Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.j (of order \(3\), degree \(2\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(-2.06288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.211 |
Dual form | 630.2.j.l.421.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.70236 | − | 0.319344i | −0.982856 | − | 0.184373i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0.574618 | + | 1.63396i | 0.234587 | + | 0.667060i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.79604 | + | 1.08728i | 0.932013 | + | 0.362425i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.83010 | − | 3.16982i | −0.551795 | − | 0.955736i | −0.998145 | − | 0.0608781i | \(-0.980610\pi\) |
0.446351 | − | 0.894858i | \(-0.352723\pi\) | |||||||
\(12\) | 1.12774 | − | 1.31461i | 0.325550 | − | 0.379496i | ||||
\(13\) | −1.78651 | + | 3.09432i | −0.495488 | + | 0.858210i | −0.999986 | − | 0.00520227i | \(-0.998344\pi\) |
0.504499 | + | 0.863413i | \(0.331677\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | −1.12774 | + | 1.31461i | −0.291181 | + | 0.339431i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.46677 | 1.08335 | 0.541676 | − | 0.840587i | \(-0.317790\pi\) | ||||
0.541676 | + | 0.840587i | \(0.317790\pi\) | |||||||
\(18\) | −0.456412 | − | 2.96508i | −0.107577 | − | 0.698876i | ||||
\(19\) | 5.59208 | 1.28291 | 0.641455 | − | 0.767160i | \(-0.278331\pi\) | ||||
0.641455 | + | 0.767160i | \(0.278331\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −0.574618 | − | 1.63396i | −0.125392 | − | 0.356559i | ||||
\(22\) | −1.83010 | + | 3.16982i | −0.390178 | + | 0.675808i | ||||
\(23\) | 1.33010 | − | 2.30379i | 0.277344 | − | 0.480374i | −0.693380 | − | 0.720572i | \(-0.743879\pi\) |
0.970724 | + | 0.240198i | \(0.0772125\pi\) | |||||||
\(24\) | −1.70236 | − | 0.319344i | −0.347492 | − | 0.0651858i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 3.57301 | 0.700726 | ||||||||
\(27\) | −4.41264 | − | 2.74383i | −0.849213 | − | 0.528050i | ||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 0.223855 | + | 0.387729i | 0.0415689 | + | 0.0719995i | 0.886061 | − | 0.463568i | \(-0.153431\pi\) |
−0.844492 | + | 0.535568i | \(0.820098\pi\) | |||||||
\(30\) | 1.70236 | + | 0.319344i | 0.310806 | + | 0.0583040i | ||||
\(31\) | 4.59208 | − | 7.95371i | 0.824761 | − | 1.42853i | −0.0773400 | − | 0.997005i | \(-0.524643\pi\) |
0.902101 | − | 0.431524i | \(-0.142024\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 2.10321 | + | 5.98059i | 0.366122 | + | 1.04109i | ||||
\(34\) | −2.23339 | − | 3.86834i | −0.383023 | − | 0.663415i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.33963 | + | 1.87780i | −0.389938 | + | 0.312967i | ||||
\(37\) | −10.1651 | −1.67113 | −0.835565 | − | 0.549391i | \(-0.814860\pi\) | ||||
−0.835565 | + | 0.549391i | \(0.814860\pi\) | |||||||
\(38\) | −2.79604 | − | 4.84288i | −0.453577 | − | 0.785619i | ||||
\(39\) | 4.02943 | − | 4.69713i | 0.645225 | − | 0.752143i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 2.28651 | − | 3.96035i | 0.357092 | − | 0.618502i | −0.630381 | − | 0.776286i | \(-0.717101\pi\) |
0.987474 | + | 0.157783i | \(0.0504348\pi\) | |||||||
\(42\) | −1.12774 | + | 1.31461i | −0.174014 | + | 0.202849i | ||||
\(43\) | −3.61660 | − | 6.26414i | −0.551527 | − | 0.955272i | −0.998165 | − | 0.0605576i | \(-0.980712\pi\) |
0.446638 | − | 0.894715i | \(-0.352621\pi\) | |||||||
\(44\) | 3.66019 | 0.551795 | ||||||||
\(45\) | 2.33963 | − | 1.87780i | 0.348771 | − | 0.279926i | ||||
\(46\) | −2.66019 | −0.392224 | ||||||||
\(47\) | −6.13567 | − | 10.6273i | −0.894979 | − | 1.55015i | −0.833831 | − | 0.552020i | \(-0.813857\pi\) |
−0.0611481 | − | 0.998129i | \(-0.519476\pi\) | |||||||
\(48\) | 0.574618 | + | 1.63396i | 0.0829390 | + | 0.235841i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −7.60404 | − | 1.42644i | −1.06478 | − | 0.199741i | ||||
\(52\) | −1.78651 | − | 3.09432i | −0.247744 | − | 0.429105i | ||||
\(53\) | 4.98094 | 0.684184 | 0.342092 | − | 0.939666i | \(-0.388865\pi\) | ||||
0.342092 | + | 0.939666i | \(0.388865\pi\) | |||||||
\(54\) | −0.169904 | + | 5.19337i | −0.0231211 | + | 0.706729i | ||||
\(55\) | −3.66019 | −0.493540 | ||||||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | −9.51971 | − | 1.78580i | −1.26092 | − | 0.236535i | ||||
\(58\) | 0.223855 | − | 0.387729i | 0.0293937 | − | 0.0509113i | ||||
\(59\) | 6.45623 | − | 11.1825i | 0.840530 | − | 1.45584i | −0.0489181 | − | 0.998803i | \(-0.515577\pi\) |
0.889448 | − | 0.457037i | \(-0.151089\pi\) | |||||||
\(60\) | −0.574618 | − | 1.63396i | −0.0741829 | − | 0.210943i | ||||
\(61\) | −0.596708 | − | 1.03353i | −0.0764007 | − | 0.132330i | 0.825294 | − | 0.564704i | \(-0.191009\pi\) |
−0.901695 | + | 0.432374i | \(0.857676\pi\) | |||||||
\(62\) | −9.18416 | −1.16639 | ||||||||
\(63\) | 0.456412 | + | 2.96508i | 0.0575025 | + | 0.373565i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.78651 | + | 3.09432i | 0.221589 | + | 0.383803i | ||||
\(66\) | 4.12774 | − | 4.81173i | 0.508089 | − | 0.592283i | ||||
\(67\) | −4.88322 | + | 8.45798i | −0.596580 | + | 1.03331i | 0.396742 | + | 0.917930i | \(0.370141\pi\) |
−0.993322 | + | 0.115376i | \(0.963193\pi\) | |||||||
\(68\) | −2.23339 | + | 3.86834i | −0.270838 | + | 0.469105i | ||||
\(69\) | −3.00000 | + | 3.49712i | −0.361158 | + | 0.421004i | ||||
\(70\) | −0.500000 | − | 0.866025i | −0.0597614 | − | 0.103510i | ||||
\(71\) | 3.89376 | 0.462104 | 0.231052 | − | 0.972941i | \(-0.425783\pi\) | ||||
0.231052 | + | 0.972941i | \(0.425783\pi\) | |||||||
\(72\) | 2.79604 | + | 1.08728i | 0.329516 | + | 0.128137i | ||||
\(73\) | 6.14603 | 0.719338 | 0.359669 | − | 0.933080i | \(-0.382890\pi\) | ||||
0.359669 | + | 0.933080i | \(0.382890\pi\) | |||||||
\(74\) | 5.08255 | + | 8.80323i | 0.590834 | + | 1.02335i | ||||
\(75\) | 0.574618 | + | 1.63396i | 0.0663512 | + | 0.188673i | ||||
\(76\) | −2.79604 | + | 4.84288i | −0.320728 | + | 0.555517i | ||||
\(77\) | 1.83010 | − | 3.16982i | 0.208559 | − | 0.361234i | ||||
\(78\) | −6.08255 | − | 1.14102i | −0.688713 | − | 0.129195i | ||||
\(79\) | 1.11660 | + | 1.93401i | 0.125628 | + | 0.217593i | 0.921978 | − | 0.387242i | \(-0.126572\pi\) |
−0.796350 | + | 0.604835i | \(0.793239\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 6.63567 | + | 6.08013i | 0.737296 | + | 0.675570i | ||||
\(82\) | −4.57301 | −0.505005 | ||||||||
\(83\) | 5.68962 | + | 9.85471i | 0.624517 | + | 1.08169i | 0.988634 | + | 0.150341i | \(0.0480373\pi\) |
−0.364118 | + | 0.931353i | \(0.618629\pi\) | |||||||
\(84\) | 1.70236 | + | 0.319344i | 0.185742 | + | 0.0348433i | ||||
\(85\) | 2.23339 | − | 3.86834i | 0.242245 | − | 0.419580i | ||||
\(86\) | −3.61660 | + | 6.26414i | −0.389988 | + | 0.675480i | ||||
\(87\) | −0.257263 | − | 0.731540i | −0.0275815 | − | 0.0784293i | ||||
\(88\) | −1.83010 | − | 3.16982i | −0.195089 | − | 0.337904i | ||||
\(89\) | 13.3585 | 1.41600 | 0.708000 | − | 0.706213i | \(-0.249598\pi\) | ||||
0.708000 | + | 0.706213i | \(0.249598\pi\) | |||||||
\(90\) | −2.79604 | − | 1.08728i | −0.294728 | − | 0.114609i | ||||
\(91\) | −3.57301 | −0.374554 | ||||||||
\(92\) | 1.33010 | + | 2.30379i | 0.138672 | + | 0.240187i | ||||
\(93\) | −10.3573 | + | 12.0736i | −1.07400 | + | 1.25197i | ||||
\(94\) | −6.13567 | + | 10.6273i | −0.632846 | + | 1.09612i | ||||
\(95\) | 2.79604 | − | 4.84288i | 0.286868 | − | 0.496869i | ||||
\(96\) | 1.12774 | − | 1.31461i | 0.115099 | − | 0.134172i | ||||
\(97\) | 4.26643 | + | 7.38968i | 0.433190 | + | 0.750308i | 0.997146 | − | 0.0754973i | \(-0.0240544\pi\) |
−0.563956 | + | 0.825805i | \(0.690721\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.67055 | − | 10.8528i | −0.167897 | − | 1.09074i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.64113 | − | 11.5028i | −0.660817 | − | 1.14457i | −0.980401 | − | 0.197011i | \(-0.936877\pi\) |
0.319584 | − | 0.947558i | \(-0.396457\pi\) | |||||||
\(102\) | 2.56669 | + | 7.29851i | 0.254140 | + | 0.722661i | ||||
\(103\) | 7.15066 | − | 12.3853i | 0.704575 | − | 1.22036i | −0.262269 | − | 0.964995i | \(-0.584471\pi\) |
0.966845 | − | 0.255366i | \(-0.0821958\pi\) | |||||||
\(104\) | −1.78651 | + | 3.09432i | −0.175181 | + | 0.303423i | ||||
\(105\) | −1.70236 | − | 0.319344i | −0.166133 | − | 0.0311648i | ||||
\(106\) | −2.49047 | − | 4.31362i | −0.241896 | − | 0.418976i | ||||
\(107\) | 9.51582 | 0.919929 | 0.459965 | − | 0.887937i | \(-0.347862\pi\) | ||||
0.459965 | + | 0.887937i | \(0.347862\pi\) | |||||||
\(108\) | 4.58255 | − | 2.44955i | 0.440956 | − | 0.235708i | ||||
\(109\) | 0.465112 | 0.0445497 | 0.0222748 | − | 0.999752i | \(-0.492909\pi\) | ||||
0.0222748 | + | 0.999752i | \(0.492909\pi\) | |||||||
\(110\) | 1.83010 | + | 3.16982i | 0.174493 | + | 0.302230i | ||||
\(111\) | 17.3046 | + | 3.24616i | 1.64248 | + | 0.308112i | ||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | −1.07320 | + | 1.85883i | −0.100958 | + | 0.174864i | −0.912080 | − | 0.410013i | \(-0.865524\pi\) |
0.811122 | + | 0.584877i | \(0.198857\pi\) | |||||||
\(114\) | 3.21331 | + | 9.13721i | 0.300954 | + | 0.855778i | ||||
\(115\) | −1.33010 | − | 2.30379i | −0.124032 | − | 0.214830i | ||||
\(116\) | −0.447711 | −0.0415689 | ||||||||
\(117\) | −8.35952 | + | 6.70942i | −0.772838 | + | 0.620286i | ||||
\(118\) | −12.9125 | −1.18869 | ||||||||
\(119\) | 2.23339 | + | 3.86834i | 0.204734 | + | 0.354610i | ||||
\(120\) | −1.12774 | + | 1.31461i | −0.102948 | + | 0.120007i | ||||
\(121\) | −1.19850 | + | 2.07586i | −0.108954 | + | 0.188715i | ||||
\(122\) | −0.596708 | + | 1.03353i | −0.0540234 | + | 0.0935714i | ||||
\(123\) | −5.15716 | + | 6.01174i | −0.465006 | + | 0.542060i | ||||
