Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), degree \(2\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + 40 x^{2} + 8 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.6 | ||
Root | \(1.13633 - 1.96819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.277 |
Dual form | 483.2.i.f.415.6 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13633 | + | 1.96819i | 0.803510 | + | 1.39172i | 0.917292 | + | 0.398215i | \(0.130370\pi\) |
−0.113782 | + | 0.993506i | \(0.536297\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −1.58251 | + | 2.74099i | −0.791257 | + | 1.37050i | ||||
\(5\) | −2.07560 | − | 3.59505i | −0.928237 | − | 1.60775i | −0.786270 | − | 0.617883i | \(-0.787991\pi\) |
−0.141967 | − | 0.989871i | \(-0.545343\pi\) | |||||||
\(6\) | 2.27267 | 0.927814 | ||||||||
\(7\) | −1.69175 | − | 2.03420i | −0.639422 | − | 0.768856i | ||||
\(8\) | −2.64772 | −0.936112 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 4.71716 | − | 8.17036i | 1.49170 | − | 2.58369i | ||||
\(11\) | 1.59353 | − | 2.76007i | 0.480467 | − | 0.832193i | −0.519282 | − | 0.854603i | \(-0.673801\pi\) |
0.999749 | + | 0.0224099i | \(0.00713388\pi\) | |||||||
\(12\) | 1.58251 | + | 2.74099i | 0.456832 | + | 0.791257i | ||||
\(13\) | 0.175661 | 0.0487197 | 0.0243598 | − | 0.999703i | \(-0.492245\pi\) | ||||
0.0243598 | + | 0.999703i | \(0.492245\pi\) | |||||||
\(14\) | 2.08130 | − | 5.64122i | 0.556251 | − | 1.50768i | ||||
\(15\) | −4.15120 | −1.07184 | ||||||||
\(16\) | 0.156327 | + | 0.270766i | 0.0390817 | + | 0.0676915i | ||||
\(17\) | 0.663433 | − | 1.14910i | 0.160906 | − | 0.278697i | −0.774288 | − | 0.632834i | \(-0.781892\pi\) |
0.935194 | + | 0.354136i | \(0.115225\pi\) | |||||||
\(18\) | 1.13633 | − | 1.96819i | 0.267837 | − | 0.463907i | ||||
\(19\) | −0.0252131 | − | 0.0436703i | −0.00578427 | − | 0.0100187i | 0.863119 | − | 0.505001i | \(-0.168508\pi\) |
−0.868903 | + | 0.494982i | \(0.835175\pi\) | |||||||
\(20\) | 13.1387 | 2.93790 | ||||||||
\(21\) | −2.60755 | + | 0.447998i | −0.569013 | + | 0.0977613i | ||||
\(22\) | 7.24313 | 1.54424 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | −1.32386 | + | 2.29300i | −0.270232 | + | 0.468056i | ||||
\(25\) | −6.11625 | + | 10.5937i | −1.22325 | + | 2.11873i | ||||
\(26\) | 0.199610 | + | 0.345735i | 0.0391467 | + | 0.0678042i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 8.25296 | − | 1.41793i | 1.55966 | − | 0.267963i | ||||
\(29\) | 1.10049 | 0.204356 | 0.102178 | − | 0.994766i | \(-0.467419\pi\) | ||||
0.102178 | + | 0.994766i | \(0.467419\pi\) | |||||||
\(30\) | −4.71716 | − | 8.17036i | −0.861231 | − | 1.49170i | ||||
\(31\) | 4.35518 | − | 7.54340i | 0.782214 | − | 1.35483i | −0.148435 | − | 0.988922i | \(-0.547424\pi\) |
0.930649 | − | 0.365912i | \(-0.119243\pi\) | |||||||
\(32\) | −3.00300 | + | 5.20135i | −0.530861 | + | 0.919478i | ||||
\(33\) | −1.59353 | − | 2.76007i | −0.277398 | − | 0.480467i | ||||
\(34\) | 3.01553 | 0.517159 | ||||||||
\(35\) | −3.80165 | + | 10.3041i | −0.642597 | + | 1.74171i | ||||
\(36\) | 3.16503 | 0.527505 | ||||||||
\(37\) | −1.88116 | − | 3.25827i | −0.309261 | − | 0.535656i | 0.668940 | − | 0.743317i | \(-0.266748\pi\) |
−0.978201 | + | 0.207660i | \(0.933415\pi\) | |||||||
\(38\) | 0.0573009 | − | 0.0992482i | 0.00929544 | − | 0.0161002i | ||||
\(39\) | 0.0878306 | − | 0.152127i | 0.0140642 | − | 0.0243598i | ||||
\(40\) | 5.49562 | + | 9.51870i | 0.868934 | + | 1.50504i | ||||
\(41\) | 4.84719 | 0.757004 | 0.378502 | − | 0.925601i | \(-0.376439\pi\) | ||||
0.378502 | + | 0.925601i | \(0.376439\pi\) | |||||||
\(42\) | −3.84479 | − | 4.62307i | −0.593264 | − | 0.713355i | ||||
\(43\) | −10.5958 | −1.61584 | −0.807920 | − | 0.589293i | \(-0.799406\pi\) | ||||
−0.807920 | + | 0.589293i | \(0.799406\pi\) | |||||||
\(44\) | 5.04356 | + | 8.73571i | 0.760346 | + | 1.31696i | ||||
\(45\) | −2.07560 | + | 3.59505i | −0.309412 | + | 0.535918i | ||||
\(46\) | −1.13633 | + | 1.96819i | −0.167543 | + | 0.290194i | ||||
\(47\) | 4.47507 | + | 7.75104i | 0.652755 | + | 1.13061i | 0.982451 | + | 0.186518i | \(0.0597204\pi\) |
−0.329696 | + | 0.944087i | \(0.606946\pi\) | |||||||
\(48\) | 0.312654 | 0.0451277 | ||||||||
\(49\) | −1.27596 | + | 6.88273i | −0.182279 | + | 0.983247i | ||||
\(50\) | −27.8004 | −3.93157 | ||||||||
\(51\) | −0.663433 | − | 1.14910i | −0.0928992 | − | 0.160906i | ||||
\(52\) | −0.277986 | + | 0.481487i | −0.0385498 | + | 0.0667702i | ||||
\(53\) | 4.98815 | − | 8.63972i | 0.685175 | − | 1.18676i | −0.288207 | − | 0.957568i | \(-0.593059\pi\) |
0.973382 | − | 0.229189i | \(-0.0736074\pi\) | |||||||
\(54\) | −1.13633 | − | 1.96819i | −0.154636 | − | 0.267837i | ||||
\(55\) | −13.2301 | −1.78395 | ||||||||
\(56\) | 4.47929 | + | 5.38601i | 0.598570 | + | 0.719735i | ||||
\(57\) | −0.0504261 | −0.00667910 | ||||||||
\(58\) | 1.25053 | + | 2.16597i | 0.164202 | + | 0.284406i | ||||
\(59\) | 3.19449 | − | 5.53301i | 0.415887 | − | 0.720337i | −0.579634 | − | 0.814877i | \(-0.696805\pi\) |
0.995521 | + | 0.0945397i | \(0.0301379\pi\) | |||||||
\(60\) | 6.56934 | − | 11.3784i | 0.848098 | − | 1.46895i | ||||
\(61\) | 3.61631 | + | 6.26363i | 0.463021 | + | 0.801975i | 0.999110 | − | 0.0421861i | \(-0.0134323\pi\) |
−0.536089 | + | 0.844161i | \(0.680099\pi\) | |||||||
\(62\) | 19.7958 | 2.51407 | ||||||||
\(63\) | −0.915795 | + | 2.48220i | −0.115379 | + | 0.312728i | ||||
\(64\) | −13.0244 | −1.62805 | ||||||||
\(65\) | −0.364603 | − | 0.631511i | −0.0452234 | − | 0.0783293i | ||||
\(66\) | 3.62156 | − | 6.27273i | 0.445784 | − | 0.772120i | ||||
\(67\) | −3.01030 | + | 5.21399i | −0.367766 | + | 0.636990i | −0.989216 | − | 0.146464i | \(-0.953211\pi\) |
0.621450 | + | 0.783454i | \(0.286544\pi\) | |||||||
\(68\) | 2.09978 | + | 3.63693i | 0.254636 | + | 0.441043i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −24.6004 | + | 4.22656i | −2.94031 | + | 0.505170i | ||||
\(71\) | 6.71519 | 0.796947 | 0.398473 | − | 0.917180i | \(-0.369540\pi\) | ||||
0.398473 | + | 0.917180i | \(0.369540\pi\) | |||||||
\(72\) | 1.32386 | + | 2.29300i | 0.156019 | + | 0.270232i | ||||
\(73\) | 2.30686 | − | 3.99560i | 0.269998 | − | 0.467650i | −0.698863 | − | 0.715255i | \(-0.746310\pi\) |
0.968861 | + | 0.247606i | \(0.0796438\pi\) | |||||||
\(74\) | 4.27526 | − | 7.40497i | 0.496989 | − | 0.860810i | ||||
\(75\) | 6.11625 | + | 10.5937i | 0.706243 | + | 1.22325i | ||||
\(76\) | 0.159600 | 0.0183074 | ||||||||
\(77\) | −8.31040 | + | 1.42780i | −0.947058 | + | 0.162713i | ||||
\(78\) | 0.399220 | 0.0452028 | ||||||||
\(79\) | 7.74272 | + | 13.4108i | 0.871124 | + | 1.50883i | 0.860835 | + | 0.508883i | \(0.169942\pi\) |
0.0102883 | + | 0.999947i | \(0.496725\pi\) | |||||||
\(80\) | 0.648945 | − | 1.12401i | 0.0725542 | − | 0.125668i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.50803 | + | 9.54019i | 0.608260 | + | 1.05354i | ||||
\(83\) | 7.21102 | 0.791512 | 0.395756 | − | 0.918356i | \(-0.370483\pi\) | ||||
0.395756 | + | 0.918356i | \(0.370483\pi\) | |||||||
\(84\) | 2.89852 | − | 7.85623i | 0.316254 | − | 0.857185i | ||||
\(85\) | −5.50809 | −0.597436 | ||||||||
\(86\) | −12.0403 | − | 20.8545i | −1.29834 | − | 2.24880i | ||||
\(87\) | 0.550245 | − | 0.953053i | 0.0589925 | − | 0.102178i | ||||
\(88\) | −4.21922 | + | 7.30791i | −0.449771 | + | 0.779026i | ||||
\(89\) | 0.970735 | + | 1.68136i | 0.102898 | + | 0.178224i | 0.912877 | − | 0.408234i | \(-0.133855\pi\) |
−0.809980 | + | 0.586458i | \(0.800522\pi\) | |||||||
\(90\) | −9.43432 | −0.994464 | ||||||||
\(91\) | −0.297175 | − | 0.357331i | −0.0311524 | − | 0.0374584i | ||||
\(92\) | −3.16503 | −0.329977 | ||||||||
\(93\) | −4.35518 | − | 7.54340i | −0.451612 | − | 0.782214i | ||||
\(94\) | −10.1703 | + | 17.6156i | −1.04899 | + | 1.81691i | ||||
\(95\) | −0.104665 | + | 0.181284i | −0.0107384 | + | 0.0185994i | ||||
\(96\) | 3.00300 | + | 5.20135i | 0.306493 | + | 0.530861i | ||||
\(97\) | −12.7879 | −1.29841 | −0.649207 | − | 0.760612i | \(-0.724899\pi\) | ||||
−0.649207 | + | 0.760612i | \(0.724899\pi\) | |||||||
\(98\) | −14.9964 | + | 5.30976i | −1.51487 | + | 0.536367i | ||||
\(99\) | −3.18706 | −0.320311 | ||||||||
\(100\) | −19.3581 | − | 33.5292i | −1.93581 | − | 3.35292i | ||||
\(101\) | 0.822915 | − | 1.42533i | 0.0818831 | − | 0.141826i | −0.822176 | − | 0.569234i | \(-0.807240\pi\) |
0.904059 | + | 0.427408i | \(0.140573\pi\) | |||||||
\(102\) | 1.50776 | − | 2.61152i | 0.149291 | − | 0.258579i | ||||
\(103\) | −4.49638 | − | 7.78795i | −0.443041 | − | 0.767370i | 0.554872 | − | 0.831936i | \(-0.312767\pi\) |
−0.997913 | + | 0.0645657i | \(0.979434\pi\) | |||||||
\(104\) | −0.465103 | −0.0456071 | ||||||||
\(105\) | 7.02280 | + | 8.44439i | 0.685356 | + | 0.824088i | ||||
\(106\) | 22.6728 | 2.20218 | ||||||||
\(107\) | 9.49153 | + | 16.4398i | 0.917581 | + | 1.58930i | 0.803078 | + | 0.595874i | \(0.203194\pi\) |
0.114503 | + | 0.993423i | \(0.463472\pi\) | |||||||
\(108\) | 1.58251 | − | 2.74099i | 0.152277 | − | 0.263752i | ||||
\(109\) | 5.85913 | − | 10.1483i | 0.561203 | − | 0.972033i | −0.436189 | − | 0.899855i | \(-0.643672\pi\) |
0.997392 | − | 0.0721773i | \(-0.0229947\pi\) | |||||||
\(110\) | −15.0339 | − | 26.0394i | −1.43342 | − | 2.48276i | ||||
\(111\) | −3.76233 | −0.357104 | ||||||||
\(112\) | 0.286327 | − | 0.776069i | 0.0270553 | − | 0.0733317i | ||||
\(113\) | 16.6028 | 1.56186 | 0.780931 | − | 0.624617i | \(-0.214745\pi\) | ||||
0.780931 | + | 0.624617i | \(0.214745\pi\) | |||||||
\(114\) | −0.0573009 | − | 0.0992482i | −0.00536673 | − | 0.00929544i | ||||
\(115\) | 2.07560 | − | 3.59505i | 0.193551 | − | 0.335240i | ||||
