Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,2,Mod(169,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("471.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.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: | \(3.76095393520\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Character | \(\chi\) | \(=\) | 471.169 |
Dual form | 471.2.e.b.301.1 |
$q$-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 \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).
\(n\) | \(158\) | \(319\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48879 | −1.75984 | −0.879919 | − | 0.475124i | \(-0.842403\pi\) | ||||
−0.879919 | + | 0.475124i | \(0.842403\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 4.19406 | 2.09703 | ||||||||
\(5\) | −1.91720 | − | 3.32070i | −0.857400 | − | 1.48506i | −0.874401 | − | 0.485205i | \(-0.838745\pi\) |
0.0170005 | − | 0.999855i | \(-0.494588\pi\) | |||||||
\(6\) | −1.24439 | − | 2.15535i | −0.508021 | − | 0.879919i | ||||
\(7\) | 3.28748 | 1.24255 | 0.621275 | − | 0.783593i | \(-0.286615\pi\) | ||||
0.621275 | + | 0.783593i | \(0.286615\pi\) | |||||||
\(8\) | −5.46054 | −1.93059 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 4.77151 | + | 8.26450i | 1.50888 | + | 2.61346i | ||||
\(11\) | 2.86691 | + | 4.96564i | 0.864406 | + | 1.49720i | 0.867635 | + | 0.497201i | \(0.165639\pi\) |
−0.00322889 | + | 0.999995i | \(0.501028\pi\) | |||||||
\(12\) | 2.09703 | + | 3.63216i | 0.605360 | + | 1.04851i | ||||
\(13\) | 0.294686 | − | 0.510411i | 0.0817311 | − | 0.141562i | −0.822262 | − | 0.569108i | \(-0.807288\pi\) |
0.903994 | + | 0.427546i | \(0.140622\pi\) | |||||||
\(14\) | −8.18183 | −2.18669 | ||||||||
\(15\) | 1.91720 | − | 3.32070i | 0.495020 | − | 0.857400i | ||||
\(16\) | 5.20199 | 1.30050 | ||||||||
\(17\) | −1.45406 | − | 2.51851i | −0.352662 | − | 0.610829i | 0.634053 | − | 0.773290i | \(-0.281390\pi\) |
−0.986715 | + | 0.162461i | \(0.948057\pi\) | |||||||
\(18\) | 1.24439 | − | 2.15535i | 0.293306 | − | 0.508021i | ||||
\(19\) | −3.24844 | − | 5.62646i | −0.745242 | − | 1.29080i | −0.950081 | − | 0.312002i | \(-0.899000\pi\) |
0.204839 | − | 0.978796i | \(-0.434333\pi\) | |||||||
\(20\) | −8.04086 | − | 13.9272i | −1.79799 | − | 3.11421i | ||||
\(21\) | 1.64374 | + | 2.84704i | 0.358693 | + | 0.621275i | ||||
\(22\) | −7.13513 | − | 12.3584i | −1.52121 | − | 2.63482i | ||||
\(23\) | 4.26360 | 0.889023 | 0.444511 | − | 0.895773i | \(-0.353377\pi\) | ||||
0.444511 | + | 0.895773i | \(0.353377\pi\) | |||||||
\(24\) | −2.73027 | − | 4.72896i | −0.557314 | − | 0.965295i | ||||
\(25\) | −4.85135 | + | 8.40278i | −0.970269 | + | 1.68056i | ||||
\(26\) | −0.733410 | + | 1.27030i | −0.143834 | + | 0.249127i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 13.7879 | 2.60566 | ||||||||
\(29\) | 5.15961 | 0.958116 | 0.479058 | − | 0.877783i | \(-0.340978\pi\) | ||||
0.479058 | + | 0.877783i | \(0.340978\pi\) | |||||||
\(30\) | −4.77151 | + | 8.26450i | −0.871155 | + | 1.50888i | ||||
\(31\) | 2.41760 | − | 4.18740i | 0.434213 | − | 0.752079i | −0.563018 | − | 0.826445i | \(-0.690360\pi\) |
0.997231 | + | 0.0743653i | \(0.0236931\pi\) | |||||||
\(32\) | −2.02557 | −0.358074 | ||||||||
\(33\) | −2.86691 | + | 4.96564i | −0.499065 | + | 0.864406i | ||||
\(34\) | 3.61885 | + | 6.26804i | 0.620628 | + | 1.07496i | ||||
\(35\) | −6.30277 | − | 10.9167i | −1.06536 | − | 1.84526i | ||||
\(36\) | −2.09703 | + | 3.63216i | −0.349505 | + | 0.605360i | ||||
\(37\) | −1.51929 | + | 2.63149i | −0.249770 | + | 0.432615i | −0.963462 | − | 0.267845i | \(-0.913688\pi\) |
0.713692 | + | 0.700460i | \(0.247022\pi\) | |||||||
\(38\) | 8.08466 | + | 14.0030i | 1.31151 | + | 2.27159i | ||||
\(39\) | 0.589372 | 0.0943750 | ||||||||
\(40\) | 10.4690 | + | 18.1328i | 1.65529 | + | 2.86704i | ||||
\(41\) | 5.55271 | 0.867187 | 0.433594 | − | 0.901108i | \(-0.357245\pi\) | ||||
0.433594 | + | 0.901108i | \(0.357245\pi\) | |||||||
\(42\) | −4.09091 | − | 7.08567i | −0.631242 | − | 1.09334i | ||||
\(43\) | 1.19864 | − | 2.07610i | 0.182791 | − | 0.316603i | −0.760039 | − | 0.649877i | \(-0.774820\pi\) |
0.942830 | + | 0.333274i | \(0.108154\pi\) | |||||||
\(44\) | 12.0240 | + | 20.8262i | 1.81268 | + | 3.13966i | ||||
\(45\) | 3.83441 | 0.571600 | ||||||||
\(46\) | −10.6112 | −1.56454 | ||||||||
\(47\) | 3.10809 | − | 5.38337i | 0.453362 | − | 0.785245i | −0.545231 | − | 0.838286i | \(-0.683558\pi\) |
0.998592 | + | 0.0530407i | \(0.0168913\pi\) | |||||||
\(48\) | 2.60100 | + | 4.50506i | 0.375421 | + | 0.650249i | ||||
\(49\) | 3.80751 | 0.543930 | ||||||||
\(50\) | 12.0740 | − | 20.9127i | 1.70752 | − | 2.95751i | ||||
\(51\) | 1.45406 | − | 2.51851i | 0.203610 | − | 0.352662i | ||||
\(52\) | 1.23593 | − | 2.14069i | 0.171392 | − | 0.296860i | ||||
\(53\) | 4.32275 | − | 7.48722i | 0.593775 | − | 1.02845i | −0.399943 | − | 0.916540i | \(-0.630970\pi\) |
0.993718 | − | 0.111909i | \(-0.0356964\pi\) | |||||||
\(54\) | 2.48879 | 0.338681 | ||||||||
\(55\) | 10.9929 | − | 19.0403i | 1.48228 | − | 2.56739i | ||||
\(56\) | −17.9514 | −2.39885 | ||||||||
\(57\) | 3.24844 | − | 5.62646i | 0.430266 | − | 0.745242i | ||||
\(58\) | −12.8412 | −1.68613 | ||||||||
\(59\) | −7.89086 | −1.02730 | −0.513651 | − | 0.857999i | \(-0.671708\pi\) | ||||
−0.513651 | + | 0.857999i | \(0.671708\pi\) | |||||||
\(60\) | 8.04086 | − | 13.9272i | 1.03807 | − | 1.79799i | ||||
\(61\) | 7.10113 | + | 12.2995i | 0.909207 | + | 1.57479i | 0.815169 | + | 0.579224i | \(0.196644\pi\) |
0.0940379 | + | 0.995569i | \(0.470023\pi\) | |||||||
\(62\) | −6.01688 | + | 10.4215i | −0.764145 | + | 1.32354i | ||||
\(63\) | −1.64374 | + | 2.84704i | −0.207092 | + | 0.358693i | ||||
\(64\) | −5.36276 | −0.670345 | ||||||||
\(65\) | −2.25989 | −0.280305 | ||||||||
\(66\) | 7.13513 | − | 12.3584i | 0.878274 | − | 1.52121i | ||||
\(67\) | 11.4780 | 1.40226 | 0.701131 | − | 0.713033i | \(-0.252679\pi\) | ||||
0.701131 | + | 0.713033i | \(0.252679\pi\) | |||||||
\(68\) | −6.09843 | − | 10.5628i | −0.739543 | − | 1.28093i | ||||
\(69\) | 2.13180 | + | 3.69239i | 0.256639 | + | 0.444511i | ||||
\(70\) | 15.6862 | + | 27.1694i | 1.87486 | + | 3.24736i | ||||
\(71\) | 1.26829 | − | 2.19675i | 0.150518 | − | 0.260706i | −0.780900 | − | 0.624656i | \(-0.785239\pi\) |
0.931418 | + | 0.363951i | \(0.118572\pi\) | |||||||
\(72\) | 2.73027 | − | 4.72896i | 0.321765 | − | 0.557314i | ||||
\(73\) | −7.03106 | − | 12.1781i | −0.822923 | − | 1.42534i | −0.903496 | − | 0.428596i | \(-0.859009\pi\) |
0.0805735 | − | 0.996749i | \(-0.474325\pi\) | |||||||
\(74\) | 3.78120 | − | 6.54922i | 0.439555 | − | 0.761332i | ||||
\(75\) | −9.70269 | −1.12037 | ||||||||
\(76\) | −13.6241 | − | 23.5977i | −1.56279 | − | 2.70684i | ||||
\(77\) | 9.42491 | + | 16.3244i | 1.07407 | + | 1.86034i | ||||
\(78\) | −1.46682 | −0.166085 | ||||||||
\(79\) | 2.02742 | 0.228103 | 0.114052 | − | 0.993475i | \(-0.463617\pi\) | ||||
0.114052 | + | 0.993475i | \(0.463617\pi\) | |||||||
\(80\) | −9.97328 | − | 17.2742i | −1.11505 | − | 1.93132i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −13.8195 | −1.52611 | ||||||||
\(83\) | 5.53712 | − | 9.59057i | 0.607778 | − | 1.05270i | −0.383828 | − | 0.923405i | \(-0.625394\pi\) |
0.991606 | − | 0.129297i | \(-0.0412722\pi\) | |||||||
\(84\) | 6.89393 | + | 11.9406i | 0.752190 | + | 1.30283i | ||||
\(85\) | −5.57548 | + | 9.65701i | −0.604745 | + | 1.04745i | ||||
\(86\) | −2.98316 | + | 5.16698i | −0.321682 | + | 0.557170i | ||||
\(87\) | 2.57981 | + | 4.46836i | 0.276584 | + | 0.479058i | ||||
\(88\) | −15.6549 | − | 27.1150i | −1.66882 | − | 2.89047i | ||||
\(89\) | 4.67557 | + | 8.09833i | 0.495610 | + | 0.858421i | 0.999987 | − | 0.00506201i | \(-0.00161130\pi\) |
−0.504377 | + | 0.863483i | \(0.668278\pi\) | |||||||
\(90\) | −9.54302 | −1.00592 | ||||||||
\(91\) | 0.968773 | − | 1.67796i | 0.101555 | − | 0.175898i | ||||
\(92\) | 17.8818 | 1.86431 | ||||||||
\(93\) | 4.83519 | 0.501386 | ||||||||
\(94\) | −7.73537 | + | 13.3981i | −0.797843 | + | 1.38190i | ||||
\(95\) | −12.4558 | + | 21.5741i | −1.27794 | + | 2.21346i | ||||
\(96\) | −1.01279 | − | 1.75420i | −0.103367 | − | 0.179037i | ||||
\(97\) | 7.98334 | − | 13.8275i | 0.810585 | − | 1.40397i | −0.101870 | − | 0.994798i | \(-0.532482\pi\) |
0.912455 | − | 0.409177i | \(-0.134184\pi\) | |||||||
\(98\) | −9.47607 | −0.957228 | ||||||||
\(99\) | −5.73382 | −0.576271 | ||||||||
\(100\) | −20.3468 | + | 35.2417i | −2.03468 | + | 3.52417i | ||||
\(101\) | −8.87995 | −0.883588 | −0.441794 | − | 0.897117i | \(-0.645658\pi\) | ||||
−0.441794 | + | 0.897117i | \(0.645658\pi\) | |||||||
\(102\) | −3.61885 | + | 6.26804i | −0.358320 | + | 0.620628i | ||||
\(103\) | −1.20897 | −0.119124 | −0.0595619 | − | 0.998225i | \(-0.518970\pi\) | ||||
−0.0595619 | + | 0.998225i | \(0.518970\pi\) | |||||||
\(104\) | −1.60914 | + | 2.78712i | −0.157789 | + | 0.273299i | ||||
\(105\) | 6.30277 | − | 10.9167i | 0.615087 | − | 1.06536i | ||||
\(106\) | −10.7584 | + | 18.6341i | −1.04495 | + | 1.80990i | ||||
\(107\) | −4.68099 | + | 8.10771i | −0.452528 | + | 0.783801i | −0.998542 | − | 0.0539744i | \(-0.982811\pi\) |
0.546014 | + | 0.837776i | \(0.316144\pi\) | |||||||
\(108\) | −4.19406 | −0.403573 | ||||||||
\(109\) | 1.20401 | + | 2.08540i | 0.115323 | + | 0.199745i | 0.917909 | − | 0.396791i | \(-0.129876\pi\) |
−0.802586 | + | 0.596537i | \(0.796543\pi\) | |||||||
