Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32740 | −1.64572 | −0.822859 | − | 0.568246i | \(-0.807622\pi\) | ||||
−0.822859 | + | 0.568246i | \(0.807622\pi\) | |||||||
\(3\) | −3.07559 | −1.77569 | −0.887847 | − | 0.460138i | \(-0.847800\pi\) | ||||
−0.887847 | + | 0.460138i | \(0.847800\pi\) | |||||||
\(4\) | 3.41677 | 1.70839 | ||||||||
\(5\) | −1.26158 | −0.564196 | −0.282098 | − | 0.959386i | \(-0.591030\pi\) | ||||
−0.282098 | + | 0.959386i | \(0.591030\pi\) | |||||||
\(6\) | 7.15812 | 2.92229 | ||||||||
\(7\) | 0.599145 | 0.226456 | 0.113228 | − | 0.993569i | \(-0.463881\pi\) | ||||
0.113228 | + | 0.993569i | \(0.463881\pi\) | |||||||
\(8\) | −3.29739 | −1.16580 | ||||||||
\(9\) | 6.45928 | 2.15309 | ||||||||
\(10\) | 2.93620 | 0.928506 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −10.5086 | −3.03357 | ||||||||
\(13\) | 1.48585 | 0.412101 | 0.206051 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206051 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(14\) | −1.39445 | −0.372682 | ||||||||
\(15\) | 3.88011 | 1.00184 | ||||||||
\(16\) | 0.840783 | 0.210196 | ||||||||
\(17\) | 3.03080 | 0.735077 | 0.367539 | − | 0.930008i | \(-0.380201\pi\) | ||||
0.367539 | + | 0.930008i | \(0.380201\pi\) | |||||||
\(18\) | −15.0333 | −3.54338 | ||||||||
\(19\) | 5.86101 | 1.34461 | 0.672303 | − | 0.740276i | \(-0.265305\pi\) | ||||
0.672303 | + | 0.740276i | \(0.265305\pi\) | |||||||
\(20\) | −4.31053 | −0.963864 | ||||||||
\(21\) | −1.84273 | −0.402116 | ||||||||
\(22\) | −2.32740 | −0.496202 | ||||||||
\(23\) | −1.31387 | −0.273961 | −0.136981 | − | 0.990574i | \(-0.543740\pi\) | ||||
−0.136981 | + | 0.990574i | \(0.543740\pi\) | |||||||
\(24\) | 10.1414 | 2.07011 | ||||||||
\(25\) | −3.40842 | −0.681683 | ||||||||
\(26\) | −3.45817 | −0.678202 | ||||||||
\(27\) | −10.6393 | −2.04754 | ||||||||
\(28\) | 2.04714 | 0.386873 | ||||||||
\(29\) | 6.74213 | 1.25198 | 0.625991 | − | 0.779830i | \(-0.284695\pi\) | ||||
0.625991 | + | 0.779830i | \(0.284695\pi\) | |||||||
\(30\) | −9.03054 | −1.64874 | ||||||||
\(31\) | 2.93038 | 0.526312 | 0.263156 | − | 0.964753i | \(-0.415237\pi\) | ||||
0.263156 | + | 0.964753i | \(0.415237\pi\) | |||||||
\(32\) | 4.63794 | 0.819880 | ||||||||
\(33\) | −3.07559 | −0.535392 | ||||||||
\(34\) | −7.05387 | −1.20973 | ||||||||
\(35\) | −0.755869 | −0.127765 | ||||||||
\(36\) | 22.0699 | 3.67831 | ||||||||
\(37\) | 0.755218 | 0.124157 | 0.0620786 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620786 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(38\) | −13.6409 | −2.21284 | ||||||||
\(39\) | −4.56988 | −0.731766 | ||||||||
\(40\) | 4.15992 | 0.657741 | ||||||||
\(41\) | 5.51301 | 0.860988 | 0.430494 | − | 0.902593i | \(-0.358339\pi\) | ||||
0.430494 | + | 0.902593i | \(0.358339\pi\) | |||||||
\(42\) | 4.28876 | 0.661769 | ||||||||
\(43\) | −9.33971 | −1.42429 | −0.712146 | − | 0.702031i | \(-0.752277\pi\) | ||||
−0.712146 | + | 0.702031i | \(0.752277\pi\) | |||||||
\(44\) | 3.41677 | 0.515098 | ||||||||
\(45\) | −8.14889 | −1.21477 | ||||||||
\(46\) | 3.05790 | 0.450863 | ||||||||
\(47\) | 8.42855 | 1.22943 | 0.614715 | − | 0.788749i | \(-0.289271\pi\) | ||||
0.614715 | + | 0.788749i | \(0.289271\pi\) | |||||||
\(48\) | −2.58591 | −0.373244 | ||||||||
\(49\) | −6.64103 | −0.948718 | ||||||||
\(50\) | 7.93273 | 1.12186 | ||||||||
\(51\) | −9.32151 | −1.30527 | ||||||||
\(52\) | 5.07682 | 0.704028 | ||||||||
\(53\) | −11.8926 | −1.63358 | −0.816788 | − | 0.576938i | \(-0.804247\pi\) | ||||
−0.816788 | + | 0.576938i | \(0.804247\pi\) | |||||||
\(54\) | 24.7619 | 3.36967 | ||||||||
\(55\) | −1.26158 | −0.170111 | ||||||||
\(56\) | −1.97561 | −0.264003 | ||||||||
\(57\) | −18.0261 | −2.38761 | ||||||||
\(58\) | −15.6916 | −2.06041 | ||||||||
\(59\) | −2.97044 | −0.386719 | −0.193359 | − | 0.981128i | \(-0.561938\pi\) | ||||
−0.193359 | + | 0.981128i | \(0.561938\pi\) | |||||||
\(60\) | 13.2574 | 1.71153 | ||||||||
\(61\) | −1.92843 | −0.246910 | −0.123455 | − | 0.992350i | \(-0.539397\pi\) | ||||
−0.123455 | + | 0.992350i | \(0.539397\pi\) | |||||||
\(62\) | −6.82016 | −0.866162 | ||||||||
\(63\) | 3.87005 | 0.487580 | ||||||||
\(64\) | −12.4759 | −1.55949 | ||||||||
\(65\) | −1.87452 | −0.232506 | ||||||||
\(66\) | 7.15812 | 0.881104 | ||||||||
\(67\) | −6.53515 | −0.798396 | −0.399198 | − | 0.916865i | \(-0.630711\pi\) | ||||
−0.399198 | + | 0.916865i | \(0.630711\pi\) | |||||||
\(68\) | 10.3556 | 1.25580 | ||||||||
\(69\) | 4.04094 | 0.486472 | ||||||||
\(70\) | 1.75921 | 0.210265 | ||||||||
\(71\) | −8.59133 | −1.01960 | −0.509802 | − | 0.860292i | \(-0.670281\pi\) | ||||
−0.509802 | + | 0.860292i | \(0.670281\pi\) | |||||||
\(72\) | −21.2987 | −2.51008 | ||||||||
\(73\) | −5.44367 | −0.637134 | −0.318567 | − | 0.947900i | \(-0.603202\pi\) | ||||
−0.318567 | + | 0.947900i | \(0.603202\pi\) | |||||||
\(74\) | −1.75769 | −0.204328 | ||||||||
\(75\) | 10.4829 | 1.21046 | ||||||||
\(76\) | 20.0257 | 2.29711 | ||||||||
\(77\) | 0.599145 | 0.0682789 | ||||||||
\(78\) | 10.6359 | 1.20428 | ||||||||
\(79\) | −2.92252 | −0.328809 | −0.164404 | − | 0.986393i | \(-0.552570\pi\) | ||||
−0.164404 | + | 0.986393i | \(0.552570\pi\) | |||||||
\(80\) | −1.06072 | −0.118592 | ||||||||
\(81\) | 13.3444 | 1.48272 | ||||||||
\(82\) | −12.8310 | −1.41694 | ||||||||
\(83\) | 6.65119 | 0.730063 | 0.365031 | − | 0.930995i | \(-0.381058\pi\) | ||||
0.365031 | + | 0.930995i | \(0.381058\pi\) | |||||||
\(84\) | −6.29618 | −0.686969 | ||||||||
\(85\) | −3.82360 | −0.414727 | ||||||||
\(86\) | 21.7372 | 2.34398 | ||||||||
\(87\) | −20.7361 | −2.22314 | ||||||||
\(88\) | −3.29739 | −0.351503 | ||||||||
\(89\) | −6.64813 | −0.704700 | −0.352350 | − | 0.935868i | \(-0.614617\pi\) | ||||
−0.352350 | + | 0.935868i | \(0.614617\pi\) | |||||||
\(90\) | 18.9657 | 1.99916 | ||||||||
\(91\) | 0.890242 | 0.0933227 | ||||||||
\(92\) | −4.48920 | −0.468032 | ||||||||
\(93\) | −9.01267 | −0.934570 | ||||||||
\(94\) | −19.6166 | −2.02330 | ||||||||
\(95\) | −7.39413 | −0.758621 | ||||||||
\(96\) | −14.2644 | −1.45586 | ||||||||
\(97\) | −12.4665 | −1.26578 | −0.632891 | − | 0.774241i | \(-0.718132\pi\) | ||||
−0.632891 | + | 0.774241i | \(0.718132\pi\) | |||||||
\(98\) | 15.4563 | 1.56132 | ||||||||
\(99\) | 6.45928 | 0.649182 | ||||||||
\(100\) | −11.6458 | −1.16458 | ||||||||
\(101\) | 4.01472 | 0.399479 | 0.199740 | − | 0.979849i | \(-0.435990\pi\) | ||||
0.199740 | + | 0.979849i | \(0.435990\pi\) | |||||||
\(102\) | 21.6948 | 2.14811 | ||||||||
\(103\) | −9.06336 | −0.893040 | −0.446520 | − | 0.894774i | \(-0.647337\pi\) | ||||
−0.446520 | + | 0.894774i | \(0.647337\pi\) | |||||||
\(104\) | −4.89943 | −0.480429 | ||||||||
\(105\) | 2.32475 | 0.226872 | ||||||||
\(106\) | 27.6788 | 2.68840 | ||||||||
\(107\) | 4.43708 | 0.428949 | 0.214474 | − | 0.976730i | \(-0.431196\pi\) | ||||
0.214474 | + | 0.976730i | \(0.431196\pi\) | |||||||
\(108\) | −36.3522 | −3.49799 | ||||||||
\(109\) | 13.3755 | 1.28114 | 0.640570 | − | 0.767900i | \(-0.278698\pi\) | ||||
0.640570 | + | 0.767900i | \(0.278698\pi\) | |||||||
\(110\) | 2.93620 | 0.279955 | ||||||||
