Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
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: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.3 | ||
Root | \(-0.132804 + 0.230024i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.f.508.3 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.632804 | − | 1.09605i | 0.447460 | − | 0.775024i | −0.550760 | − | 0.834664i | \(-0.685662\pi\) |
0.998220 | + | 0.0596401i | \(0.0189953\pi\) | |||||||
\(3\) | 1.31364 | + | 2.27529i | 0.758430 | + | 1.31364i | 0.943651 | + | 0.330943i | \(0.107367\pi\) |
−0.185220 | + | 0.982697i | \(0.559300\pi\) | |||||||
\(4\) | 0.199118 | + | 0.344882i | 0.0995588 | + | 0.172441i | ||||
\(5\) | −1.45130 | + | 2.51373i | −0.649041 | + | 1.12417i | 0.334311 | + | 0.942463i | \(0.391496\pi\) |
−0.983352 | + | 0.181709i | \(0.941837\pi\) | |||||||
\(6\) | 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 | \(-0.0673336\pi\) |
−0.670686 | + | 0.741741i | \(0.734000\pi\) | |||||||
\(12\) | −0.523138 | + | 0.906101i | −0.151017 | + | 0.261569i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 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 | 0.514941 | − | 0.857226i | \(-0.327814\pi\) |
−0.999850 | + | 0.0173386i | \(0.994481\pi\) | |||||||
\(18\) | 2.46958 | + | 4.27744i | 0.582086 | + | 1.00820i | ||||
\(19\) | 3.48105 | − | 6.02935i | 0.798608 | − | 1.38323i | −0.121915 | − | 0.992540i | \(-0.538904\pi\) |
0.920523 | − | 0.390688i | \(-0.127763\pi\) | |||||||
\(20\) | −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 | −0.831472 | − | 0.555566i | \(-0.812501\pi\) |
0.896871 | + | 0.442293i | \(0.145835\pi\) | |||||||
\(24\) | 3.98720 | + | 6.90602i | 0.813883 | + | 1.40969i | ||||
\(25\) | −1.71254 | − | 2.96621i | −0.342509 | − | 0.593243i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −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 | −0.771275 | − | 0.636502i | \(-0.780381\pi\) |
−0.165589 | − | 0.986195i | \(-0.552953\pi\) | |||||||
\(32\) | 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 | \(-0.914953\pi\) |
0.710903 | + | 0.703290i | \(0.248287\pi\) | |||||||
\(38\) | −4.40565 | − | 7.63080i | −0.714690 | − | 1.23788i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.40502 | + | 7.62973i | −0.696496 | + | 1.20637i | ||||
\(41\) | 0.521150 | 0.0813900 | 0.0406950 | − | 0.999172i | \(-0.487043\pi\) | ||||
0.0406950 | + | 0.999172i | \(0.487043\pi\) | |||||||
\(42\) | 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 | −0.168916 | − | 0.985630i | \(-0.554027\pi\) |
0.938039 | − | 0.346530i | \(-0.112640\pi\) | |||||||
\(48\) | 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 | 0 | ||||||||
\(53\) | −3.55950 | − | 6.16523i | −0.488935 | − | 0.846860i | 0.510984 | − | 0.859590i | \(-0.329281\pi\) |
−0.999919 | + | 0.0127302i | \(0.995948\pi\) | |||||||
\(54\) | −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 | \(-0.124344\pi\) |
−0.792097 | + | 0.610395i | \(0.791011\pi\) | |||||||
\(60\) | −1.51846 | − | 2.63005i | −0.196032 | − | 0.339538i | ||||
\(61\) | −1.20041 | + | 2.07917i | −0.153696 | + | 0.266210i | −0.932584 | − | 0.360954i | \(-0.882451\pi\) |
0.778887 | + | 0.627164i | \(0.215784\pi\) | |||||||
\(62\) | −13.2034 | −1.67684 | ||||||||
\(63\) | −10.3246 | − | 0.123576i | −1.30077 | − | 0.0155691i | ||||
\(64\) | 8.89542 | 1.11193 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.38590 | + | 5.86455i | 0.416775 | + | 0.721876i | ||||
\(67\) | 7.34709 | + | 12.7255i | 0.897589 | + | 1.55467i | 0.830567 | + | 0.556919i | \(0.188017\pi\) |
0.0670226 | + | 0.997751i | \(0.478650\pi\) | |||||||
\(68\) | 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 | \(-0.568553\pi\) | ||||
−0.213704 | + | 0.976898i | \(0.568553\pi\) | |||||||
\(72\) | −5.92264 | + | 10.2583i | −0.697990 | + | 1.20895i | ||||
\(73\) | 1.48786 | + | 2.57706i | 0.174141 | + | 0.301622i | 0.939864 | − | 0.341550i | \(-0.110952\pi\) |
−0.765722 | + | 0.643171i | \(0.777618\pi\) | |||||||
\(74\) | 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 | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.38075 | − | 7.58769i | 0.492873 | − | 0.853681i | −0.507093 | − | 0.861891i | \(-0.669280\pi\) |
0.999966 | + | 0.00820995i | \(0.00261334\pi\) | |||||||
