Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + 15624 x^{4} + 2116 x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.20 | ||
Root | \(2.74619i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.e.694.1 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74619i | 1.94185i | 0.239389 | + | 0.970924i | \(0.423053\pi\) | ||||
−0.239389 | + | 0.970924i | \(0.576947\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −5.54154 | −2.77077 | ||||||||
\(5\) | 2.23561 | − | 0.0452669i | 0.999795 | − | 0.0202440i | ||||
\(6\) | 2.74619 | 1.12113 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 9.72574i | − | 3.43857i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.124311 | + | 6.13940i | 0.0393107 | + | 1.94145i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 5.54154i | 1.59971i | ||||||||
\(13\) | − | 0.748249i | − | 0.207527i | −0.994602 | − | 0.103763i | \(-0.966911\pi\) | ||
0.994602 | − | 0.103763i | \(-0.0330885\pi\) | |||||||
\(14\) | −2.74619 | −0.733949 | ||||||||
\(15\) | −0.0452669 | − | 2.23561i | −0.0116879 | − | 0.577232i | ||||
\(16\) | 15.6256 | 3.90640 | ||||||||
\(17\) | 6.15353i | 1.49245i | 0.665694 | + | 0.746225i | \(0.268136\pi\) | ||||
−0.665694 | + | 0.746225i | \(0.731864\pi\) | |||||||
\(18\) | − | 2.74619i | − | 0.647282i | ||||||
\(19\) | 1.43933 | 0.330205 | 0.165103 | − | 0.986276i | \(-0.447204\pi\) | ||||
0.165103 | + | 0.986276i | \(0.447204\pi\) | |||||||
\(20\) | −12.3887 | + | 0.250849i | −2.77020 | + | 0.0560914i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | − | 2.74619i | − | 0.585489i | ||||||
\(23\) | 5.82872i | 1.21537i | 0.794177 | + | 0.607686i | \(0.207902\pi\) | ||||
−0.794177 | + | 0.607686i | \(0.792098\pi\) | |||||||
\(24\) | −9.72574 | −1.98526 | ||||||||
\(25\) | 4.99590 | − | 0.202398i | 0.999180 | − | 0.0404797i | ||||
\(26\) | 2.05483 | 0.402986 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 5.54154i | − | 1.04725i | ||||||
\(29\) | 0.913059 | 0.169551 | 0.0847754 | − | 0.996400i | \(-0.472983\pi\) | ||||
0.0847754 | + | 0.996400i | \(0.472983\pi\) | |||||||
\(30\) | 6.13940 | − | 0.124311i | 1.12090 | − | 0.0226961i | ||||
\(31\) | 2.25971 | 0.405856 | 0.202928 | − | 0.979194i | \(-0.434954\pi\) | ||||
0.202928 | + | 0.979194i | \(0.434954\pi\) | |||||||
\(32\) | 23.4594i | 4.14707i | ||||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −16.8987 | −2.89811 | ||||||||
\(35\) | 0.0452669 | + | 2.23561i | 0.00765151 | + | 0.377887i | ||||
\(36\) | 5.54154 | 0.923590 | ||||||||
\(37\) | 3.26260i | 0.536369i | 0.963368 | + | 0.268184i | \(0.0864236\pi\) | ||||
−0.963368 | + | 0.268184i | \(0.913576\pi\) | |||||||
\(38\) | 3.95267i | 0.641208i | ||||||||
\(39\) | −0.748249 | −0.119816 | ||||||||
\(40\) | −0.440254 | − | 21.7430i | −0.0696103 | − | 3.43786i | ||||
\(41\) | −11.5056 | −1.79687 | −0.898437 | − | 0.439103i | \(-0.855296\pi\) | ||||
−0.898437 | + | 0.439103i | \(0.855296\pi\) | |||||||
\(42\) | 2.74619i | 0.423746i | ||||||||
\(43\) | 9.99697i | 1.52452i | 0.647269 | + | 0.762262i | \(0.275911\pi\) | ||||
−0.647269 | + | 0.762262i | \(0.724089\pi\) | |||||||
\(44\) | 5.54154 | 0.835419 | ||||||||
\(45\) | −2.23561 | + | 0.0452669i | −0.333265 | + | 0.00674799i | ||||
\(46\) | −16.0068 | −2.36007 | ||||||||
\(47\) | 8.43122i | 1.22982i | 0.788597 | + | 0.614910i | \(0.210808\pi\) | ||||
−0.788597 | + | 0.614910i | \(0.789192\pi\) | |||||||
\(48\) | − | 15.6256i | − | 2.25536i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0.555824 | + | 13.7197i | 0.0786053 | + | 1.94026i | ||||
\(51\) | 6.15353 | 0.861666 | ||||||||
\(52\) | 4.14645i | 0.575010i | ||||||||
\(53\) | 5.64500i | 0.775400i | 0.921786 | + | 0.387700i | \(0.126730\pi\) | ||||
−0.921786 | + | 0.387700i | \(0.873270\pi\) | |||||||
\(54\) | −2.74619 | −0.373709 | ||||||||
\(55\) | −2.23561 | + | 0.0452669i | −0.301450 | + | 0.00610379i | ||||
\(56\) | 9.72574 | 1.29966 | ||||||||
\(57\) | − | 1.43933i | − | 0.190644i | ||||||
\(58\) | 2.50743i | 0.329242i | ||||||||
\(59\) | 4.37632 | 0.569748 | 0.284874 | − | 0.958565i | \(-0.408048\pi\) | ||||
0.284874 | + | 0.958565i | \(0.408048\pi\) | |||||||
\(60\) | 0.250849 | + | 12.3887i | 0.0323844 | + | 1.59938i | ||||
\(61\) | −9.75318 | −1.24877 | −0.624383 | − | 0.781118i | \(-0.714650\pi\) | ||||
−0.624383 | + | 0.781118i | \(0.714650\pi\) | |||||||
\(62\) | 6.20558i | 0.788110i | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −33.1726 | −4.14657 | ||||||||
\(65\) | −0.0338709 | − | 1.67279i | −0.00420117 | − | 0.207484i | ||||
\(66\) | −2.74619 | −0.338032 | ||||||||
\(67\) | − | 6.69285i | − | 0.817661i | −0.912610 | − | 0.408831i | \(-0.865937\pi\) | ||
0.912610 | − | 0.408831i | \(-0.134063\pi\) | |||||||
\(68\) | − | 34.1000i | − | 4.13524i | ||||||
\(69\) | 5.82872 | 0.701696 | ||||||||
\(70\) | −6.13940 | + | 0.124311i | −0.733799 | + | 0.0148581i | ||||
\(71\) | 10.8314 | 1.28545 | 0.642726 | − | 0.766096i | \(-0.277803\pi\) | ||||
0.642726 | + | 0.766096i | \(0.277803\pi\) | |||||||
\(72\) | 9.72574i | 1.14619i | ||||||||
\(73\) | − | 3.60606i | − | 0.422057i | −0.977480 | − | 0.211028i | \(-0.932319\pi\) | ||
0.977480 | − | 0.211028i | \(-0.0676813\pi\) | |||||||
\(74\) | −8.95972 | −1.04155 | ||||||||
\(75\) | −0.202398 | − | 4.99590i | −0.0233709 | − | 0.576877i | ||||
\(76\) | −7.97612 | −0.914923 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | − | 2.05483i | − | 0.232664i | ||||||
\(79\) | 10.6281 | 1.19575 | 0.597877 | − | 0.801588i | \(-0.296011\pi\) | ||||
0.597877 | + | 0.801588i | \(0.296011\pi\) | |||||||
\(80\) | 34.9328 | − | 0.707323i | 3.90560 | − | 0.0790811i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 31.5965i | − | 3.48925i | ||||||
\(83\) | − | 13.4443i | − | 1.47571i | −0.674961 | − | 0.737854i | \(-0.735839\pi\) | ||
0.674961 | − | 0.737854i | \(-0.264161\pi\) | |||||||
\(84\) | −5.54154 | −0.604632 | ||||||||
\(85\) | 0.278551 | + | 13.7569i | 0.0302131 | + | 1.49214i | ||||
\(86\) | −27.4535 | −2.96039 | ||||||||
\(87\) | − | 0.913059i | − | 0.0978902i | ||||||
\(88\) | 9.72574i | 1.03677i | ||||||||
\(89\) | 5.61820 | 0.595528 | 0.297764 | − | 0.954640i | \(-0.403759\pi\) | ||||
0.297764 | + | 0.954640i | \(0.403759\pi\) | |||||||
\(90\) | −0.124311 | − | 6.13940i | −0.0131036 | − | 0.647150i | ||||
\(91\) | 0.748249 | 0.0784378 | ||||||||
\(92\) | − | 32.3001i | − | 3.36752i | ||||||
\(93\) | − | 2.25971i | − | 0.234321i | ||||||
\(94\) | −23.1537 | −2.38812 | ||||||||
\(95\) | 3.21778 | − | 0.0651541i | 0.330138 | − | 0.00668467i | ||||
\(96\) | 23.4594 | 2.39431 | ||||||||
\(97\) | 14.0142i | 1.42293i | 0.702723 | + | 0.711464i | \(0.251967\pi\) | ||||
−0.702723 | + | 0.711464i | \(0.748033\pi\) | |||||||
\(98\) | − | 2.74619i | − | 0.277407i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −27.6850 | + | 1.12160i | −2.76850 | + | 0.112160i | ||||
\(101\) | −2.63227 | −0.261921 | −0.130960 | − | 0.991388i | \(-0.541806\pi\) | ||||
−0.130960 | + | 0.991388i | \(0.541806\pi\) | |||||||
\(102\) | 16.8987i | 1.67322i | ||||||||
\(103\) | − | 0.913885i | − | 0.0900478i | −0.998986 | − | 0.0450239i | \(-0.985664\pi\) | ||
0.998986 | − | 0.0450239i | \(-0.0143364\pi\) | |||||||
\(104\) | −7.27727 | −0.713596 | ||||||||
\(105\) | 2.23561 | − | 0.0452669i | 0.218173 | − | 0.00441760i | ||||
\(106\) | −15.5022 | −1.50571 | ||||||||
\(107\) | − | 12.1001i | − | 1.16976i | −0.811121 | − | 0.584879i | \(-0.801142\pi\) | ||
0.811121 | − | 0.584879i | \(-0.198858\pi\) | |||||||
\(108\) | − | 5.54154i | − | 0.533235i | ||||||
\(109\) | −20.2083 | −1.93561 | −0.967803 | − | 0.251707i | \(-0.919008\pi\) | ||||
−0.967803 | + | 0.251707i | \(0.919008\pi\) | |||||||
\(110\) | −0.124311 | − | 6.13940i | −0.0118526 | − | 0.585369i | ||||
\(111\) | 3.26260 | 0.309673 | ||||||||
\(112\) | 15.6256i | 1.47648i | ||||||||
\(113\) | − | 0.0930496i | − | 0.00875337i | −0.999990 | − | 0.00437669i | \(-0.998607\pi\) | ||
0.999990 | − | 0.00437669i | \(-0.00139315\pi\) | |||||||
\(114\) | 3.95267 | 0.370202 | ||||||||
\(115\) | 0.263848 | + | 13.0307i | 0.0246040 | + | 1.21512i | ||||
