Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.c (of order \(2\), degree \(1\), 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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.20 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.7 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.72893i | 1.01274i | 0.862316 | + | 0.506370i | \(0.169013\pi\) | ||||
−0.862316 | + | 0.506370i | \(0.830987\pi\) | |||||||
\(3\) | − | 9.00000i | − | 0.577350i | ||||||
\(4\) | −0.820586 | −0.0256433 | ||||||||
\(5\) | −32.0393 | − | 45.8092i | −0.573137 | − | 0.819460i | ||||
\(6\) | 51.5603 | 0.584706 | ||||||||
\(7\) | − | 158.171i | − | 1.22006i | −0.792377 | − | 0.610032i | \(-0.791156\pi\) | ||
0.792377 | − | 0.610032i | \(-0.208844\pi\) | |||||||
\(8\) | 178.625i | 0.986770i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 262.437 | − | 183.551i | 0.829900 | − | 0.580439i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 7.38528i | 0.0148052i | ||||||||
\(13\) | 78.2418i | 0.128405i | 0.997937 | + | 0.0642023i | \(0.0204503\pi\) | ||||
−0.997937 | + | 0.0642023i | \(0.979550\pi\) | |||||||
\(14\) | 906.152 | 1.23561 | ||||||||
\(15\) | −412.283 | + | 288.354i | −0.473115 | + | 0.330901i | ||||
\(16\) | −1049.59 | −1.02499 | ||||||||
\(17\) | 88.2340i | 0.0740480i | 0.999314 | + | 0.0370240i | \(0.0117878\pi\) | ||||
−0.999314 | + | 0.0370240i | \(0.988212\pi\) | |||||||
\(18\) | − | 464.043i | − | 0.337580i | ||||||
\(19\) | −1865.42 | −1.18548 | −0.592738 | − | 0.805395i | \(-0.701953\pi\) | ||||
−0.592738 | + | 0.805395i | \(0.701953\pi\) | |||||||
\(20\) | 26.2910 | + | 37.5904i | 0.0146971 | + | 0.0210137i | ||||
\(21\) | −1423.54 | −0.704405 | ||||||||
\(22\) | 693.200i | 0.305353i | ||||||||
\(23\) | 503.122i | 0.198314i | 0.995072 | + | 0.0991571i | \(0.0316146\pi\) | ||||
−0.995072 | + | 0.0991571i | \(0.968385\pi\) | |||||||
\(24\) | 1607.62 | 0.569712 | ||||||||
\(25\) | −1071.96 | + | 2935.39i | −0.343028 | + | 0.939325i | ||||
\(26\) | −448.241 | −0.130040 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | 129.793i | 0.0312865i | ||||||||
\(29\) | −1050.22 | −0.231892 | −0.115946 | − | 0.993255i | \(-0.536990\pi\) | ||||
−0.115946 | + | 0.993255i | \(0.536990\pi\) | |||||||
\(30\) | −1651.96 | − | 2361.94i | −0.335117 | − | 0.479143i | ||||
\(31\) | −9057.51 | −1.69280 | −0.846398 | − | 0.532550i | \(-0.821234\pi\) | ||||
−0.846398 | + | 0.532550i | \(0.821234\pi\) | |||||||
\(32\) | − | 297.011i | − | 0.0512741i | ||||||
\(33\) | − | 1089.00i | − | 0.174078i | ||||||
\(34\) | −505.486 | −0.0749914 | ||||||||
\(35\) | −7245.70 | + | 5067.70i | −0.999794 | + | 0.699264i | ||||
\(36\) | 66.4675 | 0.00854778 | ||||||||
\(37\) | 3899.39i | 0.468266i | 0.972205 | + | 0.234133i | \(0.0752251\pi\) | ||||
−0.972205 | + | 0.234133i | \(0.924775\pi\) | |||||||
\(38\) | − | 10686.9i | − | 1.20058i | ||||||
\(39\) | 704.176 | 0.0741344 | ||||||||
\(40\) | 8182.64 | − | 5723.01i | 0.808619 | − | 0.565555i | ||||
\(41\) | −9454.73 | −0.878394 | −0.439197 | − | 0.898391i | \(-0.644737\pi\) | ||||
−0.439197 | + | 0.898391i | \(0.644737\pi\) | |||||||
\(42\) | − | 8155.37i | − | 0.713379i | ||||||
\(43\) | − | 8918.80i | − | 0.735589i | −0.929907 | − | 0.367795i | \(-0.880113\pi\) | ||
0.929907 | − | 0.367795i | \(-0.119887\pi\) | |||||||
\(44\) | −99.2910 | −0.00773175 | ||||||||
\(45\) | 2595.19 | + | 3710.54i | 0.191046 | + | 0.273153i | ||||
\(46\) | −2882.35 | −0.200841 | ||||||||
\(47\) | 9431.40i | 0.622776i | 0.950283 | + | 0.311388i | \(0.100794\pi\) | ||||
−0.950283 | + | 0.311388i | \(0.899206\pi\) | |||||||
\(48\) | 9446.27i | 0.591776i | ||||||||
\(49\) | −8211.19 | −0.488558 | ||||||||
\(50\) | −16816.6 | − | 6141.20i | −0.951293 | − | 0.347399i | ||||
\(51\) | 794.106 | 0.0427516 | ||||||||
\(52\) | − | 64.2042i | − | 0.00329272i | ||||||
\(53\) | − | 25507.5i | − | 1.24732i | −0.781695 | − | 0.623661i | \(-0.785645\pi\) | ||
0.781695 | − | 0.623661i | \(-0.214355\pi\) | |||||||
\(54\) | −4176.39 | −0.194902 | ||||||||
\(55\) | −3876.76 | − | 5542.91i | −0.172807 | − | 0.247076i | ||||
\(56\) | 28253.3 | 1.20392 | ||||||||
\(57\) | 16788.8i | 0.684435i | ||||||||
\(58\) | − | 6016.65i | − | 0.234847i | ||||||
\(59\) | −9907.66 | −0.370545 | −0.185273 | − | 0.982687i | \(-0.559317\pi\) | ||||
−0.185273 | + | 0.982687i | \(0.559317\pi\) | |||||||
\(60\) | 338.314 | − | 236.619i | 0.0121322 | − | 0.00848540i | ||||
\(61\) | −15614.3 | −0.537278 | −0.268639 | − | 0.963241i | \(-0.586574\pi\) | ||||
−0.268639 | + | 0.963241i | \(0.586574\pi\) | |||||||
\(62\) | − | 51889.8i | − | 1.71436i | ||||||
\(63\) | 12811.9i | 0.406688i | ||||||||
\(64\) | −31885.2 | −0.973058 | ||||||||
\(65\) | 3584.19 | − | 2506.81i | 0.105222 | − | 0.0735934i | ||||
\(66\) | 6238.80 | 0.176295 | ||||||||
\(67\) | − | 16879.9i | − | 0.459392i | −0.973262 | − | 0.229696i | \(-0.926227\pi\) | ||
0.973262 | − | 0.229696i | \(-0.0737732\pi\) | |||||||
\(68\) | − | 72.4036i | − | 0.00189884i | ||||||
\(69\) | 4528.10 | 0.114497 | ||||||||
\(70\) | −29032.5 | − | 41510.1i | −0.708173 | − | 1.01253i | ||||
\(71\) | 71467.7 | 1.68253 | 0.841267 | − | 0.540620i | \(-0.181810\pi\) | ||||
0.841267 | + | 0.540620i | \(0.181810\pi\) | |||||||
\(72\) | − | 14468.6i | − | 0.328923i | ||||||
\(73\) | − | 65733.0i | − | 1.44370i | −0.692050 | − | 0.721849i | \(-0.743292\pi\) | ||
0.692050 | − | 0.721849i | \(-0.256708\pi\) | |||||||
\(74\) | −22339.3 | −0.474232 | ||||||||
\(75\) | 26418.5 | + | 9647.67i | 0.542320 | + | 0.198047i | ||||
\(76\) | 1530.74 | 0.0303995 | ||||||||
\(77\) | − | 19138.7i | − | 0.367863i | ||||||
\(78\) | 4034.17i | 0.0750789i | ||||||||
\(79\) | −104481. | −1.88352 | −0.941762 | − | 0.336281i | \(-0.890831\pi\) | ||||
−0.941762 | + | 0.336281i | \(0.890831\pi\) | |||||||
\(80\) | 33628.0 | + | 48080.7i | 0.587457 | + | 0.839934i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − | 54165.4i | − | 0.889585i | ||||||
\(83\) | 15457.9i | 0.246294i | 0.992388 | + | 0.123147i | \(0.0392987\pi\) | ||||
−0.992388 | + | 0.123147i | \(0.960701\pi\) | |||||||
\(84\) | 1168.14 | 0.0180633 | ||||||||
\(85\) | 4041.93 | − | 2826.96i | 0.0606794 | − | 0.0424397i | ||||
\(86\) | 51095.2 | 0.744961 | ||||||||
\(87\) | 9452.01i | 0.133883i | ||||||||
\(88\) | 21613.6i | 0.297522i | ||||||||
\(89\) | −2774.62 | −0.0371303 | −0.0185651 | − | 0.999828i | \(-0.505910\pi\) | ||||
−0.0185651 | + | 0.999828i | \(0.505910\pi\) | |||||||
\(90\) | −21257.4 | + | 14867.6i | −0.276633 | + | 0.193480i | ||||
\(91\) | 12375.6 | 0.156662 | ||||||||
\(92\) | − | 412.855i | − | 0.00508544i | ||||||
\(93\) | 81517.6i | 0.977336i | ||||||||
\(94\) | −54031.8 | −0.630710 | ||||||||
\(95\) | 59766.8 | + | 85453.4i | 0.679440 | + | 0.971450i | ||||
\(96\) | −2673.10 | −0.0296031 | ||||||||
\(97\) | 125401.i | 1.35323i | 0.736338 | + | 0.676614i | \(0.236553\pi\) | ||||
−0.736338 | + | 0.676614i | \(0.763447\pi\) | |||||||
\(98\) | − | 47041.3i | − | 0.494782i | ||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 879.638 | − | 2408.74i | 0.00879638 | − | 0.0240874i | ||||
\(101\) | 50984.8 | 0.497322 | 0.248661 | − | 0.968591i | \(-0.420010\pi\) | ||||
0.248661 | + | 0.968591i | \(0.420010\pi\) | |||||||
\(102\) | 4549.37i | 0.0432963i | ||||||||
\(103\) | 51464.8i | 0.477989i | 0.971021 | + | 0.238994i | \(0.0768177\pi\) | ||||
−0.971021 | + | 0.238994i | \(0.923182\pi\) | |||||||
\(104\) | −13975.9 | −0.126706 | ||||||||
\(105\) | 45609.3 | + | 65211.3i | 0.403720 | + | 0.577231i | ||||
\(106\) | 146131. | 1.26321 | ||||||||
\(107\) | 139655.i | 1.17923i | 0.807686 | + | 0.589613i | \(0.200720\pi\) | ||||
−0.807686 | + | 0.589613i | \(0.799280\pi\) | |||||||
\(108\) | − | 598.208i | − | 0.00493506i | ||||||
\(109\) | −144034. | −1.16118 | −0.580591 | − | 0.814195i | \(-0.697178\pi\) | ||||
−0.580591 | + | 0.814195i | \(0.697178\pi\) | |||||||
\(110\) | 31754.9 | − | 22209.7i | 0.250224 | − | 0.175009i | ||||
\(111\) | 35094.5 | 0.270353 | ||||||||
\(112\) | 166014.i | 1.25055i | ||||||||
\(113\) | − | 62064.4i | − | 0.457242i | −0.973515 | − | 0.228621i | \(-0.926578\pi\) | ||
0.973515 | − | 0.228621i | \(-0.0734217\pi\) | |||||||
\(114\) | −96181.7 | −0.693155 | ||||||||
