Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,5,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(31.0109889252\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + \cdots + 4294967296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.5 | ||
Root | \(-1.06635 + 3.85524i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.5.c.b.151.6 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80556 | − | 2.85111i | −0.701390 | − | 0.712778i | ||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | −0.257663 | + | 15.9979i | −0.0161040 | + | 0.999870i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.8148 | + | 14.5781i | −0.411522 | + | 0.404948i | ||||
\(7\) | 63.6232i | 1.29843i | 0.760604 | + | 0.649216i | \(0.224903\pi\) | ||||
−0.760604 | + | 0.649216i | \(0.775097\pi\) | |||||||
\(8\) | 46.3347 | − | 44.1485i | 0.723980 | − | 0.689821i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 220.737i | − | 1.82427i | −0.409888 | − | 0.912136i | \(-0.634432\pi\) | ||
0.409888 | − | 0.912136i | \(-0.365568\pi\) | |||||||
\(12\) | 83.1277 | + | 1.33886i | 0.577275 | + | 0.00929762i | ||||
\(13\) | −236.856 | −1.40151 | −0.700756 | − | 0.713401i | \(-0.747154\pi\) | ||||
−0.700756 | + | 0.713401i | \(0.747154\pi\) | |||||||
\(14\) | 181.397 | − | 178.499i | 0.925493 | − | 0.910707i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −255.867 | − | 8.24415i | −0.999481 | − | 0.0322037i | ||||
\(17\) | 46.7414 | 0.161735 | 0.0808674 | − | 0.996725i | \(-0.474231\pi\) | ||||
0.0808674 | + | 0.996725i | \(0.474231\pi\) | |||||||
\(18\) | 75.7501 | + | 76.9800i | 0.233797 | + | 0.237593i | ||||
\(19\) | − | 195.899i | − | 0.542656i | −0.962487 | − | 0.271328i | \(-0.912537\pi\) | ||
0.962487 | − | 0.271328i | \(-0.0874629\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 330.596 | 0.749650 | ||||||||
\(22\) | −629.345 | + | 619.291i | −1.30030 | + | 1.27953i | ||||
\(23\) | 741.830i | 1.40232i | 0.713002 | + | 0.701162i | \(0.247335\pi\) | ||||
−0.713002 | + | 0.701162i | \(0.752665\pi\) | |||||||
\(24\) | −229.402 | − | 240.762i | −0.398268 | − | 0.417990i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 664.512 | + | 675.301i | 0.983007 | + | 0.998966i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | −1017.84 | − | 16.3934i | −1.29826 | − | 0.0209099i | ||||
\(29\) | 1059.06 | 1.25928 | 0.629641 | − | 0.776886i | \(-0.283202\pi\) | ||||
0.629641 | + | 0.776886i | \(0.283202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1067.12i | 1.11042i | 0.831709 | + | 0.555212i | \(0.187363\pi\) | ||||
−0.831709 | + | 0.555212i | \(0.812637\pi\) | |||||||
\(32\) | 694.346 | + | 752.635i | 0.678072 | + | 0.734995i | ||||
\(33\) | −1146.98 | −1.05324 | ||||||||
\(34\) | −131.136 | − | 133.265i | −0.113439 | − | 0.115281i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.95691 | − | 431.944i | 0.00536798 | − | 0.333290i | ||||
\(37\) | 2287.23 | 1.67073 | 0.835366 | − | 0.549695i | \(-0.185256\pi\) | ||||
0.835366 | + | 0.549695i | \(0.185256\pi\) | |||||||
\(38\) | −558.530 | + | 549.606i | −0.386793 | + | 0.380614i | ||||
\(39\) | 1230.74i | 0.809163i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1141.57 | −0.679105 | −0.339552 | − | 0.940587i | \(-0.610276\pi\) | ||||
−0.339552 | + | 0.940587i | \(0.610276\pi\) | |||||||
\(42\) | −927.506 | − | 942.565i | −0.525797 | − | 0.534334i | ||||
\(43\) | 1245.24i | 0.673468i | 0.941600 | + | 0.336734i | \(0.109322\pi\) | ||||
−0.941600 | + | 0.336734i | \(0.890678\pi\) | |||||||
\(44\) | 3531.33 | + | 56.8758i | 1.82404 | + | 0.0293780i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2115.04 | − | 2081.25i | 0.999546 | − | 0.983577i | ||||
\(47\) | − | 406.719i | − | 0.184119i | −0.995754 | − | 0.0920595i | \(-0.970655\pi\) | ||
0.995754 | − | 0.0920595i | \(-0.0293450\pi\) | |||||||
\(48\) | −42.8379 | + | 1329.53i | −0.0185928 | + | 0.577051i | ||||
\(49\) | −1646.91 | −0.685926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 242.875i | − | 0.0933777i | ||||||
\(52\) | 61.0290 | − | 3789.20i | 0.0225699 | − | 1.40133i | ||||
\(53\) | −1442.39 | −0.513488 | −0.256744 | − | 0.966479i | \(-0.582650\pi\) | ||||
−0.256744 | + | 0.966479i | \(0.582650\pi\) | |||||||
\(54\) | 400.000 | − | 393.609i | 0.137174 | − | 0.134983i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2808.87 | + | 2947.96i | 0.895685 | + | 0.940039i | ||||
\(57\) | −1017.92 | −0.313303 | ||||||||
\(58\) | −2971.25 | − | 3019.49i | −0.883248 | − | 0.897588i | ||||
\(59\) | 2472.02i | 0.710147i | 0.934838 | + | 0.355074i | \(0.115544\pi\) | ||||
−0.934838 | + | 0.355074i | \(0.884456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4819.29 | 1.29516 | 0.647579 | − | 0.761998i | \(-0.275781\pi\) | ||||
0.647579 | + | 0.761998i | \(0.275781\pi\) | |||||||
\(62\) | 3042.47 | − | 2993.86i | 0.791486 | − | 0.778841i | ||||
\(63\) | − | 1717.83i | − | 0.432811i | ||||||
\(64\) | 197.817 | − | 4091.22i | 0.0482951 | − | 0.998833i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3217.93 | + | 3270.17i | 0.738735 | + | 0.750729i | ||||
\(67\) | 5792.14i | 1.29030i | 0.764057 | + | 0.645149i | \(0.223205\pi\) | ||||
−0.764057 | + | 0.645149i | \(0.776795\pi\) | |||||||
\(68\) | −12.0435 | + | 747.765i | −0.00260457 | + | 0.161714i | ||||
\(69\) | 3854.66 | 0.809633 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 309.369i | − | 0.0613706i | −0.999529 | − | 0.0306853i | \(-0.990231\pi\) | ||
0.999529 | − | 0.0306853i | \(-0.00976897\pi\) | |||||||
\(72\) | −1251.04 | + | 1192.01i | −0.241327 | + | 0.229940i | ||||
\(73\) | −996.733 | −0.187039 | −0.0935197 | − | 0.995617i | \(-0.529812\pi\) | ||||
−0.0935197 | + | 0.995617i | \(0.529812\pi\) | |||||||
\(74\) | −6416.96 | − | 6521.15i | −1.17183 | − | 1.19086i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3133.98 | + | 50.4759i | 0.542586 | + | 0.00873891i | ||||
\(77\) | 14044.0 | 2.36869 | ||||||||
\(78\) | 3508.97 | − | 3452.91i | 0.576754 | − | 0.567539i | ||||
\(79\) | − | 1096.99i | − | 0.175772i | −0.996131 | − | 0.0878860i | \(-0.971989\pi\) | ||
0.996131 | − | 0.0878860i | \(-0.0280111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 3202.76 | + | 3254.76i | 0.476317 | + | 0.484051i | ||||
\(83\) | 3097.31i | 0.449603i | 0.974405 | + | 0.224801i | \(0.0721733\pi\) | ||||
−0.974405 | + | 0.224801i | \(0.927827\pi\) | |||||||
\(84\) | −85.1824 | + | 5288.85i | −0.0120723 | + | 0.749553i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3550.32 | − | 3493.60i | 0.480033 | − | 0.472364i | ||||
\(87\) | − | 5503.02i | − | 0.727047i | ||||||
\(88\) | −9745.21 | − | 10227.8i | −1.25842 | − | 1.32074i | ||||
\(89\) | 10965.3 | 1.38433 | 0.692167 | − | 0.721738i | \(-0.256656\pi\) | ||||
0.692167 | + | 0.721738i | \(0.256656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15069.5i | − | 1.81977i | ||||||
\(92\) | −11867.7 | − | 191.142i | −1.40214 | − | 0.0225830i | ||||
\(93\) | 5544.91 | 0.641104 | ||||||||
\(94\) | −1159.60 | + | 1141.07i | −0.131236 | + | 0.129139i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3910.81 | − | 3607.93i | 0.424350 | − | 0.391485i | ||||
\(97\) | 12339.0 | 1.31140 | 0.655701 | − | 0.755020i | \(-0.272373\pi\) | ||||
0.655701 | + | 0.755020i | \(0.272373\pi\) | |||||||
\(98\) | 4620.50 | + | 4695.52i | 0.481102 | + | 0.488913i | ||||
\(99\) | 5959.90i | 0.608091i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14918.3 | 1.46244 | 0.731219 | − | 0.682143i | \(-0.238952\pi\) | ||||
0.731219 | + | 0.682143i | \(0.238952\pi\) | |||||||
\(102\) | −692.464 | + | 681.401i | −0.0665575 | + | 0.0654942i | ||||
\(103\) | − | 10083.1i | − | 0.950433i | −0.879869 | − | 0.475216i | \(-0.842370\pi\) | ||
0.879869 | − | 0.475216i | \(-0.157630\pi\) | |||||||
\(104\) | −10974.6 | + | 10456.8i | −1.01467 | + | 0.966792i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4046.71 | + | 4112.41i | 0.360155 | + | 0.366003i | ||||
\(107\) | 18475.7i | 1.61374i | 0.590731 | + | 0.806869i | \(0.298839\pi\) | ||||
−0.590731 | + | 0.806869i | \(0.701161\pi\) | |||||||
\(108\) | −2244.45 | − | 36.1491i | −0.192425 | − | 0.00309921i | ||||
\(109\) | −676.882 | −0.0569718 | −0.0284859 | − | 0.999594i | \(-0.509069\pi\) | ||||
−0.0284859 | + | 0.999594i | \(0.509069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11884.8i | − | 0.964597i | ||||||
\(112\) | 524.519 | − | 16279.1i | 0.0418144 | − | 1.29776i | ||||
\(113\) | 5693.92 | 0.445917 | 0.222959 | − | 0.974828i | \(-0.428429\pi\) | ||||