\(111\) | −2.32274 | −0.220465 | ||||||||
\(112\) | 0.503751 | 0.0476000 | ||||||||
\(113\) | −7.11965 | −0.669760 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(114\) | 41.9538 | 3.92933 | ||||||||
\(115\) | 1.65756 | 0.154568 | ||||||||
\(116\) | 23.0363 | 2.13887 | ||||||||
\(117\) | 9.59754 | 0.887293 | ||||||||
\(118\) | 6.91339 | 0.636430 | ||||||||
\(119\) | 1.81589 | 0.166462 | ||||||||
\(120\) | −12.7942 | −1.16795 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.48821 | 0.406343 | ||||||||
\(123\) | −16.9558 | −1.52885 | ||||||||
\(124\) | 10.0125 | 0.899145 | ||||||||
\(125\) | 10.6079 | 0.948798 | ||||||||
\(126\) | −9.00713 | −0.802419 | ||||||||
\(127\) | −1.34382 | −0.119245 | −0.0596223 | − | 0.998221i | \(-0.518990\pi\) | ||||
−0.0596223 | + | 0.998221i | \(0.518990\pi\) | |||||||
\(128\) | 19.7604 | 1.74659 | ||||||||
\(129\) | 28.7252 | 2.52911 | ||||||||
\(130\) | 4.36275 | 0.382639 | ||||||||
\(131\) | −2.41096 | −0.210646 | −0.105323 | − | 0.994438i | \(-0.533588\pi\) | ||||
−0.105323 | + | 0.994438i | \(0.533588\pi\) | |||||||
\(132\) | −10.5086 | −0.914656 | ||||||||
\(133\) | 3.51159 | 0.304494 | ||||||||
\(134\) | 15.2099 | 1.31393 | ||||||||
\(135\) | 13.4224 | 1.15521 | ||||||||
\(136\) | −9.99372 | −0.856955 | ||||||||
\(137\) | −4.70465 | −0.401945 | −0.200973 | − | 0.979597i | \(-0.564410\pi\) | ||||
−0.200973 | + | 0.979597i | \(0.564410\pi\) | |||||||
\(138\) | −9.40486 | −0.800595 | ||||||||
\(139\) | −8.67075 | −0.735443 | −0.367722 | − | 0.929936i | \(-0.619862\pi\) | ||||
−0.367722 | + | 0.929936i | \(0.619862\pi\) | |||||||
\(140\) | −2.58263 | −0.218272 | ||||||||
\(141\) | −25.9228 | −2.18309 | ||||||||
\(142\) | 19.9954 | 1.67798 | ||||||||
\(143\) | 1.48585 | 0.124253 | ||||||||
\(144\) | 5.43085 | 0.452571 | ||||||||
\(145\) | −8.50573 | −0.706363 | ||||||||
\(146\) | 12.6696 | 1.04854 | ||||||||
\(147\) | 20.4251 | 1.68463 | ||||||||
\(148\) | 2.58041 | 0.212108 | ||||||||
\(149\) | 15.8353 | 1.29728 | 0.648641 | − | 0.761094i | \(-0.275338\pi\) | ||||
0.648641 | + | 0.761094i | \(0.275338\pi\) | |||||||
\(150\) | −24.3979 | −1.99208 | ||||||||
\(151\) | −7.08609 | −0.576658 | −0.288329 | − | 0.957531i | \(-0.593100\pi\) | ||||
−0.288329 | + | 0.957531i | \(0.593100\pi\) | |||||||
\(152\) | −19.3260 | −1.56755 | ||||||||
\(153\) | 19.5768 | 1.58269 | ||||||||
\(154\) | −1.39445 | −0.112368 | ||||||||
\(155\) | −3.69691 | −0.296943 | ||||||||
\(156\) | −15.6142 | −1.25014 | ||||||||
\(157\) | 9.84115 | 0.785409 | 0.392704 | − | 0.919665i | \(-0.371540\pi\) | ||||
0.392704 | + | 0.919665i | \(0.371540\pi\) | |||||||
\(158\) | 6.80186 | 0.541127 | ||||||||
\(159\) | 36.5768 | 2.90073 | ||||||||
\(160\) | −5.85113 | −0.462572 | ||||||||
\(161\) | −0.787201 | −0.0620401 | ||||||||
\(162\) | −31.0578 | −2.44013 | ||||||||
\(163\) | −19.5654 | −1.53248 | −0.766240 | − | 0.642554i | \(-0.777875\pi\) | ||||
−0.766240 | + | 0.642554i | \(0.777875\pi\) | |||||||
\(164\) | 18.8367 | 1.47090 | ||||||||
\(165\) | 3.88011 | 0.302066 | ||||||||
\(166\) | −15.4800 | −1.20148 | ||||||||
\(167\) | 6.46145 | 0.500002 | 0.250001 | − | 0.968246i | \(-0.419569\pi\) | ||||
0.250001 | + | 0.968246i | \(0.419569\pi\) | |||||||
\(168\) | 6.07619 | 0.468788 | ||||||||
\(169\) | −10.7922 | −0.830172 | ||||||||
\(170\) | 8.89902 | 0.682524 | ||||||||
\(171\) | 37.8579 | 2.89506 | ||||||||
\(172\) | −31.9117 | −2.43324 | ||||||||
\(173\) | −7.20310 | −0.547642 | −0.273821 | − | 0.961781i | \(-0.588288\pi\) | ||||
−0.273821 | + | 0.961781i | \(0.588288\pi\) | |||||||
\(174\) | 48.2610 | 3.65866 | ||||||||
\(175\) | −2.04214 | −0.154371 | ||||||||
\(176\) | 0.840783 | 0.0633764 | ||||||||
\(177\) | 9.13587 | 0.686694 | ||||||||
\(178\) | 15.4728 | 1.15974 | ||||||||
\(179\) | −8.81980 | −0.659223 | −0.329612 | − | 0.944117i | \(-0.606918\pi\) | ||||
−0.329612 | + | 0.944117i | \(0.606918\pi\) | |||||||
\(180\) | −27.8429 | −2.07529 | ||||||||
\(181\) | −9.19110 | −0.683169 | −0.341585 | − | 0.939851i | \(-0.610964\pi\) | ||||
−0.341585 | + | 0.939851i | \(0.610964\pi\) | |||||||
\(182\) | −2.07194 | −0.153583 | ||||||||
\(183\) | 5.93105 | 0.438436 | ||||||||
\(184\) | 4.33235 | 0.319385 | ||||||||
\(185\) | −0.952768 | −0.0700489 | ||||||||
\(186\) | 20.9761 | 1.53804 | ||||||||
\(187\) | 3.03080 | 0.221634 | ||||||||
\(188\) | 28.7984 | 2.10034 | ||||||||
\(189\) | −6.37451 | −0.463677 | ||||||||
\(190\) | 17.2091 | 1.24848 | ||||||||
\(191\) | 5.68987 | 0.411704 | 0.205852 | − | 0.978583i | \(-0.434003\pi\) | ||||
0.205852 | + | 0.978583i | \(0.434003\pi\) | |||||||
\(192\) | 38.3708 | 2.76917 | ||||||||
\(193\) | 12.9483 | 0.932037 | 0.466019 | − | 0.884775i | \(-0.345688\pi\) | ||||
0.466019 | + | 0.884775i | \(0.345688\pi\) | |||||||
\(194\) | 29.0145 | 2.08312 | ||||||||
\(195\) | 5.76527 | 0.412859 | ||||||||
\(196\) | −22.6909 | −1.62078 | ||||||||
\(197\) | 22.2473 | 1.58505 | 0.792527 | − | 0.609837i | \(-0.208765\pi\) | ||||
0.792527 | + | 0.609837i | \(0.208765\pi\) | |||||||
\(198\) | −15.0333 | −1.06837 | ||||||||
\(199\) | 14.0715 | 0.997500 | 0.498750 | − | 0.866746i | \(-0.333793\pi\) | ||||
0.498750 | + | 0.866746i | \(0.333793\pi\) | |||||||
\(200\) | 11.2389 | 0.794708 | ||||||||
\(201\) | 20.0995 | 1.41771 | ||||||||
\(202\) | −9.34383 | −0.657430 | ||||||||
\(203\) | 4.03951 | 0.283518 | ||||||||
\(204\) | −31.8495 | −2.22991 | ||||||||
\(205\) | −6.95511 | −0.485766 | ||||||||
\(206\) | 21.0940 | 1.46969 | ||||||||
\(207\) | −8.48667 | −0.589864 | ||||||||
\(208\) | 1.24928 | 0.0866220 | ||||||||
\(209\) | 5.86101 | 0.405414 | ||||||||
\(210\) | −5.41061 | −0.373367 | ||||||||
\(211\) | −11.8254 | −0.814093 | −0.407046 | − | 0.913408i | \(-0.633441\pi\) | ||||
−0.407046 | + | 0.913408i | \(0.633441\pi\) | |||||||
\(212\) | −40.6343 | −2.79078 | ||||||||
\(213\) | 26.4234 | 1.81050 | ||||||||
\(214\) | −10.3268 | −0.705928 | ||||||||
\(215\) | 11.7828 | 0.803580 | ||||||||
\(216\) | 35.0820 | 2.38703 | ||||||||
\(217\) | 1.75573 | 0.119186 | ||||||||
\(218\) | −31.1301 | −2.10839 | ||||||||
\(219\) | 16.7425 | 1.13135 | ||||||||
\(220\) | −4.31053 | −0.290616 | ||||||||
\(221\) | 4.50332 | 0.302926 | ||||||||
\(222\) | 5.40595 | 0.362823 | ||||||||
\(223\) | −12.8055 | −0.857519 | −0.428759 | − | 0.903419i | \(-0.641049\pi\) | ||||
−0.428759 | + | 0.903419i | \(0.641049\pi\) | |||||||
\(224\) | 2.77880 | 0.185666 | ||||||||
\(225\) | −22.0159 | −1.46773 | ||||||||
\(226\) | 16.5702 | 1.10224 | ||||||||
\(227\) | −14.5984 | −0.968930 | −0.484465 | − | 0.874811i | \(-0.660986\pi\) | ||||
−0.484465 | + | 0.874811i | \(0.660986\pi\) | |||||||
\(228\) | −61.5910 | −4.07896 | ||||||||
\(229\) | 21.5271 | 1.42255 | 0.711276 | − | 0.702913i | \(-0.248118\pi\) | ||||
0.711276 | + | 0.702913i | \(0.248118\pi\) | |||||||
\(230\) | −3.85779 | −0.254375 | ||||||||
\(231\) | −1.84273 | −0.121243 | ||||||||
\(232\) | −22.2314 | −1.45956 | ||||||||
\(233\) | −15.4722 | −1.01362 | −0.506808 | − | 0.862059i | \(-0.669175\pi\) | ||||
−0.506808 | + | 0.862059i | \(0.669175\pi\) | |||||||
\(234\) | −22.3373 | −1.46023 | ||||||||
\(235\) | −10.6333 | −0.693639 | ||||||||
