Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [357,2,Mod(16,357)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(357, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("357.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 357 = 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 357.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.85065935216\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 16.3 | ||
Character | \(\chi\) | \(=\) | 357.16 |
Dual form | 357.2.p.a.67.3 |
$q$-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 \(\left(\mathbb{Z}/357\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(190\) | \(239\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11091 | + | 1.92416i | −0.785534 | + | 1.36058i | 0.143145 | + | 0.989702i | \(0.454278\pi\) |
−0.928679 | + | 0.370883i | \(0.879055\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −1.46826 | − | 2.54309i | −0.734128 | − | 1.27155i | ||||
\(5\) | 0.551608 | + | 0.318471i | 0.246687 | + | 0.142425i | 0.618246 | − | 0.785985i | \(-0.287843\pi\) |
−0.371560 | + | 0.928409i | \(0.621177\pi\) | |||||||
\(6\) | − | 2.22183i | − | 0.907057i | ||||||
\(7\) | 1.27391 | + | 2.31887i | 0.481494 | + | 0.876449i | ||||
\(8\) | 2.08076 | 0.735661 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.22558 | + | 0.707587i | −0.387561 | + | 0.223759i | ||||
\(11\) | −3.85464 | + | 2.22548i | −1.16222 | + | 0.671007i | −0.951835 | − | 0.306612i | \(-0.900805\pi\) |
−0.210384 | + | 0.977619i | \(0.567471\pi\) | |||||||
\(12\) | 2.54309 | + | 1.46826i | 0.734128 | + | 0.423849i | ||||
\(13\) | −4.96153 | −1.37608 | −0.688040 | − | 0.725673i | \(-0.741529\pi\) | ||||
−0.688040 | + | 0.725673i | \(0.741529\pi\) | |||||||
\(14\) | −5.87707 | − | 0.124849i | −1.57071 | − | 0.0333673i | ||||
\(15\) | −0.636942 | −0.164458 | ||||||||
\(16\) | 0.624963 | − | 1.08247i | 0.156241 | − | 0.270617i | ||||
\(17\) | −1.55173 | + | 3.81997i | −0.376349 | + | 0.926478i | ||||
\(18\) | 1.11091 | + | 1.92416i | 0.261845 | + | 0.453528i | ||||
\(19\) | 2.85195 | − | 4.93972i | 0.654282 | − | 1.13325i | −0.327791 | − | 0.944750i | \(-0.606304\pi\) |
0.982073 | − | 0.188500i | \(-0.0603624\pi\) | |||||||
\(20\) | − | 1.87039i | − | 0.418231i | ||||||
\(21\) | −2.26267 | − | 1.37124i | −0.493756 | − | 0.299229i | ||||
\(22\) | − | 9.88925i | − | 2.10840i | ||||||
\(23\) | −1.06733 | − | 0.616221i | −0.222553 | − | 0.128491i | 0.384579 | − | 0.923092i | \(-0.374347\pi\) |
−0.607132 | + | 0.794601i | \(0.707680\pi\) | |||||||
\(24\) | −1.80199 | + | 1.04038i | −0.367830 | + | 0.212367i | ||||
\(25\) | −2.29715 | − | 3.97878i | −0.459430 | − | 0.795757i | ||||
\(26\) | 5.51183 | − | 9.54676i | 1.08096 | − | 1.87227i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 4.02666 | − | 6.64437i | 0.760968 | − | 1.25567i | ||||
\(29\) | 3.35828i | 0.623618i | 0.950145 | + | 0.311809i | \(0.100935\pi\) | ||||
−0.950145 | + | 0.311809i | \(0.899065\pi\) | |||||||
\(30\) | 0.707587 | − | 1.22558i | 0.129187 | − | 0.223759i | ||||
\(31\) | −3.14993 | + | 1.81861i | −0.565745 | + | 0.326633i | −0.755448 | − | 0.655209i | \(-0.772581\pi\) |
0.189703 | + | 0.981841i | \(0.439247\pi\) | |||||||
\(32\) | 3.46932 | + | 6.00904i | 0.613296 | + | 1.06226i | ||||
\(33\) | 2.22548 | − | 3.85464i | 0.387406 | − | 0.671007i | ||||
\(34\) | −5.62638 | − | 7.22942i | −0.964917 | − | 1.23983i | ||||
\(35\) | −0.0357911 | + | 1.68481i | −0.00604980 | + | 0.284785i | ||||
\(36\) | −2.93651 | −0.489418 | ||||||||
\(37\) | 2.86890 | + | 1.65636i | 0.471644 | + | 0.272304i | 0.716928 | − | 0.697147i | \(-0.245548\pi\) |
−0.245283 | + | 0.969451i | \(0.578881\pi\) | |||||||
\(38\) | 6.33653 | + | 10.9752i | 1.02792 | + | 1.78041i | ||||
\(39\) | 4.29681 | − | 2.48076i | 0.688040 | − | 0.397240i | ||||
\(40\) | 1.14777 | + | 0.662663i | 0.181478 | + | 0.104776i | ||||
\(41\) | − | 8.40547i | − | 1.31271i | −0.754450 | − | 0.656357i | \(-0.772097\pi\) | ||
0.754450 | − | 0.656357i | \(-0.227903\pi\) | |||||||
\(42\) | 5.15212 | − | 2.83041i | 0.794989 | − | 0.436742i | ||||
\(43\) | 2.95338 | 0.450386 | 0.225193 | − | 0.974314i | \(-0.427699\pi\) | ||||
0.225193 | + | 0.974314i | \(0.427699\pi\) | |||||||
\(44\) | 11.3192 | + | 6.53514i | 1.70643 | + | 0.985210i | ||||
\(45\) | 0.551608 | − | 0.318471i | 0.0822289 | − | 0.0474749i | ||||
\(46\) | 2.37141 | − | 1.36914i | 0.349646 | − | 0.201868i | ||||
\(47\) | −5.19336 | + | 8.99516i | −0.757529 | + | 1.31208i | 0.186578 | + | 0.982440i | \(0.440260\pi\) |
−0.944107 | + | 0.329639i | \(0.893073\pi\) | |||||||
\(48\) | 1.24993i | 0.180411i | ||||||||
\(49\) | −3.75429 | + | 5.90807i | −0.536327 | + | 0.844010i | ||||
\(50\) | 10.2077 | 1.44359 | ||||||||
\(51\) | −0.566148 | − | 4.08405i | −0.0792766 | − | 0.571882i | ||||
\(52\) | 7.28479 | + | 12.6176i | 1.01022 | + | 1.74975i | ||||
\(53\) | −6.14162 | − | 10.6376i | −0.843616 | − | 1.46119i | −0.886818 | − | 0.462119i | \(-0.847089\pi\) |
0.0432018 | − | 0.999066i | \(-0.486244\pi\) | |||||||
\(54\) | −1.92416 | − | 1.11091i | −0.261845 | − | 0.151176i | ||||
\(55\) | −2.83500 | −0.382272 | ||||||||
\(56\) | 2.65071 | + | 4.82501i | 0.354216 | + | 0.644770i | ||||
\(57\) | 5.70390i | 0.755500i | ||||||||
\(58\) | −6.46187 | − | 3.73076i | −0.848485 | − | 0.489873i | ||||
\(59\) | −0.809436 | − | 1.40198i | −0.105380 | − | 0.182523i | 0.808514 | − | 0.588477i | \(-0.200272\pi\) |
−0.913893 | + | 0.405955i | \(0.866939\pi\) | |||||||
\(60\) | 0.935194 | + | 1.61980i | 0.120733 | + | 0.209116i | ||||
\(61\) | −6.67049 | − | 3.85121i | −0.854069 | − | 0.493097i | 0.00795289 | − | 0.999968i | \(-0.497468\pi\) |
−0.862022 | + | 0.506872i | \(0.830802\pi\) | |||||||
\(62\) | − | 8.08129i | − | 1.02632i | ||||||
\(63\) | 2.64515 | + | 0.0561921i | 0.333258 | + | 0.00707954i | ||||
\(64\) | −12.9166 | −1.61458 | ||||||||
\(65\) | −2.73682 | − | 1.58010i | −0.339461 | − | 0.195988i | ||||
\(66\) | 4.94463 | + | 8.56434i | 0.608641 | + | 1.05420i | ||||
\(67\) | 4.43382 | + | 7.67960i | 0.541677 | + | 0.938213i | 0.998808 | + | 0.0488132i | \(0.0155439\pi\) |
−0.457130 | + | 0.889400i | \(0.651123\pi\) | |||||||
\(68\) | 11.9929 | − | 1.66250i | 1.45435 | − | 0.201608i | ||||
\(69\) | 1.23244 | 0.148369 | ||||||||
\(70\) | −3.20208 | − | 1.94055i | −0.382722 | − | 0.231940i | ||||
\(71\) | 9.35212i | 1.10989i | 0.831886 | + | 0.554946i | \(0.187261\pi\) | ||||
−0.831886 | + | 0.554946i | \(0.812739\pi\) | |||||||
\(72\) | 1.04038 | − | 1.80199i | 0.122610 | − | 0.212367i | ||||
\(73\) | −7.34831 | + | 4.24255i | −0.860055 | + | 0.496553i | −0.864031 | − | 0.503439i | \(-0.832068\pi\) |
0.00397574 | + | 0.999992i | \(0.498734\pi\) | |||||||
\(74\) | −6.37420 | + | 3.68015i | −0.740986 | + | 0.427808i | ||||
\(75\) | 3.97878 | + | 2.29715i | 0.459430 | + | 0.265252i | ||||
\(76\) | −16.7496 | −1.92131 | ||||||||
\(77\) | −10.0711 | − | 6.10333i | −1.14770 | − | 0.695540i | ||||
\(78\) | 11.0237i | 1.24818i | ||||||||
\(79\) | 12.5774 | + | 7.26158i | 1.41507 | + | 0.816992i | 0.995860 | − | 0.0908965i | \(-0.0289733\pi\) |
0.419211 | + | 0.907889i | \(0.362307\pi\) | |||||||
\(80\) | 0.689470 | − | 0.398066i | 0.0770851 | − | 0.0445051i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 16.1735 | + | 9.33775i | 1.78606 | + | 1.03118i | ||||
\(83\) | 1.17614 | 0.129098 | 0.0645491 | − | 0.997915i | \(-0.479439\pi\) | ||||
0.0645491 | + | 0.997915i | \(0.479439\pi\) | |||||||
\(84\) | −0.165009 | + | 7.76752i | −0.0180039 | + | 0.847506i | ||||
\(85\) | −2.07249 | + | 1.61294i | −0.224794 | + | 0.174948i | ||||
\(86\) | −3.28095 | + | 5.68276i | −0.353793 | + | 0.612788i | ||||
\(87\) | −1.67914 | − | 2.90836i | −0.180023 | − | 0.311809i | ||||
\(88\) | −8.02060 | + | 4.63069i | −0.854999 | + | 0.493634i | ||||
\(89\) | −1.92963 | + | 3.34222i | −0.204541 | + | 0.354275i | −0.949986 | − | 0.312292i | \(-0.898903\pi\) |
0.745446 | + | 0.666566i | \(0.232237\pi\) | |||||||
\(90\) | 1.41517i | 0.149172i | ||||||||
\(91\) | −6.32056 | − | 11.5051i | −0.662575 | − | 1.20606i | ||||
\(92\) | 3.61908i | 0.377315i | ||||||||
\(93\) | 1.81861 | − | 3.14993i | 0.188582 | − | 0.326633i | ||||
\(94\) | −11.5387 | − | 19.9857i | −1.19013 | − | 2.06137i | ||||
\(95\) | 3.14632 | − | 1.81653i | 0.322805 | − | 0.186372i | ||||
\(96\) | −6.00904 | − | 3.46932i | −0.613296 | − | 0.354086i | ||||
\(97\) | 12.9435i | 1.31421i | 0.753800 | + | 0.657104i | \(0.228219\pi\) | ||||
−0.753800 | + | 0.657104i | \(0.771781\pi\) | |||||||
\(98\) | −7.19737 | − | 13.7872i | −0.727045 | − | 1.39272i | ||||
\(99\) | 4.45096i | 0.447338i | ||||||||
\(100\) | −6.74561 | + | 11.6837i | −0.674561 | + | 1.16837i | ||||
\(101\) | 2.72077 | + | 4.71251i | 0.270727 | + | 0.468912i | 0.969048 | − | 0.246872i | \(-0.0794027\pi\) |
−0.698321 | + | 0.715784i | \(0.746069\pi\) | |||||||
\(102\) | 8.48730 | + | 3.44767i | 0.840368 | + | 0.341370i | ||||
\(103\) | −5.70540 | + | 9.88205i | −0.562170 | + | 0.973707i | 0.435137 | + | 0.900364i | \(0.356700\pi\) |
−0.997307 | + | 0.0733429i | \(0.976633\pi\) | |||||||
\(104\) | −10.3238 | −1.01233 | ||||||||
\(105\) | −0.811409 | − | 1.47698i | −0.0791854 | − | 0.144139i | ||||
\(106\) | 27.2912 | 2.65076 | ||||||||
\(107\) | 10.4912 | + | 6.05708i | 1.01422 | + | 0.585560i | 0.912424 | − | 0.409245i | \(-0.134208\pi\) |
0.101795 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(108\) | 2.54309 | − | 1.46826i | 0.244709 | − | 0.141283i | ||||
\(109\) | −10.1103 | + | 5.83720i | −0.968394 | + | 0.559103i | −0.898746 | − | 0.438469i | \(-0.855521\pi\) |
−0.0696480 | + | 0.997572i | \(0.522188\pi\) | |||||||
\(110\) | 3.14944 | − | 5.45499i | 0.300287 | − | 0.520113i | ||||
\(111\) | −3.31272 | −0.314430 | ||||||||
\(112\) | 3.30625 | + | 0.0702360i | 0.312411 | + | 0.00663668i | ||||
