Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(29,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.i (of order \(10\), degree \(4\), 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: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 29.19 | ||
Character | \(\chi\) | \(=\) | 150.29 |
Dual form | 150.3.i.a.119.19 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.437016 | − | 1.34500i | 0.218508 | − | 0.672499i | ||||
\(3\) | 2.06877 | + | 2.17260i | 0.689590 | + | 0.724200i | ||||
\(4\) | −1.61803 | − | 1.17557i | −0.404508 | − | 0.293893i | ||||
\(5\) | 2.68239 | + | 4.21957i | 0.536477 | + | 0.843915i | ||||
\(6\) | 3.82622 | − | 1.83303i | 0.637704 | − | 0.305505i | ||||
\(7\) | 8.88015i | 1.26859i | 0.773090 | + | 0.634297i | \(0.218710\pi\) | ||||
−0.773090 | + | 0.634297i | \(0.781290\pi\) | |||||||
\(8\) | −2.28825 | + | 1.66251i | −0.286031 | + | 0.207813i | ||||
\(9\) | −0.440370 | + | 8.98922i | −0.0489300 | + | 0.998802i | ||||
\(10\) | 6.84756 | − | 1.76378i | 0.684756 | − | 0.176378i | ||||
\(11\) | −16.5303 | − | 5.37102i | −1.50275 | − | 0.488274i | −0.561934 | − | 0.827182i | \(-0.689943\pi\) |
−0.940820 | + | 0.338908i | \(0.889943\pi\) | |||||||
\(12\) | −0.793300 | − | 5.94733i | −0.0661083 | − | 0.495610i | ||||
\(13\) | 14.5516 | − | 4.72811i | 1.11936 | − | 0.363701i | 0.309834 | − | 0.950791i | \(-0.399727\pi\) |
0.809522 | + | 0.587090i | \(0.199727\pi\) | |||||||
\(14\) | 11.9438 | + | 3.88077i | 0.853127 | + | 0.277198i | ||||
\(15\) | −3.61819 | + | 14.5571i | −0.241213 | + | 0.970472i | ||||
\(16\) | 1.23607 | + | 3.80423i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 8.28643 | − | 6.02044i | 0.487437 | − | 0.354144i | −0.316761 | − | 0.948505i | \(-0.602595\pi\) |
0.804198 | + | 0.594362i | \(0.202595\pi\) | |||||||
\(18\) | 11.8980 | + | 4.52073i | 0.661001 | + | 0.251152i | ||||
\(19\) | 14.2114 | − | 10.3252i | 0.747970 | − | 0.543432i | −0.147227 | − | 0.989103i | \(-0.547035\pi\) |
0.895197 | + | 0.445671i | \(0.147035\pi\) | |||||||
\(20\) | 0.620212 | − | 9.98075i | 0.0310106 | − | 0.499037i | ||||
\(21\) | −19.2930 | + | 18.3710i | −0.918715 | + | 0.874810i | ||||
\(22\) | −14.4480 | + | 19.8860i | −0.656728 | + | 0.903908i | ||||
\(23\) | 8.91122 | − | 27.4259i | 0.387444 | − | 1.19243i | −0.547247 | − | 0.836971i | \(-0.684324\pi\) |
0.934691 | − | 0.355460i | \(-0.115676\pi\) | |||||||
\(24\) | −8.34582 | − | 1.53209i | −0.347742 | − | 0.0638371i | ||||
\(25\) | −10.6096 | + | 22.6371i | −0.424384 | + | 0.905482i | ||||
\(26\) | − | 21.6381i | − | 0.832236i | ||||||
\(27\) | −20.4410 | + | 17.6399i | −0.757074 | + | 0.653329i | ||||
\(28\) | 10.4392 | − | 14.3684i | 0.372830 | − | 0.513157i | ||||
\(29\) | 6.68922 | − | 9.20692i | 0.230663 | − | 0.317480i | −0.677959 | − | 0.735099i | \(-0.737135\pi\) |
0.908622 | + | 0.417619i | \(0.137135\pi\) | |||||||
\(30\) | 17.9980 | + | 11.2281i | 0.599934 | + | 0.374271i | ||||
\(31\) | 33.0715 | − | 24.0278i | 1.06682 | − | 0.775092i | 0.0914841 | − | 0.995807i | \(-0.470839\pi\) |
0.975338 | + | 0.220715i | \(0.0708389\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | −22.5283 | − | 47.0251i | −0.682677 | − | 1.42500i | ||||
\(34\) | −4.47618 | − | 13.7763i | −0.131652 | − | 0.405184i | ||||
\(35\) | −37.4705 | + | 23.8200i | −1.07058 | + | 0.680572i | ||||
\(36\) | 11.2800 | − | 14.0272i | 0.313333 | − | 0.389644i | ||||
\(37\) | 1.47164 | − | 0.478166i | 0.0397741 | − | 0.0129234i | −0.289062 | − | 0.957310i | \(-0.593343\pi\) |
0.328836 | + | 0.944387i | \(0.393343\pi\) | |||||||
\(38\) | −7.67675 | − | 23.6266i | −0.202020 | − | 0.621753i | ||||
\(39\) | 40.3763 | + | 21.8335i | 1.03529 | + | 0.559832i | ||||
\(40\) | −13.1530 | − | 5.19593i | −0.328826 | − | 0.129898i | ||||
\(41\) | −5.18186 | + | 1.68369i | −0.126387 | + | 0.0410656i | −0.371528 | − | 0.928422i | \(-0.621166\pi\) |
0.245141 | + | 0.969488i | \(0.421166\pi\) | |||||||
\(42\) | 16.2776 | + | 33.9775i | 0.387562 | + | 0.808987i | ||||
\(43\) | 27.1575i | 0.631569i | 0.948831 | + | 0.315784i | \(0.102268\pi\) | ||||
−0.948831 | + | 0.315784i | \(0.897732\pi\) | |||||||
\(44\) | 20.4326 | + | 28.1230i | 0.464376 | + | 0.639159i | ||||
\(45\) | −39.1119 | + | 22.2544i | −0.869154 | + | 0.494542i | ||||
\(46\) | −32.9934 | − | 23.9711i | −0.717249 | − | 0.521112i | ||||
\(47\) | −73.3819 | − | 53.3151i | −1.56132 | − | 1.13436i | −0.934920 | − | 0.354859i | \(-0.884529\pi\) |
−0.626397 | − | 0.779504i | \(-0.715471\pi\) | |||||||
\(48\) | −5.70791 | + | 10.5556i | −0.118915 | + | 0.219907i | ||||
\(49\) | −29.8571 | −0.609329 | ||||||||
\(50\) | 25.8102 | + | 24.1626i | 0.516204 | + | 0.483253i | ||||
\(51\) | 30.2227 | + | 5.54816i | 0.592603 | + | 0.108788i | ||||
\(52\) | −29.1032 | − | 9.45621i | −0.559678 | − | 0.181850i | ||||
\(53\) | 15.4590 | + | 11.2316i | 0.291680 | + | 0.211918i | 0.723996 | − | 0.689804i | \(-0.242303\pi\) |
−0.432316 | + | 0.901722i | \(0.642303\pi\) | |||||||
\(54\) | 14.7926 | + | 35.2020i | 0.273936 | + | 0.651889i | ||||
\(55\) | −21.6772 | − | 84.1579i | −0.394132 | − | 1.53014i | ||||
\(56\) | −14.7633 | − | 20.3200i | −0.263631 | − | 0.362857i | ||||
\(57\) | 51.8327 | + | 9.51523i | 0.909346 | + | 0.166934i | ||||
\(58\) | −9.45998 | − | 13.0205i | −0.163103 | − | 0.224492i | ||||
\(59\) | −36.4710 | + | 11.8502i | −0.618153 | + | 0.200850i | −0.601320 | − | 0.799008i | \(-0.705358\pi\) |
−0.0168331 | + | 0.999858i | \(0.505358\pi\) | |||||||
\(60\) | 22.9672 | − | 19.3004i | 0.382787 | − | 0.321674i | ||||
\(61\) | −23.6592 | + | 72.8155i | −0.387856 | + | 1.19370i | 0.546532 | + | 0.837438i | \(0.315948\pi\) |
−0.934387 | + | 0.356258i | \(0.884052\pi\) | |||||||
\(62\) | −17.8646 | − | 54.9816i | −0.288139 | − | 0.886800i | ||||
\(63\) | −79.8257 | − | 3.91055i | −1.26707 | − | 0.0620723i | ||||
\(64\) | 2.47214 | − | 7.60845i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 58.9837 | + | 48.7190i | 0.907441 | + | 0.749523i | ||||
\(66\) | −73.0939 | + | 9.74982i | −1.10748 | + | 0.147724i | ||||
\(67\) | −29.7411 | − | 40.9351i | −0.443897 | − | 0.610972i | 0.527175 | − | 0.849756i | \(-0.323251\pi\) |
−0.971073 | + | 0.238784i | \(0.923251\pi\) | |||||||
\(68\) | −20.4852 | −0.301253 | ||||||||
\(69\) | 78.0208 | − | 37.3775i | 1.13074 | − | 0.541702i | ||||
\(70\) | 15.6627 | + | 60.8074i | 0.223752 | + | 0.868677i | ||||
\(71\) | −47.1092 | + | 64.8403i | −0.663510 | + | 0.913244i | −0.999591 | − | 0.0285896i | \(-0.990898\pi\) |
0.336081 | + | 0.941833i | \(0.390898\pi\) | |||||||
\(72\) | −13.9370 | − | 21.3017i | −0.193569 | − | 0.295856i | ||||
\(73\) | −20.6289 | − | 6.70273i | −0.282587 | − | 0.0918182i | 0.164294 | − | 0.986411i | \(-0.447465\pi\) |
−0.446881 | + | 0.894593i | \(0.647465\pi\) | |||||||
\(74\) | − | 2.18832i | − | 0.0295719i | ||||||
\(75\) | −71.1301 | + | 23.7805i | −0.948401 | + | 0.317073i | ||||
\(76\) | −35.1326 | −0.462271 | ||||||||
\(77\) | 47.6955 | − | 146.792i | 0.619422 | − | 1.90638i | ||||
\(78\) | 47.0110 | − | 44.7644i | 0.602705 | − | 0.573902i | ||||
\(79\) | 56.9806 | + | 41.3989i | 0.721274 | + | 0.524036i | 0.886791 | − | 0.462171i | \(-0.152929\pi\) |
−0.165517 | + | 0.986207i | \(0.552929\pi\) | |||||||
\(80\) | −12.7366 | + | 15.4201i | −0.159207 | + | 0.192751i | ||||
\(81\) | −80.6121 | − | 7.91716i | −0.995212 | − | 0.0977428i | ||||
\(82\) | 7.70539i | 0.0939682i | ||||||||
\(83\) | 94.9893 | − | 69.0138i | 1.14445 | − | 0.831491i | 0.156717 | − | 0.987644i | \(-0.449909\pi\) |
0.987733 | + | 0.156152i | \(0.0499091\pi\) | |||||||
\(84\) | 52.8132 | − | 7.04462i | 0.628728 | − | 0.0838645i | ||||
\(85\) | 47.6311 | + | 18.8160i | 0.560366 | + | 0.221365i | ||||
\(86\) | 36.5267 | + | 11.8682i | 0.424729 | + | 0.138003i | ||||
\(87\) | 33.8414 | − | 4.51402i | 0.388982 | − | 0.0518853i | ||||
\(88\) | 46.7547 | − | 15.1915i | 0.531304 | − | 0.172631i | ||||
\(89\) | 135.505 | + | 44.0283i | 1.52253 | + | 0.494701i | 0.946494 | − | 0.322722i | \(-0.104598\pi\) |
0.576038 | + | 0.817423i | \(0.304598\pi\) | |||||||
\(90\) | 12.8396 | + | 62.3309i | 0.142662 | + | 0.692566i | ||||
\(91\) | 41.9863 | + | 129.221i | 0.461388 | + | 1.42001i | ||||
\(92\) | −46.6598 | + | 33.9003i | −0.507171 | + | 0.368482i | ||||
\(93\) | 120.620 | + | 22.1430i | 1.29699 | + | 0.238096i | ||||
\(94\) | −103.778 | + | 75.3989i | −1.10402 | + | 0.802116i | ||||
\(95\) | 81.6885 | + | 32.2699i | 0.859879 | + | 0.339684i | ||||
\(96\) | 11.7027 | + | 12.2901i | 0.121904 | + | 0.128022i | ||||
\(97\) | 102.989 | − | 141.752i | 1.06174 | − | 1.46136i | 0.183580 | − | 0.983005i | \(-0.441231\pi\) |
0.878164 | − | 0.478360i | \(-0.158769\pi\) | |||||||
\(98\) | −13.0480 | + | 40.1577i | −0.133143 | + | 0.409773i | ||||
\(99\) | 55.5607 | − | 146.229i | 0.561219 | − | 1.47706i | ||||
\(100\) | 43.7781 | − | 24.1552i | 0.437781 | − | 0.241552i | ||||
\(101\) | − | 67.3023i | − | 0.666359i | −0.942863 | − | 0.333180i | \(-0.891878\pi\) | ||
0.942863 | − | 0.333180i | \(-0.108122\pi\) | |||||||
\(102\) | 20.6701 | − | 38.2248i | 0.202648 | − | 0.374753i | ||||
\(103\) | −50.7074 | + | 69.7927i | −0.492305 | + | 0.677599i | −0.980811 | − | 0.194961i | \(-0.937542\pi\) |
0.488506 | + | 0.872560i | \(0.337542\pi\) | |||||||
\(104\) | −25.4372 | + | 35.0112i | −0.244588 | + | 0.336647i | ||||
\(105\) | −129.269 | − | 32.1301i | −1.23113 | − | 0.306001i | ||||
\(106\) | 21.8624 | − | 15.8839i | 0.206249 | − | 0.149849i | ||||
\(107\) | −116.245 | −1.08640 | −0.543201 | − | 0.839603i | \(-0.682788\pi\) | ||||
−0.543201 | + | 0.839603i | \(0.682788\pi\) | |||||||
\(108\) | 53.8112 | − | 4.51212i | 0.498251 | − | 0.0417789i | ||||
\(109\) | −17.6420 | − | 54.2965i | −0.161853 | − | 0.498133i | 0.836937 | − | 0.547299i | \(-0.184344\pi\) |
−0.998791 | + | 0.0491655i | \(0.984344\pi\) | |||||||
\(110\) | −122.665 | − | 7.62253i | −1.11514 | − | 0.0692957i | ||||
\(111\) | 4.08335 | + | 2.20807i | 0.0367870 | + | 0.0198926i | ||||
\(112\) | −33.7821 | + | 10.9765i | −0.301626 | + | 0.0980042i | ||||
\(113\) | 2.96339 | + | 9.12036i | 0.0262247 | + | 0.0807112i | 0.963312 | − | 0.268383i | \(-0.0864893\pi\) |
−0.937088 | + | 0.349094i | \(0.886489\pi\) | |||||||
\(114\) | 35.4497 | − | 65.5565i | 0.310962 | − | 0.575057i | ||||