\(124\) | 4.59208 | + | 7.95371i | 0.412381 | + | 0.714264i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.33963 | − | 1.87780i | 0.208431 | − | 0.167288i | ||||
\(127\) | −4.66019 | −0.413525 | −0.206763 | − | 0.978391i | \(-0.566293\pi\) | ||||
−0.206763 | + | 0.978391i | \(0.566293\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.15633 | + | 11.8187i | 0.365945 | + | 1.04058i | ||||
\(130\) | 1.78651 | − | 3.09432i | 0.156687 | − | 0.271390i | ||||
\(131\) | −7.83963 | + | 13.5786i | −0.684951 | + | 1.18637i | 0.288501 | + | 0.957480i | \(0.406843\pi\) |
−0.973452 | + | 0.228891i | \(0.926490\pi\) | |||||||
\(132\) | −6.23095 | − | 1.16886i | −0.542335 | − | 0.101736i | ||||
\(133\) | 2.79604 | + | 4.84288i | 0.242447 | + | 0.419931i | ||||
\(134\) | 9.76643 | 0.843691 | ||||||||
\(135\) | −4.58255 | + | 2.44955i | −0.394403 | + | 0.210823i | ||||
\(136\) | 4.46677 | 0.383023 | ||||||||
\(137\) | −6.55312 | − | 11.3503i | −0.559871 | − | 0.969725i | −0.997507 | − | 0.0705724i | \(-0.977517\pi\) |
0.437636 | − | 0.899152i | \(-0.355816\pi\) | |||||||
\(138\) | 4.52859 | + | 0.849516i | 0.385500 | + | 0.0723156i | ||||
\(139\) | −8.51036 | + | 14.7404i | −0.721840 | + | 1.25026i | 0.238422 | + | 0.971162i | \(0.423370\pi\) |
−0.960262 | + | 0.279101i | \(0.909964\pi\) | |||||||
\(140\) | −0.500000 | + | 0.866025i | −0.0422577 | + | 0.0731925i | ||||
\(141\) | 7.05133 | + | 20.0508i | 0.593829 | + | 1.68858i | ||||
\(142\) | −1.94688 | − | 3.37209i | −0.163379 | − | 0.282980i | ||||
\(143\) | 13.0779 | 1.09363 | ||||||||
\(144\) | −0.456412 | − | 2.96508i | −0.0380343 | − | 0.247090i | ||||
\(145\) | 0.447711 | 0.0371804 | ||||||||
\(146\) | −3.07301 | − | 5.32262i | −0.254324 | − | 0.440503i | ||||
\(147\) | 1.12774 | − | 1.31461i | 0.0930143 | − | 0.108427i | ||||
\(148\) | 5.08255 | − | 8.80323i | 0.417783 | − | 0.723621i | ||||
\(149\) | −7.15473 | + | 12.3924i | −0.586138 | + | 1.01522i | 0.408594 | + | 0.912716i | \(0.366019\pi\) |
−0.994732 | + | 0.102505i | \(0.967314\pi\) | |||||||
\(150\) | 1.12774 | − | 1.31461i | 0.0920795 | − | 0.107338i | ||||
\(151\) | −6.01036 | − | 10.4103i | −0.489116 | − | 0.847174i | 0.510805 | − | 0.859696i | \(-0.329347\pi\) |
−0.999922 | + | 0.0125221i | \(0.996014\pi\) | |||||||
\(152\) | 5.59208 | 0.453577 | ||||||||
\(153\) | 12.4893 | + | 4.85661i | 1.00970 | + | 0.392634i | ||||
\(154\) | −3.66019 | −0.294947 | ||||||||
\(155\) | −4.59208 | − | 7.95371i | −0.368845 | − | 0.638858i | ||||
\(156\) | 2.05312 | + | 5.83815i | 0.164381 | + | 0.467426i | ||||
\(157\) | 3.31973 | − | 5.74995i | 0.264944 | − | 0.458896i | −0.702605 | − | 0.711580i | \(-0.747980\pi\) |
0.967549 | + | 0.252684i | \(0.0813133\pi\) | |||||||
\(158\) | 1.11660 | − | 1.93401i | 0.0888321 | − | 0.153862i | ||||
\(159\) | −8.47933 | − | 1.59063i | −0.672455 | − | 0.126145i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 2.66019 | 0.209652 | ||||||||
\(162\) | 1.94771 | − | 8.78672i | 0.153027 | − | 0.690350i | ||||
\(163\) | 7.46677 | 0.584843 | 0.292421 | − | 0.956290i | \(-0.405539\pi\) | ||||
0.292421 | + | 0.956290i | \(0.405539\pi\) | |||||||
\(164\) | 2.28651 | + | 3.96035i | 0.178546 | + | 0.309251i | ||||
\(165\) | 6.23095 | + | 1.16886i | 0.485079 | + | 0.0909956i | ||||
\(166\) | 5.68962 | − | 9.85471i | 0.441600 | − | 0.764874i | ||||
\(167\) | −1.98501 | + | 3.43813i | −0.153604 | + | 0.266051i | −0.932550 | − | 0.361041i | \(-0.882421\pi\) |
0.778946 | + | 0.627092i | \(0.215755\pi\) | |||||||
\(168\) | −0.574618 | − | 1.63396i | −0.0443328 | − | 0.126062i | ||||
\(169\) | 0.116784 | + | 0.202277i | 0.00898342 | + | 0.0155597i | ||||
\(170\) | −4.46677 | −0.342586 | ||||||||
\(171\) | 15.6357 | + | 6.08013i | 1.19569 | + | 0.464959i | ||||
\(172\) | 7.23321 | 0.551527 | ||||||||
\(173\) | 4.59208 | + | 7.95371i | 0.349129 | + | 0.604710i | 0.986095 | − | 0.166183i | \(-0.0531441\pi\) |
−0.636966 | + | 0.770892i | \(0.719811\pi\) | |||||||
\(174\) | −0.504901 | + | 0.588566i | −0.0382764 | + | 0.0446191i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.83010 | + | 3.16982i | −0.137949 | + | 0.238934i | ||||
\(177\) | −14.5619 | + | 16.9749i | −1.09454 | + | 1.27591i | ||||
\(178\) | −6.67925 | − | 11.5688i | −0.500631 | − | 0.867119i | ||||
\(179\) | 2.34147 | 0.175010 | 0.0875049 | − | 0.996164i | \(-0.472111\pi\) | ||||
0.0875049 | + | 0.996164i | \(0.472111\pi\) | |||||||
\(180\) | 0.456412 | + | 2.96508i | 0.0340189 | + | 0.221004i | ||||
\(181\) | 18.6789 | 1.38839 | 0.694196 | − | 0.719786i | \(-0.255760\pi\) | ||||
0.694196 | + | 0.719786i | \(0.255760\pi\) | |||||||
\(182\) | 1.78651 | + | 3.09432i | 0.132425 | + | 0.229366i | ||||
\(183\) | 0.685759 | + | 1.94999i | 0.0506928 | + | 0.144147i | ||||
\(184\) | 1.33010 | − | 2.30379i | 0.0980559 | − | 0.169838i | ||||
\(185\) | −5.08255 | + | 8.80323i | −0.373676 | + | 0.647226i | ||||
\(186\) | 15.6347 | + | 2.93290i | 1.14639 | + | 0.215051i | ||||
\(187\) | −8.17462 | − | 14.1589i | −0.597788 | − | 1.03540i | ||||
\(188\) | 12.2713 | 0.894979 | ||||||||
\(189\) | 0.169904 | − | 5.19337i | 0.0123587 | − | 0.377762i | ||||
\(190\) | −5.59208 | −0.405692 | ||||||||
\(191\) | −9.37960 | − | 16.2459i | −0.678684 | − | 1.17551i | −0.975377 | − | 0.220542i | \(-0.929217\pi\) |
0.296694 | − | 0.954973i | \(-0.404116\pi\) | |||||||
\(192\) | −1.70236 | − | 0.319344i | −0.122857 | − | 0.0230467i | ||||
\(193\) | −4.01989 | + | 6.96266i | −0.289358 | + | 0.501183i | −0.973657 | − | 0.228019i | \(-0.926775\pi\) |
0.684298 | + | 0.729202i | \(0.260109\pi\) | |||||||
\(194\) | 4.26643 | − | 7.38968i | 0.306312 | − | 0.530548i | ||||
\(195\) | −2.05312 | − | 5.83815i | −0.147027 | − | 0.418079i | ||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 7.15529 | 0.509793 | 0.254897 | − | 0.966968i | \(-0.417959\pi\) | ||||
0.254897 | + | 0.966968i | \(0.417959\pi\) | |||||||
\(198\) | −8.56348 | + | 6.87312i | −0.608580 | + | 0.488451i | ||||
\(199\) | 6.87267 | 0.487191 | 0.243595 | − | 0.969877i | \(-0.421673\pi\) | ||||
0.243595 | + | 0.969877i | \(0.421673\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 11.0140 | − | 12.8391i | 0.776866 | − | 0.905598i | ||||
\(202\) | −6.64113 | + | 11.5028i | −0.467268 | + | 0.809332i | ||||
\(203\) | −0.223855 | + | 0.387729i | −0.0157116 | + | 0.0272132i | ||||
\(204\) | 5.03735 | − | 5.87208i | 0.352685 | − | 0.411128i | ||||
\(205\) | −2.28651 | − | 3.96035i | −0.159697 | − | 0.276603i | ||||
\(206\) | −14.3013 | −0.996420 | ||||||||
\(207\) | 6.22386 | − | 4.99532i | 0.432588 | − | 0.347198i | ||||
\(208\) | 3.57301 | 0.247744 | ||||||||
\(209\) | −10.2340 | − | 17.7259i | −0.707903 | − | 1.22612i | ||||
\(210\) | 0.574618 | + | 1.63396i | 0.0396524 | + | 0.112754i | ||||
\(211\) | −12.3879 | + | 21.4565i | −0.852821 | + | 1.47713i | 0.0258316 | + | 0.999666i | \(0.491777\pi\) |
−0.878652 | + | 0.477462i | \(0.841557\pi\) | |||||||
\(212\) | −2.49047 | + | 4.31362i | −0.171046 | + | 0.296260i | ||||
\(213\) | −6.62857 | − | 1.24345i | −0.454182 | − | 0.0851997i | ||||
\(214\) | −4.75791 | − | 8.24095i | −0.325244 | − | 0.563339i | ||||
\(215\) | −7.23321 | −0.493301 | ||||||||
\(216\) | −4.41264 | − | 2.74383i | −0.300242 | − | 0.186694i | ||||
\(217\) | 9.18416 | 0.623461 | ||||||||
\(218\) | −0.232556 | − | 0.402799i | −0.0157507 | − | 0.0272810i | ||||
\(219\) | −10.4627 | − | 1.96270i | −0.707006 | − | 0.132627i | ||||
\(220\) | 1.83010 | − | 3.16982i | 0.123385 | − | 0.213709i | ||||
\(221\) | −7.97992 | + | 13.8216i | −0.536788 | + | 0.929744i | ||||
\(222\) | −5.84105 | − | 16.6093i | −0.392026 | − | 1.11474i | ||||
\(223\) | 14.8784 | + | 25.7702i | 0.996332 | + | 1.72570i | 0.572278 | + | 0.820060i | \(0.306060\pi\) |
0.424054 | + | 0.905637i | \(0.360607\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −0.456412 | − | 2.96508i | −0.0304274 | − | 0.197672i | ||||
\(226\) | 2.14639 | 0.142776 | ||||||||
\(227\) | −7.32991 | − | 12.6958i | −0.486503 | − | 0.842649i | 0.513376 | − | 0.858164i | \(-0.328395\pi\) |
−0.999880 | + | 0.0155150i | \(0.995061\pi\) | |||||||
\(228\) | 6.30640 | − | 7.35141i | 0.417652 | − | 0.486859i | ||||
\(229\) | 9.74274 | − | 16.8749i | 0.643818 | − | 1.11513i | −0.340755 | − | 0.940152i | \(-0.610683\pi\) |
0.984573 | − | 0.174974i | \(-0.0559840\pi\) | |||||||
\(230\) | −1.33010 | + | 2.30379i | −0.0877039 | + | 0.151908i | ||||
\(231\) | −4.12774 | + | 4.81173i | −0.271585 | + | 0.316589i | ||||
\(232\) | 0.223855 | + | 0.387729i | 0.0146968 | + | 0.0254557i | ||||
\(233\) | −11.7572 | −0.770238 | −0.385119 | − | 0.922867i | \(-0.625840\pi\) | ||||
−0.385119 | + | 0.922867i | \(0.625840\pi\) | |||||||
\(234\) | 9.99029 | + | 3.88485i | 0.653085 | + | 0.253961i | ||||
\(235\) | −12.2713 | −0.800493 | ||||||||
\(236\) | 6.45623 | + | 11.1825i | 0.420265 | + | 0.727920i | ||||
\(237\) | −1.28324 | − | 3.64896i | −0.0833555 | − | 0.237025i | ||||
\(238\) | 2.23339 | − | 3.86834i | 0.144769 | − | 0.250747i | ||||
\(239\) | 2.03813 | − | 3.53014i | 0.131835 | − | 0.228346i | −0.792549 | − | 0.609809i | \(-0.791246\pi\) |
0.924384 | + | 0.381463i | \(0.124580\pi\) | |||||||
\(240\) | 1.70236 | + | 0.319344i | 0.109887 | + | 0.0206136i | ||||
\(241\) | 11.5057 | + | 19.9285i | 0.741149 | + | 1.28371i | 0.951972 | + | 0.306184i | \(0.0990523\pi\) |
−0.210823 | + | 0.977524i | \(0.567614\pi\) | |||||||
\(242\) | 2.39700 | 0.154085 | ||||||||
\(243\) | −9.35462 | − | 12.4696i | −0.600099 | − | 0.799926i | ||||
\(244\) | 1.19342 | 0.0764007 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | 7.78490 | + | 1.46036i | 0.496347 | + | 0.0931095i | ||||
\(247\) | −9.99029 | + | 17.3037i | −0.635667 | + | 1.10101i | ||||
\(248\) | 4.59208 | − | 7.95371i | 0.291597 | − | 0.505061i | ||||
