Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.296108 | −0.170958 | −0.0854790 | − | 0.996340i | \(-0.527242\pi\) | ||||
−0.0854790 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.296108 | 0.120886 | ||||||||
\(7\) | −4.13577 | −1.56317 | −0.781586 | − | 0.623797i | \(-0.785589\pi\) | ||||
−0.781586 | + | 0.623797i | \(0.785589\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.91232 | −0.970773 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.822860 | −0.248102 | −0.124051 | − | 0.992276i | \(-0.539589\pi\) | ||||
−0.124051 | + | 0.992276i | \(0.539589\pi\) | |||||||
\(12\) | −0.296108 | −0.0854790 | ||||||||
\(13\) | 3.99861 | 1.10902 | 0.554508 | − | 0.832179i | \(-0.312907\pi\) | ||||
0.554508 | + | 0.832179i | \(0.312907\pi\) | |||||||
\(14\) | 4.13577 | 1.10533 | ||||||||
\(15\) | 0.296108 | 0.0764548 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.706145 | 0.171265 | 0.0856326 | − | 0.996327i | \(-0.472709\pi\) | ||||
0.0856326 | + | 0.996327i | \(0.472709\pi\) | |||||||
\(18\) | 2.91232 | 0.686440 | ||||||||
\(19\) | −7.10481 | −1.62995 | −0.814977 | − | 0.579493i | \(-0.803251\pi\) | ||||
−0.814977 | + | 0.579493i | \(0.803251\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.22463 | 0.267237 | ||||||||
\(22\) | 0.822860 | 0.175434 | ||||||||
\(23\) | 1.64986 | 0.344019 | 0.172009 | − | 0.985095i | \(-0.444974\pi\) | ||||
0.172009 | + | 0.985095i | \(0.444974\pi\) | |||||||
\(24\) | 0.296108 | 0.0604428 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.99861 | −0.784192 | ||||||||
\(27\) | 1.75069 | 0.336920 | ||||||||
\(28\) | −4.13577 | −0.781586 | ||||||||
\(29\) | 5.42043 | 1.00655 | 0.503274 | − | 0.864127i | \(-0.332129\pi\) | ||||
0.503274 | + | 0.864127i | \(0.332129\pi\) | |||||||
\(30\) | −0.296108 | −0.0540617 | ||||||||
\(31\) | 9.32030 | 1.67397 | 0.836987 | − | 0.547222i | \(-0.184315\pi\) | ||||
0.836987 | + | 0.547222i | \(0.184315\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.243656 | 0.0424150 | ||||||||
\(34\) | −0.706145 | −0.121103 | ||||||||
\(35\) | 4.13577 | 0.699072 | ||||||||
\(36\) | −2.91232 | −0.485387 | ||||||||
\(37\) | 8.12172 | 1.33520 | 0.667601 | − | 0.744519i | \(-0.267321\pi\) | ||||
0.667601 | + | 0.744519i | \(0.267321\pi\) | |||||||
\(38\) | 7.10481 | 1.15255 | ||||||||
\(39\) | −1.18402 | −0.189595 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.09551 | −0.483437 | −0.241719 | − | 0.970346i | \(-0.577711\pi\) | ||||
−0.241719 | + | 0.970346i | \(0.577711\pi\) | |||||||
\(42\) | −1.22463 | −0.188965 | ||||||||
\(43\) | 1.99945 | 0.304914 | 0.152457 | − | 0.988310i | \(-0.451281\pi\) | ||||
0.152457 | + | 0.988310i | \(0.451281\pi\) | |||||||
\(44\) | −0.822860 | −0.124051 | ||||||||
\(45\) | 2.91232 | 0.434143 | ||||||||
\(46\) | −1.64986 | −0.243258 | ||||||||
\(47\) | −6.03806 | −0.880741 | −0.440370 | − | 0.897816i | \(-0.645153\pi\) | ||||
−0.440370 | + | 0.897816i | \(0.645153\pi\) | |||||||
\(48\) | −0.296108 | −0.0427395 | ||||||||
\(49\) | 10.1046 | 1.44351 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.209095 | −0.0292792 | ||||||||
\(52\) | 3.99861 | 0.554508 | ||||||||
\(53\) | −9.56029 | −1.31321 | −0.656604 | − | 0.754236i | \(-0.728007\pi\) | ||||
−0.656604 | + | 0.754236i | \(0.728007\pi\) | |||||||
\(54\) | −1.75069 | −0.238238 | ||||||||
\(55\) | 0.822860 | 0.110954 | ||||||||
\(56\) | 4.13577 | 0.552665 | ||||||||
\(57\) | 2.10379 | 0.278654 | ||||||||
\(58\) | −5.42043 | −0.711737 | ||||||||
\(59\) | 13.5316 | 1.76166 | 0.880832 | − | 0.473428i | \(-0.156984\pi\) | ||||
0.880832 | + | 0.473428i | \(0.156984\pi\) | |||||||
\(60\) | 0.296108 | 0.0382274 | ||||||||
\(61\) | 1.75683 | 0.224939 | 0.112470 | − | 0.993655i | \(-0.464124\pi\) | ||||
0.112470 | + | 0.993655i | \(0.464124\pi\) | |||||||
\(62\) | −9.32030 | −1.18368 | ||||||||
\(63\) | 12.0447 | 1.51749 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.99861 | −0.495967 | ||||||||
\(66\) | −0.243656 | −0.0299919 | ||||||||
\(67\) | 3.37580 | 0.412419 | 0.206210 | − | 0.978508i | \(-0.433887\pi\) | ||||
0.206210 | + | 0.978508i | \(0.433887\pi\) | |||||||
\(68\) | 0.706145 | 0.0856326 | ||||||||
\(69\) | −0.488536 | −0.0588128 | ||||||||
\(70\) | −4.13577 | −0.494319 | ||||||||
\(71\) | −9.49307 | −1.12662 | −0.563310 | − | 0.826246i | \(-0.690472\pi\) | ||||
−0.563310 | + | 0.826246i | \(0.690472\pi\) | |||||||
\(72\) | 2.91232 | 0.343220 | ||||||||
\(73\) | −2.28444 | −0.267373 | −0.133686 | − | 0.991024i | \(-0.542682\pi\) | ||||
−0.133686 | + | 0.991024i | \(0.542682\pi\) | |||||||
\(74\) | −8.12172 | −0.944131 | ||||||||
\(75\) | −0.296108 | −0.0341916 | ||||||||
\(76\) | −7.10481 | −0.814977 | ||||||||
\(77\) | 3.40316 | 0.387826 | ||||||||
\(78\) | 1.18402 | 0.134064 | ||||||||
\(79\) | −10.1450 | −1.14140 | −0.570700 | − | 0.821159i | \(-0.693328\pi\) | ||||
−0.570700 | + | 0.821159i | \(0.693328\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.21857 | 0.913174 | ||||||||
\(82\) | 3.09551 | 0.341842 | ||||||||
\(83\) | 4.37454 | 0.480168 | 0.240084 | − | 0.970752i | \(-0.422825\pi\) | ||||
0.240084 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(84\) | 1.22463 | 0.133618 | ||||||||
\(85\) | −0.706145 | −0.0765922 | ||||||||
\(86\) | −1.99945 | −0.215607 | ||||||||
\(87\) | −1.60503 | −0.172077 | ||||||||
\(88\) | 0.822860 | 0.0877172 | ||||||||
\(89\) | 17.8609 | 1.89325 | 0.946627 | − | 0.322332i | \(-0.104467\pi\) | ||||
0.946627 | + | 0.322332i | \(0.104467\pi\) | |||||||
\(90\) | −2.91232 | −0.306985 | ||||||||
\(91\) | −16.5373 | −1.73358 | ||||||||
\(92\) | 1.64986 | 0.172009 | ||||||||
\(93\) | −2.75981 | −0.286179 | ||||||||
\(94\) | 6.03806 | 0.622778 | ||||||||
\(95\) | 7.10481 | 0.728938 | ||||||||
\(96\) | 0.296108 | 0.0302214 | ||||||||
\(97\) | −4.31564 | −0.438187 | −0.219093 | − | 0.975704i | \(-0.570310\pi\) | ||||
−0.219093 | + | 0.975704i | \(0.570310\pi\) | |||||||
\(98\) | −10.1046 | −1.02071 | ||||||||
\(99\) | 2.39643 | 0.240851 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.44498 | 0.243285 | 0.121642 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121642 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(102\) | 0.209095 | 0.0207035 | ||||||||
\(103\) | 4.50202 | 0.443597 | 0.221799 | − | 0.975092i | \(-0.428807\pi\) | ||||
0.221799 | + | 0.975092i | \(0.428807\pi\) | |||||||
\(104\) | −3.99861 | −0.392096 | ||||||||
\(105\) | −1.22463 | −0.119512 | ||||||||
\(106\) | 9.56029 | 0.928578 | ||||||||
\(107\) | −11.3731 | −1.09948 | −0.549738 | − | 0.835337i | \(-0.685273\pi\) | ||||
−0.549738 | + | 0.835337i | \(0.685273\pi\) | |||||||
\(108\) | 1.75069 | 0.168460 | ||||||||
\(109\) | 10.0190 | 0.959644 | 0.479822 | − | 0.877366i | \(-0.340701\pi\) | ||||
0.479822 | + | 0.877366i | \(0.340701\pi\) | |||||||
\(110\) | −0.822860 | −0.0784567 | ||||||||
\(111\) | −2.40491 | −0.228264 | ||||||||
\(112\) | −4.13577 | −0.390793 | ||||||||
\(113\) | 4.40252 | 0.414154 | 0.207077 | − | 0.978325i | \(-0.433605\pi\) | ||||
0.207077 | + | 0.978325i | \(0.433605\pi\) | |||||||
\(114\) | −2.10379 | −0.197038 | ||||||||
\(115\) | −1.64986 | −0.153850 | ||||||||
