Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
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: | \( x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + \cdots - 43744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.69357\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.69357 | −0.757387 | −0.378694 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378694 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.25998 | 1.23216 | 0.616078 | − | 0.787685i | \(-0.288721\pi\) | ||||
0.616078 | + | 0.787685i | \(0.288721\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.69357 | −0.535553 | ||||||||
\(11\) | 5.34841 | 1.61261 | 0.806304 | − | 0.591502i | \(-0.201465\pi\) | ||||
0.806304 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.872188 | −0.241902 | −0.120951 | − | 0.992659i | \(-0.538594\pi\) | ||||
−0.120951 | + | 0.992659i | \(0.538594\pi\) | |||||||
\(14\) | 3.25998 | 0.871265 | ||||||||
\(15\) | 1.69357 | 0.437278 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −8.19698 | −1.88052 | −0.940258 | − | 0.340461i | \(-0.889417\pi\) | ||||
−0.940258 | + | 0.340461i | \(0.889417\pi\) | |||||||
\(20\) | −1.69357 | −0.378694 | ||||||||
\(21\) | −3.25998 | −0.711385 | ||||||||
\(22\) | 5.34841 | 1.14029 | ||||||||
\(23\) | 6.81251 | 1.42051 | 0.710253 | − | 0.703947i | \(-0.248581\pi\) | ||||
0.710253 | + | 0.703947i | \(0.248581\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.13182 | −0.426365 | ||||||||
\(26\) | −0.872188 | −0.171050 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.25998 | 0.616078 | ||||||||
\(29\) | 7.06454 | 1.31185 | 0.655926 | − | 0.754825i | \(-0.272278\pi\) | ||||
0.655926 | + | 0.754825i | \(0.272278\pi\) | |||||||
\(30\) | 1.69357 | 0.309202 | ||||||||
\(31\) | 8.08471 | 1.45206 | 0.726028 | − | 0.687665i | \(-0.241364\pi\) | ||||
0.726028 | + | 0.687665i | \(0.241364\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.34841 | −0.931039 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −5.52099 | −0.933218 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.23414 | 0.860487 | 0.430244 | − | 0.902713i | \(-0.358428\pi\) | ||||
0.430244 | + | 0.902713i | \(0.358428\pi\) | |||||||
\(38\) | −8.19698 | −1.32973 | ||||||||
\(39\) | 0.872188 | 0.139662 | ||||||||
\(40\) | −1.69357 | −0.267777 | ||||||||
\(41\) | −11.8798 | −1.85532 | −0.927659 | − | 0.373429i | \(-0.878182\pi\) | ||||
−0.927659 | + | 0.373429i | \(0.878182\pi\) | |||||||
\(42\) | −3.25998 | −0.503025 | ||||||||
\(43\) | 8.64072 | 1.31770 | 0.658848 | − | 0.752276i | \(-0.271044\pi\) | ||||
0.658848 | + | 0.752276i | \(0.271044\pi\) | |||||||
\(44\) | 5.34841 | 0.806304 | ||||||||
\(45\) | −1.69357 | −0.252462 | ||||||||
\(46\) | 6.81251 | 1.00445 | ||||||||
\(47\) | 2.11402 | 0.308361 | 0.154180 | − | 0.988043i | \(-0.450726\pi\) | ||||
0.154180 | + | 0.988043i | \(0.450726\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.62744 | 0.518206 | ||||||||
\(50\) | −2.13182 | −0.301486 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −0.872188 | −0.120951 | ||||||||
\(53\) | −9.00406 | −1.23680 | −0.618402 | − | 0.785862i | \(-0.712219\pi\) | ||||
−0.618402 | + | 0.785862i | \(0.712219\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −9.05791 | −1.22137 | ||||||||
\(56\) | 3.25998 | 0.435633 | ||||||||
\(57\) | 8.19698 | 1.08572 | ||||||||
\(58\) | 7.06454 | 0.927620 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 1.69357 | 0.218639 | ||||||||
\(61\) | 13.5963 | 1.74083 | 0.870415 | − | 0.492319i | \(-0.163851\pi\) | ||||
0.870415 | + | 0.492319i | \(0.163851\pi\) | |||||||
\(62\) | 8.08471 | 1.02676 | ||||||||
\(63\) | 3.25998 | 0.410718 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.47711 | 0.183213 | ||||||||
\(66\) | −5.34841 | −0.658344 | ||||||||
\(67\) | −8.42336 | −1.02908 | −0.514539 | − | 0.857467i | \(-0.672037\pi\) | ||||
−0.514539 | + | 0.857467i | \(0.672037\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −6.81251 | −0.820129 | ||||||||
\(70\) | −5.52099 | −0.659885 | ||||||||
\(71\) | 4.49841 | 0.533863 | 0.266932 | − | 0.963715i | \(-0.413990\pi\) | ||||
0.266932 | + | 0.963715i | \(0.413990\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.42134 | −0.985643 | −0.492822 | − | 0.870130i | \(-0.664034\pi\) | ||||
−0.492822 | + | 0.870130i | \(0.664034\pi\) | |||||||
\(74\) | 5.23414 | 0.608456 | ||||||||
\(75\) | 2.13182 | 0.246162 | ||||||||
\(76\) | −8.19698 | −0.940258 | ||||||||
\(77\) | 17.4357 | 1.98698 | ||||||||
\(78\) | 0.872188 | 0.0987559 | ||||||||
\(79\) | −4.21233 | −0.473924 | −0.236962 | − | 0.971519i | \(-0.576152\pi\) | ||||
−0.236962 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(80\) | −1.69357 | −0.189347 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.8798 | −1.31191 | ||||||||
\(83\) | 11.0390 | 1.21169 | 0.605843 | − | 0.795584i | \(-0.292836\pi\) | ||||
0.605843 | + | 0.795584i | \(0.292836\pi\) | |||||||
\(84\) | −3.25998 | −0.355693 | ||||||||
\(85\) | −1.69357 | −0.183693 | ||||||||
\(86\) | 8.64072 | 0.931752 | ||||||||
\(87\) | −7.06454 | −0.757398 | ||||||||
\(88\) | 5.34841 | 0.570143 | ||||||||
\(89\) | −10.7178 | −1.13608 | −0.568041 | − | 0.823000i | \(-0.692299\pi\) | ||||
−0.568041 | + | 0.823000i | \(0.692299\pi\) | |||||||
\(90\) | −1.69357 | −0.178518 | ||||||||
\(91\) | −2.84331 | −0.298060 | ||||||||
\(92\) | 6.81251 | 0.710253 | ||||||||
\(93\) | −8.08471 | −0.838345 | ||||||||
\(94\) | 2.11402 | 0.218044 | ||||||||
\(95\) | 13.8822 | 1.42428 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.447712 | −0.0454583 | −0.0227291 | − | 0.999742i | \(-0.507236\pi\) | ||||
−0.0227291 | + | 0.999742i | \(0.507236\pi\) | |||||||
\(98\) | 3.62744 | 0.366427 | ||||||||
\(99\) | 5.34841 | 0.537536 | ||||||||
\(100\) | −2.13182 | −0.213182 | ||||||||
\(101\) | −15.2331 | −1.51575 | −0.757877 | − | 0.652397i | \(-0.773763\pi\) | ||||
−0.757877 | + | 0.652397i | \(0.773763\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −13.1296 | −1.29370 | −0.646848 | − | 0.762619i | \(-0.723913\pi\) | ||||
−0.646848 | + | 0.762619i | \(0.723913\pi\) | |||||||
\(104\) | −0.872188 | −0.0855251 | ||||||||
\(105\) | 5.52099 | 0.538794 | ||||||||
\(106\) | −9.00406 | −0.874552 | ||||||||
\(107\) | 4.99176 | 0.482572 | 0.241286 | − | 0.970454i | \(-0.422431\pi\) | ||||
0.241286 | + | 0.970454i | \(0.422431\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −3.85965 | −0.369687 | −0.184844 | − | 0.982768i | \(-0.559178\pi\) | ||||
−0.184844 | + | 0.982768i | \(0.559178\pi\) | |||||||
\(110\) | −9.05791 | −0.863637 | ||||||||
\(111\) | −5.23414 | −0.496803 | ||||||||
\(112\) | 3.25998 | 0.308039 | ||||||||
\(113\) | 2.85200 | 0.268293 | 0.134147 | − | 0.990961i | \(-0.457171\pi\) | ||||
0.134147 | + | 0.990961i | \(0.457171\pi\) | |||||||
\(114\) | 8.19698 | 0.767718 | ||||||||
\(115\) | −11.5374 | −1.07587 | ||||||||
\(116\) | 7.06454 | 0.655926 | ||||||||
\(117\) | −0.872188 | −0.0806338 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 3.25998 | 0.298842 | ||||||||
