Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (of order \(2\), degree \(1\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 103 x^{10} + 14 x^{9} + 7600 x^{8} + 1474 x^{7} + 229961 x^{6} + 442438 x^{5} + \cdots + 69739201 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.7 | ||
Root | \(-1.37625 - 2.38373i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.d.601.10 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −6.84490 | + | 1.46536i | −0.977844 | + | 0.209337i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.87800 | −0.534363 | −0.267182 | − | 0.963646i | \(-0.586092\pi\) | ||||
−0.267182 | + | 0.963646i | \(0.586092\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | 2.06416i | 0.158781i | 0.996844 | + | 0.0793906i | \(0.0252974\pi\) | ||||
−0.996844 | + | 0.0793906i | \(0.974703\pi\) | |||||||
\(14\) | −9.68016 | + | 2.07233i | −0.691440 | + | 0.148024i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 2.59754i | 0.152796i | 0.997077 | + | 0.0763982i | \(0.0243420\pi\) | ||||
−0.997077 | + | 0.0763982i | \(0.975658\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 14.3990i | 0.757840i | 0.925429 | + | 0.378920i | \(0.123704\pi\) | ||||
−0.925429 | + | 0.378920i | \(0.876296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53808 | + | 11.8557i | 0.120861 | + | 0.564558i | ||||
\(22\) | −8.31274 | −0.377852 | ||||||||
\(23\) | 4.73565 | 0.205898 | 0.102949 | − | 0.994687i | \(-0.467172\pi\) | ||||
0.102949 | + | 0.994687i | \(0.467172\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.91916i | 0.112275i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −13.6898 | + | 2.93072i | −0.488922 | + | 0.104669i | ||||
\(29\) | −16.1571 | −0.557140 | −0.278570 | − | 0.960416i | \(-0.589860\pi\) | ||||
−0.278570 | + | 0.960416i | \(0.589860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.3772i | 1.56055i | 0.625434 | + | 0.780277i | \(0.284922\pi\) | ||||
−0.625434 | + | 0.780277i | \(0.715078\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 10.1810i | 0.308515i | ||||||||
\(34\) | 3.67347i | 0.108043i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −46.3013 | −1.25139 | −0.625694 | − | 0.780069i | \(-0.715184\pi\) | ||||
−0.625694 | + | 0.780069i | \(0.715184\pi\) | |||||||
\(38\) | 20.3632i | 0.535874i | ||||||||
\(39\) | 3.57522 | 0.0916724 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 74.7122i | 1.82225i | 0.412132 | + | 0.911124i | \(0.364784\pi\) | ||||
−0.412132 | + | 0.911124i | \(0.635216\pi\) | |||||||
\(42\) | 3.58939 | + | 16.7665i | 0.0854616 | + | 0.399203i | ||||
\(43\) | 10.4038 | 0.241950 | 0.120975 | − | 0.992656i | \(-0.461398\pi\) | ||||
0.120975 | + | 0.992656i | \(0.461398\pi\) | |||||||
\(44\) | −11.7560 | −0.267182 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.69723 | 0.145592 | ||||||||
\(47\) | 35.0672i | 0.746111i | 0.927809 | + | 0.373055i | \(0.121690\pi\) | ||||
−0.927809 | + | 0.373055i | \(0.878310\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | 44.7054 | − | 20.0605i | 0.912356 | − | 0.409398i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.49907 | 0.0882170 | ||||||||
\(52\) | 4.12831i | 0.0793906i | ||||||||
\(53\) | −39.9926 | −0.754578 | −0.377289 | − | 0.926096i | \(-0.623144\pi\) | ||||
−0.377289 | + | 0.926096i | \(0.623144\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.3603 | + | 4.14467i | −0.345720 | + | 0.0740119i | ||||
\(57\) | 24.9397 | 0.437539 | ||||||||
\(58\) | −22.8495 | −0.393958 | ||||||||
\(59\) | − | 60.1573i | − | 1.01962i | −0.860288 | − | 0.509808i | \(-0.829716\pi\) | ||
0.860288 | − | 0.509808i | \(-0.170284\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 73.1619i | 1.19938i | 0.800234 | + | 0.599688i | \(0.204709\pi\) | ||||
−0.800234 | + | 0.599688i | \(0.795291\pi\) | |||||||
\(62\) | 68.4156i | 1.10348i | ||||||||
\(63\) | 20.5347 | − | 4.39608i | 0.325948 | − | 0.0697791i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 14.3981i | 0.218153i | ||||||||
\(67\) | −39.5941 | −0.590956 | −0.295478 | − | 0.955350i | \(-0.595479\pi\) | ||||
−0.295478 | + | 0.955350i | \(0.595479\pi\) | |||||||
\(68\) | 5.19507i | 0.0763982i | ||||||||
\(69\) | − | 8.20239i | − | 0.118875i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −39.3463 | −0.554173 | −0.277087 | − | 0.960845i | \(-0.589369\pi\) | ||||
−0.277087 | + | 0.960845i | \(0.589369\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 11.8315i | 0.162075i | 0.996711 | + | 0.0810377i | \(0.0258234\pi\) | ||||
−0.996711 | + | 0.0810377i | \(0.974177\pi\) | |||||||
\(74\) | −65.4800 | −0.884864 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.7979i | 0.378920i | ||||||||
\(77\) | 40.2343 | − | 8.61339i | 0.522524 | − | 0.111862i | ||||
\(78\) | 5.05613 | 0.0648222 | ||||||||
\(79\) | 41.2398 | 0.522023 | 0.261012 | − | 0.965336i | \(-0.415944\pi\) | ||||
0.261012 | + | 0.965336i | \(0.415944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 105.659i | 1.28852i | ||||||||
\(83\) | − | 126.222i | − | 1.52075i | −0.649485 | − | 0.760374i | \(-0.725016\pi\) | ||
0.649485 | − | 0.760374i | \(-0.274984\pi\) | |||||||
\(84\) | 5.07616 | + | 23.7114i | 0.0604304 | + | 0.282279i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.7133 | 0.171084 | ||||||||
\(87\) | 27.9849i | 0.321665i | ||||||||
\(88\) | −16.6255 | −0.188926 | ||||||||
\(89\) | 92.1225i | 1.03508i | 0.855658 | + | 0.517542i | \(0.173153\pi\) | ||||
−0.855658 | + | 0.517542i | \(0.826847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.02473 | − | 14.1290i | −0.0332388 | − | 0.155263i | ||||
\(92\) | 9.47131 | 0.102949 | ||||||||
\(93\) | 83.7917 | 0.900986 | ||||||||
\(94\) | 49.5925i | 0.527580i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | 4.26795i | 0.0439995i | 0.999758 | + | 0.0219997i | \(0.00700330\pi\) | ||||
−0.999758 | + | 0.0219997i | \(0.992997\pi\) | |||||||
\(98\) | 63.2230 | − | 28.3698i | 0.645133 | − | 0.289488i | ||||
\(99\) | 17.6340 | 0.178121 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 90.7089i | 0.898108i | 0.893505 | + | 0.449054i | \(0.148239\pi\) | ||||
−0.893505 | + | 0.449054i | \(0.851761\pi\) | |||||||
\(102\) | 6.36264 | 0.0623788 | ||||||||
\(103\) | − | 136.976i | − | 1.32986i | −0.746904 | − | 0.664932i | \(-0.768460\pi\) | ||
0.746904 | − | 0.664932i | \(-0.231540\pi\) | |||||||
\(104\) | 5.83832i | 0.0561377i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −56.5581 | −0.533567 | ||||||||
\(107\) | 23.3746 | 0.218454 | 0.109227 | − | 0.994017i | \(-0.465162\pi\) | ||||
0.109227 | + | 0.994017i | \(0.465162\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | −25.6873 | −0.235663 | −0.117832 | − | 0.993034i | \(-0.537594\pi\) | ||||
−0.117832 | + | 0.993034i | \(0.537594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 80.1962i | 0.722489i | ||||||||
\(112\) | −27.3796 | + | 5.86144i | −0.244461 | + | 0.0523343i | ||||
\(113\) | 2.51092 | 0.0222205 | 0.0111103 | − | 0.999938i | \(-0.496463\pi\) | ||||
0.0111103 | + | 0.999938i | \(0.496463\pi\) | |||||||
\(114\) | 35.2701 | 0.309387 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.3141 | −0.278570 | ||||||||
\(117\) | − | 6.19247i | − | 0.0529271i | ||||||
\(118\) | − | 85.0753i | − | 0.720977i | ||||||
\(119\) | −3.80633 | − | 17.7799i | −0.0319860 | − | 0.149411i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −86.4491 | −0.714456 | ||||||||
\(122\) | 103.467i | 0.848087i | ||||||||
