Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1205,2,Mod(1,1205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1205.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1205 = 5 \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1205.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: | \(9.62197344356\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.96562\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.96562 | 1.38991 | 0.694953 | − | 0.719055i | \(-0.255425\pi\) | ||||
0.694953 | + | 0.719055i | \(0.255425\pi\) | |||||||
\(3\) | −0.551502 | −0.318410 | −0.159205 | − | 0.987246i | \(-0.550893\pi\) | ||||
−0.159205 | + | 0.987246i | \(0.550893\pi\) | |||||||
\(4\) | 1.86368 | 0.931840 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.08405 | −0.442560 | ||||||||
\(7\) | 1.56703 | 0.592281 | 0.296140 | − | 0.955144i | \(-0.404300\pi\) | ||||
0.296140 | + | 0.955144i | \(0.404300\pi\) | |||||||
\(8\) | −0.267954 | −0.0947362 | ||||||||
\(9\) | −2.69585 | −0.898615 | ||||||||
\(10\) | −1.96562 | −0.621585 | ||||||||
\(11\) | −3.99112 | −1.20337 | −0.601684 | − | 0.798735i | \(-0.705503\pi\) | ||||
−0.601684 | + | 0.798735i | \(0.705503\pi\) | |||||||
\(12\) | −1.02782 | −0.296707 | ||||||||
\(13\) | −2.71047 | −0.751749 | −0.375874 | − | 0.926671i | \(-0.622658\pi\) | ||||
−0.375874 | + | 0.926671i | \(0.622658\pi\) | |||||||
\(14\) | 3.08019 | 0.823215 | ||||||||
\(15\) | 0.551502 | 0.142397 | ||||||||
\(16\) | −4.25406 | −1.06351 | ||||||||
\(17\) | −7.60012 | −1.84330 | −0.921650 | − | 0.388021i | \(-0.873159\pi\) | ||||
−0.921650 | + | 0.388021i | \(0.873159\pi\) | |||||||
\(18\) | −5.29902 | −1.24899 | ||||||||
\(19\) | 0.708589 | 0.162561 | 0.0812807 | − | 0.996691i | \(-0.474099\pi\) | ||||
0.0812807 | + | 0.996691i | \(0.474099\pi\) | |||||||
\(20\) | −1.86368 | −0.416731 | ||||||||
\(21\) | −0.864219 | −0.188588 | ||||||||
\(22\) | −7.84504 | −1.67257 | ||||||||
\(23\) | 8.61987 | 1.79737 | 0.898684 | − | 0.438597i | \(-0.144524\pi\) | ||||
0.898684 | + | 0.438597i | \(0.144524\pi\) | |||||||
\(24\) | 0.147777 | 0.0301649 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.32776 | −1.04486 | ||||||||
\(27\) | 3.14127 | 0.604538 | ||||||||
\(28\) | 2.92044 | 0.551911 | ||||||||
\(29\) | −5.83317 | −1.08319 | −0.541596 | − | 0.840639i | \(-0.682180\pi\) | ||||
−0.541596 | + | 0.840639i | \(0.682180\pi\) | |||||||
\(30\) | 1.08405 | 0.197919 | ||||||||
\(31\) | 7.20499 | 1.29405 | 0.647027 | − | 0.762467i | \(-0.276012\pi\) | ||||
0.647027 | + | 0.762467i | \(0.276012\pi\) | |||||||
\(32\) | −7.82597 | −1.38345 | ||||||||
\(33\) | 2.20111 | 0.383164 | ||||||||
\(34\) | −14.9390 | −2.56202 | ||||||||
\(35\) | −1.56703 | −0.264876 | ||||||||
\(36\) | −5.02419 | −0.837365 | ||||||||
\(37\) | −11.5871 | −1.90491 | −0.952456 | − | 0.304677i | \(-0.901452\pi\) | ||||
−0.952456 | + | 0.304677i | \(0.901452\pi\) | |||||||
\(38\) | 1.39282 | 0.225945 | ||||||||
\(39\) | 1.49483 | 0.239364 | ||||||||
\(40\) | 0.267954 | 0.0423673 | ||||||||
\(41\) | 9.24605 | 1.44399 | 0.721995 | − | 0.691898i | \(-0.243225\pi\) | ||||
0.721995 | + | 0.691898i | \(0.243225\pi\) | |||||||
\(42\) | −1.69873 | −0.262120 | ||||||||
\(43\) | 0.217644 | 0.0331904 | 0.0165952 | − | 0.999862i | \(-0.494717\pi\) | ||||
0.0165952 | + | 0.999862i | \(0.494717\pi\) | |||||||
\(44\) | −7.43816 | −1.12135 | ||||||||
\(45\) | 2.69585 | 0.401873 | ||||||||
\(46\) | 16.9434 | 2.49817 | ||||||||
\(47\) | −2.29372 | −0.334573 | −0.167287 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167287 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(48\) | 2.34612 | 0.338634 | ||||||||
\(49\) | −4.54442 | −0.649204 | ||||||||
\(50\) | 1.96562 | 0.277981 | ||||||||
\(51\) | 4.19149 | 0.586925 | ||||||||
\(52\) | −5.05145 | −0.700510 | ||||||||
\(53\) | 13.2571 | 1.82101 | 0.910504 | − | 0.413500i | \(-0.135694\pi\) | ||||
0.910504 | + | 0.413500i | \(0.135694\pi\) | |||||||
\(54\) | 6.17456 | 0.840251 | ||||||||
\(55\) | 3.99112 | 0.538162 | ||||||||
\(56\) | −0.419892 | −0.0561104 | ||||||||
\(57\) | −0.390788 | −0.0517612 | ||||||||
\(58\) | −11.4658 | −1.50554 | ||||||||
\(59\) | 1.31384 | 0.171048 | 0.0855239 | − | 0.996336i | \(-0.472744\pi\) | ||||
0.0855239 | + | 0.996336i | \(0.472744\pi\) | |||||||
\(60\) | 1.02782 | 0.132691 | ||||||||
\(61\) | −13.1201 | −1.67985 | −0.839927 | − | 0.542699i | \(-0.817402\pi\) | ||||
−0.839927 | + | 0.542699i | \(0.817402\pi\) | |||||||
\(62\) | 14.1623 | 1.79861 | ||||||||
\(63\) | −4.22446 | −0.532232 | ||||||||
\(64\) | −6.87481 | −0.859351 | ||||||||
\(65\) | 2.71047 | 0.336192 | ||||||||
\(66\) | 4.32656 | 0.532562 | ||||||||
\(67\) | −2.79005 | −0.340859 | −0.170430 | − | 0.985370i | \(-0.554516\pi\) | ||||
−0.170430 | + | 0.985370i | \(0.554516\pi\) | |||||||
\(68\) | −14.1642 | −1.71766 | ||||||||
\(69\) | −4.75388 | −0.572300 | ||||||||
\(70\) | −3.08019 | −0.368153 | ||||||||
\(71\) | −3.67764 | −0.436456 | −0.218228 | − | 0.975898i | \(-0.570028\pi\) | ||||
−0.218228 | + | 0.975898i | \(0.570028\pi\) | |||||||
\(72\) | 0.722363 | 0.0851313 | ||||||||
\(73\) | −8.82698 | −1.03312 | −0.516560 | − | 0.856251i | \(-0.672788\pi\) | ||||
−0.516560 | + | 0.856251i | \(0.672788\pi\) | |||||||
\(74\) | −22.7759 | −2.64765 | ||||||||
\(75\) | −0.551502 | −0.0636820 | ||||||||
\(76\) | 1.32058 | 0.151481 | ||||||||
\(77\) | −6.25419 | −0.712731 | ||||||||
\(78\) | 2.93827 | 0.332694 | ||||||||
\(79\) | 7.53594 | 0.847859 | 0.423930 | − | 0.905695i | \(-0.360650\pi\) | ||||
0.423930 | + | 0.905695i | \(0.360650\pi\) | |||||||
\(80\) | 4.25406 | 0.475618 | ||||||||
\(81\) | 6.35512 | 0.706124 | ||||||||
\(82\) | 18.1743 | 2.00701 | ||||||||
\(83\) | −5.42978 | −0.595996 | −0.297998 | − | 0.954566i | \(-0.596319\pi\) | ||||
−0.297998 | + | 0.954566i | \(0.596319\pi\) | |||||||
\(84\) | −1.61063 | −0.175734 | ||||||||
\(85\) | 7.60012 | 0.824349 | ||||||||
\(86\) | 0.427806 | 0.0461315 | ||||||||
\(87\) | 3.21701 | 0.344899 | ||||||||
\(88\) | 1.06944 | 0.114002 | ||||||||
\(89\) | 13.1423 | 1.39308 | 0.696539 | − | 0.717519i | \(-0.254722\pi\) | ||||
0.696539 | + | 0.717519i | \(0.254722\pi\) | |||||||
\(90\) | 5.29902 | 0.558566 | ||||||||
\(91\) | −4.24738 | −0.445246 | ||||||||
\(92\) | 16.0647 | 1.67486 | ||||||||
\(93\) | −3.97357 | −0.412040 | ||||||||
\(94\) | −4.50859 | −0.465026 | ||||||||
\(95\) | −0.708589 | −0.0726997 | ||||||||
\(96\) | 4.31604 | 0.440504 | ||||||||
\(97\) | −13.0935 | −1.32945 | −0.664723 | − | 0.747090i | \(-0.731451\pi\) | ||||
−0.664723 | + | 0.747090i | \(0.731451\pi\) | |||||||
\(98\) | −8.93263 | −0.902332 | ||||||||
\(99\) | 10.7594 | 1.08136 | ||||||||
\(100\) | 1.86368 | 0.186368 | ||||||||
\(101\) | −4.73983 | −0.471631 | −0.235815 | − | 0.971798i | \(-0.575776\pi\) | ||||
−0.235815 | + | 0.971798i | \(0.575776\pi\) | |||||||
\(102\) | 8.23889 | 0.815771 | ||||||||
\(103\) | −5.08831 | −0.501366 | −0.250683 | − | 0.968069i | \(-0.580655\pi\) | ||||
−0.250683 | + | 0.968069i | \(0.580655\pi\) | |||||||
\(104\) | 0.726282 | 0.0712178 | ||||||||
\(105\) | 0.864219 | 0.0843391 | ||||||||
\(106\) | 26.0586 | 2.53103 | ||||||||
\(107\) | −4.89049 | −0.472781 | −0.236391 | − | 0.971658i | \(-0.575965\pi\) | ||||