\(120\) | 1.69357 | 0.154601 | ||||||||
\(121\) | 17.6055 | 1.60050 | ||||||||
\(122\) | 13.5963 | 1.23095 | ||||||||
\(123\) | 11.8798 | 1.07117 | ||||||||
\(124\) | 8.08471 | 0.726028 | ||||||||
\(125\) | 12.0782 | 1.08031 | ||||||||
\(126\) | 3.25998 | 0.290422 | ||||||||
\(127\) | 13.0162 | 1.15500 | 0.577502 | − | 0.816389i | \(-0.304027\pi\) | ||||
0.577502 | + | 0.816389i | \(0.304027\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.64072 | −0.760773 | ||||||||
\(130\) | 1.47711 | 0.129551 | ||||||||
\(131\) | 5.81999 | 0.508495 | 0.254247 | − | 0.967139i | \(-0.418172\pi\) | ||||
0.254247 | + | 0.967139i | \(0.418172\pi\) | |||||||
\(132\) | −5.34841 | −0.465520 | ||||||||
\(133\) | −26.7220 | −2.31709 | ||||||||
\(134\) | −8.42336 | −0.727668 | ||||||||
\(135\) | 1.69357 | 0.145759 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −6.73352 | −0.575283 | −0.287642 | − | 0.957738i | \(-0.592871\pi\) | ||||
−0.287642 | + | 0.957738i | \(0.592871\pi\) | |||||||
\(138\) | −6.81251 | −0.579919 | ||||||||
\(139\) | 11.5918 | 0.983207 | 0.491603 | − | 0.870819i | \(-0.336411\pi\) | ||||
0.491603 | + | 0.870819i | \(0.336411\pi\) | |||||||
\(140\) | −5.52099 | −0.466609 | ||||||||
\(141\) | −2.11402 | −0.178032 | ||||||||
\(142\) | 4.49841 | 0.377498 | ||||||||
\(143\) | −4.66482 | −0.390092 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −11.9643 | −0.993580 | ||||||||
\(146\) | −8.42134 | −0.696955 | ||||||||
\(147\) | −3.62744 | −0.299187 | ||||||||
\(148\) | 5.23414 | 0.430244 | ||||||||
\(149\) | 14.2808 | 1.16993 | 0.584964 | − | 0.811059i | \(-0.301108\pi\) | ||||
0.584964 | + | 0.811059i | \(0.301108\pi\) | |||||||
\(150\) | 2.13182 | 0.174063 | ||||||||
\(151\) | 10.6867 | 0.869669 | 0.434835 | − | 0.900510i | \(-0.356807\pi\) | ||||
0.434835 | + | 0.900510i | \(0.356807\pi\) | |||||||
\(152\) | −8.19698 | −0.664863 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 17.4357 | 1.40501 | ||||||||
\(155\) | −13.6920 | −1.09977 | ||||||||
\(156\) | 0.872188 | 0.0698309 | ||||||||
\(157\) | 19.3407 | 1.54356 | 0.771780 | − | 0.635890i | \(-0.219367\pi\) | ||||
0.771780 | + | 0.635890i | \(0.219367\pi\) | |||||||
\(158\) | −4.21233 | −0.335115 | ||||||||
\(159\) | 9.00406 | 0.714069 | ||||||||
\(160\) | −1.69357 | −0.133888 | ||||||||
\(161\) | 22.2086 | 1.75028 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 11.5555 | 0.905095 | 0.452547 | − | 0.891740i | \(-0.350515\pi\) | ||||
0.452547 | + | 0.891740i | \(0.350515\pi\) | |||||||
\(164\) | −11.8798 | −0.927659 | ||||||||
\(165\) | 9.05791 | 0.705157 | ||||||||
\(166\) | 11.0390 | 0.856791 | ||||||||
\(167\) | 0.0924743 | 0.00715587 | 0.00357794 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357794 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(168\) | −3.25998 | −0.251513 | ||||||||
\(169\) | −12.2393 | −0.941484 | ||||||||
\(170\) | −1.69357 | −0.129891 | ||||||||
\(171\) | −8.19698 | −0.626839 | ||||||||
\(172\) | 8.64072 | 0.658848 | ||||||||
\(173\) | −19.6366 | −1.49295 | −0.746473 | − | 0.665416i | \(-0.768254\pi\) | ||||
−0.746473 | + | 0.665416i | \(0.768254\pi\) | |||||||
\(174\) | −7.06454 | −0.535561 | ||||||||
\(175\) | −6.94970 | −0.525348 | ||||||||
\(176\) | 5.34841 | 0.403152 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −10.7178 | −0.803332 | ||||||||
\(179\) | 0.451919 | 0.0337780 | 0.0168890 | − | 0.999857i | \(-0.494624\pi\) | ||||
0.0168890 | + | 0.999857i | \(0.494624\pi\) | |||||||
\(180\) | −1.69357 | −0.126231 | ||||||||
\(181\) | 11.0413 | 0.820690 | 0.410345 | − | 0.911930i | \(-0.365408\pi\) | ||||
0.410345 | + | 0.911930i | \(0.365408\pi\) | |||||||
\(182\) | −2.84331 | −0.210760 | ||||||||
\(183\) | −13.5963 | −1.00507 | ||||||||
\(184\) | 6.81251 | 0.502225 | ||||||||
\(185\) | −8.86438 | −0.651722 | ||||||||
\(186\) | −8.08471 | −0.592800 | ||||||||
\(187\) | 5.34841 | 0.391115 | ||||||||
\(188\) | 2.11402 | 0.154180 | ||||||||
\(189\) | −3.25998 | −0.237128 | ||||||||
\(190\) | 13.8822 | 1.00712 | ||||||||
\(191\) | 10.8266 | 0.783386 | 0.391693 | − | 0.920096i | \(-0.371890\pi\) | ||||
0.391693 | + | 0.920096i | \(0.371890\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.00971922 | −0.000699605 0 | −0.000349802 | − | 1.00000i | \(-0.500111\pi\) | ||||
−0.000349802 | 1.00000i | \(0.500111\pi\) | ||||||||
\(194\) | −0.447712 | −0.0321439 | ||||||||
\(195\) | −1.47711 | −0.105778 | ||||||||
\(196\) | 3.62744 | 0.259103 | ||||||||
\(197\) | −23.4333 | −1.66955 | −0.834776 | − | 0.550590i | \(-0.814403\pi\) | ||||
−0.834776 | + | 0.550590i | \(0.814403\pi\) | |||||||
\(198\) | 5.34841 | 0.380095 | ||||||||
\(199\) | 13.7943 | 0.977851 | 0.488926 | − | 0.872325i | \(-0.337389\pi\) | ||||
0.488926 | + | 0.872325i | \(0.337389\pi\) | |||||||
\(200\) | −2.13182 | −0.150743 | ||||||||
\(201\) | 8.42336 | 0.594138 | ||||||||
\(202\) | −15.2331 | −1.07180 | ||||||||
\(203\) | 23.0302 | 1.61641 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 20.1193 | 1.40519 | ||||||||
\(206\) | −13.1296 | −0.914781 | ||||||||
\(207\) | 6.81251 | 0.473502 | ||||||||
\(208\) | −0.872188 | −0.0604754 | ||||||||
\(209\) | −43.8409 | −3.03254 | ||||||||
\(210\) | 5.52099 | 0.380985 | ||||||||
\(211\) | 12.7991 | 0.881124 | 0.440562 | − | 0.897722i | \(-0.354779\pi\) | ||||
0.440562 | + | 0.897722i | \(0.354779\pi\) | |||||||
\(212\) | −9.00406 | −0.618402 | ||||||||
\(213\) | −4.49841 | −0.308226 | ||||||||
\(214\) | 4.99176 | 0.341230 | ||||||||
\(215\) | −14.6336 | −0.998006 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 26.3560 | 1.78916 | ||||||||
\(218\) | −3.85965 | −0.261408 | ||||||||
\(219\) | 8.42134 | 0.569061 | ||||||||
\(220\) | −9.05791 | −0.610684 | ||||||||
\(221\) | −0.872188 | −0.0586697 | ||||||||
\(222\) | −5.23414 | −0.351292 | ||||||||
\(223\) | 4.15974 | 0.278557 | 0.139278 | − | 0.990253i | \(-0.455522\pi\) | ||||
0.139278 | + | 0.990253i | \(0.455522\pi\) | |||||||
\(224\) | 3.25998 | 0.217816 | ||||||||
\(225\) | −2.13182 | −0.142122 | ||||||||
\(226\) | 2.85200 | 0.189712 | ||||||||
\(227\) | −8.45801 | −0.561378 | −0.280689 | − | 0.959799i | \(-0.590563\pi\) | ||||
−0.280689 | + | 0.959799i | \(0.590563\pi\) | |||||||
\(228\) | 8.19698 | 0.542858 | ||||||||
\(229\) | 18.5289 | 1.22442 | 0.612212 | − | 0.790694i | \(-0.290280\pi\) | ||||
0.612212 | + | 0.790694i | \(0.290280\pi\) | |||||||
\(230\) | −11.5374 | −0.760757 | ||||||||
\(231\) | −17.4357 | −1.14718 | ||||||||
\(232\) | 7.06454 | 0.463810 | ||||||||
\(233\) | −0.749085 | −0.0490742 | −0.0245371 | − | 0.999699i | \(-0.507811\pi\) | ||||
−0.0245371 | + | 0.999699i | \(0.507811\pi\) | |||||||
\(234\) | −0.872188 | −0.0570167 | ||||||||
\(235\) | −3.58023 | −0.233548 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 4.21233 | 0.273620 | ||||||||
\(238\) | 3.25998 | 0.211313 | ||||||||
\(239\) | −15.0757 | −0.975167 | −0.487584 | − | 0.873076i | \(-0.662122\pi\) | ||||
−0.487584 | + | 0.873076i | \(0.662122\pi\) | |||||||
\(240\) | 1.69357 | 0.109319 | ||||||||
\(241\) | −23.0265 | −1.48327 | −0.741633 | − | 0.670805i | \(-0.765949\pi\) | ||||