\(116\) | −5.05975 | −0.469786 | ||||||||
\(117\) | 0.748249i | 0.0691757i | ||||||||
\(118\) | 12.0182i | 1.10636i | ||||||||
\(119\) | −6.15353 | −0.564093 | ||||||||
\(120\) | −21.7430 | + | 0.440254i | −1.98485 | + | 0.0401895i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 26.7840i | − | 2.42491i | ||||||
\(123\) | 11.5056i | 1.03743i | ||||||||
\(124\) | −12.5223 | −1.12453 | ||||||||
\(125\) | 11.1597 | − | 0.678633i | 0.998156 | − | 0.0606988i | ||||
\(126\) | 2.74619 | 0.244650 | ||||||||
\(127\) | − | 14.7548i | − | 1.30928i | −0.755941 | − | 0.654640i | \(-0.772820\pi\) | ||
0.755941 | − | 0.654640i | \(-0.227180\pi\) | |||||||
\(128\) | − | 44.1794i | − | 3.90494i | ||||||
\(129\) | 9.99697 | 0.880184 | ||||||||
\(130\) | 4.59380 | − | 0.0930159i | 0.402903 | − | 0.00815804i | ||||
\(131\) | 16.5007 | 1.44168 | 0.720838 | − | 0.693104i | \(-0.243757\pi\) | ||||
0.720838 | + | 0.693104i | \(0.243757\pi\) | |||||||
\(132\) | − | 5.54154i | − | 0.482329i | ||||||
\(133\) | 1.43933i | 0.124806i | ||||||||
\(134\) | 18.3798 | 1.58777 | ||||||||
\(135\) | 0.0452669 | + | 2.23561i | 0.00389596 | + | 0.192411i | ||||
\(136\) | 59.8476 | 5.13189 | ||||||||
\(137\) | 20.1409i | 1.72076i | 0.509656 | + | 0.860378i | \(0.329773\pi\) | ||||
−0.509656 | + | 0.860378i | \(0.670227\pi\) | |||||||
\(138\) | 16.0068i | 1.36259i | ||||||||
\(139\) | −1.80356 | −0.152976 | −0.0764881 | − | 0.997070i | \(-0.524371\pi\) | ||||
−0.0764881 | + | 0.997070i | \(0.524371\pi\) | |||||||
\(140\) | −0.250849 | − | 12.3887i | −0.0212006 | − | 1.04704i | ||||
\(141\) | 8.43122 | 0.710037 | ||||||||
\(142\) | 29.7451i | 2.49615i | ||||||||
\(143\) | 0.748249i | 0.0625717i | ||||||||
\(144\) | −15.6256 | −1.30213 | ||||||||
\(145\) | 2.04124 | − | 0.0413314i | 0.169516 | − | 0.00343238i | ||||
\(146\) | 9.90290 | 0.819570 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 18.0799i | − | 1.48616i | ||||||
\(149\) | −6.52258 | −0.534350 | −0.267175 | − | 0.963648i | \(-0.586090\pi\) | ||||
−0.267175 | + | 0.963648i | \(0.586090\pi\) | |||||||
\(150\) | 13.7197 | − | 0.555824i | 1.12021 | − | 0.0453828i | ||||
\(151\) | −3.83724 | −0.312270 | −0.156135 | − | 0.987736i | \(-0.549903\pi\) | ||||
−0.156135 | + | 0.987736i | \(0.549903\pi\) | |||||||
\(152\) | − | 13.9986i | − | 1.13543i | ||||||
\(153\) | − | 6.15353i | − | 0.497483i | ||||||
\(154\) | 2.74619 | 0.221294 | ||||||||
\(155\) | 5.05183 | − | 0.102290i | 0.405772 | − | 0.00821613i | ||||
\(156\) | 4.14645 | 0.331982 | ||||||||
\(157\) | − | 20.5461i | − | 1.63976i | −0.572538 | − | 0.819878i | \(-0.694041\pi\) | ||
0.572538 | − | 0.819878i | \(-0.305959\pi\) | |||||||
\(158\) | 29.1867i | 2.32197i | ||||||||
\(159\) | 5.64500 | 0.447678 | ||||||||
\(160\) | 1.06193 | + | 52.4460i | 0.0839532 | + | 4.14622i | ||||
\(161\) | −5.82872 | −0.459368 | ||||||||
\(162\) | 2.74619i | 0.215761i | ||||||||
\(163\) | 1.68575i | 0.132038i | 0.997818 | + | 0.0660189i | \(0.0210298\pi\) | ||||
−0.997818 | + | 0.0660189i | \(0.978970\pi\) | |||||||
\(164\) | 63.7588 | 4.97872 | ||||||||
\(165\) | 0.0452669 | + | 2.23561i | 0.00352403 | + | 0.174042i | ||||
\(166\) | 36.9206 | 2.86560 | ||||||||
\(167\) | 14.1425i | 1.09438i | 0.837008 | + | 0.547190i | \(0.184303\pi\) | ||||
−0.837008 | + | 0.547190i | \(0.815697\pi\) | |||||||
\(168\) | − | 9.72574i | − | 0.750357i | ||||||
\(169\) | 12.4401 | 0.956933 | ||||||||
\(170\) | −37.7790 | + | 0.764954i | −2.89752 | + | 0.0586693i | ||||
\(171\) | −1.43933 | −0.110068 | ||||||||
\(172\) | − | 55.3986i | − | 4.22411i | ||||||
\(173\) | 13.3765i | 1.01700i | 0.861063 | + | 0.508499i | \(0.169799\pi\) | ||||
−0.861063 | + | 0.508499i | \(0.830201\pi\) | |||||||
\(174\) | 2.50743 | 0.190088 | ||||||||
\(175\) | 0.202398 | + | 4.99590i | 0.0152999 | + | 0.377655i | ||||
\(176\) | −15.6256 | −1.17782 | ||||||||
\(177\) | − | 4.37632i | − | 0.328944i | ||||||
\(178\) | 15.4286i | 1.15642i | ||||||||
\(179\) | 21.2621 | 1.58920 | 0.794602 | − | 0.607131i | \(-0.207680\pi\) | ||||
0.794602 | + | 0.607131i | \(0.207680\pi\) | |||||||
\(180\) | 12.3887 | − | 0.250849i | 0.923401 | − | 0.0186971i | ||||
\(181\) | 10.6061 | 0.788348 | 0.394174 | − | 0.919036i | \(-0.371031\pi\) | ||||
0.394174 | + | 0.919036i | \(0.371031\pi\) | |||||||
\(182\) | 2.05483i | 0.152314i | ||||||||
\(183\) | 9.75318i | 0.720976i | ||||||||
\(184\) | 56.6886 | 4.17914 | ||||||||
\(185\) | 0.147688 | + | 7.29391i | 0.0108582 | + | 0.536259i | ||||
\(186\) | 6.20558 | 0.455015 | ||||||||
\(187\) | − | 6.15353i | − | 0.449991i | ||||||
\(188\) | − | 46.7220i | − | 3.40755i | ||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0.178925 | + | 8.83664i | 0.0129806 | + | 0.641077i | ||||
\(191\) | 0.660904 | 0.0478213 | 0.0239107 | − | 0.999714i | \(-0.492388\pi\) | ||||
0.0239107 | + | 0.999714i | \(0.492388\pi\) | |||||||
\(192\) | 33.1726i | 2.39402i | ||||||||
\(193\) | 6.34668i | 0.456844i | 0.973562 | + | 0.228422i | \(0.0733566\pi\) | ||||
−0.973562 | + | 0.228422i | \(0.926643\pi\) | |||||||
\(194\) | −38.4856 | −2.76311 | ||||||||
\(195\) | −1.67279 | + | 0.0338709i | −0.119791 | + | 0.00242555i | ||||
\(196\) | 5.54154 | 0.395824 | ||||||||
\(197\) | − | 12.6891i | − | 0.904059i | −0.892003 | − | 0.452029i | \(-0.850700\pi\) | ||
0.892003 | − | 0.452029i | \(-0.149300\pi\) | |||||||
\(198\) | 2.74619i | 0.195163i | ||||||||
\(199\) | −7.00407 | −0.496505 | −0.248253 | − | 0.968695i | \(-0.579856\pi\) | ||||
−0.248253 | + | 0.968695i | \(0.579856\pi\) | |||||||
\(200\) | −1.96847 | − | 48.5888i | −0.139192 | − | 3.43575i | ||||
\(201\) | −6.69285 | −0.472077 | ||||||||
\(202\) | − | 7.22871i | − | 0.508610i | ||||||
\(203\) | 0.913059i | 0.0640842i | ||||||||
\(204\) | −34.1000 | −2.38748 | ||||||||
\(205\) | −25.7220 | + | 0.520823i | −1.79650 | + | 0.0363759i | ||||
\(206\) | 2.50970 | 0.174859 | ||||||||
\(207\) | − | 5.82872i | − | 0.405124i | ||||||
\(208\) | − | 11.6918i | − | 0.810684i | ||||||
\(209\) | −1.43933 | −0.0995606 | ||||||||
\(210\) | 0.124311 | + | 6.13940i | 0.00857830 | + | 0.423659i | ||||
\(211\) | −24.9569 | −1.71811 | −0.859053 | − | 0.511887i | \(-0.828947\pi\) | ||||
−0.859053 | + | 0.511887i | \(0.828947\pi\) | |||||||
\(212\) | − | 31.2820i | − | 2.14846i | ||||||
\(213\) | − | 10.8314i | − | 0.742156i | ||||||
\(214\) | 33.2290 | 2.27149 | ||||||||
\(215\) | 0.452532 | + | 22.3493i | 0.0308624 | + | 1.52421i | ||||
\(216\) | 9.72574 | 0.661753 | ||||||||
\(217\) | 2.25971i | 0.153399i | ||||||||
\(218\) | − | 55.4958i | − | 3.75865i | ||||||
\(219\) | −3.60606 | −0.243675 | ||||||||
\(220\) | 12.3887 | − | 0.250849i | 0.835248 | − | 0.0169122i | ||||
\(221\) | 4.60437 | 0.309724 | ||||||||
\(222\) | 8.95972i | 0.601337i | ||||||||
\(223\) | − | 15.2962i | − | 1.02431i | −0.858892 | − | 0.512156i | \(-0.828847\pi\) | ||
0.858892 | − | 0.512156i | \(-0.171153\pi\) | |||||||
\(224\) | −23.4594 | −1.56744 | ||||||||
\(225\) | −4.99590 | + | 0.202398i | −0.333060 | + | 0.0134932i | ||||
\(226\) | 0.255532 | 0.0169977 | ||||||||
\(227\) | 23.0182i | 1.52777i | 0.645350 | + | 0.763887i | \(0.276711\pi\) | ||||
−0.645350 | + | 0.763887i | \(0.723289\pi\) | |||||||
\(228\) | 7.97612i | 0.528231i | ||||||||
\(229\) | −6.83386 | −0.451594 | −0.225797 | − | 0.974174i | \(-0.572499\pi\) | ||||
−0.225797 | + | 0.974174i | \(0.572499\pi\) | |||||||
\(230\) | −35.7849 | + | 0.724577i | −2.35958 | + | 0.0477772i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | − | 8.88017i | − | 0.583012i | ||||||
\(233\) | 17.9663i | 1.17701i | 0.808494 | + | 0.588504i | \(0.200283\pi\) | ||||
−0.808494 | + | 0.588504i | \(0.799717\pi\) | |||||||
\(234\) | −2.05483 | −0.134329 | ||||||||
\(235\) | 0.381655 | + | 18.8489i | 0.0248965 | + | 1.22957i | ||||
\(236\) | −24.2516 | −1.57864 | ||||||||
\(237\) | − | 10.6281i | − | 0.690369i | ||||||
\(238\) | − | 16.8987i | − | 1.09538i | ||||||
\(239\) | 17.8108 | 1.15208 | 0.576041 | − | 0.817421i | \(-0.304597\pi\) | ||||
0.576041 | + | 0.817421i | \(0.304597\pi\) | |||||||