\(110\) | −27.3590 | + | 47.3872i | −2.60858 | + | 4.51819i | ||||
\(111\) | −3.03859 | −0.288410 | ||||||||
\(112\) | 17.1014 | 1.61593 | ||||||||
\(113\) | −8.43059 | − | 14.6022i | −0.793083 | − | 1.37366i | −0.924049 | − | 0.382273i | \(-0.875141\pi\) |
0.130966 | − | 0.991387i | \(-0.458192\pi\) | |||||||
\(114\) | −8.08466 | + | 14.0030i | −0.757198 | + | 1.31151i | ||||
\(115\) | −8.17420 | − | 14.1581i | −0.762248 | − | 1.32025i | ||||
\(116\) | 21.6397 | 2.00920 | ||||||||
\(117\) | 0.294686 | + | 0.510411i | 0.0272437 | + | 0.0471875i | ||||
\(118\) | 19.6387 | 1.80789 | ||||||||
\(119\) | −4.78020 | − | 8.27956i | −0.438201 | − | 0.758986i | ||||
\(120\) | −10.4690 | + | 18.1328i | −0.955681 | + | 1.65529i | ||||
\(121\) | −10.9384 | + | 18.9458i | −0.994397 | + | 1.72235i | ||||
\(122\) | −17.6732 | − | 30.6109i | −1.60006 | − | 2.77138i | ||||
\(123\) | 2.77635 | + | 4.80879i | 0.250335 | + | 0.433594i | ||||
\(124\) | 10.1395 | − | 17.5622i | 0.910557 | − | 1.57713i | ||||
\(125\) | 18.0321 | 1.61284 | ||||||||
\(126\) | 4.09091 | − | 7.08567i | 0.364448 | − | 0.631242i | ||||
\(127\) | 4.52807 | − | 7.84284i | 0.401801 | − | 0.695940i | −0.592142 | − | 0.805833i | \(-0.701718\pi\) |
0.993943 | + | 0.109894i | \(0.0350510\pi\) | |||||||
\(128\) | 17.3979 | 1.53777 | ||||||||
\(129\) | 2.39728 | 0.211069 | ||||||||
\(130\) | 5.62439 | 0.493291 | ||||||||
\(131\) | −3.39639 | + | 5.88272i | −0.296744 | + | 0.513975i | −0.975389 | − | 0.220491i | \(-0.929234\pi\) |
0.678645 | + | 0.734466i | \(0.262567\pi\) | |||||||
\(132\) | −12.0240 | + | 20.8262i | −1.04655 | + | 1.81268i | ||||
\(133\) | −10.6792 | − | 18.4968i | −0.926001 | − | 1.60388i | ||||
\(134\) | −28.5663 | −2.46775 | ||||||||
\(135\) | 1.91720 | + | 3.32070i | 0.165007 | + | 0.285800i | ||||
\(136\) | 7.93997 | + | 13.7524i | 0.680847 | + | 1.17926i | ||||
\(137\) | 4.23509 | + | 7.33539i | 0.361828 | + | 0.626705i | 0.988262 | − | 0.152770i | \(-0.0488194\pi\) |
−0.626434 | + | 0.779475i | \(0.715486\pi\) | |||||||
\(138\) | −5.30560 | − | 9.18957i | −0.451643 | − | 0.782268i | ||||
\(139\) | −2.86496 | + | 4.96226i | −0.243003 | + | 0.420893i | −0.961568 | − | 0.274566i | \(-0.911466\pi\) |
0.718565 | + | 0.695459i | \(0.244799\pi\) | |||||||
\(140\) | −26.4342 | − | 45.7853i | −2.23409 | − | 3.86956i | ||||
\(141\) | 6.21618 | 0.523497 | ||||||||
\(142\) | −3.15651 | + | 5.46723i | −0.264888 | + | 0.458800i | ||||
\(143\) | 3.37935 | 0.282596 | ||||||||
\(144\) | −2.60100 | + | 4.50506i | −0.216750 | + | 0.375421i | ||||
\(145\) | −9.89204 | − | 17.1335i | −0.821489 | − | 1.42286i | ||||
\(146\) | 17.4988 | + | 30.3088i | 1.44821 | + | 2.50837i | ||||
\(147\) | 1.90375 | + | 3.29740i | 0.157019 | + | 0.271965i | ||||
\(148\) | −6.37200 | + | 11.0366i | −0.523775 | + | 0.907205i | ||||
\(149\) | −18.4925 | −1.51496 | −0.757480 | − | 0.652858i | \(-0.773570\pi\) | ||||
−0.757480 | + | 0.652858i | \(0.773570\pi\) | |||||||
\(150\) | 24.1479 | 1.97167 | ||||||||
\(151\) | 7.85088 | + | 13.5981i | 0.638895 | + | 1.10660i | 0.985676 | + | 0.168653i | \(0.0539417\pi\) |
−0.346780 | + | 0.937946i | \(0.612725\pi\) | |||||||
\(152\) | 17.7382 | + | 30.7235i | 1.43876 | + | 2.49200i | ||||
\(153\) | 2.90813 | 0.235108 | ||||||||
\(154\) | −23.4566 | − | 40.6280i | −1.89018 | − | 3.27390i | ||||
\(155\) | −18.5401 | −1.48918 | ||||||||
\(156\) | 2.47186 | 0.197907 | ||||||||
\(157\) | −12.3818 | + | 1.92102i | −0.988178 | + | 0.153314i | ||||
\(158\) | −5.04583 | −0.401424 | ||||||||
\(159\) | 8.64550 | 0.685632 | ||||||||
\(160\) | 3.88344 | + | 6.72632i | 0.307013 | + | 0.531762i | ||||
\(161\) | 14.0165 | 1.10465 | ||||||||
\(162\) | 1.24439 | + | 2.15535i | 0.0977687 | + | 0.169340i | ||||
\(163\) | 5.50827 | + | 9.54060i | 0.431441 | + | 0.747278i | 0.996998 | − | 0.0774318i | \(-0.0246720\pi\) |
−0.565557 | + | 0.824709i | \(0.691339\pi\) | |||||||
\(164\) | 23.2884 | 1.81852 | ||||||||
\(165\) | 21.9858 | 1.71159 | ||||||||
\(166\) | −13.7807 | + | 23.8689i | −1.06959 | + | 1.85258i | ||||
\(167\) | 0.551802 | + | 0.955750i | 0.0426998 | + | 0.0739581i | 0.886585 | − | 0.462565i | \(-0.153071\pi\) |
−0.843886 | + | 0.536523i | \(0.819737\pi\) | |||||||
\(168\) | −8.97569 | − | 15.5464i | −0.692490 | − | 1.19943i | ||||
\(169\) | 6.32632 | + | 10.9575i | 0.486640 | + | 0.842885i | ||||
\(170\) | 13.8762 | − | 24.0342i | 1.06425 | − | 1.84334i | ||||
\(171\) | 6.49687 | 0.496828 | ||||||||
\(172\) | 5.02716 | − | 8.70730i | 0.383317 | − | 0.663925i | ||||
\(173\) | −16.1574 | −1.22842 | −0.614211 | − | 0.789142i | \(-0.710526\pi\) | ||||
−0.614211 | + | 0.789142i | \(0.710526\pi\) | |||||||
\(174\) | −6.42059 | − | 11.1208i | −0.486744 | − | 0.843065i | ||||
\(175\) | −15.9487 | + | 27.6239i | −1.20561 | + | 2.08817i | ||||
\(176\) | 14.9137 | + | 25.8312i | 1.12416 | + | 1.94710i | ||||
\(177\) | −3.94543 | − | 6.83369i | −0.296557 | − | 0.513651i | ||||
\(178\) | −11.6365 | − | 20.1550i | −0.872193 | − | 1.51068i | ||||
\(179\) | 3.49081 | + | 6.04626i | 0.260916 | + | 0.451919i | 0.966485 | − | 0.256721i | \(-0.0826422\pi\) |
−0.705570 | + | 0.708640i | \(0.749309\pi\) | |||||||
\(180\) | 16.0817 | 1.19866 | ||||||||
\(181\) | 5.35794 | + | 9.28023i | 0.398253 | + | 0.689794i | 0.993510 | − | 0.113741i | \(-0.0362834\pi\) |
−0.595258 | + | 0.803535i | \(0.702950\pi\) | |||||||
\(182\) | −2.41107 | + | 4.17609i | −0.178720 | + | 0.309553i | ||||
\(183\) | −7.10113 | + | 12.2995i | −0.524931 | + | 0.909207i | ||||
\(184\) | −23.2816 | −1.71634 | ||||||||
\(185\) | 11.6512 | 0.856612 | ||||||||
\(186\) | −12.0338 | −0.882358 | ||||||||
\(187\) | 8.33735 | − | 14.4407i | 0.609687 | − | 1.05601i | ||||
\(188\) | 13.0355 | − | 22.5782i | 0.950712 | − | 1.64668i | ||||
\(189\) | −3.28748 | −0.239129 | ||||||||
\(190\) | 30.9999 | − | 53.6934i | 2.24897 | − | 3.89533i | ||||
\(191\) | 1.25436 | + | 2.17262i | 0.0907624 | + | 0.157205i | 0.907832 | − | 0.419334i | \(-0.137736\pi\) |
−0.817070 | + | 0.576539i | \(0.804403\pi\) | |||||||
\(192\) | −2.68138 | − | 4.64429i | −0.193512 | − | 0.335173i | ||||
\(193\) | 0.445945 | − | 0.772400i | 0.0320998 | − | 0.0555985i | −0.849529 | − | 0.527542i | \(-0.823114\pi\) |
0.881629 | + | 0.471943i | \(0.156447\pi\) | |||||||
\(194\) | −19.8688 | + | 34.4138i | −1.42650 | + | 2.47077i | ||||
\(195\) | −1.12995 | − | 1.95712i | −0.0809171 | − | 0.140153i | ||||
\(196\) | 15.9689 | 1.14064 | ||||||||
\(197\) | 2.34936 | + | 4.06922i | 0.167385 | + | 0.289920i | 0.937500 | − | 0.347986i | \(-0.113134\pi\) |
−0.770114 | + | 0.637906i | \(0.779801\pi\) | |||||||
\(198\) | 14.2703 | 1.01414 | ||||||||
\(199\) | −8.91188 | − | 15.4358i | −0.631746 | − | 1.09422i | −0.987195 | − | 0.159521i | \(-0.949005\pi\) |
0.355448 | − | 0.934696i | \(-0.384328\pi\) | |||||||
\(200\) | 26.4910 | − | 45.8837i | 1.87319 | − | 3.24447i | ||||
\(201\) | 5.73900 | + | 9.94024i | 0.404798 | + | 0.701131i | ||||
\(202\) | 22.1003 | 1.55497 | ||||||||
\(203\) | 16.9621 | 1.19051 | ||||||||
\(204\) | 6.09843 | − | 10.5628i | 0.426975 | − | 0.739543i | ||||
\(205\) | −10.6457 | − | 18.4389i | −0.743526 | − | 1.28783i | ||||
\(206\) | 3.00888 | 0.209639 | ||||||||
\(207\) | −2.13180 | + | 3.69239i | −0.148170 | + | 0.256639i | ||||
\(208\) | 1.53295 | − | 2.65515i | 0.106291 | − | 0.184102i | ||||
\(209\) | 18.6260 | − | 32.2611i | 1.28838 | − | 2.23155i | ||||
\(210\) | −15.6862 | + | 27.1694i | −1.08245 | + | 1.87486i | ||||
\(211\) | −19.3188 | −1.32996 | −0.664980 | − | 0.746861i | \(-0.731560\pi\) | ||||
−0.664980 | + | 0.746861i | \(0.731560\pi\) | |||||||
\(212\) | 18.1298 | − | 31.4018i | 1.24516 | − | 2.15669i | ||||
\(213\) | 2.53658 | 0.173804 | ||||||||
\(214\) | 11.6500 | − | 20.1783i | 0.796376 | − | 1.37936i | ||||
\(215\) | −9.19215 | −0.626899 | ||||||||
\(216\) | 5.46054 | 0.371542 | ||||||||
\(217\) | 7.94780 | − | 13.7660i | 0.539532 | − | 0.934496i | ||||
\(218\) | −2.99652 | − | 5.19012i | −0.202950 | − | 0.351519i | ||||
\(219\) | 7.03106 | − | 12.1781i | 0.475115 | − | 0.822923i | ||||
\(220\) | 46.1049 | − | 79.8560i | 3.10839 | − | 5.38389i | ||||
\(221\) | −1.71397 | −0.115294 | ||||||||
\(222\) | 7.56239 | 0.507555 | ||||||||
\(223\) | −4.66315 | + | 8.07682i | −0.312268 | + | 0.540864i | −0.978853 | − | 0.204565i | \(-0.934422\pi\) |
0.666585 | + | 0.745429i | \(0.267755\pi\) | |||||||
\(224\) | −6.65903 | −0.444925 | ||||||||
\(225\) | −4.85135 | − | 8.40278i | −0.323423 | − | 0.560185i | ||||
\(226\) | 20.9819 | + | 36.3418i | 1.39570 | + | 2.41742i | ||||
\(227\) | 2.40625 | + | 4.16774i | 0.159708 | + | 0.276623i | 0.934763 | − | 0.355271i | \(-0.115611\pi\) |
−0.775055 | + | 0.631894i | \(0.782278\pi\) | |||||||
\(228\) | 13.6241 | − | 23.5977i | 0.902280 | − | 1.56279i | ||||
\(229\) | 4.17311 | − | 7.22803i | 0.275767 | − | 0.477642i | −0.694562 | − | 0.719433i | \(-0.744402\pi\) |
0.970328 | + | 0.241791i | \(0.0777350\pi\) | |||||||
\(230\) | 20.3438 | + | 35.2366i | 1.34143 | + | 2.32343i | ||||
\(231\) | −9.42491 | + | 16.3244i | −0.620113 | + | 1.07407i | ||||
\(232\) | −28.1743 | −1.84973 | ||||||||
\(233\) | 7.23733 | + | 12.5354i | 0.474133 | + | 0.821223i | 0.999561 | − | 0.0296153i | \(-0.00942822\pi\) |
−0.525428 | + | 0.850838i | \(0.676095\pi\) | |||||||
\(234\) | −0.733410 | − | 1.27030i | −0.0479445 | − | 0.0830423i | ||||
\(235\) | −23.8354 | −1.55485 | ||||||||
\(236\) | −33.0947 | −2.15428 | ||||||||