\(116\) | −1.74154 | + | 3.01644i | −0.161698 | + | 0.280069i | ||||
\(117\) | −0.0878306 | − | 0.152127i | −0.00811995 | − | 0.0140642i | ||||
\(118\) | 14.5200 | 1.33668 | ||||||||
\(119\) | −3.45986 | + | 0.594434i | −0.317165 | + | 0.0544916i | ||||
\(120\) | 10.9912 | 1.00336 | ||||||||
\(121\) | 0.421334 | + | 0.729772i | 0.0383031 | + | 0.0663429i | ||||
\(122\) | −8.21867 | + | 14.2352i | −0.744083 | + | 1.28879i | ||||
\(123\) | 2.42359 | − | 4.19779i | 0.218528 | − | 0.378502i | ||||
\(124\) | 13.7843 | + | 23.8751i | 1.23786 | + | 2.14404i | ||||
\(125\) | 30.0236 | 2.68539 | ||||||||
\(126\) | −5.92609 | + | 1.01815i | −0.527938 | + | 0.0907042i | ||||
\(127\) | 17.8466 | 1.58363 | 0.791815 | − | 0.610761i | \(-0.209136\pi\) | ||||
0.791815 | + | 0.610761i | \(0.209136\pi\) | |||||||
\(128\) | −8.79403 | − | 15.2317i | −0.777290 | − | 1.34631i | ||||
\(129\) | −5.29788 | + | 9.17620i | −0.466453 | + | 0.807920i | ||||
\(130\) | 0.828622 | − | 1.43522i | 0.0726750 | − | 0.125877i | ||||
\(131\) | −10.7810 | − | 18.6732i | −0.941940 | − | 1.63149i | −0.761765 | − | 0.647854i | \(-0.775667\pi\) |
−0.180176 | − | 0.983634i | \(-0.557667\pi\) | |||||||
\(132\) | 10.0871 | 0.877971 | ||||||||
\(133\) | −0.0461800 | + | 0.125168i | −0.00400431 | + | 0.0108534i | ||||
\(134\) | −13.6828 | −1.18202 | ||||||||
\(135\) | 2.07560 | + | 3.59505i | 0.178639 | + | 0.309412i | ||||
\(136\) | −1.75659 | + | 3.04250i | −0.150626 | + | 0.260892i | ||||
\(137\) | −0.282766 | + | 0.489765i | −0.0241583 | + | 0.0418434i | −0.877852 | − | 0.478932i | \(-0.841024\pi\) |
0.853693 | + | 0.520776i | \(0.174357\pi\) | |||||||
\(138\) | 1.13633 | + | 1.96819i | 0.0967313 | + | 0.167543i | ||||
\(139\) | −19.5670 | −1.65965 | −0.829825 | − | 0.558024i | \(-0.811560\pi\) | ||||
−0.829825 | + | 0.558024i | \(0.811560\pi\) | |||||||
\(140\) | −22.2274 | − | 26.7267i | −1.87856 | − | 2.25882i | ||||
\(141\) | 8.95013 | 0.753737 | ||||||||
\(142\) | 7.63071 | + | 13.2168i | 0.640355 | + | 1.10913i | ||||
\(143\) | 0.279921 | − | 0.484838i | 0.0234082 | − | 0.0405442i | ||||
\(144\) | 0.156327 | − | 0.270766i | 0.0130272 | − | 0.0225638i | ||||
\(145\) | −2.28418 | − | 3.95632i | −0.189691 | − | 0.328554i | ||||
\(146\) | 10.4855 | 0.867783 | ||||||||
\(147\) | 5.32264 | + | 4.54637i | 0.439004 | + | 0.374979i | ||||
\(148\) | 11.9079 | 0.978821 | ||||||||
\(149\) | −3.76363 | − | 6.51880i | −0.308329 | − | 0.534041i | 0.669668 | − | 0.742660i | \(-0.266436\pi\) |
−0.977997 | + | 0.208619i | \(0.933103\pi\) | |||||||
\(150\) | −13.9002 | + | 24.0759i | −1.13495 | + | 1.96579i | ||||
\(151\) | 10.6811 | − | 18.5002i | 0.869213 | − | 1.50552i | 0.00641149 | − | 0.999979i | \(-0.497959\pi\) |
0.862802 | − | 0.505542i | \(-0.168708\pi\) | |||||||
\(152\) | 0.0667572 | + | 0.115627i | 0.00541472 | + | 0.00937858i | ||||
\(153\) | −1.32687 | −0.107271 | ||||||||
\(154\) | −12.2536 | − | 14.7340i | −0.987421 | − | 1.18730i | ||||
\(155\) | −36.1585 | −2.90432 | ||||||||
\(156\) | 0.277986 | + | 0.481487i | 0.0222567 | + | 0.0385498i | ||||
\(157\) | −5.87970 | + | 10.1839i | −0.469251 | + | 0.812767i | −0.999382 | − | 0.0351487i | \(-0.988810\pi\) |
0.530131 | + | 0.847916i | \(0.322143\pi\) | |||||||
\(158\) | −17.5966 | + | 30.4783i | −1.39991 | + | 2.42472i | ||||
\(159\) | −4.98815 | − | 8.63972i | −0.395586 | − | 0.685175i | ||||
\(160\) | 24.9322 | 1.97106 | ||||||||
\(161\) | 0.915795 | − | 2.48220i | 0.0721748 | − | 0.195625i | ||||
\(162\) | −2.27267 | −0.178558 | ||||||||
\(163\) | 7.66094 | + | 13.2691i | 0.600051 | + | 1.03932i | 0.992813 | + | 0.119678i | \(0.0381864\pi\) |
−0.392762 | + | 0.919640i | \(0.628480\pi\) | |||||||
\(164\) | −7.67075 | + | 13.2861i | −0.598985 | + | 1.03747i | ||||
\(165\) | −6.61506 | + | 11.4576i | −0.514982 | + | 0.891975i | ||||
\(166\) | 8.19413 | + | 14.1927i | 0.635988 | + | 1.10156i | ||||
\(167\) | −8.02472 | −0.620972 | −0.310486 | − | 0.950578i | \(-0.600492\pi\) | ||||
−0.310486 | + | 0.950578i | \(0.600492\pi\) | |||||||
\(168\) | 6.90406 | − | 1.18618i | 0.532660 | − | 0.0915155i | ||||
\(169\) | −12.9691 | −0.997626 | ||||||||
\(170\) | −6.25903 | − | 10.8410i | −0.480046 | − | 0.831464i | ||||
\(171\) | −0.0252131 | + | 0.0436703i | −0.00192809 | + | 0.00333955i | ||||
\(172\) | 16.7679 | − | 29.0429i | 1.27854 | − | 2.21450i | ||||
\(173\) | −7.76126 | − | 13.4429i | −0.590078 | − | 1.02205i | −0.994221 | − | 0.107349i | \(-0.965764\pi\) |
0.404143 | − | 0.914696i | \(-0.367570\pi\) | |||||||
\(174\) | 2.50105 | 0.189604 | ||||||||
\(175\) | 31.8968 | − | 5.48014i | 2.41117 | − | 0.414260i | ||||
\(176\) | 0.996445 | 0.0751099 | ||||||||
\(177\) | −3.19449 | − | 5.53301i | −0.240112 | − | 0.415887i | ||||
\(178\) | −2.20616 | + | 3.82118i | −0.165359 | + | 0.286410i | ||||
\(179\) | −4.14140 | + | 7.17312i | −0.309543 | + | 0.536144i | −0.978262 | − | 0.207371i | \(-0.933509\pi\) |
0.668720 | + | 0.743515i | \(0.266843\pi\) | |||||||
\(180\) | −6.56934 | − | 11.3784i | −0.489650 | − | 0.848098i | ||||
\(181\) | −5.71189 | −0.424561 | −0.212281 | − | 0.977209i | \(-0.568089\pi\) | ||||
−0.212281 | + | 0.977209i | \(0.568089\pi\) | |||||||
\(182\) | 0.365604 | − | 0.990944i | 0.0271004 | − | 0.0734537i | ||||
\(183\) | 7.23261 | 0.534650 | ||||||||
\(184\) | −1.32386 | − | 2.29300i | −0.0975964 | − | 0.169042i | ||||
\(185\) | −7.80909 | + | 13.5257i | −0.574136 | + | 0.994432i | ||||
\(186\) | 9.89789 | − | 17.1437i | 0.725749 | − | 1.25703i | ||||
\(187\) | −2.11440 | − | 3.66224i | −0.154620 | − | 0.267810i | ||||
\(188\) | −28.3274 | −2.06599 | ||||||||
\(189\) | 1.69175 | + | 2.03420i | 0.123057 | + | 0.147966i | ||||
\(190\) | −0.475736 | −0.0345135 | ||||||||
\(191\) | 0.775762 | + | 1.34366i | 0.0561322 | + | 0.0972238i | 0.892726 | − | 0.450600i | \(-0.148790\pi\) |
−0.836594 | + | 0.547824i | \(0.815457\pi\) | |||||||
\(192\) | −6.51218 | + | 11.2794i | −0.469976 | + | 0.814023i | ||||
\(193\) | −3.66145 | + | 6.34182i | −0.263557 | + | 0.456494i | −0.967185 | − | 0.254075i | \(-0.918229\pi\) |
0.703627 | + | 0.710569i | \(0.251562\pi\) | |||||||
\(194\) | −14.5313 | − | 25.1690i | −1.04329 | − | 1.80703i | ||||
\(195\) | −0.729206 | −0.0522195 | ||||||||
\(196\) | −16.8463 | − | 14.3894i | −1.20331 | − | 1.02781i | ||||
\(197\) | −6.84137 | −0.487427 | −0.243714 | − | 0.969847i | \(-0.578366\pi\) | ||||
−0.243714 | + | 0.969847i | \(0.578366\pi\) | |||||||
\(198\) | −3.62156 | − | 6.27273i | −0.257373 | − | 0.445784i | ||||
\(199\) | −3.82183 | + | 6.61961i | −0.270922 | + | 0.469251i | −0.969098 | − | 0.246675i | \(-0.920662\pi\) |
0.698176 | + | 0.715926i | \(0.253995\pi\) | |||||||
\(200\) | 16.1941 | − | 28.0491i | 1.14510 | − | 1.98337i | ||||
\(201\) | 3.01030 | + | 5.21399i | 0.212330 | + | 0.367766i | ||||
\(202\) | 3.74043 | 0.263176 | ||||||||
\(203\) | −1.86176 | − | 2.23862i | −0.130670 | − | 0.157120i | ||||
\(204\) | 4.19957 | 0.294028 | ||||||||
\(205\) | −10.0608 | − | 17.4259i | −0.702679 | − | 1.21708i | ||||
\(206\) | 10.2188 | − | 17.6994i | 0.711976 | − | 1.23318i | ||||
\(207\) | 0.500000 | − | 0.866025i | 0.0347524 | − | 0.0601929i | ||||
\(208\) | 0.0274606 | + | 0.0475631i | 0.00190405 | + | 0.00329791i | ||||
\(209\) | −0.160711 | −0.0111166 | ||||||||
\(210\) | −8.63990 | + | 23.4179i | −0.596210 | + | 1.61599i | ||||
\(211\) | −4.69603 | −0.323288 | −0.161644 | − | 0.986849i | \(-0.551680\pi\) | ||||
−0.161644 | + | 0.986849i | \(0.551680\pi\) | |||||||
\(212\) | 15.7876 | + | 27.3450i | 1.08430 | + | 1.87806i | ||||
\(213\) | 3.35760 | − | 5.81553i | 0.230059 | − | 0.398473i | ||||
\(214\) | −21.5711 | + | 37.3623i | −1.47457 | + | 2.55403i | ||||
\(215\) | 21.9926 | + | 38.0923i | 1.49988 | + | 2.59787i | ||||
\(216\) | 2.64772 | 0.180155 | ||||||||
\(217\) | −22.7127 | + | 3.90223i | −1.54184 | + | 0.264901i | ||||
\(218\) | 26.6318 | 1.80373 | ||||||||
\(219\) | −2.30686 | − | 3.99560i | −0.155883 | − | 0.269998i | ||||
\(220\) | 20.9369 | − | 36.2637i | 1.41156 | − | 2.44490i | ||||
\(221\) | 0.116539 | − | 0.201852i | 0.00783929 | − | 0.0135780i | ||||
\(222\) | −4.27526 | − | 7.40497i | −0.286937 | − | 0.496989i | ||||
\(223\) | 24.2891 | 1.62652 | 0.813260 | − | 0.581900i | \(-0.197690\pi\) | ||||
0.813260 | + | 0.581900i | \(0.197690\pi\) | |||||||
\(224\) | 15.6609 | − | 2.69068i | 1.04639 | − | 0.179779i | ||||
\(225\) | 12.2325 | 0.815500 | ||||||||
\(226\) | 18.8664 | + | 32.6775i | 1.25497 | + | 2.17368i | ||||
\(227\) | −2.16652 | + | 3.75252i | −0.143797 | + | 0.249063i | −0.928923 | − | 0.370272i | \(-0.879264\pi\) |
0.785127 | + | 0.619335i | \(0.212598\pi\) | |||||||
\(228\) | 0.0798000 | − | 0.138218i | 0.00528489 | − | 0.00915369i | ||||
\(229\) | 6.22185 | + | 10.7766i | 0.411152 | + | 0.712135i | 0.995016 | − | 0.0997158i | \(-0.0317934\pi\) |
−0.583864 | + | 0.811851i | \(0.698460\pi\) | |||||||
\(230\) | 9.43432 | 0.622080 | ||||||||
\(231\) | −2.91869 | + | 7.91091i | −0.192036 | + | 0.520500i | ||||
\(232\) | −2.91380 | −0.191300 | ||||||||
\(233\) | −1.62382 | − | 2.81254i | −0.106380 | − | 0.184255i | 0.807921 | − | 0.589291i | \(-0.200593\pi\) |
−0.914301 | + | 0.405035i | \(0.867259\pi\) | |||||||
\(234\) | 0.199610 | − | 0.345735i | 0.0130489 | − | 0.0226014i | ||||
\(235\) | 18.5769 | − | 32.1762i | 1.21182 | − | 2.09894i | ||||
\(236\) | 10.1106 | + | 17.5121i | 0.658147 | + | 1.13994i | ||||
\(237\) | 15.4854 | 1.00589 | ||||||||
\(238\) | −5.10152 | − | 6.13419i | −0.330682 | − | 0.397621i | ||||
\(239\) | 26.4823 | 1.71300 | 0.856500 | − | 0.516147i | \(-0.172634\pi\) | ||||
0.856500 | + | 0.516147i | \(0.172634\pi\) | |||||||
