Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.84779568.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 13x^{4} - 4x^{3} + 152x^{2} - 96x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(1.83685 + 3.18152i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.v.271.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29244 | + | 2.23857i | −0.456946 | + | 0.791454i | −0.998798 | − | 0.0490204i | \(-0.984390\pi\) |
0.541852 | + | 0.840474i | \(0.317723\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.659207 | + | 1.14178i | 0.0824008 | + | 0.142722i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.4468 | − | 19.8264i | 0.618067 | − | 1.07052i | −0.371771 | − | 0.928324i | \(-0.621249\pi\) |
0.989838 | − | 0.142199i | \(-0.0454174\pi\) | |||||||
\(8\) | −24.0869 | −1.06450 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −12.9244 | −0.408705 | ||||||||
\(11\) | 5.54140 | − | 9.59799i | 0.151891 | − | 0.263082i | −0.780032 | − | 0.625740i | \(-0.784797\pi\) |
0.931922 | + | 0.362658i | \(0.118131\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.81841 | + | 10.0778i | 0.124134 | + | 0.215006i | 0.921394 | − | 0.388630i | \(-0.127052\pi\) |
−0.797260 | + | 0.603636i | \(0.793718\pi\) | |||||||
\(14\) | 29.5885 | + | 51.2487i | 0.564847 | + | 0.978343i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 25.8572 | − | 44.7861i | 0.404019 | − | 0.699782i | ||||
\(17\) | −10.0643 | −0.143585 | −0.0717926 | − | 0.997420i | \(-0.522872\pi\) | ||||
−0.0717926 | + | 0.997420i | \(0.522872\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 117.865 | 1.42316 | 0.711579 | − | 0.702606i | \(-0.247980\pi\) | ||||
0.711579 | + | 0.702606i | \(0.247980\pi\) | |||||||
\(20\) | −3.29603 | + | 5.70890i | −0.0368508 | + | 0.0638274i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.3238 | + | 24.8096i | 0.138812 | + | 0.240429i | ||||
\(23\) | 86.2204 | + | 149.338i | 0.781661 | + | 1.35388i | 0.930974 | + | 0.365086i | \(0.118961\pi\) |
−0.149313 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −30.0798 | −0.226889 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 30.1831 | 0.203717 | ||||||||
\(29\) | 89.1603 | − | 154.430i | 0.570919 | − | 0.988860i | −0.425553 | − | 0.904933i | \(-0.639920\pi\) |
0.996472 | − | 0.0839270i | \(-0.0267462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −70.2642 | − | 121.701i | −0.407091 | − | 0.705102i | 0.587471 | − | 0.809245i | \(-0.300123\pi\) |
−0.994562 | + | 0.104143i | \(0.966790\pi\) | |||||||
\(32\) | −29.5100 | − | 51.1128i | −0.163021 | − | 0.282361i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.0075 | − | 22.5296i | 0.0656107 | − | 0.113641i | ||||
\(35\) | 114.468 | 0.552816 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 250.074 | 1.11113 | 0.555566 | − | 0.831473i | \(-0.312502\pi\) | ||||
0.555566 | + | 0.831473i | \(0.312502\pi\) | |||||||
\(38\) | −152.333 | + | 263.848i | −0.650307 | + | 1.12636i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −60.2174 | − | 104.300i | −0.238030 | − | 0.412280i | ||||
\(41\) | 180.784 | + | 313.128i | 0.688629 | + | 1.19274i | 0.972281 | + | 0.233813i | \(0.0751205\pi\) |
−0.283652 | + | 0.958927i | \(0.591546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 180.354 | − | 312.382i | 0.639620 | − | 1.10786i | −0.345896 | − | 0.938273i | \(-0.612425\pi\) |
0.985516 | − | 0.169582i | \(-0.0542418\pi\) | |||||||
\(44\) | 14.6117 | 0.0500636 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −445.738 | −1.42871 | ||||||||
\(47\) | −300.060 | + | 519.720i | −0.931241 | + | 1.61296i | −0.150037 | + | 0.988680i | \(0.547939\pi\) |
−0.781204 | + | 0.624276i | \(0.785394\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −90.5568 | − | 156.849i | −0.264014 | − | 0.457286i | ||||
\(50\) | −32.3110 | − | 55.9642i | −0.0913892 | − | 0.158291i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.67107 | + | 13.2867i | −0.0204574 | + | 0.0354333i | ||||
\(53\) | −201.312 | −0.521742 | −0.260871 | − | 0.965374i | \(-0.584010\pi\) | ||||
−0.260871 | + | 0.965374i | \(0.584010\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 55.4140 | 0.135855 | ||||||||
\(56\) | −275.718 | + | 477.557i | −0.657934 | + | 1.13958i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 230.468 | + | 399.183i | 0.521758 | + | 0.903712i | ||||
\(59\) | 207.886 | + | 360.069i | 0.458719 | + | 0.794525i | 0.998894 | − | 0.0470283i | \(-0.0149751\pi\) |
−0.540174 | + | 0.841553i | \(0.681642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.3135 | − | 47.3083i | 0.0573301 | − | 0.0992986i | −0.835936 | − | 0.548827i | \(-0.815075\pi\) |
0.893266 | + | 0.449528i | \(0.148408\pi\) | |||||||
\(62\) | 363.248 | 0.744074 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 566.275 | 1.10601 | ||||||||
\(65\) | −29.0921 | + | 50.3889i | −0.0555143 | + | 0.0961535i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 265.539 | + | 459.928i | 0.484191 | + | 0.838643i | 0.999835 | − | 0.0181595i | \(-0.00578066\pi\) |
−0.515644 | + | 0.856803i | \(0.672447\pi\) | |||||||
\(68\) | −6.63444 | − | 11.4912i | −0.0118315 | − | 0.0204928i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −147.942 | + | 256.244i | −0.252607 | + | 0.437528i | ||||
\(71\) | 933.534 | 1.56042 | 0.780212 | − | 0.625515i | \(-0.215111\pi\) | ||||
0.780212 | + | 0.625515i | \(0.215111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −560.199 | −0.898169 | −0.449085 | − | 0.893489i | \(-0.648250\pi\) | ||||
−0.449085 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(74\) | −323.205 | + | 559.807i | −0.507727 | + | 0.879409i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 77.6972 | + | 134.575i | 0.117269 | + | 0.203117i | ||||
\(77\) | −126.862 | − | 219.732i | −0.187757 | − | 0.325205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −405.391 | + | 702.157i | −0.577342 | + | 0.999985i | 0.418441 | + | 0.908244i | \(0.362577\pi\) |
−0.995783 | + | 0.0917413i | \(0.970757\pi\) | |||||||
\(80\) | 258.572 | 0.361366 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −934.611 | −1.25867 | ||||||||
\(83\) | 269.105 | − | 466.104i | 0.355881 | − | 0.616404i | −0.631387 | − | 0.775468i | \(-0.717514\pi\) |
0.987268 | + | 0.159064i | \(0.0508475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.1607 | − | 43.5796i | −0.0321066 | − | 0.0556103i | ||||
\(86\) | 466.192 | + | 807.468i | 0.584544 | + | 1.01246i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −133.475 | + | 231.186i | −0.161688 | + | 0.280052i | ||||
\(89\) | −686.173 | −0.817238 | −0.408619 | − | 0.912705i | \(-0.633990\pi\) | ||||
−0.408619 | + | 0.912705i | \(0.633990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 266.408 | 0.306892 | ||||||||
\(92\) | −113.674 | + | 196.889i | −0.128819 | + | 0.223121i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −775.619 | − | 1343.41i | −0.851053 | − | 1.47407i | ||||
\(95\) | 294.662 | + | 510.369i | 0.318228 | + | 0.551187i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −357.327 | + | 618.909i | −0.374032 | + | 0.647842i | −0.990182 | − | 0.139787i | \(-0.955358\pi\) |
0.616150 | + | 0.787629i | \(0.288692\pi\) | |||||||
\(98\) | 468.156 | 0.482560 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −32.9603 | −0.0329603 | ||||||||
\(101\) | 486.953 | − | 843.428i | 0.479739 | − | 0.830933i | −0.519991 | − | 0.854172i | \(-0.674065\pi\) |
0.999730 | + | 0.0232390i | \(0.00739786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 379.614 | + | 657.511i | 0.363151 | + | 0.628995i | 0.988478 | − | 0.151368i | \(-0.0483677\pi\) |
−0.625327 | + | 0.780363i | \(0.715034\pi\) | |||||||
\(104\) | −140.148 | − | 242.743i | −0.132141 | − | 0.228874i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 260.183 | − | 450.650i | 0.238408 | − | 0.412934i | ||||
\(107\) | −1832.06 | −1.65525 | −0.827625 | − | 0.561282i | \(-0.810308\pi\) | ||||
−0.827625 | + | 0.561282i | \(0.810308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1370.91 | 1.20467 | 0.602335 | − | 0.798244i | \(-0.294237\pi\) | ||||
0.602335 | + | 0.798244i | \(0.294237\pi\) | |||||||
\(110\) | −71.6192 | + | 124.048i | −0.0620784 | + | 0.107523i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −591.963 | − | 1025.31i | −0.499422 | − | 0.865025i | ||||
\(113\) | 291.783 | + | 505.384i | 0.242909 | + | 0.420730i | 0.961542 | − | 0.274659i | \(-0.0885651\pi\) |
