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 | 263.8 | ||
Character | \(\chi\) | \(=\) | 735.263 |
Dual form | 735.2.y.j.422.8 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.127030 | − | 0.474084i | 0.0898241 | − | 0.335228i | −0.906360 | − | 0.422507i | \(-0.861150\pi\) |
0.996184 | + | 0.0872785i | \(0.0278170\pi\) | |||||||
\(3\) | −1.58040 | − | 0.708759i | −0.912444 | − | 0.409202i | ||||
\(4\) | 1.52343 | + | 0.879554i | 0.761716 | + | 0.439777i | ||||
\(5\) | 1.06741 | − | 1.96485i | 0.477361 | − | 0.878707i | ||||
\(6\) | −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 | ||||
\(10\) | −0.795910 | − | 0.755638i | −0.251689 | − | 0.238954i | ||||
\(11\) | 2.31347 | + | 1.33568i | 0.697538 | + | 0.402724i | 0.806430 | − | 0.591330i | \(-0.201397\pi\) |
−0.108892 | + | 0.994054i | \(0.534730\pi\) | |||||||
\(12\) | −1.78424 | − | 2.46979i | −0.515065 | − | 0.712968i | ||||
\(13\) | 2.14945 | + | 2.14945i | 0.596149 | + | 0.596149i | 0.939285 | − | 0.343137i | \(-0.111489\pi\) |
−0.343137 | + | 0.939285i | \(0.611489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.07954 | + | 2.34871i | −0.795134 | + | 0.606434i | ||||
\(16\) | 1.30634 | + | 2.26264i | 0.326584 | + | 0.565661i | ||||
\(17\) | 4.46307 | − | 1.19588i | 1.08245 | − | 0.290042i | 0.326852 | − | 0.945075i | \(-0.394012\pi\) |
0.755600 | + | 0.655033i | \(0.227345\pi\) | |||||||
\(18\) | 1.31553 | − | 0.661370i | 0.310074 | − | 0.155886i | ||||
\(19\) | −4.54082 | + | 2.62164i | −1.04174 | + | 0.601446i | −0.920324 | − | 0.391156i | \(-0.872075\pi\) |
−0.121411 | + | 0.992602i | \(0.538742\pi\) | |||||||
\(20\) | 3.35432 | − | 2.05447i | 0.750049 | − | 0.459393i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.927108 | − | 0.927108i | 0.197660 | − | 0.197660i | ||||
\(23\) | −3.48084 | − | 0.932688i | −0.725805 | − | 0.194479i | −0.123045 | − | 0.992401i | \(-0.539266\pi\) |
−0.602760 | + | 0.797922i | \(0.705932\pi\) | |||||||
\(24\) | −2.98646 | + | 1.13715i | −0.609609 | + | 0.232120i | ||||
\(25\) | −2.72127 | − | 4.19461i | −0.544253 | − | 0.838921i | ||||
\(26\) | 1.29206 | − | 0.745973i | 0.253394 | − | 0.146297i | ||||
\(27\) | −1.56561 | − | 4.95468i | −0.301301 | − | 0.953529i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.86924 | 0.532804 | 0.266402 | − | 0.963862i | \(-0.414165\pi\) | ||||
0.266402 | + | 0.963862i | \(0.414165\pi\) | |||||||
\(30\) | 0.722289 | + | 1.75832i | 0.131871 | + | 0.321024i | ||||
\(31\) | 2.64299 | − | 4.57780i | 0.474696 | − | 0.822197i | −0.524884 | − | 0.851174i | \(-0.675891\pi\) |
0.999580 | + | 0.0289764i | \(0.00922477\pi\) | |||||||
\(32\) | 4.80289 | − | 1.28693i | 0.849040 | − | 0.227499i | ||||
\(33\) | −2.70953 | − | 3.75061i | −0.471669 | − | 0.652897i | ||||
\(34\) | − | 2.26778i | − | 0.388921i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.06932 | + | 5.16785i | 0.178220 | + | 0.861309i | ||||
\(37\) | 2.92720 | + | 0.784341i | 0.481229 | + | 0.128945i | 0.491275 | − | 0.871005i | \(-0.336531\pi\) |
−0.0100459 | + | 0.999950i | \(0.503198\pi\) | |||||||
\(38\) | 0.666057 | + | 2.48576i | 0.108049 | + | 0.403243i | ||||
\(39\) | −1.87354 | − | 4.92042i | −0.300007 | − | 0.787898i | ||||
\(40\) | −1.17081 | − | 3.95592i | −0.185121 | − | 0.625486i | ||||
\(41\) | 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 | ||||
\(45\) | 6.53157 | − | 1.52924i | 0.973669 | − | 0.227966i | ||||
\(46\) | −0.884344 | + | 1.53173i | −0.130389 | + | 0.225841i | ||||
\(47\) | 2.80388 | − | 10.4642i | 0.408988 | − | 1.52636i | −0.387593 | − | 0.921831i | \(-0.626693\pi\) |
0.796580 | − | 0.604533i | \(-0.206640\pi\) | |||||||
\(48\) | −0.460865 | − | 4.50176i | −0.0665201 | − | 0.649773i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.33428 | + | 0.757266i | −0.330117 | + | 0.107094i | ||||
\(51\) | −7.90101 | − | 1.27328i | −1.10636 | − | 0.178295i | ||||
\(52\) | 1.38398 | + | 5.16509i | 0.191924 | + | 0.716269i | ||||
\(53\) | −1.62361 | − | 6.05938i | −0.223019 | − | 0.832319i | −0.983188 | − | 0.182594i | \(-0.941551\pi\) |
0.760169 | − | 0.649725i | \(-0.225116\pi\) | |||||||
\(54\) | −2.54782 | + | 0.112835i | −0.346714 | + | 0.0153548i | ||||
\(55\) | 5.09384 | − | 3.11990i | 0.686854 | − | 0.420687i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.03442 | − | 0.924894i | 1.19664 | − | 0.122505i | ||||
\(58\) | 0.364480 | − | 1.36026i | 0.0478586 | − | 0.178611i | ||||
\(59\) | 0.0797185 | − | 0.138077i | 0.0103785 | − | 0.0179760i | −0.860790 | − | 0.508961i | \(-0.830030\pi\) |
0.871168 | + | 0.490985i | \(0.163363\pi\) | |||||||
\(60\) | −6.75729 | + | 0.869475i | −0.872362 | + | 0.112249i | ||||
\(61\) | −2.36267 | − | 4.09227i | −0.302509 | − | 0.523961i | 0.674195 | − | 0.738554i | \(-0.264491\pi\) |
−0.976704 | + | 0.214593i | \(0.931158\pi\) | |||||||
\(62\) | −1.83452 | − | 1.83452i | −0.232984 | − | 0.232984i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.78490i | 0.348112i | ||||||||
\(65\) | 6.51768 | − | 1.92899i | 0.808418 | − | 0.239262i | ||||
\(66\) | −2.12230 | + | 0.808104i | −0.261237 | + | 0.0994707i | ||||
\(67\) | −1.98077 | − | 7.39232i | −0.241989 | − | 0.903116i | −0.974873 | − | 0.222762i | \(-0.928493\pi\) |
0.732884 | − | 0.680354i | \(-0.238174\pi\) | |||||||
\(68\) | 7.85101 | + | 2.10367i | 0.952075 | + | 0.255108i | ||||
\(69\) | 4.84006 | + | 3.94109i | 0.582675 | + | 0.474452i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.5880i | − | 1.61260i | −0.591508 | − | 0.806299i | \(-0.701467\pi\) | ||
0.591508 | − | 0.806299i | \(-0.298533\pi\) | |||||||
\(72\) | 5.52577 | + | 0.319531i | 0.651218 | + | 0.0376570i | ||||
\(73\) | −5.68930 | + | 1.52444i | −0.665882 | + | 0.178423i | −0.575899 | − | 0.817521i | \(-0.695348\pi\) |
−0.0899831 | + | 0.995943i | \(0.528681\pi\) | |||||||
\(74\) | 0.743687 | − | 1.28810i | 0.0864519 | − | 0.149739i | ||||
\(75\) | 1.32772 | + | 8.55787i | 0.153312 | + | 0.988178i | ||||
\(76\) | −9.22351 | −1.05801 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.57069 | + | 0.263173i | −0.291073 | + | 0.0297985i | ||||
\(79\) | −3.37499 | + | 1.94855i | −0.379716 | + | 0.219229i | −0.677695 | − | 0.735344i | \(-0.737021\pi\) |
0.297979 | + | 0.954572i | \(0.403687\pi\) | |||||||
\(80\) | 5.84015 | − | 0.151586i | 0.652949 | − | 0.0169478i | ||||
\(81\) | −1.03739 | + | 8.94001i | −0.115266 | + | 0.993335i | ||||
\(82\) | 5.48839 | + | 1.47061i | 0.606091 | + | 0.162402i | ||||
\(83\) | −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 | ||||
\(87\) | −4.53454 | − | 2.03360i | −0.486154 | − | 0.218025i | ||||
\(88\) | 4.76073 | − | 1.27563i | 0.507496 | − | 0.135983i | ||||
\(89\) | 1.97563 | + | 3.42189i | 0.209416 | + | 0.362719i | 0.951531 | − | 0.307554i | \(-0.0995104\pi\) |
−0.742115 | + | 0.670273i | \(0.766177\pi\) | |||||||
\(90\) | 0.104719 | − | 3.29077i | 0.0110384 | − | 0.346878i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.48247 | − | 4.48247i | −0.467330 | − | 0.467330i | ||||
\(93\) | −7.42154 | + | 5.36150i | −0.769578 | + | 0.555962i | ||||
\(94\) | −4.60474 | − | 2.65855i | −0.474943 | − | 0.274208i | ||||
\(95\) | 0.304212 | + | 11.7204i | 0.0312115 | + | 1.20249i | ||||
\(96\) | −8.50261 | − | 1.37023i | −0.867794 | − | 0.139849i | ||||
\(97\) | −1.86878 | + | 1.86878i | −0.189746 | + | 0.189746i | −0.795586 | − | 0.605840i | \(-0.792837\pi\) |
0.605840 | + | 0.795586i | \(0.292837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.62386 | + | 7.84786i | 0.163204 | + | 0.788740i | ||||
\(100\) | −0.456282 | − | 8.78369i | −0.0456282 | − | 0.878369i | ||||
\(101\) | −3.25725 | − | 1.88058i | −0.324109 | − | 0.187124i | 0.329114 | − | 0.944290i | \(-0.393250\pi\) |
−0.653222 | + | 0.757166i | \(0.726583\pi\) | |||||||
\(102\) | −1.60731 | + | 3.58400i | −0.159147 | + | 0.354869i | ||||
\(103\) | −3.24189 | + | 12.0989i | −0.319433 | + | 1.19214i | 0.600358 | + | 0.799731i | \(0.295025\pi\) |
−0.919791 | + | 0.392409i | \(0.871642\pi\) | |||||||
\(104\) | 5.60838 | 0.549947 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.07890 | −0.299049 | ||||||||
\(107\) | 0.260023 | − | 0.970420i | 0.0251374 | − | 0.0938140i | −0.952218 | − | 0.305421i | \(-0.901203\pi\) |
0.977355 | + | 0.211607i | \(0.0678696\pi\) | |||||||
\(108\) | 1.97281 | − | 8.92516i | 0.189834 | − | 0.858824i | ||||
\(109\) | 16.4669 | + | 9.50719i | 1.57725 | + | 0.910623i | 0.995242 | + | 0.0974376i | \(0.0310646\pi\) |
0.582004 | + | 0.813186i | \(0.302269\pi\) | |||||||
\(110\) | −0.832022 | − | 2.81123i | −0.0793301 | − | 0.268040i | ||||
\(111\) | −4.07024 | − | 3.31425i | −0.386330 | − | 0.314575i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.69132 | − | 5.69132i | 0.535394 | − | 0.535394i | −0.386779 | − | 0.922173i | \(-0.626412\pi\) |
0.922173 | + | 0.386779i | \(0.126412\pi\) | |||||||
\(114\) | 0.709169 | − | 4.40057i | 0.0664198 | − | 0.412151i | ||||
