Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.32973\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.06562 | −1.53666 | −0.768330 | − | 0.640054i | \(-0.778912\pi\) | ||||
−0.768330 | + | 0.640054i | \(0.778912\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.65945 | −0.801856 | −0.400928 | − | 0.916110i | \(-0.631312\pi\) | ||||
−0.400928 | + | 0.916110i | \(0.631312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.91023 | −1.63920 | −0.819602 | − | 0.572933i | \(-0.805805\pi\) | ||||
−0.819602 | + | 0.572933i | \(0.805805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.40617 | −0.826117 | −0.413058 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413058 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.65945 | 0.610121 | 0.305060 | − | 0.952333i | \(-0.401323\pi\) | ||||
0.305060 | + | 0.952333i | \(0.401323\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.34868 | 1.38540 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.84461 | 1.08532 | 0.542659 | − | 0.839953i | \(-0.317418\pi\) | ||||
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.31640 | 1.67327 | 0.836637 | − | 0.547757i | \(-0.184518\pi\) | ||||
0.836637 | + | 0.547757i | \(0.184518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.15288 | 0.722923 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.06562 | −0.687215 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.18059 | −0.687285 | −0.343642 | − | 0.939101i | \(-0.611661\pi\) | ||||
−0.343642 | + | 0.939101i | \(0.611661\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.22914 | 1.47785 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.15539 | 0.336615 | 0.168307 | − | 0.985735i | \(-0.446170\pi\) | ||||
0.168307 | + | 0.985735i | \(0.446170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34868 | −0.358171 | −0.179085 | − | 0.983834i | \(-0.557314\pi\) | ||||
−0.179085 | + | 0.983834i | \(0.557314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.242644 | −0.0353933 | −0.0176966 | − | 0.999843i | \(-0.505633\pi\) | ||||
−0.0176966 | + | 0.999843i | \(0.505633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.52927 | 1.36132 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.31891 | 0.744796 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.03585 | 1.24117 | 0.620585 | − | 0.784140i | \(-0.286895\pi\) | ||||
0.620585 | + | 0.784140i | \(0.286895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.65945 | −0.358601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.15288 | −0.550062 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.4143 | −1.87658 | −0.938291 | − | 0.345846i | \(-0.887592\pi\) | ||||
−0.938291 | + | 0.345846i | \(0.887592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.46365 | 0.315438 | 0.157719 | − | 0.987484i | \(-0.449586\pi\) | ||||
0.157719 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.28306 | 0.287639 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.91023 | −0.733074 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.75485 | 0.947405 | 0.473703 | − | 0.880685i | \(-0.342917\pi\) | ||||
0.473703 | + | 0.880685i | \(0.342917\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.56155 | −0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4395 | −1.47630 | −0.738149 | − | 0.674638i | \(-0.764300\pi\) | ||||
−0.738149 | + | 0.674638i | \(0.764300\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.08977 | −0.244589 | −0.122294 | − | 0.992494i | \(-0.539025\pi\) | ||||
−0.122294 | + | 0.992494i | \(0.539025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8123 | 1.23218 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.15288 | 0.467235 | 0.233618 | − | 0.972329i | \(-0.424944\pi\) | ||||
0.233618 | + | 0.972329i | \(0.424944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5293 | 1.37527 | 0.687633 | − | 0.726058i | \(-0.258650\pi\) | ||||
0.687633 | + | 0.726058i | \(0.258650\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40617 | −0.369451 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.12667 | −0.978482 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.35682 | −0.991821 | −0.495910 | − | 0.868374i | \(-0.665166\pi\) | ||||
−0.495910 | + | 0.868374i | \(0.665166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.0288 | 2.51890 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.5481 | −1.50856 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.65945 | 0.272854 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.47179 | 0.352507 | 0.176253 | − | 0.984345i | \(-0.443602\pi\) | ||||
0.176253 | + | 0.984345i | \(0.443602\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.49342 | 0.150095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.21036 | 0.916465 | 0.458233 | − | 0.888832i | \(-0.348483\pi\) | ||||
0.458233 | + | 0.888832i | \(0.348483\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.69736 | −0.462845 | −0.231422 | − | 0.972853i | \(-0.574338\pi\) | ||||
−0.231422 | + | 0.972853i | \(0.574338\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.34868 | 0.619568 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.376394 | 0.0363873 | 0.0181937 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181937 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.0369 | 1.82340 | 0.911702 | − | 0.410851i | \(-0.134768\pi\) | ||||
0.911702 | + | 0.410851i | \(0.134768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.52821 | 0.619631 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.94252 | 0.276809 | 0.138404 | − | 0.990376i | \(-0.455803\pi\) | ||||
0.138404 | + | 0.990376i | \(0.455803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.31891 | 0.306833 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.8482 | 1.26946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.92730 | −0.357028 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.36575 | −0.303479 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00357 | −0.532730 | −0.266365 | − | 0.963872i | \(-0.585823\pi\) | ||||
−0.266365 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.66759 | 0.322913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.9606 | 1.74397 | 0.871985 | − | 0.489533i | \(-0.162833\pi\) | ||||