\(115\) | 139.629 | − | 35.9654i | 1.21417 | − | 0.312743i | ||||
\(116\) | −21.6468 | + | 7.03346i | −0.186610 | + | 0.0606333i | ||||
\(117\) | 36.0939 | + | 132.890i | 0.308495 | + | 1.13581i | ||||
\(118\) | 54.2322i | 0.459595i | ||||||||
\(119\) | 53.4625 | + | 73.5848i | 0.449264 | + | 0.618359i | ||||
\(120\) | −15.9220 | − | 39.3255i | −0.132683 | − | 0.327712i | ||||
\(121\) | 146.512 | + | 106.447i | 1.21084 | + | 0.879727i | ||||
\(122\) | 87.5972 | + | 63.6431i | 0.718010 | + | 0.521665i | ||||
\(123\) | −14.3781 | − | 7.77494i | −0.116895 | − | 0.0632109i | ||||
\(124\) | −81.7572 | −0.659333 | ||||||||
\(125\) | −123.978 | + | 15.9534i | −0.991822 | + | 0.127627i | ||||
\(126\) | −40.1448 | + | 105.656i | −0.318609 | + | 0.838542i | ||||
\(127\) | −130.689 | − | 42.4634i | −1.02905 | − | 0.334357i | −0.254633 | − | 0.967038i | \(-0.581955\pi\) |
−0.774413 | + | 0.632681i | \(0.781955\pi\) | |||||||
\(128\) | −9.15298 | − | 6.65003i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | −59.0023 | + | 56.1826i | −0.457382 | + | 0.435524i | ||||
\(130\) | 91.3037 | − | 58.0419i | 0.702336 | − | 0.446476i | ||||
\(131\) | −33.6017 | − | 46.2488i | −0.256502 | − | 0.353044i | 0.661273 | − | 0.750145i | \(-0.270016\pi\) |
−0.917775 | + | 0.397101i | \(0.870016\pi\) | |||||||
\(132\) | −18.8297 | + | 102.572i | −0.142649 | + | 0.777059i | ||||
\(133\) | 91.6894 | + | 126.200i | 0.689394 | + | 0.948869i | ||||
\(134\) | −68.0550 | + | 22.1124i | −0.507873 | + | 0.165018i | ||||
\(135\) | −129.263 | − | 38.9352i | −0.957507 | − | 0.288409i | ||||
\(136\) | −8.95235 | + | 27.5525i | −0.0658261 | + | 0.202592i | ||||
\(137\) | 51.2370 | + | 157.691i | 0.373992 | + | 1.15103i | 0.944156 | + | 0.329499i | \(0.106880\pi\) |
−0.570164 | + | 0.821531i | \(0.693120\pi\) | |||||||
\(138\) | −16.1762 | − | 121.272i | −0.117219 | − | 0.878785i | ||||
\(139\) | −1.12127 | + | 3.45092i | −0.00806671 | + | 0.0248268i | −0.955009 | − | 0.296577i | \(-0.904155\pi\) |
0.946942 | + | 0.321404i | \(0.104155\pi\) | |||||||
\(140\) | 88.6306 | + | 5.50757i | 0.633076 | + | 0.0393398i | ||||
\(141\) | −35.9781 | − | 269.726i | −0.255164 | − | 1.91295i | ||||
\(142\) | 66.6225 | + | 91.6980i | 0.469173 | + | 0.645761i | ||||
\(143\) | −265.937 | −1.85970 | ||||||||
\(144\) | −34.7414 | + | 9.43602i | −0.241259 | + | 0.0655279i | ||||
\(145\) | 56.7923 | + | 3.52912i | 0.391671 | + | 0.0243388i | ||||
\(146\) | −18.0303 | + | 24.8166i | −0.123495 | + | 0.169977i | ||||
\(147\) | −61.7676 | − | 64.8676i | −0.420188 | − | 0.441276i | ||||
\(148\) | −2.94329 | − | 0.956332i | −0.0198871 | − | 0.00646170i | ||||
\(149\) | 30.0596i | 0.201742i | 0.994900 | + | 0.100871i | \(0.0321630\pi\) | ||||
−0.994900 | + | 0.100871i | \(0.967837\pi\) | |||||||
\(150\) | 0.899735 | + | 106.062i | 0.00599823 | + | 0.707081i | ||||
\(151\) | −239.756 | −1.58779 | −0.793893 | − | 0.608058i | \(-0.791949\pi\) | ||||
−0.793893 | + | 0.608058i | \(0.791949\pi\) | |||||||
\(152\) | −15.3535 | + | 47.2532i | −0.101010 | + | 0.310876i | ||||
\(153\) | 50.4700 | + | 77.1397i | 0.329869 | + | 0.504181i | ||||
\(154\) | −176.591 | − | 128.301i | −1.14669 | − | 0.833120i | ||||
\(155\) | 190.098 | + | 75.0956i | 1.22644 | + | 0.484488i | ||||
\(156\) | −39.6634 | − | 82.7924i | −0.254252 | − | 0.530720i | ||||
\(157\) | − | 285.668i | − | 1.81954i | −0.415108 | − | 0.909772i | \(-0.636256\pi\) | ||
0.415108 | − | 0.909772i | \(-0.363744\pi\) | |||||||
\(158\) | 80.5828 | − | 58.5468i | 0.510018 | − | 0.370550i | ||||
\(159\) | 7.57935 | + | 56.8220i | 0.0476689 | + | 0.357371i | ||||
\(160\) | 15.1739 | + | 23.8695i | 0.0948367 | + | 0.149184i | ||||
\(161\) | 243.546 | + | 79.1330i | 1.51271 | + | 0.491510i | ||||
\(162\) | −45.8774 | + | 104.963i | −0.283194 | + | 0.647921i | ||||
\(163\) | 111.924 | − | 36.3663i | 0.686650 | − | 0.223106i | 0.0551454 | − | 0.998478i | \(-0.482438\pi\) |
0.631504 | + | 0.775372i | \(0.282438\pi\) | |||||||
\(164\) | 10.3637 | + | 3.36738i | 0.0631935 | + | 0.0205328i | ||||
\(165\) | 137.996 | − | 221.199i | 0.836340 | − | 1.34060i | ||||
\(166\) | −51.3115 | − | 157.920i | −0.309105 | − | 0.951328i | ||||
\(167\) | 16.3909 | − | 11.9087i | 0.0981492 | − | 0.0713096i | −0.537628 | − | 0.843182i | \(-0.680680\pi\) |
0.635777 | + | 0.771872i | \(0.280680\pi\) | |||||||
\(168\) | 13.6052 | − | 74.1122i | 0.0809833 | − | 0.441144i | ||||
\(169\) | 52.6707 | − | 38.2675i | 0.311661 | − | 0.226435i | ||||
\(170\) | 46.1231 | − | 55.8408i | 0.271312 | − | 0.328475i | ||||
\(171\) | 86.5572 | + | 132.297i | 0.506183 | + | 0.773664i | ||||
\(172\) | 31.9255 | − | 43.9417i | 0.185613 | − | 0.255475i | ||||
\(173\) | −38.6233 | + | 118.870i | −0.223256 | + | 0.687111i | 0.775208 | + | 0.631706i | \(0.217645\pi\) |
−0.998464 | + | 0.0554049i | \(0.982355\pi\) | |||||||
\(174\) | 8.71789 | − | 47.4893i | 0.0501028 | − | 0.272927i | ||||
\(175\) | −201.021 | − | 94.2148i | −1.14869 | − | 0.538370i | ||||
\(176\) | − | 69.5239i | − | 0.395022i | ||||||
\(177\) | −101.196 | − | 54.7217i | −0.571728 | − | 0.309162i | ||||
\(178\) | 118.436 | − | 163.013i | 0.665371 | − | 0.915804i | ||||
\(179\) | 56.5615 | − | 77.8503i | 0.315986 | − | 0.434918i | −0.621250 | − | 0.783612i | \(-0.713375\pi\) |
0.937236 | + | 0.348695i | \(0.113375\pi\) | |||||||
\(180\) | 89.4460 | + | 9.97044i | 0.496922 | + | 0.0553913i | ||||
\(181\) | −68.8447 | + | 50.0186i | −0.380357 | + | 0.276346i | −0.761493 | − | 0.648173i | \(-0.775533\pi\) |
0.381135 | + | 0.924519i | \(0.375533\pi\) | |||||||
\(182\) | 192.150 | 1.05577 | ||||||||
\(183\) | −207.144 | + | 99.2367i | −1.13194 | + | 0.542277i | ||||
\(184\) | 25.2047 | + | 77.5722i | 0.136982 | + | 0.421588i | ||||
\(185\) | 5.96517 | + | 4.92708i | 0.0322442 | + | 0.0266329i | ||||
\(186\) | 82.4952 | − | 152.557i | 0.443523 | − | 0.820199i | ||||
\(187\) | −169.313 | + | 55.0131i | −0.905417 | + | 0.294188i | ||||
\(188\) | 56.0588 | + | 172.531i | 0.298185 | + | 0.917719i | ||||
\(189\) | −156.645 | − | 181.519i | −0.828809 | − | 0.960419i | ||||
\(190\) | 79.1022 | − | 95.7683i | 0.416327 | − | 0.504044i | ||||
\(191\) | −115.633 | + | 37.5714i | −0.605407 | + | 0.196709i | −0.595651 | − | 0.803244i | \(-0.703106\pi\) |
−0.00975672 | + | 0.999952i | \(0.503106\pi\) | |||||||
\(192\) | 21.6444 | − | 10.3692i | 0.112731 | − | 0.0540062i | ||||
\(193\) | − | 67.7539i | − | 0.351056i | −0.984474 | − | 0.175528i | \(-0.943837\pi\) | ||
0.984474 | − | 0.175528i | \(-0.0561633\pi\) | |||||||
\(194\) | −145.649 | − | 200.468i | −0.750766 | − | 1.03334i | ||||
\(195\) | 16.1769 | + | 228.936i | 0.0829585 | + | 1.17403i | ||||
\(196\) | 48.3098 | + | 35.0992i | 0.246479 | + | 0.179077i | ||||
\(197\) | −133.793 | − | 97.2065i | −0.679154 | − | 0.493434i | 0.193923 | − | 0.981017i | \(-0.437879\pi\) |
−0.873077 | + | 0.487583i | \(0.837879\pi\) | |||||||
\(198\) | −172.397 | − | 138.633i | −0.870692 | − | 0.700169i | ||||
\(199\) | −299.615 | −1.50561 | −0.752803 | − | 0.658246i | \(-0.771298\pi\) | ||||
−0.752803 | + | 0.658246i | \(0.771298\pi\) | |||||||
\(200\) | −13.3569 | − | 69.4377i | −0.0667846 | − | 0.347188i | ||||
\(201\) | 27.4080 | − | 149.301i | 0.136358 | − | 0.742791i | ||||
\(202\) | −90.5214 | − | 29.4122i | −0.448126 | − | 0.145605i | ||||
\(203\) | 81.7588 | + | 59.4013i | 0.402753 | + | 0.292617i | ||||
\(204\) | −42.3791 | − | 44.5061i | −0.207741 | − | 0.218167i | ||||
\(205\) | −21.0042 | − | 17.3489i | −0.102460 | − | 0.0846290i | ||||
\(206\) | 71.7111 | + | 98.7018i | 0.348112 | + | 0.479135i | ||||
\(207\) | 242.613 | + | 92.1825i | 1.17205 | + | 0.445326i | ||||
\(208\) | 35.9736 | + | 49.5134i | 0.172950 | + | 0.238045i | ||||
\(209\) | −290.376 | + | 94.3488i | −1.38936 | + | 0.451430i | ||||
\(210\) | −99.7076 | + | 159.825i | −0.474798 | + | 0.761073i | ||||
\(211\) | −45.0795 | + | 138.740i | −0.213647 | + | 0.657538i | 0.785600 | + | 0.618735i | \(0.212354\pi\) |
−0.999247 | + | 0.0388029i | \(0.987646\pi\) | |||||||
\(212\) | −11.8097 | − | 36.3464i | −0.0557059 | − | 0.171445i | ||||
\(213\) | −238.330 | + | 31.7903i | −1.11892 | + | 0.149250i | ||||
\(214\) | −50.8009 | + | 156.349i | −0.237387 | + | 0.730603i | ||||
\(215\) | −114.593 | + | 72.8468i | −0.532990 | + | 0.338823i | ||||
\(216\) | 17.4475 | − | 74.3477i | 0.0807757 | − | 0.344202i | ||||
\(217\) | 213.371 | + | 293.680i | 0.983276 | + | 1.35336i | ||||
\(218\) | −80.7385 | −0.370360 | ||||||||
\(219\) | −28.1141 | − | 58.6847i | −0.128375 | − | 0.267967i | ||||
\(220\) | −63.8591 | + | 161.654i | −0.290268 | + | 0.734789i | ||||
\(221\) | 92.1156 | − | 126.786i | 0.416813 | − | 0.573694i | ||||
\(222\) | 4.75434 | − | 4.52714i | 0.0214160 | − | 0.0203925i | ||||
\(223\) | 338.042 | + | 109.836i | 1.51588 | + | 0.492540i | 0.944603 | − | 0.328216i | \(-0.106447\pi\) |
0.571279 | + | 0.820756i | \(0.306447\pi\) | |||||||
\(224\) | 50.2337i | 0.224258i | ||||||||
\(225\) | −198.817 | − | 105.341i | −0.883633 | − | 0.468181i | ||||
\(226\) | 13.5619 | 0.0600085 | ||||||||
\(227\) | −115.661 | + | 355.968i | −0.509519 | + | 1.56814i | 0.283518 | + | 0.958967i | \(0.408498\pi\) |
−0.793038 | + | 0.609173i | \(0.791502\pi\) | |||||||
\(228\) | −72.6813 | − | 76.3290i | −0.318777 | − | 0.334776i | ||||
\(229\) | 145.582 | + | 105.771i | 0.635729 | + | 0.461884i | 0.858380 | − | 0.513014i | \(-0.171471\pi\) |
−0.222651 | + | 0.974898i | \(0.571471\pi\) | |||||||
\(230\) | 12.6468 | − | 203.518i | 0.0549860 | − | 0.884861i | ||||
\(231\) | 417.590 | − | 200.055i | 1.80775 | − | 0.866039i | ||||
\(232\) | 32.1886i | 0.138744i | ||||||||
\(233\) | −20.8576 | + | 15.1539i | −0.0895177 | + | 0.0650384i | −0.631644 | − | 0.775259i | \(-0.717619\pi\) |
0.542126 | + | 0.840297i | \(0.317619\pi\) | |||||||
\(234\) | 194.510 | + | 9.52879i | 0.831239 | + | 0.0407213i | ||||
\(235\) | 28.1282 | − | 452.652i | 0.119694 | − | 1.92618i | ||||
\(236\) | 72.9421 | + | 23.7003i | 0.309077 | + | 0.100425i | ||||
\(237\) | 27.9368 | + | 209.441i | 0.117877 | + | 0.883717i | ||||
\(238\) | 122.335 | − | 39.7491i | 0.514014 | − | 0.167013i | ||||
\(239\) | −56.1423 | − | 18.2417i | −0.234905 | − | 0.0763253i | 0.189199 | − | 0.981939i | \(-0.439411\pi\) |