0.222959 | + | 0.974828i | \(0.428429\pi\) | |||||||
\(114\) | 2855.84 | + | 2902.20i | 0.219747 | + | 0.223315i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −272.880 | + | 16942.7i | −0.0202794 | + | 1.25912i | ||||
\(117\) | 6395.10 | 0.467171 | ||||||||
\(118\) | 7048.01 | − | 6935.41i | 0.506177 | − | 0.498090i | ||||
\(119\) | 2973.83i | 0.210002i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −34083.8 | −2.32797 | ||||||||
\(122\) | −13520.8 | − | 13740.3i | −0.908412 | − | 0.923160i | ||||
\(123\) | 5931.80i | 0.392081i | ||||||||
\(124\) | −17071.7 | − | 274.957i | −1.11028 | − | 0.0178822i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4897.71 | + | 4819.46i | −0.308498 | + | 0.303569i | ||||
\(127\) | 21834.4i | 1.35374i | 0.736103 | + | 0.676869i | \(0.236664\pi\) | ||||
−0.736103 | + | 0.676869i | \(0.763336\pi\) | |||||||
\(128\) | −12219.5 | + | 10914.2i | −0.745820 | + | 0.666148i | ||||
\(129\) | 6470.47 | 0.388827 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6919.28i | 0.403198i | 0.979468 | + | 0.201599i | \(0.0646138\pi\) | ||||
−0.979468 | + | 0.201599i | \(0.935386\pi\) | |||||||
\(132\) | 295.535 | − | 18349.3i | 0.0169614 | − | 1.05311i | ||||
\(133\) | 12463.7 | 0.704602 | ||||||||
\(134\) | 16514.0 | − | 16250.2i | 0.919695 | − | 0.905002i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2165.75 | − | 2063.56i | 0.117093 | − | 0.111568i | ||||
\(137\) | −24619.2 | −1.31169 | −0.655846 | − | 0.754895i | \(-0.727688\pi\) | ||||
−0.655846 | + | 0.754895i | \(0.727688\pi\) | |||||||
\(138\) | −10814.5 | − | 10990.1i | −0.567868 | − | 0.577088i | ||||
\(139\) | 18767.2i | 0.971336i | 0.874143 | + | 0.485668i | \(0.161424\pi\) | ||||
−0.874143 | + | 0.485668i | \(0.838576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2113.37 | −0.106301 | ||||||||
\(142\) | −882.046 | + | 867.954i | −0.0437436 | + | 0.0430447i | ||||
\(143\) | 52282.8i | 2.55674i | ||||||||
\(144\) | 6908.41 | + | 222.592i | 0.333160 | + | 0.0107346i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2796.39 | + | 2841.80i | 0.131188 | + | 0.133318i | ||||
\(147\) | 8557.59i | 0.396020i | ||||||||
\(148\) | −589.335 | + | 36590.9i | −0.0269054 | + | 1.67051i | ||||
\(149\) | 6573.00 | 0.296068 | 0.148034 | − | 0.988982i | \(-0.452706\pi\) | ||||
0.148034 | + | 0.988982i | \(0.452706\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7823.28i | 0.343111i | 0.985174 | + | 0.171556i | \(0.0548793\pi\) | ||||
−0.985174 | + | 0.171556i | \(0.945121\pi\) | |||||||
\(152\) | −8648.65 | − | 9076.93i | −0.374335 | − | 0.392873i | ||||
\(153\) | −1262.02 | −0.0539116 | ||||||||
\(154\) | −39401.2 | − | 40041.0i | −1.66138 | − | 1.68835i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −19689.2 | − | 317.116i | −0.809058 | − | 0.0130307i | ||||
\(157\) | 9202.59 | 0.373346 | 0.186673 | − | 0.982422i | \(-0.440230\pi\) | ||||
0.186673 | + | 0.982422i | \(0.440230\pi\) | |||||||
\(158\) | −3127.65 | + | 3077.68i | −0.125286 | + | 0.123285i | ||||
\(159\) | 7494.87i | 0.296462i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47197.6 | −1.82082 | ||||||||
\(162\) | −2045.25 | − | 2078.46i | −0.0779322 | − | 0.0791975i | ||||
\(163\) | − | 43667.2i | − | 1.64354i | −0.569820 | − | 0.821769i | \(-0.692987\pi\) | ||
0.569820 | − | 0.821769i | \(-0.307013\pi\) | |||||||
\(164\) | 294.142 | − | 18262.8i | 0.0109363 | − | 0.679017i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8830.78 | − | 8689.70i | 0.320467 | − | 0.315347i | ||||
\(167\) | 19662.7i | 0.705034i | 0.935805 | + | 0.352517i | \(0.114674\pi\) | ||||
−0.935805 | + | 0.352517i | \(0.885326\pi\) | |||||||
\(168\) | 15318.1 | − | 14595.3i | 0.542732 | − | 0.517124i | ||||
\(169\) | 27539.5 | 0.964236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5289.27i | 0.180885i | ||||||||
\(172\) | −19921.3 | − | 320.853i | −0.673381 | − | 0.0108455i | ||||
\(173\) | 31871.9 | 1.06492 | 0.532459 | − | 0.846456i | \(-0.321268\pi\) | ||||
0.532459 | + | 0.846456i | \(0.321268\pi\) | |||||||
\(174\) | −15689.7 | + | 15439.1i | −0.518223 | + | 0.509944i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1819.79 | + | 56479.3i | −0.0587484 | + | 1.82333i | ||||
\(177\) | 12845.0 | 0.410004 | ||||||||
\(178\) | −30763.8 | − | 31263.3i | −0.970958 | − | 0.986722i | ||||
\(179\) | − | 52843.2i | − | 1.64924i | −0.565689 | − | 0.824619i | \(-0.691390\pi\) | ||
0.565689 | − | 0.824619i | \(-0.308610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −63045.0 | −1.92439 | −0.962197 | − | 0.272356i | \(-0.912197\pi\) | ||||
−0.962197 | + | 0.272356i | \(0.912197\pi\) | |||||||
\(182\) | −42964.8 | + | 42278.4i | −1.29709 | + | 1.27637i | ||||
\(183\) | − | 25041.7i | − | 0.747760i | ||||||
\(184\) | 32750.7 | + | 34372.5i | 0.967352 | + | 1.01526i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15556.6 | − | 15809.1i | −0.449664 | − | 0.456964i | ||||
\(187\) | − | 10317.5i | − | 0.295048i | ||||||
\(188\) | 6506.66 | + | 104.796i | 0.184095 | + | 0.00296504i | ||||
\(189\) | −8926.08 | −0.249883 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20730.2i | − | 0.568246i | −0.958788 | − | 0.284123i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284123i | \(-0.0917024\pi\) | |||||||
\(192\) | −21258.6 | − | 1027.89i | −0.576677 | − | 0.0278832i | ||||
\(193\) | −17567.6 | −0.471627 | −0.235813 | − | 0.971798i | \(-0.575775\pi\) | ||||
−0.235813 | + | 0.971798i | \(0.575775\pi\) | |||||||
\(194\) | −34617.8 | − | 35179.8i | −0.919805 | − | 0.934739i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 424.348 | − | 26347.1i | 0.0110461 | − | 0.685837i | ||||
\(197\) | 50800.9 | 1.30900 | 0.654499 | − | 0.756063i | \(-0.272880\pi\) | ||||
0.654499 | + | 0.756063i | \(0.272880\pi\) | |||||||
\(198\) | 16992.3 | − | 16720.8i | 0.433433 | − | 0.426509i | ||||
\(199\) | 32141.3i | 0.811629i | 0.913955 | + | 0.405814i | \(0.133012\pi\) | ||||
−0.913955 | + | 0.405814i | \(0.866988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30096.9 | 0.744953 | ||||||||
\(202\) | −41854.3 | − | 42533.8i | −1.02574 | − | 1.04239i | ||||
\(203\) | 67380.5i | 1.63509i | ||||||||
\(204\) | 3885.50 | + | 62.5800i | 0.0933656 | + | 0.00150375i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −28748.1 | + | 28288.9i | −0.677447 | + | 0.666624i | ||||
\(207\) | − | 20029.4i | − | 0.467442i | ||||||
\(208\) | 60603.6 | + | 1952.67i | 1.40079 | + | 0.0451339i | ||||
\(209\) | −43242.1 | −0.989953 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9541.34i | − | 0.214311i | −0.994242 | − | 0.107156i | \(-0.965826\pi\) | ||
0.994242 | − | 0.107156i | \(-0.0341743\pi\) | |||||||
\(212\) | 371.650 | − | 23075.2i | 0.00826919 | − | 0.513421i | ||||
\(213\) | −1607.53 | −0.0354323 | ||||||||
\(214\) | 52676.2 | − | 51834.6i | 1.15024 | − | 1.13186i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6193.87 | + | 6500.58i | 0.132756 | + | 0.139330i | ||||
\(217\) | −67893.4 | −1.44181 | ||||||||
\(218\) | 1899.03 | + | 1929.86i | 0.0399594 | + | 0.0406082i | ||||
\(219\) | 5179.18i | 0.107987i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11071.0 | −0.226673 | ||||||||
\(222\) | −33884.9 | + | 33343.5i | −0.687543 | + | 0.676559i | ||||
\(223\) | 33469.4i | 0.673037i | 0.941677 | + | 0.336518i | \(0.109249\pi\) | ||||
−0.941677 | + | 0.336518i | \(0.890751\pi\) | |||||||
\(224\) | −47885.0 | + | 44176.5i | −0.954342 | + | 0.880431i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15974.6 | − | 16234.0i | −0.312762 | − | 0.317840i | ||||
\(227\) | 1149.27i | 0.0223033i | 0.999938 | + | 0.0111517i | \(0.00354976\pi\) | ||||
−0.999938 | + | 0.0111517i | \(0.996450\pi\) | |||||||
\(228\) | 262.281 | − | 16284.6i | 0.00504541 | − | 0.313262i | ||||
\(229\) | −49392.2 | −0.941863 | −0.470931 | − | 0.882170i | \(-0.656082\pi\) | ||||
−0.470931 | + | 0.882170i | \(0.656082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 72974.7i | − | 1.36757i | ||||||
\(232\) | 49071.1 | − | 46755.8i | 0.911696 | − | 0.868679i | ||||
\(233\) | −42084.0 | −0.775184 | −0.387592 | − | 0.921831i | \(-0.626693\pi\) | ||||
−0.387592 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(234\) | −17941.8 | − | 18233.1i | −0.327669 | − | 0.332989i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −39547.2 | − | 636.949i | −0.710055 | − | 0.0114362i | ||||
\(237\) | −5700.14 | −0.101482 | ||||||||
\(238\) | 8478.73 | − | 8343.27i | 0.149685 | − | 0.147293i | ||||
\(239\) | 34540.4i | 0.604689i | 0.953199 | + | 0.302345i | \(0.0977693\pi\) | ||||
