Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(349,1050)]
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, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.349");
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.h (of order \(2\), degree \(1\), not 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: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.18 | ||
Character | \(\chi\) | \(=\) | 1050.349 |
Dual form | 1050.3.h.c.349.17 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 1.46536 | − | 6.84490i | 0.209337 | − | 0.977844i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.87800 | −0.534363 | −0.267182 | − | 0.963646i | \(-0.586092\pi\) | ||||
−0.267182 | + | 0.963646i | \(0.586092\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | −2.06416 | −0.158781 | −0.0793906 | − | 0.996844i | \(-0.525297\pi\) | ||||
−0.0793906 | + | 0.996844i | \(0.525297\pi\) | |||||||
\(14\) | 9.68016 | + | 2.07233i | 0.691440 | + | 0.148024i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 2.59754 | 0.152796 | 0.0763982 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763982 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | 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 | ||||
\(22\) | − | 8.31274i | − | 0.377852i | ||||||
\(23\) | − | 4.73565i | − | 0.205898i | −0.994687 | − | 0.102949i | \(-0.967172\pi\) | ||
0.994687 | − | 0.102949i | \(-0.0328278\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 2.91916i | − | 0.112275i | ||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −2.93072 | + | 13.6898i | −0.104669 | + | 0.488922i | ||||
\(29\) | 16.1571 | 0.557140 | 0.278570 | − | 0.960416i | \(-0.410140\pi\) | ||||
0.278570 | + | 0.960416i | \(0.410140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 48.3772i | − | 1.56055i | −0.625434 | − | 0.780277i | \(-0.715078\pi\) | ||
0.625434 | − | 0.780277i | \(-0.284922\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −10.1810 | −0.308515 | ||||||||
\(34\) | 3.67347i | 0.108043i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | − | 46.3013i | − | 1.25139i | −0.780069 | − | 0.625694i | \(-0.784816\pi\) | ||
0.780069 | − | 0.625694i | \(-0.215184\pi\) | |||||||
\(38\) | −20.3632 | −0.535874 | ||||||||
\(39\) | −3.57522 | −0.0916724 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 74.7122i | − | 1.82225i | −0.412132 | − | 0.911124i | \(-0.635216\pi\) | ||
0.412132 | − | 0.911124i | \(-0.364784\pi\) | |||||||
\(42\) | 16.7665 | + | 3.58939i | 0.399203 | + | 0.0854616i | ||||
\(43\) | − | 10.4038i | − | 0.241950i | −0.992656 | − | 0.120975i | \(-0.961398\pi\) | ||
0.992656 | − | 0.120975i | \(-0.0386021\pi\) | |||||||
\(44\) | 11.7560 | 0.267182 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.69723 | 0.145592 | ||||||||
\(47\) | 35.0672 | 0.746111 | 0.373055 | − | 0.927809i | \(-0.378310\pi\) | ||||
0.373055 | + | 0.927809i | \(0.378310\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −44.7054 | − | 20.0605i | −0.912356 | − | 0.409398i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.49907 | 0.0882170 | ||||||||
\(52\) | 4.12831 | 0.0793906 | ||||||||
\(53\) | 39.9926i | 0.754578i | 0.926096 | + | 0.377289i | \(0.123144\pi\) | ||||
−0.926096 | + | 0.377289i | \(0.876856\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.3603 | − | 4.14467i | −0.345720 | − | 0.0740119i | ||||
\(57\) | 24.9397i | 0.437539i | ||||||||
\(58\) | 22.8495i | 0.393958i | ||||||||
\(59\) | − | 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 | \(-0.795291\pi\) | ||
0.800234 | − | 0.599688i | \(-0.204709\pi\) | |||||||
\(62\) | 68.4156 | 1.10348 | ||||||||
\(63\) | 4.39608 | − | 20.5347i | 0.0697791 | − | 0.325948i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 14.3981i | − | 0.218153i | ||||||
\(67\) | − | 39.5941i | − | 0.590956i | −0.955350 | − | 0.295478i | \(-0.904521\pi\) | ||
0.955350 | − | 0.295478i | \(-0.0954789\pi\) | |||||||
\(68\) | −5.19507 | −0.0763982 | ||||||||
\(69\) | − | 8.20239i | − | 0.118875i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −39.3463 | −0.554173 | −0.277087 | − | 0.960845i | \(-0.589369\pi\) | ||||
−0.277087 | + | 0.960845i | \(0.589369\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | −11.8315 | −0.162075 | −0.0810377 | − | 0.996711i | \(-0.525823\pi\) | ||||
−0.0810377 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(74\) | 65.4800 | 0.884864 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 28.7979i | − | 0.378920i | ||||||
\(77\) | −8.61339 | + | 40.2343i | −0.111862 | + | 0.522524i | ||||
\(78\) | − | 5.05613i | − | 0.0648222i | ||||||
\(79\) | −41.2398 | −0.522023 | −0.261012 | − | 0.965336i | \(-0.584056\pi\) | ||||
−0.261012 | + | 0.965336i | \(0.584056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 105.659 | 1.28852 | ||||||||
\(83\) | 126.222 | 1.52075 | 0.760374 | − | 0.649485i | \(-0.225016\pi\) | ||||
0.760374 | + | 0.649485i | \(0.225016\pi\) | |||||||
\(84\) | −5.07616 | + | 23.7114i | −0.0604304 | + | 0.282279i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.7133 | 0.171084 | ||||||||
\(87\) | 27.9849 | 0.321665 | ||||||||
\(88\) | 16.6255i | 0.188926i | ||||||||
\(89\) | 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 | ||||
\(92\) | 9.47131i | 0.102949i | ||||||||
\(93\) | − | 83.7917i | − | 0.900986i | ||||||
\(94\) | 49.5925i | 0.527580i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | 4.26795 | 0.0439995 | 0.0219997 | − | 0.999758i | \(-0.492997\pi\) | ||||
0.0219997 | + | 0.999758i | \(0.492997\pi\) | |||||||
\(98\) | 28.3698 | − | 63.2230i | 0.289488 | − | 0.645133i | ||||
\(99\) | −17.6340 | −0.178121 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 90.7089i | − | 0.898108i | −0.893505 | − | 0.449054i | \(-0.851761\pi\) | ||
0.893505 | − | 0.449054i | \(-0.148239\pi\) | |||||||
\(102\) | 6.36264i | 0.0623788i | ||||||||
\(103\) | 136.976 | 1.32986 | 0.664932 | − | 0.746904i | \(-0.268460\pi\) | ||||
0.664932 | + | 0.746904i | \(0.268460\pi\) | |||||||
\(104\) | 5.83832i | 0.0561377i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −56.5581 | −0.533567 | ||||||||
\(107\) | 23.3746i | 0.218454i | 0.994017 | + | 0.109227i | \(0.0348375\pi\) | ||||
−0.994017 | + | 0.109227i | \(0.965162\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | 25.6873 | 0.235663 | 0.117832 | − | 0.993034i | \(-0.462406\pi\) | ||||
0.117832 | + | 0.993034i | \(0.462406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 80.1962i | − | 0.722489i | ||||||
\(112\) | 5.86144 | − | 27.3796i | 0.0523343 | − | 0.244461i | ||||
\(113\) | − | 2.51092i | − | 0.0222205i | −0.999938 | − | 0.0111103i | \(-0.996463\pi\) | ||
0.999938 | − | 0.0111103i | \(-0.00353658\pi\) | |||||||
\(114\) | −35.2701 | −0.309387 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.3141 | −0.278570 | ||||||||
\(117\) | −6.19247 | −0.0529271 | ||||||||
\(118\) | 85.0753 | 0.720977 | ||||||||