\(113\) | 4.19208i | 0.394358i | 0.980367 | + | 0.197179i | \(0.0631780\pi\) | ||||
−0.980367 | + | 0.197179i | \(0.936822\pi\) | |||||||
\(114\) | −10.9752 | − | 6.33653i | −1.02792 | − | 0.593471i | ||||
\(115\) | −0.392497 | − | 0.679825i | −0.0366006 | − | 0.0633940i | ||||
\(116\) | 8.54043 | − | 4.93082i | 0.792959 | − | 0.457815i | ||||
\(117\) | −2.48076 | + | 4.29681i | −0.229347 | + | 0.397240i | ||||
\(118\) | 3.59685 | 0.331117 | ||||||||
\(119\) | −10.8348 | + | 1.26806i | −0.993221 | + | 0.116243i | ||||
\(120\) | −1.32533 | −0.120985 | ||||||||
\(121\) | 4.40551 | − | 7.63056i | 0.400501 | − | 0.693688i | ||||
\(122\) | 14.8207 | − | 8.55672i | 1.34180 | − | 0.774689i | ||||
\(123\) | 4.20274 | + | 7.27935i | 0.378948 | + | 0.656357i | ||||
\(124\) | 9.24981 | + | 5.34038i | 0.830658 | + | 0.479580i | ||||
\(125\) | − | 6.11102i | − | 0.546586i | ||||||
\(126\) | −3.04666 | + | 5.02727i | −0.271418 | + | 0.447865i | ||||
\(127\) | 17.6363 | 1.56497 | 0.782485 | − | 0.622669i | \(-0.213952\pi\) | ||||
0.782485 | + | 0.622669i | \(0.213952\pi\) | |||||||
\(128\) | 7.41058 | − | 12.8355i | 0.655009 | − | 1.13451i | ||||
\(129\) | −2.55770 | + | 1.47669i | −0.225193 | + | 0.130015i | ||||
\(130\) | 6.08074 | − | 3.51071i | 0.533316 | − | 0.307910i | ||||
\(131\) | −10.7894 | − | 6.22924i | −0.942671 | − | 0.544251i | −0.0518742 | − | 0.998654i | \(-0.516519\pi\) |
−0.890797 | + | 0.454402i | \(0.849853\pi\) | |||||||
\(132\) | −13.0703 | −1.13762 | ||||||||
\(133\) | 15.0877 | + | 0.320514i | 1.30827 | + | 0.0277921i | ||||
\(134\) | −19.7024 | −1.70202 | ||||||||
\(135\) | −0.318471 | + | 0.551608i | −0.0274096 | + | 0.0474749i | ||||
\(136\) | −3.22878 | + | 7.94845i | −0.276865 | + | 0.681574i | ||||
\(137\) | 9.11657 | + | 15.7904i | 0.778882 | + | 1.34906i | 0.932587 | + | 0.360946i | \(0.117546\pi\) |
−0.153705 | + | 0.988117i | \(0.549121\pi\) | |||||||
\(138\) | −1.36914 | + | 2.37141i | −0.116549 | + | 0.201868i | ||||
\(139\) | − | 11.7920i | − | 1.00019i | −0.865971 | − | 0.500094i | \(-0.833299\pi\) | ||
0.865971 | − | 0.500094i | \(-0.166701\pi\) | |||||||
\(140\) | 4.33718 | − | 2.38271i | 0.366559 | − | 0.201376i | ||||
\(141\) | − | 10.3867i | − | 0.874720i | ||||||
\(142\) | −17.9950 | − | 10.3894i | −1.51010 | − | 0.871858i | ||||
\(143\) | 19.1249 | − | 11.0418i | 1.59931 | − | 0.923360i | ||||
\(144\) | −0.624963 | − | 1.08247i | −0.0520803 | − | 0.0902057i | ||||
\(145\) | −1.06952 | + | 1.85246i | −0.0888185 | + | 0.153838i | ||||
\(146\) | − | 18.8524i | − | 1.56024i | ||||||
\(147\) | 0.297274 | − | 6.99368i | 0.0245187 | − | 0.576829i | ||||
\(148\) | − | 9.72784i | − | 0.799624i | ||||||
\(149\) | −5.60174 | + | 9.70250i | −0.458912 | + | 0.794860i | −0.998904 | − | 0.0468109i | \(-0.985094\pi\) |
0.539991 | + | 0.841671i | \(0.318428\pi\) | |||||||
\(150\) | −8.84017 | + | 5.10387i | −0.721797 | + | 0.416729i | ||||
\(151\) | 6.82085 | + | 11.8141i | 0.555073 | + | 0.961414i | 0.997898 | + | 0.0648064i | \(0.0206430\pi\) |
−0.442825 | + | 0.896608i | \(0.646024\pi\) | |||||||
\(152\) | 5.93423 | − | 10.2784i | 0.481330 | − | 0.833688i | ||||
\(153\) | 2.53232 | + | 3.25382i | 0.204726 | + | 0.263056i | ||||
\(154\) | 22.9319 | − | 12.5981i | 1.84790 | − | 1.01518i | ||||
\(155\) | −2.31670 | −0.186082 | ||||||||
\(156\) | −12.6176 | − | 7.28479i | −1.01022 | − | 0.583250i | ||||
\(157\) | −0.168499 | − | 0.291848i | −0.0134476 | − | 0.0232920i | 0.859223 | − | 0.511601i | \(-0.170947\pi\) |
−0.872671 | + | 0.488309i | \(0.837614\pi\) | |||||||
\(158\) | −27.9449 | + | 16.1340i | −2.22317 | + | 1.28355i | ||||
\(159\) | 10.6376 | + | 6.14162i | 0.843616 | + | 0.487062i | ||||
\(160\) | 4.41952i | 0.349393i | ||||||||
\(161\) | 0.0692535 | − | 3.26000i | 0.00545794 | − | 0.256924i | ||||
\(162\) | 2.22183 | 0.174563 | ||||||||
\(163\) | 4.52040 | + | 2.60985i | 0.354065 | + | 0.204420i | 0.666474 | − | 0.745528i | \(-0.267803\pi\) |
−0.312409 | + | 0.949948i | \(0.601136\pi\) | |||||||
\(164\) | −21.3759 | + | 12.3414i | −1.66918 | + | 0.963700i | ||||
\(165\) | 2.45518 | − | 1.41750i | 0.191136 | − | 0.110352i | ||||
\(166\) | −1.30659 | + | 2.26308i | −0.101411 | + | 0.175649i | ||||
\(167\) | − | 19.6234i | − | 1.51850i | −0.650797 | − | 0.759252i | \(-0.725565\pi\) | ||
0.650797 | − | 0.759252i | \(-0.274435\pi\) | |||||||
\(168\) | −4.70809 | − | 2.85323i | −0.363237 | − | 0.220131i | ||||
\(169\) | 11.6168 | 0.893597 | ||||||||
\(170\) | −0.801198 | − | 5.77965i | −0.0614491 | − | 0.443279i | ||||
\(171\) | −2.85195 | − | 4.93972i | −0.218094 | − | 0.377750i | ||||
\(172\) | −4.33631 | − | 7.51071i | −0.330641 | − | 0.572687i | ||||
\(173\) | −9.57633 | − | 5.52890i | −0.728075 | − | 0.420354i | 0.0896424 | − | 0.995974i | \(-0.471428\pi\) |
−0.817718 | + | 0.575620i | \(0.804761\pi\) | |||||||
\(174\) | 7.46152 | 0.565657 | ||||||||
\(175\) | 6.29990 | − | 10.3954i | 0.476228 | − | 0.785820i | ||||
\(176\) | 5.56337i | 0.419355i | ||||||||
\(177\) | 1.40198 | + | 0.809436i | 0.105380 | + | 0.0608409i | ||||
\(178\) | −4.28731 | − | 7.42584i | −0.321347 | − | 0.556590i | ||||
\(179\) | 2.93488 | + | 5.08337i | 0.219364 | + | 0.379949i | 0.954614 | − | 0.297847i | \(-0.0962686\pi\) |
−0.735250 | + | 0.677796i | \(0.762935\pi\) | |||||||
\(180\) | −1.61980 | − | 0.935194i | −0.120733 | − | 0.0697052i | ||||
\(181\) | 11.6689i | 0.867343i | 0.901071 | + | 0.433672i | \(0.142782\pi\) | ||||
−0.901071 | + | 0.433672i | \(0.857218\pi\) | |||||||
\(182\) | 29.1593 | + | 0.619442i | 2.16143 | + | 0.0459161i | ||||
\(183\) | 7.70242 | 0.569379 | ||||||||
\(184\) | −2.22085 | − | 1.28221i | −0.163724 | − | 0.0945258i | ||||
\(185\) | 1.05501 | + | 1.82732i | 0.0775656 | + | 0.134348i | ||||
\(186\) | 4.04065 | + | 6.99860i | 0.296274 | + | 0.513162i | ||||
\(187\) | −2.51990 | − | 18.1779i | −0.184273 | − | 1.32930i | ||||
\(188\) | 30.5007 | 2.22449 | ||||||||
\(189\) | −2.31887 | + | 1.27391i | −0.168673 | + | 0.0926636i | ||||
\(190\) | 8.07201i | 0.585605i | ||||||||
\(191\) | 7.88271 | − | 13.6533i | 0.570373 | − | 0.987915i | −0.426154 | − | 0.904651i | \(-0.640132\pi\) |
0.996527 | − | 0.0832649i | \(-0.0265348\pi\) | |||||||
\(192\) | 11.1861 | − | 6.45831i | 0.807288 | − | 0.466088i | ||||
\(193\) | −1.58028 | + | 0.912377i | −0.113751 | + | 0.0656743i | −0.555796 | − | 0.831319i | \(-0.687587\pi\) |
0.442045 | + | 0.896993i | \(0.354253\pi\) | |||||||
\(194\) | −24.9052 | − | 14.3791i | −1.78809 | − | 1.03236i | ||||
\(195\) | 3.16021 | 0.226307 | ||||||||
\(196\) | 20.5370 | + | 0.872947i | 1.46693 | + | 0.0623534i | ||||
\(197\) | − | 17.5404i | − | 1.24970i | −0.780743 | − | 0.624852i | \(-0.785159\pi\) | ||
0.780743 | − | 0.624852i | \(-0.214841\pi\) | |||||||
\(198\) | −8.56434 | − | 4.94463i | −0.608641 | − | 0.351399i | ||||
\(199\) | −10.5663 | + | 6.10043i | −0.749022 | + | 0.432448i | −0.825340 | − | 0.564636i | \(-0.809017\pi\) |
0.0763186 | + | 0.997083i | \(0.475683\pi\) | |||||||
\(200\) | −4.77983 | − | 8.27891i | −0.337985 | − | 0.585407i | ||||
\(201\) | −7.67960 | − | 4.43382i | −0.541677 | − | 0.312738i | ||||
\(202\) | −12.0902 | −0.850660 | ||||||||
\(203\) | −7.78741 | + | 4.27816i | −0.546569 | + | 0.300268i | ||||
\(204\) | −9.55487 | + | 7.43620i | −0.668975 | + | 0.520638i | ||||
\(205\) | 2.67690 | − | 4.63653i | 0.186963 | − | 0.323829i | ||||
\(206\) | −12.6764 | − | 21.9562i | −0.883208 | − | 1.52976i | ||||
\(207\) | −1.06733 | + | 0.616221i | −0.0741843 | + | 0.0428303i | ||||
\(208\) | −3.10077 | + | 5.37070i | −0.215000 | + | 0.372391i | ||||
\(209\) | 25.3878i | 1.75611i | ||||||||
\(210\) | 3.74336 | + | 0.0795216i | 0.258316 | + | 0.00548751i | ||||
\(211\) | 3.74811i | 0.258030i | 0.991643 | + | 0.129015i | \(0.0411816\pi\) | ||||
−0.991643 | + | 0.129015i | \(0.958818\pi\) | |||||||
\(212\) | −18.0349 | + | 31.2374i | −1.23864 | + | 2.14539i | ||||
\(213\) | −4.67606 | − | 8.09917i | −0.320398 | − | 0.554946i | ||||
\(214\) | −23.3096 | + | 13.4578i | −1.59341 | + | 0.919955i | ||||
\(215\) | 1.62911 | + | 0.940565i | 0.111104 | + | 0.0641460i | ||||
\(216\) | 2.08076i | 0.141578i | ||||||||
\(217\) | −8.22987 | − | 4.98752i | −0.558680 | − | 0.338575i | ||||
\(218\) | − | 25.9385i | − | 1.75678i | ||||||
\(219\) | 4.24255 | − | 7.34831i | 0.286685 | − | 0.496553i | ||||
\(220\) | 4.16251 | + | 7.20967i | 0.280636 | + | 0.486076i | ||||
\(221\) | 7.69894 | − | 18.9529i | 0.517887 | − | 1.27491i | ||||
\(222\) | 3.68015 | − | 6.37420i | 0.246995 | − | 0.427808i | ||||
\(223\) | −10.9773 | −0.735097 | −0.367548 | − | 0.930004i | \(-0.619803\pi\) | ||||
−0.367548 | + | 0.930004i | \(0.619803\pi\) | |||||||
\(224\) | −9.51456 | + | 15.6999i | −0.635718 | + | 1.04899i | ||||
\(225\) | −4.59430 | −0.306287 | ||||||||
\(226\) | −8.06623 | − | 4.65704i | −0.536558 | − | 0.309782i | ||||
\(227\) | 9.40856 | − | 5.43203i | 0.624468 | − | 0.360537i | −0.154139 | − | 0.988049i | \(-0.549260\pi\) |
0.778606 | + | 0.627513i | \(0.215927\pi\) | |||||||
\(228\) | 14.5055 | − | 8.37478i | 0.960653 | − | 0.554633i | ||||
\(229\) | 4.77603 | − | 8.27234i | 0.315609 | − | 0.546651i | −0.663958 | − | 0.747770i | \(-0.731124\pi\) |
0.979567 | + | 0.201119i | \(0.0644578\pi\) | |||||||
\(230\) | 1.74412 | 0.115004 | ||||||||
\(231\) | 11.7735 | + | 0.250109i | 0.774637 | + | 0.0164559i | ||||
\(232\) | 6.98779i | 0.458771i | ||||||||
\(233\) | −8.22414 | − | 4.74821i | −0.538782 | − | 0.311066i | 0.205803 | − | 0.978593i | \(-0.434019\pi\) |
−0.744585 | + | 0.667528i | \(0.767353\pi\) | |||||||
\(234\) | −5.51183 | − | 9.54676i | −0.360319 | − | 0.624091i | ||||
\(235\) | −5.72940 | + | 3.30787i | −0.373745 | + | 0.215782i | ||||
\(236\) | −2.37692 | + | 4.11694i | −0.154724 | + | 0.267990i | ||||