−0.236391 | + | 0.971658i | \(0.575965\pi\) | |||||||
\(108\) | 5.85432 | 0.563333 | ||||||||
\(109\) | −14.1111 | −1.35160 | −0.675801 | − | 0.737084i | \(-0.736202\pi\) | ||||
−0.675801 | + | 0.737084i | \(0.736202\pi\) | |||||||
\(110\) | 7.84504 | 0.747995 | ||||||||
\(111\) | 6.39033 | 0.606543 | ||||||||
\(112\) | −6.66622 | −0.629899 | ||||||||
\(113\) | 15.0059 | 1.41164 | 0.705820 | − | 0.708391i | \(-0.250579\pi\) | ||||
0.705820 | + | 0.708391i | \(0.250579\pi\) | |||||||
\(114\) | −0.768143 | −0.0719432 | ||||||||
\(115\) | −8.61987 | −0.803807 | ||||||||
\(116\) | −10.8712 | −1.00936 | ||||||||
\(117\) | 7.30701 | 0.675533 | ||||||||
\(118\) | 2.58252 | 0.237741 | ||||||||
\(119\) | −11.9096 | −1.09175 | ||||||||
\(120\) | −0.147777 | −0.0134902 | ||||||||
\(121\) | 4.92902 | 0.448092 | ||||||||
\(122\) | −25.7892 | −2.33484 | ||||||||
\(123\) | −5.09922 | −0.459781 | ||||||||
\(124\) | 13.4278 | 1.20585 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −8.30371 | −0.739753 | ||||||||
\(127\) | 6.37046 | 0.565287 | 0.282644 | − | 0.959225i | \(-0.408789\pi\) | ||||
0.282644 | + | 0.959225i | \(0.408789\pi\) | |||||||
\(128\) | 2.13866 | 0.189032 | ||||||||
\(129\) | −0.120031 | −0.0105681 | ||||||||
\(130\) | 5.32776 | 0.467276 | ||||||||
\(131\) | 15.5677 | 1.36015 | 0.680076 | − | 0.733142i | \(-0.261947\pi\) | ||||
0.680076 | + | 0.733142i | \(0.261947\pi\) | |||||||
\(132\) | 4.10216 | 0.357048 | ||||||||
\(133\) | 1.11038 | 0.0962820 | ||||||||
\(134\) | −5.48420 | −0.473763 | ||||||||
\(135\) | −3.14127 | −0.270358 | ||||||||
\(136\) | 2.03649 | 0.174627 | ||||||||
\(137\) | 2.80386 | 0.239550 | 0.119775 | − | 0.992801i | \(-0.461783\pi\) | ||||
0.119775 | + | 0.992801i | \(0.461783\pi\) | |||||||
\(138\) | −9.34434 | −0.795443 | ||||||||
\(139\) | −14.7772 | −1.25339 | −0.626694 | − | 0.779266i | \(-0.715592\pi\) | ||||
−0.626694 | + | 0.779266i | \(0.715592\pi\) | |||||||
\(140\) | −2.92044 | −0.246822 | ||||||||
\(141\) | 1.26499 | 0.106532 | ||||||||
\(142\) | −7.22887 | −0.606633 | ||||||||
\(143\) | 10.8178 | 0.904630 | ||||||||
\(144\) | 11.4683 | 0.955690 | ||||||||
\(145\) | 5.83317 | 0.484419 | ||||||||
\(146\) | −17.3505 | −1.43594 | ||||||||
\(147\) | 2.50626 | 0.206713 | ||||||||
\(148\) | −21.5947 | −1.77507 | ||||||||
\(149\) | 8.79693 | 0.720672 | 0.360336 | − | 0.932823i | \(-0.382662\pi\) | ||||
0.360336 | + | 0.932823i | \(0.382662\pi\) | |||||||
\(150\) | −1.08405 | −0.0885120 | ||||||||
\(151\) | −16.9267 | −1.37748 | −0.688739 | − | 0.725010i | \(-0.741835\pi\) | ||||
−0.688739 | + | 0.725010i | \(0.741835\pi\) | |||||||
\(152\) | −0.189869 | −0.0154004 | ||||||||
\(153\) | 20.4888 | 1.65642 | ||||||||
\(154\) | −12.2934 | −0.990630 | ||||||||
\(155\) | −7.20499 | −0.578718 | ||||||||
\(156\) | 2.78588 | 0.223049 | ||||||||
\(157\) | −1.17357 | −0.0936615 | −0.0468307 | − | 0.998903i | \(-0.514912\pi\) | ||||
−0.0468307 | + | 0.998903i | \(0.514912\pi\) | |||||||
\(158\) | 14.8128 | 1.17844 | ||||||||
\(159\) | −7.31134 | −0.579827 | ||||||||
\(160\) | 7.82597 | 0.618697 | ||||||||
\(161\) | 13.5076 | 1.06455 | ||||||||
\(162\) | 12.4918 | 0.981447 | ||||||||
\(163\) | 7.37084 | 0.577328 | 0.288664 | − | 0.957430i | \(-0.406789\pi\) | ||||
0.288664 | + | 0.957430i | \(0.406789\pi\) | |||||||
\(164\) | 17.2317 | 1.34557 | ||||||||
\(165\) | −2.20111 | −0.171356 | ||||||||
\(166\) | −10.6729 | −0.828379 | ||||||||
\(167\) | 15.7056 | 1.21534 | 0.607669 | − | 0.794191i | \(-0.292105\pi\) | ||||
0.607669 | + | 0.794191i | \(0.292105\pi\) | |||||||
\(168\) | 0.231571 | 0.0178661 | ||||||||
\(169\) | −5.65336 | −0.434874 | ||||||||
\(170\) | 14.9390 | 1.14577 | ||||||||
\(171\) | −1.91025 | −0.146080 | ||||||||
\(172\) | 0.405618 | 0.0309281 | ||||||||
\(173\) | −8.83998 | −0.672091 | −0.336046 | − | 0.941846i | \(-0.609090\pi\) | ||||
−0.336046 | + | 0.941846i | \(0.609090\pi\) | |||||||
\(174\) | 6.32343 | 0.479378 | ||||||||
\(175\) | 1.56703 | 0.118456 | ||||||||
\(176\) | 16.9784 | 1.27980 | ||||||||
\(177\) | −0.724588 | −0.0544633 | ||||||||
\(178\) | 25.8328 | 1.93625 | ||||||||
\(179\) | 6.07612 | 0.454151 | 0.227075 | − | 0.973877i | \(-0.427084\pi\) | ||||
0.227075 | + | 0.973877i | \(0.427084\pi\) | |||||||
\(180\) | 5.02419 | 0.374481 | ||||||||
\(181\) | 5.98011 | 0.444498 | 0.222249 | − | 0.974990i | \(-0.428660\pi\) | ||||
0.222249 | + | 0.974990i | \(0.428660\pi\) | |||||||
\(182\) | −8.34875 | −0.618851 | ||||||||
\(183\) | 7.23575 | 0.534882 | ||||||||
\(184\) | −2.30973 | −0.170276 | ||||||||
\(185\) | 11.5871 | 0.851902 | ||||||||
\(186\) | −7.81054 | −0.572696 | ||||||||
\(187\) | 30.3330 | 2.21817 | ||||||||
\(188\) | −4.27476 | −0.311769 | ||||||||
\(189\) | 4.92246 | 0.358056 | ||||||||
\(190\) | −1.39282 | −0.101046 | ||||||||
\(191\) | −8.04857 | −0.582374 | −0.291187 | − | 0.956666i | \(-0.594050\pi\) | ||||
−0.291187 | + | 0.956666i | \(0.594050\pi\) | |||||||
\(192\) | 3.79147 | 0.273626 | ||||||||
\(193\) | 5.00147 | 0.360014 | 0.180007 | − | 0.983665i | \(-0.442388\pi\) | ||||
0.180007 | + | 0.983665i | \(0.442388\pi\) | |||||||
\(194\) | −25.7370 | −1.84781 | ||||||||
\(195\) | −1.49483 | −0.107047 | ||||||||
\(196\) | −8.46935 | −0.604954 | ||||||||
\(197\) | 11.3742 | 0.810376 | 0.405188 | − | 0.914233i | \(-0.367206\pi\) | ||||
0.405188 | + | 0.914233i | \(0.367206\pi\) | |||||||
\(198\) | 21.1490 | 1.50299 | ||||||||
\(199\) | −21.8929 | −1.55195 | −0.775973 | − | 0.630767i | \(-0.782741\pi\) | ||||
−0.775973 | + | 0.630767i | \(0.782741\pi\) | |||||||
\(200\) | −0.267954 | −0.0189472 | ||||||||
\(201\) | 1.53872 | 0.108533 | ||||||||
\(202\) | −9.31673 | −0.655523 | ||||||||
\(203\) | −9.14074 | −0.641554 | ||||||||
\(204\) | 7.81159 | 0.546920 | ||||||||
\(205\) | −9.24605 | −0.645772 | ||||||||
\(206\) | −10.0017 | −0.696852 | ||||||||
\(207\) | −23.2378 | −1.61514 | ||||||||
\(208\) | 11.5305 | 0.799496 | ||||||||
\(209\) | −2.82806 | −0.195621 | ||||||||
\(210\) | 1.69873 | 0.117224 | ||||||||
\(211\) | −11.2687 | −0.775770 | −0.387885 | − | 0.921708i | \(-0.626794\pi\) | ||||
−0.387885 | + | 0.921708i | \(0.626794\pi\) | |||||||
\(212\) | 24.7071 | 1.69689 | ||||||||
\(213\) | 2.02823 | 0.138972 | ||||||||
\(214\) | −9.61286 | −0.657122 | ||||||||
\(215\) | −0.217644 | −0.0148432 | ||||||||
\(216\) | −0.841717 | −0.0572716 | ||||||||
\(217\) | 11.2904 | 0.766443 | ||||||||
\(218\) | −27.7372 | −1.87860 | ||||||||
\(219\) | 4.86810 | 0.328956 | ||||||||
\(220\) | 7.43816 | 0.501481 | ||||||||
\(221\) | 20.5999 | 1.38570 | ||||||||
\(222\) | 12.5610 | 0.843038 | ||||||||
\(223\) | 1.74920 | 0.117135 | 0.0585674 | − | 0.998283i | \(-0.481347\pi\) | ||||
0.0585674 | + | 0.998283i | \(0.481347\pi\) | |||||||
\(224\) | −12.2635 | −0.819390 | ||||||||
\(225\) | −2.69585 | −0.179723 | ||||||||
\(226\) | 29.4960 | 1.96205 | ||||||||
\(227\) | 4.95808 | 0.329079 | 0.164540 | − | 0.986370i | \(-0.447386\pi\) | ||||
0.164540 | + | 0.986370i | \(0.447386\pi\) | |||||||
\(228\) | −0.728304 | −0.0482331 | ||||||||
\(229\) | 12.7250 | 0.840890 | 0.420445 | − | 0.907318i | \(-0.361874\pi\) | ||||
0.420445 | + | 0.907318i | \(0.361874\pi\) | |||||||