\(115\) | −5.54808 | + | 5.84376i | −0.517361 | + | 0.544933i | ||||
\(116\) | 4.37109 | + | 2.52365i | 0.405845 | + | 0.234315i | ||||
\(117\) | −0.526450 | + | 9.10411i | −0.0486704 | + | 0.841676i | ||||
\(118\) | −0.0553332 | − | 0.0553332i | −0.00509383 | − | 0.00509383i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.953453 | + | 7.08176i | −0.0870380 | + | 0.646473i | ||||
\(121\) | −1.93190 | − | 3.34615i | −0.175627 | − | 0.304195i | ||||
\(122\) | −2.24021 | + | 0.600262i | −0.202819 | + | 0.0543452i | ||||
\(123\) | 8.20518 | − | 18.2960i | 0.739836 | − | 1.64969i | ||||
\(124\) | 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 | \(0.974455\pi\) | |||||||
\(128\) | 10.9261 | + | 2.92763i | 0.965736 | + | 0.258768i | ||||
\(129\) | −0.661668 | − | 1.73772i | −0.0582566 | − | 0.152997i | ||||
\(130\) | −0.0865616 | − | 3.33497i | −0.00759196 | − | 0.292496i | ||||
\(131\) | −8.61072 | + | 4.97140i | −0.752322 | + | 0.434353i | −0.826532 | − | 0.562889i | \(-0.809690\pi\) |
0.0742105 | + | 0.997243i | \(0.476356\pi\) | |||||||
\(132\) | −0.828923 | − | 8.09697i | −0.0721485 | − | 0.704751i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.75620 | −0.324486 | ||||||||
\(135\) | −11.4064 | − | 2.21250i | −0.981702 | − | 0.190422i | ||||
\(136\) | 4.26242 | − | 7.38272i | 0.365499 | − | 0.633063i | ||||
\(137\) | −18.6661 | + | 5.00156i | −1.59475 | + | 0.427312i | −0.943452 | − | 0.331510i | \(-0.892442\pi\) |
−0.651298 | + | 0.758822i | \(0.725775\pi\) | |||||||
\(138\) | 2.48324 | − | 1.79396i | 0.211388 | − | 0.152712i | ||||
\(139\) | 16.7933i | 1.42439i | 0.701982 | + | 0.712195i | \(0.252299\pi\) | ||||
−0.701982 | + | 0.712195i | \(0.747701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8479 | + | 14.5504i | −0.997770 | + | 1.22536i | ||||
\(142\) | −6.44185 | − | 1.72609i | −0.540588 | − | 0.144850i | ||||
\(143\) | 2.10170 | + | 7.84366i | 0.175753 | + | 0.655920i | ||||
\(144\) | −2.46231 | + | 7.44121i | −0.205193 | + | 0.620101i | ||||
\(145\) | 3.06266 | − | 5.63762i | 0.254340 | − | 0.468179i | ||||
\(146\) | 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 | \(-0.291244\pi\) |
−0.991271 | + | 0.131841i | \(0.957911\pi\) | |||||||
\(150\) | 4.22581 | + | 0.457659i | 0.345036 | + | 0.0373677i | ||||
\(151\) | −10.1934 | + | 17.6555i | −0.829527 | + | 1.43678i | 0.0688822 | + | 0.997625i | \(0.478057\pi\) |
−0.898410 | + | 0.439159i | \(0.855277\pi\) | |||||||
\(152\) | −2.50378 | + | 9.34424i | −0.203083 | + | 0.757918i | ||||
\(153\) | 11.5843 | + | 7.61221i | 0.936535 | + | 0.615410i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.17353 | − | 10.0795i | −0.495869 | − | 0.809603i | ||||
\(156\) | 1.47356 | − | 9.14380i | 0.117979 | − | 0.732090i | ||||
\(157\) | 2.31653 | + | 8.64539i | 0.184879 | + | 0.689977i | 0.994656 | + | 0.103240i | \(0.0329211\pi\) |
−0.809778 | + | 0.586737i | \(0.800412\pi\) | |||||||
\(158\) | 0.495050 | + | 1.84755i | 0.0393841 | + | 0.146983i | ||||
\(159\) | −1.72870 | + | 10.7270i | −0.137094 | + | 0.850705i | ||||
\(160\) | 2.59804 | − | 10.8106i | 0.205393 | − | 0.854657i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.10654 | + | 1.62746i | 0.322640 | + | 0.127866i | ||||
\(163\) | −2.36320 | + | 8.81958i | −0.185100 | + | 0.690803i | 0.809509 | + | 0.587108i | \(0.199733\pi\) |
−0.994609 | + | 0.103696i | \(0.966933\pi\) | |||||||
\(164\) | −10.1824 | + | 17.6365i | −0.795115 | + | 1.37718i | ||||
\(165\) | −10.2616 | + | 1.32038i | −0.798862 | + | 0.102791i | ||||
\(166\) | 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 | ||||||
\(170\) | −4.45585 | − | 2.42066i | −0.341748 | − | 0.185656i | ||||
\(171\) | −14.9335 | − | 4.94153i | −1.14199 | − | 0.377888i | ||||
\(172\) | 0.488773 | + | 1.82412i | 0.0372686 | + | 0.139088i | ||||
\(173\) | 2.32183 | + | 0.622134i | 0.176526 | + | 0.0472999i | 0.345999 | − | 0.938235i | \(-0.387540\pi\) |
−0.169473 | + | 0.985535i | \(0.554207\pi\) | |||||||
\(174\) | −1.54012 | + | 1.89142i | −0.116756 | + | 0.143388i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.97941i | 0.526093i | ||||||||
\(177\) | −0.223850 | + | 0.161715i | −0.0168256 | + | 0.0121552i | ||||
\(178\) | 1.87323 | − | 0.501929i | 0.140404 | − | 0.0376212i | ||||
\(179\) | 4.22190 | − | 7.31255i | 0.315560 | − | 0.546565i | −0.663997 | − | 0.747736i | \(-0.731141\pi\) |
0.979556 | + | 0.201170i | \(0.0644744\pi\) | |||||||
\(180\) | 11.2955 | + | 3.41517i | 0.841913 | + | 0.254552i | ||||
\(181\) | 5.51483 | 0.409914 | 0.204957 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204957 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.833531 | + | 8.14198i | 0.0616164 | + | 0.601872i | ||||
\(184\) | −5.75794 | + | 3.32435i | −0.424481 | + | 0.245074i | ||||
\(185\) | 4.66564 | − | 4.91429i | 0.343025 | − | 0.361306i | ||||
\(186\) | 1.59904 | + | 4.19951i | 0.117247 | + | 0.307923i | ||||
\(187\) | 11.9225 | + | 3.19462i | 0.871859 | + | 0.233614i | ||||
\(188\) | 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 | −0.517428 | − | 0.855727i | \(-0.673111\pi\) |
0.482367 | + | 0.875969i | \(0.339777\pi\) | |||||||
\(192\) | 1.97382 | − | 4.40125i | 0.142448 | − | 0.317633i | ||||
\(193\) | −9.63320 | + | 2.58121i | −0.693413 | + | 0.185799i | −0.588278 | − | 0.808659i | \(-0.700194\pi\) |
−0.105135 | + | 0.994458i | \(0.533527\pi\) | |||||||
\(194\) | 0.648566 | + | 1.12335i | 0.0465643 | + | 0.0806518i | ||||
\(195\) | −11.6677 | − | 1.57089i | −0.835543 | − | 0.112493i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1505 | − | 10.1505i | −0.723190 | − | 0.723190i | 0.246064 | − | 0.969254i | \(-0.420863\pi\) |
−0.969254 | + | 0.246064i | \(0.920863\pi\) | |||||||
\(198\) | 3.92682 | + | 0.227071i | 0.279067 | + | 0.0161372i | ||||
\(199\) | 10.1107 | + | 5.83740i | 0.716726 | + | 0.413802i | 0.813547 | − | 0.581500i | \(-0.197534\pi\) |
−0.0968203 | + | 0.995302i | \(0.530867\pi\) | |||||||
\(200\) | −9.02253 | − | 1.92214i | −0.637989 | − | 0.135916i | ||||
\(201\) | −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 | ||||
\(205\) | 22.7467 | + | 12.3572i | 1.58870 | + | 0.863066i | ||||
\(206\) | 5.32408 | + | 3.07386i | 0.370946 | + | 0.214166i | ||||
\(207\) | −4.85594 | − | 9.65894i | −0.337511 | − | 0.671343i | ||||
\(208\) | −2.05553 | + | 7.67133i | −0.142525 | + | 0.531911i | ||||
\(209\) | −14.0067 | −0.968867 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.777102 | −0.0534979 | −0.0267490 | − | 0.999642i | \(-0.508515\pi\) | ||||
−0.0267490 | + | 0.999642i | \(0.508515\pi\) | |||||||
\(212\) | 2.85610 | − | 10.6591i | 0.196157 | − | 0.732070i | ||||
\(213\) | −9.63061 | + | 21.4744i | −0.659879 | + | 1.47140i | ||||
\(214\) | −0.427030 | − | 0.246546i | −0.0291911 | − | 0.0168535i | ||||
\(215\) | 2.30181 | − | 0.681252i | 0.156982 | − | 0.0464610i | ||||
\(216\) | −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 | ||||
\(220\) | 10.5042 | − | 0.272646i | 0.708196 | − | 0.0183818i | ||||
\(221\) | 12.1636 | + | 7.02265i | 0.818211 | + | 0.472394i | ||||
\(222\) | −2.08828 | + | 1.50862i | −0.140156 | + | 0.101252i | ||||
\(223\) | −3.33811 | − | 3.33811i | −0.223536 | − | 0.223536i | 0.586450 | − | 0.809986i | \(-0.300525\pi\) |
−0.809986 | + | 0.586450i | \(0.800525\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.96714 | − | 14.4659i | 0.264476 | − | 0.964392i | ||||
\(226\) | −1.97519 | − | 3.42113i | −0.131388 | − | 0.227570i | ||||
\(227\) | −0.331024 | + | 0.0886976i | −0.0219708 | + | 0.00588706i | −0.269788 | − | 0.962920i | \(-0.586954\pi\) |
0.247817 | + | 0.968807i | \(0.420287\pi\) | |||||||
\(228\) | 14.5768 | + | 6.53725i | 0.965374 | + | 0.432940i | ||||
\(229\) | 11.6734 | − | 6.73964i | 0.771400 | − | 0.445368i | −0.0619741 | − | 0.998078i | \(-0.519740\pi\) |
0.833374 | + | 0.552710i | \(0.186406\pi\) | |||||||
\(230\) | 2.06566 | + | 3.37259i | 0.136205 | + | 0.222382i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.74324 | − | 3.74324i | 0.245756 | − | 0.245756i | ||||
\(233\) | −1.62913 | − | 0.436524i | −0.106728 | − | 0.0285976i | 0.205060 | − | 0.978749i | \(-0.434261\pi\) |
−0.311788 | + | 0.950152i | \(0.600928\pi\) | |||||||
\(234\) | 4.24924 | + | 1.40608i | 0.277782 | + | 0.0919184i | ||||
\(235\) | −17.5677 | − | 16.6788i | −1.14599 | − | 1.08801i | ||||
\(236\) | 0.242891 | − | 0.140233i | 0.0158109 | − | 0.00912842i | ||||
\(237\) | 6.71488 | − | 0.687432i | 0.436178 | − | 0.0446535i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.15325 | 0.333336 | 0.166668 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166668 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(240\) | −9.33721 | − | 3.89970i | −0.602714 | − | 0.251724i | ||||
\(241\) | 7.45869 | − | 12.9188i | 0.480457 | − | 0.832176i | −0.519292 | − | 0.854597i | \(-0.673804\pi\) |
0.999749 | + | 0.0224214i | \(0.00713757\pi\) | |||||||