\(237\) | 1.01371 | + | 1.75580i | 0.0658477 | + | 0.114052i | ||||
\(238\) | 11.8969 | + | 20.6060i | 0.771162 | + | 1.33569i | ||||
\(239\) | −3.57167 | −0.231032 | −0.115516 | − | 0.993306i | \(-0.536852\pi\) | ||||
−0.115516 | + | 0.993306i | \(0.536852\pi\) | |||||||
\(240\) | 9.97328 | − | 17.2742i | 0.643773 | − | 1.11505i | ||||
\(241\) | 13.3312 | + | 23.0902i | 0.858735 | + | 1.48737i | 0.873136 | + | 0.487476i | \(0.162082\pi\) |
−0.0144011 | + | 0.999896i | \(0.504584\pi\) | |||||||
\(242\) | 27.2233 | − | 47.1521i | 1.74998 | − | 3.03105i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 29.7825 | + | 51.5849i | 1.90663 | + | 3.30238i | ||||
\(245\) | −7.29977 | − | 12.6436i | −0.466365 | − | 0.807768i | ||||
\(246\) | −6.90975 | − | 11.9680i | −0.440550 | − | 0.763054i | ||||
\(247\) | −3.82907 | −0.243638 | ||||||||
\(248\) | −13.2014 | + | 22.8655i | −0.838288 | + | 1.45196i | ||||
\(249\) | 11.0742 | 0.701801 | ||||||||
\(250\) | −44.8779 | −2.83833 | ||||||||
\(251\) | 5.01215 | − | 8.68130i | 0.316364 | − | 0.547959i | −0.663362 | − | 0.748298i | \(-0.730871\pi\) |
0.979727 | + | 0.200339i | \(0.0642045\pi\) | |||||||
\(252\) | −6.89393 | + | 11.9406i | −0.434277 | + | 0.752190i | ||||
\(253\) | 12.2234 | + | 21.1715i | 0.768477 | + | 1.33104i | ||||
\(254\) | −11.2694 | + | 19.5192i | −0.707104 | + | 1.22474i | ||||
\(255\) | −11.1510 | −0.698300 | ||||||||
\(256\) | −32.5742 | −2.03589 | ||||||||
\(257\) | −2.77874 | + | 4.81291i | −0.173333 | + | 0.300221i | −0.939583 | − | 0.342321i | \(-0.888787\pi\) |
0.766250 | + | 0.642542i | \(0.222120\pi\) | |||||||
\(258\) | −5.96631 | −0.371446 | ||||||||
\(259\) | −4.99464 | + | 8.65097i | −0.310352 | + | 0.537545i | ||||
\(260\) | −9.47811 | −0.587808 | ||||||||
\(261\) | −2.57981 | + | 4.46836i | −0.159686 | + | 0.276584i | ||||
\(262\) | 8.45288 | − | 14.6408i | 0.522221 | − | 0.904513i | ||||
\(263\) | −3.93830 | + | 6.82133i | −0.242846 | + | 0.420621i | −0.961524 | − | 0.274722i | \(-0.911414\pi\) |
0.718678 | + | 0.695343i | \(0.244748\pi\) | |||||||
\(264\) | 15.6549 | − | 27.1150i | 0.963491 | − | 1.66882i | ||||
\(265\) | −33.1504 | −2.03641 | ||||||||
\(266\) | 26.5781 | + | 46.0347i | 1.62961 | + | 2.82257i | ||||
\(267\) | −4.67557 | + | 8.09833i | −0.286140 | + | 0.495610i | ||||
\(268\) | 48.1394 | 2.94058 | ||||||||
\(269\) | −27.3968 | −1.67041 | −0.835206 | − | 0.549937i | \(-0.814652\pi\) | ||||
−0.835206 | + | 0.549937i | \(0.814652\pi\) | |||||||
\(270\) | −4.77151 | − | 8.26450i | −0.290385 | − | 0.502962i | ||||
\(271\) | −6.74815 | + | 11.6881i | −0.409921 | + | 0.710004i | −0.994880 | − | 0.101058i | \(-0.967777\pi\) |
0.584959 | + | 0.811063i | \(0.301110\pi\) | |||||||
\(272\) | −7.56403 | − | 13.1013i | −0.458637 | − | 0.794382i | ||||
\(273\) | 1.93755 | 0.117266 | ||||||||
\(274\) | −10.5402 | − | 18.2562i | −0.636759 | − | 1.10290i | ||||
\(275\) | −55.6335 | −3.35483 | ||||||||
\(276\) | 8.94090 | + | 15.4861i | 0.538179 | + | 0.932153i | ||||
\(277\) | −5.13464 | + | 8.89345i | −0.308511 | + | 0.534356i | −0.978037 | − | 0.208433i | \(-0.933164\pi\) |
0.669526 | + | 0.742788i | \(0.266497\pi\) | |||||||
\(278\) | 7.13028 | − | 12.3500i | 0.427645 | − | 0.740704i | ||||
\(279\) | 2.41760 | + | 4.18740i | 0.144738 | + | 0.250693i | ||||
\(280\) | 34.4165 | + | 59.6111i | 2.05678 | + | 3.56244i | ||||
\(281\) | 4.06455 | − | 7.04000i | 0.242470 | − | 0.419971i | −0.718947 | − | 0.695065i | \(-0.755376\pi\) |
0.961417 | + | 0.275094i | \(0.0887089\pi\) | |||||||
\(282\) | −15.4707 | −0.921269 | ||||||||
\(283\) | −7.65842 | + | 13.2648i | −0.455246 | + | 0.788508i | −0.998702 | − | 0.0509287i | \(-0.983782\pi\) |
0.543457 | + | 0.839437i | \(0.317115\pi\) | |||||||
\(284\) | 5.31928 | − | 9.21327i | 0.315641 | − | 0.546707i | ||||
\(285\) | −24.9117 | −1.47564 | ||||||||
\(286\) | −8.41049 | −0.497322 | ||||||||
\(287\) | 18.2544 | 1.07752 | ||||||||
\(288\) | 1.01279 | − | 1.75420i | 0.0596791 | − | 0.103367i | ||||
\(289\) | 4.27139 | − | 7.39827i | 0.251258 | − | 0.435192i | ||||
\(290\) | 24.6192 | + | 42.6416i | 1.44569 | + | 2.50400i | ||||
\(291\) | 15.9667 | 0.935983 | ||||||||
\(292\) | −29.4886 | − | 51.0758i | −1.72569 | − | 2.98899i | ||||
\(293\) | 9.43404 | + | 16.3402i | 0.551142 | + | 0.954606i | 0.998193 | + | 0.0600975i | \(0.0191412\pi\) |
−0.447050 | + | 0.894509i | \(0.647526\pi\) | |||||||
\(294\) | −4.73803 | − | 8.20652i | −0.276328 | − | 0.478614i | ||||
\(295\) | 15.1284 | + | 26.2032i | 0.880809 | + | 1.52561i | ||||
\(296\) | 8.29616 | − | 14.3694i | 0.482204 | − | 0.835202i | ||||
\(297\) | −2.86691 | − | 4.96564i | −0.166355 | − | 0.288135i | ||||
\(298\) | 46.0238 | 2.66608 | ||||||||
\(299\) | 1.25642 | − | 2.17619i | 0.0726608 | − | 0.125852i | ||||
\(300\) | −40.6936 | −2.34945 | ||||||||
\(301\) | 3.94050 | − | 6.82515i | 0.227127 | − | 0.393395i | ||||
\(302\) | −19.5392 | − | 33.8428i | −1.12435 | − | 1.94744i | ||||
\(303\) | −4.43997 | − | 7.69026i | −0.255070 | − | 0.441794i | ||||
\(304\) | −16.8983 | − | 29.2688i | −0.969186 | − | 1.67868i | ||||
\(305\) | 27.2286 | − | 47.1614i | 1.55911 | − | 2.70045i | ||||
\(306\) | −7.23771 | −0.413752 | ||||||||
\(307\) | −14.1069 | −0.805126 | −0.402563 | − | 0.915392i | \(-0.631881\pi\) | ||||
−0.402563 | + | 0.915392i | \(0.631881\pi\) | |||||||
\(308\) | 39.5286 | + | 68.4655i | 2.25235 | + | 3.90119i | ||||
\(309\) | −0.604487 | − | 1.04700i | −0.0343881 | − | 0.0595619i | ||||
\(310\) | 46.1424 | 2.62071 | ||||||||
\(311\) | 11.8967 | + | 20.6058i | 0.674602 | + | 1.16845i | 0.976585 | + | 0.215132i | \(0.0690182\pi\) |
−0.301983 | + | 0.953313i | \(0.597648\pi\) | |||||||
\(312\) | −3.21828 | −0.182199 | ||||||||
\(313\) | −18.6516 | −1.05425 | −0.527125 | − | 0.849788i | \(-0.676730\pi\) | ||||
−0.527125 | + | 0.849788i | \(0.676730\pi\) | |||||||
\(314\) | 30.8157 | − | 4.78101i | 1.73903 | − | 0.269808i | ||||
\(315\) | 12.6055 | 0.710241 | ||||||||
\(316\) | 8.50313 | 0.478338 | ||||||||
\(317\) | 8.28354 | + | 14.3475i | 0.465250 | + | 0.805836i | 0.999213 | − | 0.0396716i | \(-0.0126312\pi\) |
−0.533963 | + | 0.845508i | \(0.679298\pi\) | |||||||
\(318\) | −21.5168 | −1.20660 | ||||||||
\(319\) | 14.7922 | + | 25.6208i | 0.828202 | + | 1.43449i | ||||
\(320\) | 10.2815 | + | 17.8081i | 0.574754 | + | 0.995503i | ||||
\(321\) | −9.36197 | −0.522534 | ||||||||
\(322\) | −34.8841 | −1.94401 | ||||||||
\(323\) | −9.44687 | + | 16.3625i | −0.525638 | + | 0.910432i | ||||
\(324\) | −2.09703 | − | 3.63216i | −0.116502 | − | 0.201787i | ||||
\(325\) | 2.85925 | + | 4.95236i | 0.158602 | + | 0.274707i | ||||
\(326\) | −13.7089 | − | 23.7445i | −0.759266 | − | 1.31509i | ||||
\(327\) | −1.20401 | + | 2.08540i | −0.0665817 | + | 0.115323i | ||||
\(328\) | −30.3208 | −1.67418 | ||||||||
\(329\) | 10.2178 | − | 17.6977i | 0.563324 | − | 0.975706i | ||||
\(330\) | −54.7180 | −3.01213 | ||||||||
\(331\) | −12.6550 | − | 21.9190i | −0.695579 | − | 1.20478i | −0.969985 | − | 0.243164i | \(-0.921815\pi\) |
0.274406 | − | 0.961614i | \(-0.411519\pi\) | |||||||
\(332\) | 23.2230 | − | 40.2234i | 1.27453 | − | 2.20755i | ||||
\(333\) | −1.51929 | − | 2.63149i | −0.0832568 | − | 0.144205i | ||||
\(334\) | −1.37332 | − | 2.37866i | −0.0751446 | − | 0.130154i | ||||
\(335\) | −22.0057 | − | 38.1150i | −1.20230 | − | 2.08244i | ||||
\(336\) | 8.55071 | + | 14.8103i | 0.466480 | + | 0.807967i | ||||
\(337\) | 6.34464 | 0.345614 | 0.172807 | − | 0.984956i | \(-0.444716\pi\) | ||||
0.172807 | + | 0.984956i | \(0.444716\pi\) | |||||||
\(338\) | −15.7449 | − | 27.2709i | −0.856407 | − | 1.48334i | ||||
\(339\) | 8.43059 | − | 14.6022i | 0.457887 | − | 0.793083i | ||||
\(340\) | −23.3839 | + | 40.5020i | −1.26817 | + | 2.19653i | ||||
\(341\) | 27.7242 | 1.50135 | ||||||||
\(342\) | −16.1693 | −0.874337 | ||||||||
\(343\) | −10.4952 | −0.566690 | ||||||||
\(344\) | −6.54521 | + | 11.3366i | −0.352894 | + | 0.611231i | ||||
\(345\) | 8.17420 | − | 14.1581i | 0.440084 | − | 0.762248i | ||||
\(346\) | 40.2122 | 2.16182 | ||||||||
\(347\) | −14.7283 | + | 25.5102i | −0.790657 | + | 1.36946i | 0.134904 | + | 0.990859i | \(0.456927\pi\) |
−0.925561 | + | 0.378599i | \(0.876406\pi\) | |||||||
\(348\) | 10.8199 | + | 18.7405i | 0.580005 | + | 1.00460i | ||||
\(349\) | 5.61868 | + | 9.73184i | 0.300761 | + | 0.520934i | 0.976309 | − | 0.216383i | \(-0.0694260\pi\) |
−0.675547 | + | 0.737317i | \(0.736093\pi\) | |||||||
\(350\) | 39.6929 | − | 68.7501i | 2.12167 | − | 3.67485i | ||||
\(351\) | −0.294686 | + | 0.510411i | −0.0157292 | + | 0.0272437i | ||||
\(352\) | −5.80714 | − | 10.0583i | −0.309522 | − | 0.536107i | ||||
\(353\) | −9.75310 | −0.519105 | −0.259553 | − | 0.965729i | \(-0.583575\pi\) | ||||
−0.259553 | + | 0.965729i | \(0.583575\pi\) | |||||||
\(354\) | 9.81933 | + | 17.0076i | 0.521892 | + | 0.903943i | ||||
\(355\) | −9.72630 | −0.516218 | ||||||||
\(356\) | 19.6096 | + | 33.9648i | 1.03931 | + | 1.80013i | ||||
\(357\) | 4.78020 | − | 8.27956i | 0.252995 | − | 0.438201i | ||||
\(358\) | −8.68789 | − | 15.0479i | −0.459169 | − | 0.795304i | ||||
\(359\) | 14.1939 | 0.749124 | 0.374562 | − | 0.927202i | \(-0.377793\pi\) | ||||
0.374562 | + | 0.927202i | \(0.377793\pi\) | |||||||
\(360\) | −20.9379 | −1.10353 | ||||||||
\(361\) | −11.6047 | + | 20.0999i | −0.610772 | + | 1.05789i | ||||
\(362\) | −13.3348 | − | 23.0965i | −0.700860 | − | 1.21393i | ||||
