Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.25 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.26 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.299460 | 0.149730 | 0.0748650 | − | 0.997194i | \(-0.476147\pi\) | ||||
0.0748650 | + | 0.997194i | \(0.476147\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.91032 | −0.977581 | ||||||||
\(5\) | − | 2.23813i | − | 0.447626i | −0.974632 | − | 0.223813i | \(-0.928150\pi\) | ||
0.974632 | − | 0.223813i | \(-0.0718505\pi\) | |||||||
\(6\) | −0.518680 | −0.0864466 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −2.36883 | −0.296103 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 0.670230i | − | 0.0670230i | ||||||
\(11\) | − | 17.7479i | − | 1.61344i | −0.590931 | − | 0.806722i | \(-0.701239\pi\) | ||
0.590931 | − | 0.806722i | \(-0.298761\pi\) | |||||||
\(12\) | 6.77288 | 0.564407 | ||||||||
\(13\) | −2.29555 | −0.176581 | −0.0882906 | − | 0.996095i | \(-0.528140\pi\) | ||||
−0.0882906 | + | 0.996095i | \(0.528140\pi\) | |||||||
\(14\) | − | 0.792297i | − | 0.0565926i | ||||||
\(15\) | 3.87655i | 0.258437i | ||||||||
\(16\) | 14.9319 | 0.933245 | ||||||||
\(17\) | 25.6106i | 1.50650i | 0.657732 | + | 0.753252i | \(0.271516\pi\) | ||||
−0.657732 | + | 0.753252i | \(0.728484\pi\) | |||||||
\(18\) | 0.898380 | 0.0499100 | ||||||||
\(19\) | 5.56819i | 0.293063i | 0.989206 | + | 0.146531i | \(0.0468109\pi\) | ||||
−0.989206 | + | 0.146531i | \(0.953189\pi\) | |||||||
\(20\) | 8.75181i | 0.437591i | ||||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | − | 5.31478i | − | 0.241581i | ||||||
\(23\) | −20.7248 | + | 9.97418i | −0.901077 | + | 0.433660i | ||||
\(24\) | 4.10293 | 0.170955 | ||||||||
\(25\) | 19.9908 | 0.799631 | ||||||||
\(26\) | −0.687427 | −0.0264395 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 10.3457i | 0.369491i | ||||||||
\(29\) | −32.8502 | −1.13277 | −0.566383 | − | 0.824142i | \(-0.691658\pi\) | ||||
−0.566383 | + | 0.824142i | \(0.691658\pi\) | |||||||
\(30\) | 1.16087i | 0.0386958i | ||||||||
\(31\) | −53.8161 | −1.73600 | −0.868002 | − | 0.496561i | \(-0.834596\pi\) | ||||
−0.868002 | + | 0.496561i | \(0.834596\pi\) | |||||||
\(32\) | 13.9468 | 0.435838 | ||||||||
\(33\) | 30.7402i | 0.931522i | ||||||||
\(34\) | 7.66934i | 0.225569i | ||||||||
\(35\) | −5.92153 | −0.169187 | ||||||||
\(36\) | −11.7310 | −0.325860 | ||||||||
\(37\) | 11.4053i | 0.308253i | 0.988051 | + | 0.154126i | \(0.0492563\pi\) | ||||
−0.988051 | + | 0.154126i | \(0.950744\pi\) | |||||||
\(38\) | 1.66745i | 0.0438803i | ||||||||
\(39\) | 3.97602 | 0.101949 | ||||||||
\(40\) | 5.30174i | 0.132543i | ||||||||
\(41\) | −20.9701 | −0.511466 | −0.255733 | − | 0.966747i | \(-0.582317\pi\) | ||||
−0.255733 | + | 0.966747i | \(0.582317\pi\) | |||||||
\(42\) | 1.37230i | 0.0326738i | ||||||||
\(43\) | 52.8779i | 1.22972i | 0.788637 | + | 0.614859i | \(0.210787\pi\) | ||||
−0.788637 | + | 0.614859i | \(0.789213\pi\) | |||||||
\(44\) | 69.4000i | 1.57727i | ||||||||
\(45\) | − | 6.71439i | − | 0.149209i | ||||||
\(46\) | −6.20624 | + | 2.98687i | −0.134918 | + | 0.0649319i | ||||
\(47\) | 72.5217 | 1.54302 | 0.771508 | − | 0.636220i | \(-0.219503\pi\) | ||||
0.771508 | + | 0.636220i | \(0.219503\pi\) | |||||||
\(48\) | −25.8629 | −0.538809 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 5.98644 | 0.119729 | ||||||||
\(51\) | − | 44.3588i | − | 0.869781i | ||||||
\(52\) | 8.97636 | 0.172622 | ||||||||
\(53\) | 72.9954i | 1.37727i | 0.725107 | + | 0.688636i | \(0.241790\pi\) | ||||
−0.725107 | + | 0.688636i | \(0.758210\pi\) | |||||||
\(54\) | −1.55604 | −0.0288155 | ||||||||
\(55\) | −39.7221 | −0.722219 | ||||||||
\(56\) | 6.26732i | 0.111916i | ||||||||
\(57\) | − | 9.64439i | − | 0.169200i | ||||||
\(58\) | −9.83732 | −0.169609 | ||||||||
\(59\) | 42.7209 | 0.724083 | 0.362042 | − | 0.932162i | \(-0.382080\pi\) | ||||
0.362042 | + | 0.932162i | \(0.382080\pi\) | |||||||
\(60\) | − | 15.1586i | − | 0.252643i | ||||||
\(61\) | 98.2277i | 1.61029i | 0.593078 | + | 0.805145i | \(0.297913\pi\) | ||||
−0.593078 | + | 0.805145i | \(0.702087\pi\) | |||||||
\(62\) | −16.1158 | −0.259932 | ||||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | −55.5512 | −0.867987 | ||||||||
\(65\) | 5.13775i | 0.0790423i | ||||||||
\(66\) | 9.20547i | 0.139477i | ||||||||
\(67\) | 7.20999i | 0.107612i | 0.998551 | + | 0.0538059i | \(0.0171352\pi\) | ||||
−0.998551 | + | 0.0538059i | \(0.982865\pi\) | |||||||
\(68\) | − | 100.146i | − | 1.47273i | ||||||
\(69\) | 35.8963 | − | 17.2758i | 0.520237 | − | 0.250374i | ||||
\(70\) | −1.77326 | −0.0253323 | ||||||||
\(71\) | −113.813 | −1.60300 | −0.801500 | − | 0.597995i | \(-0.795964\pi\) | ||||
−0.801500 | + | 0.597995i | \(0.795964\pi\) | |||||||
\(72\) | −7.10648 | −0.0987011 | ||||||||
\(73\) | 43.6776 | 0.598323 | 0.299161 | − | 0.954203i | \(-0.403293\pi\) | ||||
0.299161 | + | 0.954203i | \(0.403293\pi\) | |||||||
\(74\) | 3.41544i | 0.0461547i | ||||||||
\(75\) | −34.6250 | −0.461667 | ||||||||
\(76\) | − | 21.7734i | − | 0.286493i | ||||||
\(77\) | −46.9565 | −0.609825 | ||||||||
\(78\) | 1.19066 | 0.0152648 | ||||||||
\(79\) | − | 24.0288i | − | 0.304162i | −0.988368 | − | 0.152081i | \(-0.951403\pi\) | ||
0.988368 | − | 0.152081i | \(-0.0485975\pi\) | |||||||
\(80\) | − | 33.4196i | − | 0.417745i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −6.27971 | −0.0765818 | ||||||||
\(83\) | − | 44.2213i | − | 0.532786i | −0.963864 | − | 0.266393i | \(-0.914168\pi\) | ||
0.963864 | − | 0.266393i | \(-0.0858320\pi\) | |||||||
\(84\) | − | 17.9194i | − | 0.213326i | ||||||
\(85\) | 57.3198 | 0.674350 | ||||||||
\(86\) | 15.8348i | 0.184126i | ||||||||
\(87\) | 56.8982 | 0.654003 | ||||||||
\(88\) | 42.0416i | 0.477746i | ||||||||
\(89\) | − | 21.5910i | − | 0.242595i | −0.992616 | − | 0.121298i | \(-0.961294\pi\) | ||
0.992616 | − | 0.121298i | \(-0.0387055\pi\) | |||||||
\(90\) | − | 2.01069i | − | 0.0223410i | ||||||
\(91\) | 6.07347i | 0.0667414i | ||||||||
\(92\) | 81.0405 | − | 39.0023i | 0.880875 | − | 0.423938i | ||||
\(93\) | 93.2122 | 1.00228 | ||||||||
\(94\) | 21.7174 | 0.231036 | ||||||||
\(95\) | 12.4623 | 0.131183 | ||||||||
\(96\) | −24.1566 | −0.251631 | ||||||||
\(97\) | − | 59.2662i | − | 0.610992i | −0.952193 | − | 0.305496i | \(-0.901178\pi\) | ||
0.952193 | − | 0.305496i | \(-0.0988222\pi\) | |||||||
\(98\) | −2.09622 | −0.0213900 | ||||||||
\(99\) | − | 53.2437i | − | 0.537815i | ||||||
\(100\) | −78.1704 | −0.781704 | ||||||||
\(101\) | 29.2064 | 0.289173 | 0.144586 | − | 0.989492i | \(-0.453815\pi\) | ||||
0.144586 | + | 0.989492i | \(0.453815\pi\) | |||||||
\(102\) | − | 13.2837i | − | 0.130232i | ||||||
\(103\) | 158.707i | 1.54085i | 0.637533 | + | 0.770423i | \(0.279955\pi\) | ||||
−0.637533 | + | 0.770423i | \(0.720045\pi\) | |||||||
\(104\) | 5.43777 | 0.0522862 | ||||||||
\(105\) | 10.2564 | 0.0976800 | ||||||||
\(106\) | 21.8592i | 0.206219i | ||||||||
\(107\) | − | 120.885i | − | 1.12976i | −0.825172 | − | 0.564882i | \(-0.808922\pi\) | ||
0.825172 | − | 0.564882i | \(-0.191078\pi\) | |||||||
\(108\) | 20.3186 | 0.188136 | ||||||||
\(109\) | 105.904i | 0.971600i | 0.874070 | + | 0.485800i | \(0.161472\pi\) | ||||
−0.874070 | + | 0.485800i | \(0.838528\pi\) | |||||||
\(110\) | −11.8952 | −0.108138 | ||||||||
\(111\) | − | 19.7546i | − | 0.177970i | ||||||
\(112\) | − | 39.5062i | − | 0.352734i | ||||||
\(113\) | − | 133.536i | − | 1.18173i | −0.806769 | − | 0.590867i | \(-0.798786\pi\) | ||
0.806769 | − | 0.590867i | \(-0.201214\pi\) | |||||||