\(123\) | 129.405 | 1.05208 | ||||||||
\(124\) | 96.7543i | 0.780277i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 29.0405 | − | 6.21700i | 0.230480 | − | 0.0493413i | ||||
\(127\) | −19.5421 | −0.153875 | −0.0769375 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769375 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 18.0200i | − | 0.139690i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 45.5826i | 0.347959i | 0.984749 | + | 0.173980i | \(0.0556627\pi\) | ||||
−0.984749 | + | 0.173980i | \(0.944337\pi\) | |||||||
\(132\) | 20.3620i | 0.154257i | ||||||||
\(133\) | −21.0997 | − | 98.5595i | −0.158644 | − | 0.741049i | ||||
\(134\) | −55.9945 | −0.417869 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.34694i | 0.0540217i | ||||||||
\(137\) | 177.239 | 1.29372 | 0.646859 | − | 0.762610i | \(-0.276082\pi\) | ||||
0.646859 | + | 0.762610i | \(0.276082\pi\) | |||||||
\(138\) | − | 11.5999i | − | 0.0840575i | ||||||
\(139\) | 33.1908i | 0.238783i | 0.992847 | + | 0.119391i | \(0.0380944\pi\) | ||||
−0.992847 | + | 0.119391i | \(0.961906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 60.7382 | 0.430767 | ||||||||
\(142\) | −55.6441 | −0.391860 | ||||||||
\(143\) | − | 12.1331i | − | 0.0848469i | ||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.7323i | 0.114605i | ||||||||
\(147\) | −34.7458 | − | 77.4321i | −0.236366 | − | 0.526749i | ||||
\(148\) | −92.6026 | −0.625694 | ||||||||
\(149\) | −43.9593 | −0.295029 | −0.147514 | − | 0.989060i | \(-0.547127\pi\) | ||||
−0.147514 | + | 0.989060i | \(0.547127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −182.752 | −1.21028 | −0.605139 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605139 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(152\) | 40.7264i | 0.267937i | ||||||||
\(153\) | − | 7.79261i | − | 0.0509321i | ||||||
\(154\) | 56.8999 | − | 12.1812i | 0.369480 | − | 0.0790985i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.15045 | 0.0458362 | ||||||||
\(157\) | − | 50.4042i | − | 0.321046i | −0.987032 | − | 0.160523i | \(-0.948682\pi\) | ||
0.987032 | − | 0.160523i | \(-0.0513180\pi\) | |||||||
\(158\) | 58.3219 | 0.369126 | ||||||||
\(159\) | 69.2693i | 0.435656i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32.4151 | + | 6.93944i | −0.201336 | + | 0.0431021i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −101.758 | −0.624281 | −0.312140 | − | 0.950036i | \(-0.601046\pi\) | ||||
−0.312140 | + | 0.950036i | \(0.601046\pi\) | |||||||
\(164\) | 149.424i | 0.911124i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 178.505i | − | 1.07533i | ||||||
\(167\) | − | 129.715i | − | 0.776738i | −0.921504 | − | 0.388369i | \(-0.873039\pi\) | ||
0.921504 | − | 0.388369i | \(-0.126961\pi\) | |||||||
\(168\) | 7.17877 | + | 33.5330i | 0.0427308 | + | 0.199601i | ||||
\(169\) | 164.739 | 0.974789 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 43.1969i | − | 0.252613i | ||||||
\(172\) | 20.8077 | 0.120975 | ||||||||
\(173\) | − | 80.2634i | − | 0.463950i | −0.972722 | − | 0.231975i | \(-0.925481\pi\) | ||
0.972722 | − | 0.231975i | \(-0.0745188\pi\) | |||||||
\(174\) | 39.5766i | 0.227452i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −23.5120 | −0.133591 | ||||||||
\(177\) | −104.196 | −0.588676 | ||||||||
\(178\) | 130.281i | 0.731915i | ||||||||
\(179\) | −145.799 | −0.814519 | −0.407260 | − | 0.913312i | \(-0.633516\pi\) | ||||
−0.407260 | + | 0.913312i | \(0.633516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 323.062i | 1.78487i | 0.451175 | + | 0.892435i | \(0.351005\pi\) | ||||
−0.451175 | + | 0.892435i | \(0.648995\pi\) | |||||||
\(182\) | −4.27762 | − | 19.9814i | −0.0235034 | − | 0.109788i | ||||
\(183\) | 126.720 | 0.692460 | ||||||||
\(184\) | 13.3945 | 0.0727959 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 118.499 | 0.637093 | ||||||||
\(187\) | − | 15.2683i | − | 0.0816488i | ||||||
\(188\) | 70.1344i | 0.373055i | ||||||||
\(189\) | −7.61424 | − | 35.5672i | −0.0402870 | − | 0.188186i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 309.035 | 1.61799 | 0.808993 | − | 0.587818i | \(-0.200013\pi\) | ||||
0.808993 | + | 0.587818i | \(0.200013\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | −353.480 | −1.83150 | −0.915752 | − | 0.401743i | \(-0.868404\pi\) | ||||
−0.915752 | + | 0.401743i | \(0.868404\pi\) | |||||||
\(194\) | 6.03579i | 0.0311123i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 89.4109 | − | 40.1210i | 0.456178 | − | 0.204699i | ||||
\(197\) | 136.303 | 0.691892 | 0.345946 | − | 0.938254i | \(-0.387558\pi\) | ||||
0.345946 | + | 0.938254i | \(0.387558\pi\) | |||||||
\(198\) | 24.9382 | 0.125951 | ||||||||
\(199\) | − | 62.4881i | − | 0.314011i | −0.987598 | − | 0.157005i | \(-0.949816\pi\) | ||
0.987598 | − | 0.157005i | \(-0.0501840\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 68.5789i | 0.341189i | ||||||||
\(202\) | 128.282i | 0.635058i | ||||||||
\(203\) | 110.594 | − | 23.6759i | 0.544796 | − | 0.116630i | ||||
\(204\) | 8.99813 | 0.0441085 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 193.713i | − | 0.940356i | ||||||
\(207\) | −14.2070 | −0.0686327 | ||||||||
\(208\) | 8.25663i | 0.0396953i | ||||||||
\(209\) | − | 84.6371i | − | 0.404962i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −188.967 | −0.895579 | −0.447790 | − | 0.894139i | \(-0.647789\pi\) | ||||
−0.447790 | + | 0.894139i | \(0.647789\pi\) | |||||||
\(212\) | −79.9853 | −0.377289 | ||||||||
\(213\) | 68.1498i | 0.319952i | ||||||||
\(214\) | 33.0566 | 0.154470 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −70.8900 | − | 331.137i | −0.326682 | − | 1.52598i | ||||
\(218\) | −36.3273 | −0.166639 | ||||||||
\(219\) | 20.4928 | 0.0935742 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.36172 | −0.0242612 | ||||||||
\(222\) | 113.415i | 0.510877i | ||||||||
\(223\) | − | 264.391i | − | 1.18561i | −0.805346 | − | 0.592805i | \(-0.798020\pi\) | ||
0.805346 | − | 0.592805i | \(-0.201980\pi\) | |||||||
\(224\) | −38.7206 | + | 8.28933i | −0.172860 | + | 0.0370059i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.55098 | 0.0157123 | ||||||||
\(227\) | − | 24.7955i | − | 0.109231i | −0.998507 | − | 0.0546157i | \(-0.982607\pi\) | ||
0.998507 | − | 0.0546157i | \(-0.0173934\pi\) | |||||||
\(228\) | 49.8795 | 0.218770 | ||||||||
\(229\) | 131.811i | 0.575595i | 0.957691 | + | 0.287798i | \(0.0929230\pi\) | ||||
−0.957691 | + | 0.287798i | \(0.907077\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.9188 | − | 69.6879i | −0.0645836 | − | 0.301679i | ||||
\(232\) | −45.6991 | −0.196979 | ||||||||
\(233\) | 145.909 | 0.626217 | 0.313109 | − | 0.949717i | \(-0.398630\pi\) | ||||
0.313109 | + | 0.949717i | \(0.398630\pi\) | |||||||
\(234\) | − | 8.75747i | − | 0.0374251i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 120.315i | − | 0.509808i | ||||||
\(237\) | − | 71.4295i | − | 0.301390i | ||||||
\(238\) | −5.38296 | − | 25.1446i | −0.0226175 | − | 0.105649i | ||||
\(239\) | −411.485 | −1.72169 | −0.860847 | − | 0.508864i | \(-0.830066\pi\) | ||||
−0.860847 | + | 0.508864i | \(0.830066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 381.587i | − | 1.58335i | −0.610943 | − | 0.791675i | \(-0.709209\pi\) | ||
0.610943 | − | 0.791675i | \(-0.290791\pi\) | |||||||
\(242\) | −122.258 | −0.505196 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 146.324i | 0.599688i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 183.007 | 0.743930 | ||||||||