−0.741633 | + | 0.670805i | \(0.765949\pi\) | |||||||
\(242\) | 17.6055 | 1.13173 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.5963 | 0.870415 | ||||||||
\(245\) | −6.14333 | −0.392483 | ||||||||
\(246\) | 11.8798 | 0.757430 | ||||||||
\(247\) | 7.14931 | 0.454900 | ||||||||
\(248\) | 8.08471 | 0.513379 | ||||||||
\(249\) | −11.0390 | −0.699567 | ||||||||
\(250\) | 12.0782 | 0.763895 | ||||||||
\(251\) | 1.14905 | 0.0725273 | 0.0362637 | − | 0.999342i | \(-0.488454\pi\) | ||||
0.0362637 | + | 0.999342i | \(0.488454\pi\) | |||||||
\(252\) | 3.25998 | 0.205359 | ||||||||
\(253\) | 36.4361 | 2.29072 | ||||||||
\(254\) | 13.0162 | 0.816712 | ||||||||
\(255\) | 1.69357 | 0.106055 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.01500 | −0.312827 | −0.156414 | − | 0.987692i | \(-0.549993\pi\) | ||||
−0.156414 | + | 0.987692i | \(0.549993\pi\) | |||||||
\(258\) | −8.64072 | −0.537947 | ||||||||
\(259\) | 17.0632 | 1.06025 | ||||||||
\(260\) | 1.47711 | 0.0916065 | ||||||||
\(261\) | 7.06454 | 0.437284 | ||||||||
\(262\) | 5.81999 | 0.359560 | ||||||||
\(263\) | 27.6970 | 1.70787 | 0.853935 | − | 0.520380i | \(-0.174210\pi\) | ||||
0.853935 | + | 0.520380i | \(0.174210\pi\) | |||||||
\(264\) | −5.34841 | −0.329172 | ||||||||
\(265\) | 15.2490 | 0.936739 | ||||||||
\(266\) | −26.7220 | −1.63843 | ||||||||
\(267\) | 10.7178 | 0.655918 | ||||||||
\(268\) | −8.42336 | −0.514539 | ||||||||
\(269\) | 23.4650 | 1.43069 | 0.715343 | − | 0.698774i | \(-0.246270\pi\) | ||||
0.715343 | + | 0.698774i | \(0.246270\pi\) | |||||||
\(270\) | 1.69357 | 0.103067 | ||||||||
\(271\) | 12.9670 | 0.787689 | 0.393844 | − | 0.919177i | \(-0.371145\pi\) | ||||
0.393844 | + | 0.919177i | \(0.371145\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 2.84331 | 0.172085 | ||||||||
\(274\) | −6.73352 | −0.406787 | ||||||||
\(275\) | −11.4019 | −0.687559 | ||||||||
\(276\) | −6.81251 | −0.410065 | ||||||||
\(277\) | 6.44021 | 0.386955 | 0.193477 | − | 0.981105i | \(-0.438023\pi\) | ||||
0.193477 | + | 0.981105i | \(0.438023\pi\) | |||||||
\(278\) | 11.5918 | 0.695232 | ||||||||
\(279\) | 8.08471 | 0.484019 | ||||||||
\(280\) | −5.52099 | −0.329943 | ||||||||
\(281\) | 2.49667 | 0.148939 | 0.0744696 | − | 0.997223i | \(-0.476274\pi\) | ||||
0.0744696 | + | 0.997223i | \(0.476274\pi\) | |||||||
\(282\) | −2.11402 | −0.125888 | ||||||||
\(283\) | 5.33765 | 0.317290 | 0.158645 | − | 0.987336i | \(-0.449287\pi\) | ||||
0.158645 | + | 0.987336i | \(0.449287\pi\) | |||||||
\(284\) | 4.49841 | 0.266932 | ||||||||
\(285\) | −13.8822 | −0.822308 | ||||||||
\(286\) | −4.66482 | −0.275837 | ||||||||
\(287\) | −38.7280 | −2.28604 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −11.9643 | −0.702567 | ||||||||
\(291\) | 0.447712 | 0.0262454 | ||||||||
\(292\) | −8.42134 | −0.492822 | ||||||||
\(293\) | 32.0747 | 1.87382 | 0.936912 | − | 0.349566i | \(-0.113671\pi\) | ||||
0.936912 | + | 0.349566i | \(0.113671\pi\) | |||||||
\(294\) | −3.62744 | −0.211557 | ||||||||
\(295\) | −1.69357 | −0.0986034 | ||||||||
\(296\) | 5.23414 | 0.304228 | ||||||||
\(297\) | −5.34841 | −0.310346 | ||||||||
\(298\) | 14.2808 | 0.827265 | ||||||||
\(299\) | −5.94179 | −0.343622 | ||||||||
\(300\) | 2.13182 | 0.123081 | ||||||||
\(301\) | 28.1685 | 1.62361 | ||||||||
\(302\) | 10.6867 | 0.614949 | ||||||||
\(303\) | 15.2331 | 0.875121 | ||||||||
\(304\) | −8.19698 | −0.470129 | ||||||||
\(305\) | −23.0263 | −1.31848 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −4.21824 | −0.240748 | −0.120374 | − | 0.992729i | \(-0.538409\pi\) | ||||
−0.120374 | + | 0.992729i | \(0.538409\pi\) | |||||||
\(308\) | 17.4357 | 0.993491 | ||||||||
\(309\) | 13.1296 | 0.746915 | ||||||||
\(310\) | −13.6920 | −0.777654 | ||||||||
\(311\) | 29.6866 | 1.68337 | 0.841686 | − | 0.539967i | \(-0.181563\pi\) | ||||
0.841686 | + | 0.539967i | \(0.181563\pi\) | |||||||
\(312\) | 0.872188 | 0.0493779 | ||||||||
\(313\) | 2.46778 | 0.139487 | 0.0697437 | − | 0.997565i | \(-0.477782\pi\) | ||||
0.0697437 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(314\) | 19.3407 | 1.09146 | ||||||||
\(315\) | −5.52099 | −0.311073 | ||||||||
\(316\) | −4.21233 | −0.236962 | ||||||||
\(317\) | −17.5247 | −0.984286 | −0.492143 | − | 0.870514i | \(-0.663786\pi\) | ||||
−0.492143 | + | 0.870514i | \(0.663786\pi\) | |||||||
\(318\) | 9.00406 | 0.504923 | ||||||||
\(319\) | 37.7841 | 2.11550 | ||||||||
\(320\) | −1.69357 | −0.0946734 | ||||||||
\(321\) | −4.99176 | −0.278613 | ||||||||
\(322\) | 22.2086 | 1.23764 | ||||||||
\(323\) | −8.19698 | −0.456092 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.85935 | 0.103138 | ||||||||
\(326\) | 11.5555 | 0.639999 | ||||||||
\(327\) | 3.85965 | 0.213439 | ||||||||
\(328\) | −11.8798 | −0.655954 | ||||||||
\(329\) | 6.89164 | 0.379948 | ||||||||
\(330\) | 9.05791 | 0.498621 | ||||||||
\(331\) | −2.76351 | −0.151897 | −0.0759483 | − | 0.997112i | \(-0.524198\pi\) | ||||
−0.0759483 | + | 0.997112i | \(0.524198\pi\) | |||||||
\(332\) | 11.0390 | 0.605843 | ||||||||
\(333\) | 5.23414 | 0.286829 | ||||||||
\(334\) | 0.0924743 | 0.00505997 | ||||||||
\(335\) | 14.2655 | 0.779410 | ||||||||
\(336\) | −3.25998 | −0.177846 | ||||||||
\(337\) | −17.1206 | −0.932620 | −0.466310 | − | 0.884621i | \(-0.654417\pi\) | ||||
−0.466310 | + | 0.884621i | \(0.654417\pi\) | |||||||
\(338\) | −12.2393 | −0.665729 | ||||||||
\(339\) | −2.85200 | −0.154899 | ||||||||
\(340\) | −1.69357 | −0.0918467 | ||||||||
\(341\) | 43.2404 | 2.34160 | ||||||||
\(342\) | −8.19698 | −0.443242 | ||||||||
\(343\) | −10.9944 | −0.593644 | ||||||||
\(344\) | 8.64072 | 0.465876 | ||||||||
\(345\) | 11.5374 | 0.621155 | ||||||||
\(346\) | −19.6366 | −1.05567 | ||||||||
\(347\) | 14.8909 | 0.799385 | 0.399693 | − | 0.916649i | \(-0.369117\pi\) | ||||
0.399693 | + | 0.916649i | \(0.369117\pi\) | |||||||
\(348\) | −7.06454 | −0.378699 | ||||||||
\(349\) | 7.01012 | 0.375243 | 0.187622 | − | 0.982241i | \(-0.439922\pi\) | ||||
0.187622 | + | 0.982241i | \(0.439922\pi\) | |||||||
\(350\) | −6.94970 | −0.371477 | ||||||||
\(351\) | 0.872188 | 0.0465540 | ||||||||
\(352\) | 5.34841 | 0.285071 | ||||||||
\(353\) | −9.62932 | −0.512517 | −0.256259 | − | 0.966608i | \(-0.582490\pi\) | ||||
−0.256259 | + | 0.966608i | \(0.582490\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | −7.61837 | −0.404341 | ||||||||
\(356\) | −10.7178 | −0.568041 | ||||||||
\(357\) | −3.25998 | −0.172536 | ||||||||
\(358\) | 0.451919 | 0.0238847 | ||||||||
\(359\) | 23.3764 | 1.23376 | 0.616879 | − | 0.787058i | \(-0.288397\pi\) | ||||
0.616879 | + | 0.787058i | \(0.288397\pi\) | |||||||
\(360\) | −1.69357 | −0.0892589 | ||||||||
\(361\) | 48.1905 | 2.53634 | ||||||||
\(362\) | 11.0413 | 0.580316 | ||||||||
\(363\) | −17.6055 | −0.924051 | ||||||||
\(364\) | −2.84331 | −0.149030 | ||||||||
\(365\) | 14.2621 | 0.746513 | ||||||||
\(366\) | −13.5963 | −0.710691 | ||||||||
\(367\) | 24.6623 | 1.28736 | 0.643679 | − | 0.765295i | \(-0.277407\pi\) | ||||
0.643679 | + | 0.765295i | \(0.277407\pi\) | |||||||
