Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.a (trivial) |
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: | yes |
Analytic conductor: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.03566\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.03566 | −0.597939 | −0.298969 | − | 0.954263i | \(-0.596643\pi\) | ||||
−0.298969 | + | 0.954263i | \(0.596643\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.52120 | 1.12752 | 0.563758 | − | 0.825940i | \(-0.309355\pi\) | ||||
0.563758 | + | 0.825940i | \(0.309355\pi\) | |||||||
\(6\) | 1.03566 | 0.422807 | ||||||||
\(7\) | −1.73580 | −0.656070 | −0.328035 | − | 0.944666i | \(-0.606386\pi\) | ||||
−0.328035 | + | 0.944666i | \(0.606386\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.92741 | −0.642469 | ||||||||
\(10\) | −2.52120 | −0.797274 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.03566 | −0.298969 | ||||||||
\(13\) | −0.661596 | −0.183494 | −0.0917468 | − | 0.995782i | \(-0.529245\pi\) | ||||
−0.0917468 | + | 0.995782i | \(0.529245\pi\) | |||||||
\(14\) | 1.73580 | 0.463911 | ||||||||
\(15\) | −2.61111 | −0.674185 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.09650 | −0.508475 | −0.254237 | − | 0.967142i | \(-0.581824\pi\) | ||||
−0.254237 | + | 0.967142i | \(0.581824\pi\) | |||||||
\(18\) | 1.92741 | 0.454294 | ||||||||
\(19\) | 0.592039 | 0.135823 | 0.0679116 | − | 0.997691i | \(-0.478366\pi\) | ||||
0.0679116 | + | 0.997691i | \(0.478366\pi\) | |||||||
\(20\) | 2.52120 | 0.563758 | ||||||||
\(21\) | 1.79770 | 0.392290 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.91698 | −0.399718 | −0.199859 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199859 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(24\) | 1.03566 | 0.211403 | ||||||||
\(25\) | 1.35646 | 0.271291 | ||||||||
\(26\) | 0.661596 | 0.129750 | ||||||||
\(27\) | 5.10312 | 0.982096 | ||||||||
\(28\) | −1.73580 | −0.328035 | ||||||||
\(29\) | 5.77853 | 1.07305 | 0.536523 | − | 0.843885i | \(-0.319737\pi\) | ||||
0.536523 | + | 0.843885i | \(0.319737\pi\) | |||||||
\(30\) | 2.61111 | 0.476721 | ||||||||
\(31\) | 4.37227 | 0.785283 | 0.392642 | − | 0.919692i | \(-0.371561\pi\) | ||||
0.392642 | + | 0.919692i | \(0.371561\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.03566 | −0.180285 | ||||||||
\(34\) | 2.09650 | 0.359546 | ||||||||
\(35\) | −4.37630 | −0.739729 | ||||||||
\(36\) | −1.92741 | −0.321235 | ||||||||
\(37\) | −7.16641 | −1.17815 | −0.589075 | − | 0.808078i | \(-0.700508\pi\) | ||||
−0.589075 | + | 0.808078i | \(0.700508\pi\) | |||||||
\(38\) | −0.592039 | −0.0960415 | ||||||||
\(39\) | 0.685188 | 0.109718 | ||||||||
\(40\) | −2.52120 | −0.398637 | ||||||||
\(41\) | −1.33596 | −0.208642 | −0.104321 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104321 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(42\) | −1.79770 | −0.277391 | ||||||||
\(43\) | 9.79286 | 1.49340 | 0.746698 | − | 0.665163i | \(-0.231638\pi\) | ||||
0.746698 | + | 0.665163i | \(0.231638\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −4.85938 | −0.724394 | ||||||||
\(46\) | 1.91698 | 0.282644 | ||||||||
\(47\) | 1.79226 | 0.261427 | 0.130714 | − | 0.991420i | \(-0.458273\pi\) | ||||
0.130714 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(48\) | −1.03566 | −0.149485 | ||||||||
\(49\) | −3.98701 | −0.569572 | ||||||||
\(50\) | −1.35646 | −0.191832 | ||||||||
\(51\) | 2.17126 | 0.304037 | ||||||||
\(52\) | −0.661596 | −0.0917468 | ||||||||
\(53\) | 9.08836 | 1.24838 | 0.624191 | − | 0.781272i | \(-0.285429\pi\) | ||||
0.624191 | + | 0.781272i | \(0.285429\pi\) | |||||||
\(54\) | −5.10312 | −0.694447 | ||||||||
\(55\) | 2.52120 | 0.339959 | ||||||||
\(56\) | 1.73580 | 0.231956 | ||||||||
\(57\) | −0.613152 | −0.0812139 | ||||||||
\(58\) | −5.77853 | −0.758759 | ||||||||
\(59\) | −9.26718 | −1.20648 | −0.603242 | − | 0.797558i | \(-0.706125\pi\) | ||||
−0.603242 | + | 0.797558i | \(0.706125\pi\) | |||||||
\(60\) | −2.61111 | −0.337093 | ||||||||
\(61\) | −2.08729 | −0.267250 | −0.133625 | − | 0.991032i | \(-0.542662\pi\) | ||||
−0.133625 | + | 0.991032i | \(0.542662\pi\) | |||||||
\(62\) | −4.37227 | −0.555279 | ||||||||
\(63\) | 3.34559 | 0.421505 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.66802 | −0.206892 | ||||||||
\(66\) | 1.03566 | 0.127481 | ||||||||
\(67\) | 0.726579 | 0.0887657 | 0.0443829 | − | 0.999015i | \(-0.485868\pi\) | ||||
0.0443829 | + | 0.999015i | \(0.485868\pi\) | |||||||
\(68\) | −2.09650 | −0.254237 | ||||||||
\(69\) | 1.98534 | 0.239007 | ||||||||
\(70\) | 4.37630 | 0.523067 | ||||||||
\(71\) | −7.98201 | −0.947290 | −0.473645 | − | 0.880716i | \(-0.657062\pi\) | ||||
−0.473645 | + | 0.880716i | \(0.657062\pi\) | |||||||
\(72\) | 1.92741 | 0.227147 | ||||||||
\(73\) | 11.4544 | 1.34063 | 0.670316 | − | 0.742076i | \(-0.266159\pi\) | ||||
0.670316 | + | 0.742076i | \(0.266159\pi\) | |||||||
\(74\) | 7.16641 | 0.833078 | ||||||||
\(75\) | −1.40483 | −0.162216 | ||||||||
\(76\) | 0.592039 | 0.0679116 | ||||||||
\(77\) | −1.73580 | −0.197813 | ||||||||
\(78\) | −0.685188 | −0.0775823 | ||||||||
\(79\) | −14.6692 | −1.65041 | −0.825205 | − | 0.564833i | \(-0.808940\pi\) | ||||
−0.825205 | + | 0.564833i | \(0.808940\pi\) | |||||||
\(80\) | 2.52120 | 0.281879 | ||||||||
\(81\) | 0.497122 | 0.0552358 | ||||||||
\(82\) | 1.33596 | 0.147532 | ||||||||
\(83\) | −3.52418 | −0.386829 | −0.193414 | − | 0.981117i | \(-0.561956\pi\) | ||||
−0.193414 | + | 0.981117i | \(0.561956\pi\) | |||||||
\(84\) | 1.79770 | 0.196145 | ||||||||
\(85\) | −5.28569 | −0.573313 | ||||||||
\(86\) | −9.79286 | −1.05599 | ||||||||
\(87\) | −5.98460 | −0.641616 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −13.6381 | −1.44563 | −0.722816 | − | 0.691040i | \(-0.757153\pi\) | ||||
−0.722816 | + | 0.691040i | \(0.757153\pi\) | |||||||
\(90\) | 4.85938 | 0.512224 | ||||||||
\(91\) | 1.14840 | 0.120385 | ||||||||
\(92\) | −1.91698 | −0.199859 | ||||||||
\(93\) | −4.52819 | −0.469551 | ||||||||
\(94\) | −1.79226 | −0.184857 | ||||||||
\(95\) | 1.49265 | 0.153143 | ||||||||
\(96\) | 1.03566 | 0.105702 | ||||||||
\(97\) | −3.68679 | −0.374337 | −0.187168 | − | 0.982328i | \(-0.559931\pi\) | ||||
−0.187168 | + | 0.982328i | \(0.559931\pi\) | |||||||
\(98\) | 3.98701 | 0.402748 | ||||||||
\(99\) | −1.92741 | −0.193712 | ||||||||
\(100\) | 1.35646 | 0.135646 | ||||||||
\(101\) | −11.3290 | −1.12728 | −0.563641 | − | 0.826020i | \(-0.690600\pi\) | ||||
−0.563641 | + | 0.826020i | \(0.690600\pi\) | |||||||
\(102\) | −2.17126 | −0.214987 | ||||||||
\(103\) | −3.18047 | −0.313381 | −0.156690 | − | 0.987648i | \(-0.550082\pi\) | ||||
−0.156690 | + | 0.987648i | \(0.550082\pi\) | |||||||
\(104\) | 0.661596 | 0.0648748 | ||||||||
\(105\) | 4.53236 | 0.442313 | ||||||||
\(106\) | −9.08836 | −0.882740 | ||||||||
\(107\) | −7.42503 | −0.717805 | −0.358902 | − | 0.933375i | \(-0.616849\pi\) | ||||
−0.358902 | + | 0.933375i | \(0.616849\pi\) | |||||||
\(108\) | 5.10312 | 0.491048 | ||||||||
\(109\) | −9.03529 | −0.865423 | −0.432712 | − | 0.901532i | \(-0.642443\pi\) | ||||
−0.432712 | + | 0.901532i | \(0.642443\pi\) | |||||||
