Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,3,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (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: | \(9.64580135835\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.4 | ||
Root | \(6.82349 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.3.d.a.235.14 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 6.82349 | 1.36470 | 0.682349 | − | 0.731027i | \(-0.260959\pi\) | ||||
0.682349 | + | 0.731027i | \(0.260959\pi\) | |||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 2.37240 | 0.338915 | 0.169457 | − | 0.985538i | \(-0.445799\pi\) | ||||
0.169457 | + | 0.985538i | \(0.445799\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 9.64987i | − | 0.964987i | ||||||
\(11\) | 7.57182i | 0.688347i | 0.938906 | + | 0.344174i | \(0.111841\pi\) | ||||
−0.938906 | + | 0.344174i | \(0.888159\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | 19.3586i | 1.48912i | 0.667553 | + | 0.744562i | \(0.267342\pi\) | ||||
−0.667553 | + | 0.744562i | \(0.732658\pi\) | |||||||
\(14\) | − | 3.35508i | − | 0.239649i | ||||||
\(15\) | −11.8186 | −0.787909 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −21.1983 | −1.24696 | −0.623479 | − | 0.781840i | \(-0.714281\pi\) | ||||
−0.623479 | + | 0.781840i | \(0.714281\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | 33.6908 | 1.77320 | 0.886600 | − | 0.462536i | \(-0.153060\pi\) | ||||
0.886600 | + | 0.462536i | \(0.153060\pi\) | |||||||
\(20\) | −13.6470 | −0.682349 | ||||||||
\(21\) | −4.10912 | −0.195672 | ||||||||
\(22\) | 10.7082 | 0.486735 | ||||||||
\(23\) | 13.4237i | 0.583640i | 0.956473 | + | 0.291820i | \(0.0942608\pi\) | ||||
−0.956473 | + | 0.291820i | \(0.905739\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 21.5600 | 0.862400 | ||||||||
\(26\) | 27.3772 | 1.05297 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −4.74481 | −0.169457 | ||||||||
\(29\) | 42.0061 | 1.44849 | 0.724244 | − | 0.689544i | \(-0.242189\pi\) | ||||
0.724244 | + | 0.689544i | \(0.242189\pi\) | |||||||
\(30\) | 16.7141i | 0.557135i | ||||||||
\(31\) | − | 35.8645i | − | 1.15692i | −0.815711 | − | 0.578460i | \(-0.803654\pi\) | ||
0.815711 | − | 0.578460i | \(-0.196346\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | − | 13.1148i | − | 0.397417i | ||||||
\(34\) | 29.9789i | 0.881733i | ||||||||
\(35\) | 16.1881 | 0.462516 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 39.6746i | 1.07229i | 0.844127 | + | 0.536144i | \(0.180119\pi\) | ||||
−0.844127 | + | 0.536144i | \(0.819881\pi\) | |||||||
\(38\) | − | 47.6460i | − | 1.25384i | ||||||
\(39\) | − | 33.5301i | − | 0.859746i | ||||||
\(40\) | 19.2997i | 0.482493i | ||||||||
\(41\) | 63.8528 | 1.55739 | 0.778693 | − | 0.627405i | \(-0.215883\pi\) | ||||
0.778693 | + | 0.627405i | \(0.215883\pi\) | |||||||
\(42\) | 5.81118i | 0.138361i | ||||||||
\(43\) | − | 7.54954i | − | 0.175571i | −0.996139 | − | 0.0877854i | \(-0.972021\pi\) | ||
0.996139 | − | 0.0877854i | \(-0.0279790\pi\) | |||||||
\(44\) | − | 15.1436i | − | 0.344174i | ||||||
\(45\) | 20.4705 | 0.454899 | ||||||||
\(46\) | 18.9840 | 0.412696 | ||||||||
\(47\) | − | 73.6850i | − | 1.56777i | −0.620909 | − | 0.783883i | \(-0.713236\pi\) | ||
0.620909 | − | 0.783883i | \(-0.286764\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | −43.3717 | −0.885137 | ||||||||
\(50\) | − | 30.4904i | − | 0.609809i | ||||||
\(51\) | 36.7165 | 0.719932 | ||||||||
\(52\) | − | 38.7172i | − | 0.744562i | ||||||
\(53\) | 51.3823 | 0.969477 | 0.484739 | − | 0.874659i | \(-0.338915\pi\) | ||||
0.484739 | + | 0.874659i | \(0.338915\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 51.6662i | 0.939386i | ||||||||
\(56\) | 6.71017i | 0.119824i | ||||||||
\(57\) | −58.3542 | −1.02376 | ||||||||
\(58\) | − | 59.4056i | − | 1.02424i | ||||||
\(59\) | 13.0424 | − | 57.5404i | 0.221058 | − | 0.975261i | ||||
\(60\) | 23.6373 | 0.393954 | ||||||||
\(61\) | 108.823i | 1.78399i | 0.452047 | + | 0.891994i | \(0.350694\pi\) | ||||
−0.452047 | + | 0.891994i | \(0.649306\pi\) | |||||||
\(62\) | −50.7201 | −0.818066 | ||||||||
\(63\) | 7.11721 | 0.112972 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 132.093i | 2.03220i | ||||||||
\(66\) | −18.5471 | −0.281017 | ||||||||
\(67\) | − | 78.9112i | − | 1.17778i | −0.808213 | − | 0.588890i | \(-0.799565\pi\) | ||
0.808213 | − | 0.588890i | \(-0.200435\pi\) | |||||||
\(68\) | 42.3966 | 0.623479 | ||||||||
\(69\) | − | 23.2506i | − | 0.336965i | ||||||
\(70\) | − | 22.8934i | − | 0.327048i | ||||||
\(71\) | −89.3631 | −1.25864 | −0.629318 | − | 0.777148i | \(-0.716666\pi\) | ||||
−0.629318 | + | 0.777148i | \(0.716666\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | 88.7054i | 1.21514i | 0.794265 | + | 0.607571i | \(0.207856\pi\) | ||||
−0.794265 | + | 0.607571i | \(0.792144\pi\) | |||||||
\(74\) | 56.1084 | 0.758222 | ||||||||
\(75\) | −37.3430 | −0.497907 | ||||||||
\(76\) | −67.3816 | −0.886600 | ||||||||
\(77\) | 17.9634i | 0.233291i | ||||||||
\(78\) | −47.4187 | −0.607932 | ||||||||
\(79\) | −97.3488 | −1.23226 | −0.616132 | − | 0.787643i | \(-0.711301\pi\) | ||||
−0.616132 | + | 0.787643i | \(0.711301\pi\) | |||||||
\(80\) | 27.2940 | 0.341174 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 90.3016i | − | 1.10124i | ||||||
\(83\) | 87.0205i | 1.04844i | 0.851583 | + | 0.524220i | \(0.175643\pi\) | ||||
−0.851583 | + | 0.524220i | \(0.824357\pi\) | |||||||
\(84\) | 8.21824 | 0.0978362 | ||||||||
\(85\) | −144.646 | −1.70172 | ||||||||
\(86\) | −10.6767 | −0.124147 | ||||||||
\(87\) | −72.7567 | −0.836284 | ||||||||
\(88\) | −21.4163 | −0.243367 | ||||||||
\(89\) | − | 145.287i | − | 1.63244i | −0.577745 | − | 0.816218i | \(-0.696067\pi\) | ||
0.577745 | − | 0.816218i | \(-0.303933\pi\) | |||||||
\(90\) | − | 28.9496i | − | 0.321662i | ||||||
\(91\) | 45.9264i | 0.504686i | ||||||||
\(92\) | − | 26.8474i | − | 0.291820i | ||||||
\(93\) | 62.1192i | 0.667948i | ||||||||
\(94\) | −104.206 | −1.10858 | ||||||||
\(95\) | 229.889 | 2.41988 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 5.99767i | 0.0618316i | 0.999522 | + | 0.0309158i | \(0.00984237\pi\) | ||||
−0.999522 | + | 0.0309158i | \(0.990158\pi\) | |||||||
\(98\) | 61.3369i | 0.625886i | ||||||||
\(99\) | 22.7155i | 0.229449i | ||||||||
\(100\) | −43.1200 | −0.431200 | ||||||||
\(101\) | − | 75.8104i | − | 0.750598i | −0.926904 | − | 0.375299i | \(-0.877540\pi\) | ||
0.926904 | − | 0.375299i | \(-0.122460\pi\) | |||||||
\(102\) | − | 51.9250i | − | 0.509069i | ||||||
\(103\) | 38.2291i | 0.371156i | 0.982630 | + | 0.185578i | \(0.0594158\pi\) | ||||
−0.982630 | + | 0.185578i | \(0.940584\pi\) | |||||||
\(104\) | −54.7544 | −0.526485 | ||||||||
\(105\) | −28.0385 | −0.267034 | ||||||||
\(106\) | − | 72.6655i | − | 0.685524i | ||||||
\(107\) | 56.4480 | 0.527551 | 0.263775 | − | 0.964584i | \(-0.415032\pi\) | ||||
0.263775 | + | 0.964584i | \(0.415032\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | 88.5015i | 0.811940i | 0.913886 | + | 0.405970i | \(0.133066\pi\) | ||||
−0.913886 | + | 0.405970i | \(0.866934\pi\) | |||||||
\(110\) | 73.0671 | 0.664246 | ||||||||
\(111\) | − | 68.7185i | − | 0.619085i | ||||||
\(112\) | 9.48961 | 0.0847287 | ||||||||
\(113\) | 133.762i | 1.18373i | 0.806036 | + | 0.591866i | \(0.201608\pi\) | ||||
−0.806036 | + | 0.591866i | \(0.798392\pi\) | |||||||
\(114\) | 82.5253i | 0.723906i | ||||||||
