Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 \) |
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 | 1.11 | ||
Root | \(0.173392\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.173392 | −0.122607 | −0.0613034 | − | 0.998119i | \(-0.519526\pi\) | ||||
−0.0613034 | + | 0.998119i | \(0.519526\pi\) | |||||||
\(3\) | −0.896458 | −0.517570 | −0.258785 | − | 0.965935i | \(-0.583322\pi\) | ||||
−0.258785 | + | 0.965935i | \(0.583322\pi\) | |||||||
\(4\) | −1.96994 | −0.984968 | ||||||||
\(5\) | 3.74986 | 1.67699 | 0.838494 | − | 0.544911i | \(-0.183437\pi\) | ||||
0.838494 | + | 0.544911i | \(0.183437\pi\) | |||||||
\(6\) | 0.155439 | 0.0634576 | ||||||||
\(7\) | 1.28742 | 0.486599 | 0.243299 | − | 0.969951i | \(-0.421770\pi\) | ||||
0.243299 | + | 0.969951i | \(0.421770\pi\) | |||||||
\(8\) | 0.688355 | 0.243370 | ||||||||
\(9\) | −2.19636 | −0.732121 | ||||||||
\(10\) | −0.650196 | −0.205610 | ||||||||
\(11\) | −4.72000 | −1.42313 | −0.711567 | − | 0.702618i | \(-0.752014\pi\) | ||||
−0.711567 | + | 0.702618i | \(0.752014\pi\) | |||||||
\(12\) | 1.76596 | 0.509790 | ||||||||
\(13\) | −4.53842 | −1.25873 | −0.629366 | − | 0.777109i | \(-0.716685\pi\) | ||||
−0.629366 | + | 0.777109i | \(0.716685\pi\) | |||||||
\(14\) | −0.223228 | −0.0596603 | ||||||||
\(15\) | −3.36159 | −0.867959 | ||||||||
\(16\) | 3.82051 | 0.955129 | ||||||||
\(17\) | 2.76011 | 0.669425 | 0.334713 | − | 0.942320i | \(-0.391361\pi\) | ||||
0.334713 | + | 0.942320i | \(0.391361\pi\) | |||||||
\(18\) | 0.380832 | 0.0897629 | ||||||||
\(19\) | 2.71957 | 0.623913 | 0.311957 | − | 0.950096i | \(-0.399016\pi\) | ||||
0.311957 | + | 0.950096i | \(0.399016\pi\) | |||||||
\(20\) | −7.38698 | −1.65178 | ||||||||
\(21\) | −1.15412 | −0.251849 | ||||||||
\(22\) | 0.818411 | 0.174486 | ||||||||
\(23\) | 4.99155 | 1.04081 | 0.520405 | − | 0.853920i | \(-0.325781\pi\) | ||||
0.520405 | + | 0.853920i | \(0.325781\pi\) | |||||||
\(24\) | −0.617082 | −0.125961 | ||||||||
\(25\) | 9.06144 | 1.81229 | ||||||||
\(26\) | 0.786927 | 0.154329 | ||||||||
\(27\) | 4.65832 | 0.896495 | ||||||||
\(28\) | −2.53613 | −0.479284 | ||||||||
\(29\) | 1.47874 | 0.274594 | 0.137297 | − | 0.990530i | \(-0.456158\pi\) | ||||
0.137297 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(30\) | 0.582873 | 0.106418 | ||||||||
\(31\) | 3.76324 | 0.675898 | 0.337949 | − | 0.941164i | \(-0.390267\pi\) | ||||
0.337949 | + | 0.941164i | \(0.390267\pi\) | |||||||
\(32\) | −2.03916 | −0.360476 | ||||||||
\(33\) | 4.23129 | 0.736572 | ||||||||
\(34\) | −0.478581 | −0.0820760 | ||||||||
\(35\) | 4.82764 | 0.816020 | ||||||||
\(36\) | 4.32669 | 0.721115 | ||||||||
\(37\) | −5.53528 | −0.909994 | −0.454997 | − | 0.890493i | \(-0.650360\pi\) | ||||
−0.454997 | + | 0.890493i | \(0.650360\pi\) | |||||||
\(38\) | −0.471553 | −0.0764960 | ||||||||
\(39\) | 4.06851 | 0.651483 | ||||||||
\(40\) | 2.58124 | 0.408129 | ||||||||
\(41\) | 1.04756 | 0.163601 | 0.0818004 | − | 0.996649i | \(-0.473933\pi\) | ||||
0.0818004 | + | 0.996649i | \(0.473933\pi\) | |||||||
\(42\) | 0.200115 | 0.0308784 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 9.29810 | 1.40174 | ||||||||
\(45\) | −8.23605 | −1.22776 | ||||||||
\(46\) | −0.865495 | −0.127610 | ||||||||
\(47\) | 2.04767 | 0.298683 | 0.149341 | − | 0.988786i | \(-0.452285\pi\) | ||||
0.149341 | + | 0.988786i | \(0.452285\pi\) | |||||||
\(48\) | −3.42493 | −0.494346 | ||||||||
\(49\) | −5.34255 | −0.763222 | ||||||||
\(50\) | −1.57118 | −0.222199 | ||||||||
\(51\) | −2.47432 | −0.346475 | ||||||||
\(52\) | 8.94040 | 1.23981 | ||||||||
\(53\) | 1.20753 | 0.165867 | 0.0829337 | − | 0.996555i | \(-0.473571\pi\) | ||||
0.0829337 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(54\) | −0.807716 | −0.109916 | ||||||||
\(55\) | −17.6993 | −2.38658 | ||||||||
\(56\) | 0.886202 | 0.118424 | ||||||||
\(57\) | −2.43799 | −0.322919 | ||||||||
\(58\) | −0.256401 | −0.0336671 | ||||||||
\(59\) | −0.436150 | −0.0567818 | −0.0283909 | − | 0.999597i | \(-0.509038\pi\) | ||||
−0.0283909 | + | 0.999597i | \(0.509038\pi\) | |||||||
\(60\) | 6.62212 | 0.854912 | ||||||||
\(61\) | 11.1148 | 1.42311 | 0.711553 | − | 0.702632i | \(-0.247992\pi\) | ||||
0.711553 | + | 0.702632i | \(0.247992\pi\) | |||||||
\(62\) | −0.652516 | −0.0828696 | ||||||||
\(63\) | −2.82764 | −0.356249 | ||||||||
\(64\) | −7.28746 | −0.910932 | ||||||||
\(65\) | −17.0184 | −2.11088 | ||||||||
\(66\) | −0.733672 | −0.0903087 | ||||||||
\(67\) | 7.86202 | 0.960499 | 0.480249 | − | 0.877132i | \(-0.340546\pi\) | ||||
0.480249 | + | 0.877132i | \(0.340546\pi\) | |||||||
\(68\) | −5.43724 | −0.659362 | ||||||||
\(69\) | −4.47472 | −0.538692 | ||||||||
\(70\) | −0.837074 | −0.100050 | ||||||||
\(71\) | 15.4494 | 1.83351 | 0.916756 | − | 0.399448i | \(-0.130798\pi\) | ||||
0.916756 | + | 0.399448i | \(0.130798\pi\) | |||||||
\(72\) | −1.51188 | −0.178177 | ||||||||
\(73\) | 15.5029 | 1.81448 | 0.907240 | − | 0.420613i | \(-0.138185\pi\) | ||||
0.907240 | + | 0.420613i | \(0.138185\pi\) | |||||||
\(74\) | 0.959773 | 0.111571 | ||||||||
\(75\) | −8.12320 | −0.937987 | ||||||||
\(76\) | −5.35739 | −0.614534 | ||||||||
\(77\) | −6.07662 | −0.692495 | ||||||||
\(78\) | −0.705447 | −0.0798762 | ||||||||
\(79\) | −10.7742 | −1.21219 | −0.606096 | − | 0.795391i | \(-0.707265\pi\) | ||||
−0.606096 | + | 0.795391i | \(0.707265\pi\) | |||||||
\(80\) | 14.3264 | 1.60174 | ||||||||
\(81\) | 2.41310 | 0.268122 | ||||||||
\(82\) | −0.181638 | −0.0200586 | ||||||||
\(83\) | 0.437792 | 0.0480540 | 0.0240270 | − | 0.999711i | \(-0.492351\pi\) | ||||
0.0240270 | + | 0.999711i | \(0.492351\pi\) | |||||||
\(84\) | 2.27354 | 0.248063 | ||||||||
\(85\) | 10.3500 | 1.12262 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.32562 | −0.142122 | ||||||||
\(88\) | −3.24904 | −0.346349 | ||||||||
\(89\) | −5.41590 | −0.574084 | −0.287042 | − | 0.957918i | \(-0.592672\pi\) | ||||
−0.287042 | + | 0.957918i | \(0.592672\pi\) | |||||||
\(90\) | 1.42807 | 0.150531 | ||||||||
\(91\) | −5.84285 | −0.612497 | ||||||||
\(92\) | −9.83303 | −1.02516 | ||||||||
\(93\) | −3.37359 | −0.349825 | ||||||||
\(94\) | −0.355049 | −0.0366205 | ||||||||
\(95\) | 10.1980 | 1.04629 | ||||||||
\(96\) | 1.82802 | 0.186572 | ||||||||
\(97\) | 6.46227 | 0.656144 | 0.328072 | − | 0.944653i | \(-0.393601\pi\) | ||||
0.328072 | + | 0.944653i | \(0.393601\pi\) | |||||||
\(98\) | 0.926356 | 0.0935761 | ||||||||
\(99\) | 10.3668 | 1.04191 | ||||||||
\(100\) | −17.8504 | −1.78504 | ||||||||
\(101\) | 6.57781 | 0.654516 | 0.327258 | − | 0.944935i | \(-0.393875\pi\) | ||||
0.327258 | + | 0.944935i | \(0.393875\pi\) | |||||||
\(102\) | 0.429028 | 0.0424801 | ||||||||
\(103\) | 11.8784 | 1.17042 | 0.585209 | − | 0.810883i | \(-0.301013\pi\) | ||||
0.585209 | + | 0.810883i | \(0.301013\pi\) | |||||||
\(104\) | −3.12405 | −0.306338 | ||||||||
\(105\) | −4.32778 | −0.422348 | ||||||||
\(106\) | −0.209377 | −0.0203365 | ||||||||
\(107\) | −10.9156 | −1.05525 | −0.527623 | − | 0.849479i | \(-0.676917\pi\) | ||||
−0.527623 | + | 0.849479i | \(0.676917\pi\) | |||||||
\(108\) | −9.17659 | −0.883018 | ||||||||
\(109\) | −0.903480 | −0.0865377 | −0.0432689 | − | 0.999063i | \(-0.513777\pi\) | ||||