\(247\) | −29.7217 | −0.120331 | ||||||||
\(248\) | 136.831i | 0.551739i | ||||||||
\(249\) | −218.623 | −0.878004 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 236.750i | 0.943229i | 0.881805 | + | 0.471614i | \(0.156329\pi\) | ||||
−0.881805 | + | 0.471614i | \(0.843671\pi\) | |||||||
\(252\) | 41.0694 | − | 8.79216i | 0.162974 | − | 0.0348895i | ||||
\(253\) | −27.8362 | −0.110024 | ||||||||
\(254\) | −27.6367 | −0.108806 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 187.550i | 0.729768i | 0.931053 | + | 0.364884i | \(0.118891\pi\) | ||||
−0.931053 | + | 0.364884i | \(0.881109\pi\) | |||||||
\(258\) | − | 25.4841i | − | 0.0987756i | ||||||
\(259\) | 316.928 | − | 67.8481i | 1.22366 | − | 0.261962i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 48.4712 | 0.185713 | ||||||||
\(262\) | 64.4636i | 0.246044i | ||||||||
\(263\) | −167.502 | −0.636890 | −0.318445 | − | 0.947941i | \(-0.603161\pi\) | ||||
−0.318445 | + | 0.947941i | \(0.603161\pi\) | |||||||
\(264\) | 28.7962i | 0.109076i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −29.8394 | − | 139.384i | −0.112178 | − | 0.524001i | ||||
\(267\) | 159.561 | 0.597606 | ||||||||
\(268\) | −79.1881 | −0.295478 | ||||||||
\(269\) | − | 373.386i | − | 1.38805i | −0.719950 | − | 0.694026i | \(-0.755835\pi\) | ||
0.719950 | − | 0.694026i | \(-0.244165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 395.308i | − | 1.45870i | −0.684141 | − | 0.729350i | \(-0.739823\pi\) | ||
0.684141 | − | 0.729350i | \(-0.260177\pi\) | |||||||
\(272\) | 10.3901i | 0.0381991i | ||||||||
\(273\) | −24.4721 | + | 5.23899i | −0.0896413 | + | 0.0191904i | ||||
\(274\) | 250.654 | 0.914796 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 16.4048i | − | 0.0594376i | ||||||
\(277\) | −50.0168 | −0.180566 | −0.0902830 | − | 0.995916i | \(-0.528777\pi\) | ||||
−0.0902830 | + | 0.995916i | \(0.528777\pi\) | |||||||
\(278\) | 46.9389i | 0.168845i | ||||||||
\(279\) | − | 145.132i | − | 0.520185i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 414.869 | 1.47640 | 0.738201 | − | 0.674580i | \(-0.235675\pi\) | ||||
0.738201 | + | 0.674580i | \(0.235675\pi\) | |||||||
\(282\) | 85.8968 | 0.304598 | ||||||||
\(283\) | 40.4964i | 0.143097i | 0.997437 | + | 0.0715484i | \(0.0227940\pi\) | ||||
−0.997437 | + | 0.0715484i | \(0.977206\pi\) | |||||||
\(284\) | −78.6926 | −0.277087 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 17.1588i | − | 0.0599958i | ||||||
\(287\) | −109.480 | − | 511.398i | −0.381464 | − | 1.78187i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 282.253 | 0.976653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.39230 | 0.0254031 | ||||||||
\(292\) | 23.6630i | 0.0810377i | ||||||||
\(293\) | 23.5736i | 0.0804560i | 0.999191 | + | 0.0402280i | \(0.0128084\pi\) | ||||
−0.999191 | + | 0.0402280i | \(0.987192\pi\) | |||||||
\(294\) | −49.1380 | − | 109.506i | −0.167136 | − | 0.372468i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −130.960 | −0.442432 | ||||||||
\(297\) | − | 30.5430i | − | 0.102838i | ||||||
\(298\) | −62.1679 | −0.208617 | ||||||||
\(299\) | 9.77513i | 0.0326927i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −71.2133 | + | 15.2454i | −0.236589 | + | 0.0506491i | ||||
\(302\) | −258.450 | −0.855796 | ||||||||
\(303\) | 157.112 | 0.518523 | ||||||||
\(304\) | 57.5958i | 0.189460i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 11.0204i | − | 0.0360144i | ||||||
\(307\) | − | 313.711i | − | 1.02186i | −0.859622 | − | 0.510930i | \(-0.829301\pi\) | ||
0.859622 | − | 0.510930i | \(-0.170699\pi\) | |||||||
\(308\) | 80.4687 | − | 17.2268i | 0.261262 | − | 0.0559311i | ||||
\(309\) | −237.249 | −0.767798 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 341.192i | − | 1.09708i | −0.836125 | − | 0.548539i | \(-0.815184\pi\) | ||
0.836125 | − | 0.548539i | \(-0.184816\pi\) | |||||||
\(312\) | 10.1123 | 0.0324111 | ||||||||
\(313\) | 508.988i | 1.62616i | 0.582151 | + | 0.813081i | \(0.302211\pi\) | ||||
−0.582151 | + | 0.813081i | \(0.697789\pi\) | |||||||
\(314\) | − | 71.2823i | − | 0.227014i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 82.4797 | 0.261012 | ||||||||
\(317\) | 355.980 | 1.12297 | 0.561483 | − | 0.827488i | \(-0.310231\pi\) | ||||
0.561483 | + | 0.827488i | \(0.310231\pi\) | |||||||
\(318\) | 97.9616i | 0.308055i | ||||||||
\(319\) | 94.9712 | 0.297715 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 40.4860i | − | 0.126124i | ||||||
\(322\) | −45.8419 | + | 9.81385i | −0.142366 | + | 0.0304778i | ||||
\(323\) | −37.4018 | −0.115795 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −143.907 | −0.441433 | ||||||||
\(327\) | 44.4917i | 0.136060i | ||||||||
\(328\) | 211.318i | 0.644262i | ||||||||
\(329\) | −51.3861 | − | 240.032i | −0.156189 | − | 0.729579i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −568.964 | −1.71892 | −0.859462 | − | 0.511199i | \(-0.829201\pi\) | ||||
−0.859462 | + | 0.511199i | \(0.829201\pi\) | |||||||
\(332\) | − | 252.444i | − | 0.760374i | ||||||
\(333\) | 138.904 | 0.417129 | ||||||||
\(334\) | − | 183.445i | − | 0.549237i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.1523 | + | 47.4229i | 0.0302152 | + | 0.141140i | ||||
\(337\) | −292.641 | −0.868372 | −0.434186 | − | 0.900823i | \(-0.642964\pi\) | ||||
−0.434186 | + | 0.900823i | \(0.642964\pi\) | |||||||
\(338\) | 232.976 | 0.689280 | ||||||||
\(339\) | − | 4.34904i | − | 0.0128290i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 284.361i | − | 0.833903i | ||||||
\(342\) | − | 61.0896i | − | 0.178625i | ||||||
\(343\) | −276.609 | + | 202.822i | −0.806439 | + | 0.591317i | ||||
\(344\) | 29.4265 | 0.0855422 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 113.510i | − | 0.328063i | ||||||
\(347\) | 175.594 | 0.506036 | 0.253018 | − | 0.967462i | \(-0.418577\pi\) | ||||
0.253018 | + | 0.967462i | \(0.418577\pi\) | |||||||
\(348\) | 55.9697i | 0.160833i | ||||||||
\(349\) | − | 451.738i | − | 1.29438i | −0.762329 | − | 0.647190i | \(-0.775944\pi\) | ||
0.762329 | − | 0.647190i | \(-0.224056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.7257 | −0.0305575 | ||||||||
\(352\) | −33.2510 | −0.0944630 | ||||||||
\(353\) | 539.172i | 1.52740i | 0.645571 | + | 0.763700i | \(0.276619\pi\) | ||||
−0.645571 | + | 0.763700i | \(0.723381\pi\) | |||||||
\(354\) | −147.355 | −0.416256 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 184.245i | 0.517542i | ||||||||
\(357\) | −30.7957 | + | 6.59275i | −0.0862624 | + | 0.0184671i | ||||
\(358\) | −206.191 | −0.575952 | ||||||||
\(359\) | 166.475 | 0.463720 | 0.231860 | − | 0.972749i | \(-0.425519\pi\) | ||||
0.231860 | + | 0.972749i | \(0.425519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 153.670 | 0.425678 | ||||||||
\(362\) | 456.878i | 1.26209i | ||||||||
\(363\) | 149.734i | 0.412491i | ||||||||
\(364\) | −6.04947 | − | 28.2579i | −0.0166194 | − | 0.0776316i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 179.209 | 0.489643 | ||||||||
\(367\) | − | 129.246i | − | 0.352169i | −0.984375 | − | 0.176084i | \(-0.943657\pi\) | ||
0.984375 | − | 0.176084i | \(-0.0563432\pi\) | |||||||
\(368\) | 18.9426 | 0.0514745 | ||||||||
\(369\) | − | 224.137i | − | 0.607416i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 273.746 | − | 58.6036i | 0.737859 | − | 0.157961i | ||||
\(372\) | 167.583 | 0.450493 | ||||||||