−0.718633 | + | 0.695390i | \(0.755232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −431.102 | + | 746.691i | −0.349569 | + | 0.605472i | ||||
\(116\) | 235.100 | 0.188177 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1074.72 | −0.838439 | ||||||||
\(119\) | −115.204 | + | 199.538i | −0.0887453 | + | 0.153711i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 604.086 | + | 1046.31i | 0.453859 | + | 0.786106i | ||||
\(122\) | 70.6020 | + | 122.286i | 0.0523935 | + | 0.0907482i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 92.6372 | − | 160.452i | 0.0670892 | − | 0.116202i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2432.76 | −1.69978 | −0.849891 | − | 0.526958i | \(-0.823333\pi\) | ||||
−0.849891 | + | 0.526958i | \(0.823333\pi\) | |||||||
\(128\) | −495.796 | + | 858.744i | −0.342364 | + | 0.592992i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −75.1994 | − | 130.249i | −0.0507340 | − | 0.0878739i | ||||
\(131\) | 250.537 | + | 433.942i | 0.167095 | + | 0.289418i | 0.937397 | − | 0.348262i | \(-0.113228\pi\) |
−0.770302 | + | 0.637679i | \(0.779895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1349.17 | − | 2336.83i | 0.879608 | − | 1.52353i | ||||
\(134\) | −1372.77 | −0.884996 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 242.418 | 0.152847 | ||||||||
\(137\) | 1261.53 | − | 2185.04i | 0.786716 | − | 1.36263i | −0.141253 | − | 0.989973i | \(-0.545113\pi\) |
0.927969 | − | 0.372658i | \(-0.121553\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 319.421 | + | 553.253i | 0.194913 | + | 0.337599i | 0.946872 | − | 0.321611i | \(-0.104224\pi\) |
−0.751959 | + | 0.659210i | \(0.770891\pi\) | |||||||
\(140\) | 75.4578 | + | 130.697i | 0.0455525 | + | 0.0788992i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1206.54 | + | 2089.78i | −0.713029 | + | 1.23500i | ||||
\(143\) | 128.969 | 0.0754189 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 891.603 | 0.510645 | ||||||||
\(146\) | 724.023 | − | 1254.04i | 0.410415 | − | 0.710859i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 164.850 | + | 285.529i | 0.0915581 | + | 0.158583i | ||||
\(149\) | −1337.07 | − | 2315.87i | −0.735146 | − | 1.27331i | −0.954659 | − | 0.297701i | \(-0.903780\pi\) |
0.219513 | − | 0.975610i | \(-0.429553\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 518.339 | − | 897.790i | 0.279350 | − | 0.483848i | −0.691873 | − | 0.722019i | \(-0.743214\pi\) |
0.971223 | + | 0.238171i | \(0.0765477\pi\) | |||||||
\(152\) | −2839.00 | −1.51496 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 655.847 | 0.343179 | ||||||||
\(155\) | 351.321 | − | 608.506i | 0.182057 | − | 0.315331i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 190.929 | + | 330.699i | 0.0970560 | + | 0.168106i | 0.910465 | − | 0.413586i | \(-0.135724\pi\) |
−0.813409 | + | 0.581692i | \(0.802391\pi\) | |||||||
\(158\) | −1047.88 | − | 1814.99i | −0.527628 | − | 0.913878i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 147.550 | − | 255.564i | 0.0729054 | − | 0.126276i | ||||
\(161\) | 3947.78 | 1.93248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2421.17 | 1.16344 | 0.581719 | − | 0.813390i | \(-0.302380\pi\) | ||||
0.581719 | + | 0.813390i | \(0.302380\pi\) | |||||||
\(164\) | −238.349 | + | 412.832i | −0.113487 | + | 0.196566i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 695.603 | + | 1204.82i | 0.325237 | + | 0.563326i | ||||
\(167\) | −1767.88 | − | 3062.06i | −0.819178 | − | 1.41886i | −0.906289 | − | 0.422659i | \(-0.861097\pi\) |
0.0871109 | − | 0.996199i | \(-0.472237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1030.79 | − | 1785.38i | 0.469182 | − | 0.812646i | ||||
\(170\) | 130.075 | 0.0586840 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 475.561 | 0.210821 | ||||||||
\(173\) | 1571.94 | − | 2722.68i | 0.690824 | − | 1.19654i | −0.280745 | − | 0.959783i | \(-0.590581\pi\) |
0.971568 | − | 0.236759i | \(-0.0760853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 286.169 | + | 495.659i | 0.123613 | + | 0.214105i | ||||
\(176\) | −286.571 | − | 496.355i | −0.122733 | − | 0.212581i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 886.836 | − | 1536.05i | 0.373434 | − | 0.646806i | ||||
\(179\) | 3299.06 | 1.37756 | 0.688780 | − | 0.724970i | \(-0.258147\pi\) | ||||
0.688780 | + | 0.724970i | \(0.258147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1875.10 | 0.770026 | 0.385013 | − | 0.922911i | \(-0.374197\pi\) | ||||
0.385013 | + | 0.922911i | \(0.374197\pi\) | |||||||
\(182\) | −344.316 | + | 596.373i | −0.140233 | + | 0.242891i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2076.79 | − | 3597.10i | −0.832080 | − | 1.44121i | ||||
\(185\) | 625.184 | + | 1082.85i | 0.248456 | + | 0.430339i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −55.7703 | + | 96.5969i | −0.0218092 | + | 0.0377747i | ||||
\(188\) | −791.207 | −0.306940 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1523.33 | −0.581652 | ||||||||
\(191\) | −680.810 | + | 1179.20i | −0.257915 | + | 0.446721i | −0.965683 | − | 0.259723i | \(-0.916369\pi\) |
0.707768 | + | 0.706445i | \(0.249702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1117.10 | − | 1934.88i | −0.416636 | − | 0.721634i | 0.578963 | − | 0.815354i | \(-0.303458\pi\) |
−0.995599 | + | 0.0937198i | \(0.970124\pi\) | |||||||
\(194\) | −923.647 | − | 1599.80i | −0.341825 | − | 0.592058i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 119.391 | − | 206.792i | 0.0435099 | − | 0.0753614i | ||||
\(197\) | 346.625 | 0.125360 | 0.0626801 | − | 0.998034i | \(-0.480035\pi\) | ||||
0.0626801 | + | 0.998034i | \(0.480035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4198.77 | 1.49569 | 0.747846 | − | 0.663872i | \(-0.231088\pi\) | ||||
0.747846 | + | 0.663872i | \(0.231088\pi\) | |||||||
\(200\) | 301.087 | − | 521.498i | 0.106450 | − | 0.184377i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1258.71 | + | 2180.16i | 0.438430 | + | 0.759383i | ||||
\(203\) | −2041.19 | − | 3535.45i | −0.705732 | − | 1.22236i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −903.922 | + | 1565.64i | −0.307964 | + | 0.533410i | ||||
\(206\) | −1962.51 | −0.663761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 601.792 | 0.200610 | ||||||||
\(209\) | 653.136 | − | 1131.26i | 0.216164 | − | 0.374408i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2364.23 | − | 4094.96i | −0.771375 | − | 1.33606i | −0.936809 | − | 0.349841i | \(-0.886236\pi\) |
0.165434 | − | 0.986221i | \(-0.447098\pi\) | |||||||
\(212\) | −132.706 | − | 229.854i | −0.0429919 | − | 0.0744642i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2367.82 | − | 4101.19i | 0.756360 | − | 1.31005i | ||||
\(215\) | 1803.54 | 0.572094 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3217.19 | −1.00644 | ||||||||
\(218\) | −1771.81 | + | 3068.87i | −0.550469 | + | 0.953440i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 36.5293 | + | 63.2706i | 0.0111946 | + | 0.0193896i | ||||
\(221\) | −58.5582 | − | 101.426i | −0.0178238 | − | 0.0308716i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1215.08 | + | 2104.58i | −0.364878 | + | 0.631987i | −0.988757 | − | 0.149534i | \(-0.952223\pi\) |
0.623879 | + | 0.781521i | \(0.285556\pi\) | |||||||
\(224\) | −1351.18 | −0.403032 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1508.45 | −0.443985 | ||||||||
\(227\) | −292.343 | + | 506.354i | −0.0854780 | + | 0.148052i | −0.905595 | − | 0.424144i | \(-0.860575\pi\) |
0.820117 | + | 0.572196i | \(0.193908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2365.89 | + | 4097.84i | 0.682717 | + | 1.18250i | 0.974148 | + | 0.225909i | \(0.0725351\pi\) |
−0.291431 | + | 0.956592i | \(0.594132\pi\) | |||||||
\(230\) | −1114.35 | − | 1930.10i | −0.319469 | − | 0.553336i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2147.60 | + | 3719.75i | −0.607745 | + | 1.05264i | ||||
\(233\) | −1228.45 | −0.345401 | −0.172701 | − | 0.984974i | \(-0.555249\pi\) | ||||
−0.172701 | + | 0.984974i | \(0.555249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3000.60 | −0.832927 | ||||||||
\(236\) | −274.079 | + | 474.719i | −0.0755977 | + | 0.130939i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −297.787 | − | 515.782i | −0.0811036 | − | 0.140476i | ||||
\(239\) | −60.2727 | − | 104.395i | −0.0163126 | − | 0.0282543i | 0.857754 | − | 0.514061i | \(-0.171859\pi\) |