\(110\) | −2.52120 | −0.240387 | ||||||||
\(111\) | 7.42196 | 0.704462 | ||||||||
\(112\) | −1.73580 | −0.164017 | ||||||||
\(113\) | 0.179700 | 0.0169048 | 0.00845239 | − | 0.999964i | \(-0.497309\pi\) | ||||
0.00845239 | + | 0.999964i | \(0.497309\pi\) | |||||||
\(114\) | 0.613152 | 0.0574269 | ||||||||
\(115\) | −4.83310 | −0.450689 | ||||||||
\(116\) | 5.77853 | 0.536523 | ||||||||
\(117\) | 1.27516 | 0.117889 | ||||||||
\(118\) | 9.26718 | 0.853113 | ||||||||
\(119\) | 3.63909 | 0.333595 | ||||||||
\(120\) | 2.61111 | 0.238360 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.08729 | 0.188974 | ||||||||
\(123\) | 1.38360 | 0.124755 | ||||||||
\(124\) | 4.37227 | 0.392642 | ||||||||
\(125\) | −9.18611 | −0.821630 | ||||||||
\(126\) | −3.34559 | −0.298049 | ||||||||
\(127\) | 18.8269 | 1.67062 | 0.835309 | − | 0.549781i | \(-0.185289\pi\) | ||||
0.835309 | + | 0.549781i | \(0.185289\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.1421 | −0.892960 | ||||||||
\(130\) | 1.66802 | 0.146295 | ||||||||
\(131\) | −6.83617 | −0.597279 | −0.298639 | − | 0.954366i | \(-0.596533\pi\) | ||||
−0.298639 | + | 0.954366i | \(0.596533\pi\) | |||||||
\(132\) | −1.03566 | −0.0901427 | ||||||||
\(133\) | −1.02766 | −0.0891095 | ||||||||
\(134\) | −0.726579 | −0.0627668 | ||||||||
\(135\) | 12.8660 | 1.10733 | ||||||||
\(136\) | 2.09650 | 0.179773 | ||||||||
\(137\) | 6.70217 | 0.572605 | 0.286302 | − | 0.958139i | \(-0.407574\pi\) | ||||
0.286302 | + | 0.958139i | \(0.407574\pi\) | |||||||
\(138\) | −1.98534 | −0.169004 | ||||||||
\(139\) | −4.47060 | −0.379191 | −0.189596 | − | 0.981862i | \(-0.560718\pi\) | ||||
−0.189596 | + | 0.981862i | \(0.560718\pi\) | |||||||
\(140\) | −4.37630 | −0.369864 | ||||||||
\(141\) | −1.85617 | −0.156318 | ||||||||
\(142\) | 7.98201 | 0.669835 | ||||||||
\(143\) | −0.661596 | −0.0553254 | ||||||||
\(144\) | −1.92741 | −0.160617 | ||||||||
\(145\) | 14.5688 | 1.20988 | ||||||||
\(146\) | −11.4544 | −0.947970 | ||||||||
\(147\) | 4.12918 | 0.340569 | ||||||||
\(148\) | −7.16641 | −0.589075 | ||||||||
\(149\) | −3.72372 | −0.305059 | −0.152530 | − | 0.988299i | \(-0.548742\pi\) | ||||
−0.152530 | + | 0.988299i | \(0.548742\pi\) | |||||||
\(150\) | 1.40483 | 0.114704 | ||||||||
\(151\) | 22.8119 | 1.85641 | 0.928204 | − | 0.372072i | \(-0.121353\pi\) | ||||
0.928204 | + | 0.372072i | \(0.121353\pi\) | |||||||
\(152\) | −0.592039 | −0.0480207 | ||||||||
\(153\) | 4.04080 | 0.326680 | ||||||||
\(154\) | 1.73580 | 0.139875 | ||||||||
\(155\) | 11.0234 | 0.885419 | ||||||||
\(156\) | 0.685188 | 0.0548590 | ||||||||
\(157\) | −11.3580 | −0.906468 | −0.453234 | − | 0.891392i | \(-0.649730\pi\) | ||||
−0.453234 | + | 0.891392i | \(0.649730\pi\) | |||||||
\(158\) | 14.6692 | 1.16702 | ||||||||
\(159\) | −9.41246 | −0.746456 | ||||||||
\(160\) | −2.52120 | −0.199318 | ||||||||
\(161\) | 3.32749 | 0.262243 | ||||||||
\(162\) | −0.497122 | −0.0390576 | ||||||||
\(163\) | −16.5868 | −1.29918 | −0.649590 | − | 0.760285i | \(-0.725059\pi\) | ||||
−0.649590 | + | 0.760285i | \(0.725059\pi\) | |||||||
\(164\) | −1.33596 | −0.104321 | ||||||||
\(165\) | −2.61111 | −0.203275 | ||||||||
\(166\) | 3.52418 | 0.273529 | ||||||||
\(167\) | −11.2683 | −0.871970 | −0.435985 | − | 0.899954i | \(-0.643600\pi\) | ||||
−0.435985 | + | 0.899954i | \(0.643600\pi\) | |||||||
\(168\) | −1.79770 | −0.138695 | ||||||||
\(169\) | −12.5623 | −0.966330 | ||||||||
\(170\) | 5.28569 | 0.405394 | ||||||||
\(171\) | −1.14110 | −0.0872622 | ||||||||
\(172\) | 9.79286 | 0.746698 | ||||||||
\(173\) | 22.3955 | 1.70270 | 0.851348 | − | 0.524601i | \(-0.175785\pi\) | ||||
0.851348 | + | 0.524601i | \(0.175785\pi\) | |||||||
\(174\) | 5.98460 | 0.453691 | ||||||||
\(175\) | −2.35453 | −0.177986 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 9.59765 | 0.721404 | ||||||||
\(178\) | 13.6381 | 1.02222 | ||||||||
\(179\) | 10.1374 | 0.757708 | 0.378854 | − | 0.925456i | \(-0.376318\pi\) | ||||
0.378854 | + | 0.925456i | \(0.376318\pi\) | |||||||
\(180\) | −4.85938 | −0.362197 | ||||||||
\(181\) | −7.64184 | −0.568013 | −0.284007 | − | 0.958822i | \(-0.591664\pi\) | ||||
−0.284007 | + | 0.958822i | \(0.591664\pi\) | |||||||
\(182\) | −1.14840 | −0.0851248 | ||||||||
\(183\) | 2.16172 | 0.159799 | ||||||||
\(184\) | 1.91698 | 0.141322 | ||||||||
\(185\) | −18.0680 | −1.32838 | ||||||||
\(186\) | 4.52819 | 0.332023 | ||||||||
\(187\) | −2.09650 | −0.153311 | ||||||||
\(188\) | 1.79226 | 0.130714 | ||||||||
\(189\) | −8.85799 | −0.644324 | ||||||||
\(190\) | −1.49265 | −0.108288 | ||||||||
\(191\) | 0.618048 | 0.0447204 | 0.0223602 | − | 0.999750i | \(-0.492882\pi\) | ||||
0.0223602 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(192\) | −1.03566 | −0.0747424 | ||||||||
\(193\) | −16.5394 | −1.19053 | −0.595265 | − | 0.803529i | \(-0.702953\pi\) | ||||
−0.595265 | + | 0.803529i | \(0.702953\pi\) | |||||||
\(194\) | 3.68679 | 0.264696 | ||||||||
\(195\) | 1.72750 | 0.123709 | ||||||||
\(196\) | −3.98701 | −0.284786 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 1.92741 | 0.136975 | ||||||||
\(199\) | −3.36737 | −0.238706 | −0.119353 | − | 0.992852i | \(-0.538082\pi\) | ||||
−0.119353 | + | 0.992852i | \(0.538082\pi\) | |||||||
\(200\) | −1.35646 | −0.0959159 | ||||||||
\(201\) | −0.752489 | −0.0530765 | ||||||||
\(202\) | 11.3290 | 0.797109 | ||||||||
\(203\) | −10.0304 | −0.703994 | ||||||||
\(204\) | 2.17126 | 0.152018 | ||||||||
\(205\) | −3.36822 | −0.235247 | ||||||||
\(206\) | 3.18047 | 0.221594 | ||||||||
\(207\) | 3.69481 | 0.256807 | ||||||||
\(208\) | −0.661596 | −0.0458734 | ||||||||
\(209\) | 0.592039 | 0.0409522 | ||||||||
\(210\) | −4.53236 | −0.312762 | ||||||||
\(211\) | 15.0329 | 1.03491 | 0.517453 | − | 0.855712i | \(-0.326880\pi\) | ||||
0.517453 | + | 0.855712i | \(0.326880\pi\) | |||||||
\(212\) | 9.08836 | 0.624191 | ||||||||
\(213\) | 8.26665 | 0.566421 | ||||||||
\(214\) | 7.42503 | 0.507565 | ||||||||
\(215\) | 24.6898 | 1.68383 | ||||||||
\(216\) | −5.10312 | −0.347223 | ||||||||
\(217\) | −7.58938 | −0.515201 | ||||||||
\(218\) | 9.03529 | 0.611947 | ||||||||
\(219\) | −11.8628 | −0.801616 | ||||||||
\(220\) | 2.52120 | 0.169979 | ||||||||
\(221\) | 1.38703 | 0.0933019 | ||||||||
\(222\) | −7.42196 | −0.498130 | ||||||||
\(223\) | 3.89916 | 0.261107 | 0.130553 | − | 0.991441i | \(-0.458325\pi\) | ||||
0.130553 | + | 0.991441i | \(0.458325\pi\) | |||||||
\(224\) | 1.73580 | 0.115978 | ||||||||
\(225\) | −2.61444 | −0.174296 | ||||||||
\(226\) | −0.179700 | −0.0119535 | ||||||||
\(227\) | 15.1464 | 1.00530 | 0.502652 | − | 0.864489i | \(-0.332358\pi\) | ||||
0.502652 | + | 0.864489i | \(0.332358\pi\) | |||||||
\(228\) | −0.613152 | −0.0406070 | ||||||||
\(229\) | −24.1376 | −1.59506 | −0.797529 | − | 0.603281i | \(-0.793860\pi\) | ||||
−0.797529 | + | 0.603281i | \(0.793860\pi\) | |||||||
\(230\) | 4.83310 | 0.318685 | ||||||||
\(231\) | 1.79770 | 0.118280 | ||||||||
\(232\) | −5.77853 | −0.379379 | ||||||||
\(233\) | −8.42912 | −0.552210 | −0.276105 | − | 0.961127i | \(-0.589044\pi\) | ||||
−0.276105 | + | 0.961127i | \(0.589044\pi\) | |||||||
\(234\) | −1.27516 | −0.0833601 | ||||||||