\(242\) | −1.83176 | + | 0.490820i | −0.117750 | + | 0.0315511i | ||||
\(243\) | 7.97581 | − | 13.3935i | 0.511648 | − | 0.859195i | ||||
\(244\) | − | 8.31238i | − | 0.532146i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.63153 | − | 6.21409i | −0.486569 | − | 0.396196i | ||||
\(247\) | −15.3953 | − | 4.12517i | −0.979581 | − | 0.262478i | ||||
\(248\) | −2.52417 | − | 9.42033i | −0.160285 | − | 0.598192i | ||||
\(249\) | 9.24313 | − | 3.51949i | 0.585759 | − | 0.223039i | ||||
\(250\) | −1.00372 | + | 5.39482i | −0.0634809 | + | 0.341198i | ||||
\(251\) | − | 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 | ||||
\(255\) | −10.9354 | + | 14.1652i | −0.684803 | + | 0.887058i | ||||
\(256\) | −0.00901148 | + | 0.0156083i | −0.000563218 | + | 0.000975522i | ||||
\(257\) | −2.13351 | + | 7.96236i | −0.133085 | + | 0.496678i | −0.999998 | − | 0.00177964i | \(-0.999434\pi\) |
0.866914 | + | 0.498458i | \(0.166100\pi\) | |||||||
\(258\) | −0.907876 | + | 0.0929433i | −0.0565219 | + | 0.00578640i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.6259 | + | 2.79396i | 0.721007 | + | 0.173274i | ||||
\(261\) | 5.72505 | + | 6.42779i | 0.354372 | + | 0.397870i | ||||
\(262\) | 1.26304 | + | 4.71372i | 0.0780307 | + | 0.291215i | ||||
\(263\) | −0.0228732 | − | 0.0853641i | −0.00141042 | − | 0.00526378i | 0.965217 | − | 0.261450i | \(-0.0842006\pi\) |
−0.966627 | + | 0.256186i | \(0.917534\pi\) | |||||||
\(264\) | −8.42797 | − | 1.35820i | −0.518706 | − | 0.0835915i | ||||
\(265\) | −13.6388 | − | 3.27771i | −0.837826 | − | 0.201348i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.696985 | − | 6.80819i | −0.0426548 | − | 0.416654i | ||||
\(268\) | 3.48438 | − | 13.0039i | 0.212843 | − | 0.794339i | ||||
\(269\) | 14.8350 | − | 25.6949i | 0.904504 | − | 1.56665i | 0.0829230 | − | 0.996556i | \(-0.473574\pi\) |
0.821581 | − | 0.570091i | \(-0.193092\pi\) | |||||||
\(270\) | −2.49786 | + | 5.12651i | −0.152015 | + | 0.311990i | ||||
\(271\) | −11.3188 | − | 19.6048i | −0.687571 | − | 1.19091i | −0.972621 | − | 0.232396i | \(-0.925344\pi\) |
0.285050 | − | 0.958513i | \(-0.407990\pi\) | |||||||
\(272\) | 8.53611 | + | 8.53611i | 0.517578 | + | 0.517578i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.48463i | 0.572988i | ||||||||
\(275\) | −0.692907 | − | 13.3389i | −0.0417839 | − | 0.804363i | ||||
\(276\) | 3.90710 | + | 10.2611i | 0.235180 | + | 0.617645i | ||||
\(277\) | 1.54147 | + | 5.75283i | 0.0926177 | + | 0.345654i | 0.996647 | − | 0.0818155i | \(-0.0260718\pi\) |
−0.904030 | + | 0.427469i | \(0.859405\pi\) | |||||||
\(278\) | 7.96144 | + | 2.13326i | 0.477495 | + | 0.127944i | ||||
\(279\) | 15.5290 | − | 3.21323i | 0.929698 | − | 0.192371i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0093i | 1.31297i | 0.754341 | + | 0.656483i | \(0.227957\pi\) | ||||
−0.754341 | + | 0.656483i | \(0.772043\pi\) | |||||||
\(282\) | 5.39306 | + | 7.46522i | 0.321152 | + | 0.444547i | ||||
\(283\) | −13.1125 | + | 3.51348i | −0.779455 | + | 0.208854i | −0.626545 | − | 0.779386i | \(-0.715531\pi\) |
−0.152911 | + | 0.988240i | \(0.548865\pi\) | |||||||
\(284\) | 11.9514 | − | 20.7004i | 0.709183 | − | 1.22834i | ||||
\(285\) | 7.82617 | − | 18.7385i | 0.463582 | − | 1.10997i | ||||
\(286\) | 3.98553 | 0.235670 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.4664 | + | 8.19181i | 0.734587 | + | 0.482707i | ||||
\(289\) | 3.76641 | − | 2.17454i | 0.221554 | − | 0.127914i | ||||
\(290\) | −2.28365 | − | 2.16811i | −0.134101 | − | 0.127316i | ||||
\(291\) | 4.27793 | − | 1.62890i | 0.250777 | − | 0.0954879i | ||||
\(292\) | −10.0081 | − | 2.68166i | −0.585679 | − | 0.156932i | ||||
\(293\) | 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 | ||||
\(297\) | 2.99590 | − | 13.5537i | 0.173840 | − | 0.786464i | ||||
\(298\) | −4.41494 | + | 1.18298i | −0.255750 | + | 0.0685281i | ||||
\(299\) | −5.47711 | − | 9.48663i | −0.316749 | − | 0.548626i | ||||
\(300\) | −5.50442 | + | 14.2051i | −0.317798 | + | 0.820134i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.07531 | + | 7.07531i | 0.407139 | + | 0.407139i | ||||
\(303\) | 3.81488 | + | 5.28067i | 0.219159 | + | 0.303366i | ||||
\(304\) | −11.8637 | − | 6.84950i | −0.680429 | − | 0.392846i | ||||
\(305\) | −10.5626 | + | 0.274161i | −0.604814 | + | 0.0156984i | ||||
\(306\) | 5.08038 | − | 4.52495i | 0.290426 | − | 0.258674i | ||||
\(307\) | 10.4746 | − | 10.4746i | 0.597814 | − | 0.597814i | −0.341916 | − | 0.939730i | \(-0.611076\pi\) |
0.939730 | + | 0.341916i | \(0.111076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6987 | − | 16.8234i | 0.779291 | − | 0.957048i | ||||
\(310\) | −5.56275 | + | 1.64637i | −0.315943 | + | 0.0935075i | ||||
\(311\) | −17.6967 | − | 10.2172i | −1.00349 | − | 0.579365i | −0.0942109 | − | 0.995552i | \(-0.530033\pi\) |
−0.909279 | + | 0.416187i | \(0.863366\pi\) | |||||||
\(312\) | −8.86348 | − | 3.97499i | −0.501796 | − | 0.225040i | ||||
\(313\) | −6.03317 | + | 22.5161i | −0.341015 | + | 1.27268i | 0.556185 | + | 0.831059i | \(0.312265\pi\) |
−0.897199 | + | 0.441626i | \(0.854402\pi\) | |||||||
\(314\) | 4.39291 | 0.247906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.85542 | −0.385647 | ||||||||
\(317\) | −8.40174 | + | 31.3557i | −0.471889 | + | 1.76111i | 0.161087 | + | 0.986940i | \(0.448500\pi\) |
−0.632975 | + | 0.774172i | \(0.718167\pi\) | |||||||
\(318\) | 4.86589 | + | 2.18220i | 0.272866 | + | 0.122372i | ||||
\(319\) | 6.63790 | + | 3.83239i | 0.371651 | + | 0.214573i | ||||
\(320\) | 5.47190 | + | 2.97263i | 0.305889 | + | 0.166175i | ||||
\(321\) | −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 | ||||
\(325\) | 3.16686 | − | 14.8653i | 0.175666 | − | 0.824578i | ||||
\(326\) | 3.88103 | + | 2.24071i | 0.214950 | + | 0.124102i | ||||
\(327\) | −19.2860 | − | 26.6962i | −1.06652 | − | 1.47631i | ||||
\(328\) | 15.1033 | + | 15.1033i | 0.833938 | + | 0.833938i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.677561 | + | 5.03257i | −0.0372985 | + | 0.277034i | ||||
\(331\) | 1.10731 | + | 1.91791i | 0.0608631 | + | 0.105418i | 0.894851 | − | 0.446364i | \(-0.147281\pi\) |
−0.833988 | + | 0.551782i | \(0.813948\pi\) | |||||||
\(332\) | −9.70274 | + | 2.59984i | −0.532507 | + | 0.142685i | ||||
\(333\) | 4.08359 | + | 8.12266i | 0.223779 | + | 0.445119i | ||||
\(334\) | 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 | \(0.112701\pi\) | |||||||
\(338\) | −1.78245 | − | 0.477605i | −0.0969524 | − | 0.0259783i | ||||
\(339\) | −13.0283 | + | 4.96078i | −0.707601 | + | 0.269432i | ||||
\(340\) | 12.5137 | − | 13.1806i | 0.678649 | − | 0.714817i | ||||
\(341\) | 12.2290 | − | 7.06041i | 0.662237 | − | 0.382343i | ||||
\(342\) | −4.23971 | + | 6.45202i | −0.229257 | + | 0.348885i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.98068 | 0.106791 | ||||||||
\(345\) | 12.9100 | − | 5.30322i | 0.695051 | − | 0.285516i | ||||
\(346\) | 0.589887 | − | 1.02171i | 0.0317125 | − | 0.0549277i | ||||
\(347\) | 6.91675 | − | 1.85334i | 0.371310 | − | 0.0994923i | −0.0683381 | − | 0.997662i | \(-0.521770\pi\) |
0.439649 | + | 0.898170i | \(0.355103\pi\) | |||||||
\(348\) | −5.11940 | − | 7.08642i | −0.274429 | − | 0.379872i | ||||
\(349\) | 7.42733i | 0.397576i | 0.980043 | + | 0.198788i | \(0.0637005\pi\) | ||||
−0.980043 | + | 0.198788i | \(0.936300\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.28463 | − | 14.0150i | 0.388825 | − | 0.748066i | ||||
\(352\) | 12.8303 | + | 3.43787i | 0.683857 | + | 0.183239i | ||||
\(353\) | 3.32729 | + | 12.4176i | 0.177094 | + | 0.660922i | 0.996186 | + | 0.0872601i | \(0.0278111\pi\) |
−0.819092 | + | 0.573662i | \(0.805522\pi\) | |||||||
\(354\) | 0.0482306 | + | 0.126666i | 0.00256343 | + | 0.00673224i | ||||
\(355\) | −26.6984 | − | 14.5040i | −1.41700 | − | 0.769791i | ||||
\(356\) | 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 | −0.978824 | − | 0.204705i | \(-0.934376\pi\) |
0.312132 | − | 0.950039i | \(-0.398957\pi\) | |||||||
\(360\) | 6.52610 | − | 10.5162i | 0.343956 | − | 0.554254i | ||||
\(361\) | 4.24604 | − | 7.35435i | 0.223476 | − | 0.387071i | ||||
\(362\) | 0.700551 | − | 2.61449i | 0.0368201 | − | 0.137415i | ||||
\(363\) | 0.681558 | + | 6.65750i | 0.0357725 | + | 0.349428i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.07752 | + | 12.8058i | −0.161085 | + | 0.670288i | ||||
\(366\) | 3.96586 | + | 0.639115i | 0.207299 | + | 0.0334071i | ||||
\(367\) | 0.589992 | + | 2.20188i | 0.0307973 | + | 0.114937i | 0.979613 | − | 0.200892i | \(-0.0643840\pi\) |
−0.948816 | + | 0.315829i | \(0.897717\pi\) | |||||||
\(368\) | −2.43681 | − | 9.09430i | −0.127027 | − | 0.474073i | ||||
\(369\) | −25.9349 | + | 23.0995i | −1.35012 | + | 1.20251i | ||||
\(370\) | −1.73711 | − | 2.83617i | −0.0903081 | − | 0.147445i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −16.0219 | + | 1.64024i | −0.830699 | + | 0.0850424i | ||||