\(249\) | −6.53872 | − | 18.5932i | −0.414374 | − | 1.17829i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −22.5155 | −1.42116 | −0.710582 | − | 0.703615i | \(-0.751568\pi\) | ||||
−0.710582 | + | 0.703615i | \(0.751568\pi\) | |||||||
\(252\) | −2.79604 | − | 1.08728i | −0.176134 | − | 0.0684919i | ||||
\(253\) | −9.73681 | −0.612148 | ||||||||
\(254\) | 2.33010 | + | 4.03584i | 0.146203 | + | 0.253231i | ||||
\(255\) | −5.03735 | + | 5.87208i | −0.315451 | + | 0.367724i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.32565 | − | 4.02814i | 0.145070 | − | 0.251268i | −0.784329 | − | 0.620345i | \(-0.786993\pi\) |
0.929399 | + | 0.369077i | \(0.120326\pi\) | |||||||
\(258\) | 8.15716 | − | 9.50886i | 0.507843 | − | 0.591996i | ||||
\(259\) | −5.08255 | − | 8.80323i | −0.315814 | − | 0.547006i | ||||
\(260\) | −3.57301 | −0.221589 | ||||||||
\(261\) | 0.204340 | + | 1.32750i | 0.0126484 | + | 0.0821700i | ||||
\(262\) | 15.6793 | 0.968668 | ||||||||
\(263\) | −6.24292 | − | 10.8131i | −0.384955 | − | 0.666761i | 0.606808 | − | 0.794848i | \(-0.292450\pi\) |
−0.991763 | + | 0.128087i | \(0.959116\pi\) | |||||||
\(264\) | 2.10321 | + | 5.98059i | 0.129444 | + | 0.368080i | ||||
\(265\) | 2.49047 | − | 4.31362i | 0.152988 | − | 0.264983i | ||||
\(266\) | 2.79604 | − | 4.84288i | 0.171436 | − | 0.296936i | ||||
\(267\) | −22.7410 | − | 4.26596i | −1.39172 | − | 0.261072i | ||||
\(268\) | −4.88322 | − | 8.45798i | −0.298290 | − | 0.516653i | ||||
\(269\) | −10.3394 | −0.630407 | −0.315204 | − | 0.949024i | \(-0.602073\pi\) | ||||
−0.315204 | + | 0.949024i | \(0.602073\pi\) | |||||||
\(270\) | 4.41264 | + | 2.74383i | 0.268545 | + | 0.166984i | ||||
\(271\) | −6.94892 | −0.422117 | −0.211059 | − | 0.977473i | \(-0.567691\pi\) | ||||
−0.211059 | + | 0.977473i | \(0.567691\pi\) | |||||||
\(272\) | −2.23339 | − | 3.86834i | −0.135419 | − | 0.234553i | ||||
\(273\) | 6.08255 | + | 1.14102i | 0.368132 | + | 0.0690577i | ||||
\(274\) | −6.55312 | + | 11.3503i | −0.395888 | + | 0.685699i | ||||
\(275\) | −1.83010 | + | 3.16982i | −0.110359 | + | 0.191147i | ||||
\(276\) | −1.52859 | − | 4.34664i | −0.0920106 | − | 0.261637i | ||||
\(277\) | 6.64113 | + | 11.5028i | 0.399027 | + | 0.691135i | 0.993606 | − | 0.112902i | \(-0.0360147\pi\) |
−0.594579 | + | 0.804037i | \(0.702681\pi\) | |||||||
\(278\) | 17.0207 | 1.02084 | ||||||||
\(279\) | 21.4875 | − | 17.2460i | 1.28642 | − | 1.03249i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 9.65455 | + | 16.7222i | 0.575942 | + | 0.997561i | 0.995939 | + | 0.0900352i | \(0.0286979\pi\) |
−0.419997 | + | 0.907526i | \(0.637969\pi\) | |||||||
\(282\) | 13.8389 | − | 16.1320i | 0.824092 | − | 0.960649i | ||||
\(283\) | 7.13567 | − | 12.3593i | 0.424171 | − | 0.734686i | −0.572171 | − | 0.820134i | \(-0.693899\pi\) |
0.996343 | + | 0.0854478i | \(0.0272321\pi\) | |||||||
\(284\) | −1.94688 | + | 3.37209i | −0.115526 | + | 0.200097i | ||||
\(285\) | −6.30640 | + | 7.35141i | −0.373559 | + | 0.435460i | ||||
\(286\) | −6.53896 | − | 11.3258i | −0.386657 | − | 0.669709i | ||||
\(287\) | 4.57301 | 0.269936 | ||||||||
\(288\) | −2.33963 | + | 1.87780i | −0.137864 | + | 0.110651i | ||||
\(289\) | 2.95207 | 0.173651 | ||||||||
\(290\) | −0.223855 | − | 0.387729i | −0.0131452 | − | 0.0227682i | ||||
\(291\) | −4.90314 | − | 13.9423i | −0.287427 | − | 0.817314i | ||||
\(292\) | −3.07301 | + | 5.32262i | −0.179835 | + | 0.311483i | ||||
\(293\) | −4.56164 | + | 7.90099i | −0.266494 | + | 0.461581i | −0.967954 | − | 0.251128i | \(-0.919199\pi\) |
0.701460 | + | 0.712709i | \(0.252532\pi\) | |||||||
\(294\) | −1.70236 | − | 0.319344i | −0.0992835 | − | 0.0186245i | ||||
\(295\) | −6.45623 | − | 11.1825i | −0.375896 | − | 0.651071i | ||||
\(296\) | −10.1651 | −0.590834 | ||||||||
\(297\) | −0.621883 | + | 19.0087i | −0.0360853 | + | 1.10300i | ||||
\(298\) | 14.3095 | 0.828925 | ||||||||
\(299\) | 4.75245 | + | 8.23149i | 0.274841 | + | 0.476039i | ||||
\(300\) | −1.70236 | − | 0.319344i | −0.0982856 | − | 0.0184373i | ||||
\(301\) | 3.61660 | − | 6.26414i | 0.208458 | − | 0.361059i | ||||
\(302\) | −6.01036 | + | 10.4103i | −0.345858 | + | 0.599043i | ||||
\(303\) | 7.63223 | + | 21.7026i | 0.438460 | + | 1.24678i | ||||
\(304\) | −2.79604 | − | 4.84288i | −0.160364 | − | 0.277758i | ||||
\(305\) | −1.19342 | −0.0683349 | ||||||||
\(306\) | −2.03869 | − | 13.2443i | −0.116544 | − | 0.757128i | ||||
\(307\) | −13.4892 | −0.769867 | −0.384934 | − | 0.922944i | \(-0.625776\pi\) | ||||
−0.384934 | + | 0.922944i | \(0.625776\pi\) | |||||||
\(308\) | 1.83010 | + | 3.16982i | 0.104279 | + | 0.180617i | ||||
\(309\) | −16.1281 | + | 18.8007i | −0.917498 | + | 1.06953i | ||||
\(310\) | −4.59208 | + | 7.95371i | −0.260812 | + | 0.451740i | ||||
\(311\) | −4.87267 | + | 8.43971i | −0.276304 | + | 0.478572i | −0.970463 | − | 0.241249i | \(-0.922443\pi\) |
0.694159 | + | 0.719821i | \(0.255776\pi\) | |||||||
\(312\) | 4.02943 | − | 4.69713i | 0.228121 | − | 0.265923i | ||||
\(313\) | 2.58356 | + | 4.47485i | 0.146031 | + | 0.252934i | 0.929757 | − | 0.368173i | \(-0.120017\pi\) |
−0.783726 | + | 0.621107i | \(0.786683\pi\) | |||||||
\(314\) | −6.63947 | −0.374687 | ||||||||
\(315\) | 2.79604 | + | 1.08728i | 0.157539 | + | 0.0612610i | ||||
\(316\) | −2.23321 | −0.125628 | ||||||||
\(317\) | 3.04442 | + | 5.27309i | 0.170992 | + | 0.296166i | 0.938767 | − | 0.344553i | \(-0.111970\pi\) |
−0.767775 | + | 0.640719i | \(0.778636\pi\) | |||||||
\(318\) | 2.86214 | + | 8.13863i | 0.160501 | + | 0.456392i | ||||
\(319\) | 0.819354 | − | 1.41916i | 0.0458750 | − | 0.0794578i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −16.1993 | − | 3.03882i | −0.904158 | − | 0.169610i | ||||
\(322\) | −1.33010 | − | 2.30379i | −0.0741233 | − | 0.128385i | ||||
\(323\) | 24.9785 | 1.38984 | ||||||||
\(324\) | −8.58338 | + | 2.70659i | −0.476854 | + | 0.150366i | ||||
\(325\) | 3.57301 | 0.198195 | ||||||||
\(326\) | −3.73339 | − | 6.46642i | −0.206773 | − | 0.358142i | ||||
\(327\) | −0.791787 | − | 0.148531i | −0.0437859 | − | 0.00821377i | ||||
\(328\) | 2.28651 | − | 3.96035i | 0.126251 | − | 0.218674i | ||||
\(329\) | 6.13567 | − | 10.6273i | 0.338270 | − | 0.585901i | ||||
\(330\) | −2.10321 | − | 5.98059i | −0.115778 | − | 0.329221i | ||||
\(331\) | −15.7277 | − | 27.2413i | −0.864475 | − | 1.49731i | −0.867568 | − | 0.497319i | \(-0.834318\pi\) |
0.00309258 | − | 0.999995i | \(-0.499016\pi\) | |||||||
\(332\) | −11.3792 | −0.624517 | ||||||||
\(333\) | −28.4220 | − | 11.0523i | −1.55752 | − | 0.605660i | ||||
\(334\) | 3.97001 | 0.217229 | ||||||||
\(335\) | 4.88322 | + | 8.45798i | 0.266799 | + | 0.462109i | ||||
\(336\) | −1.12774 | + | 1.31461i | −0.0615232 | + | 0.0717180i | ||||
\(337\) | 11.6991 | − | 20.2635i | 0.637293 | − | 1.10382i | −0.348731 | − | 0.937223i | \(-0.613387\pi\) |
0.986024 | − | 0.166601i | \(-0.0532793\pi\) | |||||||
\(338\) | 0.116784 | − | 0.202277i | 0.00635223 | − | 0.0110024i | ||||
\(339\) | 2.42057 | − | 2.82167i | 0.131467 | − | 0.153252i | ||||
\(340\) | 2.23339 | + | 3.86834i | 0.121122 | + | 0.209790i | ||||
\(341\) | −33.6158 | −1.82040 | ||||||||
\(342\) | −2.55229 | − | 16.5809i | −0.138012 | − | 0.896595i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.61660 | − | 6.26414i | −0.194994 | − | 0.337740i | ||||
\(345\) | 1.52859 | + | 4.34664i | 0.0822968 | + | 0.234015i | ||||
\(346\) | 4.59208 | − | 7.95371i | 0.246872 | − | 0.427594i | ||||
\(347\) | 7.56247 | − | 13.0986i | 0.405975 | − | 0.703169i | −0.588460 | − | 0.808527i | \(-0.700265\pi\) |
0.994434 | + | 0.105358i | \(0.0335988\pi\) | |||||||
\(348\) | 0.762164 | + | 0.142974i | 0.0408563 | + | 0.00766420i | ||||
\(349\) | 9.68555 | + | 16.7759i | 0.518455 | + | 0.897991i | 0.999770 | + | 0.0214433i | \(0.00682613\pi\) |
−0.481315 | + | 0.876548i | \(0.659841\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 16.3735 | − | 8.75226i | 0.873953 | − | 0.467161i | ||||
\(352\) | 3.66019 | 0.195089 | ||||||||
\(353\) | −14.7626 | − | 25.5696i | −0.785736 | − | 1.36093i | −0.928559 | − | 0.371186i | \(-0.878951\pi\) |
0.142823 | − | 0.989748i | \(-0.454382\pi\) | |||||||
\(354\) | 21.9816 | + | 4.12352i | 1.16831 | + | 0.219162i | ||||
\(355\) | 1.94688 | − | 3.37209i | 0.103330 | − | 0.178972i | ||||
\(356\) | −6.67925 | + | 11.5688i | −0.354000 | + | 0.613146i | ||||
\(357\) | −2.56669 | − | 7.29851i | −0.135844 | − | 0.386278i | ||||
\(358\) | −1.17074 | − | 2.02777i | −0.0618753 | − | 0.107171i | ||||
\(359\) | −15.6217 | −0.824482 | −0.412241 | − | 0.911075i | \(-0.635254\pi\) | ||||
−0.412241 | + | 0.911075i | \(0.635254\pi\) | |||||||
\(360\) | 2.33963 | − | 1.87780i | 0.123309 | − | 0.0989689i | ||||
\(361\) | 12.2713 | 0.645860 | ||||||||
\(362\) | −9.33945 | − | 16.1764i | −0.490870 | − | 0.850212i | ||||
\(363\) | 2.70319 | − | 3.15112i | 0.141881 | − | 0.165391i | ||||
\(364\) | 1.78651 | − | 3.09432i | 0.0936384 | − | 0.162186i | ||||
\(365\) | 3.07301 | − | 5.32262i | 0.160849 | − | 0.278599i | ||||
\(366\) | 1.34586 | − | 1.56888i | 0.0703493 | − | 0.0820067i | ||||
\(367\) | 12.6659 | + | 21.9380i | 0.661156 | + | 1.14516i | 0.980312 | + | 0.197453i | \(0.0632671\pi\) |
−0.319156 | + | 0.947702i | \(0.603400\pi\) | |||||||
\(368\) | −2.66019 | −0.138672 | ||||||||
\(369\) | 10.6991 | − | 8.58722i | 0.556975 | − | 0.447033i | ||||
\(370\) | 10.1651 | 0.528458 | ||||||||
\(371\) | 2.49047 | + | 4.31362i | 0.129299 | + | 0.223952i | ||||
\(372\) | −5.27739 | − | 15.0065i | −0.273620 | − | 0.778051i | ||||
\(373\) | 8.00000 | − | 13.8564i | 0.414224 | − | 0.717458i | −0.581122 | − | 0.813816i | \(-0.697386\pi\) |
0.995347 | + | 0.0963587i | \(0.0307196\pi\) | |||||||