\(115\) | 91.5965i | 0.796492i | ||||||||
\(116\) | −84.0123 | −0.724244 | ||||||||
\(117\) | 58.0758i | 0.496375i | ||||||||
\(118\) | −81.3744 | − | 18.4447i | −0.689613 | − | 0.156311i | ||||
\(119\) | −50.2909 | −0.422613 | ||||||||
\(120\) | − | 33.4281i | − | 0.278568i | ||||||
\(121\) | 63.6676 | 0.526178 | ||||||||
\(122\) | 153.899 | 1.26147 | ||||||||
\(123\) | −110.596 | −0.899158 | ||||||||
\(124\) | 71.7291i | 0.578460i | ||||||||
\(125\) | −23.4729 | −0.187783 | ||||||||
\(126\) | − | 10.0653i | − | 0.0798830i | ||||||
\(127\) | 24.1795 | 0.190390 | 0.0951948 | − | 0.995459i | \(-0.469653\pi\) | ||||
0.0951948 | + | 0.995459i | \(0.469653\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 13.0762i | 0.101366i | ||||||||
\(130\) | 186.808 | 1.43699 | ||||||||
\(131\) | 63.1713i | 0.482223i | 0.970497 | + | 0.241112i | \(0.0775120\pi\) | ||||
−0.970497 | + | 0.241112i | \(0.922488\pi\) | |||||||
\(132\) | 26.2295i | 0.198709i | ||||||||
\(133\) | 79.9282 | 0.600964 | ||||||||
\(134\) | −111.597 | −0.832816 | ||||||||
\(135\) | −35.4559 | −0.262636 | ||||||||
\(136\) | − | 59.9578i | − | 0.440866i | ||||||
\(137\) | −25.1684 | −0.183711 | −0.0918554 | − | 0.995772i | \(-0.529280\pi\) | ||||
−0.0918554 | + | 0.995772i | \(0.529280\pi\) | |||||||
\(138\) | −32.8812 | −0.238270 | ||||||||
\(139\) | −192.394 | −1.38413 | −0.692066 | − | 0.721834i | \(-0.743299\pi\) | ||||
−0.692066 | + | 0.721834i | \(0.743299\pi\) | |||||||
\(140\) | −32.3761 | −0.231258 | ||||||||
\(141\) | 127.626i | 0.905150i | ||||||||
\(142\) | 126.379i | 0.889990i | ||||||||
\(143\) | −146.580 | −1.02503 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 286.628 | 1.97675 | ||||||||
\(146\) | 125.448 | 0.859235 | ||||||||
\(147\) | 75.1220 | 0.511034 | ||||||||
\(148\) | − | 79.3493i | − | 0.536144i | ||||||
\(149\) | − | 282.691i | − | 1.89726i | −0.316394 | − | 0.948628i | \(-0.602472\pi\) | ||
0.316394 | − | 0.948628i | \(-0.397528\pi\) | |||||||
\(150\) | 52.8110i | 0.352073i | ||||||||
\(151\) | − | 213.278i | − | 1.41244i | −0.707993 | − | 0.706219i | \(-0.750399\pi\) | ||
0.707993 | − | 0.706219i | \(-0.249601\pi\) | |||||||
\(152\) | 95.2920i | 0.626921i | ||||||||
\(153\) | −63.5949 | −0.415653 | ||||||||
\(154\) | 25.4041 | 0.164962 | ||||||||
\(155\) | − | 244.721i | − | 1.57885i | ||||||
\(156\) | 67.0602i | 0.429873i | ||||||||
\(157\) | 29.1212i | 0.185486i | 0.995690 | + | 0.0927428i | \(0.0295634\pi\) | ||||
−0.995690 | + | 0.0927428i | \(0.970437\pi\) | |||||||
\(158\) | 137.672i | 0.871342i | ||||||||
\(159\) | −88.9967 | −0.559728 | ||||||||
\(160\) | − | 38.5995i | − | 0.241247i | ||||||
\(161\) | 31.8465i | 0.197804i | ||||||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 4.78094 | 0.0293309 | 0.0146655 | − | 0.999892i | \(-0.495332\pi\) | ||||
0.0146655 | + | 0.999892i | \(0.495332\pi\) | |||||||
\(164\) | −127.706 | −0.778693 | ||||||||
\(165\) | − | 89.4885i | − | 0.542355i | ||||||
\(166\) | 123.066 | 0.741359 | ||||||||
\(167\) | −111.489 | −0.667601 | −0.333801 | − | 0.942644i | \(-0.608331\pi\) | ||||
−0.333801 | + | 0.942644i | \(0.608331\pi\) | |||||||
\(168\) | − | 11.6224i | − | 0.0691807i | ||||||
\(169\) | −205.756 | −1.21749 | ||||||||
\(170\) | 204.561i | 1.20330i | ||||||||
\(171\) | 101.072 | 0.591067 | ||||||||
\(172\) | 15.0991i | 0.0877854i | ||||||||
\(173\) | − | 205.464i | − | 1.18765i | −0.804592 | − | 0.593827i | \(-0.797616\pi\) | ||
0.804592 | − | 0.593827i | \(-0.202384\pi\) | |||||||
\(174\) | 102.894i | 0.591342i | ||||||||
\(175\) | 51.1490 | 0.292280 | ||||||||
\(176\) | 30.2873i | 0.172087i | ||||||||
\(177\) | −22.5901 | + | 99.6629i | −0.127628 | + | 0.563067i | ||||
\(178\) | −205.466 | −1.15431 | ||||||||
\(179\) | 208.921i | 1.16716i | 0.812056 | + | 0.583579i | \(0.198348\pi\) | ||||
−0.812056 | + | 0.583579i | \(0.801652\pi\) | |||||||
\(180\) | −40.9409 | −0.227450 | ||||||||
\(181\) | −268.817 | −1.48518 | −0.742589 | − | 0.669747i | \(-0.766402\pi\) | ||||
−0.742589 | + | 0.669747i | \(0.766402\pi\) | |||||||
\(182\) | 64.9498 | 0.356867 | ||||||||
\(183\) | − | 188.487i | − | 1.02999i | ||||||
\(184\) | −37.9680 | −0.206348 | ||||||||
\(185\) | 270.719i | 1.46335i | ||||||||
\(186\) | 87.8498 | 0.472311 | ||||||||
\(187\) | − | 160.510i | − | 0.858340i | ||||||
\(188\) | 147.370i | 0.783883i | ||||||||
\(189\) | −12.3274 | −0.0652242 | ||||||||
\(190\) | − | 325.112i | − | 1.71112i | ||||||
\(191\) | − | 194.399i | − | 1.01780i | −0.860827 | − | 0.508898i | \(-0.830053\pi\) | ||
0.860827 | − | 0.508898i | \(-0.169947\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | −177.848 | −0.921490 | −0.460745 | − | 0.887533i | \(-0.652418\pi\) | ||||
−0.460745 | + | 0.887533i | \(0.652418\pi\) | |||||||
\(194\) | 8.48198 | 0.0437215 | ||||||||
\(195\) | − | 228.792i | − | 1.17329i | ||||||
\(196\) | 86.7434 | 0.442568 | ||||||||
\(197\) | 46.2937 | 0.234993 | 0.117497 | − | 0.993073i | \(-0.462513\pi\) | ||||
0.117497 | + | 0.993073i | \(0.462513\pi\) | |||||||
\(198\) | 32.1245 | 0.162245 | ||||||||
\(199\) | 177.279 | 0.890849 | 0.445425 | − | 0.895319i | \(-0.353053\pi\) | ||||
0.445425 | + | 0.895319i | \(0.353053\pi\) | |||||||
\(200\) | 60.9809i | 0.304904i | ||||||||
\(201\) | 136.678i | 0.679991i | ||||||||
\(202\) | −107.212 | −0.530753 | ||||||||
\(203\) | 99.6555 | 0.490914 | ||||||||
\(204\) | −73.4331 | −0.359966 | ||||||||
\(205\) | 435.699 | 2.12536 | ||||||||
\(206\) | 54.0641 | 0.262447 | ||||||||
\(207\) | 40.2711i | 0.194547i | ||||||||
\(208\) | 77.4344i | 0.372281i | ||||||||
\(209\) | 255.101i | 1.22058i | ||||||||
\(210\) | 39.6525i | 0.188821i | ||||||||
\(211\) | 138.502i | 0.656406i | 0.944607 | + | 0.328203i | \(0.106443\pi\) | ||||
−0.944607 | + | 0.328203i | \(0.893557\pi\) | |||||||
\(212\) | −102.765 | −0.484739 | ||||||||
\(213\) | 154.781 | 0.726674 | ||||||||
\(214\) | − | 79.8295i | − | 0.373035i | ||||||
\(215\) | − | 51.5142i | − | 0.239601i | ||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | − | 85.0851i | − | 0.392097i | ||||||
\(218\) | 125.160 | 0.574128 | ||||||||
\(219\) | − | 153.642i | − | 0.701563i | ||||||
\(220\) | − | 103.332i | − | 0.469693i | ||||||
\(221\) | − | 410.370i | − | 1.85688i | ||||||
\(222\) | −97.1826 | −0.437759 | ||||||||
\(223\) | −49.0872 | −0.220122 | −0.110061 | − | 0.993925i | \(-0.535105\pi\) | ||||
−0.110061 | + | 0.993925i | \(0.535105\pi\) | |||||||
\(224\) | − | 13.4203i | − | 0.0599122i | ||||||
\(225\) | 64.6800 | 0.287467 | ||||||||
\(226\) | 189.168 | 0.837025 | ||||||||
\(227\) | − | 85.5435i | − | 0.376843i | −0.982088 | − | 0.188422i | \(-0.939663\pi\) | ||
0.982088 | − | 0.188422i | \(-0.0603372\pi\) | |||||||
\(228\) | 116.708 | 0.511879 | ||||||||
\(229\) | − | 143.420i | − | 0.626287i | −0.949706 | − | 0.313144i | \(-0.898618\pi\) | ||
0.949706 | − | 0.313144i | \(-0.101382\pi\) | |||||||
\(230\) | 129.537 | 0.563205 | ||||||||
\(231\) | − | 31.1135i | − | 0.134691i | ||||||
\(232\) | 118.811i | 0.512118i | ||||||||
\(233\) | − | 154.300i | − | 0.662233i | −0.943590 | − | 0.331116i | \(-0.892575\pi\) | ||
0.943590 | − | 0.331116i | \(-0.107425\pi\) | |||||||
\(234\) | 82.1316 | 0.350990 | ||||||||
\(235\) | − | 502.789i | − | 2.13953i | ||||||
\(236\) | −26.0848 | + | 115.081i | −0.110529 | + | 0.487630i | ||||
\(237\) | 168.613 | 0.711447 | ||||||||
\(238\) | 71.1221i | 0.298832i | ||||||||
\(239\) | 189.129 | 0.791334 | 0.395667 | − | 0.918394i | \(-0.370513\pi\) | ||||