\(373\) | 4.77498 | − | 17.8205i | 0.247239 | − | 0.922708i | −0.725006 | − | 0.688742i | \(-0.758163\pi\) |
0.972245 | − | 0.233965i | \(-0.0751703\pi\) | |||||||
\(374\) | 3.02904 | − | 5.24645i | 0.156628 | − | 0.271287i | ||||
\(375\) | 18.2322 | + | 6.52600i | 0.941504 | + | 0.337001i | ||||
\(376\) | −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 | \(0.837138\pi\) | |||||||
\(380\) | −9.84528 | + | 18.1228i | −0.505052 | + | 0.929680i | ||||
\(381\) | 27.7826 | − | 10.5787i | 1.42334 | − | 0.541965i | ||||
\(382\) | 0.0710766 | + | 0.265262i | 0.00363660 | + | 0.0135720i | ||||
\(383\) | −24.2119 | − | 6.48757i | −1.23717 | − | 0.331499i | −0.419804 | − | 0.907615i | \(-0.637901\pi\) |
−0.817368 | + | 0.576115i | \(0.804568\pi\) | |||||||
\(384\) | −15.1925 | − | 12.3708i | −0.775291 | − | 0.631293i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.89484i | 0.249141i | ||||||||
\(387\) | −0.185924 | + | 3.21525i | −0.00945103 | + | 0.163440i | ||||
\(388\) | −4.49065 | + | 1.20327i | −0.227978 | + | 0.0610865i | ||||
\(389\) | −9.17563 | + | 15.8927i | −0.465223 | + | 0.805790i | −0.999212 | − | 0.0397016i | \(-0.987359\pi\) |
0.533988 | + | 0.845492i | \(0.320693\pi\) | |||||||
\(390\) | −2.22689 | + | 5.33193i | −0.112763 | + | 0.269993i | ||||
\(391\) | −16.6506 | −0.842056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.1319 | − | 1.75387i | 0.864189 | − | 0.0884710i | ||||
\(394\) | −6.10159 | + | 3.52275i | −0.307393 | + | 0.177474i | ||||
\(395\) | 0.226107 | + | 8.71124i | 0.0113767 | + | 0.438310i | ||||
\(396\) | −4.42877 | + | 13.3840i | −0.222554 | + | 0.672569i | ||||
\(397\) | 14.9067 | + | 3.99423i | 0.748144 | + | 0.200465i | 0.612695 | − | 0.790320i | \(-0.290086\pi\) |
0.135449 | + | 0.990784i | \(0.456752\pi\) | |||||||
\(398\) | 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 | −0.999918 | − | 0.0128408i | \(-0.995913\pi\) |
−0.488838 | + | 0.872374i | \(0.662579\pi\) | |||||||
\(402\) | 5.93629 | + | 2.66224i | 0.296075 | + | 0.132781i | ||||
\(403\) | 15.5207 | − | 4.15876i | 0.773141 | − | 0.207163i | ||||
\(404\) | −3.30813 | − | 5.72986i | −0.164586 | − | 0.285071i | ||||
\(405\) | 16.4585 | + | 11.5810i | 0.817827 | + | 0.575464i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.72437 | + | 5.72437i | 0.283746 | + | 0.283746i | ||||
\(408\) | −11.9689 | + | 8.64662i | −0.592548 | + | 0.428071i | ||||
\(409\) | −6.57533 | − | 3.79627i | −0.325129 | − | 0.187714i | 0.328547 | − | 0.944488i | \(-0.393441\pi\) |
−0.653677 | + | 0.756774i | \(0.726774\pi\) | |||||||
\(410\) | 8.74789 | − | 9.21411i | 0.432027 | − | 0.455052i | ||||
\(411\) | 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 | ||||
\(415\) | 3.62366 | + | 12.2436i | 0.177879 | + | 0.601015i | ||||
\(416\) | 13.0897 | + | 7.55737i | 0.641777 | + | 0.370530i | ||||
\(417\) | 11.9024 | − | 26.5401i | 0.582863 | − | 1.29967i | ||||
\(418\) | −1.77928 | + | 6.64038i | −0.0870276 | + | 0.324791i | ||||
\(419\) | 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 | \(0.290174\pi\) | |||||||
\(422\) | −0.0987156 | + | 0.368412i | −0.00480540 | + | 0.0179340i | ||||
\(423\) | 29.0370 | − | 14.5981i | 1.41183 | − | 0.709784i | ||||
\(424\) | −10.0233 | − | 5.78696i | −0.486775 | − | 0.281040i | ||||
\(425\) | −17.1614 | − | 15.4665i | −0.832451 | − | 0.750236i | ||||
\(426\) | 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 | ||||
\(430\) | −0.0305705 | − | 1.17779i | −0.00147424 | − | 0.0567982i | ||||
\(431\) | −7.30254 | − | 4.21613i | −0.351751 | − | 0.203084i | 0.313705 | − | 0.949520i | \(-0.398430\pi\) |
−0.665456 | + | 0.746437i | \(0.731763\pi\) | |||||||
\(432\) | 9.16546 | − | 10.0149i | 0.440974 | − | 0.481842i | ||||
\(433\) | −18.8277 | − | 18.8277i | −0.904802 | − | 0.904802i | 0.0910444 | − | 0.995847i | \(-0.470979\pi\) |
−0.995847 | + | 0.0910444i | \(0.970979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.83593 | + | 6.73900i | −0.423651 | + | 0.323110i | ||||
\(436\) | 16.7242 | + | 28.9671i | 0.800942 | + | 1.38727i | ||||
\(437\) | 18.2510 | − | 4.89035i | 0.873065 | − | 0.233937i | ||||
\(438\) | 2.04892 | − | 4.56871i | 0.0979013 | − | 0.218301i | ||||
\(439\) | 4.22855 | − | 2.44135i | 0.201818 | − | 0.116519i | −0.395685 | − | 0.918386i | \(-0.629493\pi\) |
0.597503 | + | 0.801867i | \(0.296160\pi\) | |||||||
\(440\) | 2.57523 | − | 10.7157i | 0.122769 | − | 0.510853i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.87447 | − | 4.87447i | 0.231855 | − | 0.231855i | ||||
\(443\) | 32.6426 | + | 8.74656i | 1.55090 | + | 0.415561i | 0.929768 | − | 0.368147i | \(-0.120008\pi\) |
0.621129 | + | 0.783708i | \(0.286674\pi\) | |||||||
\(444\) | −3.28566 | − | 8.62903i | −0.155931 | − | 0.409516i | ||||
\(445\) | 8.83230 | − | 0.229249i | 0.418691 | − | 0.0108674i | ||||
\(446\) | −2.00658 | + | 1.15850i | −0.0950145 | + | 0.0548567i | ||||
\(447\) | 1.64270 | + | 16.0460i | 0.0776970 | + | 0.758948i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.6736 | 1.11723 | 0.558613 | − | 0.829428i | \(-0.311334\pi\) | ||||
0.558613 | + | 0.829428i | \(0.311334\pi\) | |||||||
\(450\) | −6.35410 | − | 3.71837i | −0.299535 | − | 0.175285i | ||||
\(451\) | −15.4630 | + | 26.7826i | −0.728123 | + | 1.26115i | ||||
\(452\) | 13.6762 | − | 3.66451i | 0.643272 | − | 0.172364i | ||||
\(453\) | 28.6231 | − | 20.6780i | 1.34483 | − | 0.971539i | ||||
\(454\) | 0.168200i | 0.00789404i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5798 | − | 12.9930i | 0.495444 | − | 0.608455i | ||||
\(457\) | −14.0127 | − | 3.75469i | −0.655486 | − | 0.175637i | −0.0842782 | − | 0.996442i | \(-0.526858\pi\) |
−0.571208 | + | 0.820805i | \(0.693525\pi\) | |||||||
\(458\) | −1.71228 | − | 6.39031i | −0.0800095 | − | 0.298599i | ||||
\(459\) | −12.9126 | − | 20.2408i | −0.602708 | − | 0.944760i | ||||
\(460\) | −13.5920 | + | 4.02274i | −0.633731 | + | 0.187561i | ||||
\(461\) | − | 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 | ||||
\(465\) | 2.61271 | + | 20.3051i | 0.121161 | + | 0.941628i | ||||
\(466\) | −0.413898 | + | 0.716892i | −0.0191734 | + | 0.0332094i | ||||
\(467\) | 2.93048 | − | 10.9367i | 0.135606 | − | 0.506090i | −0.864388 | − | 0.502825i | \(-0.832294\pi\) |
0.999995 | − | 0.00326486i | \(-0.00103924\pi\) | |||||||
\(468\) | −8.80957 | + | 13.4065i | −0.407223 | + | 0.619714i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.1388 | + | 6.20986i | −0.467668 | + | 0.286439i | ||||
\(471\) | 2.46647 | − | 15.3050i | 0.113649 | − | 0.705218i | ||||
\(472\) | −0.0761345 | − | 0.284138i | −0.00350438 | − | 0.0130785i | ||||
\(473\) | 0.742247 | + | 2.77010i | 0.0341285 | + | 0.127369i | ||||
\(474\) | 0.527093 | − | 3.27074i | 0.0242102 | − | 0.150230i | ||||
\(475\) | 23.3535 | + | 11.9128i | 1.07153 | + | 0.546595i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3349 | − | 15.7277i | 0.473201 | − | 0.720121i | ||||
\(478\) | 0.654619 | − | 2.44307i | 0.0299416 | − | 0.111743i | ||||
\(479\) | −10.0600 | + | 17.4244i | −0.459652 | + | 0.796140i | −0.998942 | − | 0.0459795i | \(-0.985359\pi\) |
0.539291 | + | 0.842120i | \(0.318692\pi\) | |||||||
\(480\) | −11.7681 | + | 15.2437i | −0.537137 | + | 0.695779i | ||||
\(481\) | 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 | ||||||
\(485\) | 1.67711 | + | 5.66662i | 0.0761538 | + | 0.257308i | ||||
\(486\) | −5.33649 | − | 5.48259i | −0.242068 | − | 0.248695i | ||||
\(487\) | 2.84753 | + | 10.6271i | 0.129034 | + | 0.481561i | 0.999951 | − | 0.00986850i | \(-0.00314129\pi\) |
−0.870917 | + | 0.491429i | \(0.836475\pi\) | |||||||
\(488\) | −8.42119 | − | 2.25645i | −0.381209 | − | 0.102145i | ||||
\(489\) | 9.98576 | − | 12.2635i | 0.451572 | − | 0.554576i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.29546i | 0.103593i | 0.998658 | + | 0.0517963i | \(0.0164947\pi\) | ||||
−0.998658 | + | 0.0517963i | \(0.983505\pi\) | |||||||
\(492\) | 28.5923 | − | 20.6558i | 1.28904 | − | 0.931235i | ||||
\(493\) | 12.8056 | − | 3.43125i | 0.576735 | − | 0.154536i | ||||
\(494\) | −3.91135 | + | 6.77466i | −0.175980 | + | 0.304806i | ||||
\(495\) | 17.1532 | + | 5.18625i | 0.770979 | + | 0.233105i | ||||
\(496\) | 13.8106 | 0.620113 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.494377 | − | 4.82910i | −0.0221536 | − | 0.216397i | ||||
\(499\) | 10.6750 | − | 6.16321i | 0.477878 | − | 0.275903i | −0.241654 | − | 0.970363i | \(-0.577690\pi\) |
0.719532 | + | 0.694459i | \(0.244356\pi\) | |||||||
\(500\) | −17.7457 | − | 8.47929i | −0.793611 | − | 0.379205i | ||||
\(501\) | −1.37723 | − | 3.61697i | −0.0615301 | − | 0.161594i | ||||
\(502\) | −2.04000 | − | 0.546616i | −0.0910496 | − | 0.0243967i | ||||
\(503\) | −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 | ||||
\(507\) | −2.66477 | + | 5.94194i | −0.118347 | + | 0.263891i | ||||