\(374\) | −8.17462 | + | 14.1589i | −0.422700 | + | 0.732137i | ||||
\(375\) | 1.70236 | + | 0.319344i | 0.0879093 | + | 0.0164909i | ||||
\(376\) | −6.13567 | − | 10.6273i | −0.316423 | − | 0.548060i | ||||
\(377\) | −1.59968 | −0.0823876 | ||||||||
\(378\) | −4.58255 | + | 2.44955i | −0.235701 | + | 0.125991i | ||||
\(379\) | 23.4571 | 1.20491 | 0.602456 | − | 0.798152i | \(-0.294189\pi\) | ||||
0.602456 | + | 0.798152i | \(0.294189\pi\) | |||||||
\(380\) | 2.79604 | + | 4.84288i | 0.143434 | + | 0.248435i | ||||
\(381\) | 7.93331 | + | 1.48820i | 0.406436 | + | 0.0762430i | ||||
\(382\) | −9.37960 | + | 16.2459i | −0.479902 | + | 0.831215i | ||||
\(383\) | −5.99130 | + | 10.3772i | −0.306141 | + | 0.530252i | −0.977515 | − | 0.210867i | \(-0.932371\pi\) |
0.671374 | + | 0.741119i | \(0.265705\pi\) | |||||||
\(384\) | 0.574618 | + | 1.63396i | 0.0293234 | + | 0.0833825i | ||||
\(385\) | −1.83010 | − | 3.16982i | −0.0932703 | − | 0.161549i | ||||
\(386\) | 8.03979 | 0.409214 | ||||||||
\(387\) | −3.30132 | − | 21.4470i | −0.167815 | − | 1.09021i | ||||
\(388\) | −8.53286 | −0.433190 | ||||||||
\(389\) | −15.3008 | − | 26.5017i | −0.775779 | − | 1.34369i | −0.934355 | − | 0.356342i | \(-0.884024\pi\) |
0.158576 | − | 0.987347i | \(-0.449310\pi\) | |||||||
\(390\) | −4.02943 | + | 4.69713i | −0.204038 | + | 0.237848i | ||||
\(391\) | 5.94124 | − | 10.2905i | 0.300461 | − | 0.520414i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | 17.6821 | − | 20.6121i | 0.891944 | − | 1.03975i | ||||
\(394\) | −3.57765 | − | 6.19666i | −0.180239 | − | 0.312183i | ||||
\(395\) | 2.23321 | 0.112365 | ||||||||
\(396\) | 10.2340 | + | 3.97963i | 0.514280 | + | 0.199984i | ||||
\(397\) | −9.76477 | −0.490080 | −0.245040 | − | 0.969513i | \(-0.578801\pi\) | ||||
−0.245040 | + | 0.969513i | \(0.578801\pi\) | |||||||
\(398\) | −3.43634 | − | 5.95191i | −0.172248 | − | 0.298342i | ||||
\(399\) | −3.21331 | − | 9.13721i | −0.160867 | − | 0.457433i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −17.1706 | + | 29.7403i | −0.857457 | + | 1.48516i | 0.0168907 | + | 0.999857i | \(0.494623\pi\) |
−0.874347 | + | 0.485301i | \(0.838710\pi\) | |||||||
\(402\) | −16.6260 | − | 3.11885i | −0.829227 | − | 0.155554i | ||||
\(403\) | 16.4076 | + | 28.4187i | 0.817319 | + | 1.41564i | ||||
\(404\) | 13.2823 | 0.660817 | ||||||||
\(405\) | 8.58338 | − | 2.70659i | 0.426511 | − | 0.134492i | ||||
\(406\) | 0.447711 | 0.0222195 | ||||||||
\(407\) | 18.6031 | + | 32.2215i | 0.922121 | + | 1.59716i | ||||
\(408\) | −7.60404 | − | 1.42644i | −0.376456 | − | 0.0706192i | ||||
\(409\) | −8.68517 | + | 15.0432i | −0.429454 | + | 0.743836i | −0.996825 | − | 0.0796264i | \(-0.974627\pi\) |
0.567371 | + | 0.823462i | \(0.307961\pi\) | |||||||
\(410\) | −2.28651 | + | 3.96035i | −0.112923 | + | 0.195588i | ||||
\(411\) | 7.53109 | + | 21.4150i | 0.371481 | + | 1.05633i | ||||
\(412\) | 7.15066 | + | 12.3853i | 0.352288 | + | 0.610180i | ||||
\(413\) | 12.9125 | 0.635381 | ||||||||
\(414\) | −7.43800 | − | 2.89236i | −0.365558 | − | 0.142152i | ||||
\(415\) | 11.3792 | 0.558585 | ||||||||
\(416\) | −1.78651 | − | 3.09432i | −0.0875907 | − | 0.151712i | ||||
\(417\) | 19.1949 | − | 22.3757i | 0.939980 | − | 1.09574i | ||||
\(418\) | −10.2340 | + | 17.7259i | −0.500563 | + | 0.867001i | ||||
\(419\) | 11.6653 | − | 20.2048i | 0.569886 | − | 0.987071i | −0.426691 | − | 0.904398i | \(-0.640321\pi\) |
0.996577 | − | 0.0826738i | \(-0.0263459\pi\) | |||||||
\(420\) | 1.12774 | − | 1.31461i | 0.0550280 | − | 0.0641465i | ||||
\(421\) | −5.66120 | − | 9.80549i | −0.275910 | − | 0.477890i | 0.694454 | − | 0.719537i | \(-0.255646\pi\) |
−0.970364 | + | 0.241646i | \(0.922313\pi\) | |||||||
\(422\) | 24.7759 | 1.20607 | ||||||||
\(423\) | −5.60078 | − | 36.3855i | −0.272319 | − | 1.76912i | ||||
\(424\) | 4.98094 | 0.241896 | ||||||||
\(425\) | −2.23339 | − | 3.86834i | −0.108335 | − | 0.187642i | ||||
\(426\) | 2.23743 | + | 6.36223i | 0.108404 | + | 0.308251i | ||||
\(427\) | 0.596708 | − | 1.03353i | 0.0288767 | − | 0.0500160i | ||||
\(428\) | −4.75791 | + | 8.24095i | −0.229982 | + | 0.398341i | ||||
\(429\) | −22.2633 | − | 4.17635i | −1.07488 | − | 0.201636i | ||||
\(430\) | 3.61660 | + | 6.26414i | 0.174408 | + | 0.302084i | ||||
\(431\) | 7.97927 | 0.384348 | 0.192174 | − | 0.981361i | \(-0.438446\pi\) | ||||
0.192174 | + | 0.981361i | \(0.438446\pi\) | |||||||
\(432\) | −0.169904 | + | 5.19337i | −0.00817453 | + | 0.249866i | ||||
\(433\) | −23.7799 | −1.14279 | −0.571395 | − | 0.820675i | \(-0.693598\pi\) | ||||
−0.571395 | + | 0.820675i | \(0.693598\pi\) | |||||||
\(434\) | −4.59208 | − | 7.95371i | −0.220427 | − | 0.381790i | ||||
\(435\) | −0.762164 | − | 0.142974i | −0.0365430 | − | 0.00685507i | ||||
\(436\) | −0.232556 | + | 0.402799i | −0.0111374 | + | 0.0192906i | ||||
\(437\) | 7.43800 | − | 12.8830i | 0.355808 | − | 0.616277i | ||||
\(438\) | 3.53162 | + | 10.0423i | 0.168747 | + | 0.479842i | ||||
\(439\) | 12.9412 | + | 22.4149i | 0.617652 | + | 1.06980i | 0.989913 | + | 0.141676i | \(0.0452491\pi\) |
−0.372262 | + | 0.928128i | \(0.621418\pi\) | |||||||
\(440\) | −3.66019 | −0.174493 | ||||||||
\(441\) | −2.33963 | + | 1.87780i | −0.111411 | + | 0.0894192i | ||||
\(442\) | 15.9598 | 0.759133 | ||||||||
\(443\) | 4.95807 | + | 8.58764i | 0.235565 | + | 0.408011i | 0.959437 | − | 0.281924i | \(-0.0909726\pi\) |
−0.723872 | + | 0.689935i | \(0.757639\pi\) | |||||||
\(444\) | −11.4636 | + | 13.3632i | −0.544037 | + | 0.634187i | ||||
\(445\) | 6.67925 | − | 11.5688i | 0.316627 | − | 0.548414i | ||||
\(446\) | 14.8784 | − | 25.7702i | 0.704513 | − | 1.22025i | ||||
\(447\) | 16.1373 | − | 18.8114i | 0.763269 | − | 0.889748i | ||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −4.19544 | −0.197995 | −0.0989976 | − | 0.995088i | \(-0.531564\pi\) | ||||
−0.0989976 | + | 0.995088i | \(0.531564\pi\) | |||||||
\(450\) | −2.33963 | + | 1.87780i | −0.110291 | + | 0.0885205i | ||||
\(451\) | −16.7381 | −0.788167 | ||||||||
\(452\) | −1.07320 | − | 1.85883i | −0.0504789 | − | 0.0874320i | ||||
\(453\) | 6.90733 | + | 19.6413i | 0.324535 | + | 0.922831i | ||||
\(454\) | −7.32991 | + | 12.6958i | −0.344010 | + | 0.595843i | ||||
\(455\) | −1.78651 | + | 3.09432i | −0.0837527 | + | 0.145064i | ||||
\(456\) | −9.51971 | − | 1.78580i | −0.445801 | − | 0.0836276i | ||||
\(457\) | 6.43087 | + | 11.1386i | 0.300824 | + | 0.521042i | 0.976323 | − | 0.216319i | \(-0.0694051\pi\) |
−0.675499 | + | 0.737361i | \(0.736072\pi\) | |||||||
\(458\) | −19.4855 | −0.910496 | ||||||||
\(459\) | −19.7103 | − | 12.2561i | −0.919997 | − | 0.572064i | ||||
\(460\) | 2.66019 | 0.124032 | ||||||||
\(461\) | −7.49213 | − | 12.9768i | −0.348943 | − | 0.604388i | 0.637119 | − | 0.770766i | \(-0.280126\pi\) |
−0.986062 | + | 0.166378i | \(0.946793\pi\) | |||||||
\(462\) | 6.23095 | + | 1.16886i | 0.289890 | + | 0.0543803i | ||||
\(463\) | 1.72830 | − | 2.99351i | 0.0803211 | − | 0.139120i | −0.823067 | − | 0.567945i | \(-0.807739\pi\) |
0.903388 | + | 0.428824i | \(0.141072\pi\) | |||||||
\(464\) | 0.223855 | − | 0.387729i | 0.0103922 | − | 0.0179999i | ||||
\(465\) | 5.27739 | + | 15.0065i | 0.244733 | + | 0.695910i | ||||
\(466\) | 5.87858 | + | 10.1820i | 0.272320 | + | 0.471672i | ||||
\(467\) | 14.1586 | 0.655183 | 0.327591 | − | 0.944820i | \(-0.393763\pi\) | ||||
0.327591 | + | 0.944820i | \(0.393763\pi\) | |||||||
\(468\) | −1.63077 | − | 10.5943i | −0.0753821 | − | 0.489720i | ||||
\(469\) | −9.76643 | −0.450972 | ||||||||
\(470\) | 6.13567 | + | 10.6273i | 0.283017 | + | 0.490200i | ||||
\(471\) | −7.48758 | + | 8.72832i | −0.345010 | + | 0.402180i | ||||
\(472\) | 6.45623 | − | 11.1825i | 0.297172 | − | 0.514717i | ||||
\(473\) | −13.2375 | + | 22.9279i | −0.608659 | + | 1.05423i | ||||
\(474\) | −2.51847 | + | 2.93580i | −0.115677 | + | 0.134846i | ||||
\(475\) | −2.79604 | − | 4.84288i | −0.128291 | − | 0.222207i | ||||
\(476\) | −4.46677 | −0.204734 | ||||||||
\(477\) | 13.9269 | + | 5.41565i | 0.637669 | + | 0.247965i | ||||
\(478\) | −4.07625 | −0.186443 | ||||||||
\(479\) | 17.8346 | + | 30.8905i | 0.814885 | + | 1.41142i | 0.909410 | + | 0.415900i | \(0.136533\pi\) |
−0.0945251 | + | 0.995522i | \(0.530133\pi\) | |||||||
\(480\) | −0.574618 | − | 1.63396i | −0.0262276 | − | 0.0745796i | ||||
\(481\) | 18.1600 | − | 31.4541i | 0.828025 | − | 1.43418i | ||||
\(482\) | 11.5057 | − | 19.9285i | 0.524072 | − | 0.907719i | ||||
\(483\) | −4.52859 | − | 0.849516i | −0.206058 | − | 0.0386543i | ||||
\(484\) | −1.19850 | − | 2.07586i | −0.0544772 | − | 0.0943574i | ||||
\(485\) | 8.53286 | 0.387457 | ||||||||
\(486\) | −6.12169 | + | 14.3361i | −0.277685 | + | 0.650301i | ||||
\(487\) | −21.8290 | −0.989165 | −0.494583 | − | 0.869131i | \(-0.664679\pi\) | ||||
−0.494583 | + | 0.869131i | \(0.664679\pi\) | |||||||
\(488\) | −0.596708 | − | 1.03353i | −0.0270117 | − | 0.0467857i | ||||
\(489\) | −12.7111 | − | 2.38447i | −0.574817 | − | 0.107829i | ||||
\(490\) | 0.500000 | − | 0.866025i | 0.0225877 | − | 0.0391230i | ||||
\(491\) | −11.0874 | + | 19.2040i | −0.500369 | + | 0.866665i | 0.499630 | + | 0.866239i | \(0.333469\pi\) |
−1.00000 | 0.000426678i | \(0.999864\pi\) | ||||||||
\(492\) | −2.62774 | − | 7.47211i | −0.118468 | − | 0.336869i | ||||
\(493\) | 0.999912 | + | 1.73190i | 0.0450338 | + | 0.0780008i | ||||
\(494\) | 19.9806 | 0.898968 | ||||||||
\(495\) | −10.2340 | − | 3.97963i | −0.459986 | − | 0.178871i | ||||
\(496\) | −9.18416 | −0.412381 | ||||||||
\(497\) | 1.94688 | + | 3.37209i | 0.0873295 | + | 0.151259i | ||||
\(498\) | −12.8328 | + | 14.9593i | −0.575052 | + | 0.670341i | ||||
