Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(829,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 27x^{12} + 283x^{10} + 1441x^{8} + 3596x^{6} + 3740x^{4} + 772x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.4 | ||
Root | \(-2.04690i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.829 |
Dual form | 1380.2.f.b.829.11 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.181772 | + | 2.22867i | −0.0812909 | + | 0.996690i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.189781i | 0.0717305i | 0.999357 | + | 0.0358652i | \(0.0114187\pi\) | ||||
−0.999357 | + | 0.0358652i | \(0.988581\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.33196 | 1.30613 | 0.653067 | − | 0.757300i | \(-0.273482\pi\) | ||||
0.653067 | + | 0.757300i | \(0.273482\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.67083i | 1.29546i | 0.761872 | + | 0.647728i | \(0.224281\pi\) | ||||
−0.761872 | + | 0.647728i | \(0.775719\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.22867 | + | 0.181772i | 0.575439 | + | 0.0469333i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.0397340i | − | 0.00963691i | −0.999988 | − | 0.00481845i | \(-0.998466\pi\) | ||
0.999988 | − | 0.00481845i | \(-0.00153377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.19716 | −1.65114 | −0.825571 | − | 0.564298i | \(-0.809147\pi\) | ||||
−0.825571 | + | 0.564298i | \(0.809147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.189781 | 0.0414136 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93392 | − | 0.810219i | −0.986784 | − | 0.162044i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.49707 | −1.20648 | −0.603238 | − | 0.797561i | \(-0.706123\pi\) | ||||
−0.603238 | + | 0.797561i | \(0.706123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.17655 | 1.64816 | 0.824079 | − | 0.566475i | \(-0.191693\pi\) | ||||
0.824079 | + | 0.566475i | \(0.191693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.33196i | − | 0.754097i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.422959 | − | 0.0344969i | −0.0714931 | − | 0.00583104i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.03881i | 0.499577i | 0.968300 | + | 0.249788i | \(0.0803611\pi\) | ||||
−0.968300 | + | 0.249788i | \(0.919639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.67083 | 0.747932 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.69330 | −1.35767 | −0.678833 | − | 0.734293i | \(-0.737514\pi\) | ||||
−0.678833 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.83269i | 1.19447i | 0.802065 | + | 0.597237i | \(0.203735\pi\) | ||||
−0.802065 | + | 0.597237i | \(0.796265\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.181772 | − | 2.22867i | 0.0270970 | − | 0.332230i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.03127i | 0.733886i | 0.930243 | + | 0.366943i | \(0.119596\pi\) | ||||
−0.930243 | + | 0.366943i | \(0.880404\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.96398 | 0.994855 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0397340 | −0.00556387 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.96306i | 0.956449i | 0.878238 | + | 0.478225i | \(0.158720\pi\) | ||||
−0.878238 | + | 0.478225i | \(0.841280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.787429 | + | 9.65450i | −0.106177 | + | 1.30181i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.19716i | 0.953287i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.64368 | −0.604555 | −0.302278 | − | 0.953220i | \(-0.597747\pi\) | ||||
−0.302278 | + | 0.953220i | \(0.597747\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.86428 | 1.00692 | 0.503459 | − | 0.864019i | \(-0.332061\pi\) | ||||
0.503459 | + | 0.864019i | \(0.332061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.189781i | − | 0.0239102i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4097 | − | 0.849027i | −1.29117 | − | 0.105309i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.52865i | 0.308924i | 0.987999 | + | 0.154462i | \(0.0493645\pi\) | ||||
−0.987999 | + | 0.154462i | \(0.950636\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.70964 | −0.202897 | −0.101448 | − | 0.994841i | \(-0.532348\pi\) | ||||
−0.101448 | + | 0.994841i | \(0.532348\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.29127i | 0.736337i | 0.929759 | + | 0.368169i | \(0.120015\pi\) | ||||
−0.929759 | + | 0.368169i | \(0.879985\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.810219 | + | 4.93392i | −0.0935560 | + | 0.569720i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.822124i | 0.0936897i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.82056 | 1.10490 | 0.552450 | − | 0.833546i | \(-0.313693\pi\) | ||||
0.552450 | + | 0.833546i | \(0.313693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.417601i | 0.0458377i | 0.999737 | + | 0.0229188i | \(0.00729593\pi\) | ||||
−0.999737 | + | 0.0229188i | \(0.992704\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0885538 | + | 0.00722253i | 0.00960501 | + | 0.000783393i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.49707i | 0.696559i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.92081 | 0.415605 | 0.207803 | − | 0.978171i | \(-0.433369\pi\) | ||||
0.207803 | + | 0.978171i | \(0.433369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.886435 | −0.0929237 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.17655i | − | 0.951564i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.30824 | − | 16.0401i | 0.134223 | − | 1.64568i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0584885i | 0.00593861i | 0.999996 | + | 0.00296930i | \(0.000945160\pi\) | ||||
−0.999996 | + | 0.00296930i | \(0.999055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.33196 | −0.435378 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.61569 | −0.658286 | −0.329143 | − | 0.944280i | \(-0.606760\pi\) | ||||
−0.329143 | + | 0.944280i | \(0.606760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.9236i | − | 1.66753i | −0.552118 | − | 0.833766i | \(-0.686180\pi\) | ||
0.552118 | − | 0.833766i | \(-0.313820\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0344969 | + | 0.422959i | −0.00336655 | + | 0.0412766i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.5775i | 1.69928i | 0.527364 | + | 0.849639i | \(0.323180\pi\) | ||||
−0.527364 | + | 0.849639i | \(0.676820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.243838 | 0.0233554 | 0.0116777 | − | 0.999932i | \(-0.496283\pi\) | ||||
0.0116777 | + | 0.999932i | \(0.496283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.03881 | 0.288431 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.22452i | − | 0.115194i | −0.998340 | − | 0.0575968i | \(-0.981656\pi\) | ||