−0.0432689 | + | 0.999063i | \(0.513777\pi\) | |||||||
\(110\) | 3.06893 | 0.292611 | ||||||||
\(111\) | 4.96215 | 0.470986 | ||||||||
\(112\) | 4.91860 | 0.464764 | ||||||||
\(113\) | 9.40706 | 0.884942 | 0.442471 | − | 0.896783i | \(-0.354102\pi\) | ||||
0.442471 | + | 0.896783i | \(0.354102\pi\) | |||||||
\(114\) | 0.422727 | 0.0395920 | ||||||||
\(115\) | 18.7176 | 1.74543 | ||||||||
\(116\) | −2.91301 | −0.270466 | ||||||||
\(117\) | 9.96802 | 0.921544 | ||||||||
\(118\) | 0.0756249 | 0.00696184 | ||||||||
\(119\) | 3.55342 | 0.325741 | ||||||||
\(120\) | −2.31397 | −0.211236 | ||||||||
\(121\) | 11.2784 | 1.02531 | ||||||||
\(122\) | −1.92722 | −0.174482 | ||||||||
\(123\) | −0.939091 | −0.0846750 | ||||||||
\(124\) | −7.41334 | −0.665737 | ||||||||
\(125\) | 15.2298 | 1.36220 | ||||||||
\(126\) | 0.490290 | 0.0436785 | ||||||||
\(127\) | 11.0737 | 0.982632 | 0.491316 | − | 0.870981i | \(-0.336516\pi\) | ||||
0.491316 | + | 0.870981i | \(0.336516\pi\) | |||||||
\(128\) | 5.34190 | 0.472162 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.95086 | 0.258808 | ||||||||
\(131\) | −13.1041 | −1.14491 | −0.572456 | − | 0.819936i | \(-0.694009\pi\) | ||||
−0.572456 | + | 0.819936i | \(0.694009\pi\) | |||||||
\(132\) | −8.33536 | −0.725500 | ||||||||
\(133\) | 3.50123 | 0.303595 | ||||||||
\(134\) | −1.36321 | −0.117764 | ||||||||
\(135\) | 17.4680 | 1.50341 | ||||||||
\(136\) | 1.89994 | 0.162918 | ||||||||
\(137\) | −8.92430 | −0.762455 | −0.381227 | − | 0.924481i | \(-0.624498\pi\) | ||||
−0.381227 | + | 0.924481i | \(0.624498\pi\) | |||||||
\(138\) | 0.775880 | 0.0660473 | ||||||||
\(139\) | 8.98053 | 0.761719 | 0.380859 | − | 0.924633i | \(-0.375628\pi\) | ||||
0.380859 | + | 0.924633i | \(0.375628\pi\) | |||||||
\(140\) | −9.51014 | −0.803753 | ||||||||
\(141\) | −1.83565 | −0.154589 | ||||||||
\(142\) | −2.67881 | −0.224801 | ||||||||
\(143\) | 21.4214 | 1.79135 | ||||||||
\(144\) | −8.39124 | −0.699270 | ||||||||
\(145\) | 5.54505 | 0.460491 | ||||||||
\(146\) | −2.68808 | −0.222467 | ||||||||
\(147\) | 4.78938 | 0.395021 | ||||||||
\(148\) | 10.9041 | 0.896314 | ||||||||
\(149\) | −11.3492 | −0.929765 | −0.464883 | − | 0.885372i | \(-0.653903\pi\) | ||||
−0.464883 | + | 0.885372i | \(0.653903\pi\) | |||||||
\(150\) | 1.40850 | 0.115003 | ||||||||
\(151\) | 18.8508 | 1.53406 | 0.767028 | − | 0.641613i | \(-0.221735\pi\) | ||||
0.767028 | + | 0.641613i | \(0.221735\pi\) | |||||||
\(152\) | 1.87203 | 0.151842 | ||||||||
\(153\) | −6.06220 | −0.490100 | ||||||||
\(154\) | 1.05364 | 0.0849046 | ||||||||
\(155\) | 14.1116 | 1.13347 | ||||||||
\(156\) | −8.01470 | −0.641689 | ||||||||
\(157\) | −9.78678 | −0.781070 | −0.390535 | − | 0.920588i | \(-0.627710\pi\) | ||||
−0.390535 | + | 0.920588i | \(0.627710\pi\) | |||||||
\(158\) | 1.86816 | 0.148623 | ||||||||
\(159\) | −1.08250 | −0.0858480 | ||||||||
\(160\) | −7.64655 | −0.604513 | ||||||||
\(161\) | 6.42621 | 0.506457 | ||||||||
\(162\) | −0.418412 | −0.0328735 | ||||||||
\(163\) | 18.5725 | 1.45471 | 0.727355 | − | 0.686261i | \(-0.240749\pi\) | ||||
0.727355 | + | 0.686261i | \(0.240749\pi\) | |||||||
\(164\) | −2.06362 | −0.161142 | ||||||||
\(165\) | 15.8667 | 1.23522 | ||||||||
\(166\) | −0.0759098 | −0.00589174 | ||||||||
\(167\) | 22.2200 | 1.71944 | 0.859718 | − | 0.510769i | \(-0.170639\pi\) | ||||
0.859718 | + | 0.510769i | \(0.170639\pi\) | |||||||
\(168\) | −0.794443 | −0.0612926 | ||||||||
\(169\) | 7.59729 | 0.584407 | ||||||||
\(170\) | −1.79461 | −0.137640 | ||||||||
\(171\) | −5.97317 | −0.456780 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.55703 | −0.118379 | −0.0591893 | − | 0.998247i | \(-0.518852\pi\) | ||||
−0.0591893 | + | 0.998247i | \(0.518852\pi\) | |||||||
\(174\) | 0.229853 | 0.0174251 | ||||||||
\(175\) | 11.6659 | 0.881857 | ||||||||
\(176\) | −18.0328 | −1.35928 | ||||||||
\(177\) | 0.390990 | 0.0293886 | ||||||||
\(178\) | 0.939075 | 0.0703866 | ||||||||
\(179\) | −0.918675 | −0.0686650 | −0.0343325 | − | 0.999410i | \(-0.510931\pi\) | ||||
−0.0343325 | + | 0.999410i | \(0.510931\pi\) | |||||||
\(180\) | 16.2245 | 1.20930 | ||||||||
\(181\) | −17.6681 | −1.31326 | −0.656629 | − | 0.754214i | \(-0.728018\pi\) | ||||
−0.656629 | + | 0.754214i | \(0.728018\pi\) | |||||||
\(182\) | 1.01310 | 0.0750963 | ||||||||
\(183\) | −9.96397 | −0.736558 | ||||||||
\(184\) | 3.43596 | 0.253302 | ||||||||
\(185\) | −20.7565 | −1.52605 | ||||||||
\(186\) | 0.584953 | 0.0428909 | ||||||||
\(187\) | −13.0277 | −0.952682 | ||||||||
\(188\) | −4.03377 | −0.294193 | ||||||||
\(189\) | 5.99721 | 0.436233 | ||||||||
\(190\) | −1.76826 | −0.128283 | ||||||||
\(191\) | −0.513569 | −0.0371606 | −0.0185803 | − | 0.999827i | \(-0.505915\pi\) | ||||
−0.0185803 | + | 0.999827i | \(0.505915\pi\) | |||||||
\(192\) | 6.53290 | 0.471471 | ||||||||
\(193\) | 11.9313 | 0.858835 | 0.429417 | − | 0.903106i | \(-0.358719\pi\) | ||||
0.429417 | + | 0.903106i | \(0.358719\pi\) | |||||||
\(194\) | −1.12051 | −0.0804477 | ||||||||
\(195\) | 15.2563 | 1.09253 | ||||||||
\(196\) | 10.5245 | 0.751749 | ||||||||
\(197\) | 19.0131 | 1.35463 | 0.677314 | − | 0.735694i | \(-0.263144\pi\) | ||||
0.677314 | + | 0.735694i | \(0.263144\pi\) | |||||||
\(198\) | −1.79753 | −0.127745 | ||||||||
\(199\) | 2.59383 | 0.183871 | 0.0919357 | − | 0.995765i | \(-0.470695\pi\) | ||||
0.0919357 | + | 0.995765i | \(0.470695\pi\) | |||||||
\(200\) | 6.23749 | 0.441057 | ||||||||
\(201\) | −7.04798 | −0.497126 | ||||||||
\(202\) | −1.14054 | −0.0802481 | ||||||||
\(203\) | 1.90375 | 0.133617 | ||||||||
\(204\) | 4.87426 | 0.341266 | ||||||||
\(205\) | 3.92819 | 0.274357 | ||||||||
\(206\) | −2.05963 | −0.143501 | ||||||||
\(207\) | −10.9633 | −0.761999 | ||||||||
\(208\) | −17.3391 | −1.20225 | ||||||||
\(209\) | −12.8364 | −0.887912 | ||||||||
\(210\) | 0.750402 | 0.0517827 | ||||||||
\(211\) | −2.50530 | −0.172472 | −0.0862360 | − | 0.996275i | \(-0.527484\pi\) | ||||
−0.0862360 | + | 0.996275i | \(0.527484\pi\) | |||||||
\(212\) | −2.37876 | −0.163374 | ||||||||
\(213\) | −13.8498 | −0.948972 | ||||||||
\(214\) | 1.89267 | 0.129380 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.20658 | 0.218180 | ||||||||
\(217\) | 4.84487 | 0.328891 | ||||||||
\(218\) | 0.156656 | 0.0106101 | ||||||||
\(219\) | −13.8977 | −0.939121 | ||||||||
\(220\) | 34.8666 | 2.35070 | ||||||||
\(221\) | −12.5265 | −0.842627 | ||||||||
\(222\) | −0.860397 | −0.0577461 | ||||||||
\(223\) | 6.22422 | 0.416805 | 0.208402 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208402 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(224\) | −2.62525 | −0.175407 | ||||||||
\(225\) | −19.9022 | −1.32681 | ||||||||
\(226\) | −1.63111 | −0.108500 | ||||||||
\(227\) | 20.0963 | 1.33384 | 0.666918 | − | 0.745131i | \(-0.267613\pi\) | ||||
0.666918 | + | 0.745131i | \(0.267613\pi\) | |||||||
\(228\) | 4.80267 | 0.318065 | ||||||||
\(229\) | −1.98863 | −0.131413 | −0.0657063 | − | 0.997839i | \(-0.520930\pi\) | ||||
−0.0657063 | + | 0.997839i | \(0.520930\pi\) | |||||||
\(230\) | −3.24548 | −0.214001 | ||||||||
\(231\) | 5.44744 | 0.358415 | ||||||||
\(232\) | 1.01790 | 0.0668281 | ||||||||