−0.874066 | + | 0.485806i | \(0.838526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −866.278 | + | 1500.44i | −0.231543 | + | 0.401044i | −0.958262 | − | 0.285890i | \(-0.907711\pi\) |
0.726719 | + | 0.686935i | \(0.241044\pi\) | |||||||
\(242\) | −3122.97 | −0.829555 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 72.0209 | 0.0188962 | ||||||||
\(245\) | 452.784 | − | 784.245i | 0.118071 | − | 0.204504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 685.786 | + | 1187.82i | 0.176662 | + | 0.305987i | ||||
\(248\) | 1692.45 | + | 2931.41i | 0.433349 | + | 0.750583i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 161.555 | − | 279.821i | 0.0408705 | − | 0.0707898i | ||||
\(251\) | 3287.82 | 0.826793 | 0.413397 | − | 0.910551i | \(-0.364342\pi\) | ||||
0.413397 | + | 0.910551i | \(0.364342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1911.13 | 0.474908 | ||||||||
\(254\) | 3144.19 | − | 5445.90i | 0.776709 | − | 1.34530i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 983.530 | + | 1703.52i | 0.240120 | + | 0.415900i | ||||
\(257\) | −744.912 | − | 1290.22i | −0.180803 | − | 0.313160i | 0.761351 | − | 0.648339i | \(-0.224536\pi\) |
−0.942154 | + | 0.335180i | \(0.891203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2862.53 | − | 4958.05i | 0.686754 | − | 1.18949i | ||||
\(260\) | −76.7107 | −0.0182977 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1295.21 | −0.305414 | ||||||||
\(263\) | 355.072 | − | 615.003i | 0.0832497 | − | 0.144193i | −0.821394 | − | 0.570361i | \(-0.806803\pi\) |
0.904644 | + | 0.426168i | \(0.140137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −503.280 | − | 871.706i | −0.116665 | − | 0.202070i | ||||
\(266\) | 3487.44 | + | 6040.42i | 0.803866 | + | 1.39234i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −350.091 | + | 606.375i | −0.0797955 | + | 0.138210i | ||||
\(269\) | −3667.61 | −0.831294 | −0.415647 | − | 0.909526i | \(-0.636445\pi\) | ||||
−0.415647 | + | 0.909526i | \(0.636445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1990.45 | −0.446166 | −0.223083 | − | 0.974799i | \(-0.571612\pi\) | ||||
−0.223083 | + | 0.974799i | \(0.571612\pi\) | |||||||
\(272\) | −260.235 | + | 450.740i | −0.0580112 | + | 0.100478i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3260.91 | + | 5648.06i | 0.718973 | + | 1.24530i | ||||
\(275\) | 138.535 | + | 239.950i | 0.0303781 | + | 0.0526164i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4157.34 | + | 7200.73i | −0.901770 | + | 1.56191i | −0.0765757 | + | 0.997064i | \(0.524399\pi\) |
−0.825195 | + | 0.564848i | \(0.808935\pi\) | |||||||
\(278\) | −1651.33 | −0.356259 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2757.18 | −0.588474 | ||||||||
\(281\) | 2882.56 | − | 4992.75i | 0.611955 | − | 1.05994i | −0.378955 | − | 0.925415i | \(-0.623717\pi\) |
0.990911 | − | 0.134522i | \(-0.0429500\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −228.780 | − | 396.259i | −0.0480551 | − | 0.0832338i | 0.840997 | − | 0.541039i | \(-0.181969\pi\) |
−0.889052 | + | 0.457805i | \(0.848636\pi\) | |||||||
\(284\) | 615.392 | + | 1065.89i | 0.128580 | + | 0.222707i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −166.684 | + | 288.705i | −0.0344624 | + | 0.0596906i | ||||
\(287\) | 8277.59 | 1.70248 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4811.71 | −0.979383 | ||||||||
\(290\) | −1152.34 | + | 1995.91i | −0.233337 | + | 0.404152i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −369.287 | − | 639.624i | −0.0740099 | − | 0.128189i | ||||
\(293\) | 2651.41 | + | 4592.38i | 0.528659 | + | 0.915664i | 0.999442 | + | 0.0334147i | \(0.0106382\pi\) |
−0.470783 | + | 0.882249i | \(0.656028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1039.43 | + | 1800.34i | −0.205145 | + | 0.355322i | ||||
\(296\) | −6023.51 | −1.18280 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6912.30 | 1.34369 | ||||||||
\(299\) | −1003.33 | + | 1737.82i | −0.194061 | + | 0.336123i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4128.93 | − | 7151.52i | −0.790657 | − | 1.36946i | ||||
\(302\) | 1339.84 | + | 2320.68i | 0.255296 | + | 0.442185i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3047.66 | − | 5278.70i | 0.574984 | − | 0.995901i | ||||
\(305\) | 273.135 | 0.0512776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6583.54 | −1.22392 | −0.611959 | − | 0.790890i | \(-0.709618\pi\) | ||||
−0.611959 | + | 0.790890i | \(0.709618\pi\) | |||||||
\(308\) | 167.257 | − | 289.697i | 0.0309427 | − | 0.0535943i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 908.121 | + | 1572.91i | 0.166380 | + | 0.288179i | ||||
\(311\) | −4064.02 | − | 7039.10i | −0.740996 | − | 1.28344i | −0.952042 | − | 0.305966i | \(-0.901021\pi\) |
0.211047 | − | 0.977476i | \(-0.432313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2603.82 | − | 4509.94i | 0.470212 | − | 0.814431i | −0.529208 | − | 0.848492i | \(-0.677511\pi\) |
0.999420 | + | 0.0340613i | \(0.0108441\pi\) | |||||||
\(314\) | −987.056 | −0.177397 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1068.94 | −0.190294 | ||||||||
\(317\) | −1631.17 | + | 2825.27i | −0.289008 | + | 0.500577i | −0.973573 | − | 0.228375i | \(-0.926659\pi\) |
0.684565 | + | 0.728952i | \(0.259992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −988.146 | − | 1711.52i | −0.173434 | − | 0.300397i | ||||
\(320\) | 1415.69 | + | 2452.04i | 0.247311 | + | 0.428354i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5102.26 | + | 8837.37i | −0.883037 | + | 1.52946i | ||||
\(323\) | −1186.22 | −0.204345 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −290.921 | −0.0496535 | ||||||||
\(326\) | −3129.21 | + | 5419.95i | −0.531628 | + | 0.920807i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4354.55 | − | 7542.30i | −0.733048 | − | 1.26968i | ||||
\(329\) | 6869.44 | + | 11898.2i | 1.15114 | + | 1.99383i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5180.23 | + | 8972.43i | −0.860216 | + | 1.48994i | 0.0115047 | + | 0.999934i | \(0.496338\pi\) |
−0.871720 | + | 0.490004i | \(0.836995\pi\) | |||||||
\(332\) | 709.583 | 0.117299 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9139.51 | 1.49728 | ||||||||
\(335\) | −1327.70 | + | 2299.64i | −0.216537 | + | 0.375053i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1867.63 | + | 3234.83i | 0.301888 | + | 0.522886i | 0.976564 | − | 0.215229i | \(-0.0690497\pi\) |
−0.674675 | + | 0.738115i | \(0.735716\pi\) | |||||||
\(338\) | 2664.47 | + | 4615.00i | 0.428781 | + | 0.742671i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 33.1722 | − | 57.4560i | 0.00529122 | − | 0.00916467i | ||||
\(341\) | −1557.45 | −0.247333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3706.15 | 0.583421 | ||||||||
\(344\) | −4344.17 | + | 7524.32i | −0.680878 | + | 1.17931i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4063.28 | + | 7037.80i | 0.631338 | + | 1.09351i | ||||
\(347\) | 98.5050 | + | 170.616i | 0.0152393 | + | 0.0263952i | 0.873544 | − | 0.486744i | \(-0.161816\pi\) |
−0.858305 | + | 0.513140i | \(0.828482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3667.10 | − | 6351.60i | 0.562451 | − | 0.974193i | −0.434831 | − | 0.900512i | \(-0.643192\pi\) |
0.997282 | − | 0.0736811i | \(-0.0234747\pi\) | |||||||
\(350\) | −1479.42 | −0.225939 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −654.107 | −0.0990456 | ||||||||
\(353\) | 2308.14 | − | 3997.82i | 0.348017 | − | 0.602783i | −0.637880 | − | 0.770136i | \(-0.720188\pi\) |
0.985897 | + | 0.167352i | \(0.0535218\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2333.84 | + | 4042.32i | 0.348921 | + | 0.604350i | ||||
\(356\) | −452.330 | − | 783.458i | −0.0673411 | − | 0.116638i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4263.83 | + | 7385.17i | −0.629470 | + | 1.09027i | ||||
\(359\) | 1153.79 | 0.169623 | 0.0848115 | − | 0.996397i | \(-0.472971\pi\) | ||||
0.0848115 | + | 0.996397i | \(0.472971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7033.09 | 1.02538 | ||||||||
\(362\) | −2423.44 | + | 4197.53i | −0.351860 | + | 0.609440i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 175.618 | + | 304.179i | 0.0252881 | + | 0.0438003i | ||||
\(365\) | −1400.50 | − | 2425.73i | −0.200837 | − | 0.347859i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1724.52 | − | 2986.96i | 0.245285 | − | 0.424845i | −0.716927 | − | 0.697148i | \(-0.754452\pi\) |
