Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.29 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.4 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44691i | 1.73023i | 0.501575 | + | 0.865114i | \(0.332754\pi\) | ||||
−0.501575 | + | 0.865114i | \(0.667246\pi\) | |||||||
\(3\) | 2.35527 | 1.35981 | 0.679907 | − | 0.733298i | \(-0.262020\pi\) | ||||
0.679907 | + | 0.733298i | \(0.262020\pi\) | |||||||
\(4\) | −3.98738 | −1.99369 | ||||||||
\(5\) | 2.67528i | 1.19642i | 0.801339 | + | 0.598210i | \(0.204121\pi\) | ||||
−0.801339 | + | 0.598210i | \(0.795879\pi\) | |||||||
\(6\) | 5.76313i | 2.35279i | ||||||||
\(7\) | − | 0.955539i | − | 0.361160i | −0.983560 | − | 0.180580i | \(-0.942203\pi\) | ||
0.983560 | − | 0.180580i | \(-0.0577974\pi\) | |||||||
\(8\) | − | 4.86294i | − | 1.71931i | ||||||
\(9\) | 2.54728 | 0.849094 | ||||||||
\(10\) | −6.54617 | −2.07008 | ||||||||
\(11\) | − | 0.164829i | − | 0.0496979i | −0.999691 | − | 0.0248490i | \(-0.992090\pi\) | ||
0.999691 | − | 0.0248490i | \(-0.00791049\pi\) | |||||||
\(12\) | −9.39134 | −2.71105 | ||||||||
\(13\) | −0.630924 | + | 3.54992i | −0.174987 | + | 0.984571i | ||||
\(14\) | 2.33812 | 0.624889 | ||||||||
\(15\) | 6.30099i | 1.62691i | ||||||||
\(16\) | 3.92444 | 0.981110 | ||||||||
\(17\) | 0.846913 | 0.205407 | 0.102703 | − | 0.994712i | \(-0.467251\pi\) | ||||
0.102703 | + | 0.994712i | \(0.467251\pi\) | |||||||
\(18\) | 6.23297i | 1.46913i | ||||||||
\(19\) | − | 4.61345i | − | 1.05840i | −0.848498 | − | 0.529199i | \(-0.822493\pi\) | ||
0.848498 | − | 0.529199i | \(-0.177507\pi\) | |||||||
\(20\) | − | 10.6674i | − | 2.38529i | ||||||
\(21\) | − | 2.25055i | − | 0.491110i | ||||||
\(22\) | 0.403323 | 0.0859888 | ||||||||
\(23\) | 3.55282 | 0.740814 | 0.370407 | − | 0.928870i | \(-0.379218\pi\) | ||||
0.370407 | + | 0.928870i | \(0.379218\pi\) | |||||||
\(24\) | − | 11.4535i | − | 2.33794i | ||||||
\(25\) | −2.15711 | −0.431423 | ||||||||
\(26\) | −8.68634 | − | 1.54381i | −1.70353 | − | 0.302767i | ||||
\(27\) | −1.06627 | −0.205205 | ||||||||
\(28\) | 3.81010i | 0.720041i | ||||||||
\(29\) | 5.07494 | 0.942393 | 0.471197 | − | 0.882028i | \(-0.343822\pi\) | ||||
0.471197 | + | 0.882028i | \(0.343822\pi\) | |||||||
\(30\) | −15.4180 | −2.81492 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | − | 0.123131i | − | 0.0217667i | ||||||
\(33\) | − | 0.388217i | − | 0.0675799i | ||||||
\(34\) | 2.07232i | 0.355400i | ||||||||
\(35\) | 2.55633 | 0.432099 | ||||||||
\(36\) | −10.1570 | −1.69283 | ||||||||
\(37\) | 7.21115i | 1.18551i | 0.805384 | + | 0.592753i | \(0.201959\pi\) | ||||
−0.805384 | + | 0.592753i | \(0.798041\pi\) | |||||||
\(38\) | 11.2887 | 1.83127 | ||||||||
\(39\) | −1.48599 | + | 8.36101i | −0.237949 | + | 1.33883i | ||||
\(40\) | 13.0097 | 2.05702 | ||||||||
\(41\) | 0.599311i | 0.0935967i | 0.998904 | + | 0.0467984i | \(0.0149018\pi\) | ||||
−0.998904 | + | 0.0467984i | \(0.985098\pi\) | |||||||
\(42\) | 5.50690 | 0.849733 | ||||||||
\(43\) | −4.14544 | −0.632173 | −0.316087 | − | 0.948730i | \(-0.602369\pi\) | ||||
−0.316087 | + | 0.948730i | \(0.602369\pi\) | |||||||
\(44\) | 0.657238i | 0.0990823i | ||||||||
\(45\) | 6.81468i | 1.01587i | ||||||||
\(46\) | 8.69344i | 1.28178i | ||||||||
\(47\) | − | 11.9496i | − | 1.74303i | −0.490373 | − | 0.871513i | \(-0.663139\pi\) | ||
0.490373 | − | 0.871513i | \(-0.336861\pi\) | |||||||
\(48\) | 9.24310 | 1.33413 | ||||||||
\(49\) | 6.08695 | 0.869564 | ||||||||
\(50\) | − | 5.27827i | − | 0.746460i | ||||||
\(51\) | 1.99471 | 0.279315 | ||||||||
\(52\) | 2.51573 | − | 14.1549i | 0.348869 | − | 1.96293i | ||||
\(53\) | 9.33924 | 1.28284 | 0.641421 | − | 0.767189i | \(-0.278345\pi\) | ||||
0.641421 | + | 0.767189i | \(0.278345\pi\) | |||||||
\(54\) | − | 2.60908i | − | 0.355051i | ||||||
\(55\) | 0.440965 | 0.0594596 | ||||||||
\(56\) | −4.64673 | −0.620946 | ||||||||
\(57\) | − | 10.8659i | − | 1.43922i | ||||||
\(58\) | 12.4179i | 1.63056i | ||||||||
\(59\) | − | 7.75933i | − | 1.01018i | −0.863067 | − | 0.505089i | \(-0.831459\pi\) | ||
0.863067 | − | 0.505089i | \(-0.168541\pi\) | |||||||
\(60\) | − | 25.1245i | − | 3.24355i | ||||||
\(61\) | −6.21514 | −0.795768 | −0.397884 | − | 0.917436i | \(-0.630255\pi\) | ||||
−0.397884 | + | 0.917436i | \(0.630255\pi\) | |||||||
\(62\) | 2.44691 | 0.310758 | ||||||||
\(63\) | − | 2.43403i | − | 0.306658i | ||||||
\(64\) | 8.15017 | 1.01877 | ||||||||
\(65\) | −9.49702 | − | 1.68790i | −1.17796 | − | 0.209358i | ||||
\(66\) | 0.949934 | 0.116929 | ||||||||
\(67\) | − | 0.784589i | − | 0.0958528i | −0.998851 | − | 0.0479264i | \(-0.984739\pi\) | ||
0.998851 | − | 0.0479264i | \(-0.0152613\pi\) | |||||||
\(68\) | −3.37696 | −0.409517 | ||||||||
\(69\) | 8.36783 | 1.00737 | ||||||||
\(70\) | 6.25512i | 0.747630i | ||||||||
\(71\) | 2.65426i | 0.315002i | 0.987519 | + | 0.157501i | \(0.0503438\pi\) | ||||
−0.987519 | + | 0.157501i | \(0.949656\pi\) | |||||||
\(72\) | − | 12.3873i | − | 1.45986i | ||||||
\(73\) | − | 0.941589i | − | 0.110205i | −0.998481 | − | 0.0551023i | \(-0.982451\pi\) | ||
0.998481 | − | 0.0551023i | \(-0.0175485\pi\) | |||||||
\(74\) | −17.6451 | −2.05120 | ||||||||
\(75\) | −5.08058 | −0.586654 | ||||||||
\(76\) | 18.3956i | 2.11012i | ||||||||
\(77\) | −0.157501 | −0.0179489 | ||||||||
\(78\) | −20.4587 | − | 3.63610i | −2.31649 | − | 0.411707i | ||||
\(79\) | 10.0747 | 1.13349 | 0.566746 | − | 0.823893i | \(-0.308202\pi\) | ||||
0.566746 | + | 0.823893i | \(0.308202\pi\) | |||||||
\(80\) | 10.4990i | 1.17382i | ||||||||
\(81\) | −10.1532 | −1.12813 | ||||||||
\(82\) | −1.46646 | −0.161944 | ||||||||
\(83\) | − | 7.61624i | − | 0.835991i | −0.908449 | − | 0.417995i | \(-0.862733\pi\) | ||
0.908449 | − | 0.417995i | \(-0.137267\pi\) | |||||||
\(84\) | 8.97379i | 0.979121i | ||||||||
\(85\) | 2.26573i | 0.245753i | ||||||||
\(86\) | − | 10.1435i | − | 1.09380i | ||||||
\(87\) | 11.9528 | 1.28148 | ||||||||
\(88\) | −0.801556 | −0.0854462 | ||||||||
\(89\) | 17.3013i | 1.83394i | 0.398958 | + | 0.916969i | \(0.369372\pi\) | ||||
−0.398958 | + | 0.916969i | \(0.630628\pi\) | |||||||
\(90\) | −16.6749 | −1.75769 | ||||||||
\(91\) | 3.39209 | + | 0.602872i | 0.355587 | + | 0.0631982i | ||||
\(92\) | −14.1664 | −1.47695 | ||||||||
\(93\) | − | 2.35527i | − | 0.244230i | ||||||
\(94\) | 29.2396 | 3.01583 | ||||||||
\(95\) | 12.3423 | 1.26629 | ||||||||
\(96\) | − | 0.290007i | − | 0.0295987i | ||||||
\(97\) | 6.09051i | 0.618398i | 0.950997 | + | 0.309199i | \(0.100061\pi\) | ||||
−0.950997 | + | 0.309199i | \(0.899939\pi\) | |||||||
\(98\) | 14.8942i | 1.50454i | ||||||||
\(99\) | − | 0.419867i | − | 0.0421982i | ||||||
\(100\) | 8.60123 | 0.860123 | ||||||||
\(101\) | 19.4595 | 1.93629 | 0.968144 | − | 0.250394i | \(-0.0805601\pi\) | ||||
0.968144 | + | 0.250394i | \(0.0805601\pi\) | |||||||
\(102\) | 4.88087i | 0.483278i | ||||||||
\(103\) | −14.9051 | −1.46864 | −0.734322 | − | 0.678802i | \(-0.762500\pi\) | ||||
−0.734322 | + | 0.678802i | \(0.762500\pi\) | |||||||
\(104\) | 17.2631 | + | 3.06815i | 1.69278 | + | 0.300857i | ||||
\(105\) | 6.02084 | 0.587574 | ||||||||
\(106\) | 22.8523i | 2.21961i | ||||||||
\(107\) | −14.5314 | −1.40480 | −0.702400 | − | 0.711783i | \(-0.747888\pi\) | ||||
−0.702400 | + | 0.711783i | \(0.747888\pi\) | |||||||
\(108\) | 4.25164 | 0.409114 | ||||||||
\(109\) | 0.473449i | 0.0453482i | 0.999743 | + | 0.0226741i | \(0.00721801\pi\) | ||||
−0.999743 | + | 0.0226741i | \(0.992782\pi\) | |||||||
\(110\) | 1.07900i | 0.102879i | ||||||||
\(111\) | 16.9842i | 1.61207i | ||||||||
\(112\) | − | 3.74995i | − | 0.354337i | ||||||
\(113\) | −6.36649 | −0.598909 | −0.299455 | − | 0.954111i | \(-0.596805\pi\) | ||||