\(240\) | −0.648945 | − | 1.12401i | −0.0418892 | − | 0.0725542i | ||||
\(241\) | −1.28075 | + | 2.21832i | −0.0825001 | + | 0.142894i | −0.904323 | − | 0.426848i | \(-0.859624\pi\) |
0.821823 | + | 0.569743i | \(0.192957\pi\) | |||||||
\(242\) | −0.957553 | + | 1.65853i | −0.0615539 | + | 0.106614i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −22.8914 | −1.46547 | ||||||||
\(245\) | 27.3921 | − | 9.69868i | 1.75002 | − | 0.619626i | ||||
\(246\) | 11.0161 | 0.702358 | ||||||||
\(247\) | −0.00442896 | − | 0.00767118i | −0.000281808 | − | 0.000488105i | ||||
\(248\) | −11.5313 | + | 19.9728i | −0.732240 | + | 1.26828i | ||||
\(249\) | 3.60551 | − | 6.24493i | 0.228490 | − | 0.395756i | ||||
\(250\) | 34.1168 | + | 59.0921i | 2.15774 | + | 3.73731i | ||||
\(251\) | 14.6123 | 0.922317 | 0.461159 | − | 0.887318i | \(-0.347434\pi\) | ||||
0.461159 | + | 0.887318i | \(0.347434\pi\) | |||||||
\(252\) | −5.35444 | − | 6.43831i | −0.337298 | − | 0.405575i | ||||
\(253\) | 3.18706 | 0.200369 | ||||||||
\(254\) | 20.2797 | + | 35.1255i | 1.27246 | + | 2.20397i | ||||
\(255\) | −2.75404 | + | 4.77014i | −0.172465 | + | 0.298718i | ||||
\(256\) | 6.96157 | − | 12.0578i | 0.435098 | − | 0.753612i | ||||
\(257\) | 2.56428 | + | 4.44147i | 0.159956 | + | 0.277051i | 0.934852 | − | 0.355036i | \(-0.115532\pi\) |
−0.774897 | + | 0.632088i | \(0.782198\pi\) | |||||||
\(258\) | −24.0807 | −1.49920 | ||||||||
\(259\) | −3.44552 | + | 9.33885i | −0.214094 | + | 0.580288i | ||||
\(260\) | 2.30796 | 0.143133 | ||||||||
\(261\) | −0.550245 | − | 0.953053i | −0.0340593 | − | 0.0589925i | ||||
\(262\) | 24.5017 | − | 42.4381i | 1.51372 | − | 2.62183i | ||||
\(263\) | −1.62406 | + | 2.81296i | −0.100144 | + | 0.173454i | −0.911744 | − | 0.410759i | \(-0.865264\pi\) |
0.811600 | + | 0.584214i | \(0.198597\pi\) | |||||||
\(264\) | 4.21922 | + | 7.30791i | 0.259675 | + | 0.449771i | ||||
\(265\) | −41.4136 | −2.54402 | ||||||||
\(266\) | −0.298830 | + | 0.0513415i | −0.0183224 | + | 0.00314795i | ||||
\(267\) | 1.94147 | 0.118816 | ||||||||
\(268\) | −9.52767 | − | 16.5024i | −0.581995 | − | 1.00805i | ||||
\(269\) | 2.41550 | − | 4.18377i | 0.147276 | − | 0.255089i | −0.782944 | − | 0.622092i | \(-0.786283\pi\) |
0.930220 | + | 0.367003i | \(0.119616\pi\) | |||||||
\(270\) | −4.71716 | + | 8.17036i | −0.287077 | + | 0.497232i | ||||
\(271\) | 6.06194 | + | 10.4996i | 0.368236 | + | 0.637804i | 0.989290 | − | 0.145964i | \(-0.0466284\pi\) |
−0.621053 | + | 0.783768i | \(0.713295\pi\) | |||||||
\(272\) | 0.414849 | 0.0251539 | ||||||||
\(273\) | −0.458045 | + | 0.0786960i | −0.0277221 | + | 0.00476290i | ||||
\(274\) | −1.28527 | −0.0776458 | ||||||||
\(275\) | 19.4928 | + | 33.7626i | 1.17546 | + | 2.03596i | ||||
\(276\) | −1.58251 | + | 2.74099i | −0.0952561 | + | 0.164988i | ||||
\(277\) | 10.9507 | − | 18.9672i | 0.657964 | − | 1.13963i | −0.323178 | − | 0.946338i | \(-0.604751\pi\) |
0.981142 | − | 0.193288i | \(-0.0619153\pi\) | |||||||
\(278\) | −22.2346 | − | 38.5115i | −1.33355 | − | 2.30977i | ||||
\(279\) | −8.71037 | −0.521476 | ||||||||
\(280\) | 10.0657 | − | 27.2825i | 0.601542 | − | 1.63044i | ||||
\(281\) | −24.2364 | −1.44582 | −0.722912 | − | 0.690940i | \(-0.757197\pi\) | ||||
−0.722912 | + | 0.690940i | \(0.757197\pi\) | |||||||
\(282\) | 10.1703 | + | 17.6156i | 0.605635 | + | 1.04899i | ||||
\(283\) | −2.57291 | + | 4.45641i | −0.152943 | + | 0.264906i | −0.932308 | − | 0.361665i | \(-0.882209\pi\) |
0.779365 | + | 0.626570i | \(0.215542\pi\) | |||||||
\(284\) | −10.6269 | + | 18.4063i | −0.630590 | + | 1.09221i | ||||
\(285\) | 0.104665 | + | 0.181284i | 0.00619979 | + | 0.0107384i | ||||
\(286\) | 1.27234 | 0.0752349 | ||||||||
\(287\) | −8.20024 | − | 9.86016i | −0.484045 | − | 0.582027i | ||||
\(288\) | 6.00601 | 0.353907 | ||||||||
\(289\) | 7.61971 | + | 13.1977i | 0.448218 | + | 0.776337i | ||||
\(290\) | 5.19119 | − | 8.99140i | 0.304837 | − | 0.527993i | ||||
\(291\) | −6.39394 | + | 11.0746i | −0.374820 | + | 0.649207i | ||||
\(292\) | 7.30128 | + | 12.6462i | 0.427275 | + | 0.740062i | ||||
\(293\) | −24.5374 | −1.43349 | −0.716745 | − | 0.697335i | \(-0.754369\pi\) | ||||
−0.716745 | + | 0.697335i | \(0.754369\pi\) | |||||||
\(294\) | −2.89983 | + | 15.6422i | −0.169121 | + | 0.912270i | ||||
\(295\) | −26.5219 | −1.54417 | ||||||||
\(296\) | 4.98080 | + | 8.62700i | 0.289503 | + | 0.501434i | ||||
\(297\) | −1.59353 | + | 2.76007i | −0.0924659 | + | 0.160156i | ||||
\(298\) | 8.55349 | − | 14.8151i | 0.495491 | − | 0.858215i | ||||
\(299\) | 0.0878306 | + | 0.152127i | 0.00507938 | + | 0.00879774i | ||||
\(300\) | −38.7162 | −2.23528 | ||||||||
\(301\) | 17.9254 | + | 21.5539i | 1.03320 | + | 1.24235i | ||||
\(302\) | 48.5491 | 2.79369 | ||||||||
\(303\) | −0.822915 | − | 1.42533i | −0.0472752 | − | 0.0818831i | ||||
\(304\) | 0.00788296 | − | 0.0136537i | 0.000452119 | − | 0.000783092i | ||||
\(305\) | 15.0120 | − | 26.0016i | 0.859586 | − | 1.48885i | ||||
\(306\) | −1.50776 | − | 2.61152i | −0.0861931 | − | 0.149291i | ||||
\(307\) | 7.16659 | 0.409019 | 0.204509 | − | 0.978865i | \(-0.434440\pi\) | ||||
0.204509 | + | 0.978865i | \(0.434440\pi\) | |||||||
\(308\) | 9.23774 | − | 25.0383i | 0.526369 | − | 1.42669i | ||||
\(309\) | −8.99275 | −0.511580 | ||||||||
\(310\) | −41.0882 | − | 71.1668i | −2.33365 | − | 4.04200i | ||||
\(311\) | −2.93640 | + | 5.08599i | −0.166508 | + | 0.288400i | −0.937190 | − | 0.348820i | \(-0.886582\pi\) |
0.770682 | + | 0.637220i | \(0.219916\pi\) | |||||||
\(312\) | −0.232551 | + | 0.402791i | −0.0131656 | + | 0.0228035i | ||||
\(313\) | 1.90182 | + | 3.29405i | 0.107497 | + | 0.186191i | 0.914756 | − | 0.404007i | \(-0.132383\pi\) |
−0.807259 | + | 0.590198i | \(0.799050\pi\) | |||||||
\(314\) | −26.7252 | −1.50819 | ||||||||
\(315\) | 10.8245 | − | 1.85973i | 0.609889 | − | 0.104784i | ||||
\(316\) | −49.0118 | −2.75713 | ||||||||
\(317\) | −4.90142 | − | 8.48951i | −0.275291 | − | 0.476818i | 0.694917 | − | 0.719090i | \(-0.255441\pi\) |
−0.970209 | + | 0.242271i | \(0.922108\pi\) | |||||||
\(318\) | 11.3364 | − | 19.6352i | 0.635714 | − | 1.10109i | ||||
\(319\) | 1.75366 | − | 3.03743i | 0.0981863 | − | 0.170064i | ||||
\(320\) | 27.0334 | + | 46.8232i | 1.51121 | + | 2.61750i | ||||
\(321\) | 18.9831 | 1.05953 | ||||||||
\(322\) | 5.92609 | − | 1.01815i | 0.330248 | − | 0.0567394i | ||||
\(323\) | −0.0669087 | −0.00372290 | ||||||||
\(324\) | −1.58251 | − | 2.74099i | −0.0879174 | − | 0.152277i | ||||
\(325\) | −1.07439 | + | 1.86089i | −0.0595963 | + | 0.103224i | ||||
\(326\) | −17.4108 | + | 30.1564i | −0.964294 | + | 1.67021i | ||||
\(327\) | −5.85913 | − | 10.1483i | −0.324011 | − | 0.561203i | ||||
\(328\) | −12.8340 | −0.708640 | ||||||||
\(329\) | 8.19649 | − | 22.2160i | 0.451887 | − | 1.22481i | ||||
\(330\) | −30.0677 | −1.65517 | ||||||||
\(331\) | 5.59480 | + | 9.69048i | 0.307518 | + | 0.532637i | 0.977819 | − | 0.209452i | \(-0.0671682\pi\) |
−0.670301 | + | 0.742090i | \(0.733835\pi\) | |||||||
\(332\) | −11.4115 | + | 19.7654i | −0.626290 | + | 1.08477i | ||||
\(333\) | −1.88116 | + | 3.25827i | −0.103087 | + | 0.178552i | ||||
\(334\) | −9.11877 | − | 15.7942i | −0.498957 | − | 0.864219i | ||||
\(335\) | 24.9927 | 1.36550 | ||||||||
\(336\) | −0.528932 | − | 0.636001i | −0.0288556 | − | 0.0346967i | ||||
\(337\) | −31.7991 | −1.73221 | −0.866103 | − | 0.499865i | \(-0.833383\pi\) | ||||
−0.866103 | + | 0.499865i | \(0.833383\pi\) | |||||||
\(338\) | −14.7373 | − | 25.5257i | −0.801603 | − | 1.38842i | ||||
\(339\) | 8.30141 | − | 14.3785i | 0.450871 | − | 0.780931i | ||||
\(340\) | 8.71663 | − | 15.0976i | 0.472725 | − | 0.818785i | ||||
\(341\) | −13.8802 | − | 24.0412i | −0.751656 | − | 1.30191i | ||||
\(342\) | −0.114602 | −0.00619696 | ||||||||
\(343\) | 16.1595 | − | 9.04831i | 0.872529 | − | 0.488563i | ||||
\(344\) | 28.0547 | 1.51261 | ||||||||
\(345\) | −2.07560 | − | 3.59505i | −0.111747 | − | 0.193551i | ||||
\(346\) | 17.6388 | − | 30.5513i | 0.948267 | − | 1.64245i | ||||
\(347\) | 0.686942 | − | 1.18982i | 0.0368770 | − | 0.0638728i | −0.846998 | − | 0.531596i | \(-0.821592\pi\) |
0.883875 | + | 0.467724i | \(0.154926\pi\) | |||||||
\(348\) | 1.74154 | + | 3.01644i | 0.0933564 | + | 0.161698i | ||||
\(349\) | −6.43146 | −0.344268 | −0.172134 | − | 0.985074i | \(-0.555066\pi\) | ||||
−0.172134 | + | 0.985074i | \(0.555066\pi\) | |||||||
\(350\) | 47.0314 | + | 56.5517i | 2.51393 | + | 3.02281i | ||||
\(351\) | −0.175661 | −0.00937611 | ||||||||
\(352\) | 9.57074 | + | 16.5770i | 0.510122 | + | 0.883558i | ||||
\(353\) | −12.8683 | + | 22.2885i | −0.684910 | + | 1.18630i | 0.288555 | + | 0.957463i | \(0.406825\pi\) |
−0.973465 | + | 0.228835i | \(0.926508\pi\) | |||||||
\(354\) | 7.26001 | − | 12.5747i | 0.385865 | − | 0.668339i | ||||
\(355\) | −13.9381 | − | 24.1414i | −0.739756 | − | 1.28129i | ||||
\(356\) | −6.14480 | −0.325674 | ||||||||
\(357\) | −1.21514 | + | 3.29355i | −0.0643119 | + | 0.174313i | ||||
\(358\) | −18.8241 | −0.994883 | ||||||||
\(359\) | 11.9817 | + | 20.7529i | 0.632369 | + | 1.09530i | 0.987066 | + | 0.160314i | \(0.0512508\pi\) |
−0.354697 | + | 0.934981i | \(0.615416\pi\) | |||||||
\(360\) | 5.49562 | − | 9.51870i | 0.289645 | − | 0.501679i | ||||
\(361\) | 9.49873 | − | 16.4523i | 0.499933 | − | 0.865910i | ||||
\(362\) | −6.49062 | − | 11.2421i | −0.341139 | − | 0.590870i | ||||
\(363\) | 0.842668 | 0.0442286 | ||||||||
\(364\) | 1.44972 | − | 0.249075i | 0.0759862 | − | 0.0130551i | ||||
\(365\) | −19.1525 | −1.00249 | ||||||||
\(366\) | 8.21867 | + | 14.2352i | 0.429597 | + | 0.744083i | ||||