\(230\) | −16.9434 | −1.11722 | ||||||||
\(231\) | 3.44920 | 0.226941 | ||||||||
\(232\) | 1.56302 | 0.102618 | ||||||||
\(233\) | 16.6923 | 1.09355 | 0.546773 | − | 0.837281i | \(-0.315856\pi\) | ||||
0.546773 | + | 0.837281i | \(0.315856\pi\) | |||||||
\(234\) | 14.3628 | 0.938928 | ||||||||
\(235\) | 2.29372 | 0.149626 | ||||||||
\(236\) | 2.44858 | 0.159389 | ||||||||
\(237\) | −4.15609 | −0.269967 | ||||||||
\(238\) | −23.4098 | −1.51743 | ||||||||
\(239\) | −16.8047 | −1.08701 | −0.543504 | − | 0.839407i | \(-0.682903\pi\) | ||||
−0.543504 | + | 0.839407i | \(0.682903\pi\) | |||||||
\(240\) | −2.34612 | −0.151442 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 9.68860 | 0.622807 | ||||||||
\(243\) | −12.9287 | −0.829375 | ||||||||
\(244\) | −24.4516 | −1.56536 | ||||||||
\(245\) | 4.54442 | 0.290333 | ||||||||
\(246\) | −10.0231 | −0.639053 | ||||||||
\(247\) | −1.92061 | −0.122205 | ||||||||
\(248\) | −1.93061 | −0.122594 | ||||||||
\(249\) | 2.99454 | 0.189771 | ||||||||
\(250\) | −1.96562 | −0.124317 | ||||||||
\(251\) | −17.2016 | −1.08576 | −0.542879 | − | 0.839811i | \(-0.682666\pi\) | ||||
−0.542879 | + | 0.839811i | \(0.682666\pi\) | |||||||
\(252\) | −7.87305 | −0.495955 | ||||||||
\(253\) | −34.4029 | −2.16289 | ||||||||
\(254\) | 12.5219 | 0.785696 | ||||||||
\(255\) | −4.19149 | −0.262481 | ||||||||
\(256\) | 17.9534 | 1.12209 | ||||||||
\(257\) | −20.4849 | −1.27781 | −0.638905 | − | 0.769285i | \(-0.720612\pi\) | ||||
−0.638905 | + | 0.769285i | \(0.720612\pi\) | |||||||
\(258\) | −0.235936 | −0.0146887 | ||||||||
\(259\) | −18.1573 | −1.12824 | ||||||||
\(260\) | 5.05145 | 0.313277 | ||||||||
\(261\) | 15.7253 | 0.973373 | ||||||||
\(262\) | 30.6002 | 1.89048 | ||||||||
\(263\) | 27.6830 | 1.70701 | 0.853503 | − | 0.521088i | \(-0.174474\pi\) | ||||
0.853503 | + | 0.521088i | \(0.174474\pi\) | |||||||
\(264\) | −0.589797 | −0.0362995 | ||||||||
\(265\) | −13.2571 | −0.814379 | ||||||||
\(266\) | 2.18259 | 0.133823 | ||||||||
\(267\) | −7.24799 | −0.443570 | ||||||||
\(268\) | −5.19977 | −0.317626 | ||||||||
\(269\) | −2.83160 | −0.172646 | −0.0863228 | − | 0.996267i | \(-0.527512\pi\) | ||||
−0.0863228 | + | 0.996267i | \(0.527512\pi\) | |||||||
\(270\) | −6.17456 | −0.375772 | ||||||||
\(271\) | 11.6911 | 0.710181 | 0.355090 | − | 0.934832i | \(-0.384450\pi\) | ||||
0.355090 | + | 0.934832i | \(0.384450\pi\) | |||||||
\(272\) | 32.3314 | 1.96038 | ||||||||
\(273\) | 2.34244 | 0.141771 | ||||||||
\(274\) | 5.51135 | 0.332953 | ||||||||
\(275\) | −3.99112 | −0.240673 | ||||||||
\(276\) | −8.85971 | −0.533292 | ||||||||
\(277\) | −12.8089 | −0.769610 | −0.384805 | − | 0.922998i | \(-0.625731\pi\) | ||||
−0.384805 | + | 0.922998i | \(0.625731\pi\) | |||||||
\(278\) | −29.0465 | −1.74209 | ||||||||
\(279\) | −19.4235 | −1.16286 | ||||||||
\(280\) | 0.419892 | 0.0250933 | ||||||||
\(281\) | −12.7989 | −0.763518 | −0.381759 | − | 0.924262i | \(-0.624681\pi\) | ||||
−0.381759 | + | 0.924262i | \(0.624681\pi\) | |||||||
\(282\) | 2.48650 | 0.148069 | ||||||||
\(283\) | −13.7630 | −0.818127 | −0.409064 | − | 0.912506i | \(-0.634145\pi\) | ||||
−0.409064 | + | 0.912506i | \(0.634145\pi\) | |||||||
\(284\) | −6.85395 | −0.406707 | ||||||||
\(285\) | 0.390788 | 0.0231483 | ||||||||
\(286\) | 21.2637 | 1.25735 | ||||||||
\(287\) | 14.4888 | 0.855248 | ||||||||
\(288\) | 21.0976 | 1.24319 | ||||||||
\(289\) | 40.7619 | 2.39776 | ||||||||
\(290\) | 11.4658 | 0.673296 | ||||||||
\(291\) | 7.22111 | 0.423309 | ||||||||
\(292\) | −16.4507 | −0.962702 | ||||||||
\(293\) | −16.5394 | −0.966241 | −0.483121 | − | 0.875554i | \(-0.660497\pi\) | ||||
−0.483121 | + | 0.875554i | \(0.660497\pi\) | |||||||
\(294\) | 4.92637 | 0.287312 | ||||||||
\(295\) | −1.31384 | −0.0764949 | ||||||||
\(296\) | 3.10482 | 0.180464 | ||||||||
\(297\) | −12.5372 | −0.727481 | ||||||||
\(298\) | 17.2915 | 1.00167 | ||||||||
\(299\) | −23.3639 | −1.35117 | ||||||||
\(300\) | −1.02782 | −0.0593414 | ||||||||
\(301\) | 0.341054 | 0.0196580 | ||||||||
\(302\) | −33.2716 | −1.91456 | ||||||||
\(303\) | 2.61403 | 0.150172 | ||||||||
\(304\) | −3.01438 | −0.172886 | ||||||||
\(305\) | 13.1201 | 0.751254 | ||||||||
\(306\) | 40.2732 | 2.30227 | ||||||||
\(307\) | −11.5276 | −0.657914 | −0.328957 | − | 0.944345i | \(-0.606697\pi\) | ||||
−0.328957 | + | 0.944345i | \(0.606697\pi\) | |||||||
\(308\) | −11.6558 | −0.664151 | ||||||||
\(309\) | 2.80621 | 0.159640 | ||||||||
\(310\) | −14.1623 | −0.804364 | ||||||||
\(311\) | −31.2894 | −1.77426 | −0.887131 | − | 0.461519i | \(-0.847305\pi\) | ||||
−0.887131 | + | 0.461519i | \(0.847305\pi\) | |||||||
\(312\) | −0.400546 | −0.0226765 | ||||||||
\(313\) | −12.4308 | −0.702629 | −0.351314 | − | 0.936258i | \(-0.614265\pi\) | ||||
−0.351314 | + | 0.936258i | \(0.614265\pi\) | |||||||
\(314\) | −2.30681 | −0.130181 | ||||||||
\(315\) | 4.22446 | 0.238022 | ||||||||
\(316\) | 14.0446 | 0.790069 | ||||||||
\(317\) | −24.6631 | −1.38522 | −0.692609 | − | 0.721313i | \(-0.743539\pi\) | ||||
−0.692609 | + | 0.721313i | \(0.743539\pi\) | |||||||
\(318\) | −14.3713 | −0.805905 | ||||||||
\(319\) | 23.2809 | 1.30348 | ||||||||
\(320\) | 6.87481 | 0.384313 | ||||||||
\(321\) | 2.69711 | 0.150538 | ||||||||
\(322\) | 26.5508 | 1.47962 | ||||||||
\(323\) | −5.38536 | −0.299650 | ||||||||
\(324\) | 11.8439 | 0.657995 | ||||||||
\(325\) | −2.71047 | −0.150350 | ||||||||
\(326\) | 14.4883 | 0.802432 | ||||||||
\(327\) | 7.78232 | 0.430363 | ||||||||
\(328\) | −2.47752 | −0.136798 | ||||||||
\(329\) | −3.59432 | −0.198161 | ||||||||
\(330\) | −4.32656 | −0.238169 | ||||||||
\(331\) | 34.0217 | 1.87000 | 0.935000 | − | 0.354648i | \(-0.115399\pi\) | ||||
0.935000 | + | 0.354648i | \(0.115399\pi\) | |||||||
\(332\) | −10.1194 | −0.555373 | ||||||||
\(333\) | 31.2371 | 1.71178 | ||||||||
\(334\) | 30.8713 | 1.68920 | ||||||||
\(335\) | 2.79005 | 0.152437 | ||||||||
\(336\) | 3.67644 | 0.200566 | ||||||||
\(337\) | −1.52041 | −0.0828222 | −0.0414111 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414111 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(338\) | −11.1124 | −0.604434 | ||||||||
\(339\) | −8.27581 | −0.449480 | ||||||||
\(340\) | 14.1642 | 0.768162 | ||||||||
\(341\) | −28.7559 | −1.55722 | ||||||||
\(342\) | −3.75483 | −0.203038 | ||||||||
\(343\) | −18.0904 | −0.976791 | ||||||||
\(344\) | −0.0583186 | −0.00314433 | ||||||||
\(345\) | 4.75388 | 0.255940 | ||||||||
\(346\) | −17.3761 | −0.934144 | ||||||||
\(347\) | 27.9625 | 1.50111 | 0.750553 | − | 0.660810i | \(-0.229787\pi\) | ||||
0.750553 | + | 0.660810i | \(0.229787\pi\) | |||||||
\(348\) | 5.99547 | 0.321391 | ||||||||
\(349\) | −5.47515 | −0.293078 | −0.146539 | − | 0.989205i | \(-0.546813\pi\) | ||||
−0.146539 | + | 0.989205i | \(0.546813\pi\) | |||||||
\(350\) | 3.08019 | 0.164643 | ||||||||
\(351\) | −8.51432 | −0.454461 | ||||||||
\(352\) | 31.2344 | 1.66480 | ||||||||
\(353\) | 15.0275 | 0.799834 | 0.399917 | − | 0.916551i | \(-0.369039\pi\) | ||||
0.399917 | + | 0.916551i | \(0.369039\pi\) | |||||||
\(354\) | −1.42427 | −0.0756990 | ||||||||
\(355\) | 3.67764 | 0.195189 | ||||||||
\(356\) | 24.4930 | 1.29812 | ||||||||
\(357\) | 6.56817 | 0.347625 | ||||||||