\(80\) | 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 | \(-0.748024\pi\) | ||||
−0.702703 | + | 0.711483i | \(0.748024\pi\) | |||||||
\(84\) | −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 | \(-0.878716\pi\) |
0.786192 | + | 0.617982i | \(0.212050\pi\) | |||||||
\(90\) | −14.3364 | −1.51119 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 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 | \(-0.462275\pi\) | ||||
0.118238 | + | 0.992985i | \(0.462275\pi\) | |||||||
\(98\) | 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 | 0.827608 | − | 0.561306i | \(-0.189701\pi\) |
−0.899910 | + | 0.436077i | \(0.856368\pi\) | |||||||
\(102\) | −6.64799 | − | 11.5147i | −0.658249 | − | 1.14012i | ||||
\(103\) | 5.81765 | − | 10.0765i | 0.573230 | − | 0.992864i | −0.423001 | − | 0.906129i | \(-0.639023\pi\) |
0.996231 | − | 0.0867346i | \(-0.0276432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.87833 | − | 17.5927i | −0.964026 | − | 1.71687i | ||||
\(106\) | −9.00987 | −0.875115 | ||||||||
\(107\) | −9.81297 | + | 16.9966i | −0.948656 | + | 1.64312i | −0.200395 | + | 0.979715i | \(0.564223\pi\) |
−0.748261 | + | 0.663405i | \(0.769111\pi\) | |||||||
\(108\) | −0.472184 | − | 0.817847i | −0.0454359 | − | 0.0786973i | ||||
\(109\) | −0.553378 | − | 0.958479i | −0.0530040 | − | 0.0918057i | 0.838306 | − | 0.545200i | \(-0.183546\pi\) |
−0.891310 | + | 0.453394i | \(0.850213\pi\) | |||||||
\(110\) | −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 | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.28335 | + | 9.15103i | −0.461609 | + | 0.799530i | −0.999041 | − | 0.0437770i | \(-0.986061\pi\) |
0.537433 | + | 0.843307i | \(0.319394\pi\) | |||||||
\(132\) | −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 | \(-0.247370\pi\) |
−0.963754 | + | 0.266791i | \(0.914037\pi\) | |||||||
\(138\) | 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 | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 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 | \(-0.969179\pi\) |
0.581382 | + | 0.813631i | \(0.302512\pi\) | |||||||
\(150\) | −5.69439 | − | 9.86298i | −0.464945 | − | 0.805309i | ||||
\(151\) | −0.0938631 | − | 0.162576i | −0.00763847 | − | 0.0132302i | 0.862181 | − | 0.506601i | \(-0.169098\pi\) |
−0.869819 | + | 0.493370i | \(0.835765\pi\) | |||||||
\(152\) | 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 | 0 | ||||||||
\(157\) | 6.03590 | + | 10.4545i | 0.481717 | + | 0.834358i | 0.999780 | − | 0.0209844i | \(-0.00668003\pi\) |
−0.518063 | + | 0.855343i | \(0.673347\pi\) | |||||||
\(158\) | −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 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) |
0.994992 | − | 0.0999554i | \(-0.0318700\pi\) | |||||||
\(164\) | 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 | \(-0.562681\pi\) | ||||
−0.195647 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(168\) | −10.7671 | + | 18.1441i | −0.830696 | + | 1.39984i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 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 | −0.854482 | − | 0.519480i | \(-0.826126\pi\) |
0.877124 | + | 0.480263i | \(0.159459\pi\) | |||||||
\(174\) | 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 | 0.674714 | − | 0.738079i | \(-0.264267\pi\) |
−0.976552 | + | 0.215280i | \(0.930934\pi\) | |||||||
\(180\) | 2.25554 | − | 3.90671i | 0.168118 | − | 0.291189i | ||||
\(181\) | 1.89324 | 0.140724 | 0.0703618 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703618 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −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 | −0.925186 | − | 0.379514i | \(-0.876091\pi\) |
0.791262 | + | 0.611478i | \(0.209425\pi\) | |||||||
\(192\) | 11.6854 | + | 20.2397i | 0.843320 | + | 1.46067i | ||||
\(193\) | 6.79373 | + | 11.7671i | 0.489024 | + | 0.847014i | 0.999920 | − | 0.0126285i | \(-0.00401987\pi\) |
−0.510897 | + | 0.859642i | \(0.670687\pi\) | |||||||
\(194\) | 1.47382 | − | 2.55272i | 0.105814 | − | 0.183275i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.78685 | − | 0.0667218i | −0.199061 | − | 0.00476585i | ||||
\(197\) | 9.70258 | 0.691280 | 0.345640 | − | 0.938367i | \(-0.387662\pi\) | ||||