\(114\) | − | 2.88811i | − | 0.0253343i | ||||||
\(115\) | 22.3235 | + | 46.3847i | 0.194117 | + | 0.403345i | ||||
\(116\) | 128.455 | 1.10737 | ||||||||
\(117\) | −6.88666 | −0.0588604 | ||||||||
\(118\) | 12.7932 | 0.108417 | ||||||||
\(119\) | 67.7592 | 0.569405 | ||||||||
\(120\) | − | 9.18288i | − | 0.0765240i | ||||||
\(121\) | −193.987 | −1.60320 | ||||||||
\(122\) | 29.4153i | 0.241109i | ||||||||
\(123\) | 36.3213 | 0.295295 | ||||||||
\(124\) | 210.438 | 1.69708 | ||||||||
\(125\) | − | 100.695i | − | 0.805562i | ||||||
\(126\) | − | 2.37689i | − | 0.0188642i | ||||||
\(127\) | −52.8091 | −0.415820 | −0.207910 | − | 0.978148i | \(-0.566666\pi\) | ||||
−0.207910 | + | 0.978148i | \(0.566666\pi\) | |||||||
\(128\) | −72.4226 | −0.565802 | ||||||||
\(129\) | − | 91.5872i | − | 0.709978i | ||||||
\(130\) | 1.53855i | 0.0118350i | ||||||||
\(131\) | 138.095 | 1.05416 | 0.527081 | − | 0.849815i | \(-0.323287\pi\) | ||||
0.527081 | + | 0.849815i | \(0.323287\pi\) | |||||||
\(132\) | − | 120.204i | − | 0.910639i | ||||||
\(133\) | 14.7321 | 0.110767 | ||||||||
\(134\) | 2.15910i | 0.0161127i | ||||||||
\(135\) | 11.6297i | 0.0861457i | ||||||||
\(136\) | − | 60.6670i | − | 0.446081i | ||||||
\(137\) | − | 84.9718i | − | 0.620232i | −0.950699 | − | 0.310116i | \(-0.899632\pi\) | ||
0.950699 | − | 0.310116i | \(-0.100368\pi\) | |||||||
\(138\) | 10.7495 | − | 5.17341i | 0.0778951 | − | 0.0374884i | ||||
\(139\) | −242.796 | −1.74673 | −0.873367 | − | 0.487063i | \(-0.838068\pi\) | ||||
−0.873367 | + | 0.487063i | \(0.838068\pi\) | |||||||
\(140\) | 23.1551 | 0.165394 | ||||||||
\(141\) | −125.611 | −0.890860 | ||||||||
\(142\) | −34.0824 | −0.240017 | ||||||||
\(143\) | 40.7412i | 0.284904i | ||||||||
\(144\) | 44.7958 | 0.311082 | ||||||||
\(145\) | 73.5230i | 0.507055i | ||||||||
\(146\) | 13.0797 | 0.0895868 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | − | 44.5986i | − | 0.301342i | ||||||
\(149\) | 32.4768i | 0.217965i | 0.994044 | + | 0.108982i | \(0.0347592\pi\) | ||||
−0.994044 | + | 0.108982i | \(0.965241\pi\) | |||||||
\(150\) | −10.3688 | −0.0691254 | ||||||||
\(151\) | −105.977 | −0.701832 | −0.350916 | − | 0.936407i | \(-0.614130\pi\) | ||||
−0.350916 | + | 0.936407i | \(0.614130\pi\) | |||||||
\(152\) | − | 13.1901i | − | 0.0867768i | ||||||
\(153\) | 76.8317i | 0.502168i | ||||||||
\(154\) | −14.0616 | −0.0913090 | ||||||||
\(155\) | 120.447i | 0.777080i | ||||||||
\(156\) | −15.5475 | −0.0996636 | ||||||||
\(157\) | 235.156i | 1.49781i | 0.662677 | + | 0.748906i | \(0.269420\pi\) | ||||
−0.662677 | + | 0.748906i | \(0.730580\pi\) | |||||||
\(158\) | − | 7.19567i | − | 0.0455422i | ||||||
\(159\) | − | 126.432i | − | 0.795168i | ||||||
\(160\) | − | 31.2148i | − | 0.195092i | ||||||
\(161\) | 26.3892 | + | 54.8326i | 0.163908 | + | 0.340575i | ||||
\(162\) | 2.69514 | 0.0166367 | ||||||||
\(163\) | 76.8192 | 0.471284 | 0.235642 | − | 0.971840i | \(-0.424281\pi\) | ||||
0.235642 | + | 0.971840i | \(0.424281\pi\) | |||||||
\(164\) | 81.9999 | 0.500000 | ||||||||
\(165\) | 68.8006 | 0.416974 | ||||||||
\(166\) | − | 13.2425i | − | 0.0797741i | ||||||
\(167\) | 152.168 | 0.911183 | 0.455592 | − | 0.890189i | \(-0.349428\pi\) | ||||
0.455592 | + | 0.890189i | \(0.349428\pi\) | |||||||
\(168\) | − | 10.8553i | − | 0.0646150i | ||||||
\(169\) | −163.730 | −0.968819 | ||||||||
\(170\) | 17.1650 | 0.100970 | ||||||||
\(171\) | 16.7046i | 0.0976876i | ||||||||
\(172\) | − | 206.770i | − | 1.20215i | ||||||
\(173\) | −182.069 | −1.05242 | −0.526211 | − | 0.850354i | \(-0.676388\pi\) | ||||
−0.526211 | + | 0.850354i | \(0.676388\pi\) | |||||||
\(174\) | 17.0387 | 0.0979238 | ||||||||
\(175\) | − | 52.8906i | − | 0.302232i | ||||||
\(176\) | − | 265.010i | − | 1.50574i | ||||||
\(177\) | −73.9948 | −0.418050 | ||||||||
\(178\) | − | 6.46563i | − | 0.0363238i | ||||||
\(179\) | 178.229 | 0.995694 | 0.497847 | − | 0.867265i | \(-0.334124\pi\) | ||||
0.497847 | + | 0.867265i | \(0.334124\pi\) | |||||||
\(180\) | 26.2554i | 0.145864i | ||||||||
\(181\) | 316.640i | 1.74939i | 0.484671 | + | 0.874697i | \(0.338940\pi\) | ||||
−0.484671 | + | 0.874697i | \(0.661060\pi\) | |||||||
\(182\) | 1.81876i | 0.00999319i | ||||||||
\(183\) | − | 170.135i | − | 0.929701i | ||||||
\(184\) | 49.0933 | − | 23.6271i | 0.266812 | − | 0.128408i | ||||
\(185\) | 25.5266 | 0.137982 | ||||||||
\(186\) | 27.9133 | 0.150072 | ||||||||
\(187\) | 454.533 | 2.43066 | ||||||||
\(188\) | −283.583 | −1.50842 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 3.73197 | 0.0196420 | ||||||||
\(191\) | − | 244.300i | − | 1.27906i | −0.768767 | − | 0.639529i | \(-0.779129\pi\) | ||
0.768767 | − | 0.639529i | \(-0.220871\pi\) | |||||||
\(192\) | 96.2175 | 0.501133 | ||||||||
\(193\) | −248.629 | −1.28823 | −0.644116 | − | 0.764928i | \(-0.722775\pi\) | ||||
−0.644116 | + | 0.764928i | \(0.722775\pi\) | |||||||
\(194\) | − | 17.7479i | − | 0.0914838i | ||||||
\(195\) | − | 8.89884i | − | 0.0456351i | ||||||
\(196\) | 27.3723 | 0.139654 | ||||||||
\(197\) | −32.1526 | −0.163211 | −0.0816056 | − | 0.996665i | \(-0.526005\pi\) | ||||
−0.0816056 | + | 0.996665i | \(0.526005\pi\) | |||||||
\(198\) | − | 15.9443i | − | 0.0805270i | ||||||
\(199\) | − | 28.6501i | − | 0.143970i | −0.997406 | − | 0.0719852i | \(-0.977067\pi\) | ||
0.997406 | − | 0.0719852i | \(-0.0229334\pi\) | |||||||
\(200\) | −47.3547 | −0.236773 | ||||||||
\(201\) | − | 12.4881i | − | 0.0621297i | ||||||
\(202\) | 8.74616 | 0.0432978 | ||||||||
\(203\) | 86.9135i | 0.428145i | ||||||||
\(204\) | 173.457i | 0.850281i | ||||||||
\(205\) | 46.9338i | 0.228946i | ||||||||
\(206\) | 47.5264i | 0.230711i | ||||||||
\(207\) | −62.1743 | + | 29.9225i | −0.300359 | + | 0.144553i | ||||
\(208\) | −34.2771 | −0.164794 | ||||||||
\(209\) | 98.8237 | 0.472840 | ||||||||
\(210\) | 3.07138 | 0.0146256 | ||||||||
\(211\) | 186.669 | 0.884687 | 0.442343 | − | 0.896846i | \(-0.354147\pi\) | ||||
0.442343 | + | 0.896846i | \(0.354147\pi\) | |||||||
\(212\) | − | 285.436i | − | 1.34639i | ||||||
\(213\) | 197.130 | 0.925493 | ||||||||
\(214\) | − | 36.2001i | − | 0.169159i | ||||||
\(215\) | 118.348 | 0.550454 | ||||||||
\(216\) | 12.3088 | 0.0569851 | ||||||||
\(217\) | 142.384i | 0.656148i | ||||||||
\(218\) | 31.7141i | 0.145478i | ||||||||
\(219\) | −75.6517 | −0.345442 | ||||||||
\(220\) | 155.326 | 0.706028 | ||||||||
\(221\) | − | 58.7905i | − | 0.266020i | ||||||
\(222\) | − | 5.91572i | − | 0.0266474i | ||||||
\(223\) | −242.763 | −1.08862 | −0.544311 | − | 0.838884i | \(-0.683209\pi\) | ||||
−0.544311 | + | 0.838884i | \(0.683209\pi\) | |||||||
\(224\) | − | 36.8998i | − | 0.164731i | ||||||
\(225\) | 59.9723 | 0.266544 | ||||||||
\(226\) | − | 39.9886i | − | 0.176941i | ||||||
\(227\) | 95.4916i | 0.420668i | 0.977630 | + | 0.210334i | \(0.0674551\pi\) | ||||
−0.977630 | + | 0.210334i | \(0.932545\pi\) | |||||||
\(228\) | 37.7127i | 0.165407i | ||||||||
\(229\) | − | 128.624i | − | 0.561677i | −0.959755 | − | 0.280838i | \(-0.909387\pi\) | ||
0.959755 | − | 0.280838i | \(-0.0906125\pi\) | |||||||
\(230\) | 6.68500 | + | 13.8904i | 0.0290652 | + | 0.0603929i | ||||
\(231\) | 81.3310 | 0.352082 | ||||||||
\(232\) | 77.8164 | 0.335416 | ||||||||
\(233\) | −374.207 | −1.60604 | −0.803019 | − | 0.595953i | \(-0.796774\pi\) | ||||
−0.803019 | + | 0.595953i | \(0.796774\pi\) | |||||||
\(234\) | −2.06228 | −0.00881316 | ||||||||
\(235\) | − | 162.313i | − | 0.690694i | ||||||
\(236\) | −167.053 | −0.707850 | ||||||||
\(237\) | 41.6191i | 0.175608i | ||||||||
\(238\) | 20.2912 | 0.0852570 | ||||||||