−0.953199 | + | 0.302345i | \(0.902231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 68666.9 | 1.18226 | 0.591131 | − | 0.806576i | \(-0.298682\pi\) | ||||
0.591131 | + | 0.806576i | \(0.298682\pi\) | |||||||
\(242\) | 95624.1 | + | 97176.6i | 1.63281 | + | 1.65932i | ||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | −1241.75 | + | 77098.6i | −0.0208572 | + | 1.29499i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 16912.2 | − | 16642.0i | 0.279467 | − | 0.275002i | ||||
\(247\) | 46399.7i | 0.760539i | ||||||||
\(248\) | 47111.7 | + | 49444.6i | 0.765994 | + | 0.803925i | ||||
\(249\) | 16094.1 | 0.259578 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 62003.3i | 0.984163i | 0.870549 | + | 0.492082i | \(0.163764\pi\) | ||||
−0.870549 | + | 0.492082i | \(0.836236\pi\) | |||||||
\(252\) | 27481.6 | + | 442.621i | 0.432755 | + | 0.00696996i | ||||
\(253\) | 163749. | 2.55822 | ||||||||
\(254\) | 62252.4 | − | 61257.9i | 0.964914 | − | 0.949499i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65400.1 | + | 4218.82i | 0.997926 | + | 0.0643740i | ||||
\(257\) | 65977.4 | 0.998916 | 0.499458 | − | 0.866338i | \(-0.333532\pi\) | ||||
0.499458 | + | 0.866338i | \(0.333532\pi\) | |||||||
\(258\) | −18153.3 | − | 18448.0i | −0.272719 | − | 0.277147i | ||||
\(259\) | 145521.i | 2.16933i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28594.5 | −0.419761 | ||||||||
\(262\) | 19727.6 | − | 19412.5i | 0.287391 | − | 0.282799i | ||||
\(263\) | − | 45889.4i | − | 0.663439i | −0.943378 | − | 0.331719i | \(-0.892371\pi\) | ||
0.943378 | − | 0.331719i | \(-0.107629\pi\) | |||||||
\(264\) | −53145.1 | + | 50637.6i | −0.762528 | + | 0.726549i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −34967.7 | − | 35535.4i | −0.494201 | − | 0.502225i | ||||
\(267\) | − | 56977.4i | − | 0.799245i | ||||||
\(268\) | −92662.3 | − | 1492.42i | −1.29013 | − | 0.0207789i | ||||
\(269\) | 66600.2 | 0.920388 | 0.460194 | − | 0.887818i | \(-0.347780\pi\) | ||||
0.460194 | + | 0.887818i | \(0.347780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 107846.i | 1.46848i | 0.678892 | + | 0.734239i | \(0.262461\pi\) | ||||
−0.678892 | + | 0.734239i | \(0.737539\pi\) | |||||||
\(272\) | −11959.6 | − | 385.343i | −0.161651 | − | 0.00520847i | ||||
\(273\) | −78303.4 | −1.05064 | ||||||||
\(274\) | 69070.5 | + | 70191.9i | 0.920008 | + | 0.934945i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −993.204 | + | 61666.6i | −0.0130383 | + | 0.809528i | ||||
\(277\) | −76120.9 | −0.992074 | −0.496037 | − | 0.868301i | \(-0.665212\pi\) | ||||
−0.496037 | + | 0.868301i | \(0.665212\pi\) | |||||||
\(278\) | 53507.3 | − | 52652.5i | 0.692347 | − | 0.681286i | ||||
\(279\) | − | 28812.2i | − | 0.370141i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 127936. | 1.62024 | 0.810120 | − | 0.586264i | \(-0.199402\pi\) | ||||
0.810120 | + | 0.586264i | \(0.199402\pi\) | |||||||
\(282\) | 5929.19 | + | 6025.46i | 0.0745586 | + | 0.0757691i | ||||
\(283\) | − | 117792.i | − | 1.47076i | −0.677655 | − | 0.735380i | \(-0.737004\pi\) | ||
0.677655 | − | 0.735380i | \(-0.262996\pi\) | |||||||
\(284\) | 4949.27 | + | 79.7131i | 0.0613627 | + | 0.000988310i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 149064. | − | 146682.i | 1.82239 | − | 1.79327i | ||||
\(287\) | − | 72630.6i | − | 0.881771i | ||||||
\(288\) | −18747.3 | − | 20321.2i | −0.226024 | − | 0.244998i | ||||
\(289\) | −81336.2 | −0.973842 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 64115.3i | − | 0.757139i | ||||||
\(292\) | 256.821 | − | 15945.7i | 0.00301207 | − | 0.187015i | ||||
\(293\) | −120518. | −1.40384 | −0.701918 | − | 0.712258i | \(-0.747673\pi\) | ||||
−0.701918 | + | 0.712258i | \(0.747673\pi\) | |||||||
\(294\) | 24398.6 | − | 24008.8i | 0.282274 | − | 0.277764i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 105978. | − | 100978.i | 1.20958 | − | 1.15250i | ||||
\(297\) | 30968.5 | 0.351081 | ||||||||
\(298\) | −18441.0 | − | 18740.4i | −0.207659 | − | 0.211031i | ||||
\(299\) | − | 175706.i | − | 1.96537i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −79226.3 | −0.874453 | ||||||||
\(302\) | 22305.0 | − | 21948.7i | 0.244562 | − | 0.240655i | ||||
\(303\) | − | 77517.9i | − | 0.844339i | ||||||
\(304\) | −1615.02 | + | 50124.1i | −0.0174756 | + | 0.542375i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3540.67 | + | 3598.15i | 0.0378131 | + | 0.0384270i | ||||
\(307\) | − | 90003.1i | − | 0.954950i | −0.878645 | − | 0.477475i | \(-0.841552\pi\) | ||
0.878645 | − | 0.477475i | \(-0.158448\pi\) | |||||||
\(308\) | −3618.62 | + | 224675.i | −0.0381453 | + | 2.36839i | ||||
\(309\) | −52393.5 | −0.548732 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 35944.1i | − | 0.371627i | −0.982585 | − | 0.185813i | \(-0.940508\pi\) | ||
0.982585 | − | 0.185813i | \(-0.0594920\pi\) | |||||||
\(312\) | 54335.2 | + | 57025.9i | 0.558178 | + | 0.585818i | ||||
\(313\) | 10420.7 | 0.106368 | 0.0531838 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531838 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(314\) | −25818.4 | − | 26237.6i | −0.261861 | − | 0.266112i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17549.6 | + | 282.655i | 0.175749 | + | 0.00283062i | ||||
\(317\) | −44276.9 | −0.440614 | −0.220307 | − | 0.975431i | \(-0.570706\pi\) | ||||
−0.220307 | + | 0.975431i | \(0.570706\pi\) | |||||||
\(318\) | 21368.7 | − | 21027.3i | 0.211312 | − | 0.207936i | ||||
\(319\) | − | 233773.i | − | 2.29727i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 96002.4 | 0.931692 | ||||||||
\(322\) | 132416. | + | 134565.i | 1.27711 | + | 1.29784i | ||||
\(323\) | − | 9156.59i | − | 0.0877664i | ||||||
\(324\) | −187.836 | + | 11662.5i | −0.00178933 | + | 0.111097i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −124500. | + | 122511.i | −1.17148 | + | 1.15276i | ||||
\(327\) | 3517.18i | 0.0328927i | ||||||||
\(328\) | −52894.6 | + | 50398.8i | −0.491658 | + | 0.468460i | ||||
\(329\) | 25876.7 | 0.239066 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 219017.i | 1.99904i | 0.0309493 | + | 0.999521i | \(0.490147\pi\) | ||||
−0.0309493 | + | 0.999521i | \(0.509853\pi\) | |||||||
\(332\) | −49550.6 | − | 798.064i | −0.449544 | − | 0.00724038i | ||||
\(333\) | −61755.2 | −0.556910 | ||||||||
\(334\) | 56060.5 | − | 55164.9i | 0.502533 | − | 0.494504i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −84588.6 | − | 2725.48i | −0.749261 | − | 0.0241415i | ||||
\(337\) | −51173.5 | −0.450594 | −0.225297 | − | 0.974290i | \(-0.572335\pi\) | ||||
−0.225297 | + | 0.974290i | \(0.572335\pi\) | |||||||
\(338\) | −77263.9 | − | 78518.3i | −0.676306 | − | 0.687286i | ||||
\(339\) | − | 29586.5i | − | 0.257450i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 235552. | 2.02572 | ||||||||
\(342\) | 15080.3 | − | 14839.4i | 0.128931 | − | 0.126871i | ||||
\(343\) | 47977.7i | 0.407804i | ||||||||
\(344\) | 54975.6 | + | 57698.0i | 0.464572 | + | 0.487578i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −89418.7 | − | 90870.4i | −0.746923 | − | 0.759050i | ||||
\(347\) | 78897.6i | 0.655247i | 0.944808 | + | 0.327623i | \(0.106248\pi\) | ||||
−0.944808 | + | 0.327623i | \(0.893752\pi\) | |||||||
\(348\) | 88036.9 | + | 1417.93i | 0.726953 | + | 0.0117083i | ||||
\(349\) | 187086. | 1.53599 | 0.767997 | − | 0.640454i | \(-0.221254\pi\) | ||||
0.767997 | + | 0.640454i | \(0.221254\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 33229.9i | − | 0.269721i | ||||||
\(352\) | 166134. | − | 153268.i | 1.34083 | − | 1.23699i | ||||
\(353\) | −26576.3 | −0.213278 | −0.106639 | − | 0.994298i | \(-0.534009\pi\) | ||||
−0.106639 | + | 0.994298i | \(0.534009\pi\) | |||||||
\(354\) | −36037.4 | − | 36622.5i | −0.287573 | − | 0.292242i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2825.36 | + | 175422.i | −0.0222932 | + | 1.38415i | ||||
\(357\) | 15452.5 | 0.121245 | ||||||||
\(358\) | −150662. | + | 148255.i | −1.17554 | + | 1.15676i | ||||
\(359\) | − | 13211.6i | − | 0.102510i | −0.998686 | − | 0.0512552i | \(-0.983678\pi\) | ||
0.998686 | − | 0.0512552i | \(-0.0163222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 91944.6 | 0.705524 | ||||||||
\(362\) | 176877. | + | 179748.i | 1.34975 | + | 1.37166i | ||||
\(363\) | 177105.i | 1.34405i | ||||||||
\(364\) | 241081. | + | 3882.86i | 1.81953 | + | 0.0293055i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −71396.8 | + | 70256.1i | −0.532987 | + | 0.524472i | ||||