0.962212 | + | 0.272303i | \(0.0877853\pi\) | |||||||
\(368\) | 8917.69 | 1.26322 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3232.05 | −0.454125 | ||||||||
\(371\) | −2304.37 | + | 3991.28i | −0.322471 | + | 0.558537i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −181.440 | − | 314.263i | −0.0251866 | − | 0.0436245i | 0.853157 | − | 0.521654i | \(-0.174685\pi\) |
−0.878344 | + | 0.478029i | \(0.841351\pi\) | |||||||
\(374\) | −144.159 | − | 249.691i | −0.0199313 | − | 0.0345220i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7227.54 | − | 12518.5i | 0.991308 | − | 1.71700i | ||||
\(377\) | 2075.09 | 0.283481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7719.79 | −1.04628 | −0.523139 | − | 0.852248i | \(-0.675239\pi\) | ||||
−0.523139 | + | 0.852248i | \(0.675239\pi\) | |||||||
\(380\) | −388.486 | + | 672.877i | −0.0524445 | + | 0.0908365i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1759.81 | − | 3048.08i | −0.235706 | − | 0.408255i | ||||
\(383\) | −2836.83 | − | 4913.53i | −0.378473 | − | 0.655534i | 0.612367 | − | 0.790573i | \(-0.290217\pi\) |
−0.990840 | + | 0.135039i | \(0.956884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 634.311 | − | 1098.66i | 0.0839675 | − | 0.145436i | ||||
\(386\) | 5775.13 | 0.761520 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −942.210 | −0.123282 | ||||||||
\(389\) | −4090.23 | + | 7084.48i | −0.533117 | + | 0.923386i | 0.466135 | + | 0.884714i | \(0.345646\pi\) |
−0.999252 | + | 0.0386726i | \(0.987687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −867.747 | − | 1502.98i | −0.112235 | − | 0.194397i | ||||
\(392\) | 2181.24 | + | 3778.01i | 0.281044 | + | 0.486782i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −447.991 | + | 775.943i | −0.0572829 | + | 0.0992169i | ||||
\(395\) | −4053.91 | −0.516390 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12940.5 | −1.63594 | −0.817968 | − | 0.575263i | \(-0.804900\pi\) | ||||
−0.817968 | + | 0.575263i | \(0.804900\pi\) | |||||||
\(398\) | −5426.65 | + | 9399.23i | −0.683450 | + | 1.18377i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 646.431 | + | 1119.65i | 0.0808039 | + | 0.139956i | ||||
\(401\) | 3290.65 | + | 5699.56i | 0.409793 | + | 0.709782i | 0.994866 | − | 0.101198i | \(-0.0322676\pi\) |
−0.585073 | + | 0.810980i | \(0.698934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 817.652 | − | 1416.21i | 0.101067 | − | 0.175054i | ||||
\(404\) | 1284.01 | 0.158124 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10552.5 | 1.28993 | ||||||||
\(407\) | 1385.76 | − | 2400.20i | 0.168770 | − | 0.292319i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2460.92 | − | 4262.44i | −0.297518 | − | 0.515316i | 0.678050 | − | 0.735016i | \(-0.262825\pi\) |
−0.975567 | + | 0.219700i | \(0.929492\pi\) | |||||||
\(410\) | −2336.53 | − | 4046.98i | −0.281446 | − | 0.487479i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −500.488 | + | 866.871i | −0.0598478 | + | 0.103659i | ||||
\(413\) | 9518.48 | 1.13408 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2691.05 | 0.318310 | ||||||||
\(416\) | 343.403 | − | 594.791i | 0.0404729 | − | 0.0701011i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1688.28 | + | 2924.18i | 0.197551 | + | 0.342168i | ||||
\(419\) | −1957.14 | − | 3389.87i | −0.228193 | − | 0.395241i | 0.729080 | − | 0.684429i | \(-0.239948\pi\) |
−0.957273 | + | 0.289187i | \(0.906615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2629.38 | − | 4554.22i | 0.304390 | − | 0.527219i | −0.672735 | − | 0.739883i | \(-0.734881\pi\) |
0.977125 | + | 0.212664i | \(0.0682140\pi\) | |||||||
\(422\) | 12222.5 | 1.40991 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4848.99 | 0.555395 | ||||||||
\(425\) | 125.804 | − | 217.898i | 0.0143585 | − | 0.0248697i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −625.302 | − | 1083.05i | −0.0708677 | − | 0.122746i | ||||
\(428\) | −1207.70 | − | 2091.81i | −0.136394 | − | 0.236241i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2330.96 | + | 4037.34i | −0.261416 | + | 0.452786i | ||||
\(431\) | −14350.1 | −1.60376 | −0.801881 | − | 0.597484i | \(-0.796167\pi\) | ||||
−0.801881 | + | 0.597484i | \(0.796167\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 863.149 | 0.0957974 | 0.0478987 | − | 0.998852i | \(-0.484748\pi\) | ||||
0.0478987 | + | 0.998852i | \(0.484748\pi\) | |||||||
\(434\) | 4158.02 | − | 7201.90i | 0.459888 | − | 0.796549i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 903.710 | + | 1565.27i | 0.0992658 | + | 0.171933i | ||||
\(437\) | 10162.3 | + | 17601.7i | 1.11243 | + | 1.92678i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8071.03 | − | 13979.4i | 0.877470 | − | 1.51982i | 0.0233618 | − | 0.999727i | \(-0.492563\pi\) |
0.854108 | − | 0.520095i | \(-0.174104\pi\) | |||||||
\(440\) | −1334.75 | −0.144618 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 302.731 | 0.0325780 | ||||||||
\(443\) | 2942.05 | − | 5095.77i | 0.315532 | − | 0.546518i | −0.664018 | − | 0.747716i | \(-0.731150\pi\) |
0.979551 | + | 0.201198i | \(0.0644836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1715.43 | − | 2971.22i | −0.182740 | − | 0.316515i | ||||
\(446\) | −3140.83 | − | 5440.08i | −0.333459 | − | 0.577568i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6482.02 | − | 11227.2i | 0.683586 | − | 1.18401i | ||||
\(449\) | 16858.4 | 1.77193 | 0.885965 | − | 0.463753i | \(-0.153497\pi\) | ||||
0.885965 | + | 0.463753i | \(0.153497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4007.20 | 0.418385 | ||||||||
\(452\) | −384.691 | + | 666.305i | −0.0400317 | + | 0.0693370i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −755.672 | − | 1308.86i | −0.0781177 | − | 0.135304i | ||||
\(455\) | 666.020 | + | 1153.58i | 0.0686231 | + | 0.118859i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3811.52 | + | 6601.74i | −0.390143 | + | 0.675747i | −0.992468 | − | 0.122504i | \(-0.960908\pi\) |
0.602325 | + | 0.798251i | \(0.294241\pi\) | |||||||
\(458\) | −12231.1 | −1.24786 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1136.74 | −0.115219 | ||||||||
\(461\) | −2039.70 | + | 3532.86i | −0.206070 | + | 0.356923i | −0.950473 | − | 0.310807i | \(-0.899401\pi\) |
0.744403 | + | 0.667730i | \(0.232734\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2749.61 | + | 4762.46i | 0.275994 | + | 0.478035i | 0.970385 | − | 0.241562i | \(-0.0776597\pi\) |
−0.694392 | + | 0.719597i | \(0.744326\pi\) | |||||||
\(464\) | −4610.88 | − | 7986.27i | −0.461325 | − | 0.799038i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1587.70 | − | 2749.97i | 0.157830 | − | 0.273369i | ||||
\(467\) | −6422.51 | −0.636399 | −0.318199 | − | 0.948024i | \(-0.603078\pi\) | ||||
−0.318199 | + | 0.948024i | \(0.603078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12158.3 | 1.19705 | ||||||||
\(470\) | 3878.10 | − | 6717.06i | 0.380603 | − | 0.659223i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5007.33 | − | 8672.96i | −0.488308 | − | 0.845774i | ||||
\(473\) | −1998.82 | − | 3462.07i | −0.194305 | − | 0.336545i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1473.31 | + | 2551.85i | −0.142316 | + | 0.246498i | ||||
\(476\) | −303.772 | −0.0292507 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 311.595 | 0.0298160 | ||||||||
\(479\) | 99.3800 | − | 172.131i | 0.00947973 | − | 0.0164194i | −0.861247 | − | 0.508187i | \(-0.830316\pi\) |
0.870726 | + | 0.491768i | \(0.163649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1455.03 | + | 2520.19i | 0.137929 | + | 0.238900i | ||||
\(482\) | −2239.22 | − | 3878.45i | −0.211605 | − | 0.366511i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −796.434 | + | 1379.46i | −0.0747966 | + | 0.129552i | ||||
\(485\) | −3573.27 | −0.334544 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1308.73 | −0.121774 | −0.0608871 | − | 0.998145i | \(-0.519393\pi\) | ||||
−0.0608871 | + | 0.998145i | \(0.519393\pi\) | |||||||
\(488\) | −657.899 | + | 1139.51i | −0.0610280 | + | 0.105704i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1170.39 | + | 2027.18i | 0.107904 | + | 0.186895i | ||||
\(491\) | −6237.41 | − | 10803.5i | −0.573300 | − | 0.992984i | −0.996224 | − | 0.0868193i | \(-0.972330\pi\) |
0.422924 | − | 0.906165i | \(-0.361004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −897.335 | + | 1554.23i | −0.0819755 | + | 0.141986i | ||||
