683460 | + | 1.18379i | ||||
\(892\) | −86878.8 | − | 50159.5i | −3.26112 | − | 1.88281i | ||||
\(893\) | −20073.8 | − | 11589.6i | −0.752231 | − | 0.434301i | ||||
\(894\) | −30677.3 | − | 53134.6i | −1.14765 | − | 1.98779i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1629.73 | − | 5401.19i | −0.0607651 | − | 0.201385i | ||||
\(897\) | 11403.6i | 0.424476i | ||||||||
\(898\) | −42864.9 | + | 24748.1i | −1.59290 | + | 0.919659i | ||||
\(899\) | −1831.28 | + | 3171.87i | −0.0679384 | + | 0.117673i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 513.344 | + | 889.138i | 0.0189811 | + | 0.0328762i | ||||
\(902\) | 86137.6i | 3.17968i | ||||||||
\(903\) | 24237.7 | + | 22768.3i | 0.893221 | + | 0.839071i | ||||
\(904\) | −41192.6 | −1.51554 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15757.9 | + | 27293.4i | −0.577836 | + | 1.00084i | ||||
\(907\) | 6688.58 | + | 3861.66i | 0.244863 | + | 0.141372i | 0.617410 | − | 0.786642i | \(-0.288182\pi\) |
−0.372547 | + | 0.928013i | \(0.621515\pi\) | |||||||
\(908\) | 110826. | − | 63985.2i | 4.05053 | − | 2.33857i | ||||
\(909\) | 227.009 | 0.00828318 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6805.43 | 0.247502 | 0.123751 | − | 0.992313i | \(-0.460508\pi\) | ||||
0.123751 | + | 0.992313i | \(0.460508\pi\) | |||||||
\(912\) | 32798.0 | − | 18936.0i | 1.19085 | − | 0.687535i | ||||
\(913\) | 14547.1 | + | 8398.76i | 0.527314 | + | 0.304445i | ||||
\(914\) | −3557.23 | + | 6161.30i | −0.128734 | + | 0.222974i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22898.0 | 0.825953 | ||||||||
\(917\) | −3260.83 | + | 983.909i | −0.117429 | + | 0.0354324i | ||||
\(918\) | − | 30439.3i | − | 1.09438i | ||||||
\(919\) | −22590.1 | − | 39127.2i | −0.810858 | − | 1.40445i | −0.912264 | − | 0.409602i | \(-0.865667\pi\) |
0.101406 | − | 0.994845i | \(-0.467666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2076.80 | + | 3597.12i | −0.0743027 | + | 0.128696i | ||||
\(922\) | 39479.4 | − | 22793.4i | 1.41018 | − | 0.814167i | ||||
\(923\) | 5857.84i | 0.208898i | ||||||||
\(924\) | 95655.2 | + | 22452.6i | 3.40566 | + | 0.799389i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26948.1 | − | 46675.4i | −0.956337 | − | 1.65643i | ||||
\(927\) | 2883.20 | + | 1664.61i | 0.102154 | + | 0.0589785i | ||||
\(928\) | 13134.1 | + | 7582.96i | 0.464598 | + | 0.268236i | ||||
\(929\) | 2596.11 | + | 4496.59i | 0.0916852 | + | 0.158803i | 0.908220 | − | 0.418492i | \(-0.137441\pi\) |
−0.816535 | + | 0.577296i | \(0.804108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1122.31 | − | 17934.0i | −0.0395081 | − | 0.631325i | ||||
\(932\) | 121171.i | 4.25866i | ||||||||
\(933\) | −8335.11 | + | 4812.28i | −0.292475 | + | 0.168861i | ||||
\(934\) | −22114.7 | + | 38303.8i | −0.774749 | + | 1.34191i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3662.69 | − | 6343.97i | −0.127905 | − | 0.221538i | ||||
\(937\) | − | 7107.58i | − | 0.247806i | −0.992294 | − | 0.123903i | \(-0.960459\pi\) | ||
0.992294 | − | 0.123903i | \(-0.0395412\pi\) | |||||||
\(938\) | −11255.6 | + | 47952.5i | −0.391800 | + | 1.66920i | ||||