\(358\) | 11.9434 | 0.631227 | ||||||||
\(359\) | −3.29197 | −0.173743 | −0.0868717 | − | 0.996220i | \(-0.527687\pi\) | ||||
−0.0868717 | + | 0.996220i | \(0.527687\pi\) | |||||||
\(360\) | −0.722363 | −0.0380719 | ||||||||
\(361\) | −18.4979 | −0.973574 | ||||||||
\(362\) | 11.7547 | 0.617811 | ||||||||
\(363\) | −2.71836 | −0.142677 | ||||||||
\(364\) | −7.91576 | −0.414898 | ||||||||
\(365\) | 8.82698 | 0.462025 | ||||||||
\(366\) | 14.2228 | 0.743436 | ||||||||
\(367\) | 1.25892 | 0.0657149 | 0.0328574 | − | 0.999460i | \(-0.489539\pi\) | ||||
0.0328574 | + | 0.999460i | \(0.489539\pi\) | |||||||
\(368\) | −36.6694 | −1.91153 | ||||||||
\(369\) | −24.9259 | −1.29759 | ||||||||
\(370\) | 22.7759 | 1.18406 | ||||||||
\(371\) | 20.7743 | 1.07855 | ||||||||
\(372\) | −7.40545 | −0.383955 | ||||||||
\(373\) | −11.0430 | −0.571785 | −0.285893 | − | 0.958262i | \(-0.592290\pi\) | ||||
−0.285893 | + | 0.958262i | \(0.592290\pi\) | |||||||
\(374\) | 59.6233 | 3.08305 | ||||||||
\(375\) | 0.551502 | 0.0284794 | ||||||||
\(376\) | 0.614612 | 0.0316962 | ||||||||
\(377\) | 15.8106 | 0.814289 | ||||||||
\(378\) | 9.67570 | 0.497665 | ||||||||
\(379\) | 13.9623 | 0.717193 | 0.358597 | − | 0.933493i | \(-0.383255\pi\) | ||||
0.358597 | + | 0.933493i | \(0.383255\pi\) | |||||||
\(380\) | −1.32058 | −0.0677445 | ||||||||
\(381\) | −3.51332 | −0.179993 | ||||||||
\(382\) | −15.8205 | −0.809445 | ||||||||
\(383\) | −29.4806 | −1.50639 | −0.753195 | − | 0.657798i | \(-0.771488\pi\) | ||||
−0.753195 | + | 0.657798i | \(0.771488\pi\) | |||||||
\(384\) | −1.17947 | −0.0601897 | ||||||||
\(385\) | 6.25419 | 0.318743 | ||||||||
\(386\) | 9.83101 | 0.500385 | ||||||||
\(387\) | −0.586734 | −0.0298254 | ||||||||
\(388\) | −24.4021 | −1.23883 | ||||||||
\(389\) | −34.1786 | −1.73292 | −0.866462 | − | 0.499243i | \(-0.833611\pi\) | ||||
−0.866462 | + | 0.499243i | \(0.833611\pi\) | |||||||
\(390\) | −2.93827 | −0.148785 | ||||||||
\(391\) | −65.5121 | −3.31309 | ||||||||
\(392\) | 1.21770 | 0.0615031 | ||||||||
\(393\) | −8.58559 | −0.433086 | ||||||||
\(394\) | 22.3573 | 1.12635 | ||||||||
\(395\) | −7.53594 | −0.379174 | ||||||||
\(396\) | 20.0521 | 1.00766 | ||||||||
\(397\) | 2.87635 | 0.144360 | 0.0721799 | − | 0.997392i | \(-0.477004\pi\) | ||||
0.0721799 | + | 0.997392i | \(0.477004\pi\) | |||||||
\(398\) | −43.0332 | −2.15706 | ||||||||
\(399\) | −0.612376 | −0.0306571 | ||||||||
\(400\) | −4.25406 | −0.212703 | ||||||||
\(401\) | 2.45963 | 0.122828 | 0.0614140 | − | 0.998112i | \(-0.480439\pi\) | ||||
0.0614140 | + | 0.998112i | \(0.480439\pi\) | |||||||
\(402\) | 3.02455 | 0.150851 | ||||||||
\(403\) | −19.5289 | −0.972803 | ||||||||
\(404\) | −8.83353 | −0.439484 | ||||||||
\(405\) | −6.35512 | −0.315788 | ||||||||
\(406\) | −17.9673 | −0.891700 | ||||||||
\(407\) | 46.2456 | 2.29231 | ||||||||
\(408\) | −1.12313 | −0.0556031 | ||||||||
\(409\) | 15.0357 | 0.743469 | 0.371734 | − | 0.928339i | \(-0.378763\pi\) | ||||
0.371734 | + | 0.928339i | \(0.378763\pi\) | |||||||
\(410\) | −18.1743 | −0.897563 | ||||||||
\(411\) | −1.54634 | −0.0762752 | ||||||||
\(412\) | −9.48298 | −0.467193 | ||||||||
\(413\) | 2.05883 | 0.101308 | ||||||||
\(414\) | −45.6769 | −2.24490 | ||||||||
\(415\) | 5.42978 | 0.266538 | ||||||||
\(416\) | 21.2121 | 1.04001 | ||||||||
\(417\) | 8.14967 | 0.399091 | ||||||||
\(418\) | −5.55891 | −0.271895 | ||||||||
\(419\) | −20.7860 | −1.01546 | −0.507732 | − | 0.861515i | \(-0.669516\pi\) | ||||
−0.507732 | + | 0.861515i | \(0.669516\pi\) | |||||||
\(420\) | 1.61063 | 0.0785906 | ||||||||
\(421\) | −26.9568 | −1.31380 | −0.656898 | − | 0.753980i | \(-0.728132\pi\) | ||||
−0.656898 | + | 0.753980i | \(0.728132\pi\) | |||||||
\(422\) | −22.1501 | −1.07825 | ||||||||
\(423\) | 6.18351 | 0.300653 | ||||||||
\(424\) | −3.55231 | −0.172515 | ||||||||
\(425\) | −7.60012 | −0.368660 | ||||||||
\(426\) | 3.98673 | 0.193158 | ||||||||
\(427\) | −20.5595 | −0.994945 | ||||||||
\(428\) | −9.11430 | −0.440557 | ||||||||
\(429\) | −5.96604 | −0.288043 | ||||||||
\(430\) | −0.427806 | −0.0206306 | ||||||||
\(431\) | −19.5871 | −0.943475 | −0.471738 | − | 0.881739i | \(-0.656373\pi\) | ||||
−0.471738 | + | 0.881739i | \(0.656373\pi\) | |||||||
\(432\) | −13.3631 | −0.642935 | ||||||||
\(433\) | −15.5844 | −0.748940 | −0.374470 | − | 0.927239i | \(-0.622175\pi\) | ||||
−0.374470 | + | 0.927239i | \(0.622175\pi\) | |||||||
\(434\) | 22.1927 | 1.06528 | ||||||||
\(435\) | −3.21701 | −0.154244 | ||||||||
\(436\) | −26.2986 | −1.25948 | ||||||||
\(437\) | 6.10795 | 0.292183 | ||||||||
\(438\) | 9.56885 | 0.457218 | ||||||||
\(439\) | −10.7485 | −0.512997 | −0.256498 | − | 0.966545i | \(-0.582569\pi\) | ||||
−0.256498 | + | 0.966545i | \(0.582569\pi\) | |||||||
\(440\) | −1.06944 | −0.0509834 | ||||||||
\(441\) | 12.2511 | 0.583384 | ||||||||
\(442\) | 40.4917 | 1.92599 | ||||||||
\(443\) | 9.12309 | 0.433451 | 0.216726 | − | 0.976233i | \(-0.430462\pi\) | ||||
0.216726 | + | 0.976233i | \(0.430462\pi\) | |||||||
\(444\) | 11.9095 | 0.565201 | ||||||||
\(445\) | −13.1423 | −0.623003 | ||||||||
\(446\) | 3.43826 | 0.162806 | ||||||||
\(447\) | −4.85152 | −0.229469 | ||||||||
\(448\) | −10.7730 | −0.508977 | ||||||||
\(449\) | −27.1275 | −1.28023 | −0.640113 | − | 0.768280i | \(-0.721113\pi\) | ||||
−0.640113 | + | 0.768280i | \(0.721113\pi\) | |||||||
\(450\) | −5.29902 | −0.249798 | ||||||||
\(451\) | −36.9021 | −1.73765 | ||||||||
\(452\) | 27.9663 | 1.31542 | ||||||||
\(453\) | 9.33513 | 0.438602 | ||||||||
\(454\) | 9.74571 | 0.457389 | ||||||||
\(455\) | 4.24738 | 0.199120 | ||||||||
\(456\) | 0.104713 | 0.00490366 | ||||||||
\(457\) | 22.9878 | 1.07533 | 0.537663 | − | 0.843160i | \(-0.319307\pi\) | ||||
0.537663 | + | 0.843160i | \(0.319307\pi\) | |||||||
\(458\) | 25.0125 | 1.16876 | ||||||||
\(459\) | −23.8741 | −1.11435 | ||||||||
\(460\) | −16.0647 | −0.749020 | ||||||||
\(461\) | 11.7356 | 0.546582 | 0.273291 | − | 0.961931i | \(-0.411888\pi\) | ||||
0.273291 | + | 0.961931i | \(0.411888\pi\) | |||||||
\(462\) | 6.77983 | 0.315426 | ||||||||
\(463\) | 32.0892 | 1.49131 | 0.745656 | − | 0.666331i | \(-0.232136\pi\) | ||||
0.745656 | + | 0.666331i | \(0.232136\pi\) | |||||||
\(464\) | 24.8146 | 1.15199 | ||||||||
\(465\) | 3.97357 | 0.184270 | ||||||||
\(466\) | 32.8107 | 1.51993 | ||||||||
\(467\) | −9.59495 | −0.444001 | −0.222001 | − | 0.975047i | \(-0.571259\pi\) | ||||
−0.222001 | + | 0.975047i | \(0.571259\pi\) | |||||||
\(468\) | 13.6179 | 0.629489 | ||||||||
\(469\) | −4.37209 | −0.201884 | ||||||||
\(470\) | 4.50859 | 0.207966 | ||||||||
\(471\) | 0.647229 | 0.0298227 | ||||||||
\(472\) | −0.352050 | −0.0162044 | ||||||||
\(473\) | −0.868642 | −0.0399402 | ||||||||
\(474\) | −8.16930 | −0.375229 | ||||||||
\(475\) | 0.708589 | 0.0325123 | ||||||||
\(476\) | −22.1957 | −1.01734 | ||||||||
\(477\) | −35.7392 | −1.63639 | ||||||||
\(478\) | −33.0318 | −1.51084 | ||||||||
\(479\) | −15.2874 | −0.698500 | −0.349250 | − | 0.937030i | \(-0.613564\pi\) | ||||
−0.349250 | + | 0.937030i | \(0.613564\pi\) | |||||||
\(480\) | −4.31604 | −0.196999 | ||||||||
\(481\) | 31.4065 | 1.43202 | ||||||||
\(482\) | −1.96562 | −0.0895317 | ||||||||
\(483\) | −7.44946 | −0.338962 | ||||||||
