Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(143,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.o (of order \(12\), degree \(4\), 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: | \(2.79476407074\) |
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: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(-0.587308 - 2.01725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.257 |
Dual form | 350.2.o.c.143.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | 0.752300 | − | 2.80762i | 0.434341 | − | 1.62098i | −0.308298 | − | 0.951290i | \(-0.599759\pi\) |
0.742639 | − | 0.669692i | \(-0.233574\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.90667i | 1.18664i | ||||||||
\(7\) | −2.58583 | − | 0.559876i | −0.977353 | − | 0.211613i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −4.71872 | − | 2.72435i | −1.57291 | − | 0.908118i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.83557 | − | 3.17930i | −0.553445 | − | 0.958596i | −0.998023 | − | 0.0628551i | \(-0.979979\pi\) |
0.444577 | − | 0.895741i | \(-0.353354\pi\) | |||||||
\(12\) | −0.752300 | − | 2.80762i | −0.217170 | − | 0.810491i | ||||
\(13\) | 0.830578 | + | 0.830578i | 0.230361 | + | 0.230361i | 0.812843 | − | 0.582482i | \(-0.197918\pi\) |
−0.582482 | + | 0.812843i | \(0.697918\pi\) | |||||||
\(14\) | 2.64263 | − | 0.128464i | 0.706273 | − | 0.0343335i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 0.761471 | + | 0.204036i | 0.184684 | + | 0.0494859i | 0.349976 | − | 0.936759i | \(-0.386190\pi\) |
−0.165292 | + | 0.986245i | \(0.552857\pi\) | |||||||
\(18\) | 5.26305 | + | 1.41023i | 1.24051 | + | 0.332394i | ||||
\(19\) | −1.09461 | + | 1.89593i | −0.251122 | + | 0.434955i | −0.963835 | − | 0.266500i | \(-0.914133\pi\) |
0.712713 | + | 0.701455i | \(0.247466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.51725 | + | 6.83885i | −0.767526 | + | 1.49236i | ||||
\(22\) | 2.59589 | + | 2.59589i | 0.553445 | + | 0.553445i | ||||
\(23\) | −1.21791 | − | 4.54529i | −0.253951 | − | 0.947759i | −0.968671 | − | 0.248348i | \(-0.920112\pi\) |
0.714719 | − | 0.699411i | \(-0.246554\pi\) | |||||||
\(24\) | 1.45333 | + | 2.51725i | 0.296660 | + | 0.513831i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.01725 | − | 0.587308i | −0.199498 | − | 0.115180i | ||||
\(27\) | −5.03288 | + | 5.03288i | −0.968579 | + | 0.968579i | ||||
\(28\) | −2.51934 | + | 0.808050i | −0.476110 | + | 0.152707i | ||||
\(29\) | 2.62236i | 0.486960i | 0.969906 | + | 0.243480i | \(0.0782891\pi\) | ||||
−0.969906 | + | 0.243480i | \(0.921711\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0359651 | − | 0.0207644i | 0.00645952 | − | 0.00372940i | −0.496767 | − | 0.867884i | \(-0.665480\pi\) |
0.503226 | + | 0.864155i | \(0.332146\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | −10.3072 | + | 2.76180i | −1.79425 | + | 0.480768i | ||||
\(34\) | −0.788333 | −0.135198 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.44871 | −0.908118 | ||||||||
\(37\) | 0.248174 | − | 0.0664979i | 0.0407995 | − | 0.0109322i | −0.238362 | − | 0.971176i | \(-0.576610\pi\) |
0.279161 | + | 0.960244i | \(0.409944\pi\) | |||||||
\(38\) | 0.566614 | − | 2.11463i | 0.0919169 | − | 0.343038i | ||||
\(39\) | 2.95680 | − | 1.70711i | 0.473466 | − | 0.273356i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.98026i | − | 1.40248i | −0.712925 | − | 0.701241i | \(-0.752630\pi\) | ||
0.712925 | − | 0.701241i | \(-0.247370\pi\) | |||||||
\(42\) | 1.62737 | − | 7.51616i | 0.251109 | − | 1.15977i | ||||
\(43\) | 0.474569 | − | 0.474569i | 0.0723711 | − | 0.0723711i | −0.669995 | − | 0.742366i | \(-0.733704\pi\) |
0.742366 | + | 0.669995i | \(0.233704\pi\) | |||||||
\(44\) | −3.17930 | − | 1.83557i | −0.479298 | − | 0.276723i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.35282 | + | 4.07520i | 0.346904 | + | 0.600855i | ||||
\(47\) | −1.65648 | − | 6.18205i | −0.241622 | − | 0.901745i | −0.975051 | − | 0.221980i | \(-0.928748\pi\) |
0.733429 | − | 0.679766i | \(-0.237919\pi\) | |||||||
\(48\) | −2.05532 | − | 2.05532i | −0.296660 | − | 0.296660i | ||||
\(49\) | 6.37308 | + | 2.89549i | 0.910440 | + | 0.413642i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.14571 | − | 1.98443i | 0.160432 | − | 0.277876i | ||||
\(52\) | 1.13459 | + | 0.304013i | 0.157339 | + | 0.0421590i | ||||
\(53\) | 7.64413 | + | 2.04824i | 1.05000 | + | 0.281347i | 0.742252 | − | 0.670120i | \(-0.233758\pi\) |
0.307749 | + | 0.951468i | \(0.400424\pi\) | |||||||
\(54\) | 3.55879 | − | 6.16400i | 0.484289 | − | 0.838814i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.22435 | − | 1.43257i | 0.297242 | − | 0.191435i | ||||
\(57\) | 4.49957 | + | 4.49957i | 0.595982 | + | 0.595982i | ||||
\(58\) | −0.678717 | − | 2.53301i | −0.0891199 | − | 0.332600i | ||||
\(59\) | −5.35616 | − | 9.27713i | −0.697312 | − | 1.20778i | −0.969395 | − | 0.245506i | \(-0.921046\pi\) |
0.272083 | − | 0.962274i | \(-0.412287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72539 | + | 0.996157i | 0.220914 | + | 0.127545i | 0.606373 | − | 0.795180i | \(-0.292624\pi\) |
−0.385459 | + | 0.922725i | \(0.625957\pi\) | |||||||
\(62\) | −0.0293654 | + | 0.0293654i | −0.00372940 | + | 0.00372940i | ||||
\(63\) | 10.6765 | + | 9.68662i | 1.34512 | + | 1.22040i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.24117 | − | 5.33539i | 1.13751 | − | 0.656741i | ||||
\(67\) | 1.71399 | − | 6.39671i | 0.209398 | − | 0.781482i | −0.778666 | − | 0.627438i | \(-0.784103\pi\) |
0.988064 | − | 0.154044i | \(-0.0492298\pi\) | |||||||
\(68\) | 0.761471 | − | 0.204036i | 0.0923420 | − | 0.0247430i | ||||
\(69\) | −13.6777 | −1.64660 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.11777 | 0.963402 | 0.481701 | − | 0.876336i | \(-0.340019\pi\) | ||||
0.481701 | + | 0.876336i | \(0.340019\pi\) | |||||||
\(72\) | 5.26305 | − | 1.41023i | 0.620256 | − | 0.166197i | ||||
\(73\) | −2.55331 | + | 9.52910i | −0.298843 | + | 1.11530i | 0.639274 | + | 0.768979i | \(0.279235\pi\) |
−0.938117 | + | 0.346318i | \(0.887432\pi\) | |||||||
\(74\) | −0.222506 | + | 0.128464i | −0.0258658 | + | 0.0149336i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.18923i | 0.251122i | ||||||||
\(77\) | 2.96647 | + | 9.24884i | 0.338060 | + | 1.05400i | ||||
\(78\) | −2.41421 | + | 2.41421i | −0.273356 | + | 0.273356i | ||||
\(79\) | 11.6145 | + | 6.70563i | 1.30673 | + | 0.754443i | 0.981550 | − | 0.191208i | \(-0.0612405\pi\) |
0.325184 | + | 0.945651i | \(0.394574\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.17114 | + | 3.76053i | 0.241238 | + | 0.417836i | ||||
\(82\) | 2.32426 | + | 8.67427i | 0.256672 | + | 0.957912i | ||||
\(83\) | −9.73033 | − | 9.73033i | −1.06804 | − | 1.06804i | −0.997509 | − | 0.0705331i | \(-0.977530\pi\) |
−0.0705331 | − | 0.997509i | \(-0.522470\pi\) | |||||||
\(84\) | 0.373402 | + | 7.68124i | 0.0407415 | + | 0.838092i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.335571 | + | 0.581226i | −0.0361855 | + | 0.0626752i | ||||
\(87\) | 7.36260 | + | 1.97280i | 0.789354 | + | 0.211507i | ||||
\(88\) | 3.54605 | + | 0.950161i | 0.378010 | + | 0.101288i | ||||
\(89\) | −0.715130 | + | 1.23864i | −0.0758036 | + | 0.131296i | −0.901435 | − | 0.432914i | \(-0.857486\pi\) |
0.825632 | + | 0.564209i | \(0.190819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68272 | − | 2.61276i | −0.176397 | − | 0.273892i | ||||
\(92\) | −3.32739 | − | 3.32739i | −0.346904 | − | 0.346904i | ||||
\(93\) | −0.0312422 | − | 0.116597i | −0.00323967 | − | 0.0120906i | ||||
\(94\) | 3.20007 | + | 5.54268i | 0.330062 | + | 0.571684i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.51725 | + | 1.45333i | 0.256915 | + | 0.148330i | ||||
\(97\) | −3.16693 | + | 3.16693i | −0.321553 | + | 0.321553i | −0.849363 | − | 0.527810i | \(-0.823013\pi\) |
0.527810 | + | 0.849363i | \(0.323013\pi\) | |||||||
\(98\) | −6.90533 | − | 1.14736i | −0.697544 | − | 0.115901i | ||||
\(99\) | 20.0030i | 2.01037i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0622734 | + | 0.0359536i | −0.00619644 | + | 0.00357751i | −0.503095 | − | 0.864231i | \(-0.667805\pi\) |
0.496899 | + | 0.867809i | \(0.334472\pi\) | |||||||
\(102\) | −0.593063 | + | 2.21334i | −0.0587220 | + | 0.219154i | ||||
\(103\) | 16.0148 | − | 4.29116i | 1.57799 | − | 0.422820i | 0.639685 | − | 0.768638i | \(-0.279065\pi\) |
0.938302 | + | 0.345817i | \(0.112398\pi\) | |||||||
\(104\) | −1.17462 | −0.115180 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.91378 | −0.768654 | ||||||||
\(107\) | 4.41372 | − | 1.18265i | 0.426690 | − | 0.114331i | −0.0390819 | − | 0.999236i | \(-0.512443\pi\) |
0.465772 | + | 0.884905i | \(0.345777\pi\) | |||||||
\(108\) | −1.84216 | + | 6.87505i | −0.177262 | + | 0.661552i | ||||
\(109\) | 15.6773 | − | 9.05131i | 1.50162 | − | 0.866958i | 0.501617 | − | 0.865090i | \(-0.332739\pi\) |
0.999998 | − | 0.00186842i | \(-0.000594737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.746804i | − | 0.0708835i | ||||||
\(112\) | −1.77778 | + | 1.95946i | −0.167985 | + | 0.185152i | ||||
\(113\) | −1.52064 | + | 1.52064i | −0.143049 | + | 0.143049i | −0.775005 | − | 0.631955i | \(-0.782253\pi\) |
0.631955 | + | 0.775005i | \(0.282253\pi\) | |||||||
\(114\) | −5.51082 | − | 3.18168i | −0.516136 | − | 0.297991i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.31118 | + | 2.27103i | 0.121740 | + | 0.210860i | ||||
\(117\) | −1.65648 | − | 6.18205i | −0.153141 | − | 0.571531i | ||||
\(118\) | 7.57475 | + | 7.57475i | 0.697312 | + | 0.697312i | ||||