\(367\) | − | 46921.2i | − | 0.348367i | −0.984713 | − | 0.174184i | \(-0.944271\pi\) | ||
0.984713 | − | 0.174184i | \(-0.0557286\pi\) | |||||||
\(368\) | 6115.76 | − | 189810.i | 0.0451601 | − | 1.40160i | ||||
\(369\) | 30822.5 | 0.226368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 91769.3i | − | 0.666729i | ||||||
\(372\) | −1428.72 | + | 88707.0i | −0.0103243 | + | 0.641021i | ||||
\(373\) | −237489. | −1.70697 | −0.853487 | − | 0.521115i | \(-0.825516\pi\) | ||||
−0.853487 | + | 0.521115i | \(0.825516\pi\) | |||||||
\(374\) | −29416.5 | + | 28946.5i | −0.210304 | + | 0.206944i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17956.0 | − | 18845.2i | −0.127009 | − | 0.133299i | ||||
\(377\) | −250843. | −1.76490 | ||||||||
\(378\) | 25042.7 | + | 25449.3i | 0.175266 | + | 0.178111i | ||||
\(379\) | 108145.i | 0.752885i | 0.926440 | + | 0.376442i | \(0.122853\pi\) | ||||
−0.926440 | + | 0.376442i | \(0.877147\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 113455. | 0.781581 | ||||||||
\(382\) | −59104.0 | + | 58159.8i | −0.405033 | + | 0.398562i | ||||
\(383\) | 143109.i | 0.975594i | 0.872957 | + | 0.487797i | \(0.162199\pi\) | ||||
−0.872957 | + | 0.487797i | \(0.837801\pi\) | |||||||
\(384\) | 56711.7 | + | 63494.4i | 0.384601 | + | 0.430599i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 49287.0 | + | 50087.3i | 0.330794 | + | 0.336165i | ||||
\(387\) | − | 33621.6i | − | 0.224489i | ||||||
\(388\) | −3179.30 | + | 197398.i | −0.0211188 | + | 1.31123i | ||||
\(389\) | −132061. | −0.872720 | −0.436360 | − | 0.899772i | \(-0.643733\pi\) | ||||
−0.436360 | + | 0.899772i | \(0.643733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34674.1i | 0.226805i | ||||||||
\(392\) | −76309.1 | + | 72708.6i | −0.496597 | + | 0.473166i | ||||
\(393\) | 35953.6 | 0.232787 | ||||||||
\(394\) | −142525. | − | 144839.i | −0.918118 | − | 0.933024i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −95346.0 | − | 1535.65i | −0.608012 | − | 0.00979266i | ||||
\(397\) | −46139.3 | −0.292745 | −0.146373 | − | 0.989230i | \(-0.546760\pi\) | ||||
−0.146373 | + | 0.989230i | \(0.546760\pi\) | |||||||
\(398\) | 91638.5 | − | 90174.4i | 0.578511 | − | 0.569269i | ||||
\(399\) | − | 64763.3i | − | 0.406802i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3244.97 | 0.0201800 | 0.0100900 | − | 0.999949i | \(-0.496788\pi\) | ||||
0.0100900 | + | 0.999949i | \(0.496788\pi\) | |||||||
\(402\) | −84438.6 | − | 85809.5i | −0.522503 | − | 0.530986i | ||||
\(403\) | − | 252753.i | − | 1.55627i | ||||||
\(404\) | −3843.90 | + | 238662.i | −0.0235510 | + | 1.46225i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 192109. | − | 189040.i | 1.16546 | − | 1.14684i | ||||
\(407\) | − | 504876.i | − | 3.04787i | ||||||
\(408\) | −10722.6 | − | 11253.6i | −0.0644138 | − | 0.0676036i | ||||
\(409\) | −190227. | −1.13717 | −0.568585 | − | 0.822625i | \(-0.692509\pi\) | ||||
−0.568585 | + | 0.822625i | \(0.692509\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 127925.i | 0.757306i | ||||||||
\(412\) | 161309. | + | 2598.05i | 0.950309 | + | 0.0153057i | ||||
\(413\) | −157278. | −0.922078 | ||||||||
\(414\) | −57106.0 | + | 56193.7i | −0.333182 | + | 0.327859i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −164460. | − | 178266.i | −0.950326 | − | 1.03010i | ||||
\(417\) | 97517.2 | 0.560801 | ||||||||
\(418\) | 121318. | + | 123288.i | 0.694343 | + | 0.705616i | ||||
\(419\) | − | 38663.2i | − | 0.220226i | −0.993919 | − | 0.110113i | \(-0.964879\pi\) | ||
0.993919 | − | 0.110113i | \(-0.0351213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −215220. | −1.21428 | −0.607140 | − | 0.794595i | \(-0.707683\pi\) | ||||
−0.607140 | + | 0.794595i | \(0.707683\pi\) | |||||||
\(422\) | −27203.4 | + | 26768.8i | −0.152756 | + | 0.150316i | ||||
\(423\) | 10981.4i | 0.0613730i | ||||||||
\(424\) | −66832.7 | + | 63679.3i | −0.371755 | + | 0.354215i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4510.02 | + | 4583.25i | 0.0248519 | + | 0.0252554i | ||||
\(427\) | 306618.i | 1.68168i | ||||||||
\(428\) | −295572. | − | 4760.50i | −1.61353 | − | 0.0259875i | ||||
\(429\) | 271669. | 1.47613 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12832.4i | − | 0.0690804i | −0.999403 | − | 0.0345402i | \(-0.989003\pi\) | ||
0.999403 | − | 0.0345402i | \(-0.0109967\pi\) | |||||||
\(432\) | 1156.62 | − | 35897.2i | 0.00619761 | − | 0.192350i | ||||
\(433\) | 245264. | 1.30815 | 0.654076 | − | 0.756429i | \(-0.273058\pi\) | ||||
0.654076 | + | 0.756429i | \(0.273058\pi\) | |||||||
\(434\) | 190479. | + | 193572.i | 1.01127 | + | 1.02769i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 174.408 | − | 10828.7i | 0.000917471 | − | 0.0569644i | ||||
\(437\) | 145324. | 0.760980 | ||||||||
\(438\) | 14766.4 | − | 14530.5i | 0.0769709 | − | 0.0757412i | ||||
\(439\) | 8320.58i | 0.0431742i | 0.999767 | + | 0.0215871i | \(0.00687192\pi\) | ||||
−0.999767 | + | 0.0215871i | \(0.993128\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44466.5 | 0.228642 | ||||||||
\(442\) | 31060.2 | + | 31564.5i | 0.158986 | + | 0.161568i | ||||
\(443\) | − | 141239.i | − | 0.719695i | −0.933011 | − | 0.359847i | \(-0.882829\pi\) | ||
0.933011 | − | 0.359847i | \(-0.117171\pi\) | |||||||
\(444\) | 190132. | + | 3062.28i | 0.964472 | + | 0.0155338i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 95425.1 | − | 93900.6i | 0.479726 | − | 0.472061i | ||||
\(447\) | − | 34154.3i | − | 0.170935i | ||||||
\(448\) | 260296. | + | 12585.7i | 1.29692 | + | 0.0627080i | ||||
\(449\) | −197626. | −0.980282 | −0.490141 | − | 0.871643i | \(-0.663055\pi\) | ||||
−0.490141 | + | 0.871643i | \(0.663055\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 251988.i | 1.23887i | ||||||||
\(452\) | −1467.11 | + | 91090.9i | −0.00718103 | + | 0.445859i | ||||
\(453\) | 40651.0 | 0.198095 | ||||||||
\(454\) | 3276.69 | − | 3224.34i | 0.0158973 | − | 0.0156433i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −47165.1 | + | 44939.7i | −0.226825 | + | 0.216123i | ||||
\(457\) | −331333. | −1.58647 | −0.793236 | − | 0.608915i | \(-0.791605\pi\) | ||||
−0.793236 | + | 0.608915i | \(0.791605\pi\) | |||||||
\(458\) | 138573. | + | 140823.i | 0.660613 | + | 0.671339i | ||||
\(459\) | 6557.63i | 0.0311259i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −196090. | −0.922687 | −0.461343 | − | 0.887222i | \(-0.652632\pi\) | ||||
−0.461343 | + | 0.887222i | \(0.652632\pi\) | |||||||
\(462\) | −208059. | + | 204735.i | −0.974770 | + | 0.959197i | ||||
\(463\) | − | 168744.i | − | 0.787164i | −0.919289 | − | 0.393582i | \(-0.871236\pi\) | ||
0.919289 | − | 0.393582i | \(-0.128764\pi\) | |||||||
\(464\) | −270978. | − | 8731.03i | −1.25863 | − | 0.0405536i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 118069. | + | 119986.i | 0.543706 | + | 0.552534i | ||||
\(467\) | 58203.8i | 0.266881i | 0.991057 | + | 0.133440i | \(0.0426025\pi\) | ||||
−0.991057 | + | 0.133440i | \(0.957398\pi\) | |||||||
\(468\) | −1647.78 | + | 102308.i | −0.00752329 | + | 0.467110i | ||||
\(469\) | −368515. | −1.67536 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 47818.1i | − | 0.215551i | ||||||
\(472\) | 109136. | + | 114541.i | 0.489874 | + | 0.514133i | ||||
\(473\) | 274871. | 1.22859 | ||||||||
\(474\) | 15992.1 | + | 16251.7i | 0.0711785 | + | 0.0723341i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −47575.2 | − | 766.248i | −0.209975 | − | 0.00338186i | ||||
\(477\) | 38944.5 | 0.171163 | ||||||||
\(478\) | 98478.6 | − | 96905.3i | 0.431009 | − | 0.424123i | ||||
\(479\) | 221700.i | 0.966260i | 0.875549 | + | 0.483130i | \(0.160500\pi\) | ||||
−0.875549 | + | 0.483130i | \(0.839500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −541743. | −2.34155 | ||||||||
\(482\) | −192649. | − | 195777.i | −0.829227 | − | 0.842690i | ||||
\(483\) | 245246.i | 1.05125i | ||||||||
\(484\) | 8782.14 | − | 545270.i | 0.0374895 | − | 2.32767i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10800.0 | + | 10627.4i | −0.0457247 | + | 0.0449942i | ||||
\(487\) | 145571.i | 0.613788i | 0.951744 | + | 0.306894i | \(0.0992897\pi\) | ||||
−0.951744 | + | 0.306894i | \(0.900710\pi\) | |||||||
\(488\) | 223300. | − | 212764.i | 0.937670 | − | 0.893427i | ||||
\(489\) | −226901. | −0.948897 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 244597.i | − | 1.01458i | −0.861774 | − | 0.507292i | \(-0.830646\pi\) | ||
0.861774 | − | 0.507292i | \(-0.169354\pi\) | |||||||