−0.424104 | + | 0.905613i | \(0.639411\pi\) | |||||||
\(240\) | −59.8508 | + | 4.22912i | −0.249378 | + | 0.0176213i | ||||
\(241\) | −45.3121 | − | 139.456i | −0.188017 | − | 0.578657i | 0.811970 | − | 0.583699i | \(-0.198395\pi\) |
−0.999987 | + | 0.00504186i | \(0.998395\pi\) | |||||||
\(242\) | 207.199 | − | 150.539i | 0.856193 | − | 0.622061i | ||||
\(243\) | −149.567 | − | 191.517i | −0.615503 | − | 0.788134i | ||||
\(244\) | 123.881 | − | 90.0049i | 0.507710 | − | 0.368873i | ||||
\(245\) | −80.0884 | − | 125.984i | −0.326891 | − | 0.514222i | ||||
\(246\) | −16.7407 | + | 15.9407i | −0.0680517 | + | 0.0647996i | ||||
\(247\) | 157.981 | − | 217.442i | 0.639597 | − | 0.880330i | ||||
\(248\) | −35.7292 | + | 109.963i | −0.144069 | + | 0.443400i | ||||
\(249\) | 346.450 | + | 63.5999i | 1.39137 | + | 0.255421i | ||||
\(250\) | −32.7230 | + | 173.722i | −0.130892 | + | 0.694887i | ||||
\(251\) | − | 101.467i | − | 0.404252i | −0.979359 | − | 0.202126i | \(-0.935215\pi\) | ||
0.979359 | − | 0.202126i | \(-0.0647851\pi\) | |||||||
\(252\) | 124.563 | + | 100.168i | 0.494300 | + | 0.397492i | ||||
\(253\) | −294.610 | + | 405.496i | −1.16447 | + | 1.60275i | ||||
\(254\) | −114.226 | + | 157.219i | −0.449709 | + | 0.618972i | ||||
\(255\) | 57.6582 | + | 142.409i | 0.226111 | + | 0.558468i | ||||
\(256\) | −12.9443 | + | 9.40456i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 125.099 | 0.486765 | 0.243383 | − | 0.969930i | \(-0.421743\pi\) | ||||
0.243383 | + | 0.969930i | \(0.421743\pi\) | |||||||
\(258\) | 49.7805 | + | 103.911i | 0.192948 | + | 0.402754i | ||||
\(259\) | 4.24619 | + | 13.0684i | 0.0163945 | + | 0.0504572i | ||||
\(260\) | −38.1650 | − | 148.168i | −0.146788 | − | 0.569879i | ||||
\(261\) | 79.8173 | + | 64.1853i | 0.305813 | + | 0.245921i | ||||
\(262\) | −76.8890 | + | 24.9827i | −0.293469 | + | 0.0953540i | ||||
\(263\) | −66.7110 | − | 205.315i | −0.253654 | − | 0.780667i | −0.994092 | − | 0.108542i | \(-0.965382\pi\) |
0.740438 | − | 0.672125i | \(-0.234618\pi\) | |||||||
\(264\) | 129.730 | + | 70.1515i | 0.491401 | + | 0.265725i | ||||
\(265\) | −5.92563 | + | 95.3582i | −0.0223609 | + | 0.359842i | ||||
\(266\) | 209.808 | − | 68.1707i | 0.788751 | − | 0.256281i | ||||
\(267\) | 184.674 | + | 385.483i | 0.691661 | + | 1.44376i | ||||
\(268\) | 101.197i | 0.377601i | ||||||||
\(269\) | −14.5225 | − | 19.9886i | −0.0539871 | − | 0.0743069i | 0.781170 | − | 0.624319i | \(-0.214623\pi\) |
−0.835157 | + | 0.550012i | \(0.814623\pi\) | |||||||
\(270\) | −108.858 | + | 156.844i | −0.403178 | + | 0.580903i | ||||
\(271\) | 375.863 | + | 273.080i | 1.38695 | + | 1.00768i | 0.996192 | + | 0.0871815i | \(0.0277860\pi\) |
0.390755 | + | 0.920495i | \(0.372214\pi\) | |||||||
\(272\) | 33.1457 | + | 24.0818i | 0.121859 | + | 0.0885359i | ||||
\(273\) | −193.884 | + | 358.547i | −0.710199 | + | 1.31336i | ||||
\(274\) | 234.485 | 0.855786 | ||||||||
\(275\) | 296.964 | − | 317.213i | 1.07987 | − | 1.15350i | ||||
\(276\) | −170.180 | − | 31.2410i | −0.616595 | − | 0.113192i | ||||
\(277\) | −225.091 | − | 73.1364i | −0.812601 | − | 0.264030i | −0.126902 | − | 0.991915i | \(-0.540503\pi\) |
−0.685699 | + | 0.727885i | \(0.740503\pi\) | |||||||
\(278\) | 4.15147 | + | 3.01622i | 0.0149333 | + | 0.0108497i | ||||
\(279\) | 201.428 | + | 307.868i | 0.721964 | + | 1.10347i | ||||
\(280\) | 46.1407 | − | 116.801i | 0.164788 | − | 0.417146i | ||||
\(281\) | 52.7516 | + | 72.6064i | 0.187728 | + | 0.258386i | 0.892499 | − | 0.451049i | \(-0.148950\pi\) |
−0.704771 | + | 0.709435i | \(0.748950\pi\) | |||||||
\(282\) | −378.504 | − | 69.4842i | −1.34221 | − | 0.246398i | ||||
\(283\) | −296.551 | − | 408.168i | −1.04789 | − | 1.44229i | −0.890628 | − | 0.454732i | \(-0.849735\pi\) |
−0.157257 | − | 0.987558i | \(-0.550265\pi\) | |||||||
\(284\) | 152.449 | − | 49.5336i | 0.536791 | − | 0.174414i | ||||
\(285\) | 98.8852 | + | 244.235i | 0.346966 | + | 0.856966i | ||||
\(286\) | −116.219 | + | 357.685i | −0.406360 | + | 1.25065i | ||||
\(287\) | −14.9514 | − | 46.0157i | −0.0520955 | − | 0.160334i | ||||
\(288\) | −2.49111 | + | 50.8507i | −0.00864968 | + | 0.176565i | ||||
\(289\) | −56.8867 | + | 175.079i | −0.196840 | + | 0.605811i | ||||
\(290\) | 29.5658 | − | 74.8432i | 0.101951 | − | 0.258080i | ||||
\(291\) | 521.032 | − | 69.4992i | 1.79049 | − | 0.238829i | ||||
\(292\) | 25.4987 | + | 35.0959i | 0.0873243 | + | 0.120192i | ||||
\(293\) | −45.9329 | −0.156768 | −0.0783838 | − | 0.996923i | \(-0.524976\pi\) | ||||
−0.0783838 | + | 0.996923i | \(0.524976\pi\) | |||||||
\(294\) | −114.240 | + | 54.7290i | −0.388572 | + | 0.186153i | ||||
\(295\) | −147.832 | − | 122.106i | −0.501126 | − | 0.413917i | ||||
\(296\) | −2.57253 | + | 3.54078i | −0.00869097 | + | 0.0119621i | ||||
\(297\) | 432.640 | − | 181.804i | 1.45670 | − | 0.612134i | ||||
\(298\) | 40.4300 | + | 13.1365i | 0.135671 | + | 0.0440823i | ||||
\(299\) | − | 441.225i | − | 1.47567i | ||||||
\(300\) | 143.047 | + | 45.1407i | 0.476822 | + | 0.150469i | ||||
\(301\) | −241.162 | −0.801204 | ||||||||
\(302\) | −104.777 | + | 322.471i | −0.346944 | + | 1.06778i | ||||
\(303\) | 146.221 | − | 139.233i | 0.482577 | − | 0.459515i | ||||
\(304\) | 56.8457 | + | 41.3008i | 0.186992 | + | 0.135858i | ||||
\(305\) | −370.713 | + | 95.4877i | −1.21545 | + | 0.313074i | ||||
\(306\) | 125.809 | − | 34.1707i | 0.411140 | − | 0.111669i | ||||
\(307\) | 110.694i | 0.360567i | 0.983615 | + | 0.180284i | \(0.0577015\pi\) | ||||
−0.983615 | + | 0.180284i | \(0.942298\pi\) | |||||||
\(308\) | −249.737 | + | 181.444i | −0.810833 | + | 0.589105i | ||||
\(309\) | −256.534 | + | 34.2184i | −0.830206 | + | 0.110739i | ||||
\(310\) | 184.079 | − | 222.863i | 0.593804 | − | 0.718913i | ||||
\(311\) | 320.823 | + | 104.242i | 1.03159 | + | 0.335182i | 0.775417 | − | 0.631450i | \(-0.217540\pi\) |
0.256169 | + | 0.966632i | \(0.417540\pi\) | |||||||
\(312\) | −128.689 | + | 17.1655i | −0.412465 | + | 0.0550177i | ||||
\(313\) | 27.0113 | − | 8.77650i | 0.0862981 | − | 0.0280399i | −0.265550 | − | 0.964097i | \(-0.585553\pi\) |
0.351848 | + | 0.936057i | \(0.385553\pi\) | |||||||
\(314\) | −384.223 | − | 124.842i | −1.22364 | − | 0.397585i | ||||
\(315\) | −197.622 | − | 347.320i | −0.627373 | − | 1.10260i | ||||
\(316\) | −43.5293 | − | 133.970i | −0.137751 | − | 0.423954i | ||||
\(317\) | 19.4846 | − | 14.1564i | 0.0614655 | − | 0.0446573i | −0.556628 | − | 0.830762i | \(-0.687905\pi\) |
0.618094 | + | 0.786104i | \(0.287905\pi\) | |||||||
\(318\) | 79.7377 | + | 14.6379i | 0.250747 | + | 0.0460312i | ||||
\(319\) | −160.025 | + | 116.265i | −0.501647 | + | 0.364468i | ||||
\(320\) | 38.7356 | − | 9.97746i | 0.121049 | − | 0.0311796i | ||||
\(321\) | −240.484 | − | 252.554i | −0.749172 | − | 0.786772i | ||||
\(322\) | 212.867 | − | 292.987i | 0.661079 | − | 0.909897i | ||||
\(323\) | 55.5996 | − | 171.118i | 0.172135 | − | 0.529777i | ||||
\(324\) | 121.126 | + | 107.576i | 0.373846 | + | 0.332023i | ||||
\(325\) | −47.3563 | + | 379.569i | −0.145712 | + | 1.16791i | ||||
\(326\) | − | 166.430i | − | 0.510521i | ||||||
\(327\) | 81.4673 | − | 150.656i | 0.249135 | − | 0.460722i | ||||
\(328\) | 9.05823 | − | 12.4676i | 0.0276166 | − | 0.0380109i | ||||
\(329\) | 473.446 | − | 651.643i | 1.43905 | − | 1.98068i | ||||
\(330\) | −237.206 | − | 282.272i | −0.718806 | − | 0.855370i | ||||
\(331\) | 201.740 | − | 146.572i | 0.609486 | − | 0.442817i | −0.239748 | − | 0.970835i | \(-0.577065\pi\) |
0.849233 | + | 0.528018i | \(0.177065\pi\) | |||||||
\(332\) | −234.826 | −0.707309 | ||||||||
\(333\) | 3.65027 | + | 13.4395i | 0.0109618 | + | 0.0403588i | ||||
\(334\) | −8.85407 | − | 27.2500i | −0.0265092 | − | 0.0815869i | ||||
\(335\) | 92.9516 | − | 235.299i | 0.277467 | − | 0.702384i | ||||
\(336\) | −93.7349 | − | 50.6872i | −0.278973 | − | 0.150855i | ||||
\(337\) | −108.391 | + | 35.2183i | −0.321634 | + | 0.104505i | −0.465384 | − | 0.885109i | \(-0.654084\pi\) |
0.143750 | + | 0.989614i | \(0.454084\pi\) | |||||||
\(338\) | −28.4517 | − | 87.5655i | −0.0841768 | − | 0.259069i | ||||
\(339\) | −13.6843 | + | 25.3062i | −0.0403667 | + | 0.0746496i | ||||
\(340\) | −54.9492 | − | 86.4387i | −0.161615 | − | 0.254231i | ||||
\(341\) | −675.736 | + | 219.560i | −1.98163 | + | 0.643870i | ||||
\(342\) | 215.765 | − | 58.6035i | 0.630893 | − | 0.171355i | ||||
\(343\) | 169.992i | 0.495602i | ||||||||
\(344\) | −45.1495 | − | 62.1430i | −0.131249 | − | 0.180648i | ||||
\(345\) | 366.999 | + | 228.954i | 1.06377 | + | 0.663634i | ||||
\(346\) | 143.001 | + | 103.896i | 0.413298 | + | 0.300278i | ||||
\(347\) | 293.966 | + | 213.579i | 0.847166 | + | 0.615502i | 0.924363 | − | 0.381514i | \(-0.124597\pi\) |
−0.0771974 | + | 0.997016i | \(0.524597\pi\) | |||||||
\(348\) | −60.0631 | − | 32.4791i | −0.172595 | − | 0.0933308i | ||||
\(349\) | −188.390 | −0.539799 | −0.269899 | − | 0.962889i | \(-0.586990\pi\) | ||||
−0.269899 | + | 0.962889i | \(0.586990\pi\) | |||||||
\(350\) | −214.568 | + | 229.199i | −0.613051 | + | 0.654853i | ||||
\(351\) | −214.046 | + | 353.336i | −0.609818 | + | 1.00666i | ||||
\(352\) | −93.5095 | − | 30.3831i | −0.265652 | − | 0.0863155i | ||||
\(353\) | 146.982 | + | 106.789i | 0.416380 | + | 0.302518i | 0.776180 | − | 0.630512i | \(-0.217155\pi\) |
−0.359799 | + | 0.933030i | \(0.617155\pi\) | |||||||
\(354\) | −117.825 | + | 112.194i | −0.332838 | + | 0.316932i | ||||
\(355\) | −399.964 | − | 24.8541i | −1.12666 | − | 0.0700114i | ||||
\(356\) | −167.494 | − | 230.535i | −0.470488 | − | 0.647571i | ||||
\(357\) | −49.2685 | + | 268.382i | −0.138007 | + | 0.751772i | ||||
\(358\) | −79.9901 | − | 110.097i | −0.223436 | − | 0.307533i | ||||
\(359\) | 274.660 | − | 89.2425i | 0.765070 | − | 0.248586i | 0.0996170 | − | 0.995026i | \(-0.468238\pi\) |
0.665453 | + | 0.746439i | \(0.268238\pi\) | |||||||
\(360\) | 52.4996 | − | 115.947i | 0.145832 | − | 0.322076i | ||||
\(361\) | −16.2004 | + | 49.8598i | −0.0448765 | + | 0.138116i | ||||
\(362\) | 37.1886 | + | 114.455i | 0.102731 | + | 0.316174i | ||||
\(363\) | 71.8326 | + | 538.526i | 0.197886 | + | 1.48354i | ||||
\(364\) | 83.9726 | − | 258.441i | 0.230694 | − | 0.710003i | ||||
\(365\) | −27.0520 | − | 105.024i | −0.0741151 | − | 0.287738i | ||||