\(236\) | −10.1493 | −0.660665 | ||||||||
\(237\) | 8.98848 | 0.583864 | ||||||||
\(238\) | −4.22629 | −0.273950 | ||||||||
\(239\) | −25.8610 | −1.67281 | −0.836406 | − | 0.548111i | \(-0.815347\pi\) | ||||
−0.836406 | + | 0.548111i | \(0.815347\pi\) | |||||||
\(240\) | 3.26233 | 0.210582 | ||||||||
\(241\) | 20.7697 | 1.33790 | 0.668948 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668948 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(242\) | −2.32740 | −0.149611 | ||||||||
\(243\) | −9.12407 | −0.585309 | ||||||||
\(244\) | −6.58899 | −0.421817 | ||||||||
\(245\) | 8.37818 | 0.535262 | ||||||||
\(246\) | 39.4628 | 2.51606 | ||||||||
\(247\) | 8.70859 | 0.554114 | ||||||||
\(248\) | −9.66261 | −0.613576 | ||||||||
\(249\) | −20.4564 | −1.29637 | ||||||||
\(250\) | −24.6888 | −1.56145 | ||||||||
\(251\) | −1.62608 | −0.102637 | −0.0513185 | − | 0.998682i | \(-0.516342\pi\) | ||||
−0.0513185 | + | 0.998682i | \(0.516342\pi\) | |||||||
\(252\) | 13.2231 | 0.832974 | ||||||||
\(253\) | −1.31387 | −0.0826025 | ||||||||
\(254\) | 3.12760 | 0.196243 | ||||||||
\(255\) | 11.7598 | 0.736429 | ||||||||
\(256\) | −21.0386 | −1.31491 | ||||||||
\(257\) | 26.8034 | 1.67195 | 0.835975 | − | 0.548768i | \(-0.184903\pi\) | ||||
0.835975 | + | 0.548768i | \(0.184903\pi\) | |||||||
\(258\) | −66.8548 | −4.16220 | ||||||||
\(259\) | 0.452485 | 0.0281161 | ||||||||
\(260\) | −6.40481 | −0.397210 | ||||||||
\(261\) | 43.5493 | 2.69563 | ||||||||
\(262\) | 5.61125 | 0.346664 | ||||||||
\(263\) | 4.93641 | 0.304392 | 0.152196 | − | 0.988350i | \(-0.451366\pi\) | ||||
0.152196 | + | 0.988350i | \(0.451366\pi\) | |||||||
\(264\) | 10.1414 | 0.624162 | ||||||||
\(265\) | 15.0035 | 0.921656 | ||||||||
\(266\) | −8.17287 | −0.501111 | ||||||||
\(267\) | 20.4469 | 1.25133 | ||||||||
\(268\) | −22.3291 | −1.36397 | ||||||||
\(269\) | −4.98870 | −0.304167 | −0.152083 | − | 0.988368i | \(-0.548598\pi\) | ||||
−0.152083 | + | 0.988368i | \(0.548598\pi\) | |||||||
\(270\) | −31.2392 | −1.90115 | ||||||||
\(271\) | 25.3831 | 1.54191 | 0.770957 | − | 0.636888i | \(-0.219778\pi\) | ||||
0.770957 | + | 0.636888i | \(0.219778\pi\) | |||||||
\(272\) | 2.54825 | 0.154510 | ||||||||
\(273\) | −2.73802 | −0.165713 | ||||||||
\(274\) | 10.9496 | 0.661488 | ||||||||
\(275\) | −3.40842 | −0.205535 | ||||||||
\(276\) | 13.8070 | 0.831082 | ||||||||
\(277\) | −21.5445 | −1.29448 | −0.647242 | − | 0.762284i | \(-0.724078\pi\) | ||||
−0.647242 | + | 0.762284i | \(0.724078\pi\) | |||||||
\(278\) | 20.1803 | 1.21033 | ||||||||
\(279\) | 18.9282 | 1.13320 | ||||||||
\(280\) | 2.49239 | 0.148949 | ||||||||
\(281\) | 25.9749 | 1.54953 | 0.774767 | − | 0.632247i | \(-0.217867\pi\) | ||||
0.774767 | + | 0.632247i | \(0.217867\pi\) | |||||||
\(282\) | 60.3326 | 3.59276 | ||||||||
\(283\) | −18.8315 | −1.11942 | −0.559709 | − | 0.828689i | \(-0.689087\pi\) | ||||
−0.559709 | + | 0.828689i | \(0.689087\pi\) | |||||||
\(284\) | −29.3546 | −1.74188 | ||||||||
\(285\) | 22.7413 | 1.34708 | ||||||||
\(286\) | −3.45817 | −0.204486 | ||||||||
\(287\) | 3.30310 | 0.194976 | ||||||||
\(288\) | 29.9577 | 1.76528 | ||||||||
\(289\) | −7.81425 | −0.459662 | ||||||||
\(290\) | 19.7962 | 1.16247 | ||||||||
\(291\) | 38.3419 | 2.24764 | ||||||||
\(292\) | −18.5998 | −1.08847 | ||||||||
\(293\) | −17.7174 | −1.03506 | −0.517532 | − | 0.855664i | \(-0.673149\pi\) | ||||
−0.517532 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(294\) | −47.5373 | −2.77243 | ||||||||
\(295\) | 3.74745 | 0.218185 | ||||||||
\(296\) | −2.49025 | −0.144743 | ||||||||
\(297\) | −10.6393 | −0.617357 | ||||||||
\(298\) | −36.8551 | −2.13496 | ||||||||
\(299\) | −1.95222 | −0.112900 | ||||||||
\(300\) | 35.8177 | 2.06794 | ||||||||
\(301\) | −5.59584 | −0.322539 | ||||||||
\(302\) | 16.4921 | 0.949016 | ||||||||
\(303\) | −12.3476 | −0.709353 | ||||||||
\(304\) | 4.92784 | 0.282631 | ||||||||
\(305\) | 2.43286 | 0.139305 | ||||||||
\(306\) | −45.5629 | −2.60466 | ||||||||
\(307\) | 9.95065 | 0.567914 | 0.283957 | − | 0.958837i | \(-0.408353\pi\) | ||||
0.283957 | + | 0.958837i | \(0.408353\pi\) | |||||||
\(308\) | 2.04714 | 0.116647 | ||||||||
\(309\) | 27.8752 | 1.58577 | ||||||||
\(310\) | 8.60418 | 0.488685 | ||||||||
\(311\) | −6.58665 | −0.373495 | −0.186747 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186747 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(312\) | 15.0687 | 0.853095 | ||||||||
\(313\) | −34.8239 | −1.96837 | −0.984183 | − | 0.177156i | \(-0.943310\pi\) | ||||
−0.984183 | + | 0.177156i | \(0.943310\pi\) | |||||||
\(314\) | −22.9042 | −1.29256 | ||||||||
\(315\) | −4.88237 | −0.275090 | ||||||||
\(316\) | −9.98557 | −0.561732 | ||||||||
\(317\) | 13.2304 | 0.743093 | 0.371546 | − | 0.928414i | \(-0.378828\pi\) | ||||
0.371546 | + | 0.928414i | \(0.378828\pi\) | |||||||
\(318\) | −85.1288 | −4.77379 | ||||||||
\(319\) | 6.74213 | 0.377487 | ||||||||
\(320\) | 15.7393 | 0.879855 | ||||||||
\(321\) | −13.6467 | −0.761682 | ||||||||
\(322\) | 1.83213 | 0.102100 | ||||||||
\(323\) | 17.7635 | 0.988390 | ||||||||
\(324\) | 45.5949 | 2.53305 | ||||||||
\(325\) | −5.06441 | −0.280923 | ||||||||
\(326\) | 45.5364 | 2.52203 | ||||||||
\(327\) | −41.1376 | −2.27491 | ||||||||
\(328\) | −18.1785 | −1.00374 | ||||||||
\(329\) | 5.04993 | 0.278411 | ||||||||
\(330\) | −9.03054 | −0.497115 | ||||||||
\(331\) | 10.5750 | 0.581254 | 0.290627 | − | 0.956836i | \(-0.406136\pi\) | ||||
0.290627 | + | 0.956836i | \(0.406136\pi\) | |||||||
\(332\) | 22.7256 | 1.24723 | ||||||||
\(333\) | 4.87817 | 0.267322 | ||||||||
\(334\) | −15.0383 | −0.822862 | ||||||||
\(335\) | 8.24462 | 0.450452 | ||||||||
\(336\) | −1.54933 | −0.0845231 | ||||||||
\(337\) | 14.6928 | 0.800365 | 0.400183 | − | 0.916435i | \(-0.368947\pi\) | ||||
0.400183 | + | 0.916435i | \(0.368947\pi\) | |||||||
\(338\) | 25.1178 | 1.36623 | ||||||||
\(339\) | 21.8972 | 1.18929 | ||||||||
\(340\) | −13.0644 | −0.708514 | ||||||||
\(341\) | 2.93038 | 0.158689 | ||||||||
\(342\) | −88.1102 | −4.76446 | ||||||||
\(343\) | −8.17295 | −0.441298 | ||||||||
\(344\) | 30.7966 | 1.66044 | ||||||||
\(345\) | −5.09797 | −0.274465 | ||||||||
\(346\) | 16.7645 | 0.901263 | ||||||||
\(347\) | 11.0607 | 0.593768 | 0.296884 | − | 0.954914i | \(-0.404052\pi\) | ||||
0.296884 | + | 0.954914i | \(0.404052\pi\) | |||||||
\(348\) | −70.8503 | −3.79798 | ||||||||
\(349\) | −19.6971 | −1.05436 | −0.527180 | − | 0.849754i | \(-0.676751\pi\) | ||||
−0.527180 | + | 0.849754i | \(0.676751\pi\) | |||||||
\(350\) | 4.75286 | 0.254051 | ||||||||
\(351\) | −15.8085 | −0.843794 | ||||||||
\(352\) | 4.63794 | 0.247203 | ||||||||
\(353\) | 6.06512 | 0.322814 | 0.161407 | − | 0.986888i | \(-0.448397\pi\) | ||||
0.161407 | + | 0.986888i | \(0.448397\pi\) | |||||||
\(354\) | −21.2628 | −1.13010 | ||||||||
\(355\) | 10.8387 | 0.575256 | ||||||||
\(356\) | −22.7151 | −1.20390 | ||||||||
\(357\) | −5.58494 | −0.295586 | ||||||||
\(358\) | 20.5272 | 1.08489 | ||||||||
\(359\) | 18.9962 | 1.00258 | 0.501290 | − | 0.865279i | \(-0.332859\pi\) | ||||
0.501290 | + | 0.865279i | \(0.332859\pi\) | |||||||