\(115\) | 23047.6 | − | 16119.7i | 0.162510 | − | 0.113661i | ||||
\(116\) | 861.799 | 0.00594649 | ||||||||
\(117\) | − | 6337.59i | − | 0.0428015i | ||||||
\(118\) | − | 56760.3i | − | 0.375266i | ||||||
\(119\) | 13956.1 | 0.0903434 | ||||||||
\(120\) | −51507.1 | − | 73643.8i | −0.326523 | − | 0.466856i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | − | 89453.4i | − | 0.544124i | ||||||
\(123\) | 85092.5i | 0.507141i | ||||||||
\(124\) | 7432.47 | 0.0434089 | ||||||||
\(125\) | 168813. | − | 44942.2i | 0.966341 | − | 0.257264i | ||||
\(126\) | −73398.3 | −0.411870 | ||||||||
\(127\) | 285166.i | 1.56888i | 0.620207 | + | 0.784438i | \(0.287049\pi\) | ||||
−0.620207 | + | 0.784438i | \(0.712951\pi\) | |||||||
\(128\) | − | 192172.i | − | 1.03673i | ||||||
\(129\) | −80269.2 | −0.424693 | ||||||||
\(130\) | 14361.4 | + | 20533.6i | 0.0745310 | + | 0.106563i | ||||
\(131\) | −198363. | −1.00991 | −0.504954 | − | 0.863146i | \(-0.668491\pi\) | ||||
−0.504954 | + | 0.863146i | \(0.668491\pi\) | |||||||
\(132\) | 893.619i | 0.00446393i | ||||||||
\(133\) | 295056.i | 1.44636i | ||||||||
\(134\) | 96703.8 | 0.465245 | ||||||||
\(135\) | 33394.9 | − | 23356.7i | 0.157705 | − | 0.110300i | ||||
\(136\) | −15760.7 | −0.0730684 | ||||||||
\(137\) | − | 166328.i | − | 0.757120i | −0.925577 | − | 0.378560i | \(-0.876419\pi\) | ||
0.925577 | − | 0.378560i | \(-0.123581\pi\) | |||||||
\(138\) | 25941.1i | 0.115955i | ||||||||
\(139\) | 301037. | 1.32155 | 0.660774 | − | 0.750585i | \(-0.270228\pi\) | ||||
0.660774 | + | 0.750585i | \(0.270228\pi\) | |||||||
\(140\) | 5945.73 | − | 4158.49i | 0.0256380 | − | 0.0179315i | ||||
\(141\) | 84882.6 | 0.359560 | ||||||||
\(142\) | 409433.i | 1.70397i | ||||||||
\(143\) | 9467.26i | 0.0387154i | ||||||||
\(144\) | 85016.4 | 0.341662 | ||||||||
\(145\) | 33648.4 | + | 48109.9i | 0.132906 | + | 0.190027i | ||||
\(146\) | 376580. | 1.46209 | ||||||||
\(147\) | 73900.7i | 0.282069i | ||||||||
\(148\) | − | 3199.79i | − | 0.0120079i | ||||||
\(149\) | −107457. | −0.396525 | −0.198263 | − | 0.980149i | \(-0.563530\pi\) | ||||
−0.198263 | + | 0.980149i | \(0.563530\pi\) | |||||||
\(150\) | −55270.8 | + | 151350.i | −0.200571 | + | 0.549229i | ||||
\(151\) | 24082.4 | 0.0859522 | 0.0429761 | − | 0.999076i | \(-0.486316\pi\) | ||||
0.0429761 | + | 0.999076i | \(0.486316\pi\) | |||||||
\(152\) | − | 333210.i | − | 1.16979i | ||||||
\(153\) | − | 7146.95i | − | 0.0246827i | ||||||
\(154\) | 109644. | 0.372550 | ||||||||
\(155\) | 290197. | + | 414917.i | 0.970204 | + | 1.38718i | ||||
\(156\) | −577.837 | −0.00190105 | ||||||||
\(157\) | − | 479707.i | − | 1.55320i | −0.629994 | − | 0.776600i | \(-0.716943\pi\) | ||
0.629994 | − | 0.776600i | \(-0.283057\pi\) | |||||||
\(158\) | − | 598566.i | − | 1.90752i | ||||||
\(159\) | −229568. | −0.720142 | ||||||||
\(160\) | −13605.9 | + | 9516.05i | −0.0420171 | + | 0.0293871i | ||||
\(161\) | 79579.5 | 0.241956 | ||||||||
\(162\) | 37587.5i | 0.112527i | ||||||||
\(163\) | − | 437032.i | − | 1.28838i | −0.764866 | − | 0.644190i | \(-0.777195\pi\) | ||
0.764866 | − | 0.644190i | \(-0.222805\pi\) | |||||||
\(164\) | 7758.42 | 0.0225249 | ||||||||
\(165\) | −49886.2 | + | 34890.8i | −0.142650 | + | 0.0997703i | ||||
\(166\) | −88557.0 | −0.249432 | ||||||||
\(167\) | − | 592592.i | − | 1.64424i | −0.569316 | − | 0.822119i | \(-0.692792\pi\) | ||
0.569316 | − | 0.822119i | \(-0.307208\pi\) | |||||||
\(168\) | − | 254280.i | − | 0.695086i | ||||||
\(169\) | 365171. | 0.983512 | ||||||||
\(170\) | 16195.4 | + | 23155.9i | 0.0429804 | + | 0.0614524i | ||||
\(171\) | 151099. | 0.395159 | ||||||||
\(172\) | 7318.65i | 0.0188630i | ||||||||
\(173\) | − | 193454.i | − | 0.491432i | −0.969342 | − | 0.245716i | \(-0.920977\pi\) | ||
0.969342 | − | 0.245716i | \(-0.0790231\pi\) | |||||||
\(174\) | −54149.9 | −0.135589 | ||||||||
\(175\) | 464295. | + | 169554.i | 1.14604 | + | 0.418517i | ||||
\(176\) | −127000. | −0.309045 | ||||||||
\(177\) | 89169.0i | 0.213934i | ||||||||
\(178\) | − | 15895.6i | − | 0.0376033i | ||||||
\(179\) | 373735. | 0.871828 | 0.435914 | − | 0.899988i | \(-0.356425\pi\) | ||||
0.435914 | + | 0.899988i | \(0.356425\pi\) | |||||||
\(180\) | −2129.57 | − | 3044.82i | −0.00489905 | − | 0.00700456i | ||||
\(181\) | −234887. | −0.532921 | −0.266461 | − | 0.963846i | \(-0.585854\pi\) | ||||
−0.266461 | + | 0.963846i | \(0.585854\pi\) | |||||||
\(182\) | 70899.0i | 0.158658i | ||||||||
\(183\) | 140529.i | 0.310198i | ||||||||
\(184\) | −89869.9 | −0.195691 | ||||||||
\(185\) | 178628. | − | 124934.i | 0.383725 | − | 0.268380i | ||||
\(186\) | −467008. | −0.989788 | ||||||||
\(187\) | 10676.3i | 0.0223263i | ||||||||
\(188\) | − | 7739.28i | − | 0.0159700i | ||||||
\(189\) | 115307. | 0.234802 | ||||||||
\(190\) | −489556. | + | 342400.i | −0.983826 | + | 0.688096i | ||||
\(191\) | 261514. | 0.518695 | 0.259348 | − | 0.965784i | \(-0.416492\pi\) | ||||
0.259348 | + | 0.965784i | \(0.416492\pi\) | |||||||
\(192\) | 286967.i | 0.561796i | ||||||||
\(193\) | − | 688977.i | − | 1.33141i | −0.746215 | − | 0.665705i | \(-0.768131\pi\) | ||
0.746215 | − | 0.665705i | \(-0.231869\pi\) | |||||||
\(194\) | −718412. | −1.37047 | ||||||||
\(195\) | −22561.3 | − | 32257.7i | −0.0424892 | − | 0.0607502i | ||||
\(196\) | 6737.99 | 0.0125282 | ||||||||
\(197\) | 625063.i | 1.14752i | 0.819025 | + | 0.573758i | \(0.194515\pi\) | ||||
−0.819025 | + | 0.573758i | \(0.805485\pi\) | |||||||
\(198\) | − | 56149.2i | − | 0.101784i | ||||||
\(199\) | −1.02019e6 | −1.82619 | −0.913097 | − | 0.407742i | \(-0.866316\pi\) | ||||
−0.913097 | + | 0.407742i | \(0.866316\pi\) | |||||||
\(200\) | −524333. | − | 191479.i | −0.926898 | − | 0.338490i | ||||
\(201\) | −151919. | −0.265230 | ||||||||
\(202\) | 292088.i | 0.503658i | ||||||||
\(203\) | 166115.i | 0.282924i | ||||||||
\(204\) | −651.632 | −0.00109629 | ||||||||
\(205\) | 302923. | + | 433113.i | 0.503440 | + | 0.719808i | ||||
\(206\) | −294838. | −0.484079 | ||||||||
\(207\) | − | 40752.9i | − | 0.0661047i | ||||||
\(208\) | − | 82121.4i | − | 0.131613i | ||||||
\(209\) | −225716. | −0.357434 | ||||||||
\(210\) | −373591. | + | 261293.i | −0.584585 | + | 0.408864i | ||||
\(211\) | −544322. | −0.841685 | −0.420843 | − | 0.907134i | \(-0.638266\pi\) | ||||
−0.420843 | + | 0.907134i | \(0.638266\pi\) | |||||||
\(212\) | 20931.1i | 0.0319855i | ||||||||
\(213\) | − | 643209.i | − | 0.971412i | ||||||
\(214\) | −800073. | −1.19425 | ||||||||
\(215\) | −408563. | + | 285752.i | −0.602786 | + | 0.421593i | ||||
\(216\) | −130217. | −0.189904 | ||||||||
\(217\) | 1.43264e6i | 2.06532i | ||||||||
\(218\) | − | 825163.i | − | 1.17598i | ||||||
\(219\) | −591597. | −0.833520 | ||||||||
\(220\) | 3181.22 | + | 4548.44i | 0.00443135 | + | 0.00633586i | ||||
\(221\) | −6903.58 | −0.00950810 | ||||||||
\(222\) | 201054.i | 0.273798i | ||||||||
\(223\) | − | 852497.i | − | 1.14797i | −0.818866 | − | 0.573985i | \(-0.805397\pi\) | ||
0.818866 | − | 0.573985i | \(-0.194603\pi\) | |||||||
\(224\) | −46978.7 | −0.0625577 | ||||||||
\(225\) | 86829.0 | − | 237767.i | 0.114343 | − | 0.313108i | ||||
\(226\) | 355562. | 0.463068 | ||||||||
\(227\) | − | 909729.i | − | 1.17178i | −0.810390 | − | 0.585891i | \(-0.800744\pi\) | ||
0.810390 | − | 0.585891i | \(-0.199256\pi\) | |||||||
\(228\) | − | 13776.6i | − | 0.0175512i | ||||||
\(229\) | 561762. | 0.707886 | 0.353943 | − | 0.935267i | \(-0.384841\pi\) | ||||
0.353943 | + | 0.935267i | \(0.384841\pi\) | |||||||
\(230\) | 92348.5 | + | 132038.i | 0.115109 | + | 0.164581i | ||||
\(231\) | −172249. | −0.212386 | ||||||||
\(232\) | − | 187596.i | − | 0.228825i | ||||||
\(233\) | 604654.i | 0.729654i | 0.931075 | + | 0.364827i | \(0.118872\pi\) | ||||
−0.931075 | + | 0.364827i | \(0.881128\pi\) | |||||||
\(234\) | 36307.6 | 0.0433468 | ||||||||
\(235\) | 432045. | − | 302176.i | 0.510340 | − | 0.356936i | ||||
\(236\) | 8130.10 | 0.00950201 | ||||||||
\(237\) | 940332.i | 1.08745i | ||||||||
\(238\) | 79953.4i | 0.0914944i | ||||||||
\(239\) | 1.13697e6 | 1.28752 | 0.643760 | − | 0.765227i | \(-0.277373\pi\) | ||||
0.643760 | + | 0.765227i | \(0.277373\pi\) | |||||||
\(240\) | 432726. | − | 302652.i | 0.484936 | − | 0.339169i | ||||