\(119\) | −1.85480 | − | 0.953932i | −0.170030 | − | 0.0874468i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.23864 | + | 2.14539i | −0.112604 | + | 0.195035i | ||||
\(122\) | −1.92443 | − | 0.515649i | −0.174229 | − | 0.0466846i | ||||
\(123\) | −25.2132 | − | 6.75585i | −2.27340 | − | 0.609155i | ||||
\(124\) | 0.0207644 | − | 0.0359651i | 0.00186470 | − | 0.00322976i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.8198 | − | 6.59327i | −1.14208 | − | 0.587376i | ||||
\(127\) | 13.2527 | + | 13.2527i | 1.17599 | + | 1.17599i | 0.980757 | + | 0.195234i | \(0.0625467\pi\) |
0.195234 | + | 0.980757i | \(0.437453\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | −0.975392 | − | 1.68943i | −0.0858785 | − | 0.148746i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2929 | + | 7.09731i | 1.07404 | + | 0.620095i | 0.929281 | − | 0.369372i | \(-0.120427\pi\) |
0.144755 | + | 0.989468i | \(0.453761\pi\) | |||||||
\(132\) | −7.54538 | + | 7.54538i | −0.656741 | + | 0.656741i | ||||
\(133\) | 3.89197 | − | 4.28970i | 0.337477 | − | 0.371964i | ||||
\(134\) | 6.62236i | 0.572085i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.682717 | + | 0.394167i | −0.0585425 | + | 0.0337995i | ||||
\(137\) | 4.90887 | − | 18.3201i | 0.419393 | − | 1.56519i | −0.356479 | − | 0.934303i | \(-0.616023\pi\) |
0.775871 | − | 0.630891i | \(-0.217311\pi\) | |||||||
\(138\) | 13.2117 | − | 3.54005i | 1.12465 | − | 0.301349i | ||||
\(139\) | −8.23706 | −0.698658 | −0.349329 | − | 0.937000i | \(-0.613591\pi\) | ||||
−0.349329 | + | 0.937000i | \(0.613591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.6030 | −1.56666 | ||||||||
\(142\) | −7.84116 | + | 2.10103i | −0.658016 | + | 0.176315i | ||||
\(143\) | 1.11607 | − | 4.16524i | 0.0933308 | − | 0.348315i | ||||
\(144\) | −4.71872 | + | 2.72435i | −0.393227 | + | 0.227029i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 9.86525i | − | 0.816454i | ||||||
\(147\) | 12.9239 | − | 15.7149i | 1.06595 | − | 1.29614i | ||||
\(148\) | 0.181676 | − | 0.181676i | 0.0149336 | − | 0.0149336i | ||||
\(149\) | −4.19317 | − | 2.42093i | −0.343518 | − | 0.198330i | 0.318309 | − | 0.947987i | \(-0.396885\pi\) |
−0.661826 | + | 0.749657i | \(0.730218\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.02292 | − | 8.69995i | −0.408759 | − | 0.707992i | 0.585992 | − | 0.810317i | \(-0.300705\pi\) |
−0.994751 | + | 0.102325i | \(0.967372\pi\) | |||||||
\(152\) | −0.566614 | − | 2.11463i | −0.0459584 | − | 0.171519i | ||||
\(153\) | −3.03730 | − | 3.03730i | −0.245551 | − | 0.245551i | ||||
\(154\) | −5.25916 | − | 8.16592i | −0.423795 | − | 0.658028i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.70711 | − | 2.95680i | 0.136678 | − | 0.236733i | ||||
\(157\) | −23.6523 | − | 6.33762i | −1.88766 | − | 0.505797i | −0.998872 | − | 0.0474774i | \(-0.984882\pi\) |
−0.888788 | − | 0.458320i | \(-0.848452\pi\) | |||||||
\(158\) | −12.9543 | − | 3.47109i | −1.03059 | − | 0.276145i | ||||
\(159\) | 11.5014 | − | 19.9209i | 0.912117 | − | 1.57983i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.604505 | + | 12.4353i | 0.0476417 | + | 0.980035i | ||||
\(162\) | −3.07046 | − | 3.07046i | −0.241238 | − | 0.241238i | ||||
\(163\) | 5.68510 | + | 21.2171i | 0.445291 | + | 1.66185i | 0.715166 | + | 0.698954i | \(0.246351\pi\) |
−0.269875 | + | 0.962895i | \(0.586982\pi\) | |||||||
\(164\) | −4.49013 | − | 7.77713i | −0.350620 | − | 0.607292i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.9172 | + | 6.88038i | 0.924952 | + | 0.534021i | ||||
\(167\) | −3.14616 | + | 3.14616i | −0.243457 | + | 0.243457i | −0.818279 | − | 0.574821i | \(-0.805072\pi\) |
0.574821 | + | 0.818279i | \(0.305072\pi\) | |||||||
\(168\) | −2.34873 | − | 7.32287i | −0.181209 | − | 0.564972i | ||||
\(169\) | − | 11.6203i | − | 0.893868i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3303 | − | 5.96423i | 0.789981 | − | 0.456096i | ||||
\(172\) | 0.173704 | − | 0.648273i | 0.0132448 | − | 0.0494304i | ||||
\(173\) | 5.04844 | − | 1.35273i | 0.383826 | − | 0.102846i | −0.0617463 | − | 0.998092i | \(-0.519667\pi\) |
0.445572 | + | 0.895246i | \(0.353000\pi\) | |||||||
\(174\) | −7.62233 | −0.577847 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.67114 | −0.276723 | ||||||||
\(177\) | −30.0761 | + | 8.05888i | −2.26066 | + | 0.605742i | ||||
\(178\) | 0.370178 | − | 1.38152i | 0.0277460 | − | 0.103550i | ||||
\(179\) | −10.8847 | + | 6.28428i | −0.813560 | + | 0.469709i | −0.848191 | − | 0.529691i | \(-0.822308\pi\) |
0.0346308 | + | 0.999400i | \(0.488974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6742i | 0.867740i | 0.900976 | + | 0.433870i | \(0.142852\pi\) | ||||
−0.900976 | + | 0.433870i | \(0.857148\pi\) | |||||||
\(182\) | 2.30161 | + | 2.08821i | 0.170607 | + | 0.154789i | ||||
\(183\) | 4.09485 | − | 4.09485i | 0.302700 | − | 0.302700i | ||||
\(184\) | 4.07520 | + | 2.35282i | 0.300428 | + | 0.173452i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0603553 | + | 0.104538i | 0.00442546 | + | 0.00766513i | ||||
\(187\) | −0.749044 | − | 2.79547i | −0.0547755 | − | 0.204425i | ||||
\(188\) | −4.52558 | − | 4.52558i | −0.330062 | − | 0.330062i | ||||
\(189\) | 15.8320 | − | 10.1964i | 1.15161 | − | 0.741680i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.75170 | + | 13.4263i | −0.560894 | + | 0.971496i | 0.436525 | + | 0.899692i | \(0.356209\pi\) |
−0.997419 | + | 0.0718040i | \(0.977124\pi\) | |||||||
\(192\) | −2.80762 | − | 0.752300i | −0.202623 | − | 0.0542926i | ||||
\(193\) | 8.69132 | + | 2.32883i | 0.625615 | + | 0.167633i | 0.557679 | − | 0.830057i | \(-0.311692\pi\) |
0.0679359 | + | 0.997690i | \(0.478359\pi\) | |||||||
\(194\) | 2.23936 | − | 3.87868i | 0.160776 | − | 0.278473i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.96699 | − | 0.678966i | 0.497642 | − | 0.0484976i | ||||
\(197\) | −12.1951 | − | 12.1951i | −0.868865 | − | 0.868865i | 0.123482 | − | 0.992347i | \(-0.460594\pi\) |
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(198\) | −5.17715 | − | 19.3214i | −0.367924 | − | 1.37311i | ||||
\(199\) | −4.36557 | − | 7.56140i | −0.309467 | − | 0.536013i | 0.668779 | − | 0.743462i | \(-0.266817\pi\) |
−0.978246 | + | 0.207448i | \(0.933484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6701 | − | 9.62450i | −1.17582 | − | 0.678860i | ||||
\(202\) | 0.0508460 | − | 0.0508460i | 0.00357751 | − | 0.00357751i | ||||
\(203\) | 1.46820 | − | 6.78099i | 0.103047 | − | 0.475932i | ||||
\(204\) | − | 2.29142i | − | 0.160432i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.3585 | + | 8.28988i | −1.00040 | + | 0.577583i | ||||
\(207\) | −6.63602 | + | 24.7660i | −0.461235 | + | 1.72135i | ||||
\(208\) | 1.13459 | − | 0.304013i | 0.0786697 | − | 0.0210795i | ||||
\(209\) | 8.03696 | 0.555928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1745 | −0.769288 | −0.384644 | − | 0.923065i | \(-0.625676\pi\) | ||||
−0.384644 | + | 0.923065i | \(0.625676\pi\) | |||||||
\(212\) | 7.64413 | − | 2.04824i | 0.525001 | − | 0.140674i | ||||
\(213\) | 6.10700 | − | 22.7916i | 0.418445 | − | 1.56166i | ||||
\(214\) | −3.95723 | + | 2.28471i | −0.270511 | + | 0.156179i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 7.11757i | − | 0.484289i | ||||||
\(217\) | −0.104625 | + | 0.0335574i | −0.00710242 | + | 0.00227803i | ||||
\(218\) | −12.8005 | + | 12.8005i | −0.866958 | + | 0.866958i | ||||
\(219\) | 24.8333 | + | 14.3375i | 1.67808 | + | 0.968838i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.462994 | + | 0.801929i | 0.0311443 | + | 0.0539436i | ||||
\(222\) | 0.193287 | + | 0.721358i | 0.0129726 | + | 0.0484143i | ||||
\(223\) | 0.746804 | + | 0.746804i | 0.0500097 | + | 0.0500097i | 0.731669 | − | 0.681660i | \(-0.238742\pi\) |
−0.681660 | + | 0.731669i | \(0.738742\pi\) | |||||||
\(224\) | 1.21006 | − | 2.35282i | 0.0808507 | − | 0.157204i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.07525 | − | 1.86239i | 0.0715247 | − | 0.123884i | ||||
\(227\) | 3.01404 | + | 0.807609i | 0.200049 | + | 0.0536029i | 0.357452 | − | 0.933932i | \(-0.383646\pi\) |
−0.157403 | + | 0.987534i | \(0.550312\pi\) | |||||||
\(228\) | 6.14653 | + | 1.64696i | 0.407064 | + | 0.109072i | ||||
\(229\) | −4.21091 | + | 7.29350i | −0.278264 | + | 0.481968i | −0.970954 | − | 0.239268i | \(-0.923093\pi\) |
0.692689 | + | 0.721236i | \(0.256426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.1989 | − | 1.37081i | 1.85535 | − | 0.0901928i | ||||
\(232\) | −1.85429 | − | 1.85429i | −0.121740 | − | 0.121740i | ||||
\(233\) | 5.90027 | + | 22.0201i | 0.386540 | + | 1.44259i | 0.835725 | + | 0.549148i | \(0.185048\pi\) |
−0.449186 | + | 0.893439i | \(0.648286\pi\) | |||||||
\(234\) | 3.20007 | + | 5.54268i | 0.209195 | + | 0.362336i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.27713 | − | 5.35616i | −0.603890 | − | 0.348656i | ||||
\(237\) | 27.5645 | − | 27.5645i | 1.79051 | − | 1.79051i | ||||
\(238\) | 2.03850 | + | 0.441369i | 0.132136 | + | 0.0286097i | ||||
\(239\) | 23.9971i | 1.55224i | 0.630585 | + | 0.776120i | \(0.282815\pi\) | ||||
−0.630585 | + | 0.776120i | \(0.717185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4666 | + | 12.3937i | −1.38278 | + | 0.798350i | −0.992488 | − | 0.122340i | \(-0.960960\pi\) |
−0.390295 | + | 0.920690i | \(0.627627\pi\) | |||||||
\(242\) | 0.641168 | − | 2.39287i | 0.0412158 | − | 0.153820i | ||||
\(243\) | −8.43364 | + | 2.25979i | −0.541018 | + | 0.144965i | ||||
\(244\) | 1.99231 | 0.127545 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.1026 | 1.66424 | ||||||||