\(239\) | −212.635 | −0.889688 | −0.444844 | − | 0.895608i | \(-0.646741\pi\) | ||||
−0.444844 | + | 0.895608i | \(0.646741\pi\) | |||||||
\(240\) | 57.8844i | 0.241185i | ||||||||
\(241\) | − | 221.950i | − | 0.920956i | −0.887671 | − | 0.460478i | \(-0.847678\pi\) | ||
0.887671 | − | 0.460478i | \(-0.152322\pi\) | |||||||
\(242\) | −58.0915 | −0.240047 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 384.102i | − | 1.57419i | ||||||
\(245\) | 15.6669i | 0.0639466i | ||||||||
\(246\) | 10.8768 | 0.0442145 | ||||||||
\(247\) | − | 12.7821i | − | 0.0517494i | ||||||
\(248\) | 127.481 | 0.514036 | ||||||||
\(249\) | 76.5935i | 0.307604i | ||||||||
\(250\) | − | 30.1542i | − | 0.120617i | ||||||
\(251\) | 169.084i | 0.673642i | 0.941569 | + | 0.336821i | \(0.109352\pi\) | ||||
−0.941569 | + | 0.336821i | \(0.890648\pi\) | |||||||
\(252\) | 31.0372i | 0.123164i | ||||||||
\(253\) | 177.021 | + | 367.821i | 0.699686 | + | 1.45384i | ||||
\(254\) | −15.8142 | −0.0622607 | ||||||||
\(255\) | −99.2808 | −0.389336 | ||||||||
\(256\) | 200.517 | 0.783270 | ||||||||
\(257\) | −56.7589 | −0.220852 | −0.110426 | − | 0.993884i | \(-0.535222\pi\) | ||||
−0.110426 | + | 0.993884i | \(0.535222\pi\) | |||||||
\(258\) | − | 27.4267i | − | 0.106305i | ||||||
\(259\) | 30.1757 | 0.116509 | ||||||||
\(260\) | − | 20.0903i | − | 0.0772702i | ||||||
\(261\) | −98.5506 | −0.377589 | ||||||||
\(262\) | 41.3540 | 0.157840 | ||||||||
\(263\) | 51.9956i | 0.197702i | 0.995102 | + | 0.0988509i | \(0.0315167\pi\) | ||||
−0.995102 | + | 0.0988509i | \(0.968483\pi\) | |||||||
\(264\) | − | 72.8183i | − | 0.275827i | ||||||
\(265\) | 163.373 | 0.616503 | ||||||||
\(266\) | 4.41166 | 0.0165852 | ||||||||
\(267\) | 37.3967i | 0.140062i | ||||||||
\(268\) | − | 28.1934i | − | 0.105199i | ||||||
\(269\) | −0.616990 | −0.00229364 | −0.00114682 | − | 0.999999i | \(-0.500365\pi\) | ||||
−0.00114682 | + | 0.999999i | \(0.500365\pi\) | |||||||
\(270\) | 3.48262i | 0.0128986i | ||||||||
\(271\) | 225.807 | 0.833237 | 0.416619 | − | 0.909081i | \(-0.363215\pi\) | ||||
0.416619 | + | 0.909081i | \(0.363215\pi\) | |||||||
\(272\) | 382.415i | 1.40594i | ||||||||
\(273\) | − | 10.5196i | − | 0.0385332i | ||||||
\(274\) | − | 25.4457i | − | 0.0928674i | ||||||
\(275\) | − | 354.794i | − | 1.29016i | ||||||
\(276\) | −140.366 | + | 67.5539i | −0.508574 | + | 0.244761i | ||||
\(277\) | −483.225 | −1.74450 | −0.872248 | − | 0.489064i | \(-0.837338\pi\) | ||||
−0.872248 | + | 0.489064i | \(0.837338\pi\) | |||||||
\(278\) | −72.7077 | −0.261538 | ||||||||
\(279\) | −161.448 | −0.578668 | ||||||||
\(280\) | 14.0271 | 0.0500967 | ||||||||
\(281\) | 478.838i | 1.70405i | 0.523501 | + | 0.852025i | \(0.324626\pi\) | ||||
−0.523501 | + | 0.852025i | \(0.675374\pi\) | |||||||
\(282\) | −37.6156 | −0.133388 | ||||||||
\(283\) | 242.939i | 0.858440i | 0.903200 | + | 0.429220i | \(0.141212\pi\) | ||||
−0.903200 | + | 0.429220i | \(0.858788\pi\) | |||||||
\(284\) | 445.046 | 1.56706 | ||||||||
\(285\) | −21.5854 | −0.0757383 | ||||||||
\(286\) | 12.2004i | 0.0426586i | ||||||||
\(287\) | 55.4817i | 0.193316i | ||||||||
\(288\) | 41.8404 | 0.145279 | ||||||||
\(289\) | −366.901 | −1.26956 | ||||||||
\(290\) | 22.0172i | 0.0759214i | ||||||||
\(291\) | 102.652i | 0.352756i | ||||||||
\(292\) | −170.793 | −0.584909 | ||||||||
\(293\) | − | 191.192i | − | 0.652532i | −0.945278 | − | 0.326266i | \(-0.894210\pi\) | ||
0.945278 | − | 0.326266i | \(-0.105790\pi\) | |||||||
\(294\) | 3.63076 | 0.0123495 | ||||||||
\(295\) | − | 95.6149i | − | 0.324118i | ||||||
\(296\) | − | 27.0173i | − | 0.0912746i | ||||||
\(297\) | 92.2207i | 0.310507i | ||||||||
\(298\) | 9.72549i | 0.0326359i | ||||||||
\(299\) | 47.5748 | − | 22.8963i | 0.159113 | − | 0.0765762i | ||||
\(300\) | 135.395 | 0.451317 | ||||||||
\(301\) | 139.902 | 0.464790 | ||||||||
\(302\) | −31.7358 | −0.105085 | ||||||||
\(303\) | −50.5870 | −0.166954 | ||||||||
\(304\) | 83.1439i | 0.273500i | ||||||||
\(305\) | 219.846 | 0.720808 | ||||||||
\(306\) | 23.0080i | 0.0751896i | ||||||||
\(307\) | 117.388 | 0.382372 | 0.191186 | − | 0.981554i | \(-0.438767\pi\) | ||||
0.191186 | + | 0.981554i | \(0.438767\pi\) | |||||||
\(308\) | 183.615 | 0.596153 | ||||||||
\(309\) | − | 274.889i | − | 0.889608i | ||||||
\(310\) | 36.0692i | 0.116352i | ||||||||
\(311\) | 299.729 | 0.963760 | 0.481880 | − | 0.876237i | \(-0.339954\pi\) | ||||
0.481880 | + | 0.876237i | \(0.339954\pi\) | |||||||
\(312\) | −9.41849 | −0.0301875 | ||||||||
\(313\) | 207.793i | 0.663877i | 0.943301 | + | 0.331938i | \(0.107703\pi\) | ||||
−0.943301 | + | 0.331938i | \(0.892297\pi\) | |||||||
\(314\) | 70.4199i | 0.224267i | ||||||||
\(315\) | −17.7646 | −0.0563956 | ||||||||
\(316\) | 93.9604i | 0.297343i | ||||||||
\(317\) | −211.154 | −0.666100 | −0.333050 | − | 0.942909i | \(-0.608078\pi\) | ||||
−0.333050 | + | 0.942909i | \(0.608078\pi\) | |||||||
\(318\) | − | 37.8612i | − | 0.119061i | ||||||
\(319\) | 583.022i | 1.82765i | ||||||||
\(320\) | 124.331i | 0.388534i | ||||||||
\(321\) | 209.378i | 0.652269i | ||||||||
\(322\) | 7.90251 | + | 16.4202i | 0.0245420 | + | 0.0509943i | ||||
\(323\) | −142.605 | −0.441500 | ||||||||
\(324\) | −35.1929 | −0.108620 | ||||||||
\(325\) | −45.8899 | −0.141200 | ||||||||
\(326\) | 23.0043 | 0.0705653 | ||||||||
\(327\) | − | 183.432i | − | 0.560954i | ||||||
\(328\) | 49.6745 | 0.151447 | ||||||||
\(329\) | − | 191.874i | − | 0.583205i | ||||||
\(330\) | 20.6030 | 0.0624334 | ||||||||
\(331\) | −508.921 | −1.53752 | −0.768762 | − | 0.639534i | \(-0.779127\pi\) | ||||
−0.768762 | + | 0.639534i | \(0.779127\pi\) | |||||||
\(332\) | 172.919i | 0.520842i | ||||||||
\(333\) | 34.2160i | 0.102751i | ||||||||
\(334\) | 45.5681 | 0.136431 | ||||||||
\(335\) | 16.1369 | 0.0481698 | ||||||||
\(336\) | 68.4267i | 0.203651i | ||||||||
\(337\) | − | 646.068i | − | 1.91712i | −0.284896 | − | 0.958558i | \(-0.591959\pi\) | ||
0.284896 | − | 0.958558i | \(-0.408041\pi\) | |||||||
\(338\) | −49.0307 | −0.145061 | ||||||||
\(339\) | 231.291i | 0.682274i | ||||||||
\(340\) | −224.139 | −0.659232 | ||||||||
\(341\) | 955.122i | 2.80094i | ||||||||
\(342\) | 5.00235i | 0.0146268i | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 125.258i | − | 0.364123i | ||||||
\(345\) | −38.6654 | − | 80.3407i | −0.112074 | − | 0.232872i | ||||
\(346\) | −54.5224 | −0.157579 | ||||||||
\(347\) | −412.479 | −1.18870 | −0.594350 | − | 0.804207i | \(-0.702591\pi\) | ||||
−0.594350 | + | 0.804207i | \(0.702591\pi\) | |||||||
\(348\) | −222.491 | −0.639341 | ||||||||
\(349\) | −411.715 | −1.17970 | −0.589850 | − | 0.807513i | \(-0.700813\pi\) | ||||
−0.589850 | + | 0.807513i | \(0.700813\pi\) | |||||||
\(350\) | − | 15.8386i | − | 0.0452532i | ||||||
\(351\) | 11.9281 | 0.0339831 | ||||||||
\(352\) | − | 247.526i | − | 0.703200i | ||||||
\(353\) | −119.691 | −0.339067 | −0.169533 | − | 0.985524i | \(-0.554226\pi\) | ||||
−0.169533 | + | 0.985524i | \(0.554226\pi\) | |||||||
\(354\) | −22.1585 | −0.0625946 | ||||||||
\(355\) | 254.728i | 0.717544i | ||||||||
\(356\) | 84.4277i | 0.237156i | ||||||||
\(357\) | −117.362 | −0.328746 | ||||||||
\(358\) | 53.3725 | 0.149085 | ||||||||
\(359\) | 318.418i | 0.886959i | 0.896284 | + | 0.443480i | \(0.146256\pi\) | ||||
−0.896284 | + | 0.443480i | \(0.853744\pi\) | |||||||
\(360\) | 15.9052i | 0.0441812i | ||||||||
\(361\) | 329.995 | 0.914114 | ||||||||
\(362\) | 94.8211i | 0.261937i | ||||||||
\(363\) | 335.996 | 0.925609 | ||||||||
\(364\) | − | 23.7492i | − | 0.0652451i | ||||||