\(241\) | 261399. | 0.289909 | 0.144954 | − | 0.989438i | \(-0.453696\pi\) | ||||
0.144954 | + | 0.989438i | \(0.453696\pi\) | |||||||
\(242\) | 83877.2i | 0.0920673i | ||||||||
\(243\) | − | 59049.0i | − | 0.0641500i | ||||||
\(244\) | 12812.9 | 0.0137776 | ||||||||
\(245\) | 263081. | + | 376148.i | 0.280010 | + | 0.400353i | ||||
\(246\) | −487489. | −0.513602 | ||||||||
\(247\) | − | 145954.i | − | 0.152220i | ||||||
\(248\) | − | 1.61789e6i | − | 1.67040i | ||||||
\(249\) | 139121. | 0.142198 | ||||||||
\(250\) | 257471. | + | 967116.i | 0.260542 | + | 0.978653i | ||||
\(251\) | 565375. | 0.566438 | 0.283219 | − | 0.959055i | \(-0.408598\pi\) | ||||
0.283219 | + | 0.959055i | \(0.408598\pi\) | |||||||
\(252\) | − | 10513.3i | − | 0.0104288i | ||||||
\(253\) | 60877.8i | 0.0597940i | ||||||||
\(254\) | −1.63370e6 | −1.58886 | ||||||||
\(255\) | −25442.6 | − | 36377.3i | −0.0245025 | − | 0.0350332i | ||||
\(256\) | 80614.3 | 0.0768798 | ||||||||
\(257\) | − | 1.51946e6i | − | 1.43501i | −0.696551 | − | 0.717507i | \(-0.745283\pi\) | ||
0.696551 | − | 0.717507i | \(-0.254717\pi\) | |||||||
\(258\) | − | 459856.i | − | 0.430103i | ||||||
\(259\) | 616772. | 0.571315 | ||||||||
\(260\) | −2941.14 | + | 2057.06i | −0.00269825 | + | 0.00188718i | ||||
\(261\) | 85068.1 | 0.0772975 | ||||||||
\(262\) | − | 1.13641e6i | − | 1.02278i | ||||||
\(263\) | 730370.i | 0.651109i | 0.945523 | + | 0.325554i | \(0.105551\pi\) | ||||
−0.945523 | + | 0.325554i | \(0.894449\pi\) | |||||||
\(264\) | 194522. | 0.171775 | ||||||||
\(265\) | −1.16848e6 | + | 817244.i | −1.02213 | + | 0.714886i | ||||
\(266\) | −1.69035e6 | −1.46478 | ||||||||
\(267\) | 24971.6i | 0.0214372i | ||||||||
\(268\) | 13851.4i | 0.0117803i | ||||||||
\(269\) | 475262. | 0.400453 | 0.200227 | − | 0.979750i | \(-0.435832\pi\) | ||||
0.200227 | + | 0.979750i | \(0.435832\pi\) | |||||||
\(270\) | 133809. | + | 191317.i | 0.111706 | + | 0.159714i | ||||
\(271\) | −961313. | −0.795136 | −0.397568 | − | 0.917573i | \(-0.630146\pi\) | ||||
−0.397568 | + | 0.917573i | \(0.630146\pi\) | |||||||
\(272\) | − | 92609.1i | − | 0.0758982i | ||||||
\(273\) | − | 111381.i | − | 0.0904488i | ||||||
\(274\) | 952883. | 0.766766 | ||||||||
\(275\) | −129708. | + | 355182.i | −0.103427 | + | 0.283217i | ||||
\(276\) | −3715.70 | −0.00293608 | ||||||||
\(277\) | 428260.i | 0.335358i | 0.985842 | + | 0.167679i | \(0.0536272\pi\) | ||||
−0.985842 | + | 0.167679i | \(0.946373\pi\) | |||||||
\(278\) | 1.72462e6i | 1.33839i | ||||||||
\(279\) | 733659. | 0.564265 | ||||||||
\(280\) | −905216. | − | 1.29426e6i | −0.690013 | − | 0.986567i | ||||
\(281\) | −212752. | −0.160734 | −0.0803670 | − | 0.996765i | \(-0.525609\pi\) | ||||
−0.0803670 | + | 0.996765i | \(0.525609\pi\) | |||||||
\(282\) | 486286.i | 0.364141i | ||||||||
\(283\) | 563864.i | 0.418512i | 0.977861 | + | 0.209256i | \(0.0671043\pi\) | ||||
−0.977861 | + | 0.209256i | \(0.932896\pi\) | |||||||
\(284\) | −58645.4 | −0.0431458 | ||||||||
\(285\) | 769080. | − | 537901.i | 0.560867 | − | 0.392275i | ||||
\(286\) | −54237.2 | −0.0392087 | ||||||||
\(287\) | 1.49547e6i | 1.07170i | ||||||||
\(288\) | 24057.9i | 0.0170914i | ||||||||
\(289\) | 1.41207e6 | 0.994517 | ||||||||
\(290\) | −275618. | + | 192769.i | −0.192448 | + | 0.134599i | ||||
\(291\) | 1.12861e6 | 0.781287 | ||||||||
\(292\) | 53939.6i | 0.0370212i | ||||||||
\(293\) | − | 1.80961e6i | − | 1.23145i | −0.787963 | − | 0.615723i | \(-0.788864\pi\) | ||
0.787963 | − | 0.615723i | \(-0.211136\pi\) | |||||||
\(294\) | −423371. | −0.285663 | ||||||||
\(295\) | 317435. | + | 453862.i | 0.212373 | + | 0.303647i | ||||
\(296\) | −696527. | −0.462071 | ||||||||
\(297\) | 88209.0i | 0.0580259i | ||||||||
\(298\) | − | 615616.i | − | 0.401577i | ||||||
\(299\) | −39365.2 | −0.0254644 | ||||||||
\(300\) | −21678.7 | − | 7916.75i | −0.0139069 | − | 0.00507859i | ||||
\(301\) | −1.41070e6 | −0.897466 | ||||||||
\(302\) | 137966.i | 0.0870473i | ||||||||
\(303\) | − | 458863.i | − | 0.287129i | ||||||
\(304\) | 1.95792e6 | 1.21510 | ||||||||
\(305\) | 500273. | + | 715281.i | 0.307934 | + | 0.440278i | ||||
\(306\) | 40944.3 | 0.0249971 | ||||||||
\(307\) | − | 774049.i | − | 0.468730i | −0.972149 | − | 0.234365i | \(-0.924699\pi\) | ||
0.972149 | − | 0.234365i | \(-0.0753011\pi\) | |||||||
\(308\) | 15705.0i | 0.00943324i | ||||||||
\(309\) | 463184. | 0.275967 | ||||||||
\(310\) | −2.37703e6 | + | 1.66251e6i | −1.40485 | + | 0.982565i | ||||
\(311\) | 1.35808e6 | 0.796205 | 0.398102 | − | 0.917341i | \(-0.369669\pi\) | ||||
0.398102 | + | 0.917341i | \(0.369669\pi\) | |||||||
\(312\) | 125783.i | 0.0731536i | ||||||||
\(313\) | − | 3.38315e6i | − | 1.95191i | −0.217968 | − | 0.975956i | \(-0.569943\pi\) | ||
0.217968 | − | 0.975956i | \(-0.430057\pi\) | |||||||
\(314\) | 2.74821e6 | 1.57299 | ||||||||
\(315\) | 586902. | − | 410484.i | 0.333265 | − | 0.233088i | ||||
\(316\) | 85736.0 | 0.0482998 | ||||||||
\(317\) | 668139.i | 0.373438i | 0.982413 | + | 0.186719i | \(0.0597854\pi\) | ||||
−0.982413 | + | 0.186719i | \(0.940215\pi\) | |||||||
\(318\) | − | 1.31518e6i | − | 0.729317i | ||||||
\(319\) | −127077. | −0.0699182 | ||||||||
\(320\) | 1.02158e6 | + | 1.46063e6i | 0.557696 | + | 0.797382i | ||||
\(321\) | 1.25689e6 | 0.680826 | ||||||||
\(322\) | 455905.i | 0.245039i | ||||||||
\(323\) | − | 164593.i | − | 0.0877821i | ||||||
\(324\) | −5383.87 | −0.00284926 | ||||||||
\(325\) | −229670. | − | 83872.3i | −0.120614 | − | 0.0440464i | ||||
\(326\) | 2.50372e6 | 1.30479 | ||||||||
\(327\) | 1.29631e6i | 0.670409i | ||||||||
\(328\) | − | 1.68885e6i | − | 0.866773i | ||||||
\(329\) | 1.49178e6 | 0.759827 | ||||||||
\(330\) | −199887. | − | 285794.i | −0.101041 | − | 0.144467i | ||||
\(331\) | 94884.0 | 0.0476018 | 0.0238009 | − | 0.999717i | \(-0.492423\pi\) | ||||
0.0238009 | + | 0.999717i | \(0.492423\pi\) | |||||||
\(332\) | − | 12684.5i | − | 0.00631581i | ||||||
\(333\) | − | 315851.i | − | 0.156089i | ||||||
\(334\) | 3.39491e6 | 1.66519 | ||||||||
\(335\) | −773256. | + | 540822.i | −0.376453 | + | 0.263295i | ||||
\(336\) | 1.49413e6 | 0.722005 | ||||||||
\(337\) | 507319.i | 0.243336i | 0.992571 | + | 0.121668i | \(0.0388243\pi\) | ||||
−0.992571 | + | 0.121668i | \(0.961176\pi\) | |||||||
\(338\) | 2.09204e6i | 0.996043i | ||||||||
\(339\) | −558580. | −0.263989 | ||||||||
\(340\) | −3316.75 | + | 2319.76i | −0.00155602 | + | 0.00108829i | ||||
\(341\) | −1.09596e6 | −0.510397 | ||||||||
\(342\) | 865635.i | 0.400193i | ||||||||
\(343\) | − | 1.35961e6i | − | 0.623993i | ||||||
\(344\) | 1.59312e6 | 0.725858 | ||||||||
\(345\) | −145077. | − | 207429.i | −0.0656223 | − | 0.0938255i | ||||
\(346\) | 1.10829e6 | 0.497693 | ||||||||
\(347\) | 2.91869e6i | 1.30126i | 0.759394 | + | 0.650631i | \(0.225495\pi\) | ||||
−0.759394 | + | 0.650631i | \(0.774505\pi\) | |||||||
\(348\) | − | 7756.19i | − | 0.00343321i | ||||||
\(349\) | 1.69598e6 | 0.745346 | 0.372673 | − | 0.927963i | \(-0.378441\pi\) | ||||
0.372673 | + | 0.927963i | \(0.378441\pi\) | |||||||
\(350\) | −971361. | + | 2.65991e6i | −0.423849 | + | 1.16064i | ||||
\(351\) | −57038.3 | −0.0247115 | ||||||||
\(352\) | − | 35938.4i | − | 0.0154597i | ||||||
\(353\) | 2.54669e6i | 1.08777i | 0.839159 | + | 0.543887i | \(0.183048\pi\) | ||||
−0.839159 | + | 0.543887i | \(0.816952\pi\) | |||||||
\(354\) | −510842. | −0.216660 | ||||||||
\(355\) | −2.28978e6 | − | 3.27388e6i | −0.964322 | − | 1.37877i | ||||
\(356\) | 2276.81 | 0.000952144 | ||||||||
\(357\) | − | 125605.i | − | 0.0521598i | ||||||
\(358\) | 2.14110e6i | 0.882936i | ||||||||
\(359\) | 425376. | 0.174196 | 0.0870978 | − | 0.996200i | \(-0.472241\pi\) | ||||
0.0870978 | + | 0.996200i | \(0.472241\pi\) | |||||||
\(360\) | −662794. | + | 463564.i | −0.269540 | + | 0.188518i | ||||
\(361\) | 1.00369e6 | 0.405353 | ||||||||
\(362\) | − | 1.34565e6i | − | 0.539711i | ||||||
\(363\) | − | 131769.i | − | 0.0524864i | ||||||
\(364\) | −10155.3 | −0.00401733 | ||||||||
\(365\) | −3.01118e6 | + | 2.10604e6i | −1.18305 | + | 0.827437i | ||||
\(366\) | −805081. | −0.314150 | ||||||||
\(367\) | − | 1.88623e6i | − | 0.731019i | −0.930808 | − | 0.365509i | \(-0.880895\pi\) | ||
0.930808 | − | 0.365509i | \(-0.119105\pi\) | |||||||
\(368\) | − | 528070.i | − | 0.203269i | ||||||