\(360\) | 26.8701 | 1.41618 | ||||||||
\(361\) | 15.3514 | 0.807968 | ||||||||
\(362\) | 21.3913 | 1.12430 | ||||||||
\(363\) | −3.07559 | −0.161427 | ||||||||
\(364\) | 3.04175 | 0.159431 | ||||||||
\(365\) | 6.86763 | 0.359468 | ||||||||
\(366\) | −13.8039 | −0.721542 | ||||||||
\(367\) | −18.4004 | −0.960494 | −0.480247 | − | 0.877133i | \(-0.659453\pi\) | ||||
−0.480247 | + | 0.877133i | \(0.659453\pi\) | |||||||
\(368\) | −1.10468 | −0.0575855 | ||||||||
\(369\) | 35.6101 | 1.85379 | ||||||||
\(370\) | 2.21747 | 0.115281 | ||||||||
\(371\) | −7.12540 | −0.369932 | ||||||||
\(372\) | −30.7942 | −1.59661 | ||||||||
\(373\) | 30.0371 | 1.55526 | 0.777632 | − | 0.628720i | \(-0.216421\pi\) | ||||
0.777632 | + | 0.628720i | \(0.216421\pi\) | |||||||
\(374\) | −7.05387 | −0.364747 | ||||||||
\(375\) | −32.6256 | −1.68478 | ||||||||
\(376\) | −27.7922 | −1.43327 | ||||||||
\(377\) | 10.0178 | 0.515944 | ||||||||
\(378\) | 14.8360 | 0.763081 | ||||||||
\(379\) | 8.65654 | 0.444656 | 0.222328 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222328 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(380\) | −25.2640 | −1.29602 | ||||||||
\(381\) | 4.13304 | 0.211742 | ||||||||
\(382\) | −13.2426 | −0.677549 | ||||||||
\(383\) | −18.6866 | −0.954843 | −0.477421 | − | 0.878674i | \(-0.658428\pi\) | ||||
−0.477421 | + | 0.878674i | \(0.658428\pi\) | |||||||
\(384\) | −60.7751 | −3.10142 | ||||||||
\(385\) | −0.755869 | −0.0385227 | ||||||||
\(386\) | −30.1358 | −1.53387 | ||||||||
\(387\) | −60.3278 | −3.06663 | ||||||||
\(388\) | −42.5952 | −2.16245 | ||||||||
\(389\) | 31.3284 | 1.58841 | 0.794206 | − | 0.607648i | \(-0.207887\pi\) | ||||
0.794206 | + | 0.607648i | \(0.207887\pi\) | |||||||
\(390\) | −13.4181 | −0.679450 | ||||||||
\(391\) | −3.98209 | −0.201383 | ||||||||
\(392\) | 21.8980 | 1.10602 | ||||||||
\(393\) | 7.41512 | 0.374044 | ||||||||
\(394\) | −51.7782 | −2.60855 | ||||||||
\(395\) | 3.68699 | 0.185513 | ||||||||
\(396\) | 22.0699 | 1.10905 | ||||||||
\(397\) | −4.38014 | −0.219833 | −0.109916 | − | 0.993941i | \(-0.535058\pi\) | ||||
−0.109916 | + | 0.993941i | \(0.535058\pi\) | |||||||
\(398\) | −32.7499 | −1.64160 | ||||||||
\(399\) | −10.8002 | −0.540688 | ||||||||
\(400\) | −2.86574 | −0.143287 | ||||||||
\(401\) | −0.895888 | −0.0447385 | −0.0223693 | − | 0.999750i | \(-0.507121\pi\) | ||||
−0.0223693 | + | 0.999750i | \(0.507121\pi\) | |||||||
\(402\) | −46.7794 | −2.33315 | ||||||||
\(403\) | 4.35412 | 0.216894 | ||||||||
\(404\) | 13.7174 | 0.682464 | ||||||||
\(405\) | −16.8351 | −0.836541 | ||||||||
\(406\) | −9.40155 | −0.466591 | ||||||||
\(407\) | 0.755218 | 0.0374348 | ||||||||
\(408\) | 30.7366 | 1.52169 | ||||||||
\(409\) | 8.26149 | 0.408504 | 0.204252 | − | 0.978918i | \(-0.434524\pi\) | ||||
0.204252 | + | 0.978918i | \(0.434524\pi\) | |||||||
\(410\) | 16.1873 | 0.799433 | ||||||||
\(411\) | 14.4696 | 0.713732 | ||||||||
\(412\) | −30.9674 | −1.52566 | ||||||||
\(413\) | −1.77973 | −0.0875746 | ||||||||
\(414\) | 19.7518 | 0.970750 | ||||||||
\(415\) | −8.39101 | −0.411898 | ||||||||
\(416\) | 6.89130 | 0.337874 | ||||||||
\(417\) | 26.6677 | 1.30592 | ||||||||
\(418\) | −13.6409 | −0.667197 | ||||||||
\(419\) | −32.8640 | −1.60551 | −0.802756 | − | 0.596307i | \(-0.796634\pi\) | ||||
−0.802756 | + | 0.596307i | \(0.796634\pi\) | |||||||
\(420\) | 7.94313 | 0.387585 | ||||||||
\(421\) | 1.08937 | 0.0530928 | 0.0265464 | − | 0.999648i | \(-0.491549\pi\) | ||||
0.0265464 | + | 0.999648i | \(0.491549\pi\) | |||||||
\(422\) | 27.5223 | 1.33977 | ||||||||
\(423\) | 54.4424 | 2.64708 | ||||||||
\(424\) | 39.2145 | 1.90443 | ||||||||
\(425\) | −10.3302 | −0.501090 | ||||||||
\(426\) | −61.4978 | −2.97958 | ||||||||
\(427\) | −1.15541 | −0.0559141 | ||||||||
\(428\) | 15.1605 | 0.732810 | ||||||||
\(429\) | −4.56988 | −0.220636 | ||||||||
\(430\) | −27.4232 | −1.32247 | ||||||||
\(431\) | −24.5816 | −1.18406 | −0.592028 | − | 0.805917i | \(-0.701672\pi\) | ||||
−0.592028 | + | 0.805917i | \(0.701672\pi\) | |||||||
\(432\) | −8.94537 | −0.430385 | ||||||||
\(433\) | −25.5381 | −1.22728 | −0.613641 | − | 0.789585i | \(-0.710296\pi\) | ||||
−0.613641 | + | 0.789585i | \(0.710296\pi\) | |||||||
\(434\) | −4.08627 | −0.196147 | ||||||||
\(435\) | 26.1602 | 1.25428 | ||||||||
\(436\) | 45.7010 | 2.18868 | ||||||||
\(437\) | −7.70062 | −0.368370 | ||||||||
\(438\) | −38.9665 | −1.86189 | ||||||||
\(439\) | −5.15845 | −0.246199 | −0.123100 | − | 0.992394i | \(-0.539283\pi\) | ||||
−0.123100 | + | 0.992394i | \(0.539283\pi\) | |||||||
\(440\) | 4.15992 | 0.198316 | ||||||||
\(441\) | −42.8962 | −2.04268 | ||||||||
\(442\) | −10.4810 | −0.498531 | ||||||||
\(443\) | −27.1359 | −1.28926 | −0.644632 | − | 0.764493i | \(-0.722990\pi\) | ||||
−0.644632 | + | 0.764493i | \(0.722990\pi\) | |||||||
\(444\) | −7.93629 | −0.376640 | ||||||||
\(445\) | 8.38714 | 0.397589 | ||||||||
\(446\) | 29.8034 | 1.41123 | ||||||||
\(447\) | −48.7031 | −2.30358 | ||||||||
\(448\) | −7.47487 | −0.353154 | ||||||||
\(449\) | −24.9526 | −1.17758 | −0.588792 | − | 0.808284i | \(-0.700396\pi\) | ||||
−0.588792 | + | 0.808284i | \(0.700396\pi\) | |||||||
\(450\) | 51.2397 | 2.41546 | ||||||||
\(451\) | 5.51301 | 0.259598 | ||||||||
\(452\) | −24.3262 | −1.14421 | ||||||||
\(453\) | 21.7939 | 1.02397 | ||||||||
\(454\) | 33.9763 | 1.59459 | ||||||||
\(455\) | −1.12311 | −0.0526522 | ||||||||
\(456\) | 59.4389 | 2.78348 | ||||||||
\(457\) | −16.2422 | −0.759779 | −0.379889 | − | 0.925032i | \(-0.624038\pi\) | ||||
−0.379889 | + | 0.925032i | \(0.624038\pi\) | |||||||
\(458\) | −50.1021 | −2.34112 | ||||||||
\(459\) | −32.2457 | −1.50510 | ||||||||
\(460\) | 5.66349 | 0.264061 | ||||||||
\(461\) | −3.86531 | −0.180025 | −0.0900127 | − | 0.995941i | \(-0.528691\pi\) | ||||
−0.0900127 | + | 0.995941i | \(0.528691\pi\) | |||||||
\(462\) | 4.28876 | 0.199531 | ||||||||
\(463\) | 9.76584 | 0.453857 | 0.226928 | − | 0.973911i | \(-0.427132\pi\) | ||||
0.226928 | + | 0.973911i | \(0.427132\pi\) | |||||||
\(464\) | 5.66867 | 0.263161 | ||||||||
\(465\) | 11.3702 | 0.527281 | ||||||||
\(466\) | 36.0099 | 1.66813 | ||||||||
\(467\) | −5.12102 | −0.236973 | −0.118486 | − | 0.992956i | \(-0.537804\pi\) | ||||
−0.118486 | + | 0.992956i | \(0.537804\pi\) | |||||||
\(468\) | 32.7926 | 1.51584 | ||||||||
\(469\) | −3.91551 | −0.180801 | ||||||||
\(470\) | 24.7479 | 1.14153 | ||||||||
\(471\) | −30.2674 | −1.39465 | ||||||||
\(472\) | 9.79470 | 0.450838 | ||||||||
\(473\) | −9.33971 | −0.429440 | ||||||||
\(474\) | −20.9197 | −0.960876 | ||||||||
\(475\) | −19.9767 | −0.916596 | ||||||||
\(476\) | 6.20448 | 0.284382 | ||||||||
\(477\) | −76.8177 | −3.51724 | ||||||||
\(478\) | 60.1889 | 2.75297 | ||||||||
\(479\) | −33.9782 | −1.55250 | −0.776252 | − | 0.630423i | \(-0.782882\pi\) | ||||
−0.776252 | + | 0.630423i | \(0.782882\pi\) | |||||||
\(480\) | 17.9957 | 0.821388 | ||||||||
\(481\) | 1.12214 | 0.0511653 | ||||||||
\(482\) | −48.3394 | −2.20180 | ||||||||
\(483\) | 2.42111 | 0.110164 | ||||||||
\(484\) | 3.41677 | 0.155308 | ||||||||
\(485\) | 15.7275 | 0.714149 | ||||||||
\(486\) | 21.2353 | 0.963254 | ||||||||