\(368\) | 6.81251 | 0.355126 | ||||||||
\(369\) | −11.8798 | −0.618439 | ||||||||
\(370\) | −8.86438 | −0.460837 | ||||||||
\(371\) | −29.3530 | −1.52393 | ||||||||
\(372\) | −8.08471 | −0.419173 | ||||||||
\(373\) | 22.3356 | 1.15649 | 0.578246 | − | 0.815863i | \(-0.303737\pi\) | ||||
0.578246 | + | 0.815863i | \(0.303737\pi\) | |||||||
\(374\) | 5.34841 | 0.276560 | ||||||||
\(375\) | −12.0782 | −0.623717 | ||||||||
\(376\) | 2.11402 | 0.109022 | ||||||||
\(377\) | −6.16161 | −0.317339 | ||||||||
\(378\) | −3.25998 | −0.167675 | ||||||||
\(379\) | 5.75391 | 0.295559 | 0.147779 | − | 0.989020i | \(-0.452787\pi\) | ||||
0.147779 | + | 0.989020i | \(0.452787\pi\) | |||||||
\(380\) | 13.8822 | 0.712140 | ||||||||
\(381\) | −13.0162 | −0.666842 | ||||||||
\(382\) | 10.8266 | 0.553938 | ||||||||
\(383\) | −26.5189 | −1.35505 | −0.677527 | − | 0.735498i | \(-0.736948\pi\) | ||||
−0.677527 | + | 0.735498i | \(0.736948\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −29.5286 | −1.50491 | ||||||||
\(386\) | −0.00971922 | −0.000494695 0 | ||||||||
\(387\) | 8.64072 | 0.439232 | ||||||||
\(388\) | −0.447712 | −0.0227291 | ||||||||
\(389\) | −10.4405 | −0.529354 | −0.264677 | − | 0.964337i | \(-0.585265\pi\) | ||||
−0.264677 | + | 0.964337i | \(0.585265\pi\) | |||||||
\(390\) | −1.47711 | −0.0747964 | ||||||||
\(391\) | 6.81251 | 0.344523 | ||||||||
\(392\) | 3.62744 | 0.183214 | ||||||||
\(393\) | −5.81999 | −0.293580 | ||||||||
\(394\) | −23.4333 | −1.18055 | ||||||||
\(395\) | 7.13387 | 0.358944 | ||||||||
\(396\) | 5.34841 | 0.268768 | ||||||||
\(397\) | 20.0503 | 1.00630 | 0.503148 | − | 0.864200i | \(-0.332175\pi\) | ||||
0.503148 | + | 0.864200i | \(0.332175\pi\) | |||||||
\(398\) | 13.7943 | 0.691445 | ||||||||
\(399\) | 26.7220 | 1.33777 | ||||||||
\(400\) | −2.13182 | −0.106591 | ||||||||
\(401\) | 27.4728 | 1.37193 | 0.685963 | − | 0.727636i | \(-0.259381\pi\) | ||||
0.685963 | + | 0.727636i | \(0.259381\pi\) | |||||||
\(402\) | 8.42336 | 0.420119 | ||||||||
\(403\) | −7.05139 | −0.351255 | ||||||||
\(404\) | −15.2331 | −0.757877 | ||||||||
\(405\) | −1.69357 | −0.0841541 | ||||||||
\(406\) | 23.0302 | 1.14297 | ||||||||
\(407\) | 27.9943 | 1.38763 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −26.2901 | −1.29996 | −0.649981 | − | 0.759950i | \(-0.725223\pi\) | ||||
−0.649981 | + | 0.759950i | \(0.725223\pi\) | |||||||
\(410\) | 20.1193 | 0.993622 | ||||||||
\(411\) | 6.73352 | 0.332140 | ||||||||
\(412\) | −13.1296 | −0.646848 | ||||||||
\(413\) | 3.25998 | 0.160413 | ||||||||
\(414\) | 6.81251 | 0.334816 | ||||||||
\(415\) | −18.6953 | −0.917715 | ||||||||
\(416\) | −0.872188 | −0.0427625 | ||||||||
\(417\) | −11.5918 | −0.567655 | ||||||||
\(418\) | −43.8409 | −2.14433 | ||||||||
\(419\) | −21.7764 | −1.06385 | −0.531923 | − | 0.846793i | \(-0.678530\pi\) | ||||
−0.531923 | + | 0.846793i | \(0.678530\pi\) | |||||||
\(420\) | 5.52099 | 0.269397 | ||||||||
\(421\) | −22.5632 | −1.09966 | −0.549832 | − | 0.835276i | \(-0.685308\pi\) | ||||
−0.549832 | + | 0.835276i | \(0.685308\pi\) | |||||||
\(422\) | 12.7991 | 0.623049 | ||||||||
\(423\) | 2.11402 | 0.102787 | ||||||||
\(424\) | −9.00406 | −0.437276 | ||||||||
\(425\) | −2.13182 | −0.103409 | ||||||||
\(426\) | −4.49841 | −0.217949 | ||||||||
\(427\) | 44.3237 | 2.14497 | ||||||||
\(428\) | 4.99176 | 0.241286 | ||||||||
\(429\) | 4.66482 | 0.225220 | ||||||||
\(430\) | −14.6336 | −0.705697 | ||||||||
\(431\) | −20.8086 | −1.00231 | −0.501157 | − | 0.865356i | \(-0.667092\pi\) | ||||
−0.501157 | + | 0.865356i | \(0.667092\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −10.9005 | −0.523842 | −0.261921 | − | 0.965089i | \(-0.584356\pi\) | ||||
−0.261921 | + | 0.965089i | \(0.584356\pi\) | |||||||
\(434\) | 26.3560 | 1.26513 | ||||||||
\(435\) | 11.9643 | 0.573644 | ||||||||
\(436\) | −3.85965 | −0.184844 | ||||||||
\(437\) | −55.8420 | −2.67129 | ||||||||
\(438\) | 8.42134 | 0.402387 | ||||||||
\(439\) | 8.77870 | 0.418984 | 0.209492 | − | 0.977810i | \(-0.432819\pi\) | ||||
0.209492 | + | 0.977810i | \(0.432819\pi\) | |||||||
\(440\) | −9.05791 | −0.431819 | ||||||||
\(441\) | 3.62744 | 0.172735 | ||||||||
\(442\) | −0.872188 | −0.0414858 | ||||||||
\(443\) | −36.9950 | −1.75769 | −0.878843 | − | 0.477111i | \(-0.841684\pi\) | ||||
−0.878843 | + | 0.477111i | \(0.841684\pi\) | |||||||
\(444\) | −5.23414 | −0.248401 | ||||||||
\(445\) | 18.1513 | 0.860454 | ||||||||
\(446\) | 4.15974 | 0.196969 | ||||||||
\(447\) | −14.2808 | −0.675459 | ||||||||
\(448\) | 3.25998 | 0.154019 | ||||||||
\(449\) | −35.1087 | −1.65688 | −0.828442 | − | 0.560075i | \(-0.810772\pi\) | ||||
−0.828442 | + | 0.560075i | \(0.810772\pi\) | |||||||
\(450\) | −2.13182 | −0.100495 | ||||||||
\(451\) | −63.5382 | −2.99190 | ||||||||
\(452\) | 2.85200 | 0.134147 | ||||||||
\(453\) | −10.6867 | −0.502104 | ||||||||
\(454\) | −8.45801 | −0.396954 | ||||||||
\(455\) | 4.81535 | 0.225747 | ||||||||
\(456\) | 8.19698 | 0.383859 | ||||||||
\(457\) | 21.7100 | 1.01555 | 0.507776 | − | 0.861489i | \(-0.330468\pi\) | ||||
0.507776 | + | 0.861489i | \(0.330468\pi\) | |||||||
\(458\) | 18.5289 | 0.865798 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −11.5374 | −0.537936 | ||||||||
\(461\) | 4.25372 | 0.198115 | 0.0990577 | − | 0.995082i | \(-0.468417\pi\) | ||||
0.0990577 | + | 0.995082i | \(0.468417\pi\) | |||||||
\(462\) | −17.4357 | −0.811182 | ||||||||
\(463\) | −31.3122 | −1.45520 | −0.727602 | − | 0.686000i | \(-0.759365\pi\) | ||||
−0.727602 | + | 0.686000i | \(0.759365\pi\) | |||||||
\(464\) | 7.06454 | 0.327963 | ||||||||
\(465\) | 13.6920 | 0.634952 | ||||||||
\(466\) | −0.749085 | −0.0347007 | ||||||||
\(467\) | −17.8953 | −0.828096 | −0.414048 | − | 0.910255i | \(-0.635885\pi\) | ||||
−0.414048 | + | 0.910255i | \(0.635885\pi\) | |||||||
\(468\) | −0.872188 | −0.0403169 | ||||||||
\(469\) | −27.4600 | −1.26798 | ||||||||
\(470\) | −3.58023 | −0.165144 | ||||||||
\(471\) | −19.3407 | −0.891175 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 46.2141 | 2.12493 | ||||||||
\(474\) | 4.21233 | 0.193479 | ||||||||
\(475\) | 17.4745 | 0.801786 | ||||||||
\(476\) | 3.25998 | 0.149421 | ||||||||
\(477\) | −9.00406 | −0.412268 | ||||||||
\(478\) | −15.0757 | −0.689547 | ||||||||
\(479\) | −13.5206 | −0.617772 | −0.308886 | − | 0.951099i | \(-0.599956\pi\) | ||||
−0.308886 | + | 0.951099i | \(0.599956\pi\) | |||||||
\(480\) | 1.69357 | 0.0773005 | ||||||||
\(481\) | −4.56515 | −0.208153 | ||||||||
\(482\) | −23.0265 | −1.04883 | ||||||||
\(483\) | −22.2086 | −1.01053 | ||||||||
\(484\) | 17.6055 | 0.800251 | ||||||||
\(485\) | 0.758232 | 0.0344295 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 28.7702 | 1.30370 | 0.651851 | − | 0.758347i | \(-0.273993\pi\) | ||||
0.651851 | + | 0.758347i | \(0.273993\pi\) | |||||||
\(488\) | 13.5963 | 0.615476 | ||||||||
\(489\) | −11.5555 | −0.522557 | ||||||||
\(490\) | −6.14333 | −0.277527 | ||||||||
\(491\) | −38.9666 | −1.75854 | −0.879269 | − | 0.476326i | \(-0.841968\pi\) | ||||