0.395667 | + | 0.918394i | \(0.370513\pi\) | |||||||
\(240\) | −47.2745 | −0.196977 | ||||||||
\(241\) | −40.7199 | −0.168962 | −0.0844811 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844811 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(242\) | − | 90.0395i | − | 0.372064i | ||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 217.647i | − | 0.891994i | ||||||
\(245\) | −295.946 | −1.20794 | ||||||||
\(246\) | 156.407i | 0.635800i | ||||||||
\(247\) | 652.207i | 2.64052i | ||||||||
\(248\) | 101.440 | 0.409033 | ||||||||
\(249\) | − | 150.724i | − | 0.605317i | ||||||
\(250\) | 33.1957i | 0.132783i | ||||||||
\(251\) | 143.103 | 0.570130 | 0.285065 | − | 0.958508i | \(-0.407985\pi\) | ||||
0.285065 | + | 0.958508i | \(0.407985\pi\) | |||||||
\(252\) | −14.2344 | −0.0564858 | ||||||||
\(253\) | −101.642 | −0.401747 | ||||||||
\(254\) | − | 34.1950i | − | 0.134626i | ||||||
\(255\) | 250.535 | 0.982489 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −120.585 | −0.469200 | −0.234600 | − | 0.972092i | \(-0.575378\pi\) | ||||
−0.234600 | + | 0.972092i | \(0.575378\pi\) | |||||||
\(258\) | 18.4925 | 0.0716765 | ||||||||
\(259\) | 94.1242i | 0.363414i | ||||||||
\(260\) | − | 264.186i | − | 1.01610i | ||||||
\(261\) | 126.018 | 0.482829 | ||||||||
\(262\) | 89.3377 | 0.340983 | ||||||||
\(263\) | 176.620 | 0.671561 | 0.335780 | − | 0.941940i | \(-0.391000\pi\) | ||||
0.335780 | + | 0.941940i | \(0.391000\pi\) | |||||||
\(264\) | 37.0942 | 0.140508 | ||||||||
\(265\) | 350.606 | 1.32304 | ||||||||
\(266\) | − | 113.036i | − | 0.424946i | ||||||
\(267\) | 251.644i | 0.942487i | ||||||||
\(268\) | 157.822i | 0.588890i | ||||||||
\(269\) | 10.9673i | 0.0407706i | 0.999792 | + | 0.0203853i | \(0.00648930\pi\) | ||||
−0.999792 | + | 0.0203853i | \(0.993511\pi\) | |||||||
\(270\) | 50.1422i | 0.185712i | ||||||||
\(271\) | −69.4590 | −0.256306 | −0.128153 | − | 0.991754i | \(-0.540905\pi\) | ||||
−0.128153 | + | 0.991754i | \(0.540905\pi\) | |||||||
\(272\) | −84.7932 | −0.311740 | ||||||||
\(273\) | − | 79.5469i | − | 0.291381i | ||||||
\(274\) | 35.5935i | 0.129903i | ||||||||
\(275\) | 163.248i | 0.593630i | ||||||||
\(276\) | 46.5011i | 0.168482i | ||||||||
\(277\) | 151.203 | 0.545859 | 0.272930 | − | 0.962034i | \(-0.412007\pi\) | ||||
0.272930 | + | 0.962034i | \(0.412007\pi\) | |||||||
\(278\) | 272.087i | 0.978729i | ||||||||
\(279\) | − | 107.594i | − | 0.385640i | ||||||
\(280\) | 45.7868i | 0.163524i | ||||||||
\(281\) | 294.887 | 1.04942 | 0.524710 | − | 0.851281i | \(-0.324174\pi\) | ||||
0.524710 | + | 0.851281i | \(0.324174\pi\) | |||||||
\(282\) | 180.491 | 0.640038 | ||||||||
\(283\) | 344.674i | 1.21793i | 0.793198 | + | 0.608964i | \(0.208415\pi\) | ||||
−0.793198 | + | 0.608964i | \(0.791585\pi\) | |||||||
\(284\) | 178.726 | 0.629318 | ||||||||
\(285\) | −398.179 | −1.39712 | ||||||||
\(286\) | 207.295i | 0.724809i | ||||||||
\(287\) | 151.485 | 0.527821 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 160.368 | 0.554906 | ||||||||
\(290\) | − | 405.354i | − | 1.39777i | ||||||
\(291\) | − | 10.3883i | − | 0.0356985i | ||||||
\(292\) | − | 177.411i | − | 0.607571i | ||||||
\(293\) | −324.880 | −1.10881 | −0.554403 | − | 0.832248i | \(-0.687053\pi\) | ||||
−0.554403 | + | 0.832248i | \(0.687053\pi\) | |||||||
\(294\) | − | 106.239i | − | 0.361356i | ||||||
\(295\) | 88.9947 | − | 392.626i | 0.301677 | − | 1.33094i | ||||
\(296\) | −112.217 | −0.379111 | ||||||||
\(297\) | − | 39.3443i | − | 0.132472i | ||||||
\(298\) | −399.786 | −1.34156 | ||||||||
\(299\) | −259.864 | −0.869112 | ||||||||
\(300\) | 74.6860 | 0.248953 | ||||||||
\(301\) | − | 17.9106i | − | 0.0595035i | ||||||
\(302\) | −301.621 | −0.998745 | ||||||||
\(303\) | 131.307i | 0.433358i | ||||||||
\(304\) | 134.763 | 0.443300 | ||||||||
\(305\) | 742.554i | 2.43460i | ||||||||
\(306\) | 89.9368i | 0.293911i | ||||||||
\(307\) | 138.870 | 0.452347 | 0.226173 | − | 0.974087i | \(-0.427378\pi\) | ||||
0.226173 | + | 0.974087i | \(0.427378\pi\) | |||||||
\(308\) | − | 35.9268i | − | 0.116645i | ||||||
\(309\) | − | 66.2147i | − | 0.214287i | ||||||
\(310\) | −346.088 | −1.11641 | ||||||||
\(311\) | 179.330 | 0.576624 | 0.288312 | − | 0.957536i | \(-0.406906\pi\) | ||||
0.288312 | + | 0.957536i | \(0.406906\pi\) | |||||||
\(312\) | 94.8374 | 0.303966 | ||||||||
\(313\) | − | 104.926i | − | 0.335225i | −0.985853 | − | 0.167613i | \(-0.946394\pi\) | ||
0.985853 | − | 0.167613i | \(-0.0536058\pi\) | |||||||
\(314\) | 41.1836 | 0.131158 | ||||||||
\(315\) | 48.5642 | 0.154172 | ||||||||
\(316\) | 194.698 | 0.616132 | ||||||||
\(317\) | 36.1325 | 0.113983 | 0.0569913 | − | 0.998375i | \(-0.481849\pi\) | ||||
0.0569913 | + | 0.998375i | \(0.481849\pi\) | |||||||
\(318\) | 125.860i | 0.395787i | ||||||||
\(319\) | 318.063i | 0.997062i | ||||||||
\(320\) | −54.5879 | −0.170587 | ||||||||
\(321\) | −97.7707 | −0.304582 | ||||||||
\(322\) | 45.0377 | 0.139869 | ||||||||
\(323\) | −714.188 | −2.21111 | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 417.371i | 1.28422i | ||||||||
\(326\) | − | 6.76128i | − | 0.0207401i | ||||||
\(327\) | − | 153.289i | − | 0.468774i | ||||||
\(328\) | 180.603i | 0.550619i | ||||||||
\(329\) | − | 174.810i | − | 0.531339i | ||||||
\(330\) | −126.556 | −0.383503 | ||||||||
\(331\) | 28.5848 | 0.0863590 | 0.0431795 | − | 0.999067i | \(-0.486251\pi\) | ||||
0.0431795 | + | 0.999067i | \(0.486251\pi\) | |||||||
\(332\) | − | 174.041i | − | 0.524220i | ||||||
\(333\) | 119.024i | 0.357429i | ||||||||
\(334\) | 157.670i | 0.472065i | ||||||||
\(335\) | − | 538.450i | − | 1.60731i | ||||||
\(336\) | −16.4365 | −0.0489181 | ||||||||
\(337\) | − | 73.4010i | − | 0.217807i | −0.994052 | − | 0.108904i | \(-0.965266\pi\) | ||
0.994052 | − | 0.108904i | \(-0.0347340\pi\) | |||||||
\(338\) | 290.983i | 0.860895i | ||||||||
\(339\) | − | 231.682i | − | 0.683428i | ||||||
\(340\) | 289.293 | 0.850861 | ||||||||
\(341\) | 271.560 | 0.796363 | ||||||||
\(342\) | − | 142.938i | − | 0.417947i | ||||||
\(343\) | −219.143 | −0.638901 | ||||||||
\(344\) | 21.3533 | 0.0620736 | ||||||||
\(345\) | − | 158.650i | − | 0.459855i | ||||||
\(346\) | −290.570 | −0.839799 | ||||||||
\(347\) | − | 197.915i | − | 0.570360i | −0.958474 | − | 0.285180i | \(-0.907947\pi\) | ||
0.958474 | − | 0.285180i | \(-0.0920534\pi\) | |||||||
\(348\) | 145.513 | 0.418142 | ||||||||
\(349\) | − | 196.556i | − | 0.563197i | −0.959532 | − | 0.281598i | \(-0.909135\pi\) | ||
0.959532 | − | 0.281598i | \(-0.0908646\pi\) | |||||||
\(350\) | − | 72.3356i | − | 0.206673i | ||||||
\(351\) | − | 100.590i | − | 0.286582i | ||||||
\(352\) | 42.8327 | 0.121684 | ||||||||
\(353\) | 84.2261i | 0.238601i | 0.992858 | + | 0.119300i | \(0.0380652\pi\) | ||||
−0.992858 | + | 0.119300i | \(0.961935\pi\) | |||||||
\(354\) | 140.945 | + | 31.9472i | 0.398149 | + | 0.0902465i | ||||
\(355\) | −609.768 | −1.71766 | ||||||||
\(356\) | 290.573i | 0.816218i | ||||||||
\(357\) | 87.1064 | 0.243996 | ||||||||
\(358\) | 295.459 | 0.825306 | ||||||||
\(359\) | −408.251 | −1.13719 | −0.568595 | − | 0.822618i | \(-0.692513\pi\) | ||||
−0.568595 | + | 0.822618i | \(0.692513\pi\) | |||||||
\(360\) | 57.8992i | 0.160831i | ||||||||
\(361\) | 774.071 | 2.14424 | ||||||||
\(362\) | 380.165i | 1.05018i | ||||||||
\(363\) | −110.275 | −0.303789 | ||||||||
\(364\) | − | 91.8528i | − | 0.252343i | ||||||