\(939\) | −32039.4 | −1.11349 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21831.5 | − | 37813.3i | 0.756309 | − | 1.30997i | −0.188411 | − | 0.982090i | \(-0.560334\pi\) |
0.944721 | − | 0.327876i | \(-0.106333\pi\) | |||||||
\(942\) | −31673.9 | − | 18286.9i | −1.09553 | − | 0.632505i | ||||
\(943\) | 13536.0 | − | 7815.03i | 0.467438 | − | 0.269875i | ||||
\(944\) | −55487.2 | −1.91309 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −107930. | −3.70943 | ||||||||
\(947\) | 13373.2 | − | 7721.04i | 0.458893 | − | 0.264942i | −0.252686 | − | 0.967548i | \(-0.581314\pi\) |
0.711579 | + | 0.702606i | \(0.247980\pi\) | |||||||
\(948\) | −75134.3 | − | 43378.8i | −2.57410 | − | 1.48616i | ||||
\(949\) | −8890.39 | + | 15398.6i | −0.304104 | + | 0.526723i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37733.7 | −1.28664 | ||||||||
\(952\) | −30999.0 | − | 29119.8i | −1.05534 | − | 0.991363i | ||||
\(953\) | − | 44561.5i | − | 1.51468i | −0.653022 | − | 0.757339i | \(-0.726499\pi\) | ||
0.653022 | − | 0.757339i | \(-0.273501\pi\) | |||||||
\(954\) | −196.200 | − | 339.828i | −0.00665848 | − | 0.0115328i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28652.1 | − | 49627.0i | 0.969327 | − | 1.67892i | ||||
\(957\) | 11954.3 | − | 6901.79i | 0.403789 | − | 0.233128i | ||||
\(958\) | 3762.08i | 0.126876i | ||||||||
\(959\) | −11256.8 | + | 11983.3i | −0.379043 | + | 0.403505i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12173.3 | + | 21084.8i | 0.408624 | + | 0.707757i | ||||
\(962\) | −60099.9 | − | 34698.7i | −2.01424 | − | 1.16292i | ||||
\(963\) | −190.411 | − | 109.934i | −0.00637167 | − | 0.00367869i | ||||
\(964\) | 54298.2 | + | 94047.2i | 1.81414 | + | 3.14218i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7309.94 | − | 24226.3i | −0.243472 | − | 0.806903i | ||||
\(967\) | − | 34733.3i | − | 1.15506i | −0.816368 | − | 0.577532i | \(-0.804016\pi\) | ||
0.816368 | − | 0.577532i | \(-0.195984\pi\) | |||||||
\(968\) | −93917.1 | + | 54223.1i | −3.11840 | + | 1.80041i | ||||
\(969\) | −5120.12 | + | 8868.31i | −0.169744 | + | 0.294005i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8855.15 | + | 15337.6i | 0.292662 | + | 0.506906i | 0.974438 | − | 0.224655i | \(-0.0721255\pi\) |
−0.681776 | + | 0.731561i | \(0.738792\pi\) | |||||||
\(972\) | 15591.9i | 0.514517i | ||||||||
\(973\) | 9883.08 | − | 42105.1i | 0.325629 | − | 1.38729i | ||||
\(974\) | −12006.4 | −0.394979 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46600.8 | + | 80715.0i | −1.52834 | + | 2.64716i | ||||
\(977\) | 49846.2 | + | 28778.7i | 1.63226 | + | 0.942387i | 0.983393 | + | 0.181488i | \(0.0580912\pi\) |
0.648870 | + | 0.760900i | \(0.275242\pi\) | |||||||
\(978\) | 19033.9 | − | 10989.2i | 0.622327 | − | 0.359301i | ||||
\(979\) | −27702.7 | −0.904375 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −242.675 | −0.00789806 | ||||||||
\(982\) | −39065.5 | + | 22554.5i | −1.26948 | + | 0.732936i | ||||
\(983\) | −21640.9 | − | 12494.4i | −0.702175 | − | 0.405401i | 0.105982 | − | 0.994368i | \(-0.466202\pi\) |
