Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.22 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.24 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 3.16709 | + | 3.86905i | 0.633417 | + | 0.773810i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −4.38904 | −0.627005 | −0.313503 | − | 0.949587i | \(-0.601502\pi\) | ||||
−0.313503 | + | 0.949587i | \(0.601502\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 5.47167 | − | 4.47894i | 0.547167 | − | 0.447894i | ||||
\(11\) | − | 2.89637i | − | 0.263306i | −0.991296 | − | 0.131653i | \(-0.957971\pi\) | ||
0.991296 | − | 0.131653i | \(-0.0420285\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | − | 1.58189i | − | 0.121684i | −0.998147 | − | 0.0608420i | \(-0.980621\pi\) | ||
0.998147 | − | 0.0608420i | \(-0.0193786\pi\) | |||||||
\(14\) | 6.20704i | 0.443360i | ||||||||
\(15\) | −6.70139 | + | 5.48556i | −0.446760 | + | 0.365704i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 3.92071 | 0.230630 | 0.115315 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115315 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | 23.3725i | 1.23013i | 0.788476 | + | 0.615066i | \(0.210871\pi\) | ||||
−0.788476 | + | 0.615066i | \(0.789129\pi\) | |||||||
\(20\) | −6.33417 | − | 7.73810i | −0.316709 | − | 0.386905i | ||||
\(21\) | − | 7.60204i | − | 0.362002i | ||||||
\(22\) | −4.09608 | −0.186186 | ||||||||
\(23\) | 22.3520 | + | 5.42118i | 0.971825 | + | 0.235704i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −4.93912 | + | 24.5072i | −0.197565 | + | 0.980290i | ||||
\(26\) | −2.23713 | −0.0860436 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 8.77808 | 0.313503 | ||||||||
\(29\) | −8.38570 | −0.289162 | −0.144581 | − | 0.989493i | \(-0.546183\pi\) | ||||
−0.144581 | + | 0.989493i | \(0.546183\pi\) | |||||||
\(30\) | 7.75775 | + | 9.47720i | 0.258592 | + | 0.315907i | ||||
\(31\) | −32.5278 | −1.04929 | −0.524643 | − | 0.851323i | \(-0.675801\pi\) | ||||
−0.524643 | + | 0.851323i | \(0.675801\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 5.01666 | 0.152020 | ||||||||
\(34\) | − | 5.54473i | − | 0.163080i | ||||||
\(35\) | −13.9005 | − | 16.9814i | −0.397156 | − | 0.485183i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −49.8194 | −1.34647 | −0.673236 | − | 0.739428i | \(-0.735096\pi\) | ||||
−0.673236 | + | 0.739428i | \(0.735096\pi\) | |||||||
\(38\) | 33.0537 | 0.869834 | ||||||||
\(39\) | 2.73992 | 0.0702543 | ||||||||
\(40\) | −10.9433 | + | 8.95787i | −0.273583 | + | 0.223947i | ||||
\(41\) | −67.7817 | −1.65321 | −0.826606 | − | 0.562781i | \(-0.809731\pi\) | ||||
−0.826606 | + | 0.562781i | \(0.809731\pi\) | |||||||
\(42\) | −10.7509 | −0.255974 | ||||||||
\(43\) | −16.2354 | −0.377566 | −0.188783 | − | 0.982019i | \(-0.560454\pi\) | ||||
−0.188783 | + | 0.982019i | \(0.560454\pi\) | |||||||
\(44\) | 5.79274i | 0.131653i | ||||||||
\(45\) | −9.50126 | − | 11.6072i | −0.211139 | − | 0.257937i | ||||
\(46\) | 7.66671 | − | 31.6105i | 0.166668 | − | 0.687184i | ||||
\(47\) | 84.9146i | 1.80669i | 0.428912 | + | 0.903347i | \(0.358897\pi\) | ||||
−0.428912 | + | 0.903347i | \(0.641103\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −29.7363 | −0.606864 | ||||||||
\(50\) | 34.6585 | + | 6.98497i | 0.693170 | + | 0.139699i | ||||
\(51\) | 6.79088i | 0.133154i | ||||||||
\(52\) | 3.16378i | 0.0608420i | ||||||||
\(53\) | 1.17306 | 0.0221333 | 0.0110666 | − | 0.999939i | \(-0.496477\pi\) | ||||
0.0110666 | + | 0.999939i | \(0.496477\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | 11.2062 | − | 9.17305i | 0.203749 | − | 0.166783i | ||||
\(56\) | − | 12.4141i | − | 0.221680i | ||||||
\(57\) | −40.4824 | −0.710217 | ||||||||
\(58\) | 11.8592i | 0.204468i | ||||||||
\(59\) | −103.019 | −1.74608 | −0.873041 | − | 0.487647i | \(-0.837855\pi\) | ||||
−0.873041 | + | 0.487647i | \(0.837855\pi\) | |||||||
\(60\) | 13.4028 | − | 10.9711i | 0.223380 | − | 0.182852i | ||||
\(61\) | − | 12.6631i | − | 0.207592i | −0.994599 | − | 0.103796i | \(-0.966901\pi\) | ||
0.994599 | − | 0.103796i | \(-0.0330989\pi\) | |||||||
\(62\) | 46.0013i | 0.741957i | ||||||||
\(63\) | 13.1671 | 0.209002 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 6.12042 | − | 5.00999i | 0.0941603 | − | 0.0770767i | ||||
\(66\) | − | 7.09463i | − | 0.107494i | ||||||
\(67\) | 125.456 | 1.87247 | 0.936236 | − | 0.351371i | \(-0.114284\pi\) | ||||
0.936236 | + | 0.351371i | \(0.114284\pi\) | |||||||
\(68\) | −7.84143 | −0.115315 | ||||||||
\(69\) | −9.38976 | + | 38.7148i | −0.136084 | + | 0.561083i | ||||
\(70\) | −24.0153 | + | 19.6582i | −0.343076 | + | 0.280832i | ||||
\(71\) | −27.4629 | −0.386801 | −0.193400 | − | 0.981120i | \(-0.561952\pi\) | ||||
−0.193400 | + | 0.981120i | \(0.561952\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | 25.1610i | 0.344672i | 0.985038 | + | 0.172336i | \(0.0551314\pi\) | ||||
−0.985038 | + | 0.172336i | \(0.944869\pi\) | |||||||
\(74\) | 70.4553i | 0.952099i | ||||||||
\(75\) | −42.4478 | − | 8.55481i | −0.565971 | − | 0.114064i | ||||
\(76\) | − | 46.7450i | − | 0.615066i | ||||||
\(77\) | 12.7123i | 0.165094i | ||||||||
\(78\) | − | 3.87483i | − | 0.0496773i | ||||||
\(79\) | 25.5000i | 0.322785i | 0.986890 | + | 0.161392i | \(0.0515985\pi\) | ||||
−0.986890 | + | 0.161392i | \(0.948402\pi\) | |||||||
\(80\) | 12.6683 | + | 15.4762i | 0.158354 | + | 0.193453i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 95.8578i | 1.16900i | ||||||||
\(83\) | 110.184 | 1.32751 | 0.663757 | − | 0.747948i | \(-0.268961\pi\) | ||||
0.663757 | + | 0.747948i | \(0.268961\pi\) | |||||||
\(84\) | 15.2041i | 0.181001i | ||||||||
\(85\) | 12.4172 | + | 15.1694i | 0.146085 | + | 0.178464i | ||||
\(86\) | 22.9603i | 0.266980i | ||||||||
\(87\) | − | 14.5245i | − | 0.166948i | ||||||
\(88\) | 8.19217 | 0.0930928 | ||||||||
\(89\) | 14.4878i | 0.162785i | 0.996682 | + | 0.0813923i | \(0.0259367\pi\) | ||||
−0.996682 | + | 0.0813923i | \(0.974063\pi\) | |||||||
\(90\) | −16.4150 | + | 13.4368i | −0.182389 | + | 0.149298i | ||||
\(91\) | 6.94298i | 0.0762965i | ||||||||
\(92\) | −44.7039 | − | 10.8424i | −0.485912 | − | 0.117852i | ||||
\(93\) | − | 56.3399i | − | 0.605805i | ||||||
\(94\) | 120.087 | 1.27752 | ||||||||
\(95\) | −90.4294 | + | 74.0227i | −0.951888 | + | 0.779187i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −63.9628 | −0.659410 | −0.329705 | − | 0.944084i | \(-0.606949\pi\) | ||||
−0.329705 | + | 0.944084i | \(0.606949\pi\) | |||||||
\(98\) | 42.0535i | 0.429118i | ||||||||
\(99\) | 8.68911i | 0.0877687i | ||||||||
\(100\) | 9.87824 | − | 49.0145i | 0.0987824 | − | 0.490145i | ||||
\(101\) | −87.1443 | −0.862815 | −0.431407 | − | 0.902157i | \(-0.641983\pi\) | ||||
−0.431407 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(102\) | 9.60375 | 0.0941544 | ||||||||
\(103\) | 135.577 | 1.31628 | 0.658141 | − | 0.752894i | \(-0.271343\pi\) | ||||
0.658141 | + | 0.752894i | \(0.271343\pi\) | |||||||
\(104\) | 4.47426 | 0.0430218 | ||||||||
\(105\) | 29.4127 | − | 24.0763i | 0.280121 | − | 0.229298i | ||||
\(106\) | − | 1.65896i | − | 0.0156506i | ||||||
\(107\) | −124.682 | −1.16525 | −0.582627 | − | 0.812740i | \(-0.697975\pi\) | ||||
−0.582627 | + | 0.812740i | \(0.697975\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 99.8206i | 0.915785i | 0.889008 | + | 0.457893i | \(0.151396\pi\) | ||||
−0.889008 | + | 0.457893i | \(0.848604\pi\) | |||||||
\(110\) | −12.9727 | − | 15.8480i | −0.117933 | − | 0.144072i | ||||
\(111\) | − | 86.2898i | − | 0.777386i | ||||||
\(112\) | −17.5562 | −0.156751 | ||||||||
\(113\) | −43.7120 | −0.386832 | −0.193416 | − | 0.981117i | \(-0.561957\pi\) | ||||
−0.193416 | + | 0.981117i | \(0.561957\pi\) | |||||||
\(114\) | 57.2507i | 0.502199i | ||||||||
\(115\) | 49.8158 | + | 103.650i | 0.433181 | + | 0.901307i | ||||
\(116\) | 16.7714 | 0.144581 | ||||||||
\(117\) | 4.74567i | 0.0405613i | ||||||||
\(118\) | 145.691i | 1.23467i | ||||||||
\(119\) | −17.2082 | −0.144606 | ||||||||
\(120\) | −15.5155 | − | 18.9544i | −0.129296 | − | 0.157953i | ||||
\(121\) | 112.611 | 0.930670 | ||||||||
\(122\) | −17.9083 | −0.146789 | ||||||||