\(373\) | −423.280 | −1.13480 | −0.567399 | − | 0.823443i | \(-0.692050\pi\) | ||||
−0.567399 | + | 0.823443i | \(0.692050\pi\) | |||||||
\(374\) | − | 21.5927i | − | 0.0577344i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 99.1850i | 0.263790i | ||||||||
\(377\) | − | 33.3507i | − | 0.0884634i | ||||||
\(378\) | −10.7682 | − | 50.2996i | −0.0284872 | − | 0.133068i | ||||
\(379\) | 30.5074 | 0.0804944 | 0.0402472 | − | 0.999190i | \(-0.487185\pi\) | ||||
0.0402472 | + | 0.999190i | \(0.487185\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.8479i | 0.0888398i | ||||||||
\(382\) | 437.042 | 1.14409 | ||||||||
\(383\) | 367.882i | 0.960529i | 0.877124 | + | 0.480264i | \(0.159459\pi\) | ||||
−0.877124 | + | 0.480264i | \(0.840541\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −499.897 | −1.29507 | ||||||||
\(387\) | −31.2115 | −0.0806500 | ||||||||
\(388\) | 8.53590i | 0.0219997i | ||||||||
\(389\) | 583.606 | 1.50027 | 0.750136 | − | 0.661283i | \(-0.229988\pi\) | ||||
0.750136 | + | 0.661283i | \(0.229988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3010i | 0.0314605i | ||||||||
\(392\) | 126.446 | − | 56.7397i | 0.322567 | − | 0.144744i | ||||
\(393\) | 78.9515 | 0.200894 | ||||||||
\(394\) | 192.761 | 0.489241 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 35.2680 | 0.0890606 | ||||||||
\(397\) | 618.783i | 1.55865i | 0.626622 | + | 0.779323i | \(0.284437\pi\) | ||||
−0.626622 | + | 0.779323i | \(0.715563\pi\) | |||||||
\(398\) | − | 88.3715i | − | 0.222039i | ||||||
\(399\) | −170.710 | + | 36.5457i | −0.427845 | + | 0.0915932i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 577.546 | 1.44026 | 0.720132 | − | 0.693837i | \(-0.244081\pi\) | ||||
0.720132 | + | 0.693837i | \(0.244081\pi\) | |||||||
\(402\) | 96.9852i | 0.241257i | ||||||||
\(403\) | −99.8580 | −0.247787 | ||||||||
\(404\) | 181.418i | 0.449054i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 156.403 | − | 33.4828i | 0.385229 | − | 0.0824700i | ||||
\(407\) | 272.159 | 0.668696 | ||||||||
\(408\) | 12.7253 | 0.0311894 | ||||||||
\(409\) | − | 488.227i | − | 1.19371i | −0.802349 | − | 0.596855i | \(-0.796417\pi\) | ||
0.802349 | − | 0.596855i | \(-0.203583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 306.987i | − | 0.746928i | ||||||
\(412\) | − | 273.952i | − | 0.664932i | ||||||
\(413\) | 88.1522 | + | 411.771i | 0.213444 | + | 0.997025i | ||||
\(414\) | −20.0917 | −0.0485306 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11.6766i | 0.0280688i | ||||||||
\(417\) | 57.4882 | 0.137861 | ||||||||
\(418\) | − | 119.695i | − | 0.286351i | ||||||
\(419\) | − | 131.348i | − | 0.313481i | −0.987640 | − | 0.156740i | \(-0.949901\pi\) | ||
0.987640 | − | 0.156740i | \(-0.0500986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −556.789 | −1.32254 | −0.661270 | − | 0.750148i | \(-0.729982\pi\) | ||||
−0.661270 | + | 0.750148i | \(0.729982\pi\) | |||||||
\(422\) | −267.240 | −0.633270 | ||||||||
\(423\) | − | 105.202i | − | 0.248704i | ||||||
\(424\) | −113.116 | −0.266784 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 96.3784i | 0.226240i | ||||||||
\(427\) | −107.209 | − | 500.787i | −0.251074 | − | 1.17280i | ||||
\(428\) | 46.7492 | 0.109227 | ||||||||
\(429\) | −21.0152 | −0.0489864 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −167.379 | −0.388351 | −0.194175 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194175 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | − | 57.5429i | − | 0.132894i | −0.997790 | − | 0.0664468i | \(-0.978834\pi\) | ||
0.997790 | − | 0.0664468i | \(-0.0211663\pi\) | |||||||
\(434\) | −100.254 | − | 468.299i | −0.230999 | − | 1.07903i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −51.3746 | −0.117832 | ||||||||
\(437\) | 68.1885i | 0.156038i | ||||||||
\(438\) | 28.9811 | 0.0661670 | ||||||||
\(439\) | 838.459i | 1.90993i | 0.296719 | + | 0.954965i | \(0.404107\pi\) | ||||
−0.296719 | + | 0.954965i | \(0.595893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −134.116 | + | 60.1815i | −0.304119 | + | 0.136466i | ||||
\(442\) | −7.58262 | −0.0171553 | ||||||||
\(443\) | 435.742 | 0.983616 | 0.491808 | − | 0.870704i | \(-0.336336\pi\) | ||||
0.491808 | + | 0.870704i | \(0.336336\pi\) | |||||||
\(444\) | 160.392i | 0.361244i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 373.905i | − | 0.838353i | ||||||
\(447\) | 76.1398i | 0.170335i | ||||||||
\(448\) | −54.7592 | + | 11.7229i | −0.122230 | + | 0.0261672i | ||||
\(449\) | 612.776 | 1.36476 | 0.682378 | − | 0.730999i | \(-0.260946\pi\) | ||||
0.682378 | + | 0.730999i | \(0.260946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 439.158i | − | 0.973743i | ||||||
\(452\) | 5.02184 | 0.0111103 | ||||||||
\(453\) | 316.536i | 0.698754i | ||||||||
\(454\) | − | 35.0662i | − | 0.0772382i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 70.5402 | 0.154693 | ||||||||
\(457\) | −3.25143 | −0.00711473 | −0.00355736 | − | 0.999994i | \(-0.501132\pi\) | ||||
−0.00355736 | + | 0.999994i | \(0.501132\pi\) | |||||||
\(458\) | 186.409i | 0.407007i | ||||||||
\(459\) | −13.4972 | −0.0294057 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 662.733i | 1.43760i | 0.695218 | + | 0.718799i | \(0.255308\pi\) | ||||
−0.695218 | + | 0.718799i | \(0.744692\pi\) | |||||||
\(462\) | −21.0984 | − | 98.5536i | −0.0456675 | − | 0.213319i | ||||
\(463\) | 193.306 | 0.417507 | 0.208754 | − | 0.977968i | \(-0.433059\pi\) | ||||
0.208754 | + | 0.977968i | \(0.433059\pi\) | |||||||
\(464\) | −64.6283 | −0.139285 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 206.346 | 0.442802 | ||||||||
\(467\) | 353.116i | 0.756138i | 0.925777 | + | 0.378069i | \(0.123412\pi\) | ||||
−0.925777 | + | 0.378069i | \(0.876588\pi\) | |||||||
\(468\) | − | 12.3849i | − | 0.0264635i | ||||||
\(469\) | 271.018 | − | 58.0196i | 0.577863 | − | 0.123709i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −87.3026 | −0.185356 | ||||||||
\(472\) | − | 170.151i | − | 0.360489i | ||||||
\(473\) | −61.1538 | −0.129289 | ||||||||
\(474\) | − | 101.017i | − | 0.213115i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.61266 | − | 35.5598i | −0.0159930 | − | 0.0747054i | ||||
\(477\) | 119.978 | 0.251526 | ||||||||
\(478\) | −581.927 | −1.21742 | ||||||||
\(479\) | 608.762i | 1.27090i | 0.772141 | + | 0.635451i | \(0.219186\pi\) | ||||
−0.772141 | + | 0.635451i | \(0.780814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 95.5732i | − | 0.198697i | ||||||
\(482\) | − | 539.646i | − | 1.11960i | ||||||
\(483\) | 12.0195 | + | 56.1446i | 0.0248850 | + | 0.116241i | ||||
\(484\) | −172.898 | −0.357228 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | 185.222 | 0.380333 | 0.190167 | − | 0.981752i | \(-0.439097\pi\) | ||||
0.190167 | + | 0.981752i | \(0.439097\pi\) | |||||||
\(488\) | 206.933i | 0.424044i | ||||||||
\(489\) | 176.250i | 0.360429i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 924.656 | 1.88321 | 0.941605 | − | 0.336720i | \(-0.109317\pi\) | ||||
0.941605 | + | 0.336720i | \(0.109317\pi\) | |||||||
\(492\) | 258.811 | 0.526038 | ||||||||
\(493\) | − | 41.9686i | − | 0.0851290i | ||||||
\(494\) | −42.0328 | −0.0850867 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 193.509i | 0.390138i | ||||||||
\(497\) | 269.322 | − | 57.6565i | 0.541895 | − | 0.116009i | ||||
\(498\) | −309.180 | −0.620843 | ||||||||
\(499\) | −644.190 | −1.29096 | −0.645481 | − | 0.763776i | \(-0.723343\pi\) | ||||