\(365\) | 605.280i | 1.65830i | ||||||||
\(366\) | −266.561 | −0.728310 | ||||||||
\(367\) | − | 711.701i | − | 1.93924i | −0.244619 | − | 0.969619i | \(-0.578663\pi\) | ||
0.244619 | − | 0.969619i | \(-0.421337\pi\) | |||||||
\(368\) | 53.6949i | 0.145910i | ||||||||
\(369\) | 191.559 | 0.519129 | ||||||||
\(370\) | 382.855 | 1.03474 | ||||||||
\(371\) | 121.900 | 0.328570 | ||||||||
\(372\) | − | 124.238i | − | 0.333974i | ||||||
\(373\) | −608.929 | −1.63252 | −0.816259 | − | 0.577686i | \(-0.803956\pi\) | ||||
−0.816259 | + | 0.577686i | \(0.803956\pi\) | |||||||
\(374\) | −226.995 | −0.606938 | ||||||||
\(375\) | 40.6562 | 0.108417 | ||||||||
\(376\) | 208.413 | 0.554289 | ||||||||
\(377\) | 813.180i | 2.15698i | ||||||||
\(378\) | 17.4335i | 0.0461204i | ||||||||
\(379\) | 472.069 | 1.24556 | 0.622782 | − | 0.782396i | \(-0.286002\pi\) | ||||
0.622782 | + | 0.782396i | \(0.286002\pi\) | |||||||
\(380\) | −459.778 | −1.20994 | ||||||||
\(381\) | −41.8801 | −0.109922 | ||||||||
\(382\) | −274.922 | −0.719690 | ||||||||
\(383\) | −94.4909 | −0.246712 | −0.123356 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123356 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 122.573i | 0.318372i | ||||||||
\(386\) | 251.514i | 0.651592i | ||||||||
\(387\) | − | 22.6486i | − | 0.0585236i | ||||||
\(388\) | − | 11.9953i | − | 0.0309158i | ||||||
\(389\) | −393.780 | −1.01229 | −0.506144 | − | 0.862449i | \(-0.668930\pi\) | ||||
−0.506144 | + | 0.862449i | \(0.668930\pi\) | |||||||
\(390\) | −323.561 | −0.829644 | ||||||||
\(391\) | − | 284.560i | − | 0.727775i | ||||||
\(392\) | − | 122.674i | − | 0.312943i | ||||||
\(393\) | − | 109.416i | − | 0.278412i | ||||||
\(394\) | − | 65.4692i | − | 0.166165i | ||||||
\(395\) | −664.258 | −1.68167 | ||||||||
\(396\) | − | 45.4309i | − | 0.114725i | ||||||
\(397\) | 372.063i | 0.937187i | 0.883414 | + | 0.468594i | \(0.155239\pi\) | ||||
−0.883414 | + | 0.468594i | \(0.844761\pi\) | |||||||
\(398\) | − | 250.710i | − | 0.629926i | ||||||
\(399\) | −138.440 | −0.346967 | ||||||||
\(400\) | 86.2400 | 0.215600 | ||||||||
\(401\) | − | 414.824i | − | 1.03447i | −0.855842 | − | 0.517237i | \(-0.826961\pi\) | ||
0.855842 | − | 0.517237i | \(-0.173039\pi\) | |||||||
\(402\) | 193.292 | 0.480826 | ||||||||
\(403\) | 694.287 | 1.72280 | ||||||||
\(404\) | 151.621i | 0.375299i | ||||||||
\(405\) | 61.4114 | 0.151633 | ||||||||
\(406\) | − | 140.934i | − | 0.347128i | ||||||
\(407\) | −300.409 | −0.738106 | ||||||||
\(408\) | 103.850i | 0.254534i | ||||||||
\(409\) | 258.475i | 0.631969i | 0.948764 | + | 0.315985i | \(0.102335\pi\) | ||||
−0.948764 | + | 0.315985i | \(0.897665\pi\) | |||||||
\(410\) | − | 616.172i | − | 1.50286i | ||||||
\(411\) | 43.5929 | 0.106065 | ||||||||
\(412\) | − | 76.4582i | − | 0.185578i | ||||||
\(413\) | 30.9418 | − | 136.509i | 0.0749197 | − | 0.330530i | ||||
\(414\) | 56.9520 | 0.137565 | ||||||||
\(415\) | 593.783i | 1.43080i | ||||||||
\(416\) | 109.509 | 0.263242 | ||||||||
\(417\) | 333.237 | 0.799129 | ||||||||
\(418\) | 360.767 | 0.863079 | ||||||||
\(419\) | − | 603.955i | − | 1.44142i | −0.693237 | − | 0.720710i | \(-0.743816\pi\) | ||
0.693237 | − | 0.720710i | \(-0.256184\pi\) | |||||||
\(420\) | 56.0771 | 0.133517 | ||||||||
\(421\) | 700.525i | 1.66395i | 0.554810 | + | 0.831977i | \(0.312791\pi\) | ||||
−0.554810 | + | 0.831977i | \(0.687209\pi\) | |||||||
\(422\) | 195.871 | 0.464149 | ||||||||
\(423\) | − | 221.055i | − | 0.522588i | ||||||
\(424\) | 145.331i | 0.342762i | ||||||||
\(425\) | −457.035 | −1.07538 | ||||||||
\(426\) | − | 218.894i | − | 0.513836i | ||||||
\(427\) | 258.173i | 0.604620i | ||||||||
\(428\) | −112.896 | −0.263775 | ||||||||
\(429\) | 253.884 | 0.591804 | ||||||||
\(430\) | −72.8521 | −0.169423 | ||||||||
\(431\) | 27.6778i | 0.0642177i | 0.999484 | + | 0.0321089i | \(0.0102223\pi\) | ||||
−0.999484 | + | 0.0321089i | \(0.989778\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | −706.334 | −1.63126 | −0.815628 | − | 0.578576i | \(-0.803609\pi\) | ||||
−0.815628 | + | 0.578576i | \(0.803609\pi\) | |||||||
\(434\) | −120.329 | −0.277255 | ||||||||
\(435\) | −496.455 | −1.14128 | ||||||||
\(436\) | − | 177.003i | − | 0.405970i | ||||||
\(437\) | 452.256i | 1.03491i | ||||||||
\(438\) | −217.283 | −0.496080 | ||||||||
\(439\) | 424.519 | 0.967014 | 0.483507 | − | 0.875340i | \(-0.339363\pi\) | ||||
0.483507 | + | 0.875340i | \(0.339363\pi\) | |||||||
\(440\) | −146.134 | −0.332123 | ||||||||
\(441\) | −130.115 | −0.295046 | ||||||||
\(442\) | −580.350 | −1.31301 | ||||||||
\(443\) | − | 577.461i | − | 1.30352i | −0.758424 | − | 0.651762i | \(-0.774030\pi\) | ||
0.758424 | − | 0.651762i | \(-0.225970\pi\) | |||||||
\(444\) | 137.437i | 0.309543i | ||||||||
\(445\) | − | 991.362i | − | 2.22778i | ||||||
\(446\) | 69.4197i | 0.155650i | ||||||||
\(447\) | 489.635i | 1.09538i | ||||||||
\(448\) | −18.9792 | −0.0423643 | ||||||||
\(449\) | −344.511 | −0.767286 | −0.383643 | − | 0.923482i | \(-0.625331\pi\) | ||||
−0.383643 | + | 0.923482i | \(0.625331\pi\) | |||||||
\(450\) | − | 91.4713i | − | 0.203270i | ||||||
\(451\) | 483.482i | 1.07202i | ||||||||
\(452\) | − | 267.523i | − | 0.591866i | ||||||
\(453\) | 369.409i | 0.815472i | ||||||||
\(454\) | −120.977 | −0.266469 | ||||||||
\(455\) | 313.378i | 0.688744i | ||||||||
\(456\) | − | 165.051i | − | 0.361953i | ||||||
\(457\) | − | 618.248i | − | 1.35284i | −0.736516 | − | 0.676420i | \(-0.763530\pi\) | ||
0.736516 | − | 0.676420i | \(-0.236470\pi\) | |||||||
\(458\) | −202.826 | −0.442852 | ||||||||
\(459\) | 110.150 | 0.239977 | ||||||||
\(460\) | − | 183.193i | − | 0.398246i | ||||||
\(461\) | 492.444 | 1.06821 | 0.534105 | − | 0.845418i | \(-0.320649\pi\) | ||||
0.534105 | + | 0.845418i | \(0.320649\pi\) | |||||||
\(462\) | −44.0012 | −0.0952406 | ||||||||
\(463\) | 577.047i | 1.24632i | 0.782094 | + | 0.623161i | \(0.214152\pi\) | ||||
−0.782094 | + | 0.623161i | \(0.785848\pi\) | |||||||
\(464\) | 168.025 | 0.362122 | ||||||||
\(465\) | 423.870i | 0.911547i | ||||||||
\(466\) | −218.213 | −0.468269 | ||||||||
\(467\) | − | 663.085i | − | 1.41988i | −0.704261 | − | 0.709942i | \(-0.748721\pi\) | ||
0.704261 | − | 0.709942i | \(-0.251279\pi\) | |||||||
\(468\) | − | 116.152i | − | 0.248187i | ||||||
\(469\) | − | 187.209i | − | 0.399167i | ||||||
\(470\) | −711.050 | −1.51287 | ||||||||
\(471\) | − | 50.4395i | − | 0.107090i | ||||||
\(472\) | 162.749 | + | 36.8895i | 0.344807 | + | 0.0781557i | ||||
\(473\) | 57.1638 | 0.120854 | ||||||||
\(474\) | − | 238.455i | − | 0.503069i | ||||||
\(475\) | 726.374 | 1.52921 | ||||||||
\(476\) | 100.582 | 0.211306 | ||||||||
\(477\) | 154.147 | 0.323159 | ||||||||
\(478\) | − | 267.469i | − | 0.559558i | ||||||
\(479\) | −266.958 | −0.557324 | −0.278662 | − | 0.960389i | \(-0.589891\pi\) | ||||
−0.278662 | + | 0.960389i | \(0.589891\pi\) | |||||||
\(480\) | 66.8563i | 0.139284i | ||||||||
\(481\) | −768.046 | −1.59677 | ||||||||
\(482\) | 57.5866i | 0.119474i | ||||||||
\(483\) | − | 55.1597i | − | 0.114202i | ||||||
\(484\) | −127.335 | −0.263089 | ||||||||
\(485\) | 40.9250i | 0.0843814i | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −841.157 | −1.72722 | −0.863611 | − | 0.504158i | \(-0.831803\pi\) | ||||
−0.863611 | + | 0.504158i | \(0.831803\pi\) | |||||||
\(488\) | −307.799 | −0.630735 | ||||||||
\(489\) | −8.28084 | −0.0169342 | ||||||||
\(490\) | 418.531i | 0.854145i | ||||||||