0.345640 | + | 0.938367i | \(0.387662\pi\) | |||||||
\(198\) | −5.02946 | + | 8.71128i | −0.357428 | + | 0.619084i | ||||
\(199\) | −13.1360 | − | 22.7522i | −0.931185 | − | 1.61286i | −0.781299 | − | 0.624156i | \(-0.785443\pi\) |
−0.149885 | − | 0.988703i | \(-0.547891\pi\) | |||||||
\(200\) | −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 | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 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 | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.12959 | + | 8.88472i | −0.344276 | + | 0.596303i | ||||
\(223\) | −17.4961 | −1.17163 | −0.585813 | − | 0.810446i | \(-0.699225\pi\) | ||||
−0.585813 | + | 0.810446i | \(0.699225\pi\) | |||||||
\(224\) | −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 | \(-0.268943\pi\) |
−0.979609 | + | 0.200912i | \(0.935609\pi\) | |||||||
\(228\) | 3.64214 | + | 6.30837i | 0.241206 | + | 0.417782i | ||||
\(229\) | 10.5585 | − | 18.2878i | 0.697725 | − | 1.20849i | −0.271529 | − | 0.962430i | \(-0.587529\pi\) |
0.969254 | − | 0.246064i | \(-0.0791374\pi\) | |||||||
\(230\) | 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 | −0.999176 | − | 0.0405847i | \(-0.987078\pi\) |
0.534735 | + | 0.845020i | \(0.320411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 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 | \(-0.320486\pi\) | ||||
0.534536 | + | 0.845145i | \(0.320486\pi\) | |||||||
\(240\) | −11.6103 | + | 20.1096i | −0.749439 | + | 1.29807i | ||||
\(241\) | −6.84450 | − | 11.8550i | −0.440893 | − | 0.763649i | 0.556863 | − | 0.830604i | \(-0.312005\pi\) |
−0.997756 | + | 0.0669552i | \(0.978672\pi\) | |||||||
\(242\) | −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 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −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 | −0.837397 | − | 0.546596i | \(-0.815923\pi\) |
0.892064 | + | 0.451909i | \(0.149257\pi\) | |||||||
\(258\) | 1.09404 | 0.0681120 | ||||||||
\(259\) | −8.16254 | − | 0.0976985i | −0.507195 | − | 0.00607069i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −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 | −0.897527 | − | 0.440959i | \(-0.854639\pi\) |
0.0668823 | − | 0.997761i | \(-0.478695\pi\) | |||||||
\(264\) | −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 | 0.977110 | + | 0.212735i | \(0.0682371\pi\) |
−0.304321 | + | 0.952570i | \(0.598430\pi\) | |||||||
\(270\) | −4.35570 | − | 7.54430i | −0.265080 | − | 0.459131i | ||||
\(271\) | −4.48105 | + | 7.76141i | −0.272204 | + | 0.471472i | −0.969426 | − | 0.245384i | \(-0.921086\pi\) |
0.697222 | + | 0.716856i | \(0.254419\pi\) | |||||||
\(272\) | −12.1757 | −0.738259 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −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 | 0.956677 | − | 0.291151i | \(-0.0940382\pi\) |
−0.730483 | + | 0.682931i | \(0.760705\pi\) | |||||||
\(278\) | −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 | \(-0.848010\pi\) | ||||
−0.888151 | + | 0.459553i | \(0.848010\pi\) | |||||||
\(282\) | 17.5328 | − | 30.3676i | 1.04406 | − | 1.80837i | ||||
\(283\) | −0.150726 | − | 0.261064i | −0.00895970 | − | 0.0155187i | 0.861511 | − | 0.507739i | \(-0.169519\pi\) |
−0.870470 | + | 0.492221i | \(0.836185\pi\) | |||||||
\(284\) | −0.717104 | − | 1.24206i | −0.0425523 | − | 0.0737027i | ||||
\(285\) | −26.5463 | + | 45.9795i | −1.57247 | + | 2.72359i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 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 | \(-0.309950\pi\) | ||||
0.562214 | + | 0.826992i | \(0.309950\pi\) | |||||||
\(294\) | −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 | 0 | ||||||||
\(300\) | 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 | \(-0.467445\pi\) | ||||
0.102098 | + | 0.994774i | \(0.467445\pi\) | |||||||
\(308\) | −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 | 0.976277 | + | 0.216526i | \(0.0694725\pi\) |
−0.300622 | + | 0.953743i | \(0.597194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.04068 | − | 15.6589i | 0.511009 | − | 0.885094i | −0.488909 | − | 0.872335i | \(-0.662605\pi\) |
0.999919 | − | 0.0127596i | \(-0.00406161\pi\) | |||||||
\(314\) | 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 | 0.161931 | + | 0.986802i | \(0.448228\pi\) |