−0.879269 | + | 0.476326i | \(0.841968\pi\) | |||||||
\(492\) | 11.8798 | 0.535584 | ||||||||
\(493\) | 7.06454 | 0.318171 | ||||||||
\(494\) | 7.14931 | 0.321663 | ||||||||
\(495\) | −9.05791 | −0.407123 | ||||||||
\(496\) | 8.08471 | 0.363014 | ||||||||
\(497\) | 14.6647 | 0.657802 | ||||||||
\(498\) | −11.0390 | −0.494669 | ||||||||
\(499\) | −8.87761 | −0.397416 | −0.198708 | − | 0.980059i | \(-0.563675\pi\) | ||||
−0.198708 | + | 0.980059i | \(0.563675\pi\) | |||||||
\(500\) | 12.0782 | 0.540155 | ||||||||
\(501\) | −0.0924743 | −0.00413145 | ||||||||
\(502\) | 1.14905 | 0.0512846 | ||||||||
\(503\) | −19.2085 | −0.856463 | −0.428232 | − | 0.903669i | \(-0.640863\pi\) | ||||
−0.428232 | + | 0.903669i | \(0.640863\pi\) | |||||||
\(504\) | 3.25998 | 0.145211 | ||||||||
\(505\) | 25.7984 | 1.14801 | ||||||||
\(506\) | 36.4361 | 1.61978 | ||||||||
\(507\) | 12.2393 | 0.543566 | ||||||||
\(508\) | 13.0162 | 0.577502 | ||||||||
\(509\) | 19.3842 | 0.859190 | 0.429595 | − | 0.903022i | \(-0.358656\pi\) | ||||
0.429595 | + | 0.903022i | \(0.358656\pi\) | |||||||
\(510\) | 1.69357 | 0.0749925 | ||||||||
\(511\) | −27.4534 | −1.21447 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.19698 | 0.361906 | ||||||||
\(514\) | −5.01500 | −0.221202 | ||||||||
\(515\) | 22.2358 | 0.979828 | ||||||||
\(516\) | −8.64072 | −0.380386 | ||||||||
\(517\) | 11.3066 | 0.497265 | ||||||||
\(518\) | 17.0632 | 0.749713 | ||||||||
\(519\) | 19.6366 | 0.861953 | ||||||||
\(520\) | 1.47711 | 0.0647756 | ||||||||
\(521\) | −36.4590 | −1.59730 | −0.798650 | − | 0.601796i | \(-0.794452\pi\) | ||||
−0.798650 | + | 0.601796i | \(0.794452\pi\) | |||||||
\(522\) | 7.06454 | 0.309207 | ||||||||
\(523\) | 0.852629 | 0.0372829 | 0.0186414 | − | 0.999826i | \(-0.494066\pi\) | ||||
0.0186414 | + | 0.999826i | \(0.494066\pi\) | |||||||
\(524\) | 5.81999 | 0.254247 | ||||||||
\(525\) | 6.94970 | 0.303310 | ||||||||
\(526\) | 27.6970 | 1.20765 | ||||||||
\(527\) | 8.08471 | 0.352175 | ||||||||
\(528\) | −5.34841 | −0.232760 | ||||||||
\(529\) | 23.4102 | 1.01784 | ||||||||
\(530\) | 15.2490 | 0.662374 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | −26.7220 | −1.15854 | ||||||||
\(533\) | 10.3614 | 0.448804 | ||||||||
\(534\) | 10.7178 | 0.463804 | ||||||||
\(535\) | −8.45389 | −0.365493 | ||||||||
\(536\) | −8.42336 | −0.363834 | ||||||||
\(537\) | −0.451919 | −0.0195017 | ||||||||
\(538\) | 23.4650 | 1.01165 | ||||||||
\(539\) | 19.4011 | 0.835663 | ||||||||
\(540\) | 1.69357 | 0.0728796 | ||||||||
\(541\) | −1.19156 | −0.0512290 | −0.0256145 | − | 0.999672i | \(-0.508154\pi\) | ||||
−0.0256145 | + | 0.999672i | \(0.508154\pi\) | |||||||
\(542\) | 12.9670 | 0.556980 | ||||||||
\(543\) | −11.0413 | −0.473826 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 6.53658 | 0.279996 | ||||||||
\(546\) | 2.84331 | 0.121683 | ||||||||
\(547\) | 20.7868 | 0.888779 | 0.444390 | − | 0.895834i | \(-0.353421\pi\) | ||||
0.444390 | + | 0.895834i | \(0.353421\pi\) | |||||||
\(548\) | −6.73352 | −0.287642 | ||||||||
\(549\) | 13.5963 | 0.580277 | ||||||||
\(550\) | −11.4019 | −0.486178 | ||||||||
\(551\) | −57.9079 | −2.46696 | ||||||||
\(552\) | −6.81251 | −0.289960 | ||||||||
\(553\) | −13.7321 | −0.583948 | ||||||||
\(554\) | 6.44021 | 0.273618 | ||||||||
\(555\) | 8.86438 | 0.376272 | ||||||||
\(556\) | 11.5918 | 0.491603 | ||||||||
\(557\) | −31.3490 | −1.32830 | −0.664150 | − | 0.747599i | \(-0.731206\pi\) | ||||
−0.664150 | + | 0.747599i | \(0.731206\pi\) | |||||||
\(558\) | 8.08471 | 0.342253 | ||||||||
\(559\) | −7.53633 | −0.318753 | ||||||||
\(560\) | −5.52099 | −0.233305 | ||||||||
\(561\) | −5.34841 | −0.225810 | ||||||||
\(562\) | 2.49667 | 0.105316 | ||||||||
\(563\) | 16.1945 | 0.682517 | 0.341258 | − | 0.939970i | \(-0.389147\pi\) | ||||
0.341258 | + | 0.939970i | \(0.389147\pi\) | |||||||
\(564\) | −2.11402 | −0.0890161 | ||||||||
\(565\) | −4.83005 | −0.203202 | ||||||||
\(566\) | 5.33765 | 0.224358 | ||||||||
\(567\) | 3.25998 | 0.136906 | ||||||||
\(568\) | 4.49841 | 0.188749 | ||||||||
\(569\) | −42.3281 | −1.77448 | −0.887242 | − | 0.461303i | \(-0.847382\pi\) | ||||
−0.887242 | + | 0.461303i | \(0.847382\pi\) | |||||||
\(570\) | −13.8822 | −0.581460 | ||||||||
\(571\) | 27.8340 | 1.16481 | 0.582407 | − | 0.812897i | \(-0.302111\pi\) | ||||
0.582407 | + | 0.812897i | \(0.302111\pi\) | |||||||
\(572\) | −4.66482 | −0.195046 | ||||||||
\(573\) | −10.8266 | −0.452288 | ||||||||
\(574\) | −38.7280 | −1.61647 | ||||||||
\(575\) | −14.5231 | −0.605654 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.6901 | −0.653187 | −0.326593 | − | 0.945165i | \(-0.605901\pi\) | ||||
−0.326593 | + | 0.945165i | \(0.605901\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 0.00971922 | 0.000403917 0 | ||||||||
\(580\) | −11.9643 | −0.496790 | ||||||||
\(581\) | 35.9868 | 1.49298 | ||||||||
\(582\) | 0.447712 | 0.0185583 | ||||||||
\(583\) | −48.1575 | −1.99448 | ||||||||
\(584\) | −8.42134 | −0.348478 | ||||||||
\(585\) | 1.47711 | 0.0610710 | ||||||||
\(586\) | 32.0747 | 1.32499 | ||||||||
\(587\) | 22.6597 | 0.935264 | 0.467632 | − | 0.883923i | \(-0.345107\pi\) | ||||
0.467632 | + | 0.883923i | \(0.345107\pi\) | |||||||
\(588\) | −3.62744 | −0.149593 | ||||||||
\(589\) | −66.2702 | −2.73062 | ||||||||
\(590\) | −1.69357 | −0.0697231 | ||||||||
\(591\) | 23.4333 | 0.963916 | ||||||||
\(592\) | 5.23414 | 0.215122 | ||||||||
\(593\) | −35.3406 | −1.45126 | −0.725631 | − | 0.688084i | \(-0.758452\pi\) | ||||
−0.725631 | + | 0.688084i | \(0.758452\pi\) | |||||||
\(594\) | −5.34841 | −0.219448 | ||||||||
\(595\) | −5.52099 | −0.226339 | ||||||||
\(596\) | 14.2808 | 0.584964 | ||||||||
\(597\) | −13.7943 | −0.564563 | ||||||||
\(598\) | −5.94179 | −0.242978 | ||||||||
\(599\) | −45.3261 | −1.85198 | −0.925988 | − | 0.377554i | \(-0.876765\pi\) | ||||
−0.925988 | + | 0.377554i | \(0.876765\pi\) | |||||||
\(600\) | 2.13182 | 0.0870314 | ||||||||
\(601\) | −10.3727 | −0.423110 | −0.211555 | − | 0.977366i | \(-0.567853\pi\) | ||||
−0.211555 | + | 0.977366i | \(0.567853\pi\) | |||||||
\(602\) | 28.1685 | 1.14806 | ||||||||
\(603\) | −8.42336 | −0.343026 | ||||||||
\(604\) | 10.6867 | 0.434835 | ||||||||
\(605\) | −29.8162 | −1.21220 | ||||||||
\(606\) | 15.2331 | 0.618804 | ||||||||
\(607\) | 45.5614 | 1.84928 | 0.924640 | − | 0.380843i | \(-0.124366\pi\) | ||||
0.924640 | + | 0.380843i | \(0.124366\pi\) | |||||||
\(608\) | −8.19698 | −0.332432 | ||||||||
\(609\) | −23.0302 | −0.933232 | ||||||||
\(610\) | −23.0263 | −0.932308 | ||||||||
\(611\) | −1.84382 | −0.0745929 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −9.65543 | −0.389979 | −0.194989 | − | 0.980805i | \(-0.562467\pi\) | ||||
−0.194989 | + | 0.980805i | \(0.562467\pi\) | |||||||
\(614\) | −4.21824 | −0.170234 | ||||||||
\(615\) | −20.1193 | −0.811289 | ||||||||
\(616\) | 17.4357 | 0.702504 | ||||||||
\(617\) | −2.90063 | −0.116775 | −0.0583875 | − | 0.998294i | \(-0.518596\pi\) | ||||
−0.0583875 | + | 0.998294i | \(0.518596\pi\) | |||||||
\(618\) | 13.1296 | 0.528149 | ||||||||