\(119\) | 3.80633 | − | 17.7799i | 0.0319860 | − | 0.149411i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −86.4491 | −0.714456 | ||||||||
\(122\) | 103.467 | 0.848087 | ||||||||
\(123\) | − | 129.405i | − | 1.05208i | ||||||
\(124\) | 96.7543i | 0.780277i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 29.0405 | + | 6.21700i | 0.230480 | + | 0.0493413i | ||||
\(127\) | − | 19.5421i | − | 0.153875i | −0.997036 | − | 0.0769375i | \(-0.975486\pi\) | ||
0.997036 | − | 0.0769375i | \(-0.0245142\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | − | 18.0200i | − | 0.139690i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 45.5826i | − | 0.347959i | −0.984749 | − | 0.173980i | \(-0.944337\pi\) | ||
0.984749 | − | 0.173980i | \(-0.0556627\pi\) | |||||||
\(132\) | 20.3620 | 0.154257 | ||||||||
\(133\) | 98.5595 | + | 21.0997i | 0.741049 | + | 0.158644i | ||||
\(134\) | 55.9945 | 0.417869 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 7.34694i | − | 0.0540217i | ||||||
\(137\) | 177.239i | 1.29372i | 0.762610 | + | 0.646859i | \(0.223918\pi\) | ||||
−0.762610 | + | 0.646859i | \(0.776082\pi\) | |||||||
\(138\) | 11.5999 | 0.0840575 | ||||||||
\(139\) | 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 | ||||||||
\(142\) | − | 55.6441i | − | 0.391860i | ||||||
\(143\) | 12.1331 | 0.0848469 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 16.7323i | − | 0.114605i | ||||||
\(147\) | −77.4321 | − | 34.7458i | −0.526749 | − | 0.236366i | ||||
\(148\) | 92.6026i | 0.625694i | ||||||||
\(149\) | 43.9593 | 0.295029 | 0.147514 | − | 0.989060i | \(-0.452873\pi\) | ||||
0.147514 | + | 0.989060i | \(0.452873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −182.752 | −1.21028 | −0.605139 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605139 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(152\) | 40.7264 | 0.267937 | ||||||||
\(153\) | 7.79261 | 0.0509321 | ||||||||
\(154\) | −56.8999 | − | 12.1812i | −0.369480 | − | 0.0790985i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.15045 | 0.0458362 | ||||||||
\(157\) | −50.4042 | −0.321046 | −0.160523 | − | 0.987032i | \(-0.551318\pi\) | ||||
−0.160523 | + | 0.987032i | \(0.551318\pi\) | |||||||
\(158\) | − | 58.3219i | − | 0.369126i | ||||||
\(159\) | 69.2693i | 0.435656i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32.4151 | − | 6.93944i | −0.201336 | − | 0.0431021i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | 101.758i | 0.624281i | 0.950036 | + | 0.312140i | \(0.101046\pi\) | ||||
−0.950036 | + | 0.312140i | \(0.898954\pi\) | |||||||
\(164\) | 149.424i | 0.911124i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 178.505i | 1.07533i | ||||||||
\(167\) | −129.715 | −0.776738 | −0.388369 | − | 0.921504i | \(-0.626961\pi\) | ||||
−0.388369 | + | 0.921504i | \(0.626961\pi\) | |||||||
\(168\) | −33.5330 | − | 7.17877i | −0.199601 | − | 0.0427308i | ||||
\(169\) | −164.739 | −0.974789 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.1969i | 0.252613i | ||||||||
\(172\) | 20.8077i | 0.120975i | ||||||||
\(173\) | 80.2634 | 0.463950 | 0.231975 | − | 0.972722i | \(-0.425481\pi\) | ||||
0.231975 | + | 0.972722i | \(0.425481\pi\) | |||||||
\(174\) | 39.5766i | 0.227452i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −23.5120 | −0.133591 | ||||||||
\(177\) | − | 104.196i | − | 0.588676i | ||||||
\(178\) | −130.281 | −0.731915 | ||||||||
\(179\) | 145.799 | 0.814519 | 0.407260 | − | 0.913312i | \(-0.366484\pi\) | ||||
0.407260 | + | 0.913312i | \(0.366484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 323.062i | − | 1.78487i | −0.451175 | − | 0.892435i | \(-0.648995\pi\) | ||
0.451175 | − | 0.892435i | \(-0.351005\pi\) | |||||||
\(182\) | −19.9814 | − | 4.27762i | −0.109788 | − | 0.0235034i | ||||
\(183\) | − | 126.720i | − | 0.692460i | ||||||
\(184\) | −13.3945 | −0.0727959 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 118.499 | 0.637093 | ||||||||
\(187\) | −15.2683 | −0.0816488 | ||||||||
\(188\) | −70.1344 | −0.373055 | ||||||||
\(189\) | 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 | \(0.200013\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | 353.480i | 1.83150i | 0.401743 | + | 0.915752i | \(0.368404\pi\) | ||||
−0.401743 | + | 0.915752i | \(0.631596\pi\) | |||||||
\(194\) | 6.03579i | 0.0311123i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 89.4109 | + | 40.1210i | 0.456178 | + | 0.204699i | ||||
\(197\) | 136.303i | 0.691892i | 0.938254 | + | 0.345946i | \(0.112442\pi\) | ||||
−0.938254 | + | 0.345946i | \(0.887558\pi\) | |||||||
\(198\) | − | 24.9382i | − | 0.125951i | ||||||
\(199\) | − | 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 | ||||||
\(202\) | 128.282 | 0.635058 | ||||||||
\(203\) | 23.6759 | − | 110.594i | 0.116630 | − | 0.544796i | ||||
\(204\) | −8.99813 | −0.0441085 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 193.713i | 0.940356i | ||||||||
\(207\) | − | 14.2070i | − | 0.0686327i | ||||||
\(208\) | −8.25663 | −0.0396953 | ||||||||
\(209\) | − | 84.6371i | − | 0.404962i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −188.967 | −0.895579 | −0.447790 | − | 0.894139i | \(-0.647789\pi\) | ||||
−0.447790 | + | 0.894139i | \(0.647789\pi\) | |||||||
\(212\) | − | 79.9853i | − | 0.377289i | ||||||
\(213\) | −68.1498 | −0.319952 | ||||||||
\(214\) | −33.0566 | −0.154470 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −331.137 | − | 70.8900i | −1.52598 | − | 0.326682i | ||||
\(218\) | 36.3273i | 0.166639i | ||||||||
\(219\) | −20.4928 | −0.0935742 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.36172 | −0.0242612 | ||||||||
\(222\) | 113.415 | 0.510877 | ||||||||
\(223\) | 264.391 | 1.18561 | 0.592805 | − | 0.805346i | \(-0.298020\pi\) | ||||
0.592805 | + | 0.805346i | \(0.298020\pi\) | |||||||
\(224\) | 38.7206 | + | 8.28933i | 0.172860 | + | 0.0370059i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.55098 | 0.0157123 | ||||||||
\(227\) | −24.7955 | −0.109231 | −0.0546157 | − | 0.998507i | \(-0.517393\pi\) | ||||
−0.0546157 | + | 0.998507i | \(0.517393\pi\) | |||||||
\(228\) | − | 49.8795i | − | 0.218770i | ||||||
\(229\) | 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 | ||||
\(232\) | − | 45.6991i | − | 0.196979i | ||||||
\(233\) | − | 145.909i | − | 0.626217i | −0.949717 | − | 0.313109i | \(-0.898630\pi\) | ||
0.949717 | − | 0.313109i | \(-0.101370\pi\) | |||||||
\(234\) | − | 8.75747i | − | 0.0374251i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 120.315i | 0.509808i | ||||||||
\(237\) | −71.4295 | −0.301390 | ||||||||
\(238\) | 25.1446 | + | 5.38296i | 0.105649 | + | 0.0226175i | ||||
\(239\) | 411.485 | 1.72169 | 0.860847 | − | 0.508864i | \(-0.169934\pi\) | ||||
0.860847 | + | 0.508864i | \(0.169934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 381.587i | 1.58335i | 0.610943 | + | 0.791675i | \(0.290791\pi\) | ||||
−0.610943 | + | 0.791675i | \(0.709209\pi\) | |||||||
