Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(53,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 53.3 | ||
Root | \(-0.132804 - 0.230024i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.53 |
Dual form | 91.2.e.c.79.3 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.632804 | − | 1.09605i | −0.447460 | − | 0.775024i | 0.550760 | − | 0.834664i | \(-0.314338\pi\) |
−0.998220 | + | 0.0596401i | \(0.981005\pi\) | |||||||
\(3\) | 1.31364 | − | 2.27529i | 0.758430 | − | 1.31364i | −0.185220 | − | 0.982697i | \(-0.559300\pi\) |
0.943651 | − | 0.330943i | \(-0.107367\pi\) | |||||||
\(4\) | 0.199118 | − | 0.344882i | 0.0995588 | − | 0.172441i | ||||
\(5\) | 1.45130 | + | 2.51373i | 0.649041 | + | 1.12417i | 0.983352 | + | 0.181709i | \(0.0581630\pi\) |
−0.334311 | + | 0.942463i | \(0.608504\pi\) | |||||||
\(6\) | −3.32511 | −1.35747 | ||||||||
\(7\) | −1.29536 | + | 2.30696i | −0.489599 | + | 0.871948i | ||||
\(8\) | −3.03523 | −1.07311 | ||||||||
\(9\) | −1.95130 | − | 3.37975i | −0.650433 | − | 1.12658i | ||||
\(10\) | 1.83678 | − | 3.18139i | 0.580840 | − | 1.00604i | ||||
\(11\) | −1.01828 | + | 1.76372i | −0.307024 | + | 0.531780i | −0.977710 | − | 0.209961i | \(-0.932666\pi\) |
0.670686 | + | 0.741741i | \(0.266000\pi\) | |||||||
\(12\) | −0.523138 | − | 0.906101i | −0.151017 | − | 0.261569i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.34825 | − | 0.0400756i | 0.894856 | − | 0.0107107i | ||||
\(15\) | 7.62594 | 1.96901 | ||||||||
\(16\) | 1.52247 | + | 2.63699i | 0.380617 | + | 0.659249i | ||||
\(17\) | −1.99933 | + | 3.46294i | −0.484909 | + | 0.839887i | −0.999850 | − | 0.0173386i | \(-0.994481\pi\) |
0.514941 | + | 0.857226i | \(0.327814\pi\) | |||||||
\(18\) | −2.46958 | + | 4.27744i | −0.582086 | + | 1.00820i | ||||
\(19\) | −3.48105 | − | 6.02935i | −0.798608 | − | 1.38323i | −0.920523 | − | 0.390688i | \(-0.872237\pi\) |
0.121915 | − | 0.992540i | \(-0.461096\pi\) | |||||||
\(20\) | 1.15592 | 0.258471 | ||||||||
\(21\) | 3.54736 | + | 5.97783i | 0.774098 | + | 1.30447i | ||||
\(22\) | 2.57749 | 0.549523 | ||||||||
\(23\) | 0.313640 | + | 0.543240i | 0.0653985 | + | 0.113273i | 0.896871 | − | 0.442293i | \(-0.145835\pi\) |
−0.831472 | + | 0.555566i | \(0.812501\pi\) | |||||||
\(24\) | −3.98720 | + | 6.90602i | −0.813883 | + | 1.40969i | ||||
\(25\) | −1.71254 | + | 2.96621i | −0.342509 | + | 0.593243i | ||||
\(26\) | −0.632804 | − | 1.09605i | −0.124103 | − | 0.214953i | ||||
\(27\) | −2.37138 | −0.456373 | ||||||||
\(28\) | 0.537699 | + | 0.906101i | 0.101615 | + | 0.171237i | ||||
\(29\) | 1.09606 | 0.203534 | 0.101767 | − | 0.994808i | \(-0.467550\pi\) | ||||
0.101767 | + | 0.994808i | \(0.467550\pi\) | |||||||
\(30\) | −4.82573 | − | 8.35841i | −0.881054 | − | 1.52603i | ||||
\(31\) | 5.21624 | − | 9.03479i | 0.936864 | − | 1.62270i | 0.165589 | − | 0.986195i | \(-0.447047\pi\) |
0.771275 | − | 0.636502i | \(-0.219619\pi\) | |||||||
\(32\) | −1.10838 | + | 1.91977i | −0.195935 | + | 0.339370i | ||||
\(33\) | 2.67531 | + | 4.63378i | 0.465712 | + | 0.806637i | ||||
\(34\) | 5.06074 | 0.867910 | ||||||||
\(35\) | −7.67901 | + | 0.0919110i | −1.29799 | + | 0.0155358i | ||||
\(36\) | −1.55415 | −0.259025 | ||||||||
\(37\) | 1.54268 | + | 2.67201i | 0.253616 | + | 0.439275i | 0.964519 | − | 0.264015i | \(-0.0850468\pi\) |
−0.710903 | + | 0.703290i | \(0.751713\pi\) | |||||||
\(38\) | −4.40565 | + | 7.63080i | −0.714690 | + | 1.23788i | ||||
\(39\) | 1.31364 | − | 2.27529i | 0.210351 | − | 0.364338i | ||||
\(40\) | −4.40502 | − | 7.62973i | −0.696496 | − | 1.20637i | ||||
\(41\) | −0.521150 | −0.0813900 | −0.0406950 | − | 0.999172i | \(-0.512957\pi\) | ||||
−0.0406950 | + | 0.999172i | \(0.512957\pi\) | |||||||
\(42\) | 4.30721 | − | 7.67088i | 0.664616 | − | 1.18364i | ||||
\(43\) | 0.329024 | 0.0501757 | 0.0250879 | − | 0.999685i | \(-0.492013\pi\) | ||||
0.0250879 | + | 0.999685i | \(0.492013\pi\) | |||||||
\(44\) | 0.405516 | + | 0.702374i | 0.0611338 | + | 0.105887i | ||||
\(45\) | 5.66384 | − | 9.81006i | 0.844316 | − | 1.46240i | ||||
\(46\) | 0.396945 | − | 0.687530i | 0.0585264 | − | 0.101371i | ||||
\(47\) | −5.27284 | − | 9.13283i | −0.769123 | − | 1.33216i | −0.938039 | − | 0.346530i | \(-0.887360\pi\) |
0.168916 | − | 0.985630i | \(-0.445973\pi\) | |||||||
\(48\) | 7.99991 | 1.15469 | ||||||||
\(49\) | −3.64409 | − | 5.97667i | −0.520585 | − | 0.853810i | ||||
\(50\) | 4.33482 | 0.613036 | ||||||||
\(51\) | 5.25280 | + | 9.09812i | 0.735540 | + | 1.27399i | ||||
\(52\) | 0.199118 | − | 0.344882i | 0.0276126 | − | 0.0478265i | ||||
\(53\) | −3.55950 | + | 6.16523i | −0.488935 | + | 0.846860i | −0.999919 | − | 0.0127302i | \(-0.995948\pi\) |
0.510984 | + | 0.859590i | \(0.329281\pi\) | |||||||
\(54\) | 1.50062 | + | 2.59915i | 0.204209 | + | 0.353700i | ||||
\(55\) | −5.91133 | −0.797084 | ||||||||
\(56\) | 3.93171 | − | 7.00214i | 0.525396 | − | 0.935700i | ||||
\(57\) | −18.2914 | −2.42275 | ||||||||
\(58\) | −0.693593 | − | 1.20134i | −0.0910733 | − | 0.157744i | ||||
\(59\) | −1.01828 | + | 1.76372i | −0.132569 | + | 0.229616i | −0.924666 | − | 0.380779i | \(-0.875656\pi\) |
0.792097 | + | 0.610395i | \(0.208989\pi\) | |||||||
\(60\) | 1.51846 | − | 2.63005i | 0.196032 | − | 0.339538i | ||||
\(61\) | −1.20041 | − | 2.07917i | −0.153696 | − | 0.266210i | 0.778887 | − | 0.627164i | \(-0.215784\pi\) |
−0.932584 | + | 0.360954i | \(0.882451\pi\) | |||||||
\(62\) | −13.2034 | −1.67684 | ||||||||
\(63\) | 10.3246 | − | 0.123576i | 1.30077 | − | 0.0155691i | ||||
\(64\) | 8.89542 | 1.11193 | ||||||||
\(65\) | 1.45130 | + | 2.51373i | 0.180012 | + | 0.311789i | ||||
\(66\) | 3.38590 | − | 5.86455i | 0.416775 | − | 0.721876i | ||||
\(67\) | −7.34709 | + | 12.7255i | −0.897589 | + | 1.55467i | −0.0670226 | + | 0.997751i | \(0.521350\pi\) |
−0.830567 | + | 0.556919i | \(0.811983\pi\) | |||||||
\(68\) | 0.796204 | + | 1.37907i | 0.0965539 | + | 0.167236i | ||||
\(69\) | 1.64804 | 0.198401 | ||||||||
\(70\) | 4.96005 | + | 8.35841i | 0.592839 | + | 0.999021i | ||||
\(71\) | 3.60141 | 0.427409 | 0.213704 | − | 0.976898i | \(-0.431447\pi\) | ||||
0.213704 | + | 0.976898i | \(0.431447\pi\) | |||||||
\(72\) | 5.92264 | + | 10.2583i | 0.697990 | + | 1.20895i | ||||
\(73\) | −1.48786 | + | 2.57706i | −0.174141 | + | 0.301622i | −0.939864 | − | 0.341550i | \(-0.889048\pi\) |
0.765722 | + | 0.643171i | \(0.222382\pi\) | |||||||
\(74\) | 1.95243 | − | 3.38172i | 0.226966 | − | 0.393117i | ||||
\(75\) | 4.49933 | + | 7.79307i | 0.519538 | + | 0.899866i | ||||
\(76\) | −2.77255 | −0.318034 | ||||||||
\(77\) | −2.74978 | − | 4.63378i | −0.313366 | − | 0.528068i | ||||
\(78\) | −3.32511 | −0.376494 | ||||||||
\(79\) | 4.38075 | + | 7.58769i | 0.492873 | + | 0.853681i | 0.999966 | − | 0.00820995i | \(-0.00261334\pi\) |
−0.507093 | + | 0.861891i | \(0.669280\pi\) | |||||||
\(80\) | −4.41912 | + | 7.65414i | −0.494073 | + | 0.855759i | ||||
\(81\) | 2.73876 | − | 4.74367i | 0.304306 | − | 0.527074i | ||||
\(82\) | 0.329786 | + | 0.571206i | 0.0364188 | + | 0.0630792i | ||||
\(83\) | 12.8039 | 1.40541 | 0.702703 | − | 0.711483i | \(-0.251976\pi\) | ||||
0.702703 | + | 0.711483i | \(0.251976\pi\) | |||||||
\(84\) | 2.76799 | − | 0.0331304i | 0.302012 | − | 0.00361482i | ||||
\(85\) | −11.6065 | −1.25890 | ||||||||
\(86\) | −0.208208 | − | 0.360627i | −0.0224516 | − | 0.0388874i | ||||
\(87\) | 1.43983 | − | 2.49386i | 0.154366 | − | 0.267370i | ||||
\(88\) | 3.09072 | − | 5.35328i | 0.329471 | − | 0.570661i | ||||
\(89\) | 1.34049 | + | 2.32180i | 0.142092 | + | 0.246110i | 0.928284 | − | 0.371872i | \(-0.121284\pi\) |
−0.786192 | + | 0.617982i | \(0.787950\pi\) | |||||||
\(90\) | −14.3364 | −1.51119 | ||||||||
\(91\) | −1.29536 | + | 2.30696i | −0.135790 | + | 0.241835i | ||||
\(92\) | 0.249805 | 0.0260440 | ||||||||
\(93\) | −13.7045 | − | 23.7369i | −1.42109 | − | 2.46141i | ||||
\(94\) | −6.67335 | + | 11.5586i | −0.688304 | + | 1.19218i | ||||
\(95\) | 10.1041 | − | 17.5008i | 1.03666 | − | 1.79554i | ||||
\(96\) | 2.91202 | + | 5.04376i | 0.297206 | + | 0.514777i | ||||
\(97\) | −2.32902 | −0.236477 | −0.118238 | − | 0.992985i | \(-0.537725\pi\) | ||||
−0.118238 | + | 0.992985i | \(0.537725\pi\) | |||||||
\(98\) | −4.24472 | + | 7.77617i | −0.428782 | + | 0.785512i | ||||
\(99\) | 7.94789 | 0.798793 | ||||||||
\(100\) | 0.681995 | + | 1.18125i | 0.0681995 | + | 0.118125i | ||||
\(101\) | −0.726620 | + | 1.25854i | −0.0723014 | + | 0.125230i | −0.899910 | − | 0.436077i | \(-0.856368\pi\) |
0.827608 | + | 0.561306i | \(0.189701\pi\) | |||||||
\(102\) | 6.64799 | − | 11.5147i | 0.658249 | − | 1.14012i | ||||
\(103\) | 5.81765 | + | 10.0765i | 0.573230 | + | 0.992864i | 0.996231 | + | 0.0867346i | \(0.0276432\pi\) |
−0.423001 | + | 0.906129i | \(0.639023\pi\) | |||||||
\(104\) | −3.03523 | −0.297628 | ||||||||
\(105\) | −9.87833 | + | 17.5927i | −0.964026 | + | 1.71687i | ||||
\(106\) | 9.00987 | 0.875115 | ||||||||
\(107\) | −9.81297 | − | 16.9966i | −0.948656 | − | 1.64312i | −0.748261 | − | 0.663405i | \(-0.769111\pi\) |
−0.200395 | − | 0.979715i | \(-0.564223\pi\) | |||||||
\(108\) | −0.472184 | + | 0.817847i | −0.0454359 | + | 0.0786973i | ||||
\(109\) | 0.553378 | − | 0.958479i | 0.0530040 | − | 0.0918057i | −0.838306 | − | 0.545200i | \(-0.816454\pi\) |
0.891310 | + | 0.453394i | \(0.149787\pi\) | |||||||
\(110\) | 3.74071 | + | 6.47911i | 0.356663 | + | 0.617759i | ||||
\(111\) | 8.10613 | 0.769400 | ||||||||
\(112\) | −8.05557 | + | 0.0964182i | −0.761180 | + | 0.00911066i | ||||
\(113\) | −1.09606 | −0.103109 | −0.0515545 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515545 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(114\) | 11.5749 | + | 20.0483i | 1.08409 | + | 1.87769i | ||||