\(237\) | −14.5232 | −0.943381 | ||||||||
\(238\) | 9.59653 | − | 22.2565i | 0.622051 | − | 1.44267i | ||||
\(239\) | 11.4897 | 0.743209 | 0.371605 | − | 0.928391i | \(-0.378808\pi\) | ||||
0.371605 | + | 0.928391i | \(0.378808\pi\) | |||||||
\(240\) | −0.398066 | + | 0.689470i | −0.0256950 | + | 0.0445051i | ||||
\(241\) | 11.4533 | − | 6.61255i | 0.737771 | − | 0.425952i | −0.0834876 | − | 0.996509i | \(-0.526606\pi\) |
0.821258 | + | 0.570557i | \(0.193273\pi\) | |||||||
\(242\) | 9.78827 | + | 16.9538i | 0.629214 | + | 1.08983i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 22.6182i | 1.44798i | ||||||||
\(245\) | −3.95245 | + | 2.06331i | −0.252512 | + | 0.131820i | ||||
\(246\) | −18.6755 | −1.19071 | ||||||||
\(247\) | −14.1500 | + | 24.5086i | −0.900345 | + | 1.55944i | ||||
\(248\) | −6.55427 | + | 3.78411i | −0.416196 | + | 0.240291i | ||||
\(249\) | −1.01857 | + | 0.588071i | −0.0645491 | + | 0.0372675i | ||||
\(250\) | 11.7586 | + | 6.78881i | 0.743677 | + | 0.429362i | ||||
\(251\) | 1.84848 | 0.116675 | 0.0583376 | − | 0.998297i | \(-0.481420\pi\) | ||||
0.0583376 | + | 0.998297i | \(0.481420\pi\) | |||||||
\(252\) | −3.74086 | − | 6.80938i | −0.235652 | − | 0.428950i | ||||
\(253\) | 5.48555 | 0.344873 | ||||||||
\(254\) | −19.5924 | + | 33.9351i | −1.22934 | + | 2.12927i | ||||
\(255\) | 0.988360 | − | 2.43310i | 0.0618935 | − | 0.152366i | ||||
\(256\) | 3.54842 | + | 6.14604i | 0.221776 | + | 0.384128i | ||||
\(257\) | 3.50196 | − | 6.06558i | 0.218446 | − | 0.378360i | −0.735887 | − | 0.677105i | \(-0.763234\pi\) |
0.954333 | + | 0.298744i | \(0.0965678\pi\) | |||||||
\(258\) | − | 6.56189i | − | 0.408526i | ||||||
\(259\) | −0.186149 | + | 8.76266i | −0.0115667 | + | 0.544485i | ||||
\(260\) | 9.27998i | 0.575520i | ||||||||
\(261\) | 2.90836 | + | 1.67914i | 0.180023 | + | 0.103936i | ||||
\(262\) | 23.9721 | − | 13.8403i | 1.48100 | − | 0.855056i | ||||
\(263\) | 2.41099 | + | 4.17595i | 0.148668 | + | 0.257500i | 0.930735 | − | 0.365694i | \(-0.119168\pi\) |
−0.782068 | + | 0.623194i | \(0.785835\pi\) | |||||||
\(264\) | 4.63069 | − | 8.02060i | 0.285000 | − | 0.493634i | ||||
\(265\) | − | 7.82371i | − | 0.480607i | ||||||
\(266\) | −17.3778 | + | 28.6750i | −1.06550 | + | 1.75818i | ||||
\(267\) | − | 3.85927i | − | 0.236183i | ||||||
\(268\) | 13.0200 | − | 22.5512i | 0.795321 | − | 1.37754i | ||||
\(269\) | −13.9286 | + | 8.04171i | −0.849244 | + | 0.490311i | −0.860396 | − | 0.509626i | \(-0.829784\pi\) |
0.0111515 | + | 0.999938i | \(0.496450\pi\) | |||||||
\(270\) | −0.707587 | − | 1.22558i | −0.0430624 | − | 0.0745862i | ||||
\(271\) | −14.1230 | + | 24.4617i | −0.857909 | + | 1.48594i | 0.0160101 | + | 0.999872i | \(0.494904\pi\) |
−0.873919 | + | 0.486071i | \(0.838430\pi\) | |||||||
\(272\) | 3.16522 | + | 4.06703i | 0.191920 | + | 0.246600i | ||||
\(273\) | 11.2263 | + | 6.80345i | 0.679448 | + | 0.411764i | ||||
\(274\) | −40.5109 | −2.44735 | ||||||||
\(275\) | 17.7094 | + | 10.2245i | 1.06792 | + | 0.616562i | ||||
\(276\) | −1.80954 | − | 3.13422i | −0.108922 | − | 0.188658i | ||||
\(277\) | −9.82327 | + | 5.67146i | −0.590223 | + | 0.340765i | −0.765186 | − | 0.643810i | \(-0.777353\pi\) |
0.174963 | + | 0.984575i | \(0.444019\pi\) | |||||||
\(278\) | 22.6898 | + | 13.0999i | 1.36084 | + | 0.785682i | ||||
\(279\) | 3.63723i | 0.217755i | ||||||||
\(280\) | −0.0744728 | + | 3.50569i | −0.00445060 | + | 0.209505i | ||||
\(281\) | 0.839507 | 0.0500808 | 0.0250404 | − | 0.999686i | \(-0.492029\pi\) | ||||
0.0250404 | + | 0.999686i | \(0.492029\pi\) | |||||||
\(282\) | 19.9857 | + | 11.5387i | 1.19013 | + | 0.687122i | ||||
\(283\) | 16.1532 | − | 9.32607i | 0.960210 | − | 0.554377i | 0.0639721 | − | 0.997952i | \(-0.479623\pi\) |
0.896238 | + | 0.443574i | \(0.146290\pi\) | |||||||
\(284\) | 23.7833 | − | 13.7313i | 1.41128 | − | 0.814803i | ||||
\(285\) | −1.81653 | + | 3.14632i | −0.107602 | + | 0.186372i | ||||
\(286\) | 49.0658i | 2.90132i | ||||||||
\(287\) | 19.4912 | − | 10.7078i | 1.15053 | − | 0.632064i | ||||
\(288\) | 6.93865 | 0.408864 | ||||||||
\(289\) | −12.1843 | − | 11.8551i | −0.716723 | − | 0.697358i | ||||
\(290\) | −2.37628 | − | 4.11584i | −0.139540 | − | 0.241690i | ||||
\(291\) | −6.47173 | − | 11.2094i | −0.379379 | − | 0.657104i | ||||
\(292\) | 21.5784 | + | 12.4583i | 1.26278 | + | 0.729066i | ||||
\(293\) | −2.99309 | −0.174858 | −0.0874292 | − | 0.996171i | \(-0.527865\pi\) | ||||
−0.0874292 | + | 0.996171i | \(0.527865\pi\) | |||||||
\(294\) | 13.1267 | + | 8.34138i | 0.765565 | + | 0.486479i | ||||
\(295\) | − | 1.03113i | − | 0.0600346i | ||||||
\(296\) | 5.96950 | + | 3.44649i | 0.346970 | + | 0.200323i | ||||
\(297\) | −2.22548 | − | 3.85464i | −0.129135 | − | 0.223669i | ||||
\(298\) | −12.4461 | − | 21.5573i | −0.720983 | − | 1.24878i | ||||
\(299\) | 5.29557 | + | 3.05740i | 0.306251 | + | 0.176814i | ||||
\(300\) | − | 13.4912i | − | 0.778916i | ||||||
\(301\) | 3.76235 | + | 6.84849i | 0.216858 | + | 0.394740i | ||||
\(302\) | −30.3095 | −1.74411 | ||||||||
\(303\) | −4.71251 | − | 2.72077i | −0.270727 | − | 0.156304i | ||||
\(304\) | −3.56473 | − | 6.17429i | −0.204451 | − | 0.354120i | ||||
\(305\) | −2.45300 | − | 4.24872i | −0.140458 | − | 0.243281i | ||||
\(306\) | −9.07405 | + | 1.25788i | −0.518729 | + | 0.0719083i | ||||
\(307\) | 25.0511 | 1.42974 | 0.714871 | − | 0.699256i | \(-0.246485\pi\) | ||||
0.714871 | + | 0.699256i | \(0.246485\pi\) | |||||||
\(308\) | −0.734447 | + | 34.5729i | −0.0418490 | + | 1.96997i | ||||
\(309\) | − | 11.4108i | − | 0.649138i | ||||||
\(310\) | 2.57366 | − | 4.45770i | 0.146174 | − | 0.253181i | ||||
\(311\) | −1.39150 | + | 0.803381i | −0.0789045 | + | 0.0455555i | −0.538933 | − | 0.842349i | \(-0.681172\pi\) |
0.460029 | + | 0.887904i | \(0.347839\pi\) | |||||||
\(312\) | 8.94064 | − | 5.16188i | 0.506164 | − | 0.292234i | ||||
\(313\) | 8.09544 | + | 4.67390i | 0.457581 | + | 0.264185i | 0.711027 | − | 0.703165i | \(-0.248231\pi\) |
−0.253446 | + | 0.967350i | \(0.581564\pi\) | |||||||
\(314\) | 0.748749 | 0.0422543 | ||||||||
\(315\) | 1.44119 | + | 0.873401i | 0.0812020 | + | 0.0492106i | ||||
\(316\) | − | 42.6474i | − | 2.39911i | ||||||
\(317\) | −19.3820 | − | 11.1902i | −1.08860 | − | 0.628506i | −0.155399 | − | 0.987852i | \(-0.549666\pi\) |
−0.933204 | + | 0.359346i | \(0.883000\pi\) | |||||||
\(318\) | −23.6349 | + | 13.6456i | −1.32538 | + | 0.765207i | ||||
\(319\) | −7.47379 | − | 12.9450i | −0.418452 | − | 0.724780i | ||||
\(320\) | −7.12491 | − | 4.11357i | −0.398294 | − | 0.229955i | ||||
\(321\) | −12.1142 | −0.676146 | ||||||||
\(322\) | 6.19582 | + | 3.75483i | 0.345280 | + | 0.209249i | ||||
\(323\) | 14.4441 | + | 18.5594i | 0.803692 | + | 1.03268i | ||||
\(324\) | −1.46826 | + | 2.54309i | −0.0815697 | + | 0.141283i | ||||
\(325\) | 11.3974 | + | 19.7409i | 0.632213 | + | 1.09503i | ||||
\(326\) | −10.0435 | + | 5.79864i | −0.556260 | + | 0.321157i | ||||
\(327\) | 5.83720 | − | 10.1103i | 0.322798 | − | 0.559103i | ||||
\(328\) | − | 17.4898i | − | 0.965712i | ||||||
\(329\) | −27.4745 | − | 0.583652i | −1.51472 | − | 0.0321778i | ||||
\(330\) | 6.29888i | 0.346742i | ||||||||
\(331\) | −9.19545 | + | 15.9270i | −0.505427 | + | 0.875426i | 0.494553 | + | 0.869148i | \(0.335332\pi\) |
−0.999980 | + | 0.00627837i | \(0.998002\pi\) | |||||||
\(332\) | −1.72688 | − | 2.99104i | −0.0947746 | − | 0.164154i | ||||
\(333\) | 2.86890 | − | 1.65636i | 0.157215 | − | 0.0907680i | ||||
\(334\) | 37.7585 | + | 21.7999i | 2.06605 | + | 1.19284i | ||||
\(335\) | 5.64817i | 0.308593i | ||||||||
\(336\) | −2.89841 | + | 1.59230i | −0.158121 | + | 0.0868670i | ||||
\(337\) | 11.8137i | 0.643535i | 0.946819 | + | 0.321768i | \(0.104277\pi\) | ||||
−0.946819 | + | 0.321768i | \(0.895723\pi\) | |||||||
\(338\) | −12.9052 | + | 22.3525i | −0.701951 | + | 1.21582i | ||||
\(339\) | −2.09604 | − | 3.63045i | −0.113841 | − | 0.197179i | ||||
\(340\) | 7.14482 | + | 2.90233i | 0.387482 | + | 0.157401i | ||||
\(341\) | 8.09458 | − | 14.0202i | 0.438346 | − | 0.759237i | ||||
\(342\) | 12.6731 | 0.685281 | ||||||||
\(343\) | −18.4827 | − | 1.17932i | −0.997971 | − | 0.0636775i | ||||
\(344\) | 6.14528 | 0.331331 | ||||||||
\(345\) | 0.679825 | + | 0.392497i | 0.0366006 | + | 0.0211313i | ||||
\(346\) | 21.2769 | − | 12.2843i | 1.14386 | − | 0.660405i | ||||
\(347\) | −14.5661 | + | 8.40971i | −0.781947 | + | 0.451457i | −0.837120 | − | 0.547020i | \(-0.815762\pi\) |
0.0551731 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(348\) | −4.93082 | + | 8.54043i | −0.264320 | + | 0.457815i | ||||
\(349\) | 26.7376 | 1.43123 | 0.715616 | − | 0.698494i | \(-0.246146\pi\) | ||||
0.715616 | + | 0.698494i | \(0.246146\pi\) | |||||||
\(350\) | 13.0038 | + | 23.6704i | 0.695082 | + | 1.26524i | ||||
\(351\) | − | 4.96153i | − | 0.264827i | ||||||
\(352\) | −26.7460 | − | 15.4418i | −1.42557 | − | 0.823051i | ||||
\(353\) | −5.56692 | − | 9.64219i | −0.296297 | − | 0.513202i | 0.678989 | − | 0.734149i | \(-0.262419\pi\) |
−0.975286 | + | 0.220947i | \(0.929085\pi\) | |||||||
\(354\) | −3.11496 | + | 1.79843i | −0.165558 | + | 0.0955852i | ||||
\(355\) | −2.97838 | + | 5.15870i | −0.158076 | + | 0.273796i | ||||
\(356\) | 11.3328 | 0.600636 | ||||||||
\(357\) | 8.74915 | − | 6.51555i | 0.463054 | − | 0.344839i | ||||
\(358\) | −13.0416 | −0.689270 | ||||||||
\(359\) | 3.39000 | − | 5.87165i | 0.178917 | − | 0.309894i | −0.762593 | − | 0.646879i | \(-0.776074\pi\) |
0.941510 | + | 0.336985i | \(0.109407\pi\) | |||||||
\(360\) | 1.14777 | − | 0.662663i | 0.0604926 | − | 0.0349254i | ||||
\(361\) | −6.76723 | − | 11.7212i | −0.356170 | − | 0.616904i | ||||
\(362\) | −22.4528 | − | 12.9631i | −1.18009 | − | 0.681328i | ||||
\(363\) | 8.81102i | 0.462458i | ||||||||