\(233\) | −20.7218 | −1.35753 | −0.678765 | − | 0.734356i | \(-0.737484\pi\) | ||||
−0.678765 | + | 0.734356i | \(0.737484\pi\) | |||||||
\(234\) | −1.72838 | −0.112988 | ||||||||
\(235\) | 7.67845 | 0.500887 | ||||||||
\(236\) | 0.859186 | 0.0559283 | ||||||||
\(237\) | 9.65863 | 0.627395 | ||||||||
\(238\) | −0.616135 | −0.0399381 | ||||||||
\(239\) | −7.80550 | −0.504896 | −0.252448 | − | 0.967610i | \(-0.581236\pi\) | ||||
−0.252448 | + | 0.967610i | \(0.581236\pi\) | |||||||
\(240\) | −12.8430 | −0.829013 | ||||||||
\(241\) | −0.497502 | −0.0320469 | −0.0160235 | − | 0.999872i | \(-0.505101\pi\) | ||||
−0.0160235 | + | 0.999872i | \(0.505101\pi\) | |||||||
\(242\) | −1.95559 | −0.125710 | ||||||||
\(243\) | −16.1382 | −1.03527 | ||||||||
\(244\) | −21.8955 | −1.40171 | ||||||||
\(245\) | −20.0338 | −1.27991 | ||||||||
\(246\) | 0.162831 | 0.0103817 | ||||||||
\(247\) | −12.3426 | −0.785340 | ||||||||
\(248\) | 2.59045 | 0.164493 | ||||||||
\(249\) | −0.392463 | −0.0248713 | ||||||||
\(250\) | −2.64073 | −0.167014 | ||||||||
\(251\) | 8.56269 | 0.540472 | 0.270236 | − | 0.962794i | \(-0.412898\pi\) | ||||
0.270236 | + | 0.962794i | \(0.412898\pi\) | |||||||
\(252\) | 5.57026 | 0.350894 | ||||||||
\(253\) | −23.5601 | −1.48121 | ||||||||
\(254\) | −1.92009 | −0.120477 | ||||||||
\(255\) | −9.27836 | −0.581034 | ||||||||
\(256\) | 13.6487 | 0.853042 | ||||||||
\(257\) | −23.6967 | −1.47816 | −0.739080 | − | 0.673617i | \(-0.764740\pi\) | ||||
−0.739080 | + | 0.673617i | \(0.764740\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.12622 | −0.442802 | ||||||||
\(260\) | 33.5252 | 2.07915 | ||||||||
\(261\) | −3.24784 | −0.201036 | ||||||||
\(262\) | 2.27215 | 0.140374 | ||||||||
\(263\) | −14.2516 | −0.878790 | −0.439395 | − | 0.898294i | \(-0.644807\pi\) | ||||
−0.439395 | + | 0.898294i | \(0.644807\pi\) | |||||||
\(264\) | 2.91263 | 0.179260 | ||||||||
\(265\) | 4.52808 | 0.278157 | ||||||||
\(266\) | −0.607086 | −0.0372228 | ||||||||
\(267\) | 4.85513 | 0.297129 | ||||||||
\(268\) | −15.4877 | −0.946060 | ||||||||
\(269\) | −1.59532 | −0.0972684 | −0.0486342 | − | 0.998817i | \(-0.515487\pi\) | ||||
−0.0486342 | + | 0.998817i | \(0.515487\pi\) | |||||||
\(270\) | −3.02882 | −0.184328 | ||||||||
\(271\) | 6.02629 | 0.366071 | 0.183035 | − | 0.983106i | \(-0.441408\pi\) | ||||
0.183035 | + | 0.983106i | \(0.441408\pi\) | |||||||
\(272\) | 10.5450 | 0.639387 | ||||||||
\(273\) | 5.23787 | 0.317011 | ||||||||
\(274\) | 1.54740 | 0.0934821 | ||||||||
\(275\) | −42.7700 | −2.57913 | ||||||||
\(276\) | 8.81490 | 0.530595 | ||||||||
\(277\) | 7.30551 | 0.438946 | 0.219473 | − | 0.975619i | \(-0.429566\pi\) | ||||
0.219473 | + | 0.975619i | \(0.429566\pi\) | |||||||
\(278\) | −1.55715 | −0.0933918 | ||||||||
\(279\) | −8.26544 | −0.494839 | ||||||||
\(280\) | 3.32313 | 0.198595 | ||||||||
\(281\) | −18.6946 | −1.11523 | −0.557613 | − | 0.830101i | \(-0.688283\pi\) | ||||
−0.557613 | + | 0.830101i | \(0.688283\pi\) | |||||||
\(282\) | 0.318287 | 0.0189537 | ||||||||
\(283\) | −18.6920 | −1.11113 | −0.555563 | − | 0.831475i | \(-0.687497\pi\) | ||||
−0.555563 | + | 0.831475i | \(0.687497\pi\) | |||||||
\(284\) | −30.4344 | −1.80595 | ||||||||
\(285\) | −9.14210 | −0.541531 | ||||||||
\(286\) | −3.71430 | −0.219631 | ||||||||
\(287\) | 1.34864 | 0.0796080 | ||||||||
\(288\) | 4.47873 | 0.263912 | ||||||||
\(289\) | −9.38179 | −0.551870 | ||||||||
\(290\) | −0.961468 | −0.0564593 | ||||||||
\(291\) | −5.79316 | −0.339601 | ||||||||
\(292\) | −30.5398 | −1.78720 | ||||||||
\(293\) | 13.4321 | 0.784714 | 0.392357 | − | 0.919813i | \(-0.371660\pi\) | ||||
0.392357 | + | 0.919813i | \(0.371660\pi\) | |||||||
\(294\) | −0.830440 | −0.0484322 | ||||||||
\(295\) | −1.63550 | −0.0952224 | ||||||||
\(296\) | −3.81024 | −0.221466 | ||||||||
\(297\) | −21.9873 | −1.27583 | ||||||||
\(298\) | 1.96787 | 0.113995 | ||||||||
\(299\) | −22.6538 | −1.31010 | ||||||||
\(300\) | 16.0022 | 0.923886 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.26858 | −0.188086 | ||||||||
\(303\) | −5.89673 | −0.338758 | ||||||||
\(304\) | 10.3902 | 0.595917 | ||||||||
\(305\) | 41.6790 | 2.38653 | ||||||||
\(306\) | 1.05114 | 0.0600896 | ||||||||
\(307\) | 0.447461 | 0.0255380 | 0.0127690 | − | 0.999918i | \(-0.495935\pi\) | ||||
0.0127690 | + | 0.999918i | \(0.495935\pi\) | |||||||
\(308\) | 11.9706 | 0.682085 | ||||||||
\(309\) | −10.6485 | −0.605773 | ||||||||
\(310\) | −2.44684 | −0.138971 | ||||||||
\(311\) | 23.9641 | 1.35888 | 0.679440 | − | 0.733731i | \(-0.262223\pi\) | ||||
0.679440 | + | 0.733731i | \(0.262223\pi\) | |||||||
\(312\) | 2.80058 | 0.158552 | ||||||||
\(313\) | −5.90628 | −0.333843 | −0.166921 | − | 0.985970i | \(-0.553383\pi\) | ||||
−0.166921 | + | 0.985970i | \(0.553383\pi\) | |||||||
\(314\) | 1.69695 | 0.0957645 | ||||||||
\(315\) | −10.6032 | −0.597425 | ||||||||
\(316\) | 21.2245 | 1.19397 | ||||||||
\(317\) | −12.9476 | −0.727207 | −0.363604 | − | 0.931554i | \(-0.618454\pi\) | ||||
−0.363604 | + | 0.931554i | \(0.618454\pi\) | |||||||
\(318\) | 0.187697 | 0.0105255 | ||||||||
\(319\) | −6.97964 | −0.390785 | ||||||||
\(320\) | −27.3269 | −1.52762 | ||||||||
\(321\) | 9.78534 | 0.546164 | ||||||||
\(322\) | −1.11425 | −0.0620950 | ||||||||
\(323\) | 7.50632 | 0.417663 | ||||||||
\(324\) | −4.75364 | −0.264091 | ||||||||
\(325\) | −41.1246 | −2.28118 | ||||||||
\(326\) | −3.22033 | −0.178357 | ||||||||
\(327\) | 0.809932 | 0.0447894 | ||||||||
\(328\) | 0.721091 | 0.0398156 | ||||||||
\(329\) | 2.63620 | 0.145339 | ||||||||
\(330\) | −2.75116 | −0.151447 | ||||||||
\(331\) | 13.7626 | 0.756463 | 0.378232 | − | 0.925711i | \(-0.376532\pi\) | ||||
0.378232 | + | 0.925711i | \(0.376532\pi\) | |||||||
\(332\) | −0.862423 | −0.0473316 | ||||||||
\(333\) | 12.1575 | 0.666225 | ||||||||
\(334\) | −3.85277 | −0.210814 | ||||||||
\(335\) | 29.4815 | 1.61074 | ||||||||
\(336\) | −4.40932 | −0.240548 | ||||||||
\(337\) | 30.4226 | 1.65723 | 0.828613 | − | 0.559821i | \(-0.189130\pi\) | ||||
0.828613 | + | 0.559821i | \(0.189130\pi\) | |||||||
\(338\) | −1.31731 | −0.0716522 | ||||||||
\(339\) | −8.43304 | −0.458020 | ||||||||
\(340\) | −20.3889 | −1.10574 | ||||||||
\(341\) | −17.7625 | −0.961893 | ||||||||
\(342\) | 1.03570 | 0.0560043 | ||||||||
\(343\) | −15.8900 | −0.857981 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.7795 | −0.903381 | ||||||||
\(346\) | 0.269976 | 0.0145140 | ||||||||
\(347\) | 17.9851 | 0.965489 | 0.482744 | − | 0.875761i | \(-0.339640\pi\) | ||||
0.482744 | + | 0.875761i | \(0.339640\pi\) | |||||||
\(348\) | 2.61140 | 0.139985 | ||||||||
\(349\) | −29.8015 | −1.59524 | −0.797619 | − | 0.603161i | \(-0.793907\pi\) | ||||
−0.797619 | + | 0.603161i | \(0.793907\pi\) | |||||||
\(350\) | −2.02277 | −0.108122 | ||||||||
\(351\) | −21.1414 | −1.12845 | ||||||||
\(352\) | 9.62483 | 0.513005 | ||||||||
\(353\) | 12.9853 | 0.691140 | 0.345570 | − | 0.938393i | \(-0.387686\pi\) | ||||
0.345570 | + | 0.938393i | \(0.387686\pi\) | |||||||
\(354\) | −0.0677946 | −0.00360324 | ||||||||
\(355\) | 57.9332 | 3.07478 | ||||||||
\(356\) | 10.6690 | 0.565455 | ||||||||
\(357\) | −3.18549 | −0.168594 | ||||||||