\(494\) | −3545.34 | −0.322900 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7267.35 | −0.657890 | ||||||||
\(497\) | 10685.9 | − | 18508.6i | 0.964447 | − | 1.67047i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1573.41 | − | 2725.23i | −0.141153 | − | 0.244485i | 0.786778 | − | 0.617236i | \(-0.211748\pi\) |
−0.927931 | + | 0.372751i | \(0.878414\pi\) | |||||||
\(500\) | −82.4008 | − | 142.722i | −0.00737015 | − | 0.0127655i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4249.30 | + | 7360.00i | −0.377800 | + | 0.654369i | ||||
\(503\) | −5419.35 | −0.480391 | −0.240196 | − | 0.970725i | \(-0.577212\pi\) | ||||
−0.240196 | + | 0.970725i | \(0.577212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4869.53 | 0.429092 | ||||||||
\(506\) | −2470.02 | + | 4278.19i | −0.217007 | + | 0.375867i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1603.69 | − | 2777.67i | −0.140063 | − | 0.242597i | ||||
\(509\) | 8597.28 | + | 14890.9i | 0.748660 | + | 1.29672i | 0.948465 | + | 0.316881i | \(0.102636\pi\) |
−0.199805 | + | 0.979836i | \(0.564031\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6412.47 | + | 11106.7i | −0.555129 | + | 0.961511i | ||||
\(512\) | −13017.3 | −1.12361 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3851.01 | 0.330468 | ||||||||
\(515\) | −1898.07 | + | 3287.56i | −0.162406 | + | 0.281295i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3325.51 | + | 5759.96i | 0.282893 | + | 0.489986i | ||||
\(518\) | 7399.30 | + | 12816.0i | 0.627619 | + | 1.08707i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 700.739 | − | 1213.72i | 0.0590951 | − | 0.102356i | ||||
\(521\) | −19829.5 | −1.66746 | −0.833730 | − | 0.552172i | \(-0.813799\pi\) | ||||
−0.833730 | + | 0.552172i | \(0.813799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5392.82 | 0.450882 | 0.225441 | − | 0.974257i | \(-0.427618\pi\) | ||||
0.225441 | + | 0.974257i | \(0.427618\pi\) | |||||||
\(524\) | −330.311 | + | 572.115i | −0.0275376 | + | 0.0476965i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 917.817 | + | 1589.71i | 0.0760812 | + | 0.131777i | ||||
\(527\) | 707.159 | + | 1224.83i | 0.0584522 | + | 0.101242i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8784.42 | + | 15215.1i | −0.721987 | + | 1.25052i | ||||
\(530\) | 2601.83 | 0.213238 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3557.53 | 0.289922 | ||||||||
\(533\) | −2103.76 | + | 3643.81i | −0.170964 | + | 0.296118i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4580.14 | − | 7933.04i | −0.370125 | − | 0.641075i | ||||
\(536\) | −6396.03 | − | 11078.3i | −0.515423 | − | 0.892738i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4740.16 | − | 8210.20i | 0.379856 | − | 0.657931i | ||||
\(539\) | −2007.25 | −0.160405 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11475.8 | −0.911984 | −0.455992 | − | 0.889984i | \(-0.650715\pi\) | ||||
−0.455992 | + | 0.889984i | \(0.650715\pi\) | |||||||
\(542\) | 2572.53 | − | 4455.75i | 0.203874 | − | 0.353120i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 296.997 | + | 514.414i | 0.0234074 | + | 0.0405429i | ||||
\(545\) | 3427.27 | + | 5936.20i | 0.269372 | + | 0.466567i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3964.55 | − | 6866.79i | 0.309893 | − | 0.536751i | −0.668445 | − | 0.743761i | \(-0.733040\pi\) |
0.978339 | + | 0.207010i | \(0.0663733\pi\) | |||||||
\(548\) | 3326.44 | 0.259304 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −716.192 | −0.0555246 | ||||||||
\(551\) | 10508.8 | − | 18201.9i | 0.812508 | − | 1.40731i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9280.82 | + | 16074.8i | 0.713672 | + | 1.23612i | ||||
\(554\) | −10746.2 | − | 18613.0i | −0.824121 | − | 1.42742i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −421.128 | + | 729.416i | −0.0321220 | + | 0.0556369i | ||||
\(557\) | 9519.36 | 0.724144 | 0.362072 | − | 0.932150i | \(-0.382069\pi\) | ||||
0.362072 | + | 0.932150i | \(0.382069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4197.49 | 0.317594 | ||||||||
\(560\) | 2959.82 | − | 5126.55i | 0.223348 | − | 0.386851i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7451.07 | + | 12905.6i | 0.559261 | + | 0.968668i | ||||
\(563\) | −5961.14 | − | 10325.0i | −0.446238 | − | 0.772907i | 0.551899 | − | 0.833911i | \(-0.313903\pi\) |
−0.998138 | + | 0.0610035i | \(0.980570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1458.92 | + | 2526.92i | −0.108632 | + | 0.188156i | ||||
\(566\) | 1182.74 | 0.0878343 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22486.0 | −1.66108 | ||||||||
\(569\) | 8795.72 | − | 15234.6i | 0.648042 | − | 1.12244i | −0.335548 | − | 0.942023i | \(-0.608922\pi\) |
0.983590 | − | 0.180418i | \(-0.0577452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4125.37 | − | 7145.34i | −0.302349 | − | 0.523684i | 0.674319 | − | 0.738440i | \(-0.264437\pi\) |
−0.976668 | + | 0.214757i | \(0.931104\pi\) | |||||||
\(572\) | 85.0170 | + | 147.254i | 0.00621458 | + | 0.0107640i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10698.3 | + | 18530.0i | −0.777939 | + | 1.34743i | ||||
\(575\) | −4311.02 | −0.312664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15922.4 | −1.14880 | −0.574401 | − | 0.818574i | \(-0.694765\pi\) | ||||
−0.574401 | + | 0.818574i | \(0.694765\pi\) | |||||||
\(578\) | 6218.84 | − | 10771.3i | 0.447525 | − | 0.775136i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 587.750 | + | 1018.01i | 0.0420776 | + | 0.0728805i | ||||
\(581\) | −6160.76 | − | 10670.8i | −0.439917 | − | 0.761958i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1115.55 | + | 1932.19i | −0.0792476 | + | 0.137261i | ||||
\(584\) | 13493.5 | 0.956103 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13707.1 | −0.966274 | ||||||||
\(587\) | −4794.83 | + | 8304.88i | −0.337144 | + | 0.583951i | −0.983894 | − | 0.178751i | \(-0.942794\pi\) |
0.646750 | + | 0.762702i | \(0.276128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8281.67 | − | 14344.3i | −0.579355 | − | 1.00347i | ||||
\(590\) | −2686.80 | − | 4653.67i | −0.187481 | − | 0.324726i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6466.21 | − | 11199.8i | 0.448919 | − | 0.777550i | ||||
\(593\) | −5311.77 | −0.367838 | −0.183919 | − | 0.982941i | \(-0.558878\pi\) | ||||
−0.183919 | + | 0.982941i | \(0.558878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1152.04 | −0.0793762 | ||||||||
\(596\) | 1762.81 | − | 3053.27i | 0.121153 | − | 0.209844i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2593.49 | − | 4492.06i | −0.177351 | − | 0.307180i | ||||
\(599\) | −3173.02 | − | 5495.83i | −0.216437 | − | 0.374881i | 0.737279 | − | 0.675589i | \(-0.236110\pi\) |
−0.953716 | + | 0.300708i | \(0.902777\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4906.67 | − | 8498.60i | 0.333023 | − | 0.576814i | −0.650080 | − | 0.759866i | \(-0.725265\pi\) |
0.983103 | + | 0.183053i | \(0.0585978\pi\) | |||||||
\(602\) | 21345.6 | 1.44515 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1366.77 | 0.0920746 | ||||||||
\(605\) | −3020.43 | + | 5231.54i | −0.202972 | + | 0.351557i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2085.48 | + | 3612.15i | 0.139451 | + | 0.241537i | 0.927289 | − | 0.374346i | \(-0.122133\pi\) |
−0.787838 | + | 0.615883i | \(0.788800\pi\) | |||||||
\(608\) | −3478.19 | − | 6024.40i | −0.232005 | − | 0.401845i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −353.010 | + | 611.431i | −0.0234311 | + | 0.0405838i | ||||
\(611\) | −6983.50 | −0.462393 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3157.32 | −0.208031 | −0.104016 | − | 0.994576i | \(-0.533169\pi\) | ||||
−0.104016 | + | 0.994576i | \(0.533169\pi\) | |||||||
\(614\) | 8508.82 | − | 14737.7i | 0.559264 | − | 0.968674i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3055.72 | + | 5292.67i | 0.199868 | + | 0.346181i | ||||
\(617\) | −1481.47 | − | 2565.99i | −0.0966643 | − | 0.167428i | 0.813638 | − | 0.581372i | \(-0.197484\pi\) |
−0.910302 | + | 0.413945i | \(0.864151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2347.86 | + | 4066.62i | −0.152453 | + | 0.264057i | −0.932129 | − | 0.362127i | \(-0.882051\pi\) |
0.779676 | + | 0.626184i | \(0.215384\pi\) | |||||||
\(620\) | 926.372 | 0.0600064 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21010.0 | 1.35438 | ||||||||