\(247\) | −2.48388 | + | 0.665553i | −0.158045 | + | 0.0423481i | ||||
\(248\) | −0.0107485 | + | 0.0401138i | −0.000682528 | + | 0.00254723i | ||||
\(249\) | −34.6392 | + | 19.9990i | −2.19517 | + | 1.26738i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.1158i | − | 0.701623i | −0.936446 | − | 0.350811i | \(-0.885906\pi\) | ||
0.936446 | − | 0.350811i | \(-0.114094\pi\) | |||||||
\(252\) | 14.0895 | + | 3.05060i | 0.887552 | + | 0.192170i | ||||
\(253\) | −12.2153 | + | 12.2153i | −0.767970 | + | 0.767970i | ||||
\(254\) | −16.2312 | − | 9.37110i | −1.01844 | − | 0.587995i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.54637 | + | 24.4314i | 0.408351 | + | 1.52399i | 0.797790 | + | 0.602935i | \(0.206002\pi\) |
−0.389439 | + | 0.921052i | \(0.627331\pi\) | |||||||
\(258\) | 1.37941 | + | 1.37941i | 0.0858785 | + | 0.0858785i | ||||
\(259\) | −0.678966 | + | 0.0330060i | −0.0421889 | + | 0.00205090i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.14424 | − | 12.3742i | 0.442217 | − | 0.765943i | ||||
\(262\) | −13.7110 | − | 3.67384i | −0.847066 | − | 0.226971i | ||||
\(263\) | 10.9595 | + | 2.93659i | 0.675792 | + | 0.181078i | 0.580363 | − | 0.814358i | \(-0.302911\pi\) |
0.0954297 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(264\) | 5.33539 | − | 9.24117i | 0.328371 | − | 0.568755i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.64910 | + | 5.15085i | −0.162427 | + | 0.315819i | ||||
\(267\) | 2.93964 | + | 2.93964i | 0.179903 | + | 0.179903i | ||||
\(268\) | −1.71399 | − | 6.39671i | −0.104699 | − | 0.390741i | ||||
\(269\) | 4.03346 | + | 6.98616i | 0.245924 | + | 0.425954i | 0.962391 | − | 0.271668i | \(-0.0875752\pi\) |
−0.716467 | + | 0.697621i | \(0.754242\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.27419 | + | 4.19976i | 0.441876 | + | 0.255117i | 0.704393 | − | 0.709810i | \(-0.251219\pi\) |
−0.262517 | + | 0.964927i | \(0.584553\pi\) | |||||||
\(272\) | 0.557436 | − | 0.557436i | 0.0337995 | − | 0.0337995i | ||||
\(273\) | −8.60155 | + | 2.75885i | −0.520590 | + | 0.166974i | ||||
\(274\) | 18.9664i | 1.14580i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.8452 | + | 6.83885i | −0.713000 | + | 0.411651i | ||||
\(277\) | −1.47009 | + | 5.48646i | −0.0883293 | + | 0.329650i | −0.995924 | − | 0.0901983i | \(-0.971250\pi\) |
0.907594 | + | 0.419848i | \(0.137917\pi\) | |||||||
\(278\) | 7.95639 | − | 2.13191i | 0.477193 | − | 0.127863i | ||||
\(279\) | −0.226279 | −0.0135470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.27627 | 0.434066 | 0.217033 | − | 0.976164i | \(-0.430362\pi\) | ||||
0.217033 | + | 0.976164i | \(0.430362\pi\) | |||||||
\(282\) | 17.9692 | − | 4.81482i | 1.07005 | − | 0.286719i | ||||
\(283\) | 1.99550 | − | 7.44729i | 0.118620 | − | 0.442696i | −0.880912 | − | 0.473280i | \(-0.843070\pi\) |
0.999532 | + | 0.0305840i | \(0.00973671\pi\) | |||||||
\(284\) | 7.03019 | − | 4.05888i | 0.417165 | − | 0.240850i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.31218i | 0.254984i | ||||||||
\(287\) | −5.02784 | + | 23.2215i | −0.296784 | + | 1.37072i | ||||
\(288\) | 3.85282 | − | 3.85282i | 0.227029 | − | 0.227029i | ||||
\(289\) | −14.1842 | − | 8.18927i | −0.834366 | − | 0.481721i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.50906 | + | 11.2740i | 0.381568 | + | 0.660895i | ||||
\(292\) | 2.55331 | + | 9.52910i | 0.149421 | + | 0.557648i | ||||
\(293\) | 3.35198 | + | 3.35198i | 0.195824 | + | 0.195824i | 0.798207 | − | 0.602383i | \(-0.205782\pi\) |
−0.602383 | + | 0.798207i | \(0.705782\pi\) | |||||||
\(294\) | −8.41624 | + | 18.5244i | −0.490845 | + | 1.08037i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.128464 | + | 0.222506i | −0.00746682 | + | 0.0129329i | ||||
\(297\) | 25.2393 | + | 6.76284i | 1.46453 | + | 0.392420i | ||||
\(298\) | 4.67687 | + | 1.25316i | 0.270924 | + | 0.0725938i | ||||
\(299\) | 2.76365 | − | 4.78679i | 0.159826 | − | 0.276827i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49286 | + | 0.961456i | −0.0860468 | + | 0.0554174i | ||||
\(302\) | 7.10348 | + | 7.10348i | 0.408759 | + | 0.408759i | ||||
\(303\) | 0.0540958 | + | 0.201888i | 0.00310772 | + | 0.0115982i | ||||
\(304\) | 1.09461 | + | 1.89593i | 0.0627804 | + | 0.108739i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.71992 | + | 2.14770i | 0.212654 | + | 0.122776i | ||||
\(307\) | −1.06546 | + | 1.06546i | −0.0608089 | + | 0.0608089i | −0.736857 | − | 0.676048i | \(-0.763691\pi\) |
0.676048 | + | 0.736857i | \(0.263691\pi\) | |||||||
\(308\) | 7.19345 | + | 6.52650i | 0.409885 | + | 0.371882i | ||||
\(309\) | − | 48.1918i | − | 2.74154i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9584 | − | 6.90417i | 0.678097 | − | 0.391500i | −0.121040 | − | 0.992648i | \(-0.538623\pi\) |
0.799138 | + | 0.601148i | \(0.205290\pi\) | |||||||
\(312\) | −0.883663 | + | 3.29788i | −0.0500276 | + | 0.186706i | ||||
\(313\) | −22.5515 | + | 6.04266i | −1.27469 | + | 0.341551i | −0.831825 | − | 0.555038i | \(-0.812704\pi\) |
−0.442863 | + | 0.896590i | \(0.646037\pi\) | |||||||
\(314\) | 24.4867 | 1.38186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4113 | 0.754443 | ||||||||
\(317\) | 12.7394 | − | 3.41352i | 0.715518 | − | 0.191722i | 0.117347 | − | 0.993091i | \(-0.462561\pi\) |
0.598171 | + | 0.801369i | \(0.295894\pi\) | |||||||
\(318\) | −5.95354 | + | 22.2189i | −0.333858 | + | 1.24598i | ||||
\(319\) | 8.33728 | − | 4.81353i | 0.466798 | − | 0.269506i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 13.2818i | − | 0.741316i | ||||||
\(322\) | −3.80239 | − | 11.8551i | −0.211899 | − | 0.660658i | ||||
\(323\) | −1.22035 | + | 1.22035i | −0.0679023 | + | 0.0679023i | ||||
\(324\) | 3.76053 | + | 2.17114i | 0.208918 | + | 0.120619i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.9828 | − | 19.0227i | −0.608279 | − | 1.05357i | ||||
\(327\) | −13.6186 | − | 50.8253i | −0.753111 | − | 2.81065i | ||||
\(328\) | 6.35000 | + | 6.35000i | 0.350620 | + | 0.350620i | ||||
\(329\) | 0.822187 | + | 16.9132i | 0.0453286 | + | 0.932454i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.54799 | − | 16.5376i | 0.524805 | − | 0.908989i | −0.474778 | − | 0.880106i | \(-0.657472\pi\) |
0.999583 | − | 0.0288830i | \(-0.00919501\pi\) | |||||||
\(332\) | −13.2919 | − | 3.56155i | −0.729487 | − | 0.195465i | ||||
\(333\) | −1.35222 | − | 0.362328i | −0.0741015 | − | 0.0198554i | ||||
\(334\) | 2.22467 | − | 3.85325i | 0.121729 | − | 0.210840i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.16400 | + | 6.46545i | 0.227165 | + | 0.352719i | ||||
\(337\) | −0.488226 | − | 0.488226i | −0.0265953 | − | 0.0265953i | 0.693684 | − | 0.720279i | \(-0.255986\pi\) |
−0.720279 | + | 0.693684i | \(0.755986\pi\) | |||||||
\(338\) | 3.00755 | + | 11.2243i | 0.163589 | + | 0.610523i | ||||
\(339\) | 3.12540 | + | 5.41335i | 0.169748 | + | 0.294013i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.132033 | − | 0.0762292i | −0.00714998 | − | 0.00412804i | ||||
\(342\) | −8.43469 | + | 8.43469i | −0.456096 | + | 0.456096i | ||||
\(343\) | −14.8586 | − | 11.0554i | −0.802289 | − | 0.596936i | ||||
\(344\) | 0.671142i | 0.0361855i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.52631 | + | 2.61327i | −0.243336 | + | 0.140490i | ||||
\(347\) | −0.986094 | + | 3.68015i | −0.0529363 | + | 0.197561i | −0.987330 | − | 0.158682i | \(-0.949276\pi\) |
0.934393 | + | 0.356243i | \(0.115942\pi\) | |||||||
\(348\) | 7.36260 | − | 1.97280i | 0.394677 | − | 0.105753i | ||||
\(349\) | 7.91303 | 0.423575 | 0.211787 | − | 0.977316i | \(-0.432072\pi\) | ||||
0.211787 | + | 0.977316i | \(0.432072\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.36041 | −0.446246 | ||||||||
\(352\) | 3.54605 | − | 0.950161i | 0.189005 | − | 0.0506438i | ||||
\(353\) | 6.67203 | − | 24.9004i | 0.355116 | − | 1.32531i | −0.525222 | − | 0.850965i | \(-0.676018\pi\) |
0.880338 | − | 0.474347i | \(-0.157316\pi\) | |||||||
\(354\) | 26.9655 | − | 15.5686i | 1.43320 | − | 0.827459i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.43026i | 0.0758036i | ||||||||
\(357\) | −4.07365 | + | 4.48995i | −0.215601 | + | 0.237633i | ||||
\(358\) | 8.88731 | − | 8.88731i | 0.469709 | − | 0.469709i | ||||
\(359\) | −8.99497 | − | 5.19325i | −0.474737 | − | 0.274089i | 0.243484 | − | 0.969905i | \(-0.421710\pi\) |
−0.718220 | + | 0.695816i | \(0.755043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.10364 | + | 12.3039i | 0.373876 | + | 0.647572i | ||||
\(362\) | −3.02152 | − | 11.2765i | −0.158807 | − | 0.592677i | ||||
\(363\) | 5.09161 | + | 5.09161i | 0.267240 | + | 0.267240i | ||||
\(364\) | −2.76365 | − | 1.42136i | −0.144855 | − | 0.0744994i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.89549 | + | 5.01514i | −0.151350 | + | 0.262146i | ||||
\(367\) | 8.39004 | + | 2.24811i | 0.437957 | + | 0.117350i | 0.471059 | − | 0.882102i | \(-0.343872\pi\) |
−0.0331020 | + | 0.999452i | \(0.510539\pi\) | |||||||
\(368\) | −4.54529 | − | 1.21791i | −0.236940 | − | 0.0634878i | ||||
\(369\) | −24.4654 | + | 42.3753i | −1.27362 | + | 2.20597i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.6197 | − | 9.57617i | −0.966686 | − | 0.497170i | ||||
\(372\) | −0.0853553 | − | 0.0853553i | −0.00442546 | − | 0.00442546i | ||||
\(373\) | −3.44476 | − | 12.8560i | −0.178363 | − | 0.665660i | −0.995954 | − | 0.0898611i | \(-0.971358\pi\) |
0.817591 | − | 0.575799i | \(-0.195309\pi\) | |||||||
\(374\) | 1.44704 | + | 2.50635i | 0.0748247 | + | 0.129600i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.54268 | + | 3.20007i | 0.285842 | + | 0.165031i | ||||