\(365\) | − | 97.7560i | − | 0.267825i | ||||||
\(366\) | − | 50.9487i | − | 0.139204i | ||||||
\(367\) | − | 509.344i | − | 1.38786i | −0.720043 | − | 0.693929i | \(-0.755878\pi\) | ||
0.720043 | − | 0.693929i | \(-0.244122\pi\) | |||||||
\(368\) | −309.461 | + | 148.934i | −0.840926 | + | 0.404711i | ||||
\(369\) | −62.9103 | −0.170489 | ||||||||
\(370\) | 7.64421 | 0.0206600 | ||||||||
\(371\) | 193.128 | 0.520560 | ||||||||
\(372\) | −364.490 | −0.979812 | ||||||||
\(373\) | 246.136i | 0.659882i | 0.944002 | + | 0.329941i | \(0.107029\pi\) | ||||
−0.944002 | + | 0.329941i | \(0.892971\pi\) | |||||||
\(374\) | 136.115 | 0.363943 | ||||||||
\(375\) | 174.409i | 0.465091i | ||||||||
\(376\) | −171.791 | −0.456892 | ||||||||
\(377\) | 75.4095 | 0.200025 | ||||||||
\(378\) | 4.11689i | 0.0108913i | ||||||||
\(379\) | − | 137.963i | − | 0.364019i | −0.983297 | − | 0.182010i | \(-0.941740\pi\) | ||
0.983297 | − | 0.182010i | \(-0.0582602\pi\) | |||||||
\(380\) | −48.7318 | −0.128242 | ||||||||
\(381\) | 91.4681 | 0.240074 | ||||||||
\(382\) | − | 73.1581i | − | 0.191513i | ||||||
\(383\) | − | 688.826i | − | 1.79850i | −0.437434 | − | 0.899251i | \(-0.644113\pi\) | ||
0.437434 | − | 0.899251i | \(-0.355887\pi\) | |||||||
\(384\) | 125.440 | 0.326666 | ||||||||
\(385\) | 105.095i | 0.272973i | ||||||||
\(386\) | −74.4544 | −0.192887 | ||||||||
\(387\) | 158.634i | 0.409906i | ||||||||
\(388\) | 231.750i | 0.597294i | ||||||||
\(389\) | − | 404.932i | − | 1.04096i | −0.853875 | − | 0.520479i | \(-0.825753\pi\) | ||
0.853875 | − | 0.520479i | \(-0.174247\pi\) | |||||||
\(390\) | − | 2.66485i | − | 0.00683294i | ||||||
\(391\) | −255.444 | − | 530.773i | −0.653311 | − | 1.35748i | ||||
\(392\) | 16.5818 | 0.0423005 | ||||||||
\(393\) | −239.188 | −0.608620 | ||||||||
\(394\) | −9.62842 | −0.0244376 | ||||||||
\(395\) | −53.7796 | −0.136151 | ||||||||
\(396\) | 208.200i | 0.525757i | ||||||||
\(397\) | 785.576 | 1.97878 | 0.989391 | − | 0.145277i | \(-0.0464073\pi\) | ||||
0.989391 | + | 0.145277i | \(0.0464073\pi\) | |||||||
\(398\) | − | 8.57956i | − | 0.0215567i | ||||||
\(399\) | −25.5167 | −0.0639515 | ||||||||
\(400\) | 298.501 | 0.746252 | ||||||||
\(401\) | 659.729i | 1.64521i | 0.568614 | + | 0.822605i | \(0.307480\pi\) | ||||
−0.568614 | + | 0.822605i | \(0.692520\pi\) | |||||||
\(402\) | − | 3.73968i | − | 0.00930268i | ||||||
\(403\) | 123.538 | 0.306545 | ||||||||
\(404\) | −114.207 | −0.282690 | ||||||||
\(405\) | − | 20.1432i | − | 0.0497362i | ||||||
\(406\) | 26.0271i | 0.0641062i | ||||||||
\(407\) | 202.421 | 0.497348 | ||||||||
\(408\) | 105.078i | 0.257545i | ||||||||
\(409\) | −111.629 | −0.272930 | −0.136465 | − | 0.990645i | \(-0.543574\pi\) | ||||
−0.136465 | + | 0.990645i | \(0.543574\pi\) | |||||||
\(410\) | 14.0548i | 0.0342800i | ||||||||
\(411\) | 147.175i | 0.358091i | ||||||||
\(412\) | − | 620.596i | − | 1.50630i | ||||||
\(413\) | − | 113.029i | − | 0.273678i | ||||||
\(414\) | −18.6187 | + | 8.96060i | −0.0449727 | + | 0.0216440i | ||||
\(415\) | −98.9729 | −0.238489 | ||||||||
\(416\) | −32.0157 | −0.0769608 | ||||||||
\(417\) | 420.535 | 1.00848 | ||||||||
\(418\) | 29.5937 | 0.0707984 | ||||||||
\(419\) | − | 343.072i | − | 0.818787i | −0.912358 | − | 0.409394i | \(-0.865740\pi\) | ||
0.912358 | − | 0.409394i | \(-0.134260\pi\) | |||||||
\(420\) | −40.1058 | −0.0954901 | ||||||||
\(421\) | 786.898i | 1.86912i | 0.355811 | + | 0.934558i | \(0.384205\pi\) | ||||
−0.355811 | + | 0.934558i | \(0.615795\pi\) | |||||||
\(422\) | 55.8999 | 0.132464 | ||||||||
\(423\) | 217.565 | 0.514338 | ||||||||
\(424\) | − | 172.913i | − | 0.407815i | ||||||
\(425\) | 511.975i | 1.20465i | ||||||||
\(426\) | 59.0325 | 0.138574 | ||||||||
\(427\) | 259.886 | 0.608632 | ||||||||
\(428\) | 472.698i | 1.10443i | ||||||||
\(429\) | − | 70.5659i | − | 0.164489i | ||||||
\(430\) | 35.4404 | 0.0824194 | ||||||||
\(431\) | 33.8925i | 0.0786370i | 0.999227 | + | 0.0393185i | \(0.0125187\pi\) | ||||
−0.999227 | + | 0.0393185i | \(0.987481\pi\) | |||||||
\(432\) | −77.5886 | −0.179603 | ||||||||
\(433\) | 847.725i | 1.95780i | 0.204351 | + | 0.978898i | \(0.434492\pi\) | ||||
−0.204351 | + | 0.978898i | \(0.565508\pi\) | |||||||
\(434\) | 42.6383i | 0.0982450i | ||||||||
\(435\) | − | 127.346i | − | 0.292749i | ||||||
\(436\) | − | 414.120i | − | 0.949818i | ||||||
\(437\) | −55.5382 | − | 115.399i | −0.127090 | − | 0.264072i | ||||
\(438\) | −22.6547 | −0.0517230 | ||||||||
\(439\) | 419.290 | 0.955103 | 0.477552 | − | 0.878604i | \(-0.341524\pi\) | ||||
0.477552 | + | 0.878604i | \(0.341524\pi\) | |||||||
\(440\) | 94.0946 | 0.213851 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | − | 17.6054i | − | 0.0398312i | ||||||
\(443\) | −652.816 | −1.47362 | −0.736812 | − | 0.676097i | \(-0.763670\pi\) | ||||
−0.736812 | + | 0.676097i | \(0.763670\pi\) | |||||||
\(444\) | 77.2470i | 0.173980i | ||||||||
\(445\) | −48.3234 | −0.108592 | ||||||||
\(446\) | −72.6977 | −0.162999 | ||||||||
\(447\) | − | 56.2514i | − | 0.125842i | ||||||
\(448\) | 146.975i | 0.328068i | ||||||||
\(449\) | 175.921 | 0.391806 | 0.195903 | − | 0.980623i | \(-0.437236\pi\) | ||||
0.195903 | + | 0.980623i | \(0.437236\pi\) | |||||||
\(450\) | 17.9593 | 0.0399096 | ||||||||
\(451\) | 372.175i | 0.825222i | ||||||||
\(452\) | 522.168i | 1.15524i | ||||||||
\(453\) | 183.557 | 0.405203 | ||||||||
\(454\) | 28.5959i | 0.0629866i | ||||||||
\(455\) | 13.5932 | 0.0298752 | ||||||||
\(456\) | 22.8459i | 0.0501006i | ||||||||
\(457\) | − | 466.627i | − | 1.02107i | −0.859858 | − | 0.510533i | \(-0.829448\pi\) | ||
0.859858 | − | 0.510533i | \(-0.170552\pi\) | |||||||
\(458\) | − | 38.5177i | − | 0.0840999i | ||||||
\(459\) | − | 133.076i | − | 0.289927i | ||||||
\(460\) | −87.2921 | − | 181.379i | −0.189766 | − | 0.394303i | ||||
\(461\) | −152.082 | −0.329896 | −0.164948 | − | 0.986302i | \(-0.552746\pi\) | ||||
−0.164948 | + | 0.986302i | \(0.552746\pi\) | |||||||
\(462\) | 24.3554 | 0.0527173 | ||||||||
\(463\) | −156.569 | −0.338163 | −0.169082 | − | 0.985602i | \(-0.554080\pi\) | ||||
−0.169082 | + | 0.985602i | \(0.554080\pi\) | |||||||
\(464\) | −490.517 | −1.05715 | ||||||||
\(465\) | − | 208.621i | − | 0.448647i | ||||||
\(466\) | −112.060 | −0.240472 | ||||||||
\(467\) | − | 699.315i | − | 1.49746i | −0.662874 | − | 0.748731i | \(-0.730664\pi\) | ||
0.662874 | − | 0.748731i | \(-0.269336\pi\) | |||||||
\(468\) | 26.9291 | 0.0575408 | ||||||||
\(469\) | 19.0758 | 0.0406734 | ||||||||
\(470\) | − | 48.6063i | − | 0.103418i | ||||||
\(471\) | − | 407.303i | − | 0.864762i | ||||||
\(472\) | −101.198 | −0.214403 | ||||||||
\(473\) | 938.471 | 1.98408 | ||||||||
\(474\) | 12.4633i | 0.0262938i | ||||||||
\(475\) | 111.313i | 0.234342i | ||||||||
\(476\) | −264.960 | −0.556640 | ||||||||
\(477\) | 218.986i | 0.459091i | ||||||||
\(478\) | −63.6758 | −0.133213 | ||||||||
\(479\) | − | 356.147i | − | 0.743523i | −0.928328 | − | 0.371761i | \(-0.878754\pi\) | ||
0.928328 | − | 0.371761i | \(-0.121246\pi\) | |||||||
\(480\) | 54.0656i | 0.112637i | ||||||||
\(481\) | − | 26.1816i | − | 0.0544316i | ||||||
\(482\) | − | 66.4653i | − | 0.137895i | ||||||
\(483\) | −45.7074 | − | 94.9728i | −0.0946324 | − | 0.196631i | ||||
\(484\) | 758.554 | 1.56726 | ||||||||
\(485\) | −132.645 | −0.273496 | ||||||||
\(486\) | −4.66812 | −0.00960518 | ||||||||
\(487\) | 194.007 | 0.398372 | 0.199186 | − | 0.979962i | \(-0.436170\pi\) | ||||
0.199186 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(488\) | − | 232.684i | − | 0.476812i | ||||||
