Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(18,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.18");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.f (of order \(4\), 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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 111x^{12} + 329x^{8} + 168x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 18.5 | ||
Root | \(-2.27933 + 2.27933i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.18 |
Dual form | 325.2.f.d.307.4 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.438725i | 0.310225i | 0.987897 | + | 0.155113i | \(0.0495740\pi\) | ||||
−0.987897 | + | 0.155113i | \(0.950426\pi\) | |||||||
\(3\) | 0.242722 | + | 0.242722i | 0.140135 | + | 0.140135i | 0.773694 | − | 0.633559i | \(-0.218407\pi\) |
−0.633559 | + | 0.773694i | \(0.718407\pi\) | |||||||
\(4\) | 1.80752 | 0.903760 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.106488 | + | 0.106488i | −0.0434736 | + | 0.0434736i | ||||
\(7\) | −0.438725 | −0.165822 | −0.0829112 | − | 0.996557i | \(-0.526422\pi\) | ||||
−0.0829112 | + | 0.996557i | \(0.526422\pi\) | |||||||
\(8\) | 1.67045i | 0.590594i | ||||||||
\(9\) | − | 2.88217i | − | 0.960724i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.04588 | + | 3.04588i | 0.918367 | + | 0.918367i | 0.996911 | − | 0.0785436i | \(-0.0250270\pi\) |
−0.0785436 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(12\) | 0.438725 | + | 0.438725i | 0.126649 | + | 0.126649i | ||||
\(13\) | 2.89520 | + | 2.14891i | 0.802983 | + | 0.596001i | ||||
\(14\) | − | 0.192479i | − | 0.0514423i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.88217 | 0.720543 | ||||||||
\(17\) | −3.09120 | − | 3.09120i | −0.749726 | − | 0.749726i | 0.224701 | − | 0.974428i | \(-0.427859\pi\) |
−0.974428 | + | 0.224701i | \(0.927859\pi\) | |||||||
\(18\) | 1.26448 | 0.298041 | ||||||||
\(19\) | −1.59454 | − | 1.59454i | −0.365814 | − | 0.365814i | 0.500134 | − | 0.865948i | \(-0.333284\pi\) |
−0.865948 | + | 0.500134i | \(0.833284\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.106488 | − | 0.106488i | −0.0232376 | − | 0.0232376i | ||||
\(22\) | −1.33630 | + | 1.33630i | −0.284901 | + | 0.284901i | ||||
\(23\) | −2.95305 | + | 2.95305i | −0.615754 | + | 0.615754i | −0.944439 | − | 0.328685i | \(-0.893394\pi\) |
0.328685 | + | 0.944439i | \(0.393394\pi\) | |||||||
\(24\) | −0.405455 | + | 0.405455i | −0.0827632 | + | 0.0827632i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.942781 | + | 1.27019i | −0.184895 | + | 0.249106i | ||||
\(27\) | 1.42773 | − | 1.42773i | 0.274767 | − | 0.274767i | ||||
\(28\) | −0.793004 | −0.149864 | ||||||||
\(29\) | − | 0.138324i | − | 0.0256862i | −0.999918 | − | 0.0128431i | \(-0.995912\pi\) | ||
0.999918 | − | 0.0128431i | \(-0.00408820\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.27019 | + | 1.27019i | −0.228134 | + | 0.228134i | −0.811913 | − | 0.583779i | \(-0.801573\pi\) |
0.583779 | + | 0.811913i | \(0.301573\pi\) | |||||||
\(32\) | 4.60539i | 0.814125i | ||||||||
\(33\) | 1.47860i | 0.257392i | ||||||||
\(34\) | 1.35619 | − | 1.35619i | 0.232584 | − | 0.232584i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 5.20959i | − | 0.868264i | ||||||
\(37\) | 7.13783 | 1.17345 | 0.586726 | − | 0.809785i | \(-0.300416\pi\) | ||||
0.586726 | + | 0.809785i | \(0.300416\pi\) | |||||||
\(38\) | 0.699566 | − | 0.699566i | 0.113485 | − | 0.113485i | ||||
\(39\) | 0.181140 | + | 1.22432i | 0.0290056 | + | 0.196047i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0318365 | − | 0.0318365i | 0.00497202 | − | 0.00497202i | −0.704616 | − | 0.709588i | \(-0.748881\pi\) |
0.709588 | + | 0.704616i | \(0.248881\pi\) | |||||||
\(42\) | 0.0467189 | − | 0.0467189i | 0.00720889 | − | 0.00720889i | ||||
\(43\) | 2.20677 | − | 2.20677i | 0.336529 | − | 0.336529i | −0.518530 | − | 0.855059i | \(-0.673521\pi\) |
0.855059 | + | 0.518530i | \(0.173521\pi\) | |||||||
\(44\) | 5.50549 | + | 5.50549i | 0.829984 | + | 0.829984i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.29558 | − | 1.29558i | −0.191022 | − | 0.191022i | ||||
\(47\) | −7.44688 | −1.08624 | −0.543120 | − | 0.839655i | \(-0.682757\pi\) | ||||
−0.543120 | + | 0.839655i | \(0.682757\pi\) | |||||||
\(48\) | 0.699566 | + | 0.699566i | 0.100974 | + | 0.100974i | ||||
\(49\) | −6.80752 | −0.972503 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.50060i | − | 0.210127i | ||||||
\(52\) | 5.23313 | + | 3.88420i | 0.725705 | + | 0.538642i | ||||
\(53\) | −7.84090 | − | 7.84090i | −1.07703 | − | 1.07703i | −0.996774 | − | 0.0802557i | \(-0.974426\pi\) |
−0.0802557 | − | 0.996774i | \(-0.525574\pi\) | |||||||
\(54\) | 0.626381 | + | 0.626381i | 0.0852397 | + | 0.0852397i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 0.732869i | − | 0.0979337i | ||||||
\(57\) | − | 0.774061i | − | 0.102527i | ||||||
\(58\) | 0.0606864 | 0.00796851 | ||||||||
\(59\) | −6.01404 | + | 6.01404i | −0.782962 | + | 0.782962i | −0.980330 | − | 0.197368i | \(-0.936761\pi\) |
0.197368 | + | 0.980330i | \(0.436761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.35550 | −1.19785 | −0.598924 | − | 0.800806i | \(-0.704405\pi\) | ||||
−0.598924 | + | 0.800806i | \(0.704405\pi\) | |||||||
\(62\) | −0.557266 | − | 0.557266i | −0.0707728 | − | 0.0707728i | ||||
\(63\) | 1.26448i | 0.159310i | ||||||||
\(64\) | 3.74385 | 0.467981 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.648699 | −0.0798494 | ||||||||
\(67\) | − | 11.1798i | − | 1.36583i | −0.730498 | − | 0.682915i | \(-0.760712\pi\) | ||
0.730498 | − | 0.682915i | \(-0.239288\pi\) | |||||||
\(68\) | −5.58741 | − | 5.58741i | −0.677573 | − | 0.677573i | ||||
\(69\) | −1.43354 | −0.172578 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.51194 | + | 1.51194i | −0.179435 | + | 0.179435i | −0.791109 | − | 0.611675i | \(-0.790496\pi\) |
0.611675 | + | 0.791109i | \(0.290496\pi\) | |||||||
\(72\) | 4.81453 | 0.567398 | ||||||||
\(73\) | − | 15.1546i | − | 1.77371i | −0.462046 | − | 0.886856i | \(-0.652884\pi\) | ||
0.462046 | − | 0.886856i | \(-0.347116\pi\) | |||||||
\(74\) | 3.13154i | 0.364035i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.88217 | − | 2.88217i | −0.330608 | − | 0.330608i | ||||
\(77\) | −1.33630 | − | 1.33630i | −0.152286 | − | 0.152286i | ||||
\(78\) | −0.537138 | + | 0.0794704i | −0.0608189 | + | 0.00899825i | ||||
\(79\) | − | 10.0951i | − | 1.13579i | −0.823100 | − | 0.567896i | \(-0.807757\pi\) | ||
0.823100 | − | 0.567896i | \(-0.192243\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.95343 | −0.883715 | ||||||||
\(82\) | 0.0139674 | + | 0.0139674i | 0.00154245 | + | 0.00154245i | ||||
\(83\) | 15.7648 | 1.73041 | 0.865203 | − | 0.501422i | \(-0.167189\pi\) | ||||
0.865203 | + | 0.501422i | \(0.167189\pi\) | |||||||
\(84\) | −0.192479 | − | 0.192479i | −0.0210012 | − | 0.0210012i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.968164 | + | 0.968164i | 0.104400 | + | 0.104400i | ||||
\(87\) | 0.0335744 | − | 0.0335744i | 0.00359955 | − | 0.00359955i | ||||
\(88\) | −5.08800 | + | 5.08800i | −0.542382 | + | 0.542382i | ||||
\(89\) | −9.98527 | + | 9.98527i | −1.05844 | + | 1.05844i | −0.0602534 | + | 0.998183i | \(0.519191\pi\) |
−0.998183 | + | 0.0602534i | \(0.980809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.27019 | − | 0.942781i | −0.133153 | − | 0.0988303i | ||||
\(92\) | −5.33770 | + | 5.33770i | −0.556494 | + | 0.556494i | ||||
\(93\) | −0.616608 | −0.0639393 | ||||||||
\(94\) | − | 3.26713i | − | 0.336979i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.11783 | + | 1.11783i | −0.114088 | + | 0.114088i | ||||
\(97\) | − | 1.50802i | − | 0.153117i | −0.997065 | − | 0.0765584i | \(-0.975607\pi\) | ||
0.997065 | − | 0.0765584i | \(-0.0243932\pi\) | |||||||
\(98\) | − | 2.98663i | − | 0.301695i | ||||||
\(99\) | 8.77875 | − | 8.77875i | 0.882297 | − | 0.882297i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.55137i | − | 0.452878i | −0.974025 | − | 0.226439i | \(-0.927292\pi\) | ||
0.974025 | − | 0.226439i | \(-0.0727084\pi\) | |||||||
\(102\) | 0.658352 | 0.0651866 | ||||||||
\(103\) | −5.64609 | + | 5.64609i | −0.556326 | + | 0.556326i | −0.928259 | − | 0.371934i | \(-0.878695\pi\) |
0.371934 | + | 0.928259i | \(0.378695\pi\) | |||||||
\(104\) | −3.58966 | + | 4.83629i | −0.351995 | + | 0.474238i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.43999 | − | 3.43999i | 0.334122 | − | 0.334122i | ||||
\(107\) | −7.73632 | + | 7.73632i | −0.747899 | + | 0.747899i | −0.974084 | − | 0.226186i | \(-0.927374\pi\) |
0.226186 | + | 0.974084i | \(0.427374\pi\) | |||||||
\(108\) | 2.58065 | − | 2.58065i | 0.248324 | − | 0.248324i | ||||
