Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [361,2,Mod(68,361)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(361, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("361.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 361 = 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 361.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.88259951297\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 292.1 | ||
Root | \(0.809017 + 1.40126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 361.292 |
Dual form | 361.2.c.d.68.1 |
$q$-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 \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 1.40126i | −0.572061 | − | 0.990839i | −0.996354 | − | 0.0853143i | \(-0.972811\pi\) |
0.424293 | − | 0.905525i | \(-0.360523\pi\) | |||||||
\(3\) | −0.190983 | − | 0.330792i | −0.110264 | − | 0.190983i | 0.805613 | − | 0.592443i | \(-0.201836\pi\) |
−0.915877 | + | 0.401460i | \(0.868503\pi\) | |||||||
\(4\) | −0.309017 | + | 0.535233i | −0.154508 | + | 0.267617i | ||||
\(5\) | −1.61803 | − | 2.80252i | −0.723607 | − | 1.25332i | −0.959545 | − | 0.281556i | \(-0.909150\pi\) |
0.235938 | − | 0.971768i | \(-0.424184\pi\) | |||||||
\(6\) | −0.309017 | + | 0.535233i | −0.126156 | + | 0.218508i | ||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.42705 | − | 2.47172i | 0.475684 | − | 0.823908i | ||||
\(10\) | −2.61803 | + | 4.53457i | −0.827895 | + | 1.43396i | ||||
\(11\) | −1.61803 | −0.487856 | −0.243928 | − | 0.969793i | \(-0.578436\pi\) | ||||
−0.243928 | + | 0.969793i | \(0.578436\pi\) | |||||||
\(12\) | 0.236068 | 0.0681470 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | −2.42705 | − | 4.20378i | −0.648657 | − | 1.12351i | ||||
\(15\) | −0.618034 | + | 1.07047i | −0.159576 | + | 0.276393i | ||||
\(16\) | 2.42705 | + | 4.20378i | 0.606763 | + | 1.05094i | ||||
\(17\) | −0.381966 | − | 0.661585i | −0.0926404 | − | 0.160458i | 0.815981 | − | 0.578079i | \(-0.196197\pi\) |
−0.908621 | + | 0.417621i | \(0.862864\pi\) | |||||||
\(18\) | −4.61803 | −1.08848 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −0.572949 | − | 0.992377i | −0.125028 | − | 0.216554i | ||||
\(22\) | 1.30902 | + | 2.26728i | 0.279083 | + | 0.483387i | ||||
\(23\) | −2.69098 | + | 4.66092i | −0.561109 | + | 0.971869i | 0.436291 | + | 0.899805i | \(0.356292\pi\) |
−0.997400 | + | 0.0720634i | \(0.977042\pi\) | |||||||
\(24\) | 0.427051 | + | 0.739674i | 0.0871714 | + | 0.150985i | ||||
\(25\) | −2.73607 | + | 4.73901i | −0.547214 | + | 0.947802i | ||||
\(26\) | −1.61803 | −0.317323 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −0.927051 | + | 1.60570i | −0.175196 | + | 0.303449i | ||||
\(29\) | 1.80902 | − | 3.13331i | 0.335926 | − | 0.581841i | −0.647736 | − | 0.761865i | \(-0.724284\pi\) |
0.983662 | + | 0.180024i | \(0.0576175\pi\) | |||||||
\(30\) | 2.00000 | 0.365148 | ||||||||
\(31\) | −8.85410 | −1.59024 | −0.795122 | − | 0.606450i | \(-0.792593\pi\) | ||||
−0.795122 | + | 0.606450i | \(0.792593\pi\) | |||||||
\(32\) | 1.69098 | − | 2.92887i | 0.298926 | − | 0.517756i | ||||
\(33\) | 0.309017 | + | 0.535233i | 0.0537930 | + | 0.0931721i | ||||
\(34\) | −0.618034 | + | 1.07047i | −0.105992 | + | 0.183583i | ||||
\(35\) | −4.85410 | − | 8.40755i | −0.820493 | − | 1.42114i | ||||
\(36\) | 0.881966 | + | 1.52761i | 0.146994 | + | 0.254602i | ||||
\(37\) | 8.85410 | 1.45561 | 0.727803 | − | 0.685787i | \(-0.240542\pi\) | ||||
0.727803 | + | 0.685787i | \(0.240542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.381966 | −0.0611635 | ||||||||
\(40\) | 3.61803 | + | 6.26662i | 0.572061 | + | 0.990839i | ||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | −0.927051 | + | 1.60570i | −0.143047 | + | 0.247765i | ||||
\(43\) | 0.0729490 | + | 0.126351i | 0.0111246 | + | 0.0192684i | 0.871534 | − | 0.490335i | \(-0.163126\pi\) |
−0.860410 | + | 0.509603i | \(0.829792\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | −9.23607 | −1.37683 | ||||||||
\(46\) | 8.70820 | 1.28395 | ||||||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | 0.927051 | − | 1.60570i | 0.133808 | − | 0.231763i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 8.85410 | 1.25216 | ||||||||
\(51\) | −0.145898 | + | 0.252703i | −0.0204298 | + | 0.0353855i | ||||
\(52\) | 0.309017 | + | 0.535233i | 0.0428529 | + | 0.0742235i | ||||
\(53\) | 3.16312 | − | 5.47868i | 0.434488 | − | 0.752555i | −0.562766 | − | 0.826616i | \(-0.690263\pi\) |
0.997254 | + | 0.0740614i | \(0.0235961\pi\) | |||||||
\(54\) | 1.80902 | + | 3.13331i | 0.246176 | + | 0.426389i | ||||
\(55\) | 2.61803 | + | 4.53457i | 0.353016 | + | 0.611441i | ||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | −0.163119 | − | 0.282530i | −0.0212363 | − | 0.0367823i | 0.855212 | − | 0.518278i | \(-0.173427\pi\) |
−0.876448 | + | 0.481496i | \(0.840094\pi\) | |||||||
\(60\) | −0.381966 | − | 0.661585i | −0.0493116 | − | 0.0854102i | ||||
\(61\) | 5.11803 | − | 8.86469i | 0.655297 | − | 1.13501i | −0.326522 | − | 0.945190i | \(-0.605877\pi\) |
0.981819 | − | 0.189818i | \(-0.0607899\pi\) | |||||||
\(62\) | 7.16312 | + | 12.4069i | 0.909717 | + | 1.57568i | ||||
\(63\) | 4.28115 | − | 7.41517i | 0.539375 | − | 0.934224i | ||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −3.23607 | −0.401385 | ||||||||
\(66\) | 0.500000 | − | 0.866025i | 0.0615457 | − | 0.106600i | ||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0.472136 | 0.0572549 | ||||||||
\(69\) | 2.05573 | 0.247481 | ||||||||
\(70\) | −7.85410 | + | 13.6037i | −0.938745 | + | 1.62595i | ||||
\(71\) | 3.73607 | + | 6.47106i | 0.443390 | + | 0.767973i | 0.997938 | − | 0.0641777i | \(-0.0204425\pi\) |
−0.554549 | + | 0.832151i | \(0.687109\pi\) | |||||||
\(72\) | −3.19098 | + | 5.52694i | −0.376061 | + | 0.651357i | ||||
\(73\) | 1.35410 | + | 2.34537i | 0.158486 | + | 0.274505i | 0.934323 | − | 0.356428i | \(-0.116006\pi\) |
−0.775837 | + | 0.630933i | \(0.782672\pi\) | |||||||
\(74\) | −7.16312 | − | 12.4069i | −0.832696 | − | 1.44227i | ||||
\(75\) | 2.09017 | 0.241352 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.85410 | −0.553176 | ||||||||
\(78\) | 0.309017 | + | 0.535233i | 0.0349893 | + | 0.0606032i | ||||
\(79\) | −6.70820 | − | 11.6190i | −0.754732 | − | 1.30723i | −0.945507 | − | 0.325600i | \(-0.894434\pi\) |
0.190776 | − | 0.981634i | \(-0.438900\pi\) | |||||||
\(80\) | 7.85410 | − | 13.6037i | 0.878115 | − | 1.52094i | ||||
\(81\) | −3.85410 | − | 6.67550i | −0.428234 | − | 0.741722i | ||||
\(82\) | 2.42705 | − | 4.20378i | 0.268023 | − | 0.464229i | ||||
\(83\) | 8.47214 | 0.929938 | 0.464969 | − | 0.885327i | \(-0.346066\pi\) | ||||
0.464969 | + | 0.885327i | \(0.346066\pi\) | |||||||
\(84\) | 0.708204 | 0.0772714 | ||||||||
\(85\) | −1.23607 | + | 2.14093i | −0.134070 | + | 0.232217i | ||||
\(86\) | 0.118034 | − | 0.204441i | 0.0127279 | − | 0.0220454i | ||||
\(87\) | −1.38197 | −0.148162 | ||||||||
\(88\) | 3.61803 | 0.385684 | ||||||||
\(89\) | 3.88197 | − | 6.72376i | 0.411488 | − | 0.712717i | −0.583565 | − | 0.812066i | \(-0.698343\pi\) |
0.995053 | + | 0.0993490i | \(0.0316760\pi\) | |||||||
\(90\) | 7.47214 | + | 12.9421i | 0.787632 | + | 1.36422i | ||||
\(91\) | 1.50000 | − | 2.59808i | 0.157243 | − | 0.272352i | ||||
\(92\) | −1.66312 | − | 2.88061i | −0.173392 | − | 0.300324i | ||||
\(93\) | 1.69098 | + | 2.92887i | 0.175347 | + | 0.303710i | ||||
\(94\) | 4.85410 | 0.500662 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.29180 | −0.131843 | ||||||||
\(97\) | −6.92705 | − | 11.9980i | −0.703335 | − | 1.21821i | −0.967289 | − | 0.253677i | \(-0.918360\pi\) |
0.263953 | − | 0.964535i | \(-0.414973\pi\) | |||||||
\(98\) | −1.61803 | − | 2.80252i | −0.163446 | − | 0.283097i | ||||
\(99\) | −2.30902 | + | 3.99933i | −0.232065 | + | 0.401948i | ||||
\(100\) | −1.69098 | − | 2.92887i | −0.169098 | − | 0.292887i | ||||
\(101\) | 4.59017 | − | 7.95041i | 0.456739 | − | 0.791095i | −0.542047 | − | 0.840348i | \(-0.682351\pi\) |
0.998786 | + | 0.0492528i | \(0.0156840\pi\) | |||||||
\(102\) | 0.472136 | 0.0467484 | ||||||||
\(103\) | 14.3262 | 1.41161 | 0.705803 | − | 0.708408i | \(-0.250586\pi\) | ||||
0.705803 | + | 0.708408i | \(0.250586\pi\) | |||||||
\(104\) | −1.11803 | + | 1.93649i | −0.109632 | + | 0.189889i | ||||
\(105\) | −1.85410 | + | 3.21140i | −0.180942 | + | 0.313400i | ||||
\(106\) | −10.2361 | −0.994215 | ||||||||
\(107\) | 16.4164 | 1.58703 | 0.793517 | − | 0.608548i | \(-0.208248\pi\) | ||||
0.793517 | + | 0.608548i | \(0.208248\pi\) | |||||||
\(108\) | 0.690983 | − | 1.19682i | 0.0664899 | − | 0.115164i | ||||
\(109\) | 1.64590 | + | 2.85078i | 0.157648 | + | 0.273055i | 0.934020 | − | 0.357220i | \(-0.116275\pi\) |
−0.776372 | + | 0.630275i | \(0.782942\pi\) | |||||||
\(110\) | 4.23607 | − | 7.33708i | 0.403893 | − | 0.699564i | ||||
\(111\) | −1.69098 | − | 2.92887i | −0.160501 | − | 0.277996i | ||||
\(112\) | 7.28115 | + | 12.6113i | 0.688004 | + | 1.19166i | ||||
\(113\) | 6.76393 | 0.636297 | 0.318149 | − | 0.948041i | \(-0.396939\pi\) | ||||
0.318149 | + | 0.948041i | \(0.396939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.4164 | 1.62409 | ||||||||
\(116\) | 1.11803 | + | 1.93649i | 0.103807 | + | 0.179799i | ||||
\(117\) | −1.42705 | − | 2.47172i | −0.131931 | − | 0.228511i | ||||
\(118\) | −0.263932 | + | 0.457144i | −0.0242969 | + | 0.0420835i | ||||
\(119\) | −1.14590 | − | 1.98475i | −0.105044 | − | 0.181942i | ||||