\(491\) | −588.805 | −1.19920 | −0.599598 | − | 0.800302i | \(-0.704673\pi\) | ||||
−0.599598 | + | 0.800302i | \(0.704673\pi\) | |||||||
\(492\) | 221.193 | 0.449579 | ||||||||
\(493\) | −890.458 | −1.80620 | ||||||||
\(494\) | 922.360 | 1.86713 | ||||||||
\(495\) | 154.999i | 0.313129i | ||||||||
\(496\) | − | 143.458i | − | 0.289230i | ||||||
\(497\) | −212.005 | −0.426570 | ||||||||
\(498\) | −213.156 | −0.428024 | ||||||||
\(499\) | −701.976 | −1.40677 | −0.703383 | − | 0.710811i | \(-0.748328\pi\) | ||||
−0.703383 | + | 0.710811i | \(0.748328\pi\) | |||||||
\(500\) | 46.9458 | 0.0938915 | ||||||||
\(501\) | 193.105 | 0.385440 | ||||||||
\(502\) | − | 202.378i | − | 0.403143i | ||||||
\(503\) | − | 43.4949i | − | 0.0864711i | −0.999065 | − | 0.0432355i | \(-0.986233\pi\) | ||
0.999065 | − | 0.0432355i | \(-0.0137666\pi\) | |||||||
\(504\) | 20.1305i | 0.0399415i | ||||||||
\(505\) | − | 517.291i | − | 1.02434i | ||||||
\(506\) | 143.743i | 0.284078i | ||||||||
\(507\) | 356.379 | 0.702918 | ||||||||
\(508\) | −48.3590 | −0.0951948 | ||||||||
\(509\) | − | 307.529i | − | 0.604183i | −0.953279 | − | 0.302091i | \(-0.902315\pi\) | ||
0.953279 | − | 0.302091i | \(-0.0976847\pi\) | |||||||
\(510\) | − | 354.310i | − | 0.694725i | ||||||
\(511\) | 210.445i | 0.411829i | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −175.063 | −0.341253 | ||||||||
\(514\) | 170.532i | 0.331775i | ||||||||
\(515\) | 260.856i | 0.506516i | ||||||||
\(516\) | − | 26.1524i | − | 0.0506829i | ||||||
\(517\) | 557.929 | 1.07917 | ||||||||
\(518\) | 133.112 | 0.256972 | ||||||||
\(519\) | 355.875i | 0.685693i | ||||||||
\(520\) | −373.616 | −0.718493 | ||||||||
\(521\) | 651.248 | 1.25000 | 0.624998 | − | 0.780626i | \(-0.285100\pi\) | ||||
0.624998 | + | 0.780626i | \(0.285100\pi\) | |||||||
\(522\) | − | 178.217i | − | 0.341412i | ||||||
\(523\) | 644.126 | 1.23160 | 0.615799 | − | 0.787903i | \(-0.288833\pi\) | ||||
0.615799 | + | 0.787903i | \(0.288833\pi\) | |||||||
\(524\) | − | 126.343i | − | 0.241112i | ||||||
\(525\) | −88.5926 | −0.168748 | ||||||||
\(526\) | − | 249.779i | − | 0.474865i | ||||||
\(527\) | 760.267i | 1.44263i | ||||||||
\(528\) | − | 52.4591i | − | 0.0993544i | ||||||
\(529\) | 348.804 | 0.659365 | ||||||||
\(530\) | − | 495.832i | − | 0.935533i | ||||||
\(531\) | 39.1272 | − | 172.621i | 0.0736859 | − | 0.325087i | ||||
\(532\) | −159.856 | −0.300482 | ||||||||
\(533\) | 1236.10i | 2.31914i | ||||||||
\(534\) | 355.878 | 0.666439 | ||||||||
\(535\) | 385.172 | 0.719948 | ||||||||
\(536\) | 223.195 | 0.416408 | ||||||||
\(537\) | − | 361.862i | − | 0.673859i | ||||||
\(538\) | 15.5101 | 0.0288292 | ||||||||
\(539\) | − | 328.403i | − | 0.609281i | ||||||
\(540\) | 70.9118 | 0.131318 | ||||||||
\(541\) | − | 386.732i | − | 0.714847i | −0.933942 | − | 0.357423i | \(-0.883655\pi\) | ||
0.933942 | − | 0.357423i | \(-0.116345\pi\) | |||||||
\(542\) | 98.2299i | 0.181236i | ||||||||
\(543\) | 465.605 | 0.857468 | ||||||||
\(544\) | 119.916i | 0.220433i | ||||||||
\(545\) | 603.889i | 1.10805i | ||||||||
\(546\) | −112.496 | −0.206037 | ||||||||
\(547\) | 64.8143 | 0.118491 | 0.0592453 | − | 0.998243i | \(-0.481131\pi\) | ||||
0.0592453 | + | 0.998243i | \(0.481131\pi\) | |||||||
\(548\) | 50.3368 | 0.0918554 | ||||||||
\(549\) | 326.470i | 0.594663i | ||||||||
\(550\) | 230.868 | 0.419760 | ||||||||
\(551\) | 1415.22 | 2.56846 | ||||||||
\(552\) | 65.7625 | 0.119135 | ||||||||
\(553\) | −230.951 | −0.417632 | ||||||||
\(554\) | − | 213.833i | − | 0.385981i | ||||||
\(555\) | − | 468.900i | − | 0.844864i | ||||||
\(556\) | 384.789 | 0.692066 | ||||||||
\(557\) | 807.019 | 1.44887 | 0.724434 | − | 0.689344i | \(-0.242101\pi\) | ||||
0.724434 | + | 0.689344i | \(0.242101\pi\) | |||||||
\(558\) | −152.160 | −0.272689 | ||||||||
\(559\) | 146.149 | 0.261447 | ||||||||
\(560\) | 64.7523 | 0.115629 | ||||||||
\(561\) | 278.011i | 0.495563i | ||||||||
\(562\) | − | 417.033i | − | 0.742052i | ||||||
\(563\) | 297.619i | 0.528631i | 0.964436 | + | 0.264315i | \(0.0851460\pi\) | ||||
−0.964436 | + | 0.264315i | \(0.914854\pi\) | |||||||
\(564\) | − | 255.252i | − | 0.452575i | ||||||
\(565\) | 912.721i | 1.61544i | ||||||||
\(566\) | 487.442 | 0.861205 | ||||||||
\(567\) | 21.3516 | 0.0376572 | ||||||||
\(568\) | − | 252.757i | − | 0.444995i | ||||||
\(569\) | − | 234.197i | − | 0.411594i | −0.978595 | − | 0.205797i | \(-0.934021\pi\) | ||
0.978595 | − | 0.205797i | \(-0.0659787\pi\) | |||||||
\(570\) | 563.110i | 0.987913i | ||||||||
\(571\) | − | 154.775i | − | 0.271060i | −0.990773 | − | 0.135530i | \(-0.956726\pi\) | ||
0.990773 | − | 0.135530i | \(-0.0432737\pi\) | |||||||
\(572\) | 293.160 | 0.512517 | ||||||||
\(573\) | 336.709i | 0.587624i | ||||||||
\(574\) | − | 214.232i | − | 0.373226i | ||||||
\(575\) | 289.415i | 0.503331i | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 621.596 | 1.07729 | 0.538645 | − | 0.842533i | \(-0.318937\pi\) | ||||
0.538645 | + | 0.842533i | \(0.318937\pi\) | |||||||
\(578\) | − | 226.794i | − | 0.392378i | ||||||
\(579\) | 308.041 | 0.532022 | ||||||||
\(580\) | −573.257 | −0.988373 | ||||||||
\(581\) | 206.448i | 0.355332i | ||||||||
\(582\) | −14.6912 | −0.0252426 | ||||||||
\(583\) | 389.057i | 0.667337i | ||||||||
\(584\) | −250.897 | −0.429618 | ||||||||
\(585\) | 396.280i | 0.677401i | ||||||||
\(586\) | 459.450i | 0.784044i | ||||||||
\(587\) | − | 44.5232i | − | 0.0758487i | −0.999281 | − | 0.0379244i | \(-0.987925\pi\) | ||
0.999281 | − | 0.0379244i | \(-0.0120746\pi\) | |||||||
\(588\) | −150.244 | −0.255517 | ||||||||
\(589\) | − | 1208.31i | − | 2.05145i | ||||||
\(590\) | −555.257 | − | 125.858i | −0.941114 | − | 0.213318i | ||||
\(591\) | −80.1830 | −0.135673 | ||||||||
\(592\) | 158.699i | 0.268072i | ||||||||
\(593\) | 431.323 | 0.727357 | 0.363679 | − | 0.931525i | \(-0.381521\pi\) | ||||
0.363679 | + | 0.931525i | \(0.381521\pi\) | |||||||
\(594\) | −55.6413 | −0.0936722 | ||||||||
\(595\) | −343.159 | −0.576738 | ||||||||
\(596\) | 565.382i | 0.948628i | ||||||||
\(597\) | −307.056 | −0.514332 | ||||||||
\(598\) | 367.504i | 0.614555i | ||||||||
\(599\) | −67.6183 | −0.112885 | −0.0564427 | − | 0.998406i | \(-0.517976\pi\) | ||||
−0.0564427 | + | 0.998406i | \(0.517976\pi\) | |||||||
\(600\) | − | 105.622i | − | 0.176037i | ||||||
\(601\) | − | 160.916i | − | 0.267747i | −0.990998 | − | 0.133874i | \(-0.957258\pi\) | ||
0.990998 | − | 0.133874i | \(-0.0427416\pi\) | |||||||
\(602\) | −25.3294 | −0.0420753 | ||||||||
\(603\) | − | 236.734i | − | 0.392593i | ||||||
\(604\) | 426.556i | 0.706219i | ||||||||
\(605\) | 434.435 | 0.718074 | ||||||||
\(606\) | 185.697 | 0.306430 | ||||||||
\(607\) | 641.724 | 1.05721 | 0.528603 | − | 0.848869i | \(-0.322716\pi\) | ||||
0.528603 | + | 0.848869i | \(0.322716\pi\) | |||||||
\(608\) | − | 190.584i | − | 0.313461i | ||||||
\(609\) | −172.608 | −0.283429 | ||||||||
\(610\) | 1050.13 | 1.72153 | ||||||||
\(611\) | 1426.44 | 2.33460 | ||||||||
\(612\) | 127.190 | 0.207826 | ||||||||
\(613\) | − | 229.162i | − | 0.373837i | −0.982375 | − | 0.186919i | \(-0.940150\pi\) | ||
0.982375 | − | 0.186919i | \(-0.0598501\pi\) | |||||||
\(614\) | − | 196.393i | − | 0.319858i | ||||||
\(615\) | −754.653 | −1.22708 | ||||||||
\(616\) | −50.8082 | −0.0824808 | ||||||||
\(617\) | −404.449 | −0.655508 | −0.327754 | − | 0.944763i | \(-0.606292\pi\) | ||||
−0.327754 | + | 0.944763i | \(0.606292\pi\) | |||||||