\(484\) | 9.18611 | 0.417550 | ||||||||
\(485\) | 13.0935 | 0.594547 | ||||||||
\(486\) | −25.4129 | −1.15275 | ||||||||
\(487\) | 9.59709 | 0.434886 | 0.217443 | − | 0.976073i | \(-0.430228\pi\) | ||||
0.217443 | + | 0.976073i | \(0.430228\pi\) | |||||||
\(488\) | 3.51558 | 0.159143 | ||||||||
\(489\) | −4.06503 | −0.183827 | ||||||||
\(490\) | 8.93263 | 0.403535 | ||||||||
\(491\) | 31.8169 | 1.43588 | 0.717938 | − | 0.696107i | \(-0.245086\pi\) | ||||
0.717938 | + | 0.696107i | \(0.245086\pi\) | |||||||
\(492\) | −9.50331 | −0.428442 | ||||||||
\(493\) | 44.3328 | 1.99665 | ||||||||
\(494\) | −3.77520 | −0.169854 | ||||||||
\(495\) | −10.7594 | −0.483601 | ||||||||
\(496\) | −30.6504 | −1.37624 | ||||||||
\(497\) | −5.76297 | −0.258504 | ||||||||
\(498\) | 5.88614 | 0.263764 | ||||||||
\(499\) | 8.33168 | 0.372977 | 0.186489 | − | 0.982457i | \(-0.440289\pi\) | ||||
0.186489 | + | 0.982457i | \(0.440289\pi\) | |||||||
\(500\) | −1.86368 | −0.0833463 | ||||||||
\(501\) | −8.66168 | −0.386975 | ||||||||
\(502\) | −33.8119 | −1.50910 | ||||||||
\(503\) | 43.1306 | 1.92310 | 0.961550 | − | 0.274630i | \(-0.0885555\pi\) | ||||
0.961550 | + | 0.274630i | \(0.0885555\pi\) | |||||||
\(504\) | 1.13196 | 0.0504217 | ||||||||
\(505\) | 4.73983 | 0.210920 | ||||||||
\(506\) | −67.6232 | −3.00622 | ||||||||
\(507\) | 3.11784 | 0.138468 | ||||||||
\(508\) | 11.8725 | 0.526757 | ||||||||
\(509\) | −15.3672 | −0.681140 | −0.340570 | − | 0.940219i | \(-0.610620\pi\) | ||||
−0.340570 | + | 0.940219i | \(0.610620\pi\) | |||||||
\(510\) | −8.23889 | −0.364824 | ||||||||
\(511\) | −13.8321 | −0.611897 | ||||||||
\(512\) | 31.0123 | 1.37056 | ||||||||
\(513\) | 2.22587 | 0.0982746 | ||||||||
\(514\) | −40.2656 | −1.77604 | ||||||||
\(515\) | 5.08831 | 0.224218 | ||||||||
\(516\) | −0.223699 | −0.00984782 | ||||||||
\(517\) | 9.15451 | 0.402615 | ||||||||
\(518\) | −35.6905 | −1.56815 | ||||||||
\(519\) | 4.87527 | 0.214001 | ||||||||
\(520\) | −0.726282 | −0.0318496 | ||||||||
\(521\) | −25.4224 | −1.11378 | −0.556888 | − | 0.830588i | \(-0.688005\pi\) | ||||
−0.556888 | + | 0.830588i | \(0.688005\pi\) | |||||||
\(522\) | 30.9101 | 1.35290 | ||||||||
\(523\) | 41.1572 | 1.79968 | 0.899838 | − | 0.436223i | \(-0.143684\pi\) | ||||
0.899838 | + | 0.436223i | \(0.143684\pi\) | |||||||
\(524\) | 29.0131 | 1.26744 | ||||||||
\(525\) | −0.864219 | −0.0377176 | ||||||||
\(526\) | 54.4144 | 2.37258 | ||||||||
\(527\) | −54.7588 | −2.38533 | ||||||||
\(528\) | −9.36365 | −0.407500 | ||||||||
\(529\) | 51.3022 | 2.23053 | ||||||||
\(530\) | −26.0586 | −1.13191 | ||||||||
\(531\) | −3.54192 | −0.153706 | ||||||||
\(532\) | 2.06939 | 0.0897194 | ||||||||
\(533\) | −25.0611 | −1.08552 | ||||||||
\(534\) | −14.2468 | −0.616520 | ||||||||
\(535\) | 4.89049 | 0.211434 | ||||||||
\(536\) | 0.747607 | 0.0322917 | ||||||||
\(537\) | −3.35100 | −0.144606 | ||||||||
\(538\) | −5.56586 | −0.239961 | ||||||||
\(539\) | 18.1373 | 0.781230 | ||||||||
\(540\) | −5.85432 | −0.251930 | ||||||||
\(541\) | 0.834623 | 0.0358833 | 0.0179416 | − | 0.999839i | \(-0.494289\pi\) | ||||
0.0179416 | + | 0.999839i | \(0.494289\pi\) | |||||||
\(542\) | 22.9802 | 0.987085 | ||||||||
\(543\) | −3.29805 | −0.141533 | ||||||||
\(544\) | 59.4784 | 2.55011 | ||||||||
\(545\) | 14.1111 | 0.604455 | ||||||||
\(546\) | 4.60436 | 0.197048 | ||||||||
\(547\) | 22.2646 | 0.951964 | 0.475982 | − | 0.879455i | \(-0.342093\pi\) | ||||
0.475982 | + | 0.879455i | \(0.342093\pi\) | |||||||
\(548\) | 5.22551 | 0.223223 | ||||||||
\(549\) | 35.3697 | 1.50954 | ||||||||
\(550\) | −7.84504 | −0.334514 | ||||||||
\(551\) | −4.13332 | −0.176085 | ||||||||
\(552\) | 1.27382 | 0.0542175 | ||||||||
\(553\) | 11.8090 | 0.502171 | ||||||||
\(554\) | −25.1774 | −1.06969 | ||||||||
\(555\) | −6.39033 | −0.271254 | ||||||||
\(556\) | −27.5400 | −1.16796 | ||||||||
\(557\) | 18.7626 | 0.794996 | 0.397498 | − | 0.917603i | \(-0.369879\pi\) | ||||
0.397498 | + | 0.917603i | \(0.369879\pi\) | |||||||
\(558\) | −38.1794 | −1.61626 | ||||||||
\(559\) | −0.589917 | −0.0249508 | ||||||||
\(560\) | 6.66622 | 0.281699 | ||||||||
\(561\) | −16.7287 | −0.706287 | ||||||||
\(562\) | −25.1578 | −1.06122 | ||||||||
\(563\) | −2.67002 | −0.112528 | −0.0562640 | − | 0.998416i | \(-0.517919\pi\) | ||||
−0.0562640 | + | 0.998416i | \(0.517919\pi\) | |||||||
\(564\) | 2.35754 | 0.0992703 | ||||||||
\(565\) | −15.0059 | −0.631304 | ||||||||
\(566\) | −27.0529 | −1.13712 | ||||||||
\(567\) | 9.95864 | 0.418224 | ||||||||
\(568\) | 0.985440 | 0.0413482 | ||||||||
\(569\) | −25.6604 | −1.07574 | −0.537869 | − | 0.843028i | \(-0.680771\pi\) | ||||
−0.537869 | + | 0.843028i | \(0.680771\pi\) | |||||||
\(570\) | 0.768143 | 0.0321740 | ||||||||
\(571\) | 17.4339 | 0.729585 | 0.364792 | − | 0.931089i | \(-0.381140\pi\) | ||||
0.364792 | + | 0.931089i | \(0.381140\pi\) | |||||||
\(572\) | 20.1609 | 0.842970 | ||||||||
\(573\) | 4.43880 | 0.185434 | ||||||||
\(574\) | 28.4796 | 1.18871 | ||||||||
\(575\) | 8.61987 | 0.359474 | ||||||||
\(576\) | 18.5334 | 0.772225 | ||||||||
\(577\) | −24.5091 | −1.02033 | −0.510163 | − | 0.860078i | \(-0.670415\pi\) | ||||
−0.510163 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(578\) | 80.1226 | 3.33266 | ||||||||
\(579\) | −2.75832 | −0.114632 | ||||||||
\(580\) | 10.8712 | 0.451400 | ||||||||
\(581\) | −8.50862 | −0.352997 | ||||||||
\(582\) | 14.1940 | 0.588360 | ||||||||
\(583\) | −52.9108 | −2.19134 | ||||||||
\(584\) | 2.36523 | 0.0978738 | ||||||||
\(585\) | −7.30701 | −0.302108 | ||||||||
\(586\) | −32.5102 | −1.34299 | ||||||||
\(587\) | −2.12931 | −0.0878860 | −0.0439430 | − | 0.999034i | \(-0.513992\pi\) | ||||
−0.0439430 | + | 0.999034i | \(0.513992\pi\) | |||||||
\(588\) | 4.67087 | 0.192623 | ||||||||
\(589\) | 5.10537 | 0.210363 | ||||||||
\(590\) | −2.58252 | −0.106321 | ||||||||
\(591\) | −6.27288 | −0.258032 | ||||||||
\(592\) | 49.2923 | 2.02590 | ||||||||
\(593\) | 21.6722 | 0.889971 | 0.444986 | − | 0.895538i | \(-0.353209\pi\) | ||||
0.444986 | + | 0.895538i | \(0.353209\pi\) | |||||||
\(594\) | −24.6434 | −1.01113 | ||||||||
\(595\) | 11.9096 | 0.488246 | ||||||||
\(596\) | 16.3947 | 0.671551 | ||||||||
\(597\) | 12.0740 | 0.494155 | ||||||||
\(598\) | −45.9247 | −1.87800 | ||||||||
\(599\) | −36.9513 | −1.50979 | −0.754895 | − | 0.655846i | \(-0.772312\pi\) | ||||
−0.754895 | + | 0.655846i | \(0.772312\pi\) | |||||||
\(600\) | 0.147777 | 0.00603299 | ||||||||
\(601\) | 20.9295 | 0.853731 | 0.426866 | − | 0.904315i | \(-0.359618\pi\) | ||||
0.426866 | + | 0.904315i | \(0.359618\pi\) | |||||||
\(602\) | 0.670384 | 0.0273228 | ||||||||
\(603\) | 7.52155 | 0.306301 | ||||||||
\(604\) | −31.5460 | −1.28359 | ||||||||
\(605\) | −4.92902 | −0.200393 | ||||||||
\(606\) | 5.13820 | 0.208725 | ||||||||
\(607\) | 34.6528 | 1.40652 | 0.703258 | − | 0.710935i | \(-0.251728\pi\) | ||||
0.703258 | + | 0.710935i | \(0.251728\pi\) | |||||||
\(608\) | −5.54540 | −0.224896 | ||||||||
\(609\) | 5.04114 | 0.204277 | ||||||||
\(610\) | 25.7892 | 1.04417 | ||||||||
\(611\) | 6.21706 | 0.251515 | ||||||||
\(612\) | 38.1845 | 1.54352 | ||||||||
\(613\) | 11.7398 | 0.474166 | 0.237083 | − | 0.971489i | \(-0.423809\pi\) | ||||