\(120\) | 1.38197 | − | 2.39364i | 0.126156 | − | 0.218508i | ||||
\(121\) | −8.38197 | −0.761997 | ||||||||
\(122\) | −16.5623 | −1.49948 | ||||||||
\(123\) | 0.572949 | − | 0.992377i | 0.0516611 | − | 0.0894796i | ||||
\(124\) | 2.73607 | − | 4.73901i | 0.245706 | − | 0.425576i | ||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | −13.8541 | −1.23422 | ||||||||
\(127\) | −2.88197 | + | 4.99171i | −0.255733 | + | 0.442943i | −0.965094 | − | 0.261902i | \(-0.915650\pi\) |
0.709361 | + | 0.704845i | \(0.248984\pi\) | |||||||
\(128\) | −6.80902 | − | 11.7936i | −0.601838 | − | 1.04241i | ||||
\(129\) | 0.0278640 | − | 0.0482619i | 0.00245329 | − | 0.00424923i | ||||
\(130\) | 2.61803 | + | 4.53457i | 0.229617 | + | 0.397708i | ||||
\(131\) | −7.54508 | − | 13.0685i | −0.659217 | − | 1.14180i | −0.980819 | − | 0.194922i | \(-0.937554\pi\) |
0.321602 | − | 0.946875i | \(-0.395779\pi\) | |||||||
\(132\) | −0.381966 | −0.0332459 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.3262 | −0.978438 | ||||||||
\(135\) | 3.61803 | + | 6.26662i | 0.311391 | + | 0.539345i | ||||
\(136\) | 0.854102 | + | 1.47935i | 0.0732386 | + | 0.126853i | ||||
\(137\) | −3.73607 | + | 6.47106i | −0.319194 | + | 0.552860i | −0.980320 | − | 0.197415i | \(-0.936745\pi\) |
0.661126 | + | 0.750275i | \(0.270079\pi\) | |||||||
\(138\) | −1.66312 | − | 2.88061i | −0.141574 | − | 0.245214i | ||||
\(139\) | −7.39919 | + | 12.8158i | −0.627591 | + | 1.08702i | 0.360443 | + | 0.932781i | \(0.382626\pi\) |
−0.988034 | + | 0.154238i | \(0.950708\pi\) | |||||||
\(140\) | 6.00000 | 0.507093 | ||||||||
\(141\) | 1.14590 | 0.0965020 | ||||||||
\(142\) | 6.04508 | − | 10.4704i | 0.507292 | − | 0.878656i | ||||
\(143\) | −0.809017 | + | 1.40126i | −0.0676534 | + | 0.117179i | ||||
\(144\) | 13.8541 | 1.15451 | ||||||||
\(145\) | −11.7082 | −0.972313 | ||||||||
\(146\) | 2.19098 | − | 3.79489i | 0.181327 | − | 0.314068i | ||||
\(147\) | −0.381966 | − | 0.661585i | −0.0315040 | − | 0.0545666i | ||||
\(148\) | −2.73607 | + | 4.73901i | −0.224903 | + | 0.389544i | ||||
\(149\) | 0.954915 | + | 1.65396i | 0.0782297 | + | 0.135498i | 0.902486 | − | 0.430719i | \(-0.141740\pi\) |
−0.824257 | + | 0.566217i | \(0.808407\pi\) | |||||||
\(150\) | −1.69098 | − | 2.92887i | −0.138068 | − | 0.239141i | ||||
\(151\) | −21.0902 | −1.71629 | −0.858147 | − | 0.513404i | \(-0.828384\pi\) | ||||
−0.858147 | + | 0.513404i | \(0.828384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.18034 | −0.176270 | ||||||||
\(154\) | 3.92705 | + | 6.80185i | 0.316451 | + | 0.548109i | ||||
\(155\) | 14.3262 | + | 24.8138i | 1.15071 | + | 1.99309i | ||||
\(156\) | 0.118034 | − | 0.204441i | 0.00945028 | − | 0.0163684i | ||||
\(157\) | 8.92705 | + | 15.4621i | 0.712456 | + | 1.23401i | 0.963932 | + | 0.266147i | \(0.0857506\pi\) |
−0.251476 | + | 0.967863i | \(0.580916\pi\) | |||||||
\(158\) | −10.8541 | + | 18.7999i | −0.863506 | + | 1.49564i | ||||
\(159\) | −2.41641 | −0.191634 | ||||||||
\(160\) | −10.9443 | −0.865221 | ||||||||
\(161\) | −8.07295 | + | 13.9828i | −0.636238 | + | 1.10200i | ||||
\(162\) | −6.23607 | + | 10.8012i | −0.489952 | + | 0.848621i | ||||
\(163\) | 1.76393 | 0.138162 | 0.0690809 | − | 0.997611i | \(-0.477993\pi\) | ||||
0.0690809 | + | 0.997611i | \(0.477993\pi\) | |||||||
\(164\) | −1.85410 | −0.144781 | ||||||||
\(165\) | 1.00000 | − | 1.73205i | 0.0778499 | − | 0.134840i | ||||
\(166\) | −6.85410 | − | 11.8717i | −0.531981 | − | 0.921419i | ||||
\(167\) | −10.1180 | + | 17.5249i | −0.782957 | + | 1.35612i | 0.147255 | + | 0.989099i | \(0.452956\pi\) |
−0.930212 | + | 0.367023i | \(0.880377\pi\) | |||||||
\(168\) | 1.28115 | + | 2.21902i | 0.0988431 | + | 0.171201i | ||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0901699 | −0.00687539 | ||||||||
\(173\) | 0.236068 | + | 0.408882i | 0.0179479 | + | 0.0310867i | 0.874860 | − | 0.484376i | \(-0.160953\pi\) |
−0.856912 | + | 0.515463i | \(0.827620\pi\) | |||||||
\(174\) | 1.11803 | + | 1.93649i | 0.0847579 | + | 0.146805i | ||||
\(175\) | −8.20820 | + | 14.2170i | −0.620482 | + | 1.07471i | ||||
\(176\) | −3.92705 | − | 6.80185i | −0.296013 | − | 0.512709i | ||||
\(177\) | −0.0623059 | + | 0.107917i | −0.00468320 | + | 0.00811154i | ||||
\(178\) | −12.5623 | −0.941585 | ||||||||
\(179\) | 12.2361 | 0.914567 | 0.457283 | − | 0.889321i | \(-0.348823\pi\) | ||||
0.457283 | + | 0.889321i | \(0.348823\pi\) | |||||||
\(180\) | 2.85410 | − | 4.94345i | 0.212732 | − | 0.368463i | ||||
\(181\) | −6.00000 | + | 10.3923i | −0.445976 | + | 0.772454i | −0.998120 | − | 0.0612954i | \(-0.980477\pi\) |
0.552143 | + | 0.833749i | \(0.313810\pi\) | |||||||
\(182\) | −4.85410 | −0.359810 | ||||||||
\(183\) | −3.90983 | −0.289023 | ||||||||
\(184\) | 6.01722 | − | 10.4221i | 0.443595 | − | 0.768330i | ||||
\(185\) | −14.3262 | − | 24.8138i | −1.05329 | − | 1.82434i | ||||
\(186\) | 2.73607 | − | 4.73901i | 0.200618 | − | 0.347481i | ||||
\(187\) | 0.618034 | + | 1.07047i | 0.0451951 | + | 0.0782802i | ||||
\(188\) | −0.927051 | − | 1.60570i | −0.0676121 | − | 0.117108i | ||||
\(189\) | −6.70820 | −0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2361 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(192\) | −0.809017 | − | 1.40126i | −0.0583858 | − | 0.101127i | ||||
\(193\) | −2.52786 | − | 4.37839i | −0.181960 | − | 0.315163i | 0.760588 | − | 0.649235i | \(-0.224911\pi\) |
−0.942548 | + | 0.334071i | \(0.891577\pi\) | |||||||
\(194\) | −11.2082 | + | 19.4132i | −0.804702 | + | 1.39379i | ||||
\(195\) | 0.618034 | + | 1.07047i | 0.0442583 | + | 0.0766577i | ||||
\(196\) | −0.618034 | + | 1.07047i | −0.0441453 | + | 0.0764619i | ||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 7.47214 | 0.531022 | ||||||||
\(199\) | 6.70820 | − | 11.6190i | 0.475532 | − | 0.823646i | −0.524075 | − | 0.851672i | \(-0.675589\pi\) |
0.999607 | + | 0.0280265i | \(0.00892227\pi\) | |||||||
\(200\) | 6.11803 | − | 10.5967i | 0.432610 | − | 0.749303i | ||||
\(201\) | −2.67376 | −0.188593 | ||||||||
\(202\) | −14.8541 | −1.04513 | ||||||||
\(203\) | 5.42705 | − | 9.39993i | 0.380904 | − | 0.659746i | ||||
\(204\) | −0.0901699 | − | 0.156179i | −0.00631316 | − | 0.0109347i | ||||
\(205\) | 4.85410 | − | 8.40755i | 0.339025 | − | 0.587209i | ||||
\(206\) | −11.5902 | − | 20.0748i | −0.807525 | − | 1.39868i | ||||
\(207\) | 7.68034 | + | 13.3027i | 0.533821 | + | 0.924604i | ||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.00000 | 0.414039 | ||||||||
\(211\) | 1.92705 | + | 3.33775i | 0.132664 | + | 0.229780i | 0.924703 | − | 0.380690i | \(-0.124314\pi\) |
−0.792039 | + | 0.610471i | \(0.790980\pi\) | |||||||
\(212\) | 1.95492 | + | 3.38601i | 0.134264 | + | 0.232552i | ||||
\(213\) | 1.42705 | − | 2.47172i | 0.0977799 | − | 0.169360i | ||||
\(214\) | −13.2812 | − | 23.0036i | −0.907881 | − | 1.57250i | ||||
\(215\) | 0.236068 | − | 0.408882i | 0.0160997 | − | 0.0278855i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | −26.5623 | −1.80317 | ||||||||
\(218\) | 2.66312 | − | 4.61266i | 0.180369 | − | 0.312409i | ||||
\(219\) | 0.517221 | − | 0.895853i | 0.0349506 | − | 0.0605361i | ||||
\(220\) | −3.23607 | −0.218176 | ||||||||
\(221\) | −0.763932 | −0.0513876 | ||||||||
\(222\) | −2.73607 | + | 4.73901i | −0.183633 | + | 0.318061i | ||||
\(223\) | 5.82624 | + | 10.0913i | 0.390154 | + | 0.675766i | 0.992470 | − | 0.122492i | \(-0.0390885\pi\) |
−0.602316 | + | 0.798258i | \(0.705755\pi\) | |||||||
\(224\) | 5.07295 | − | 8.78661i | 0.338951 | − | 0.587080i | ||||
\(225\) | 7.80902 | + | 13.5256i | 0.520601 | + | 0.901708i | ||||
\(226\) | −5.47214 | − | 9.47802i | −0.364001 | − | 0.630468i | ||||
\(227\) | 16.4164 | 1.08960 | 0.544798 | − | 0.838568i | \(-0.316606\pi\) | ||||
0.544798 | + | 0.838568i | \(0.316606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6180 | −0.899905 | −0.449953 | − | 0.893052i | \(-0.648559\pi\) | ||||
−0.449953 | + | 0.893052i | \(0.648559\pi\) | |||||||
\(230\) | −14.0902 | − | 24.4049i | −0.929078 | − | 1.60921i | ||||
\(231\) | 0.927051 | + | 1.60570i | 0.0609955 | + | 0.105647i | ||||
\(232\) | −4.04508 | + | 7.00629i | −0.265573 | + | 0.459986i | ||||
\(233\) | −2.26393 | − | 3.92125i | −0.148315 | − | 0.256889i | 0.782290 | − | 0.622915i | \(-0.214052\pi\) |
−0.930605 | + | 0.366025i | \(0.880718\pi\) | |||||||
\(234\) | −2.30902 | + | 3.99933i | −0.150945 | + | 0.261445i | ||||
\(235\) | 9.70820 | 0.633293 | ||||||||
\(236\) | 0.201626 | 0.0131247 | ||||||||
\(237\) | −2.56231 | + | 4.43804i | −0.166440 | + | 0.288282i | ||||
\(238\) | −1.85410 | + | 3.21140i | −0.120184 | + | 0.208164i | ||||
\(239\) | −0.326238 | −0.0211026 | −0.0105513 | − | 0.999944i | \(-0.503359\pi\) | ||||
−0.0105513 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(240\) | −6.00000 | −0.387298 | ||||||||
\(241\) | −1.59017 | + | 2.75426i | −0.102432 | + | 0.177417i | −0.912686 | − | 0.408661i | \(-0.865996\pi\) |
0.810254 | + | 0.586079i | \(0.199329\pi\) | |||||||
\(242\) | 6.78115 | + | 11.7453i | 0.435909 | + | 0.755017i | ||||
\(243\) | −4.82624 | + | 8.35929i | −0.309603 | + | 0.536249i | ||||
\(244\) | 3.16312 | + | 5.47868i | 0.202498 | + | 0.350737i | ||||
\(245\) | −3.23607 | − | 5.60503i | −0.206745 | − | 0.358092i | ||||
\(246\) | −1.85410 | −0.118213 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 19.7984 | 1.25720 | ||||||||
\(249\) | −1.61803 | − | 2.80252i | −0.102539 | − | 0.177602i | ||||