\(364\) | −19.9784 | + | 32.9662i | −1.04715 | + | 1.72790i | ||||
\(365\) | −5.40452 | −0.282885 | ||||||||
\(366\) | −8.55672 | + | 14.8207i | −0.447267 | + | 0.774689i | ||||
\(367\) | −23.9881 | + | 13.8495i | −1.25217 | + | 0.722940i | −0.971540 | − | 0.236876i | \(-0.923876\pi\) |
−0.280629 | + | 0.959816i | \(0.590543\pi\) | |||||||
\(368\) | −1.33408 | + | 0.770232i | −0.0695437 | + | 0.0401511i | ||||
\(369\) | −7.27935 | − | 4.20274i | −0.378948 | − | 0.218786i | ||||
\(370\) | −4.68808 | −0.243722 | ||||||||
\(371\) | 16.8433 | − | 27.7930i | 0.874459 | − | 1.44294i | ||||
\(372\) | −10.6808 | −0.553772 | ||||||||
\(373\) | 14.3114 | − | 24.7881i | 0.741016 | − | 1.28348i | −0.211018 | − | 0.977482i | \(-0.567678\pi\) |
0.952033 | − | 0.305994i | \(-0.0989889\pi\) | |||||||
\(374\) | 37.7766 | + | 15.3454i | 1.95338 | + | 0.793493i | ||||
\(375\) | 3.05551 | + | 5.29230i | 0.157786 | + | 0.273293i | ||||
\(376\) | −10.8062 | + | 18.7168i | −0.557285 | + | 0.965246i | ||||
\(377\) | − | 16.6622i | − | 0.858148i | ||||||
\(378\) | 0.124849 | − | 5.87707i | 0.00642154 | − | 0.302284i | ||||
\(379\) | − | 27.2491i | − | 1.39969i | −0.714294 | − | 0.699845i | \(-0.753252\pi\) | ||
0.714294 | − | 0.699845i | \(-0.246748\pi\) | |||||||
\(380\) | −9.23919 | − | 5.33425i | −0.473960 | − | 0.273641i | ||||
\(381\) | −15.2735 | + | 8.81816i | −0.782485 | + | 0.451768i | ||||
\(382\) | 17.5140 | + | 30.3352i | 0.896095 | + | 1.55208i | ||||
\(383\) | −17.7384 | + | 30.7238i | −0.906391 | + | 1.56991i | −0.0873512 | + | 0.996178i | \(0.527840\pi\) |
−0.819039 | + | 0.573737i | \(0.805493\pi\) | |||||||
\(384\) | 14.8212i | 0.756340i | ||||||||
\(385\) | −3.61155 | − | 6.57399i | −0.184061 | − | 0.335042i | ||||
\(386\) | − | 4.05428i | − | 0.206358i | ||||||
\(387\) | 1.47669 | − | 2.55770i | 0.0750643 | − | 0.130015i | ||||
\(388\) | 32.9164 | − | 19.0043i | 1.67108 | − | 0.964797i | ||||
\(389\) | −8.97450 | − | 15.5443i | −0.455025 | − | 0.788126i | 0.543665 | − | 0.839303i | \(-0.317036\pi\) |
−0.998690 | + | 0.0511761i | \(0.983703\pi\) | |||||||
\(390\) | −3.51071 | + | 6.08074i | −0.177772 | + | 0.307910i | ||||
\(391\) | 4.01014 | − | 3.12094i | 0.202802 | − | 0.157833i | ||||
\(392\) | −7.81179 | + | 12.2933i | −0.394555 | + | 0.620905i | ||||
\(393\) | 12.4585 | 0.628447 | ||||||||
\(394\) | 33.7506 | + | 19.4859i | 1.70033 | + | 0.981686i | ||||
\(395\) | 4.62521 | + | 8.01110i | 0.232720 | + | 0.403082i | ||||
\(396\) | 11.3192 | − | 6.53514i | 0.568811 | − | 0.328403i | ||||
\(397\) | 14.5890 | + | 8.42296i | 0.732201 | + | 0.422736i | 0.819227 | − | 0.573470i | \(-0.194403\pi\) |
−0.0870261 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(398\) | − | 27.1082i | − | 1.35881i | ||||||
\(399\) | −13.2266 | + | 7.26627i | −0.662157 | + | 0.363769i | ||||
\(400\) | −5.74255 | −0.287127 | ||||||||
\(401\) | 27.4843 | + | 15.8681i | 1.37250 | + | 0.792413i | 0.991242 | − | 0.132056i | \(-0.0421579\pi\) |
0.381257 | + | 0.924469i | \(0.375491\pi\) | |||||||
\(402\) | 17.0627 | − | 9.85118i | 0.851012 | − | 0.491332i | ||||
\(403\) | 15.6285 | − | 9.02311i | 0.778510 | − | 0.449473i | ||||
\(404\) | 7.98957 | − | 13.8383i | 0.397496 | − | 0.688483i | ||||
\(405\) | − | 0.636942i | − | 0.0316499i | ||||||
\(406\) | 0.419279 | − | 19.7369i | 0.0208084 | − | 0.979525i | ||||
\(407\) | −14.7448 | −0.730872 | ||||||||
\(408\) | −1.17802 | − | 8.49795i | −0.0583207 | − | 0.420711i | ||||
\(409\) | −7.11957 | − | 12.3315i | −0.352040 | − | 0.609751i | 0.634567 | − | 0.772868i | \(-0.281179\pi\) |
−0.986607 | + | 0.163117i | \(0.947845\pi\) | |||||||
\(410\) | 5.94760 | + | 10.3016i | 0.293731 | + | 0.508757i | ||||
\(411\) | −15.7904 | − | 9.11657i | −0.778882 | − | 0.449687i | ||||
\(412\) | 33.5080 | 1.65082 | ||||||||
\(413\) | 2.21986 | − | 3.66298i | 0.109232 | − | 0.180243i | ||||
\(414\) | − | 2.73827i | − | 0.134579i | ||||||
\(415\) | 0.648769 | + | 0.374567i | 0.0318468 | + | 0.0183868i | ||||
\(416\) | −17.2131 | − | 29.8140i | −0.843944 | − | 1.46175i | ||||
\(417\) | 5.89602 | + | 10.2122i | 0.288729 | + | 0.500094i | ||||
\(418\) | −48.8501 | − | 28.2036i | −2.38934 | − | 1.37949i | ||||
\(419\) | − | 2.91045i | − | 0.142185i | −0.997470 | − | 0.0710923i | \(-0.977352\pi\) | ||
0.997470 | − | 0.0710923i | \(-0.0226485\pi\) | |||||||
\(420\) | −2.56475 | + | 4.23208i | −0.125147 | + | 0.206504i | ||||
\(421\) | 0.521247 | 0.0254040 | 0.0127020 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127020 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(422\) | −7.21195 | − | 4.16382i | −0.351072 | − | 0.202692i | ||||
\(423\) | 5.19336 | + | 8.99516i | 0.252510 | + | 0.437360i | ||||
\(424\) | −12.7793 | − | 22.1343i | −0.620615 | − | 1.07494i | ||||
\(425\) | 18.7634 | − | 2.60106i | 0.910157 | − | 0.126170i | ||||
\(426\) | 20.7788 | 1.00674 | ||||||||
\(427\) | 0.432815 | − | 20.3741i | 0.0209454 | − | 0.985971i | ||||
\(428\) | − | 35.5734i | − | 1.71950i | ||||||
\(429\) | −11.0418 | + | 19.1249i | −0.533102 | + | 0.923360i | ||||
\(430\) | −3.61959 | + | 2.08977i | −0.174552 | + | 0.100778i | ||||
\(431\) | 21.6103 | − | 12.4767i | 1.04093 | − | 0.600981i | 0.120834 | − | 0.992673i | \(-0.461443\pi\) |
0.920097 | + | 0.391691i | \(0.128110\pi\) | |||||||
\(432\) | 1.08247 | + | 0.624963i | 0.0520803 | + | 0.0300686i | ||||
\(433\) | −8.79699 | −0.422756 | −0.211378 | − | 0.977404i | \(-0.567795\pi\) | ||||
−0.211378 | + | 0.977404i | \(0.567795\pi\) | |||||||
\(434\) | 18.7394 | − | 10.2949i | 0.899522 | − | 0.494169i | ||||
\(435\) | − | 2.13903i | − | 0.102559i | ||||||
\(436\) | 29.6891 | + | 17.1410i | 1.42185 | + | 0.820906i | ||||
\(437\) | −6.08792 | + | 3.51486i | −0.291225 | + | 0.168139i | ||||
\(438\) | 9.42621 | + | 16.3267i | 0.450402 | + | 0.780119i | ||||
\(439\) | −3.85640 | − | 2.22649i | −0.184056 | − | 0.106265i | 0.405141 | − | 0.914254i | \(-0.367222\pi\) |
−0.589197 | + | 0.807989i | \(0.700556\pi\) | |||||||
\(440\) | −5.89897 | −0.281222 | ||||||||
\(441\) | 3.23940 | + | 6.20535i | 0.154257 | + | 0.295493i | ||||
\(442\) | 27.9155 | + | 35.8690i | 1.32780 | + | 1.70611i | ||||
\(443\) | 15.5992 | − | 27.0186i | 0.741141 | − | 1.28369i | −0.210835 | − | 0.977522i | \(-0.567618\pi\) |
0.951976 | − | 0.306173i | \(-0.0990485\pi\) | |||||||
\(444\) | 4.86392 | + | 8.42456i | 0.230831 | + | 0.399812i | ||||
\(445\) | −2.12880 | + | 1.22906i | −0.100915 | + | 0.0582632i | ||||
\(446\) | 12.1949 | − | 21.1221i | 0.577444 | − | 1.00016i | ||||
\(447\) | − | 11.2035i | − | 0.529906i | ||||||
\(448\) | −16.4546 | − | 29.9519i | −0.777409 | − | 1.41509i | ||||
\(449\) | 35.1190i | 1.65737i | 0.559716 | + | 0.828685i | \(0.310910\pi\) | ||||
−0.559716 | + | 0.828685i | \(0.689090\pi\) | |||||||
\(450\) | 5.10387 | − | 8.84017i | 0.240599 | − | 0.416729i | ||||
\(451\) | 18.7062 | + | 32.4001i | 0.880840 | + | 1.52566i | ||||
\(452\) | 10.6609 | − | 6.15505i | 0.501445 | − | 0.289509i | ||||
\(453\) | −11.8141 | − | 6.82085i | −0.555073 | − | 0.320471i | ||||
\(454\) | 24.1381i | 1.13286i | ||||||||
\(455\) | 0.177579 | − | 8.35923i | 0.00832501 | − | 0.391887i | ||||
\(456\) | 11.8685i | 0.555792i | ||||||||
\(457\) | 4.26769 | − | 7.39186i | 0.199634 | − | 0.345777i | −0.748776 | − | 0.662824i | \(-0.769358\pi\) |
0.948410 | + | 0.317047i | \(0.102691\pi\) | |||||||
\(458\) | 10.6115 | + | 18.3797i | 0.495844 | + | 0.858826i | ||||
\(459\) | −3.81997 | − | 1.55173i | −0.178301 | − | 0.0724284i | ||||
\(460\) | −1.15257 | + | 1.99631i | −0.0537390 | + | 0.0930786i | ||||
\(461\) | 16.5716 | 0.771819 | 0.385909 | − | 0.922537i | \(-0.373888\pi\) | ||||
0.385909 | + | 0.922537i | \(0.373888\pi\) | |||||||
\(462\) | −13.5605 | + | 22.3762i | −0.630894 | + | 1.04103i | ||||
\(463\) | −9.46742 | −0.439989 | −0.219994 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219994 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(464\) | 3.63524 | + | 2.09880i | 0.168762 | + | 0.0974346i | ||||
\(465\) | 2.00632 | − | 1.15835i | 0.0930411 | − | 0.0537173i | ||||
\(466\) | 18.2726 | − | 10.5497i | 0.846463 | − | 0.488705i | ||||
\(467\) | −4.59009 | + | 7.95027i | −0.212404 | + | 0.367895i | −0.952466 | − | 0.304644i | \(-0.901463\pi\) |
0.740062 | + | 0.672538i | \(0.234796\pi\) | |||||||
\(468\) | 14.5696 | 0.673479 | ||||||||
\(469\) | −12.1597 | + | 20.0646i | −0.561482 | + | 0.926497i | ||||
\(470\) | − | 14.6990i | − | 0.678015i | ||||||
\(471\) | 0.291848 | + | 0.168499i | 0.0134476 | + | 0.00776400i | ||||
\(472\) | −1.68424 | − | 2.91720i | −0.0775236 | − | 0.134275i | ||||
\(473\) | −11.3842 | + | 6.57268i | −0.523447 | + | 0.302212i | ||||
\(474\) | 16.1340 | − | 27.9449i | 0.741058 | − | 1.28355i | ||||
\(475\) | −26.2054 | −1.20239 | ||||||||
\(476\) | 19.1330 | + | 25.6920i | 0.876959 | + | 1.17759i | ||||
\(477\) | −12.2832 | −0.562411 | ||||||||
\(478\) | −12.7641 | + | 22.1081i | −0.583816 | + | 1.01120i | ||||
\(479\) | 17.4440 | − | 10.0713i | 0.797037 | − | 0.460169i | −0.0453972 | − | 0.998969i | \(-0.514455\pi\) |
0.842434 | + | 0.538800i | \(0.181122\pi\) | |||||||
\(480\) | −2.20976 | − | 3.82741i | −0.100861 | − | 0.174697i | ||||
\(481\) | −14.2341 | − | 8.21808i | −0.649021 | − | 0.374712i | ||||
\(482\) | 29.3839i | 1.33840i | ||||||||
\(483\) | 1.57003 | + | 2.85787i | 0.0714386 | + | 0.130038i | ||||
\(484\) | −25.8736 | −1.17607 | ||||||||
\(485\) | −4.12212 | + | 7.13971i | −0.187176 | + | 0.324198i | ||||
\(486\) | −1.92416 | + | 1.11091i | −0.0872816 | + | 0.0503920i | ||||
\(487\) | 4.67401 | − | 2.69854i | 0.211800 | − | 0.122283i | −0.390348 | − | 0.920667i | \(-0.627645\pi\) |
0.602148 | + | 0.798385i | \(0.294312\pi\) | |||||||
\(488\) | −13.8797 | − | 8.01345i | −0.628305 | − | 0.362752i | ||||