0.871985 | + | 0.489533i | \(0.162833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.8123 | −0.937548 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7609 | −1.00480 | −0.502402 | − | 0.864634i | \(-0.667550\pi\) | ||||
−0.502402 | + | 0.864634i | \(0.667550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3891 | −1.05083 | −0.525415 | − | 0.850846i | \(-0.676090\pi\) | ||||
−0.525415 | + | 0.850846i | \(0.676090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.378902 | 0.0319093 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.7180 | 1.31441 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.84461 | 0.485369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.8805 | −1.22732 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.13124 | −0.174598 | −0.0872991 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0872991 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.787129 | 0.0640556 | 0.0320278 | − | 0.999487i | \(-0.489803\pi\) | ||||
0.0320278 | + | 0.999487i | \(0.489803\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.91274 | 0.154636 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.31640 | 0.748311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.18873 | −0.733340 | −0.366670 | − | 0.930351i | \(-0.619502\pi\) | ||||
−0.366670 | + | 0.930351i | \(0.619502\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1100 | −1.11899 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.06562 | −0.320416 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6928 | 1.38581 | 0.692903 | − | 0.721031i | \(-0.256331\pi\) | ||||
0.692903 | + | 0.721031i | \(0.256331\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.15288 | 0.323301 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.2462 | −1.10240 | −0.551202 | − | 0.834372i | \(-0.685831\pi\) | ||||
−0.551202 | + | 0.834372i | \(0.685831\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.9309 | 1.68699 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.49342 | −0.114205 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.20394 | −0.0915338 | −0.0457669 | − | 0.998952i | \(-0.514573\pi\) | ||||
−0.0457669 | + | 0.998952i | \(0.514573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.06562 | −0.307332 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.5087 | 1.69186 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.42495 | −0.554967 | −0.277483 | − | 0.960730i | \(-0.589500\pi\) | ||||
−0.277483 | + | 0.960730i | \(0.589500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0450 | 1.78725 | 0.893627 | − | 0.448810i | \(-0.148152\pi\) | ||||
0.893627 | + | 0.448810i | \(0.148152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.84712 | −0.284387 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.18059 | −0.307363 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.05854 | 0.662426 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.6112 | −1.64472 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.87689 | 0.352880 | 0.176440 | − | 0.984311i | \(-0.443542\pi\) | ||||
0.176440 | + | 0.984311i | \(0.443542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2714 | 0.739353 | 0.369676 | − | 0.929161i | \(-0.379469\pi\) | ||||
0.369676 | + | 0.929161i | \(0.379469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.22914 | 0.660913 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.28557 | 0.305334 | 0.152667 | − | 0.988278i | \(-0.451214\pi\) | ||||
0.152667 | + | 0.988278i | \(0.451214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.02164 | −0.285086 | −0.142543 | − | 0.989789i | \(-0.545528\pi\) | ||||
−0.142543 | + | 0.989789i | \(0.545528\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.1096 | −0.854146 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.7620 | −1.66776 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.15539 | 0.150539 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.561553 | −0.0390306 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.07270 | −0.489229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3416 | −1.05616 | −0.528080 | − | 0.849195i | \(-0.677088\pi\) | ||||
−0.528080 | + | 0.849195i | \(0.677088\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.4249 | 1.33098 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.34868 | −0.160179 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.8770 | −2.57126 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.26328 | 0.220512 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.1312 | 1.35417 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6801 | 1.18395 | 0.591973 | − | 0.805958i | \(-0.298349\pi\) | ||||
0.591973 | + | 0.805958i | \(0.298349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.63817 | −0.573335 | −0.286668 | − | 0.958030i | \(-0.592548\pi\) | ||||
−0.286668 | + | 0.958030i | \(0.592548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.34055 | −0.220749 | −0.110375 | − | 0.993890i | \(-0.535205\pi\) | ||||
−0.110375 | + | 0.993890i | \(0.535205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.8840 | −1.11089 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.23728 | 0.539642 | 0.269821 | − | 0.962910i | \(-0.413035\pi\) | ||||
0.269821 | + | 0.962910i | \(0.413035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.242644 | −0.0158284 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.48494 | −0.421242 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.86525 | 0.185338 | 0.0926688 | − | 0.995697i | \(-0.470460\pi\) | ||||
0.0926688 | + | 0.995697i | \(0.470460\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.68109 | 0.301536 | 0.150768 | − | 0.988569i | \(-0.451825\pi\) | ||||
0.150768 | + | 0.988569i | \(0.451825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.52927 | 0.608803 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.7180 | −1.00011 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.5651 | −1.23989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.5824 | 1.17291 | 0.586455 | − | 0.809982i | \(-0.300523\pi\) | ||||