\(250\) | −1.23607 | − | 2.14093i | −0.0781758 | − | 0.135404i | ||||
\(251\) | 12.6803 | − | 21.9630i | 0.800376 | − | 1.38629i | −0.118993 | − | 0.992895i | \(-0.537967\pi\) |
0.919369 | − | 0.393397i | \(-0.128700\pi\) | |||||||
\(252\) | 2.64590 | + | 4.58283i | 0.166676 | + | 0.288691i | ||||
\(253\) | 4.35410 | − | 7.54153i | 0.273740 | − | 0.474132i | ||||
\(254\) | 9.32624 | 0.585180 | ||||||||
\(255\) | 0.944272 | 0.0591326 | ||||||||
\(256\) | −6.78115 | + | 11.7453i | −0.423822 | + | 0.734081i | ||||
\(257\) | −10.1803 | + | 17.6329i | −0.635032 | + | 1.09991i | 0.351476 | + | 0.936197i | \(0.385680\pi\) |
−0.986508 | + | 0.163711i | \(0.947654\pi\) | |||||||
\(258\) | −0.0901699 | −0.00561374 | ||||||||
\(259\) | 26.5623 | 1.65050 | ||||||||
\(260\) | 1.00000 | − | 1.73205i | 0.0620174 | − | 0.107417i | ||||
\(261\) | −5.16312 | − | 8.94278i | −0.319589 | − | 0.553544i | ||||
\(262\) | −12.2082 | + | 21.1452i | −0.754225 | + | 1.30636i | ||||
\(263\) | 7.47214 | + | 12.9421i | 0.460752 | + | 0.798045i | 0.998999 | − | 0.0447419i | \(-0.0142466\pi\) |
−0.538247 | + | 0.842787i | \(0.680913\pi\) | |||||||
\(264\) | −0.690983 | − | 1.19682i | −0.0425271 | − | 0.0736590i | ||||
\(265\) | −20.4721 | −1.25759 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.96556 | −0.181489 | ||||||||
\(268\) | 2.16312 | + | 3.74663i | 0.132134 | + | 0.228862i | ||||
\(269\) | −15.1631 | − | 26.2633i | −0.924512 | − | 1.60130i | −0.792345 | − | 0.610074i | \(-0.791140\pi\) |
−0.132167 | − | 0.991227i | \(-0.542194\pi\) | |||||||
\(270\) | 5.85410 | − | 10.1396i | 0.356269 | − | 0.617077i | ||||
\(271\) | −0.572949 | − | 0.992377i | −0.0348042 | − | 0.0602826i | 0.848099 | − | 0.529838i | \(-0.177747\pi\) |
−0.882903 | + | 0.469556i | \(0.844414\pi\) | |||||||
\(272\) | 1.85410 | − | 3.21140i | 0.112421 | − | 0.194720i | ||||
\(273\) | −1.14590 | −0.0693529 | ||||||||
\(274\) | 12.0902 | 0.730394 | ||||||||
\(275\) | 4.42705 | − | 7.66788i | 0.266961 | − | 0.462390i | ||||
\(276\) | −0.635255 | + | 1.10029i | −0.0382379 | + | 0.0662299i | ||||
\(277\) | 11.4164 | 0.685945 | 0.342973 | − | 0.939345i | \(-0.388566\pi\) | ||||
0.342973 | + | 0.939345i | \(0.388566\pi\) | |||||||
\(278\) | 23.9443 | 1.43608 | ||||||||
\(279\) | −12.6353 | + | 21.8849i | −0.756453 | + | 1.31021i | ||||
\(280\) | 10.8541 | + | 18.7999i | 0.648657 | + | 1.12351i | ||||
\(281\) | 14.7533 | − | 25.5534i | 0.880107 | − | 1.52439i | 0.0288869 | − | 0.999583i | \(-0.490804\pi\) |
0.851221 | − | 0.524808i | \(-0.175863\pi\) | |||||||
\(282\) | −0.927051 | − | 1.60570i | −0.0552051 | − | 0.0956180i | ||||
\(283\) | −13.0172 | − | 22.5465i | −0.773793 | − | 1.34025i | −0.935470 | − | 0.353406i | \(-0.885023\pi\) |
0.161677 | − | 0.986844i | \(-0.448310\pi\) | |||||||
\(284\) | −4.61803 | −0.274030 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.61803 | 0.154808 | ||||||||
\(287\) | 4.50000 | + | 7.79423i | 0.265627 | + | 0.460079i | ||||
\(288\) | −4.82624 | − | 8.35929i | −0.284389 | − | 0.492576i | ||||
\(289\) | 8.20820 | − | 14.2170i | 0.482836 | − | 0.836296i | ||||
\(290\) | 9.47214 | + | 16.4062i | 0.556223 | + | 0.963406i | ||||
\(291\) | −2.64590 | + | 4.58283i | −0.155105 | + | 0.268650i | ||||
\(292\) | −1.67376 | −0.0979495 | ||||||||
\(293\) | −10.1459 | −0.592730 | −0.296365 | − | 0.955075i | \(-0.595774\pi\) | ||||
−0.296365 | + | 0.955075i | \(0.595774\pi\) | |||||||
\(294\) | −0.618034 | + | 1.07047i | −0.0360445 | + | 0.0624309i | ||||
\(295\) | −0.527864 | + | 0.914287i | −0.0307334 | + | 0.0532319i | ||||
\(296\) | −19.7984 | −1.15076 | ||||||||
\(297\) | 3.61803 | 0.209940 | ||||||||
\(298\) | 1.54508 | − | 2.67617i | 0.0895044 | − | 0.155026i | ||||
\(299\) | 2.69098 | + | 4.66092i | 0.155624 | + | 0.269548i | ||||
\(300\) | −0.645898 | + | 1.11873i | −0.0372909 | + | 0.0645898i | ||||
\(301\) | 0.218847 | + | 0.379054i | 0.0126141 | + | 0.0218483i | ||||
\(302\) | 17.0623 | + | 29.5528i | 0.981825 | + | 1.70057i | ||||
\(303\) | −3.50658 | −0.201448 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.1246 | −1.89671 | ||||||||
\(306\) | 1.76393 | + | 3.05522i | 0.100837 | + | 0.174655i | ||||
\(307\) | 8.66312 | + | 15.0050i | 0.494430 | + | 0.856378i | 0.999979 | − | 0.00641942i | \(-0.00204338\pi\) |
−0.505549 | + | 0.862798i | \(0.668710\pi\) | |||||||
\(308\) | 1.50000 | − | 2.59808i | 0.0854704 | − | 0.148039i | ||||
\(309\) | −2.73607 | − | 4.73901i | −0.155649 | − | 0.269593i | ||||
\(310\) | 23.1803 | − | 40.1495i | 1.31655 | − | 2.28034i | ||||
\(311\) | 12.6525 | 0.717456 | 0.358728 | − | 0.933442i | \(-0.383211\pi\) | ||||
0.358728 | + | 0.933442i | \(0.383211\pi\) | |||||||
\(312\) | 0.854102 | 0.0483540 | ||||||||
\(313\) | 5.66312 | − | 9.80881i | 0.320098 | − | 0.554427i | −0.660410 | − | 0.750906i | \(-0.729617\pi\) |
0.980508 | + | 0.196479i | \(0.0629507\pi\) | |||||||
\(314\) | 14.4443 | − | 25.0182i | 0.815137 | − | 1.41186i | ||||
\(315\) | −27.7082 | −1.56118 | ||||||||
\(316\) | 8.29180 | 0.466450 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 1.95492 | + | 3.38601i | 0.109626 | + | 0.189878i | ||||
\(319\) | −2.92705 | + | 5.06980i | −0.163883 | + | 0.283854i | ||||
\(320\) | −6.85410 | − | 11.8717i | −0.383156 | − | 0.663646i | ||||
\(321\) | −3.13525 | − | 5.43042i | −0.174993 | − | 0.303097i | ||||
\(322\) | 26.1246 | 1.45587 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.76393 | 0.264663 | ||||||||
\(325\) | 2.73607 | + | 4.73901i | 0.151770 | + | 0.262873i | ||||
\(326\) | −1.42705 | − | 2.47172i | −0.0790370 | − | 0.136896i | ||||
\(327\) | 0.628677 | − | 1.08890i | 0.0347659 | − | 0.0602163i | ||||
\(328\) | −3.35410 | − | 5.80948i | −0.185199 | − | 0.320775i | ||||
\(329\) | −4.50000 | + | 7.79423i | −0.248093 | + | 0.429710i | ||||
\(330\) | −3.23607 | −0.178140 | ||||||||
\(331\) | 10.9443 | 0.601552 | 0.300776 | − | 0.953695i | \(-0.402754\pi\) | ||||
0.300776 | + | 0.953695i | \(0.402754\pi\) | |||||||
\(332\) | −2.61803 | + | 4.53457i | −0.143683 | + | 0.248867i | ||||
\(333\) | 12.6353 | − | 21.8849i | 0.692408 | − | 1.19929i | ||||
\(334\) | 32.7426 | 1.79160 | ||||||||
\(335\) | −22.6525 | −1.23764 | ||||||||
\(336\) | 2.78115 | − | 4.81710i | 0.151724 | − | 0.262794i | ||||
\(337\) | 8.56231 | + | 14.8303i | 0.466419 | + | 0.807861i | 0.999264 | − | 0.0383518i | \(-0.0122107\pi\) |
−0.532846 | + | 0.846212i | \(0.678877\pi\) | |||||||
\(338\) | 9.70820 | − | 16.8151i | 0.528057 | − | 0.914621i | ||||
\(339\) | −1.29180 | − | 2.23746i | −0.0701607 | − | 0.121522i | ||||
\(340\) | −0.763932 | − | 1.32317i | −0.0414300 | − | 0.0717589i | ||||
\(341\) | 14.3262 | 0.775809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −0.163119 | − | 0.282530i | −0.00879478 | − | 0.0152330i | ||||
\(345\) | −3.32624 | − | 5.76121i | −0.179079 | − | 0.310173i | ||||
\(346\) | 0.381966 | − | 0.661585i | 0.0205346 | − | 0.0355670i | ||||
\(347\) | 12.7082 | + | 22.0113i | 0.682212 | + | 1.18163i | 0.974304 | + | 0.225236i | \(0.0723153\pi\) |
−0.292092 | + | 0.956390i | \(0.594351\pi\) | |||||||
\(348\) | 0.427051 | − | 0.739674i | 0.0228923 | − | 0.0396507i | ||||
\(349\) | −20.9787 | −1.12296 | −0.561482 | − | 0.827489i | \(-0.689769\pi\) | ||||
−0.561482 | + | 0.827489i | \(0.689769\pi\) | |||||||
\(350\) | 26.5623 | 1.41981 | ||||||||
\(351\) | −1.11803 | + | 1.93649i | −0.0596762 | + | 0.103362i | ||||
\(352\) | −2.73607 | + | 4.73901i | −0.145833 | + | 0.252590i | ||||
\(353\) | 24.4508 | 1.30139 | 0.650694 | − | 0.759340i | \(-0.274478\pi\) | ||||
0.650694 | + | 0.759340i | \(0.274478\pi\) | |||||||
\(354\) | 0.201626 | 0.0107163 | ||||||||
\(355\) | 12.0902 | − | 20.9408i | 0.641680 | − | 1.11142i | ||||
\(356\) | 2.39919 | + | 4.15551i | 0.127157 | + | 0.220242i | ||||
\(357\) | −0.437694 | + | 0.758108i | −0.0231652 | + | 0.0401234i | ||||
\(358\) | −9.89919 | − | 17.1459i | −0.523188 | − | 0.906189i | ||||
\(359\) | −3.51722 | − | 6.09201i | −0.185632 | − | 0.321524i | 0.758157 | − | 0.652072i | \(-0.226100\pi\) |
−0.943789 | + | 0.330548i | \(0.892767\pi\) | |||||||
\(360\) | 20.6525 | 1.08848 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 19.4164 | 1.02050 | ||||||||
\(363\) | 1.60081 | + | 2.77269i | 0.0840209 | + | 0.145528i | ||||
\(364\) | 0.927051 | + | 1.60570i | 0.0485907 | + | 0.0841615i | ||||
\(365\) | 4.38197 | − | 7.58979i | 0.229363 | − | 0.397268i | ||||
\(366\) | 3.16312 | + | 5.47868i | 0.165339 | + | 0.286375i | ||||
\(367\) | 7.97214 | − | 13.8081i | 0.416142 | − | 0.720779i | −0.579405 | − | 0.815039i | \(-0.696715\pi\) |
0.995548 | + | 0.0942602i | \(0.0300485\pi\) | |||||||
\(368\) | −26.1246 | −1.36184 | ||||||||
\(369\) | 8.56231 | 0.445736 | ||||||||
\(370\) | −23.1803 | + | 40.1495i | −1.20509 | + | 2.08727i | ||||
\(371\) | 9.48936 | − | 16.4360i | 0.492663 | − | 0.853317i | ||||
\(372\) | −2.09017 | −0.108370 | ||||||||
\(373\) | −5.47214 | −0.283336 | −0.141668 | − | 0.989914i | \(-0.545247\pi\) | ||||
−0.141668 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(374\) | 1.00000 | − | 1.73205i | 0.0517088 | − | 0.0895622i | ||||
\(375\) | −0.291796 | − | 0.505406i | −0.0150683 | − | 0.0260990i | ||||
\(376\) | 3.35410 | − | 5.80948i | 0.172975 | − | 0.299601i | ||||
\(377\) | −1.80902 | − | 3.13331i | −0.0931691 | − | 0.161374i | ||||
\(378\) | 5.42705 | + | 9.39993i | 0.279137 | + | 0.483480i | ||||
