Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(2,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.d (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(3.86166i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.9 |
Dual form | 17.4.d.a.2.1 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.43772 | + | 3.43772i | −1.21542 | + | 1.21542i | −0.246196 | + | 0.969220i | \(0.579181\pi\) |
−0.969220 | + | 0.246196i | \(0.920819\pi\) | |||||||
\(3\) | −4.67995 | − | 1.93850i | −0.900656 | − | 0.373064i | −0.116184 | − | 0.993228i | \(-0.537066\pi\) |
−0.784472 | + | 0.620164i | \(0.787066\pi\) | |||||||
\(4\) | − | 15.6358i | − | 1.95447i | ||||||
\(5\) | −7.10390 | + | 17.1503i | −0.635392 | + | 1.53397i | 0.197364 | + | 0.980330i | \(0.436762\pi\) |
−0.832755 | + | 0.553641i | \(0.813238\pi\) | |||||||
\(6\) | 22.7523 | − | 9.42432i | 1.54810 | − | 0.641244i | ||||
\(7\) | 5.36561 | + | 12.9537i | 0.289716 | + | 0.699436i | 0.999990 | − | 0.00448945i | \(-0.00142904\pi\) |
−0.710274 | + | 0.703925i | \(0.751429\pi\) | |||||||
\(8\) | 26.2496 | + | 26.2496i | 1.16008 | + | 1.16008i | ||||
\(9\) | −0.947753 | − | 0.947753i | −0.0351020 | − | 0.0351020i | ||||
\(10\) | −34.5367 | − | 83.3791i | −1.09215 | − | 2.63668i | ||||
\(11\) | 17.9963 | − | 7.45431i | 0.493281 | − | 0.204324i | −0.122154 | − | 0.992511i | \(-0.538980\pi\) |
0.615435 | + | 0.788187i | \(0.288980\pi\) | |||||||
\(12\) | −30.3099 | + | 73.1746i | −0.729143 | + | 1.76031i | ||||
\(13\) | 29.9060i | 0.638033i | 0.947749 | + | 0.319016i | \(0.103352\pi\) | ||||
−0.947749 | + | 0.319016i | \(0.896648\pi\) | |||||||
\(14\) | −62.9767 | − | 26.0858i | −1.20223 | − | 0.497980i | ||||
\(15\) | 66.4917 | − | 66.4917i | 1.14454 | − | 1.14454i | ||||
\(16\) | −55.3912 | −0.865487 | ||||||||
\(17\) | −56.0566 | + | 42.0792i | −0.799748 | + | 0.600335i | ||||
\(18\) | 6.51621 | 0.0853269 | ||||||||
\(19\) | −32.3771 | + | 32.3771i | −0.390938 | + | 0.390938i | −0.875022 | − | 0.484084i | \(-0.839153\pi\) |
0.484084 | + | 0.875022i | \(0.339153\pi\) | |||||||
\(20\) | 268.158 | + | 111.075i | 2.99810 | + | 1.24185i | ||||
\(21\) | − | 71.0240i | − | 0.738034i | ||||||
\(22\) | −36.2404 | + | 87.4920i | −0.351203 | + | 0.847880i | ||||
\(23\) | 82.5263 | − | 34.1835i | 0.748171 | − | 0.309903i | 0.0241759 | − | 0.999708i | \(-0.492304\pi\) |
0.723995 | + | 0.689805i | \(0.242304\pi\) | |||||||
\(24\) | −71.9620 | − | 173.732i | −0.612049 | − | 1.47762i | ||||
\(25\) | −155.280 | − | 155.280i | −1.24224 | − | 1.24224i | ||||
\(26\) | −102.808 | − | 102.808i | −0.775475 | − | 0.775475i | ||||
\(27\) | 54.9376 | + | 132.631i | 0.391584 | + | 0.945366i | ||||
\(28\) | 202.542 | − | 83.8955i | 1.36703 | − | 0.566241i | ||||
\(29\) | −22.1603 | + | 53.4998i | −0.141899 | + | 0.342574i | −0.978812 | − | 0.204762i | \(-0.934358\pi\) |
0.836913 | + | 0.547336i | \(0.184358\pi\) | |||||||
\(30\) | 457.159i | 2.78218i | ||||||||
\(31\) | 149.621 | + | 61.9751i | 0.866863 | + | 0.359067i | 0.771388 | − | 0.636365i | \(-0.219563\pi\) |
0.0954754 | + | 0.995432i | \(0.469563\pi\) | |||||||
\(32\) | −19.5778 | + | 19.5778i | −0.108153 | + | 0.108153i | ||||
\(33\) | −98.6719 | −0.520502 | ||||||||
\(34\) | 48.0504 | − | 337.363i | 0.242370 | − | 1.70168i | ||||
\(35\) | −260.277 | −1.25700 | ||||||||
\(36\) | −14.8188 | + | 14.8188i | −0.0686058 | + | 0.0686058i | ||||
\(37\) | 125.263 | + | 51.8855i | 0.556569 | + | 0.230538i | 0.643195 | − | 0.765702i | \(-0.277608\pi\) |
−0.0866259 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(38\) | − | 222.607i | − | 0.950304i | ||||||
\(39\) | 57.9726 | − | 139.958i | 0.238027 | − | 0.574648i | ||||
\(40\) | −636.664 | + | 263.715i | −2.51663 | + | 1.04242i | ||||
\(41\) | −21.7716 | − | 52.5612i | −0.0829304 | − | 0.200212i | 0.876975 | − | 0.480536i | \(-0.159558\pi\) |
−0.959905 | + | 0.280324i | \(0.909558\pi\) | |||||||
\(42\) | 244.160 | + | 244.160i | 0.897018 | + | 0.897018i | ||||
\(43\) | 36.8715 | + | 36.8715i | 0.130764 | + | 0.130764i | 0.769460 | − | 0.638695i | \(-0.220526\pi\) |
−0.638695 | + | 0.769460i | \(0.720526\pi\) | |||||||
\(44\) | −116.554 | − | 281.386i | −0.399345 | − | 0.964104i | ||||
\(45\) | 22.9870 | − | 9.52153i | 0.0761489 | − | 0.0315419i | ||||
\(46\) | −166.189 | + | 401.215i | −0.532678 | + | 1.28600i | ||||
\(47\) | − | 482.699i | − | 1.49806i | −0.662536 | − | 0.749030i | \(-0.730520\pi\) | ||
0.662536 | − | 0.749030i | \(-0.269480\pi\) | |||||||
\(48\) | 259.228 | + | 107.376i | 0.779506 | + | 0.322882i | ||||
\(49\) | 103.528 | − | 103.528i | 0.301832 | − | 0.301832i | ||||
\(50\) | 1067.62 | 3.01967 | ||||||||
\(51\) | 343.912 | − | 88.2627i | 0.944262 | − | 0.242338i | ||||
\(52\) | 467.603 | 1.24702 | ||||||||
\(53\) | −374.747 | + | 374.747i | −0.971234 | + | 0.971234i | −0.999598 | − | 0.0283638i | \(-0.990970\pi\) |
0.0283638 | + | 0.999598i | \(0.490970\pi\) | |||||||
\(54\) | −644.808 | − | 267.088i | −1.62495 | − | 0.673076i | ||||
\(55\) | 361.597i | 0.886504i | ||||||||
\(56\) | −199.185 | + | 480.875i | −0.475308 | + | 1.14749i | ||||
\(57\) | 214.286 | − | 88.7602i | 0.497945 | − | 0.206256i | ||||
\(58\) | −107.736 | − | 260.098i | −0.243904 | − | 0.588836i | ||||
\(59\) | 198.031 | + | 198.031i | 0.436973 | + | 0.436973i | 0.890992 | − | 0.454019i | \(-0.150010\pi\) |
−0.454019 | + | 0.890992i | \(0.650010\pi\) | |||||||
\(60\) | −1039.65 | − | 1039.65i | −2.23697 | − | 2.23697i | ||||
\(61\) | 224.504 | + | 542.000i | 0.471226 | + | 1.13764i | 0.963622 | + | 0.267268i | \(0.0861209\pi\) |
−0.492397 | + | 0.870371i | \(0.663879\pi\) | |||||||
\(62\) | −727.408 | + | 301.302i | −1.49001 | + | 0.617184i | ||||
\(63\) | 7.19166 | − | 17.3622i | 0.0143820 | − | 0.0347211i | ||||
\(64\) | − | 577.735i | − | 1.12839i | ||||||
\(65\) | −512.897 | − | 212.449i | −0.978724 | − | 0.405401i | ||||
\(66\) | 339.206 | − | 339.206i | 0.632627 | − | 0.632627i | ||||
\(67\) | −367.471 | −0.670056 | −0.335028 | − | 0.942208i | \(-0.608746\pi\) | ||||
−0.335028 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(68\) | 657.940 | + | 876.488i | 1.17334 | + | 1.56309i | ||||
\(69\) | −452.484 | −0.789458 | ||||||||
\(70\) | 894.759 | − | 894.759i | 1.52777 | − | 1.52777i | ||||
\(71\) | −55.9406 | − | 23.1713i | −0.0935060 | − | 0.0387314i | 0.335440 | − | 0.942062i | \(-0.391115\pi\) |
−0.428946 | + | 0.903330i | \(0.641115\pi\) | |||||||
\(72\) | − | 49.7563i | − | 0.0814421i | ||||||
\(73\) | −140.861 | + | 340.067i | −0.225842 | + | 0.545231i | −0.995663 | − | 0.0930283i | \(-0.970345\pi\) |
0.769821 | + | 0.638259i | \(0.220345\pi\) | |||||||
\(74\) | −608.985 | + | 252.250i | −0.956663 | + | 0.396263i | ||||
\(75\) | 425.692 | + | 1027.71i | 0.655395 | + | 1.58226i | ||||
\(76\) | 506.241 | + | 506.241i | 0.764077 | + | 0.764077i | ||||
\(77\) | 193.122 | + | 193.122i | 0.285823 | + | 0.285823i | ||||
\(78\) | 281.843 | + | 680.430i | 0.409134 | + | 0.987738i | ||||
\(79\) | 201.148 | − | 83.3181i | 0.286467 | − | 0.118659i | −0.234823 | − | 0.972038i | \(-0.575451\pi\) |
0.521290 | + | 0.853380i | \(0.325451\pi\) | |||||||
\(80\) | 393.493 | − | 949.976i | 0.549923 | − | 1.32763i | ||||
\(81\) | − | 691.015i | − | 0.947894i | ||||||
\(82\) | 255.535 | + | 105.846i | 0.344136 | + | 0.142546i | ||||
\(83\) | 420.131 | − | 420.131i | 0.555606 | − | 0.555606i | −0.372447 | − | 0.928053i | \(-0.621481\pi\) |
0.928053 | + | 0.372447i | \(0.121481\pi\) | |||||||
\(84\) | −1110.51 | −1.44247 | ||||||||
\(85\) | −323.451 | − | 1260.31i | −0.412743 | − | 1.60824i | ||||
\(86\) | −253.508 | −0.317866 | ||||||||
\(87\) | 207.418 | − | 207.418i | 0.255604 | − | 0.255604i | ||||
\(88\) | 668.069 | + | 276.723i | 0.809277 | + | 0.335213i | ||||
\(89\) | 887.553i | 1.05708i | 0.848907 | + | 0.528542i | \(0.177261\pi\) | ||||
−0.848907 | + | 0.528542i | \(0.822739\pi\) | |||||||
\(90\) | −46.2905 | + | 111.755i | −0.0542160 | + | 0.130889i | ||||
\(91\) | −387.394 | + | 160.464i | −0.446263 | + | 0.184848i | ||||
\(92\) | −534.486 | − | 1290.36i | −0.605696 | − | 1.46228i | ||||
\(93\) | −580.081 | − | 580.081i | −0.646791 | − | 0.646791i | ||||
\(94\) | 1659.38 | + | 1659.38i | 1.82077 | + | 1.82077i | ||||
\(95\) | −325.274 | − | 785.281i | −0.351289 | − | 0.848086i | ||||
\(96\) | 129.575 | − | 53.6716i | 0.137757 | − | 0.0570607i | ||||
\(97\) | 338.553 | − | 817.340i | 0.354380 | − | 0.855549i | −0.641688 | − | 0.766965i | \(-0.721766\pi\) |
0.996069 | − | 0.0885841i | \(-0.0282342\pi\) | |||||||
\(98\) | 711.801i | 0.733702i | ||||||||
\(99\) | −24.1209 | − | 9.99120i | −0.0244873 | − | 0.0101430i | ||||
\(100\) | −2427.92 | + | 2427.92i | −2.42792 | + | 2.42792i | ||||
\(101\) | 1845.31 | 1.81798 | 0.908988 | − | 0.416822i | \(-0.136856\pi\) | ||||
0.908988 | + | 0.416822i | \(0.136856\pi\) | |||||||
\(102\) | −878.851 | + | 1485.69i | −0.853129 | + | 1.44221i | ||||
\(103\) | −1823.07 | −1.74400 | −0.872002 | − | 0.489502i | \(-0.837178\pi\) | ||||
−0.872002 | + | 0.489502i | \(0.837178\pi\) | |||||||
\(104\) | −785.020 | + | 785.020i | −0.740169 | + | 0.740169i | ||||
\(105\) | 1218.08 | + | 504.547i | 1.13212 | + | 0.468940i | ||||
\(106\) | − | 2576.54i | − | 2.36091i | ||||||
\(107\) | 710.011 | − | 1714.12i | 0.641490 | − | 1.54869i | −0.183181 | − | 0.983079i | \(-0.558639\pi\) |
0.824670 | − | 0.565613i | \(-0.191361\pi\) | |||||||
\(108\) | 2073.79 | − | 858.992i | 1.84769 | − | 0.765339i | ||||
\(109\) | 530.959 | + | 1281.85i | 0.466575 | + | 1.12641i | 0.965648 | + | 0.259852i | \(0.0836739\pi\) |
−0.499073 | + | 0.866560i | \(0.666326\pi\) | |||||||
\(110\) | −1243.07 | − | 1243.07i | −1.07747 | − | 1.07747i | ||||
\(111\) | −485.643 | − | 485.643i | −0.415272 | − | 0.415272i | ||||
\(112\) | −297.207 | − | 717.522i | −0.250745 | − | 0.605352i | ||||
\(113\) | −566.444 | + | 234.629i | −0.471563 | + | 0.195328i | −0.605793 | − | 0.795623i | \(-0.707144\pi\) |