−0.935561 | + | 0.353164i | \(0.885106\pi\) | |||||||
\(318\) | −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 | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −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 | \(-0.999878\pi\) | |
0.500331 | + | 0.865834i | \(0.333212\pi\) | |||||||
\(332\) | −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 | 0 | ||||||||
\(339\) | −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 | −0.993156 | − | 0.116794i | \(-0.962738\pi\) |
0.395431 | − | 0.918496i | \(-0.370595\pi\) | |||||||
\(348\) | −0.573392 | + | 0.993144i | −0.0307370 | + | 0.0532381i | ||||
\(349\) | −19.9368 | −1.06719 | −0.533595 | − | 0.845740i | \(-0.679159\pi\) | ||||
−0.533595 | + | 0.845740i | \(0.679159\pi\) | |||||||
\(350\) | −5.61514 | − | 10.0002i | −0.300142 | − | 0.534535i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.25728 | + | 3.90972i | −0.120313 | + | 0.208389i | ||||
\(353\) | 11.4576 | + | 19.8451i | 0.609825 | + | 1.05625i | 0.991269 | + | 0.131856i | \(0.0420937\pi\) |
−0.381444 | + | 0.924392i | \(0.624573\pi\) | |||||||
\(354\) | 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 | −0.242940 | − | 0.970041i | \(-0.578112\pi\) |
0.961551 | − | 0.274628i | \(-0.0885547\pi\) | |||||||
\(360\) | −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 | 0 | ||||||||
\(365\) | −8.63735 | −0.452099 | ||||||||
\(366\) | −3.99148 | + | 6.91345i | −0.208638 | + | 0.361372i | ||||
\(367\) | 5.42822 | + | 9.40195i | 0.283351 | + | 0.490778i | 0.972208 | − | 0.234119i | \(-0.0752206\pi\) |
−0.688857 | + | 0.724897i | \(0.741887\pi\) | |||||||
\(368\) | −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 | −0.833695 | − | 0.552226i | \(-0.813779\pi\) |
0.895089 | + | 0.445888i | \(0.147112\pi\) | |||||||
\(374\) | −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 | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7.93997 | − | 0.0950346i | −0.408388 | − | 0.00488805i | ||||
\(379\) | 29.2197 | 1.50092 | 0.750458 | − | 0.660918i | \(-0.229833\pi\) | ||||
0.750458 | + | 0.660918i | \(0.229833\pi\) | |||||||
\(380\) | −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 | \(-0.858293\pi\) |
0.824199 | + | 0.566301i | \(0.191626\pi\) | |||||||
\(384\) | 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 | −0.967315 | − | 0.253576i | \(-0.918393\pi\) |
0.264054 | − | 0.964508i | \(-0.414940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −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 | \(-0.690999\pi\) |
0.997080 | + | 0.0763669i | \(0.0243320\pi\) | |||||||
\(398\) | −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 | \(-0.696911\pi\) |
0.995489 | + | 0.0948737i | \(0.0302447\pi\) | |||||||
\(402\) | 24.4299 | + | 42.3137i | 1.21845 | + | 2.11042i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 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 | \(-0.276104\pi\) |
−0.983881 | + | 0.178825i | \(0.942770\pi\) | |||||||
\(410\) | 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 | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −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 | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.604344 | + | 1.04676i | 0.0291441 | + | 0.0504790i | ||||
\(431\) | 0.604764 | + | 1.04748i | 0.0291304 | + | 0.0504554i | 0.880223 | − | 0.474560i | \(-0.157393\pi\) |
−0.851093 | + | 0.525016i | \(0.824060\pi\) | |||||||
\(432\) | −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 | −0.528860 | − | 0.848709i | \(-0.677381\pi\) |
0.999434 | + | 0.0336522i | \(0.0107139\pi\) | |||||||
\(440\) | −17.9422 | −0.855362 | ||||||||
\(441\) | −13.0889 | − | 23.9784i | −0.623282 | − | 1.14183i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1155 | + | 19.2526i | −0.528113 | + | 0.914719i | 0.471350 | + | 0.881946i | \(0.343767\pi\) |
−0.999463 | + | 0.0327726i | \(0.989566\pi\) | |||||||
\(444\) | −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 | \(-0.643443\pi\) | ||||
−0.435541 | + | 0.900169i | \(0.643443\pi\) | |||||||
\(450\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 55.5185 | 2.59989 | ||||||||
\(457\) | −14.9910 | + | 25.9651i | −0.701248 | + | 1.21460i | 0.266781 | + | 0.963757i | \(0.414040\pi\) |
