Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (of order \(12\), degree \(4\), not 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 227.3 | ||
Character | \(\chi\) | \(=\) | 784.227 |
Dual form | 784.2.w.e.411.3 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.613848 | − | 1.27404i | 0.434056 | − | 0.900886i | ||||
\(3\) | −2.05749 | + | 0.551303i | −1.18789 | + | 0.318295i | −0.798053 | − | 0.602587i | \(-0.794137\pi\) |
−0.389841 | + | 0.920882i | \(0.627470\pi\) | |||||||
\(4\) | −1.24638 | − | 1.56414i | −0.623190 | − | 0.782070i | ||||
\(5\) | −0.929901 | + | 3.47044i | −0.415864 | + | 1.55203i | 0.367233 | + | 0.930129i | \(0.380305\pi\) |
−0.783098 | + | 0.621898i | \(0.786362\pi\) | |||||||
\(6\) | −0.560603 | + | 2.95975i | −0.228865 | + | 1.20831i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.75787 | + | 0.627801i | −0.975056 | + | 0.221961i | ||||
\(9\) | 1.33126 | − | 0.768605i | 0.443754 | − | 0.256202i | ||||
\(10\) | 3.85068 | + | 3.31506i | 1.21769 | + | 1.04831i | ||||
\(11\) | 2.73205 | − | 0.732051i | 0.823744 | − | 0.220722i | 0.177762 | − | 0.984074i | \(-0.443114\pi\) |
0.645983 | + | 0.763352i | \(0.276448\pi\) | |||||||
\(12\) | 3.42674 | + | 2.53107i | 0.989213 | + | 0.730658i | ||||
\(13\) | 1.17573 | − | 1.17573i | 0.326090 | − | 0.326090i | −0.525008 | − | 0.851098i | \(-0.675938\pi\) |
0.851098 | + | 0.525008i | \(0.175938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.65306i | − | 1.97601i | ||||||
\(16\) | −0.893069 | + | 3.89903i | −0.223267 | + | 0.974757i | ||||
\(17\) | −5.31204 | − | 3.06691i | −1.28836 | − | 0.743834i | −0.309997 | − | 0.950737i | \(-0.600328\pi\) |
−0.978361 | + | 0.206903i | \(0.933661\pi\) | |||||||
\(18\) | −0.162044 | − | 2.16790i | −0.0381942 | − | 0.510978i | ||||
\(19\) | 0.358639 | − | 1.33846i | 0.0822774 | − | 0.307063i | −0.912507 | − | 0.409060i | \(-0.865857\pi\) |
0.994785 | + | 0.101997i | \(0.0325232\pi\) | |||||||
\(20\) | 6.58726 | − | 2.87099i | 1.47296 | − | 0.641973i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.744399 | − | 3.93012i | 0.158706 | − | 0.837905i | ||||
\(23\) | −0.103594 | − | 0.179430i | −0.0216009 | − | 0.0374138i | 0.855023 | − | 0.518590i | \(-0.173543\pi\) |
−0.876624 | + | 0.481176i | \(0.840210\pi\) | |||||||
\(24\) | 5.32820 | − | 2.81212i | 1.08761 | − | 0.574022i | ||||
\(25\) | −6.84910 | − | 3.95433i | −1.36982 | − | 0.790866i | ||||
\(26\) | −0.776216 | − | 2.21966i | −0.152228 | − | 0.435311i | ||||
\(27\) | 2.20324 | − | 2.20324i | 0.424013 | − | 0.424013i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46733 | − | 3.46733i | −0.643868 | − | 0.643868i | 0.307636 | − | 0.951504i | \(-0.400462\pi\) |
−0.951504 | + | 0.307636i | \(0.900462\pi\) | |||||||
\(30\) | −9.75034 | − | 4.69782i | −1.78016 | − | 0.857700i | ||||
\(31\) | 2.87099 | − | 4.97270i | 0.515645 | − | 0.893124i | −0.484190 | − | 0.874963i | \(-0.660886\pi\) |
0.999835 | − | 0.0181610i | \(-0.00578115\pi\) | |||||||
\(32\) | 4.41933 | + | 3.53122i | 0.781234 | + | 0.624238i | ||||
\(33\) | −5.21759 | + | 3.01238i | −0.908266 | + | 0.524388i | ||||
\(34\) | −7.16816 | + | 4.88516i | −1.22933 | + | 0.837798i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.86147 | − | 1.12431i | −0.476911 | − | 0.187385i | ||||
\(37\) | 0.349158 | + | 0.0935566i | 0.0574012 | + | 0.0153806i | 0.287405 | − | 0.957809i | \(-0.407207\pi\) |
−0.230004 | + | 0.973190i | \(0.573874\pi\) | |||||||
\(38\) | −1.48511 | − | 1.27853i | −0.240916 | − | 0.207405i | ||||
\(39\) | −1.77088 | + | 3.06725i | −0.283567 | + | 0.491153i | ||||
\(40\) | 0.385806 | − | 10.1548i | 0.0610013 | − | 1.60562i | ||||
\(41\) | −6.75794 | −1.05541 | −0.527707 | − | 0.849427i | \(-0.676948\pi\) | ||||
−0.527707 | + | 0.849427i | \(0.676948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.207188 | + | 0.207188i | 0.0315959 | + | 0.0315959i | 0.722728 | − | 0.691132i | \(-0.242888\pi\) |
−0.691132 | + | 0.722728i | \(0.742888\pi\) | |||||||
\(44\) | −4.55021 | − | 3.36090i | −0.685969 | − | 0.506674i | ||||
\(45\) | 1.42945 | + | 5.33479i | 0.213090 | + | 0.795264i | ||||
\(46\) | −0.292193 | + | 0.0218406i | −0.0430815 | + | 0.00322022i | ||||
\(47\) | −5.46606 | − | 9.46749i | −0.797307 | − | 1.38098i | −0.921364 | − | 0.388700i | \(-0.872924\pi\) |
0.124058 | − | 0.992275i | \(-0.460409\pi\) | |||||||
\(48\) | −0.312065 | − | 8.51457i | −0.0450426 | − | 1.22897i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.24230 | + | 6.29870i | −1.30706 | + | 0.890771i | ||||
\(51\) | 12.6203 | + | 3.38159i | 1.76719 | + | 0.473518i | ||||
\(52\) | −3.30443 | − | 0.373600i | −0.458241 | − | 0.0518091i | ||||
\(53\) | −2.63182 | − | 9.82209i | −0.361508 | − | 1.34917i | −0.872093 | − | 0.489340i | \(-0.837238\pi\) |
0.510584 | − | 0.859828i | \(-0.329429\pi\) | |||||||
\(54\) | −1.45457 | − | 4.15948i | −0.197942 | − | 0.566033i | ||||
\(55\) | 10.1621i | 1.37026i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.95159i | 0.390947i | ||||||||
\(58\) | −6.54596 | + | 2.28912i | −0.859526 | + | 0.300577i | ||||
\(59\) | 0.743968 | + | 2.77653i | 0.0968564 | + | 0.361473i | 0.997294 | − | 0.0735115i | \(-0.0234205\pi\) |
−0.900438 | + | 0.434984i | \(0.856754\pi\) | |||||||
\(60\) | −11.9705 | + | 9.53863i | −1.54538 | + | 1.23143i | ||||
\(61\) | 10.2623 | + | 2.74979i | 1.31396 | + | 0.352074i | 0.846711 | − | 0.532053i | \(-0.178579\pi\) |
0.467247 | + | 0.884127i | \(0.345246\pi\) | |||||||
\(62\) | −4.57310 | − | 6.71026i | −0.580784 | − | 0.852204i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.21173 | − | 3.46279i | 0.901467 | − | 0.432849i | ||||
\(65\) | 2.98700 | + | 5.17363i | 0.370491 | + | 0.641710i | ||||
\(66\) | 0.635096 | + | 8.49659i | 0.0781749 | + | 1.04586i | ||||
\(67\) | 0.358169 | + | 1.33671i | 0.0437573 | + | 0.163305i | 0.984347 | − | 0.176240i | \(-0.0563936\pi\) |
−0.940590 | + | 0.339545i | \(0.889727\pi\) | |||||||
\(68\) | 1.82375 | + | 12.1313i | 0.221162 | + | 1.47114i | ||||
\(69\) | 0.312065 | + | 0.312065i | 0.0375682 | + | 0.0375682i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.09683 | 0.248847 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(72\) | −3.18893 | + | 2.95548i | −0.375818 | + | 0.348307i | ||||
\(73\) | −1.36480 | + | 2.36391i | −0.159738 | + | 0.276675i | −0.934774 | − | 0.355242i | \(-0.884398\pi\) |
0.775036 | + | 0.631917i | \(0.217732\pi\) | |||||||
\(74\) | 0.333525 | − | 0.387413i | 0.0387715 | − | 0.0450359i | ||||
\(75\) | 16.2720 | + | 4.36007i | 1.87893 | + | 0.503458i | ||||
\(76\) | −2.54054 | + | 1.10727i | −0.291420 | + | 0.127012i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.82076 | + | 4.13900i | 0.319389 | + | 0.468650i | ||||
\(79\) | 9.55355 | − | 5.51575i | 1.07486 | − | 0.620570i | 0.145354 | − | 0.989380i | \(-0.453568\pi\) |
0.929505 | + | 0.368810i | \(0.120235\pi\) | |||||||
\(80\) | −12.7009 | − | 6.72505i | −1.42000 | − | 0.751884i | ||||
\(81\) | −5.62431 | + | 9.74159i | −0.624923 | + | 1.08240i | ||||
\(82\) | −4.14835 | + | 8.60992i | −0.458109 | + | 0.950807i | ||||
\(83\) | 2.27616 | + | 2.27616i | 0.249841 | + | 0.249841i | 0.820905 | − | 0.571065i | \(-0.193469\pi\) |
−0.571065 | + | 0.820905i | \(0.693469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.5832 | − | 15.5832i | 1.69023 | − | 1.69023i | ||||
\(86\) | 0.391149 | − | 0.136785i | 0.0421787 | − | 0.0147499i | ||||
\(87\) | 9.04557 | + | 5.22246i | 0.969787 | + | 0.559907i | ||||
\(88\) | −7.07507 | + | 3.73409i | −0.754205 | + | 0.398055i | ||||
\(89\) | −7.04071 | − | 12.1949i | −0.746314 | − | 1.29265i | −0.949578 | − | 0.313530i | \(-0.898488\pi\) |
0.203264 | − | 0.979124i | \(-0.434845\pi\) | |||||||
\(90\) | 7.67424 | + | 1.45357i | 0.808935 | + | 0.153219i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.151536 | + | 0.385674i | −0.0157988 | + | 0.0402093i | ||||
\(93\) | −3.16558 | + | 11.8141i | −0.328255 | + | 1.22506i | ||||
\(94\) | −15.4173 | + | 1.15240i | −1.59018 | + | 0.118861i | ||||
\(95\) | 4.31154 | + | 2.48927i | 0.442355 | + | 0.255394i | ||||
\(96\) | −11.0395 | − | 4.82907i | −1.12672 | − | 0.492865i | ||||
\(97\) | − | 2.83866i | − | 0.288223i | −0.989561 | − | 0.144111i | \(-0.953968\pi\) | ||
0.989561 | − | 0.144111i | \(-0.0460323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.07442 | − | 3.07442i | 0.308991 | − | 0.308991i | ||||
\(100\) | 2.35146 | + | 15.6416i | 0.235146 | + | 1.56416i | ||||
\(101\) | 6.77286 | − | 1.81478i | 0.673925 | − | 0.180578i | 0.0944028 | − | 0.995534i | \(-0.469906\pi\) |
0.579522 | + | 0.814956i | \(0.303239\pi\) | |||||||
\(102\) | 12.0552 | − | 14.0030i | 1.19365 | − | 1.38650i | ||||
\(103\) | −11.9500 | + | 6.89933i | −1.17747 | + | 0.679811i | −0.955427 | − | 0.295227i | \(-0.904605\pi\) |
−0.222040 | + | 0.975038i | \(0.571272\pi\) | |||||||
\(104\) | −2.50440 | + | 3.98065i | −0.245577 | + | 0.390335i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.1293 | − | 2.67621i | −1.37236 | − | 0.259937i | ||||
\(107\) | 3.60910 | − | 13.4693i | 0.348905 | − | 1.30213i | −0.539078 | − | 0.842256i | \(-0.681227\pi\) |
0.887983 | − | 0.459875i | \(-0.152106\pi\) | |||||||
\(108\) | −6.19225 | − | 0.700099i | −0.595849 | − | 0.0673671i | ||||
\(109\) | −6.37931 | + | 1.70933i | −0.611027 | + | 0.163724i | −0.551045 | − | 0.834475i | \(-0.685771\pi\) |
−0.0599816 | + | 0.998199i | \(0.519104\pi\) | |||||||
\(110\) | 12.9470 | + | 6.23802i | 1.23445 | + | 0.594772i | ||||
\(111\) | −0.769968 | −0.0730821 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2577 | −1.34125 | −0.670626 | − | 0.741796i | \(-0.733974\pi\) | ||||
−0.670626 | + | 0.741796i | \(0.733974\pi\) | |||||||
\(114\) | 3.76045 | + | 1.81183i | 0.352199 | + | 0.169693i | ||||
\(115\) | 0.719034 | − | 0.192665i | 0.0670503 | − | 0.0179661i | ||||
\(116\) | −1.10178 | + | 9.74502i | −0.102298 | + | 0.904802i | ||||
\(117\) | 0.661536 | − | 2.46889i | 0.0611590 | − | 0.228249i | ||||