−0.299455 | + | 0.954111i | \(0.596805\pi\) | |||||||
\(114\) | 26.5879 | 2.49019 | ||||||||
\(115\) | 9.50478i | 0.886325i | ||||||||
\(116\) | −20.2357 | −1.87884 | ||||||||
\(117\) | −1.60714 | + | 9.04264i | −0.148580 | + | 0.835993i | ||||
\(118\) | 18.9864 | 1.74784 | ||||||||
\(119\) | − | 0.809258i | − | 0.0741846i | ||||||
\(120\) | 30.6414 | 2.79716 | ||||||||
\(121\) | 10.9728 | 0.997530 | ||||||||
\(122\) | − | 15.2079i | − | 1.37686i | ||||||
\(123\) | 1.41154i | 0.127274i | ||||||||
\(124\) | 3.98738i | 0.358077i | ||||||||
\(125\) | 7.60551i | 0.680258i | ||||||||
\(126\) | 5.95585 | 0.530589 | ||||||||
\(127\) | −21.1327 | −1.87522 | −0.937611 | − | 0.347687i | \(-0.886967\pi\) | ||||
−0.937611 | + | 0.347687i | \(0.886967\pi\) | |||||||
\(128\) | 19.6965i | 1.74094i | ||||||||
\(129\) | −9.76361 | −0.859638 | ||||||||
\(130\) | 4.13013 | − | 23.2384i | 0.362237 | − | 2.03814i | ||||
\(131\) | −12.9701 | −1.13320 | −0.566601 | − | 0.823992i | \(-0.691742\pi\) | ||||
−0.566601 | + | 0.823992i | \(0.691742\pi\) | |||||||
\(132\) | 1.54797i | 0.134733i | ||||||||
\(133\) | −4.40833 | −0.382251 | ||||||||
\(134\) | 1.91982 | 0.165847 | ||||||||
\(135\) | − | 2.85258i | − | 0.245511i | ||||||
\(136\) | − | 4.11849i | − | 0.353158i | ||||||
\(137\) | − | 19.3568i | − | 1.65376i | −0.562379 | − | 0.826880i | \(-0.690114\pi\) | ||
0.562379 | − | 0.826880i | \(-0.309886\pi\) | |||||||
\(138\) | 20.4754i | 1.74298i | ||||||||
\(139\) | −0.820777 | −0.0696174 | −0.0348087 | − | 0.999394i | \(-0.511082\pi\) | ||||
−0.0348087 | + | 0.999394i | \(0.511082\pi\) | |||||||
\(140\) | −10.1931 | −0.861472 | ||||||||
\(141\) | − | 28.1445i | − | 2.37019i | ||||||
\(142\) | −6.49473 | −0.545026 | ||||||||
\(143\) | 0.585131 | + | 0.103995i | 0.0489311 | + | 0.00869648i | ||||
\(144\) | 9.99665 | 0.833054 | ||||||||
\(145\) | 13.5769i | 1.12750i | ||||||||
\(146\) | 2.30399 | 0.190679 | ||||||||
\(147\) | 14.3364 | 1.18244 | ||||||||
\(148\) | − | 28.7536i | − | 2.36353i | ||||||
\(149\) | − | 10.4194i | − | 0.853589i | −0.904349 | − | 0.426795i | \(-0.859643\pi\) | ||
0.904349 | − | 0.426795i | \(-0.140357\pi\) | |||||||
\(150\) | − | 12.4317i | − | 1.01505i | ||||||
\(151\) | − | 1.28956i | − | 0.104943i | −0.998622 | − | 0.0524713i | \(-0.983290\pi\) | ||
0.998622 | − | 0.0524713i | \(-0.0167098\pi\) | |||||||
\(152\) | −22.4349 | −1.81971 | ||||||||
\(153\) | 2.15732 | 0.174409 | ||||||||
\(154\) | − | 0.385391i | − | 0.0310557i | ||||||
\(155\) | 2.67528 | 0.214884 | ||||||||
\(156\) | 5.92522 | − | 33.3385i | 0.474397 | − | 2.66922i | ||||
\(157\) | 3.21524 | 0.256604 | 0.128302 | − | 0.991735i | \(-0.459047\pi\) | ||||
0.128302 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(158\) | 24.6519i | 1.96120i | ||||||||
\(159\) | 21.9964 | 1.74443 | ||||||||
\(160\) | 0.329410 | 0.0260422 | ||||||||
\(161\) | − | 3.39486i | − | 0.267552i | ||||||
\(162\) | − | 24.8440i | − | 1.95193i | ||||||
\(163\) | 3.97579i | 0.311408i | 0.987804 | + | 0.155704i | \(0.0497646\pi\) | ||||
−0.987804 | + | 0.155704i | \(0.950235\pi\) | |||||||
\(164\) | − | 2.38968i | − | 0.186603i | ||||||
\(165\) | 1.03859 | 0.0808541 | ||||||||
\(166\) | 18.6363 | 1.44646 | ||||||||
\(167\) | − | 14.6209i | − | 1.13140i | −0.824612 | − | 0.565699i | \(-0.808606\pi\) | ||
0.824612 | − | 0.565699i | \(-0.191394\pi\) | |||||||
\(168\) | −10.9443 | −0.844371 | ||||||||
\(169\) | −12.2039 | − | 4.47946i | −0.938759 | − | 0.344574i | ||||
\(170\) | −5.54404 | −0.425208 | ||||||||
\(171\) | − | 11.7517i | − | 0.898679i | ||||||
\(172\) | 16.5294 | 1.26036 | ||||||||
\(173\) | 2.37223 | 0.180357 | 0.0901787 | − | 0.995926i | \(-0.471256\pi\) | ||||
0.0901787 | + | 0.995926i | \(0.471256\pi\) | |||||||
\(174\) | 29.2476i | 2.21725i | ||||||||
\(175\) | 2.06121i | 0.155812i | ||||||||
\(176\) | − | 0.646863i | − | 0.0487591i | ||||||
\(177\) | − | 18.2753i | − | 1.37366i | ||||||
\(178\) | −42.3349 | −3.17313 | ||||||||
\(179\) | 7.91369 | 0.591497 | 0.295749 | − | 0.955266i | \(-0.404431\pi\) | ||||
0.295749 | + | 0.955266i | \(0.404431\pi\) | |||||||
\(180\) | − | 27.1727i | − | 2.02534i | ||||||
\(181\) | −13.0489 | −0.969919 | −0.484960 | − | 0.874537i | \(-0.661166\pi\) | ||||
−0.484960 | + | 0.874537i | \(0.661166\pi\) | |||||||
\(182\) | −1.47518 | + | 8.30014i | −0.109347 | + | 0.615247i | ||||
\(183\) | −14.6383 | −1.08210 | ||||||||
\(184\) | − | 17.2772i | − | 1.27369i | ||||||
\(185\) | −19.2918 | −1.41836 | ||||||||
\(186\) | 5.76313 | 0.422573 | ||||||||
\(187\) | − | 0.139596i | − | 0.0102083i | ||||||
\(188\) | 47.6475i | 3.47505i | ||||||||
\(189\) | 1.01887i | 0.0741117i | ||||||||
\(190\) | 30.2004i | 2.19097i | ||||||||
\(191\) | −9.81737 | −0.710360 | −0.355180 | − | 0.934798i | \(-0.615580\pi\) | ||||
−0.355180 | + | 0.934798i | \(0.615580\pi\) | |||||||
\(192\) | 19.1958 | 1.38534 | ||||||||
\(193\) | − | 19.9690i | − | 1.43740i | −0.695321 | − | 0.718699i | \(-0.744738\pi\) | ||
0.695321 | − | 0.718699i | \(-0.255262\pi\) | |||||||
\(194\) | −14.9030 | −1.06997 | ||||||||
\(195\) | −22.3680 | − | 3.97545i | −1.60181 | − | 0.284688i | ||||
\(196\) | −24.2710 | −1.73364 | ||||||||
\(197\) | 16.5253i | 1.17738i | 0.808359 | + | 0.588689i | \(0.200356\pi\) | ||||
−0.808359 | + | 0.588689i | \(0.799644\pi\) | |||||||
\(198\) | 1.02738 | 0.0730125 | ||||||||
\(199\) | 20.6068 | 1.46078 | 0.730388 | − | 0.683032i | \(-0.239339\pi\) | ||||
0.730388 | + | 0.683032i | \(0.239339\pi\) | |||||||
\(200\) | 10.4899i | 0.741749i | ||||||||
\(201\) | − | 1.84792i | − | 0.130342i | ||||||
\(202\) | 47.6156i | 3.35022i | ||||||||
\(203\) | − | 4.84930i | − | 0.340354i | ||||||
\(204\) | −7.95365 | −0.556867 | ||||||||
\(205\) | −1.60332 | −0.111981 | ||||||||
\(206\) | − | 36.4715i | − | 2.54109i | ||||||
\(207\) | 9.05003 | 0.629020 | ||||||||
\(208\) | −2.47602 | + | 13.9314i | −0.171681 | + | 0.965972i | ||||
\(209\) | −0.760432 | −0.0526002 | ||||||||
\(210\) | 14.7325i | 1.01664i | ||||||||
\(211\) | −20.3309 | −1.39964 | −0.699819 | − | 0.714320i | \(-0.746736\pi\) | ||||
−0.699819 | + | 0.714320i | \(0.746736\pi\) | |||||||
\(212\) | −37.2391 | −2.55759 | ||||||||
\(213\) | 6.25148i | 0.428344i | ||||||||
\(214\) | − | 35.5570i | − | 2.43062i | ||||||
\(215\) | − | 11.0902i | − | 0.756345i | ||||||
\(216\) | 5.18523i | 0.352810i | ||||||||
\(217\) | −0.955539 | −0.0648662 | ||||||||
\(218\) | −1.15849 | −0.0784627 | ||||||||
\(219\) | − | 2.21769i | − | 0.149858i | ||||||
\(220\) | −1.75829 | −0.118544 | ||||||||
\(221\) | −0.534337 | + | 3.00647i | −0.0359434 | + | 0.202237i | ||||
\(222\) | −41.5588 | −2.78924 | ||||||||
\(223\) | − | 3.70952i | − | 0.248408i | −0.992257 | − | 0.124204i | \(-0.960362\pi\) | ||
0.992257 | − | 0.124204i | \(-0.0396377\pi\) | |||||||
\(224\) | −0.117657 | −0.00786127 | ||||||||
\(225\) | −5.49477 | −0.366318 | ||||||||
\(226\) | − | 15.5782i | − | 1.03625i | ||||||
\(227\) | 13.1733i | 0.874340i | 0.899379 | + | 0.437170i | \(0.144019\pi\) | ||||
−0.899379 | + | 0.437170i | \(0.855981\pi\) | |||||||
\(228\) | 43.3265i | 2.86937i | ||||||||
\(229\) | − | 19.1936i | − | 1.26835i | −0.773191 | − | 0.634173i | \(-0.781341\pi\) | ||
0.773191 | − | 0.634173i | \(-0.218659\pi\) | |||||||
\(230\) | −23.2574 | −1.53354 | ||||||||
\(231\) | −0.370957 | −0.0244072 | ||||||||
\(232\) | − | 24.6792i | − | 1.62027i | ||||||
\(233\) | −1.99780 | −0.130880 | −0.0654401 | − | 0.997856i | \(-0.520845\pi\) | ||||
−0.0654401 | + | 0.997856i | \(0.520845\pi\) | |||||||
\(234\) | −22.1266 | − | 3.93253i | −1.44646 | − | 0.257078i | ||||
\(235\) | 31.9685 | 2.08539 | ||||||||
\(236\) | 30.9394i | 2.01398i | ||||||||