\(116\) | 5.42043 | 0.503274 | ||||||||
\(117\) | −11.6452 | −1.07660 | ||||||||
\(118\) | −13.5316 | −1.24569 | ||||||||
\(119\) | −2.92045 | −0.267717 | ||||||||
\(120\) | −0.296108 | −0.0270308 | ||||||||
\(121\) | −10.3229 | −0.938446 | ||||||||
\(122\) | −1.75683 | −0.159056 | ||||||||
\(123\) | 0.916605 | 0.0826475 | ||||||||
\(124\) | 9.32030 | 0.836987 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −12.0447 | −1.07302 | ||||||||
\(127\) | −15.2948 | −1.35720 | −0.678598 | − | 0.734510i | \(-0.737412\pi\) | ||||
−0.678598 | + | 0.734510i | \(0.737412\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.592055 | −0.0521275 | ||||||||
\(130\) | 3.99861 | 0.350701 | ||||||||
\(131\) | 3.96317 | 0.346263 | 0.173132 | − | 0.984899i | \(-0.444611\pi\) | ||||
0.173132 | + | 0.984899i | \(0.444611\pi\) | |||||||
\(132\) | 0.243656 | 0.0212075 | ||||||||
\(133\) | 29.3838 | 2.54790 | ||||||||
\(134\) | −3.37580 | −0.291624 | ||||||||
\(135\) | −1.75069 | −0.150675 | ||||||||
\(136\) | −0.706145 | −0.0605514 | ||||||||
\(137\) | −4.62278 | −0.394951 | −0.197475 | − | 0.980308i | \(-0.563274\pi\) | ||||
−0.197475 | + | 0.980308i | \(0.563274\pi\) | |||||||
\(138\) | 0.488536 | 0.0415869 | ||||||||
\(139\) | 14.5029 | 1.23012 | 0.615061 | − | 0.788479i | \(-0.289131\pi\) | ||||
0.615061 | + | 0.788479i | \(0.289131\pi\) | |||||||
\(140\) | 4.13577 | 0.349536 | ||||||||
\(141\) | 1.78792 | 0.150570 | ||||||||
\(142\) | 9.49307 | 0.796641 | ||||||||
\(143\) | −3.29030 | −0.275149 | ||||||||
\(144\) | −2.91232 | −0.242693 | ||||||||
\(145\) | −5.42043 | −0.450142 | ||||||||
\(146\) | 2.28444 | 0.189061 | ||||||||
\(147\) | −2.99204 | −0.246779 | ||||||||
\(148\) | 8.12172 | 0.667601 | ||||||||
\(149\) | −1.37553 | −0.112688 | −0.0563438 | − | 0.998411i | \(-0.517944\pi\) | ||||
−0.0563438 | + | 0.998411i | \(0.517944\pi\) | |||||||
\(150\) | 0.296108 | 0.0241771 | ||||||||
\(151\) | −20.5910 | −1.67567 | −0.837834 | − | 0.545925i | \(-0.816178\pi\) | ||||
−0.837834 | + | 0.545925i | \(0.816178\pi\) | |||||||
\(152\) | 7.10481 | 0.576276 | ||||||||
\(153\) | −2.05652 | −0.166260 | ||||||||
\(154\) | −3.40316 | −0.274234 | ||||||||
\(155\) | −9.32030 | −0.748624 | ||||||||
\(156\) | −1.18402 | −0.0947975 | ||||||||
\(157\) | −10.0317 | −0.800619 | −0.400310 | − | 0.916380i | \(-0.631097\pi\) | ||||
−0.400310 | + | 0.916380i | \(0.631097\pi\) | |||||||
\(158\) | 10.1450 | 0.807092 | ||||||||
\(159\) | 2.83088 | 0.224503 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −6.82342 | −0.537761 | ||||||||
\(162\) | −8.21857 | −0.645712 | ||||||||
\(163\) | 6.90312 | 0.540694 | 0.270347 | − | 0.962763i | \(-0.412862\pi\) | ||||
0.270347 | + | 0.962763i | \(0.412862\pi\) | |||||||
\(164\) | −3.09551 | −0.241719 | ||||||||
\(165\) | −0.243656 | −0.0189686 | ||||||||
\(166\) | −4.37454 | −0.339530 | ||||||||
\(167\) | −11.7018 | −0.905510 | −0.452755 | − | 0.891635i | \(-0.649559\pi\) | ||||
−0.452755 | + | 0.891635i | \(0.649559\pi\) | |||||||
\(168\) | −1.22463 | −0.0944825 | ||||||||
\(169\) | 2.98889 | 0.229915 | ||||||||
\(170\) | 0.706145 | 0.0541588 | ||||||||
\(171\) | 20.6915 | 1.58232 | ||||||||
\(172\) | 1.99945 | 0.152457 | ||||||||
\(173\) | −17.2942 | −1.31485 | −0.657425 | − | 0.753520i | \(-0.728354\pi\) | ||||
−0.657425 | + | 0.753520i | \(0.728354\pi\) | |||||||
\(174\) | 1.60503 | 0.121677 | ||||||||
\(175\) | −4.13577 | −0.312635 | ||||||||
\(176\) | −0.822860 | −0.0620254 | ||||||||
\(177\) | −4.00682 | −0.301171 | ||||||||
\(178\) | −17.8609 | −1.33873 | ||||||||
\(179\) | −13.4637 | −1.00633 | −0.503163 | − | 0.864192i | \(-0.667830\pi\) | ||||
−0.503163 | + | 0.864192i | \(0.667830\pi\) | |||||||
\(180\) | 2.91232 | 0.217072 | ||||||||
\(181\) | −8.63696 | −0.641980 | −0.320990 | − | 0.947083i | \(-0.604016\pi\) | ||||
−0.320990 | + | 0.947083i | \(0.604016\pi\) | |||||||
\(182\) | 16.5373 | 1.22583 | ||||||||
\(183\) | −0.520212 | −0.0384551 | ||||||||
\(184\) | −1.64986 | −0.121629 | ||||||||
\(185\) | −8.12172 | −0.597121 | ||||||||
\(186\) | 2.75981 | 0.202359 | ||||||||
\(187\) | −0.581059 | −0.0424912 | ||||||||
\(188\) | −6.03806 | −0.440370 | ||||||||
\(189\) | −7.24042 | −0.526663 | ||||||||
\(190\) | −7.10481 | −0.515437 | ||||||||
\(191\) | 19.6582 | 1.42241 | 0.711207 | − | 0.702983i | \(-0.248149\pi\) | ||||
0.711207 | + | 0.702983i | \(0.248149\pi\) | |||||||
\(192\) | −0.296108 | −0.0213698 | ||||||||
\(193\) | 8.04192 | 0.578870 | 0.289435 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289435 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(194\) | 4.31564 | 0.309845 | ||||||||
\(195\) | 1.18402 | 0.0847895 | ||||||||
\(196\) | 10.1046 | 0.721754 | ||||||||
\(197\) | 5.98586 | 0.426475 | 0.213237 | − | 0.977000i | \(-0.431599\pi\) | ||||
0.213237 | + | 0.977000i | \(0.431599\pi\) | |||||||
\(198\) | −2.39643 | −0.170307 | ||||||||
\(199\) | −14.4209 | −1.02227 | −0.511135 | − | 0.859500i | \(-0.670775\pi\) | ||||
−0.511135 | + | 0.859500i | \(0.670775\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −0.999600 | −0.0705064 | ||||||||
\(202\) | −2.44498 | −0.172028 | ||||||||
\(203\) | −22.4176 | −1.57341 | ||||||||
\(204\) | −0.209095 | −0.0146396 | ||||||||
\(205\) | 3.09551 | 0.216200 | ||||||||
\(206\) | −4.50202 | −0.313671 | ||||||||
\(207\) | −4.80491 | −0.333964 | ||||||||
\(208\) | 3.99861 | 0.277254 | ||||||||
\(209\) | 5.84626 | 0.404394 | ||||||||
\(210\) | 1.22463 | 0.0845077 | ||||||||
\(211\) | −15.9423 | −1.09752 | −0.548758 | − | 0.835981i | \(-0.684899\pi\) | ||||
−0.548758 | + | 0.835981i | \(0.684899\pi\) | |||||||
\(212\) | −9.56029 | −0.656604 | ||||||||
\(213\) | 2.81097 | 0.192605 | ||||||||
\(214\) | 11.3731 | 0.777447 | ||||||||
\(215\) | −1.99945 | −0.136362 | ||||||||
\(216\) | −1.75069 | −0.119119 | ||||||||
\(217\) | −38.5466 | −2.61671 | ||||||||
\(218\) | −10.0190 | −0.678570 | ||||||||
\(219\) | 0.676439 | 0.0457095 | ||||||||
\(220\) | 0.822860 | 0.0554772 | ||||||||
\(221\) | 2.82360 | 0.189936 | ||||||||
\(222\) | 2.40491 | 0.161407 | ||||||||
\(223\) | −22.3927 | −1.49952 | −0.749761 | − | 0.661708i | \(-0.769832\pi\) | ||||
−0.749761 | + | 0.661708i | \(0.769832\pi\) | |||||||
\(224\) | 4.13577 | 0.276332 | ||||||||
\(225\) | −2.91232 | −0.194155 | ||||||||
\(226\) | −4.40252 | −0.292851 | ||||||||
\(227\) | −25.4914 | −1.69193 | −0.845963 | − | 0.533242i | \(-0.820973\pi\) | ||||
−0.845963 | + | 0.533242i | \(0.820973\pi\) | |||||||
\(228\) | 2.10379 | 0.139327 | ||||||||
\(229\) | 14.2915 | 0.944406 | 0.472203 | − | 0.881490i | \(-0.343459\pi\) | ||||
0.472203 | + | 0.881490i | \(0.343459\pi\) | |||||||
\(230\) | 1.64986 | 0.108788 | ||||||||
\(231\) | −1.00770 | −0.0663019 | ||||||||
\(232\) | −5.42043 | −0.355868 | ||||||||
\(233\) | −8.74153 | −0.572677 | −0.286338 | − | 0.958129i | \(-0.592438\pi\) | ||||
−0.286338 | + | 0.958129i | \(0.592438\pi\) | |||||||
\(234\) | 11.6452 | 0.761273 | ||||||||
\(235\) | 6.03806 | 0.393879 | ||||||||
\(236\) | 13.5316 | 0.880832 | ||||||||
\(237\) | 3.00401 | 0.195132 | ||||||||
\(238\) | 2.92045 | 0.189305 | ||||||||