−0.645481 | + | 0.763776i | \(0.723343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −224.674 | −0.448450 | ||||||||
\(502\) | 334.816i | 0.666963i | ||||||||
\(503\) | − | 774.419i | − | 1.53960i | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||
0.638285 | − | 0.769800i | \(-0.279644\pi\) | |||||||
\(504\) | 58.0809 | − | 12.4340i | 0.115240 | − | 0.0246706i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −39.3663 | −0.0777990 | ||||||||
\(507\) | − | 285.337i | − | 0.562794i | ||||||
\(508\) | −39.0842 | −0.0769375 | ||||||||
\(509\) | 675.381i | 1.32688i | 0.748231 | + | 0.663439i | \(0.230904\pi\) | ||||
−0.748231 | + | 0.663439i | \(0.769096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.3374 | − | 80.9855i | −0.0339284 | − | 0.158484i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −74.8192 | −0.145846 | ||||||||
\(514\) | 265.236i | 0.516024i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 36.0400i | − | 0.0698449i | ||||||
\(517\) | − | 206.125i | − | 0.398694i | ||||||
\(518\) | 448.204 | − | 95.9517i | 0.865259 | − | 0.185235i | ||||
\(519\) | −139.020 | −0.267862 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 572.162i | − | 1.09820i | −0.835757 | − | 0.549100i | \(-0.814971\pi\) | ||
0.835757 | − | 0.549100i | \(-0.185029\pi\) | |||||||
\(522\) | 68.5486 | 0.131319 | ||||||||
\(523\) | − | 85.2596i | − | 0.163020i | −0.996673 | − | 0.0815102i | \(-0.974026\pi\) | ||
0.996673 | − | 0.0815102i | \(-0.0259743\pi\) | |||||||
\(524\) | 91.1653i | 0.173980i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −236.884 | −0.450349 | ||||||||
\(527\) | −125.661 | −0.238447 | ||||||||
\(528\) | 40.7240i | 0.0771287i | ||||||||
\(529\) | −506.574 | −0.957606 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 180.472i | 0.339872i | ||||||||
\(532\) | −42.1993 | − | 197.119i | −0.0793221 | − | 0.370524i | ||||
\(533\) | −154.218 | −0.289339 | ||||||||
\(534\) | 225.653 | 0.422571 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −111.989 | −0.208935 | ||||||||
\(537\) | 252.531i | 0.470263i | ||||||||
\(538\) | − | 528.048i | − | 0.981501i | ||||||
\(539\) | −262.778 | + | 117.916i | −0.487530 | + | 0.218767i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −347.233 | −0.641836 | −0.320918 | − | 0.947107i | \(-0.603991\pi\) | ||||
−0.320918 | + | 0.947107i | \(0.603991\pi\) | |||||||
\(542\) | − | 559.049i | − | 1.03146i | ||||||
\(543\) | 559.559 | 1.03050 | ||||||||
\(544\) | 14.6939i | 0.0270108i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −34.6087 | + | 7.40905i | −0.0633859 | + | 0.0135697i | ||||
\(547\) | −593.025 | −1.08414 | −0.542070 | − | 0.840333i | \(-0.682359\pi\) | ||||
−0.542070 | + | 0.840333i | \(0.682359\pi\) | |||||||
\(548\) | 354.479 | 0.646859 | ||||||||
\(549\) | − | 219.486i | − | 0.399792i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 232.645i | − | 0.422223i | ||||||
\(552\) | − | 23.1999i | − | 0.0420288i | ||||||
\(553\) | −282.283 | + | 60.4312i | −0.510457 | + | 0.109279i | ||||
\(554\) | −70.7344 | −0.127679 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 66.3817i | 0.119391i | ||||||||
\(557\) | −836.159 | −1.50118 | −0.750591 | − | 0.660767i | \(-0.770231\pi\) | ||||
−0.750591 | + | 0.660767i | \(0.770231\pi\) | |||||||
\(558\) | − | 205.247i | − | 0.367826i | ||||||
\(559\) | 21.4752i | 0.0384171i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.4455 | −0.0471399 | ||||||||
\(562\) | 586.714 | 1.04397 | ||||||||
\(563\) | − | 894.630i | − | 1.58904i | −0.607238 | − | 0.794520i | \(-0.707722\pi\) | ||
0.607238 | − | 0.794520i | \(-0.292278\pi\) | |||||||
\(564\) | 121.476 | 0.215384 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 57.2706i | 0.101185i | ||||||||
\(567\) | −61.6041 | + | 13.1882i | −0.108649 | + | 0.0232597i | ||||
\(568\) | −111.288 | −0.195930 | ||||||||
\(569\) | 559.583 | 0.983450 | 0.491725 | − | 0.870751i | \(-0.336367\pi\) | ||||
0.491725 | + | 0.870751i | \(0.336367\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 439.360 | 0.769457 | 0.384729 | − | 0.923030i | \(-0.374295\pi\) | ||||
0.384729 | + | 0.923030i | \(0.374295\pi\) | |||||||
\(572\) | − | 24.2662i | − | 0.0424235i | ||||||
\(573\) | − | 535.265i | − | 0.934145i | ||||||
\(574\) | −154.828 | − | 723.226i | −0.269736 | − | 1.25998i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 704.688i | 1.22130i | 0.791902 | + | 0.610648i | \(0.209091\pi\) | ||||
−0.791902 | + | 0.610648i | \(0.790909\pi\) | |||||||
\(578\) | 399.166 | 0.690598 | ||||||||
\(579\) | 612.246i | 1.05742i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 184.961 | + | 863.978i | 0.318349 | + | 1.48705i | ||||
\(582\) | 10.4543 | 0.0179627 | ||||||||
\(583\) | 235.077 | 0.403219 | ||||||||
\(584\) | 33.4645i | 0.0573023i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.3381i | 0.0568910i | ||||||||
\(587\) | − | 144.103i | − | 0.245491i | −0.992438 | − | 0.122746i | \(-0.960830\pi\) | ||
0.992438 | − | 0.122746i | \(-0.0391699\pi\) | |||||||
\(588\) | −69.4916 | − | 154.864i | −0.118183 | − | 0.263374i | ||||
\(589\) | −696.581 | −1.18265 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 236.083i | − | 0.399464i | ||||||
\(592\) | −185.205 | −0.312847 | ||||||||
\(593\) | 612.101i | 1.03221i | 0.856525 | + | 0.516105i | \(0.172619\pi\) | ||||
−0.856525 | + | 0.516105i | \(0.827381\pi\) | |||||||
\(594\) | − | 43.1943i | − | 0.0727177i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −87.9186 | −0.147514 | ||||||||
\(597\) | −108.233 | −0.181294 | ||||||||
\(598\) | 13.8241i | 0.0231173i | ||||||||
\(599\) | 435.517 | 0.727074 | 0.363537 | − | 0.931580i | \(-0.381569\pi\) | ||||
0.363537 | + | 0.931580i | \(0.381569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 412.897i | 0.687017i | 0.939150 | + | 0.343508i | \(0.111615\pi\) | ||||
−0.939150 | + | 0.343508i | \(0.888385\pi\) | |||||||
\(602\) | −100.711 | + | 21.5602i | −0.167294 | + | 0.0358143i | ||||
\(603\) | 118.782 | 0.196985 | ||||||||
\(604\) | −365.504 | −0.605139 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 222.190 | 0.366651 | ||||||||
\(607\) | 868.480i | 1.43077i | 0.698728 | + | 0.715387i | \(0.253750\pi\) | ||||
−0.698728 | + | 0.715387i | \(0.746250\pi\) | |||||||
\(608\) | 81.4528i | 0.133968i | ||||||||
\(609\) | −41.0079 | − | 191.554i | −0.0673365 | − | 0.314538i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −72.3842 | −0.118468 | ||||||||
\(612\) | − | 15.5852i | − | 0.0254661i | ||||||
\(613\) | −320.085 | −0.522161 | −0.261080 | − | 0.965317i | \(-0.584079\pi\) | ||||
−0.261080 | + | 0.965317i | \(0.584079\pi\) | |||||||
\(614\) | − | 443.654i | − | 0.722564i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 113.800 | − | 24.3623i | 0.184740 | − | 0.0395492i | ||||
\(617\) | −287.002 | −0.465157 | −0.232578 | − | 0.972578i | \(-0.574716\pi\) | ||||
−0.232578 | + | 0.972578i | \(0.574716\pi\) | |||||||
\(618\) | −335.521 | −0.542915 | ||||||||
\(619\) | 461.836i | 0.746100i | 0.927811 | + | 0.373050i | \(0.121688\pi\) | ||||
−0.927811 | + | 0.373050i | \(0.878312\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.6072i | 0.0396251i | ||||||||
\(622\) | − | 482.518i | − | 0.775752i | ||||||
\(623\) | −134.993 | − | 630.570i | −0.216682 | − | 1.01215i | ||||
\(624\) | 14.3009 | 0.0229181 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 719.818i | 1.14987i | ||||||||