\(487\) | −34.9174 | −1.58226 | −0.791130 | − | 0.611648i | \(-0.790507\pi\) | ||||
−0.791130 | + | 0.611648i | \(0.790507\pi\) | |||||||
\(488\) | 6.35877 | 0.287848 | ||||||||
\(489\) | 60.1752 | 2.72122 | ||||||||
\(490\) | −19.4993 | −0.880891 | ||||||||
\(491\) | −0.442418 | −0.0199660 | −0.00998302 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998302 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(492\) | −57.9341 | −2.61187 | ||||||||
\(493\) | 20.4340 | 0.920303 | ||||||||
\(494\) | −20.2683 | −0.911916 | ||||||||
\(495\) | −8.14889 | −0.366266 | ||||||||
\(496\) | 2.46382 | 0.110629 | ||||||||
\(497\) | −5.14746 | −0.230895 | ||||||||
\(498\) | 47.6100 | 2.13346 | ||||||||
\(499\) | −23.7518 | −1.06328 | −0.531638 | − | 0.846972i | \(-0.678423\pi\) | ||||
−0.531638 | + | 0.846972i | \(0.678423\pi\) | |||||||
\(500\) | 36.2447 | 1.62091 | ||||||||
\(501\) | −19.8728 | −0.887851 | ||||||||
\(502\) | 3.78452 | 0.168911 | ||||||||
\(503\) | 29.1178 | 1.29830 | 0.649149 | − | 0.760662i | \(-0.275125\pi\) | ||||
0.649149 | + | 0.760662i | \(0.275125\pi\) | |||||||
\(504\) | −12.7610 | −0.568422 | ||||||||
\(505\) | −5.06488 | −0.225384 | ||||||||
\(506\) | 3.05790 | 0.135940 | ||||||||
\(507\) | 33.1926 | 1.47413 | ||||||||
\(508\) | −4.59152 | −0.203716 | ||||||||
\(509\) | 0.324499 | 0.0143832 | 0.00719158 | − | 0.999974i | \(-0.497711\pi\) | ||||
0.00719158 | + | 0.999974i | \(0.497711\pi\) | |||||||
\(510\) | −27.3698 | −1.21195 | ||||||||
\(511\) | −3.26155 | −0.144282 | ||||||||
\(512\) | 9.44428 | 0.417382 | ||||||||
\(513\) | −62.3572 | −2.75314 | ||||||||
\(514\) | −62.3821 | −2.75156 | ||||||||
\(515\) | 11.4342 | 0.503849 | ||||||||
\(516\) | 98.1473 | 4.32069 | ||||||||
\(517\) | 8.42855 | 0.370687 | ||||||||
\(518\) | −1.05311 | −0.0462711 | ||||||||
\(519\) | 22.1538 | 0.972445 | ||||||||
\(520\) | 6.18102 | 0.271056 | ||||||||
\(521\) | −23.3740 | −1.02403 | −0.512017 | − | 0.858975i | \(-0.671102\pi\) | ||||
−0.512017 | + | 0.858975i | \(0.671102\pi\) | |||||||
\(522\) | −101.356 | −4.43625 | ||||||||
\(523\) | −37.8723 | −1.65604 | −0.828020 | − | 0.560698i | \(-0.810533\pi\) | ||||
−0.828020 | + | 0.560698i | \(0.810533\pi\) | |||||||
\(524\) | −8.23769 | −0.359865 | ||||||||
\(525\) | 6.28078 | 0.274116 | ||||||||
\(526\) | −11.4890 | −0.500943 | ||||||||
\(527\) | 8.88141 | 0.386880 | ||||||||
\(528\) | −2.58591 | −0.112537 | ||||||||
\(529\) | −21.2737 | −0.924945 | ||||||||
\(530\) | −34.9190 | −1.51679 | ||||||||
\(531\) | −19.1869 | −0.832641 | ||||||||
\(532\) | 11.9983 | 0.520193 | ||||||||
\(533\) | 8.19153 | 0.354814 | ||||||||
\(534\) | −47.5881 | −2.05934 | ||||||||
\(535\) | −5.59773 | −0.242011 | ||||||||
\(536\) | 21.5489 | 0.930772 | ||||||||
\(537\) | 27.1261 | 1.17058 | ||||||||
\(538\) | 11.6107 | 0.500572 | ||||||||
\(539\) | −6.64103 | −0.286049 | ||||||||
\(540\) | 45.8612 | 1.97355 | ||||||||
\(541\) | −4.25778 | −0.183056 | −0.0915281 | − | 0.995802i | \(-0.529175\pi\) | ||||
−0.0915281 | + | 0.995802i | \(0.529175\pi\) | |||||||
\(542\) | −59.0765 | −2.53755 | ||||||||
\(543\) | 28.2681 | 1.21310 | ||||||||
\(544\) | 14.0567 | 0.602675 | ||||||||
\(545\) | −16.8742 | −0.722813 | ||||||||
\(546\) | 6.37246 | 0.272716 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | −16.0747 | −0.686677 | ||||||||
\(549\) | −12.4562 | −0.531619 | ||||||||
\(550\) | 7.93273 | 0.338253 | ||||||||
\(551\) | 39.5157 | 1.68342 | ||||||||
\(552\) | −13.3245 | −0.567130 | ||||||||
\(553\) | −1.75101 | −0.0744606 | ||||||||
\(554\) | 50.1426 | 2.13036 | ||||||||
\(555\) | 2.93033 | 0.124385 | ||||||||
\(556\) | −29.6260 | −1.25642 | ||||||||
\(557\) | 11.6817 | 0.494969 | 0.247485 | − | 0.968892i | \(-0.420396\pi\) | ||||
0.247485 | + | 0.968892i | \(0.420396\pi\) | |||||||
\(558\) | −44.0533 | −1.86493 | ||||||||
\(559\) | −13.8774 | −0.586953 | ||||||||
\(560\) | −0.635522 | −0.0268557 | ||||||||
\(561\) | −9.32151 | −0.393555 | ||||||||
\(562\) | −60.4539 | −2.55010 | ||||||||
\(563\) | −19.6636 | −0.828721 | −0.414360 | − | 0.910113i | \(-0.635995\pi\) | ||||
−0.414360 | + | 0.910113i | \(0.635995\pi\) | |||||||
\(564\) | −88.5723 | −3.72957 | ||||||||
\(565\) | 8.98201 | 0.377876 | ||||||||
\(566\) | 43.8284 | 1.84225 | ||||||||
\(567\) | 7.99526 | 0.335769 | ||||||||
\(568\) | 28.3290 | 1.18866 | ||||||||
\(569\) | 6.22920 | 0.261142 | 0.130571 | − | 0.991439i | \(-0.458319\pi\) | ||||
0.130571 | + | 0.991439i | \(0.458319\pi\) | |||||||
\(570\) | −52.9281 | −2.21691 | ||||||||
\(571\) | 29.0965 | 1.21765 | 0.608826 | − | 0.793304i | \(-0.291641\pi\) | ||||
0.608826 | + | 0.793304i | \(0.291641\pi\) | |||||||
\(572\) | 5.07682 | 0.212272 | ||||||||
\(573\) | −17.4997 | −0.731061 | ||||||||
\(574\) | −7.68761 | −0.320875 | ||||||||
\(575\) | 4.47823 | 0.186755 | ||||||||
\(576\) | −80.5852 | −3.35772 | ||||||||
\(577\) | −2.46159 | −0.102477 | −0.0512387 | − | 0.998686i | \(-0.516317\pi\) | ||||
−0.0512387 | + | 0.998686i | \(0.516317\pi\) | |||||||
\(578\) | 18.1868 | 0.756473 | ||||||||
\(579\) | −39.8236 | −1.65501 | ||||||||
\(580\) | −29.0621 | −1.20674 | ||||||||
\(581\) | 3.98503 | 0.165327 | ||||||||
\(582\) | −89.2369 | −3.69899 | ||||||||
\(583\) | −11.8926 | −0.492542 | ||||||||
\(584\) | 17.9499 | 0.742772 | ||||||||
\(585\) | −12.1081 | −0.500607 | ||||||||
\(586\) | 41.2355 | 1.70342 | ||||||||
\(587\) | 15.9484 | 0.658261 | 0.329130 | − | 0.944285i | \(-0.393244\pi\) | ||||
0.329130 | + | 0.944285i | \(0.393244\pi\) | |||||||
\(588\) | 69.7879 | 2.87800 | ||||||||
\(589\) | 17.1750 | 0.707683 | ||||||||
\(590\) | −8.72180 | −0.359071 | ||||||||
\(591\) | −68.4236 | −2.81457 | ||||||||
\(592\) | 0.634975 | 0.0260973 | ||||||||
\(593\) | −12.7634 | −0.524130 | −0.262065 | − | 0.965050i | \(-0.584403\pi\) | ||||
−0.262065 | + | 0.965050i | \(0.584403\pi\) | |||||||
\(594\) | 24.7619 | 1.01599 | ||||||||
\(595\) | −2.29089 | −0.0939173 | ||||||||
\(596\) | 54.1058 | 2.21626 | ||||||||
\(597\) | −43.2781 | −1.77126 | ||||||||
\(598\) | 4.54359 | 0.185801 | ||||||||
\(599\) | 9.87514 | 0.403487 | 0.201744 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201744 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(600\) | −34.5662 | −1.41116 | ||||||||
\(601\) | −6.94106 | −0.283132 | −0.141566 | − | 0.989929i | \(-0.545214\pi\) | ||||
−0.141566 | + | 0.989929i | \(0.545214\pi\) | |||||||
\(602\) | 13.0237 | 0.530808 | ||||||||
\(603\) | −42.2124 | −1.71902 | ||||||||
\(604\) | −24.2115 | −0.985154 | ||||||||
\(605\) | −1.26158 | −0.0512905 | ||||||||
\(606\) | 28.7378 | 1.16739 | ||||||||
\(607\) | 29.2989 | 1.18921 | 0.594603 | − | 0.804019i | \(-0.297309\pi\) | ||||
0.594603 | + | 0.804019i | \(0.297309\pi\) | |||||||
\(608\) | 27.1830 | 1.10242 | ||||||||
\(609\) | −12.4239 | −0.503442 | ||||||||
\(610\) | −5.66223 | −0.229257 | ||||||||
\(611\) | 12.5236 | 0.506650 | ||||||||
\(612\) | 66.8894 | 2.70384 | ||||||||
\(613\) | 31.3333 | 1.26554 | 0.632770 | − | 0.774340i | \(-0.281918\pi\) | ||||
0.632770 | + | 0.774340i | \(0.281918\pi\) | |||||||
\(614\) | −23.1591 | −0.934625 | ||||||||