\(115\) | −0.910371 | + | 1.57681i | −0.0848926 | + | 0.147038i | ||||
\(116\) | 0.218245 | − | 0.378012i | 0.0202636 | − | 0.0350975i | ||||
\(117\) | −1.95130 | − | 3.37975i | −0.180398 | − | 0.312458i | ||||
\(118\) | 2.57749 | 0.237277 | ||||||||
\(119\) | −5.39901 | − | 9.09812i | −0.494926 | − | 0.834024i | ||||
\(120\) | −23.1465 | −2.11297 | ||||||||
\(121\) | 3.42620 | + | 5.93436i | 0.311473 | + | 0.539487i | ||||
\(122\) | −1.51925 | + | 2.63141i | −0.137546 | + | 0.238237i | ||||
\(123\) | −0.684604 | + | 1.18577i | −0.0617286 | + | 0.106917i | ||||
\(124\) | −2.07729 | − | 3.59797i | −0.186546 | − | 0.323107i | ||||
\(125\) | 4.57134 | 0.408873 | ||||||||
\(126\) | −6.66888 | − | 11.2380i | −0.594111 | − | 1.00116i | ||||
\(127\) | 5.18143 | 0.459778 | 0.229889 | − | 0.973217i | \(-0.426164\pi\) | ||||
0.229889 | + | 0.973217i | \(0.426164\pi\) | |||||||
\(128\) | −3.41231 | − | 5.91029i | −0.301608 | − | 0.522400i | ||||
\(129\) | 0.432219 | − | 0.748626i | 0.0380548 | − | 0.0659128i | ||||
\(130\) | 1.83678 | − | 3.18139i | 0.161096 | − | 0.279027i | ||||
\(131\) | −5.28335 | − | 9.15103i | −0.461609 | − | 0.799530i | 0.537433 | − | 0.843307i | \(-0.319394\pi\) |
−0.999041 | + | 0.0437770i | \(0.986061\pi\) | |||||||
\(132\) | 2.13081 | 0.185463 | ||||||||
\(133\) | 18.4187 | − | 0.220455i | 1.59710 | − | 0.0191159i | ||||
\(134\) | 18.5971 | 1.60654 | ||||||||
\(135\) | −3.44159 | − | 5.96101i | −0.296205 | − | 0.513042i | ||||
\(136\) | 6.06842 | − | 10.5108i | 0.520363 | − | 0.901295i | ||||
\(137\) | 2.93589 | − | 5.08510i | 0.250830 | − | 0.434450i | −0.712925 | − | 0.701241i | \(-0.752630\pi\) |
0.963754 | + | 0.266791i | \(0.0859632\pi\) | |||||||
\(138\) | −1.04289 | − | 1.80633i | −0.0887764 | − | 0.153765i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −1.49733 | + | 2.66665i | −0.126547 | + | 0.225373i | ||||
\(141\) | −27.7065 | −2.33331 | ||||||||
\(142\) | −2.27899 | − | 3.94732i | −0.191248 | − | 0.331252i | ||||
\(143\) | −1.01828 | + | 1.76372i | −0.0851530 | + | 0.147489i | ||||
\(144\) | 5.94159 | − | 10.2911i | 0.495132 | − | 0.857594i | ||||
\(145\) | 1.59072 | + | 2.75520i | 0.132102 | + | 0.228807i | ||||
\(146\) | 3.76611 | 0.311685 | ||||||||
\(147\) | −18.3857 | + | 0.440185i | −1.51643 | + | 0.0363058i | ||||
\(148\) | 1.22870 | 0.100999 | ||||||||
\(149\) | 5.05271 | + | 8.75155i | 0.413934 | + | 0.716955i | 0.995316 | − | 0.0966760i | \(-0.0308211\pi\) |
−0.581382 | + | 0.813631i | \(0.697488\pi\) | |||||||
\(150\) | 5.69439 | − | 9.86298i | 0.464945 | − | 0.805309i | ||||
\(151\) | 0.0938631 | − | 0.162576i | 0.00763847 | − | 0.0132302i | −0.862181 | − | 0.506601i | \(-0.830902\pi\) |
0.869819 | + | 0.493370i | \(0.164235\pi\) | |||||||
\(152\) | 10.5658 | + | 18.3005i | 0.856998 | + | 1.48436i | ||||
\(153\) | 15.6052 | 1.26160 | ||||||||
\(154\) | −3.33878 | + | 5.94616i | −0.269046 | + | 0.479155i | ||||
\(155\) | 30.2813 | 2.43225 | ||||||||
\(156\) | −0.523138 | − | 0.906101i | −0.0418845 | − | 0.0725461i | ||||
\(157\) | 6.03590 | − | 10.4545i | 0.481717 | − | 0.834358i | −0.518063 | − | 0.855343i | \(-0.673347\pi\) |
0.999780 | + | 0.0209844i | \(0.00668003\pi\) | |||||||
\(158\) | 5.54432 | − | 9.60304i | 0.441082 | − | 0.763977i | ||||
\(159\) | 9.35180 | + | 16.1978i | 0.741646 | + | 1.28457i | ||||
\(160\) | −6.43435 | −0.508680 | ||||||||
\(161\) | −1.65951 | + | 0.0198629i | −0.130788 | + | 0.00156541i | ||||
\(162\) | −6.93239 | −0.544660 | ||||||||
\(163\) | −7.45678 | − | 12.9155i | −0.584060 | − | 1.01162i | −0.994992 | − | 0.0999554i | \(-0.968130\pi\) |
0.410932 | − | 0.911666i | \(-0.365203\pi\) | |||||||
\(164\) | −0.103770 | + | 0.179735i | −0.00810309 | + | 0.0140350i | ||||
\(165\) | −7.76536 | + | 13.4500i | −0.604532 | + | 1.04708i | ||||
\(166\) | −8.10234 | − | 14.0337i | −0.628863 | − | 1.08922i | ||||
\(167\) | 5.05664 | 0.391294 | 0.195647 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195647 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(168\) | −10.7671 | − | 18.1441i | −0.830696 | − | 1.39984i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 7.34465 | + | 12.7213i | 0.563309 | + | 0.975680i | ||||
\(171\) | −13.5851 | + | 23.5302i | −1.03888 | + | 1.79940i | ||||
\(172\) | 0.0655145 | − | 0.113474i | 0.00499543 | − | 0.00865235i | ||||
\(173\) | 0.297807 | + | 0.515817i | 0.0226419 | + | 0.0392169i | 0.877124 | − | 0.480263i | \(-0.159459\pi\) |
−0.854482 | + | 0.519480i | \(0.826126\pi\) | |||||||
\(174\) | −3.64453 | −0.276291 | ||||||||
\(175\) | −4.62457 | − | 7.79307i | −0.349584 | − | 0.589101i | ||||
\(176\) | −6.20121 | −0.467434 | ||||||||
\(177\) | 2.67531 | + | 4.63378i | 0.201089 | + | 0.348296i | ||||
\(178\) | 1.69654 | − | 2.93849i | 0.127161 | − | 0.220249i | ||||
\(179\) | −4.03832 | + | 6.99458i | −0.301838 | + | 0.522799i | −0.976552 | − | 0.215280i | \(-0.930934\pi\) |
0.674714 | + | 0.738079i | \(0.264267\pi\) | |||||||
\(180\) | −2.25554 | − | 3.90671i | −0.168118 | − | 0.291189i | ||||
\(181\) | 1.89324 | 0.140724 | 0.0703618 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703618 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(182\) | 3.34825 | − | 0.0400756i | 0.248188 | − | 0.00297060i | ||||
\(183\) | −6.30761 | −0.466272 | ||||||||
\(184\) | −0.951968 | − | 1.64886i | −0.0701800 | − | 0.121555i | ||||
\(185\) | −4.47780 | + | 7.75577i | −0.329214 | + | 0.570216i | ||||
\(186\) | −17.3446 | + | 30.0417i | −1.27176 | + | 2.20276i | ||||
\(187\) | −4.07177 | − | 7.05251i | −0.297757 | − | 0.515730i | ||||
\(188\) | −4.19966 | −0.306292 | ||||||||
\(189\) | 3.07179 | − | 5.47068i | 0.223440 | − | 0.397933i | ||||
\(190\) | −25.5757 | −1.85545 | ||||||||
\(191\) | −1.85087 | − | 3.20580i | −0.133924 | − | 0.231964i | 0.791262 | − | 0.611478i | \(-0.209425\pi\) |
−0.925186 | + | 0.379514i | \(0.876091\pi\) | |||||||
\(192\) | 11.6854 | − | 20.2397i | 0.843320 | − | 1.46067i | ||||
\(193\) | −6.79373 | + | 11.7671i | −0.489024 | + | 0.847014i | −0.999920 | − | 0.0126285i | \(-0.995980\pi\) |
0.510897 | + | 0.859642i | \(0.329313\pi\) | |||||||
\(194\) | 1.47382 | + | 2.55272i | 0.105814 | + | 0.183275i | ||||
\(195\) | 7.62594 | 0.546105 | ||||||||
\(196\) | −2.78685 | + | 0.0667218i | −0.199061 | + | 0.00476585i | ||||
\(197\) | −9.70258 | −0.691280 | −0.345640 | − | 0.938367i | \(-0.612338\pi\) | ||||
−0.345640 | + | 0.938367i | \(0.612338\pi\) | |||||||
\(198\) | −5.02946 | − | 8.71128i | −0.357428 | − | 0.619084i | ||||
\(199\) | −13.1360 | + | 22.7522i | −0.931185 | + | 1.61286i | −0.149885 | + | 0.988703i | \(0.547891\pi\) |
−0.781299 | + | 0.624156i | \(0.785443\pi\) | |||||||
\(200\) | 5.19796 | − | 9.00313i | 0.367551 | − | 0.636617i | ||||
\(201\) | 19.3029 | + | 33.4335i | 1.36152 | + | 2.35822i | ||||
\(202\) | 1.83923 | 0.129408 | ||||||||
\(203\) | −1.41979 | + | 2.52857i | −0.0996500 | + | 0.177471i | ||||
\(204\) | 4.18370 | 0.292918 | ||||||||
\(205\) | −0.756345 | − | 1.31003i | −0.0528255 | − | 0.0914964i | ||||
\(206\) | 7.36287 | − | 12.7529i | 0.512995 | − | 0.888534i | ||||
\(207\) | 1.22401 | − | 2.12005i | 0.0850747 | − | 0.147354i | ||||
\(208\) | 1.52247 | + | 2.63699i | 0.105564 | + | 0.182843i | ||||
\(209\) | 14.1788 | 0.980765 | ||||||||
\(210\) | 25.5335 | − | 0.305614i | 1.76198 | − | 0.0210894i | ||||
\(211\) | 10.0338 | 0.690758 | 0.345379 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345379 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(212\) | 1.41752 | + | 2.45521i | 0.0973555 | + | 0.168625i | ||||
\(213\) | 4.73096 | − | 8.19426i | 0.324160 | − | 0.561461i | ||||
\(214\) | −12.4194 | + | 21.5110i | −0.848971 | + | 1.47046i | ||||
\(215\) | 0.477513 | + | 0.827077i | 0.0325661 | + | 0.0564062i | ||||
\(216\) | 7.19769 | 0.489740 | ||||||||
\(217\) | 14.0860 | + | 23.7369i | 0.956218 | + | 1.61137i | ||||
\(218\) | −1.40072 | −0.0948688 | ||||||||
\(219\) | 3.90903 | + | 6.77065i | 0.264148 | + | 0.457518i | ||||
\(220\) | −1.17705 | + | 2.03871i | −0.0793567 | + | 0.137450i | ||||
\(221\) | −1.99933 | + | 3.46294i | −0.134490 | + | 0.232943i | ||||
\(222\) | −5.12959 | − | 8.88472i | −0.344276 | − | 0.596303i | ||||
\(223\) | 17.4961 | 1.17163 | 0.585813 | − | 0.810446i | \(-0.300775\pi\) | ||||
0.585813 | + | 0.810446i | \(0.300775\pi\) | |||||||
\(224\) | −2.99307 | − | 5.04376i | −0.199983 | − | 0.337000i | ||||
\(225\) | 13.3667 | 0.891116 | ||||||||
\(226\) | 0.693593 | + | 1.20134i | 0.0461371 | + | 0.0799119i | ||||
\(227\) | 4.75815 | − | 8.24136i | 0.315810 | − | 0.546998i | −0.663800 | − | 0.747910i | \(-0.731057\pi\) |
0.979609 | + | 0.200912i | \(0.0643906\pi\) | |||||||
\(228\) | −3.64214 | + | 6.30837i | −0.241206 | + | 0.417782i | ||||
\(229\) | −10.5585 | − | 18.2878i | −0.697725 | − | 1.20849i | −0.969254 | − | 0.246064i | \(-0.920863\pi\) |
0.271529 | − | 0.962430i | \(-0.412471\pi\) | |||||||
\(230\) | 2.30435 | 0.151944 | ||||||||
\(231\) | −14.1554 | + | 0.169428i | −0.931357 | + | 0.0111475i | ||||
\(232\) | −3.32680 | −0.218415 | ||||||||
\(233\) | −7.08938 | − | 12.2792i | −0.464441 | − | 0.804435i | 0.534735 | − | 0.845020i | \(-0.320411\pi\) |
−0.999176 | + | 0.0405847i | \(0.987078\pi\) | |||||||
\(234\) | −2.46958 | + | 4.27744i | −0.161442 | + | 0.279625i | ||||
\(235\) | 15.3050 | − | 26.5090i | 0.998385 | − | 1.72925i | ||||
\(236\) | 0.405516 | + | 0.702374i | 0.0263968 | + | 0.0457206i | ||||
\(237\) | 23.0189 | 1.49524 | ||||||||
\(238\) | −6.55547 | + | 11.6749i | −0.424928 | + | 0.756772i | ||||
\(239\) | −16.5275 | −1.06907 | −0.534536 | − | 0.845145i | \(-0.679514\pi\) | ||||
−0.534536 | + | 0.845145i | \(0.679514\pi\) | |||||||
\(240\) | 11.6103 | + | 20.1096i | 0.749439 | + | 1.29807i | ||||
\(241\) | 6.84450 | − | 11.8550i | 0.440893 | − | 0.763649i | −0.556863 | − | 0.830604i | \(-0.687995\pi\) |