\(242\) | − | 122.258i | − | 0.505196i | ||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 146.324i | 0.599688i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 183.007 | 0.743930 | ||||||||
\(247\) | − | 29.7217i | − | 0.120331i | ||||||
\(248\) | −136.831 | −0.551739 | ||||||||
\(249\) | 218.623 | 0.878004 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 236.750i | − | 0.943229i | −0.881805 | − | 0.471614i | \(-0.843671\pi\) | ||
0.881805 | − | 0.471614i | \(-0.156329\pi\) | |||||||
\(252\) | −8.79216 | + | 41.0694i | −0.0348895 | + | 0.162974i | ||||
\(253\) | 27.8362i | 0.110024i | ||||||||
\(254\) | 27.6367 | 0.108806 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 187.550 | 0.729768 | 0.364884 | − | 0.931053i | \(-0.381109\pi\) | ||||
0.364884 | + | 0.931053i | \(0.381109\pi\) | |||||||
\(258\) | 25.4841 | 0.0987756 | ||||||||
\(259\) | −316.928 | − | 67.8481i | −1.22366 | − | 0.261962i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 48.4712 | 0.185713 | ||||||||
\(262\) | 64.4636 | 0.246044 | ||||||||
\(263\) | 167.502i | 0.636890i | 0.947941 | + | 0.318445i | \(0.103161\pi\) | ||||
−0.947941 | + | 0.318445i | \(0.896839\pi\) | |||||||
\(264\) | 28.7962i | 0.109076i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −29.8394 | + | 139.384i | −0.112178 | + | 0.524001i | ||||
\(267\) | 159.561i | 0.597606i | ||||||||
\(268\) | 79.1881i | 0.295478i | ||||||||
\(269\) | − | 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 | \(0.260177\pi\) | ||||
−0.684141 | + | 0.729350i | \(0.739823\pi\) | |||||||
\(272\) | 10.3901 | 0.0381991 | ||||||||
\(273\) | −5.23899 | + | 24.4721i | −0.0191904 | + | 0.0896413i | ||||
\(274\) | −250.654 | −0.914796 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 16.4048i | 0.0594376i | ||||||||
\(277\) | − | 50.0168i | − | 0.180566i | −0.995916 | − | 0.0902830i | \(-0.971223\pi\) | ||
0.995916 | − | 0.0902830i | \(-0.0287772\pi\) | |||||||
\(278\) | −46.9389 | −0.168845 | ||||||||
\(279\) | − | 145.132i | − | 0.520185i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 414.869 | 1.47640 | 0.738201 | − | 0.674580i | \(-0.235675\pi\) | ||||
0.738201 | + | 0.674580i | \(0.235675\pi\) | |||||||
\(282\) | 85.8968i | 0.304598i | ||||||||
\(283\) | −40.4964 | −0.143097 | −0.0715484 | − | 0.997437i | \(-0.522794\pi\) | ||||
−0.0715484 | + | 0.997437i | \(0.522794\pi\) | |||||||
\(284\) | 78.6926 | 0.277087 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.1588i | 0.0599958i | ||||||||
\(287\) | −511.398 | − | 109.480i | −1.78187 | − | 0.381464i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | −282.253 | −0.976653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.39230 | 0.0254031 | ||||||||
\(292\) | 23.6630 | 0.0810377 | ||||||||
\(293\) | −23.5736 | −0.0804560 | −0.0402280 | − | 0.999191i | \(-0.512808\pi\) | ||||
−0.0402280 | + | 0.999191i | \(0.512808\pi\) | |||||||
\(294\) | 49.1380 | − | 109.506i | 0.167136 | − | 0.372468i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −130.960 | −0.442432 | ||||||||
\(297\) | −30.5430 | −0.102838 | ||||||||
\(298\) | 62.1679i | 0.208617i | ||||||||
\(299\) | 9.77513i | 0.0326927i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −71.2133 | − | 15.2454i | −0.236589 | − | 0.0506491i | ||||
\(302\) | − | 258.450i | − | 0.855796i | ||||||
\(303\) | − | 157.112i | − | 0.518523i | ||||||
\(304\) | 57.5958i | 0.189460i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.0204i | 0.0360144i | ||||||||
\(307\) | −313.711 | −1.02186 | −0.510930 | − | 0.859622i | \(-0.670699\pi\) | ||||
−0.510930 | + | 0.859622i | \(0.670699\pi\) | |||||||
\(308\) | 17.2268 | − | 80.4687i | 0.0559311 | − | 0.261262i | ||||
\(309\) | 237.249 | 0.767798 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 341.192i | 1.09708i | 0.836125 | + | 0.548539i | \(0.184816\pi\) | ||||
−0.836125 | + | 0.548539i | \(0.815184\pi\) | |||||||
\(312\) | 10.1123i | 0.0324111i | ||||||||
\(313\) | −508.988 | −1.62616 | −0.813081 | − | 0.582151i | \(-0.802211\pi\) | ||||
−0.813081 | + | 0.582151i | \(0.802211\pi\) | |||||||
\(314\) | − | 71.2823i | − | 0.227014i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 82.4797 | 0.261012 | ||||||||
\(317\) | 355.980i | 1.12297i | 0.827488 | + | 0.561483i | \(0.189769\pi\) | ||||
−0.827488 | + | 0.561483i | \(0.810231\pi\) | |||||||
\(318\) | −97.9616 | −0.308055 | ||||||||
\(319\) | −94.9712 | −0.297715 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.4860i | 0.126124i | ||||||||
\(322\) | 9.81385 | − | 45.8419i | 0.0304778 | − | 0.142366i | ||||
\(323\) | 37.4018i | 0.115795i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −143.907 | −0.441433 | ||||||||
\(327\) | 44.4917 | 0.136060 | ||||||||
\(328\) | −211.318 | −0.644262 | ||||||||
\(329\) | 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 | \(0.829201\pi\) | |||||||
\(332\) | −252.444 | −0.760374 | ||||||||
\(333\) | − | 138.904i | − | 0.417129i | ||||||
\(334\) | − | 183.445i | − | 0.549237i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.1523 | − | 47.4229i | 0.0302152 | − | 0.141140i | ||||
\(337\) | − | 292.641i | − | 0.868372i | −0.900823 | − | 0.434186i | \(-0.857036\pi\) | ||
0.900823 | − | 0.434186i | \(-0.142964\pi\) | |||||||
\(338\) | − | 232.976i | − | 0.689280i | ||||||
\(339\) | − | 4.34904i | − | 0.0128290i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 284.361i | 0.833903i | ||||||||
\(342\) | −61.0896 | −0.178625 | ||||||||
\(343\) | −202.822 | + | 276.609i | −0.591317 | + | 0.806439i | ||||
\(344\) | −29.4265 | −0.0855422 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 113.510i | 0.328063i | ||||||||
\(347\) | 175.594i | 0.506036i | 0.967462 | + | 0.253018i | \(0.0814232\pi\) | ||||
−0.967462 | + | 0.253018i | \(0.918577\pi\) | |||||||
\(348\) | −55.9697 | −0.160833 | ||||||||
\(349\) | − | 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 | ||||||||
\(352\) | − | 33.2510i | − | 0.0944630i | ||||||
\(353\) | −539.172 | −1.52740 | −0.763700 | − | 0.645571i | \(-0.776619\pi\) | ||||
−0.763700 | + | 0.645571i | \(0.776619\pi\) | |||||||
\(354\) | 147.355 | 0.416256 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 184.245i | − | 0.517542i | ||||||
\(357\) | 6.59275 | − | 30.7957i | 0.0184671 | − | 0.0862624i | ||||
\(358\) | 206.191i | 0.575952i | ||||||||
\(359\) | −166.475 | −0.463720 | −0.231860 | − | 0.972749i | \(-0.574481\pi\) | ||||
−0.231860 | + | 0.972749i | \(0.574481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 153.670 | 0.425678 | ||||||||
\(362\) | 456.878 | 1.26209 | ||||||||
\(363\) | −149.734 | −0.412491 | ||||||||
\(364\) | 6.04947 | − | 28.2579i | 0.0166194 | − | 0.0776316i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 179.209 | 0.489643 | ||||||||
\(367\) | −129.246 | −0.352169 | −0.176084 | − | 0.984375i | \(-0.556343\pi\) | ||||
−0.176084 | + | 0.984375i | \(0.556343\pi\) | |||||||
\(368\) | − | 18.9426i | − | 0.0514745i | ||||||