\(492\) | −94896.4 | − | 1528.41i | −0.392030 | − | 0.00631406i | ||||
\(493\) | 49501.8 | 0.203670 | ||||||||
\(494\) | 132291. | − | 130177.i | 0.542095 | − | 0.533435i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8797.48 | − | 273040.i | 0.0357598 | − | 1.10985i | ||||
\(497\) | 19683.1 | 0.0796856 | ||||||||
\(498\) | −45153.0 | − | 45886.1i | −0.182066 | − | 0.185022i | ||||
\(499\) | 113422.i | 0.455507i | 0.973719 | + | 0.227754i | \(0.0731381\pi\) | ||||
−0.973719 | + | 0.227754i | \(0.926862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 102170. | 0.407052 | ||||||||
\(502\) | 176778. | − | 173954.i | 0.701490 | − | 0.690282i | ||||
\(503\) | − | 135516.i | − | 0.535616i | −0.963472 | − | 0.267808i | \(-0.913701\pi\) | ||
0.963472 | − | 0.267808i | \(-0.0862993\pi\) | |||||||
\(504\) | −75839.5 | − | 79595.0i | −0.298562 | − | 0.313346i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −459408. | − | 466867.i | −1.79431 | − | 1.82344i | ||||
\(507\) | − | 143100.i | − | 0.556702i | ||||||
\(508\) | −349306. | − | 5625.93i | −1.35356 | − | 0.0218005i | ||||
\(509\) | 393520. | 1.51891 | 0.759454 | − | 0.650561i | \(-0.225466\pi\) | ||||
0.759454 | + | 0.650561i | \(0.225466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 63415.3i | − | 0.242858i | ||||||
\(512\) | −171456. | − | 198299.i | −0.654051 | − | 0.756451i | ||||
\(513\) | 27483.9 | 0.104434 | ||||||||
\(514\) | −185104. | − | 188109.i | −0.700630 | − | 0.712005i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1667.20 | + | 103514.i | −0.00626165 | + | 0.388777i | ||||
\(517\) | −89777.9 | −0.335883 | ||||||||
\(518\) | 414896. | − | 408268.i | 1.54625 | − | 1.52155i | ||||
\(519\) | − | 165611.i | − | 0.614831i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 309126. | 1.13883 | 0.569416 | − | 0.822049i | \(-0.307169\pi\) | ||||
0.569416 | + | 0.822049i | \(0.307169\pi\) | |||||||
\(522\) | 80223.7 | + | 81526.2i | 0.294416 | + | 0.299196i | ||||
\(523\) | 49369.3i | 0.180490i | 0.995920 | + | 0.0902452i | \(0.0287651\pi\) | ||||
−0.995920 | + | 0.0902452i | \(0.971235\pi\) | |||||||
\(524\) | −110694. | − | 1782.84i | −0.403146 | − | 0.00649308i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −130836. | + | 128745.i | −0.472884 | + | 0.465329i | ||||
\(527\) | 49878.6i | 0.179594i | ||||||||
\(528\) | 293475. | + | 9455.90i | 1.05270 | + | 0.0339184i | ||||
\(529\) | −270470. | −0.966514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 66744.6i | − | 0.236716i | ||||||
\(532\) | −3211.44 | + | 199394.i | −0.0113469 | + | 0.704511i | ||||
\(533\) | 270388. | 0.951773 | ||||||||
\(534\) | −162449. | + | 159854.i | −0.569684 | + | 0.560583i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 255715. | + | 268377.i | 0.890073 | + | 0.934150i | ||||
\(537\) | −274581. | −0.952188 | ||||||||
\(538\) | −186851. | − | 189885.i | −0.645551 | − | 0.656032i | ||||
\(539\) | 363533.i | 1.25132i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −102454. | −0.350053 | −0.175027 | − | 0.984564i | \(-0.556001\pi\) | ||||
−0.175027 | + | 0.984564i | \(0.556001\pi\) | |||||||
\(542\) | 307482. | − | 302570.i | 1.04670 | − | 1.02998i | ||||
\(543\) | 327592.i | 1.11105i | ||||||||
\(544\) | 32454.7 | + | 35179.2i | 0.109668 | + | 0.118874i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 219685. | + | 223252.i | 0.736911 | + | 0.748875i | ||||
\(547\) | − | 66168.6i | − | 0.221145i | −0.993868 | − | 0.110573i | \(-0.964732\pi\) | ||
0.993868 | − | 0.110573i | \(-0.0352685\pi\) | |||||||
\(548\) | 6343.45 | − | 393855.i | 0.0211234 | − | 1.31152i | ||||
\(549\) | −130121. | −0.431720 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 207468.i | − | 0.683358i | ||||||
\(552\) | 178605. | − | 170178.i | 0.586158 | − | 0.558501i | ||||
\(553\) | 69794.2 | 0.228228 | ||||||||
\(554\) | 213562. | + | 217029.i | 0.695831 | + | 0.707128i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −300236. | − | 4835.61i | −0.971210 | − | 0.0156424i | ||||
\(557\) | 344220. | 1.10950 | 0.554749 | − | 0.832018i | \(-0.312814\pi\) | ||||
0.554749 | + | 0.832018i | \(0.312814\pi\) | |||||||
\(558\) | −82146.7 | + | 80834.3i | −0.263829 | + | 0.259614i | ||||
\(559\) | − | 294943.i | − | 0.943874i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −53611.6 | −0.170346 | ||||||||
\(562\) | −358931. | − | 364759.i | −1.13642 | − | 1.15487i | ||||
\(563\) | − | 581940.i | − | 1.83595i | −0.396637 | − | 0.917976i | \(-0.629823\pi\) | ||
0.396637 | − | 0.917976i | \(-0.370177\pi\) | |||||||
\(564\) | 544.538 | − | 33809.6i | 0.00171187 | − | 0.106287i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −335837. | + | 330472.i | −1.04833 | + | 1.03158i | ||||
\(567\) | 46381.3i | 0.144270i | ||||||||
\(568\) | −13658.2 | − | 14334.5i | −0.0423347 | − | 0.0444311i | ||||
\(569\) | 269874. | 0.833559 | 0.416779 | − | 0.909008i | \(-0.363159\pi\) | ||||
0.416779 | + | 0.909008i | \(0.363159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 248959.i | 0.763581i | 0.924249 | + | 0.381790i | \(0.124692\pi\) | ||||
−0.924249 | + | 0.381790i | \(0.875308\pi\) | |||||||
\(572\) | −836416. | − | 13471.3i | −2.55641 | − | 0.0411736i | ||||
\(573\) | −107717. | −0.328077 | ||||||||
\(574\) | −207078. | + | 203770.i | −0.628507 | + | 0.618466i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5341.06 | + | 110463.i | −0.0160984 | + | 0.332944i | ||||
\(577\) | 389168. | 1.16892 | 0.584461 | − | 0.811422i | \(-0.301306\pi\) | ||||
0.584461 | + | 0.811422i | \(0.301306\pi\) | |||||||
\(578\) | 228194. | + | 231899.i | 0.683043 | + | 0.694133i | ||||
\(579\) | 91284.1i | 0.272294i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −197061. | −0.583779 | ||||||||
\(582\) | −182800. | + | 179879.i | −0.539672 | + | 0.531050i | ||||
\(583\) | 318388.i | 0.936742i | ||||||||
\(584\) | −46183.4 | + | 44004.3i | −0.135413 | + | 0.129024i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 338120. | + | 343610.i | 0.984636 | + | 1.00062i | ||||
\(587\) | − | 67273.5i | − | 0.195240i | −0.995224 | − | 0.0976198i | \(-0.968877\pi\) | ||
0.995224 | − | 0.0976198i | \(-0.0311229\pi\) | |||||||
\(588\) | −136904. | − | 2204.98i | −0.395968 | − | 0.00637748i | ||||
\(589\) | 209047. | 0.602579 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 263969.i | − | 0.755750i | ||||||
\(592\) | −585227. | − | 18856.3i | −1.66986 | − | 0.0538038i | ||||
\(593\) | −483157. | −1.37398 | −0.686988 | − | 0.726669i | \(-0.741067\pi\) | ||||
−0.686988 | + | 0.726669i | \(0.741067\pi\) | |||||||
\(594\) | −86884.1 | − | 88294.7i | −0.246245 | − | 0.250243i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1693.62 | + | 105154.i | −0.00476786 | + | 0.296029i | ||||
\(597\) | 167011. | 0.468594 | ||||||||
\(598\) | −500959. | + | 492955.i | −1.40088 | + | 1.37849i | ||||
\(599\) | 361016.i | 1.00617i | 0.864236 | + | 0.503086i | \(0.167802\pi\) | ||||
−0.864236 | + | 0.503086i | \(0.832198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −329300. | −0.911681 | −0.455841 | − | 0.890061i | \(-0.650661\pi\) | ||||
−0.455841 | + | 0.890061i | \(0.650661\pi\) | |||||||
\(602\) | 222274. | + | 225883.i | 0.613333 | + | 0.623290i | ||||
\(603\) | − | 156388.i | − | 0.430099i | ||||||
\(604\) | −125156. | − | 2015.77i | −0.343067 | − | 0.00552545i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −221012. | + | 217481.i | −0.601826 | + | 0.592211i | ||||
\(607\) | 347112.i | 0.942090i | 0.882109 | + | 0.471045i | \(0.156123\pi\) | ||||
−0.882109 | + | 0.471045i | \(0.843877\pi\) | |||||||
\(608\) | 147440. | − | 136022.i | 0.398850 | − | 0.367960i | ||||
\(609\) | 350120. | 0.944021 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 96333.6i | 0.258045i | ||||||||
\(612\) | 325.175 | − | 20189.7i | 0.000868190 | − | 0.0539046i | ||||
\(613\) | 315831. | 0.840492 | 0.420246 | − | 0.907410i | \(-0.361944\pi\) | ||||
0.420246 | + | 0.907410i | \(0.361944\pi\) | |||||||
\(614\) | −256609. | + | 252509.i | −0.680667 | + | 0.669792i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 650724. | − | 620021.i | 1.71489 | − | 1.63397i | ||||
\(617\) | 302237. | 0.793920 | 0.396960 | − | 0.917836i | \(-0.370065\pi\) | ||||
0.396960 | + | 0.917836i | \(0.370065\pi\) | |||||||
\(618\) | 146993. | + | 149380.i | 0.384876 | + | 0.391124i | ||||
\(619\) | − | 367141.i | − | 0.958190i | −0.877763 | − | 0.479095i | \(-0.840965\pi\) | ||
0.877763 | − | 0.479095i | \(-0.159035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −104076. | −0.269878 | ||||||||