\(358\) | 0.159291 | 0.00841880 | ||||||||
\(359\) | 33.4100 | 1.76331 | 0.881655 | − | 0.471894i | \(-0.156429\pi\) | ||||
0.881655 | + | 0.471894i | \(0.156429\pi\) | |||||||
\(360\) | −5.66933 | −0.298800 | ||||||||
\(361\) | −11.6039 | −0.610732 | ||||||||
\(362\) | 3.06350 | 0.161014 | ||||||||
\(363\) | −10.1106 | −0.530671 | ||||||||
\(364\) | 11.5100 | 0.603290 | ||||||||
\(365\) | 58.1338 | 3.04286 | ||||||||
\(366\) | 1.72767 | 0.0903070 | ||||||||
\(367\) | −23.8201 | −1.24340 | −0.621700 | − | 0.783256i | \(-0.713558\pi\) | ||||
−0.621700 | + | 0.783256i | \(0.713558\pi\) | |||||||
\(368\) | 19.0703 | 0.994107 | ||||||||
\(369\) | −2.30081 | −0.119776 | ||||||||
\(370\) | 3.59901 | 0.187104 | ||||||||
\(371\) | 1.55460 | 0.0807108 | ||||||||
\(372\) | 6.64575 | 0.344566 | ||||||||
\(373\) | −22.0022 | −1.13923 | −0.569615 | − | 0.821911i | \(-0.692908\pi\) | ||||
−0.569615 | + | 0.821911i | \(0.692908\pi\) | |||||||
\(374\) | 2.25891 | 0.116805 | ||||||||
\(375\) | −13.6529 | −0.705033 | ||||||||
\(376\) | 1.40952 | 0.0726905 | ||||||||
\(377\) | −6.71113 | −0.345641 | ||||||||
\(378\) | −1.03987 | −0.0534851 | ||||||||
\(379\) | −26.6146 | −1.36710 | −0.683550 | − | 0.729903i | \(-0.739565\pi\) | ||||
−0.683550 | + | 0.729903i | \(0.739565\pi\) | |||||||
\(380\) | −20.0894 | −1.03057 | ||||||||
\(381\) | −9.92711 | −0.508582 | ||||||||
\(382\) | 0.0890489 | 0.00455614 | ||||||||
\(383\) | −4.01558 | −0.205186 | −0.102593 | − | 0.994723i | \(-0.532714\pi\) | ||||
−0.102593 | + | 0.994723i | \(0.532714\pi\) | |||||||
\(384\) | −4.78879 | −0.244377 | ||||||||
\(385\) | −22.7865 | −1.16131 | ||||||||
\(386\) | −2.06880 | −0.105299 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.7303 | −0.646281 | ||||||||
\(389\) | 5.01939 | 0.254493 | 0.127246 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127246 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(390\) | −2.64533 | −0.133951 | ||||||||
\(391\) | 13.7772 | 0.696744 | ||||||||
\(392\) | −3.67758 | −0.185746 | ||||||||
\(393\) | 11.7473 | 0.592573 | ||||||||
\(394\) | −3.29672 | −0.166086 | ||||||||
\(395\) | −40.4017 | −2.03283 | ||||||||
\(396\) | −20.4220 | −1.02624 | ||||||||
\(397\) | 0.953961 | 0.0478779 | 0.0239390 | − | 0.999713i | \(-0.492379\pi\) | ||||
0.0239390 | + | 0.999713i | \(0.492379\pi\) | |||||||
\(398\) | −0.449749 | −0.0225439 | ||||||||
\(399\) | −3.13871 | −0.157132 | ||||||||
\(400\) | 34.6194 | 1.73097 | ||||||||
\(401\) | −5.05098 | −0.252234 | −0.126117 | − | 0.992015i | \(-0.540251\pi\) | ||||
−0.126117 | + | 0.992015i | \(0.540251\pi\) | |||||||
\(402\) | 1.22206 | 0.0609510 | ||||||||
\(403\) | −17.0792 | −0.850774 | ||||||||
\(404\) | −12.9579 | −0.644677 | ||||||||
\(405\) | 9.04877 | 0.449637 | ||||||||
\(406\) | −0.330096 | −0.0163824 | ||||||||
\(407\) | 26.1265 | 1.29504 | ||||||||
\(408\) | −1.70321 | −0.0843217 | ||||||||
\(409\) | −3.11544 | −0.154048 | −0.0770242 | − | 0.997029i | \(-0.524542\pi\) | ||||
−0.0770242 | + | 0.997029i | \(0.524542\pi\) | |||||||
\(410\) | −0.681117 | −0.0336380 | ||||||||
\(411\) | 8.00027 | 0.394624 | ||||||||
\(412\) | −23.3998 | −1.15282 | ||||||||
\(413\) | −0.561507 | −0.0276300 | ||||||||
\(414\) | 1.90094 | 0.0934262 | ||||||||
\(415\) | 1.64166 | 0.0805859 | ||||||||
\(416\) | 9.25456 | 0.453742 | ||||||||
\(417\) | −8.05067 | −0.394243 | ||||||||
\(418\) | 2.22573 | 0.108864 | ||||||||
\(419\) | 14.9155 | 0.728672 | 0.364336 | − | 0.931268i | \(-0.381296\pi\) | ||||
0.364336 | + | 0.931268i | \(0.381296\pi\) | |||||||
\(420\) | 8.52544 | 0.415999 | ||||||||
\(421\) | −8.61076 | −0.419663 | −0.209831 | − | 0.977738i | \(-0.567291\pi\) | ||||
−0.209831 | + | 0.977738i | \(0.567291\pi\) | |||||||
\(422\) | 0.434399 | 0.0211462 | ||||||||
\(423\) | −4.49741 | −0.218672 | ||||||||
\(424\) | 0.831211 | 0.0403672 | ||||||||
\(425\) | 25.0106 | 1.21319 | ||||||||
\(426\) | 2.40144 | 0.116350 | ||||||||
\(427\) | 14.3094 | 0.692482 | ||||||||
\(428\) | 21.5029 | 1.03938 | ||||||||
\(429\) | −19.2034 | −0.927147 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.33423 | −0.0642676 | −0.0321338 | − | 0.999484i | \(-0.510230\pi\) | ||||
−0.0321338 | + | 0.999484i | \(0.510230\pi\) | |||||||
\(432\) | 17.7972 | 0.856268 | ||||||||
\(433\) | −13.5246 | −0.649951 | −0.324976 | − | 0.945722i | \(-0.605356\pi\) | ||||
−0.324976 | + | 0.945722i | \(0.605356\pi\) | |||||||
\(434\) | −0.840061 | −0.0403242 | ||||||||
\(435\) | −4.97091 | −0.238337 | ||||||||
\(436\) | 1.77980 | 0.0852368 | ||||||||
\(437\) | 13.5749 | 0.649375 | ||||||||
\(438\) | 2.40976 | 0.115143 | ||||||||
\(439\) | −24.1197 | −1.15117 | −0.575586 | − | 0.817741i | \(-0.695226\pi\) | ||||
−0.575586 | + | 0.817741i | \(0.695226\pi\) | |||||||
\(440\) | −12.1834 | −0.580823 | ||||||||
\(441\) | 11.7342 | 0.558771 | ||||||||
\(442\) | 2.17200 | 0.103312 | ||||||||
\(443\) | 0.319346 | 0.0151726 | 0.00758629 | − | 0.999971i | \(-0.497585\pi\) | ||||
0.00758629 | + | 0.999971i | \(0.497585\pi\) | |||||||
\(444\) | −9.77510 | −0.463906 | ||||||||
\(445\) | −20.3089 | −0.962733 | ||||||||
\(446\) | −1.07923 | −0.0511030 | ||||||||
\(447\) | 10.1741 | 0.481219 | ||||||||
\(448\) | −9.38201 | −0.443258 | ||||||||
\(449\) | 36.3704 | 1.71643 | 0.858213 | − | 0.513294i | \(-0.171575\pi\) | ||||
0.858213 | + | 0.513294i | \(0.171575\pi\) | |||||||
\(450\) | 3.45088 | 0.162676 | ||||||||
\(451\) | −4.94447 | −0.232826 | ||||||||
\(452\) | −18.5313 | −0.871639 | ||||||||
\(453\) | −16.8990 | −0.793983 | ||||||||
\(454\) | −3.48453 | −0.163537 | ||||||||
\(455\) | −21.9099 | −1.02715 | ||||||||
\(456\) | −1.67820 | −0.0785889 | ||||||||
\(457\) | −21.6311 | −1.01186 | −0.505929 | − | 0.862575i | \(-0.668850\pi\) | ||||
−0.505929 | + | 0.862575i | \(0.668850\pi\) | |||||||
\(458\) | 0.344813 | 0.0161121 | ||||||||
\(459\) | 12.8575 | 0.600136 | ||||||||
\(460\) | −36.8725 | −1.71919 | ||||||||
\(461\) | −32.6478 | −1.52056 | −0.760281 | − | 0.649595i | \(-0.774939\pi\) | ||||
−0.760281 | + | 0.649595i | \(0.774939\pi\) | |||||||
\(462\) | −0.944543 | −0.0439441 | ||||||||
\(463\) | −9.74471 | −0.452875 | −0.226438 | − | 0.974026i | \(-0.572708\pi\) | ||||
−0.226438 | + | 0.974026i | \(0.572708\pi\) | |||||||
\(464\) | 5.64953 | 0.262273 | ||||||||
\(465\) | −12.6505 | −0.586652 | ||||||||
\(466\) | 3.59300 | 0.166442 | ||||||||
\(467\) | 12.6828 | 0.586888 | 0.293444 | − | 0.955976i | \(-0.405199\pi\) | ||||
0.293444 | + | 0.955976i | \(0.405199\pi\) | |||||||
\(468\) | −19.6364 | −0.907691 | ||||||||
\(469\) | 10.1217 | 0.467377 | ||||||||
\(470\) | −1.33138 | −0.0614121 | ||||||||
\(471\) | 8.77344 | 0.404259 | ||||||||
\(472\) | −0.300226 | −0.0138190 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.67473 | −0.0769229 | ||||||||
\(475\) | 24.6433 | 1.13071 | ||||||||
\(476\) | −7.00000 | −0.320845 | ||||||||
\(477\) | −2.65218 | −0.121435 | ||||||||
\(478\) | 1.35341 | 0.0619036 | ||||||||
\(479\) | 14.5454 | 0.664594 | 0.332297 | − | 0.943175i | \(-0.392176\pi\) | ||||
0.332297 | + | 0.943175i | \(0.392176\pi\) | |||||||
\(480\) | 6.85482 | 0.312878 | ||||||||
\(481\) | 25.1214 | 1.14544 | ||||||||
\(482\) | 0.0862629 | 0.00392917 | ||||||||