\(369\) | − | 224.137i | − | 0.607416i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 273.746 | + | 58.6036i | 0.737859 | + | 0.157961i | ||||
\(372\) | 167.583i | 0.450493i | ||||||||
\(373\) | 423.280i | 1.13480i | 0.823443 | + | 0.567399i | \(0.192050\pi\) | ||||
−0.823443 | + | 0.567399i | \(0.807950\pi\) | |||||||
\(374\) | − | 21.5927i | − | 0.0577344i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 99.1850i | − | 0.263790i | ||||||
\(377\) | −33.3507 | −0.0884634 | ||||||||
\(378\) | 50.2996 | + | 10.7682i | 0.133068 | + | 0.0284872i | ||||
\(379\) | −30.5074 | −0.0804944 | −0.0402472 | − | 0.999190i | \(-0.512815\pi\) | ||||
−0.0402472 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 33.8479i | − | 0.0888398i | ||||||
\(382\) | 437.042i | 1.14409i | ||||||||
\(383\) | −367.882 | −0.960529 | −0.480264 | − | 0.877124i | \(-0.659459\pi\) | ||||
−0.480264 | + | 0.877124i | \(0.659459\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −499.897 | −1.29507 | ||||||||
\(387\) | − | 31.2115i | − | 0.0806500i | ||||||
\(388\) | −8.53590 | −0.0219997 | ||||||||
\(389\) | −583.606 | −1.50027 | −0.750136 | − | 0.661283i | \(-0.770012\pi\) | ||||
−0.750136 | + | 0.661283i | \(0.770012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.3010i | − | 0.0314605i | ||||||
\(392\) | −56.7397 | + | 126.446i | −0.144744 | + | 0.322567i | ||||
\(393\) | − | 78.9515i | − | 0.200894i | ||||||
\(394\) | −192.761 | −0.489241 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 35.2680 | 0.0890606 | ||||||||
\(397\) | 618.783 | 1.55865 | 0.779323 | − | 0.626622i | \(-0.215563\pi\) | ||||
0.779323 | + | 0.626622i | \(0.215563\pi\) | |||||||
\(398\) | 88.3715 | 0.222039 | ||||||||
\(399\) | 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 | \(0.244081\pi\) | |||||||
\(402\) | 96.9852 | 0.241257 | ||||||||
\(403\) | 99.8580i | 0.247787i | ||||||||
\(404\) | 181.418i | 0.449054i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 156.403 | + | 33.4828i | 0.385229 | + | 0.0824700i | ||||
\(407\) | 272.159i | 0.668696i | ||||||||
\(408\) | − | 12.7253i | − | 0.0311894i | ||||||
\(409\) | − | 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 | ||||||||
\(412\) | −273.952 | −0.664932 | ||||||||
\(413\) | −411.771 | − | 88.1522i | −0.997025 | − | 0.213444i | ||||
\(414\) | 20.0917 | 0.0485306 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 11.6766i | − | 0.0280688i | ||||||
\(417\) | 57.4882i | 0.137861i | ||||||||
\(418\) | 119.695 | 0.286351 | ||||||||
\(419\) | − | 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 | \(0.729982\pi\) | |||||||
\(422\) | − | 267.240i | − | 0.633270i | ||||||
\(423\) | 105.202 | 0.248704 | ||||||||
\(424\) | 113.116 | 0.266784 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 96.3784i | − | 0.226240i | ||||||
\(427\) | −500.787 | − | 107.209i | −1.17280 | − | 0.251074i | ||||
\(428\) | − | 46.7492i | − | 0.109227i | ||||||
\(429\) | 21.0152 | 0.0489864 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −167.379 | −0.388351 | −0.194175 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194175 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 57.5429 | 0.132894 | 0.0664468 | − | 0.997790i | \(-0.478834\pi\) | ||||
0.0664468 | + | 0.997790i | \(0.478834\pi\) | |||||||
\(434\) | 100.254 | − | 468.299i | 0.230999 | − | 1.07903i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −51.3746 | −0.117832 | ||||||||
\(437\) | 68.1885 | 0.156038 | ||||||||
\(438\) | − | 28.9811i | − | 0.0661670i | ||||||
\(439\) | 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 | ||||
\(442\) | − | 7.58262i | − | 0.0171553i | ||||||
\(443\) | − | 435.742i | − | 0.983616i | −0.870704 | − | 0.491808i | \(-0.836336\pi\) | ||
0.870704 | − | 0.491808i | \(-0.163664\pi\) | |||||||
\(444\) | 160.392i | 0.361244i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 373.905i | 0.838353i | ||||||||
\(447\) | 76.1398 | 0.170335 | ||||||||
\(448\) | −11.7229 | + | 54.7592i | −0.0261672 | + | 0.122230i | ||||
\(449\) | −612.776 | −1.36476 | −0.682378 | − | 0.730999i | \(-0.739054\pi\) | ||||
−0.682378 | + | 0.730999i | \(0.739054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 439.158i | 0.973743i | ||||||||
\(452\) | 5.02184i | 0.0111103i | ||||||||
\(453\) | −316.536 | −0.698754 | ||||||||
\(454\) | − | 35.0662i | − | 0.0772382i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 70.5402 | 0.154693 | ||||||||
\(457\) | − | 3.25143i | − | 0.00711473i | −0.999994 | − | 0.00355736i | \(-0.998868\pi\) | ||
0.999994 | − | 0.00355736i | \(-0.00113235\pi\) | |||||||
\(458\) | −186.409 | −0.407007 | ||||||||
\(459\) | 13.4972 | 0.0294057 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 662.733i | − | 1.43760i | −0.695218 | − | 0.718799i | \(-0.744692\pi\) | ||
0.695218 | − | 0.718799i | \(-0.255308\pi\) | |||||||
\(462\) | −98.5536 | − | 21.0984i | −0.213319 | − | 0.0456675i | ||||
\(463\) | − | 193.306i | − | 0.417507i | −0.977968 | − | 0.208754i | \(-0.933059\pi\) | ||
0.977968 | − | 0.208754i | \(-0.0669407\pi\) | |||||||
\(464\) | 64.6283 | 0.139285 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 206.346 | 0.442802 | ||||||||
\(467\) | 353.116 | 0.756138 | 0.378069 | − | 0.925777i | \(-0.376588\pi\) | ||||
0.378069 | + | 0.925777i | \(0.376588\pi\) | |||||||
\(468\) | 12.3849 | 0.0264635 | ||||||||
\(469\) | −271.018 | − | 58.0196i | −0.577863 | − | 0.123709i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −87.3026 | −0.185356 | ||||||||
\(472\) | −170.151 | −0.360489 | ||||||||
\(473\) | 61.1538i | 0.129289i | ||||||||
\(474\) | − | 101.017i | − | 0.213115i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.61266 | + | 35.5598i | −0.0159930 | + | 0.0747054i | ||||
\(477\) | 119.978i | 0.251526i | ||||||||
\(478\) | 581.927i | 1.21742i | ||||||||
\(479\) | 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 | ||||||||
\(482\) | −539.646 | −1.11960 | ||||||||
\(483\) | −56.1446 | − | 12.0195i | −0.116241 | − | 0.0248850i | ||||
\(484\) | 172.898 | 0.357228 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 185.222i | 0.380333i | 0.981752 | + | 0.190167i | \(0.0609028\pi\) | ||||
−0.981752 | + | 0.190167i | \(0.939097\pi\) | |||||||
\(488\) | −206.933 | −0.424044 | ||||||||
\(489\) | 176.250i | 0.360429i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 924.656 | 1.88321 | 0.941605 | − | 0.336720i | \(-0.109317\pi\) | ||||
0.941605 | + | 0.336720i | \(0.109317\pi\) | |||||||
\(492\) | 258.811i | 0.526038i | ||||||||
\(493\) | 41.9686 | 0.0851290 | ||||||||
\(494\) | 42.0328 | 0.0850867 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 193.509i | − | 0.390138i | ||||||
\(497\) | −57.6565 | + | 269.322i | −0.116009 | + | 0.541895i | ||||
\(498\) | 309.180i | 0.620843i | ||||||||
\(499\) | 644.190 | 1.29096 | 0.645481 | − | 0.763776i | \(-0.276657\pi\) | ||||
0.645481 | + | 0.763776i | \(0.276657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −224.674 | −0.448450 | ||||||||