\(240\) | −0.707323 | − | 34.9328i | −0.0456575 | − | 2.25490i | ||||
\(241\) | 10.4906 | 0.675758 | 0.337879 | − | 0.941190i | \(-0.390291\pi\) | ||||
0.337879 | + | 0.941190i | \(0.390291\pi\) | |||||||
\(242\) | 2.74619i | 0.176532i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 54.0476 | 3.46005 | ||||||||
\(245\) | −2.23561 | + | 0.0452669i | −0.142828 | + | 0.00289200i | ||||
\(246\) | −31.5965 | −2.01452 | ||||||||
\(247\) | − | 1.07698i | − | 0.0685265i | ||||||
\(248\) | − | 21.9773i | − | 1.39556i | ||||||
\(249\) | −13.4443 | −0.852000 | ||||||||
\(250\) | 1.86365 | + | 30.6467i | 0.117868 | + | 1.93827i | ||||
\(251\) | −5.13076 | −0.323851 | −0.161926 | − | 0.986803i | \(-0.551770\pi\) | ||||
−0.161926 | + | 0.986803i | \(0.551770\pi\) | |||||||
\(252\) | 5.54154i | 0.349084i | ||||||||
\(253\) | − | 5.82872i | − | 0.366449i | ||||||
\(254\) | 40.5195 | 2.54242 | ||||||||
\(255\) | 13.7569 | − | 0.278551i | 0.861490 | − | 0.0174436i | ||||
\(256\) | 54.9797 | 3.43623 | ||||||||
\(257\) | − | 21.1767i | − | 1.32097i | −0.750840 | − | 0.660485i | \(-0.770351\pi\) | ||
0.750840 | − | 0.660485i | \(-0.229649\pi\) | |||||||
\(258\) | 27.4535i | 1.70918i | ||||||||
\(259\) | −3.26260 | −0.202728 | ||||||||
\(260\) | 0.187697 | + | 9.26985i | 0.0116405 | + | 0.574892i | ||||
\(261\) | −0.913059 | −0.0565169 | ||||||||
\(262\) | 45.3141i | 2.79951i | ||||||||
\(263\) | 1.58627i | 0.0978133i | 0.998803 | + | 0.0489067i | \(0.0155737\pi\) | ||||
−0.998803 | + | 0.0489067i | \(0.984426\pi\) | |||||||
\(264\) | 9.72574 | 0.598578 | ||||||||
\(265\) | 0.255532 | + | 12.6200i | 0.0156972 | + | 0.775242i | ||||
\(266\) | −3.95267 | −0.242354 | ||||||||
\(267\) | − | 5.61820i | − | 0.343828i | ||||||
\(268\) | 37.0887i | 2.26555i | ||||||||
\(269\) | 3.62855 | 0.221237 | 0.110618 | − | 0.993863i | \(-0.464717\pi\) | ||||
0.110618 | + | 0.993863i | \(0.464717\pi\) | |||||||
\(270\) | −6.13940 | + | 0.124311i | −0.373632 | + | 0.00756535i | ||||
\(271\) | 8.16357 | 0.495902 | 0.247951 | − | 0.968773i | \(-0.420243\pi\) | ||||
0.247951 | + | 0.968773i | \(0.420243\pi\) | |||||||
\(272\) | 96.1526i | 5.83011i | ||||||||
\(273\) | − | 0.748249i | − | 0.0452861i | ||||||
\(274\) | −55.3108 | −3.34145 | ||||||||
\(275\) | −4.99590 | + | 0.202398i | −0.301264 | + | 0.0122051i | ||||
\(276\) | −32.3001 | −1.94424 | ||||||||
\(277\) | 8.82549i | 0.530272i | 0.964211 | + | 0.265136i | \(0.0854169\pi\) | ||||
−0.964211 | + | 0.265136i | \(0.914583\pi\) | |||||||
\(278\) | − | 4.95292i | − | 0.297056i | ||||||
\(279\) | −2.25971 | −0.135285 | ||||||||
\(280\) | 21.7430 | − | 0.440254i | 1.29939 | − | 0.0263102i | ||||
\(281\) | 16.3437 | 0.974985 | 0.487492 | − | 0.873127i | \(-0.337912\pi\) | ||||
0.487492 | + | 0.873127i | \(0.337912\pi\) | |||||||
\(282\) | 23.1537i | 1.37878i | ||||||||
\(283\) | − | 11.6256i | − | 0.691073i | −0.938405 | − | 0.345536i | \(-0.887697\pi\) | ||
0.938405 | − | 0.345536i | \(-0.112303\pi\) | |||||||
\(284\) | −60.0227 | −3.56169 | ||||||||
\(285\) | −0.0651541 | − | 3.21778i | −0.00385940 | − | 0.190605i | ||||
\(286\) | −2.05483 | −0.121505 | ||||||||
\(287\) | − | 11.5056i | − | 0.679154i | ||||||
\(288\) | − | 23.4594i | − | 1.38236i | ||||||
\(289\) | −20.8659 | −1.22741 | ||||||||
\(290\) | 0.113504 | + | 5.60563i | 0.00666516 | + | 0.329174i | ||||
\(291\) | 14.0142 | 0.821527 | ||||||||
\(292\) | 19.9831i | 1.16942i | ||||||||
\(293\) | − | 8.77092i | − | 0.512403i | −0.966623 | − | 0.256201i | \(-0.917529\pi\) | ||
0.966623 | − | 0.256201i | \(-0.0824710\pi\) | |||||||
\(294\) | −2.74619 | −0.160161 | ||||||||
\(295\) | 9.78375 | − | 0.198103i | 0.569632 | − | 0.0115340i | ||||
\(296\) | 31.7312 | 1.84434 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | − | 17.9122i | − | 1.03763i | ||||||
\(299\) | 4.36134 | 0.252223 | ||||||||
\(300\) | 1.12160 | + | 27.6850i | 0.0647555 | + | 1.59839i | ||||
\(301\) | −9.99697 | −0.576216 | ||||||||
\(302\) | − | 10.5378i | − | 0.606380i | ||||||
\(303\) | 2.63227i | 0.151220i | ||||||||
\(304\) | 22.4904 | 1.28991 | ||||||||
\(305\) | −21.8043 | + | 0.441496i | −1.24851 | + | 0.0252800i | ||||
\(306\) | 16.8987 | 0.966037 | ||||||||
\(307\) | − | 28.1213i | − | 1.60497i | −0.596675 | − | 0.802483i | \(-0.703512\pi\) | ||
0.596675 | − | 0.802483i | \(-0.296488\pi\) | |||||||
\(308\) | 5.54154i | 0.315759i | ||||||||
\(309\) | −0.913885 | −0.0519891 | ||||||||
\(310\) | 0.280908 | + | 13.8733i | 0.0159545 | + | 0.787948i | ||||
\(311\) | −7.52137 | −0.426498 | −0.213249 | − | 0.976998i | \(-0.568404\pi\) | ||||
−0.213249 | + | 0.976998i | \(0.568404\pi\) | |||||||
\(312\) | 7.27727i | 0.411995i | ||||||||
\(313\) | 10.1735i | 0.575039i | 0.957775 | + | 0.287520i | \(0.0928307\pi\) | ||||
−0.957775 | + | 0.287520i | \(0.907169\pi\) | |||||||
\(314\) | 56.4234 | 3.18416 | ||||||||
\(315\) | −0.0452669 | − | 2.23561i | −0.00255050 | − | 0.125962i | ||||
\(316\) | −58.8961 | −3.31316 | ||||||||
\(317\) | − | 1.97131i | − | 0.110720i | −0.998466 | − | 0.0553599i | \(-0.982369\pi\) | ||
0.998466 | − | 0.0553599i | \(-0.0176306\pi\) | |||||||
\(318\) | 15.5022i | 0.869322i | ||||||||
\(319\) | −0.913059 | −0.0511215 | ||||||||
\(320\) | −74.1609 | + | 1.50162i | −4.14572 | + | 0.0839431i | ||||
\(321\) | −12.1001 | −0.675360 | ||||||||
\(322\) | − | 16.0068i | − | 0.892022i | ||||||
\(323\) | 8.85697i | 0.492815i | ||||||||
\(324\) | −5.54154 | −0.307863 | ||||||||
\(325\) | −0.151444 | − | 3.73818i | −0.00840062 | − | 0.207357i | ||||
\(326\) | −4.62938 | −0.256397 | ||||||||
\(327\) | 20.2083i | 1.11752i | ||||||||
\(328\) | 111.900i | 6.17867i | ||||||||
\(329\) | −8.43122 | −0.464828 | ||||||||
\(330\) | −6.13940 | + | 0.124311i | −0.337963 | + | 0.00684312i | ||||
\(331\) | −19.5659 | −1.07544 | −0.537721 | − | 0.843123i | \(-0.680714\pi\) | ||||
−0.537721 | + | 0.843123i | \(0.680714\pi\) | |||||||
\(332\) | 74.5023i | 4.08885i | ||||||||
\(333\) | − | 3.26260i | − | 0.178790i | ||||||
\(334\) | −38.8380 | −2.12512 | ||||||||
\(335\) | −0.302965 | − | 14.9626i | −0.0165527 | − | 0.817494i | ||||
\(336\) | 15.6256 | 0.852447 | ||||||||
\(337\) | 28.8041i | 1.56906i | 0.620093 | + | 0.784528i | \(0.287095\pi\) | ||||
−0.620093 | + | 0.784528i | \(0.712905\pi\) | |||||||
\(338\) | 34.1629i | 1.85822i | ||||||||
\(339\) | −0.0930496 | −0.00505376 | ||||||||
\(340\) | −1.54360 | − | 76.2344i | −0.0837137 | − | 4.13439i | ||||
\(341\) | −2.25971 | −0.122370 | ||||||||
\(342\) | − | 3.95267i | − | 0.213736i | ||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 97.2279 | 5.24218 | ||||||||
\(345\) | 13.0307 | − | 0.263848i | 0.701552 | − | 0.0142051i | ||||
\(346\) | −36.7344 | −1.97486 | ||||||||
\(347\) | − | 21.1332i | − | 1.13449i | −0.823549 | − | 0.567246i | \(-0.808009\pi\) | ||
0.823549 | − | 0.567246i | \(-0.191991\pi\) | |||||||
\(348\) | 5.05975i | 0.271231i | ||||||||
\(349\) | 19.1331 | 1.02417 | 0.512085 | − | 0.858935i | \(-0.328873\pi\) | ||||
0.512085 | + | 0.858935i | \(0.328873\pi\) | |||||||
\(350\) | −13.7197 | + | 0.555824i | −0.733348 | + | 0.0297100i | ||||
\(351\) | 0.748249 | 0.0399386 | ||||||||
\(352\) | − | 23.4594i | − | 1.25039i | ||||||
\(353\) | − | 30.7309i | − | 1.63564i | −0.575475 | − | 0.817820i | \(-0.695183\pi\) | ||
0.575475 | − | 0.817820i | \(-0.304817\pi\) | |||||||
\(354\) | 12.0182 | 0.638760 | ||||||||
\(355\) | 24.2148 | − | 0.490305i | 1.28519 | − | 0.0260227i | ||||
\(356\) | −31.1335 | −1.65007 | ||||||||
\(357\) | 6.15353i | 0.325679i | ||||||||
\(358\) | 58.3897i | 3.08599i | ||||||||
\(359\) | 16.5201 | 0.871899 | 0.435950 | − | 0.899971i | \(-0.356413\pi\) | ||||
0.435950 | + | 0.899971i | \(0.356413\pi\) | |||||||
\(360\) | 0.440254 | + | 21.7430i | 0.0232034 | + | 1.14595i | ||||
\(361\) | −16.9283 | −0.890964 | ||||||||
\(362\) | 29.1264i | 1.53085i | ||||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | −4.14645 | −0.217333 | ||||||||
\(365\) | −0.163235 | − | 8.06173i | −0.00854411 | − | 0.421970i | ||||
\(366\) | −26.7840 | −1.40002 | ||||||||