\(239\) | 12.0802 | 0.781403 | 0.390702 | − | 0.920517i | \(-0.372232\pi\) | ||||
0.390702 | + | 0.920517i | \(0.372232\pi\) | |||||||
\(240\) | 0.296108 | 0.0191137 | ||||||||
\(241\) | 26.0973 | 1.68107 | 0.840537 | − | 0.541754i | \(-0.182240\pi\) | ||||
0.840537 | + | 0.541754i | \(0.182240\pi\) | |||||||
\(242\) | 10.3229 | 0.663581 | ||||||||
\(243\) | −7.68564 | −0.493034 | ||||||||
\(244\) | 1.75683 | 0.112470 | ||||||||
\(245\) | −10.1046 | −0.645557 | ||||||||
\(246\) | −0.916605 | −0.0584406 | ||||||||
\(247\) | −28.4094 | −1.80764 | ||||||||
\(248\) | −9.32030 | −0.591839 | ||||||||
\(249\) | −1.29534 | −0.0820886 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −20.6946 | −1.30623 | −0.653115 | − | 0.757259i | \(-0.726538\pi\) | ||||
−0.653115 | + | 0.757259i | \(0.726538\pi\) | |||||||
\(252\) | 12.0447 | 0.758743 | ||||||||
\(253\) | −1.35760 | −0.0853517 | ||||||||
\(254\) | 15.2948 | 0.959682 | ||||||||
\(255\) | 0.209095 | 0.0130940 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.82529 | 0.488128 | 0.244064 | − | 0.969759i | \(-0.421519\pi\) | ||||
0.244064 | + | 0.969759i | \(0.421519\pi\) | |||||||
\(258\) | 0.592055 | 0.0368597 | ||||||||
\(259\) | −33.5895 | −2.08715 | ||||||||
\(260\) | −3.99861 | −0.247983 | ||||||||
\(261\) | −15.7860 | −0.977130 | ||||||||
\(262\) | −3.96317 | −0.244845 | ||||||||
\(263\) | 15.9940 | 0.986232 | 0.493116 | − | 0.869964i | \(-0.335858\pi\) | ||||
0.493116 | + | 0.869964i | \(0.335858\pi\) | |||||||
\(264\) | −0.243656 | −0.0149960 | ||||||||
\(265\) | 9.56029 | 0.587284 | ||||||||
\(266\) | −29.3838 | −1.80164 | ||||||||
\(267\) | −5.28876 | −0.323667 | ||||||||
\(268\) | 3.37580 | 0.206210 | ||||||||
\(269\) | 17.2558 | 1.05210 | 0.526051 | − | 0.850453i | \(-0.323672\pi\) | ||||
0.526051 | + | 0.850453i | \(0.323672\pi\) | |||||||
\(270\) | 1.75069 | 0.106543 | ||||||||
\(271\) | 11.3627 | 0.690236 | 0.345118 | − | 0.938559i | \(-0.387839\pi\) | ||||
0.345118 | + | 0.938559i | \(0.387839\pi\) | |||||||
\(272\) | 0.706145 | 0.0428163 | ||||||||
\(273\) | 4.89683 | 0.296370 | ||||||||
\(274\) | 4.62278 | 0.279272 | ||||||||
\(275\) | −0.822860 | −0.0496204 | ||||||||
\(276\) | −0.488536 | −0.0294064 | ||||||||
\(277\) | 18.4155 | 1.10648 | 0.553240 | − | 0.833022i | \(-0.313391\pi\) | ||||
0.553240 | + | 0.833022i | \(0.313391\pi\) | |||||||
\(278\) | −14.5029 | −0.869828 | ||||||||
\(279\) | −27.1437 | −1.62505 | ||||||||
\(280\) | −4.13577 | −0.247159 | ||||||||
\(281\) | 1.48925 | 0.0888410 | 0.0444205 | − | 0.999013i | \(-0.485856\pi\) | ||||
0.0444205 | + | 0.999013i | \(0.485856\pi\) | |||||||
\(282\) | −1.78792 | −0.106469 | ||||||||
\(283\) | 19.5290 | 1.16088 | 0.580438 | − | 0.814304i | \(-0.302881\pi\) | ||||
0.580438 | + | 0.814304i | \(0.302881\pi\) | |||||||
\(284\) | −9.49307 | −0.563310 | ||||||||
\(285\) | −2.10379 | −0.124618 | ||||||||
\(286\) | 3.29030 | 0.194559 | ||||||||
\(287\) | 12.8023 | 0.755696 | ||||||||
\(288\) | 2.91232 | 0.171610 | ||||||||
\(289\) | −16.5014 | −0.970668 | ||||||||
\(290\) | 5.42043 | 0.318298 | ||||||||
\(291\) | 1.27790 | 0.0749115 | ||||||||
\(292\) | −2.28444 | −0.133686 | ||||||||
\(293\) | −20.1562 | −1.17754 | −0.588770 | − | 0.808301i | \(-0.700388\pi\) | ||||
−0.588770 | + | 0.808301i | \(0.700388\pi\) | |||||||
\(294\) | 2.99204 | 0.174499 | ||||||||
\(295\) | −13.5316 | −0.787840 | ||||||||
\(296\) | −8.12172 | −0.472065 | ||||||||
\(297\) | −1.44057 | −0.0835903 | ||||||||
\(298\) | 1.37553 | 0.0796822 | ||||||||
\(299\) | 6.59714 | 0.381522 | ||||||||
\(300\) | −0.296108 | −0.0170958 | ||||||||
\(301\) | −8.26928 | −0.476633 | ||||||||
\(302\) | 20.5910 | 1.18488 | ||||||||
\(303\) | −0.723978 | −0.0415914 | ||||||||
\(304\) | −7.10481 | −0.407489 | ||||||||
\(305\) | −1.75683 | −0.100596 | ||||||||
\(306\) | 2.05652 | 0.117563 | ||||||||
\(307\) | −29.9663 | −1.71027 | −0.855133 | − | 0.518408i | \(-0.826525\pi\) | ||||
−0.855133 | + | 0.518408i | \(0.826525\pi\) | |||||||
\(308\) | 3.40316 | 0.193913 | ||||||||
\(309\) | −1.33308 | −0.0758365 | ||||||||
\(310\) | 9.32030 | 0.529357 | ||||||||
\(311\) | −0.121878 | −0.00691105 | −0.00345553 | − | 0.999994i | \(-0.501100\pi\) | ||||
−0.00345553 | + | 0.999994i | \(0.501100\pi\) | |||||||
\(312\) | 1.18402 | 0.0670320 | ||||||||
\(313\) | 12.5030 | 0.706714 | 0.353357 | − | 0.935489i | \(-0.385040\pi\) | ||||
0.353357 | + | 0.935489i | \(0.385040\pi\) | |||||||
\(314\) | 10.0317 | 0.566123 | ||||||||
\(315\) | −12.0447 | −0.678640 | ||||||||
\(316\) | −10.1450 | −0.570700 | ||||||||
\(317\) | −22.3371 | −1.25458 | −0.627288 | − | 0.778787i | \(-0.715835\pi\) | ||||
−0.627288 | + | 0.778787i | \(0.715835\pi\) | |||||||
\(318\) | −2.83088 | −0.158748 | ||||||||
\(319\) | −4.46025 | −0.249726 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 3.36766 | 0.187964 | ||||||||
\(322\) | 6.82342 | 0.380254 | ||||||||
\(323\) | −5.01702 | −0.279155 | ||||||||
\(324\) | 8.21857 | 0.456587 | ||||||||
\(325\) | 3.99861 | 0.221803 | ||||||||
\(326\) | −6.90312 | −0.382329 | ||||||||
\(327\) | −2.96670 | −0.164059 | ||||||||
\(328\) | 3.09551 | 0.170921 | ||||||||
\(329\) | 24.9720 | 1.37675 | ||||||||
\(330\) | 0.243656 | 0.0134128 | ||||||||
\(331\) | 25.6526 | 1.40999 | 0.704997 | − | 0.709210i | \(-0.250948\pi\) | ||||
0.704997 | + | 0.709210i | \(0.250948\pi\) | |||||||
\(332\) | 4.37454 | 0.240084 | ||||||||
\(333\) | −23.6530 | −1.29618 | ||||||||
\(334\) | 11.7018 | 0.640292 | ||||||||
\(335\) | −3.37580 | −0.184439 | ||||||||
\(336\) | 1.22463 | 0.0668092 | ||||||||
\(337\) | −19.2644 | −1.04940 | −0.524700 | − | 0.851287i | \(-0.675823\pi\) | ||||
−0.524700 | + | 0.851287i | \(0.675823\pi\) | |||||||
\(338\) | −2.98889 | −0.162574 | ||||||||
\(339\) | −1.30362 | −0.0708030 | ||||||||
\(340\) | −0.706145 | −0.0382961 | ||||||||
\(341\) | −7.66930 | −0.415316 | ||||||||
\(342\) | −20.6915 | −1.11887 | ||||||||
\(343\) | −12.8397 | −0.693280 | ||||||||
\(344\) | −1.99945 | −0.107803 | ||||||||
\(345\) | 0.488536 | 0.0263019 | ||||||||
\(346\) | 17.2942 | 0.929740 | ||||||||
\(347\) | −17.9569 | −0.963977 | −0.481989 | − | 0.876177i | \(-0.660085\pi\) | ||||
−0.481989 | + | 0.876177i | \(0.660085\pi\) | |||||||
\(348\) | −1.60503 | −0.0860387 | ||||||||
\(349\) | −4.82970 | −0.258528 | −0.129264 | − | 0.991610i | \(-0.541261\pi\) | ||||
−0.129264 | + | 0.991610i | \(0.541261\pi\) | |||||||
\(350\) | 4.13577 | 0.221066 | ||||||||
\(351\) | 7.00031 | 0.373649 | ||||||||
\(352\) | 0.822860 | 0.0438586 | ||||||||
\(353\) | 8.09667 | 0.430942 | 0.215471 | − | 0.976510i | \(-0.430871\pi\) | ||||
0.215471 | + | 0.976510i | \(0.430871\pi\) | |||||||
\(354\) | 4.00682 | 0.212960 | ||||||||
\(355\) | 9.49307 | 0.503840 | ||||||||
\(356\) | 17.8609 | 0.946627 | ||||||||
\(357\) | 0.864768 | 0.0457684 | ||||||||
\(358\) | 13.4637 | 0.711579 | ||||||||
\(359\) | −3.71498 | −0.196069 | −0.0980347 | − | 0.995183i | \(-0.531256\pi\) | ||||
−0.0980347 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(360\) | −2.91232 | −0.153493 | ||||||||
\(361\) | 31.4783 | 1.65675 | ||||||||
\(362\) | 8.63696 | 0.453949 | ||||||||