\(499\) | −2.97649 | + | 5.15543i | −0.133246 | + | 0.230789i | −0.924926 | − | 0.380147i | \(-0.875873\pi\) |
0.791680 | + | 0.610936i | \(0.209207\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 4.47714 | − | 5.21903i | 0.200024 | − | 0.233169i | ||||
\(502\) | 11.2577 | + | 19.4990i | 0.502457 | + | 0.870281i | ||||
\(503\) | −41.4795 | −1.84948 | −0.924741 | − | 0.380598i | \(-0.875718\pi\) | ||||
−0.924741 | + | 0.380598i | \(0.875718\pi\) | |||||||
\(504\) | 0.456412 | + | 2.96508i | 0.0203302 | + | 0.132075i | ||||
\(505\) | −13.2823 | −0.591053 | ||||||||
\(506\) | 4.86840 | + | 8.43232i | 0.216427 | + | 0.374862i | ||||
\(507\) | −0.134213 | − | 0.381641i | −0.00596061 | − | 0.0169493i | ||||
\(508\) | 2.33010 | − | 4.03584i | 0.103381 | − | 0.179062i | ||||
\(509\) | −0.596708 | + | 1.03353i | −0.0264486 | + | 0.0458104i | −0.878947 | − | 0.476920i | \(-0.841753\pi\) |
0.852498 | + | 0.522730i | \(0.175087\pi\) | |||||||
\(510\) | 7.60404 | + | 1.42644i | 0.336713 | + | 0.0631637i | ||||
\(511\) | 3.07301 | + | 5.32262i | 0.135942 | + | 0.235459i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −24.6758 | − | 15.3437i | −1.08946 | − | 0.677441i | ||||
\(514\) | −4.65129 | −0.205160 | ||||||||
\(515\) | −7.15066 | − | 12.3853i | −0.315096 | − | 0.545762i | ||||
\(516\) | −12.3135 | − | 2.30988i | −0.542072 | − | 0.101687i | ||||
\(517\) | −22.4577 | + | 38.8979i | −0.987689 | + | 1.71073i | ||||
\(518\) | −5.08255 | + | 8.80323i | −0.223314 | + | 0.386792i | ||||
\(519\) | −5.27739 | − | 15.0065i | −0.231652 | − | 0.658713i | ||||
\(520\) | 1.78651 | + | 3.09432i | 0.0783435 | + | 0.135695i | ||||
\(521\) | −1.53452 | −0.0672287 | −0.0336144 | − | 0.999435i | \(-0.510702\pi\) | ||||
−0.0336144 | + | 0.999435i | \(0.510702\pi\) | |||||||
\(522\) | 1.04748 | − | 0.840713i | 0.0458468 | − | 0.0367970i | ||||
\(523\) | 8.66833 | 0.379040 | 0.189520 | − | 0.981877i | \(-0.439307\pi\) | ||||
0.189520 | + | 0.981877i | \(0.439307\pi\) | |||||||
\(524\) | −7.83963 | − | 13.5786i | −0.342476 | − | 0.593185i | ||||
\(525\) | −1.12774 | + | 1.31461i | −0.0492185 | + | 0.0573744i | ||||
\(526\) | −6.24292 | + | 10.8131i | −0.272204 | + | 0.471471i | ||||
\(527\) | 20.5118 | − | 35.5274i | 0.893507 | − | 1.54760i | ||||
\(528\) | 4.12774 | − | 4.81173i | 0.179637 | − | 0.209404i | ||||
\(529\) | 7.96169 | + | 13.7901i | 0.346161 | + | 0.599568i | ||||
\(530\) | −4.98094 | −0.216358 | ||||||||
\(531\) | 30.2103 | − | 24.2471i | 1.31102 | − | 1.05223i | ||||
\(532\) | −5.59208 | −0.242447 | ||||||||
\(533\) | 8.16972 | + | 14.1504i | 0.353870 | + | 0.612921i | ||||
\(534\) | 7.67605 | + | 21.8272i | 0.332175 | + | 0.944556i | ||||
\(535\) | 4.75791 | − | 8.24095i | 0.205702 | − | 0.356287i | ||||
\(536\) | −4.88322 | + | 8.45798i | −0.210923 | + | 0.365329i | ||||
\(537\) | −3.98602 | − | 0.747735i | −0.172009 | − | 0.0322671i | ||||
\(538\) | 5.16972 | + | 8.95422i | 0.222883 | + | 0.386044i | ||||
\(539\) | 3.66019 | 0.157656 | ||||||||
\(540\) | 0.169904 | − | 5.19337i | 0.00731152 | − | 0.223487i | ||||
\(541\) | 30.0622 | 1.29247 | 0.646237 | − | 0.763137i | \(-0.276342\pi\) | ||||
0.646237 | + | 0.763137i | \(0.276342\pi\) | |||||||
\(542\) | 3.47446 | + | 6.01795i | 0.149241 | + | 0.258493i | ||||
\(543\) | −31.7981 | − | 5.96499i | −1.36459 | − | 0.255982i | ||||
\(544\) | −2.23339 | + | 3.86834i | −0.0957557 | + | 0.165854i | ||||
\(545\) | 0.232556 | − | 0.402799i | 0.00996161 | − | 0.0172540i | ||||
\(546\) | −2.05312 | − | 5.83815i | −0.0878654 | − | 0.249850i | ||||
\(547\) | 19.9070 | + | 34.4799i | 0.851162 | + | 1.47426i | 0.880161 | + | 0.474676i | \(0.157435\pi\) |
−0.0289988 | + | 0.999579i | \(0.509232\pi\) | |||||||
\(548\) | 13.1062 | 0.559871 | ||||||||
\(549\) | −0.544689 | − | 3.53857i | −0.0232468 | − | 0.151023i | ||||
\(550\) | 3.66019 | 0.156071 | ||||||||
\(551\) | 1.25182 | + | 2.16821i | 0.0533292 | + | 0.0923689i | ||||
\(552\) | −3.00000 | + | 3.49712i | −0.127688 | + | 0.148847i | ||||
\(553\) | −1.11660 | + | 1.93401i | −0.0474828 | + | 0.0822426i | ||||
\(554\) | 6.64113 | − | 11.5028i | 0.282154 | − | 0.488706i | ||||
\(555\) | 11.4636 | − | 13.3632i | 0.486601 | − | 0.567234i | ||||
\(556\) | −8.51036 | − | 14.7404i | −0.360920 | − | 0.625131i | ||||
\(557\) | 18.9717 | 0.803856 | 0.401928 | − | 0.915671i | \(-0.368340\pi\) | ||||
0.401928 | + | 0.915671i | \(0.368340\pi\) | |||||||
\(558\) | −25.6793 | − | 9.98570i | −1.08709 | − | 0.422729i | ||||
\(559\) | 25.8443 | 1.09310 | ||||||||
\(560\) | −0.500000 | − | 0.866025i | −0.0211289 | − | 0.0365963i | ||||
\(561\) | 9.39458 | + | 26.7140i | 0.396639 | + | 1.12786i | ||||
\(562\) | 9.65455 | − | 16.7222i | 0.407253 | − | 0.705382i | ||||
\(563\) | −5.79197 | + | 10.0320i | −0.244102 | + | 0.422798i | −0.961879 | − | 0.273476i | \(-0.911827\pi\) |
0.717776 | + | 0.696274i | \(0.245160\pi\) | |||||||
\(564\) | −20.8902 | − | 3.91878i | −0.879636 | − | 0.165010i | ||||
\(565\) | 1.07320 | + | 1.85883i | 0.0451497 | + | 0.0782016i | ||||
\(566\) | −14.2713 | −0.599869 | ||||||||
\(567\) | −1.94771 | + | 8.78672i | −0.0817962 | + | 0.369007i | ||||
\(568\) | 3.89376 | 0.163379 | ||||||||
\(569\) | 2.53304 | + | 4.38736i | 0.106191 | + | 0.183928i | 0.914224 | − | 0.405209i | \(-0.132801\pi\) |
−0.808033 | + | 0.589137i | \(0.799468\pi\) | |||||||
\(570\) | 9.51971 | + | 1.78580i | 0.398737 | + | 0.0747988i | ||||
\(571\) | −22.6012 | + | 39.1465i | −0.945833 | + | 1.63823i | −0.191757 | + | 0.981442i | \(0.561419\pi\) |
−0.754075 | + | 0.656788i | \(0.771915\pi\) | |||||||
\(572\) | −6.53896 | + | 11.3258i | −0.273408 | + | 0.473556i | ||||
\(573\) | 10.7794 | + | 30.6517i | 0.450315 | + | 1.28049i | ||||
\(574\) | −2.28651 | − | 3.96035i | −0.0954370 | − | 0.165302i | ||||
\(575\) | −2.66019 | −0.110938 | ||||||||
\(576\) | 2.79604 | + | 1.08728i | 0.116502 | + | 0.0453031i | ||||
\(577\) | 35.8246 | 1.49140 | 0.745698 | − | 0.666284i | \(-0.232116\pi\) | ||||
0.745698 | + | 0.666284i | \(0.232116\pi\) | |||||||
\(578\) | −1.47604 | − | 2.55657i | −0.0613950 | − | 0.106339i | ||||
\(579\) | 9.06678 | − | 10.5692i | 0.376802 | − | 0.439241i | ||||
\(580\) | −0.223855 | + | 0.387729i | −0.00929509 | + | 0.0160996i | ||||
\(581\) | −5.68962 | + | 9.85471i | −0.236045 | + | 0.408842i | ||||
\(582\) | −9.62284 | + | 11.2174i | −0.398879 | + | 0.464976i | ||||
\(583\) | −9.11559 | − | 15.7887i | −0.377529 | − | 0.653900i | ||||
\(584\) | 6.14603 | 0.254324 | ||||||||
\(585\) | 1.63077 | + | 10.5943i | 0.0674238 | + | 0.438019i | ||||
\(586\) | 9.12328 | 0.376879 | ||||||||
\(587\) | 1.85988 | + | 3.22142i | 0.0767657 | + | 0.132962i | 0.901853 | − | 0.432044i | \(-0.142207\pi\) |
−0.825087 | + | 0.565006i | \(0.808874\pi\) | |||||||
\(588\) | 0.574618 | + | 1.63396i | 0.0236969 | + | 0.0673832i | ||||
\(589\) | 25.6793 | − | 44.4778i | 1.05810 | − | 1.83267i | ||||
\(590\) | −6.45623 | + | 11.1825i | −0.265799 | + | 0.460377i | ||||
\(591\) | −12.1809 | − | 2.28500i | −0.501054 | − | 0.0939923i | ||||
\(592\) | 5.08255 | + | 8.80323i | 0.208891 | + | 0.361810i | ||||
\(593\) | 21.5845 | 0.886368 | 0.443184 | − | 0.896431i | \(-0.353849\pi\) | ||||
0.443184 | + | 0.896431i | \(0.353849\pi\) | |||||||
\(594\) | 16.7730 | − | 8.96580i | 0.688204 | − | 0.367871i | ||||
\(595\) | 4.46677 | 0.183120 | ||||||||
\(596\) | −7.15473 | − | 12.3924i | −0.293069 | − | 0.507611i | ||||
\(597\) | −11.6997 | − | 2.19475i | −0.478838 | − | 0.0898250i | ||||
\(598\) | 4.75245 | − | 8.23149i | 0.194342 | − | 0.336610i | ||||
\(599\) | −8.32908 | + | 14.4264i | −0.340317 | + | 0.589447i | −0.984492 | − | 0.175432i | \(-0.943868\pi\) |
0.644174 | + | 0.764879i | \(0.277201\pi\) | |||||||
\(600\) | 0.574618 | + | 1.63396i | 0.0234587 | + | 0.0667060i | ||||
\(601\) | 7.98685 | + | 13.8336i | 0.325790 | + | 0.564286i | 0.981672 | − | 0.190578i | \(-0.0610363\pi\) |
−0.655882 | + | 0.754864i | \(0.727703\pi\) | |||||||
\(602\) | −7.23321 | −0.294803 | ||||||||
\(603\) | −22.8498 | + | 18.3394i | −0.930516 | + | 0.746840i | ||||
\(604\) | 12.0207 | 0.489116 | ||||||||
\(605\) | 1.19850 | + | 2.07586i | 0.0487259 | + | 0.0843958i | ||||
\(606\) | 14.9789 | − | 17.4610i | 0.608477 | − | 0.709305i | ||||
\(607\) | 1.78752 | − | 3.09608i | 0.0725532 | − | 0.125666i | −0.827466 | − | 0.561515i | \(-0.810219\pi\) |
0.900020 | + | 0.435849i | \(0.143552\pi\) | |||||||
\(608\) | −2.79604 | + | 4.84288i | −0.113394 | + | 0.196405i | ||||
\(609\) | 0.504901 | − | 0.588566i | 0.0204596 | − | 0.0238499i | ||||
\(610\) | 0.596708 | + | 1.03353i | 0.0241600 | + | 0.0418464i | ||||
\(611\) | 43.8456 | 1.77380 | ||||||||
\(612\) | −10.4506 | + | 8.38772i | −0.422440 | + | 0.339054i | ||||
\(613\) | −19.4388 | −0.785126 | −0.392563 | − | 0.919725i | \(-0.628412\pi\) | ||||
−0.392563 | + | 0.919725i | \(0.628412\pi\) | |||||||
\(614\) | 6.74458 | + | 11.6820i | 0.272189 | + | 0.471445i | ||||
\(615\) | 2.62774 | + | 7.47211i | 0.105961 | + | 0.301304i | ||||
\(616\) | 1.83010 | − | 3.16982i | 0.0737367 | − | 0.127716i | ||||
\(617\) | −6.48667 | + | 11.2352i | −0.261143 | + | 0.452314i | −0.966546 | − | 0.256493i | \(-0.917433\pi\) |
0.705403 | + | 0.708807i | \(0.250766\pi\) | |||||||
\(618\) | 24.3460 | + | 4.56704i | 0.979338 | + | 0.183713i | ||||
\(619\) | 17.7225 | + | 30.6962i | 0.712327 | + | 1.23379i | 0.963982 | + | 0.265969i | \(0.0856918\pi\) |
−0.251655 | + | 0.967817i | \(0.580975\pi\) | |||||||
\(620\) | 9.18416 | 0.368845 | ||||||||
\(621\) | −12.1904 | + | 6.51626i | −0.489186 | + | 0.261488i | ||||
\(622\) | 9.74534 | 0.390753 | ||||||||
\(623\) | 6.67925 | + | 11.5688i | 0.267599 | + | 0.463495i | ||||