0.586455 | + | 0.809982i | \(0.300523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.65945 | −0.167198 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.31891 | 0.333083 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.7226 | −1.79166 | −0.895832 | − | 0.444392i | \(-0.853420\pi\) | ||||
−0.895832 | + | 0.444392i | \(0.853420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.9967 | 1.05612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.28206 | −0.203154 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.20500 | 0.567604 | 0.283802 | − | 0.958883i | \(-0.408404\pi\) | ||||
0.283802 | + | 0.958883i | \(0.408404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.03585 | 0.555068 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6112 | 0.894189 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.9194 | 1.03160 | 0.515798 | − | 0.856710i | \(-0.327496\pi\) | ||||
0.515798 | + | 0.856710i | \(0.327496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.15082 | −0.0699072 | −0.0349536 | − | 0.999389i | \(-0.511128\pi\) | ||||
−0.0349536 | + | 0.999389i | \(0.511128\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −37.5222 | −2.27095 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.65945 | −0.160371 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.57505 | 0.154720 | 0.0773600 | − | 0.997003i | \(-0.475351\pi\) | ||||
0.0773600 | + | 0.997003i | \(0.475351\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.23165 | −0.313211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.4718 | 1.63883 | 0.819415 | − | 0.573201i | \(-0.194299\pi\) | ||||
0.819415 | + | 0.573201i | \(0.194299\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.36389 | 0.140519 | 0.0702595 | − | 0.997529i | \(-0.477617\pi\) | ||||
0.0702595 | + | 0.997529i | \(0.477617\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.15288 | −0.245995 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.76298 | −0.517263 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.39803 | −0.317531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.42138 | −0.317807 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 34.1198 | 1.99330 | 0.996650 | − | 0.0817846i | \(-0.0260619\pi\) | ||||
0.996650 | + | 0.0817846i | \(0.0260619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4143 | −0.839233 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.7907 | −0.858243 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.91023 | −0.341798 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.54885 | 0.550386 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.3825 | −0.826251 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.46365 | 0.141068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.49342 | −0.0852342 | −0.0426171 | − | 0.999091i | \(-0.513570\pi\) | ||||
−0.0426171 | + | 0.999091i | \(0.513570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.33518 | 0.417284 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1060 | 0.799880 | 0.399940 | − | 0.916541i | \(-0.369031\pi\) | ||||
0.399940 | + | 0.916541i | \(0.369031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.8563 | −1.85715 | −0.928574 | − | 0.371146i | \(-0.878965\pi\) | ||||
−0.928574 | + | 0.371146i | \(0.878965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.28306 | 0.128636 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5824 | 0.706698 | 0.353349 | − | 0.935492i | \(-0.385043\pi\) | ||||
0.353349 | + | 0.935492i | \(0.385043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5435 | −0.870268 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.587758 | −0.0328055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.05854 | −0.504031 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.91023 | −0.327841 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.7271 | −1.64391 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.986499 | 0.0543874 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.57677 | −0.0866669 | −0.0433334 | − | 0.999061i | \(-0.513798\pi\) | ||||
−0.0433334 | + | 0.999061i | \(0.513798\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.34762 | 0.128649 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.75485 | 0.423693 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4718 | −0.842802 | −0.421401 | − | 0.906874i | \(-0.638461\pi\) | ||||
−0.421401 | + | 0.906874i | \(0.638461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.59489 | −0.249560 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.7765 | −1.34172 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.2831 | −0.555233 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.56155 | −0.0840712 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.00312 | 0.483313 | 0.241656 | − | 0.970362i | \(-0.422309\pi\) | ||||
0.241656 | + | 0.970362i | \(0.422309\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.10398 | 0.0590945 | 0.0295473 | − | 0.999563i | \(-0.490593\pi\) | ||||
0.0295473 | + | 0.999563i | \(0.490593\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.8701 | −1.75448 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.96566 | 0.104621 | 0.0523107 | − | 0.998631i | \(-0.483341\pi\) | ||||
0.0523107 | + | 0.998631i | \(0.483341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4395 | −0.660220 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.6247 | −1.14450 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.60403 | 0.137435 | 0.0687177 | − | 0.997636i | \(-0.478109\pi\) | ||||
0.0687177 | + | 0.997636i | \(0.478109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9273 | −0.627753 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.13269 | 0.321883 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.08977 | −0.109383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.98042 | −0.364375 | −0.182188 | − | 0.983264i | \(-0.558318\pi\) | ||||
−0.182188 | + | 0.983264i | \(0.558318\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.21036 | −0.0630090 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.7363 | −1.90726 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3220 | 1.25935 | 0.629673 | − | 0.776860i | \(-0.283189\pi\) | ||||