\(377\) | −2.17808 | + | 2.17808i | −0.112177 | + | 0.112177i | ||||
\(378\) | −12.6535 | + | 13.9466i | −0.650826 | + | 0.717336i | ||||
\(379\) | − | 25.3453i | − | 1.30190i | −0.759121 | − | 0.650949i | \(-0.774371\pi\) | ||
0.759121 | − | 0.650949i | \(-0.225629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 47.1788 | − | 27.2387i | 2.41704 | − | 1.39548i | ||||
\(382\) | 4.01258 | − | 14.9751i | 0.205301 | − | 0.766195i | ||||
\(383\) | −17.7739 | + | 4.76251i | −0.908205 | + | 0.243353i | −0.682537 | − | 0.730851i | \(-0.739123\pi\) |
−0.225668 | + | 0.974204i | \(0.572457\pi\) | |||||||
\(384\) | 2.90667 | 0.148330 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.99792 | −0.457982 | ||||||||
\(387\) | −3.53225 | + | 0.946464i | −0.179554 | + | 0.0481114i | ||||
\(388\) | −1.15918 | + | 4.32611i | −0.0588483 | + | 0.219625i | ||||
\(389\) | 19.3621 | − | 11.1787i | 0.981699 | − | 0.566784i | 0.0789164 | − | 0.996881i | \(-0.474854\pi\) |
0.902783 | + | 0.430097i | \(0.141521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.70961i | − | 0.187603i | ||||||
\(392\) | −6.55387 | + | 2.45902i | −0.331020 | + | 0.124199i | ||||
\(393\) | 29.1745 | − | 29.1745i | 1.47166 | − | 1.47166i | ||||
\(394\) | 14.9359 | + | 8.62324i | 0.752459 | + | 0.434432i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.0015 | + | 17.3231i | 0.502594 | + | 0.870518i | ||||
\(397\) | 4.08518 | + | 15.2461i | 0.205029 | + | 0.765181i | 0.989441 | + | 0.144939i | \(0.0462987\pi\) |
−0.784411 | + | 0.620241i | \(0.787035\pi\) | |||||||
\(398\) | 6.17385 | + | 6.17385i | 0.309467 | + | 0.309467i | ||||
\(399\) | −9.11594 | − | 14.1543i | −0.456368 | − | 0.708603i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.98528 | + | 12.0989i | −0.348828 | + | 0.604188i | −0.986042 | − | 0.166499i | \(-0.946754\pi\) |
0.637213 | + | 0.770687i | \(0.280087\pi\) | |||||||
\(402\) | 18.5931 | + | 4.98201i | 0.927339 | + | 0.248480i | ||||
\(403\) | 0.0471183 | + | 0.0126253i | 0.00234713 | + | 0.000628911i | ||||
\(404\) | −0.0359536 | + | 0.0622734i | −0.00178876 | + | 0.00309822i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.336879 | + | 6.92993i | 0.0167190 | + | 0.343927i | ||||
\(407\) | −0.666957 | − | 0.666957i | −0.0330598 | − | 0.0330598i | ||||
\(408\) | 0.593063 | + | 2.21334i | 0.0293610 | + | 0.109577i | ||||
\(409\) | 0.156681 | + | 0.271379i | 0.00774737 | + | 0.0134188i | 0.869873 | − | 0.493276i | \(-0.164201\pi\) |
−0.862126 | + | 0.506694i | \(0.830867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −47.7431 | − | 27.5645i | −2.35499 | − | 1.35966i | ||||
\(412\) | 11.7237 | − | 11.7237i | 0.577583 | − | 0.577583i | ||||
\(413\) | 8.65608 | + | 26.9879i | 0.425938 | + | 1.32799i | ||||
\(414\) | − | 25.6396i | − | 1.26012i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.01725 | + | 0.587308i | −0.0498746 | + | 0.0287951i | ||||
\(417\) | −6.19675 | + | 23.1266i | −0.303456 | + | 1.13251i | ||||
\(418\) | −7.76311 | + | 2.08012i | −0.379706 | + | 0.101742i | ||||
\(419\) | −31.6254 | −1.54500 | −0.772501 | − | 0.635014i | \(-0.780994\pi\) | ||||
−0.772501 | + | 0.635014i | \(0.780994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2137 | 1.18011 | 0.590053 | − | 0.807365i | \(-0.299107\pi\) | ||||
0.590053 | + | 0.807365i | \(0.299107\pi\) | |||||||
\(422\) | 10.7938 | − | 2.89219i | 0.525433 | − | 0.140789i | ||||
\(423\) | −9.02565 | + | 33.6842i | −0.438842 | + | 1.63778i | ||||
\(424\) | −6.85354 | + | 3.95689i | −0.332837 | + | 0.192164i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23.5956i | 1.14321i | ||||||||
\(427\) | −3.90386 | − | 3.54190i | −0.188921 | − | 0.171405i | ||||
\(428\) | 3.23107 | − | 3.23107i | 0.156179 | − | 0.156179i | ||||
\(429\) | −10.8548 | − | 6.26703i | −0.524075 | − | 0.302575i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.779037 | − | 1.34933i | −0.0375249 | − | 0.0649950i | 0.846653 | − | 0.532145i | \(-0.178614\pi\) |
−0.884178 | + | 0.467150i | \(0.845281\pi\) | |||||||
\(432\) | 1.84216 | + | 6.87505i | 0.0886311 | + | 0.330776i | ||||
\(433\) | 6.28166 | + | 6.28166i | 0.301877 | + | 0.301877i | 0.841748 | − | 0.539871i | \(-0.181527\pi\) |
−0.539871 | + | 0.841748i | \(0.681527\pi\) | |||||||
\(434\) | 0.0923749 | − | 0.0594930i | 0.00443414 | − | 0.00285575i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.05131 | − | 15.6773i | 0.433479 | − | 0.750808i | ||||
\(437\) | 9.95068 | + | 2.66628i | 0.476006 | + | 0.127545i | ||||
\(438\) | −27.6979 | − | 7.42163i | −1.32346 | − | 0.354619i | ||||
\(439\) | −11.9571 | + | 20.7103i | −0.570681 | + | 0.988449i | 0.425815 | + | 0.904810i | \(0.359988\pi\) |
−0.996496 | + | 0.0836389i | \(0.973346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.1844 | − | 31.0255i | −1.05640 | − | 1.47741i | ||||
\(442\) | −0.654772 | − | 0.654772i | −0.0311443 | − | 0.0311443i | ||||
\(443\) | −3.32895 | − | 12.4238i | −0.158163 | − | 0.590272i | −0.998814 | − | 0.0486946i | \(-0.984494\pi\) |
0.840651 | − | 0.541578i | \(-0.182173\pi\) | |||||||
\(444\) | −0.373402 | − | 0.646751i | −0.0177209 | − | 0.0306935i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.914645 | − | 0.528070i | −0.0433097 | − | 0.0250049i | ||||
\(447\) | −9.95157 | + | 9.95157i | −0.470693 | + | 0.470693i | ||||
\(448\) | −0.559876 | + | 2.58583i | −0.0264517 | + | 0.122169i | ||||
\(449\) | 17.8932i | 0.844435i | 0.906495 | + | 0.422217i | \(0.138748\pi\) | ||||
−0.906495 | + | 0.422217i | \(0.861252\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.5510 | + | 16.4839i | −1.34441 | + | 0.776197i | ||||
\(452\) | −0.556592 | + | 2.07723i | −0.0261799 | + | 0.0977046i | ||||
\(453\) | −28.2049 | + | 7.55749i | −1.32518 | + | 0.355082i | ||||
\(454\) | −3.12036 | −0.146446 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.36335 | −0.297991 | ||||||||
\(457\) | 33.0454 | − | 8.85449i | 1.54580 | − | 0.414196i | 0.617665 | − | 0.786442i | \(-0.288079\pi\) |
0.928134 | + | 0.372246i | \(0.121412\pi\) | |||||||
\(458\) | 2.17973 | − | 8.13485i | 0.101852 | − | 0.380116i | ||||
\(459\) | −4.85928 | + | 2.80551i | −0.226812 | + | 0.130950i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3471i | 1.08738i | 0.839286 | + | 0.543690i | \(0.182973\pi\) | ||||
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(462\) | −26.8833 | + | 8.62252i | −1.25072 | + | 0.401156i | ||||
\(463\) | −3.98510 | + | 3.98510i | −0.185203 | + | 0.185203i | −0.793619 | − | 0.608415i | \(-0.791805\pi\) |
0.608415 | + | 0.793619i | \(0.291805\pi\) | |||||||
\(464\) | 2.27103 | + | 1.31118i | 0.105430 | + | 0.0608700i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.3985 | − | 19.7427i | −0.528023 | − | 0.914563i | ||||
\(467\) | 1.26454 | + | 4.71932i | 0.0585159 | + | 0.218384i | 0.988992 | − | 0.147968i | \(-0.0472732\pi\) |
−0.930476 | + | 0.366352i | \(0.880607\pi\) | |||||||
\(468\) | −4.52558 | − | 4.52558i | −0.209195 | − | 0.209195i | ||||
\(469\) | −8.01347 | + | 15.5812i | −0.370028 | + | 0.719473i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.5873 | + | 61.6390i | −1.63978 | + | 2.84017i | ||||
\(472\) | 10.3473 | + | 2.77255i | 0.476273 | + | 0.127617i | ||||
\(473\) | −2.37990 | − | 0.637693i | −0.109428 | − | 0.0293212i | ||||
\(474\) | −19.4910 | + | 33.7595i | −0.895253 | + | 1.55062i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.08327 | + | 0.101272i | −0.0954867 | + | 0.00464182i | ||||
\(477\) | −30.4904 | − | 30.4904i | −1.39606 | − | 1.39606i | ||||
\(478\) | −6.21090 | − | 23.1794i | −0.284080 | − | 1.06020i | ||||
\(479\) | 8.55572 | + | 14.8189i | 0.390921 | + | 0.677094i | 0.992571 | − | 0.121665i | \(-0.0388234\pi\) |
−0.601651 | + | 0.798759i | \(0.705490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.261359 | + | 0.150896i | 0.0119170 | + | 0.00688026i | ||||
\(482\) | 17.5274 | − | 17.5274i | 0.798350 | − | 0.798350i | ||||
\(483\) | 35.3683 | + | 7.65783i | 1.60931 | + | 0.348443i | ||||
\(484\) | 2.47728i | 0.112604i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.56140 | − | 4.36557i | 0.342992 | − | 0.198026i | ||||
\(487\) | −0.0337240 | + | 0.125860i | −0.00152818 | + | 0.00570325i | −0.966686 | − | 0.255966i | \(-0.917606\pi\) |
0.965158 | + | 0.261670i | \(0.0842731\pi\) | |||||||
\(488\) | −1.92443 | + | 0.515649i | −0.0871147 | + | 0.0233423i | ||||
\(489\) | 63.8465 | 2.88724 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9895 | 1.21802 | 0.609011 | − | 0.793162i | \(-0.291567\pi\) | ||||
0.609011 | + | 0.793162i | \(0.291567\pi\) | |||||||
\(492\) | −25.2132 | + | 6.75585i | −1.13670 | + | 0.304577i | ||||
\(493\) | −0.535055 | + | 1.99685i | −0.0240977 | + | 0.0899337i | ||||
\(494\) | 2.22698 | − | 1.28575i | 0.100197 | − | 0.0578486i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.0415289i | − | 0.00186470i | ||||||
\(497\) | −20.9912 | − | 4.54495i | −0.941584 | − | 0.203869i | ||||
\(498\) | 28.2828 | − | 28.2828i | 1.26738 | − | 1.26738i | ||||
\(499\) | 0.0833977 | + | 0.0481497i | 0.00373339 | + | 0.00215548i | 0.501866 | − | 0.864946i | \(-0.332647\pi\) |
−0.498132 | + | 0.867101i | \(0.665981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.46638 | + | 11.2001i | 0.288897 | + | 0.500384i | ||||
\(502\) | 2.87698 | + | 10.7370i | 0.128406 | + | 0.479217i | ||||
\(503\) | −13.6334 | − | 13.6334i | −0.607883 | − | 0.607883i | 0.334509 | − | 0.942392i | \(-0.391429\pi\) |
−0.942392 | + | 0.334509i | \(0.891429\pi\) | |||||||