\(615\) | 21.3911 | 0.862572 | ||||||||
\(616\) | −1.97561 | −0.0795998 | ||||||||
\(617\) | 20.2638 | 0.815792 | 0.407896 | − | 0.913028i | \(-0.366263\pi\) | ||||
0.407896 | + | 0.913028i | \(0.366263\pi\) | |||||||
\(618\) | −64.8767 | −2.60972 | ||||||||
\(619\) | −14.3073 | −0.575058 | −0.287529 | − | 0.957772i | \(-0.592834\pi\) | ||||
−0.287529 | + | 0.957772i | \(0.592834\pi\) | |||||||
\(620\) | −12.6315 | −0.507293 | ||||||||
\(621\) | 13.9787 | 0.560947 | ||||||||
\(622\) | 15.3297 | 0.614666 | ||||||||
\(623\) | −3.98319 | −0.159583 | ||||||||
\(624\) | −3.84228 | −0.153814 | ||||||||
\(625\) | 3.65939 | 0.146376 | ||||||||
\(626\) | 81.0491 | 3.23937 | ||||||||
\(627\) | −18.0261 | −0.719892 | ||||||||
\(628\) | 33.6249 | 1.34178 | ||||||||
\(629\) | 2.28892 | 0.0912651 | ||||||||
\(630\) | 11.3632 | 0.452721 | ||||||||
\(631\) | −3.15968 | −0.125785 | −0.0628924 | − | 0.998020i | \(-0.520033\pi\) | ||||
−0.0628924 | + | 0.998020i | \(0.520033\pi\) | |||||||
\(632\) | 9.63667 | 0.383326 | ||||||||
\(633\) | 36.3701 | 1.44558 | ||||||||
\(634\) | −30.7924 | −1.22292 | ||||||||
\(635\) | 1.69533 | 0.0672773 | ||||||||
\(636\) | 124.975 | 4.95557 | ||||||||
\(637\) | −9.86759 | −0.390968 | ||||||||
\(638\) | −15.6916 | −0.621237 | ||||||||
\(639\) | −55.4938 | −2.19530 | ||||||||
\(640\) | −24.9294 | −0.985420 | ||||||||
\(641\) | 32.0601 | 1.26630 | 0.633150 | − | 0.774029i | \(-0.281762\pi\) | ||||
0.633150 | + | 0.774029i | \(0.281762\pi\) | |||||||
\(642\) | 31.7612 | 1.25351 | ||||||||
\(643\) | −16.4784 | −0.649844 | −0.324922 | − | 0.945741i | \(-0.605338\pi\) | ||||
−0.324922 | + | 0.945741i | \(0.605338\pi\) | |||||||
\(644\) | −2.68968 | −0.105988 | ||||||||
\(645\) | −36.2391 | −1.42691 | ||||||||
\(646\) | −41.3428 | −1.62661 | ||||||||
\(647\) | −10.4922 | −0.412491 | −0.206245 | − | 0.978500i | \(-0.566125\pi\) | ||||
−0.206245 | + | 0.978500i | \(0.566125\pi\) | |||||||
\(648\) | −44.0018 | −1.72855 | ||||||||
\(649\) | −2.97044 | −0.116600 | ||||||||
\(650\) | 11.7869 | 0.462319 | ||||||||
\(651\) | −5.39990 | −0.211639 | ||||||||
\(652\) | −66.8505 | −2.61807 | ||||||||
\(653\) | −34.9327 | −1.36702 | −0.683511 | − | 0.729940i | \(-0.739548\pi\) | ||||
−0.683511 | + | 0.729940i | \(0.739548\pi\) | |||||||
\(654\) | 95.7434 | 3.74386 | ||||||||
\(655\) | 3.04161 | 0.118846 | ||||||||
\(656\) | 4.63525 | 0.180976 | ||||||||
\(657\) | −35.1622 | −1.37181 | ||||||||
\(658\) | −11.7532 | −0.458187 | ||||||||
\(659\) | −15.5209 | −0.604608 | −0.302304 | − | 0.953212i | \(-0.597756\pi\) | ||||
−0.302304 | + | 0.953212i | \(0.597756\pi\) | |||||||
\(660\) | 13.2574 | 0.516045 | ||||||||
\(661\) | 27.8124 | 1.08178 | 0.540888 | − | 0.841095i | \(-0.318088\pi\) | ||||
0.540888 | + | 0.841095i | \(0.318088\pi\) | |||||||
\(662\) | −24.6122 | −0.956579 | ||||||||
\(663\) | −13.8504 | −0.537905 | ||||||||
\(664\) | −21.9316 | −0.851109 | ||||||||
\(665\) | −4.43015 | −0.171794 | ||||||||
\(666\) | −11.3534 | −0.439936 | ||||||||
\(667\) | −8.85830 | −0.342995 | ||||||||
\(668\) | 22.0773 | 0.854196 | ||||||||
\(669\) | 39.3845 | 1.52269 | ||||||||
\(670\) | −19.1885 | −0.741316 | ||||||||
\(671\) | −1.92843 | −0.0744460 | ||||||||
\(672\) | −8.54646 | −0.329687 | ||||||||
\(673\) | −16.6229 | −0.640764 | −0.320382 | − | 0.947288i | \(-0.603811\pi\) | ||||
−0.320382 | + | 0.947288i | \(0.603811\pi\) | |||||||
\(674\) | −34.1959 | −1.31718 | ||||||||
\(675\) | 36.2633 | 1.39577 | ||||||||
\(676\) | −36.8746 | −1.41825 | ||||||||
\(677\) | 13.3423 | 0.512785 | 0.256393 | − | 0.966573i | \(-0.417466\pi\) | ||||
0.256393 | + | 0.966573i | \(0.417466\pi\) | |||||||
\(678\) | −50.9633 | −1.95724 | ||||||||
\(679\) | −7.46925 | −0.286644 | ||||||||
\(680\) | 12.6079 | 0.483490 | ||||||||
\(681\) | 44.8988 | 1.72052 | ||||||||
\(682\) | −6.82016 | −0.261158 | ||||||||
\(683\) | 26.4190 | 1.01090 | 0.505448 | − | 0.862857i | \(-0.331327\pi\) | ||||
0.505448 | + | 0.862857i | \(0.331327\pi\) | |||||||
\(684\) | 129.352 | 4.94588 | ||||||||
\(685\) | 5.93529 | 0.226776 | ||||||||
\(686\) | 19.0217 | 0.726252 | ||||||||
\(687\) | −66.2086 | −2.52602 | ||||||||
\(688\) | −7.85267 | −0.299380 | ||||||||
\(689\) | −17.6707 | −0.673199 | ||||||||
\(690\) | 11.8650 | 0.451692 | ||||||||
\(691\) | 10.5924 | 0.402952 | 0.201476 | − | 0.979493i | \(-0.435426\pi\) | ||||
0.201476 | + | 0.979493i | \(0.435426\pi\) | |||||||
\(692\) | −24.6114 | −0.935583 | ||||||||
\(693\) | 3.87005 | 0.147011 | ||||||||
\(694\) | −25.7426 | −0.977175 | ||||||||
\(695\) | 10.9388 | 0.414934 | ||||||||
\(696\) | 68.3748 | 2.59174 | ||||||||
\(697\) | 16.7088 | 0.632893 | ||||||||
\(698\) | 45.8428 | 1.73518 | ||||||||
\(699\) | 47.5861 | 1.79987 | ||||||||
\(700\) | −6.97751 | −0.263725 | ||||||||
\(701\) | −45.5990 | −1.72225 | −0.861125 | − | 0.508394i | \(-0.830239\pi\) | ||||
−0.861125 | + | 0.508394i | \(0.830239\pi\) | |||||||
\(702\) | 36.7926 | 1.38865 | ||||||||
\(703\) | 4.42634 | 0.166943 | ||||||||
\(704\) | −12.4759 | −0.470203 | ||||||||
\(705\) | 32.7037 | 1.23169 | ||||||||
\(706\) | −14.1159 | −0.531260 | ||||||||
\(707\) | 2.40540 | 0.0904643 | ||||||||
\(708\) | 31.2152 | 1.17314 | ||||||||
\(709\) | 35.5322 | 1.33444 | 0.667220 | − | 0.744861i | \(-0.267484\pi\) | ||||
0.667220 | + | 0.744861i | \(0.267484\pi\) | |||||||
\(710\) | −25.2258 | −0.946708 | ||||||||
\(711\) | −18.8774 | −0.707956 | ||||||||
\(712\) | 21.9215 | 0.821541 | ||||||||
\(713\) | −3.85015 | −0.144189 | ||||||||
\(714\) | 12.9984 | 0.486452 | ||||||||
\(715\) | −1.87452 | −0.0701031 | ||||||||
\(716\) | −30.1353 | −1.12621 | ||||||||
\(717\) | 79.5380 | 2.97040 | ||||||||
\(718\) | −44.2116 | −1.64996 | ||||||||
\(719\) | −18.5736 | −0.692680 | −0.346340 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346340 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(720\) | −6.85145 | −0.255339 | ||||||||
\(721\) | −5.43027 | −0.202234 | ||||||||
\(722\) | −35.7288 | −1.32969 | ||||||||
\(723\) | −63.8793 | −2.37570 | ||||||||
\(724\) | −31.4039 | −1.16712 | ||||||||
\(725\) | −22.9800 | −0.853455 | ||||||||
\(726\) | 7.15812 | 0.265663 | ||||||||
\(727\) | −17.0223 | −0.631321 | −0.315660 | − | 0.948872i | \(-0.602226\pi\) | ||||
−0.315660 | + | 0.948872i | \(0.602226\pi\) | |||||||
\(728\) | −2.93547 | −0.108796 | ||||||||
\(729\) | −11.9714 | −0.443384 | ||||||||
\(730\) | −15.9837 | −0.591583 | ||||||||
\(731\) | −28.3068 | −1.04697 | ||||||||
\(732\) | 20.2651 | 0.749018 | ||||||||
\(733\) | 31.7063 | 1.17110 | 0.585550 | − | 0.810636i | \(-0.300879\pi\) | ||||
0.585550 | + | 0.810636i | \(0.300879\pi\) | |||||||
\(734\) | 42.8250 | 1.58070 | ||||||||
\(735\) | −25.7679 | −0.950463 | ||||||||
\(736\) | −6.09366 | −0.224615 | ||||||||
\(737\) | −6.53515 | −0.240725 | ||||||||
\(738\) | −82.8788 | −3.05081 | ||||||||
\(739\) | 10.5885 | 0.389503 | 0.194751 | − | 0.980853i | \(-0.437610\pi\) | ||||
0.194751 | + | 0.980853i | \(0.437610\pi\) | |||||||
\(740\) | −3.25539 | −0.119671 | ||||||||
\(741\) | −26.7841 | −0.983938 | ||||||||
\(742\) | 16.5836 | 0.608804 | ||||||||