−0.808157 | + | 0.588967i | \(0.799535\pi\) | |||||||
\(984\) | 41302.6 | − | 71538.2i | 1.33809 | − | 2.31764i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10290.1 | −0.332358 | ||||||||
\(987\) | −9187.51 | + | 39141.8i | −0.296294 | + | 1.26231i | ||||
\(988\) | 43405.5i | 1.39769i | ||||||||
\(989\) | 9792.23 | + | 16960.6i | 0.314838 | + | 0.545315i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30786.6 | + | 53324.0i | −0.986850 | + | 1.70927i | −0.353443 | + | 0.935456i | \(0.614989\pi\) |
−0.633407 | + | 0.773819i | \(0.718344\pi\) | |||||||
\(992\) | −19523.7 | + | 11272.0i | −0.624879 | + | 0.360774i | ||||
\(993\) | − | 32021.2i | − | 1.02333i | ||||||
\(994\) | −3754.99 | − | 12444.6i | −0.119820 | − | 0.397103i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13871.0 | − | 24025.2i | −0.441283 | − | 0.764325i | ||||
\(997\) | 8134.74 | + | 4696.60i | 0.258405 | + | 0.149190i | 0.623607 | − | 0.781738i | \(-0.285667\pi\) |
−0.365202 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(998\) | 89776.7 | + | 51832.6i | 2.84753 | + | 1.64402i | ||||
\(999\) | 22544.7 | + | 39048.5i | 0.713995 | + | 1.23668i |
(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 | 175.4.k.d.74.10 | 20 | ||
5.2 | odd | 4 | 175.4.e.d.151.5 | 10 | |||
5.3 | odd | 4 | 35.4.e.c.11.1 | ✓ | 10 | ||
5.4 | even | 2 | inner | 175.4.k.d.74.1 | 20 | ||
7.2 | even | 3 | inner | 175.4.k.d.149.1 | 20 | ||
15.8 | even | 4 | 315.4.j.g.46.5 | 10 | |||
20.3 | even | 4 | 560.4.q.n.81.4 | 10 | |||
35.2 | odd | 12 | 175.4.e.d.51.5 | 10 | |||
35.3 | even | 12 | 245.4.a.n.1.5 | 5 | |||
35.9 | even | 6 | inner | 175.4.k.d.149.10 | 20 | ||
35.13 | even | 4 | 245.4.e.o.116.1 | 10 | |||
35.17 | even | 12 | 1225.4.a.bf.1.1 | 5 | |||
35.18 | odd | 12 | 245.4.a.m.1.5 | 5 | |||
35.23 | odd | 12 | 35.4.e.c.16.1 | yes | 10 | ||
35.32 | odd | 12 | 1225.4.a.bg.1.1 | 5 | |||
35.33 | even | 12 | 245.4.e.o.226.1 | 10 | |||
105.23 | even | 12 | 315.4.j.g.226.5 | 10 | |||
105.38 | odd | 12 | 2205.4.a.bt.1.1 | 5 | |||
105.53 | even | 12 | 2205.4.a.bu.1.1 | 5 | |||
140.23 | even | 12 | 560.4.q.n.401.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.c.11.1 | ✓ | 10 | 5.3 | odd | 4 | ||
35.4.e.c.16.1 | yes | 10 | 35.23 | odd | 12 | ||
175.4.e.d.51.5 | 10 | 35.2 | odd | 12 | |||
175.4.e.d.151.5 | 10 | 5.2 | odd | 4 | |||
175.4.k.d.74.1 | 20 | 5.4 | even | 2 | inner | ||
175.4.k.d.74.10 | 20 | 1.1 | even | 1 | trivial | ||
175.4.k.d.149.1 | 20 | 7.2 | even | 3 | inner | ||
175.4.k.d.149.10 | 20 | 35.9 | even | 6 | inner | ||
245.4.a.m.1.5 | 5 | 35.18 | odd | 12 | |||
245.4.a.n.1.5 | 5 | 35.3 | even | 12 | |||
245.4.e.o.116.1 | 10 | 35.13 | even | 4 | |||
245.4.e.o.226.1 | 10 | 35.33 | even | 12 | |||
315.4.j.g.46.5 | 10 | 15.8 | even | 4 | |||
315.4.j.g.226.5 | 10 | 105.23 | even | 12 | |||
560.4.q.n.81.4 | 10 | 20.3 | even | 4 | |||
560.4.q.n.401.4 | 10 | 140.23 | even | 12 | |||
1225.4.a.bf.1.1 | 5 | 35.17 | even | 12 | |||
1225.4.a.bg.1.1 | 5 | 35.32 | odd | 12 | |||
2205.4.a.bt.1.1 | 5 | 105.38 | odd | 12 | |||
2205.4.a.bu.1.1 | 5 | 105.53 | even | 12 |