\(367\) | −12.8392 | + | 22.2381i | −0.670199 | + | 1.16082i | 0.307648 | + | 0.951500i | \(0.400458\pi\) |
−0.977847 | + | 0.209319i | \(0.932875\pi\) | |||||||
\(368\) | −0.156327 | + | 0.270766i | −0.00814910 | + | 0.0141147i | ||||
\(369\) | −2.42359 | − | 4.19779i | −0.126167 | − | 0.218528i | ||||
\(370\) | −35.4950 | −1.84530 | ||||||||
\(371\) | −26.0136 | + | 4.46936i | −1.35056 | + | 0.232038i | ||||
\(372\) | 27.5686 | 1.42936 | ||||||||
\(373\) | −2.90046 | − | 5.02374i | −0.150180 | − | 0.260120i | 0.781113 | − | 0.624389i | \(-0.214652\pi\) |
−0.931294 | + | 0.364270i | \(0.881319\pi\) | |||||||
\(374\) | 4.80533 | − | 8.32307i | 0.248478 | − | 0.430376i | ||||
\(375\) | 15.0118 | − | 26.0012i | 0.775205 | − | 1.34269i | ||||
\(376\) | −11.8487 | − | 20.5226i | −0.611052 | − | 1.05837i | ||||
\(377\) | 0.193314 | 0.00995616 | ||||||||
\(378\) | −2.08130 | + | 5.64122i | −0.107051 | + | 0.290153i | ||||
\(379\) | 21.0504 | 1.08129 | 0.540643 | − | 0.841252i | \(-0.318181\pi\) | ||||
0.540643 | + | 0.841252i | \(0.318181\pi\) | |||||||
\(380\) | −0.331266 | − | 0.573770i | −0.0169936 | − | 0.0294338i | ||||
\(381\) | 8.92330 | − | 15.4556i | 0.457155 | − | 0.791815i | ||||
\(382\) | −1.76305 | + | 3.05369i | −0.0902056 | + | 0.156241i | ||||
\(383\) | 2.41145 | + | 4.17675i | 0.123219 | + | 0.213422i | 0.921035 | − | 0.389479i | \(-0.127345\pi\) |
−0.797816 | + | 0.602901i | \(0.794012\pi\) | |||||||
\(384\) | −17.5881 | −0.897537 | ||||||||
\(385\) | 22.3821 | + | 26.9127i | 1.14070 | + | 1.37160i | ||||
\(386\) | −16.6425 | −0.847083 | ||||||||
\(387\) | 5.29788 | + | 9.17620i | 0.269307 | + | 0.466453i | ||||
\(388\) | 20.2370 | − | 35.0515i | 1.02738 | − | 1.77947i | ||||
\(389\) | 9.77072 | − | 16.9234i | 0.495395 | − | 0.858049i | −0.504591 | − | 0.863359i | \(-0.668357\pi\) |
0.999986 | + | 0.00530928i | \(0.00169000\pi\) | |||||||
\(390\) | −0.828622 | − | 1.43522i | −0.0419589 | − | 0.0726750i | ||||
\(391\) | 1.32687 | 0.0671025 | ||||||||
\(392\) | 3.37838 | − | 18.2236i | 0.170634 | − | 0.920429i | ||||
\(393\) | −21.5620 | −1.08766 | ||||||||
\(394\) | −7.77408 | − | 13.4651i | −0.391653 | − | 0.678362i | ||||
\(395\) | 32.1416 | − | 55.6709i | 1.61722 | − | 2.80111i | ||||
\(396\) | 5.04356 | − | 8.73571i | 0.253449 | − | 0.438986i | ||||
\(397\) | −18.2925 | − | 31.6835i | −0.918072 | − | 1.59015i | −0.802340 | − | 0.596868i | \(-0.796412\pi\) |
−0.115733 | − | 0.993280i | \(-0.536922\pi\) | |||||||
\(398\) | −17.3715 | −0.870756 | ||||||||
\(399\) | 0.0853084 | + | 0.102577i | 0.00427076 | + | 0.00513527i | ||||
\(400\) | −3.82454 | −0.191227 | ||||||||
\(401\) | 2.33744 | + | 4.04856i | 0.116726 | + | 0.202176i | 0.918468 | − | 0.395494i | \(-0.129427\pi\) |
−0.801742 | + | 0.597670i | \(0.796093\pi\) | |||||||
\(402\) | −6.84141 | + | 11.8497i | −0.341219 | + | 0.591008i | ||||
\(403\) | 0.765037 | − | 1.32508i | 0.0381092 | − | 0.0660071i | ||||
\(404\) | 2.60455 | + | 4.51121i | 0.129581 | + | 0.224441i | ||||
\(405\) | 4.15120 | 0.206275 | ||||||||
\(406\) | 2.29045 | − | 6.20811i | 0.113673 | − | 0.308103i | ||||
\(407\) | −11.9907 | −0.594359 | ||||||||
\(408\) | 1.75659 | + | 3.04250i | 0.0869640 | + | 0.150626i | ||||
\(409\) | −5.50296 | + | 9.53141i | −0.272104 | + | 0.471298i | −0.969400 | − | 0.245485i | \(-0.921053\pi\) |
0.697296 | + | 0.716783i | \(0.254386\pi\) | |||||||
\(410\) | 22.8650 | − | 39.6033i | 1.12922 | − | 1.95587i | ||||
\(411\) | 0.282766 | + | 0.489765i | 0.0139478 | + | 0.0241583i | ||||
\(412\) | 28.4623 | 1.40224 | ||||||||
\(413\) | −16.6595 | + | 2.86225i | −0.819763 | + | 0.140842i | ||||
\(414\) | 2.27267 | 0.111696 | ||||||||
\(415\) | −14.9672 | − | 25.9240i | −0.734711 | − | 1.27256i | ||||
\(416\) | −0.527511 | + | 0.913677i | −0.0258634 | + | 0.0447967i | ||||
\(417\) | −9.78349 | + | 16.9455i | −0.479100 | + | 0.829825i | ||||
\(418\) | −0.182621 | − | 0.316310i | −0.00893230 | − | 0.0154712i | ||||
\(419\) | 18.8771 | 0.922206 | 0.461103 | − | 0.887347i | \(-0.347454\pi\) | ||||
0.461103 | + | 0.887347i | \(0.347454\pi\) | |||||||
\(420\) | −34.2597 | + | 5.88611i | −1.67170 | + | 0.287213i | ||||
\(421\) | −10.1341 | −0.493905 | −0.246952 | − | 0.969028i | \(-0.579429\pi\) | ||||
−0.246952 | + | 0.969028i | \(0.579429\pi\) | |||||||
\(422\) | −5.33627 | − | 9.24269i | −0.259765 | − | 0.449927i | ||||
\(423\) | 4.47507 | − | 7.75104i | 0.217585 | − | 0.376869i | ||||
\(424\) | −13.2072 | + | 22.8756i | −0.641400 | + | 1.11094i | ||||
\(425\) | 8.11544 | + | 14.0563i | 0.393656 | + | 0.681833i | ||||
\(426\) | 15.2614 | 0.739418 | ||||||||
\(427\) | 6.62359 | − | 17.9528i | 0.320538 | − | 0.868797i | ||||
\(428\) | −60.0819 | −2.90417 | ||||||||
\(429\) | −0.279921 | − | 0.484838i | −0.0135147 | − | 0.0234082i | ||||
\(430\) | −49.9819 | + | 86.5712i | −2.41034 | + | 4.17483i | ||||
\(431\) | −3.93591 | + | 6.81720i | −0.189586 | + | 0.328373i | −0.945112 | − | 0.326745i | \(-0.894048\pi\) |
0.755526 | + | 0.655119i | \(0.227381\pi\) | |||||||
\(432\) | −0.156327 | − | 0.270766i | −0.00752128 | − | 0.0130272i | ||||
\(433\) | −20.5867 | −0.989335 | −0.494668 | − | 0.869082i | \(-0.664710\pi\) | ||||
−0.494668 | + | 0.869082i | \(0.664710\pi\) | |||||||
\(434\) | −33.4895 | − | 40.2686i | −1.60755 | − | 1.93296i | ||||
\(435\) | −4.56836 | −0.219036 | ||||||||
\(436\) | 18.5443 | + | 32.1197i | 0.888112 | + | 1.53826i | ||||
\(437\) | 0.0252131 | − | 0.0436703i | 0.00120610 | − | 0.00208903i | ||||
\(438\) | 5.24273 | − | 9.08068i | 0.250507 | − | 0.433892i | ||||
\(439\) | −16.8339 | − | 29.1571i | −0.803437 | − | 1.39159i | −0.917341 | − | 0.398102i | \(-0.869669\pi\) |
0.113904 | − | 0.993492i | \(-0.463664\pi\) | |||||||
\(440\) | 35.0297 | 1.66998 | ||||||||
\(441\) | 6.59859 | − | 2.33635i | 0.314219 | − | 0.111255i | ||||
\(442\) | 0.529711 | 0.0251958 | ||||||||
\(443\) | −3.66764 | − | 6.35254i | −0.174255 | − | 0.301818i | 0.765648 | − | 0.643259i | \(-0.222418\pi\) |
−0.939903 | + | 0.341441i | \(0.889085\pi\) | |||||||
\(444\) | 5.95393 | − | 10.3125i | 0.282561 | − | 0.489410i | ||||
\(445\) | 4.02972 | − | 6.97968i | 0.191027 | − | 0.330868i | ||||
\(446\) | 27.6006 | + | 47.8056i | 1.30693 | + | 2.26366i | ||||
\(447\) | −7.52726 | −0.356027 | ||||||||
\(448\) | 22.0340 | + | 26.4942i | 1.04101 | + | 1.25173i | ||||
\(449\) | −21.1508 | −0.998170 | −0.499085 | − | 0.866553i | \(-0.666330\pi\) | ||||
−0.499085 | + | 0.866553i | \(0.666330\pi\) | |||||||
\(450\) | 13.9002 | + | 24.0759i | 0.655262 | + | 1.13495i | ||||
\(451\) | 7.72413 | − | 13.3786i | 0.363715 | − | 0.629973i | ||||
\(452\) | −26.2742 | + | 45.5083i | −1.23583 | + | 2.14053i | ||||
\(453\) | −10.6811 | − | 18.5002i | −0.501841 | − | 0.869213i | ||||
\(454\) | −9.84755 | −0.462168 | ||||||||
\(455\) | −0.667803 | + | 1.81004i | −0.0313071 | + | 0.0848558i | ||||
\(456\) | 0.133514 | 0.00625239 | ||||||||
\(457\) | −4.48391 | − | 7.76636i | −0.209748 | − | 0.363295i | 0.741887 | − | 0.670525i | \(-0.233931\pi\) |
−0.951635 | + | 0.307230i | \(0.900598\pi\) | |||||||
\(458\) | −14.1402 | + | 24.4916i | −0.660729 | + | 1.14442i | ||||
\(459\) | −0.663433 | + | 1.14910i | −0.0309664 | + | 0.0536354i | ||||
\(460\) | 6.56934 | + | 11.3784i | 0.306297 | + | 0.530522i | ||||
\(461\) | 6.30195 | 0.293511 | 0.146756 | − | 0.989173i | \(-0.453117\pi\) | ||||
0.146756 | + | 0.989173i | \(0.453117\pi\) | |||||||
\(462\) | −18.8868 | + | 3.24491i | −0.878693 | + | 0.150967i | ||||
\(463\) | −15.1092 | −0.702183 | −0.351092 | − | 0.936341i | \(-0.614189\pi\) | ||||
−0.351092 | + | 0.936341i | \(0.614189\pi\) | |||||||
\(464\) | 0.172036 | + | 0.297976i | 0.00798658 | + | 0.0138332i | ||||
\(465\) | −18.0793 | + | 31.3142i | −0.838405 | + | 1.45216i | ||||
\(466\) | 3.69041 | − | 6.39197i | 0.170955 | − | 0.296102i | ||||
\(467\) | 9.48025 | + | 16.4203i | 0.438694 | + | 0.759840i | 0.997589 | − | 0.0693985i | \(-0.0221080\pi\) |
−0.558895 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(468\) | 0.555973 | 0.0256999 | ||||||||
\(469\) | 15.6990 | − | 2.69722i | 0.724911 | − | 0.124546i | ||||
\(470\) | 84.4384 | 3.89485 | ||||||||
\(471\) | 5.87970 | + | 10.1839i | 0.270922 | + | 0.469251i | ||||
\(472\) | −8.45812 | + | 14.6499i | −0.389317 | + | 0.674316i | ||||
\(473\) | −16.8847 | + | 29.2451i | −0.776357 | + | 1.34469i | ||||
\(474\) | 17.5966 | + | 30.4783i | 0.808240 | + | 1.39991i | ||||
\(475\) | 0.616837 | 0.0283024 | ||||||||
\(476\) | 3.84594 | − | 10.4242i | 0.176278 | − | 0.477791i | ||||
\(477\) | −9.97629 | −0.456783 | ||||||||
\(478\) | 30.0928 | + | 52.1223i | 1.37641 | + | 2.38402i | ||||
\(479\) | 14.2886 | − | 24.7486i | 0.652862 | − | 1.13079i | −0.329563 | − | 0.944134i | \(-0.606901\pi\) |
0.982425 | − | 0.186657i | \(-0.0597653\pi\) | |||||||
\(480\) | 12.4661 | − | 21.5919i | 0.568996 | − | 0.985530i | ||||
\(481\) | −0.330447 | − | 0.572352i | −0.0150671 | − | 0.0260970i | ||||
\(482\) | −5.82143 | −0.265159 | ||||||||
\(483\) | −1.69175 | − | 2.03420i | −0.0769773 | − | 0.0925594i | ||||
\(484\) | −2.66707 | −0.121230 | ||||||||
\(485\) | 26.5426 | + | 45.9731i | 1.20524 | + | 2.08753i | ||||
\(486\) | −1.13633 | + | 1.96819i | −0.0515452 | + | 0.0892789i | ||||
\(487\) | −12.4964 | + | 21.6443i | −0.566264 | + | 0.980799i | 0.430666 | + | 0.902511i | \(0.358279\pi\) |
−0.996931 | + | 0.0782875i | \(0.975055\pi\) | |||||||
\(488\) | −9.57498 | − | 16.5844i | −0.433439 | − | 0.750738i | ||||
\(489\) | 15.3219 | 0.692879 | ||||||||
\(490\) | 50.2155 | + | 42.8919i | 2.26850 | + | 1.93766i | ||||
\(491\) | −22.0515 | −0.995170 | −0.497585 | − | 0.867415i | \(-0.665780\pi\) | ||||