\(379\) | −15.1246 | −0.776899 | −0.388450 | − | 0.921470i | \(-0.626989\pi\) | ||||
−0.388450 | + | 0.921470i | \(0.626989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.20163 | 0.112793 | ||||||||
\(382\) | −11.5172 | − | 19.9484i | −0.589272 | − | 1.02065i | ||||
\(383\) | −0.190983 | − | 0.330792i | −0.00975878 | − | 0.0169027i | 0.861105 | − | 0.508428i | \(-0.169773\pi\) |
−0.870864 | + | 0.491525i | \(0.836440\pi\) | |||||||
\(384\) | −2.60081 | + | 4.50474i | −0.132722 | + | 0.229882i | ||||
\(385\) | 7.85410 | + | 13.6037i | 0.400282 | + | 0.693309i | ||||
\(386\) | −4.09017 | + | 7.08438i | −0.208184 | + | 0.360586i | ||||
\(387\) | 0.416408 | 0.0211672 | ||||||||
\(388\) | 8.56231 | 0.434685 | ||||||||
\(389\) | −4.63525 | + | 8.02850i | −0.235017 | + | 0.407061i | −0.959278 | − | 0.282465i | \(-0.908848\pi\) |
0.724261 | + | 0.689526i | \(0.242181\pi\) | |||||||
\(390\) | 1.00000 | − | 1.73205i | 0.0506370 | − | 0.0877058i | ||||
\(391\) | 4.11146 | 0.207925 | ||||||||
\(392\) | −4.47214 | −0.225877 | ||||||||
\(393\) | −2.88197 | + | 4.99171i | −0.145376 | + | 0.251799i | ||||
\(394\) | −2.42705 | − | 4.20378i | −0.122273 | − | 0.211783i | ||||
\(395\) | −21.7082 | + | 37.5997i | −1.09226 | + | 1.89185i | ||||
\(396\) | −1.42705 | − | 2.47172i | −0.0717120 | − | 0.124209i | ||||
\(397\) | 5.73607 | + | 9.93516i | 0.287885 | + | 0.498631i | 0.973305 | − | 0.229517i | \(-0.0737146\pi\) |
−0.685420 | + | 0.728148i | \(0.740381\pi\) | |||||||
\(398\) | −21.7082 | −1.08813 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.5623 | −1.32812 | ||||||||
\(401\) | 17.9443 | + | 31.0804i | 0.896094 | + | 1.55208i | 0.832445 | + | 0.554108i | \(0.186941\pi\) |
0.0636496 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(402\) | 2.16312 | + | 3.74663i | 0.107887 | + | 0.186865i | ||||
\(403\) | −4.42705 | + | 7.66788i | −0.220527 | + | 0.381964i | ||||
\(404\) | 2.83688 | + | 4.91362i | 0.141140 | + | 0.244462i | ||||
\(405\) | −12.4721 | + | 21.6024i | −0.619745 | + | 1.07343i | ||||
\(406\) | −17.5623 | −0.871603 | ||||||||
\(407\) | −14.3262 | −0.710125 | ||||||||
\(408\) | 0.326238 | − | 0.565061i | 0.0161512 | − | 0.0279747i | ||||
\(409\) | 4.14590 | − | 7.18091i | 0.205001 | − | 0.355073i | −0.745132 | − | 0.666917i | \(-0.767613\pi\) |
0.950133 | + | 0.311844i | \(0.100947\pi\) | |||||||
\(410\) | −15.7082 | −0.775773 | ||||||||
\(411\) | 2.85410 | 0.140782 | ||||||||
\(412\) | −4.42705 | + | 7.66788i | −0.218105 | + | 0.377769i | ||||
\(413\) | −0.489357 | − | 0.847591i | −0.0240797 | − | 0.0417072i | ||||
\(414\) | 12.4271 | − | 21.5243i | 0.610756 | − | 1.05786i | ||||
\(415\) | −13.7082 | − | 23.7433i | −0.672909 | − | 1.16551i | ||||
\(416\) | −1.69098 | − | 2.92887i | −0.0829073 | − | 0.143600i | ||||
\(417\) | 5.65248 | 0.276803 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.94427 | −0.436956 | −0.218478 | − | 0.975842i | \(-0.570109\pi\) | ||||
−0.218478 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(420\) | −1.14590 | − | 1.98475i | −0.0559141 | − | 0.0968461i | ||||
\(421\) | 13.7361 | + | 23.7916i | 0.669455 | + | 1.15953i | 0.978057 | + | 0.208339i | \(0.0668056\pi\) |
−0.308602 | + | 0.951191i | \(0.599861\pi\) | |||||||
\(422\) | 3.11803 | − | 5.40059i | 0.151784 | − | 0.262897i | ||||
\(423\) | 4.28115 | + | 7.41517i | 0.208157 | + | 0.360538i | ||||
\(424\) | −7.07295 | + | 12.2507i | −0.343493 | + | 0.594947i | ||||
\(425\) | 4.18034 | 0.202776 | ||||||||
\(426\) | −4.61803 | −0.223744 | ||||||||
\(427\) | 15.3541 | − | 26.5941i | 0.743037 | − | 1.28698i | ||||
\(428\) | −5.07295 | + | 8.78661i | −0.245210 | + | 0.424717i | ||||
\(429\) | 0.618034 | 0.0298390 | ||||||||
\(430\) | −0.763932 | −0.0368401 | ||||||||
\(431\) | −13.8262 | + | 23.9477i | −0.665986 | + | 1.15352i | 0.313030 | + | 0.949743i | \(0.398656\pi\) |
−0.979017 | + | 0.203779i | \(0.934678\pi\) | |||||||
\(432\) | −5.42705 | − | 9.39993i | −0.261109 | − | 0.452254i | ||||
\(433\) | 1.71885 | − | 2.97713i | 0.0826025 | − | 0.143072i | −0.821765 | − | 0.569827i | \(-0.807010\pi\) |
0.904367 | + | 0.426755i | \(0.140343\pi\) | |||||||
\(434\) | 21.4894 | + | 37.2207i | 1.03152 | + | 1.78665i | ||||
\(435\) | 2.23607 | + | 3.87298i | 0.107211 | + | 0.185695i | ||||
\(436\) | −2.03444 | −0.0974321 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.67376 | −0.0799754 | ||||||||
\(439\) | 17.2984 | + | 29.9617i | 0.825606 | + | 1.42999i | 0.901455 | + | 0.432873i | \(0.142500\pi\) |
−0.0758487 | + | 0.997119i | \(0.524167\pi\) | |||||||
\(440\) | −5.85410 | − | 10.1396i | −0.279083 | − | 0.483387i | ||||
\(441\) | 2.85410 | − | 4.94345i | 0.135910 | − | 0.235402i | ||||
\(442\) | 0.618034 | + | 1.07047i | 0.0293969 | + | 0.0509169i | ||||
\(443\) | 3.79180 | − | 6.56758i | 0.180154 | − | 0.312035i | −0.761779 | − | 0.647837i | \(-0.775674\pi\) |
0.941933 | + | 0.335802i | \(0.109007\pi\) | |||||||
\(444\) | 2.09017 | 0.0991951 | ||||||||
\(445\) | −25.1246 | −1.19102 | ||||||||
\(446\) | 9.42705 | − | 16.3281i | 0.446384 | − | 0.773159i | ||||
\(447\) | 0.364745 | − | 0.631757i | 0.0172519 | − | 0.0298811i | ||||
\(448\) | 12.7082 | 0.600406 | ||||||||
\(449\) | 2.88854 | 0.136319 | 0.0681594 | − | 0.997674i | \(-0.478287\pi\) | ||||
0.0681594 | + | 0.997674i | \(0.478287\pi\) | |||||||
\(450\) | 12.6353 | − | 21.8849i | 0.595632 | − | 1.03166i | ||||
\(451\) | −2.42705 | − | 4.20378i | −0.114285 | − | 0.197948i | ||||
\(452\) | −2.09017 | + | 3.62028i | −0.0983133 | + | 0.170284i | ||||
\(453\) | 4.02786 | + | 6.97647i | 0.189246 | + | 0.327783i | ||||
\(454\) | −13.2812 | − | 23.0036i | −0.623315 | − | 1.07961i | ||||
\(455\) | −9.70820 | −0.455128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.7082 | 0.921911 | 0.460955 | − | 0.887423i | \(-0.347507\pi\) | ||||
0.460955 | + | 0.887423i | \(0.347507\pi\) | |||||||
\(458\) | 11.0172 | + | 19.0824i | 0.514801 | + | 0.891661i | ||||
\(459\) | 0.854102 | + | 1.47935i | 0.0398661 | + | 0.0690501i | ||||
\(460\) | −5.38197 | + | 9.32184i | −0.250935 | + | 0.434633i | ||||
\(461\) | −10.4721 | − | 18.1383i | −0.487736 | − | 0.844784i | 0.512165 | − | 0.858887i | \(-0.328844\pi\) |
−0.999901 | + | 0.0141038i | \(0.995510\pi\) | |||||||
\(462\) | 1.50000 | − | 2.59808i | 0.0697863 | − | 0.120873i | ||||
\(463\) | 28.2705 | 1.31384 | 0.656921 | − | 0.753959i | \(-0.271858\pi\) | ||||
0.656921 | + | 0.753959i | \(0.271858\pi\) | |||||||
\(464\) | 17.5623 | 0.815310 | ||||||||
\(465\) | 5.47214 | − | 9.47802i | 0.253764 | − | 0.439533i | ||||
\(466\) | −3.66312 | + | 6.34471i | −0.169691 | + | 0.293913i | ||||
\(467\) | −15.9443 | −0.737813 | −0.368906 | − | 0.929467i | \(-0.620268\pi\) | ||||
−0.368906 | + | 0.929467i | \(0.620268\pi\) | |||||||
\(468\) | 1.76393 | 0.0815378 | ||||||||
\(469\) | 10.5000 | − | 18.1865i | 0.484845 | − | 0.839776i | ||||
\(470\) | −7.85410 | − | 13.6037i | −0.362283 | − | 0.627492i | ||||
\(471\) | 3.40983 | − | 5.90600i | 0.157117 | − | 0.272134i | ||||
\(472\) | 0.364745 | + | 0.631757i | 0.0167888 | + | 0.0290790i | ||||
\(473\) | −0.118034 | − | 0.204441i | −0.00542721 | − | 0.00940020i | ||||
\(474\) | 8.29180 | 0.380855 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.41641 | 0.0649209 | ||||||||
\(477\) | −9.02786 | − | 15.6367i | −0.413357 | − | 0.715956i | ||||
\(478\) | 0.263932 | + | 0.457144i | 0.0120720 | + | 0.0209093i | ||||
\(479\) | −11.5451 | + | 19.9967i | −0.527508 | + | 0.913671i | 0.471978 | + | 0.881611i | \(0.343540\pi\) |
−0.999486 | + | 0.0320608i | \(0.989793\pi\) | |||||||
\(480\) | 2.09017 | + | 3.62028i | 0.0954028 | + | 0.165242i | ||||
\(481\) | 4.42705 | − | 7.66788i | 0.201856 | − | 0.349625i | ||||
\(482\) | 5.14590 | 0.234389 | ||||||||
\(483\) | 6.16718 | 0.280617 | ||||||||
\(484\) | 2.59017 | − | 4.48631i | 0.117735 | − | 0.203923i | ||||
\(485\) | −22.4164 | + | 38.8264i | −1.01788 | + | 1.76301i | ||||
\(486\) | 15.6180 | 0.708448 | ||||||||
\(487\) | 4.18034 | 0.189429 | 0.0947146 | − | 0.995504i | \(-0.469806\pi\) | ||||
0.0947146 | + | 0.995504i | \(0.469806\pi\) | |||||||
\(488\) | −11.4443 | + | 19.8221i | −0.518058 | + | 0.897303i | ||||
\(489\) | −0.336881 | − | 0.583495i | −0.0152343 | − | 0.0263866i | ||||
\(490\) | −5.23607 | + | 9.06914i | −0.236541 | + | 0.409702i | ||||
\(491\) | 10.6074 | + | 18.3725i | 0.478705 | + | 0.829141i | 0.999702 | − | 0.0244174i | \(-0.00777307\pi\) |
−0.520997 | + | 0.853559i | \(0.674440\pi\) | |||||||
\(492\) | 0.354102 | + | 0.613323i | 0.0159641 | + | 0.0276507i | ||||
\(493\) | −2.76393 | −0.124481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.9443 | 0.671695 | ||||||||
\(496\) | −21.4894 | − | 37.2207i | −0.964901 | − | 1.67126i | ||||
\(497\) | 11.2082 | + | 19.4132i | 0.502757 | + | 0.870800i | ||||
\(498\) | −2.61803 | + | 4.53457i | −0.117317 | + | 0.203199i | ||||
\(499\) | −12.5623 | − | 21.7586i | −0.562366 | − | 0.974047i | −0.997289 | − | 0.0735791i | \(-0.976558\pi\) |
0.434923 | − | 0.900467i | \(-0.356775\pi\) | |||||||
\(500\) | −0.472136 | + | 0.817763i | −0.0211146 | + | 0.0365715i | ||||
\(501\) | 7.72949 | 0.345328 | ||||||||
\(502\) | −41.0344 | −1.83146 | ||||||||
\(503\) | −17.9164 | + | 31.0321i | −0.798853 | + | 1.38365i | 0.121510 | + | 0.992590i | \(0.461226\pi\) |
−0.920363 | + | 0.391064i | \(0.872107\pi\) | |||||||
\(504\) | −9.57295 | + | 16.5808i | −0.426413 | + | 0.738569i | ||||
\(505\) | −29.7082 | −1.32200 | ||||||||