\(483\) | −5.76083 | −0.262127 | ||||||||
\(484\) | −22.2178 | −1.00990 | ||||||||
\(485\) | 24.2326 | 1.10035 | ||||||||
\(486\) | 2.79824 | 0.126931 | ||||||||
\(487\) | 37.8405 | 1.71472 | 0.857359 | − | 0.514719i | \(-0.172104\pi\) | ||||
0.857359 | + | 0.514719i | \(0.172104\pi\) | |||||||
\(488\) | 7.65095 | 0.346342 | ||||||||
\(489\) | −16.6495 | −0.752915 | ||||||||
\(490\) | 3.47371 | 0.156926 | ||||||||
\(491\) | −28.2201 | −1.27355 | −0.636777 | − | 0.771048i | \(-0.719733\pi\) | ||||
−0.636777 | + | 0.771048i | \(0.719733\pi\) | |||||||
\(492\) | 1.84995 | 0.0834021 | ||||||||
\(493\) | 4.08147 | 0.183820 | ||||||||
\(494\) | 2.14011 | 0.0962879 | ||||||||
\(495\) | 38.8742 | 1.74726 | ||||||||
\(496\) | 14.3775 | 0.645569 | ||||||||
\(497\) | 19.8899 | 0.892184 | ||||||||
\(498\) | 0.0680499 | 0.00304939 | ||||||||
\(499\) | 8.26465 | 0.369977 | 0.184988 | − | 0.982741i | \(-0.440775\pi\) | ||||
0.184988 | + | 0.982741i | \(0.440775\pi\) | |||||||
\(500\) | −30.0018 | −1.34172 | ||||||||
\(501\) | −19.9193 | −0.889929 | ||||||||
\(502\) | −1.48470 | −0.0662656 | ||||||||
\(503\) | −29.8923 | −1.33283 | −0.666415 | − | 0.745581i | \(-0.732172\pi\) | ||||
−0.666415 | + | 0.745581i | \(0.732172\pi\) | |||||||
\(504\) | −1.94642 | −0.0867005 | ||||||||
\(505\) | 24.6658 | 1.09762 | ||||||||
\(506\) | 4.08514 | 0.181607 | ||||||||
\(507\) | −6.81065 | −0.302472 | ||||||||
\(508\) | −21.8145 | −0.967861 | ||||||||
\(509\) | −22.2426 | −0.985884 | −0.492942 | − | 0.870062i | \(-0.664079\pi\) | ||||
−0.492942 | + | 0.870062i | \(0.664079\pi\) | |||||||
\(510\) | 1.60880 | 0.0712386 | ||||||||
\(511\) | 19.9588 | 0.882923 | ||||||||
\(512\) | −13.0504 | −0.576751 | ||||||||
\(513\) | 12.6687 | 0.559335 | ||||||||
\(514\) | 4.10882 | 0.181232 | ||||||||
\(515\) | 44.5425 | 1.96278 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.66499 | −0.425066 | ||||||||
\(518\) | 1.23563 | 0.0542905 | ||||||||
\(519\) | 1.39581 | 0.0612692 | ||||||||
\(520\) | −11.7147 | −0.513725 | ||||||||
\(521\) | 17.8713 | 0.782954 | 0.391477 | − | 0.920188i | \(-0.371964\pi\) | ||||
0.391477 | + | 0.920188i | \(0.371964\pi\) | |||||||
\(522\) | 0.563150 | 0.0246484 | ||||||||
\(523\) | 9.87947 | 0.431999 | 0.216000 | − | 0.976393i | \(-0.430699\pi\) | ||||
0.216000 | + | 0.976393i | \(0.430699\pi\) | |||||||
\(524\) | 25.8143 | 1.12770 | ||||||||
\(525\) | −10.4580 | −0.456423 | ||||||||
\(526\) | 2.47111 | 0.107746 | ||||||||
\(527\) | 10.3870 | 0.452463 | ||||||||
\(528\) | 16.1657 | 0.703521 | ||||||||
\(529\) | 1.91556 | 0.0832852 | ||||||||
\(530\) | −0.785133 | −0.0341040 | ||||||||
\(531\) | 0.957943 | 0.0415712 | ||||||||
\(532\) | −6.89720 | −0.299031 | ||||||||
\(533\) | −4.75426 | −0.205930 | ||||||||
\(534\) | −0.841841 | −0.0364300 | ||||||||
\(535\) | −40.9318 | −1.76964 | ||||||||
\(536\) | 5.41187 | 0.233757 | ||||||||
\(537\) | 0.823554 | 0.0355390 | ||||||||
\(538\) | 0.276616 | 0.0119258 | ||||||||
\(539\) | 25.2169 | 1.08617 | ||||||||
\(540\) | −34.4109 | −1.48081 | ||||||||
\(541\) | 15.4611 | 0.664726 | 0.332363 | − | 0.943152i | \(-0.392154\pi\) | ||||
0.332363 | + | 0.943152i | \(0.392154\pi\) | |||||||
\(542\) | −1.04491 | −0.0448828 | ||||||||
\(543\) | 15.8387 | 0.679703 | ||||||||
\(544\) | −5.62830 | −0.241311 | ||||||||
\(545\) | −3.38792 | −0.145123 | ||||||||
\(546\) | −0.908206 | −0.0388676 | ||||||||
\(547\) | 38.6245 | 1.65146 | 0.825732 | − | 0.564063i | \(-0.190762\pi\) | ||||
0.825732 | + | 0.564063i | \(0.190762\pi\) | |||||||
\(548\) | 17.5803 | 0.750993 | ||||||||
\(549\) | −24.4122 | −1.04189 | ||||||||
\(550\) | 7.41598 | 0.316219 | ||||||||
\(551\) | 4.02153 | 0.171323 | ||||||||
\(552\) | −3.08019 | −0.131102 | ||||||||
\(553\) | −13.8709 | −0.589851 | ||||||||
\(554\) | −1.26672 | −0.0538177 | ||||||||
\(555\) | 18.6073 | 0.789838 | ||||||||
\(556\) | −17.6911 | −0.750268 | ||||||||
\(557\) | −3.85403 | −0.163300 | −0.0816502 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816502 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(558\) | 1.43316 | 0.0606706 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 18.4441 | 0.779404 | ||||||||
\(561\) | 11.6788 | 0.493080 | ||||||||
\(562\) | 3.24149 | 0.136734 | ||||||||
\(563\) | −47.2566 | −1.99163 | −0.995815 | − | 0.0913962i | \(-0.970867\pi\) | ||||
−0.995815 | + | 0.0913962i | \(0.970867\pi\) | |||||||
\(564\) | 3.61610 | 0.152265 | ||||||||
\(565\) | 35.2751 | 1.48404 | ||||||||
\(566\) | 3.24105 | 0.136231 | ||||||||
\(567\) | 3.10666 | 0.130468 | ||||||||
\(568\) | 10.6347 | 0.446222 | ||||||||
\(569\) | 36.0982 | 1.51331 | 0.756657 | − | 0.653811i | \(-0.226831\pi\) | ||||
0.756657 | + | 0.653811i | \(0.226831\pi\) | |||||||
\(570\) | 1.58517 | 0.0663954 | ||||||||
\(571\) | 31.8292 | 1.33201 | 0.666006 | − | 0.745946i | \(-0.268002\pi\) | ||||
0.666006 | + | 0.745946i | \(0.268002\pi\) | |||||||
\(572\) | −42.1987 | −1.76442 | ||||||||
\(573\) | 0.460394 | 0.0192332 | ||||||||
\(574\) | −0.233844 | −0.00976047 | ||||||||
\(575\) | 45.2306 | 1.88625 | ||||||||
\(576\) | 16.0059 | 0.666912 | ||||||||
\(577\) | 17.1365 | 0.713403 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(578\) | 1.62673 | 0.0676630 | ||||||||
\(579\) | −10.6959 | −0.444508 | ||||||||
\(580\) | −10.9234 | −0.453569 | ||||||||
\(581\) | 0.563622 | 0.0233830 | ||||||||
\(582\) | 1.00449 | 0.0416374 | ||||||||
\(583\) | −5.69956 | −0.236052 | ||||||||
\(584\) | 10.6715 | 0.441591 | ||||||||
\(585\) | 37.3787 | 1.54542 | ||||||||
\(586\) | −2.32903 | −0.0962112 | ||||||||
\(587\) | −23.8807 | −0.985662 | −0.492831 | − | 0.870125i | \(-0.664038\pi\) | ||||
−0.492831 | + | 0.870125i | \(0.664038\pi\) | |||||||
\(588\) | −9.43476 | −0.389083 | ||||||||
\(589\) | 10.2344 | 0.421701 | ||||||||
\(590\) | 0.283583 | 0.0116749 | ||||||||
\(591\) | −17.0445 | −0.701115 | ||||||||
\(592\) | −21.1476 | −0.869161 | ||||||||
\(593\) | 10.8615 | 0.446028 | 0.223014 | − | 0.974815i | \(-0.428410\pi\) | ||||
0.223014 | + | 0.974815i | \(0.428410\pi\) | |||||||
\(594\) | 3.81242 | 0.156426 | ||||||||
\(595\) | 13.3248 | 0.546264 | ||||||||
\(596\) | 22.3572 | 0.915788 | ||||||||
\(597\) | −2.32526 | −0.0951664 | ||||||||
\(598\) | 3.92798 | 0.160627 | ||||||||
\(599\) | 21.5460 | 0.880345 | 0.440172 | − | 0.897913i | \(-0.354917\pi\) | ||||
0.440172 | + | 0.897913i | \(0.354917\pi\) | |||||||
\(600\) | −5.59165 | −0.228278 | ||||||||
\(601\) | −35.3358 | −1.44138 | −0.720690 | − | 0.693258i | \(-0.756175\pi\) | ||||
−0.720690 | + | 0.693258i | \(0.756175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.2679 | −0.703201 | ||||||||
\(604\) | −37.1349 | −1.51100 | ||||||||
\(605\) | 42.2925 | 1.71944 | ||||||||
\(606\) | 1.02245 | 0.0415340 | ||||||||
\(607\) | −0.431261 | −0.0175044 | −0.00875218 | − | 0.999962i | \(-0.502786\pi\) | ||||
−0.00875218 | + | 0.999962i | \(0.502786\pi\) | |||||||
\(608\) | −5.54564 | −0.224905 | ||||||||
\(609\) | −1.70663 | −0.0691563 | ||||||||
\(610\) | −7.22681 | −0.292605 | ||||||||
\(611\) | −9.29317 | −0.375961 | ||||||||
\(612\) | 11.9421 | 0.482733 | ||||||||
\(613\) | −39.4834 | −1.59472 | −0.797359 | − | 0.603506i | \(-0.793770\pi\) | ||||
