Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(128,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.128");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.y (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 128.8 | ||
Character | \(\chi\) | \(=\) | 735.128 |
Dual form | 735.2.y.g.557.8 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.474084 | − | 0.127030i | 0.335228 | − | 0.0898241i | −0.0872785 | − | 0.996184i | \(-0.527817\pi\) |
0.422507 | + | 0.906360i | \(0.361150\pi\) | |||||||
\(3\) | 0.708759 | + | 1.58040i | 0.409202 | + | 0.912444i | ||||
\(4\) | −1.52343 | + | 0.879554i | −0.761716 | + | 0.439777i | ||||
\(5\) | −2.23532 | + | 0.0580193i | −0.999663 | + | 0.0259470i | ||||
\(6\) | 0.536770 | + | 0.659208i | 0.219135 | + | 0.269120i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.30461 | + | 1.30461i | −0.461250 | + | 0.461250i | ||||
\(9\) | −1.99532 | + | 2.24024i | −0.665107 | + | 0.746748i | ||||
\(10\) | −1.05236 | + | 0.311459i | −0.332784 | + | 0.0984920i | ||||
\(11\) | 2.31347 | − | 1.33568i | 0.697538 | − | 0.402724i | −0.108892 | − | 0.994054i | \(-0.534730\pi\) |
0.806430 | + | 0.591330i | \(0.201397\pi\) | |||||||
\(12\) | −2.46979 | − | 1.78424i | −0.712968 | − | 0.515065i | ||||
\(13\) | −2.14945 | − | 2.14945i | −0.596149 | − | 0.596149i | 0.343137 | − | 0.939285i | \(-0.388511\pi\) |
−0.939285 | + | 0.343137i | \(0.888511\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67599 | − | 3.49157i | −0.432740 | − | 0.901519i | ||||
\(16\) | 1.30634 | − | 2.26264i | 0.326584 | − | 0.565661i | ||||
\(17\) | −1.19588 | + | 4.46307i | −0.290042 | + | 1.08245i | 0.655033 | + | 0.755600i | \(0.272655\pi\) |
−0.945075 | + | 0.326852i | \(0.894012\pi\) | |||||||
\(18\) | −0.661370 | + | 1.31553i | −0.155886 | + | 0.310074i | ||||
\(19\) | −4.54082 | − | 2.62164i | −1.04174 | − | 0.601446i | −0.121411 | − | 0.992602i | \(-0.538742\pi\) |
−0.920324 | + | 0.391156i | \(0.872075\pi\) | |||||||
\(20\) | 3.35432 | − | 2.05447i | 0.750049 | − | 0.459393i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.927108 | − | 0.927108i | 0.197660 | − | 0.197660i | ||||
\(23\) | −0.932688 | − | 3.48084i | −0.194479 | − | 0.725805i | −0.992401 | − | 0.123045i | \(-0.960734\pi\) |
0.797922 | − | 0.602760i | \(-0.205932\pi\) | |||||||
\(24\) | −2.98646 | − | 1.13715i | −0.609609 | − | 0.232120i | ||||
\(25\) | 4.99327 | − | 0.259383i | 0.998654 | − | 0.0518766i | ||||
\(26\) | −1.29206 | − | 0.745973i | −0.253394 | − | 0.146297i | ||||
\(27\) | −4.95468 | − | 1.56561i | −0.953529 | − | 0.301301i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.86924 | −0.532804 | −0.266402 | − | 0.963862i | \(-0.585835\pi\) | ||||
−0.266402 | + | 0.963862i | \(0.585835\pi\) | |||||||
\(30\) | −1.23810 | − | 1.44239i | −0.226045 | − | 0.263344i | ||||
\(31\) | −2.64299 | − | 4.57780i | −0.474696 | − | 0.822197i | 0.524884 | − | 0.851174i | \(-0.324109\pi\) |
−0.999580 | + | 0.0289764i | \(0.990775\pi\) | |||||||
\(32\) | 1.28693 | − | 4.80289i | 0.227499 | − | 0.849040i | ||||
\(33\) | 3.75061 | + | 2.70953i | 0.652897 | + | 0.471669i | ||||
\(34\) | 2.26778i | 0.388921i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.06932 | − | 5.16785i | 0.178220 | − | 0.861309i | ||||
\(37\) | −0.784341 | − | 2.92720i | −0.128945 | − | 0.481229i | 0.871005 | − | 0.491275i | \(-0.163469\pi\) |
−0.999950 | + | 0.0100459i | \(0.996802\pi\) | |||||||
\(38\) | −2.48576 | − | 0.666057i | −0.403243 | − | 0.108049i | ||||
\(39\) | 1.87354 | − | 4.92042i | 0.300007 | − | 0.787898i | ||||
\(40\) | 2.84053 | − | 2.99191i | 0.449127 | − | 0.473063i | ||||
\(41\) | 11.5768i | 1.80800i | 0.427537 | + | 0.903998i | \(0.359381\pi\) | ||||
−0.427537 | + | 0.903998i | \(0.640619\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.759108 | + | 0.759108i | 0.115763 | + | 0.115763i | 0.762615 | − | 0.646852i | \(-0.223915\pi\) |
−0.646852 | + | 0.762615i | \(0.723915\pi\) | |||||||
\(44\) | −2.34961 | + | 4.06965i | −0.354217 | + | 0.613522i | ||||
\(45\) | 4.33019 | − | 5.12342i | 0.645507 | − | 0.763754i | ||||
\(46\) | −0.884344 | − | 1.53173i | −0.130389 | − | 0.225841i | ||||
\(47\) | −10.4642 | + | 2.80388i | −1.52636 | + | 0.408988i | −0.921831 | − | 0.387593i | \(-0.873307\pi\) |
−0.604533 | + | 0.796580i | \(0.706640\pi\) | |||||||
\(48\) | 4.50176 | + | 0.460865i | 0.649773 | + | 0.0665201i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.33428 | − | 0.757266i | 0.330117 | − | 0.107094i | ||||
\(51\) | −7.90101 | + | 1.27328i | −1.10636 | + | 0.178295i | ||||
\(52\) | 5.16509 | + | 1.38398i | 0.716269 | + | 0.191924i | ||||
\(53\) | −6.05938 | − | 1.62361i | −0.832319 | − | 0.223019i | −0.182594 | − | 0.983188i | \(-0.558449\pi\) |
−0.649725 | + | 0.760169i | \(0.725116\pi\) | |||||||
\(54\) | −2.54782 | − | 0.112835i | −0.346714 | − | 0.0153548i | ||||
\(55\) | −5.09384 | + | 3.11990i | −0.686854 | + | 0.420687i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.924894 | − | 9.03442i | 0.122505 | − | 1.19664i | ||||
\(58\) | −1.36026 | + | 0.364480i | −0.178611 | + | 0.0478586i | ||||
\(59\) | 0.0797185 | + | 0.138077i | 0.0103785 | + | 0.0179760i | 0.871168 | − | 0.490985i | \(-0.163363\pi\) |
−0.860790 | + | 0.508961i | \(0.830030\pi\) | |||||||
\(60\) | 5.62428 | + | 3.84504i | 0.726092 | + | 0.496392i | ||||
\(61\) | 2.36267 | − | 4.09227i | 0.302509 | − | 0.523961i | −0.674195 | − | 0.738554i | \(-0.735509\pi\) |
0.976704 | + | 0.214593i | \(0.0688424\pi\) | |||||||
\(62\) | −1.83452 | − | 1.83452i | −0.232984 | − | 0.232984i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.78490i | 0.348112i | ||||||||
\(65\) | 4.92940 | + | 4.67998i | 0.611416 | + | 0.580480i | ||||
\(66\) | 2.12230 | + | 0.808104i | 0.261237 | + | 0.0994707i | ||||
\(67\) | 7.39232 | + | 1.98077i | 0.903116 | + | 0.241989i | 0.680354 | − | 0.732884i | \(-0.261826\pi\) |
0.222762 | + | 0.974873i | \(0.428493\pi\) | |||||||
\(68\) | −2.10367 | − | 7.85101i | −0.255108 | − | 0.952075i | ||||
\(69\) | 4.84006 | − | 3.94109i | 0.582675 | − | 0.474452i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5880i | 1.61260i | 0.591508 | + | 0.806299i | \(0.298533\pi\) | ||||
−0.591508 | + | 0.806299i | \(0.701467\pi\) | |||||||
\(72\) | −0.319531 | − | 5.52577i | −0.0376570 | − | 0.651218i | ||||
\(73\) | −1.52444 | + | 5.68930i | −0.178423 | + | 0.665882i | 0.817521 | + | 0.575899i | \(0.195348\pi\) |
−0.995943 | + | 0.0899831i | \(0.971319\pi\) | |||||||
\(74\) | −0.743687 | − | 1.28810i | −0.0864519 | − | 0.149739i | ||||
\(75\) | 3.94895 | + | 7.70751i | 0.455986 | + | 0.889987i | ||||
\(76\) | 9.22351 | 1.05801 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.263173 | − | 2.57069i | 0.0297985 | − | 0.291073i | ||||
\(79\) | 3.37499 | + | 1.94855i | 0.379716 | + | 0.219229i | 0.677695 | − | 0.735344i | \(-0.262979\pi\) |
−0.297979 | + | 0.954572i | \(0.596313\pi\) | |||||||
\(80\) | −2.78880 | + | 5.13351i | −0.311797 | + | 0.573944i | ||||
\(81\) | −1.03739 | − | 8.94001i | −0.115266 | − | 0.993335i | ||||
\(82\) | 1.47061 | + | 5.48839i | 0.162402 | + | 0.606091i | ||||
\(83\) | −4.03778 | + | 4.03778i | −0.443204 | + | 0.443204i | −0.893087 | − | 0.449883i | \(-0.851466\pi\) |
0.449883 | + | 0.893087i | \(0.351466\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41421 | − | 10.0457i | 0.261858 | − | 1.08961i | ||||
\(86\) | 0.456311 | + | 0.263451i | 0.0492052 | + | 0.0284087i | ||||
\(87\) | −2.03360 | − | 4.53454i | −0.218025 | − | 0.486154i | ||||
\(88\) | −1.27563 | + | 4.76073i | −0.135983 | + | 0.507496i | ||||
\(89\) | 1.97563 | − | 3.42189i | 0.209416 | − | 0.362719i | −0.742115 | − | 0.670273i | \(-0.766177\pi\) |
0.951531 | + | 0.307554i | \(0.0995104\pi\) | |||||||
\(90\) | 1.40205 | − | 2.97900i | 0.147789 | − | 0.314014i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.48247 | + | 4.48247i | 0.467330 | + | 0.467330i | ||||
\(93\) | 5.36150 | − | 7.42154i | 0.555962 | − | 0.769578i | ||||
\(94\) | −4.60474 | + | 2.65855i | −0.474943 | + | 0.274208i | ||||
\(95\) | 10.3023 | + | 5.59675i | 1.05699 | + | 0.574214i | ||||
\(96\) | 8.50261 | − | 1.37023i | 0.867794 | − | 0.139849i | ||||
\(97\) | 1.86878 | − | 1.86878i | 0.189746 | − | 0.189746i | −0.605840 | − | 0.795586i | \(-0.707163\pi\) |
0.795586 | + | 0.605840i | \(0.207163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.62386 | + | 7.84786i | −0.163204 | + | 0.788740i | ||||
\(100\) | −7.37876 | + | 4.78700i | −0.737876 | + | 0.478700i | ||||
\(101\) | 3.25725 | − | 1.88058i | 0.324109 | − | 0.187124i | −0.329114 | − | 0.944290i | \(-0.606750\pi\) |
0.653222 | + | 0.757166i | \(0.273417\pi\) | |||||||
\(102\) | −3.58400 | + | 1.60731i | −0.354869 | + | 0.159147i | ||||
\(103\) | −12.0989 | + | 3.24189i | −1.19214 | + | 0.319433i | −0.799731 | − | 0.600358i | \(-0.795025\pi\) |
−0.392409 | + | 0.919791i | \(0.628358\pi\) | |||||||
\(104\) | 5.60838 | 0.549947 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.07890 | −0.299049 | ||||||||
\(107\) | 0.970420 | − | 0.260023i | 0.0938140 | − | 0.0251374i | −0.211607 | − | 0.977355i | \(-0.567870\pi\) |
0.305421 | + | 0.952218i | \(0.401203\pi\) | |||||||
\(108\) | 8.92516 | − | 1.97281i | 0.858824 | − | 0.189834i | ||||
\(109\) | −16.4669 | + | 9.50719i | −1.57725 | + | 0.910623i | −0.582004 | + | 0.813186i | \(0.697731\pi\) |
−0.995242 | + | 0.0974376i | \(0.968935\pi\) | |||||||
\(110\) | −2.01859 | + | 2.12617i | −0.192465 | + | 0.202722i | ||||
\(111\) | 4.07024 | − | 3.31425i | 0.386330 | − | 0.314575i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.69132 | + | 5.69132i | −0.535394 | + | 0.535394i | −0.922173 | − | 0.386779i | \(-0.873588\pi\) |
0.386779 | + | 0.922173i | \(0.373588\pi\) | |||||||
\(114\) | −0.709169 | − | 4.40057i | −0.0664198 | − | 0.412151i | ||||
\(115\) | 2.28681 | + | 7.72665i | 0.213246 | + | 0.720514i | ||||
\(116\) | 4.37109 | − | 2.52365i | 0.405845 | − | 0.234315i | ||||
\(117\) | 9.10411 | − | 0.526450i | 0.841676 | − | 0.0486704i | ||||