0.629673 | + | 0.776860i | \(0.283189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.5430 | −1.77906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.6541 | 1.26640 | 0.633198 | − | 0.773990i | \(-0.281742\pi\) | ||||
0.633198 | + | 0.773990i | \(0.281742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.37489 | 0.480290 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.99292 | 0.255126 | 0.127563 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127563 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.8123 | 0.551048 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.31891 | 0.0670439 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.0234 | −1.62365 | −0.811826 | − | 0.583900i | \(-0.801526\pi\) | ||||
−0.811826 | + | 0.583900i | \(0.801526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.40617 | −0.172257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.1696 | −1.57230 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.15288 | 0.208954 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.3441 | −0.870476 | −0.435238 | − | 0.900315i | \(-0.643336\pi\) | ||||
−0.435238 | + | 0.900315i | \(0.643336\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.8840 | 0.845259 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.3352 | −1.06543 | −0.532714 | − | 0.846295i | \(-0.678828\pi\) | ||||
−0.532714 | + | 0.846295i | \(0.678828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −55.0621 | −2.74284 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.1181 | 0.551103 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5328 | −0.619709 | −0.309855 | − | 0.950784i | \(-0.600280\pi\) | ||||
−0.309855 | + | 0.950784i | \(0.600280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.3653 | 0.905894 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 58.6031 | 2.88367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.5293 | 0.615038 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.3462 | 0.947389 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0288 | −0.587644 | −0.293822 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293822 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.3721 | −1.87014 | −0.935071 | − | 0.354462i | \(-0.884664\pi\) | ||||
−0.935071 | + | 0.354462i | \(0.884664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.136257 | 0.00662507 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.40617 | −0.165223 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0163 | −0.484721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.5445 | −1.18502 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.4789 | 1.41995 | 0.709975 | − | 0.704227i | \(-0.248706\pi\) | ||||
0.709975 | + | 0.704227i | \(0.248706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0531 | −0.579236 | −0.289618 | − | 0.957142i | \(-0.593528\pi\) | ||||
−0.289618 | + | 0.957142i | \(0.593528\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.12667 | −0.437590 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.65945 | 0.127219 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.1656 | −0.771541 | −0.385771 | − | 0.922595i | \(-0.626064\pi\) | ||||
−0.385771 | + | 0.922595i | \(0.626064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.35119 | −0.254819 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.3729 | −0.920433 | −0.460217 | − | 0.887807i | \(-0.652228\pi\) | ||||
−0.460217 | + | 0.887807i | \(0.652228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.35682 | −0.443556 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.32805 | 0.157411 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4728 | 1.01337 | 0.506683 | − | 0.862132i | \(-0.330871\pi\) | ||||
0.506683 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.73215 | −0.269916 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.22914 | −0.0577502 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0288 | 1.12649 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.95602 | −0.278611 | −0.139305 | − | 0.990249i | \(-0.544487\pi\) | ||||
−0.139305 | + | 0.990249i | \(0.544487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.9436 | −0.884210 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.6918 | 1.61576 | 0.807879 | − | 0.589348i | \(-0.200615\pi\) | ||||
0.807879 | + | 0.589348i | \(0.200615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.6399 | 1.42396 | 0.711979 | − | 0.702200i | \(-0.247799\pi\) | ||||
0.711979 | + | 0.702200i | \(0.247799\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.5481 | −0.674650 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.89547 | 0.411633 | 0.205817 | − | 0.978591i | \(-0.434015\pi\) | ||||
0.205817 | + | 0.978591i | \(0.434015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.5283 | −1.45584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.3487 | 0.661152 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.24621 | 0.287201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.65945 | 0.122024 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.07411 | −0.232327 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.13224 | 0.417263 | 0.208631 | − | 0.977994i | \(-0.433099\pi\) | ||||
0.208631 | + | 0.977994i | \(0.433099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.7083 | 1.12660 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.34868 | 0.288875 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.47179 | 0.157646 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2085 | −0.643849 | −0.321924 | − | 0.946765i | \(-0.604330\pi\) | ||||
−0.321924 | + | 0.946765i | \(0.604330\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.6282 | −1.24939 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.1760 | 1.04592 | 0.522960 | − | 0.852357i | \(-0.324828\pi\) | ||||
0.522960 | + | 0.852357i | \(0.324828\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.9077 | −0.896599 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.49342 | 0.0671244 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 50.5743 | 2.26857 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.19831 | 0.0984099 | 0.0492050 | − | 0.998789i | \(-0.484331\pi\) | ||||
0.0492050 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.2462 | 0.993887 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 44.0461 | 1.96392 | 0.981959 | − | 0.189092i | \(-0.0605545\pi\) | ||||