0.998340 | − | 0.0575968i | \(-0.0183438\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.22867 | − | 0.181772i | −0.207824 | − | 0.0169503i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4.67083i | − | 0.431819i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.00754075 | 0.000691260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.76587 | 0.705988 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.69330i | 0.783849i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.70256 | − | 10.8488i | 0.241724 | − | 0.970345i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6764i | 1.83474i | 0.398041 | + | 0.917368i | \(0.369690\pi\) | ||||
−0.398041 | + | 0.917368i | \(0.630310\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.83269 | 0.689630 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.3253 | 1.60109 | 0.800546 | − | 0.599272i | \(-0.204543\pi\) | ||||
0.800546 | + | 0.599272i | \(0.204543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.36588i | − | 0.118437i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.22867 | − | 0.181772i | −0.191813 | − | 0.0156444i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.46899i | − | 0.296376i | −0.988959 | − | 0.148188i | \(-0.952656\pi\) | ||
0.988959 | − | 0.148188i | \(-0.0473440\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.40878 | −0.543585 | −0.271793 | − | 0.962356i | \(-0.587617\pi\) | ||||
−0.271793 | + | 0.962356i | \(0.587617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.03127 | 0.423709 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.2339i | 1.69204i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.18099 | − | 14.4798i | 0.0980755 | − | 1.20248i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.96398i | − | 0.574380i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9989 | −1.14684 | −0.573418 | − | 0.819263i | \(-0.694383\pi\) | ||||
−0.573418 | + | 0.819263i | \(0.694383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5758 | 1.18616 | 0.593081 | − | 0.805143i | \(-0.297911\pi\) | ||||
0.593081 | + | 0.805143i | \(0.297911\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0397340i | 0.00321230i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.66804 | + | 20.4515i | −0.133980 | + | 1.64270i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.9563i | − | 1.51287i | −0.654066 | − | 0.756437i | \(-0.726938\pi\) | ||
0.654066 | − | 0.756437i | \(-0.273062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.96306 | 0.552206 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.189781 | −0.0149568 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.2785i | − | 1.04005i | −0.854150 | − | 0.520026i | \(-0.825922\pi\) | ||
0.854150 | − | 0.520026i | \(-0.174078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.65450 | + | 0.787429i | 0.751601 | + | 0.0613013i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.9737i | 1.08132i | 0.841242 | + | 0.540659i | \(0.181825\pi\) | ||||
−0.841242 | + | 0.540659i | \(0.818175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.81667 | −0.678206 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.19716 | 0.550381 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.7917i | − | 0.972534i | −0.873810 | − | 0.486267i | \(-0.838358\pi\) | ||
0.873810 | − | 0.486267i | \(-0.161642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.153764 | − | 0.936364i | 0.0116235 | − | 0.0707825i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.64368i | 0.349040i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0511629 | −0.00382410 | −0.00191205 | − | 0.999998i | \(-0.500609\pi\) | ||||
−0.00191205 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7448 | 1.61628 | 0.808141 | − | 0.588989i | \(-0.200474\pi\) | ||||
0.808141 | + | 0.588989i | \(0.200474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.86428i | − | 0.581344i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.77249 | − | 0.552370i | −0.497924 | − | 0.0406111i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.172126i | − | 0.0125871i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.189781 | −0.0138045 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.3680 | −1.47378 | −0.736890 | − | 0.676013i | \(-0.763706\pi\) | ||||
−0.736890 | + | 0.676013i | \(0.763706\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8592i | 1.14157i | 0.821099 | + | 0.570786i | \(0.193361\pi\) | ||||
−0.821099 | + | 0.570786i | \(0.806639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.849027 | + | 10.4097i | −0.0608001 | + | 0.745456i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.16978i | − | 0.439579i | −0.975547 | − | 0.219789i | \(-0.929463\pi\) | ||
0.975547 | − | 0.219789i | \(-0.0705370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.81534 | 0.341350 | 0.170675 | − | 0.985327i | \(-0.445405\pi\) | ||||
0.170675 | + | 0.985327i | \(0.445405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.52865 | 0.178358 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.23302i | − | 0.0865411i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.58020 | − | 19.3745i | 0.110366 | − | 1.35317i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.00000i | − | 0.0695048i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.1778 | −2.15661 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9874 | −1.65136 | −0.825679 | − | 0.564140i | \(-0.809208\pi\) | ||||
−0.825679 | + | 0.564140i | \(0.809208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.70964i | 0.117143i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.4565 | − | 1.42376i | −1.19052 | − | 0.0970999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.74154i | 0.118223i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.29127 | 0.425125 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.185591 | 0.0124842 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.4215i | − | 0.764840i | −0.923989 | − | 0.382420i | \(-0.875091\pi\) | ||
0.923989 | − | 0.382420i | \(-0.124909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.93392 | + | 0.810219i | 0.328928 | + | 0.0540146i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 15.7360i | − | 1.04443i | −0.852813 | − | 0.522217i | \(-0.825105\pi\) | ||
0.852813 | − | 0.522217i | \(-0.174895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.46335 | −0.228865 | −0.114432 | − | 0.993431i | \(-0.536505\pi\) | ||||
−0.114432 | + | 0.993431i | \(0.536505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.822124 | 0.0540918 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.319746i | − | 0.0209473i | −0.999945 | − | 0.0104736i | \(-0.996666\pi\) | ||
0.999945 | − | 0.0104736i | \(-0.00333392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2130 | − | 0.914544i | −0.731457 | − | 0.0596583i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.82056i | − | 0.637914i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.93697 | 0.189977 | 0.0949885 | − | 0.995478i | \(-0.469719\pi\) | ||||