\(623\) | −7854.46 | + | 13604.3i | −0.505108 | + | 0.874873i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 6730.54 | + | 11657.6i | 0.429723 | + | 0.744302i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −251.723 | + | 435.998i | −0.0159950 | + | 0.0277041i | ||||
\(629\) | −2516.81 | −0.159542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17397.6 | −1.09760 | −0.548800 | − | 0.835954i | \(-0.684915\pi\) | ||||
−0.548800 | + | 0.835954i | \(0.684915\pi\) | |||||||
\(632\) | 9764.62 | − | 16912.8i | 0.614582 | − | 1.06449i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4216.37 | − | 7302.97i | −0.264122 | − | 0.457473i | ||||
\(635\) | −6081.90 | − | 10534.2i | −0.380083 | − | 0.658323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1053.79 | − | 1825.22i | 0.0655460 | − | 0.113529i | ||||
\(638\) | 5108.47 | 0.317000 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4957.96 | −0.306220 | ||||||||
\(641\) | −3451.73 | + | 5978.57i | −0.212691 | + | 0.368392i | −0.952556 | − | 0.304364i | \(-0.901556\pi\) |
0.739865 | + | 0.672756i | \(0.234890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6066.04 | + | 10506.7i | 0.372039 | + | 0.644391i | 0.989879 | − | 0.141913i | \(-0.0453253\pi\) |
−0.617840 | + | 0.786304i | \(0.711992\pi\) | |||||||
\(644\) | 2602.40 | + | 4507.49i | 0.159238 | + | 0.275808i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1533.12 | − | 2655.44i | 0.0933744 | − | 0.161729i | ||||
\(647\) | −16784.3 | −1.01988 | −0.509939 | − | 0.860211i | \(-0.670332\pi\) | ||||
−0.509939 | + | 0.860211i | \(0.670332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4607.92 | 0.278700 | ||||||||
\(650\) | 375.997 | − | 651.246i | 0.0226889 | − | 0.0392984i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1596.05 | + | 2764.44i | 0.0958682 | + | 0.166049i | ||||
\(653\) | −7855.76 | − | 13606.6i | −0.470781 | − | 0.815416i | 0.528661 | − | 0.848833i | \(-0.322694\pi\) |
−0.999441 | + | 0.0334172i | \(0.989361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1252.68 | + | 2169.71i | −0.0747273 | + | 0.129431i | ||||
\(656\) | 18698.4 | 1.11288 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −35513.3 | −2.10403 | ||||||||
\(659\) | −10113.5 | + | 17517.1i | −0.597825 | + | 1.03546i | 0.395316 | + | 0.918545i | \(0.370635\pi\) |
−0.993141 | + | 0.116919i | \(0.962698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7493.41 | − | 12979.0i | −0.440938 | − | 0.763727i | 0.556822 | − | 0.830632i | \(-0.312021\pi\) |
−0.997759 | + | 0.0669056i | \(0.978687\pi\) | |||||||
\(662\) | −13390.3 | − | 23192.6i | −0.786144 | − | 1.36164i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6481.92 | + | 11227.0i | −0.378836 | + | 0.656164i | ||||
\(665\) | 13491.7 | 0.786745 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30749.7 | 1.78506 | ||||||||
\(668\) | 2330.80 | − | 4037.06i | 0.135002 | − | 0.233830i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3431.93 | − | 5944.28i | −0.197891 | − | 0.342758i | ||||
\(671\) | −302.710 | − | 524.309i | −0.0174158 | − | 0.0301650i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3416.87 | + | 5918.20i | −0.195707 | + | 0.338974i | −0.947132 | − | 0.320844i | \(-0.896033\pi\) |
0.751425 | + | 0.659818i | \(0.229367\pi\) | |||||||
\(674\) | −9655.19 | −0.551787 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2718.02 | 0.154644 | ||||||||
\(677\) | −15219.6 | + | 26361.2i | −0.864015 | + | 1.49652i | 0.00400745 | + | 0.999992i | \(0.498724\pi\) |
−0.868022 | + | 0.496525i | \(0.834609\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8180.48 | + | 14169.0i | 0.462354 | + | 0.800820i | ||||
\(680\) | 606.045 | + | 1049.70i | 0.0341776 | + | 0.0591973i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2012.91 | − | 3486.46i | 0.113018 | − | 0.195753i | ||||
\(683\) | 9675.88 | 0.542075 | 0.271038 | − | 0.962569i | \(-0.412633\pi\) | ||||
0.271038 | + | 0.962569i | \(0.412633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12615.3 | 0.703660 | ||||||||
\(686\) | −4789.97 | + | 8296.47i | −0.266592 | + | 0.461751i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9326.90 | − | 16154.7i | −0.516838 | − | 0.895190i | ||||
\(689\) | −1171.32 | − | 2028.78i | −0.0647657 | − | 0.112177i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6705.28 | + | 11613.9i | −0.369147 | + | 0.639382i | −0.989432 | − | 0.144994i | \(-0.953684\pi\) |
0.620285 | + | 0.784376i | \(0.287017\pi\) | |||||||
\(692\) | 4144.94 | 0.227698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −509.247 | −0.0278541 | ||||||||
\(695\) | −1597.10 | + | 2766.26i | −0.0871678 | + | 0.150979i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1819.47 | − | 3151.41i | −0.0988769 | − | 0.171260i | ||||
\(698\) | 9479.00 | + | 16418.1i | 0.514019 | + | 0.890307i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −377.289 | + | 653.484i | −0.0203717 | + | 0.0352848i | ||||
\(701\) | 12796.5 | 0.689466 | 0.344733 | − | 0.938701i | \(-0.387969\pi\) | ||||
0.344733 | + | 0.938701i | \(0.387969\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29474.9 | 1.58132 | ||||||||
\(704\) | 3137.96 | − | 5435.11i | 0.167992 | − | 0.290971i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5966.26 | + | 10333.9i | 0.318050 | + | 0.550879i | ||||
\(707\) | −11148.1 | − | 19309.0i | −0.593022 | − | 1.02714i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2424.66 | + | 4199.64i | −0.128435 | + | 0.222455i | −0.923070 | − | 0.384631i | \(-0.874329\pi\) |
0.794636 | + | 0.607087i | \(0.207662\pi\) | |||||||
\(710\) | −12065.4 | −0.637753 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16527.8 | 0.869952 | ||||||||
\(713\) | 12116.4 | − | 20986.2i | 0.636414 | − | 1.10230i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 322.422 | + | 558.451i | 0.0168642 | + | 0.0292096i | ||||
\(716\) | 2174.76 | + | 3766.80i | 0.113512 | + | 0.196609i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1491.20 | + | 2582.83i | −0.0775085 | + | 0.134249i | ||||
\(719\) | −33988.7 | −1.76296 | −0.881479 | − | 0.472224i | \(-0.843451\pi\) | ||||
−0.881479 | + | 0.472224i | \(0.843451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17381.4 | 0.897806 | ||||||||
\(722\) | −9089.83 | + | 15744.1i | −0.468544 | + | 0.811542i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1236.07 | + | 2140.94i | 0.0634508 | + | 0.109900i | ||||
\(725\) | 2229.01 | + | 3860.75i | 0.114184 | + | 0.197772i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8156.13 | − | 14126.8i | 0.416085 | − | 0.720681i | −0.579456 | − | 0.815003i | \(-0.696735\pi\) |
0.995542 | + | 0.0943224i | \(0.0300685\pi\) | |||||||
\(728\) | −6416.96 | −0.326687 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7240.23 | 0.367086 | ||||||||
\(731\) | −1815.13 | + | 3143.90i | −0.0918400 | + | 0.159072i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18915.9 | + | 32763.3i | 0.953172 | + | 1.65094i | 0.738498 | + | 0.674256i | \(0.235535\pi\) |
0.214673 | + | 0.976686i | \(0.431131\pi\) | |||||||
\(734\) | 4457.68 | + | 7720.93i | 0.224164 | + | 0.388263i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5088.73 | − | 8813.94i | 0.254855 | − | 0.441421i | ||||
\(737\) | 5885.84 | 0.294176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16860.9 | −0.839295 | −0.419647 | − | 0.907687i | \(-0.637846\pi\) | ||||
−0.419647 | + | 0.907687i | \(0.637846\pi\) | |||||||
\(740\) | −824.251 | + | 1427.64i | −0.0409460 | + | 0.0709206i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5956.51 | − | 10317.0i | −0.294704 | − | 0.510442i | ||||
\(743\) | 203.039 | + | 351.673i | 0.0100253 | + | 0.0173643i | 0.870995 | − | 0.491293i | \(-0.163475\pi\) |
−0.860969 | + | 0.508657i | \(0.830142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6685.33 | − | 11579.3i | 0.328767 | − | 0.569442i | ||||
\(746\) | 937.999 | 0.0460357 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −147.056 | −0.00718839 | ||||||||
\(749\) | −20971.1 | + | 36323.1i | −1.02306 | + | 1.77198i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7553.15 | + | 13082.4i | 0.367002 | + | 0.635666i | 0.989095 | − | 0.147277i | \(-0.0470509\pi\) |
−0.622093 | + | 0.782943i | \(0.713718\pi\) | |||||||
\(752\) | 15517.5 | + | 26877.0i | 0.752479 | + | 1.30333i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2681.92 | + | 4645.22i | −0.129535 | + | 0.224362i | ||||