−0.968029 | + | 0.250840i | \(0.919293\pi\) | |||||||
\(458\) | −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 | \(-0.737509\pi\) | ||||
−0.678821 | + | 0.734304i | \(0.737509\pi\) | |||||||
\(462\) | −9.14330 | + | 15.4078i | −0.425385 | + | 0.716836i | ||||
\(463\) | −1.55900 | −0.0724530 | −0.0362265 | − | 0.999344i | \(-0.511534\pi\) | ||||
−0.0362265 | + | 0.999344i | \(0.511534\pi\) | |||||||
\(464\) | 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 | −0.973197 | − | 0.229972i | \(-0.926136\pi\) |
0.685760 | + | 0.727827i | \(0.259470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −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 | 0.902897 | + | 0.429857i | \(0.141436\pi\) |
−0.0791811 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(480\) | −8.45242 | − | 14.6400i | −0.385798 | − | 0.668222i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −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 | \(-0.113776\pi\) |
−0.771398 | + | 0.636352i | \(0.780442\pi\) | |||||||
\(488\) | −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 | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 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 | \(-0.751443\pi\) |
0.964742 | + | 0.263196i | \(0.0847766\pi\) | |||||||
\(500\) | −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 | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.03171 | + | 1.78698i | 0.0457749 | + | 0.0792845i | ||||
\(509\) | 1.64142 | − | 2.84303i | 0.0727547 | − | 0.126015i | −0.827353 | − | 0.561682i | \(-0.810154\pi\) |
0.900108 | + | 0.435667i | \(0.143488\pi\) | |||||||
\(510\) | 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 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.38530 | + | 4.13147i | 0.104502 | + | 0.181003i | 0.913535 | − | 0.406761i | \(-0.133342\pi\) |
−0.809033 | + | 0.587764i | \(0.800008\pi\) | |||||||
\(522\) | 2.70682 | + | 4.68835i | 0.118474 | + | 0.205203i | ||||
\(523\) | −12.7562 | + | 22.0944i | −0.557789 | + | 0.966119i | 0.439892 | + | 0.898051i | \(0.355017\pi\) |
−0.997681 | + | 0.0680682i | \(0.978316\pi\) | |||||||
\(524\) | −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 | 0 | ||||||||
\(534\) | −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 | \(-0.948863\pi\) |
0.632091 | + | 0.774894i | \(0.282197\pi\) | |||||||
\(542\) | 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 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | \(-0.306291\pi\) |
−0.996393 | + | 0.0848540i | \(0.972958\pi\) | |||||||
\(558\) | 25.7639 | − | 44.6243i | 1.09067 | − | 1.88910i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −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 | 0.877539 | + | 0.479506i | \(0.159184\pi\) |
−0.0235047 | + | 0.999724i | \(0.507482\pi\) | |||||||
\(564\) | 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 | −0.548739 | − | 0.835994i | \(-0.684892\pi\) |
0.998361 | + | 0.0572245i | \(0.0182251\pi\) | |||||||
\(570\) | 33.5972 | + | 58.1921i | 1.40723 | + | 2.43740i | ||||
\(571\) | 5.47793 | + | 9.48806i | 0.229244 | + | 0.397063i | 0.957584 | − | 0.288153i | \(-0.0930412\pi\) |
−0.728340 | + | 0.685216i | \(0.759708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −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 | 0.959729 | + | 0.280927i | \(0.0906418\pi\) |
−0.236575 | + | 0.971613i | \(0.576025\pi\) | |||||||
\(578\) | −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 | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1796 | − | 21.0958i | 0.503136 | − | 0.871458i | ||||
\(587\) | 22.8463 | 0.942967 | 0.471483 | − | 0.881875i | \(-0.343719\pi\) | ||||
0.471483 | + | 0.881875i | \(0.343719\pi\) | |||||||
\(588\) | −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 | \(-0.715687\pi\) |
0.988165 | + | 0.153394i | \(0.0490202\pi\) | |||||||
\(594\) | −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 | 0 | ||||||||
\(599\) | −15.5036 | − | 26.8531i | −0.633461 | − | 1.09719i | −0.986839 | − | 0.161706i | \(-0.948300\pi\) |
0.353378 | − | 0.935481i | \(-0.385033\pi\) | |||||||
\(600\) | 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 | −0.307826 | − | 0.951443i | \(-0.599601\pi\) |
0.977887 | − | 0.209136i | \(-0.0670652\pi\) | |||||||