\(489\) | −5.21971 | −0.236043 | ||||||||
\(490\) | 0.420694 | − | 9.89728i | 0.0190050 | − | 0.447114i | ||||
\(491\) | −4.61469 | −0.208258 | −0.104129 | − | 0.994564i | \(-0.533206\pi\) | ||||
−0.104129 | + | 0.994564i | \(0.533206\pi\) | |||||||
\(492\) | 12.3414 | − | 21.3759i | 0.556392 | − | 0.963700i | ||||
\(493\) | −12.8285 | − | 5.21114i | −0.577768 | − | 0.234698i | ||||
\(494\) | −31.4389 | − | 54.4538i | −1.41450 | − | 2.44999i | ||||
\(495\) | −1.41750 | + | 2.45518i | −0.0637119 | + | 0.110352i | ||||
\(496\) | 4.54627i | 0.204134i | ||||||||
\(497\) | −21.6863 | + | 11.9138i | −0.972765 | + | 0.534407i | ||||
\(498\) | − | 2.61318i | − | 0.117099i | ||||||
\(499\) | −35.0782 | − | 20.2524i | −1.57031 | − | 0.906621i | −0.996130 | − | 0.0878956i | \(-0.971986\pi\) |
−0.574185 | − | 0.818726i | \(-0.694681\pi\) | |||||||
\(500\) | −15.5409 | + | 8.97253i | −0.695009 | + | 0.401264i | ||||
\(501\) | 9.81170 | + | 16.9944i | 0.438354 | + | 0.759252i | ||||
\(502\) | −2.05350 | + | 3.55677i | −0.0916523 | + | 0.158746i | ||||
\(503\) | − | 0.342609i | − | 0.0152762i | −0.999971 | − | 0.00763808i | \(-0.997569\pi\) | ||
0.999971 | − | 0.00763808i | \(-0.00243130\pi\) | |||||||
\(504\) | 5.50394 | + | 0.116922i | 0.245165 | + | 0.00520814i | ||||
\(505\) | 3.46595i | 0.154233i | ||||||||
\(506\) | −6.09397 | + | 10.5551i | −0.270910 | + | 0.469230i | ||||
\(507\) | −10.0604 | + | 5.80838i | −0.446799 | + | 0.257959i | ||||
\(508\) | −25.8946 | − | 44.8508i | −1.14889 | − | 1.98993i | ||||
\(509\) | 9.05619 | − | 15.6858i | 0.401409 | − | 0.695260i | −0.592488 | − | 0.805580i | \(-0.701854\pi\) |
0.993896 | + | 0.110320i | \(0.0351874\pi\) | |||||||
\(510\) | 3.58368 | + | 4.60472i | 0.158688 | + | 0.203900i | ||||
\(511\) | −19.1990 | − | 11.6351i | −0.849315 | − | 0.514707i | ||||
\(512\) | 13.8744 | 0.613168 | ||||||||
\(513\) | 4.93972 | + | 2.85195i | 0.218094 | + | 0.125917i | ||||
\(514\) | 7.78075 | + | 13.4767i | 0.343194 | + | 0.594430i | ||||
\(515\) | −6.29429 | + | 3.63401i | −0.277360 | + | 0.160134i | ||||
\(516\) | 7.51071 | + | 4.33631i | 0.330641 | + | 0.190896i | ||||
\(517\) | − | 46.2308i | − | 2.03323i | ||||||
\(518\) | −16.6539 | − | 10.0927i | −0.731732 | − | 0.443449i | ||||
\(519\) | 11.0578 | 0.485383 | ||||||||
\(520\) | −5.69467 | − | 3.28782i | −0.249728 | − | 0.144180i | ||||
\(521\) | −1.69820 | + | 0.980458i | −0.0743996 | + | 0.0429546i | −0.536738 | − | 0.843749i | \(-0.680344\pi\) |
0.462339 | + | 0.886703i | \(0.347010\pi\) | |||||||
\(522\) | −6.46187 | + | 3.73076i | −0.282828 | + | 0.163291i | ||||
\(523\) | −17.6024 | + | 30.4883i | −0.769700 | + | 1.33316i | 0.168026 | + | 0.985783i | \(0.446261\pi\) |
−0.937726 | + | 0.347377i | \(0.887073\pi\) | |||||||
\(524\) | 36.5845i | 1.59820i | ||||||||
\(525\) | −0.258164 | + | 12.1526i | −0.0112672 | + | 0.530385i | ||||
\(526\) | −10.7136 | −0.467134 | ||||||||
\(527\) | −2.05921 | − | 14.8546i | −0.0897006 | − | 0.647078i | ||||
\(528\) | −2.78169 | − | 4.81802i | −0.121057 | − | 0.209677i | ||||
\(529\) | −10.7405 | − | 18.6032i | −0.466980 | − | 0.808833i | ||||
\(530\) | 15.0540 | + | 8.69146i | 0.653906 | + | 0.377533i | ||||
\(531\) | −1.61887 | −0.0702530 | ||||||||
\(532\) | −21.3375 | − | 38.8400i | −0.925097 | − | 1.68393i | ||||
\(533\) | 41.7040i | 1.80640i | ||||||||
\(534\) | 7.42584 | + | 4.28731i | 0.321347 | + | 0.185530i | ||||
\(535\) | 3.85801 | + | 6.68227i | 0.166796 | + | 0.288900i | ||||
\(536\) | 9.22573 | + | 15.9794i | 0.398491 | + | 0.690207i | ||||
\(537\) | −5.08337 | − | 2.93488i | −0.219364 | − | 0.126650i | ||||
\(538\) | − | 35.7345i | − | 1.54063i | ||||||
\(539\) | 1.32315 | − | 31.1286i | 0.0569922 | − | 1.34080i | ||||
\(540\) | 1.87039 | 0.0804886 | ||||||||
\(541\) | 15.6944 | + | 9.06116i | 0.674754 | + | 0.389570i | 0.797876 | − | 0.602822i | \(-0.205957\pi\) |
−0.123121 | + | 0.992392i | \(0.539290\pi\) | |||||||
\(542\) | −31.3788 | − | 54.3496i | −1.34783 | − | 2.33452i | ||||
\(543\) | −5.83446 | − | 10.1056i | −0.250380 | − | 0.433672i | ||||
\(544\) | −28.3378 | + | 3.92830i | −1.21497 | + | 0.168425i | ||||
\(545\) | −7.43592 | −0.318520 | ||||||||
\(546\) | −25.5624 | + | 14.0432i | −1.09397 | + | 0.600993i | ||||
\(547\) | 3.48512i | 0.149013i | 0.997221 | + | 0.0745065i | \(0.0237382\pi\) | ||||
−0.997221 | + | 0.0745065i | \(0.976262\pi\) | |||||||
\(548\) | 26.7709 | − | 46.3686i | 1.14360 | − | 1.98077i | ||||
\(549\) | −6.67049 | + | 3.85121i | −0.284690 | + | 0.164366i | ||||
\(550\) | −39.3472 | + | 22.7171i | −1.67777 | + | 0.968661i | ||||
\(551\) | 16.5890 | + | 9.57766i | 0.706715 | + | 0.408022i | ||||
\(552\) | 2.56442 | 0.109149 | ||||||||
\(553\) | −0.816087 | + | 38.4160i | −0.0347036 | + | 1.63362i | ||||
\(554\) | − | 25.2020i | − | 1.07073i | ||||||
\(555\) | −1.82732 | − | 1.05501i | −0.0775656 | − | 0.0447825i | ||||
\(556\) | −29.9883 | + | 17.3137i | −1.27179 | + | 0.734266i | ||||
\(557\) | 11.3343 | + | 19.6315i | 0.480249 | + | 0.831815i | 0.999743 | − | 0.0226584i | \(-0.00721302\pi\) |
−0.519494 | + | 0.854474i | \(0.673880\pi\) | |||||||
\(558\) | −6.99860 | − | 4.04065i | −0.296274 | − | 0.171054i | ||||
\(559\) | −14.6533 | −0.619767 | ||||||||
\(560\) | 1.80139 | + | 1.09169i | 0.0761224 | + | 0.0461322i | ||||
\(561\) | 11.2713 | + | 14.4826i | 0.475873 | + | 0.611456i | ||||
\(562\) | −0.932619 | + | 1.61534i | −0.0393402 | + | 0.0681392i | ||||
\(563\) | −4.36066 | − | 7.55289i | −0.183780 | − | 0.318316i | 0.759385 | − | 0.650642i | \(-0.225500\pi\) |
−0.943165 | + | 0.332326i | \(0.892167\pi\) | |||||||
\(564\) | −26.4144 | + | 15.2504i | −1.11225 | + | 0.642156i | ||||
\(565\) | −1.33506 | + | 2.31239i | −0.0561663 | + | 0.0972829i | ||||
\(566\) | 41.4418i | 1.74193i | ||||||||
\(567\) | 1.37124 | − | 2.26267i | 0.0575867 | − | 0.0950234i | ||||
\(568\) | 19.4595i | 0.816505i | ||||||||
\(569\) | 18.9894 | − | 32.8906i | 0.796078 | − | 1.37885i | −0.126074 | − | 0.992021i | \(-0.540238\pi\) |
0.922152 | − | 0.386827i | \(-0.126429\pi\) | |||||||
\(570\) | −4.03601 | − | 6.99057i | −0.169050 | − | 0.292803i | ||||
\(571\) | −35.6117 | + | 20.5604i | −1.49030 | + | 0.860426i | −0.999938 | − | 0.0110921i | \(-0.996469\pi\) |
−0.490363 | + | 0.871518i | \(0.663136\pi\) | |||||||
\(572\) | −56.1605 | − | 32.4243i | −2.34819 | − | 1.35573i | ||||
\(573\) | 15.7654i | 0.658610i | ||||||||
\(574\) | −1.04942 | + | 49.3996i | −0.0438017 | + | 2.06190i | ||||
\(575\) | 5.66222i | 0.236131i | ||||||||
\(576\) | −6.45831 | + | 11.1861i | −0.269096 | + | 0.466088i | ||||
\(577\) | −11.7385 | − | 20.3316i | −0.488679 | − | 0.846417i | 0.511236 | − | 0.859440i | \(-0.329188\pi\) |
−0.999915 | + | 0.0130235i | \(0.995854\pi\) | |||||||
\(578\) | 36.3467 | − | 10.2745i | 1.51183 | − | 0.427363i | ||||
\(579\) | 0.912377 | − | 1.58028i | 0.0379171 | − | 0.0656743i | ||||
\(580\) | 6.28129 | 0.260816 | ||||||||
\(581\) | 1.49830 | + | 2.72732i | 0.0621600 | + | 0.113148i | ||||
\(582\) | 28.7581 | 1.19206 | ||||||||
\(583\) | 47.3475 | + | 27.3361i | 1.96093 | + | 1.13214i | ||||
\(584\) | −15.2901 | + | 8.82774i | −0.632709 | + | 0.365295i | ||||
\(585\) | −2.73682 | + | 1.58010i | −0.113154 | + | 0.0653292i | ||||
\(586\) | 3.32507 | − | 5.75918i | 0.137357 | − | 0.237910i | ||||
\(587\) | −23.3181 | −0.962443 | −0.481221 | − | 0.876599i | \(-0.659807\pi\) | ||||
−0.481221 | + | 0.876599i | \(0.659807\pi\) | |||||||
\(588\) | −18.2221 | + | 9.51252i | −0.751465 | + | 0.392290i | ||||
\(589\) | 20.7464i | 0.854840i | ||||||||
\(590\) | 1.98405 | + | 1.14549i | 0.0816821 | + | 0.0471592i | ||||
\(591\) | 8.77022 | + | 15.1905i | 0.360759 | + | 0.624852i | ||||
\(592\) | 3.58592 | − | 2.07033i | 0.147380 | − | 0.0850900i | ||||
\(593\) | −7.23725 | + | 12.5353i | −0.297198 | + | 0.514763i | −0.975494 | − | 0.220026i | \(-0.929386\pi\) |
0.678295 | + | 0.734789i | \(0.262719\pi\) | |||||||
\(594\) | 9.88925 | 0.405761 | ||||||||
\(595\) | −6.38038 | − | 2.75109i | −0.261570 | − | 0.112784i | ||||
\(596\) | 32.8991 | 1.34760 | ||||||||
\(597\) | 6.10043 | − | 10.5663i | 0.249674 | − | 0.432448i | ||||
\(598\) | −11.7658 | + | 6.79301i | −0.481141 | + | 0.277787i | ||||
\(599\) | 0.156806 | + | 0.271596i | 0.00640692 | + | 0.0110971i | 0.869211 | − | 0.494441i | \(-0.164627\pi\) |
−0.862804 | + | 0.505538i | \(0.831294\pi\) | |||||||
\(600\) | 8.27891 | + | 4.77983i | 0.337985 | + | 0.195136i | ||||
\(601\) | − | 39.9343i | − | 1.62896i | −0.580195 | − | 0.814478i | \(-0.697024\pi\) | ||
0.580195 | − | 0.814478i | \(-0.302976\pi\) | |||||||
\(602\) | −17.3572 | − | 0.368726i | −0.707427 | − | 0.0150282i | ||||
\(603\) | 8.86764 | 0.361118 | ||||||||
\(604\) | 20.0295 | − | 34.6921i | 0.814989 | − | 1.41160i | ||||
\(605\) | 4.86023 | − | 2.80605i | 0.197596 | − | 0.114082i | ||||
\(606\) | 10.4704 | − | 6.04508i | 0.425330 | − | 0.245564i | ||||
\(607\) | 7.80981 | + | 4.50900i | 0.316990 | + | 0.183015i | 0.650050 | − | 0.759891i | \(-0.274748\pi\) |
−0.333060 | + | 0.942906i | \(0.608081\pi\) | |||||||
\(608\) | 39.5773 | 1.60507 | ||||||||
\(609\) | 4.60502 | − | 7.59871i | 0.186605 | − | 0.307915i | ||||
\(610\) | 10.9003 | 0.441339 | ||||||||
\(611\) | 25.7670 | − | 44.6298i | 1.04242 | − | 1.80553i | ||||
\(612\) | 4.55666 | − | 11.2174i | 0.184192 | − | 0.453435i | ||||
\(613\) | 9.03406 | + | 15.6475i | 0.364882 | + | 0.631995i | 0.988757 | − | 0.149529i | \(-0.0477759\pi\) |
−0.623875 | + | 0.781524i | \(0.714443\pi\) | |||||||
\(614\) | −27.8296 | + | 48.2023i | −1.12311 | + | 1.94529i | ||||
\(615\) | 5.35380i | 0.215886i | ||||||||
\(616\) | −20.9555 | − | 12.6996i | −0.844322 | − | 0.511681i | ||||
\(617\) | − | 44.6374i | − | 1.79703i | −0.438938 | − | 0.898517i | \(-0.644645\pi\) | ||