\(118\) | 0.0553332 | + | 0.0553332i | 0.00509383 | + | 0.00509383i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.74166 | + | 2.36862i | 0.615427 | + | 0.216224i | ||||
\(121\) | −1.93190 | + | 3.34615i | −0.175627 | + | 0.304195i | ||||
\(122\) | 0.600262 | − | 2.24021i | 0.0543452 | − | 0.202819i | ||||
\(123\) | −18.2960 | + | 8.20518i | −1.64969 | + | 0.739836i | ||||
\(124\) | 8.05284 | + | 4.64931i | 0.723167 | + | 0.417520i | ||||
\(125\) | −11.1465 | + | 0.869508i | −0.996971 | + | 0.0777712i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1366 | + | 12.1366i | −1.07695 | + | 1.07695i | −0.0801668 | + | 0.996781i | \(0.525545\pi\) |
−0.996781 | + | 0.0801668i | \(0.974455\pi\) | |||||||
\(128\) | 2.92763 | + | 10.9261i | 0.258768 | + | 0.965736i | ||||
\(129\) | −0.661668 | + | 1.73772i | −0.0582566 | + | 0.152997i | ||||
\(130\) | 2.93145 | + | 1.59252i | 0.257105 | + | 0.139673i | ||||
\(131\) | 8.61072 | + | 4.97140i | 0.752322 | + | 0.434353i | 0.826532 | − | 0.562889i | \(-0.190310\pi\) |
−0.0742105 | + | 0.997243i | \(0.523644\pi\) | |||||||
\(132\) | −8.09697 | − | 0.828923i | −0.704751 | − | 0.0721485i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.75620 | 0.324486 | ||||||||
\(135\) | 11.1661 | + | 3.21216i | 0.961026 | + | 0.276459i | ||||
\(136\) | −4.26242 | − | 7.38272i | −0.365499 | − | 0.633063i | ||||
\(137\) | −5.00156 | + | 18.6661i | −0.427312 | + | 1.59475i | 0.331510 | + | 0.943452i | \(0.392442\pi\) |
−0.758822 | + | 0.651298i | \(0.774225\pi\) | |||||||
\(138\) | 1.79396 | − | 2.48324i | 0.152712 | − | 0.211388i | ||||
\(139\) | − | 16.7933i | − | 1.42439i | −0.701982 | − | 0.712195i | \(-0.747701\pi\) | ||
0.701982 | − | 0.712195i | \(-0.252299\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8479 | − | 14.5504i | −0.997770 | − | 1.22536i | ||||
\(142\) | 1.72609 | + | 6.44185i | 0.144850 | + | 0.540588i | ||||
\(143\) | −7.84366 | − | 2.10170i | −0.655920 | − | 0.175753i | ||||
\(144\) | 2.46231 | + | 7.44121i | 0.205193 | + | 0.620101i | ||||
\(145\) | 6.41365 | − | 0.166471i | 0.532625 | − | 0.0138247i | ||||
\(146\) | 2.89086i | 0.239249i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.76952 | + | 3.76952i | 0.309853 | + | 0.309853i | ||||
\(149\) | 4.65628 | − | 8.06492i | 0.381458 | − | 0.660704i | −0.609813 | − | 0.792545i | \(-0.708756\pi\) |
0.991271 | + | 0.131841i | \(0.0420889\pi\) | |||||||
\(150\) | 2.85122 | + | 3.15237i | 0.232801 | + | 0.257390i | ||||
\(151\) | −10.1934 | − | 17.6555i | −0.829527 | − | 1.43678i | −0.898410 | − | 0.439159i | \(-0.855277\pi\) |
0.0688822 | − | 0.997625i | \(-0.478057\pi\) | |||||||
\(152\) | 9.34424 | − | 2.50378i | 0.757918 | − | 0.203083i | ||||
\(153\) | −7.61221 | − | 11.5843i | −0.615410 | − | 0.936535i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.17353 | + | 10.0795i | 0.495869 | + | 0.809603i | ||||
\(156\) | 1.47356 | + | 9.14380i | 0.117979 | + | 0.732090i | ||||
\(157\) | 8.64539 | + | 2.31653i | 0.689977 | + | 0.184879i | 0.586737 | − | 0.809778i | \(-0.300412\pi\) |
0.103240 | + | 0.994656i | \(0.467079\pi\) | |||||||
\(158\) | 1.84755 | + | 0.495050i | 0.146983 | + | 0.0393841i | ||||
\(159\) | −1.72870 | − | 10.7270i | −0.137094 | − | 0.850705i | ||||
\(160\) | −2.59804 | + | 10.8106i | −0.205393 | + | 0.854657i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.62746 | − | 4.10654i | −0.127866 | − | 0.322640i | ||||
\(163\) | 8.81958 | − | 2.36320i | 0.690803 | − | 0.185100i | 0.103696 | − | 0.994609i | \(-0.466933\pi\) |
0.587108 | + | 0.809509i | \(0.300267\pi\) | |||||||
\(164\) | −10.1824 | − | 17.6365i | −0.795115 | − | 1.37718i | ||||
\(165\) | −8.54099 | − | 5.83905i | −0.664916 | − | 0.454569i | ||||
\(166\) | −1.40133 | + | 2.42717i | −0.108764 | + | 0.188385i | ||||
\(167\) | 1.58004 | + | 1.58004i | 0.122268 | + | 0.122268i | 0.765593 | − | 0.643325i | \(-0.222446\pi\) |
−0.643325 | + | 0.765593i | \(0.722446\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.75977i | − | 0.289213i | ||||||
\(170\) | −0.131575 | − | 5.06920i | −0.0100913 | − | 0.388790i | ||||
\(171\) | 14.9335 | − | 4.94153i | 1.14199 | − | 0.377888i | ||||
\(172\) | −1.82412 | − | 0.488773i | −0.139088 | − | 0.0372686i | ||||
\(173\) | −0.622134 | − | 2.32183i | −0.0472999 | − | 0.176526i | 0.938235 | − | 0.345999i | \(-0.112460\pi\) |
−0.985535 | + | 0.169473i | \(0.945793\pi\) | |||||||
\(174\) | −1.54012 | − | 1.89142i | −0.116756 | − | 0.143388i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 6.97941i | − | 0.526093i | ||||||
\(177\) | −0.161715 | + | 0.223850i | −0.0121552 | + | 0.0168256i | ||||
\(178\) | 0.501929 | − | 1.87323i | 0.0376212 | − | 0.140404i | ||||
\(179\) | −4.22190 | − | 7.31255i | −0.315560 | − | 0.546565i | 0.663997 | − | 0.747736i | \(-0.268859\pi\) |
−0.979556 | + | 0.201170i | \(0.935526\pi\) | |||||||
\(180\) | −2.09043 | + | 11.6138i | −0.155812 | + | 0.865643i | ||||
\(181\) | −5.51483 | −0.409914 | −0.204957 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204957 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.14198 | + | 0.833531i | 0.601872 | + | 0.0616164i | ||||
\(184\) | 5.75794 | + | 3.32435i | 0.424481 | + | 0.245074i | ||||
\(185\) | 1.92308 | + | 6.49771i | 0.141388 | + | 0.477721i | ||||
\(186\) | 1.59904 | − | 4.19951i | 0.117247 | − | 0.307923i | ||||
\(187\) | 3.19462 | + | 11.9225i | 0.233614 | + | 0.871859i | ||||
\(188\) | 13.4754 | − | 13.4754i | 0.982792 | − | 0.982792i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.59510 | + | 1.34463i | 0.405911 | + | 0.0975494i | ||||
\(191\) | −0.484562 | − | 0.279762i | −0.0350617 | − | 0.0202429i | 0.482367 | − | 0.875969i | \(-0.339777\pi\) |
−0.517428 | + | 0.855727i | \(0.673111\pi\) | |||||||
\(192\) | −4.40125 | + | 1.97382i | −0.317633 | + | 0.142448i | ||||
\(193\) | 2.58121 | − | 9.63320i | 0.185799 | − | 0.693413i | −0.808659 | − | 0.588278i | \(-0.799806\pi\) |
0.994458 | − | 0.105135i | \(-0.0335273\pi\) | |||||||
\(194\) | 0.648566 | − | 1.12335i | 0.0465643 | − | 0.0806518i | ||||
\(195\) | −3.90248 | + | 11.1074i | −0.279462 | + | 0.795417i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1505 | + | 10.1505i | 0.723190 | + | 0.723190i | 0.969254 | − | 0.246064i | \(-0.0791372\pi\) |
−0.246064 | + | 0.969254i | \(0.579137\pi\) | |||||||
\(198\) | 0.227071 | + | 3.92682i | 0.0161372 | + | 0.279067i | ||||
\(199\) | 10.1107 | − | 5.83740i | 0.716726 | − | 0.413802i | −0.0968203 | − | 0.995302i | \(-0.530867\pi\) |
0.813547 | + | 0.581500i | \(0.197534\pi\) | |||||||
\(200\) | −6.17588 | + | 6.85267i | −0.436701 | + | 0.484557i | ||||
\(201\) | 2.10898 | + | 13.0867i | 0.148756 | + | 0.923065i | ||||
\(202\) | 1.30532 | − | 1.30532i | 0.0918421 | − | 0.0918421i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.9167 | − | 8.88912i | 0.764324 | − | 0.622363i | ||||
\(205\) | −0.671679 | − | 25.8778i | −0.0469121 | − | 1.80739i | ||||
\(206\) | −5.32408 | + | 3.07386i | −0.370946 | + | 0.214166i | ||||
\(207\) | 9.65894 | + | 4.85594i | 0.671343 | + | 0.337511i | ||||
\(208\) | −7.67133 | + | 2.05553i | −0.531911 | + | 0.142525i | ||||
\(209\) | −14.0067 | −0.968867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.777102 | −0.0534979 | −0.0267490 | − | 0.999642i | \(-0.508515\pi\) | ||||
−0.0267490 | + | 0.999642i | \(0.508515\pi\) | |||||||
\(212\) | 10.6591 | − | 2.85610i | 0.732070 | − | 0.196157i | ||||
\(213\) | −21.4744 | + | 9.63061i | −1.47140 | + | 0.659879i | ||||
\(214\) | 0.427030 | − | 0.246546i | 0.0291911 | − | 0.0168535i | ||||
\(215\) | −1.74089 | − | 1.65280i | −0.118728 | − | 0.112720i | ||||
\(216\) | 8.50645 | − | 4.42142i | 0.578790 | − | 0.300840i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.59901 | + | 6.59901i | −0.446941 | + | 0.446941i | ||||
\(219\) | −10.0718 | + | 1.62312i | −0.680591 | + | 0.109680i | ||||
\(220\) | 5.01600 | − | 9.23326i | 0.338179 | − | 0.622507i | ||||
\(221\) | 12.1636 | − | 7.02265i | 0.818211 | − | 0.472394i | ||||
\(222\) | 1.50862 | − | 2.08828i | 0.101252 | − | 0.140156i | ||||
\(223\) | 3.33811 | + | 3.33811i | 0.223536 | + | 0.223536i | 0.809986 | − | 0.586450i | \(-0.199475\pi\) |
−0.586450 | + | 0.809986i | \(0.699475\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.38209 | + | 11.7037i | −0.625473 | + | 0.780246i | ||||
\(226\) | −1.97519 | + | 3.42113i | −0.131388 | + | 0.227570i | ||||
\(227\) | 0.0886976 | − | 0.331024i | 0.00588706 | − | 0.0219708i | −0.962920 | − | 0.269788i | \(-0.913046\pi\) |
0.968807 | + | 0.247817i | \(0.0797131\pi\) | |||||||
\(228\) | 6.53725 | + | 14.5768i | 0.432940 | + | 0.965374i | ||||
\(229\) | 11.6734 | + | 6.73964i | 0.771400 | + | 0.445368i | 0.833374 | − | 0.552710i | \(-0.186406\pi\) |
−0.0619741 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(230\) | 2.06566 | + | 3.37259i | 0.136205 | + | 0.222382i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.74324 | − | 3.74324i | 0.245756 | − | 0.245756i | ||||
\(233\) | −0.436524 | − | 1.62913i | −0.0285976 | − | 0.106728i | 0.950152 | − | 0.311788i | \(-0.100928\pi\) |
−0.978749 | + | 0.205060i | \(0.934261\pi\) | |||||||
\(234\) | 4.24924 | − | 1.40608i | 0.277782 | − | 0.0919184i | ||||
\(235\) | 23.2282 | − | 6.87468i | 1.51524 | − | 0.448455i | ||||
\(236\) | −0.242891 | − | 0.140233i | −0.0158109 | − | 0.00912842i | ||||
\(237\) | −0.687432 | + | 6.71488i | −0.0446535 | + | 0.436178i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.15325 | −0.333336 | −0.166668 | − | 0.986013i | \(-0.553301\pi\) | ||||
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(240\) | −10.0896 | − | 0.768990i | −0.651280 | − | 0.0496381i | ||||
\(241\) | −7.45869 | − | 12.9188i | −0.480457 | − | 0.832176i | 0.519292 | − | 0.854597i | \(-0.326196\pi\) |
−0.999749 | + | 0.0224214i | \(0.992862\pi\) | |||||||
\(242\) | −0.490820 | + | 1.83176i | −0.0315511 | + | 0.117750i | ||||
\(243\) | 13.3935 | − | 7.97581i | 0.859195 | − | 0.511648i | ||||