\(369\) | 765833. | 0.292798 | ||||||||
\(370\) | 715737. | + | 1.02335e6i | 0.271800 | + | 0.388614i | ||||
\(371\) | −4.03456e6 | −1.52181 | ||||||||
\(372\) | − | 66892.3i | − | 0.0250622i | ||||||
\(373\) | − | 903282.i | − | 0.336164i | −0.985773 | − | 0.168082i | \(-0.946243\pi\) | ||
0.985773 | − | 0.168082i | \(-0.0537574\pi\) | |||||||
\(374\) | −61163.8 | −0.0226108 | ||||||||
\(375\) | −404480. | − | 1.51932e6i | −0.148532 | − | 0.557917i | ||||
\(376\) | −1.68468e6 | −0.614537 | ||||||||
\(377\) | − | 82171.3i | − | 0.0297760i | ||||||
\(378\) | 660585.i | 0.237793i | ||||||||
\(379\) | −4.94830e6 | −1.76953 | −0.884766 | − | 0.466036i | \(-0.845682\pi\) | ||||
−0.884766 | + | 0.466036i | \(0.845682\pi\) | |||||||
\(380\) | −49043.8 | − | 70121.9i | −0.0174231 | − | 0.0249112i | ||||
\(381\) | 2.56650e6 | 0.905791 | ||||||||
\(382\) | 1.49820e6i | 0.525304i | ||||||||
\(383\) | 1.62974e6i | 0.567703i | 0.958868 | + | 0.283851i | \(0.0916123\pi\) | ||||
−0.958868 | + | 0.283851i | \(0.908388\pi\) | |||||||
\(384\) | −1.72955e6 | −0.598556 | ||||||||
\(385\) | −876730. | + | 613192.i | −0.301449 | + | 0.210836i | ||||
\(386\) | 3.94710e6 | 1.34837 | ||||||||
\(387\) | 722423.i | 0.245196i | ||||||||
\(388\) | − | 102902.i | − | 0.0347013i | ||||||
\(389\) | −5.33558e6 | −1.78775 | −0.893877 | − | 0.448311i | \(-0.852026\pi\) | ||||
−0.893877 | + | 0.448311i | \(0.852026\pi\) | |||||||
\(390\) | 184802. | − | 129252.i | 0.0615241 | − | 0.0430305i | ||||
\(391\) | −44392.4 | −0.0146848 | ||||||||
\(392\) | − | 1.46672e6i | − | 0.482094i | ||||||
\(393\) | 1.78527e6i | 0.583071i | ||||||||
\(394\) | −3.58094e6 | −1.16214 | ||||||||
\(395\) | 3.34751e6 | + | 4.78620e6i | 1.07952 | + | 1.54347i | ||||
\(396\) | 8042.57 | 0.00257725 | ||||||||
\(397\) | 3.89341e6i | 1.23981i | 0.784678 | + | 0.619903i | \(0.212828\pi\) | ||||
−0.784678 | + | 0.619903i | \(0.787172\pi\) | |||||||
\(398\) | − | 5.84457e6i | − | 1.84946i | ||||||
\(399\) | 2.65550e6 | 0.835055 | ||||||||
\(400\) | 1.12512e6 | − | 3.08094e6i | 0.351599 | − | 0.962795i | ||||
\(401\) | 401457. | 0.124675 | 0.0623374 | − | 0.998055i | \(-0.480145\pi\) | ||||
0.0623374 | + | 0.998055i | \(0.480145\pi\) | |||||||
\(402\) | − | 870335.i | − | 0.268609i | ||||||
\(403\) | − | 708676.i | − | 0.217363i | ||||||
\(404\) | −41837.5 | −0.0127530 | ||||||||
\(405\) | −210210. | − | 300554.i | −0.0636819 | − | 0.0910511i | ||||
\(406\) | −951662. | −0.286528 | ||||||||
\(407\) | 471826.i | 0.141187i | ||||||||
\(408\) | 141847.i | 0.0421861i | ||||||||
\(409\) | 5.92484e6 | 1.75133 | 0.875666 | − | 0.482918i | \(-0.160423\pi\) | ||||
0.875666 | + | 0.482918i | \(0.160423\pi\) | |||||||
\(410\) | −2.48127e6 | + | 1.73542e6i | −0.728979 | + | 0.509854i | ||||
\(411\) | −1.49695e6 | −0.437124 | ||||||||
\(412\) | − | 42231.4i | − | 0.0122572i | ||||||
\(413\) | 1.56711e6i | 0.452089i | ||||||||
\(414\) | 233470. | 0.0669469 | ||||||||
\(415\) | 708113. | − | 495260.i | 0.201828 | − | 0.141160i | ||||
\(416\) | 23238.7 | 0.00658383 | ||||||||
\(417\) | − | 2.70933e6i | − | 0.762996i | ||||||
\(418\) | − | 1.29311e6i | − | 0.361988i | ||||||
\(419\) | −4.23888e6 | −1.17955 | −0.589774 | − | 0.807568i | \(-0.700783\pi\) | ||||
−0.589774 | + | 0.807568i | \(0.700783\pi\) | |||||||
\(420\) | −37426.4 | − | 53511.5i | −0.0103527 | − | 0.0148021i | ||||
\(421\) | 5.04583e6 | 1.38748 | 0.693740 | − | 0.720225i | \(-0.255962\pi\) | ||||
0.693740 | + | 0.720225i | \(0.255962\pi\) | |||||||
\(422\) | − | 3.11838e6i | − | 0.852409i | ||||||
\(423\) | − | 763944.i | − | 0.207592i | ||||||
\(424\) | 4.55627e6 | 1.23082 | ||||||||
\(425\) | −259001. | − | 94583.5i | −0.0695552 | − | 0.0254006i | ||||
\(426\) | 3.68490e6 | 0.983788 | ||||||||
\(427\) | 2.46974e6i | 0.655514i | ||||||||
\(428\) | − | 114599.i | − | 0.0302393i | ||||||
\(429\) | 85205.3 | 0.0223524 | ||||||||
\(430\) | −1.63705e6 | − | 2.34063e6i | −0.426965 | − | 0.610466i | ||||
\(431\) | −7.38745e6 | −1.91558 | −0.957792 | − | 0.287461i | \(-0.907189\pi\) | ||||
−0.957792 | + | 0.287461i | \(0.907189\pi\) | |||||||
\(432\) | − | 765148.i | − | 0.197259i | ||||||
\(433\) | − | 1.66687e6i | − | 0.427249i | −0.976916 | − | 0.213625i | \(-0.931473\pi\) | ||
0.976916 | − | 0.213625i | \(-0.0685270\pi\) | |||||||
\(434\) | −8.20748e6 | −2.09163 | ||||||||
\(435\) | 432989. | − | 302836.i | 0.109712 | − | 0.0767334i | ||||
\(436\) | 118193. | 0.0297766 | ||||||||
\(437\) | − | 938534.i | − | 0.235097i | ||||||
\(438\) | − | 3.38922e6i | − | 0.844139i | ||||||
\(439\) | −7.00345e6 | −1.73441 | −0.867203 | − | 0.497956i | \(-0.834084\pi\) | ||||
−0.867203 | + | 0.497956i | \(0.834084\pi\) | |||||||
\(440\) | 990100. | − | 692484.i | 0.243808 | − | 0.170521i | ||||
\(441\) | 665106. | 0.162853 | ||||||||
\(442\) | − | 39550.1i | − | 0.00962924i | ||||||
\(443\) | 1.09721e6i | 0.265633i | 0.991141 | + | 0.132816i | \(0.0424020\pi\) | ||||
−0.991141 | + | 0.132816i | \(0.957598\pi\) | |||||||
\(444\) | −28798.1 | −0.00693276 | ||||||||
\(445\) | 88896.9 | + | 127103.i | 0.0212807 | + | 0.0304268i | ||||
\(446\) | 4.88389e6 | 1.16260 | ||||||||
\(447\) | 967117.i | 0.228934i | ||||||||
\(448\) | 5.04332e6i | 1.18719i | ||||||||
\(449\) | 1.62691e6 | 0.380844 | 0.190422 | − | 0.981702i | \(-0.439014\pi\) | ||||
0.190422 | + | 0.981702i | \(0.439014\pi\) | |||||||
\(450\) | 1.36215e6 | + | 497437.i | 0.317098 | + | 0.115800i | ||||
\(451\) | −1.14402e6 | −0.264846 | ||||||||
\(452\) | 50929.2i | 0.0117252i | ||||||||
\(453\) | − | 216741.i | − | 0.0496245i | ||||||
\(454\) | 5.21177e6 | 1.18671 | ||||||||
\(455\) | −396506. | − | 566917.i | −0.0897887 | − | 0.128378i | ||||
\(456\) | −2.99889e6 | −0.675380 | ||||||||
\(457\) | − | 857428.i | − | 0.192047i | −0.995379 | − | 0.0960235i | \(-0.969388\pi\) | ||
0.995379 | − | 0.0960235i | \(-0.0306124\pi\) | |||||||
\(458\) | 3.21829e6i | 0.716905i | ||||||||
\(459\) | −64322.6 | −0.0142505 | ||||||||
\(460\) | −18912.6 | + | 13227.6i | −0.00416731 | + | 0.00291465i | ||||
\(461\) | −5.70696e6 | −1.25070 | −0.625349 | − | 0.780345i | \(-0.715043\pi\) | ||||
−0.625349 | + | 0.780345i | \(0.715043\pi\) | |||||||
\(462\) | − | 986800.i | − | 0.215092i | ||||||
\(463\) | − | 5.95157e6i | − | 1.29027i | −0.764070 | − | 0.645133i | \(-0.776802\pi\) | ||
0.764070 | − | 0.645133i | \(-0.223198\pi\) | |||||||
\(464\) | 1.10230e6 | 0.237686 | ||||||||
\(465\) | 3.73426e6 | − | 2.61177e6i | 0.800888 | − | 0.560148i | ||||
\(466\) | −3.46402e6 | −0.738950 | ||||||||
\(467\) | − | 5.25283e6i | − | 1.11455i | −0.830326 | − | 0.557277i | \(-0.811846\pi\) | ||
0.830326 | − | 0.557277i | \(-0.188154\pi\) | |||||||
\(468\) | 5200.54i | 0.00109757i | ||||||||
\(469\) | −2.66992e6 | −0.560488 | ||||||||
\(470\) | 1.73114e6 | + | 2.47515e6i | 0.361483 | + | 0.516841i | ||||
\(471\) | −4.31737e6 | −0.896740 | ||||||||
\(472\) | − | 1.76975e6i | − | 0.365643i | ||||||
\(473\) | − | 1.07918e6i | − | 0.221789i | ||||||
\(474\) | −5.38709e6 | −1.10131 | ||||||||
\(475\) | 1.99966e6 | − | 5.47574e6i | 0.406652 | − | 1.11355i | ||||
\(476\) | −11452.2 | −0.00231670 | ||||||||
\(477\) | 2.06611e6i | 0.415774i | ||||||||
\(478\) | 6.51361e6i | 1.30392i | ||||||||
\(479\) | −8.82420e6 | −1.75726 | −0.878631 | − | 0.477502i | \(-0.841542\pi\) | ||||
−0.878631 | + | 0.477502i | \(0.841542\pi\) | |||||||
\(480\) | 85644.4 | + | 122453.i | 0.0169666 | + | 0.0242586i | ||||
\(481\) | −305095. | −0.0601275 | ||||||||
\(482\) | 1.49754e6i | 0.293602i | ||||||||
\(483\) | − | 716216.i | − | 0.139693i | ||||||
\(484\) | −12014.2 | −0.00233121 | ||||||||
\(485\) | 5.74451e6 | − | 4.01776e6i | 1.10892 | − | 0.775585i | ||||
\(486\) | 338287. | 0.0649673 | ||||||||
\(487\) | 5.99283e6i | 1.14501i | 0.819901 | + | 0.572506i | \(0.194029\pi\) | ||||
−0.819901 | + | 0.572506i | \(0.805971\pi\) | |||||||
\(488\) | − | 2.78911e6i | − | 0.530170i | ||||||
\(489\) | −3.93328e6 | −0.743846 | ||||||||
\(490\) | −2.15492e6 | + | 1.50717e6i | −0.405454 | + | 0.283578i | ||||
\(491\) | 6.17263e6 | 1.15549 | 0.577745 | − | 0.816217i | \(-0.303933\pi\) | ||||
0.577745 | + | 0.816217i | \(0.303933\pi\) | |||||||
\(492\) | − | 69825.8i | − | 0.0130048i | ||||||