\(619\) | 19.5455 | 0.785598 | 0.392799 | − | 0.919624i | \(-0.371507\pi\) | ||||
0.392799 | + | 0.919624i | \(0.371507\pi\) | |||||||
\(620\) | −13.6920 | −0.549884 | ||||||||
\(621\) | −6.81251 | −0.273376 | ||||||||
\(622\) | 29.6866 | 1.19032 | ||||||||
\(623\) | −34.9397 | −1.39983 | ||||||||
\(624\) | 0.872188 | 0.0349155 | ||||||||
\(625\) | −9.79620 | −0.391848 | ||||||||
\(626\) | 2.46778 | 0.0986325 | ||||||||
\(627\) | 43.8409 | 1.75084 | ||||||||
\(628\) | 19.3407 | 0.771780 | ||||||||
\(629\) | 5.23414 | 0.208699 | ||||||||
\(630\) | −5.52099 | −0.219962 | ||||||||
\(631\) | −29.3601 | −1.16881 | −0.584403 | − | 0.811463i | \(-0.698671\pi\) | ||||
−0.584403 | + | 0.811463i | \(0.698671\pi\) | |||||||
\(632\) | −4.21233 | −0.167557 | ||||||||
\(633\) | −12.7991 | −0.508717 | ||||||||
\(634\) | −17.5247 | −0.695995 | ||||||||
\(635\) | −22.0439 | −0.874786 | ||||||||
\(636\) | 9.00406 | 0.357034 | ||||||||
\(637\) | −3.16381 | −0.125355 | ||||||||
\(638\) | 37.7841 | 1.49589 | ||||||||
\(639\) | 4.49841 | 0.177954 | ||||||||
\(640\) | −1.69357 | −0.0669442 | ||||||||
\(641\) | 3.41394 | 0.134843 | 0.0674214 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674214 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(642\) | −4.99176 | −0.197009 | ||||||||
\(643\) | −10.3725 | −0.409053 | −0.204526 | − | 0.978861i | \(-0.565565\pi\) | ||||
−0.204526 | + | 0.978861i | \(0.565565\pi\) | |||||||
\(644\) | 22.2086 | 0.875142 | ||||||||
\(645\) | 14.6336 | 0.576199 | ||||||||
\(646\) | −8.19698 | −0.322506 | ||||||||
\(647\) | 12.7423 | 0.500950 | 0.250475 | − | 0.968123i | \(-0.419413\pi\) | ||||
0.250475 | + | 0.968123i | \(0.419413\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 5.34841 | 0.209944 | ||||||||
\(650\) | 1.85935 | 0.0729298 | ||||||||
\(651\) | −26.3560 | −1.03297 | ||||||||
\(652\) | 11.5555 | 0.452547 | ||||||||
\(653\) | 12.7096 | 0.497365 | 0.248683 | − | 0.968585i | \(-0.420002\pi\) | ||||
0.248683 | + | 0.968585i | \(0.420002\pi\) | |||||||
\(654\) | 3.85965 | 0.150924 | ||||||||
\(655\) | −9.85655 | −0.385127 | ||||||||
\(656\) | −11.8798 | −0.463829 | ||||||||
\(657\) | −8.42134 | −0.328548 | ||||||||
\(658\) | 6.89164 | 0.268664 | ||||||||
\(659\) | 18.2871 | 0.712363 | 0.356182 | − | 0.934417i | \(-0.384078\pi\) | ||||
0.356182 | + | 0.934417i | \(0.384078\pi\) | |||||||
\(660\) | 9.05791 | 0.352579 | ||||||||
\(661\) | 32.4373 | 1.26166 | 0.630832 | − | 0.775919i | \(-0.282714\pi\) | ||||
0.630832 | + | 0.775919i | \(0.282714\pi\) | |||||||
\(662\) | −2.76351 | −0.107407 | ||||||||
\(663\) | 0.872188 | 0.0338730 | ||||||||
\(664\) | 11.0390 | 0.428395 | ||||||||
\(665\) | 45.2555 | 1.75493 | ||||||||
\(666\) | 5.23414 | 0.202819 | ||||||||
\(667\) | 48.1272 | 1.86349 | ||||||||
\(668\) | 0.0924743 | 0.00357794 | ||||||||
\(669\) | −4.15974 | −0.160825 | ||||||||
\(670\) | 14.2655 | 0.551126 | ||||||||
\(671\) | 72.7187 | 2.80727 | ||||||||
\(672\) | −3.25998 | −0.125756 | ||||||||
\(673\) | −31.9094 | −1.23002 | −0.615008 | − | 0.788521i | \(-0.710847\pi\) | ||||
−0.615008 | + | 0.788521i | \(0.710847\pi\) | |||||||
\(674\) | −17.1206 | −0.659462 | ||||||||
\(675\) | 2.13182 | 0.0820540 | ||||||||
\(676\) | −12.2393 | −0.470742 | ||||||||
\(677\) | 6.97296 | 0.267993 | 0.133996 | − | 0.990982i | \(-0.457219\pi\) | ||||
0.133996 | + | 0.990982i | \(0.457219\pi\) | |||||||
\(678\) | −2.85200 | −0.109530 | ||||||||
\(679\) | −1.45953 | −0.0560117 | ||||||||
\(680\) | −1.69357 | −0.0649454 | ||||||||
\(681\) | 8.45801 | 0.324111 | ||||||||
\(682\) | 43.2404 | 1.65576 | ||||||||
\(683\) | 28.6314 | 1.09555 | 0.547775 | − | 0.836626i | \(-0.315475\pi\) | ||||
0.547775 | + | 0.836626i | \(0.315475\pi\) | |||||||
\(684\) | −8.19698 | −0.313419 | ||||||||
\(685\) | 11.4037 | 0.435712 | ||||||||
\(686\) | −10.9944 | −0.419770 | ||||||||
\(687\) | −18.5289 | −0.706921 | ||||||||
\(688\) | 8.64072 | 0.329424 | ||||||||
\(689\) | 7.85324 | 0.299185 | ||||||||
\(690\) | 11.5374 | 0.439223 | ||||||||
\(691\) | −25.8516 | −0.983440 | −0.491720 | − | 0.870753i | \(-0.663632\pi\) | ||||
−0.491720 | + | 0.870753i | \(0.663632\pi\) | |||||||
\(692\) | −19.6366 | −0.746473 | ||||||||
\(693\) | 17.4357 | 0.662328 | ||||||||
\(694\) | 14.8909 | 0.565251 | ||||||||
\(695\) | −19.6316 | −0.744668 | ||||||||
\(696\) | −7.06454 | −0.267781 | ||||||||
\(697\) | −11.8798 | −0.449981 | ||||||||
\(698\) | 7.01012 | 0.265337 | ||||||||
\(699\) | 0.749085 | 0.0283330 | ||||||||
\(700\) | −6.94970 | −0.262674 | ||||||||
\(701\) | −19.1129 | −0.721886 | −0.360943 | − | 0.932588i | \(-0.617545\pi\) | ||||
−0.360943 | + | 0.932588i | \(0.617545\pi\) | |||||||
\(702\) | 0.872188 | 0.0329186 | ||||||||
\(703\) | −42.9042 | −1.61816 | ||||||||
\(704\) | 5.34841 | 0.201576 | ||||||||
\(705\) | 3.58023 | 0.134839 | ||||||||
\(706\) | −9.62932 | −0.362404 | ||||||||
\(707\) | −49.6597 | −1.86764 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 41.3007 | 1.55108 | 0.775540 | − | 0.631299i | \(-0.217478\pi\) | ||||
0.775540 | + | 0.631299i | \(0.217478\pi\) | |||||||
\(710\) | −7.61837 | −0.285912 | ||||||||
\(711\) | −4.21233 | −0.157975 | ||||||||
\(712\) | −10.7178 | −0.401666 | ||||||||
\(713\) | 55.0771 | 2.06265 | ||||||||
\(714\) | −3.25998 | −0.122002 | ||||||||
\(715\) | 7.90020 | 0.295451 | ||||||||
\(716\) | 0.451919 | 0.0168890 | ||||||||
\(717\) | 15.0757 | 0.563013 | ||||||||
\(718\) | 23.3764 | 0.872399 | ||||||||
\(719\) | 27.5366 | 1.02694 | 0.513470 | − | 0.858107i | \(-0.328360\pi\) | ||||
0.513470 | + | 0.858107i | \(0.328360\pi\) | |||||||
\(720\) | −1.69357 | −0.0631156 | ||||||||
\(721\) | −42.8021 | −1.59403 | ||||||||
\(722\) | 48.1905 | 1.79347 | ||||||||
\(723\) | 23.0265 | 0.856365 | ||||||||
\(724\) | 11.0413 | 0.410345 | ||||||||
\(725\) | −15.0604 | −0.559328 | ||||||||
\(726\) | −17.6055 | −0.653402 | ||||||||
\(727\) | −23.3004 | −0.864165 | −0.432083 | − | 0.901834i | \(-0.642221\pi\) | ||||
−0.432083 | + | 0.901834i | \(0.642221\pi\) | |||||||
\(728\) | −2.84331 | −0.105380 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.2621 | 0.527865 | ||||||||
\(731\) | 8.64072 | 0.319588 | ||||||||
\(732\) | −13.5963 | −0.502534 | ||||||||
\(733\) | 15.6247 | 0.577111 | 0.288555 | − | 0.957463i | \(-0.406825\pi\) | ||||
0.288555 | + | 0.957463i | \(0.406825\pi\) | |||||||
\(734\) | 24.6623 | 0.910300 | ||||||||
\(735\) | 6.14333 | 0.226600 | ||||||||
\(736\) | 6.81251 | 0.251112 | ||||||||
\(737\) | −45.0516 | −1.65950 | ||||||||
\(738\) | −11.8798 | −0.437303 | ||||||||
\(739\) | −42.7669 | −1.57320 | −0.786602 | − | 0.617460i | \(-0.788162\pi\) | ||||
−0.786602 | + | 0.617460i | \(0.788162\pi\) | |||||||
\(740\) | −8.86438 | −0.325861 | ||||||||
\(741\) | −7.14931 | −0.262637 | ||||||||
\(742\) | −29.3530 | −1.07758 | ||||||||
\(743\) | −19.0678 | −0.699531 | −0.349766 | − | 0.936837i | \(-0.613739\pi\) | ||||
−0.349766 | + | 0.936837i | \(0.613739\pi\) | |||||||
\(744\) | −8.08471 | −0.296400 | ||||||||
\(745\) | −24.1855 | −0.886089 | ||||||||
\(746\) | 22.3356 | 0.817763 | ||||||||