\(123\) | − | 117.401i | − | 0.954482i | ||||||
\(124\) | 65.0557 | 0.524643 | ||||||||
\(125\) | −110.462 | + | 58.5069i | −0.883699 | + | 0.468055i | ||||
\(126\) | − | 18.6211i | − | 0.147787i | ||||||
\(127\) | − | 90.0283i | − | 0.708884i | −0.935078 | − | 0.354442i | \(-0.884671\pi\) | ||
0.935078 | − | 0.354442i | \(-0.115329\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | − | 28.1205i | − | 0.217988i | ||||||
\(130\) | −7.08519 | − | 8.65558i | −0.0545015 | − | 0.0665814i | ||||
\(131\) | 127.511 | 0.973363 | 0.486681 | − | 0.873580i | \(-0.338207\pi\) | ||||
0.486681 | + | 0.873580i | \(0.338207\pi\) | |||||||
\(132\) | −10.0333 | −0.0760100 | ||||||||
\(133\) | − | 102.583i | − | 0.771299i | ||||||
\(134\) | − | 177.421i | − | 1.32404i | ||||||
\(135\) | 20.1042 | − | 16.4567i | 0.148920 | − | 0.121901i | ||||
\(136\) | 11.0895i | 0.0815401i | ||||||||
\(137\) | 113.969 | 0.831891 | 0.415945 | − | 0.909390i | \(-0.363451\pi\) | ||||
0.415945 | + | 0.909390i | \(0.363451\pi\) | |||||||
\(138\) | 54.7509 | + | 13.2791i | 0.396746 | + | 0.0962256i | ||||
\(139\) | 202.788 | 1.45890 | 0.729452 | − | 0.684032i | \(-0.239775\pi\) | ||||
0.729452 | + | 0.684032i | \(0.239775\pi\) | |||||||
\(140\) | 27.8009 | + | 33.9628i | 0.198578 | + | 0.242592i | ||||
\(141\) | −147.076 | −1.04309 | ||||||||
\(142\) | 38.8384i | 0.273510i | ||||||||
\(143\) | −4.58174 | −0.0320401 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −26.5582 | − | 32.4447i | −0.183160 | − | 0.223757i | ||||
\(146\) | 35.5831 | 0.243720 | ||||||||
\(147\) | − | 51.5049i | − | 0.350373i | ||||||
\(148\) | 99.6389 | 0.673236 | ||||||||
\(149\) | 88.7811i | 0.595846i | 0.954590 | + | 0.297923i | \(0.0962939\pi\) | ||||
−0.954590 | + | 0.297923i | \(0.903706\pi\) | |||||||
\(150\) | −12.0983 | + | 60.0302i | −0.0806555 | + | 0.400202i | ||||
\(151\) | 106.644 | 0.706250 | 0.353125 | − | 0.935576i | \(-0.385119\pi\) | ||||
0.353125 | + | 0.935576i | \(0.385119\pi\) | |||||||
\(152\) | −66.1074 | −0.434917 | ||||||||
\(153\) | −11.7621 | −0.0768768 | ||||||||
\(154\) | 17.9779 | 0.116739 | ||||||||
\(155\) | −103.018 | − | 125.852i | −0.664635 | − | 0.811948i | ||||
\(156\) | −5.47983 | −0.0351271 | ||||||||
\(157\) | 33.6167 | 0.214119 | 0.107060 | − | 0.994253i | \(-0.465856\pi\) | ||||
0.107060 | + | 0.994253i | \(0.465856\pi\) | |||||||
\(158\) | 36.0624 | 0.228243 | ||||||||
\(159\) | 2.03181i | 0.0127787i | ||||||||
\(160\) | 21.8867 | − | 17.9157i | 0.136792 | − | 0.111973i | ||||
\(161\) | −98.1037 | − | 23.7938i | −0.609339 | − | 0.147787i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 273.536i | 1.67813i | 0.544027 | + | 0.839067i | \(0.316899\pi\) | ||||
−0.544027 | + | 0.839067i | \(0.683101\pi\) | |||||||
\(164\) | 135.563 | 0.826606 | ||||||||
\(165\) | 15.8882 | + | 19.4097i | 0.0962921 | + | 0.117635i | ||||
\(166\) | − | 155.823i | − | 0.938695i | ||||||
\(167\) | − | 62.4430i | − | 0.373910i | −0.982368 | − | 0.186955i | \(-0.940138\pi\) | ||
0.982368 | − | 0.186955i | \(-0.0598619\pi\) | |||||||
\(168\) | 21.5018 | 0.127987 | ||||||||
\(169\) | 166.498 | 0.985193 | ||||||||
\(170\) | 21.4528 | − | 17.5606i | 0.126193 | − | 0.103298i | ||||
\(171\) | − | 70.1175i | − | 0.410044i | ||||||
\(172\) | 32.4707 | 0.188783 | ||||||||
\(173\) | − | 187.243i | − | 1.08233i | −0.840917 | − | 0.541164i | \(-0.817984\pi\) | ||
0.840917 | − | 0.541164i | \(-0.182016\pi\) | |||||||
\(174\) | −20.5407 | −0.118050 | ||||||||
\(175\) | 21.6780 | − | 107.563i | 0.123874 | − | 0.614647i | ||||
\(176\) | − | 11.5855i | − | 0.0658266i | ||||||
\(177\) | − | 178.434i | − | 1.00810i | ||||||
\(178\) | 20.4889 | 0.115106 | ||||||||
\(179\) | −151.065 | −0.843937 | −0.421968 | − | 0.906611i | \(-0.638661\pi\) | ||||
−0.421968 | + | 0.906611i | \(0.638661\pi\) | |||||||
\(180\) | 19.0025 | + | 23.2143i | 0.105570 | + | 0.128968i | ||||
\(181\) | − | 295.157i | − | 1.63070i | −0.578968 | − | 0.815350i | \(-0.696544\pi\) | ||
0.578968 | − | 0.815350i | \(-0.303456\pi\) | |||||||
\(182\) | 9.81886 | 0.0539498 | ||||||||
\(183\) | 21.9331 | 0.119853 | ||||||||
\(184\) | −15.3334 | + | 63.2209i | −0.0833338 | + | 0.343592i | ||||
\(185\) | −157.782 | − | 192.754i | −0.852878 | − | 1.04191i | ||||
\(186\) | −79.6766 | −0.428369 | ||||||||
\(187\) | − | 11.3558i | − | 0.0607264i | ||||||
\(188\) | − | 169.829i | − | 0.903347i | ||||||
\(189\) | 22.8061i | 0.120667i | ||||||||
\(190\) | 104.684 | + | 127.886i | 0.550968 | + | 0.673087i | ||||
\(191\) | 339.920i | 1.77969i | 0.456267 | + | 0.889843i | \(0.349186\pi\) | ||||
−0.456267 | + | 0.889843i | \(0.650814\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | − | 205.591i | − | 1.06524i | −0.846354 | − | 0.532620i | \(-0.821207\pi\) | ||
0.846354 | − | 0.532620i | \(-0.178793\pi\) | |||||||
\(194\) | 90.4570i | 0.466273i | ||||||||
\(195\) | 8.67755 | + | 10.6009i | 0.0445003 | + | 0.0543635i | ||||
\(196\) | 59.4727 | 0.303432 | ||||||||
\(197\) | 239.594i | 1.21621i | 0.793856 | + | 0.608106i | \(0.208070\pi\) | ||||
−0.793856 | + | 0.608106i | \(0.791930\pi\) | |||||||
\(198\) | 12.2883 | 0.0620619 | ||||||||
\(199\) | − | 12.7701i | − | 0.0641713i | −0.999485 | − | 0.0320856i | \(-0.989785\pi\) | ||
0.999485 | − | 0.0320856i | \(-0.0102149\pi\) | |||||||
\(200\) | −69.3170 | − | 13.9699i | −0.346585 | − | 0.0698497i | ||||
\(201\) | 217.296i | 1.08107i | ||||||||
\(202\) | 123.241i | 0.610102i | ||||||||
\(203\) | 36.8052 | 0.181306 | ||||||||
\(204\) | − | 13.5818i | − | 0.0665772i | ||||||
\(205\) | −214.670 | − | 262.251i | −1.04717 | − | 1.27927i | ||||
\(206\) | − | 191.735i | − | 0.930753i | ||||||
\(207\) | −67.0559 | − | 16.2635i | −0.323942 | − | 0.0785679i | ||||
\(208\) | − | 6.32757i | − | 0.0304210i | ||||||
\(209\) | 67.6954 | 0.323901 | ||||||||
\(210\) | −34.0490 | − | 41.5958i | −0.162138 | − | 0.198075i | ||||
\(211\) | −84.8656 | −0.402207 | −0.201103 | − | 0.979570i | \(-0.564453\pi\) | ||||
−0.201103 | + | 0.979570i | \(0.564453\pi\) | |||||||
\(212\) | −2.34613 | −0.0110666 | ||||||||
\(213\) | − | 47.5671i | − | 0.223320i | ||||||
\(214\) | 176.327i | 0.823959i | ||||||||
\(215\) | −51.4188 | − | 62.8154i | −0.239157 | − | 0.292165i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 142.766 | 0.657907 | ||||||||
\(218\) | 141.168 | 0.647558 | ||||||||
\(219\) | −43.5802 | −0.198996 | ||||||||
\(220\) | −22.4124 | + | 18.3461i | −0.101875 | + | 0.0833914i | ||||
\(221\) | − | 6.20214i | − | 0.0280640i | ||||||
\(222\) | −122.032 | −0.549695 | ||||||||
\(223\) | − | 44.0312i | − | 0.197449i | −0.995115 | − | 0.0987246i | \(-0.968524\pi\) | ||
0.995115 | − | 0.0987246i | \(-0.0314763\pi\) | |||||||
\(224\) | 24.8281i | 0.110840i | ||||||||
\(225\) | 14.8174 | − | 73.5217i | 0.0658549 | − | 0.326763i | ||||
\(226\) | 61.8181i | 0.273532i | ||||||||
\(227\) | −343.150 | −1.51167 | −0.755837 | − | 0.654760i | \(-0.772770\pi\) | ||||
−0.755837 | + | 0.654760i | \(0.772770\pi\) | |||||||
\(228\) | 80.9647 | 0.355108 | ||||||||
\(229\) | − | 54.4435i | − | 0.237745i | −0.992910 | − | 0.118872i | \(-0.962072\pi\) | ||
0.992910 | − | 0.118872i | \(-0.0379279\pi\) | |||||||
\(230\) | 146.584 | − | 70.4502i | 0.637320 | − | 0.306305i | ||||
\(231\) | −22.0183 | −0.0953173 | ||||||||
\(232\) | − | 23.7183i | − | 0.102234i | ||||||
\(233\) | − | 118.133i | − | 0.507010i | −0.967334 | − | 0.253505i | \(-0.918417\pi\) | ||
0.967334 | − | 0.253505i | \(-0.0815834\pi\) | |||||||
\(234\) | 6.71140 | 0.0286812 | ||||||||
\(235\) | −328.539 | + | 268.932i | −1.39804 | + | 1.14439i | ||||
\(236\) | 206.038 | 0.873041 | ||||||||
\(237\) | −44.1673 | −0.186360 | ||||||||
\(238\) | 24.3360i | 0.102252i | ||||||||
\(239\) | 34.1084 | 0.142713 | 0.0713564 | − | 0.997451i | \(-0.477267\pi\) | ||||
0.0713564 | + | 0.997451i | \(0.477267\pi\) | |||||||
\(240\) | −26.8056 | + | 21.9422i | −0.111690 | + | 0.0914259i | ||||
\(241\) | 151.731i | 0.629590i | 0.949160 | + | 0.314795i | \(0.101936\pi\) | ||||
−0.949160 | + | 0.314795i | \(0.898064\pi\) | |||||||