\(618\) | −93.6418 | −0.151524 | ||||||||
\(619\) | −254.624 | −0.411347 | −0.205674 | − | 0.978621i | \(-0.565938\pi\) | ||||
−0.205674 | + | 0.978621i | \(0.565938\pi\) | |||||||
\(620\) | 489.442i | 0.789423i | ||||||||
\(621\) | − | 69.7517i | − | 0.112322i | ||||||
\(622\) | − | 253.611i | − | 0.407735i | ||||||
\(623\) | − | 344.679i | − | 0.553256i | ||||||
\(624\) | − | 134.120i | − | 0.214937i | ||||||
\(625\) | −699.167 | −1.11867 | ||||||||
\(626\) | −148.387 | −0.237040 | ||||||||
\(627\) | − | 441.847i | − | 0.704701i | ||||||
\(628\) | − | 58.2425i | − | 0.0927428i | ||||||
\(629\) | − | 841.035i | − | 1.33710i | ||||||
\(630\) | − | 68.6801i | − | 0.109016i | ||||||
\(631\) | −979.288 | −1.55196 | −0.775981 | − | 0.630756i | \(-0.782745\pi\) | ||||
−0.775981 | + | 0.630756i | \(0.782745\pi\) | |||||||
\(632\) | − | 275.344i | − | 0.435671i | ||||||
\(633\) | − | 239.892i | − | 0.378976i | ||||||
\(634\) | − | 51.0990i | − | 0.0805978i | ||||||
\(635\) | 164.988 | 0.259824 | ||||||||
\(636\) | 177.993 | 0.279864 | ||||||||
\(637\) | − | 839.616i | − | 1.31808i | ||||||
\(638\) | 449.809 | 0.705029 | ||||||||
\(639\) | −268.089 | −0.419545 | ||||||||
\(640\) | 77.1990i | 0.120623i | ||||||||
\(641\) | 861.293 | 1.34367 | 0.671835 | − | 0.740701i | \(-0.265506\pi\) | ||||
0.671835 | + | 0.740701i | \(0.265506\pi\) | |||||||
\(642\) | 138.269i | 0.215372i | ||||||||
\(643\) | 463.059 | 0.720154 | 0.360077 | − | 0.932923i | \(-0.382750\pi\) | ||||
0.360077 | + | 0.932923i | \(0.382750\pi\) | |||||||
\(644\) | − | 63.6929i | − | 0.0989020i | ||||||
\(645\) | 89.2252i | 0.138334i | ||||||||
\(646\) | 1010.01i | 1.56349i | ||||||||
\(647\) | 613.775 | 0.948647 | 0.474324 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474324 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | 435.685 | + | 98.7547i | 0.671318 | + | 0.152164i | ||||
\(650\) | 590.252 | 0.908080 | ||||||||
\(651\) | 147.372i | 0.226377i | ||||||||
\(652\) | −9.56189 | −0.0146655 | ||||||||
\(653\) | −952.358 | −1.45843 | −0.729217 | − | 0.684282i | \(-0.760116\pi\) | ||||
−0.729217 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(654\) | −216.783 | −0.331473 | ||||||||
\(655\) | 431.048i | 0.658089i | ||||||||
\(656\) | 255.411 | 0.389347 | ||||||||
\(657\) | 266.116i | 0.405047i | ||||||||
\(658\) | −247.219 | −0.375713 | ||||||||
\(659\) | − | 310.121i | − | 0.470593i | −0.971924 | − | 0.235296i | \(-0.924394\pi\) | ||
0.971924 | − | 0.235296i | \(-0.0756061\pi\) | |||||||
\(660\) | 178.977i | 0.271177i | ||||||||
\(661\) | 771.991 | 1.16791 | 0.583957 | − | 0.811785i | \(-0.301504\pi\) | ||||
0.583957 | + | 0.811785i | \(0.301504\pi\) | |||||||
\(662\) | − | 40.4250i | − | 0.0610650i | ||||||
\(663\) | 710.781i | 1.07207i | ||||||||
\(664\) | −246.131 | −0.370679 | ||||||||
\(665\) | 545.389 | 0.820134 | ||||||||
\(666\) | 168.325 | 0.252741 | ||||||||
\(667\) | 563.878i | 0.845395i | ||||||||
\(668\) | 222.979 | 0.333801 | ||||||||
\(669\) | 85.0215 | 0.127087 | ||||||||
\(670\) | −761.483 | −1.13654 | ||||||||
\(671\) | −823.990 | −1.22800 | ||||||||
\(672\) | 23.2447i | 0.0345903i | ||||||||
\(673\) | − | 945.650i | − | 1.40513i | −0.711622 | − | 0.702563i | \(-0.752039\pi\) | ||
0.711622 | − | 0.702563i | \(-0.247961\pi\) | |||||||
\(674\) | −103.805 | −0.154013 | ||||||||
\(675\) | −112.029 | −0.165969 | ||||||||
\(676\) | 411.512 | 0.608745 | ||||||||
\(677\) | −562.988 | −0.831593 | −0.415796 | − | 0.909458i | \(-0.636497\pi\) | ||||
−0.415796 | + | 0.909458i | \(0.636497\pi\) | |||||||
\(678\) | −327.648 | −0.483256 | ||||||||
\(679\) | 14.2289i | 0.0209556i | ||||||||
\(680\) | − | 409.122i | − | 0.601649i | ||||||
\(681\) | 148.166i | 0.217571i | ||||||||
\(682\) | − | 384.043i | − | 0.563114i | ||||||
\(683\) | − | 388.352i | − | 0.568597i | −0.958736 | − | 0.284298i | \(-0.908239\pi\) | ||
0.958736 | − | 0.284298i | \(-0.0917606\pi\) | |||||||
\(684\) | −202.145 | −0.295533 | ||||||||
\(685\) | −171.736 | −0.250710 | ||||||||
\(686\) | 309.915i | 0.451771i | ||||||||
\(687\) | 248.410i | 0.361587i | ||||||||
\(688\) | − | 30.1982i | − | 0.0438927i | ||||||
\(689\) | 994.690i | 1.44367i | ||||||||
\(690\) | −224.365 | −0.325166 | ||||||||
\(691\) | − | 430.154i | − | 0.622509i | −0.950327 | − | 0.311254i | \(-0.899251\pi\) | ||
0.950327 | − | 0.311254i | \(-0.100749\pi\) | |||||||
\(692\) | 410.929i | 0.593827i | ||||||||
\(693\) | 53.8902i | 0.0777637i | ||||||||
\(694\) | −279.894 | −0.403305 | ||||||||
\(695\) | −1312.80 | −1.88892 | ||||||||
\(696\) | − | 205.787i | − | 0.295671i | ||||||
\(697\) | −1353.57 | −1.94200 | ||||||||
\(698\) | −277.972 | −0.398240 | ||||||||
\(699\) | 267.256i | 0.382340i | ||||||||
\(700\) | −102.298 | −0.146140 | ||||||||
\(701\) | − | 1091.34i | − | 1.55684i | −0.627744 | − | 0.778420i | \(-0.716021\pi\) | ||
0.627744 | − | 0.778420i | \(-0.283979\pi\) | |||||||
\(702\) | −142.256 | −0.202644 | ||||||||
\(703\) | 1336.67i | 1.90138i | ||||||||
\(704\) | − | 60.5745i | − | 0.0860434i | ||||||
\(705\) | 870.855i | 1.23526i | ||||||||
\(706\) | 119.114 | 0.168716 | ||||||||
\(707\) | − | 179.853i | − | 0.254389i | ||||||
\(708\) | 45.1802 | − | 199.326i | 0.0638139 | − | 0.281534i | ||||
\(709\) | 91.8453 | 0.129542 | 0.0647710 | − | 0.997900i | \(-0.479368\pi\) | ||||
0.0647710 | + | 0.997900i | \(0.479368\pi\) | |||||||
\(710\) | 862.342i | 1.21457i | ||||||||
\(711\) | −292.046 | −0.410754 | ||||||||
\(712\) | 410.933 | 0.577153 | ||||||||
\(713\) | 481.435 | 0.675225 | ||||||||
\(714\) | − | 123.187i | − | 0.172531i | ||||||
\(715\) | −1000.19 | −1.39886 | ||||||||
\(716\) | − | 417.843i | − | 0.583579i | ||||||
\(717\) | −327.581 | −0.456877 | ||||||||
\(718\) | 577.354i | 0.804115i | ||||||||
\(719\) | 1252.19i | 1.74157i | 0.491664 | + | 0.870785i | \(0.336389\pi\) | ||||
−0.491664 | + | 0.870785i | \(0.663611\pi\) | |||||||
\(720\) | 81.8819 | 0.113725 | ||||||||
\(721\) | 90.6948i | 0.125790i | ||||||||
\(722\) | − | 1094.70i | − | 1.51621i | ||||||
\(723\) | 70.5289 | 0.0975504 | ||||||||
\(724\) | 537.634 | 0.742589 | ||||||||
\(725\) | 905.652 | 1.24917 | ||||||||
\(726\) | 155.953i | 0.214811i | ||||||||
\(727\) | 330.075 | 0.454023 | 0.227012 | − | 0.973892i | \(-0.427104\pi\) | ||||
0.227012 | + | 0.973892i | \(0.427104\pi\) | |||||||
\(728\) | −129.900 | −0.178433 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 855.995 | 1.17260 | ||||||||
\(731\) | 160.037i | 0.218929i | ||||||||
\(732\) | 376.975i | 0.514993i | ||||||||
\(733\) | 95.7808 | 0.130670 | 0.0653348 | − | 0.997863i | \(-0.479188\pi\) | ||||
0.0653348 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(734\) | −1006.50 | −1.37125 | ||||||||
\(735\) | 512.594 | 0.697407 | ||||||||
\(736\) | 75.9360 | 0.103174 | ||||||||
\(737\) | 597.501 | 0.810721 | ||||||||
\(738\) | − | 270.905i | − | 0.367080i | ||||||
\(739\) | − | 1338.91i | − | 1.81179i | −0.423500 | − | 0.905896i | \(-0.639199\pi\) | ||
0.423500 | − | 0.905896i | \(-0.360801\pi\) | |||||||
\(740\) | − | 541.439i | − | 0.731674i | ||||||
\(741\) | − | 1129.66i | − | 1.52450i | ||||||
\(742\) | − | 172.392i | − | 0.232334i | ||||||
\(743\) | 759.998 | 1.02288 | 0.511439 | − | 0.859320i | \(-0.329113\pi\) | ||||
0.511439 | + | 0.859320i | \(0.329113\pi\) | |||||||
\(744\) | −175.700 | −0.236155 | ||||||||
\(745\) | − | 1928.94i | − | 2.58918i | ||||||
\(746\) | 861.156i | 1.15436i | ||||||||