\(367\) | − | 22.8531i | − | 1.19292i | −0.802641 | − | 0.596462i | \(-0.796573\pi\) | ||
0.802641 | − | 0.596462i | \(-0.203427\pi\) | |||||||
\(368\) | 91.0773i | 4.74773i | ||||||||
\(369\) | 11.5056 | 0.598958 | ||||||||
\(370\) | −20.0304 | + | 0.405579i | −1.04133 | + | 0.0210850i | ||||
\(371\) | −5.64500 | −0.293074 | ||||||||
\(372\) | 12.5223i | 0.649249i | ||||||||
\(373\) | − | 19.1864i | − | 0.993436i | −0.867912 | − | 0.496718i | \(-0.834538\pi\) | ||
0.867912 | − | 0.496718i | \(-0.165462\pi\) | |||||||
\(374\) | 16.8987 | 0.873813 | ||||||||
\(375\) | −0.678633 | − | 11.1597i | −0.0350444 | − | 0.576286i | ||||
\(376\) | 81.9998 | 4.22882 | ||||||||
\(377\) | − | 0.683195i | − | 0.0351864i | ||||||
\(378\) | − | 2.74619i | − | 0.141249i | ||||||
\(379\) | 30.4582 | 1.56453 | 0.782265 | − | 0.622945i | \(-0.214064\pi\) | ||||
0.782265 | + | 0.622945i | \(0.214064\pi\) | |||||||
\(380\) | −17.8315 | + | 0.361054i | −0.914736 | + | 0.0185217i | ||||
\(381\) | −14.7548 | −0.755913 | ||||||||
\(382\) | 1.81497i | 0.0928617i | ||||||||
\(383\) | 19.3943i | 0.991004i | 0.868607 | + | 0.495502i | \(0.165016\pi\) | ||||
−0.868607 | + | 0.495502i | \(0.834984\pi\) | |||||||
\(384\) | −44.1794 | −2.25452 | ||||||||
\(385\) | −0.0452669 | − | 2.23561i | −0.00230702 | − | 0.113937i | ||||
\(386\) | −17.4292 | −0.887122 | ||||||||
\(387\) | − | 9.99697i | − | 0.508175i | ||||||
\(388\) | − | 77.6603i | − | 3.94261i | ||||||
\(389\) | −30.0679 | −1.52450 | −0.762251 | − | 0.647281i | \(-0.775906\pi\) | ||||
−0.762251 | + | 0.647281i | \(0.775906\pi\) | |||||||
\(390\) | −0.0930159 | − | 4.59380i | −0.00471004 | − | 0.232616i | ||||
\(391\) | −35.8672 | −1.81388 | ||||||||
\(392\) | 9.72574i | 0.491224i | ||||||||
\(393\) | − | 16.5007i | − | 0.832352i | ||||||
\(394\) | 34.8466 | 1.75554 | ||||||||
\(395\) | 23.7603 | − | 0.481101i | 1.19551 | − | 0.0242068i | ||||
\(396\) | −5.54154 | −0.278473 | ||||||||
\(397\) | − | 25.3301i | − | 1.27128i | −0.771985 | − | 0.635640i | \(-0.780736\pi\) | ||
0.771985 | − | 0.635640i | \(-0.219264\pi\) | |||||||
\(398\) | − | 19.2345i | − | 0.964137i | ||||||
\(399\) | 1.43933 | 0.0720567 | ||||||||
\(400\) | 78.0640 | − | 3.16260i | 3.90320 | − | 0.158130i | ||||
\(401\) | 20.6349 | 1.03046 | 0.515228 | − | 0.857053i | \(-0.327707\pi\) | ||||
0.515228 | + | 0.857053i | \(0.327707\pi\) | |||||||
\(402\) | − | 18.3798i | − | 0.916701i | ||||||
\(403\) | − | 1.69082i | − | 0.0842260i | ||||||
\(404\) | 14.5868 | 0.725723 | ||||||||
\(405\) | 2.23561 | − | 0.0452669i | 0.111088 | − | 0.00224933i | ||||
\(406\) | −2.50743 | −0.124442 | ||||||||
\(407\) | − | 3.26260i | − | 0.161721i | ||||||
\(408\) | − | 59.8476i | − | 2.96290i | ||||||
\(409\) | −26.0758 | −1.28937 | −0.644683 | − | 0.764450i | \(-0.723011\pi\) | ||||
−0.644683 | + | 0.764450i | \(0.723011\pi\) | |||||||
\(410\) | −1.43028 | − | 70.6375i | −0.0706364 | − | 3.48854i | ||||
\(411\) | 20.1409 | 0.993479 | ||||||||
\(412\) | 5.06433i | 0.249502i | ||||||||
\(413\) | 4.37632i | 0.215345i | ||||||||
\(414\) | 16.0068 | 0.786689 | ||||||||
\(415\) | −0.608584 | − | 30.0563i | −0.0298742 | − | 1.47540i | ||||
\(416\) | 17.5534 | 0.860629 | ||||||||
\(417\) | 1.80356i | 0.0883208i | ||||||||
\(418\) | − | 3.95267i | − | 0.193332i | ||||||
\(419\) | 21.9235 | 1.07103 | 0.535517 | − | 0.844525i | \(-0.320117\pi\) | ||||
0.535517 | + | 0.844525i | \(0.320117\pi\) | |||||||
\(420\) | −12.3887 | + | 0.250849i | −0.604508 | + | 0.0122402i | ||||
\(421\) | −9.30230 | −0.453366 | −0.226683 | − | 0.973969i | \(-0.572788\pi\) | ||||
−0.226683 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(422\) | − | 68.5364i | − | 3.33630i | ||||||
\(423\) | − | 8.43122i | − | 0.409940i | ||||||
\(424\) | 54.9018 | 2.66627 | ||||||||
\(425\) | 1.24546 | + | 30.7424i | 0.0604139 | + | 1.49123i | ||||
\(426\) | 29.7451 | 1.44115 | ||||||||
\(427\) | − | 9.75318i | − | 0.471989i | ||||||
\(428\) | 67.0530i | 3.24113i | ||||||||
\(429\) | 0.748249 | 0.0361258 | ||||||||
\(430\) | −61.3754 | + | 1.24274i | −2.95979 | + | 0.0599301i | ||||
\(431\) | 28.2950 | 1.36292 | 0.681462 | − | 0.731854i | \(-0.261345\pi\) | ||||
0.681462 | + | 0.731854i | \(0.261345\pi\) | |||||||
\(432\) | 15.6256i | 0.751787i | ||||||||
\(433\) | − | 11.9658i | − | 0.575042i | −0.957774 | − | 0.287521i | \(-0.907169\pi\) | ||
0.957774 | − | 0.287521i | \(-0.0928310\pi\) | |||||||
\(434\) | −6.20558 | −0.297877 | ||||||||
\(435\) | −0.0413314 | − | 2.04124i | −0.00198169 | − | 0.0978701i | ||||
\(436\) | 111.985 | 5.36312 | ||||||||
\(437\) | 8.38946i | 0.401322i | ||||||||
\(438\) | − | 9.90290i | − | 0.473179i | ||||||
\(439\) | 21.4648 | 1.02446 | 0.512229 | − | 0.858849i | \(-0.328820\pi\) | ||||
0.512229 | + | 0.858849i | \(0.328820\pi\) | |||||||
\(440\) | 0.440254 | + | 21.7430i | 0.0209883 | + | 1.03655i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 12.6445i | 0.601436i | ||||||||
\(443\) | − | 23.8247i | − | 1.13195i | −0.824424 | − | 0.565973i | \(-0.808501\pi\) | ||
0.824424 | − | 0.565973i | \(-0.191499\pi\) | |||||||
\(444\) | −18.0799 | −0.858032 | ||||||||
\(445\) | 12.5601 | − | 0.254319i | 0.595406 | − | 0.0120559i | ||||
\(446\) | 42.0064 | 1.98906 | ||||||||
\(447\) | 6.52258i | 0.308507i | ||||||||
\(448\) | − | 33.1726i | − | 1.56726i | ||||||
\(449\) | 13.3576 | 0.630383 | 0.315192 | − | 0.949028i | \(-0.397931\pi\) | ||||
0.315192 | + | 0.949028i | \(0.397931\pi\) | |||||||
\(450\) | −0.555824 | − | 13.7197i | −0.0262018 | − | 0.646752i | ||||
\(451\) | 11.5056 | 0.541778 | ||||||||
\(452\) | 0.515638i | 0.0242536i | ||||||||
\(453\) | 3.83724i | 0.180289i | ||||||||
\(454\) | −63.2124 | −2.96670 | ||||||||
\(455\) | 1.67279 | − | 0.0338709i | 0.0784217 | − | 0.00158789i | ||||
\(456\) | −13.9986 | −0.655543 | ||||||||
\(457\) | − | 36.4496i | − | 1.70504i | −0.522695 | − | 0.852520i | \(-0.675073\pi\) | ||
0.522695 | − | 0.852520i | \(-0.324927\pi\) | |||||||
\(458\) | − | 18.7670i | − | 0.876927i | ||||||
\(459\) | −6.15353 | −0.287222 | ||||||||
\(460\) | −1.46213 | − | 72.2104i | −0.0681720 | − | 3.36683i | ||||
\(461\) | 25.8103 | 1.20211 | 0.601053 | − | 0.799209i | \(-0.294748\pi\) | ||||
0.601053 | + | 0.799209i | \(0.294748\pi\) | |||||||
\(462\) | − | 2.74619i | − | 0.127764i | ||||||
\(463\) | 12.5698i | 0.584170i | 0.956392 | + | 0.292085i | \(0.0943489\pi\) | ||||
−0.956392 | + | 0.292085i | \(0.905651\pi\) | |||||||
\(464\) | 14.2671 | 0.662333 | ||||||||
\(465\) | −0.102290 | − | 5.05183i | −0.00474359 | − | 0.234273i | ||||
\(466\) | −49.3387 | −2.28557 | ||||||||
\(467\) | − | 26.1670i | − | 1.21087i | −0.795896 | − | 0.605433i | \(-0.793000\pi\) | ||
0.795896 | − | 0.605433i | \(-0.207000\pi\) | |||||||
\(468\) | − | 4.14645i | − | 0.191670i | ||||||
\(469\) | 6.69285 | 0.309047 | ||||||||
\(470\) | −51.7627 | + | 1.04810i | −2.38763 | + | 0.0483451i | ||||
\(471\) | −20.5461 | −0.946714 | ||||||||
\(472\) | − | 42.5629i | − | 1.95912i | ||||||
\(473\) | − | 9.99697i | − | 0.459661i | ||||||
\(474\) | 29.1867 | 1.34059 | ||||||||
\(475\) | 7.19076 | − | 0.291318i | 0.329935 | − | 0.0133666i | ||||
\(476\) | 34.1000 | 1.56297 | ||||||||
\(477\) | − | 5.64500i | − | 0.258467i | ||||||
\(478\) | 48.9117i | 2.23717i | ||||||||
\(479\) | −39.7023 | −1.81404 | −0.907022 | − | 0.421082i | \(-0.861650\pi\) | ||||
−0.907022 | + | 0.421082i | \(0.861650\pi\) | |||||||
\(480\) | 52.4460 | − | 1.06193i | 2.39382 | − | 0.0484704i | ||||
\(481\) | 2.44124 | 0.111311 | ||||||||
\(482\) | 28.8091i | 1.31222i | ||||||||
\(483\) | 5.82872i | 0.265216i | ||||||||
\(484\) | −5.54154 | −0.251888 | ||||||||
\(485\) | 0.634380 | + | 31.3303i | 0.0288057 | + | 1.42264i | ||||
\(486\) | 2.74619 | 0.124570 | ||||||||
\(487\) | 13.3271i | 0.603909i | 0.953322 | + | 0.301954i | \(0.0976391\pi\) | ||||
−0.953322 | + | 0.301954i | \(0.902361\pi\) | |||||||
\(488\) | 94.8568i | 4.29397i | ||||||||
\(489\) | 1.68575 | 0.0762321 | ||||||||
\(490\) | −0.124311 | − | 6.13940i | −0.00561582 | − | 0.277350i | ||||