\(242\) | − | 159.256i | − | 0.658083i | ||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 25.3262i | 0.103796i | ||||||||
\(245\) | −94.1776 | − | 115.051i | −0.384398 | − | 0.469598i | ||||
\(246\) | −166.031 | −0.674921 | ||||||||
\(247\) | 36.9728 | 0.149687 | ||||||||
\(248\) | − | 92.0026i | − | 0.370978i | ||||||
\(249\) | 190.844i | 0.766441i | ||||||||
\(250\) | 82.7412 | + | 156.217i | 0.330965 | + | 0.624870i | ||||
\(251\) | − | 31.1868i | − | 0.124250i | −0.998068 | − | 0.0621252i | \(-0.980212\pi\) | ||
0.998068 | − | 0.0621252i | \(-0.0197878\pi\) | |||||||
\(252\) | −26.3342 | −0.104501 | ||||||||
\(253\) | 15.7017 | − | 64.7396i | 0.0620622 | − | 0.255888i | ||||
\(254\) | −127.319 | −0.501257 | ||||||||
\(255\) | −26.2743 | + | 21.5073i | −0.103036 | + | 0.0843423i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 487.515i | − | 1.89695i | −0.316858 | − | 0.948473i | \(-0.602628\pi\) | ||
0.316858 | − | 0.948473i | \(-0.397372\pi\) | |||||||
\(258\) | −39.7683 | −0.154141 | ||||||||
\(259\) | 218.659 | 0.844245 | ||||||||
\(260\) | −12.2408 | + | 10.0200i | −0.0470802 | + | 0.0385384i | ||||
\(261\) | 25.1571 | 0.0963874 | ||||||||
\(262\) | − | 180.327i | − | 0.688272i | ||||||
\(263\) | 296.073 | 1.12575 | 0.562876 | − | 0.826541i | \(-0.309695\pi\) | ||||
0.562876 | + | 0.826541i | \(0.309695\pi\) | |||||||
\(264\) | 14.1893i | 0.0537472i | ||||||||
\(265\) | 3.71520 | + | 4.53865i | 0.0140196 | + | 0.0171270i | ||||
\(266\) | −145.074 | −0.545391 | ||||||||
\(267\) | −25.0936 | −0.0939837 | ||||||||
\(268\) | −250.911 | −0.936236 | ||||||||
\(269\) | −69.7280 | −0.259212 | −0.129606 | − | 0.991566i | \(-0.541371\pi\) | ||||
−0.129606 | + | 0.991566i | \(0.541371\pi\) | |||||||
\(270\) | −23.2732 | − | 28.4316i | −0.0861972 | − | 0.105302i | ||||
\(271\) | 356.089 | 1.31398 | 0.656991 | − | 0.753898i | \(-0.271829\pi\) | ||||
0.656991 | + | 0.753898i | \(0.271829\pi\) | |||||||
\(272\) | 15.6829 | 0.0576576 | ||||||||
\(273\) | −12.0256 | −0.0440498 | ||||||||
\(274\) | − | 161.177i | − | 0.588235i | ||||||
\(275\) | 70.9820 | + | 14.3055i | 0.258116 | + | 0.0520201i | ||||
\(276\) | 18.7795 | − | 77.4295i | 0.0680418 | − | 0.280542i | ||||
\(277\) | 38.0169i | 0.137245i | 0.997643 | + | 0.0686225i | \(0.0218604\pi\) | ||||
−0.997643 | + | 0.0686225i | \(0.978140\pi\) | |||||||
\(278\) | − | 286.785i | − | 1.03160i | ||||||
\(279\) | 97.5835 | 0.349762 | ||||||||
\(280\) | 48.0307 | − | 39.3164i | 0.171538 | − | 0.140416i | ||||
\(281\) | 311.125i | 1.10721i | 0.832781 | + | 0.553603i | \(0.186747\pi\) | ||||
−0.832781 | + | 0.553603i | \(0.813253\pi\) | |||||||
\(282\) | 207.997i | 0.737579i | ||||||||
\(283\) | 106.374 | 0.375879 | 0.187939 | − | 0.982181i | \(-0.439819\pi\) | ||||
0.187939 | + | 0.982181i | \(0.439819\pi\) | |||||||
\(284\) | 54.9257 | 0.193400 | ||||||||
\(285\) | −128.211 | − | 156.628i | −0.449864 | − | 0.549573i | ||||
\(286\) | 6.47956i | 0.0226558i | ||||||||
\(287\) | 297.496 | 1.03657 | ||||||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | −273.628 | −0.946810 | ||||||||
\(290\) | −45.8837 | + | 37.5590i | −0.158220 | + | 0.129514i | ||||
\(291\) | − | 110.787i | − | 0.380710i | ||||||
\(292\) | − | 50.3221i | − | 0.172336i | ||||||
\(293\) | 235.464 | 0.803631 | 0.401815 | − | 0.915721i | \(-0.368379\pi\) | ||||
0.401815 | + | 0.915721i | \(0.368379\pi\) | |||||||
\(294\) | −72.8389 | −0.247751 | ||||||||
\(295\) | −326.270 | − | 398.585i | −1.10600 | − | 1.35114i | ||||
\(296\) | − | 140.911i | − | 0.476050i | ||||||
\(297\) | −15.0500 | −0.0506733 | ||||||||
\(298\) | 125.555 | 0.421327 | ||||||||
\(299\) | 8.57572 | − | 35.3584i | 0.0286813 | − | 0.118256i | ||||
\(300\) | 84.8956 | + | 17.1096i | 0.282985 | + | 0.0570321i | ||||
\(301\) | 71.2576 | 0.236736 | ||||||||
\(302\) | − | 150.817i | − | 0.499394i | ||||||
\(303\) | − | 150.938i | − | 0.498146i | ||||||
\(304\) | 93.4900i | 0.307533i | ||||||||
\(305\) | 48.9942 | − | 40.1051i | 0.160637 | − | 0.131492i | ||||
\(306\) | 16.6342i | 0.0543601i | ||||||||
\(307\) | 35.2062i | 0.114678i | 0.998355 | + | 0.0573391i | \(0.0182616\pi\) | ||||
−0.998355 | + | 0.0573391i | \(0.981738\pi\) | |||||||
\(308\) | − | 25.4245i | − | 0.0825472i | ||||||
\(309\) | 234.826i | 0.759956i | ||||||||
\(310\) | −177.981 | + | 145.690i | −0.574134 | + | 0.469968i | ||||
\(311\) | −174.212 | −0.560166 | −0.280083 | − | 0.959976i | \(-0.590362\pi\) | ||||
−0.280083 | + | 0.959976i | \(0.590362\pi\) | |||||||
\(312\) | 7.74965i | 0.0248386i | ||||||||
\(313\) | 212.916 | 0.680244 | 0.340122 | − | 0.940381i | \(-0.389532\pi\) | ||||
0.340122 | + | 0.940381i | \(0.389532\pi\) | |||||||
\(314\) | − | 47.5412i | − | 0.151405i | ||||||
\(315\) | 41.7014 | + | 50.9442i | 0.132385 | + | 0.161728i | ||||
\(316\) | − | 51.0000i | − | 0.161392i | ||||||
\(317\) | − | 220.794i | − | 0.696511i | −0.937400 | − | 0.348256i | \(-0.886774\pi\) | ||
0.937400 | − | 0.348256i | \(-0.113226\pi\) | |||||||
\(318\) | 2.87341 | 0.00903588 | ||||||||
\(319\) | 24.2881i | 0.0761382i | ||||||||
\(320\) | −25.3367 | − | 30.9524i | −0.0791772 | − | 0.0967263i | ||||
\(321\) | − | 215.956i | − | 0.672759i | ||||||
\(322\) | −33.6495 | + | 138.740i | −0.104501 | + | 0.430868i | ||||
\(323\) | 91.6369i | 0.283706i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 38.7678 | + | 7.81315i | 0.119286 | + | 0.0240405i | ||||
\(326\) | 386.838 | 1.18662 | ||||||||
\(327\) | −172.894 | −0.528729 | ||||||||
\(328\) | − | 191.716i | − | 0.584499i | ||||||
\(329\) | − | 372.693i | − | 1.13281i | ||||||
\(330\) | 27.4495 | − | 22.4693i | 0.0831802 | − | 0.0680888i | ||||
\(331\) | 328.021 | 0.990999 | 0.495499 | − | 0.868608i | \(-0.334985\pi\) | ||||
0.495499 | + | 0.868608i | \(0.334985\pi\) | |||||||
\(332\) | −220.367 | −0.663757 | ||||||||
\(333\) | 149.458 | 0.448824 | ||||||||
\(334\) | −88.3078 | −0.264395 | ||||||||
\(335\) | 397.329 | + | 485.395i | 1.18606 | + | 1.44894i | ||||
\(336\) | − | 30.4081i | − | 0.0905004i | ||||||
\(337\) | −97.1617 | −0.288314 | −0.144157 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144157 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(338\) | − | 235.463i | − | 0.696637i | ||||||
\(339\) | − | 75.7115i | − | 0.223338i | ||||||
\(340\) | −24.8345 | − | 30.3389i | −0.0730426 | − | 0.0892320i | ||||
\(341\) | 94.2126i | 0.276283i | ||||||||
\(342\) | −99.1611 | −0.289945 | ||||||||
\(343\) | 345.577 | 1.00751 | ||||||||
\(344\) | − | 45.9205i | − | 0.133490i | ||||||
\(345\) | −179.528 | + | 86.2835i | −0.520370 | + | 0.250097i | ||||
\(346\) | −264.801 | −0.765321 | ||||||||
\(347\) | 346.996i | 0.999987i | 0.866029 | + | 0.499994i | \(0.166664\pi\) | ||||
−0.866029 | + | 0.499994i | \(0.833336\pi\) | |||||||
\(348\) | 29.0489i | 0.0834739i | ||||||||
\(349\) | −428.347 | −1.22735 | −0.613677 | − | 0.789557i | \(-0.710310\pi\) | ||||
−0.613677 | + | 0.789557i | \(0.710310\pi\) | |||||||
\(350\) | −152.117 | − | 30.6573i | −0.434621 | − | 0.0875923i | ||||
\(351\) | −8.21975 | −0.0234181 | ||||||||
\(352\) | −16.3843 | −0.0465464 | ||||||||
\(353\) | 285.410i | 0.808527i | 0.914643 | + | 0.404263i | \(0.132472\pi\) | ||||
−0.914643 | + | 0.404263i | \(0.867528\pi\) | |||||||
\(354\) | −252.344 | −0.712835 | ||||||||
\(355\) | −86.9773 | − | 106.255i | −0.245006 | − | 0.299311i | ||||
\(356\) | − | 28.9756i | − | 0.0813923i | ||||||
\(357\) | − | 29.8054i | − | 0.0834885i | ||||||
\(358\) | 213.638i | 0.596753i | ||||||||
\(359\) | − | 448.742i | − | 1.24998i | −0.780634 | − | 0.624988i | \(-0.785104\pi\) | ||
0.780634 | − | 0.624988i | \(-0.214896\pi\) | |||||||
\(360\) | 32.8300 | − | 26.8736i | 0.0911944 | − | 0.0746490i | ||||
\(361\) | −185.274 | −0.513224 | ||||||||
\(362\) | −417.415 | −1.15308 | ||||||||
\(363\) | 195.048i | 0.537322i | ||||||||
\(364\) | − | 13.8860i | − | 0.0381482i | ||||||
\(365\) | −97.3493 | + | 79.6872i | −0.266710 | + | 0.218321i | ||||
\(366\) | − | 31.0181i | − | 0.0847489i | ||||||
\(367\) | 259.468 | 0.706998 | 0.353499 | − | 0.935435i | \(-0.384992\pi\) | ||||
0.353499 | + | 0.935435i | \(0.384992\pi\) | |||||||
\(368\) | 89.4079 | + | 21.6847i | 0.242956 | + | 0.0589259i | ||||