\(363\) | −21.8767 | −1.14823 | ||||||||
\(364\) | 4.06309 | − | 7.03747i | 0.212964 | − | 0.368864i | ||||
\(365\) | −26.9599 | + | 46.6960i | −1.41115 | + | 2.44418i | ||||
\(366\) | 17.6732 | − | 30.6109i | 0.923793 | − | 1.60006i | ||||
\(367\) | 6.68889 | − | 11.5855i | 0.349157 | − | 0.604758i | −0.636943 | − | 0.770911i | \(-0.719801\pi\) |
0.986100 | + | 0.166153i | \(0.0531347\pi\) | |||||||
\(368\) | 22.1792 | 1.15617 | ||||||||
\(369\) | −2.77635 | + | 4.80879i | −0.144531 | + | 0.250335i | ||||
\(370\) | −28.9973 | −1.50750 | ||||||||
\(371\) | 14.2109 | − | 24.6141i | 0.737795 | − | 1.27790i | ||||
\(372\) | 20.2791 | 1.05142 | ||||||||
\(373\) | 33.6429 | 1.74196 | 0.870981 | − | 0.491316i | \(-0.163484\pi\) | ||||
0.870981 | + | 0.491316i | \(0.163484\pi\) | |||||||
\(374\) | −20.7499 | + | 35.9398i | −1.07295 | + | 1.85840i | ||||
\(375\) | 9.01603 | + | 15.6162i | 0.465586 | + | 0.806418i | ||||
\(376\) | −16.9718 | + | 29.3961i | −0.875256 | + | 1.51599i | ||||
\(377\) | 1.52047 | − | 2.63352i | 0.0783079 | − | 0.135633i | ||||
\(378\) | 8.18183 | 0.420828 | ||||||||
\(379\) | 23.2927 | 1.19646 | 0.598232 | − | 0.801323i | \(-0.295870\pi\) | ||||
0.598232 | + | 0.801323i | \(0.295870\pi\) | |||||||
\(380\) | −52.2405 | + | 90.4831i | −2.67988 | + | 4.64169i | ||||
\(381\) | 9.05614 | 0.463960 | ||||||||
\(382\) | −3.12184 | − | 5.40718i | −0.159727 | − | 0.276655i | ||||
\(383\) | 1.07467 | + | 1.86138i | 0.0549130 | + | 0.0951121i | 0.892175 | − | 0.451690i | \(-0.149179\pi\) |
−0.837262 | + | 0.546802i | \(0.815845\pi\) | |||||||
\(384\) | 8.69896 | + | 15.0670i | 0.443917 | + | 0.768887i | ||||
\(385\) | 36.1390 | − | 62.5945i | 1.84181 | − | 3.19011i | ||||
\(386\) | −1.10986 | + | 1.92234i | −0.0564905 | + | 0.0978444i | ||||
\(387\) | 1.19864 | + | 2.07610i | 0.0609303 | + | 0.105534i | ||||
\(388\) | 33.4826 | − | 57.9935i | 1.69982 | − | 2.94417i | ||||
\(389\) | −22.3660 | −1.13400 | −0.567002 | − | 0.823717i | \(-0.691897\pi\) | ||||
−0.567002 | + | 0.823717i | \(0.691897\pi\) | |||||||
\(390\) | 2.81219 | + | 4.87086i | 0.142401 | + | 0.246646i | ||||
\(391\) | −6.19955 | − | 10.7379i | −0.313525 | − | 0.543041i | ||||
\(392\) | −20.7910 | −1.05011 | ||||||||
\(393\) | −6.79278 | −0.342650 | ||||||||
\(394\) | −5.84707 | − | 10.1274i | −0.294571 | − | 0.510212i | ||||
\(395\) | −3.88699 | − | 6.73246i | −0.195576 | − | 0.338747i | ||||
\(396\) | −24.0480 | −1.20846 | ||||||||
\(397\) | 12.1086 | − | 20.9727i | 0.607713 | − | 1.05259i | −0.383904 | − | 0.923373i | \(-0.625421\pi\) |
0.991616 | − | 0.129216i | \(-0.0412461\pi\) | |||||||
\(398\) | 22.1798 | + | 38.4165i | 1.11177 | + | 1.92564i | ||||
\(399\) | 10.6792 | − | 18.4968i | 0.534627 | − | 0.926001i | ||||
\(400\) | −25.2367 | + | 43.7112i | −1.26183 | + | 2.18556i | ||||
\(401\) | −9.72418 | − | 16.8428i | −0.485602 | − | 0.841088i | 0.514261 | − | 0.857634i | \(-0.328066\pi\) |
−0.999863 | + | 0.0165459i | \(0.994733\pi\) | |||||||
\(402\) | −14.2832 | − | 24.7391i | −0.712379 | − | 1.23388i | ||||
\(403\) | −1.42486 | − | 2.46794i | −0.0709775 | − | 0.122937i | ||||
\(404\) | −37.2430 | −1.85291 | ||||||||
\(405\) | −1.91720 | + | 3.32070i | −0.0952667 | + | 0.165007i | ||||
\(406\) | −42.2151 | −2.09510 | ||||||||
\(407\) | −17.4227 | −0.863612 | ||||||||
\(408\) | −7.93997 | + | 13.7524i | −0.393087 | + | 0.680847i | ||||
\(409\) | 11.0695 | − | 19.1730i | 0.547353 | − | 0.948044i | −0.451101 | − | 0.892473i | \(-0.648969\pi\) |
0.998455 | − | 0.0555710i | \(-0.0176979\pi\) | |||||||
\(410\) | 26.4948 | + | 45.8904i | 1.30849 | + | 2.26636i | ||||
\(411\) | −4.23509 | + | 7.33539i | −0.208902 | + | 0.361828i | ||||
\(412\) | −5.07051 | −0.249806 | ||||||||
\(413\) | −25.9410 | −1.27647 | ||||||||
\(414\) | 5.30560 | − | 9.18957i | 0.260756 | − | 0.451643i | ||||
\(415\) | −42.4632 | −2.08443 | ||||||||
\(416\) | −0.596908 | + | 1.03387i | −0.0292658 | + | 0.0506899i | ||||
\(417\) | −5.72992 | −0.280595 | ||||||||
\(418\) | −46.3560 | + | 80.2910i | −2.26735 | + | 3.92716i | ||||
\(419\) | 19.3914 | − | 33.5869i | 0.947331 | − | 1.64083i | 0.196317 | − | 0.980540i | \(-0.437102\pi\) |
0.751015 | − | 0.660286i | \(-0.229565\pi\) | |||||||
\(420\) | 26.4342 | − | 45.7853i | 1.28985 | − | 2.23409i | ||||
\(421\) | −13.0515 | + | 22.6059i | −0.636091 | + | 1.10174i | 0.350192 | + | 0.936678i | \(0.386116\pi\) |
−0.986283 | + | 0.165064i | \(0.947217\pi\) | |||||||
\(422\) | 48.0803 | 2.34051 | ||||||||
\(423\) | 3.10809 | + | 5.38337i | 0.151121 | + | 0.261748i | ||||
\(424\) | −23.6045 | + | 40.8842i | −1.14634 | + | 1.98551i | ||||
\(425\) | 28.2167 | 1.36871 | ||||||||
\(426\) | −6.31301 | −0.305866 | ||||||||
\(427\) | 23.3448 | + | 40.4344i | 1.12973 | + | 1.95676i | ||||
\(428\) | −19.6323 | + | 34.0042i | −0.948964 | + | 1.64365i | ||||
\(429\) | 1.68968 | + | 2.92661i | 0.0815783 | + | 0.141298i | ||||
\(430\) | 22.8773 | 1.10324 | ||||||||
\(431\) | −2.71856 | − | 4.70868i | −0.130948 | − | 0.226809i | 0.793094 | − | 0.609099i | \(-0.208469\pi\) |
−0.924042 | + | 0.382290i | \(0.875136\pi\) | |||||||
\(432\) | −5.20199 | −0.250281 | ||||||||
\(433\) | −11.1341 | − | 19.2848i | −0.535070 | − | 0.926768i | −0.999160 | − | 0.0409798i | \(-0.986952\pi\) |
0.464090 | − | 0.885788i | \(-0.346381\pi\) | |||||||
\(434\) | −19.7804 | + | 34.2606i | −0.949488 | + | 1.64456i | ||||
\(435\) | 9.89204 | − | 17.1335i | 0.474287 | − | 0.821489i | ||||
\(436\) | 5.04967 | + | 8.74629i | 0.241835 | + | 0.418871i | ||||
\(437\) | −13.8500 | − | 23.9890i | −0.662537 | − | 1.14755i | ||||
\(438\) | −17.4988 | + | 30.3088i | −0.836125 | + | 1.44821i | ||||
\(439\) | 35.3580 | 1.68754 | 0.843772 | − | 0.536701i | \(-0.180330\pi\) | ||||
0.843772 | + | 0.536701i | \(0.180330\pi\) | |||||||
\(440\) | −60.0272 | + | 103.970i | −2.86168 | + | 4.95658i | ||||
\(441\) | −1.90375 | + | 3.29740i | −0.0906549 | + | 0.157019i | ||||
\(442\) | 4.26570 | 0.202899 | ||||||||
\(443\) | −9.82780 | −0.466933 | −0.233466 | − | 0.972365i | \(-0.575007\pi\) | ||||
−0.233466 | + | 0.972365i | \(0.575007\pi\) | |||||||
\(444\) | −12.7440 | −0.604804 | ||||||||
\(445\) | 17.9281 | − | 31.0523i | 0.849872 | − | 1.47202i | ||||
\(446\) | 11.6056 | − | 20.1015i | 0.549540 | − | 0.951832i | ||||
\(447\) | −9.24623 | − | 16.0149i | −0.437331 | − | 0.757480i | ||||
\(448\) | −17.6300 | −0.832937 | ||||||||
\(449\) | −3.48340 | − | 6.03342i | −0.164392 | − | 0.284735i | 0.772047 | − | 0.635565i | \(-0.219233\pi\) |
−0.936439 | + | 0.350830i | \(0.885899\pi\) | |||||||
\(450\) | 12.0740 | + | 20.9127i | 0.569172 | + | 0.985835i | ||||
\(451\) | 15.9191 | + | 27.5727i | 0.749602 | + | 1.29835i | ||||
\(452\) | −35.3584 | − | 61.2425i | −1.66312 | − | 2.88060i | ||||
\(453\) | −7.85088 | + | 13.5981i | −0.368866 | + | 0.638895i | ||||
\(454\) | −5.98863 | − | 10.3726i | −0.281061 | − | 0.486811i | ||||
\(455\) | −7.42934 | −0.348293 | ||||||||
\(456\) | −17.7382 | + | 30.7235i | −0.830667 | + | 1.43876i | ||||
\(457\) | −2.17767 | −0.101867 | −0.0509336 | − | 0.998702i | \(-0.516220\pi\) | ||||
−0.0509336 | + | 0.998702i | \(0.516220\pi\) | |||||||
\(458\) | −10.3860 | + | 17.9890i | −0.485304 | + | 0.840572i | ||||
\(459\) | 1.45406 | + | 2.51851i | 0.0678699 | + | 0.117554i | ||||
\(460\) | −34.2831 | − | 59.3800i | −1.59846 | − | 2.76861i | ||||
\(461\) | 8.88563 | + | 15.3904i | 0.413845 | + | 0.716801i | 0.995306 | − | 0.0967733i | \(-0.0308522\pi\) |
−0.581461 | + | 0.813574i | \(0.697519\pi\) | |||||||
\(462\) | 23.4566 | − | 40.6280i | 1.09130 | − | 1.89018i | ||||
\(463\) | 23.6891 | 1.10093 | 0.550463 | − | 0.834860i | \(-0.314451\pi\) | ||||
0.550463 | + | 0.834860i | \(0.314451\pi\) | |||||||
\(464\) | 26.8403 | 1.24603 | ||||||||
\(465\) | −9.27006 | − | 16.0562i | −0.429889 | − | 0.744589i | ||||
\(466\) | −18.0122 | − | 31.1980i | −0.834397 | − | 1.44522i | ||||
\(467\) | −23.0629 | −1.06722 | −0.533611 | − | 0.845730i | \(-0.679165\pi\) | ||||
−0.533611 | + | 0.845730i | \(0.679165\pi\) | |||||||
\(468\) | 1.23593 | + | 2.14069i | 0.0571308 | + | 0.0989535i | ||||
\(469\) | 37.7337 | 1.74238 | ||||||||
\(470\) | 59.3212 | 2.73628 | ||||||||
\(471\) | −7.85457 | − | 9.76247i | −0.361919 | − | 0.449831i | ||||
\(472\) | 43.0883 | 1.98330 | ||||||||
\(473\) | 13.7456 | 0.632022 | ||||||||
\(474\) | −2.52291 | − | 4.36981i | −0.115881 | − | 0.200712i | ||||
\(475\) | 63.0372 | 2.89234 | ||||||||
\(476\) | −20.0484 | − | 34.7249i | −0.918919 | − | 1.59161i | ||||
\(477\) | 4.32275 | + | 7.48722i | 0.197925 | + | 0.342816i | ||||
\(478\) | 8.88913 | 0.406579 | ||||||||
\(479\) | −36.9952 | −1.69035 | −0.845177 | − | 0.534487i | \(-0.820505\pi\) | ||||
−0.845177 | + | 0.534487i | \(0.820505\pi\) | |||||||
\(480\) | −3.88344 | + | 6.72632i | −0.177254 | + | 0.307013i | ||||
\(481\) | 0.895428 | + | 1.55093i | 0.0408280 | + | 0.0707162i | ||||
\(482\) | −33.1784 | − | 57.4666i | −1.51123 | − | 2.61753i | ||||
\(483\) | 7.00825 | + | 12.1386i | 0.318886 | + | 0.552327i | ||||
\(484\) | −45.8761 | + | 79.4598i | −2.08528 | + | 3.61181i | ||||
\(485\) | −61.2228 | −2.77998 | ||||||||
\(486\) | −1.24439 | + | 2.15535i | −0.0564468 | + | 0.0977687i | ||||
\(487\) | −13.0169 | −0.589850 | −0.294925 | − | 0.955520i | \(-0.595295\pi\) | ||||
−0.294925 | + | 0.955520i | \(0.595295\pi\) | |||||||
\(488\) | −38.7760 | − | 67.1620i | −1.75531 | − | 3.04028i | ||||