−0.497585 | + | 0.867415i | \(0.665780\pi\) | |||||||
\(492\) | 7.67075 | + | 13.2861i | 0.345824 | + | 0.598985i | ||||
\(493\) | 0.730101 | − | 1.26457i | 0.0328821 | − | 0.0569535i | ||||
\(494\) | 0.0100656 | − | 0.0174341i | 0.000452871 | − | 0.000784395i | ||||
\(495\) | 6.61506 | + | 11.4576i | 0.297325 | + | 0.514982i | ||||
\(496\) | 2.72333 | 0.122281 | ||||||||
\(497\) | −11.3604 | − | 13.6601i | −0.509585 | − | 0.612737i | ||||
\(498\) | 16.3883 | 0.734376 | ||||||||
\(499\) | 19.7125 | + | 34.1431i | 0.882455 | + | 1.52846i | 0.848603 | + | 0.529030i | \(0.177444\pi\) |
0.0338517 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(500\) | −47.5127 | + | 82.2944i | −2.12483 | + | 3.68032i | ||||
\(501\) | −4.01236 | + | 6.94961i | −0.179259 | + | 0.310486i | ||||
\(502\) | 16.6044 | + | 28.7597i | 0.741091 | + | 1.28361i | ||||
\(503\) | −31.3079 | −1.39595 | −0.697975 | − | 0.716122i | \(-0.745915\pi\) | ||||
−0.697975 | + | 0.716122i | \(0.745915\pi\) | |||||||
\(504\) | 2.42477 | − | 6.57218i | 0.108008 | − | 0.292748i | ||||
\(505\) | −6.83218 | −0.304028 | ||||||||
\(506\) | 3.62156 | + | 6.27273i | 0.160998 | + | 0.278857i | ||||
\(507\) | −6.48457 | + | 11.2316i | −0.287990 | + | 0.498813i | ||||
\(508\) | −28.2425 | + | 48.9174i | −1.25306 | + | 2.17036i | ||||
\(509\) | −7.73301 | − | 13.3940i | −0.342760 | − | 0.593677i | 0.642184 | − | 0.766550i | \(-0.278028\pi\) |
−0.984944 | + | 0.172873i | \(0.944695\pi\) | |||||||
\(510\) | −12.5181 | −0.554309 | ||||||||
\(511\) | −12.0305 | + | 2.06694i | −0.532198 | + | 0.0914360i | ||||
\(512\) | −3.53344 | −0.156158 | ||||||||
\(513\) | 0.0252131 | + | 0.0436703i | 0.00111318 | + | 0.00192809i | ||||
\(514\) | −5.82777 | + | 10.0940i | −0.257052 | + | 0.445227i | ||||
\(515\) | −18.6654 | + | 32.3294i | −0.822495 | + | 1.42460i | ||||
\(516\) | −16.7679 | − | 29.0429i | −0.738168 | − | 1.27854i | ||||
\(517\) | 28.5246 | 1.25451 | ||||||||
\(518\) | −22.2959 | + | 3.83062i | −0.979625 | + | 0.168308i | ||||
\(519\) | −15.5225 | −0.681363 | ||||||||
\(520\) | 0.965368 | + | 1.67207i | 0.0423342 | + | 0.0733250i | ||||
\(521\) | 3.40802 | − | 5.90287i | 0.149308 | − | 0.258609i | −0.781664 | − | 0.623700i | \(-0.785629\pi\) |
0.930972 | + | 0.365091i | \(0.118962\pi\) | |||||||
\(522\) | 1.25053 | − | 2.16597i | 0.0547340 | − | 0.0948021i | ||||
\(523\) | 4.26780 | + | 7.39205i | 0.186618 | + | 0.323232i | 0.944121 | − | 0.329600i | \(-0.106914\pi\) |
−0.757503 | + | 0.652832i | \(0.773581\pi\) | |||||||
\(524\) | 68.2443 | 2.98127 | ||||||||
\(525\) | 11.2025 | − | 30.3635i | 0.488915 | − | 1.32517i | ||||
\(526\) | −7.38192 | −0.321867 | ||||||||
\(527\) | −5.77874 | − | 10.0091i | −0.251726 | − | 0.436002i | ||||
\(528\) | 0.498223 | − | 0.862947i | 0.0216824 | − | 0.0375549i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −47.0597 | − | 81.5099i | −2.04414 | − | 3.54056i | ||||
\(531\) | −6.38897 | −0.277258 | ||||||||
\(532\) | −0.270004 | − | 0.324659i | −0.0117061 | − | 0.0140757i | ||||
\(533\) | 0.851464 | 0.0368810 | ||||||||
\(534\) | 2.20616 | + | 3.82118i | 0.0954698 | + | 0.165359i | ||||
\(535\) | 39.4013 | − | 68.2450i | 1.70347 | − | 2.95049i | ||||
\(536\) | 7.97043 | − | 13.8052i | 0.344270 | − | 0.596294i | ||||
\(537\) | 4.14140 | + | 7.17312i | 0.178715 | + | 0.309543i | ||||
\(538\) | 10.9793 | 0.473350 | ||||||||
\(539\) | 16.9636 | + | 14.4896i | 0.730672 | + | 0.624109i | ||||
\(540\) | −13.1387 | −0.565399 | ||||||||
\(541\) | −0.617312 | − | 1.06921i | −0.0265403 | − | 0.0459691i | 0.852450 | − | 0.522808i | \(-0.175116\pi\) |
−0.878990 | + | 0.476839i | \(0.841782\pi\) | |||||||
\(542\) | −13.7768 | + | 23.8621i | −0.591763 | + | 1.02496i | ||||
\(543\) | −2.85594 | + | 4.94664i | −0.122560 | + | 0.212281i | ||||
\(544\) | 3.98458 | + | 6.90150i | 0.170837 | + | 0.295899i | ||||
\(545\) | −48.6449 | −2.08372 | ||||||||
\(546\) | −0.675381 | − | 0.812094i | −0.0289036 | − | 0.0347544i | ||||
\(547\) | 26.1193 | 1.11678 | 0.558390 | − | 0.829578i | \(-0.311419\pi\) | ||||
0.558390 | + | 0.829578i | \(0.311419\pi\) | |||||||
\(548\) | −0.894962 | − | 1.55012i | −0.0382309 | − | 0.0662178i | ||||
\(549\) | 3.61631 | − | 6.26363i | 0.154340 | − | 0.267325i | ||||
\(550\) | −44.3008 | + | 76.7312i | −1.88899 | + | 3.27183i | ||||
\(551\) | −0.0277467 | − | 0.0480587i | −0.00118205 | − | 0.00204737i | ||||
\(552\) | −2.64772 | −0.112695 | ||||||||
\(553\) | 14.1815 | − | 38.4380i | 0.603058 | − | 1.63455i | ||||
\(554\) | 49.7746 | 2.11472 | ||||||||
\(555\) | 7.80909 | + | 13.5257i | 0.331477 | + | 0.574136i | ||||
\(556\) | 30.9650 | − | 53.6330i | 1.31321 | − | 2.27455i | ||||
\(557\) | 12.8872 | − | 22.3213i | 0.546049 | − | 0.945785i | −0.452491 | − | 0.891769i | \(-0.649465\pi\) |
0.998540 | − | 0.0540157i | \(-0.0172021\pi\) | |||||||
\(558\) | −9.89789 | − | 17.1437i | −0.419011 | − | 0.725749i | ||||
\(559\) | −1.86127 | −0.0787232 | ||||||||
\(560\) | −3.38431 | + | 0.581452i | −0.143013 | + | 0.0245709i | ||||
\(561\) | −4.22880 | −0.178540 | ||||||||
\(562\) | −27.5407 | − | 47.7019i | −1.16173 | − | 2.01218i | ||||
\(563\) | −5.57519 | + | 9.65651i | −0.234966 | + | 0.406973i | −0.959263 | − | 0.282515i | \(-0.908831\pi\) |
0.724297 | + | 0.689488i | \(0.242165\pi\) | |||||||
\(564\) | −14.1637 | + | 24.5323i | −0.596400 | + | 1.03299i | ||||
\(565\) | −34.4609 | − | 59.6880i | −1.44978 | − | 2.51109i | ||||
\(566\) | −11.6947 | −0.491567 | ||||||||
\(567\) | 2.60755 | − | 0.447998i | 0.109507 | − | 0.0188142i | ||||
\(568\) | −17.7800 | −0.746031 | ||||||||
\(569\) | 4.74876 | + | 8.22509i | 0.199078 | + | 0.344814i | 0.948230 | − | 0.317585i | \(-0.102872\pi\) |
−0.749152 | + | 0.662399i | \(0.769539\pi\) | |||||||
\(570\) | −0.237868 | + | 0.411999i | −0.00996319 | + | 0.0172568i | ||||
\(571\) | 12.7812 | − | 22.1378i | 0.534878 | − | 0.926436i | −0.464291 | − | 0.885683i | \(-0.653691\pi\) |
0.999169 | − | 0.0407535i | \(-0.0129758\pi\) | |||||||
\(572\) | 0.885959 | + | 1.53453i | 0.0370438 | + | 0.0641617i | ||||
\(573\) | 1.55152 | 0.0648159 | ||||||||
\(574\) | 10.0885 | − | 27.3441i | 0.421084 | − | 1.14132i | ||||
\(575\) | −12.2325 | −0.510130 | ||||||||
\(576\) | 6.51218 | + | 11.2794i | 0.271341 | + | 0.469976i | ||||
\(577\) | −7.67828 | + | 13.2992i | −0.319651 | + | 0.553652i | −0.980415 | − | 0.196942i | \(-0.936899\pi\) |
0.660764 | + | 0.750594i | \(0.270232\pi\) | |||||||
\(578\) | −17.3171 | + | 29.9941i | −0.720296 | + | 1.24759i | ||||
\(579\) | 3.66145 | + | 6.34182i | 0.152165 | + | 0.263557i | ||||
\(580\) | 14.4590 | 0.600377 | ||||||||
\(581\) | −12.1992 | − | 14.6687i | −0.506110 | − | 0.608559i | ||||
\(582\) | −29.0626 | −1.20469 | ||||||||
\(583\) | −15.8975 | − | 27.5353i | −0.658407 | − | 1.14040i | ||||
\(584\) | −6.10793 | + | 10.5792i | −0.252748 | + | 0.437772i | ||||
\(585\) | −0.364603 | + | 0.631511i | −0.0150745 | + | 0.0261098i | ||||
\(586\) | −27.8827 | − | 48.2943i | −1.15182 | − | 1.99502i | ||||
\(587\) | −2.88985 | −0.119277 | −0.0596384 | − | 0.998220i | \(-0.518995\pi\) | ||||
−0.0596384 | + | 0.998220i | \(0.518995\pi\) | |||||||
\(588\) | −20.8847 | + | 7.39462i | −0.861272 | + | 0.304949i | ||||
\(589\) | −0.439230 | −0.0180982 | ||||||||
\(590\) | −30.1378 | − | 52.2002i | −1.24075 | − | 2.14905i | ||||
\(591\) | −3.42068 | + | 5.92480i | −0.140708 | + | 0.243714i | ||||
\(592\) | 0.588153 | − | 1.01871i | 0.0241729 | − | 0.0418687i | ||||
\(593\) | −10.4889 | − | 18.1673i | −0.430727 | − | 0.746041i | 0.566209 | − | 0.824262i | \(-0.308410\pi\) |
−0.996936 | + | 0.0782203i | \(0.975076\pi\) | |||||||
\(594\) | −7.24313 | −0.297189 | ||||||||
\(595\) | 9.31832 | + | 11.2046i | 0.382014 | + | 0.459342i | ||||
\(596\) | 23.8240 | 0.975869 | ||||||||
\(597\) | 3.82183 | + | 6.61961i | 0.156417 | + | 0.270922i | ||||
\(598\) | −0.199610 | + | 0.345735i | −0.00816266 | + | 0.0141381i | ||||
\(599\) | −4.05406 | + | 7.02184i | −0.165644 | + | 0.286905i | −0.936884 | − | 0.349640i | \(-0.886304\pi\) |
0.771240 | + | 0.636545i | \(0.219637\pi\) | |||||||
\(600\) | −16.1941 | − | 28.0491i | −0.661123 | − | 1.14510i | ||||
\(601\) | 31.3113 | 1.27721 | 0.638607 | − | 0.769533i | \(-0.279511\pi\) | ||||
0.638607 | + | 0.769533i | \(0.279511\pi\) | |||||||
\(602\) | −22.0530 | + | 59.7731i | −0.898812 | + | 2.43617i | ||||
\(603\) | 6.02059 | 0.245178 | ||||||||
\(604\) | 33.8059 | + | 58.5535i | 1.37554 | + | 2.38251i | ||||
\(605\) | 1.74904 | − | 3.02943i | 0.0711087 | − | 0.123164i | ||||
\(606\) | 1.87021 | − | 3.23931i | 0.0759723 | − | 0.131588i | ||||
\(607\) | 12.8283 | + | 22.2193i | 0.520685 | + | 0.901852i | 0.999711 | + | 0.0240514i | \(0.00765654\pi\) |
−0.479026 | + | 0.877801i | \(0.659010\pi\) | |||||||
\(608\) | 0.302860 | 0.0122826 | ||||||||
\(609\) | −2.86958 | + | 0.493018i | −0.116281 | + | 0.0199781i | ||||
\(610\) | 68.2348 | 2.76274 | ||||||||
\(611\) | 0.786096 | + | 1.36156i | 0.0318020 | + | 0.0550827i | ||||
\(612\) | 2.09978 | − | 3.63693i | 0.0848787 | − | 0.147014i | ||||
\(613\) | −14.6981 | + | 25.4579i | −0.593651 | + | 1.02823i | 0.400084 | + | 0.916478i | \(0.368981\pi\) |
−0.993736 | + | 0.111756i | \(0.964353\pi\) | |||||||
\(614\) | 8.14364 | + | 14.1052i | 0.328651 | + | 0.569240i | ||||
\(615\) | −20.1217 | −0.811384 | ||||||||
\(616\) | 22.0036 | − | 3.78041i | 0.886552 | − | 0.152317i | ||||
\(617\) | 36.1711 | 1.45619 | 0.728097 | − | 0.685474i | \(-0.240405\pi\) | ||||
0.728097 | + | 0.685474i | \(0.240405\pi\) | |||||||
\(618\) | −10.2188 | − | 17.6994i | −0.411060 | − | 0.711976i | ||||