\(627\) | −146.596 | −0.233805 | ||||||||
\(628\) | − | 100.808i | − | 0.160523i | ||||||
\(629\) | − | 120.269i | − | 0.191207i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.3642 | −0.0211794 | −0.0105897 | − | 0.999944i | \(-0.503371\pi\) | ||||
−0.0105897 | + | 0.999944i | \(0.503371\pi\) | |||||||
\(632\) | 116.644 | 0.184563 | ||||||||
\(633\) | 327.301i | 0.517063i | ||||||||
\(634\) | 503.432 | 0.794057 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 138.539i | 0.217828i | ||||||||
\(637\) | 41.4080 | + | 92.2790i | 0.0650047 | + | 0.144865i | ||||
\(638\) | 134.310 | 0.210517 | ||||||||
\(639\) | 118.039 | 0.184724 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −248.329 | −0.387408 | −0.193704 | − | 0.981060i | \(-0.562050\pi\) | ||||
−0.193704 | + | 0.981060i | \(0.562050\pi\) | |||||||
\(642\) | − | 57.2558i | − | 0.0891835i | ||||||
\(643\) | − | 1084.03i | − | 1.68590i | −0.537991 | − | 0.842950i | \(-0.680817\pi\) | ||
0.537991 | − | 0.842950i | \(-0.319183\pi\) | |||||||
\(644\) | −64.8302 | + | 13.8789i | −0.100668 | + | 0.0215511i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −52.8942 | −0.0818795 | ||||||||
\(647\) | 1131.40i | 1.74868i | 0.485312 | + | 0.874341i | \(0.338706\pi\) | ||||
−0.485312 | + | 0.874341i | \(0.661294\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 353.605i | 0.544845i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −573.546 | + | 122.785i | −0.881023 | + | 0.188610i | ||||
\(652\) | −203.515 | −0.312140 | ||||||||
\(653\) | 239.818 | 0.367256 | 0.183628 | − | 0.982996i | \(-0.441216\pi\) | ||||
0.183628 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(654\) | 62.9207i | 0.0962091i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 298.849i | 0.455562i | ||||||||
\(657\) | − | 35.4945i | − | 0.0540251i | ||||||
\(658\) | −72.6709 | − | 339.456i | −0.110442 | − | 0.515891i | ||||
\(659\) | 340.662 | 0.516938 | 0.258469 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258469 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 88.1855i | 0.133412i | 0.997773 | + | 0.0667061i | \(0.0212490\pi\) | ||||
−0.997773 | + | 0.0667061i | \(0.978751\pi\) | |||||||
\(662\) | −804.637 | −1.21546 | ||||||||
\(663\) | 9.28678i | 0.0140072i | ||||||||
\(664\) | − | 357.010i | − | 0.537666i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 196.440 | 0.294955 | ||||||||
\(667\) | −76.5143 | −0.114714 | ||||||||
\(668\) | − | 259.431i | − | 0.388369i | ||||||
\(669\) | −457.939 | −0.684512 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 430.046i | − | 0.640903i | ||||||
\(672\) | 14.3575 | + | 67.0661i | 0.0213654 | + | 0.0998007i | ||||
\(673\) | 1258.19 | 1.86952 | 0.934759 | − | 0.355283i | \(-0.115616\pi\) | ||||
0.934759 | + | 0.355283i | \(0.115616\pi\) | |||||||
\(674\) | −413.857 | −0.614032 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 329.479 | 0.487394 | ||||||||
\(677\) | 1194.41i | 1.76427i | 0.470999 | + | 0.882134i | \(0.343893\pi\) | ||||
−0.470999 | + | 0.882134i | \(0.656107\pi\) | |||||||
\(678\) | − | 6.15047i | − | 0.00907149i | ||||||
\(679\) | −6.25408 | − | 29.2137i | −0.00921073 | − | 0.0430246i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.9471 | −0.0630647 | ||||||||
\(682\) | − | 402.147i | − | 0.589658i | ||||||
\(683\) | −890.365 | −1.30361 | −0.651804 | − | 0.758387i | \(-0.725988\pi\) | ||||
−0.651804 | + | 0.758387i | \(0.725988\pi\) | |||||||
\(684\) | − | 86.3938i | − | 0.126307i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −391.184 | + | 286.833i | −0.570239 | + | 0.418124i | ||||
\(687\) | 228.304 | 0.332320 | ||||||||
\(688\) | 41.6154 | 0.0604875 | ||||||||
\(689\) | − | 82.5511i | − | 0.119813i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 328.636i | − | 0.475595i | −0.971315 | − | 0.237798i | \(-0.923575\pi\) | ||
0.971315 | − | 0.237798i | \(-0.0764255\pi\) | |||||||
\(692\) | − | 160.527i | − | 0.231975i | ||||||
\(693\) | −120.703 | + | 25.8402i | −0.174175 | + | 0.0372874i | ||||
\(694\) | 248.328 | 0.357821 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 79.1531i | 0.113726i | ||||||||
\(697\) | −194.068 | −0.278433 | ||||||||
\(698\) | − | 638.855i | − | 0.915265i | ||||||
\(699\) | − | 252.721i | − | 0.361547i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 144.549 | 0.206204 | 0.103102 | − | 0.994671i | \(-0.467123\pi\) | ||||
0.103102 | + | 0.994671i | \(0.467123\pi\) | |||||||
\(702\) | −15.1684 | −0.0216074 | ||||||||
\(703\) | − | 666.691i | − | 0.948351i | ||||||
\(704\) | −47.0240 | −0.0667954 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 762.505i | 1.08004i | ||||||||
\(707\) | −132.921 | − | 620.894i | −0.188007 | − | 0.878209i | ||||
\(708\) | −208.391 | −0.294338 | ||||||||
\(709\) | −1014.70 | −1.43117 | −0.715585 | − | 0.698526i | \(-0.753840\pi\) | ||||
−0.715585 | + | 0.698526i | \(0.753840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −123.719 | −0.174008 | ||||||||
\(712\) | 260.562i | 0.365958i | ||||||||
\(713\) | 229.098i | 0.321315i | ||||||||
\(714\) | −43.5517 | + | 9.32356i | −0.0609967 | + | 0.0130582i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −291.598 | −0.407260 | ||||||||
\(717\) | 712.713i | 0.994020i | ||||||||
\(718\) | 235.432 | 0.327899 | ||||||||
\(719\) | 1364.28i | 1.89747i | 0.316076 | + | 0.948734i | \(0.397635\pi\) | ||||
−0.316076 | + | 0.948734i | \(0.602365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 200.719 | + | 937.588i | 0.278390 | + | 1.30040i | ||||
\(722\) | 217.322 | 0.301000 | ||||||||
\(723\) | −660.928 | −0.914147 | ||||||||
\(724\) | 646.123i | 0.892435i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 211.756i | 0.291675i | ||||||||
\(727\) | 121.107i | 0.166584i | 0.996525 | + | 0.0832922i | \(0.0265435\pi\) | ||||
−0.996525 | + | 0.0832922i | \(0.973457\pi\) | |||||||
\(728\) | −8.55524 | − | 39.9627i | −0.0117517 | − | 0.0548938i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.0244i | 0.0369690i | ||||||||
\(732\) | 253.440 | 0.346230 | ||||||||
\(733\) | 1064.94i | 1.45285i | 0.687245 | + | 0.726426i | \(0.258820\pi\) | ||||
−0.687245 | + | 0.726426i | \(0.741180\pi\) | |||||||
\(734\) | − | 182.781i | − | 0.249021i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.7889 | 0.0363980 | ||||||||
\(737\) | 232.734 | 0.315785 | ||||||||
\(738\) | − | 316.977i | − | 0.429508i | ||||||
\(739\) | 658.565 | 0.891156 | 0.445578 | − | 0.895243i | \(-0.352998\pi\) | ||||
0.445578 | + | 0.895243i | \(0.352998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.4795i | 0.0694730i | ||||||||
\(742\) | 387.135 | − | 82.8781i | 0.521745 | − | 0.111695i | ||||
\(743\) | −844.054 | −1.13601 | −0.568004 | − | 0.823026i | \(-0.692284\pi\) | ||||
−0.568004 | + | 0.823026i | \(0.692284\pi\) | |||||||
\(744\) | 236.999 | 0.318547 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −598.608 | −0.802424 | ||||||||
\(747\) | 378.666i | 0.506916i | ||||||||
\(748\) | − | 30.5366i | − | 0.0408244i | ||||||
\(749\) | −159.997 | + | 34.2522i | −0.213614 | + | 0.0457305i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 802.681 | 1.06882 | 0.534408 | − | 0.845227i | \(-0.320535\pi\) | ||||
0.534408 | + | 0.845227i | \(0.320535\pi\) | |||||||
\(752\) | 140.269i | 0.186528i | ||||||||
\(753\) | 410.064 | 0.544573 | ||||||||
\(754\) | − | 47.1650i | − | 0.0625531i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.2285 | − | 71.1343i | −0.0201435 | − | 0.0940930i | ||||