\(235\) | 4.51864 | 0.294764 | ||||||||
\(236\) | −9.26718 | −0.603242 | ||||||||
\(237\) | 15.1923 | 0.986844 | ||||||||
\(238\) | −3.63909 | −0.235887 | ||||||||
\(239\) | 17.0649 | 1.10384 | 0.551918 | − | 0.833899i | \(-0.313896\pi\) | ||||
0.551918 | + | 0.833899i | \(0.313896\pi\) | |||||||
\(240\) | −2.61111 | −0.168546 | ||||||||
\(241\) | −2.91512 | −0.187779 | −0.0938896 | − | 0.995583i | \(-0.529930\pi\) | ||||
−0.0938896 | + | 0.995583i | \(0.529930\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −15.8242 | −1.01512 | ||||||||
\(244\) | −2.08729 | −0.133625 | ||||||||
\(245\) | −10.0520 | −0.642202 | ||||||||
\(246\) | −1.38360 | −0.0882151 | ||||||||
\(247\) | −0.391691 | −0.0249227 | ||||||||
\(248\) | −4.37227 | −0.277640 | ||||||||
\(249\) | 3.64985 | 0.231300 | ||||||||
\(250\) | 9.18611 | 0.580980 | ||||||||
\(251\) | −26.6776 | −1.68387 | −0.841936 | − | 0.539577i | \(-0.818584\pi\) | ||||
−0.841936 | + | 0.539577i | \(0.818584\pi\) | |||||||
\(252\) | 3.34559 | 0.210752 | ||||||||
\(253\) | −1.91698 | −0.120520 | ||||||||
\(254\) | −18.8269 | −1.18130 | ||||||||
\(255\) | 5.47418 | 0.342806 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.66062 | 0.290722 | 0.145361 | − | 0.989379i | \(-0.453566\pi\) | ||||
0.145361 | + | 0.989379i | \(0.453566\pi\) | |||||||
\(258\) | 10.1421 | 0.631418 | ||||||||
\(259\) | 12.4394 | 0.772949 | ||||||||
\(260\) | −1.66802 | −0.103446 | ||||||||
\(261\) | −11.1376 | −0.689400 | ||||||||
\(262\) | 6.83617 | 0.422340 | ||||||||
\(263\) | 9.70084 | 0.598179 | 0.299090 | − | 0.954225i | \(-0.403317\pi\) | ||||
0.299090 | + | 0.954225i | \(0.403317\pi\) | |||||||
\(264\) | 1.03566 | 0.0637405 | ||||||||
\(265\) | 22.9136 | 1.40757 | ||||||||
\(266\) | 1.02766 | 0.0630099 | ||||||||
\(267\) | 14.1244 | 0.864400 | ||||||||
\(268\) | 0.726579 | 0.0443829 | ||||||||
\(269\) | −5.70499 | −0.347839 | −0.173920 | − | 0.984760i | \(-0.555643\pi\) | ||||
−0.173920 | + | 0.984760i | \(0.555643\pi\) | |||||||
\(270\) | −12.8660 | −0.783000 | ||||||||
\(271\) | −15.8705 | −0.964065 | −0.482032 | − | 0.876153i | \(-0.660101\pi\) | ||||
−0.482032 | + | 0.876153i | \(0.660101\pi\) | |||||||
\(272\) | −2.09650 | −0.127119 | ||||||||
\(273\) | −1.18935 | −0.0719826 | ||||||||
\(274\) | −6.70217 | −0.404893 | ||||||||
\(275\) | 1.35646 | 0.0817974 | ||||||||
\(276\) | 1.98534 | 0.119504 | ||||||||
\(277\) | −29.8963 | −1.79630 | −0.898148 | − | 0.439693i | \(-0.855087\pi\) | ||||
−0.898148 | + | 0.439693i | \(0.855087\pi\) | |||||||
\(278\) | 4.47060 | 0.268129 | ||||||||
\(279\) | −8.42715 | −0.504520 | ||||||||
\(280\) | 4.37630 | 0.261534 | ||||||||
\(281\) | −29.3852 | −1.75297 | −0.876486 | − | 0.481428i | \(-0.840118\pi\) | ||||
−0.876486 | + | 0.481428i | \(0.840118\pi\) | |||||||
\(282\) | 1.85617 | 0.110533 | ||||||||
\(283\) | 21.0954 | 1.25399 | 0.626996 | − | 0.779023i | \(-0.284284\pi\) | ||||
0.626996 | + | 0.779023i | \(0.284284\pi\) | |||||||
\(284\) | −7.98201 | −0.473645 | ||||||||
\(285\) | −1.54588 | −0.0915700 | ||||||||
\(286\) | 0.661596 | 0.0391210 | ||||||||
\(287\) | 2.31896 | 0.136884 | ||||||||
\(288\) | 1.92741 | 0.113574 | ||||||||
\(289\) | −12.6047 | −0.741453 | ||||||||
\(290\) | −14.5688 | −0.855512 | ||||||||
\(291\) | 3.81826 | 0.223830 | ||||||||
\(292\) | 11.4544 | 0.670316 | ||||||||
\(293\) | −22.8019 | −1.33210 | −0.666051 | − | 0.745906i | \(-0.732017\pi\) | ||||
−0.666051 | + | 0.745906i | \(0.732017\pi\) | |||||||
\(294\) | −4.12918 | −0.240819 | ||||||||
\(295\) | −23.3644 | −1.36033 | ||||||||
\(296\) | 7.16641 | 0.416539 | ||||||||
\(297\) | 5.10312 | 0.296113 | ||||||||
\(298\) | 3.72372 | 0.215710 | ||||||||
\(299\) | 1.26827 | 0.0733458 | ||||||||
\(300\) | −1.40483 | −0.0811078 | ||||||||
\(301\) | −16.9984 | −0.979773 | ||||||||
\(302\) | −22.8119 | −1.31268 | ||||||||
\(303\) | 11.7330 | 0.674046 | ||||||||
\(304\) | 0.592039 | 0.0339558 | ||||||||
\(305\) | −5.26248 | −0.301329 | ||||||||
\(306\) | −4.04080 | −0.230997 | ||||||||
\(307\) | 21.6573 | 1.23605 | 0.618023 | − | 0.786160i | \(-0.287934\pi\) | ||||
0.618023 | + | 0.786160i | \(0.287934\pi\) | |||||||
\(308\) | −1.73580 | −0.0989063 | ||||||||
\(309\) | 3.29388 | 0.187383 | ||||||||
\(310\) | −11.0234 | −0.626086 | ||||||||
\(311\) | 5.96867 | 0.338452 | 0.169226 | − | 0.985577i | \(-0.445873\pi\) | ||||
0.169226 | + | 0.985577i | \(0.445873\pi\) | |||||||
\(312\) | −0.685188 | −0.0387911 | ||||||||
\(313\) | 23.2868 | 1.31625 | 0.658124 | − | 0.752909i | \(-0.271350\pi\) | ||||
0.658124 | + | 0.752909i | \(0.271350\pi\) | |||||||
\(314\) | 11.3580 | 0.640970 | ||||||||
\(315\) | 8.43491 | 0.475253 | ||||||||
\(316\) | −14.6692 | −0.825205 | ||||||||
\(317\) | −17.5188 | −0.983954 | −0.491977 | − | 0.870608i | \(-0.663726\pi\) | ||||
−0.491977 | + | 0.870608i | \(0.663726\pi\) | |||||||
\(318\) | 9.41246 | 0.527824 | ||||||||
\(319\) | 5.77853 | 0.323536 | ||||||||
\(320\) | 2.52120 | 0.140939 | ||||||||
\(321\) | 7.68981 | 0.429203 | ||||||||
\(322\) | −3.32749 | −0.185434 | ||||||||
\(323\) | −1.24121 | −0.0690627 | ||||||||
\(324\) | 0.497122 | 0.0276179 | ||||||||
\(325\) | −0.897425 | −0.0497802 | ||||||||
\(326\) | 16.5868 | 0.918658 | ||||||||
\(327\) | 9.35749 | 0.517470 | ||||||||
\(328\) | 1.33596 | 0.0737660 | ||||||||
\(329\) | −3.11100 | −0.171515 | ||||||||
\(330\) | 2.61111 | 0.143737 | ||||||||
\(331\) | −19.7977 | −1.08818 | −0.544089 | − | 0.839027i | \(-0.683125\pi\) | ||||
−0.544089 | + | 0.839027i | \(0.683125\pi\) | |||||||
\(332\) | −3.52418 | −0.193414 | ||||||||
\(333\) | 13.8126 | 0.756925 | ||||||||
\(334\) | 11.2683 | 0.616576 | ||||||||
\(335\) | 1.83185 | 0.100085 | ||||||||
\(336\) | 1.79770 | 0.0980724 | ||||||||
\(337\) | 5.87540 | 0.320053 | 0.160027 | − | 0.987113i | \(-0.448842\pi\) | ||||
0.160027 | + | 0.987113i | \(0.448842\pi\) | |||||||
\(338\) | 12.5623 | 0.683299 | ||||||||
\(339\) | −0.186109 | −0.0101080 | ||||||||
\(340\) | −5.28569 | −0.286657 | ||||||||
\(341\) | 4.37227 | 0.236772 | ||||||||
\(342\) | 1.14110 | 0.0617037 | ||||||||
\(343\) | 19.0712 | 1.02975 | ||||||||
\(344\) | −9.79286 | −0.527996 | ||||||||
\(345\) | 5.00545 | 0.269484 | ||||||||
\(346\) | −22.3955 | −1.20399 | ||||||||
\(347\) | −15.4392 | −0.828818 | −0.414409 | − | 0.910091i | \(-0.636012\pi\) | ||||
−0.414409 | + | 0.910091i | \(0.636012\pi\) | |||||||
\(348\) | −5.98460 | −0.320808 | ||||||||
\(349\) | −14.7457 | −0.789319 | −0.394659 | − | 0.918828i | \(-0.629137\pi\) | ||||
−0.394659 | + | 0.918828i | \(0.629137\pi\) | |||||||
\(350\) | 2.35453 | 0.125855 | ||||||||
\(351\) | −3.37620 | −0.180208 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 24.4420 | 1.30092 | 0.650458 | − | 0.759542i | \(-0.274577\pi\) | ||||
0.650458 | + | 0.759542i | \(0.274577\pi\) | |||||||
\(354\) | −9.59765 | −0.510109 | ||||||||
\(355\) | −20.1242 | −1.06808 | ||||||||
\(356\) | −13.6381 | −0.722816 | ||||||||
\(357\) | −3.76886 | −0.199469 | ||||||||
\(358\) | −10.1374 | −0.535780 | ||||||||
\(359\) | 5.59776 | 0.295438 | 0.147719 | − | 0.989029i | \(-0.452807\pi\) | ||||
0.147719 | + | 0.989029i | \(0.452807\pi\) | |||||||