\(237\) | 23.7286 | 1.54134 | ||||||||
\(238\) | 1.98018 | 0.128356 | ||||||||
\(239\) | − | 12.1146i | − | 0.783631i | −0.920044 | − | 0.391816i | \(-0.871847\pi\) | ||
0.920044 | − | 0.391816i | \(-0.128153\pi\) | |||||||
\(240\) | 24.7279i | 1.59618i | ||||||||
\(241\) | − | 16.0688i | − | 1.03509i | −0.855657 | − | 0.517543i | \(-0.826847\pi\) | ||
0.855657 | − | 0.517543i | \(-0.173153\pi\) | |||||||
\(242\) | 26.8496i | 1.72595i | ||||||||
\(243\) | −20.7147 | −1.32885 | ||||||||
\(244\) | 24.7821 | 1.58651 | ||||||||
\(245\) | 16.2843i | 1.04036i | ||||||||
\(246\) | −3.45391 | −0.220213 | ||||||||
\(247\) | 16.3774 | + | 2.91073i | 1.04207 | + | 0.185206i | ||||
\(248\) | −4.86294 | −0.308797 | ||||||||
\(249\) | − | 17.9383i | − | 1.13679i | ||||||
\(250\) | −18.6100 | −1.17700 | ||||||||
\(251\) | 18.8448 | 1.18947 | 0.594737 | − | 0.803921i | \(-0.297256\pi\) | ||||
0.594737 | + | 0.803921i | \(0.297256\pi\) | |||||||
\(252\) | 9.70539i | 0.611382i | ||||||||
\(253\) | − | 0.585609i | − | 0.0368169i | ||||||
\(254\) | − | 51.7098i | − | 3.24456i | ||||||
\(255\) | 5.33639i | 0.334178i | ||||||||
\(256\) | −31.8952 | −1.99345 | ||||||||
\(257\) | −28.0808 | −1.75163 | −0.875816 | − | 0.482645i | \(-0.839676\pi\) | ||||
−0.875816 | + | 0.482645i | \(0.839676\pi\) | |||||||
\(258\) | − | 23.8907i | − | 1.48737i | ||||||
\(259\) | 6.89054 | 0.428157 | ||||||||
\(260\) | 37.8682 | + | 6.73028i | 2.34849 | + | 0.417394i | ||||
\(261\) | 12.9273 | 0.800180 | ||||||||
\(262\) | − | 31.7367i | − | 1.96070i | ||||||
\(263\) | 21.4892 | 1.32508 | 0.662540 | − | 0.749026i | \(-0.269478\pi\) | ||||
0.662540 | + | 0.749026i | \(0.269478\pi\) | |||||||
\(264\) | −1.88788 | −0.116191 | ||||||||
\(265\) | 24.9851i | 1.53482i | ||||||||
\(266\) | − | 10.7868i | − | 0.661381i | ||||||
\(267\) | 40.7493i | 2.49381i | ||||||||
\(268\) | 3.12845i | 0.191101i | ||||||||
\(269\) | −22.7854 | −1.38925 | −0.694626 | − | 0.719371i | \(-0.744430\pi\) | ||||
−0.694626 | + | 0.719371i | \(0.744430\pi\) | |||||||
\(270\) | 6.98002 | 0.424790 | ||||||||
\(271\) | − | 22.7290i | − | 1.38069i | −0.723480 | − | 0.690345i | \(-0.757459\pi\) | ||
0.723480 | − | 0.690345i | \(-0.242541\pi\) | |||||||
\(272\) | 3.32366 | 0.201526 | ||||||||
\(273\) | 7.98927 | + | 1.41992i | 0.483533 | + | 0.0859377i | ||||
\(274\) | 47.3643 | 2.86138 | ||||||||
\(275\) | 0.355556i | 0.0214408i | ||||||||
\(276\) | −33.3657 | −2.00838 | ||||||||
\(277\) | −1.05029 | −0.0631057 | −0.0315529 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315529 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(278\) | − | 2.00837i | − | 0.120454i | ||||||
\(279\) | − | 2.54728i | − | 0.152502i | ||||||
\(280\) | − | 12.4313i | − | 0.742912i | ||||||
\(281\) | − | 5.80404i | − | 0.346240i | −0.984901 | − | 0.173120i | \(-0.944615\pi\) | ||
0.984901 | − | 0.173120i | \(-0.0553849\pi\) | |||||||
\(282\) | 68.8670 | 4.10097 | ||||||||
\(283\) | −16.0917 | −0.956551 | −0.478275 | − | 0.878210i | \(-0.658738\pi\) | ||||
−0.478275 | + | 0.878210i | \(0.658738\pi\) | |||||||
\(284\) | − | 10.5835i | − | 0.628017i | ||||||
\(285\) | 29.0693 | 1.72192 | ||||||||
\(286\) | −0.254466 | + | 1.43177i | −0.0150469 | + | 0.0846620i | ||||
\(287\) | 0.572665 | 0.0338034 | ||||||||
\(288\) | − | 0.313650i | − | 0.0184820i | ||||||
\(289\) | −16.2827 | −0.957808 | ||||||||
\(290\) | −33.2214 | −1.95083 | ||||||||
\(291\) | 14.3448i | 0.840906i | ||||||||
\(292\) | 3.75447i | 0.219714i | ||||||||
\(293\) | − | 19.3398i | − | 1.12984i | −0.825145 | − | 0.564922i | \(-0.808906\pi\) | ||
0.825145 | − | 0.564922i | \(-0.191094\pi\) | |||||||
\(294\) | 35.0799i | 2.04590i | ||||||||
\(295\) | 20.7584 | 1.20860 | ||||||||
\(296\) | 35.0674 | 2.03825 | ||||||||
\(297\) | 0.175753i | 0.0101982i | ||||||||
\(298\) | 25.4953 | 1.47690 | ||||||||
\(299\) | −2.24156 | + | 12.6122i | −0.129633 | + | 0.729384i | ||||
\(300\) | 20.2582 | 1.16961 | ||||||||
\(301\) | 3.96113i | 0.228316i | ||||||||
\(302\) | 3.15543 | 0.181575 | ||||||||
\(303\) | 45.8322 | 2.63299 | ||||||||
\(304\) | − | 18.1052i | − | 1.03840i | ||||||
\(305\) | − | 16.6272i | − | 0.952073i | ||||||
\(306\) | 5.27878i | 0.301768i | ||||||||
\(307\) | 15.2126i | 0.868227i | 0.900858 | + | 0.434113i | \(0.142938\pi\) | ||||
−0.900858 | + | 0.434113i | \(0.857062\pi\) | |||||||
\(308\) | 0.628016 | 0.0357845 | ||||||||
\(309\) | −35.1055 | −1.99708 | ||||||||
\(310\) | 6.54617i | 0.371798i | ||||||||
\(311\) | −2.16175 | −0.122582 | −0.0612908 | − | 0.998120i | \(-0.519522\pi\) | ||||
−0.0612908 | + | 0.998120i | \(0.519522\pi\) | |||||||
\(312\) | 40.6591 | + | 7.22630i | 2.30187 | + | 0.409109i | ||||
\(313\) | 13.3466 | 0.754396 | 0.377198 | − | 0.926133i | \(-0.376888\pi\) | ||||
0.377198 | + | 0.926133i | \(0.376888\pi\) | |||||||
\(314\) | 7.86740i | 0.443983i | ||||||||
\(315\) | 6.51170 | 0.366893 | ||||||||
\(316\) | −40.1716 | −2.25983 | ||||||||
\(317\) | 30.2692i | 1.70009i | 0.526714 | + | 0.850043i | \(0.323424\pi\) | ||||
−0.526714 | + | 0.850043i | \(0.676576\pi\) | |||||||
\(318\) | 53.8232i | 3.01826i | ||||||||
\(319\) | − | 0.836500i | − | 0.0468350i | ||||||
\(320\) | 21.8040i | 1.21888i | ||||||||
\(321\) | −34.2252 | −1.91027 | ||||||||
\(322\) | 8.30692 | 0.462926 | ||||||||
\(323\) | − | 3.90719i | − | 0.217402i | ||||||
\(324\) | 40.4847 | 2.24915 | ||||||||
\(325\) | 1.36097 | − | 7.65758i | 0.0754932 | − | 0.424766i | ||||
\(326\) | −9.72842 | −0.538807 | ||||||||
\(327\) | 1.11510i | 0.0616651i | ||||||||
\(328\) | 2.91442 | 0.160922 | ||||||||
\(329\) | −11.4183 | −0.629511 | ||||||||
\(330\) | 2.54134i | 0.139896i | ||||||||
\(331\) | 7.60712i | 0.418125i | 0.977902 | + | 0.209063i | \(0.0670412\pi\) | ||||
−0.977902 | + | 0.209063i | \(0.932959\pi\) | |||||||
\(332\) | 30.3688i | 1.66671i | ||||||||
\(333\) | 18.3688i | 1.00661i | ||||||||
\(334\) | 35.7760 | 1.95758 | ||||||||
\(335\) | 2.09899 | 0.114680 | ||||||||
\(336\) | − | 8.83214i | − | 0.481833i | ||||||
\(337\) | −13.7524 | −0.749139 | −0.374569 | − | 0.927199i | \(-0.622209\pi\) | ||||
−0.374569 | + | 0.927199i | \(0.622209\pi\) | |||||||
\(338\) | 10.9608 | − | 29.8618i | 0.596191 | − | 1.62427i | ||||
\(339\) | −14.9948 | −0.814405 | ||||||||
\(340\) | − | 9.03432i | − | 0.489955i | ||||||
\(341\) | −0.164829 | −0.00892601 | ||||||||
\(342\) | 28.7555 | 1.55492 | ||||||||
\(343\) | − | 12.5051i | − | 0.675211i | ||||||
\(344\) | 20.1590i | 1.08690i | ||||||||
\(345\) | 22.3863i | 1.20524i | ||||||||
\(346\) | 5.80464i | 0.312060i | ||||||||
\(347\) | −14.5798 | −0.782687 | −0.391344 | − | 0.920245i | \(-0.627990\pi\) | ||||
−0.391344 | + | 0.920245i | \(0.627990\pi\) | |||||||
\(348\) | −47.6605 | −2.55487 | ||||||||
\(349\) | 13.7796i | 0.737606i | 0.929508 | + | 0.368803i | \(0.120232\pi\) | ||||
−0.929508 | + | 0.368803i | \(0.879768\pi\) | |||||||
\(350\) | −5.04359 | −0.269591 | ||||||||
\(351\) | 0.672738 | − | 3.78519i | 0.0359081 | − | 0.202038i | ||||
\(352\) | −0.0202957 | −0.00108176 | ||||||||
\(353\) | − | 13.5153i | − | 0.719348i | −0.933078 | − | 0.359674i | \(-0.882888\pi\) | ||
0.933078 | − | 0.359674i | \(-0.117112\pi\) | |||||||
\(354\) | 44.7180 | 2.37674 | ||||||||
\(355\) | −7.10087 | −0.376875 | ||||||||
\(356\) | − | 68.9870i | − | 3.65630i | ||||||
\(357\) | − | 1.90602i | − | 0.100877i | ||||||
\(358\) | 19.3641i | 1.02343i | ||||||||
\(359\) | 15.0739i | 0.795569i | 0.917479 | + | 0.397784i | \(0.130221\pi\) | ||||
−0.917479 | + | 0.397784i | \(0.869779\pi\) | |||||||
\(360\) | 33.1394 | 1.74660 | ||||||||
\(361\) | −2.28390 | −0.120205 | ||||||||
\(362\) | − | 31.9296i | − | 1.67818i | ||||||