0.997756 | + | 0.0669552i | \(0.0213284\pi\) | |||||||
\(242\) | 4.33623 | − | 7.51058i | 0.278744 | − | 0.482798i | ||||
\(243\) | −10.7526 | − | 18.6240i | −0.689777 | − | 1.19473i | ||||
\(244\) | −0.956089 | −0.0612073 | ||||||||
\(245\) | 9.73503 | − | 17.8342i | 0.621948 | − | 1.13938i | ||||
\(246\) | 1.73288 | 0.110484 | ||||||||
\(247\) | −3.48105 | − | 6.02935i | −0.221494 | − | 0.383639i | ||||
\(248\) | −15.8325 | + | 27.4226i | −1.00536 | + | 1.74134i | ||||
\(249\) | 16.8197 | − | 29.1325i | 1.06590 | − | 1.84620i | ||||
\(250\) | −2.89276 | − | 5.01042i | −0.182954 | − | 0.316886i | ||||
\(251\) | −14.6603 | −0.925349 | −0.462674 | − | 0.886528i | \(-0.653110\pi\) | ||||
−0.462674 | + | 0.886528i | \(0.653110\pi\) | |||||||
\(252\) | 2.01318 | − | 3.58536i | 0.126819 | − | 0.225857i | ||||
\(253\) | −1.27750 | −0.0803155 | ||||||||
\(254\) | −3.27883 | − | 5.67910i | −0.205732 | − | 0.356339i | ||||
\(255\) | −15.2468 | + | 26.4082i | −0.954791 | + | 1.65375i | ||||
\(256\) | 4.57678 | − | 7.92721i | 0.286049 | − | 0.495451i | ||||
\(257\) | 0.876387 | + | 1.51795i | 0.0546675 | + | 0.0946869i | 0.892064 | − | 0.451909i | \(-0.149257\pi\) |
−0.837397 | + | 0.546596i | \(0.815923\pi\) | |||||||
\(258\) | −1.09404 | −0.0681120 | ||||||||
\(259\) | −8.16254 | + | 0.0976985i | −0.507195 | + | 0.00607069i | ||||
\(260\) | 1.15592 | 0.0716870 | ||||||||
\(261\) | −2.13875 | − | 3.70442i | −0.132385 | − | 0.229298i | ||||
\(262\) | −6.68666 | + | 11.5816i | −0.413103 | + | 0.715515i | ||||
\(263\) | −13.4708 | + | 23.3321i | −0.830645 | + | 1.43872i | 0.0668823 | + | 0.997761i | \(0.478695\pi\) |
−0.897527 | + | 0.440959i | \(0.854639\pi\) | |||||||
\(264\) | −8.12018 | − | 14.0646i | −0.499762 | − | 0.865614i | ||||
\(265\) | −20.6636 | −1.26936 | ||||||||
\(266\) | −11.8970 | − | 20.0483i | −0.729454 | − | 1.22924i | ||||
\(267\) | 7.04370 | 0.431067 | ||||||||
\(268\) | 2.92587 | + | 5.06775i | 0.178726 | + | 0.309562i | ||||
\(269\) | 11.0346 | − | 19.1124i | 0.672789 | − | 1.16530i | −0.304321 | − | 0.952570i | \(-0.598430\pi\) |
0.977110 | − | 0.212735i | \(-0.0682371\pi\) | |||||||
\(270\) | −4.35570 | + | 7.54430i | −0.265080 | + | 0.459131i | ||||
\(271\) | 4.48105 | + | 7.76141i | 0.272204 | + | 0.471472i | 0.969426 | − | 0.245384i | \(-0.0789140\pi\) |
−0.697222 | + | 0.716856i | \(0.745581\pi\) | |||||||
\(272\) | −12.1757 | −0.738259 | ||||||||
\(273\) | 3.54736 | + | 5.97783i | 0.214696 | + | 0.361795i | ||||
\(274\) | −7.43137 | −0.448945 | ||||||||
\(275\) | −3.48770 | − | 6.04088i | −0.210316 | − | 0.364279i | ||||
\(276\) | 0.328154 | − | 0.568379i | 0.0197525 | − | 0.0342124i | ||||
\(277\) | 3.76463 | − | 6.52052i | 0.226194 | − | 0.391780i | −0.730483 | − | 0.682931i | \(-0.760705\pi\) |
0.956677 | + | 0.291151i | \(0.0940382\pi\) | |||||||
\(278\) | 2.53122 | + | 4.38420i | 0.151812 | + | 0.262947i | ||||
\(279\) | −40.7138 | −2.43747 | ||||||||
\(280\) | 23.3075 | − | 0.278971i | 1.39289 | − | 0.0166717i | ||||
\(281\) | 29.7762 | 1.77630 | 0.888151 | − | 0.459553i | \(-0.151990\pi\) | ||||
0.888151 | + | 0.459553i | \(0.151990\pi\) | |||||||
\(282\) | 17.5328 | + | 30.3676i | 1.04406 | + | 1.80837i | ||||
\(283\) | −0.150726 | + | 0.261064i | −0.00895970 | + | 0.0155187i | −0.870470 | − | 0.492221i | \(-0.836185\pi\) |
0.861511 | + | 0.507739i | \(0.169519\pi\) | |||||||
\(284\) | 0.717104 | − | 1.24206i | 0.0425523 | − | 0.0737027i | ||||
\(285\) | −26.5463 | − | 45.9795i | −1.57247 | − | 2.72359i | ||||
\(286\) | 2.57749 | 0.152410 | ||||||||
\(287\) | 0.675076 | − | 1.20227i | 0.0398485 | − | 0.0709678i | ||||
\(288\) | 8.65110 | 0.509771 | ||||||||
\(289\) | 0.505347 | + | 0.875286i | 0.0297263 | + | 0.0514874i | ||||
\(290\) | 2.01322 | − | 3.48701i | 0.118221 | − | 0.204764i | ||||
\(291\) | −3.05950 | + | 5.29921i | −0.179351 | + | 0.310645i | ||||
\(292\) | 0.592520 | + | 1.02627i | 0.0346746 | + | 0.0600582i | ||||
\(293\) | −19.2471 | −1.12443 | −0.562214 | − | 0.826992i | \(-0.690050\pi\) | ||||
−0.562214 | + | 0.826992i | \(0.690050\pi\) | |||||||
\(294\) | 12.1170 | + | 19.8731i | 0.706678 | + | 1.15902i | ||||
\(295\) | −5.91133 | −0.344171 | ||||||||
\(296\) | −4.68240 | − | 8.11015i | −0.272159 | − | 0.471393i | ||||
\(297\) | 2.41474 | − | 4.18245i | 0.140117 | − | 0.242690i | ||||
\(298\) | 6.39475 | − | 11.0760i | 0.370438 | − | 0.641618i | ||||
\(299\) | 0.313640 | + | 0.543240i | 0.0181383 | + | 0.0314164i | ||||
\(300\) | 3.58358 | 0.206898 | ||||||||
\(301\) | −0.426204 | + | 0.759044i | −0.0245660 | + | 0.0437506i | ||||
\(302\) | −0.237588 | −0.0136716 | ||||||||
\(303\) | 1.90903 | + | 3.30654i | 0.109671 | + | 0.189956i | ||||
\(304\) | 10.5996 | − | 18.3590i | 0.607928 | − | 1.05296i | ||||
\(305\) | 3.48430 | − | 6.03499i | 0.199511 | − | 0.345562i | ||||
\(306\) | −9.87503 | − | 17.1040i | −0.564518 | − | 0.977773i | ||||
\(307\) | −3.57779 | −0.204195 | −0.102098 | − | 0.994774i | \(-0.532555\pi\) | ||||
−0.102098 | + | 0.994774i | \(0.532555\pi\) | |||||||
\(308\) | −2.14563 | + | 0.0256814i | −0.122259 | + | 0.00146333i | ||||
\(309\) | 30.5692 | 1.73902 | ||||||||
\(310\) | −19.1621 | − | 33.1898i | −1.08834 | − | 1.88505i | ||||
\(311\) | 11.9153 | − | 20.6379i | 0.675655 | − | 1.17027i | −0.300622 | − | 0.953743i | \(-0.597194\pi\) |
0.976277 | − | 0.216526i | \(-0.0694725\pi\) | |||||||
\(312\) | −3.98720 | + | 6.90602i | −0.225730 | + | 0.390977i | ||||
\(313\) | 9.04068 | + | 15.6589i | 0.511009 | + | 0.885094i | 0.999919 | + | 0.0127596i | \(0.00406161\pi\) |
−0.488909 | + | 0.872335i | \(0.662605\pi\) | |||||||
\(314\) | −15.2782 | −0.862196 | ||||||||
\(315\) | 15.2947 | + | 25.7738i | 0.861758 | + | 1.45219i | ||||
\(316\) | 3.48914 | 0.196279 | ||||||||
\(317\) | 13.7741 | + | 23.8574i | 0.773630 | + | 1.33997i | 0.935561 | + | 0.353164i | \(0.114894\pi\) |
−0.161931 | + | 0.986802i | \(0.551772\pi\) | |||||||
\(318\) | 11.8357 | − | 20.5001i | 0.663714 | − | 1.14959i | ||||
\(319\) | −1.11610 | + | 1.93314i | −0.0624897 | + | 0.108235i | ||||
\(320\) | 12.9099 | + | 22.3606i | 0.721687 | + | 1.25000i | ||||
\(321\) | −51.5628 | −2.87796 | ||||||||
\(322\) | 1.07191 | + | 1.80633i | 0.0597355 | + | 0.100663i | ||||
\(323\) | 27.8391 | 1.54901 | ||||||||
\(324\) | −1.09067 | − | 1.88909i | −0.0605927 | − | 0.104950i | ||||
\(325\) | −1.71254 | + | 2.96621i | −0.0949948 | + | 0.164536i | ||||
\(326\) | −9.43736 | + | 16.3460i | −0.522687 | + | 0.905321i | ||||
\(327\) | −1.45388 | − | 2.51819i | −0.0803997 | − | 0.139256i | ||||
\(328\) | 1.58181 | 0.0873408 | ||||||||
\(329\) | 27.8993 | − | 0.333930i | 1.53814 | − | 0.0184101i | ||||
\(330\) | 19.6558 | 1.08202 | ||||||||
\(331\) | 9.09069 | + | 15.7455i | 0.499669 | + | 0.865453i | 1.00000 | 0.000381757i | \(-0.000121517\pi\) | |
−0.500331 | + | 0.865834i | \(0.666788\pi\) | |||||||
\(332\) | 2.54947 | − | 4.41582i | 0.139921 | − | 0.242350i | ||||
\(333\) | 6.02048 | − | 10.4278i | 0.329920 | − | 0.571439i | ||||
\(334\) | −3.19986 | − | 5.54232i | −0.175089 | − | 0.303262i | ||||
\(335\) | −42.6513 | −2.33029 | ||||||||
\(336\) | −10.3627 | + | 18.4554i | −0.565334 | + | 1.00683i | ||||
\(337\) | −17.1381 | −0.933572 | −0.466786 | − | 0.884370i | \(-0.654588\pi\) | ||||
−0.466786 | + | 0.884370i | \(0.654588\pi\) | |||||||
\(338\) | −0.632804 | − | 1.09605i | −0.0344200 | − | 0.0596172i | ||||
\(339\) | −1.43983 | + | 2.49386i | −0.0782010 | + | 0.135448i | ||||
\(340\) | −2.31106 | + | 4.00288i | −0.125335 | + | 0.217086i | ||||
\(341\) | 10.6232 | + | 18.3999i | 0.575279 | + | 0.996412i | ||||
\(342\) | 34.3869 | 1.85943 | ||||||||
\(343\) | 18.5083 | − | 0.664840i | 0.999355 | − | 0.0358980i | ||||
\(344\) | −0.998663 | −0.0538443 | ||||||||
\(345\) | 2.39180 | + | 4.14272i | 0.128770 | + | 0.223037i | ||||
\(346\) | 0.376907 | − | 0.652823i | 0.0202627 | − | 0.0350960i | ||||
\(347\) | −11.1344 | + | 19.2853i | −0.597725 | + | 1.03529i | 0.395431 | + | 0.918496i | \(0.370595\pi\) |
−0.993156 | + | 0.116794i | \(0.962738\pi\) | |||||||
\(348\) | −0.573392 | − | 0.993144i | −0.0307370 | − | 0.0532381i | ||||
\(349\) | 19.9368 | 1.06719 | 0.533595 | − | 0.845740i | \(-0.320841\pi\) | ||||
0.533595 | + | 0.845740i | \(0.320841\pi\) | |||||||
\(350\) | −5.61514 | + | 10.0002i | −0.300142 | + | 0.534535i | ||||
\(351\) | −2.37138 | −0.126575 | ||||||||
\(352\) | −2.25728 | − | 3.90972i | −0.120313 | − | 0.208389i | ||||
\(353\) | −11.4576 | + | 19.8451i | −0.609825 | + | 1.05625i | 0.381444 | + | 0.924392i | \(0.375427\pi\) |
−0.991269 | + | 0.131856i | \(0.957906\pi\) | |||||||
\(354\) | 3.38590 | − | 5.86455i | 0.179958 | − | 0.311697i | ||||
\(355\) | 5.22673 | + | 9.05296i | 0.277406 | + | 0.480481i | ||||
\(356\) | 1.06766 | 0.0565860 | ||||||||
\(357\) | −27.7932 | + | 0.332661i | −1.47097 | + | 0.0176063i | ||||
\(358\) | 10.2219 | 0.540242 | ||||||||
\(359\) | −13.6157 | − | 23.5831i | −0.718610 | − | 1.24467i | −0.961551 | − | 0.274628i | \(-0.911445\pi\) |
0.242940 | − | 0.970041i | \(-0.421888\pi\) | |||||||
\(360\) | −17.1910 | + | 29.7758i | −0.906048 | + | 1.56932i | ||||
\(361\) | −14.7354 | + | 25.5225i | −0.775548 | + | 1.34329i | ||||
\(362\) | −1.19805 | − | 2.07509i | −0.0629682 | − | 0.109064i | ||||
\(363\) | 18.0032 | 0.944923 | ||||||||
\(364\) | 0.537699 | + | 0.906101i | 0.0281831 | + | 0.0474926i | ||||
\(365\) | −8.63735 | −0.452099 | ||||||||
\(366\) | 3.99148 | + | 6.91345i | 0.208638 | + | 0.361372i | ||||
\(367\) | 5.42822 | − | 9.40195i | 0.283351 | − | 0.490778i | −0.688857 | − | 0.724897i | \(-0.741887\pi\) |
0.972208 | + | 0.234119i | \(0.0752206\pi\) | |||||||
\(368\) | −0.955014 | + | 1.65413i | −0.0497836 | + | 0.0862277i | ||||