\(502\) | 334.816 | 0.666963 | ||||||||
\(503\) | 774.419 | 1.53960 | 0.769800 | − | 0.638285i | \(-0.220356\pi\) | ||||
0.769800 | + | 0.638285i | \(0.220356\pi\) | |||||||
\(504\) | −58.0809 | − | 12.4340i | −0.115240 | − | 0.0246706i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −39.3663 | −0.0777990 | ||||||||
\(507\) | −285.337 | −0.562794 | ||||||||
\(508\) | 39.0842i | 0.0769375i | ||||||||
\(509\) | 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 | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 74.8192i | 0.145846i | ||||||||
\(514\) | 265.236i | 0.516024i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 36.0400i | 0.0698449i | ||||||||
\(517\) | −206.125 | −0.398694 | ||||||||
\(518\) | 95.9517 | − | 448.204i | 0.185235 | − | 0.865259i | ||||
\(519\) | 139.020 | 0.267862 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 572.162i | 1.09820i | 0.835757 | + | 0.549100i | \(0.185029\pi\) | ||||
−0.835757 | + | 0.549100i | \(0.814971\pi\) | |||||||
\(522\) | 68.5486i | 0.131319i | ||||||||
\(523\) | 85.2596 | 0.163020 | 0.0815102 | − | 0.996673i | \(-0.474026\pi\) | ||||
0.0815102 | + | 0.996673i | \(0.474026\pi\) | |||||||
\(524\) | 91.1653i | 0.173980i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −236.884 | −0.450349 | ||||||||
\(527\) | − | 125.661i | − | 0.238447i | ||||||
\(528\) | −40.7240 | −0.0771287 | ||||||||
\(529\) | 506.574 | 0.957606 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 180.472i | − | 0.339872i | ||||||
\(532\) | −197.119 | − | 42.1993i | −0.370524 | − | 0.0793221i | ||||
\(533\) | 154.218i | 0.289339i | ||||||||
\(534\) | −225.653 | −0.422571 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −111.989 | −0.208935 | ||||||||
\(537\) | 252.531 | 0.470263 | ||||||||
\(538\) | 528.048 | 0.981501 | ||||||||
\(539\) | 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 | \(0.603991\pi\) | |||||||
\(542\) | −559.049 | −1.03146 | ||||||||
\(543\) | − | 559.559i | − | 1.03050i | ||||||
\(544\) | 14.6939i | 0.0270108i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −34.6087 | − | 7.40905i | −0.0633859 | − | 0.0135697i | ||||
\(547\) | − | 593.025i | − | 1.08414i | −0.840333 | − | 0.542070i | \(-0.817641\pi\) | ||
0.840333 | − | 0.542070i | \(-0.182359\pi\) | |||||||
\(548\) | − | 354.479i | − | 0.646859i | ||||||
\(549\) | − | 219.486i | − | 0.399792i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 232.645i | 0.422223i | ||||||||
\(552\) | −23.1999 | −0.0420288 | ||||||||
\(553\) | −60.4312 | + | 282.283i | −0.109279 | + | 0.510457i | ||||
\(554\) | 70.7344 | 0.127679 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 66.3817i | − | 0.119391i | ||||||
\(557\) | − | 836.159i | − | 1.50118i | −0.660767 | − | 0.750591i | \(-0.729769\pi\) | ||
0.660767 | − | 0.750591i | \(-0.270231\pi\) | |||||||
\(558\) | 205.247 | 0.367826 | ||||||||
\(559\) | 21.4752i | 0.0384171i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.4455 | −0.0471399 | ||||||||
\(562\) | 586.714i | 1.04397i | ||||||||
\(563\) | 894.630 | 1.58904 | 0.794520 | − | 0.607238i | \(-0.207722\pi\) | ||||
0.794520 | + | 0.607238i | \(0.207722\pi\) | |||||||
\(564\) | −121.476 | −0.215384 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 57.2706i | − | 0.101185i | ||||||
\(567\) | 13.1882 | − | 61.6041i | 0.0232597 | − | 0.108649i | ||||
\(568\) | 111.288i | 0.195930i | ||||||||
\(569\) | −559.583 | −0.983450 | −0.491725 | − | 0.870751i | \(-0.663633\pi\) | ||||
−0.491725 | + | 0.870751i | \(0.663633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 439.360 | 0.769457 | 0.384729 | − | 0.923030i | \(-0.374295\pi\) | ||||
0.384729 | + | 0.923030i | \(0.374295\pi\) | |||||||
\(572\) | −24.2662 | −0.0424235 | ||||||||
\(573\) | 535.265 | 0.934145 | ||||||||
\(574\) | 154.828 | − | 723.226i | 0.269736 | − | 1.25998i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 704.688 | 1.22130 | 0.610648 | − | 0.791902i | \(-0.290909\pi\) | ||||
0.610648 | + | 0.791902i | \(0.290909\pi\) | |||||||
\(578\) | − | 399.166i | − | 0.690598i | ||||||
\(579\) | 612.246i | 1.05742i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 184.961 | − | 863.978i | 0.318349 | − | 1.48705i | ||||
\(582\) | 10.4543i | 0.0179627i | ||||||||
\(583\) | − | 235.077i | − | 0.403219i | ||||||
\(584\) | 33.4645i | 0.0573023i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 33.3381i | − | 0.0568910i | ||||||
\(587\) | −144.103 | −0.245491 | −0.122746 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122746 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(588\) | 154.864 | + | 69.4916i | 0.263374 | + | 0.118183i | ||||
\(589\) | 696.581 | 1.18265 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 236.083i | 0.399464i | ||||||||
\(592\) | − | 185.205i | − | 0.312847i | ||||||
\(593\) | −612.101 | −1.03221 | −0.516105 | − | 0.856525i | \(-0.672619\pi\) | ||||
−0.516105 | + | 0.856525i | \(0.672619\pi\) | |||||||
\(594\) | − | 43.1943i | − | 0.0727177i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −87.9186 | −0.147514 | ||||||||
\(597\) | − | 108.233i | − | 0.181294i | ||||||
\(598\) | −13.8241 | −0.0231173 | ||||||||
\(599\) | −435.517 | −0.727074 | −0.363537 | − | 0.931580i | \(-0.618431\pi\) | ||||
−0.363537 | + | 0.931580i | \(0.618431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 412.897i | − | 0.687017i | −0.939150 | − | 0.343508i | \(-0.888385\pi\) | ||
0.939150 | − | 0.343508i | \(-0.111615\pi\) | |||||||
\(602\) | 21.5602 | − | 100.711i | 0.0358143 | − | 0.167294i | ||||
\(603\) | − | 118.782i | − | 0.196985i | ||||||
\(604\) | 365.504 | 0.605139 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 222.190 | 0.366651 | ||||||||
\(607\) | 868.480 | 1.43077 | 0.715387 | − | 0.698728i | \(-0.246250\pi\) | ||||
0.715387 | + | 0.698728i | \(0.246250\pi\) | |||||||
\(608\) | −81.4528 | −0.133968 | ||||||||
\(609\) | 41.0079 | − | 191.554i | 0.0673365 | − | 0.314538i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −72.3842 | −0.118468 | ||||||||
\(612\) | −15.5852 | −0.0254661 | ||||||||
\(613\) | 320.085i | 0.522161i | 0.965317 | + | 0.261080i | \(0.0840788\pi\) | ||||
−0.965317 | + | 0.261080i | \(0.915921\pi\) | |||||||
\(614\) | − | 443.654i | − | 0.722564i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 113.800 | + | 24.3623i | 0.184740 | + | 0.0395492i | ||||
\(617\) | − | 287.002i | − | 0.465157i | −0.972578 | − | 0.232578i | \(-0.925284\pi\) | ||
0.972578 | − | 0.232578i | \(-0.0747162\pi\) | |||||||
\(618\) | 335.521i | 0.542915i | ||||||||
\(619\) | 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 | ||||||
\(622\) | −482.518 | −0.775752 | ||||||||
\(623\) | 630.570 | + | 134.993i | 1.01215 | + | 0.216682i | ||||
\(624\) | −14.3009 | −0.0229181 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 719.818i | − | 1.14987i | ||||||
\(627\) | − | 146.596i | − | 0.233805i | ||||||
\(628\) | 100.808 | 0.160523 | ||||||||