\(363\) | 3.05669 | 0.160435 | ||||||||
\(364\) | −16.5373 | −0.866791 | ||||||||
\(365\) | 2.28444 | 0.119573 | ||||||||
\(366\) | 0.520212 | 0.0271919 | ||||||||
\(367\) | −5.56678 | −0.290584 | −0.145292 | − | 0.989389i | \(-0.546412\pi\) | ||||
−0.145292 | + | 0.989389i | \(0.546412\pi\) | |||||||
\(368\) | 1.64986 | 0.0860047 | ||||||||
\(369\) | 9.01511 | 0.469308 | ||||||||
\(370\) | 8.12172 | 0.422228 | ||||||||
\(371\) | 39.5391 | 2.05277 | ||||||||
\(372\) | −2.75981 | −0.143090 | ||||||||
\(373\) | 0.0486608 | 0.00251956 | 0.00125978 | − | 0.999999i | \(-0.499599\pi\) | ||||
0.00125978 | + | 0.999999i | \(0.499599\pi\) | |||||||
\(374\) | 0.581059 | 0.0300458 | ||||||||
\(375\) | 0.296108 | 0.0152910 | ||||||||
\(376\) | 6.03806 | 0.311389 | ||||||||
\(377\) | 21.6742 | 1.11628 | ||||||||
\(378\) | 7.24042 | 0.372407 | ||||||||
\(379\) | 31.7768 | 1.63227 | 0.816133 | − | 0.577863i | \(-0.196113\pi\) | ||||
0.816133 | + | 0.577863i | \(0.196113\pi\) | |||||||
\(380\) | 7.10481 | 0.364469 | ||||||||
\(381\) | 4.52892 | 0.232024 | ||||||||
\(382\) | −19.6582 | −1.00580 | ||||||||
\(383\) | 31.6798 | 1.61876 | 0.809380 | − | 0.587285i | \(-0.199803\pi\) | ||||
0.809380 | + | 0.587285i | \(0.199803\pi\) | |||||||
\(384\) | 0.296108 | 0.0151107 | ||||||||
\(385\) | −3.40316 | −0.173441 | ||||||||
\(386\) | −8.04192 | −0.409323 | ||||||||
\(387\) | −5.82305 | −0.296002 | ||||||||
\(388\) | −4.31564 | −0.219093 | ||||||||
\(389\) | 39.1623 | 1.98561 | 0.992803 | − | 0.119756i | \(-0.0382114\pi\) | ||||
0.992803 | + | 0.119756i | \(0.0382114\pi\) | |||||||
\(390\) | −1.18402 | −0.0599552 | ||||||||
\(391\) | 1.16504 | 0.0589185 | ||||||||
\(392\) | −10.1046 | −0.510357 | ||||||||
\(393\) | −1.17353 | −0.0591965 | ||||||||
\(394\) | −5.98586 | −0.301563 | ||||||||
\(395\) | 10.1450 | 0.510450 | ||||||||
\(396\) | 2.39643 | 0.120425 | ||||||||
\(397\) | 8.06487 | 0.404764 | 0.202382 | − | 0.979307i | \(-0.435132\pi\) | ||||
0.202382 | + | 0.979307i | \(0.435132\pi\) | |||||||
\(398\) | 14.4209 | 0.722854 | ||||||||
\(399\) | −8.70078 | −0.435584 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −12.4473 | −0.621588 | −0.310794 | − | 0.950477i | \(-0.600595\pi\) | ||||
−0.310794 | + | 0.950477i | \(0.600595\pi\) | |||||||
\(402\) | 0.999600 | 0.0498555 | ||||||||
\(403\) | 37.2682 | 1.85646 | ||||||||
\(404\) | 2.44498 | 0.121642 | ||||||||
\(405\) | −8.21857 | −0.408384 | ||||||||
\(406\) | 22.4176 | 1.11257 | ||||||||
\(407\) | −6.68304 | −0.331266 | ||||||||
\(408\) | 0.209095 | 0.0103517 | ||||||||
\(409\) | 13.8530 | 0.684987 | 0.342493 | − | 0.939520i | \(-0.388729\pi\) | ||||
0.342493 | + | 0.939520i | \(0.388729\pi\) | |||||||
\(410\) | −3.09551 | −0.152876 | ||||||||
\(411\) | 1.36884 | 0.0675200 | ||||||||
\(412\) | 4.50202 | 0.221799 | ||||||||
\(413\) | −55.9635 | −2.75379 | ||||||||
\(414\) | 4.80491 | 0.236148 | ||||||||
\(415\) | −4.37454 | −0.214738 | ||||||||
\(416\) | −3.99861 | −0.196048 | ||||||||
\(417\) | −4.29443 | −0.210299 | ||||||||
\(418\) | −5.84626 | −0.285950 | ||||||||
\(419\) | 33.8364 | 1.65302 | 0.826508 | − | 0.562925i | \(-0.190324\pi\) | ||||
0.826508 | + | 0.562925i | \(0.190324\pi\) | |||||||
\(420\) | −1.22463 | −0.0597560 | ||||||||
\(421\) | 29.1105 | 1.41876 | 0.709379 | − | 0.704827i | \(-0.248976\pi\) | ||||
0.709379 | + | 0.704827i | \(0.248976\pi\) | |||||||
\(422\) | 15.9423 | 0.776061 | ||||||||
\(423\) | 17.5847 | 0.855000 | ||||||||
\(424\) | 9.56029 | 0.464289 | ||||||||
\(425\) | 0.706145 | 0.0342531 | ||||||||
\(426\) | −2.81097 | −0.136192 | ||||||||
\(427\) | −7.26584 | −0.351619 | ||||||||
\(428\) | −11.3731 | −0.549738 | ||||||||
\(429\) | 0.974284 | 0.0470389 | ||||||||
\(430\) | 1.99945 | 0.0964223 | ||||||||
\(431\) | −27.7288 | −1.33565 | −0.667825 | − | 0.744318i | \(-0.732775\pi\) | ||||
−0.667825 | + | 0.744318i | \(0.732775\pi\) | |||||||
\(432\) | 1.75069 | 0.0842299 | ||||||||
\(433\) | −20.0254 | −0.962361 | −0.481180 | − | 0.876622i | \(-0.659792\pi\) | ||||
−0.481180 | + | 0.876622i | \(0.659792\pi\) | |||||||
\(434\) | 38.5466 | 1.85029 | ||||||||
\(435\) | 1.60503 | 0.0769554 | ||||||||
\(436\) | 10.0190 | 0.479822 | ||||||||
\(437\) | −11.7219 | −0.560735 | ||||||||
\(438\) | −0.676439 | −0.0323215 | ||||||||
\(439\) | 17.4058 | 0.830734 | 0.415367 | − | 0.909654i | \(-0.363653\pi\) | ||||
0.415367 | + | 0.909654i | \(0.363653\pi\) | |||||||
\(440\) | −0.822860 | −0.0392283 | ||||||||
\(441\) | −29.4277 | −1.40132 | ||||||||
\(442\) | −2.82360 | −0.134305 | ||||||||
\(443\) | −34.8435 | −1.65546 | −0.827732 | − | 0.561123i | \(-0.810369\pi\) | ||||
−0.827732 | + | 0.561123i | \(0.810369\pi\) | |||||||
\(444\) | −2.40491 | −0.114132 | ||||||||
\(445\) | −17.8609 | −0.846689 | ||||||||
\(446\) | 22.3927 | 1.06032 | ||||||||
\(447\) | 0.407305 | 0.0192648 | ||||||||
\(448\) | −4.13577 | −0.195397 | ||||||||
\(449\) | −32.0077 | −1.51053 | −0.755267 | − | 0.655417i | \(-0.772493\pi\) | ||||
−0.755267 | + | 0.655417i | \(0.772493\pi\) | |||||||
\(450\) | 2.91232 | 0.137288 | ||||||||
\(451\) | 2.54717 | 0.119942 | ||||||||
\(452\) | 4.40252 | 0.207077 | ||||||||
\(453\) | 6.09715 | 0.286469 | ||||||||
\(454\) | 25.4914 | 1.19637 | ||||||||
\(455\) | 16.5373 | 0.775282 | ||||||||
\(456\) | −2.10379 | −0.0985190 | ||||||||
\(457\) | −10.1150 | −0.473158 | −0.236579 | − | 0.971612i | \(-0.576026\pi\) | ||||
−0.236579 | + | 0.971612i | \(0.576026\pi\) | |||||||
\(458\) | −14.2915 | −0.667796 | ||||||||
\(459\) | 1.23624 | 0.0577026 | ||||||||
\(460\) | −1.64986 | −0.0769250 | ||||||||
\(461\) | −25.7053 | −1.19721 | −0.598607 | − | 0.801043i | \(-0.704279\pi\) | ||||
−0.598607 | + | 0.801043i | \(0.704279\pi\) | |||||||
\(462\) | 1.00770 | 0.0468826 | ||||||||
\(463\) | −26.4196 | −1.22782 | −0.613912 | − | 0.789374i | \(-0.710405\pi\) | ||||
−0.613912 | + | 0.789374i | \(0.710405\pi\) | |||||||
\(464\) | 5.42043 | 0.251637 | ||||||||
\(465\) | 2.75981 | 0.127983 | ||||||||
\(466\) | 8.74153 | 0.404944 | ||||||||
\(467\) | 5.55271 | 0.256949 | 0.128474 | − | 0.991713i | \(-0.458992\pi\) | ||||
0.128474 | + | 0.991713i | \(0.458992\pi\) | |||||||
\(468\) | −11.6452 | −0.538301 | ||||||||
\(469\) | −13.9615 | −0.644682 | ||||||||
\(470\) | −6.03806 | −0.278515 | ||||||||
\(471\) | 2.97048 | 0.136872 | ||||||||
\(472\) | −13.5316 | −0.622843 | ||||||||
\(473\) | −1.64527 | −0.0756497 | ||||||||
\(474\) | −3.00401 | −0.137979 | ||||||||
\(475\) | −7.10481 | −0.325991 | ||||||||
\(476\) | −2.92045 | −0.133859 | ||||||||
\(477\) | 27.8426 | 1.27483 | ||||||||
\(478\) | −12.0802 | −0.552535 | ||||||||
\(479\) | −33.0201 | −1.50873 | −0.754363 | − | 0.656458i | \(-0.772054\pi\) | ||||
−0.754363 | + | 0.656458i | \(0.772054\pi\) | |||||||
\(480\) | −0.296108 | −0.0135154 | ||||||||
\(481\) | 32.4756 | 1.48076 | ||||||||
\(482\) | −26.0973 | −1.18870 | ||||||||
\(483\) | 2.02047 | 0.0919345 | ||||||||
\(484\) | −10.3229 | −0.469223 | ||||||||
\(485\) | 4.31564 | 0.195963 | ||||||||
\(486\) | 7.68564 | 0.348628 | ||||||||
\(487\) | 12.6051 | 0.571192 | 0.285596 | − | 0.958350i | \(-0.407808\pi\) | ||||