\(109\) | 10.2876 | + | 10.2876i | 0.985376 | + | 0.985376i | 0.999895 | − | 0.0145186i | \(-0.00462157\pi\) |
−0.0145186 | + | 0.999895i | \(0.504622\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.73251 | + | 1.73251i | 0.164442 | + | 0.164442i | ||||
\(112\) | −1.26448 | −0.119482 | ||||||||
\(113\) | −2.25349 | − | 2.25349i | −0.211990 | − | 0.211990i | 0.593122 | − | 0.805112i | \(-0.297895\pi\) |
−0.805112 | + | 0.593122i | \(0.797895\pi\) | |||||||
\(114\) | 0.339600 | 0.0318064 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 0.250024i | − | 0.0232142i | ||||||
\(117\) | 6.19354 | − | 8.34446i | 0.572593 | − | 0.771446i | ||||
\(118\) | −2.63851 | − | 2.63851i | −0.242894 | − | 0.242894i | ||||
\(119\) | 1.35619 | + | 1.35619i | 0.124321 | + | 0.124321i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.55476i | 0.686796i | ||||||||
\(122\) | − | 4.10449i | − | 0.371603i | ||||||
\(123\) | 0.0154548 | 0.00139351 | ||||||||
\(124\) | −2.29590 | + | 2.29590i | −0.206178 | + | 0.206178i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.554759 | −0.0494218 | ||||||||
\(127\) | 12.7337 | + | 12.7337i | 1.12993 | + | 1.12993i | 0.990187 | + | 0.139747i | \(0.0446290\pi\) |
0.139747 | + | 0.990187i | \(0.455371\pi\) | |||||||
\(128\) | 10.8533i | 0.959305i | ||||||||
\(129\) | 1.07126 | 0.0943193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.9329 | 1.04259 | 0.521293 | − | 0.853378i | \(-0.325450\pi\) | ||||
0.521293 | + | 0.853378i | \(0.325450\pi\) | |||||||
\(132\) | 2.67260i | 0.232620i | ||||||||
\(133\) | 0.699566 | + | 0.699566i | 0.0606601 | + | 0.0606601i | ||||
\(134\) | 4.90485 | 0.423715 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.16371 | − | 5.16371i | 0.442784 | − | 0.442784i | ||||
\(137\) | −3.37863 | −0.288656 | −0.144328 | − | 0.989530i | \(-0.546102\pi\) | ||||
−0.144328 | + | 0.989530i | \(0.546102\pi\) | |||||||
\(138\) | − | 0.628930i | − | 0.0535380i | ||||||
\(139\) | − | 15.3123i | − | 1.29877i | −0.760458 | − | 0.649387i | \(-0.775025\pi\) | ||
0.760458 | − | 0.649387i | \(-0.224975\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.80752 | − | 1.80752i | −0.152221 | − | 0.152221i | ||||
\(142\) | −0.663327 | − | 0.663327i | −0.0556652 | − | 0.0556652i | ||||
\(143\) | 2.27309 | + | 15.3638i | 0.190086 | + | 1.28478i | ||||
\(144\) | − | 8.30692i | − | 0.692243i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.64870 | 0.550250 | ||||||||
\(147\) | −1.65233 | − | 1.65233i | −0.136282 | − | 0.136282i | ||||
\(148\) | 12.9018 | 1.06052 | ||||||||
\(149\) | −6.72153 | − | 6.72153i | −0.550649 | − | 0.550649i | 0.375979 | − | 0.926628i | \(-0.377306\pi\) |
−0.926628 | + | 0.375979i | \(0.877306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.88524 | + | 5.88524i | 0.478934 | + | 0.478934i | 0.904791 | − | 0.425857i | \(-0.140027\pi\) |
−0.425857 | + | 0.904791i | \(0.640027\pi\) | |||||||
\(152\) | 2.66361 | − | 2.66361i | 0.216047 | − | 0.216047i | ||||
\(153\) | −8.90937 | + | 8.90937i | −0.720280 | + | 0.720280i | ||||
\(154\) | 0.586269 | − | 0.586269i | 0.0472429 | − | 0.0472429i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.327414 | + | 2.21298i | 0.0262141 | + | 0.177180i | ||||
\(157\) | −8.26499 | + | 8.26499i | −0.659618 | + | 0.659618i | −0.955290 | − | 0.295672i | \(-0.904457\pi\) |
0.295672 | + | 0.955290i | \(0.404457\pi\) | |||||||
\(158\) | 4.42899 | 0.352352 | ||||||||
\(159\) | − | 3.80631i | − | 0.301860i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.29558 | − | 1.29558i | 0.102106 | − | 0.102106i | ||||
\(162\) | − | 3.48937i | − | 0.274151i | ||||||
\(163\) | 20.6325i | 1.61606i | 0.589142 | + | 0.808030i | \(0.299466\pi\) | ||||
−0.589142 | + | 0.808030i | \(0.700534\pi\) | |||||||
\(164\) | 0.0575450 | − | 0.0575450i | 0.00449351 | − | 0.00449351i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.91639i | 0.536816i | ||||||||
\(167\) | −6.02897 | −0.466535 | −0.233268 | − | 0.972413i | \(-0.574942\pi\) | ||||
−0.233268 | + | 0.972413i | \(0.574942\pi\) | |||||||
\(168\) | 0.177883 | − | 0.177883i | 0.0137240 | − | 0.0137240i | ||||
\(169\) | 3.76434 | + | 12.4431i | 0.289565 | + | 0.957158i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.59575 | + | 4.59575i | −0.351446 | + | 0.351446i | ||||
\(172\) | 3.98878 | − | 3.98878i | 0.304142 | − | 0.304142i | ||||
\(173\) | 14.1676 | − | 14.1676i | 1.07714 | − | 1.07714i | 0.0803789 | − | 0.996764i | \(-0.474387\pi\) |
0.996764 | − | 0.0803789i | \(-0.0256130\pi\) | |||||||
\(174\) | 0.0147299 | + | 0.0147299i | 0.00111667 | + | 0.00111667i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.77875 | + | 8.77875i | 0.661723 | + | 0.661723i | ||||
\(177\) | −2.91948 | −0.219441 | ||||||||
\(178\) | −4.38078 | − | 4.38078i | −0.328354 | − | 0.328354i | ||||
\(179\) | −16.0951 | −1.20301 | −0.601504 | − | 0.798870i | \(-0.705432\pi\) | ||||
−0.601504 | + | 0.798870i | \(0.705432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.55476i | 0.487211i | 0.969874 | + | 0.243606i | \(0.0783303\pi\) | ||||
−0.969874 | + | 0.243606i | \(0.921670\pi\) | |||||||
\(182\) | 0.413621 | − | 0.557266i | 0.0306597 | − | 0.0413073i | ||||
\(183\) | −2.27078 | − | 2.27078i | −0.167861 | − | 0.167861i | ||||
\(184\) | −4.93294 | − | 4.93294i | −0.363661 | − | 0.363661i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 0.270521i | − | 0.0198356i | ||||||
\(187\) | − | 18.8308i | − | 1.37705i | ||||||
\(188\) | −13.4604 | −0.981700 | ||||||||
\(189\) | −0.626381 | + | 0.626381i | −0.0455625 | + | 0.0455625i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.0657 | 1.59662 | 0.798309 | − | 0.602249i | \(-0.205728\pi\) | ||||
0.798309 | + | 0.602249i | \(0.205728\pi\) | |||||||
\(192\) | 0.908713 | + | 0.908713i | 0.0655807 | + | 0.0655807i | ||||
\(193\) | 10.5065i | 0.756276i | 0.925749 | + | 0.378138i | \(0.123435\pi\) | ||||
−0.925749 | + | 0.378138i | \(0.876565\pi\) | |||||||
\(194\) | 0.661608 | 0.0475007 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.3047 | −0.878910 | ||||||||
\(197\) | 10.3630i | 0.738335i | 0.929363 | + | 0.369168i | \(0.120357\pi\) | ||||
−0.929363 | + | 0.369168i | \(0.879643\pi\) | |||||||
\(198\) | 3.85145 | + | 3.85145i | 0.273711 | + | 0.273711i | ||||
\(199\) | 19.2548 | 1.36493 | 0.682467 | − | 0.730916i | \(-0.260907\pi\) | ||||
0.682467 | + | 0.730916i | \(0.260907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.71358 | − | 2.71358i | 0.191401 | − | 0.191401i | ||||
\(202\) | 1.99680 | 0.140494 | ||||||||
\(203\) | 0.0606864i | 0.00425935i | ||||||||
\(204\) | − | 2.71237i | − | 0.189904i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.47708 | − | 2.47708i | −0.172586 | − | 0.172586i | ||||
\(207\) | 8.51121 | + | 8.51121i | 0.591570 | + | 0.591570i | ||||
\(208\) | 8.34446 | + | 6.19354i | 0.578584 | + | 0.429445i | ||||
\(209\) | − | 9.71358i | − | 0.671902i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.04519 | 0.622697 | 0.311348 | − | 0.950296i | \(-0.399219\pi\) | ||||
0.311348 | + | 0.950296i | \(0.399219\pi\) | |||||||
\(212\) | −14.1726 | − | 14.1726i | −0.973377 | − | 0.973377i | ||||
\(213\) | −0.733963 | −0.0502903 | ||||||||
\(214\) | −3.39412 | − | 3.39412i | −0.232017 | − | 0.232017i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.38496 | + | 2.38496i | 0.162276 | + | 0.162276i | ||||
\(217\) | 0.557266 | − | 0.557266i | 0.0378297 | − | 0.0378297i | ||||
\(218\) | −4.51344 | + | 4.51344i | −0.305688 | + | 0.305688i | ||||
\(219\) | 3.67835 | − | 3.67835i | 0.248560 | − | 0.248560i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.30692 | − | 15.5924i | −0.155180 | − | 1.04886i | ||||
\(222\) | −0.760094 | + | 0.760094i | −0.0510142 | + | 0.0510142i | ||||
\(223\) | 8.93448 | 0.598297 | 0.299148 | − | 0.954207i | \(-0.403297\pi\) | ||||
0.299148 | + | 0.954207i | \(0.403297\pi\) | |||||||
\(224\) | − | 2.02050i | − | 0.135000i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.988660 | − | 0.988660i | 0.0657647 | − | 0.0657647i | ||||
\(227\) | 22.4564i | 1.49048i | 0.666796 | + | 0.745240i | \(0.267665\pi\) | ||||
−0.666796 | + | 0.745240i | \(0.732335\pi\) | |||||||
\(228\) | − | 1.39913i | − | 0.0926598i | ||||||
\(229\) | 7.22432 | − | 7.22432i | 0.477396 | − | 0.477396i | −0.426902 | − | 0.904298i | \(-0.640395\pi\) |
0.904298 | + | 0.426902i | \(0.140395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.648699i | − | 0.0426813i | ||||||
\(232\) | 0.231065 | 0.0151701 | ||||||||
\(233\) | 13.1537 | − | 13.1537i | 0.861725 | − | 0.861725i | −0.129814 | − | 0.991538i | \(-0.541438\pi\) |
0.991538 | + | 0.129814i | \(0.0414379\pi\) | |||||||