0.134230 | + | 0.990950i | \(0.457144\pi\) | |||||||
\(114\) | −431.522 | + | 1041.79i | −0.354524 | + | 0.855897i | ||||
\(115\) | 1658.19i | 1.34458i | ||||||||
\(116\) | 836.510 | + | 346.494i | 0.669552 | + | 0.277337i | ||||
\(117\) | 28.3435 | − | 28.3435i | 0.0223962 | − | 0.0223962i | ||||
\(118\) | −1361.55 | −1.06221 | ||||||||
\(119\) | −845.860 | − | 500.362i | −0.651596 | − | 0.385446i | ||||
\(120\) | 3490.76 | 2.65551 | ||||||||
\(121\) | −672.859 | + | 672.859i | −0.505529 | + | 0.505529i | ||||
\(122\) | −2635.02 | − | 1091.46i | −1.95544 | − | 0.809970i | ||||
\(123\) | 288.188i | 0.211260i | ||||||||
\(124\) | 969.029 | − | 2339.44i | 0.701785 | − | 1.69426i | ||||
\(125\) | 1622.40 | − | 672.020i | 1.16089 | − | 0.480858i | ||||
\(126\) | 34.9634 | + | 84.4092i | 0.0247206 | + | 0.0596807i | ||||
\(127\) | −78.9750 | − | 78.9750i | −0.0551803 | − | 0.0551803i | 0.678978 | − | 0.734158i | \(-0.262423\pi\) |
−0.734158 | + | 0.678978i | \(0.762423\pi\) | |||||||
\(128\) | 1829.47 | + | 1829.47i | 1.26331 | + | 1.26331i | ||||
\(129\) | −101.081 | − | 244.032i | −0.0689901 | − | 0.166557i | ||||
\(130\) | 2493.53 | − | 1032.85i | 1.68229 | − | 0.696826i | ||||
\(131\) | −815.895 | + | 1969.75i | −0.544161 | + | 1.31372i | 0.377602 | + | 0.925968i | \(0.376749\pi\) |
−0.921763 | + | 0.387753i | \(0.873251\pi\) | |||||||
\(132\) | 1542.81i | 1.01731i | ||||||||
\(133\) | −593.127 | − | 245.681i | −0.386697 | − | 0.160175i | ||||
\(134\) | 1263.26 | − | 1263.26i | 0.814397 | − | 0.814397i | ||||
\(135\) | −2664.94 | −1.69897 | ||||||||
\(136\) | −2576.03 | − | 366.902i | −1.62421 | − | 0.231335i | ||||
\(137\) | 3087.68 | 1.92554 | 0.962769 | − | 0.270327i | \(-0.0871317\pi\) | ||||
0.962769 | + | 0.270327i | \(0.0871317\pi\) | |||||||
\(138\) | 1555.51 | − | 1555.51i | 0.959520 | − | 0.959520i | ||||
\(139\) | 434.062 | + | 179.794i | 0.264868 | + | 0.109712i | 0.511165 | − | 0.859482i | \(-0.329214\pi\) |
−0.246297 | + | 0.969194i | \(0.579214\pi\) | |||||||
\(140\) | 4069.64i | 2.45677i | ||||||||
\(141\) | −935.710 | + | 2259.00i | −0.558872 | + | 1.34924i | ||||
\(142\) | 271.964 | − | 112.651i | 0.160723 | − | 0.0665738i | ||||
\(143\) | 222.929 | + | 538.197i | 0.130365 | + | 0.314729i | ||||
\(144\) | 52.4971 | + | 52.4971i | 0.0303803 | + | 0.0303803i | ||||
\(145\) | −760.113 | − | 760.113i | −0.435338 | − | 0.435338i | ||||
\(146\) | −684.816 | − | 1653.29i | −0.388190 | − | 0.937175i | ||||
\(147\) | −685.196 | + | 283.818i | −0.384449 | + | 0.159244i | ||||
\(148\) | 811.270 | − | 1958.58i | 0.450581 | − | 1.08780i | ||||
\(149\) | − | 2209.36i | − | 1.21475i | −0.794416 | − | 0.607374i | \(-0.792223\pi\) | ||
0.794416 | − | 0.607374i | \(-0.207777\pi\) | |||||||
\(150\) | −4996.38 | − | 2069.57i | −2.71969 | − | 1.12653i | ||||
\(151\) | 532.003 | − | 532.003i | 0.286714 | − | 0.286714i | −0.549065 | − | 0.835779i | \(-0.685016\pi\) |
0.835779 | + | 0.549065i | \(0.185016\pi\) | |||||||
\(152\) | −1699.77 | −0.907038 | ||||||||
\(153\) | 93.0085 | + | 13.2471i | 0.0491457 | + | 0.00699979i | ||||
\(154\) | −1327.80 | −0.694787 | ||||||||
\(155\) | −2125.79 | + | 2125.79i | −1.10160 | + | 1.10160i | ||||
\(156\) | −2188.36 | − | 906.447i | −1.12313 | − | 0.465217i | ||||
\(157\) | − | 579.544i | − | 0.294603i | −0.989092 | − | 0.147301i | \(-0.952941\pi\) | ||
0.989092 | − | 0.147301i | \(-0.0470587\pi\) | |||||||
\(158\) | −405.065 | + | 977.913i | −0.203957 | + | 0.492396i | ||||
\(159\) | 2480.24 | − | 1027.35i | 1.23708 | − | 0.512415i | ||||
\(160\) | −196.687 | − | 474.844i | −0.0971842 | − | 0.234623i | ||||
\(161\) | 885.609 | + | 885.609i | 0.433514 | + | 0.433514i | ||||
\(162\) | 2375.51 | + | 2375.51i | 1.15209 | + | 1.15209i | ||||
\(163\) | 680.311 | + | 1642.42i | 0.326908 | + | 0.789227i | 0.998819 | + | 0.0485941i | \(0.0154741\pi\) |
−0.671910 | + | 0.740633i | \(0.734526\pi\) | |||||||
\(164\) | −821.835 | + | 340.415i | −0.391308 | + | 0.162085i | ||||
\(165\) | 700.955 | − | 1692.26i | 0.330723 | − | 0.798436i | ||||
\(166\) | 2888.58i | 1.35059i | ||||||||
\(167\) | 2896.21 | + | 1199.65i | 1.34201 | + | 0.555879i | 0.934057 | − | 0.357124i | \(-0.116243\pi\) |
0.407953 | + | 0.913003i | \(0.366243\pi\) | |||||||
\(168\) | 1864.35 | − | 1864.35i | 0.856178 | − | 0.856178i | ||||
\(169\) | 1302.63 | 0.592914 | ||||||||
\(170\) | 5444.54 | + | 3220.67i | 2.45633 | + | 1.45302i | ||||
\(171\) | 61.3710 | 0.0274454 | ||||||||
\(172\) | 576.515 | − | 576.515i | 0.255575 | − | 0.255575i | ||||
\(173\) | −1080.32 | − | 447.482i | −0.474768 | − | 0.196656i | 0.132451 | − | 0.991190i | \(-0.457715\pi\) |
−0.607220 | + | 0.794534i | \(0.707715\pi\) | |||||||
\(174\) | 1426.09i | 0.621331i | ||||||||
\(175\) | 1178.28 | − | 2844.62i | 0.508970 | − | 1.22876i | ||||
\(176\) | −996.836 | + | 412.903i | −0.426928 | + | 0.176839i | ||||
\(177\) | −542.891 | − | 1310.65i | −0.230543 | − | 0.556581i | ||||
\(178\) | −3051.16 | − | 3051.16i | −1.28480 | − | 1.28480i | ||||
\(179\) | −1097.81 | − | 1097.81i | −0.458404 | − | 0.458404i | 0.439727 | − | 0.898131i | \(-0.355075\pi\) |
−0.898131 | + | 0.439727i | \(0.855075\pi\) | |||||||
\(180\) | −148.876 | − | 359.419i | −0.0616477 | − | 0.148831i | ||||
\(181\) | −1382.05 | + | 572.462i | −0.567551 | + | 0.235087i | −0.647960 | − | 0.761675i | \(-0.724377\pi\) |
0.0804087 | + | 0.996762i | \(0.474377\pi\) | |||||||
\(182\) | 780.121 | − | 1883.38i | 0.317728 | − | 0.767062i | ||||
\(183\) | − | 2971.73i | − | 1.20042i | ||||||
\(184\) | 3063.59 | + | 1268.98i | 1.22745 | + | 0.508426i | ||||
\(185\) | −1779.71 | + | 1779.71i | −0.707279 | + | 0.707279i | ||||
\(186\) | 3988.30 | 1.57224 | ||||||||
\(187\) | −695.141 | + | 1175.13i | −0.271838 | + | 0.459542i | ||||
\(188\) | −7547.37 | −2.92792 | ||||||||
\(189\) | −1423.29 | + | 1423.29i | −0.547775 | + | 0.547775i | ||||
\(190\) | 3817.77 | + | 1581.37i | 1.45774 | + | 0.603815i | ||||
\(191\) | − | 3008.79i | − | 1.13983i | −0.821702 | − | 0.569917i | \(-0.806975\pi\) | ||
0.821702 | − | 0.569917i | \(-0.193025\pi\) | |||||||
\(192\) | −1119.94 | + | 2703.77i | −0.420961 | + | 1.01629i | ||||
\(193\) | −3597.18 | + | 1490.00i | −1.34161 | + | 0.555713i | −0.933945 | − | 0.357418i | \(-0.883657\pi\) |
−0.407666 | + | 0.913131i | \(0.633657\pi\) | |||||||
\(194\) | 1645.93 | + | 3973.63i | 0.609129 | + | 1.47057i | ||||
\(195\) | 1988.50 | + | 1988.50i | 0.730253 | + | 0.730253i | ||||
\(196\) | −1618.74 | − | 1618.74i | −0.589921 | − | 0.589921i | ||||
\(197\) | −362.277 | − | 874.614i | −0.131021 | − | 0.316313i | 0.844731 | − | 0.535191i | \(-0.179760\pi\) |
−0.975752 | + | 0.218878i | \(0.929760\pi\) | |||||||
\(198\) | 117.268 | − | 48.5739i | 0.0420902 | − | 0.0174343i | ||||
\(199\) | 675.758 | − | 1631.42i | 0.240720 | − | 0.581149i | −0.756635 | − | 0.653837i | \(-0.773158\pi\) |
0.997355 | + | 0.0726889i | \(0.0231580\pi\) | |||||||
\(200\) | − | 8152.07i | − | 2.88219i | ||||||
\(201\) | 1719.75 | + | 712.342i | 0.603490 | + | 0.249974i | ||||
\(202\) | −6343.66 | + | 6343.66i | −2.20960 | + | 2.20960i | ||||
\(203\) | −811.925 | −0.280719 | ||||||||
\(204\) | −1380.06 | − | 5377.33i | −0.473643 | − | 1.84553i | ||||
\(205\) | 1056.10 | 0.359812 | ||||||||
\(206\) | 6267.19 | − | 6267.19i | 2.11969 | − | 2.11969i | ||||
\(207\) | −110.612 | − | 45.8170i | −0.0371404 | − | 0.0153841i | ||||
\(208\) | − | 1656.53i | − | 0.552209i | ||||||
\(209\) | −341.319 | + | 824.018i | −0.112964 | + | 0.272720i | ||||
\(210\) | −5921.92 | + | 2452.94i | −1.94596 | + | 0.806042i | ||||
\(211\) | −142.128 | − | 343.127i | −0.0463720 | − | 0.111952i | 0.898996 | − | 0.437956i | \(-0.144298\pi\) |
−0.945368 | + | 0.326004i | \(0.894298\pi\) | |||||||
\(212\) | 5859.45 | + | 5859.45i | 1.89825 | + | 1.89825i | ||||
\(213\) | 216.881 | + | 216.881i | 0.0697674 | + | 0.0697674i | ||||
\(214\) | 3451.84 | + | 8333.47i | 1.10263 | + | 2.66198i | ||||
\(215\) | −894.290 | + | 370.427i | −0.283675 | + | 0.117502i | ||||
\(216\) | −2039.43 | + | 4923.61i | −0.642432 | + | 1.55097i | ||||
\(217\) | 2270.69i | 0.710342i | ||||||||
\(218\) | −6231.92 | − | 2581.35i | −1.93614 | − | 0.801976i | ||||
\(219\) | 1318.44 | − | 1318.44i | 0.406812 | − | 0.406812i | ||||
\(220\) | 5653.85 | 1.73265 | ||||||||
\(221\) | −1258.42 | − | 1676.43i | −0.383033 | − | 0.510266i | ||||
\(222\) | 3339.00 | 1.00946 | ||||||||
\(223\) | 1820.02 | − | 1820.02i | 0.546536 | − | 0.546536i | −0.378901 | − | 0.925437i | \(-0.623698\pi\) |
0.925437 | + | 0.378901i | \(0.123698\pi\) | |||||||
\(224\) | −358.653 | − | 148.559i | −0.106980 | − | 0.0443125i | ||||
\(225\) | 294.334i | 0.0872100i | ||||||||
\(226\) | 1140.69 | − | 2753.86i | 0.335740 | − | 0.810549i | ||||
\(227\) | −4808.47 | + | 1991.73i | −1.40594 | + | 0.582361i | −0.951288 | − | 0.308305i | \(-0.900238\pi\) |
−0.454657 | + | 0.890666i | \(0.650238\pi\) | |||||||
\(228\) | −1387.83 | − | 3350.53i | −0.403121 | − | 0.973220i | ||||
\(229\) | −2261.84 | − | 2261.84i | −0.652694 | − | 0.652694i | 0.300947 | − | 0.953641i | \(-0.402697\pi\) |
−0.953641 | + | 0.300947i | \(0.902697\pi\) | |||||||
\(230\) | −5700.38 | − | 5700.38i | −1.63423 | − | 1.63423i | ||||
\(231\) | −529.435 | − | 1278.17i | −0.150798 | − | 0.364058i | ||||
\(232\) | −1986.05 | + | 822.648i | −0.562027 | + | 0.232799i | ||||
\(233\) | 326.467 | − | 788.162i | 0.0917923 | − | 0.221606i | −0.871315 | − | 0.490724i | \(-0.836732\pi\) |
0.963107 | + | 0.269118i | \(0.0867322\pi\) | |||||||
\(234\) | 194.873i | 0.0544414i | ||||||||
\(235\) | 8278.44 | + | 3429.04i | 2.29798 | + | 0.951855i | ||||
\(236\) | 3096.36 | − | 3096.36i | 0.854051 | − | 0.854051i | ||||
\(237\) | −1102.87 | −0.302276 | ||||||||
\(238\) | 4627.93 | − | 1187.73i | 1.26044 | − | 0.323482i | ||||
\(239\) | 1892.67 | 0.512246 | 0.256123 | − | 0.966644i | \(-0.417555\pi\) | ||||
0.256123 | + | 0.966644i | \(0.417555\pi\) | |||||||
\(240\) | −3683.05 | + | 3683.05i | −0.990583 | + | 0.990583i | ||||
\(241\) | 1708.64 | + | 707.742i | 0.456694 | + | 0.189169i | 0.599157 | − | 0.800631i | \(-0.295502\pi\) |
−0.142464 | + | 0.989800i | \(0.545502\pi\) | |||||||
\(242\) | − | 4626.19i | − | 1.22886i | ||||||
\(243\) | 143.786 | − | 347.130i | 0.0379584 | − | 0.0916396i | ||||
\(244\) | 8474.59 | − | 3510.29i | 2.22348 | − | 0.920997i | ||||
\(245\) | 1040.09 | + | 2511.00i | 0.271220 | + | 0.654783i | ||||
\(246\) | −990.708 | − | 990.708i | −0.256769 | − | 0.256769i | ||||
\(247\) | −968.269 | − | 968.269i | −0.249431 | − | 0.249431i | ||||
\(248\) | 2300.67 | + | 5554.32i | 0.589085 | + | 1.42218i | ||||
\(249\) | −2780.61 | + | 1151.77i | −0.707687 | + | 0.293134i | ||||
\(250\) | −3267.13 | + | 7887.56i | −0.826527 | + | 1.99541i | ||||
\(251\) | 1026.39i | 0.258109i | 0.991637 | + | 0.129055i | \(0.0411942\pi\) | ||||
−0.991637 | + | 0.129055i | \(0.958806\pi\) | |||||||
\(252\) | −271.471 | − | 112.447i | −0.0678615 | − | 0.0281091i | ||||
\(253\) | 1230.35 | − | 1230.35i | 0.305738 | − | 0.305738i | ||||
\(254\) | 542.987 | 0.134134 | ||||||||
\(255\) | −929.383 | + | 6525.22i | −0.228236 | + | 1.60245i | ||||
\(256\) | −7956.49 | −1.94250 | ||||||||
\(257\) | 1849.68 | − | 1849.68i | 0.448949 | − | 0.448949i | −0.446056 | − | 0.895005i | \(-0.647172\pi\) |
0.895005 | + | 0.446056i | \(0.147172\pi\) | |||||||
\(258\) | 1186.40 | + | 491.424i | 0.286288 | + | 0.118584i | ||||
\(259\) | 1901.02i | 0.456075i | ||||||||
\(260\) | −3321.80 | + | 8019.54i | −0.792344 | + | 1.91289i | ||||
\(261\) | 71.7070 | − | 29.7020i | 0.0170060 | − | 0.00704410i | ||||
\(262\) | −3966.61 | − | 9576.24i | −0.935335 | − | 2.25810i | ||||
\(263\) | 3529.99 | + | 3529.99i | 0.827637 | + | 0.827637i | 0.987189 | − | 0.159553i | \(-0.0510052\pi\) |
−0.159553 | + | 0.987189i | \(0.551005\pi\) | |||||||
\(264\) | −2590.10 | − | 2590.10i | −0.603824 | − | 0.603824i | ||||
\(265\) | −3764.86 | − | 9089.18i | −0.872731 | − | 2.10696i | ||||
\(266\) | 2883.59 | − | 1194.42i | 0.664677 | − | 0.275318i | ||||
\(267\) | 1720.52 | − | 4153.70i | 0.394360 | − | 0.952069i | ||||
\(268\) | 5745.70i | 1.30961i | ||||||||
\(269\) | −3150.91 | − | 1305.15i | −0.714181 | − | 0.295823i | −0.00414728 | − | 0.999991i | \(-0.501320\pi\) |
−0.710033 | + | 0.704168i | \(0.751320\pi\) | |||||||
\(270\) | 9161.30 | − | 9161.30i | 2.06496 | − | 2.06496i | ||||
\(271\) | −75.0911 | −0.0168319 | −0.00841597 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841597 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(272\) | 3105.04 | − | 2330.81i | 0.692172 | − | 0.519582i | ||||
\(273\) | 2124.04 | 0.470889 | ||||||||
\(274\) | −10614.6 | + | 10614.6i | −2.34033 | + | 2.34033i | ||||
\(275\) | −3951.97 | − | 1636.96i | −0.866591 | − | 0.358954i | ||||
\(276\) | 7074.93i | 1.54297i | ||||||||
\(277\) | −1317.15 | + | 3179.88i | −0.285704 | + | 0.689750i | −0.999949 | − | 0.0101463i | \(-0.996770\pi\) |
0.714245 | + | 0.699896i | \(0.246770\pi\) | |||||||
\(278\) | −2110.26 | + | 874.099i | −0.455270 | + | 0.188579i | ||||
\(279\) | −83.0668 | − | 200.541i | −0.0178247 | − | 0.0430325i | ||||
\(280\) | −6832.18 | − | 6832.18i | −1.45822 | − | 1.45822i | ||||
\(281\) | 1183.03 | + | 1183.03i | 0.251151 | + | 0.251151i | 0.821443 | − | 0.570291i | \(-0.193170\pi\) |
−0.570291 | + | 0.821443i | \(0.693170\pi\) | |||||||
\(282\) | −4549.11 | − | 10982.5i | −0.960622 | − | 2.31915i | ||||
\(283\) | 6275.19 | − | 2599.27i | 1.31810 | − | 0.545973i | 0.390860 | − | 0.920450i | \(-0.372178\pi\) |
0.927236 | + | 0.374477i | \(0.122178\pi\) | |||||||
\(284\) | −362.302 | + | 874.674i | −0.0756995 | + | 0.182755i | ||||
\(285\) | 4305.62i | 0.894887i | ||||||||
\(286\) | −2616.53 | − | 1083.80i | −0.540975 | − | 0.224079i | ||||
\(287\) | 564.046 | − | 564.046i | 0.116009 | − | 0.116009i | ||||
\(288\) | 37.1098 | 0.00759277 | ||||||||
\(289\) | 1371.69 | − | 4717.63i | 0.279195 | − | 0.960234i | ||||
\(290\) | 5226.11 | 1.05823 | ||||||||
\(291\) | −3168.82 | + | 3168.82i | −0.638349 | + | 0.638349i | ||||
\(292\) | 5317.22 | + | 2202.46i | 1.06564 | + | 0.441402i | ||||
\(293\) | 6436.90i | 1.28344i | 0.766939 | + | 0.641720i | \(0.221779\pi\) | ||||
−0.766939 | + | 0.641720i | \(0.778221\pi\) | |||||||
\(294\) | 1379.83 | − | 3331.19i | 0.273718 | − | 0.660813i | ||||
\(295\) | −4803.08 | + | 1989.50i | −0.947952 | + | 0.392655i | ||||
\(296\) | 1926.12 | + | 4650.07i | 0.378221 | + | 0.913107i | ||||
\(297\) | 1977.35 | + | 1977.35i | 0.386321 | + | 0.386321i | ||||
\(298\) | 7595.14 | + | 7595.14i | 1.47643 | + | 1.47643i | ||||
\(299\) | 1022.29 | + | 2468.03i | 0.197728 | + | 0.477357i | ||||
\(300\) | 16069.0 | − | 6656.02i | 3.09249 | − | 1.28095i | ||||
\(301\) | −279.786 | + | 675.462i | −0.0535767 | + | 0.129346i | ||||
\(302\) | 3657.75i | 0.696953i | ||||||||
\(303\) | −8635.97 | − | 3577.14i | −1.63737 | − | 0.678221i | ||||
\(304\) | 1793.41 | − | 1793.41i | 0.338352 | − | 0.338352i | ||||
\(305\) | −10890.3 | −2.04452 | ||||||||
\(306\) | −365.276 | + | 274.197i | −0.0682401 | + | 0.0512248i | ||||
\(307\) | 5129.87 | 0.953672 | 0.476836 | − | 0.878992i | \(-0.341784\pi\) | ||||
0.476836 | + | 0.878992i | \(0.341784\pi\) | |||||||
\(308\) | 3019.62 | − | 3019.62i | 0.558632 | − | 0.558632i | ||||
\(309\) | 8531.87 | + | 3534.02i | 1.57075 | + | 0.650625i | ||||
\(310\) | − | 14615.7i | − | 2.67779i | ||||||
\(311\) | −1309.80 | + | 3162.14i | −0.238816 | + | 0.576554i | −0.997161 | − | 0.0753000i | \(-0.976009\pi\) |
0.758344 | + | 0.651854i | \(0.226009\pi\) | |||||||
\(312\) | 5195.61 | − | 2152.09i | 0.942768 | − | 0.390507i | ||||
\(313\) | −1639.23 | − | 3957.46i | −0.296022 | − | 0.714661i | −0.999990 | − | 0.00442950i | \(-0.998590\pi\) |
0.703968 | − | 0.710232i | \(-0.251410\pi\) | |||||||
\(314\) | 1992.31 | + | 1992.31i | 0.358065 | + | 0.358065i | ||||
\(315\) | 246.679 | + | 246.679i | 0.0441231 | + | 0.0441231i | ||||
\(316\) | −1302.74 | − | 3145.10i | −0.231915 | − | 0.559892i | ||||
\(317\) | 360.637 | − | 149.381i | 0.0638971 | − | 0.0264670i | −0.350506 | − | 0.936560i | \(-0.613990\pi\) |
0.414403 | + | 0.910093i | \(0.363990\pi\) | |||||||
\(318\) | −4994.62 | + | 12058.1i | −0.880769 | + | 2.12636i | ||||
\(319\) | 1127.99i | 0.197979i | ||||||||
\(320\) | 9908.34 | + | 4104.17i | 1.73092 | + | 0.716969i | ||||
\(321\) | −6645.63 | + | 6645.63i | −1.15552 | + | 1.15552i | ||||
\(322\) | −6088.94 | −1.05380 | ||||||||
\(323\) | 452.549 | − | 3177.35i | 0.0779582 | − | 0.547346i | ||||
\(324\) | −10804.5 | −1.85263 | ||||||||
\(325\) | 4643.79 | − | 4643.79i | 0.792589 | − | 0.792589i | ||||
\(326\) | −7984.87 | − | 3307.44i | −1.35657 | − | 0.561909i | ||||
\(327\) | − | 7028.25i | − | 1.18857i | ||||||
\(328\) | 808.216 | − | 1951.21i | 0.136056 | − | 0.328467i | ||||
\(329\) | 6252.75 | − | 2589.97i | 1.04780 | − | 0.434012i | ||||
\(330\) | 3407.81 | + | 8227.18i | 0.568466 | + | 1.37240i | ||||
\(331\) | −2704.60 | − | 2704.60i | −0.449119 | − | 0.449119i | 0.445942 | − | 0.895062i | \(-0.352869\pi\) |
−0.895062 | + | 0.445942i | \(0.852869\pi\) | |||||||
\(332\) | −6569.07 | − | 6569.07i | −1.08592 | − | 1.08592i | ||||
\(333\) | −69.5434 | − | 167.893i | −0.0114443 | − | 0.0276290i | ||||
\(334\) | −14080.4 | + | 5832.30i | −2.30672 | + | 0.955477i | ||||
\(335\) | 2610.48 | − | 6302.25i | 0.425748 | − | 1.02785i | ||||
\(336\) | 3934.10i | 0.638758i | ||||||||
\(337\) | 2195.97 | + | 909.601i | 0.354962 | + | 0.147030i | 0.553037 | − | 0.833157i | \(-0.313469\pi\) |
−0.198075 | + | 0.980187i | \(0.563469\pi\) | |||||||
\(338\) | −4478.08 | + | 4478.08i | −0.720638 | + | 0.720638i | ||||
\(339\) | 3105.76 | 0.497586 | ||||||||
\(340\) | −19706.0 | + | 5057.41i | −3.14326 | + | 0.806695i | ||||
\(341\) | 3154.61 | 0.500973 | ||||||||
\(342\) | −210.976 | + | 210.976i | −0.0333575 | + | 0.0333575i | ||||
\(343\) | 6339.70 | + | 2625.99i | 0.997993 | + | 0.413382i | ||||
\(344\) | 1935.73i | 0.303394i | ||||||||
\(345\) | 3214.40 | − | 7760.24i | 0.501615 | − | 1.21101i | ||||
\(346\) | 5252.13 | − | 2175.51i | 0.816059 | − | 0.338023i | ||||
\(347\) | −4562.82 | − | 11015.6i | −0.705893 | − | 1.70418i | −0.710017 | − | 0.704184i | \(-0.751313\pi\) |
0.00412480 | − | 0.999991i | \(-0.498687\pi\) | |||||||
\(348\) | −3243.14 | − | 3243.14i | −0.499571 | − | 0.499571i | ||||
\(349\) | −5225.48 | − | 5225.48i | −0.801471 | − | 0.801471i | 0.181854 | − | 0.983326i | \(-0.441790\pi\) |
−0.983326 | + | 0.181854i | \(0.941790\pi\) | |||||||
\(350\) | 5728.41 | + | 13829.6i | 0.874847 | + | 2.11207i | ||||
\(351\) | −3966.46 | + | 1642.96i | −0.603174 | + | 0.249843i | ||||
\(352\) | −206.389 | + | 498.267i | −0.0312516 | + | 0.0754481i | ||||
\(353\) | 2966.18i | 0.447235i | 0.974677 | + | 0.223617i | \(0.0717866\pi\) | ||||
−0.974677 | + | 0.223617i | \(0.928213\pi\) | |||||||
\(354\) | 6371.96 | + | 2639.35i | 0.956684 | + | 0.396271i | ||||
\(355\) | 794.792 | − | 794.792i | 0.118826 | − | 0.118826i | ||||
\(356\) | 13877.6 | 2.06604 | ||||||||
\(357\) | 2988.63 | + | 3981.36i | 0.443068 | + | 0.590241i | ||||
\(358\) | 7547.93 | 1.11430 | ||||||||
\(359\) | −4614.81 | + | 4614.81i | −0.678441 | + | 0.678441i | −0.959647 | − | 0.281206i | \(-0.909265\pi\) |
0.281206 | + | 0.959647i | \(0.409265\pi\) | |||||||
\(360\) | 853.336 | + | 353.463i | 0.124930 | + | 0.0517476i | ||||
\(361\) | 4762.44i | 0.694335i | ||||||||
\(362\) | 2783.12 | − | 6719.05i | 0.404082 | − | 0.975539i | ||||
\(363\) | 4453.28 | − | 1844.61i | 0.643902 | − | 0.266713i | ||||
\(364\) | 2508.97 | + | 6057.20i | 0.361280 | + | 0.872208i | ||||
\(365\) | −4831.61 | − | 4831.61i | −0.692871 | − | 0.692871i | ||||
\(366\) | 10216.0 | + | 10216.0i | 1.45901 | + | 1.45901i | ||||
\(367\) | 2256.50 | + | 5447.66i | 0.320949 | + | 0.774838i | 0.999199 | + | 0.0400079i | \(0.0127383\pi\) |
−0.678251 | + | 0.734831i | \(0.737262\pi\) | |||||||
\(368\) | −4571.23 | + | 1893.47i | −0.647532 | + | 0.268217i | ||||
\(369\) | −29.1810 | + | 70.4491i | −0.00411680 | + | 0.00993884i | ||||
\(370\) | − | 12236.2i | − | 1.71928i | ||||||
\(371\) | −6865.11 | − | 2843.62i | −0.960697 | − | 0.397934i | ||||
\(372\) | −9070.01 | + | 9070.01i | −1.26413 | + | 1.26413i | ||||
\(373\) | 9234.98 | 1.28195 | 0.640977 | − | 0.767560i | \(-0.278529\pi\) | ||||
0.640977 | + | 0.767560i | \(0.278529\pi\) | |||||||
\(374\) | −1650.08 | − | 6429.47i | −0.228138 | − | 0.888930i | ||||
\(375\) | −8895.45 | −1.22496 | ||||||||
\(376\) | 12670.6 | − | 12670.6i | 1.73787 | − | 1.73787i | ||||
\(377\) | −1599.96 | − | 662.726i | −0.218574 | − | 0.0905361i | ||||
\(378\) | − | 9785.77i | − | 1.33155i | ||||||
\(379\) | −554.759 | + | 1339.31i | −0.0751875 | + | 0.181519i | −0.957005 | − | 0.290073i | \(-0.906320\pi\) |
0.881817 | + | 0.471592i | \(0.156320\pi\) | |||||||
\(380\) | −12278.5 | + | 5085.91i | −1.65756 | + | 0.686584i | ||||
\(381\) | 216.506 | + | 522.692i | 0.0291127 | + | 0.0702843i | ||||
\(382\) | 10343.4 | + | 10343.4i | 1.38537 | + | 1.38537i | ||||
\(383\) | 5769.34 | + | 5769.34i | 0.769711 | + | 0.769711i | 0.978056 | − | 0.208344i | \(-0.0668075\pi\) |
−0.208344 | + | 0.978056i | \(0.566808\pi\) | |||||||
\(384\) | −5015.39 | − | 12108.2i | −0.666512 | − | 1.60910i | ||||
\(385\) | −4684.03 | + | 1940.19i | −0.620053 | + | 0.256834i | ||||
\(386\) | 7243.89 | − | 17488.3i | 0.955192 | − | 2.30604i | ||||
\(387\) | − | 69.8902i | − | 0.00918015i | ||||||
\(388\) | −12779.7 | − | 5293.54i | −1.67215 | − | 0.692626i | ||||
\(389\) | 1037.93 | − | 1037.93i | 0.135283 | − | 0.135283i | −0.636222 | − | 0.771506i | \(-0.719504\pi\) |
0.771506 | + | 0.636222i | \(0.219504\pi\) | |||||||
\(390\) | −13671.8 | −1.77512 | ||||||||
\(391\) | −3187.73 | + | 5388.85i | −0.412303 | + | 0.696998i | ||||
\(392\) | 5435.15 | 0.700298 | ||||||||
\(393\) | 7636.69 | − | 7636.69i | 0.980204 | − | 0.980204i | ||||
\(394\) | 4252.08 | + | 1761.27i | 0.543697 | + | 0.225207i | ||||
\(395\) | 4041.63i | 0.514827i | ||||||||
\(396\) | −156.220 | + | 377.149i | −0.0198241 | + | 0.0478597i | ||||
\(397\) | −5560.11 | + | 2303.07i | −0.702907 | + | 0.291154i | −0.705366 | − | 0.708843i | \(-0.749217\pi\) |
0.00245887 | + | 0.999997i | \(0.499217\pi\) | |||||||
\(398\) | 3285.31 | + | 7931.43i | 0.413763 | + | 0.998912i | ||||
\(399\) | 2299.55 | + | 2299.55i | 0.288525 | + | 0.288525i | ||||
\(400\) | 8601.13 | + | 8601.13i | 1.07514 | + | 1.07514i | ||||
\(401\) | 2257.50 | + | 5450.08i | 0.281132 | + | 0.678713i | 0.999863 | − | 0.0165756i | \(-0.00527641\pi\) |
−0.718730 | + | 0.695289i | \(0.755276\pi\) | |||||||
\(402\) | −8360.83 | + | 3463.17i | −1.03731 | + | 0.429670i | ||||
\(403\) | −1853.43 | + | 4474.57i | −0.229096 | + | 0.553087i | ||||
\(404\) | − | 28852.9i | − | 3.55318i | ||||||
\(405\) | 11851.1 | + | 4908.90i | 1.45404 | + | 0.602284i | ||||
\(406\) | 2791.17 | − | 2791.17i | 0.341190 | − | 0.341190i | ||||
\(407\) | 2641.04 | 0.321649 | ||||||||
\(408\) | 11344.4 | + | 6710.70i | 1.37655 | + | 0.814287i | ||||
\(409\) | −9261.09 | −1.11964 | −0.559818 | − | 0.828616i | \(-0.689129\pi\) | ||||
−0.559818 | + | 0.828616i | \(0.689129\pi\) | |||||||
\(410\) | −3630.59 | + | 3630.59i | −0.437322 | + | 0.437322i | ||||
\(411\) | −14450.2 | − | 5985.47i | −1.73425 | − | 0.718349i | ||||
\(412\) | 28505.1i | 3.40861i | ||||||||
\(413\) | −1502.68 | + | 3627.79i | −0.179036 | + | 0.432232i | ||||
\(414\) | 537.759 | − | 222.747i | 0.0638391 | − | 0.0264430i | ||||
\(415\) | 4220.81 | + | 10189.9i | 0.499257 | + | 1.20531i | ||||
\(416\) | −585.493 | − | 585.493i | −0.0690052 | − | 0.0690052i | ||||
\(417\) | −1682.86 | − | 1682.86i | −0.197625 | − | 0.197625i | ||||
\(418\) | −1659.38 | − | 4006.10i | −0.194170 | − | 0.468767i | ||||
\(419\) | 7888.15 | − | 3267.38i | 0.919716 | − | 0.380959i | 0.127948 | − | 0.991781i | \(-0.459161\pi\) |
0.791768 | + | 0.610822i | \(0.209161\pi\) | |||||||
\(420\) | 7888.98 | − | 19045.7i | 0.916531 | − | 2.21270i | ||||
\(421\) | − | 1617.31i | − | 0.187228i | −0.995609 | − | 0.0936140i | \(-0.970158\pi\) | ||
0.995609 | − | 0.0936140i | \(-0.0298420\pi\) | |||||||
\(422\) | 1668.17 | + | 690.978i | 0.192429 | + | 0.0797068i | ||||
\(423\) | −457.479 | + | 457.479i | −0.0525848 | + | 0.0525848i | ||||
\(424\) | −19673.9 | −2.25342 | ||||||||
\(425\) | 15238.5 | + | 2170.41i | 1.73924 | + | 0.247719i | ||||
\(426\) | −1491.15 | −0.169593 | ||||||||
\(427\) | −5816.32 | + | 5816.32i | −0.659184 | + | 0.659184i | ||||
\(428\) | −26801.6 | − | 11101.6i | −3.02688 | − | 1.25377i | ||||
\(429\) | − | 2950.88i | − | 0.332097i | ||||||
\(430\) | 1800.89 | − | 4347.74i | 0.201969 | − | 0.487597i | ||||
\(431\) | 2343.97 | − | 970.905i | 0.261961 | − | 0.108508i | −0.247838 | − | 0.968802i | \(-0.579720\pi\) |
0.509799 | + | 0.860294i | \(0.329720\pi\) | |||||||
\(432\) | −3043.06 | − | 7346.60i | −0.338910 | − | 0.818202i | ||||
\(433\) | −1296.36 | − | 1296.36i | −0.143878 | − | 0.143878i | 0.631499 | − | 0.775377i | \(-0.282440\pi\) |
−0.775377 | + | 0.631499i | \(0.782440\pi\) | |||||||
\(434\) | −7805.98 | − | 7805.98i | −0.863361 | − | 0.863361i | ||||
\(435\) | 2083.81 | + | 5030.77i | 0.229681 | + | 0.554498i | ||||
\(436\) | 20042.7 | − | 8301.96i | 2.20154 | − | 0.911908i | ||||
\(437\) | −1565.20 | + | 3778.73i | −0.171336 | + | 0.413641i | ||||
\(438\) | 9064.84i | 0.988892i | ||||||||
\(439\) | −9607.00 | − | 3979.35i | −1.04446 | − | 0.432629i | −0.206548 | − | 0.978436i | \(-0.566223\pi\) |
−0.837911 | + | 0.545808i | \(0.816223\pi\) | |||||||
\(440\) | −9491.78 | + | 9491.78i | −1.02842 | + | 1.02842i | ||||
\(441\) | −196.238 | −0.0211898 | ||||||||
\(442\) | 10089.2 | + | 1436.99i | 1.08573 | + | 0.154640i | ||||
\(443\) | −3984.14 | −0.427296 | −0.213648 | − | 0.976911i | \(-0.568535\pi\) | ||||
−0.213648 | + | 0.976911i | \(0.568535\pi\) | |||||||
\(444\) | −7593.40 | + | 7593.40i | −0.811637 | + | 0.811637i | ||||
\(445\) | −15221.8 | − | 6305.09i | −1.62154 | − | 0.671662i | ||||
\(446\) | 12513.4i | 1.32854i | ||||||||
\(447\) | −4282.83 | + | 10339.7i | −0.453179 | + | 1.09407i | ||||
\(448\) | 7483.82 | − | 3099.90i | 0.789235 | − | 0.326912i | ||||
\(449\) | 5045.33 | + | 12180.5i | 0.530298 | + | 1.28025i | 0.931326 | + | 0.364187i | \(0.118653\pi\) |
−0.401027 | + | 0.916066i | \(0.631347\pi\) | |||||||
\(450\) | −1011.84 | − | 1011.84i | −0.105996 | − | 0.105996i | ||||
\(451\) | −783.616 | − | 783.616i | −0.0818160 | − | 0.0818160i | ||||
\(452\) | 3668.60 | + | 8856.79i | 0.381762 | + | 0.921656i | ||||
\(453\) | −3521.03 | + | 1458.46i | −0.365193 | + | 0.151268i | ||||
\(454\) | 9683.14 | − | 23377.2i | 1.00100 | − | 2.41662i | ||||
\(455\) | − | 7783.85i | − | 0.802005i | ||||||
\(456\) | 7954.85 | + | 3295.01i | 0.816929 | + | 0.338383i | ||||
\(457\) | 11484.8 | − | 11484.8i | 1.17557 | − | 1.17557i | 0.194706 | − | 0.980862i | \(-0.437625\pi\) |
0.980862 | − | 0.194706i | \(-0.0623754\pi\) | |||||||
\(458\) | 15551.2 | 1.58659 | ||||||||
\(459\) | −8660.63 | − | 5123.12i | −0.880705 | − | 0.520974i | ||||
\(460\) | 25927.1 | 2.62795 | ||||||||
\(461\) | 7816.84 | − | 7816.84i | 0.789732 | − | 0.789732i | −0.191718 | − | 0.981450i | \(-0.561406\pi\) |
0.981450 | + | 0.191718i | \(0.0614058\pi\) | |||||||
\(462\) | 6214.03 | + | 2573.94i | 0.625764 | + | 0.259200i | ||||
\(463\) | − | 14185.7i | − | 1.42390i | −0.702228 | − | 0.711952i | \(-0.747811\pi\) | ||
0.702228 | − | 0.711952i | \(-0.252189\pi\) | |||||||
\(464\) | 1227.49 | − | 2963.41i | 0.122812 | − | 0.296494i | ||||
\(465\) | 14069.4 | − | 5827.74i | 1.40312 | − | 0.581193i | ||||
\(466\) | 1587.18 | + | 3831.78i | 0.157778 | + | 0.380909i | ||||
\(467\) | −6851.43 | − | 6851.43i | −0.678900 | − | 0.678900i | 0.280851 | − | 0.959751i | \(-0.409383\pi\) |
−0.959751 | + | 0.280851i | \(0.909383\pi\) | |||||||
\(468\) | −443.172 | − | 443.172i | −0.0437727 | − | 0.0437727i | ||||
\(469\) | −1971.71 | − | 4760.13i | −0.194126 | − | 0.468661i | ||||
\(470\) | −40247.0 | + | 16670.8i | −3.94990 | + | 1.63610i | ||||
\(471\) | −1123.44 | + | 2712.23i | −0.109906 | + | 0.265336i | ||||
\(472\) | 10396.5i | 1.01385i | ||||||||
\(473\) | 938.404 | + | 388.699i | 0.0912217 | + | 0.0377852i | ||||
\(474\) | 3791.36 | − | 3791.36i | 0.367390 | − | 0.367390i | ||||
\(475\) | 10055.0 | 0.971276 | ||||||||
\(476\) | −7823.54 | + | 13225.7i | −0.753343 | + | 1.27352i | ||||
\(477\) | 710.334 | 0.0681844 | ||||||||
\(478\) | −6506.47 | + | 6506.47i | −0.622592 | + | 0.622592i | ||||
\(479\) | 12229.4 | + | 5065.58i | 1.16655 | + | 0.483199i | 0.880049 | − | 0.474882i | \(-0.157509\pi\) |
0.286497 | + | 0.958081i | \(0.407509\pi\) | |||||||
\(480\) | 2603.52i | 0.247571i | ||||||||
\(481\) | −1551.69 | + | 3746.10i | −0.147091 | + | 0.355109i | ||||
\(482\) | −8306.83 | + | 3440.80i | −0.784992 | + | 0.325154i | ||||
\(483\) | −2427.85 | − | 5861.35i | −0.228719 | − | 0.552175i | ||||
\(484\) | 10520.7 | + | 10520.7i | 0.988042 | + | 0.988042i | ||||
\(485\) | 11612.6 | + | 11612.6i | 1.08722 | + | 1.08722i | ||||
\(486\) | 699.040 | + | 1687.63i | 0.0652450 | + | 0.157515i | ||||
\(487\) | 17831.1 | − | 7385.89i | 1.65915 | − | 0.687242i | 0.661136 | − | 0.750266i | \(-0.270075\pi\) |
0.998012 | + | 0.0630247i | \(0.0200747\pi\) | |||||||
\(488\) | −8334.15 | + | 20120.4i | −0.773093 | + | 1.86641i | ||||
\(489\) | − | 9005.20i | − | 0.832780i | ||||||
\(490\) | −12207.6 | − | 5056.56i | −1.12548 | − | 0.466188i | ||||
\(491\) | 51.1031 | − | 51.1031i | 0.00469705 | − | 0.00469705i | −0.704754 | − | 0.709451i | \(-0.748943\pi\) |