0.285596 | + | 0.958350i | \(0.407808\pi\) | |||||||
\(488\) | −1.75683 | −0.0795280 | ||||||||
\(489\) | −2.04407 | −0.0924360 | ||||||||
\(490\) | 10.1046 | 0.456477 | ||||||||
\(491\) | 9.50398 | 0.428909 | 0.214454 | − | 0.976734i | \(-0.431203\pi\) | ||||
0.214454 | + | 0.976734i | \(0.431203\pi\) | |||||||
\(492\) | 0.916605 | 0.0413237 | ||||||||
\(493\) | 3.82761 | 0.172387 | ||||||||
\(494\) | 28.4094 | 1.27820 | ||||||||
\(495\) | −2.39643 | −0.107712 | ||||||||
\(496\) | 9.32030 | 0.418494 | ||||||||
\(497\) | 39.2611 | 1.76110 | ||||||||
\(498\) | 1.29534 | 0.0580454 | ||||||||
\(499\) | 1.73969 | 0.0778793 | 0.0389396 | − | 0.999242i | \(-0.487602\pi\) | ||||
0.0389396 | + | 0.999242i | \(0.487602\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 3.46499 | 0.154804 | ||||||||
\(502\) | 20.6946 | 0.923644 | ||||||||
\(503\) | −37.4195 | −1.66845 | −0.834226 | − | 0.551422i | \(-0.814085\pi\) | ||||
−0.834226 | + | 0.551422i | \(0.814085\pi\) | |||||||
\(504\) | −12.0447 | −0.536512 | ||||||||
\(505\) | −2.44498 | −0.108800 | ||||||||
\(506\) | 1.35760 | 0.0603528 | ||||||||
\(507\) | −0.885036 | −0.0393058 | ||||||||
\(508\) | −15.2948 | −0.678598 | ||||||||
\(509\) | −22.4908 | −0.996886 | −0.498443 | − | 0.866923i | \(-0.666095\pi\) | ||||
−0.498443 | + | 0.866923i | \(0.666095\pi\) | |||||||
\(510\) | −0.209095 | −0.00925889 | ||||||||
\(511\) | 9.44789 | 0.417950 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −12.4383 | −0.549163 | ||||||||
\(514\) | −7.82529 | −0.345159 | ||||||||
\(515\) | −4.50202 | −0.198383 | ||||||||
\(516\) | −0.592055 | −0.0260637 | ||||||||
\(517\) | 4.96848 | 0.218513 | ||||||||
\(518\) | 33.5895 | 1.47584 | ||||||||
\(519\) | 5.12094 | 0.224784 | ||||||||
\(520\) | 3.99861 | 0.175351 | ||||||||
\(521\) | −37.5682 | −1.64589 | −0.822947 | − | 0.568118i | \(-0.807672\pi\) | ||||
−0.822947 | + | 0.568118i | \(0.807672\pi\) | |||||||
\(522\) | 15.7860 | 0.690935 | ||||||||
\(523\) | 6.93113 | 0.303077 | 0.151539 | − | 0.988451i | \(-0.451577\pi\) | ||||
0.151539 | + | 0.988451i | \(0.451577\pi\) | |||||||
\(524\) | 3.96317 | 0.173132 | ||||||||
\(525\) | 1.22463 | 0.0534474 | ||||||||
\(526\) | −15.9940 | −0.697371 | ||||||||
\(527\) | 6.58148 | 0.286694 | ||||||||
\(528\) | 0.243656 | 0.0106037 | ||||||||
\(529\) | −20.2780 | −0.881651 | ||||||||
\(530\) | −9.56029 | −0.415273 | ||||||||
\(531\) | −39.4084 | −1.71018 | ||||||||
\(532\) | 29.3838 | 1.27395 | ||||||||
\(533\) | −12.3777 | −0.536139 | ||||||||
\(534\) | 5.28876 | 0.228867 | ||||||||
\(535\) | 11.3731 | 0.491701 | ||||||||
\(536\) | −3.37580 | −0.145812 | ||||||||
\(537\) | 3.98671 | 0.172039 | ||||||||
\(538\) | −17.2558 | −0.743948 | ||||||||
\(539\) | −8.31464 | −0.358137 | ||||||||
\(540\) | −1.75069 | −0.0753375 | ||||||||
\(541\) | −11.1664 | −0.480080 | −0.240040 | − | 0.970763i | \(-0.577161\pi\) | ||||
−0.240040 | + | 0.970763i | \(0.577161\pi\) | |||||||
\(542\) | −11.3627 | −0.488071 | ||||||||
\(543\) | 2.55747 | 0.109752 | ||||||||
\(544\) | −0.706145 | −0.0302757 | ||||||||
\(545\) | −10.0190 | −0.429166 | ||||||||
\(546\) | −4.89683 | −0.209565 | ||||||||
\(547\) | 11.7714 | 0.503311 | 0.251655 | − | 0.967817i | \(-0.419025\pi\) | ||||
0.251655 | + | 0.967817i | \(0.419025\pi\) | |||||||
\(548\) | −4.62278 | −0.197475 | ||||||||
\(549\) | −5.11645 | −0.218365 | ||||||||
\(550\) | 0.822860 | 0.0350869 | ||||||||
\(551\) | −38.5111 | −1.64063 | ||||||||
\(552\) | 0.488536 | 0.0207935 | ||||||||
\(553\) | 41.9573 | 1.78421 | ||||||||
\(554\) | −18.4155 | −0.782400 | ||||||||
\(555\) | 2.40491 | 0.102083 | ||||||||
\(556\) | 14.5029 | 0.615061 | ||||||||
\(557\) | −21.8550 | −0.926028 | −0.463014 | − | 0.886351i | \(-0.653232\pi\) | ||||
−0.463014 | + | 0.886351i | \(0.653232\pi\) | |||||||
\(558\) | 27.1437 | 1.14908 | ||||||||
\(559\) | 7.99504 | 0.338154 | ||||||||
\(560\) | 4.13577 | 0.174768 | ||||||||
\(561\) | 0.172056 | 0.00726421 | ||||||||
\(562\) | −1.48925 | −0.0628200 | ||||||||
\(563\) | −11.2852 | −0.475616 | −0.237808 | − | 0.971312i | \(-0.576429\pi\) | ||||
−0.237808 | + | 0.971312i | \(0.576429\pi\) | |||||||
\(564\) | 1.78792 | 0.0752849 | ||||||||
\(565\) | −4.40252 | −0.185216 | ||||||||
\(566\) | −19.5290 | −0.820863 | ||||||||
\(567\) | −33.9901 | −1.42745 | ||||||||
\(568\) | 9.49307 | 0.398320 | ||||||||
\(569\) | −3.54576 | −0.148646 | −0.0743229 | − | 0.997234i | \(-0.523680\pi\) | ||||
−0.0743229 | + | 0.997234i | \(0.523680\pi\) | |||||||
\(570\) | 2.10379 | 0.0881181 | ||||||||
\(571\) | 6.12529 | 0.256335 | 0.128168 | − | 0.991753i | \(-0.459090\pi\) | ||||
0.128168 | + | 0.991753i | \(0.459090\pi\) | |||||||
\(572\) | −3.29030 | −0.137574 | ||||||||
\(573\) | −5.82094 | −0.243173 | ||||||||
\(574\) | −12.8023 | −0.534358 | ||||||||
\(575\) | 1.64986 | 0.0688038 | ||||||||
\(576\) | −2.91232 | −0.121347 | ||||||||
\(577\) | −5.43131 | −0.226108 | −0.113054 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113054 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(578\) | 16.5014 | 0.686366 | ||||||||
\(579\) | −2.38128 | −0.0989625 | ||||||||
\(580\) | −5.42043 | −0.225071 | ||||||||
\(581\) | −18.0921 | −0.750586 | ||||||||
\(582\) | −1.27790 | −0.0529705 | ||||||||
\(583\) | 7.86679 | 0.325809 | ||||||||
\(584\) | 2.28444 | 0.0945306 | ||||||||
\(585\) | 11.6452 | 0.481471 | ||||||||
\(586\) | 20.1562 | 0.832646 | ||||||||
\(587\) | −10.7921 | −0.445438 | −0.222719 | − | 0.974883i | \(-0.571493\pi\) | ||||
−0.222719 | + | 0.974883i | \(0.571493\pi\) | |||||||
\(588\) | −2.99204 | −0.123390 | ||||||||
\(589\) | −66.2189 | −2.72850 | ||||||||
\(590\) | 13.5316 | 0.557087 | ||||||||
\(591\) | −1.77246 | −0.0729093 | ||||||||
\(592\) | 8.12172 | 0.333801 | ||||||||
\(593\) | −15.6129 | −0.641144 | −0.320572 | − | 0.947224i | \(-0.603875\pi\) | ||||
−0.320572 | + | 0.947224i | \(0.603875\pi\) | |||||||
\(594\) | 1.44057 | 0.0591073 | ||||||||
\(595\) | 2.92045 | 0.119727 | ||||||||
\(596\) | −1.37553 | −0.0563438 | ||||||||
\(597\) | 4.27014 | 0.174765 | ||||||||
\(598\) | −6.59714 | −0.269777 | ||||||||
\(599\) | 16.2243 | 0.662907 | 0.331454 | − | 0.943472i | \(-0.392461\pi\) | ||||
0.331454 | + | 0.943472i | \(0.392461\pi\) | |||||||
\(600\) | 0.296108 | 0.0120886 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 8.26928 | 0.337031 | ||||||||
\(603\) | −9.83140 | −0.400366 | ||||||||
\(604\) | −20.5910 | −0.837834 | ||||||||
\(605\) | 10.3229 | 0.419686 | ||||||||
\(606\) | 0.723978 | 0.0294096 | ||||||||
\(607\) | −28.6329 | −1.16217 | −0.581087 | − | 0.813841i | \(-0.697372\pi\) | ||||
−0.581087 | + | 0.813841i | \(0.697372\pi\) | |||||||
\(608\) | 7.10481 | 0.288138 | ||||||||
\(609\) | 6.63803 | 0.268987 | ||||||||
\(610\) | 1.75683 | 0.0711320 | ||||||||
\(611\) | −24.1438 | −0.976755 | ||||||||
\(612\) | −2.05652 | −0.0831299 | ||||||||
\(613\) | 38.8736 | 1.57009 | 0.785046 | − | 0.619438i | \(-0.212639\pi\) | ||||
0.785046 | + | 0.619438i | \(0.212639\pi\) | |||||||
\(614\) | 29.9663 | 1.20934 | ||||||||
\(615\) | −0.916605 | −0.0369611 | ||||||||
\(616\) | −3.40316 | −0.137117 | ||||||||