\(360\) | 4.85938 | 0.256112 | ||||||||
\(361\) | −18.6495 | −0.981552 | ||||||||
\(362\) | 7.64184 | 0.401646 | ||||||||
\(363\) | −1.03566 | −0.0543581 | ||||||||
\(364\) | 1.14840 | 0.0601923 | ||||||||
\(365\) | 28.8787 | 1.51158 | ||||||||
\(366\) | −2.16172 | −0.112995 | ||||||||
\(367\) | 8.51249 | 0.444348 | 0.222174 | − | 0.975007i | \(-0.428685\pi\) | ||||
0.222174 | + | 0.975007i | \(0.428685\pi\) | |||||||
\(368\) | −1.91698 | −0.0999296 | ||||||||
\(369\) | 2.57494 | 0.134046 | ||||||||
\(370\) | 18.0680 | 0.939308 | ||||||||
\(371\) | −15.7756 | −0.819026 | ||||||||
\(372\) | −4.52819 | −0.234776 | ||||||||
\(373\) | −37.2003 | −1.92616 | −0.963080 | − | 0.269217i | \(-0.913235\pi\) | ||||
−0.963080 | + | 0.269217i | \(0.913235\pi\) | |||||||
\(374\) | 2.09650 | 0.108407 | ||||||||
\(375\) | 9.51369 | 0.491285 | ||||||||
\(376\) | −1.79226 | −0.0924286 | ||||||||
\(377\) | −3.82305 | −0.196897 | ||||||||
\(378\) | 8.85799 | 0.455606 | ||||||||
\(379\) | 12.1776 | 0.625519 | 0.312760 | − | 0.949832i | \(-0.398747\pi\) | ||||
0.312760 | + | 0.949832i | \(0.398747\pi\) | |||||||
\(380\) | 1.49265 | 0.0765714 | ||||||||
\(381\) | −19.4983 | −0.998927 | ||||||||
\(382\) | −0.618048 | −0.0316221 | ||||||||
\(383\) | −25.9801 | −1.32752 | −0.663761 | − | 0.747944i | \(-0.731041\pi\) | ||||
−0.663761 | + | 0.747944i | \(0.731041\pi\) | |||||||
\(384\) | 1.03566 | 0.0528508 | ||||||||
\(385\) | −4.37630 | −0.223037 | ||||||||
\(386\) | 16.5394 | 0.841832 | ||||||||
\(387\) | −18.8748 | −0.959461 | ||||||||
\(388\) | −3.68679 | −0.187168 | ||||||||
\(389\) | 24.9045 | 1.26271 | 0.631354 | − | 0.775495i | \(-0.282500\pi\) | ||||
0.631354 | + | 0.775495i | \(0.282500\pi\) | |||||||
\(390\) | −1.72750 | −0.0874752 | ||||||||
\(391\) | 4.01895 | 0.203247 | ||||||||
\(392\) | 3.98701 | 0.201374 | ||||||||
\(393\) | 7.07995 | 0.357136 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | −36.9839 | −1.86086 | ||||||||
\(396\) | −1.92741 | −0.0968559 | ||||||||
\(397\) | 14.9156 | 0.748593 | 0.374297 | − | 0.927309i | \(-0.377884\pi\) | ||||
0.374297 | + | 0.927309i | \(0.377884\pi\) | |||||||
\(398\) | 3.36737 | 0.168791 | ||||||||
\(399\) | 1.06431 | 0.0532820 | ||||||||
\(400\) | 1.35646 | 0.0678228 | ||||||||
\(401\) | −4.56349 | −0.227890 | −0.113945 | − | 0.993487i | \(-0.536349\pi\) | ||||
−0.113945 | + | 0.993487i | \(0.536349\pi\) | |||||||
\(402\) | 0.752489 | 0.0375307 | ||||||||
\(403\) | −2.89268 | −0.144094 | ||||||||
\(404\) | −11.3290 | −0.563641 | ||||||||
\(405\) | 1.25334 | 0.0622792 | ||||||||
\(406\) | 10.0304 | 0.497799 | ||||||||
\(407\) | −7.16641 | −0.355226 | ||||||||
\(408\) | −2.17126 | −0.107493 | ||||||||
\(409\) | 1.19069 | 0.0588758 | 0.0294379 | − | 0.999567i | \(-0.490628\pi\) | ||||
0.0294379 | + | 0.999567i | \(0.490628\pi\) | |||||||
\(410\) | 3.36822 | 0.166345 | ||||||||
\(411\) | −6.94117 | −0.342383 | ||||||||
\(412\) | −3.18047 | −0.156690 | ||||||||
\(413\) | 16.0859 | 0.791538 | ||||||||
\(414\) | −3.69481 | −0.181590 | ||||||||
\(415\) | −8.88516 | −0.436155 | ||||||||
\(416\) | 0.661596 | 0.0324374 | ||||||||
\(417\) | 4.63002 | 0.226733 | ||||||||
\(418\) | −0.592039 | −0.0289576 | ||||||||
\(419\) | −12.1040 | −0.591319 | −0.295659 | − | 0.955293i | \(-0.595539\pi\) | ||||
−0.295659 | + | 0.955293i | \(0.595539\pi\) | |||||||
\(420\) | 4.53236 | 0.221156 | ||||||||
\(421\) | −30.6982 | −1.49614 | −0.748069 | − | 0.663621i | \(-0.769019\pi\) | ||||
−0.748069 | + | 0.663621i | \(0.769019\pi\) | |||||||
\(422\) | −15.0329 | −0.731789 | ||||||||
\(423\) | −3.45441 | −0.167959 | ||||||||
\(424\) | −9.08836 | −0.441370 | ||||||||
\(425\) | −2.84380 | −0.137945 | ||||||||
\(426\) | −8.26665 | −0.400520 | ||||||||
\(427\) | 3.62311 | 0.175335 | ||||||||
\(428\) | −7.42503 | −0.358902 | ||||||||
\(429\) | 0.685188 | 0.0330812 | ||||||||
\(430\) | −24.6898 | −1.19065 | ||||||||
\(431\) | −9.16476 | −0.441451 | −0.220725 | − | 0.975336i | \(-0.570842\pi\) | ||||
−0.220725 | + | 0.975336i | \(0.570842\pi\) | |||||||
\(432\) | 5.10312 | 0.245524 | ||||||||
\(433\) | −20.5838 | −0.989193 | −0.494596 | − | 0.869123i | \(-0.664684\pi\) | ||||
−0.494596 | + | 0.869123i | \(0.664684\pi\) | |||||||
\(434\) | 7.58938 | 0.364302 | ||||||||
\(435\) | −15.0884 | −0.723432 | ||||||||
\(436\) | −9.03529 | −0.432712 | ||||||||
\(437\) | −1.13493 | −0.0542910 | ||||||||
\(438\) | 11.8628 | 0.566828 | ||||||||
\(439\) | −19.8541 | −0.947586 | −0.473793 | − | 0.880636i | \(-0.657115\pi\) | ||||
−0.473793 | + | 0.880636i | \(0.657115\pi\) | |||||||
\(440\) | −2.52120 | −0.120194 | ||||||||
\(441\) | 7.68459 | 0.365933 | ||||||||
\(442\) | −1.38703 | −0.0659744 | ||||||||
\(443\) | 1.65311 | 0.0785416 | 0.0392708 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392708 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(444\) | 7.42196 | 0.352231 | ||||||||
\(445\) | −34.3843 | −1.62997 | ||||||||
\(446\) | −3.89916 | −0.184630 | ||||||||
\(447\) | 3.85651 | 0.182407 | ||||||||
\(448\) | −1.73580 | −0.0820087 | ||||||||
\(449\) | −34.3912 | −1.62302 | −0.811511 | − | 0.584338i | \(-0.801354\pi\) | ||||
−0.811511 | + | 0.584338i | \(0.801354\pi\) | |||||||
\(450\) | 2.61444 | 0.123246 | ||||||||
\(451\) | −1.33596 | −0.0629079 | ||||||||
\(452\) | 0.179700 | 0.00845239 | ||||||||
\(453\) | −23.6254 | −1.11002 | ||||||||
\(454\) | −15.1464 | −0.710858 | ||||||||
\(455\) | 2.89534 | 0.135736 | ||||||||
\(456\) | 0.613152 | 0.0287135 | ||||||||
\(457\) | −9.36018 | −0.437851 | −0.218925 | − | 0.975742i | \(-0.570255\pi\) | ||||
−0.218925 | + | 0.975742i | \(0.570255\pi\) | |||||||
\(458\) | 24.1376 | 1.12788 | ||||||||
\(459\) | −10.6987 | −0.499371 | ||||||||
\(460\) | −4.83310 | −0.225344 | ||||||||
\(461\) | −31.5116 | −1.46764 | −0.733821 | − | 0.679343i | \(-0.762265\pi\) | ||||
−0.733821 | + | 0.679343i | \(0.762265\pi\) | |||||||
\(462\) | −1.79770 | −0.0836364 | ||||||||
\(463\) | −31.6852 | −1.47254 | −0.736268 | − | 0.676690i | \(-0.763414\pi\) | ||||
−0.736268 | + | 0.676690i | \(0.763414\pi\) | |||||||
\(464\) | 5.77853 | 0.268262 | ||||||||
\(465\) | −11.4165 | −0.529426 | ||||||||
\(466\) | 8.42912 | 0.390472 | ||||||||
\(467\) | 8.22554 | 0.380632 | 0.190316 | − | 0.981723i | \(-0.439049\pi\) | ||||
0.190316 | + | 0.981723i | \(0.439049\pi\) | |||||||
\(468\) | 1.27516 | 0.0589445 | ||||||||
\(469\) | −1.26119 | −0.0582365 | ||||||||
\(470\) | −4.51864 | −0.208429 | ||||||||
\(471\) | 11.7630 | 0.542012 | ||||||||
\(472\) | 9.26718 | 0.426556 | ||||||||
\(473\) | 9.79286 | 0.450276 | ||||||||
\(474\) | −15.1923 | −0.697804 | ||||||||
\(475\) | 0.803075 | 0.0368476 | ||||||||
\(476\) | 3.63909 | 0.166798 | ||||||||
\(477\) | −17.5170 | −0.802047 | ||||||||
\(478\) | −17.0649 | −0.780529 | ||||||||
\(479\) | −28.3633 | −1.29595 | −0.647976 | − | 0.761661i | \(-0.724384\pi\) | ||||
−0.647976 | + | 0.761661i | \(0.724384\pi\) | |||||||
\(480\) | 2.61111 | 0.119180 | ||||||||
\(481\) | 4.74126 | 0.216183 | ||||||||
\(482\) | 2.91512 | 0.132780 | ||||||||
\(483\) | −3.44615 | −0.156805 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −9.29514 | −0.422070 | ||||||||