\(118\) | 3.99410 | + | 0.756517i | 0.367687 | + | 0.0696430i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.80460 | + | 21.1062i | 0.438598 | + | 1.92672i | ||||
\(121\) | −2.59808 | + | 1.50000i | −0.236189 | + | 0.136364i | ||||
\(122\) | 9.80287 | − | 11.3867i | 0.887510 | − | 1.03091i | ||||
\(123\) | 13.9044 | − | 3.72568i | 1.25372 | − | 0.335933i | ||||
\(124\) | −11.3564 | + | 1.70725i | −1.01983 | + | 0.153316i | ||||
\(125\) | 7.38956 | − | 7.38956i | 0.660942 | − | 0.660942i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.16426i | − | 0.546990i | −0.961873 | − | 0.273495i | \(-0.911820\pi\) | ||
0.961873 | − | 0.273495i | \(-0.0881797\pi\) | |||||||
\(128\) | 0.0151595 | − | 11.3137i | 0.00133992 | − | 0.999999i | ||||
\(129\) | −0.540512 | − | 0.312065i | −0.0475894 | − | 0.0274758i | ||||
\(130\) | 8.42500 | − | 0.629745i | 0.738921 | − | 0.0552323i | ||||
\(131\) | −0.447802 | + | 1.67122i | −0.0391246 | + | 0.146015i | −0.982725 | − | 0.185071i | \(-0.940748\pi\) |
0.943600 | + | 0.331086i | \(0.107415\pi\) | |||||||
\(132\) | 11.2149 | + | 4.40647i | 0.976131 | + | 0.383534i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.92288 | + | 0.364211i | 0.166112 | + | 0.0314630i | ||||
\(135\) | 5.59741 | + | 9.69499i | 0.481748 | + | 0.834412i | ||||
\(136\) | 16.5753 | + | 5.12324i | 1.42132 | + | 0.439314i | ||||
\(137\) | 6.72332 | + | 3.88171i | 0.574412 | + | 0.331637i | 0.758910 | − | 0.651196i | \(-0.225732\pi\) |
−0.184498 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(138\) | 0.589145 | − | 0.206024i | 0.0501513 | − | 0.0175379i | ||||
\(139\) | 6.45272 | − | 6.45272i | 0.547313 | − | 0.547313i | −0.378350 | − | 0.925663i | \(-0.623508\pi\) |
0.925663 | + | 0.378350i | \(0.123508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4658 | + | 16.4658i | 1.38667 | + | 1.38667i | ||||
\(142\) | 1.28713 | − | 2.67145i | 0.108014 | − | 0.224183i | ||||
\(143\) | 2.35147 | − | 4.07286i | 0.196640 | − | 0.340590i | ||||
\(144\) | 1.80790 | + | 5.87705i | 0.150659 | + | 0.489754i | ||||
\(145\) | 15.2574 | − | 8.80889i | 1.26706 | − | 0.731539i | ||||
\(146\) | 2.17394 | + | 3.18990i | 0.179917 | + | 0.263998i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.288848 | − | 0.662739i | −0.0237432 | − | 0.0544768i | ||||
\(149\) | −7.97593 | − | 2.13714i | −0.653413 | − | 0.175082i | −0.0831417 | − | 0.996538i | \(-0.526495\pi\) |
−0.570272 | + | 0.821456i | \(0.693162\pi\) | |||||||
\(150\) | 15.5435 | − | 18.0548i | 1.26912 | − | 1.47417i | ||||
\(151\) | −0.778116 | + | 1.34774i | −0.0633222 | + | 0.109677i | −0.895949 | − | 0.444158i | \(-0.853503\pi\) |
0.832626 | + | 0.553835i | \(0.186836\pi\) | |||||||
\(152\) | −0.148796 | + | 3.91645i | −0.0120689 | + | 0.317666i | ||||
\(153\) | −9.42896 | −0.762286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5877 | + | 14.5877i | 1.17171 | + | 1.17171i | ||||
\(156\) | 7.00480 | − | 1.05306i | 0.560833 | − | 0.0843123i | ||||
\(157\) | −1.04412 | − | 3.89673i | −0.0833302 | − | 0.310993i | 0.911663 | − | 0.410940i | \(-0.134799\pi\) |
−0.994993 | + | 0.0999470i | \(0.968133\pi\) | |||||||
\(158\) | −1.16288 | − | 15.5575i | −0.0925136 | − | 1.23769i | ||||
\(159\) | 10.8299 | + | 18.7579i | 0.858867 | + | 1.48760i | ||||
\(160\) | −16.3644 | + | 12.0533i | −1.29372 | + | 0.952899i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.95875 | + | 13.1455i | 0.703866 | + | 1.03281i | ||||
\(163\) | −1.11232 | − | 0.298045i | −0.0871237 | − | 0.0233447i | 0.214994 | − | 0.976615i | \(-0.431027\pi\) |
−0.302118 | + | 0.953271i | \(0.597694\pi\) | |||||||
\(164\) | 8.42297 | + | 10.5704i | 0.657724 | + | 0.825407i | ||||
\(165\) | −5.60243 | − | 20.9085i | −0.436148 | − | 1.62773i | ||||
\(166\) | 4.29714 | − | 1.50271i | 0.333523 | − | 0.116633i | ||||
\(167\) | − | 6.52564i | − | 0.504969i | −0.967601 | − | 0.252485i | \(-0.918752\pi\) | ||
0.967601 | − | 0.252485i | \(-0.0812477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2353i | 0.787331i | ||||||||
\(170\) | −10.2880 | − | 29.4194i | −0.789051 | − | 2.25636i | ||||
\(171\) | −0.551303 | − | 2.05749i | −0.0421592 | − | 0.157340i | ||||
\(172\) | 0.0658360 | − | 0.582307i | 0.00501995 | − | 0.0444005i | ||||
\(173\) | −5.18582 | − | 1.38954i | −0.394271 | − | 0.105644i | 0.0562362 | − | 0.998417i | \(-0.482090\pi\) |
−0.450507 | + | 0.892773i | \(0.648757\pi\) | |||||||
\(174\) | 12.2063 | − | 8.31866i | 0.925354 | − | 0.630636i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.414376 | + | 11.3061i | 0.0312348 | + | 0.852231i | ||||
\(177\) | −3.06142 | − | 5.30253i | −0.230110 | − | 0.398563i | ||||
\(178\) | −19.8587 | + | 1.48438i | −1.48848 | + | 0.111259i | ||||
\(179\) | 5.91986 | + | 22.0932i | 0.442471 | + | 1.65132i | 0.722529 | + | 0.691341i | \(0.242980\pi\) |
−0.280058 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(180\) | 6.56272 | − | 8.88505i | 0.489156 | − | 0.662253i | ||||
\(181\) | 3.70233 | + | 3.70233i | 0.275192 | + | 0.275192i | 0.831186 | − | 0.555994i | \(-0.187662\pi\) |
−0.555994 | + | 0.831186i | \(0.687662\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.6307 | −1.67291 | ||||||||
\(184\) | 0.398346 | + | 0.429810i | 0.0293664 | + | 0.0316860i | ||||
\(185\) | −0.649365 | + | 1.12473i | −0.0477422 | + | 0.0826920i | ||||
\(186\) | 13.1085 | + | 11.2851i | 0.961162 | + | 0.827467i | ||||
\(187\) | −16.7579 | − | 4.49026i | −1.22546 | − | 0.328361i | ||||
\(188\) | −7.99569 | + | 20.3498i | −0.583146 | + | 1.48416i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.81807 | − | 3.96506i | 0.422087 | − | 0.287656i | ||||
\(191\) | 1.38573 | − | 0.800051i | 0.100268 | − | 0.0578896i | −0.449028 | − | 0.893518i | \(-0.648230\pi\) |
0.549295 | + | 0.835628i | \(0.314896\pi\) | |||||||
\(192\) | −12.9290 | + | 11.1005i | −0.933073 | + | 0.801111i | ||||
\(193\) | 8.25169 | − | 14.2923i | 0.593969 | − | 1.02879i | −0.399722 | − | 0.916636i | \(-0.630893\pi\) |
0.993691 | − | 0.112149i | \(-0.0357733\pi\) | |||||||
\(194\) | −3.61659 | − | 1.74251i | −0.259656 | − | 0.125105i | ||||
\(195\) | −8.99796 | − | 8.99796i | −0.644357 | − | 0.644357i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2127 | + | 12.2127i | −0.870117 | + | 0.870117i | −0.992485 | − | 0.122368i | \(-0.960951\pi\) |
0.122368 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(198\) | −2.02972 | − | 5.80418i | −0.144246 | − | 0.412485i | ||||
\(199\) | −14.0301 | − | 8.10030i | −0.994569 | − | 0.574215i | −0.0879323 | − | 0.996126i | \(-0.528026\pi\) |
−0.906637 | + | 0.421912i | \(0.861359\pi\) | |||||||
\(200\) | 21.3715 | + | 6.60567i | 1.51119 | + | 0.467092i | ||||
\(201\) | −1.47386 | − | 2.55280i | −0.103958 | − | 0.180061i | ||||
\(202\) | 1.84539 | − | 9.74293i | 0.129841 | − | 0.685510i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.4404 | − | 23.9546i | −0.730973 | − | 1.67716i | ||||
\(205\) | 6.28422 | − | 23.4530i | 0.438909 | − | 1.63803i | ||||
\(206\) | 1.45458 | + | 19.4600i | 0.101345 | + | 1.35584i | ||||
\(207\) | −0.275822 | − | 0.159246i | −0.0191710 | − | 0.0110684i | ||||
\(208\) | 3.53421 | + | 5.63423i | 0.245053 | + | 0.390664i | ||||
\(209\) | − | 3.91928i | − | 0.271102i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.22959 | + | 1.22959i | −0.0846487 | + | 0.0846487i | −0.748163 | − | 0.663515i | \(-0.769064\pi\) |
0.663515 | + | 0.748163i | \(0.269064\pi\) | |||||||
\(212\) | −12.0829 | + | 16.3586i | −0.829855 | + | 1.12351i | ||||
\(213\) | −4.31420 | + | 1.15599i | −0.295604 | + | 0.0792070i | ||||
\(214\) | −14.9451 | − | 12.8663i | −1.02163 | − | 0.879522i | ||||
\(215\) | −0.911699 | + | 0.526369i | −0.0621773 | + | 0.0358981i | ||||
\(216\) | −4.69306 | + | 7.45944i | −0.319322 | + | 0.507551i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.73816 | + | 9.17679i | −0.117723 | + | 0.621531i | ||||
\(219\) | 1.50484 | − | 5.61615i | 0.101688 | − | 0.379504i | ||||
\(220\) | 15.8950 | − | 12.6659i | 1.07164 | − | 0.853935i | ||||
\(221\) | −9.85141 | + | 2.63968i | −0.662678 | + | 0.177564i | ||||
\(222\) | −0.472643 | + | 0.980973i | −0.0317217 | + | 0.0658386i | ||||
\(223\) | −3.08465 | −0.206564 | −0.103282 | − | 0.994652i | \(-0.532934\pi\) | ||||
−0.103282 | + | 0.994652i | \(0.532934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.1573 | −0.810485 | ||||||||
\(226\) | −8.75207 | + | 18.1650i | −0.582179 | + | 1.20831i | ||||
\(227\) | −8.42831 | + | 2.25836i | −0.559407 | + | 0.149893i | −0.527434 | − | 0.849596i | \(-0.676846\pi\) |
−0.0319729 | + | 0.999489i | \(0.510179\pi\) | |||||||
\(228\) | 4.61670 | − | 3.67880i | 0.305748 | − | 0.243635i | ||||
\(229\) | −4.36541 | + | 16.2919i | −0.288474 | + | 1.07660i | 0.657789 | + | 0.753203i | \(0.271492\pi\) |
−0.946263 | + | 0.323398i | \(0.895175\pi\) | |||||||
\(230\) | 0.195914 | − | 1.03435i | 0.0129182 | − | 0.0682029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.7393 | + | 7.38567i | 0.770720 | + | 0.484893i | ||||
\(233\) | −12.9805 | + | 7.49428i | −0.850380 | + | 0.490967i | −0.860779 | − | 0.508979i | \(-0.830023\pi\) |
0.0103994 | + | 0.999946i | \(0.496690\pi\) | |||||||
\(234\) | −2.73939 | − | 2.35835i | −0.179080 | − | 0.154170i | ||||
\(235\) | 37.9392 | − | 10.1658i | 2.47488 | − | 0.663143i | ||||
\(236\) | 3.41561 | − | 4.62428i | 0.222337 | − | 0.301015i | ||||
\(237\) | −16.6155 | + | 16.6155i | −1.07929 | + | 1.07929i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.9930i | − | 1.22856i | −0.789090 | − | 0.614278i | \(-0.789447\pi\) | ||
0.789090 | − | 0.614278i | \(-0.210553\pi\) | |||||||
\(240\) | 29.8395 | + | 6.83471i | 1.92613 | + | 0.441179i | ||||
\(241\) | 21.0900 | + | 12.1763i | 1.35853 | + | 0.784346i | 0.989425 | − | 0.145044i | \(-0.0463323\pi\) |
0.369101 | + | 0.929389i | \(0.379666\pi\) | |||||||
\(242\) | 0.316243 | + | 4.23084i | 0.0203289 | + | 0.271969i | ||||
\(243\) | 3.78208 | − | 14.1149i | 0.242620 | − | 0.905472i | ||||
\(244\) | −8.48973 | − | 19.4790i | −0.543500 | − | 1.24702i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.78852 | − | 20.0019i | 0.241547 | − | 1.27527i | ||||
\(247\) | −1.15201 | − | 1.99533i | −0.0733005 | − | 0.126960i | ||||
\(248\) | −4.79597 | + | 15.5165i | −0.304544 | + | 0.985299i | ||||
\(249\) | −5.93803 | − | 3.42832i | −0.376307 | − | 0.217261i | ||||
\(250\) | −4.87856 | − | 13.9507i | −0.308547 | − | 0.882320i | ||||
\(251\) | −13.3452 | + | 13.3452i | −0.842342 | + | 0.842342i | −0.989163 | − | 0.146821i | \(-0.953096\pi\) |
0.146821 | + | 0.989163i | \(0.453096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.414376 | − | 0.414376i | −0.0260516 | − | 0.0260516i | ||||
\(254\) | −7.85355 | − | 3.78392i | −0.492775 | − | 0.237424i | ||||
\(255\) | −23.4712 | + | 40.6533i | −1.46982 | + | 2.54581i | ||||
\(256\) | −14.4049 | − | 6.96421i | −0.900303 | − | 0.435263i | ||||
\(257\) | −4.67708 | + | 2.70031i | −0.291748 | + | 0.168441i | −0.638730 | − | 0.769431i | \(-0.720540\pi\) |
0.346982 | + | 0.937872i | \(0.387207\pi\) | |||||||
\(258\) | −0.729376 | + | 0.497076i | −0.0454090 | + | 0.0309466i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.36935 | − | 11.1204i | 0.270975 | − | 0.689657i | ||||
\(261\) | −7.28095 | − | 1.95092i | −0.450679 | − | 0.120759i | ||||
\(262\) | 1.85433 | + | 1.59640i | 0.114561 | + | 0.0986256i | ||||
\(263\) | 0.181180 | − | 0.313813i | 0.0111721 | − | 0.0193506i | −0.860385 | − | 0.509644i | \(-0.829777\pi\) |
0.871557 | + | 0.490294i | \(0.163110\pi\) | |||||||
\(264\) | 12.4983 | − | 11.5834i | 0.769216 | − | 0.712907i | ||||
\(265\) | 36.5343 | 2.24428 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.2093 | + | 21.2093i | 1.29799 | + | 1.29799i | ||||
\(268\) | 1.64438 | − | 2.22627i | 0.100446 | − | 0.135991i | ||||
\(269\) | −6.91882 | − | 25.8214i | −0.421848 | − | 1.57436i | −0.770711 | − | 0.637185i | \(-0.780099\pi\) |
0.348863 | − | 0.937174i | \(-0.386568\pi\) | |||||||
\(270\) | 15.7878 | − | 1.18009i | 0.960816 | − | 0.0718182i | ||||
\(271\) | −4.83748 | − | 8.37876i | −0.293856 | − | 0.508973i | 0.680862 | − | 0.732411i | \(-0.261605\pi\) |
−0.974718 | + | 0.223438i | \(0.928272\pi\) | |||||||
\(272\) | 16.7020 | − | 17.9728i | 1.01271 | − | 1.08976i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.07257 | − | 6.18303i | 0.548094 | − | 0.373531i | ||||
\(275\) | −21.6069 | − | 5.78954i | −1.30294 | − | 0.349122i | ||||
\(276\) | 0.0991614 | − | 0.877064i | 0.00596882 | − | 0.0527931i | ||||
\(277\) | −1.08202 | − | 4.03815i | −0.0650122 | − | 0.242629i | 0.925771 | − | 0.378084i | \(-0.123417\pi\) |
−0.990783 | + | 0.135455i | \(0.956750\pi\) | |||||||
\(278\) | −4.26007 | − | 12.1821i | −0.255502 | − | 0.730631i | ||||
\(279\) | − | 8.82664i | − | 0.528437i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.8602i | 1.18476i | 0.805658 | + | 0.592382i | \(0.201812\pi\) | ||||
−0.805658 | + | 0.592382i | \(0.798188\pi\) | |||||||
\(282\) | 31.0857 | − | 10.8707i | 1.85113 | − | 0.647340i | ||||
\(283\) | −7.14328 | − | 26.6591i | −0.424624 | − | 1.58472i | −0.764743 | − | 0.644335i | \(-0.777134\pi\) |
0.340119 | − | 0.940382i | \(-0.389533\pi\) | |||||||
\(284\) | −2.61344 | − | 3.27973i | −0.155079 | − | 0.194616i | ||||
\(285\) | −10.2433 | − | 2.74468i | −0.606761 | − | 0.162581i | ||||
\(286\) | −3.74556 | − | 5.49599i | −0.221480 | − | 0.324985i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.59741 | + | 1.30427i | 0.506607 | + | 0.0768547i | ||||
\(289\) | 10.3118 | + | 17.8606i | 0.606578 | + | 1.05062i | ||||
\(290\) | −1.85717 | − | 24.8460i | −0.109057 | − | 1.45901i | ||||
\(291\) | 1.56497 | + | 5.84053i | 0.0917399 | + | 0.342378i | ||||
\(292\) | 5.39855 | − | 0.811587i | 0.315926 | − | 0.0474945i | ||||
\(293\) | 18.3063 | + | 18.3063i | 1.06947 | + | 1.06947i | 0.997400 | + | 0.0720669i | \(0.0229595\pi\) |
0.0720669 | + | 0.997400i | \(0.477041\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3276 | −0.601295 | ||||||||
\(296\) | −1.02167 | − | 0.0388156i | −0.0593832 | − | 0.00225611i | ||||
\(297\) | 4.40647 | − | 7.63224i | 0.255690 | − | 0.442867i | ||||
\(298\) | −7.61882 | + | 8.84981i | −0.441347 | + | 0.512656i | ||||
\(299\) | −0.332761 | − | 0.0891631i | −0.0192441 | − | 0.00515644i | ||||
\(300\) | −13.4614 | − | 30.8860i | −0.777192 | − | 1.78320i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.23943 | + | 1.81866i | 0.0713213 | + | 0.104652i | ||||
\(303\) | −12.9346 | + | 7.46780i | −0.743074 | + | 0.429014i | ||||
\(304\) | 4.89840 | + | 2.59368i | 0.280942 | + | 0.148758i | ||||
\(305\) | −19.0859 | + | 33.0578i | −1.09286 | + | 1.89288i | ||||
\(306\) | −5.78795 | + | 12.0129i | −0.330875 | + | 0.686733i | ||||
\(307\) | −10.7614 | − | 10.7614i | −0.614188 | − | 0.614188i | 0.329847 | − | 0.944034i | \(-0.393003\pi\) |
−0.944034 | + | 0.329847i | \(0.893003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.7834 | − | 20.7834i | 1.18233 | − | 1.18233i | ||||
\(310\) | 27.5401 | − | 9.63077i | 1.56417 | − | 0.546991i | ||||
\(311\) | −1.63450 | − | 0.943681i | −0.0926842 | − | 0.0535113i | 0.452942 | − | 0.891540i | \(-0.350375\pi\) |
−0.545626 | + | 0.838029i | \(0.683708\pi\) | |||||||
\(312\) | 2.95823 | − | 9.57085i | 0.167477 | − | 0.541842i | ||||
\(313\) | 10.9206 | + | 18.9150i | 0.617267 | + | 1.06914i | 0.989982 | + | 0.141192i | \(0.0450936\pi\) |
−0.372715 | + | 0.927946i | \(0.621573\pi\) | |||||||
\(314\) | −5.60554 | − | 1.06174i | −0.316339 | − | 0.0599173i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.5348 | − | 8.06838i | −1.15517 | − | 0.453882i | ||||
\(317\) | −5.22124 | + | 19.4859i | −0.293254 | + | 1.09444i | 0.649340 | + | 0.760498i | \(0.275045\pi\) |
−0.942594 | + | 0.333941i | \(0.891621\pi\) | |||||||
\(318\) | 30.5464 | − | 2.28325i | 1.71296 | − | 0.128039i | ||||
\(319\) | −12.0112 | − | 6.93467i | −0.672498 | − | 0.388267i | ||||
\(320\) | 5.31120 | + | 28.2479i | 0.296905 | + | 1.57911i | ||||
\(321\) | 29.7028i | 1.65785i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.01003 | + | 6.01003i | −0.334407 | + | 0.334407i | ||||
\(324\) | 22.2472 | − | 3.34452i | 1.23596 | − | 0.185807i | ||||
\(325\) | −12.7020 | + | 3.40348i | −0.704578 | + | 0.188791i | ||||
\(326\) | −1.06252 | + | 1.23419i | −0.0588475 | + | 0.0683556i | ||||
\(327\) | 12.1830 | − | 7.03387i | 0.673722 | − | 0.388974i | ||||
\(328\) | 18.6376 | − | 4.24264i | 1.02909 | − | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −30.0775 | − | 5.69693i | −1.65571 | − | 0.313606i | ||||
\(331\) | −1.92279 | + | 7.17595i | −0.105686 | + | 0.394426i | −0.998422 | − | 0.0561542i | \(-0.982116\pi\) |
0.892736 | + | 0.450580i | \(0.148783\pi\) | |||||||
\(332\) | 0.723270 | − | 6.39719i | 0.0396946 | − | 0.351091i | ||||
\(333\) | 0.536729 | − | 0.143816i | 0.0294126 | − | 0.00788107i | ||||
\(334\) | −8.31396 | − | 4.00575i | −0.454920 | − | 0.219185i | ||||
\(335\) | −4.97202 | −0.271650 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0799 | −0.658034 | −0.329017 | − | 0.944324i | \(-0.606717\pi\) | ||||
−0.329017 | + | 0.944324i | \(0.606717\pi\) | |||||||
\(338\) | 13.0402 | + | 6.28292i | 0.709295 | + | 0.341746i | ||||
\(339\) | 29.3351 | − | 7.86032i | 1.59326 | − | 0.426914i | ||||
\(340\) | −43.7969 | − | 4.95170i | −2.37522 | − | 0.268544i | ||||
\(341\) | 4.20342 | − | 15.6874i | 0.227628 | − | 0.849520i | ||||
\(342\) | −2.95975 | − | 0.560603i | −0.160045 | − | 0.0303139i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.701472 | − | 0.441326i | −0.0378208 | − | 0.0237947i | ||||
\(345\) | −1.37319 | + | 0.792812i | −0.0739301 | + | 0.0426836i | ||||
\(346\) | −4.95364 | + | 5.75400i | −0.266309 | + | 0.309337i | ||||
\(347\) | −26.4326 | + | 7.08259i | −1.41897 | + | 0.380213i | −0.885120 | − | 0.465363i | \(-0.845924\pi\) |
−0.533855 | + | 0.845576i | \(0.679257\pi\) | |||||||
\(348\) | −3.10556 | − | 20.6577i | −0.166476 | − | 1.10737i | ||||
\(349\) | 2.96915 | − | 2.96915i | 0.158935 | − | 0.158935i | −0.623160 | − | 0.782095i | \(-0.714151\pi\) |
0.782095 | + | 0.623160i | \(0.214151\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.18084i | − | 0.276533i | ||||||
\(352\) | 14.6589 | + | 6.41231i | 0.781320 | + | 0.341777i | ||||
\(353\) | 14.1327 | + | 8.15953i | 0.752209 | + | 0.434288i | 0.826491 | − | 0.562949i | \(-0.190333\pi\) |
−0.0742828 | + | 0.997237i | \(0.523667\pi\) | |||||||
\(354\) | −8.63491 | + | 0.645435i | −0.458940 | + | 0.0343045i | ||||
\(355\) | −1.94984 | + | 7.27691i | −0.103487 | + | 0.386218i | ||||
\(356\) | −10.2991 | + | 26.2121i | −0.545850 | + | 1.38924i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 31.7816 | + | 6.01971i | 1.67971 | + | 0.318152i | ||||
\(359\) | −8.26786 | − | 14.3203i | −0.436361 | − | 0.755799i | 0.561045 | − | 0.827785i | \(-0.310400\pi\) |
−0.997406 | + | 0.0719864i | \(0.977066\pi\) | |||||||
\(360\) | −7.29144 | − | 13.8153i | −0.384293 | − | 0.728129i | ||||
\(361\) | 14.7916 | + | 8.53995i | 0.778507 | + | 0.449471i | ||||
\(362\) | 6.98961 | − | 2.44427i | 0.367366 | − | 0.128468i | ||||
\(363\) | 4.51857 | − | 4.51857i | 0.237163 | − | 0.237163i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.93467 | − | 6.93467i | −0.362977 | − | 0.362977i | ||||
\(366\) | −13.8918 | + | 28.8325i | −0.726135 | + | 1.50710i | ||||
\(367\) | 11.8390 | − | 20.5058i | 0.617992 | − | 1.07039i | −0.371860 | − | 0.928289i | \(-0.621280\pi\) |
0.989852 | − | 0.142104i | \(-0.0453868\pi\) | |||||||
\(368\) | 0.792120 | − | 0.243673i | 0.0412921 | − | 0.0127023i | ||||
\(369\) | −8.99660 | + | 5.19419i | −0.468344 | + | 0.270399i | ||||
\(370\) | 1.03435 | + | 1.51773i | 0.0537732 | + | 0.0789033i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 22.4244 | − | 9.77345i | 1.16265 | − | 0.506730i | ||||
\(373\) | −30.0357 | − | 8.04803i | −1.55519 | − | 0.416711i | −0.624051 | − | 0.781383i | \(-0.714514\pi\) |
−0.931136 | + | 0.364672i | \(0.881181\pi\) | |||||||
\(374\) | −16.0076 | + | 18.5940i | −0.827733 | + | 0.961471i | ||||
\(375\) | −11.1301 | + | 19.2779i | −0.574754 | + | 0.995504i | ||||
\(376\) | 21.0184 | + | 22.6785i | 1.08394 | + | 1.16956i | ||||
\(377\) | −8.15332 | −0.419918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0100 | − | 20.0100i | −1.02785 | − | 1.02785i | −0.999601 | − | 0.0282452i | \(-0.991008\pi\) |
−0.0282452 | − | 0.999601i | \(-0.508992\pi\) | |||||||
\(380\) | −1.48026 | − | 9.84643i | −0.0759355 | − | 0.505111i | ||||
\(381\) | 3.39838 | + | 12.6829i | 0.174104 | + | 0.649766i | ||||
\(382\) | −0.168674 | − | 2.25659i | −0.00863009 | − | 0.115457i | ||||
\(383\) | 2.58822 | + | 4.48293i | 0.132252 | + | 0.229067i | 0.924544 | − | 0.381075i | \(-0.124446\pi\) |
−0.792292 | + | 0.610142i | \(0.791113\pi\) | |||||||
\(384\) | 6.20609 | + | 23.2862i | 0.316703 | + | 1.18832i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.1438 | − | 19.2863i | −0.669002 | − | 0.981649i | ||||
\(387\) | 0.435068 | + | 0.116576i | 0.0221158 | + | 0.00592590i | ||||
\(388\) | −4.44007 | + | 3.53806i | −0.225410 | + | 0.179618i | ||||
\(389\) | −1.52222 | − | 5.68099i | −0.0771795 | − | 0.288038i | 0.916539 | − | 0.399945i | \(-0.130971\pi\) |
−0.993719 | + | 0.111907i | \(0.964304\pi\) | |||||||
\(390\) | −16.9872 | + | 5.94042i | −0.860180 | + | 0.300805i | ||||
\(391\) | 1.27085i | 0.0642698i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.68540i | − | 0.185904i | ||||||
\(394\) | 8.06277 | + | 23.0562i | 0.406196 | + | 1.16156i | ||||
\(395\) | 10.2582 | + | 38.2841i | 0.516146 | + | 1.92628i | ||||
\(396\) | −8.64073 | − | 0.976926i | −0.434213 | − | 0.0490924i | ||||
\(397\) | −20.2664 | − | 5.43037i | −1.01714 | − | 0.272542i | −0.288531 | − | 0.957470i | \(-0.593167\pi\) |
−0.728611 | + | 0.684928i | \(0.759834\pi\) | |||||||
\(398\) | −18.9325 | + | 12.9027i | −0.949001 | + | 0.646752i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5348 | − | 23.1734i | 1.07674 | − | 1.15867i | ||||
\(401\) | −11.0544 | − | 19.1468i | −0.552032 | − | 0.956147i | −0.998128 | − | 0.0611622i | \(-0.980519\pi\) |
0.446096 | − | 0.894985i | \(-0.352814\pi\) | |||||||
\(402\) | −4.15711 | + | 0.310732i | −0.207338 | + | 0.0154979i | ||||
\(403\) | −2.47105 | − | 9.22210i | −0.123092 | − | 0.459386i | ||||
\(404\) | −11.2801 | − | 8.33180i | −0.561208 | − | 0.414522i | ||||
\(405\) | −28.5775 | − | 28.5775i | −1.42003 | − | 1.42003i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.02241 | 0.0506787 | ||||||||
\(408\) | −36.9281 | − | 1.40299i | −1.82821 | − | 0.0694582i | ||||
\(409\) | 0.729129 | − | 1.26289i | 0.0360531 | − | 0.0624458i | −0.847436 | − | 0.530898i | \(-0.821855\pi\) |
0.883489 | + | 0.468452i | \(0.155188\pi\) | |||||||
\(410\) | −26.0227 | − | 22.4030i | −1.28517 | − | 1.10640i | ||||
\(411\) | −15.9732 | − | 4.28000i | −0.787899 | − | 0.211117i | ||||
\(412\) | 25.6858 | + | 10.0923i | 1.26545 | + | 0.497210i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.372199 | + | 0.253657i | −0.0182926 | + | 0.0124666i | ||||
\(415\) | −10.0159 | + | 5.78266i | −0.491659 | + | 0.283860i | ||||
\(416\) | 9.34773 | − | 1.04418i | 0.458310 | − | 0.0511950i | ||||
\(417\) | −9.71902 | + | 16.8338i | −0.475942 | + | 0.824357i | ||||
\(418\) | −4.99334 | − | 2.40584i | −0.244232 | − | 0.117674i | ||||
\(419\) | 24.2050 | + | 24.2050i | 1.18249 | + | 1.18249i | 0.979096 | + | 0.203398i | \(0.0651984\pi\) |
0.203398 | + | 0.979096i | \(0.434802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1878 | − | 19.1878i | 0.935158 | − | 0.935158i | −0.0628646 | − | 0.998022i | \(-0.520024\pi\) |
0.998022 | + | 0.0628646i | \(0.0200236\pi\) | |||||||
\(422\) | 0.811773 | + | 2.32134i | 0.0395165 | + | 0.113001i | ||||
\(423\) | −14.5535 | − | 8.40248i | −0.707617 | − | 0.408543i | ||||
\(424\) | 13.4245 | + | 25.4358i | 0.651954 | + | 1.23527i | ||||
\(425\) | 24.2551 | + | 42.0111i | 1.17655 | + | 2.03784i | ||||
\(426\) | −1.17549 | + | 6.20609i | −0.0569525 | + | 0.300686i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −25.5663 | + | 11.1428i | −1.23579 | + | 0.538607i | ||||
\(429\) | −2.59274 | + | 9.67625i | −0.125179 | + | 0.467174i | ||||
\(430\) | 0.110974 | + | 1.48466i | 0.00535163 | + | 0.0715965i | ||||
\(431\) | −17.6927 | − | 10.2149i | −0.852228 | − | 0.492034i | 0.00917369 | − | 0.999958i | \(-0.497080\pi\) |
−0.861402 | + | 0.507924i | \(0.830413\pi\) | |||||||
\(432\) | 6.62284 | + | 10.5581i | 0.318642 | + | 0.507978i | ||||
\(433\) | − | 22.7267i | − | 1.09218i | −0.837727 | − | 0.546089i | \(-0.816116\pi\) | ||
0.837727 | − | 0.546089i | \(-0.183884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.5357 | + | 26.5357i | −1.27229 | + | 1.27229i | ||||
\(436\) | 10.6247 | + | 7.84766i | 0.508830 | + | 0.375835i | ||||
\(437\) | −0.277313 | + | 0.0743057i | −0.0132657 | + | 0.00355453i | ||||
\(438\) | −6.23148 | − | 5.36470i | −0.297751 | − | 0.256335i | ||||
\(439\) | 30.8968 | − | 17.8383i | 1.47462 | − | 0.851375i | 0.475034 | − | 0.879968i | \(-0.342436\pi\) |
0.999591 | + | 0.0285924i | \(0.00910248\pi\) | |||||||
\(440\) | −6.37980 | − | 28.0259i | −0.304145 | − | 1.33608i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.68420 | + | 14.1715i | −0.127674 | + | 0.674070i | ||||
\(443\) | −1.87342 | + | 6.99171i | −0.0890091 | + | 0.332186i | −0.996043 | − | 0.0888708i | \(-0.971674\pi\) |
0.907034 | + | 0.421057i | \(0.138341\pi\) | |||||||
\(444\) | 0.959673 | + | 1.20434i | 0.0455441 | + | 0.0571553i | ||||
\(445\) | 48.8687 | − | 13.0943i | 2.31660 | − | 0.620731i | ||||
\(446\) | −1.89351 | + | 3.92999i | −0.0896603 | + | 0.186090i | ||||
\(447\) | 17.5886 | 0.831913 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.6346 | −1.68170 | −0.840851 | − | 0.541266i | \(-0.817945\pi\) | ||||
−0.840851 | + | 0.541266i | \(0.817945\pi\) | |||||||
\(450\) | −7.46272 | + | 15.4889i | −0.351796 | + | 0.730154i | ||||
\(451\) | −18.4630 | + | 4.94716i | −0.869391 | + | 0.232953i | ||||
\(452\) | 17.7705 | + | 22.3010i | 0.835855 | + | 1.04895i | ||||
\(453\) | 0.857956 | − | 3.20194i | 0.0403103 | − | 0.150440i | ||||
\(454\) | −2.29645 | + | 12.1243i | −0.107778 | + | 0.569023i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.85301 | − | 8.14010i | −0.0867751 | − | 0.381195i | ||||
\(457\) | 4.14209 | − | 2.39144i | 0.193759 | − | 0.111867i | −0.399982 | − | 0.916523i | \(-0.630984\pi\) |
0.593741 | + | 0.804656i | \(0.297650\pi\) | |||||||
\(458\) | 18.0769 | + | 15.5625i | 0.844680 | + | 0.727188i | ||||
\(459\) | −18.4608 | + | 4.94656i | −0.861677 | + | 0.230886i | ||||
\(460\) | −1.19754 | − | 0.884537i | −0.0558358 | − | 0.0412417i | ||||
\(461\) | 6.54100 | − | 6.54100i | 0.304645 | − | 0.304645i | −0.538183 | − | 0.842828i | \(-0.680889\pi\) |
0.842828 | + | 0.538183i | \(0.180889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.771348i | − | 0.0358476i | −0.999839 | − | 0.0179238i | \(-0.994294\pi\) | ||
0.999839 | − | 0.0179238i | \(-0.00570563\pi\) | |||||||
\(464\) | 16.6158 | − | 10.4227i | 0.771369 | − | 0.483860i | ||||
\(465\) | −38.0564 | − | 21.9719i | −1.76482 | − | 1.01892i | ||||
\(466\) | 1.58001 | + | 21.1381i | 0.0731926 | + | 0.979202i | ||||
\(467\) | −0.919035 | + | 3.42988i | −0.0425278 | + | 0.158716i | −0.983924 | − | 0.178586i | \(-0.942848\pi\) |
0.941396 | + | 0.337302i | \(0.109514\pi\) | |||||||
\(468\) | −4.68621 | + | 2.04244i | −0.216620 | + | 0.0944117i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.3373 | − | 54.5765i | 0.476822 | − | 2.51743i | ||||
\(471\) | 4.29656 | + | 7.44186i | 0.197975 | + | 0.342903i | ||||
\(472\) | −3.79487 | − | 7.19025i | −0.174673 | − | 0.330958i | ||||
\(473\) | 0.717721 | + | 0.414376i | 0.0330008 | + | 0.0190530i | ||||
\(474\) | 10.9695 | + | 31.3683i | 0.503846 | + | 1.44079i | ||||
\(475\) | −7.74906 | + | 7.74906i | −0.355551 | + | 0.355551i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.0530 | − | 11.0530i | −0.506080 | − | 0.506080i | ||||
\(478\) | −24.1980 | − | 11.6588i | −1.10679 | − | 0.533262i | ||||
\(479\) | 4.96517 | − | 8.59993i | 0.226865 | − | 0.392941i | −0.730013 | − | 0.683434i | \(-0.760486\pi\) |
0.956877 | + | 0.290493i | \(0.0938192\pi\) | |||||||
\(480\) | 27.0247 | − | 33.8214i | 1.23350 | − | 1.54373i | ||||
\(481\) | 0.520514 | − | 0.300519i | 0.0237334 | − | 0.0137025i | ||||
\(482\) | 28.4592 | − | 19.3952i | 1.29628 | − | 0.883427i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.58440 | + | 2.19418i | 0.253836 | + | 0.0997356i | ||||
\(485\) | 9.85141 | + | 2.63968i | 0.447329 | + | 0.119862i | ||||
\(486\) | −15.6614 | − | 13.4829i | −0.710416 | − | 0.611599i | ||||
\(487\) | −3.70370 | + | 6.41499i | −0.167830 | + | 0.290691i | −0.937657 | − | 0.347563i | \(-0.887009\pi\) |
0.769826 | + | 0.638253i | \(0.220343\pi\) | |||||||
\(488\) | −30.0286 | − | 1.14086i | −1.35933 | − | 0.0516442i | ||||
\(489\) | 2.45290 | 0.110924 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.4988 | + | 21.4988i | 0.970229 | + | 0.970229i | 0.999569 | − | 0.0293409i | \(-0.00934085\pi\) |
−0.0293409 | + | 0.999569i | \(0.509341\pi\) | |||||||
\(492\) | −23.1577 | − | 17.1048i | −1.04403 | − | 0.771146i | ||||
\(493\) | 7.78462 | + | 29.0526i | 0.350602 | + | 1.30846i | ||||
\(494\) | −3.24930 | + | 0.242876i | −0.146193 | + | 0.0109275i | ||||
\(495\) | 7.81068 | + | 13.5285i | 0.351064 | + | 0.608061i | ||||
\(496\) | 16.8247 | + | 15.6351i | 0.755452 | + | 0.702035i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.01288 | + | 5.46085i | −0.359066 | + | 0.244706i | ||||
\(499\) | 31.8565 | + | 8.53593i | 1.42609 | + | 0.382121i | 0.887641 | − | 0.460535i | \(-0.152342\pi\) |
0.538452 | + | 0.842656i | \(0.319009\pi\) | |||||||
\(500\) | −20.7685 | − | 2.34810i | −0.928796 | − | 0.105010i | ||||
\(501\) | 3.59761 | + | 13.4265i | 0.160729 | + | 0.599850i | ||||
\(502\) | 8.81046 | + | 25.1943i | 0.393230 | + | 1.12448i | ||||
\(503\) | − | 38.8858i | − | 1.73383i | −0.498456 | − | 0.866915i | \(-0.666099\pi\) | ||
0.498456 | − | 0.866915i | \(-0.333901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.1924i | 1.12105i | ||||||||
\(506\) | −0.782298 | + | 0.273570i | −0.0347774 | + | 0.0121617i | ||||
\(507\) | −5.64276 | − | 21.0591i | −0.250604 | − | 0.935265i | ||||
\(508\) | −9.64177 | + | 7.68302i | −0.427784 | + | 0.340879i | ||||
\(509\) | 11.2154 | + | 3.00516i | 0.497114 | + | 0.133201i | 0.498660 | − | 0.866798i | \(-0.333826\pi\) |
−0.00154626 | + | 0.999999i | \(0.500492\pi\) | |||||||
\(510\) | 37.3864 | + | 54.8584i | 1.65550 | + | 2.42917i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.7151 | + | 14.0775i | −0.782904 | + | 0.622142i | ||||
\(513\) | −2.15878 | − | 3.73911i | −0.0953123 | − | 0.165086i | ||||
\(514\) | 0.569304 | + | 7.61639i | 0.0251109 | + | 0.335945i | ||||
\(515\) | −12.8314 | − | 47.8874i | −0.565418 | − | 2.11017i | ||||
\(516\) | 0.185571 | + | 1.23439i | 0.00816930 | + | 0.0543409i | ||||
\(517\) | −21.8642 | − | 21.8642i | −0.961588 | − | 0.961588i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.4358 | 0.501978 | ||||||||
\(520\) | −11.4858 | − | 12.3930i | −0.503684 | − | 0.543468i | ||||
\(521\) | −5.97165 | + | 10.3432i | −0.261623 | + | 0.453144i | −0.966673 | − | 0.256013i | \(-0.917591\pi\) |
0.705051 | + | 0.709157i | \(0.250924\pi\) | |||||||
\(522\) | −6.95496 | + | 8.07868i | −0.304410 | + | 0.353594i | ||||
\(523\) | −18.1764 | − | 4.87035i | −0.794798 | − | 0.212965i | −0.161499 | − | 0.986873i | \(-0.551633\pi\) |
−0.633299 | + | 0.773908i | \(0.718300\pi\) | |||||||
\(524\) | 3.17215 | − | 1.38255i | 0.138576 | − | 0.0603970i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.288595 | − | 0.423465i | −0.0125833 | − | 0.0184640i | ||||
\(527\) | −30.5016 | + | 17.6101i | −1.32867 | + | 0.767109i | ||||
\(528\) | −7.08568 | − | 23.0338i | −0.308365 | − | 1.00242i | ||||
\(529\) | 11.4785 | − | 19.8814i | 0.499067 | − | 0.864409i | ||||
\(530\) | 22.4265 | − | 46.5463i | 0.974145 | − | 2.02184i | ||||
\(531\) | 3.12447 | + | 3.12447i | 0.135590 | + | 0.135590i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.94554 | + | 7.94554i | −0.344160 | + | 0.344160i | ||||
\(534\) | 40.0409 | − | 14.0023i | 1.73274 | − | 0.605939i | ||||
\(535\) | 43.3884 | + | 25.0503i | 1.87585 | + | 1.08302i | ||||
\(536\) | −1.82697 | − | 3.46161i | −0.0789131 | − | 0.149519i | ||||
\(537\) | −24.3601 | − | 42.1930i | −1.05122 | − | 1.82076i | ||||
\(538\) | −37.1447 | − | 7.03553i | −1.60142 | − | 0.303323i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.18783 | − | 20.8388i | 0.352348 | − | 0.896758i | ||||
\(541\) | 4.43893 | − | 16.5663i | 0.190844 | − | 0.712241i | −0.802459 | − | 0.596707i | \(-0.796475\pi\) |
0.993304 | − | 0.115534i | \(-0.0368579\pi\) | |||||||
\(542\) | −13.6444 | + | 1.01988i | −0.586077 | + | 0.0438076i | ||||
\(543\) | −9.65863 | − | 5.57641i | −0.414492 | − | 0.239307i | ||||
\(544\) | −12.6457 | − | 32.3117i | −0.542181 | − | 1.38535i | ||||
\(545\) | − | 23.7285i | − | 1.01642i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7858 | − | 16.7858i | 0.717710 | − | 0.717710i | −0.250426 | − | 0.968136i | \(-0.580571\pi\) |
0.968136 | + | 0.250426i | \(0.0805706\pi\) | |||||||
\(548\) | −2.30828 | − | 15.3543i | −0.0986047 | − | 0.655903i | ||||
\(549\) | 15.7754 | − | 4.22700i | 0.673277 | − | 0.180404i | ||||
\(550\) | −20.6395 | + | 23.9742i | −0.880070 | + | 1.02226i | ||||
\(551\) | −5.88440 | + | 3.39736i | −0.250684 | + | 0.144732i | ||||
\(552\) | −1.05655 | − | 0.664720i | −0.0449697 | − | 0.0282924i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.80898 | − | 1.10027i | −0.246800 | − | 0.0467460i | ||||
\(555\) | 0.715994 | − | 2.67213i | 0.0303922 | − | 0.113425i | ||||
\(556\) | −18.1355 | − | 2.05041i | −0.769117 | − | 0.0869569i | ||||
\(557\) | −13.9632 | + | 3.74143i | −0.591639 | + | 0.158529i | −0.542202 | − | 0.840248i | \(-0.682409\pi\) |
−0.0494370 | + | 0.998777i | \(0.515743\pi\) | |||||||
\(558\) | −11.2455 | − | 5.41822i | −0.476061 | − | 0.229371i | ||||
\(559\) | 0.487196 | 0.0206062 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.9547 | 1.56023 | ||||||||
\(562\) | 25.3028 | + | 12.1912i | 1.06734 | + | 0.514254i | ||||
\(563\) | 29.3012 | − | 7.85123i | 1.23490 | − | 0.330890i | 0.418413 | − | 0.908257i | \(-0.362586\pi\) |
0.816485 | + | 0.577367i | \(0.195920\pi\) | |||||||
\(564\) | 5.23217 | − | 46.2776i | 0.220314 | − | 1.94864i | ||||
\(565\) | 13.2583 | − | 49.4805i | 0.557779 | − | 2.08166i | ||||
\(566\) | −38.3498 | − | 7.26377i | −1.61196 | − | 0.305319i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.78278 | + | 1.31639i | −0.242640 | + | 0.0552344i | ||||
\(569\) | 34.5771 | − | 19.9631i | 1.44955 | − | 0.836896i | 0.451093 | − | 0.892477i | \(-0.351034\pi\) |
0.998454 | + | 0.0555808i | \(0.0177010\pi\) | |||||||
\(570\) | −9.78468 | + | 11.3656i | −0.409835 | + | 0.476053i | ||||
\(571\) | 28.1970 | − | 7.55536i | 1.18001 | − | 0.316182i | 0.385078 | − | 0.922884i | \(-0.374175\pi\) |
0.794929 | + | 0.606702i | \(0.207508\pi\) | |||||||
\(572\) | −9.30135 | + | 1.39831i | −0.388909 | + | 0.0584663i | ||||
\(573\) | −2.41005 | + | 2.41005i | −0.100681 | + | 0.100681i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.63858i | 0.0683336i | ||||||||
\(576\) | 6.93920 | − | 10.1529i | 0.289133 | − | 0.423036i | ||||
\(577\) | −0.793111 | − | 0.457903i | −0.0330177 | − | 0.0190628i | 0.483400 | − | 0.875399i | \(-0.339402\pi\) |
−0.516418 | + | 0.856337i | \(0.672735\pi\) | |||||||
\(578\) | 29.0851 | − | 2.17403i | 1.20978 | − | 0.0904278i | ||||
\(579\) | −9.09837 | + | 33.9556i | −0.378115 | + | 1.41115i | ||||
\(580\) | −32.7949 | − | 12.8856i | −1.36174 | − | 0.535043i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.40175 | + | 1.59136i | 0.348264 | + | 0.0659641i | ||||
\(583\) | −14.3805 | − | 24.9078i | −0.595581 | − | 1.03158i | ||||
\(584\) | 2.27989 | − | 7.37619i | 0.0943426 | − | 0.305229i | ||||
\(585\) | 7.95296 | + | 4.59164i | 0.328814 | + | 0.189841i | ||||
\(586\) | 34.5604 | − | 12.0858i | 1.42768 | − | 0.499259i | ||||
\(587\) | −19.0031 | + | 19.0031i | −0.784343 | + | 0.784343i | −0.980560 | − | 0.196218i | \(-0.937134\pi\) |
0.196218 | + | 0.980560i | \(0.437134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.62611 | − | 5.62611i | −0.231820 | − | 0.231820i | ||||
\(590\) | −6.33957 | + | 13.1578i | −0.260996 | + | 0.541698i | ||||
\(591\) | 18.3946 | − | 31.8604i | 0.756653 | − | 1.31056i | ||||
\(592\) | −0.676602 | + | 1.27782i | −0.0278082 | + | 0.0525182i | ||||
\(593\) | 31.5452 | − | 18.2126i | 1.29541 | − | 0.747903i | 0.315798 | − | 0.948826i | \(-0.397728\pi\) |
0.979607 | + | 0.200924i | \(0.0643943\pi\) | |||||||
\(594\) | −7.01891 | − | 10.2991i | −0.287989 | − | 0.422576i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.59825 | + | 15.1392i | 0.270275 | + | 0.620124i | ||||
\(597\) | 33.3326 | + | 8.93144i | 1.36421 | + | 0.365540i | ||||
\(598\) | −0.317863 | + | 0.369220i | −0.0129984 | + | 0.0150985i | ||||
\(599\) | 2.13462 | − | 3.69727i | 0.0872181 | − | 0.151066i | −0.819116 | − | 0.573628i | \(-0.805536\pi\) |
0.906334 | + | 0.422562i | \(0.138869\pi\) | |||||||
\(600\) | −47.6134 | − | 1.80895i | −1.94381 | − | 0.0738500i | ||||
\(601\) | −26.3491 | −1.07480 | −0.537400 | − | 0.843327i | \(-0.680594\pi\) | ||||
−0.537400 | + | 0.843327i | \(0.680594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.50422 | + | 1.50422i | 0.0612564 | + | 0.0612564i | ||||
\(604\) | 3.07788 | − | 0.462711i | 0.125237 | − | 0.0188274i | ||||
\(605\) | −2.78970 | − | 10.4113i | −0.113418 | − | 0.423280i | ||||
\(606\) | 1.57443 | + | 21.0634i | 0.0639568 | + | 0.855641i | ||||
\(607\) | −15.4145 | − | 26.6988i | −0.625657 | − | 1.08367i | −0.988413 | − | 0.151786i | \(-0.951498\pi\) |
0.362756 | − | 0.931884i | \(-0.381836\pi\) | |||||||
\(608\) | 6.31134 | − | 4.64865i | 0.255959 | − | 0.188528i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.4013 | + | 44.6088i | 1.23091 | + | 1.80616i | ||||
\(611\) | −17.5579 | − | 4.70462i | −0.710316 | − | 0.190329i | ||||
\(612\) | 11.7521 | + | 14.7482i | 0.475050 | + | 0.596161i | ||||
\(613\) | 0.794387 | + | 2.96469i | 0.0320850 | + | 0.119743i | 0.980111 | − | 0.198450i | \(-0.0635907\pi\) |
−0.948026 | + | 0.318193i | \(0.896924\pi\) | |||||||
\(614\) | −20.3164 | + | 7.10467i | −0.819905 | + | 0.286721i | ||||
\(615\) | 51.7189i | 2.08551i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 36.8410i | − | 1.48316i | −0.670863 | − | 0.741581i | \(-0.734076\pi\) | ||
0.670863 | − | 0.741581i | \(-0.265924\pi\) | |||||||
\(618\) | −13.7211 | − | 39.2368i | −0.551945 | − | 1.57834i | ||||
\(619\) | 11.3782 | + | 42.4639i | 0.457327 | + | 1.70677i | 0.681155 | + | 0.732140i | \(0.261478\pi\) |
−0.223827 | + | 0.974629i | \(0.571855\pi\) | |||||||
\(620\) | 4.63539 | − | 40.9991i | 0.186162 | − | 1.64656i | ||||
\(621\) | −0.623570 | − | 0.167085i | −0.0250230 | − | 0.00670489i | ||||
\(622\) | −2.20563 | + | 1.50315i | −0.0884377 | + | 0.0602710i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.3778 | − | 9.64397i | −0.415444 | − | 0.386068i | ||||
\(625\) | −0.998199 | − | 1.72893i | −0.0399279 | − | 0.0691572i | ||||
\(626\) | 30.8021 | − | 2.30237i | 1.23110 | − | 0.0920212i | ||||
\(627\) | 2.16071 | + | 8.06389i | 0.0862905 | + | 0.322041i | ||||
\(628\) | −4.79365 | + | 6.48996i | −0.191287 | + | 0.258978i | ||||
\(629\) | −1.56781 | − | 1.56781i | −0.0625127 | − | 0.0625127i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6001 | −1.17836 | −0.589181 | − | 0.808001i | \(-0.700549\pi\) | ||||
−0.589181 | + | 0.808001i | \(0.700549\pi\) | |||||||
\(632\) | −22.8847 | + | 21.2095i | −0.910305 | + | 0.843667i | ||||
\(633\) | 1.85200 | − | 3.20776i | 0.0736104 | − | 0.127497i | ||||
\(634\) | 21.6209 | + | 18.6135i | 0.858676 | + | 0.739236i | ||||
\(635\) | 21.3927 | + | 5.73215i | 0.848943 | + | 0.227474i | ||||
\(636\) | 15.8419 | − | 40.3190i | 0.628171 | − | 1.59875i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.2081 | + | 11.0460i | −0.641686 | + | 0.437314i | ||||
\(639\) | 2.79143 | − | 1.61163i | 0.110427 | − | 0.0637552i | ||||
\(640\) | 39.2494 | + | 10.5732i | 1.55147 | + | 0.417944i | ||||
\(641\) | −6.92621 | + | 11.9965i | −0.273569 | + | 0.473835i | −0.969773 | − | 0.244009i | \(-0.921537\pi\) |
0.696204 | + | 0.717844i | \(0.254871\pi\) | |||||||
\(642\) | 37.8427 | + | 18.2330i | 1.49353 | + | 0.719599i | ||||
\(643\) | 27.3875 | + | 27.3875i | 1.08006 | + | 1.08006i | 0.996503 | + | 0.0835527i | \(0.0266267\pi\) |
0.0835527 | + | 0.996503i | \(0.473373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.58562 | − | 1.58562i | 0.0624339 | − | 0.0624339i | ||||
\(646\) | 3.96780 | + | 11.3463i | 0.156111 | + | 0.446414i | ||||
\(647\) | −19.7138 | − | 11.3818i | −0.775029 | − | 0.447463i | 0.0596369 | − | 0.998220i | \(-0.481006\pi\) |
−0.834666 | + | 0.550757i | \(0.814339\pi\) | |||||||
\(648\) | 9.39535 | − | 30.3970i | 0.369084 | − | 1.19411i | ||||
\(649\) | 4.06512 | + | 7.04099i | 0.159570 | + | 0.276383i | ||||
\(650\) | −3.46089 | + | 18.2721i | −0.135747 | + | 0.716690i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.920190 | + | 2.11130i | 0.0360374 | + | 0.0826850i | ||||
\(653\) | −0.724195 | + | 2.70273i | −0.0283399 | + | 0.105766i | −0.978647 | − | 0.205548i | \(-0.934102\pi\) |
0.950307 | + | 0.311314i | \(0.100769\pi\) | |||||||
\(654\) | −1.48294 | − | 19.8394i | −0.0579876 | − | 0.775783i | ||||
\(655\) | −5.38345 | − | 3.10814i | −0.210349 | − | 0.121445i | ||||
\(656\) | 6.03531 | − | 26.3494i | 0.235639 | − | 1.02877i | ||||
\(657\) | 4.19598i | 0.163701i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.71933 | − | 2.71933i | 0.105930 | − | 0.105930i | −0.652155 | − | 0.758085i | \(-0.726135\pi\) |
0.758085 | + | 0.652155i | \(0.226135\pi\) | |||||||
\(660\) | −25.7211 | + | 34.8230i | −1.00119 | + | 1.35548i | ||||
\(661\) | −26.9300 | + | 7.21586i | −1.04745 | + | 0.280665i | −0.741199 | − | 0.671285i | \(-0.765743\pi\) |
−0.306255 | + | 0.951949i | \(0.599076\pi\) | |||||||
\(662\) | 7.96218 | + | 6.85466i | 0.309459 | + | 0.266414i | ||||
\(663\) | 18.8139 | − | 10.8622i | 0.730673 | − | 0.421854i | ||||
\(664\) | −7.70632 | − | 4.84838i | −0.299063 | − | 0.188154i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.146242 | − | 0.772098i | 0.00566676 | − | 0.0299182i | ||||
\(667\) | −0.262949 | + | 0.981340i | −0.0101814 | + | 0.0379976i | ||||
\(668\) | −10.2070 | + | 8.13344i | −0.394921 | + | 0.314692i | ||||
\(669\) | 6.34665 | − | 1.70058i | 0.245376 | − | 0.0657482i | ||||
\(670\) | −3.05206 | + | 6.33457i | −0.117912 | + | 0.244726i | ||||
\(671\) | 30.0502 | 1.16008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.95707 | 0.152534 | 0.0762670 | − | 0.997087i | \(-0.475700\pi\) | ||||
0.0762670 | + | 0.997087i | \(0.475700\pi\) | |||||||
\(674\) | −7.41523 | + | 15.3903i | −0.285624 | + | 0.592814i | ||||
\(675\) | −23.8025 | + | 6.37787i | −0.916160 | + | 0.245484i | ||||
\(676\) | 16.0094 | − | 12.7571i | 0.615748 | − | 0.490657i | ||||
\(677\) | −2.95679 | + | 11.0349i | −0.113639 | + | 0.424105i | −0.999181 | − | 0.0404526i | \(-0.987120\pi\) |
0.885543 | + | 0.464558i | \(0.153787\pi\) | |||||||
\(678\) | 7.99291 | − | 42.1993i | 0.306966 | − | 1.62065i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −33.1933 | + | 52.7596i | −1.27291 | + | 2.02324i | ||||
\(681\) | 16.0961 | − | 9.29311i | 0.616806 | − | 0.356113i | ||||
\(682\) | −17.4062 | − | 14.9850i | −0.666517 | − | 0.573806i | ||||
\(683\) | 23.4497 | − | 6.28333i | 0.897277 | − | 0.240425i | 0.219431 | − | 0.975628i | \(-0.429580\pi\) |
0.677847 | + | 0.735203i | \(0.262913\pi\) | |||||||
\(684\) | −2.53107 | + | 3.42674i | −0.0967780 | + | 0.131024i | ||||
\(685\) | −19.7233 | + | 19.7233i | −0.753587 | + | 0.753587i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 35.9272i | − | 1.37071i | ||||||
\(688\) | −0.992866 | + | 0.622799i | −0.0378527 | + | 0.0237440i | ||||
\(689\) | −14.6425 | − | 8.45384i | −0.557834 | − | 0.322066i | ||||
\(690\) | 0.167147 | + | 2.23617i | 0.00636320 | + | 0.0851296i | ||||
\(691\) | −4.31928 | + | 16.1198i | −0.164313 | + | 0.613225i | 0.833814 | + | 0.552046i | \(0.186153\pi\) |
−0.998127 | + | 0.0611789i | \(0.980514\pi\) | |||||||
\(692\) | 4.29008 | + | 9.84324i | 0.163084 | + | 0.374184i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.20205 | + | 38.0239i | −0.273386 | + | 1.44337i | ||||
\(695\) | 16.3934 | + | 28.3942i | 0.621836 | + | 1.07705i | ||||
\(696\) | −28.2252 | − | 8.72407i | −1.06987 | − | 0.330685i | ||||
\(697\) | 35.8985 | + | 20.7260i | 1.35975 | + | 0.785052i | ||||
\(698\) | −1.96022 | − | 5.60543i | −0.0741955 | − | 0.212169i | ||||
\(699\) | 22.5756 | − | 22.5756i | 0.853888 | − | 0.853888i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.7735 | + | 22.7735i | 0.860141 | + | 0.860141i | 0.991354 | − | 0.131213i | \(-0.0418871\pi\) |
−0.131213 | + | 0.991354i | \(0.541887\pi\) | |||||||
\(702\) | −6.60063 | − | 3.18025i | −0.249125 | − | 0.120031i | ||||
\(703\) | 0.250443 | − | 0.433780i | 0.00944564 | − | 0.0163603i | ||||
\(704\) | 17.1679 | − | 14.7399i | 0.647039 | − | 0.555530i | ||||
\(705\) | −72.4553 | + | 41.8321i | −2.72882 | + | 1.57549i | ||||
\(706\) | 19.0709 | − | 12.9970i | 0.717744 | − | 0.489149i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.47821 | + | 11.3975i | −0.168301 | + | 0.428343i | ||||
\(709\) | 25.5187 | + | 6.83770i | 0.958373 | + | 0.256795i | 0.703912 | − | 0.710288i | \(-0.251435\pi\) |
0.254462 | + | 0.967083i | \(0.418102\pi\) | |||||||
\(710\) | 8.07420 | + | 6.95110i | 0.303019 | + | 0.260870i | ||||
\(711\) | 8.47886 | − | 14.6858i | 0.317982 | − | 0.550761i | ||||
\(712\) | 27.0733 | + | 29.2118i | 1.01462 | + | 1.09476i | ||||
\(713\) | −1.18967 | −0.0445536 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9480 | + | 11.9480i | 0.446829 | + | 0.446829i | ||||
\(716\) | 27.1785 | − | 36.7960i | 1.01571 | − | 1.37513i | ||||
\(717\) | 10.4709 | + | 39.0780i | 0.391043 | + | 1.45939i | ||||
\(718\) | −23.3200 | + | 1.74310i | −0.870294 | + | 0.0650520i | ||||
\(719\) | −6.50750 | − | 11.2713i | −0.242689 | − | 0.420349i | 0.718790 | − | 0.695227i | \(-0.244696\pi\) |
−0.961479 | + | 0.274877i | \(0.911363\pi\) | |||||||
\(720\) | −22.0771 | + | 0.809141i | −0.822766 | + | 0.0301549i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.9601 | − | 13.6030i | 0.742838 | − | 0.506250i | ||||
\(723\) | −50.1054 | − | 13.4257i | −1.86344 | − | 0.499307i | ||||
\(724\) | 1.17645 | − | 10.4055i | 0.0437225 | − | 0.386717i | ||||
\(725\) | 10.0371 | + | 37.4591i | 0.372770 | + | 1.39120i | ||||
\(726\) | −2.98314 | − | 8.53057i | −0.110715 | − | 0.316599i | ||||
\(727\) | 19.1133i | 0.708874i | 0.935080 | + | 0.354437i | \(0.115327\pi\) | ||||
−0.935080 | + | 0.354437i | \(0.884673\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 2.61946i | − | 0.0970171i | ||||||
\(730\) | −13.0919 | + | 4.57825i | −0.484553 | + | 0.169448i | ||||
\(731\) | −0.465165 | − | 1.73602i | −0.0172047 | − | 0.0642090i | ||||
\(732\) | 28.2064 | + | 35.3975i | 1.04254 | + | 1.30833i | ||||
\(733\) | 45.7708 | + | 12.2643i | 1.69058 | + | 0.452991i | 0.970540 | − | 0.240939i | \(-0.0774553\pi\) |
0.720043 | + | 0.693929i | \(0.244122\pi\) | |||||||
\(734\) | −18.8579 | − | 27.6709i | −0.696059 | − | 1.02135i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.175792 | − | 1.15878i | 0.00647977 | − | 0.0427130i | ||||
\(737\) | 1.95707 | + | 3.38975i | 0.0720897 | + | 0.124863i | ||||
\(738\) | 1.09508 | + | 14.6505i | 0.0403106 | + | 0.539293i | ||||
\(739\) | 2.93350 | + | 10.9480i | 0.107911 | + | 0.402728i | 0.998659 | − | 0.0517686i | \(-0.0164858\pi\) |
−0.890748 | + | 0.454497i | \(0.849819\pi\) | |||||||
\(740\) | 2.56859 | − | 0.386148i | 0.0944234 | − | 0.0141951i | ||||
\(741\) | 3.47028 | + | 3.47028i | 0.127484 | + | 0.127484i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.9072 | 1.42737 | 0.713683 | − | 0.700469i | \(-0.247026\pi\) | ||||
0.713683 | + | 0.700469i | \(0.247026\pi\) | |||||||
\(744\) | 1.31336 | − | 34.5691i | 0.0481503 | − | 1.26737i | ||||
\(745\) | 14.8336 | − | 25.6926i | 0.543463 | − | 0.941305i | ||||
\(746\) | −28.6909 | + | 33.3265i | −1.05045 | + | 1.22017i | ||||
\(747\) | 4.77963 | + | 1.28070i | 0.174878 | + | 0.0468583i | ||||
\(748\) | 13.8633 | + | 31.8083i | 0.506893 | + | 1.16303i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.7287 | + | 26.0139i | 0.647360 | + | 0.949893i | ||||
\(751\) | 15.2975 | − | 8.83202i | 0.558214 | − | 0.322285i | −0.194215 | − | 0.980959i | \(-0.562216\pi\) |
0.752428 | + | 0.658674i | \(0.228882\pi\) | |||||||
\(752\) | 41.7956 | − | 12.8572i | 1.52413 | − | 0.468854i | ||||
\(753\) | 20.1004 | − | 34.8149i | 0.732499 | − | 1.26873i | ||||
\(754\) | −5.00490 | + | 10.3877i | −0.182268 | + | 0.378298i | ||||
\(755\) | −3.95367 | − | 3.95367i | −0.143889 | − | 0.143889i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.2828 | + | 21.2828i | −0.773535 | + | 0.773535i | −0.978723 | − | 0.205187i | \(-0.934220\pi\) |
0.205187 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(758\) | −37.7768 | + | 13.2106i | −1.37212 | + | 0.479829i | ||||
\(759\) | 1.08102 | + | 0.624129i | 0.0392387 | + | 0.0226545i | ||||
\(760\) | −13.4534 | − | 4.15830i | −0.488008 | − | 0.150837i | ||||
\(761\) | 7.59613 | + | 13.1569i | 0.275359 | + | 0.476937i | 0.970226 | − | 0.242202i | \(-0.0778698\pi\) |
−0.694866 | + | 0.719139i | \(0.744536\pi\) | |||||||
\(762\) | 18.2447 | + | 3.45570i | 0.660936 | + | 0.125187i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.97854 | − | 1.17031i | −0.107760 | − | 0.0423402i | ||||
\(765\) | 8.76800 | − | 32.7226i | 0.317008 | − | 1.18309i | ||||
\(766\) | 7.30023 | − | 0.545671i | 0.263768 | − | 0.0197159i | ||||
\(767\) | 4.13916 | + | 2.38975i | 0.149457 | + | 0.0862888i | ||||
\(768\) | 33.4773 | + | 6.38736i | 1.20801 | + | 0.230484i | ||||
\(769\) | 40.3950i | 1.45668i | 0.685216 | + | 0.728340i | \(0.259708\pi\) | ||||
−0.685216 | + | 0.728340i | \(0.740292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.13436 | − | 8.13436i | 0.292952 | − | 0.292952i | ||||
\(772\) | −32.6400 | + | 4.90690i | −1.17474 | + | 0.176603i | ||||
\(773\) | 18.5723 | − | 4.97644i | 0.668001 | − | 0.178990i | 0.0911466 | − | 0.995837i | \(-0.470947\pi\) |
0.576854 | + | 0.816847i | \(0.304280\pi\) | |||||||
\(774\) | 0.415589 | − | 0.482736i | 0.0149380 | − | 0.0173516i | ||||
\(775\) | −39.3274 | + | 22.7057i | −1.41268 | + | 0.815613i | ||||
\(776\) | 1.78212 | + | 7.82868i | 0.0639742 | + | 0.281033i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.17225 | − | 1.54789i | −0.292989 | − | 0.0554947i | ||||
\(779\) | −2.42366 | + | 9.04523i | −0.0868367 | + | 0.324079i | ||||
\(780\) | −2.85919 | + | 25.2890i | −0.102375 | + | 0.905490i | ||||
\(781\) | 5.72864 | − | 1.53498i | 0.204987 | − | 0.0549260i | ||||
\(782\) | 1.61912 | + | 0.780111i | 0.0578998 | + | 0.0278967i | ||||
\(783\) | −15.2787 | −0.546017 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.4943 | 0.517323 | ||||||||
\(786\) | −4.69536 | − | 2.26227i | −0.167478 | − | 0.0806926i | ||||
\(787\) | −39.6347 | + | 10.6201i | −1.41283 | + | 0.378566i | −0.882933 | − | 0.469499i | \(-0.844435\pi\) |
−0.529893 | + | 0.848064i | \(0.677768\pi\) | |||||||
\(788\) | 34.3240 | + | 3.88069i | 1.22274 | + | 0.138244i | ||||
\(789\) | −0.199771 | + | 0.745554i | −0.00711202 | + | 0.0265424i | ||||
\(790\) | 55.0727 | + | 10.4312i | 1.95940 | + | 0.371127i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.54874 | + | 10.4090i | −0.232699 | + | 0.369867i | ||||
\(793\) | 15.2988 | − | 8.83277i | 0.543276 | − | 0.313661i | ||||
\(794\) | −19.3590 | + | 22.4869i | −0.687026 | + | 0.798030i | ||||
\(795\) | −75.1690 | + | 20.1415i | −2.66597 | + | 0.714345i | ||||
\(796\) | 4.81688 | + | 32.0411i | 0.170730 | + | 1.13567i | ||||
\(797\) | 21.9291 | − | 21.9291i | 0.776770 | − | 0.776770i | −0.202510 | − | 0.979280i | \(-0.564910\pi\) |
0.979280 | + | 0.202510i | \(0.0649099\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.0556i | 2.37226i | ||||||||
\(800\) | −16.3048 | − | 41.6612i | −0.576462 | − | 1.47295i | ||||
\(801\) | −18.7461 | − | 10.8231i | −0.662360 | − | 0.382414i | ||||
\(802\) | −31.1797 | + | 2.33059i | −1.10099 | + | 0.0822961i | ||||
\(803\) | −1.99821 | + | 7.45742i | −0.0705153 | + | 0.263167i | ||||
\(804\) | −2.15595 | + | 5.48709i | −0.0760344 | + | 0.193515i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2662 | − | 2.51274i | −0.467283 | − | 0.0885073i | ||||
\(807\) | 28.4708 | + | 49.3130i | 1.00222 | + | 1.73590i | ||||
\(808\) | −17.5394 | + | 9.25695i | −0.617033 | + | 0.325658i | ||||
\(809\) | −2.56402 | − | 1.48034i | −0.0901462 | − | 0.0520459i | 0.454249 | − | 0.890875i | \(-0.349908\pi\) |
−0.544395 | + | 0.838829i | \(0.683241\pi\) | |||||||
\(810\) | −53.9513 | + | 18.8668i | −1.89566 | + | 0.662911i | ||||
\(811\) | 10.4787 | − | 10.4787i | 0.367956 | − | 0.367956i | −0.498775 | − | 0.866731i | \(-0.666217\pi\) |
0.866731 | + | 0.498775i | \(0.166217\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.5723 | + | 14.5723i | 0.511073 | + | 0.511073i | ||||
\(814\) | 0.627601 | − | 1.30259i | 0.0219974 | − | 0.0456558i | ||||
\(815\) | 2.06870 | − | 3.58309i | 0.0724633 | − | 0.125510i | ||||
\(816\) | −24.4557 | + | 46.1868i | −0.856121 | + | 1.61686i | ||||
\(817\) | 0.351619 | − | 0.203007i | 0.0123016 | − | 0.00710232i | ||||
\(818\) | −1.16140 | − | 1.70416i | −0.0406075 | − | 0.0595847i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −44.5164 | + | 19.4020i | −1.55458 | + | 0.677547i | ||||
\(821\) | 14.6458 | + | 3.92432i | 0.511140 | + | 0.136960i | 0.505165 | − | 0.863023i | \(-0.331431\pi\) |
0.00597486 | + | 0.999982i | \(0.498098\pi\) | |||||||
\(822\) | −15.2580 | + | 17.7233i | −0.532185 | + | 0.618170i | ||||
\(823\) | −4.94250 | + | 8.56066i | −0.172285 | + | 0.298406i | −0.939218 | − | 0.343321i | \(-0.888448\pi\) |
0.766934 | + | 0.641726i | \(0.221782\pi\) | |||||||
\(824\) | 28.6252 | − | 26.5297i | 0.997204 | − | 0.924205i | ||||
\(825\) | 47.6477 | 1.65888 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.5166 | − | 16.5166i | −0.574338 | − | 0.574338i | 0.359000 | − | 0.933338i | \(-0.383118\pi\) |
−0.933338 | + | 0.359000i | \(0.883118\pi\) | |||||||
\(828\) | 0.0946964 | + | 0.629906i | 0.00329093 | + | 0.0218907i | ||||
\(829\) | −8.73597 | − | 32.6031i | −0.303413 | − | 1.13235i | −0.934303 | − | 0.356480i | \(-0.883977\pi\) |
0.630890 | − | 0.775872i | \(-0.282690\pi\) | |||||||
\(830\) | 1.21915 | + | 16.3103i | 0.0423173 | + | 0.566140i | ||||
\(831\) | 4.45249 | + | 7.71194i | 0.154455 | + | 0.267524i | ||||
\(832\) | 4.40776 | − | 12.5504i | 0.152812 | − | 0.435107i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.4811 | + | 22.7159i | 0.536065 | + | 0.786587i | ||||
\(835\) | 22.6468 | + | 6.06820i | 0.783726 | + | 0.209999i | ||||
\(836\) | −6.13030 | + | 4.88491i | −0.212021 | + | 0.168948i | ||||
\(837\) | −4.63057 | − | 17.2815i | −0.160056 | − | 0.597337i | ||||
\(838\) | 45.6965 | − | 15.9801i | 1.57856 | − | 0.552023i | ||||
\(839\) | − | 30.3282i | − | 1.04705i | −0.852012 | − | 0.523523i | \(-0.824617\pi\) | ||
0.852012 | − | 0.523523i | \(-0.175383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 4.95519i | − | 0.170869i | ||||||
\(842\) | −12.6677 | − | 36.2246i | −0.436559 | − | 1.24838i | ||||
\(843\) | −10.9490 | − | 40.8623i | −0.377104 | − | 1.40737i | ||||
\(844\) | 3.45580 | + | 0.390715i | 0.118953 | + | 0.0134490i | ||||
\(845\) | −35.5210 | − | 9.51782i | −1.22196 | − | 0.327423i | ||||
\(846\) | −19.6388 | + | 13.3840i | −0.675196 | + | 0.460151i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40.6470 | − | 1.48974i | 1.39582 | − | 0.0511578i | ||||
\(849\) | 29.3945 | + | 50.9127i | 1.00882 | + | 1.74732i | ||||
\(850\) | 68.4130 | − | 5.11368i | 2.34655 | − | 0.175398i | ||||
\(851\) | −0.0193838 | − | 0.0723414i | −0.000664469 | − | 0.00247983i | ||||
\(852\) | 7.18527 | + | 5.30722i | 0.246163 | + | 0.181822i | ||||
\(853\) | 10.6402 | + | 10.6402i | 0.364313 | + | 0.364313i | 0.865398 | − | 0.501085i | \(-0.167066\pi\) |
−0.501085 | + | 0.865398i | \(0.667066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.65306 | 0.261729 | ||||||||
\(856\) | −1.49738 | + | 39.4126i | −0.0511793 | + | 1.34709i | ||||
\(857\) | −18.3762 | + | 31.8285i | −0.627719 | + | 1.08724i | 0.360289 | + | 0.932841i | \(0.382678\pi\) |
−0.988008 | + | 0.154401i | \(0.950655\pi\) | |||||||
\(858\) | 10.7364 | + | 9.24302i | 0.366536 | + | 0.315552i | ||||
\(859\) | 26.6404 | + | 7.13827i | 0.908958 | + | 0.243555i | 0.682859 | − | 0.730550i | \(-0.260736\pi\) |
0.226099 | + | 0.974104i | \(0.427403\pi\) | |||||||
\(860\) | 1.95964 | + | 0.769968i | 0.0668231 | + | 0.0262557i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.8749 | + | 16.2709i | −0.813182 | + | 0.554190i | ||||
\(863\) | 32.5024 | − | 18.7653i | 1.10639 | − | 0.638777i | 0.168501 | − | 0.985701i | \(-0.446107\pi\) |
0.937893 | + | 0.346924i | \(0.112774\pi\) | |||||||
\(864\) | 17.5170 | − | 1.95671i | 0.595939 | − | 0.0665686i | ||||
\(865\) | 9.64460 | − | 16.7049i | 0.327926 | − | 0.567985i | ||||
\(866\) | −28.9549 | − | 13.9508i | −0.983927 | − | 0.474066i | ||||
\(867\) | −31.0631 | − | 31.0631i | −1.05496 | − | 1.05496i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.0630 | − | 22.0630i | 0.748436 | − | 0.748436i | ||||
\(870\) | 17.5188 | + | 50.0966i | 0.593943 | + | 1.69843i | ||||
\(871\) | 1.99272 | + | 1.15050i | 0.0675208 | + | 0.0389832i | ||||
\(872\) | 16.5202 | − | 8.71905i | 0.559445 | − | 0.295264i | ||||
\(873\) | −2.18181 | − | 3.77901i | −0.0738432 | − | 0.127900i | ||||
\(874\) | −0.0755591 | + | 0.398921i | −0.00255582 | + | 0.0134937i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6600 | + | 4.64607i | −0.360170 | + | 0.156976i | ||||
\(877\) | 8.86399 | − | 33.0809i | 0.299316 | − | 1.11706i | −0.638413 | − | 0.769694i | \(-0.720409\pi\) |
0.937729 | − | 0.347368i | \(-0.112924\pi\) | |||||||
\(878\) | −3.76082 | − | 50.3139i | −0.126922 | − | 1.69801i | ||||
\(879\) | −47.7575 | − | 27.5728i | −1.61082 | − | 0.930007i | ||||
\(880\) | −39.6225 | − | 9.07550i | −1.33567 | − | 0.305935i | ||||
\(881\) | 11.3518i | 0.382453i | 0.981546 | + | 0.191226i | \(0.0612464\pi\) | ||||
−0.981546 | + | 0.191226i | \(0.938754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.21956 | + | 3.21956i | −0.108347 | + | 0.108347i | −0.759202 | − | 0.650855i | \(-0.774411\pi\) |
0.650855 | + | 0.759202i | \(0.274411\pi\) | |||||||
\(884\) | 16.4074 | + | 12.1189i | 0.551842 | + | 0.407604i | ||||
\(885\) | 21.2489 | − | 5.69363i | 0.714275 | − | 0.191389i | ||||
\(886\) | 7.75776 | + | 6.67868i | 0.260627 | + | 0.224375i | ||||
\(887\) | −23.4899 | + | 13.5619i | −0.788714 | + | 0.455364i | −0.839510 | − | 0.543345i | \(-0.817158\pi\) |
0.0507957 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(888\) | 2.12347 | − | 0.483386i | 0.0712591 | − | 0.0162214i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.3152 | − | 70.2989i | 0.446327 | − | 2.35642i | ||||
\(891\) | −8.23456 | + | 30.7318i | −0.275868 | + | 1.02955i | ||||
\(892\) | 3.84465 | + | 4.82483i | 0.128729 | + | 0.161547i | ||||
\(893\) | −14.6322 | + | 3.92068i | −0.489647 | + | 0.131201i | ||||
\(894\) | 10.7967 | − | 22.4087i | 0.361097 | − | 0.749459i | ||||
\(895\) | −82.1780 | −2.74691 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.733810 | 0.0245012 | ||||||||
\(898\) | −21.8743 | + | 45.4001i | −0.729953 | + | 1.51502i | ||||
\(899\) | −27.1967 | + | 7.28734i | −0.907061 | + | 0.243046i | ||||
\(900\) | 15.1526 | + | 19.0157i | 0.505087 | + | 0.633856i | ||||
\(901\) | −16.1431 | + | 60.2469i | −0.537805 | + | 2.00711i | ||||
\(902\) | −5.03060 | + | 26.5595i | −0.167501 | + | 0.884336i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.3209 | − | 8.95100i | 1.30780 | − | 0.297706i | ||||
\(905\) | −16.2915 | + | 9.40592i | −0.541549 | + | 0.312663i | ||||
\(906\) | −3.55276 | − | 3.05858i | −0.118032 | − | 0.101614i | ||||
\(907\) | −50.8747 | + | 13.6318i | −1.68927 | + | 0.452638i | −0.970201 | − | 0.242303i | \(-0.922097\pi\) |
−0.719067 | + | 0.694941i | \(0.755431\pi\) | |||||||
\(908\) | 14.0373 | + | 10.3683i | 0.465843 | + | 0.344084i | ||||
\(909\) | 7.62161 | − | 7.62161i | 0.252793 | − | 0.252793i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3761i | 0.608827i | 0.952540 | + | 0.304414i | \(0.0984605\pi\) | ||||
−0.952540 | + | 0.304414i | \(0.901540\pi\) | |||||||
\(912\) | −11.5083 | − | 2.63597i | −0.381079 | − | 0.0872858i | ||||
\(913\) | 7.88484 | + | 4.55231i | 0.260950 | + | 0.150660i | ||||
\(914\) | −0.504184 | − | 6.74520i | −0.0166769 | − | 0.223111i | ||||
\(915\) | 21.0443 | − | 78.5383i | 0.695702 | − | 2.59640i | ||||
\(916\) | 30.9238 | − | 13.4778i | 1.02175 | − | 0.445320i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.02999 | + | 26.5563i | −0.166015 | + | 0.876490i | ||||
\(919\) | −22.0221 | − | 38.1433i | −0.726441 | − | 1.25823i | −0.958378 | − | 0.285502i | \(-0.907840\pi\) |
0.231937 | − | 0.972731i | \(-0.425494\pi\) | |||||||
\(920\) | −1.86205 | + | 0.982754i | −0.0613900 | + | 0.0324005i | ||||
\(921\) | 28.0744 | + | 16.2088i | 0.925083 | + | 0.534097i | ||||
\(922\) | −4.31835 | − | 12.3487i | −0.142217 | − | 0.406683i | ||||
\(923\) | 2.46531 | − | 2.46531i | 0.0811467 | − | 0.0811467i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.02146 | − | 2.02146i | −0.0664653 | − | 0.0664653i | ||||
\(926\) | −0.982732 | − | 0.473491i | −0.0322946 | − | 0.0155599i | ||||
\(927\) | −10.6057 | + | 18.3696i | −0.348338 | + | 0.603338i | ||||
\(928\) | −3.07936 | − | 27.5672i | −0.101085 | − | 0.904938i | ||||
\(929\) | 18.4252 | − | 10.6378i | 0.604512 | − | 0.349015i | −0.166303 | − | 0.986075i | \(-0.553183\pi\) |
0.770814 | + | 0.637060i | \(0.219850\pi\) | |||||||
\(930\) | −51.3540 | + | 34.9982i | −1.68396 | + | 1.14764i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.9007 | + | 10.9626i | 0.913919 | + | 0.359091i | ||||
\(933\) | 3.88323 | + | 1.04051i | 0.127131 | + | 0.0340647i | ||||
\(934\) | 3.80568 | + | 3.27632i | 0.124526 | + | 0.107204i | ||||
\(935\) | 31.1664 | − | 53.9817i | 1.01925 | − | 1.76539i | ||||
\(936\) | −0.274465 | + | 7.22419i | −0.00897115 | + | 0.236130i | ||||
\(937\) | −1.53994 | −0.0503075 | −0.0251537 | − | 0.999684i | \(-0.508008\pi\) | ||||
−0.0251537 | + | 0.999684i | \(0.508008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.8969 | − | 32.8969i | −1.07355 | − | 1.07355i | ||||
\(940\) | −63.1875 | − | 46.6718i | −2.06095 | − | 1.52227i | ||||
\(941\) | −5.60595 | − | 20.9217i | −0.182749 | − | 0.682028i | −0.995101 | − | 0.0988611i | \(-0.968480\pi\) |
0.812352 | − | 0.583167i | \(-0.198187\pi\) | |||||||
\(942\) | 12.1187 | − | 0.905838i | 0.394848 | − | 0.0295138i | ||||
\(943\) | 0.700083 | + | 1.21258i | 0.0227978 | + | 0.0394870i | ||||
\(944\) | −11.4902 | + | 0.421122i | −0.373973 | + | 0.0137064i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.968506 | − | 0.660045i | 0.0314888 | − | 0.0214599i | ||||
\(947\) | 44.2550 | + | 11.8581i | 1.43809 | + | 0.385336i | 0.891866 | − | 0.452300i | \(-0.149396\pi\) |
0.546228 | + | 0.837636i | \(0.316063\pi\) | |||||||
\(948\) | 46.6983 | + | 5.27974i | 1.51669 | + | 0.171478i | ||||
\(949\) | 1.17468 | + | 4.38397i | 0.0381318 | + | 0.142310i | ||||
\(950\) | 5.11590 | + | 14.6294i | 0.165982 | + | 0.474640i | ||||
\(951\) | − | 42.9706i | − | 1.39342i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 41.8875i | − | 1.35687i | −0.734661 | − | 0.678435i | \(-0.762659\pi\) | ||
0.734661 | − | 0.678435i | \(-0.237341\pi\) | |||||||
\(954\) | −20.8668 | + | 7.29713i | −0.675588 | + | 0.236253i | ||||
\(955\) | 1.48794 | + | 5.55305i | 0.0481485 | + | 0.179693i | ||||
\(956\) | −29.7077 | + | 23.6725i | −0.960817 | + | 0.765624i | ||||
\(957\) | 28.5361 | + | 7.64621i | 0.922440 | + | 0.247167i | ||||
\(958\) | −7.90884 | − | 11.6049i | −0.255523 | − | 0.374937i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −26.5009 | − | 55.1918i | −0.855314 | − | 1.78131i | ||||
\(961\) | −0.985195 | − | 1.70641i | −0.0317805 | − | 0.0550454i | ||||
\(962\) | −0.0633581 | − | 0.847632i | −0.00204275 | − | 0.0273287i | ||||
\(963\) | −5.54795 | − | 20.7052i | −0.178780 | − | 0.667216i | ||||
\(964\) | −7.24071 | − | 48.1640i | −0.233207 | − | 1.55126i | ||||
\(965\) | 41.9274 | + | 41.9274i | 1.34969 | + | 1.34969i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.99067 | −0.0640156 | −0.0320078 | − | 0.999488i | \(-0.510190\pi\) | ||||
−0.0320078 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(968\) | 6.22346 | − | 5.76788i | 0.200030 | − | 0.185387i | ||||
\(969\) | 9.05224 | − | 15.6789i | 0.290800 | − | 0.503680i | ||||
\(970\) | 9.41034 | − | 10.9308i | 0.302148 | − | 0.350966i | ||||
\(971\) | 5.53347 | + | 1.48269i | 0.177578 | + | 0.0475818i | 0.346512 | − | 0.938045i | \(-0.387366\pi\) |
−0.168934 | + | 0.985627i | \(0.554033\pi\) | |||||||
\(972\) | −26.7916 | + | 11.6768i | −0.859341 | + | 0.374535i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.89948 | + | 8.65650i | 0.189031 | + | 0.277372i | ||||
\(975\) | 24.2578 | − | 14.0053i | 0.776873 | − | 0.448528i | ||||
\(976\) | −19.8865 | + | 37.5574i | −0.636551 | + | 1.20218i | ||||
\(977\) | −12.5203 | + | 21.6858i | −0.400560 | + | 0.693790i | −0.993794 | − | 0.111241i | \(-0.964518\pi\) |
0.593234 | + | 0.805030i | \(0.297851\pi\) | |||||||
\(978\) | 1.50571 | − | 3.12511i | 0.0481473 | − | 0.0999300i | ||||
\(979\) | −28.1629 | − | 28.1629i | −0.900089 | − | 0.900089i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.17874 | + | 7.17874i | −0.229199 | + | 0.229199i | ||||
\(982\) | 40.5875 | − | 14.1935i | 1.29520 | − | 0.452931i | ||||
\(983\) | −27.2577 | − | 15.7373i | −0.869387 | − | 0.501941i | −0.00224251 | − | 0.999997i | \(-0.500714\pi\) |
−0.867144 | + | 0.498057i | \(0.834047\pi\) | |||||||
\(984\) | −36.0076 | + | 19.0041i | −1.14788 | + | 0.605830i | ||||
\(985\) | −31.0268 | − | 53.7399i | −0.988595 | − | 1.71230i | ||||
\(986\) | 41.7929 | + | 7.91593i | 1.33096 | + | 0.252095i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.68514 | + | 4.28885i | −0.0536116 | + | 0.136446i | ||||
\(989\) | 0.0157124 | − | 0.0586393i | 0.000499624 | − | 0.00186462i | ||||
\(990\) | 22.0305 | − | 1.64672i | 0.700175 | − | 0.0523361i | ||||
\(991\) | 45.8894 | + | 26.4943i | 1.45773 | + | 0.841619i | 0.998899 | − | 0.0469070i | \(-0.0149364\pi\) |
0.458827 | + | 0.888526i | \(0.348270\pi\) | |||||||
\(992\) | 30.2476 | − | 11.8379i | 0.960362 | − | 0.375854i | ||||
\(993\) | − | 15.8245i | − | 0.502175i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.1582 | − | 41.1582i | 1.30480 | − | 1.30480i | ||||
\(996\) | 2.03867 | + | 13.5609i | 0.0645977 | + | 0.429694i | ||||
\(997\) | 9.78775 | − | 2.62262i | 0.309981 | − | 0.0830592i | −0.100475 | − | 0.994940i | \(-0.532036\pi\) |
0.410456 | + | 0.911880i | \(0.365370\pi\) | |||||||
\(998\) | 30.4302 | − | 35.3469i | 0.963252 | − | 1.11889i | ||||
\(999\) | 0.975405 | − | 0.563150i | 0.0308604 | − | 0.0178173i |
(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 | 784.2.w.e.227.3 | 32 | ||
7.2 | even | 3 | inner | 784.2.w.e.19.2 | 32 | ||
7.3 | odd | 6 | 112.2.j.d.83.7 | yes | 16 | ||
7.4 | even | 3 | 112.2.j.d.83.8 | yes | 16 | ||
7.5 | odd | 6 | inner | 784.2.w.e.19.1 | 32 | ||
7.6 | odd | 2 | inner | 784.2.w.e.227.4 | 32 | ||
16.11 | odd | 4 | inner | 784.2.w.e.619.1 | 32 | ||
28.3 | even | 6 | 448.2.j.d.111.7 | 16 | |||
28.11 | odd | 6 | 448.2.j.d.111.2 | 16 | |||
56.3 | even | 6 | 896.2.j.g.223.2 | 16 | |||
56.11 | odd | 6 | 896.2.j.g.223.7 | 16 | |||
56.45 | odd | 6 | 896.2.j.h.223.7 | 16 | |||
56.53 | even | 6 | 896.2.j.h.223.2 | 16 | |||
112.3 | even | 12 | 896.2.j.h.671.2 | 16 | |||
112.11 | odd | 12 | 112.2.j.d.27.7 | ✓ | 16 | ||
112.27 | even | 4 | inner | 784.2.w.e.619.2 | 32 | ||
112.45 | odd | 12 | 896.2.j.g.671.7 | 16 | |||
112.53 | even | 12 | 448.2.j.d.335.7 | 16 | |||
112.59 | even | 12 | 112.2.j.d.27.8 | yes | 16 | ||
112.67 | odd | 12 | 896.2.j.h.671.7 | 16 | |||
112.75 | even | 12 | inner | 784.2.w.e.411.3 | 32 | ||
112.101 | odd | 12 | 448.2.j.d.335.2 | 16 | |||
112.107 | odd | 12 | inner | 784.2.w.e.411.4 | 32 | ||
112.109 | even | 12 | 896.2.j.g.671.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.7 | ✓ | 16 | 112.11 | odd | 12 | ||
112.2.j.d.27.8 | yes | 16 | 112.59 | even | 12 | ||
112.2.j.d.83.7 | yes | 16 | 7.3 | odd | 6 | ||
112.2.j.d.83.8 | yes | 16 | 7.4 | even | 3 | ||
448.2.j.d.111.2 | 16 | 28.11 | odd | 6 | |||
448.2.j.d.111.7 | 16 | 28.3 | even | 6 | |||
448.2.j.d.335.2 | 16 | 112.101 | odd | 12 | |||
448.2.j.d.335.7 | 16 | 112.53 | even | 12 | |||
784.2.w.e.19.1 | 32 | 7.5 | odd | 6 | inner | ||
784.2.w.e.19.2 | 32 | 7.2 | even | 3 | inner | ||
784.2.w.e.227.3 | 32 | 1.1 | even | 1 | trivial | ||
784.2.w.e.227.4 | 32 | 7.6 | odd | 2 | inner | ||
784.2.w.e.411.3 | 32 | 112.75 | even | 12 | inner | ||
784.2.w.e.411.4 | 32 | 112.107 | odd | 12 | inner | ||
784.2.w.e.619.1 | 32 | 16.11 | odd | 4 | inner | ||
784.2.w.e.619.2 | 32 | 112.27 | even | 4 | inner | ||
896.2.j.g.223.2 | 16 | 56.3 | even | 6 | |||
896.2.j.g.223.7 | 16 | 56.11 | odd | 6 | |||
896.2.j.g.671.2 | 16 | 112.109 | even | 12 | |||
896.2.j.g.671.7 | 16 | 112.45 | odd | 12 | |||
896.2.j.h.223.2 | 16 | 56.53 | even | 6 | |||
896.2.j.h.223.7 | 16 | 56.45 | odd | 6 | |||
896.2.j.h.671.2 | 16 | 112.3 | even | 12 | |||
896.2.j.h.671.7 | 16 | 112.67 | odd | 12 |