\(366\) | 42.9477 | + | 321.977i | 0.117343 | + | 0.879717i | ||||
\(367\) | −104.081 | − | 143.255i | −0.283598 | − | 0.390340i | 0.643323 | − | 0.765595i | \(-0.277555\pi\) |
−0.926922 | + | 0.375255i | \(0.877555\pi\) | |||||||
\(368\) | 115.349 | 0.313449 | ||||||||
\(369\) | −12.8531 | − | 47.3224i | −0.0348323 | − | 0.128245i | ||||
\(370\) | 9.23378 | − | 5.86993i | 0.0249562 | − | 0.0158647i | ||||
\(371\) | −99.7387 | + | 137.279i | −0.268838 | + | 0.370023i | ||||
\(372\) | −169.137 | − | 177.626i | −0.454669 | − | 0.477488i | ||||
\(373\) | 278.407 | + | 90.4598i | 0.746399 | + | 0.242520i | 0.657431 | − | 0.753515i | \(-0.271643\pi\) |
0.0889679 | + | 0.996034i | \(0.471643\pi\) | |||||||
\(374\) | 251.767i | 0.673174i | ||||||||
\(375\) | −291.142 | − | 236.350i | −0.776379 | − | 0.630267i | ||||
\(376\) | 256.553 | 0.682321 | ||||||||
\(377\) | 53.8076 | − | 165.603i | 0.142726 | − | 0.439265i | ||||
\(378\) | −312.599 | + | 131.360i | −0.826982 | + | 0.347514i | ||||
\(379\) | −456.223 | − | 331.465i | −1.20375 | − | 0.874579i | −0.209106 | − | 0.977893i | \(-0.567055\pi\) |
−0.994649 | + | 0.103314i | \(0.967055\pi\) | |||||||
\(380\) | −94.2392 | − | 148.244i | −0.247998 | − | 0.390117i | ||||
\(381\) | −178.109 | − | 371.781i | −0.467479 | − | 0.975804i | ||||
\(382\) | 171.945i | 0.450118i | ||||||||
\(383\) | 363.176 | − | 263.863i | 0.948241 | − | 0.688937i | −0.00214932 | − | 0.999998i | \(-0.500684\pi\) |
0.950390 | + | 0.311060i | \(0.100684\pi\) | |||||||
\(384\) | −4.48758 | − | 33.6432i | −0.0116864 | − | 0.0876124i | ||||
\(385\) | 747.335 | − | 192.497i | 1.94113 | − | 0.499993i | ||||
\(386\) | −91.1288 | − | 29.6095i | −0.236085 | − | 0.0767086i | ||||
\(387\) | −244.124 | − | 11.9593i | −0.630813 | − | 0.0309027i | ||||
\(388\) | −333.280 | + | 108.289i | −0.858969 | + | 0.279096i | ||||
\(389\) | −512.841 | − | 166.632i | −1.31836 | − | 0.428360i | −0.436427 | − | 0.899740i | \(-0.643756\pi\) |
−0.881931 | + | 0.471379i | \(0.843756\pi\) | |||||||
\(390\) | 314.988 | + | 78.2910i | 0.807662 | + | 0.200746i | ||||
\(391\) | −91.2740 | − | 280.912i | −0.233437 | − | 0.718446i | ||||
\(392\) | 68.3204 | − | 49.6377i | 0.174287 | − | 0.126627i | ||||
\(393\) | 30.9658 | − | 168.681i | 0.0787934 | − | 0.429214i | ||||
\(394\) | −189.212 | + | 137.471i | −0.480234 | + | 0.348911i | ||||
\(395\) | −21.8414 | + | 351.482i | −0.0552946 | + | 0.889827i | ||||
\(396\) | −261.802 | + | 171.288i | −0.661116 | + | 0.432546i | ||||
\(397\) | 311.278 | − | 428.438i | 0.784076 | − | 1.07919i | −0.210744 | − | 0.977541i | \(-0.567589\pi\) |
0.994821 | − | 0.101647i | \(-0.0324112\pi\) | |||||||
\(398\) | −130.937 | + | 402.982i | −0.328987 | + | 1.01252i | ||||
\(399\) | −84.4967 | + | 460.282i | −0.211771 | + | 1.15359i | ||||
\(400\) | −99.2307 | − | 12.3804i | −0.248077 | − | 0.0309509i | ||||
\(401\) | 362.105i | 0.903006i | 0.892270 | + | 0.451503i | \(0.149112\pi\) | ||||
−0.892270 | + | 0.451503i | \(0.850888\pi\) | |||||||
\(402\) | −188.832 | − | 102.111i | −0.469730 | − | 0.254007i | ||||
\(403\) | 367.638 | − | 506.010i | 0.912252 | − | 1.25561i | ||||
\(404\) | −79.1186 | + | 108.897i | −0.195838 | + | 0.269548i | ||||
\(405\) | −182.826 | − | 361.386i | −0.451422 | − | 0.892311i | ||||
\(406\) | 115.624 | − | 84.0061i | 0.284789 | − | 0.206912i | ||||
\(407\) | −26.8949 | −0.0660809 | ||||||||
\(408\) | −78.3809 | + | 37.5500i | −0.192110 | + | 0.0920342i | ||||
\(409\) | −118.845 | − | 365.769i | −0.290576 | − | 0.894300i | −0.984672 | − | 0.174418i | \(-0.944196\pi\) |
0.694096 | − | 0.719882i | \(-0.255804\pi\) | |||||||
\(410\) | −32.5135 | + | 20.6688i | −0.0793011 | + | 0.0504118i | ||||
\(411\) | −236.602 | + | 437.544i | −0.575674 | + | 1.06458i | ||||
\(412\) | 164.093 | − | 53.3169i | 0.398283 | − | 0.129410i | ||||
\(413\) | −105.231 | − | 323.868i | −0.254797 | − | 0.784185i | ||||
\(414\) | 230.011 | − | 286.029i | 0.555582 | − | 0.690892i | ||||
\(415\) | 546.007 | + | 215.693i | 1.31568 | + | 0.519741i | ||||
\(416\) | 82.3164 | − | 26.7462i | 0.197876 | − | 0.0642938i | ||||
\(417\) | −9.81713 | + | 4.70310i | −0.0235423 | + | 0.0112784i | ||||
\(418\) | 431.787i | 1.03298i | ||||||||
\(419\) | 476.023 | + | 655.189i | 1.13609 | + | 1.56370i | 0.775943 | + | 0.630804i | \(0.217275\pi\) |
0.360150 | + | 0.932894i | \(0.382725\pi\) | |||||||
\(420\) | 171.391 | + | 203.953i | 0.408073 | + | 0.485601i | ||||
\(421\) | −501.538 | − | 364.388i | −1.19130 | − | 0.865531i | −0.197899 | − | 0.980222i | \(-0.563412\pi\) |
−0.993401 | + | 0.114692i | \(0.963412\pi\) | |||||||
\(422\) | 166.905 | + | 121.264i | 0.395510 | + | 0.287355i | ||||
\(423\) | 511.576 | − | 636.168i | 1.20940 | − | 1.50394i | ||||
\(424\) | −54.0468 | −0.127469 | ||||||||
\(425\) | 48.3695 | + | 251.455i | 0.113811 | + | 0.591658i | ||||
\(426\) | −61.3962 | + | 334.446i | −0.144123 | + | 0.785085i | ||||
\(427\) | −646.613 | − | 210.097i | −1.51432 | − | 0.492031i | ||||
\(428\) | 188.088 | + | 136.654i | 0.439459 | + | 0.319285i | ||||
\(429\) | −550.163 | − | 577.775i | −1.28243 | − | 1.34679i | ||||
\(430\) | 47.8999 | + | 185.962i | 0.111395 | + | 0.432471i | ||||
\(431\) | −57.0800 | − | 78.5638i | −0.132436 | − | 0.182283i | 0.737649 | − | 0.675185i | \(-0.235936\pi\) |
−0.870085 | + | 0.492902i | \(0.835936\pi\) | |||||||
\(432\) | −92.3726 | − | 55.9580i | −0.213825 | − | 0.129533i | ||||
\(433\) | 47.8218 | + | 65.8210i | 0.110443 | + | 0.152012i | 0.860660 | − | 0.509180i | \(-0.170051\pi\) |
−0.750217 | + | 0.661191i | \(0.770051\pi\) | |||||||
\(434\) | 488.245 | − | 158.640i | 1.12499 | − | 0.365531i | ||||
\(435\) | 109.823 | + | 130.688i | 0.252467 | + | 0.300432i | ||||
\(436\) | −35.2840 | + | 108.593i | −0.0809266 | + | 0.249067i | ||||
\(437\) | −156.537 | − | 481.772i | −0.358208 | − | 1.10245i | ||||
\(438\) | −91.2171 | + | 12.1672i | −0.208258 | + | 0.0277791i | ||||
\(439\) | −176.553 | + | 543.374i | −0.402171 | + | 1.23775i | 0.521064 | + | 0.853518i | \(0.325535\pi\) |
−0.923235 | + | 0.384236i | \(0.874465\pi\) | |||||||
\(440\) | 189.516 | + | 156.535i | 0.430718 | + | 0.355762i | ||||
\(441\) | 13.1482 | − | 268.392i | 0.0298145 | − | 0.608599i | ||||
\(442\) | −130.271 | − | 179.303i | −0.294731 | − | 0.405663i | ||||
\(443\) | 307.905 | 0.695044 | 0.347522 | − | 0.937672i | \(-0.387023\pi\) | ||||
0.347522 | + | 0.937672i | \(0.387023\pi\) | |||||||
\(444\) | −4.01126 | − | 8.37301i | −0.00903437 | − | 0.0188581i | ||||
\(445\) | 177.697 | + | 689.876i | 0.399319 | + | 1.55028i | ||||
\(446\) | 295.459 | − | 406.665i | 0.662465 | − | 0.911805i | ||||
\(447\) | −65.3074 | + | 62.1864i | −0.146102 | + | 0.139119i | ||||
\(448\) | 67.5642 | + | 21.9529i | 0.150813 | + | 0.0490021i | ||||
\(449\) | 730.520i | 1.62699i | 0.581570 | + | 0.813497i | \(0.302439\pi\) | ||||
−0.581570 | + | 0.813497i | \(0.697561\pi\) | |||||||
\(450\) | −228.569 | + | 221.373i | −0.507932 | + | 0.491940i | ||||
\(451\) | 94.7008 | 0.209980 | ||||||||
\(452\) | 5.92677 | − | 18.2407i | 0.0131123 | − | 0.0403556i | ||||
\(453\) | −496.000 | − | 520.893i | −1.09492 | − | 1.14987i | ||||
\(454\) | 428.230 | + | 311.127i | 0.943237 | + | 0.685302i | ||||
\(455\) | −432.632 | + | 523.784i | −0.950840 | + | 1.15117i | ||||
\(456\) | −134.425 | + | 64.3991i | −0.294792 | + | 0.141226i | ||||
\(457\) | 334.758i | 0.732513i | 0.930514 | + | 0.366256i | \(0.119361\pi\) | ||||
−0.930514 | + | 0.366256i | \(0.880639\pi\) | |||||||
\(458\) | 205.884 | − | 149.583i | 0.449528 | − | 0.326601i | ||||
\(459\) | −63.1828 | + | 269.236i | −0.137653 | + | 0.586570i | ||||
\(460\) | −268.204 | − | 105.951i | −0.583053 | − | 0.230327i | ||||
\(461\) | −385.182 | − | 125.153i | −0.835536 | − | 0.271482i | −0.140160 | − | 0.990129i | \(-0.544762\pi\) |
−0.695375 | + | 0.718647i | \(0.744762\pi\) | |||||||
\(462\) | −86.5799 | − | 649.085i | −0.187402 | − | 1.40495i | ||||
\(463\) | 403.917 | − | 131.241i | 0.872392 | − | 0.283457i | 0.161597 | − | 0.986857i | \(-0.448336\pi\) |
0.710795 | + | 0.703400i | \(0.248336\pi\) | |||||||
\(464\) | 43.2935 | + | 14.0669i | 0.0933050 | + | 0.0303166i | ||||
\(465\) | 230.116 | + | 568.362i | 0.494874 | + | 1.22228i | ||||
\(466\) | 11.2669 | + | 34.6759i | 0.0241779 | + | 0.0744119i | ||||
\(467\) | −251.589 | + | 182.790i | −0.538734 | + | 0.391413i | −0.823615 | − | 0.567150i | \(-0.808046\pi\) |
0.284881 | + | 0.958563i | \(0.408046\pi\) | |||||||
\(468\) | 97.8202 | − | 257.451i | 0.209017 | − | 0.550109i | ||||
\(469\) | 363.510 | − | 264.106i | 0.775075 | − | 0.563125i | ||||
\(470\) | −596.523 | − | 235.648i | −1.26920 | − | 0.501380i | ||||
\(471\) | 620.643 | − | 590.983i | 1.31771 | − | 1.25474i | ||||
\(472\) | 63.7537 | − | 87.7495i | 0.135071 | − | 0.185910i | ||||
\(473\) | 145.863 | − | 448.921i | 0.308379 | − | 0.949093i | ||||
\(474\) | 293.906 | + | 53.9541i | 0.620055 | + | 0.113827i | ||||
\(475\) | 82.9548 | + | 431.251i | 0.174642 | + | 0.907897i | ||||
\(476\) | − | 181.912i | − | 0.382167i | ||||||
\(477\) | −107.771 | + | 134.019i | −0.225936 | + | 0.280961i | ||||
\(478\) | −49.0702 | + | 67.5393i | −0.102657 | + | 0.141296i | ||||
\(479\) | −113.399 | + | 156.080i | −0.236741 | + | 0.325846i | −0.910813 | − | 0.412820i | \(-0.864544\pi\) |
0.674071 | + | 0.738666i | \(0.264544\pi\) | |||||||
\(480\) | −20.4676 | + | 82.3473i | −0.0426408 | + | 0.171557i | ||||
\(481\) | 19.1540 | − | 13.9162i | 0.0398211 | − | 0.0289317i | ||||
\(482\) | −207.370 | −0.430229 | ||||||||
\(483\) | 331.918 | + | 692.837i | 0.687200 | + | 1.43444i | ||||
\(484\) | −111.925 | − | 344.470i | −0.231250 | − | 0.711714i | ||||
\(485\) | 874.391 | + | 54.3354i | 1.80287 | + | 0.112032i | ||||
\(486\) | −322.953 | + | 117.472i | −0.664512 | + | 0.241711i | ||||
\(487\) | −485.583 | + | 157.776i | −0.997091 | + | 0.323974i | −0.761702 | − | 0.647927i | \(-0.775636\pi\) |
−0.235388 | + | 0.971901i | \(0.575636\pi\) | |||||||
\(488\) | −66.9183 | − | 205.953i | −0.137128 | − | 0.422036i | ||||
\(489\) | 310.554 | + | 167.932i | 0.635080 | + | 0.343420i | ||||
\(490\) | −204.448 | + | 52.6615i | −0.417242 | + | 0.107472i | ||||
\(491\) | −553.144 | + | 179.727i | −1.12657 | + | 0.366043i | −0.812270 | − | 0.583282i | \(-0.801768\pi\) |