\(489\) | −133.055 | −0.272096 | ||||||||
\(490\) | 4.69161i | 0.00957472i | ||||||||
\(491\) | −438.471 | −0.893017 | −0.446508 | − | 0.894779i | \(-0.647333\pi\) | ||||
−0.446508 | + | 0.894779i | \(0.647333\pi\) | |||||||
\(492\) | −142.028 | −0.288675 | ||||||||
\(493\) | − | 841.313i | − | 1.70652i | ||||||
\(494\) | − | 3.82773i | − | 0.00774843i | ||||||
\(495\) | −119.166 | −0.240740 | ||||||||
\(496\) | −803.578 | −1.62012 | ||||||||
\(497\) | 301.121i | 0.605877i | ||||||||
\(498\) | 22.9367i | 0.0460576i | ||||||||
\(499\) | −78.4964 | −0.157307 | −0.0786537 | − | 0.996902i | \(-0.525062\pi\) | ||||
−0.0786537 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(500\) | 393.751i | 0.787502i | ||||||||
\(501\) | −263.562 | −0.526072 | ||||||||
\(502\) | 50.6340i | 0.100864i | ||||||||
\(503\) | 123.657i | 0.245839i | 0.992417 | + | 0.122919i | \(0.0392256\pi\) | ||||
−0.992417 | + | 0.122919i | \(0.960774\pi\) | |||||||
\(504\) | 18.8020i | 0.0373055i | ||||||||
\(505\) | − | 65.3678i | − | 0.129441i | ||||||
\(506\) | 53.0106 | + | 110.148i | 0.104764 | + | 0.217683i | ||||
\(507\) | 283.589 | 0.559348 | ||||||||
\(508\) | 206.501 | 0.406498 | ||||||||
\(509\) | 162.390 | 0.319037 | 0.159519 | − | 0.987195i | \(-0.449006\pi\) | ||||
0.159519 | + | 0.987195i | \(0.449006\pi\) | |||||||
\(510\) | −29.7306 | −0.0582953 | ||||||||
\(511\) | − | 115.560i | − | 0.226145i | ||||||
\(512\) | 349.737 | 0.683081 | ||||||||
\(513\) | − | 28.9332i | − | 0.0564000i | ||||||
\(514\) | −16.9970 | −0.0330682 | ||||||||
\(515\) | 355.207 | 0.689723 | ||||||||
\(516\) | 358.136i | 0.694061i | ||||||||
\(517\) | − | 1287.11i | − | 2.48957i | ||||||
\(518\) | 9.03642 | 0.0174448 | ||||||||
\(519\) | 315.353 | 0.607616 | ||||||||
\(520\) | − | 12.1704i | − | 0.0234047i | ||||||
\(521\) | − | 372.783i | − | 0.715514i | −0.933815 | − | 0.357757i | \(-0.883542\pi\) | ||
0.933815 | − | 0.357757i | \(-0.116458\pi\) | |||||||
\(522\) | −29.5120 | −0.0565363 | ||||||||
\(523\) | − | 4.17483i | − | 0.00798246i | −0.999992 | − | 0.00399123i | \(-0.998730\pi\) | ||
0.999992 | − | 0.00399123i | \(-0.00127045\pi\) | |||||||
\(524\) | −539.997 | −1.03053 | ||||||||
\(525\) | 91.6092i | 0.174494i | ||||||||
\(526\) | 15.5706i | 0.0296019i | ||||||||
\(527\) | − | 1378.26i | − | 2.61530i | ||||||
\(528\) | 459.011i | 0.869339i | ||||||||
\(529\) | 330.032 | − | 413.425i | 0.623878 | − | 0.781522i | ||||
\(530\) | 48.9237 | 0.0923089 | ||||||||
\(531\) | 128.163 | 0.241361 | ||||||||
\(532\) | −57.6071 | −0.108284 | ||||||||
\(533\) | 48.1380 | 0.0903153 | ||||||||
\(534\) | 11.1988i | 0.0209715i | ||||||||
\(535\) | −270.556 | −0.505711 | ||||||||
\(536\) | − | 17.0792i | − | 0.0318642i | ||||||
\(537\) | −308.702 | −0.574864 | ||||||||
\(538\) | −0.184764 | −0.000343427 | ||||||||
\(539\) | 124.235i | 0.230492i | ||||||||
\(540\) | − | 45.4757i | − | 0.0842143i | ||||||
\(541\) | 533.262 | 0.985697 | 0.492849 | − | 0.870115i | \(-0.335956\pi\) | ||||
0.492849 | + | 0.870115i | \(0.335956\pi\) | |||||||
\(542\) | 67.6202 | 0.124761 | ||||||||
\(543\) | − | 548.437i | − | 1.01001i | ||||||
\(544\) | 357.186i | 0.656592i | ||||||||
\(545\) | 237.028 | 0.434913 | ||||||||
\(546\) | − | 3.15019i | − | 0.00576957i | ||||||
\(547\) | −12.0226 | −0.0219792 | −0.0109896 | − | 0.999940i | \(-0.503498\pi\) | ||||
−0.0109896 | + | 0.999940i | \(0.503498\pi\) | |||||||
\(548\) | 332.267i | 0.606327i | ||||||||
\(549\) | 294.683i | 0.536763i | ||||||||
\(550\) | − | 106.247i | − | 0.193176i | ||||||
\(551\) | − | 182.916i | − | 0.331972i | ||||||
\(552\) | −85.0322 | + | 40.9233i | −0.154044 | + | 0.0741364i | ||||
\(553\) | −63.5743 | −0.114963 | ||||||||
\(554\) | −144.707 | −0.261203 | ||||||||
\(555\) | −44.2134 | −0.0796639 | ||||||||
\(556\) | 949.411 | 1.70757 | ||||||||
\(557\) | 840.063i | 1.50819i | 0.656764 | + | 0.754096i | \(0.271925\pi\) | ||||
−0.656764 | + | 0.754096i | \(0.728075\pi\) | |||||||
\(558\) | −48.3473 | −0.0866439 | ||||||||
\(559\) | − | 121.384i | − | 0.217145i | ||||||
\(560\) | −88.4199 | −0.157893 | ||||||||
\(561\) | −787.275 | −1.40334 | ||||||||
\(562\) | 143.393i | 0.255147i | ||||||||
\(563\) | − | 166.070i | − | 0.294973i | −0.989064 | − | 0.147486i | \(-0.952882\pi\) | ||
0.989064 | − | 0.147486i | \(-0.0471182\pi\) | |||||||
\(564\) | 491.181 | 0.870888 | ||||||||
\(565\) | −298.871 | −0.528974 | ||||||||
\(566\) | 72.7504i | 0.128534i | ||||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | 269.603 | 0.474653 | ||||||||
\(569\) | 107.590i | 0.189086i | 0.995521 | + | 0.0945428i | \(0.0301389\pi\) | ||||
−0.995521 | + | 0.0945428i | \(0.969861\pi\) | |||||||
\(570\) | −6.46396 | −0.0113403 | ||||||||
\(571\) | − | 620.345i | − | 1.08642i | −0.839597 | − | 0.543210i | \(-0.817209\pi\) | ||
0.839597 | − | 0.543210i | \(-0.182791\pi\) | |||||||
\(572\) | − | 159.311i | − | 0.278517i | ||||||
\(573\) | 423.140i | 0.738465i | ||||||||
\(574\) | 16.6145i | 0.0289452i | ||||||||
\(575\) | −414.304 | + | 199.392i | −0.720529 | + | 0.346768i | ||||
\(576\) | −166.654 | −0.289329 | ||||||||
\(577\) | −439.039 | −0.760900 | −0.380450 | − | 0.924802i | \(-0.624231\pi\) | ||||
−0.380450 | + | 0.924802i | \(0.624231\pi\) | |||||||
\(578\) | −109.872 | −0.190090 | ||||||||
\(579\) | 430.638 | 0.743761 | ||||||||
\(580\) | − | 287.499i | − | 0.495688i | ||||||
\(581\) | −116.998 | −0.201374 | ||||||||
\(582\) | 30.7402i | 0.0528182i | ||||||||
\(583\) | 1295.51 | 2.22215 | ||||||||
\(584\) | −103.464 | −0.177165 | ||||||||
\(585\) | 15.4132i | 0.0263474i | ||||||||
\(586\) | − | 57.2543i | − | 0.0977035i | ||||||
\(587\) | −295.927 | −0.504134 | −0.252067 | − | 0.967710i | \(-0.581110\pi\) | ||||
−0.252067 | + | 0.967710i | \(0.581110\pi\) | |||||||
\(588\) | −47.4102 | −0.0806295 | ||||||||
\(589\) | − | 299.659i | − | 0.508758i | ||||||
\(590\) | − | 28.6328i | − | 0.0485302i | ||||||
\(591\) | 55.6899 | 0.0942300 | ||||||||
\(592\) | 170.304i | 0.287675i | ||||||||
\(593\) | 981.889 | 1.65580 | 0.827900 | − | 0.560876i | \(-0.189535\pi\) | ||||
0.827900 | + | 0.560876i | \(0.189535\pi\) | |||||||
\(594\) | 27.6164i | 0.0464923i | ||||||||
\(595\) | − | 151.654i | − | 0.254881i | ||||||
\(596\) | − | 126.995i | − | 0.213078i | ||||||
\(597\) | 49.6234i | 0.0831213i | ||||||||
\(598\) | 14.2468 | − | 6.85652i | 0.0238240 | − | 0.0114657i | ||||
\(599\) | 491.151 | 0.819952 | 0.409976 | − | 0.912096i | \(-0.365537\pi\) | ||||
0.409976 | + | 0.912096i | \(0.365537\pi\) | |||||||
\(600\) | 82.0207 | 0.136701 | ||||||||
\(601\) | −1122.37 | −1.86751 | −0.933753 | − | 0.357918i | \(-0.883487\pi\) | ||||
−0.933753 | + | 0.357918i | \(0.883487\pi\) | |||||||
\(602\) | 41.8950 | 0.0695930 | ||||||||
\(603\) | 21.6300i | 0.0358706i | ||||||||
\(604\) | 414.403 | 0.686098 | ||||||||
\(605\) | 434.169i | 0.717635i | ||||||||
\(606\) | −15.1488 | −0.0249980 | ||||||||
\(607\) | 237.456 | 0.391196 | 0.195598 | − | 0.980684i | \(-0.437335\pi\) | ||||
0.195598 | + | 0.980684i | \(0.437335\pi\) | |||||||
\(608\) | 77.6586i | 0.127728i | ||||||||
\(609\) | − | 150.539i | − | 0.247190i | ||||||
\(610\) | 65.8352 | 0.107927 | ||||||||
\(611\) | −166.478 | −0.272467 | ||||||||
\(612\) | − | 300.437i | − | 0.490910i | ||||||
\(613\) | − | 687.849i | − | 1.12210i | −0.827781 | − | 0.561051i | \(-0.810397\pi\) | ||
0.827781 | − | 0.561051i | \(-0.189603\pi\) | |||||||
\(614\) | 35.1531 | 0.0572525 | ||||||||
\(615\) | − | 81.2918i | − | 0.132182i | ||||||
\(616\) | 111.232 | 0.180571 | ||||||||