\(486\) | 15.8242 | 0.717801 | ||||||||
\(487\) | 3.84730 | 0.174338 | 0.0871689 | − | 0.996194i | \(-0.472218\pi\) | ||||
0.0871689 | + | 0.996194i | \(0.472218\pi\) | |||||||
\(488\) | 2.08729 | 0.0944871 | ||||||||
\(489\) | 17.1783 | 0.776830 | ||||||||
\(490\) | 10.0520 | 0.454105 | ||||||||
\(491\) | 26.6876 | 1.20439 | 0.602197 | − | 0.798347i | \(-0.294292\pi\) | ||||
0.602197 | + | 0.798347i | \(0.294292\pi\) | |||||||
\(492\) | 1.38360 | 0.0623775 | ||||||||
\(493\) | −12.1147 | −0.545618 | ||||||||
\(494\) | 0.391691 | 0.0176230 | ||||||||
\(495\) | −4.85938 | −0.218413 | ||||||||
\(496\) | 4.37227 | 0.196321 | ||||||||
\(497\) | 13.8551 | 0.621488 | ||||||||
\(498\) | −3.64985 | −0.163554 | ||||||||
\(499\) | 10.1351 | 0.453708 | 0.226854 | − | 0.973929i | \(-0.427156\pi\) | ||||
0.226854 | + | 0.973929i | \(0.427156\pi\) | |||||||
\(500\) | −9.18611 | −0.410815 | ||||||||
\(501\) | 11.6702 | 0.521385 | ||||||||
\(502\) | 26.6776 | 1.19068 | ||||||||
\(503\) | 16.8789 | 0.752595 | 0.376297 | − | 0.926499i | \(-0.377197\pi\) | ||||
0.376297 | + | 0.926499i | \(0.377197\pi\) | |||||||
\(504\) | −3.34559 | −0.149024 | ||||||||
\(505\) | −28.5628 | −1.27103 | ||||||||
\(506\) | 1.91698 | 0.0852203 | ||||||||
\(507\) | 13.0103 | 0.577806 | ||||||||
\(508\) | 18.8269 | 0.835309 | ||||||||
\(509\) | 20.4750 | 0.907536 | 0.453768 | − | 0.891120i | \(-0.350079\pi\) | ||||
0.453768 | + | 0.891120i | \(0.350079\pi\) | |||||||
\(510\) | −5.47418 | −0.242401 | ||||||||
\(511\) | −19.8825 | −0.879548 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.02125 | 0.133391 | ||||||||
\(514\) | −4.66062 | −0.205571 | ||||||||
\(515\) | −8.01860 | −0.353342 | ||||||||
\(516\) | −10.1421 | −0.446480 | ||||||||
\(517\) | 1.79226 | 0.0788234 | ||||||||
\(518\) | −12.4394 | −0.546557 | ||||||||
\(519\) | −23.1941 | −1.01811 | ||||||||
\(520\) | 1.66802 | 0.0731473 | ||||||||
\(521\) | 17.7597 | 0.778068 | 0.389034 | − | 0.921223i | \(-0.372809\pi\) | ||||
0.389034 | + | 0.921223i | \(0.372809\pi\) | |||||||
\(522\) | 11.1376 | 0.487479 | ||||||||
\(523\) | −8.12089 | −0.355102 | −0.177551 | − | 0.984112i | \(-0.556817\pi\) | ||||
−0.177551 | + | 0.984112i | \(0.556817\pi\) | |||||||
\(524\) | −6.83617 | −0.298639 | ||||||||
\(525\) | 2.43850 | 0.106425 | ||||||||
\(526\) | −9.70084 | −0.422977 | ||||||||
\(527\) | −9.16645 | −0.399297 | ||||||||
\(528\) | −1.03566 | −0.0450713 | ||||||||
\(529\) | −19.3252 | −0.840225 | ||||||||
\(530\) | −22.9136 | −0.995303 | ||||||||
\(531\) | 17.8616 | 0.775129 | ||||||||
\(532\) | −1.02766 | −0.0445547 | ||||||||
\(533\) | 0.883865 | 0.0382844 | ||||||||
\(534\) | −14.1244 | −0.611223 | ||||||||
\(535\) | −18.7200 | −0.809336 | ||||||||
\(536\) | −0.726579 | −0.0313834 | ||||||||
\(537\) | −10.4989 | −0.453063 | ||||||||
\(538\) | 5.70499 | 0.245960 | ||||||||
\(539\) | −3.98701 | −0.171733 | ||||||||
\(540\) | 12.8660 | 0.553664 | ||||||||
\(541\) | 40.4394 | 1.73863 | 0.869313 | − | 0.494262i | \(-0.164562\pi\) | ||||
0.869313 | + | 0.494262i | \(0.164562\pi\) | |||||||
\(542\) | 15.8705 | 0.681697 | ||||||||
\(543\) | 7.91435 | 0.339637 | ||||||||
\(544\) | 2.09650 | 0.0898865 | ||||||||
\(545\) | −22.7798 | −0.975778 | ||||||||
\(546\) | 1.18935 | 0.0508994 | ||||||||
\(547\) | −1.92266 | −0.0822072 | −0.0411036 | − | 0.999155i | \(-0.513087\pi\) | ||||
−0.0411036 | + | 0.999155i | \(0.513087\pi\) | |||||||
\(548\) | 6.70217 | 0.286302 | ||||||||
\(549\) | 4.02306 | 0.171700 | ||||||||
\(550\) | −1.35646 | −0.0578395 | ||||||||
\(551\) | 3.42112 | 0.145745 | ||||||||
\(552\) | −1.98534 | −0.0845018 | ||||||||
\(553\) | 25.4627 | 1.08278 | ||||||||
\(554\) | 29.8963 | 1.27017 | ||||||||
\(555\) | 18.7123 | 0.794291 | ||||||||
\(556\) | −4.47060 | −0.189596 | ||||||||
\(557\) | −8.43674 | −0.357476 | −0.178738 | − | 0.983897i | \(-0.557201\pi\) | ||||
−0.178738 | + | 0.983897i | \(0.557201\pi\) | |||||||
\(558\) | 8.42715 | 0.356750 | ||||||||
\(559\) | −6.47891 | −0.274029 | ||||||||
\(560\) | −4.37630 | −0.184932 | ||||||||
\(561\) | 2.17126 | 0.0916706 | ||||||||
\(562\) | 29.3852 | 1.23954 | ||||||||
\(563\) | 8.87788 | 0.374158 | 0.187079 | − | 0.982345i | \(-0.440098\pi\) | ||||
0.187079 | + | 0.982345i | \(0.440098\pi\) | |||||||
\(564\) | −1.85617 | −0.0781588 | ||||||||
\(565\) | 0.453061 | 0.0190604 | ||||||||
\(566\) | −21.0954 | −0.886706 | ||||||||
\(567\) | −0.862903 | −0.0362385 | ||||||||
\(568\) | 7.98201 | 0.334918 | ||||||||
\(569\) | 10.6005 | 0.444397 | 0.222199 | − | 0.975001i | \(-0.428677\pi\) | ||||
0.222199 | + | 0.975001i | \(0.428677\pi\) | |||||||
\(570\) | 1.54588 | 0.0647497 | ||||||||
\(571\) | 14.0366 | 0.587411 | 0.293706 | − | 0.955896i | \(-0.405111\pi\) | ||||
0.293706 | + | 0.955896i | \(0.405111\pi\) | |||||||
\(572\) | −0.661596 | −0.0276627 | ||||||||
\(573\) | −0.640088 | −0.0267401 | ||||||||
\(574\) | −2.31896 | −0.0967913 | ||||||||
\(575\) | −2.60030 | −0.108440 | ||||||||
\(576\) | −1.92741 | −0.0803086 | ||||||||
\(577\) | −33.8714 | −1.41009 | −0.705043 | − | 0.709164i | \(-0.749072\pi\) | ||||
−0.705043 | + | 0.709164i | \(0.749072\pi\) | |||||||
\(578\) | 12.6047 | 0.524287 | ||||||||
\(579\) | 17.1292 | 0.711864 | ||||||||
\(580\) | 14.5688 | 0.604939 | ||||||||
\(581\) | 6.11726 | 0.253787 | ||||||||
\(582\) | −3.81826 | −0.158272 | ||||||||
\(583\) | 9.08836 | 0.376401 | ||||||||
\(584\) | −11.4544 | −0.473985 | ||||||||
\(585\) | 3.21495 | 0.132922 | ||||||||
\(586\) | 22.8019 | 0.941939 | ||||||||
\(587\) | −39.3259 | −1.62315 | −0.811577 | − | 0.584245i | \(-0.801391\pi\) | ||||
−0.811577 | + | 0.584245i | \(0.801391\pi\) | |||||||
\(588\) | 4.12918 | 0.170285 | ||||||||
\(589\) | 2.58856 | 0.106660 | ||||||||
\(590\) | 23.3644 | 0.961898 | ||||||||
\(591\) | −1.03566 | −0.0426014 | ||||||||
\(592\) | −7.16641 | −0.294537 | ||||||||
\(593\) | 23.3274 | 0.957943 | 0.478972 | − | 0.877830i | \(-0.341010\pi\) | ||||
0.478972 | + | 0.877830i | \(0.341010\pi\) | |||||||
\(594\) | −5.10312 | −0.209384 | ||||||||
\(595\) | 9.17489 | 0.376134 | ||||||||
\(596\) | −3.72372 | −0.152530 | ||||||||
\(597\) | 3.48745 | 0.142732 | ||||||||
\(598\) | −1.26827 | −0.0518633 | ||||||||
\(599\) | 11.5160 | 0.470530 | 0.235265 | − | 0.971931i | \(-0.424404\pi\) | ||||
0.235265 | + | 0.971931i | \(0.424404\pi\) | |||||||
\(600\) | 1.40483 | 0.0573519 | ||||||||
\(601\) | 15.7163 | 0.641082 | 0.320541 | − | 0.947235i | \(-0.396135\pi\) | ||||
0.320541 | + | 0.947235i | \(0.396135\pi\) | |||||||
\(602\) | 16.9984 | 0.692804 | ||||||||
\(603\) | −1.40041 | −0.0570292 | ||||||||
\(604\) | 22.8119 | 0.928204 | ||||||||
\(605\) | 2.52120 | 0.102501 | ||||||||
\(606\) | −11.7330 | −0.476622 | ||||||||
\(607\) | 2.39409 | 0.0971733 | 0.0485866 | − | 0.998819i | \(-0.484528\pi\) | ||||
0.0485866 | + | 0.998819i | \(0.484528\pi\) | |||||||
\(608\) | −0.592039 | −0.0240104 | ||||||||
\(609\) | 10.3881 | 0.420945 | ||||||||
\(610\) | 5.26248 | 0.213071 | ||||||||
\(611\) | −1.18575 | −0.0479703 | ||||||||
\(612\) | 4.04080 | 0.163340 | ||||||||
\(613\) | −20.8827 | −0.843445 | −0.421722 | − | 0.906725i | \(-0.638574\pi\) | ||||