0.981959 | + | 0.189092i | \(0.0605545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.21036 | 0.409856 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34.2462 | −1.52093 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.09254 | −0.403020 | −0.201510 | − | 0.979486i | \(-0.564585\pi\) | ||||
−0.201510 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.49619 | 0.375850 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.7907 | 0.653025 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.69736 | −0.206991 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.645301 | 0.0283803 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.88001 | 0.0825235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.1231 | −0.750177 | −0.375088 | − | 0.926989i | \(-0.622388\pi\) | ||||
−0.375088 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.6112 | 1.16362 | 0.581812 | − | 0.813323i | \(-0.302344\pi\) | ||||
0.581812 | + | 0.813323i | \(0.302344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.34868 | 0.277079 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.7332 | −1.38232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.09439 | 0.351267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7388 | −0.551780 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.376394 | 0.0162729 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.5944 | 0.500337 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.3427 | −1.09159 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.5941 | 1.35834 | 0.679168 | − | 0.733983i | \(-0.262341\pi\) | ||||
0.679168 | + | 0.733983i | \(0.262341\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −37.5476 | −1.61132 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.0369 | 0.815452 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7009 | −0.970622 | −0.485311 | − | 0.874342i | \(-0.661294\pi\) | ||||
−0.485311 | + | 0.874342i | \(0.661294\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.38347 | −0.0590451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5435 | 0.662175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.8840 | −0.717982 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.52821 | 0.277107 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.1292 | 1.48847 | 0.744236 | − | 0.667917i | \(-0.232814\pi\) | ||||
0.744236 | + | 0.667917i | \(0.232814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8813 | 0.587115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1454 | −0.597219 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.0511 | −1.35079 | −0.675397 | − | 0.737455i | \(-0.736028\pi\) | ||||
−0.675397 | + | 0.737455i | \(0.736028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.94252 | 0.123793 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.4593 | 1.19518 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.0575 | −0.924700 | −0.462350 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462350 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.49242 | −0.355397 | −0.177698 | − | 0.984085i | \(-0.556865\pi\) | ||||
−0.177698 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.61553 | −0.318143 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.1554 | 1.13050 | 0.565248 | − | 0.824921i | \(-0.308780\pi\) | ||||
0.565248 | + | 0.824921i | \(0.308780\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.0394 | −0.666573 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.9393 | −2.11332 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.0304 | −0.995239 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.31891 | 0.137220 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.8322 | 1.27258 | 0.636290 | − | 0.771450i | \(-0.280468\pi\) | ||||
0.636290 | + | 0.771450i | \(0.280468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.7765 | 1.02090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.69214 | −0.275278 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.7559 | −1.13980 | −0.569899 | − | 0.821715i | \(-0.693018\pi\) | ||||
−0.569899 | + | 0.821715i | \(0.693018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8482 | 0.567720 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.28000 | 0.257023 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.7712 | 1.25728 | 0.628638 | − | 0.777698i | \(-0.283613\pi\) | ||||
0.628638 | + | 0.777698i | \(0.283613\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.9830 | −0.733541 | −0.366771 | − | 0.930311i | \(-0.619537\pi\) | ||||
−0.366771 | + | 0.930311i | \(0.619537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.35476 | −0.177339 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.92730 | −0.159668 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.3220 | 0.743668 | 0.371834 | − | 0.928299i | \(-0.378729\pi\) | ||||
0.371834 | + | 0.928299i | \(0.378729\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 37.1056 | 1.50359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.43408 | 0.0580168 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.4451 | 1.43162 | 0.715808 | − | 0.698297i | \(-0.246059\pi\) | ||||
0.715808 | + | 0.698297i | \(0.246059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.36575 | −0.135720 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.1567 | 1.73742 | 0.868712 | − | 0.495318i | \(-0.164948\pi\) | ||||
0.868712 | + | 0.495318i | \(0.164948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.81133 | −0.233577 | −0.116789 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116789 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56155 | 0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.0413 | 1.52409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0444 | 0.441070 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.2398 | 0.567777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.4626 | 1.09327 | 0.546635 | − | 0.837371i | \(-0.315908\pi\) | ||||