\(755\) | 5183.39 | 0.249858 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14265.4 | −0.684919 | −0.342460 | − | 0.939533i | \(-0.611260\pi\) | ||||
−0.342460 | + | 0.939533i | \(0.611260\pi\) | |||||||
\(758\) | 9977.36 | − | 17281.3i | 0.478092 | − | 0.828080i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7097.50 | − | 12293.2i | −0.338755 | − | 0.586740i | ||||
\(761\) | 11500.6 | + | 19919.7i | 0.547828 | + | 0.948867i | 0.998423 | + | 0.0561380i | \(0.0178787\pi\) |
−0.450595 | + | 0.892729i | \(0.648788\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15692.4 | − | 27180.1i | 0.744567 | − | 1.28963i | ||||
\(764\) | −1795.18 | −0.0850095 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14665.7 | 0.691767 | ||||||||
\(767\) | −2419.13 | + | 4190.06i | −0.113885 | + | 0.197255i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6147.31 | − | 10647.5i | −0.288267 | − | 0.499294i | 0.685129 | − | 0.728422i | \(-0.259746\pi\) |
−0.973396 | + | 0.229128i | \(0.926413\pi\) | |||||||
\(770\) | 1639.62 | + | 2839.90i | 0.0767372 | + | 0.132913i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1472.80 | − | 2550.96i | 0.0686622 | − | 0.118926i | ||||
\(773\) | −5938.46 | −0.276315 | −0.138158 | − | 0.990410i | \(-0.544118\pi\) | ||||
−0.138158 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3513.21 | 0.162836 | ||||||||
\(776\) | 8606.93 | − | 14907.6i | 0.398158 | − | 0.689630i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10572.7 | − | 18312.5i | −0.487212 | − | 0.843875i | ||||
\(779\) | 21308.1 | + | 36906.7i | 0.980029 | + | 1.69746i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5173.09 | − | 8960.05i | 0.237014 | − | 0.410520i | ||||
\(782\) | 4486.04 | 0.205141 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9366.19 | −0.426667 | ||||||||
\(785\) | −954.645 | + | 1653.49i | −0.0434048 | + | 0.0751793i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16212.5 | − | 28080.9i | −0.734325 | − | 1.27189i | −0.955019 | − | 0.296545i | \(-0.904166\pi\) |
0.220694 | − | 0.975343i | \(-0.429168\pi\) | |||||||
\(788\) | 228.497 | + | 395.769i | 0.0103298 | + | 0.0178917i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5239.42 | − | 9074.95i | 0.235962 | − | 0.408699i | ||||
\(791\) | 13359.9 | 0.600535 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 635.685 | 0.0284664 | ||||||||
\(794\) | 16724.8 | − | 28968.3i | 0.747535 | − | 1.29477i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2767.85 | + | 4794.06i | 0.123246 | + | 0.213469i | ||||
\(797\) | −10495.2 | − | 18178.2i | −0.466449 | − | 0.807913i | 0.532817 | − | 0.846231i | \(-0.321133\pi\) |
−0.999266 | + | 0.0383177i | \(0.987800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3019.89 | − | 5230.61i | 0.133712 | − | 0.231597i | ||||
\(800\) | 1475.50 | 0.0652085 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17011.8 | −0.749013 | ||||||||
\(803\) | −3104.29 | + | 5376.79i | −0.136423 | + | 0.236292i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9869.45 | + | 17094.4i | 0.432115 | + | 0.748445i | ||||
\(806\) | 2113.53 | + | 3660.74i | 0.0923646 | + | 0.159980i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11729.2 | + | 20315.6i | −0.510684 | + | 0.884531i | ||||
\(809\) | 4943.95 | 0.214858 | 0.107429 | − | 0.994213i | \(-0.465738\pi\) | ||||
0.107429 | + | 0.994213i | \(0.465738\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19844.5 | −0.859230 | −0.429615 | − | 0.903012i | \(-0.641351\pi\) | ||||
−0.429615 | + | 0.903012i | \(0.641351\pi\) | |||||||
\(812\) | 2691.14 | − | 4661.18i | 0.116306 | − | 0.201448i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3582.02 | + | 6204.23i | 0.154238 | + | 0.267148i | ||||
\(815\) | 6052.91 | + | 10484.0i | 0.260153 | + | 0.450597i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21257.3 | − | 36818.8i | 0.910282 | − | 1.57665i | ||||
\(818\) | 12722.4 | 0.543798 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2383.49 | −0.101506 | ||||||||
\(821\) | 6304.12 | − | 10919.1i | 0.267985 | − | 0.464163i | −0.700357 | − | 0.713793i | \(-0.746976\pi\) |
0.968341 | + | 0.249630i | \(0.0803090\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12421.7 | − | 21515.0i | −0.526116 | − | 0.911260i | −0.999537 | − | 0.0304237i | \(-0.990314\pi\) |
0.473421 | − | 0.880836i | \(-0.343019\pi\) | |||||||
\(824\) | −9143.75 | − | 15837.4i | −0.386575 | − | 0.669567i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12302.0 | + | 21307.8i | −0.518212 | + | 0.897569i | ||||
\(827\) | −33361.1 | −1.40276 | −0.701379 | − | 0.712789i | \(-0.747432\pi\) | ||||
−0.701379 | + | 0.712789i | \(0.747432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5049.62 | −0.211557 | −0.105778 | − | 0.994390i | \(-0.533733\pi\) | ||||
−0.105778 | + | 0.994390i | \(0.533733\pi\) | |||||||
\(830\) | −3478.02 | + | 6024.10i | −0.145450 | + | 0.251927i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3294.82 | + | 5706.80i | 0.137293 | + | 0.237798i | ||||
\(833\) | 911.389 | + | 1578.57i | 0.0379085 | + | 0.0656594i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8839.40 | − | 15310.3i | 0.366347 | − | 0.634532i | ||||
\(836\) | 1722.21 | 0.0712485 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10117.9 | 0.417087 | ||||||||
\(839\) | −8732.33 | + | 15124.8i | −0.359325 | + | 0.622369i | −0.987848 | − | 0.155422i | \(-0.950326\pi\) |
0.628523 | + | 0.777791i | \(0.283660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3704.61 | − | 6416.57i | −0.151897 | − | 0.263093i | ||||
\(842\) | 6796.63 | + | 11772.1i | 0.278180 | + | 0.481821i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3117.03 | − | 5398.85i | 0.127124 | − | 0.220185i | ||||
\(845\) | 10307.9 | 0.419649 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27659.3 | 1.12206 | ||||||||
\(848\) | −5205.37 | + | 9015.96i | −0.210794 | + | 0.365105i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 325.187 | + | 563.240i | 0.0131221 | + | 0.0227282i | ||||
\(851\) | 21561.5 | + | 37345.5i | 0.868528 | + | 1.50433i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1373.24 | + | 2378.51i | −0.0551216 | + | 0.0954734i | −0.892270 | − | 0.451503i | \(-0.850888\pi\) |
0.837148 | + | 0.546977i | \(0.184221\pi\) | |||||||
\(854\) | 3232.66 | 0.129531 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44128.7 | 1.76202 | ||||||||
\(857\) | 7828.41 | − | 13559.2i | 0.312034 | − | 0.540459i | −0.666768 | − | 0.745265i | \(-0.732323\pi\) |
0.978803 | + | 0.204806i | \(0.0656562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17253.7 | + | 29884.2i | 0.685317 | + | 1.18700i | 0.973337 | + | 0.229379i | \(0.0736695\pi\) |
−0.288021 | + | 0.957624i | \(0.592997\pi\) | |||||||
\(860\) | 1188.90 | + | 2059.24i | 0.0471410 | + | 0.0816506i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18546.7 | − | 32123.8i | 0.732833 | − | 1.26930i | ||||
\(863\) | −26576.7 | −1.04830 | −0.524150 | − | 0.851626i | \(-0.675617\pi\) | ||||
−0.524150 | + | 0.851626i | \(0.675617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15719.4 | 0.617892 | ||||||||
\(866\) | −1115.57 | + | 1932.22i | −0.0437742 | + | 0.0758192i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2120.79 | − | 3673.32i | −0.0829313 | − | 0.143641i | ||||
\(869\) | 4492.86 | + | 7781.87i | 0.175385 | + | 0.303777i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3090.04 | + | 5352.10i | −0.120209 | + | 0.208208i | ||||
\(872\) | −33020.9 | −1.28237 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −52536.8 | −2.03328 | ||||||||
\(875\) | −1430.85 | + | 2478.30i | −0.0552816 | + | 0.0957505i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6699.73 | + | 11604.3i | 0.257963 | + | 0.446806i | 0.965696 | − | 0.259674i | \(-0.0836153\pi\) |
−0.707733 | + | 0.706480i | \(0.750282\pi\) | |||||||
\(878\) | 20862.6 | + | 36135.1i | 0.801913 | + | 1.38895i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1432.85 | − | 2481.78i | 0.0548881 | − | 0.0950689i | ||||
\(881\) | 44435.4 | 1.69928 | 0.849641 | − | 0.527362i | \(-0.176819\pi\) | ||||
0.849641 | + | 0.527362i | \(0.176819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11162.1 | −0.425408 | −0.212704 | − | 0.977117i | \(-0.568227\pi\) | ||||
−0.212704 | + | 0.977117i | \(0.568227\pi\) | |||||||
\(884\) | 77.2039 | − | 133.721i | 0.00293738 | − | 0.00508770i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7604.83 | + | 13171.9i | 0.288362 | + | 0.499458i | ||||