\(244\) | 8.31238i | 0.532146i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.63153 | + | 6.21409i | −0.486569 | + | 0.396196i | ||||
\(247\) | 4.12517 | + | 15.3953i | 0.262478 | + | 0.979581i | ||||
\(248\) | 9.42033 | + | 2.52417i | 0.598192 | + | 0.160285i | ||||
\(249\) | −9.24313 | − | 3.51949i | −0.585759 | − | 0.223039i | ||||
\(250\) | −5.17391 | + | 1.82816i | −0.327227 | + | 0.115623i | ||||
\(251\) | − | 4.30303i | − | 0.271605i | −0.990736 | − | 0.135802i | \(-0.956639\pi\) | ||
0.990736 | − | 0.135802i | \(-0.0433613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80704 | − | 6.80704i | −0.427955 | − | 0.427955i | ||||
\(254\) | −4.21205 | + | 7.29548i | −0.264287 | + | 0.457759i | ||||
\(255\) | 17.5874 | − | 3.30459i | 1.10136 | − | 0.206942i | ||||
\(256\) | −0.00901148 | − | 0.0156083i | −0.000563218 | − | 0.000975522i | ||||
\(257\) | 7.96236 | − | 2.13351i | 0.496678 | − | 0.133085i | −0.00177964 | − | 0.999998i | \(-0.500566\pi\) |
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(258\) | −0.0929433 | + | 0.907876i | −0.00578640 | + | 0.0565219i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.6259 | − | 2.79396i | −0.721007 | − | 0.173274i | ||||
\(261\) | 5.72505 | − | 6.42779i | 0.354372 | − | 0.397870i | ||||
\(262\) | 4.71372 | + | 1.26304i | 0.291215 | + | 0.0780307i | ||||
\(263\) | −0.0853641 | − | 0.0228732i | −0.00526378 | − | 0.00141042i | 0.256186 | − | 0.966627i | \(-0.417534\pi\) |
−0.261450 | + | 0.965217i | \(0.584201\pi\) | |||||||
\(264\) | −8.42797 | + | 1.35820i | −0.518706 | + | 0.0835915i | ||||
\(265\) | 13.6388 | + | 3.27771i | 0.837826 | + | 0.201348i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.80819 | + | 0.696985i | 0.416654 | + | 0.0426548i | ||||
\(268\) | −13.0039 | + | 3.48438i | −0.794339 | + | 0.212843i | ||||
\(269\) | 14.8350 | + | 25.6949i | 0.904504 | + | 1.56665i | 0.821581 | + | 0.570091i | \(0.193092\pi\) |
0.0829230 | + | 0.996556i | \(0.473574\pi\) | |||||||
\(270\) | 5.70172 | + | 0.104398i | 0.346995 | + | 0.00635348i | ||||
\(271\) | 11.3188 | − | 19.6048i | 0.687571 | − | 1.19091i | −0.285050 | − | 0.958513i | \(-0.592010\pi\) |
0.972621 | − | 0.232396i | \(-0.0746564\pi\) | |||||||
\(272\) | 8.53611 | + | 8.53611i | 0.517578 | + | 0.517578i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.48463i | 0.572988i | ||||||||
\(275\) | 11.2053 | − | 7.26950i | 0.675707 | − | 0.438367i | ||||
\(276\) | −3.90710 | + | 10.2611i | −0.235180 | + | 0.617645i | ||||
\(277\) | −5.75283 | − | 1.54147i | −0.345654 | − | 0.0926177i | 0.0818155 | − | 0.996647i | \(-0.473928\pi\) |
−0.427469 | + | 0.904030i | \(0.640595\pi\) | |||||||
\(278\) | −2.13326 | − | 7.96144i | −0.127944 | − | 0.477495i | ||||
\(279\) | 15.5290 | + | 3.21323i | 0.929698 | + | 0.192371i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.0093i | − | 1.31297i | −0.754341 | − | 0.656483i | \(-0.772043\pi\) | ||
0.754341 | − | 0.656483i | \(-0.227957\pi\) | |||||||
\(282\) | −7.46522 | − | 5.39306i | −0.444547 | − | 0.321152i | ||||
\(283\) | −3.51348 | + | 13.1125i | −0.208854 | + | 0.779455i | 0.779386 | + | 0.626545i | \(0.215531\pi\) |
−0.988240 | + | 0.152911i | \(0.951135\pi\) | |||||||
\(284\) | −11.9514 | − | 20.7004i | −0.709183 | − | 1.22834i | ||||
\(285\) | −1.54326 | + | 20.2484i | −0.0914148 | + | 1.19941i | ||||
\(286\) | −3.98553 | −0.235670 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.19181 | + | 12.4664i | 0.482707 | + | 0.734587i | ||||
\(289\) | −3.76641 | − | 2.17454i | −0.221554 | − | 0.127914i | ||||
\(290\) | 3.01946 | − | 0.893650i | 0.177309 | − | 0.0524769i | ||||
\(291\) | 4.27793 | + | 1.62890i | 0.250777 | + | 0.0954879i | ||||
\(292\) | −2.68166 | − | 10.0081i | −0.156932 | − | 0.585679i | ||||
\(293\) | 3.56359 | − | 3.56359i | 0.208187 | − | 0.208187i | −0.595309 | − | 0.803497i | \(-0.702970\pi\) |
0.803497 | + | 0.595309i | \(0.202970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.186207 | − | 0.304019i | −0.0108414 | − | 0.0177007i | ||||
\(296\) | 4.84212 | + | 2.79560i | 0.281443 | + | 0.162491i | ||||
\(297\) | −13.5537 | + | 2.99590i | −0.786464 | + | 0.173840i | ||||
\(298\) | 1.18298 | − | 4.41494i | 0.0685281 | − | 0.255750i | ||||
\(299\) | −5.47711 | + | 9.48663i | −0.316749 | + | 0.548626i | ||||
\(300\) | −12.7951 | − | 8.26856i | −0.738727 | − | 0.477385i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.07531 | − | 7.07531i | −0.407139 | − | 0.407139i | ||||
\(303\) | 5.28067 | + | 3.81488i | 0.303366 | + | 0.219159i | ||||
\(304\) | −11.8637 | + | 6.84950i | −0.680429 | + | 0.392846i | ||||
\(305\) | −5.04388 | + | 9.28458i | −0.288812 | + | 0.531634i | ||||
\(306\) | −5.08038 | − | 4.52495i | −0.290426 | − | 0.258674i | ||||
\(307\) | −10.4746 | + | 10.4746i | −0.597814 | + | 0.597814i | −0.939730 | − | 0.341916i | \(-0.888924\pi\) |
0.341916 | + | 0.939730i | \(0.388924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6987 | − | 16.8234i | −0.779291 | − | 0.957048i | ||||
\(310\) | 4.20717 | + | 3.99430i | 0.238951 | + | 0.226861i | ||||
\(311\) | 17.6967 | − | 10.2172i | 1.00349 | − | 0.579365i | 0.0942109 | − | 0.995552i | \(-0.469967\pi\) |
0.909279 | + | 0.416187i | \(0.136634\pi\) | |||||||
\(312\) | 3.97499 | + | 8.86348i | 0.225040 | + | 0.501796i | ||||
\(313\) | −22.5161 | + | 6.03317i | −1.27268 | + | 0.341015i | −0.831059 | − | 0.556185i | \(-0.812265\pi\) |
−0.441626 | + | 0.897199i | \(0.645598\pi\) | |||||||
\(314\) | 4.39291 | 0.247906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.85542 | −0.385647 | ||||||||
\(317\) | −31.3557 | + | 8.40174i | −1.76111 | + | 0.471889i | −0.986940 | − | 0.161087i | \(-0.948500\pi\) |
−0.774172 | + | 0.632975i | \(0.781833\pi\) | |||||||
\(318\) | −2.18220 | − | 4.86589i | −0.122372 | − | 0.272866i | ||||
\(319\) | −6.63790 | + | 3.83239i | −0.371651 | + | 0.214573i | ||||
\(320\) | −0.161578 | − | 6.22512i | −0.00903247 | − | 0.347995i | ||||
\(321\) | 1.09873 | + | 1.34936i | 0.0613254 | + | 0.0753137i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.1308 | − | 17.1308i | 0.953185 | − | 0.953185i | ||||
\(324\) | 9.44362 | + | 12.7071i | 0.524645 | + | 0.705948i | ||||
\(325\) | −11.2903 | − | 10.1752i | −0.626272 | − | 0.564420i | ||||
\(326\) | 3.88103 | − | 2.24071i | 0.214950 | − | 0.124102i | ||||
\(327\) | −26.6962 | − | 19.2860i | −1.47631 | − | 1.06652i | ||||
\(328\) | −15.1033 | − | 15.1033i | −0.833938 | − | 0.833938i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.79089 | − | 1.68323i | −0.263730 | − | 0.0926589i | ||||
\(331\) | 1.10731 | − | 1.91791i | 0.0608631 | − | 0.105418i | −0.833988 | − | 0.551782i | \(-0.813948\pi\) |
0.894851 | + | 0.446364i | \(0.147281\pi\) | |||||||
\(332\) | 2.59984 | − | 9.70274i | 0.142685 | − | 0.532507i | ||||
\(333\) | 8.12266 | + | 4.08359i | 0.445119 | + | 0.223779i | ||||
\(334\) | 0.949788 | + | 0.548360i | 0.0519701 | + | 0.0300049i | ||||
\(335\) | −16.6391 | − | 3.99874i | −0.909091 | − | 0.218475i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8541 | − | 10.8541i | 0.591263 | − | 0.591263i | −0.346710 | − | 0.937972i | \(-0.612701\pi\) |
0.937972 | + | 0.346710i | \(0.112701\pi\) | |||||||
\(338\) | −0.477605 | − | 1.78245i | −0.0259783 | − | 0.0969524i | ||||
\(339\) | −13.0283 | − | 4.96078i | −0.707601 | − | 0.269432i | ||||
\(340\) | 5.15788 | + | 17.4274i | 0.279725 | + | 0.945135i | ||||
\(341\) | −12.2290 | − | 7.06041i | −0.662237 | − | 0.382343i | ||||
\(342\) | 6.45202 | − | 4.23971i | 0.348885 | − | 0.229257i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.98068 | −0.106791 | ||||||||
\(345\) | −10.5904 | + | 9.09040i | −0.570168 | + | 0.489411i | ||||
\(346\) | −0.589887 | − | 1.02171i | −0.0317125 | − | 0.0549277i | ||||
\(347\) | 1.85334 | − | 6.91675i | 0.0994923 | − | 0.371310i | −0.898170 | − | 0.439649i | \(-0.855103\pi\) |
0.997662 | + | 0.0683381i | \(0.0217697\pi\) | |||||||
\(348\) | 7.08642 | + | 5.11940i | 0.379872 | + | 0.274429i | ||||
\(349\) | − | 7.42733i | − | 0.397576i | −0.980043 | − | 0.198788i | \(-0.936300\pi\) | ||
0.980043 | − | 0.198788i | \(-0.0637005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.28463 | + | 14.0150i | 0.388825 | + | 0.748066i | ||||
\(352\) | −3.43787 | − | 12.8303i | −0.183239 | − | 0.683857i | ||||
\(353\) | −12.4176 | − | 3.32729i | −0.660922 | − | 0.177094i | −0.0872601 | − | 0.996186i | \(-0.527811\pi\) |
−0.573662 | + | 0.819092i | \(0.694478\pi\) | |||||||
\(354\) | −0.0482306 | + | 0.126666i | −0.00256343 | + | 0.00673224i | ||||
\(355\) | −0.788366 | − | 30.3734i | −0.0418421 | − | 1.61205i | ||||
\(356\) | 6.95068i | 0.368385i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.93045 | − | 2.93045i | −0.154879 | − | 0.154879i | ||||
\(359\) | 12.6320 | − | 21.8793i | 0.666692 | − | 1.15474i | −0.312132 | − | 0.950039i | \(-0.601043\pi\) |
0.978824 | − | 0.204705i | \(-0.0656237\pi\) | |||||||
\(360\) | 1.03485 | + | 12.3333i | 0.0545415 | + | 0.650022i | ||||
\(361\) | 4.24604 | + | 7.35435i | 0.223476 | + | 0.387071i | ||||
\(362\) | −2.61449 | + | 0.700551i | −0.137415 | + | 0.0368201i | ||||
\(363\) | −6.65750 | − | 0.681558i | −0.349428 | − | 0.0357725i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.07752 | − | 12.8058i | 0.161085 | − | 0.670288i | ||||
\(366\) | 3.96586 | − | 0.639115i | 0.207299 | − | 0.0334071i | ||||
\(367\) | 2.20188 | + | 0.589992i | 0.114937 | + | 0.0307973i | 0.315829 | − | 0.948816i | \(-0.397717\pi\) |
−0.200892 | + | 0.979613i | \(0.564384\pi\) | |||||||
\(368\) | −9.09430 | − | 2.43681i | −0.474073 | − | 0.127027i | ||||
\(369\) | −25.9349 | − | 23.0995i | −1.35012 | − | 1.20251i | ||||
\(370\) | 1.73711 | + | 2.83617i | 0.0903081 | + | 0.147445i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.64024 | + | 16.0219i | −0.0850424 | + | 0.830699i | ||||
\(373\) | −17.8205 | + | 4.77498i | −0.922708 | + | 0.247239i | −0.688742 | − | 0.725006i | \(-0.741837\pi\) |
−0.233965 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(374\) | 3.02904 | + | 5.24645i | 0.156628 | + | 0.271287i | ||||