0.546635 | + | 0.837371i | \(0.315908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.9567 | 0.952194 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00357 | −0.238244 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −56.3202 | −2.23149 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.98544 | 0.276340 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.7938 | 1.49277 | 0.746383 | − | 0.665517i | \(-0.231789\pi\) | ||||
0.746383 | + | 0.665517i | \(0.231789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.5343 | −0.494304 | −0.247152 | − | 0.968977i | \(-0.579495\pi\) | ||||
−0.247152 | + | 0.968977i | \(0.579495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.66759 | 0.144411 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5133 | 0.845774 | 0.422887 | − | 0.906183i | \(-0.361017\pi\) | ||||
0.422887 | + | 0.906183i | \(0.361017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.3342 | 1.50475 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.1469 | 2.31815 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.9011 | 0.778790 | 0.389395 | − | 0.921071i | \(-0.372684\pi\) | ||||
0.389395 | + | 0.921071i | \(0.372684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.9606 | 0.779927 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.17351 | 0.0457831 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.95773 | 0.193126 | 0.0965628 | − | 0.995327i | \(-0.469215\pi\) | ||||
0.0965628 | + | 0.995327i | \(0.469215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.4360 | −1.22087 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.8123 | −0.419284 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.84461 | 0.226304 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.6084 | −1.06740 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.55197 | −0.252936 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.5176 | −1.09927 | −0.549637 | − | 0.835404i | \(-0.685234\pi\) | ||||
−0.549637 | + | 0.835404i | \(0.685234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.6214 | 1.10001 | 0.550004 | − | 0.835162i | \(-0.314626\pi\) | ||||
0.550004 | + | 0.835162i | \(0.314626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1150 | −0.541683 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.4890 | 0.516898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.3983 | −0.436144 | −0.218072 | − | 0.975933i | \(-0.569977\pi\) | ||||
−0.218072 | + | 0.975933i | \(0.569977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.7609 | −0.449362 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.21644 | 0.199020 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53.4040 | −2.03453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.1898 | −1.71910 | −0.859550 | − | 0.511051i | \(-0.829256\pi\) | ||||
−0.859550 | + | 0.511051i | \(0.829256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.07170 | −0.230645 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.3891 | −0.469945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.34160 | −0.278083 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.8629 | −0.486521 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4871 | 1.52918 | 0.764588 | − | 0.644520i | \(-0.222943\pi\) | ||||
0.764588 | + | 0.644520i | \(0.222943\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.1181 | −0.419327 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.378902 | 0.0142703 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.4458 | −1.40830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6443 | −1.56398 | −0.781992 | − | 0.623288i | \(-0.785796\pi\) | ||||
−0.781992 | + | 0.623288i | \(0.785796\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.33206 | −0.0874591 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.31640 | 0.348902 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.7180 | 0.587820 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.47424 | −0.167093 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.2288 | −1.83592 | −0.917961 | − | 0.396670i | \(-0.870166\pi\) | ||||
−0.917961 | + | 0.396670i | \(0.870166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.0977 | 0.711235 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.30977 | −0.271853 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.84461 | 0.217063 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.9581 | −1.03691 | −0.518455 | − | 0.855105i | \(-0.673493\pi\) | ||||
−0.518455 | + | 0.855105i | \(0.673493\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.6655 | −0.689427 | −0.344714 | − | 0.938708i | \(-0.612024\pi\) | ||||
−0.344714 | + | 0.938708i | \(0.612024\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.8805 | −0.548874 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.6237 | −0.759682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50407 | −0.0921136 | −0.0460568 | − | 0.998939i | \(-0.514666\pi\) | ||||
−0.0460568 | + | 0.998939i | \(0.514666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.5445 | 0.901664 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.69736 | −0.172330 | −0.0861648 | − | 0.996281i | \(-0.527461\pi\) | ||||
−0.0861648 | + | 0.996281i | \(0.527461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.13124 | −0.0780826 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.03585 | −0.257428 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.53027 | −0.0559150 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0720 | 0.586477 | 0.293239 | − | 0.956039i | \(-0.405267\pi\) | ||||
0.293239 | + | 0.956039i | \(0.405267\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.0174 | −1.05745 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.787129 | 0.0286465 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.8357 | −0.939014 | −0.469507 | − | 0.882929i | \(-0.655568\pi\) | ||||
−0.469507 | + | 0.882929i | \(0.655568\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.15288 | 0.150740 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.6005 | 0.565518 | 0.282759 | − | 0.959191i | \(-0.408750\pi\) | ||||
0.282759 | + | 0.959191i | \(0.408750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −77.3968 | −2.80195 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.91274 | 0.0691553 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 85.1919 | 3.07610 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.7722 | −1.36210 | −0.681050 | − | 0.732237i | \(-0.738476\pi\) | ||||