\(747\) | 261.062i | 0.349480i | ||||||||
\(748\) | 321.019i | 0.429170i | ||||||||
\(749\) | 133.917 | 0.178795 | ||||||||
\(750\) | − | 57.4966i | − | 0.0766621i | ||||||
\(751\) | − | 1141.06i | − | 1.51939i | −0.650280 | − | 0.759695i | \(-0.725348\pi\) | ||
0.650280 | − | 0.759695i | \(-0.274652\pi\) | |||||||
\(752\) | − | 294.740i | − | 0.391941i | ||||||
\(753\) | −247.861 | −0.329165 | ||||||||
\(754\) | 1150.01 | 1.52521 | ||||||||
\(755\) | − | 1455.30i | − | 1.92755i | ||||||
\(756\) | 24.6547 | 0.0326121 | ||||||||
\(757\) | 1315.00 | 1.73712 | 0.868559 | − | 0.495585i | \(-0.165046\pi\) | ||||
0.868559 | + | 0.495585i | \(0.165046\pi\) | |||||||
\(758\) | − | 667.606i | − | 0.880747i | ||||||
\(759\) | 176.049 | 0.231949 | ||||||||
\(760\) | 650.224i | 0.855558i | ||||||||
\(761\) | −478.698 | −0.629038 | −0.314519 | − | 0.949251i | \(-0.601843\pi\) | ||||
−0.314519 | + | 0.949251i | \(0.601843\pi\) | |||||||
\(762\) | 59.2274i | 0.0777263i | ||||||||
\(763\) | 209.961i | 0.275178i | ||||||||
\(764\) | 388.798i | 0.508898i | ||||||||
\(765\) | −433.939 | −0.567241 | ||||||||
\(766\) | 133.630i | 0.174452i | ||||||||
\(767\) | 1113.90 | + | 252.483i | 1.45228 | + | 0.329182i | ||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | − | 856.443i | − | 1.11371i | −0.830610 | − | 0.556855i | \(-0.812008\pi\) | ||
0.830610 | − | 0.556855i | \(-0.187992\pi\) | |||||||
\(770\) | 173.345 | 0.225123 | ||||||||
\(771\) | 208.858 | 0.270893 | ||||||||
\(772\) | 355.695 | 0.460745 | ||||||||
\(773\) | − | 107.668i | − | 0.139286i | −0.997572 | − | 0.0696432i | \(-0.977814\pi\) | ||
0.997572 | − | 0.0696432i | \(-0.0221861\pi\) | |||||||
\(774\) | −32.0300 | −0.0413824 | ||||||||
\(775\) | − | 773.239i | − | 0.997728i | ||||||
\(776\) | −16.9640 | −0.0218608 | ||||||||
\(777\) | − | 163.028i | − | 0.209817i | ||||||
\(778\) | 556.889i | 0.715796i | ||||||||
\(779\) | 2151.25 | 2.76156 | ||||||||
\(780\) | 457.584i | 0.586647i | ||||||||
\(781\) | − | 676.641i | − | 0.866378i | ||||||
\(782\) | −402.428 | −0.514614 | ||||||||
\(783\) | −218.270 | −0.278761 | ||||||||
\(784\) | −173.487 | −0.221284 | ||||||||
\(785\) | 198.708i | 0.253132i | ||||||||
\(786\) | −154.737 | −0.196867 | ||||||||
\(787\) | −672.728 | −0.854800 | −0.427400 | − | 0.904063i | \(-0.640570\pi\) | ||||
−0.427400 | + | 0.904063i | \(0.640570\pi\) | |||||||
\(788\) | −92.5874 | −0.117497 | ||||||||
\(789\) | −305.916 | −0.387726 | ||||||||
\(790\) | 939.403i | 1.18912i | ||||||||
\(791\) | 317.337i | 0.401184i | ||||||||
\(792\) | −64.2490 | −0.0811225 | ||||||||
\(793\) | −2106.67 | −2.65658 | ||||||||
\(794\) | 526.177 | 0.662691 | ||||||||
\(795\) | −607.268 | −0.763859 | ||||||||
\(796\) | −354.558 | −0.445425 | ||||||||
\(797\) | 960.865i | 1.20560i | 0.797892 | + | 0.602801i | \(0.205949\pi\) | ||||
−0.797892 | + | 0.602801i | \(0.794051\pi\) | |||||||
\(798\) | 195.783i | 0.245342i | ||||||||
\(799\) | 1562.00i | 1.95494i | ||||||||
\(800\) | − | 121.962i | − | 0.152452i | ||||||
\(801\) | − | 435.860i | − | 0.544145i | ||||||
\(802\) | −586.649 | −0.731483 | ||||||||
\(803\) | −671.661 | −0.836440 | ||||||||
\(804\) | − | 273.356i | − | 0.339996i | ||||||
\(805\) | 217.304i | 0.269943i | ||||||||
\(806\) | − | 981.871i | − | 1.21820i | ||||||
\(807\) | − | 18.9959i | − | 0.0235389i | ||||||
\(808\) | 214.424 | 0.265377 | ||||||||
\(809\) | 677.160i | 0.837034i | 0.908209 | + | 0.418517i | \(0.137450\pi\) | ||||
−0.908209 | + | 0.418517i | \(0.862550\pi\) | |||||||
\(810\) | − | 86.8488i | − | 0.107221i | ||||||
\(811\) | − | 569.272i | − | 0.701939i | −0.936387 | − | 0.350969i | \(-0.885852\pi\) | ||
0.936387 | − | 0.350969i | \(-0.114148\pi\) | |||||||
\(812\) | −199.311 | −0.245457 | ||||||||
\(813\) | 120.307 | 0.147979 | ||||||||
\(814\) | 424.843i | 0.521920i | ||||||||
\(815\) | 32.6227 | 0.0400279 | ||||||||
\(816\) | 146.866 | 0.179983 | ||||||||
\(817\) | − | 254.350i | − | 0.311322i | ||||||
\(818\) | 365.540 | 0.446870 | ||||||||
\(819\) | 137.779i | 0.168229i | ||||||||
\(820\) | −871.398 | −1.06268 | ||||||||
\(821\) | − | 1171.29i | − | 1.42666i | −0.700827 | − | 0.713332i | \(-0.747185\pi\) | ||
0.700827 | − | 0.713332i | \(-0.252815\pi\) | |||||||
\(822\) | − | 61.6497i | − | 0.0749996i | ||||||
\(823\) | 313.575i | 0.381015i | 0.981686 | + | 0.190507i | \(0.0610133\pi\) | ||||
−0.981686 | + | 0.190507i | \(0.938987\pi\) | |||||||
\(824\) | −108.128 | −0.131224 | ||||||||
\(825\) | − | 282.754i | − | 0.342733i | ||||||
\(826\) | −193.053 | − | 43.7584i | −0.233720 | − | 0.0529762i | ||||
\(827\) | −1140.49 | −1.37907 | −0.689536 | − | 0.724251i | \(-0.742186\pi\) | ||||
−0.689536 | + | 0.724251i | \(0.742186\pi\) | |||||||
\(828\) | − | 80.5423i | − | 0.0972733i | ||||||
\(829\) | 704.237 | 0.849502 | 0.424751 | − | 0.905310i | \(-0.360362\pi\) | ||||
0.424751 | + | 0.905310i | \(0.360362\pi\) | |||||||
\(830\) | 839.737 | 1.01173 | ||||||||
\(831\) | −261.891 | −0.315152 | ||||||||
\(832\) | − | 154.869i | − | 0.186140i | ||||||
\(833\) | 919.406 | 1.10373 | ||||||||
\(834\) | − | 471.268i | − | 0.565070i | ||||||
\(835\) | −760.747 | −0.911074 | ||||||||
\(836\) | − | 510.201i | − | 0.610289i | ||||||
\(837\) | 186.358i | 0.222649i | ||||||||
\(838\) | −854.121 | −1.01924 | ||||||||
\(839\) | 1437.04i | 1.71280i | 0.516309 | + | 0.856402i | \(0.327306\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(840\) | − | 79.3050i | − | 0.0944107i | ||||||
\(841\) | 923.515 | 1.09811 | ||||||||
\(842\) | 990.691 | 1.17659 | ||||||||
\(843\) | −510.759 | −0.605883 | ||||||||
\(844\) | − | 277.003i | − | 0.328203i | ||||||
\(845\) | −1403.97 | −1.66151 | ||||||||
\(846\) | −312.619 | −0.369526 | ||||||||
\(847\) | 151.045 | 0.178330 | ||||||||
\(848\) | 205.529 | 0.242369 | ||||||||
\(849\) | − | 596.992i | − | 0.703171i | ||||||
\(850\) | 646.345i | 0.760406i | ||||||||
\(851\) | −532.581 | −0.625829 | ||||||||
\(852\) | −309.563 | −0.363337 | ||||||||
\(853\) | 870.900 | 1.02099 | 0.510493 | − | 0.859882i | \(-0.329463\pi\) | ||||
0.510493 | + | 0.859882i | \(0.329463\pi\) | |||||||
\(854\) | 365.111 | 0.427531 | ||||||||
\(855\) | 689.667 | 0.806628 | ||||||||
\(856\) | 159.659i | 0.186517i | ||||||||
\(857\) | 384.900i | 0.449125i | 0.974460 | + | 0.224563i | \(0.0720953\pi\) | ||||
−0.974460 | + | 0.224563i | \(0.927905\pi\) | |||||||
\(858\) | − | 359.046i | − | 0.418468i | ||||||
\(859\) | 612.020i | 0.712479i | 0.934395 | + | 0.356240i | \(0.115941\pi\) | ||||
−0.934395 | + | 0.356240i | \(0.884059\pi\) | |||||||
\(860\) | 103.028i | 0.119800i | ||||||||
\(861\) | −262.379 | −0.304738 | ||||||||
\(862\) | 39.1424 | 0.0454088 | ||||||||
\(863\) | 901.798i | 1.04496i | 0.852653 | + | 0.522478i | \(0.174992\pi\) | ||||
−0.852653 | + | 0.522478i | \(0.825008\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | − | 1401.98i | − | 1.62079i | ||||||
\(866\) | 998.907i | 1.15347i | ||||||||
\(867\) | −277.765 | −0.320375 | ||||||||
\(868\) | 170.170i | 0.196049i | ||||||||
\(869\) | − | 737.107i | − | 0.848225i | ||||||
\(870\) | 702.093i | 0.807004i | ||||||||
\(871\) | 1527.61 | 1.75386 | ||||||||
\(872\) | −250.320 | −0.287064 | ||||||||
\(873\) | 17.9930i | 0.0206105i | ||||||||
\(874\) | 639.586 | 0.731792 | ||||||||
\(875\) | −55.6871 | −0.0636424 | ||||||||
\(876\) | 307.284i | 0.350781i | ||||||||
\(877\) | −1331.15 | −1.51784 | −0.758921 | − | 0.651183i | \(-0.774273\pi\) | ||||