\(747\) | 11.0390 | 0.403895 | ||||||||
\(748\) | 5.34841 | 0.195557 | ||||||||
\(749\) | 16.2730 | 0.594603 | ||||||||
\(750\) | −12.0782 | −0.441035 | ||||||||
\(751\) | −23.1655 | −0.845321 | −0.422661 | − | 0.906288i | \(-0.638904\pi\) | ||||
−0.422661 | + | 0.906288i | \(0.638904\pi\) | |||||||
\(752\) | 2.11402 | 0.0770902 | ||||||||
\(753\) | −1.14905 | −0.0418737 | ||||||||
\(754\) | −6.16161 | −0.224393 | ||||||||
\(755\) | −18.0986 | −0.658676 | ||||||||
\(756\) | −3.25998 | −0.118564 | ||||||||
\(757\) | 1.95453 | 0.0710384 | 0.0355192 | − | 0.999369i | \(-0.488692\pi\) | ||||
0.0355192 | + | 0.999369i | \(0.488692\pi\) | |||||||
\(758\) | 5.75391 | 0.208992 | ||||||||
\(759\) | −36.4361 | −1.32255 | ||||||||
\(760\) | 13.8822 | 0.503559 | ||||||||
\(761\) | 6.30047 | 0.228392 | 0.114196 | − | 0.993458i | \(-0.463571\pi\) | ||||
0.114196 | + | 0.993458i | \(0.463571\pi\) | |||||||
\(762\) | −13.0162 | −0.471529 | ||||||||
\(763\) | −12.5824 | −0.455512 | ||||||||
\(764\) | 10.8266 | 0.391693 | ||||||||
\(765\) | −1.69357 | −0.0612311 | ||||||||
\(766\) | −26.5189 | −0.958168 | ||||||||
\(767\) | −0.872188 | −0.0314929 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −36.2604 | −1.30758 | −0.653791 | − | 0.756675i | \(-0.726823\pi\) | ||||
−0.653791 | + | 0.756675i | \(0.726823\pi\) | |||||||
\(770\) | −29.5286 | −1.06414 | ||||||||
\(771\) | 5.01500 | 0.180611 | ||||||||
\(772\) | −0.00971922 | −0.000349802 0 | ||||||||
\(773\) | −15.6856 | −0.564171 | −0.282086 | − | 0.959389i | \(-0.591026\pi\) | ||||
−0.282086 | + | 0.959389i | \(0.591026\pi\) | |||||||
\(774\) | 8.64072 | 0.310584 | ||||||||
\(775\) | −17.2352 | −0.619106 | ||||||||
\(776\) | −0.447712 | −0.0160719 | ||||||||
\(777\) | −17.0632 | −0.612138 | ||||||||
\(778\) | −10.4405 | −0.374310 | ||||||||
\(779\) | 97.3788 | 3.48896 | ||||||||
\(780\) | −1.47711 | −0.0528891 | ||||||||
\(781\) | 24.0594 | 0.860912 | ||||||||
\(782\) | 6.81251 | 0.243615 | ||||||||
\(783\) | −7.06454 | −0.252466 | ||||||||
\(784\) | 3.62744 | 0.129552 | ||||||||
\(785\) | −32.7549 | −1.16907 | ||||||||
\(786\) | −5.81999 | −0.207592 | ||||||||
\(787\) | −40.0891 | −1.42902 | −0.714511 | − | 0.699624i | \(-0.753351\pi\) | ||||
−0.714511 | + | 0.699624i | \(0.753351\pi\) | |||||||
\(788\) | −23.4333 | −0.834776 | ||||||||
\(789\) | −27.6970 | −0.986039 | ||||||||
\(790\) | 7.13387 | 0.253812 | ||||||||
\(791\) | 9.29744 | 0.330579 | ||||||||
\(792\) | 5.34841 | 0.190048 | ||||||||
\(793\) | −11.8585 | −0.421109 | ||||||||
\(794\) | 20.0503 | 0.711559 | ||||||||
\(795\) | −15.2490 | −0.540826 | ||||||||
\(796\) | 13.7943 | 0.488926 | ||||||||
\(797\) | 0.717534 | 0.0254164 | 0.0127082 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127082 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(798\) | 26.7220 | 0.945947 | ||||||||
\(799\) | 2.11402 | 0.0747885 | ||||||||
\(800\) | −2.13182 | −0.0753714 | ||||||||
\(801\) | −10.7178 | −0.378694 | ||||||||
\(802\) | 27.4728 | 0.970098 | ||||||||
\(803\) | −45.0408 | −1.58946 | ||||||||
\(804\) | 8.42336 | 0.297069 | ||||||||
\(805\) | −37.6118 | −1.32564 | ||||||||
\(806\) | −7.05139 | −0.248375 | ||||||||
\(807\) | −23.4650 | −0.826007 | ||||||||
\(808\) | −15.2331 | −0.535900 | ||||||||
\(809\) | −29.9676 | −1.05361 | −0.526803 | − | 0.849988i | \(-0.676609\pi\) | ||||
−0.526803 | + | 0.849988i | \(0.676609\pi\) | |||||||
\(810\) | −1.69357 | −0.0595059 | ||||||||
\(811\) | −43.0911 | −1.51313 | −0.756566 | − | 0.653918i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653918i | \(0.773124\pi\) | |||||||
\(812\) | 23.0302 | 0.808203 | ||||||||
\(813\) | −12.9670 | −0.454772 | ||||||||
\(814\) | 27.9943 | 0.981201 | ||||||||
\(815\) | −19.5700 | −0.685507 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −70.8278 | −2.47795 | ||||||||
\(818\) | −26.2901 | −0.919212 | ||||||||
\(819\) | −2.84331 | −0.0993534 | ||||||||
\(820\) | 20.1193 | 0.702597 | ||||||||
\(821\) | −0.422522 | −0.0147461 | −0.00737305 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737305 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(822\) | 6.73352 | 0.234859 | ||||||||
\(823\) | −10.6003 | −0.369504 | −0.184752 | − | 0.982785i | \(-0.559148\pi\) | ||||
−0.184752 | + | 0.982785i | \(0.559148\pi\) | |||||||
\(824\) | −13.1296 | −0.457390 | ||||||||
\(825\) | 11.4019 | 0.396962 | ||||||||
\(826\) | 3.25998 | 0.113429 | ||||||||
\(827\) | −47.2538 | −1.64317 | −0.821587 | − | 0.570083i | \(-0.806911\pi\) | ||||
−0.821587 | + | 0.570083i | \(0.806911\pi\) | |||||||
\(828\) | 6.81251 | 0.236751 | ||||||||
\(829\) | −0.450112 | −0.0156330 | −0.00781652 | − | 0.999969i | \(-0.502488\pi\) | ||||
−0.00781652 | + | 0.999969i | \(0.502488\pi\) | |||||||
\(830\) | −18.6953 | −0.648922 | ||||||||
\(831\) | −6.44021 | −0.223409 | ||||||||
\(832\) | −0.872188 | −0.0302377 | ||||||||
\(833\) | 3.62744 | 0.125684 | ||||||||
\(834\) | −11.5918 | −0.401393 | ||||||||
\(835\) | −0.156612 | −0.00541977 | ||||||||
\(836\) | −43.8409 | −1.51627 | ||||||||
\(837\) | −8.08471 | −0.279448 | ||||||||
\(838\) | −21.7764 | −0.752253 | ||||||||
\(839\) | −4.77877 | −0.164981 | −0.0824907 | − | 0.996592i | \(-0.526287\pi\) | ||||
−0.0824907 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(840\) | 5.52099 | 0.190492 | ||||||||
\(841\) | 20.9077 | 0.720956 | ||||||||
\(842\) | −22.5632 | −0.777579 | ||||||||
\(843\) | −2.49667 | −0.0859900 | ||||||||
\(844\) | 12.7991 | 0.440562 | ||||||||
\(845\) | 20.7281 | 0.713068 | ||||||||
\(846\) | 2.11402 | 0.0726813 | ||||||||
\(847\) | 57.3936 | 1.97207 | ||||||||
\(848\) | −9.00406 | −0.309201 | ||||||||
\(849\) | −5.33765 | −0.183188 | ||||||||
\(850\) | −2.13182 | −0.0731210 | ||||||||
\(851\) | 35.6576 | 1.22233 | ||||||||
\(852\) | −4.49841 | −0.154113 | ||||||||
\(853\) | 53.1197 | 1.81878 | 0.909392 | − | 0.415939i | \(-0.136547\pi\) | ||||
0.909392 | + | 0.415939i | \(0.136547\pi\) | |||||||
\(854\) | 44.3237 | 1.51672 | ||||||||
\(855\) | 13.8822 | 0.474760 | ||||||||
\(856\) | 4.99176 | 0.170615 | ||||||||
\(857\) | −30.3500 | −1.03674 | −0.518369 | − | 0.855157i | \(-0.673461\pi\) | ||||
−0.518369 | + | 0.855157i | \(0.673461\pi\) | |||||||
\(858\) | 4.66482 | 0.159254 | ||||||||
\(859\) | −17.4264 | −0.594582 | −0.297291 | − | 0.954787i | \(-0.596083\pi\) | ||||
−0.297291 | + | 0.954787i | \(0.596083\pi\) | |||||||
\(860\) | −14.6336 | −0.499003 | ||||||||
\(861\) | 38.7280 | 1.31985 | ||||||||
\(862\) | −20.8086 | −0.708743 | ||||||||
\(863\) | −14.9876 | −0.510184 | −0.255092 | − | 0.966917i | \(-0.582106\pi\) | ||||
−0.255092 | + | 0.966917i | \(0.582106\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 33.2560 | 1.13074 | ||||||||
\(866\) | −10.9005 | −0.370413 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 26.3560 | 0.894579 | ||||||||
\(869\) | −22.5293 | −0.764253 | ||||||||
\(870\) | 11.9643 | 0.405627 | ||||||||
\(871\) | 7.34676 | 0.248935 | ||||||||
\(872\) | −3.85965 | −0.130704 | ||||||||
\(873\) | −0.447712 | −0.0151528 | ||||||||