0.709451 | + | 0.704754i | \(0.248943\pi\) | |||||||
\(492\) | 4506.04 | 0.412902 | ||||||||
\(493\) | −1008.99 | − | 3931.50i | −0.0921760 | − | 0.359160i | ||||
\(494\) | 6657.27 | 0.606325 | ||||||||
\(495\) | 342.705 | − | 342.705i | 0.0311180 | − | 0.0311180i | ||||
\(496\) | −8287.69 | − | 3432.87i | −0.750259 | − | 0.310767i | ||||
\(497\) | − | 848.967i | − | 0.0766225i | ||||||
\(498\) | 5599.50 | − | 13518.4i | 0.503855 | − | 1.21641i | ||||
\(499\) | −13678.5 | + | 5665.84i | −1.22713 | + | 0.508292i | −0.899668 | − | 0.436574i | \(-0.856192\pi\) |
−0.327457 | + | 0.944866i | \(0.606192\pi\) | |||||||
\(500\) | −10507.5 | − | 25367.5i | −0.939824 | − | 2.26894i | ||||
\(501\) | −11228.6 | − | 11228.6i | −1.00131 | − | 1.00131i | ||||
\(502\) | −3528.45 | − | 3528.45i | −0.313710 | − | 0.313710i | ||||
\(503\) | 2561.65 | + | 6184.36i | 0.227074 | + | 0.548205i | 0.995819 | − | 0.0913508i | \(-0.0291184\pi\) |
−0.768745 | + | 0.639555i | \(0.779118\pi\) | |||||||
\(504\) | 644.529 | − | 266.973i | 0.0569635 | − | 0.0235951i | ||||
\(505\) | −13108.9 | + | 31647.7i | −1.15513 | + | 2.78872i | ||||
\(506\) | 8459.22i | 0.743198i | ||||||||
\(507\) | −6096.25 | − | 2525.15i | −0.534012 | − | 0.221195i | ||||
\(508\) | −1234.84 | + | 1234.84i | −0.107848 | + | 0.107848i | ||||
\(509\) | −4414.17 | −0.384390 | −0.192195 | − | 0.981357i | \(-0.561561\pi\) | ||||
−0.192195 | + | 0.981357i | \(0.561561\pi\) | |||||||
\(510\) | −19236.9 | − | 25626.8i | −1.67024 | − | 2.22505i | ||||
\(511\) | −5160.94 | −0.446784 | ||||||||
\(512\) | 12716.4 | − | 12716.4i | 1.09764 | − | 1.09764i | ||||
\(513\) | −6072.94 | − | 2515.49i | −0.522664 | − | 0.216495i | ||||
\(514\) | 12717.4i | 1.09132i | ||||||||
\(515\) | 12950.9 | − | 31266.2i | 1.10813 | − | 2.67525i | ||||
\(516\) | −3815.63 | + | 1580.49i | −0.325531 | + | 0.134839i | ||||
\(517\) | −3598.19 | − | 8686.79i | −0.306089 | − | 0.738965i | ||||
\(518\) | −6535.15 | − | 6535.15i | −0.554321 | − | 0.554321i | ||||
\(519\) | 4188.38 | + | 4188.38i | 0.354238 | + | 0.354238i | ||||
\(520\) | −7886.64 | − | 19040.0i | −0.665100 | − | 1.60569i | ||||
\(521\) | −1064.38 | + | 440.882i | −0.0895037 | + | 0.0370736i | −0.426986 | − | 0.904258i | \(-0.640425\pi\) |
0.337482 | + | 0.941332i | \(0.390425\pi\) | |||||||
\(522\) | −144.401 | + | 348.615i | −0.0121078 | + | 0.0292308i | ||||
\(523\) | 8548.79i | 0.714747i | 0.933962 | + | 0.357373i | \(0.116328\pi\) | ||||
−0.933962 | + | 0.357373i | \(0.883672\pi\) | |||||||
\(524\) | 30798.5 | + | 12757.2i | 2.56763 | + | 1.06355i | ||||
\(525\) | −11028.6 | + | 11028.6i | −0.916814 | + | 0.916814i | ||||
\(526\) | −24270.2 | −2.01185 | ||||||||
\(527\) | −10995.1 | + | 2821.82i | −0.908833 | + | 0.233246i | ||||
\(528\) | 5465.55 | 0.450488 | ||||||||
\(529\) | −2961.28 | + | 2961.28i | −0.243387 | + | 0.243387i | ||||
\(530\) | 44188.5 | + | 18303.5i | 3.62156 | + | 1.50010i | ||||
\(531\) | − | 375.368i | − | 0.0306772i | ||||||
\(532\) | −3841.42 | + | 9274.00i | −0.313058 | + | 0.755788i | ||||
\(533\) | 1571.89 | − | 651.100i | 0.127742 | − | 0.0529123i | ||||
\(534\) | 8364.59 | + | 20193.9i | 0.677849 | + | 1.63647i | ||||
\(535\) | 24353.8 | + | 24353.8i | 1.96805 | + | 1.96805i | ||||
\(536\) | −9645.98 | − | 9645.98i | −0.777319 | − | 0.777319i | ||||
\(537\) | 3009.59 | + | 7265.80i | 0.241850 | + | 0.583878i | ||||
\(538\) | 15318.7 | − | 6345.20i | 1.22757 | − | 0.508478i | ||||
\(539\) | 1091.39 | − | 2634.86i | 0.0872165 | − | 0.210559i | ||||
\(540\) | 41668.4i | 3.32060i | ||||||||
\(541\) | −1681.96 | − | 696.690i | −0.133666 | − | 0.0553661i | 0.314848 | − | 0.949142i | \(-0.398046\pi\) |
−0.448514 | + | 0.893776i | \(0.648046\pi\) | |||||||
\(542\) | 258.142 | − | 258.142i | 0.0204578 | − | 0.0204578i | ||||
\(543\) | 7577.62 | 0.598871 | ||||||||
\(544\) | 273.647 | − | 1921.28i | 0.0215672 | − | 0.151423i | ||||
\(545\) | −25756.0 | −2.02434 | ||||||||
\(546\) | −7301.85 | + | 7301.85i | −0.572327 | + | 0.572327i | ||||
\(547\) | −76.4832 | − | 31.6804i | −0.00597840 | − | 0.00247633i | 0.379692 | − | 0.925113i | \(-0.376030\pi\) |
−0.385671 | + | 0.922637i | \(0.626030\pi\) | |||||||
\(548\) | − | 48278.3i | − | 3.76341i | ||||||
\(549\) | 300.908 | − | 726.456i | 0.0233924 | − | 0.0564743i | ||||
\(550\) | 19213.1 | − | 7958.34i | 1.48955 | − | 0.616991i | ||||
\(551\) | −1014.68 | − | 2449.65i | −0.0784516 | − | 0.189399i | ||||
\(552\) | −11877.5 | − | 11877.5i | −0.915835 | − | 0.915835i | ||||
\(553\) | 2158.56 | + | 2158.56i | 0.165988 | + | 0.165988i | ||||
\(554\) | −6403.54 | − | 15459.5i | −0.491084 | − | 1.18558i | ||||
\(555\) | 11778.9 | − | 4878.97i | 0.900875 | − | 0.373155i | ||||
\(556\) | 2811.22 | − | 6786.89i | 0.214429 | − | 0.517677i | ||||
\(557\) | − | 12671.9i | − | 0.963963i | −0.876181 | − | 0.481981i | \(-0.839917\pi\) | ||
0.876181 | − | 0.481981i | \(-0.160083\pi\) | |||||||
\(558\) | 974.963 | + | 403.843i | 0.0739668 | + | 0.0306380i | ||||
\(559\) | −1102.68 | + | 1102.68i | −0.0834318 | + | 0.0834318i | ||||
\(560\) | 14417.1 | 1.08791 | ||||||||
\(561\) | 5531.21 | − | 4152.03i | 0.416271 | − | 0.312476i | ||||
\(562\) | −8133.82 | −0.610506 | ||||||||
\(563\) | 3329.39 | − | 3329.39i | 0.249231 | − | 0.249231i | −0.571424 | − | 0.820655i | \(-0.693609\pi\) |
0.820655 | + | 0.571424i | \(0.193609\pi\) | |||||||
\(564\) | 35321.3 | + | 14630.5i | 2.63705 | + | 1.09230i | ||||
\(565\) | − | 11381.5i | − | 0.847473i | ||||||
\(566\) | −12636.8 | + | 30507.9i | −0.938451 | + | 2.26562i | ||||
\(567\) | 8951.22 | − | 3707.72i | 0.662991 | − | 0.274620i | ||||
\(568\) | −860.179 | − | 2076.66i | −0.0635428 | − | 0.153406i | ||||
\(569\) | −6005.28 | − | 6005.28i | −0.442450 | − | 0.442450i | 0.450384 | − | 0.892835i | \(-0.351287\pi\) |
−0.892835 | + | 0.450384i | \(0.851287\pi\) | |||||||
\(570\) | −14801.5 | − | 14801.5i | −1.08766 | − | 1.08766i | ||||
\(571\) | 431.903 | + | 1042.71i | 0.0316543 | + | 0.0764202i | 0.938916 | − | 0.344146i | \(-0.111831\pi\) |
−0.907262 | + | 0.420566i | \(0.861831\pi\) | |||||||
\(572\) | 8415.13 | − | 3485.66i | 0.615129 | − | 0.254795i | ||||
\(573\) | −5832.53 | + | 14081.0i | −0.425231 | + | 1.02660i | ||||
\(574\) | 3878.06i | 0.281998i | ||||||||
\(575\) | −18122.7 | − | 7506.66i | −1.31438 | − | 0.544434i | ||||
\(576\) | −547.550 | + | 547.550i | −0.0396087 | + | 0.0396087i | ||||
\(577\) | −18288.9 | −1.31955 | −0.659773 | − | 0.751465i | \(-0.729348\pi\) | ||||
−0.659773 | + | 0.751465i | \(0.729348\pi\) | |||||||
\(578\) | 11502.4 | + | 20933.3i | 0.827746 | + | 1.50642i | ||||
\(579\) | 19723.0 | 1.41565 | ||||||||
\(580\) | −11885.0 | + | 11885.0i | −0.850855 | + | 0.850855i | ||||
\(581\) | 7696.52 | + | 3188.00i | 0.549579 | + | 0.227643i | ||||
\(582\) | − | 21787.0i | − | 1.55172i | ||||||
\(583\) | −3950.58 | + | 9537.53i | −0.280645 | + | 0.677537i | ||||
\(584\) | −12624.2 | + | 5229.10i | −0.894506 | + | 0.370517i | ||||
\(585\) | 284.750 | + | 687.448i | 0.0201248 | + | 0.0485855i | ||||
\(586\) | −22128.2 | − | 22128.2i | −1.55991 | − | 1.55991i | ||||
\(587\) | 7997.50 | + | 7997.50i | 0.562338 | + | 0.562338i | 0.929971 | − | 0.367633i | \(-0.119832\pi\) |
−0.367633 | + | 0.929971i | \(0.619832\pi\) | |||||||
\(588\) | 4437.71 | + | 10713.6i | 0.311238 | + | 0.751395i | ||||
\(589\) | −6850.88 | + | 2837.73i | −0.479262 | + | 0.198517i | ||||
\(590\) | 9672.28 | − | 23350.9i | 0.674918 | − | 1.62940i | ||||
\(591\) | 4795.42i | 0.333769i | ||||||||
\(592\) | −6938.44 | − | 2874.00i | −0.481703 | − | 0.199528i | ||||
\(593\) | −3735.98 | + | 3735.98i | −0.258715 | + | 0.258715i | −0.824532 | − | 0.565816i | \(-0.808561\pi\) |
0.565816 | + | 0.824532i | \(0.308561\pi\) | |||||||
\(594\) | −13595.1 | −0.939082 | ||||||||
\(595\) | 14590.3 | − | 10952.3i | 1.00528 | − | 0.754620i | ||||
\(596\) | −34545.0 | −2.37419 | ||||||||
\(597\) | −6325.02 | + | 6325.02i | −0.433611 | + | 0.433611i | ||||
\(598\) | −11998.7 | − | 4970.04i | −0.820509 | − | 0.339866i | ||||
\(599\) | 22287.6i | 1.52028i | 0.649762 | + | 0.760138i | \(0.274869\pi\) | ||||
−0.649762 | + | 0.760138i | \(0.725131\pi\) | |||||||
\(600\) | −15802.8 | + | 38151.2i | −1.07524 | + | 2.59586i | ||||
\(601\) | 13901.4 | − | 5758.15i | 0.943511 | − | 0.390815i | 0.142723 | − | 0.989763i | \(-0.454414\pi\) |
0.800788 | + | 0.598947i | \(0.204414\pi\) | |||||||
\(602\) | −1360.22 | − | 3283.87i | −0.0920907 | − | 0.222326i | ||||
\(603\) | 348.272 | + | 348.272i | 0.0235203 | + | 0.0235203i | ||||
\(604\) | −8318.28 | − | 8318.28i | −0.560374 | − | 0.560374i | ||||
\(605\) | −6759.83 | − | 16319.7i | −0.454258 | − | 1.09668i | ||||
\(606\) | 41985.2 | − | 17390.8i | 2.81441 | − | 1.16577i | ||||
\(607\) | −4319.98 | + | 10429.4i | −0.288868 | + | 0.697388i | −0.999984 | − | 0.00568627i | \(-0.998190\pi\) |
0.711116 | + | 0.703075i | \(0.248190\pi\) | |||||||
\(608\) | − | 1267.75i | − | 0.0845623i | ||||||
\(609\) | 3799.77 | + | 1573.91i | 0.252831 | + | 0.104726i | ||||
\(610\) | 37437.8 | − | 37437.8i | 2.48494 | − | 2.48494i | ||||
\(611\) | 14435.6 | 0.955811 | ||||||||
\(612\) | 207.129 | − | 1454.26i | 0.0136809 | − | 0.0960538i | ||||
\(613\) | 14753.0 | 0.972054 | 0.486027 | − | 0.873944i | \(-0.338446\pi\) | ||||
0.486027 | + | 0.873944i | \(0.338446\pi\) | |||||||
\(614\) | −17635.0 | + | 17635.0i | −1.15911 | + | 1.15911i | ||||
\(615\) | −4942.51 | − | 2047.26i | −0.324067 | − | 0.134233i | ||||
\(616\) | 10138.8i | 0.663154i | ||||||||
\(617\) | 2561.52 | − | 6184.04i | 0.167136 | − | 0.403501i | −0.818014 | − | 0.575198i | \(-0.804925\pi\) |
0.985150 | + | 0.171697i | \(0.0549250\pi\) | |||||||
\(618\) | −41479.1 | + | 17181.2i | −2.69989 | + | 1.11833i | ||||
\(619\) | 491.884 | + | 1187.51i | 0.0319394 | + | 0.0771085i | 0.939044 | − | 0.343796i | \(-0.111713\pi\) |