\(489\) | −5.50827 | + | 9.54060i | −0.249093 | + | 0.431441i | ||||
\(490\) | 18.1676 | + | 31.4671i | 0.820727 | + | 1.42154i | ||||
\(491\) | 17.0799 | + | 29.5833i | 0.770805 | + | 1.33507i | 0.937122 | + | 0.349001i | \(0.113479\pi\) |
−0.166317 | + | 0.986072i | \(0.553187\pi\) | |||||||
\(492\) | 11.6442 | + | 20.1683i | 0.524960 | + | 0.909258i | ||||
\(493\) | −7.50241 | − | 12.9946i | −0.337892 | − | 0.585245i | ||||
\(494\) | 9.52974 | 0.428763 | ||||||||
\(495\) | 10.9929 | + | 19.0403i | 0.494095 | + | 0.855797i | ||||
\(496\) | 12.5763 | − | 21.7828i | 0.564694 | − | 0.978078i | ||||
\(497\) | 4.16948 | − | 7.22175i | 0.187027 | − | 0.323940i | ||||
\(498\) | −27.5614 | −1.23506 | ||||||||
\(499\) | −18.3704 | −0.822370 | −0.411185 | − | 0.911552i | \(-0.634885\pi\) | ||||
−0.411185 | + | 0.911552i | \(0.634885\pi\) | |||||||
\(500\) | 75.6274 | 3.38216 | ||||||||
\(501\) | −0.551802 | + | 0.955750i | −0.0246527 | + | 0.0426998i | ||||
\(502\) | −12.4742 | + | 21.6059i | −0.556750 | + | 0.964319i | ||||
\(503\) | 1.56322 | 0.0697006 | 0.0348503 | − | 0.999393i | \(-0.488905\pi\) | ||||
0.0348503 | + | 0.999393i | \(0.488905\pi\) | |||||||
\(504\) | 8.97569 | − | 15.5464i | 0.399809 | − | 0.692490i | ||||
\(505\) | 17.0247 | + | 29.4876i | 0.757588 | + | 1.31218i | ||||
\(506\) | −30.4214 | − | 52.6914i | −1.35239 | − | 2.34242i | ||||
\(507\) | −6.32632 | + | 10.9575i | −0.280962 | + | 0.486640i | ||||
\(508\) | 18.9910 | − | 32.8933i | 0.842588 | − | 1.45941i | ||||
\(509\) | −3.15901 | − | 5.47156i | −0.140021 | − | 0.242523i | 0.787484 | − | 0.616336i | \(-0.211384\pi\) |
−0.927504 | + | 0.373813i | \(0.878050\pi\) | |||||||
\(510\) | 27.7523 | 1.22889 | ||||||||
\(511\) | −23.1144 | − | 40.0354i | −1.02252 | − | 1.77106i | ||||
\(512\) | 46.2743 | 2.04505 | ||||||||
\(513\) | 3.24844 | + | 5.62646i | 0.143422 | + | 0.248414i | ||||
\(514\) | 6.91568 | − | 11.9783i | 0.305037 | − | 0.528340i | ||||
\(515\) | 2.31785 | + | 4.01464i | 0.102137 | + | 0.176906i | ||||
\(516\) | 10.0543 | 0.442617 | ||||||||
\(517\) | 35.6425 | 1.56755 | ||||||||
\(518\) | 12.4306 | − | 21.5304i | 0.546169 | − | 0.945993i | ||||
\(519\) | −8.07868 | − | 13.9927i | −0.354615 | − | 0.614211i | ||||
\(520\) | 12.3402 | 0.541154 | ||||||||
\(521\) | −3.69810 | + | 6.40529i | −0.162017 | + | 0.280621i | −0.935592 | − | 0.353084i | \(-0.885133\pi\) |
0.773575 | + | 0.633704i | \(0.218466\pi\) | |||||||
\(522\) | 6.42059 | − | 11.1208i | 0.281022 | − | 0.486744i | ||||
\(523\) | −1.92776 | + | 3.33899i | −0.0842953 | + | 0.146004i | −0.905091 | − | 0.425219i | \(-0.860197\pi\) |
0.820795 | + | 0.571222i | \(0.193531\pi\) | |||||||
\(524\) | −14.2446 | + | 24.6724i | −0.622280 | + | 1.07782i | ||||
\(525\) | −31.8974 | −1.39212 | ||||||||
\(526\) | 9.80158 | − | 16.9768i | 0.427369 | − | 0.740225i | ||||
\(527\) | −14.0614 | −0.612523 | ||||||||
\(528\) | −14.9137 | + | 25.8312i | −0.649033 | + | 1.12416i | ||||
\(529\) | −4.82168 | −0.209638 | ||||||||
\(530\) | 82.5042 | 3.58375 | ||||||||
\(531\) | 3.94543 | − | 6.83369i | 0.171217 | − | 0.296557i | ||||
\(532\) | −44.7890 | − | 77.5768i | −1.94185 | − | 3.36338i | ||||
\(533\) | 1.63630 | − | 2.83416i | 0.0708762 | − | 0.122761i | ||||
\(534\) | 11.6365 | − | 20.1550i | 0.503561 | − | 0.872193i | ||||
\(535\) | 35.8976 | 1.55199 | ||||||||
\(536\) | −62.6761 | −2.70719 | ||||||||
\(537\) | −3.49081 | + | 6.04626i | −0.150640 | + | 0.260916i | ||||
\(538\) | 68.1848 | 2.93965 | ||||||||
\(539\) | 10.9158 | + | 18.9067i | 0.470176 | + | 0.814369i | ||||
\(540\) | 8.04086 | + | 13.9272i | 0.346024 | + | 0.599331i | ||||
\(541\) | 12.9904 | + | 22.5001i | 0.558502 | + | 0.967354i | 0.997622 | + | 0.0689253i | \(0.0219570\pi\) |
−0.439120 | + | 0.898429i | \(0.644710\pi\) | |||||||
\(542\) | 16.7947 | − | 29.0893i | 0.721394 | − | 1.24949i | ||||
\(543\) | −5.35794 | + | 9.28023i | −0.229931 | + | 0.398253i | ||||
\(544\) | 2.94532 | + | 5.10144i | 0.126279 | + | 0.218722i | ||||
\(545\) | 4.61665 | − | 7.99628i | 0.197756 | − | 0.342523i | ||||
\(546\) | −4.82214 | −0.206368 | ||||||||
\(547\) | 3.57210 | + | 6.18706i | 0.152732 | + | 0.264540i | 0.932231 | − | 0.361864i | \(-0.117860\pi\) |
−0.779499 | + | 0.626404i | \(0.784526\pi\) | |||||||
\(548\) | 17.7622 | + | 30.7650i | 0.758764 | + | 1.31422i | ||||
\(549\) | −14.2023 | −0.606138 | ||||||||
\(550\) | 138.460 | 5.90395 | ||||||||
\(551\) | −16.7607 | − | 29.0303i | −0.714029 | − | 1.23673i | ||||
\(552\) | −11.6408 | − | 20.1624i | −0.495464 | − | 0.858170i | ||||
\(553\) | 6.66511 | 0.283429 | ||||||||
\(554\) | 12.7790 | − | 22.1339i | 0.542928 | − | 0.940380i | ||||
\(555\) | 5.82559 | + | 10.0902i | 0.247283 | + | 0.428306i | ||||
\(556\) | −12.0158 | + | 20.8120i | −0.509584 | + | 0.882625i | ||||
\(557\) | −4.99582 | + | 8.65302i | −0.211680 | + | 0.366640i | −0.952240 | − | 0.305349i | \(-0.901227\pi\) |
0.740561 | + | 0.671990i | \(0.234560\pi\) | |||||||
\(558\) | −6.01688 | − | 10.4215i | −0.254715 | − | 0.441179i | ||||
\(559\) | −0.706444 | − | 1.22360i | −0.0298794 | − | 0.0517526i | ||||
\(560\) | −32.7869 | − | 56.7886i | −1.38550 | − | 2.39976i | ||||
\(561\) | 16.6747 | 0.704006 | ||||||||
\(562\) | −10.1158 | + | 17.5210i | −0.426709 | + | 0.739081i | ||||
\(563\) | −17.6613 | −0.744334 | −0.372167 | − | 0.928166i | \(-0.621385\pi\) | ||||
−0.372167 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(564\) | 26.0710 | 1.09779 | ||||||||
\(565\) | −32.3263 | + | 55.9908i | −1.35998 | + | 2.35555i | ||||
\(566\) | 19.0602 | − | 33.0132i | 0.801158 | − | 1.38765i | ||||
\(567\) | −1.64374 | − | 2.84704i | −0.0690305 | − | 0.119564i | ||||
\(568\) | −6.92555 | + | 11.9954i | −0.290590 | + | 0.503316i | ||||
\(569\) | 39.5299 | 1.65718 | 0.828591 | − | 0.559855i | \(-0.189143\pi\) | ||||
0.828591 | + | 0.559855i | \(0.189143\pi\) | |||||||
\(570\) | 61.9998 | 2.59689 | ||||||||
\(571\) | −8.62894 | + | 14.9458i | −0.361110 | + | 0.625461i | −0.988144 | − | 0.153531i | \(-0.950935\pi\) |
0.627034 | + | 0.778992i | \(0.284269\pi\) | |||||||
\(572\) | 14.1732 | 0.592611 | ||||||||
\(573\) | −1.25436 | + | 2.17262i | −0.0524017 | + | 0.0907624i | ||||
\(574\) | −45.4313 | −1.89627 | ||||||||
\(575\) | −20.6842 | + | 35.8261i | −0.862592 | + | 1.49405i | ||||
\(576\) | 2.68138 | − | 4.64429i | 0.111724 | − | 0.193512i | ||||
\(577\) | −4.78704 | + | 8.29139i | −0.199287 | + | 0.345175i | −0.948297 | − | 0.317383i | \(-0.897196\pi\) |
0.749010 | + | 0.662558i | \(0.230529\pi\) | |||||||
\(578\) | −10.6306 | + | 18.4127i | −0.442174 | + | 0.765868i | ||||
\(579\) | 0.891890 | 0.0370657 | ||||||||
\(580\) | −41.4878 | − | 71.8589i | −1.72269 | − | 2.98378i | ||||
\(581\) | 18.2032 | − | 31.5288i | 0.755194 | − | 1.30803i | ||||
\(582\) | −39.7376 | −1.64718 | ||||||||
\(583\) | 49.5717 | 2.05305 | ||||||||
\(584\) | 38.3933 | + | 66.4992i | 1.58873 | + | 2.75176i | ||||
\(585\) | 1.12995 | − | 1.95712i | 0.0467175 | − | 0.0809171i | ||||
\(586\) | −23.4793 | − | 40.6673i | −0.969921 | − | 1.67995i | ||||
\(587\) | −7.51888 | −0.310337 | −0.155169 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155169 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(588\) | 7.98445 | + | 13.8295i | 0.329273 | + | 0.570318i | ||||
\(589\) | −31.4136 | −1.29438 | ||||||||
\(590\) | −37.6513 | − | 65.2140i | −1.55008 | − | 2.68482i | ||||
\(591\) | −2.34936 | + | 4.06922i | −0.0966400 | + | 0.167385i | ||||
\(592\) | −7.90335 | + | 13.6890i | −0.324826 | + | 0.562615i | ||||
\(593\) | 11.1514 | + | 19.3148i | 0.457934 | + | 0.793166i | 0.998852 | − | 0.0479102i | \(-0.0152561\pi\) |
−0.540917 | + | 0.841076i | \(0.681923\pi\) | |||||||
\(594\) | 7.13513 | + | 12.3584i | 0.292758 | + | 0.507072i | ||||
\(595\) | −18.3293 | + | 31.7472i | −0.751426 | + | 1.30151i | ||||
\(596\) | −77.5584 | −3.17691 | ||||||||
\(597\) | 8.91188 | − | 15.4358i | 0.364739 | − | 0.631746i | ||||
\(598\) | −3.12697 | + | 5.41607i | −0.127871 | + | 0.221480i | ||||
\(599\) | −25.0601 | −1.02393 | −0.511963 | − | 0.859007i | \(-0.671082\pi\) | ||||
−0.511963 | + | 0.859007i | \(0.671082\pi\) | |||||||
\(600\) | 52.9819 | 2.16298 | ||||||||
\(601\) | −41.5483 | −1.69479 | −0.847395 | − | 0.530962i | \(-0.821831\pi\) | ||||
−0.847395 | + | 0.530962i | \(0.821831\pi\) | |||||||
\(602\) | −9.80706 | + | 16.9863i | −0.399706 | + | 0.692311i | ||||
\(603\) | −5.73900 | + | 9.94024i | −0.233710 | + | 0.404798i | ||||
\(604\) | 32.9270 | + | 57.0313i | 1.33978 | + | 2.32057i | ||||
\(605\) | 83.8844 | 3.41038 | ||||||||
\(606\) | 11.0501 | + | 19.1394i | 0.448881 | + | 0.777485i | ||||
\(607\) | −0.316472 | − | 0.548146i | −0.0128452 | − | 0.0222485i | 0.859531 | − | 0.511083i | \(-0.170756\pi\) |
−0.872377 | + | 0.488834i | \(0.837422\pi\) | |||||||
\(608\) | 6.57995 | + | 11.3968i | 0.266852 | + | 0.462201i | ||||
\(609\) | 8.48106 | + | 14.6896i | 0.343670 | + | 0.595254i | ||||
\(610\) | −67.7663 | + | 117.375i | −2.74378 | + | 4.75236i | ||||
\(611\) | −1.83182 | − | 3.17281i | −0.0741075 | − | 0.128358i | ||||
\(612\) | 12.1969 | 0.493029 | ||||||||
\(613\) | −5.44772 | + | 9.43572i | −0.220031 | + | 0.381105i | −0.954817 | − | 0.297194i | \(-0.903949\pi\) |
0.734786 | + | 0.678299i | \(0.237283\pi\) | |||||||
\(614\) | 35.1092 | 1.41689 | ||||||||
\(615\) | 10.6457 | − | 18.4389i | 0.429275 | − | 0.743526i | ||||
\(616\) | −51.4650 | − | 89.1401i | −2.07359 | − | 3.59156i | ||||