−0.421722 | + | 0.906725i | \(0.638574\pi\) | |||||||
\(614\) | −21.6573 | −0.874016 | ||||||||
\(615\) | 3.48833 | 0.140663 | ||||||||
\(616\) | 1.73580 | 0.0699373 | ||||||||
\(617\) | −32.4607 | −1.30682 | −0.653410 | − | 0.757004i | \(-0.726662\pi\) | ||||
−0.653410 | + | 0.757004i | \(0.726662\pi\) | |||||||
\(618\) | −3.29388 | −0.132499 | ||||||||
\(619\) | 10.5885 | 0.425590 | 0.212795 | − | 0.977097i | \(-0.431743\pi\) | ||||
0.212795 | + | 0.977097i | \(0.431743\pi\) | |||||||
\(620\) | 11.0234 | 0.442710 | ||||||||
\(621\) | −9.78259 | −0.392562 | ||||||||
\(622\) | −5.96867 | −0.239322 | ||||||||
\(623\) | 23.6729 | 0.948436 | ||||||||
\(624\) | 0.685188 | 0.0274295 | ||||||||
\(625\) | −29.9423 | −1.19769 | ||||||||
\(626\) | −23.2868 | −0.930728 | ||||||||
\(627\) | −0.613152 | −0.0244869 | ||||||||
\(628\) | −11.3580 | −0.453234 | ||||||||
\(629\) | 15.0243 | 0.599060 | ||||||||
\(630\) | −8.43491 | −0.336055 | ||||||||
\(631\) | 44.3252 | 1.76456 | 0.882279 | − | 0.470727i | \(-0.156008\pi\) | ||||
0.882279 | + | 0.470727i | \(0.156008\pi\) | |||||||
\(632\) | 14.6692 | 0.583508 | ||||||||
\(633\) | −15.5690 | −0.618810 | ||||||||
\(634\) | 17.5188 | 0.695760 | ||||||||
\(635\) | 47.4664 | 1.88365 | ||||||||
\(636\) | −9.41246 | −0.373228 | ||||||||
\(637\) | 2.63779 | 0.104513 | ||||||||
\(638\) | −5.77853 | −0.228774 | ||||||||
\(639\) | 15.3846 | 0.608604 | ||||||||
\(640\) | −2.52120 | −0.0996592 | ||||||||
\(641\) | −27.7088 | −1.09443 | −0.547215 | − | 0.836992i | \(-0.684312\pi\) | ||||
−0.547215 | + | 0.836992i | \(0.684312\pi\) | |||||||
\(642\) | −7.68981 | −0.303493 | ||||||||
\(643\) | −11.9777 | −0.472355 | −0.236178 | − | 0.971710i | \(-0.575895\pi\) | ||||
−0.236178 | + | 0.971710i | \(0.575895\pi\) | |||||||
\(644\) | 3.32749 | 0.131122 | ||||||||
\(645\) | −25.5702 | −1.00683 | ||||||||
\(646\) | 1.24121 | 0.0488347 | ||||||||
\(647\) | 7.51854 | 0.295584 | 0.147792 | − | 0.989018i | \(-0.452783\pi\) | ||||
0.147792 | + | 0.989018i | \(0.452783\pi\) | |||||||
\(648\) | −0.497122 | −0.0195288 | ||||||||
\(649\) | −9.26718 | −0.363769 | ||||||||
\(650\) | 0.897425 | 0.0351999 | ||||||||
\(651\) | 7.86002 | 0.308059 | ||||||||
\(652\) | −16.5868 | −0.649590 | ||||||||
\(653\) | −7.55273 | −0.295561 | −0.147781 | − | 0.989020i | \(-0.547213\pi\) | ||||
−0.147781 | + | 0.989020i | \(0.547213\pi\) | |||||||
\(654\) | −9.35749 | −0.365907 | ||||||||
\(655\) | −17.2354 | −0.673441 | ||||||||
\(656\) | −1.33596 | −0.0521605 | ||||||||
\(657\) | −22.0772 | −0.861314 | ||||||||
\(658\) | 3.11100 | 0.121279 | ||||||||
\(659\) | 32.6551 | 1.27206 | 0.636031 | − | 0.771663i | \(-0.280575\pi\) | ||||
0.636031 | + | 0.771663i | \(0.280575\pi\) | |||||||
\(660\) | −2.61111 | −0.101637 | ||||||||
\(661\) | −41.2651 | −1.60503 | −0.802513 | − | 0.596634i | \(-0.796504\pi\) | ||||
−0.802513 | + | 0.596634i | \(0.796504\pi\) | |||||||
\(662\) | 19.7977 | 0.769458 | ||||||||
\(663\) | −1.43649 | −0.0557888 | ||||||||
\(664\) | 3.52418 | 0.136765 | ||||||||
\(665\) | −2.59094 | −0.100472 | ||||||||
\(666\) | −13.8126 | −0.535227 | ||||||||
\(667\) | −11.0773 | −0.428917 | ||||||||
\(668\) | −11.2683 | −0.435985 | ||||||||
\(669\) | −4.03820 | −0.156126 | ||||||||
\(670\) | −1.83185 | −0.0707706 | ||||||||
\(671\) | −2.08729 | −0.0805789 | ||||||||
\(672\) | −1.79770 | −0.0693477 | ||||||||
\(673\) | 26.2045 | 1.01011 | 0.505055 | − | 0.863087i | \(-0.331472\pi\) | ||||
0.505055 | + | 0.863087i | \(0.331472\pi\) | |||||||
\(674\) | −5.87540 | −0.226312 | ||||||||
\(675\) | 6.92216 | 0.266434 | ||||||||
\(676\) | −12.5623 | −0.483165 | ||||||||
\(677\) | 1.09914 | 0.0422433 | 0.0211216 | − | 0.999777i | \(-0.493276\pi\) | ||||
0.0211216 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(678\) | 0.186109 | 0.00714746 | ||||||||
\(679\) | 6.39952 | 0.245591 | ||||||||
\(680\) | 5.28569 | 0.202697 | ||||||||
\(681\) | −15.6866 | −0.601111 | ||||||||
\(682\) | −4.37227 | −0.167423 | ||||||||
\(683\) | 46.5909 | 1.78275 | 0.891376 | − | 0.453265i | \(-0.149741\pi\) | ||||
0.891376 | + | 0.453265i | \(0.149741\pi\) | |||||||
\(684\) | −1.14110 | −0.0436311 | ||||||||
\(685\) | 16.8975 | 0.645621 | ||||||||
\(686\) | −19.0712 | −0.728143 | ||||||||
\(687\) | 24.9984 | 0.953747 | ||||||||
\(688\) | 9.79286 | 0.373349 | ||||||||
\(689\) | −6.01282 | −0.229070 | ||||||||
\(690\) | −5.00545 | −0.190554 | ||||||||
\(691\) | −14.3112 | −0.544425 | −0.272212 | − | 0.962237i | \(-0.587755\pi\) | ||||
−0.272212 | + | 0.962237i | \(0.587755\pi\) | |||||||
\(692\) | 22.3955 | 0.851348 | ||||||||
\(693\) | 3.34559 | 0.127088 | ||||||||
\(694\) | 15.4392 | 0.586063 | ||||||||
\(695\) | −11.2713 | −0.427544 | ||||||||
\(696\) | 5.98460 | 0.226846 | ||||||||
\(697\) | 2.80083 | 0.106089 | ||||||||
\(698\) | 14.7457 | 0.558133 | ||||||||
\(699\) | 8.72971 | 0.330188 | ||||||||
\(700\) | −2.35453 | −0.0889930 | ||||||||
\(701\) | 45.7544 | 1.72812 | 0.864059 | − | 0.503390i | \(-0.167914\pi\) | ||||
0.864059 | + | 0.503390i | \(0.167914\pi\) | |||||||
\(702\) | 3.37620 | 0.127427 | ||||||||
\(703\) | −4.24280 | −0.160020 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −4.67978 | −0.176251 | ||||||||
\(706\) | −24.4420 | −0.919887 | ||||||||
\(707\) | 19.6649 | 0.739576 | ||||||||
\(708\) | 9.59765 | 0.360702 | ||||||||
\(709\) | 0.740212 | 0.0277993 | 0.0138996 | − | 0.999903i | \(-0.495575\pi\) | ||||
0.0138996 | + | 0.999903i | \(0.495575\pi\) | |||||||
\(710\) | 20.1242 | 0.755249 | ||||||||
\(711\) | 28.2735 | 1.06034 | ||||||||
\(712\) | 13.6381 | 0.511108 | ||||||||
\(713\) | −8.38157 | −0.313892 | ||||||||
\(714\) | 3.76886 | 0.141046 | ||||||||
\(715\) | −1.66802 | −0.0623802 | ||||||||
\(716\) | 10.1374 | 0.378854 | ||||||||
\(717\) | −17.6734 | −0.660026 | ||||||||
\(718\) | −5.59776 | −0.208906 | ||||||||
\(719\) | 44.6697 | 1.66590 | 0.832950 | − | 0.553348i | \(-0.186650\pi\) | ||||
0.832950 | + | 0.553348i | \(0.186650\pi\) | |||||||
\(720\) | −4.85938 | −0.181098 | ||||||||
\(721\) | 5.52065 | 0.205600 | ||||||||
\(722\) | 18.6495 | 0.694062 | ||||||||
\(723\) | 3.01907 | 0.112280 | ||||||||
\(724\) | −7.64184 | −0.284007 | ||||||||
\(725\) | 7.83833 | 0.291108 | ||||||||
\(726\) | 1.03566 | 0.0384370 | ||||||||
\(727\) | 38.8867 | 1.44223 | 0.721113 | − | 0.692817i | \(-0.243631\pi\) | ||||
0.721113 | + | 0.692817i | \(0.243631\pi\) | |||||||
\(728\) | −1.14840 | −0.0425624 | ||||||||
\(729\) | 14.8971 | 0.551746 | ||||||||
\(730\) | −28.8787 | −1.06885 | ||||||||
\(731\) | −20.5307 | −0.759355 | ||||||||
\(732\) | 2.16172 | 0.0798996 | ||||||||
\(733\) | 24.5229 | 0.905775 | 0.452888 | − | 0.891568i | \(-0.350394\pi\) | ||||
0.452888 | + | 0.891568i | \(0.350394\pi\) | |||||||
\(734\) | −8.51249 | −0.314202 | ||||||||
\(735\) | 10.4105 | 0.383997 | ||||||||
\(736\) | 1.91698 | 0.0706609 | ||||||||
\(737\) | 0.726579 | 0.0267639 | ||||||||
\(738\) | −2.57494 | −0.0947848 | ||||||||
\(739\) | −37.8714 | −1.39312 | −0.696560 | − | 0.717498i | \(-0.745287\pi\) | ||||
−0.696560 | + | 0.717498i | \(0.745287\pi\) | |||||||
\(740\) | −18.0680 | −0.664191 | ||||||||
\(741\) | 0.405658 | 0.0149022 | ||||||||