\(757\) | 207.749 | 0.274437 | 0.137219 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137219 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(758\) | 43.1440 | 0.0569182 | ||||||||
\(759\) | 48.2136i | 0.0635226i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 135.451i | 0.177991i | 0.996032 | + | 0.0889956i | \(0.0283657\pi\) | ||||
−0.996032 | + | 0.0889956i | \(0.971634\pi\) | |||||||
\(762\) | 47.8682i | 0.0628192i | ||||||||
\(763\) | 175.827 | − | 37.6411i | 0.230442 | − | 0.0493331i | ||||
\(764\) | 618.071 | 0.808993 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 520.264i | 0.679196i | ||||||||
\(767\) | 124.174 | 0.161896 | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | 12.5945i | 0.0163778i | 0.999966 | + | 0.00818890i | \(0.00260664\pi\) | ||||
−0.999966 | + | 0.00818890i | \(0.997393\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 324.847 | 0.421332 | ||||||||
\(772\) | −706.961 | −0.915752 | ||||||||
\(773\) | − | 614.951i | − | 0.795538i | −0.917486 | − | 0.397769i | \(-0.869785\pi\) | ||
0.917486 | − | 0.397769i | \(-0.130215\pi\) | |||||||
\(774\) | −44.1398 | −0.0570281 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.0716i | 0.0155562i | ||||||||
\(777\) | −117.516 | − | 548.936i | −0.151244 | − | 0.706481i | ||||
\(778\) | 825.343 | 1.06085 | ||||||||
\(779\) | −1075.78 | −1.38097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 231.278 | 0.296130 | ||||||||
\(782\) | 17.3963i | 0.0222459i | ||||||||
\(783\) | − | 83.9546i | − | 0.107222i | ||||||
\(784\) | 178.822 | − | 80.2420i | 0.228089 | − | 0.102350i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 111.654 | 0.142054 | ||||||||
\(787\) | 783.038i | 0.994966i | 0.867474 | + | 0.497483i | \(0.165742\pi\) | ||||
−0.867474 | + | 0.497483i | \(0.834258\pi\) | |||||||
\(788\) | 272.605 | 0.345946 | ||||||||
\(789\) | 290.122i | 0.367708i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.1870 | + | 3.67940i | −0.0217282 | + | 0.00465158i | ||||
\(792\) | 49.8765 | 0.0629753 | ||||||||
\(793\) | −151.018 | −0.190438 | ||||||||
\(794\) | 875.091i | 1.10213i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 124.976i | − | 0.157005i | ||||||
\(797\) | − | 50.5740i | − | 0.0634554i | −0.999497 | − | 0.0317277i | \(-0.989899\pi\) | ||
0.999497 | − | 0.0317277i | \(-0.0101009\pi\) | |||||||
\(798\) | −241.421 | + | 51.6834i | −0.302532 | + | 0.0647662i | ||||
\(799\) | −91.0884 | −0.114003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 276.367i | − | 0.345028i | ||||||
\(802\) | 816.773 | 1.01842 | ||||||||
\(803\) | − | 69.5455i | − | 0.0866071i | ||||||
\(804\) | 137.158i | 0.170594i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −141.221 | −0.175212 | ||||||||
\(807\) | −646.724 | −0.801393 | ||||||||
\(808\) | 256.563i | 0.317529i | ||||||||
\(809\) | 908.730 | 1.12328 | 0.561638 | − | 0.827383i | \(-0.310172\pi\) | ||||
0.561638 | + | 0.827383i | \(0.310172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 195.796i | 0.241426i | 0.992687 | + | 0.120713i | \(0.0385181\pi\) | ||||
−0.992687 | + | 0.120713i | \(0.961482\pi\) | |||||||
\(812\) | 221.187 | − | 47.3518i | 0.272398 | − | 0.0583151i | ||||
\(813\) | −684.693 | −0.842181 | ||||||||
\(814\) | 384.891 | 0.472839 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.9963 | 0.0220542 | ||||||||
\(817\) | 149.805i | 0.183359i | ||||||||
\(818\) | − | 690.458i | − | 0.844080i | ||||||
\(819\) | 9.07420 | + | 42.3869i | 0.0110796 | + | 0.0517544i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −239.589 | −0.291826 | −0.145913 | − | 0.989297i | \(-0.546612\pi\) | ||||
−0.145913 | + | 0.989297i | \(0.546612\pi\) | |||||||
\(822\) | − | 434.146i | − | 0.528158i | ||||||
\(823\) | 1493.19 | 1.81432 | 0.907162 | − | 0.420781i | \(-0.138244\pi\) | ||||
0.907162 | + | 0.420781i | \(0.138244\pi\) | |||||||
\(824\) | − | 387.427i | − | 0.470178i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 124.666 | + | 582.332i | 0.150927 | + | 0.705003i | ||||
\(827\) | 1031.14 | 1.24685 | 0.623424 | − | 0.781884i | \(-0.285741\pi\) | ||||
0.623424 | + | 0.781884i | \(0.285741\pi\) | |||||||
\(828\) | −28.4139 | −0.0343163 | ||||||||
\(829\) | 113.418i | 0.136814i | 0.997658 | + | 0.0684068i | \(0.0217916\pi\) | ||||
−0.997658 | + | 0.0684068i | \(0.978208\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 86.6316i | 0.104250i | ||||||||
\(832\) | 16.5133i | 0.0198477i | ||||||||
\(833\) | 52.1079 | + | 116.124i | 0.0625545 | + | 0.139405i | ||||
\(834\) | 81.3006 | 0.0974827 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 169.274i | − | 0.202481i | ||||||
\(837\) | −251.375 | −0.300329 | ||||||||
\(838\) | − | 185.755i | − | 0.221664i | ||||||
\(839\) | − | 252.998i | − | 0.301548i | −0.988568 | − | 0.150774i | \(-0.951823\pi\) | ||
0.988568 | − | 0.150774i | \(-0.0481765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −579.949 | −0.689595 | ||||||||
\(842\) | −787.419 | −0.935177 | ||||||||
\(843\) | − | 718.575i | − | 0.852402i | ||||||
\(844\) | −377.934 | −0.447790 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 148.778i | − | 0.175860i | ||||||
\(847\) | 591.736 | − | 126.679i | 0.698626 | − | 0.149562i | ||||
\(848\) | −159.971 | −0.188645 | ||||||||
\(849\) | 70.1418 | 0.0826170 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −219.267 | −0.257658 | ||||||||
\(852\) | 136.300i | 0.159976i | ||||||||
\(853\) | 911.188i | 1.06822i | 0.845416 | + | 0.534108i | \(0.179352\pi\) | ||||
−0.845416 | + | 0.534108i | \(0.820648\pi\) | |||||||
\(854\) | −151.616 | − | 708.219i | −0.177536 | − | 0.829296i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 66.1133 | 0.0772352 | ||||||||
\(857\) | 638.434i | 0.744963i | 0.928040 | + | 0.372482i | \(0.121493\pi\) | ||||
−0.928040 | + | 0.372482i | \(0.878507\pi\) | |||||||
\(858\) | −29.7199 | −0.0346386 | ||||||||
\(859\) | 644.249i | 0.749999i | 0.927025 | + | 0.374999i | \(0.122357\pi\) | ||||
−0.927025 | + | 0.374999i | \(0.877643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −885.767 | + | 189.625i | −1.02877 | + | 0.220239i | ||||
\(862\) | −236.710 | −0.274605 | ||||||||
\(863\) | −623.500 | −0.722480 | −0.361240 | − | 0.932473i | \(-0.617647\pi\) | ||||
−0.361240 | + | 0.932473i | \(0.617647\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 81.3779i | − | 0.0939699i | ||||||
\(867\) | − | 488.876i | − | 0.563871i | ||||||
\(868\) | −141.780 | − | 662.274i | −0.163341 | − | 0.762989i | ||||
\(869\) | −242.408 | −0.278950 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 81.7283i | − | 0.0938328i | ||||||
\(872\) | −72.6546 | −0.0833195 | ||||||||
\(873\) | − | 12.8038i | − | 0.0146665i | ||||||
\(874\) | 96.4331i | 0.110335i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 40.9855 | 0.0467871 | ||||||||
\(877\) | 204.837 | 0.233566 | 0.116783 | − | 0.993157i | \(-0.462742\pi\) | ||||
0.116783 | + | 0.993157i | \(0.462742\pi\) | |||||||
\(878\) | 1185.76i | 1.35052i | ||||||||
\(879\) | 40.8307 | 0.0464513 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1294.76i | 1.46964i | 0.678260 | + | 0.734822i | \(0.262734\pi\) | ||||
−0.678260 | + | 0.734822i | \(0.737266\pi\) | |||||||
\(882\) | −189.669 | + | 85.1095i | −0.215044 | + | 0.0964960i | ||||
\(883\) | 1600.29 | 1.81233 | 0.906165 | − | 0.422925i | \(-0.138997\pi\) | ||||