−0.797359 | + | 0.603506i | \(0.793770\pi\) | |||||||
\(614\) | −0.0775863 | −0.00313113 | ||||||||
\(615\) | −3.52146 | −0.141999 | ||||||||
\(616\) | −4.18288 | −0.168533 | ||||||||
\(617\) | −21.5383 | −0.867099 | −0.433549 | − | 0.901130i | \(-0.642739\pi\) | ||||
−0.433549 | + | 0.901130i | \(0.642739\pi\) | |||||||
\(618\) | 1.84637 | 0.0742719 | ||||||||
\(619\) | −30.8064 | −1.23821 | −0.619106 | − | 0.785308i | \(-0.712505\pi\) | ||||
−0.619106 | + | 0.785308i | \(0.712505\pi\) | |||||||
\(620\) | −27.7990 | −1.11643 | ||||||||
\(621\) | 23.2522 | 0.933080 | ||||||||
\(622\) | −4.15519 | −0.166608 | ||||||||
\(623\) | −6.97254 | −0.279349 | ||||||||
\(624\) | 15.5438 | 0.622250 | ||||||||
\(625\) | 11.8025 | 0.472099 | ||||||||
\(626\) | 1.02410 | 0.0409314 | ||||||||
\(627\) | 11.5073 | 0.459557 | ||||||||
\(628\) | 19.2793 | 0.769329 | ||||||||
\(629\) | −15.2780 | −0.609173 | ||||||||
\(630\) | 1.83852 | 0.0732483 | ||||||||
\(631\) | 32.5214 | 1.29466 | 0.647328 | − | 0.762211i | \(-0.275886\pi\) | ||||
0.647328 | + | 0.762211i | \(0.275886\pi\) | |||||||
\(632\) | −7.41648 | −0.295012 | ||||||||
\(633\) | 2.24590 | 0.0892664 | ||||||||
\(634\) | 2.24500 | 0.0891605 | ||||||||
\(635\) | 41.5248 | 1.64786 | ||||||||
\(636\) | 2.13246 | 0.0845575 | ||||||||
\(637\) | 24.2468 | 0.960692 | ||||||||
\(638\) | 1.21021 | 0.0479128 | ||||||||
\(639\) | −33.9326 | −1.34235 | ||||||||
\(640\) | 20.0314 | 0.791810 | ||||||||
\(641\) | −5.46273 | −0.215765 | −0.107882 | − | 0.994164i | \(-0.534407\pi\) | ||||
−0.107882 | + | 0.994164i | \(0.534407\pi\) | |||||||
\(642\) | −1.69670 | −0.0669634 | ||||||||
\(643\) | −28.5630 | −1.12641 | −0.563207 | − | 0.826316i | \(-0.690432\pi\) | ||||
−0.563207 | + | 0.826316i | \(0.690432\pi\) | |||||||
\(644\) | −12.6592 | −0.498843 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.30154 | −0.0512083 | ||||||||
\(647\) | −6.49241 | −0.255243 | −0.127622 | − | 0.991823i | \(-0.540734\pi\) | ||||
−0.127622 | + | 0.991823i | \(0.540734\pi\) | |||||||
\(648\) | 1.66107 | 0.0652529 | ||||||||
\(649\) | 2.05863 | 0.0808082 | ||||||||
\(650\) | 7.13069 | 0.279689 | ||||||||
\(651\) | −4.34322 | −0.170224 | ||||||||
\(652\) | −36.5866 | −1.43284 | ||||||||
\(653\) | −24.2888 | −0.950493 | −0.475246 | − | 0.879853i | \(-0.657641\pi\) | ||||
−0.475246 | + | 0.879853i | \(0.657641\pi\) | |||||||
\(654\) | −0.140436 | −0.00549148 | ||||||||
\(655\) | −49.1386 | −1.92000 | ||||||||
\(656\) | 4.00221 | 0.156260 | ||||||||
\(657\) | −34.0500 | −1.32842 | ||||||||
\(658\) | −0.457097 | −0.0178195 | ||||||||
\(659\) | 36.4889 | 1.42140 | 0.710702 | − | 0.703493i | \(-0.248377\pi\) | ||||
0.710702 | + | 0.703493i | \(0.248377\pi\) | |||||||
\(660\) | −31.2564 | −1.21665 | ||||||||
\(661\) | −25.3533 | −0.986131 | −0.493065 | − | 0.869992i | \(-0.664124\pi\) | ||||
−0.493065 | + | 0.869992i | \(0.664124\pi\) | |||||||
\(662\) | −2.38633 | −0.0927475 | ||||||||
\(663\) | 11.2295 | 0.436119 | ||||||||
\(664\) | 0.301357 | 0.0116949 | ||||||||
\(665\) | 13.1291 | 0.509126 | ||||||||
\(666\) | −2.10801 | −0.0816837 | ||||||||
\(667\) | 7.38118 | 0.285800 | ||||||||
\(668\) | −43.7720 | −1.69359 | ||||||||
\(669\) | −5.57975 | −0.215726 | ||||||||
\(670\) | −5.11185 | −0.197488 | ||||||||
\(671\) | −52.4620 | −2.02527 | ||||||||
\(672\) | 2.35343 | 0.0907854 | ||||||||
\(673\) | 31.1668 | 1.20139 | 0.600696 | − | 0.799477i | \(-0.294890\pi\) | ||||
0.600696 | + | 0.799477i | \(0.294890\pi\) | |||||||
\(674\) | −5.27504 | −0.203187 | ||||||||
\(675\) | 42.2111 | 1.62471 | ||||||||
\(676\) | −14.9662 | −0.575622 | ||||||||
\(677\) | −25.5584 | −0.982291 | −0.491145 | − | 0.871078i | \(-0.663422\pi\) | ||||
−0.491145 | + | 0.871078i | \(0.663422\pi\) | |||||||
\(678\) | 1.46222 | 0.0561563 | ||||||||
\(679\) | 8.31965 | 0.319279 | ||||||||
\(680\) | 7.12449 | 0.273212 | ||||||||
\(681\) | −18.0155 | −0.690354 | ||||||||
\(682\) | 3.07988 | 0.117935 | ||||||||
\(683\) | −23.1944 | −0.887510 | −0.443755 | − | 0.896148i | \(-0.646354\pi\) | ||||
−0.443755 | + | 0.896148i | \(0.646354\pi\) | |||||||
\(684\) | 11.7668 | 0.449913 | ||||||||
\(685\) | −33.4649 | −1.27863 | ||||||||
\(686\) | 2.75521 | 0.105194 | ||||||||
\(687\) | 1.78273 | 0.0680153 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.48029 | −0.208783 | ||||||||
\(690\) | 2.90944 | 0.110761 | ||||||||
\(691\) | −35.7877 | −1.36143 | −0.680714 | − | 0.732549i | \(-0.738331\pi\) | ||||
−0.680714 | + | 0.732549i | \(0.738331\pi\) | |||||||
\(692\) | 3.06724 | 0.116599 | ||||||||
\(693\) | 13.3465 | 0.506990 | ||||||||
\(694\) | −3.11847 | −0.118375 | ||||||||
\(695\) | 33.6757 | 1.27739 | ||||||||
\(696\) | −0.912501 | −0.0345883 | ||||||||
\(697\) | 2.89137 | 0.109519 | ||||||||
\(698\) | 5.16735 | 0.195587 | ||||||||
\(699\) | 18.5762 | 0.702617 | ||||||||
\(700\) | −22.9810 | −0.868600 | ||||||||
\(701\) | 14.7767 | 0.558107 | 0.279053 | − | 0.960276i | \(-0.409979\pi\) | ||||
0.279053 | + | 0.960276i | \(0.409979\pi\) | |||||||
\(702\) | 3.66576 | 0.138355 | ||||||||
\(703\) | −15.0536 | −0.567757 | ||||||||
\(704\) | 34.3968 | 1.29638 | ||||||||
\(705\) | −6.88341 | −0.259244 | ||||||||
\(706\) | −2.25155 | −0.0847384 | ||||||||
\(707\) | 8.46839 | 0.318487 | ||||||||
\(708\) | −0.770225 | −0.0289468 | ||||||||
\(709\) | −25.9700 | −0.975324 | −0.487662 | − | 0.873032i | \(-0.662150\pi\) | ||||
−0.487662 | + | 0.873032i | \(0.662150\pi\) | |||||||
\(710\) | −10.0452 | −0.376988 | ||||||||
\(711\) | 23.6641 | 0.887472 | ||||||||
\(712\) | −3.72807 | −0.139715 | ||||||||
\(713\) | 18.7844 | 0.703481 | ||||||||
\(714\) | 0.552339 | 0.0206708 | ||||||||
\(715\) | 80.3271 | 3.00406 | ||||||||
\(716\) | 1.80973 | 0.0676328 | ||||||||
\(717\) | 6.99730 | 0.261319 | ||||||||
\(718\) | −5.79303 | −0.216194 | ||||||||
\(719\) | −4.03692 | −0.150552 | −0.0752759 | − | 0.997163i | \(-0.523984\pi\) | ||||
−0.0752759 | + | 0.997163i | \(0.523984\pi\) | |||||||
\(720\) | −31.4659 | −1.17267 | ||||||||
\(721\) | 15.2925 | 0.569523 | ||||||||
\(722\) | 2.01203 | 0.0748799 | ||||||||
\(723\) | 0.445990 | 0.0165865 | ||||||||
\(724\) | 34.8050 | 1.29352 | ||||||||
\(725\) | 13.3995 | 0.497644 | ||||||||
\(726\) | 1.75311 | 0.0650639 | ||||||||
\(727\) | −14.6132 | −0.541973 | −0.270987 | − | 0.962583i | \(-0.587350\pi\) | ||||
−0.270987 | + | 0.962583i | \(0.587350\pi\) | |||||||
\(728\) | −4.02196 | −0.149064 | ||||||||
\(729\) | 7.22794 | 0.267702 | ||||||||
\(730\) | −10.0799 | −0.373075 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 19.6284 | 0.725486 | ||||||||
\(733\) | −26.2291 | −0.968794 | −0.484397 | − | 0.874848i | \(-0.660961\pi\) | ||||
−0.484397 | + | 0.874848i | \(0.660961\pi\) | |||||||
\(734\) | 4.13022 | 0.152449 | ||||||||
\(735\) | 17.9595 | 0.662445 | ||||||||
\(736\) | −10.1786 | −0.375187 | ||||||||
\(737\) | −37.1088 | −1.36692 | ||||||||
\(738\) | 0.398943 | 0.0146853 | ||||||||
\(739\) | 5.99448 | 0.220510 | 0.110255 | − | 0.993903i | \(-0.464833\pi\) | ||||
0.110255 | + | 0.993903i | \(0.464833\pi\) | |||||||
\(740\) | 40.8890 | 1.50311 | ||||||||
\(741\) | 11.0646 | 0.406469 | ||||||||