−0.681050 | + | 0.732237i | \(0.738476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.8518 | 1.61530 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.9078 | −1.54329 | −0.771643 | − | 0.636056i | \(-0.780565\pi\) | ||||
−0.771643 | + | 0.636056i | \(0.780565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.31640 | 0.334655 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.5412 | −0.952162 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.73215 | 0.205376 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.0823 | 1.18378 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.5051 | 1.16164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.18873 | −0.327960 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.5324 | 1.19530 | 0.597650 | − | 0.801757i | \(-0.296101\pi\) | ||||
0.597650 | + | 0.801757i | \(0.296101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.3741 | −0.511731 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9632 | −0.425361 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.5608 | −0.517068 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.1100 | −0.500428 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.7488 | 1.16002 | 0.580012 | − | 0.814608i | \(-0.303048\pi\) | ||||
0.580012 | + | 0.814608i | \(0.303048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.826486 | 0.0292390 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.25435 | 0.185653 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.55764 | 0.196125 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.06562 | −0.143294 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.4206 | −0.930049 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8513 | 1.01436 | 0.507179 | − | 0.861841i | \(-0.330688\pi\) | ||||
0.507179 | + | 0.861841i | \(0.330688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.1791 | −1.27042 | −0.635211 | − | 0.772339i | \(-0.719087\pi\) | ||||
−0.635211 | + | 0.772339i | \(0.719087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.79706 | 0.0630257 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.6928 | 0.619752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.24621 | −0.218527 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.4934 | −0.471498 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.73752 | 0.200241 | 0.100120 | − | 0.994975i | \(-0.468077\pi\) | ||||
0.100120 | + | 0.994975i | \(0.468077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.87333 | 0.239589 | 0.119795 | − | 0.992799i | \(-0.461776\pi\) | ||||
0.119795 | + | 0.992799i | \(0.461776\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.15288 | 0.144585 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7332 | 0.686191 | 0.343095 | − | 0.939301i | \(-0.388525\pi\) | ||||
0.343095 | + | 0.939301i | \(0.388525\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.88833 | −0.100316 | −0.0501580 | − | 0.998741i | \(-0.515972\pi\) | ||||
−0.0501580 | + | 0.998741i | \(0.515972\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.02108 | −0.139490 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.4583 | −1.12461 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.2462 | −0.493010 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.8137 | 1.79094 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.1904 | −0.835147 | −0.417573 | − | 0.908643i | \(-0.637119\pi\) | ||||
−0.417573 | + | 0.908643i | \(0.637119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.15951 | 0.177914 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −42.8986 | −1.47751 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9309 | 0.754445 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.9669 | 0.548630 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.69135 | −0.126687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.18059 | −0.143309 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.5381 | 0.942887 | 0.471444 | − | 0.881896i | \(-0.343733\pi\) | ||||
0.471444 | + | 0.881896i | \(0.343733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.49342 | −0.0510740 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.3995 | −0.594357 | −0.297178 | − | 0.954822i | \(-0.596046\pi\) | ||||
−0.297178 | + | 0.954822i | \(0.596046\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.24560 | −0.0424993 | −0.0212497 | − | 0.999774i | \(-0.506764\pi\) | ||||
−0.0212497 | + | 0.999774i | \(0.506764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6839 | 0.466345 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.60383 | 0.156716 | 0.0783580 | − | 0.996925i | \(-0.475032\pi\) | ||||
0.0783580 | + | 0.996925i | \(0.475032\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.20394 | −0.0409352 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.42931 | 0.286274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0444 | −0.374655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.8330 | −1.55299 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.94959 | −0.0659837 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.06562 | −0.137443 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.8276 | 1.14228 | 0.571138 | − | 0.820854i | \(-0.306502\pi\) | ||||
0.571138 | + | 0.820854i | \(0.306502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −53.2799 | −1.79709 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.1134 | 0.879782 | 0.439891 | − | 0.898051i | \(-0.355017\pi\) | ||||
0.439891 | + | 0.898051i | \(0.355017\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.5412 | 1.83546 | 0.917729 | − | 0.397206i | \(-0.130020\pi\) | ||||