0.906165 | + | 0.422925i | \(0.138997\pi\) | |||||||
\(884\) | −10.7234 | −0.0121306 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 616.232 | 0.695521 | ||||||||
\(887\) | 822.386i | 0.927154i | 0.886057 | + | 0.463577i | \(0.153434\pi\) | ||||
−0.886057 | + | 0.463577i | \(0.846566\pi\) | |||||||
\(888\) | 226.829i | 0.255438i | ||||||||
\(889\) | 133.764 | − | 28.6362i | 0.150466 | − | 0.0322118i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −52.9020 | −0.0593737 | ||||||||
\(892\) | − | 528.782i | − | 0.592805i | ||||||
\(893\) | −504.931 | −0.565433 | ||||||||
\(894\) | 107.678i | 0.120445i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −77.4413 | + | 16.5787i | −0.0864300 | + | 0.0185030i | ||||
\(897\) | 16.9310 | 0.0188752 | ||||||||
\(898\) | 866.596 | 0.965028 | ||||||||
\(899\) | − | 781.633i | − | 0.869447i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 103.882i | − | 0.115297i | ||||||
\(902\) | − | 621.063i | − | 0.688540i | ||||||
\(903\) | 26.4058 | + | 123.345i | 0.0292423 | + | 0.136595i | ||||
\(904\) | 7.10195 | 0.00785614 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 447.649i | 0.494094i | ||||||||
\(907\) | 803.919 | 0.886350 | 0.443175 | − | 0.896435i | \(-0.353852\pi\) | ||||
0.443175 | + | 0.896435i | \(0.353852\pi\) | |||||||
\(908\) | − | 49.5910i | − | 0.0546157i | ||||||
\(909\) | − | 272.127i | − | 0.299369i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −604.804 | −0.663891 | −0.331945 | − | 0.943299i | \(-0.607705\pi\) | ||||
−0.331945 | + | 0.943299i | \(0.607705\pi\) | |||||||
\(912\) | 99.7589 | 0.109385 | ||||||||
\(913\) | 741.933i | 0.812632i | ||||||||
\(914\) | −4.59822 | −0.00503087 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 263.623i | 0.287798i | ||||||||
\(917\) | −66.7950 | − | 312.009i | −0.0728408 | − | 0.340250i | ||||
\(918\) | −19.0879 | −0.0207929 | ||||||||
\(919\) | 152.377 | 0.165807 | 0.0829035 | − | 0.996558i | \(-0.473581\pi\) | ||||
0.0829035 | + | 0.996558i | \(0.473581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −543.363 | −0.589971 | ||||||||
\(922\) | 937.246i | 1.01654i | ||||||||
\(923\) | − | 81.2169i | − | 0.0879923i | ||||||
\(924\) | −29.8376 | − | 139.376i | −0.0322918 | − | 0.150840i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 273.376 | 0.295222 | ||||||||
\(927\) | 410.928i | 0.443288i | ||||||||
\(928\) | −91.3982 | −0.0984894 | ||||||||
\(929\) | 756.423i | 0.814233i | 0.913376 | + | 0.407117i | \(0.133466\pi\) | ||||
−0.913376 | + | 0.407117i | \(0.866534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 288.850 | + | 643.712i | 0.310258 | + | 0.691420i | ||||
\(932\) | 291.817 | 0.313109 | ||||||||
\(933\) | −590.961 | −0.633399 | ||||||||
\(934\) | 499.382i | 0.534670i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 17.5149i | − | 0.0187126i | ||||||
\(937\) | − | 62.9589i | − | 0.0671920i | −0.999435 | − | 0.0335960i | \(-0.989304\pi\) | ||
0.999435 | − | 0.0335960i | \(-0.0106960\pi\) | |||||||
\(938\) | 383.277 | − | 82.0521i | 0.408611 | − | 0.0874755i | ||||
\(939\) | 881.594 | 0.938865 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 513.455i | 0.545648i | 0.962064 | + | 0.272824i | \(0.0879577\pi\) | ||||
−0.962064 | + | 0.272824i | \(0.912042\pi\) | |||||||
\(942\) | −123.465 | −0.131066 | ||||||||
\(943\) | 353.811i | 0.375197i | ||||||||
\(944\) | − | 240.629i | − | 0.254904i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −86.4845 | −0.0914212 | ||||||||
\(947\) | 1612.21 | 1.70243 | 0.851217 | − | 0.524813i | \(-0.175865\pi\) | ||||
0.851217 | + | 0.524813i | \(0.175865\pi\) | |||||||
\(948\) | − | 142.859i | − | 0.150695i | ||||||
\(949\) | −24.4221 | −0.0257345 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 616.576i | − | 0.648345i | ||||||
\(952\) | −10.7659 | − | 50.2891i | −0.0113087 | − | 0.0528247i | ||||
\(953\) | −1350.65 | −1.41726 | −0.708629 | − | 0.705582i | \(-0.750686\pi\) | ||||
−0.708629 | + | 0.705582i | \(0.750686\pi\) | |||||||
\(954\) | 169.674 | 0.177856 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −822.970 | −0.860847 | ||||||||
\(957\) | − | 164.495i | − | 0.171886i | ||||||
\(958\) | 860.920i | 0.898664i | ||||||||
\(959\) | −1213.19 | + | 259.719i | −1.26505 | + | 0.270823i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1379.35 | −1.43533 | ||||||||
\(962\) | − | 135.161i | − | 0.140500i | ||||||
\(963\) | −70.1237 | −0.0728180 | ||||||||
\(964\) | − | 763.174i | − | 0.791675i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.9981 | + | 79.4004i | 0.0175964 | + | 0.0821951i | ||||
\(967\) | −936.177 | −0.968125 | −0.484063 | − | 0.875033i | \(-0.660839\pi\) | ||||
−0.484063 | + | 0.875033i | \(0.660839\pi\) | |||||||
\(968\) | −244.515 | −0.252598 | ||||||||
\(969\) | 64.7819i | 0.0668544i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 135.578i | − | 0.139627i | −0.997560 | − | 0.0698133i | \(-0.977760\pi\) | ||
0.997560 | − | 0.0698133i | \(-0.0222404\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −48.6365 | − | 227.188i | −0.0499862 | − | 0.233492i | ||||
\(974\) | 261.944 | 0.268936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 292.648i | 0.299844i | ||||||||
\(977\) | −1726.37 | −1.76701 | −0.883506 | − | 0.468420i | \(-0.844823\pi\) | ||||
−0.883506 | + | 0.468420i | \(0.844823\pi\) | |||||||
\(978\) | 249.255i | 0.254861i | ||||||||
\(979\) | − | 541.496i | − | 0.553111i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 77.0619 | 0.0785544 | ||||||||
\(982\) | 1307.66 | 1.33163 | ||||||||
\(983\) | − | 73.5367i | − | 0.0748085i | −0.999300 | − | 0.0374042i | \(-0.988091\pi\) | ||
0.999300 | − | 0.0374042i | \(-0.0119089\pi\) | |||||||
\(984\) | 366.013 | 0.371965 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 59.3525i | − | 0.0601953i | ||||||
\(987\) | −415.747 | + | 89.0033i | −0.421223 | + | 0.0901756i | ||||
\(988\) | −59.4434 | −0.0601654 | ||||||||
\(989\) | 49.2690 | 0.0498170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1809.34 | 1.82578 | 0.912888 | − | 0.408209i | \(-0.133847\pi\) | ||||
0.912888 | + | 0.408209i | \(0.133847\pi\) | |||||||
\(992\) | 273.663i | 0.275870i | ||||||||
\(993\) | 985.474i | 0.992421i | ||||||||
\(994\) | 380.878 | − | 81.5386i | 0.383178 | − | 0.0820308i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −437.246 | −0.439002 | ||||||||
\(997\) | 1094.62i | 1.09792i | 0.835850 | + | 0.548958i | \(0.184975\pi\) | ||||
−0.835850 | + | 0.548958i | \(0.815025\pi\) | |||||||
\(998\) | −911.023 | −0.912849 | ||||||||
\(999\) | − | 240.589i | − | 0.240830i |
(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 | 1050.3.f.d.601.7 | yes | 12 | |
5.2 | odd | 4 | 1050.3.h.c.349.10 | 24 | |||
5.3 | odd | 4 | 1050.3.h.c.349.17 | 24 | |||
5.4 | even | 2 | 1050.3.f.c.601.6 | yes | 12 | ||
7.6 | odd | 2 | inner | 1050.3.f.d.601.10 | yes | 12 | |
35.13 | even | 4 | 1050.3.h.c.349.9 | 24 | |||
35.27 | even | 4 | 1050.3.h.c.349.18 | 24 | |||
35.34 | odd | 2 | 1050.3.f.c.601.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.f.c.601.3 | ✓ | 12 | 35.34 | odd | 2 | ||
1050.3.f.c.601.6 | yes | 12 | 5.4 | even | 2 | ||
1050.3.f.d.601.7 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.3.f.d.601.10 | yes | 12 | 7.6 | odd | 2 | inner | |
1050.3.h.c.349.9 | 24 | 35.13 | even | 4 | |||
1050.3.h.c.349.10 | 24 | 5.2 | odd | 4 | |||
1050.3.h.c.349.17 | 24 | 5.3 | odd | 4 | |||
1050.3.h.c.349.18 | 24 | 35.27 | even | 4 |