−0.907105 | + | 0.420904i | \(0.861713\pi\) | |||||||
\(620\) | 33238.3 | + | 33238.3i | 2.15304 | + | 2.15304i | ||||
\(621\) | 9067.61 | + | 9067.61i | 0.585943 | + | 0.585943i | ||||
\(622\) | −6367.81 | − | 15373.2i | −0.410492 | − | 0.991014i | ||||
\(623\) | −11497.1 | + | 4762.27i | −0.739362 | + | 0.306254i | ||||
\(624\) | −3211.17 | + | 7752.46i | −0.206009 | + | 0.497350i | ||||
\(625\) | 5148.78i | 0.329522i | ||||||||
\(626\) | 19239.9 | + | 7969.41i | 1.22840 | + | 0.508820i | ||||
\(627\) | 3194.71 | − | 3194.71i | 0.203484 | − | 0.203484i | ||||
\(628\) | −9061.61 | −0.575792 | ||||||||
\(629\) | −9205.10 | + | 2362.42i | −0.583516 | + | 0.149755i | ||||
\(630\) | −1696.02 | −0.107256 | ||||||||
\(631\) | 19224.0 | − | 19224.0i | 1.21283 | − | 1.21283i | 0.242734 | − | 0.970093i | \(-0.421956\pi\) |
0.970093 | − | 0.242734i | \(-0.0780442\pi\) | |||||||
\(632\) | 7467.12 | + | 3092.98i | 0.469978 | + | 0.194671i | ||||
\(633\) | 1881.33i | 0.118130i | ||||||||
\(634\) | −726.238 | + | 1753.29i | −0.0454931 | + | 0.109830i | ||||
\(635\) | 1915.48 | − | 793.417i | 0.119706 | − | 0.0495839i | ||||
\(636\) | −16063.4 | − | 38780.5i | −1.00150 | − | 2.41784i | ||||
\(637\) | 3096.11 | + | 3096.11i | 0.192578 | + | 0.192578i | ||||
\(638\) | −3877.70 | − | 3877.70i | −0.240626 | − | 0.240626i | ||||
\(639\) | 31.0571 | + | 74.9785i | 0.00192269 | + | 0.00464179i | ||||
\(640\) | −44372.3 | + | 18379.6i | −2.74057 | + | 1.13518i | ||||
\(641\) | −4715.24 | + | 11383.6i | −0.290547 | + | 0.701442i | −0.999995 | − | 0.00331580i | \(-0.998945\pi\) |
0.709448 | + | 0.704758i | \(0.248945\pi\) | |||||||
\(642\) | − | 45691.6i | − | 2.80888i | ||||||
\(643\) | −23630.2 | − | 9787.93i | −1.44927 | − | 0.600308i | −0.487246 | − | 0.873265i | \(-0.661999\pi\) |
−0.962026 | + | 0.272956i | \(0.911999\pi\) | |||||||
\(644\) | 13847.2 | − | 13847.2i | 0.847290 | − | 0.847290i | ||||
\(645\) | 4903.30 | 0.299329 | ||||||||
\(646\) | 9367.10 | + | 12478.6i | 0.570501 | + | 0.760004i | ||||
\(647\) | −28275.5 | −1.71812 | −0.859062 | − | 0.511872i | \(-0.828952\pi\) | ||||
−0.859062 | + | 0.511872i | \(0.828952\pi\) | |||||||
\(648\) | 18138.9 | − | 18138.9i | 1.09963 | − | 1.09963i | ||||
\(649\) | 5040.00 | + | 2087.64i | 0.304834 | + | 0.126266i | ||||
\(650\) | 31928.1i | 1.92665i | ||||||||
\(651\) | 4401.72 | − | 10626.7i | 0.265003 | − | 0.639774i | ||||
\(652\) | 25680.4 | − | 10637.2i | 1.54252 | − | 0.638933i | ||||
\(653\) | 900.910 | + | 2174.99i | 0.0539898 | + | 0.130343i | 0.948573 | − | 0.316559i | \(-0.102527\pi\) |
−0.894583 | + | 0.446902i | \(0.852527\pi\) | |||||||
\(654\) | 24161.1 | + | 24161.1i | 1.44461 | + | 1.44461i | ||||
\(655\) | −27985.7 | − | 27985.7i | −1.66945 | − | 1.66945i | ||||
\(656\) | 1205.95 | + | 2911.43i | 0.0717752 | + | 0.173281i | ||||
\(657\) | 455.801 | − | 188.799i | 0.0270662 | − | 0.0112112i | ||||
\(658\) | −12591.6 | + | 30398.8i | −0.746004 | + | 1.80101i | ||||
\(659\) | 21272.6i | 1.25745i | 0.777626 | + | 0.628727i | \(0.216424\pi\) | ||||
−0.777626 | + | 0.628727i | \(0.783576\pi\) | |||||||
\(660\) | −26459.7 | − | 10960.0i | −1.56052 | − | 0.646388i | ||||
\(661\) | 11753.0 | − | 11753.0i | 0.691587 | − | 0.691587i | −0.270994 | − | 0.962581i | \(-0.587352\pi\) |
0.962581 | + | 0.270994i | \(0.0873525\pi\) | |||||||
\(662\) | 18595.3 | 1.09173 | ||||||||
\(663\) | 2639.58 | + | 10285.0i | 0.154620 | + | 0.602470i | ||||
\(664\) | 22056.5 | 1.28910 | ||||||||
\(665\) | 8427.03 | − | 8427.03i | 0.491408 | − | 0.491408i | ||||
\(666\) | 816.238 | + | 338.097i | 0.0474903 | + | 0.0196711i | ||||
\(667\) | 5172.66i | 0.300279i | ||||||||
\(668\) | 18757.5 | − | 45284.5i | 1.08645 | − | 2.62292i | ||||
\(669\) | −12045.7 | + | 4989.49i | −0.696134 | + | 0.288348i | ||||
\(670\) | 12691.3 | + | 30639.4i | 0.731801 | + | 1.76672i | ||||
\(671\) | 8080.48 | + | 8080.48i | 0.464893 | + | 0.464893i | ||||
\(672\) | 1390.49 | + | 1390.49i | 0.0798206 | + | 0.0798206i | ||||
\(673\) | −87.5115 | − | 211.271i | −0.00501236 | − | 0.0121009i | 0.921354 | − | 0.388726i | \(-0.127085\pi\) |
−0.926366 | + | 0.376625i | \(0.877085\pi\) | |||||||
\(674\) | −10676.1 | + | 4422.17i | −0.610129 | + | 0.252724i | ||||
\(675\) | 12064.2 | − | 29125.7i | 0.687930 | − | 1.66081i | ||||
\(676\) | − | 20367.7i | − | 1.15883i | ||||||
\(677\) | 9216.32 | + | 3817.52i | 0.523208 | + | 0.216720i | 0.628625 | − | 0.777708i | \(-0.283618\pi\) |
−0.105417 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(678\) | −10676.7 | + | 10676.7i | −0.604773 | + | 0.604773i | ||||
\(679\) | 12404.1 | 0.701071 | ||||||||
\(680\) | 24592.3 | − | 41573.2i | 1.38687 | − | 2.34450i | ||||
\(681\) | 26364.4 | 1.48353 | ||||||||
\(682\) | −10844.7 | + | 10844.7i | −0.608890 | + | 0.608890i | ||||
\(683\) | −28742.6 | − | 11905.6i | −1.61026 | − | 0.666990i | −0.617437 | − | 0.786620i | \(-0.711829\pi\) |
−0.992819 | + | 0.119630i | \(0.961829\pi\) | |||||||
\(684\) | − | 959.583i | − | 0.0536412i | ||||||
\(685\) | −21934.6 | + | 52954.8i | −1.22347 | + | 2.95372i | ||||
\(686\) | −30821.5 | + | 12766.7i | −1.71541 | + | 0.710545i | ||||
\(687\) | 6200.73 | + | 14969.9i | 0.344356 | + | 0.831349i | ||||
\(688\) | −2042.36 | − | 2042.36i | −0.113175 | − | 0.113175i | ||||
\(689\) | −11207.2 | − | 11207.2i | −0.619679 | − | 0.619679i | ||||
\(690\) | 15627.3 | + | 37727.7i | 0.862205 | + | 2.08155i | ||||
\(691\) | −4720.02 | + | 1955.10i | −0.259852 | + | 0.107634i | −0.508807 | − | 0.860881i | \(-0.669913\pi\) |
0.248954 | + | 0.968515i | \(0.419913\pi\) | |||||||
\(692\) | −6996.72 | + | 16891.6i | −0.384358 | + | 0.927921i | ||||
\(693\) | − | 366.064i | − | 0.0200659i | ||||||
\(694\) | 53554.2 | + | 22182.9i | 2.92924 | + | 1.21333i | ||||
\(695\) | −6167.06 | + | 6167.06i | −0.336590 | + | 0.336590i | ||||
\(696\) | 10889.3 | 0.593043 | ||||||||
\(697\) | 3432.17 | + | 2030.27i | 0.186518 | + | 0.110333i | ||||
\(698\) | 35927.4 | 1.94824 | ||||||||
\(699\) | −3055.70 | + | 3055.70i | −0.165347 | + | 0.165347i | ||||
\(700\) | −44477.9 | − | 18423.3i | −2.40158 | − | 0.994767i | ||||
\(701\) | − | 11204.5i | − | 0.603691i | −0.953357 | − | 0.301846i | \(-0.902397\pi\) | ||
0.953357 | − | 0.301846i | \(-0.0976027\pi\) | |||||||
\(702\) | 7987.54 | − | 19283.6i | 0.429445 | − | 1.03677i | ||||
\(703\) | −5735.55 | + | 2375.74i | −0.307710 | + | 0.127458i | ||||
\(704\) | −4306.62 | − | 10397.1i | −0.230557 | − | 0.556613i | ||||
\(705\) | −32095.5 | − | 32095.5i | −1.71459 | − | 1.71459i | ||||
\(706\) | −10196.9 | − | 10196.9i | −0.543576 | − | 0.543576i | ||||
\(707\) | 9901.24 | + | 23903.7i | 0.526696 | + | 1.27156i | ||||
\(708\) | −20493.1 | + | 8488.52i | −1.08782 | + | 0.450590i | ||||
\(709\) | 12992.1 | − | 31365.7i | 0.688193 | − | 1.66144i | −0.0601983 | − | 0.998186i | \(-0.519173\pi\) |
0.748391 | − | 0.663258i | \(-0.230827\pi\) | |||||||
\(710\) | 5464.54i | 0.288846i | ||||||||
\(711\) | −269.603 | − | 111.673i | −0.0142207 | − | 0.00589041i | ||||
\(712\) | −23297.9 | + | 23297.9i | −1.22630 | + | 1.22630i | ||||
\(713\) | 14466.2 | 0.759838 | ||||||||
\(714\) | −23960.9 | − | 3412.73i | −1.25590 | − | 0.178877i | ||||
\(715\) | −10813.9 | −0.565619 | ||||||||
\(716\) | −17165.1 | + | 17165.1i | −0.895937 | + | 0.895937i | ||||
\(717\) | −8857.61 | − | 3668.94i | −0.461358 | − | 0.191101i | ||||
\(718\) | − | 31728.8i | − | 1.64918i | ||||||
\(719\) | 2384.53 | − | 5756.76i | 0.123683 | − | 0.298596i | −0.849895 | − | 0.526952i | \(-0.823335\pi\) |
0.973578 | + | 0.228355i | \(0.0733348\pi\) | |||||||
\(720\) | −1273.28 | + | 527.408i | −0.0659059 | + | 0.0272991i | ||||
\(721\) | −9781.88 | − | 23615.6i | −0.505265 | − | 1.21982i | ||||
\(722\) | −16371.9 | − | 16371.9i | −0.843906 | − | 0.843906i | ||||
\(723\) | −6624.39 | − | 6624.39i | −0.340752 | − | 0.340752i | ||||
\(724\) | 8950.89 | + | 21609.4i | 0.459471 | + | 1.10926i | ||||
\(725\) | 11748.5 | − | 4866.38i | 0.601831 | − | 0.249287i | ||||
\(726\) | −8967.87 | + | 21650.3i | −0.458442 | + | 1.10678i | ||||
\(727\) | − | 5206.88i | − | 0.265629i | −0.991141 | − | 0.132815i | \(-0.957598\pi\) | ||
0.991141 | − | 0.132815i | \(-0.0424015\pi\) | |||||||
\(728\) | −14381.0 | − | 5956.82i | −0.732139 | − | 0.303262i | ||||
\(729\) | −14538.6 | + | 14538.6i | −0.738637 | + | 0.738637i | ||||
\(730\) | 33219.4 | 1.68425 | ||||||||
\(731\) | −3618.42 | − | 515.369i | −0.183081 | − | 0.0260761i | ||||
\(732\) | −46465.3 | −2.34618 | ||||||||
\(733\) | 2699.43 | − | 2699.43i | 0.136024 | − | 0.136024i | −0.635816 | − | 0.771840i | \(-0.719336\pi\) |
0.771840 | + | 0.635816i | \(0.219336\pi\) | |||||||
\(734\) | −26484.7 | − | 10970.3i | −1.33184 | − | 0.551665i | ||||
\(735\) | − | 13767.5i | − | 0.690916i | ||||||
\(736\) | −946.446 | + | 2284.92i | −0.0474001 | + | 0.114434i | ||||
\(737\) | −6613.13 | + | 2739.25i | −0.330526 | + | 0.136908i | ||||
\(738\) | −141.868 | − | 342.500i | −0.00707620 | − | 0.0170835i | ||||
\(739\) | 6513.44 | + | 6513.44i | 0.324223 | + | 0.324223i | 0.850385 | − | 0.526162i | \(-0.176369\pi\) |
−0.526162 | + | 0.850385i | \(0.676369\pi\) | |||||||
\(740\) | 27827.1 | + | 27827.1i | 1.38236 | + | 1.38236i | ||||
\(741\) | 2654.46 | + | 6408.43i | 0.131598 | + | 0.317705i | ||||
\(742\) | 33375.9 | − | 13824.7i | 1.65130 | − | 0.683992i | ||||
\(743\) | 8854.88 | − | 21377.6i | 0.437219 | − | 1.05554i | −0.539686 | − | 0.841867i | \(-0.681457\pi\) |
0.976905 | − | 0.213674i | \(-0.0685431\pi\) | |||||||
\(744\) | − | 30453.8i | − | 1.50066i | ||||||
\(745\) | 37891.2 | + | 15695.0i | 1.86339 | + | 0.771841i | ||||
\(746\) | −31747.2 | + | 31747.2i | −1.55811 | + | 1.55811i | ||||
\(747\) | −796.360 | −0.0390057 | ||||||||
\(748\) | 18374.1 | + | 10869.1i | 0.898161 | + | 0.531300i | ||||
\(749\) | 26013.9 | 1.26906 | ||||||||
\(750\) | 30580.0 | − | 30580.0i | 1.48883 | − | 1.48883i | ||||