\(493\) | − | 92665.3i | − | 0.0171712i | ||||||
\(494\) | 836159. | 0.154160 | ||||||||
\(495\) | 314017. | + | 448976.i | 0.0576024 | + | 0.0823588i | ||||
\(496\) | 9.50663e6 | 1.73509 | ||||||||
\(497\) | − | 1.13041e7i | − | 2.05280i | ||||||
\(498\) | 797013.i | 0.144010i | ||||||||
\(499\) | 2.47210e6 | 0.444441 | 0.222221 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222221 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(500\) | −138526. | + | 36879.0i | −0.0247802 | + | 0.00659711i | ||||
\(501\) | −5.33333e6 | −0.949301 | ||||||||
\(502\) | 3.23899e6i | 0.573655i | ||||||||
\(503\) | 8.18126e6i | 1.44178i | 0.693047 | + | 0.720892i | \(0.256268\pi\) | ||||
−0.693047 | + | 0.720892i | \(0.743732\pi\) | |||||||
\(504\) | −2.28852e6 | −0.401308 | ||||||||
\(505\) | −1.63352e6 | − | 2.33557e6i | −0.285034 | − | 0.407535i | ||||
\(506\) | −348764. | −0.0605558 | ||||||||
\(507\) | − | 3.28654e6i | − | 0.567831i | ||||||
\(508\) | − | 234003.i | − | 0.0402312i | ||||||
\(509\) | −1.19487e6 | −0.204421 | −0.102211 | − | 0.994763i | \(-0.532592\pi\) | ||||
−0.102211 | + | 0.994763i | \(0.532592\pi\) | |||||||
\(510\) | 208403. | − | 145759.i | 0.0354796 | − | 0.0248147i | ||||
\(511\) | −1.03971e7 | −1.76141 | ||||||||
\(512\) | − | 5.68768e6i | − | 0.958870i | ||||||
\(513\) | − | 1.35989e6i | − | 0.228145i | ||||||
\(514\) | 8.70486e6 | 1.45330 | ||||||||
\(515\) | 2.35756e6 | − | 1.64890e6i | 0.391692 | − | 0.273953i | ||||
\(516\) | 65867.8 | 0.0108905 | ||||||||
\(517\) | 1.14120e6i | 0.187774i | ||||||||
\(518\) | 3.53344e6i | 0.578593i | ||||||||
\(519\) | −1.74109e6 | −0.283728 | ||||||||
\(520\) | 447779. | + | 640225.i | 0.0726198 | + | 0.103830i | ||||
\(521\) | 1.09929e6 | 0.177426 | 0.0887128 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887128 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(522\) | 487349.i | 0.0782823i | ||||||||
\(523\) | − | 7.07488e6i | − | 1.13101i | −0.824746 | − | 0.565503i | \(-0.808682\pi\) | ||
0.824746 | − | 0.565503i | \(-0.191318\pi\) | |||||||
\(524\) | 162774. | 0.0258974 | ||||||||
\(525\) | 1.52598e6 | − | 4.17865e6i | 0.241631 | − | 0.661665i | ||||
\(526\) | −4.18424e6 | −0.659404 | ||||||||
\(527\) | − | 799180.i | − | 0.125348i | ||||||
\(528\) | 1.14300e6i | 0.178427i | ||||||||
\(529\) | 6.18321e6 | 0.960671 | ||||||||
\(530\) | −4.68193e6 | − | 6.69413e6i | −0.723994 | − | 1.03515i | ||||
\(531\) | 802521. | 0.123515 | ||||||||
\(532\) | − | 242119.i | − | 0.0370894i | ||||||
\(533\) | − | 739755.i | − | 0.112790i | ||||||
\(534\) | −143060. | −0.0217103 | ||||||||
\(535\) | 6.39748e6 | − | 4.47445e6i | 0.966327 | − | 0.675857i | ||||
\(536\) | 3.01517e6 | 0.453315 | ||||||||
\(537\) | − | 3.36361e6i | − | 0.503350i | ||||||
\(538\) | 2.72274e6i | 0.405555i | ||||||||
\(539\) | −993554. | −0.147306 | ||||||||
\(540\) | −27403.4 | + | 19166.2i | −0.00404408 | + | 0.00282847i | ||||
\(541\) | −3.53440e6 | −0.519186 | −0.259593 | − | 0.965718i | \(-0.583588\pi\) | ||||
−0.259593 | + | 0.965718i | \(0.583588\pi\) | |||||||
\(542\) | − | 5.50729e6i | − | 0.805267i | ||||||
\(543\) | 2.11398e6i | 0.307682i | ||||||||
\(544\) | 26206.5 | 0.00379675 | ||||||||
\(545\) | 4.61477e6 | + | 6.59810e6i | 0.665516 | + | 0.951542i | ||||
\(546\) | 638091. | 0.0916011 | ||||||||
\(547\) | 1.37763e6i | 0.196863i | 0.995144 | + | 0.0984316i | \(0.0313826\pi\) | ||||
−0.995144 | + | 0.0984316i | \(0.968617\pi\) | |||||||
\(548\) | 136487.i | 0.0194151i | ||||||||
\(549\) | 1.26476e6 | 0.179093 | ||||||||
\(550\) | −2.03481e6 | − | 743085.i | −0.286826 | − | 0.104745i | ||||
\(551\) | 1.95911e6 | 0.274903 | ||||||||
\(552\) | 808829.i | 0.112982i | ||||||||
\(553\) | 1.65260e7i | 2.29802i | ||||||||
\(554\) | −2.45347e6 | −0.339630 | ||||||||
\(555\) | −1.12440e6 | − | 1.60765e6i | −0.154950 | − | 0.221544i | ||||
\(556\) | −247027. | −0.0338889 | ||||||||
\(557\) | 9.57607e6i | 1.30782i | 0.756571 | + | 0.653912i | \(0.226873\pi\) | ||||
−0.756571 | + | 0.653912i | \(0.773127\pi\) | |||||||
\(558\) | 4.20308e6i | 0.571455i | ||||||||
\(559\) | 697823. | 0.0944530 | ||||||||
\(560\) | 7.60498e6 | − | 5.31899e6i | 1.02477 | − | 0.716736i | ||||
\(561\) | 96086.8 | 0.0128901 | ||||||||
\(562\) | − | 1.21884e6i | − | 0.162782i | ||||||
\(563\) | − | 4.58027e6i | − | 0.609003i | −0.952512 | − | 0.304502i | \(-0.901510\pi\) | ||
0.952512 | − | 0.304502i | \(-0.0984899\pi\) | |||||||
\(564\) | −69653.5 | −0.00922031 | ||||||||
\(565\) | −2.84312e6 | + | 1.98850e6i | −0.374692 | + | 0.262062i | ||||
\(566\) | −3.23033e6 | −0.423844 | ||||||||
\(567\) | − | 1.03776e6i | − | 0.135563i | ||||||
\(568\) | 1.27659e7i | 1.66027i | ||||||||
\(569\) | 943189. | 0.122129 | 0.0610644 | − | 0.998134i | \(-0.480550\pi\) | ||||
0.0610644 | + | 0.998134i | \(0.480550\pi\) | |||||||
\(570\) | 3.08160e6 | + | 4.40600e6i | 0.397273 | + | 0.568012i | ||||
\(571\) | −581249. | −0.0746057 | −0.0373029 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373029 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(572\) | − | 7768.70i | − | 0.000992792i | ||||||
\(573\) | − | 2.35363e6i | − | 0.299469i | ||||||
\(574\) | −8.56742e6 | −1.08535 | ||||||||
\(575\) | −1.47686e6 | − | 539328.i | −0.186281 | − | 0.0680273i | ||||
\(576\) | 2.58270e6 | 0.324353 | ||||||||
\(577\) | − | 3.08163e6i | − | 0.385338i | −0.981264 | − | 0.192669i | \(-0.938286\pi\) | ||
0.981264 | − | 0.192669i | \(-0.0617143\pi\) | |||||||
\(578\) | 8.08965e6i | 1.00719i | ||||||||
\(579\) | −6.20079e6 | −0.768689 | ||||||||
\(580\) | −27611.5 | − | 39478.3i | −0.00340816 | − | 0.00487291i | ||||
\(581\) | 2.44499e6 | 0.300495 | ||||||||
\(582\) | 6.46571e6i | 0.791241i | ||||||||
\(583\) | − | 3.08641e6i | − | 0.376082i | ||||||
\(584\) | 1.17415e7 | 1.42460 | ||||||||
\(585\) | −290320. | + | 203052.i | −0.0350741 | + | 0.0245311i | ||||
\(586\) | 1.03671e7 | 1.24713 | ||||||||
\(587\) | 5.79374e6i | 0.694007i | 0.937864 | + | 0.347004i | \(0.112801\pi\) | ||||
−0.937864 | + | 0.347004i | \(0.887199\pi\) | |||||||
\(588\) | − | 60641.9i | − | 0.00723318i | ||||||
\(589\) | 1.68961e7 | 2.00677 | ||||||||
\(590\) | −2.60014e6 | + | 1.81856e6i | −0.307515 | + | 0.215079i | ||||
\(591\) | 5.62557e6 | 0.662518 | ||||||||
\(592\) | − | 4.09274e6i | − | 0.479966i | ||||||
\(593\) | 1.14174e7i | 1.33331i | 0.745366 | + | 0.666656i | \(0.232275\pi\) | ||||
−0.745366 | + | 0.666656i | \(0.767725\pi\) | |||||||
\(594\) | −505343. | −0.0587652 | ||||||||
\(595\) | −447144. | − | 639317.i | −0.0517791 | − | 0.0740327i | ||||
\(596\) | 88178.1 | 0.0101682 | ||||||||
\(597\) | 9.18168e6i | 1.05435i | ||||||||
\(598\) | − | 225520.i | − | 0.0257889i | ||||||
\(599\) | −1.33518e7 | −1.52045 | −0.760224 | − | 0.649661i | \(-0.774911\pi\) | ||||
−0.760224 | + | 0.649661i | \(0.774911\pi\) | |||||||
\(600\) | −1.72331e6 | + | 4.71900e6i | −0.195427 | + | 0.535145i | ||||
\(601\) | 1774.23 | 0.000200366 | 0.000100183 | − | 1.00000i | \(-0.499968\pi\) | ||||
0.000100183 | 1.00000i | \(0.499968\pi\) | ||||||||
\(602\) | − | 8.08179e6i | − | 0.908901i | ||||||
\(603\) | 1.36727e6i | 0.153131i | ||||||||
\(604\) | −19761.7 | −0.00220410 | ||||||||
\(605\) | −469088. | − | 670692.i | −0.0521034 | − | 0.0744963i | ||||
\(606\) | 2.62879e6 | 0.290787 | ||||||||
\(607\) | − | 2.48398e6i | − | 0.273638i | −0.990596 | − | 0.136819i | \(-0.956312\pi\) | ||
0.990596 | − | 0.136819i | \(-0.0436879\pi\) | |||||||
\(608\) | 554051.i | 0.0607842i | ||||||||
\(609\) | 1.49504e6 | 0.163346 | ||||||||
\(610\) | −4.09779e6 | + | 2.86603e6i | −0.445887 | + | 0.311857i | ||||
\(611\) | −737930. | −0.0799672 | ||||||||
\(612\) | 5864.69i | 0.000632946i | ||||||||
\(613\) | − | 3.19717e6i | − | 0.343649i | −0.985128 | − | 0.171824i | \(-0.945034\pi\) | ||
0.985128 | − | 0.171824i | \(-0.0549662\pi\) | |||||||
\(614\) | 4.43447e6 | 0.474702 | ||||||||
\(615\) | 3.89802e6 | − | 2.72631e6i | 0.415582 | − | 0.290661i | ||||
\(616\) | 3.41865e6 | 0.362997 | ||||||||
\(617\) | − | 3.43973e6i | − | 0.363757i | −0.983321 | − | 0.181878i | \(-0.941782\pi\) | ||
0.983321 | − | 0.181878i | \(-0.0582177\pi\) | |||||||
\(618\) | 2.65354e6i | 0.279483i | ||||||||
\(619\) | 580297. | 0.0608729 | 0.0304364 | − | 0.999537i | \(-0.490310\pi\) | ||||