\(491\) | 22.1471 | 0.999487 | 0.499743 | − | 0.866173i | \(-0.333428\pi\) | ||||
0.499743 | + | 0.866173i | \(0.333428\pi\) | |||||||
\(492\) | − | 63.7588i | − | 2.87447i | ||||||
\(493\) | 5.61853i | 0.253046i | ||||||||
\(494\) | 2.95758 | 0.133068 | ||||||||
\(495\) | 2.23561 | − | 0.0452669i | 0.100483 | − | 0.00203460i | ||||
\(496\) | 35.3093 | 1.58543 | ||||||||
\(497\) | 10.8314i | 0.485855i | ||||||||
\(498\) | − | 36.9206i | − | 1.65445i | ||||||
\(499\) | −15.4018 | −0.689479 | −0.344739 | − | 0.938698i | \(-0.612033\pi\) | ||||
−0.344739 | + | 0.938698i | \(0.612033\pi\) | |||||||
\(500\) | −61.8421 | + | 3.76067i | −2.76566 | + | 0.168182i | ||||
\(501\) | 14.1425 | 0.631841 | ||||||||
\(502\) | − | 14.0900i | − | 0.628869i | ||||||
\(503\) | 13.1271i | 0.585308i | 0.956218 | + | 0.292654i | \(0.0945384\pi\) | ||||
−0.956218 | + | 0.292654i | \(0.905462\pi\) | |||||||
\(504\) | −9.72574 | −0.433219 | ||||||||
\(505\) | −5.88473 | + | 0.119155i | −0.261867 | + | 0.00530232i | ||||
\(506\) | 16.0068 | 0.711587 | ||||||||
\(507\) | − | 12.4401i | − | 0.552485i | ||||||
\(508\) | 81.7646i | 3.62772i | ||||||||
\(509\) | −28.6739 | −1.27095 | −0.635475 | − | 0.772121i | \(-0.719196\pi\) | ||||
−0.635475 | + | 0.772121i | \(0.719196\pi\) | |||||||
\(510\) | 0.764954 | + | 37.7790i | 0.0338727 | + | 1.67288i | ||||
\(511\) | 3.60606 | 0.159523 | ||||||||
\(512\) | 62.6257i | 2.76769i | ||||||||
\(513\) | 1.43933i | 0.0635480i | ||||||||
\(514\) | 58.1553 | 2.56512 | ||||||||
\(515\) | −0.0413688 | − | 2.04309i | −0.00182293 | − | 0.0900293i | ||||
\(516\) | −55.3986 | −2.43879 | ||||||||
\(517\) | − | 8.43122i | − | 0.370805i | ||||||
\(518\) | − | 8.95972i | − | 0.393667i | ||||||
\(519\) | 13.3765 | 0.587164 | ||||||||
\(520\) | −16.2691 | + | 0.329420i | −0.713449 | + | 0.0144460i | ||||
\(521\) | 24.7030 | 1.08226 | 0.541128 | − | 0.840940i | \(-0.317997\pi\) | ||||
0.541128 | + | 0.840940i | \(0.317997\pi\) | |||||||
\(522\) | − | 2.50743i | − | 0.109747i | ||||||
\(523\) | − | 4.81571i | − | 0.210576i | −0.994442 | − | 0.105288i | \(-0.966423\pi\) | ||
0.994442 | − | 0.105288i | \(-0.0335765\pi\) | |||||||
\(524\) | −91.4395 | −3.99455 | ||||||||
\(525\) | 4.99590 | − | 0.202398i | 0.218039 | − | 0.00883339i | ||||
\(526\) | −4.35618 | −0.189939 | ||||||||
\(527\) | 13.9052i | 0.605719i | ||||||||
\(528\) | 15.6256i | 0.680017i | ||||||||
\(529\) | −10.9740 | −0.477130 | ||||||||
\(530\) | −34.6569 | + | 0.701738i | −1.50540 | + | 0.0304816i | ||||
\(531\) | −4.37632 | −0.189916 | ||||||||
\(532\) | − | 7.97612i | − | 0.345809i | ||||||
\(533\) | 8.60906i | 0.372900i | ||||||||
\(534\) | 15.4286 | 0.667662 | ||||||||
\(535\) | −0.547733 | − | 27.0510i | −0.0236805 | − | 1.16952i | ||||
\(536\) | −65.0929 | −2.81158 | ||||||||
\(537\) | − | 21.2621i | − | 0.917527i | ||||||
\(538\) | 9.96467i | 0.429608i | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −0.250849 | − | 12.3887i | −0.0107948 | − | 0.533126i | ||||
\(541\) | −21.8196 | −0.938096 | −0.469048 | − | 0.883173i | \(-0.655403\pi\) | ||||
−0.469048 | + | 0.883173i | \(0.655403\pi\) | |||||||
\(542\) | 22.4187i | 0.962966i | ||||||||
\(543\) | − | 10.6061i | − | 0.455153i | ||||||
\(544\) | −144.358 | −6.18929 | ||||||||
\(545\) | −45.1779 | + | 0.914769i | −1.93521 | + | 0.0391844i | ||||
\(546\) | 2.05483 | 0.0879387 | ||||||||
\(547\) | 6.70571i | 0.286715i | 0.989671 | + | 0.143358i | \(0.0457899\pi\) | ||||
−0.989671 | + | 0.143358i | \(0.954210\pi\) | |||||||
\(548\) | − | 111.612i | − | 4.76782i | ||||||
\(549\) | 9.75318 | 0.416255 | ||||||||
\(550\) | −0.555824 | − | 13.7197i | −0.0237004 | − | 0.585009i | ||||
\(551\) | 1.31419 | 0.0559866 | ||||||||
\(552\) | − | 56.6886i | − | 2.41283i | ||||||
\(553\) | 10.6281i | 0.451953i | ||||||||
\(554\) | −24.2364 | −1.02971 | ||||||||
\(555\) | 7.29391 | − | 0.147688i | 0.309609 | − | 0.00626901i | ||||
\(556\) | 9.99452 | 0.423862 | ||||||||
\(557\) | − | 17.9230i | − | 0.759421i | −0.925105 | − | 0.379710i | \(-0.876024\pi\) | ||
0.925105 | − | 0.379710i | \(-0.123976\pi\) | |||||||
\(558\) | − | 6.20558i | − | 0.262703i | ||||||
\(559\) | 7.48022 | 0.316380 | ||||||||
\(560\) | 0.707323 | + | 34.9328i | 0.0298899 | + | 1.47618i | ||||
\(561\) | −6.15353 | −0.259802 | ||||||||
\(562\) | 44.8829i | 1.89327i | ||||||||
\(563\) | − | 8.34113i | − | 0.351537i | −0.984432 | − | 0.175768i | \(-0.943759\pi\) | ||
0.984432 | − | 0.175768i | \(-0.0562409\pi\) | |||||||
\(564\) | −46.7220 | −1.96735 | ||||||||
\(565\) | −0.00421207 | − | 0.208023i | −0.000177203 | − | 0.00875158i | ||||
\(566\) | 31.9262 | 1.34196 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 105.343i | − | 4.42011i | ||||||
\(569\) | −33.2594 | −1.39431 | −0.697154 | − | 0.716922i | \(-0.745550\pi\) | ||||
−0.697154 | + | 0.716922i | \(0.745550\pi\) | |||||||
\(570\) | 8.83664 | − | 0.178925i | 0.370126 | − | 0.00749436i | ||||
\(571\) | −37.7037 | −1.57785 | −0.788926 | − | 0.614489i | \(-0.789362\pi\) | ||||
−0.788926 | + | 0.614489i | \(0.789362\pi\) | |||||||
\(572\) | − | 4.14645i | − | 0.173372i | ||||||
\(573\) | − | 0.660904i | − | 0.0276097i | ||||||
\(574\) | 31.5965 | 1.31881 | ||||||||
\(575\) | 1.17972 | + | 29.1197i | 0.0491979 | + | 1.21438i | ||||
\(576\) | 33.1726 | 1.38219 | ||||||||
\(577\) | − | 17.4572i | − | 0.726752i | −0.931643 | − | 0.363376i | \(-0.881624\pi\) | ||
0.931643 | − | 0.363376i | \(-0.118376\pi\) | |||||||
\(578\) | − | 57.3017i | − | 2.38344i | ||||||
\(579\) | 6.34668 | 0.263759 | ||||||||
\(580\) | −11.3116 | + | 0.229039i | −0.469690 | + | 0.00951035i | ||||
\(581\) | 13.4443 | 0.557765 | ||||||||
\(582\) | 38.4856i | 1.59528i | ||||||||
\(583\) | − | 5.64500i | − | 0.233792i | ||||||
\(584\) | −35.0716 | −1.45127 | ||||||||
\(585\) | 0.0338709 | + | 1.67279i | 0.00140039 | + | 0.0691615i | ||||
\(586\) | 24.0866 | 0.995008 | ||||||||
\(587\) | − | 14.2485i | − | 0.588100i | −0.955790 | − | 0.294050i | \(-0.904997\pi\) | ||
0.955790 | − | 0.294050i | \(-0.0950032\pi\) | |||||||
\(588\) | − | 5.54154i | − | 0.228529i | ||||||
\(589\) | 3.25247 | 0.134016 | ||||||||
\(590\) | 0.544027 | + | 26.8680i | 0.0223972 | + | 1.10614i | ||||
\(591\) | −12.6891 | −0.521959 | ||||||||
\(592\) | 50.9802i | 2.09527i | ||||||||
\(593\) | 32.3418i | 1.32812i | 0.747680 | + | 0.664059i | \(0.231168\pi\) | ||||
−0.747680 | + | 0.664059i | \(0.768832\pi\) | |||||||
\(594\) | 2.74619 | 0.112677 | ||||||||
\(595\) | −13.7569 | + | 0.278551i | −0.563977 | + | 0.0114195i | ||||
\(596\) | 36.1451 | 1.48056 | ||||||||
\(597\) | 7.00407i | 0.286657i | ||||||||
\(598\) | 11.9770i | 0.489778i | ||||||||
\(599\) | −16.0797 | −0.656998 | −0.328499 | − | 0.944504i | \(-0.606543\pi\) | ||||
−0.328499 | + | 0.944504i | \(0.606543\pi\) | |||||||
\(600\) | −48.5888 | + | 1.96847i | −1.98363 | + | 0.0803626i | ||||
\(601\) | 43.1542 | 1.76030 | 0.880149 | − | 0.474698i | \(-0.157443\pi\) | ||||
0.880149 | + | 0.474698i | \(0.157443\pi\) | |||||||
\(602\) | − | 27.4535i | − | 1.11892i | ||||||
\(603\) | 6.69285i | 0.272554i | ||||||||
\(604\) | 21.2642 | 0.865228 | ||||||||
\(605\) | 2.23561 | − | 0.0452669i | 0.0908905 | − | 0.00184036i | ||||
\(606\) | −7.22871 | −0.293646 | ||||||||
\(607\) | 2.85844i | 0.116020i | 0.998316 | + | 0.0580102i | \(0.0184756\pi\) | ||||
−0.998316 | + | 0.0580102i | \(0.981524\pi\) | |||||||
\(608\) | 33.7658i | 1.36938i | ||||||||
\(609\) | 0.913059 | 0.0369990 | ||||||||
\(610\) | −1.21243 | − | 59.8787i | −0.0490899 | − | 2.42442i | ||||
\(611\) | 6.30865 | 0.255221 | ||||||||
\(612\) | 34.1000i | 1.37841i | ||||||||
\(613\) | 36.8928i | 1.49009i | 0.667016 | + | 0.745043i | \(0.267571\pi\) | ||||
−0.667016 | + | 0.745043i | \(0.732429\pi\) | |||||||
\(614\) | 77.2263 | 3.11660 | ||||||||
\(615\) | 0.520823 | + | 25.7220i | 0.0210016 | + | 1.03721i | ||||
\(616\) | −9.72574 | −0.391861 | ||||||||
\(617\) | − | 12.9981i | − | 0.523285i | −0.965165 | − | 0.261642i | \(-0.915736\pi\) | ||
0.965165 | − | 0.261642i | \(-0.0842641\pi\) | |||||||
\(618\) | − | 2.50970i | − | 0.100955i | ||||||