\(369\) | 1.01692 | + | 1.76136i | 0.0529388 | + | 0.0916926i | ||||
\(370\) | 11.3343 | 0.589241 | ||||||||
\(371\) | −9.61210 | − | 16.1978i | −0.499035 | − | 0.840948i | ||||
\(372\) | −10.9152 | −0.565929 | ||||||||
\(373\) | 1.18572 | + | 2.05373i | 0.0613943 | + | 0.106338i | 0.895089 | − | 0.445888i | \(-0.147112\pi\) |
−0.833695 | + | 0.552226i | \(0.813779\pi\) | |||||||
\(374\) | −5.15326 | + | 8.92571i | −0.266469 | + | 0.461538i | ||||
\(375\) | 6.00510 | − | 10.4011i | 0.310102 | − | 0.537112i | ||||
\(376\) | 16.0043 | + | 27.7202i | 0.825357 | + | 1.42956i | ||||
\(377\) | 1.09606 | 0.0564501 | ||||||||
\(378\) | −7.93997 | + | 0.0950346i | −0.408388 | + | 0.00488805i | ||||
\(379\) | −29.2197 | −1.50092 | −0.750458 | − | 0.660918i | \(-0.770167\pi\) | ||||
−0.750458 | + | 0.660918i | \(0.770167\pi\) | |||||||
\(380\) | −4.02381 | − | 6.96944i | −0.206417 | − | 0.357525i | ||||
\(381\) | 6.80654 | − | 11.7893i | 0.348709 | − | 0.603982i | ||||
\(382\) | −2.34248 | + | 4.05729i | −0.119852 | + | 0.207589i | ||||
\(383\) | 1.53297 | + | 2.65519i | 0.0783313 | + | 0.135674i | 0.902530 | − | 0.430627i | \(-0.141707\pi\) |
−0.824199 | + | 0.566301i | \(0.808374\pi\) | |||||||
\(384\) | −17.9302 | −0.914995 | ||||||||
\(385\) | 7.65729 | − | 13.6372i | 0.390252 | − | 0.695015i | ||||
\(386\) | 17.1964 | 0.875274 | ||||||||
\(387\) | −0.642025 | − | 1.11202i | −0.0326360 | − | 0.0565271i | ||||
\(388\) | −0.463750 | + | 0.803238i | −0.0235433 | + | 0.0407782i | ||||
\(389\) | −13.8705 | + | 24.0244i | −0.703261 | + | 1.21808i | 0.264054 | + | 0.964508i | \(0.414940\pi\) |
−0.967315 | + | 0.253576i | \(0.918393\pi\) | |||||||
\(390\) | −4.82573 | − | 8.35841i | −0.244360 | − | 0.423244i | ||||
\(391\) | −2.50828 | −0.126849 | ||||||||
\(392\) | 11.0607 | + | 18.1405i | 0.558647 | + | 0.916236i | ||||
\(393\) | −27.7617 | −1.40039 | ||||||||
\(394\) | 6.13984 | + | 10.6345i | 0.309320 | + | 0.535759i | ||||
\(395\) | −12.7156 | + | 22.0240i | −0.639790 | + | 1.10815i | ||||
\(396\) | 1.58257 | − | 2.74108i | 0.0795269 | − | 0.137745i | ||||
\(397\) | −8.61559 | − | 14.9226i | −0.432404 | − | 0.748946i | 0.564676 | − | 0.825313i | \(-0.309001\pi\) |
−0.997080 | + | 0.0763669i | \(0.975668\pi\) | |||||||
\(398\) | 33.2500 | 1.66667 | ||||||||
\(399\) | 23.6939 | − | 42.1974i | 1.18618 | − | 2.11251i | ||||
\(400\) | −10.4292 | −0.521459 | ||||||||
\(401\) | −8.32201 | − | 14.4142i | −0.415582 | − | 0.719808i | 0.579908 | − | 0.814682i | \(-0.303089\pi\) |
−0.995489 | + | 0.0948737i | \(0.969755\pi\) | |||||||
\(402\) | 24.4299 | − | 42.3137i | 1.21845 | − | 2.11042i | ||||
\(403\) | 5.21624 | − | 9.03479i | 0.259839 | − | 0.450055i | ||||
\(404\) | 0.289366 | + | 0.501196i | 0.0143965 | + | 0.0249354i | ||||
\(405\) | 15.8990 | 0.790029 | ||||||||
\(406\) | 3.66989 | − | 0.0439254i | 0.182133 | − | 0.00217998i | ||||
\(407\) | −6.28355 | −0.311464 | ||||||||
\(408\) | −15.9435 | − | 27.6149i | −0.789318 | − | 1.36714i | ||||
\(409\) | 6.81689 | − | 11.8072i | 0.337073 | − | 0.583828i | −0.646807 | − | 0.762653i | \(-0.723896\pi\) |
0.983881 | + | 0.178825i | \(0.0572296\pi\) | |||||||
\(410\) | −0.957237 | + | 1.65798i | −0.0472746 | + | 0.0818820i | ||||
\(411\) | −7.71340 | − | 13.3600i | −0.380474 | − | 0.659000i | ||||
\(412\) | 4.63359 | 0.228280 | ||||||||
\(413\) | −2.74978 | − | 4.63378i | −0.135308 | − | 0.228013i | ||||
\(414\) | −3.09824 | −0.152270 | ||||||||
\(415\) | 18.5822 | + | 32.1854i | 0.912167 | + | 1.57992i | ||||
\(416\) | −1.10838 | + | 1.91977i | −0.0543426 | + | 0.0941242i | ||||
\(417\) | −5.25456 | + | 9.10116i | −0.257317 | + | 0.445686i | ||||
\(418\) | −8.97238 | − | 15.5406i | −0.438853 | − | 0.760116i | ||||
\(419\) | −10.8502 | −0.530066 | −0.265033 | − | 0.964239i | \(-0.585383\pi\) | ||||
−0.265033 | + | 0.964239i | \(0.585383\pi\) | |||||||
\(420\) | 4.10046 | + | 6.90987i | 0.200082 | + | 0.337167i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −6.34946 | − | 10.9976i | −0.309087 | − | 0.535354i | ||||
\(423\) | −20.5778 | + | 35.6418i | −1.00053 | + | 1.73296i | ||||
\(424\) | 10.8039 | − | 18.7129i | 0.524683 | − | 0.908778i | ||||
\(425\) | −6.84788 | − | 11.8609i | −0.332171 | − | 0.575337i | ||||
\(426\) | −11.9751 | −0.580194 | ||||||||
\(427\) | 6.35150 | − | 0.0760220i | 0.307371 | − | 0.00367896i | ||||
\(428\) | −7.81574 | −0.377788 | ||||||||
\(429\) | 2.67531 | + | 4.63378i | 0.129165 | + | 0.223721i | ||||
\(430\) | 0.604344 | − | 1.04676i | 0.0291441 | − | 0.0504790i | ||||
\(431\) | −0.604764 | + | 1.04748i | −0.0291304 | + | 0.0504554i | −0.880223 | − | 0.474560i | \(-0.842607\pi\) |
0.851093 | + | 0.525016i | \(0.175940\pi\) | |||||||
\(432\) | −3.61036 | − | 6.25332i | −0.173703 | − | 0.300863i | ||||
\(433\) | −5.56422 | −0.267399 | −0.133700 | − | 0.991022i | \(-0.542686\pi\) | ||||
−0.133700 | + | 0.991022i | \(0.542686\pi\) | |||||||
\(434\) | 17.1032 | − | 30.4597i | 0.820979 | − | 1.46211i | ||||
\(435\) | 8.35851 | 0.400760 | ||||||||
\(436\) | −0.220375 | − | 0.381700i | −0.0105540 | − | 0.0182801i | ||||
\(437\) | 2.18359 | − | 3.78209i | 0.104455 | − | 0.180922i | ||||
\(438\) | 4.94731 | − | 8.56899i | 0.236391 | − | 0.409442i | ||||
\(439\) | 9.85960 | + | 17.0773i | 0.470573 | + | 0.815057i | 0.999434 | − | 0.0336522i | \(-0.0107139\pi\) |
−0.528860 | + | 0.848709i | \(0.677381\pi\) | |||||||
\(440\) | 17.9422 | 0.855362 | ||||||||
\(441\) | −13.0889 | + | 23.9784i | −0.623282 | + | 1.14183i | ||||
\(442\) | 5.06074 | 0.240715 | ||||||||
\(443\) | −11.1155 | − | 19.2526i | −0.528113 | − | 0.914719i | −0.999463 | − | 0.0327726i | \(-0.989566\pi\) |
0.471350 | − | 0.881946i | \(-0.343767\pi\) | |||||||
\(444\) | 1.61407 | − | 2.79566i | 0.0766005 | − | 0.132676i | ||||
\(445\) | −3.89091 | + | 6.73926i | −0.184447 | + | 0.319471i | ||||
\(446\) | −11.0716 | − | 19.1766i | −0.524256 | − | 0.908039i | ||||
\(447\) | 26.5498 | 1.25576 | ||||||||
\(448\) | −11.5228 | + | 20.5213i | −0.544399 | + | 0.969542i | ||||
\(449\) | 18.4579 | 0.871082 | 0.435541 | − | 0.900169i | \(-0.356557\pi\) | ||||
0.435541 | + | 0.900169i | \(0.356557\pi\) | |||||||
\(450\) | −8.45853 | − | 14.6506i | −0.398739 | − | 0.690636i | ||||
\(451\) | 0.530678 | − | 0.919161i | 0.0249886 | − | 0.0432816i | ||||
\(452\) | −0.218245 | + | 0.378012i | −0.0102654 | + | 0.0177802i | ||||
\(453\) | −0.246605 | − | 0.427132i | −0.0115865 | − | 0.0200684i | ||||
\(454\) | −12.0439 | −0.565249 | ||||||||
\(455\) | −7.67901 | + | 0.0919110i | −0.359997 | + | 0.00430886i | ||||
\(456\) | 55.5185 | 2.59989 | ||||||||
\(457\) | 14.9910 | + | 25.9651i | 0.701248 | + | 1.21460i | 0.968029 | + | 0.250840i | \(0.0807067\pi\) |
−0.266781 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(458\) | −13.3629 | + | 23.1452i | −0.624408 | + | 1.08151i | ||||
\(459\) | 4.74118 | − | 8.21197i | 0.221299 | − | 0.383302i | ||||
\(460\) | 0.362542 | + | 0.627941i | 0.0169036 | + | 0.0292779i | ||||
\(461\) | 29.1498 | 1.35764 | 0.678821 | − | 0.734304i | \(-0.262491\pi\) | ||||
0.678821 | + | 0.734304i | \(0.262491\pi\) | |||||||
\(462\) | 9.14330 | + | 15.4078i | 0.425385 | + | 0.716836i | ||||
\(463\) | 1.55900 | 0.0724530 | 0.0362265 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362265 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(464\) | 1.66872 | + | 2.89031i | 0.0774685 | + | 0.134179i | ||||
\(465\) | 39.7787 | − | 68.8988i | 1.84470 | − | 3.19511i | ||||
\(466\) | −8.97238 | + | 15.5406i | −0.415637 | + | 0.719905i | ||||
\(467\) | −6.21156 | − | 10.7587i | −0.287437 | − | 0.497855i | 0.685760 | − | 0.727827i | \(-0.259470\pi\) |
−0.973197 | + | 0.229972i | \(0.926136\pi\) | |||||||
\(468\) | −1.55415 | −0.0718407 | ||||||||
\(469\) | −19.8401 | − | 33.4335i | −0.916132 | − | 1.54382i | ||||
\(470\) | −38.7402 | −1.78695 | ||||||||
\(471\) | −15.8580 | − | 27.4668i | −0.730697 | − | 1.26561i | ||||
\(472\) | 3.09072 | − | 5.35328i | 0.142262 | − | 0.246405i | ||||
\(473\) | −0.335039 | + | 0.580305i | −0.0154051 | + | 0.0266825i | ||||
\(474\) | −14.5665 | − | 25.2299i | −0.669060 | − | 1.15885i | ||||
\(475\) | 23.8458 | 1.09412 | ||||||||
\(476\) | −4.21281 | + | 0.0504237i | −0.193094 | + | 0.00231117i | ||||
\(477\) | 27.7826 | 1.27208 | ||||||||
\(478\) | 10.4587 | + | 18.1149i | 0.478368 | + | 0.828557i | ||||
\(479\) | −18.0279 | + | 31.2252i | −0.823716 | + | 1.42672i | 0.0791811 | + | 0.996860i | \(0.474769\pi\) |
−0.902897 | + | 0.429857i | \(0.858564\pi\) | |||||||
\(480\) | −8.45242 | + | 14.6400i | −0.385798 | + | 0.668222i | ||||
\(481\) | 1.54268 | + | 2.67201i | 0.0703404 | + | 0.121833i | ||||
\(482\) | −17.3249 | −0.789128 | ||||||||
\(483\) | −2.13480 | + | 3.80196i | −0.0971369 | + | 0.172995i | ||||
\(484\) | 2.72887 | 0.124040 | ||||||||
\(485\) | −3.38011 | − | 5.85453i | −0.153483 | − | 0.265840i | ||||
\(486\) | −13.6085 | + | 23.5707i | −0.617295 | + | 1.06919i | ||||
\(487\) | −3.65002 | + | 6.32202i | −0.165398 | + | 0.286478i | −0.936797 | − | 0.349874i | \(-0.886224\pi\) |
0.771398 | + | 0.636352i | \(0.219558\pi\) | |||||||
\(488\) | 3.64351 | + | 6.31074i | 0.164934 | + | 0.285674i | ||||
\(489\) | −39.1821 | −1.77188 | ||||||||
\(490\) | −25.7075 | + | 0.615481i | −1.16135 | + | 0.0278046i | ||||
\(491\) | 4.49178 | 0.202711 | 0.101356 | − | 0.994850i | \(-0.467682\pi\) | ||||
0.101356 | + | 0.994850i | \(0.467682\pi\) | |||||||
\(492\) | 0.272633 | + | 0.472215i | 0.0122913 | + | 0.0212891i | ||||
\(493\) | −2.19139 | + | 3.79560i | −0.0986954 | + | 0.170945i | ||||
\(494\) | −4.40565 | + | 7.63080i | −0.198219 | + | 0.343326i | ||||
\(495\) | 11.5348 | + | 19.9788i | 0.518450 | + | 0.897981i | ||||
\(496\) | 31.7663 | 1.42635 | ||||||||
\(497\) | −4.66512 | + | 8.30829i | −0.209259 | + | 0.372678i | ||||