0.237083 | + | 0.971489i | \(0.423809\pi\) | |||||||
\(614\) | −22.6589 | −0.914439 | ||||||||
\(615\) | 5.09922 | 0.205620 | ||||||||
\(616\) | 1.67584 | 0.0675214 | ||||||||
\(617\) | −5.06089 | −0.203744 | −0.101872 | − | 0.994798i | \(-0.532483\pi\) | ||||
−0.101872 | + | 0.994798i | \(0.532483\pi\) | |||||||
\(618\) | 5.51596 | 0.221884 | ||||||||
\(619\) | −28.6627 | −1.15205 | −0.576025 | − | 0.817432i | \(-0.695397\pi\) | ||||
−0.576025 | + | 0.817432i | \(0.695397\pi\) | |||||||
\(620\) | −13.4278 | −0.539273 | ||||||||
\(621\) | 27.0774 | 1.08658 | ||||||||
\(622\) | −61.5033 | −2.46606 | ||||||||
\(623\) | 20.5943 | 0.825093 | ||||||||
\(624\) | −6.35909 | −0.254567 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.4342 | −0.976588 | ||||||||
\(627\) | 1.55968 | 0.0622877 | ||||||||
\(628\) | −2.18717 | −0.0872775 | ||||||||
\(629\) | 88.0636 | 3.51133 | ||||||||
\(630\) | 8.30371 | 0.330828 | ||||||||
\(631\) | −22.6225 | −0.900586 | −0.450293 | − | 0.892881i | \(-0.648681\pi\) | ||||
−0.450293 | + | 0.892881i | \(0.648681\pi\) | |||||||
\(632\) | −2.01929 | −0.0803229 | ||||||||
\(633\) | 6.21472 | 0.247013 | ||||||||
\(634\) | −48.4784 | −1.92532 | ||||||||
\(635\) | −6.37046 | −0.252804 | ||||||||
\(636\) | −13.6260 | −0.540306 | ||||||||
\(637\) | 12.3175 | 0.488038 | ||||||||
\(638\) | 45.7615 | 1.81171 | ||||||||
\(639\) | 9.91436 | 0.392206 | ||||||||
\(640\) | −2.13866 | −0.0845378 | ||||||||
\(641\) | −24.3789 | −0.962909 | −0.481454 | − | 0.876471i | \(-0.659891\pi\) | ||||
−0.481454 | + | 0.876471i | \(0.659891\pi\) | |||||||
\(642\) | 5.30152 | 0.209234 | ||||||||
\(643\) | −31.9931 | −1.26168 | −0.630842 | − | 0.775911i | \(-0.717290\pi\) | ||||
−0.630842 | + | 0.775911i | \(0.717290\pi\) | |||||||
\(644\) | 25.1738 | 0.991987 | ||||||||
\(645\) | 0.120031 | 0.00472622 | ||||||||
\(646\) | −10.5856 | −0.416485 | ||||||||
\(647\) | 3.55450 | 0.139742 | 0.0698710 | − | 0.997556i | \(-0.477741\pi\) | ||||
0.0698710 | + | 0.997556i | \(0.477741\pi\) | |||||||
\(648\) | −1.70288 | −0.0668955 | ||||||||
\(649\) | −5.24370 | −0.205833 | ||||||||
\(650\) | −5.32776 | −0.208972 | ||||||||
\(651\) | −6.22669 | −0.244043 | ||||||||
\(652\) | 13.7369 | 0.537978 | ||||||||
\(653\) | 26.0330 | 1.01875 | 0.509375 | − | 0.860545i | \(-0.329877\pi\) | ||||
0.509375 | + | 0.860545i | \(0.329877\pi\) | |||||||
\(654\) | 15.2971 | 0.598165 | ||||||||
\(655\) | −15.5677 | −0.608278 | ||||||||
\(656\) | −39.3332 | −1.53571 | ||||||||
\(657\) | 23.7962 | 0.928377 | ||||||||
\(658\) | −7.06509 | −0.275426 | ||||||||
\(659\) | −13.9243 | −0.542412 | −0.271206 | − | 0.962521i | \(-0.587423\pi\) | ||||
−0.271206 | + | 0.962521i | \(0.587423\pi\) | |||||||
\(660\) | −4.10216 | −0.159677 | ||||||||
\(661\) | 18.4645 | 0.718186 | 0.359093 | − | 0.933302i | \(-0.383086\pi\) | ||||
0.359093 | + | 0.933302i | \(0.383086\pi\) | |||||||
\(662\) | 66.8738 | 2.59912 | ||||||||
\(663\) | −11.3609 | −0.441220 | ||||||||
\(664\) | 1.45493 | 0.0564624 | ||||||||
\(665\) | −1.11038 | −0.0430586 | ||||||||
\(666\) | 61.4004 | 2.37922 | ||||||||
\(667\) | −50.2812 | −1.94690 | ||||||||
\(668\) | 29.2702 | 1.13250 | ||||||||
\(669\) | −0.964685 | −0.0372969 | ||||||||
\(670\) | 5.48420 | 0.211873 | ||||||||
\(671\) | 52.3638 | 2.02148 | ||||||||
\(672\) | 6.76335 | 0.260902 | ||||||||
\(673\) | 21.8721 | 0.843108 | 0.421554 | − | 0.906803i | \(-0.361485\pi\) | ||||
0.421554 | + | 0.906803i | \(0.361485\pi\) | |||||||
\(674\) | −2.98856 | −0.115115 | ||||||||
\(675\) | 3.14127 | 0.120908 | ||||||||
\(676\) | −10.5360 | −0.405233 | ||||||||
\(677\) | −28.5839 | −1.09857 | −0.549285 | − | 0.835635i | \(-0.685100\pi\) | ||||
−0.549285 | + | 0.835635i | \(0.685100\pi\) | |||||||
\(678\) | −16.2671 | −0.624735 | ||||||||
\(679\) | −20.5179 | −0.787406 | ||||||||
\(680\) | −2.03649 | −0.0780957 | ||||||||
\(681\) | −2.73439 | −0.104782 | ||||||||
\(682\) | −56.5234 | −2.16439 | ||||||||
\(683\) | −2.47564 | −0.0947278 | −0.0473639 | − | 0.998878i | \(-0.515082\pi\) | ||||
−0.0473639 | + | 0.998878i | \(0.515082\pi\) | |||||||
\(684\) | −3.56009 | −0.136123 | ||||||||
\(685\) | −2.80386 | −0.107130 | ||||||||
\(686\) | −35.5590 | −1.35765 | ||||||||
\(687\) | −7.01785 | −0.267748 | ||||||||
\(688\) | −0.925869 | −0.0352984 | ||||||||
\(689\) | −35.9331 | −1.36894 | ||||||||
\(690\) | 9.34434 | 0.355733 | ||||||||
\(691\) | −39.9523 | −1.51986 | −0.759929 | − | 0.650006i | \(-0.774767\pi\) | ||||
−0.759929 | + | 0.650006i | \(0.774767\pi\) | |||||||
\(692\) | −16.4749 | −0.626282 | ||||||||
\(693\) | 16.8603 | 0.640471 | ||||||||
\(694\) | 54.9638 | 2.08640 | ||||||||
\(695\) | 14.7772 | 0.560532 | ||||||||
\(696\) | −0.862011 | −0.0326744 | ||||||||
\(697\) | −70.2712 | −2.66171 | ||||||||
\(698\) | −10.7621 | −0.407351 | ||||||||
\(699\) | −9.20582 | −0.348196 | ||||||||
\(700\) | 2.92044 | 0.110382 | ||||||||
\(701\) | −5.61138 | −0.211939 | −0.105969 | − | 0.994369i | \(-0.533795\pi\) | ||||
−0.105969 | + | 0.994369i | \(0.533795\pi\) | |||||||
\(702\) | −16.7360 | −0.631658 | ||||||||
\(703\) | −8.21051 | −0.309665 | ||||||||
\(704\) | 27.4382 | 1.03411 | ||||||||
\(705\) | −1.26499 | −0.0476423 | ||||||||
\(706\) | 29.5384 | 1.11169 | ||||||||
\(707\) | −7.42745 | −0.279338 | ||||||||
\(708\) | −1.35040 | −0.0507511 | ||||||||
\(709\) | 28.4660 | 1.06906 | 0.534532 | − | 0.845148i | \(-0.320488\pi\) | ||||
0.534532 | + | 0.845148i | \(0.320488\pi\) | |||||||
\(710\) | 7.22887 | 0.271294 | ||||||||
\(711\) | −20.3157 | −0.761899 | ||||||||
\(712\) | −3.52153 | −0.131975 | ||||||||
\(713\) | 62.1061 | 2.32589 | ||||||||
\(714\) | 12.9106 | 0.483166 | ||||||||
\(715\) | −10.8178 | −0.404563 | ||||||||
\(716\) | 11.3239 | 0.423196 | ||||||||
\(717\) | 9.26785 | 0.346114 | ||||||||
\(718\) | −6.47077 | −0.241487 | ||||||||
\(719\) | −5.05643 | −0.188573 | −0.0942864 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942864 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(720\) | −11.4683 | −0.427398 | ||||||||
\(721\) | −7.97352 | −0.296949 | ||||||||
\(722\) | −36.3599 | −1.35318 | ||||||||
\(723\) | 0.551502 | 0.0205106 | ||||||||
\(724\) | 11.1450 | 0.414201 | ||||||||
\(725\) | −5.83317 | −0.216639 | ||||||||
\(726\) | −5.34328 | −0.198308 | ||||||||
\(727\) | −47.1191 | −1.74755 | −0.873776 | − | 0.486328i | \(-0.838336\pi\) | ||||
−0.873776 | + | 0.486328i | \(0.838336\pi\) | |||||||
\(728\) | 1.13810 | 0.0421809 | ||||||||
\(729\) | −11.9352 | −0.442043 | ||||||||
\(730\) | 17.3505 | 0.642172 | ||||||||
\(731\) | −1.65412 | −0.0611798 | ||||||||
\(732\) | 13.4851 | 0.498425 | ||||||||
\(733\) | 37.7391 | 1.39392 | 0.696962 | − | 0.717108i | \(-0.254535\pi\) | ||||
0.696962 | + | 0.717108i | \(0.254535\pi\) | |||||||
\(734\) | 2.47456 | 0.0913375 | ||||||||
\(735\) | −2.50626 | −0.0924448 | ||||||||
\(736\) | −67.4589 | −2.48657 | ||||||||
\(737\) | 11.1354 | 0.410179 | ||||||||
\(738\) | −48.9950 | −1.80353 | ||||||||
\(739\) | −5.83089 | −0.214493 | −0.107246 | − | 0.994232i | \(-0.534203\pi\) | ||||
−0.107246 | + | 0.994232i | \(0.534203\pi\) | |||||||
\(740\) | 21.5947 | 0.793837 | ||||||||
\(741\) | 1.05922 | 0.0389114 | ||||||||
\(742\) | 40.8345 | 1.49908 | ||||||||