\(508\) | −29.1641 | + | 7.81448i | −1.29395 | + | 0.346712i | ||||
\(509\) | 6.80807 | + | 11.7919i | 0.301762 | + | 0.522668i | 0.976535 | − | 0.215358i | \(-0.0690918\pi\) |
−0.674773 | + | 0.738025i | \(0.735758\pi\) | |||||||
\(510\) | 5.32635 | + | 6.98372i | 0.235855 | + | 0.309244i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0031 | + | 16.0031i | 0.707245 | + | 0.707245i | ||||
\(513\) | 20.0986 | + | 18.3939i | 0.887373 | + | 0.812109i | ||||
\(514\) | 3.50381 | + | 2.02292i | 0.154546 | + | 0.0892273i | ||||
\(515\) | 20.3121 | + | 19.2843i | 0.895057 | + | 0.849769i | ||||
\(516\) | 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 | ||||
\(520\) | 5.98645 | − | 11.0196i | 0.262523 | − | 0.483243i | ||||
\(521\) | −15.9236 | − | 9.19351i | −0.697626 | − | 0.402775i | 0.108836 | − | 0.994060i | \(-0.465288\pi\) |
−0.806463 | + | 0.591285i | \(0.798621\pi\) | |||||||
\(522\) | 3.77457 | − | 1.89763i | 0.165208 | − | 0.0830570i | ||||
\(523\) | −3.26144 | + | 12.1719i | −0.142613 | + | 0.532239i | 0.857237 | + | 0.514922i | \(0.172179\pi\) |
−0.999850 | + | 0.0173168i | \(0.994488\pi\) | |||||||
\(524\) | −17.4905 | −0.764074 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0433754 | −0.00189126 | ||||||||
\(527\) | 6.32138 | − | 23.5917i | 0.275364 | − | 1.02767i | ||||
\(528\) | 4.94672 | − | 11.0303i | 0.215279 | − | 0.480030i | ||||
\(529\) | −8.67226 | − | 5.00693i | −0.377055 | − | 0.217693i | ||||
\(530\) | −3.28645 | + | 6.04958i | −0.142754 | + | 0.262777i | ||||
\(531\) | 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 | ||||
\(535\) | −1.62918 | − | 1.54674i | −0.0704355 | − | 0.0668716i | ||||
\(536\) | −12.2282 | − | 7.05998i | −0.528180 | − | 0.304945i | ||||
\(537\) | −11.8551 | + | 8.56443i | −0.511586 | + | 0.369582i | ||||
\(538\) | −10.2971 | − | 10.2971i | −0.443938 | − | 0.443938i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −15.4308 | − | 13.4031i | −0.664035 | − | 0.576777i | ||||
\(541\) | −13.9129 | − | 24.0979i | −0.598162 | − | 1.03605i | −0.993092 | − | 0.117336i | \(-0.962564\pi\) |
0.394930 | − | 0.918711i | \(-0.370769\pi\) | |||||||
\(542\) | −10.7322 | + | 2.87568i | −0.460986 | + | 0.123521i | ||||
\(543\) | −8.71563 | − | 3.90868i | −0.374023 | − | 0.167738i | ||||
\(544\) | 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 | \(0.381483\pi\) | |||||||
\(548\) | −32.8356 | − | 8.79828i | −1.40267 | − | 0.375844i | ||||
\(549\) | 4.45339 | − | 13.4583i | 0.190066 | − | 0.574388i | ||||
\(550\) | −6.41176 | − | 1.36594i | −0.273398 | − | 0.0582440i | ||||
\(551\) | −13.0287 | + | 7.52212i | −0.555041 | + | 0.320453i | ||||
\(552\) | 11.4560 | − | 1.17280i | 0.487600 | − | 0.0499178i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.92314 | 0.124192 | ||||||||
\(555\) | −10.8566 | + | 4.45973i | −0.460838 | + | 0.189305i | ||||
\(556\) | −14.7706 | + | 25.5834i | −0.626413 | + | 1.08498i | ||||
\(557\) | −14.2070 | + | 3.80675i | −0.601969 | + | 0.161297i | −0.546917 | − | 0.837187i | \(-0.684199\pi\) |
−0.0550511 | + | 0.998484i | \(0.517532\pi\) | |||||||
\(558\) | 0.449318 | − | 7.77023i | 0.0190211 | − | 0.328940i | ||||
\(559\) | 3.26332i | 0.138024i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.5781 | − | 13.4990i | −0.699927 | − | 0.569926i | ||||
\(562\) | 10.4343 | + | 2.79585i | 0.440143 | + | 0.117936i | ||||
\(563\) | −3.71967 | − | 13.8820i | −0.156766 | − | 0.585057i | −0.998948 | − | 0.0458638i | \(-0.985396\pi\) |
0.842182 | − | 0.539193i | \(-0.181271\pi\) | |||||||
\(564\) | −30.8472 | + | 11.7457i | −1.29890 | + | 0.494581i | ||||
\(565\) | −5.10760 | − | 17.2576i | −0.214879 | − | 0.726031i | ||||
\(566\) | 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 | 0.894171 | + | 0.447726i | \(0.147766\pi\) |
−0.0593435 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(570\) | −7.88947 | − | 6.09062i | −0.330454 | − | 0.255108i | ||||
\(571\) | 21.9157 | − | 37.9591i | 0.917143 | − | 1.58854i | 0.113410 | − | 0.993548i | \(-0.463823\pi\) |
0.803733 | − | 0.594990i | \(-0.202844\pi\) | |||||||
\(572\) | −3.69712 | + | 13.7978i | −0.154584 | + | 0.576917i | ||||
\(573\) | 0.964086 | − | 0.0986978i | 0.0402753 | − | 0.00412316i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.56003 | + | 17.1388i | 0.231869 | + | 0.714739i | ||||
\(576\) | −6.23885 | + | 5.55676i | −0.259952 | + | 0.231532i | ||||
\(577\) | −10.1822 | − | 38.0004i | −0.423890 | − | 1.58198i | −0.766336 | − | 0.642441i | \(-0.777922\pi\) |
0.342446 | − | 0.939538i | \(-0.388745\pi\) | |||||||
\(578\) | −0.552465 | − | 2.06183i | −0.0229795 | − | 0.0857607i | ||||
\(579\) | 17.0537 | + | 2.74828i | 0.708730 | + | 0.114215i | ||||
\(580\) | 9.62434 | − | 5.89476i | 0.399629 | − | 0.244767i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.228809 | − | 2.23502i | −0.00948443 | − | 0.0926445i | ||||
\(583\) | 4.33725 | − | 16.1868i | 0.179630 | − | 0.670390i | ||||
\(584\) | −5.43352 | + | 9.41114i | −0.224841 | + | 0.389436i | ||||
\(585\) | 17.3263 | + | 10.7522i | 0.716353 | + | 0.444550i | ||||
\(586\) | −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 | ||||||||
\(590\) | −0.167785 | + | 0.0496581i | −0.00690758 | + | 0.00204439i | ||||
\(591\) | 8.84754 | + | 23.2360i | 0.363939 | + | 0.955801i | ||||
\(592\) | 2.04923 | + | 7.64782i | 0.0842228 | + | 0.314324i | ||||
\(593\) | −1.65289 | − | 0.442890i | −0.0678759 | − | 0.0181873i | 0.224721 | − | 0.974423i | \(-0.427853\pi\) |
−0.292597 | + | 0.956236i | \(0.594520\pi\) | |||||||
\(594\) | −6.04501 | − | 3.14204i | −0.248030 | − | 0.128919i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.3818i | − | 0.671025i | ||||||
\(597\) | −11.8416 | − | 16.3914i | −0.484644 | − | 0.670857i | ||||
\(598\) | −5.19322 | + | 1.39152i | −0.212366 | + | 0.0569034i | ||||
\(599\) | −7.80027 | + | 13.5105i | −0.318710 | + | 0.552022i | −0.980219 | − | 0.197915i | \(-0.936583\pi\) |
0.661509 | + | 0.749937i | \(0.269916\pi\) | |||||||
\(600\) | 12.8969 | + | 9.43254i | 0.526512 | + | 0.385082i | ||||
\(601\) | 14.2954 | 0.583122 | 0.291561 | − | 0.956552i | \(-0.405825\pi\) | ||||
0.291561 | + | 0.956552i | \(0.405825\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.6083 | − | 19.1875i | 0.513452 | − | 0.781374i | ||||
\(604\) | −31.0579 | + | 17.9313i | −1.26373 | + | 0.729614i | ||||
\(605\) | −8.63680 | + | 0.224175i | −0.351136 | + | 0.00911400i | ||||
\(606\) | 2.98809 | − | 1.13777i | 0.121383 | − | 0.0462187i | ||||
\(607\) | 36.7166 | + | 9.83819i | 1.49028 | + | 0.399320i | 0.909832 | − | 0.414976i | \(-0.136210\pi\) |
0.580450 | + | 0.814296i | \(0.302877\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 10.9525 | + | 21.7857i | 0.442731 | + | 0.880634i | ||||
\(613\) | −3.79405 | + | 1.01661i | −0.153240 | + | 0.0410606i | −0.334624 | − | 0.942352i | \(-0.608609\pi\) |
0.181383 | + | 0.983412i | \(0.441943\pi\) | |||||||
\(614\) | −3.63523 | − | 6.29641i | −0.146706 | − | 0.254102i | ||||
\(615\) | −27.1906 | − | 35.6513i | −1.09643 | − | 1.43760i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.21465 | + | 3.21465i | 0.129417 | + | 0.129417i | 0.768848 | − | 0.639431i | \(-0.220830\pi\) |
−0.639431 | + | 0.768848i | \(0.720830\pi\) | |||||||
\(618\) | −6.23554 | − | 8.63141i | −0.250830 | − | 0.347206i | ||||
\(619\) | 42.1764 | + | 24.3506i | 1.69521 | + | 0.978731i | 0.950179 | + | 0.311704i | \(0.100900\pi\) |
0.745033 | + | 0.667027i | \(0.232434\pi\) | |||||||
\(620\) | −0.539499 | − | 20.7853i | −0.0216668 | − | 0.834760i | ||||
\(621\) | 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 | ||||
\(625\) | −10.1894 | + | 22.8293i | −0.407577 | + | 0.913171i | ||||
\(626\) | 9.90812 | + | 5.72046i | 0.396008 | + | 0.228635i | ||||
\(627\) | 22.1363 | + | 9.92741i | 0.884037 | + | 0.396463i | ||||
\(628\) | −4.07502 | + | 15.2082i | −0.162611 | + | 0.606872i | ||||
\(629\) | 14.0023 | 0.558307 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0588 | 0.599480 | 0.299740 | − | 0.954021i | \(-0.403100\pi\) | ||||
0.299740 | + | 0.954021i | \(0.403100\pi\) | |||||||
\(632\) | −1.86095 | + | 6.94515i | −0.0740245 | + | 0.276263i | ||||
\(633\) | 1.22813 | + | 0.550778i | 0.0488138 | + | 0.0218915i | ||||
\(634\) | 13.7980 | + | 7.96626i | 0.547987 | + | 0.316381i | ||||
\(635\) | 10.8918 | + | 36.8013i | 0.432229 | + | 1.46042i | ||||
\(636\) | −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 | ||||
\(640\) | 17.4150 | − | 18.3431i | 0.688386 | − | 0.725074i | ||||
\(641\) | −39.8129 | − | 22.9860i | −1.57252 | − | 0.907892i | −0.995860 | − | 0.0909048i | \(-0.971024\pi\) |
−0.576656 | − | 0.816987i | \(-0.695643\pi\) | |||||||
\(642\) | 0.500136 | + | 0.692302i | 0.0197388 | + | 0.0273230i | ||||
\(643\) | −5.91991 | − | 5.91991i | −0.233458 | − | 0.233458i | 0.580676 | − | 0.814135i | \(-0.302788\pi\) |