\(363\) | 25.8439 | 1.35646 | ||||||||
\(364\) | −13.5255 | − | 2.40388i | −0.708931 | − | 0.125998i | ||||
\(365\) | 2.51901 | 0.131851 | ||||||||
\(366\) | − | 35.8187i | − | 1.87227i | ||||||
\(367\) | −18.5321 | −0.967367 | −0.483684 | − | 0.875243i | \(-0.660701\pi\) | ||||
−0.483684 | + | 0.875243i | \(0.660701\pi\) | |||||||
\(368\) | 13.9428 | 0.726820 | ||||||||
\(369\) | 1.52661i | 0.0794724i | ||||||||
\(370\) | − | 47.2054i | − | 2.45409i | ||||||
\(371\) | − | 8.92400i | − | 0.463311i | ||||||
\(372\) | 9.39134i | 0.486918i | ||||||||
\(373\) | 13.1741 | 0.682129 | 0.341065 | − | 0.940040i | \(-0.389212\pi\) | ||||
0.341065 | + | 0.940040i | \(0.389212\pi\) | |||||||
\(374\) | 0.341580 | 0.0176627 | ||||||||
\(375\) | 17.9130i | 0.925024i | ||||||||
\(376\) | −58.1102 | −2.99680 | ||||||||
\(377\) | −3.20190 | + | 18.0156i | −0.164906 | + | 0.927853i | ||||
\(378\) | −2.49308 | −0.128230 | ||||||||
\(379\) | 0.643695i | 0.0330644i | 0.999863 | + | 0.0165322i | \(0.00526260\pi\) | ||||
−0.999863 | + | 0.0165322i | \(0.994737\pi\) | |||||||
\(380\) | −49.2133 | −2.52459 | ||||||||
\(381\) | −49.7731 | −2.54995 | ||||||||
\(382\) | − | 24.0222i | − | 1.22909i | ||||||
\(383\) | 0.638046i | 0.0326027i | 0.999867 | + | 0.0163013i | \(0.00518910\pi\) | ||||
−0.999867 | + | 0.0163013i | \(0.994811\pi\) | |||||||
\(384\) | 46.3905i | 2.36735i | ||||||||
\(385\) | − | 0.421359i | − | 0.0214744i | ||||||
\(386\) | 48.8623 | 2.48703 | ||||||||
\(387\) | −10.5596 | −0.536774 | ||||||||
\(388\) | − | 24.2852i | − | 1.23289i | ||||||
\(389\) | 3.50021 | 0.177468 | 0.0887339 | − | 0.996055i | \(-0.471718\pi\) | ||||
0.0887339 | + | 0.996055i | \(0.471718\pi\) | |||||||
\(390\) | 9.72757 | − | 54.7326i | 0.492574 | − | 2.77149i | ||||
\(391\) | 3.00893 | 0.152168 | ||||||||
\(392\) | − | 29.6005i | − | 1.49505i | ||||||
\(393\) | −30.5480 | −1.54094 | ||||||||
\(394\) | −40.4359 | −2.03713 | ||||||||
\(395\) | 26.9526i | 1.35613i | ||||||||
\(396\) | 1.67417i | 0.0841301i | ||||||||
\(397\) | 36.5004i | 1.83190i | 0.401287 | + | 0.915952i | \(0.368563\pi\) | ||||
−0.401287 | + | 0.915952i | \(0.631437\pi\) | |||||||
\(398\) | 50.4230i | 2.52748i | ||||||||
\(399\) | −10.3828 | −0.519790 | ||||||||
\(400\) | −8.46546 | −0.423273 | ||||||||
\(401\) | 5.71571i | 0.285429i | 0.989764 | + | 0.142715i | \(0.0455831\pi\) | ||||
−0.989764 | + | 0.142715i | \(0.954417\pi\) | |||||||
\(402\) | 4.52169 | 0.225521 | ||||||||
\(403\) | 3.54992 | + | 0.630924i | 0.176834 | + | 0.0314285i | ||||
\(404\) | −77.5922 | −3.86036 | ||||||||
\(405\) | − | 27.1626i | − | 1.34972i | ||||||
\(406\) | 11.8658 | 0.588891 | ||||||||
\(407\) | 1.18861 | 0.0589172 | ||||||||
\(408\) | − | 9.70014i | − | 0.480229i | ||||||
\(409\) | 32.8297i | 1.62333i | 0.584126 | + | 0.811663i | \(0.301438\pi\) | ||||
−0.584126 | + | 0.811663i | \(0.698562\pi\) | |||||||
\(410\) | − | 3.92320i | − | 0.193753i | ||||||
\(411\) | − | 45.5903i | − | 2.24881i | ||||||
\(412\) | 59.4323 | 2.92802 | ||||||||
\(413\) | −7.41434 | −0.364836 | ||||||||
\(414\) | 22.1446i | 1.08835i | ||||||||
\(415\) | 20.3756 | 1.00020 | ||||||||
\(416\) | 0.437106 | + | 0.0776864i | 0.0214309 | + | 0.00380889i | ||||
\(417\) | −1.93315 | −0.0946667 | ||||||||
\(418\) | − | 1.86071i | − | 0.0910103i | ||||||
\(419\) | 33.3911 | 1.63126 | 0.815630 | − | 0.578573i | \(-0.196390\pi\) | ||||
0.815630 | + | 0.578573i | \(0.196390\pi\) | |||||||
\(420\) | −24.0074 | −1.17144 | ||||||||
\(421\) | 31.5645i | 1.53836i | 0.639033 | + | 0.769179i | \(0.279335\pi\) | ||||
−0.639033 | + | 0.769179i | \(0.720665\pi\) | |||||||
\(422\) | − | 49.7480i | − | 2.42169i | ||||||
\(423\) | − | 30.4389i | − | 1.47999i | ||||||
\(424\) | − | 45.4162i | − | 2.20561i | ||||||
\(425\) | −1.82689 | −0.0886170 | ||||||||
\(426\) | −15.2968 | −0.741134 | ||||||||
\(427\) | 5.93881i | 0.287399i | ||||||||
\(428\) | 57.9420 | 2.80073 | ||||||||
\(429\) | 1.37814 | + | 0.244935i | 0.0665372 | + | 0.0118256i | ||||
\(430\) | 27.1368 | 1.30865 | ||||||||
\(431\) | 13.7218i | 0.660954i | 0.943814 | + | 0.330477i | \(0.107210\pi\) | ||||
−0.943814 | + | 0.330477i | \(0.892790\pi\) | |||||||
\(432\) | −4.18453 | −0.201328 | ||||||||
\(433\) | 4.35155 | 0.209122 | 0.104561 | − | 0.994518i | \(-0.466656\pi\) | ||||
0.104561 | + | 0.994518i | \(0.466656\pi\) | |||||||
\(434\) | − | 2.33812i | − | 0.112233i | ||||||
\(435\) | 31.9772i | 1.53319i | ||||||||
\(436\) | − | 1.88782i | − | 0.0904103i | ||||||
\(437\) | − | 16.3907i | − | 0.784075i | ||||||
\(438\) | 5.42650 | 0.259288 | ||||||||
\(439\) | 1.65440 | 0.0789601 | 0.0394800 | − | 0.999220i | \(-0.487430\pi\) | ||||
0.0394800 | + | 0.999220i | \(0.487430\pi\) | |||||||
\(440\) | − | 2.14439i | − | 0.102230i | ||||||
\(441\) | 15.5052 | 0.738341 | ||||||||
\(442\) | −7.35658 | − | 1.30748i | −0.349917 | − | 0.0621903i | ||||
\(443\) | −10.9699 | −0.521194 | −0.260597 | − | 0.965448i | \(-0.583919\pi\) | ||||
−0.260597 | + | 0.965448i | \(0.583919\pi\) | |||||||
\(444\) | − | 67.7224i | − | 3.21396i | ||||||
\(445\) | −46.2859 | −2.19416 | ||||||||
\(446\) | 9.07687 | 0.429802 | ||||||||
\(447\) | − | 24.5404i | − | 1.16072i | ||||||
\(448\) | − | 7.78780i | − | 0.367939i | ||||||
\(449\) | − | 2.08348i | − | 0.0983254i | −0.998791 | − | 0.0491627i | \(-0.984345\pi\) | ||
0.998791 | − | 0.0491627i | \(-0.0156553\pi\) | |||||||
\(450\) | − | 13.4452i | − | 0.633814i | ||||||
\(451\) | 0.0987842 | 0.00465156 | ||||||||
\(452\) | 25.3856 | 1.19404 | ||||||||
\(453\) | − | 3.03725i | − | 0.142702i | ||||||
\(454\) | −32.2338 | −1.51281 | ||||||||
\(455\) | −1.61285 | + | 9.07478i | −0.0756116 | + | 0.425432i | ||||
\(456\) | −52.8403 | −2.47447 | ||||||||
\(457\) | 5.71250i | 0.267220i | 0.991034 | + | 0.133610i | \(0.0426569\pi\) | ||||
−0.991034 | + | 0.133610i | \(0.957343\pi\) | |||||||
\(458\) | 46.9650 | 2.19453 | ||||||||
\(459\) | −0.903042 | −0.0421504 | ||||||||
\(460\) | − | 37.8992i | − | 1.76706i | ||||||
\(461\) | − | 11.8887i | − | 0.553713i | −0.960911 | − | 0.276856i | \(-0.910707\pi\) | ||
0.960911 | − | 0.276856i | \(-0.0892926\pi\) | |||||||
\(462\) | − | 0.907699i | − | 0.0422300i | ||||||
\(463\) | − | 0.451563i | − | 0.0209859i | −0.999945 | − | 0.0104930i | \(-0.996660\pi\) | ||
0.999945 | − | 0.0104930i | \(-0.00334007\pi\) | |||||||
\(464\) | 19.9163 | 0.924591 | ||||||||
\(465\) | 6.30099 | 0.292202 | ||||||||
\(466\) | − | 4.88844i | − | 0.226453i | ||||||
\(467\) | 26.5720 | 1.22960 | 0.614802 | − | 0.788682i | \(-0.289236\pi\) | ||||
0.614802 | + | 0.788682i | \(0.289236\pi\) | |||||||
\(468\) | 6.40828 | − | 36.0565i | 0.296223 | − | 1.66671i | ||||
\(469\) | −0.749705 | −0.0346182 | ||||||||
\(470\) | 78.2240i | 3.60820i | ||||||||
\(471\) | 7.57274 | 0.348934 | ||||||||
\(472\) | −37.7332 | −1.73681 | ||||||||
\(473\) | 0.683290i | 0.0314177i | ||||||||
\(474\) | 58.0618i | 2.66687i | ||||||||
\(475\) | 9.95173i | 0.456617i | ||||||||
\(476\) | 3.22682i | 0.147901i | ||||||||
\(477\) | 23.7897 | 1.08925 | ||||||||
\(478\) | 29.6435 | 1.35586 | ||||||||
\(479\) | 11.7579i | 0.537233i | 0.963247 | + | 0.268617i | \(0.0865665\pi\) | ||||
−0.963247 | + | 0.268617i | \(0.913433\pi\) | |||||||
\(480\) | 0.775849 | 0.0354125 | ||||||||
\(481\) | −25.5990 | − | 4.54969i | −1.16721 | − | 0.207448i | ||||
\(482\) | 39.3191 | 1.79093 | ||||||||
\(483\) | − | 7.99579i | − | 0.363821i | ||||||
\(484\) | −43.7528 | −1.98877 | ||||||||
\(485\) | −16.2938 | −0.739864 | ||||||||
\(486\) | − | 50.6870i | − | 2.29921i | ||||||
\(487\) | 21.1168i | 0.956894i | 0.878116 | + | 0.478447i | \(0.158800\pi\) | ||||
−0.878116 | + | 0.478447i | \(0.841200\pi\) | |||||||