\(742\) | 15.7756 | 0.579139 | ||||||||
\(743\) | 9.06047 | 0.332396 | 0.166198 | − | 0.986092i | \(-0.446851\pi\) | ||||
0.166198 | + | 0.986092i | \(0.446851\pi\) | |||||||
\(744\) | 4.52819 | 0.166011 | ||||||||
\(745\) | −9.38826 | −0.343959 | ||||||||
\(746\) | 37.2003 | 1.36200 | ||||||||
\(747\) | 6.79252 | 0.248525 | ||||||||
\(748\) | −2.09650 | −0.0766555 | ||||||||
\(749\) | 12.8884 | 0.470930 | ||||||||
\(750\) | −9.51369 | −0.347391 | ||||||||
\(751\) | 4.38806 | 0.160123 | 0.0800614 | − | 0.996790i | \(-0.474488\pi\) | ||||
0.0800614 | + | 0.996790i | \(0.474488\pi\) | |||||||
\(752\) | 1.79226 | 0.0653569 | ||||||||
\(753\) | 27.6289 | 1.00685 | ||||||||
\(754\) | 3.82305 | 0.139227 | ||||||||
\(755\) | 57.5134 | 2.09313 | ||||||||
\(756\) | −8.85799 | −0.322162 | ||||||||
\(757\) | −27.9012 | −1.01409 | −0.507043 | − | 0.861921i | \(-0.669261\pi\) | ||||
−0.507043 | + | 0.861921i | \(0.669261\pi\) | |||||||
\(758\) | −12.1776 | −0.442309 | ||||||||
\(759\) | 1.98534 | 0.0720634 | ||||||||
\(760\) | −1.49265 | −0.0541441 | ||||||||
\(761\) | 23.6515 | 0.857367 | 0.428684 | − | 0.903455i | \(-0.358978\pi\) | ||||
0.428684 | + | 0.903455i | \(0.358978\pi\) | |||||||
\(762\) | 19.4983 | 0.706348 | ||||||||
\(763\) | 15.6834 | 0.567778 | ||||||||
\(764\) | 0.618048 | 0.0223602 | ||||||||
\(765\) | 10.1877 | 0.368336 | ||||||||
\(766\) | 25.9801 | 0.938700 | ||||||||
\(767\) | 6.13112 | 0.221382 | ||||||||
\(768\) | −1.03566 | −0.0373712 | ||||||||
\(769\) | −21.6221 | −0.779712 | −0.389856 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389856 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(770\) | 4.37630 | 0.157711 | ||||||||
\(771\) | −4.82682 | −0.173834 | ||||||||
\(772\) | −16.5394 | −0.595265 | ||||||||
\(773\) | −16.1644 | −0.581392 | −0.290696 | − | 0.956816i | \(-0.593887\pi\) | ||||
−0.290696 | + | 0.956816i | \(0.593887\pi\) | |||||||
\(774\) | 18.8748 | 0.678442 | ||||||||
\(775\) | 5.93080 | 0.213040 | ||||||||
\(776\) | 3.68679 | 0.132348 | ||||||||
\(777\) | −12.8830 | −0.462176 | ||||||||
\(778\) | −24.9045 | −0.892869 | ||||||||
\(779\) | −0.790941 | −0.0283384 | ||||||||
\(780\) | 1.72750 | 0.0618543 | ||||||||
\(781\) | −7.98201 | −0.285619 | ||||||||
\(782\) | −4.01895 | −0.143717 | ||||||||
\(783\) | 29.4886 | 1.05384 | ||||||||
\(784\) | −3.98701 | −0.142393 | ||||||||
\(785\) | −28.6358 | −1.02206 | ||||||||
\(786\) | −7.07995 | −0.252533 | ||||||||
\(787\) | 4.06955 | 0.145064 | 0.0725318 | − | 0.997366i | \(-0.476892\pi\) | ||||
0.0725318 | + | 0.997366i | \(0.476892\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | −10.0468 | −0.357675 | ||||||||
\(790\) | 36.9839 | 1.31583 | ||||||||
\(791\) | −0.311924 | −0.0110907 | ||||||||
\(792\) | 1.92741 | 0.0684874 | ||||||||
\(793\) | 1.38094 | 0.0490387 | ||||||||
\(794\) | −14.9156 | −0.529335 | ||||||||
\(795\) | −23.7307 | −0.841641 | ||||||||
\(796\) | −3.36737 | −0.119353 | ||||||||
\(797\) | −4.88414 | −0.173005 | −0.0865026 | − | 0.996252i | \(-0.527569\pi\) | ||||
−0.0865026 | + | 0.996252i | \(0.527569\pi\) | |||||||
\(798\) | −1.06431 | −0.0376761 | ||||||||
\(799\) | −3.75746 | −0.132929 | ||||||||
\(800\) | −1.35646 | −0.0479580 | ||||||||
\(801\) | 26.2861 | 0.928774 | ||||||||
\(802\) | 4.56349 | 0.161142 | ||||||||
\(803\) | 11.4544 | 0.404216 | ||||||||
\(804\) | −0.752489 | −0.0265382 | ||||||||
\(805\) | 8.38928 | 0.295683 | ||||||||
\(806\) | 2.89268 | 0.101890 | ||||||||
\(807\) | 5.90843 | 0.207987 | ||||||||
\(808\) | 11.3290 | 0.398554 | ||||||||
\(809\) | 24.8920 | 0.875155 | 0.437577 | − | 0.899181i | \(-0.355837\pi\) | ||||
0.437577 | + | 0.899181i | \(0.355837\pi\) | |||||||
\(810\) | −1.25334 | −0.0440380 | ||||||||
\(811\) | −48.8768 | −1.71630 | −0.858148 | − | 0.513402i | \(-0.828385\pi\) | ||||
−0.858148 | + | 0.513402i | \(0.828385\pi\) | |||||||
\(812\) | −10.0304 | −0.351997 | ||||||||
\(813\) | 16.4365 | 0.576452 | ||||||||
\(814\) | 7.16641 | 0.251182 | ||||||||
\(815\) | −41.8187 | −1.46484 | ||||||||
\(816\) | 2.17126 | 0.0760092 | ||||||||
\(817\) | 5.79776 | 0.202838 | ||||||||
\(818\) | −1.19069 | −0.0416315 | ||||||||
\(819\) | −2.21343 | −0.0773434 | ||||||||
\(820\) | −3.36822 | −0.117623 | ||||||||
\(821\) | 44.9222 | 1.56779 | 0.783897 | − | 0.620891i | \(-0.213229\pi\) | ||||
0.783897 | + | 0.620891i | \(0.213229\pi\) | |||||||
\(822\) | 6.94117 | 0.242101 | ||||||||
\(823\) | 9.49265 | 0.330893 | 0.165446 | − | 0.986219i | \(-0.447094\pi\) | ||||
0.165446 | + | 0.986219i | \(0.447094\pi\) | |||||||
\(824\) | 3.18047 | 0.110797 | ||||||||
\(825\) | −1.40483 | −0.0489098 | ||||||||
\(826\) | −16.0859 | −0.559702 | ||||||||
\(827\) | −34.7253 | −1.20752 | −0.603759 | − | 0.797167i | \(-0.706331\pi\) | ||||
−0.603759 | + | 0.797167i | \(0.706331\pi\) | |||||||
\(828\) | 3.69481 | 0.128403 | ||||||||
\(829\) | −20.4794 | −0.711278 | −0.355639 | − | 0.934623i | \(-0.615737\pi\) | ||||
−0.355639 | + | 0.934623i | \(0.615737\pi\) | |||||||
\(830\) | 8.88516 | 0.308408 | ||||||||
\(831\) | 30.9625 | 1.07408 | ||||||||
\(832\) | −0.661596 | −0.0229367 | ||||||||
\(833\) | 8.35874 | 0.289613 | ||||||||
\(834\) | −4.63002 | −0.160324 | ||||||||
\(835\) | −28.4097 | −0.983160 | ||||||||
\(836\) | 0.592039 | 0.0204761 | ||||||||
\(837\) | 22.3122 | 0.771224 | ||||||||
\(838\) | 12.1040 | 0.418125 | ||||||||
\(839\) | 32.1767 | 1.11086 | 0.555431 | − | 0.831563i | \(-0.312553\pi\) | ||||
0.555431 | + | 0.831563i | \(0.312553\pi\) | |||||||
\(840\) | −4.53236 | −0.156381 | ||||||||
\(841\) | 4.39146 | 0.151430 | ||||||||
\(842\) | 30.6982 | 1.05793 | ||||||||
\(843\) | 30.4330 | 1.04817 | ||||||||
\(844\) | 15.0329 | 0.517453 | ||||||||
\(845\) | −31.6721 | −1.08955 | ||||||||
\(846\) | 3.45441 | 0.118765 | ||||||||
\(847\) | −1.73580 | −0.0596427 | ||||||||
\(848\) | 9.08836 | 0.312096 | ||||||||
\(849\) | −21.8477 | −0.749810 | ||||||||
\(850\) | 2.84380 | 0.0975417 | ||||||||
\(851\) | 13.7379 | 0.470928 | ||||||||
\(852\) | 8.26665 | 0.283211 | ||||||||
\(853\) | −26.5986 | −0.910718 | −0.455359 | − | 0.890308i | \(-0.650489\pi\) | ||||
−0.455359 | + | 0.890308i | \(0.650489\pi\) | |||||||
\(854\) | −3.62311 | −0.123980 | ||||||||
\(855\) | −2.87695 | −0.0983895 | ||||||||
\(856\) | 7.42503 | 0.253782 | ||||||||
\(857\) | −9.38910 | −0.320725 | −0.160363 | − | 0.987058i | \(-0.551266\pi\) | ||||
−0.160363 | + | 0.987058i | \(0.551266\pi\) | |||||||
\(858\) | −0.685188 | −0.0233919 | ||||||||
\(859\) | 42.6884 | 1.45651 | 0.728254 | − | 0.685307i | \(-0.240332\pi\) | ||||
0.728254 | + | 0.685307i | \(0.240332\pi\) | |||||||
\(860\) | 24.6898 | 0.841914 | ||||||||
\(861\) | −2.40165 | −0.0818480 | ||||||||
\(862\) | 9.16476 | 0.312153 | ||||||||
\(863\) | 18.8089 | 0.640263 | 0.320131 | − | 0.947373i | \(-0.396273\pi\) | ||||
0.320131 | + | 0.947373i | \(0.396273\pi\) | |||||||
\(864\) | −5.10312 | −0.173612 | ||||||||
\(865\) | 56.4635 | 1.91982 | ||||||||
\(866\) | 20.5838 | 0.699465 | ||||||||
\(867\) | 13.0542 | 0.443344 | ||||||||
\(868\) | −7.58938 | −0.257600 | ||||||||
\(869\) | −14.6692 | −0.497617 | ||||||||
\(870\) | 15.0884 | 0.511544 | ||||||||