−0.814135 | + | 0.580676i | \(0.802788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.12062 | − | 0.554781i | −0.162249 | − | 0.0218445i | ||||
\(646\) | 5.94531 | + | 10.2976i | 0.233915 | + | 0.405153i | ||||
\(647\) | −15.1870 | + | 4.06933i | −0.597061 | + | 0.159982i | −0.544678 | − | 0.838645i | \(-0.683348\pi\) |
−0.0523826 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(648\) | 10.3099 | + | 13.0166i | 0.405009 | + | 0.511342i | ||||
\(649\) | 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 | ||||
\(653\) | −41.8686 | − | 11.2187i | −1.63845 | − | 0.439020i | −0.682101 | − | 0.731258i | \(-0.738934\pi\) |
−0.956346 | + | 0.292238i | \(0.905600\pi\) | |||||||
\(654\) | −15.1062 | + | 5.75195i | −0.590698 | + | 0.224919i | ||||
\(655\) | 0.576874 | + | 22.2253i | 0.0225403 | + | 0.868414i | ||||
\(656\) | −26.1942 | + | 15.1232i | −1.02271 | + | 0.590463i | ||||
\(657\) | −14.7671 | − | 9.70367i | −0.576120 | − | 0.378576i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −50.9397 | −1.98433 | −0.992165 | − | 0.124933i | \(-0.960129\pi\) | ||||
−0.992165 | + | 0.124933i | \(0.960129\pi\) | |||||||
\(660\) | −16.7941 | − | 7.01409i | −0.653711 | − | 0.273023i | ||||
\(661\) | 10.2697 | − | 17.7876i | 0.399445 | − | 0.691858i | −0.594213 | − | 0.804308i | \(-0.702536\pi\) |
0.993657 | + | 0.112449i | \(0.0358696\pi\) | |||||||
\(662\) | 1.04991 | − | 0.281323i | 0.0408060 | − | 0.0109339i | ||||
\(663\) | −14.2459 | − | 19.7196i | −0.553267 | − | 0.765847i | ||||
\(664\) | 10.5355i | 0.408856i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.36956 | − | 0.904139i | 0.169317 | − | 0.0350347i | ||||
\(667\) | −9.98735 | − | 2.67610i | −0.386712 | − | 0.103619i | ||||
\(668\) | 1.01736 | + | 3.79683i | 0.0393627 | + | 0.146904i | ||||
\(669\) | 2.90963 | + | 7.64146i | 0.112493 | + | 0.295436i | ||||
\(670\) | −4.00941 | + | 7.38037i | −0.154897 | + | 0.285128i | ||||
\(671\) | − | 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 | ||||
\(675\) | −16.5225 | + | 20.0501i | −0.635951 | + | 0.771729i | ||||
\(676\) | 3.30692 | − | 5.72776i | 0.127189 | − | 0.220298i | ||||
\(677\) | −3.17568 | + | 11.8518i | −0.122051 | + | 0.455502i | −0.999717 | − | 0.0237707i | \(-0.992433\pi\) |
0.877666 | + | 0.479273i | \(0.159100\pi\) | |||||||
\(678\) | 0.696831 | + | 6.80669i | 0.0267616 | + | 0.261409i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.95618 | − | 16.2554i | −0.381802 | − | 0.623366i | ||||
\(681\) | 0.586015 | + | 0.0944387i | 0.0224561 | + | 0.00361890i | ||||
\(682\) | −1.79377 | − | 6.69445i | −0.0686871 | − | 0.256344i | ||||
\(683\) | 8.78498 | + | 32.7860i | 0.336148 | + | 1.25452i | 0.902619 | + | 0.430440i | \(0.141642\pi\) |
−0.566471 | + | 0.824081i | \(0.691692\pi\) | |||||||
\(684\) | −18.4039 | − | 20.6629i | −0.703689 | − | 0.790066i | ||||
\(685\) | −10.0971 | + | 42.0147i | −0.385789 | + | 1.60530i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.2254 | + | 2.37769i | −0.886104 | + | 0.0907145i | ||||
\(688\) | −0.725939 | + | 2.70924i | −0.0276762 | + | 0.103289i | ||||
\(689\) | 9.53445 | − | 16.5141i | 0.363234 | − | 0.629139i | ||||
\(690\) | −0.874210 | − | 6.79409i | −0.0332806 | − | 0.258647i | ||||
\(691\) | 16.2840 | + | 28.2047i | 0.619472 | + | 1.07296i | 0.989582 | + | 0.143969i | \(0.0459867\pi\) |
−0.370110 | + | 0.928988i | \(0.620680\pi\) | |||||||
\(692\) | 2.98996 | + | 2.98996i | 0.113661 | + | 0.113661i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 3.51455i | − | 0.133410i | ||||||
\(695\) | 32.9963 | + | 17.9254i | 1.25162 | + | 0.679948i | ||||
\(696\) | −8.56887 | + | 3.26276i | −0.324802 | + | 0.123674i | ||||
\(697\) | 13.8444 | + | 51.6681i | 0.524395 | + | 1.95707i | ||||
\(698\) | 3.52118 | + | 0.943497i | 0.133279 | + | 0.0357119i | ||||
\(699\) | 2.26528 | + | 1.84454i | 0.0856808 | + | 0.0697670i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.43359i | − | 0.0919155i | −0.998943 | − | 0.0459577i | \(-0.985366\pi\) | ||
0.998943 | − | 0.0459577i | \(-0.0146340\pi\) | |||||||
\(702\) | −5.71892 | − | 5.23386i | −0.215847 | − | 0.197539i | ||||
\(703\) | −15.3482 | + | 4.11253i | −0.578867 | + | 0.155107i | ||||
\(704\) | −3.71974 | + | 6.44278i | −0.140193 | + | 0.242821i | ||||
\(705\) | 15.9427 | + | 38.8105i | 0.600438 | + | 1.46169i | ||||
\(706\) | 6.30965 | 0.237467 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.483257 | + | 0.0494732i | −0.0181619 | + | 0.00185932i | ||||
\(709\) | −10.6934 | + | 6.17386i | −0.401601 | + | 0.231864i | −0.687174 | − | 0.726493i | \(-0.741149\pi\) |
0.285574 | + | 0.958357i | \(0.407816\pi\) | |||||||
\(710\) | −10.2676 | + | 10.8148i | −0.385336 | + | 0.405873i | ||||
\(711\) | −11.0994 | − | 3.67281i | −0.416260 | − | 0.137741i | ||||
\(712\) | 7.04166 | + | 1.88681i | 0.263897 | + | 0.0707111i | ||||
\(713\) | −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 | ||||
\(717\) | −8.14418 | − | 3.65241i | −0.304150 | − | 0.136402i | ||||
\(718\) | −11.9773 | + | 3.20930i | −0.446988 | + | 0.119770i | ||||
\(719\) | 12.1083 | + | 20.9721i | 0.451562 | + | 0.782129i | 0.998483 | − | 0.0550554i | \(-0.0175335\pi\) |
−0.546921 | + | 0.837184i | \(0.684200\pi\) | |||||||
\(720\) | 11.9926 | + | 12.7809i | 0.446936 | + | 0.476316i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.94721 | − | 2.94721i | −0.109684 | − | 0.109684i | ||||
\(723\) | −20.9441 | + | 15.1305i | −0.778918 | + | 0.562709i | ||||
\(724\) | 8.40146 | + | 4.85059i | 0.312238 | + | 0.180271i | ||||
\(725\) | −7.80796 | − | 12.0353i | −0.289980 | − | 0.446981i | ||||
\(726\) | 3.24279 | + | 0.522589i | 0.120351 | + | 0.0193951i | ||||
\(727\) | −25.8923 | + | 25.8923i | −0.960293 | + | 0.960293i | −0.999241 | − | 0.0389483i | \(-0.987599\pi\) |
0.0389483 | + | 0.999241i | \(0.487599\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.0977 | + | 15.5142i | −0.818435 | + | 0.574599i | ||||
\(730\) | 5.68010 | + | 3.08573i | 0.210230 | + | 0.114208i | ||||
\(731\) | 4.29575 | + | 2.48015i | 0.158884 | + | 0.0917317i | ||||
\(732\) | −5.89148 | + | 13.1369i | −0.217755 | + | 0.485553i | ||||
\(733\) | 4.92434 | − | 18.3779i | 0.181885 | − | 0.678803i | −0.813391 | − | 0.581717i | \(-0.802381\pi\) |
0.995276 | − | 0.0970859i | \(-0.0309521\pi\) | |||||||
\(734\) | 1.11882 | 0.0412965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.9184 | −0.660481 | ||||||||
\(737\) | 5.29136 | − | 19.7476i | 0.194910 | − | 0.727413i | ||||
\(738\) | 7.65657 | + | 15.2297i | 0.281842 | + | 0.560612i | ||||
\(739\) | 1.70445 | + | 0.984064i | 0.0626991 | + | 0.0361994i | 0.531022 | − | 0.847358i | \(-0.321808\pi\) |
−0.468323 | + | 0.883557i | \(0.655142\pi\) | |||||||
\(740\) | 11.4302 | − | 3.38291i | 0.420181 | − | 0.124358i | ||||
\(741\) | 21.4070 | + | 17.4310i | 0.786406 | + | 0.640343i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.54680 | − | 4.54680i | 0.166806 | − | 0.166806i | −0.618768 | − | 0.785574i | \(-0.712368\pi\) |
0.785574 | + | 0.618768i | \(0.212368\pi\) | |||||||
\(744\) | −2.68755 | + | 16.6769i | −0.0985304 | + | 0.611405i | ||||
\(745\) | −20.8165 | + | 0.540308i | −0.762658 | + | 0.0197954i | ||||
\(746\) | −7.84182 | − | 4.52748i | −0.287110 | − | 0.165763i | ||||
\(747\) | −17.1023 | − | 0.988950i | −0.625740 | − | 0.0361838i | ||||
\(748\) | 15.3533 | + | 15.3533i | 0.561371 | + | 0.561371i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.40991 | − | 7.81457i | 0.197542 | − | 0.285348i | ||||
\(751\) | 0.245859 | + | 0.425840i | 0.00897152 | + | 0.0155391i | 0.870476 | − | 0.492210i | \(-0.163811\pi\) |
−0.861505 | + | 0.507749i | \(0.830478\pi\) | |||||||
\(752\) | 27.3396 | − | 7.32563i | 0.996973 | − | 0.267138i | ||||
\(753\) | −3.04981 | + | 6.80051i | −0.111141 | + | 0.247824i | ||||
\(754\) | 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 | \(0.221250\pi\) | |||||||
\(758\) | 9.03771 | + | 2.42165i | 0.328265 | + | 0.0879582i | ||||
\(759\) | 5.93329 | + | 15.5824i | 0.215365 | + | 0.565605i | ||||
\(760\) | 15.6875 | + | 14.8937i | 0.569044 | + | 0.540251i | ||||
\(761\) | 23.3151 | − | 13.4610i | 0.845173 | − | 0.487961i | −0.0138461 | − | 0.999904i | \(-0.504407\pi\) |
0.859019 | + | 0.511943i | \(0.171074\pi\) | |||||||
\(762\) | −1.48598 | − | 14.5151i | −0.0538312 | − | 0.525826i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.984264 | −0.0356094 | ||||||||
\(765\) | 27.3221 | − | 14.6361i | 0.987831 | − | 0.529168i | ||||
\(766\) | −6.15131 | + | 10.6544i | −0.222256 | + | 0.384958i | ||||
\(767\) | 0.468138 | − | 0.125437i | 0.0169035 | − | 0.00452928i | ||||
\(768\) | 0.0253043 | − | 0.0182804i | 0.000913090 | − | 0.000659638i | ||||
\(769\) | − | 31.3935i | − | 1.13208i | −0.824378 | − | 0.566040i | \(-0.808475\pi\) | ||
0.824378 | − | 0.566040i | \(-0.191525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.01519 | − | 11.0716i | 0.324674 | − | 0.398733i | ||||