\(617\) | −14.3262 | −0.576751 | −0.288375 | − | 0.957517i | \(-0.593115\pi\) | ||||
−0.288375 | + | 0.957517i | \(0.593115\pi\) | |||||||
\(618\) | 1.33308 | 0.0536245 | ||||||||
\(619\) | 28.5541 | 1.14769 | 0.573843 | − | 0.818965i | \(-0.305452\pi\) | ||||
0.573843 | + | 0.818965i | \(0.305452\pi\) | |||||||
\(620\) | −9.32030 | −0.374312 | ||||||||
\(621\) | 2.88838 | 0.115907 | ||||||||
\(622\) | 0.121878 | 0.00488685 | ||||||||
\(623\) | −73.8686 | −2.95948 | ||||||||
\(624\) | −1.18402 | −0.0473988 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.5030 | −0.499722 | ||||||||
\(627\) | −1.73113 | −0.0691345 | ||||||||
\(628\) | −10.0317 | −0.400310 | ||||||||
\(629\) | 5.73511 | 0.228674 | ||||||||
\(630\) | 12.0447 | 0.479871 | ||||||||
\(631\) | −31.2959 | −1.24587 | −0.622936 | − | 0.782273i | \(-0.714060\pi\) | ||||
−0.622936 | + | 0.782273i | \(0.714060\pi\) | |||||||
\(632\) | 10.1450 | 0.403546 | ||||||||
\(633\) | 4.72066 | 0.187629 | ||||||||
\(634\) | 22.3371 | 0.887119 | ||||||||
\(635\) | 15.2948 | 0.606956 | ||||||||
\(636\) | 2.83088 | 0.112252 | ||||||||
\(637\) | 40.4042 | 1.60087 | ||||||||
\(638\) | 4.46025 | 0.176583 | ||||||||
\(639\) | 27.6469 | 1.09369 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −12.3622 | −0.488277 | −0.244138 | − | 0.969740i | \(-0.578505\pi\) | ||||
−0.244138 | + | 0.969740i | \(0.578505\pi\) | |||||||
\(642\) | −3.36766 | −0.132911 | ||||||||
\(643\) | −16.2820 | −0.642099 | −0.321050 | − | 0.947062i | \(-0.604036\pi\) | ||||
−0.321050 | + | 0.947062i | \(0.604036\pi\) | |||||||
\(644\) | −6.82342 | −0.268880 | ||||||||
\(645\) | 0.592055 | 0.0233121 | ||||||||
\(646\) | 5.01702 | 0.197392 | ||||||||
\(647\) | −18.3327 | −0.720731 | −0.360366 | − | 0.932811i | \(-0.617348\pi\) | ||||
−0.360366 | + | 0.932811i | \(0.617348\pi\) | |||||||
\(648\) | −8.21857 | −0.322856 | ||||||||
\(649\) | −11.1346 | −0.437072 | ||||||||
\(650\) | −3.99861 | −0.156838 | ||||||||
\(651\) | 11.4139 | 0.447348 | ||||||||
\(652\) | 6.90312 | 0.270347 | ||||||||
\(653\) | −38.2637 | −1.49737 | −0.748687 | − | 0.662924i | \(-0.769315\pi\) | ||||
−0.748687 | + | 0.662924i | \(0.769315\pi\) | |||||||
\(654\) | 2.96670 | 0.116007 | ||||||||
\(655\) | −3.96317 | −0.154854 | ||||||||
\(656\) | −3.09551 | −0.120859 | ||||||||
\(657\) | 6.65301 | 0.259558 | ||||||||
\(658\) | −24.9720 | −0.973509 | ||||||||
\(659\) | −33.5330 | −1.30626 | −0.653131 | − | 0.757245i | \(-0.726545\pi\) | ||||
−0.653131 | + | 0.757245i | \(0.726545\pi\) | |||||||
\(660\) | −0.243656 | −0.00948428 | ||||||||
\(661\) | 24.9749 | 0.971412 | 0.485706 | − | 0.874122i | \(-0.338563\pi\) | ||||
0.485706 | + | 0.874122i | \(0.338563\pi\) | |||||||
\(662\) | −25.6526 | −0.997016 | ||||||||
\(663\) | −0.836090 | −0.0324710 | ||||||||
\(664\) | −4.37454 | −0.169765 | ||||||||
\(665\) | −29.3838 | −1.13946 | ||||||||
\(666\) | 23.6530 | 0.916537 | ||||||||
\(667\) | 8.94293 | 0.346271 | ||||||||
\(668\) | −11.7018 | −0.452755 | ||||||||
\(669\) | 6.63064 | 0.256355 | ||||||||
\(670\) | 3.37580 | 0.130418 | ||||||||
\(671\) | −1.44563 | −0.0558078 | ||||||||
\(672\) | −1.22463 | −0.0472413 | ||||||||
\(673\) | 30.6584 | 1.18179 | 0.590897 | − | 0.806747i | \(-0.298774\pi\) | ||||
0.590897 | + | 0.806747i | \(0.298774\pi\) | |||||||
\(674\) | 19.2644 | 0.742038 | ||||||||
\(675\) | 1.75069 | 0.0673839 | ||||||||
\(676\) | 2.98889 | 0.114957 | ||||||||
\(677\) | −22.2925 | −0.856769 | −0.428384 | − | 0.903597i | \(-0.640917\pi\) | ||||
−0.428384 | + | 0.903597i | \(0.640917\pi\) | |||||||
\(678\) | 1.30362 | 0.0500653 | ||||||||
\(679\) | 17.8485 | 0.684961 | ||||||||
\(680\) | 0.706145 | 0.0270794 | ||||||||
\(681\) | 7.54821 | 0.289248 | ||||||||
\(682\) | 7.66930 | 0.293673 | ||||||||
\(683\) | 21.3750 | 0.817892 | 0.408946 | − | 0.912559i | \(-0.365896\pi\) | ||||
0.408946 | + | 0.912559i | \(0.365896\pi\) | |||||||
\(684\) | 20.6915 | 0.791158 | ||||||||
\(685\) | 4.62278 | 0.176627 | ||||||||
\(686\) | 12.8397 | 0.490223 | ||||||||
\(687\) | −4.23181 | −0.161454 | ||||||||
\(688\) | 1.99945 | 0.0762285 | ||||||||
\(689\) | −38.2279 | −1.45637 | ||||||||
\(690\) | −0.488536 | −0.0185982 | ||||||||
\(691\) | 5.34740 | 0.203425 | 0.101712 | − | 0.994814i | \(-0.467568\pi\) | ||||
0.101712 | + | 0.994814i | \(0.467568\pi\) | |||||||
\(692\) | −17.2942 | −0.657425 | ||||||||
\(693\) | −9.91109 | −0.376491 | ||||||||
\(694\) | 17.9569 | 0.681635 | ||||||||
\(695\) | −14.5029 | −0.550127 | ||||||||
\(696\) | 1.60503 | 0.0608386 | ||||||||
\(697\) | −2.18588 | −0.0827960 | ||||||||
\(698\) | 4.82970 | 0.182807 | ||||||||
\(699\) | 2.58844 | 0.0979037 | ||||||||
\(700\) | −4.13577 | −0.156317 | ||||||||
\(701\) | −27.4229 | −1.03575 | −0.517874 | − | 0.855457i | \(-0.673276\pi\) | ||||
−0.517874 | + | 0.855457i | \(0.673276\pi\) | |||||||
\(702\) | −7.00031 | −0.264210 | ||||||||
\(703\) | −57.7032 | −2.17632 | ||||||||
\(704\) | −0.822860 | −0.0310127 | ||||||||
\(705\) | −1.78792 | −0.0673368 | ||||||||
\(706\) | −8.09667 | −0.304722 | ||||||||
\(707\) | −10.1119 | −0.380296 | ||||||||
\(708\) | −4.00682 | −0.150585 | ||||||||
\(709\) | 21.1429 | 0.794039 | 0.397019 | − | 0.917810i | \(-0.370045\pi\) | ||||
0.397019 | + | 0.917810i | \(0.370045\pi\) | |||||||
\(710\) | −9.49307 | −0.356269 | ||||||||
\(711\) | 29.5454 | 1.10804 | ||||||||
\(712\) | −17.8609 | −0.669366 | ||||||||
\(713\) | 15.3772 | 0.575879 | ||||||||
\(714\) | −0.864768 | −0.0323631 | ||||||||
\(715\) | 3.29030 | 0.123050 | ||||||||
\(716\) | −13.4637 | −0.503163 | ||||||||
\(717\) | −3.57704 | −0.133587 | ||||||||
\(718\) | 3.71498 | 0.138642 | ||||||||
\(719\) | −20.2239 | −0.754223 | −0.377111 | − | 0.926168i | \(-0.623083\pi\) | ||||
−0.377111 | + | 0.926168i | \(0.623083\pi\) | |||||||
\(720\) | 2.91232 | 0.108536 | ||||||||
\(721\) | −18.6193 | −0.693419 | ||||||||
\(722\) | −31.4783 | −1.17150 | ||||||||
\(723\) | −7.72762 | −0.287393 | ||||||||
\(724\) | −8.63696 | −0.320990 | ||||||||
\(725\) | 5.42043 | 0.201310 | ||||||||
\(726\) | −3.05669 | −0.113445 | ||||||||
\(727\) | −27.1280 | −1.00612 | −0.503062 | − | 0.864251i | \(-0.667793\pi\) | ||||
−0.503062 | + | 0.864251i | \(0.667793\pi\) | |||||||
\(728\) | 16.5373 | 0.612914 | ||||||||
\(729\) | −22.3799 | −0.828886 | ||||||||
\(730\) | −2.28444 | −0.0845507 | ||||||||
\(731\) | 1.41190 | 0.0522212 | ||||||||
\(732\) | −0.520212 | −0.0192276 | ||||||||
\(733\) | 27.9836 | 1.03360 | 0.516800 | − | 0.856106i | \(-0.327123\pi\) | ||||
0.516800 | + | 0.856106i | \(0.327123\pi\) | |||||||
\(734\) | 5.56678 | 0.205474 | ||||||||
\(735\) | 2.99204 | 0.110363 | ||||||||
\(736\) | −1.64986 | −0.0608145 | ||||||||
\(737\) | −2.77781 | −0.102322 | ||||||||
\(738\) | −9.01511 | −0.331851 | ||||||||
\(739\) | −33.7585 | −1.24183 | −0.620913 | − | 0.783880i | \(-0.713238\pi\) | ||||
−0.620913 | + | 0.783880i | \(0.713238\pi\) | |||||||
\(740\) | −8.12172 | −0.298560 | ||||||||
\(741\) | 8.41224 | 0.309031 | ||||||||
\(742\) | −39.5391 | −1.45153 | ||||||||
\(743\) | 19.2666 | 0.706821 | 0.353411 | − | 0.935468i | \(-0.385022\pi\) | ||||