\(624\) | −6.08255 | − | 1.14102i | −0.243497 | − | 0.0456774i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 2.58356 | − | 4.47485i | 0.103260 | − | 0.178851i | ||||
\(627\) | 11.7613 | + | 33.4439i | 0.469702 | + | 1.33562i | ||||
\(628\) | 3.31973 | + | 5.74995i | 0.132472 | + | 0.229448i | ||||
\(629\) | −45.4052 | −1.81042 | ||||||||
\(630\) | −0.456412 | − | 2.96508i | −0.0181839 | − | 0.118132i | ||||
\(631\) | 1.54505 | 0.0615076 | 0.0307538 | − | 0.999527i | \(-0.490209\pi\) | ||||
0.0307538 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(632\) | 1.11660 | + | 1.93401i | 0.0444161 | + | 0.0769309i | ||||
\(633\) | 27.9407 | − | 32.5707i | 1.11054 | − | 1.29457i | ||||
\(634\) | 3.04442 | − | 5.27309i | 0.120909 | − | 0.209421i | ||||
\(635\) | −2.33010 | + | 4.03584i | −0.0924670 | + | 0.160158i | ||||
\(636\) | 5.61719 | − | 6.54800i | 0.222736 | − | 0.259645i | ||||
\(637\) | −1.78651 | − | 3.09432i | −0.0707840 | − | 0.122601i | ||||
\(638\) | −1.63871 | −0.0648770 | ||||||||
\(639\) | 10.8871 | + | 4.23359i | 0.430687 | + | 0.167478i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 7.62132 | + | 13.2005i | 0.301024 | + | 0.521389i | 0.976368 | − | 0.216114i | \(-0.0693382\pi\) |
−0.675344 | + | 0.737503i | \(0.736005\pi\) | |||||||
\(642\) | 5.46797 | + | 15.5484i | 0.215804 | + | 0.613648i | ||||
\(643\) | −8.32991 | + | 14.4278i | −0.328500 | + | 0.568978i | −0.982214 | − | 0.187763i | \(-0.939876\pi\) |
0.653715 | + | 0.756741i | \(0.273210\pi\) | |||||||
\(644\) | −1.33010 | + | 2.30379i | −0.0524131 | + | 0.0907822i | ||||
\(645\) | 12.3135 | + | 2.30988i | 0.484844 | + | 0.0909515i | ||||
\(646\) | −12.4893 | − | 21.6321i | −0.491384 | − | 0.851102i | ||||
\(647\) | −3.40995 | −0.134059 | −0.0670294 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670294 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(648\) | 6.63567 | + | 6.08013i | 0.260674 | + | 0.238850i | ||||
\(649\) | −47.2621 | −1.85520 | ||||||||
\(650\) | −1.78651 | − | 3.09432i | −0.0700726 | − | 0.121369i | ||||
\(651\) | −15.6347 | − | 2.93290i | −0.612773 | − | 0.114950i | ||||
\(652\) | −3.73339 | + | 6.46642i | −0.146211 | + | 0.253244i | ||||
\(653\) | 14.8845 | − | 25.7807i | 0.582475 | − | 1.00888i | −0.412710 | − | 0.910863i | \(-0.635418\pi\) |
0.995185 | − | 0.0980144i | \(-0.0312491\pi\) | |||||||
\(654\) | 0.267262 | + | 0.759973i | 0.0104508 | + | 0.0297173i | ||||
\(655\) | 7.83963 | + | 13.5786i | 0.306320 | + | 0.530561i | ||||
\(656\) | −4.57301 | −0.178546 | ||||||||
\(657\) | 17.1845 | + | 6.68242i | 0.670433 | + | 0.260706i | ||||
\(658\) | −12.2713 | −0.478386 | ||||||||
\(659\) | 1.29132 | + | 2.23663i | 0.0503027 | + | 0.0871268i | 0.890080 | − | 0.455804i | \(-0.150648\pi\) |
−0.839778 | + | 0.542930i | \(0.817315\pi\) | |||||||
\(660\) | −4.12774 | + | 4.81173i | −0.160672 | + | 0.187296i | ||||
\(661\) | −4.75717 | + | 8.23966i | −0.185032 | + | 0.320486i | −0.943587 | − | 0.331123i | \(-0.892572\pi\) |
0.758555 | + | 0.651609i | \(0.225906\pi\) | |||||||
\(662\) | −15.7277 | + | 27.2413i | −0.611276 | + | 1.05876i | ||||
\(663\) | 17.9985 | − | 20.9810i | 0.699005 | − | 0.814835i | ||||
\(664\) | 5.68962 | + | 9.85471i | 0.220800 | + | 0.382437i | ||||
\(665\) | 5.59208 | 0.216851 | ||||||||
\(666\) | 4.63947 | + | 30.1403i | 0.179776 | + | 1.16791i | ||||
\(667\) | 1.19100 | 0.0461156 | ||||||||
\(668\) | −1.98501 | − | 3.43813i | −0.0768022 | − | 0.133025i | ||||
\(669\) | −17.0988 | − | 48.6213i | −0.661078 | − | 1.87981i | ||||
\(670\) | 4.88322 | − | 8.45798i | 0.188655 | − | 0.326760i | ||||
\(671\) | −2.18407 | + | 3.78291i | −0.0843150 | + | 0.146038i | ||||
\(672\) | 1.70236 | + | 0.319344i | 0.0656698 | + | 0.0123190i | ||||
\(673\) | 6.93189 | + | 12.0064i | 0.267205 | + | 0.462812i | 0.968139 | − | 0.250414i | \(-0.0805667\pi\) |
−0.700934 | + | 0.713226i | \(0.747233\pi\) | |||||||
\(674\) | −23.3983 | −0.901269 | ||||||||
\(675\) | −0.169904 | + | 5.19337i | −0.00653963 | + | 0.199893i | ||||
\(676\) | −0.233569 | −0.00898342 | ||||||||
\(677\) | −19.1069 | − | 33.0941i | −0.734337 | − | 1.27191i | −0.955013 | − | 0.296563i | \(-0.904160\pi\) |
0.220676 | − | 0.975347i | \(-0.429174\pi\) | |||||||
\(678\) | −3.65393 | − | 0.685437i | −0.140328 | − | 0.0263241i | ||||
\(679\) | −4.26643 | + | 7.38968i | −0.163731 | + | 0.283590i | ||||
\(680\) | 2.23339 | − | 3.86834i | 0.0856465 | − | 0.148344i | ||||
\(681\) | 8.42381 | + | 23.9535i | 0.322801 | + | 0.917901i | ||||
\(682\) | 16.8079 | + | 29.1121i | 0.643607 | + | 1.11476i | ||||
\(683\) | 33.0106 | 1.26311 | 0.631557 | − | 0.775329i | \(-0.282416\pi\) | ||||
0.631557 | + | 0.775329i | \(0.282416\pi\) | |||||||
\(684\) | −13.0834 | + | 10.5008i | −0.500255 | + | 0.401509i | ||||
\(685\) | −13.1062 | −0.500764 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −21.9745 | + | 25.6158i | −0.838380 | + | 0.977305i | ||||
\(688\) | −3.61660 | + | 6.26414i | −0.137882 | + | 0.238818i | ||||
\(689\) | −8.89848 | + | 15.4126i | −0.339005 | + | 0.587174i | ||||
\(690\) | 3.00000 | − | 3.49712i | 0.114208 | − | 0.133133i | ||||
\(691\) | −23.3411 | − | 40.4280i | −0.887938 | − | 1.53795i | −0.842309 | − | 0.538995i | \(-0.818804\pi\) |
−0.0456283 | − | 0.998958i | \(-0.514529\pi\) | |||||||
\(692\) | −9.18416 | −0.349129 | ||||||||
\(693\) | 8.56348 | − | 6.87312i | 0.325300 | − | 0.261088i | ||||
\(694\) | −15.1249 | −0.574135 | ||||||||
\(695\) | 8.51036 | + | 14.7404i | 0.322816 | + | 0.559134i | ||||
\(696\) | −0.257263 | − | 0.731540i | −0.00975153 | − | 0.0277290i | ||||
\(697\) | 10.2133 | − | 17.6900i | 0.386857 | − | 0.670056i | ||||
\(698\) | 9.68555 | − | 16.7759i | 0.366603 | − | 0.634976i | ||||
\(699\) | 20.0149 | + | 3.75458i | 0.757033 | + | 0.142011i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | −18.8553 | −0.712154 | −0.356077 | − | 0.934457i | \(-0.615886\pi\) | ||||
−0.356077 | + | 0.934457i | \(0.615886\pi\) | |||||||
\(702\) | −15.7664 | − | 9.80374i | −0.595066 | − | 0.370018i | ||||
\(703\) | −56.8440 | −2.14391 | ||||||||
\(704\) | −1.83010 | − | 3.16982i | −0.0689743 | − | 0.119467i | ||||
\(705\) | 20.8902 | + | 3.91878i | 0.786770 | + | 0.147590i | ||||
\(706\) | −14.7626 | + | 25.5696i | −0.555599 | + | 0.962326i | ||||
\(707\) | 6.64113 | − | 11.5028i | 0.249765 | − | 0.432606i | ||||
\(708\) | −7.41974 | − | 21.0984i | −0.278851 | − | 0.792926i | ||||
\(709\) | −1.90145 | − | 3.29340i | −0.0714104 | − | 0.123686i | 0.828109 | − | 0.560567i | \(-0.189417\pi\) |
−0.899520 | + | 0.436880i | \(0.856083\pi\) | |||||||
\(710\) | −3.89376 | −0.146130 | ||||||||
\(711\) | 1.01926 | + | 6.62163i | 0.0382253 | + | 0.248330i | ||||
\(712\) | 13.3585 | 0.500631 | ||||||||
\(713\) | −12.2158 | − | 21.1584i | −0.457485 | − | 0.792388i | ||||
\(714\) | −5.03735 | + | 5.87208i | −0.188518 | + | 0.219757i | ||||
\(715\) | 6.53896 | − | 11.3258i | 0.244543 | − | 0.423561i | ||||
\(716\) | −1.17074 | + | 2.02777i | −0.0437524 | + | 0.0757814i | ||||
\(717\) | −4.59695 | + | 5.35869i | −0.171676 | + | 0.200124i | ||||
\(718\) | 7.81085 | + | 13.5288i | 0.291498 | + | 0.504890i | ||||
\(719\) | −14.9530 | −0.557652 | −0.278826 | − | 0.960342i | \(-0.589945\pi\) | ||||
−0.278826 | + | 0.960342i | \(0.589945\pi\) | |||||||
\(720\) | −2.79604 | − | 1.08728i | −0.104202 | − | 0.0405203i | ||||
\(721\) | 14.3013 | 0.532609 | ||||||||
\(722\) | −6.13567 | − | 10.6273i | −0.228346 | − | 0.395507i | ||||
\(723\) | −13.2228 | − | 37.5997i | −0.491762 | − | 1.39835i | ||||
\(724\) | −9.33945 | + | 16.1764i | −0.347098 | + | 0.601191i | ||||
\(725\) | 0.223855 | − | 0.387729i | 0.00831378 | − | 0.0143999i | ||||
\(726\) | −4.08055 | − | 0.765467i | −0.151443 | − | 0.0284092i | ||||
\(727\) | −16.1627 | − | 27.9946i | −0.599441 | − | 1.03826i | −0.992904 | − | 0.118921i | \(-0.962056\pi\) |
0.393463 | − | 0.919340i | \(-0.371277\pi\) | |||||||
\(728\) | −3.57301 | −0.132425 | ||||||||
\(729\) | 11.9428 | + | 24.2151i | 0.442326 | + | 0.896854i | ||||
\(730\) | −6.14603 | −0.227475 | ||||||||
\(731\) | −16.1545 | − | 27.9805i | −0.597498 | − | 1.03490i | ||||
\(732\) | −2.03162 | − | 0.381111i | −0.0750909 | − | 0.0140863i | ||||
\(733\) | 9.96233 | − | 17.2553i | 0.367967 | − | 0.637337i | −0.621281 | − | 0.783588i | \(-0.713387\pi\) |
0.989248 | + | 0.146251i | \(0.0467206\pi\) | |||||||
\(734\) | 12.6659 | − | 21.9380i | 0.467508 | − | 0.809747i | ||||
\(735\) | −0.574618 | − | 1.63396i | −0.0211951 | − | 0.0602694i | ||||
\(736\) | 1.33010 | + | 2.30379i | 0.0490280 | + | 0.0849189i | ||||
\(737\) | 35.7470 | 1.31676 | ||||||||
\(738\) | −12.7863 | − | 4.97212i | −0.470671 | − | 0.183026i | ||||
\(739\) | −50.3032 | −1.85043 | −0.925216 | − | 0.379441i | \(-0.876116\pi\) | ||||
−0.925216 | + | 0.379441i | \(0.876116\pi\) | |||||||
\(740\) | −5.08255 | − | 8.80323i | −0.186838 | − | 0.323613i | ||||
\(741\) | 22.5329 | − | 26.2667i | 0.827765 | − | 0.964932i | ||||
\(742\) | 2.49047 | − | 4.31362i | 0.0914280 | − | 0.158358i | ||||
\(743\) | −9.23321 | + | 15.9924i | −0.338733 | + | 0.586704i | −0.984195 | − | 0.177089i | \(-0.943332\pi\) |
0.645461 | + | 0.763793i | \(0.276665\pi\) | |||||||
\(744\) | −10.3573 | + | 12.0736i | −0.379718 | + | 0.442640i | ||||
\(745\) | 7.15473 | + | 12.3924i | 0.262129 | + | 0.454021i | ||||
\(746\) | −16.0000 | −0.585802 | ||||||||
\(747\) | 5.19361 | + | 33.7403i | 0.190024 | + | 1.23449i | ||||
\(748\) | 16.3492 | 0.597788 | ||||||||
\(749\) | 4.75791 | + | 8.24095i | 0.173850 | + | 0.301118i | ||||
\(750\) | −0.574618 | − | 1.63396i | −0.0209821 | − | 0.0596637i | ||||
\(751\) | 19.0348 | − | 32.9692i | 0.694590 | − | 1.20306i | −0.275729 | − | 0.961235i | \(-0.588919\pi\) |
0.970319 | − | 0.241829i | \(-0.0777473\pi\) | |||||||