\(751\) | 28770.9 | + | 11917.3i | 1.39796 | + | 0.579053i | 0.949221 | − | 0.314612i | \(-0.101874\pi\) |
0.448736 | + | 0.893664i | \(0.351874\pi\) | |||||||
\(752\) | 26737.2i | 1.29655i | ||||||||
\(753\) | 1989.66 | − | 4803.47i | 0.0962912 | − | 0.232468i | ||||
\(754\) | 7778.48 | − | 3221.95i | 0.375697 | − | 0.155619i | ||||
\(755\) | 5344.73 | + | 12903.3i | 0.257635 | + | 0.621986i | ||||
\(756\) | 22254.3 | + | 22254.3i | 1.07061 | + | 1.07061i | ||||
\(757\) | 21914.1 | + | 21914.1i | 1.05216 | + | 1.05216i | 0.998563 | + | 0.0535946i | \(0.0170679\pi\) |
0.0535946 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(758\) | −2697.05 | − | 6511.26i | −0.129237 | − | 0.312005i | ||||
\(759\) | −8143.03 | + | 3372.96i | −0.389425 | + | 0.161305i | ||||
\(760\) | 12075.0 | − | 29151.6i | 0.576324 | − | 1.39137i | ||||
\(761\) | − | 14150.5i | − | 0.674053i | −0.941495 | − | 0.337026i | \(-0.890579\pi\) | ||
0.941495 | − | 0.337026i | \(-0.109421\pi\) | |||||||
\(762\) | −2541.15 | − | 1052.58i | −0.120809 | − | 0.0500406i | ||||
\(763\) | −13755.8 | + | 13755.8i | −0.652679 | + | 0.652679i | ||||
\(764\) | −47044.7 | −2.22777 | ||||||||
\(765\) | −887.915 | + | 1501.02i | −0.0419642 | + | 0.0709404i | ||||
\(766\) | −39666.7 | −1.87104 | ||||||||
\(767\) | −5922.30 | + | 5922.30i | −0.278803 | + | 0.278803i | ||||
\(768\) | 37235.9 | + | 15423.6i | 1.74953 | + | 0.724677i | ||||
\(769\) | 619.823i | 0.0290655i | 0.999894 | + | 0.0145328i | \(0.00462608\pi\) | ||||
−0.999894 | + | 0.0145328i | \(0.995374\pi\) | |||||||
\(770\) | 9432.55 | − | 22772.2i | 0.441462 | − | 1.06578i | ||||
\(771\) | −12242.0 | + | 5070.81i | −0.571836 | + | 0.236862i | ||||
\(772\) | 23297.3 | + | 56244.7i | 1.08613 | + | 2.62214i | ||||
\(773\) | −7209.95 | − | 7209.95i | −0.335477 | − | 0.335477i | 0.519185 | − | 0.854662i | \(-0.326236\pi\) |
−0.854662 | + | 0.519185i | \(0.826236\pi\) | |||||||
\(774\) | 240.263 | + | 240.263i | 0.0111577 | + | 0.0111577i | ||||
\(775\) | −13609.7 | − | 32856.6i | −0.630805 | − | 1.52290i | ||||
\(776\) | 30341.7 | − | 12568.0i | 1.40361 | − | 0.581396i | ||||
\(777\) | 3685.11 | − | 8896.65i | 0.170145 | − | 0.410767i | ||||
\(778\) | 7136.23i | 0.328851i | ||||||||
\(779\) | 2406.68 | + | 996.880i | 0.110691 | + | 0.0458497i | ||||
\(780\) | 31091.7 | − | 31091.7i | 1.42726 | − | 1.42726i | ||||
\(781\) | −1179.45 | −0.0540385 | ||||||||
\(782\) | −7566.83 | − | 29483.9i | −0.346022 | − | 1.34826i | ||||
\(783\) | −8313.17 | −0.379423 | ||||||||
\(784\) | −5734.55 | + | 5734.55i | −0.261231 | + | 0.261231i | ||||
\(785\) | 9939.36 | + | 4117.02i | 0.451912 | + | 0.187188i | ||||
\(786\) | 52505.5i | 2.38271i | ||||||||
\(787\) | 12707.6 | − | 30679.0i | 0.575577 | − | 1.38956i | −0.321171 | − | 0.947021i | \(-0.604076\pi\) |
0.896747 | − | 0.442543i | \(-0.145924\pi\) | |||||||
\(788\) | −13675.3 | + | 5664.48i | −0.618225 | + | 0.256077i | ||||
\(789\) | −9677.29 | − | 23363.0i | −0.436655 | − | 1.05418i | ||||
\(790\) | −13894.0 | − | 13894.0i | −0.625729 | − | 0.625729i | ||||
\(791\) | −6078.64 | − | 6078.64i | −0.273238 | − | 0.273238i | ||||
\(792\) | −370.899 | − | 895.429i | −0.0166406 | − | 0.0401738i | ||||
\(793\) | −16209.0 | + | 6714.00i | −0.725851 | + | 0.300657i | ||||
\(794\) | 11196.8 | − | 27031.4i | 0.500452 | − | 1.20820i | ||||
\(795\) | 49835.1i | 2.22323i | ||||||||
\(796\) | −25508.6 | − | 10566.0i | −1.13584 | − | 0.470480i | ||||
\(797\) | 3077.08 | − | 3077.08i | 0.136757 | − | 0.136757i | −0.635414 | − | 0.772172i | \(-0.719171\pi\) |
0.772172 | + | 0.635414i | \(0.219171\pi\) | |||||||
\(798\) | −15810.4 | −0.701356 | ||||||||
\(799\) | 20311.6 | + | 27058.4i | 0.899338 | + | 1.19807i | ||||
\(800\) | 6080.08 | 0.268704 | ||||||||
\(801\) | 841.181 | − | 841.181i | 0.0371057 | − | 0.0371057i | ||||
\(802\) | −26496.5 | − | 10975.2i | −1.16661 | − | 0.483226i | ||||
\(803\) | 7169.98i | 0.315097i | ||||||||
\(804\) | 11138.0 | − | 26889.6i | 0.488567 | − | 1.17950i | ||||
\(805\) | −21479.7 | + | 8897.20i | −0.940449 | + | 0.389547i | ||||
\(806\) | −9010.73 | − | 21753.8i | −0.393784 | − | 0.950678i | ||||
\(807\) | 12216.1 | + | 12216.1i | 0.532870 | + | 0.532870i | ||||
\(808\) | 48438.8 | + | 48438.8i | 2.10900 | + | 2.10900i | ||||
\(809\) | −5172.06 | − | 12486.4i | −0.224771 | − | 0.542645i | 0.770755 | − | 0.637132i | \(-0.219879\pi\) |
−0.995526 | + | 0.0944862i | \(0.969879\pi\) | |||||||
\(810\) | −57616.2 | + | 23865.4i | −2.49929 | + | 1.03524i | ||||
\(811\) | −2203.64 | + | 5320.06i | −0.0954135 | + | 0.230348i | −0.964379 | − | 0.264524i | \(-0.914785\pi\) |
0.868966 | + | 0.494872i | \(0.164785\pi\) | |||||||
\(812\) | 12695.1i | 0.548657i | ||||||||
\(813\) | 351.422 | + | 145.564i | 0.0151598 | + | 0.00627939i | ||||
\(814\) | −9079.13 | + | 9079.13i | −0.390938 | + | 0.390938i | ||||
\(815\) | −33000.8 | −1.41837 | ||||||||
\(816\) | −19049.7 | + | 4888.97i | −0.817246 | + | 0.209741i | ||||
\(817\) | −2387.59 | −0.102241 | ||||||||
\(818\) | 31837.0 | − | 31837.0i | 1.36082 | − | 1.36082i | ||||
\(819\) | 519.234 | + | 215.074i | 0.0221532 | + | 0.00917616i | ||||
\(820\) | − | 16513.0i | − | 0.703243i | ||||||
\(821\) | −10698.4 | + | 25828.3i | −0.454783 | + | 1.09794i | 0.515699 | + | 0.856770i | \(0.327532\pi\) |
−0.970482 | + | 0.241174i | \(0.922468\pi\) | |||||||
\(822\) | 70252.0 | − | 29099.3i | 2.98092 | − | 1.23474i | ||||
\(823\) | −14557.5 | − | 35144.9i | −0.616576 | − | 1.48855i | −0.855655 | − | 0.517547i | \(-0.826845\pi\) |
0.239078 | − | 0.971000i | \(-0.423155\pi\) | |||||||
\(824\) | −47854.9 | − | 47854.9i | −2.02318 | − | 2.02318i | ||||
\(825\) | 15321.8 | + | 15321.8i | 0.646588 | + | 0.646588i | ||||
\(826\) | −7305.52 | − | 17637.1i | −0.307738 | − | 0.742946i | ||||
\(827\) | 13366.2 | − | 5536.47i | 0.562018 | − | 0.232795i | −0.0835432 | − | 0.996504i | \(-0.526624\pi\) |
0.645561 | + | 0.763709i | \(0.276624\pi\) | |||||||
\(828\) | −716.385 | + | 1729.51i | −0.0300677 | + | 0.0725899i | ||||
\(829\) | − | 24519.4i | − | 1.02726i | −0.858013 | − | 0.513628i | \(-0.828301\pi\) | ||
0.858013 | − | 0.513628i | \(-0.171699\pi\) | |||||||
\(830\) | −49540.1 | − | 20520.2i | −2.07176 | − | 0.858151i | ||||
\(831\) | 12328.4 | − | 12328.4i | 0.514642 | − | 0.514642i | ||||
\(832\) | 17277.7 | 0.719949 | ||||||||
\(833\) | −1447.06 | + | 10159.8i | −0.0601892 | + | 0.422590i | ||||
\(834\) | 11570.4 | 0.480394 | ||||||||
\(835\) | −41148.8 | + | 41148.8i | −1.70540 | + | 1.70540i | ||||
\(836\) | 12884.2 | + | 5336.79i | 0.533024 | + | 0.220786i | ||||
\(837\) | 23249.2i | 0.960108i | ||||||||
\(838\) | −15884.9 | + | 38349.5i | −0.654814 | + | 1.58086i | ||||
\(839\) | 35168.5 | − | 14567.3i | 1.44714 | − | 0.599426i | 0.485625 | − | 0.874167i | \(-0.338592\pi\) |
0.961518 | + | 0.274741i | \(0.0885921\pi\) | |||||||
\(840\) | 18730.1 | + | 45218.4i | 0.769344 | + | 1.85736i | ||||
\(841\) | 14874.5 | + | 14874.5i | 0.609885 | + | 0.609885i | ||||
\(842\) | 5559.86 | + | 5559.86i | 0.227560 | + | 0.227560i | ||||
\(843\) | −3243.21 | − | 7829.80i | −0.132505 | − | 0.319896i | ||||
\(844\) | −5365.06 | + | 2222.28i | −0.218807 | + | 0.0906327i | ||||
\(845\) | −9253.77 | + | 22340.6i | −0.376733 | + | 0.909514i | ||||
\(846\) | − | 3145.36i | − | 0.127825i | ||||||
\(847\) | −12326.3 | − | 5105.73i | −0.500045 | − | 0.207125i | ||||
\(848\) | 20757.6 | − | 20757.6i | 0.840590 | − | 0.840590i | ||||
\(849\) | −34406.2 | −1.39083 | ||||||||
\(850\) | −59846.9 | + | 44924.4i | −2.41498 | + | 1.81282i | ||||
\(851\) | 12111.1 | 0.487853 | ||||||||
\(852\) | 3391.11 | − | 3391.11i | 0.136358 | − | 0.136358i | ||||
\(853\) | 34565.1 | + | 14317.3i | 1.38744 | + | 0.574696i | 0.946460 | − | 0.322821i | \(-0.104631\pi\) |
0.440979 | + | 0.897517i | \(0.354631\pi\) | |||||||
\(854\) | − | 39989.7i | − | 1.60237i | ||||||
\(855\) | −435.973 | + | 1052.53i | −0.0174386 | + | 0.0421004i | ||||
\(856\) | 63632.5 | − | 26357.4i | 2.54079 | − | 1.05243i | ||||
\(857\) | 11132.3 | + | 26875.7i | 0.443723 | + | 1.07124i | 0.974632 | + | 0.223814i | \(0.0718508\pi\) |
−0.530908 | + | 0.847429i | \(0.678149\pi\) | |||||||
\(858\) | 10144.3 | + | 10144.3i | 0.403637 | + | 0.403637i | ||||
\(859\) | −30775.9 | − | 30775.9i | −1.22242 | − | 1.22242i | −0.966769 | − | 0.255651i | \(-0.917710\pi\) |
−0.255651 | − | 0.966769i | \(-0.582290\pi\) | |||||||
\(860\) | 5791.91 | + | 13982.9i | 0.229654 | + | 0.554434i | ||||
\(861\) | −3733.11 | + | 1546.30i | −0.147763 | + | 0.0612054i | ||||
\(862\) | −4720.21 | + | 11395.6i | −0.186509 | + | 0.450274i | ||||
\(863\) | 15659.4i | 0.617672i | 0.951115 | + | 0.308836i | \(0.0999394\pi\) | ||||
−0.951115 | + | 0.308836i | \(0.900061\pi\) | |||||||
\(864\) | −3672.19 | − | 1521.07i | −0.144595 | − | 0.0598933i | ||||
\(865\) | 15348.9 | − | 15348.9i | 0.603328 | − | 0.603328i | ||||
\(866\) | 8913.05 | 0.349743 | ||||||||
\(867\) | −15564.5 | + | 19419.3i | −0.609688 | + | 0.760683i | ||||
\(868\) | 35503.9 | 1.38834 | ||||||||
\(869\) | 2998.84 | − | 2998.84i | 0.117064 | − | 0.117064i | ||||
\(870\) | −24457.9 | − | 10130.8i | −0.953104 | − | 0.394789i | ||||
\(871\) | − | 10989.6i | − | 0.427518i | ||||||
\(872\) | −19710.6 | + | 47585.5i | −0.765463 | + | 1.84799i | ||||
\(873\) | −1095.50 | + | 453.771i | −0.0424709 | + | 0.0175920i | ||||
\(874\) | −7609.48 | − | 18370.9i | −0.294502 | − | 0.710990i | ||||
\(875\) | 17410.3 | + | 17410.3i | 0.672659 | + | 0.672659i | ||||
\(876\) | −20614.8 | − | 20614.8i | −0.795103 | − | 0.795103i | ||||
\(877\) | 11056.4 | + | 26692.6i | 0.425712 | + | 1.02776i | 0.980633 | + | 0.195856i | \(0.0627485\pi\) |
−0.554921 | + | 0.831903i | \(0.687252\pi\) | |||||||
\(878\) | 46706.0 | − | 19346.3i | 1.79528 | − | 0.743627i | ||||
\(879\) | 12477.9 | − | 30124.4i | 0.478805 | − | 1.15594i | ||||