0.438938 | − | 0.898517i | \(-0.355355\pi\) | |||||||
\(618\) | 21.9562 | + | 12.6764i | 0.883208 | + | 0.509920i | ||||
\(619\) | 29.1522 | − | 16.8310i | 1.17173 | − | 0.676496i | 0.217639 | − | 0.976029i | \(-0.430164\pi\) |
0.954086 | + | 0.299533i | \(0.0968310\pi\) | |||||||
\(620\) | 3.40151 | + | 5.89159i | 0.136608 | + | 0.236612i | ||||
\(621\) | 0.616221 | − | 1.06733i | 0.0247281 | − | 0.0428303i | ||||
\(622\) | − | 3.56994i | − | 0.143142i | ||||||
\(623\) | −10.2084 | − | 0.216860i | −0.408989 | − | 0.00868832i | ||||
\(624\) | − | 6.20155i | − | 0.248261i | ||||||
\(625\) | −9.53958 | + | 16.5230i | −0.381583 | + | 0.660922i | ||||
\(626\) | −17.9867 | + | 10.3846i | −0.718891 | + | 0.415052i | ||||
\(627\) | −12.6939 | − | 21.9865i | −0.506946 | − | 0.878056i | ||||
\(628\) | −0.494798 | + | 0.857015i | −0.0197446 | + | 0.0341986i | ||||
\(629\) | −10.7790 | + | 8.38888i | −0.429787 | + | 0.334487i | ||||
\(630\) | −3.28160 | + | 1.80281i | −0.130742 | + | 0.0718257i | ||||
\(631\) | 46.1081 | 1.83553 | 0.917767 | − | 0.397120i | \(-0.129990\pi\) | ||||
0.917767 | + | 0.397120i | \(0.129990\pi\) | |||||||
\(632\) | 26.1707 | + | 15.1096i | 1.04101 | + | 0.601029i | ||||
\(633\) | −1.87405 | − | 3.24596i | −0.0744869 | − | 0.129015i | ||||
\(634\) | 43.0635 | − | 24.8627i | 1.71027 | − | 0.987425i | ||||
\(635\) | 9.72833 | + | 5.61666i | 0.386057 | + | 0.222890i | ||||
\(636\) | − | 36.0698i | − | 1.43026i | ||||||
\(637\) | 18.6270 | − | 29.3131i | 0.738029 | − | 1.16143i | ||||
\(638\) | 33.2109 | 1.31483 | ||||||||
\(639\) | 8.09917 | + | 4.67606i | 0.320398 | + | 0.184982i | ||||
\(640\) | 8.17548 | − | 4.72011i | 0.323164 | − | 0.186579i | ||||
\(641\) | 31.3749 | − | 18.1143i | 1.23924 | − | 0.715473i | 0.270298 | − | 0.962777i | \(-0.412878\pi\) |
0.968938 | + | 0.247304i | \(0.0795446\pi\) | |||||||
\(642\) | 13.4578 | − | 23.3096i | 0.531136 | − | 0.919955i | ||||
\(643\) | 42.9418i | 1.69346i | 0.532022 | + | 0.846731i | \(0.321432\pi\) | ||||
−0.532022 | + | 0.846731i | \(0.678568\pi\) | |||||||
\(644\) | −8.39217 | + | 4.61040i | −0.330698 | + | 0.181675i | ||||
\(645\) | −1.88113 | −0.0740694 | ||||||||
\(646\) | −51.7575 | + | 7.17483i | −2.03637 | + | 0.282290i | ||||
\(647\) | 11.9012 | + | 20.6134i | 0.467884 | + | 0.810398i | 0.999326 | − | 0.0366959i | \(-0.0116833\pi\) |
−0.531443 | + | 0.847094i | \(0.678350\pi\) | |||||||
\(648\) | −1.04038 | − | 1.80199i | −0.0408701 | − | 0.0707890i | ||||
\(649\) | 6.24017 | + | 3.60276i | 0.244948 | + | 0.141421i | ||||
\(650\) | −50.6460 | −1.98650 | ||||||||
\(651\) | 9.62103 | + | 0.204384i | 0.377078 | + | 0.00801042i | ||||
\(652\) | − | 15.3277i | − | 0.600280i | ||||||
\(653\) | 16.8061 | + | 9.70301i | 0.657673 | + | 0.379708i | 0.791390 | − | 0.611312i | \(-0.209358\pi\) |
−0.133716 | + | 0.991020i | \(0.542691\pi\) | |||||||
\(654\) | 12.9693 | + | 22.4634i | 0.507138 | + | 0.878389i | ||||
\(655\) | −3.96766 | − | 6.87220i | −0.155029 | − | 0.268519i | ||||
\(656\) | −9.09866 | − | 5.25311i | −0.355243 | − | 0.205100i | ||||
\(657\) | 8.48510i | 0.331035i | ||||||||
\(658\) | 31.6448 | − | 52.2168i | 1.23364 | − | 2.03562i | ||||
\(659\) | −5.28871 | −0.206019 | −0.103009 | − | 0.994680i | \(-0.532847\pi\) | ||||
−0.103009 | + | 0.994680i | \(0.532847\pi\) | |||||||
\(660\) | −7.20967 | − | 4.16251i | −0.280636 | − | 0.162025i | ||||
\(661\) | 4.45043 | + | 7.70836i | 0.173102 | + | 0.299821i | 0.939503 | − | 0.342542i | \(-0.111288\pi\) |
−0.766401 | + | 0.642362i | \(0.777954\pi\) | |||||||
\(662\) | −20.4307 | − | 35.3870i | −0.794061 | − | 1.37535i | ||||
\(663\) | 2.80896 | + | 20.2631i | 0.109091 | + | 0.786955i | ||||
\(664\) | 2.44727 | 0.0949726 | ||||||||
\(665\) | 8.22042 | + | 4.98179i | 0.318774 | + | 0.193186i | ||||
\(666\) | 7.36029i | 0.285205i | ||||||||
\(667\) | 2.06945 | − | 3.58439i | 0.0801293 | − | 0.138788i | ||||
\(668\) | −49.9041 | + | 28.8122i | −1.93085 | + | 1.11478i | ||||
\(669\) | 9.50665 | − | 5.48867i | 0.367548 | − | 0.212204i | ||||
\(670\) | −10.8680 | − | 6.27463i | −0.419867 | − | 0.242410i | ||||
\(671\) | 34.2831 | 1.32349 | ||||||||
\(672\) | 0.389897 | − | 18.3538i | 0.0150406 | − | 0.708013i | ||||
\(673\) | − | 25.1549i | − | 0.969650i | −0.874611 | − | 0.484825i | \(-0.838883\pi\) | ||
0.874611 | − | 0.484825i | \(-0.161117\pi\) | |||||||
\(674\) | −22.7315 | − | 13.1240i | −0.875584 | − | 0.505519i | ||||
\(675\) | 3.97878 | − | 2.29715i | 0.153143 | − | 0.0884174i | ||||
\(676\) | −17.0564 | − | 29.5425i | −0.656015 | − | 1.13625i | ||||
\(677\) | 20.9761 | + | 12.1106i | 0.806178 | + | 0.465447i | 0.845627 | − | 0.533775i | \(-0.179227\pi\) |
−0.0394489 | + | 0.999222i | \(0.512560\pi\) | |||||||
\(678\) | 9.31408 | 0.357705 | ||||||||
\(679\) | −30.0142 | + | 16.4888i | −1.15184 | + | 0.632784i | ||||
\(680\) | −4.31237 | + | 3.35615i | −0.165372 | + | 0.128703i | ||||
\(681\) | −5.43203 | + | 9.40856i | −0.208156 | + | 0.360537i | ||||
\(682\) | 17.9847 | + | 31.1505i | 0.688671 | + | 1.19281i | ||||
\(683\) | −10.2643 | + | 5.92609i | −0.392752 | + | 0.226756i | −0.683352 | − | 0.730089i | \(-0.739479\pi\) |
0.290600 | + | 0.956845i | \(0.406145\pi\) | |||||||
\(684\) | −8.37478 | + | 14.5055i | −0.320218 | + | 0.554633i | ||||
\(685\) | 11.6135i | 0.443727i | ||||||||
\(686\) | 22.8018 | − | 34.2535i | 0.870579 | − | 1.30780i | ||||
\(687\) | 9.55207i | 0.364434i | ||||||||
\(688\) | 1.84575 | − | 3.19694i | 0.0703687 | − | 0.121882i | ||||
\(689\) | 30.4718 | + | 52.7787i | 1.16088 | + | 2.01071i | ||||
\(690\) | −1.51045 | + | 0.872061i | −0.0575020 | + | 0.0331988i | ||||
\(691\) | −33.3914 | − | 19.2785i | −1.27027 | − | 0.733390i | −0.295230 | − | 0.955426i | \(-0.595396\pi\) |
−0.975038 | + | 0.222036i | \(0.928730\pi\) | |||||||
\(692\) | 32.4713i | 1.23438i | ||||||||
\(693\) | −10.3212 | + | 5.67013i | −0.392069 | + | 0.215391i | ||||
\(694\) | − | 37.3698i | − | 1.41854i | ||||||
\(695\) | 3.75542 | − | 6.50459i | 0.142451 | − | 0.246733i | ||||
\(696\) | −3.49390 | − | 6.05161i | −0.132436 | − | 0.229386i | ||||
\(697\) | 32.1086 | + | 13.0430i | 1.21620 | + | 0.494039i | ||||
\(698\) | −29.7032 | + | 51.4474i | −1.12428 | + | 1.94731i | ||||
\(699\) | 9.49642 | 0.359188 | ||||||||
\(700\) | −35.6864 | − | 0.758100i | −1.34882 | − | 0.0286535i | ||||
\(701\) | −25.5314 | −0.964308 | −0.482154 | − | 0.876087i | \(-0.660145\pi\) | ||||
−0.482154 | + | 0.876087i | \(0.660145\pi\) | |||||||
\(702\) | 9.54676 | + | 5.51183i | 0.360319 | + | 0.208030i | ||||
\(703\) | 16.3639 | − | 9.44771i | 0.617177 | − | 0.356327i | ||||
\(704\) | 49.7889 | − | 28.7456i | 1.87649 | − | 1.08339i | ||||
\(705\) | 3.30787 | − | 5.72940i | 0.124582 | − | 0.215782i | ||||
\(706\) | 24.7375 | 0.931007 | ||||||||
\(707\) | −7.46166 | + | 12.3124i | −0.280625 | + | 0.463057i | ||||
\(708\) | − | 4.75383i | − | 0.178660i | ||||||
\(709\) | 30.6327 | + | 17.6858i | 1.15043 | + | 0.664203i | 0.948993 | − | 0.315297i | \(-0.102104\pi\) |
0.201441 | + | 0.979501i | \(0.435438\pi\) | |||||||
\(710\) | −6.61744 | − | 11.4617i | −0.248348 | − | 0.430152i | ||||
\(711\) | 12.5774 | − | 7.26158i | 0.471691 | − | 0.272331i | ||||
\(712\) | −4.01511 | + | 6.95438i | −0.150473 | + | 0.260626i | ||||
\(713\) | 4.48268 | 0.167878 | ||||||||
\(714\) | 2.81740 | + | 24.0730i | 0.105439 | + | 0.900908i | ||||
\(715\) | 14.0659 | 0.526036 | ||||||||
\(716\) | 8.61832 | − | 14.9274i | 0.322082 | − | 0.557862i | ||||
\(717\) | −9.95040 | + | 5.74487i | −0.371605 | + | 0.214546i | ||||
\(718\) | 7.53199 | + | 13.0458i | 0.281091 | + | 0.486864i | ||||
\(719\) | 0.253848 | + | 0.146559i | 0.00946693 | + | 0.00546573i | 0.504726 | − | 0.863280i | \(-0.331594\pi\) |
−0.495259 | + | 0.868745i | \(0.664927\pi\) | |||||||
\(720\) | − | 0.796131i | − | 0.0296701i | ||||||
\(721\) | −30.1834 | − | 0.641197i | −1.12409 | − | 0.0238794i | ||||
\(722\) | 30.0712 | 1.11913 | ||||||||
\(723\) | −6.61255 | + | 11.4533i | −0.245924 | + | 0.425952i | ||||
\(724\) | 29.6751 | − | 17.1329i | 1.10287 | − | 0.636741i | ||||
\(725\) | 13.3619 | − | 7.71449i | 0.496248 | − | 0.286509i | ||||
\(726\) | −16.9538 | − | 9.78827i | −0.629214 | − | 0.363277i | ||||
\(727\) | −8.78145 | −0.325686 | −0.162843 | − | 0.986652i | \(-0.552066\pi\) | ||||
−0.162843 | + | 0.986652i | \(0.552066\pi\) | |||||||
\(728\) | −13.1516 | − | 23.9394i | −0.487430 | − | 0.887255i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 6.00395 | − | 10.3991i | 0.222216 | − | 0.384890i | ||||
\(731\) | −4.58284 | + | 11.2818i | −0.169502 | + | 0.417273i | ||||
\(732\) | −11.3091 | − | 19.5880i | −0.417997 | − | 0.723992i | ||||
\(733\) | 17.9304 | − | 31.0564i | 0.662275 | − | 1.14709i | −0.317741 | − | 0.948177i | \(-0.602924\pi\) |
0.980016 | − | 0.198917i | \(-0.0637423\pi\) | |||||||
\(734\) | − | 61.5425i | − | 2.27158i | ||||||
\(735\) | 2.39126 | − | 3.76310i | 0.0882031 | − | 0.138804i | ||||
\(736\) | − | 8.55148i | − | 0.315212i | ||||||
\(737\) | −34.1816 | − | 19.7347i | −1.25909 | − | 0.726939i | ||||
\(738\) | 16.1735 | − | 9.33775i | 0.595353 | − | 0.343727i | ||||
\(739\) | −11.0541 | − | 19.1462i | −0.406631 | − | 0.704306i | 0.587879 | − | 0.808949i | \(-0.299963\pi\) |
−0.994510 | + | 0.104643i | \(0.966630\pi\) | |||||||
\(740\) | 3.09804 | − | 5.36596i | 0.113886 | − | 0.197256i | ||||
\(741\) | − | 28.3001i | − | 1.03963i | ||||||
\(742\) | 34.7666 | + | 63.2847i | 1.27632 | + | 2.32325i | ||||
\(743\) | 22.7670i | 0.835241i | 0.908622 | + | 0.417620i | \(0.137136\pi\) | ||||
−0.908622 | + | 0.417620i | \(0.862864\pi\) | |||||||
\(744\) | 3.78411 | − | 6.55427i | 0.138732 | − | 0.240291i | ||||
\(745\) | −6.17993 | + | 3.56798i | −0.226415 | + | 0.130721i | ||||
\(746\) | 31.7974 | + | 55.0747i | 1.16419 | + | 2.01643i | ||||