0.917729 | + | 0.397206i | \(0.130020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.5087 | 0.756621 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6201 | −0.759509 | −0.379754 | − | 0.925087i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925087i | \(0.623991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.4082 | 0.818626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.6162 | 0.623666 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.645301 | −0.0215942 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.42495 | −0.248189 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.22914 | 0.308152 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54.4508 | 1.81603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.7776 | −1.02535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.9110 | −0.496208 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0450 | 0.799284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.62149 | 0.120250 | 0.0601248 | − | 0.998191i | \(-0.480850\pi\) | ||||
0.0601248 | + | 0.998191i | \(0.480850\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.17211 | −0.171548 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.9241 | −0.892034 | −0.446017 | − | 0.895025i | \(-0.647158\pi\) | ||||
−0.446017 | + | 0.895025i | \(0.647158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.3210 | −1.10277 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.84712 | −0.127182 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −81.1524 | −2.67989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.5059 | 0.643441 | 0.321721 | − | 0.946835i | \(-0.395739\pi\) | ||||
0.321721 | + | 0.946835i | \(0.395739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.33206 | 0.0768440 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 73.5204 | 2.41995 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.18059 | −0.137457 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.63782 | 0.0866373 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.2139 | 0.892860 | 0.446430 | − | 0.894819i | \(-0.352695\pi\) | ||||
0.446430 | + | 0.894819i | \(0.352695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.3427 | 0.830572 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.0273 | −0.721142 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.05854 | 0.296246 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85626 | 0.125978 | 0.0629892 | − | 0.998014i | \(-0.479937\pi\) | ||||
0.0629892 | + | 0.998014i | \(0.479937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 51.3069 | 1.67434 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.6471 | −1.97704 | −0.988519 | − | 0.151097i | \(-0.951720\pi\) | ||||
−0.988519 | + | 0.151097i | \(0.951720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.15539 | 0.0701890 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.6112 | −0.735541 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.11954 | 0.0363801 | 0.0181901 | − | 0.999835i | \(-0.494210\pi\) | ||||
0.0181901 | + | 0.999835i | \(0.494210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.3510 | 0.400931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6481 | −0.637132 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.8590 | 0.481331 | 0.240666 | − | 0.970608i | \(-0.422634\pi\) | ||||
0.240666 | + | 0.970608i | \(0.422634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.87689 | 0.157813 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.2720 | 0.784601 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.8155 | 1.54404 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.7953 | 1.79985 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.211365 | −0.00681114 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.2714 | 0.330649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.5718 | −1.24039 | −0.620193 | − | 0.784449i | \(-0.712946\pi\) | ||||
−0.620193 | + | 0.784449i | \(0.712946\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.1454 | 0.454416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.4984 | 0.818284 | 0.409142 | − | 0.912471i | \(-0.365828\pi\) | ||||
0.409142 | + | 0.912471i | \(0.365828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.3694 | 1.61477 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.22914 | 0.295569 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.8952 | −0.508533 | −0.254267 | − | 0.967134i | \(-0.581834\pi\) | ||||
−0.254267 | + | 0.967134i | \(0.581834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.8840 | 0.795297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6902 | −0.341313 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.50587 | 0.0799247 | 0.0399624 | − | 0.999201i | \(-0.487276\pi\) | ||||
0.0399624 | + | 0.999201i | \(0.487276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.28557 | 0.136550 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.54047 | −0.0490337 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.34868 | −0.0746837 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5272 | −0.397938 | −0.198969 | − | 0.980006i | \(-0.563759\pi\) | ||||
−0.198969 | + | 0.980006i | \(0.563759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.46220 | 0.0781356 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.02164 | −0.127494 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.34803 | −0.296055 | −0.148028 | − | 0.988983i | \(-0.547292\pi\) | ||||
−0.148028 | + | 0.988983i | \(0.547292\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.2506 | −0.735616 |
(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 | 1840.2.a.u.1.1 | 4 | ||
4.3 | odd | 2 | 115.2.a.c.1.2 | ✓ | 4 | ||
5.4 | even | 2 | 9200.2.a.cl.1.4 | 4 | |||
8.3 | odd | 2 | 7360.2.a.cj.1.2 | 4 | |||
8.5 | even | 2 | 7360.2.a.cg.1.3 | 4 | |||
12.11 | even | 2 | 1035.2.a.o.1.3 | 4 | |||
20.3 | even | 4 | 575.2.b.e.24.5 | 8 | |||
20.7 | even | 4 | 575.2.b.e.24.4 | 8 | |||
20.19 | odd | 2 | 575.2.a.h.1.3 | 4 | |||
28.27 | even | 2 | 5635.2.a.v.1.2 | 4 | |||
60.59 | even | 2 | 5175.2.a.bx.1.2 | 4 | |||
92.91 | even | 2 | 2645.2.a.m.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.a.c.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
575.2.a.h.1.3 | 4 | 20.19 | odd | 2 | |||
575.2.b.e.24.4 | 8 | 20.7 | even | 4 | |||
575.2.b.e.24.5 | 8 | 20.3 | even | 4 | |||
1035.2.a.o.1.3 | 4 | 12.11 | even | 2 | |||
1840.2.a.u.1.1 | 4 | 1.1 | even | 1 | trivial | ||
2645.2.a.m.1.2 | 4 | 92.91 | even | 2 | |||
5175.2.a.bx.1.2 | 4 | 60.59 | even | 2 | |||
5635.2.a.v.1.2 | 4 | 28.27 | even | 2 | |||
7360.2.a.cg.1.3 | 4 | 8.5 | even | 2 | |||
7360.2.a.cj.1.2 | 4 | 8.3 | odd | 2 | |||
9200.2.a.cl.1.4 | 4 | 5.4 | even | 2 |