\(506\) | −14.0902 | −0.626384 | ||||||||
\(507\) | 2.29180 | − | 3.96951i | 0.101782 | − | 0.176292i | ||||
\(508\) | −1.78115 | − | 3.08505i | −0.0790259 | − | 0.136877i | ||||
\(509\) | −1.01722 | + | 1.76188i | −0.0450875 | + | 0.0780939i | −0.887688 | − | 0.460445i | \(-0.847690\pi\) |
0.842601 | + | 0.538538i | \(0.181023\pi\) | |||||||
\(510\) | −0.763932 | − | 1.32317i | −0.0338275 | − | 0.0585909i | ||||
\(511\) | 4.06231 | + | 7.03612i | 0.179706 | + | 0.311260i | ||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.9443 | 1.45311 | ||||||||
\(515\) | −23.1803 | − | 40.1495i | −1.02145 | − | 1.76920i | ||||
\(516\) | 0.0172209 | + | 0.0298275i | 0.000758109 | + | 0.00131308i | ||||
\(517\) | 2.42705 | − | 4.20378i | 0.106742 | − | 0.184882i | ||||
\(518\) | −21.4894 | − | 37.2207i | −0.944188 | − | 1.63538i | ||||
\(519\) | 0.0901699 | − | 0.156179i | 0.00395802 | − | 0.00685549i | ||||
\(520\) | 7.23607 | 0.317323 | ||||||||
\(521\) | 6.27051 | 0.274716 | 0.137358 | − | 0.990521i | \(-0.456139\pi\) | ||||
0.137358 | + | 0.990521i | \(0.456139\pi\) | |||||||
\(522\) | −8.35410 | + | 14.4697i | −0.365649 | + | 0.633323i | ||||
\(523\) | 2.20820 | − | 3.82472i | 0.0965580 | − | 0.167243i | −0.813700 | − | 0.581285i | \(-0.802550\pi\) |
0.910258 | + | 0.414042i | \(0.135883\pi\) | |||||||
\(524\) | 9.32624 | 0.407419 | ||||||||
\(525\) | 6.27051 | 0.273667 | ||||||||
\(526\) | 12.0902 | − | 20.9408i | 0.527156 | − | 0.913062i | ||||
\(527\) | 3.38197 | + | 5.85774i | 0.147321 | + | 0.255167i | ||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | −2.98278 | − | 5.16632i | −0.129686 | − | 0.224623i | ||||
\(530\) | 16.5623 | + | 28.6868i | 0.719421 | + | 1.24607i | ||||
\(531\) | −0.931116 | −0.0404070 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 2.39919 | + | 4.15551i | 0.103823 | + | 0.179827i | ||||
\(535\) | −26.5623 | − | 46.0073i | −1.14839 | − | 1.98907i | ||||
\(536\) | −7.82624 | + | 13.5554i | −0.338042 | + | 0.585506i | ||||
\(537\) | −2.33688 | − | 4.04760i | −0.100844 | − | 0.174667i | ||||
\(538\) | −24.5344 | + | 42.4949i | −1.05775 | + | 1.83209i | ||||
\(539\) | −3.23607 | −0.139387 | ||||||||
\(540\) | −4.47214 | −0.192450 | ||||||||
\(541\) | 14.9164 | − | 25.8360i | 0.641306 | − | 1.11078i | −0.343835 | − | 0.939030i | \(-0.611726\pi\) |
0.985141 | − | 0.171745i | \(-0.0549406\pi\) | |||||||
\(542\) | −0.927051 | + | 1.60570i | −0.0398202 | + | 0.0689707i | ||||
\(543\) | 4.58359 | 0.196701 | ||||||||
\(544\) | −2.58359 | −0.110771 | ||||||||
\(545\) | 5.32624 | − | 9.22531i | 0.228151 | − | 0.395169i | ||||
\(546\) | 0.927051 | + | 1.60570i | 0.0396741 | + | 0.0687176i | ||||
\(547\) | 13.4615 | − | 23.3160i | 0.575572 | − | 0.996920i | −0.420407 | − | 0.907335i | \(-0.638113\pi\) |
0.995979 | − | 0.0895843i | \(-0.0285538\pi\) | |||||||
\(548\) | −2.30902 | − | 3.99933i | −0.0986363 | − | 0.170843i | ||||
\(549\) | −14.6074 | − | 25.3007i | −0.623428 | − | 1.07981i | ||||
\(550\) | −14.3262 | −0.610873 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −4.59675 | −0.195651 | ||||||||
\(553\) | −20.1246 | − | 34.8569i | −0.855786 | − | 1.48226i | ||||
\(554\) | −9.23607 | − | 15.9973i | −0.392403 | − | 0.679662i | ||||
\(555\) | −5.47214 | + | 9.47802i | −0.232279 | + | 0.402319i | ||||
\(556\) | −4.57295 | − | 7.92058i | −0.193936 | − | 0.335907i | ||||
\(557\) | 0.409830 | − | 0.709846i | 0.0173651 | − | 0.0300772i | −0.857212 | − | 0.514963i | \(-0.827806\pi\) |
0.874577 | + | 0.484886i | \(0.161139\pi\) | |||||||
\(558\) | 40.8885 | 1.73095 | ||||||||
\(559\) | 0.145898 | 0.00617083 | ||||||||
\(560\) | 23.5623 | − | 40.8111i | 0.995689 | − | 1.72458i | ||||
\(561\) | 0.236068 | − | 0.408882i | 0.00996680 | − | 0.0172630i | ||||
\(562\) | −47.7426 | −2.01390 | ||||||||
\(563\) | −32.8328 | −1.38374 | −0.691869 | − | 0.722023i | \(-0.743212\pi\) | ||||
−0.691869 | + | 0.722023i | \(0.743212\pi\) | |||||||
\(564\) | −0.354102 | + | 0.613323i | −0.0149104 | + | 0.0258255i | ||||
\(565\) | −10.9443 | − | 18.9560i | −0.460429 | − | 0.797486i | ||||
\(566\) | −21.0623 | + | 36.4810i | −0.885315 | + | 1.53341i | ||||
\(567\) | −11.5623 | − | 20.0265i | −0.485571 | − | 0.841034i | ||||
\(568\) | −8.35410 | − | 14.4697i | −0.350530 | − | 0.607136i | ||||
\(569\) | 16.9098 | 0.708897 | 0.354448 | − | 0.935076i | \(-0.384669\pi\) | ||||
0.354448 | + | 0.935076i | \(0.384669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.67376 | 0.279288 | 0.139644 | − | 0.990202i | \(-0.455404\pi\) | ||||
0.139644 | + | 0.990202i | \(0.455404\pi\) | |||||||
\(572\) | −0.500000 | − | 0.866025i | −0.0209061 | − | 0.0362103i | ||||
\(573\) | −2.71885 | − | 4.70918i | −0.113581 | − | 0.196729i | ||||
\(574\) | 7.28115 | − | 12.6113i | 0.303909 | − | 0.526387i | ||||
\(575\) | −14.7254 | − | 25.5052i | −0.614093 | − | 1.06364i | ||||
\(576\) | 6.04508 | − | 10.4704i | 0.251879 | − | 0.436266i | ||||
\(577\) | −12.1246 | −0.504754 | −0.252377 | − | 0.967629i | \(-0.581212\pi\) | ||||
−0.252377 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(578\) | −26.5623 | −1.10485 | ||||||||
\(579\) | −0.965558 | + | 1.67240i | −0.0401272 | + | 0.0695024i | ||||
\(580\) | 3.61803 | − | 6.26662i | 0.150231 | − | 0.260207i | ||||
\(581\) | 25.4164 | 1.05445 | ||||||||
\(582\) | 8.56231 | 0.354919 | ||||||||
\(583\) | −5.11803 | + | 8.86469i | −0.211967 | + | 0.367138i | ||||
\(584\) | −3.02786 | − | 5.24441i | −0.125294 | − | 0.217015i | ||||
\(585\) | −4.61803 | + | 7.99867i | −0.190932 | + | 0.330704i | ||||
\(586\) | 8.20820 | + | 14.2170i | 0.339078 | + | 0.587300i | ||||
\(587\) | 1.06231 | + | 1.83997i | 0.0438461 | + | 0.0759436i | 0.887116 | − | 0.461547i | \(-0.152706\pi\) |
−0.843270 | + | 0.537491i | \(0.819372\pi\) | |||||||
\(588\) | 0.472136 | 0.0194706 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.70820 | 0.0703256 | ||||||||
\(591\) | −0.572949 | − | 0.992377i | −0.0235680 | − | 0.0408209i | ||||
\(592\) | 21.4894 | + | 37.2207i | 0.883207 | + | 1.52976i | ||||
\(593\) | −0.354102 | + | 0.613323i | −0.0145412 | + | 0.0251861i | −0.873204 | − | 0.487354i | \(-0.837962\pi\) |
0.858663 | + | 0.512540i | \(0.171295\pi\) | |||||||
\(594\) | −2.92705 | − | 5.06980i | −0.120098 | − | 0.208016i | ||||
\(595\) | −3.70820 | + | 6.42280i | −0.152022 | + | 0.263309i | ||||
\(596\) | −1.18034 | −0.0483486 | ||||||||
\(597\) | −5.12461 | −0.209736 | ||||||||
\(598\) | 4.35410 | − | 7.54153i | 0.178052 | − | 0.308396i | ||||
\(599\) | −14.2082 | + | 24.6093i | −0.580531 | + | 1.00551i | 0.414885 | + | 0.909874i | \(0.363822\pi\) |
−0.995416 | + | 0.0956361i | \(0.969511\pi\) | |||||||
\(600\) | −4.67376 | −0.190806 | ||||||||
\(601\) | 20.2918 | 0.827720 | 0.413860 | − | 0.910341i | \(-0.364180\pi\) | ||||
0.413860 | + | 0.910341i | \(0.364180\pi\) | |||||||
\(602\) | 0.354102 | − | 0.613323i | 0.0144321 | − | 0.0249972i | ||||
\(603\) | −9.98936 | − | 17.3021i | −0.406798 | − | 0.704595i | ||||
\(604\) | 6.51722 | − | 11.2882i | 0.265182 | − | 0.459309i | ||||
\(605\) | 13.5623 | + | 23.4906i | 0.551386 | + | 0.955029i | ||||
\(606\) | 2.83688 | + | 4.91362i | 0.115240 | + | 0.199602i | ||||
\(607\) | −6.27051 | −0.254512 | −0.127256 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127256 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.14590 | −0.168000 | ||||||||
\(610\) | 26.7984 | + | 46.4161i | 1.08503 | + | 1.87933i | ||||
\(611\) | 1.50000 | + | 2.59808i | 0.0606835 | + | 0.105107i | ||||
\(612\) | 0.673762 | − | 1.16699i | 0.0272352 | − | 0.0471728i | ||||
\(613\) | 9.97214 | + | 17.2722i | 0.402771 | + | 0.697619i | 0.994059 | − | 0.108841i | \(-0.0347138\pi\) |
−0.591288 | + | 0.806460i | \(0.701381\pi\) | |||||||
\(614\) | 14.0172 | − | 24.2785i | 0.565689 | − | 0.979802i | ||||
\(615\) | −3.70820 | −0.149529 | ||||||||
\(616\) | 10.8541 | 0.437324 | ||||||||
\(617\) | −3.83688 | + | 6.64567i | −0.154467 | + | 0.267545i | −0.932865 | − | 0.360227i | \(-0.882699\pi\) |
0.778398 | + | 0.627771i | \(0.216033\pi\) | |||||||
\(618\) | −4.42705 | + | 7.66788i | −0.178082 | + | 0.308447i | ||||
\(619\) | 10.1246 | 0.406943 | 0.203471 | − | 0.979081i | \(-0.434778\pi\) | ||||
0.203471 | + | 0.979081i | \(0.434778\pi\) | |||||||
\(620\) | −17.7082 | −0.711179 | ||||||||
\(621\) | 6.01722 | − | 10.4221i | 0.241463 | − | 0.418226i | ||||
\(622\) | −10.2361 | − | 17.7294i | −0.410429 | − | 0.710884i | ||||
\(623\) | 11.6459 | − | 20.1713i | 0.466583 | − | 0.808146i | ||||
\(624\) | −0.927051 | − | 1.60570i | −0.0371117 | − | 0.0642794i | ||||
\(625\) | 11.2082 | + | 19.4132i | 0.448328 | + | 0.776527i | ||||
\(626\) | −18.3262 | −0.732464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0344 | −0.440322 | ||||||||
\(629\) | −3.38197 | − | 5.85774i | −0.134848 | − | 0.233563i | ||||
\(630\) | 22.4164 | + | 38.8264i | 0.893091 | + | 1.54688i | ||||
\(631\) | −14.6803 | + | 25.4271i | −0.584415 | + | 1.01224i | 0.410533 | + | 0.911846i | \(0.365343\pi\) |
−0.994948 | + | 0.100391i | \(0.967991\pi\) | |||||||
\(632\) | 15.0000 | + | 25.9808i | 0.596668 | + | 1.03346i | ||||
\(633\) | 0.736068 | − | 1.27491i | 0.0292561 | − | 0.0506730i | ||||
\(634\) | 29.1246 | 1.15669 | ||||||||
\(635\) | 18.6525 | 0.740201 | ||||||||
\(636\) | 0.746711 | − | 1.29334i | 0.0296090 | − | 0.0512843i | ||||
\(637\) | 1.00000 | − | 1.73205i | 0.0396214 | − | 0.0686264i | ||||