\(874\) | −55.8420 | −1.88888 | ||||||||
\(875\) | 39.3748 | 1.33111 | ||||||||
\(876\) | 8.42134 | 0.284531 | ||||||||
\(877\) | 18.1154 | 0.611713 | 0.305856 | − | 0.952078i | \(-0.401057\pi\) | ||||
0.305856 | + | 0.952078i | \(0.401057\pi\) | |||||||
\(878\) | 8.77870 | 0.296267 | ||||||||
\(879\) | −32.0747 | −1.08185 | ||||||||
\(880\) | −9.05791 | −0.305342 | ||||||||
\(881\) | 14.0626 | 0.473782 | 0.236891 | − | 0.971536i | \(-0.423872\pi\) | ||||
0.236891 | + | 0.971536i | \(0.423872\pi\) | |||||||
\(882\) | 3.62744 | 0.122142 | ||||||||
\(883\) | 40.5859 | 1.36582 | 0.682912 | − | 0.730501i | \(-0.260713\pi\) | ||||
0.682912 | + | 0.730501i | \(0.260713\pi\) | |||||||
\(884\) | −0.872188 | −0.0293349 | ||||||||
\(885\) | 1.69357 | 0.0569287 | ||||||||
\(886\) | −36.9950 | −1.24287 | ||||||||
\(887\) | −12.5256 | −0.420567 | −0.210283 | − | 0.977640i | \(-0.567439\pi\) | ||||
−0.210283 | + | 0.977640i | \(0.567439\pi\) | |||||||
\(888\) | −5.23414 | −0.175646 | ||||||||
\(889\) | 42.4326 | 1.42314 | ||||||||
\(890\) | 18.1513 | 0.608433 | ||||||||
\(891\) | 5.34841 | 0.179179 | ||||||||
\(892\) | 4.15974 | 0.139278 | ||||||||
\(893\) | −17.3285 | −0.579878 | ||||||||
\(894\) | −14.2808 | −0.477621 | ||||||||
\(895\) | −0.765356 | −0.0255830 | ||||||||
\(896\) | 3.25998 | 0.108908 | ||||||||
\(897\) | 5.94179 | 0.198391 | ||||||||
\(898\) | −35.1087 | −1.17159 | ||||||||
\(899\) | 57.1147 | 1.90488 | ||||||||
\(900\) | −2.13182 | −0.0710608 | ||||||||
\(901\) | −9.00406 | −0.299969 | ||||||||
\(902\) | −63.5382 | −2.11559 | ||||||||
\(903\) | −28.1685 | −0.937390 | ||||||||
\(904\) | 2.85200 | 0.0948560 | ||||||||
\(905\) | −18.6991 | −0.621580 | ||||||||
\(906\) | −10.6867 | −0.355041 | ||||||||
\(907\) | 10.3762 | 0.344535 | 0.172268 | − | 0.985050i | \(-0.444891\pi\) | ||||
0.172268 | + | 0.985050i | \(0.444891\pi\) | |||||||
\(908\) | −8.45801 | −0.280689 | ||||||||
\(909\) | −15.2331 | −0.505251 | ||||||||
\(910\) | 4.81535 | 0.159627 | ||||||||
\(911\) | 15.4998 | 0.513532 | 0.256766 | − | 0.966474i | \(-0.417343\pi\) | ||||
0.256766 | + | 0.966474i | \(0.417343\pi\) | |||||||
\(912\) | 8.19698 | 0.271429 | ||||||||
\(913\) | 59.0410 | 1.95397 | ||||||||
\(914\) | 21.7100 | 0.718103 | ||||||||
\(915\) | 23.0263 | 0.761226 | ||||||||
\(916\) | 18.5289 | 0.612212 | ||||||||
\(917\) | 18.9730 | 0.626545 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −30.8058 | −1.01619 | −0.508095 | − | 0.861301i | \(-0.669650\pi\) | ||||
−0.508095 | + | 0.861301i | \(0.669650\pi\) | |||||||
\(920\) | −11.5374 | −0.380378 | ||||||||
\(921\) | 4.21824 | 0.138996 | ||||||||
\(922\) | 4.25372 | 0.140089 | ||||||||
\(923\) | −3.92346 | −0.129142 | ||||||||
\(924\) | −17.4357 | −0.573592 | ||||||||
\(925\) | −11.1583 | −0.366882 | ||||||||
\(926\) | −31.3122 | −1.02898 | ||||||||
\(927\) | −13.1296 | −0.431232 | ||||||||
\(928\) | 7.06454 | 0.231905 | ||||||||
\(929\) | −46.7723 | −1.53455 | −0.767275 | − | 0.641318i | \(-0.778388\pi\) | ||||
−0.767275 | + | 0.641318i | \(0.778388\pi\) | |||||||
\(930\) | 13.6920 | 0.448979 | ||||||||
\(931\) | −29.7341 | −0.974496 | ||||||||
\(932\) | −0.749085 | −0.0245371 | ||||||||
\(933\) | −29.6866 | −0.971895 | ||||||||
\(934\) | −17.8953 | −0.585553 | ||||||||
\(935\) | −9.05791 | −0.296225 | ||||||||
\(936\) | −0.872188 | −0.0285084 | ||||||||
\(937\) | 20.7990 | 0.679474 | 0.339737 | − | 0.940520i | \(-0.389662\pi\) | ||||
0.339737 | + | 0.940520i | \(0.389662\pi\) | |||||||
\(938\) | −27.4600 | −0.896599 | ||||||||
\(939\) | −2.46778 | −0.0805331 | ||||||||
\(940\) | −3.58023 | −0.116774 | ||||||||
\(941\) | 15.5612 | 0.507281 | 0.253641 | − | 0.967299i | \(-0.418372\pi\) | ||||
0.253641 | + | 0.967299i | \(0.418372\pi\) | |||||||
\(942\) | −19.3407 | −0.630156 | ||||||||
\(943\) | −80.9314 | −2.63549 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 5.52099 | 0.179598 | ||||||||
\(946\) | 46.2141 | 1.50255 | ||||||||
\(947\) | −54.5603 | −1.77297 | −0.886485 | − | 0.462756i | \(-0.846860\pi\) | ||||
−0.886485 | + | 0.462756i | \(0.846860\pi\) | |||||||
\(948\) | 4.21233 | 0.136810 | ||||||||
\(949\) | 7.34499 | 0.238429 | ||||||||
\(950\) | 17.4745 | 0.566949 | ||||||||
\(951\) | 17.5247 | 0.568278 | ||||||||
\(952\) | 3.25998 | 0.105656 | ||||||||
\(953\) | 42.0794 | 1.36309 | 0.681543 | − | 0.731778i | \(-0.261309\pi\) | ||||
0.681543 | + | 0.731778i | \(0.261309\pi\) | |||||||
\(954\) | −9.00406 | −0.291517 | ||||||||
\(955\) | −18.3356 | −0.593326 | ||||||||
\(956\) | −15.0757 | −0.487584 | ||||||||
\(957\) | −37.7841 | −1.22139 | ||||||||
\(958\) | −13.5206 | −0.436831 | ||||||||
\(959\) | −21.9511 | −0.708839 | ||||||||
\(960\) | 1.69357 | 0.0546597 | ||||||||
\(961\) | 34.3625 | 1.10847 | ||||||||
\(962\) | −4.56515 | −0.147186 | ||||||||
\(963\) | 4.99176 | 0.160857 | ||||||||
\(964\) | −23.0265 | −0.741633 | ||||||||
\(965\) | 0.0164602 | 0.000529872 0 | ||||||||
\(966\) | −22.2086 | −0.714550 | ||||||||
\(967\) | −23.7985 | −0.765309 | −0.382654 | − | 0.923892i | \(-0.624990\pi\) | ||||
−0.382654 | + | 0.923892i | \(0.624990\pi\) | |||||||
\(968\) | 17.6055 | 0.565863 | ||||||||
\(969\) | 8.19698 | 0.263325 | ||||||||
\(970\) | 0.758232 | 0.0243453 | ||||||||
\(971\) | 4.38164 | 0.140613 | 0.0703067 | − | 0.997525i | \(-0.477602\pi\) | ||||
0.0703067 | + | 0.997525i | \(0.477602\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 37.7891 | 1.21146 | ||||||||
\(974\) | 28.7702 | 0.921856 | ||||||||
\(975\) | −1.85935 | −0.0595469 | ||||||||
\(976\) | 13.5963 | 0.435207 | ||||||||
\(977\) | 34.7203 | 1.11080 | 0.555400 | − | 0.831584i | \(-0.312565\pi\) | ||||
0.555400 | + | 0.831584i | \(0.312565\pi\) | |||||||
\(978\) | −11.5555 | −0.369503 | ||||||||
\(979\) | −57.3231 | −1.83206 | ||||||||
\(980\) | −6.14333 | −0.196241 | ||||||||
\(981\) | −3.85965 | −0.123229 | ||||||||
\(982\) | −38.9666 | −1.24347 | ||||||||
\(983\) | −13.4071 | −0.427621 | −0.213811 | − | 0.976875i | \(-0.568588\pi\) | ||||
−0.213811 | + | 0.976875i | \(0.568588\pi\) | |||||||
\(984\) | 11.8798 | 0.378715 | ||||||||
\(985\) | 39.6859 | 1.26450 | ||||||||
\(986\) | 7.06454 | 0.224981 | ||||||||
\(987\) | −6.89164 | −0.219363 | ||||||||
\(988\) | 7.14931 | 0.227450 | ||||||||
\(989\) | 58.8649 | 1.87180 | ||||||||
\(990\) | −9.05791 | −0.287879 | ||||||||
\(991\) | −8.09941 | −0.257286 | −0.128643 | − | 0.991691i | \(-0.541062\pi\) | ||||
−0.128643 | + | 0.991691i | \(0.541062\pi\) | |||||||
\(992\) | 8.08471 | 0.256690 | ||||||||
\(993\) | 2.76351 | 0.0876975 | ||||||||
\(994\) | 14.6647 | 0.465136 | ||||||||
\(995\) | −23.3616 | −0.740612 | ||||||||
\(996\) | −11.0390 | −0.349783 | ||||||||
\(997\) | −34.1018 | −1.08002 | −0.540008 | − | 0.841660i | \(-0.681579\pi\) | ||||
−0.540008 | + | 0.841660i | \(0.681579\pi\) | |||||||
\(998\) | −8.87761 | −0.281016 | ||||||||
\(999\) | −5.23414 | −0.165601 |
(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 | 6018.2.a.bc.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.bc.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial |