Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
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([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (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: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(-1.33068 - 0.478848i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.k.765.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19412 | + | 0.757684i | −0.844368 | + | 0.535763i | ||||
\(3\) | 0.538823 | + | 2.01092i | 0.311090 | + | 1.16100i | 0.927575 | + | 0.373636i | \(0.121889\pi\) |
−0.616486 | + | 0.787366i | \(0.711444\pi\) | |||||||
\(4\) | 0.851831 | − | 1.80953i | 0.425915 | − | 0.904763i | ||||
\(5\) | 0.129523 | − | 0.483385i | 0.0579243 | − | 0.216177i | −0.930897 | − | 0.365282i | \(-0.880973\pi\) |
0.988821 | + | 0.149105i | \(0.0476393\pi\) | |||||||
\(6\) | −2.16706 | − | 1.99301i | −0.884697 | − | 0.813643i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.353863 | + | 2.80620i | 0.125109 | + | 0.992143i | ||||
\(9\) | −1.15537 | + | 0.667056i | −0.385125 | + | 0.222352i | ||||
\(10\) | 0.211588 | + | 0.675356i | 0.0669100 | + | 0.213566i | ||||
\(11\) | −0.456405 | + | 0.122293i | −0.137611 | + | 0.0368728i | −0.326967 | − | 0.945036i | \(-0.606027\pi\) |
0.189356 | + | 0.981909i | \(0.439360\pi\) | |||||||
\(12\) | 4.09779 | + | 0.737945i | 1.18293 | + | 0.213026i | ||||
\(13\) | −3.17982 | + | 3.17982i | −0.881923 | + | 0.881923i | −0.993730 | − | 0.111807i | \(-0.964336\pi\) |
0.111807 | + | 0.993730i | \(0.464336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.04184 | 0.269001 | ||||||||
\(16\) | −2.54877 | − | 3.08282i | −0.637192 | − | 0.770705i | ||||
\(17\) | −0.646137 | + | 1.11914i | −0.156711 | + | 0.271432i | −0.933681 | − | 0.358106i | \(-0.883423\pi\) |
0.776970 | + | 0.629538i | \(0.216756\pi\) | |||||||
\(18\) | 0.874235 | − | 1.67195i | 0.206059 | − | 0.394083i | ||||
\(19\) | −3.59560 | − | 0.963437i | −0.824886 | − | 0.221028i | −0.178405 | − | 0.983957i | \(-0.557094\pi\) |
−0.646482 | + | 0.762930i | \(0.723760\pi\) | |||||||
\(20\) | −0.764367 | − | 0.646137i | −0.170918 | − | 0.144481i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.452341 | − | 0.491843i | 0.0964395 | − | 0.104861i | ||||
\(23\) | 2.26039 | − | 1.30504i | 0.471324 | − | 0.272119i | −0.245470 | − | 0.969404i | \(-0.578942\pi\) |
0.716794 | + | 0.697285i | \(0.245609\pi\) | |||||||
\(24\) | −5.45237 | + | 2.22364i | −1.11296 | + | 0.453898i | ||||
\(25\) | 4.11324 | + | 2.37478i | 0.822648 | + | 0.474956i | ||||
\(26\) | 1.38778 | − | 6.20637i | 0.272166 | − | 1.21717i | ||||
\(27\) | 2.45234 | + | 2.45234i | 0.471953 | + | 0.471953i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.98602 | + | 6.98602i | −1.29727 | + | 1.29727i | −0.367084 | + | 0.930188i | \(0.619644\pi\) |
−0.930188 | + | 0.367084i | \(0.880356\pi\) | |||||||
\(30\) | −1.24408 | + | 0.789383i | −0.227136 | + | 0.144121i | ||||
\(31\) | −4.17982 | + | 7.23966i | −0.750717 | + | 1.30028i | 0.196758 | + | 0.980452i | \(0.436959\pi\) |
−0.947475 | + | 0.319829i | \(0.896375\pi\) | |||||||
\(32\) | 5.37933 | + | 1.75009i | 0.950940 | + | 0.309375i | ||||
\(33\) | −0.491843 | − | 0.851898i | −0.0856189 | − | 0.148296i | ||||
\(34\) | −0.0763926 | − | 1.82596i | −0.0131012 | − | 0.313149i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.222871 | + | 2.65890i | 0.0371452 | + | 0.443150i | ||||
\(37\) | −1.21525 | + | 4.53539i | −0.199786 | + | 0.745613i | 0.791189 | + | 0.611571i | \(0.209462\pi\) |
−0.990976 | + | 0.134042i | \(0.957204\pi\) | |||||||
\(38\) | 5.02354 | − | 1.57387i | 0.814926 | − | 0.255315i | ||||
\(39\) | −8.10770 | − | 4.68099i | −1.29827 | − | 0.749558i | ||||
\(40\) | 1.40231 | + | 0.192415i | 0.221725 | + | 0.0304235i | ||||
\(41\) | 9.93254i | 1.55120i | 0.631223 | + | 0.775601i | \(0.282553\pi\) | ||||
−0.631223 | + | 0.775601i | \(0.717447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.61241 | − | 7.61241i | −1.16088 | − | 1.16088i | −0.984283 | − | 0.176598i | \(-0.943491\pi\) |
−0.176598 | − | 0.984283i | \(-0.556509\pi\) | |||||||
\(44\) | −0.167487 | + | 0.930050i | −0.0252496 | + | 0.140210i | ||||
\(45\) | 0.172798 | + | 0.644890i | 0.0257592 | + | 0.0961345i | ||||
\(46\) | −1.71036 | + | 3.27103i | −0.252180 | + | 0.482287i | ||||
\(47\) | 2.29805 | + | 3.98033i | 0.335205 | + | 0.580591i | 0.983524 | − | 0.180777i | \(-0.0578612\pi\) |
−0.648319 | + | 0.761368i | \(0.724528\pi\) | |||||||
\(48\) | 4.82596 | − | 6.78645i | 0.696567 | − | 0.979540i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.71102 | + | 0.280770i | −0.949082 | + | 0.0397068i | ||||
\(51\) | −2.59866 | − | 0.696308i | −0.363885 | − | 0.0975026i | ||||
\(52\) | 3.04530 | + | 8.46263i | 0.422307 | + | 1.17356i | ||||
\(53\) | 5.38786 | − | 1.44367i | 0.740079 | − | 0.198304i | 0.130966 | − | 0.991387i | \(-0.458192\pi\) |
0.609113 | + | 0.793083i | \(0.291526\pi\) | |||||||
\(54\) | −4.78648 | − | 1.07028i | −0.651358 | − | 0.145647i | ||||
\(55\) | 0.236459i | 0.0318842i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.74956i | − | 1.02645i | ||||||
\(58\) | 3.04893 | − | 13.6353i | 0.400344 | − | 1.79041i | ||||
\(59\) | 8.73669 | − | 2.34099i | 1.13742 | − | 0.304771i | 0.359507 | − | 0.933142i | \(-0.382945\pi\) |
0.777913 | + | 0.628372i | \(0.216278\pi\) | |||||||
\(60\) | 0.887469 | − | 1.88523i | 0.114572 | − | 0.243382i | ||||
\(61\) | −5.94749 | − | 1.59362i | −0.761498 | − | 0.204043i | −0.142886 | − | 0.989739i | \(-0.545638\pi\) |
−0.618612 | + | 0.785697i | \(0.712305\pi\) | |||||||
\(62\) | −0.494178 | − | 11.8120i | −0.0627607 | − | 1.50012i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.74956 | + | 1.98602i | −0.968695 | + | 0.248253i | ||||
\(65\) | 1.12522 | + | 1.94894i | 0.139566 | + | 0.241736i | ||||
\(66\) | 1.23279 | + | 0.644604i | 0.151746 | + | 0.0793452i | ||||
\(67\) | −3.65002 | − | 13.6221i | −0.445921 | − | 1.66420i | −0.713493 | − | 0.700662i | \(-0.752888\pi\) |
0.267572 | − | 0.963538i | \(-0.413779\pi\) | |||||||
\(68\) | 1.47472 | + | 2.12252i | 0.178836 | + | 0.257394i | ||||
\(69\) | 3.84227 | + | 3.84227i | 0.462555 | + | 0.462555i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.62395i | − | 0.904797i | −0.891816 | − | 0.452398i | \(-0.850569\pi\) | ||
0.891816 | − | 0.452398i | \(-0.149431\pi\) | |||||||
\(72\) | −2.28074 | − | 3.00617i | −0.268788 | − | 0.354281i | ||||
\(73\) | 0.482023 | + | 0.278296i | 0.0564166 | + | 0.0325721i | 0.527943 | − | 0.849280i | \(-0.322963\pi\) |
−0.471526 | + | 0.881852i | \(0.656297\pi\) | |||||||
\(74\) | −1.98523 | − | 6.33656i | −0.230779 | − | 0.736610i | ||||
\(75\) | −2.55917 | + | 9.55097i | −0.295508 | + | 1.10285i | ||||
\(76\) | −4.80620 | + | 5.68564i | −0.551309 | + | 0.652188i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.2283 | − | 0.553431i | 1.49780 | − | 0.0626638i | ||||
\(79\) | 0.744616 | + | 1.28971i | 0.0837758 | + | 0.145104i | 0.904869 | − | 0.425690i | \(-0.139969\pi\) |
−0.821093 | + | 0.570794i | \(0.806635\pi\) | |||||||
\(80\) | −1.82031 | + | 0.832742i | −0.203517 | + | 0.0931034i | ||||
\(81\) | −5.61124 | + | 9.71895i | −0.623471 | + | 1.07988i | ||||
\(82\) | −7.52572 | − | 11.8606i | −0.831077 | − | 1.30979i | ||||
\(83\) | 1.47209 | − | 1.47209i | 0.161583 | − | 0.161583i | −0.621685 | − | 0.783268i | \(-0.713551\pi\) |
0.783268 | + | 0.621685i | \(0.213551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.457288 | + | 0.457288i | 0.0495998 | + | 0.0495998i | ||||
\(86\) | 14.8579 | + | 3.32231i | 1.60217 | + | 0.358254i | ||||
\(87\) | −17.8125 | − | 10.2841i | −1.90970 | − | 1.10257i | ||||
\(88\) | −0.504685 | − | 1.23749i | −0.0537996 | − | 0.131917i | ||||
\(89\) | 10.6453 | − | 6.14609i | 1.12840 | − | 0.651484i | 0.184871 | − | 0.982763i | \(-0.440813\pi\) |
0.943533 | + | 0.331279i | \(0.107480\pi\) | |||||||
\(90\) | −0.694964 | − | 0.639148i | −0.0732556 | − | 0.0673721i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.436028 | − | 5.20190i | −0.0454591 | − | 0.542336i | ||||
\(93\) | −16.8105 | − | 4.50437i | −1.74317 | − | 0.467081i | ||||
\(94\) | −5.75997 | − | 3.01179i | −0.594096 | − | 0.310643i | ||||
\(95\) | −0.931423 | + | 1.61327i | −0.0955620 | + | 0.165518i | ||||
\(96\) | −0.620770 | + | 11.7604i | −0.0633571 | + | 1.20029i | ||||
\(97\) | 5.50078 | 0.558519 | 0.279260 | − | 0.960216i | \(-0.409911\pi\) | ||||
0.279260 | + | 0.960216i | \(0.409911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.445742 | − | 0.445742i | 0.0447988 | − | 0.0447988i | ||||
\(100\) | 7.80101 | − | 5.42011i | 0.780101 | − | 0.542011i | ||||
\(101\) | −9.60136 | + | 2.57268i | −0.955371 | + | 0.255991i | −0.702640 | − | 0.711546i | \(-0.747996\pi\) |
−0.252731 | + | 0.967537i | \(0.581329\pi\) | |||||||
\(102\) | 3.63068 | − | 1.13749i | 0.359491 | − | 0.112628i | ||||
\(103\) | −12.6446 | + | 7.30038i | −1.24591 | + | 0.719328i | −0.970292 | − | 0.241938i | \(-0.922217\pi\) |
−0.275621 | + | 0.961266i | \(0.588884\pi\) | |||||||
\(104\) | −10.0484 | − | 7.79800i | −0.985330 | − | 0.764657i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.33988 | + | 5.80620i | −0.518655 | + | 0.563948i | ||||
\(107\) | 0.381339 | − | 1.42318i | 0.0368654 | − | 0.137584i | −0.945040 | − | 0.326954i | \(-0.893978\pi\) |
0.981906 | + | 0.189370i | \(0.0606446\pi\) | |||||||
\(108\) | 6.52656 | − | 2.34860i | 0.628018 | − | 0.225994i | ||||
\(109\) | −1.58554 | − | 5.91732i | −0.151867 | − | 0.566776i | −0.999353 | − | 0.0359585i | \(-0.988552\pi\) |
0.847486 | − | 0.530818i | \(-0.178115\pi\) | |||||||
\(110\) | −0.179161 | − | 0.282360i | −0.0170824 | − | 0.0269220i | ||||
\(111\) | −9.77509 | −0.927810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6379 | 1.65924 | 0.829619 | − | 0.558331i | \(-0.188558\pi\) | ||||
0.829619 | + | 0.558331i | \(0.188558\pi\) | |||||||
\(114\) | 5.87172 | + | 9.25388i | 0.549937 | + | 0.866706i | ||||
\(115\) | −0.338064 | − | 1.26167i | −0.0315246 | − | 0.117651i | ||||
\(116\) | 6.69048 | + | 18.5923i | 0.621195 | + | 1.72625i | ||||
\(117\) | 1.55276 | − | 5.79500i | 0.143553 | − | 0.535748i | ||||
\(118\) | −8.65890 | + | 9.41506i | −0.797116 | + | 0.866727i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.368667 | + | 2.92361i | 0.0336546 | + | 0.266888i | ||||
\(121\) | −9.33293 | + | 5.38837i | −0.848448 | + | 0.489852i | ||||
\(122\) | 8.30946 | − | 2.60334i | 0.752303 | − | 0.235695i | ||||
\(123\) | −19.9735 | + | 5.35188i | −1.80095 | + | 0.482563i | ||||
\(124\) | 9.53985 | + | 13.7305i | 0.856704 | + | 1.23303i | ||||
\(125\) | 3.45001 | − | 3.45001i | 0.308578 | − | 0.308578i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.75122 | 0.687809 | 0.343905 | − | 0.939005i | \(-0.388250\pi\) | ||||
0.343905 | + | 0.939005i | \(0.388250\pi\) | |||||||
\(128\) | 7.74911 | − | 8.24326i | 0.684931 | − | 0.728608i | ||||
\(129\) | 11.2062 | − | 19.4097i | 0.986648 | − | 1.70892i | ||||
\(130\) | −2.82032 | − | 1.47470i | −0.247358 | − | 0.129340i | ||||
\(131\) | −2.07126 | − | 0.554991i | −0.180966 | − | 0.0484898i | 0.167198 | − | 0.985923i | \(-0.446528\pi\) |
−0.348164 | + | 0.937434i | \(0.613195\pi\) | |||||||
\(132\) | −1.96050 | + | 0.164331i | −0.170639 | + | 0.0143031i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.6798 | + | 13.5008i | 1.26814 | + | 1.16629i | ||||
\(135\) | 1.50306 | − | 0.867792i | 0.129363 | − | 0.0746877i | ||||
\(136\) | −3.36919 | − | 1.41717i | −0.288905 | − | 0.121521i | ||||
\(137\) | 5.17194 | + | 2.98602i | 0.441869 | + | 0.255113i | 0.704390 | − | 0.709813i | \(-0.251221\pi\) |
−0.262521 | + | 0.964926i | \(0.584554\pi\) | |||||||
\(138\) | −7.49934 | − | 1.67689i | −0.638386 | − | 0.142747i | ||||
\(139\) | 9.10343 | + | 9.10343i | 0.772142 | + | 0.772142i | 0.978481 | − | 0.206338i | \(-0.0661547\pi\) |
−0.206338 | + | 0.978481i | \(0.566155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.76588 | + | 6.76588i | −0.569790 | + | 0.569790i | ||||
\(142\) | 5.77655 | + | 9.10389i | 0.484757 | + | 0.763982i | ||||
\(143\) | 1.06241 | − | 1.84016i | 0.0888436 | − | 0.153882i | ||||
\(144\) | 5.00120 | + | 1.86164i | 0.416766 | + | 0.155137i | ||||
\(145\) | 2.47209 | + | 4.28179i | 0.205296 | + | 0.355583i | ||||
\(146\) | −0.786453 | + | 0.0329029i | −0.0650873 | + | 0.00272306i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.17171 | + | 6.06241i | 0.589511 | + | 0.498327i | ||||
\(149\) | −1.14828 | + | 4.28543i | −0.0940706 | + | 0.351076i | −0.996877 | − | 0.0789711i | \(-0.974837\pi\) |
0.902806 | + | 0.430047i | \(0.141503\pi\) | |||||||
\(150\) | −4.18066 | − | 13.3440i | −0.341349 | − | 1.08953i | ||||
\(151\) | 10.4144 | + | 6.01276i | 0.847513 | + | 0.489312i | 0.859811 | − | 0.510613i | \(-0.170581\pi\) |
−0.0122982 | + | 0.999924i | \(0.503915\pi\) | |||||||
\(152\) | 1.43125 | − | 10.4309i | 0.116090 | − | 0.846058i | ||||
\(153\) | − | 1.72404i | − | 0.139380i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.95816 | + | 2.95816i | 0.237605 | + | 0.237605i | ||||
\(156\) | −15.3768 | + | 10.6837i | −1.23113 | + | 0.855380i | ||||
\(157\) | 3.05954 | + | 11.4183i | 0.244178 | + | 0.911283i | 0.973795 | + | 0.227428i | \(0.0730315\pi\) |
−0.729617 | + | 0.683856i | \(0.760302\pi\) | |||||||
\(158\) | −1.86635 | − | 0.975885i | −0.148479 | − | 0.0776372i | ||||
\(159\) | 5.80620 | + | 10.0566i | 0.460462 | + | 0.797543i | ||||
\(160\) | 1.54271 | − | 2.37361i | 0.121962 | − | 0.187651i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.663415 | − | 15.8571i | −0.0521228 | − | 1.24585i | ||||
\(163\) | 1.25491 | + | 0.336253i | 0.0982925 | + | 0.0263374i | 0.307630 | − | 0.951506i | \(-0.400464\pi\) |
−0.209338 | + | 0.977843i | \(0.567131\pi\) | |||||||
\(164\) | 17.9732 | + | 8.46085i | 1.40347 | + | 0.660681i | ||||
\(165\) | −0.475500 | + | 0.127410i | −0.0370176 | + | 0.00991884i | ||||
\(166\) | −0.642470 | + | 2.87323i | −0.0498654 | + | 0.223006i | ||||
\(167\) | − | 13.0690i | − | 1.01131i | −0.862736 | − | 0.505655i | \(-0.831251\pi\) | ||
0.862736 | − | 0.505655i | \(-0.168749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.22248i | − | 0.555575i | ||||||
\(170\) | −0.892535 | − | 0.199576i | −0.0684543 | − | 0.0153068i | ||||
\(171\) | 4.79693 | − | 1.28533i | 0.366830 | − | 0.0982918i | ||||
\(172\) | −20.2593 | + | 7.29037i | −1.54476 | + | 0.555885i | ||||
\(173\) | 5.20256 | + | 1.39402i | 0.395543 | + | 0.105986i | 0.451108 | − | 0.892470i | \(-0.351029\pi\) |
−0.0555642 | + | 0.998455i | \(0.517696\pi\) | |||||||
\(174\) | 29.0623 | − | 1.21588i | 2.20321 | − | 0.0921758i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.54028 | + | 1.09532i | 0.116103 | + | 0.0825626i | ||||
\(177\) | 9.41506 | + | 16.3074i | 0.707679 | + | 1.22574i | ||||
\(178\) | −8.05499 | + | 15.4049i | −0.603747 | + | 1.15465i | ||||
\(179\) | 3.23233 | + | 12.0632i | 0.241596 | + | 0.901649i | 0.975064 | + | 0.221924i | \(0.0712338\pi\) |
−0.733468 | + | 0.679724i | \(0.762100\pi\) | |||||||
\(180\) | 1.31414 | + | 0.236655i | 0.0979502 | + | 0.0176392i | ||||
\(181\) | −1.37018 | − | 1.37018i | −0.101844 | − | 0.101844i | 0.654349 | − | 0.756193i | \(-0.272943\pi\) |
−0.756193 | + | 0.654349i | \(0.772943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.8186i | − | 0.947576i | ||||||
\(184\) | 4.46207 | + | 5.88131i | 0.328948 | + | 0.433576i | ||||
\(185\) | 2.03494 | + | 1.17487i | 0.149612 | + | 0.0863783i | ||||
\(186\) | 23.4866 | − | 7.35832i | 1.72212 | − | 0.539538i | ||||
\(187\) | 0.158037 | − | 0.589801i | 0.0115568 | − | 0.0431305i | ||||
\(188\) | 9.16007 | − | 0.767805i | 0.668067 | − | 0.0559979i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.110122 | − | 2.63216i | −0.00798908 | − | 0.190957i | ||||
\(191\) | 0.707725 | + | 1.22582i | 0.0512092 | + | 0.0886970i | 0.890494 | − | 0.454995i | \(-0.150359\pi\) |
−0.839285 | + | 0.543692i | \(0.817026\pi\) | |||||||
\(192\) | −8.16937 | − | 14.5136i | −0.589573 | − | 1.04743i | ||||
\(193\) | 5.48485 | − | 9.50005i | 0.394808 | − | 0.683828i | −0.598268 | − | 0.801296i | \(-0.704144\pi\) |
0.993077 | + | 0.117468i | \(0.0374776\pi\) | |||||||
\(194\) | −6.56857 | + | 4.16785i | −0.471596 | + | 0.299234i | ||||
\(195\) | −3.31285 | + | 3.31285i | −0.237238 | + | 0.237238i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.92787 | + | 8.92787i | 0.636084 | + | 0.636084i | 0.949587 | − | 0.313503i | \(-0.101503\pi\) |
−0.313503 | + | 0.949587i | \(0.601503\pi\) | |||||||
\(198\) | −0.194537 | + | 0.870000i | −0.0138251 | + | 0.0618282i | ||||
\(199\) | −7.58080 | − | 4.37678i | −0.537388 | − | 0.310261i | 0.206631 | − | 0.978419i | \(-0.433750\pi\) |
−0.744020 | + | 0.668157i | \(0.767083\pi\) | |||||||
\(200\) | −5.20860 | + | 12.3829i | −0.368303 | + | 0.875606i | ||||
\(201\) | 25.4261 | − | 14.6798i | 1.79342 | − | 1.03543i | ||||
\(202\) | 9.51587 | − | 10.3469i | 0.669535 | − | 0.728003i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.47360 | + | 4.10920i | −0.243201 | + | 0.287701i | ||||
\(205\) | 4.80125 | + | 1.28649i | 0.335334 | + | 0.0898524i | ||||
\(206\) | 9.56779 | − | 18.2981i | 0.666620 | − | 1.27489i | ||||
\(207\) | −1.74106 | + | 3.01561i | −0.121012 | + | 0.209600i | ||||
\(208\) | 17.9074 | + | 1.69819i | 1.24166 | + | 0.117748i | ||||
\(209\) | 1.75887 | 0.121664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.88837 | + | 9.88837i | −0.680743 | + | 0.680743i | −0.960168 | − | 0.279424i | \(-0.909856\pi\) |
0.279424 | + | 0.960168i | \(0.409856\pi\) | |||||||
\(212\) | 1.97718 | − | 10.9792i | 0.135793 | − | 0.754057i | ||||
\(213\) | 15.3311 | − | 4.10796i | 1.05047 | − | 0.281473i | ||||
\(214\) | 0.622954 | + | 1.98837i | 0.0425843 | + | 0.135922i | ||||
\(215\) | −4.66571 | + | 2.69375i | −0.318199 | + | 0.183712i | ||||
\(216\) | −6.01398 | + | 7.74956i | −0.409199 | + | 0.527291i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.37678 | + | 5.86463i | 0.431890 | + | 0.397203i | ||||
\(219\) | −0.299905 | + | 1.11926i | −0.0202657 | + | 0.0756327i | ||||
\(220\) | 0.427879 | + | 0.201423i | 0.0288476 | + | 0.0135800i | ||||
\(221\) | −1.50407 | − | 5.61327i | −0.101175 | − | 0.377589i | ||||
\(222\) | 11.6726 | − | 7.40642i | 0.783413 | − | 0.497087i | ||||
\(223\) | 6.12483 | 0.410149 | 0.205074 | − | 0.978746i | \(-0.434256\pi\) | ||||
0.205074 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.33645 | −0.422430 | ||||||||
\(226\) | −21.0618 | + | 13.3640i | −1.40101 | + | 0.888958i | ||||
\(227\) | −2.02602 | − | 7.56121i | −0.134472 | − | 0.501855i | −1.00000 | 0.000994262i | \(-0.999684\pi\) | |
0.865528 | − | 0.500861i | \(-0.166983\pi\) | |||||||
\(228\) | −14.0230 | − | 6.60132i | −0.928698 | − | 0.437183i | ||||
\(229\) | 4.68228 | − | 17.4745i | 0.309414 | − | 1.15475i | −0.619665 | − | 0.784866i | \(-0.712732\pi\) |
0.929079 | − | 0.369882i | \(-0.120602\pi\) | |||||||
\(230\) | 1.35964 | + | 1.25044i | 0.0896517 | + | 0.0824514i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −22.0763 | − | 17.1321i | −1.44938 | − | 1.12478i | ||||
\(233\) | 21.3351 | − | 12.3178i | 1.39771 | − | 0.806966i | 0.403554 | − | 0.914956i | \(-0.367775\pi\) |
0.994152 | + | 0.107990i | \(0.0344415\pi\) | |||||||
\(234\) | 2.53659 | + | 8.09641i | 0.165822 | + | 0.529279i | ||||
\(235\) | 2.22169 | − | 0.595299i | 0.144927 | − | 0.0388330i | ||||
\(236\) | 3.20610 | − | 17.8034i | 0.208699 | − | 1.15890i | ||||
\(237\) | −2.19229 | + | 2.19229i | −0.142404 | + | 0.142404i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.8844 | −0.704052 | −0.352026 | − | 0.935990i | \(-0.614507\pi\) | ||||
−0.352026 | + | 0.935990i | \(0.614507\pi\) | |||||||
\(240\) | −2.65540 | − | 3.21180i | −0.171405 | − | 0.207321i | ||||
\(241\) | 7.57634 | − | 13.1226i | 0.488035 | − | 0.845302i | −0.511870 | − | 0.859063i | \(-0.671047\pi\) |
0.999905 | + | 0.0137611i | \(0.00438043\pi\) | |||||||
\(242\) | 7.06193 | − | 13.5058i | 0.453958 | − | 0.868183i | ||||
\(243\) | −12.5176 | − | 3.35408i | −0.803003 | − | 0.215164i | ||||
\(244\) | −7.94996 | + | 9.40463i | −0.508944 | + | 0.602070i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.7957 | − | 21.5244i | 1.26213 | − | 1.37234i | ||||
\(247\) | 14.4969 | − | 8.36979i | 0.922415 | − | 0.532557i | ||||
\(248\) | −21.7950 | − | 9.16758i | −1.38399 | − | 0.582142i | ||||
\(249\) | 3.75345 | + | 2.16706i | 0.237865 | + | 0.137332i | ||||
\(250\) | −1.50570 | + | 6.73372i | −0.0952287 | + | 0.425878i | ||||
\(251\) | −0.848041 | − | 0.848041i | −0.0535279 | − | 0.0535279i | 0.679836 | − | 0.733364i | \(-0.262051\pi\) |
−0.733364 | + | 0.679836i | \(0.762051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.872056 | + | 0.872056i | −0.0548257 | + | 0.0548257i | ||||
\(254\) | −9.25586 | + | 5.87297i | −0.580764 | + | 0.368503i | ||||
\(255\) | −0.673170 | + | 1.16596i | −0.0421555 | + | 0.0730155i | ||||
\(256\) | −3.00756 | + | 15.7148i | −0.187972 | + | 0.982174i | ||||
\(257\) | 5.82596 | + | 10.0909i | 0.363413 | + | 0.629450i | 0.988520 | − | 0.151089i | \(-0.0482780\pi\) |
−0.625107 | + | 0.780539i | \(0.714945\pi\) | |||||||
\(258\) | 1.32490 | + | 31.6681i | 0.0824848 | + | 1.97157i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.48515 | − | 0.375949i | 0.278157 | − | 0.0233154i | ||||
\(261\) | 3.41141 | − | 12.7315i | 0.211161 | − | 0.788062i | ||||
\(262\) | 2.89383 | − | 0.906632i | 0.178781 | − | 0.0560119i | ||||
\(263\) | 15.7448 | + | 9.09027i | 0.970867 | + | 0.560530i | 0.899500 | − | 0.436920i | \(-0.143931\pi\) |
0.0713665 | + | 0.997450i | \(0.477264\pi\) | |||||||
\(264\) | 2.21655 | − | 1.68167i | 0.136419 | − | 0.103499i | ||||
\(265\) | − | 2.79140i | − | 0.171474i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0952 | + | 18.0952i | 1.10741 | + | 1.10741i | ||||
\(268\) | −27.7587 | − | 4.99889i | −1.69563 | − | 0.305356i | ||||
\(269\) | 8.21935 | + | 30.6750i | 0.501143 | + | 1.87029i | 0.492474 | + | 0.870327i | \(0.336093\pi\) |
0.00866872 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(270\) | −1.13732 | + | 2.17509i | −0.0692149 | + | 0.132372i | ||||
\(271\) | −11.1066 | − | 19.2372i | −0.674677 | − | 1.16857i | −0.976563 | − | 0.215231i | \(-0.930950\pi\) |
0.301886 | − | 0.953344i | \(-0.402384\pi\) | |||||||
\(272\) | 5.09697 | − | 0.860511i | 0.309049 | − | 0.0521761i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.43836 | + | 0.353036i | −0.509780 | + | 0.0213277i | ||||
\(275\) | −2.16772 | − | 0.580840i | −0.130719 | − | 0.0350260i | ||||
\(276\) | 10.2256 | − | 3.67972i | 0.615512 | − | 0.221493i | ||||
\(277\) | 11.1559 | − | 2.98921i | 0.670291 | − | 0.179604i | 0.0924053 | − | 0.995721i | \(-0.470544\pi\) |
0.577886 | + | 0.816117i | \(0.303878\pi\) | |||||||
\(278\) | −17.7681 | − | 3.97304i | −1.06566 | − | 0.238287i | ||||
\(279\) | − | 11.1527i | − | 0.667694i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7783i | 1.59746i | 0.601690 | + | 0.798730i | \(0.294494\pi\) | ||||
−0.601690 | + | 0.798730i | \(0.705506\pi\) | |||||||
\(282\) | 2.95285 | − | 13.2056i | 0.175840 | − | 0.786384i | ||||
\(283\) | 16.0481 | − | 4.30009i | 0.953963 | − | 0.255614i | 0.251920 | − | 0.967748i | \(-0.418938\pi\) |
0.702043 | + | 0.712135i | \(0.252271\pi\) | |||||||
\(284\) | −13.7957 | − | 6.49432i | −0.818627 | − | 0.385367i | ||||
\(285\) | −3.74603 | − | 1.00374i | −0.221895 | − | 0.0594567i | ||||
\(286\) | 0.125609 | + | 3.00234i | 0.00742741 | + | 0.177532i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.38255 | + | 1.56631i | −0.435021 | + | 0.0922955i | ||||
\(289\) | 7.66501 | + | 13.2762i | 0.450883 | + | 0.780952i | ||||
\(290\) | −6.19621 | − | 3.23989i | −0.363854 | − | 0.190253i | ||||
\(291\) | 2.96395 | + | 11.0616i | 0.173750 | + | 0.648442i | ||||
\(292\) | 0.914187 | − | 0.635173i | 0.0534987 | − | 0.0371707i | ||||
\(293\) | −15.2256 | − | 15.2256i | −0.889492 | − | 0.889492i | 0.104983 | − | 0.994474i | \(-0.466521\pi\) |
−0.994474 | + | 0.104983i | \(0.966521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.52640i | − | 0.263537i | ||||||
\(296\) | −13.1573 | − | 1.80534i | −0.764750 | − | 0.104934i | ||||
\(297\) | −1.41917 | − | 0.819356i | −0.0823484 | − | 0.0475439i | ||||
\(298\) | −1.87582 | − | 5.98734i | −0.108664 | − | 0.346837i | ||||
\(299\) | −3.03785 | + | 11.3374i | −0.175683 | + | 0.655659i | ||||
\(300\) | 15.1027 | + | 12.7667i | 0.871957 | + | 0.737086i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.9918 | + | 0.710887i | −0.977768 | + | 0.0409069i | ||||
\(303\) | −10.3469 | − | 17.9213i | −0.594412 | − | 1.02955i | ||||
\(304\) | 6.19424 | + | 13.5402i | 0.355264 | + | 0.776581i | ||||
\(305\) | −1.54067 | + | 2.66852i | −0.0882185 | + | 0.152799i | ||||
\(306\) | 1.30628 | + | 2.05870i | 0.0746748 | + | 0.117688i | ||||
\(307\) | −13.7596 | + | 13.7596i | −0.785302 | + | 0.785302i | −0.980720 | − | 0.195418i | \(-0.937394\pi\) |
0.195418 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.4937 | − | 21.4937i | −1.22273 | − | 1.22273i | ||||
\(310\) | −5.77374 | − | 1.29104i | −0.327927 | − | 0.0733262i | ||||
\(311\) | −9.07434 | − | 5.23907i | −0.514558 | − | 0.297080i | 0.220147 | − | 0.975467i | \(-0.429346\pi\) |
−0.734705 | + | 0.678386i | \(0.762680\pi\) | |||||||
\(312\) | 10.2668 | − | 24.4083i | 0.581242 | − | 1.38185i | ||||
\(313\) | −28.4453 | + | 16.4229i | −1.60782 | + | 0.928276i | −0.617964 | + | 0.786206i | \(0.712042\pi\) |
−0.989857 | + | 0.142070i | \(0.954624\pi\) | |||||||
\(314\) | −12.3049 | − | 11.3167i | −0.694408 | − | 0.638637i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.96806 | − | 0.248785i | 0.166966 | − | 0.0139952i | ||||
\(317\) | −8.11991 | − | 2.17572i | −0.456059 | − | 0.122201i | 0.0234738 | − | 0.999724i | \(-0.492527\pi\) |
−0.479533 | + | 0.877524i | \(0.659194\pi\) | |||||||
\(318\) | −14.5530 | − | 7.60954i | −0.816094 | − | 0.426722i | ||||
\(319\) | 2.33411 | − | 4.04280i | 0.130685 | − | 0.226353i | ||||
\(320\) | −0.0437305 | + | 4.00326i | −0.00244461 | + | 0.223789i | ||||
\(321\) | 3.06736 | 0.171203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.40147 | − | 3.40147i | 0.189263 | − | 0.189263i | ||||
\(324\) | 12.8069 | + | 18.4326i | 0.711493 | + | 1.02403i | ||||
\(325\) | −20.6307 | + | 5.52799i | −1.14439 | + | 0.306638i | ||||
\(326\) | −1.75329 | + | 0.549302i | −0.0971056 | + | 0.0304230i | ||||
\(327\) | 11.0449 | − | 6.37678i | 0.610784 | − | 0.352636i | ||||
\(328\) | −27.8727 | + | 3.51476i | −1.53901 | + | 0.194070i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.471266 | − | 0.512421i | 0.0259423 | − | 0.0282078i | ||||
\(331\) | −0.131636 | + | 0.491271i | −0.00723535 | + | 0.0270027i | −0.969449 | − | 0.245292i | \(-0.921116\pi\) |
0.962214 | + | 0.272295i | \(0.0877827\pi\) | |||||||
\(332\) | −1.40982 | − | 3.91776i | −0.0773737 | − | 0.215015i | ||||
\(333\) | −1.62128 | − | 6.05071i | −0.0888458 | − | 0.331577i | ||||
\(334\) | 9.90218 | + | 15.6059i | 0.541823 | + | 0.853919i | ||||
\(335\) | −7.05747 | −0.385591 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0287 | 1.47235 | 0.736174 | − | 0.676792i | \(-0.236630\pi\) | ||||
0.736174 | + | 0.676792i | \(0.236630\pi\) | |||||||
\(338\) | 5.47236 | + | 8.62449i | 0.297657 | + | 0.469110i | ||||
\(339\) | 9.50373 | + | 35.4684i | 0.516172 | + | 1.92638i | ||||
\(340\) | 1.21701 | − | 0.437942i | 0.0660014 | − | 0.0237508i | ||||
\(341\) | 1.02233 | − | 3.81538i | 0.0553622 | − | 0.206614i | ||||
\(342\) | −4.75422 | + | 5.16939i | −0.257079 | + | 0.279529i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.6682 | − | 24.0557i | 1.00652 | − | 1.29700i | ||||
\(345\) | 2.35496 | − | 1.35964i | 0.126787 | − | 0.0732003i | ||||
\(346\) | −7.26869 | + | 2.27727i | −0.390767 | + | 0.122427i | ||||
\(347\) | −3.49011 | + | 0.935173i | −0.187359 | + | 0.0502027i | −0.351278 | − | 0.936271i | \(-0.614253\pi\) |
0.163919 | + | 0.986474i | \(0.447586\pi\) | |||||||
\(348\) | −33.7826 | + | 23.4719i | −1.81093 | + | 1.25823i | ||||
\(349\) | 2.82678 | − | 2.82678i | 0.151314 | − | 0.151314i | −0.627391 | − | 0.778705i | \(-0.715877\pi\) |
0.778705 | + | 0.627391i | \(0.215877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5960 | −0.832453 | ||||||||
\(352\) | −2.66918 | − | 0.140892i | −0.142268 | − | 0.00750959i | ||||
\(353\) | 0.424483 | − | 0.735225i | 0.0225929 | − | 0.0391321i | −0.854508 | − | 0.519438i | \(-0.826141\pi\) |
0.877101 | + | 0.480306i | \(0.159475\pi\) | |||||||
\(354\) | −23.5985 | − | 12.3393i | −1.25425 | − | 0.655824i | ||||
\(355\) | −3.68531 | − | 0.987475i | −0.195596 | − | 0.0524097i | ||||
\(356\) | −2.05348 | − | 24.4984i | −0.108834 | − | 1.29841i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9999 | − | 11.9558i | −0.687066 | − | 0.631885i | ||||
\(359\) | 24.8695 | − | 14.3584i | 1.31256 | − | 0.757808i | 0.330043 | − | 0.943966i | \(-0.392937\pi\) |
0.982520 | + | 0.186158i | \(0.0596035\pi\) | |||||||
\(360\) | −1.74855 | + | 0.713108i | −0.0921565 | + | 0.0375841i | ||||
\(361\) | −4.45438 | − | 2.57174i | −0.234441 | − | 0.135355i | ||||
\(362\) | 2.67431 | + | 0.597990i | 0.140559 | + | 0.0314297i | ||||
\(363\) | −15.8644 | − | 15.8644i | −0.832663 | − | 0.832663i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.196957 | − | 0.196957i | 0.0103092 | − | 0.0103092i | ||||
\(366\) | 9.71243 | + | 15.3069i | 0.507677 | + | 0.800103i | ||||
\(367\) | −10.6496 | + | 18.4456i | −0.555903 | + | 0.962853i | 0.441929 | + | 0.897050i | \(0.354294\pi\) |
−0.997833 | + | 0.0658029i | \(0.979039\pi\) | |||||||
\(368\) | −9.78440 | − | 3.64214i | −0.510047 | − | 0.189860i | ||||
\(369\) | −6.62556 | − | 11.4758i | −0.344913 | − | 0.597407i | ||||
\(370\) | −3.32013 | + | 0.138905i | −0.172606 | + | 0.00722131i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −22.4705 | + | 26.5821i | −1.16504 | + | 1.37822i | ||||
\(373\) | 2.04320 | − | 7.62531i | 0.105793 | − | 0.394824i | −0.892641 | − | 0.450768i | \(-0.851150\pi\) |
0.998434 | + | 0.0559442i | \(0.0178169\pi\) | |||||||
\(374\) | 0.258168 | + | 0.824033i | 0.0133496 | + | 0.0426097i | ||||
\(375\) | 8.79661 | + | 5.07873i | 0.454255 | + | 0.262264i | ||||
\(376\) | −10.3564 | + | 7.85728i | −0.534093 | + | 0.405208i | ||||
\(377\) | − | 44.4286i | − | 2.28819i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0442 | + | 12.0442i | 0.618668 | + | 0.618668i | 0.945190 | − | 0.326522i | \(-0.105877\pi\) |
−0.326522 | + | 0.945190i | \(0.605877\pi\) | |||||||
\(380\) | 2.12584 | + | 3.05967i | 0.109053 | + | 0.156958i | ||||
\(381\) | 4.17653 | + | 15.5870i | 0.213970 | + | 0.798548i | ||||
\(382\) | −1.77389 | − | 0.927536i | −0.0907600 | − | 0.0474569i | ||||
\(383\) | 0.0426634 | + | 0.0738952i | 0.00218000 | + | 0.00377587i | 0.867113 | − | 0.498111i | \(-0.165973\pi\) |
−0.864933 | + | 0.501887i | \(0.832639\pi\) | |||||||
\(384\) | 20.7519 | + | 11.1411i | 1.05899 | + | 0.568544i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.648472 | + | 15.5000i | 0.0330064 | + | 0.788927i | ||||
\(387\) | 13.8731 | + | 3.71728i | 0.705209 | + | 0.188960i | ||||
\(388\) | 4.68573 | − | 9.95380i | 0.237882 | − | 0.505328i | ||||
\(389\) | −0.720006 | + | 0.192925i | −0.0365058 | + | 0.00978169i | −0.277026 | − | 0.960863i | \(-0.589349\pi\) |
0.240520 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(390\) | 1.44584 | − | 6.46603i | 0.0732129 | − | 0.327420i | ||||
\(391\) | 3.37293i | 0.170576i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.46416i | − | 0.225187i | ||||||
\(394\) | −17.4254 | − | 3.89642i | −0.877880 | − | 0.196299i | ||||
\(395\) | 0.719873 | − | 0.192889i | 0.0362207 | − | 0.00970532i | ||||
\(396\) | −0.426885 | − | 1.18628i | −0.0214518 | − | 0.0596128i | ||||
\(397\) | 20.6847 | + | 5.54245i | 1.03813 | + | 0.278167i | 0.737340 | − | 0.675522i | \(-0.236081\pi\) |
0.300795 | + | 0.953689i | \(0.402748\pi\) | |||||||
\(398\) | 12.3686 | − | 0.517465i | 0.619980 | − | 0.0259382i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.16268 | − | 18.7332i | −0.158134 | − | 0.936658i | ||||
\(401\) | −17.1809 | − | 29.7583i | −0.857975 | − | 1.48606i | −0.873857 | − | 0.486182i | \(-0.838389\pi\) |
0.0158823 | − | 0.999874i | \(-0.494944\pi\) | |||||||
\(402\) | −19.2391 | + | 36.7943i | −0.959560 | + | 1.83513i | ||||
\(403\) | −9.72973 | − | 36.3118i | −0.484672 | − | 1.80882i | ||||
\(404\) | −3.52341 | + | 19.5654i | −0.175296 | + | 0.973415i | ||||
\(405\) | 3.97122 | + | 3.97122i | 0.197331 | + | 0.197331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.21859i | − | 0.109971i | ||||||
\(408\) | 1.03441 | − | 7.53875i | 0.0512111 | − | 0.373224i | ||||
\(409\) | −13.3958 | − | 7.73408i | −0.662380 | − | 0.382425i | 0.130803 | − | 0.991408i | \(-0.458244\pi\) |
−0.793183 | + | 0.608983i | \(0.791578\pi\) | |||||||
\(410\) | −6.70800 | + | 2.10161i | −0.331285 | + | 0.103791i | ||||
\(411\) | −3.21788 | + | 12.0093i | −0.158726 | + | 0.592374i | ||||
\(412\) | 2.43914 | + | 29.0995i | 0.120168 | + | 1.43363i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.205845 | − | 4.92017i | −0.0101168 | − | 0.241813i | ||||
\(415\) | −0.520919 | − | 0.902257i | −0.0255709 | − | 0.0442901i | ||||
\(416\) | −22.6702 | + | 11.5403i | −1.11150 | + | 0.565811i | ||||
\(417\) | −13.4011 | + | 23.2114i | −0.656254 | + | 1.13666i | ||||
\(418\) | −2.10030 | + | 1.33267i | −0.102729 | + | 0.0651829i | ||||
\(419\) | 26.1914 | − | 26.1914i | 1.27953 | − | 1.27953i | 0.338602 | − | 0.940930i | \(-0.390046\pi\) |
0.940930 | − | 0.338602i | \(-0.109954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3620 | + | 20.3620i | 0.992382 | + | 0.992382i | 0.999971 | − | 0.00758948i | \(-0.00241583\pi\) |
−0.00758948 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(422\) | 4.31561 | − | 19.3001i | 0.210081 | − | 0.939515i | ||||
\(423\) | −5.31021 | − | 3.06585i | −0.258191 | − | 0.149067i | ||||
\(424\) | 5.95780 | + | 14.6086i | 0.289336 | + | 0.709455i | ||||
\(425\) | −5.31544 | + | 3.06887i | −0.257837 | + | 0.148862i | ||||
\(426\) | −15.1946 | + | 16.5215i | −0.736182 | + | 0.800471i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.25044 | − | 1.90235i | −0.108779 | − | 0.0919534i | ||||
\(429\) | 4.27285 | + | 1.14491i | 0.206295 | + | 0.0552766i | ||||
\(430\) | 3.53039 | − | 6.75178i | 0.170251 | − | 0.325600i | ||||
\(431\) | 12.6089 | − | 21.8392i | 0.607347 | − | 1.05196i | −0.384329 | − | 0.923196i | \(-0.625567\pi\) |
0.991676 | − | 0.128760i | \(-0.0410997\pi\) | |||||||
\(432\) | 1.30968 | − | 13.8106i | 0.0630118 | − | 0.664462i | ||||
\(433\) | 11.8077 | 0.567442 | 0.283721 | − | 0.958907i | \(-0.408431\pi\) | ||||
0.283721 | + | 0.958907i | \(0.408431\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.27830 | + | 7.27830i | −0.348968 | + | 0.348968i | ||||
\(436\) | −12.0582 | − | 2.17148i | −0.577481 | − | 0.103995i | ||||
\(437\) | −9.38477 | + | 2.51464i | −0.448934 | + | 0.120292i | ||||
\(438\) | −0.489924 | − | 1.56376i | −0.0234095 | − | 0.0747194i | ||||
\(439\) | 23.7665 | − | 13.7216i | 1.13431 | − | 0.654897i | 0.189298 | − | 0.981920i | \(-0.439379\pi\) |
0.945016 | + | 0.327023i | \(0.106046\pi\) | |||||||
\(440\) | −0.663553 | + | 0.0836741i | −0.0316337 | + | 0.00398901i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.04912 | + | 5.56329i | 0.287727 | + | 0.264619i | ||||
\(443\) | −7.48700 | + | 27.9419i | −0.355718 | + | 1.32756i | 0.523861 | + | 0.851804i | \(0.324491\pi\) |
−0.879579 | + | 0.475753i | \(0.842175\pi\) | |||||||
\(444\) | −8.32672 | + | 17.6883i | −0.395169 | + | 0.839448i | ||||
\(445\) | −1.59212 | − | 5.94186i | −0.0754736 | − | 0.281671i | ||||
\(446\) | −7.31376 | + | 4.64068i | −0.346317 | + | 0.219743i | ||||
\(447\) | −9.23636 | −0.436865 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.2497 | −1.14441 | −0.572206 | − | 0.820110i | \(-0.693912\pi\) | ||||
−0.572206 | + | 0.820110i | \(0.693912\pi\) | |||||||
\(450\) | 7.56646 | − | 4.80102i | 0.356686 | − | 0.226322i | ||||
\(451\) | −1.21468 | − | 4.53326i | −0.0571972 | − | 0.213463i | ||||
\(452\) | 15.0245 | − | 31.9163i | 0.706695 | − | 1.50122i | ||||
\(453\) | −6.47963 | + | 24.1823i | −0.304440 | + | 1.13618i | ||||
\(454\) | 8.14831 | + | 7.49389i | 0.382419 | + | 0.351705i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21.7469 | − | 2.74228i | 1.01839 | − | 0.128419i | ||||
\(457\) | −11.7825 | + | 6.80265i | −0.551164 | + | 0.318215i | −0.749591 | − | 0.661901i | \(-0.769750\pi\) |
0.198427 | + | 0.980116i | \(0.436417\pi\) | |||||||
\(458\) | 7.64896 | + | 24.4143i | 0.357412 | + | 1.14080i | ||||
\(459\) | −4.32907 | + | 1.15997i | −0.202064 | + | 0.0541428i | ||||
\(460\) | −2.57100 | − | 0.462995i | −0.119873 | − | 0.0215873i | ||||
\(461\) | −28.1748 | + | 28.1748i | −1.31223 | + | 1.31223i | −0.392462 | + | 0.919768i | \(0.628376\pi\) |
−0.919768 | + | 0.392462i | \(0.871624\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2805 | −1.36078 | −0.680391 | − | 0.732849i | \(-0.738190\pi\) | ||||
−0.680391 | + | 0.732849i | \(0.738190\pi\) | |||||||
\(464\) | 39.3424 | + | 3.73090i | 1.82643 | + | 0.173202i | ||||
\(465\) | −4.35469 | + | 7.54254i | −0.201944 | + | 0.349777i | ||||
\(466\) | −16.1436 | + | 30.8741i | −0.747836 | + | 1.43022i | ||||
\(467\) | 30.3485 | + | 8.13184i | 1.40436 | + | 0.376297i | 0.879908 | − | 0.475144i | \(-0.157604\pi\) |
0.524451 | + | 0.851441i | \(0.324271\pi\) | |||||||
\(468\) | −9.16350 | − | 7.74612i | −0.423583 | − | 0.358065i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.20190 | + | 2.39419i | −0.101566 | + | 0.110436i | ||||
\(471\) | −21.3128 | + | 12.3049i | −0.982041 | + | 0.566982i | ||||
\(472\) | 9.66088 | + | 23.6885i | 0.444678 | + | 1.09035i | ||||
\(473\) | 4.40529 | + | 2.54339i | 0.202555 | + | 0.116945i | ||||
\(474\) | 0.956787 | − | 4.27891i | 0.0439467 | − | 0.196537i | ||||
\(475\) | −12.5016 | − | 12.5016i | −0.573613 | − | 0.573613i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.26198 | + | 5.26198i | −0.240930 | + | 0.240930i | ||||
\(478\) | 12.9972 | − | 8.24692i | 0.594479 | − | 0.377205i | ||||
\(479\) | 16.8012 | − | 29.1005i | 0.767665 | − | 1.32963i | −0.171162 | − | 0.985243i | \(-0.554752\pi\) |
0.938826 | − | 0.344391i | \(-0.111915\pi\) | |||||||
\(480\) | 5.60439 | + | 1.82331i | 0.255804 | + | 0.0832221i | ||||
\(481\) | −10.5574 | − | 18.2860i | −0.481377 | − | 0.833769i | ||||
\(482\) | 0.895749 | + | 21.4104i | 0.0408002 | + | 0.975217i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.80032 | + | 21.4782i | 0.0818326 | + | 0.976280i | ||||
\(485\) | 0.712476 | − | 2.65900i | 0.0323519 | − | 0.120739i | ||||
\(486\) | 17.4888 | − | 5.47921i | 0.793307 | − | 0.248542i | ||||
\(487\) | −11.1651 | − | 6.44618i | −0.505939 | − | 0.292104i | 0.225224 | − | 0.974307i | \(-0.427689\pi\) |
−0.731163 | + | 0.682203i | \(0.761022\pi\) | |||||||
\(488\) | 2.36744 | − | 17.2538i | 0.107169 | − | 0.781042i | ||||
\(489\) | 2.70471i | 0.122311i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.46128 | + | 5.46128i | 0.246464 | + | 0.246464i | 0.819518 | − | 0.573054i | \(-0.194241\pi\) |
−0.573054 | + | 0.819518i | \(0.694241\pi\) | |||||||
\(492\) | −7.32967 | + | 40.7015i | −0.330447 | + | 1.83496i | ||||
\(493\) | −3.30443 | − | 12.3323i | −0.148824 | − | 0.555418i | ||||
\(494\) | −10.9693 | + | 20.9786i | −0.493534 | + | 0.943870i | ||||
\(495\) | −0.157732 | − | 0.273199i | −0.00708951 | − | 0.0122794i | ||||
\(496\) | 32.9719 | − | 5.56658i | 1.48048 | − | 0.249947i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.12400 | + | 0.256210i | −0.274423 | + | 0.0114811i | ||||
\(499\) | −21.6691 | − | 5.80620i | −0.970040 | − | 0.259921i | −0.261195 | − | 0.965286i | \(-0.584117\pi\) |
−0.708845 | + | 0.705365i | \(0.750783\pi\) | |||||||
\(500\) | −3.30405 | − | 9.18170i | −0.147762 | − | 0.410618i | ||||
\(501\) | 26.2807 | − | 7.04189i | 1.17413 | − | 0.314608i | ||||
\(502\) | 1.65521 | + | 0.370113i | 0.0738755 | + | 0.0165190i | ||||
\(503\) | − | 2.46825i | − | 0.110054i | −0.998485 | − | 0.0550269i | \(-0.982476\pi\) | ||
0.998485 | − | 0.0550269i | \(-0.0175245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.97438i | 0.221357i | ||||||||
\(506\) | 0.380594 | − | 1.70208i | 0.0169195 | − | 0.0756667i | ||||
\(507\) | 14.5238 | − | 3.89164i | 0.645025 | − | 0.172834i | ||||
\(508\) | 6.60272 | − | 14.0260i | 0.292949 | − | 0.622304i | ||||
\(509\) | −18.2978 | − | 4.90288i | −0.811036 | − | 0.217316i | −0.170612 | − | 0.985338i | \(-0.554575\pi\) |
−0.640424 | + | 0.768022i | \(0.721241\pi\) | |||||||
\(510\) | −0.0795886 | − | 1.90235i | −0.00352424 | − | 0.0842374i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.31546 | − | 21.0441i | −0.367495 | − | 0.930025i | ||||
\(513\) | −6.45495 | − | 11.1803i | −0.284993 | − | 0.493623i | ||||
\(514\) | −14.6025 | − | 7.63542i | −0.644091 | − | 0.336784i | ||||
\(515\) | 1.89113 | + | 7.05780i | 0.0833332 | + | 0.311004i | ||||
\(516\) | −25.5765 | − | 36.8116i | −1.12594 | − | 1.62054i | ||||
\(517\) | −1.53561 | − | 1.53561i | −0.0675360 | − | 0.0675360i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.2130i | 0.492198i | ||||||||
\(520\) | −5.07094 | + | 3.84725i | −0.222375 | + | 0.168713i | ||||
\(521\) | −11.2226 | − | 6.47937i | −0.491671 | − | 0.283867i | 0.233596 | − | 0.972334i | \(-0.424951\pi\) |
−0.725268 | + | 0.688467i | \(0.758284\pi\) | |||||||
\(522\) | 5.57286 | + | 17.7877i | 0.243918 | + | 0.778547i | ||||
\(523\) | 6.94125 | − | 25.9051i | 0.303520 | − | 1.13275i | −0.630693 | − | 0.776033i | \(-0.717229\pi\) |
0.934212 | − | 0.356718i | \(-0.116104\pi\) | |||||||
\(524\) | −2.76863 | + | 3.27523i | −0.120948 | + | 0.143079i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.6887 | + | 1.07474i | −1.12008 | + | 0.0468609i | ||||
\(527\) | −5.40147 | − | 9.35562i | −0.235292 | − | 0.407537i | ||||
\(528\) | −1.37265 | + | 3.68755i | −0.0597370 | + | 0.160480i | ||||
\(529\) | −8.09376 | + | 14.0188i | −0.351903 | + | 0.609513i | ||||
\(530\) | 2.11500 | + | 3.33326i | 0.0918696 | + | 0.144787i | ||||
\(531\) | −8.53258 | + | 8.53258i | −0.370282 | + | 0.370282i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.5837 | − | 31.5837i | −1.36804 | − | 1.36804i | ||||
\(534\) | −35.3183 | − | 7.89736i | −1.52837 | − | 0.341752i | ||||
\(535\) | −0.638550 | − | 0.368667i | −0.0276069 | − | 0.0159389i | ||||
\(536\) | 36.9347 | − | 15.0630i | 1.59534 | − | 0.650624i | ||||
\(537\) | −22.5165 | + | 12.9999i | −0.971658 | + | 0.560987i | ||||
\(538\) | −33.0568 | − | 30.4019i | −1.42518 | − | 1.31072i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.289940 | − | 3.45904i | −0.0124770 | − | 0.148853i | ||||
\(541\) | 15.3523 | + | 4.11365i | 0.660049 | + | 0.176860i | 0.573268 | − | 0.819368i | \(-0.305675\pi\) |
0.0867808 | + | 0.996227i | \(0.472342\pi\) | |||||||
\(542\) | 27.8383 | + | 14.5562i | 1.19576 | + | 0.625240i | ||||
\(543\) | 2.01703 | − | 3.49359i | 0.0865589 | − | 0.149924i | ||||
\(544\) | −5.43438 | + | 4.88944i | −0.232997 | + | 0.209633i | ||||
\(545\) | −3.06571 | −0.131321 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2062 | − | 19.2062i | 0.821196 | − | 0.821196i | −0.165083 | − | 0.986280i | \(-0.552789\pi\) |
0.986280 | + | 0.165083i | \(0.0527893\pi\) | |||||||
\(548\) | 9.80890 | − | 6.81518i | 0.419016 | − | 0.291130i | ||||
\(549\) | 7.93461 | − | 2.12607i | 0.338641 | − | 0.0907386i | ||||
\(550\) | 3.02861 | − | 0.948859i | 0.129140 | − | 0.0404595i | ||||
\(551\) | 31.8495 | − | 18.3883i | 1.35683 | − | 0.783369i | ||||
\(552\) | −9.42255 | + | 12.1418i | −0.401051 | + | 0.516790i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.0565 | + | 12.0221i | −0.469748 | + | 0.510769i | ||||
\(555\) | −1.26610 | + | 4.72513i | −0.0537428 | + | 0.200571i | ||||
\(556\) | 24.2275 | − | 8.71831i | 1.02747 | − | 0.369739i | ||||
\(557\) | 1.54045 | + | 5.74906i | 0.0652712 | + | 0.243595i | 0.990852 | − | 0.134956i | \(-0.0430892\pi\) |
−0.925580 | + | 0.378551i | \(0.876423\pi\) | |||||||
\(558\) | 8.45021 | + | 13.3176i | 0.357726 | + | 0.563780i | ||||
\(559\) | 48.4121 | 2.04762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.27119 | 0.0536698 | ||||||||
\(562\) | −20.2895 | − | 31.9764i | −0.855860 | − | 1.34884i | ||||
\(563\) | 4.19155 | + | 15.6431i | 0.176653 | + | 0.659276i | 0.996264 | + | 0.0863570i | \(0.0275226\pi\) |
−0.819612 | + | 0.572919i | \(0.805811\pi\) | |||||||
\(564\) | 6.47965 | + | 18.0064i | 0.272842 | + | 0.758207i | ||||
\(565\) | 2.28451 | − | 8.52592i | 0.0961102 | − | 0.358688i | ||||
\(566\) | −15.9053 | + | 17.2942i | −0.668548 | + | 0.726930i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.3944 | − | 2.69783i | 0.897688 | − | 0.113199i | ||||
\(569\) | −13.0326 | + | 7.52436i | −0.546354 | + | 0.315437i | −0.747650 | − | 0.664093i | \(-0.768818\pi\) |
0.201296 | + | 0.979530i | \(0.435485\pi\) | |||||||
\(570\) | 5.23371 | − | 1.63971i | 0.219216 | − | 0.0686801i | ||||
\(571\) | 17.1302 | − | 4.59003i | 0.716877 | − | 0.192087i | 0.118099 | − | 0.993002i | \(-0.462320\pi\) |
0.598778 | + | 0.800915i | \(0.295653\pi\) | |||||||
\(572\) | −2.42481 | − | 3.48997i | −0.101386 | − | 0.145923i | ||||
\(573\) | −2.08367 | + | 2.08367i | −0.0870467 | + | 0.0870467i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.3967 | 0.516978 | ||||||||
\(576\) | 7.62886 | − | 7.46399i | 0.317869 | − | 0.311000i | ||||
\(577\) | 23.1600 | − | 40.1142i | 0.964162 | − | 1.66998i | 0.252313 | − | 0.967646i | \(-0.418809\pi\) |
0.711850 | − | 0.702332i | \(-0.247858\pi\) | |||||||
\(578\) | −19.2121 | − | 10.0457i | −0.799117 | − | 0.417845i | ||||
\(579\) | 22.0592 | + | 5.91073i | 0.916747 | + | 0.245642i | ||||
\(580\) | 9.85381 | − | 0.825955i | 0.409157 | − | 0.0342959i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.9205 | − | 10.9631i | −0.494120 | − | 0.454436i | ||||
\(583\) | −2.28249 | + | 1.31780i | −0.0945312 | + | 0.0545776i | ||||
\(584\) | −0.610386 | + | 1.45114i | −0.0252580 | + | 0.0600484i | ||||
\(585\) | −2.60010 | − | 1.50117i | −0.107501 | − | 0.0620656i | ||||
\(586\) | 29.7174 | + | 6.64498i | 1.22762 | + | 0.274501i | ||||
\(587\) | 4.90812 | + | 4.90812i | 0.202580 | + | 0.202580i | 0.801104 | − | 0.598525i | \(-0.204246\pi\) |
−0.598525 | + | 0.801104i | \(0.704246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.0039 | − | 22.0039i | 0.906654 | − | 0.906654i | ||||
\(590\) | 3.42958 | + | 5.40505i | 0.141194 | + | 0.222522i | ||||
\(591\) | −13.1427 | + | 22.7637i | −0.540616 | + | 0.936375i | ||||
\(592\) | 17.0792 | − | 7.81324i | 0.701950 | − | 0.321122i | ||||
\(593\) | 12.0345 | + | 20.8443i | 0.494196 | + | 0.855972i | 0.999978 | − | 0.00668902i | \(-0.00212920\pi\) |
−0.505782 | + | 0.862662i | \(0.668796\pi\) | |||||||
\(594\) | 2.31546 | − | 0.0968722i | 0.0950046 | − | 0.00397471i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.77646 | + | 5.72830i | 0.277575 | + | 0.234640i | ||||
\(597\) | 4.71662 | − | 17.6027i | 0.193038 | − | 0.720429i | ||||
\(598\) | −4.96262 | − | 15.8399i | −0.202937 | − | 0.647742i | ||||
\(599\) | 5.33990 | + | 3.08299i | 0.218182 | + | 0.125968i | 0.605108 | − | 0.796143i | \(-0.293130\pi\) |
−0.386926 | + | 0.922111i | \(0.626463\pi\) | |||||||
\(600\) | −27.7076 | − | 3.80183i | −1.13116 | − | 0.155209i | ||||
\(601\) | 16.2922i | 0.664572i | 0.943179 | + | 0.332286i | \(0.107820\pi\) | ||||
−0.943179 | + | 0.332286i | \(0.892180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3038 | + | 13.3038i | 0.541773 | + | 0.541773i | ||||
\(604\) | 19.7516 | − | 13.7233i | 0.803680 | − | 0.558393i | ||||
\(605\) | 1.39583 | + | 5.20932i | 0.0567487 | + | 0.211789i | ||||
\(606\) | 25.9341 | + | 13.5605i | 1.05350 | + | 0.550857i | ||||
\(607\) | −17.4917 | − | 30.2966i | −0.709968 | − | 1.22970i | −0.964868 | − | 0.262733i | \(-0.915376\pi\) |
0.254900 | − | 0.966967i | \(-0.417957\pi\) | |||||||
\(608\) | −17.6558 | − | 11.4753i | −0.716037 | − | 0.465383i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.182153 | − | 4.35386i | −0.00737515 | − | 0.176283i | ||||
\(611\) | −19.9641 | − | 5.34937i | −0.807661 | − | 0.216412i | ||||
\(612\) | −3.11969 | − | 1.46859i | −0.126106 | − | 0.0593642i | ||||
\(613\) | −20.6418 | + | 5.53096i | −0.833715 | + | 0.223393i | −0.650334 | − | 0.759649i | \(-0.725371\pi\) |
−0.183381 | + | 0.983042i | \(0.558704\pi\) | |||||||
\(614\) | 6.00515 | − | 26.8560i | 0.242348 | − | 1.08382i | ||||
\(615\) | 10.3481i | 0.417275i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.21451i | 0.0891526i | 0.999006 | + | 0.0445763i | \(0.0141938\pi\) | ||||
−0.999006 | + | 0.0445763i | \(0.985806\pi\) | |||||||
\(618\) | 41.9514 | + | 9.38056i | 1.68753 | + | 0.377341i | ||||
\(619\) | 2.70864 | − | 0.725777i | 0.108869 | − | 0.0291714i | −0.203973 | − | 0.978977i | \(-0.565385\pi\) |
0.312842 | + | 0.949805i | \(0.398719\pi\) | |||||||
\(620\) | 7.87273 | − | 2.83302i | 0.316176 | − | 0.113777i | ||||
\(621\) | 8.74364 | + | 2.34285i | 0.350870 | + | 0.0940154i | ||||
\(622\) | 14.8054 | − | 0.619414i | 0.593642 | − | 0.0248362i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.23403 | + | 36.9253i | 0.249561 | + | 1.47820i | ||||
\(625\) | 10.6531 | + | 18.4517i | 0.426123 | + | 0.738067i | ||||
\(626\) | 21.5236 | − | 41.1633i | 0.860257 | − | 1.64522i | ||||
\(627\) | 0.947720 | + | 3.53694i | 0.0378483 | + | 0.141252i | ||||
\(628\) | 23.2680 | + | 4.19019i | 0.928494 | + | 0.167207i | ||||
\(629\) | −4.29052 | − | 4.29052i | −0.171074 | − | 0.171074i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.6123i | − | 0.979801i | −0.871778 | − | 0.489900i | \(-0.837033\pi\) | ||
0.871778 | − | 0.489900i | \(-0.162967\pi\) | |||||||
\(632\) | −3.35571 | + | 2.54593i | −0.133483 | + | 0.101271i | ||||
\(633\) | −25.2128 | − | 14.5566i | −1.00212 | − | 0.578573i | ||||
\(634\) | 11.3446 | − | 3.55425i | 0.450553 | − | 0.141157i | ||||
\(635\) | 1.00396 | − | 3.74682i | 0.0398409 | − | 0.148688i | ||||
\(636\) | 23.1437 | − | 1.93992i | 0.917706 | − | 0.0769229i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.275961 | + | 6.59609i | 0.0109254 | + | 0.261142i | ||||
\(639\) | 5.08560 | + | 8.80852i | 0.201183 | + | 0.348460i | ||||
\(640\) | −2.98099 | − | 4.81350i | −0.117834 | − | 0.190270i | ||||
\(641\) | 11.7655 | − | 20.3784i | 0.464709 | − | 0.804899i | −0.534480 | − | 0.845181i | \(-0.679492\pi\) |
0.999188 | + | 0.0402822i | \(0.0128257\pi\) | |||||||
\(642\) | −3.66279 | + | 2.32409i | −0.144559 | + | 0.0917245i | ||||
\(643\) | −8.79484 | + | 8.79484i | −0.346835 | + | 0.346835i | −0.858929 | − | 0.512095i | \(-0.828870\pi\) |
0.512095 | + | 0.858929i | \(0.328870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.93089 | − | 7.93089i | −0.312278 | − | 0.312278i | ||||
\(646\) | −1.48452 | + | 6.63900i | −0.0584075 | + | 0.261208i | ||||
\(647\) | 18.3033 | + | 10.5674i | 0.719577 | + | 0.415448i | 0.814597 | − | 0.580028i | \(-0.196958\pi\) |
−0.0950202 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(648\) | −29.2590 | − | 12.3071i | −1.14940 | − | 0.483469i | ||||
\(649\) | −3.70118 | + | 2.13688i | −0.145284 | + | 0.0838798i | ||||
\(650\) | 20.4470 | − | 22.2326i | 0.801999 | − | 0.872036i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.67743 | − | 1.98437i | 0.0656934 | − | 0.0777139i | ||||
\(653\) | −9.11215 | − | 2.44159i | −0.356586 | − | 0.0955470i | 0.0760787 | − | 0.997102i | \(-0.475760\pi\) |
−0.432665 | + | 0.901555i | \(0.642427\pi\) | |||||||
\(654\) | −8.35732 | + | 15.9832i | −0.326797 | + | 0.624991i | ||||
\(655\) | −0.536549 | + | 0.929331i | −0.0209647 | + | 0.0363120i | ||||
\(656\) | 30.6202 | − | 25.3157i | 1.19552 | − | 0.988414i | ||||
\(657\) | −0.742557 | −0.0289699 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.68220 | + | 2.68220i | −0.104484 | + | 0.104484i | −0.757416 | − | 0.652932i | \(-0.773539\pi\) |
0.652932 | + | 0.757416i | \(0.273539\pi\) | |||||||
\(660\) | −0.174494 | + | 0.968961i | −0.00679217 | + | 0.0377167i | ||||
\(661\) | 0.793258 | − | 0.212553i | 0.0308542 | − | 0.00826735i | −0.243359 | − | 0.969936i | \(-0.578249\pi\) |
0.274213 | + | 0.961669i | \(0.411583\pi\) | |||||||
\(662\) | −0.215040 | − | 0.686373i | −0.00835775 | − | 0.0266767i | ||||
\(663\) | 10.4774 | − | 6.04912i | 0.406908 | − | 0.234928i | ||||
\(664\) | 4.65191 | + | 3.61007i | 0.180529 | + | 0.140098i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.52053 | + | 5.99684i | 0.252665 | + | 0.232373i | ||||
\(667\) | −6.67412 | + | 24.9081i | −0.258423 | + | 0.964447i | ||||
\(668\) | −23.6487 | − | 11.1326i | −0.914996 | − | 0.430733i | ||||
\(669\) | 3.30020 | + | 12.3165i | 0.127593 | + | 0.476184i | ||||
\(670\) | 8.42744 | − | 5.34733i | 0.325581 | − | 0.206585i | ||||
\(671\) | 2.90935 | 0.112314 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.60472 | −0.293140 | −0.146570 | − | 0.989200i | \(-0.546823\pi\) | ||||
−0.146570 | + | 0.989200i | \(0.546823\pi\) | |||||||
\(674\) | −32.2755 | + | 20.4792i | −1.24320 | + | 0.788830i | ||||
\(675\) | 4.26330 | + | 15.9108i | 0.164094 | + | 0.612409i | ||||
\(676\) | −13.0693 | − | 6.15233i | −0.502664 | − | 0.236628i | ||||
\(677\) | −7.74876 | + | 28.9188i | −0.297809 | + | 1.11144i | 0.641152 | + | 0.767414i | \(0.278457\pi\) |
−0.938961 | + | 0.344024i | \(0.888210\pi\) | |||||||
\(678\) | −38.2224 | − | 35.1526i | −1.46792 | − | 1.35003i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.12143 | + | 1.44506i | −0.0430047 | + | 0.0554155i | ||||
\(681\) | 14.1133 | − | 8.14831i | 0.540822 | − | 0.312244i | ||||
\(682\) | 1.67007 | + | 5.33061i | 0.0639504 | + | 0.204120i | ||||
\(683\) | −8.04672 | + | 2.15611i | −0.307899 | + | 0.0825013i | −0.409460 | − | 0.912328i | \(-0.634283\pi\) |
0.101561 | + | 0.994829i | \(0.467616\pi\) | |||||||
\(684\) | 1.76033 | − | 9.77505i | 0.0673078 | − | 0.373758i | ||||
\(685\) | 2.11328 | − | 2.11328i | 0.0807444 | − | 0.0807444i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.6627 | 1.43692 | ||||||||
\(688\) | −4.06542 | + | 42.8699i | −0.154993 | + | 1.63440i | ||||
\(689\) | −12.5418 | + | 21.7230i | −0.477804 | + | 0.827581i | ||||
\(690\) | −1.78192 | + | 3.40788i | −0.0678366 | + | 0.129736i | ||||
\(691\) | −16.3753 | − | 4.38774i | −0.622945 | − | 0.166918i | −0.0664786 | − | 0.997788i | \(-0.521176\pi\) |
−0.556466 | + | 0.830870i | \(0.687843\pi\) | |||||||
\(692\) | 6.95422 | − | 8.22670i | 0.264360 | − | 0.312732i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.45904 | − | 3.76111i | 0.131303 | − | 0.142770i | ||||
\(695\) | 5.57956 | − | 3.22136i | 0.211645 | − | 0.122193i | ||||
\(696\) | 22.5560 | − | 53.6247i | 0.854983 | − | 2.03264i | ||||
\(697\) | −11.1159 | − | 6.41779i | −0.421046 | − | 0.243091i | ||||
\(698\) | −1.23370 | + | 5.51731i | −0.0466963 | + | 0.208833i | ||||
\(699\) | 36.2659 | + | 36.2659i | 1.37170 | + | 1.37170i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6791 | + | 12.6791i | −0.478882 | + | 0.478882i | −0.904774 | − | 0.425892i | \(-0.859960\pi\) |
0.425892 | + | 0.904774i | \(0.359960\pi\) | |||||||
\(702\) | 18.6234 | − | 11.8168i | 0.702897 | − | 0.445998i | ||||
\(703\) | 8.73912 | − | 15.1366i | 0.329602 | − | 0.570888i | ||||
\(704\) | 3.29406 | − | 1.85415i | 0.124150 | − | 0.0698809i | ||||
\(705\) | 2.39419 | + | 4.14686i | 0.0901704 | + | 0.156180i | ||||
\(706\) | 0.0501864 | + | 1.19957i | 0.00188879 | + | 0.0451464i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 37.5286 | − | 3.14568i | 1.41041 | − | 0.118222i | ||||
\(709\) | −4.14517 | + | 15.4700i | −0.155675 | + | 0.580987i | 0.843372 | + | 0.537331i | \(0.180567\pi\) |
−0.999047 | + | 0.0436562i | \(0.986099\pi\) | |||||||
\(710\) | 5.14888 | − | 1.61314i | 0.193234 | − | 0.0605399i | ||||
\(711\) | −1.72062 | − | 0.993401i | −0.0645283 | − | 0.0372554i | ||||
\(712\) | 21.0142 | + | 27.6981i | 0.787539 | + | 1.03803i | ||||
\(713\) | 21.8193i | 0.817138i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.751898 | − | 0.751898i | −0.0281194 | − | 0.0281194i | ||||
\(716\) | 24.5821 | + | 4.42684i | 0.918678 | + | 0.165439i | ||||
\(717\) | −5.86476 | − | 21.8876i | −0.219023 | − | 0.817406i | ||||
\(718\) | −18.8180 | + | 35.9889i | −0.702280 | + | 1.34309i | ||||
\(719\) | 0.669732 | + | 1.16001i | 0.0249768 | + | 0.0432611i | 0.878244 | − | 0.478213i | \(-0.158715\pi\) |
−0.853267 | + | 0.521475i | \(0.825382\pi\) | |||||||
\(720\) | 1.54766 | − | 2.17638i | 0.0576778 | − | 0.0811089i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.26762 | − | 0.304056i | 0.270473 | − | 0.0113158i | ||||
\(723\) | 30.4708 | + | 8.16462i | 1.13322 | + | 0.303645i | ||||
\(724\) | −3.64653 | + | 1.31221i | −0.135522 | + | 0.0487679i | ||||
\(725\) | −45.3255 | + | 12.1449i | −1.68335 | + | 0.451051i | ||||
\(726\) | 30.9641 | + | 6.92373i | 1.14918 | + | 0.256964i | ||||
\(727\) | − | 3.87352i | − | 0.143661i | −0.997417 | − | 0.0718304i | \(-0.977116\pi\) | ||
0.997417 | − | 0.0718304i | \(-0.0228840\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.68839i | 0.247718i | ||||||||
\(730\) | −0.0859588 | + | 0.384422i | −0.00318148 | + | 0.0142281i | ||||
\(731\) | 13.4380 | − | 3.60071i | 0.497024 | − | 0.133177i | ||||
\(732\) | −23.1955 | − | 10.9193i | −0.857332 | − | 0.403587i | ||||
\(733\) | −41.2353 | − | 11.0490i | −1.52306 | − | 0.408103i | −0.602312 | − | 0.798261i | \(-0.705754\pi\) |
−0.920748 | + | 0.390158i | \(0.872420\pi\) | |||||||
\(734\) | −1.25910 | − | 30.0952i | −0.0464741 | − | 1.11083i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.4433 | − | 3.06434i | 0.532387 | − | 0.112953i | ||||
\(737\) | 3.33178 | + | 5.77081i | 0.122728 | + | 0.212570i | ||||
\(738\) | 16.6067 | + | 8.68338i | 0.611302 | + | 0.319640i | ||||
\(739\) | 6.97402 | + | 26.0274i | 0.256544 | + | 0.957434i | 0.967225 | + | 0.253920i | \(0.0817200\pi\) |
−0.710682 | + | 0.703514i | \(0.751613\pi\) | |||||||
\(740\) | 3.85938 | − | 2.68148i | 0.141874 | − | 0.0985731i | ||||
\(741\) | 24.6422 | + | 24.6422i | 0.905254 | + | 0.905254i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.4783i | 0.494470i | 0.968956 | + | 0.247235i | \(0.0795219\pi\) | ||||
−0.968956 | + | 0.247235i | \(0.920478\pi\) | |||||||
\(744\) | 6.69155 | − | 48.7677i | 0.245324 | − | 1.78791i | ||||
\(745\) | 1.92279 | + | 1.11012i | 0.0704455 | + | 0.0406717i | ||||
\(746\) | 3.33776 | + | 10.6536i | 0.122204 | + | 0.390056i | ||||
\(747\) | −0.718850 | + | 2.68279i | −0.0263014 | + | 0.0981580i | ||||
\(748\) | −0.932639 | − | 0.788382i | −0.0341007 | − | 0.0288261i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.3523 | + | 0.600456i | −0.524070 | + | 0.0219256i | ||||
\(751\) | 17.8616 | + | 30.9372i | 0.651780 | + | 1.12892i | 0.982691 | + | 0.185254i | \(0.0593108\pi\) |
−0.330911 | + | 0.943662i | \(0.607356\pi\) | |||||||
\(752\) | 6.41346 | − | 17.2294i | 0.233875 | − | 0.628292i | ||||
\(753\) | 1.24839 | − | 2.16228i | 0.0454940 | − | 0.0787980i | ||||
\(754\) | 33.6628 | + | 53.0529i | 1.22593 | + | 1.93207i | ||||
\(755\) | 4.25538 | − | 4.25538i | 0.154869 | − | 0.154869i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1603 | + | 10.1603i | 0.369284 | + | 0.369284i | 0.867216 | − | 0.497932i | \(-0.165907\pi\) |
−0.497932 | + | 0.867216i | \(0.665907\pi\) | |||||||
\(758\) | −23.5078 | − | 5.25648i | −0.853843 | − | 0.190924i | ||||
\(759\) | −2.22351 | − | 1.28375i | −0.0807085 | − | 0.0465971i | ||||
\(760\) | −4.85677 | − | 2.04289i | −0.176173 | − | 0.0741033i | ||||
\(761\) | −19.1505 | + | 11.0565i | −0.694205 | + | 0.400799i | −0.805185 | − | 0.593023i | \(-0.797934\pi\) |
0.110980 | + | 0.993823i | \(0.464601\pi\) | |||||||
\(762\) | −16.7973 | − | 15.4483i | −0.608503 | − | 0.559631i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.82101 | − | 0.236459i | 0.102061 | − | 0.00855480i | ||||
\(765\) | −0.833375 | − | 0.223302i | −0.0301307 | − | 0.00807351i | ||||
\(766\) | −0.106934 | − | 0.0559141i | −0.00386369 | − | 0.00202026i | ||||
\(767\) | −20.3372 | + | 35.2250i | −0.734332 | + | 1.27190i | ||||
\(768\) | −33.2217 | + | 2.41955i | −1.19878 | + | 0.0873079i | ||||
\(769\) | 18.2859 | 0.659405 | 0.329702 | − | 0.944085i | \(-0.393052\pi\) | ||||
0.329702 | + | 0.944085i | \(0.393052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.1527 | + | 17.1527i | −0.617739 | + | 0.617739i | ||||
\(772\) | −12.5184 | − | 18.0174i | −0.450548 | − | 0.648461i | ||||
\(773\) | −12.5013 | + | 3.34971i | −0.449640 | + | 0.120481i | −0.476531 | − | 0.879158i | \(-0.658106\pi\) |
0.0268907 | + | 0.999638i | \(0.491439\pi\) | |||||||
\(774\) | −19.3826 | + | 6.07254i | −0.696694 | + | 0.218273i | ||||
\(775\) | −34.3852 | + | 19.8523i | −1.23515 | + | 0.713116i | ||||
\(776\) | 1.94652 | + | 15.4363i | 0.0698760 | + | 0.554131i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.713596 | − | 0.775912i | 0.0255836 | − | 0.0278178i | ||||
\(779\) | 9.56938 | − | 35.7134i | 0.342859 | − | 1.27957i | ||||
\(780\) | 3.17270 | + | 8.81668i | 0.113601 | + | 0.315688i | ||||
\(781\) | 0.932359 | + | 3.47961i | 0.0333624 | + | 0.124510i | ||||
\(782\) | −2.55561 | − | 4.02767i | −0.0913886 | − | 0.144029i | ||||
\(783\) | −34.2642 | −1.22450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.91574 | 0.211142 | ||||||||
\(786\) | 3.38242 | + | 5.33073i | 0.120647 | + | 0.190141i | ||||
\(787\) | −8.86450 | − | 33.0828i | −0.315985 | − | 1.17927i | −0.923069 | − | 0.384635i | \(-0.874327\pi\) |
0.607083 | − | 0.794638i | \(-0.292339\pi\) | |||||||
\(788\) | 23.7603 | − | 8.55018i | 0.846424 | − | 0.304588i | ||||
\(789\) | −9.79610 | + | 36.5595i | −0.348750 | + | 1.30155i | ||||
\(790\) | −0.713463 | + | 0.775769i | −0.0253839 | + | 0.0276006i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.40858 | + | 1.09311i | 0.0500516 | + | 0.0388421i | ||||
\(793\) | 23.9794 | − | 13.8445i | 0.851532 | − | 0.491632i | ||||
\(794\) | −28.8994 | + | 9.05412i | −1.02560 | + | 0.321319i | ||||
\(795\) | 5.61327 | − | 1.50407i | 0.199082 | − | 0.0533439i | ||||
\(796\) | −14.3774 | + | 9.98938i | −0.509595 | + | 0.354064i | ||||
\(797\) | 12.6836 | − | 12.6836i | 0.449277 | − | 0.449277i | −0.445837 | − | 0.895114i | \(-0.647094\pi\) |
0.895114 | + | 0.445837i | \(0.147094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.93942 | −0.210121 | ||||||||
\(800\) | 17.9704 | + | 19.9733i | 0.635350 | + | 0.706162i | ||||
\(801\) | −8.19957 | + | 14.2021i | −0.289718 | + | 0.501805i | ||||
\(802\) | 43.0634 | + | 22.5171i | 1.52062 | + | 0.795107i | ||||
\(803\) | −0.254032 | − | 0.0680676i | −0.00896459 | − | 0.00240205i | ||||
\(804\) | −4.90468 | − | 58.5139i | −0.172975 | − | 2.06363i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 39.1313 | + | 35.9885i | 1.37834 | + | 1.26764i | ||||
\(807\) | −57.2561 | + | 33.0568i | −2.01551 | + | 1.16366i | ||||
\(808\) | −10.6170 | − | 26.0330i | −0.373506 | − | 0.915838i | ||||
\(809\) | −7.52353 | − | 4.34371i | −0.264513 | − | 0.152717i | 0.361878 | − | 0.932225i | \(-0.382136\pi\) |
−0.626392 | + | 0.779509i | \(0.715469\pi\) | |||||||
\(810\) | −7.75102 | − | 1.73317i | −0.272343 | − | 0.0608974i | ||||
\(811\) | −2.41161 | − | 2.41161i | −0.0846830 | − | 0.0846830i | 0.663496 | − | 0.748179i | \(-0.269072\pi\) |
−0.748179 | + | 0.663496i | \(0.769072\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.6998 | − | 32.6998i | 1.14683 | − | 1.14683i | ||||
\(814\) | 1.68099 | + | 2.64926i | 0.0589187 | + | 0.0928564i | ||||
\(815\) | 0.325080 | − | 0.563055i | 0.0113871 | − | 0.0197229i | ||||
\(816\) | 4.47678 | + | 9.78591i | 0.156719 | + | 0.342575i | ||||
\(817\) | 20.0371 | + | 34.7052i | 0.701008 | + | 1.21418i | ||||
\(818\) | 21.8561 | − | 0.914397i | 0.764182 | − | 0.0319711i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.41779 | − | 7.59211i | 0.224119 | − | 0.265128i | ||||
\(821\) | −2.42543 | + | 9.05181i | −0.0846479 | + | 0.315910i | −0.995247 | − | 0.0973798i | \(-0.968954\pi\) |
0.910599 | + | 0.413290i | \(0.135621\pi\) | |||||||
\(822\) | −5.25671 | − | 16.7786i | −0.183349 | − | 0.585221i | ||||
\(823\) | 8.76954 | + | 5.06310i | 0.305687 | + | 0.176488i | 0.644995 | − | 0.764187i | \(-0.276860\pi\) |
−0.339308 | + | 0.940675i | \(0.610193\pi\) | |||||||
\(824\) | −24.9608 | − | 32.9001i | −0.869552 | − | 1.14613i | ||||
\(825\) | − | 4.67208i | − | 0.162661i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.96806 | + | 2.96806i | 0.103209 | + | 0.103209i | 0.756826 | − | 0.653617i | \(-0.226749\pi\) |
−0.653617 | + | 0.756826i | \(0.726749\pi\) | |||||||
\(828\) | 3.97374 | + | 5.71929i | 0.138097 | + | 0.198759i | ||||
\(829\) | −11.2070 | − | 41.8251i | −0.389235 | − | 1.45265i | −0.831381 | − | 0.555702i | \(-0.812449\pi\) |
0.442146 | − | 0.896943i | \(-0.354217\pi\) | |||||||
\(830\) | 1.30566 | + | 0.682709i | 0.0453202 | + | 0.0236972i | ||||
\(831\) | 12.0221 | + | 20.8229i | 0.417042 | + | 0.722337i | ||||
\(832\) | 18.3270 | − | 30.9574i | 0.635375 | − | 1.07325i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.58441 | − | 37.8709i | −0.0548635 | − | 1.31136i | ||||
\(835\) | −6.31737 | − | 1.69273i | −0.218622 | − | 0.0585795i | ||||
\(836\) | 1.49826 | − | 3.18272i | 0.0518184 | − | 0.110077i | ||||
\(837\) | −28.0044 | + | 7.50377i | −0.967975 | + | 0.259368i | ||||
\(838\) | −11.4308 | + | 51.1203i | −0.394870 | + | 1.76592i | ||||
\(839\) | 51.7749i | 1.78747i | 0.448598 | + | 0.893734i | \(0.351924\pi\) | ||||
−0.448598 | + | 0.893734i | \(0.648076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 68.6090i | − | 2.36583i | ||||||
\(842\) | −39.7425 | − | 8.88664i | −1.36962 | − | 0.306254i | ||||
\(843\) | −53.8489 | + | 14.4288i | −1.85465 | + | 0.496953i | ||||
\(844\) | 9.47004 | + | 26.3165i | 0.325972 | + | 0.905851i | ||||
\(845\) | −3.49124 | − | 0.935475i | −0.120102 | − | 0.0321813i | ||||
\(846\) | 8.66396 | − | 0.362475i | 0.297873 | − | 0.0124621i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.1830 | − | 12.9302i | −0.624406 | − | 0.444025i | ||||
\(849\) | 17.2942 | + | 29.9545i | 0.593536 | + | 1.02803i | ||||
\(850\) | 4.02202 | − | 7.69201i | 0.137954 | − | 0.263834i | ||||
\(851\) | 3.17190 | + | 11.8377i | 0.108731 | + | 0.405791i | ||||
\(852\) | 5.62606 | − | 31.2414i | 0.192746 | − | 1.07031i | ||||
\(853\) | −5.56576 | − | 5.56576i | −0.190568 | − | 0.190568i | 0.605374 | − | 0.795941i | \(-0.293024\pi\) |
−0.795941 | + | 0.605374i | \(0.793024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.48524i | − | 0.0849936i | ||||||
\(856\) | 4.12866 | + | 0.566506i | 0.141115 | + | 0.0193628i | ||||
\(857\) | 28.0770 | + | 16.2103i | 0.959093 | + | 0.553733i | 0.895894 | − | 0.444268i | \(-0.146536\pi\) |
0.0631996 | + | 0.998001i | \(0.479870\pi\) | |||||||
\(858\) | −5.96976 | + | 1.87032i | −0.203804 | + | 0.0638516i | ||||
\(859\) | 2.80958 | − | 10.4855i | 0.0958618 | − | 0.357761i | −0.901287 | − | 0.433223i | \(-0.857376\pi\) |
0.997149 | + | 0.0754617i | \(0.0240431\pi\) | |||||||
\(860\) | 0.900012 | + | 10.7373i | 0.0306902 | + | 0.366140i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.49074 | + | 35.6321i | 0.0507748 | + | 1.21363i | ||||
\(863\) | 16.5015 | + | 28.5814i | 0.561716 | + | 0.972921i | 0.997347 | + | 0.0727955i | \(0.0231921\pi\) |
−0.435631 | + | 0.900126i | \(0.643475\pi\) | |||||||
\(864\) | 8.90014 | + | 17.4838i | 0.302789 | + | 0.594810i | ||||
\(865\) | 1.34770 | − | 2.33428i | 0.0458232 | − | 0.0793681i | ||||
\(866\) | −14.0998 | + | 8.94651i | −0.479130 | + | 0.304015i | ||||
\(867\) | −22.5672 | + | 22.5672i | −0.766423 | + | 0.766423i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.497570 | − | 0.497570i | −0.0168789 | − | 0.0168789i | ||||
\(870\) | 3.17649 | − | 14.2058i | 0.107693 | − | 0.481621i | ||||
\(871\) | 54.9221 | + | 31.7093i | 1.86096 | + | 1.07443i | ||||
\(872\) | 16.0441 | − | 6.54327i | 0.543323 | − | 0.221583i | ||||
\(873\) | −6.35546 | + | 3.66933i | −0.215100 | + | 0.124188i | ||||
\(874\) | 9.30121 | − | 10.1135i | 0.314618 | − | 0.342093i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.76986 | + | 1.49611i | 0.0597981 | + | 0.0505488i | ||||
\(877\) | 46.1420 | + | 12.3637i | 1.55810 | + | 0.417493i | 0.932063 | − | 0.362296i | \(-0.118007\pi\) |
0.626042 | + | 0.779789i | \(0.284674\pi\) | |||||||
\(878\) | −17.9834 | + | 34.3927i | −0.606909 | + | 1.16070i | ||||
\(879\) | 22.4136 | − | 38.8214i | 0.755990 | − | 1.30941i | ||||
\(880\) | 0.728962 | − | 0.602680i | 0.0245733 | − | 0.0203163i | ||||
\(881\) | −46.9509 | −1.58181 | −0.790907 | − | 0.611936i | \(-0.790391\pi\) | ||||
−0.790907 | + | 0.611936i | \(0.790391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8628 | − | 13.8628i | 0.466522 | − | 0.466522i | −0.434264 | − | 0.900786i | \(-0.642991\pi\) |
0.900786 | + | 0.434264i | \(0.142991\pi\) | |||||||
\(884\) | −11.4386 | − | 2.05990i | −0.384721 | − | 0.0692819i | ||||
\(885\) | 9.10221 | − | 2.43893i | 0.305967 | − | 0.0819837i | ||||
\(886\) | −12.2307 | − | 39.0386i | −0.410900 | − | 1.31153i | ||||
\(887\) | −6.75025 | + | 3.89726i | −0.226651 | + | 0.130857i | −0.609026 | − | 0.793150i | \(-0.708440\pi\) |
0.382375 | + | 0.924007i | \(0.375106\pi\) | |||||||
\(888\) | −3.45904 | − | 27.4309i | −0.116078 | − | 0.920520i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.40322 | + | 5.88895i | 0.214637 | + | 0.197398i | ||||
\(891\) | 1.37244 | − | 5.12200i | 0.0459783 | − | 0.171593i | ||||
\(892\) | 5.21732 | − | 11.0830i | 0.174689 | − | 0.371088i | ||||
\(893\) | −4.42805 | − | 16.5257i | −0.148179 | − | 0.553011i | ||||
\(894\) | 11.0293 | − | 6.99824i | 0.368875 | − | 0.234056i | ||||
\(895\) | 6.24985 | 0.208910 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.4354 | −0.815875 | ||||||||
\(898\) | 28.9569 | − | 18.3736i | 0.966305 | − | 0.613134i | ||||
\(899\) | −21.3761 | − | 79.7767i | −0.712933 | − | 2.66070i | ||||
\(900\) | −5.39758 | + | 11.4660i | −0.179919 | + | 0.382199i | ||||
\(901\) | −1.86562 | + | 6.96259i | −0.0621528 | + | 0.231958i | ||||
\(902\) | 4.88525 | + | 4.49290i | 0.162661 | + | 0.149597i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.24141 | + | 49.4956i | 0.207586 | + | 1.64620i | ||||
\(905\) | −0.839792 | + | 0.484854i | −0.0279156 | + | 0.0161171i | ||||
\(906\) | −10.5851 | − | 33.7860i | −0.351667 | − | 1.12247i | ||||
\(907\) | 9.28586 | − | 2.48814i | 0.308332 | − | 0.0826173i | −0.101335 | − | 0.994852i | \(-0.532311\pi\) |
0.409667 | + | 0.912235i | \(0.365645\pi\) | |||||||
\(908\) | −15.4080 | − | 2.77474i | −0.511333 | − | 0.0920828i | ||||
\(909\) | 9.37705 | − | 9.37705i | 0.311017 | − | 0.311017i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.36372 | −0.210839 | −0.105420 | − | 0.994428i | \(-0.533619\pi\) | ||||
−0.105420 | + | 0.994428i | \(0.533619\pi\) | |||||||
\(912\) | −23.8905 | + | 19.7518i | −0.791094 | + | 0.654049i | ||||
\(913\) | −0.491843 | + | 0.851898i | −0.0162776 | + | 0.0281937i | ||||
\(914\) | 8.91547 | − | 17.0506i | 0.294898 | − | 0.563984i | ||||
\(915\) | −6.19631 | − | 1.66030i | −0.204844 | − | 0.0548877i | ||||
\(916\) | −27.6321 | − | 23.3580i | −0.912989 | − | 0.771771i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.29052 | − | 4.66521i | 0.141608 | − | 0.153975i | ||||
\(919\) | 14.5846 | − | 8.42040i | 0.481100 | − | 0.277763i | −0.239775 | − | 0.970829i | \(-0.577074\pi\) |
0.720875 | + | 0.693065i | \(0.243740\pi\) | |||||||
\(920\) | 3.42088 | − | 1.39513i | 0.112783 | − | 0.0459962i | ||||
\(921\) | −35.0834 | − | 20.2554i | −1.15604 | − | 0.667438i | ||||
\(922\) | 12.2964 | − | 54.9915i | 0.404961 | − | 1.81105i | ||||
\(923\) | 24.2428 | + | 24.2428i | 0.797961 | + | 0.797961i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.7692 | + | 15.7692i | −0.518487 | + | 0.518487i | ||||
\(926\) | 34.9644 | − | 22.1854i | 1.14900 | − | 0.729057i | ||||
\(927\) | 9.73953 | − | 16.8694i | 0.319888 | − | 0.554062i | ||||
\(928\) | −49.8063 | + | 25.3540i | −1.63497 | + | 0.832285i | ||||
\(929\) | −10.8991 | − | 18.8778i | −0.357587 | − | 0.619360i | 0.629970 | − | 0.776620i | \(-0.283067\pi\) |
−0.987557 | + | 0.157260i | \(0.949734\pi\) | |||||||
\(930\) | −0.514853 | − | 12.3062i | −0.0168827 | − | 0.403535i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.11552 | − | 49.0990i | −0.134808 | − | 1.60829i | ||||
\(933\) | 5.64587 | − | 21.0707i | 0.184837 | − | 0.689822i | ||||
\(934\) | −42.4010 | + | 13.2842i | −1.38740 | + | 0.434671i | ||||
\(935\) | −0.264632 | − | 0.152785i | −0.00865438 | − | 0.00499661i | ||||
\(936\) | 16.8114 | + | 2.30674i | 0.549498 | + | 0.0753982i | ||||
\(937\) | 21.3450i | 0.697310i | 0.937251 | + | 0.348655i | \(0.113361\pi\) | ||||
−0.937251 | + | 0.348655i | \(0.886639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.3520 | − | 48.3520i | −1.57791 | − | 1.57791i | ||||
\(940\) | 0.815291 | − | 4.52729i | 0.0265919 | − | 0.147664i | ||||
\(941\) | 13.4819 | + | 50.3151i | 0.439497 | + | 1.64022i | 0.730071 | + | 0.683372i | \(0.239487\pi\) |
−0.290574 | + | 0.956853i | \(0.593846\pi\) | |||||||
\(942\) | 16.1267 | − | 30.8419i | 0.525436 | − | 1.00488i | ||||
\(943\) | 12.9623 | + | 22.4514i | 0.422112 | + | 0.731119i | ||||
\(944\) | −29.4846 | − | 20.9670i | −0.959643 | − | 0.682418i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.18752 | + | 0.300705i | −0.233686 | + | 0.00977675i | ||||
\(947\) | −2.10513 | − | 0.564067i | −0.0684074 | − | 0.0183297i | 0.224453 | − | 0.974485i | \(-0.427940\pi\) |
−0.292860 | + | 0.956155i | \(0.594607\pi\) | |||||||
\(948\) | 2.09954 | + | 5.83446i | 0.0681900 | + | 0.189494i | ||||
\(949\) | −2.41768 | + | 0.647815i | −0.0784812 | + | 0.0210290i | ||||
\(950\) | 24.4006 | + | 5.45612i | 0.791661 | + | 0.177020i | ||||
\(951\) | − | 17.5008i | − | 0.567502i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.31316i | − | 0.236897i | −0.992960 | − | 0.118448i | \(-0.962208\pi\) | ||
0.992960 | − | 0.118448i | \(-0.0377920\pi\) | |||||||
\(954\) | 2.29650 | − | 10.2703i | 0.0743521 | − | 0.332515i | ||||
\(955\) | 0.684208 | − | 0.183333i | 0.0221405 | − | 0.00593252i | ||||
\(956\) | −9.27165 | + | 19.6956i | −0.299867 | + | 0.637000i | ||||
\(957\) | 9.38740 | + | 2.51535i | 0.303452 | + | 0.0813096i | ||||
\(958\) | 1.98640 | + | 47.4793i | 0.0641775 | + | 1.53399i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.07378 | + | 2.06911i | −0.260580 | + | 0.0667803i | ||||
\(961\) | −19.4418 | − | 33.6741i | −0.627153 | − | 1.08626i | ||||
\(962\) | 26.4618 | + | 13.8364i | 0.853162 | + | 0.446104i | ||||
\(963\) | 0.508749 | + | 1.89868i | 0.0163942 | + | 0.0611840i | ||||
\(964\) | −17.2919 | − | 24.8878i | −0.556936 | − | 0.801583i | ||||
\(965\) | −3.88177 | − | 3.88177i | −0.124959 | − | 0.124959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.1882i | 1.35668i | 0.734748 | + | 0.678341i | \(0.237301\pi\) | ||||
−0.734748 | + | 0.678341i | \(0.762699\pi\) | |||||||
\(968\) | −18.4234 | − | 24.2834i | −0.592152 | − | 0.780497i | ||||
\(969\) | 8.67287 | + | 5.00728i | 0.278613 | + | 0.160857i | ||||
\(970\) | 1.16390 | + | 3.71498i | 0.0373705 | + | 0.119281i | ||||
\(971\) | 15.4813 | − | 57.7769i | 0.496818 | − | 1.85415i | −0.0227850 | − | 0.999740i | \(-0.507253\pi\) |
0.519603 | − | 0.854408i | \(-0.326080\pi\) | |||||||
\(972\) | −16.7321 | + | 19.7938i | −0.536684 | + | 0.634886i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.2166 | − | 0.762130i | 0.583698 | − | 0.0244202i | ||||
\(975\) | −22.2326 | − | 38.5080i | −0.712014 | − | 1.23324i | ||||
\(976\) | 10.2459 | + | 22.3968i | 0.327964 | + | 0.716904i | ||||
\(977\) | 3.53396 | − | 6.12099i | 0.113061 | − | 0.195828i | −0.803942 | − | 0.594708i | \(-0.797268\pi\) |
0.917003 | + | 0.398880i | \(0.130601\pi\) | |||||||
\(978\) | −2.04931 | − | 3.22974i | −0.0655298 | − | 0.103276i | ||||
\(979\) | −4.10696 | + | 4.10696i | −0.131259 | + | 0.131259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.77907 | + | 5.77907i | 0.184512 | + | 0.184512i | ||||
\(982\) | −10.6593 | − | 2.38348i | −0.340153 | − | 0.0760600i | ||||
\(983\) | −36.6563 | − | 21.1635i | −1.16915 | − | 0.675011i | −0.215673 | − | 0.976466i | \(-0.569194\pi\) |
−0.953480 | + | 0.301455i | \(0.902528\pi\) | |||||||
\(984\) | −22.0864 | − | 54.1559i | −0.704087 | − | 1.72643i | ||||
\(985\) | 5.47196 | − | 3.15924i | 0.174351 | − | 0.100662i | ||||
\(986\) | 13.2898 | + | 12.2225i | 0.423235 | + | 0.389243i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.79644 | − | 33.3621i | −0.0889667 | − | 1.06139i | ||||
\(989\) | −27.1415 | − | 7.27254i | −0.863049 | − | 0.231253i | ||||
\(990\) | 0.395348 | + | 0.206721i | 0.0125650 | + | 0.00657003i | ||||
\(991\) | −8.73586 | + | 15.1310i | −0.277504 | + | 0.480651i | −0.970764 | − | 0.240037i | \(-0.922840\pi\) |
0.693260 | + | 0.720688i | \(0.256174\pi\) | |||||||
\(992\) | −35.1547 | + | 31.6295i | −1.11616 | + | 1.00424i | ||||
\(993\) | −1.05883 | −0.0336010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.09755 | + | 3.09755i | −0.0981991 | + | 0.0981991i | ||||
\(996\) | 7.11865 | − | 4.94600i | 0.225563 | − | 0.156720i | ||||
\(997\) | 4.77839 | − | 1.28037i | 0.151333 | − | 0.0405496i | −0.182357 | − | 0.983232i | \(-0.558373\pi\) |
0.333690 | + | 0.942683i | \(0.391706\pi\) | |||||||
\(998\) | 30.2746 | − | 9.48500i | 0.958327 | − | 0.300242i | ||||
\(999\) | −14.1025 | + | 8.14210i | −0.446184 | + | 0.257605i |
(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.x.k.165.1 | 16 | ||
7.2 | even | 3 | inner | 784.2.x.k.373.4 | 16 | ||
7.3 | odd | 6 | 784.2.m.g.197.2 | 8 | |||
7.4 | even | 3 | 112.2.m.c.85.2 | yes | 8 | ||
7.5 | odd | 6 | 784.2.x.j.373.4 | 16 | |||
7.6 | odd | 2 | 784.2.x.j.165.1 | 16 | |||
16.13 | even | 4 | inner | 784.2.x.k.557.4 | 16 | ||
28.11 | odd | 6 | 448.2.m.c.113.1 | 8 | |||
56.11 | odd | 6 | 896.2.m.f.225.4 | 8 | |||
56.53 | even | 6 | 896.2.m.e.225.1 | 8 | |||
112.11 | odd | 12 | 896.2.m.f.673.4 | 8 | |||
112.13 | odd | 4 | 784.2.x.j.557.4 | 16 | |||
112.45 | odd | 12 | 784.2.m.g.589.2 | 8 | |||
112.53 | even | 12 | 896.2.m.e.673.1 | 8 | |||
112.61 | odd | 12 | 784.2.x.j.765.1 | 16 | |||
112.67 | odd | 12 | 448.2.m.c.337.1 | 8 | |||
112.93 | even | 12 | inner | 784.2.x.k.765.1 | 16 | ||
112.109 | even | 12 | 112.2.m.c.29.2 | ✓ | 8 | ||
224.67 | odd | 24 | 7168.2.a.bd.1.2 | 8 | |||
224.109 | even | 24 | 7168.2.a.bc.1.2 | 8 | |||
224.179 | odd | 24 | 7168.2.a.bd.1.7 | 8 | |||
224.221 | even | 24 | 7168.2.a.bc.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.c.29.2 | ✓ | 8 | 112.109 | even | 12 | ||
112.2.m.c.85.2 | yes | 8 | 7.4 | even | 3 | ||
448.2.m.c.113.1 | 8 | 28.11 | odd | 6 | |||
448.2.m.c.337.1 | 8 | 112.67 | odd | 12 | |||
784.2.m.g.197.2 | 8 | 7.3 | odd | 6 | |||
784.2.m.g.589.2 | 8 | 112.45 | odd | 12 | |||
784.2.x.j.165.1 | 16 | 7.6 | odd | 2 | |||
784.2.x.j.373.4 | 16 | 7.5 | odd | 6 | |||
784.2.x.j.557.4 | 16 | 112.13 | odd | 4 | |||
784.2.x.j.765.1 | 16 | 112.61 | odd | 12 | |||
784.2.x.k.165.1 | 16 | 1.1 | even | 1 | trivial | ||
784.2.x.k.373.4 | 16 | 7.2 | even | 3 | inner | ||
784.2.x.k.557.4 | 16 | 16.13 | even | 4 | inner | ||
784.2.x.k.765.1 | 16 | 112.93 | even | 12 | inner | ||
896.2.m.e.225.1 | 8 | 56.53 | even | 6 | |||
896.2.m.e.673.1 | 8 | 112.53 | even | 12 | |||
896.2.m.f.225.4 | 8 | 56.11 | odd | 6 | |||
896.2.m.f.673.4 | 8 | 112.11 | odd | 12 | |||
7168.2.a.bc.1.2 | 8 | 224.109 | even | 24 | |||
7168.2.a.bc.1.7 | 8 | 224.221 | even | 24 | |||
7168.2.a.bd.1.2 | 8 | 224.67 | odd | 24 | |||
7168.2.a.bd.1.7 | 8 | 224.179 | odd | 24 |