\(743\) | −0.934902 | −0.0342982 | −0.0171491 | − | 0.999853i | \(-0.505459\pi\) | ||||
−0.0171491 | + | 0.999853i | \(0.505459\pi\) | |||||||
\(744\) | 29.7183 | 1.08952 | ||||||||
\(745\) | −19.9776 | −0.731921 | ||||||||
\(746\) | −69.9083 | −2.55952 | ||||||||
\(747\) | 42.9619 | 1.57189 | ||||||||
\(748\) | 10.3556 | 0.378636 | ||||||||
\(749\) | 2.65845 | 0.0971378 | ||||||||
\(750\) | 75.9326 | 2.77267 | ||||||||
\(751\) | 20.9014 | 0.762702 | 0.381351 | − | 0.924430i | \(-0.375459\pi\) | ||||
0.381351 | + | 0.924430i | \(0.375459\pi\) | |||||||
\(752\) | 7.08659 | 0.258421 | ||||||||
\(753\) | 5.00115 | 0.182252 | ||||||||
\(754\) | −23.3154 | −0.849097 | ||||||||
\(755\) | 8.93967 | 0.325348 | ||||||||
\(756\) | −21.7802 | −0.792139 | ||||||||
\(757\) | −47.3148 | −1.71969 | −0.859844 | − | 0.510558i | \(-0.829439\pi\) | ||||
−0.859844 | + | 0.510558i | \(0.829439\pi\) | |||||||
\(758\) | −20.1472 | −0.731779 | ||||||||
\(759\) | 4.04094 | 0.146677 | ||||||||
\(760\) | 24.3813 | 0.884403 | ||||||||
\(761\) | −6.35314 | −0.230301 | −0.115151 | − | 0.993348i | \(-0.536735\pi\) | ||||
−0.115151 | + | 0.993348i | \(0.536735\pi\) | |||||||
\(762\) | −9.61922 | −0.348468 | ||||||||
\(763\) | 8.01386 | 0.290121 | ||||||||
\(764\) | 19.4410 | 0.703350 | ||||||||
\(765\) | −24.6977 | −0.892946 | ||||||||
\(766\) | 43.4912 | 1.57140 | ||||||||
\(767\) | −4.41364 | −0.159367 | ||||||||
\(768\) | 64.7062 | 2.33488 | ||||||||
\(769\) | −36.6873 | −1.32298 | −0.661490 | − | 0.749954i | \(-0.730075\pi\) | ||||
−0.661490 | + | 0.749954i | \(0.730075\pi\) | |||||||
\(770\) | 1.75921 | 0.0633974 | ||||||||
\(771\) | −82.4364 | −2.96887 | ||||||||
\(772\) | 44.2413 | 1.59228 | ||||||||
\(773\) | 1.47629 | 0.0530984 | 0.0265492 | − | 0.999648i | \(-0.491548\pi\) | ||||
0.0265492 | + | 0.999648i | \(0.491548\pi\) | |||||||
\(774\) | 140.407 | 5.04681 | ||||||||
\(775\) | −9.98797 | −0.358778 | ||||||||
\(776\) | 41.1069 | 1.47565 | ||||||||
\(777\) | −1.39166 | −0.0499256 | ||||||||
\(778\) | −72.9136 | −2.61408 | ||||||||
\(779\) | 32.3118 | 1.15769 | ||||||||
\(780\) | 19.6986 | 0.705323 | ||||||||
\(781\) | −8.59133 | −0.307422 | ||||||||
\(782\) | 9.26789 | 0.331419 | ||||||||
\(783\) | −71.7318 | −2.56348 | ||||||||
\(784\) | −5.58366 | −0.199417 | ||||||||
\(785\) | −12.4154 | −0.443124 | ||||||||
\(786\) | −17.2579 | −0.615570 | ||||||||
\(787\) | 20.5342 | 0.731965 | 0.365982 | − | 0.930622i | \(-0.380733\pi\) | ||||
0.365982 | + | 0.930622i | \(0.380733\pi\) | |||||||
\(788\) | 76.0139 | 2.70788 | ||||||||
\(789\) | −15.1824 | −0.540507 | ||||||||
\(790\) | −8.58108 | −0.305301 | ||||||||
\(791\) | −4.26570 | −0.151671 | ||||||||
\(792\) | −21.2987 | −0.756818 | ||||||||
\(793\) | −2.86536 | −0.101752 | ||||||||
\(794\) | 10.1943 | 0.361782 | ||||||||
\(795\) | −46.1446 | −1.63658 | ||||||||
\(796\) | 48.0790 | 1.70411 | ||||||||
\(797\) | −12.5303 | −0.443845 | −0.221922 | − | 0.975064i | \(-0.571233\pi\) | ||||
−0.221922 | + | 0.975064i | \(0.571233\pi\) | |||||||
\(798\) | 25.1364 | 0.889820 | ||||||||
\(799\) | 25.5453 | 0.903726 | ||||||||
\(800\) | −15.8080 | −0.558898 | ||||||||
\(801\) | −42.9421 | −1.51728 | ||||||||
\(802\) | 2.08509 | 0.0736270 | ||||||||
\(803\) | −5.44367 | −0.192103 | ||||||||
\(804\) | 68.6753 | 2.42199 | ||||||||
\(805\) | 0.993116 | 0.0350027 | ||||||||
\(806\) | −10.1338 | −0.356946 | ||||||||
\(807\) | 15.3432 | 0.540107 | ||||||||
\(808\) | −13.2381 | −0.465714 | ||||||||
\(809\) | −25.2177 | −0.886608 | −0.443304 | − | 0.896371i | \(-0.646194\pi\) | ||||
−0.443304 | + | 0.896371i | \(0.646194\pi\) | |||||||
\(810\) | 39.1819 | 1.37671 | ||||||||
\(811\) | 35.4366 | 1.24435 | 0.622175 | − | 0.782879i | \(-0.286249\pi\) | ||||
0.622175 | + | 0.782879i | \(0.286249\pi\) | |||||||
\(812\) | 13.8021 | 0.484359 | ||||||||
\(813\) | −78.0681 | −2.73797 | ||||||||
\(814\) | −1.75769 | −0.0616071 | ||||||||
\(815\) | 24.6833 | 0.864619 | ||||||||
\(816\) | −7.83737 | −0.274363 | ||||||||
\(817\) | −54.7401 | −1.91511 | ||||||||
\(818\) | −19.2277 | −0.672282 | ||||||||
\(819\) | 5.75032 | 0.200932 | ||||||||
\(820\) | −23.7640 | −0.829875 | ||||||||
\(821\) | 41.1793 | 1.43717 | 0.718584 | − | 0.695441i | \(-0.244791\pi\) | ||||
0.718584 | + | 0.695441i | \(0.244791\pi\) | |||||||
\(822\) | −33.6764 | −1.17460 | ||||||||
\(823\) | −29.0771 | −1.01356 | −0.506782 | − | 0.862074i | \(-0.669165\pi\) | ||||
−0.506782 | + | 0.862074i | \(0.669165\pi\) | |||||||
\(824\) | 29.8854 | 1.04111 | ||||||||
\(825\) | 10.4829 | 0.364968 | ||||||||
\(826\) | 4.14213 | 0.144123 | ||||||||
\(827\) | 43.2599 | 1.50429 | 0.752147 | − | 0.658996i | \(-0.229019\pi\) | ||||
0.752147 | + | 0.658996i | \(0.229019\pi\) | |||||||
\(828\) | −28.9970 | −1.00772 | ||||||||
\(829\) | 33.4857 | 1.16301 | 0.581503 | − | 0.813544i | \(-0.302465\pi\) | ||||
0.581503 | + | 0.813544i | \(0.302465\pi\) | |||||||
\(830\) | 19.5292 | 0.677868 | ||||||||
\(831\) | 66.2622 | 2.29861 | ||||||||
\(832\) | −18.5373 | −0.642666 | ||||||||
\(833\) | −20.1276 | −0.697381 | ||||||||
\(834\) | −62.0663 | −2.14918 | ||||||||
\(835\) | −8.15163 | −0.282099 | ||||||||
\(836\) | 20.0257 | 0.692604 | ||||||||
\(837\) | −31.1773 | −1.07765 | ||||||||
\(838\) | 76.4876 | 2.64222 | ||||||||
\(839\) | 8.70338 | 0.300474 | 0.150237 | − | 0.988650i | \(-0.451996\pi\) | ||||
0.150237 | + | 0.988650i | \(0.451996\pi\) | |||||||
\(840\) | −7.66559 | −0.264488 | ||||||||
\(841\) | 16.4563 | 0.567459 | ||||||||
\(842\) | −2.53540 | −0.0873758 | ||||||||
\(843\) | −79.8883 | −2.75150 | ||||||||
\(844\) | −40.4046 | −1.39078 | ||||||||
\(845\) | 13.6153 | 0.468380 | ||||||||
\(846\) | −126.709 | −4.35634 | ||||||||
\(847\) | 0.599145 | 0.0205869 | ||||||||
\(848\) | −9.99911 | −0.343371 | ||||||||
\(849\) | 57.9182 | 1.98775 | ||||||||
\(850\) | 24.0425 | 0.824652 | ||||||||
\(851\) | −0.992261 | −0.0340143 | ||||||||
\(852\) | 90.2829 | 3.09304 | ||||||||
\(853\) | 15.0584 | 0.515590 | 0.257795 | − | 0.966200i | \(-0.417004\pi\) | ||||
0.257795 | + | 0.966200i | \(0.417004\pi\) | |||||||
\(854\) | 2.68909 | 0.0920187 | ||||||||
\(855\) | −47.7607 | −1.63338 | ||||||||
\(856\) | −14.6308 | −0.500069 | ||||||||
\(857\) | −16.9262 | −0.578189 | −0.289094 | − | 0.957301i | \(-0.593354\pi\) | ||||
−0.289094 | + | 0.957301i | \(0.593354\pi\) | |||||||
\(858\) | 10.6359 | 0.363104 | ||||||||
\(859\) | −35.4021 | −1.20791 | −0.603953 | − | 0.797020i | \(-0.706408\pi\) | ||||
−0.603953 | + | 0.797020i | \(0.706408\pi\) | |||||||
\(860\) | 40.2591 | 1.37282 | ||||||||
\(861\) | −10.1590 | −0.346217 | ||||||||
\(862\) | 57.2112 | 1.94862 | ||||||||
\(863\) | −42.8410 | −1.45833 | −0.729163 | − | 0.684340i | \(-0.760090\pi\) | ||||
−0.729163 | + | 0.684340i | \(0.760090\pi\) | |||||||
\(864\) | −49.3446 | −1.67874 | ||||||||
\(865\) | 9.08729 | 0.308977 | ||||||||
\(866\) | 59.4372 | 2.01976 | ||||||||
\(867\) | 24.0335 | 0.816219 | ||||||||
\(868\) | 5.99891 | 0.203616 | ||||||||
\(869\) | −2.92252 | −0.0991396 | ||||||||
\(870\) | −60.8851 | −2.06420 | ||||||||
\(871\) | −9.71028 | −0.329020 | ||||||||
\(872\) | −44.1042 | −1.49356 | ||||||||