\(772\) | −16.9458 | − | 4.54062i | −0.609894 | − | 0.163421i | ||||
\(773\) | −4.90198 | − | 18.2944i | −0.176312 | − | 0.658005i | −0.996324 | − | 0.0856597i | \(-0.972700\pi\) |
0.820012 | − | 0.572346i | \(-0.193966\pi\) | |||||||
\(774\) | 1.50068 | + | 0.496578i | 0.0539408 | + | 0.0178491i | ||||
\(775\) | −26.3944 | + | 1.37109i | −0.948113 | + | 0.0492512i | ||||
\(776\) | 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 | ||||
\(780\) | −16.3933 | − | 12.6555i | −0.586974 | − | 0.453141i | ||||
\(781\) | 18.1493 | − | 31.4354i | 0.649431 | − | 1.12485i | ||||
\(782\) | −2.11513 | + | 7.89378i | −0.0756369 | + | 0.282281i | ||||
\(783\) | −4.49210 | − | 14.2162i | −0.160535 | − | 0.508044i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.4596 | + | 4.67657i | 0.694542 | + | 0.166914i | ||||
\(786\) | 1.34479 | − | 8.34475i | 0.0479671 | − | 0.297647i | ||||
\(787\) | 8.22502 | + | 30.6962i | 0.293190 | + | 1.09420i | 0.942644 | + | 0.333800i | \(0.108331\pi\) |
−0.649454 | + | 0.760401i | \(0.725002\pi\) | |||||||
\(788\) | −6.53566 | − | 24.3914i | −0.232823 | − | 0.868908i | ||||
\(789\) | −0.0243538 | + | 0.151121i | −0.000867017 | + | 0.00538005i | ||||
\(790\) | 4.15858 | + | 0.999399i | 0.147956 | + | 0.0355570i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.3569 | + | 8.11990i | 0.439084 | + | 0.288528i | ||||
\(793\) | 3.71767 | − | 13.8745i | 0.132018 | − | 0.492699i | ||||
\(794\) | 3.78720 | − | 6.55962i | 0.134403 | − | 0.232792i | ||||
\(795\) | 19.2317 | + | 14.8467i | 0.682077 | + | 0.526559i | ||||
\(796\) | 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 | ||||||
\(800\) | −18.4681 | − | 16.6442i | −0.652947 | − | 0.588460i | ||||
\(801\) | −3.72385 | + | 11.2536i | −0.131576 | + | 0.397628i | ||||
\(802\) | 4.37293 | + | 16.3200i | 0.154414 | + | 0.576279i | ||||
\(803\) | −15.1982 | − | 4.07235i | −0.536333 | − | 0.143710i | ||||
\(804\) | −14.7233 | + | 18.0817i | −0.519252 | + | 0.637694i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 7.88640i | − | 0.277787i | ||||||
\(807\) | −41.6567 | + | 30.0938i | −1.46638 | + | 1.05935i | ||||
\(808\) | −6.70287 | + | 1.79603i | −0.235806 | + | 0.0631841i | ||||
\(809\) | −3.13513 | + | 5.43021i | −0.110225 | + | 0.190916i | −0.915861 | − | 0.401495i | \(-0.868491\pi\) |
0.805636 | + | 0.592411i | \(0.201824\pi\) | |||||||
\(810\) | 7.58109 | − | 6.33155i | 0.266372 | − | 0.222468i | ||||
\(811\) | −8.90138 | −0.312570 | −0.156285 | − | 0.987712i | \(-0.549952\pi\) | ||||
−0.156285 | + | 0.987712i | \(0.549952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.99320 | + | 39.0058i | 0.140048 | + | 1.36799i | ||||
\(814\) | 3.44100 | − | 1.98666i | 0.120607 | − | 0.0696325i | ||||
\(815\) | 14.8066 | + | 14.0575i | 0.518654 | + | 0.492411i | ||||
\(816\) | −7.44041 | − | 19.5405i | −0.260466 | − | 0.684054i | ||||
\(817\) | −5.43708 | − | 1.45686i | −0.190219 | − | 0.0509691i | ||||
\(818\) | −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 | −0.732467 | − | 0.680803i | \(-0.761631\pi\) |
0.223359 | + | 0.974736i | \(0.428298\pi\) | |||||||
\(822\) | 6.72232 | − | 14.9895i | 0.234468 | − | 0.522819i | ||||
\(823\) | −44.3795 | + | 11.8914i | −1.54697 | + | 0.414510i | −0.928510 | − | 0.371306i | \(-0.878910\pi\) |
−0.618461 | + | 0.785816i | \(0.712243\pi\) | |||||||
\(824\) | 11.5550 | + | 20.0138i | 0.402536 | + | 0.697213i | ||||
\(825\) | −8.35897 | + | 21.5718i | −0.291022 | + | 0.751034i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.87454 | + | 4.87454i | 0.169504 | + | 0.169504i | 0.786762 | − | 0.617257i | \(-0.211756\pi\) |
−0.617257 | + | 0.786762i | \(0.711756\pi\) | |||||||
\(828\) | 1.09786 | − | 18.9858i | 0.0381534 | − | 0.659802i | ||||
\(829\) | 8.50889 | + | 4.91261i | 0.295526 | + | 0.170622i | 0.640431 | − | 0.768015i | \(-0.278756\pi\) |
−0.344905 | + | 0.938638i | \(0.612089\pi\) | |||||||
\(830\) | 6.26482 | − | 0.162608i | 0.217455 | − | 0.00564421i | ||||
\(831\) | 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 | ||||
\(835\) | 4.79111 | − | 1.41799i | 0.165803 | − | 0.0490716i | ||||
\(836\) | −21.3383 | − | 12.3197i | −0.738002 | − | 0.426085i | ||||
\(837\) | −26.8194 | − | 5.92815i | −0.927015 | − | 0.204907i | ||||
\(838\) | 0.788406 | − | 2.94237i | 0.0272350 | − | 0.101643i | ||||
\(839\) | −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 | ||||||||
\(842\) | 3.19276 | − | 11.9156i | 0.110030 | − | 0.410637i | ||||
\(843\) | 15.5993 | − | 34.7835i | 0.537269 | − | 1.19801i | ||||
\(844\) | −1.18386 | − | 0.683503i | −0.0407502 | − | 0.0235271i | ||||
\(845\) | −7.38739 | − | 4.01322i | −0.254134 | − | 0.138059i | ||||
\(846\) | −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 | ||||
\(850\) | −9.51245 | + | 6.17123i | −0.326274 | + | 0.211672i | ||||
\(851\) | −9.45756 | − | 5.46033i | −0.324201 | − | 0.187178i | ||||
\(852\) | −33.5595 | + | 24.2442i | −1.14973 | + | 0.830593i | ||||
\(853\) | −36.7177 | − | 36.7177i | −1.25719 | − | 1.25719i | −0.952429 | − | 0.304761i | \(-0.901424\pi\) |
−0.304761 | − | 0.952429i | \(-0.598576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.6496 | + | 24.0675i | −0.877197 | + | 0.823090i | ||||
\(856\) | −0.926792 | − | 1.60525i | −0.0316771 | − | 0.0548663i | ||||
\(857\) | −34.9520 | + | 9.36537i | −1.19394 | + | 0.319915i | −0.800442 | − | 0.599411i | \(-0.795402\pi\) |
−0.393497 | + | 0.919326i | \(0.628735\pi\) | |||||||
\(858\) | −6.29873 | − | 2.82478i | −0.215035 | − | 0.0964365i | ||||
\(859\) | 13.6081 | − | 7.85667i | 0.464304 | − | 0.268066i | −0.249548 | − | 0.968362i | \(-0.580282\pi\) |
0.713852 | + | 0.700296i | \(0.246949\pi\) | |||||||
\(860\) | 4.10585 | + | 0.986727i | 0.140008 | + | 0.0336471i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.92644 | + | 2.92644i | −0.0996751 | + | 0.0996751i | ||||
\(863\) | 15.1749 | + | 4.06609i | 0.516559 | + | 0.138411i | 0.507674 | − | 0.861549i | \(-0.330505\pi\) |
0.00888427 | + | 0.999961i | \(0.497172\pi\) | |||||||
\(864\) | −13.8958 | − | 21.7820i | −0.472744 | − | 0.741038i | ||||
\(865\) | 3.70075 | − | 3.89798i | 0.125829 | − | 0.132535i | ||||
\(866\) | −11.3176 | + | 6.53423i | −0.384588 | + | 0.222042i | ||||
\(867\) | −7.49366 | + | 0.767159i | −0.254498 | + | 0.0260541i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4106 | −0.353155 | ||||||||
\(870\) | 2.07242 | + | 5.04503i | 0.0702616 | + | 0.171043i | ||||
\(871\) | 11.6318 | − | 20.1469i | 0.394130 | − | 0.682653i | ||||
\(872\) | 33.8861 | − | 9.07976i | 1.14753 | − | 0.307480i | ||||
\(873\) | −7.91533 | − | 0.457708i | −0.267893 | − | 0.0154911i | ||||
\(874\) | − | 9.27375i | − | 0.313689i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.9161 | + | 11.3314i | 0.470182 | + | 0.382853i | ||||
\(877\) | 28.3179 | + | 7.58775i | 0.956226 | + | 0.256220i | 0.703002 | − | 0.711188i | \(-0.251842\pi\) |
0.253224 | + | 0.967408i | \(0.418509\pi\) | |||||||
\(878\) | −0.620252 | − | 2.31481i | −0.0209325 | − | 0.0781211i | ||||
\(879\) | −8.15763 | + | 3.10617i | −0.275150 | + | 0.104769i | ||||
\(880\) | 13.7135 | + | 7.44991i | 0.462282 | + | 0.251136i | ||||
\(881\) | − | 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 | ||||
\(885\) | 0.0788050 | + | 0.612448i | 0.00264900 | + | 0.0205872i | ||||
\(886\) | 8.29321 | − | 14.3643i | 0.278616 | − | 0.482577i | ||||
\(887\) | 0.494122 | − | 1.84409i | 0.0165910 | − | 0.0619185i | −0.957134 | − | 0.289645i | \(-0.906463\pi\) |
0.973725 | + | 0.227727i | \(0.0731293\pi\) | |||||||
\(888\) | −9.63389 | + | 0.986265i | −0.323292 | + | 0.0330969i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.01329 | − | 4.21637i | 0.0339655 | − | 0.141333i | ||||
\(891\) | −14.3410 | + | 19.2968i | −0.480442 | + | 0.646469i | ||||
\(892\) | −2.14933 | − | 8.02142i | −0.0719650 | − | 0.268577i | ||||
\(893\) | 14.7015 | + | 54.8669i | 0.491969 | + | 1.83605i | ||||
\(894\) | 7.81581 | + | 1.25955i | 0.261400 | + | 0.0421256i | ||||
\(895\) | −9.86155 | − | 16.1009i | −0.329635 | − | 0.538194i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.93228 | + | 18.8746i | 0.0645169 | + | 0.630205i | ||||
\(898\) | 3.00727 | − | 11.2233i | 0.100354 | − | 0.374526i | ||||
\(899\) | 7.58338 | − | 13.1348i | 0.252920 | − | 0.438070i | ||||
\(900\) | 18.7672 | − | 18.5485i | 0.625573 | − | 0.618282i | ||||
\(901\) | −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 | ||||||
\(905\) | 5.88659 | − | 10.8358i | 0.195677 | − | 0.360194i | ||||
\(906\) | −6.16712 | − | 16.1965i | −0.204889 | − | 0.538093i | ||||
\(907\) | −10.4993 | − | 39.1839i | −0.348623 | − | 1.30108i | −0.888322 | − | 0.459221i | \(-0.848129\pi\) |
0.539699 | − | 0.841858i | \(-0.318538\pi\) | |||||||
\(908\) | −0.582307 | − | 0.156029i | −0.0193245 | − | 0.00517799i | ||||