\(488\) | 30.2239i | 1.36817i | ||||||||
\(489\) | 9.36405i | 0.423457i | ||||||||
\(490\) | −39.8462 | −1.80007 | ||||||||
\(491\) | 24.8938 | 1.12344 | 0.561722 | − | 0.827326i | \(-0.310139\pi\) | ||||
0.561722 | + | 0.827326i | \(0.310139\pi\) | |||||||
\(492\) | − | 5.62834i | − | 0.253745i | ||||||
\(493\) | 4.29803 | 0.193574 | ||||||||
\(494\) | −7.12231 | + | 40.0740i | −0.320448 | + | 1.80301i | ||||
\(495\) | 1.12326 | 0.0504868 | ||||||||
\(496\) | − | 3.92444i | − | 0.176213i | ||||||
\(497\) | 2.53625 | 0.113766 | ||||||||
\(498\) | 43.8934 | 1.96691 | ||||||||
\(499\) | 18.5383i | 0.829890i | 0.909847 | + | 0.414945i | \(0.136199\pi\) | ||||
−0.909847 | + | 0.414945i | \(0.863801\pi\) | |||||||
\(500\) | − | 30.3261i | − | 1.35622i | ||||||
\(501\) | − | 34.4361i | − | 1.53849i | ||||||
\(502\) | 46.1116i | 2.05806i | ||||||||
\(503\) | 36.0174 | 1.60593 | 0.802967 | − | 0.596023i | \(-0.203253\pi\) | ||||
0.802967 | + | 0.596023i | \(0.203253\pi\) | |||||||
\(504\) | −11.8365 | −0.527241 | ||||||||
\(505\) | 52.0595i | 2.31662i | ||||||||
\(506\) | 1.43293 | 0.0637017 | ||||||||
\(507\) | −28.7434 | − | 10.5503i | −1.27654 | − | 0.468556i | ||||
\(508\) | 84.2640 | 3.73861 | ||||||||
\(509\) | − | 20.9608i | − | 0.929072i | −0.885554 | − | 0.464536i | \(-0.846221\pi\) | ||
0.885554 | − | 0.464536i | \(-0.153779\pi\) | |||||||
\(510\) | −13.0577 | −0.578204 | ||||||||
\(511\) | −0.899725 | −0.0398015 | ||||||||
\(512\) | − | 38.6519i | − | 1.70819i | ||||||
\(513\) | 4.91920i | 0.217188i | ||||||||
\(514\) | − | 68.7113i | − | 3.03072i | ||||||
\(515\) | − | 39.8753i | − | 1.75712i | ||||||
\(516\) | 38.9312 | 1.71385 | ||||||||
\(517\) | −1.96964 | −0.0866248 | ||||||||
\(518\) | 16.8605i | 0.740809i | ||||||||
\(519\) | 5.58724 | 0.245253 | ||||||||
\(520\) | −8.20815 | + | 46.1835i | −0.359951 | + | 2.02528i | ||||
\(521\) | 25.4300 | 1.11411 | 0.557054 | − | 0.830476i | \(-0.311931\pi\) | ||||
0.557054 | + | 0.830476i | \(0.311931\pi\) | |||||||
\(522\) | 31.6320i | 1.38449i | ||||||||
\(523\) | −3.07473 | −0.134449 | −0.0672244 | − | 0.997738i | \(-0.521414\pi\) | ||||
−0.0672244 | + | 0.997738i | \(0.521414\pi\) | |||||||
\(524\) | 51.7167 | 2.25926 | ||||||||
\(525\) | 4.85469i | 0.211876i | ||||||||
\(526\) | 52.5822i | 2.29269i | ||||||||
\(527\) | − | 0.846913i | − | 0.0368921i | ||||||
\(528\) | − | 1.52353i | − | 0.0663033i | ||||||
\(529\) | −10.3775 | −0.451195 | ||||||||
\(530\) | −61.1362 | −2.65559 | ||||||||
\(531\) | − | 19.7652i | − | 0.857736i | ||||||
\(532\) | 17.5777 | 0.762089 | ||||||||
\(533\) | −2.12751 | − | 0.378120i | −0.0921526 | − | 0.0163782i | ||||
\(534\) | −99.7099 | −4.31487 | ||||||||
\(535\) | − | 38.8754i | − | 1.68073i | ||||||
\(536\) | −3.81541 | −0.164801 | ||||||||
\(537\) | 18.6389 | 0.804326 | ||||||||
\(538\) | − | 55.7539i | − | 2.40372i | ||||||
\(539\) | − | 1.00331i | − | 0.0432155i | ||||||
\(540\) | 11.3743i | 0.489473i | ||||||||
\(541\) | − | 9.16670i | − | 0.394107i | −0.980393 | − | 0.197054i | \(-0.936863\pi\) | ||
0.980393 | − | 0.197054i | \(-0.0631373\pi\) | |||||||
\(542\) | 55.6159 | 2.38891 | ||||||||
\(543\) | −30.7337 | −1.31891 | ||||||||
\(544\) | − | 0.104281i | − | 0.00447103i | ||||||
\(545\) | −1.26661 | −0.0542555 | ||||||||
\(546\) | −3.47443 | + | 19.5490i | −0.148692 | + | 0.836622i | ||||
\(547\) | −24.3063 | −1.03926 | −0.519630 | − | 0.854391i | \(-0.673930\pi\) | ||||
−0.519630 | + | 0.854391i | \(0.673930\pi\) | |||||||
\(548\) | 77.1828i | 3.29708i | ||||||||
\(549\) | −15.8317 | −0.675681 | ||||||||
\(550\) | −0.870014 | −0.0370975 | ||||||||
\(551\) | − | 23.4130i | − | 0.997426i | ||||||
\(552\) | − | 40.6923i | − | 1.73198i | ||||||
\(553\) | − | 9.62677i | − | 0.409372i | ||||||
\(554\) | − | 2.56997i | − | 0.109187i | ||||||
\(555\) | −45.4374 | −1.92871 | ||||||||
\(556\) | 3.27275 | 0.138796 | ||||||||
\(557\) | − | 9.13477i | − | 0.387052i | −0.981095 | − | 0.193526i | \(-0.938008\pi\) | ||
0.981095 | − | 0.193526i | \(-0.0619925\pi\) | |||||||
\(558\) | 6.23297 | 0.263863 | ||||||||
\(559\) | 2.61546 | − | 14.7160i | 0.110622 | − | 0.622420i | ||||
\(560\) | 10.0322 | 0.423937 | ||||||||
\(561\) | − | 0.328786i | − | 0.0138814i | ||||||
\(562\) | 14.2020 | 0.599074 | ||||||||
\(563\) | 30.1418 | 1.27032 | 0.635162 | − | 0.772379i | \(-0.280933\pi\) | ||||
0.635162 | + | 0.772379i | \(0.280933\pi\) | |||||||
\(564\) | 112.223i | 4.72542i | ||||||||
\(565\) | − | 17.0321i | − | 0.716547i | ||||||
\(566\) | − | 39.3749i | − | 1.65505i | ||||||
\(567\) | 9.70178i | 0.407437i | ||||||||
\(568\) | 12.9075 | 0.541587 | ||||||||
\(569\) | 29.0683 | 1.21861 | 0.609303 | − | 0.792937i | \(-0.291449\pi\) | ||||
0.609303 | + | 0.792937i | \(0.291449\pi\) | |||||||
\(570\) | 71.1300i | 2.97931i | ||||||||
\(571\) | −20.7284 | −0.867454 | −0.433727 | − | 0.901044i | \(-0.642802\pi\) | ||||
−0.433727 | + | 0.901044i | \(0.642802\pi\) | |||||||
\(572\) | −2.33314 | − | 0.414667i | −0.0975535 | − | 0.0173381i | ||||
\(573\) | −23.1225 | −0.965957 | ||||||||
\(574\) | 1.40126i | 0.0584876i | ||||||||
\(575\) | −7.66383 | −0.319604 | ||||||||
\(576\) | 20.7608 | 0.865032 | ||||||||
\(577\) | − | 14.0634i | − | 0.585469i | −0.956194 | − | 0.292734i | \(-0.905435\pi\) | ||
0.956194 | − | 0.292734i | \(-0.0945652\pi\) | |||||||
\(578\) | − | 39.8424i | − | 1.65723i | ||||||
\(579\) | − | 47.0323i | − | 1.95459i | ||||||
\(580\) | − | 54.1362i | − | 2.24788i | ||||||
\(581\) | −7.27761 | −0.301926 | ||||||||
\(582\) | −35.1004 | −1.45496 | ||||||||
\(583\) | − | 1.53938i | − | 0.0637546i | ||||||
\(584\) | −4.57890 | −0.189476 | ||||||||
\(585\) | −24.1916 | − | 4.29955i | −1.00020 | − | 0.177764i | ||||
\(586\) | 47.3228 | 1.95489 | ||||||||
\(587\) | 38.4922i | 1.58874i | 0.607431 | + | 0.794372i | \(0.292200\pi\) | ||||
−0.607431 | + | 0.794372i | \(0.707800\pi\) | |||||||
\(588\) | −57.1646 | −2.35743 | ||||||||
\(589\) | −4.61345 | −0.190094 | ||||||||
\(590\) | 50.7939i | 2.09115i | ||||||||
\(591\) | 38.9215i | 1.60102i | ||||||||
\(592\) | 28.2997i | 1.16311i | ||||||||
\(593\) | − | 18.7114i | − | 0.768387i | −0.923253 | − | 0.384193i | \(-0.874480\pi\) | ||
0.923253 | − | 0.384193i | \(-0.125520\pi\) | |||||||
\(594\) | −0.430053 | −0.0176453 | ||||||||
\(595\) | 2.16499 | 0.0887560 | ||||||||
\(596\) | 41.5460i | 1.70179i | ||||||||
\(597\) | 48.5345 | 1.98638 | ||||||||
\(598\) | −30.8610 | − | 5.48489i | −1.26200 | − | 0.224294i | ||||
\(599\) | 37.0994 | 1.51584 | 0.757919 | − | 0.652348i | \(-0.226216\pi\) | ||||
0.757919 | + | 0.652348i | \(0.226216\pi\) | |||||||
\(600\) | 24.7066i | 1.00864i | ||||||||
\(601\) | −11.2787 | −0.460069 | −0.230035 | − | 0.973182i | \(-0.573884\pi\) | ||||
−0.230035 | + | 0.973182i | \(0.573884\pi\) | |||||||
\(602\) | −9.69253 | −0.395038 | ||||||||
\(603\) | − | 1.99857i | − | 0.0813880i | ||||||
\(604\) | 5.14195i | 0.209223i | ||||||||
\(605\) | 29.3554i | 1.19347i | ||||||||
\(606\) | 112.147i | 4.55568i | ||||||||
\(607\) | −6.57246 | −0.266768 | −0.133384 | − | 0.991064i | \(-0.542584\pi\) | ||||
−0.133384 | + | 0.991064i | \(0.542584\pi\) | |||||||
\(608\) | −0.568060 | −0.0230379 | ||||||||
\(609\) | − | 11.4214i | − | 0.462819i | ||||||
\(610\) | 40.6854 | 1.64730 | ||||||||
\(611\) | 42.4201 | + | 7.53927i | 1.71613 | + | 0.305006i | ||||
\(612\) | −8.60207 | −0.347718 | ||||||||
\(613\) | 37.0931i | 1.49817i | 0.662471 | + | 0.749087i | \(0.269508\pi\) | ||||
−0.662471 | + | 0.749087i | \(0.730492\pi\) | |||||||
\(614\) | −37.2238 | −1.50223 | ||||||||
\(615\) | −3.77626 | −0.152273 | ||||||||
\(616\) | 0.765918i | 0.0308597i | ||||||||