\(608\) | 15.4333 | 0.625901 | ||||||||
\(609\) | −3.88813 | + | 6.55208i | −0.157555 | + | 0.265503i | ||||
\(610\) | −8.81953 | −0.357092 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.10727 | + | 5.38194i | 0.125604 | + | 0.217552i | ||||
\(613\) | −21.5829 | − | 37.3826i | −0.871723 | − | 1.50987i | −0.860213 | − | 0.509935i | \(-0.829669\pi\) |
−0.0115102 | − | 0.999934i | \(-0.503664\pi\) | |||||||
\(614\) | 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 | \(-0.515754\pi\) | ||||
−0.0494721 | + | 0.998776i | \(0.515754\pi\) | |||||||
\(618\) | 19.3443 | − | 33.5053i | 0.778142 | − | 1.34778i | ||||
\(619\) | 18.8894 | + | 32.7175i | 0.759231 | + | 1.31503i | 0.943243 | + | 0.332102i | \(0.107758\pi\) |
−0.184013 | + | 0.982924i | \(0.558909\pi\) | |||||||
\(620\) | 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 | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 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 | \(-0.308126\pi\) | ||||
0.566942 | + | 0.823758i | \(0.308126\pi\) | |||||||
\(632\) | 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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | 0.999063 | + | 0.0432812i | \(0.0137811\pi\) |
−0.462049 | + | 0.886854i | \(0.652886\pi\) | |||||||
\(642\) | −32.6292 | + | 56.5154i | −1.28777 | + | 2.23049i | ||||
\(643\) | 37.1664 | 1.46570 | 0.732849 | − | 0.680391i | \(-0.238190\pi\) | ||||
0.732849 | + | 0.680391i | \(0.238190\pi\) | |||||||
\(644\) | 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 | 0.619414 | − | 0.785064i | \(-0.287370\pi\) |
−0.989593 | + | 0.143896i | \(0.954037\pi\) | |||||||
\(648\) | 8.31275 | + | 14.3981i | 0.326556 | + | 0.565611i | ||||
\(649\) | −2.07380 | + | 3.59192i | −0.0814036 | + | 0.140995i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 72.5123 | + | 0.867909i | 2.84198 | + | 0.0340161i | ||||
\(652\) | 5.93910 | 0.232593 | ||||||||
\(653\) | 13.0092 | − | 22.5326i | 0.509090 | − | 0.881770i | −0.490854 | − | 0.871242i | \(-0.663315\pi\) |
0.999945 | − | 0.0105286i | \(-0.00335143\pi\) | |||||||
\(654\) | −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 | \(-0.127579\pi\) |
−0.798259 | + | 0.602314i | \(0.794245\pi\) | |||||||
\(662\) | 11.5053 | + | 19.9277i | 0.447164 | + | 0.774511i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −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 | 0 | ||||||||
\(677\) | −12.1696 | + | 21.0783i | −0.467715 | + | 0.810106i | −0.999319 | − | 0.0368866i | \(-0.988256\pi\) |
0.531604 | + | 0.846993i | \(0.321589\pi\) | |||||||
\(678\) | −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 | \(-0.0943799\pi\) |
−0.731215 | + | 0.682147i | \(0.761047\pi\) | |||||||
\(684\) | −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 | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.02708 | + | 5.24306i | 0.115239 | + | 0.199600i | ||||
\(691\) | 0.588923 | − | 1.02004i | 0.0224037 | − | 0.0388043i | −0.854606 | − | 0.519277i | \(-0.826201\pi\) |
0.877010 | + | 0.480472i | \(0.159535\pi\) | |||||||
\(692\) | 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 | \(0.701204\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 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 | \(-0.740108\pi\) |
0.973501 | + | 0.228682i | \(0.0734418\pi\) | |||||||
\(710\) | −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 | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | −0.743250 | − | 0.669014i | \(-0.766717\pi\) |
0.951008 | + | 0.309166i | \(0.100050\pi\) | |||||||
\(720\) | −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 | \(0.536959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −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 | −0.424477 | − | 0.905439i | \(-0.639542\pi\) |
0.996371 | − | 0.0851111i | \(-0.0271245\pi\) | |||||||
\(734\) | 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 | \(-0.152978\pi\) |
−0.843729 | + | 0.536770i | \(0.819644\pi\) | |||||||
\(740\) | 1.78322 | − | 3.08862i | 0.0655523 | − | 0.113540i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.6710 | − | 20.7854i | −0.428456 | − | 0.763055i | ||||
\(743\) | −24.3612 | −0.893726 | −0.446863 | − | 0.894603i | \(-0.647459\pi\) | ||||
−0.446863 | + | 0.894603i | \(0.647459\pi\) | |||||||