\(619\) | −13.3094 | −0.534951 | −0.267475 | − | 0.963565i | \(-0.586189\pi\) | ||||
−0.267475 | + | 0.963565i | \(0.586189\pi\) | |||||||
\(620\) | −27.9949 | + | 0.566845i | −1.12430 | + | 0.0227650i | ||||
\(621\) | −5.82872 | −0.233899 | ||||||||
\(622\) | − | 20.6551i | − | 0.828193i | ||||||
\(623\) | 5.61820i | 0.225088i | ||||||||
\(624\) | −11.6918 | −0.468048 | ||||||||
\(625\) | 24.9181 | − | 2.02232i | 0.996723 | − | 0.0808930i | ||||
\(626\) | −27.9383 | −1.11664 | ||||||||
\(627\) | 1.43933i | 0.0574814i | ||||||||
\(628\) | 113.857i | 4.54339i | ||||||||
\(629\) | −20.0765 | −0.800503 | ||||||||
\(630\) | 6.13940 | − | 0.124311i | 0.244600 | − | 0.00495269i | ||||
\(631\) | 33.2052 | 1.32188 | 0.660939 | − | 0.750440i | \(-0.270158\pi\) | ||||
0.660939 | + | 0.750440i | \(0.270158\pi\) | |||||||
\(632\) | − | 103.366i | − | 4.11168i | ||||||
\(633\) | 24.9569i | 0.991949i | ||||||||
\(634\) | 5.41358 | 0.215001 | ||||||||
\(635\) | −0.667906 | − | 32.9861i | −0.0265050 | − | 1.30901i | ||||
\(636\) | −31.2820 | −1.24041 | ||||||||
\(637\) | 0.748249i | 0.0296467i | ||||||||
\(638\) | − | 2.50743i | − | 0.0992701i | ||||||
\(639\) | −10.8314 | −0.428484 | ||||||||
\(640\) | −1.99986 | − | 98.7679i | −0.0790516 | − | 3.90414i | ||||
\(641\) | 18.8363 | 0.743991 | 0.371996 | − | 0.928235i | \(-0.378674\pi\) | ||||
0.371996 | + | 0.928235i | \(0.378674\pi\) | |||||||
\(642\) | − | 33.2290i | − | 1.31145i | ||||||
\(643\) | − | 24.9394i | − | 0.983512i | −0.870733 | − | 0.491756i | \(-0.836355\pi\) | ||
0.870733 | − | 0.491756i | \(-0.163645\pi\) | |||||||
\(644\) | 32.3001 | 1.27280 | ||||||||
\(645\) | 22.3493 | − | 0.452532i | 0.880004 | − | 0.0178184i | ||||
\(646\) | −24.3229 | −0.956971 | ||||||||
\(647\) | − | 8.94306i | − | 0.351588i | −0.984427 | − | 0.175794i | \(-0.943751\pi\) | ||
0.984427 | − | 0.175794i | \(-0.0562493\pi\) | |||||||
\(648\) | − | 9.72574i | − | 0.382063i | ||||||
\(649\) | −4.37632 | −0.171786 | ||||||||
\(650\) | 10.2657 | − | 0.415895i | 0.402655 | − | 0.0163127i | ||||
\(651\) | 2.25971 | 0.0885649 | ||||||||
\(652\) | − | 9.34164i | − | 0.365847i | ||||||
\(653\) | 1.77376i | 0.0694126i | 0.999398 | + | 0.0347063i | \(0.0110496\pi\) | ||||
−0.999398 | + | 0.0347063i | \(0.988950\pi\) | |||||||
\(654\) | −55.4958 | −2.17006 | ||||||||
\(655\) | 36.8892 | − | 0.746937i | 1.44138 | − | 0.0291853i | ||||
\(656\) | −179.782 | −7.01931 | ||||||||
\(657\) | 3.60606i | 0.140686i | ||||||||
\(658\) | − | 23.1537i | − | 0.902626i | ||||||
\(659\) | 5.71183 | 0.222501 | 0.111251 | − | 0.993792i | \(-0.464514\pi\) | ||||
0.111251 | + | 0.993792i | \(0.464514\pi\) | |||||||
\(660\) | −0.250849 | − | 12.3887i | −0.00976427 | − | 0.482231i | ||||
\(661\) | −2.38412 | −0.0927315 | −0.0463657 | − | 0.998925i | \(-0.514764\pi\) | ||||
−0.0463657 | + | 0.998925i | \(0.514764\pi\) | |||||||
\(662\) | − | 53.7317i | − | 2.08834i | ||||||
\(663\) | − | 4.60437i | − | 0.178819i | ||||||
\(664\) | −130.756 | −5.07432 | ||||||||
\(665\) | 0.0651541 | + | 3.21778i | 0.00252657 | + | 0.124780i | ||||
\(666\) | 8.95972 | 0.347182 | ||||||||
\(667\) | 5.32197i | 0.206067i | ||||||||
\(668\) | − | 78.3713i | − | 3.03228i | ||||||
\(669\) | −15.2962 | −0.591387 | ||||||||
\(670\) | 41.0901 | − | 0.831997i | 1.58745 | − | 0.0321429i | ||||
\(671\) | 9.75318 | 0.376517 | ||||||||
\(672\) | 23.4594i | 0.904965i | ||||||||
\(673\) | 11.8632i | 0.457292i | 0.973510 | + | 0.228646i | \(0.0734298\pi\) | ||||
−0.973510 | + | 0.228646i | \(0.926570\pi\) | |||||||
\(674\) | −79.1013 | −3.04687 | ||||||||
\(675\) | 0.202398 | + | 4.99590i | 0.00779032 | + | 0.192292i | ||||
\(676\) | −68.9375 | −2.65144 | ||||||||
\(677\) | 7.00471i | 0.269213i | 0.990899 | + | 0.134606i | \(0.0429770\pi\) | ||||
−0.990899 | + | 0.134606i | \(0.957023\pi\) | |||||||
\(678\) | − | 0.255532i | − | 0.00981363i | ||||||
\(679\) | −14.0142 | −0.537816 | ||||||||
\(680\) | 133.796 | − | 2.70912i | 5.13084 | − | 0.103890i | ||||
\(681\) | 23.0182 | 0.882061 | ||||||||
\(682\) | − | 6.20558i | − | 0.237624i | ||||||
\(683\) | − | 13.4790i | − | 0.515759i | −0.966177 | − | 0.257879i | \(-0.916976\pi\) | ||
0.966177 | − | 0.257879i | \(-0.0830237\pi\) | |||||||
\(684\) | 7.97612 | 0.304974 | ||||||||
\(685\) | 0.911718 | + | 45.0273i | 0.0348350 | + | 1.72040i | ||||
\(686\) | 2.74619 | 0.104850 | ||||||||
\(687\) | 6.83386i | 0.260728i | ||||||||
\(688\) | 156.209i | 5.95540i | ||||||||
\(689\) | 4.22387 | 0.160917 | ||||||||
\(690\) | 0.724577 | + | 35.7849i | 0.0275842 | + | 1.36231i | ||||
\(691\) | 43.3563 | 1.64935 | 0.824676 | − | 0.565605i | \(-0.191357\pi\) | ||||
0.824676 | + | 0.565605i | \(0.191357\pi\) | |||||||
\(692\) | − | 74.1266i | − | 2.81787i | ||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | 58.0358 | 2.20301 | ||||||||
\(695\) | −4.03206 | + | 0.0816417i | −0.152945 | + | 0.00309685i | ||||
\(696\) | −8.88017 | −0.336602 | ||||||||
\(697\) | − | 70.8000i | − | 2.68174i | ||||||
\(698\) | 52.5430i | 1.98878i | ||||||||
\(699\) | 17.9663 | 0.679546 | ||||||||
\(700\) | −1.12160 | − | 27.6850i | −0.0423925 | − | 1.04639i | ||||
\(701\) | −49.3615 | −1.86436 | −0.932178 | − | 0.361999i | \(-0.882094\pi\) | ||||
−0.932178 | + | 0.361999i | \(0.882094\pi\) | |||||||
\(702\) | 2.05483i | 0.0775546i | ||||||||
\(703\) | 4.69597i | 0.177112i | ||||||||
\(704\) | 33.1726 | 1.25024 | ||||||||
\(705\) | 18.8489 | − | 0.381655i | 0.709891 | − | 0.0143740i | ||||
\(706\) | 84.3927 | 3.17616 | ||||||||
\(707\) | − | 2.63227i | − | 0.0989968i | ||||||
\(708\) | 24.2516i | 0.911430i | ||||||||
\(709\) | −39.2337 | −1.47345 | −0.736727 | − | 0.676190i | \(-0.763630\pi\) | ||||
−0.736727 | + | 0.676190i | \(0.763630\pi\) | |||||||
\(710\) | 1.34647 | + | 66.4984i | 0.0505321 | + | 2.49564i | ||||
\(711\) | −10.6281 | −0.398585 | ||||||||
\(712\) | − | 54.6411i | − | 2.04776i | ||||||
\(713\) | 13.1712i | 0.493266i | ||||||||
\(714\) | −16.8987 | −0.632419 | ||||||||
\(715\) | 0.0338709 | + | 1.67279i | 0.00126670 | + | 0.0625589i | ||||
\(716\) | −117.825 | −4.40332 | ||||||||
\(717\) | − | 17.8108i | − | 0.665155i | ||||||
\(718\) | 45.3674i | 1.69310i | ||||||||
\(719\) | 18.6722 | 0.696357 | 0.348178 | − | 0.937428i | \(-0.386800\pi\) | ||||
0.348178 | + | 0.937428i | \(0.386800\pi\) | |||||||
\(720\) | −34.9328 | + | 0.707323i | −1.30187 | + | 0.0263604i | ||||
\(721\) | 0.913885 | 0.0340349 | ||||||||
\(722\) | − | 46.4883i | − | 1.73012i | ||||||
\(723\) | − | 10.4906i | − | 0.390149i | ||||||
\(724\) | −58.7743 | −2.18433 | ||||||||
\(725\) | 4.56155 | − | 0.184802i | 0.169412 | − | 0.00686336i | ||||
\(726\) | 2.74619 | 0.101921 | ||||||||
\(727\) | − | 12.7687i | − | 0.473566i | −0.971563 | − | 0.236783i | \(-0.923907\pi\) | ||
0.971563 | − | 0.236783i | \(-0.0760931\pi\) | |||||||
\(728\) | − | 7.27727i | − | 0.269714i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 22.1390 | − | 0.448274i | 0.819402 | − | 0.0165914i | ||||
\(731\) | −61.5166 | −2.27527 | ||||||||
\(732\) | − | 54.0476i | − | 1.99766i | ||||||
\(733\) | − | 13.7757i | − | 0.508818i | −0.967097 | − | 0.254409i | \(-0.918119\pi\) | ||
0.967097 | − | 0.254409i | \(-0.0818810\pi\) | |||||||
\(734\) | 62.7590 | 2.31648 | ||||||||
\(735\) | 0.0452669 | + | 2.23561i | 0.00166970 | + | 0.0824617i | ||||
\(736\) | −136.738 | −5.04023 | ||||||||
\(737\) | 6.69285i | 0.246534i | ||||||||
\(738\) | 31.5965i | 1.16308i | ||||||||
\(739\) | −23.4848 | −0.863901 | −0.431951 | − | 0.901897i | \(-0.642175\pi\) | ||||
−0.431951 | + | 0.901897i | \(0.642175\pi\) | |||||||
\(740\) | −0.818419 | − | 40.4195i | −0.0300857 | − | 1.48585i | ||||
\(741\) | −1.07698 | −0.0395638 | ||||||||
\(742\) | − | 15.5022i | − | 0.569105i | ||||||
\(743\) | − | 15.1428i | − | 0.555536i | −0.960648 | − | 0.277768i | \(-0.910405\pi\) | ||
0.960648 | − | 0.277768i | \(-0.0895946\pi\) | |||||||
\(744\) | −21.9773 | −0.805728 | ||||||||
\(745\) | −14.5819 | + | 0.295257i | −0.534241 | + | 0.0108174i | ||||
\(746\) | 52.6896 | 1.92910 | ||||||||