\(619\) | 11.4789 | − | 19.8821i | 0.461376 | − | 0.799127i | −0.537654 | − | 0.843166i | \(-0.680689\pi\) |
0.999030 | + | 0.0440388i | \(0.0140225\pi\) | |||||||
\(620\) | 57.2214 | − | 99.1103i | 2.29806 | − | 3.98037i | ||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | −13.3469 | −0.535163 | ||||||||
\(623\) | 1.77799 | − | 4.81912i | 0.0712336 | − | 0.193074i | ||||
\(624\) | 0.0549212 | 0.00219861 | ||||||||
\(625\) | −31.7357 | − | 54.9679i | −1.26943 | − | 2.19872i | ||||
\(626\) | −4.32221 | + | 7.48628i | −0.172750 | + | 0.299212i | ||||
\(627\) | −0.0803554 | + | 0.139180i | −0.00320909 | + | 0.00555830i | ||||
\(628\) | −18.6094 | − | 32.2325i | −0.742597 | − | 1.28622i | ||||
\(629\) | −4.99210 | −0.199048 | ||||||||
\(630\) | 15.9605 | + | 19.1913i | 0.635882 | + | 0.764600i | ||||
\(631\) | −13.3609 | −0.531890 | −0.265945 | − | 0.963988i | \(-0.585684\pi\) | ||||
−0.265945 | + | 0.963988i | \(0.585684\pi\) | |||||||
\(632\) | −20.5006 | − | 35.5080i | −0.815469 | − | 1.41243i | ||||
\(633\) | −2.34802 | + | 4.06688i | −0.0933253 | + | 0.161644i | ||||
\(634\) | 11.1393 | − | 19.2939i | 0.442399 | − | 0.766257i | ||||
\(635\) | −37.0424 | − | 64.1594i | −1.46998 | − | 2.54609i | ||||
\(636\) | 31.5752 | 1.25204 | ||||||||
\(637\) | −0.224136 | + | 1.20903i | −0.00888059 | + | 0.0479035i | ||||
\(638\) | 7.97099 | 0.315575 | ||||||||
\(639\) | −3.35760 | − | 5.81553i | −0.132824 | − | 0.230059i | ||||
\(640\) | −36.5058 | + | 63.2299i | −1.44302 | + | 2.49938i | ||||
\(641\) | 17.5479 | − | 30.3939i | 0.693102 | − | 1.20049i | −0.277714 | − | 0.960664i | \(-0.589577\pi\) |
0.970816 | − | 0.239824i | \(-0.0770898\pi\) | |||||||
\(642\) | 21.5711 | + | 37.3623i | 0.851344 | + | 1.47457i | ||||
\(643\) | 15.1822 | 0.598726 | 0.299363 | − | 0.954139i | \(-0.403226\pi\) | ||||
0.299363 | + | 0.954139i | \(0.403226\pi\) | |||||||
\(644\) | 5.35444 | + | 6.43831i | 0.210994 | + | 0.253705i | ||||
\(645\) | 43.9852 | 1.73191 | ||||||||
\(646\) | −0.0760306 | − | 0.131689i | −0.00299139 | − | 0.00518123i | ||||
\(647\) | −10.0328 | + | 17.3773i | −0.394430 | + | 0.683174i | −0.993028 | − | 0.117876i | \(-0.962391\pi\) |
0.598598 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(648\) | 1.32386 | − | 2.29300i | 0.0520062 | − | 0.0900774i | ||||
\(649\) | −10.1810 | − | 17.6340i | −0.399640 | − | 0.692196i | ||||
\(650\) | −4.88346 | −0.191545 | ||||||||
\(651\) | −7.97691 | + | 21.6209i | −0.312640 | + | 0.847389i | ||||
\(652\) | −48.4942 | −1.89918 | ||||||||
\(653\) | 2.06883 | + | 3.58331i | 0.0809594 | + | 0.140226i | 0.903662 | − | 0.428246i | \(-0.140868\pi\) |
−0.822703 | + | 0.568472i | \(0.807535\pi\) | |||||||
\(654\) | 13.3159 | − | 23.0638i | 0.520692 | − | 0.901865i | ||||
\(655\) | −44.7541 | + | 77.5164i | −1.74869 | + | 3.02882i | ||||
\(656\) | 0.757746 | + | 1.31245i | 0.0295850 | + | 0.0512427i | ||||
\(657\) | −4.61372 | −0.179998 | ||||||||
\(658\) | 53.0393 | − | 9.11260i | 2.06769 | − | 0.355246i | ||||
\(659\) | 14.7450 | 0.574383 | 0.287192 | − | 0.957873i | \(-0.407278\pi\) | ||||
0.287192 | + | 0.957873i | \(0.407278\pi\) | |||||||
\(660\) | −20.9369 | − | 36.2637i | −0.814966 | − | 1.41156i | ||||
\(661\) | −12.9996 | + | 22.5159i | −0.505625 | + | 0.875768i | 0.494354 | + | 0.869261i | \(0.335405\pi\) |
−0.999979 | + | 0.00650733i | \(0.997929\pi\) | |||||||
\(662\) | −12.7151 | + | 22.0233i | −0.494188 | + | 0.855959i | ||||
\(663\) | −0.116539 | − | 0.201852i | −0.00452602 | − | 0.00783929i | ||||
\(664\) | −19.0928 | −0.740944 | ||||||||
\(665\) | 0.545835 | − | 0.0937791i | 0.0211666 | − | 0.00363660i | ||||
\(666\) | −8.55052 | −0.331326 | ||||||||
\(667\) | 0.550245 | + | 0.953053i | 0.0213056 | + | 0.0369024i | ||||
\(668\) | 12.6992 | − | 21.9957i | 0.491348 | − | 0.851040i | ||||
\(669\) | 12.1446 | − | 21.0350i | 0.469536 | − | 0.813260i | ||||
\(670\) | 28.4001 | + | 49.1904i | 1.09719 | + | 1.90039i | ||||
\(671\) | 23.0507 | 0.889864 | ||||||||
\(672\) | 5.50027 | − | 14.9081i | 0.212178 | − | 0.575093i | ||||
\(673\) | 8.46300 | 0.326225 | 0.163112 | − | 0.986608i | \(-0.447847\pi\) | ||||
0.163112 | + | 0.986608i | \(0.447847\pi\) | |||||||
\(674\) | −36.1344 | − | 62.5866i | −1.39185 | − | 2.41075i | ||||
\(675\) | 6.11625 | − | 10.5937i | 0.235414 | − | 0.407750i | ||||
\(676\) | 20.5239 | − | 35.5484i | 0.789379 | − | 1.36724i | ||||
\(677\) | −9.36149 | − | 16.2146i | −0.359791 | − | 0.623177i | 0.628134 | − | 0.778105i | \(-0.283819\pi\) |
−0.987926 | + | 0.154928i | \(0.950485\pi\) | |||||||
\(678\) | 37.7327 | 1.44912 | ||||||||
\(679\) | 21.6339 | + | 26.0132i | 0.830234 | + | 0.998293i | ||||
\(680\) | 14.5839 | 0.559267 | ||||||||
\(681\) | 2.16652 | + | 3.75252i | 0.0830211 | + | 0.143797i | ||||
\(682\) | 31.5452 | − | 54.6378i | 1.20793 | − | 2.09219i | ||||
\(683\) | 0.150927 | − | 0.261414i | 0.00577508 | − | 0.0100027i | −0.863123 | − | 0.504993i | \(-0.831495\pi\) |
0.868899 | + | 0.494990i | \(0.164828\pi\) | |||||||
\(684\) | −0.0798000 | − | 0.138218i | −0.00305123 | − | 0.00528489i | ||||
\(685\) | 2.34764 | 0.0896986 | ||||||||
\(686\) | 36.1713 | + | 21.5230i | 1.38103 | + | 0.821751i | ||||
\(687\) | 12.4437 | 0.474757 | ||||||||
\(688\) | −1.65640 | − | 2.86897i | −0.0631498 | − | 0.109379i | ||||
\(689\) | 0.876224 | − | 1.51766i | 0.0333815 | − | 0.0578184i | ||||
\(690\) | 4.71716 | − | 8.17036i | 0.179579 | − | 0.311040i | ||||
\(691\) | 15.7619 | + | 27.3004i | 0.599610 | + | 1.03855i | 0.992879 | + | 0.119131i | \(0.0380108\pi\) |
−0.393269 | + | 0.919424i | \(0.628656\pi\) | |||||||
\(692\) | 49.1292 | 1.86761 | ||||||||
\(693\) | 5.39171 | + | 6.48312i | 0.204814 | + | 0.246273i | ||||
\(694\) | 3.12238 | 0.118524 | ||||||||
\(695\) | 40.6133 | + | 70.3443i | 1.54055 | + | 2.66831i | ||||
\(696\) | −1.45690 | + | 2.52342i | −0.0552236 | + | 0.0956500i | ||||
\(697\) | 3.21578 | − | 5.56990i | 0.121806 | − | 0.210975i | ||||
\(698\) | −7.30829 | − | 12.6583i | −0.276623 | − | 0.479125i | ||||
\(699\) | −3.24764 | −0.122837 | ||||||||
\(700\) | −35.4561 | + | 96.1013i | −1.34011 | + | 3.63229i | ||||
\(701\) | −17.6579 | −0.666928 | −0.333464 | − | 0.942763i | \(-0.608218\pi\) | ||||
−0.333464 | + | 0.942763i | \(0.608218\pi\) | |||||||
\(702\) | −0.199610 | − | 0.345735i | −0.00753380 | − | 0.0130489i | ||||
\(703\) | −0.0948597 | + | 0.164302i | −0.00357770 | + | 0.00619676i | ||||
\(704\) | −20.7547 | + | 35.9482i | −0.782222 | + | 1.35485i | ||||
\(705\) | −18.5769 | − | 32.1762i | −0.699647 | − | 1.21182i | ||||
\(706\) | −58.4907 | −2.20133 | ||||||||
\(707\) | −4.29158 | + | 0.737329i | −0.161401 | + | 0.0277301i | ||||
\(708\) | 20.2213 | 0.759962 | ||||||||
\(709\) | −3.86961 | − | 6.70235i | −0.145326 | − | 0.251712i | 0.784168 | − | 0.620548i | \(-0.213090\pi\) |
−0.929495 | + | 0.368836i | \(0.879756\pi\) | |||||||
\(710\) | 31.6766 | − | 54.8655i | 1.18880 | − | 2.05907i | ||||
\(711\) | 7.74272 | − | 13.4108i | 0.290375 | − | 0.502944i | ||||
\(712\) | −2.57024 | − | 4.45178i | −0.0963237 | − | 0.166838i | ||||
\(713\) | 8.71037 | 0.326206 | ||||||||
\(714\) | −7.86313 | + | 1.35095i | −0.294270 | + | 0.0505581i | ||||
\(715\) | −2.32402 | −0.0869134 | ||||||||
\(716\) | −13.1077 | − | 22.7031i | −0.489856 | − | 0.848455i | ||||
\(717\) | 13.2412 | − | 22.9344i | 0.494501 | − | 0.856500i | ||||
\(718\) | −27.2304 | + | 47.1645i | −1.01623 | + | 1.76016i | ||||
\(719\) | 11.7071 | + | 20.2773i | 0.436602 | + | 0.756216i | 0.997425 | − | 0.0717194i | \(-0.0228486\pi\) |
−0.560823 | + | 0.827936i | \(0.689515\pi\) | |||||||
\(720\) | −1.29789 | −0.0483695 | ||||||||
\(721\) | −8.23552 | + | 22.3218i | −0.306707 | + | 0.831308i | ||||
\(722\) | 43.1749 | 1.60681 | ||||||||
\(723\) | 1.28075 | + | 2.21832i | 0.0476315 | + | 0.0825001i | ||||
\(724\) | 9.03914 | − | 15.6563i | 0.335937 | − | 0.581860i | ||||
\(725\) | −6.73087 | + | 11.6582i | −0.249978 | + | 0.432975i | ||||
\(726\) | 0.957553 | + | 1.65853i | 0.0355381 | + | 0.0615539i | ||||
\(727\) | −43.6574 | −1.61916 | −0.809582 | − | 0.587007i | \(-0.800306\pi\) | ||||
−0.809582 | + | 0.587007i | \(0.800306\pi\) | |||||||
\(728\) | 0.786838 | + | 0.946113i | 0.0291621 | + | 0.0350653i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.7636 | − | 37.6957i | −0.805509 | − | 1.39518i | ||||
\(731\) | −7.02958 | + | 12.1756i | −0.259998 | + | 0.450330i | ||||
\(732\) | −11.4457 | + | 19.8246i | −0.423046 | + | 0.732737i | ||||
\(733\) | 21.1238 | + | 36.5875i | 0.780226 | + | 1.35139i | 0.931810 | + | 0.362947i | \(0.118229\pi\) |
−0.151584 | + | 0.988444i | \(0.548437\pi\) | |||||||
\(734\) | −58.3584 | −2.15405 | ||||||||
\(735\) | 5.29675 | − | 28.5716i | 0.195374 | − | 1.05388i | ||||
\(736\) | −6.00601 | −0.221384 | ||||||||
\(737\) | 9.59399 | + | 16.6173i | 0.353399 | + | 0.612105i | ||||
\(738\) | 5.50803 | − | 9.54019i | 0.202753 | − | 0.351179i | ||||
\(739\) | 19.6253 | − | 33.9921i | 0.721929 | − | 1.25042i | −0.238296 | − | 0.971192i | \(-0.576589\pi\) |
0.960226 | − | 0.279225i | \(-0.0900777\pi\) | |||||||
\(740\) | −24.7160 | − | 42.8094i | −0.908578 | − | 1.57370i | ||||
\(741\) | −0.00885791 | −0.000325404 | ||||||||
\(742\) | −38.3568 | − | 46.1211i | −1.40812 | − | 1.69316i | ||||
\(743\) | 20.7027 | 0.759507 | 0.379754 | − | 0.925088i | \(-0.376009\pi\) | ||||
0.379754 | + | 0.925088i | \(0.376009\pi\) | |||||||
\(744\) | 11.5313 | + | 19.9728i | 0.422759 | + | 0.732240i | ||||
\(745\) | −15.6236 | + | 27.0609i | −0.572405 | + | 0.991434i | ||||
\(746\) | 6.59179 | − | 11.4173i | 0.241342 | − | 0.418017i | ||||
\(747\) | −3.60551 | − | 6.24493i | −0.131919 | − | 0.228490i | ||||