\(638\) | 9.47214 | 0.375005 | ||||||||
\(639\) | 21.3262 | 0.843653 | ||||||||
\(640\) | −22.0344 | + | 38.1648i | −0.870988 | + | 1.50860i | ||||
\(641\) | 19.7533 | + | 34.2137i | 0.780208 | + | 1.35136i | 0.931820 | + | 0.362920i | \(0.118220\pi\) |
−0.151612 | + | 0.988440i | \(0.548447\pi\) | |||||||
\(642\) | −5.07295 | + | 8.78661i | −0.200213 | + | 0.346780i | ||||
\(643\) | 12.1459 | + | 21.0373i | 0.478987 | + | 0.829631i | 0.999710 | − | 0.0240956i | \(-0.00767060\pi\) |
−0.520722 | + | 0.853726i | \(0.674337\pi\) | |||||||
\(644\) | −4.98936 | − | 8.64182i | −0.196608 | − | 0.340535i | ||||
\(645\) | −0.180340 | −0.00710088 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.47214 | 0.293760 | 0.146880 | − | 0.989154i | \(-0.453077\pi\) | ||||
0.146880 | + | 0.989154i | \(0.453077\pi\) | |||||||
\(648\) | 8.61803 | + | 14.9269i | 0.338548 | + | 0.586383i | ||||
\(649\) | 0.263932 | + | 0.457144i | 0.0103602 | + | 0.0179445i | ||||
\(650\) | 4.42705 | − | 7.66788i | 0.173643 | − | 0.300759i | ||||
\(651\) | 5.07295 | + | 8.78661i | 0.198825 | + | 0.344374i | ||||
\(652\) | −0.545085 | + | 0.944115i | −0.0213472 | + | 0.0369744i | ||||
\(653\) | −23.5623 | −0.922064 | −0.461032 | − | 0.887383i | \(-0.652521\pi\) | ||||
−0.461032 | + | 0.887383i | \(0.652521\pi\) | |||||||
\(654\) | −2.03444 | −0.0795530 | ||||||||
\(655\) | −24.4164 | + | 42.2905i | −0.954028 | + | 1.65242i | ||||
\(656\) | −7.28115 | + | 12.6113i | −0.284281 | + | 0.492390i | ||||
\(657\) | 7.72949 | 0.301556 | ||||||||
\(658\) | 14.5623 | 0.567698 | ||||||||
\(659\) | 12.8885 | − | 22.3236i | 0.502066 | − | 0.869604i | −0.497931 | − | 0.867217i | \(-0.665907\pi\) |
0.999997 | − | 0.00238770i | \(-0.000760030\pi\) | |||||||
\(660\) | 0.618034 | + | 1.07047i | 0.0240569 | + | 0.0416678i | ||||
\(661\) | −2.70820 | + | 4.69075i | −0.105337 | + | 0.182449i | −0.913876 | − | 0.405994i | \(-0.866925\pi\) |
0.808539 | + | 0.588443i | \(0.200259\pi\) | |||||||
\(662\) | −8.85410 | − | 15.3358i | −0.344124 | − | 0.596041i | ||||
\(663\) | 0.145898 | + | 0.252703i | 0.00566621 | + | 0.00981416i | ||||
\(664\) | −18.9443 | −0.735180 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −40.8885 | −1.58440 | ||||||||
\(667\) | 9.73607 | + | 16.8634i | 0.376982 | + | 0.652952i | ||||
\(668\) | −6.25329 | − | 10.8310i | −0.241947 | − | 0.419065i | ||||
\(669\) | 2.22542 | − | 3.85455i | 0.0860399 | − | 0.149025i | ||||
\(670\) | 18.3262 | + | 31.7420i | 0.708004 | + | 1.22630i | ||||
\(671\) | −8.28115 | + | 14.3434i | −0.319690 | + | 0.553720i | ||||
\(672\) | −3.87539 | −0.149496 | ||||||||
\(673\) | 34.1246 | 1.31541 | 0.657704 | − | 0.753277i | \(-0.271528\pi\) | ||||
0.657704 | + | 0.753277i | \(0.271528\pi\) | |||||||
\(674\) | 13.8541 | − | 23.9960i | 0.533640 | − | 0.924292i | ||||
\(675\) | 6.11803 | − | 10.5967i | 0.235483 | − | 0.407869i | ||||
\(676\) | −7.41641 | −0.285246 | ||||||||
\(677\) | −30.7426 | −1.18154 | −0.590768 | − | 0.806842i | \(-0.701175\pi\) | ||||
−0.590768 | + | 0.806842i | \(0.701175\pi\) | |||||||
\(678\) | −2.09017 | + | 3.62028i | −0.0802725 | + | 0.139036i | ||||
\(679\) | −20.7812 | − | 35.9940i | −0.797507 | − | 1.38132i | ||||
\(680\) | 2.76393 | − | 4.78727i | 0.105992 | − | 0.183583i | ||||
\(681\) | −3.13525 | − | 5.43042i | −0.120143 | − | 0.208094i | ||||
\(682\) | −11.5902 | − | 20.0748i | −0.443811 | − | 0.768702i | ||||
\(683\) | 9.65248 | 0.369342 | 0.184671 | − | 0.982800i | \(-0.440878\pi\) | ||||
0.184671 | + | 0.982800i | \(0.440878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1803 | 0.923883 | ||||||||
\(686\) | 12.1353 | + | 21.0189i | 0.463326 | + | 0.802504i | ||||
\(687\) | 2.60081 | + | 4.50474i | 0.0992272 | + | 0.171867i | ||||
\(688\) | −0.354102 | + | 0.613323i | −0.0135000 | + | 0.0233827i | ||||
\(689\) | −3.16312 | − | 5.47868i | −0.120505 | − | 0.208721i | ||||
\(690\) | −5.38197 | + | 9.32184i | −0.204888 | + | 0.354876i | ||||
\(691\) | −39.1803 | −1.49049 | −0.745245 | − | 0.666791i | \(-0.767668\pi\) | ||||
−0.745245 | + | 0.666791i | \(0.767668\pi\) | |||||||
\(692\) | −0.291796 | −0.0110924 | ||||||||
\(693\) | −6.92705 | + | 11.9980i | −0.263137 | + | 0.455766i | ||||
\(694\) | 20.5623 | − | 35.6150i | 0.780534 | − | 1.35193i | ||||
\(695\) | 47.8885 | 1.81652 | ||||||||
\(696\) | 3.09017 | 0.117133 | ||||||||
\(697\) | 1.14590 | − | 1.98475i | 0.0434040 | − | 0.0751779i | ||||
\(698\) | 16.9721 | + | 29.3966i | 0.642405 | + | 1.11268i | ||||
\(699\) | −0.864745 | + | 1.49778i | −0.0327077 | + | 0.0566513i | ||||
\(700\) | −5.07295 | − | 8.78661i | −0.191739 | − | 0.332102i | ||||
\(701\) | 19.8156 | + | 34.3216i | 0.748425 | + | 1.29631i | 0.948578 | + | 0.316545i | \(0.102523\pi\) |
−0.200153 | + | 0.979765i | \(0.564144\pi\) | |||||||
\(702\) | 3.61803 | 0.136554 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −6.85410 | −0.258324 | ||||||||
\(705\) | −1.85410 | − | 3.21140i | −0.0698295 | − | 0.120948i | ||||
\(706\) | −19.7812 | − | 34.2620i | −0.744474 | − | 1.28947i | ||||
\(707\) | 13.7705 | − | 23.8512i | 0.517893 | − | 0.897018i | ||||
\(708\) | −0.0385072 | − | 0.0666964i | −0.00144719 | − | 0.00250660i | ||||
\(709\) | −8.29180 | + | 14.3618i | −0.311405 | + | 0.539369i | −0.978667 | − | 0.205454i | \(-0.934133\pi\) |
0.667262 | + | 0.744823i | \(0.267466\pi\) | |||||||
\(710\) | −39.1246 | −1.46832 | ||||||||
\(711\) | −38.2918 | −1.43605 | ||||||||
\(712\) | −8.68034 | + | 15.0348i | −0.325309 | + | 0.563453i | ||||
\(713\) | 23.8262 | − | 41.2683i | 0.892300 | − | 1.54551i | ||||
\(714\) | 1.41641 | 0.0530077 | ||||||||
\(715\) | 5.23607 | 0.195818 | ||||||||
\(716\) | −3.78115 | + | 6.54915i | −0.141308 | + | 0.244753i | ||||
\(717\) | 0.0623059 | + | 0.107917i | 0.00232686 | + | 0.00403023i | ||||
\(718\) | −5.69098 | + | 9.85707i | −0.212386 | + | 0.367863i | ||||
\(719\) | −23.5172 | − | 40.7330i | −0.877044 | − | 1.51909i | −0.854569 | − | 0.519338i | \(-0.826179\pi\) |
−0.0224754 | − | 0.999747i | \(-0.507155\pi\) | |||||||
\(720\) | −22.4164 | − | 38.8264i | −0.835410 | − | 1.44697i | ||||
\(721\) | 42.9787 | 1.60061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.21478 | 0.0451782 | ||||||||
\(724\) | −3.70820 | − | 6.42280i | −0.137814 | − | 0.238701i | ||||
\(725\) | 9.89919 | + | 17.1459i | 0.367647 | + | 0.636783i | ||||
\(726\) | 2.59017 | − | 4.48631i | 0.0961302 | − | 0.166502i | ||||
\(727\) | 8.03444 | + | 13.9161i | 0.297981 | + | 0.516118i | 0.975674 | − | 0.219227i | \(-0.0703535\pi\) |
−0.677693 | + | 0.735345i | \(0.737020\pi\) | |||||||
\(728\) | −3.35410 | + | 5.80948i | −0.124311 | + | 0.215313i | ||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | −14.1803 | −0.524838 | ||||||||
\(731\) | 0.0557281 | − | 0.0965239i | 0.00206118 | − | 0.00357006i | ||||
\(732\) | 1.20820 | − | 2.09267i | 0.0446565 | − | 0.0773473i | ||||
\(733\) | −52.9574 | −1.95603 | −0.978014 | − | 0.208541i | \(-0.933129\pi\) | ||||
−0.978014 | + | 0.208541i | \(0.933129\pi\) | |||||||
\(734\) | −25.7984 | −0.952235 | ||||||||
\(735\) | −1.23607 | + | 2.14093i | −0.0455931 | + | 0.0789695i | ||||
\(736\) | 9.10081 | + | 15.7631i | 0.335460 | + | 0.581034i | ||||
\(737\) | −5.66312 | + | 9.80881i | −0.208604 | + | 0.361312i | ||||
\(738\) | −6.92705 | − | 11.9980i | −0.254988 | − | 0.441653i | ||||
\(739\) | 12.5000 | + | 21.6506i | 0.459820 | + | 0.796431i | 0.998951 | − | 0.0457903i | \(-0.0145806\pi\) |
−0.539131 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(740\) | 17.7082 | 0.650967 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.7082 | −1.12733 | ||||||||
\(743\) | 1.68034 | + | 2.91043i | 0.0616457 | + | 0.106773i | 0.895201 | − | 0.445662i | \(-0.147032\pi\) |
−0.833555 | + | 0.552436i | \(0.813698\pi\) | |||||||
\(744\) | −3.78115 | − | 6.54915i | −0.138624 | − | 0.240103i | ||||
\(745\) | 3.09017 | − | 5.35233i | 0.113215 | − | 0.196094i | ||||
\(746\) | 4.42705 | + | 7.66788i | 0.162086 | + | 0.280741i | ||||
\(747\) | 12.0902 | − | 20.9408i | 0.442356 | − | 0.766183i | ||||
\(748\) | −0.763932 | −0.0279321 | ||||||||
\(749\) | 49.2492 | 1.79953 | ||||||||
\(750\) | −0.472136 | + | 0.817763i | −0.0172400 | + | 0.0298605i | ||||
\(751\) | 8.57295 | − | 14.8488i | 0.312831 | − | 0.541840i | −0.666143 | − | 0.745824i | \(-0.732056\pi\) |
0.978974 | + | 0.203984i | \(0.0653892\pi\) | |||||||
\(752\) | −14.5623 | −0.531033 | ||||||||
\(753\) | −9.68692 | −0.353011 | ||||||||
\(754\) | −2.92705 | + | 5.06980i | −0.106597 | + | 0.184631i | ||||
\(755\) | 34.1246 | + | 59.1056i | 1.24192 | + | 2.15107i | ||||
\(756\) | 2.07295 | − | 3.59045i | 0.0753924 | − | 0.130584i | ||||
\(757\) | −13.3713 | − | 23.1598i | −0.485989 | − | 0.841758i | 0.513881 | − | 0.857861i | \(-0.328207\pi\) |
−0.999870 | + | 0.0161036i | \(0.994874\pi\) | |||||||
\(758\) | 12.2361 | + | 21.1935i | 0.444434 | + | 0.769782i | ||||
\(759\) | −3.32624 | −0.120735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.88854 | 0.177210 | 0.0886048 | − | 0.996067i | \(-0.471759\pi\) | ||||
0.0886048 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(762\) | −1.78115 | − | 3.08505i | −0.0645244 | − | 0.111759i | ||||
\(763\) | 4.93769 | + | 8.55234i | 0.178757 | + | 0.309615i | ||||
\(764\) | −4.39919 | + | 7.61962i | −0.159157 | + | 0.275668i | ||||
\(765\) | 3.52786 | + | 6.11044i | 0.127550 | + | 0.220923i | ||||
\(766\) | −0.309017 | + | 0.535233i | −0.0111652 | + | 0.0193388i | ||||