\(617\) | 13.0949i | 0.527182i | 0.964635 | + | 0.263591i | \(0.0849069\pi\) | ||||
−0.964635 | + | 0.263591i | \(0.915093\pi\) | |||||||
\(618\) | − | 85.9001i | − | 3.45541i | ||||||
\(619\) | 20.6820i | 0.831281i | 0.909529 | + | 0.415640i | \(0.136443\pi\) | ||||
−0.909529 | + | 0.415640i | \(0.863557\pi\) | |||||||
\(620\) | −10.6674 | −0.428411 | ||||||||
\(621\) | −3.78828 | −0.152018 | ||||||||
\(622\) | − | 5.28962i | − | 0.212094i | ||||||
\(623\) | 16.5321 | 0.662345 | ||||||||
\(624\) | −5.83169 | + | 32.8123i | −0.233454 | + | 1.31354i | ||||
\(625\) | −31.1324 | −1.24530 | ||||||||
\(626\) | 32.6580i | 1.30528i | ||||||||
\(627\) | −1.79102 | −0.0715264 | ||||||||
\(628\) | −12.8204 | −0.511589 | ||||||||
\(629\) | 6.10722i | 0.243511i | ||||||||
\(630\) | 15.9336i | 0.634808i | ||||||||
\(631\) | 46.6562i | 1.85736i | 0.370888 | + | 0.928678i | \(0.379053\pi\) | ||||
−0.370888 | + | 0.928678i | \(0.620947\pi\) | |||||||
\(632\) | − | 48.9927i | − | 1.94882i | ||||||
\(633\) | −47.8848 | −1.90325 | ||||||||
\(634\) | −74.0660 | −2.94154 | ||||||||
\(635\) | − | 56.5358i | − | 2.24355i | ||||||
\(636\) | −87.7080 | −3.47785 | ||||||||
\(637\) | −3.84040 | + | 21.6082i | −0.152162 | + | 0.856147i | ||||
\(638\) | 2.04684 | 0.0810352 | ||||||||
\(639\) | 6.76114i | 0.267466i | ||||||||
\(640\) | −52.6936 | −2.08290 | ||||||||
\(641\) | −46.4680 | −1.83537 | −0.917687 | − | 0.397304i | \(-0.869946\pi\) | ||||
−0.917687 | + | 0.397304i | \(0.869946\pi\) | |||||||
\(642\) | − | 83.7461i | − | 3.30520i | ||||||
\(643\) | 18.1376i | 0.715278i | 0.933860 | + | 0.357639i | \(0.116418\pi\) | ||||
−0.933860 | + | 0.357639i | \(0.883582\pi\) | |||||||
\(644\) | 13.5366i | 0.533416i | ||||||||
\(645\) | − | 26.1204i | − | 1.02849i | ||||||
\(646\) | 9.56055 | 0.376155 | ||||||||
\(647\) | −27.8566 | −1.09516 | −0.547578 | − | 0.836755i | \(-0.684450\pi\) | ||||
−0.547578 | + | 0.836755i | \(0.684450\pi\) | |||||||
\(648\) | 49.3745i | 1.93961i | ||||||||
\(649\) | −1.27897 | −0.0502038 | ||||||||
\(650\) | 18.7374 | + | 3.33018i | 0.734942 | + | 0.130621i | ||||
\(651\) | −2.25055 | −0.0882060 | ||||||||
\(652\) | − | 15.8530i | − | 0.620851i | ||||||
\(653\) | −7.49659 | −0.293364 | −0.146682 | − | 0.989184i | \(-0.546859\pi\) | ||||
−0.146682 | + | 0.989184i | \(0.546859\pi\) | |||||||
\(654\) | −2.72855 | −0.106695 | ||||||||
\(655\) | − | 34.6986i | − | 1.35579i | ||||||
\(656\) | 2.35196i | 0.0918286i | ||||||||
\(657\) | − | 2.39849i | − | 0.0935741i | ||||||
\(658\) | − | 27.9396i | − | 1.08920i | ||||||
\(659\) | −18.8622 | −0.734768 | −0.367384 | − | 0.930069i | \(-0.619747\pi\) | ||||
−0.367384 | + | 0.930069i | \(0.619747\pi\) | |||||||
\(660\) | −4.14125 | −0.161198 | ||||||||
\(661\) | − | 0.0711000i | − | 0.00276547i | −0.999999 | − | 0.00138274i | \(-0.999560\pi\) | ||
0.999999 | − | 0.00138274i | \(-0.000440139\pi\) | |||||||
\(662\) | −18.6140 | −0.723452 | ||||||||
\(663\) | −1.25851 | + | 7.08105i | −0.0488764 | + | 0.275005i | ||||
\(664\) | −37.0374 | −1.43733 | ||||||||
\(665\) | − | 11.7935i | − | 0.457333i | ||||||
\(666\) | −44.9469 | −1.74166 | ||||||||
\(667\) | 18.0303 | 0.698138 | ||||||||
\(668\) | 58.2990i | 2.25566i | ||||||||
\(669\) | − | 8.73690i | − | 0.337788i | ||||||
\(670\) | 5.13605i | 0.198423i | ||||||||
\(671\) | 1.02444i | 0.0395480i | ||||||||
\(672\) | −0.277113 | −0.0106899 | ||||||||
\(673\) | 13.3225 | 0.513545 | 0.256773 | − | 0.966472i | \(-0.417341\pi\) | ||||
0.256773 | + | 0.966472i | \(0.417341\pi\) | |||||||
\(674\) | − | 33.6508i | − | 1.29618i | ||||||
\(675\) | 2.30007 | 0.0885299 | ||||||||
\(676\) | 48.6615 | + | 17.8613i | 1.87159 | + | 0.686973i | ||||
\(677\) | −28.6510 | −1.10115 | −0.550574 | − | 0.834786i | \(-0.685591\pi\) | ||||
−0.550574 | + | 0.834786i | \(0.685591\pi\) | |||||||
\(678\) | − | 36.6909i | − | 1.40911i | ||||||
\(679\) | 5.81972 | 0.223340 | ||||||||
\(680\) | 11.0181 | 0.422525 | ||||||||
\(681\) | 31.0265i | 1.18894i | ||||||||
\(682\) | − | 0.403323i | − | 0.0154440i | ||||||
\(683\) | 18.5015i | 0.707939i | 0.935257 | + | 0.353970i | \(0.115168\pi\) | ||||
−0.935257 | + | 0.353970i | \(0.884832\pi\) | |||||||
\(684\) | 46.8587i | 1.79169i | ||||||||
\(685\) | 51.7847 | 1.97859 | ||||||||
\(686\) | 30.5989 | 1.16827 | ||||||||
\(687\) | − | 45.2060i | − | 1.72472i | ||||||
\(688\) | −16.2685 | −0.620232 | ||||||||
\(689\) | −5.89234 | + | 33.1535i | −0.224480 | + | 1.26305i | ||||
\(690\) | −54.7773 | −2.08534 | ||||||||
\(691\) | − | 3.41864i | − | 0.130051i | −0.997884 | − | 0.0650255i | \(-0.979287\pi\) | ||
0.997884 | − | 0.0650255i | \(-0.0207129\pi\) | |||||||
\(692\) | −9.45899 | −0.359577 | ||||||||
\(693\) | −0.401199 | −0.0152403 | ||||||||
\(694\) | − | 35.6756i | − | 1.35423i | ||||||
\(695\) | − | 2.19581i | − | 0.0832917i | ||||||
\(696\) | − | 58.1260i | − | 2.20326i | ||||||
\(697\) | 0.507565i | 0.0192254i | ||||||||
\(698\) | −33.7175 | −1.27623 | ||||||||
\(699\) | −4.70535 | −0.177973 | ||||||||
\(700\) | − | 8.21881i | − | 0.310642i | ||||||
\(701\) | 18.7003 | 0.706301 | 0.353151 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353151 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(702\) | 9.26203 | + | 1.64613i | 0.349573 | + | 0.0621292i | ||||
\(703\) | 33.2683 | 1.25474 | ||||||||
\(704\) | − | 1.34339i | − | 0.0506308i | ||||||
\(705\) | 75.2942 | 2.83574 | ||||||||
\(706\) | 33.0708 | 1.24464 | ||||||||
\(707\) | − | 18.5943i | − | 0.699309i | ||||||
\(708\) | 72.8705i | 2.73864i | ||||||||
\(709\) | − | 2.87246i | − | 0.107878i | −0.998544 | − | 0.0539388i | \(-0.982822\pi\) | ||
0.998544 | − | 0.0539388i | \(-0.0171776\pi\) | |||||||
\(710\) | − | 17.3752i | − | 0.652080i | ||||||
\(711\) | 25.6631 | 0.962441 | ||||||||
\(712\) | 84.1355 | 3.15311 | ||||||||
\(713\) | − | 3.55282i | − | 0.133054i | ||||||
\(714\) | 4.66386 | 0.174541 | ||||||||
\(715\) | −0.278215 | + | 1.56539i | −0.0104046 | + | 0.0585422i | ||||
\(716\) | −31.5549 | −1.17926 | ||||||||
\(717\) | − | 28.5332i | − | 1.06559i | ||||||
\(718\) | −36.8844 | −1.37652 | ||||||||
\(719\) | 27.9855 | 1.04368 | 0.521842 | − | 0.853042i | \(-0.325245\pi\) | ||||
0.521842 | + | 0.853042i | \(0.325245\pi\) | |||||||
\(720\) | 26.7438i | 0.996683i | ||||||||
\(721\) | 14.2424i | 0.530415i | ||||||||
\(722\) | − | 5.58850i | − | 0.207982i | ||||||
\(723\) | − | 37.8464i | − | 1.40752i | ||||||
\(724\) | 52.0310 | 1.93372 | ||||||||
\(725\) | −10.9472 | −0.406570 | ||||||||
\(726\) | 63.2379i | 2.34698i | ||||||||
\(727\) | −52.3092 | −1.94004 | −0.970021 | − | 0.243020i | \(-0.921862\pi\) | ||||
−0.970021 | + | 0.243020i | \(0.921862\pi\) | |||||||
\(728\) | 2.93173 | − | 16.4955i | 0.108657 | − | 0.611365i | ||||
\(729\) | −18.3290 | −0.678851 | ||||||||
\(730\) | 6.16380i | 0.228133i | ||||||||
\(731\) | −3.51083 | −0.129853 | ||||||||
\(732\) | 58.3686 | 2.15736 | ||||||||
\(733\) | 31.3469i | 1.15782i | 0.815390 | + | 0.578912i | \(0.196522\pi\) | ||||
−0.815390 | + | 0.578912i | \(0.803478\pi\) | |||||||
\(734\) | − | 45.3464i | − | 1.67377i | ||||||
\(735\) | 38.3538i | 1.41470i | ||||||||
\(736\) | − | 0.437463i | − | 0.0161251i | ||||||
\(737\) | −0.129323 | −0.00476368 | ||||||||
\(738\) | −3.73549 | −0.137505 | ||||||||
\(739\) | − | 34.1803i | − | 1.25734i | −0.777671 | − | 0.628671i | \(-0.783599\pi\) | ||
0.777671 | − | 0.628671i | \(-0.216401\pi\) | |||||||
\(740\) | 76.9239 | 2.82778 | ||||||||
\(741\) | 38.5731 | + | 6.85555i | 1.41702 | + | 0.251845i | ||||
\(742\) | 21.8363 | 0.801634 | ||||||||
\(743\) | 0.574231i | 0.0210665i | 0.999945 | + | 0.0105332i | \(0.00335290\pi\) | ||||
−0.999945 | + | 0.0105332i | \(0.996647\pi\) | |||||||