\(622\) | −102481. | + | 100843.i | −0.264887 | + | 0.260655i | ||||
\(623\) | 697647.i | 1.79746i | ||||||||
\(624\) | 10146.4 | − | 314905.i | 0.0260581 | − | 0.808744i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −29236.0 | − | 29710.7i | −0.0746052 | − | 0.0758165i | ||||
\(627\) | 224693.i | 0.571549i | ||||||||
\(628\) | −2371.17 | + | 147222.i | −0.00601234 | + | 0.373297i | ||||
\(629\) | 106908. | 0.270215 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 210709.i | − | 0.529206i | −0.964357 | − | 0.264603i | \(-0.914759\pi\) | ||
0.964357 | − | 0.264603i | \(-0.0852409\pi\) | |||||||
\(632\) | −48430.6 | − | 50828.9i | −0.121251 | − | 0.127255i | ||||
\(633\) | −49578.3 | −0.123733 | ||||||||
\(634\) | 124221. | + | 126238.i | 0.309043 | + | 0.314060i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −119902. | − | 1931.15i | −0.296424 | − | 0.00477422i | ||||
\(637\) | 390079. | 0.961334 | ||||||||
\(638\) | −666512. | + | 655864.i | −1.63745 | + | 1.61129i | ||||
\(639\) | 8352.97i | 0.0204569i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −415962. | −1.01237 | −0.506183 | − | 0.862426i | \(-0.668944\pi\) | ||||
−0.506183 | + | 0.862426i | \(0.668944\pi\) | |||||||
\(642\) | −269341. | − | 273714.i | −0.653479 | − | 0.664089i | ||||
\(643\) | 732294.i | 1.77118i | 0.464465 | + | 0.885592i | \(0.346247\pi\) | ||||
−0.464465 | + | 0.885592i | \(0.653753\pi\) | |||||||
\(644\) | 12161.1 | − | 755063.i | 0.0293225 | − | 1.82059i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26106.4 | + | 25689.4i | −0.0625580 | + | 0.0615585i | ||||
\(647\) | 96321.2i | 0.230098i | 0.993360 | + | 0.115049i | \(0.0367025\pi\) | ||||
−0.993360 | + | 0.115049i | \(0.963297\pi\) | |||||||
\(648\) | 33778.0 | − | 32184.3i | 0.0804423 | − | 0.0766467i | ||||
\(649\) | 545667. | 1.29550 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 352785.i | 0.832430i | ||||||||
\(652\) | 698584. | + | 11251.4i | 1.64333 | + | 0.0264675i | ||||
\(653\) | 274691. | 0.644196 | 0.322098 | − | 0.946706i | \(-0.395612\pi\) | ||||
0.322098 | + | 0.946706i | \(0.395612\pi\) | |||||||
\(654\) | 10027.9 | − | 9867.66i | 0.0234452 | − | 0.0230706i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 292092. | + | 9411.32i | 0.678752 | + | 0.0218697i | ||||
\(657\) | 26911.8 | 0.0623465 | ||||||||
\(658\) | −72598.8 | − | 73777.5i | −0.167679 | − | 0.170401i | ||||
\(659\) | − | 360421.i | − | 0.829927i | −0.909838 | − | 0.414963i | \(-0.863794\pi\) | ||
0.909838 | − | 0.414963i | \(-0.136206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 461663. | 1.05663 | 0.528314 | − | 0.849049i | \(-0.322824\pi\) | ||||
0.528314 | + | 0.849049i | \(0.322824\pi\) | |||||||
\(662\) | 624442. | − | 614465.i | 1.42487 | − | 1.40211i | ||||
\(663\) | 57526.4i | 0.130870i | ||||||||
\(664\) | 136742. | + | 143513.i | 0.310145 | + | 0.325504i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 173258. | + | 176071.i | 0.390611 | + | 0.396953i | ||||
\(667\) | 785640.i | 1.76592i | ||||||||
\(668\) | −314562. | − | 5066.35i | −0.704943 | − | 0.0113538i | ||||
\(669\) | 173912. | 0.388578 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.06379e6i | − | 2.36272i | ||||||
\(672\) | 229548. | + | 248818.i | 0.508317 | + | 0.550989i | ||||
\(673\) | 295518. | 0.652459 | 0.326230 | − | 0.945291i | \(-0.394222\pi\) | ||||
0.326230 | + | 0.945291i | \(0.394222\pi\) | |||||||
\(674\) | 143570. | + | 145901.i | 0.316042 | + | 0.321173i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7095.93 | + | 440576.i | −0.0155280 | + | 0.964111i | ||||
\(677\) | −865789. | −1.88901 | −0.944506 | − | 0.328494i | \(-0.893459\pi\) | ||||
−0.944506 | + | 0.328494i | \(0.893459\pi\) | |||||||
\(678\) | −84354.3 | + | 83006.6i | −0.183505 | + | 0.180573i | ||||
\(679\) | 785046.i | 1.70277i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5971.77 | 0.0128768 | ||||||||
\(682\) | −660856. | − | 671586.i | −1.42082 | − | 1.44389i | ||||
\(683\) | − | 631289.i | − | 1.35328i | −0.736316 | − | 0.676638i | \(-0.763436\pi\) | ||
0.736316 | − | 0.676638i | \(-0.236564\pi\) | |||||||
\(684\) | −84617.4 | − | 1362.85i | −0.180862 | − | 0.00291297i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 136790. | − | 134604.i | 0.290673 | − | 0.286029i | ||||
\(687\) | 256650.i | 0.543785i | ||||||||
\(688\) | 10266.0 | − | 318617.i | 0.0216882 | − | 0.673119i | ||||
\(689\) | 341638. | 0.719660 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 692970.i | 1.45130i | 0.688062 | + | 0.725652i | \(0.258462\pi\) | ||||
−0.688062 | + | 0.725652i | \(0.741538\pi\) | |||||||
\(692\) | −8212.23 | + | 509885.i | −0.0171494 | + | 1.06478i | ||||
\(693\) | −379188. | −0.789564 | ||||||||
\(694\) | 224946. | − | 221352.i | 0.467045 | − | 0.459584i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −242950. | − | 254981.i | −0.501532 | − | 0.526368i | ||||
\(697\) | −53358.8 | −0.109835 | ||||||||
\(698\) | −524880. | − | 533402.i | −1.07733 | − | 1.09482i | ||||
\(699\) | 218675.i | 0.447553i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −106868. | −0.217477 | −0.108739 | − | 0.994070i | \(-0.534681\pi\) | ||||
−0.108739 | + | 0.994070i | \(0.534681\pi\) | |||||||
\(702\) | −94742.2 | + | 93228.5i | −0.192251 | + | 0.189180i | ||||
\(703\) | − | 448066.i | − | 0.906633i | ||||||
\(704\) | −903083. | − | 43665.5i | −1.82214 | − | 0.0881035i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 74561.4 | + | 75772.0i | 0.149591 | + | 0.152020i | ||||
\(707\) | 949151.i | 1.89888i | ||||||||
\(708\) | −3309.69 | + | 205493.i | −0.00660268 | + | 0.409951i | ||||
\(709\) | 71602.5 | 0.142441 | 0.0712207 | − | 0.997461i | \(-0.477311\pi\) | ||||
0.0712207 | + | 0.997461i | \(0.477311\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29618.8i | 0.0585906i | ||||||||
\(712\) | 508075. | − | 484102.i | 1.00223 | − | 0.954942i | ||||
\(713\) | −791620. | −1.55718 | ||||||||
\(714\) | −43352.9 | − | 44056.8i | −0.0850397 | − | 0.0864204i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 845382. | + | 13615.8i | 1.64902 | + | 0.0265592i | ||||
\(717\) | 179477. | 0.349117 | ||||||||
\(718\) | −37667.8 | + | 37066.0i | −0.0730671 | + | 0.0718997i | ||||
\(719\) | − | 84839.0i | − | 0.164111i | −0.996628 | − | 0.0820555i | \(-0.973852\pi\) | ||
0.996628 | − | 0.0820555i | \(-0.0261485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 641521. | 1.23407 | ||||||||
\(722\) | −257956. | − | 262144.i | −0.494848 | − | 0.502882i | ||||
\(723\) | − | 356804.i | − | 0.682579i | ||||||
\(724\) | 16244.4 | − | 1.00859e6i | 0.0309903 | − | 1.92414i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 504945. | − | 496877.i | 0.958011 | − | 0.942706i | ||||
\(727\) | − | 80916.8i | − | 0.153098i | −0.997066 | − | 0.0765491i | \(-0.975610\pi\) | ||
0.997066 | − | 0.0765491i | \(-0.0243902\pi\) | |||||||
\(728\) | −665296. | − | 698241.i | −1.25531 | − | 1.31748i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58204.4i | 0.108923i | ||||||||
\(732\) | 400616. | + | 6452.34i | 0.747663 | + | 0.0120419i | ||||
\(733\) | 62103.9 | 0.115588 | 0.0577938 | − | 0.998329i | \(-0.481593\pi\) | ||||
0.0577938 | + | 0.998329i | \(0.481593\pi\) | |||||||
\(734\) | −133778. | + | 131640.i | −0.248308 | + | 0.244341i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −558327. | + | 515086.i | −1.03070 | + | 0.950877i | ||||
\(737\) | 1.27854e6 | 2.35385 | ||||||||
\(738\) | −86474.4 | − | 87878.4i | −0.158772 | − | 0.161350i | ||||
\(739\) | 268031.i | 0.490790i | 0.969423 | + | 0.245395i | \(0.0789176\pi\) | ||||
−0.969423 | + | 0.245395i | \(0.921082\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 241100. | 0.439098 | ||||||||
\(742\) | −261644. | + | 257464.i | −0.475230 | + | 0.467637i | ||||
\(743\) | 348633.i | 0.631525i | 0.948838 | + | 0.315763i | \(0.102260\pi\) | ||||
−0.948838 | + | 0.315763i | \(0.897740\pi\) | |||||||
\(744\) | 256922. | − | 244799.i | 0.464147 | − | 0.442247i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 666291. | + | 677109.i | 1.19725 | + | 1.21669i | ||||
\(747\) | − | 83627.5i | − | 0.149868i | ||||||
\(748\) | 165059. | + | 2658.45i | 0.295010 | + | 0.00475145i | ||||
\(749\) | −1.17548e6 | −2.09533 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 757069.i | − | 1.34232i | −0.741313 | − | 0.671159i | \(-0.765797\pi\) | ||
0.741313 | − | 0.671159i | \(-0.234203\pi\) | |||||||
\(752\) | −3353.05 | + | 104066.i | −0.00592932 | + | 0.184023i | ||||