−0.314296 | + | 0.949325i | \(0.601768\pi\) | |||||||
\(492\) | 14.1242 | + | 29.4826i | 0.0287078 | + | 0.0599239i | ||||
\(493\) | − | 116.565i | − | 0.236439i | ||||||
\(494\) | −223.418 | − | 307.509i | −0.452264 | − | 0.622487i | ||||
\(495\) | 766.060 | − | 157.801i | 1.54760 | − | 0.318790i | ||||
\(496\) | 132.286 | + | 96.1114i | 0.266706 | + | 0.193773i | ||||
\(497\) | −575.792 | − | 418.337i | −1.15853 | − | 0.841725i | ||||
\(498\) | 236.946 | − | 438.181i | 0.475795 | − | 0.879881i | ||||
\(499\) | 281.894 | 0.564918 | 0.282459 | − | 0.959279i | \(-0.408850\pi\) | ||||
0.282459 | + | 0.959279i | \(0.408850\pi\) | |||||||
\(500\) | 219.355 | + | 119.931i | 0.438709 | + | 0.239863i | ||||
\(501\) | 59.7819 | + | 10.9745i | 0.119325 | + | 0.0219052i | ||||
\(502\) | −136.473 | − | 44.3429i | −0.271859 | − | 0.0883324i | ||||
\(503\) | 78.1333 | + | 56.7672i | 0.155335 | + | 0.112857i | 0.662738 | − | 0.748852i | \(-0.269394\pi\) |
−0.507403 | + | 0.861709i | \(0.669394\pi\) | |||||||
\(504\) | 189.162 | − | 123.762i | 0.375321 | − | 0.245560i | ||||
\(505\) | 283.987 | − | 180.531i | 0.562350 | − | 0.357487i | ||||
\(506\) | 416.642 | + | 573.458i | 0.823403 | + | 1.13332i | ||||
\(507\) | 192.104 | + | 35.2656i | 0.378903 | + | 0.0695574i | ||||
\(508\) | 161.540 | + | 222.341i | 0.317993 | + | 0.437679i | ||||
\(509\) | 42.5947 | − | 13.8399i | 0.0836832 | − | 0.0271903i | −0.266876 | − | 0.963731i | \(-0.585991\pi\) |
0.350559 | + | 0.936541i | \(0.385991\pi\) | |||||||
\(510\) | 216.738 | − | 15.3149i | 0.424976 | − | 0.0300293i | ||||
\(511\) | 59.5213 | − | 183.188i | 0.116480 | − | 0.358489i | ||||
\(512\) | 6.99226 | + | 21.5200i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | −108.360 | + | 461.745i | −0.211228 | + | 0.900088i | ||||
\(514\) | 54.6701 | − | 168.257i | 0.106362 | − | 0.327349i | ||||
\(515\) | −430.512 | − | 26.7524i | −0.835946 | − | 0.0519464i | ||||
\(516\) | 161.514 | − | 21.5440i | 0.313012 | − | 0.0417519i | ||||
\(517\) | 926.668 | + | 1275.45i | 1.79239 | + | 2.46702i | ||||
\(518\) | 19.4326 | 0.0375147 | ||||||||
\(519\) | −338.160 | + | 162.002i | −0.651560 | + | 0.312143i | ||||
\(520\) | −215.965 | − | 13.4202i | −0.415317 | − | 0.0258081i | ||||
\(521\) | −437.726 | + | 602.478i | −0.840164 | + | 1.15639i | 0.145781 | + | 0.989317i | \(0.453431\pi\) |
−0.985945 | + | 0.167070i | \(0.946569\pi\) | |||||||
\(522\) | 121.210 | − | 79.3040i | 0.232204 | − | 0.151923i | ||||
\(523\) | −427.802 | − | 139.001i | −0.817977 | − | 0.265777i | −0.130005 | − | 0.991513i | \(-0.541499\pi\) |
−0.687973 | + | 0.725736i | \(0.741499\pi\) | |||||||
\(524\) | 114.333i | 0.218193i | ||||||||
\(525\) | −211.175 | − | 631.646i | −0.402237 | − | 1.20314i | ||||
\(526\) | −305.302 | −0.580423 | ||||||||
\(527\) | 129.386 | − | 398.210i | 0.245515 | − | 0.755617i | ||||
\(528\) | 151.048 | − | 143.829i | 0.286075 | − | 0.272404i | ||||
\(529\) | −244.801 | − | 177.859i | −0.462763 | − | 0.336217i | ||||
\(530\) | 125.667 | + | 49.6430i | 0.237107 | + | 0.0936660i | ||||
\(531\) | −90.4630 | − | 333.065i | −0.170363 | − | 0.627240i | ||||
\(532\) | − | 311.983i | − | 0.586433i | ||||||
\(533\) | −67.4438 | + | 49.0008i | −0.126536 | + | 0.0919340i | ||||
\(534\) | 599.179 | − | 79.9231i | 1.12206 | − | 0.149669i | ||||
\(535\) | −311.814 | − | 490.504i | −0.582830 | − | 0.916830i | ||||
\(536\) | 136.110 | + | 44.2248i | 0.253936 | + | 0.0825089i | ||||
\(537\) | 286.150 | − | 38.1689i | 0.532868 | − | 0.0710780i | ||||
\(538\) | −33.2311 | + | 10.7975i | −0.0617679 | + | 0.0200696i | ||||
\(539\) | 493.547 | + | 160.363i | 0.915672 | + | 0.297520i | ||||
\(540\) | 163.382 | + | 214.957i | 0.302559 | + | 0.398068i | ||||
\(541\) | 52.9898 | + | 163.086i | 0.0979480 | + | 0.301453i | 0.988011 | − | 0.154385i | \(-0.0493397\pi\) |
−0.890063 | + | 0.455838i | \(0.849340\pi\) | |||||||
\(542\) | 531.550 | − | 386.194i | 0.980720 | − | 0.712535i | ||||
\(543\) | −251.094 | − | 46.0949i | −0.462420 | − | 0.0848892i | ||||
\(544\) | 46.8751 | − | 34.0568i | 0.0861675 | − | 0.0626043i | ||||
\(545\) | 181.785 | − | 220.086i | 0.333551 | − | 0.403828i | ||||
\(546\) | 397.514 | + | 417.465i | 0.728048 | + | 0.764588i | ||||
\(547\) | −223.225 | + | 307.243i | −0.408090 | + | 0.561687i | −0.962751 | − | 0.270389i | \(-0.912848\pi\) |
0.554661 | + | 0.832076i | \(0.312848\pi\) | |||||||
\(548\) | 102.474 | − | 315.382i | 0.186996 | − | 0.575515i | ||||
\(549\) | −644.136 | − | 244.743i | −1.17329 | − | 0.445799i | ||||
\(550\) | −296.872 | − | 538.042i | −0.539768 | − | 0.978259i | ||||
\(551\) | − | 199.911i | − | 0.362815i | ||||||
\(552\) | −116.390 | + | 215.239i | −0.210852 | + | 0.389926i | ||||
\(553\) | −367.628 | + | 505.997i | −0.664789 | + | 0.915003i | ||||
\(554\) | −196.736 | + | 270.784i | −0.355120 | + | 0.488780i | ||||
\(555\) | 1.63601 | + | 23.1529i | 0.00294777 | + | 0.0417170i | ||||
\(556\) | 5.87106 | − | 4.26558i | 0.0105595 | − | 0.00767190i | ||||
\(557\) | −162.914 | −0.292485 | −0.146243 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146243 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(558\) | 502.109 | − | 136.377i | 0.899837 | − | 0.244403i | ||||
\(559\) | 128.403 | + | 395.185i | 0.229702 | + | 0.706950i | ||||
\(560\) | −136.933 | − | 113.103i | −0.244523 | − | 0.201970i | ||||
\(561\) | −469.791 | − | 254.040i | −0.837418 | − | 0.452833i | ||||
\(562\) | 120.709 | − | 39.2206i | 0.214784 | − | 0.0697876i | ||||
\(563\) | 18.6650 | + | 57.4448i | 0.0331527 | + | 0.102033i | 0.966264 | − | 0.257555i | \(-0.0829170\pi\) |
−0.933111 | + | 0.359589i | \(0.882917\pi\) | |||||||
\(564\) | −258.868 | + | 478.721i | −0.458986 | + | 0.848796i | ||||
\(565\) | −30.5351 | + | 36.9686i | −0.0540444 | + | 0.0654311i | ||||
\(566\) | −678.583 | + | 220.485i | −1.19891 | + | 0.389549i | ||||
\(567\) | 70.3056 | − | 715.848i | 0.123996 | − | 1.26252i | ||||
\(568\) | − | 226.690i | − | 0.399102i | ||||||
\(569\) | 306.353 | + | 421.658i | 0.538405 | + | 0.741051i | 0.988382 | − | 0.151989i | \(-0.0485678\pi\) |
−0.449977 | + | 0.893040i | \(0.648568\pi\) | |||||||
\(570\) | 371.710 | − | 26.2655i | 0.652123 | − | 0.0460798i | ||||
\(571\) | 438.487 | + | 318.579i | 0.767928 | + | 0.557932i | 0.901332 | − | 0.433129i | \(-0.142591\pi\) |
−0.133404 | + | 0.991062i | \(0.542591\pi\) | |||||||
\(572\) | 430.296 | + | 312.628i | 0.752265 | + | 0.546552i | ||||
\(573\) | −320.845 | − | 173.497i | −0.559940 | − | 0.302787i | ||||
\(574\) | −68.4251 | −0.119207 | ||||||||
\(575\) | 526.298 | + | 492.702i | 0.915301 | + | 0.856873i | ||||
\(576\) | 67.3054 | + | 25.5731i | 0.116850 | + | 0.0443978i | ||||
\(577\) | 789.861 | + | 256.641i | 1.36891 | + | 0.444786i | 0.899008 | − | 0.437933i | \(-0.144289\pi\) |
0.469902 | + | 0.882719i | \(0.344289\pi\) | |||||||
\(578\) | 210.621 | + | 153.025i | 0.364396 | + | 0.264749i | ||||
\(579\) | 147.202 | − | 140.167i | 0.254235 | − | 0.242085i | ||||
\(580\) | −87.7432 | − | 72.4736i | −0.151281 | − | 0.124955i | ||||
\(581\) | 612.853 | + | 843.520i | 1.05482 | + | 1.45184i | ||||
\(582\) | 134.223 | − | 731.159i | 0.230624 | − | 1.25629i | ||||
\(583\) | −195.217 | − | 268.693i | −0.334849 | − | 0.460880i | ||||
\(584\) | 58.3473 | − | 18.9582i | 0.0999097 | − | 0.0324626i | ||||
\(585\) | −463.920 | + | 508.763i | −0.793026 | + | 0.869680i | ||||
\(586\) | −20.0734 | + | 61.7796i | −0.0342550 | + | 0.105426i | ||||
\(587\) | 87.1657 | + | 268.268i | 0.148494 | + | 0.457016i | 0.997444 | − | 0.0714568i | \(-0.0227648\pi\) |
−0.848950 | + | 0.528473i | \(0.822765\pi\) | |||||||
\(588\) | 23.6856 | + | 177.570i | 0.0402817 | + | 0.301990i | ||||
\(589\) | 221.901 | − | 682.940i | 0.376741 | − | 1.15949i | ||||
\(590\) | −228.837 | + | 145.472i | −0.387859 | + | 0.246562i | ||||
\(591\) | −65.5970 | − | 491.777i | −0.110993 | − | 0.832111i | ||||
\(592\) | 3.63810 | + | 5.00742i | 0.00614544 | + | 0.00845847i | ||||
\(593\) | 737.541 | 1.24374 | 0.621872 | − | 0.783119i | \(-0.286372\pi\) | ||||
0.621872 | + | 0.783119i | \(0.286372\pi\) | |||||||
\(594\) | −55.4549 | − | 661.350i | −0.0933584 | − | 1.11338i | ||||
\(595\) | −167.089 | + | 422.972i | −0.280822 | + | 0.710877i | ||||
\(596\) | 35.3372 | − | 48.6374i | 0.0592905 | − | 0.0816064i | ||||
\(597\) | −619.836 | − | 650.944i | −1.03825 | − | 1.09036i | ||||
\(598\) | −593.446 | − | 192.822i | −0.992385 | − | 0.322445i | ||||
\(599\) | − | 494.412i | − | 0.825396i | −0.910868 | − | 0.412698i | \(-0.864586\pi\) | ||
0.910868 | − | 0.412698i | \(-0.135414\pi\) | |||||||
\(600\) | 123.228 | − | 172.670i | 0.205380 | − | 0.287783i | ||||
\(601\) | −547.684 | −0.911288 | −0.455644 | − | 0.890162i | \(-0.650591\pi\) | ||||
−0.455644 | + | 0.890162i | \(0.650591\pi\) | |||||||
\(602\) | −105.392 | + | 324.363i | −0.175070 | + | 0.538809i | ||||
\(603\) | 381.072 | − | 249.323i | 0.631960 | − | 0.413471i | ||||
\(604\) | 387.933 | + | 281.850i | 0.642273 | + | 0.466639i | ||||
\(605\) | −56.1597 | + | 903.749i | −0.0928259 | + | 1.49380i | ||||
\(606\) | −123.367 | − | 257.514i | −0.203576 | − | 0.424940i | ||||
\(607\) | 414.860i | 0.683459i | 0.939798 | + | 0.341729i | \(0.111013\pi\) | ||||
−0.939798 | + | 0.341729i | \(0.888987\pi\) | |||||||
\(608\) | 80.3919 | − | 58.4082i | 0.132224 | − | 0.0960661i | ||||
\(609\) | 40.0852 | + | 300.517i | 0.0658214 | + | 0.493459i | ||||
\(610\) | −33.5770 | + | 540.338i | −0.0550443 | + | 0.885800i | ||||
\(611\) | −1319.90 | − | 428.863i | −2.16024 | − | 0.701903i | ||||
\(612\) | 9.02106 | − | 184.146i | 0.0147403 | − | 0.300892i | ||||
\(613\) | 569.176 | − | 184.937i | 0.928509 | − | 0.301691i | 0.194556 | − | 0.980891i | \(-0.437673\pi\) |
0.733953 | + | 0.679200i | \(0.237673\pi\) | |||||||
\(614\) | 148.883 | + | 48.3751i | 0.242481 | + | 0.0787868i | ||||
\(615\) | −5.76063 | − | 81.5247i | −0.00936688 | − | 0.132561i | ||||
\(616\) | 134.903 | + | 415.189i | 0.218999 | + | 0.674008i | ||||
\(617\) | −95.2613 | + | 69.2114i | −0.154394 | + | 0.112174i | −0.662300 | − | 0.749238i | \(-0.730420\pi\) |
0.507906 | + | 0.861412i | \(0.330420\pi\) | |||||||
\(618\) | −66.0856 | + | 359.991i | −0.106935 | + | 0.582509i | ||||