\(375\) | −9.27434 | − | 16.9996i | −0.478925 | − | 0.877856i | ||||
\(376\) | 9.99377 | − | 17.3097i | 0.515389 | − | 0.892681i | ||||
\(377\) | 6.16727 | + | 6.16727i | 0.317630 | + | 0.317630i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0635i | 0.979228i | 0.871939 | + | 0.489614i | \(0.162862\pi\) | ||||
−0.871939 | + | 0.489614i | \(0.837138\pi\) | |||||||
\(380\) | −20.6174 | + | 0.535141i | −1.05765 | + | 0.0274522i | ||||
\(381\) | −27.7826 | − | 10.5787i | −1.42334 | − | 0.541965i | ||||
\(382\) | −0.265262 | − | 0.0710766i | −0.0135720 | − | 0.00363660i | ||||
\(383\) | 6.48757 | + | 24.2119i | 0.331499 | + | 1.23717i | 0.907615 | + | 0.419804i | \(0.137901\pi\) |
−0.576115 | + | 0.817368i | \(0.695432\pi\) | |||||||
\(384\) | −15.1925 | + | 12.3708i | −0.775291 | + | 0.631293i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.89484i | − | 0.249141i | ||||||
\(387\) | −3.21525 | + | 0.185924i | −0.163440 | + | 0.00945103i | ||||
\(388\) | −1.20327 | + | 4.49065i | −0.0610865 | + | 0.227978i | ||||
\(389\) | 9.17563 | + | 15.8927i | 0.465223 | + | 0.805790i | 0.999212 | − | 0.0397016i | \(-0.0126407\pi\) |
−0.533988 | + | 0.845492i | \(0.679307\pi\) | |||||||
\(390\) | −0.439125 | + | 5.76157i | −0.0222360 | + | 0.291748i | ||||
\(391\) | 16.6506 | 0.842056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.75387 | + | 17.1319i | −0.0884710 | + | 0.864189i | ||||
\(394\) | 6.10159 | + | 3.52275i | 0.307393 | + | 0.177474i | ||||
\(395\) | −7.65721 | − | 4.15981i | −0.385276 | − | 0.209303i | ||||
\(396\) | −4.42877 | − | 13.3840i | −0.222554 | − | 0.672569i | ||||
\(397\) | 3.99423 | + | 14.9067i | 0.200465 | + | 0.748144i | 0.990784 | + | 0.135449i | \(0.0432478\pi\) |
−0.790320 | + | 0.612695i | \(0.790086\pi\) | |||||||
\(398\) | 4.05178 | − | 4.05178i | 0.203097 | − | 0.203097i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.93600 | − | 11.6368i | 0.296800 | − | 0.581841i | ||||
\(401\) | −29.8123 | − | 17.2121i | −1.48876 | − | 0.859534i | −0.488838 | − | 0.872374i | \(-0.662579\pi\) |
−0.999918 | + | 0.0128408i | \(0.995913\pi\) | |||||||
\(402\) | 2.66224 | + | 5.93629i | 0.132781 | + | 0.296075i | ||||
\(403\) | −4.15876 | + | 15.5207i | −0.207163 | + | 0.773141i | ||||
\(404\) | −3.30813 | + | 5.72986i | −0.164586 | + | 0.285071i | ||||
\(405\) | 2.83759 | + | 19.9236i | 0.141001 | + | 0.990009i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.72437 | − | 5.72437i | −0.283746 | − | 0.283746i | ||||
\(408\) | 8.64662 | − | 11.9689i | 0.428071 | − | 0.592548i | ||||
\(409\) | −6.57533 | + | 3.79627i | −0.325129 | + | 0.187714i | −0.653677 | − | 0.756774i | \(-0.726774\pi\) |
0.328547 | + | 0.944488i | \(0.393441\pi\) | |||||||
\(410\) | −3.60571 | − | 12.1829i | −0.178073 | − | 0.601673i | ||||
\(411\) | −33.0447 | + | 5.32529i | −1.62998 | + | 0.262677i | ||||
\(412\) | 15.5804 | − | 15.5804i | 0.767593 | − | 0.767593i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.19600 | + | 1.07514i | 0.255369 | + | 0.0528404i | ||||
\(415\) | 8.79145 | − | 9.25999i | 0.431555 | − | 0.454555i | ||||
\(416\) | −13.0897 | + | 7.55737i | −0.641777 | + | 0.370530i | ||||
\(417\) | 26.5401 | − | 11.9024i | 1.29967 | − | 0.582863i | ||||
\(418\) | −6.64038 | + | 1.77928i | −0.324791 | + | 0.0870276i | ||||
\(419\) | 6.20644 | 0.303204 | 0.151602 | − | 0.988442i | \(-0.451557\pi\) | ||||
0.151602 | + | 0.988442i | \(0.451557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1339 | 1.22495 | 0.612474 | − | 0.790490i | \(-0.290174\pi\) | ||||
0.612474 | + | 0.790490i | \(0.290174\pi\) | |||||||
\(422\) | −0.368412 | + | 0.0987156i | −0.0179340 | + | 0.00480540i | ||||
\(423\) | 14.5981 | − | 29.0370i | 0.709784 | − | 1.41183i | ||||
\(424\) | 10.0233 | − | 5.78696i | 0.486775 | − | 0.281040i | ||||
\(425\) | −4.81368 | + | 22.5955i | −0.233498 | + | 1.09604i | ||||
\(426\) | −8.95731 | + | 7.29363i | −0.433983 | + | 0.353377i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.24966 | + | 1.24966i | −0.0604048 | + | 0.0604048i | ||||
\(429\) | −2.23774 | − | 13.8857i | −0.108039 | − | 0.670408i | ||||
\(430\) | −1.03528 | − | 0.562421i | −0.0499258 | − | 0.0271224i | ||||
\(431\) | −7.30254 | + | 4.21613i | −0.351751 | + | 0.203084i | −0.665456 | − | 0.746437i | \(-0.731763\pi\) |
0.313705 | + | 0.949520i | \(0.398430\pi\) | |||||||
\(432\) | −10.0149 | + | 9.16546i | −0.481842 | + | 0.440974i | ||||
\(433\) | 18.8277 | + | 18.8277i | 0.904802 | + | 0.904802i | 0.995847 | − | 0.0910444i | \(-0.0290205\pi\) |
−0.0910444 | + | 0.995847i | \(0.529021\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.80882 | + | 10.0181i | 0.230566 | + | 0.480333i | ||||
\(436\) | 16.7242 | − | 28.9671i | 0.800942 | − | 1.38727i | ||||
\(437\) | −4.89035 | + | 18.2510i | −0.233937 | + | 0.873065i | ||||
\(438\) | −4.56871 | + | 2.04892i | −0.218301 | + | 0.0979013i | ||||
\(439\) | 4.22855 | + | 2.44135i | 0.201818 | + | 0.116519i | 0.597503 | − | 0.801867i | \(-0.296160\pi\) |
−0.395685 | + | 0.918386i | \(0.629493\pi\) | |||||||
\(440\) | 2.57523 | − | 10.7157i | 0.122769 | − | 0.510853i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.87447 | − | 4.87447i | 0.231855 | − | 0.231855i | ||||
\(443\) | 8.74656 | + | 32.6426i | 0.415561 | + | 1.55090i | 0.783708 | + | 0.621129i | \(0.213326\pi\) |
−0.368147 | + | 0.929768i | \(0.620008\pi\) | |||||||
\(444\) | −3.28566 | + | 8.62903i | −0.155931 | + | 0.409516i | ||||
\(445\) | −4.21761 | + | 7.76362i | −0.199934 | + | 0.368031i | ||||
\(446\) | 2.00658 | + | 1.15850i | 0.0950145 | + | 0.0548567i | ||||
\(447\) | 16.0460 | + | 1.64270i | 0.758948 | + | 0.0776970i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.6736 | −1.11723 | −0.558613 | − | 0.829428i | \(-0.688666\pi\) | ||||
−0.558613 | + | 0.829428i | \(0.688666\pi\) | |||||||
\(450\) | −2.96117 | + | 6.74034i | −0.139591 | + | 0.317743i | ||||
\(451\) | 15.4630 | + | 26.7826i | 0.728123 | + | 1.26115i | ||||
\(452\) | 3.66451 | − | 13.6762i | 0.172364 | − | 0.643272i | ||||
\(453\) | 20.6780 | − | 28.6231i | 0.971539 | − | 1.34483i | ||||
\(454\) | − | 0.168200i | − | 0.00789404i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5798 | + | 12.9930i | 0.495444 | + | 0.608455i | ||||
\(457\) | 3.75469 | + | 14.0127i | 0.175637 | + | 0.655486i | 0.996442 | + | 0.0842782i | \(0.0268584\pi\) |
−0.820805 | + | 0.571208i | \(0.806475\pi\) | |||||||
\(458\) | 6.39031 | + | 1.71228i | 0.298599 | + | 0.0800095i | ||||
\(459\) | 12.9126 | − | 20.2408i | 0.602708 | − | 0.944760i | ||||
\(460\) | −10.2798 | − | 9.75966i | −0.479298 | − | 0.455047i | ||||
\(461\) | − | 23.3153i | − | 1.08590i | −0.839764 | − | 0.542951i | \(-0.817307\pi\) | ||
0.839764 | − | 0.542951i | \(-0.182693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.0563 | − | 17.0563i | −0.792672 | − | 0.792672i | 0.189256 | − | 0.981928i | \(-0.439392\pi\) |
−0.981928 | + | 0.189256i | \(0.939392\pi\) | |||||||
\(464\) | −3.74819 | + | 6.49206i | −0.174005 | + | 0.301386i | ||||
\(465\) | −11.5541 | + | 16.9006i | −0.535807 | + | 0.783745i | ||||
\(466\) | −0.413898 | − | 0.716892i | −0.0191734 | − | 0.0332094i | ||||
\(467\) | −10.9367 | + | 2.93048i | −0.506090 | + | 0.135606i | −0.502825 | − | 0.864388i | \(-0.667706\pi\) |
−0.00326486 | + | 0.999995i | \(0.501039\pi\) | |||||||
\(468\) | −13.4065 | + | 8.80957i | −0.619714 | + | 0.407223i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.1388 | − | 6.20986i | 0.467668 | − | 0.286439i | ||||
\(471\) | 2.46647 | + | 15.3050i | 0.113649 | + | 0.705218i | ||||
\(472\) | −0.284138 | − | 0.0761345i | −0.0130785 | − | 0.00350438i | ||||
\(473\) | 2.77010 | + | 0.742247i | 0.127369 | + | 0.0341285i | ||||
\(474\) | 0.527093 | + | 3.27074i | 0.0242102 | + | 0.150230i | ||||
\(475\) | −23.3535 | − | 11.9128i | −1.07153 | − | 0.546595i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.7277 | − | 10.3349i | 0.720121 | − | 0.473201i | ||||
\(478\) | −2.44307 | + | 0.654619i | −0.111743 | + | 0.0299416i | ||||
\(479\) | −10.0600 | − | 17.4244i | −0.459652 | − | 0.796140i | 0.539291 | − | 0.842120i | \(-0.318692\pi\) |
−0.998942 | + | 0.0459795i | \(0.985359\pi\) | |||||||
\(480\) | −18.9265 | + | 3.55621i | −0.863873 | + | 0.162318i | ||||
\(481\) | −4.60596 | + | 7.97776i | −0.210014 | + | 0.363754i | ||||
\(482\) | −5.17713 | − | 5.17713i | −0.235812 | − | 0.235812i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 6.79683i | − | 0.308947i | ||||||
\(485\) | −4.06888 | + | 4.28573i | −0.184758 | + | 0.194605i | ||||
\(486\) | 5.33649 | − | 5.48259i | 0.242068 | − | 0.248695i | ||||
\(487\) | −10.6271 | − | 2.84753i | −0.481561 | − | 0.129034i | 0.00986850 | − | 0.999951i | \(-0.496859\pi\) |
−0.491429 | + | 0.870917i | \(0.663525\pi\) | |||||||
\(488\) | 2.25645 | + | 8.42119i | 0.102145 | + | 0.381209i | ||||
\(489\) | 9.98576 | + | 12.2635i | 0.451572 | + | 0.554576i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.29546i | − | 0.103593i | −0.998658 | − | 0.0517963i | \(-0.983505\pi\) | ||
0.998658 | − | 0.0517963i | \(-0.0164947\pi\) | |||||||
\(492\) | 20.6558 | − | 28.5923i | 0.931235 | − | 1.28904i | ||||
\(493\) | 3.43125 | − | 12.8056i | 0.154536 | − | 0.576735i | ||||
\(494\) | 3.91135 | + | 6.77466i | 0.175980 | + | 0.304806i | ||||
\(495\) | 3.17451 | − | 17.6367i | 0.142684 | − | 0.792709i | ||||
\(496\) | −13.8106 | −0.620113 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.82910 | − | 0.494377i | −0.216397 | − | 0.0221536i | ||||
\(499\) | −10.6750 | − | 6.16321i | −0.477878 | − | 0.275903i | 0.241654 | − | 0.970363i | \(-0.422310\pi\) |
−0.719532 | + | 0.694459i | \(0.755644\pi\) | |||||||
\(500\) | 16.2161 | − | 11.1286i | 0.725207 | − | 0.497684i | ||||
\(501\) | −1.37723 | + | 3.61697i | −0.0615301 | + | 0.161594i | ||||
\(502\) | −0.546616 | − | 2.04000i | −0.0243967 | − | 0.0910496i | ||||
\(503\) | −4.62523 | + | 4.62523i | −0.206229 | + | 0.206229i | −0.802662 | − | 0.596434i | \(-0.796584\pi\) |