\(504\) | −14.3989 | + | 0.699963i | −0.641379 | + | 0.0311788i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.63753 | − | 14.9606i | 0.383985 | − | 0.665081i | ||||
\(507\) | −32.6254 | − | 8.74194i | −1.44894 | − | 0.388243i | ||||
\(508\) | 18.1036 | + | 4.85084i | 0.803217 | + | 0.215221i | ||||
\(509\) | 6.16366 | − | 10.6758i | 0.273199 | − | 0.473195i | −0.696480 | − | 0.717576i | \(-0.745251\pi\) |
0.969679 | + | 0.244381i | \(0.0785848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9376 | − | 23.2111i | 0.528087 | − | 1.02680i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.03291 | − | 15.0510i | −0.178057 | − | 0.664520i | ||||
\(514\) | −12.6466 | − | 21.9046i | −0.557818 | − | 0.966169i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.68943 | − | 0.975392i | −0.0743730 | − | 0.0429393i | ||||
\(517\) | −16.6140 | + | 16.6140i | −0.730684 | + | 0.730684i | ||||
\(518\) | 0.647288 | − | 0.207611i | 0.0284402 | − | 0.00912189i | ||||
\(519\) | − | 15.1918i | − | 0.666845i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.1415 | − | 8.16461i | 0.619551 | − | 0.357698i | −0.157143 | − | 0.987576i | \(-0.550228\pi\) |
0.776694 | + | 0.629878i | \(0.216895\pi\) | |||||||
\(522\) | −3.69813 | + | 13.8016i | −0.161863 | + | 0.604080i | ||||
\(523\) | 26.4703 | − | 7.09270i | 1.15747 | − | 0.310142i | 0.371512 | − | 0.928428i | \(-0.378839\pi\) |
0.785953 | + | 0.618286i | \(0.212173\pi\) | |||||||
\(524\) | 14.1946 | 0.620095 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3461 | −0.494714 | ||||||||
\(527\) | 0.0316231 | − | 0.00847337i | 0.00137752 | − | 0.000369106i | ||||
\(528\) | −2.76180 | + | 10.3072i | −0.120192 | + | 0.448563i | ||||
\(529\) | 0.742186 | − | 0.428501i | 0.0322689 | − | 0.0186305i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 58.3682i | 2.53297i | ||||||||
\(532\) | 1.22570 | − | 5.66098i | 0.0531407 | − | 0.245435i | ||||
\(533\) | 7.45881 | − | 7.45881i | 0.323077 | − | 0.323077i | ||||
\(534\) | −3.60031 | − | 2.07864i | −0.155801 | − | 0.0899517i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.31118 | + | 5.73513i | 0.143021 | + | 0.247720i | ||||
\(537\) | 9.45533 | + | 35.2878i | 0.408028 | + | 1.52278i | ||||
\(538\) | −5.70417 | − | 5.70417i | −0.245924 | − | 0.245924i | ||||
\(539\) | −2.49258 | − | 25.5768i | −0.107363 | − | 1.10167i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5773 | − | 35.6410i | 0.884689 | − | 1.53233i | 0.0386200 | − | 0.999254i | \(-0.487704\pi\) |
0.846069 | − | 0.533073i | \(-0.178963\pi\) | |||||||
\(542\) | −8.11330 | − | 2.17395i | −0.348496 | − | 0.0933793i | ||||
\(543\) | 32.7769 | + | 8.78254i | 1.40659 | + | 0.376895i | ||||
\(544\) | −0.394167 | + | 0.682717i | −0.0168998 | + | 0.0292712i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.59442 | − | 4.89109i | 0.325011 | − | 0.209320i | ||||
\(547\) | −8.06541 | − | 8.06541i | −0.344852 | − | 0.344852i | 0.513336 | − | 0.858188i | \(-0.328410\pi\) |
−0.858188 | + | 0.513336i | \(0.828410\pi\) | |||||||
\(548\) | −4.90887 | − | 18.3201i | −0.209696 | − | 0.782597i | ||||
\(549\) | −5.42777 | − | 9.40117i | −0.231651 | − | 0.401232i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.97180 | − | 2.87047i | −0.211806 | − | 0.122286i | ||||
\(552\) | 9.67160 | − | 9.67160i | 0.411651 | − | 0.411651i | ||||
\(553\) | −26.2788 | − | 23.8423i | −1.11749 | − | 1.01388i | ||||
\(554\) | − | 5.68000i | − | 0.241320i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.13350 | + | 4.11853i | −0.302528 | + | 0.174665i | ||||
\(557\) | 6.64049 | − | 24.7826i | 0.281367 | − | 1.05007i | −0.670087 | − | 0.742282i | \(-0.733743\pi\) |
0.951454 | − | 0.307792i | \(-0.0995901\pi\) | |||||||
\(558\) | 0.218568 | − | 0.0585652i | 0.00925274 | − | 0.00247926i | ||||
\(559\) | 0.788333 | 0.0333429 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.41213 | −0.355160 | ||||||||
\(562\) | −7.02834 | + | 1.88324i | −0.296473 | + | 0.0794396i | ||||
\(563\) | 3.31584 | − | 12.3749i | 0.139746 | − | 0.521539i | −0.860187 | − | 0.509978i | \(-0.829653\pi\) |
0.999933 | − | 0.0115606i | \(-0.00367993\pi\) | |||||||
\(564\) | −16.1107 | + | 9.30152i | −0.678383 | + | 0.391665i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.71000i | 0.324076i | ||||||||
\(567\) | −3.50878 | − | 10.9397i | −0.147355 | − | 0.459423i | ||||
\(568\) | −5.74013 | + | 5.74013i | −0.240850 | + | 0.240850i | ||||
\(569\) | 29.8291 | + | 17.2218i | 1.25050 | + | 0.721977i | 0.971209 | − | 0.238229i | \(-0.0765669\pi\) |
0.279292 | + | 0.960206i | \(0.409900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.11985 | + | 7.13579i | 0.172410 | + | 0.298623i | 0.939262 | − | 0.343201i | \(-0.111511\pi\) |
−0.766852 | + | 0.641824i | \(0.778178\pi\) | |||||||
\(572\) | −1.11607 | − | 4.16524i | −0.0466654 | − | 0.174158i | ||||
\(573\) | 31.8645 | + | 31.8645i | 1.33116 | + | 1.33116i | ||||
\(574\) | −1.15364 | − | 23.7315i | −0.0481520 | − | 0.990534i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.72435 | + | 4.71872i | −0.113515 | + | 0.196613i | ||||
\(577\) | 3.39649 | + | 0.910086i | 0.141398 | + | 0.0378874i | 0.328824 | − | 0.944391i | \(-0.393348\pi\) |
−0.187426 | + | 0.982279i | \(0.560015\pi\) | |||||||
\(578\) | 15.8204 | + | 4.23908i | 0.658044 | + | 0.176322i | ||||
\(579\) | 13.0770 | − | 22.6500i | 0.543460 | − | 0.941301i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.7132 | + | 30.6088i | 0.817843 | + | 1.26987i | ||||
\(582\) | −9.20520 | − | 9.20520i | −0.381568 | − | 0.381568i | ||||
\(583\) | −7.51937 | − | 28.0627i | −0.311421 | − | 1.16224i | ||||
\(584\) | −4.93262 | − | 8.54355i | −0.204113 | − | 0.353535i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.10531 | − | 2.37020i | −0.169589 | − | 0.0979122i | ||||
\(587\) | −5.37485 | + | 5.37485i | −0.221844 | + | 0.221844i | −0.809275 | − | 0.587431i | \(-0.800139\pi\) |
0.587431 | + | 0.809275i | \(0.300139\pi\) | |||||||
\(588\) | 3.33499 | − | 20.0715i | 0.137533 | − | 0.827734i | ||||
\(589\) | 0.0909162i | 0.00374613i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.4136 | + | 25.0649i | −1.78580 | + | 1.03103i | ||||
\(592\) | 0.0664979 | − | 0.248174i | 0.00273305 | − | 0.0101999i | ||||
\(593\) | −0.709668 | + | 0.190155i | −0.0291426 | + | 0.00780872i | −0.273361 | − | 0.961912i | \(-0.588135\pi\) |
0.244218 | + | 0.969720i | \(0.421469\pi\) | |||||||
\(594\) | −26.1296 | −1.07211 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.84185 | −0.198330 | ||||||||
\(597\) | −24.5138 | + | 6.56845i | −1.00328 | + | 0.268829i | ||||
\(598\) | −1.43057 | + | 5.33897i | −0.0585005 | + | 0.218327i | ||||
\(599\) | −7.23778 | + | 4.17873i | −0.295727 | + | 0.170738i | −0.640522 | − | 0.767940i | \(-0.721282\pi\) |
0.344794 | + | 0.938678i | \(0.387949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.9236i | − | 1.62852i | −0.580501 | − | 0.814259i | \(-0.697143\pi\) | ||
0.580501 | − | 0.814259i | \(-0.302857\pi\) | |||||||
\(602\) | 1.19315 | − | 1.31508i | 0.0486290 | − | 0.0535985i | ||||
\(603\) | −25.5147 | + | 25.5147i | −1.03904 | + | 1.03904i | ||||
\(604\) | −8.69995 | − | 5.02292i | −0.353996 | − | 0.204380i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.104505 | − | 0.181008i | −0.00424523 | − | 0.00735295i | ||||
\(607\) | −8.91623 | − | 33.2758i | −0.361899 | − | 1.35062i | −0.871577 | − | 0.490259i | \(-0.836902\pi\) |
0.509678 | − | 0.860365i | \(-0.329765\pi\) | |||||||
\(608\) | −1.54802 | − | 1.54802i | −0.0627804 | − | 0.0627804i | ||||
\(609\) | −17.9339 | − | 9.22349i | −0.726720 | − | 0.373755i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.75885 | − | 6.51051i | 0.152067 | − | 0.263387i | ||||
\(612\) | −4.14903 | − | 1.11173i | −0.167715 | − | 0.0449390i | ||||
\(613\) | −31.6042 | − | 8.46832i | −1.27648 | − | 0.342032i | −0.443971 | − | 0.896041i | \(-0.646431\pi\) |
−0.832510 | + | 0.554009i | \(0.813097\pi\) | |||||||
\(614\) | 0.753393 | − | 1.30491i | 0.0304044 | − | 0.0526620i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.63753 | − | 4.44231i | −0.348016 | − | 0.178986i | ||||
\(617\) | 15.5005 | + | 15.5005i | 0.624025 | + | 0.624025i | 0.946558 | − | 0.322533i | \(-0.104534\pi\) |
−0.322533 | + | 0.946558i | \(0.604534\pi\) | |||||||
\(618\) | 12.4730 | + | 46.5497i | 0.501736 | + | 1.87250i | ||||
\(619\) | −4.31138 | − | 7.46752i | −0.173289 | − | 0.300145i | 0.766279 | − | 0.642508i | \(-0.222106\pi\) |
−0.939568 | + | 0.342363i | \(0.888773\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.0055 | + | 16.7463i | 1.16395 | + | 0.672008i | ||||
\(622\) | −9.76397 | + | 9.76397i | −0.391500 | + | 0.391500i | ||||
\(623\) | 2.54269 | − | 2.80254i | 0.101871 | − | 0.112281i | ||||
\(624\) | − | 3.41421i | − | 0.136678i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.2191 | − | 11.6735i | 0.808119 | − | 0.466568i | ||||
\(627\) | 6.04621 | − | 22.5648i | 0.241462 | − | 0.901150i | ||||
\(628\) | −23.6523 | + | 6.33762i | −0.943830 | + | 0.252898i | ||||
\(629\) | 0.202545 | 0.00807600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.13675 | −0.164682 | −0.0823408 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823408 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(632\) | −12.9543 | + | 3.47109i | −0.515294 | + | 0.138073i | ||||
\(633\) | −8.40662 | + | 31.3739i | −0.334133 | + | 1.24700i | ||||
\(634\) | −11.4219 | + | 6.59442i | −0.453620 | + | 0.261898i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 23.0027i | − | 0.912117i | ||||||