\(871\) | −0.480701 | −0.0162879 | ||||||||
\(872\) | 9.03529 | 0.305973 | ||||||||
\(873\) | 7.10594 | 0.240500 | ||||||||
\(874\) | 1.13493 | 0.0383895 | ||||||||
\(875\) | 15.9452 | 0.539047 | ||||||||
\(876\) | −11.8628 | −0.400808 | ||||||||
\(877\) | 32.3311 | 1.09174 | 0.545872 | − | 0.837868i | \(-0.316198\pi\) | ||||
0.545872 | + | 0.837868i | \(0.316198\pi\) | |||||||
\(878\) | 19.8541 | 0.670044 | ||||||||
\(879\) | 23.6151 | 0.796516 | ||||||||
\(880\) | 2.52120 | 0.0849897 | ||||||||
\(881\) | 34.1548 | 1.15070 | 0.575351 | − | 0.817906i | \(-0.304865\pi\) | ||||
0.575351 | + | 0.817906i | \(0.304865\pi\) | |||||||
\(882\) | −7.68459 | −0.258753 | ||||||||
\(883\) | −25.3413 | −0.852802 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(884\) | 1.38703 | 0.0466509 | ||||||||
\(885\) | 24.1976 | 0.813394 | ||||||||
\(886\) | −1.65311 | −0.0555373 | ||||||||
\(887\) | 11.0158 | 0.369874 | 0.184937 | − | 0.982750i | \(-0.440792\pi\) | ||||
0.184937 | + | 0.982750i | \(0.440792\pi\) | |||||||
\(888\) | −7.42196 | −0.249065 | ||||||||
\(889\) | −32.6797 | −1.09604 | ||||||||
\(890\) | 34.3843 | 1.15256 | ||||||||
\(891\) | 0.497122 | 0.0166542 | ||||||||
\(892\) | 3.89916 | 0.130553 | ||||||||
\(893\) | 1.06109 | 0.0355079 | ||||||||
\(894\) | −3.85651 | −0.128981 | ||||||||
\(895\) | 25.5585 | 0.854328 | ||||||||
\(896\) | 1.73580 | 0.0579889 | ||||||||
\(897\) | −1.31349 | −0.0438563 | ||||||||
\(898\) | 34.3912 | 1.14765 | ||||||||
\(899\) | 25.2653 | 0.842646 | ||||||||
\(900\) | −2.61444 | −0.0871481 | ||||||||
\(901\) | −19.0537 | −0.634771 | ||||||||
\(902\) | 1.33596 | 0.0444826 | ||||||||
\(903\) | 17.6046 | 0.585844 | ||||||||
\(904\) | −0.179700 | −0.00597675 | ||||||||
\(905\) | −19.2666 | −0.640444 | ||||||||
\(906\) | 23.6254 | 0.784901 | ||||||||
\(907\) | −9.23996 | −0.306808 | −0.153404 | − | 0.988164i | \(-0.549024\pi\) | ||||
−0.153404 | + | 0.988164i | \(0.549024\pi\) | |||||||
\(908\) | 15.1464 | 0.502652 | ||||||||
\(909\) | 21.8357 | 0.724244 | ||||||||
\(910\) | −2.89534 | −0.0959795 | ||||||||
\(911\) | −46.6779 | −1.54651 | −0.773254 | − | 0.634097i | \(-0.781372\pi\) | ||||
−0.773254 | + | 0.634097i | \(0.781372\pi\) | |||||||
\(912\) | −0.613152 | −0.0203035 | ||||||||
\(913\) | −3.52418 | −0.116633 | ||||||||
\(914\) | 9.36018 | 0.309607 | ||||||||
\(915\) | 5.45014 | 0.180176 | ||||||||
\(916\) | −24.1376 | −0.797529 | ||||||||
\(917\) | 11.8662 | 0.391857 | ||||||||
\(918\) | 10.6987 | 0.353109 | ||||||||
\(919\) | 7.79819 | 0.257239 | 0.128619 | − | 0.991694i | \(-0.458945\pi\) | ||||
0.128619 | + | 0.991694i | \(0.458945\pi\) | |||||||
\(920\) | 4.83310 | 0.159343 | ||||||||
\(921\) | −22.4296 | −0.739080 | ||||||||
\(922\) | 31.5116 | 1.03778 | ||||||||
\(923\) | 5.28086 | 0.173822 | ||||||||
\(924\) | 1.79770 | 0.0591399 | ||||||||
\(925\) | −9.72092 | −0.319622 | ||||||||
\(926\) | 31.6852 | 1.04124 | ||||||||
\(927\) | 6.13006 | 0.201338 | ||||||||
\(928\) | −5.77853 | −0.189690 | ||||||||
\(929\) | 12.0048 | 0.393866 | 0.196933 | − | 0.980417i | \(-0.436902\pi\) | ||||
0.196933 | + | 0.980417i | \(0.436902\pi\) | |||||||
\(930\) | 11.4165 | 0.374361 | ||||||||
\(931\) | −2.36046 | −0.0773611 | ||||||||
\(932\) | −8.42912 | −0.276105 | ||||||||
\(933\) | −6.18151 | −0.202374 | ||||||||
\(934\) | −8.22554 | −0.269148 | ||||||||
\(935\) | −5.28569 | −0.172861 | ||||||||
\(936\) | −1.27516 | −0.0416800 | ||||||||
\(937\) | −7.27247 | −0.237581 | −0.118791 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118791 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(938\) | 1.26119 | 0.0411794 | ||||||||
\(939\) | −24.1172 | −0.787036 | ||||||||
\(940\) | 4.51864 | 0.147382 | ||||||||
\(941\) | 56.0480 | 1.82711 | 0.913556 | − | 0.406714i | \(-0.133325\pi\) | ||||
0.913556 | + | 0.406714i | \(0.133325\pi\) | |||||||
\(942\) | −11.7630 | −0.383261 | ||||||||
\(943\) | 2.56101 | 0.0833980 | ||||||||
\(944\) | −9.26718 | −0.301621 | ||||||||
\(945\) | −22.3328 | −0.726485 | ||||||||
\(946\) | −9.79286 | −0.318393 | ||||||||
\(947\) | 20.6617 | 0.671415 | 0.335707 | − | 0.941966i | \(-0.391025\pi\) | ||||
0.335707 | + | 0.941966i | \(0.391025\pi\) | |||||||
\(948\) | 15.1923 | 0.493422 | ||||||||
\(949\) | −7.57815 | −0.245997 | ||||||||
\(950\) | −0.803075 | −0.0260552 | ||||||||
\(951\) | 18.1435 | 0.588344 | ||||||||
\(952\) | −3.63909 | −0.117944 | ||||||||
\(953\) | 51.5227 | 1.66898 | 0.834492 | − | 0.551020i | \(-0.185761\pi\) | ||||
0.834492 | + | 0.551020i | \(0.185761\pi\) | |||||||
\(954\) | 17.5170 | 0.567133 | ||||||||
\(955\) | 1.55822 | 0.0504229 | ||||||||
\(956\) | 17.0649 | 0.551918 | ||||||||
\(957\) | −5.98460 | −0.193455 | ||||||||
\(958\) | 28.3633 | 0.916377 | ||||||||
\(959\) | −11.6336 | −0.375669 | ||||||||
\(960\) | −2.61111 | −0.0842732 | ||||||||
\(961\) | −11.8832 | −0.383330 | ||||||||
\(962\) | −4.74126 | −0.152864 | ||||||||
\(963\) | 14.3111 | 0.461167 | ||||||||
\(964\) | −2.91512 | −0.0938896 | ||||||||
\(965\) | −41.6991 | −1.34234 | ||||||||
\(966\) | 3.44615 | 0.110878 | ||||||||
\(967\) | 10.1949 | 0.327845 | 0.163922 | − | 0.986473i | \(-0.447585\pi\) | ||||
0.163922 | + | 0.986473i | \(0.447585\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 1.28547 | 0.0412953 | ||||||||
\(970\) | 9.29514 | 0.298449 | ||||||||
\(971\) | 38.2263 | 1.22674 | 0.613369 | − | 0.789796i | \(-0.289814\pi\) | ||||
0.613369 | + | 0.789796i | \(0.289814\pi\) | |||||||
\(972\) | −15.8242 | −0.507562 | ||||||||
\(973\) | 7.76005 | 0.248776 | ||||||||
\(974\) | −3.84730 | −0.123275 | ||||||||
\(975\) | 0.929428 | 0.0297655 | ||||||||
\(976\) | −2.08729 | −0.0668125 | ||||||||
\(977\) | −0.921778 | −0.0294903 | −0.0147452 | − | 0.999891i | \(-0.504694\pi\) | ||||
−0.0147452 | + | 0.999891i | \(0.504694\pi\) | |||||||
\(978\) | −17.1783 | −0.549302 | ||||||||
\(979\) | −13.6381 | −0.435875 | ||||||||
\(980\) | −10.0520 | −0.321101 | ||||||||
\(981\) | 17.4147 | 0.556008 | ||||||||
\(982\) | −26.6876 | −0.851636 | ||||||||
\(983\) | −10.6976 | −0.341199 | −0.170600 | − | 0.985340i | \(-0.554570\pi\) | ||||
−0.170600 | + | 0.985340i | \(0.554570\pi\) | |||||||
\(984\) | −1.38360 | −0.0441076 | ||||||||
\(985\) | 2.52120 | 0.0803322 | ||||||||
\(986\) | 12.1147 | 0.385810 | ||||||||
\(987\) | 3.22193 | 0.102555 | ||||||||
\(988\) | −0.391691 | −0.0124613 | ||||||||
\(989\) | −18.7727 | −0.596938 | ||||||||
\(990\) | 4.85938 | 0.154441 | ||||||||
\(991\) | 38.0455 | 1.20855 | 0.604277 | − | 0.796774i | \(-0.293462\pi\) | ||||
0.604277 | + | 0.796774i | \(0.293462\pi\) | |||||||
\(992\) | −4.37227 | −0.138820 | ||||||||
\(993\) | 20.5037 | 0.650664 | ||||||||
\(994\) | −13.8551 | −0.439459 | ||||||||
\(995\) | −8.48981 | −0.269145 | ||||||||
\(996\) | 3.64985 | 0.115650 | ||||||||
\(997\) | −53.6949 | −1.70053 | −0.850267 | − | 0.526352i | \(-0.823559\pi\) | ||||
−0.850267 | + | 0.526352i | \(0.823559\pi\) | |||||||
\(998\) | −10.1351 | −0.320820 | ||||||||
\(999\) | −36.5710 | −1.15706 |
(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 | 4334.2.a.a.1.5 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.5 | ✓ | 15 | 1.1 | even | 1 | trivial |