\(873\) | −80.5247 | −2.72535 | ||||||||
\(874\) | 17.9224 | 0.606234 | ||||||||
\(875\) | 6.35567 | 0.214861 | ||||||||
\(876\) | 57.2054 | 1.93279 | ||||||||
\(877\) | −26.2919 | −0.887816 | −0.443908 | − | 0.896072i | \(-0.646408\pi\) | ||||
−0.443908 | + | 0.896072i | \(0.646408\pi\) | |||||||
\(878\) | 12.0057 | 0.405174 | ||||||||
\(879\) | 54.4916 | 1.83796 | ||||||||
\(880\) | −1.06072 | −0.0357567 | ||||||||
\(881\) | −34.4620 | −1.16106 | −0.580528 | − | 0.814240i | \(-0.697154\pi\) | ||||
−0.580528 | + | 0.814240i | \(0.697154\pi\) | |||||||
\(882\) | 99.8365 | 3.36167 | ||||||||
\(883\) | −4.28090 | −0.144064 | −0.0720318 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720318 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(884\) | 15.3868 | 0.517515 | ||||||||
\(885\) | −11.5256 | −0.387430 | ||||||||
\(886\) | 63.1559 | 2.12177 | ||||||||
\(887\) | 16.7400 | 0.562073 | 0.281037 | − | 0.959697i | \(-0.409322\pi\) | ||||
0.281037 | + | 0.959697i | \(0.409322\pi\) | |||||||
\(888\) | 7.65899 | 0.257019 | ||||||||
\(889\) | −0.805143 | −0.0270036 | ||||||||
\(890\) | −19.5202 | −0.654319 | ||||||||
\(891\) | 13.3444 | 0.447056 | ||||||||
\(892\) | −43.7534 | −1.46497 | ||||||||
\(893\) | 49.3998 | 1.65310 | ||||||||
\(894\) | 113.351 | 3.79104 | ||||||||
\(895\) | 11.1269 | 0.371931 | ||||||||
\(896\) | 11.8394 | 0.395526 | ||||||||
\(897\) | 6.00424 | 0.200476 | ||||||||
\(898\) | 58.0745 | 1.93797 | ||||||||
\(899\) | 19.7570 | 0.658934 | ||||||||
\(900\) | −75.2233 | −2.50744 | ||||||||
\(901\) | −36.0441 | −1.20080 | ||||||||
\(902\) | −12.8310 | −0.427224 | ||||||||
\(903\) | 17.2105 | 0.572731 | ||||||||
\(904\) | 23.4762 | 0.780808 | ||||||||
\(905\) | 11.5953 | 0.385441 | ||||||||
\(906\) | −50.7231 | −1.68516 | ||||||||
\(907\) | 22.4839 | 0.746566 | 0.373283 | − | 0.927717i | \(-0.378232\pi\) | ||||
0.373283 | + | 0.927717i | \(0.378232\pi\) | |||||||
\(908\) | −49.8794 | −1.65531 | ||||||||
\(909\) | 25.9322 | 0.860116 | ||||||||
\(910\) | 2.61392 | 0.0866507 | ||||||||
\(911\) | −24.5921 | −0.814772 | −0.407386 | − | 0.913256i | \(-0.633560\pi\) | ||||
−0.407386 | + | 0.913256i | \(0.633560\pi\) | |||||||
\(912\) | −15.1560 | −0.501866 | ||||||||
\(913\) | 6.65119 | 0.220122 | ||||||||
\(914\) | 37.8021 | 1.25038 | ||||||||
\(915\) | −7.48250 | −0.247364 | ||||||||
\(916\) | 73.5532 | 2.43027 | ||||||||
\(917\) | −1.44451 | −0.0477020 | ||||||||
\(918\) | 75.0485 | 2.47697 | ||||||||
\(919\) | −4.09733 | −0.135158 | −0.0675792 | − | 0.997714i | \(-0.521528\pi\) | ||||
−0.0675792 | + | 0.997714i | \(0.521528\pi\) | |||||||
\(920\) | −5.46560 | −0.180196 | ||||||||
\(921\) | −30.6042 | −1.00844 | ||||||||
\(922\) | 8.99611 | 0.296271 | ||||||||
\(923\) | −12.7655 | −0.420180 | ||||||||
\(924\) | −6.29618 | −0.207129 | ||||||||
\(925\) | −2.57410 | −0.0846358 | ||||||||
\(926\) | −22.7290 | −0.746920 | ||||||||
\(927\) | −58.5428 | −1.92280 | ||||||||
\(928\) | 31.2696 | 1.02647 | ||||||||
\(929\) | −30.4192 | −0.998020 | −0.499010 | − | 0.866596i | \(-0.666303\pi\) | ||||
−0.499010 | + | 0.866596i | \(0.666303\pi\) | |||||||
\(930\) | −26.4630 | −0.867755 | ||||||||
\(931\) | −38.9231 | −1.27565 | ||||||||
\(932\) | −52.8649 | −1.73165 | ||||||||
\(933\) | 20.2579 | 0.663212 | ||||||||
\(934\) | 11.9187 | 0.389990 | ||||||||
\(935\) | −3.82360 | −0.125045 | ||||||||
\(936\) | −31.6468 | −1.03441 | ||||||||
\(937\) | −25.3829 | −0.829224 | −0.414612 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414612 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(938\) | 9.11293 | 0.297548 | ||||||||
\(939\) | 107.104 | 3.49522 | ||||||||
\(940\) | −36.3315 | −1.18500 | ||||||||
\(941\) | 29.7991 | 0.971422 | 0.485711 | − | 0.874119i | \(-0.338561\pi\) | ||||
0.485711 | + | 0.874119i | \(0.338561\pi\) | |||||||
\(942\) | 70.4441 | 2.29519 | ||||||||
\(943\) | −7.24340 | −0.235877 | ||||||||
\(944\) | −2.49750 | −0.0812866 | ||||||||
\(945\) | 8.04195 | 0.261605 | ||||||||
\(946\) | 21.7372 | 0.706738 | ||||||||
\(947\) | 32.2793 | 1.04893 | 0.524467 | − | 0.851430i | \(-0.324264\pi\) | ||||
0.524467 | + | 0.851430i | \(0.324264\pi\) | |||||||
\(948\) | 30.7116 | 0.997466 | ||||||||
\(949\) | −8.08849 | −0.262564 | ||||||||
\(950\) | 46.4938 | 1.50846 | ||||||||
\(951\) | −40.6913 | −1.31951 | ||||||||
\(952\) | −5.98769 | −0.194062 | ||||||||
\(953\) | −41.6583 | −1.34945 | −0.674723 | − | 0.738071i | \(-0.735737\pi\) | ||||
−0.674723 | + | 0.738071i | \(0.735737\pi\) | |||||||
\(954\) | 178.785 | 5.78838 | ||||||||
\(955\) | −7.17822 | −0.232282 | ||||||||
\(956\) | −88.3612 | −2.85781 | ||||||||
\(957\) | −20.7361 | −0.670301 | ||||||||
\(958\) | 79.0807 | 2.55498 | ||||||||
\(959\) | −2.81877 | −0.0910227 | ||||||||
\(960\) | −48.4078 | −1.56235 | ||||||||
\(961\) | −22.4129 | −0.722995 | ||||||||
\(962\) | −2.61167 | −0.0842037 | ||||||||
\(963\) | 28.6603 | 0.923566 | ||||||||
\(964\) | 70.9655 | 2.28564 | ||||||||
\(965\) | −16.3353 | −0.525851 | ||||||||
\(966\) | −5.63488 | −0.181299 | ||||||||
\(967\) | 10.2163 | 0.328534 | 0.164267 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164267 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(968\) | −3.29739 | −0.105982 | ||||||||
\(969\) | −54.6334 | −1.75508 | ||||||||
\(970\) | −36.6041 | −1.17529 | ||||||||
\(971\) | 22.4164 | 0.719375 | 0.359687 | − | 0.933073i | \(-0.382883\pi\) | ||||
0.359687 | + | 0.933073i | \(0.382883\pi\) | |||||||
\(972\) | −31.1749 | −0.999934 | ||||||||
\(973\) | −5.19504 | −0.166545 | ||||||||
\(974\) | 81.2667 | 2.60395 | ||||||||
\(975\) | 15.5761 | 0.498833 | ||||||||
\(976\) | −1.62139 | −0.0518994 | ||||||||
\(977\) | 34.1828 | 1.09360 | 0.546802 | − | 0.837262i | \(-0.315845\pi\) | ||||
0.546802 | + | 0.837262i | \(0.315845\pi\) | |||||||
\(978\) | −140.052 | −4.47836 | ||||||||
\(979\) | −6.64813 | −0.212475 | ||||||||
\(980\) | 28.6263 | 0.914435 | ||||||||
\(981\) | 86.3960 | 2.75841 | ||||||||
\(982\) | 1.02968 | 0.0328585 | ||||||||
\(983\) | −37.1639 | −1.18535 | −0.592673 | − | 0.805443i | \(-0.701927\pi\) | ||||
−0.592673 | + | 0.805443i | \(0.701927\pi\) | |||||||
\(984\) | 55.9098 | 1.78234 | ||||||||
\(985\) | −28.0667 | −0.894280 | ||||||||
\(986\) | −47.5581 | −1.51456 | ||||||||
\(987\) | −15.5315 | −0.494374 | ||||||||
\(988\) | 29.7553 | 0.946641 | ||||||||
\(989\) | 12.2712 | 0.390201 | ||||||||
\(990\) | 18.9657 | 0.602770 | ||||||||
\(991\) | 15.1619 | 0.481634 | 0.240817 | − | 0.970571i | \(-0.422585\pi\) | ||||
0.240817 | + | 0.970571i | \(0.422585\pi\) | |||||||
\(992\) | 13.5909 | 0.431513 | ||||||||
\(993\) | −32.5244 | −1.03213 | ||||||||
\(994\) | 11.9802 | 0.379988 | ||||||||
\(995\) | −17.7523 | −0.562785 | ||||||||
\(996\) | −69.8947 | −2.21470 | ||||||||
\(997\) | 5.77715 | 0.182964 | 0.0914821 | − | 0.995807i | \(-0.470840\pi\) | ||||
0.0914821 | + | 0.995807i | \(0.470840\pi\) | |||||||
\(998\) | 55.2798 | 1.74985 | ||||||||
\(999\) | −8.03502 | −0.254217 |
(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 | 6017.2.a.c.1.14 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.14 | ✓ | 106 | 1.1 | even | 1 | trivial |