\(743\) | 30.8566 | 1.13202 | 0.566010 | − | 0.824398i | \(-0.308486\pi\) | ||||
0.566010 | + | 0.824398i | \(0.308486\pi\) | |||||||
\(744\) | 1.06473 | 0.0390350 | ||||||||
\(745\) | −8.79693 | −0.322294 | ||||||||
\(746\) | −21.7064 | −0.794728 | ||||||||
\(747\) | 14.6379 | 0.535571 | ||||||||
\(748\) | 56.5310 | 2.06698 | ||||||||
\(749\) | −7.66353 | −0.280019 | ||||||||
\(750\) | 1.08405 | 0.0395838 | ||||||||
\(751\) | 37.0538 | 1.35211 | 0.676057 | − | 0.736849i | \(-0.263687\pi\) | ||||
0.676057 | + | 0.736849i | \(0.263687\pi\) | |||||||
\(752\) | 9.75762 | 0.355824 | ||||||||
\(753\) | 9.48674 | 0.345716 | ||||||||
\(754\) | 31.0778 | 1.13179 | ||||||||
\(755\) | 16.9267 | 0.616027 | ||||||||
\(756\) | 9.17389 | 0.333651 | ||||||||
\(757\) | 39.7535 | 1.44487 | 0.722433 | − | 0.691441i | \(-0.243024\pi\) | ||||
0.722433 | + | 0.691441i | \(0.243024\pi\) | |||||||
\(758\) | 27.4446 | 0.996832 | ||||||||
\(759\) | 18.9733 | 0.688687 | ||||||||
\(760\) | 0.189869 | 0.00688729 | ||||||||
\(761\) | 31.2801 | 1.13390 | 0.566952 | − | 0.823751i | \(-0.308123\pi\) | ||||
0.566952 | + | 0.823751i | \(0.308123\pi\) | |||||||
\(762\) | −6.90588 | −0.250174 | ||||||||
\(763\) | −22.1125 | −0.800527 | ||||||||
\(764\) | −15.0000 | −0.542679 | ||||||||
\(765\) | −20.4888 | −0.740773 | ||||||||
\(766\) | −57.9478 | −2.09374 | ||||||||
\(767\) | −3.56113 | −0.128585 | ||||||||
\(768\) | −9.90134 | −0.357284 | ||||||||
\(769\) | 3.13978 | 0.113223 | 0.0566117 | − | 0.998396i | \(-0.481970\pi\) | ||||
0.0566117 | + | 0.998396i | \(0.481970\pi\) | |||||||
\(770\) | 12.2934 | 0.443023 | ||||||||
\(771\) | 11.2974 | 0.406868 | ||||||||
\(772\) | 9.32114 | 0.335475 | ||||||||
\(773\) | −22.6071 | −0.813121 | −0.406561 | − | 0.913624i | \(-0.633272\pi\) | ||||
−0.406561 | + | 0.913624i | \(0.633272\pi\) | |||||||
\(774\) | −1.15330 | −0.0414545 | ||||||||
\(775\) | 7.20499 | 0.258811 | ||||||||
\(776\) | 3.50847 | 0.125947 | ||||||||
\(777\) | 10.0138 | 0.359244 | ||||||||
\(778\) | −67.1823 | −2.40860 | ||||||||
\(779\) | 6.55165 | 0.234737 | ||||||||
\(780\) | −2.78588 | −0.0997506 | ||||||||
\(781\) | 14.6779 | 0.525217 | ||||||||
\(782\) | −128.772 | −4.60488 | ||||||||
\(783\) | −18.3236 | −0.654831 | ||||||||
\(784\) | 19.3322 | 0.690437 | ||||||||
\(785\) | 1.17357 | 0.0418867 | ||||||||
\(786\) | −16.8761 | −0.601949 | ||||||||
\(787\) | 41.4390 | 1.47714 | 0.738571 | − | 0.674176i | \(-0.235501\pi\) | ||||
0.738571 | + | 0.674176i | \(0.235501\pi\) | |||||||
\(788\) | 21.1978 | 0.755141 | ||||||||
\(789\) | −15.2672 | −0.543528 | ||||||||
\(790\) | −14.8128 | −0.527017 | ||||||||
\(791\) | 23.5147 | 0.836087 | ||||||||
\(792\) | −2.88304 | −0.102444 | ||||||||
\(793\) | 35.5616 | 1.26283 | ||||||||
\(794\) | 5.65382 | 0.200647 | ||||||||
\(795\) | 7.31134 | 0.259307 | ||||||||
\(796\) | −40.8013 | −1.44616 | ||||||||
\(797\) | −22.3178 | −0.790536 | −0.395268 | − | 0.918566i | \(-0.629348\pi\) | ||||
−0.395268 | + | 0.918566i | \(0.629348\pi\) | |||||||
\(798\) | −1.20370 | −0.0426106 | ||||||||
\(799\) | 17.4326 | 0.616720 | ||||||||
\(800\) | −7.82597 | −0.276690 | ||||||||
\(801\) | −35.4295 | −1.25184 | ||||||||
\(802\) | 4.83471 | 0.170719 | ||||||||
\(803\) | 35.2295 | 1.24322 | ||||||||
\(804\) | 2.86768 | 0.101135 | ||||||||
\(805\) | −13.5076 | −0.476080 | ||||||||
\(806\) | −38.3865 | −1.35211 | ||||||||
\(807\) | 1.56163 | 0.0549721 | ||||||||
\(808\) | 1.27006 | 0.0446805 | ||||||||
\(809\) | −5.65747 | −0.198906 | −0.0994531 | − | 0.995042i | \(-0.531709\pi\) | ||||
−0.0994531 | + | 0.995042i | \(0.531709\pi\) | |||||||
\(810\) | −12.4918 | −0.438916 | ||||||||
\(811\) | −47.8682 | −1.68088 | −0.840441 | − | 0.541904i | \(-0.817704\pi\) | ||||
−0.840441 | + | 0.541904i | \(0.817704\pi\) | |||||||
\(812\) | −17.0354 | −0.597826 | ||||||||
\(813\) | −6.44764 | −0.226129 | ||||||||
\(814\) | 90.9014 | 3.18609 | ||||||||
\(815\) | −7.37084 | −0.258189 | ||||||||
\(816\) | −17.8308 | −0.624203 | ||||||||
\(817\) | 0.154220 | 0.00539547 | ||||||||
\(818\) | 29.5546 | 1.03335 | ||||||||
\(819\) | 11.4503 | 0.400105 | ||||||||
\(820\) | −17.2317 | −0.601756 | ||||||||
\(821\) | −3.39747 | −0.118572 | −0.0592862 | − | 0.998241i | \(-0.518882\pi\) | ||||
−0.0592862 | + | 0.998241i | \(0.518882\pi\) | |||||||
\(822\) | −3.03952 | −0.106015 | ||||||||
\(823\) | −1.21618 | −0.0423933 | −0.0211967 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211967 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(824\) | 1.36343 | 0.0474975 | ||||||||
\(825\) | 2.20111 | 0.0766328 | ||||||||
\(826\) | 4.04689 | 0.140809 | ||||||||
\(827\) | 55.7826 | 1.93975 | 0.969875 | − | 0.243603i | \(-0.0783295\pi\) | ||||
0.969875 | + | 0.243603i | \(0.0783295\pi\) | |||||||
\(828\) | −43.3079 | −1.50505 | ||||||||
\(829\) | −47.8332 | −1.66132 | −0.830659 | − | 0.556782i | \(-0.812036\pi\) | ||||
−0.830659 | + | 0.556782i | \(0.812036\pi\) | |||||||
\(830\) | 10.6729 | 0.370462 | ||||||||
\(831\) | 7.06412 | 0.245051 | ||||||||
\(832\) | 18.6339 | 0.646016 | ||||||||
\(833\) | 34.5382 | 1.19668 | ||||||||
\(834\) | 16.0192 | 0.554699 | ||||||||
\(835\) | −15.7056 | −0.543515 | ||||||||
\(836\) | −5.27060 | −0.182288 | ||||||||
\(837\) | 22.6328 | 0.782304 | ||||||||
\(838\) | −40.8576 | −1.41140 | ||||||||
\(839\) | −35.3573 | −1.22067 | −0.610334 | − | 0.792144i | \(-0.708965\pi\) | ||||
−0.610334 | + | 0.792144i | \(0.708965\pi\) | |||||||
\(840\) | −0.231571 | −0.00798997 | ||||||||
\(841\) | 5.02589 | 0.173306 | ||||||||
\(842\) | −52.9870 | −1.82605 | ||||||||
\(843\) | 7.05861 | 0.243112 | ||||||||
\(844\) | −21.0013 | −0.722894 | ||||||||
\(845\) | 5.65336 | 0.194481 | ||||||||
\(846\) | 12.1545 | 0.417879 | ||||||||
\(847\) | 7.72391 | 0.265397 | ||||||||
\(848\) | −56.3966 | −1.93667 | ||||||||
\(849\) | 7.59034 | 0.260500 | ||||||||
\(850\) | −14.9390 | −0.512403 | ||||||||
\(851\) | −99.8795 | −3.42383 | ||||||||
\(852\) | 3.77997 | 0.129500 | ||||||||
\(853\) | −38.5021 | −1.31829 | −0.659143 | − | 0.752018i | \(-0.729081\pi\) | ||||
−0.659143 | + | 0.752018i | \(0.729081\pi\) | |||||||
\(854\) | −40.4123 | −1.38288 | ||||||||
\(855\) | 1.91025 | 0.0653290 | ||||||||
\(856\) | 1.31043 | 0.0447895 | ||||||||
\(857\) | 3.21574 | 0.109848 | 0.0549238 | − | 0.998491i | \(-0.482508\pi\) | ||||
0.0549238 | + | 0.998491i | \(0.482508\pi\) | |||||||
\(858\) | −11.7270 | −0.400353 | ||||||||
\(859\) | 8.56250 | 0.292149 | 0.146074 | − | 0.989274i | \(-0.453336\pi\) | ||||
0.146074 | + | 0.989274i | \(0.453336\pi\) | |||||||
\(860\) | −0.405618 | −0.0138315 | ||||||||
\(861\) | −7.99062 | −0.272319 | ||||||||
\(862\) | −38.5008 | −1.31134 | ||||||||
\(863\) | −21.7491 | −0.740350 | −0.370175 | − | 0.928962i | \(-0.620702\pi\) | ||||
−0.370175 | + | 0.928962i | \(0.620702\pi\) | |||||||
\(864\) | −24.5835 | −0.836347 | ||||||||
\(865\) | 8.83998 | 0.300568 | ||||||||
\(866\) | −30.6331 | −1.04096 | ||||||||
\(867\) | −22.4803 | −0.763470 | ||||||||
\(868\) | 21.0417 | 0.714202 | ||||||||
\(869\) | −30.0768 | −1.02029 | ||||||||
\(870\) | −6.32343 | −0.214384 | ||||||||
\(871\) | 7.56236 | 0.256241 | ||||||||
\(872\) | 3.78114 | 0.128046 | ||||||||