\(747\) | 0.588071 | − | 1.01857i | 0.0215164 | − | 0.0372675i | ||||
\(748\) | −42.5283 | + | 33.0982i | −1.55499 | + | 1.21019i | ||||
\(749\) | −0.680720 | + | 32.0438i | −0.0248730 | + | 1.17086i | ||||
\(750\) | −13.5776 | −0.495784 | ||||||||
\(751\) | 29.3570 | + | 16.9493i | 1.07125 | + | 0.618488i | 0.928523 | − | 0.371274i | \(-0.121079\pi\) |
0.142729 | + | 0.989762i | \(0.454412\pi\) | |||||||
\(752\) | 6.49132 | + | 11.2433i | 0.236714 | + | 0.410001i | ||||
\(753\) | −1.60083 | + | 0.924241i | −0.0583376 | + | 0.0336812i | ||||
\(754\) | 32.0607 | + | 18.5103i | 1.16758 | + | 0.674105i | ||||
\(755\) | 8.68897i | 0.316224i | ||||||||
\(756\) | 6.64437 | + | 4.02666i | 0.241653 | + | 0.146448i | ||||
\(757\) | −47.8187 | −1.73800 | −0.869000 | − | 0.494813i | \(-0.835237\pi\) | ||||
−0.869000 | + | 0.494813i | \(0.835237\pi\) | |||||||
\(758\) | 52.4315 | + | 30.2713i | 1.90440 | + | 1.09950i | ||||
\(759\) | −4.75062 | + | 2.74277i | −0.172437 | + | 0.0995564i | ||||
\(760\) | 6.54674 | − | 3.77976i | 0.237475 | − | 0.137106i | ||||
\(761\) | −8.17259 | + | 14.1553i | −0.296256 | + | 0.513131i | −0.975276 | − | 0.220989i | \(-0.929072\pi\) |
0.679020 | + | 0.734120i | \(0.262405\pi\) | |||||||
\(762\) | − | 39.1848i | − | 1.41952i | ||||||
\(763\) | −26.4154 | − | 16.0084i | −0.956301 | − | 0.579544i | ||||
\(764\) | −46.2954 | −1.67491 | ||||||||
\(765\) | 0.360603 | + | 2.60130i | 0.0130376 | + | 0.0940504i | ||||
\(766\) | −39.4117 | − | 68.2630i | −1.42400 | − | 2.46644i | ||||
\(767\) | 4.01604 | + | 6.95598i | 0.145011 | + | 0.251166i | ||||
\(768\) | −6.14604 | − | 3.54842i | −0.221776 | − | 0.128043i | ||||
\(769\) | 4.74962 | 0.171276 | 0.0856378 | − | 0.996326i | \(-0.472707\pi\) | ||||
0.0856378 | + | 0.996326i | \(0.472707\pi\) | |||||||
\(770\) | 16.6615 | + | 0.353947i | 0.600439 | + | 0.0127554i | ||||
\(771\) | 7.00393i | 0.252240i | ||||||||
\(772\) | 4.64052 | + | 2.67920i | 0.167016 | + | 0.0964267i | ||||
\(773\) | 6.84878 | + | 11.8624i | 0.246333 | + | 0.426662i | 0.962506 | − | 0.271262i | \(-0.0874408\pi\) |
−0.716172 | + | 0.697924i | \(0.754108\pi\) | |||||||
\(774\) | 3.28095 | + | 5.68276i | 0.117931 | + | 0.204263i | ||||
\(775\) | 14.4718 | + | 8.35527i | 0.519841 | + | 0.300130i | ||||
\(776\) | 26.9323i | 0.966812i | ||||||||
\(777\) | −4.22012 | − | 7.68176i | −0.151396 | − | 0.275582i | ||||
\(778\) | 39.8795 | 1.42975 | ||||||||
\(779\) | −41.5207 | − | 23.9720i | −1.48763 | − | 0.858885i | ||||
\(780\) | −4.63999 | − | 8.03670i | −0.166138 | − | 0.287760i | ||||
\(781\) | −20.8129 | − | 36.0491i | −0.744746 | − | 1.28994i | ||||
\(782\) | 1.55027 | + | 11.1832i | 0.0554375 | + | 0.399912i | ||||
\(783\) | −3.35828 | −0.120015 | ||||||||
\(784\) | 4.04901 | + | 7.75623i | 0.144607 | + | 0.277008i | ||||
\(785\) | − | 0.214648i | − | 0.00766110i | ||||||
\(786\) | −13.8403 | + | 23.9721i | −0.493667 | + | 0.855056i | ||||
\(787\) | −42.8464 | + | 24.7374i | −1.52731 | + | 0.881793i | −0.527838 | + | 0.849345i | \(0.676997\pi\) |
−0.999473 | + | 0.0324481i | \(0.989670\pi\) | |||||||
\(788\) | −44.6070 | + | 25.7538i | −1.58906 | + | 0.917443i | ||||
\(789\) | −4.17595 | − | 2.41099i | −0.148668 | − | 0.0858333i | ||||
\(790\) | −20.5528 | −0.731236 | ||||||||
\(791\) | −9.72089 | + | 5.34035i | −0.345635 | + | 0.189881i | ||||
\(792\) | 9.26139i | 0.329089i | ||||||||
\(793\) | 33.0958 | + | 19.1079i | 1.17527 | + | 0.678541i | ||||
\(794\) | −32.4142 | + | 18.7143i | −1.15034 | + | 0.664147i | ||||
\(795\) | 3.91185 | + | 6.77553i | 0.138739 | + | 0.240303i | ||||
\(796\) | 31.0279 | + | 17.9140i | 1.09976 | + | 0.634944i | ||||
\(797\) | −19.8771 | −0.704082 | −0.352041 | − | 0.935985i | \(-0.614512\pi\) | ||||
−0.352041 | + | 0.935985i | \(0.614512\pi\) | |||||||
\(798\) | 0.712126 | − | 33.5222i | 0.0252090 | − | 1.18667i | ||||
\(799\) | −26.3025 | − | 33.7965i | −0.930517 | − | 1.19563i | ||||
\(800\) | 15.9391 | − | 27.6074i | 0.563533 | − | 0.976068i | ||||
\(801\) | 1.92963 | + | 3.34222i | 0.0681802 | + | 0.118092i | ||||
\(802\) | −61.0653 | + | 35.2561i | −2.15629 | + | 1.24493i | ||||
\(803\) | 18.8834 | − | 32.7070i | 0.666381 | − | 1.15421i | ||||
\(804\) | 26.0399i | 0.918357i | ||||||||
\(805\) | 1.07642 | − | 1.77619i | 0.0379387 | − | 0.0626024i | ||||
\(806\) | 40.0956i | 1.41231i | ||||||||
\(807\) | 8.04171 | − | 13.9286i | 0.283081 | − | 0.490311i | ||||
\(808\) | 5.66128 | + | 9.80562i | 0.199163 | + | 0.344961i | ||||
\(809\) | 18.8332 | − | 10.8734i | 0.662140 | − | 0.382287i | −0.130952 | − | 0.991389i | \(-0.541803\pi\) |
0.793092 | + | 0.609102i | \(0.208470\pi\) | |||||||
\(810\) | 1.22558 | + | 0.707587i | 0.0430624 | + | 0.0248621i | ||||
\(811\) | 1.15024i | 0.0403905i | 0.999796 | + | 0.0201952i | \(0.00642878\pi\) | ||||
−0.999796 | + | 0.0201952i | \(0.993571\pi\) | |||||||
\(812\) | 22.3137 | + | 13.5227i | 0.783057 | + | 0.474553i | ||||
\(813\) | − | 28.2459i | − | 0.990628i | ||||||
\(814\) | 16.3802 | − | 28.3713i | 0.574125 | − | 0.994413i | ||||
\(815\) | 1.66233 | + | 2.87923i | 0.0582287 | + | 0.100855i | ||||
\(816\) | −4.77468 | − | 1.93955i | −0.167147 | − | 0.0678977i | ||||
\(817\) | 8.42288 | − | 14.5889i | 0.294679 | − | 0.510400i | ||||
\(818\) | 31.6369 | 1.10616 | ||||||||
\(819\) | −13.1240 | − | 0.278799i | −0.458590 | − | 0.00974201i | ||||
\(820\) | −15.7215 | −0.549018 | ||||||||
\(821\) | −42.8081 | − | 24.7153i | −1.49401 | − | 0.862569i | −0.494038 | − | 0.869441i | \(-0.664479\pi\) |
−0.999976 | + | 0.00687127i | \(0.997813\pi\) | |||||||
\(822\) | 35.0835 | − | 20.2554i | 1.22368 | − | 0.706490i | ||||
\(823\) | 8.27176 | − | 4.77570i | 0.288335 | − | 0.166471i | −0.348856 | − | 0.937177i | \(-0.613430\pi\) |
0.637191 | + | 0.770706i | \(0.280096\pi\) | |||||||
\(824\) | −11.8716 | + | 20.5622i | −0.413567 | + | 0.716318i | ||||
\(825\) | −20.4491 | −0.711945 | ||||||||
\(826\) | 4.58208 | + | 8.34062i | 0.159431 | + | 0.290207i | ||||
\(827\) | 56.8626i | 1.97731i | 0.150219 | + | 0.988653i | \(0.452002\pi\) | ||||
−0.150219 | + | 0.988653i | \(0.547998\pi\) | |||||||
\(828\) | 3.13422 | + | 1.80954i | 0.108922 | + | 0.0628859i | ||||
\(829\) | 21.4785 | + | 37.2019i | 0.745981 | + | 1.29208i | 0.949735 | + | 0.313055i | \(0.101352\pi\) |
−0.203754 | + | 0.979022i | \(0.565314\pi\) | |||||||
\(830\) | −1.44145 | + | 0.832223i | −0.0500335 | + | 0.0288869i | ||||
\(831\) | 5.67146 | − | 9.82327i | 0.196741 | − | 0.340765i | ||||
\(832\) | 64.0861 | 2.22179 | ||||||||
\(833\) | −16.7430 | − | 23.5090i | −0.580111 | − | 0.814538i | ||||
\(834\) | −26.1999 | −0.907227 | ||||||||
\(835\) | 6.24948 | − | 10.8244i | 0.216272 | − | 0.374595i | ||||
\(836\) | 64.5635 | − | 37.2758i | 2.23298 | − | 1.28921i | ||||
\(837\) | −1.81861 | − | 3.14993i | −0.0628605 | − | 0.108878i | ||||
\(838\) | 5.60016 | + | 3.23325i | 0.193454 | + | 0.111691i | ||||
\(839\) | 47.9465i | 1.65530i | 0.561246 | + | 0.827649i | \(0.310322\pi\) | ||||
−0.561246 | + | 0.827649i | \(0.689678\pi\) | |||||||
\(840\) | −1.68835 | − | 3.07325i | −0.0582536 | − | 0.106037i | ||||
\(841\) | 17.7219 | 0.611101 | ||||||||
\(842\) | −0.579061 | + | 1.00296i | −0.0199557 | + | 0.0345644i | ||||
\(843\) | −0.727034 | + | 0.419754i | −0.0250404 | + | 0.0144571i | ||||
\(844\) | 9.53178 | − | 5.50318i | 0.328097 | − | 0.189427i | ||||
\(845\) | 6.40790 | + | 3.69960i | 0.220438 | + | 0.127270i | ||||
\(846\) | −23.0775 | −0.793420 | ||||||||
\(847\) | 23.3065 | + | 0.495110i | 0.800821 | + | 0.0170122i | ||||
\(848\) | −15.3531 | −0.527229 | ||||||||
\(849\) | −9.32607 | + | 16.1532i | −0.320070 | + | 0.554377i | ||||
\(850\) | −15.8396 | + | 38.9932i | −0.543295 | + | 1.33746i | ||||
\(851\) | −2.04137 | − | 3.53576i | −0.0699772 | − | 0.121204i | ||||
\(852\) | −13.7313 | + | 23.7833i | −0.470427 | + | 0.814803i | ||||
\(853\) | − | 22.5926i | − | 0.773556i | −0.922173 | − | 0.386778i | \(-0.873588\pi\) | ||
0.922173 | − | 0.386778i | \(-0.126412\pi\) | |||||||
\(854\) | 38.7221 | + | 23.4666i | 1.32504 | + | 0.803012i | ||||
\(855\) | − | 3.63305i | − | 0.124248i | ||||||
\(856\) | 21.8296 | + | 12.6034i | 0.746122 | + | 0.430774i | ||||
\(857\) | −36.3637 | + | 20.9946i | −1.24216 | + | 0.717161i | −0.969533 | − | 0.244959i | \(-0.921225\pi\) |
−0.272626 | + | 0.962120i | \(0.587892\pi\) | |||||||
\(858\) | −24.5329 | − | 42.4922i | −0.837539 | − | 1.45066i | ||||
\(859\) | 27.1729 | − | 47.0649i | 0.927128 | − | 1.60583i | 0.139024 | − | 0.990289i | \(-0.455603\pi\) |
0.788103 | − | 0.615543i | \(-0.211063\pi\) | |||||||
\(860\) | − | 5.52396i | − | 0.188365i | ||||||
\(861\) | −11.5259 | + | 19.0188i | −0.392803 | + | 0.648161i | ||||
\(862\) | 55.4421i | 1.88837i | ||||||||
\(863\) | −27.7443 | + | 48.0545i | −0.944426 | + | 1.63579i | −0.187530 | + | 0.982259i | \(0.560048\pi\) |
−0.756896 | + | 0.653535i | \(0.773285\pi\) | |||||||
\(864\) | −6.00904 | + | 3.46932i | −0.204432 | + | 0.118029i | ||||
\(865\) | −3.52159 | − | 6.09957i | −0.119738 | − | 0.207392i | ||||
\(866\) | 9.77269 | − | 16.9268i | 0.332089 | − | 0.575196i | ||||
\(867\) | 16.4794 | + | 4.17467i | 0.559671 | + | 0.141779i | ||||
\(868\) | −0.600174 | + | 28.2523i | −0.0203712 | + | 0.958944i | ||||
\(869\) | −64.6420 | −2.19283 | ||||||||
\(870\) | 4.11584 | + | 2.37628i | 0.139540 | + | 0.0805634i | ||||
\(871\) | −21.9985 | − | 38.1026i | −0.745392 | − | 1.29106i | ||||
\(872\) | −21.0372 | + | 12.1458i | −0.712410 | + | 0.411310i | ||||
\(873\) | 11.2094 | + | 6.47173i | 0.379379 | + | 0.219035i | ||||
\(874\) | − | 15.6188i | − | 0.528315i | ||||||
\(875\) | 14.1706 | − | 7.78491i | 0.479055 | − | 0.263178i | ||||
\(876\) | −24.9166 | −0.841853 | ||||||||
\(877\) | 9.07889 | + | 5.24170i | 0.306572 | + | 0.177000i | 0.645392 | − | 0.763852i | \(-0.276694\pi\) |