\(637\) | 2.88840 | + | 7.69827i | 0.114443 | + | 0.305017i | ||||
\(638\) | −6.80736 | + | 6.80736i | −0.269506 | + | 0.269506i | ||||
\(639\) | −38.3055 | − | 22.1157i | −1.51534 | − | 0.874882i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.42807 | − | 9.40169i | −0.214396 | − | 0.371345i | 0.738690 | − | 0.674046i | \(-0.235445\pi\) |
−0.953086 | + | 0.302701i | \(0.902112\pi\) | |||||||
\(642\) | 3.43757 | + | 12.8292i | 0.135670 | + | 0.506328i | ||||
\(643\) | −8.06230 | − | 8.06230i | −0.317946 | − | 0.317946i | 0.530032 | − | 0.847978i | \(-0.322180\pi\) |
−0.847978 | + | 0.530032i | \(0.822180\pi\) | |||||||
\(644\) | 6.74114 | + | 10.4670i | 0.265638 | + | 0.412457i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.862920 | − | 1.49462i | 0.0339511 | − | 0.0588051i | ||||
\(647\) | 10.0715 | + | 2.69865i | 0.395951 | + | 0.106095i | 0.451300 | − | 0.892372i | \(-0.350960\pi\) |
−0.0553490 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(648\) | −4.19432 | − | 1.12387i | −0.164769 | − | 0.0441496i | ||||
\(649\) | −19.6632 | + | 34.0577i | −0.771848 | + | 1.33688i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0155070 | + | 0.318994i | 0.000607766 | + | 0.0125023i | ||||
\(652\) | 15.5320 | + | 15.5320i | 0.608279 | + | 0.608279i | ||||
\(653\) | 1.72009 | + | 6.41946i | 0.0673123 | + | 0.251213i | 0.991380 | − | 0.131015i | \(-0.0418236\pi\) |
−0.924068 | + | 0.382228i | \(0.875157\pi\) | |||||||
\(654\) | 26.3091 | + | 45.5687i | 1.02877 | + | 1.78188i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.77713 | − | 4.49013i | −0.303646 | − | 0.175310i | ||||
\(657\) | 38.0090 | − | 38.0090i | 1.48287 | − | 1.48287i | ||||
\(658\) | −5.17163 | − | 16.1241i | −0.201611 | − | 0.628582i | ||||
\(659\) | − | 22.0345i | − | 0.858343i | −0.903223 | − | 0.429172i | \(-0.858806\pi\) | ||
0.903223 | − | 0.429172i | \(-0.141194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.94278 | + | 5.74047i | −0.386729 | + | 0.223278i | −0.680742 | − | 0.732523i | \(-0.738343\pi\) |
0.294013 | + | 0.955802i | \(0.405009\pi\) | |||||||
\(662\) | −4.94240 | + | 18.4453i | −0.192092 | + | 0.716897i | ||||
\(663\) | 2.59983 | − | 0.696621i | 0.100969 | − | 0.0270545i | ||||
\(664\) | 13.7608 | 0.534021 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.39993 | 0.0542460 | ||||||||
\(667\) | 11.9194 | − | 3.19379i | 0.461521 | − | 0.123664i | ||||
\(668\) | −1.15158 | + | 4.29774i | −0.0445558 | + | 0.166285i | ||||
\(669\) | 2.65857 | − | 1.53492i | 0.102786 | − | 0.0593436i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.31407i | − | 0.282356i | ||||||
\(672\) | −5.69550 | − | 5.16742i | −0.219708 | − | 0.199338i | ||||
\(673\) | 15.2073 | − | 15.2073i | 0.586198 | − | 0.586198i | −0.350402 | − | 0.936600i | \(-0.613955\pi\) |
0.936600 | + | 0.350402i | \(0.113955\pi\) | |||||||
\(674\) | 0.597952 | + | 0.345228i | 0.0230322 | + | 0.0132977i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.81014 | − | 10.0635i | −0.223467 | − | 0.387056i | ||||
\(677\) | 1.48523 | + | 5.54296i | 0.0570821 | + | 0.213033i | 0.988576 | − | 0.150724i | \(-0.0481604\pi\) |
−0.931494 | + | 0.363757i | \(0.881494\pi\) | |||||||
\(678\) | −4.41998 | − | 4.41998i | −0.169748 | − | 0.169748i | ||||
\(679\) | 9.96224 | − | 6.41606i | 0.382316 | − | 0.246226i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.53492 | − | 7.85472i | 0.173779 | − | 0.300993i | ||||
\(682\) | 0.147264 | + | 0.0394591i | 0.00563901 | + | 0.00151097i | ||||
\(683\) | 18.7685 | + | 5.02900i | 0.718157 | + | 0.192430i | 0.599349 | − | 0.800488i | \(-0.295426\pi\) |
0.118808 | + | 0.992917i | \(0.462093\pi\) | |||||||
\(684\) | 5.96423 | − | 10.3303i | 0.228048 | − | 0.394991i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.2137 | + | 6.83301i | 0.657220 | + | 0.260886i | ||||
\(687\) | 17.3095 | + | 17.3095i | 0.660400 | + | 0.660400i | ||||
\(688\) | −0.173704 | − | 0.648273i | −0.00662241 | − | 0.0247152i | ||||
\(689\) | 4.64782 | + | 8.05027i | 0.177068 | + | 0.306691i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0914 | + | 11.0224i | 0.726270 | + | 0.419312i | 0.817056 | − | 0.576558i | \(-0.195605\pi\) |
−0.0907861 | + | 0.995870i | \(0.528938\pi\) | |||||||
\(692\) | 3.69572 | − | 3.69572i | 0.140490 | − | 0.140490i | ||||
\(693\) | 11.1992 | − | 51.7244i | 0.425422 | − | 1.96485i | ||||
\(694\) | − | 3.80998i | − | 0.144625i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.60113 | + | 3.81116i | −0.250215 | + | 0.144462i | ||||
\(697\) | 1.83229 | − | 6.83821i | 0.0694031 | − | 0.259016i | ||||
\(698\) | −7.64340 | + | 2.04804i | −0.289307 | + | 0.0775196i | ||||
\(699\) | 66.2630 | 2.50630 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0270 | −0.680870 | −0.340435 | − | 0.940268i | \(-0.610574\pi\) | ||||
−0.340435 | + | 0.940268i | \(0.610574\pi\) | |||||||
\(702\) | 8.07553 | − | 2.16383i | 0.304791 | − | 0.0816686i | ||||
\(703\) | −0.145579 | + | 0.543308i | −0.00549062 | + | 0.0204913i | ||||
\(704\) | −3.17930 | + | 1.83557i | −0.119824 | + | 0.0691807i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.7787i | 0.970196i | ||||||||
\(707\) | 0.181158 | − | 0.0581046i | 0.00681316 | − | 0.00218525i | ||||
\(708\) | −22.0173 | + | 22.0173i | −0.827459 | + | 0.827459i | ||||
\(709\) | 37.0614 | + | 21.3974i | 1.39187 | + | 0.803597i | 0.993522 | − | 0.113637i | \(-0.0362500\pi\) |
0.398349 | + | 0.917234i | \(0.369583\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.5370 | − | 63.2840i | −1.37025 | − | 2.37334i | ||||
\(712\) | −0.370178 | − | 1.38152i | −0.0138730 | − | 0.0517748i | ||||
\(713\) | −0.138183 | − | 0.138183i | −0.00517498 | − | 0.00517498i | ||||
\(714\) | 2.77276 | − | 5.39130i | 0.103768 | − | 0.201764i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.28428 | + | 10.8847i | −0.234854 | + | 0.406780i | ||||
\(717\) | 67.3747 | + | 18.0530i | 2.51615 | + | 0.674202i | ||||
\(718\) | 10.0326 | + | 2.68822i | 0.374413 | + | 0.100324i | ||||
\(719\) | 2.72691 | − | 4.72315i | 0.101697 | − | 0.176144i | −0.810687 | − | 0.585480i | \(-0.800906\pi\) |
0.912384 | + | 0.409336i | \(0.134240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.8142 | + | 2.12990i | −1.63172 | + | 0.0793217i | ||||
\(722\) | −10.0461 | − | 10.0461i | −0.373876 | − | 0.373876i | ||||
\(723\) | 18.6476 | + | 69.5938i | 0.693512 | + | 2.58822i | ||||
\(724\) | 5.83712 | + | 10.1102i | 0.216935 | + | 0.375742i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.23593 | − | 3.60031i | −0.231437 | − | 0.133620i | ||||
\(727\) | 16.6781 | − | 16.6781i | 0.618555 | − | 0.618555i | −0.326606 | − | 0.945161i | \(-0.605905\pi\) |
0.945161 | + | 0.326606i | \(0.105905\pi\) | |||||||
\(728\) | 3.03736 | + | 0.657639i | 0.112572 | + | 0.0243737i | ||||
\(729\) | 38.4054i | 1.42242i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.458200 | − | 0.264542i | 0.0169471 | − | 0.00978443i | ||||
\(732\) | 1.49882 | − | 5.59367i | 0.0553979 | − | 0.206748i | ||||
\(733\) | 32.8405 | − | 8.79960i | 1.21299 | − | 0.325021i | 0.405057 | − | 0.914291i | \(-0.367252\pi\) |
0.807936 | + | 0.589271i | \(0.200585\pi\) | |||||||
\(734\) | −8.68601 | −0.320607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.70563 | 0.173452 | ||||||||
\(737\) | −23.4832 | + | 6.29231i | −0.865016 | + | 0.231780i | ||||
\(738\) | 12.6642 | − | 47.2635i | 0.466177 | − | 1.73979i | ||||
\(739\) | −25.0733 | + | 14.4761i | −0.922335 | + | 0.532510i | −0.884379 | − | 0.466769i | \(-0.845418\pi\) |
−0.0379557 | + | 0.999279i | \(0.512085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.47449i | 0.274582i | ||||||||
\(742\) | 20.4637 | + | 4.43074i | 0.751247 | + | 0.162658i | ||||
\(743\) | −34.0351 | + | 34.0351i | −1.24863 | + | 1.24863i | −0.292300 | + | 0.956327i | \(0.594421\pi\) |
−0.956327 | + | 0.292300i | \(0.905579\pi\) | |||||||
\(744\) | 0.104538 | + | 0.0603553i | 0.00383257 | + | 0.00221273i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.65477 | + | 11.5264i | 0.243649 | + | 0.422012i | ||||
\(747\) | 19.4058 | + | 72.4235i | 0.710022 | + | 2.64984i | ||||
\(748\) | −2.04643 | − | 2.04643i | −0.0748247 | − | 0.0748247i | ||||
\(749\) | −12.0753 | + | 0.587006i | −0.441221 | + | 0.0214487i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.30569 | − | 16.1179i | 0.339569 | − | 0.588151i | −0.644782 | − | 0.764366i | \(-0.723052\pi\) |
0.984352 | + | 0.176215i | \(0.0563853\pi\) | |||||||
\(752\) | −6.18205 | − | 1.65648i | −0.225436 | − | 0.0604055i | ||||
\(753\) | −31.2090 | − | 8.36242i | −1.13732 | − | 0.304743i | ||||
\(754\) | 1.54013 | − | 2.66759i | 0.0560883 | − | 0.0971478i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.61270 | − | 16.7463i | 0.313241 | − | 0.609059i | ||||
\(757\) | −29.7422 | − | 29.7422i | −1.08100 | − | 1.08100i | −0.996416 | − | 0.0845825i | \(-0.973044\pi\) |
−0.0845825 | − | 0.996416i | \(-0.526956\pi\) | |||||||
\(758\) | 6.55984 | + | 24.4816i | 0.238264 | + | 0.889213i | ||||
\(759\) | 25.1064 | + | 43.4856i | 0.911305 | + | 1.57843i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.6474 | + | 10.1887i | 0.639718 | + | 0.369341i | 0.784506 | − | 0.620122i | \(-0.212917\pi\) |
−0.144788 | + | 0.989463i | \(0.546250\pi\) | |||||||
\(762\) | −38.5213 | + | 38.5213i | −1.39548 | + | 1.39548i | ||||
\(763\) | −45.6066 | + | 14.6278i | −1.65107 | + | 0.529563i | ||||
\(764\) | 15.5034i | 0.560894i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.9357 | − | 9.20046i | 0.575779 | − | 0.332426i | ||||