\(747\) | 13.4443i | 0.491902i | ||||||||
\(748\) | 34.1000i | 1.24682i | ||||||||
\(749\) | 12.1001 | 0.442127 | ||||||||
\(750\) | 30.6467 | − | 1.86365i | 1.11906 | − | 0.0680510i | ||||
\(751\) | 22.7886 | 0.831569 | 0.415784 | − | 0.909463i | \(-0.363507\pi\) | ||||
0.415784 | + | 0.909463i | \(0.363507\pi\) | |||||||
\(752\) | 131.743i | 4.80417i | ||||||||
\(753\) | 5.13076i | 0.186975i | ||||||||
\(754\) | 1.87618 | 0.0683265 | ||||||||
\(755\) | −8.57856 | + | 0.173700i | −0.312206 | + | 0.00632159i | ||||
\(756\) | 5.54154 | 0.201544 | ||||||||
\(757\) | 15.8664i | 0.576675i | 0.957529 | + | 0.288338i | \(0.0931026\pi\) | ||||
−0.957529 | + | 0.288338i | \(0.906897\pi\) | |||||||
\(758\) | 83.6438i | 3.03808i | ||||||||
\(759\) | −5.82872 | −0.211569 | ||||||||
\(760\) | −0.633672 | − | 31.2953i | −0.0229857 | − | 1.13520i | ||||
\(761\) | 36.6802 | 1.32966 | 0.664829 | − | 0.746996i | \(-0.268504\pi\) | ||||
0.664829 | + | 0.746996i | \(0.268504\pi\) | |||||||
\(762\) | − | 40.5195i | − | 1.46787i | ||||||
\(763\) | − | 20.2083i | − | 0.731591i | ||||||
\(764\) | −3.66243 | −0.132502 | ||||||||
\(765\) | −0.278551 | − | 13.7569i | −0.0100710 | − | 0.497381i | ||||
\(766\) | −53.2605 | −1.92438 | ||||||||
\(767\) | − | 3.27458i | − | 0.118238i | ||||||
\(768\) | − | 54.9797i | − | 1.98391i | ||||||
\(769\) | −18.1791 | −0.655555 | −0.327778 | − | 0.944755i | \(-0.606300\pi\) | ||||
−0.327778 | + | 0.944755i | \(0.606300\pi\) | |||||||
\(770\) | 6.13940 | − | 0.124311i | 0.221249 | − | 0.00447987i | ||||
\(771\) | −21.1767 | −0.762662 | ||||||||
\(772\) | − | 35.1704i | − | 1.26581i | ||||||
\(773\) | 49.4475i | 1.77850i | 0.457418 | + | 0.889252i | \(0.348774\pi\) | ||||
−0.457418 | + | 0.889252i | \(0.651226\pi\) | |||||||
\(774\) | 27.4535 | 0.986797 | ||||||||
\(775\) | 11.2893 | − | 0.457361i | 0.405523 | − | 0.0164289i | ||||
\(776\) | 136.298 | 4.89283 | ||||||||
\(777\) | 3.26260i | 0.117045i | ||||||||
\(778\) | − | 82.5720i | − | 2.96035i | ||||||
\(779\) | −16.5604 | −0.593337 | ||||||||
\(780\) | 9.26985 | − | 0.187697i | 0.331914 | − | 0.00672064i | ||||
\(781\) | −10.8314 | −0.387578 | ||||||||
\(782\) | − | 98.4980i | − | 3.52228i | ||||||
\(783\) | 0.913059i | 0.0326301i | ||||||||
\(784\) | −15.6256 | −0.558057 | ||||||||
\(785\) | −0.930058 | − | 45.9330i | −0.0331952 | − | 1.63942i | ||||
\(786\) | 45.3141 | 1.61630 | ||||||||
\(787\) | 5.07894i | 0.181045i | 0.995894 | + | 0.0905224i | \(0.0288537\pi\) | ||||
−0.995894 | + | 0.0905224i | \(0.971146\pi\) | |||||||
\(788\) | 70.3170i | 2.50494i | ||||||||
\(789\) | 1.58627 | 0.0564726 | ||||||||
\(790\) | 1.32119 | + | 65.2502i | 0.0470060 | + | 2.32150i | ||||
\(791\) | 0.0930496 | 0.00330846 | ||||||||
\(792\) | − | 9.72574i | − | 0.345589i | ||||||
\(793\) | 7.29781i | 0.259153i | ||||||||
\(794\) | 69.5612 | 2.46863 | ||||||||
\(795\) | 12.6200 | − | 0.255532i | 0.447586 | − | 0.00906278i | ||||
\(796\) | 38.8133 | 1.37570 | ||||||||
\(797\) | 21.0140i | 0.744354i | 0.928162 | + | 0.372177i | \(0.121389\pi\) | ||||
−0.928162 | + | 0.372177i | \(0.878611\pi\) | |||||||
\(798\) | 3.95267i | 0.139923i | ||||||||
\(799\) | −51.8818 | −1.83544 | ||||||||
\(800\) | 4.74814 | + | 117.201i | 0.167872 | + | 4.14367i | ||||
\(801\) | −5.61820 | −0.198509 | ||||||||
\(802\) | 56.6672i | 2.00099i | ||||||||
\(803\) | 3.60606i | 0.127255i | ||||||||
\(804\) | 37.0887 | 1.30802 | ||||||||
\(805\) | −13.0307 | + | 0.263848i | −0.459273 | + | 0.00929943i | ||||
\(806\) | 4.64332 | 0.163554 | ||||||||
\(807\) | − | 3.62855i | − | 0.127731i | ||||||
\(808\) | 25.6008i | 0.900633i | ||||||||
\(809\) | −42.3417 | −1.48866 | −0.744328 | − | 0.667814i | \(-0.767230\pi\) | ||||
−0.744328 | + | 0.667814i | \(0.767230\pi\) | |||||||
\(810\) | 0.124311 | + | 6.13940i | 0.00436786 | + | 0.215717i | ||||
\(811\) | 8.26639 | 0.290272 | 0.145136 | − | 0.989412i | \(-0.453638\pi\) | ||||
0.145136 | + | 0.989412i | \(0.453638\pi\) | |||||||
\(812\) | − | 5.05975i | − | 0.177563i | ||||||
\(813\) | − | 8.16357i | − | 0.286309i | ||||||
\(814\) | 8.95972 | 0.314038 | ||||||||
\(815\) | 0.0763086 | + | 3.76867i | 0.00267297 | + | 0.132011i | ||||
\(816\) | 96.1526 | 3.36601 | ||||||||
\(817\) | 14.3890i | 0.503406i | ||||||||
\(818\) | − | 71.6090i | − | 2.50375i | ||||||
\(819\) | −0.748249 | −0.0261459 | ||||||||
\(820\) | 142.540 | − | 2.88616i | 4.97770 | − | 0.100789i | ||||
\(821\) | 12.6391 | 0.441107 | 0.220553 | − | 0.975375i | \(-0.429214\pi\) | ||||
0.220553 | + | 0.975375i | \(0.429214\pi\) | |||||||
\(822\) | 55.3108i | 1.92918i | ||||||||
\(823\) | 26.7117i | 0.931111i | 0.885019 | + | 0.465555i | \(0.154145\pi\) | ||||
−0.885019 | + | 0.465555i | \(0.845855\pi\) | |||||||
\(824\) | −8.88821 | −0.309635 | ||||||||
\(825\) | 0.202398 | + | 4.99590i | 0.00704661 | + | 0.173935i | ||||
\(826\) | −12.0182 | −0.418166 | ||||||||
\(827\) | 54.8572i | 1.90757i | 0.300486 | + | 0.953786i | \(0.402851\pi\) | ||||
−0.300486 | + | 0.953786i | \(0.597149\pi\) | |||||||
\(828\) | 32.3001i | 1.12251i | ||||||||
\(829\) | 22.6349 | 0.786144 | 0.393072 | − | 0.919508i | \(-0.371412\pi\) | ||||
0.393072 | + | 0.919508i | \(0.371412\pi\) | |||||||
\(830\) | 82.5402 | − | 1.67128i | 2.86501 | − | 0.0580111i | ||||
\(831\) | 8.82549 | 0.306153 | ||||||||
\(832\) | 24.8214i | 0.860526i | ||||||||
\(833\) | − | 6.15353i | − | 0.213207i | ||||||
\(834\) | −4.95292 | −0.171506 | ||||||||
\(835\) | 0.640188 | + | 31.6171i | 0.0221546 | + | 1.09416i | ||||
\(836\) | 7.97612 | 0.275860 | ||||||||
\(837\) | 2.25971i | 0.0781069i | ||||||||
\(838\) | 60.2061i | 2.07978i | ||||||||
\(839\) | 8.57558 | 0.296062 | 0.148031 | − | 0.988983i | \(-0.452706\pi\) | ||||
0.148031 | + | 0.988983i | \(0.452706\pi\) | |||||||
\(840\) | −0.440254 | − | 21.7430i | −0.0151902 | − | 0.750203i | ||||
\(841\) | −28.1663 | −0.971253 | ||||||||
\(842\) | − | 25.5459i | − | 0.880369i | ||||||
\(843\) | − | 16.3437i | − | 0.562908i | ||||||
\(844\) | 138.300 | 4.76048 | ||||||||
\(845\) | 27.8113 | − | 0.563126i | 0.956736 | − | 0.0193721i | ||||
\(846\) | 23.1537 | 0.796041 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 88.2066i | 3.02903i | ||||||||
\(849\) | −11.6256 | −0.398991 | ||||||||
\(850\) | −84.4244 | + | 3.42028i | −2.89573 | + | 0.117315i | ||||
\(851\) | −19.0168 | −0.651888 | ||||||||
\(852\) | 60.0227i | 2.05635i | ||||||||
\(853\) | − | 36.0856i | − | 1.23555i | −0.786356 | − | 0.617774i | \(-0.788035\pi\) | ||
0.786356 | − | 0.617774i | \(-0.211965\pi\) | |||||||
\(854\) | 26.7840 | 0.916531 | ||||||||
\(855\) | −3.21778 | + | 0.0651541i | −0.110046 | + | 0.00222822i | ||||
\(856\) | −117.682 | −4.02229 | ||||||||
\(857\) | − | 35.6459i | − | 1.21764i | −0.793308 | − | 0.608820i | \(-0.791643\pi\) | ||
0.793308 | − | 0.608820i | \(-0.208357\pi\) | |||||||
\(858\) | 2.05483i | 0.0701508i | ||||||||
\(859\) | −25.2433 | −0.861289 | −0.430644 | − | 0.902522i | \(-0.641714\pi\) | ||||
−0.430644 | + | 0.902522i | \(0.641714\pi\) | |||||||
\(860\) | −2.50773 | − | 123.850i | −0.0855127 | − | 4.22324i | ||||
\(861\) | −11.5056 | −0.392110 | ||||||||
\(862\) | 77.7034i | 2.64659i | ||||||||
\(863\) | − | 10.9658i | − | 0.373281i | −0.982428 | − | 0.186641i | \(-0.940240\pi\) | ||
0.982428 | − | 0.186641i | \(-0.0597600\pi\) | |||||||
\(864\) | −23.4594 | −0.798104 | ||||||||
\(865\) | 0.605514 | + | 29.9047i | 0.0205881 | + | 1.01679i | ||||
\(866\) | 32.8604 | 1.11664 | ||||||||
\(867\) | 20.8659i | 0.708643i | ||||||||
\(868\) | − | 12.5223i | − | 0.425033i | ||||||
\(869\) | −10.6281 | −0.360534 | ||||||||
\(870\) | 5.60563 | − | 0.113504i | 0.190049 | − | 0.00384813i | ||||
\(871\) | −5.00792 | −0.169687 | ||||||||
\(872\) | 196.541i | 6.65571i | ||||||||
\(873\) | − | 14.0142i | − | 0.474309i | ||||||
\(874\) | −23.0390 | −0.779307 | ||||||||
\(875\) | 0.678633 | + | 11.1597i | 0.0229420 | + | 0.377268i | ||||
\(876\) | 19.9831 | 0.675167 | ||||||||
\(877\) | − | 11.8214i | − | 0.399179i | −0.979880 | − | 0.199589i | \(-0.936039\pi\) | ||