\(753\) | 322179. | 0.568207 | ||||||||
\(754\) | 703756. | + | 715182.i | 1.23788 | + | 1.25798i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2299.92 | − | 142799.i | 0.00402411 | − | 0.249851i | ||||
\(757\) | 128542. | 0.224312 | 0.112156 | − | 0.993691i | \(-0.464224\pi\) | ||||
0.112156 | + | 0.993691i | \(0.464224\pi\) | |||||||
\(758\) | 308334. | − | 303408.i | 0.536639 | − | 0.528066i | ||||
\(759\) | − | 850866.i | − | 1.47699i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 460176. | 0.794611 | 0.397306 | − | 0.917686i | \(-0.369945\pi\) | ||||
0.397306 | + | 0.917686i | \(0.369945\pi\) | |||||||
\(762\) | −318305. | − | 323473.i | −0.548193 | − | 0.557094i | ||||
\(763\) | − | 43065.4i | − | 0.0739740i | ||||||
\(764\) | 331640. | + | 5341.40i | 0.568172 | + | 0.00915100i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 408019. | − | 401501.i | 0.695382 | − | 0.684272i | ||||
\(767\) | − | 585512.i | − | 0.995280i | ||||||
\(768\) | 21921.6 | − | 339829.i | 0.0371664 | − | 0.576153i | ||||
\(769\) | 1.10194e6 | 1.86340 | 0.931701 | − | 0.363226i | \(-0.118325\pi\) | ||||
0.931701 | + | 0.363226i | \(0.118325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 342829.i | − | 0.576725i | ||||||
\(772\) | 4526.53 | − | 281046.i | 0.00759506 | − | 0.471566i | ||||
\(773\) | 809541. | 1.35481 | 0.677407 | − | 0.735608i | \(-0.263103\pi\) | ||||
0.677407 | + | 0.735608i | \(0.263103\pi\) | |||||||
\(774\) | −95858.8 | + | 94327.3i | −0.160011 | + | 0.157455i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 571724. | − | 544748.i | 0.949430 | − | 0.904633i | ||||
\(777\) | 756149. | 1.25246 | ||||||||
\(778\) | 370505. | + | 376520.i | 0.612117 | + | 0.622055i | ||||
\(779\) | 223633.i | 0.368520i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68289.2 | −0.111957 | ||||||||
\(782\) | 98859.8 | − | 97280.4i | 0.161661 | − | 0.159079i | ||||
\(783\) | 148582.i | 0.242349i | ||||||||
\(784\) | 421390. | + | 13577.4i | 0.685570 | + | 0.0220894i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −100870. | − | 102508.i | −0.163274 | − | 0.165925i | ||||
\(787\) | − | 363079.i | − | 0.586207i | −0.956081 | − | 0.293104i | \(-0.905312\pi\) | ||
0.956081 | − | 0.293104i | \(-0.0946881\pi\) | |||||||
\(788\) | −13089.5 | + | 812709.i | −0.0210800 | + | 1.30883i | ||||
\(789\) | −238448. | −0.383036 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 362265.i | 0.578993i | ||||||||
\(792\) | 263121. | + | 276150.i | 0.419473 | + | 0.440246i | ||||
\(793\) | −1.14147e6 | −1.81518 | ||||||||
\(794\) | 129446. | + | 131548.i | 0.205328 | + | 0.208662i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −514194. | − | 8281.64i | −0.811524 | − | 0.0130704i | ||||
\(797\) | 483796. | 0.761633 | 0.380816 | − | 0.924651i | \(-0.375643\pi\) | ||||
0.380816 | + | 0.924651i | \(0.375643\pi\) | |||||||
\(798\) | −184647. | + | 181697.i | −0.289960 | + | 0.285327i | ||||
\(799\) | − | 19010.6i | − | 0.0297785i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −296063. | −0.461444 | ||||||||
\(802\) | −9103.96 | − | 9251.77i | −0.0141541 | − | 0.0143839i | ||||
\(803\) | 220016.i | 0.341211i | ||||||||
\(804\) | −7754.85 | + | 481487.i | −0.0119967 | + | 0.744857i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −720626. | + | 709113.i | −1.10928 | + | 1.09155i | ||||
\(807\) | − | 346065.i | − | 0.531386i | ||||||
\(808\) | 691237. | − | 658622.i | 1.05878 | − | 1.00882i | ||||
\(809\) | 483640. | 0.738966 | 0.369483 | − | 0.929237i | \(-0.379535\pi\) | ||||
0.369483 | + | 0.929237i | \(0.379535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 406318.i | − | 0.617767i | −0.951100 | − | 0.308883i | \(-0.900045\pi\) | ||
0.951100 | − | 0.308883i | \(-0.0999553\pi\) | |||||||
\(812\) | −1.07795e6 | − | 17361.5i | −1.63488 | − | 0.0263315i | ||||
\(813\) | 560386. | 0.847826 | ||||||||
\(814\) | −1.43946e6 | + | 1.41646e6i | −2.17245 | + | 2.13774i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2002.30 | + | 62143.8i | −0.00300711 | + | 0.0933292i | ||||
\(817\) | 243942. | 0.365462 | ||||||||
\(818\) | 533693. | + | 542358.i | 0.797599 | + | 0.810549i | ||||
\(819\) | 406877.i | 0.606589i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 489931. | 0.726857 | 0.363428 | − | 0.931622i | \(-0.381606\pi\) | ||||
0.363428 | + | 0.931622i | \(0.381606\pi\) | |||||||
\(822\) | 364728. | − | 358901.i | 0.539791 | − | 0.531167i | ||||
\(823\) | 372808.i | 0.550408i | 0.961386 | + | 0.275204i | \(0.0887455\pi\) | ||||
−0.961386 | + | 0.275204i | \(0.911255\pi\) | |||||||
\(824\) | −445156. | − | 467200.i | −0.655628 | − | 0.688095i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 441253. | + | 448417.i | 0.646736 | + | 0.657237i | ||||
\(827\) | − | 222364.i | − | 0.325127i | −0.986698 | − | 0.162563i | \(-0.948024\pi\) | ||
0.986698 | − | 0.162563i | \(-0.0519762\pi\) | |||||||
\(828\) | 320429. | + | 5160.84i | 0.467381 | + | 0.00752766i | ||||
\(829\) | 127764. | 0.185908 | 0.0929542 | − | 0.995670i | \(-0.470369\pi\) | ||||
0.0929542 | + | 0.995670i | \(0.470369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 395536.i | 0.572774i | ||||||||
\(832\) | −46854.0 | + | 969028.i | −0.0676862 | + | 1.39988i | ||||
\(833\) | −76978.8 | −0.110938 | ||||||||
\(834\) | −273590. | − | 278032.i | −0.393341 | − | 0.399727i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11141.9 | − | 691784.i | 0.0159422 | − | 0.989824i | ||||
\(837\) | −149712. | −0.213701 | ||||||||
\(838\) | −110233. | + | 108472.i | −0.156972 | + | 0.154465i | ||||
\(839\) | − | 981082.i | − | 1.39374i | −0.717198 | − | 0.696870i | \(-0.754576\pi\) | ||
0.717198 | − | 0.696870i | \(-0.245424\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 414320. | 0.585793 | ||||||||
\(842\) | 603814. | + | 613617.i | 0.851684 | + | 0.865512i | ||||
\(843\) | − | 664774.i | − | 0.935446i | ||||||
\(844\) | 152642. | + | 2458.45i | 0.214283 | + | 0.00345125i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 31309.2 | − | 30809.0i | 0.0437453 | − | 0.0430464i | ||||
\(847\) | − | 2.16852e6i | − | 3.02271i | ||||||
\(848\) | 369060. | + | 11891.3i | 0.513222 | + | 0.0165362i | ||||
\(849\) | −612064. | −0.849144 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.69674e6i | 2.34291i | ||||||||
\(852\) | 414.201 | − | 25717.1i | 0.000570601 | − | 0.0354278i | ||||
\(853\) | −192525. | −0.264599 | −0.132299 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132299 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(854\) | 874203. | − | 860236.i | 1.19866 | − | 1.17951i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 815674. | + | 856066.i | 1.11319 | + | 1.16831i | ||||
\(857\) | −1.20031e6 | −1.63430 | −0.817151 | − | 0.576424i | \(-0.804448\pi\) | ||||
−0.817151 | + | 0.576424i | \(0.804448\pi\) | |||||||
\(858\) | −762184. | − | 774559.i | −1.03535 | − | 1.05216i | ||||
\(859\) | 1.29982e6i | 1.76156i | 0.473529 | + | 0.880778i | \(0.342980\pi\) | ||||
−0.473529 | + | 0.880778i | \(0.657020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −377400. | −0.509091 | ||||||||
\(862\) | −36586.7 | + | 36002.2i | −0.0492390 | + | 0.0484523i | ||||
\(863\) | 148386.i | 0.199238i | 0.995026 | + | 0.0996188i | \(0.0317623\pi\) | ||||
−0.995026 | + | 0.0996188i | \(0.968238\pi\) | |||||||
\(864\) | −105592. | + | 97414.0i | −0.141450 | + | 0.130495i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −688103. | − | 699275.i | −0.917525 | − | 0.932421i | ||||
\(867\) | 422636.i | 0.562248i | ||||||||
\(868\) | 17493.6 | − | 1.08615e6i | 0.0232188 | − | 1.44162i | ||||
\(869\) | −242147. | −0.320656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.37190e6i | − | 1.80837i | ||||||
\(872\) | −31363.1 | + | 29883.3i | −0.0412465 | + | 0.0393003i | ||||
\(873\) | −333153. | −0.437134 | ||||||||
\(874\) | −407714. | − | 414334.i | −0.533744 | − | 0.542410i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −82856.1 | − | 1334.48i | −0.107973 | − | 0.00173902i | ||||
\(877\) | −144747. | −0.188196 | −0.0940981 | − | 0.995563i | \(-0.529997\pi\) | ||||
−0.0940981 | + | 0.995563i | \(0.529997\pi\) | |||||||
\(878\) | 23722.9 | − | 23343.9i | 0.0307736 | − | 0.0302820i | ||||
\(879\) | 626229.i | 0.810505i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 281633. | 0.362853 | 0.181427 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181427 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(882\) | −124754. | − | 126779.i | −0.160367 | − | 0.162971i | ||||