\(752\) | −6.13567 | + | 10.6273i | −0.223745 | + | 0.387537i | ||||
\(753\) | 38.3294 | + | 7.19018i | 1.39680 | + | 0.262025i | ||||
\(754\) | 0.799839 | + | 1.38536i | 0.0291284 | + | 0.0504519i | ||||
\(755\) | −12.0207 | −0.437479 | ||||||||
\(756\) | 4.41264 | + | 2.74383i | 0.160486 | + | 0.0997921i | ||||
\(757\) | −50.4531 | −1.83375 | −0.916875 | − | 0.399176i | \(-0.869296\pi\) | ||||
−0.916875 | + | 0.399176i | \(0.869296\pi\) | |||||||
\(758\) | −11.7286 | − | 20.3145i | −0.426001 | − | 0.737855i | ||||
\(759\) | 16.5755 | + | 3.10939i | 0.601653 | + | 0.112864i | ||||
\(760\) | 2.79604 | − | 4.84288i | 0.101423 | − | 0.175670i | ||||
\(761\) | −10.4286 | + | 18.0629i | −0.378038 | + | 0.654781i | −0.990777 | − | 0.135504i | \(-0.956735\pi\) |
0.612739 | + | 0.790286i | \(0.290068\pi\) | |||||||
\(762\) | −2.67783 | − | 7.61455i | −0.0970076 | − | 0.275846i | ||||
\(763\) | 0.232556 | + | 0.402799i | 0.00841910 | + | 0.0145823i | ||||
\(764\) | 18.7592 | 0.678684 | ||||||||
\(765\) | 10.4506 | − | 8.38772i | 0.377842 | − | 0.303259i | ||||
\(766\) | 11.9826 | 0.432949 | ||||||||
\(767\) | 23.0682 | + | 39.9553i | 0.832944 | + | 1.44270i | ||||
\(768\) | 1.12774 | − | 1.31461i | 0.0406938 | − | 0.0474370i | ||||
\(769\) | 11.5777 | − | 20.0532i | 0.417504 | − | 0.723138i | −0.578184 | − | 0.815906i | \(-0.696238\pi\) |
0.995688 | + | 0.0927688i | \(0.0295717\pi\) | |||||||
\(770\) | −1.83010 | + | 3.16982i | −0.0659521 | + | 0.114232i | ||||
\(771\) | −5.24544 | + | 6.11465i | −0.188910 | + | 0.220214i | ||||
\(772\) | −4.01989 | − | 6.96266i | −0.144679 | − | 0.250592i | ||||
\(773\) | −47.8229 | −1.72007 | −0.860035 | − | 0.510235i | \(-0.829558\pi\) | ||||
−0.860035 | + | 0.510235i | \(0.829558\pi\) | |||||||
\(774\) | −16.9230 | + | 13.5825i | −0.608285 | + | 0.488214i | ||||
\(775\) | −9.18416 | −0.329905 | ||||||||
\(776\) | 4.26643 | + | 7.38968i | 0.153156 | + | 0.265274i | ||||
\(777\) | 5.84105 | + | 16.6093i | 0.209546 | + | 0.595856i | ||||
\(778\) | −15.3008 | + | 26.5017i | −0.548559 | + | 0.950132i | ||||
\(779\) | 12.7863 | − | 22.1466i | 0.458118 | − | 0.793483i | ||||
\(780\) | 6.08255 | + | 1.14102i | 0.217790 | + | 0.0408551i | ||||
\(781\) | −7.12595 | − | 12.3425i | −0.254987 | − | 0.441650i | ||||
\(782\) | −11.8825 | −0.424916 | ||||||||
\(783\) | 0.0760681 | − | 2.32513i | 0.00271845 | − | 0.0830934i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −3.31973 | − | 5.74995i | −0.118486 | − | 0.205224i | ||||
\(786\) | −26.6917 | − | 5.00708i | −0.952061 | − | 0.178596i | ||||
\(787\) | 4.28169 | − | 7.41611i | 0.152626 | − | 0.264356i | −0.779566 | − | 0.626320i | \(-0.784560\pi\) |
0.932192 | + | 0.361964i | \(0.117894\pi\) | |||||||
\(788\) | −3.57765 | + | 6.19666i | −0.127448 | + | 0.220747i | ||||
\(789\) | 7.17459 | + | 20.4013i | 0.255422 | + | 0.726306i | ||||
\(790\) | −1.11660 | − | 1.93401i | −0.0397269 | − | 0.0688091i | ||||
\(791\) | −2.14639 | −0.0763169 | ||||||||
\(792\) | −1.67055 | − | 10.8528i | −0.0593605 | − | 0.385636i | ||||
\(793\) | 4.26410 | 0.151422 | ||||||||
\(794\) | 4.88238 | + | 8.45654i | 0.173269 | + | 0.300111i | ||||
\(795\) | −5.61719 | + | 6.54800i | −0.199221 | + | 0.232234i | ||||
\(796\) | −3.43634 | + | 5.95191i | −0.121798 | + | 0.210960i | ||||
\(797\) | 20.2038 | − | 34.9940i | 0.715655 | − | 1.23955i | −0.247052 | − | 0.969002i | \(-0.579462\pi\) |
0.962707 | − | 0.270548i | \(-0.0872048\pi\) | |||||||
\(798\) | −6.30640 | + | 7.35141i | −0.223244 | + | 0.260237i | ||||
\(799\) | −27.4066 | − | 47.4697i | −0.969577 | − | 1.67936i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 37.3509 | + | 14.5244i | 1.31973 | + | 0.513193i | ||||
\(802\) | 34.3411 | 1.21263 | ||||||||
\(803\) | −11.2478 | − | 19.4818i | −0.396927 | − | 0.687498i | ||||
\(804\) | 5.61197 | + | 15.9579i | 0.197919 | + | 0.562793i | ||||
\(805\) | 1.33010 | − | 2.30379i | 0.0468797 | − | 0.0811980i | ||||
\(806\) | 16.4076 | − | 28.4187i | 0.577932 | − | 1.00101i | ||||
\(807\) | 17.6014 | + | 3.30184i | 0.619600 | + | 0.116230i | ||||
\(808\) | −6.64113 | − | 11.5028i | −0.233634 | − | 0.404666i | ||||
\(809\) | −28.9325 | −1.01721 | −0.508606 | − | 0.861000i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.861000i | \(0.669839\pi\) | |||||||
\(810\) | −6.63567 | − | 6.08013i | −0.233154 | − | 0.213634i | ||||
\(811\) | 2.27170 | 0.0797700 | 0.0398850 | − | 0.999204i | \(-0.487301\pi\) | ||||
0.0398850 | + | 0.999204i | \(0.487301\pi\) | |||||||
\(812\) | −0.223855 | − | 0.387729i | −0.00785579 | − | 0.0136066i | ||||
\(813\) | 11.8296 | + | 2.21910i | 0.414880 | + | 0.0778271i | ||||
\(814\) | 18.6031 | − | 32.2215i | 0.652038 | − | 1.12936i | ||||
\(815\) | 3.73339 | − | 6.46642i | 0.130775 | − | 0.226509i | ||||
\(816\) | 2.56669 | + | 7.29851i | 0.0898522 | + | 0.255499i | ||||
\(817\) | −20.2243 | − | 35.0296i | −0.707559 | − | 1.22553i | ||||
\(818\) | 17.3703 | 0.607340 | ||||||||
\(819\) | −9.99029 | − | 3.88485i | −0.349089 | − | 0.135748i | ||||
\(820\) | 4.57301 | 0.159697 | ||||||||
\(821\) | 1.72932 | + | 2.99527i | 0.0603536 | + | 0.104535i | 0.894623 | − | 0.446821i | \(-0.147444\pi\) |
−0.834270 | + | 0.551356i | \(0.814111\pi\) | |||||||
\(822\) | 14.7804 | − | 17.2296i | 0.515526 | − | 0.600952i | ||||
\(823\) | −7.64122 | + | 13.2350i | −0.266356 | + | 0.461342i | −0.967918 | − | 0.251266i | \(-0.919153\pi\) |
0.701562 | + | 0.712608i | \(0.252486\pi\) | |||||||
\(824\) | 7.15066 | − | 12.3853i | 0.249105 | − | 0.431463i | ||||
\(825\) | 4.12774 | − | 4.81173i | 0.143709 | − | 0.167523i | ||||
\(826\) | −6.45623 | − | 11.1825i | −0.224641 | − | 0.389090i | ||||
\(827\) | 48.8246 | 1.69780 | 0.848898 | − | 0.528557i | \(-0.177267\pi\) | ||||
0.848898 | + | 0.528557i | \(0.177267\pi\) | |||||||
\(828\) | 1.21414 | + | 7.88767i | 0.0421944 | + | 0.274116i | ||||
\(829\) | 1.04793 | 0.0363961 | 0.0181980 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181980 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(830\) | −5.68962 | − | 9.85471i | −0.197489 | − | 0.342062i | ||||
\(831\) | −7.63223 | − | 21.7026i | −0.264759 | − | 0.752856i | ||||
\(832\) | −1.78651 | + | 3.09432i | −0.0619360 | + | 0.107276i | ||||
\(833\) | −2.23339 | + | 3.86834i | −0.0773823 | + | 0.134030i | ||||
\(834\) | −28.9754 | − | 5.43547i | −1.00333 | − | 0.188215i | ||||
\(835\) | 1.98501 | + | 3.43813i | 0.0686940 | + | 0.118981i | ||||
\(836\) | 20.4681 | 0.707903 | ||||||||
\(837\) | −42.0868 | + | 22.4970i | −1.45473 | + | 0.777610i | ||||
\(838\) | −23.3305 | −0.805940 | ||||||||
\(839\) | 8.68897 | + | 15.0497i | 0.299976 | + | 0.519575i | 0.976130 | − | 0.217186i | \(-0.0696878\pi\) |
−0.676154 | + | 0.736761i | \(0.736354\pi\) | |||||||
\(840\) | −1.70236 | − | 0.319344i | −0.0587369 | − | 0.0110184i | ||||
\(841\) | 14.3998 | − | 24.9411i | 0.496544 | − | 0.860040i | ||||
\(842\) | −5.66120 | + | 9.80549i | −0.195098 | + | 0.337920i | ||||
\(843\) | −11.0954 | − | 31.5502i | −0.382145 | − | 1.08665i | ||||
\(844\) | −12.3879 | − | 21.4565i | −0.426410 | − | 0.738564i | ||||
\(845\) | 0.233569 | 0.00803501 | ||||||||
\(846\) | −28.7103 | + | 23.0431i | −0.987082 | + | 0.792240i | ||||
\(847\) | −2.39700 | −0.0823619 | ||||||||
\(848\) | −2.49047 | − | 4.31362i | −0.0855230 | − | 0.148130i | ||||
\(849\) | −16.0943 | + | 18.7613i | −0.552356 | + | 0.643885i | ||||
\(850\) | −2.23339 | + | 3.86834i | −0.0766045 | + | 0.132683i | ||||
\(851\) | −13.5205 | + | 23.4183i | −0.463478 | + | 0.802768i | ||||
\(852\) | 4.39114 | − | 5.11879i | 0.150438 | − | 0.175367i | ||||
\(853\) | 7.78549 | + | 13.4849i | 0.266570 | + | 0.461713i | 0.967974 | − | 0.251051i | \(-0.0807762\pi\) |
−0.701404 | + | 0.712764i | \(0.747443\pi\) | |||||||
\(854\) | −1.19342 | −0.0408379 | ||||||||
\(855\) | 13.0834 | − | 10.5008i | 0.447442 | − | 0.359120i | ||||
\(856\) | 9.51582 | 0.325244 | ||||||||
\(857\) | 17.6753 | + | 30.6145i | 0.603776 | + | 1.04577i | 0.992244 | + | 0.124308i | \(0.0396711\pi\) |
−0.388468 | + | 0.921462i | \(0.626996\pi\) | |||||||
\(858\) | 7.51481 | + | 21.3687i | 0.256551 | + | 0.729517i | ||||
\(859\) | −16.4940 | + | 28.5684i | −0.562768 | + | 0.974742i | 0.434486 | + | 0.900679i | \(0.356930\pi\) |
−0.997254 | + | 0.0740637i | \(0.976403\pi\) | |||||||
\(860\) | 3.61660 | − | 6.26414i | 0.123325 | − | 0.213605i | ||||
\(861\) | −7.78490 | − | 1.46036i | −0.265309 | − | 0.0497691i | ||||
\(862\) | −3.98964 | − | 6.91025i | −0.135888 | − | 0.235364i | ||||
\(863\) | 25.1656 | 0.856648 | 0.428324 | − | 0.903625i | \(-0.359104\pi\) | ||||
0.428324 | + | 0.903625i | \(0.359104\pi\) | |||||||
\(864\) | 4.58255 | − | 2.44955i | 0.155901 | − | 0.0833352i | ||||
\(865\) | 9.18416 | 0.312271 | ||||||||
\(866\) | 11.8900 | + | 20.5940i | 0.404037 | + | 0.699813i | ||||
\(867\) | −5.02548 | − | 0.942726i | −0.170674 | − | 0.0320167i | ||||
\(868\) | −4.59208 | + | 7.95371i | −0.155865 | + | 0.269967i | ||||
\(869\) | 4.08698 | − | 7.07886i | 0.138641 | − | 0.240134i | ||||
\(870\) | 0.257263 | + | 0.731540i | 0.00872203 | + | 0.0248015i | ||||
\(871\) | −17.4478 | − | 30.2205i | −0.591196 | − | 1.02398i | ||||
\(872\) | 0.465112 | 0.0157507 | ||||||||
\(873\) | 3.89450 | + | 25.3006i | 0.131809 | + | 0.856296i | ||||
\(874\) | −14.8760 | −0.503188 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | 6.93111 | − | 8.07965i | 0.234181 | − | 0.272986i | ||||
\(877\) | −24.6535 | + | 42.7012i | −0.832491 | + | 1.44192i | 0.0635665 | + | 0.997978i | \(0.479753\pi\) |
−0.896057 | + | 0.443939i | \(0.853581\pi\) | |||||||
\(878\) | 12.9412 | − | 22.4149i | 0.436746 | − | 0.756466i | ||||
\(879\) | 10.2887 | − | 11.9936i | 0.347028 | − | 0.404533i | ||||