\(767\) | −0.326238 | −0.0117798 | ||||||||
\(768\) | 5.18034 | 0.186929 | ||||||||
\(769\) | −18.3156 | + | 31.7235i | −0.660477 | + | 1.14398i | 0.320013 | + | 0.947413i | \(0.396313\pi\) |
−0.980490 | + | 0.196567i | \(0.937021\pi\) | |||||||
\(770\) | 12.7082 | − | 22.0113i | 0.457972 | − | 0.793231i | ||||
\(771\) | 7.77709 | 0.280085 | ||||||||
\(772\) | 3.12461 | 0.112457 | ||||||||
\(773\) | 17.9615 | − | 31.1102i | 0.646030 | − | 1.11896i | −0.338033 | − | 0.941134i | \(-0.609761\pi\) |
0.984063 | − | 0.177822i | \(-0.0569052\pi\) | |||||||
\(774\) | −0.336881 | − | 0.583495i | −0.0121089 | − | 0.0209733i | ||||
\(775\) | 24.2254 | − | 41.9597i | 0.870203 | − | 1.50724i | ||||
\(776\) | 15.4894 | + | 26.8284i | 0.556036 | + | 0.963082i | ||||
\(777\) | −5.07295 | − | 8.78661i | −0.181991 | − | 0.315218i | ||||
\(778\) | 15.0000 | 0.537776 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.763932 | −0.0273532 | ||||||||
\(781\) | −6.04508 | − | 10.4704i | −0.216310 | − | 0.374660i | ||||
\(782\) | −3.32624 | − | 5.76121i | −0.118946 | − | 0.206021i | ||||
\(783\) | −4.04508 | + | 7.00629i | −0.144560 | + | 0.250384i | ||||
\(784\) | 4.85410 | + | 8.40755i | 0.173361 | + | 0.300270i | ||||
\(785\) | 28.8885 | − | 50.0364i | 1.03108 | − | 1.78588i | ||||
\(786\) | 9.32624 | 0.332656 | ||||||||
\(787\) | 38.0000 | 1.35455 | 0.677277 | − | 0.735728i | \(-0.263160\pi\) | ||||
0.677277 | + | 0.735728i | \(0.263160\pi\) | |||||||
\(788\) | −0.927051 | + | 1.60570i | −0.0330248 | + | 0.0572007i | ||||
\(789\) | 2.85410 | − | 4.94345i | 0.101609 | − | 0.175991i | ||||
\(790\) | 70.2492 | 2.49936 | ||||||||
\(791\) | 20.2918 | 0.721493 | ||||||||
\(792\) | 5.16312 | − | 8.94278i | 0.183463 | − | 0.317768i | ||||
\(793\) | −5.11803 | − | 8.86469i | −0.181747 | − | 0.314795i | ||||
\(794\) | 9.28115 | − | 16.0754i | 0.329376 | − | 0.570496i | ||||
\(795\) | 3.90983 | + | 6.77202i | 0.138667 | + | 0.240179i | ||||
\(796\) | 4.14590 | + | 7.18091i | 0.146947 | + | 0.254520i | ||||
\(797\) | −20.2918 | −0.718772 | −0.359386 | − | 0.933189i | \(-0.617014\pi\) | ||||
−0.359386 | + | 0.933189i | \(0.617014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.29180 | 0.0810779 | ||||||||
\(800\) | 9.25329 | + | 16.0272i | 0.327153 | + | 0.566646i | ||||
\(801\) | −11.0795 | − | 19.1903i | −0.391476 | − | 0.678056i | ||||
\(802\) | 29.0344 | − | 50.2891i | 1.02524 | − | 1.77577i | ||||
\(803\) | −2.19098 | − | 3.79489i | −0.0773181 | − | 0.133919i | ||||
\(804\) | 0.826238 | − | 1.43109i | 0.0291392 | − | 0.0504705i | ||||
\(805\) | 52.2492 | 1.84154 | ||||||||
\(806\) | 14.3262 | 0.504620 | ||||||||
\(807\) | −5.79180 | + | 10.0317i | −0.203881 | + | 0.353132i | ||||
\(808\) | −10.2639 | + | 17.7777i | −0.361084 | + | 0.625416i | ||||
\(809\) | −24.7984 | −0.871864 | −0.435932 | − | 0.899980i | \(-0.643581\pi\) | ||||
−0.435932 | + | 0.899980i | \(0.643581\pi\) | |||||||
\(810\) | 40.3607 | 1.41813 | ||||||||
\(811\) | −11.4894 | + | 19.9001i | −0.403446 | + | 0.698789i | −0.994139 | − | 0.108107i | \(-0.965521\pi\) |
0.590693 | + | 0.806896i | \(0.298854\pi\) | |||||||
\(812\) | 3.35410 | + | 5.80948i | 0.117706 | + | 0.203873i | ||||
\(813\) | −0.218847 | + | 0.379054i | −0.00767530 | + | 0.0132940i | ||||
\(814\) | 11.5902 | + | 20.0748i | 0.406235 | + | 0.703620i | ||||
\(815\) | −2.85410 | − | 4.94345i | −0.0999748 | − | 0.173161i | ||||
\(816\) | −1.41641 | −0.0495842 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −13.4164 | −0.469094 | ||||||||
\(819\) | −4.28115 | − | 7.41517i | −0.149596 | − | 0.259107i | ||||
\(820\) | 3.00000 | + | 5.19615i | 0.104765 | + | 0.181458i | ||||
\(821\) | −26.0238 | + | 45.0745i | −0.908237 | + | 1.57311i | −0.0917245 | + | 0.995784i | \(0.529238\pi\) |
−0.816512 | + | 0.577328i | \(0.804095\pi\) | |||||||
\(822\) | −2.30902 | − | 3.99933i | −0.0805362 | − | 0.139493i | ||||
\(823\) | 12.7984 | − | 22.1674i | 0.446123 | − | 0.772708i | −0.552006 | − | 0.833840i | \(-0.686138\pi\) |
0.998130 | + | 0.0611317i | \(0.0194710\pi\) | |||||||
\(824\) | −32.0344 | −1.11597 | ||||||||
\(825\) | −3.38197 | −0.117745 | ||||||||
\(826\) | −0.791796 | + | 1.37143i | −0.0275501 | + | 0.0477182i | ||||
\(827\) | −16.2984 | + | 28.2296i | −0.566750 | + | 0.981640i | 0.430135 | + | 0.902765i | \(0.358466\pi\) |
−0.996885 | + | 0.0788750i | \(0.974867\pi\) | |||||||
\(828\) | −9.49342 | −0.329919 | ||||||||
\(829\) | 4.67376 | 0.162326 | 0.0811632 | − | 0.996701i | \(-0.474136\pi\) | ||||
0.0811632 | + | 0.996701i | \(0.474136\pi\) | |||||||
\(830\) | −22.1803 | + | 38.4175i | −0.769891 | + | 1.33349i | ||||
\(831\) | −2.18034 | − | 3.77646i | −0.0756352 | − | 0.131004i | ||||
\(832\) | 2.11803 | − | 3.66854i | 0.0734296 | − | 0.127184i | ||||
\(833\) | −0.763932 | − | 1.32317i | −0.0264687 | − | 0.0458451i | ||||
\(834\) | −4.57295 | − | 7.92058i | −0.158348 | − | 0.274267i | ||||
\(835\) | 65.4853 | 2.26621 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7984 | 0.684332 | ||||||||
\(838\) | 7.23607 | + | 12.5332i | 0.249966 | + | 0.432954i | ||||
\(839\) | −7.60081 | − | 13.1650i | −0.262409 | − | 0.454506i | 0.704472 | − | 0.709731i | \(-0.251184\pi\) |
−0.966882 | + | 0.255225i | \(0.917850\pi\) | |||||||
\(840\) | 4.14590 | − | 7.18091i | 0.143047 | − | 0.247765i | ||||
\(841\) | 7.95492 | + | 13.7783i | 0.274307 | + | 0.475114i | ||||
\(842\) | 22.2254 | − | 38.4956i | 0.765939 | − | 1.32664i | ||||
\(843\) | −11.2705 | −0.388177 | ||||||||
\(844\) | −2.38197 | −0.0819907 | ||||||||
\(845\) | 19.4164 | − | 33.6302i | 0.667945 | − | 1.15691i | ||||
\(846\) | 6.92705 | − | 11.9980i | 0.238157 | − | 0.412500i | ||||
\(847\) | −25.1459 | −0.864023 | ||||||||
\(848\) | 30.7082 | 1.05452 | ||||||||
\(849\) | −4.97214 | + | 8.61199i | −0.170643 | + | 0.295563i | ||||
\(850\) | −3.38197 | − | 5.85774i | −0.116000 | − | 0.200919i | ||||
\(851\) | −23.8262 | + | 41.2683i | −0.816753 | + | 1.41466i | ||||
\(852\) | 0.881966 | + | 1.52761i | 0.0302157 | + | 0.0523351i | ||||
\(853\) | −15.3541 | − | 26.5941i | −0.525714 | − | 0.910564i | −0.999551 | − | 0.0299515i | \(-0.990465\pi\) |
0.473837 | − | 0.880613i | \(-0.342869\pi\) | |||||||
\(854\) | −49.6869 | −1.70025 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.7082 | −1.25466 | ||||||||
\(857\) | 5.30902 | + | 9.19549i | 0.181353 | + | 0.314112i | 0.942341 | − | 0.334653i | \(-0.108619\pi\) |
−0.760989 | + | 0.648765i | \(0.775286\pi\) | |||||||
\(858\) | −0.500000 | − | 0.866025i | −0.0170697 | − | 0.0295656i | ||||
\(859\) | 24.2705 | − | 42.0378i | 0.828099 | − | 1.43431i | −0.0714285 | − | 0.997446i | \(-0.522756\pi\) |
0.899528 | − | 0.436864i | \(-0.143911\pi\) | |||||||
\(860\) | 0.145898 | + | 0.252703i | 0.00497508 | + | 0.00861709i | ||||
\(861\) | 1.71885 | − | 2.97713i | 0.0585782 | − | 0.101460i | ||||
\(862\) | 44.7426 | 1.52394 | ||||||||
\(863\) | −27.0557 | −0.920988 | −0.460494 | − | 0.887663i | \(-0.652328\pi\) | ||||
−0.460494 | + | 0.887663i | \(0.652328\pi\) | |||||||
\(864\) | −3.78115 | + | 6.54915i | −0.128637 | + | 0.222807i | ||||
\(865\) | 0.763932 | − | 1.32317i | 0.0259745 | − | 0.0449891i | ||||
\(866\) | −5.56231 | −0.189015 | ||||||||
\(867\) | −6.27051 | −0.212958 | ||||||||
\(868\) | 8.20820 | − | 14.2170i | 0.278605 | − | 0.482557i | ||||
\(869\) | 10.8541 | + | 18.7999i | 0.368200 | + | 0.637741i | ||||
\(870\) | 3.61803 | − | 6.26662i | 0.122663 | − | 0.212458i | ||||
\(871\) | −3.50000 | − | 6.06218i | −0.118593 | − | 0.205409i | ||||
\(872\) | −3.68034 | − | 6.37454i | −0.124632 | − | 0.215869i | ||||
\(873\) | −39.5410 | −1.33826 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.58359 | 0.154954 | ||||||||
\(876\) | 0.319660 | + | 0.553668i | 0.0108003 | + | 0.0187067i | ||||
\(877\) | −5.90983 | − | 10.2361i | −0.199561 | − | 0.345649i | 0.748825 | − | 0.662767i | \(-0.230618\pi\) |
−0.948386 | + | 0.317118i | \(0.897285\pi\) | |||||||
\(878\) | 27.9894 | − | 48.4790i | 0.944595 | − | 1.63609i | ||||
\(879\) | 1.93769 | + | 3.35618i | 0.0653568 | + | 0.113201i | ||||
\(880\) | −12.7082 | + | 22.0113i | −0.428393 | + | 0.741999i | ||||
\(881\) | 32.4508 | 1.09330 | 0.546648 | − | 0.837362i | \(-0.315903\pi\) | ||||
0.546648 | + | 0.837362i | \(0.315903\pi\) | |||||||
\(882\) | −9.23607 | −0.310995 | ||||||||
\(883\) | 25.4615 | − | 44.1006i | 0.856847 | − | 1.48410i | −0.0180730 | − | 0.999837i | \(-0.505753\pi\) |
0.874920 | − | 0.484267i | \(-0.160914\pi\) | |||||||
\(884\) | 0.236068 | − | 0.408882i | 0.00793983 | − | 0.0137522i | ||||
\(885\) | 0.403252 | 0.0135552 | ||||||||
\(886\) | −12.2705 | −0.412236 | ||||||||
\(887\) | −13.6738 | + | 23.6837i | −0.459120 | + | 0.795219i | −0.998915 | − | 0.0465775i | \(-0.985169\pi\) |
0.539795 | + | 0.841797i | \(0.318502\pi\) | |||||||
\(888\) | 3.78115 | + | 6.54915i | 0.126887 | + | 0.219775i | ||||
\(889\) | −8.64590 | + | 14.9751i | −0.289974 | + | 0.502250i | ||||
\(890\) | 20.3262 | + | 35.2061i | 0.681337 | + | 1.18011i | ||||
\(891\) | 6.23607 | + | 10.8012i | 0.208916 | + | 0.361853i | ||||
\(892\) | −7.20163 | −0.241128 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.18034 | −0.0394765 | ||||||||
\(895\) | −19.7984 | − | 34.2918i | −0.661787 | − | 1.14625i | ||||
\(896\) | −20.4271 | − | 35.3807i | −0.682420 | − | 1.18199i | ||||
\(897\) | 1.02786 | − | 1.78031i | 0.0343194 | − | 0.0594429i | ||||