−0.758921 | + | 0.651183i | \(0.774273\pi\) | |||||||
\(878\) | − | 600.361i | − | 0.683782i | ||||||
\(879\) | 562.709 | 0.640170 | ||||||||
\(880\) | 206.665i | 0.234846i | ||||||||
\(881\) | 81.0344i | 0.0919801i | 0.998942 | + | 0.0459900i | \(0.0146442\pi\) | ||||
−0.998942 | + | 0.0459900i | \(0.985356\pi\) | |||||||
\(882\) | 184.011i | 0.208629i | ||||||||
\(883\) | −669.176 | −0.757844 | −0.378922 | − | 0.925429i | \(-0.623705\pi\) | ||||
−0.378922 | + | 0.925429i | \(0.623705\pi\) | |||||||
\(884\) | 820.739i | 0.928438i | ||||||||
\(885\) | −154.143 | + | 680.048i | −0.174173 | + | 0.768416i | ||||
\(886\) | −816.653 | −0.921730 | ||||||||
\(887\) | 1311.00i | 1.47801i | 0.673699 | + | 0.739006i | \(0.264704\pi\) | ||||
−0.673699 | + | 0.739006i | \(0.735296\pi\) | |||||||
\(888\) | 194.365 | 0.218880 | ||||||||
\(889\) | 57.3635 | 0.0645259 | ||||||||
\(890\) | −1402.00 | −1.57528 | ||||||||
\(891\) | 68.1464i | 0.0764830i | ||||||||
\(892\) | 98.1743 | 0.110061 | ||||||||
\(893\) | − | 2482.51i | − | 2.77996i | ||||||
\(894\) | 692.449 | 0.774551 | ||||||||
\(895\) | 1425.57i | 1.59282i | ||||||||
\(896\) | 26.8407i | 0.0299561i | ||||||||
\(897\) | 450.098 | 0.501782 | ||||||||
\(898\) | 487.212i | 0.542553i | ||||||||
\(899\) | − | 1506.53i | − | 1.67578i | ||||||
\(900\) | −129.360 | −0.143733 | ||||||||
\(901\) | −1089.22 | −1.20890 | ||||||||
\(902\) | 683.747 | 0.758034 | ||||||||
\(903\) | 31.0220i | 0.0343544i | ||||||||
\(904\) | −378.335 | −0.418512 | ||||||||
\(905\) | −1834.27 | −2.02682 | ||||||||
\(906\) | 522.423 | 0.576625 | ||||||||
\(907\) | −443.586 | −0.489069 | −0.244534 | − | 0.969641i | \(-0.578635\pi\) | ||||
−0.244534 | + | 0.969641i | \(0.578635\pi\) | |||||||
\(908\) | 171.087i | 0.188422i | ||||||||
\(909\) | − | 227.431i | − | 0.250199i | ||||||
\(910\) | 443.184 | 0.487015 | ||||||||
\(911\) | −202.130 | −0.221877 | −0.110939 | − | 0.993827i | \(-0.535386\pi\) | ||||
−0.110939 | + | 0.993827i | \(0.535386\pi\) | |||||||
\(912\) | −233.417 | −0.255939 | ||||||||
\(913\) | −658.903 | −0.721691 | ||||||||
\(914\) | −874.335 | −0.956603 | ||||||||
\(915\) | − | 1286.14i | − | 1.40562i | ||||||
\(916\) | 286.840i | 0.313144i | ||||||||
\(917\) | 149.868i | 0.163433i | ||||||||
\(918\) | − | 155.775i | − | 0.169690i | ||||||
\(919\) | 451.851i | 0.491677i | 0.969311 | + | 0.245839i | \(0.0790633\pi\) | ||||
−0.969311 | + | 0.245839i | \(0.920937\pi\) | |||||||
\(920\) | −259.074 | −0.281602 | ||||||||
\(921\) | −240.531 | −0.261163 | ||||||||
\(922\) | − | 696.422i | − | 0.755338i | ||||||
\(923\) | − | 1729.95i | − | 1.87426i | ||||||
\(924\) | 62.2271i | 0.0673453i | ||||||||
\(925\) | 855.385i | 0.924740i | ||||||||
\(926\) | 816.068 | 0.881283 | ||||||||
\(927\) | 114.687i | 0.123719i | ||||||||
\(928\) | − | 237.623i | − | 0.256059i | ||||||
\(929\) | − | 766.666i | − | 0.825259i | −0.910899 | − | 0.412629i | \(-0.864610\pi\) | ||
0.910899 | − | 0.412629i | \(-0.135390\pi\) | |||||||
\(930\) | 599.442 | 0.644561 | ||||||||
\(931\) | −1461.23 | −1.56953 | ||||||||
\(932\) | 308.600i | 0.331116i | ||||||||
\(933\) | −310.609 | −0.332914 | ||||||||
\(934\) | −937.744 | −1.00401 | ||||||||
\(935\) | − | 1095.24i | − | 1.17138i | ||||||
\(936\) | −164.263 | −0.175495 | ||||||||
\(937\) | 1737.39i | 1.85420i | 0.374810 | + | 0.927102i | \(0.377708\pi\) | ||||
−0.374810 | + | 0.927102i | \(0.622292\pi\) | |||||||
\(938\) | −264.754 | −0.282254 | ||||||||
\(939\) | 181.736i | 0.193543i | ||||||||
\(940\) | 1005.58i | 1.06976i | ||||||||
\(941\) | 943.475i | 1.00263i | 0.865265 | + | 0.501315i | \(0.167150\pi\) | ||||
−0.865265 | + | 0.501315i | \(0.832850\pi\) | |||||||
\(942\) | −71.3322 | −0.0757242 | ||||||||
\(943\) | 857.142i | 0.908953i | ||||||||
\(944\) | 52.1696 | − | 230.162i | 0.0552644 | − | 0.243815i | ||||
\(945\) | −84.1156 | −0.0890113 | ||||||||
\(946\) | − | 80.8418i | − | 0.0854564i | ||||||
\(947\) | −317.569 | −0.335342 | −0.167671 | − | 0.985843i | \(-0.553625\pi\) | ||||
−0.167671 | + | 0.985843i | \(0.553625\pi\) | |||||||
\(948\) | −337.226 | −0.355724 | ||||||||
\(949\) | −1717.21 | −1.80950 | ||||||||
\(950\) | − | 1027.25i | − | 1.08131i | ||||||
\(951\) | −62.5833 | −0.0658079 | ||||||||
\(952\) | − | 142.244i | − | 0.149416i | ||||||
\(953\) | −1739.86 | −1.82567 | −0.912835 | − | 0.408329i | \(-0.866111\pi\) | ||||
−0.912835 | + | 0.408329i | \(0.866111\pi\) | |||||||
\(954\) | − | 217.997i | − | 0.228508i | ||||||
\(955\) | − | 1326.48i | − | 1.38898i | ||||||
\(956\) | −378.258 | −0.395667 | ||||||||
\(957\) | − | 550.901i | − | 0.575654i | ||||||
\(958\) | 377.536i | 0.394088i | ||||||||
\(959\) | −59.7095 | −0.0622623 | ||||||||
\(960\) | 94.5490 | 0.0984886 | ||||||||
\(961\) | −325.265 | −0.338465 | ||||||||
\(962\) | 1086.18i | 1.12909i | ||||||||
\(963\) | 169.344 | 0.175850 | ||||||||
\(964\) | 81.4398 | 0.0844811 | ||||||||
\(965\) | −1213.54 | −1.25755 | ||||||||
\(966\) | −78.0076 | −0.0807532 | ||||||||
\(967\) | 1095.86i | 1.13326i | 0.823972 | + | 0.566630i | \(0.191753\pi\) | ||||
−0.823972 | + | 0.566630i | \(0.808247\pi\) | |||||||
\(968\) | 180.079i | 0.186032i | ||||||||
\(969\) | 1237.01 | 1.27658 | ||||||||
\(970\) | 57.8767 | 0.0596667 | ||||||||
\(971\) | 528.256 | 0.544032 | 0.272016 | − | 0.962293i | \(-0.412310\pi\) | ||||
0.272016 | + | 0.962293i | \(0.412310\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | −456.437 | −0.469103 | ||||||||
\(974\) | 1189.58i | 1.22133i | ||||||||
\(975\) | − | 722.908i | − | 0.741445i | ||||||
\(976\) | 435.293i | 0.445997i | ||||||||
\(977\) | 857.002i | 0.877177i | 0.898688 | + | 0.438588i | \(0.144521\pi\) | ||||
−0.898688 | + | 0.438588i | \(0.855479\pi\) | |||||||
\(978\) | 11.7109i | 0.0119743i | ||||||||
\(979\) | 1100.08 | 1.12368 | ||||||||
\(980\) | 591.893 | 0.603972 | ||||||||
\(981\) | 265.504i | 0.270647i | ||||||||
\(982\) | 832.696i | 0.847959i | ||||||||
\(983\) | 415.207i | 0.422388i | 0.977444 | + | 0.211194i | \(0.0677351\pi\) | ||||
−0.977444 | + | 0.211194i | \(0.932265\pi\) | |||||||
\(984\) | − | 312.814i | − | 0.317900i | ||||||
\(985\) | 315.884 | 0.320695 | ||||||||
\(986\) | 1259.30i | 1.27718i | ||||||||
\(987\) | 302.781i | 0.306769i | ||||||||
\(988\) | − | 1304.41i | − | 1.32026i | ||||||
\(989\) | 101.343 | 0.102470 | ||||||||
\(990\) | 219.201 | 0.221415 | ||||||||
\(991\) | 87.4808i | 0.0882753i | 0.999025 | + | 0.0441376i | \(0.0140540\pi\) | ||||
−0.999025 | + | 0.0441376i | \(0.985946\pi\) | |||||||
\(992\) | −202.880 | −0.204517 | ||||||||
\(993\) | −49.5104 | −0.0498594 | ||||||||
\(994\) | 299.821i | 0.301631i | ||||||||
\(995\) | 1209.66 | 1.21574 | ||||||||
\(996\) | 301.448i | 0.302659i | ||||||||
\(997\) | 1593.12 | 1.59792 | 0.798958 | − | 0.601387i | \(-0.205385\pi\) | ||||
0.798958 | + | 0.601387i | \(0.205385\pi\) | |||||||
\(998\) | 992.744i | 0.994733i | ||||||||
\(999\) | − | 206.155i | − | 0.206362i |
(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 | 354.3.d.a.235.4 | ✓ | 20 | |
3.2 | odd | 2 | 1062.3.d.f.235.13 | 20 | |||
59.58 | odd | 2 | inner | 354.3.d.a.235.14 | yes | 20 | |
177.176 | even | 2 | 1062.3.d.f.235.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.3.d.a.235.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
354.3.d.a.235.14 | yes | 20 | 59.58 | odd | 2 | inner | |
1062.3.d.f.235.3 | 20 | 177.176 | even | 2 | |||
1062.3.d.f.235.13 | 20 | 3.2 | odd | 2 |