\(619\) | 279.977 | − | 203.415i | 0.452305 | − | 0.328619i | −0.338200 | − | 0.941074i | \(-0.609818\pi\) |
0.790505 | + | 0.612455i | \(0.209818\pi\) | |||||||
\(620\) | −219.305 | − | 344.981i | −0.353717 | − | 0.556420i | ||||
\(621\) | 301.636 | + | 717.806i | 0.485727 | + | 1.15589i | ||||
\(622\) | 280.410 | − | 385.951i | 0.450819 | − | 0.620500i | ||||
\(623\) | −390.979 | + | 1203.31i | −0.627574 | + | 1.93147i | ||||
\(624\) | −33.1516 | + | 180.588i | −0.0531276 | + | 0.289404i | ||||
\(625\) | −399.873 | − | 480.340i | −0.639797 | − | 0.768544i | ||||
\(626\) | − | 40.1656i | − | 0.0641623i | ||||||
\(627\) | −805.703 | − | 435.684i | −1.28501 | − | 0.694871i | ||||
\(628\) | −335.823 | + | 462.221i | −0.534751 | + | 0.736021i | ||||
\(629\) | 9.31589 | − | 12.8222i | 0.0148106 | − | 0.0203851i | ||||
\(630\) | −553.508 | + | 114.017i | −0.878585 | + | 0.180980i | ||||
\(631\) | −70.4052 | + | 51.1524i | −0.111577 | + | 0.0810656i | −0.642175 | − | 0.766558i | \(-0.721968\pi\) |
0.530597 | + | 0.847624i | \(0.321968\pi\) | |||||||
\(632\) | −199.212 | −0.315208 | ||||||||
\(633\) | −394.687 | + | 189.083i | −0.623517 | + | 0.298709i | ||||
\(634\) | −10.5252 | − | 32.3932i | −0.0166013 | − | 0.0510934i | ||||
\(635\) | −171.381 | − | 665.354i | −0.269891 | − | 1.04780i | ||||
\(636\) | 54.5346 | − | 100.850i | 0.0857462 | − | 0.158569i | ||||
\(637\) | −434.470 | + | 141.168i | −0.682056 | + | 0.221613i | ||||
\(638\) | 86.4427 | + | 266.043i | 0.135490 | + | 0.416996i | ||||
\(639\) | −562.118 | − | 452.029i | −0.879684 | − | 0.707401i | ||||
\(640\) | 3.50845 | − | 56.4596i | 0.00548195 | − | 0.0882182i | ||||
\(641\) | 564.370 | − | 183.375i | 0.880452 | − | 0.286076i | 0.166307 | − | 0.986074i | \(-0.446816\pi\) |
0.714145 | + | 0.699998i | \(0.246816\pi\) | |||||||
\(642\) | −444.779 | + | 213.081i | −0.692803 | + | 0.331901i | ||||
\(643\) | − | 555.696i | − | 0.864224i | −0.901820 | − | 0.432112i | \(-0.857768\pi\) | ||
0.901820 | − | 0.432112i | \(-0.142232\pi\) | |||||||
\(644\) | −301.040 | − | 414.346i | −0.467453 | − | 0.643394i | ||||
\(645\) | −395.334 | − | 98.2609i | −0.612920 | − | 0.152343i | ||||
\(646\) | −205.855 | − | 149.563i | −0.318662 | − | 0.231521i | ||||
\(647\) | −862.659 | − | 626.758i | −1.33332 | − | 0.968715i | −0.999661 | − | 0.0260212i | \(-0.991716\pi\) |
−0.333660 | − | 0.942693i | \(-0.608284\pi\) | |||||||
\(648\) | 197.623 | − | 115.902i | 0.304973 | − | 0.178861i | ||||
\(649\) | 666.524 | 1.02700 | ||||||||
\(650\) | 489.824 | + | 229.572i | 0.753575 | + | 0.353188i | ||||
\(651\) | −196.633 | + | 1071.13i | −0.302048 | + | 1.64536i | ||||
\(652\) | −223.848 | − | 72.7326i | −0.343325 | − | 0.111553i | ||||
\(653\) | −636.997 | − | 462.806i | −0.975494 | − | 0.708738i | −0.0187968 | − | 0.999823i | \(-0.505984\pi\) |
−0.956697 | + | 0.291086i | \(0.905984\pi\) | |||||||
\(654\) | −167.029 | − | 175.412i | −0.255397 | − | 0.268215i | ||||
\(655\) | 105.017 | − | 265.842i | 0.160332 | − | 0.405866i | ||||
\(656\) | −12.8103 | − | 17.6318i | −0.0195279 | − | 0.0268778i | ||||
\(657\) | 69.3367 | − | 182.486i | 0.105535 | − | 0.277756i | ||||
\(658\) | −669.554 | − | 921.562i | −1.01756 | − | 1.40055i | ||||
\(659\) | 233.655 | − | 75.9192i | 0.354560 | − | 0.115204i | −0.126321 | − | 0.991989i | \(-0.540317\pi\) |
0.480881 | + | 0.876786i | \(0.340317\pi\) | |||||||
\(660\) | −483.318 | + | 195.684i | −0.732300 | + | 0.296491i | ||||
\(661\) | 177.145 | − | 545.195i | 0.267995 | − | 0.824804i | −0.722993 | − | 0.690855i | \(-0.757234\pi\) |
0.990988 | − | 0.133949i | \(-0.0427657\pi\) | |||||||
\(662\) | −108.976 | − | 335.394i | −0.164616 | − | 0.506637i | ||||
\(663\) | 466.022 | − | 62.1616i | 0.702899 | − | 0.0937580i | ||||
\(664\) | −102.623 | + | 315.841i | −0.154553 | + | 0.475664i | ||||
\(665\) | −286.562 | + | 725.406i | −0.430920 | + | 1.09084i | ||||
\(666\) | 19.6713 | + | 0.963671i | 0.0295365 | + | 0.00144695i | ||||
\(667\) | −192.899 | − | 265.503i | −0.289204 | − | 0.398055i | ||||
\(668\) | −40.5206 | −0.0606595 | ||||||||
\(669\) | 460.701 | + | 961.655i | 0.688641 | + | 1.43745i | ||||
\(670\) | −275.855 | − | 227.849i | −0.411723 | − | 0.340073i | ||||
\(671\) | 782.187 | − | 1076.59i | 1.16570 | − | 1.60445i | ||||
\(672\) | −109.138 | + | 103.922i | −0.162407 | + | 0.154646i | ||||
\(673\) | −1217.43 | − | 395.567i | −1.80896 | − | 0.587767i | −0.808961 | − | 0.587862i | \(-0.799970\pi\) |
−1.00000 | 9.49759e-5i | \(0.999970\pi\) | ||||||||
\(674\) | 161.176i | 0.239134i | ||||||||
\(675\) | −182.445 | − | 649.876i | −0.270288 | − | 0.962779i | ||||
\(676\) | −130.209 | −0.192617 | ||||||||
\(677\) | 21.7680 | − | 66.9952i | 0.0321537 | − | 0.0989589i | −0.933692 | − | 0.358078i | \(-0.883432\pi\) |
0.965845 | + | 0.259119i | \(0.0834322\pi\) | |||||||
\(678\) | 28.0565 | + | 29.4646i | 0.0413813 | + | 0.0434581i | ||||
\(679\) | 1258.78 | + | 914.559i | 1.85388 | + | 1.34692i | ||||
\(680\) | −140.273 | + | 36.1314i | −0.206285 | + | 0.0531344i | ||||
\(681\) | −1012.65 | + | 485.131i | −1.48701 | + | 0.712380i | ||||
\(682\) | 1004.81i | 1.47333i | ||||||||
\(683\) | −50.6807 | + | 36.8217i | −0.0742031 | + | 0.0539117i | −0.624268 | − | 0.781210i | \(-0.714603\pi\) |
0.550065 | + | 0.835122i | \(0.314603\pi\) | |||||||
\(684\) | 15.4713 | − | 315.814i | 0.0226189 | − | 0.461717i | ||||
\(685\) | −527.952 | + | 639.187i | −0.770733 | + | 0.933119i | ||||
\(686\) | 228.638 | + | 74.2891i | 0.333292 | + | 0.108293i | ||||
\(687\) | 71.3768 | + | 535.108i | 0.103896 | + | 0.778906i | ||||
\(688\) | −103.313 | + | 33.5685i | −0.150164 | + | 0.0487914i | ||||
\(689\) | 278.058 | + | 90.3467i | 0.403568 | + | 0.131127i | ||||
\(690\) | 468.326 | − | 393.556i | 0.678734 | − | 0.570371i | ||||
\(691\) | −293.365 | − | 902.886i | −0.424552 | − | 1.30664i | −0.903423 | − | 0.428751i | \(-0.858954\pi\) |
0.478871 | − | 0.877885i | \(-0.341046\pi\) | |||||||
\(692\) | 202.234 | − | 146.932i | 0.292246 | − | 0.212329i | ||||
\(693\) | 1298.54 | + | 493.388i | 1.87379 | + | 0.711959i | ||||
\(694\) | 415.731 | − | 302.047i | 0.599037 | − | 0.435226i | ||||
\(695\) | −17.5691 | + | 4.52542i | −0.0252793 | + | 0.00651140i | ||||
\(696\) | −69.9328 | + | 66.5908i | −0.100478 | + | 0.0956764i | ||||
\(697\) | −32.8026 | + | 45.1489i | −0.0470625 | + | 0.0647760i | ||||
\(698\) | −82.3293 | + | 253.384i | −0.117950 | + | 0.363014i | ||||
\(699\) | −76.0731 | − | 13.9652i | −0.108831 | − | 0.0199788i | ||||
\(700\) | 214.502 | + | 388.757i | 0.306431 | + | 0.555367i | ||||
\(701\) | − | 1169.75i | − | 1.66868i | −0.551247 | − | 0.834342i | \(-0.685848\pi\) | ||
0.551247 | − | 0.834342i | \(-0.314152\pi\) | |||||||
\(702\) | 381.695 | + | 442.305i | 0.543724 | + | 0.630064i | ||||
\(703\) | 15.9770 | − | 21.9904i | 0.0227269 | − | 0.0312808i | ||||
\(704\) | −81.7303 | + | 112.492i | −0.116094 | + | 0.159790i | ||||
\(705\) | 1041.62 | − | 875.322i | 1.47748 | − | 1.24159i | ||||
\(706\) | 207.864 | − | 151.022i | 0.294425 | − | 0.213913i | ||||
\(707\) | 597.655 | 0.845339 | ||||||||
\(708\) | 99.4092 | + | 207.504i | 0.140409 | + | 0.293085i | ||||
\(709\) | −153.546 | − | 472.565i | −0.216566 | − | 0.666523i | −0.999039 | − | 0.0438374i | \(-0.986042\pi\) |
0.782472 | − | 0.622685i | \(-0.213958\pi\) | |||||||
\(710\) | −208.219 | + | 527.088i | −0.293266 | + | 0.742378i | ||||
\(711\) | −397.236 | + | 493.981i | −0.558700 | + | 0.694769i | ||||
\(712\) | −383.267 | + | 124.531i | −0.538296 | + | 0.174903i | ||||
\(713\) | −364.279 | − | 1121.13i | −0.510910 | − | 1.57242i | ||||
\(714\) | 339.443 | + | 183.553i | 0.475410 | + | 0.257078i | ||||
\(715\) | −713.347 | − | 1122.14i | −0.997688 | − | 1.56943i | ||||
\(716\) | −183.037 | + | 59.4723i | −0.255638 | + | 0.0830619i | ||||
\(717\) | −76.5136 | − | 159.713i | −0.106714 | − | 0.222751i | ||||
\(718\) | − | 408.418i | − | 0.568827i | ||||||
\(719\) | 404.305 | + | 556.477i | 0.562315 | + | 0.773960i | 0.991619 | − | 0.129200i | \(-0.0412409\pi\) |
−0.429303 | + | 0.903160i | \(0.641241\pi\) | |||||||
\(720\) | −133.006 | − | 121.283i | −0.184730 | − | 0.168448i | ||||
\(721\) | −619.770 | − | 450.289i | −0.859598 | − | 0.624534i | ||||
\(722\) | 59.9814 | + | 43.5790i | 0.0830767 | + | 0.0603588i | ||||
\(723\) | 209.242 | − | 386.948i | 0.289408 | − | 0.535198i | ||||
\(724\) | 170.193 | 0.235074 | ||||||||
\(725\) | 137.448 | + | 249.106i | 0.189583 | + | 0.343594i | ||||
\(726\) | 755.707 | + | 138.730i | 1.04092 | + | 0.191088i | ||||
\(727\) | 883.026 | + | 286.913i | 1.21462 | + | 0.394653i | 0.845119 | − | 0.534579i | \(-0.179530\pi\) |
0.369498 | + | 0.929232i | \(0.379530\pi\) | |||||||
\(728\) | −310.905 | − | 225.886i | −0.427068 | − | 0.310283i | ||||
\(729\) | 106.668 | − | 721.154i | 0.146321 | − | 0.989237i | ||||
\(730\) | −153.080 | − | 9.51249i | −0.209698 | − | 0.0130308i | ||||
\(731\) | 163.500 | + | 225.038i | 0.223666 | + | 0.307850i | ||||
\(732\) | 451.826 | + | 82.9444i | 0.617249 | + | 0.113312i | ||||
\(733\) | −143.420 | − | 197.401i | −0.195662 | − | 0.269306i | 0.699902 | − | 0.714239i | \(-0.253227\pi\) |
−0.895563 | + | 0.444934i | \(0.853227\pi\) | |||||||
\(734\) | −238.162 | + | 77.3835i | −0.324471 | + | 0.105427i | ||||
\(735\) | 108.029 | − | 434.633i | 0.146978 | − | 0.591337i | ||||
\(736\) | 50.4095 | − | 155.144i | 0.0684912 | − | 0.210794i | ||||
\(737\) | 271.766 | + | 836.410i | 0.368746 | + | 1.13488i | ||||
\(738\) | −69.2654 | − | 3.39322i | −0.0938556 | − | 0.00459786i | ||||
\(739\) | −349.812 | + | 1076.61i | −0.473359 | + | 1.45685i | 0.374800 | + | 0.927106i | \(0.377711\pi\) |
−0.848159 | + | 0.529742i | \(0.822289\pi\) | |||||||
\(740\) | −3.85972 | − | 14.9847i | −0.00521584 | − | 0.0202495i | ||||
\(741\) | 799.239 | − | 106.609i | 1.07859 | − | 0.143871i | ||||
\(742\) | 141.052 | + | 194.141i | 0.190097 | + | 0.261646i | ||||
\(743\) | −711.688 | −0.957857 | −0.478929 | − | 0.877854i | \(-0.658975\pi\) | ||||
−0.478929 | + | 0.877854i | \(0.658975\pi\) | |||||||
\(744\) | −312.822 | + | 149.864i | −0.420459 | + | 0.201430i | ||||
\(745\) | −126.839 | + | 80.6314i | −0.170253 | + | 0.108230i | ||||
\(746\) | 243.336 | − | 334.924i | 0.326188 | − | 0.448960i | ||||
\(747\) | 578.550 | + | 884.271i | 0.774497 | + | 1.18376i | ||||