0.979880 | − | 0.199589i | \(-0.0639608\pi\) | |||||||
\(878\) | 58.9463i | 1.98934i | ||||||||
\(879\) | −8.77092 | −0.295836 | ||||||||
\(880\) | −34.9328 | + | 0.707323i | −1.17758 | + | 0.0238439i | ||||
\(881\) | 0.829270 | 0.0279388 | 0.0139694 | − | 0.999902i | \(-0.495553\pi\) | ||||
0.0139694 | + | 0.999902i | \(0.495553\pi\) | |||||||
\(882\) | 2.74619i | 0.0924689i | ||||||||
\(883\) | 19.6106i | 0.659950i | 0.943990 | + | 0.329975i | \(0.107040\pi\) | ||||
−0.943990 | + | 0.329975i | \(0.892960\pi\) | |||||||
\(884\) | −25.5153 | −0.858173 | ||||||||
\(885\) | −0.198103 | − | 9.78375i | −0.00665915 | − | 0.328877i | ||||
\(886\) | 65.4271 | 2.19807 | ||||||||
\(887\) | − | 28.2995i | − | 0.950205i | −0.879930 | − | 0.475103i | \(-0.842411\pi\) | ||
0.879930 | − | 0.475103i | \(-0.157589\pi\) | |||||||
\(888\) | − | 31.7312i | − | 1.06483i | ||||||
\(889\) | 14.7548 | 0.494861 | ||||||||
\(890\) | 0.698406 | + | 34.4924i | 0.0234106 | + | 1.15619i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 84.7648i | 2.83814i | ||||||||
\(893\) | 12.1353i | 0.406093i | ||||||||
\(894\) | −17.9122 | −0.599074 | ||||||||
\(895\) | 47.5338 | − | 0.962470i | 1.58888 | − | 0.0321718i | ||||
\(896\) | 44.1794 | 1.47593 | ||||||||
\(897\) | − | 4.36134i | − | 0.145621i | ||||||
\(898\) | 36.6824i | 1.22411i | ||||||||
\(899\) | 2.06325 | 0.0688131 | ||||||||
\(900\) | 27.6850 | − | 1.12160i | 0.922833 | − | 0.0373866i | ||||
\(901\) | −34.7367 | −1.15725 | ||||||||
\(902\) | 31.5965i | 1.05205i | ||||||||
\(903\) | 9.99697i | 0.332678i | ||||||||
\(904\) | −0.904976 | −0.0300991 | ||||||||
\(905\) | 23.7112 | − | 0.480107i | 0.788186 | − | 0.0159593i | ||||
\(906\) | −10.5378 | −0.350094 | ||||||||
\(907\) | − | 0.464498i | − | 0.0154234i | −0.999970 | − | 0.00771170i | \(-0.997545\pi\) | ||
0.999970 | − | 0.00771170i | \(-0.00245473\pi\) | |||||||
\(908\) | − | 127.557i | − | 4.23311i | ||||||
\(909\) | 2.63227 | 0.0873070 | ||||||||
\(910\) | 0.0930159 | + | 4.59380i | 0.00308345 | + | 0.152283i | ||||
\(911\) | 3.65543 | 0.121110 | 0.0605549 | − | 0.998165i | \(-0.480713\pi\) | ||||
0.0605549 | + | 0.998165i | \(0.480713\pi\) | |||||||
\(912\) | − | 22.4904i | − | 0.744733i | ||||||
\(913\) | 13.4443i | 0.444942i | ||||||||
\(914\) | 100.097 | 3.31093 | ||||||||
\(915\) | 0.441496 | + | 21.8043i | 0.0145954 | + | 0.720828i | ||||
\(916\) | 37.8701 | 1.25126 | ||||||||
\(917\) | 16.5007i | 0.544902i | ||||||||
\(918\) | − | 16.8987i | − | 0.557741i | ||||||
\(919\) | −4.13390 | −0.136365 | −0.0681823 | − | 0.997673i | \(-0.521720\pi\) | ||||
−0.0681823 | + | 0.997673i | \(0.521720\pi\) | |||||||
\(920\) | 126.734 | − | 2.56612i | 4.17828 | − | 0.0846024i | ||||
\(921\) | −28.1213 | −0.926628 | ||||||||
\(922\) | 70.8799i | 2.33431i | ||||||||
\(923\) | − | 8.10460i | − | 0.266766i | ||||||
\(924\) | 5.54154 | 0.182303 | ||||||||
\(925\) | 0.660346 | + | 16.2996i | 0.0217120 | + | 0.535929i | ||||
\(926\) | −34.5191 | −1.13437 | ||||||||
\(927\) | 0.913885i | 0.0300159i | ||||||||
\(928\) | 21.4198i | 0.703139i | ||||||||
\(929\) | 11.8017 | 0.387202 | 0.193601 | − | 0.981080i | \(-0.437983\pi\) | ||||
0.193601 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(930\) | 13.8733 | − | 0.280908i | 0.454922 | − | 0.00921132i | ||||
\(931\) | −1.43933 | −0.0471722 | ||||||||
\(932\) | − | 99.5608i | − | 3.26122i | ||||||
\(933\) | 7.52137i | 0.246239i | ||||||||
\(934\) | 71.8596 | 2.35132 | ||||||||
\(935\) | −0.278551 | − | 13.7569i | −0.00910960 | − | 0.449898i | ||||
\(936\) | 7.27727 | 0.237865 | ||||||||
\(937\) | − | 17.1766i | − | 0.561136i | −0.959834 | − | 0.280568i | \(-0.909477\pi\) | ||
0.959834 | − | 0.280568i | \(-0.0905229\pi\) | |||||||
\(938\) | 18.3798i | 0.600122i | ||||||||
\(939\) | 10.1735 | 0.331999 | ||||||||
\(940\) | −2.11496 | − | 104.452i | −0.0689824 | − | 3.40685i | ||||
\(941\) | −9.65994 | −0.314905 | −0.157453 | − | 0.987527i | \(-0.550328\pi\) | ||||
−0.157453 | + | 0.987527i | \(0.550328\pi\) | |||||||
\(942\) | − | 56.4234i | − | 1.83837i | ||||||
\(943\) | − | 67.0630i | − | 2.18387i | ||||||
\(944\) | 68.3827 | 2.22567 | ||||||||
\(945\) | −2.23561 | + | 0.0452669i | −0.0727244 | + | 0.00147253i | ||||
\(946\) | 27.4535 | 0.892592 | ||||||||
\(947\) | 22.0118i | 0.715287i | 0.933858 | + | 0.357643i | \(0.116420\pi\) | ||||
−0.933858 | + | 0.357643i | \(0.883580\pi\) | |||||||
\(948\) | 58.8961i | 1.91285i | ||||||||
\(949\) | −2.69823 | −0.0875882 | ||||||||
\(950\) | 0.800015 | + | 19.7472i | 0.0259559 | + | 0.640683i | ||||
\(951\) | −1.97131 | −0.0639241 | ||||||||
\(952\) | 59.8476i | 1.93967i | ||||||||
\(953\) | 16.2420i | 0.526131i | 0.964778 | + | 0.263065i | \(0.0847335\pi\) | ||||
−0.964778 | + | 0.263065i | \(0.915267\pi\) | |||||||
\(954\) | 15.5022 | 0.501903 | ||||||||
\(955\) | 1.47752 | − | 0.0299171i | 0.0478115 | − | 0.000968094i | ||||
\(956\) | −98.6990 | −3.19215 | ||||||||
\(957\) | 0.913059i | 0.0295150i | ||||||||
\(958\) | − | 109.030i | − | 3.52260i | ||||||
\(959\) | −20.1409 | −0.650385 | ||||||||
\(960\) | 1.50162 | + | 74.1609i | 0.0484646 | + | 2.39353i | ||||
\(961\) | −25.8937 | −0.835281 | ||||||||
\(962\) | 6.70410i | 0.216149i | ||||||||
\(963\) | 12.1001i | 0.389919i | ||||||||
\(964\) | −58.1340 | −1.87237 | ||||||||
\(965\) | 0.287295 | + | 14.1887i | 0.00924835 | + | 0.456751i | ||||
\(966\) | −16.0068 | −0.515009 | ||||||||
\(967\) | 28.7859i | 0.925691i | 0.886439 | + | 0.462846i | \(0.153172\pi\) | ||||
−0.886439 | + | 0.462846i | \(0.846828\pi\) | |||||||
\(968\) | − | 9.72574i | − | 0.312597i | ||||||
\(969\) | 8.85697 | 0.284527 | ||||||||
\(970\) | −86.0389 | + | 1.74213i | −2.76254 | + | 0.0559363i | ||||
\(971\) | 28.6005 | 0.917833 | 0.458916 | − | 0.888479i | \(-0.348238\pi\) | ||||
0.458916 | + | 0.888479i | \(0.348238\pi\) | |||||||
\(972\) | 5.54154i | 0.177745i | ||||||||
\(973\) | − | 1.80356i | − | 0.0578196i | ||||||
\(974\) | −36.5987 | −1.17270 | ||||||||
\(975\) | −3.73818 | + | 0.151444i | −0.119718 | + | 0.00485010i | ||||
\(976\) | −152.399 | −4.87818 | ||||||||
\(977\) | 61.8504i | 1.97877i | 0.145322 | + | 0.989384i | \(0.453578\pi\) | ||||
−0.145322 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(978\) | 4.62938i | 0.148031i | ||||||||
\(979\) | −5.61820 | −0.179558 | ||||||||
\(980\) | 12.3887 | − | 0.250849i | 0.395743 | − | 0.00801306i | ||||
\(981\) | 20.2083 | 0.645202 | ||||||||
\(982\) | 60.8202i | 1.94085i | ||||||||
\(983\) | − | 7.66340i | − | 0.244425i | −0.992504 | − | 0.122212i | \(-0.961001\pi\) | ||
0.992504 | − | 0.122212i | \(-0.0389989\pi\) | |||||||
\(984\) | 111.900 | 3.56726 | ||||||||
\(985\) | −0.574395 | − | 28.3678i | −0.0183018 | − | 0.903874i | ||||
\(986\) | −15.4295 | −0.491377 | ||||||||
\(987\) | 8.43122i | 0.268369i | ||||||||
\(988\) | 5.96812i | 0.189871i | ||||||||
\(989\) | −58.2696 | −1.85286 | ||||||||
\(990\) | 0.124311 | + | 6.13940i | 0.00395088 | + | 0.195123i | ||||
\(991\) | 1.79343 | 0.0569703 | 0.0284851 | − | 0.999594i | \(-0.490932\pi\) | ||||
0.0284851 | + | 0.999594i | \(0.490932\pi\) | |||||||
\(992\) | 53.0113i | 1.68311i | ||||||||
\(993\) | 19.5659i | 0.620906i | ||||||||
\(994\) | −29.7451 | −0.943457 | ||||||||
\(995\) | −15.6584 | + | 0.317052i | −0.496403 | + | 0.0100512i | ||||
\(996\) | 74.5023 | 2.36070 | ||||||||
\(997\) | − | 24.0260i | − | 0.760911i | −0.924799 | − | 0.380456i | \(-0.875767\pi\) | ||
0.924799 | − | 0.380456i | \(-0.124233\pi\) | |||||||
\(998\) | − | 42.2962i | − | 1.33886i | ||||||
\(999\) | −3.26260 | −0.103224 |
(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 | 1155.2.c.e.694.20 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.cm.1.1 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cp.1.10 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.e.694.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.e.694.1 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.e.694.20 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cm.1.1 | 10 | 5.2 | odd | 4 | |||
5775.2.a.cp.1.10 | 10 | 5.3 | odd | 4 |