\(883\) | − | 334210.i | − | 0.428645i | −0.976763 | − | 0.214323i | \(-0.931246\pi\) | ||
0.976763 | − | 0.214323i | \(-0.0687544\pi\) | |||||||
\(884\) | 2852.58 | − | 177112.i | 0.00365034 | − | 0.226644i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −402689. | + | 396255.i | −0.512982 | + | 0.504787i | ||||
\(887\) | 504313.i | 0.640992i | 0.947250 | + | 0.320496i | \(0.103850\pi\) | ||||
−0.947250 | + | 0.320496i | \(0.896150\pi\) | |||||||
\(888\) | −524696. | − | 550679.i | −0.665399 | − | 0.698349i | ||||
\(889\) | −1.38918e6 | −1.75774 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 160917.i | − | 0.202697i | ||||||
\(892\) | −535442. | − | 8623.85i | −0.672950 | − | 0.0108386i | ||||
\(893\) | −79675.8 | −0.0999133 | ||||||||
\(894\) | −97377.7 | + | 95822.0i | −0.121839 | + | 0.119892i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −694394. | − | 777444.i | −0.864948 | − | 0.968396i | ||||
\(897\) | −912998. | −1.13471 | ||||||||
\(898\) | 554451. | + | 563453.i | 0.687560 | + | 0.698723i | ||||
\(899\) | 1.13014e6i | 1.39834i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −67419.2 | −0.0830489 | ||||||||
\(902\) | 718445. | − | 706967.i | 0.883040 | − | 0.868932i | ||||
\(903\) | 411672.i | 0.504866i | ||||||||
\(904\) | 263826. | − | 251378.i | 0.322835 | − | 0.307603i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −114049. | − | 115900.i | −0.138942 | − | 0.141198i | ||||
\(907\) | 83306.2i | 0.101266i | 0.998717 | + | 0.0506329i | \(0.0161239\pi\) | ||||
−0.998717 | + | 0.0506329i | \(0.983876\pi\) | |||||||
\(908\) | −18385.9 | − | 296.124i | −0.0223004 | − | 0.000359172i | ||||
\(909\) | −402795. | −0.487479 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 115795.i | − | 0.139525i | −0.997564 | − | 0.0697626i | \(-0.977776\pi\) | ||
0.997564 | − | 0.0697626i | \(-0.0222242\pi\) | |||||||
\(912\) | 260453. | + | 8391.89i | 0.313140 | + | 0.0100895i | ||||
\(913\) | 683691. | 0.820198 | ||||||||
\(914\) | 929574. | + | 944667.i | 1.11274 | + | 1.13080i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12726.6 | − | 790173.i | 0.0151677 | − | 0.941741i | ||||
\(917\) | −440227. | −0.523525 | ||||||||
\(918\) | 18696.5 | − | 18397.8i | 0.0221858 | − | 0.0218314i | ||||
\(919\) | − | 788234.i | − | 0.933306i | −0.884441 | − | 0.466653i | \(-0.845460\pi\) | ||
0.884441 | − | 0.466653i | \(-0.154540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −467670. | −0.551341 | ||||||||
\(922\) | 550143. | + | 559075.i | 0.647163 | + | 0.657671i | ||||
\(923\) | 73275.8i | 0.0860117i | ||||||||
\(924\) | 1.16744e6 | + | 18802.9i | 1.36739 | + | 0.0220232i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −481107. | + | 473420.i | −0.561073 | + | 0.552109i | ||||
\(927\) | 272245.i | 0.316811i | ||||||||
\(928\) | 735352. | + | 797083.i | 0.853884 | + | 0.925567i | ||||
\(929\) | −15865.8 | −0.0183837 | −0.00919183 | − | 0.999958i | \(-0.502926\pi\) | ||||
−0.00919183 | + | 0.999958i | \(0.502926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 322628.i | 0.372222i | ||||||||
\(932\) | 10843.5 | − | 673256.i | 0.0124835 | − | 0.775084i | ||||
\(933\) | −186771. | −0.214559 | ||||||||
\(934\) | 165945. | − | 163294.i | 0.190227 | − | 0.187188i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 296315. | − | 282334.i | 0.338222 | − | 0.322264i | ||||
\(937\) | −15433.2 | −0.0175783 | −0.00878913 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00878913 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(938\) | 1.03389e6 | + | 1.05068e6i | 1.17508 | + | 1.19416i | ||||
\(939\) | − | 54147.7i | − | 0.0614114i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −550507. | −0.621704 | −0.310852 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310852 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(942\) | −136335. | + | 134157.i | −0.153640 | + | 0.151185i | ||||
\(943\) | − | 846854.i | − | 0.952325i | ||||||
\(944\) | 20379.7 | − | 632510.i | 0.0228694 | − | 0.709779i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −771167. | − | 783688.i | −0.861720 | − | 0.875711i | ||||
\(947\) | 1.27984e6i | 1.42710i | 0.700602 | + | 0.713552i | \(0.252915\pi\) | ||||
−0.700602 | + | 0.713552i | \(0.747085\pi\) | |||||||
\(948\) | 1468.72 | − | 91190.4i | 0.00163426 | − | 0.101469i | ||||
\(949\) | 236082. | 0.262138 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 230069.i | 0.254389i | ||||||||
\(952\) | 131290. | + | 137792.i | 0.144864 | + | 0.152037i | ||||
\(953\) | 491859. | 0.541571 | 0.270785 | − | 0.962640i | \(-0.412717\pi\) | ||||
0.270785 | + | 0.962640i | \(0.412717\pi\) | |||||||
\(954\) | −109261. | − | 111035.i | −0.120052 | − | 0.122001i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −552575. | − | 8899.80i | −0.604611 | − | 0.00973788i | ||||
\(957\) | −1.21472e6 | −1.32633 | ||||||||
\(958\) | 632090. | − | 621992.i | 0.688729 | − | 0.677725i | ||||
\(959\) | − | 1.56635e6i | − | 1.70314i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −215219. | −0.233042 | ||||||||
\(962\) | 1.51989e6 | + | 1.54457e6i | 1.64234 | + | 1.66900i | ||||
\(963\) | − | 498843.i | − | 0.537912i | ||||||
\(964\) | −17692.9 | + | 1.09853e6i | −0.0190391 | + | 1.18211i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 699223. | − | 688052.i | 0.749310 | − | 0.737338i | ||||
\(967\) | − | 628976.i | − | 0.672638i | −0.941748 | − | 0.336319i | \(-0.890818\pi\) | ||
0.941748 | − | 0.336319i | \(-0.109182\pi\) | |||||||
\(968\) | −1.57926e6 | + | 1.50475e6i | −1.68540 | + | 1.60588i | ||||
\(969\) | −47579.0 | −0.0506720 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.78700e6i | 1.89533i | 0.319264 | + | 0.947666i | \(0.396564\pi\) | ||||
−0.319264 | + | 0.947666i | \(0.603436\pi\) | |||||||
\(972\) | 60600.1 | + | 976.027i | 0.0641417 | + | 0.00103307i | ||||
\(973\) | −1.19403e6 | −1.26121 | ||||||||
\(974\) | 415040. | − | 408409.i | 0.437494 | − | 0.430505i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.23310e6 | − | 39730.9i | −1.29449 | − | 0.0417089i | ||||
\(977\) | −842171. | −0.882289 | −0.441145 | − | 0.897436i | \(-0.645427\pi\) | ||||
−0.441145 | + | 0.897436i | \(0.645427\pi\) | |||||||
\(978\) | 636585. | + | 646921.i | 0.665547 | + | 0.676353i | ||||
\(979\) | − | 2.42045e6i | − | 2.52540i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18275.8 | 0.0189906 | ||||||||
\(982\) | −697373. | + | 686232.i | −0.723173 | + | 0.711620i | ||||
\(983\) | 877633.i | 0.908251i | 0.890938 | + | 0.454125i | \(0.150048\pi\) | ||||
−0.890938 | + | 0.454125i | \(0.849952\pi\) | |||||||
\(984\) | 261880. | + | 274848.i | 0.270466 | + | 0.283859i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −138880. | − | 141135.i | −0.142852 | − | 0.145171i | ||||
\(987\) | − | 134459.i | − | 0.138025i | ||||||
\(988\) | −742300. | − | 11955.5i | −0.760441 | − | 0.0122477i | ||||
\(989\) | −923758. | −0.944421 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 326910.i | − | 0.332875i | −0.986052 | − | 0.166437i | \(-0.946774\pi\) | ||
0.986052 | − | 0.166437i | \(-0.0532264\pi\) | |||||||
\(992\) | −803150. | + | 740949.i | −0.816157 | + | 0.752948i | ||||
\(993\) | 1.13805e6 | 1.15415 | ||||||||
\(994\) | −55222.0 | − | 56118.6i | −0.0558907 | − | 0.0567981i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4146.86 | + | 257472.i | −0.00418024 | + | 0.259545i | ||||
\(997\) | −935659. | −0.941298 | −0.470649 | − | 0.882320i | \(-0.655980\pi\) | ||||
−0.470649 | + | 0.882320i | \(0.655980\pi\) | |||||||
\(998\) | 323378. | − | 318212.i | 0.324676 | − | 0.319488i | ||||
\(999\) | 320890.i | 0.321532i |
(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 | 300.5.c.b.151.5 | ✓ | 16 | |
4.3 | odd | 2 | inner | 300.5.c.b.151.6 | yes | 16 | |
5.2 | odd | 4 | 300.5.f.c.199.25 | 32 | |||
5.3 | odd | 4 | 300.5.f.c.199.8 | 32 | |||
5.4 | even | 2 | 300.5.c.c.151.12 | yes | 16 | ||
20.3 | even | 4 | 300.5.f.c.199.26 | 32 | |||
20.7 | even | 4 | 300.5.f.c.199.7 | 32 | |||
20.19 | odd | 2 | 300.5.c.c.151.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.5.c.b.151.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
300.5.c.b.151.6 | yes | 16 | 4.3 | odd | 2 | inner | |
300.5.c.c.151.11 | yes | 16 | 20.19 | odd | 2 | ||
300.5.c.c.151.12 | yes | 16 | 5.4 | even | 2 | ||
300.5.f.c.199.7 | 32 | 20.7 | even | 4 | |||
300.5.f.c.199.8 | 32 | 5.3 | odd | 4 | |||
300.5.f.c.199.25 | 32 | 5.2 | odd | 4 | |||
300.5.f.c.199.26 | 32 | 20.3 | even | 4 |