\(742\) | −0.269555 | −0.00989569 | ||||||||
\(743\) | −28.1441 | −1.03251 | −0.516253 | − | 0.856436i | \(-0.672674\pi\) | ||||
−0.516253 | + | 0.856436i | \(0.672674\pi\) | |||||||
\(744\) | −2.32223 | −0.0851370 | ||||||||
\(745\) | −42.5580 | −1.55920 | ||||||||
\(746\) | 3.81501 | 0.139677 | ||||||||
\(747\) | −0.961551 | −0.0351813 | ||||||||
\(748\) | 25.6638 | 0.938361 | ||||||||
\(749\) | −14.0529 | −0.513481 | ||||||||
\(750\) | 2.36730 | 0.0864417 | ||||||||
\(751\) | −27.5881 | −1.00670 | −0.503352 | − | 0.864081i | \(-0.667900\pi\) | ||||
−0.503352 | + | 0.864081i | \(0.667900\pi\) | |||||||
\(752\) | 7.82313 | 0.285280 | ||||||||
\(753\) | −7.67610 | −0.279733 | ||||||||
\(754\) | 1.16366 | 0.0423779 | ||||||||
\(755\) | 70.6879 | 2.57259 | ||||||||
\(756\) | −11.8141 | −0.429675 | ||||||||
\(757\) | −22.9603 | −0.834507 | −0.417254 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(758\) | 4.61476 | 0.167616 | ||||||||
\(759\) | 21.1207 | 0.766632 | ||||||||
\(760\) | 7.01986 | 0.254637 | ||||||||
\(761\) | 31.0617 | 1.12598 | 0.562992 | − | 0.826462i | \(-0.309650\pi\) | ||||
0.562992 | + | 0.826462i | \(0.309650\pi\) | |||||||
\(762\) | 1.72128 | 0.0623555 | ||||||||
\(763\) | −1.16316 | −0.0421091 | ||||||||
\(764\) | 1.01170 | 0.0366020 | ||||||||
\(765\) | −22.7324 | −0.821892 | ||||||||
\(766\) | 0.696270 | 0.0251572 | ||||||||
\(767\) | 1.97943 | 0.0714731 | ||||||||
\(768\) | −12.2355 | −0.441509 | ||||||||
\(769\) | −13.0535 | −0.470722 | −0.235361 | − | 0.971908i | \(-0.575627\pi\) | ||||
−0.235361 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(770\) | 3.95099 | 0.142384 | ||||||||
\(771\) | 21.2431 | 0.765052 | ||||||||
\(772\) | −23.5039 | −0.845925 | ||||||||
\(773\) | 48.6075 | 1.74829 | 0.874145 | − | 0.485666i | \(-0.161423\pi\) | ||||
0.874145 | + | 0.485666i | \(0.161423\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.1004 | 1.22492 | ||||||||
\(776\) | 4.44834 | 0.159686 | ||||||||
\(777\) | 6.38836 | 0.229181 | ||||||||
\(778\) | −0.870322 | −0.0312026 | ||||||||
\(779\) | 2.84891 | 0.102073 | ||||||||
\(780\) | −30.0540 | −1.07611 | ||||||||
\(781\) | −72.9214 | −2.60933 | ||||||||
\(782\) | −2.38886 | −0.0854255 | ||||||||
\(783\) | 6.88843 | 0.246172 | ||||||||
\(784\) | −20.4113 | −0.728975 | ||||||||
\(785\) | −36.6990 | −1.30985 | ||||||||
\(786\) | −2.03689 | −0.0726534 | ||||||||
\(787\) | 24.5540 | 0.875257 | 0.437628 | − | 0.899156i | \(-0.355819\pi\) | ||||
0.437628 | + | 0.899156i | \(0.355819\pi\) | |||||||
\(788\) | −37.4546 | −1.33426 | ||||||||
\(789\) | 12.7759 | 0.454836 | ||||||||
\(790\) | 7.00534 | 0.249239 | ||||||||
\(791\) | 12.1108 | 0.430611 | ||||||||
\(792\) | 7.13607 | 0.253569 | ||||||||
\(793\) | −50.4438 | −1.79131 | ||||||||
\(794\) | −0.165409 | −0.00587015 | ||||||||
\(795\) | −4.05923 | −0.143966 | ||||||||
\(796\) | −5.10967 | −0.181107 | ||||||||
\(797\) | 31.5442 | 1.11735 | 0.558676 | − | 0.829386i | \(-0.311310\pi\) | ||||
0.558676 | + | 0.829386i | \(0.311310\pi\) | |||||||
\(798\) | 0.544227 | 0.0192654 | ||||||||
\(799\) | 5.65178 | 0.199946 | ||||||||
\(800\) | −18.4777 | −0.653285 | ||||||||
\(801\) | 11.8953 | 0.420299 | ||||||||
\(802\) | 0.875799 | 0.0309256 | ||||||||
\(803\) | −73.1739 | −2.58225 | ||||||||
\(804\) | 13.8841 | 0.489653 | ||||||||
\(805\) | 24.0974 | 0.849322 | ||||||||
\(806\) | 2.96139 | 0.104311 | ||||||||
\(807\) | 1.43014 | 0.0503433 | ||||||||
\(808\) | 4.52787 | 0.159290 | ||||||||
\(809\) | 35.1426 | 1.23555 | 0.617774 | − | 0.786356i | \(-0.288035\pi\) | ||||
0.617774 | + | 0.786356i | \(0.288035\pi\) | |||||||
\(810\) | −1.56898 | −0.0551285 | ||||||||
\(811\) | 43.7911 | 1.53771 | 0.768857 | − | 0.639421i | \(-0.220826\pi\) | ||||
0.768857 | + | 0.639421i | \(0.220826\pi\) | |||||||
\(812\) | −3.75027 | −0.131609 | ||||||||
\(813\) | −5.40231 | −0.189467 | ||||||||
\(814\) | −4.53013 | −0.158781 | ||||||||
\(815\) | 69.6442 | 2.43953 | ||||||||
\(816\) | −9.45319 | −0.330928 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.540192 | 0.0188874 | ||||||||
\(819\) | 12.8330 | 0.448422 | ||||||||
\(820\) | −7.73828 | −0.270232 | ||||||||
\(821\) | 42.0166 | 1.46639 | 0.733195 | − | 0.680018i | \(-0.238028\pi\) | ||||
0.733195 | + | 0.680018i | \(0.238028\pi\) | |||||||
\(822\) | −1.38718 | −0.0483836 | ||||||||
\(823\) | −15.1340 | −0.527539 | −0.263770 | − | 0.964586i | \(-0.584966\pi\) | ||||
−0.263770 | + | 0.964586i | \(0.584966\pi\) | |||||||
\(824\) | 8.17659 | 0.284845 | ||||||||
\(825\) | 38.3415 | 1.33488 | ||||||||
\(826\) | 0.0973609 | 0.00338762 | ||||||||
\(827\) | 20.2018 | 0.702486 | 0.351243 | − | 0.936284i | \(-0.385759\pi\) | ||||
0.351243 | + | 0.936284i | \(0.385759\pi\) | |||||||
\(828\) | 21.5969 | 0.750544 | ||||||||
\(829\) | −25.3002 | −0.878713 | −0.439356 | − | 0.898313i | \(-0.644793\pi\) | ||||
−0.439356 | + | 0.898313i | \(0.644793\pi\) | |||||||
\(830\) | −0.284651 | −0.00988037 | ||||||||
\(831\) | −6.54909 | −0.227185 | ||||||||
\(832\) | 33.0736 | 1.14662 | ||||||||
\(833\) | −14.7460 | −0.510920 | ||||||||
\(834\) | 1.39592 | 0.0483369 | ||||||||
\(835\) | 83.3219 | 2.88347 | ||||||||
\(836\) | 25.2869 | 0.874565 | ||||||||
\(837\) | 17.5304 | 0.605939 | ||||||||
\(838\) | −2.58624 | −0.0893401 | ||||||||
\(839\) | −42.6109 | −1.47109 | −0.735546 | − | 0.677474i | \(-0.763074\pi\) | ||||
−0.735546 | + | 0.677474i | \(0.763074\pi\) | |||||||
\(840\) | −2.97905 | −0.102787 | ||||||||
\(841\) | −26.8133 | −0.924598 | ||||||||
\(842\) | 1.49304 | 0.0514535 | ||||||||
\(843\) | 16.7589 | 0.577208 | ||||||||
\(844\) | 4.93528 | 0.169879 | ||||||||
\(845\) | 28.4888 | 0.980043 | ||||||||
\(846\) | 0.779816 | 0.0268106 | ||||||||
\(847\) | 14.5201 | 0.498915 | ||||||||
\(848\) | 4.61340 | 0.158425 | ||||||||
\(849\) | 16.7566 | 0.575086 | ||||||||
\(850\) | −4.33663 | −0.148745 | ||||||||
\(851\) | −27.6296 | −0.947131 | ||||||||
\(852\) | 27.2832 | 0.934706 | ||||||||
\(853\) | −18.7681 | −0.642607 | −0.321304 | − | 0.946976i | \(-0.604121\pi\) | ||||
−0.321304 | + | 0.946976i | \(0.604121\pi\) | |||||||
\(854\) | −2.48114 | −0.0849029 | ||||||||
\(855\) | −22.3985 | −0.766014 | ||||||||
\(856\) | −7.51378 | −0.256816 | ||||||||
\(857\) | −21.8895 | −0.747731 | −0.373865 | − | 0.927483i | \(-0.621968\pi\) | ||||
−0.373865 | + | 0.927483i | \(0.621968\pi\) | |||||||
\(858\) | 3.32971 | 0.113675 | ||||||||
\(859\) | 7.09658 | 0.242132 | 0.121066 | − | 0.992644i | \(-0.461369\pi\) | ||||
0.121066 | + | 0.992644i | \(0.461369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.20900 | −0.0412027 | ||||||||
\(862\) | 0.231345 | 0.00787964 | ||||||||
\(863\) | 15.5005 | 0.527643 | 0.263822 | − | 0.964571i | \(-0.415017\pi\) | ||||
0.263822 | + | 0.964571i | \(0.415017\pi\) | |||||||
\(864\) | −9.49906 | −0.323164 | ||||||||
\(865\) | −5.83863 | −0.198519 | ||||||||
\(866\) | 2.34506 | 0.0796884 | ||||||||
\(867\) | 8.41039 | 0.285632 | ||||||||
\(868\) | −9.54407 | −0.323947 | ||||||||
\(869\) | 50.8543 | 1.72511 | ||||||||
\(870\) | 0.861916 | 0.0292217 | ||||||||
\(871\) | −35.6812 | −1.20901 | ||||||||
\(872\) | −0.621916 | −0.0210607 | ||||||||
\(873\) | −14.1935 | −0.480377 | ||||||||