0.0949885 | + | 0.995478i | \(0.469719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6764 | −1.20305 | −0.601527 | − | 0.798853i | \(-0.705441\pi\) | ||||
−0.601527 | + | 0.798853i | \(0.705441\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.26586 | + | 15.5204i | −0.0808727 | + | 0.991562i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.6167i | − | 2.13898i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.417601 | 0.0264644 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.76059 | −0.237366 | −0.118683 | − | 0.992932i | \(-0.537867\pi\) | ||||
−0.118683 | + | 0.992932i | \(0.537867\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.33196i | 0.272348i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.00722253 | − | 0.0885538i | 0.000452292 | − | 0.00554546i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 26.1810i | − | 1.63312i | −0.577259 | − | 0.816561i | \(-0.695878\pi\) | ||
0.577259 | − | 0.816561i | \(-0.304122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.576708 | −0.0358349 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.49707 | 0.402158 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.6844i | − | 1.39878i | −0.714739 | − | 0.699391i | \(-0.753455\pi\) | ||
0.714739 | − | 0.699391i | \(-0.246545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.5183 | − | 1.26569i | −0.953284 | − | 0.0777507i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.92081i | − | 0.239950i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.570220 | −0.0347669 | −0.0173835 | − | 0.999849i | \(-0.505534\pi\) | ||||
−0.0173835 | + | 0.999849i | \(0.505534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9506 | 1.33341 | 0.666703 | − | 0.745323i | \(-0.267705\pi\) | ||||
0.666703 | + | 0.745323i | \(0.267705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.886435i | 0.0536495i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.3735 | − | 3.50984i | −1.28887 | − | 0.211651i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5514i | 0.754141i | 0.926185 | + | 0.377070i | \(0.123069\pi\) | ||||
−0.926185 | + | 0.377070i | \(0.876931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.17655 | −0.549386 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7956 | 1.30022 | 0.650108 | − | 0.759842i | \(-0.274724\pi\) | ||||
0.650108 | + | 0.759842i | \(0.274724\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0765i | 1.43120i | 0.698510 | + | 0.715601i | \(0.253847\pi\) | ||||
−0.698510 | + | 0.715601i | \(0.746153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.0401 | − | 1.30824i | −0.950132 | − | 0.0774936i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.64982i | − | 0.0973860i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9984 | 0.999907 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0584885 | 0.00342866 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 27.2212i | − | 1.59028i | −0.606427 | − | 0.795139i | \(-0.707398\pi\) | ||
0.606427 | − | 0.795139i | \(-0.292602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.844091 | − | 10.3492i | 0.0491449 | − | 0.602555i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.33196i | 0.251366i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.67083 | −0.270121 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.48650 | −0.0856802 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.61569i | 0.380061i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.42951 | + | 17.5269i | −0.0818533 | + | 1.00358i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.48076i | 0.369877i | 0.982750 | + | 0.184938i | \(0.0592085\pi\) | ||||
−0.982750 | + | 0.184938i | \(0.940791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.9236 | −0.962750 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.11457 | 0.233316 | 0.116658 | − | 0.993172i | \(-0.462782\pi\) | ||||
0.116658 | + | 0.993172i | \(0.462782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.760034i | − | 0.0429597i | −0.999769 | − | 0.0214798i | \(-0.993162\pi\) | ||
0.999769 | − | 0.0214798i | \(-0.00683777\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.422959 | + | 0.0344969i | 0.0238310 | + | 0.00194368i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.48188i | 0.420224i | 0.977677 | + | 0.210112i | \(0.0673829\pi\) | ||||
−0.977677 | + | 0.210112i | \(0.932617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.1450 | −1.57582 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.5775 | 0.981079 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.285972i | 0.0159119i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.78440 | − | 23.0455i | 0.209921 | − | 1.27833i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 0.243838i | − | 0.0134843i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.954839 | −0.0526420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.5981 | 1.57189 | 0.785946 | − | 0.618295i | \(-0.212176\pi\) | ||||
0.785946 | + | 0.618295i | \(0.212176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.03881i | − | 0.166526i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.63553 | − | 0.459639i | −0.307902 | − | 0.0251127i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.9098i | − | 1.24798i | −0.781434 | − | 0.623988i | \(-0.785512\pi\) | ||
0.781434 | − | 0.623988i | \(-0.214488\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.22452 | −0.0665071 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.7525 | 2.15272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.65010i | 0.143092i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.181772 | + | 2.22867i | −0.00978628 | + | 0.119987i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7314i | 0.576090i | 0.957617 | + | 0.288045i | \(0.0930053\pi\) | ||||
−0.957617 | + | 0.288045i | \(0.906995\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.67523 | 0.517903 | 0.258952 | − | 0.965890i | \(-0.416623\pi\) | ||||
0.258952 | + | 0.965890i | \(0.416623\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.67083 | −0.249311 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.4875i | − | 1.56946i | −0.619838 | − | 0.784730i | \(-0.712802\pi\) | ||
0.619838 | − | 0.784730i | \(-0.287198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.310765 | − | 3.81022i | 0.0164937 | − | 0.202225i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.00754075i | − | 0.000399099i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.53528 | −0.239363 | −0.119681 | − | 0.992812i | \(-0.538187\pi\) | ||||
−0.119681 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.7991 | 1.72627 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.76587i | − | 0.407602i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0211 | − | 1.14358i | −0.733900 | − | 0.0598576i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.15285i | − | 0.425576i | −0.977098 | − | 0.212788i | \(-0.931746\pi\) | ||