\(617\) | −3.80760 | − | 6.59495i | −0.153288 | − | 0.265503i | 0.779146 | − | 0.626842i | \(-0.215653\pi\) |
−0.932434 | + | 0.361339i | \(0.882320\pi\) | |||||||
\(618\) | 1.50444 | + | 2.60577i | 0.0605175 | + | 0.104819i | ||||
\(619\) | −0.481687 | + | 0.834306i | −0.0193606 | + | 0.0335336i | −0.875543 | − | 0.483139i | \(-0.839496\pi\) |
0.856183 | + | 0.516673i | \(0.172830\pi\) | |||||||
\(620\) | −77.7583 | −3.12285 | ||||||||
\(621\) | −4.26360 | −0.171093 | ||||||||
\(622\) | −29.6084 | − | 51.2833i | −1.18719 | − | 2.05627i | ||||
\(623\) | 15.3708 | + | 26.6231i | 0.615820 | + | 1.06663i | ||||
\(624\) | 3.06591 | 0.122734 | ||||||||
\(625\) | −10.3144 | − | 17.8651i | −0.412576 | − | 0.714603i | ||||
\(626\) | 46.4198 | 1.85531 | ||||||||
\(627\) | 37.2519 | 1.48770 | ||||||||
\(628\) | −51.9301 | + | 8.05687i | −2.07224 | + | 0.321504i | ||||
\(629\) | 8.83660 | 0.352338 | ||||||||
\(630\) | −31.3725 | −1.24991 | ||||||||
\(631\) | −2.58795 | − | 4.48247i | −0.103025 | − | 0.178444i | 0.809905 | − | 0.586562i | \(-0.199519\pi\) |
−0.912930 | + | 0.408117i | \(0.866185\pi\) | |||||||
\(632\) | −11.0708 | −0.440374 | ||||||||
\(633\) | −9.65939 | − | 16.7306i | −0.383926 | − | 0.664980i | ||||
\(634\) | −20.6160 | − | 35.7079i | −0.818764 | − | 1.41814i | ||||
\(635\) | −34.7249 | −1.37802 | ||||||||
\(636\) | 36.2597 | 1.43779 | ||||||||
\(637\) | 1.12202 | − | 1.94339i | 0.0444560 | − | 0.0770000i | ||||
\(638\) | −36.8145 | − | 63.7646i | −1.45750 | − | 2.52447i | ||||
\(639\) | 1.26829 | + | 2.19675i | 0.0501728 | + | 0.0869019i | ||||
\(640\) | −33.3554 | − | 57.7732i | −1.31849 | − | 2.28369i | ||||
\(641\) | 5.43538 | − | 9.41436i | 0.214685 | − | 0.371845i | −0.738490 | − | 0.674264i | \(-0.764461\pi\) |
0.953175 | + | 0.302419i | \(0.0977943\pi\) | |||||||
\(642\) | 23.2999 | 0.919575 | ||||||||
\(643\) | 1.21577 | − | 2.10577i | 0.0479452 | − | 0.0830435i | −0.841057 | − | 0.540947i | \(-0.818066\pi\) |
0.889002 | + | 0.457903i | \(0.151399\pi\) | |||||||
\(644\) | 58.7860 | 2.31649 | ||||||||
\(645\) | −4.59607 | − | 7.96063i | −0.180970 | − | 0.313450i | ||||
\(646\) | 23.5112 | − | 40.7227i | 0.925037 | − | 1.60221i | ||||
\(647\) | 11.0196 | + | 19.0866i | 0.433227 | + | 0.750371i | 0.997149 | − | 0.0754572i | \(-0.0240416\pi\) |
−0.563922 | + | 0.825828i | \(0.690708\pi\) | |||||||
\(648\) | 2.73027 | + | 4.72896i | 0.107255 | + | 0.185771i | ||||
\(649\) | −22.6224 | − | 39.1832i | −0.888007 | − | 1.53807i | ||||
\(650\) | −7.11605 | − | 12.3254i | −0.279114 | − | 0.483440i | ||||
\(651\) | 15.8956 | 0.622997 | ||||||||
\(652\) | 23.1020 | + | 40.0138i | 0.904744 | + | 1.56706i | ||||
\(653\) | 18.4465 | − | 31.9502i | 0.721866 | − | 1.25031i | −0.238386 | − | 0.971171i | \(-0.576618\pi\) |
0.960251 | − | 0.279137i | \(-0.0900485\pi\) | |||||||
\(654\) | 2.99652 | − | 5.19012i | 0.117173 | − | 0.202950i | ||||
\(655\) | 26.0463 | 1.01771 | ||||||||
\(656\) | 28.8851 | 1.12778 | ||||||||
\(657\) | 14.0621 | 0.548615 | ||||||||
\(658\) | −25.4299 | + | 44.0458i | −0.991359 | + | 1.71708i | ||||
\(659\) | 5.16026 | − | 8.93784i | 0.201015 | − | 0.348169i | −0.747841 | − | 0.663878i | \(-0.768909\pi\) |
0.948856 | + | 0.315710i | \(0.102243\pi\) | |||||||
\(660\) | 92.2098 | 3.58926 | ||||||||
\(661\) | 18.5193 | − | 32.0764i | 0.720319 | − | 1.24763i | −0.240553 | − | 0.970636i | \(-0.577329\pi\) |
0.960872 | − | 0.276993i | \(-0.0893379\pi\) | |||||||
\(662\) | 31.4955 | + | 54.5518i | 1.22411 | + | 2.12021i | ||||
\(663\) | −0.856984 | − | 1.48434i | −0.0332825 | − | 0.0576470i | ||||
\(664\) | −30.2356 | + | 52.3697i | −1.17337 | + | 2.03234i | ||||
\(665\) | −40.9483 | + | 70.9245i | −1.58791 | + | 2.75033i | ||||
\(666\) | 3.78120 | + | 6.54922i | 0.146518 | + | 0.253777i | ||||
\(667\) | 21.9986 | 0.851787 | ||||||||
\(668\) | 2.31429 | + | 4.00847i | 0.0895426 | + | 0.155092i | ||||
\(669\) | −9.32630 | −0.360576 | ||||||||
\(670\) | 54.7674 | + | 94.8600i | 2.11585 | + | 3.66476i | ||||
\(671\) | −40.7166 | + | 70.5233i | −1.57185 | + | 2.72252i | ||||
\(672\) | −3.32951 | − | 5.76689i | −0.128439 | − | 0.222463i | ||||
\(673\) | −32.9404 | −1.26976 | −0.634879 | − | 0.772612i | \(-0.718950\pi\) | ||||
−0.634879 | + | 0.772612i | \(0.718950\pi\) | |||||||
\(674\) | −15.7904 | −0.608225 | ||||||||
\(675\) | 4.85135 | − | 8.40278i | 0.186728 | − | 0.323423i | ||||
\(676\) | 26.5329 | + | 45.9564i | 1.02050 | + | 1.76755i | ||||
\(677\) | 3.52049 | 0.135303 | 0.0676517 | − | 0.997709i | \(-0.478449\pi\) | ||||
0.0676517 | + | 0.997709i | \(0.478449\pi\) | |||||||
\(678\) | −20.9819 | + | 36.3418i | −0.805806 | + | 1.39570i | ||||
\(679\) | 26.2450 | − | 45.4578i | 1.00719 | − | 1.74451i | ||||
\(680\) | 30.4451 | − | 52.7324i | 1.16752 | − | 2.02220i | ||||
\(681\) | −2.40625 | + | 4.16774i | −0.0922076 | + | 0.159708i | ||||
\(682\) | −68.9995 | −2.64213 | ||||||||
\(683\) | 14.5295 | − | 25.1658i | 0.555955 | − | 0.962942i | −0.441874 | − | 0.897077i | \(-0.645686\pi\) |
0.997829 | − | 0.0658648i | \(-0.0209806\pi\) | |||||||
\(684\) | 27.2482 | 1.04186 | ||||||||
\(685\) | 16.2391 | − | 28.1269i | 0.620463 | − | 1.07467i | ||||
\(686\) | 26.1204 | 0.997283 | ||||||||
\(687\) | 8.34621 | 0.318428 | ||||||||
\(688\) | 6.23531 | − | 10.7999i | 0.237719 | − | 0.411741i | ||||
\(689\) | −2.54770 | − | 4.41275i | −0.0970598 | − | 0.168113i | ||||
\(690\) | −20.3438 | + | 35.2366i | −0.774477 | + | 1.34143i | ||||
\(691\) | −4.25610 | + | 7.37178i | −0.161910 | + | 0.280436i | −0.935554 | − | 0.353185i | \(-0.885099\pi\) |
0.773644 | + | 0.633621i | \(0.218432\pi\) | |||||||
\(692\) | −67.7649 | −2.57603 | ||||||||
\(693\) | −18.8498 | −0.716045 | ||||||||
\(694\) | 36.6556 | − | 63.4893i | 1.39143 | − | 2.41002i | ||||
\(695\) | 21.9709 | 0.833402 | ||||||||
\(696\) | −14.0871 | − | 24.3996i | −0.533971 | − | 0.924865i | ||||
\(697\) | −8.07400 | − | 13.9846i | −0.305824 | − | 0.529703i | ||||
\(698\) | −13.9837 | − | 24.2205i | −0.529291 | − | 0.916759i | ||||
\(699\) | −7.23733 | + | 12.5354i | −0.273741 | + | 0.474133i | ||||
\(700\) | −66.8897 | + | 115.856i | −2.52819 | + | 4.37896i | ||||
\(701\) | −0.0191693 | − | 0.0332021i | −0.000724013 | − | 0.00125403i | 0.865663 | − | 0.500627i | \(-0.166897\pi\) |
−0.866387 | + | 0.499373i | \(0.833564\pi\) | |||||||
\(702\) | 0.733410 | − | 1.27030i | 0.0276808 | − | 0.0479445i | ||||
\(703\) | 19.7413 | 0.744558 | ||||||||
\(704\) | −15.3746 | − | 26.6295i | −0.579451 | − | 1.00364i | ||||
\(705\) | −11.9177 | − | 20.6420i | −0.448846 | − | 0.777424i | ||||
\(706\) | 24.2734 | 0.913541 | ||||||||
\(707\) | −29.1926 | −1.09790 | ||||||||
\(708\) | −16.5474 | − | 28.6609i | −0.621888 | − | 1.07714i | ||||
\(709\) | −11.0409 | − | 19.1235i | −0.414651 | − | 0.718197i | 0.580741 | − | 0.814089i | \(-0.302763\pi\) |
−0.995392 | + | 0.0958918i | \(0.969430\pi\) | |||||||
\(710\) | 24.2067 | 0.908460 | ||||||||
\(711\) | −1.01371 | + | 1.75580i | −0.0380172 | + | 0.0658477i | ||||
\(712\) | −25.5311 | − | 44.2212i | −0.956820 | − | 1.65726i | ||||
\(713\) | 10.3077 | − | 17.8534i | 0.386026 | − | 0.668616i | ||||
\(714\) | −11.8969 | + | 20.6060i | −0.445230 | + | 0.771162i | ||||
\(715\) | −6.47891 | − | 11.2218i | −0.242298 | − | 0.419672i | ||||
\(716\) | 14.6407 | + | 25.3584i | 0.547147 | + | 0.947687i | ||||
\(717\) | −1.78584 | − | 3.09316i | −0.0666933 | − | 0.115516i | ||||
\(718\) | −35.3255 | −1.31834 | ||||||||
\(719\) | −0.812483 | + | 1.40726i | −0.0303005 | + | 0.0524820i | −0.880778 | − | 0.473529i | \(-0.842980\pi\) |
0.850478 | + | 0.526011i | \(0.176313\pi\) | |||||||
\(720\) | 19.9466 | 0.743365 | ||||||||
\(721\) | −3.97448 | −0.148017 | ||||||||
\(722\) | 28.8816 | − | 50.0243i | 1.07486 | − | 1.86171i | ||||
\(723\) | −13.3312 | + | 23.0902i | −0.495791 | + | 0.858735i | ||||
\(724\) | 22.4715 | + | 38.9218i | 0.835147 | + | 1.44652i | ||||
\(725\) | −25.0311 | + | 43.3551i | −0.929631 | + | 1.61017i | ||||
\(726\) | 54.4465 | 2.02070 | ||||||||
\(727\) | −39.1375 | −1.45153 | −0.725765 | − | 0.687943i | \(-0.758514\pi\) | ||||
−0.725765 | + | 0.687943i | \(0.758514\pi\) | |||||||
\(728\) | −5.29002 | + | 9.16258i | −0.196061 | + | 0.339588i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 67.0975 | − | 116.216i | 2.48339 | − | 4.30136i | ||||
\(731\) | −6.97159 | −0.257854 | ||||||||
\(732\) | −29.7825 | + | 51.5849i | −1.10079 | + | 1.90663i | ||||
\(733\) | −10.9521 | + | 18.9696i | −0.404525 | + | 0.700658i | −0.994266 | − | 0.106935i | \(-0.965896\pi\) |
0.589741 | + | 0.807592i | \(0.299230\pi\) | |||||||
\(734\) | −16.6472 | + | 28.8338i | −0.614460 | + | 1.06428i | ||||
\(735\) | 7.29977 | − | 12.6436i | 0.269256 | − | 0.466365i | ||||
\(736\) | −8.63625 | −0.318336 | ||||||||
\(737\) | 32.9064 | + | 56.9956i | 1.21212 | + | 2.09946i | ||||
\(738\) | 6.90975 | − | 11.9680i | 0.254351 | − | 0.440550i | ||||
\(739\) | −38.0764 | −1.40066 | −0.700332 | − | 0.713817i | \(-0.746965\pi\) | ||||
−0.700332 | + | 0.713817i | \(0.746965\pi\) | |||||||
\(740\) | 48.8657 | 1.79634 | ||||||||
\(741\) | −1.91454 | − | 3.31607i | −0.0703322 | − | 0.121819i | ||||
\(742\) | −35.3680 | + | 61.2591i | −1.29840 | + | 2.24889i | ||||
\(743\) | −5.24336 | − | 9.08176i | −0.192360 | − | 0.333178i | 0.753672 | − | 0.657251i | \(-0.228281\pi\) |
−0.946032 | + | 0.324073i | \(0.894948\pi\) | |||||||