\(744\) | −11.4535 | −0.419907 | ||||||||
\(745\) | 27.8747 | 1.02125 | ||||||||
\(746\) | 32.2359i | 1.18024i | ||||||||
\(747\) | − | 19.4007i | − | 0.709835i | ||||||
\(748\) | 0.556623i | 0.0203521i | ||||||||
\(749\) | 13.8853i | 0.507357i | ||||||||
\(750\) | −43.8316 | −1.60050 | ||||||||
\(751\) | 39.2613 | 1.43266 | 0.716332 | − | 0.697760i | \(-0.245820\pi\) | ||||
0.716332 | + | 0.697760i | \(0.245820\pi\) | |||||||
\(752\) | − | 46.8954i | − | 1.71010i | ||||||
\(753\) | 44.3845 | 1.61746 | ||||||||
\(754\) | −44.0827 | − | 7.83477i | −1.60540 | − | 0.285326i | ||||
\(755\) | 3.44992 | 0.125556 | ||||||||
\(756\) | − | 4.06261i | − | 0.147756i | ||||||
\(757\) | 41.5394 | 1.50978 | 0.754888 | − | 0.655854i | \(-0.227691\pi\) | ||||
0.754888 | + | 0.655854i | \(0.227691\pi\) | |||||||
\(758\) | −1.57507 | −0.0572090 | ||||||||
\(759\) | − | 1.37927i | − | 0.0500642i | ||||||
\(760\) | − | 60.0197i | − | 2.17714i | ||||||
\(761\) | − | 50.6181i | − | 1.83490i | −0.397847 | − | 0.917452i | \(-0.630243\pi\) | ||
0.397847 | − | 0.917452i | \(-0.369757\pi\) | |||||||
\(762\) | − | 121.790i | − | 4.41200i | ||||||
\(763\) | 0.452399 | 0.0163779 | ||||||||
\(764\) | 39.1456 | 1.41624 | ||||||||
\(765\) | 5.77144i | 0.208667i | ||||||||
\(766\) | −1.56124 | −0.0564100 | ||||||||
\(767\) | 27.5450 | + | 4.89555i | 0.994593 | + | 0.176768i | ||||
\(768\) | −75.1218 | −2.71072 | ||||||||
\(769\) | − | 30.6558i | − | 1.10548i | −0.833355 | − | 0.552739i | \(-0.813583\pi\) | ||
0.833355 | − | 0.552739i | \(-0.186417\pi\) | |||||||
\(770\) | 1.03103 | 0.0371557 | ||||||||
\(771\) | −66.1378 | −2.38189 | ||||||||
\(772\) | 79.6239i | 2.86573i | ||||||||
\(773\) | − | 24.6737i | − | 0.887450i | −0.896163 | − | 0.443725i | \(-0.853657\pi\) | ||
0.896163 | − | 0.443725i | \(-0.146343\pi\) | |||||||
\(774\) | − | 25.8384i | − | 0.928742i | ||||||
\(775\) | 2.15711i | 0.0774858i | ||||||||
\(776\) | 29.6178 | 1.06322 | ||||||||
\(777\) | 16.2290 | 0.582214 | ||||||||
\(778\) | 8.56472i | 0.307060i | ||||||||
\(779\) | 2.76489 | 0.0990625 | ||||||||
\(780\) | 89.1898 | + | 15.8516i | 3.19351 | + | 0.567579i | ||||
\(781\) | 0.437500 | 0.0156550 | ||||||||
\(782\) | 7.36258i | 0.263285i | ||||||||
\(783\) | −5.41128 | −0.193383 | ||||||||
\(784\) | 23.8878 | 0.853137 | ||||||||
\(785\) | 8.60165i | 0.307006i | ||||||||
\(786\) | − | 74.7484i | − | 2.66619i | ||||||
\(787\) | 4.27479i | 0.152380i | 0.997093 | + | 0.0761899i | \(0.0242755\pi\) | ||||
−0.997093 | + | 0.0761899i | \(0.975724\pi\) | |||||||
\(788\) | − | 65.8926i | − | 2.34733i | ||||||
\(789\) | 50.6128 | 1.80186 | ||||||||
\(790\) | −65.9507 | −2.34642 | ||||||||
\(791\) | 6.08343i | 0.216302i | ||||||||
\(792\) | −2.04179 | −0.0725518 | ||||||||
\(793\) | 3.92128 | − | 22.0633i | 0.139249 | − | 0.783490i | ||||
\(794\) | −89.3134 | −3.16961 | ||||||||
\(795\) | 58.8465i | 2.08707i | ||||||||
\(796\) | −82.1671 | −2.91234 | ||||||||
\(797\) | 45.6976 | 1.61869 | 0.809347 | − | 0.587331i | \(-0.199821\pi\) | ||||
0.809347 | + | 0.587331i | \(0.199821\pi\) | |||||||
\(798\) | − | 25.4058i | − | 0.899355i | ||||||
\(799\) | − | 10.1203i | − | 0.358029i | ||||||
\(800\) | 0.265608i | 0.00939066i | ||||||||
\(801\) | 44.0714i | 1.55719i | ||||||||
\(802\) | −13.9858 | −0.493857 | ||||||||
\(803\) | −0.155202 | −0.00547695 | ||||||||
\(804\) | 7.36834i | 0.259861i | ||||||||
\(805\) | 9.08219 | 0.320105 | ||||||||
\(806\) | −1.54381 | + | 8.68634i | −0.0543786 | + | 0.305963i | ||||
\(807\) | −53.6657 | −1.88912 | ||||||||
\(808\) | − | 94.6303i | − | 3.32908i | ||||||
\(809\) | −3.09548 | −0.108831 | −0.0544157 | − | 0.998518i | \(-0.517330\pi\) | ||||
−0.0544157 | + | 0.998518i | \(0.517330\pi\) | |||||||
\(810\) | 66.4646 | 2.33533 | ||||||||
\(811\) | − | 38.5887i | − | 1.35503i | −0.735508 | − | 0.677516i | \(-0.763057\pi\) | ||
0.735508 | − | 0.677516i | \(-0.236943\pi\) | |||||||
\(812\) | 19.3360i | 0.678561i | ||||||||
\(813\) | − | 53.5329i | − | 1.87748i | ||||||
\(814\) | 2.90842i | 0.101940i | ||||||||
\(815\) | −10.6364 | −0.372575 | ||||||||
\(816\) | 7.82810 | 0.274038 | ||||||||
\(817\) | 19.1248i | 0.669091i | ||||||||
\(818\) | −80.3315 | −2.80873 | ||||||||
\(819\) | 8.64060 | + | 1.53568i | 0.301927 | + | 0.0536612i | ||||
\(820\) | 6.39306 | 0.223256 | ||||||||
\(821\) | − | 45.7191i | − | 1.59561i | −0.602917 | − | 0.797804i | \(-0.705995\pi\) | ||
0.602917 | − | 0.797804i | \(-0.294005\pi\) | |||||||
\(822\) | 111.556 | 3.89095 | ||||||||
\(823\) | −45.5672 | −1.58837 | −0.794187 | − | 0.607673i | \(-0.792103\pi\) | ||||
−0.794187 | + | 0.607673i | \(0.792103\pi\) | |||||||
\(824\) | 72.4827i | 2.52505i | ||||||||
\(825\) | 0.837428i | 0.0291555i | ||||||||
\(826\) | − | 18.1422i | − | 0.631250i | ||||||
\(827\) | − | 1.77154i | − | 0.0616024i | −0.999526 | − | 0.0308012i | \(-0.990194\pi\) | ||
0.999526 | − | 0.0308012i | \(-0.00980588\pi\) | |||||||
\(828\) | −36.0859 | −1.25407 | ||||||||
\(829\) | −13.6456 | −0.473932 | −0.236966 | − | 0.971518i | \(-0.576153\pi\) | ||||
−0.236966 | + | 0.971518i | \(0.576153\pi\) | |||||||
\(830\) | 49.8572i | 1.73057i | ||||||||
\(831\) | −2.47371 | −0.0858121 | ||||||||
\(832\) | −5.14213 | + | 28.9325i | −0.178271 | + | 1.00305i | ||||
\(833\) | 5.15511 | 0.178614 | ||||||||
\(834\) | − | 4.73025i | − | 0.163795i | ||||||
\(835\) | 39.1149 | 1.35363 | ||||||||
\(836\) | 3.03213 | 0.104868 | ||||||||
\(837\) | 1.06627i | 0.0368558i | ||||||||
\(838\) | 81.7050i | 2.82245i | ||||||||
\(839\) | − | 17.4861i | − | 0.603686i | −0.953358 | − | 0.301843i | \(-0.902398\pi\) | ||
0.953358 | − | 0.301843i | \(-0.0976018\pi\) | |||||||
\(840\) | − | 29.2790i | − | 1.01022i | ||||||
\(841\) | −3.24496 | −0.111895 | ||||||||
\(842\) | −77.2355 | −2.66171 | ||||||||
\(843\) | − | 13.6701i | − | 0.470822i | ||||||
\(844\) | 81.0671 | 2.79045 | ||||||||
\(845\) | 11.9838 | − | 32.6487i | 0.412255 | − | 1.12315i | ||||
\(846\) | 74.4814 | 2.56072 | ||||||||
\(847\) | − | 10.4850i | − | 0.360268i | ||||||
\(848\) | 36.6513 | 1.25861 | ||||||||
\(849\) | −37.9002 | −1.30073 | ||||||||
\(850\) | − | 4.47023i | − | 0.153328i | ||||||
\(851\) | 25.6199i | 0.878239i | ||||||||
\(852\) | − | 24.9270i | − | 0.853986i | ||||||
\(853\) | − | 22.9767i | − | 0.786707i | −0.919387 | − | 0.393353i | \(-0.871315\pi\) | ||
0.919387 | − | 0.393353i | \(-0.128685\pi\) | |||||||
\(854\) | −14.5318 | −0.497266 | ||||||||
\(855\) | 31.4392 | 1.07520 | ||||||||
\(856\) | 70.6652i | 2.41529i | ||||||||
\(857\) | 6.41812 | 0.219239 | 0.109619 | − | 0.993974i | \(-0.465037\pi\) | ||||
0.109619 | + | 0.993974i | \(0.465037\pi\) | |||||||
\(858\) | −0.599336 | + | 3.37219i | −0.0204610 | + | 0.115125i | ||||
\(859\) | −33.4062 | −1.13980 | −0.569902 | − | 0.821713i | \(-0.693019\pi\) | ||||
−0.569902 | + | 0.821713i | \(0.693019\pi\) | |||||||
\(860\) | 44.2208i | 1.50792i | ||||||||
\(861\) | 1.34878 | 0.0459663 | ||||||||
\(862\) | −33.5760 | −1.14360 | ||||||||
\(863\) | 50.0659i | 1.70426i | 0.523327 | + | 0.852132i | \(0.324691\pi\) | ||||
−0.523327 | + | 0.852132i | \(0.675309\pi\) | |||||||
\(864\) | 0.131292i | 0.00446664i | ||||||||
\(865\) | 6.34638i | 0.215783i | ||||||||
\(866\) | 10.6479i | 0.361829i | ||||||||
\(867\) | −38.3502 | −1.30244 | ||||||||
\(868\) | 3.81010 | 0.129323 | ||||||||
\(869\) | − | 1.66061i | − | 0.0563322i | ||||||
\(870\) | −78.2453 | −2.65277 | ||||||||
\(871\) | 2.78523 | + | 0.495015i | 0.0943738 | + | 0.0167730i | ||||
\(872\) | 2.30236 | 0.0779676 | ||||||||
\(873\) | 15.5142i | 0.525078i | ||||||||
\(874\) | 40.1067 | 1.35663 | ||||||||
\(875\) | 7.26736 | 0.245682 | ||||||||
\(876\) | 8.84279i | 0.298770i | ||||||||