\(748\) | 13.3843 | 0.489377 | ||||||||
\(749\) | 17.3846 | − | 47.1198i | 0.635219 | − | 1.72172i | ||||
\(750\) | 68.2336 | 2.49154 | ||||||||
\(751\) | 0.0315813 | + | 0.0547004i | 0.00115242 | + | 0.00199605i | 0.866601 | − | 0.499002i | \(-0.166300\pi\) |
−0.865449 | + | 0.500998i | \(0.832967\pi\) | |||||||
\(752\) | −1.39915 | + | 2.42339i | −0.0510216 | + | 0.0883720i | ||||
\(753\) | 7.30613 | − | 12.6546i | 0.266250 | − | 0.461159i | ||||
\(754\) | 0.219669 | + | 0.380478i | 0.00799987 | + | 0.0138562i | ||||
\(755\) | −88.6786 | −3.22735 | ||||||||
\(756\) | −8.25296 | + | 1.41793i | −0.300157 | + | 0.0515695i | ||||
\(757\) | 37.1805 | 1.35135 | 0.675673 | − | 0.737201i | \(-0.263853\pi\) | ||||
0.675673 | + | 0.737201i | \(0.263853\pi\) | |||||||
\(758\) | 23.9203 | + | 41.4312i | 0.868824 | + | 1.50485i | ||||
\(759\) | 1.59353 | − | 2.76007i | 0.0578414 | − | 0.100184i | ||||
\(760\) | 0.277123 | − | 0.479991i | 0.0100523 | − | 0.0174111i | ||||
\(761\) | 14.1534 | + | 24.5144i | 0.513059 | + | 0.888645i | 0.999885 | + | 0.0151458i | \(0.00482125\pi\) |
−0.486826 | + | 0.873499i | \(0.661845\pi\) | |||||||
\(762\) | 40.5594 | 1.46931 | ||||||||
\(763\) | −30.5559 | + | 5.24977i | −1.10620 | + | 0.190054i | ||||
\(764\) | −4.91062 | −0.177660 | ||||||||
\(765\) | 2.75404 | + | 4.77014i | 0.0995727 | + | 0.172465i | ||||
\(766\) | −5.48042 | + | 9.49236i | −0.198016 | + | 0.342973i | ||||
\(767\) | 0.561148 | − | 0.971936i | 0.0202619 | − | 0.0350946i | ||||
\(768\) | −6.96157 | − | 12.0578i | −0.251204 | − | 0.435098i | ||||
\(769\) | 7.54568 | 0.272104 | 0.136052 | − | 0.990702i | \(-0.456559\pi\) | ||||
0.136052 | + | 0.990702i | \(0.456559\pi\) | |||||||
\(770\) | −27.5359 | + | 74.6341i | −0.992323 | + | 2.68963i | ||||
\(771\) | 5.12857 | 0.184701 | ||||||||
\(772\) | −11.5886 | − | 20.0720i | −0.417083 | − | 0.722409i | ||||
\(773\) | 9.19756 | − | 15.9306i | 0.330813 | − | 0.572985i | −0.651858 | − | 0.758341i | \(-0.726010\pi\) |
0.982672 | + | 0.185356i | \(0.0593437\pi\) | |||||||
\(774\) | −12.0403 | + | 20.8545i | −0.432781 | + | 0.749599i | ||||
\(775\) | 53.2748 | + | 92.2746i | 1.91369 | + | 3.31460i | ||||
\(776\) | 33.8588 | 1.21546 | ||||||||
\(777\) | 6.36492 | + | 7.65333i | 0.228340 | + | 0.274562i | ||||
\(778\) | 44.4112 | 1.59222 | ||||||||
\(779\) | −0.122212 | − | 0.211678i | −0.00437872 | − | 0.00758416i | ||||
\(780\) | 1.15398 | − | 1.99875i | 0.0413191 | − | 0.0715667i | ||||
\(781\) | 10.7008 | − | 18.5344i | 0.382906 | − | 0.663213i | ||||
\(782\) | 1.50776 | + | 2.61152i | 0.0539175 | + | 0.0933879i | ||||
\(783\) | −1.10049 | −0.0393283 | ||||||||
\(784\) | −2.06308 | + | 0.730470i | −0.0736813 | + | 0.0260882i | ||||
\(785\) | 48.8157 | 1.74231 | ||||||||
\(786\) | −24.5017 | − | 42.4381i | −0.873945 | − | 1.51372i | ||||
\(787\) | −8.61948 | + | 14.9294i | −0.307251 | + | 0.532175i | −0.977760 | − | 0.209727i | \(-0.932742\pi\) |
0.670509 | + | 0.741902i | \(0.266076\pi\) | |||||||
\(788\) | 10.8266 | − | 18.7521i | 0.385680 | − | 0.668018i | ||||
\(789\) | 1.62406 | + | 2.81296i | 0.0578182 | + | 0.100144i | ||||
\(790\) | 146.094 | 5.19781 | ||||||||
\(791\) | −28.0879 | − | 33.7735i | −0.998689 | − | 1.20085i | ||||
\(792\) | 8.43845 | 0.299847 | ||||||||
\(793\) | 0.635245 | + | 1.10028i | 0.0225582 | + | 0.0390720i | ||||
\(794\) | 41.5727 | − | 72.0061i | 1.47536 | − | 2.55540i | ||||
\(795\) | −20.7068 | + | 35.8652i | −0.734395 | + | 1.27201i | ||||
\(796\) | −12.0962 | − | 20.9512i | −0.428739 | − | 0.742597i | ||||
\(797\) | −52.7371 | −1.86804 | −0.934021 | − | 0.357217i | \(-0.883726\pi\) | ||||
−0.934021 | + | 0.357217i | \(0.883726\pi\) | |||||||
\(798\) | −0.104952 | + | 0.284465i | −0.00371526 | + | 0.0100699i | ||||
\(799\) | 11.8756 | 0.420129 | ||||||||
\(800\) | −36.7342 | − | 63.6255i | −1.29875 | − | 2.24950i | ||||
\(801\) | 0.970735 | − | 1.68136i | 0.0342992 | − | 0.0594080i | ||||
\(802\) | −5.31223 | + | 9.20105i | −0.187581 | + | 0.324900i | ||||
\(803\) | −7.35210 | − | 12.7342i | −0.259450 | − | 0.449380i | ||||
\(804\) | −19.0553 | −0.672030 | ||||||||
\(805\) | −10.8245 | + | 1.85973i | −0.381512 | + | 0.0655470i | ||||
\(806\) | 3.47735 | 0.122485 | ||||||||
\(807\) | −2.41550 | − | 4.18377i | −0.0850297 | − | 0.147276i | ||||
\(808\) | −2.17885 | + | 3.77388i | −0.0766517 | + | 0.132765i | ||||
\(809\) | −3.00655 | + | 5.20750i | −0.105705 | + | 0.183086i | −0.914026 | − | 0.405656i | \(-0.867043\pi\) |
0.808321 | + | 0.588742i | \(0.200376\pi\) | |||||||
\(810\) | 4.71716 | + | 8.17036i | 0.165744 | + | 0.287077i | ||||
\(811\) | 24.3539 | 0.855181 | 0.427591 | − | 0.903972i | \(-0.359362\pi\) | ||||
0.427591 | + | 0.903972i | \(0.359362\pi\) | |||||||
\(812\) | 9.08230 | − | 1.56042i | 0.318726 | − | 0.0547599i | ||||
\(813\) | 12.1239 | 0.425203 | ||||||||
\(814\) | −13.6255 | − | 23.6001i | −0.477574 | − | 0.827182i | ||||
\(815\) | 31.8021 | − | 55.0829i | 1.11398 | − | 1.92947i | ||||
\(816\) | 0.207425 | − | 0.359270i | 0.00726132 | − | 0.0125770i | ||||
\(817\) | 0.267152 | + | 0.462720i | 0.00934645 | + | 0.0161885i | ||||
\(818\) | −25.0128 | −0.874554 | ||||||||
\(819\) | −0.160870 | + | 0.436027i | −0.00562124 | + | 0.0152360i | ||||
\(820\) | 63.6857 | 2.22400 | ||||||||
\(821\) | −0.0559463 | − | 0.0969019i | −0.00195254 | − | 0.00338190i | 0.865047 | − | 0.501690i | \(-0.167288\pi\) |
−0.867000 | + | 0.498308i | \(0.833955\pi\) | |||||||
\(822\) | −0.642634 | + | 1.11307i | −0.0224144 | + | 0.0388229i | ||||
\(823\) | −9.96882 | + | 17.2665i | −0.347491 | + | 0.601873i | −0.985803 | − | 0.167905i | \(-0.946300\pi\) |
0.638312 | + | 0.769778i | \(0.279633\pi\) | |||||||
\(824\) | 11.9052 | + | 20.6204i | 0.414736 | + | 0.718344i | ||||
\(825\) | 38.9857 | 1.35731 | ||||||||
\(826\) | −24.5643 | − | 29.5367i | −0.854700 | − | 1.02771i | ||||
\(827\) | −48.7394 | −1.69483 | −0.847417 | − | 0.530928i | \(-0.821843\pi\) | ||||
−0.847417 | + | 0.530928i | \(0.821843\pi\) | |||||||
\(828\) | 1.58251 | + | 2.74099i | 0.0549962 | + | 0.0952561i | ||||
\(829\) | −5.66689 | + | 9.81533i | −0.196819 | + | 0.340901i | −0.947495 | − | 0.319770i | \(-0.896394\pi\) |
0.750676 | + | 0.660670i | \(0.229728\pi\) | |||||||
\(830\) | 34.0155 | − | 58.9166i | 1.18070 | − | 2.04502i | ||||
\(831\) | −10.9507 | − | 18.9672i | −0.379875 | − | 0.657964i | ||||
\(832\) | −2.28788 | −0.0793178 | ||||||||
\(833\) | 7.06242 | + | 6.03243i | 0.244699 | + | 0.209011i | ||||
\(834\) | −44.4693 | −1.53985 | ||||||||
\(835\) | 16.6561 | + | 28.8493i | 0.576409 | + | 0.998370i | ||||
\(836\) | 0.254327 | − | 0.440508i | 0.00879609 | − | 0.0152353i | ||||
\(837\) | −4.35518 | + | 7.54340i | −0.150537 | + | 0.260738i | ||||
\(838\) | 21.4507 | + | 37.1537i | 0.741002 | + | 1.28345i | ||||
\(839\) | 42.1263 | 1.45436 | 0.727182 | − | 0.686445i | \(-0.240830\pi\) | ||||
0.727182 | + | 0.686445i | \(0.240830\pi\) | |||||||
\(840\) | −18.5944 | − | 22.3584i | −0.641569 | − | 0.771438i | ||||
\(841\) | −27.7889 | −0.958239 | ||||||||
\(842\) | −11.5157 | − | 19.9458i | −0.396857 | − | 0.687377i | ||||
\(843\) | −12.1182 | + | 20.9894i | −0.417373 | + | 0.722912i | ||||
\(844\) | 7.43154 | − | 12.8718i | 0.255804 | − | 0.443066i | ||||
\(845\) | 26.9188 | + | 46.6247i | 0.926034 | + | 1.60394i | ||||
\(846\) | 20.3407 | 0.699327 | ||||||||
\(847\) | 0.771711 | − | 2.09167i | 0.0265163 | − | 0.0718707i | ||||
\(848\) | 3.11912 | 0.107111 | ||||||||
\(849\) | 2.57291 | + | 4.45641i | 0.0883020 | + | 0.152943i | ||||
\(850\) | −18.4437 | + | 31.9454i | −0.632614 | + | 1.09572i | ||||
\(851\) | 1.88116 | − | 3.25827i | 0.0644854 | − | 0.111692i | ||||
\(852\) | 10.6269 | + | 18.4063i | 0.364071 | + | 0.630590i | ||||
\(853\) | −37.5528 | −1.28578 | −0.642891 | − | 0.765957i | \(-0.722265\pi\) | ||||
−0.642891 | + | 0.765957i | \(0.722265\pi\) | |||||||
\(854\) | 42.8611 | − | 7.36390i | 1.46668 | − | 0.251988i | ||||
\(855\) | 0.209329 | 0.00715890 | ||||||||
\(856\) | −25.1310 | − | 43.5281i | −0.858958 | − | 1.48776i | ||||
\(857\) | −29.0360 | + | 50.2919i | −0.991852 | + | 1.71794i | −0.385597 | + | 0.922667i | \(0.626005\pi\) |
−0.606255 | + | 0.795271i | \(0.707329\pi\) | |||||||
\(858\) | 0.636169 | − | 1.10188i | 0.0217184 | − | 0.0376174i | ||||
\(859\) | 12.4928 | + | 21.6382i | 0.426250 | + | 0.738287i | 0.996536 | − | 0.0831590i | \(-0.0265009\pi\) |
−0.570286 | + | 0.821446i | \(0.693168\pi\) | |||||||
\(860\) | −139.214 | −4.74717 | ||||||||
\(861\) | −12.6393 | + | 2.17153i | −0.430745 | + | 0.0740057i | ||||
\(862\) | −17.8901 | −0.609338 | ||||||||
\(863\) | 6.96047 | + | 12.0559i | 0.236937 | + | 0.410387i | 0.959834 | − | 0.280569i | \(-0.0905231\pi\) |
−0.722897 | + | 0.690956i | \(0.757190\pi\) | |||||||
\(864\) | 3.00300 | − | 5.20135i | 0.102164 | − | 0.176954i | ||||
\(865\) | −32.2186 | + | 55.8042i | −1.09546 | + | 1.89740i | ||||
\(866\) | −23.3934 | − | 40.5186i | −0.794941 | − | 1.37688i | ||||
\(867\) | 15.2394 | 0.517558 | ||||||||
\(868\) | 25.2471 | − | 68.4307i | 0.856944 | − | 2.32269i | ||||
\(869\) | 49.3530 | 1.67418 | ||||||||
\(870\) | −5.19119 | − | 8.99140i | −0.175998 | − | 0.304837i | ||||
\(871\) | −0.528793 | + | 0.915896i | −0.0179175 | + | 0.0310339i | ||||
\(872\) | −15.5134 | + | 26.8699i | −0.525349 | + | 0.909931i | ||||
\(873\) | 6.39394 | + | 11.0746i | 0.216402 | + | 0.374820i | ||||
\(874\) | 0.114602 | 0.00387647 | ||||||||
\(875\) | −50.7924 | − | 61.0740i | −1.71710 | − | 2.06468i | ||||
\(876\) | 14.6026 | 0.493375 | ||||||||
\(877\) | 3.98769 | + | 6.90689i | 0.134655 | + | 0.233229i | 0.925466 | − | 0.378832i | \(-0.123674\pi\) |