\(617\) | − | 792.532i | − | 1.28449i | −0.766499 | − | 0.642246i | \(-0.778003\pi\) | ||
0.766499 | − | 0.642246i | \(-0.221997\pi\) | |||||||
\(618\) | − | 82.3182i | − | 0.133201i | ||||||
\(619\) | − | 152.411i | − | 0.246222i | −0.992393 | − | 0.123111i | \(-0.960713\pi\) | ||
0.992393 | − | 0.123111i | \(-0.0392871\pi\) | |||||||
\(620\) | − | 470.988i | − | 0.759659i | ||||||
\(621\) | 107.689 | − | 51.8274i | 0.173412 | − | 0.0834579i | ||||
\(622\) | 89.7569 | 0.144304 | ||||||||
\(623\) | −57.1243 | −0.0916924 | ||||||||
\(624\) | 59.3696 | 0.0951436 | ||||||||
\(625\) | 274.400 | 0.439041 | ||||||||
\(626\) | 62.2258i | 0.0994023i | ||||||||
\(627\) | −171.168 | −0.272995 | ||||||||
\(628\) | − | 919.537i | − | 1.46423i | ||||||
\(629\) | −292.097 | −0.464384 | ||||||||
\(630\) | −5.31979 | −0.00844411 | ||||||||
\(631\) | 111.205i | 0.176236i | 0.996110 | + | 0.0881181i | \(0.0280853\pi\) | ||||
−0.996110 | + | 0.0881181i | \(0.971915\pi\) | |||||||
\(632\) | 56.9201i | 0.0900634i | ||||||||
\(633\) | −323.320 | −0.510774 | ||||||||
\(634\) | −63.2321 | −0.0997352 | ||||||||
\(635\) | 118.194i | 0.186132i | ||||||||
\(636\) | 494.389i | 0.777341i | ||||||||
\(637\) | 16.0689 | 0.0252259 | ||||||||
\(638\) | 174.592i | 0.273655i | ||||||||
\(639\) | −341.439 | −0.534333 | ||||||||
\(640\) | 162.091i | 0.253268i | ||||||||
\(641\) | 576.346i | 0.899135i | 0.893246 | + | 0.449568i | \(0.148422\pi\) | ||||
−0.893246 | + | 0.449568i | \(0.851578\pi\) | |||||||
\(642\) | 62.7004i | 0.0976642i | ||||||||
\(643\) | − | 201.552i | − | 0.313456i | −0.987642 | − | 0.156728i | \(-0.949905\pi\) | ||
0.987642 | − | 0.156728i | \(-0.0500947\pi\) | |||||||
\(644\) | −103.190 | − | 214.413i | −0.160233 | − | 0.332940i | ||||
\(645\) | −204.984 | −0.317805 | ||||||||
\(646\) | −42.7044 | −0.0661058 | ||||||||
\(647\) | 438.725 | 0.678091 | 0.339046 | − | 0.940770i | \(-0.389896\pi\) | ||||
0.339046 | + | 0.940770i | \(0.389896\pi\) | |||||||
\(648\) | −21.3194 | −0.0329004 | ||||||||
\(649\) | − | 758.206i | − | 1.16827i | ||||||
\(650\) | −13.7422 | −0.0211418 | ||||||||
\(651\) | − | 246.616i | − | 0.378827i | ||||||
\(652\) | −300.388 | −0.460718 | ||||||||
\(653\) | 502.740 | 0.769893 | 0.384946 | − | 0.922939i | \(-0.374220\pi\) | ||||
0.384946 | + | 0.922939i | \(0.374220\pi\) | |||||||
\(654\) | − | 54.9305i | − | 0.0839916i | ||||||
\(655\) | − | 309.075i | − | 0.471870i | ||||||
\(656\) | −313.124 | −0.477323 | ||||||||
\(657\) | 131.033 | 0.199441 | ||||||||
\(658\) | − | 57.4587i | − | 0.0873233i | ||||||
\(659\) | − | 856.448i | − | 1.29962i | −0.760097 | − | 0.649809i | \(-0.774849\pi\) | ||
0.760097 | − | 0.649809i | \(-0.225151\pi\) | |||||||
\(660\) | −269.033 | −0.407625 | ||||||||
\(661\) | 167.376i | 0.253216i | 0.991953 | + | 0.126608i | \(0.0404091\pi\) | ||||
−0.991953 | + | 0.126608i | \(0.959591\pi\) | |||||||
\(662\) | −152.401 | −0.230214 | ||||||||
\(663\) | 101.828i | 0.153587i | ||||||||
\(664\) | 104.752i | 0.157760i | ||||||||
\(665\) | − | 32.9723i | − | 0.0495823i | ||||||
\(666\) | 10.2463i | 0.0153849i | ||||||||
\(667\) | 680.813 | − | 327.654i | 1.02071 | − | 0.491235i | ||||
\(668\) | −595.025 | −0.890755 | ||||||||
\(669\) | 420.477 | 0.628516 | ||||||||
\(670\) | 4.83236 | 0.00721247 | ||||||||
\(671\) | 1743.33 | 2.59811 | ||||||||
\(672\) | 63.9123i | 0.0951076i | ||||||||
\(673\) | −319.026 | −0.474036 | −0.237018 | − | 0.971505i | \(-0.576170\pi\) | ||||
−0.237018 | + | 0.971505i | \(0.576170\pi\) | |||||||
\(674\) | − | 193.472i | − | 0.287050i | ||||||
\(675\) | −103.875 | −0.153889 | ||||||||
\(676\) | 640.239 | 0.947099 | ||||||||
\(677\) | 808.515i | 1.19426i | 0.802144 | + | 0.597131i | \(0.203693\pi\) | ||||
−0.802144 | + | 0.597131i | \(0.796307\pi\) | |||||||
\(678\) | 69.2624i | 0.102157i | ||||||||
\(679\) | −156.804 | −0.230933 | ||||||||
\(680\) | −135.781 | −0.199677 | ||||||||
\(681\) | − | 165.396i | − | 0.242873i | ||||||
\(682\) | 286.021i | 0.419385i | ||||||||
\(683\) | −376.090 | −0.550644 | −0.275322 | − | 0.961352i | \(-0.588784\pi\) | ||||
−0.275322 | + | 0.961352i | \(0.588784\pi\) | |||||||
\(684\) | − | 65.3203i | − | 0.0954975i | ||||||
\(685\) | −190.178 | −0.277632 | ||||||||
\(686\) | 5.54608i | 0.00808466i | ||||||||
\(687\) | 222.783i | 0.324284i | ||||||||
\(688\) | 789.569i | 1.14763i | ||||||||
\(689\) | − | 167.565i | − | 0.243200i | ||||||
\(690\) | −11.5788 | − | 24.0588i | −0.0167808 | − | 0.0348678i | ||||
\(691\) | 7.98529 | 0.0115561 | 0.00577807 | − | 0.999983i | \(-0.498161\pi\) | ||||
0.00577807 | + | 0.999983i | \(0.498161\pi\) | |||||||
\(692\) | 711.949 | 1.02883 | ||||||||
\(693\) | −140.869 | −0.203275 | ||||||||
\(694\) | −123.521 | −0.177984 | ||||||||
\(695\) | 543.409i | 0.781883i | ||||||||
\(696\) | −134.782 | −0.193652 | ||||||||
\(697\) | − | 537.057i | − | 0.770526i | ||||||
\(698\) | −123.292 | −0.176637 | ||||||||
\(699\) | 648.146 | 0.927247 | ||||||||
\(700\) | 206.819i | 0.295456i | ||||||||
\(701\) | − | 973.059i | − | 1.38810i | −0.719926 | − | 0.694050i | \(-0.755825\pi\) | ||
0.719926 | − | 0.694050i | \(-0.244175\pi\) | |||||||
\(702\) | 3.57197 | 0.00508828 | ||||||||
\(703\) | −63.5072 | −0.0903374 | ||||||||
\(704\) | 985.916i | 1.40045i | ||||||||
\(705\) | 281.134i | 0.398772i | ||||||||
\(706\) | −35.8425 | −0.0507684 | ||||||||
\(707\) | − | 77.2729i | − | 0.109297i | ||||||
\(708\) | 289.344 | 0.408677 | ||||||||
\(709\) | 872.985i | 1.23129i | 0.788023 | + | 0.615645i | \(0.211105\pi\) | ||||
−0.788023 | + | 0.615645i | \(0.788895\pi\) | |||||||
\(710\) | 76.2809i | 0.107438i | ||||||||
\(711\) | − | 72.0864i | − | 0.101387i | ||||||
\(712\) | 51.1452i | 0.0718332i | ||||||||
\(713\) | 1115.33 | − | 536.771i | 1.56427 | − | 0.752835i | ||||
\(714\) | −35.1453 | −0.0492232 | ||||||||
\(715\) | 91.1842 | 0.127530 | ||||||||
\(716\) | −696.934 | −0.973372 | ||||||||
\(717\) | 368.295 | 0.513662 | ||||||||
\(718\) | 95.3535i | 0.132804i | ||||||||
\(719\) | −403.760 | −0.561558 | −0.280779 | − | 0.959772i | \(-0.590593\pi\) | ||||
−0.280779 | + | 0.959772i | \(0.590593\pi\) | |||||||
\(720\) | − | 100.259i | − | 0.139248i | ||||||
\(721\) | 419.900 | 0.582385 | ||||||||
\(722\) | 98.8204 | 0.136870 | ||||||||
\(723\) | 384.429i | 0.531714i | ||||||||
\(724\) | − | 1238.17i | − | 1.71017i | ||||||
\(725\) | −656.701 | −0.905795 | ||||||||
\(726\) | 100.617 | 0.138591 | ||||||||
\(727\) | − | 631.483i | − | 0.868615i | −0.900765 | − | 0.434308i | \(-0.856993\pi\) | ||
0.900765 | − | 0.434308i | \(-0.143007\pi\) | |||||||
\(728\) | − | 14.3870i | − | 0.0197623i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 29.2740i | − | 0.0401014i | ||||||
\(731\) | −1354.23 | −1.85258 | ||||||||
\(732\) | 665.284i | 0.908858i | ||||||||
\(733\) | 1425.23i | 1.94437i | 0.234205 | + | 0.972187i | \(0.424751\pi\) | ||||
−0.234205 | + | 0.972187i | \(0.575249\pi\) | |||||||
\(734\) | − | 152.528i | − | 0.207804i | ||||||
\(735\) | − | 27.1359i | − | 0.0369196i | ||||||
\(736\) | −289.044 | + | 139.108i | −0.392723 | + | 0.189005i | ||||
\(737\) | 127.962 | 0.173626 | ||||||||
\(738\) | −18.8391 | −0.0255273 | ||||||||
\(739\) | −732.694 | −0.991467 | −0.495734 | − | 0.868475i | \(-0.665101\pi\) | ||||
−0.495734 | + | 0.868475i | \(0.665101\pi\) | |||||||
\(740\) | −99.8174 | −0.134888 | ||||||||
\(741\) | 22.1392i | 0.0298775i | ||||||||
\(742\) | 57.8340 | 0.0779434 | ||||||||
\(743\) | − | 257.702i | − | 0.346840i | −0.984848 | − | 0.173420i | \(-0.944518\pi\) | ||
0.984848 | − | 0.173420i | \(-0.0554819\pi\) | |||||||