\(748\) | 338.626 | + | 110.026i | 0.452709 | + | 0.147094i | ||||
\(749\) | − | 1032.27i | − | 1.37820i | ||||||
\(750\) | −445.124 | + | 288.296i | −0.593498 | + | 0.384395i | ||||
\(751\) | 1293.60 | 1.72251 | 0.861254 | − | 0.508175i | \(-0.169680\pi\) | ||||
0.861254 | + | 0.508175i | \(0.169680\pi\) | |||||||
\(752\) | 112.118 | − | 345.062i | 0.149092 | − | 0.458860i | ||||
\(753\) | 220.448 | − | 209.913i | 0.292759 | − | 0.278769i | ||||
\(754\) | −199.221 | − | 144.742i | −0.264218 | − | 0.191966i | ||||
\(755\) | −643.118 | − | 1011.67i | −0.851811 | − | 1.33996i | ||||
\(756\) | 40.0683 | + | 477.851i | 0.0530004 | + | 0.632079i | ||||
\(757\) | − | 1171.95i | − | 1.54815i | −0.633092 | − | 0.774076i | \(-0.718215\pi\) | ||
0.633092 | − | 0.774076i | \(-0.281785\pi\) | |||||||
\(758\) | −645.197 | + | 468.763i | −0.851183 | + | 0.618421i | ||||
\(759\) | −1490.46 | + | 198.809i | −1.96372 | + | 0.261936i | ||||
\(760\) | −240.572 | + | 61.9662i | −0.316543 | + | 0.0815345i | ||||
\(761\) | 929.297 | + | 301.947i | 1.22115 | + | 0.396776i | 0.847502 | − | 0.530793i | \(-0.178106\pi\) |
0.373651 | + | 0.927569i | \(0.378106\pi\) | |||||||
\(762\) | −577.881 | + | 77.0822i | −0.758375 | + | 0.101158i | ||||
\(763\) | 482.161 | − | 156.664i | 0.631928 | − | 0.205326i | ||||
\(764\) | 231.266 | + | 75.1428i | 0.302704 | + | 0.0983544i | ||||
\(765\) | −190.117 | + | 419.880i | −0.248519 | + | 0.548863i | ||||
\(766\) | −196.181 | − | 603.783i | −0.256111 | − | 0.788229i | ||||
\(767\) | −474.684 | + | 344.878i | −0.618884 | + | 0.449645i | ||||
\(768\) | −47.2111 | − | 8.66681i | −0.0614728 | − | 0.0112849i | ||||
\(769\) | −6.70121 | + | 4.86871i | −0.00871418 | + | 0.00633122i | −0.592134 | − | 0.805840i | \(-0.701714\pi\) |
0.583420 | + | 0.812171i | \(0.301714\pi\) | |||||||
\(770\) | 67.6892 | − | 1089.29i | 0.0879081 | − | 1.41466i | ||||
\(771\) | 258.801 | + | 271.789i | 0.335669 | + | 0.352515i | ||||
\(772\) | −79.6494 | + | 109.628i | −0.103173 | + | 0.142005i | ||||
\(773\) | 182.178 | − | 560.686i | 0.235676 | − | 0.725337i | −0.761355 | − | 0.648336i | \(-0.775465\pi\) |
0.997031 | − | 0.0770017i | \(-0.0245347\pi\) | |||||||
\(774\) | −122.772 | + | 323.120i | −0.158620 | + | 0.417468i | ||||
\(775\) | 193.045 | + | 1003.57i | 0.249090 | + | 1.29493i | ||||
\(776\) | 495.585i | 0.638640i | ||||||||
\(777\) | −19.6080 | + | 36.2608i | −0.0252356 | + | 0.0466677i | ||||
\(778\) | −448.240 | + | 616.949i | −0.576143 | + | 0.792993i | ||||
\(779\) | −56.2572 | + | 77.4314i | −0.0722172 | + | 0.0993985i | ||||
\(780\) | 242.956 | − | 389.444i | 0.311482 | − | 0.499287i | ||||
\(781\) | 1126.99 | − | 818.804i | 1.44301 | − | 1.04841i | ||||
\(782\) | −417.715 | −0.534162 | ||||||||
\(783\) | 25.6748 | + | 306.196i | 0.0327903 | + | 0.391054i | ||||
\(784\) | −36.9054 | − | 113.583i | −0.0470733 | − | 0.144877i | ||||
\(785\) | 1205.40 | − | 766.273i | 1.53554 | − | 0.976145i | ||||
\(786\) | −213.343 | − | 115.365i | −0.271429 | − | 0.146775i | ||||
\(787\) | 1289.88 | − | 419.107i | 1.63898 | − | 0.532538i | 0.662672 | − | 0.748909i | \(-0.269422\pi\) |
0.976311 | + | 0.216371i | \(0.0694222\pi\) | |||||||
\(788\) | 102.209 | + | 314.567i | 0.129707 | + | 0.399197i | ||||
\(789\) | 308.058 | − | 569.687i | 0.390441 | − | 0.722037i | ||||
\(790\) | 463.197 | + | 182.980i | 0.586325 | + | 0.231620i | ||||
\(791\) | −80.9902 | + | 26.3153i | −0.102390 | + | 0.0332684i | ||||
\(792\) | 115.971 | + | 426.978i | 0.146428 | + | 0.539114i | ||||
\(793\) | 1171.45i | 1.47723i | ||||||||
\(794\) | −440.214 | − | 605.902i | −0.554426 | − | 0.763101i | ||||
\(795\) | −219.434 | + | 184.400i | −0.276017 | + | 0.231950i | ||||
\(796\) | 484.788 | + | 352.219i | 0.609030 | + | 0.442486i | ||||
\(797\) | 273.643 | + | 198.813i | 0.343342 | + | 0.249452i | 0.746070 | − | 0.665867i | \(-0.231938\pi\) |
−0.402729 | + | 0.915319i | \(0.631938\pi\) | |||||||
\(798\) | 582.152 | + | 314.799i | 0.729514 | + | 0.394484i | ||||
\(799\) | −929.054 | −1.16277 | ||||||||
\(800\) | −60.0169 | + | 128.055i | −0.0750212 | + | 0.160068i | ||||
\(801\) | −455.453 | + | 1198.70i | −0.568605 | + | 1.49650i | ||||
\(802\) | 487.031 | + | 158.246i | 0.607270 | + | 0.197314i | ||||
\(803\) | 305.001 | + | 221.596i | 0.379827 | + | 0.275960i | ||||
\(804\) | −219.861 | + | 209.354i | −0.273459 | + | 0.260390i | ||||
\(805\) | 319.378 | + | 1239.93i | 0.396743 | + | 1.54028i | ||||
\(806\) | −519.918 | − | 715.606i | −0.645060 | − | 0.887848i | ||||
\(807\) | 13.3833 | − | 72.9034i | 0.0165840 | − | 0.0903388i | ||||
\(808\) | 111.891 | + | 154.004i | 0.138478 | + | 0.190599i | ||||
\(809\) | −1309.19 | + | 425.381i | −1.61828 | + | 0.525811i | −0.971535 | − | 0.236895i | \(-0.923870\pi\) |
−0.646745 | + | 0.762706i | \(0.723870\pi\) | |||||||
\(810\) | −565.961 | + | 87.9690i | −0.698717 | + | 0.108604i | ||||
\(811\) | −90.6930 | + | 279.124i | −0.111829 | + | 0.344173i | −0.991272 | − | 0.131830i | \(-0.957915\pi\) |
0.879444 | + | 0.476003i | \(0.157915\pi\) | |||||||
\(812\) | −62.4582 | − | 192.227i | −0.0769190 | − | 0.236732i | ||||
\(813\) | 184.280 | + | 1381.54i | 0.226667 | + | 1.69931i | ||||
\(814\) | −11.7535 | + | 36.1736i | −0.0144392 | + | 0.0444393i | ||||
\(815\) | 453.673 | + | 374.723i | 0.556655 | + | 0.459782i | ||||
\(816\) | 16.2509 | + | 121.832i | 0.0199153 | + | 0.149304i | ||||
\(817\) | 280.406 | + | 385.946i | 0.343215 | + | 0.472394i | ||||
\(818\) | −543.895 | −0.664909 | ||||||||
\(819\) | −1180.08 | + | 320.519i | −1.44088 | + | 0.391355i | ||||
\(820\) | 13.5906 | + | 52.7631i | 0.0165739 | + | 0.0643453i | ||||
\(821\) | 212.728 | − | 292.795i | 0.259108 | − | 0.356632i | −0.659567 | − | 0.751646i | \(-0.729260\pi\) |
0.918675 | + | 0.395014i | \(0.129260\pi\) | |||||||
\(822\) | 485.097 | + | 509.443i | 0.590142 | + | 0.619760i | ||||
\(823\) | −255.585 | − | 83.0445i | −0.310553 | − | 0.100905i | 0.149594 | − | 0.988747i | \(-0.452203\pi\) |
−0.460147 | + | 0.887843i | \(0.652203\pi\) | |||||||
\(824\) | − | 244.004i | − | 0.296122i | ||||||
\(825\) | 1303.53 | − | 11.0579i | 1.58003 | − | 0.0134035i | ||||
\(826\) | −481.590 | −0.583039 | ||||||||
\(827\) | 268.822 | − | 827.349i | 0.325057 | − | 1.00042i | −0.646358 | − | 0.763034i | \(-0.723709\pi\) |
0.971415 | − | 0.237388i | \(-0.0762912\pi\) | |||||||
\(828\) | −284.190 | − | 434.364i | −0.343224 | − | 0.524594i | ||||
\(829\) | 498.059 | + | 361.861i | 0.600795 | + | 0.436503i | 0.846161 | − | 0.532927i | \(-0.178908\pi\) |
−0.245366 | + | 0.969431i | \(0.578908\pi\) | |||||||
\(830\) | 528.720 | − | 640.116i | 0.637012 | − | 0.771225i | ||||
\(831\) | −306.765 | − | 640.334i | −0.369152 | − | 0.770558i | ||||
\(832\) | − | 122.404i | − | 0.147120i | ||||||
\(833\) | −247.409 | + | 179.753i | −0.297010 | + | 0.215790i | ||||
\(834\) | 2.03541 | + | 15.2593i | 0.00244054 | + | 0.0182966i | ||||
\(835\) | 94.2164 | + | 37.2189i | 0.112834 | + | 0.0445736i | ||||
\(836\) | 580.752 | + | 188.698i | 0.694679 | + | 0.225715i | ||||
\(837\) | −252.166 | + | 1074.53i | −0.301273 | + | 1.28379i | ||||
\(838\) | 1089.26 | − | 353.921i | 1.29983 | − | 0.422340i | ||||
\(839\) | −383.519 | − | 124.613i | −0.457115 | − | 0.148526i | 0.0714035 | − | 0.997448i | \(-0.477252\pi\) |
−0.528518 | + | 0.848922i | \(0.677252\pi\) | |||||||
\(840\) | 349.216 | − | 141.389i | 0.415733 | − | 0.168321i | ||||
\(841\) | 219.862 | + | 676.664i | 0.261429 | + | 0.804595i | ||||
\(842\) | −709.281 | + | 515.323i | −0.842377 | + | 0.612023i | ||||
\(843\) | −48.6135 | + | 264.814i | −0.0576672 | + | 0.314133i | ||||
\(844\) | 236.039 | − | 171.493i | 0.279667 | − | 0.203190i | ||||
\(845\) | 302.756 | + | 119.600i | 0.358291 | + | 0.141538i | ||||
\(846\) | −632.077 | − | 966.084i | −0.747136 | − | 1.14194i | ||||
\(847\) | −945.265 | + | 1301.05i | −1.11602 | + | 1.53606i | ||||
\(848\) | −23.6193 | + | 72.6927i | −0.0278530 | + | 0.0857226i | ||||
\(849\) | 273.288 | − | 1488.69i | 0.321894 | − | 1.75347i | ||||
\(850\) | 359.344 | + | 44.8330i | 0.422758 | + | 0.0527447i | ||||
\(851\) | − | 44.6222i | − | 0.0524350i | ||||||
\(852\) | 422.998 | + | 228.736i | 0.496477 | + | 0.268470i | ||||
\(853\) | 384.635 | − | 529.404i | 0.450920 | − | 0.620638i | −0.521675 | − | 0.853144i | \(-0.674693\pi\) |
0.972595 | + | 0.232506i | \(0.0746927\pi\) | |||||||
\(854\) | −565.160 | + | 777.876i | −0.661780 | + | 0.910862i | ||||
\(855\) | −326.055 | + | 720.105i | −0.381351 | + | 0.842228i | ||||
\(856\) | 265.997 | − | 193.258i | 0.310744 | − | 0.225769i | ||||
\(857\) | 668.295 | 0.779808 | 0.389904 | − | 0.920856i | \(-0.372508\pi\) | ||||
0.389904 | + | 0.920856i | \(0.372508\pi\) | |||||||
\(858\) | −1017.54 | + | 487.471i | −1.18594 | + | 0.568148i | ||||
\(859\) | 161.884 | + | 498.228i | 0.188456 | + | 0.580009i | 0.999991 | − | 0.00429551i | \(-0.00136731\pi\) |
−0.811534 | + | 0.584305i | \(0.801367\pi\) | |||||||
\(860\) | 271.052 | + | 16.8434i | 0.315177 | + | 0.0195853i | ||||
\(861\) | 69.0427 | − | 127.679i | 0.0801889 | − | 0.148292i | ||||
\(862\) | −130.613 | + | 42.4387i | −0.151523 | + | 0.0492329i | ||||
\(863\) | −74.8592 | − | 230.393i | −0.0867430 | − | 0.266967i | 0.898271 | − | 0.439442i | \(-0.144824\pi\) |
−0.985014 | + | 0.172474i | \(0.944824\pi\) | |||||||
\(864\) | −115.632 | + | 99.7863i | −0.133833 | + | 0.115493i | ||||
\(865\) | −605.184 | + | 155.882i | −0.699635 | + | 0.180211i | ||||
\(866\) | 109.428 | − | 35.5553i | 0.126360 | − | 0.0410569i | ||||
\(867\) | −498.063 | + | 238.607i | −0.574467 | + | 0.275210i | ||||
\(868\) | − | 726.017i | − | 0.836425i | ||||||
\(869\) | −719.553 | − | 990.379i | −0.828024 | − | 1.13968i | ||||
\(870\) | 223.769 | − | 90.5989i | 0.257206 | − | 0.104137i | ||||
\(871\) | −626.327 | − | 455.053i | −0.719089 | − | 0.522449i | ||||
\(872\) | 130.638 | + | 94.9138i | 0.149814 | + | 0.108846i | ||||
\(873\) | 1228.89 | + | 988.215i | 1.40766 | + | 1.13198i | ||||
\(874\) | −716.391 | −0.819669 | ||||||||
\(875\) | −141.669 | − | 1100.94i | −0.161907 | − | 1.25822i | ||||
\(876\) | −23.4984 | + | 128.004i | −0.0268247 | + | 0.146123i | ||||
\(877\) | −521.873 | − | 169.567i | −0.595066 | − | 0.193349i | −0.00402732 | − | 0.999992i | \(-0.501282\pi\) |