\(767\) | 3.25668 | − | 12.1541i | 0.117592 | − | 0.438859i | ||||
\(768\) | −2.80762 | + | 0.752300i | −0.101311 | + | 0.0271463i | ||||
\(769\) | −40.9728 | −1.47752 | −0.738759 | − | 0.673970i | \(-0.764588\pi\) | ||||
−0.738759 | + | 0.673970i | \(0.764588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 73.5189 | 2.64772 | ||||||||
\(772\) | 8.69132 | − | 2.32883i | 0.312808 | − | 0.0838165i | ||||
\(773\) | −6.39265 | + | 23.8577i | −0.229928 | + | 0.858101i | 0.750443 | + | 0.660936i | \(0.229840\pi\) |
−0.980370 | + | 0.197166i | \(0.936826\pi\) | |||||||
\(774\) | 3.16693 | − | 1.82843i | 0.113833 | − | 0.0657215i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 4.47871i | − | 0.160776i | ||||||
\(777\) | −0.418118 | + | 1.93111i | −0.0149999 | + | 0.0692783i | ||||
\(778\) | −15.8091 | + | 15.8091i | −0.566784 | + | 0.566784i | ||||
\(779\) | 17.0259 | + | 9.82991i | 0.610017 | + | 0.352193i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9007 | − | 25.8088i | −0.533190 | − | 0.923513i | ||||
\(782\) | 0.960117 | + | 3.58321i | 0.0343337 | + | 0.128135i | ||||
\(783\) | −13.1980 | − | 13.1980i | −0.471659 | − | 0.471659i | ||||
\(784\) | 5.69411 | − | 4.07150i | 0.203361 | − | 0.145411i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −20.6295 | + | 35.7314i | −0.735831 | + | 1.27450i | ||||
\(787\) | −7.92843 | − | 2.12442i | −0.282618 | − | 0.0757273i | 0.114725 | − | 0.993397i | \(-0.463401\pi\) |
−0.397343 | + | 0.917670i | \(0.630068\pi\) | |||||||
\(788\) | −16.6588 | − | 4.46372i | −0.593446 | − | 0.159013i | ||||
\(789\) | 16.4897 | − | 28.5610i | 0.587048 | − | 1.01680i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.78348 | − | 3.08075i | 0.170081 | − | 0.109539i | ||||
\(792\) | −14.1442 | − | 14.1442i | −0.502594 | − | 0.502594i | ||||
\(793\) | 0.605689 | + | 2.26046i | 0.0215086 | + | 0.0802713i | ||||
\(794\) | −7.89197 | − | 13.6693i | −0.280076 | − | 0.485105i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.56140 | − | 4.36557i | −0.268007 | − | 0.154734i | ||||
\(797\) | 11.7928 | − | 11.7928i | 0.417722 | − | 0.417722i | −0.466696 | − | 0.884418i | \(-0.654556\pi\) |
0.884418 | + | 0.466696i | \(0.154556\pi\) | |||||||
\(798\) | 12.4687 | + | 11.3127i | 0.441388 | + | 0.400464i | ||||
\(799\) | − | 5.04544i | − | 0.178495i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.74899 | − | 3.89653i | 0.238464 | − | 0.137677i | ||||
\(802\) | 3.61585 | − | 13.4945i | 0.127680 | − | 0.476508i | ||||
\(803\) | 34.9827 | − | 9.37358i | 1.23451 | − | 0.330786i | ||||
\(804\) | −19.2490 | −0.678860 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0487805 | −0.00171822 | ||||||||
\(807\) | 22.6489 | − | 6.06875i | 0.797278 | − | 0.213630i | ||||
\(808\) | 0.0186109 | − | 0.0694570i | 0.000654730 | − | 0.00244349i | ||||
\(809\) | 28.8498 | − | 16.6564i | 1.01430 | − | 0.585609i | 0.101855 | − | 0.994799i | \(-0.467522\pi\) |
0.912449 | + | 0.409191i | \(0.134189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.2368i | 1.93963i | 0.243850 | + | 0.969813i | \(0.421590\pi\) | ||||
−0.243850 | + | 0.969813i | \(0.578410\pi\) | |||||||
\(812\) | −2.11900 | − | 6.60661i | −0.0743623 | − | 0.231847i | ||||
\(813\) | 17.2637 | − | 17.2637i | 0.605465 | − | 0.605465i | ||||
\(814\) | 0.816852 | + | 0.471610i | 0.0286307 | + | 0.0165299i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.14571 | − | 1.98443i | −0.0401079 | − | 0.0694689i | ||||
\(817\) | 0.380278 | + | 1.41922i | 0.0133042 | + | 0.0496521i | ||||
\(818\) | −0.221580 | − | 0.221580i | −0.00774737 | − | 0.00774737i | ||||
\(819\) | 0.822187 | + | 16.9132i | 0.0287295 | + | 0.590995i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.31457 | + | 16.1333i | −0.325081 | + | 0.563056i | −0.981529 | − | 0.191315i | \(-0.938725\pi\) |
0.656448 | + | 0.754371i | \(0.272058\pi\) | |||||||
\(822\) | 53.2505 | + | 14.2684i | 1.85732 | + | 0.497669i | ||||
\(823\) | −16.3139 | − | 4.37130i | −0.568668 | − | 0.152374i | −0.0369821 | − | 0.999316i | \(-0.511774\pi\) |
−0.531685 | + | 0.846942i | \(0.678441\pi\) | |||||||
\(824\) | −8.28988 | + | 14.3585i | −0.288792 | + | 0.500202i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.3461 | − | 23.8280i | −0.533960 | − | 0.829081i | ||||
\(827\) | 5.62716 | + | 5.62716i | 0.195675 | + | 0.195675i | 0.798143 | − | 0.602468i | \(-0.205816\pi\) |
−0.602468 | + | 0.798143i | \(0.705816\pi\) | |||||||
\(828\) | 6.63602 | + | 24.7660i | 0.230618 | + | 0.860677i | ||||
\(829\) | −3.29757 | − | 5.71155i | −0.114529 | − | 0.198370i | 0.803062 | − | 0.595895i | \(-0.203203\pi\) |
−0.917591 | + | 0.397525i | \(0.869869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.2980 | + | 8.25494i | 0.495991 | + | 0.286361i | ||||
\(832\) | 0.830578 | − | 0.830578i | 0.0287951 | − | 0.0287951i | ||||
\(833\) | 4.26213 | + | 3.50517i | 0.147674 | + | 0.121447i | ||||
\(834\) | − | 23.9424i | − | 0.829057i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.96021 | − | 4.01848i | 0.240724 | − | 0.138982i | ||||
\(837\) | −0.0765030 | + | 0.285513i | −0.00264433 | + | 0.00986877i | ||||
\(838\) | 30.5478 | − | 8.18525i | 1.05526 | − | 0.282755i | ||||
\(839\) | −46.0930 | −1.59131 | −0.795654 | − | 0.605752i | \(-0.792872\pi\) | ||||
−0.795654 | + | 0.605752i | \(0.792872\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.1232 | 0.762870 | ||||||||
\(842\) | −23.3887 | + | 6.26698i | −0.806027 | + | 0.215974i | ||||
\(843\) | 5.47394 | − | 20.4290i | 0.188533 | − | 0.703613i | ||||
\(844\) | −9.67744 | + | 5.58727i | −0.333111 | + | 0.192322i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 34.8724i | − | 1.19894i | ||||||
\(847\) | 4.40407 | − | 4.85413i | 0.151326 | − | 0.166790i | ||||
\(848\) | 5.59589 | − | 5.59589i | 0.192164 | − | 0.192164i | ||||
\(849\) | −19.4080 | − | 11.2052i | −0.666080 | − | 0.384562i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.604505 | − | 1.04703i | −0.0207222 | − | 0.0358918i | ||||
\(852\) | −6.10700 | − | 22.7916i | −0.209222 | − | 0.780828i | ||||
\(853\) | 14.9594 | + | 14.9594i | 0.512200 | + | 0.512200i | 0.915200 | − | 0.403000i | \(-0.132032\pi\) |
−0.403000 | + | 0.915200i | \(0.632032\pi\) | |||||||
\(854\) | 4.68755 | + | 2.41082i | 0.160405 | + | 0.0824967i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.28471 | + | 3.95723i | −0.0780897 | + | 0.135255i | ||||
\(857\) | −11.6491 | − | 3.12136i | −0.397924 | − | 0.106623i | 0.0543068 | − | 0.998524i | \(-0.482705\pi\) |
−0.452231 | + | 0.891901i | \(0.649372\pi\) | |||||||
\(858\) | 12.1070 | + | 3.24405i | 0.413325 | + | 0.110750i | ||||
\(859\) | 2.90061 | − | 5.02401i | 0.0989677 | − | 0.171417i | −0.812290 | − | 0.583254i | \(-0.801779\pi\) |
0.911258 | + | 0.411837i | \(0.135113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 61.4147 | + | 31.5858i | 2.09301 | + | 1.07644i | ||||
\(862\) | 1.10172 | + | 1.10172i | 0.0375249 | + | 0.0375249i | ||||
\(863\) | 0.778623 | + | 2.90586i | 0.0265046 | + | 0.0989167i | 0.977911 | − | 0.209021i | \(-0.0670278\pi\) |
−0.951406 | + | 0.307938i | \(0.900361\pi\) | |||||||
\(864\) | −3.55879 | − | 6.16400i | −0.121072 | − | 0.209703i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.69343 | − | 4.44180i | −0.261433 | − | 0.150939i | ||||
\(867\) | −33.6632 | + | 33.6632i | −1.14326 | + | 1.14326i | ||||
\(868\) | −0.0738294 | + | 0.0813742i | −0.00250593 | + | 0.00276202i | ||||
\(869\) | − | 49.2347i | − | 1.67017i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.73657 | − | 3.88936i | 0.228260 | − | 0.131786i | ||||
\(872\) | −4.68530 | + | 17.4858i | −0.158664 | + | 0.592143i | ||||
\(873\) | 23.5717 | − | 6.31601i | 0.797780 | − | 0.213765i | ||||
\(874\) | −10.3017 | −0.348460 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.6750 | 0.968838 | ||||||||
\(877\) | 33.8582 | − | 9.07228i | 1.14331 | − | 0.306349i | 0.363030 | − | 0.931778i | \(-0.381742\pi\) |
0.780282 | + | 0.625428i | \(0.215076\pi\) | |||||||
\(878\) | 6.18945 | − | 23.0994i | 0.208884 | − | 0.779565i | ||||
\(879\) | 11.9328 | − | 6.88939i | 0.402483 | − | 0.232373i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.7116i | − | 0.798864i | −0.916763 | − | 0.399432i | \(-0.869207\pi\) | ||
0.916763 | − | 0.399432i | \(-0.130793\pi\) | |||||||
\(882\) | 29.4585 | + | 24.2266i | 0.991919 | + | 0.815753i | ||||
\(883\) | 7.95370 | − | 7.95370i | 0.267663 | − | 0.267663i | −0.560495 | − | 0.828158i | \(-0.689389\pi\) |
0.828158 | + | 0.560495i | \(0.189389\pi\) | |||||||
\(884\) | 0.801929 | + | 0.462994i | 0.0269718 | + | 0.0155722i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.43103 | + | 11.1389i | 0.216055 | + | 0.374218i | ||||
\(887\) | 5.27738 | + | 19.6954i | 0.177197 | + | 0.661308i | 0.996167 | + | 0.0874718i | \(0.0278788\pi\) |
−0.818970 | + | 0.573836i | \(0.805455\pi\) | |||||||
\(888\) | 0.528070 | + | 0.528070i | 0.0177209 | + | 0.0177209i | ||||
\(889\) | −26.8495 | − | 41.6893i | −0.900503 | − | 1.39821i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.97057 | − | 13.8054i | 0.267024 | − | 0.462499i | ||||
\(892\) | 1.02015 | + | 0.273349i | 0.0341573 | + | 0.00915241i | ||||
\(893\) | 13.5339 | + | 3.62640i | 0.452895 | + | 0.121353i | ||||
\(894\) | 7.03682 | − | 12.1881i | 0.235347 | − | 0.407632i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.128464 | − | 2.64263i | −0.00429168 | − | 0.0882841i | ||||
\(897\) | −11.3604 | − | 11.3604i | −0.379313 | − | 0.379313i | ||||
\(898\) | −4.63111 | − | 17.2836i | −0.154542 | − | 0.576760i | ||||