0.353411 | + | 0.935468i | \(0.385022\pi\) | |||||||
\(744\) | 2.75981 | 0.101180 | ||||||||
\(745\) | 1.37553 | 0.0503954 | ||||||||
\(746\) | −0.0486608 | −0.00178160 | ||||||||
\(747\) | −12.7401 | −0.466135 | ||||||||
\(748\) | −0.581059 | −0.0212456 | ||||||||
\(749\) | 47.0364 | 1.71867 | ||||||||
\(750\) | −0.296108 | −0.0108123 | ||||||||
\(751\) | 0.636085 | 0.0232111 | 0.0116055 | − | 0.999933i | \(-0.496306\pi\) | ||||
0.0116055 | + | 0.999933i | \(0.496306\pi\) | |||||||
\(752\) | −6.03806 | −0.220185 | ||||||||
\(753\) | 6.12783 | 0.223310 | ||||||||
\(754\) | −21.6742 | −0.789327 | ||||||||
\(755\) | 20.5910 | 0.749382 | ||||||||
\(756\) | −7.24042 | −0.263332 | ||||||||
\(757\) | 6.52218 | 0.237053 | 0.118526 | − | 0.992951i | \(-0.462183\pi\) | ||||
0.118526 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(758\) | −31.7768 | −1.15419 | ||||||||
\(759\) | 0.401997 | 0.0145916 | ||||||||
\(760\) | −7.10481 | −0.257718 | ||||||||
\(761\) | 3.77881 | 0.136982 | 0.0684909 | − | 0.997652i | \(-0.478182\pi\) | ||||
0.0684909 | + | 0.997652i | \(0.478182\pi\) | |||||||
\(762\) | −4.52892 | −0.164065 | ||||||||
\(763\) | −41.4361 | −1.50009 | ||||||||
\(764\) | 19.6582 | 0.711207 | ||||||||
\(765\) | 2.05652 | 0.0743536 | ||||||||
\(766\) | −31.6798 | −1.14464 | ||||||||
\(767\) | 54.1076 | 1.95371 | ||||||||
\(768\) | −0.296108 | −0.0106849 | ||||||||
\(769\) | 0.555843 | 0.0200442 | 0.0100221 | − | 0.999950i | \(-0.496810\pi\) | ||||
0.0100221 | + | 0.999950i | \(0.496810\pi\) | |||||||
\(770\) | 3.40316 | 0.122641 | ||||||||
\(771\) | −2.31713 | −0.0834495 | ||||||||
\(772\) | 8.04192 | 0.289435 | ||||||||
\(773\) | −5.06431 | −0.182151 | −0.0910753 | − | 0.995844i | \(-0.529030\pi\) | ||||
−0.0910753 | + | 0.995844i | \(0.529030\pi\) | |||||||
\(774\) | 5.82305 | 0.209305 | ||||||||
\(775\) | 9.32030 | 0.334795 | ||||||||
\(776\) | 4.31564 | 0.154922 | ||||||||
\(777\) | 9.94613 | 0.356815 | ||||||||
\(778\) | −39.1623 | −1.40404 | ||||||||
\(779\) | 21.9930 | 0.787981 | ||||||||
\(780\) | 1.18402 | 0.0423947 | ||||||||
\(781\) | 7.81147 | 0.279516 | ||||||||
\(782\) | −1.16504 | −0.0416617 | ||||||||
\(783\) | 9.48946 | 0.339126 | ||||||||
\(784\) | 10.1046 | 0.360877 | ||||||||
\(785\) | 10.0317 | 0.358048 | ||||||||
\(786\) | 1.17353 | 0.0418583 | ||||||||
\(787\) | 33.9465 | 1.21006 | 0.605030 | − | 0.796202i | \(-0.293161\pi\) | ||||
0.605030 | + | 0.796202i | \(0.293161\pi\) | |||||||
\(788\) | 5.98586 | 0.213237 | ||||||||
\(789\) | −4.73595 | −0.168604 | ||||||||
\(790\) | −10.1450 | −0.360942 | ||||||||
\(791\) | −18.2078 | −0.647395 | ||||||||
\(792\) | −2.39643 | −0.0851535 | ||||||||
\(793\) | 7.02488 | 0.249461 | ||||||||
\(794\) | −8.06487 | −0.286212 | ||||||||
\(795\) | −2.83088 | −0.100401 | ||||||||
\(796\) | −14.4209 | −0.511135 | ||||||||
\(797\) | 29.6491 | 1.05022 | 0.525112 | − | 0.851033i | \(-0.324023\pi\) | ||||
0.525112 | + | 0.851033i | \(0.324023\pi\) | |||||||
\(798\) | 8.70078 | 0.308004 | ||||||||
\(799\) | −4.26374 | −0.150840 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −52.0167 | −1.83792 | ||||||||
\(802\) | 12.4473 | 0.439529 | ||||||||
\(803\) | 1.87977 | 0.0663357 | ||||||||
\(804\) | −0.999600 | −0.0352532 | ||||||||
\(805\) | 6.82342 | 0.240494 | ||||||||
\(806\) | −37.2682 | −1.31272 | ||||||||
\(807\) | −5.10957 | −0.179865 | ||||||||
\(808\) | −2.44498 | −0.0860141 | ||||||||
\(809\) | −51.1694 | −1.79902 | −0.899509 | − | 0.436901i | \(-0.856076\pi\) | ||||
−0.899509 | + | 0.436901i | \(0.856076\pi\) | |||||||
\(810\) | 8.21857 | 0.288771 | ||||||||
\(811\) | 9.31015 | 0.326923 | 0.163462 | − | 0.986550i | \(-0.447734\pi\) | ||||
0.163462 | + | 0.986550i | \(0.447734\pi\) | |||||||
\(812\) | −22.4176 | −0.786704 | ||||||||
\(813\) | −3.36459 | −0.118001 | ||||||||
\(814\) | 6.68304 | 0.234241 | ||||||||
\(815\) | −6.90312 | −0.241806 | ||||||||
\(816\) | −0.209095 | −0.00731979 | ||||||||
\(817\) | −14.2057 | −0.496996 | ||||||||
\(818\) | −13.8530 | −0.484359 | ||||||||
\(819\) | 48.1620 | 1.68292 | ||||||||
\(820\) | 3.09551 | 0.108100 | ||||||||
\(821\) | −29.7388 | −1.03789 | −0.518945 | − | 0.854808i | \(-0.673675\pi\) | ||||
−0.518945 | + | 0.854808i | \(0.673675\pi\) | |||||||
\(822\) | −1.36884 | −0.0477439 | ||||||||
\(823\) | −34.1657 | −1.19094 | −0.595470 | − | 0.803377i | \(-0.703034\pi\) | ||||
−0.595470 | + | 0.803377i | \(0.703034\pi\) | |||||||
\(824\) | −4.50202 | −0.156835 | ||||||||
\(825\) | 0.243656 | 0.00848300 | ||||||||
\(826\) | 55.9635 | 1.94722 | ||||||||
\(827\) | 9.18166 | 0.319278 | 0.159639 | − | 0.987175i | \(-0.448967\pi\) | ||||
0.159639 | + | 0.987175i | \(0.448967\pi\) | |||||||
\(828\) | −4.80491 | −0.166982 | ||||||||
\(829\) | 34.3418 | 1.19274 | 0.596370 | − | 0.802710i | \(-0.296609\pi\) | ||||
0.596370 | + | 0.802710i | \(0.296609\pi\) | |||||||
\(830\) | 4.37454 | 0.151843 | ||||||||
\(831\) | −5.45298 | −0.189162 | ||||||||
\(832\) | 3.99861 | 0.138627 | ||||||||
\(833\) | 7.13528 | 0.247223 | ||||||||
\(834\) | 4.29443 | 0.148704 | ||||||||
\(835\) | 11.7018 | 0.404956 | ||||||||
\(836\) | 5.84626 | 0.202197 | ||||||||
\(837\) | 16.3169 | 0.563995 | ||||||||
\(838\) | −33.8364 | −1.16886 | ||||||||
\(839\) | −25.5692 | −0.882748 | −0.441374 | − | 0.897323i | \(-0.645509\pi\) | ||||
−0.441374 | + | 0.897323i | \(0.645509\pi\) | |||||||
\(840\) | 1.22463 | 0.0422539 | ||||||||
\(841\) | 0.381014 | 0.0131384 | ||||||||
\(842\) | −29.1105 | −1.00321 | ||||||||
\(843\) | −0.440978 | −0.0151881 | ||||||||
\(844\) | −15.9423 | −0.548758 | ||||||||
\(845\) | −2.98889 | −0.102821 | ||||||||
\(846\) | −17.5847 | −0.604576 | ||||||||
\(847\) | 42.6931 | 1.46695 | ||||||||
\(848\) | −9.56029 | −0.328302 | ||||||||
\(849\) | −5.78268 | −0.198461 | ||||||||
\(850\) | −0.706145 | −0.0242206 | ||||||||
\(851\) | 13.3997 | 0.459335 | ||||||||
\(852\) | 2.81097 | 0.0963024 | ||||||||
\(853\) | −23.9968 | −0.821633 | −0.410817 | − | 0.911718i | \(-0.634756\pi\) | ||||
−0.410817 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(854\) | 7.26584 | 0.248632 | ||||||||
\(855\) | −20.6915 | −0.707633 | ||||||||
\(856\) | 11.3731 | 0.388724 | ||||||||
\(857\) | −44.2671 | −1.51214 | −0.756068 | − | 0.654493i | \(-0.772882\pi\) | ||||
−0.756068 | + | 0.654493i | \(0.772882\pi\) | |||||||
\(858\) | −0.974284 | −0.0332615 | ||||||||
\(859\) | −3.76483 | −0.128454 | −0.0642271 | − | 0.997935i | \(-0.520458\pi\) | ||||
−0.0642271 | + | 0.997935i | \(0.520458\pi\) | |||||||
\(860\) | −1.99945 | −0.0681808 | ||||||||
\(861\) | −3.79086 | −0.129192 | ||||||||
\(862\) | 27.7288 | 0.944448 | ||||||||
\(863\) | 37.7084 | 1.28361 | 0.641805 | − | 0.766868i | \(-0.278186\pi\) | ||||
0.641805 | + | 0.766868i | \(0.278186\pi\) | |||||||
\(864\) | −1.75069 | −0.0595595 | ||||||||
\(865\) | 17.2942 | 0.588019 | ||||||||
\(866\) | 20.0254 | 0.680492 | ||||||||
\(867\) | 4.88618 | 0.165944 | ||||||||
\(868\) | −38.5466 | −1.30836 | ||||||||
\(869\) | 8.34791 | 0.283183 | ||||||||
\(870\) | −1.60503 | −0.0544157 | ||||||||
\(871\) | 13.4985 | 0.457379 | ||||||||
\(872\) | −10.0190 | −0.339285 | ||||||||