\(744\) | −26.4028 | −0.967972 | ||||||||
\(745\) | 35.4538 | + | 61.4078i | 1.29893 | + | 2.24981i | ||||
\(746\) | −83.7299 | −3.06557 | ||||||||
\(747\) | 5.53712 | + | 9.59057i | 0.202593 | + | 0.350901i | ||||
\(748\) | 34.9673 | − | 60.5651i | 1.27853 | − | 2.21448i | ||||
\(749\) | −15.3886 | + | 26.6539i | −0.562288 | + | 0.973912i | ||||
\(750\) | −22.4390 | − | 38.8654i | −0.819355 | − | 1.41916i | ||||
\(751\) | −3.38405 | − | 5.86134i | −0.123486 | − | 0.213883i | 0.797654 | − | 0.603115i | \(-0.206074\pi\) |
−0.921140 | + | 0.389231i | \(0.872741\pi\) | |||||||
\(752\) | 16.1683 | − | 28.0042i | 0.589596 | − | 1.02121i | ||||
\(753\) | 10.0243 | 0.365306 | ||||||||
\(754\) | −3.78411 | + | 6.55427i | −0.137809 | + | 0.238693i | ||||
\(755\) | 30.1035 | − | 52.1408i | 1.09558 | − | 1.89760i | ||||
\(756\) | −13.7879 | −0.501460 | ||||||||
\(757\) | −12.8960 | −0.468713 | −0.234357 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234357 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(758\) | −57.9705 | −2.10558 | ||||||||
\(759\) | −12.2234 | + | 21.1715i | −0.443680 | + | 0.768477i | ||||
\(760\) | 68.0155 | − | 117.806i | 2.46718 | − | 4.27328i | ||||
\(761\) | 6.98423 | + | 12.0970i | 0.253178 | + | 0.438518i | 0.964399 | − | 0.264451i | \(-0.0851908\pi\) |
−0.711221 | + | 0.702969i | \(0.751857\pi\) | |||||||
\(762\) | −22.5388 | −0.816494 | ||||||||
\(763\) | 3.95814 | + | 6.85571i | 0.143294 | + | 0.248193i | ||||
\(764\) | 5.26086 | + | 9.11208i | 0.190331 | + | 0.329664i | ||||
\(765\) | −5.57548 | − | 9.65701i | −0.201582 | − | 0.349150i | ||||
\(766\) | −2.67462 | − | 4.63258i | −0.0966379 | − | 0.167382i | ||||
\(767\) | −2.32533 | + | 4.02758i | −0.0839626 | + | 0.145428i | ||||
\(768\) | −16.2871 | − | 28.2101i | −0.587710 | − | 1.01794i | ||||
\(769\) | 16.3346 | 0.589041 | 0.294521 | − | 0.955645i | \(-0.404840\pi\) | ||||
0.294521 | + | 0.955645i | \(0.404840\pi\) | |||||||
\(770\) | −89.9421 | + | 155.784i | −3.24129 | + | 5.61408i | ||||
\(771\) | −5.55747 | −0.200147 | ||||||||
\(772\) | 1.87032 | − | 3.23949i | 0.0673143 | − | 0.116592i | ||||
\(773\) | 12.7482 | + | 22.0805i | 0.458521 | + | 0.794181i | 0.998883 | − | 0.0472511i | \(-0.0150461\pi\) |
−0.540362 | + | 0.841433i | \(0.681713\pi\) | |||||||
\(774\) | −2.98316 | − | 5.16698i | −0.107227 | − | 0.185723i | ||||
\(775\) | 23.4572 | + | 40.6291i | 0.842608 | + | 1.45944i | ||||
\(776\) | −43.5933 | + | 75.5058i | −1.56491 | + | 2.71050i | ||||
\(777\) | −9.98929 | −0.358364 | ||||||||
\(778\) | 55.6643 | 1.99566 | ||||||||
\(779\) | −18.0376 | − | 31.2421i | −0.646265 | − | 1.11936i | ||||
\(780\) | −4.73906 | − | 8.20829i | −0.169685 | − | 0.293904i | ||||
\(781\) | 14.5443 | 0.520437 | ||||||||
\(782\) | 15.4294 | + | 26.7244i | 0.551753 | + | 0.955664i | ||||
\(783\) | −5.15961 | −0.184390 | ||||||||
\(784\) | 19.8066 | 0.707379 | ||||||||
\(785\) | 30.1176 | + | 37.4333i | 1.07494 | + | 1.33605i | ||||
\(786\) | 16.9058 | 0.603009 | ||||||||
\(787\) | −28.4468 | −1.01402 | −0.507010 | − | 0.861940i | \(-0.669249\pi\) | ||||
−0.507010 | + | 0.861940i | \(0.669249\pi\) | |||||||
\(788\) | 9.85337 | + | 17.0665i | 0.351012 | + | 0.607970i | ||||
\(789\) | −7.87660 | −0.280414 | ||||||||
\(790\) | 9.67388 | + | 16.7557i | 0.344181 | + | 0.596139i | ||||
\(791\) | −27.7154 | − | 48.0044i | −0.985445 | − | 1.70684i | ||||
\(792\) | 31.3097 | 1.11254 | ||||||||
\(793\) | 8.37041 | 0.297242 | ||||||||
\(794\) | −30.1357 | + | 52.1965i | −1.06948 | + | 1.85239i | ||||
\(795\) | −16.5752 | − | 28.7091i | −0.587861 | − | 1.01821i | ||||
\(796\) | −37.3769 | − | 64.7387i | −1.32479 | − | 2.29460i | ||||
\(797\) | 9.78759 | + | 16.9526i | 0.346694 | + | 0.600492i | 0.985660 | − | 0.168743i | \(-0.0539709\pi\) |
−0.638966 | + | 0.769235i | \(0.720638\pi\) | |||||||
\(798\) | −26.5781 | + | 46.0347i | −0.940856 | + | 1.62961i | ||||
\(799\) | −18.0775 | −0.639534 | ||||||||
\(800\) | 9.82676 | − | 17.0205i | 0.347429 | − | 0.601764i | ||||
\(801\) | −9.35115 | −0.330407 | ||||||||
\(802\) | 24.2014 | + | 41.9181i | 0.854581 | + | 1.48018i | ||||
\(803\) | 40.3148 | − | 69.8273i | 1.42268 | − | 2.46415i | ||||
\(804\) | 24.0697 | + | 41.6899i | 0.848873 | + | 1.47029i | ||||
\(805\) | −26.8725 | − | 46.5445i | −0.947131 | − | 1.64048i | ||||
\(806\) | 3.54618 | + | 6.14216i | 0.124909 | + | 0.216348i | ||||
\(807\) | −13.6984 | − | 23.7263i | −0.482207 | − | 0.835206i | ||||
\(808\) | 48.4893 | 1.70585 | ||||||||
\(809\) | −4.91749 | − | 8.51735i | −0.172890 | − | 0.299454i | 0.766539 | − | 0.642198i | \(-0.221977\pi\) |
−0.939429 | + | 0.342744i | \(0.888644\pi\) | |||||||
\(810\) | 4.77151 | − | 8.26450i | 0.167654 | − | 0.290385i | ||||
\(811\) | −8.00283 | + | 13.8613i | −0.281017 | + | 0.486736i | −0.971636 | − | 0.236483i | \(-0.924005\pi\) |
0.690618 | + | 0.723220i | \(0.257339\pi\) | |||||||
\(812\) | 71.1401 | 2.49653 | ||||||||
\(813\) | −13.4963 | −0.473336 | ||||||||
\(814\) | 43.3614 | 1.51982 | ||||||||
\(815\) | 21.1210 | − | 36.5826i | 0.739835 | − | 1.28143i | ||||
\(816\) | 7.56403 | − | 13.1013i | 0.264794 | − | 0.458637i | ||||
\(817\) | −15.5748 | −0.544894 | ||||||||
\(818\) | −27.5497 | + | 47.7175i | −0.963253 | + | 1.66840i | ||||
\(819\) | 0.968773 | + | 1.67796i | 0.0338517 | + | 0.0586328i | ||||
\(820\) | −44.6486 | − | 77.3336i | −1.55920 | − | 2.70061i | ||||
\(821\) | 3.61979 | − | 6.26965i | 0.126331 | − | 0.218812i | −0.795921 | − | 0.605400i | \(-0.793013\pi\) |
0.922253 | + | 0.386588i | \(0.126346\pi\) | |||||||
\(822\) | 10.5402 | − | 18.2562i | 0.367633 | − | 0.636759i | ||||
\(823\) | −18.6356 | − | 32.2779i | −0.649598 | − | 1.12514i | −0.983219 | − | 0.182429i | \(-0.941604\pi\) |
0.333621 | − | 0.942707i | \(-0.391729\pi\) | |||||||
\(824\) | 6.60165 | 0.229979 | ||||||||
\(825\) | −27.8168 | − | 48.1801i | −0.968456 | − | 1.67741i | ||||
\(826\) | 64.5617 | 2.24639 | ||||||||
\(827\) | −18.5756 | − | 32.1739i | −0.645937 | − | 1.11879i | −0.984084 | − | 0.177702i | \(-0.943134\pi\) |
0.338148 | − | 0.941093i | \(-0.390200\pi\) | |||||||
\(828\) | −8.94090 | + | 15.4861i | −0.310718 | + | 0.538179i | ||||
\(829\) | 1.45917 | + | 2.52735i | 0.0506789 | + | 0.0877785i | 0.890252 | − | 0.455468i | \(-0.150528\pi\) |
−0.839573 | + | 0.543247i | \(0.817195\pi\) | |||||||
\(830\) | 105.682 | 3.66827 | ||||||||
\(831\) | −10.2693 | −0.356237 | ||||||||
\(832\) | −1.58033 | + | 2.73721i | −0.0547881 | + | 0.0948957i | ||||
\(833\) | −5.53636 | − | 9.58926i | −0.191823 | − | 0.332248i | ||||
\(834\) | 14.2606 | 0.493802 | ||||||||
\(835\) | 2.11584 | − | 3.66474i | 0.0732215 | − | 0.126823i | ||||
\(836\) | 78.1183 | − | 135.305i | 2.70178 | − | 4.67962i | ||||
\(837\) | −2.41760 | + | 4.18740i | −0.0835644 | + | 0.144738i | ||||
\(838\) | −48.2610 | + | 83.5905i | −1.66715 | + | 2.88759i | ||||
\(839\) | 14.9309 | 0.515472 | 0.257736 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257736 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(840\) | −34.4165 | + | 59.6111i | −1.18748 | + | 2.05678i | ||||
\(841\) | −2.37837 | −0.0820129 | ||||||||
\(842\) | 32.4824 | − | 56.2611i | 1.11942 | − | 1.93889i | ||||
\(843\) | 8.12909 | 0.279981 | ||||||||
\(844\) | −81.0240 | −2.78896 | ||||||||
\(845\) | 24.2577 | − | 42.0156i | 0.834490 | − | 1.44538i | ||||
\(846\) | −7.73537 | − | 13.3981i | −0.265948 | − | 0.460635i | ||||
\(847\) | −35.9596 | + | 62.2839i | −1.23559 | + | 2.14010i | ||||
\(848\) | 22.4869 | − | 38.9485i | 0.772203 | − | 1.33750i | ||||
\(849\) | −15.3168 | −0.525672 | ||||||||
\(850\) | −70.2253 | −2.40871 | ||||||||
\(851\) | −6.47767 | + | 11.2196i | −0.222052 | + | 0.384604i | ||||
\(852\) | 10.6386 | 0.364471 | ||||||||
\(853\) | −3.19989 | − | 5.54238i | −0.109562 | − | 0.189767i | 0.806031 | − | 0.591874i | \(-0.201612\pi\) |
−0.915593 | + | 0.402106i | \(0.868278\pi\) | |||||||
\(854\) | −58.1002 | − | 100.633i | −1.98815 | − | 3.44357i | ||||
\(855\) | −12.4558 | − | 21.5741i | −0.425981 | − | 0.737820i | ||||
\(856\) | 25.5607 | − | 44.2724i | 0.873646 | − | 1.51320i | ||||
\(857\) | 22.7409 | − | 39.3884i | 0.776814 | − | 1.34548i | −0.156956 | − | 0.987606i | \(-0.550168\pi\) |
0.933769 | − | 0.357875i | \(-0.116499\pi\) | |||||||
\(858\) | −4.20524 | − | 7.28369i | −0.143565 | − | 0.248661i | ||||
\(859\) | −15.0402 | + | 26.0504i | −0.513165 | + | 0.888828i | 0.486718 | + | 0.873559i | \(0.338194\pi\) |
−0.999883 | + | 0.0152691i | \(0.995139\pi\) | |||||||
\(860\) | −38.5524 | −1.31463 | ||||||||
\(861\) | 9.12720 | + | 15.8088i | 0.311054 | + | 0.538762i | ||||
\(862\) | 6.76590 | + | 11.7189i | 0.230448 | + | 0.399147i | ||||
\(863\) | 55.0453 | 1.87376 | 0.936882 | − | 0.349645i | \(-0.113698\pi\) | ||||
0.936882 | + | 0.349645i | \(0.113698\pi\) | |||||||
\(864\) | 2.02557 | 0.0689114 | ||||||||
\(865\) | 30.9770 | + | 53.6537i | 1.05325 | + | 1.82428i | ||||
\(866\) | 27.7103 | + | 47.9957i | 0.941635 | + | 1.63096i | ||||
\(867\) | 8.54279 | 0.290128 | ||||||||
\(868\) | 33.3335 | − | 57.7353i | 1.13141 | − | 1.95966i | ||||
\(869\) | 5.81245 | + | 10.0675i | 0.197174 | + | 0.341515i | ||||
\(870\) | −24.6192 | + | 42.6416i | −0.834668 | + | 1.44569i | ||||
\(871\) | 3.38241 | − | 5.85850i | 0.114608 | − | 0.198508i | ||||
\(872\) | −6.57452 | − | 11.3874i | −0.222641 | − | 0.385626i | ||||
\(873\) | 7.98334 | + | 13.8275i | 0.270195 | + | 0.467992i | ||||