\(498\) | −42.5742 | −1.90780 | ||||||||
\(499\) | −5.68369 | − | 9.84443i | −0.254437 | − | 0.440697i | 0.710306 | − | 0.703893i | \(-0.248557\pi\) |
−0.964742 | + | 0.263196i | \(0.915223\pi\) | |||||||
\(500\) | 0.910235 | − | 1.57657i | 0.0407069 | − | 0.0705065i | ||||
\(501\) | 6.64260 | − | 11.5053i | 0.296770 | − | 0.514020i | ||||
\(502\) | 9.27709 | + | 16.0684i | 0.414057 | + | 0.717167i | ||||
\(503\) | 17.1080 | 0.762806 | 0.381403 | − | 0.924409i | \(-0.375441\pi\) | ||||
0.381403 | + | 0.924409i | \(0.375441\pi\) | |||||||
\(504\) | −31.3374 | + | 0.375082i | −1.39588 | + | 0.0167075i | ||||
\(505\) | −4.21818 | −0.187706 | ||||||||
\(506\) | 0.808405 | + | 1.40020i | 0.0359380 | + | 0.0622464i | ||||
\(507\) | 1.31364 | − | 2.27529i | 0.0583408 | − | 0.101049i | ||||
\(508\) | 1.03171 | − | 1.78698i | 0.0457749 | − | 0.0792845i | ||||
\(509\) | −1.64142 | − | 2.84303i | −0.0727547 | − | 0.126015i | 0.827353 | − | 0.561682i | \(-0.189846\pi\) |
−0.900108 | + | 0.435667i | \(0.856512\pi\) | |||||||
\(510\) | 38.5929 | 1.70892 | ||||||||
\(511\) | −4.01784 | − | 6.77065i | −0.177739 | − | 0.299516i | ||||
\(512\) | −25.2340 | −1.11520 | ||||||||
\(513\) | 8.25490 | + | 14.2979i | 0.364463 | + | 0.631268i | ||||
\(514\) | 1.10916 | − | 1.92113i | 0.0489231 | − | 0.0847373i | ||||
\(515\) | −16.8863 | + | 29.2479i | −0.744100 | + | 1.28882i | ||||
\(516\) | −0.172125 | − | 0.298129i | −0.00757738 | − | 0.0131244i | ||||
\(517\) | 21.4770 | 0.944555 | ||||||||
\(518\) | 5.27237 | + | 8.88472i | 0.231655 | + | 0.390372i | ||||
\(519\) | 1.56485 | 0.0686891 | ||||||||
\(520\) | −4.40502 | − | 7.62973i | −0.193173 | − | 0.334586i | ||||
\(521\) | 2.38530 | − | 4.13147i | 0.104502 | − | 0.181003i | −0.809033 | − | 0.587764i | \(-0.800008\pi\) |
0.913535 | + | 0.406761i | \(0.133342\pi\) | |||||||
\(522\) | −2.70682 | + | 4.68835i | −0.118474 | + | 0.205203i | ||||
\(523\) | −12.7562 | − | 22.0944i | −0.557789 | − | 0.966119i | −0.997681 | − | 0.0680682i | \(-0.978316\pi\) |
0.439892 | − | 0.898051i | \(-0.355017\pi\) | |||||||
\(524\) | −4.20803 | −0.183829 | ||||||||
\(525\) | −23.8065 | + | 0.284943i | −1.03900 | + | 0.0124359i | ||||
\(526\) | 34.0975 | 1.48672 | ||||||||
\(527\) | 20.8580 | + | 36.1271i | 0.908588 | + | 1.57372i | ||||
\(528\) | −8.14616 | + | 14.1096i | −0.354516 | + | 0.614040i | ||||
\(529\) | 11.3033 | − | 19.5778i | 0.491446 | − | 0.851210i | ||||
\(530\) | 13.0760 | + | 22.6483i | 0.567986 | + | 0.983780i | ||||
\(531\) | 7.94789 | 0.344909 | ||||||||
\(532\) | 3.59145 | − | 6.39616i | 0.155709 | − | 0.277309i | ||||
\(533\) | −0.521150 | −0.0225735 | ||||||||
\(534\) | −4.45728 | − | 7.72024i | −0.192885 | − | 0.334087i | ||||
\(535\) | 28.4831 | − | 49.3342i | 1.23143 | − | 2.13290i | ||||
\(536\) | 22.3001 | − | 38.6249i | 0.963216 | − | 1.66834i | ||||
\(537\) | 10.6098 | + | 18.3767i | 0.457847 | + | 0.793013i | ||||
\(538\) | −27.9309 | −1.20418 | ||||||||
\(539\) | 14.2519 | − | 0.341214i | 0.613871 | − | 0.0146971i | ||||
\(540\) | −2.74112 | −0.117959 | ||||||||
\(541\) | 8.25784 | + | 14.3030i | 0.355032 | + | 0.614934i | 0.987123 | − | 0.159960i | \(-0.0511366\pi\) |
−0.632091 | + | 0.774894i | \(0.717803\pi\) | |||||||
\(542\) | 5.67125 | − | 9.82290i | 0.243601 | − | 0.421930i | ||||
\(543\) | 2.48704 | − | 4.30768i | 0.106729 | − | 0.184860i | ||||
\(544\) | −4.43203 | − | 7.67649i | −0.190022 | − | 0.329127i | ||||
\(545\) | 3.21247 | 0.137607 | ||||||||
\(546\) | 4.30721 | − | 7.67088i | 0.184331 | − | 0.328283i | ||||
\(547\) | 23.3317 | 0.997591 | 0.498796 | − | 0.866720i | \(-0.333776\pi\) | ||||
0.498796 | + | 0.866720i | \(0.333776\pi\) | |||||||
\(548\) | −1.16917 | − | 2.02507i | −0.0499446 | − | 0.0865066i | ||||
\(549\) | −4.68471 | + | 8.11416i | −0.199939 | + | 0.346304i | ||||
\(550\) | −4.41407 | + | 7.64539i | −0.188216 | + | 0.326001i | ||||
\(551\) | −3.81545 | − | 6.60855i | −0.162544 | − | 0.281534i | ||||
\(552\) | −5.00218 | −0.212907 | ||||||||
\(553\) | −23.1791 | + | 0.277434i | −0.985676 | + | 0.0117977i | ||||
\(554\) | −9.52909 | −0.404852 | ||||||||
\(555\) | 11.7644 | + | 20.3766i | 0.499372 | + | 0.864938i | ||||
\(556\) | −0.796470 | + | 1.37953i | −0.0337779 | + | 0.0585050i | ||||
\(557\) | 10.0235 | − | 17.3613i | 0.424711 | − | 0.735621i | −0.571682 | − | 0.820475i | \(-0.693709\pi\) |
0.996393 | + | 0.0848540i | \(0.0270424\pi\) | |||||||
\(558\) | 25.7639 | + | 44.6243i | 1.09067 | + | 1.88910i | ||||
\(559\) | 0.329024 | 0.0139162 | ||||||||
\(560\) | −11.9334 | − | 20.1096i | −0.504279 | − | 0.849784i | ||||
\(561\) | −21.3953 | −0.903312 | ||||||||
\(562\) | −18.8425 | − | 32.6362i | −0.794824 | − | 1.37668i | ||||
\(563\) | 20.2642 | − | 35.0986i | 0.854034 | − | 1.47923i | −0.0235047 | − | 0.999724i | \(-0.507482\pi\) |
0.877539 | − | 0.479506i | \(-0.159184\pi\) | |||||||
\(564\) | −5.51684 | + | 9.55545i | −0.232301 | + | 0.402357i | ||||
\(565\) | −1.59072 | − | 2.75520i | −0.0669219 | − | 0.115912i | ||||
\(566\) | 0.381519 | 0.0160364 | ||||||||
\(567\) | 7.39576 | + | 12.4629i | 0.310593 | + | 0.523394i | ||||
\(568\) | −10.9311 | −0.458659 | ||||||||
\(569\) | 10.7252 | + | 18.5766i | 0.449623 | + | 0.778770i | 0.998361 | − | 0.0572245i | \(-0.0182251\pi\) |
−0.548739 | + | 0.835994i | \(0.684892\pi\) | |||||||
\(570\) | −33.5972 | + | 58.1921i | −1.40723 | + | 2.43740i | ||||
\(571\) | 5.47793 | − | 9.48806i | 0.229244 | − | 0.397063i | −0.728340 | − | 0.685216i | \(-0.759708\pi\) |
0.957584 | + | 0.288153i | \(0.0930412\pi\) | |||||||
\(572\) | 0.405516 | + | 0.702374i | 0.0169555 | + | 0.0293677i | ||||
\(573\) | −9.72552 | −0.406289 | ||||||||
\(574\) | −1.74494 | + | 0.0208854i | −0.0728323 | + | 0.000871740i | ||||
\(575\) | −2.14849 | −0.0895982 | ||||||||
\(576\) | −17.3576 | − | 30.0643i | −0.723235 | − | 1.25268i | ||||
\(577\) | −17.3708 | + | 30.0870i | −0.723154 | + | 1.25254i | 0.236575 | + | 0.971613i | \(0.423975\pi\) |
−0.959729 | + | 0.280927i | \(0.909358\pi\) | |||||||
\(578\) | 0.639571 | − | 1.10777i | 0.0266027 | − | 0.0460771i | ||||
\(579\) | 17.8490 | + | 30.9154i | 0.741781 | + | 1.28480i | ||||
\(580\) | 1.26696 | 0.0526076 | ||||||||
\(581\) | −16.5856 | + | 29.5380i | −0.688086 | + | 1.22544i | ||||
\(582\) | 7.74426 | 0.321010 | ||||||||
\(583\) | −7.24915 | − | 12.5559i | −0.300229 | − | 0.520012i | ||||
\(584\) | 4.51600 | − | 7.82195i | 0.186874 | − | 0.323675i | ||||
\(585\) | 5.66384 | − | 9.81006i | 0.234171 | − | 0.405596i | ||||
\(586\) | 12.1796 | + | 21.0958i | 0.503136 | + | 0.871458i | ||||
\(587\) | −22.8463 | −0.942967 | −0.471483 | − | 0.881875i | \(-0.656281\pi\) | ||||
−0.471483 | + | 0.881875i | \(0.656281\pi\) | |||||||
\(588\) | −3.50910 | + | 6.42854i | −0.144713 | + | 0.265108i | ||||
\(589\) | −72.6320 | −2.99275 | ||||||||
\(590\) | 3.74071 | + | 6.47911i | 0.154003 | + | 0.266741i | ||||
\(591\) | −12.7457 | + | 22.0762i | −0.524288 | + | 0.908094i | ||||
\(592\) | −4.69738 | + | 8.13610i | −0.193061 | + | 0.334392i | ||||
\(593\) | −8.79676 | − | 15.2364i | −0.361240 | − | 0.625686i | 0.626925 | − | 0.779079i | \(-0.284313\pi\) |
−0.988165 | + | 0.153394i | \(0.950980\pi\) | |||||||
\(594\) | −6.11222 | −0.250787 | ||||||||
\(595\) | 15.0346 | − | 26.7757i | 0.616359 | − | 1.09770i | ||||
\(596\) | 4.02433 | 0.164843 | ||||||||
\(597\) | 34.5119 | + | 59.7764i | 1.41248 | + | 2.44648i | ||||
\(598\) | 0.396945 | − | 0.687530i | 0.0162323 | − | 0.0281152i | ||||
\(599\) | −15.5036 | + | 26.8531i | −0.633461 | + | 1.09719i | 0.353378 | + | 0.935481i | \(0.385033\pi\) |
−0.986839 | + | 0.161706i | \(0.948300\pi\) | |||||||
\(600\) | −13.6565 | − | 23.6537i | −0.557524 | − | 0.965660i | ||||
\(601\) | −1.43754 | −0.0586385 | −0.0293193 | − | 0.999570i | \(-0.509334\pi\) | ||||
−0.0293193 | + | 0.999570i | \(0.509334\pi\) | |||||||
\(602\) | 1.10165 | − | 0.0131858i | 0.0449001 | − | 0.000537415i | ||||
\(603\) | 57.3455 | 2.33529 | ||||||||
\(604\) | −0.0373796 | − | 0.0647433i | −0.00152095 | − | 0.00263437i | ||||
\(605\) | −9.94490 | + | 17.2251i | −0.404318 | + | 0.700299i | ||||
\(606\) | 2.41609 | − | 4.18479i | 0.0981470 | − | 0.169996i | ||||
\(607\) | 16.5085 | + | 28.5936i | 0.670061 | + | 1.16058i | 0.977887 | + | 0.209136i | \(0.0670652\pi\) |
−0.307826 | + | 0.951443i | \(0.599601\pi\) | |||||||
\(608\) | 15.4333 | 0.625901 | ||||||||
\(609\) | 3.88813 | + | 6.55208i | 0.157555 | + | 0.265503i | ||||
\(610\) | −8.81953 | −0.357092 | ||||||||
\(611\) | −5.27284 | − | 9.13283i | −0.213316 | − | 0.369475i | ||||
\(612\) | 3.10727 | − | 5.38194i | 0.125604 | − | 0.217552i | ||||
\(613\) | 21.5829 | − | 37.3826i | 0.871723 | − | 1.50987i | 0.0115102 | − | 0.999934i | \(-0.496336\pi\) |
0.860213 | − | 0.509935i | \(-0.170331\pi\) | |||||||
\(614\) | 2.26404 | + | 3.92143i | 0.0913692 | + | 0.158256i | ||||
\(615\) | −3.97426 | −0.160258 | ||||||||
\(616\) | 8.34619 | + | 14.0646i | 0.336278 | + | 0.566677i | ||||
\(617\) | 2.45772 | 0.0989441 | 0.0494721 | − | 0.998776i | \(-0.484246\pi\) | ||||
0.0494721 | + | 0.998776i | \(0.484246\pi\) | |||||||
\(618\) | −19.3443 | − | 33.5053i | −0.778142 | − | 1.34778i | ||||
\(619\) | −18.8894 | + | 32.7175i | −0.759231 | + | 1.31503i | 0.184013 | + | 0.982924i | \(0.441091\pi\) |
−0.943243 | + | 0.332102i | \(0.892242\pi\) | |||||||
\(620\) | 6.02954 | − | 10.4435i | 0.242152 | − | 0.419420i | ||||
\(621\) | −0.743761 | − | 1.28823i | −0.0298461 | − | 0.0516949i | ||||
\(622\) | −30.1602 | −1.20932 | ||||||||
\(623\) | −7.09271 | + | 0.0848936i | −0.284163 | + | 0.00340119i | ||||
\(624\) | 7.99991 | 0.320253 | ||||||||
\(625\) | 15.1971 | + | 26.3222i | 0.607884 | + | 1.05289i | ||||
\(626\) | 11.4420 | − | 19.8181i | 0.457313 | − | 0.792089i | ||||