\(629\) | − | 120.269i | − | 0.191207i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.3642 | −0.0211794 | −0.0105897 | − | 0.999944i | \(-0.503371\pi\) | ||||
−0.0105897 | + | 0.999944i | \(0.503371\pi\) | |||||||
\(632\) | 116.644i | 0.184563i | ||||||||
\(633\) | −327.301 | −0.517063 | ||||||||
\(634\) | −503.432 | −0.794057 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 138.539i | − | 0.217828i | ||||||
\(637\) | 92.2790 | + | 41.4080i | 0.144865 | + | 0.0650047i | ||||
\(638\) | − | 134.310i | − | 0.210517i | ||||||
\(639\) | −118.039 | −0.184724 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −248.329 | −0.387408 | −0.193704 | − | 0.981060i | \(-0.562050\pi\) | ||||
−0.193704 | + | 0.981060i | \(0.562050\pi\) | |||||||
\(642\) | −57.2558 | −0.0891835 | ||||||||
\(643\) | 1084.03 | 1.68590 | 0.842950 | − | 0.537991i | \(-0.180817\pi\) | ||||
0.842950 | + | 0.537991i | \(0.180817\pi\) | |||||||
\(644\) | 64.8302 | + | 13.8789i | 0.100668 | + | 0.0215511i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −52.8942 | −0.0818795 | ||||||||
\(647\) | 1131.40 | 1.74868 | 0.874341 | − | 0.485312i | \(-0.161294\pi\) | ||||
0.874341 | + | 0.485312i | \(0.161294\pi\) | |||||||
\(648\) | − | 25.4558i | − | 0.0392837i | ||||||
\(649\) | 353.605i | 0.544845i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −573.546 | − | 122.785i | −0.881023 | − | 0.188610i | ||||
\(652\) | − | 203.515i | − | 0.312140i | ||||||
\(653\) | − | 239.818i | − | 0.367256i | −0.982996 | − | 0.183628i | \(-0.941216\pi\) | ||
0.982996 | − | 0.183628i | \(-0.0587843\pi\) | |||||||
\(654\) | 62.9207i | 0.0962091i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 298.849i | − | 0.455562i | ||||||
\(657\) | −35.4945 | −0.0540251 | ||||||||
\(658\) | 339.456 | + | 72.6709i | 0.515891 | + | 0.110442i | ||||
\(659\) | −340.662 | −0.516938 | −0.258469 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258469 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 88.1855i | − | 0.133412i | −0.997773 | − | 0.0667061i | \(-0.978751\pi\) | ||
0.997773 | − | 0.0667061i | \(-0.0212490\pi\) | |||||||
\(662\) | − | 804.637i | − | 1.21546i | ||||||
\(663\) | −9.28678 | −0.0140072 | ||||||||
\(664\) | − | 357.010i | − | 0.537666i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 196.440 | 0.294955 | ||||||||
\(667\) | − | 76.5143i | − | 0.114714i | ||||||
\(668\) | 259.431 | 0.388369 | ||||||||
\(669\) | 457.939 | 0.684512 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 430.046i | 0.640903i | ||||||||
\(672\) | 67.0661 | + | 14.3575i | 0.0998007 | + | 0.0213654i | ||||
\(673\) | − | 1258.19i | − | 1.86952i | −0.355283 | − | 0.934759i | \(-0.615616\pi\) | ||
0.355283 | − | 0.934759i | \(-0.384384\pi\) | |||||||
\(674\) | 413.857 | 0.614032 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 329.479 | 0.487394 | ||||||||
\(677\) | 1194.41 | 1.76427 | 0.882134 | − | 0.470999i | \(-0.156107\pi\) | ||||
0.882134 | + | 0.470999i | \(0.156107\pi\) | |||||||
\(678\) | 6.15047 | 0.00907149 | ||||||||
\(679\) | 6.25408 | − | 29.2137i | 0.00921073 | − | 0.0430246i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.9471 | −0.0630647 | ||||||||
\(682\) | −402.147 | −0.589658 | ||||||||
\(683\) | 890.365i | 1.30361i | 0.758387 | + | 0.651804i | \(0.225988\pi\) | ||||
−0.758387 | + | 0.651804i | \(0.774012\pi\) | |||||||
\(684\) | − | 86.3938i | − | 0.126307i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −391.184 | − | 286.833i | −0.570239 | − | 0.418124i | ||||
\(687\) | 228.304i | 0.332320i | ||||||||
\(688\) | − | 41.6154i | − | 0.0604875i | ||||||
\(689\) | − | 82.5511i | − | 0.119813i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 328.636i | 0.475595i | 0.971315 | + | 0.237798i | \(0.0764255\pi\) | ||||
−0.971315 | + | 0.237798i | \(0.923575\pi\) | |||||||
\(692\) | −160.527 | −0.231975 | ||||||||
\(693\) | −25.8402 | + | 120.703i | −0.0372874 | + | 0.174175i | ||||
\(694\) | −248.328 | −0.357821 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 79.1531i | − | 0.113726i | ||||||
\(697\) | − | 194.068i | − | 0.278433i | ||||||
\(698\) | 638.855 | 0.915265 | ||||||||
\(699\) | − | 252.721i | − | 0.361547i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 144.549 | 0.206204 | 0.103102 | − | 0.994671i | \(-0.467123\pi\) | ||||
0.103102 | + | 0.994671i | \(0.467123\pi\) | |||||||
\(702\) | − | 15.1684i | − | 0.0216074i | ||||||
\(703\) | 666.691 | 0.948351 | ||||||||
\(704\) | 47.0240 | 0.0667954 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 762.505i | − | 1.08004i | ||||||
\(707\) | −620.894 | − | 132.921i | −0.878209 | − | 0.188007i | ||||
\(708\) | 208.391i | 0.294338i | ||||||||
\(709\) | 1014.70 | 1.43117 | 0.715585 | − | 0.698526i | \(-0.246160\pi\) | ||||
0.715585 | + | 0.698526i | \(0.246160\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −123.719 | −0.174008 | ||||||||
\(712\) | 260.562 | 0.365958 | ||||||||
\(713\) | −229.098 | −0.321315 | ||||||||
\(714\) | 43.5517 | + | 9.32356i | 0.0609967 | + | 0.0130582i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −291.598 | −0.407260 | ||||||||
\(717\) | 712.713 | 0.994020 | ||||||||
\(718\) | − | 235.432i | − | 0.327899i | ||||||
\(719\) | 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 | ||||
\(722\) | 217.322i | 0.301000i | ||||||||
\(723\) | 660.928i | 0.914147i | ||||||||
\(724\) | 646.123i | 0.892435i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 211.756i | − | 0.291675i | ||||||
\(727\) | 121.107 | 0.166584 | 0.0832922 | − | 0.996525i | \(-0.473457\pi\) | ||||
0.0832922 | + | 0.996525i | \(0.473457\pi\) | |||||||
\(728\) | 39.9627 | + | 8.55524i | 0.0548938 | + | 0.0117517i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 27.0244i | − | 0.0369690i | ||||||
\(732\) | 253.440i | 0.346230i | ||||||||
\(733\) | −1064.94 | −1.45285 | −0.726426 | − | 0.687245i | \(-0.758820\pi\) | ||||
−0.726426 | + | 0.687245i | \(0.758820\pi\) | |||||||
\(734\) | − | 182.781i | − | 0.249021i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.7889 | 0.0363980 | ||||||||
\(737\) | 232.734i | 0.315785i | ||||||||
\(738\) | 316.977 | 0.429508 | ||||||||
\(739\) | −658.565 | −0.891156 | −0.445578 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445578 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 51.4795i | − | 0.0694730i | ||||||
\(742\) | −82.8781 | + | 387.135i | −0.111695 | + | 0.521745i | ||||
\(743\) | 844.054i | 1.13601i | 0.823026 | + | 0.568004i | \(0.192284\pi\) | ||||
−0.823026 | + | 0.568004i | \(0.807716\pi\) | |||||||
\(744\) | −236.999 | −0.318547 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −598.608 | −0.802424 | ||||||||
\(747\) | 378.666 | 0.506916 | ||||||||
\(748\) | 30.5366 | 0.0408244 | ||||||||
\(749\) | 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 | \(0.320535\pi\) | |||||||
\(752\) | 140.269 | 0.186528 | ||||||||
\(753\) | − | 410.064i | − | 0.544573i | ||||||