\(909\) | −2.28631 | − | 11.0494i | −0.0758322 | − | 0.366485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 34.0874i | − | 1.12937i | −0.825307 | − | 0.564684i | \(-0.808998\pi\) | ||
0.825307 | − | 0.564684i | \(-0.191002\pi\) | |||||||
\(912\) | 13.8947 | + | 19.2334i | 0.460100 | + | 0.636883i | ||||
\(913\) | −14.7345 | + | 3.94810i | −0.487641 | + | 0.130663i | ||||
\(914\) | −3.56008 | + | 6.16624i | −0.117757 | + | 0.203961i | ||||
\(915\) | 16.8875 | + | 7.05308i | 0.558283 | + | 0.233168i | ||||
\(916\) | 23.7115 | 0.783450 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.2361 | + | 3.55046i | −0.370848 | + | 0.117183i | ||||
\(919\) | −1.90232 | + | 1.09830i | −0.0627516 | + | 0.0362297i | −0.531048 | − | 0.847342i | \(-0.678201\pi\) |
0.468296 | + | 0.883572i | \(0.344868\pi\) | |||||||
\(920\) | 0.385752 | + | 14.8619i | 0.0127179 | + | 0.489983i | ||||
\(921\) | −23.9779 | + | 9.13004i | −0.790099 | + | 0.300845i | ||||
\(922\) | −11.0534 | − | 2.96175i | −0.364025 | − | 0.0975401i | ||||
\(923\) | 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 | ||||
\(927\) | −33.5731 | + | 16.8786i | −1.10269 | + | 0.554365i | ||||
\(928\) | 13.7806 | − | 3.69251i | 0.452372 | − | 0.121213i | ||||
\(929\) | −25.6490 | − | 44.4254i | −0.841518 | − | 1.45755i | −0.888611 | − | 0.458661i | \(-0.848329\pi\) |
0.0470938 | − | 0.998890i | \(-0.485004\pi\) | |||||||
\(930\) | 9.95824 | + | 1.34073i | 0.326543 | + | 0.0439642i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.09792 | − | 2.09792i | −0.0687197 | − | 0.0687197i | ||||
\(933\) | 20.7264 | + | 28.6900i | 0.678550 | + | 0.939268i | ||||
\(934\) | −4.81265 | − | 2.77858i | −0.157475 | − | 0.0909181i | ||||
\(935\) | 19.0032 | − | 20.0159i | 0.621469 | − | 0.654591i | ||||
\(936\) | 11.1905 | + | 12.5641i | 0.365774 | + | 0.410672i | ||||
\(937\) | 16.4279 | − | 16.4279i | 0.536675 | − | 0.536675i | −0.385876 | − | 0.922551i | \(-0.626101\pi\) |
0.922551 | + | 0.385876i | \(0.126101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.4933 | − | 31.3083i | 0.831942 | − | 1.02171i | ||||
\(940\) | −12.0933 | − | 40.8608i | −0.394440 | − | 1.33273i | ||||
\(941\) | 49.6120 | + | 28.6435i | 1.61731 | + | 0.933752i | 0.987613 | + | 0.156906i | \(0.0501521\pi\) |
0.629692 | + | 0.776845i | \(0.283181\pi\) | |||||||
\(942\) | −6.94255 | − | 3.11352i | −0.226201 | − | 0.101444i | ||||
\(943\) | 10.7976 | − | 40.2970i | 0.351617 | − | 1.31225i | ||||
\(944\) | 0.416557 | 0.0135578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.40755 | 0.0457634 | ||||||||
\(947\) | −13.1147 | + | 48.9447i | −0.426170 | + | 1.59049i | 0.335183 | + | 0.942153i | \(0.391202\pi\) |
−0.761354 | + | 0.648337i | \(0.775465\pi\) | |||||||
\(948\) | 10.8343 | + | 4.85884i | 0.351881 | + | 0.157808i | ||||
\(949\) | −15.5055 | − | 8.95213i | −0.503331 | − | 0.290599i | ||||
\(950\) | 8.61426 | − | 9.55826i | 0.279483 | − | 0.310111i | ||||
\(951\) | 35.5017 | − | 43.5997i | 1.15122 | − | 1.41382i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.4764 | − | 35.4764i | 1.14919 | − | 1.14919i | 0.162481 | − | 0.986712i | \(-0.448050\pi\) |
0.986712 | − | 0.162481i | \(-0.0519496\pi\) | |||||||
\(954\) | −6.14339 | − | 6.89749i | −0.198900 | − | 0.223315i | ||||
\(955\) | 0.0324632 | + | 1.25071i | 0.00105048 | + | 0.0404721i | ||||
\(956\) | 7.85062 | + | 4.53256i | 0.253907 | + | 0.146593i | ||||
\(957\) | −7.77429 | − | 10.7614i | −0.251307 | − | 0.347866i | ||||
\(958\) | 6.98270 | + | 6.98270i | 0.225601 | + | 0.225601i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.54091 | − | 8.57620i | −0.211107 | − | 0.276796i | ||||
\(961\) | 1.52917 | + | 2.64859i | 0.0493279 | + | 0.0854385i | ||||
\(962\) | 4.36722 | − | 1.17019i | 0.140805 | − | 0.0377286i | ||||
\(963\) | 2.69281 | − | 1.35378i | 0.0867745 | − | 0.0436251i | ||||
\(964\) | 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 | \(0.408771\pi\) | |||||||
\(968\) | −6.88580 | − | 1.84504i | −0.221318 | − | 0.0593020i | ||||
\(969\) | 39.2152 | − | 14.9319i | 1.25977 | − | 0.479682i | ||||
\(970\) | 2.89950 | − | 0.0752587i | 0.0930973 | − | 0.00241641i | ||||
\(971\) | 20.3136 | − | 11.7280i | 0.651894 | − | 0.376371i | −0.137288 | − | 0.990531i | \(-0.543838\pi\) |
0.789181 | + | 0.614160i | \(0.210505\pi\) | |||||||
\(972\) | 23.9309 | − | 13.3890i | 0.767585 | − | 0.429451i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.39987 | 0.173023 | ||||||||
\(975\) | −15.5408 | + | 21.2485i | −0.497704 | + | 0.680498i | ||||
\(976\) | 6.17289 | − | 10.6918i | 0.197589 | − | 0.342235i | ||||
\(977\) | 12.3410 | − | 3.30675i | 0.394823 | − | 0.105792i | −0.0559446 | − | 0.998434i | \(-0.517817\pi\) |
0.450767 | + | 0.892641i | \(0.351150\pi\) | |||||||
\(978\) | −4.54544 | − | 6.29193i | −0.145347 | − | 0.201194i | ||||
\(979\) | 10.5552i | 0.337347i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5584 | + | 55.8598i | 0.369031 | + | 1.78347i | ||||
\(982\) | 1.08824 | + | 0.291593i | 0.0347271 | + | 0.00930511i | ||||
\(983\) | 1.14703 | + | 4.28077i | 0.0365846 | + | 0.136535i | 0.981803 | − | 0.189904i | \(-0.0608177\pi\) |
−0.945218 | + | 0.326440i | \(0.894151\pi\) | |||||||
\(984\) | −13.1646 | − | 34.5737i | −0.419672 | − | 1.10217i | ||||
\(985\) | −30.7788 | + | 9.10940i | −0.980695 | + | 0.290250i | ||||
\(986\) | − | 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 | ||||
\(990\) | 4.63770 | − | 7.47324i | 0.147396 | − | 0.237515i | ||||
\(991\) | 14.6141 | − | 25.3124i | 0.464233 | − | 0.804076i | −0.534933 | − | 0.844894i | \(-0.679663\pi\) |
0.999167 | + | 0.0408185i | \(0.0129965\pi\) | |||||||
\(992\) | 6.80270 | − | 25.3880i | 0.215986 | − | 0.806071i | ||||
\(993\) | −0.390649 | − | 3.81588i | −0.0123969 | − | 0.121093i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.2618 | − | 13.6350i | 0.705748 | − | 0.432260i | ||||
\(996\) | 17.1769 | + | 2.76812i | 0.544270 | + | 0.0877113i | ||||
\(997\) | −1.67460 | − | 6.24970i | −0.0530352 | − | 0.197930i | 0.934325 | − | 0.356422i | \(-0.116003\pi\) |
−0.987360 | + | 0.158492i | \(0.949337\pi\) | |||||||
\(998\) | −1.56583 | − | 5.84376i | −0.0495655 | − | 0.184981i | ||||
\(999\) | −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.j.263.8 | 48 | ||
3.2 | odd | 2 | inner | 735.2.y.j.263.5 | 48 | ||
5.2 | odd | 4 | inner | 735.2.y.j.557.8 | 48 | ||
7.2 | even | 3 | inner | 735.2.y.j.128.5 | 48 | ||
7.3 | odd | 6 | 735.2.j.h.638.8 | 24 | |||
7.4 | even | 3 | 105.2.j.a.8.8 | yes | 24 | ||
7.5 | odd | 6 | 735.2.y.g.128.5 | 48 | |||
7.6 | odd | 2 | 735.2.y.g.263.8 | 48 | |||
15.2 | even | 4 | inner | 735.2.y.j.557.5 | 48 | ||
21.2 | odd | 6 | inner | 735.2.y.j.128.8 | 48 | ||
21.5 | even | 6 | 735.2.y.g.128.8 | 48 | |||
21.11 | odd | 6 | 105.2.j.a.8.5 | ✓ | 24 | ||
21.17 | even | 6 | 735.2.j.h.638.5 | 24 | |||
21.20 | even | 2 | 735.2.y.g.263.5 | 48 | |||
35.2 | odd | 12 | inner | 735.2.y.j.422.5 | 48 | ||
35.4 | even | 6 | 525.2.j.b.218.5 | 24 | |||
35.12 | even | 12 | 735.2.y.g.422.5 | 48 | |||
35.17 | even | 12 | 735.2.j.h.197.5 | 24 | |||
35.18 | odd | 12 | 525.2.j.b.407.8 | 24 | |||
35.27 | even | 4 | 735.2.y.g.557.8 | 48 | |||
35.32 | odd | 12 | 105.2.j.a.92.5 | yes | 24 | ||
105.2 | even | 12 | inner | 735.2.y.j.422.8 | 48 | ||
105.17 | odd | 12 | 735.2.j.h.197.8 | 24 | |||
105.32 | even | 12 | 105.2.j.a.92.8 | yes | 24 | ||
105.47 | odd | 12 | 735.2.y.g.422.8 | 48 | |||
105.53 | even | 12 | 525.2.j.b.407.5 | 24 | |||
105.62 | odd | 4 | 735.2.y.g.557.5 | 48 | |||
105.74 | odd | 6 | 525.2.j.b.218.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.5 | ✓ | 24 | 21.11 | odd | 6 | ||
105.2.j.a.8.8 | yes | 24 | 7.4 | even | 3 | ||
105.2.j.a.92.5 | yes | 24 | 35.32 | odd | 12 | ||
105.2.j.a.92.8 | yes | 24 | 105.32 | even | 12 | ||
525.2.j.b.218.5 | 24 | 35.4 | even | 6 | |||
525.2.j.b.218.8 | 24 | 105.74 | odd | 6 | |||
525.2.j.b.407.5 | 24 | 105.53 | even | 12 | |||
525.2.j.b.407.8 | 24 | 35.18 | odd | 12 | |||
735.2.j.h.197.5 | 24 | 35.17 | even | 12 | |||
735.2.j.h.197.8 | 24 | 105.17 | odd | 12 | |||
735.2.j.h.638.5 | 24 | 21.17 | even | 6 | |||
735.2.j.h.638.8 | 24 | 7.3 | odd | 6 | |||
735.2.y.g.128.5 | 48 | 7.5 | odd | 6 | |||
735.2.y.g.128.8 | 48 | 21.5 | even | 6 | |||
735.2.y.g.263.5 | 48 | 21.20 | even | 2 | |||
735.2.y.g.263.8 | 48 | 7.6 | odd | 2 | |||
735.2.y.g.422.5 | 48 | 35.12 | even | 12 | |||
735.2.y.g.422.8 | 48 | 105.47 | odd | 12 | |||
735.2.y.g.557.5 | 48 | 105.62 | odd | 4 | |||
735.2.y.g.557.8 | 48 | 35.27 | even | 4 | |||
735.2.y.j.128.5 | 48 | 7.2 | even | 3 | inner | ||
735.2.y.j.128.8 | 48 | 21.2 | odd | 6 | inner | ||
735.2.y.j.263.5 | 48 | 3.2 | odd | 2 | inner | ||
735.2.y.j.263.8 | 48 | 1.1 | even | 1 | trivial | ||
735.2.y.j.422.5 | 48 | 35.2 | odd | 12 | inner | ||
735.2.y.j.422.8 | 48 | 105.2 | even | 12 | inner | ||
735.2.y.j.557.5 | 48 | 15.2 | even | 4 | inner | ||
735.2.y.j.557.8 | 48 | 5.2 | odd | 4 | inner |