\(627\) | 18.6258 | − | 32.2608i | 0.743842 | − | 1.28837i | ||||
\(628\) | −2.40371 | − | 4.16334i | −0.0959183 | − | 0.166135i | ||||
\(629\) | −12.3374 | −0.491922 | ||||||||
\(630\) | 18.5708 | − | 33.0735i | 0.739878 | − | 1.31768i | ||||
\(631\) | −28.4828 | −1.13388 | −0.566942 | − | 0.823758i | \(-0.691874\pi\) | ||||
−0.566942 | + | 0.823758i | \(0.691874\pi\) | |||||||
\(632\) | −13.2966 | − | 23.0303i | −0.528909 | − | 0.916098i | ||||
\(633\) | 13.1809 | − | 22.8299i | 0.523892 | − | 0.907407i | ||||
\(634\) | 17.4326 | − | 30.1942i | 0.692337 | − | 1.19916i | ||||
\(635\) | 7.51981 | + | 13.0247i | 0.298415 | + | 0.516869i | ||||
\(636\) | 7.44843 | 0.295350 | ||||||||
\(637\) | −3.64409 | − | 5.97667i | −0.144384 | − | 0.236804i | ||||
\(638\) | 2.82509 | 0.111847 | ||||||||
\(639\) | −7.02743 | − | 12.1719i | −0.278001 | − | 0.481512i | ||||
\(640\) | 9.90456 | − | 17.1552i | 0.391512 | − | 0.678119i | ||||
\(641\) | 13.5961 | − | 23.5492i | 0.537014 | − | 0.930136i | −0.462049 | − | 0.886854i | \(-0.652886\pi\) |
0.999063 | − | 0.0432812i | \(-0.0137811\pi\) | |||||||
\(642\) | 32.6292 | + | 56.5154i | 1.28777 | + | 2.23049i | ||||
\(643\) | −37.1664 | −1.46570 | −0.732849 | − | 0.680391i | \(-0.761810\pi\) | ||||
−0.732849 | + | 0.680391i | \(0.761810\pi\) | |||||||
\(644\) | −0.323587 | + | 0.576289i | −0.0127511 | + | 0.0227090i | ||||
\(645\) | 2.50912 | 0.0987965 | ||||||||
\(646\) | −17.6167 | − | 30.5130i | −0.693120 | − | 1.20052i | ||||
\(647\) | −9.41593 | + | 16.3089i | −0.370178 | + | 0.641168i | −0.989593 | − | 0.143896i | \(-0.954037\pi\) |
0.619414 | + | 0.785064i | \(0.287370\pi\) | |||||||
\(648\) | −8.31275 | + | 14.3981i | −0.326556 | + | 0.565611i | ||||
\(649\) | −2.07380 | − | 3.59192i | −0.0814036 | − | 0.140995i | ||||
\(650\) | 4.33482 | 0.170026 | ||||||||
\(651\) | 72.5123 | − | 0.867909i | 2.84198 | − | 0.0340161i | ||||
\(652\) | −5.93910 | −0.232593 | ||||||||
\(653\) | 13.0092 | + | 22.5326i | 0.509090 | + | 0.881770i | 0.999945 | + | 0.0105286i | \(0.00335143\pi\) |
−0.490854 | + | 0.871242i | \(0.663315\pi\) | |||||||
\(654\) | −1.84004 | + | 3.18705i | −0.0719513 | + | 0.124623i | ||||
\(655\) | 15.3355 | − | 26.5618i | 0.599206 | − | 1.03786i | ||||
\(656\) | −0.793435 | − | 1.37427i | −0.0309784 | − | 0.0536562i | ||||
\(657\) | 11.6131 | 0.453069 | ||||||||
\(658\) | −18.0208 | − | 30.3676i | −0.702523 | − | 1.18385i | ||||
\(659\) | −33.3339 | −1.29851 | −0.649253 | − | 0.760573i | \(-0.724918\pi\) | ||||
−0.649253 | + | 0.760573i | \(0.724918\pi\) | |||||||
\(660\) | 3.09244 | + | 5.35626i | 0.120373 | + | 0.208492i | ||||
\(661\) | −3.14920 | + | 5.45458i | −0.122490 | + | 0.212159i | −0.920749 | − | 0.390156i | \(-0.872421\pi\) |
0.798259 | + | 0.602314i | \(0.205755\pi\) | |||||||
\(662\) | 11.5053 | − | 19.9277i | 0.447164 | − | 0.774511i | ||||
\(663\) | 5.25280 | + | 9.09812i | 0.204002 | + | 0.353342i | ||||
\(664\) | −38.8626 | −1.50816 | ||||||||
\(665\) | 27.2852 | + | 45.9795i | 1.05807 | + | 1.78301i | ||||
\(666\) | −15.2391 | −0.590505 | ||||||||
\(667\) | 0.343769 | + | 0.595426i | 0.0133108 | + | 0.0230550i | ||||
\(668\) | 1.00687 | − | 1.74394i | 0.0389568 | − | 0.0674752i | ||||
\(669\) | 22.9836 | − | 39.8088i | 0.888597 | − | 1.53910i | ||||
\(670\) | 26.9899 | + | 46.7479i | 1.04271 | + | 1.80603i | ||||
\(671\) | 4.88941 | 0.188754 | ||||||||
\(672\) | −15.4078 | + | 0.184418i | −0.594370 | + | 0.00711409i | ||||
\(673\) | 18.3188 | 0.706137 | 0.353068 | − | 0.935598i | \(-0.385138\pi\) | ||||
0.353068 | + | 0.935598i | \(0.385138\pi\) | |||||||
\(674\) | 10.8451 | + | 18.7842i | 0.417736 | + | 0.723541i | ||||
\(675\) | 4.06110 | − | 7.03403i | 0.156312 | − | 0.270740i | ||||
\(676\) | 0.199118 | − | 0.344882i | 0.00765837 | − | 0.0132647i | ||||
\(677\) | −12.1696 | − | 21.0783i | −0.467715 | − | 0.810106i | 0.531604 | − | 0.846993i | \(-0.321589\pi\) |
−0.999319 | + | 0.0368866i | \(0.988256\pi\) | |||||||
\(678\) | 3.64453 | 0.139967 | ||||||||
\(679\) | 3.01692 | − | 5.37296i | 0.115779 | − | 0.206195i | ||||
\(680\) | 35.2284 | 1.35095 | ||||||||
\(681\) | −12.5010 | − | 21.6524i | −0.479039 | − | 0.829720i | ||||
\(682\) | 13.4448 | − | 23.2871i | 0.514829 | − | 0.891709i | ||||
\(683\) | −5.88409 | + | 10.1916i | −0.225149 | + | 0.389969i | −0.956364 | − | 0.292178i | \(-0.905620\pi\) |
0.731215 | + | 0.682147i | \(0.238953\pi\) | |||||||
\(684\) | 5.41008 | + | 9.37054i | 0.206860 | + | 0.358291i | ||||
\(685\) | 17.0434 | 0.651195 | ||||||||
\(686\) | −12.4408 | − | 19.8653i | −0.474994 | − | 0.758461i | ||||
\(687\) | −55.4802 | −2.11670 | ||||||||
\(688\) | 0.500929 | + | 0.867635i | 0.0190977 | + | 0.0330783i | ||||
\(689\) | −3.55950 | + | 6.16523i | −0.135606 | + | 0.234877i | ||||
\(690\) | 3.02708 | − | 5.24306i | 0.115239 | − | 0.199600i | ||||
\(691\) | −0.588923 | − | 1.02004i | −0.0224037 | − | 0.0388043i | 0.854606 | − | 0.519277i | \(-0.173799\pi\) |
−0.877010 | + | 0.480472i | \(0.840465\pi\) | |||||||
\(692\) | 0.237195 | 0.00901679 | ||||||||
\(693\) | −10.2954 | + | 18.3354i | −0.391089 | + | 0.696506i | ||||
\(694\) | 28.1835 | 1.06983 | ||||||||
\(695\) | −5.80520 | − | 10.0549i | −0.220204 | − | 0.381404i | ||||
\(696\) | −4.37022 | + | 7.56944i | −0.165653 | + | 0.286919i | ||||
\(697\) | 1.04195 | − | 1.80471i | 0.0394668 | − | 0.0683584i | ||||
\(698\) | −12.6161 | − | 21.8517i | −0.477525 | − | 0.827097i | ||||
\(699\) | −37.2516 | −1.40898 | ||||||||
\(700\) | −3.60852 | + | 0.0431908i | −0.136389 | + | 0.00163246i | ||||
\(701\) | −31.2867 | −1.18168 | −0.590841 | − | 0.806788i | \(-0.701204\pi\) | ||||
−0.590841 | + | 0.806788i | \(0.701204\pi\) | |||||||
\(702\) | 1.50062 | + | 2.59915i | 0.0566373 | + | 0.0980987i | ||||
\(703\) | 10.7403 | − | 18.6028i | 0.405079 | − | 0.701617i | ||||
\(704\) | −9.05804 | + | 15.6890i | −0.341388 | + | 0.591301i | ||||
\(705\) | −40.2104 | − | 69.6464i | −1.51441 | − | 2.62304i | ||||
\(706\) | 29.0016 | 1.09149 | ||||||||
\(707\) | −1.96217 | − | 3.30654i | −0.0737950 | − | 0.124355i | ||||
\(708\) | 2.13081 | 0.0800806 | ||||||||
\(709\) | −7.68738 | − | 13.3149i | −0.288706 | − | 0.500053i | 0.684795 | − | 0.728735i | \(-0.259892\pi\) |
−0.973501 | + | 0.228682i | \(0.926558\pi\) | |||||||
\(710\) | 6.61499 | − | 11.4575i | 0.248256 | − | 0.429992i | ||||
\(711\) | 17.0963 | − | 29.6117i | 0.641162 | − | 1.11053i | ||||
\(712\) | −4.06870 | − | 7.04719i | −0.152481 | − | 0.264105i | ||||
\(713\) | 6.54409 | 0.245078 | ||||||||
\(714\) | 17.9523 | + | 30.2522i | 0.671848 | + | 1.13216i | ||||
\(715\) | −5.91133 | −0.221071 | ||||||||
\(716\) | 1.60820 | + | 2.78549i | 0.0601013 | + | 0.104098i | ||||
\(717\) | −21.7111 | + | 37.6048i | −0.810817 | + | 1.40438i | ||||
\(718\) | −17.2322 | + | 29.8470i | −0.643099 | + | 1.11388i | ||||
\(719\) | 5.57087 | + | 9.64904i | 0.207759 | + | 0.359848i | 0.951008 | − | 0.309166i | \(-0.100050\pi\) |
−0.743250 | + | 0.669014i | \(0.766717\pi\) | |||||||
\(720\) | 34.4921 | 1.28545 | ||||||||
\(721\) | −30.7819 | + | 0.368433i | −1.14638 | + | 0.0137211i | ||||
\(722\) | 37.2985 | 1.38811 | ||||||||
\(723\) | −17.9824 | − | 31.1465i | −0.668773 | − | 1.15835i | ||||
\(724\) | 0.376978 | − | 0.652945i | 0.0140103 | − | 0.0242665i | ||||
\(725\) | −1.87706 | + | 3.25116i | −0.0697121 | + | 0.120745i | ||||
\(726\) | −11.3925 | − | 19.7324i | −0.422815 | − | 0.732338i | ||||
\(727\) | −6.24735 | −0.231702 | −0.115851 | − | 0.993267i | \(-0.536959\pi\) | ||||
−0.115851 | + | 0.993267i | \(0.536959\pi\) | |||||||
\(728\) | 3.93171 | − | 7.00214i | 0.145719 | − | 0.259516i | ||||
\(729\) | −40.0674 | −1.48398 | ||||||||
\(730\) | 5.46575 | + | 9.46696i | 0.202296 | + | 0.350388i | ||||
\(731\) | −0.657828 | + | 1.13939i | −0.0243307 | + | 0.0421419i | ||||
\(732\) | −1.25596 | + | 2.17538i | −0.0464215 | + | 0.0804044i | ||||
\(733\) | −15.4834 | − | 26.8181i | −0.571894 | − | 0.990550i | −0.996371 | − | 0.0851111i | \(-0.972875\pi\) |
0.424477 | − | 0.905439i | \(-0.360458\pi\) | |||||||
\(734\) | −13.7400 | −0.507153 | ||||||||
\(735\) | −27.7897 | − | 45.5777i | −1.02504 | − | 1.68116i | ||||
\(736\) | −1.39053 | −0.0512554 | ||||||||
\(737\) | −14.9628 | − | 25.9163i | −0.551162 | − | 0.954641i | ||||
\(738\) | 1.28702 | − | 2.22919i | 0.0473760 | − | 0.0820576i | ||||
\(739\) | −1.16872 | + | 2.02429i | −0.0429921 | + | 0.0744646i | −0.886721 | − | 0.462305i | \(-0.847022\pi\) |
0.843729 | + | 0.536770i | \(0.180356\pi\) | |||||||
\(740\) | 1.78322 | + | 3.08862i | 0.0655523 | + | 0.113540i | ||||
\(741\) | −18.2914 | −0.671951 | ||||||||
\(742\) | −11.6710 | + | 20.7854i | −0.428456 | + | 0.763055i | ||||
\(743\) | 24.3612 | 0.893726 | 0.446863 | − | 0.894603i | \(-0.352541\pi\) | ||||
0.446863 | + | 0.894603i | \(0.352541\pi\) | |||||||
\(744\) | 41.5963 | + | 72.0470i | 1.52500 | + | 2.64137i | ||||
\(745\) | −14.6660 | + | 25.4022i | −0.537321 | + | 0.930666i | ||||
\(746\) | 1.50066 | − | 2.59922i | 0.0549430 | − | 0.0951641i | ||||
\(747\) | −24.9842 | − | 43.2739i | −0.914123 | − | 1.58331i | ||||
\(748\) | −3.24304 | −0.118577 | ||||||||
\(749\) | 51.9216 | − | 0.621457i | 1.89718 | − | 0.0227075i | ||||
\(750\) | −15.2002 | −0.555033 | ||||||||
\(751\) | 6.01266 | + | 10.4142i | 0.219405 | + | 0.380021i | 0.954626 | − | 0.297806i | \(-0.0962550\pi\) |
−0.735221 | + | 0.677827i | \(0.762922\pi\) | |||||||
\(752\) | 16.0555 | − | 27.8089i | 0.585483 | − | 1.01409i | ||||
\(753\) | −19.2583 | + | 33.3564i | −0.701813 | + | 1.21558i | ||||
\(754\) | −0.693593 | − | 1.20134i | −0.0252592 | − | 0.0437502i | ||||
\(755\) | 0.544894 | 0.0198307 | ||||||||
\(756\) | −1.27509 | − | 2.14871i | −0.0463746 | − | 0.0781479i | ||||
\(757\) | 25.9905 | 0.944641 | 0.472321 | − | 0.881427i | \(-0.343416\pi\) | ||||