\(874\) | 34.4698 | + | 59.7034i | 1.16596 | + | 2.01950i | ||||
\(875\) | 59.2800 | 2.00403 | ||||||||
\(876\) | 29.4886 | − | 51.0758i | 0.996329 | − | 1.72569i | ||||
\(877\) | 26.9421 | 0.909770 | 0.454885 | − | 0.890550i | \(-0.349680\pi\) | ||||
0.454885 | + | 0.890550i | \(0.349680\pi\) | |||||||
\(878\) | −87.9985 | −2.96980 | ||||||||
\(879\) | −9.43404 | + | 16.3402i | −0.318202 | + | 0.551142i | ||||
\(880\) | 57.1850 | − | 99.0474i | 1.92771 | − | 3.33889i | ||||
\(881\) | 11.3162 | + | 19.6002i | 0.381251 | + | 0.660347i | 0.991241 | − | 0.132062i | \(-0.0421599\pi\) |
−0.609990 | + | 0.792409i | \(0.708827\pi\) | |||||||
\(882\) | 4.73803 | − | 8.20652i | 0.159538 | − | 0.276328i | ||||
\(883\) | 0.709122 | 0.0238638 | 0.0119319 | − | 0.999929i | \(-0.496202\pi\) | ||||
0.0119319 | + | 0.999929i | \(0.496202\pi\) | |||||||
\(884\) | −7.18848 | −0.241775 | ||||||||
\(885\) | −15.1284 | + | 26.2032i | −0.508536 | + | 0.880809i | ||||
\(886\) | 24.4593 | 0.821726 | ||||||||
\(887\) | 14.5252 | − | 25.1584i | 0.487709 | − | 0.844737i | −0.512191 | − | 0.858872i | \(-0.671166\pi\) |
0.999900 | + | 0.0141344i | \(0.00449927\pi\) | |||||||
\(888\) | 16.5923 | 0.556801 | ||||||||
\(889\) | 14.8859 | − | 25.7832i | 0.499258 | − | 0.864740i | ||||
\(890\) | −44.6191 | + | 77.2826i | −1.49564 | + | 2.59052i | ||||
\(891\) | 2.86691 | − | 4.96564i | 0.0960452 | − | 0.166355i | ||||
\(892\) | −19.5575 | + | 33.8746i | −0.654834 | + | 1.13421i | ||||
\(893\) | −40.3857 | −1.35146 | ||||||||
\(894\) | 23.0119 | + | 39.8577i | 0.769632 | + | 1.33304i | ||||
\(895\) | 13.3852 | − | 23.1839i | 0.447418 | − | 0.774951i | ||||
\(896\) | 57.1953 | 1.91076 | ||||||||
\(897\) | 2.51285 | 0.0839015 | ||||||||
\(898\) | 8.66944 | + | 15.0159i | 0.289303 | + | 0.501087i | ||||
\(899\) | 12.4739 | − | 21.6054i | 0.416027 | − | 0.720580i | ||||
\(900\) | −20.3468 | − | 35.2417i | −0.678227 | − | 1.17472i | ||||
\(901\) | −25.1422 | −0.837609 | ||||||||
\(902\) | −39.6193 | − | 68.6226i | −1.31918 | − | 2.28488i | ||||
\(903\) | 7.88100 | 0.262263 | ||||||||
\(904\) | 46.0355 | + | 79.7359i | 1.53112 | + | 2.65198i | ||||
\(905\) | 20.5445 | − | 35.5842i | 0.682924 | − | 1.18286i | ||||
\(906\) | 19.5392 | − | 33.8428i | 0.649145 | − | 1.12435i | ||||
\(907\) | −4.45082 | − | 7.70904i | −0.147787 | − | 0.255975i | 0.782622 | − | 0.622497i | \(-0.213882\pi\) |
−0.930409 | + | 0.366522i | \(0.880548\pi\) | |||||||
\(908\) | 10.0919 | + | 17.4797i | 0.334913 | + | 0.580086i | ||||
\(909\) | 4.43997 | − | 7.69026i | 0.147265 | − | 0.255070i | ||||
\(910\) | 18.4900 | 0.612939 | ||||||||
\(911\) | 14.4457 | − | 25.0206i | 0.478606 | − | 0.828970i | −0.521093 | − | 0.853500i | \(-0.674476\pi\) |
0.999699 | + | 0.0245298i | \(0.00780887\pi\) | |||||||
\(912\) | 16.8983 | − | 29.2688i | 0.559560 | − | 0.969186i | ||||
\(913\) | 63.4977 | 2.10147 | ||||||||
\(914\) | 5.41976 | 0.179270 | ||||||||
\(915\) | 54.4573 | 1.80030 | ||||||||
\(916\) | 17.5022 | − | 30.3148i | 0.578290 | − | 1.00163i | ||||
\(917\) | −11.1655 | + | 19.3393i | −0.368719 | + | 0.638640i | ||||
\(918\) | −3.61885 | − | 6.26804i | −0.119440 | − | 0.206876i | ||||
\(919\) | 55.2168 | 1.82143 | 0.910716 | − | 0.413032i | \(-0.135530\pi\) | ||||
0.910716 | + | 0.413032i | \(0.135530\pi\) | |||||||
\(920\) | 44.6355 | + | 77.3110i | 1.47159 | + | 2.54887i | ||||
\(921\) | −7.05347 | − | 12.2170i | −0.232420 | − | 0.402563i | ||||
\(922\) | −22.1144 | − | 38.3033i | −0.728300 | − | 1.26145i | ||||
\(923\) | −0.747495 | − | 1.29470i | −0.0246041 | − | 0.0426155i | ||||
\(924\) | −39.5286 | + | 68.4655i | −1.30040 | + | 2.25235i | ||||
\(925\) | −14.7412 | − | 25.5326i | −0.484689 | − | 0.839506i | ||||
\(926\) | −58.9571 | −1.93745 | ||||||||
\(927\) | 0.604487 | − | 1.04700i | 0.0198540 | − | 0.0343881i | ||||
\(928\) | −10.4512 | −0.343077 | ||||||||
\(929\) | −3.56227 | + | 6.17003i | −0.116874 | + | 0.202432i | −0.918527 | − | 0.395357i | \(-0.870621\pi\) |
0.801653 | + | 0.597789i | \(0.203954\pi\) | |||||||
\(930\) | 23.0712 | + | 39.9605i | 0.756534 | + | 1.31036i | ||||
\(931\) | −12.3684 | − | 21.4228i | −0.405359 | − | 0.702103i | ||||
\(932\) | 30.3538 | + | 52.5742i | 0.994270 | + | 1.72213i | ||||
\(933\) | −11.8967 | + | 20.6058i | −0.389482 | + | 0.674602i | ||||
\(934\) | 57.3985 | 1.87814 | ||||||||
\(935\) | −63.9376 | −2.09098 | ||||||||
\(936\) | −1.60914 | − | 2.78712i | −0.0525965 | − | 0.0910997i | ||||
\(937\) | −1.02546 | − | 1.77615i | −0.0335004 | − | 0.0580243i | 0.848789 | − | 0.528732i | \(-0.177332\pi\) |
−0.882289 | + | 0.470707i | \(0.843999\pi\) | |||||||
\(938\) | −93.9111 | −3.06630 | ||||||||
\(939\) | −9.32579 | − | 16.1527i | −0.304336 | − | 0.527125i | ||||
\(940\) | −99.9669 | −3.26056 | ||||||||
\(941\) | −1.79663 | −0.0585685 | −0.0292842 | − | 0.999571i | \(-0.509323\pi\) | ||||
−0.0292842 | + | 0.999571i | \(0.509323\pi\) | |||||||
\(942\) | 19.5483 | + | 24.2967i | 0.636919 | + | 0.791629i | ||||
\(943\) | 23.6746 | 0.770949 | ||||||||
\(944\) | −41.0482 | −1.33601 | ||||||||
\(945\) | 6.30277 | + | 10.9167i | 0.205029 | + | 0.355121i | ||||
\(946\) | −34.2098 | −1.11226 | ||||||||
\(947\) | −8.31990 | − | 14.4105i | −0.270361 | − | 0.468278i | 0.698594 | − | 0.715519i | \(-0.253810\pi\) |
−0.968954 | + | 0.247240i | \(0.920476\pi\) | |||||||
\(948\) | 4.25157 | + | 7.36393i | 0.138084 | + | 0.239169i | ||||
\(949\) | −8.28781 | −0.269034 | ||||||||
\(950\) | −156.886 | −5.09005 | ||||||||
\(951\) | −8.28354 | + | 14.3475i | −0.268612 | + | 0.465250i | ||||
\(952\) | 26.1025 | + | 45.2108i | 0.845986 | + | 1.46529i | ||||
\(953\) | 20.4041 | + | 35.3409i | 0.660953 | + | 1.14480i | 0.980366 | + | 0.197188i | \(0.0631811\pi\) |
−0.319413 | + | 0.947616i | \(0.603486\pi\) | |||||||
\(954\) | −10.7584 | − | 18.6341i | −0.348316 | − | 0.603301i | ||||
\(955\) | 4.80974 | − | 8.33071i | 0.155639 | − | 0.269575i | ||||
\(956\) | −14.9798 | −0.484481 | ||||||||
\(957\) | −14.7922 | + | 25.6208i | −0.478163 | + | 0.828202i | ||||
\(958\) | 92.0731 | 2.97475 | ||||||||
\(959\) | 13.9228 | + | 24.1149i | 0.449589 | + | 0.778712i | ||||
\(960\) | −10.2815 | + | 17.8081i | −0.331834 | + | 0.574754i | ||||
\(961\) | 3.81045 | + | 6.59989i | 0.122918 | + | 0.212900i | ||||
\(962\) | −2.22853 | − | 3.85993i | −0.0718507 | − | 0.124449i | ||||
\(963\) | −4.68099 | − | 8.10771i | −0.150843 | − | 0.261267i | ||||
\(964\) | 55.9116 | + | 96.8417i | 1.80079 | + | 3.11906i | ||||
\(965\) | −3.41987 | −0.110090 | ||||||||
\(966\) | −17.4420 | − | 30.2105i | −0.561188 | − | 0.972007i | ||||
\(967\) | 0.469200 | − | 0.812678i | 0.0150884 | − | 0.0261339i | −0.858383 | − | 0.513010i | \(-0.828530\pi\) |
0.873471 | + | 0.486876i | \(0.161864\pi\) | |||||||
\(968\) | 59.7293 | − | 103.454i | 1.91977 | − | 3.32515i | ||||
\(969\) | −18.8937 | −0.606954 | ||||||||
\(970\) | 152.370 | 4.89232 | ||||||||
\(971\) | 32.9863 | 1.05858 | 0.529290 | − | 0.848441i | \(-0.322459\pi\) | ||||
0.529290 | + | 0.848441i | \(0.322459\pi\) | |||||||
\(972\) | 2.09703 | − | 3.63216i | 0.0672622 | − | 0.116502i | ||||
\(973\) | −9.41849 | + | 16.3133i | −0.301943 | + | 0.522981i | ||||
\(974\) | 32.3962 | 1.03804 | ||||||||
\(975\) | −2.85925 | + | 4.95236i | −0.0915692 | + | 0.158602i | ||||
\(976\) | 36.9400 | + | 63.9820i | 1.18242 | + | 2.04801i | ||||
\(977\) | 8.17558 | + | 14.1605i | 0.261560 | + | 0.453035i | 0.966657 | − | 0.256076i | \(-0.0824297\pi\) |
−0.705097 | + | 0.709111i | \(0.749096\pi\) | |||||||
\(978\) | 13.7089 | − | 23.7445i | 0.438362 | − | 0.759266i | ||||
\(979\) | −26.8089 | + | 46.4344i | −0.856817 | + | 1.48405i | ||||
\(980\) | −30.6156 | − | 53.0278i | −0.977981 | − | 1.69391i | ||||
\(981\) | −2.40801 | −0.0768820 | ||||||||
\(982\) | −42.5082 | − | 73.6264i | −1.35649 | − | 2.34951i | ||||
\(983\) | −20.7375 | −0.661423 | −0.330712 | − | 0.943732i | \(-0.607289\pi\) | ||||
−0.330712 | + | 0.943732i | \(0.607289\pi\) | |||||||
\(984\) | −15.1604 | − | 26.2585i | −0.483295 | − | 0.837092i | ||||
\(985\) | 9.00843 | − | 15.6031i | 0.287032 | − | 0.497155i | ||||
\(986\) | 18.6719 | + | 32.3407i | 0.594634 | + | 1.02994i | ||||
\(987\) | 20.4356 | 0.650471 | ||||||||
\(988\) | −16.0593 | −0.510916 | ||||||||
\(989\) | 5.11052 | − | 8.85169i | 0.162505 | − | 0.281467i | ||||
\(990\) | −27.3590 | − | 47.3872i | −0.869526 | − | 1.50606i | ||||
\(991\) | −5.41424 | −0.171989 | −0.0859946 | − | 0.996296i | \(-0.527407\pi\) | ||||
−0.0859946 | + | 0.996296i | \(0.527407\pi\) | |||||||
\(992\) | −4.89702 | + | 8.48189i | −0.155481 | + | 0.269300i | ||||
\(993\) | 12.6550 | − | 21.9190i | 0.401593 | − | 0.695579i | ||||
\(994\) | −10.3769 | + | 17.9734i | −0.329137 | + | 0.570081i | ||||
\(995\) | −34.1718 | + | 59.1873i | −1.08332 | + | 1.87636i | ||||
\(996\) | 46.4460 | 1.47170 | ||||||||
\(997\) | −25.3391 | + | 43.8886i | −0.802497 | + | 1.38997i | 0.115471 | + | 0.993311i | \(0.463162\pi\) |
−0.917968 | + | 0.396655i | \(0.870171\pi\) | |||||||
\(998\) | 45.7199 | 1.44724 | ||||||||
\(999\) | 1.51929 | − | 2.63149i | 0.0480683 | − | 0.0832568i |
(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 | 471.2.e.b.169.1 | ✓ | 22 | |
157.144 | even | 3 | inner | 471.2.e.b.301.1 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.2.e.b.169.1 | ✓ | 22 | 1.1 | even | 1 | trivial | |
471.2.e.b.301.1 | yes | 22 | 157.144 | even | 3 | inner |