0.596434 | + | 0.802662i | \(0.296584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.17188 | + | 4.39266i | −0.319144 | + | 0.195471i | ||||
\(506\) | −4.09181 | − | 2.36241i | −0.181903 | − | 0.105022i | ||||
\(507\) | 5.94194 | − | 2.66477i | 0.263891 | − | 0.118347i | ||||
\(508\) | 7.81448 | − | 29.1641i | 0.346712 | − | 1.29395i | ||||
\(509\) | 6.80807 | − | 11.7919i | 0.301762 | − | 0.522668i | −0.674773 | − | 0.738025i | \(-0.735758\pi\) |
0.976535 | + | 0.215358i | \(0.0690918\pi\) | |||||||
\(510\) | 7.91811 | − | 3.80079i | 0.350620 | − | 0.168302i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0031 | − | 16.0031i | −0.707245 | − | 0.707245i | ||||
\(513\) | 18.3939 | + | 20.0986i | 0.812109 | + | 0.887373i | ||||
\(514\) | 3.50381 | − | 2.02292i | 0.154546 | − | 0.0892273i | ||||
\(515\) | 26.8568 | − | 7.94862i | 1.18345 | − | 0.350258i | ||||
\(516\) | −0.520409 | − | 3.22927i | −0.0229097 | − | 0.142161i | ||||
\(517\) | −20.4636 | + | 20.4636i | −0.899987 | + | 0.899987i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.22848 | − | 2.62884i | 0.141715 | − | 0.115393i | ||||
\(520\) | −12.5365 | + | 0.325394i | −0.549762 | + | 0.0142695i | ||||
\(521\) | 15.9236 | − | 9.19351i | 0.697626 | − | 0.402775i | −0.108836 | − | 0.994060i | \(-0.534712\pi\) |
0.806463 | + | 0.591285i | \(0.201379\pi\) | |||||||
\(522\) | 1.89763 | − | 3.77457i | 0.0830570 | − | 0.165208i | ||||
\(523\) | −12.1719 | + | 3.26144i | −0.532239 | + | 0.142613i | −0.514922 | − | 0.857237i | \(-0.672179\pi\) |
−0.0173168 | + | 0.999850i | \(0.505512\pi\) | |||||||
\(524\) | −17.4905 | −0.764074 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0433754 | −0.00189126 | ||||||||
\(527\) | 23.5917 | − | 6.32138i | 1.02767 | − | 0.275364i | ||||
\(528\) | 11.0303 | − | 4.94672i | 0.480030 | − | 0.215279i | ||||
\(529\) | 8.67226 | − | 5.00693i | 0.377055 | − | 0.217693i | ||||
\(530\) | 6.88231 | − | 0.178636i | 0.298949 | − | 0.00775944i | ||||
\(531\) | −0.468389 | − | 0.0969179i | −0.0203264 | − | 0.00420588i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.8837 | − | 24.8837i | 1.07783 | − | 1.07783i | ||||
\(534\) | 3.31619 | − | 0.534418i | 0.143506 | − | 0.0231265i | ||||
\(535\) | −2.15411 | + | 0.637537i | −0.0931302 | + | 0.0275631i | ||||
\(536\) | −12.2282 | + | 7.05998i | −0.528180 | + | 0.304945i | ||||
\(537\) | 8.56443 | − | 11.8551i | 0.369582 | − | 0.511586i | ||||
\(538\) | 10.2971 | + | 10.2971i | 0.443938 | + | 0.443938i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.8361 | + | 4.92769i | −0.853609 | + | 0.212054i | ||||
\(541\) | −13.9129 | + | 24.0979i | −0.598162 | + | 1.03605i | 0.394930 | + | 0.918711i | \(0.370769\pi\) |
−0.993092 | + | 0.117336i | \(0.962564\pi\) | |||||||
\(542\) | 2.87568 | − | 10.7322i | 0.123521 | − | 0.460986i | ||||
\(543\) | −3.90868 | − | 8.71563i | −0.167738 | − | 0.374023i | ||||
\(544\) | 19.8966 | + | 11.4873i | 0.853061 | + | 0.492515i | ||||
\(545\) | 36.2572 | − | 22.2070i | 1.55309 | − | 0.951242i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.2773 | + | 13.2773i | −0.567695 | + | 0.567695i | −0.931482 | − | 0.363787i | \(-0.881483\pi\) |
0.363787 | + | 0.931482i | \(0.381483\pi\) | |||||||
\(548\) | −8.79828 | − | 32.8356i | −0.375844 | − | 1.40267i | ||||
\(549\) | 4.45339 | + | 13.4583i | 0.190066 | + | 0.574388i | ||||
\(550\) | 4.38882 | − | 4.86977i | 0.187140 | − | 0.207648i | ||||
\(551\) | 13.0287 | + | 7.52212i | 0.555041 | + | 0.320453i | ||||
\(552\) | −1.17280 | + | 11.4560i | −0.0499178 | + | 0.487600i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.92314 | −0.124192 | ||||||||
\(555\) | −8.90597 | + | 7.64455i | −0.378037 | + | 0.324493i | ||||
\(556\) | 14.7706 | + | 25.5834i | 0.626413 | + | 1.08498i | ||||
\(557\) | −3.80675 | + | 14.2070i | −0.161297 | + | 0.601969i | 0.837187 | + | 0.546917i | \(0.184199\pi\) |
−0.998484 | + | 0.0550511i | \(0.982468\pi\) | |||||||
\(558\) | 7.77023 | − | 0.449318i | 0.328940 | − | 0.0190211i | ||||
\(559\) | − | 3.26332i | − | 0.138024i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5781 | + | 13.4990i | −0.699927 | + | 0.569926i | ||||
\(562\) | −2.79585 | − | 10.4343i | −0.117936 | − | 0.440143i | ||||
\(563\) | 13.8820 | + | 3.71967i | 0.585057 | + | 0.156766i | 0.539193 | − | 0.842182i | \(-0.318729\pi\) |
0.0458638 | + | 0.998948i | \(0.485396\pi\) | |||||||
\(564\) | 30.8472 | + | 11.7457i | 1.29890 | + | 0.494581i | ||||
\(565\) | 12.3917 | − | 13.0521i | 0.521322 | − | 0.549106i | ||||
\(566\) | 6.66273i | 0.280055i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.7271 | − | 17.7271i | −0.743811 | − | 0.743811i | ||||
\(569\) | −19.9137 | + | 34.4916i | −0.834827 | + | 1.44596i | 0.0593435 | + | 0.998238i | \(0.481099\pi\) |
−0.894171 | + | 0.447726i | \(0.852234\pi\) | |||||||
\(570\) | 1.84053 | + | 9.79550i | 0.0770915 | + | 0.410289i | ||||
\(571\) | 21.9157 | + | 37.9591i | 0.917143 | + | 1.58854i | 0.803733 | + | 0.594990i | \(0.202844\pi\) |
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(572\) | 13.7978 | − | 3.69712i | 0.576917 | − | 0.154584i | ||||
\(573\) | 0.0986978 | − | 0.964086i | 0.00412316 | − | 0.0402753i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.56003 | − | 17.1388i | −0.231869 | − | 0.714739i | ||||
\(576\) | −6.23885 | − | 5.55676i | −0.259952 | − | 0.231532i | ||||
\(577\) | −38.0004 | − | 10.1822i | −1.58198 | − | 0.423890i | −0.642441 | − | 0.766336i | \(-0.722078\pi\) |
−0.939538 | + | 0.342446i | \(0.888745\pi\) | |||||||
\(578\) | −2.06183 | − | 0.552465i | −0.0857607 | − | 0.0229795i | ||||
\(579\) | 17.0537 | − | 2.74828i | 0.708730 | − | 0.114215i | ||||
\(580\) | −9.62434 | + | 5.89476i | −0.399629 | + | 0.244767i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.23502 | + | 0.228809i | 0.0926445 | + | 0.00948443i | ||||
\(583\) | −16.1868 | + | 4.33725i | −0.670390 | + | 0.179630i | ||||
\(584\) | −5.43352 | − | 9.41114i | −0.224841 | − | 0.389436i | ||||
\(585\) | −20.3200 | + | 1.70500i | −0.840129 | + | 0.0704929i | ||||
\(586\) | 1.23676 | − | 2.14213i | 0.0510900 | − | 0.0884905i | ||||
\(587\) | −27.2778 | − | 27.2778i | −1.12588 | − | 1.12588i | −0.990841 | − | 0.135034i | \(-0.956886\pi\) |
−0.135034 | − | 0.990841i | \(-0.543114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.7160i | 1.14202i | ||||||||
\(590\) | −0.126897 | − | 0.120477i | −0.00522429 | − | 0.00495995i | ||||
\(591\) | −8.84754 | + | 23.2360i | −0.363939 | + | 0.955801i | ||||
\(592\) | −7.64782 | − | 2.04923i | −0.314324 | − | 0.0842228i | ||||
\(593\) | 0.442890 | + | 1.65289i | 0.0181873 | + | 0.0678759i | 0.974423 | − | 0.224721i | \(-0.0721472\pi\) |
−0.956236 | + | 0.292597i | \(0.905480\pi\) | |||||||
\(594\) | −6.04501 | + | 3.14204i | −0.248030 | + | 0.128919i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.3818i | 0.671025i | ||||||||
\(597\) | 16.3914 | + | 11.8416i | 0.670857 | + | 0.484644i | ||||
\(598\) | −1.39152 | + | 5.19322i | −0.0569034 | + | 0.212366i | ||||
\(599\) | 7.80027 | + | 13.5105i | 0.318710 | + | 0.552022i | 0.980219 | − | 0.197915i | \(-0.0634170\pi\) |
−0.661509 | + | 0.749937i | \(0.730084\pi\) | |||||||
\(600\) | −15.2072 | − | 4.90346i | −0.620830 | − | 0.200183i | ||||
\(601\) | −14.2954 | −0.583122 | −0.291561 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291561 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.1875 | + | 12.6083i | −0.781374 | + | 0.513452i | ||||
\(604\) | 31.0579 | + | 17.9313i | 1.26373 | + | 0.729614i | ||||
\(605\) | 4.12426 | − | 7.59178i | 0.167675 | − | 0.308650i | ||||
\(606\) | 2.98809 | + | 1.13777i | 0.121383 | + | 0.0462187i | ||||
\(607\) | 9.83819 | + | 36.7166i | 0.399320 | + | 1.49028i | 0.814296 | + | 0.580450i | \(0.197123\pi\) |
−0.414976 | + | 0.909832i | \(0.636210\pi\) | |||||||
\(608\) | −18.4352 | + | 18.4352i | −0.747646 | + | 0.747646i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.21180 | + | 5.04240i | −0.0490643 | + | 0.204161i | ||||
\(611\) | 28.5191 | + | 16.4655i | 1.15376 | + | 0.666122i | ||||
\(612\) | 21.7857 | + | 10.9525i | 0.880634 | + | 0.442731i | ||||
\(613\) | 1.01661 | − | 3.79405i | 0.0410606 | − | 0.153240i | −0.942352 | − | 0.334624i | \(-0.891391\pi\) |
0.983412 | + | 0.181383i | \(0.0580575\pi\) | |||||||
\(614\) | −3.63523 | + | 6.29641i | −0.146706 | + | 0.254102i | ||||
\(615\) | 40.4212 | − | 19.4027i | 1.62994 | − | 0.782392i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.21465 | − | 3.21465i | −0.129417 | − | 0.129417i | 0.639431 | − | 0.768848i | \(-0.279170\pi\) |
−0.768848 | + | 0.639431i | \(0.779170\pi\) | |||||||
\(618\) | −8.63141 | − | 6.23554i | −0.347206 | − | 0.250830i | ||||
\(619\) | 42.1764 | − | 24.3506i | 1.69521 | − | 0.978731i | 0.745033 | − | 0.667027i | \(-0.232434\pi\) |
0.950179 | − | 0.311704i | \(-0.100900\pi\) | |||||||
\(620\) | −18.2704 | − | 9.92545i | −0.733757 | − | 0.398616i | ||||
\(621\) | −0.828458 | + | 18.7067i | −0.0332449 | + | 0.750673i | ||||
\(622\) | 7.09184 | − | 7.09184i | 0.284357 | − | 0.284357i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.68567 | − | 10.6669i | −0.347705 | − | 0.427017i | ||||
\(625\) | 24.8654 | − | 2.59034i | 0.994618 | − | 0.103613i | ||||
\(626\) | −9.90812 | + | 5.72046i | −0.396008 | + | 0.228635i | ||||
\(627\) | −9.92741 | − | 22.1363i | −0.396463 | − | 0.884037i | ||||
\(628\) | −15.2082 | + | 4.07502i | −0.606872 | + | 0.162611i | ||||
\(629\) | 14.0023 | 0.558307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0588 | 0.599480 | 0.299740 | − | 0.954021i | \(-0.403100\pi\) | ||||
0.299740 | + | 0.954021i | \(0.403100\pi\) | |||||||
\(632\) | −6.94515 | + | 1.86095i | −0.276263 | + | 0.0740245i | ||||
\(633\) | −0.550778 | − | 1.22813i | −0.0218915 | − | 0.0488138i | ||||
\(634\) | −13.7980 | + | 7.96626i | −0.547987 | + | 0.316381i | ||||
\(635\) | 26.4249 | − | 27.8333i | 1.04864 | − | 1.10453i | ||||
\(636\) | 12.0685 | + | 14.8213i | 0.478547 | + | 0.587704i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.66009 | + | 2.66009i | −0.105314 | + | 0.105314i | ||||