\(369\) | 203.345 | 0.551071 | ||||||||
\(370\) | −272.595 | + | 223.138i | −0.736744 | + | 0.603076i | ||||
\(371\) | −5.14862 | −0.0138777 | ||||||||
\(372\) | 112.680i | 0.302903i | ||||||||
\(373\) | 173.652 | 0.465555 | 0.232778 | − | 0.972530i | \(-0.425219\pi\) | ||||
0.232778 | + | 0.972530i | \(0.425219\pi\) | |||||||
\(374\) | −16.0596 | −0.0429400 | ||||||||
\(375\) | −101.337 | − | 191.327i | −0.270232 | − | 0.510204i | ||||
\(376\) | −240.175 | −0.638762 | ||||||||
\(377\) | 13.2653i | 0.0351864i | ||||||||
\(378\) | 32.2527 | 0.0853246 | ||||||||
\(379\) | 243.255i | 0.641833i | 0.947107 | + | 0.320917i | \(0.103991\pi\) | ||||
−0.947107 | + | 0.320917i | \(0.896009\pi\) | |||||||
\(380\) | 180.859 | − | 148.045i | 0.475944 | − | 0.389593i | ||||
\(381\) | 155.934 | 0.409275 | ||||||||
\(382\) | 480.720 | 1.25843 | ||||||||
\(383\) | −46.0197 | −0.120156 | −0.0600779 | − | 0.998194i | \(-0.519135\pi\) | ||||
−0.0600779 | + | 0.998194i | \(0.519135\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | −49.1844 | + | 40.2609i | −0.127752 | + | 0.104574i | ||||
\(386\) | −290.750 | −0.753239 | ||||||||
\(387\) | 48.7061 | 0.125855 | ||||||||
\(388\) | 127.926 | 0.329705 | ||||||||
\(389\) | − | 403.468i | − | 1.03719i | −0.855019 | − | 0.518597i | \(-0.826455\pi\) | ||
0.855019 | − | 0.518597i | \(-0.173545\pi\) | |||||||
\(390\) | 14.9919 | − | 12.2719i | 0.0384408 | − | 0.0314664i | ||||
\(391\) | 87.6357 | + | 21.2549i | 0.224132 | + | 0.0543604i | ||||
\(392\) | − | 84.1071i | − | 0.214559i | ||||||
\(393\) | 220.855i | 0.561971i | ||||||||
\(394\) | 338.837 | 0.859992 | ||||||||
\(395\) | −98.6608 | + | 80.7607i | −0.249774 | + | 0.204457i | ||||
\(396\) | − | 17.3782i | − | 0.0438844i | ||||||
\(397\) | 333.085i | 0.839005i | 0.907754 | + | 0.419502i | \(0.137795\pi\) | ||||
−0.907754 | + | 0.419502i | \(0.862205\pi\) | |||||||
\(398\) | −18.0596 | −0.0453760 | ||||||||
\(399\) | 177.679 | 0.445310 | ||||||||
\(400\) | −19.7565 | + | 98.0290i | −0.0493912 | + | 0.245072i | ||||
\(401\) | 498.274i | 1.24258i | 0.783582 | + | 0.621289i | \(0.213391\pi\) | ||||
−0.783582 | + | 0.621289i | \(0.786609\pi\) | |||||||
\(402\) | 307.302 | 0.764434 | ||||||||
\(403\) | 51.4555i | 0.127681i | ||||||||
\(404\) | 174.289 | 0.431407 | ||||||||
\(405\) | 28.5038 | + | 34.8215i | 0.0703797 | + | 0.0859789i | ||||
\(406\) | − | 52.0503i | − | 0.128203i | ||||||
\(407\) | 144.295i | 0.354534i | ||||||||
\(408\) | −19.2075 | −0.0470772 | ||||||||
\(409\) | 415.197 | 1.01515 | 0.507576 | − | 0.861607i | \(-0.330542\pi\) | ||||
0.507576 | + | 0.861607i | \(0.330542\pi\) | |||||||
\(410\) | −370.879 | + | 303.590i | −0.904582 | + | 0.740463i | ||||
\(411\) | 197.400i | 0.480292i | ||||||||
\(412\) | −271.154 | −0.658141 | ||||||||
\(413\) | 452.154 | 1.09480 | ||||||||
\(414\) | −23.0001 | + | 94.8314i | −0.0555559 | + | 0.229061i | ||||
\(415\) | 348.961 | + | 426.307i | 0.840871 | + | 1.02724i | ||||
\(416\) | −8.94853 | −0.0215109 | ||||||||
\(417\) | 351.238i | 0.842298i | ||||||||
\(418\) | − | 95.7357i | − | 0.229033i | ||||||
\(419\) | − | 297.163i | − | 0.709221i | −0.935014 | − | 0.354610i | \(-0.884614\pi\) | ||
0.935014 | − | 0.354610i | \(-0.115386\pi\) | |||||||
\(420\) | −58.8253 | + | 48.1526i | −0.140060 | + | 0.114649i | ||||
\(421\) | 281.558i | 0.668783i | 0.942434 | + | 0.334392i | \(0.108531\pi\) | ||||
−0.942434 | + | 0.334392i | \(0.891469\pi\) | |||||||
\(422\) | 120.018i | 0.284403i | ||||||||
\(423\) | − | 254.744i | − | 0.602231i | ||||||
\(424\) | 3.31793i | 0.00782530i | ||||||||
\(425\) | −19.3649 | + | 96.0859i | −0.0455644 | + | 0.226084i | ||||
\(426\) | −67.2700 | −0.157911 | ||||||||
\(427\) | 55.5788i | 0.130161i | ||||||||
\(428\) | 249.364 | 0.582627 | ||||||||
\(429\) | − | 7.93581i | − | 0.0184984i | ||||||
\(430\) | −88.8345 | + | 72.7172i | −0.206592 | + | 0.169110i | ||||
\(431\) | 782.410i | 1.81534i | 0.419689 | + | 0.907668i | \(0.362139\pi\) | ||||
−0.419689 | + | 0.907668i | \(0.637861\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | 153.757 | 0.355096 | 0.177548 | − | 0.984112i | \(-0.443183\pi\) | ||||
0.177548 | + | 0.984112i | \(0.443183\pi\) | |||||||
\(434\) | − | 201.901i | − | 0.465211i | ||||||
\(435\) | 56.1959 | − | 46.0002i | 0.129186 | − | 0.105748i | ||||
\(436\) | − | 199.641i | − | 0.457893i | ||||||
\(437\) | −126.707 | + | 522.421i | −0.289946 | + | 1.19547i | ||||
\(438\) | 61.6317i | 0.140712i | ||||||||
\(439\) | −446.096 | −1.01616 | −0.508082 | − | 0.861309i | \(-0.669645\pi\) | ||||
−0.508082 | + | 0.861309i | \(0.669645\pi\) | |||||||
\(440\) | 25.9453 | + | 31.6959i | 0.0589666 | + | 0.0720362i | ||||
\(441\) | 89.2090 | 0.202288 | ||||||||
\(442\) | −8.77116 | −0.0198442 | ||||||||
\(443\) | 726.162i | 1.63919i | 0.572942 | + | 0.819596i | \(0.305802\pi\) | ||||
−0.572942 | + | 0.819596i | \(0.694198\pi\) | |||||||
\(444\) | 172.580i | 0.388693i | ||||||||
\(445\) | −56.0541 | + | 45.8842i | −0.125964 | + | 0.103111i | ||||
\(446\) | −62.2695 | −0.139618 | ||||||||
\(447\) | −153.773 | −0.344012 | ||||||||
\(448\) | 35.1123 | 0.0783757 | ||||||||
\(449\) | 118.414 | 0.263728 | 0.131864 | − | 0.991268i | \(-0.457904\pi\) | ||||
0.131864 | + | 0.991268i | \(0.457904\pi\) | |||||||
\(450\) | −103.975 | − | 20.9549i | −0.231057 | − | 0.0465665i | ||||
\(451\) | 196.321i | 0.435301i | ||||||||
\(452\) | 87.4241 | 0.193416 | ||||||||
\(453\) | 184.712i | 0.407754i | ||||||||
\(454\) | 485.287i | 1.06891i | ||||||||
\(455\) | −26.8628 | + | 21.9890i | −0.0590390 | + | 0.0483275i | ||||
\(456\) | − | 114.501i | − | 0.251100i | ||||||
\(457\) | 27.9007 | 0.0610518 | 0.0305259 | − | 0.999534i | \(-0.490282\pi\) | ||||
0.0305259 | + | 0.999534i | \(0.490282\pi\) | |||||||
\(458\) | −76.9947 | −0.168111 | ||||||||
\(459\) | − | 20.3726i | − | 0.0443848i | ||||||
\(460\) | −99.6316 | − | 207.301i | −0.216590 | − | 0.450653i | ||||
\(461\) | 382.827 | 0.830427 | 0.415214 | − | 0.909724i | \(-0.363707\pi\) | ||||
0.415214 | + | 0.909724i | \(0.363707\pi\) | |||||||
\(462\) | 31.1386i | 0.0673995i | ||||||||
\(463\) | 58.0745i | 0.125431i | 0.998031 | + | 0.0627154i | \(0.0199760\pi\) | ||||
−0.998031 | + | 0.0627154i | \(0.980024\pi\) | |||||||
\(464\) | −33.5428 | −0.0722905 | ||||||||
\(465\) | 217.982 | − | 178.433i | 0.468778 | − | 0.383727i | ||||
\(466\) | −167.066 | −0.358510 | ||||||||
\(467\) | −384.852 | −0.824095 | −0.412047 | − | 0.911162i | \(-0.635186\pi\) | ||||
−0.412047 | + | 0.911162i | \(0.635186\pi\) | |||||||
\(468\) | − | 9.49135i | − | 0.0202807i | ||||||
\(469\) | −550.630 | −1.17405 | ||||||||
\(470\) | 380.327 | + | 464.624i | 0.809206 | + | 0.988562i | ||||
\(471\) | 58.2258i | 0.123622i | ||||||||
\(472\) | − | 291.381i | − | 0.617333i | ||||||
\(473\) | 47.0236i | 0.0994156i | ||||||||
\(474\) | 62.4620i | 0.131776i | ||||||||
\(475\) | −572.796 | − | 115.440i | −1.20589 | − | 0.243031i | ||||
\(476\) | 34.4163 | 0.0723032 | ||||||||
\(477\) | −3.51919 | −0.00737776 | ||||||||
\(478\) | − | 48.2365i | − | 0.100913i | ||||||
\(479\) | − | 557.765i | − | 1.16444i | −0.813033 | − | 0.582218i | \(-0.802185\pi\) | ||
0.813033 | − | 0.582218i | \(-0.197815\pi\) | |||||||
\(480\) | 31.0310 | + | 37.9088i | 0.0646479 | + | 0.0789767i | ||||
\(481\) | 78.8089i | 0.163844i | ||||||||
\(482\) | 214.580 | 0.445188 | ||||||||
\(483\) | 41.2120 | − | 169.921i | 0.0853251 | − | 0.351802i | ||||
\(484\) | −225.222 | −0.465335 | ||||||||
\(485\) | −202.576 | − | 247.475i | −0.417682 | − | 0.510258i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 651.144i | 1.33705i | 0.743689 | + | 0.668525i | \(0.233074\pi\) | ||||
−0.743689 | + | 0.668525i | \(0.766926\pi\) | |||||||
\(488\) | 35.8166 | 0.0733947 | ||||||||
\(489\) | −473.778 | −0.968872 | ||||||||
\(490\) | −162.707 | + | 133.187i | −0.332056 | + | 0.271811i | ||||
\(491\) | 492.791 | 1.00365 | 0.501824 | − | 0.864970i | \(-0.332662\pi\) | ||||
0.501824 | + | 0.864970i | \(0.332662\pi\) | |||||||
\(492\) | 234.803i | 0.477241i | ||||||||
\(493\) | −32.8779 | −0.0666895 | ||||||||
\(494\) | − | 52.2874i | − | 0.105845i | ||||||