\(744\) | 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 | −0.735221 | − | 0.677827i | \(-0.762922\pi\) |
0.954626 | + | 0.297806i | \(0.0962550\pi\) | |||||||
\(752\) | −16.0555 | − | 27.8089i | −0.585483 | − | 1.01409i | ||||
\(753\) | −19.2583 | − | 33.3564i | −0.701813 | − | 1.21558i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 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 | \(-0.755677\pi\) |
0.961156 | + | 0.276004i | \(0.0890103\pi\) | |||||||
\(762\) | 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 | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.0245 | + | 20.8270i | −0.433896 | + | 0.751530i | ||||
\(769\) | −9.24486 | −0.333378 | −0.166689 | − | 0.986010i | \(-0.553308\pi\) | ||||
−0.166689 | + | 0.986010i | \(0.553308\pi\) | |||||||
\(770\) | −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 | \(-0.225050\pi\) |
−0.942694 | + | 0.333659i | \(0.891717\pi\) | |||||||
\(774\) | 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 | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −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 | 0.914885 | + | 0.403715i | \(0.132281\pi\) |
−0.107815 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −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 | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −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 | 0.998582 | − | 0.0532388i | \(-0.0169544\pi\) |
−0.545397 | + | 0.838178i | \(0.683621\pi\) | |||||||
\(810\) | −10.0610 | + | 17.4261i | −0.353507 | + | 0.612291i | ||||
\(811\) | 25.7829 | 0.905362 | 0.452681 | − | 0.891673i | \(-0.350468\pi\) | ||||
0.452681 | + | 0.891673i | \(0.350468\pi\) | |||||||
\(812\) | −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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.602407 | −0.0210370 | ||||||||
\(821\) | −0.855366 | + | 1.48154i | −0.0298525 | + | 0.0517060i | −0.880566 | − | 0.473924i | \(-0.842837\pi\) |
0.850713 | + | 0.525630i | \(0.176170\pi\) | |||||||
\(822\) | −9.76214 | − | 16.9085i | −0.340494 | − | 0.589752i | ||||
\(823\) | 20.1887 | + | 34.9678i | 0.703733 | + | 1.21890i | 0.967147 | + | 0.254218i | \(0.0818181\pi\) |
−0.263414 | + | 0.964683i | \(0.584849\pi\) | |||||||
\(824\) | 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 | \(-0.610513\pi\) | ||||
−0.340254 | + | 0.940333i | \(0.610513\pi\) | |||||||
\(828\) | −0.487444 | + | 0.844278i | −0.0169399 | + | 0.0293407i | ||||
\(829\) | −20.7871 | − | 36.0043i | −0.721966 | − | 1.25048i | −0.960211 | − | 0.279277i | \(-0.909905\pi\) |
0.238244 | − | 0.971205i | \(-0.423428\pi\) | |||||||
\(830\) | −23.5178 | − | 40.7341i | −0.816316 | − | 1.41390i | ||||
\(831\) | −9.89073 | + | 17.1312i | −0.343106 | + | 0.594276i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 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 | \(-0.790660\pi\) | ||||
−0.791425 | + | 0.611266i | \(0.790660\pi\) | |||||||
\(840\) | −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 | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 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 | \(-0.740281\pi\) | ||||
−0.685191 | + | 0.728364i | \(0.740281\pi\) | |||||||
\(854\) | −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 | −0.997374 | − | 0.0724294i | \(-0.976925\pi\) |
0.435961 | − | 0.899966i | \(-0.356409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0252 | − | 29.4885i | 0.580891 | − | 1.00613i | −0.414483 | − | 0.910057i | \(-0.636037\pi\) |
0.995374 | − | 0.0960762i | \(-0.0306292\pi\) | |||||||
\(860\) | −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 | \(-0.910276\pi\) |
0.721160 | + | 0.692768i | \(0.243609\pi\) | |||||||
\(864\) | −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 | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −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 | −0.00759373 | − | 0.999971i | \(-0.502417\pi\) |
0.869797 | − | 0.493409i | \(-0.164249\pi\) | |||||||
\(878\) | −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 | 0 | ||||||||
\(885\) | −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 | −0.896716 | − | 0.442606i | \(-0.854054\pi\) |
0.831666 | + | 0.555276i | \(0.187387\pi\) | |||||||