\(744\) | −220.804 | −0.296779 | ||||||||
\(745\) | 72.6872 | 0.0975667 | ||||||||
\(746\) | 73.7079i | 0.0988042i | ||||||||
\(747\) | − | 132.664i | − | 0.177595i | ||||||
\(748\) | −1777.37 | −2.37617 | ||||||||
\(749\) | −319.831 | −0.427010 | ||||||||
\(750\) | 52.2286i | 0.0696381i | ||||||||
\(751\) | 685.728i | 0.913087i | 0.889701 | + | 0.456543i | \(0.150913\pi\) | ||||
−0.889701 | + | 0.456543i | \(0.849087\pi\) | |||||||
\(752\) | 1082.89 | 1.44001 | ||||||||
\(753\) | − | 292.863i | − | 0.388928i | ||||||
\(754\) | 22.5821 | 0.0299498 | ||||||||
\(755\) | 237.190i | 0.314158i | ||||||||
\(756\) | − | 53.7581i | − | 0.0711085i | ||||||
\(757\) | − | 1062.28i | − | 1.40328i | −0.712532 | − | 0.701639i | \(-0.752452\pi\) | ||
0.712532 | − | 0.701639i | \(-0.247548\pi\) | |||||||
\(758\) | − | 41.3145i | − | 0.0545046i | ||||||
\(759\) | −306.609 | − | 637.084i | −0.403964 | − | 0.839373i | ||||
\(760\) | −29.5211 | −0.0388436 | ||||||||
\(761\) | −204.509 | −0.268737 | −0.134369 | − | 0.990931i | \(-0.542901\pi\) | ||||
−0.134369 | + | 0.990931i | \(0.542901\pi\) | |||||||
\(762\) | 27.3910 | 0.0359462 | ||||||||
\(763\) | 280.197 | 0.367230 | ||||||||
\(764\) | 955.293i | 1.25038i | ||||||||
\(765\) | 171.959 | 0.224783 | ||||||||
\(766\) | − | 206.276i | − | 0.269290i | ||||||
\(767\) | −98.0682 | −0.127859 | ||||||||
\(768\) | −347.306 | −0.452221 | ||||||||
\(769\) | 1204.50i | 1.56633i | 0.621816 | + | 0.783163i | \(0.286395\pi\) | ||||
−0.621816 | + | 0.783163i | \(0.713605\pi\) | |||||||
\(770\) | 31.4717i | 0.0408723i | ||||||||
\(771\) | 98.3094 | 0.127509 | ||||||||
\(772\) | 972.219 | 1.25935 | ||||||||
\(773\) | 1319.49i | 1.70697i | 0.521116 | + | 0.853486i | \(0.325516\pi\) | ||||
−0.521116 | + | 0.853486i | \(0.674484\pi\) | |||||||
\(774\) | 47.5044i | 0.0613752i | ||||||||
\(775\) | −1075.83 | −1.38816 | ||||||||
\(776\) | 140.391i | 0.180917i | ||||||||
\(777\) | −52.2659 | −0.0672662 | ||||||||
\(778\) | − | 121.261i | − | 0.155863i | ||||||
\(779\) | − | 116.766i | − | 0.149892i | ||||||
\(780\) | 34.7974i | 0.0446120i | ||||||||
\(781\) | 2019.94i | 2.58635i | ||||||||
\(782\) | −76.4954 | − | 158.945i | −0.0978202 | − | 0.203255i | ||||
\(783\) | 170.695 | 0.218001 | ||||||||
\(784\) | −104.523 | −0.133321 | ||||||||
\(785\) | 526.310 | 0.670459 | ||||||||
\(786\) | −71.6271 | −0.0911287 | ||||||||
\(787\) | 1351.01i | 1.71666i | 0.513098 | + | 0.858330i | \(0.328498\pi\) | ||||
−0.513098 | + | 0.858330i | \(0.671502\pi\) | |||||||
\(788\) | 125.727 | 0.159552 | ||||||||
\(789\) | − | 90.0590i | − | 0.114143i | ||||||
\(790\) | −16.1048 | −0.0203859 | ||||||||
\(791\) | −353.303 | −0.446653 | ||||||||
\(792\) | 126.125i | 0.159249i | ||||||||
\(793\) | − | 225.487i | − | 0.284347i | ||||||
\(794\) | 235.249 | 0.296283 | ||||||||
\(795\) | −282.971 | −0.355938 | ||||||||
\(796\) | 112.031i | 0.140743i | ||||||||
\(797\) | 284.911i | 0.357480i | 0.983896 | + | 0.178740i | \(0.0572020\pi\) | ||||
−0.983896 | + | 0.178740i | \(0.942798\pi\) | |||||||
\(798\) | −7.64122 | −0.00957546 | ||||||||
\(799\) | 1857.32i | 2.32456i | ||||||||
\(800\) | 278.808 | 0.348510 | ||||||||
\(801\) | − | 64.7729i | − | 0.0808651i | ||||||
\(802\) | 197.562i | 0.246337i | ||||||||
\(803\) | − | 775.184i | − | 0.965360i | ||||||
\(804\) | 48.8324i | 0.0607368i | ||||||||
\(805\) | 122.722 | − | 59.0624i | 0.152450 | − | 0.0733695i | ||||
\(806\) | 36.9946 | 0.0458991 | ||||||||
\(807\) | 1.06866 | 0.00132424 | ||||||||
\(808\) | −69.1849 | −0.0856249 | ||||||||
\(809\) | −1363.76 | −1.68574 | −0.842870 | − | 0.538118i | \(-0.819136\pi\) | ||||
−0.842870 | + | 0.538118i | \(0.819136\pi\) | |||||||
\(810\) | − | 6.03207i | − | 0.00744700i | ||||||
\(811\) | −1133.87 | −1.39811 | −0.699055 | − | 0.715068i | \(-0.746396\pi\) | ||||
−0.699055 | + | 0.715068i | \(0.746396\pi\) | |||||||
\(812\) | − | 339.860i | − | 0.418547i | ||||||
\(813\) | −391.110 | −0.481070 | ||||||||
\(814\) | 60.6169 | 0.0744679 | ||||||||
\(815\) | − | 171.931i | − | 0.210959i | ||||||
\(816\) | − | 662.363i | − | 0.811719i | ||||||
\(817\) | −294.434 | −0.360385 | ||||||||
\(818\) | −33.4283 | −0.0408659 | ||||||||
\(819\) | 18.2204i | 0.0222471i | ||||||||
\(820\) | − | 183.526i | − | 0.223813i | ||||||
\(821\) | −496.142 | −0.604314 | −0.302157 | − | 0.953258i | \(-0.597707\pi\) | ||||
−0.302157 | + | 0.953258i | \(0.597707\pi\) | |||||||
\(822\) | 44.0732i | 0.0536170i | ||||||||
\(823\) | −915.395 | −1.11227 | −0.556133 | − | 0.831093i | \(-0.687716\pi\) | ||||
−0.556133 | + | 0.831093i | \(0.687716\pi\) | |||||||
\(824\) | − | 375.949i | − | 0.456249i | ||||||
\(825\) | 614.521i | 0.744874i | ||||||||
\(826\) | − | 33.8476i | − | 0.0409778i | ||||||
\(827\) | − | 610.884i | − | 0.738675i | −0.929295 | − | 0.369337i | \(-0.879585\pi\) | ||
0.929295 | − | 0.369337i | \(-0.120415\pi\) | |||||||
\(828\) | 243.122 | − | 117.007i | 0.293625 | − | 0.141313i | ||||
\(829\) | 677.701 | 0.817493 | 0.408746 | − | 0.912648i | \(-0.365966\pi\) | ||||
0.408746 | + | 0.912648i | \(0.365966\pi\) | |||||||
\(830\) | −29.6384 | −0.0357090 | ||||||||
\(831\) | 836.971 | 1.00718 | ||||||||
\(832\) | 127.521 | 0.153270 | ||||||||
\(833\) | − | 179.274i | − | 0.215215i | ||||||
\(834\) | 125.933 | 0.150999 | ||||||||
\(835\) | − | 340.571i | − | 0.407869i | ||||||
\(836\) | −386.432 | −0.462240 | ||||||||
\(837\) | 279.637 | 0.334094 | ||||||||
\(838\) | − | 102.736i | − | 0.122597i | ||||||
\(839\) | 556.507i | 0.663298i | 0.943403 | + | 0.331649i | \(0.107605\pi\) | ||||
−0.943403 | + | 0.331649i | \(0.892395\pi\) | |||||||
\(840\) | −24.2956 | −0.0289234 | ||||||||
\(841\) | 238.137 | 0.283159 | ||||||||
\(842\) | 235.644i | 0.279863i | ||||||||
\(843\) | − | 829.372i | − | 0.983834i | ||||||
\(844\) | −729.936 | −0.864853 | ||||||||
\(845\) | 366.450i | 0.433669i | ||||||||
\(846\) | 65.1521 | 0.0770119 | ||||||||
\(847\) | 513.242i | 0.605953i | ||||||||
\(848\) | 1089.96i | 1.28533i | ||||||||
\(849\) | − | 420.782i | − | 0.495621i | ||||||
\(850\) | 153.316i | 0.180372i | ||||||||
\(851\) | −113.759 | − | 236.373i | −0.133677 | − | 0.277759i | ||||
\(852\) | −770.842 | −0.904744 | ||||||||
\(853\) | 247.618 | 0.290291 | 0.145145 | − | 0.989410i | \(-0.453635\pi\) | ||||
0.145145 | + | 0.989410i | \(0.453635\pi\) | |||||||
\(854\) | 77.8255 | 0.0911305 | ||||||||
\(855\) | 37.3870 | 0.0437275 | ||||||||
\(856\) | 286.355i | 0.334526i | ||||||||
\(857\) | −820.438 | −0.957337 | −0.478668 | − | 0.877996i | \(-0.658880\pi\) | ||||
−0.478668 | + | 0.877996i | \(0.658880\pi\) | |||||||
\(858\) | − | 21.1317i | − | 0.0246290i | ||||||
\(859\) | 1109.91 | 1.29210 | 0.646048 | − | 0.763297i | \(-0.276421\pi\) | ||||
0.646048 | + | 0.763297i | \(0.276421\pi\) | |||||||
\(860\) | −462.777 | −0.538113 | ||||||||
\(861\) | − | 96.0971i | − | 0.111611i | ||||||
\(862\) | 10.1495i | 0.0117743i | ||||||||
\(863\) | 1032.56 | 1.19648 | 0.598239 | − | 0.801318i | \(-0.295868\pi\) | ||||
0.598239 | + | 0.801318i | \(0.295868\pi\) | |||||||
\(864\) | −72.4698 | −0.0838771 | ||||||||
\(865\) | 407.494i | 0.471091i | ||||||||
\(866\) | 253.860i | 0.293141i | ||||||||
\(867\) | 635.492 | 0.732978 | ||||||||
\(868\) | − | 556.768i | − | 0.641437i | ||||||
\(869\) | −426.461 | −0.490749 | ||||||||
\(870\) | − | 38.1349i | − | 0.0438332i | ||||||
\(871\) | − | 16.5509i | − | 0.0190022i | ||||||
\(872\) | − | 250.869i | − | 0.287694i | ||||||
\(873\) | − | 177.799i | − | 0.203664i | ||||||
\(874\) | −16.6315 | − | 34.5575i | −0.0190291 | − | 0.0395395i | ||||