−0.591039 | + | 0.806643i | \(0.701282\pi\) | |||||||
\(878\) | 653.680 | + | 474.926i | 0.744510 | + | 0.540918i | ||||
\(879\) | −95.0247 | − | 99.7938i | −0.108105 | − | 0.113531i | ||||
\(880\) | 293.361 | − | 186.490i | 0.333365 | − | 0.211921i | ||||
\(881\) | 659.986 | + | 908.393i | 0.749133 | + | 1.03109i | 0.998041 | + | 0.0625660i | \(0.0199284\pi\) |
−0.248908 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(882\) | −355.241 | − | 134.976i | −0.402767 | − | 0.153034i | ||||
\(883\) | 252.897 | + | 348.083i | 0.286407 | + | 0.394205i | 0.927843 | − | 0.372972i | \(-0.121661\pi\) |
−0.641436 | + | 0.767176i | \(0.721661\pi\) | |||||||
\(884\) | −298.092 | + | 96.8561i | −0.337209 | + | 0.109566i | ||||
\(885\) | −40.5445 | − | 573.788i | −0.0458130 | − | 0.648348i | ||||
\(886\) | 134.559 | − | 414.131i | 0.151873 | − | 0.467416i | ||||
\(887\) | 98.4617 | + | 303.034i | 0.111005 | + | 0.341639i | 0.991093 | − | 0.133172i | \(-0.0425163\pi\) |
−0.880088 | + | 0.474811i | \(0.842516\pi\) | |||||||
\(888\) | −13.0147 | + | 1.73599i | −0.0146561 | + | 0.00195495i | ||||
\(889\) | 377.081 | − | 1160.54i | 0.424163 | − | 1.30544i | ||||
\(890\) | 1005.54 | + | 62.4849i | 1.12982 | + | 0.0702077i | ||||
\(891\) | 1290.02 | + | 563.842i | 1.44783 | + | 0.632820i | ||||
\(892\) | −417.843 | − | 575.111i | −0.468433 | − | 0.644743i | ||||
\(893\) | −1593.35 | −1.78427 | ||||||||
\(894\) | 55.1001 | + | 115.015i | 0.0616333 | + | 0.128652i | ||||
\(895\) | 480.215 | + | 29.8409i | 0.536553 | + | 0.0333418i | ||||
\(896\) | 59.0533 | − | 81.2799i | 0.0659077 | − | 0.0907142i | ||||
\(897\) | 958.604 | − | 912.793i | 1.06868 | − | 1.01761i | ||||
\(898\) | 982.547 | + | 319.249i | 1.09415 | + | 0.355511i | ||||
\(899\) | − | 465.214i | − | 0.517480i | ||||||
\(900\) | 197.858 | + | 404.169i | 0.219842 | + | 0.449076i | ||||
\(901\) | 195.720 | 0.217225 | ||||||||
\(902\) | 41.3858 | − | 127.372i | 0.0458822 | − | 0.141211i | ||||
\(903\) | −498.910 | − | 523.949i | −0.552503 | − | 0.580232i | ||||
\(904\) | −21.9436 | − | 15.9430i | −0.0242739 | − | 0.0176360i | ||||
\(905\) | −395.725 | − | 156.326i | −0.437266 | − | 0.172736i | ||||
\(906\) | −917.359 | + | 439.480i | −1.01254 | + | 0.485077i | ||||
\(907\) | − | 87.2255i | − | 0.0961692i | −0.998843 | − | 0.0480846i | \(-0.984688\pi\) | ||
0.998843 | − | 0.0480846i | \(-0.0153117\pi\) | |||||||
\(908\) | 605.608 | − | 440.000i | 0.666970 | − | 0.484582i | ||||
\(909\) | 604.995 | + | 29.6379i | 0.665561 | + | 0.0326050i | ||||
\(910\) | 515.421 | + | 810.791i | 0.566396 | + | 0.890979i | ||||
\(911\) | 1467.29 | + | 476.753i | 1.61064 | + | 0.523329i | 0.969708 | − | 0.244267i | \(-0.0785472\pi\) |
0.640934 | + | 0.767596i | \(0.278547\pi\) | |||||||
\(912\) | 27.8706 | + | 208.945i | 0.0305599 | + | 0.229106i | ||||
\(913\) | −1940.88 | + | 630.629i | −2.12582 | + | 0.690721i | ||||
\(914\) | 450.249 | + | 146.295i | 0.492614 | + | 0.160060i | ||||
\(915\) | −974.378 | − | 607.869i | −1.06489 | − | 0.664338i | ||||
\(916\) | −111.215 | − | 342.284i | −0.121413 | − | 0.373672i | ||||
\(917\) | 410.696 | − | 298.388i | 0.447870 | − | 0.325396i | ||||
\(918\) | 334.509 | + | 202.641i | 0.364389 | + | 0.220742i | ||||
\(919\) | 851.640 | − | 618.753i | 0.926703 | − | 0.673289i | −0.0184806 | − | 0.999829i | \(-0.505883\pi\) |
0.945183 | + | 0.326540i | \(0.105883\pi\) | |||||||
\(920\) | −259.713 | + | 314.432i | −0.282297 | + | 0.341774i | ||||
\(921\) | −240.494 | + | 229.001i | −0.261123 | + | 0.248644i | ||||
\(922\) | −336.661 | + | 463.375i | −0.365142 | + | 0.502575i | ||||
\(923\) | −378.944 | + | 1166.27i | −0.410556 | + | 1.26356i | ||||
\(924\) | −910.854 | − | 167.211i | −0.985773 | − | 0.180964i | ||||
\(925\) | −4.78927 | + | 38.3868i | −0.00517759 | + | 0.0414993i | ||||
\(926\) | − | 600.622i | − | 0.648620i | ||||||
\(927\) | −605.052 | − | 486.554i | −0.652699 | − | 0.524870i | ||||
\(928\) | 37.8399 | − | 52.0822i | 0.0407758 | − | 0.0561231i | ||||
\(929\) | −495.358 | + | 681.801i | −0.533216 | + | 0.733909i | −0.987616 | − | 0.156889i | \(-0.949854\pi\) |
0.454400 | + | 0.890798i | \(0.349854\pi\) | |||||||
\(930\) | 865.010 | − | 61.1226i | 0.930118 | − | 0.0657232i | ||||
\(931\) | −424.312 | + | 308.281i | −0.455760 | + | 0.331129i | ||||
\(932\) | 51.5629 | 0.0553250 | ||||||||
\(933\) | 437.234 | + | 912.672i | 0.468632 | + | 0.978212i | ||||
\(934\) | 135.904 | + | 418.268i | 0.145507 | + | 0.447825i | ||||
\(935\) | −686.295 | − | 566.862i | −0.734005 | − | 0.606270i | ||||
\(936\) | −303.522 | − | 244.078i | −0.324276 | − | 0.260767i | ||||
\(937\) | 869.531 | − | 282.528i | 0.927995 | − | 0.301524i | 0.194252 | − | 0.980952i | \(-0.437772\pi\) |
0.733742 | + | 0.679428i | \(0.237772\pi\) | |||||||
\(938\) | −196.361 | − | 604.338i | −0.209341 | − | 0.644284i | ||||
\(939\) | 74.9480 | + | 40.5281i | 0.0798168 | + | 0.0431610i | ||||
\(940\) | −577.637 | + | 699.340i | −0.614507 | + | 0.743978i | ||||
\(941\) | −1446.35 | + | 469.947i | −1.53703 | + | 0.499412i | −0.950556 | − | 0.310553i | \(-0.899486\pi\) |
−0.586477 | + | 0.809966i | \(0.699486\pi\) | |||||||
\(942\) | −523.639 | − | 1093.03i | −0.555880 | − | 1.16033i | ||||
\(943\) | 157.121i | 0.166618i | ||||||||
\(944\) | −90.1614 | − | 124.096i | −0.0955099 | − | 0.131458i | ||||
\(945\) | 345.751 | − | 1147.88i | 0.365874 | − | 1.21469i | ||||
\(946\) | −540.053 | − | 392.371i | −0.570880 | − | 0.414769i | ||||
\(947\) | 418.835 | + | 304.301i | 0.442276 | + | 0.321332i | 0.786539 | − | 0.617541i | \(-0.211871\pi\) |
−0.344263 | + | 0.938873i | \(0.611871\pi\) | |||||||
\(948\) | 201.010 | − | 371.724i | 0.212036 | − | 0.392114i | ||||
\(949\) | −331.875 | −0.349710 | ||||||||
\(950\) | 616.284 | + | 76.8897i | 0.648720 | + | 0.0809365i | ||||
\(951\) | 71.0652 | + | 13.0459i | 0.0747268 | + | 0.0137180i | ||||
\(952\) | −244.670 | − | 79.4982i | −0.257007 | − | 0.0835066i | ||||
\(953\) | 801.548 | + | 582.359i | 0.841079 | + | 0.611080i | 0.922672 | − | 0.385586i | \(-0.126001\pi\) |
−0.0815929 | + | 0.996666i | \(0.526001\pi\) | |||||||
\(954\) | 133.157 | + | 203.521i | 0.139577 | + | 0.213334i | ||||
\(955\) | −468.707 | − | 387.140i | −0.490793 | − | 0.405382i | ||||
\(956\) | 69.3957 | + | 95.5150i | 0.0725897 | + | 0.0999111i | ||||
\(957\) | −583.653 | − | 107.145i | −0.609878 | − | 0.111959i | ||||
\(958\) | 160.371 | + | 220.731i | 0.167401 | + | 0.230408i | ||||
\(959\) | −1400.32 | + | 454.992i | −1.46019 | + | 0.474444i | ||||
\(960\) | 101.812 | + | 63.5159i | 0.106054 | + | 0.0661624i | ||||
\(961\) | 219.421 | − | 675.309i | 0.228326 | − | 0.702715i | ||||
\(962\) | −10.3466 | − | 31.8436i | −0.0107553 | − | 0.0331015i | ||||
\(963\) | 51.1908 | − | 1044.95i | 0.0531576 | − | 1.08510i | ||||
\(964\) | −90.6242 | + | 278.913i | −0.0940085 | + | 0.289328i | ||||
\(965\) | 285.892 | − | 181.742i | 0.296262 | − | 0.188334i | ||||
\(966\) | 1076.92 | − | 143.647i | 1.11482 | − | 0.148703i | ||||
\(967\) | −933.969 | − | 1285.50i | −0.965842 | − | 1.32937i | −0.944119 | − | 0.329603i | \(-0.893085\pi\) |
−0.0217225 | − | 0.999764i | \(-0.506915\pi\) | |||||||
\(968\) | −512.224 | −0.529157 | ||||||||
\(969\) | 486.794 | − | 233.209i | 0.502367 | − | 0.240669i | ||||
\(970\) | 455.204 | − | 1152.31i | 0.469282 | − | 1.18795i | ||||
\(971\) | −53.6223 | + | 73.8048i | −0.0552238 | + | 0.0760091i | −0.835736 | − | 0.549132i | \(-0.814958\pi\) |
0.780512 | + | 0.625141i | \(0.214958\pi\) | |||||||
\(972\) | 16.8636 | + | 485.707i | 0.0173494 | + | 0.499699i | ||||
\(973\) | −30.6447 | − | 9.95708i | −0.0314951 | − | 0.0102334i | ||||
\(974\) | 722.058i | 0.741333i | ||||||||
\(975\) | −922.621 | + | 682.356i | −0.946278 | + | 0.699852i | ||||
\(976\) | −306.251 | −0.313782 | ||||||||
\(977\) | −29.4896 | + | 90.7596i | −0.0301838 | + | 0.0928962i | −0.965014 | − | 0.262200i | \(-0.915552\pi\) |
0.934830 | + | 0.355096i | \(0.115552\pi\) | |||||||
\(978\) | 361.586 | − | 344.306i | 0.369719 | − | 0.352051i | ||||
\(979\) | −2003.47 | − | 1455.60i | −2.04644 | − | 1.48683i | ||||
\(980\) | −18.5177 | + | 297.996i | −0.0188957 | + | 0.304078i | ||||
\(981\) | 495.852 | − | 134.677i | 0.505456 | − | 0.137286i | ||||
\(982\) | 822.520i | 0.837597i | ||||||||
\(983\) | 566.239 | − | 411.397i | 0.576031 | − | 0.418511i | −0.261260 | − | 0.965269i | \(-0.584138\pi\) |
0.837291 | + | 0.546757i | \(0.184138\pi\) | |||||||
\(984\) | 45.8265 | − | 6.11268i | 0.0465716 | − | 0.00621208i | ||||
\(985\) | 51.2846 | − | 825.296i | 0.0520656 | − | 0.837864i | ||||
\(986\) | −156.779 | − | 50.9406i | −0.159005 | − | 0.0516639i | ||||
\(987\) | 2395.21 | − | 319.491i | 2.42676 | − | 0.323699i | ||||
\(988\) | −511.236 | + | 166.111i | −0.517445 | + | 0.168128i | ||||
\(989\) | 744.819 | + | 242.006i | 0.753103 | + | 0.244698i | ||||
\(990\) | 122.539 | − | 1099.31i | 0.123777 | − | 1.11041i | ||||
\(991\) | 410.128 | + | 1262.24i | 0.413852 | + | 1.27371i | 0.913273 | + | 0.407347i | \(0.133546\pi\) |
−0.499421 | + | 0.866359i | \(0.666454\pi\) | |||||||
\(992\) | 187.081 | − | 135.922i | 0.188589 | − | 0.137018i | ||||
\(993\) | 735.796 | + | 135.074i | 0.740983 | + | 0.136027i | ||||
\(994\) | −814.292 | + | 591.618i | −0.819208 | + | 0.595189i | ||||
\(995\) | −803.685 | − | 1264.25i | −0.807723 | − | 1.27060i | ||||
\(996\) | −485.802 | − | 510.184i | −0.487753 | − | 0.512233i | ||||
\(997\) | −873.173 | + | 1201.82i | −0.875800 | + | 1.20544i | 0.101766 | + | 0.994808i | \(0.467551\pi\) |
−0.977566 | + | 0.210628i | \(0.932449\pi\) | |||||||
\(998\) | 123.192 | − | 379.146i | 0.123439 | − | 0.379906i | ||||
\(999\) | −21.6470 | + | 35.7338i | −0.0216687 | + | 0.0357696i |
(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 | 150.3.i.a.29.19 | yes | 80 | |
3.2 | odd | 2 | inner | 150.3.i.a.29.3 | ✓ | 80 | |
25.19 | even | 10 | inner | 150.3.i.a.119.3 | yes | 80 | |
75.44 | odd | 10 | inner | 150.3.i.a.119.19 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.i.a.29.3 | ✓ | 80 | 3.2 | odd | 2 | inner | |
150.3.i.a.29.19 | yes | 80 | 1.1 | even | 1 | trivial | |
150.3.i.a.119.3 | yes | 80 | 25.19 | even | 10 | inner | |
150.3.i.a.119.19 | yes | 80 | 75.44 | odd | 10 | inner |