\(639\) | −30.4404 | − | 27.1124i | −1.20420 | − | 1.07255i | ||||
\(640\) | −7.17810 | − | 24.2533i | −0.283739 | − | 0.958697i | ||||
\(641\) | −39.8129 | + | 22.9860i | −1.57252 | + | 0.907892i | −0.576656 | + | 0.816987i | \(0.695643\pi\) |
−0.995860 | + | 0.0909048i | \(0.971024\pi\) | |||||||
\(642\) | 0.692302 | + | 0.500136i | 0.0273230 | + | 0.0197388i | ||||
\(643\) | 5.91991 | + | 5.91991i | 0.233458 | + | 0.233458i | 0.814135 | − | 0.580676i | \(-0.197212\pi\) |
−0.580676 | + | 0.814135i | \(0.697212\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.37822 | − | 3.92274i | 0.0542672 | − | 0.154458i | ||||
\(646\) | 5.94531 | − | 10.2976i | 0.233915 | − | 0.405153i | ||||
\(647\) | 4.06933 | − | 15.1870i | 0.159982 | − | 0.597061i | −0.838645 | − | 0.544678i | \(-0.816652\pi\) |
0.998627 | − | 0.0523826i | \(-0.0166815\pi\) | |||||||
\(648\) | 13.0166 | + | 10.3099i | 0.511342 | + | 0.405009i | ||||
\(649\) | 0.368853 | + | 0.212957i | 0.0144787 | + | 0.00835931i | ||||
\(650\) | −6.64511 | − | 3.38970i | −0.260642 | − | 0.132955i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.3575 | + | 11.3575i | −0.444793 | + | 0.444793i | ||||
\(653\) | −11.2187 | − | 41.8686i | −0.439020 | − | 1.63845i | −0.731258 | − | 0.682101i | \(-0.761066\pi\) |
0.292238 | − | 0.956346i | \(-0.405600\pi\) | |||||||
\(654\) | −15.1062 | − | 5.75195i | −0.590698 | − | 0.224919i | ||||
\(655\) | −19.5361 | − | 10.6131i | −0.763339 | − | 0.414686i | ||||
\(656\) | 26.1942 | + | 15.1232i | 1.02271 | + | 0.590463i | ||||
\(657\) | −9.70367 | − | 14.7671i | −0.378576 | − | 0.576120i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.9397 | 1.98433 | 0.992165 | − | 0.124933i | \(-0.0398714\pi\) | ||||
0.992165 | + | 0.124933i | \(0.0398714\pi\) | |||||||
\(660\) | 18.1474 | + | 1.38312i | 0.706386 | + | 0.0538381i | ||||
\(661\) | −10.2697 | − | 17.7876i | −0.399445 | − | 0.691858i | 0.594213 | − | 0.804308i | \(-0.297464\pi\) |
−0.993657 | + | 0.112449i | \(0.964130\pi\) | |||||||
\(662\) | 0.281323 | − | 1.04991i | 0.0109339 | − | 0.0408060i | ||||
\(663\) | 19.7196 | + | 14.2459i | 0.765847 | + | 0.553267i | ||||
\(664\) | − | 10.5355i | − | 0.408856i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.36956 | + | 0.904139i | 0.169317 | + | 0.0350347i | ||||
\(667\) | 2.67610 | + | 9.98735i | 0.103619 | + | 0.386712i | ||||
\(668\) | −3.79683 | − | 1.01736i | −0.146904 | − | 0.0393627i | ||||
\(669\) | −2.90963 | + | 7.64146i | −0.112493 | + | 0.295436i | ||||
\(670\) | −8.39629 | + | 0.217932i | −0.324377 | + | 0.00841945i | ||||
\(671\) | − | 12.6231i | − | 0.487310i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.4635 | + | 25.4635i | 0.981544 | + | 0.981544i | 0.999833 | − | 0.0182887i | \(-0.00582181\pi\) |
−0.0182887 | + | 0.999833i | \(0.505822\pi\) | |||||||
\(674\) | 3.76697 | − | 6.52458i | 0.145098 | − | 0.251317i | ||||
\(675\) | −25.1461 | − | 6.53234i | −0.967875 | − | 0.251430i | ||||
\(676\) | 3.30692 | + | 5.72776i | 0.127189 | + | 0.220298i | ||||
\(677\) | 11.8518 | − | 3.17568i | 0.455502 | − | 0.122051i | −0.0237707 | − | 0.999717i | \(-0.507567\pi\) |
0.479273 | + | 0.877666i | \(0.340900\pi\) | |||||||
\(678\) | −6.80669 | − | 0.696831i | −0.261409 | − | 0.0267616i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.95618 | + | 16.2554i | 0.381802 | + | 0.623366i | ||||
\(681\) | 0.586015 | − | 0.0944387i | 0.0224561 | − | 0.00361890i | ||||
\(682\) | −6.69445 | − | 1.79377i | −0.256344 | − | 0.0686871i | ||||
\(683\) | 32.7860 | + | 8.78498i | 1.25452 | + | 0.336148i | 0.824081 | − | 0.566471i | \(-0.191692\pi\) |
0.430440 | + | 0.902619i | \(0.358358\pi\) | |||||||
\(684\) | −18.4039 | + | 20.6629i | −0.703689 | + | 0.790066i | ||||
\(685\) | 10.0971 | − | 42.0147i | 0.385789 | − | 1.60530i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.37769 | + | 23.2254i | −0.0907145 | + | 0.886104i | ||||
\(688\) | 2.70924 | − | 0.725939i | 0.103289 | − | 0.0276762i | ||||
\(689\) | 9.53445 | + | 16.5141i | 0.363234 | + | 0.629139i | ||||
\(690\) | −3.86598 | + | 5.65492i | −0.147175 | + | 0.215279i | ||||
\(691\) | −16.2840 | + | 28.2047i | −0.619472 | + | 1.07296i | 0.370110 | + | 0.928988i | \(0.379320\pi\) |
−0.989582 | + | 0.143969i | \(0.954013\pi\) | |||||||
\(692\) | 2.98996 | + | 2.98996i | 0.113661 | + | 0.113661i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 3.51455i | − | 0.133410i | ||||||
\(695\) | 0.974335 | + | 37.5383i | 0.0369586 | + | 1.42391i | ||||
\(696\) | 8.56887 | + | 3.26276i | 0.324802 | + | 0.123674i | ||||
\(697\) | −51.6681 | − | 13.8444i | −1.95707 | − | 0.524395i | ||||
\(698\) | −0.943497 | − | 3.52118i | −0.0357119 | − | 0.133279i | ||||
\(699\) | 2.26528 | − | 1.84454i | 0.0856808 | − | 0.0697670i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.43359i | 0.0919155i | 0.998943 | + | 0.0459577i | \(0.0146340\pi\) | ||||
−0.998943 | + | 0.0459577i | \(0.985366\pi\) | |||||||
\(702\) | 5.23386 | + | 5.71892i | 0.197539 | + | 0.215847i | ||||
\(703\) | −4.11253 | + | 15.3482i | −0.155107 | + | 0.578867i | ||||
\(704\) | 3.71974 | + | 6.44278i | 0.140193 | + | 0.242821i | ||||
\(705\) | 27.3279 | + | 31.8372i | 1.02923 | + | 1.19906i | ||||
\(706\) | −6.30965 | −0.237467 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.0494732 | − | 0.483257i | 0.00185932 | − | 0.0181619i | ||||
\(709\) | 10.6934 | + | 6.17386i | 0.401601 | + | 0.231864i | 0.687174 | − | 0.726493i | \(-0.258851\pi\) |
−0.285574 | + | 0.958357i | \(0.592184\pi\) | |||||||
\(710\) | −4.23210 | − | 14.2994i | −0.158828 | − | 0.536647i | ||||
\(711\) | −11.0994 | + | 3.67281i | −0.416260 | + | 0.137741i | ||||
\(712\) | 1.88681 | + | 7.04166i | 0.0707111 | + | 0.263897i | ||||
\(713\) | −13.4695 | + | 13.4695i | −0.504436 | + | 0.504436i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.6550 | + | 4.24288i | 0.660259 | + | 0.158675i | ||||
\(716\) | 12.8636 | + | 7.42678i | 0.480734 | + | 0.277552i | ||||
\(717\) | −3.65241 | − | 8.14418i | −0.136402 | − | 0.304150i | ||||
\(718\) | 3.20930 | − | 11.9773i | 0.119770 | − | 0.446988i | ||||
\(719\) | 12.1083 | − | 20.9721i | 0.451562 | − | 0.782129i | −0.546921 | − | 0.837184i | \(-0.684200\pi\) |
0.998483 | + | 0.0550554i | \(0.0175335\pi\) | |||||||
\(720\) | −5.93578 | − | 16.4906i | −0.221213 | − | 0.614568i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.94721 | + | 2.94721i | 0.109684 | + | 0.109684i | ||||
\(723\) | 15.1305 | − | 20.9441i | 0.562709 | − | 0.778918i | ||||
\(724\) | 8.40146 | − | 4.85059i | 0.312238 | − | 0.180271i | ||||
\(725\) | −14.3269 | + | 0.744231i | −0.532087 | + | 0.0276400i | ||||
\(726\) | −3.24279 | + | 0.522589i | −0.120351 | + | 0.0193951i | ||||
\(727\) | 25.8923 | − | 25.8923i | 0.960293 | − | 0.960293i | −0.0389483 | − | 0.999241i | \(-0.512401\pi\) |
0.999241 | + | 0.0389483i | \(0.0124008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0977 | + | 15.5142i | 0.818435 | + | 0.574599i | ||||
\(730\) | −0.167725 | − | 6.46198i | −0.00620780 | − | 0.239169i | ||||
\(731\) | −4.29575 | + | 2.48015i | −0.158884 | + | 0.0917317i | ||||
\(732\) | −13.1369 | + | 5.89148i | −0.485553 | + | 0.217755i | ||||
\(733\) | 18.3779 | − | 4.92434i | 0.678803 | − | 0.181885i | 0.0970859 | − | 0.995276i | \(-0.469048\pi\) |
0.581717 | + | 0.813391i | \(0.302381\pi\) | |||||||
\(734\) | 1.11882 | 0.0412965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.9184 | −0.660481 | ||||||||
\(737\) | 19.7476 | − | 5.29136i | 0.727413 | − | 0.194910i | ||||
\(738\) | −15.2297 | − | 7.65657i | −0.560612 | − | 0.281842i | ||||
\(739\) | −1.70445 | + | 0.984064i | −0.0626991 | + | 0.0361994i | −0.531022 | − | 0.847358i | \(-0.678192\pi\) |
0.468323 | + | 0.883557i | \(0.344858\pi\) | |||||||
\(740\) | −8.64477 | − | 8.20736i | −0.317788 | − | 0.301709i | ||||
\(741\) | −21.4070 | + | 17.4310i | −0.786406 | + | 0.640343i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.54680 | + | 4.54680i | −0.166806 | + | 0.166806i | −0.785574 | − | 0.618768i | \(-0.787632\pi\) |
0.618768 | + | 0.785574i | \(0.287632\pi\) | |||||||
\(744\) | 2.68755 | + | 16.6769i | 0.0985304 | + | 0.611405i | ||||
\(745\) | −9.94034 | + | 18.2978i | −0.364186 | + | 0.670379i | ||||
\(746\) | −7.84182 | + | 4.52748i | −0.287110 | + | 0.165763i | ||||
\(747\) | −0.988950 | − | 17.1023i | −0.0361838 | − | 0.625740i | ||||
\(748\) | −15.3533 | − | 15.3533i | −0.561371 | − | 0.561371i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.55628 | − | 6.88112i | −0.239402 | − | 0.251263i | ||||
\(751\) | 0.245859 | − | 0.425840i | 0.00897152 | − | 0.0155391i | −0.861505 | − | 0.507749i | \(-0.830478\pi\) |
0.870476 | + | 0.492210i | \(0.163811\pi\) | |||||||
\(752\) | −7.32563 | + | 27.3396i | −0.267138 | + | 0.996973i | ||||
\(753\) | 6.80051 | − | 3.04981i | 0.247824 | − | 0.111141i | ||||
\(754\) | 3.70723 | + | 2.14037i | 0.135010 | + | 0.0779478i | ||||
\(755\) | 23.8098 | + | 38.8742i | 0.866528 | + | 1.41478i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.50957 | − | 3.50957i | 0.127558 | − | 0.127558i | −0.640446 | − | 0.768003i | \(-0.721250\pi\) |
0.768003 | + | 0.640446i | \(0.221250\pi\) | |||||||
\(758\) | 2.42165 | + | 9.03771i | 0.0879582 | + | 0.328265i | ||||
\(759\) | 5.93329 | − | 15.5824i | 0.215365 | − | 0.565605i | ||||
\(760\) | −20.7420 | + | 6.13888i | −0.752393 | + | 0.222681i | ||||
\(761\) | −23.3151 | − | 13.4610i | −0.845173 | − | 0.487961i | 0.0138461 | − | 0.999904i | \(-0.495593\pi\) |
−0.859019 | + | 0.511943i | \(0.828926\pi\) | |||||||
\(762\) | −14.5151 | − | 1.48598i | −0.525826 | − | 0.0538312i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.984264 | 0.0356094 | ||||||||
\(765\) | 17.6878 | + | 25.4529i | 0.639503 | + | 0.920252i | ||||
\(766\) | 6.15131 | + | 10.6544i | 0.222256 | + | 0.384958i | ||||
\(767\) | 0.125437 | − | 0.468138i | 0.00452928 | − | 0.0169035i | ||||
\(768\) | 0.0182804 | − | 0.0253043i | 0.000659638 | − | 0.000913090i | ||||