\(234\) | 3.66092 | + | 2.71726i | 0.239322 | + | 0.177633i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.8705 | + | 10.8705i | −0.707610 | + | 0.707610i | ||||
\(237\) | 2.45031 | − | 2.45031i | 0.159165 | − | 0.159165i | ||||
\(238\) | −0.594992 | + | 0.594992i | −0.0385676 | + | 0.0385676i | ||||
\(239\) | 21.7527 | + | 21.7527i | 1.40706 | + | 1.40706i | 0.774545 | + | 0.632519i | \(0.217979\pi\) |
0.632519 | + | 0.774545i | \(0.282021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3999 | − | 18.3999i | −1.18524 | − | 1.18524i | −0.978368 | − | 0.206873i | \(-0.933671\pi\) |
−0.206873 | − | 0.978368i | \(-0.566329\pi\) | |||||||
\(242\) | −3.31446 | −0.213061 | ||||||||
\(243\) | −6.21367 | − | 6.21367i | −0.398607 | − | 0.398607i | ||||
\(244\) | −16.9103 | −1.08257 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.00678040i | 0.000432303i | ||||||||
\(247\) | −1.18998 | − | 8.04306i | −0.0757169 | − | 0.511768i | ||||
\(248\) | −2.12180 | − | 2.12180i | −0.134735 | − | 0.134735i | ||||
\(249\) | 3.82645 | + | 3.82645i | 0.242491 | + | 0.242491i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.08078i | 0.573174i | 0.958054 | + | 0.286587i | \(0.0925207\pi\) | ||||
−0.958054 | + | 0.286587i | \(0.907479\pi\) | |||||||
\(252\) | 2.28557i | 0.143978i | ||||||||
\(253\) | −17.9893 | −1.13098 | ||||||||
\(254\) | −5.58660 | + | 5.58660i | −0.350534 | + | 0.350534i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.72609 | 0.170381 | ||||||||
\(257\) | 11.8624 | + | 11.8624i | 0.739958 | + | 0.739958i | 0.972570 | − | 0.232612i | \(-0.0747272\pi\) |
−0.232612 | + | 0.972570i | \(0.574727\pi\) | |||||||
\(258\) | 0.469989i | 0.0292602i | ||||||||
\(259\) | −3.13154 | −0.194585 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.398675 | −0.0246774 | ||||||||
\(262\) | 5.23527i | 0.323436i | ||||||||
\(263\) | −13.4047 | − | 13.4047i | −0.826568 | − | 0.826568i | 0.160472 | − | 0.987040i | \(-0.448698\pi\) |
−0.987040 | + | 0.160472i | \(0.948698\pi\) | |||||||
\(264\) | −2.46994 | −0.152014 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.306917 | + | 0.306917i | −0.0188183 | + | 0.0188183i | ||||
\(267\) | −4.84729 | −0.296649 | ||||||||
\(268\) | − | 20.2077i | − | 1.23438i | ||||||
\(269\) | 13.8800i | 0.846278i | 0.906065 | + | 0.423139i | \(0.139072\pi\) | ||||
−0.906065 | + | 0.423139i | \(0.860928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.00270 | − | 6.00270i | −0.364638 | − | 0.364638i | 0.500879 | − | 0.865517i | \(-0.333010\pi\) |
−0.865517 | + | 0.500879i | \(0.833010\pi\) | |||||||
\(272\) | −8.90937 | − | 8.90937i | −0.540210 | − | 0.540210i | ||||
\(273\) | −0.0794704 | − | 0.537138i | −0.00480977 | − | 0.0325090i | ||||
\(274\) | − | 1.48229i | − | 0.0895484i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.59115 | −0.155969 | ||||||||
\(277\) | 7.05072 | + | 7.05072i | 0.423637 | + | 0.423637i | 0.886454 | − | 0.462817i | \(-0.153161\pi\) |
−0.462817 | + | 0.886454i | \(0.653161\pi\) | |||||||
\(278\) | 6.71789 | 0.402912 | ||||||||
\(279\) | 3.66092 | + | 3.66092i | 0.219174 | + | 0.219174i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2285 | − | 10.2285i | −0.610182 | − | 0.610182i | 0.332811 | − | 0.942993i | \(-0.392003\pi\) |
−0.942993 | + | 0.332811i | \(0.892003\pi\) | |||||||
\(282\) | 0.793004 | − | 0.793004i | 0.0472227 | − | 0.0472227i | ||||
\(283\) | −1.69674 | + | 1.69674i | −0.100861 | + | 0.100861i | −0.755737 | − | 0.654876i | \(-0.772721\pi\) |
0.654876 | + | 0.755737i | \(0.272721\pi\) | |||||||
\(284\) | −2.73287 | + | 2.73287i | −0.162166 | + | 0.162166i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.74046 | + | 0.997262i | −0.398572 | + | 0.0589694i | ||||
\(287\) | −0.0139674 | + | 0.0139674i | −0.000824472 | + | 0.000824472i | ||||
\(288\) | 13.2735 | 0.782150 | ||||||||
\(289\) | 2.11105i | 0.124179i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.366030 | − | 0.366030i | 0.0214571 | − | 0.0214571i | ||||
\(292\) | − | 27.3923i | − | 1.60301i | ||||||
\(293\) | 0.654334i | 0.0382266i | 0.999817 | + | 0.0191133i | \(0.00608433\pi\) | ||||
−0.999817 | + | 0.0191133i | \(0.993916\pi\) | |||||||
\(294\) | 0.724920 | − | 0.724920i | 0.0422782 | − | 0.0422782i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.9234i | 0.693035i | ||||||||
\(297\) | 8.69739 | 0.504674 | ||||||||
\(298\) | 2.94890 | − | 2.94890i | 0.170825 | − | 0.170825i | ||||
\(299\) | −14.8955 | + | 2.20382i | −0.861431 | + | 0.127450i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.968164 | + | 0.968164i | −0.0558040 | + | 0.0558040i | ||||
\(302\) | −2.58200 | + | 2.58200i | −0.148577 | + | 0.148577i | ||||
\(303\) | 1.10472 | − | 1.10472i | 0.0634643 | − | 0.0634643i | ||||
\(304\) | −4.59575 | − | 4.59575i | −0.263584 | − | 0.263584i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.90876 | − | 3.90876i | −0.223449 | − | 0.223449i | ||||
\(307\) | −5.69696 | −0.325143 | −0.162571 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162571 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(308\) | −2.41539 | − | 2.41539i | −0.137630 | − | 0.137630i | ||||
\(309\) | −2.74086 | −0.155922 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.12203i | − | 0.517263i | −0.965976 | − | 0.258631i | \(-0.916729\pi\) | ||
0.965976 | − | 0.258631i | \(-0.0832715\pi\) | |||||||
\(312\) | −2.04516 | + | 0.302585i | −0.115785 | + | 0.0171305i | ||||
\(313\) | −16.2726 | − | 16.2726i | −0.919784 | − | 0.919784i | 0.0772297 | − | 0.997013i | \(-0.475393\pi\) |
−0.997013 | + | 0.0772297i | \(0.975393\pi\) | |||||||
\(314\) | −3.62605 | − | 3.62605i | −0.204630 | − | 0.204630i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 18.2472i | − | 1.02648i | ||||||
\(317\) | − | 23.5257i | − | 1.32133i | −0.750680 | − | 0.660666i | \(-0.770274\pi\) | ||
0.750680 | − | 0.660666i | \(-0.229726\pi\) | |||||||
\(318\) | 1.66992 | 0.0936447 | ||||||||
\(319\) | 0.421320 | − | 0.421320i | 0.0235894 | − | 0.0235894i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.75555 | −0.209614 | ||||||||
\(322\) | 0.568402 | + | 0.568402i | 0.0316758 | + | 0.0316758i | ||||
\(323\) | 9.85812i | 0.548520i | ||||||||
\(324\) | −14.3760 | −0.798666 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.05197 | −0.501342 | ||||||||
\(327\) | 4.99406i | 0.276172i | ||||||||
\(328\) | 0.0531813 | + | 0.0531813i | 0.00293645 | + | 0.00293645i | ||||
\(329\) | 3.26713 | 0.180123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6859 | + | 11.6859i | −0.642317 | + | 0.642317i | −0.951125 | − | 0.308807i | \(-0.900070\pi\) |
0.308807 | + | 0.951125i | \(0.400070\pi\) | |||||||
\(332\) | 28.4951 | 1.56387 | ||||||||
\(333\) | − | 20.5725i | − | 1.12736i | ||||||
\(334\) | − | 2.64506i | − | 0.144731i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.306917 | − | 0.306917i | −0.0167437 | − | 0.0167437i | ||||
\(337\) | 10.1125 | + | 10.1125i | 0.550863 | + | 0.550863i | 0.926690 | − | 0.375827i | \(-0.122641\pi\) |
−0.375827 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(338\) | −5.45908 | + | 1.65151i | −0.296935 | + | 0.0898303i | ||||
\(339\) | − | 1.09394i | − | 0.0594147i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.73772 | −0.419021 | ||||||||
\(342\) | −2.01627 | − | 2.01627i | −0.109027 | − | 0.109027i | ||||
\(343\) | 6.05770 | 0.327085 | ||||||||
\(344\) | 3.68630 | + | 3.68630i | 0.198752 | + | 0.198752i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.21568 | + | 6.21568i | 0.334157 | + | 0.334157i | ||||
\(347\) | 6.58258 | − | 6.58258i | 0.353371 | − | 0.353371i | −0.507991 | − | 0.861362i | \(-0.669612\pi\) |
0.861362 | + | 0.507991i | \(0.169612\pi\) | |||||||
\(348\) | 0.0606864 | − | 0.0606864i | 0.00325313 | − | 0.00325313i | ||||
\(349\) | −17.5571 | + | 17.5571i | −0.939812 | + | 0.939812i | −0.998289 | − | 0.0584769i | \(-0.981376\pi\) |
0.0584769 | + | 0.998289i | \(0.481376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.20164 | − | 1.06549i | 0.384395 | − | 0.0568719i | ||||
\(352\) | −14.0275 | + | 14.0275i | −0.747666 | + | 0.747666i | ||||
\(353\) | −25.0043 | −1.33084 | −0.665421 | − | 0.746468i | \(-0.731748\pi\) | ||||
−0.665421 | + | 0.746468i | \(0.731748\pi\) | |||||||
\(354\) | − | 1.28085i | − | 0.0680763i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.0486 | + | 18.0486i | −0.956573 | + | 0.956573i | ||||
\(357\) | 0.658352i | 0.0348437i | ||||||||
\(358\) | − | 7.06134i | − | 0.373203i | ||||||
\(359\) | −1.66770 | + | 1.66770i | −0.0880179 | + | 0.0880179i | −0.749745 | − | 0.661727i | \(-0.769824\pi\) |
0.661727 | + | 0.749745i | \(0.269824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.9149i | − | 0.732361i | ||||||
\(362\) | −2.87573 | −0.151145 | ||||||||
\(363\) | −1.83370 | + | 1.83370i | −0.0962445 | + | 0.0962445i | ||||
\(364\) | −2.29590 | − | 1.70410i | −0.120338 | − | 0.0893189i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.996249 | − | 0.996249i | 0.0520748 | − | 0.0520748i | ||||
\(367\) | −8.72948 | + | 8.72948i | −0.455675 | + | 0.455675i | −0.897233 | − | 0.441558i | \(-0.854426\pi\) |
0.441558 | + | 0.897233i | \(0.354426\pi\) | |||||||
\(368\) | −8.51121 | + | 8.51121i | −0.443677 | + | 0.443677i | ||||
\(369\) | −0.0917581 | − | 0.0917581i | −0.00477674 | − | 0.00477674i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.43999 | + | 3.43999i | 0.178596 | + | 0.178596i | ||||
\(372\) | −1.11453 | −0.0577858 | ||||||||
\(373\) | 9.69421 | + | 9.69421i | 0.501947 | + | 0.501947i | 0.912043 | − | 0.410096i | \(-0.134505\pi\) |
−0.410096 | + | 0.912043i | \(0.634505\pi\) | |||||||
\(374\) | 8.26156 | 0.427195 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 12.4397i | − | 0.641527i | ||||||
\(377\) | 0.297247 | − | 0.400477i | 0.0153090 | − | 0.0206256i | ||||
\(378\) | −0.274809 | − | 0.274809i | −0.0141346 | − | 0.0141346i | ||||
\(379\) | 16.8307 | + | 16.8307i | 0.864536 | + | 0.864536i | 0.991861 | − | 0.127325i | \(-0.0406391\pi\) |
−0.127325 | + | 0.991861i | \(0.540639\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.18150i | 0.316688i | ||||||||
\(382\) | 9.68076i | 0.495311i | ||||||||
\(383\) | 23.8645 | 1.21942 | 0.609709 | − | 0.792625i | \(-0.291286\pi\) | ||||
0.609709 | + | 0.792625i | \(0.291286\pi\) | |||||||
\(384\) | −2.63433 | + | 2.63433i | −0.134433 | + | 0.134433i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.60947 | −0.234616 | ||||||||
\(387\) | −6.36029 | − | 6.36029i | −0.323311 | − | 0.323311i | ||||
\(388\) | − | 2.72579i | − | 0.138381i | ||||||
\(389\) | 12.7910 | 0.648528 | 0.324264 | − | 0.945967i | \(-0.394883\pi\) | ||||
0.324264 | + | 0.945967i | \(0.394883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2570 | 0.923294 | ||||||||
\(392\) | − | 11.3716i | − | 0.574355i | ||||||
\(393\) | 2.89638 | + | 2.89638i | 0.146103 | + | 0.146103i | ||||
\(394\) | −4.54652 | −0.229050 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.8678 | − | 15.8678i | 0.797385 | − | 0.797385i | ||||
\(397\) | −15.7318 | −0.789558 | −0.394779 | − | 0.918776i | \(-0.629179\pi\) | ||||
−0.394779 | + | 0.918776i | \(0.629179\pi\) | |||||||
\(398\) | 8.44755i | 0.423437i | ||||||||
\(399\) | 0.339600i | 0.0170013i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.12698 | − | 4.12698i | −0.206092 | − | 0.206092i | 0.596512 | − | 0.802604i | \(-0.296553\pi\) |
−0.802604 | + | 0.596512i | \(0.796553\pi\) | |||||||
\(402\) | 1.19051 | + | 1.19051i | 0.0593775 | + | 0.0593775i | ||||
\(403\) | −6.40700 | + | 0.947927i | −0.319156 | + | 0.0472196i | ||||
\(404\) | − | 8.22669i | − | 0.409293i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0266246 | −0.00132136 | ||||||||
\(407\) | 21.7410 | + | 21.7410i | 1.07766 | + | 1.07766i | ||||
\(408\) | 2.50669 | 0.124100 | ||||||||
\(409\) | 3.54342 | + | 3.54342i | 0.175211 | + | 0.175211i | 0.789264 | − | 0.614054i | \(-0.210462\pi\) |
−0.614054 | + | 0.789264i | \(0.710462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.820068 | − | 0.820068i | −0.0404510 | − | 0.0404510i | ||||
\(412\) | −10.2054 | + | 10.2054i | −0.502785 | + | 0.502785i | ||||
\(413\) | 2.63851 | − | 2.63851i | 0.129833 | − | 0.129833i | ||||
\(414\) | −3.73408 | + | 3.73408i | −0.183520 | + | 0.183520i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.89658 | + | 13.3335i | −0.485220 | + | 0.653729i | ||||
\(417\) | 3.71663 | − | 3.71663i | 0.182004 | − | 0.182004i | ||||
\(418\) | 4.26159 | 0.208441 | ||||||||
\(419\) | − | 29.6710i | − | 1.44952i | −0.689001 | − | 0.724761i | \(-0.741950\pi\) | ||
0.689001 | − | 0.724761i | \(-0.258050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.57981 | − | 7.57981i | 0.369418 | − | 0.369418i | −0.497847 | − | 0.867265i | \(-0.665876\pi\) |
0.867265 | + | 0.497847i | \(0.165876\pi\) | |||||||
\(422\) | 3.96835i | 0.193176i | ||||||||
\(423\) | 21.4632i | 1.04358i | ||||||||
\(424\) | 13.0979 | − | 13.0979i | 0.636088 | − | 0.636088i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 0.322008i | − | 0.0156013i | ||||||
\(427\) | 4.10449 | 0.198630 | ||||||||
\(428\) | −13.9836 | + | 13.9836i | −0.675921 | + | 0.675921i | ||||
\(429\) | −3.17739 | + | 4.28085i | −0.153406 | + | 0.206681i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4803 | − | 28.4803i | 1.37185 | − | 1.37185i | 0.514144 | − | 0.857704i | \(-0.328110\pi\) |
0.857704 | − | 0.514144i | \(-0.171890\pi\) | |||||||
\(432\) | 4.11497 | − | 4.11497i | 0.197981 | − | 0.197981i | ||||
\(433\) | 6.79819 | − | 6.79819i | 0.326700 | − | 0.326700i | −0.524630 | − | 0.851330i | \(-0.675796\pi\) |
0.851330 | + | 0.524630i | \(0.175796\pi\) | |||||||
\(434\) | 0.244486 | + | 0.244486i | 0.0117357 | + | 0.0117357i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.5951 | + | 18.5951i | 0.890544 | + | 0.890544i | ||||
\(437\) | 9.41755 | 0.450502 | ||||||||
\(438\) | 1.61378 | + | 1.61378i | 0.0771096 | + | 0.0771096i | ||||
\(439\) | 5.31643 | 0.253740 | 0.126870 | − | 0.991919i | \(-0.459507\pi\) | ||||
0.126870 | + | 0.991919i | \(0.459507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.6204i | 0.934307i | ||||||||
\(442\) | 6.84075 | − | 1.01210i | 0.325381 | − | 0.0481408i | ||||
\(443\) | 2.05415 | + | 2.05415i | 0.0975958 | + | 0.0975958i | 0.754219 | − | 0.656623i | \(-0.228016\pi\) |
−0.656623 | + | 0.754219i | \(0.728016\pi\) | |||||||
\(444\) | 3.13154 | + | 3.13154i | 0.148617 | + | 0.148617i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.91978i | 0.185607i | ||||||||
\(447\) | − | 3.26292i | − | 0.154331i | ||||||
\(448\) | −1.64252 | −0.0776017 | ||||||||
\(449\) | 22.4041 | − | 22.4041i | 1.05731 | − | 1.05731i | 0.0590595 | − | 0.998254i | \(-0.481190\pi\) |
0.998254 | − | 0.0590595i | \(-0.0188102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.193940 | 0.00913228 | ||||||||
\(452\) | −4.07322 | − | 4.07322i | −0.191588 | − | 0.191588i | ||||
\(453\) | 2.85695i | 0.134231i | ||||||||
\(454\) | −9.85216 | −0.462385 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.29303 | 0.0605518 | ||||||||
\(457\) | − | 8.38353i | − | 0.392165i | −0.980587 | − | 0.196083i | \(-0.937178\pi\) | ||
0.980587 | − | 0.196083i | \(-0.0628220\pi\) | |||||||
\(458\) | 3.16949 | + | 3.16949i | 0.148100 | + | 0.148100i | ||||
\(459\) | −8.82681 | −0.412000 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6582 | + | 16.6582i | −0.775851 | + | 0.775851i | −0.979122 | − | 0.203272i | \(-0.934842\pi\) |
0.203272 | + | 0.979122i | \(0.434842\pi\) | |||||||
\(462\) | 0.284600 | 0.0132408 | ||||||||
\(463\) | 20.8398i | 0.968506i | 0.874928 | + | 0.484253i | \(0.160909\pi\) | ||||
−0.874928 | + | 0.484253i | \(0.839091\pi\) | |||||||
\(464\) | − | 0.398675i | − | 0.0185080i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.77083 | + | 5.77083i | 0.267329 | + | 0.267329i | ||||
\(467\) | −26.1022 | − | 26.1022i | −1.20786 | − | 1.20786i | −0.971718 | − | 0.236146i | \(-0.924116\pi\) |
−0.236146 | − | 0.971718i | \(-0.575884\pi\) | |||||||
\(468\) | 11.1949 | − | 15.0828i | 0.517487 | − | 0.697202i | ||||
\(469\) | 4.90485i | 0.226485i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.01219 | −0.184872 | ||||||||
\(472\) | −10.0462 | − | 10.0462i | −0.462413 | − | 0.462413i | ||||
\(473\) | 13.4431 | 0.618114 | ||||||||
\(474\) | 1.07501 | + | 1.07501i | 0.0493770 | + | 0.0493770i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.45133 | + | 2.45133i | 0.112357 | + | 0.112357i | ||||
\(477\) | −22.5988 | + | 22.5988i | −1.03473 | + | 1.03473i | ||||
\(478\) | −9.54344 | + | 9.54344i | −0.436507 | + | 0.436507i | ||||
\(479\) | 19.7704 | − | 19.7704i | 0.903334 | − | 0.903334i | −0.0923887 | − | 0.995723i | \(-0.529450\pi\) |
0.995723 | + | 0.0923887i | \(0.0294502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.6654 | + | 15.3386i | 0.942263 | + | 0.699379i | ||||
\(482\) | 8.07248 | − | 8.07248i | 0.367692 | − | 0.367692i | ||||
\(483\) | 0.628930 | 0.0286173 | ||||||||
\(484\) | 13.6554i | 0.620699i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.72609 | − | 2.72609i | 0.123658 | − | 0.123658i | ||||
\(487\) | 15.6213i | 0.707867i | 0.935271 | + | 0.353934i | \(0.115156\pi\) | ||||
−0.935271 | + | 0.353934i | \(0.884844\pi\) | |||||||
\(488\) | − | 15.6279i | − | 0.707443i | ||||||
\(489\) | −5.00795 | + | 5.00795i | −0.226467 | + | 0.226467i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6196i | 0.569516i | 0.958599 | + | 0.284758i | \(0.0919133\pi\) | ||||
−0.958599 | + | 0.284758i | \(0.908087\pi\) | |||||||
\(492\) | 0.0279349 | 0.00125940 | ||||||||
\(493\) | −0.427589 | + | 0.427589i | −0.0192576 | + | 0.0192576i | ||||
\(494\) | 3.52869 | − | 0.522076i | 0.158763 | − | 0.0234893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.66092 | + | 3.66092i | −0.164380 | + | 0.164380i | ||||
\(497\) | 0.663327 | − | 0.663327i | 0.0297543 | − | 0.0297543i | ||||
\(498\) | −1.67876 | + | 1.67876i | −0.0752269 | + | 0.0752269i | ||||
\(499\) | −22.5427 | − | 22.5427i | −1.00915 | − | 1.00915i | −0.999958 | − | 0.00919352i | \(-0.997074\pi\) |
−0.00919352 | − | 0.999958i | \(-0.502926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.46336 | − | 1.46336i | −0.0653782 | − | 0.0653782i | ||||
\(502\) | −3.98396 | −0.177813 | ||||||||
\(503\) | 5.50096 | + | 5.50096i | 0.245275 | + | 0.245275i | 0.819028 | − | 0.573753i | \(-0.194513\pi\) |
−0.573753 | + | 0.819028i | \(0.694513\pi\) | |||||||
\(504\) | −2.11225 | −0.0940873 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 7.89234i | − | 0.350857i | ||||||
\(507\) | −2.10651 | + | 3.93389i | −0.0935535 | + | 0.174710i | ||||
\(508\) | 23.0165 | + | 23.0165i | 1.02119 | + | 1.02119i | ||||
\(509\) | −18.5018 | − | 18.5018i | −0.820077 | − | 0.820077i | 0.166042 | − | 0.986119i | \(-0.446901\pi\) |
−0.986119 | + | 0.166042i | \(0.946901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.64870i | 0.294121i | ||||||||
\(512\) | 22.9026i | 1.01216i | ||||||||
\(513\) | −4.55316 | −0.201027 | ||||||||
\(514\) | −5.20434 | + | 5.20434i | −0.229554 | + | 0.229554i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.93633 | 0.0852420 | ||||||||
\(517\) | −22.6823 | − | 22.6823i | −0.997567 | − | 0.997567i | ||||
\(518\) | − | 1.37389i | − | 0.0603651i | ||||||
\(519\) | 6.87757 | 0.301892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.5848 | 0.638971 | 0.319485 | − | 0.947591i | \(-0.396490\pi\) | ||||
0.319485 | + | 0.947591i | \(0.396490\pi\) | |||||||
\(522\) | − | 0.174909i | − | 0.00765554i | ||||||
\(523\) | 9.37818 | + | 9.37818i | 0.410079 | + | 0.410079i | 0.881766 | − | 0.471687i | \(-0.156355\pi\) |
−0.471687 | + | 0.881766i | \(0.656355\pi\) | |||||||
\(524\) | 21.5690 | 0.942247 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.88096 | − | 5.88096i | 0.256422 | − | 0.256422i | ||||
\(527\) | 7.85286 | 0.342076 | ||||||||
\(528\) | 4.26159i | 0.185462i | ||||||||
\(529\) | 5.55896i | 0.241694i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.3335 | + | 17.3335i | 0.752210 | + | 0.752210i | ||||
\(532\) | 1.26448 | + | 1.26448i | 0.0548222 | + | 0.0548222i | ||||
\(533\) | 0.160587 | − | 0.0237591i | 0.00695578 | − | 0.00102912i | ||||
\(534\) | − | 2.12662i | − | 0.0920280i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.6753 | 0.806651 | ||||||||
\(537\) | −3.90664 | − | 3.90664i | −0.168584 | − | 0.168584i | ||||
\(538\) | −6.08949 | −0.262537 | ||||||||
\(539\) | −20.7349 | − | 20.7349i | −0.893115 | − | 0.893115i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.153054 | + | 0.153054i | 0.00658032 | + | 0.00658032i | 0.710389 | − | 0.703809i | \(-0.248519\pi\) |
−0.703809 | + | 0.710389i | \(0.748519\pi\) | |||||||
\(542\) | 2.63353 | − | 2.63353i | 0.113120 | − | 0.113120i | ||||
\(543\) | −1.59098 | + | 1.59098i | −0.0682756 | + | 0.0682756i | ||||
\(544\) | 14.2362 | − | 14.2362i | 0.610371 | − | 0.610371i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.235655 | − | 0.0348656i | 0.0100851 | − | 0.00149211i | ||||
\(547\) | 20.1505 | − | 20.1505i | 0.861574 | − | 0.861574i | −0.129947 | − | 0.991521i | \(-0.541481\pi\) |
0.991521 | + | 0.129947i | \(0.0414808\pi\) | |||||||
\(548\) | −6.10695 | −0.260876 | ||||||||
\(549\) | 26.9642i | 1.15080i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.220565 | + | 0.220565i | −0.00939637 | + | 0.00939637i | ||||
\(552\) | − | 2.39466i | − | 0.101924i | ||||||
\(553\) | 4.42899i | 0.188340i | ||||||||
\(554\) | −3.09333 | + | 3.09333i | −0.131423 | + | 0.131423i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 27.6773i | − | 1.17378i | ||||||
\(557\) | 14.6986 | 0.622799 | 0.311400 | − | 0.950279i | \(-0.399202\pi\) | ||||
0.311400 | + | 0.950279i | \(0.399202\pi\) | |||||||
\(558\) | −1.60614 | + | 1.60614i | −0.0679932 | + | 0.0679932i | ||||
\(559\) | 11.1312 | − | 1.64688i | 0.470799 | − | 0.0696555i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.57066 | − | 4.57066i | 0.192973 | − | 0.192973i | ||||
\(562\) | 4.48750 | − | 4.48750i | 0.189294 | − | 0.189294i | ||||
\(563\) | 2.85777 | − | 2.85777i | 0.120441 | − | 0.120441i | −0.644317 | − | 0.764758i | \(-0.722858\pi\) |
0.764758 | + | 0.644317i | \(0.222858\pi\) | |||||||
\(564\) | −3.26713 | − | 3.26713i | −0.137571 | − | 0.137571i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.744403 | − | 0.744403i | −0.0312896 | − | 0.0312896i | ||||
\(567\) | 3.48937 | 0.146540 | ||||||||
\(568\) | −2.52563 | − | 2.52563i | −0.105973 | − | 0.105973i | ||||
\(569\) | 4.12855 | 0.173078 | 0.0865390 | − | 0.996248i | \(-0.472419\pi\) | ||||
0.0865390 | + | 0.996248i | \(0.472419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.4821i | 1.27564i | 0.770187 | + | 0.637819i | \(0.220163\pi\) | ||||
−0.770187 | + | 0.637819i | \(0.779837\pi\) | |||||||
\(572\) | 4.10866 | + | 27.7703i | 0.171792 | + | 1.16113i | ||||
\(573\) | 5.35582 | + | 5.35582i | 0.223743 | + | 0.223743i | ||||
\(574\) | −0.00612786 | − | 0.00612786i | −0.000255772 | − | 0.000255772i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 10.7904i | − | 0.449601i | ||||||
\(577\) | 10.4982i | 0.437046i | 0.975832 | + | 0.218523i | \(0.0701239\pi\) | ||||
−0.975832 | + | 0.218523i | \(0.929876\pi\) | |||||||
\(578\) | −0.926169 | −0.0385235 | ||||||||
\(579\) | −2.55016 | + | 2.55016i | −0.105981 | + | 0.105981i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.91639 | −0.286940 | ||||||||
\(582\) | 0.160587 | + | 0.160587i | 0.00665653 | + | 0.00665653i | ||||
\(583\) | − | 47.7648i | − | 1.97822i | ||||||
\(584\) | 25.3151 | 1.04754 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.287073 | −0.0118589 | ||||||||
\(587\) | − | 30.4911i | − | 1.25850i | −0.777202 | − | 0.629251i | \(-0.783362\pi\) | ||
0.777202 | − | 0.629251i | \(-0.216638\pi\) | |||||||
\(588\) | −2.98663 | − | 2.98663i | −0.123166 | − | 0.123166i | ||||
\(589\) | 4.05076 | 0.166909 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.51533 | + | 2.51533i | −0.103467 | + | 0.103467i | ||||
\(592\) | 20.5725 | 0.845523 | ||||||||
\(593\) | 34.5161i | 1.41741i | 0.705506 | + | 0.708704i | \(0.250720\pi\) | ||||
−0.705506 | + | 0.708704i | \(0.749280\pi\) | |||||||
\(594\) | 3.81576i | 0.156563i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.1493 | − | 12.1493i | −0.497655 | − | 0.497655i | ||||
\(597\) | 4.67355 | + | 4.67355i | 0.191276 | + | 0.191276i | ||||
\(598\) | −0.966870 | − | 6.53504i | −0.0395382 | − | 0.267237i | ||||
\(599\) | 27.5663i | 1.12633i | 0.826345 | + | 0.563164i | \(0.190416\pi\) | ||||
−0.826345 | + | 0.563164i | \(0.809584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.0403 | −1.26616 | −0.633081 | − | 0.774086i | \(-0.718210\pi\) | ||||
−0.633081 | + | 0.774086i | \(0.718210\pi\) | |||||||
\(602\) | −0.424757 | − | 0.424757i | −0.0173118 | − | 0.0173118i | ||||
\(603\) | −32.2221 | −1.31219 | ||||||||
\(604\) | 10.6377 | + | 10.6377i | 0.432841 | + | 0.432841i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.484666 | + | 0.484666i | 0.0196882 | + | 0.0196882i | ||||
\(607\) | −12.6624 | + | 12.6624i | −0.513952 | + | 0.513952i | −0.915735 | − | 0.401783i | \(-0.868391\pi\) |
0.401783 | + | 0.915735i | \(0.368391\pi\) | |||||||
\(608\) | 7.34349 | − | 7.34349i | 0.297818 | − | 0.297818i | ||||
\(609\) | −0.0147299 | + | 0.0147299i | −0.000596886 | + | 0.000596886i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.5602 | − | 16.0027i | −0.872232 | − | 0.647400i | ||||
\(612\) | −16.1039 | + | 16.1039i | −0.650961 | + | 0.650961i | ||||
\(613\) | −9.95690 | −0.402155 | −0.201078 | − | 0.979575i | \(-0.564444\pi\) | ||||
−0.201078 | + | 0.979575i | \(0.564444\pi\) | |||||||
\(614\) | − | 2.49940i | − | 0.100867i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.23223 | − | 2.23223i | 0.0899391 | − | 0.0899391i | ||||
\(617\) | 23.8211i | 0.959001i | 0.877542 | + | 0.479501i | \(0.159182\pi\) | ||||
−0.877542 | + | 0.479501i | \(0.840818\pi\) | |||||||
\(618\) | − | 1.20248i | − | 0.0483709i | ||||||
\(619\) | −20.8503 | + | 20.8503i | −0.838046 | + | 0.838046i | −0.988602 | − | 0.150556i | \(-0.951894\pi\) |
0.150556 | + | 0.988602i | \(0.451894\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.43233i | 0.338378i | ||||||||
\(622\) | 4.00206 | 0.160468 | ||||||||
\(623\) | 4.38078 | − | 4.38078i | 0.175512 | − | 0.175512i | ||||
\(624\) | 0.522076 | + | 3.52869i | 0.0208998 | + | 0.141261i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.13921 | − | 7.13921i | 0.285340 | − | 0.285340i | ||||
\(627\) | 2.35770 | − | 2.35770i | 0.0941574 | − | 0.0941574i | ||||
\(628\) | −14.9391 | + | 14.9391i | −0.596137 | + | 0.596137i | ||||
\(629\) | −22.0645 | − | 22.0645i | −0.879768 | − | 0.879768i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.0474 | − | 15.0474i | −0.599027 | − | 0.599027i | 0.341027 | − | 0.940054i | \(-0.389225\pi\) |
−0.940054 | + | 0.341027i | \(0.889225\pi\) | |||||||
\(632\) | 16.8635 | 0.670793 | ||||||||
\(633\) | 2.19547 | + | 2.19547i | 0.0872619 | + | 0.0872619i | ||||
\(634\) | 10.3213 | 0.409911 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 6.87999i | − | 0.272809i | ||||||
\(637\) | −19.7091 | − | 14.6288i | −0.780904 | − | 0.579613i | ||||
\(638\) | 0.184843 | + | 0.184843i | 0.00731802 | + | 0.00731802i | ||||
\(639\) | 4.35768 | + | 4.35768i | 0.172387 | + | 0.172387i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.0567i | − | 0.871188i | −0.900143 | − | 0.435594i | \(-0.856538\pi\) | ||
0.900143 | − | 0.435594i | \(-0.143462\pi\) | |||||||
\(642\) | − | 1.64765i | − | 0.0650276i | ||||||
\(643\) | 5.50564 | 0.217121 | 0.108561 | − | 0.994090i | \(-0.465376\pi\) | ||||
0.108561 | + | 0.994090i | \(0.465376\pi\) | |||||||
\(644\) | 2.34178 | − | 2.34178i | 0.0922792 | − | 0.0922792i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.32500 | −0.170165 | ||||||||
\(647\) | 7.18604 | + | 7.18604i | 0.282512 | + | 0.282512i | 0.834110 | − | 0.551598i | \(-0.185982\pi\) |
−0.551598 | + | 0.834110i | \(0.685982\pi\) | |||||||
\(648\) | − | 13.2858i | − | 0.521917i | ||||||
\(649\) | −36.6361 | −1.43809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.270521 | 0.0106026 | ||||||||
\(652\) | 37.2936i | 1.46053i | ||||||||
\(653\) | 3.66293 | + | 3.66293i | 0.143342 | + | 0.143342i | 0.775136 | − | 0.631794i | \(-0.217681\pi\) |
−0.631794 | + | 0.775136i | \(0.717681\pi\) | |||||||
\(654\) | −2.19102 | −0.0856756 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.0917581 | − | 0.0917581i | 0.00358255 | − | 0.00358255i | ||||
\(657\) | −43.6782 | −1.70405 | ||||||||
\(658\) | 1.43337i | 0.0558786i | ||||||||
\(659\) | 5.69188i | 0.221724i | 0.993836 | + | 0.110862i | \(0.0353612\pi\) | ||||
−0.993836 | + | 0.110862i | \(0.964639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8493 | + | 24.8493i | 0.966527 | + | 0.966527i | 0.999458 | − | 0.0329310i | \(-0.0104842\pi\) |
−0.0329310 | + | 0.999458i | \(0.510484\pi\) | |||||||
\(662\) | −5.12691 | − | 5.12691i | −0.199263 | − | 0.199263i | ||||
\(663\) | 3.22467 | − | 4.34455i | 0.125236 | − | 0.168728i | ||||
\(664\) | 26.3343i | 1.02197i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.02565 | 0.349737 | ||||||||
\(667\) | 0.408480 | + | 0.408480i | 0.0158164 | + | 0.0158164i | ||||
\(668\) | −10.8975 | −0.421636 | ||||||||
\(669\) | 2.16859 | + | 2.16859i | 0.0838426 | + | 0.0838426i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.4957 | − | 28.4957i | −1.10006 | − | 1.10006i | ||||
\(672\) | 0.490419 | − | 0.490419i | 0.0189183 | − | 0.0189183i | ||||
\(673\) | 21.9648 | − | 21.9648i | 0.846679 | − | 0.846679i | −0.143038 | − | 0.989717i | \(-0.545687\pi\) |
0.989717 | + | 0.143038i | \(0.0456872\pi\) | |||||||
\(674\) | −4.43660 | + | 4.43660i | −0.170892 | + | 0.170892i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.80413 | + | 22.4911i | 0.261697 | + | 0.865042i | ||||
\(677\) | 33.7205 | − | 33.7205i | 1.29598 | − | 1.29598i | 0.364959 | − | 0.931024i | \(-0.381083\pi\) |
0.931024 | − | 0.364959i | \(-0.118917\pi\) | |||||||
\(678\) | 0.479939 | 0.0184319 | ||||||||
\(679\) | 0.661608i | 0.0253902i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.45065 | + | 5.45065i | −0.208869 | + | 0.208869i | ||||
\(682\) | − | 3.39473i | − | 0.129991i | ||||||
\(683\) | − | 19.8074i | − | 0.757909i | −0.925415 | − | 0.378955i | \(-0.876284\pi\) | ||
0.925415 | − | 0.378955i | \(-0.123716\pi\) | |||||||
\(684\) | −8.30692 | + | 8.30692i | −0.317623 | + | 0.317623i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.65766i | 0.101470i | ||||||||
\(687\) | 3.50700 | 0.133800 | ||||||||
\(688\) | 6.36029 | − | 6.36029i | 0.242484 | − | 0.242484i | ||||
\(689\) | −5.85154 | − | 39.5504i | −0.222926 | − | 1.50675i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.2449 | + | 31.2449i | −1.18861 | + | 1.18861i | −0.211162 | + | 0.977451i | \(0.567725\pi\) |
−0.977451 | + | 0.211162i | \(0.932275\pi\) | |||||||
\(692\) | 25.6082 | − | 25.6082i | 0.973479 | − | 0.973479i | ||||
\(693\) | −3.85145 | + | 3.85145i | −0.146305 | + | 0.146305i | ||||
\(694\) | 2.88794 | + | 2.88794i | 0.109625 | + | 0.109625i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0560844 | + | 0.0560844i | 0.00212587 | + | 0.00212587i | ||||
\(697\) | −0.196826 | −0.00745531 | ||||||||
\(698\) | −7.70275 | − | 7.70275i | −0.291553 | − | 0.291553i | ||||
\(699\) | 6.38536 | 0.241516 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.2135i | − | 1.29223i | −0.763241 | − | 0.646114i | \(-0.776393\pi\) | ||
0.763241 | − | 0.646114i | \(-0.223607\pi\) | |||||||
\(702\) | 0.467459 | + | 3.15954i | 0.0176431 | + | 0.119249i | ||||
\(703\) | −11.3816 | − | 11.3816i | −0.429265 | − | 0.429265i | ||||
\(704\) | 11.4033 | + | 11.4033i | 0.429778 | + | 0.429778i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 10.9700i | − | 0.412861i | ||||||
\(707\) | 1.99680i | 0.0750973i | ||||||||
\(708\) | −5.27702 | −0.198322 | ||||||||
\(709\) | 4.07045 | − | 4.07045i | 0.152869 | − | 0.152869i | −0.626529 | − | 0.779398i | \(-0.715525\pi\) |
0.779398 | + | 0.626529i | \(0.215525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.0960 | −1.09118 | ||||||||
\(712\) | −16.6799 | − | 16.6799i | −0.625107 | − | 0.625107i | ||||
\(713\) | − | 7.50191i | − | 0.280949i | ||||||
\(714\) | −0.288835 | −0.0108094 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −29.0923 | −1.08723 | ||||||||
\(717\) | 10.5597i | 0.394359i | ||||||||
\(718\) | −0.731661 | − | 0.731661i | −0.0273054 | − | 0.0273054i | ||||
\(719\) | −40.4409 | −1.50819 | −0.754095 | − | 0.656765i | \(-0.771924\pi\) | ||||
−0.754095 | + | 0.656765i | \(0.771924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.47708 | − | 2.47708i | 0.0922512 | − | 0.0922512i | ||||
\(722\) | 6.10479 | 0.227197 | ||||||||
\(723\) | − | 8.93211i | − | 0.332189i | ||||||
\(724\) | 11.8479i | 0.440322i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.804491 | − | 0.804491i | −0.0298575 | − | 0.0298575i | ||||
\(727\) | 14.6406 | + | 14.6406i | 0.542988 | + | 0.542988i | 0.924404 | − | 0.381415i | \(-0.124563\pi\) |
−0.381415 | + | 0.924404i | \(0.624563\pi\) | |||||||
\(728\) | 1.57487 | − | 2.12180i | 0.0583686 | − | 0.0786392i | ||||
\(729\) | 20.8439i | 0.771997i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6431 | −0.504609 | ||||||||
\(732\) | −4.10449 | − | 4.10449i | −0.151706 | − | 0.151706i | ||||
\(733\) | −31.6272 | −1.16818 | −0.584089 | − | 0.811690i | \(-0.698548\pi\) | ||||
−0.584089 | + | 0.811690i | \(0.698548\pi\) | |||||||
\(734\) | −3.82984 | − | 3.82984i | −0.141362 | − | 0.141362i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.6000 | − | 13.6000i | −0.501301 | − | 0.501301i | ||||
\(737\) | 34.0523 | − | 34.0523i | 1.25433 | − | 1.25433i | ||||
\(738\) | 0.0402566 | − | 0.0402566i | 0.00148186 | − | 0.00148186i | ||||
\(739\) | −10.0736 | + | 10.0736i | −0.370563 | + | 0.370563i | −0.867682 | − | 0.497119i | \(-0.834391\pi\) |
0.497119 | + | 0.867682i | \(0.334391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.66339 | − | 2.24106i | 0.0611062 | − | 0.0823274i | ||||
\(742\) | −1.50921 | + | 1.50921i | −0.0554049 | + | 0.0554049i | ||||
\(743\) | −5.70595 | −0.209331 | −0.104666 | − | 0.994507i | \(-0.533377\pi\) | ||||
−0.104666 | + | 0.994507i | \(0.533377\pi\) | |||||||
\(744\) | − | 1.03001i | − | 0.0377622i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.25309 | + | 4.25309i | −0.155717 | + | 0.155717i | ||||
\(747\) | − | 45.4367i | − | 1.66244i | ||||||
\(748\) | − | 34.0371i | − | 1.24452i | ||||||
\(749\) | 3.39412 | − | 3.39412i | 0.124018 | − | 0.124018i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.6268i | − | 0.424269i | −0.977240 | − | 0.212134i | \(-0.931959\pi\) | ||
0.977240 | − | 0.212134i | \(-0.0680415\pi\) | |||||||
\(752\) | −21.4632 | −0.782682 | ||||||||
\(753\) | −2.20410 | + | 2.20410i | −0.0803220 | + | 0.0803220i | ||||
\(754\) | 0.175699 | + | 0.130410i | 0.00639858 | + | 0.00474924i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.13220 | + | 1.13220i | −0.0411776 | + | 0.0411776i | ||||
\(757\) | −12.4158 | + | 12.4158i | −0.451261 | + | 0.451261i | −0.895773 | − | 0.444512i | \(-0.853377\pi\) |
0.444512 | + | 0.895773i | \(0.353377\pi\) | |||||||
\(758\) | −7.38405 | + | 7.38405i | −0.268201 | + | 0.268201i | ||||
\(759\) | −4.36639 | − | 4.36639i | −0.158490 | − | 0.158490i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.74841 | − | 1.74841i | −0.0633797 | − | 0.0633797i | 0.674706 | − | 0.738086i | \(-0.264270\pi\) |
−0.738086 | + | 0.674706i | \(0.764270\pi\) | |||||||
\(762\) | −2.71198 | −0.0982446 | ||||||||
\(763\) | −4.51344 | − | 4.51344i | −0.163397 | − | 0.163397i | ||||
\(764\) | 39.8842 | 1.44296 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.4699i | 0.378294i | ||||||||
\(767\) | −30.3355 | + | 4.48819i | −1.09535 | + | 0.162059i | ||||
\(768\) | 0.661681 | + | 0.661681i | 0.0238764 | + | 0.0238764i | ||||
\(769\) | −8.83323 | − | 8.83323i | −0.318534 | − | 0.318534i | 0.529670 | − | 0.848204i | \(-0.322316\pi\) |
−0.848204 | + | 0.529670i | \(0.822316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.75854i | 0.207389i | ||||||||
\(772\) | 18.9907i | 0.683492i | ||||||||
\(773\) | 49.9877 | 1.79793 | 0.898967 | − | 0.438017i | \(-0.144319\pi\) | ||||
0.898967 | + | 0.438017i | \(0.144319\pi\) | |||||||
\(774\) | 2.79041 | − | 2.79041i | 0.100299 | − | 0.100299i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.51908 | 0.0904299 | ||||||||
\(777\) | −0.760094 | − | 0.760094i | −0.0272682 | − | 0.0272682i | ||||
\(778\) | 5.61171i | 0.201190i | ||||||||
\(779\) | −0.101529 | −0.00363766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.21039 | −0.329574 | ||||||||
\(782\) | 8.00978i | 0.286429i | ||||||||
\(783\) | −0.197490 | − | 0.197490i | −0.00705773 | − | 0.00705773i | ||||
\(784\) | −19.6204 | −0.700730 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.27072 | + | 1.27072i | −0.0453249 | + | 0.0453249i | ||||
\(787\) | −11.2437 | −0.400793 | −0.200396 | − | 0.979715i | \(-0.564223\pi\) | ||||
−0.200396 | + | 0.979715i | \(0.564223\pi\) | |||||||
\(788\) | 18.7314i | 0.667278i | ||||||||
\(789\) | − | 6.50722i | − | 0.231663i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.988660 | + | 0.988660i | 0.0351527 | + | 0.0351527i | ||||
\(792\) | 14.6645 | + | 14.6645i | 0.521080 | + | 0.521080i | ||||
\(793\) | −27.0860 | − | 20.1042i | −0.961853 | − | 0.713919i | ||||
\(794\) | − | 6.90195i | − | 0.244941i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.8034 | 1.23357 | ||||||||
\(797\) | 16.9617 | + | 16.9617i | 0.600815 | + | 0.600815i | 0.940529 | − | 0.339714i | \(-0.110330\pi\) |
−0.339714 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(798\) | −0.148991 | −0.00527422 | ||||||||
\(799\) | 23.0198 | + | 23.0198i | 0.814382 | + | 0.814382i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.7793 | + | 28.7793i | 1.01687 | + | 1.01687i | ||||
\(802\) | 1.81061 | − | 1.81061i | 0.0639349 | − | 0.0639349i | ||||
\(803\) | 46.1591 | − | 46.1591i | 1.62892 | − | 1.62892i | ||||
\(804\) | 4.90485 | − | 4.90485i | 0.172981 | − | 0.172981i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.415879 | − | 2.81091i | −0.0146487 | − | 0.0990101i | ||||
\(807\) | −3.36898 | + | 3.36898i | −0.118594 | + | 0.118594i | ||||
\(808\) | 7.60285 | 0.267467 | ||||||||
\(809\) | 12.9602i | 0.455657i | 0.973701 | + | 0.227828i | \(0.0731625\pi\) | ||||
−0.973701 | + | 0.227828i | \(0.926837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.8170 | − | 10.8170i | 0.379836 | − | 0.379836i | −0.491207 | − | 0.871043i | \(-0.663444\pi\) |
0.871043 | + | 0.491207i | \(0.163444\pi\) | |||||||
\(812\) | 0.109692i | 0.00384943i | ||||||||
\(813\) | − | 2.91397i | − | 0.102198i | ||||||
\(814\) | −9.53830 | + | 9.53830i | −0.334317 | + | 0.334317i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 4.32500i | − | 0.151405i | ||||||
\(817\) | −7.03758 | −0.246214 | ||||||||
\(818\) | −1.55459 | + | 1.55459i | −0.0543548 | + | 0.0543548i | ||||
\(819\) | −2.71726 | + | 3.66092i | −0.0949487 | + | 0.127923i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.30454 | − | 5.30454i | 0.185130 | − | 0.185130i | −0.608457 | − | 0.793587i | \(-0.708211\pi\) |
0.793587 | + | 0.608457i | \(0.208211\pi\) | |||||||
\(822\) | 0.359784 | − | 0.359784i | 0.0125489 | − | 0.0125489i | ||||
\(823\) | −34.1224 | + | 34.1224i | −1.18943 | + | 1.18943i | −0.212208 | + | 0.977224i | \(0.568065\pi\) |
−0.977224 | + | 0.212208i | \(0.931935\pi\) | |||||||
\(824\) | −9.43153 | − | 9.43153i | −0.328563 | − | 0.328563i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.15758 | + | 1.15758i | 0.0402773 | + | 0.0402773i | ||||
\(827\) | 5.27056 | 0.183275 | 0.0916376 | − | 0.995792i | \(-0.470790\pi\) | ||||
0.0916376 | + | 0.995792i | \(0.470790\pi\) | |||||||
\(828\) | 15.3842 | + | 15.3842i | 0.534637 | + | 0.534637i | ||||
\(829\) | 20.9932 | 0.729125 | 0.364562 | − | 0.931179i | \(-0.381219\pi\) | ||||
0.364562 | + | 0.931179i | \(0.381219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.42273i | 0.118733i | ||||||||
\(832\) | 10.8392 | + | 8.04520i | 0.375781 | + | 0.278917i | ||||
\(833\) | 21.0434 | + | 21.0434i | 0.729111 | + | 0.729111i | ||||
\(834\) | 1.63058 | + | 1.63058i | 0.0564623 | + | 0.0564623i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 17.5575i | − | 0.607239i | ||||||
\(837\) | 3.62699i | 0.125367i | ||||||||
\(838\) | 13.0174 | 0.449678 | ||||||||
\(839\) | 7.12698 | − | 7.12698i | 0.246051 | − | 0.246051i | −0.573297 | − | 0.819348i | \(-0.694336\pi\) |
0.819348 | + | 0.573297i | \(0.194336\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9809 | 0.999340 | ||||||||
\(842\) | 3.32545 | + | 3.32545i | 0.114603 | + | 0.114603i | ||||
\(843\) | − | 4.96537i | − | 0.171016i | ||||||
\(844\) | 16.3494 | 0.562769 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.41643 | −0.323744 | ||||||||
\(847\) | − | 3.31446i | − | 0.113886i | ||||||
\(848\) | −22.5988 | − | 22.5988i | −0.776046 | − | 0.776046i | ||||
\(849\) | −0.823673 | −0.0282684 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0784 | + | 21.0784i | −0.722558 | + | 0.722558i | ||||
\(852\) | −1.32665 | −0.0454504 | ||||||||
\(853\) | 5.81669i | 0.199160i | 0.995030 | + | 0.0995798i | \(0.0317498\pi\) | ||||
−0.995030 | + | 0.0995798i | \(0.968250\pi\) | |||||||
\(854\) | 1.80074i | 0.0616201i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.9232 | − | 12.9232i | −0.441705 | − | 0.441705i | ||||
\(857\) | −1.83206 | − | 1.83206i | −0.0625819 | − | 0.0625819i | 0.675123 | − | 0.737705i | \(-0.264090\pi\) |
−0.737705 | + | 0.675123i | \(0.764090\pi\) | |||||||
\(858\) | −1.87811 | − | 1.39400i | −0.0641177 | − | 0.0475903i | ||||
\(859\) | 5.10411i | 0.174150i | 0.996202 | + | 0.0870750i | \(0.0277520\pi\) | ||||
−0.996202 | + | 0.0870750i | \(0.972248\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.00678040 | −0.000231076 | ||||||||
\(862\) | 12.4950 | + | 12.4950i | 0.425582 | + | 0.425582i | ||||
\(863\) | −51.8953 | −1.76654 | −0.883268 | − | 0.468869i | \(-0.844662\pi\) | ||||
−0.883268 | + | 0.468869i | \(0.844662\pi\) | |||||||
\(864\) | 6.57526 | + | 6.57526i | 0.223695 | + | 0.223695i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.98253 | + | 2.98253i | 0.101351 | + | 0.101351i | ||||
\(867\) | −0.512397 | + | 0.512397i | −0.0174019 | + | 0.0174019i | ||||
\(868\) | 1.00727 | − | 1.00727i | 0.0341890 | − | 0.0341890i | ||||
\(869\) | 30.7486 | − | 30.7486i | 1.04307 | − | 1.04307i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0244 | − | 32.3677i | 0.814036 | − | 1.09674i | ||||
\(872\) | −17.1850 | + | 17.1850i | −0.581958 | + | 0.581958i | ||||
\(873\) | −4.34639 | −0.147103 | ||||||||
\(874\) | 4.13171i | 0.139757i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.64870 | − | 6.64870i | 0.224639 | − | 0.224639i | ||||
\(877\) | − | 15.4765i | − | 0.522604i | −0.965257 | − | 0.261302i | \(-0.915848\pi\) | ||
0.965257 | − | 0.261302i | \(-0.0841518\pi\) | |||||||
\(878\) | 2.33245i | 0.0787164i | ||||||||
\(879\) | −0.158821 | + | 0.158821i | −0.00535691 | + | 0.00535691i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.8033i | 1.57684i | 0.615135 | + | 0.788422i | \(0.289102\pi\) | ||||
−0.615135 | + | 0.788422i | \(0.710898\pi\) | |||||||
\(882\) | −8.60797 | −0.289846 | ||||||||
\(883\) | 3.15723 | − | 3.15723i | 0.106249 | − | 0.106249i | −0.651984 | − | 0.758233i | \(-0.726063\pi\) |
0.758233 | + | 0.651984i | \(0.226063\pi\) | |||||||
\(884\) | −4.16980 | − | 28.1835i | −0.140246 | − | 0.947914i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.901208 | + | 0.901208i | −0.0302767 | + | 0.0302767i | ||||
\(887\) | −4.34803 | + | 4.34803i | −0.145993 | + | 0.145993i | −0.776325 | − | 0.630333i | \(-0.782919\pi\) |
0.630333 | + | 0.776325i | \(0.282919\pi\) | |||||||
\(888\) | −2.89407 | + | 2.89407i | −0.0971188 | + | 0.0971188i | ||||
\(889\) | −5.58660 | − | 5.58660i | −0.187368 | − | 0.187368i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.2252 | − | 24.2252i | −0.811575 | − | 0.811575i | ||||
\(892\) | 16.1493 | 0.540717 | ||||||||
\(893\) | 11.8744 | + | 11.8744i | 0.397361 | + | 0.397361i | ||||
\(894\) | 1.43153 | 0.0478774 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 4.76161i | − | 0.159074i | ||||||
\(897\) | −4.15038 | − | 3.08055i | −0.138577 | − | 0.102857i | ||||
\(898\) | 9.82922 | + | 9.82922i | 0.328005 | + | 0.328005i | ||||
\(899\) | 0.175699 | + | 0.175699i | 0.00585989 | + | 0.00585989i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.4756i | 1.61496i | ||||||||
\(902\) | 0.0850862i | 0.00283306i | ||||||||
\(903\) | −0.469989 | −0.0156402 | ||||||||
\(904\) | 3.76434 | − | 3.76434i | 0.125200 | − | 0.125200i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.25341 | −0.0416419 | ||||||||
\(907\) | −17.2267 | − | 17.2267i | −0.572004 | − | 0.572004i | 0.360684 | − | 0.932688i | \(-0.382543\pi\) |
−0.932688 | + | 0.360684i | \(0.882543\pi\) | |||||||
\(908\) | 40.5903i | 1.34704i | ||||||||
\(909\) | −13.1178 | −0.435091 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4109 | 0.709373 | 0.354687 | − | 0.934985i | \(-0.384588\pi\) | ||||
0.354687 | + | 0.934985i | \(0.384588\pi\) | |||||||
\(912\) | − | 2.23098i | − | 0.0738751i | ||||||
\(913\) | 48.0175 | + | 48.0175i | 1.58915 | + | 1.58915i | ||||
\(914\) | 3.67806 | 0.121659 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.0581 | − | 13.0581i | 0.431452 | − | 0.431452i | ||||
\(917\) | −5.23527 | −0.172884 | ||||||||
\(918\) | − | 3.87254i | − | 0.127813i | ||||||
\(919\) | 12.1389i | 0.400425i | 0.979753 | + | 0.200212i | \(0.0641632\pi\) | ||||
−0.979753 | + | 0.200212i | \(0.935837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.38278 | − | 1.38278i | −0.0455640 | − | 0.0455640i | ||||
\(922\) | −7.30837 | − | 7.30837i | −0.240688 | − | 0.240688i | ||||
\(923\) | −7.62641 | + | 1.12834i | −0.251026 | + | 0.0371398i | ||||
\(924\) | − | 1.17254i | − | 0.0385737i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.14292 | −0.300455 | ||||||||
\(927\) | 16.2730 | + | 16.2730i | 0.534475 | + | 0.534475i | ||||
\(928\) | 0.637038 | 0.0209118 | ||||||||
\(929\) | 13.8895 | + | 13.8895i | 0.455700 | + | 0.455700i | 0.897241 | − | 0.441541i | \(-0.145568\pi\) |
−0.441541 | + | 0.897241i | \(0.645568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8549 | + | 10.8549i | 0.355755 | + | 0.355755i | ||||
\(932\) | 23.7755 | − | 23.7755i | 0.778793 | − | 0.778793i | ||||
\(933\) | 2.21411 | − | 2.21411i | 0.0724869 | − | 0.0724869i | ||||
\(934\) | 11.4517 | − | 11.4517i | 0.374710 | − | 0.374710i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.9390 | + | 10.3460i | 0.455611 | + | 0.338170i | ||||
\(937\) | 21.6718 | − | 21.6718i | 0.707988 | − | 0.707988i | −0.258124 | − | 0.966112i | \(-0.583104\pi\) |
0.966112 | + | 0.258124i | \(0.0831044\pi\) | |||||||
\(938\) | −2.15188 | −0.0702614 | ||||||||
\(939\) | − | 7.89945i | − | 0.257789i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.4870 | − | 24.4870i | 0.798255 | − | 0.798255i | −0.184565 | − | 0.982820i | \(-0.559088\pi\) |
0.982820 | + | 0.184565i | \(0.0590878\pi\) | |||||||
\(942\) | − | 1.76025i | − | 0.0573519i | ||||||
\(943\) | 0.188029i | 0.00612308i | ||||||||
\(944\) | −17.3335 | + | 17.3335i | −0.564158 | + | 0.564158i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.89782i | 0.191755i | ||||||||
\(947\) | −40.4688 | −1.31506 | −0.657530 | − | 0.753429i | \(-0.728399\pi\) | ||||
−0.657530 | + | 0.753429i | \(0.728399\pi\) | |||||||
\(948\) | 4.42899 | − | 4.42899i | 0.143847 | − | 0.143847i | ||||
\(949\) | 32.5659 | − | 43.8756i | 1.05713 | − | 1.42426i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.71019 | − | 5.71019i | 0.185166 | − | 0.185166i | ||||
\(952\) | −2.26545 | + | 2.26545i | −0.0734235 | + | 0.0734235i | ||||
\(953\) | 1.33281 | − | 1.33281i | 0.0431741 | − | 0.0431741i | −0.685190 | − | 0.728364i | \(-0.740281\pi\) |
0.728364 | + | 0.685190i | \(0.240281\pi\) | |||||||
\(954\) | −9.91466 | − | 9.91466i | −0.320999 | − | 0.320999i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 39.3184 | + | 39.3184i | 1.27165 | + | 1.27165i | ||||
\(957\) | 0.204527 | 0.00661142 | ||||||||
\(958\) | 8.67378 | + | 8.67378i | 0.280237 | + | 0.280237i | ||||
\(959\) | 1.48229 | 0.0478656 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7732i | 0.895910i | ||||||||
\(962\) | −6.72942 | + | 9.06644i | −0.216965 | + | 0.292314i | ||||
\(963\) | 22.2974 | + | 22.2974i | 0.718524 | + | 0.718524i | ||||
\(964\) | −33.2582 | − | 33.2582i | −1.07117 | − | 1.07117i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.275927i | 0.00887780i | ||||||||
\(967\) | 40.2629i | 1.29477i | 0.762164 | + | 0.647384i | \(0.224137\pi\) | ||||
−0.762164 | + | 0.647384i | \(0.775863\pi\) | |||||||
\(968\) | −12.6199 | −0.405618 | ||||||||
\(969\) | −2.39278 | + | 2.39278i | −0.0768672 | + | 0.0768672i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.8739 | 0.734059 | 0.367030 | − | 0.930209i | \(-0.380375\pi\) | ||||
0.367030 | + | 0.930209i | \(0.380375\pi\) | |||||||
\(972\) | −11.2313 | − | 11.2313i | −0.360245 | − | 0.360245i | ||||
\(973\) | 6.71789i | 0.215366i | ||||||||
\(974\) | −6.85343 | −0.219598 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.9642 | −0.863102 | ||||||||
\(977\) | − | 14.0612i | − | 0.449857i | −0.974375 | − | 0.224929i | \(-0.927785\pi\) | ||
0.974375 | − | 0.224929i | \(-0.0722149\pi\) | |||||||
\(978\) | −2.19711 | − | 2.19711i | −0.0702559 | − | 0.0702559i | ||||
\(979\) | −60.8279 | −1.94407 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.6507 | − | 29.6507i | 0.946674 | − | 0.946674i | ||||
\(982\) | −5.53655 | −0.176678 | ||||||||
\(983\) | 35.4794i | 1.13162i | 0.824537 | + | 0.565808i | \(0.191436\pi\) | ||||
−0.824537 | + | 0.565808i | \(0.808564\pi\) | |||||||
\(984\) | 0.0258165i | 0.000823001i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.187594 | − | 0.187594i | −0.00597420 | − | 0.00597420i | ||||
\(987\) | 0.793004 | + | 0.793004i | 0.0252416 | + | 0.0252416i | ||||
\(988\) | −2.15092 | − | 14.5380i | −0.0684299 | − | 0.462515i | ||||
\(989\) | 13.0334i | 0.414438i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0591 | −0.351303 | −0.175652 | − | 0.984452i | \(-0.556203\pi\) | ||||
−0.175652 | + | 0.984452i | \(0.556203\pi\) | |||||||
\(992\) | −5.84974 | − | 5.84974i | −0.185729 | − | 0.185729i | ||||
\(993\) | −5.67287 | −0.180023 | ||||||||
\(994\) | 0.291018 | + | 0.291018i | 0.00923053 | + | 0.00923053i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.91639 | + | 6.91639i | 0.219154 | + | 0.219154i | ||||
\(997\) | −2.10621 | + | 2.10621i | −0.0667044 | + | 0.0667044i | −0.739672 | − | 0.672968i | \(-0.765019\pi\) |
0.672968 | + | 0.739672i | \(0.265019\pi\) | |||||||
\(998\) | 9.89005 | − | 9.89005i | 0.313064 | − | 0.313064i | ||||
\(999\) | 10.1909 | − | 10.1909i | 0.322426 | − | 0.322426i |
(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 | 325.2.f.d.18.5 | yes | 16 | |
5.2 | odd | 4 | 325.2.k.d.57.4 | yes | 16 | ||
5.3 | odd | 4 | 325.2.k.d.57.5 | yes | 16 | ||
5.4 | even | 2 | inner | 325.2.f.d.18.4 | ✓ | 16 | |
13.8 | odd | 4 | 325.2.k.d.268.4 | yes | 16 | ||
65.8 | even | 4 | inner | 325.2.f.d.307.5 | yes | 16 | |
65.34 | odd | 4 | 325.2.k.d.268.5 | yes | 16 | ||
65.47 | even | 4 | inner | 325.2.f.d.307.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.f.d.18.4 | ✓ | 16 | 5.4 | even | 2 | inner | |
325.2.f.d.18.5 | yes | 16 | 1.1 | even | 1 | trivial | |
325.2.f.d.307.4 | yes | 16 | 65.47 | even | 4 | inner | |
325.2.f.d.307.5 | yes | 16 | 65.8 | even | 4 | inner | |
325.2.k.d.57.4 | yes | 16 | 5.2 | odd | 4 | ||
325.2.k.d.57.5 | yes | 16 | 5.3 | odd | 4 | ||
325.2.k.d.268.4 | yes | 16 | 13.8 | odd | 4 | ||
325.2.k.d.268.5 | yes | 16 | 65.34 | odd | 4 |