\(887\) | 5795.60 | + | 10038.3i | 0.219388 | + | 0.379991i | 0.954621 | − | 0.297823i | \(-0.0962606\pi\) |
−0.735233 | + | 0.677814i | \(0.762927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27847.2 | + | 48232.8i | −1.05058 | + | 1.81966i | ||||
\(890\) | 8868.36 | 0.334009 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3203.96 | −0.120265 | ||||||||
\(893\) | −35366.5 | + | 61256.6i | −1.32530 | + | 2.29549i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8247.65 | + | 14285.3i | 0.308032 | + | 0.533527i | ||||
\(896\) | 11350.5 | + | 19659.7i | 0.423208 | + | 0.733017i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21788.4 | + | 37738.7i | −0.809676 | + | 1.40240i | ||||
\(899\) | −25059.1 | −0.929663 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2026.06 | 0.0749144 | ||||||||
\(902\) | −5179.06 | + | 8970.39i | −0.191179 | + | 0.331132i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7028.17 | − | 12173.2i | −0.258577 | − | 0.447868i | ||||
\(905\) | 4687.74 | + | 8119.40i | 0.172183 | + | 0.298230i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4326.19 | + | 7493.19i | −0.158378 | + | 0.274319i | −0.934284 | − | 0.356530i | \(-0.883960\pi\) |
0.775906 | + | 0.630849i | \(0.217293\pi\) | |||||||
\(908\) | −770.859 | −0.0281738 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3443.16 | −0.125428 | ||||||||
\(911\) | −18356.2 | + | 31793.9i | −0.667583 | + | 1.15629i | 0.310995 | + | 0.950411i | \(0.399338\pi\) |
−0.978578 | + | 0.205876i | \(0.933996\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2982.44 | − | 5165.74i | −0.108110 | − | 0.187252i | ||||
\(914\) | −9852.30 | − | 17064.7i | −0.356548 | − | 0.617560i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3119.22 | + | 5402.64i | −0.112513 | + | 0.194878i | ||||
\(917\) | 11471.3 | 0.413104 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42003.3 | −1.50768 | −0.753841 | − | 0.657057i | \(-0.771801\pi\) | ||||
−0.753841 | + | 0.657057i | \(0.771801\pi\) | |||||||
\(920\) | 10383.9 | − | 17985.5i | 0.372118 | − | 0.644526i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5272.36 | − | 9132.00i | −0.188325 | − | 0.326189i | ||||
\(923\) | 5431.69 | + | 9407.96i | 0.193701 | + | 0.335500i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3125.92 | + | 5414.25i | −0.111113 | + | 0.192454i | ||||
\(926\) | −14214.8 | −0.504457 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10524.5 | −0.372288 | ||||||||
\(929\) | −6556.30 | + | 11355.8i | −0.231545 | + | 0.401048i | −0.958263 | − | 0.285888i | \(-0.907711\pi\) |
0.726718 | + | 0.686936i | \(0.241045\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10673.4 | − | 18487.0i | −0.375734 | − | 0.650790i | ||||
\(932\) | −809.803 | − | 1402.62i | −0.0284614 | − | 0.0492965i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8300.69 | − | 14377.2i | 0.290800 | − | 0.503680i | ||||
\(935\) | −557.703 | −0.0195068 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49863.5 | 1.73849 | 0.869247 | − | 0.494378i | \(-0.164604\pi\) | ||||
0.869247 | + | 0.494378i | \(0.164604\pi\) | |||||||
\(938\) | −15713.8 | + | 27217.1i | −0.546987 | + | 0.947410i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1978.02 | − | 3426.03i | −0.0686339 | − | 0.118877i | ||||
\(941\) | −4676.14 | − | 8099.31i | −0.161996 | − | 0.280584i | 0.773589 | − | 0.633688i | \(-0.218460\pi\) |
−0.935584 | + | 0.353104i | \(0.885126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31174.6 | + | 53996.0i | −1.07655 | + | 1.86464i | ||||
\(944\) | 21501.4 | 0.741326 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10333.4 | 0.355147 | ||||||||
\(947\) | −2005.69 | + | 3473.96i | −0.0688239 | + | 0.119207i | −0.898384 | − | 0.439211i | \(-0.855258\pi\) |
0.829560 | + | 0.558418i | \(0.188591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3259.47 | − | 5645.57i | −0.111493 | − | 0.193112i | ||||
\(950\) | −3808.32 | − | 6596.21i | −0.130061 | − | 0.225273i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2774.90 | − | 4806.27i | 0.0944696 | − | 0.163626i | ||||
\(953\) | 39128.6 | 1.33001 | 0.665005 | − | 0.746839i | \(-0.268429\pi\) | ||||
0.665005 | + | 0.746839i | \(0.268429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6808.10 | −0.230686 | ||||||||
\(956\) | 79.4643 | − | 137.636i | 0.00268835 | − | 0.00465636i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 256.885 | + | 444.938i | 0.00866345 | + | 0.0150055i | ||||
\(959\) | −28880.9 | − | 50023.3i | −0.972486 | − | 1.68440i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5021.39 | − | 8697.31i | 0.168554 | − | 0.291944i | ||||
\(962\) | −7522.15 | −0.252104 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2284.22 | −0.0763174 | ||||||||
\(965\) | 5585.50 | − | 9674.38i | 0.186325 | − | 0.322725i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8817.49 | − | 15272.3i | −0.293228 | − | 0.507885i | 0.681343 | − | 0.731964i | \(-0.261396\pi\) |
−0.974571 | + | 0.224079i | \(0.928063\pi\) | |||||||
\(968\) | −14550.6 | − | 25202.3i | −0.483134 | − | 0.836812i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4618.24 | − | 7999.02i | 0.152869 | − | 0.264776i | ||||
\(971\) | −26827.3 | −0.886642 | −0.443321 | − | 0.896363i | \(-0.646200\pi\) | ||||
−0.443321 | + | 0.896363i | \(0.646200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14625.3 | 0.481877 | ||||||||
\(974\) | 1691.45 | − | 2929.67i | 0.0556442 | − | 0.0963787i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1412.50 | − | 2446.53i | −0.0463249 | − | 0.0802371i | ||||
\(977\) | 4171.82 | + | 7225.80i | 0.136610 | + | 0.236616i | 0.926211 | − | 0.377004i | \(-0.123046\pi\) |
−0.789601 | + | 0.613620i | \(0.789713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3802.36 | + | 6585.88i | −0.124131 | + | 0.215001i | ||||
\(980\) | 1193.91 | 0.0389165 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32245.8 | 1.04787 | ||||||||
\(983\) | 18445.0 | − | 31947.7i | 0.598479 | − | 1.03660i | −0.394567 | − | 0.918867i | \(-0.629105\pi\) |
0.993046 | − | 0.117729i | \(-0.0375614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 866.561 | + | 1500.93i | 0.0280314 | + | 0.0485518i | ||||
\(986\) | −2319.50 | − | 4017.49i | −0.0749167 | − | 0.129760i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −904.149 | + | 1566.03i | −0.0291142 | + | 0.0504272i | ||||
\(989\) | 62200.7 | 1.99987 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24259.3 | −0.777619 | −0.388810 | − | 0.921318i | \(-0.627114\pi\) | ||||
−0.388810 | + | 0.921318i | \(0.627114\pi\) | |||||||
\(992\) | −4146.99 | + | 7182.80i | −0.132729 | + | 0.229893i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27621.8 | + | 47842.4i | 0.881400 | + | 1.52663i | ||||
\(995\) | 10496.9 | + | 18181.2i | 0.334447 | + | 0.579279i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15850.1 | + | 27453.2i | −0.503488 | + | 0.872067i | 0.496504 | + | 0.868035i | \(0.334617\pi\) |
−0.999992 | + | 0.00403269i | \(0.998716\pi\) | |||||||
\(998\) | 8134.15 | 0.257998 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.4.e.v.136.1 | 6 | ||
3.2 | odd | 2 | 405.4.e.q.136.3 | 6 | |||
9.2 | odd | 6 | 135.4.a.h.1.1 | yes | 3 | ||
9.4 | even | 3 | inner | 405.4.e.v.271.1 | 6 | ||
9.5 | odd | 6 | 405.4.e.q.271.3 | 6 | |||
9.7 | even | 3 | 135.4.a.e.1.3 | ✓ | 3 | ||
36.7 | odd | 6 | 2160.4.a.bi.1.3 | 3 | |||
36.11 | even | 6 | 2160.4.a.bq.1.3 | 3 | |||
45.2 | even | 12 | 675.4.b.n.649.2 | 6 | |||
45.7 | odd | 12 | 675.4.b.m.649.5 | 6 | |||
45.29 | odd | 6 | 675.4.a.p.1.3 | 3 | |||
45.34 | even | 6 | 675.4.a.s.1.1 | 3 | |||
45.38 | even | 12 | 675.4.b.n.649.5 | 6 | |||
45.43 | odd | 12 | 675.4.b.m.649.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.e.1.3 | ✓ | 3 | 9.7 | even | 3 | ||
135.4.a.h.1.1 | yes | 3 | 9.2 | odd | 6 | ||
405.4.e.q.136.3 | 6 | 3.2 | odd | 2 | |||
405.4.e.q.271.3 | 6 | 9.5 | odd | 6 | |||
405.4.e.v.136.1 | 6 | 1.1 | even | 1 | trivial | ||
405.4.e.v.271.1 | 6 | 9.4 | even | 3 | inner | ||
675.4.a.p.1.3 | 3 | 45.29 | odd | 6 | |||
675.4.a.s.1.1 | 3 | 45.34 | even | 6 | |||
675.4.b.m.649.2 | 6 | 45.43 | odd | 12 | |||
675.4.b.m.649.5 | 6 | 45.7 | odd | 12 | |||
675.4.b.n.649.2 | 6 | 45.2 | even | 12 | |||
675.4.b.n.649.5 | 6 | 45.38 | even | 12 | |||
2160.4.a.bi.1.3 | 3 | 36.7 | odd | 6 | |||
2160.4.a.bq.1.3 | 3 | 36.11 | even | 6 |