\(877\) | − | 1.09490i | − | 0.0369722i | −0.999829 | − | 0.0184861i | \(-0.994115\pi\) | ||
0.999829 | − | 0.0184861i | \(-0.00588465\pi\) | |||||||
\(878\) | 4.04816i | 0.136619i | ||||||||
\(879\) | − | 45.5504i | − | 1.53638i | ||||||
\(880\) | 1.73054 | 0.0583364 | ||||||||
\(881\) | −38.4176 | −1.29432 | −0.647161 | − | 0.762353i | \(-0.724044\pi\) | ||||
−0.647161 | + | 0.762353i | \(0.724044\pi\) | |||||||
\(882\) | 37.9398i | 1.27750i | ||||||||
\(883\) | 51.2341 | 1.72416 | 0.862082 | − | 0.506769i | \(-0.169160\pi\) | ||||
0.862082 | + | 0.506769i | \(0.169160\pi\) | |||||||
\(884\) | 2.13061 | − | 11.9880i | 0.0716600 | − | 0.403198i | ||||
\(885\) | 48.8915 | 1.64347 | ||||||||
\(886\) | − | 26.8423i | − | 0.901785i | ||||||
\(887\) | 10.7255 | 0.360126 | 0.180063 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180063 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(888\) | 82.5931 | 2.77164 | ||||||||
\(889\) | 20.1931i | 0.677255i | ||||||||
\(890\) | − | 113.258i | − | 3.79640i | ||||||
\(891\) | 1.67355i | 0.0560659i | ||||||||
\(892\) | 14.7913i | 0.495248i | ||||||||
\(893\) | −55.1288 | −1.84481 | ||||||||
\(894\) | 60.0483 | 2.00831 | ||||||||
\(895\) | 21.1713i | 0.707680i | ||||||||
\(896\) | 18.8208 | 0.628757 | ||||||||
\(897\) | −5.27946 | + | 29.7051i | −0.176276 | + | 0.991826i | ||||
\(898\) | 5.09809 | 0.170125 | ||||||||
\(899\) | − | 5.07494i | − | 0.169259i | ||||||
\(900\) | 21.9097 | 0.730325 | ||||||||
\(901\) | 7.90952 | 0.263504 | ||||||||
\(902\) | 0.241716i | 0.00804827i | ||||||||
\(903\) | 9.32951i | 0.310467i | ||||||||
\(904\) | 30.9599i | 1.02971i | ||||||||
\(905\) | − | 34.9095i | − | 1.16043i | ||||||
\(906\) | 7.43188 | 0.246908 | ||||||||
\(907\) | 33.5827 | 1.11510 | 0.557548 | − | 0.830145i | \(-0.311742\pi\) | ||||
0.557548 | + | 0.830145i | \(0.311742\pi\) | |||||||
\(908\) | − | 52.5268i | − | 1.74316i | ||||||
\(909\) | 49.5687 | 1.64409 | ||||||||
\(910\) | −22.2052 | − | 3.94650i | −0.736095 | − | 0.130825i | ||||
\(911\) | 23.2679 | 0.770901 | 0.385450 | − | 0.922729i | \(-0.374046\pi\) | ||||
0.385450 | + | 0.922729i | \(0.374046\pi\) | |||||||
\(912\) | − | 42.6426i | − | 1.41204i | ||||||
\(913\) | −1.25538 | −0.0415470 | ||||||||
\(914\) | −13.9780 | −0.462351 | ||||||||
\(915\) | − | 39.1616i | − | 1.29464i | ||||||
\(916\) | 76.5321i | 2.52869i | ||||||||
\(917\) | 12.3934i | 0.409267i | ||||||||
\(918\) | − | 2.20966i | − | 0.0729298i | ||||||
\(919\) | −29.5244 | −0.973921 | −0.486960 | − | 0.873424i | \(-0.661894\pi\) | ||||
−0.486960 | + | 0.873424i | \(0.661894\pi\) | |||||||
\(920\) | 46.2212 | 1.52387 | ||||||||
\(921\) | 35.8296i | 1.18063i | ||||||||
\(922\) | 29.0906 | 0.958049 | ||||||||
\(923\) | −9.42240 | − | 1.67463i | −0.310142 | − | 0.0551212i | ||||
\(924\) | 1.47915 | 0.0486603 | ||||||||
\(925\) | − | 15.5553i | − | 0.511454i | ||||||
\(926\) | 1.10494 | 0.0363104 | ||||||||
\(927\) | −37.9675 | −1.24702 | ||||||||
\(928\) | − | 0.624884i | − | 0.0205128i | ||||||
\(929\) | − | 20.1052i | − | 0.659631i | −0.944045 | − | 0.329815i | \(-0.893013\pi\) | ||
0.944045 | − | 0.329815i | \(-0.106987\pi\) | |||||||
\(930\) | 15.4180i | 0.505575i | ||||||||
\(931\) | − | 28.0818i | − | 0.920344i | ||||||
\(932\) | 7.96599 | 0.260935 | ||||||||
\(933\) | −5.09150 | −0.166688 | ||||||||
\(934\) | 65.0193i | 2.12749i | ||||||||
\(935\) | 0.373459 | 0.0122134 | ||||||||
\(936\) | 43.9739 | + | 7.81543i | 1.43733 | + | 0.255455i | ||||
\(937\) | 37.5339 | 1.22618 | 0.613090 | − | 0.790013i | \(-0.289926\pi\) | ||||
0.613090 | + | 0.790013i | \(0.289926\pi\) | |||||||
\(938\) | − | 1.83446i | − | 0.0598973i | ||||||
\(939\) | 31.4349 | 1.02584 | ||||||||
\(940\) | −127.470 | −4.15763 | ||||||||
\(941\) | 28.1882i | 0.918908i | 0.888202 | + | 0.459454i | \(0.151955\pi\) | ||||
−0.888202 | + | 0.459454i | \(0.848045\pi\) | |||||||
\(942\) | 18.5298i | 0.603735i | ||||||||
\(943\) | 2.12924i | 0.0693377i | ||||||||
\(944\) | − | 30.4510i | − | 0.991096i | ||||||
\(945\) | −2.72575 | −0.0886687 | ||||||||
\(946\) | −1.67195 | −0.0543598 | ||||||||
\(947\) | − | 14.0166i | − | 0.455478i | −0.973722 | − | 0.227739i | \(-0.926867\pi\) | ||
0.973722 | − | 0.227739i | \(-0.0731333\pi\) | |||||||
\(948\) | −94.6149 | −3.07295 | ||||||||
\(949\) | 3.34257 | + | 0.594071i | 0.108504 | + | 0.0192844i | ||||
\(950\) | −24.3510 | −0.790051 | ||||||||
\(951\) | 71.2919i | 2.31180i | ||||||||
\(952\) | −3.93538 | −0.127546 | ||||||||
\(953\) | 5.61343 | 0.181837 | 0.0909184 | − | 0.995858i | \(-0.471020\pi\) | ||||
0.0909184 | + | 0.995858i | \(0.471020\pi\) | |||||||
\(954\) | 58.2112i | 1.88466i | ||||||||
\(955\) | − | 26.2642i | − | 0.849889i | ||||||
\(956\) | 48.3057i | 1.56232i | ||||||||
\(957\) | − | 1.97018i | − | 0.0636869i | ||||||
\(958\) | −28.7706 | −0.929537 | ||||||||
\(959\) | −18.4961 | −0.597271 | ||||||||
\(960\) | 51.3542i | 1.65745i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 11.1327 | − | 62.6385i | 0.358932 | − | 2.01955i | ||||
\(963\) | −37.0154 | −1.19281 | ||||||||
\(964\) | 64.0726i | 2.06364i | ||||||||
\(965\) | 53.4226 | 1.71973 | ||||||||
\(966\) | 19.5650 | 0.629494 | ||||||||
\(967\) | 20.0869i | 0.645951i | 0.946407 | + | 0.322975i | \(0.104683\pi\) | ||||
−0.946407 | + | 0.322975i | \(0.895317\pi\) | |||||||
\(968\) | − | 53.3603i | − | 1.71506i | ||||||
\(969\) | − | 9.20247i | − | 0.295626i | ||||||
\(970\) | − | 39.8695i | − | 1.28013i | ||||||
\(971\) | −13.7594 | −0.441560 | −0.220780 | − | 0.975324i | \(-0.570860\pi\) | ||||
−0.220780 | + | 0.975324i | \(0.570860\pi\) | |||||||
\(972\) | 82.5973 | 2.64931 | ||||||||
\(973\) | 0.784284i | 0.0251430i | ||||||||
\(974\) | −51.6710 | −1.65565 | ||||||||
\(975\) | 3.20546 | − | 18.0356i | 0.102657 | − | 0.577603i | ||||
\(976\) | −24.3910 | −0.780735 | ||||||||
\(977\) | 8.80988i | 0.281853i | 0.990020 | + | 0.140927i | \(0.0450081\pi\) | ||||
−0.990020 | + | 0.140927i | \(0.954992\pi\) | |||||||
\(978\) | −22.9130 | −0.732677 | ||||||||
\(979\) | 2.85177 | 0.0911430 | ||||||||
\(980\) | − | 64.9316i | − | 2.07416i | ||||||
\(981\) | 1.20601i | 0.0385049i | ||||||||
\(982\) | 60.9130i | 1.94381i | ||||||||
\(983\) | − | 0.750558i | − | 0.0239391i | −0.999928 | − | 0.0119695i | \(-0.996190\pi\) | ||
0.999928 | − | 0.0119695i | \(-0.00381012\pi\) | |||||||
\(984\) | 6.86423 | 0.218824 | ||||||||
\(985\) | −44.2098 | −1.40864 | ||||||||
\(986\) | 10.5169i | 0.334927i | ||||||||
\(987\) | −26.8931 | −0.856017 | ||||||||
\(988\) | −65.3028 | − | 11.6062i | −2.07756 | − | 0.369242i | ||||
\(989\) | −14.7280 | −0.468323 | ||||||||
\(990\) | 2.74852i | 0.0873537i | ||||||||
\(991\) | −44.1083 | −1.40115 | −0.700573 | − | 0.713581i | \(-0.747072\pi\) | ||||
−0.700573 | + | 0.713581i | \(0.747072\pi\) | |||||||
\(992\) | −0.123131 | −0.00390942 | ||||||||
\(993\) | 17.9168i | 0.568572i | ||||||||
\(994\) | 6.20597i | 0.196841i | ||||||||
\(995\) | 55.1289i | 1.74770i | ||||||||
\(996\) | 71.5267i | 2.26641i | ||||||||
\(997\) | 14.6260 | 0.463210 | 0.231605 | − | 0.972810i | \(-0.425602\pi\) | ||||
0.231605 | + | 0.972810i | \(0.425602\pi\) | |||||||
\(998\) | −45.3617 | −1.43590 | ||||||||
\(999\) | − | 7.68907i | − | 0.243271i |
(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 | 403.2.c.b.311.29 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.14 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.3 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.4 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.29 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.3 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.14 | 16 | 13.5 | odd | 4 |