\(495\) | −33.6186 | + | 27.5192i | −0.0679164 | + | 0.0555942i | ||||
\(496\) | −130.111 | −0.262321 | ||||||||
\(497\) | 120.536 | 0.242526 | ||||||||
\(498\) | 269.894 | 0.541956 | ||||||||
\(499\) | 506.096 | 1.01422 | 0.507110 | − | 0.861881i | \(-0.330714\pi\) | ||||
0.507110 | + | 0.861881i | \(0.330714\pi\) | |||||||
\(500\) | 220.925 | − | 117.014i | 0.441850 | − | 0.234027i | ||||
\(501\) | 108.154 | 0.215877 | ||||||||
\(502\) | −44.1048 | −0.0878583 | ||||||||
\(503\) | 73.5526 | 0.146228 | 0.0731139 | − | 0.997324i | \(-0.476706\pi\) | ||||
0.0731139 | + | 0.997324i | \(0.476706\pi\) | |||||||
\(504\) | 37.2422i | 0.0738933i | ||||||||
\(505\) | −275.994 | − | 337.166i | −0.546522 | − | 0.667655i | ||||
\(506\) | −91.5556 | − | 22.2056i | −0.180940 | − | 0.0438846i | ||||
\(507\) | 288.382i | 0.568801i | ||||||||
\(508\) | 180.057i | 0.354442i | ||||||||
\(509\) | −725.849 | −1.42603 | −0.713015 | − | 0.701149i | \(-0.752671\pi\) | ||||
−0.713015 | + | 0.701149i | \(0.752671\pi\) | |||||||
\(510\) | 30.4159 | + | 37.1574i | 0.0596390 | + | 0.0728577i | ||||
\(511\) | − | 110.433i | − | 0.216111i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 121.447 | 0.236739 | ||||||||
\(514\) | −689.451 | −1.34134 | ||||||||
\(515\) | 429.385 | + | 524.555i | 0.833756 | + | 1.01855i | ||||
\(516\) | 56.2409i | 0.108994i | ||||||||
\(517\) | 245.944 | 0.475714 | ||||||||
\(518\) | − | 309.231i | − | 0.596971i | ||||||
\(519\) | 324.314 | 0.624882 | ||||||||
\(520\) | 14.1704 | + | 17.3112i | 0.0272507 | + | 0.0332907i | ||||
\(521\) | 90.1740i | 0.173079i | 0.996248 | + | 0.0865394i | \(0.0275808\pi\) | ||||
−0.996248 | + | 0.0865394i | \(0.972419\pi\) | |||||||
\(522\) | − | 35.5775i | − | 0.0681562i | ||||||
\(523\) | 355.009 | 0.678794 | 0.339397 | − | 0.940643i | \(-0.389777\pi\) | ||||
0.339397 | + | 0.940643i | \(0.389777\pi\) | |||||||
\(524\) | −255.021 | −0.486681 | ||||||||
\(525\) | 186.305 | + | 37.5474i | 0.354867 | + | 0.0715188i | ||||
\(526\) | − | 418.710i | − | 0.796027i | ||||||
\(527\) | −127.532 | −0.241997 | ||||||||
\(528\) | 20.0666 | 0.0380050 | ||||||||
\(529\) | 470.222 | + | 242.348i | 0.888888 | + | 0.458125i | ||||
\(530\) | 6.41862 | − | 5.25408i | 0.0121106 | − | 0.00991336i | ||||
\(531\) | 309.057 | 0.582027 | ||||||||
\(532\) | 205.166i | 0.385650i | ||||||||
\(533\) | 107.223i | 0.201169i | ||||||||
\(534\) | 35.4878i | 0.0664565i | ||||||||
\(535\) | −394.879 | − | 482.402i | −0.738092 | − | 0.901685i | ||||
\(536\) | 354.842i | 0.662019i | ||||||||
\(537\) | − | 261.652i | − | 0.487247i | ||||||
\(538\) | 98.6102i | 0.183290i | ||||||||
\(539\) | 86.1274i | 0.159791i | ||||||||
\(540\) | −40.2084 | + | 32.9133i | −0.0744599 | + | 0.0609506i | ||||
\(541\) | −692.660 | −1.28033 | −0.640166 | − | 0.768236i | \(-0.721135\pi\) | ||||
−0.640166 | + | 0.768236i | \(0.721135\pi\) | |||||||
\(542\) | − | 503.586i | − | 0.929126i | ||||||
\(543\) | 511.226 | 0.941485 | ||||||||
\(544\) | − | 22.1789i | − | 0.0407701i | ||||||
\(545\) | −386.211 | + | 316.140i | −0.708644 | + | 0.580074i | ||||
\(546\) | 17.0068i | 0.0311479i | ||||||||
\(547\) | − | 571.267i | − | 1.04436i | −0.852834 | − | 0.522181i | \(-0.825118\pi\) | ||
0.852834 | − | 0.522181i | \(-0.174882\pi\) | |||||||
\(548\) | −227.938 | −0.415945 | ||||||||
\(549\) | 37.9893i | 0.0691972i | ||||||||
\(550\) | 20.2311 | − | 100.384i | 0.0367837 | − | 0.182516i | ||||
\(551\) | − | 195.995i | − | 0.355707i | ||||||
\(552\) | −109.502 | − | 26.5583i | −0.198373 | − | 0.0481128i | ||||
\(553\) | − | 111.920i | − | 0.202388i | ||||||
\(554\) | 53.7640 | 0.0970469 | ||||||||
\(555\) | 333.860 | − | 273.287i | 0.601549 | − | 0.492410i | ||||
\(556\) | −405.575 | −0.729452 | ||||||||
\(557\) | −614.979 | −1.10409 | −0.552045 | − | 0.833814i | \(-0.686152\pi\) | ||||
−0.552045 | + | 0.833814i | \(0.686152\pi\) | |||||||
\(558\) | − | 138.004i | − | 0.247319i | ||||||
\(559\) | 25.6826i | 0.0459438i | ||||||||
\(560\) | −55.6019 | − | 67.9257i | −0.0992890 | − | 0.121296i | ||||
\(561\) | 19.6689 | 0.0350604 | ||||||||
\(562\) | 439.997 | 0.782913 | ||||||||
\(563\) | 158.051 | 0.280731 | 0.140365 | − | 0.990100i | \(-0.455172\pi\) | ||||
0.140365 | + | 0.990100i | \(0.455172\pi\) | |||||||
\(564\) | 294.153 | 0.521547 | ||||||||
\(565\) | −138.440 | − | 169.124i | −0.245026 | − | 0.299335i | ||||
\(566\) | − | 150.435i | − | 0.265786i | ||||||
\(567\) | −39.5013 | −0.0696673 | ||||||||
\(568\) | − | 77.6767i | − | 0.136755i | ||||||
\(569\) | − | 460.419i | − | 0.809173i | −0.914500 | − | 0.404586i | \(-0.867416\pi\) | ||
0.914500 | − | 0.404586i | \(-0.132584\pi\) | |||||||
\(570\) | −221.506 | + | 181.318i | −0.388607 | + | 0.318102i | ||||
\(571\) | 1109.86i | 1.94371i | 0.235580 | + | 0.971855i | \(0.424301\pi\) | ||||
−0.235580 | + | 0.971855i | \(0.575699\pi\) | |||||||
\(572\) | 9.16348 | 0.0160201 | ||||||||
\(573\) | −588.759 | −1.02750 | ||||||||
\(574\) | − | 420.723i | − | 0.732968i | ||||||
\(575\) | −243.257 | + | 521.009i | −0.423056 | + | 0.906103i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | − | 554.867i | − | 0.961642i | −0.876819 | − | 0.480821i | \(-0.840339\pi\) | ||
0.876819 | − | 0.480821i | \(-0.159661\pi\) | |||||||
\(578\) | 386.968i | 0.669496i | ||||||||
\(579\) | 356.095 | 0.615017 | ||||||||
\(580\) | 53.1165 | + | 64.8894i | 0.0915801 | + | 0.111878i | ||||
\(581\) | −483.601 | −0.832359 | ||||||||
\(582\) | −156.676 | −0.269203 | ||||||||
\(583\) | − | 3.39763i | − | 0.00582783i | ||||||
\(584\) | −71.1661 | −0.121860 | ||||||||
\(585\) | −18.3613 | + | 15.0300i | −0.0313868 | + | 0.0256922i | ||||
\(586\) | − | 332.996i | − | 0.568253i | ||||||
\(587\) | 880.384i | 1.49980i | 0.661550 | + | 0.749901i | \(0.269899\pi\) | ||||
−0.661550 | + | 0.749901i | \(0.730101\pi\) | |||||||
\(588\) | 103.010i | 0.175187i | ||||||||
\(589\) | − | 760.257i | − | 1.29076i | ||||||
\(590\) | −563.685 | + | 461.415i | −0.955398 | + | 0.782059i | ||||
\(591\) | −414.989 | −0.702180 | ||||||||
\(592\) | −199.278 | −0.336618 | ||||||||
\(593\) | − | 474.560i | − | 0.800270i | −0.916456 | − | 0.400135i | \(-0.868963\pi\) | ||
0.916456 | − | 0.400135i | \(-0.131037\pi\) | |||||||
\(594\) | 21.2839i | 0.0358314i | ||||||||
\(595\) | −54.4997 | − | 66.5793i | −0.0915962 | − | 0.111898i | ||||
\(596\) | − | 177.562i | − | 0.297923i | ||||||
\(597\) | 22.1184 | 0.0370493 | ||||||||
\(598\) | −50.0043 | − | 12.1279i | −0.0836193 | − | 0.0202808i | ||||
\(599\) | −150.075 | −0.250542 | −0.125271 | − | 0.992123i | \(-0.539980\pi\) | ||||
−0.125271 | + | 0.992123i | \(0.539980\pi\) | |||||||
\(600\) | 24.1967 | − | 120.060i | 0.0403278 | − | 0.200101i | ||||
\(601\) | −346.698 | −0.576868 | −0.288434 | − | 0.957500i | \(-0.593135\pi\) | ||||
−0.288434 | + | 0.957500i | \(0.593135\pi\) | |||||||
\(602\) | − | 100.773i | − | 0.167398i | ||||||
\(603\) | −376.367 | −0.624158 | ||||||||
\(604\) | −213.288 | −0.353125 | ||||||||
\(605\) | 356.649 | + | 435.698i | 0.589502 | + | 0.720162i | ||||
\(606\) | −213.459 | −0.352243 | ||||||||
\(607\) | − | 717.693i | − | 1.18236i | −0.806540 | − | 0.591180i | \(-0.798662\pi\) | ||
0.806540 | − | 0.591180i | \(-0.201338\pi\) | |||||||
\(608\) | 132.215 | 0.217459 | ||||||||
\(609\) | 63.7484i | 0.104677i | ||||||||
\(610\) | −56.7172 | − | 69.2882i | −0.0929790 | − | 0.113587i | ||||
\(611\) | 134.326 | 0.219846 | ||||||||
\(612\) | 23.5243 | 0.0384384 | ||||||||
\(613\) | −1059.01 | −1.72759 | −0.863796 | − | 0.503841i | \(-0.831920\pi\) | ||||
−0.863796 | + | 0.503841i | \(0.831920\pi\) | |||||||
\(614\) | 49.7891 | 0.0810897 | ||||||||
\(615\) | 454.232 | − | 371.820i | 0.738588 | − | 0.604586i | ||||
\(616\) | −35.9557 | −0.0583697 | ||||||||
\(617\) | −832.513 | −1.34929 | −0.674646 | − | 0.738142i | \(-0.735704\pi\) | ||||
−0.674646 | + | 0.738142i | \(0.735704\pi\) | |||||||
\(618\) | 332.095 | 0.537370 | ||||||||
\(619\) | − | 1204.47i | − | 1.94583i | −0.231168 | − | 0.972914i | \(-0.574255\pi\) | ||
0.231168 | − | 0.972914i | \(-0.425745\pi\) | |||||||
\(620\) | 206.037 | + | 251.704i | 0.332318 | + | 0.405974i | ||||