−0.790811 | + | 0.612061i | \(0.790341\pi\) | |||||||
\(878\) | 38.2578 | − | 66.2645i | 1.29114 | − | 2.23632i | ||||
\(879\) | −12.2687 | + | 21.2500i | −0.413813 | + | 0.716745i | ||||
\(880\) | −2.06822 | − | 3.58227i | −0.0697198 | − | 0.120758i | ||||
\(881\) | −33.6800 | −1.13471 | −0.567354 | − | 0.823474i | \(-0.692033\pi\) | ||||
−0.567354 | + | 0.823474i | \(0.692033\pi\) | |||||||
\(882\) | 12.0966 | + | 10.3324i | 0.407314 | + | 0.347910i | ||||
\(883\) | 32.7638 | 1.10259 | 0.551294 | − | 0.834311i | \(-0.314134\pi\) | ||||
0.551294 | + | 0.834311i | \(0.314134\pi\) | |||||||
\(884\) | 0.368851 | + | 0.638868i | 0.0124058 | + | 0.0214875i | ||||
\(885\) | −13.2610 | + | 22.9687i | −0.445763 | + | 0.772083i | ||||
\(886\) | 8.33534 | − | 14.4372i | 0.280031 | − | 0.485028i | ||||
\(887\) | −4.66894 | − | 8.08685i | −0.156768 | − | 0.271530i | 0.776934 | − | 0.629583i | \(-0.216774\pi\) |
−0.933701 | + | 0.358053i | \(0.883441\pi\) | |||||||
\(888\) | 9.96160 | 0.334289 | ||||||||
\(889\) | −30.1920 | − | 36.3036i | −1.01261 | − | 1.21758i | ||||
\(890\) | 18.3164 | 0.613968 | ||||||||
\(891\) | 1.59353 | + | 2.76007i | 0.0533852 | + | 0.0924659i | ||||
\(892\) | −38.4379 | + | 66.5764i | −1.28700 | + | 2.22914i | ||||
\(893\) | 0.225660 | − | 0.390855i | 0.00755143 | − | 0.0130795i | ||||
\(894\) | −8.55349 | − | 14.8151i | −0.286072 | − | 0.495491i | ||||
\(895\) | 34.3836 | 1.14932 | ||||||||
\(896\) | −16.1071 | + | 43.6571i | −0.538099 | + | 1.45848i | ||||
\(897\) | 0.175661 | 0.00586516 | ||||||||
\(898\) | −24.0344 | − | 41.6289i | −0.802040 | − | 1.38917i | ||||
\(899\) | 4.79284 | − | 8.30144i | 0.159850 | − | 0.276869i | ||||
\(900\) | −19.3581 | + | 33.5292i | −0.645270 | + | 1.11764i | ||||
\(901\) | −6.61860 | − | 11.4637i | −0.220497 | − | 0.381913i | ||||
\(902\) | 35.1088 | 1.16900 | ||||||||
\(903\) | 27.6289 | − | 4.74689i | 0.919434 | − | 0.157966i | ||||
\(904\) | −43.9597 | −1.46208 | ||||||||
\(905\) | 11.8556 | + | 20.5345i | 0.394094 | + | 0.682590i | ||||
\(906\) | 24.2746 | − | 42.0448i | 0.806468 | − | 1.39684i | ||||
\(907\) | −9.59691 | + | 16.6223i | −0.318660 | + | 0.551935i | −0.980209 | − | 0.197967i | \(-0.936566\pi\) |
0.661549 | + | 0.749902i | \(0.269900\pi\) | |||||||
\(908\) | −6.85708 | − | 11.8768i | −0.227560 | − | 0.394146i | ||||
\(909\) | −1.64583 | −0.0545887 | ||||||||
\(910\) | −4.32134 | + | 0.742443i | −0.143251 | + | 0.0246117i | ||||
\(911\) | −18.4406 | −0.610963 | −0.305481 | − | 0.952198i | \(-0.598817\pi\) | ||||
−0.305481 | + | 0.952198i | \(0.598817\pi\) | |||||||
\(912\) | −0.00788296 | − | 0.0136537i | −0.000261031 | − | 0.000452119i | ||||
\(913\) | 11.4910 | − | 19.9029i | 0.380295 | − | 0.658691i | ||||
\(914\) | 10.1904 | − | 17.6504i | 0.337070 | − | 0.583822i | ||||
\(915\) | −15.0120 | − | 26.0016i | −0.496282 | − | 0.859586i | ||||
\(916\) | −39.3847 | −1.30131 | ||||||||
\(917\) | −19.7464 | + | 53.5212i | −0.652083 | + | 1.76743i | ||||
\(918\) | −3.01553 | −0.0995272 | ||||||||
\(919\) | 15.3453 | + | 26.5788i | 0.506194 | + | 0.876753i | 0.999974 | + | 0.00716672i | \(0.00228126\pi\) |
−0.493781 | + | 0.869587i | \(0.664385\pi\) | |||||||
\(920\) | −5.49562 | + | 9.51870i | −0.181185 | + | 0.313822i | ||||
\(921\) | 3.58329 | − | 6.20645i | 0.118074 | − | 0.204509i | ||||
\(922\) | 7.16113 | + | 12.4034i | 0.235839 | + | 0.408486i | ||||
\(923\) | 1.17960 | 0.0388270 | ||||||||
\(924\) | −17.0649 | − | 20.5192i | −0.561394 | − | 0.675034i | ||||
\(925\) | 46.0226 | 1.51321 | ||||||||
\(926\) | −17.1691 | − | 29.7377i | −0.564211 | − | 0.977243i | ||||
\(927\) | −4.49638 | + | 7.78795i | −0.147680 | + | 0.255790i | ||||
\(928\) | −3.30478 | + | 5.72404i | −0.108485 | + | 0.187901i | ||||
\(929\) | 2.09459 | + | 3.62794i | 0.0687213 | + | 0.119029i | 0.898339 | − | 0.439304i | \(-0.144775\pi\) |
−0.829617 | + | 0.558332i | \(0.811441\pi\) | |||||||
\(930\) | −82.1764 | −2.69467 | ||||||||
\(931\) | 0.332741 | − | 0.117813i | 0.0109052 | − | 0.00386117i | ||||
\(932\) | 10.2789 | 0.336696 | ||||||||
\(933\) | 2.93640 | + | 5.08599i | 0.0961334 | + | 0.166508i | ||||
\(934\) | −21.5455 | + | 37.3179i | −0.704990 | + | 1.22108i | ||||
\(935\) | −8.77730 | + | 15.2027i | −0.287048 | + | 0.497182i | ||||
\(936\) | 0.232551 | + | 0.402791i | 0.00760118 | + | 0.0131656i | ||||
\(937\) | 31.8927 | 1.04189 | 0.520945 | − | 0.853590i | \(-0.325580\pi\) | ||||
0.520945 | + | 0.853590i | \(0.325580\pi\) | |||||||
\(938\) | 23.1479 | + | 27.8336i | 0.755807 | + | 0.908800i | ||||
\(939\) | 3.80364 | 0.124127 | ||||||||
\(940\) | 58.7964 | + | 101.838i | 1.91773 | + | 3.32160i | ||||
\(941\) | 15.1790 | − | 26.2908i | 0.494822 | − | 0.857056i | −0.505160 | − | 0.863025i | \(-0.668567\pi\) |
0.999982 | + | 0.00596909i | \(0.00190003\pi\) | |||||||
\(942\) | −13.3626 | + | 23.1447i | −0.435378 | + | 0.754096i | ||||
\(943\) | 2.42359 | + | 4.19779i | 0.0789231 | + | 0.136699i | ||||
\(944\) | 1.99754 | 0.0650143 | ||||||||
\(945\) | 3.80165 | − | 10.3041i | 0.123668 | − | 0.335193i | ||||
\(946\) | −76.7465 | −2.49524 | ||||||||
\(947\) | −16.8838 | − | 29.2436i | −0.548650 | − | 0.950290i | −0.998367 | − | 0.0571191i | \(-0.981809\pi\) |
0.449717 | − | 0.893171i | \(-0.351525\pi\) | |||||||
\(948\) | −24.5059 | + | 42.4455i | −0.795915 | + | 1.37857i | ||||
\(949\) | 0.405226 | − | 0.701872i | 0.0131542 | − | 0.0227837i | ||||
\(950\) | 0.700934 | + | 1.21405i | 0.0227413 | + | 0.0393891i | ||||
\(951\) | −9.80284 | −0.317879 | ||||||||
\(952\) | 9.16076 | − | 1.57390i | 0.296902 | − | 0.0510103i | ||||
\(953\) | 6.62261 | 0.214527 | 0.107264 | − | 0.994231i | \(-0.465791\pi\) | ||||
0.107264 | + | 0.994231i | \(0.465791\pi\) | |||||||
\(954\) | −11.3364 | − | 19.6352i | −0.367030 | − | 0.635714i | ||||
\(955\) | 3.22035 | − | 5.57781i | 0.104208 | − | 0.180494i | ||||
\(956\) | −41.9087 | + | 72.5880i | −1.35542 | + | 2.34766i | ||||
\(957\) | −1.75366 | − | 3.03743i | −0.0566879 | − | 0.0981863i | ||||
\(958\) | 64.9465 | 2.09833 | ||||||||
\(959\) | 1.47465 | − | 0.253357i | 0.0476189 | − | 0.00818134i | ||||
\(960\) | 54.0668 | 1.74500 | ||||||||
\(961\) | −22.4353 | − | 38.8590i | −0.723718 | − | 1.25352i | ||||
\(962\) | 0.750998 | − | 1.30077i | 0.0242131 | − | 0.0419384i | ||||
\(963\) | 9.49153 | − | 16.4398i | 0.305860 | − | 0.529766i | ||||
\(964\) | −4.05360 | − | 7.02104i | −0.130558 | − | 0.226132i | ||||
\(965\) | 30.3989 | 0.978574 | ||||||||
\(966\) | 2.08130 | − | 5.64122i | 0.0669647 | − | 0.181503i | ||||
\(967\) | −49.1558 | −1.58074 | −0.790372 | − | 0.612628i | \(-0.790113\pi\) | ||||
−0.790372 | + | 0.612628i | \(0.790113\pi\) | |||||||
\(968\) | −1.11558 | − | 1.93223i | −0.0358560 | − | 0.0621044i | ||||
\(969\) | −0.0334543 | + | 0.0579446i | −0.00107471 | + | 0.00186145i | ||||
\(970\) | −60.3225 | + | 104.482i | −1.93684 | + | 3.35470i | ||||
\(971\) | 4.38158 | + | 7.58911i | 0.140611 | + | 0.243546i | 0.927727 | − | 0.373259i | \(-0.121760\pi\) |
−0.787116 | + | 0.616806i | \(0.788426\pi\) | |||||||
\(972\) | −3.16503 | −0.101518 | ||||||||
\(973\) | 33.1025 | + | 39.8032i | 1.06122 | + | 1.27603i | ||||
\(974\) | −56.8002 | −1.82000 | ||||||||
\(975\) | 1.07439 | + | 1.86089i | 0.0344079 | + | 0.0595963i | ||||
\(976\) | −1.13065 | + | 1.95835i | −0.0361913 | + | 0.0626851i | ||||
\(977\) | 0.173762 | − | 0.300964i | 0.00555913 | − | 0.00962869i | −0.863232 | − | 0.504807i | \(-0.831564\pi\) |
0.868792 | + | 0.495178i | \(0.164897\pi\) | |||||||
\(978\) | 17.4108 | + | 30.1564i | 0.556735 | + | 0.964294i | ||||
\(979\) | 6.18757 | 0.197756 | ||||||||
\(980\) | −16.7644 | + | 90.4299i | −0.535518 | + | 2.88868i | ||||
\(981\) | −11.7183 | −0.374136 | ||||||||
\(982\) | −25.0579 | − | 43.4015i | −0.799629 | − | 1.38500i | ||||
\(983\) | 26.6641 | − | 46.1836i | 0.850454 | − | 1.47303i | −0.0303458 | − | 0.999539i | \(-0.509661\pi\) |
0.880799 | − | 0.473490i | \(-0.157006\pi\) | |||||||
\(984\) | −6.41701 | + | 11.1146i | −0.204567 | + | 0.354320i | ||||
\(985\) | 14.2000 | + | 24.5950i | 0.452448 | + | 0.783663i | ||||
\(986\) | 3.31856 | 0.105684 | ||||||||
\(987\) | −15.1414 | − | 18.2064i | −0.481956 | − | 0.579515i | ||||
\(988\) | 0.0280355 | 0.000891930 | ||||||||
\(989\) | −5.29788 | − | 9.17620i | −0.168463 | − | 0.291786i | ||||
\(990\) | −15.0339 | + | 26.0394i | −0.477807 | + | 0.827586i | ||||
\(991\) | 2.91462 | − | 5.04827i | 0.0925860 | − | 0.160364i | −0.816013 | − | 0.578034i | \(-0.803820\pi\) |
0.908599 | + | 0.417671i | \(0.137153\pi\) | |||||||
\(992\) | 26.1573 | + | 45.3057i | 0.830494 | + | 1.43846i | ||||
\(993\) | 11.1896 | 0.355091 | ||||||||
\(994\) | 13.9763 | − | 37.8819i | 0.443302 | − | 1.20154i | ||||
\(995\) | 31.7304 | 1.00592 | ||||||||
\(996\) | 11.4115 | + | 19.7654i | 0.361588 | + | 0.626290i | ||||
\(997\) | 15.9679 | − | 27.6572i | 0.505708 | − | 0.875912i | −0.494270 | − | 0.869308i | \(-0.664565\pi\) |
0.999978 | − | 0.00660337i | \(-0.00210193\pi\) | |||||||
\(998\) | −44.8001 | + | 77.5961i | −1.41812 | + | 2.45626i | ||||
\(999\) | 1.88116 | + | 3.25827i | 0.0595174 | + | 0.103087i |
(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 | 483.2.i.f.277.6 | ✓ | 12 | |
7.2 | even | 3 | inner | 483.2.i.f.415.6 | yes | 12 | |
7.3 | odd | 6 | 3381.2.a.bd.1.1 | 6 | |||
7.4 | even | 3 | 3381.2.a.bc.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.f.277.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
483.2.i.f.415.6 | yes | 12 | 7.2 | even | 3 | inner | |
3381.2.a.bc.1.1 | 6 | 7.4 | even | 3 | |||
3381.2.a.bd.1.1 | 6 | 7.3 | odd | 6 |