\(754\) | − | 47.1650i | − | 0.0625531i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.2285 | + | 71.1343i | −0.0201435 | + | 0.0940930i | ||||
\(757\) | 207.749i | 0.274437i | 0.990541 | + | 0.137219i | \(0.0438163\pi\) | ||||
−0.990541 | + | 0.137219i | \(0.956184\pi\) | |||||||
\(758\) | − | 43.1440i | − | 0.0569182i | ||||||
\(759\) | 48.2136i | 0.0635226i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 135.451i | − | 0.177991i | −0.996032 | − | 0.0889956i | \(-0.971634\pi\) | ||
0.996032 | − | 0.0889956i | \(-0.0283657\pi\) | |||||||
\(762\) | 47.8682 | 0.0628192 | ||||||||
\(763\) | 37.6411 | − | 175.827i | 0.0493331 | − | 0.230442i | ||||
\(764\) | −618.071 | −0.808993 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 520.264i | − | 0.679196i | ||||||
\(767\) | 124.174i | 0.161896i | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | − | 706.961i | − | 0.915752i | ||||||
\(773\) | 614.951 | 0.795538 | 0.397769 | − | 0.917486i | \(-0.369785\pi\) | ||||
0.397769 | + | 0.917486i | \(0.369785\pi\) | |||||||
\(774\) | 44.1398 | 0.0570281 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 12.0716i | − | 0.0155562i | ||||||
\(777\) | −548.936 | − | 117.516i | −0.706481 | − | 0.151244i | ||||
\(778\) | − | 825.343i | − | 1.06085i | ||||||
\(779\) | 1075.78 | 1.38097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 231.278 | 0.296130 | ||||||||
\(782\) | 17.3963 | 0.0222459 | ||||||||
\(783\) | 83.9546 | 0.107222 | ||||||||
\(784\) | −178.822 | − | 80.2420i | −0.228089 | − | 0.102350i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 111.654 | 0.142054 | ||||||||
\(787\) | 783.038 | 0.994966 | 0.497483 | − | 0.867474i | \(-0.334258\pi\) | ||||
0.497483 | + | 0.867474i | \(0.334258\pi\) | |||||||
\(788\) | − | 272.605i | − | 0.345946i | ||||||
\(789\) | 290.122i | 0.367708i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.1870 | − | 3.67940i | −0.0217282 | − | 0.00465158i | ||||
\(792\) | 49.8765i | 0.0629753i | ||||||||
\(793\) | 151.018i | 0.190438i | ||||||||
\(794\) | 875.091i | 1.10213i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 124.976i | 0.157005i | ||||||||
\(797\) | −50.5740 | −0.0634554 | −0.0317277 | − | 0.999497i | \(-0.510101\pi\) | ||||
−0.0317277 | + | 0.999497i | \(0.510101\pi\) | |||||||
\(798\) | −51.6834 | + | 241.421i | −0.0647662 | + | 0.302532i | ||||
\(799\) | 91.0884 | 0.114003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 276.367i | 0.345028i | ||||||||
\(802\) | 816.773i | 1.01842i | ||||||||
\(803\) | 69.5455 | 0.0866071 | ||||||||
\(804\) | 137.158i | 0.170594i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −141.221 | −0.175212 | ||||||||
\(807\) | − | 646.724i | − | 0.801393i | ||||||
\(808\) | −256.563 | −0.317529 | ||||||||
\(809\) | −908.730 | −1.12328 | −0.561638 | − | 0.827383i | \(-0.689828\pi\) | ||||
−0.561638 | + | 0.827383i | \(0.689828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 195.796i | − | 0.241426i | −0.992687 | − | 0.120713i | \(-0.961482\pi\) | ||
0.992687 | − | 0.120713i | \(-0.0385181\pi\) | |||||||
\(812\) | −47.3518 | + | 221.187i | −0.0583151 | + | 0.272398i | ||||
\(813\) | 684.693i | 0.842181i | ||||||||
\(814\) | −384.891 | −0.472839 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.9963 | 0.0220542 | ||||||||
\(817\) | 149.805 | 0.183359 | ||||||||
\(818\) | 690.458 | 0.844080 | ||||||||
\(819\) | −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 | \(0.546612\pi\) | |||||||
\(822\) | −434.146 | −0.528158 | ||||||||
\(823\) | − | 1493.19i | − | 1.81432i | −0.420781 | − | 0.907162i | \(-0.638244\pi\) | ||
0.420781 | − | 0.907162i | \(-0.361756\pi\) | |||||||
\(824\) | − | 387.427i | − | 0.470178i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 124.666 | − | 582.332i | 0.150927 | − | 0.705003i | ||||
\(827\) | 1031.14i | 1.24685i | 0.781884 | + | 0.623424i | \(0.214259\pi\) | ||||
−0.781884 | + | 0.623424i | \(0.785741\pi\) | |||||||
\(828\) | 28.4139i | 0.0343163i | ||||||||
\(829\) | 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 | ||||||
\(832\) | 16.5133 | 0.0198477 | ||||||||
\(833\) | −116.124 | − | 52.1079i | −0.139405 | − | 0.0625545i | ||||
\(834\) | −81.3006 | −0.0974827 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 169.274i | 0.202481i | ||||||||
\(837\) | − | 251.375i | − | 0.300329i | ||||||
\(838\) | 185.755 | 0.221664 | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | − | 787.419i | − | 0.935177i | ||||||
\(843\) | 718.575 | 0.852402 | ||||||||
\(844\) | 377.934 | 0.447790 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 148.778i | 0.175860i | ||||||||
\(847\) | −126.679 | + | 591.736i | −0.149562 | + | 0.698626i | ||||
\(848\) | 159.971i | 0.188645i | ||||||||
\(849\) | −70.1418 | −0.0826170 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −219.267 | −0.257658 | ||||||||
\(852\) | 136.300 | 0.159976 | ||||||||
\(853\) | −911.188 | −1.06822 | −0.534108 | − | 0.845416i | \(-0.679352\pi\) | ||||
−0.534108 | + | 0.845416i | \(0.679352\pi\) | |||||||
\(854\) | 151.616 | − | 708.219i | 0.177536 | − | 0.829296i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 66.1133 | 0.0772352 | ||||||||
\(857\) | 638.434 | 0.744963 | 0.372482 | − | 0.928040i | \(-0.378507\pi\) | ||||
0.372482 | + | 0.928040i | \(0.378507\pi\) | |||||||
\(858\) | 29.7199i | 0.0346386i | ||||||||
\(859\) | 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 | ||||
\(862\) | − | 236.710i | − | 0.274605i | ||||||
\(863\) | 623.500i | 0.722480i | 0.932473 | + | 0.361240i | \(0.117647\pi\) | ||||
−0.932473 | + | 0.361240i | \(0.882353\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 81.3779i | 0.0939699i | ||||||||
\(867\) | −488.876 | −0.563871 | ||||||||
\(868\) | 662.274 | + | 141.780i | 0.762989 | + | 0.163341i | ||||
\(869\) | 242.408 | 0.278950 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 81.7283i | 0.0938328i | ||||||||
\(872\) | − | 72.6546i | − | 0.0833195i | ||||||
\(873\) | 12.8038 | 0.0146665 | ||||||||
\(874\) | 96.4331i | 0.110335i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 40.9855 | 0.0467871 | ||||||||
\(877\) | 204.837i | 0.233566i | 0.993157 | + | 0.116783i | \(0.0372582\pi\) | ||||
−0.993157 | + | 0.116783i | \(0.962742\pi\) | |||||||
\(878\) | −1185.76 | −1.35052 | ||||||||
\(879\) | −40.8307 | −0.0464513 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1294.76i | − | 1.46964i | −0.678260 | − | 0.734822i | \(-0.737266\pi\) | ||
0.678260 | − | 0.734822i | \(-0.262734\pi\) | |||||||
\(882\) | 85.1095 | − | 189.669i | 0.0964960 | − | 0.215044i | ||||
\(883\) | − | 1600.29i | − | 1.81233i | −0.422925 | − | 0.906165i | \(-0.638997\pi\) | ||
0.422925 | − | 0.906165i | \(-0.361003\pi\) | |||||||
\(884\) | 10.7234 | 0.0121306 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 616.232 | 0.695521 | ||||||||
\(887\) | 822.386 | 0.927154 | 0.463577 | − | 0.886057i | \(-0.346566\pi\) | ||||
0.463577 | + | 0.886057i | \(0.346566\pi\) | |||||||