\(873\) | 12.5685 | 0.425380 | ||||||||
\(874\) | 11.7219 | 0.396500 | ||||||||
\(875\) | 4.13577 | 0.139814 | ||||||||
\(876\) | 0.676439 | 0.0228548 | ||||||||
\(877\) | 20.4230 | 0.689634 | 0.344817 | − | 0.938670i | \(-0.387941\pi\) | ||||
0.344817 | + | 0.938670i | \(0.387941\pi\) | |||||||
\(878\) | −17.4058 | −0.587417 | ||||||||
\(879\) | 5.96842 | 0.201310 | ||||||||
\(880\) | 0.822860 | 0.0277386 | ||||||||
\(881\) | 47.9464 | 1.61535 | 0.807677 | − | 0.589625i | \(-0.200724\pi\) | ||||
0.807677 | + | 0.589625i | \(0.200724\pi\) | |||||||
\(882\) | 29.4277 | 0.990882 | ||||||||
\(883\) | 42.4944 | 1.43005 | 0.715025 | − | 0.699098i | \(-0.246415\pi\) | ||||
0.715025 | + | 0.699098i | \(0.246415\pi\) | |||||||
\(884\) | 2.82360 | 0.0949679 | ||||||||
\(885\) | 4.00682 | 0.134688 | ||||||||
\(886\) | 34.8435 | 1.17059 | ||||||||
\(887\) | 29.9976 | 1.00722 | 0.503610 | − | 0.863931i | \(-0.332005\pi\) | ||||
0.503610 | + | 0.863931i | \(0.332005\pi\) | |||||||
\(888\) | 2.40491 | 0.0807034 | ||||||||
\(889\) | 63.2558 | 2.12153 | ||||||||
\(890\) | 17.8609 | 0.598699 | ||||||||
\(891\) | −6.76273 | −0.226560 | ||||||||
\(892\) | −22.3927 | −0.749761 | ||||||||
\(893\) | 42.8992 | 1.43557 | ||||||||
\(894\) | −0.407305 | −0.0136223 | ||||||||
\(895\) | 13.4637 | 0.450042 | ||||||||
\(896\) | 4.13577 | 0.138166 | ||||||||
\(897\) | −1.95346 | −0.0652243 | ||||||||
\(898\) | 32.0077 | 1.06811 | ||||||||
\(899\) | 50.5200 | 1.68494 | ||||||||
\(900\) | −2.91232 | −0.0970773 | ||||||||
\(901\) | −6.75095 | −0.224907 | ||||||||
\(902\) | −2.54717 | −0.0848115 | ||||||||
\(903\) | 2.44860 | 0.0814843 | ||||||||
\(904\) | −4.40252 | −0.146426 | ||||||||
\(905\) | 8.63696 | 0.287102 | ||||||||
\(906\) | −6.09715 | −0.202564 | ||||||||
\(907\) | −53.4495 | −1.77476 | −0.887380 | − | 0.461038i | \(-0.847477\pi\) | ||||
−0.887380 | + | 0.461038i | \(0.847477\pi\) | |||||||
\(908\) | −25.4914 | −0.845963 | ||||||||
\(909\) | −7.12056 | −0.236174 | ||||||||
\(910\) | −16.5373 | −0.548207 | ||||||||
\(911\) | 15.2363 | 0.504801 | 0.252401 | − | 0.967623i | \(-0.418780\pi\) | ||||
0.252401 | + | 0.967623i | \(0.418780\pi\) | |||||||
\(912\) | 2.10379 | 0.0696634 | ||||||||
\(913\) | −3.59964 | −0.119131 | ||||||||
\(914\) | 10.1150 | 0.334573 | ||||||||
\(915\) | 0.520212 | 0.0171977 | ||||||||
\(916\) | 14.2915 | 0.472203 | ||||||||
\(917\) | −16.3907 | −0.541269 | ||||||||
\(918\) | −1.23624 | −0.0408019 | ||||||||
\(919\) | 55.2002 | 1.82089 | 0.910443 | − | 0.413634i | \(-0.135741\pi\) | ||||
0.910443 | + | 0.413634i | \(0.135741\pi\) | |||||||
\(920\) | 1.64986 | 0.0543942 | ||||||||
\(921\) | 8.87326 | 0.292384 | ||||||||
\(922\) | 25.7053 | 0.846558 | ||||||||
\(923\) | −37.9591 | −1.24944 | ||||||||
\(924\) | −1.00770 | −0.0331510 | ||||||||
\(925\) | 8.12172 | 0.267040 | ||||||||
\(926\) | 26.4196 | 0.868203 | ||||||||
\(927\) | −13.1113 | −0.430633 | ||||||||
\(928\) | −5.42043 | −0.177934 | ||||||||
\(929\) | −17.0622 | −0.559791 | −0.279896 | − | 0.960030i | \(-0.590300\pi\) | ||||
−0.279896 | + | 0.960030i | \(0.590300\pi\) | |||||||
\(930\) | −2.75981 | −0.0904979 | ||||||||
\(931\) | −71.7909 | −2.35285 | ||||||||
\(932\) | −8.74153 | −0.286338 | ||||||||
\(933\) | 0.0360890 | 0.00118150 | ||||||||
\(934\) | −5.55271 | −0.181690 | ||||||||
\(935\) | 0.581059 | 0.0190026 | ||||||||
\(936\) | 11.6452 | 0.380636 | ||||||||
\(937\) | 39.0453 | 1.27556 | 0.637778 | − | 0.770221i | \(-0.279854\pi\) | ||||
0.637778 | + | 0.770221i | \(0.279854\pi\) | |||||||
\(938\) | 13.9615 | 0.455859 | ||||||||
\(939\) | −3.70225 | −0.120818 | ||||||||
\(940\) | 6.03806 | 0.196940 | ||||||||
\(941\) | 12.4496 | 0.405844 | 0.202922 | − | 0.979195i | \(-0.434956\pi\) | ||||
0.202922 | + | 0.979195i | \(0.434956\pi\) | |||||||
\(942\) | −2.97048 | −0.0967833 | ||||||||
\(943\) | −5.10715 | −0.166312 | ||||||||
\(944\) | 13.5316 | 0.440416 | ||||||||
\(945\) | 7.24042 | 0.235531 | ||||||||
\(946\) | 1.64527 | 0.0534924 | ||||||||
\(947\) | −19.8281 | −0.644328 | −0.322164 | − | 0.946684i | \(-0.604410\pi\) | ||||
−0.322164 | + | 0.946684i | \(0.604410\pi\) | |||||||
\(948\) | 3.00401 | 0.0975658 | ||||||||
\(949\) | −9.13457 | −0.296521 | ||||||||
\(950\) | 7.10481 | 0.230510 | ||||||||
\(951\) | 6.61419 | 0.214480 | ||||||||
\(952\) | 2.92045 | 0.0946523 | ||||||||
\(953\) | 35.6756 | 1.15565 | 0.577823 | − | 0.816162i | \(-0.303902\pi\) | ||||
0.577823 | + | 0.816162i | \(0.303902\pi\) | |||||||
\(954\) | −27.8426 | −0.901438 | ||||||||
\(955\) | −19.6582 | −0.636123 | ||||||||
\(956\) | 12.0802 | 0.390702 | ||||||||
\(957\) | 1.32072 | 0.0426927 | ||||||||
\(958\) | 33.0201 | 1.06683 | ||||||||
\(959\) | 19.1187 | 0.617376 | ||||||||
\(960\) | 0.296108 | 0.00955684 | ||||||||
\(961\) | 55.8679 | 1.80219 | ||||||||
\(962\) | −32.4756 | −1.04706 | ||||||||
\(963\) | 33.1220 | 1.06734 | ||||||||
\(964\) | 26.0973 | 0.840537 | ||||||||
\(965\) | −8.04192 | −0.258879 | ||||||||
\(966\) | −2.02047 | −0.0650075 | ||||||||
\(967\) | −56.7690 | −1.82557 | −0.912784 | − | 0.408442i | \(-0.866072\pi\) | ||||
−0.912784 | + | 0.408442i | \(0.866072\pi\) | |||||||
\(968\) | 10.3229 | 0.331791 | ||||||||
\(969\) | 1.48558 | 0.0477237 | ||||||||
\(970\) | −4.31564 | −0.138567 | ||||||||
\(971\) | −30.5244 | −0.979575 | −0.489788 | − | 0.871842i | \(-0.662926\pi\) | ||||
−0.489788 | + | 0.871842i | \(0.662926\pi\) | |||||||
\(972\) | −7.68564 | −0.246517 | ||||||||
\(973\) | −59.9807 | −1.92289 | ||||||||
\(974\) | −12.6051 | −0.403894 | ||||||||
\(975\) | −1.18402 | −0.0379190 | ||||||||
\(976\) | 1.75683 | 0.0562348 | ||||||||
\(977\) | −1.53158 | −0.0489997 | −0.0244999 | − | 0.999700i | \(-0.507799\pi\) | ||||
−0.0244999 | + | 0.999700i | \(0.507799\pi\) | |||||||
\(978\) | 2.04407 | 0.0653621 | ||||||||
\(979\) | −14.6970 | −0.469719 | ||||||||
\(980\) | −10.1046 | −0.322778 | ||||||||
\(981\) | −29.1785 | −0.931596 | ||||||||
\(982\) | −9.50398 | −0.303284 | ||||||||
\(983\) | 0.964359 | 0.0307583 | 0.0153791 | − | 0.999882i | \(-0.495104\pi\) | ||||
0.0153791 | + | 0.999882i | \(0.495104\pi\) | |||||||
\(984\) | −0.916605 | −0.0292203 | ||||||||
\(985\) | −5.98586 | −0.190725 | ||||||||
\(986\) | −3.82761 | −0.121896 | ||||||||
\(987\) | −7.39440 | −0.235366 | ||||||||
\(988\) | −28.4094 | −0.903822 | ||||||||
\(989\) | 3.29881 | 0.104896 | ||||||||
\(990\) | 2.39643 | 0.0761636 | ||||||||
\(991\) | −38.5148 | −1.22346 | −0.611732 | − | 0.791065i | \(-0.709527\pi\) | ||||
−0.611732 | + | 0.791065i | \(0.709527\pi\) | |||||||
\(992\) | −9.32030 | −0.295920 | ||||||||
\(993\) | −7.59594 | −0.241050 | ||||||||
\(994\) | −39.2611 | −1.24529 | ||||||||
\(995\) | 14.4209 | 0.457173 | ||||||||
\(996\) | −1.29534 | −0.0410443 | ||||||||
\(997\) | −12.6946 | −0.402043 | −0.201021 | − | 0.979587i | \(-0.564426\pi\) | ||||
−0.201021 | + | 0.979587i | \(0.564426\pi\) | |||||||
\(998\) | −1.73969 | −0.0550690 | ||||||||
\(999\) | 14.2186 | 0.449856 |
(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 | 6010.2.a.i.1.16 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.i.1.16 | ✓ | 29 | 1.1 | even | 1 | trivial |