\(769\) | 31.3935i | 1.13208i | 0.824378 | + | 0.566040i | \(0.191525\pi\) | ||||
−0.824378 | + | 0.566040i | \(0.808475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.01519 | + | 11.0716i | 0.324674 | + | 0.398733i | ||||
\(772\) | 4.54062 | + | 16.9458i | 0.163421 | + | 0.609894i | ||||
\(773\) | 18.2944 | + | 4.90198i | 0.658005 | + | 0.176312i | 0.572346 | − | 0.820012i | \(-0.306034\pi\) |
0.0856597 | + | 0.996324i | \(0.472700\pi\) | |||||||
\(774\) | −1.50068 | + | 0.496578i | −0.0539408 | + | 0.0178491i | ||||
\(775\) | −14.3846 | − | 22.1726i | −0.516709 | − | 0.796464i | ||||
\(776\) | 4.87606i | 0.175040i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.36887 | + | 6.36887i | 0.228335 | + | 0.228335i | ||||
\(779\) | 30.3503 | − | 52.5683i | 1.08741 | − | 1.88345i | ||||
\(780\) | −3.82439 | − | 20.3538i | −0.136935 | − | 0.728783i | ||||
\(781\) | 18.1493 | + | 31.4354i | 0.649431 | + | 1.12485i | ||||
\(782\) | 7.89378 | − | 2.11513i | 0.282281 | − | 0.0756369i | ||||
\(783\) | 14.2162 | + | 4.49210i | 0.508044 | + | 0.160535i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.4596 | − | 4.67657i | −0.694542 | − | 0.166914i | ||||
\(786\) | 1.34479 | + | 8.34475i | 0.0479671 | + | 0.297647i | ||||
\(787\) | 30.6962 | + | 8.22502i | 1.09420 | + | 0.293190i | 0.760401 | − | 0.649454i | \(-0.225002\pi\) |
0.333800 | + | 0.942644i | \(0.391669\pi\) | |||||||
\(788\) | −24.3914 | − | 6.53566i | −0.868908 | − | 0.232823i | ||||
\(789\) | −0.0243538 | − | 0.151121i | −0.000867017 | − | 0.00538005i | ||||
\(790\) | −4.15858 | − | 0.999399i | −0.147956 | − | 0.0355570i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8.11990 | − | 12.3569i | −0.288528 | − | 0.439084i | ||||
\(793\) | −13.8745 | + | 3.71767i | −0.492699 | + | 0.132018i | ||||
\(794\) | 3.78720 | + | 6.55962i | 0.134403 | + | 0.232792i | ||||
\(795\) | 4.48655 | + | 23.8779i | 0.159122 | + | 0.846861i | ||||
\(796\) | −10.2686 | + | 17.7858i | −0.363961 | + | 0.630399i | ||||
\(797\) | −7.83907 | − | 7.83907i | −0.277674 | − | 0.277674i | 0.554506 | − | 0.832180i | \(-0.312907\pi\) |
−0.832180 | + | 0.554506i | \(0.812907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 50.0556i | − | 1.77084i | ||||||
\(800\) | 5.18020 | − | 24.3159i | 0.183148 | − | 0.859698i | ||||
\(801\) | 3.72385 | + | 11.2536i | 0.131576 | + | 0.397628i | ||||
\(802\) | −16.3200 | − | 4.37293i | −0.576279 | − | 0.154414i | ||||
\(803\) | 4.07235 | + | 15.1982i | 0.143710 | + | 0.536333i | ||||
\(804\) | −14.7233 | − | 18.0817i | −0.519252 | − | 0.637694i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.88640i | 0.277787i | ||||||||
\(807\) | −30.0938 | + | 41.6567i | −1.05935 | + | 1.46638i | ||||
\(808\) | −1.79603 | + | 6.70287i | −0.0631841 | + | 0.235806i | ||||
\(809\) | 3.13513 | + | 5.43021i | 0.110225 | + | 0.190916i | 0.915861 | − | 0.401495i | \(-0.131509\pi\) |
−0.805636 | + | 0.592411i | \(0.798176\pi\) | |||||||
\(810\) | 3.87615 | + | 9.08498i | 0.136194 | + | 0.319214i | ||||
\(811\) | 8.90138 | 0.312570 | 0.156285 | − | 0.987712i | \(-0.450048\pi\) | ||||
0.156285 | + | 0.987712i | \(0.450048\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.0058 | + | 3.99320i | 1.36799 | + | 0.140048i | ||||
\(814\) | −3.44100 | − | 1.98666i | −0.120607 | − | 0.0696325i | ||||
\(815\) | −19.5774 | + | 5.79420i | −0.685768 | + | 0.202962i | ||||
\(816\) | −7.44041 | + | 19.5405i | −0.260466 | + | 0.684054i | ||||
\(817\) | −1.45686 | − | 5.43708i | −0.0509691 | − | 0.190219i | ||||
\(818\) | −2.63502 | + | 2.63502i | −0.0921313 | + | 0.0921313i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.7842 | + | 38.8324i | 0.830581 | + | 1.35608i | ||||
\(821\) | −14.5875 | − | 8.42211i | −0.509108 | − | 0.293934i | 0.223359 | − | 0.974736i | \(-0.428298\pi\) |
−0.732467 | + | 0.680803i | \(0.761631\pi\) | |||||||
\(822\) | −14.9895 | + | 6.72232i | −0.522819 | + | 0.234468i | ||||
\(823\) | 11.8914 | − | 44.3795i | 0.414510 | − | 1.54697i | −0.371306 | − | 0.928510i | \(-0.621090\pi\) |
0.785816 | − | 0.618461i | \(-0.212243\pi\) | |||||||
\(824\) | 11.5550 | − | 20.0138i | 0.402536 | − | 0.697213i | ||||
\(825\) | 19.4306 | + | 12.5566i | 0.676486 | + | 0.437164i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.87454 | − | 4.87454i | −0.169504 | − | 0.169504i | 0.617257 | − | 0.786762i | \(-0.288244\pi\) |
−0.786762 | + | 0.617257i | \(0.788244\pi\) | |||||||
\(828\) | −18.9858 | + | 1.09786i | −0.659802 | + | 0.0381534i | ||||
\(829\) | 8.50889 | − | 4.91261i | 0.295526 | − | 0.170622i | −0.344905 | − | 0.938638i | \(-0.612089\pi\) |
0.640431 | + | 0.768015i | \(0.278756\pi\) | |||||||
\(830\) | 2.99159 | − | 5.50680i | 0.103839 | − | 0.191144i | ||||
\(831\) | −1.64124 | − | 10.1843i | −0.0569340 | − | 0.353289i | ||||
\(832\) | 5.98598 | − | 5.98598i | 0.207527 | − | 0.207527i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.0703 | − | 9.01414i | 0.383332 | − | 0.312134i | ||||
\(835\) | −3.62357 | − | 3.44023i | −0.125399 | − | 0.119054i | ||||
\(836\) | 21.3383 | − | 12.3197i | 0.738002 | − | 0.426085i | ||||
\(837\) | 5.92815 | + | 26.8194i | 0.204907 | + | 0.927015i | ||||
\(838\) | 2.94237 | − | 0.788406i | 0.101643 | − | 0.0272350i | ||||
\(839\) | −13.0314 | −0.449893 | −0.224947 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224947 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7675 | −0.716120 | ||||||||
\(842\) | 11.9156 | − | 3.19276i | 0.410637 | − | 0.110030i | ||||
\(843\) | 34.7835 | − | 15.5993i | 1.19801 | − | 0.537269i | ||||
\(844\) | 1.18386 | − | 0.683503i | 0.0407502 | − | 0.0235271i | ||||
\(845\) | 0.218139 | + | 8.40427i | 0.00750422 | + | 0.289116i | ||||
\(846\) | 3.23214 | − | 15.6204i | 0.111123 | − | 0.537041i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.5892 | + | 11.5892i | −0.397976 | + | 0.397976i | ||||
\(849\) | −23.2131 | + | 3.74089i | −0.796673 | + | 0.128387i | ||||
\(850\) | 0.588223 | + | 11.3236i | 0.0201759 | + | 0.388398i | ||||
\(851\) | −9.45756 | + | 5.46033i | −0.324201 | + | 0.187178i | ||||
\(852\) | 24.2442 | − | 33.5595i | 0.830593 | − | 1.14973i | ||||
\(853\) | 36.7177 | + | 36.7177i | 1.25719 | + | 1.25719i | 0.952429 | + | 0.304761i | \(0.0985765\pi\) |
0.304761 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33.0944 | + | 11.9123i | −1.13181 | + | 0.407392i | ||||
\(856\) | −0.926792 | + | 1.60525i | −0.0316771 | + | 0.0548663i | ||||
\(857\) | 9.36537 | − | 34.9520i | 0.319915 | − | 1.19394i | −0.599411 | − | 0.800442i | \(-0.704598\pi\) |
0.919326 | − | 0.393497i | \(-0.128735\pi\) | |||||||
\(858\) | −2.82478 | − | 6.29873i | −0.0964365 | − | 0.215035i | ||||
\(859\) | 13.6081 | + | 7.85667i | 0.464304 | + | 0.268066i | 0.713852 | − | 0.700296i | \(-0.246949\pi\) |
−0.249548 | + | 0.968362i | \(0.580282\pi\) | |||||||
\(860\) | 4.10585 | + | 0.986727i | 0.140008 | + | 0.0336471i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.92644 | + | 2.92644i | −0.0996751 | + | 0.0996751i | ||||
\(863\) | 4.06609 | + | 15.1749i | 0.138411 | + | 0.516559i | 0.999961 | + | 0.00888427i | \(0.00282799\pi\) |
−0.861549 | + | 0.507674i | \(0.830505\pi\) | |||||||
\(864\) | −13.8958 | + | 21.7820i | −0.472744 | + | 0.741038i | ||||
\(865\) | 1.52538 | + | 5.15393i | 0.0518643 | + | 0.175239i | ||||
\(866\) | 11.3176 | + | 6.53423i | 0.384588 | + | 0.222042i | ||||
\(867\) | 0.767159 | − | 7.49366i | 0.0260541 | − | 0.254498i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.4106 | 0.353155 | ||||||||
\(870\) | 3.55240 | + | 4.13857i | 0.120437 | + | 0.140311i | ||||
\(871\) | −11.6318 | − | 20.1469i | −0.394130 | − | 0.682653i | ||||
\(872\) | 9.07976 | − | 33.8861i | 0.307480 | − | 1.14753i | ||||
\(873\) | 0.457708 | + | 7.91533i | 0.0154911 | + | 0.267893i | ||||
\(874\) | 9.27375i | 0.313689i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.9161 | − | 11.3314i | 0.470182 | − | 0.382853i | ||||
\(877\) | −7.58775 | − | 28.3179i | −0.256220 | − | 0.956226i | −0.967408 | − | 0.253224i | \(-0.918509\pi\) |
0.711188 | − | 0.703002i | \(-0.248158\pi\) | |||||||
\(878\) | 2.31481 | + | 0.620252i | 0.0781211 | + | 0.0209325i | ||||
\(879\) | 8.15763 | + | 3.10617i | 0.275150 | + | 0.104769i | ||||
\(880\) | 0.404941 | + | 15.6012i | 0.0136505 | + | 0.525916i | ||||
\(881\) | − | 26.4774i | − | 0.892045i | −0.895022 | − | 0.446023i | \(-0.852840\pi\) | ||
0.895022 | − | 0.446023i | \(-0.147160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9720 | − | 26.9720i | −0.907681 | − | 0.907681i | 0.0884037 | − | 0.996085i | \(-0.471823\pi\) |
−0.996085 | + | 0.0884037i | \(0.971823\pi\) | |||||||
\(884\) | −12.3536 | + | 21.3971i | −0.415496 | + | 0.719661i | ||||
\(885\) | 0.348496 | − | 0.509758i | 0.0117146 | − | 0.0171353i | ||||
\(886\) | 8.29321 | + | 14.3643i | 0.278616 | + | 0.482577i | ||||
\(887\) | −1.84409 | + | 0.494122i | −0.0619185 | + | 0.0165910i | −0.289645 | − | 0.957134i | \(-0.593537\pi\) |
0.227727 | + | 0.973725i | \(0.426871\pi\) | |||||||
\(888\) | −0.986265 | + | 9.63389i | −0.0330969 | + | 0.323292i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.01329 | + | 4.21637i | −0.0339655 | + | 0.141333i | ||||
\(891\) | −14.3410 | − | 19.2968i | −0.480442 | − | 0.646469i | ||||
\(892\) | −8.02142 | − | 2.14933i | −0.268577 | − | 0.0719650i | ||||
\(893\) | 54.8669 | + | 14.7015i | 1.83605 | + | 0.491969i | ||||
\(894\) | 7.81581 | − | 1.25955i | 0.261400 | − | 0.0421256i | ||||
\(895\) | 9.86155 | + | 16.1009i | 0.329635 | + | 0.538194i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.8746 | − | 1.93228i | −0.630205 | − | 0.0645169i | ||||
\(898\) | −11.2233 | + | 3.00727i | −0.374526 | + | 0.100354i | ||||
\(899\) | 7.58338 | + | 13.1348i | 0.252920 | + | 0.438070i | ||||
\(900\) | 3.99895 | − | 26.0818i | 0.133298 | − | 0.869394i | ||||
\(901\) | 14.4925 | − | 25.1018i | 0.482816 | − | 0.836261i | ||||
\(902\) | 10.7330 | + | 10.7330i | 0.357368 | + | 0.357368i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 14.8499i | − | 0.493901i | ||||||