\(621\) | 28.1693 | − | 116.144i | 0.0453612 | − | 0.187028i | ||||
\(622\) | 246.373i | 0.396097i | ||||||||
\(623\) | − | 63.5876i | − | 0.102067i | ||||||
\(624\) | 10.9597 | 0.0175636 | ||||||||
\(625\) | −576.210 | − | 242.089i | −0.921936 | − | 0.387342i | ||||
\(626\) | − | 301.109i | − | 0.481005i | ||||||
\(627\) | 117.252i | 0.187004i | ||||||||
\(628\) | −67.2334 | −0.107060 | ||||||||
\(629\) | −195.328 | −0.310537 | ||||||||
\(630\) | 72.0460 | − | 58.9747i | 0.114359 | − | 0.0936106i | ||||
\(631\) | 383.040i | 0.607037i | 0.952826 | + | 0.303518i | \(0.0981613\pi\) | ||||
−0.952826 | + | 0.303518i | \(0.901839\pi\) | |||||||
\(632\) | −72.1249 | −0.114122 | ||||||||
\(633\) | − | 146.992i | − | 0.232214i | ||||||
\(634\) | −312.250 | −0.492508 | ||||||||
\(635\) | 348.324 | − | 285.128i | 0.548542 | − | 0.449020i | ||||
\(636\) | − | 4.06361i | − | 0.00638933i | ||||||
\(637\) | 47.0397i | 0.0738456i | ||||||||
\(638\) | 34.3485 | 0.0538378 | ||||||||
\(639\) | 82.3886 | 0.128934 | ||||||||
\(640\) | −43.7733 | + | 35.8315i | −0.0683958 | + | 0.0559867i | ||||
\(641\) | − | 439.350i | − | 0.685413i | −0.939443 | − | 0.342706i | \(-0.888656\pi\) | ||
0.939443 | − | 0.342706i | \(-0.111344\pi\) | |||||||
\(642\) | −305.408 | −0.475713 | ||||||||
\(643\) | 715.156 | 1.11222 | 0.556109 | − | 0.831109i | \(-0.312294\pi\) | ||||
0.556109 | + | 0.831109i | \(0.312294\pi\) | |||||||
\(644\) | 196.207 | + | 47.5875i | 0.304670 | + | 0.0738937i | ||||
\(645\) | 108.800 | − | 89.0600i | 0.168681 | − | 0.138077i | ||||
\(646\) | 129.594 | 0.200610 | ||||||||
\(647\) | − | 117.314i | − | 0.181319i | −0.995882 | − | 0.0906596i | \(-0.971102\pi\) | ||
0.995882 | − | 0.0906596i | \(-0.0288975\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | 298.381i | 0.459754i | ||||||||
\(650\) | 11.0495 | − | 54.8260i | 0.0169992 | − | 0.0843476i | ||||
\(651\) | 247.278i | 0.379843i | ||||||||
\(652\) | − | 547.072i | − | 0.839067i | ||||||
\(653\) | 135.228i | 0.207087i | 0.994625 | + | 0.103543i | \(0.0330181\pi\) | ||||
−0.994625 | + | 0.103543i | \(0.966982\pi\) | |||||||
\(654\) | 244.509i | 0.373868i | ||||||||
\(655\) | 403.837 | + | 493.345i | 0.616545 | + | 0.753198i | ||||
\(656\) | −271.127 | −0.413303 | ||||||||
\(657\) | − | 75.4831i | − | 0.114891i | ||||||
\(658\) | −527.068 | −0.801015 | ||||||||
\(659\) | − | 548.436i | − | 0.832224i | −0.909313 | − | 0.416112i | \(-0.863392\pi\) | ||
0.909313 | − | 0.416112i | \(-0.136608\pi\) | |||||||
\(660\) | −31.7764 | − | 38.8194i | −0.0481460 | − | 0.0588173i | ||||
\(661\) | 77.7084i | 0.117562i | 0.998271 | + | 0.0587809i | \(0.0187213\pi\) | ||||
−0.998271 | + | 0.0587809i | \(0.981279\pi\) | |||||||
\(662\) | − | 463.891i | − | 0.700742i | ||||||
\(663\) | 10.7424 | 0.0162028 | ||||||||
\(664\) | 311.647i | 0.469347i | ||||||||
\(665\) | 396.898 | − | 324.889i | 0.596839 | − | 0.488554i | ||||
\(666\) | − | 211.366i | − | 0.317366i | ||||||
\(667\) | −187.437 | − | 45.4604i | −0.281015 | − | 0.0681565i | ||||
\(668\) | 124.886i | 0.186955i | ||||||||
\(669\) | 76.2642 | 0.113997 | ||||||||
\(670\) | 686.452 | − | 561.908i | 1.02455 | − | 0.838669i | ||||
\(671\) | −36.6770 | −0.0546602 | ||||||||
\(672\) | −43.0036 | −0.0639935 | ||||||||
\(673\) | − | 384.159i | − | 0.570816i | −0.958406 | − | 0.285408i | \(-0.907871\pi\) | ||
0.958406 | − | 0.285408i | \(-0.0921291\pi\) | |||||||
\(674\) | 137.407i | 0.203869i | ||||||||
\(675\) | 127.343 | + | 25.6644i | 0.188657 | + | 0.0380214i | ||||
\(676\) | −332.995 | −0.492597 | ||||||||
\(677\) | 960.270 | 1.41842 | 0.709210 | − | 0.704998i | \(-0.249052\pi\) | ||||
0.709210 | + | 0.704998i | \(0.249052\pi\) | |||||||
\(678\) | −107.072 | −0.157924 | ||||||||
\(679\) | 280.735 | 0.413454 | ||||||||
\(680\) | −42.9057 | + | 35.1213i | −0.0630966 | + | 0.0516489i | ||||
\(681\) | − | 594.353i | − | 0.872765i | ||||||
\(682\) | 133.237 | 0.195362 | ||||||||
\(683\) | 250.745i | 0.367122i | 0.983008 | + | 0.183561i | \(0.0587626\pi\) | ||||
−0.983008 | + | 0.183561i | \(0.941237\pi\) | |||||||
\(684\) | 140.235i | 0.205022i | ||||||||
\(685\) | 360.950 | + | 440.952i | 0.526934 | + | 0.643725i | ||||
\(686\) | − | 488.719i | − | 0.712419i | ||||||
\(687\) | 94.2989 | 0.137262 | ||||||||
\(688\) | −64.9414 | −0.0943916 | ||||||||
\(689\) | − | 1.85566i | − | 0.00269327i | ||||||
\(690\) | 122.023 | + | 253.890i | 0.176845 | + | 0.367957i | ||||
\(691\) | 239.207 | 0.346175 | 0.173087 | − | 0.984906i | \(-0.444626\pi\) | ||||
0.173087 | + | 0.984906i | \(0.444626\pi\) | |||||||
\(692\) | 374.485i | 0.541164i | ||||||||
\(693\) | − | 38.1368i | − | 0.0550315i | ||||||
\(694\) | 490.726 | 0.707098 | ||||||||
\(695\) | 642.246 | + | 784.596i | 0.924095 | + | 1.12891i | ||||
\(696\) | 41.0814 | 0.0590250 | ||||||||
\(697\) | −265.753 | −0.381281 | ||||||||
\(698\) | 605.774i | 0.867870i | ||||||||
\(699\) | 204.613 | 0.292722 | ||||||||
\(700\) | −43.3560 | + | 215.126i | −0.0619371 | + | 0.307323i | ||||
\(701\) | 1147.70i | 1.63723i | 0.574339 | + | 0.818617i | \(0.305259\pi\) | ||||
−0.574339 | + | 0.818617i | \(0.694741\pi\) | |||||||
\(702\) | 11.6245i | 0.0165591i | ||||||||
\(703\) | − | 1164.40i | − | 1.65634i | ||||||
\(704\) | 23.1709i | 0.0329133i | ||||||||
\(705\) | −465.804 | − | 569.046i | −0.660714 | − | 0.807157i | ||||
\(706\) | 403.631 | 0.571715 | ||||||||
\(707\) | 382.480 | 0.540990 | ||||||||
\(708\) | 356.868i | 0.504051i | ||||||||
\(709\) | 1366.04i | 1.92671i | 0.268225 | + | 0.963356i | \(0.413563\pi\) | ||||
−0.268225 | + | 0.963356i | \(0.586437\pi\) | |||||||
\(710\) | −150.268 | + | 123.004i | −0.211645 | + | 0.173246i | ||||
\(711\) | − | 76.5000i | − | 0.107595i | ||||||
\(712\) | −40.9778 | −0.0575530 | ||||||||
\(713\) | −727.061 | − | 176.339i | −1.01972 | − | 0.247320i | ||||
\(714\) | −42.1512 | −0.0590353 | ||||||||
\(715\) | −14.5108 | − | 17.7270i | −0.0202948 | − | 0.0247930i | ||||
\(716\) | 302.129 | 0.421968 | ||||||||
\(717\) | 59.0774i | 0.0823953i | ||||||||
\(718\) | −634.616 | −0.883867 | ||||||||
\(719\) | −491.364 | −0.683400 | −0.341700 | − | 0.939809i | \(-0.611003\pi\) | ||||
−0.341700 | + | 0.939809i | \(0.611003\pi\) | |||||||
\(720\) | −38.0050 | − | 46.4286i | −0.0527848 | − | 0.0644842i | ||||
\(721\) | −595.053 | −0.825316 | ||||||||
\(722\) | 262.017i | 0.362904i | ||||||||
\(723\) | −262.806 | −0.363494 | ||||||||
\(724\) | 590.313i | 0.815350i | ||||||||
\(725\) | 41.4180 | − | 205.510i | 0.0571283 | − | 0.283463i | ||||
\(726\) | 275.840 | 0.379944 | ||||||||
\(727\) | 106.511 | 0.146507 | 0.0732536 | − | 0.997313i | \(-0.476662\pi\) | ||||
0.0732536 | + | 0.997313i | \(0.476662\pi\) | |||||||
\(728\) | −19.6377 | −0.0269749 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 112.695 | + | 137.673i | 0.154376 | + | 0.188593i | ||||
\(731\) | −63.6542 | −0.0870783 | ||||||||
\(732\) | −43.8662 | −0.0599266 | ||||||||
\(733\) | 23.9903 | 0.0327289 | 0.0163645 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163645 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(734\) | − | 366.944i | − | 0.499923i | ||||||
\(735\) | 199.275 | − | 163.120i | 0.271122 | − | 0.221933i | ||||
\(736\) | 30.6668 | − | 126.442i | 0.0416669 | − | 0.171796i | ||||
\(737\) | − | 363.366i | − | 0.493034i | ||||||
\(738\) | − | 287.573i | − | 0.389666i | ||||||
\(739\) | 256.204 | 0.346691 | 0.173345 | − | 0.984861i | \(-0.444542\pi\) | ||||
0.173345 | + | 0.984861i | \(0.444542\pi\) | |||||||
\(740\) | 315.565 | + | 385.508i | 0.426439 | + | 0.520957i | ||||
\(741\) | 64.0387i | 0.0864220i | ||||||||
\(742\) | 7.28125i | 0.00981301i | ||||||||
\(743\) | 500.539 | 0.673673 | 0.336836 | − | 0.941563i | \(-0.390643\pi\) | ||||
0.336836 | + | 0.941563i | \(0.390643\pi\) | |||||||
\(744\) | 159.353 | 0.214184 | ||||||||
\(745\) | −343.499 | + | 281.177i | −0.461072 | + | 0.377419i | ||||
\(746\) | − | 245.581i | − | 0.329197i | ||||||
\(747\) | −330.551 | −0.442505 | ||||||||
\(748\) | 22.7117i | 0.0303632i | ||||||||
\(749\) | 547.234 | 0.730620 | ||||||||
\(750\) | −270.577 | + | 143.312i | −0.360769 | + | 0.191083i | ||||