−0.338819 | + | 0.940851i | \(0.610028\pi\) | |||||||
\(878\) | 8.56825 | − | 4.94688i | 0.289165 | − | 0.166949i | ||||
\(879\) | 2.59209 | − | 1.49655i | 0.0874292 | − | 0.0504772i | ||||
\(880\) | −1.77177 | + | 3.06880i | −0.0597264 | + | 0.103449i | ||||
\(881\) | 36.9043i | 1.24334i | 0.783280 | + | 0.621669i | \(0.213545\pi\) | ||||
−0.783280 | + | 0.621669i | \(0.786455\pi\) | |||||||
\(882\) | −15.5388 | − | 0.660490i | −0.523217 | − | 0.0222399i | ||||
\(883\) | 12.2155 | 0.411086 | 0.205543 | − | 0.978648i | \(-0.434104\pi\) | ||||
0.205543 | + | 0.978648i | \(0.434104\pi\) | |||||||
\(884\) | −59.5029 | + | 8.24854i | −2.00130 | + | 0.277428i | ||||
\(885\) | 0.515564 | + | 0.892983i | 0.0173305 | + | 0.0300173i | ||||
\(886\) | 34.6587 | + | 60.0307i | 1.16438 | + | 2.01677i | ||||
\(887\) | 26.0598 | + | 15.0457i | 0.875003 | + | 0.505183i | 0.869008 | − | 0.494799i | \(-0.164758\pi\) |
0.00599576 | + | 0.999982i | \(0.498091\pi\) | |||||||
\(888\) | −6.89299 | −0.231314 | ||||||||
\(889\) | 22.4671 | + | 40.8963i | 0.753524 | + | 1.37162i | ||||
\(890\) | − | 5.46154i | − | 0.183071i | ||||||
\(891\) | 3.85464 | + | 2.22548i | 0.129135 | + | 0.0745563i | ||||
\(892\) | 16.1175 | + | 27.9164i | 0.539655 | + | 0.934710i | ||||
\(893\) | 29.6224 | + | 51.3075i | 0.991276 | + | 1.71694i | ||||
\(894\) | 21.5573 | + | 12.4461i | 0.720983 | + | 0.416260i | ||||
\(895\) | 3.73870i | 0.124971i | ||||||||
\(896\) | 39.2043 | + | 0.832833i | 1.30972 | + | 0.0278230i | ||||
\(897\) | −6.11480 | −0.204167 | ||||||||
\(898\) | −67.5745 | − | 39.0142i | −2.25499 | − | 1.30192i | ||||
\(899\) | −6.10742 | − | 10.5784i | −0.203694 | − | 0.352808i | ||||
\(900\) | 6.74561 | + | 11.6837i | 0.224854 | + | 0.389458i | ||||
\(901\) | 50.1654 | − | 6.95413i | 1.67125 | − | 0.231676i | ||||
\(902\) | −83.1238 | −2.76772 | ||||||||
\(903\) | −6.68253 | − | 4.04979i | −0.222381 | − | 0.134769i | ||||
\(904\) | 8.72273i | 0.290114i | ||||||||
\(905\) | −3.71621 | + | 6.43666i | −0.123531 | + | 0.213962i | ||||
\(906\) | 26.2488 | − | 15.1547i | 0.872057 | − | 0.503483i | ||||
\(907\) | 19.0675 | − | 11.0086i | 0.633125 | − | 0.365535i | −0.148836 | − | 0.988862i | \(-0.547553\pi\) |
0.781961 | + | 0.623327i | \(0.214219\pi\) | |||||||
\(908\) | −27.6283 | − | 15.9512i | −0.916878 | − | 0.529360i | ||||
\(909\) | 5.44154 | 0.180484 | ||||||||
\(910\) | 15.8872 | + | 9.62807i | 0.526656 | + | 0.319167i | ||||
\(911\) | 7.91228i | 0.262146i | 0.991373 | + | 0.131073i | \(0.0418422\pi\) | ||||
−0.991373 | + | 0.131073i | \(0.958158\pi\) | |||||||
\(912\) | 6.17429 | + | 3.56473i | 0.204451 | + | 0.118040i | ||||
\(913\) | −4.53360 | + | 2.61748i | −0.150040 | + | 0.0866258i | ||||
\(914\) | 9.48207 | + | 16.4234i | 0.313639 | + | 0.543239i | ||||
\(915\) | 4.24872 | + | 2.45300i | 0.140458 | + | 0.0810936i | ||||
\(916\) | −28.0498 | −0.926790 | ||||||||
\(917\) | 0.700068 | − | 32.9546i | 0.0231183 | − | 1.08826i | ||||
\(918\) | 7.22942 | − | 5.62638i | 0.238606 | − | 0.185698i | ||||
\(919\) | −27.6410 | + | 47.8756i | −0.911792 | + | 1.57927i | −0.100261 | + | 0.994961i | \(0.531968\pi\) |
−0.811531 | + | 0.584309i | \(0.801366\pi\) | |||||||
\(920\) | −0.816694 | − | 1.41456i | −0.0269256 | − | 0.0466365i | ||||
\(921\) | −21.6949 | + | 12.5256i | −0.714871 | + | 0.412731i | ||||
\(922\) | −18.4097 | + | 31.8865i | −0.606290 | + | 1.05012i | ||||
\(923\) | − | 46.4008i | − | 1.52730i | ||||||
\(924\) | −16.6504 | − | 30.3082i | −0.547758 | − | 0.997068i | ||||
\(925\) | − | 15.2197i | − | 0.500419i | ||||||
\(926\) | 10.5175 | − | 18.2168i | 0.345626 | − | 0.598642i | ||||
\(927\) | 5.70540 | + | 9.88205i | 0.187390 | + | 0.324569i | ||||
\(928\) | −20.1801 | + | 11.6510i | −0.662444 | + | 0.382462i | ||||
\(929\) | 4.83852 | + | 2.79352i | 0.158747 | + | 0.0916524i | 0.577269 | − | 0.816554i | \(-0.304118\pi\) |
−0.418522 | + | 0.908207i | \(0.637452\pi\) | |||||||
\(930\) | 5.14731i | 0.168787i | ||||||||
\(931\) | 18.4772 | + | 35.3947i | 0.605565 | + | 1.16001i | ||||
\(932\) | 27.8863i | 0.913448i | ||||||||
\(933\) | 0.803381 | − | 1.39150i | 0.0263015 | − | 0.0455555i | ||||
\(934\) | −10.1984 | − | 17.6641i | −0.333701 | − | 0.577988i | ||||
\(935\) | 4.39915 | − | 10.8296i | 0.143868 | − | 0.354166i | ||||
\(936\) | −5.16188 | + | 8.94064i | −0.168721 | + | 0.292234i | ||||
\(937\) | −35.3405 | −1.15452 | −0.577262 | − | 0.816559i | \(-0.695879\pi\) | ||||
−0.577262 | + | 0.816559i | \(0.695879\pi\) | |||||||
\(938\) | −25.0991 | − | 45.6871i | −0.819515 | − | 1.49174i | ||||
\(939\) | −9.34780 | −0.305054 | ||||||||
\(940\) | 16.8244 | + | 9.71359i | 0.548753 | + | 0.316823i | ||||
\(941\) | −1.01029 | + | 0.583291i | −0.0329345 | + | 0.0190147i | −0.516377 | − | 0.856361i | \(-0.672720\pi\) |
0.483442 | + | 0.875376i | \(0.339386\pi\) | |||||||
\(942\) | −0.648436 | + | 0.374374i | −0.0211272 | + | 0.0121978i | ||||
\(943\) | −5.17963 | + | 8.97138i | −0.168672 | + | 0.292148i | ||||
\(944\) | −2.02347 | −0.0658584 | ||||||||
\(945\) | −1.68481 | − | 0.0357911i | −0.0548069 | − | 0.00116428i | ||||
\(946\) | − | 29.2067i | − | 0.949592i | ||||||
\(947\) | −44.5572 | − | 25.7251i | −1.44792 | − | 0.835955i | −0.449558 | − | 0.893251i | \(-0.648419\pi\) |
−0.998357 | + | 0.0572964i | \(0.981752\pi\) | |||||||
\(948\) | 21.3237 | + | 36.9338i | 0.692562 | + | 1.19955i | ||||
\(949\) | 36.4589 | − | 21.0495i | 1.18350 | − | 0.683297i | ||||
\(950\) | 29.1120 | − | 50.4234i | 0.944517 | − | 1.63595i | ||||
\(951\) | 22.3804 | 0.725736 | ||||||||
\(952\) | −22.5446 | + | 2.63853i | −0.730674 | + | 0.0855152i | ||||
\(953\) | −36.9788 | −1.19786 | −0.598930 | − | 0.800801i | \(-0.704407\pi\) | ||||
−0.598930 | + | 0.800801i | \(0.704407\pi\) | |||||||
\(954\) | 13.6456 | − | 23.6349i | 0.441793 | − | 0.765207i | ||||
\(955\) | 8.69634 | − | 5.02083i | 0.281407 | − | 0.162470i | ||||
\(956\) | −16.8699 | − | 29.2195i | −0.545610 | − | 0.945025i | ||||
\(957\) | 12.9450 | + | 7.47379i | 0.418452 | + | 0.241593i | ||||
\(958\) | 44.7533i | 1.44591i | ||||||||
\(959\) | −25.0020 | + | 41.2557i | −0.807358 | + | 1.33222i | ||||
\(960\) | 8.22713 | 0.265530 | ||||||||
\(961\) | −8.88528 | + | 15.3898i | −0.286622 | + | 0.496444i | ||||
\(962\) | 31.6258 | − | 18.2591i | 1.01966 | − | 0.588698i | ||||
\(963\) | 10.4912 | − | 6.05708i | 0.338073 | − | 0.195187i | ||||
\(964\) | −33.6327 | − | 19.4178i | −1.08324 | − | 0.625406i | ||||
\(965\) | −1.16226 | −0.0374145 | ||||||||
\(966\) | −7.24315 | − | 0.153869i | −0.233045 | − | 0.00495066i | ||||
\(967\) | 11.5339 | 0.370905 | 0.185453 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185453 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(968\) | 9.16682 | − | 15.8774i | 0.294633 | − | 0.510319i | ||||
\(969\) | −21.7887 | − | 8.85089i | −0.699954 | − | 0.284332i | ||||
\(970\) | −9.15862 | − | 15.8632i | −0.294066 | − | 0.509337i | ||||
\(971\) | 4.18925 | − | 7.25599i | 0.134439 | − | 0.232856i | −0.790944 | − | 0.611889i | \(-0.790410\pi\) |
0.925383 | + | 0.379033i | \(0.123743\pi\) | |||||||
\(972\) | − | 2.93651i | − | 0.0941886i | ||||||
\(973\) | 27.3442 | − | 15.0220i | 0.876614 | − | 0.481585i | ||||
\(974\) | 11.9914i | 0.384229i | ||||||||
\(975\) | −19.7409 | − | 11.3974i | −0.632213 | − | 0.365009i | ||||
\(976\) | −8.33762 | + | 4.81373i | −0.266881 | + | 0.154084i | ||||
\(977\) | −3.37704 | − | 5.84921i | −0.108041 | − | 0.187133i | 0.806935 | − | 0.590640i | \(-0.201124\pi\) |
−0.914977 | + | 0.403507i | \(0.867791\pi\) | |||||||
\(978\) | 5.79864 | − | 10.0435i | 0.185420 | − | 0.321157i | ||||
\(979\) | − | 17.1774i | − | 0.548993i | ||||||
\(980\) | 11.0504 | + | 7.02197i | 0.352991 | + | 0.224309i | ||||
\(981\) | 11.6744i | 0.372735i | ||||||||
\(982\) | 5.12652 | − | 8.87940i | 0.163594 | − | 0.283353i | ||||
\(983\) | 11.1391 | − | 6.43115i | 0.355281 | − | 0.205122i | −0.311728 | − | 0.950171i | \(-0.600908\pi\) |
0.667009 | + | 0.745050i | \(0.267574\pi\) | |||||||
\(984\) | 8.74490 | + | 15.1466i | 0.278777 | + | 0.482856i | ||||
\(985\) | 5.58612 | − | 9.67545i | 0.177989 | − | 0.308285i | ||||
\(986\) | 24.2784 | − | 18.8950i | 0.773183 | − | 0.601739i | ||||
\(987\) | 24.0854 | − | 13.2318i | 0.766647 | − | 0.421172i | ||||
\(988\) | 83.1034 | 2.64387 | ||||||||
\(989\) | −3.15222 | − | 1.81993i | −0.100235 | − | 0.0578705i | ||||
\(990\) | −3.14944 | − | 5.45499i | −0.100096 | − | 0.173371i | ||||
\(991\) | −45.5283 | + | 26.2858i | −1.44625 | + | 0.834995i | −0.998256 | − | 0.0590392i | \(-0.981196\pi\) |
−0.447998 | + | 0.894034i | \(0.647863\pi\) | |||||||
\(992\) | −21.8563 | − | 12.6187i | −0.693937 | − | 0.400645i | ||||
\(993\) | − | 18.3909i | − | 0.583617i | ||||||
\(994\) | 1.16760 | − | 54.9631i | 0.0370341 | − | 1.74332i | ||||
\(995\) | −7.77124 | −0.246365 | ||||||||
\(996\) | 2.99104 | + | 1.72688i | 0.0947746 | + | 0.0547181i | ||||
\(997\) | −4.36058 | + | 2.51758i | −0.138101 | + | 0.0797326i | −0.567459 | − | 0.823402i | \(-0.692073\pi\) |
0.429358 | + | 0.903135i | \(0.358740\pi\) | |||||||
\(998\) | 77.9376 | − | 44.9973i | 2.46707 | − | 1.42436i | ||||
\(999\) | −1.65636 | + | 2.86890i | −0.0524049 | + | 0.0907680i |
(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 | 357.2.p.a.16.3 | ✓ | 48 | |
7.4 | even | 3 | inner | 357.2.p.a.67.4 | yes | 48 | |
17.16 | even | 2 | inner | 357.2.p.a.16.4 | yes | 48 | |
119.67 | even | 6 | inner | 357.2.p.a.67.3 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
357.2.p.a.16.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
357.2.p.a.16.4 | yes | 48 | 17.16 | even | 2 | inner | |
357.2.p.a.67.3 | yes | 48 | 119.67 | even | 6 | inner | |
357.2.p.a.67.4 | yes | 48 | 7.4 | even | 3 | inner |