0.0304364 | + | 0.999537i | \(0.490310\pi\) | |||||||
\(620\) | −238131. | − | 340476.i | −0.0248793 | − | 0.0355719i | ||||
\(621\) | −366776. | −0.0381656 | ||||||||
\(622\) | 7.78035e6i | 0.806349i | ||||||||
\(623\) | 438865.i | 0.0453013i | ||||||||
\(624\) | −739093. | −0.0759867 | ||||||||
\(625\) | −7.46742e6 | − | 6.29326e6i | −0.764663 | − | 0.644430i | ||||
\(626\) | 1.93818e7 | 1.97678 | ||||||||
\(627\) | 2.03144e6i | 0.206365i | ||||||||
\(628\) | 393641.i | 0.0398292i | ||||||||
\(629\) | −344059. | −0.0346742 | ||||||||
\(630\) | 2.35163e6 | + | 3.36232e6i | 0.236058 | + | 0.337511i | ||||
\(631\) | −1.94969e7 | −1.94936 | −0.974680 | − | 0.223604i | \(-0.928218\pi\) | ||||
−0.974680 | + | 0.223604i | \(0.928218\pi\) | |||||||
\(632\) | − | 1.86629e7i | − | 1.85861i | ||||||
\(633\) | 4.89890e6i | 0.485947i | ||||||||
\(634\) | −3.82772e6 | −0.378196 | ||||||||
\(635\) | 1.30632e7 | − | 9.13653e6i | 1.28563 | − | 0.899181i | ||||
\(636\) | 188380. | 0.0184668 | ||||||||
\(637\) | − | 642458.i | − | 0.0627330i | ||||||
\(638\) | − | 728015.i | − | 0.0708090i | ||||||
\(639\) | −5.78888e6 | −0.560845 | ||||||||
\(640\) | −8.80325e6 | + | 6.15707e6i | −0.849558 | + | 0.594188i | ||||
\(641\) | −1.50533e7 | −1.44706 | −0.723530 | − | 0.690293i | \(-0.757482\pi\) | ||||
−0.723530 | + | 0.690293i | \(0.757482\pi\) | |||||||
\(642\) | 7.20065e6i | 0.689500i | ||||||||
\(643\) | − | 1.34527e7i | − | 1.28316i | −0.767056 | − | 0.641580i | \(-0.778279\pi\) | ||
0.767056 | − | 0.641580i | \(-0.221721\pi\) | |||||||
\(644\) | −65301.9 | −0.00620456 | ||||||||
\(645\) | 2.57177e6 | + | 3.67707e6i | 0.243407 | + | 0.348019i | ||||
\(646\) | 942943. | 0.0889005 | ||||||||
\(647\) | 1.15666e7i | 1.08629i | 0.839638 | + | 0.543146i | \(0.182767\pi\) | ||||
−0.839638 | + | 0.543146i | \(0.817233\pi\) | |||||||
\(648\) | 1.17196e6i | 0.109641i | ||||||||
\(649\) | −1.19883e6 | −0.111724 | ||||||||
\(650\) | 480498. | − | 1.31576e6i | 0.0446076 | − | 0.122150i | ||||
\(651\) | 1.28938e7 | 1.19241 | ||||||||
\(652\) | 358622.i | 0.0330383i | ||||||||
\(653\) | 8.60996e6i | 0.790165i | 0.918646 | + | 0.395083i | \(0.129284\pi\) | ||||
−0.918646 | + | 0.395083i | \(0.870716\pi\) | |||||||
\(654\) | −7.42646e6 | −0.678950 | ||||||||
\(655\) | 6.35541e6 | + | 9.08684e6i | 0.578816 | + | 0.827580i | ||||
\(656\) | 9.92354e6 | 0.900341 | ||||||||
\(657\) | 5.32438e6i | 0.481233i | ||||||||
\(658\) | 8.54628e6i | 0.769507i | ||||||||
\(659\) | 3.14337e6 | 0.281957 | 0.140978 | − | 0.990013i | \(-0.454975\pi\) | ||||
0.140978 | + | 0.990013i | \(0.454975\pi\) | |||||||
\(660\) | 40935.9 | − | 28630.9i | 0.00365801 | − | 0.00255844i | ||||
\(661\) | −2.75239e6 | −0.245023 | −0.122511 | − | 0.992467i | \(-0.539095\pi\) | ||||
−0.122511 | + | 0.992467i | \(0.539095\pi\) | |||||||
\(662\) | 543584.i | 0.0482083i | ||||||||
\(663\) | 62132.2i | 0.00548951i | ||||||||
\(664\) | −2.76116e6 | −0.243036 | ||||||||
\(665\) | 1.35163e7 | − | 9.45340e6i | 1.18523 | − | 0.828961i | ||||
\(666\) | 1.80948e6 | 0.158077 | ||||||||
\(667\) | − | 528390.i | − | 0.0459876i | ||||||
\(668\) | 486273.i | 0.0421637i | ||||||||
\(669\) | −7.67247e6 | −0.662781 | ||||||||
\(670\) | −3.09833e6 | − | 4.42992e6i | −0.266649 | − | 0.381250i | ||||
\(671\) | −1.88934e6 | −0.161996 | ||||||||
\(672\) | 422808.i | 0.0361177i | ||||||||
\(673\) | 1.66398e7i | 1.41615i | 0.706136 | + | 0.708076i | \(0.250437\pi\) | ||||
−0.706136 | + | 0.708076i | \(0.749563\pi\) | |||||||
\(674\) | −2.90639e6 | −0.246436 | ||||||||
\(675\) | −2.13990e6 | − | 781461.i | −0.180773 | − | 0.0660158i | ||||
\(676\) | −299655. | −0.0252205 | ||||||||
\(677\) | 1.05991e7i | 0.888789i | 0.895831 | + | 0.444395i | \(0.146581\pi\) | ||||
−0.895831 | + | 0.444395i | \(0.853419\pi\) | |||||||
\(678\) | − | 3.20006e6i | − | 0.267352i | ||||||
\(679\) | 1.98348e7 | 1.65103 | ||||||||
\(680\) | 504964. | + | 721987.i | 0.0418782 | + | 0.0598766i | ||||
\(681\) | −8.18756e6 | −0.676529 | ||||||||
\(682\) | − | 6.27867e6i | − | 0.516900i | ||||||
\(683\) | − | 544094.i | − | 0.0446296i | −0.999751 | − | 0.0223148i | \(-0.992896\pi\) | ||
0.999751 | − | 0.0223148i | \(-0.00710360\pi\) | |||||||
\(684\) | −123990. | −0.0101332 | ||||||||
\(685\) | −7.61937e6 | + | 5.32905e6i | −0.620429 | + | 0.433933i | ||||
\(686\) | 7.78911e6 | 0.631943 | ||||||||
\(687\) | − | 5.05586e6i | − | 0.408698i | ||||||
\(688\) | 9.36104e6i | 0.753969i | ||||||||
\(689\) | 1.99575e6 | 0.160162 | ||||||||
\(690\) | 1.18834e6 | − | 831137.i | 0.0950208 | − | 0.0664584i | ||||
\(691\) | −7.88699e6 | −0.628371 | −0.314185 | − | 0.949362i | \(-0.601731\pi\) | ||||
−0.314185 | + | 0.949362i | \(0.601731\pi\) | |||||||
\(692\) | 158746.i | 0.0126020i | ||||||||
\(693\) | 1.55024e6i | 0.122621i | ||||||||
\(694\) | −1.67210e7 | −1.31784 | ||||||||
\(695\) | −9.64502e6 | − | 1.37903e7i | −0.757428 | − | 1.08296i | ||||
\(696\) | −1.68836e6 | −0.132112 | ||||||||
\(697\) | − | 834228.i | − | 0.0650433i | ||||||
\(698\) | 9.71616e6i | 0.754842i | ||||||||
\(699\) | 5.44188e6 | 0.421266 | ||||||||
\(700\) | −380994. | − | 139134.i | −0.0293882 | − | 0.0107322i | ||||
\(701\) | 2.22952e7 | 1.71363 | 0.856814 | − | 0.515625i | \(-0.172440\pi\) | ||||
0.856814 | + | 0.515625i | \(0.172440\pi\) | |||||||
\(702\) | − | 326768.i | − | 0.0250263i | ||||||
\(703\) | − | 7.27400e6i | − | 0.555118i | ||||||
\(704\) | −3.85811e6 | −0.293388 | ||||||||
\(705\) | −2.71958e6 | − | 3.88840e6i | −0.206077 | − | 0.294645i | ||||
\(706\) | −1.45898e7 | −1.10163 | ||||||||
\(707\) | − | 8.06434e6i | − | 0.606765i | ||||||
\(708\) | − | 73170.9i | − | 0.00548599i | ||||||
\(709\) | 8.40301e6 | 0.627797 | 0.313899 | − | 0.949457i | \(-0.398365\pi\) | ||||
0.313899 | + | 0.949457i | \(0.398365\pi\) | |||||||
\(710\) | 1.87558e7 | − | 1.31180e7i | 1.39633 | − | 0.976608i | ||||
\(711\) | 8.46299e6 | 0.627841 | ||||||||
\(712\) | − | 495615.i | − | 0.0366390i | ||||||
\(713\) | − | 4.55703e6i | − | 0.335706i | ||||||
\(714\) | 719580. | 0.0528243 | ||||||||
\(715\) | 433687. | − | 303325.i | 0.0317257 | − | 0.0221892i | ||||
\(716\) | −306682. | −0.0223566 | ||||||||
\(717\) | − | 1.02327e7i | − | 0.743350i | ||||||
\(718\) | 2.43695e6i | 0.176415i | ||||||||
\(719\) | −1.39897e7 | −1.00922 | −0.504612 | − | 0.863346i | \(-0.668364\pi\) | ||||
−0.504612 | + | 0.863346i | \(0.668364\pi\) | |||||||
\(720\) | −2.72387e6 | − | 3.89453e6i | −0.195819 | − | 0.279978i | ||||
\(721\) | 8.14027e6 | 0.583177 | ||||||||
\(722\) | 5.75009e6i | 0.410517i | ||||||||
\(723\) | − | 2.35259e6i | − | 0.167379i | ||||||
\(724\) | 192745. | 0.0136659 | ||||||||
\(725\) | 1.12580e6 | − | 3.08282e6i | 0.0795456 | − | 0.217822i | ||||
\(726\) | 754895. | 0.0531551 | ||||||||
\(727\) | − | 1.69990e7i | − | 1.19286i | −0.802666 | − | 0.596428i | \(-0.796586\pi\) | ||
0.802666 | − | 0.596428i | \(-0.203414\pi\) | |||||||
\(728\) | 2.21059e6i | 0.154589i | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | −1.20654e7 | − | 1.72508e7i | −0.837979 | − | 1.19813i | ||||
\(731\) | 786941. | 0.0544689 | ||||||||
\(732\) | − | 115316.i | − | 0.00795450i | ||||||
\(733\) | 9.14170e6i | 0.628445i | 0.949349 | + | 0.314222i | \(0.101744\pi\) | ||||
−0.949349 | + | 0.314222i | \(0.898256\pi\) | |||||||
\(734\) | 1.08060e7 | 0.740332 | ||||||||
\(735\) | 3.38533e6 | − | 2.36773e6i | 0.231144 | − | 0.161664i | ||||
\(736\) | 149433. | 0.0101684 | ||||||||
\(737\) | − | 2.04247e6i | − | 0.138512i | ||||||
\(738\) | 4.38740e6i | 0.296528i | ||||||||
\(739\) | 1.54222e7 | 1.03881 | 0.519405 | − | 0.854528i | \(-0.326154\pi\) | ||||
0.519405 | + | 0.854528i | \(0.326154\pi\) | |||||||
\(740\) | −146580. | + | 102519.i | −0.00983998 | + | 0.00688217i | ||||
\(741\) | −1.31358e6 | −0.0878845 | ||||||||
\(742\) | − | 2.31137e7i | − | 1.54120i | ||||||
\(743\) | − | 2.34940e7i | − | 1.56129i | −0.624973 | − | 0.780646i | \(-0.714890\pi\) | ||
0.624973 | − | 0.780646i | \(-0.285110\pi\) | |||||||
\(744\) | −1.45610e7 | −0.964407 | ||||||||
\(745\) | 3.44286e6 | + | 4.92254e6i | 0.227263 | + | 0.324936i | ||||
\(746\) | 5.17484e6 | 0.340447 | ||||||||
\(747\) | − | 1.25209e6i | − | 0.0820981i | ||||||
\(748\) | − | 8760.83i | − | 0.000572521i | ||||||