\(751\) | − | 869.309i | − | 1.15754i | −0.815492 | − | 0.578768i | \(-0.803534\pi\) | ||
0.815492 | − | 0.578768i | \(-0.196466\pi\) | |||||||
\(752\) | 339.658i | 0.451673i | ||||||||
\(753\) | 54.0172 | 0.0717360 | ||||||||
\(754\) | 18.7599 | 0.0248805 | ||||||||
\(755\) | 337.750 | + | 412.610i | 0.447351 | + | 0.546504i | ||||
\(756\) | − | 45.6122i | − | 0.0603336i | ||||||
\(757\) | 642.801 | 0.849142 | 0.424571 | − | 0.905395i | \(-0.360425\pi\) | ||||
0.424571 | + | 0.905395i | \(0.360425\pi\) | |||||||
\(758\) | 344.014 | 0.453844 | ||||||||
\(759\) | 112.132 | + | 27.1962i | 0.147737 | + | 0.0358316i | ||||
\(760\) | −209.368 | − | 255.773i | −0.275484 | − | 0.336543i | ||||
\(761\) | 985.400 | 1.29487 | 0.647437 | − | 0.762119i | \(-0.275841\pi\) | ||||
0.647437 | + | 0.762119i | \(0.275841\pi\) | |||||||
\(762\) | − | 220.523i | − | 0.289401i | ||||||
\(763\) | − | 438.116i | − | 0.574202i | ||||||
\(764\) | − | 679.840i | − | 0.889843i | ||||||
\(765\) | −37.2517 | − | 45.5083i | −0.0486951 | − | 0.0594880i | ||||
\(766\) | 65.0816i | 0.0849630i | ||||||||
\(767\) | 162.965i | 0.212470i | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 504.152i | 0.655594i | 0.944748 | + | 0.327797i | \(0.106306\pi\) | ||||
−0.944748 | + | 0.327797i | \(0.893694\pi\) | |||||||
\(770\) | 56.9375 | + | 69.5573i | 0.0739448 | + | 0.0903341i | ||||
\(771\) | 844.401 | 1.09520 | ||||||||
\(772\) | 411.183i | 0.532620i | ||||||||
\(773\) | 238.172 | 0.308114 | 0.154057 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154057 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(774\) | − | 68.8808i | − | 0.0889933i | ||||||
\(775\) | 160.659 | − | 797.168i | 0.207302 | − | 1.02860i | ||||
\(776\) | − | 180.914i | − | 0.233137i | ||||||
\(777\) | 378.729i | 0.487425i | ||||||||
\(778\) | −570.590 | −0.733406 | ||||||||
\(779\) | − | 1584.23i | − | 2.03367i | ||||||
\(780\) | −17.3551 | − | 21.2018i | −0.0222501 | − | 0.0271817i | ||||
\(781\) | 79.5426i | 0.101847i | ||||||||
\(782\) | 30.0590 | − | 123.936i | 0.0384386 | − | 0.158485i | ||||
\(783\) | 43.5734i | 0.0556493i | ||||||||
\(784\) | −118.945 | −0.151716 | ||||||||
\(785\) | 106.467 | + | 130.065i | 0.135627 | + | 0.165688i | ||||
\(786\) | 312.336 | 0.397374 | ||||||||
\(787\) | −1475.14 | −1.87439 | −0.937193 | − | 0.348811i | \(-0.886585\pi\) | ||||
−0.937193 | + | 0.348811i | \(0.886585\pi\) | |||||||
\(788\) | − | 479.187i | − | 0.608106i | ||||||
\(789\) | 512.813i | 0.649953i | ||||||||
\(790\) | 114.213 | + | 139.527i | 0.144573 | + | 0.176617i | ||||
\(791\) | 191.854 | 0.242546 | ||||||||
\(792\) | −24.5765 | −0.0310309 | ||||||||
\(793\) | −20.0316 | −0.0252606 | ||||||||
\(794\) | 471.053 | 0.593266 | ||||||||
\(795\) | −7.86117 | + | 6.43491i | −0.00988826 | + | 0.00809423i | ||||
\(796\) | 25.5402i | 0.0320856i | ||||||||
\(797\) | −711.412 | −0.892613 | −0.446306 | − | 0.894880i | \(-0.647261\pi\) | ||||
−0.446306 | + | 0.894880i | \(0.647261\pi\) | |||||||
\(798\) | − | 251.275i | − | 0.314882i | ||||||
\(799\) | 332.926i | 0.416678i | ||||||||
\(800\) | 138.634 | + | 27.9399i | 0.173292 | + | 0.0349249i | ||||
\(801\) | − | 43.4635i | − | 0.0542615i | ||||||
\(802\) | 704.666 | 0.878635 | ||||||||
\(803\) | 72.8756 | 0.0907542 | ||||||||
\(804\) | − | 434.591i | − | 0.540536i | ||||||
\(805\) | −218.643 | − | 454.925i | −0.271607 | − | 0.565124i | ||||
\(806\) | 72.7691 | 0.0902842 | ||||||||
\(807\) | − | 120.772i | − | 0.149656i | ||||||
\(808\) | − | 246.481i | − | 0.305051i | ||||||
\(809\) | −208.458 | −0.257674 | −0.128837 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128837 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(810\) | 49.2450 | − | 40.3104i | 0.0607963 | − | 0.0497660i | ||||
\(811\) | 1248.40 | 1.53934 | 0.769668 | − | 0.638445i | \(-0.220422\pi\) | ||||
0.769668 | + | 0.638445i | \(0.220422\pi\) | |||||||
\(812\) | −73.6103 | −0.0906531 | ||||||||
\(813\) | 616.765i | 0.758628i | ||||||||
\(814\) | 204.065 | 0.250694 | ||||||||
\(815\) | −1058.32 | + | 866.312i | −1.29856 | + | 1.06296i | ||||
\(816\) | 27.1635i | 0.0332886i | ||||||||
\(817\) | − | 379.461i | − | 0.464456i | ||||||
\(818\) | − | 587.177i | − | 0.717820i | ||||||
\(819\) | − | 20.8289i | − | 0.0254322i | ||||||
\(820\) | 429.341 | + | 524.502i | 0.523587 | + | 0.639636i | ||||
\(821\) | 988.320 | 1.20380 | 0.601900 | − | 0.798572i | \(-0.294411\pi\) | ||||
0.601900 | + | 0.798572i | \(0.294411\pi\) | |||||||
\(822\) | 279.166 | 0.339618 | ||||||||
\(823\) | 672.949i | 0.817677i | 0.912607 | + | 0.408839i | \(0.134066\pi\) | ||||
−0.912607 | + | 0.408839i | \(0.865934\pi\) | |||||||
\(824\) | 383.470i | 0.465376i | ||||||||
\(825\) | −24.7779 | + | 122.944i | −0.0300338 | + | 0.149024i | ||||
\(826\) | − | 639.442i | − | 0.774143i | ||||||
\(827\) | 1421.35 | 1.71868 | 0.859339 | − | 0.511406i | \(-0.170875\pi\) | ||||
0.859339 | + | 0.511406i | \(0.170875\pi\) | |||||||
\(828\) | 134.112 | + | 32.5271i | 0.161971 | + | 0.0392839i | ||||
\(829\) | −1150.45 | −1.38775 | −0.693875 | − | 0.720095i | \(-0.744098\pi\) | ||||
−0.693875 | + | 0.720095i | \(0.744098\pi\) | |||||||
\(830\) | 602.889 | − | 493.506i | 0.726372 | − | 0.594586i | ||||
\(831\) | −65.8472 | −0.0792385 | ||||||||
\(832\) | 12.6551i | 0.0152105i | ||||||||
\(833\) | −116.588 | −0.139961 | ||||||||
\(834\) | 496.726 | 0.595595 | ||||||||
\(835\) | 241.595 | − | 197.762i | 0.289336 | − | 0.236841i | ||||
\(836\) | −135.391 | −0.161951 | ||||||||
\(837\) | 169.020i | 0.201935i | ||||||||
\(838\) | −420.253 | −0.501495 | ||||||||
\(839\) | − | 967.070i | − | 1.15265i | −0.817222 | − | 0.576323i | \(-0.804487\pi\) | ||
0.817222 | − | 0.576323i | \(-0.195513\pi\) | |||||||
\(840\) | 68.0981 | + | 83.1916i | 0.0810691 | + | 0.0990376i | ||||
\(841\) | −770.680 | −0.916385 | ||||||||
\(842\) | 398.183 | 0.472901 | ||||||||
\(843\) | −538.884 | −0.639246 | ||||||||
\(844\) | 169.731 | 0.201103 | ||||||||
\(845\) | 527.312 | + | 644.188i | 0.624038 | + | 0.762353i | ||||
\(846\) | −360.262 | −0.425842 | ||||||||
\(847\) | −494.254 | −0.583535 | ||||||||
\(848\) | 4.69226 | 0.00553332 | ||||||||
\(849\) | 184.245i | 0.217014i | ||||||||
\(850\) | 135.886 | + | 27.3861i | 0.159866 | + | 0.0322189i | ||||
\(851\) | −1113.56 | − | 270.080i | −1.30853 | − | 0.317368i | ||||
\(852\) | 95.1342i | 0.111660i | ||||||||
\(853\) | − | 885.948i | − | 1.03863i | −0.854584 | − | 0.519313i | \(-0.826188\pi\) | ||
0.854584 | − | 0.519313i | \(-0.173812\pi\) | |||||||
\(854\) | 78.6003 | 0.0920378 | ||||||||
\(855\) | 271.288 | − | 222.068i | 0.317296 | − | 0.259729i | ||||
\(856\) | − | 352.654i | − | 0.411979i | ||||||
\(857\) | 219.985i | 0.256692i | 0.991729 | + | 0.128346i | \(0.0409668\pi\) | ||||
−0.991729 | + | 0.128346i | \(0.959033\pi\) | |||||||
\(858\) | −11.2229 | −0.0130803 | ||||||||
\(859\) | −248.800 | −0.289639 | −0.144820 | − | 0.989458i | \(-0.546260\pi\) | ||||
−0.144820 | + | 0.989458i | \(0.546260\pi\) | |||||||
\(860\) | 102.838 | + | 125.631i | 0.119579 | + | 0.146082i | ||||
\(861\) | 515.279i | 0.598465i | ||||||||
\(862\) | 1106.49 | 1.28364 | ||||||||
\(863\) | 730.096i | 0.845998i | 0.906130 | + | 0.422999i | \(0.139023\pi\) | ||||
−0.906130 | + | 0.422999i | \(0.860977\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | 724.452 | − | 593.014i | 0.837516 | − | 0.685565i | ||||
\(866\) | − | 217.445i | − | 0.251091i | ||||||
\(867\) | − | 473.938i | − | 0.546641i | ||||||
\(868\) | −285.532 | −0.328954 | ||||||||
\(869\) | 73.8574 | 0.0849912 | ||||||||
\(870\) | −65.0541 | − | 79.4730i | −0.0747749 | − | 0.0913482i | ||||
\(871\) | − | 198.457i | − | 0.227850i | ||||||
\(872\) | −282.335 | −0.323779 | ||||||||
\(873\) | 191.888 | 0.219803 | ||||||||
\(874\) | 738.816 | + | 179.190i | 0.845327 | + | 0.205023i | ||||
\(875\) | 484.824 | − | 256.789i | 0.554084 | − | 0.293473i | ||||
\(876\) | 87.1604 | 0.0994981 | ||||||||
\(877\) | − | 1341.09i | − | 1.52918i | −0.644514 | − | 0.764592i | \(-0.722940\pi\) | ||
0.644514 | − | 0.764592i | \(-0.277060\pi\) | |||||||