0.977098 | − | 0.212788i | \(-0.0682543\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.69330 | 0.452555 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.32146 | −0.0686066 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.9482i | 1.49888i | 0.662070 | + | 0.749442i | \(0.269678\pi\) | ||||
−0.662070 | + | 0.749442i | \(0.730322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.8488 | − | 2.70256i | −0.560229 | − | 0.139559i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 30.3467i | − | 1.56294i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.46596 | −0.126668 | −0.0633338 | − | 0.997992i | \(-0.520173\pi\) | ||||
−0.0633338 | + | 0.997992i | \(0.520173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.6764 | 1.05928 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 19.0579i | − | 0.973813i | −0.873454 | − | 0.486906i | \(-0.838125\pi\) | ||
0.873454 | − | 0.486906i | \(-0.161875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.83224 | − | 0.149439i | −0.0933796 | − | 0.00761612i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.83269i | − | 0.398158i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.4975 | −1.90120 | −0.950599 | − | 0.310421i | \(-0.899530\pi\) | ||||
−0.950599 | + | 0.310421i | \(0.899530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0397340 | 0.00200943 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.3253i | − | 0.924391i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.78510 | + | 21.8868i | −0.0898183 | + | 1.10124i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.171284i | − | 0.00859652i | −0.999991 | − | 0.00429826i | \(-0.998632\pi\) | ||
0.999991 | − | 0.00429826i | \(-0.00136818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.36588 | −0.0683798 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.7490 | −1.13603 | −0.568015 | − | 0.823018i | \(-0.692289\pi\) | ||||
−0.568015 | + | 0.823018i | \(0.692289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.8621i | 2.13512i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.181772 | + | 2.22867i | −0.00903233 | + | 0.110743i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1640i | 0.652515i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0110 | 0.544460 | 0.272230 | − | 0.962232i | \(-0.412239\pi\) | ||||
0.272230 | + | 0.962232i | \(0.412239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.46899 | −0.171113 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 0.881282i | − | 0.0433651i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.930694 | − | 0.0759082i | −0.0456860 | − | 0.00372619i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.40878i | 0.313839i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9587 | 1.51243 | 0.756215 | − | 0.654323i | \(-0.227046\pi\) | ||||
0.756215 | + | 0.654323i | \(0.227046\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0710 | 0.880727 | 0.440364 | − | 0.897819i | \(-0.354850\pi\) | ||||
0.440364 | + | 0.897819i | \(0.354850\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.03127i | − | 0.244629i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.0321932 | + | 0.196044i | −0.00156160 | + | 0.00950954i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.49249i | 0.0722267i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.2339 | 0.976900 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.0949 | 1.30512 | 0.652558 | − | 0.757738i | \(-0.273696\pi\) | ||||
0.652558 | + | 0.757738i | \(0.273696\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 35.7515i | − | 1.71811i | −0.511887 | − | 0.859053i | \(-0.671053\pi\) | ||
0.511887 | − | 0.859053i | \(-0.328947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.4798 | − | 1.18099i | −0.694254 | − | 0.0566239i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7.19716i | − | 0.344287i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.8294 | 1.32822 | 0.664112 | − | 0.747633i | \(-0.268810\pi\) | ||||
0.664112 | + | 0.747633i | \(0.268810\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.96398 | −0.331618 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.72908i | 0.414731i | 0.978264 | + | 0.207366i | \(0.0664889\pi\) | ||||
−0.978264 | + | 0.207366i | \(0.933511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.712694 | + | 8.73819i | −0.0337849 | + | 0.414230i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.9989i | 0.662126i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.6145 | −1.44479 | −0.722394 | − | 0.691481i | \(-0.756958\pi\) | ||||
−0.722394 | + | 0.691481i | \(0.756958\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.6590 | −1.77329 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 14.5758i | − | 0.684831i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.161129 | − | 1.97557i | 0.00755385 | − | 0.0926161i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 27.4809i | − | 1.28550i | −0.766074 | − | 0.642752i | \(-0.777793\pi\) | ||
0.766074 | − | 0.642752i | \(-0.222207\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0397340 | 0.00185462 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.3722 | 1.18170 | 0.590850 | − | 0.806782i | \(-0.298793\pi\) | ||||
0.590850 | + | 0.806782i | \(0.298793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2448i | 1.49854i | 0.662264 | + | 0.749271i | \(0.269596\pi\) | ||||
−0.662264 | + | 0.749271i | \(0.730404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.4515 | + | 1.66804i | 0.948415 | + | 0.0773536i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.845923i | 0.0391446i | 0.999808 | + | 0.0195723i | \(0.00623046\pi\) | ||||
−0.999808 | + | 0.0195723i | \(0.993770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.479891 | −0.0221593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.9563 | −0.873459 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.9309i | 1.56014i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.5102 | + | 5.83128i | 1.62932 | + | 0.267557i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.96306i | − | 0.318816i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.01308 | 0.366127 | 0.183063 | − | 0.983101i | \(-0.441399\pi\) | ||||
0.183063 | + | 0.983101i | \(0.441399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.1938 | −0.647180 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.189781i | 0.00863534i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.130351 | − | 0.0106316i | −0.00591895 | − | 0.000482755i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.2251i | − | 0.780544i | −0.920700 | − | 0.390272i | \(-0.872381\pi\) | ||
0.920700 | − | 0.390272i | \(-0.127619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.2785 | −0.600474 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.41331 | −0.424817 | −0.212408 | − | 0.977181i | \(-0.568131\pi\) | ||||