\(749\) | 2.20894e7 | 1.43873 | ||||||||
\(750\) | 8.70405e6 | − | 2.31723e6i | 0.565025 | − | 0.150424i | ||||
\(751\) | 9.67937e6 | 0.626250 | 0.313125 | − | 0.949712i | \(-0.398624\pi\) | ||||
0.313125 | + | 0.949712i | \(0.398624\pi\) | |||||||
\(752\) | − | 9.89906e6i | − | 0.638336i | ||||||
\(753\) | − | 5.08838e6i | − | 0.327033i | ||||||
\(754\) | 470754. | 0.0301554 | ||||||||
\(755\) | −771583. | − | 1.10319e6i | −0.0492624 | − | 0.0704343i | ||||
\(756\) | −94619.3 | −0.00602109 | ||||||||
\(757\) | 6.06490e6i | 0.384666i | 0.981330 | + | 0.192333i | \(0.0616054\pi\) | ||||
−0.981330 | + | 0.192333i | \(0.938395\pi\) | |||||||
\(758\) | − | 2.83485e7i | − | 1.79208i | ||||||
\(759\) | 547900. | 0.0345221 | ||||||||
\(760\) | −1.52641e7 | + | 1.06758e7i | −0.958598 | + | 0.670451i | ||||
\(761\) | −2.42020e7 | −1.51492 | −0.757461 | − | 0.652880i | \(-0.773561\pi\) | ||||
−0.757461 | + | 0.652880i | \(0.773561\pi\) | |||||||
\(762\) | 1.47033e7i | 0.917331i | ||||||||
\(763\) | 2.27821e7i | 1.41672i | ||||||||
\(764\) | −214595. | −0.0133011 | ||||||||
\(765\) | −327396. | + | 228983.i | −0.0202265 | + | 0.0141466i | ||||
\(766\) | −9.33665e6 | −0.574936 | ||||||||
\(767\) | − | 775193.i | − | 0.0475797i | ||||||
\(768\) | − | 725529.i | − | 0.0443866i | ||||||
\(769\) | −3.47840e6 | −0.212111 | −0.106055 | − | 0.994360i | \(-0.533822\pi\) | ||||
−0.106055 | + | 0.994360i | \(0.533822\pi\) | |||||||
\(770\) | −3.51293e6 | − | 5.02272e6i | −0.213522 | − | 0.305290i | ||||
\(771\) | −1.36751e7 | −0.828506 | ||||||||
\(772\) | 565365.i | 0.0341418i | ||||||||
\(773\) | − | 1.02630e7i | − | 0.617769i | −0.951100 | − | 0.308884i | \(-0.900044\pi\) | ||
0.951100 | − | 0.308884i | \(-0.0999556\pi\) | |||||||
\(774\) | −4.13871e6 | −0.248320 | ||||||||
\(775\) | 9.70932e6 | − | 2.65873e7i | 0.580677 | − | 1.59009i | ||||
\(776\) | −2.23997e7 | −1.33533 | ||||||||
\(777\) | − | 5.55095e6i | − | 0.329849i | ||||||
\(778\) | − | 3.05672e7i | − | 1.81053i | ||||||
\(779\) | 1.76370e7 | 1.04131 | ||||||||
\(780\) | 18513.5 | + | 26470.3i | 0.00108956 | + | 0.00155784i | ||||
\(781\) | 8.64759e6 | 0.507303 | ||||||||
\(782\) | − | 254321.i | − | 0.0148719i | ||||||
\(783\) | − | 765613.i | − | 0.0446277i | ||||||
\(784\) | 8.61834e6 | 0.500764 | ||||||||
\(785\) | −2.19750e7 | + | 1.53695e7i | −1.27278 | + | 0.890196i | ||||
\(786\) | −1.02277e7 | −0.590500 | ||||||||
\(787\) | − | 2.49651e7i | − | 1.43680i | −0.695629 | − | 0.718401i | \(-0.744874\pi\) | ||
0.695629 | − | 0.718401i | \(-0.255126\pi\) | |||||||
\(788\) | − | 512919.i | − | 0.0294261i | ||||||
\(789\) | 6.57333e6 | 0.375918 | ||||||||
\(790\) | −2.74198e7 | + | 1.91776e7i | −1.56314 | + | 1.09327i | ||||
\(791\) | −9.81681e6 | −0.557865 | ||||||||
\(792\) | − | 1.75070e6i | − | 0.0991742i | ||||||
\(793\) | − | 1.22169e6i | − | 0.0689890i | ||||||
\(794\) | −2.23050e7 | −1.25560 | ||||||||
\(795\) | 7.35519e6 | + | 1.05163e7i | 0.412740 | + | 0.590127i | ||||
\(796\) | 837151. | 0.0468297 | ||||||||
\(797\) | 2.85688e7i | 1.59311i | 0.604564 | + | 0.796557i | \(0.293347\pi\) | ||||
−0.604564 | + | 0.796557i | \(0.706653\pi\) | |||||||
\(798\) | 1.52132e7i | 0.845694i | ||||||||
\(799\) | −832170. | −0.0461153 | ||||||||
\(800\) | 871845. | + | 318385.i | 0.0481631 | + | 0.0175885i | ||||
\(801\) | 224744. | 0.0123768 | ||||||||
\(802\) | 2.29992e6i | 0.126263i | ||||||||
\(803\) | − | 7.95370e6i | − | 0.435292i | ||||||
\(804\) | 124663. | 0.00680138 | ||||||||
\(805\) | −2.54967e6 | − | 3.64547e6i | −0.138674 | − | 0.198273i | ||||
\(806\) | 4.05995e6 | 0.220132 | ||||||||
\(807\) | − | 4.27735e6i | − | 0.231202i | ||||||
\(808\) | 9.10714e6i | 0.490743i | ||||||||
\(809\) | −1.00028e7 | −0.537340 | −0.268670 | − | 0.963232i | \(-0.586584\pi\) | ||||
−0.268670 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(810\) | 1.72185e6 | − | 1.20428e6i | 0.0922111 | − | 0.0644932i | ||||
\(811\) | −7.88288e6 | −0.420855 | −0.210428 | − | 0.977609i | \(-0.567486\pi\) | ||||
−0.210428 | + | 0.977609i | \(0.567486\pi\) | |||||||
\(812\) | − | 136312.i | − | 0.00725511i | ||||||
\(813\) | 8.65181e6i | 0.459072i | ||||||||
\(814\) | −2.70306e6 | −0.142986 | ||||||||
\(815\) | −2.00201e7 | + | 1.40022e7i | −1.05578 | + | 0.738418i | ||||
\(816\) | −833482. | −0.0438198 | ||||||||
\(817\) | 1.66373e7i | 0.872023i | ||||||||
\(818\) | 3.39430e7i | 1.77364i | ||||||||
\(819\) | −1.00242e6 | −0.0522206 | ||||||||
\(820\) | −248575. | − | 355407.i | −0.0129099 | − | 0.0184583i | ||||
\(821\) | 1.84331e7 | 0.954423 | 0.477211 | − | 0.878789i | \(-0.341648\pi\) | ||||
0.477211 | + | 0.878789i | \(0.341648\pi\) | |||||||
\(822\) | − | 8.57594e6i | − | 0.442693i | ||||||
\(823\) | 1.93527e7i | 0.995961i | 0.867188 | + | 0.497981i | \(0.165925\pi\) | ||||
−0.867188 | + | 0.497981i | \(0.834075\pi\) | |||||||
\(824\) | −9.19288e6 | −0.471665 | ||||||||
\(825\) | 3.19664e6 | + | 1.16737e6i | 0.163516 | + | 0.0597135i | ||||
\(826\) | −8.97785e6 | −0.457849 | ||||||||
\(827\) | − | 1.33049e7i | − | 0.676471i | −0.941062 | − | 0.338235i | \(-0.890170\pi\) | ||
0.941062 | − | 0.338235i | \(-0.109830\pi\) | |||||||
\(828\) | 33441.3i | 0.00169515i | ||||||||
\(829\) | 1.61482e7 | 0.816090 | 0.408045 | − | 0.912962i | \(-0.366211\pi\) | ||||
0.408045 | + | 0.912962i | \(0.366211\pi\) | |||||||
\(830\) | 2.83731e6 | + | 4.05672e6i | 0.142959 | + | 0.204400i | ||||
\(831\) | 3.85434e6 | 0.193619 | ||||||||
\(832\) | − | 2.49475e6i | − | 0.124945i | ||||||
\(833\) | − | 724505.i | − | 0.0361767i | ||||||
\(834\) | 1.55216e7 | 0.772717 | ||||||||
\(835\) | −2.71461e7 | + | 1.89862e7i | −1.34739 | + | 0.942373i | ||||
\(836\) | 185219. | 0.00916581 | ||||||||
\(837\) | − | 6.60293e6i | − | 0.325779i | ||||||
\(838\) | − | 2.42842e7i | − | 1.19458i | ||||||
\(839\) | −2.17566e7 | −1.06705 | −0.533527 | − | 0.845783i | \(-0.679134\pi\) | ||||
−0.533527 | + | 0.845783i | \(0.679134\pi\) | |||||||
\(840\) | −1.16483e7 | + | 8.14695e6i | −0.569595 | + | 0.398379i | ||||
\(841\) | −1.94082e7 | −0.946226 | ||||||||
\(842\) | 2.89072e7i | 1.40516i | ||||||||
\(843\) | 1.91477e6i | 0.0927998i | ||||||||
\(844\) | 446663. | 0.0215836 | ||||||||
\(845\) | −1.16998e7 | − | 1.67282e7i | −0.563687 | − | 0.805949i | ||||
\(846\) | 4.37658e6 | 0.210237 | ||||||||
\(847\) | − | 2.31579e6i | − | 0.110915i | ||||||
\(848\) | 2.67723e7i | 1.27849i | ||||||||
\(849\) | 5.07478e6 | 0.241628 | ||||||||
\(850\) | 541862. | − | 1.48380e6i | 0.0257242 | − | 0.0704413i | ||||
\(851\) | −1.96187e6 | −0.0928638 | ||||||||
\(852\) | 527809.i | 0.0249102i | ||||||||
\(853\) | 1.29447e7i | 0.609142i | 0.952490 | + | 0.304571i | \(0.0985130\pi\) | ||||
−0.952490 | + | 0.304571i | \(0.901487\pi\) | |||||||
\(854\) | −1.41490e7 | −0.663866 | ||||||||
\(855\) | −4.84111e6 | − | 6.92172e6i | −0.226480 | − | 0.323817i | ||||
\(856\) | −2.49458e7 | −1.16362 | ||||||||
\(857\) | 3.34203e7i | 1.55438i | 0.629264 | + | 0.777192i | \(0.283356\pi\) | ||||
−0.629264 | + | 0.777192i | \(0.716644\pi\) | |||||||
\(858\) | 488135.i | 0.0226371i | ||||||||
\(859\) | 4.22247e7 | 1.95247 | 0.976234 | − | 0.216719i | \(-0.0695356\pi\) | ||||
0.976234 | + | 0.216719i | \(0.0695356\pi\) | |||||||
\(860\) | 335261. | − | 234485.i | 0.0154574 | − | 0.0108111i | ||||
\(861\) | 1.34592e7 | 0.618745 | ||||||||
\(862\) | − | 4.23221e7i | − | 1.93999i | ||||||
\(863\) | 9.62825e6i | 0.440069i | 0.975492 | + | 0.220034i | \(0.0706169\pi\) | ||||
−0.975492 | + | 0.220034i | \(0.929383\pi\) | |||||||
\(864\) | 216521. | 0.00986771 | ||||||||
\(865\) | −8.86199e6 | + | 6.19815e6i | −0.402709 | + | 0.281658i | ||||
\(866\) | 9.54936e6 | 0.432693 | ||||||||
\(867\) | − | 1.27086e7i | − | 0.574185i | ||||||
\(868\) | − | 1.17560e6i | − | 0.0529617i | ||||||
\(869\) | −1.26422e7 | −0.567904 | ||||||||
\(870\) | 1.73492e6 | + | 2.48056e6i | 0.0777110 | + | 0.111110i | ||||
\(871\) | 1.32072e6 | 0.0589880 | ||||||||
\(872\) | − | 2.57281e7i | − | 1.14582i | ||||||
\(873\) | − | 1.01575e7i | − | 0.451076i | ||||||
\(874\) | 5.37679e6 | 0.238092 | ||||||||
\(875\) | −7.10857e6 | − | 2.67014e7i | −0.313879 | − | 1.17900i | ||||
\(876\) | 485457. | 0.0213742 | ||||||||
\(877\) | 1.37201e7i | 0.602362i | 0.953567 | + | 0.301181i | \(0.0973808\pi\) | ||||