\(888\) | −226.829 | −0.255438 | ||||||||
\(889\) | −133.764 | − | 28.6362i | −0.150466 | − | 0.0322118i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −52.9020 | −0.0593737 | ||||||||
\(892\) | −528.782 | −0.592805 | ||||||||
\(893\) | 504.931i | 0.565433i | ||||||||
\(894\) | 107.678i | 0.120445i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −77.4413 | − | 16.5787i | −0.0864300 | − | 0.0185030i | ||||
\(897\) | 16.9310i | 0.0188752i | ||||||||
\(898\) | − | 866.596i | − | 0.965028i | ||||||
\(899\) | − | 781.633i | − | 0.869447i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 103.882i | 0.115297i | ||||||||
\(902\) | −621.063 | −0.688540 | ||||||||
\(903\) | −123.345 | − | 26.4058i | −0.136595 | − | 0.0292423i | ||||
\(904\) | −7.10195 | −0.00785614 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 447.649i | − | 0.494094i | ||||||
\(907\) | 803.919i | 0.886350i | 0.896435 | + | 0.443175i | \(0.146148\pi\) | ||||
−0.896435 | + | 0.443175i | \(0.853852\pi\) | |||||||
\(908\) | 49.5910 | 0.0546157 | ||||||||
\(909\) | − | 272.127i | − | 0.299369i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −604.804 | −0.663891 | −0.331945 | − | 0.943299i | \(-0.607705\pi\) | ||||
−0.331945 | + | 0.943299i | \(0.607705\pi\) | |||||||
\(912\) | 99.7589i | 0.109385i | ||||||||
\(913\) | −741.933 | −0.812632 | ||||||||
\(914\) | 4.59822 | 0.00503087 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 263.623i | − | 0.287798i | ||||||
\(917\) | −312.009 | − | 66.7950i | −0.340250 | − | 0.0728408i | ||||
\(918\) | 19.0879i | 0.0207929i | ||||||||
\(919\) | −152.377 | −0.165807 | −0.0829035 | − | 0.996558i | \(-0.526419\pi\) | ||||
−0.0829035 | + | 0.996558i | \(0.526419\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −543.363 | −0.589971 | ||||||||
\(922\) | 937.246 | 1.01654 | ||||||||
\(923\) | 81.2169 | 0.0879923 | ||||||||
\(924\) | 29.8376 | − | 139.376i | 0.0322918 | − | 0.150840i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 273.376 | 0.295222 | ||||||||
\(927\) | 410.928 | 0.443288 | ||||||||
\(928\) | 91.3982i | 0.0984894i | ||||||||
\(929\) | 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 | ||||
\(932\) | 291.817i | 0.313109i | ||||||||
\(933\) | 590.961i | 0.633399i | ||||||||
\(934\) | 499.382i | 0.534670i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.5149i | 0.0187126i | ||||||||
\(937\) | −62.9589 | −0.0671920 | −0.0335960 | − | 0.999435i | \(-0.510696\pi\) | ||||
−0.0335960 | + | 0.999435i | \(0.510696\pi\) | |||||||
\(938\) | 82.0521 | − | 383.277i | 0.0874755 | − | 0.408611i | ||||
\(939\) | −881.594 | −0.938865 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 513.455i | − | 0.545648i | −0.962064 | − | 0.272824i | \(-0.912042\pi\) | ||
0.962064 | − | 0.272824i | \(-0.0879577\pi\) | |||||||
\(942\) | − | 123.465i | − | 0.131066i | ||||||
\(943\) | −353.811 | −0.375197 | ||||||||
\(944\) | − | 240.629i | − | 0.254904i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −86.4845 | −0.0914212 | ||||||||
\(947\) | 1612.21i | 1.70243i | 0.524813 | + | 0.851217i | \(0.324135\pi\) | ||||
−0.524813 | + | 0.851217i | \(0.675865\pi\) | |||||||
\(948\) | 142.859 | 0.150695 | ||||||||
\(949\) | 24.4221 | 0.0257345 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 616.576i | 0.648345i | ||||||||
\(952\) | −50.2891 | − | 10.7659i | −0.0528247 | − | 0.0113087i | ||||
\(953\) | 1350.65i | 1.41726i | 0.705582 | + | 0.708629i | \(0.250686\pi\) | ||||
−0.705582 | + | 0.708629i | \(0.749314\pi\) | |||||||
\(954\) | −169.674 | −0.177856 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −822.970 | −0.860847 | ||||||||
\(957\) | −164.495 | −0.171886 | ||||||||
\(958\) | −860.920 | −0.898664 | ||||||||
\(959\) | 1213.19 | + | 259.719i | 1.26505 | + | 0.270823i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1379.35 | −1.43533 | ||||||||
\(962\) | −135.161 | −0.140500 | ||||||||
\(963\) | 70.1237i | 0.0728180i | ||||||||
\(964\) | − | 763.174i | − | 0.791675i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.9981 | − | 79.4004i | 0.0175964 | − | 0.0821951i | ||||
\(967\) | − | 936.177i | − | 0.968125i | −0.875033 | − | 0.484063i | \(-0.839161\pi\) | ||
0.875033 | − | 0.484063i | \(-0.160839\pi\) | |||||||
\(968\) | 244.515i | 0.252598i | ||||||||
\(969\) | 64.7819i | 0.0668544i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 135.578i | 0.139627i | 0.997560 | + | 0.0698133i | \(0.0222404\pi\) | ||||
−0.997560 | + | 0.0698133i | \(0.977760\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | 227.188 | + | 48.6365i | 0.233492 | + | 0.0499862i | ||||
\(974\) | −261.944 | −0.268936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 292.648i | − | 0.299844i | ||||||
\(977\) | − | 1726.37i | − | 1.76701i | −0.468420 | − | 0.883506i | \(-0.655177\pi\) | ||
0.468420 | − | 0.883506i | \(-0.344823\pi\) | |||||||
\(978\) | −249.255 | −0.254861 | ||||||||
\(979\) | − | 541.496i | − | 0.553111i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 77.0619 | 0.0785544 | ||||||||
\(982\) | 1307.66i | 1.33163i | ||||||||
\(983\) | 73.5367 | 0.0748085 | 0.0374042 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374042 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(984\) | −366.013 | −0.371965 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59.3525i | 0.0601953i | ||||||||
\(987\) | 89.0033 | − | 415.747i | 0.0901756 | − | 0.421223i | ||||
\(988\) | 59.4434i | 0.0601654i | ||||||||
\(989\) | −49.2690 | −0.0498170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1809.34 | 1.82578 | 0.912888 | − | 0.408209i | \(-0.133847\pi\) | ||||
0.912888 | + | 0.408209i | \(0.133847\pi\) | |||||||
\(992\) | 273.663 | 0.275870 | ||||||||
\(993\) | −985.474 | −0.992421 | ||||||||
\(994\) | −380.878 | − | 81.5386i | −0.383178 | − | 0.0820308i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −437.246 | −0.439002 | ||||||||
\(997\) | 1094.62 | 1.09792 | 0.548958 | − | 0.835850i | \(-0.315025\pi\) | ||||
0.548958 | + | 0.835850i | \(0.315025\pi\) | |||||||
\(998\) | 911.023i | 0.912849i | ||||||||
\(999\) | − | 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.h.c.349.18 | 24 | ||
5.2 | odd | 4 | 1050.3.f.c.601.3 | ✓ | 12 | ||
5.3 | odd | 4 | 1050.3.f.d.601.10 | yes | 12 | ||
5.4 | even | 2 | inner | 1050.3.h.c.349.9 | 24 | ||
7.6 | odd | 2 | inner | 1050.3.h.c.349.10 | 24 | ||
35.13 | even | 4 | 1050.3.f.d.601.7 | yes | 12 | ||
35.27 | even | 4 | 1050.3.f.c.601.6 | yes | 12 | ||
35.34 | odd | 2 | inner | 1050.3.h.c.349.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.f.c.601.3 | ✓ | 12 | 5.2 | odd | 4 | ||
1050.3.f.c.601.6 | yes | 12 | 35.27 | even | 4 | ||
1050.3.f.d.601.7 | yes | 12 | 35.13 | even | 4 | ||
1050.3.f.d.601.10 | yes | 12 | 5.3 | odd | 4 | ||
1050.3.h.c.349.9 | 24 | 5.4 | even | 2 | inner | ||
1050.3.h.c.349.10 | 24 | 7.6 | odd | 2 | inner | ||
1050.3.h.c.349.17 | 24 | 35.34 | odd | 2 | inner | ||
1050.3.h.c.349.18 | 24 | 1.1 | even | 1 | trivial |