−0.212408 | + | 0.977181i | \(0.568131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.258154i | 0.0116267i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.787429 | − | 9.65450i | 0.0353923 | − | 0.433937i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.324457i | − | 0.0145539i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.17655 | 0.410799 | 0.205399 | − | 0.978678i | \(-0.434151\pi\) | ||||
0.205399 | + | 0.978678i | \(0.434151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9737 | 0.624300 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.02474i | − | 0.224042i | −0.993706 | − | 0.112021i | \(-0.964268\pi\) | ||
0.993706 | − | 0.112021i | \(-0.0357324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.20255 | − | 14.7442i | 0.0535127 | − | 0.656107i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.81667i | 0.391562i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3326 | 0.635282 | 0.317641 | − | 0.948211i | \(-0.397109\pi\) | ||||
0.317641 | + | 0.948211i | \(0.397109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.19396 | −0.0528178 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.19716i | − | 0.317762i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.7171 | + | 3.07624i | 1.66201 | + | 0.135555i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.7952i | 0.958554i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.7917 | −0.561493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.4727 | −1.11598 | −0.557991 | − | 0.829847i | \(-0.688427\pi\) | ||||
−0.557991 | + | 0.829847i | \(0.688427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7464i | 0.688543i | 0.938870 | + | 0.344271i | \(0.111874\pi\) | ||||
−0.938870 | + | 0.344271i | \(0.888126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.936364 | − | 0.153764i | −0.0408663 | − | 0.00671082i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.364621i | − | 0.0158831i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.64368 | 0.201518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 40.6050i | − | 1.75880i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.1743 | − | 3.19509i | −1.69365 | − | 0.138136i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0511629i | 0.00220784i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.1677 | 1.29941 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.58372 | −0.240063 | −0.120031 | − | 0.992770i | \(-0.538300\pi\) | ||||
−0.120031 | + | 0.992770i | \(0.538300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 21.7448i | − | 0.933161i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0443229 | + | 0.543434i | −0.00189859 | + | 0.0232781i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.9544i | − | 0.596648i | −0.954465 | − | 0.298324i | \(-0.903572\pi\) | ||
0.954465 | − | 0.298324i | \(-0.0964276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.86428 | −0.335639 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.7605 | 1.99206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.86376i | 0.0792550i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.552370 | + | 6.77249i | −0.0234468 | + | 0.287476i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.6343i | 1.29802i | 0.760781 | + | 0.649009i | \(0.224816\pi\) | ||||
−0.760781 | + | 0.649009i | \(0.775184\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.5852 | −1.54739 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.172126 | −0.00726716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 40.9163i | − | 1.72442i | −0.506553 | − | 0.862209i | \(-0.669080\pi\) | ||
0.506553 | − | 0.862209i | \(-0.330920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.72906 | + | 0.222584i | 0.114812 | + | 0.00936420i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.189781i | 0.00797005i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.2131 | −0.721612 | −0.360806 | − | 0.932641i | \(-0.617498\pi\) | ||||
−0.360806 | + | 0.932641i | \(0.617498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.7070 | −0.615469 | −0.307734 | − | 0.951472i | \(-0.599571\pi\) | ||||
−0.307734 | + | 0.951472i | \(0.599571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.3680i | 0.850887i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.810219 | − | 4.93392i | 0.0337885 | − | 0.205759i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7617i | 0.656168i | 0.944648 | + | 0.328084i | \(0.106403\pi\) | ||||
−0.944648 | + | 0.328084i | \(0.893597\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.8592 | 0.659086 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0792528 | −0.00328796 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.1637i | 1.24925i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.4097 | + | 0.849027i | 0.430389 | + | 0.0351029i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.4757i | 1.67061i | 0.549787 | + | 0.835305i | \(0.314709\pi\) | ||||
−0.549787 | + | 0.835305i | \(0.685291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −66.0451 | −2.72134 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.16978 | −0.253791 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.8541i | 1.47235i | 0.676791 | + | 0.736175i | \(0.263370\pi\) | ||||
−0.676791 | + | 0.736175i | \(0.736630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.00137070 | + | 0.0168058i | −5.61932e−5 | + | 0.000688972i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.81534i | − | 0.197079i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0263 | 0.859112 | 0.429556 | − | 0.903040i | \(-0.358670\pi\) | ||||
0.429556 | + | 0.903040i | \(0.358670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.16524 | 0.251485 | 0.125743 | − | 0.992063i | \(-0.459869\pi\) | ||||
0.125743 | + | 0.992063i | \(0.459869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.52865i | − | 0.102975i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.41162 | + | 17.3075i | −0.0573904 | + | 0.703651i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.5809i | − | 1.11947i | −0.828671 | − | 0.559736i | \(-0.810903\pi\) | ||
0.828671 | − | 0.559736i | \(-0.189097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.23302 | −0.0499645 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.5002 | −0.950716 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.7384i | 0.878005i | 0.898486 | + | 0.439003i | \(0.144668\pi\) | ||||
−0.898486 | + | 0.439003i | \(0.855332\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.3745 | − | 1.58020i | −0.781255 | − | 0.0637198i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.2023i | 1.01461i | 0.861767 | + | 0.507304i | \(0.169358\pi\) | ||||
−0.861767 | + | 0.507304i | \(0.830642\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.45053 | −0.259269 | −0.129634 | − | 0.991562i | \(-0.541380\pi\) | ||||
−0.129634 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.744096i | 0.0298116i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.6871 | + | 7.99511i | 0.947484 | + | 0.319804i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.1778i | 1.24512i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.120744 | 0.00481438 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0614 | −0.957871 | −0.478935 | − | 0.877850i | \(-0.658977\pi\) | ||||
−0.478935 | + | 0.877850i | \(0.658977\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.9874i | 0.953412i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.0809 | − | 3.75839i | −1.82866 | − | 0.149147i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5276i | 1.28879i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.70964 | 0.0676323 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0204978 | 0.000809615 | 0.000404807 | − | 1.00000i | \(-0.499871\pi\) | ||||
0.000404807 | 1.00000i | \(0.499871\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.4037i | 1.82998i | 0.403471 | + | 0.914992i | \(0.367804\pi\) | ||||
−0.403471 | + | 0.914992i | \(0.632196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.42376 | + | 17.4565i | −0.0560607 | + | 0.687348i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.8386i | − | 0.661992i | −0.943632 | − | 0.330996i | \(-0.892615\pi\) | ||
0.943632 | − | 0.330996i | \(-0.107385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.1162 | −0.789631 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.74154 | 0.0682562 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.9087i | 1.60088i | 0.599413 | + | 0.800440i | \(0.295401\pi\) | ||||
−0.599413 | + | 0.800440i | \(0.704599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.33103 | + | 40.8411i | −0.130154 | + | 1.59579i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.29127i | − | 0.245446i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.3970 | 1.49573 | 0.747867 | − | 0.663849i | \(-0.231078\pi\) | ||||
0.747867 | + | 0.663849i | \(0.231078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8022 | −0.420155 | −0.210078 | − | 0.977685i | \(-0.567372\pi\) | ||||
−0.210078 | + | 0.977685i | \(0.567372\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.185591i | − | 0.00720775i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04410 | + | 0.248280i | 0.118045 | + | 0.00962787i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.49707i | − | 0.251568i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.4215 | −0.441581 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.0677 | 1.31517 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.3951i | − | 0.439247i | −0.975585 | − | 0.219624i | \(-0.929517\pi\) | ||
0.975585 | − | 0.219624i | \(-0.0704829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.810219 | − | 4.93392i | 0.0311853 | − | 0.189907i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.87400i | 0.148890i | 0.997225 | + | 0.0744449i | \(0.0237185\pi\) | ||||
−0.997225 | + | 0.0744449i | \(0.976282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0111000 | −0.000425979 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.7360 | −0.603004 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 27.9517i | − | 1.06954i | −0.844997 | − | 0.534770i | \(-0.820398\pi\) | ||
0.844997 | − | 0.534770i | \(-0.179602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.73122 | + | 0.630565i | 0.295395 | + | 0.0240927i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.46335i | 0.132135i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.5233 | −1.23904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1448 | 1.33697 | 0.668485 | − | 0.743726i | \(-0.266943\pi\) | ||||
0.668485 | + | 0.743726i | \(0.266943\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.822124i | − | 0.0312299i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.16494 | − | 14.2830i | 0.0441886 | − | 0.541786i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.345420i | 0.0130837i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.319746 | −0.0120939 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.89656 | −0.298249 | −0.149124 | − | 0.988818i | \(-0.547645\pi\) | ||||
−0.149124 | + | 0.988818i | \(0.547645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 21.8708i | − | 0.824872i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.914544 | + | 11.2130i | −0.0344437 | + | 0.422307i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.25553i | − | 0.0472191i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3686 | 0.614734 | 0.307367 | − | 0.951591i | \(-0.400552\pi\) | ||||
0.307367 | + | 0.951591i | \(0.400552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.82056 | −0.368300 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.17655i | 0.343665i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.0945 | − | 3.67795i | −1.68644 | − | 0.137547i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 2.93697i | − | 0.109683i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.0861 | −0.450737 | −0.225368 | − | 0.974274i | \(-0.572359\pi\) | ||||
−0.225368 | + | 0.974274i | \(0.572359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.21178 | 0.119613 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.6764i | 0.694583i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.0560 | + | 5.26405i | 1.19053 | + | 0.195502i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.89415i | − | 0.292778i | −0.989227 | − | 0.146389i | \(-0.953235\pi\) | ||
0.989227 | − | 0.146389i | \(-0.0467651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.311224 | 0.0115110 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17.1444i | − | 0.633242i | −0.948552 | − | 0.316621i | \(-0.897452\pi\) | ||
0.948552 | − | 0.316621i | \(-0.102548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.5204 | + | 1.26586i | 0.572479 | + | 0.0466919i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.9540i | 0.403497i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.1409 | 1.58696 | 0.793482 | − | 0.608593i | \(-0.208266\pi\) | ||||
0.793482 | + | 0.608593i | \(0.208266\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.6167 | −1.23494 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 41.0320i | − | 1.50532i | −0.658410 | − | 0.752660i | \(-0.728771\pi\) | ||
0.658410 | − | 0.752660i | \(-0.271229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.54461 | − | 31.1989i | 0.0932273 | − | 1.14304i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 0.417601i | − | 0.0152792i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.33587 | −0.121890 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.4190 | 1.18299 | 0.591494 | − | 0.806309i | \(-0.298538\pi\) | ||||
0.591494 | + | 0.806309i | \(0.298538\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.76059i | 0.137043i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.64947 | + | 32.4846i | −0.0964242 | + | 1.18224i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31.1373i | − | 1.13170i | −0.824507 | − | 0.565852i | \(-0.808547\pi\) | ||
0.824507 | − | 0.565852i | \(-0.191453\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.33196 | 0.157240 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.4836 | −1.57628 | −0.788139 | − | 0.615497i | \(-0.788955\pi\) | ||||
−0.788139 | + | 0.615497i | \(0.788955\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0462758i | 0.00167530i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0885538 | − | 0.00722253i | −0.00320167 | − | 0.000261131i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 21.6898i | − | 0.783175i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.35659 | 0.157103 | 0.0785514 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785514 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.1810 | −0.942884 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.3629i | 1.88336i | 0.336508 | + | 0.941681i | \(0.390754\pi\) | ||||
−0.336508 | + | 0.941681i | \(0.609246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45.2764 | − | 7.43502i | −1.62637 | − | 0.267074i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.576708i | 0.0206893i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 62.5671 | 2.24170 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.40609 | −0.265011 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.49707i | − | 0.232186i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.2472 | + | 3.44572i | 1.50787 | + | 0.122983i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0229i | 0.535507i | 0.963487 | + | 0.267754i | \(0.0862813\pi\) | ||||
−0.963487 | + | 0.267754i | \(0.913719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6844 | −0.807587 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.232392 | 0.00826289 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.7327i | 1.30442i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.26569 | + | 15.5183i | −0.0448894 | + | 0.550379i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 31.3217i | − | 1.10947i | −0.832026 | − | 0.554737i | \(-0.812819\pi\) | ||
0.832026 | − | 0.554737i | \(-0.187181\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.199912 | 0.00707239 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.92081 | −0.138535 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.2535i | 0.961756i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0344969 | − | 0.422959i | 0.00121586 | − | 0.0149073i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.570220i | 0.0200727i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.0261 | 0.774397 | 0.387198 | − | 0.921996i | \(-0.373443\pi\) | ||||
0.387198 | + | 0.921996i | \(0.373443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.2449 | 0.781125 | 0.390563 | − | 0.920576i | \(-0.372281\pi\) | ||||
0.390563 | + | 0.920576i | \(0.372281\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 21.9506i | − | 0.769843i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.5933 | + | 2.41366i | 1.03661 | + | 0.0845468i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 56.3731i | − | 1.97225i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.886435 | 0.0309746 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 55.8300 | 1.94848 | 0.974240 | − | 0.225513i | \(-0.0724058\pi\) | ||||
0.974240 | + | 0.225513i | \(0.0724058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 8.57848i | − | 0.299027i | −0.988760 | − | 0.149514i | \(-0.952229\pi\) | ||
0.988760 | − | 0.149514i | \(-0.0477708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.50984 | + | 21.3735i | −0.122197 | + | 0.744131i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4646i | 0.433437i | 0.976234 | + | 0.216718i | \(0.0695354\pi\) | ||||
−0.976234 | + | 0.216718i | \(0.930465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.83650 | 0.202710 | 0.101355 | − | 0.994850i | \(-0.467682\pi\) | ||||
0.101355 | + | 0.994850i | \(0.467682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.5514 | 0.435403 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.276707i | − | 0.00958732i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.1428 | − | 2.54003i | −1.07774 | − | 0.0879014i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.17655i | 0.317188i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.9925 | 0.759265 | 0.379633 | − | 0.925137i | \(-0.376050\pi\) | ||||
0.379633 | + | 0.925137i | \(0.376050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.2119 | 0.455583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 21.7956i | − | 0.750680i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.60262 | − | 19.6494i | 0.0551320 | − | 0.675961i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.47381i | 0.0506409i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.0765 | 0.826304 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.03881 | −0.104169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.7842i | 1.05403i | 0.849856 | + | 0.527015i | \(0.176689\pi\) | ||||
−0.849856 | + | 0.527015i | \(0.823311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.30824 | + | 16.0401i | −0.0447410 | + | 0.548559i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.0207i | 0.513098i | 0.966531 | + | 0.256549i | \(0.0825855\pi\) | ||||
−0.966531 | + | 0.256549i | \(0.917414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.352932 | −0.0120419 | −0.00602094 | − | 0.999982i | \(-0.501917\pi\) | ||||
−0.00602094 | + | 0.999982i | \(0.501917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.64982 | −0.0562259 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 8.55180i | − | 0.291107i | −0.989350 | − | 0.145553i | \(-0.953504\pi\) | ||
0.989350 | − | 0.145553i | \(-0.0464962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.5084 | + | 2.32517i | 0.969315 | + | 0.0790582i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.9984i | − | 0.577297i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.5423 | 1.44315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.8109 | −0.400198 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.0584885i | − | 0.00197954i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.05889 | + | 0.512894i | 0.0696033 | + | 0.0173390i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9633i | 1.58584i | 0.609327 | + | 0.792919i | \(0.291440\pi\) | ||||
−0.609327 | + | 0.792919i | \(0.708560\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.2212 | −0.918147 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.9481 | −1.61541 | −0.807706 | − | 0.589585i | \(-0.799291\pi\) | ||||
−0.807706 | + | 0.589585i | \(0.799291\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6286i | 1.67014i | 0.550147 | + | 0.835068i | \(0.314572\pi\) | ||||
−0.550147 | + | 0.835068i | \(0.685428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.3492 | − | 0.844091i | −0.347885 | − | 0.0283738i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.1853i | 1.31572i | 0.753142 | + | 0.657858i | \(0.228537\pi\) | ||||
−0.753142 | + | 0.657858i | \(0.771463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.92399 | −0.131606 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.33196 | 0.145126 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 36.2108i | − | 1.21175i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.00929999 | − | 0.114025i | 0.000310865 | − | 0.00381144i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.67083i | 0.155955i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −59.6207 | −1.98846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.276670 | 0.00921721 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.48650i | 0.0494675i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.95261 | + | 48.4620i | −0.131389 | + | 1.61093i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.3323i | − | 1.30601i | −0.757355 | − | 0.653004i | \(-0.773509\pi\) | ||
0.757355 | − | 0.653004i | \(-0.226491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.61569 | 0.219429 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8676 | −0.591980 | −0.295990 | − | 0.955191i | \(-0.595649\pi\) | ||||
−0.295990 | + | 0.955191i | \(0.595649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.80903i | 0.0598702i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.5269 | + | 1.42951i | 0.579420 | + | 0.0472580i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.47780i | 0.114847i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0858 | 0.662570 | 0.331285 | − | 0.943531i | \(-0.392518\pi\) | ||||
0.331285 | + | 0.943531i | \(0.392518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.48076 | 0.213548 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.98544i | − | 0.262844i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.46210 | − | 14.9932i | 0.0809533 | − | 0.492974i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.9236i | 0.555844i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.6085 | 1.85727 | 0.928633 | − | 0.371001i | \(-0.120985\pi\) | ||||
0.928633 | + | 0.371001i | \(0.120985\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50.1209 | −1.64265 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 4.11457i | − | 0.134705i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.383612 | + | 0.0312877i | 0.0125454 | + | 0.00102322i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.1869i | 1.57420i | 0.616826 | + | 0.787099i | \(0.288418\pi\) | ||||
−0.616826 | + | 0.787099i | \(0.711582\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.760034 | −0.0248028 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.7084 | −0.349083 | −0.174542 | − | 0.984650i | \(-0.555844\pi\) | ||||
−0.174542 | + | 0.984650i | \(0.555844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.69330i | − | 0.283093i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0344969 | − | 0.422959i | 0.00112218 | − | 0.0137589i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.5646i | 0.570774i | 0.958412 | + | 0.285387i | \(0.0921221\pi\) | ||||
−0.958412 | + | 0.285387i | \(0.907878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.3855 | −0.953893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.48188 | 0.242617 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.3058i | 1.17606i | 0.808839 | + | 0.588031i | \(0.200097\pi\) | ||||
−0.808839 | + | 0.588031i | \(0.799903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.70234 | − | 45.3936i | 0.119805 | − | 1.46890i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.1450i | 0.909800i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.658348 | 0.0212592 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.2091 | 1.71642 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 17.5775i | − | 0.566426i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.3449 | − | 2.88276i | −1.13779 | − | 0.0927994i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30.4808i | − | 0.980195i | −0.871668 | − | 0.490098i | \(-0.836961\pi\) | ||
0.871668 | − | 0.490098i | \(-0.163039\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.285972 | 0.00918674 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.2929 | 1.38934 | 0.694668 | − | 0.719330i | \(-0.255551\pi\) | ||||
0.694668 | + | 0.719330i | \(0.255551\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.21626i | − | 0.0389916i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.0455 | − | 3.78440i | −0.738047 | − | 0.121198i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 6.01624i | − | 0.192477i | −0.995358 | − | 0.0962383i | \(-0.969319\pi\) | ||
0.995358 | − | 0.0962383i | \(-0.0306811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9848 | 0.542836 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.243838 | −0.00778515 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0552i | 1.14998i | 0.818159 | + | 0.574992i | \(0.194995\pi\) | ||||
−0.818159 | + | 0.574992i | \(0.805005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.7504 | + | 1.12149i | 0.438124 | + | 0.0357338i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.954839i | 0.0303929i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.83269 | −0.249065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.5584 | −1.63781 | −0.818904 | − | 0.573931i | \(-0.805418\pi\) | ||||
−0.818904 | + | 0.573931i | \(0.805418\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 28.5981i | − | 0.907532i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.875293 | + | 10.7318i | −0.0277487 | + | 0.340220i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.9389i | 0.599799i | 0.953971 | + | 0.299900i | \(0.0969532\pi\) | ||||
−0.953971 | + | 0.299900i | \(0.903047\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.03881 | −0.0961436 |
(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 | 1380.2.f.b.829.4 | ✓ | 14 | |
3.2 | odd | 2 | 4140.2.f.c.829.7 | 14 | |||
5.2 | odd | 4 | 6900.2.a.bc.1.4 | 7 | |||
5.3 | odd | 4 | 6900.2.a.bd.1.4 | 7 | |||
5.4 | even | 2 | inner | 1380.2.f.b.829.11 | yes | 14 | |
15.14 | odd | 2 | 4140.2.f.c.829.8 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.f.b.829.4 | ✓ | 14 | 1.1 | even | 1 | trivial | |
1380.2.f.b.829.11 | yes | 14 | 5.4 | even | 2 | inner | |
4140.2.f.c.829.7 | 14 | 3.2 | odd | 2 | |||
4140.2.f.c.829.8 | 14 | 15.14 | odd | 2 | |||
6900.2.a.bc.1.4 | 7 | 5.2 | odd | 4 | |||
6900.2.a.bd.1.4 | 7 | 5.3 | odd | 4 |