−0.953567 | + | 0.301181i | \(0.902619\pi\) | |||||||
\(878\) | − | 4.01222e7i | − | 1.75650i | ||||||
\(879\) | −1.62865e7 | −0.710976 | ||||||||
\(880\) | 4.06899e6 | + | 5.81776e6i | 0.177125 | + | 0.253250i | ||||
\(881\) | 2.99671e7 | 1.30078 | 0.650392 | − | 0.759599i | \(-0.274605\pi\) | ||||
0.650392 | + | 0.759599i | \(0.274605\pi\) | |||||||
\(882\) | 3.81034e6i | 0.164927i | ||||||||
\(883\) | 6.57264e6i | 0.283686i | 0.989889 | + | 0.141843i | \(0.0453028\pi\) | ||||
−0.989889 | + | 0.141843i | \(0.954697\pi\) | |||||||
\(884\) | 5664.99 | 0.000243819 | ||||||||
\(885\) | 4.08476e6 | − | 2.85691e6i | 0.175311 | − | 0.122614i | ||||
\(886\) | −6.28585e6 | −0.269017 | ||||||||
\(887\) | 1.99178e7i | 0.850028i | 0.905187 | + | 0.425014i | \(0.139731\pi\) | ||||
−0.905187 | + | 0.425014i | \(0.860269\pi\) | |||||||
\(888\) | 6.26874e6i | 0.266777i | ||||||||
\(889\) | 4.51051e7 | 1.91413 | ||||||||
\(890\) | −728163. | + | 509284.i | −0.0308144 | + | 0.0215519i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 699548.i | 0.0294378i | ||||||||
\(893\) | − | 1.75935e7i | − | 0.738285i | ||||||
\(894\) | −5.54054e6 | −0.231851 | ||||||||
\(895\) | −1.19742e7 | − | 1.71205e7i | −0.499677 | − | 0.714428i | ||||
\(896\) | −3.03961e7 | −1.26488 | ||||||||
\(897\) | 354287.i | 0.0147019i | ||||||||
\(898\) | 9.32044e6i | 0.385696i | ||||||||
\(899\) | 9.51241e6 | 0.392547 | ||||||||
\(900\) | −71250.7 | + | 195108.i | −0.00293213 | + | 0.00802914i | ||||
\(901\) | 2.25063e6 | 0.0923617 | ||||||||
\(902\) | − | 6.55402e6i | − | 0.268220i | ||||||
\(903\) | 1.26963e7i | 0.518152i | ||||||||
\(904\) | 1.10862e7 | 0.451193 | ||||||||
\(905\) | 7.52563e6 | + | 1.07600e7i | 0.305437 | + | 0.436707i | ||||
\(906\) | 1.24170e6 | 0.0502568 | ||||||||
\(907\) | 4.17948e7i | 1.68696i | 0.537163 | + | 0.843478i | \(0.319496\pi\) | ||||
−0.537163 | + | 0.843478i | \(0.680504\pi\) | |||||||
\(908\) | 746511.i | 0.0300484i | ||||||||
\(909\) | −4.12977e6 | −0.165774 | ||||||||
\(910\) | 3.24782e6 | − | 2.27156e6i | 0.130014 | − | 0.0909326i | ||||
\(911\) | −2.46957e7 | −0.985882 | −0.492941 | − | 0.870063i | \(-0.664078\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(912\) | − | 1.76213e7i | − | 0.701536i | ||||||
\(913\) | 1.87040e6i | 0.0742605i | ||||||||
\(914\) | 4.91214e6 | 0.194494 | ||||||||
\(915\) | 6.43753e6 | − | 4.50246e6i | 0.254195 | − | 0.177786i | ||||
\(916\) | −460974. | −0.0181526 | ||||||||
\(917\) | 3.13753e7i | 1.23215i | ||||||||
\(918\) | − | 368499.i | − | 0.0144321i | ||||||
\(919\) | 2.76370e7 | 1.07945 | 0.539724 | − | 0.841842i | \(-0.318529\pi\) | ||||
0.539724 | + | 0.841842i | \(0.318529\pi\) | |||||||
\(920\) | 2.87937e6 | + | 4.11687e6i | 0.112157 | + | 0.160361i | ||||
\(921\) | −6.96644e6 | −0.270621 | ||||||||
\(922\) | − | 3.26947e7i | − | 1.26663i | ||||||
\(923\) | 5.59176e6i | 0.216045i | ||||||||
\(924\) | 141345. | 0.00544628 | ||||||||
\(925\) | −1.14462e7 | − | 4.18000e6i | −0.439854 | − | 0.160628i | ||||
\(926\) | 3.40961e7 | 1.30670 | ||||||||
\(927\) | − | 4.16865e6i | − | 0.159330i | ||||||
\(928\) | 311928.i | 0.0118901i | ||||||||
\(929\) | 2.99531e7 | 1.13868 | 0.569340 | − | 0.822102i | \(-0.307199\pi\) | ||||
0.569340 | + | 0.822102i | \(0.307199\pi\) | |||||||
\(930\) | 1.49626e7 | + | 2.13933e7i | 0.567284 | + | 0.811092i | ||||
\(931\) | 1.53173e7 | 0.579173 | ||||||||
\(932\) | − | 496171.i | − | 0.0187108i | ||||||
\(933\) | − | 1.22227e7i | − | 0.459689i | ||||||
\(934\) | 3.00931e7 | 1.12875 | ||||||||
\(935\) | 489073. | − | 342062.i | 0.0182955 | − | 0.0127960i | ||||
\(936\) | 1.13205e6 | 0.0422353 | ||||||||
\(937\) | 3.96082e7i | 1.47379i | 0.676006 | + | 0.736896i | \(0.263709\pi\) | ||||
−0.676006 | + | 0.736896i | \(0.736291\pi\) | |||||||
\(938\) | − | 1.52958e7i | − | 0.567629i | ||||||
\(939\) | −3.04483e7 | −1.12694 | ||||||||
\(940\) | −354530. | + | 247961.i | −0.0130868 | + | 0.00915302i | ||||
\(941\) | −3.50065e6 | −0.128877 | −0.0644383 | − | 0.997922i | \(-0.520526\pi\) | ||||
−0.0644383 | + | 0.997922i | \(0.520526\pi\) | |||||||
\(942\) | − | 2.47339e7i | − | 0.908165i | ||||||
\(943\) | − | 4.75688e6i | − | 0.174198i | ||||||
\(944\) | 1.03989e7 | 0.379804 | ||||||||
\(945\) | −3.69436e6 | − | 5.28212e6i | −0.134573 | − | 0.192410i | ||||
\(946\) | 6.18251e6 | 0.224614 | ||||||||
\(947\) | 2.56533e7i | 0.929540i | 0.885432 | + | 0.464770i | \(0.153863\pi\) | ||||
−0.885432 | + | 0.464770i | \(0.846137\pi\) | |||||||
\(948\) | − | 771624.i | − | 0.0278859i | ||||||
\(949\) | 5.14307e6 | 0.185377 | ||||||||
\(950\) | 3.13701e7 | + | 1.14559e7i | 1.12773 | + | 0.411833i | ||||
\(951\) | 6.01325e6 | 0.215604 | ||||||||
\(952\) | 2.49290e6i | 0.0891482i | ||||||||
\(953\) | 1.43726e7i | 0.512629i | 0.966593 | + | 0.256314i | \(0.0825082\pi\) | ||||
−0.966593 | + | 0.256314i | \(0.917492\pi\) | |||||||
\(954\) | −1.18366e7 | −0.421071 | ||||||||
\(955\) | −8.37875e6 | − | 1.19798e7i | −0.297283 | − | 0.425050i | ||||
\(956\) | −932982. | −0.0330163 | ||||||||
\(957\) | 1.14369e6i | 0.0403673i | ||||||||
\(958\) | − | 5.05532e7i | − | 1.77965i | ||||||
\(959\) | −2.63084e7 | −0.923735 | ||||||||
\(960\) | 1.31457e7 | − | 9.19422e6i | 0.460369 | − | 0.321986i | ||||
\(961\) | 5.34094e7 | 1.86556 | ||||||||
\(962\) | − | 1.74787e6i | − | 0.0608935i | ||||||
\(963\) | − | 1.13120e7i | − | 0.393075i | ||||||
\(964\) | −214501. | −0.00743423 | ||||||||
\(965\) | −3.15615e7 | + | 2.20744e7i | −1.09104 | + | 0.763080i | ||||
\(966\) | 4.10315e6 | 0.141473 | ||||||||
\(967\) | 3.41494e7i | 1.17440i | 0.809441 | + | 0.587201i | \(0.199770\pi\) | ||||
−0.809441 | + | 0.587201i | \(0.800230\pi\) | |||||||
\(968\) | 2.61524e6i | 0.0897064i | ||||||||
\(969\) | −1.48134e6 | −0.0506810 | ||||||||
\(970\) | 2.30174e7 | + | 3.29099e7i | 0.785466 | + | 1.12304i | ||||
\(971\) | 8.76612e6 | 0.298373 | 0.149186 | − | 0.988809i | \(-0.452335\pi\) | ||||
0.149186 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(972\) | 48454.8i | 0.00164502i | ||||||||
\(973\) | − | 4.76154e7i | − | 1.61237i | ||||||
\(974\) | −3.43325e7 | −1.15960 | ||||||||
\(975\) | −754851. | + | 2.06703e6i | −0.0254302 | + | 0.0696363i | ||||
\(976\) | 1.63886e7 | 0.550703 | ||||||||
\(977\) | 4.92659e7i | 1.65124i | 0.564227 | + | 0.825620i | \(0.309174\pi\) | ||||
−0.564227 | + | 0.825620i | \(0.690826\pi\) | |||||||
\(978\) | − | 2.25335e7i | − | 0.753323i | ||||||
\(979\) | −335729. | −0.0111952 | ||||||||
\(980\) | −215881. | − | 308662.i | −0.00718040 | − | 0.0102664i | ||||
\(981\) | 1.16668e7 | 0.387061 | ||||||||
\(982\) | 3.53625e7i | 1.17021i | ||||||||
\(983\) | − | 5.54306e7i | − | 1.82964i | −0.403861 | − | 0.914820i | \(-0.632332\pi\) | ||
0.403861 | − | 0.914820i | \(-0.367668\pi\) | |||||||
\(984\) | −1.51996e7 | −0.500432 | ||||||||
\(985\) | 2.86336e7 | − | 2.00266e7i | 0.940342 | − | 0.657683i | ||||
\(986\) | 530873. | 0.0173899 | ||||||||
\(987\) | − | 1.34260e7i | − | 0.438686i | ||||||
\(988\) | 119768.i | 0.00390344i | ||||||||
\(989\) | 4.48725e6 | 0.145878 | ||||||||
\(990\) | −2.57215e6 | + | 1.79898e6i | −0.0834081 | + | 0.0583363i | ||||
\(991\) | −1.51099e7 | −0.488739 | −0.244370 | − | 0.969682i | \(-0.578581\pi\) | ||||
−0.244370 | + | 0.969682i | \(0.578581\pi\) | |||||||
\(992\) | 2.69018e6i | 0.0867966i | ||||||||
\(993\) | − | 853956.i | − | 0.0274829i | ||||||
\(994\) | 6.47606e7 | 2.07895 | ||||||||
\(995\) | 3.26861e7 | + | 4.67339e7i | 1.04666 | + | 1.49649i | ||||
\(996\) | −114161. | −0.00364643 | ||||||||
\(997\) | − | 3.98499e7i | − | 1.26966i | −0.772650 | − | 0.634832i | \(-0.781069\pi\) | ||
0.772650 | − | 0.634832i | \(-0.218931\pi\) | |||||||
\(998\) | 1.41625e7i | 0.450104i | ||||||||
\(999\) | −2.84266e6 | −0.0901178 |
(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 | 165.6.c.b.34.20 | yes | 26 | |
5.2 | odd | 4 | 825.6.a.v.1.4 | 13 | |||
5.3 | odd | 4 | 825.6.a.y.1.10 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.7 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.7 | ✓ | 26 | 5.4 | even | 2 | inner | |
165.6.c.b.34.20 | yes | 26 | 1.1 | even | 1 | trivial | |
825.6.a.v.1.4 | 13 | 5.2 | odd | 4 | |||
825.6.a.y.1.10 | 13 | 5.3 | odd | 4 |