\(888\) | −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 | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −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 | 0.933916 | + | 0.357491i | \(0.116368\pi\) |
−0.157362 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(908\) | 1.89486 | − | 3.28200i | 0.0628832 | − | 0.108917i | ||||
\(909\) | 5.67142 | 0.188109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | −0.786481 | − | 0.617615i | \(-0.788099\pi\) |
0.928110 | + | 0.372305i | \(0.121432\pi\) | |||||||
\(920\) | 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 | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −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 | \(-0.877649\pi\) |
0.788260 | + | 0.615343i | \(0.210982\pi\) | |||||||
\(930\) | 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 | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −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 | \(-0.236775\pi\) |
−0.954342 | + | 0.298717i | \(0.903441\pi\) | |||||||
\(942\) | 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 | −0.268539 | − | 0.963269i | \(-0.586541\pi\) |
0.968485 | − | 0.249073i | \(-0.0801259\pi\) | |||||||
\(948\) | 4.58347 | + | 7.93881i | 0.148864 | + | 0.257840i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −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 | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −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 | \(-0.755713\pi\) | ||||
−0.719683 | + | 0.694303i | \(0.755713\pi\) | |||||||
\(968\) | 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 | −0.830337 | − | 0.557261i | \(-0.811852\pi\) |
0.897771 | + | 0.440463i | \(0.145186\pi\) | |||||||
\(972\) | −8.56409 | −0.274693 | ||||||||
\(973\) | −5.18143 | − | 9.22783i | −0.166109 | − | 0.295830i | ||||
\(974\) | 9.23899 | 0.296036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.65517 | + | 6.33093i | 0.116999 | + | 0.202648i | ||||
\(977\) | −12.8449 | − | 22.2481i | −0.410946 | − | 0.711779i | 0.584048 | − | 0.811719i | \(-0.301468\pi\) |
−0.994993 | + | 0.0999403i | \(0.968135\pi\) | |||||||
\(978\) | 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 | −0.999962 | − | 0.00870538i | \(-0.997229\pi\) |
0.492442 | − | 0.870345i | \(-0.336104\pi\) | |||||||
\(984\) | 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 | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 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 | 0.780919 | − | 0.624632i | \(-0.214751\pi\) |
−0.931407 | + | 0.363979i | \(0.881418\pi\) | |||||||
\(992\) | 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 | 0.638224 | − | 0.769851i | \(-0.279670\pi\) |
−0.985822 | + | 0.167792i | \(0.946336\pi\) | |||||||
\(998\) | −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 | 1183.2.e.f.170.3 | 10 | ||
7.2 | even | 3 | 8281.2.a.bw.1.3 | 5 | |||
7.4 | even | 3 | inner | 1183.2.e.f.508.3 | 10 | ||
7.5 | odd | 6 | 8281.2.a.bx.1.3 | 5 | |||
13.12 | even | 2 | 91.2.e.c.79.3 | yes | 10 | ||
39.38 | odd | 2 | 819.2.j.h.352.3 | 10 | |||
52.51 | odd | 2 | 1456.2.r.p.625.1 | 10 | |||
91.12 | odd | 6 | 637.2.a.k.1.3 | 5 | |||
91.25 | even | 6 | 91.2.e.c.53.3 | ✓ | 10 | ||
91.38 | odd | 6 | 637.2.e.m.508.3 | 10 | |||
91.51 | even | 6 | 637.2.a.l.1.3 | 5 | |||
91.90 | odd | 2 | 637.2.e.m.79.3 | 10 | |||
273.116 | odd | 6 | 819.2.j.h.235.3 | 10 | |||
273.194 | even | 6 | 5733.2.a.bm.1.3 | 5 | |||
273.233 | odd | 6 | 5733.2.a.bl.1.3 | 5 | |||
364.207 | odd | 6 | 1456.2.r.p.417.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.3 | ✓ | 10 | 91.25 | even | 6 | ||
91.2.e.c.79.3 | yes | 10 | 13.12 | even | 2 | ||
637.2.a.k.1.3 | 5 | 91.12 | odd | 6 | |||
637.2.a.l.1.3 | 5 | 91.51 | even | 6 | |||
637.2.e.m.79.3 | 10 | 91.90 | odd | 2 | |||
637.2.e.m.508.3 | 10 | 91.38 | odd | 6 | |||
819.2.j.h.235.3 | 10 | 273.116 | odd | 6 | |||
819.2.j.h.352.3 | 10 | 39.38 | odd | 2 | |||
1183.2.e.f.170.3 | 10 | 1.1 | even | 1 | trivial | ||
1183.2.e.f.508.3 | 10 | 7.4 | even | 3 | inner | ||
1456.2.r.p.417.1 | 10 | 364.207 | odd | 6 | |||
1456.2.r.p.625.1 | 10 | 52.51 | odd | 2 | |||
5733.2.a.bl.1.3 | 5 | 273.233 | odd | 6 | |||
5733.2.a.bm.1.3 | 5 | 273.194 | even | 6 | |||
8281.2.a.bw.1.3 | 5 | 7.2 | even | 3 | |||
8281.2.a.bx.1.3 | 5 | 7.5 | odd | 6 |