\(875\) | −266.414 | −0.304474 | ||||||||
\(876\) | 295.823 | 0.337697 | ||||||||
\(877\) | 625.292 | 0.712990 | 0.356495 | − | 0.934297i | \(-0.383972\pi\) | ||||
0.356495 | + | 0.934297i | \(0.383972\pi\) | |||||||
\(878\) | 125.561 | 0.143008 | ||||||||
\(879\) | 331.154i | 0.376739i | ||||||||
\(880\) | −593.127 | −0.674008 | ||||||||
\(881\) | − | 408.171i | − | 0.463304i | −0.972799 | − | 0.231652i | \(-0.925587\pi\) | ||
0.972799 | − | 0.231652i | \(-0.0744131\pi\) | |||||||
\(882\) | −6.28866 | −0.00713000 | ||||||||
\(883\) | −657.599 | −0.744733 | −0.372366 | − | 0.928086i | \(-0.621453\pi\) | ||||
−0.372366 | + | 0.928086i | \(0.621453\pi\) | |||||||
\(884\) | 229.890i | 0.260056i | ||||||||
\(885\) | 165.610i | 0.187130i | ||||||||
\(886\) | −195.492 | −0.220646 | ||||||||
\(887\) | 179.854 | 0.202767 | 0.101383 | − | 0.994847i | \(-0.467673\pi\) | ||||
0.101383 | + | 0.994847i | \(0.467673\pi\) | |||||||
\(888\) | 46.7953i | 0.0526974i | ||||||||
\(889\) | 139.720i | 0.157165i | ||||||||
\(890\) | −14.4709 | −0.0162595 | ||||||||
\(891\) | − | 159.731i | − | 0.179272i | ||||||
\(892\) | 949.280 | 1.06422 | ||||||||
\(893\) | 403.815i | 0.452200i | ||||||||
\(894\) | − | 16.8450i | − | 0.0188423i | ||||||
\(895\) | − | 398.900i | − | 0.445699i | ||||||
\(896\) | 191.612i | 0.213853i | ||||||||
\(897\) | −82.4020 | + | 39.6575i | −0.0918640 | + | 0.0442113i | ||||
\(898\) | 52.6812 | 0.0586651 | ||||||||
\(899\) | 1767.87 | 1.96649 | ||||||||
\(900\) | −234.511 | −0.260568 | ||||||||
\(901\) | −1869.45 | −2.07487 | ||||||||
\(902\) | 111.452i | 0.123560i | ||||||||
\(903\) | −242.317 | −0.268347 | ||||||||
\(904\) | 316.323i | 0.349915i | ||||||||
\(905\) | 708.682 | 0.783074 | ||||||||
\(906\) | 54.9680 | 0.0606710 | ||||||||
\(907\) | 54.2424i | 0.0598041i | 0.999553 | + | 0.0299021i | \(0.00951954\pi\) | ||||
−0.999553 | + | 0.0299021i | \(0.990480\pi\) | |||||||
\(908\) | − | 373.403i | − | 0.411237i | ||||||
\(909\) | 87.6193 | 0.0963909 | ||||||||
\(910\) | 4.07062 | 0.00447321 | ||||||||
\(911\) | 1273.20i | 1.39758i | 0.715326 | + | 0.698791i | \(0.246278\pi\) | ||||
−0.715326 | + | 0.698791i | \(0.753722\pi\) | |||||||
\(912\) | − | 144.009i | − | 0.157905i | ||||||
\(913\) | −784.834 | −0.859621 | ||||||||
\(914\) | − | 139.736i | − | 0.152884i | ||||||
\(915\) | −380.785 | −0.416159 | ||||||||
\(916\) | 502.962i | 0.549085i | ||||||||
\(917\) | − | 365.365i | − | 0.398435i | ||||||
\(918\) | − | 39.8511i | − | 0.0434107i | ||||||
\(919\) | 1646.87i | 1.79203i | 0.444026 | + | 0.896014i | \(0.353550\pi\) | ||||
−0.444026 | + | 0.896014i | \(0.646450\pi\) | |||||||
\(920\) | −52.8805 | − | 109.877i | −0.0574788 | − | 0.119432i | ||||
\(921\) | −203.322 | −0.220763 | ||||||||
\(922\) | −45.5425 | −0.0493953 | ||||||||
\(923\) | 261.264 | 0.283060 | ||||||||
\(924\) | −318.031 | −0.344189 | ||||||||
\(925\) | 228.002i | 0.246488i | ||||||||
\(926\) | −46.8863 | −0.0506331 | ||||||||
\(927\) | 476.121i | 0.513615i | ||||||||
\(928\) | −458.156 | −0.493702 | ||||||||
\(929\) | 630.405 | 0.678585 | 0.339292 | − | 0.940681i | \(-0.389812\pi\) | ||||
0.339292 | + | 0.940681i | \(0.389812\pi\) | |||||||
\(930\) | − | 62.4737i | − | 0.0671760i | ||||||
\(931\) | − | 38.9774i | − | 0.0418661i | ||||||
\(932\) | 1463.27 | 1.57003 | ||||||||
\(933\) | −519.146 | −0.556427 | ||||||||
\(934\) | − | 209.417i | − | 0.224215i | ||||||
\(935\) | − | 1017.30i | − | 1.08803i | ||||||
\(936\) | 16.3133 | 0.0174287 | ||||||||
\(937\) | 385.538i | 0.411460i | 0.978609 | + | 0.205730i | \(0.0659568\pi\) | ||||
−0.978609 | + | 0.205730i | \(0.934043\pi\) | |||||||
\(938\) | 5.71245 | 0.00609003 | ||||||||
\(939\) | − | 359.909i | − | 0.383289i | ||||||
\(940\) | 634.696i | 0.675209i | ||||||||
\(941\) | − | 1491.55i | − | 1.58507i | −0.609826 | − | 0.792535i | \(-0.708761\pi\) | ||
0.609826 | − | 0.792535i | \(-0.291239\pi\) | |||||||
\(942\) | − | 121.971i | − | 0.129481i | ||||||
\(943\) | 434.601 | − | 209.160i | 0.460870 | − | 0.221802i | ||||
\(944\) | 637.905 | 0.675747 | ||||||||
\(945\) | 30.7692 | 0.0325600 | ||||||||
\(946\) | 281.034 | 0.297077 | ||||||||
\(947\) | 437.003 | 0.461461 | 0.230730 | − | 0.973018i | \(-0.425888\pi\) | ||||
0.230730 | + | 0.973018i | \(0.425888\pi\) | |||||||
\(948\) | − | 162.744i | − | 0.171671i | ||||||
\(949\) | −100.264 | −0.105652 | ||||||||
\(950\) | 33.3336i | 0.0350880i | ||||||||
\(951\) | 365.729 | 0.384573 | ||||||||
\(952\) | −160.510 | −0.168603 | ||||||||
\(953\) | − | 1100.00i | − | 1.15425i | −0.816656 | − | 0.577124i | \(-0.804175\pi\) | ||
0.816656 | − | 0.577124i | \(-0.195825\pi\) | |||||||
\(954\) | 65.5776i | 0.0687396i | ||||||||
\(955\) | −546.775 | −0.572540 | ||||||||
\(956\) | 831.473 | 0.869742 | ||||||||
\(957\) | − | 1009.82i | − | 1.05520i | ||||||
\(958\) | − | 106.652i | − | 0.111328i | ||||||
\(959\) | −224.814 | −0.234426 | ||||||||
\(960\) | − | 215.347i | − | 0.224320i | ||||||
\(961\) | 1935.17 | 2.01371 | ||||||||
\(962\) | − | 7.84034i | − | 0.00815004i | ||||||
\(963\) | − | 362.654i | − | 0.376588i | ||||||
\(964\) | 867.898i | 0.900309i | ||||||||
\(965\) | 556.463i | 0.576646i | ||||||||
\(966\) | −13.6875 | − | 28.4405i | −0.0141693 | − | 0.0294416i | ||||
\(967\) | 1353.43 | 1.39961 | 0.699807 | − | 0.714332i | \(-0.253270\pi\) | ||||
0.699807 | + | 0.714332i | \(0.253270\pi\) | |||||||
\(968\) | 459.522 | 0.474713 | ||||||||
\(969\) | 246.998 | 0.254900 | ||||||||
\(970\) | −39.7220 | −0.0409505 | ||||||||
\(971\) | 578.234i | 0.595504i | 0.954643 | + | 0.297752i | \(0.0962369\pi\) | ||||
−0.954643 | + | 0.297752i | \(0.903763\pi\) | |||||||
\(972\) | 60.9559 | 0.0627118 | ||||||||
\(973\) | 642.378i | 0.660203i | ||||||||
\(974\) | 58.0974 | 0.0596483 | ||||||||
\(975\) | 79.4837 | 0.0815217 | ||||||||
\(976\) | 1466.73i | 1.50280i | ||||||||
\(977\) | − | 1117.15i | − | 1.14345i | −0.820446 | − | 0.571725i | \(-0.806275\pi\) | ||
0.820446 | − | 0.571725i | \(-0.193725\pi\) | |||||||
\(978\) | −39.8446 | −0.0407409 | ||||||||
\(979\) | −383.194 | −0.391414 | ||||||||
\(980\) | − | 61.2627i | − | 0.0625129i | ||||||
\(981\) | 317.713i | 0.323867i | ||||||||
\(982\) | −131.305 | −0.133711 | ||||||||
\(983\) | − | 179.686i | − | 0.182793i | −0.995815 | − | 0.0913966i | \(-0.970867\pi\) | ||
0.995815 | − | 0.0913966i | \(-0.0291331\pi\) | |||||||
\(984\) | −86.0388 | −0.0874378 | ||||||||
\(985\) | 71.9617i | 0.0730576i | ||||||||
\(986\) | − | 251.940i | − | 0.255517i | ||||||
\(987\) | 332.336i | 0.336714i | ||||||||
\(988\) | 49.9821i | 0.0505892i | ||||||||
\(989\) | −527.413 | − | 1095.88i | −0.533280 | − | 1.10807i | ||||
\(990\) | −35.6855 | −0.0360460 | ||||||||
\(991\) | −1275.15 | −1.28673 | −0.643367 | − | 0.765558i | \(-0.722463\pi\) | ||||
−0.643367 | + | 0.765558i | \(0.722463\pi\) | |||||||
\(992\) | −750.563 | −0.756616 | ||||||||
\(993\) | 881.477 | 0.887690 | ||||||||
\(994\) | 90.1737i | 0.0907180i | ||||||||
\(995\) | −64.1226 | −0.0644448 | ||||||||
\(996\) | − | 299.505i | − | 0.300708i | ||||||
\(997\) | −965.297 | −0.968201 | −0.484101 | − | 0.875012i | \(-0.660853\pi\) | ||||
−0.484101 | + | 0.875012i | \(0.660853\pi\) | |||||||
\(998\) | −23.5065 | −0.0235536 | ||||||||
\(999\) | − | 59.2639i | − | 0.0593232i |
(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 | 483.3.f.a.22.25 | ✓ | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.26 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.25 | ✓ | 48 | 1.1 | even | 1 | trivial | |
483.3.f.a.22.26 | yes | 48 | 23.22 | odd | 2 | inner |