\(873\) | 35.2981 | 1.19466 | ||||||||
\(874\) | 12.0059 | 0.406107 | ||||||||
\(875\) | −1.56703 | −0.0529752 | ||||||||
\(876\) | 9.07258 | 0.306534 | ||||||||
\(877\) | 21.9167 | 0.740074 | 0.370037 | − | 0.929017i | \(-0.379345\pi\) | ||||
0.370037 | + | 0.929017i | \(0.379345\pi\) | |||||||
\(878\) | −21.1275 | −0.713017 | ||||||||
\(879\) | 9.12151 | 0.307661 | ||||||||
\(880\) | −16.9784 | −0.572343 | ||||||||
\(881\) | 0.352879 | 0.0118888 | 0.00594441 | − | 0.999982i | \(-0.498108\pi\) | ||||
0.00594441 | + | 0.999982i | \(0.498108\pi\) | |||||||
\(882\) | 24.0810 | 0.810849 | ||||||||
\(883\) | −55.2411 | −1.85901 | −0.929505 | − | 0.368810i | \(-0.879765\pi\) | ||||
−0.929505 | + | 0.368810i | \(0.879765\pi\) | |||||||
\(884\) | 38.3916 | 1.29125 | ||||||||
\(885\) | 0.724588 | 0.0243567 | ||||||||
\(886\) | 17.9326 | 0.602457 | ||||||||
\(887\) | −6.24830 | −0.209797 | −0.104899 | − | 0.994483i | \(-0.533452\pi\) | ||||
−0.104899 | + | 0.994483i | \(0.533452\pi\) | |||||||
\(888\) | −1.71232 | −0.0574615 | ||||||||
\(889\) | 9.98269 | 0.334809 | ||||||||
\(890\) | −25.8328 | −0.865916 | ||||||||
\(891\) | −25.3640 | −0.849727 | ||||||||
\(892\) | 3.25994 | 0.109151 | ||||||||
\(893\) | −1.62530 | −0.0543887 | ||||||||
\(894\) | −9.53628 | −0.318941 | ||||||||
\(895\) | −6.07612 | −0.203102 | ||||||||
\(896\) | 3.35133 | 0.111960 | ||||||||
\(897\) | 12.8852 | 0.430226 | ||||||||
\(898\) | −53.3225 | −1.77940 | ||||||||
\(899\) | −42.0279 | −1.40171 | ||||||||
\(900\) | −5.02419 | −0.167473 | ||||||||
\(901\) | −100.756 | −3.35667 | ||||||||
\(902\) | −72.5356 | −2.41517 | ||||||||
\(903\) | −0.188092 | −0.00625931 | ||||||||
\(904\) | −4.02091 | −0.133733 | ||||||||
\(905\) | −5.98011 | −0.198786 | ||||||||
\(906\) | 18.3494 | 0.609616 | ||||||||
\(907\) | −16.6946 | −0.554335 | −0.277168 | − | 0.960822i | \(-0.589396\pi\) | ||||
−0.277168 | + | 0.960822i | \(0.589396\pi\) | |||||||
\(908\) | 9.24026 | 0.306649 | ||||||||
\(909\) | 12.7779 | 0.423815 | ||||||||
\(910\) | 8.34875 | 0.276758 | ||||||||
\(911\) | 17.3319 | 0.574232 | 0.287116 | − | 0.957896i | \(-0.407303\pi\) | ||||
0.287116 | + | 0.957896i | \(0.407303\pi\) | |||||||
\(912\) | 1.66244 | 0.0550488 | ||||||||
\(913\) | 21.6709 | 0.717202 | ||||||||
\(914\) | 45.1854 | 1.49460 | ||||||||
\(915\) | −7.23575 | −0.239207 | ||||||||
\(916\) | 23.7153 | 0.783574 | ||||||||
\(917\) | 24.3949 | 0.805592 | ||||||||
\(918\) | −46.9274 | −1.54884 | ||||||||
\(919\) | 42.2047 | 1.39220 | 0.696102 | − | 0.717943i | \(-0.254916\pi\) | ||||
0.696102 | + | 0.717943i | \(0.254916\pi\) | |||||||
\(920\) | 2.30973 | 0.0761496 | ||||||||
\(921\) | 6.35749 | 0.209486 | ||||||||
\(922\) | 23.0678 | 0.759698 | ||||||||
\(923\) | 9.96814 | 0.328105 | ||||||||
\(924\) | 6.42820 | 0.211472 | ||||||||
\(925\) | −11.5871 | −0.380982 | ||||||||
\(926\) | 63.0753 | 2.07278 | ||||||||
\(927\) | 13.7173 | 0.450535 | ||||||||
\(928\) | 45.6502 | 1.49854 | ||||||||
\(929\) | −27.1814 | −0.891794 | −0.445897 | − | 0.895084i | \(-0.647115\pi\) | ||||
−0.445897 | + | 0.895084i | \(0.647115\pi\) | |||||||
\(930\) | 7.81054 | 0.256118 | ||||||||
\(931\) | −3.22013 | −0.105535 | ||||||||
\(932\) | 31.1090 | 1.01901 | ||||||||
\(933\) | 17.2562 | 0.564942 | ||||||||
\(934\) | −18.8601 | −0.617120 | ||||||||
\(935\) | −30.3330 | −0.991995 | ||||||||
\(936\) | −1.95794 | −0.0639974 | ||||||||
\(937\) | −15.4398 | −0.504397 | −0.252199 | − | 0.967676i | \(-0.581154\pi\) | ||||
−0.252199 | + | 0.967676i | \(0.581154\pi\) | |||||||
\(938\) | −8.59389 | −0.280600 | ||||||||
\(939\) | 6.85560 | 0.223724 | ||||||||
\(940\) | 4.27476 | 0.139427 | ||||||||
\(941\) | 3.16013 | 0.103017 | 0.0515086 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515086 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(942\) | 1.27221 | 0.0414508 | ||||||||
\(943\) | 79.6998 | 2.59538 | ||||||||
\(944\) | −5.58917 | −0.181912 | ||||||||
\(945\) | −4.92246 | −0.160128 | ||||||||
\(946\) | −1.70742 | −0.0555131 | ||||||||
\(947\) | 35.0516 | 1.13902 | 0.569512 | − | 0.821983i | \(-0.307132\pi\) | ||||
0.569512 | + | 0.821983i | \(0.307132\pi\) | |||||||
\(948\) | −7.74561 | −0.251566 | ||||||||
\(949\) | 23.9253 | 0.776647 | ||||||||
\(950\) | 1.39282 | 0.0451890 | ||||||||
\(951\) | 13.6018 | 0.441067 | ||||||||
\(952\) | 3.19123 | 0.103428 | ||||||||
\(953\) | 15.8937 | 0.514848 | 0.257424 | − | 0.966298i | \(-0.417126\pi\) | ||||
0.257424 | + | 0.966298i | \(0.417126\pi\) | |||||||
\(954\) | −70.2498 | −2.27442 | ||||||||
\(955\) | 8.04857 | 0.260446 | ||||||||
\(956\) | −31.3186 | −1.01292 | ||||||||
\(957\) | −12.8395 | −0.415041 | ||||||||
\(958\) | −30.0493 | −0.970850 | ||||||||
\(959\) | 4.39373 | 0.141881 | ||||||||
\(960\) | −3.79147 | −0.122369 | ||||||||
\(961\) | 20.9118 | 0.674575 | ||||||||
\(962\) | 61.7335 | 1.99037 | ||||||||
\(963\) | 13.1840 | 0.424848 | ||||||||
\(964\) | −1.86368 | −0.0600251 | ||||||||
\(965\) | −5.00147 | −0.161003 | ||||||||
\(966\) | −14.6428 | −0.471126 | ||||||||
\(967\) | −15.7577 | −0.506733 | −0.253366 | − | 0.967370i | \(-0.581538\pi\) | ||||
−0.253366 | + | 0.967370i | \(0.581538\pi\) | |||||||
\(968\) | −1.32075 | −0.0424506 | ||||||||
\(969\) | 2.97004 | 0.0954114 | ||||||||
\(970\) | 25.7370 | 0.826364 | ||||||||
\(971\) | −5.24444 | −0.168302 | −0.0841511 | − | 0.996453i | \(-0.526818\pi\) | ||||
−0.0841511 | + | 0.996453i | \(0.526818\pi\) | |||||||
\(972\) | −24.0949 | −0.772845 | ||||||||
\(973\) | −23.1563 | −0.742357 | ||||||||
\(974\) | 18.8643 | 0.604450 | ||||||||
\(975\) | 1.49483 | 0.0478729 | ||||||||
\(976\) | 55.8136 | 1.78655 | ||||||||
\(977\) | 21.5907 | 0.690747 | 0.345374 | − | 0.938465i | \(-0.387752\pi\) | ||||
0.345374 | + | 0.938465i | \(0.387752\pi\) | |||||||
\(978\) | −7.99033 | −0.255502 | ||||||||
\(979\) | −52.4523 | −1.67638 | ||||||||
\(980\) | 8.46935 | 0.270544 | ||||||||
\(981\) | 38.0414 | 1.21457 | ||||||||
\(982\) | 62.5401 | 1.99573 | ||||||||
\(983\) | −39.1399 | −1.24837 | −0.624184 | − | 0.781277i | \(-0.714568\pi\) | ||||
−0.624184 | + | 0.781277i | \(0.714568\pi\) | |||||||
\(984\) | 1.36636 | 0.0435579 | ||||||||
\(985\) | −11.3742 | −0.362411 | ||||||||
\(986\) | 87.1417 | 2.77516 | ||||||||
\(987\) | 1.98228 | 0.0630966 | ||||||||
\(988\) | −3.57940 | −0.113876 | ||||||||
\(989\) | 1.87606 | 0.0596553 | ||||||||
\(990\) | −21.1490 | −0.672160 | ||||||||
\(991\) | −59.9001 | −1.90279 | −0.951394 | − | 0.307976i | \(-0.900348\pi\) | ||||
−0.951394 | + | 0.307976i | \(0.900348\pi\) | |||||||
\(992\) | −56.3860 | −1.79026 | ||||||||
\(993\) | −18.7630 | −0.595426 | ||||||||
\(994\) | −11.3278 | −0.359297 | ||||||||
\(995\) | 21.8929 | 0.694051 | ||||||||
\(996\) | 5.58086 | 0.176836 | ||||||||
\(997\) | 51.5191 | 1.63163 | 0.815813 | − | 0.578316i | \(-0.196290\pi\) | ||||
0.815813 | + | 0.578316i | \(0.196290\pi\) | |||||||
\(998\) | 16.3770 | 0.518403 | ||||||||
\(999\) | −36.3983 | −1.15159 |
(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 | 1205.2.a.c.1.13 | ✓ | 15 | |
5.4 | even | 2 | 6025.2.a.i.1.3 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.c.1.13 | ✓ | 15 | 1.1 | even | 1 | trivial | |
6025.2.a.i.1.3 | 15 | 5.4 | even | 2 |