\(874\) | −2.35378 | −0.0796177 | ||||||||
\(875\) | 19.6072 | 0.662843 | ||||||||
\(876\) | 27.3776 | 0.925004 | ||||||||
\(877\) | 30.1286 | 1.01737 | 0.508685 | − | 0.860953i | \(-0.330132\pi\) | ||||
0.508685 | + | 0.860953i | \(0.330132\pi\) | |||||||
\(878\) | 4.18217 | 0.141142 | ||||||||
\(879\) | −12.0414 | −0.406145 | ||||||||
\(880\) | −67.6206 | −2.27949 | ||||||||
\(881\) | −17.3905 | −0.585899 | −0.292950 | − | 0.956128i | \(-0.594637\pi\) | ||||
−0.292950 | + | 0.956128i | \(0.594637\pi\) | |||||||
\(882\) | −2.03461 | −0.0685090 | ||||||||
\(883\) | −23.7234 | −0.798357 | −0.399179 | − | 0.916873i | \(-0.630705\pi\) | ||||
−0.399179 | + | 0.916873i | \(0.630705\pi\) | |||||||
\(884\) | 24.6765 | 0.829960 | ||||||||
\(885\) | 1.46616 | 0.0492843 | ||||||||
\(886\) | −0.0553720 | −0.00186026 | ||||||||
\(887\) | −51.3944 | −1.72565 | −0.862827 | − | 0.505500i | \(-0.831308\pi\) | ||||
−0.862827 | + | 0.505500i | \(0.831308\pi\) | |||||||
\(888\) | 3.41572 | 0.114624 | ||||||||
\(889\) | 14.2565 | 0.478148 | ||||||||
\(890\) | 3.52140 | 0.118038 | ||||||||
\(891\) | −11.3898 | −0.381573 | ||||||||
\(892\) | −12.2613 | −0.410539 | ||||||||
\(893\) | 5.56878 | 0.186352 | ||||||||
\(894\) | −1.76411 | −0.0590007 | ||||||||
\(895\) | −3.44490 | −0.115150 | ||||||||
\(896\) | 6.87727 | 0.229753 | ||||||||
\(897\) | 20.3082 | 0.678070 | ||||||||
\(898\) | −6.30634 | −0.210445 | ||||||||
\(899\) | 5.56484 | 0.185598 | ||||||||
\(900\) | 39.2060 | 1.30687 | ||||||||
\(901\) | 3.33292 | 0.111036 | ||||||||
\(902\) | 0.857332 | 0.0285460 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.47540 | 0.215369 | ||||||||
\(905\) | −66.2528 | −2.20232 | ||||||||
\(906\) | 2.93015 | 0.0973476 | ||||||||
\(907\) | −7.61195 | −0.252751 | −0.126375 | − | 0.991982i | \(-0.540334\pi\) | ||||
−0.126375 | + | 0.991982i | \(0.540334\pi\) | |||||||
\(908\) | −39.5883 | −1.31379 | ||||||||
\(909\) | −14.4472 | −0.479185 | ||||||||
\(910\) | 3.79900 | 0.125936 | ||||||||
\(911\) | −35.9994 | −1.19271 | −0.596357 | − | 0.802719i | \(-0.703386\pi\) | ||||
−0.596357 | + | 0.802719i | \(0.703386\pi\) | |||||||
\(912\) | −9.31436 | −0.308429 | ||||||||
\(913\) | −2.06638 | −0.0683873 | ||||||||
\(914\) | 3.75065 | 0.124061 | ||||||||
\(915\) | −37.3635 | −1.23520 | ||||||||
\(916\) | 3.91748 | 0.129437 | ||||||||
\(917\) | −16.8705 | −0.557112 | ||||||||
\(918\) | −2.22939 | −0.0735807 | ||||||||
\(919\) | −9.73512 | −0.321132 | −0.160566 | − | 0.987025i | \(-0.551332\pi\) | ||||
−0.160566 | + | 0.987025i | \(0.551332\pi\) | |||||||
\(920\) | 12.8844 | 0.424785 | ||||||||
\(921\) | −0.401131 | −0.0132177 | ||||||||
\(922\) | 5.66088 | 0.186431 | ||||||||
\(923\) | −70.1161 | −2.30790 | ||||||||
\(924\) | −10.7311 | −0.353027 | ||||||||
\(925\) | −50.1576 | −1.64917 | ||||||||
\(926\) | 1.68966 | 0.0555255 | ||||||||
\(927\) | −26.0894 | −0.856887 | ||||||||
\(928\) | −3.01538 | −0.0989846 | ||||||||
\(929\) | 12.0728 | 0.396095 | 0.198047 | − | 0.980192i | \(-0.436540\pi\) | ||||
0.198047 | + | 0.980192i | \(0.436540\pi\) | |||||||
\(930\) | 2.19349 | 0.0719274 | ||||||||
\(931\) | −14.5295 | −0.476184 | ||||||||
\(932\) | 40.8206 | 1.33712 | ||||||||
\(933\) | −21.4828 | −0.703316 | ||||||||
\(934\) | −2.19909 | −0.0719565 | ||||||||
\(935\) | −48.8521 | −1.59764 | ||||||||
\(936\) | 6.86154 | 0.224277 | ||||||||
\(937\) | −36.6495 | −1.19729 | −0.598643 | − | 0.801016i | \(-0.704293\pi\) | ||||
−0.598643 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(938\) | −1.75503 | −0.0573036 | ||||||||
\(939\) | 5.29474 | 0.172787 | ||||||||
\(940\) | −15.1261 | −0.493358 | ||||||||
\(941\) | 29.2866 | 0.954715 | 0.477357 | − | 0.878709i | \(-0.341595\pi\) | ||||
0.477357 | + | 0.878709i | \(0.341595\pi\) | |||||||
\(942\) | −1.52125 | −0.0495649 | ||||||||
\(943\) | 5.22893 | 0.170277 | ||||||||
\(944\) | −1.66632 | −0.0542340 | ||||||||
\(945\) | 22.4887 | 0.731557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.4088 | 1.57307 | 0.786537 | − | 0.617543i | \(-0.211872\pi\) | ||||
0.786537 | + | 0.617543i | \(0.211872\pi\) | |||||||
\(948\) | −19.0269 | −0.617964 | ||||||||
\(949\) | −70.3588 | −2.28394 | ||||||||
\(950\) | −4.27295 | −0.138633 | ||||||||
\(951\) | 11.6069 | 0.376381 | ||||||||
\(952\) | 2.44601 | 0.0792758 | ||||||||
\(953\) | 56.7901 | 1.83961 | 0.919806 | − | 0.392374i | \(-0.128346\pi\) | ||||
0.919806 | + | 0.392374i | \(0.128346\pi\) | |||||||
\(954\) | 0.459867 | 0.0148887 | ||||||||
\(955\) | −1.92581 | −0.0623178 | ||||||||
\(956\) | 15.3763 | 0.497306 | ||||||||
\(957\) | 6.25695 | 0.202259 | ||||||||
\(958\) | −2.52205 | −0.0814837 | ||||||||
\(959\) | −11.4893 | −0.371009 | ||||||||
\(960\) | 24.4975 | 0.790652 | ||||||||
\(961\) | −16.8380 | −0.543162 | ||||||||
\(962\) | −4.35586 | −0.140439 | ||||||||
\(963\) | 23.9745 | 0.772568 | ||||||||
\(964\) | 0.980047 | 0.0315652 | ||||||||
\(965\) | 44.7407 | 1.44026 | ||||||||
\(966\) | 0.998883 | 0.0321385 | ||||||||
\(967\) | 10.2369 | 0.329197 | 0.164598 | − | 0.986361i | \(-0.447367\pi\) | ||||
0.164598 | + | 0.986361i | \(0.447367\pi\) | |||||||
\(968\) | 7.76357 | 0.249531 | ||||||||
\(969\) | −6.72911 | −0.216170 | ||||||||
\(970\) | −4.20174 | −0.134910 | ||||||||
\(971\) | 40.2133 | 1.29051 | 0.645253 | − | 0.763969i | \(-0.276752\pi\) | ||||
0.645253 | + | 0.763969i | \(0.276752\pi\) | |||||||
\(972\) | 31.7912 | 1.01970 | ||||||||
\(973\) | 11.5617 | 0.370651 | ||||||||
\(974\) | −6.56125 | −0.210236 | ||||||||
\(975\) | 36.8665 | 1.18067 | ||||||||
\(976\) | 42.4643 | 1.35925 | ||||||||
\(977\) | 30.9631 | 0.990596 | 0.495298 | − | 0.868723i | \(-0.335059\pi\) | ||||
0.495298 | + | 0.868723i | \(0.335059\pi\) | |||||||
\(978\) | 2.88689 | 0.0923125 | ||||||||
\(979\) | 25.5631 | 0.816999 | ||||||||
\(980\) | 39.4653 | 1.26067 | ||||||||
\(981\) | 1.98437 | 0.0633561 | ||||||||
\(982\) | 4.89314 | 0.156146 | ||||||||
\(983\) | −53.4586 | −1.70506 | −0.852532 | − | 0.522674i | \(-0.824934\pi\) | ||||
−0.852532 | + | 0.522674i | \(0.824934\pi\) | |||||||
\(984\) | −0.646428 | −0.0206074 | ||||||||
\(985\) | 71.2965 | 2.27169 | ||||||||
\(986\) | −0.707695 | −0.0225376 | ||||||||
\(987\) | −2.36325 | −0.0752229 | ||||||||
\(988\) | 24.3141 | 0.773534 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.74047 | −0.214226 | ||||||||
\(991\) | 9.04068 | 0.287187 | 0.143593 | − | 0.989637i | \(-0.454134\pi\) | ||||
0.143593 | + | 0.989637i | \(0.454134\pi\) | |||||||
\(992\) | −7.67384 | −0.243645 | ||||||||
\(993\) | −12.3376 | −0.391523 | ||||||||
\(994\) | −3.44875 | −0.109388 | ||||||||
\(995\) | 9.72648 | 0.308350 | ||||||||
\(996\) | 0.773126 | 0.0244974 | ||||||||
\(997\) | 14.0612 | 0.445321 | 0.222661 | − | 0.974896i | \(-0.428526\pi\) | ||||
0.222661 | + | 0.974896i | \(0.428526\pi\) | |||||||
\(998\) | −1.43303 | −0.0453616 | ||||||||
\(999\) | −25.7851 | −0.815805 |
(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 | 1849.2.a.p.1.11 | ✓ | 20 | |
43.42 | odd | 2 | 1849.2.a.r.1.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.p.1.11 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1849.2.a.r.1.10 | yes | 20 | 43.42 | odd | 2 |