\(905\) | 12.3274 | − | 0.319966i | 0.409776 | − | 0.0106360i | ||||
\(906\) | 6.16712 | − | 16.1965i | 0.204889 | − | 0.538093i | ||||
\(907\) | 39.1839 | + | 10.4993i | 1.30108 | + | 0.348623i | 0.841858 | − | 0.539699i | \(-0.181462\pi\) |
0.459221 | + | 0.888322i | \(0.348129\pi\) | |||||||
\(908\) | 0.156029 | + | 0.582307i | 0.00517799 | + | 0.0193245i | ||||
\(909\) | −2.28631 | + | 11.0494i | −0.0758322 | + | 0.366485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0874i | 1.12937i | 0.825307 | + | 0.564684i | \(0.191002\pi\) | ||||
−0.825307 | + | 0.564684i | \(0.808998\pi\) | |||||||
\(912\) | −19.2334 | − | 13.8947i | −0.636883 | − | 0.460100i | ||||
\(913\) | −3.94810 | + | 14.7345i | −0.130663 | + | 0.487641i | ||||
\(914\) | 3.56008 | + | 6.16624i | 0.117757 | + | 0.203961i | ||||
\(915\) | −18.2482 | − | 1.39081i | −0.603268 | − | 0.0459788i | ||||
\(916\) | −23.7115 | −0.783450 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.55046 | − | 11.2361i | 0.117183 | − | 0.370848i | ||||
\(919\) | 1.90232 | + | 1.09830i | 0.0627516 | + | 0.0362297i | 0.531048 | − | 0.847342i | \(-0.321799\pi\) |
−0.468296 | + | 0.883572i | \(0.655132\pi\) | |||||||
\(920\) | −13.0637 | − | 7.09689i | −0.430697 | − | 0.233978i | ||||
\(921\) | −23.9779 | − | 9.13004i | −0.790099 | − | 0.300845i | ||||
\(922\) | −2.96175 | − | 11.0534i | −0.0975401 | − | 0.364025i | ||||
\(923\) | 29.2066 | − | 29.2066i | 0.961348 | − | 0.961348i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.67569 | − | 14.4129i | −0.153736 | − | 0.473892i | ||||
\(926\) | −10.2528 | − | 5.91944i | −0.336927 | − | 0.194525i | ||||
\(927\) | 16.8786 | − | 33.5731i | 0.554365 | − | 1.10269i | ||||
\(928\) | −3.69251 | + | 13.7806i | −0.121213 | + | 0.452372i | ||||
\(929\) | −25.6490 | + | 44.4254i | −0.841518 | + | 1.45755i | 0.0470938 | + | 0.998890i | \(0.485004\pi\) |
−0.888611 | + | 0.458661i | \(0.848329\pi\) | |||||||
\(930\) | −3.33071 | + | 9.48000i | −0.109218 | + | 0.310861i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.09792 | + | 2.09792i | 0.0687197 | + | 0.0687197i | ||||
\(933\) | 28.6900 | + | 20.7264i | 0.939268 | + | 0.678550i | ||||
\(934\) | −4.81265 | + | 2.77858i | −0.157475 | + | 0.0909181i | ||||
\(935\) | −7.83272 | − | 26.4652i | −0.256157 | − | 0.865504i | ||||
\(936\) | −11.1905 | + | 12.5641i | −0.365774 | + | 0.410672i | ||||
\(937\) | −16.4279 | + | 16.4279i | −0.536675 | + | 0.536675i | −0.922551 | − | 0.385876i | \(-0.873899\pi\) |
0.385876 | + | 0.922551i | \(0.373899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.4933 | − | 31.3083i | −0.831942 | − | 1.02171i | ||||
\(940\) | −29.3399 | + | 30.9035i | −0.956961 | + | 1.00796i | ||||
\(941\) | −49.6120 | + | 28.6435i | −1.61731 | + | 0.933752i | −0.629692 | + | 0.776845i | \(0.716819\pi\) |
−0.987613 | + | 0.156906i | \(0.949848\pi\) | |||||||
\(942\) | 3.11352 | + | 6.94255i | 0.101444 | + | 0.226201i | ||||
\(943\) | 40.2970 | − | 10.7976i | 1.31225 | − | 0.351617i | ||||
\(944\) | 0.416557 | 0.0135578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.40755 | 0.0457634 | ||||||||
\(947\) | −48.9447 | + | 13.1147i | −1.59049 | + | 0.426170i | −0.942153 | − | 0.335183i | \(-0.891202\pi\) |
−0.648337 | + | 0.761354i | \(0.724535\pi\) | |||||||
\(948\) | −4.85884 | − | 10.8343i | −0.157808 | − | 0.351881i | ||||
\(949\) | 15.5055 | − | 8.95213i | 0.503331 | − | 0.290599i | ||||
\(950\) | −12.5848 | − | 2.68104i | −0.408306 | − | 0.0869844i | ||||
\(951\) | −35.5017 | − | 43.5997i | −1.15122 | − | 1.41382i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.4764 | + | 35.4764i | −1.14919 | + | 1.14919i | −0.162481 | + | 0.986712i | \(0.551950\pi\) |
−0.986712 | + | 0.162481i | \(0.948050\pi\) | |||||||
\(954\) | 6.14339 | − | 6.89749i | 0.198900 | − | 0.223315i | ||||
\(955\) | 1.09938 | + | 0.597243i | 0.0355751 | + | 0.0193263i | ||||
\(956\) | 7.85062 | − | 4.53256i | 0.253907 | − | 0.146593i | ||||
\(957\) | −10.7614 | − | 7.77429i | −0.347866 | − | 0.251307i | ||||
\(958\) | −6.98270 | − | 6.98270i | −0.225601 | − | 0.225601i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.72365 | − | 4.66747i | 0.313830 | − | 0.150642i | ||||
\(961\) | 1.52917 | − | 2.64859i | 0.0493279 | − | 0.0854385i | ||||
\(962\) | −1.17019 | + | 4.36722i | −0.0377286 | + | 0.140805i | ||||
\(963\) | −1.35378 | + | 2.69281i | −0.0436251 | + | 0.0867745i | ||||
\(964\) | 22.7256 | + | 13.1206i | 0.731943 | + | 0.422588i | ||||
\(965\) | −5.21090 | + | 21.6830i | −0.167745 | + | 0.698000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0372 | + | 21.0372i | −0.676511 | + | 0.676511i | −0.959209 | − | 0.282698i | \(-0.908771\pi\) |
0.282698 | + | 0.959209i | \(0.408771\pi\) | |||||||
\(968\) | −1.84504 | − | 6.88580i | −0.0593020 | − | 0.221318i | ||||
\(969\) | 39.2152 | + | 14.9319i | 1.25977 | + | 0.479682i | ||||
\(970\) | −1.38457 | + | 2.54867i | −0.0444560 | + | 0.0818329i | ||||
\(971\) | −20.3136 | − | 11.7280i | −0.651894 | − | 0.376371i | 0.137288 | − | 0.990531i | \(-0.456162\pi\) |
−0.789181 | + | 0.614160i | \(0.789495\pi\) | |||||||
\(972\) | −13.3890 | + | 23.9309i | −0.429451 | + | 0.767585i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.39987 | −0.173023 | ||||||||
\(975\) | 8.07882 | − | 25.0549i | 0.258729 | − | 0.802400i | ||||
\(976\) | −6.17289 | − | 10.6918i | −0.197589 | − | 0.342235i | ||||
\(977\) | 3.30675 | − | 12.3410i | 0.105792 | − | 0.394823i | −0.892641 | − | 0.450767i | \(-0.851150\pi\) |
0.998434 | + | 0.0559446i | \(0.0178170\pi\) | |||||||
\(978\) | 6.29193 | + | 4.54544i | 0.201194 | + | 0.145347i | ||||
\(979\) | − | 10.5552i | − | 0.337347i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5584 | − | 55.8598i | 0.369031 | − | 1.78347i | ||||
\(982\) | −0.291593 | − | 1.08824i | −0.00930511 | − | 0.0347271i | ||||
\(983\) | −4.28077 | − | 1.14703i | −0.136535 | − | 0.0365846i | 0.189904 | − | 0.981803i | \(-0.439182\pi\) |
−0.326440 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(984\) | 13.1646 | − | 34.5737i | 0.419672 | − | 1.10217i | ||||
\(985\) | −23.2784 | − | 22.1005i | −0.741711 | − | 0.704182i | ||||
\(986\) | − | 6.50680i | − | 0.207219i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.8254 | − | 19.8254i | −0.630731 | − | 0.630731i | ||||
\(989\) | 1.93432 | − | 3.35034i | 0.0615078 | − | 0.106535i | ||||
\(990\) | −0.735406 | − | 8.76452i | −0.0233727 | − | 0.278555i | ||||
\(991\) | 14.6141 | + | 25.3124i | 0.464233 | + | 0.804076i | 0.999167 | − | 0.0408185i | \(-0.0129965\pi\) |
−0.534933 | + | 0.844894i | \(0.679663\pi\) | |||||||
\(992\) | −25.3880 | + | 6.80270i | −0.806071 | + | 0.215986i | ||||
\(993\) | 3.81588 | + | 0.390649i | 0.121093 | + | 0.0123969i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.2618 | + | 13.6350i | −0.705748 | + | 0.432260i | ||||
\(996\) | 17.1769 | − | 2.76812i | 0.544270 | − | 0.0877113i | ||||
\(997\) | −6.24970 | − | 1.67460i | −0.197930 | − | 0.0530352i | 0.158492 | − | 0.987360i | \(-0.449337\pi\) |
−0.356422 | + | 0.934325i | \(0.616003\pi\) | |||||||
\(998\) | −5.84376 | − | 1.56583i | −0.184981 | − | 0.0495655i | ||||
\(999\) | −0.696689 | + | 15.7313i | −0.0220423 | + | 0.497717i |
(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 | 735.2.y.g.128.8 | 48 | ||
3.2 | odd | 2 | inner | 735.2.y.g.128.5 | 48 | ||
5.2 | odd | 4 | inner | 735.2.y.g.422.8 | 48 | ||
7.2 | even | 3 | 735.2.j.h.638.5 | 24 | |||
7.3 | odd | 6 | 735.2.y.j.263.5 | 48 | |||
7.4 | even | 3 | inner | 735.2.y.g.263.5 | 48 | ||
7.5 | odd | 6 | 105.2.j.a.8.5 | ✓ | 24 | ||
7.6 | odd | 2 | 735.2.y.j.128.8 | 48 | |||
15.2 | even | 4 | inner | 735.2.y.g.422.5 | 48 | ||
21.2 | odd | 6 | 735.2.j.h.638.8 | 24 | |||
21.5 | even | 6 | 105.2.j.a.8.8 | yes | 24 | ||
21.11 | odd | 6 | inner | 735.2.y.g.263.8 | 48 | ||
21.17 | even | 6 | 735.2.y.j.263.8 | 48 | |||
21.20 | even | 2 | 735.2.y.j.128.5 | 48 | |||
35.2 | odd | 12 | 735.2.j.h.197.8 | 24 | |||
35.12 | even | 12 | 105.2.j.a.92.8 | yes | 24 | ||
35.17 | even | 12 | 735.2.y.j.557.5 | 48 | |||
35.19 | odd | 6 | 525.2.j.b.218.8 | 24 | |||
35.27 | even | 4 | 735.2.y.j.422.8 | 48 | |||
35.32 | odd | 12 | inner | 735.2.y.g.557.5 | 48 | ||
35.33 | even | 12 | 525.2.j.b.407.5 | 24 | |||
105.2 | even | 12 | 735.2.j.h.197.5 | 24 | |||
105.17 | odd | 12 | 735.2.y.j.557.8 | 48 | |||
105.32 | even | 12 | inner | 735.2.y.g.557.8 | 48 | ||
105.47 | odd | 12 | 105.2.j.a.92.5 | yes | 24 | ||
105.62 | odd | 4 | 735.2.y.j.422.5 | 48 | |||
105.68 | odd | 12 | 525.2.j.b.407.8 | 24 | |||
105.89 | even | 6 | 525.2.j.b.218.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.5 | ✓ | 24 | 7.5 | odd | 6 | ||
105.2.j.a.8.8 | yes | 24 | 21.5 | even | 6 | ||
105.2.j.a.92.5 | yes | 24 | 105.47 | odd | 12 | ||
105.2.j.a.92.8 | yes | 24 | 35.12 | even | 12 | ||
525.2.j.b.218.5 | 24 | 105.89 | even | 6 | |||
525.2.j.b.218.8 | 24 | 35.19 | odd | 6 | |||
525.2.j.b.407.5 | 24 | 35.33 | even | 12 | |||
525.2.j.b.407.8 | 24 | 105.68 | odd | 12 | |||
735.2.j.h.197.5 | 24 | 105.2 | even | 12 | |||
735.2.j.h.197.8 | 24 | 35.2 | odd | 12 | |||
735.2.j.h.638.5 | 24 | 7.2 | even | 3 | |||
735.2.j.h.638.8 | 24 | 21.2 | odd | 6 | |||
735.2.y.g.128.5 | 48 | 3.2 | odd | 2 | inner | ||
735.2.y.g.128.8 | 48 | 1.1 | even | 1 | trivial | ||
735.2.y.g.263.5 | 48 | 7.4 | even | 3 | inner | ||
735.2.y.g.263.8 | 48 | 21.11 | odd | 6 | inner | ||
735.2.y.g.422.5 | 48 | 15.2 | even | 4 | inner | ||
735.2.y.g.422.8 | 48 | 5.2 | odd | 4 | inner | ||
735.2.y.g.557.5 | 48 | 35.32 | odd | 12 | inner | ||
735.2.y.g.557.8 | 48 | 105.32 | even | 12 | inner | ||
735.2.y.j.128.5 | 48 | 21.20 | even | 2 | |||
735.2.y.j.128.8 | 48 | 7.6 | odd | 2 | |||
735.2.y.j.263.5 | 48 | 7.3 | odd | 6 | |||
735.2.y.j.263.8 | 48 | 21.17 | even | 6 | |||
735.2.y.j.422.5 | 48 | 105.62 | odd | 4 | |||
735.2.y.j.422.8 | 48 | 35.27 | even | 4 | |||
735.2.y.j.557.5 | 48 | 35.17 | even | 12 | |||
735.2.y.j.557.8 | 48 | 105.17 | odd | 12 |