0.472321 | + | 0.881427i | \(0.343416\pi\) | |||||||
\(758\) | 18.4904 | + | 32.0263i | 0.671600 | + | 1.16325i | ||||
\(759\) | −1.67817 | + | 2.90667i | −0.0609137 | + | 0.105506i | ||||
\(760\) | −30.6682 | + | 53.1189i | −1.11245 | + | 1.92683i | ||||
\(761\) | −6.66350 | − | 11.5415i | −0.241552 | − | 0.418380i | 0.719605 | − | 0.694384i | \(-0.244323\pi\) |
−0.961156 | + | 0.276004i | \(0.910990\pi\) | |||||||
\(762\) | −17.2288 | −0.624134 | ||||||||
\(763\) | 1.49435 | + | 2.51819i | 0.0540990 | + | 0.0911647i | ||||
\(764\) | −1.47416 | −0.0533334 | ||||||||
\(765\) | 22.6478 | + | 39.2271i | 0.818833 | + | 1.41826i | ||||
\(766\) | 1.94014 | − | 3.36043i | 0.0701002 | − | 0.121417i | ||||
\(767\) | −1.01828 | + | 1.76372i | −0.0367680 | + | 0.0636841i | ||||
\(768\) | −12.0245 | − | 20.8270i | −0.433896 | − | 0.751530i | ||||
\(769\) | 9.24486 | 0.333378 | 0.166689 | − | 0.986010i | \(-0.446692\pi\) | ||||
0.166689 | + | 0.986010i | \(0.446692\pi\) | |||||||
\(770\) | −19.7926 | + | 0.236900i | −0.713275 | + | 0.00853728i | ||||
\(771\) | 4.60503 | 0.165846 | ||||||||
\(772\) | 2.70550 | + | 4.68607i | 0.0973732 | + | 0.168655i | ||||
\(773\) | 5.07097 | − | 8.78317i | 0.182390 | − | 0.315909i | −0.760304 | − | 0.649568i | \(-0.774950\pi\) |
0.942694 | + | 0.333659i | \(0.108283\pi\) | |||||||
\(774\) | −0.812552 | + | 1.40738i | −0.0292066 | + | 0.0505873i | ||||
\(775\) | 17.8661 | + | 30.9450i | 0.641768 | + | 1.11158i | ||||
\(776\) | 7.06912 | 0.253766 | ||||||||
\(777\) | −10.5003 | + | 18.7005i | −0.376698 | + | 0.670876i | ||||
\(778\) | 35.1092 | 1.25873 | ||||||||
\(779\) | 1.81415 | + | 3.14220i | 0.0649987 | + | 0.112581i | ||||
\(780\) | 1.51846 | − | 2.63005i | 0.0543696 | − | 0.0941709i | ||||
\(781\) | −3.66725 | + | 6.35186i | −0.131225 | + | 0.227288i | ||||
\(782\) | 1.58725 | + | 2.74920i | 0.0567600 | + | 0.0983112i | ||||
\(783\) | −2.59919 | −0.0928873 | ||||||||
\(784\) | 10.2124 | − | 18.7088i | 0.364729 | − | 0.668170i | ||||
\(785\) | 35.0396 | 1.25062 | ||||||||
\(786\) | 17.5677 | + | 30.4282i | 0.626620 | + | 1.08534i | ||||
\(787\) | −22.6411 | + | 39.2156i | −0.807070 | + | 1.39789i | 0.107815 | + | 0.994171i | \(0.465614\pi\) |
−0.914885 | + | 0.403715i | \(0.867719\pi\) | |||||||
\(788\) | −1.93195 | + | 3.34624i | −0.0688230 | + | 0.119205i | ||||
\(789\) | 35.3916 | + | 61.3000i | 1.25997 | + | 2.18234i | ||||
\(790\) | 32.1859 | 1.14512 | ||||||||
\(791\) | 1.41979 | − | 2.52857i | 0.0504821 | − | 0.0899056i | ||||
\(792\) | −24.1237 | −0.857197 | ||||||||
\(793\) | −1.20041 | − | 2.07917i | −0.0426277 | − | 0.0738334i | ||||
\(794\) | −10.9040 | + | 18.8862i | −0.386967 | + | 0.670247i | ||||
\(795\) | −27.1445 | + | 47.0157i | −0.962718 | + | 1.66748i | ||||
\(796\) | 5.23121 | + | 9.06072i | 0.185415 | + | 0.321149i | ||||
\(797\) | 27.0784 | 0.959165 | 0.479583 | − | 0.877497i | \(-0.340788\pi\) | ||||
0.479583 | + | 0.877497i | \(0.340788\pi\) | |||||||
\(798\) | −61.2440 | + | 0.733038i | −2.16802 | + | 0.0259493i | ||||
\(799\) | 42.1686 | 1.49182 | ||||||||
\(800\) | −3.79629 | − | 6.57536i | −0.134219 | − | 0.232474i | ||||
\(801\) | 5.23140 | − | 9.06106i | 0.184843 | − | 0.320157i | ||||
\(802\) | −10.5324 | + | 18.2427i | −0.371912 | + | 0.644171i | ||||
\(803\) | −3.03013 | − | 5.24834i | −0.106931 | − | 0.185210i | ||||
\(804\) | 15.3741 | 0.542204 | ||||||||
\(805\) | −2.45837 | − | 4.14272i | −0.0866463 | − | 0.146012i | ||||
\(806\) | −13.2034 | −0.465071 | ||||||||
\(807\) | −28.9909 | − | 50.2137i | −1.02053 | − | 1.76760i | ||||
\(808\) | 2.20546 | − | 3.81996i | 0.0775877 | − | 0.134386i | ||||
\(809\) | 12.8899 | − | 22.3260i | 0.453185 | − | 0.784939i | −0.545397 | − | 0.838178i | \(-0.683621\pi\) |
0.998582 | + | 0.0532388i | \(0.0169544\pi\) | |||||||
\(810\) | −10.0610 | − | 17.4261i | −0.353507 | − | 0.612291i | ||||
\(811\) | −25.7829 | −0.905362 | −0.452681 | − | 0.891673i | \(-0.649532\pi\) | ||||
−0.452681 | + | 0.891673i | \(0.649532\pi\) | |||||||
\(812\) | 0.589352 | + | 0.993144i | 0.0206822 | + | 0.0348525i | ||||
\(813\) | 23.5459 | 0.825792 | ||||||||
\(814\) | 3.97626 | + | 6.88708i | 0.139368 | + | 0.241392i | ||||
\(815\) | 21.6440 | − | 37.4886i | 0.758158 | − | 1.31317i | ||||
\(816\) | −15.9945 | + | 27.7032i | −0.559918 | + | 0.969807i | ||||
\(817\) | −1.14535 | − | 1.98380i | −0.0400707 | − | 0.0694045i | ||||
\(818\) | −17.2550 | −0.603308 | ||||||||
\(819\) | 10.3246 | − | 0.123576i | 0.360770 | − | 0.00431810i | ||||
\(820\) | −0.602407 | −0.0210370 | ||||||||
\(821\) | 0.855366 | + | 1.48154i | 0.0298525 | + | 0.0517060i | 0.880566 | − | 0.473924i | \(-0.157163\pi\) |
−0.850713 | + | 0.525630i | \(0.823830\pi\) | |||||||
\(822\) | −9.76214 | + | 16.9085i | −0.340494 | + | 0.589752i | ||||
\(823\) | 20.1887 | − | 34.9678i | 0.703733 | − | 1.21890i | −0.263414 | − | 0.964683i | \(-0.584849\pi\) |
0.967147 | − | 0.254218i | \(-0.0818181\pi\) | |||||||
\(824\) | −17.6579 | − | 30.5844i | −0.615142 | − | 1.06546i | ||||
\(825\) | −18.3264 | −0.638042 | ||||||||
\(826\) | −3.33878 | + | 5.94616i | −0.116171 | + | 0.206893i | ||||
\(827\) | 19.5698 | 0.680509 | 0.340254 | − | 0.940333i | \(-0.389487\pi\) | ||||
0.340254 | + | 0.940333i | \(0.389487\pi\) | |||||||
\(828\) | −0.487444 | − | 0.844278i | −0.0169399 | − | 0.0293407i | ||||
\(829\) | −20.7871 | + | 36.0043i | −0.721966 | + | 1.25048i | 0.238244 | + | 0.971205i | \(0.423428\pi\) |
−0.960211 | + | 0.279277i | \(0.909905\pi\) | |||||||
\(830\) | 23.5178 | − | 40.7341i | 0.816316 | − | 1.41390i | ||||
\(831\) | −9.89073 | − | 17.1312i | −0.343106 | − | 0.594276i | ||||
\(832\) | 8.89542 | 0.308393 | ||||||||
\(833\) | 27.9826 | − | 0.669951i | 0.969540 | − | 0.0232124i | ||||
\(834\) | 13.3004 | 0.460556 | ||||||||
\(835\) | 7.33870 | + | 12.7110i | 0.253966 | + | 0.439882i | ||||
\(836\) | 2.82324 | − | 4.89000i | 0.0976438 | − | 0.169124i | ||||
\(837\) | −12.3697 | + | 21.4250i | −0.427560 | + | 0.740555i | ||||
\(838\) | 6.86604 | + | 11.8923i | 0.237183 | + | 0.410814i | ||||
\(839\) | 45.8480 | 1.58285 | 0.791425 | − | 0.611266i | \(-0.209340\pi\) | ||||
0.791425 | + | 0.611266i | \(0.209340\pi\) | |||||||
\(840\) | 29.9830 | − | 53.3979i | 1.03451 | − | 1.84240i | ||||
\(841\) | −27.7986 | −0.958574 | ||||||||
\(842\) | 6.32804 | + | 10.9605i | 0.218079 | + | 0.377723i | ||||
\(843\) | 39.1152 | − | 67.7496i | 1.34720 | − | 2.33342i | ||||
\(844\) | 1.99791 | − | 3.46049i | 0.0687710 | − | 0.119115i | ||||
\(845\) | 1.45130 | + | 2.51373i | 0.0499262 | + | 0.0864748i | ||||
\(846\) | 52.0869 | 1.79078 | ||||||||
\(847\) | −18.1285 | + | 0.216982i | −0.622902 | + | 0.00745559i | ||||
\(848\) | −21.6769 | −0.744388 | ||||||||
\(849\) | 0.395998 | + | 0.685889i | 0.0135906 | + | 0.0235397i | ||||
\(850\) | −8.66674 | + | 15.0112i | −0.297267 | + | 0.514881i | ||||
\(851\) | −0.967695 | + | 1.67610i | −0.0331722 | + | 0.0574559i | ||||
\(852\) | −1.88403 | − | 3.26324i | −0.0645459 | − | 0.111797i | ||||
\(853\) | 40.0236 | 1.37038 | 0.685191 | − | 0.728364i | \(-0.259719\pi\) | ||||
0.685191 | + | 0.728364i | \(0.259719\pi\) | |||||||
\(854\) | −4.10258 | − | 6.91345i | −0.140387 | − | 0.236573i | ||||
\(855\) | −78.8645 | −2.69711 | ||||||||
\(856\) | 29.7846 | + | 51.5884i | 1.01802 | + | 1.76326i | ||||
\(857\) | −16.4351 | + | 28.4664i | −0.561412 | + | 0.972395i | 0.435961 | + | 0.899966i | \(0.356409\pi\) |
−0.997374 | + | 0.0724294i | \(0.976925\pi\) | |||||||
\(858\) | 3.38590 | − | 5.86455i | 0.115593 | − | 0.200212i | ||||
\(859\) | 17.0252 | + | 29.4885i | 0.580891 | + | 1.00613i | 0.995374 | + | 0.0960762i | \(0.0306292\pi\) |
−0.414483 | + | 0.910057i | \(0.636037\pi\) | |||||||
\(860\) | 0.380325 | 0.0129690 | ||||||||
\(861\) | −1.84871 | − | 3.11535i | −0.0630038 | − | 0.106171i | ||||
\(862\) | 1.53079 | 0.0521388 | ||||||||
\(863\) | 7.03208 | + | 12.1799i | 0.239375 | + | 0.414609i | 0.960535 | − | 0.278159i | \(-0.0897243\pi\) |
−0.721160 | + | 0.692768i | \(0.756391\pi\) | |||||||
\(864\) | 2.62839 | − | 4.55250i | 0.0894195 | − | 0.154879i | ||||
\(865\) | −0.864415 | + | 1.49721i | −0.0293910 | + | 0.0509067i | ||||
\(866\) | 3.52106 | + | 6.09866i | 0.119651 | + | 0.207241i | ||||
\(867\) | 2.65537 | 0.0901813 | ||||||||
\(868\) | 10.9912 | − | 0.131555i | 0.373066 | − | 0.00446527i | ||||
\(869\) | −17.8434 | −0.605295 | ||||||||
\(870\) | −5.28930 | − | 9.16134i | −0.179324 | − | 0.310599i | ||||
\(871\) | −7.34709 | + | 12.7255i | −0.248947 | + | 0.431188i | ||||
\(872\) | −1.67963 | + | 2.90920i | −0.0568794 | + | 0.0985180i | ||||
\(873\) | 4.54463 | + | 7.87152i | 0.153812 | + | 0.266411i | ||||
\(874\) | −5.52715 | −0.186959 | ||||||||
\(875\) | −5.92153 | + | 10.5459i | −0.200184 | + | 0.356516i | ||||
\(876\) | 3.11343 | 0.105193 | ||||||||
\(877\) | −25.5335 | − | 44.2252i | −0.862204 | − | 1.49338i | −0.869797 | − | 0.493409i | \(-0.835751\pi\) |
0.00759373 | − | 0.999971i | \(-0.497583\pi\) | |||||||
\(878\) | 12.4784 | − | 21.6132i | 0.421125 | − | 0.729411i | ||||
\(879\) | −25.2838 | + | 43.7927i | −0.852800 | + | 1.47709i | ||||
\(880\) | −8.99982 | − | 15.5881i | −0.303384 | − | 0.525476i | ||||
\(881\) | −18.4203 | −0.620597 | −0.310298 | − | 0.950639i | \(-0.600429\pi\) | ||||
−0.310298 | + | 0.950639i | \(0.600429\pi\) | |||||||
\(882\) | 34.5642 | − | 0.827526i | 1.16384 | − | 0.0278643i | ||||
\(883\) | 0.126678 | 0.00426305 | 0.00213153 | − | 0.999998i | \(-0.499322\pi\) | ||||
0.00213153 | + | 0.999998i | \(0.499322\pi\) | |||||||
\(884\) | 0.796204 | + | 1.37907i | 0.0267792 | + | 0.0463830i | ||||
\(885\) | −7.76536 | + | 13.4500i | −0.261030 | + | 0.452117i | ||||
\(886\) | −14.0679 | + | 24.3663i | −0.472619 | + | 0.818601i | ||||