\(880\) | − | 20029.3i | − | 0.767258i | ||||||
\(881\) | 20413.0 | + | 8455.34i | 0.780625 | + | 0.323346i | 0.737168 | − | 0.675710i | \(-0.236163\pi\) |
0.0434576 | + | 0.999055i | \(0.486163\pi\) | |||||||
\(882\) | 674.612 | − | 674.612i | 0.0257544 | − | 0.0257544i | ||||
\(883\) | −40158.3 | −1.53050 | −0.765252 | − | 0.643731i | \(-0.777385\pi\) | ||||
−0.765252 | + | 0.643731i | \(0.777385\pi\) | |||||||
\(884\) | −26212.2 | + | 19676.3i | −0.997299 | + | 0.748628i | ||||
\(885\) | 26334.8 | 1.00026 | ||||||||
\(886\) | 13696.3 | − | 13696.3i | 0.519343 | − | 0.519343i | ||||
\(887\) | −25685.4 | − | 10639.3i | −0.972303 | − | 0.402741i | −0.160734 | − | 0.986998i | \(-0.551386\pi\) |
−0.811569 | + | 0.584257i | \(0.801386\pi\) | |||||||
\(888\) | − | 25495.9i | − | 0.963497i | ||||||
\(889\) | 599.272 | − | 1446.77i | 0.0226085 | − | 0.0545817i | ||||
\(890\) | 74003.4 | − | 30653.2i | 2.78719 | − | 1.15449i | ||||
\(891\) | −5151.04 | − | 12435.7i | −0.193677 | − | 0.467578i | ||||
\(892\) | −28457.4 | − | 28457.4i | −1.06819 | − | 1.06819i | ||||
\(893\) | 15628.4 | + | 15628.4i | 0.585648 | + | 0.585648i | ||||
\(894\) | −20821.7 | − | 50268.0i | −0.778950 | − | 1.88055i | ||||
\(895\) | 26626.6 | − | 11029.1i | 0.994444 | − | 0.411912i | ||||
\(896\) | −13882.2 | + | 33514.6i | −0.517603 | + | 1.24960i | ||||
\(897\) | − | 13532.0i | − | 0.503700i | ||||||
\(898\) | −59217.5 | − | 24528.7i | −2.20057 | − | 0.911507i | ||||
\(899\) | −6631.31 | + | 6631.31i | −0.246014 | + | 0.246014i | ||||
\(900\) | 4602.13 | 0.170449 | ||||||||
\(901\) | 5237.99 | − | 36776.0i | 0.193677 | − | 1.35981i | ||||
\(902\) | 5387.70 | 0.198881 | ||||||||
\(903\) | 2618.76 | − | 2618.76i | 0.0965083 | − | 0.0965083i | ||||
\(904\) | −21027.8 | − | 8710.02i | −0.773646 | − | 0.320455i | ||||
\(905\) | − | 27769.3i | − | 1.01998i | ||||||
\(906\) | 7090.54 | − | 17118.1i | 0.260008 | − | 0.627715i | ||||
\(907\) | −17011.7 | + | 7046.48i | −0.622783 | + | 0.257965i | −0.671683 | − | 0.740839i | \(-0.734428\pi\) |
0.0489002 | + | 0.998804i | \(0.484428\pi\) | |||||||
\(908\) | 31142.3 | + | 75184.2i | 1.13821 | + | 2.74788i | ||||
\(909\) | −1748.90 | − | 1748.90i | −0.0638145 | − | 0.0638145i | ||||
\(910\) | 26758.6 | + | 26758.6i | 0.974770 | + | 0.974770i | ||||
\(911\) | −12349.9 | − | 29815.2i | −0.449143 | − | 1.08433i | −0.972644 | − | 0.232302i | \(-0.925374\pi\) |
0.523501 | − | 0.852025i | \(-0.324626\pi\) | |||||||
\(912\) | −11869.6 | + | 4916.53i | −0.430965 | + | 0.178512i | ||||
\(913\) | 4429.01 | − | 10692.6i | 0.160547 | − | 0.387594i | ||||
\(914\) | 78962.7i | 2.85761i | ||||||||
\(915\) | 50966.1 | + | 21110.9i | 1.84141 | + | 0.762736i | ||||
\(916\) | −35365.7 | + | 35365.7i | −1.27567 | + | 1.27567i | ||||
\(917\) | −29893.3 | −1.07652 | ||||||||
\(918\) | 47384.6 | − | 12160.9i | 1.70362 | − | 0.437223i | ||||
\(919\) | 19185.3 | 0.688643 | 0.344322 | − | 0.938852i | \(-0.388109\pi\) | ||||
0.344322 | + | 0.938852i | \(0.388109\pi\) | |||||||
\(920\) | −43526.8 | + | 43526.8i | −1.55982 | + | 1.55982i | ||||
\(921\) | −24007.5 | − | 9944.24i | −0.858930 | − | 0.355781i | ||||
\(922\) | 53744.2i | 1.91971i | ||||||||
\(923\) | 692.961 | − | 1672.96i | 0.0247119 | − | 0.0596599i | ||||
\(924\) | −19985.2 | + | 8278.13i | −0.711541 | + | 0.294730i | ||||
\(925\) | −11394.0 | − | 27507.5i | −0.405008 | − | 0.977775i | ||||
\(926\) | 48766.6 | + | 48766.6i | 1.73064 | + | 1.73064i | ||||
\(927\) | 1727.82 | + | 1727.82i | 0.0612179 | + | 0.0612179i | ||||
\(928\) | −613.557 | − | 1481.26i | −0.0217037 | − | 0.0523973i | ||||
\(929\) | −19238.6 | + | 7968.89i | −0.679438 | + | 0.281433i | −0.695592 | − | 0.718437i | \(-0.744858\pi\) |
0.0161538 | + | 0.999870i | \(0.494858\pi\) | |||||||
\(930\) | −28332.5 | + | 68400.7i | −0.998988 | + | 2.41177i | ||||
\(931\) | 6703.89i | 0.235995i | ||||||||
\(932\) | −12323.5 | − | 5104.57i | −0.433123 | − | 0.179405i | ||||
\(933\) | 12259.6 | − | 12259.6i | 0.430183 | − | 0.430183i | ||||
\(934\) | 47106.5 | 1.65029 | ||||||||
\(935\) | −15215.7 | − | 20269.9i | −0.532200 | − | 0.708981i | ||||
\(936\) | 1488.01 | 0.0519627 | ||||||||
\(937\) | 14900.1 | − | 14900.1i | 0.519495 | − | 0.519495i | −0.397924 | − | 0.917418i | \(-0.630269\pi\) |
0.917418 | + | 0.397924i | \(0.130269\pi\) | |||||||
\(938\) | 23142.1 | + | 9585.78i | 0.805562 | + | 0.333675i | ||||
\(939\) | 21698.4i | 0.754100i | ||||||||
\(940\) | 53615.7 | − | 129440.i | 1.86037 | − | 4.49134i | ||||
\(941\) | −10307.2 | + | 4269.37i | −0.357071 | + | 0.147904i | −0.554006 | − | 0.832513i | \(-0.686901\pi\) |
0.196935 | + | 0.980417i | \(0.436901\pi\) | |||||||
\(942\) | −5461.81 | − | 13186.0i | −0.188912 | − | 0.456074i | ||||
\(943\) | −3593.46 | − | 3593.46i | −0.124092 | − | 0.124092i | ||||
\(944\) | −10969.1 | − | 10969.1i | −0.378194 | − | 0.378194i | ||||
\(945\) | −14299.0 | − | 34520.9i | −0.492219 | − | 1.18832i | ||||
\(946\) | −4562.20 | + | 1889.73i | −0.156797 | + | 0.0649475i | ||||
\(947\) | −1165.49 | + | 2813.74i | −0.0399929 | + | 0.0965514i | −0.942614 | − | 0.333885i | \(-0.891640\pi\) |
0.902621 | + | 0.430436i | \(0.141640\pi\) | |||||||
\(948\) | 17244.3i | 0.590789i | ||||||||
\(949\) | −10170.0 | − | 4212.57i | −0.347875 | − | 0.144095i | ||||
\(950\) | −34566.3 | + | 34566.3i | −1.18050 | + | 1.18050i | ||||
\(951\) | −1977.33 | −0.0674232 | ||||||||
\(952\) | −9069.20 | − | 35337.8i | −0.308755 | − | 1.20305i | ||||
\(953\) | 6037.53 | 0.205220 | 0.102610 | − | 0.994722i | \(-0.467281\pi\) | ||||
0.102610 | + | 0.994722i | \(0.467281\pi\) | |||||||
\(954\) | −2441.93 | + | 2441.93i | −0.0828724 | + | 0.0828724i | ||||
\(955\) | 51601.7 | + | 21374.1i | 1.74847 | + | 0.724241i | ||||
\(956\) | − | 29593.4i | − | 1.00117i | ||||||
\(957\) | 2186.60 | − | 5278.92i | 0.0738587 | − | 0.178311i | ||||
\(958\) | −59455.2 | + | 24627.2i | −2.00513 | + | 0.830551i | ||||
\(959\) | 16567.3 | + | 39997.0i | 0.557858 | + | 1.34679i | ||||
\(960\) | −38414.6 | − | 38414.6i | −1.29149 | − | 1.29149i | ||||
\(961\) | −2519.83 | − | 2519.83i | −0.0845836 | − | 0.0845836i | ||||
\(962\) | −7543.77 | − | 18212.3i | −0.252829 | − | 0.610382i | ||||
\(963\) | −2297.48 | + | 951.646i | −0.0768797 | + | 0.0318446i | ||||
\(964\) | 11066.1 | − | 26715.9i | 0.369725 | − | 0.892595i | ||||
\(965\) | − | 72277.6i | − | 2.41109i | ||||||
\(966\) | 28495.9 | + | 11803.4i | 0.949111 | + | 0.393135i | ||||
\(967\) | 7884.94 | − | 7884.94i | 0.262216 | − | 0.262216i | −0.563738 | − | 0.825954i | \(-0.690637\pi\) |
0.825954 | + | 0.563738i | \(0.190637\pi\) | |||||||
\(968\) | −35324.6 | −1.17291 | ||||||||
\(969\) | −8277.20 | + | 13992.6i | −0.274409 | + | 0.463887i | ||||
\(970\) | −79841.6 | −2.64284 | ||||||||
\(971\) | 20542.5 | − | 20542.5i | 0.678930 | − | 0.678930i | −0.280828 | − | 0.959758i | \(-0.590609\pi\) |
0.959758 | + | 0.280828i | \(0.0906091\pi\) | |||||||
\(972\) | −5427.65 | − | 2248.21i | −0.179107 | − | 0.0741885i | ||||
\(973\) | 6587.43i | 0.217043i | ||||||||
\(974\) | −35907.7 | + | 86688.9i | −1.18127 | + | 2.85184i | ||||
\(975\) | −30734.7 | + | 12730.7i | −1.00954 | + | 0.418164i | ||||
\(976\) | −12435.5 | − | 30022.0i | −0.407839 | − | 0.984612i | ||||
\(977\) | −1718.38 | − | 1718.38i | −0.0562700 | − | 0.0562700i | 0.678412 | − | 0.734682i | \(-0.262669\pi\) |
−0.734682 | + | 0.678412i | \(0.762669\pi\) | |||||||
\(978\) | 30957.3 | + | 30957.3i | 1.01217 | + | 1.01217i | ||||
\(979\) | 6616.10 | + | 15972.7i | 0.215987 | + | 0.521439i | ||||
\(980\) | 39261.4 | − | 16262.6i | 1.27975 | − | 0.530091i | ||||
\(981\) | 711.658 | − | 1718.09i | 0.0231616 | − | 0.0559170i | ||||
\(982\) | 351.356i | 0.0114177i | ||||||||
\(983\) | −2002.34 | − | 829.397i | −0.0649693 | − | 0.0269112i | 0.349962 | − | 0.936764i | \(-0.386194\pi\) |
−0.414931 | + | 0.909853i | \(0.636194\pi\) | |||||||
\(984\) | −7564.82 | + | 7564.82i | −0.245079 | + | 0.245079i | ||||
\(985\) | 17573.5 | 0.568465 | ||||||||
\(986\) | 16984.0 | + | 10046.8i | 0.548561 | + | 0.324497i | ||||
\(987\) | −34283.2 | −1.10562 | ||||||||
\(988\) | −15139.6 | + | 15139.6i | −0.487506 | + | 0.487506i | ||||
\(989\) | 4303.27 | + | 1782.47i | 0.138358 | + | 0.0573098i | ||||
\(990\) | 2356.24i | 0.0756427i | ||||||||
\(991\) | 7474.99 | − | 18046.2i | 0.239607 | − | 0.578463i | −0.757635 | − | 0.652679i | \(-0.773645\pi\) |
0.997242 | + | 0.0742153i | \(0.0236452\pi\) | |||||||
\(992\) | −4142.59 | + | 1715.92i | −0.132588 | + | 0.0549198i | ||||
\(993\) | 7414.54 | + | 17900.3i | 0.236952 | + | 0.572052i | ||||
\(994\) | 2918.51 | + | 2918.51i | 0.0931282 | + | 0.0931282i | ||||
\(995\) | 23178.9 | + | 23178.9i | 0.738514 | + | 0.738514i | ||||
\(996\) | 18008.8 | + | 43477.0i | 0.572921 | + | 1.38315i | ||||
\(997\) | −8215.19 | + | 3402.84i | −0.260961 | + | 0.108093i | −0.509328 | − | 0.860572i | \(-0.670106\pi\) |
0.248367 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(998\) | 27545.4 | − | 66500.5i | 0.873682 | − | 2.10925i | ||||
\(999\) | 19464.2i | 0.616437i |
(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 | 17.4.d.a.9.1 | yes | 12 | |
3.2 | odd | 2 | 153.4.l.a.145.3 | 12 | |||
17.2 | even | 8 | inner | 17.4.d.a.2.1 | ✓ | 12 | |
17.6 | odd | 16 | 289.4.a.g.1.1 | 12 | |||
17.7 | odd | 16 | 289.4.b.e.288.12 | 12 | |||
17.10 | odd | 16 | 289.4.b.e.288.11 | 12 | |||
17.11 | odd | 16 | 289.4.a.g.1.2 | 12 | |||
51.2 | odd | 8 | 153.4.l.a.19.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.1 | ✓ | 12 | 17.2 | even | 8 | inner | |
17.4.d.a.9.1 | yes | 12 | 1.1 | even | 1 | trivial | |
153.4.l.a.19.3 | 12 | 51.2 | odd | 8 | |||
153.4.l.a.145.3 | 12 | 3.2 | odd | 2 | |||
289.4.a.g.1.1 | 12 | 17.6 | odd | 16 | |||
289.4.a.g.1.2 | 12 | 17.11 | odd | 16 | |||
289.4.b.e.288.11 | 12 | 17.10 | odd | 16 | |||
289.4.b.e.288.12 | 12 | 17.7 | odd | 16 |