\(878\) | 630.875i | 0.718536i | ||||||||
\(879\) | 407.835i | 0.463976i | ||||||||
\(880\) | 44.8248 | − | 36.6922i | 0.0509373 | − | 0.0416957i | ||||
\(881\) | 168.776i | 0.191573i | 0.995402 | + | 0.0957864i | \(0.0305366\pi\) | ||||
−0.995402 | + | 0.0957864i | \(0.969463\pi\) | |||||||
\(882\) | − | 126.161i | − | 0.143039i | ||||||
\(883\) | 516.266i | 0.584673i | 0.956316 | + | 0.292336i | \(0.0944327\pi\) | ||||
−0.956316 | + | 0.292336i | \(0.905567\pi\) | |||||||
\(884\) | 12.4043i | 0.0140320i | ||||||||
\(885\) | 690.370 | − | 565.116i | 0.780079 | − | 0.638549i | ||||
\(886\) | 1026.95 | 1.15908 | ||||||||
\(887\) | − | 531.793i | − | 0.599541i | −0.954011 | − | 0.299771i | \(-0.903090\pi\) | ||
0.954011 | − | 0.299771i | \(-0.0969102\pi\) | |||||||
\(888\) | 244.064 | 0.274847 | ||||||||
\(889\) | 395.138i | 0.444474i | ||||||||
\(890\) | 64.8901 | + | 79.2725i | 0.0729102 | + | 0.0890702i | ||||
\(891\) | − | 26.0673i | − | 0.0292562i | ||||||
\(892\) | 88.0624i | 0.0987246i | ||||||||
\(893\) | −1984.67 | −2.22247 | ||||||||
\(894\) | 217.468i | 0.243253i | ||||||||
\(895\) | −478.435 | − | 584.477i | −0.534564 | − | 0.653047i | ||||
\(896\) | − | 49.6563i | − | 0.0554200i | ||||||
\(897\) | 61.2425 | + | 14.8536i | 0.0682749 | + | 0.0165592i | ||||
\(898\) | − | 167.463i | − | 0.186484i | ||||||
\(899\) | 272.769 | 0.303413 | ||||||||
\(900\) | −29.6347 | + | 147.043i | −0.0329275 | + | 0.163382i | ||||
\(901\) | 4.59925 | 0.00510461 | ||||||||
\(902\) | 277.639 | 0.307804 | ||||||||
\(903\) | 123.422i | 0.136680i | ||||||||
\(904\) | − | 123.636i | − | 0.136766i | ||||||
\(905\) | 1141.98 | − | 934.787i | 1.26185 | − | 1.03291i | ||||
\(906\) | 261.223 | 0.288325 | ||||||||
\(907\) | 842.943 | 0.929375 | 0.464687 | − | 0.885475i | \(-0.346167\pi\) | ||||
0.464687 | + | 0.885475i | \(0.346167\pi\) | |||||||
\(908\) | 686.300 | 0.755837 | ||||||||
\(909\) | 261.433 | 0.287605 | ||||||||
\(910\) | 31.0972 | + | 37.9897i | 0.0341727 | + | 0.0417469i | ||||
\(911\) | − | 1240.10i | − | 1.36125i | −0.732631 | − | 0.680626i | \(-0.761708\pi\) | ||
0.732631 | − | 0.680626i | \(-0.238292\pi\) | |||||||
\(912\) | −161.929 | −0.177554 | ||||||||
\(913\) | − | 319.133i | − | 0.349543i | ||||||
\(914\) | − | 39.4575i | − | 0.0431701i | ||||||
\(915\) | 69.4641 | + | 84.8604i | 0.0759170 | + | 0.0927436i | ||||
\(916\) | 108.887i | 0.118872i | ||||||||
\(917\) | −559.649 | −0.610304 | ||||||||
\(918\) | −28.8112 | −0.0313848 | ||||||||
\(919\) | 293.548i | 0.319421i | 0.987164 | + | 0.159711i | \(0.0510561\pi\) | ||||
−0.987164 | + | 0.159711i | \(0.948944\pi\) | |||||||
\(920\) | −293.167 | + | 140.900i | −0.318660 | + | 0.153153i | ||||
\(921\) | −60.9789 | −0.0662094 | ||||||||
\(922\) | − | 541.399i | − | 0.587201i | ||||||
\(923\) | 43.4433i | 0.0470675i | ||||||||
\(924\) | 44.0366 | 0.0476587 | ||||||||
\(925\) | 246.064 | − | 1220.94i | 0.266015 | − | 1.31993i | ||||
\(926\) | 82.1297 | 0.0886930 | ||||||||
\(927\) | −406.731 | −0.438761 | ||||||||
\(928\) | 47.4367i | 0.0511171i | ||||||||
\(929\) | 326.931 | 0.351917 | 0.175959 | − | 0.984398i | \(-0.443698\pi\) | ||||
0.175959 | + | 0.984398i | \(0.443698\pi\) | |||||||
\(930\) | −252.343 | − | 308.273i | −0.271336 | − | 0.331476i | ||||
\(931\) | − | 695.013i | − | 0.746523i | ||||||
\(932\) | 236.267i | 0.253505i | ||||||||
\(933\) | − | 301.743i | − | 0.323412i | ||||||
\(934\) | 544.263i | 0.582723i | ||||||||
\(935\) | 43.9363 | − | 35.9649i | 0.0469907 | − | 0.0384651i | ||||
\(936\) | −13.4228 | −0.0143406 | ||||||||
\(937\) | 364.741 | 0.389265 | 0.194632 | − | 0.980876i | \(-0.437649\pi\) | ||||
0.194632 | + | 0.980876i | \(0.437649\pi\) | |||||||
\(938\) | 778.708i | 0.830179i | ||||||||
\(939\) | 368.782i | 0.392739i | ||||||||
\(940\) | 657.078 | − | 537.864i | 0.699019 | − | 0.572195i | ||||
\(941\) | − | 114.607i | − | 0.121793i | −0.998144 | − | 0.0608964i | \(-0.980604\pi\) | ||
0.998144 | − | 0.0608964i | \(-0.0193959\pi\) | |||||||
\(942\) | 82.3437 | 0.0874137 | ||||||||
\(943\) | −1515.05 | − | 367.457i | −1.60663 | − | 0.389668i | ||||
\(944\) | −412.075 | −0.436521 | ||||||||
\(945\) | −88.2380 | + | 72.2289i | −0.0933736 | + | 0.0764327i | ||||
\(946\) | 66.5014 | 0.0702975 | ||||||||
\(947\) | 352.179i | 0.371889i | 0.982560 | + | 0.185945i | \(0.0595345\pi\) | ||||
−0.982560 | + | 0.185945i | \(0.940466\pi\) | |||||||
\(948\) | 88.3346 | 0.0931799 | ||||||||
\(949\) | 39.8020 | 0.0419410 | ||||||||
\(950\) | −163.256 | + | 810.055i | −0.171849 | + | 0.852690i | ||||
\(951\) | 382.427 | 0.402131 | ||||||||
\(952\) | − | 48.6720i | − | 0.0511261i | ||||||
\(953\) | −1802.34 | −1.89123 | −0.945614 | − | 0.325290i | \(-0.894538\pi\) | ||||
−0.945614 | + | 0.325290i | \(0.894538\pi\) | |||||||
\(954\) | 4.97689i | 0.00521687i | ||||||||
\(955\) | −1315.17 | + | 1076.56i | −1.37714 | + | 1.12728i | ||||
\(956\) | −68.2167 | −0.0713564 | ||||||||
\(957\) | −42.0682 | −0.0439584 | ||||||||
\(958\) | −788.798 | −0.823380 | ||||||||
\(959\) | −500.214 | −0.521600 | ||||||||
\(960\) | 53.6112 | − | 43.8844i | 0.0558450 | − | 0.0457130i | ||||
\(961\) | 97.0602 | 0.100999 | ||||||||
\(962\) | 111.453 | 0.115855 | ||||||||
\(963\) | 374.046 | 0.388418 | ||||||||
\(964\) | − | 303.463i | − | 0.314795i | ||||||
\(965\) | 795.444 | − | 651.126i | 0.824294 | − | 0.674742i | ||||
\(966\) | −240.304 | − | 58.2826i | −0.248762 | − | 0.0603340i | ||||
\(967\) | − | 402.567i | − | 0.416305i | −0.978096 | − | 0.208152i | \(-0.933255\pi\) | ||
0.978096 | − | 0.208152i | \(-0.0667450\pi\) | |||||||
\(968\) | 318.512i | 0.329041i | ||||||||
\(969\) | −158.720 | −0.163797 | ||||||||
\(970\) | −349.983 | + | 286.485i | −0.360807 | + | 0.295346i | ||||
\(971\) | 1053.48i | 1.08494i | 0.840075 | + | 0.542470i | \(0.182511\pi\) | ||||
−0.840075 | + | 0.542470i | \(0.817489\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −890.042 | −0.914740 | ||||||||
\(974\) | 920.856 | 0.945438 | ||||||||
\(975\) | −13.5328 | + | 67.1478i | −0.0138798 | + | 0.0688695i | ||||
\(976\) | − | 50.6524i | − | 0.0518979i | ||||||
\(977\) | 1151.57 | 1.17868 | 0.589341 | − | 0.807884i | \(-0.299387\pi\) | ||||
0.589341 | + | 0.807884i | \(0.299387\pi\) | |||||||
\(978\) | 670.024i | 0.685096i | ||||||||
\(979\) | 41.9621 | 0.0428622 | ||||||||
\(980\) | 188.355 | + | 230.103i | 0.192199 | + | 0.234799i | ||||
\(981\) | − | 299.462i | − | 0.305262i | ||||||
\(982\) | − | 696.912i | − | 0.709687i | ||||||
\(983\) | −583.591 | −0.593683 | −0.296842 | − | 0.954927i | \(-0.595933\pi\) | ||||
−0.296842 | + | 0.954927i | \(0.595933\pi\) | |||||||
\(984\) | 332.061 | 0.337460 | ||||||||
\(985\) | −927.001 | + | 758.814i | −0.941117 | + | 0.770370i | ||||
\(986\) | 46.4964i | 0.0471566i | ||||||||
\(987\) | 645.524 | 0.654026 | ||||||||
\(988\) | −73.9455 | −0.0748436 | ||||||||
\(989\) | −362.892 | − | 88.0148i | −0.366929 | − | 0.0889938i | ||||
\(990\) | 38.9180 | + | 47.5439i | 0.0393111 | + | 0.0480241i | ||||
\(991\) | −970.432 | −0.979245 | −0.489622 | − | 0.871935i | \(-0.662865\pi\) | ||||
−0.489622 | + | 0.871935i | \(0.662865\pi\) | |||||||
\(992\) | 184.005i | 0.185489i | ||||||||
\(993\) | 568.148i | 0.572154i | ||||||||
\(994\) | − | 170.463i | − | 0.171492i | ||||||
\(995\) | 49.4081 | − | 40.4440i | 0.0496564 | − | 0.0406472i | ||||
\(996\) | − | 381.688i | − | 0.383221i | ||||||
\(997\) | 418.055i | 0.419312i | 0.977775 | + | 0.209656i | \(0.0672345\pi\) | ||||
−0.977775 | + | 0.209656i | \(0.932766\pi\) | |||||||
\(998\) | − | 715.728i | − | 0.717162i | ||||||
\(999\) | 258.869i | 0.259129i |
(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 | 690.3.f.a.229.22 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.23 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.21 | ✓ | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.24 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.21 | ✓ | 48 | 23.22 | odd | 2 | inner | |
690.3.f.a.229.22 | yes | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.23 | yes | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.24 | yes | 48 | 115.114 | odd | 2 | inner |