\(898\) | −2.33688 | − | 4.04760i | −0.0779827 | − | 0.135070i | ||||
\(899\) | −16.0172 | + | 27.7426i | −0.534204 | + | 0.925269i | ||||
\(900\) | −9.65248 | −0.321749 | ||||||||
\(901\) | −4.83282 | −0.161004 | ||||||||
\(902\) | −3.92705 | + | 6.80185i | −0.130756 | + | 0.226477i | ||||
\(903\) | 0.0835921 | − | 0.144786i | 0.00278177 | − | 0.00481817i | ||||
\(904\) | −15.1246 | −0.503037 | ||||||||
\(905\) | 38.8328 | 1.29085 | ||||||||
\(906\) | 6.51722 | − | 11.2882i | 0.216520 | − | 0.375024i | ||||
\(907\) | 13.2361 | + | 22.9255i | 0.439496 | + | 0.761230i | 0.997651 | − | 0.0685071i | \(-0.0218236\pi\) |
−0.558154 | + | 0.829737i | \(0.688490\pi\) | |||||||
\(908\) | −5.07295 | + | 8.78661i | −0.168352 | + | 0.291594i | ||||
\(909\) | −13.1008 | − | 22.6913i | −0.434527 | − | 0.752622i | ||||
\(910\) | 7.85410 | + | 13.6037i | 0.260361 | + | 0.450958i | ||||
\(911\) | 3.38197 | 0.112050 | 0.0560248 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560248 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7082 | −0.453675 | ||||||||
\(914\) | −15.9443 | − | 27.6163i | −0.527390 | − | 0.913466i | ||||
\(915\) | 6.32624 | + | 10.9574i | 0.209139 | + | 0.362239i | ||||
\(916\) | 4.20820 | − | 7.28882i | 0.139043 | − | 0.240829i | ||||
\(917\) | −22.6353 | − | 39.2054i | −0.747482 | − | 1.29468i | ||||
\(918\) | 1.38197 | − | 2.39364i | 0.0456117 | − | 0.0790017i | ||||
\(919\) | 23.2918 | 0.768325 | 0.384163 | − | 0.923265i | \(-0.374490\pi\) | ||||
0.384163 | + | 0.923265i | \(0.374490\pi\) | |||||||
\(920\) | −38.9443 | −1.28395 | ||||||||
\(921\) | 3.30902 | − | 5.73139i | 0.109036 | − | 0.188856i | ||||
\(922\) | −16.9443 | + | 29.3483i | −0.558030 | + | 0.966536i | ||||
\(923\) | 7.47214 | 0.245948 | ||||||||
\(924\) | −1.14590 | −0.0376973 | ||||||||
\(925\) | −24.2254 | + | 41.9597i | −0.796527 | + | 1.37963i | ||||
\(926\) | −22.8713 | − | 39.6143i | −0.751598 | − | 1.30181i | ||||
\(927\) | 20.4443 | − | 35.4105i | 0.671478 | − | 1.16303i | ||||
\(928\) | −6.11803 | − | 10.5967i | −0.200834 | − | 0.347855i | ||||
\(929\) | −8.19098 | − | 14.1872i | −0.268737 | − | 0.465467i | 0.699799 | − | 0.714340i | \(-0.253273\pi\) |
−0.968536 | + | 0.248873i | \(0.919940\pi\) | |||||||
\(930\) | −17.7082 | −0.580675 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.79837 | 0.0916638 | ||||||||
\(933\) | −2.41641 | − | 4.18534i | −0.0791096 | − | 0.137022i | ||||
\(934\) | 12.8992 | + | 22.3420i | 0.422074 | + | 0.731054i | ||||
\(935\) | 2.00000 | − | 3.46410i | 0.0654070 | − | 0.113288i | ||||
\(936\) | 3.19098 | + | 5.52694i | 0.104301 | + | 0.180654i | ||||
\(937\) | −20.2812 | + | 35.1280i | −0.662556 | + | 1.14758i | 0.317385 | + | 0.948297i | \(0.397195\pi\) |
−0.979942 | + | 0.199285i | \(0.936138\pi\) | |||||||
\(938\) | −33.9787 | −1.10944 | ||||||||
\(939\) | −4.32624 | −0.141181 | ||||||||
\(940\) | −3.00000 | + | 5.19615i | −0.0978492 | + | 0.169480i | ||||
\(941\) | 5.34346 | − | 9.25514i | 0.174192 | − | 0.301709i | −0.765689 | − | 0.643210i | \(-0.777602\pi\) |
0.939881 | + | 0.341501i | \(0.110935\pi\) | |||||||
\(942\) | −11.0344 | −0.359522 | ||||||||
\(943\) | −16.1459 | −0.525783 | ||||||||
\(944\) | 0.791796 | − | 1.37143i | 0.0257708 | − | 0.0446363i | ||||
\(945\) | 10.8541 | + | 18.7999i | 0.353084 | + | 0.611559i | ||||
\(946\) | −0.190983 | + | 0.330792i | −0.00620939 | + | 0.0107550i | ||||
\(947\) | 16.3262 | + | 28.2779i | 0.530531 | + | 0.918907i | 0.999365 | + | 0.0356211i | \(0.0113409\pi\) |
−0.468834 | + | 0.883286i | \(0.655326\pi\) | |||||||
\(948\) | −1.58359 | − | 2.74286i | −0.0514327 | − | 0.0890840i | ||||
\(949\) | 2.70820 | 0.0879120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.87539 | 0.222950 | ||||||||
\(952\) | 2.56231 | + | 4.43804i | 0.0830448 | + | 0.143838i | ||||
\(953\) | −8.64590 | − | 14.9751i | −0.280068 | − | 0.485092i | 0.691333 | − | 0.722536i | \(-0.257024\pi\) |
−0.971401 | + | 0.237444i | \(0.923690\pi\) | |||||||
\(954\) | −14.6074 | + | 25.3007i | −0.472932 | + | 0.819142i | ||||
\(955\) | −23.0344 | − | 39.8968i | −0.745377 | − | 1.29103i | ||||
\(956\) | 0.100813 | − | 0.174613i | 0.00326053 | − | 0.00564740i | ||||
\(957\) | 2.23607 | 0.0722818 | ||||||||
\(958\) | 37.3607 | 1.20707 | ||||||||
\(959\) | −11.2082 | + | 19.4132i | −0.361932 | + | 0.626884i | ||||
\(960\) | −2.61803 | + | 4.53457i | −0.0844967 | + | 0.146353i | ||||
\(961\) | 47.3951 | 1.52887 | ||||||||
\(962\) | −14.3262 | −0.461896 | ||||||||
\(963\) | 23.4271 | − | 40.5768i | 0.754926 | − | 1.30757i | ||||
\(964\) | −0.982779 | − | 1.70222i | −0.0316532 | − | 0.0548249i | ||||
\(965\) | −8.18034 | + | 14.1688i | −0.263334 | + | 0.456109i | ||||
\(966\) | −4.98936 | − | 8.64182i | −0.160530 | − | 0.278046i | ||||
\(967\) | −3.27051 | − | 5.66469i | −0.105173 | − | 0.182164i | 0.808636 | − | 0.588309i | \(-0.200206\pi\) |
−0.913809 | + | 0.406145i | \(0.866873\pi\) | |||||||
\(968\) | 18.7426 | 0.602411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.5410 | 2.32915 | ||||||||
\(971\) | −11.7533 | − | 20.3573i | −0.377181 | − | 0.653297i | 0.613470 | − | 0.789718i | \(-0.289773\pi\) |
−0.990651 | + | 0.136421i | \(0.956440\pi\) | |||||||
\(972\) | −2.98278 | − | 5.16632i | −0.0956727 | − | 0.165710i | ||||
\(973\) | −22.1976 | + | 38.4473i | −0.711621 | + | 1.23256i | ||||
\(974\) | −3.38197 | − | 5.85774i | −0.108365 | − | 0.187694i | ||||
\(975\) | 1.04508 | − | 1.81014i | 0.0334695 | − | 0.0579709i | ||||
\(976\) | 49.6869 | 1.59044 | ||||||||
\(977\) | 10.6393 | 0.340382 | 0.170191 | − | 0.985411i | \(-0.445562\pi\) | ||||
0.170191 | + | 0.985411i | \(0.445562\pi\) | |||||||
\(978\) | −0.545085 | + | 0.944115i | −0.0174299 | + | 0.0301895i | ||||
\(979\) | −6.28115 | + | 10.8793i | −0.200747 | + | 0.347703i | ||||
\(980\) | 4.00000 | 0.127775 | ||||||||
\(981\) | 9.39512 | 0.299963 | ||||||||
\(982\) | 17.1631 | − | 29.7274i | 0.547697 | − | 0.948639i | ||||
\(983\) | −16.3090 | − | 28.2480i | −0.520177 | − | 0.900973i | −0.999725 | − | 0.0234571i | \(-0.992533\pi\) |
0.479548 | − | 0.877516i | \(-0.340801\pi\) | |||||||
\(984\) | −1.28115 | + | 2.21902i | −0.0408417 | + | 0.0707398i | ||||
\(985\) | −4.85410 | − | 8.40755i | −0.154665 | − | 0.267887i | ||||
\(986\) | 2.23607 | + | 3.87298i | 0.0712109 | + | 0.123341i | ||||
\(987\) | 3.43769 | 0.109423 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.785218 | −0.0249685 | ||||||||
\(990\) | −12.0902 | − | 20.9408i | −0.384251 | − | 0.665542i | ||||
\(991\) | −3.72542 | − | 6.45263i | −0.118342 | − | 0.204974i | 0.800769 | − | 0.598974i | \(-0.204425\pi\) |
−0.919111 | + | 0.393999i | \(0.871091\pi\) | |||||||
\(992\) | −14.9721 | + | 25.9325i | −0.475366 | + | 0.823358i | ||||
\(993\) | −2.09017 | − | 3.62028i | −0.0663295 | − | 0.114886i | ||||
\(994\) | 18.1353 | − | 31.4112i | 0.575215 | − | 0.996302i | ||||
\(995\) | −43.4164 | −1.37639 | ||||||||
\(996\) | 2.00000 | 0.0633724 | ||||||||
\(997\) | −19.8541 | + | 34.3883i | −0.628786 | + | 1.08909i | 0.359010 | + | 0.933334i | \(0.383114\pi\) |
−0.987796 | + | 0.155755i | \(0.950219\pi\) | |||||||
\(998\) | −20.3262 | + | 35.2061i | −0.643416 | + | 1.11443i | ||||
\(999\) | −19.7984 | −0.626393 |
(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 | 361.2.c.d.292.1 | 4 | ||
19.2 | odd | 18 | 361.2.e.i.28.1 | 12 | |||
19.3 | odd | 18 | 361.2.e.i.234.1 | 12 | |||
19.4 | even | 9 | 361.2.e.j.245.2 | 12 | |||
19.5 | even | 9 | 361.2.e.j.99.1 | 12 | |||
19.6 | even | 9 | 361.2.e.j.62.1 | 12 | |||
19.7 | even | 3 | 361.2.a.f.1.2 | yes | 2 | ||
19.8 | odd | 6 | 361.2.c.g.68.2 | 4 | |||
19.9 | even | 9 | 361.2.e.j.54.2 | 12 | |||
19.10 | odd | 18 | 361.2.e.i.54.1 | 12 | |||
19.11 | even | 3 | inner | 361.2.c.d.68.1 | 4 | ||
19.12 | odd | 6 | 361.2.a.c.1.1 | ✓ | 2 | ||
19.13 | odd | 18 | 361.2.e.i.62.2 | 12 | |||
19.14 | odd | 18 | 361.2.e.i.99.2 | 12 | |||
19.15 | odd | 18 | 361.2.e.i.245.1 | 12 | |||
19.16 | even | 9 | 361.2.e.j.234.2 | 12 | |||
19.17 | even | 9 | 361.2.e.j.28.2 | 12 | |||
19.18 | odd | 2 | 361.2.c.g.292.2 | 4 | |||
57.26 | odd | 6 | 3249.2.a.i.1.1 | 2 | |||
57.50 | even | 6 | 3249.2.a.o.1.2 | 2 | |||
76.7 | odd | 6 | 5776.2.a.s.1.2 | 2 | |||
76.31 | even | 6 | 5776.2.a.bg.1.1 | 2 | |||
95.64 | even | 6 | 9025.2.a.n.1.1 | 2 | |||
95.69 | odd | 6 | 9025.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.c.1.1 | ✓ | 2 | 19.12 | odd | 6 | ||
361.2.a.f.1.2 | yes | 2 | 19.7 | even | 3 | ||
361.2.c.d.68.1 | 4 | 19.11 | even | 3 | inner | ||
361.2.c.d.292.1 | 4 | 1.1 | even | 1 | trivial | ||
361.2.c.g.68.2 | 4 | 19.8 | odd | 6 | |||
361.2.c.g.292.2 | 4 | 19.18 | odd | 2 | |||
361.2.e.i.28.1 | 12 | 19.2 | odd | 18 | |||
361.2.e.i.54.1 | 12 | 19.10 | odd | 18 | |||
361.2.e.i.62.2 | 12 | 19.13 | odd | 18 | |||
361.2.e.i.99.2 | 12 | 19.14 | odd | 18 | |||
361.2.e.i.234.1 | 12 | 19.3 | odd | 18 | |||
361.2.e.i.245.1 | 12 | 19.15 | odd | 18 | |||
361.2.e.j.28.2 | 12 | 19.17 | even | 9 | |||
361.2.e.j.54.2 | 12 | 19.9 | even | 9 | |||
361.2.e.j.62.1 | 12 | 19.6 | even | 9 | |||
361.2.e.j.99.1 | 12 | 19.5 | even | 9 | |||
361.2.e.j.234.2 | 12 | 19.16 | even | 9 | |||
361.2.e.j.245.2 | 12 | 19.4 | even | 9 | |||
3249.2.a.i.1.1 | 2 | 57.26 | odd | 6 | |||
3249.2.a.o.1.2 | 2 | 57.50 | even | 6 | |||
5776.2.a.s.1.2 | 2 | 76.7 | odd | 6 | |||
5776.2.a.bg.1.1 | 2 | 76.31 | even | 6 | |||
9025.2.a.n.1.1 | 2 | 95.64 | even | 6 | |||
9025.2.a.s.1.2 | 2 | 95.69 | odd | 6 |