\(899\) | 0.0544519 | + | 0.0943134i | 0.00181607 | + | 0.00314553i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.40287 | + | 3.11935i | 0.179996 | + | 0.103921i | ||||
\(902\) | 23.3118 | − | 23.3118i | 0.776197 | − | 0.776197i | ||||
\(903\) | 1.57633 | + | 4.91468i | 0.0524570 | + | 0.163550i | ||||
\(904\) | − | 2.15051i | − | 0.0715247i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 25.2878 | − | 14.5999i | 0.840132 | − | 0.485051i | ||||
\(907\) | 1.68614 | − | 6.29276i | 0.0559874 | − | 0.208948i | −0.932266 | − | 0.361775i | \(-0.882171\pi\) |
0.988253 | + | 0.152827i | \(0.0488377\pi\) | |||||||
\(908\) | 3.01404 | − | 0.807609i | 0.100024 | − | 0.0268014i | ||||
\(909\) | 0.391801 | 0.0129952 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2528 | −0.803531 | −0.401765 | − | 0.915743i | \(-0.631603\pi\) | ||||
−0.401765 | + | 0.915743i | \(0.631603\pi\) | |||||||
\(912\) | 6.14653 | − | 1.64696i | 0.203532 | − | 0.0545362i | ||||
\(913\) | −13.0749 | + | 48.7964i | −0.432718 | + | 1.61492i | ||||
\(914\) | −29.6277 | + | 17.1056i | −0.979997 | + | 0.565802i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.42181i | 0.278264i | ||||||||
\(917\) | −27.8138 | − | 25.2350i | −0.918493 | − | 0.833333i | ||||
\(918\) | 3.96759 | − | 3.96759i | 0.130950 | − | 0.130950i | ||||
\(919\) | 31.2542 | + | 18.0446i | 1.03098 | + | 0.595236i | 0.917265 | − | 0.398277i | \(-0.130392\pi\) |
0.113714 | + | 0.993513i | \(0.463725\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.18986 | + | 3.79295i | 0.0721583 | + | 0.124982i | ||||
\(922\) | −6.04266 | − | 22.5515i | −0.199004 | − | 0.742695i | ||||
\(923\) | 6.74244 | + | 6.74244i | 0.221930 | + | 0.221930i | ||||
\(924\) | 23.7356 | − | 15.2866i | 0.780844 | − | 0.502893i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.81789 | − | 4.88073i | 0.0926017 | − | 0.160391i | ||||
\(927\) | −87.2600 | − | 23.3813i | −2.86600 | − | 0.767941i | ||||
\(928\) | −2.53301 | − | 0.678717i | −0.0831500 | − | 0.0222800i | ||||
\(929\) | 21.2041 | − | 36.7266i | 0.695685 | − | 1.20496i | −0.274264 | − | 0.961654i | \(-0.588434\pi\) |
0.969949 | − | 0.243307i | \(-0.0782323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4657 | + | 8.91344i | −0.408547 | + | 0.292126i | ||||
\(932\) | 16.1198 | + | 16.1198i | 0.528023 | + | 0.528023i | ||||
\(933\) | −10.3880 | − | 38.7686i | −0.340089 | − | 1.26923i | ||||
\(934\) | −2.44290 | − | 4.23123i | −0.0799342 | − | 0.138450i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.54268 | + | 3.20007i | 0.181168 | + | 0.104597i | ||||
\(937\) | 4.06709 | − | 4.06709i | 0.132866 | − | 0.132866i | −0.637546 | − | 0.770412i | \(-0.720050\pi\) |
0.770412 | + | 0.637546i | \(0.220050\pi\) | |||||||
\(938\) | 3.70770 | − | 17.1243i | 0.121061 | − | 0.559129i | ||||
\(939\) | 67.8621i | 2.21460i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4071 | + | 10.0500i | −0.567455 | + | 0.327621i | −0.756132 | − | 0.654419i | \(-0.772913\pi\) |
0.188677 | + | 0.982039i | \(0.439580\pi\) | |||||||
\(942\) | 18.4213 | − | 68.7494i | 0.600200 | − | 2.23998i | ||||
\(943\) | −40.8179 | + | 10.9371i | −1.32921 | + | 0.356162i | ||||
\(944\) | −10.7123 | −0.348656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.46386 | 0.0801069 | ||||||||
\(947\) | −56.9449 | + | 15.2583i | −1.85046 | + | 0.495830i | −0.999565 | − | 0.0295030i | \(-0.990608\pi\) |
−0.850897 | + | 0.525333i | \(0.823941\pi\) | |||||||
\(948\) | 10.0893 | − | 37.6538i | 0.327685 | − | 1.22294i | ||||
\(949\) | −10.0354 | + | 5.79393i | −0.325762 | + | 0.188079i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 38.3355i | − | 1.24311i | ||||||
\(952\) | 1.98608 | − | 0.637013i | 0.0643691 | − | 0.0206457i | ||||
\(953\) | 31.1044 | − | 31.1044i | 1.00757 | − | 1.00757i | 0.00759828 | − | 0.999971i | \(-0.497581\pi\) |
0.999971 | − | 0.00759828i | \(-0.00241863\pi\) | |||||||
\(954\) | 37.3429 | + | 21.5599i | 1.20902 | + | 0.698029i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.9985 | + | 20.7821i | 0.388060 | + | 0.672140i | ||||
\(957\) | −7.24244 | − | 27.0292i | −0.234115 | − | 0.873729i | ||||
\(958\) | −12.0996 | − | 12.0996i | −0.390921 | − | 0.390921i | ||||
\(959\) | −22.9505 | + | 44.6245i | −0.741111 | + | 1.44100i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4991 | + | 26.8453i | −0.499972 | + | 0.865977i | ||||
\(962\) | −0.291508 | − | 0.0781094i | −0.00939861 | − | 0.00251835i | ||||
\(963\) | −24.0491 | − | 6.44392i | −0.774970 | − | 0.207653i | ||||
\(964\) | −12.3937 | + | 21.4666i | −0.399175 | + | 0.691391i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −36.1451 | + | 1.75709i | −1.16295 | + | 0.0565336i | ||||
\(967\) | 21.5036 | + | 21.5036i | 0.691510 | + | 0.691510i | 0.962564 | − | 0.271054i | \(-0.0873721\pi\) |
−0.271054 | + | 0.962564i | \(0.587372\pi\) | |||||||
\(968\) | −0.641168 | − | 2.39287i | −0.0206079 | − | 0.0769098i | ||||
\(969\) | 2.50822 | + | 4.34437i | 0.0805756 | + | 0.139561i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.3034 | − | 26.1559i | −1.45385 | − | 0.839384i | −0.455158 | − | 0.890411i | \(-0.650417\pi\) |
−0.998697 | + | 0.0510273i | \(0.983750\pi\) | |||||||
\(972\) | −6.17385 | + | 6.17385i | −0.198026 | + | 0.198026i | ||||
\(973\) | 21.2997 | + | 4.61174i | 0.682836 | + | 0.147845i | ||||
\(974\) | − | 0.130300i | − | 0.00417507i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.72539 | − | 0.996157i | 0.0552285 | − | 0.0318862i | ||||
\(977\) | −14.6477 | + | 54.6658i | −0.468620 | + | 1.74891i | 0.175979 | + | 0.984394i | \(0.443691\pi\) |
−0.644599 | + | 0.764520i | \(0.722976\pi\) | |||||||
\(978\) | −61.6710 | + | 16.5247i | −1.97202 | + | 0.528401i | ||||
\(979\) | 5.25068 | 0.167813 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −98.6358 | −3.14920 | ||||||||
\(982\) | −26.0699 | + | 6.98541i | −0.831924 | + | 0.222913i | ||||
\(983\) | −4.00621 | + | 14.9514i | −0.127778 | + | 0.476875i | −0.999923 | − | 0.0123723i | \(-0.996062\pi\) |
0.872145 | + | 0.489247i | \(0.162728\pi\) | |||||||
\(984\) | 22.6055 | − | 13.0513i | 0.720638 | − | 0.416061i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2.06729i | − | 0.0658361i | ||||||
\(987\) | 48.1044 | + | 10.4154i | 1.53118 | + | 0.331526i | ||||
\(988\) | −1.81832 | + | 1.81832i | −0.0578486 | + | 0.0578486i | ||||
\(989\) | −2.73504 | − | 1.57907i | −0.0869691 | − | 0.0502116i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.8648 | + | 46.5311i | 0.853388 | + | 1.47811i | 0.878133 | + | 0.478417i | \(0.158789\pi\) |
−0.0247453 | + | 0.999694i | \(0.507877\pi\) | |||||||
\(992\) | 0.0107485 | + | 0.0401138i | 0.000341264 | + | 0.00127362i | ||||
\(993\) | −39.2484 | − | 39.2484i | −1.24551 | − | 1.24551i | ||||
\(994\) | 21.4523 | − | 1.04284i | 0.680424 | − | 0.0330769i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.9990 | + | 34.6392i | −0.633692 | + | 1.09759i | ||||
\(997\) | −37.2167 | − | 9.97217i | −1.17866 | − | 0.315822i | −0.384267 | − | 0.923222i | \(-0.625546\pi\) |
−0.794396 | + | 0.607400i | \(0.792213\pi\) | |||||||
\(998\) | −0.0930180 | − | 0.0249241i | −0.00294443 | − | 0.000788959i | ||||
\(999\) | −0.914352 | + | 1.58370i | −0.0289288 | + | 0.0501062i |
(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 | 350.2.o.c.257.2 | 16 | ||
5.2 | odd | 4 | 70.2.k.a.33.1 | yes | 16 | ||
5.3 | odd | 4 | inner | 350.2.o.c.243.4 | 16 | ||
5.4 | even | 2 | 70.2.k.a.47.3 | yes | 16 | ||
7.3 | odd | 6 | inner | 350.2.o.c.157.4 | 16 | ||
15.2 | even | 4 | 630.2.bv.c.523.4 | 16 | |||
15.14 | odd | 2 | 630.2.bv.c.397.1 | 16 | |||
20.7 | even | 4 | 560.2.ci.c.33.4 | 16 | |||
20.19 | odd | 2 | 560.2.ci.c.257.4 | 16 | |||
35.2 | odd | 12 | 490.2.g.c.293.4 | 16 | |||
35.3 | even | 12 | inner | 350.2.o.c.143.2 | 16 | ||
35.4 | even | 6 | 490.2.l.c.227.2 | 16 | |||
35.9 | even | 6 | 490.2.g.c.97.1 | 16 | |||
35.12 | even | 12 | 490.2.g.c.293.1 | 16 | |||
35.17 | even | 12 | 70.2.k.a.3.3 | ✓ | 16 | ||
35.19 | odd | 6 | 490.2.g.c.97.4 | 16 | |||
35.24 | odd | 6 | 70.2.k.a.17.1 | yes | 16 | ||
35.27 | even | 4 | 490.2.l.c.313.2 | 16 | |||
35.32 | odd | 12 | 490.2.l.c.423.4 | 16 | |||
35.34 | odd | 2 | 490.2.l.c.117.4 | 16 | |||
105.17 | odd | 12 | 630.2.bv.c.73.1 | 16 | |||
105.59 | even | 6 | 630.2.bv.c.577.4 | 16 | |||
140.59 | even | 6 | 560.2.ci.c.17.4 | 16 | |||
140.87 | odd | 12 | 560.2.ci.c.353.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.3 | ✓ | 16 | 35.17 | even | 12 | ||
70.2.k.a.17.1 | yes | 16 | 35.24 | odd | 6 | ||
70.2.k.a.33.1 | yes | 16 | 5.2 | odd | 4 | ||
70.2.k.a.47.3 | yes | 16 | 5.4 | even | 2 | ||
350.2.o.c.143.2 | 16 | 35.3 | even | 12 | inner | ||
350.2.o.c.157.4 | 16 | 7.3 | odd | 6 | inner | ||
350.2.o.c.243.4 | 16 | 5.3 | odd | 4 | inner | ||
350.2.o.c.257.2 | 16 | 1.1 | even | 1 | trivial | ||
490.2.g.c.97.1 | 16 | 35.9 | even | 6 | |||
490.2.g.c.97.4 | 16 | 35.19 | odd | 6 | |||
490.2.g.c.293.1 | 16 | 35.12 | even | 12 | |||
490.2.g.c.293.4 | 16 | 35.2 | odd | 12 | |||
490.2.l.c.117.4 | 16 | 35.34 | odd | 2 | |||
490.2.l.c.227.2 | 16 | 35.4 | even | 6 | |||
490.2.l.c.313.2 | 16 | 35.27 | even | 4 | |||
490.2.l.c.423.4 | 16 | 35.32 | odd | 12 | |||
560.2.ci.c.17.4 | 16 | 140.59 | even | 6 | |||
560.2.ci.c.33.4 | 16 | 20.7 | even | 4 | |||
560.2.ci.c.257.4 | 16 | 20.19 | odd | 2 | |||
560.2.ci.c.353.4 | 16 | 140.87 | odd | 12 | |||
630.2.bv.c.73.1 | 16 | 105.17 | odd | 12 | |||
630.2.bv.c.397.1 | 16 | 15.14 | odd | 2 | |||
630.2.bv.c.523.4 | 16 | 15.2 | even | 4 | |||
630.2.bv.c.577.4 | 16 | 105.59 | even | 6 |