\(887\) | −1.93735 | − | 3.35559i | −0.0650498 | − | 0.112670i | 0.831666 | − | 0.555276i | \(-0.187387\pi\) |
−0.896716 | + | 0.442606i | \(0.854054\pi\) | |||||||
\(888\) | −24.6039 | −0.825654 | ||||||||
\(889\) | −6.71181 | + | 11.9533i | −0.225107 | + | 0.400902i | ||||
\(890\) | 9.84874 | 0.330131 | ||||||||
\(891\) | 5.57765 | + | 9.66078i | 0.186858 | + | 0.323648i | ||||
\(892\) | 3.48378 | − | 6.03409i | 0.116646 | − | 0.202036i | ||||
\(893\) | −36.7100 | + | 63.5837i | −1.22845 | + | 2.12775i | ||||
\(894\) | −16.8008 | − | 29.0998i | −0.561903 | − | 0.973244i | ||||
\(895\) | −23.4433 | −0.783622 | ||||||||
\(896\) | 18.0549 | − | 0.216102i | 0.603173 | − | 0.00721945i | ||||
\(897\) | 1.64804 | 0.0550265 | ||||||||
\(898\) | −11.6802 | − | 20.2308i | −0.389775 | − | 0.675109i | ||||
\(899\) | 5.71733 | − | 9.90270i | 0.190684 | − | 0.330274i | ||||
\(900\) | 2.66155 | − | 4.60995i | 0.0887185 | − | 0.153665i | ||||
\(901\) | −14.2332 | − | 24.6527i | −0.474178 | − | 0.821300i | ||||
\(902\) | −1.34326 | −0.0447257 | ||||||||
\(903\) | 1.16717 | + | 1.96685i | 0.0388409 | + | 0.0654527i | ||||
\(904\) | 3.32680 | 0.110648 | ||||||||
\(905\) | 2.74766 | + | 4.75909i | 0.0913355 | + | 0.158198i | ||||
\(906\) | −0.312105 | + | 0.540581i | −0.0103690 | + | 0.0179596i | ||||
\(907\) | 23.3871 | − | 40.5076i | 0.776555 | − | 1.34503i | −0.157362 | − | 0.987541i | \(-0.550299\pi\) |
0.933916 | − | 0.357491i | \(-0.116368\pi\) | |||||||
\(908\) | −1.89486 | − | 3.28200i | −0.0628832 | − | 0.108917i | ||||
\(909\) | 5.67142 | 0.188109 | ||||||||
\(910\) | 4.96005 | + | 8.35841i | 0.164424 | + | 0.277079i | ||||
\(911\) | 5.93675 | 0.196693 | 0.0983467 | − | 0.995152i | \(-0.468645\pi\) | ||||
0.0983467 | + | 0.995152i | \(0.468645\pi\) | |||||||
\(912\) | −27.8481 | − | 48.2343i | −0.922142 | − | 1.59720i | ||||
\(913\) | −13.0379 | + | 22.5824i | −0.431493 | + | 0.747368i | ||||
\(914\) | 18.9727 | − | 32.8617i | 0.627561 | − | 1.08697i | ||||
\(915\) | −9.15424 | − | 15.8556i | −0.302630 | − | 0.524170i | ||||
\(916\) | −8.40952 | −0.277858 | ||||||||
\(917\) | 27.9549 | − | 0.334595i | 0.923151 | − | 0.0110493i | ||||
\(918\) | −12.0010 | −0.396091 | ||||||||
\(919\) | 4.29351 | + | 7.43657i | 0.141630 | + | 0.245310i | 0.928110 | − | 0.372305i | \(-0.121432\pi\) |
−0.786481 | + | 0.617615i | \(0.788099\pi\) | |||||||
\(920\) | 2.76318 | − | 4.78597i | 0.0910995 | − | 0.157789i | ||||
\(921\) | −4.69993 | + | 8.14051i | −0.154868 | + | 0.268239i | ||||
\(922\) | −18.4461 | − | 31.9496i | −0.607490 | − | 1.05220i | ||||
\(923\) | 3.60141 | 0.118542 | ||||||||
\(924\) | −2.76016 | + | 4.91568i | −0.0908025 | + | 0.161714i | ||||
\(925\) | −10.5677 | −0.347463 | ||||||||
\(926\) | −0.986543 | − | 1.70874i | −0.0324198 | − | 0.0561528i | ||||
\(927\) | 22.7040 | − | 39.3244i | 0.745696 | − | 1.29158i | ||||
\(928\) | −1.21485 | + | 2.10418i | −0.0398794 | + | 0.0690732i | ||||
\(929\) | 4.22972 | + | 7.32610i | 0.138773 | + | 0.240361i | 0.927032 | − | 0.374981i | \(-0.122351\pi\) |
−0.788260 | + | 0.615343i | \(0.789018\pi\) | |||||||
\(930\) | −100.689 | −3.30171 | ||||||||
\(931\) | −23.3502 | + | 42.7766i | −0.765271 | + | 1.40195i | ||||
\(932\) | −5.64648 | −0.184957 | ||||||||
\(933\) | −31.3049 | − | 54.2216i | −1.02487 | − | 1.77514i | ||||
\(934\) | −7.86141 | + | 13.6164i | −0.257233 | + | 0.445541i | ||||
\(935\) | 11.8187 | − | 20.4706i | 0.386513 | − | 0.669460i | ||||
\(936\) | 5.92264 | + | 10.2583i | 0.193587 | + | 0.335303i | ||||
\(937\) | −33.3596 | −1.08981 | −0.544905 | − | 0.838498i | \(-0.683434\pi\) | ||||
−0.544905 | + | 0.838498i | \(0.683434\pi\) | |||||||
\(938\) | −24.0899 | + | 42.9026i | −0.786562 | + | 1.40082i | ||||
\(939\) | 47.5048 | 1.55026 | ||||||||
\(940\) | −6.09497 | − | 10.5568i | −0.198796 | − | 0.344325i | ||||
\(941\) | 6.70187 | − | 11.6080i | 0.218475 | − | 0.378409i | −0.735867 | − | 0.677126i | \(-0.763225\pi\) |
0.954342 | + | 0.298717i | \(0.0965586\pi\) | |||||||
\(942\) | −20.0700 | + | 34.7623i | −0.653916 | + | 1.13262i | ||||
\(943\) | −0.163454 | − | 0.283110i | −0.00532278 | − | 0.00921933i | ||||
\(944\) | −6.20121 | −0.201832 | ||||||||
\(945\) | 18.2099 | − | 0.217956i | 0.592367 | − | 0.00709012i | ||||
\(946\) | 0.848057 | 0.0275727 | ||||||||
\(947\) | −21.5397 | − | 37.3078i | −0.699946 | − | 1.21234i | −0.968485 | − | 0.249073i | \(-0.919874\pi\) |
0.268539 | − | 0.963269i | \(-0.413459\pi\) | |||||||
\(948\) | 4.58347 | − | 7.93881i | 0.148864 | − | 0.257840i | ||||
\(949\) | −1.48786 | + | 2.57706i | −0.0482981 | + | 0.0836548i | ||||
\(950\) | −15.0897 | − | 26.1362i | −0.489575 | − | 0.847969i | ||||
\(951\) | 72.3768 | 2.34698 | ||||||||
\(952\) | 16.3872 | + | 27.6149i | 0.531113 | + | 0.895003i | ||||
\(953\) | 16.7332 | 0.542040 | 0.271020 | − | 0.962574i | \(-0.412639\pi\) | ||||
0.271020 | + | 0.962574i | \(0.412639\pi\) | |||||||
\(954\) | −17.5810 | − | 30.4511i | −0.569204 | − | 0.985891i | ||||
\(955\) | 5.37234 | − | 9.30517i | 0.173845 | − | 0.301108i | ||||
\(956\) | −3.29091 | + | 5.70002i | −0.106436 | + | 0.184352i | ||||
\(957\) | 2.93231 | + | 5.07891i | 0.0947881 | + | 0.164178i | ||||
\(958\) | 45.6325 | 1.47432 | ||||||||
\(959\) | 7.92809 | + | 13.3600i | 0.256011 | + | 0.431417i | ||||
\(960\) | 67.8360 | 2.18940 | ||||||||
\(961\) | −38.9183 | − | 67.4085i | −1.25543 | − | 2.17447i | ||||
\(962\) | 1.95243 | − | 3.38172i | 0.0629490 | − | 0.109031i | ||||
\(963\) | −38.2961 | + | 66.3308i | −1.23407 | + | 2.13748i | ||||
\(964\) | −2.72572 | − | 4.72109i | −0.0877896 | − | 0.152056i | ||||
\(965\) | −39.4390 | −1.26959 | ||||||||
\(966\) | 5.51804 | − | 0.0660462i | 0.177540 | − | 0.00212500i | ||||
\(967\) | 44.7594 | 1.43937 | 0.719683 | − | 0.694303i | \(-0.244287\pi\) | ||||
0.719683 | + | 0.694303i | \(0.244287\pi\) | |||||||
\(968\) | −10.3993 | − | 18.0121i | −0.334246 | − | 0.578932i | ||||
\(969\) | 36.5705 | − | 63.3420i | 1.17482 | − | 2.03484i | ||||
\(970\) | −4.27790 | + | 7.40954i | −0.137355 | + | 0.237906i | ||||
\(971\) | 2.10129 | + | 3.63955i | 0.0674337 | + | 0.116799i | 0.897771 | − | 0.440463i | \(-0.145186\pi\) |
−0.830337 | + | 0.557261i | \(0.811852\pi\) | |||||||
\(972\) | −8.56409 | −0.274693 | ||||||||
\(973\) | 5.18143 | − | 9.22783i | 0.166109 | − | 0.295830i | ||||
\(974\) | 9.23899 | 0.296036 | ||||||||
\(975\) | 4.49933 | + | 7.79307i | 0.144094 | + | 0.249578i | ||||
\(976\) | 3.65517 | − | 6.33093i | 0.116999 | − | 0.202648i | ||||
\(977\) | 12.8449 | − | 22.2481i | 0.410946 | − | 0.711779i | −0.584048 | − | 0.811719i | \(-0.698532\pi\) |
0.994993 | + | 0.0999403i | \(0.0318652\pi\) | |||||||
\(978\) | 24.7946 | + | 42.9455i | 0.792843 | + | 1.37325i | ||||
\(979\) | −5.45999 | −0.174502 | ||||||||
\(980\) | −4.21227 | − | 6.90854i | −0.134556 | − | 0.220685i | ||||
\(981\) | −4.31923 | −0.137902 | ||||||||
\(982\) | −2.84242 | − | 4.92321i | −0.0907051 | − | 0.157106i | ||||
\(983\) | 15.9122 | − | 27.5607i | 0.507520 | − | 0.879051i | −0.492442 | − | 0.870345i | \(-0.663896\pi\) |
0.999962 | − | 0.00870538i | \(-0.00277104\pi\) | |||||||
\(984\) | 2.07793 | − | 3.59908i | 0.0662419 | − | 0.114734i | ||||
\(985\) | −14.0814 | − | 24.3896i | −0.448669 | − | 0.777118i | ||||
\(986\) | 5.54689 | 0.176649 | ||||||||
\(987\) | 35.8898 | − | 63.9176i | 1.14238 | − | 2.03452i | ||||
\(988\) | −2.77255 | −0.0882067 | ||||||||
\(989\) | 0.103195 | + | 0.178739i | 0.00328141 | + | 0.00568358i | ||||
\(990\) | 14.5985 | − | 25.2854i | 0.463971 | − | 0.803622i | ||||
\(991\) | −4.73739 | + | 8.20540i | −0.150488 | + | 0.260653i | −0.931407 | − | 0.363979i | \(-0.881418\pi\) |
0.780919 | + | 0.624632i | \(0.214751\pi\) | |||||||
\(992\) | 11.5631 | + | 20.0279i | 0.367129 | + | 0.635887i | ||||
\(993\) | 47.7676 | 1.51586 | ||||||||
\(994\) | 12.0584 | − | 0.144329i | 0.382469 | − | 0.00457783i | ||||
\(995\) | −76.2570 | −2.41751 | ||||||||
\(996\) | −6.69818 | − | 11.6016i | −0.212240 | − | 0.367611i | ||||
\(997\) | −10.9755 | + | 19.0102i | −0.347599 | + | 0.602059i | −0.985822 | − | 0.167792i | \(-0.946336\pi\) |
0.638224 | + | 0.769851i | \(0.279670\pi\) | |||||||
\(998\) | −7.19332 | + | 12.4592i | −0.227701 | + | 0.394389i | ||||
\(999\) | −3.65830 | − | 6.33636i | −0.115743 | − | 0.200473i |
(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 | 91.2.e.c.53.3 | ✓ | 10 | |
3.2 | odd | 2 | 819.2.j.h.235.3 | 10 | |||
4.3 | odd | 2 | 1456.2.r.p.417.1 | 10 | |||
7.2 | even | 3 | inner | 91.2.e.c.79.3 | yes | 10 | |
7.3 | odd | 6 | 637.2.a.k.1.3 | 5 | |||
7.4 | even | 3 | 637.2.a.l.1.3 | 5 | |||
7.5 | odd | 6 | 637.2.e.m.79.3 | 10 | |||
7.6 | odd | 2 | 637.2.e.m.508.3 | 10 | |||
13.12 | even | 2 | 1183.2.e.f.508.3 | 10 | |||
21.2 | odd | 6 | 819.2.j.h.352.3 | 10 | |||
21.11 | odd | 6 | 5733.2.a.bl.1.3 | 5 | |||
21.17 | even | 6 | 5733.2.a.bm.1.3 | 5 | |||
28.23 | odd | 6 | 1456.2.r.p.625.1 | 10 | |||
91.25 | even | 6 | 8281.2.a.bw.1.3 | 5 | |||
91.38 | odd | 6 | 8281.2.a.bx.1.3 | 5 | |||
91.51 | even | 6 | 1183.2.e.f.170.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
91.2.e.c.79.3 | yes | 10 | 7.2 | even | 3 | inner | |
637.2.a.k.1.3 | 5 | 7.3 | odd | 6 | |||
637.2.a.l.1.3 | 5 | 7.4 | even | 3 | |||
637.2.e.m.79.3 | 10 | 7.5 | odd | 6 | |||
637.2.e.m.508.3 | 10 | 7.6 | odd | 2 | |||
819.2.j.h.235.3 | 10 | 3.2 | odd | 2 | |||
819.2.j.h.352.3 | 10 | 21.2 | odd | 6 | |||
1183.2.e.f.170.3 | 10 | 91.51 | even | 6 | |||
1183.2.e.f.508.3 | 10 | 13.12 | even | 2 | |||
1456.2.r.p.417.1 | 10 | 4.3 | odd | 2 | |||
1456.2.r.p.625.1 | 10 | 28.23 | odd | 6 | |||
5733.2.a.bl.1.3 | 5 | 21.11 | odd | 6 | |||
5733.2.a.bm.1.3 | 5 | 21.17 | even | 6 | |||
8281.2.a.bw.1.3 | 5 | 91.25 | even | 6 | |||
8281.2.a.bx.1.3 | 5 | 91.38 | odd | 6 |