\(880\) | 1.83010 | + | 3.16982i | 0.0616925 | + | 0.106855i | ||||
\(881\) | 24.9811 | 0.841635 | 0.420818 | − | 0.907145i | \(-0.361743\pi\) | ||||
0.420818 | + | 0.907145i | \(0.361743\pi\) | |||||||
\(882\) | 2.79604 | + | 1.08728i | 0.0941475 | + | 0.0366105i | ||||
\(883\) | −12.8743 | −0.433256 | −0.216628 | − | 0.976254i | \(-0.569506\pi\) | ||||
−0.216628 | + | 0.976254i | \(0.569506\pi\) | |||||||
\(884\) | −7.97992 | − | 13.8216i | −0.268394 | − | 0.464872i | ||||
\(885\) | 7.41974 | + | 21.0984i | 0.249412 | + | 0.709215i | ||||
\(886\) | 4.95807 | − | 8.58764i | 0.166570 | − | 0.288507i | ||||
\(887\) | −4.65853 | + | 8.06881i | −0.156418 | + | 0.270924i | −0.933574 | − | 0.358383i | \(-0.883328\pi\) |
0.777156 | + | 0.629308i | \(0.216661\pi\) | |||||||
\(888\) | 17.3046 | + | 3.24616i | 0.580705 | + | 0.108934i | ||||
\(889\) | −2.33010 | − | 4.03584i | −0.0781489 | − | 0.135358i | ||||
\(890\) | −13.3585 | −0.447778 | ||||||||
\(891\) | 7.12899 | − | 32.1611i | 0.238830 | − | 1.07744i | ||||
\(892\) | −29.7568 | −0.996332 | ||||||||
\(893\) | −34.3111 | − | 59.4286i | −1.14818 | − | 1.98870i | ||||
\(894\) | −24.3598 | − | 4.56964i | −0.814714 | − | 0.152832i | ||||
\(895\) | 1.17074 | − | 2.02777i | 0.0391334 | − | 0.0677810i | ||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | −5.46169 | − | 15.5306i | −0.182361 | − | 0.518551i | ||||
\(898\) | 2.09772 | + | 3.63336i | 0.0700019 | + | 0.121247i | ||||
\(899\) | 4.11185 | 0.137138 | ||||||||
\(900\) | 2.79604 | + | 1.08728i | 0.0932013 | + | 0.0362425i | ||||
\(901\) | 22.2487 | 0.741212 | ||||||||
\(902\) | 8.36905 | + | 14.4956i | 0.278659 | + | 0.482652i | ||||
\(903\) | −8.15716 | + | 9.50886i | −0.271453 | + | 0.316435i | ||||
\(904\) | −1.07320 | + | 1.85883i | −0.0356940 | + | 0.0618238i | ||||
\(905\) | 9.33945 | − | 16.1764i | 0.310454 | − | 0.537722i | ||||
\(906\) | 13.5562 | − | 15.8026i | 0.450376 | − | 0.525006i | ||||
\(907\) | 3.98019 | + | 6.89390i | 0.132160 | + | 0.228908i | 0.924509 | − | 0.381160i | \(-0.124475\pi\) |
−0.792349 | + | 0.610068i | \(0.791142\pi\) | |||||||
\(908\) | 14.6598 | 0.486503 | ||||||||
\(909\) | −6.06218 | − | 39.3829i | −0.201070 | − | 1.30625i | ||||
\(910\) | 3.57301 | 0.118444 | ||||||||
\(911\) | −16.6067 | − | 28.7637i | −0.550205 | − | 0.952983i | −0.998259 | − | 0.0589764i | \(-0.981216\pi\) |
0.448055 | − | 0.894006i | \(-0.352117\pi\) | |||||||
\(912\) | 3.21331 | + | 9.13721i | 0.106403 | + | 0.302563i | ||||
\(913\) | 20.8251 | − | 36.0701i | 0.689210 | − | 1.19375i | ||||
\(914\) | 6.43087 | − | 11.1386i | 0.212714 | − | 0.368432i | ||||
\(915\) | 2.03162 | + | 0.381111i | 0.0671633 | + | 0.0125991i | ||||
\(916\) | 9.74274 | + | 16.8749i | 0.321909 | + | 0.557563i | ||||
\(917\) | −15.6793 | −0.517775 | ||||||||
\(918\) | −0.758925 | + | 23.1976i | −0.0250483 | + | 0.765636i | ||||
\(919\) | 41.7394 | 1.37686 | 0.688428 | − | 0.725305i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725305i | \(0.258301\pi\) | |||||||
\(920\) | −1.33010 | − | 2.30379i | −0.0438520 | − | 0.0759538i | ||||
\(921\) | 22.9634 | + | 4.30768i | 0.756669 | + | 0.141943i | ||||
\(922\) | −7.49213 | + | 12.9768i | −0.246740 | + | 0.427367i | ||||
\(923\) | −6.95623 | + | 12.0485i | −0.228967 | + | 0.396583i | ||||
\(924\) | −2.10321 | − | 5.98059i | −0.0691906 | − | 0.196747i | ||||
\(925\) | 5.08255 | + | 8.80323i | 0.167113 | + | 0.289448i | ||||
\(926\) | −3.45661 | −0.113591 | ||||||||
\(927\) | 33.4598 | − | 26.8551i | 1.09896 | − | 0.882036i | ||||
\(928\) | −0.447711 | −0.0146968 | ||||||||
\(929\) | 12.0191 | + | 20.8176i | 0.394333 | + | 0.683004i | 0.993016 | − | 0.117982i | \(-0.0376424\pi\) |
−0.598683 | + | 0.800986i | \(0.704309\pi\) | |||||||
\(930\) | 10.3573 | − | 12.0736i | 0.339630 | − | 0.395909i | ||||
\(931\) | −2.79604 | + | 4.84288i | −0.0916365 | + | 0.158719i | ||||
\(932\) | 5.87858 | − | 10.1820i | 0.192559 | − | 0.333523i | ||||
\(933\) | 10.9902 | − | 12.8113i | 0.359803 | − | 0.419425i | ||||
\(934\) | −7.07931 | − | 12.2617i | −0.231642 | − | 0.401216i | ||||
\(935\) | −16.3492 | −0.534678 | ||||||||
\(936\) | −8.35952 | + | 6.70942i | −0.273240 | + | 0.219304i | ||||
\(937\) | 24.0309 | 0.785055 | 0.392527 | − | 0.919740i | \(-0.371601\pi\) | ||||
0.392527 | + | 0.919740i | \(0.371601\pi\) | |||||||
\(938\) | 4.88322 | + | 8.45798i | 0.159443 | + | 0.276163i | ||||
\(939\) | −2.96912 | − | 8.44284i | −0.0968936 | − | 0.275522i | ||||
\(940\) | 6.13567 | − | 10.6273i | 0.200123 | − | 0.346624i | ||||
\(941\) | 18.6696 | − | 32.3367i | 0.608613 | − | 1.05415i | −0.382857 | − | 0.923808i | \(-0.625060\pi\) |
0.991469 | − | 0.130340i | \(-0.0416069\pi\) | |||||||
\(942\) | 11.3027 | + | 2.12027i | 0.368263 | + | 0.0690822i | ||||
\(943\) | −6.08255 | − | 10.5353i | −0.198075 | − | 0.343076i | ||||
\(944\) | −12.9125 | −0.420265 | ||||||||
\(945\) | −4.41264 | − | 2.74383i | −0.143543 | − | 0.0892567i | ||||
\(946\) | 26.4749 | 0.860774 | ||||||||
\(947\) | 26.1248 | + | 45.2495i | 0.848943 | + | 1.47041i | 0.882153 | + | 0.470964i | \(0.156094\pi\) |
−0.0332098 | + | 0.999448i | \(0.510573\pi\) | |||||||
\(948\) | 3.80171 | + | 0.713161i | 0.123474 | + | 0.0231624i | ||||
\(949\) | −10.9799 | + | 19.0178i | −0.356423 | + | 0.617343i | ||||
\(950\) | −2.79604 | + | 4.84288i | −0.0907155 | + | 0.157124i | ||||
\(951\) | −3.49876 | − | 9.94890i | −0.113455 | − | 0.322615i | ||||
\(952\) | 2.23339 | + | 3.86834i | 0.0723845 | + | 0.125374i | ||||
\(953\) | −9.95337 | −0.322421 | −0.161211 | − | 0.986920i | \(-0.551540\pi\) | ||||
−0.161211 | + | 0.986920i | \(0.551540\pi\) | |||||||
\(954\) | −2.27336 | − | 14.7689i | −0.0736027 | − | 0.478160i | ||||
\(955\) | −18.7592 | −0.607033 | ||||||||
\(956\) | 2.03813 | + | 3.53014i | 0.0659177 | + | 0.114173i | ||||
\(957\) | −1.84803 | + | 2.15427i | −0.0597384 | + | 0.0696375i | ||||
\(958\) | 17.8346 | − | 30.8905i | 0.576211 | − | 0.998026i | ||||
\(959\) | 6.55312 | − | 11.3503i | 0.211611 | − | 0.366521i | ||||
\(960\) | −1.12774 | + | 1.31461i | −0.0363976 | + | 0.0424289i | ||||
\(961\) | −26.6744 | − | 46.2013i | −0.860463 | − | 1.49037i | ||||
\(962\) | −36.3200 | −1.17100 | ||||||||
\(963\) | 26.6066 | + | 10.3463i | 0.857386 | + | 0.333405i | ||||
\(964\) | −23.0115 | −0.741149 | ||||||||
\(965\) | 4.01989 | + | 6.96266i | 0.129405 | + | 0.224136i | ||||
\(966\) | 1.52859 | + | 4.34664i | 0.0491817 | + | 0.139851i | ||||
\(967\) | 15.8362 | − | 27.4291i | 0.509258 | − | 0.882061i | −0.490684 | − | 0.871337i | \(-0.663253\pi\) |
0.999943 | − | 0.0107235i | \(-0.00341346\pi\) | |||||||
\(968\) | −1.19850 | + | 2.07586i | −0.0385212 | + | 0.0667207i | ||||
\(969\) | −42.5224 | − | 7.97675i | −1.36602 | − | 0.256250i | ||||
\(970\) | −4.26643 | − | 7.38968i | −0.136987 | − | 0.237268i | ||||
\(971\) | 25.8256 | 0.828784 | 0.414392 | − | 0.910098i | \(-0.363994\pi\) | ||||
0.414392 | + | 0.910098i | \(0.363994\pi\) | |||||||
\(972\) | 15.4763 | − | 1.86654i | 0.496403 | − | 0.0598692i | ||||
\(973\) | −17.0207 | −0.545659 | ||||||||
\(974\) | 10.9145 | + | 18.9044i | 0.349723 | + | 0.605737i | ||||
\(975\) | −6.08255 | − | 1.14102i | −0.194797 | − | 0.0365419i | ||||
\(976\) | −0.596708 | + | 1.03353i | −0.0191002 | + | 0.0330825i | ||||
\(977\) | 15.4863 | − | 26.8231i | 0.495451 | − | 0.858146i | −0.504535 | − | 0.863391i | \(-0.668336\pi\) |
0.999986 | + | 0.00524503i | \(0.00166955\pi\) | |||||||
\(978\) | 4.29055 | + | 12.2004i | 0.137197 | + | 0.390125i | ||||
\(979\) | −24.4473 | − | 42.3440i | −0.781341 | − | 1.35332i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 1.30047 | + | 0.505705i | 0.0415209 | + | 0.0161459i | ||||
\(982\) | 22.1749 | 0.707629 | ||||||||
\(983\) | 22.8449 | + | 39.5685i | 0.728639 | + | 1.26204i | 0.957458 | + | 0.288571i | \(0.0931803\pi\) |
−0.228819 | + | 0.973469i | \(0.573486\pi\) | |||||||
\(984\) | −5.15716 | + | 6.01174i | −0.164404 | + | 0.191647i | ||||
\(985\) | 3.57765 | − | 6.19666i | 0.113993 | − | 0.197442i | ||||
\(986\) | 0.999912 | − | 1.73190i | 0.0318437 | − | 0.0551549i | ||||
\(987\) | −13.8389 | + | 16.1320i | −0.440496 | + | 0.513489i | ||||
\(988\) | −9.99029 | − | 17.3037i | −0.317833 | − | 0.550504i | ||||
\(989\) | −19.2417 | −0.611851 | ||||||||
\(990\) | 1.67055 | + | 10.8528i | 0.0530937 | + | 0.344923i | ||||
\(991\) | −38.4068 | −1.22003 | −0.610017 | − | 0.792389i | \(-0.708837\pi\) | ||||
−0.610017 | + | 0.792389i | \(0.708837\pi\) | |||||||
\(992\) | 4.59208 | + | 7.95371i | 0.145799 | + | 0.252531i | ||||
\(993\) | 18.0749 | + | 51.3969i | 0.573590 | + | 1.63103i | ||||
\(994\) | 1.94688 | − | 3.37209i | 0.0617513 | − | 0.106956i | ||||
\(995\) | 3.43634 | − | 5.95191i | 0.108939 | − | 0.188688i | ||||
\(996\) | 19.3715 | + | 3.63389i | 0.613810 | + | 0.115144i | ||||
\(997\) | −28.4170 | − | 49.2197i | −0.899975 | − | 1.55880i | −0.827523 | − | 0.561431i | \(-0.810251\pi\) |
−0.0724518 | − | 0.997372i | \(-0.523082\pi\) | |||||||
\(998\) | 5.95298 | 0.188438 | ||||||||
\(999\) | 44.8549 | + | 27.8913i | 1.41915 | + | 0.882441i |
(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 | 630.2.j.l.211.1 | ✓ | 8 | |
3.2 | odd | 2 | 1890.2.j.l.631.4 | 8 | |||
9.2 | odd | 6 | 1890.2.j.l.1261.4 | 8 | |||
9.4 | even | 3 | 5670.2.a.bw.1.4 | 4 | |||
9.5 | odd | 6 | 5670.2.a.bv.1.1 | 4 | |||
9.7 | even | 3 | inner | 630.2.j.l.421.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.l.211.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
630.2.j.l.421.1 | yes | 8 | 9.7 | even | 3 | inner | |
1890.2.j.l.631.4 | 8 | 3.2 | odd | 2 | |||
1890.2.j.l.1261.4 | 8 | 9.2 | odd | 6 | |||
5670.2.a.bv.1.1 | 4 | 9.5 | odd | 6 | |||
5670.2.a.bw.1.4 | 4 | 9.4 | even | 3 |