Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(22,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 22.12 | ||
Character | \(\chi\) | \(=\) | 105.22 |
Dual form | 105.3.l.a.43.12 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74240 | + | 2.74240i | 1.37120 | + | 1.37120i | 0.858671 | + | 0.512527i | \(0.171291\pi\) |
0.512527 | + | 0.858671i | \(0.328709\pi\) | |||||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 11.0415i | 2.76037i | ||||||||
\(5\) | −0.683416 | − | 4.95307i | −0.136683 | − | 0.990615i | ||||
\(6\) | −6.71747 | −1.11958 | ||||||||
\(7\) | 1.87083 | + | 1.87083i | 0.267261 | + | 0.267261i | ||||
\(8\) | −19.3105 | + | 19.3105i | −2.41382 | + | 2.41382i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 11.7091 | − | 15.4575i | 1.17091 | − | 1.54575i | ||||
\(11\) | 10.9331 | 0.993917 | 0.496958 | − | 0.867774i | \(-0.334450\pi\) | ||||
0.496958 | + | 0.867774i | \(0.334450\pi\) | |||||||
\(12\) | −13.5230 | − | 13.5230i | −1.12692 | − | 1.12692i | ||||
\(13\) | 8.10523 | − | 8.10523i | 0.623479 | − | 0.623479i | −0.322940 | − | 0.946419i | \(-0.604671\pi\) |
0.946419 | + | 0.322940i | \(0.104671\pi\) | |||||||
\(14\) | 10.2611i | 0.732936i | ||||||||
\(15\) | 6.90326 | + | 5.22924i | 0.460217 | + | 0.348616i | ||||
\(16\) | −61.7483 | −3.85927 | ||||||||
\(17\) | −5.51018 | − | 5.51018i | −0.324128 | − | 0.324128i | 0.526220 | − | 0.850348i | \(-0.323609\pi\) |
−0.850348 | + | 0.526220i | \(0.823609\pi\) | |||||||
\(18\) | 8.22719 | − | 8.22719i | 0.457066 | − | 0.457066i | ||||
\(19\) | 12.1318i | 0.638513i | 0.947668 | + | 0.319257i | \(0.103433\pi\) | ||||
−0.947668 | + | 0.319257i | \(0.896567\pi\) | |||||||
\(20\) | 54.6893 | − | 7.54592i | 2.73446 | − | 0.377296i | ||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 29.9829 | + | 29.9829i | 1.36286 | + | 1.36286i | ||||
\(23\) | 24.3210 | − | 24.3210i | 1.05743 | − | 1.05743i | 0.0591858 | − | 0.998247i | \(-0.481150\pi\) |
0.998247 | − | 0.0591858i | \(-0.0188504\pi\) | |||||||
\(24\) | − | 47.3009i | − | 1.97087i | ||||||
\(25\) | −24.0659 | + | 6.77002i | −0.962635 | + | 0.270801i | ||||
\(26\) | 44.4555 | 1.70983 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −20.6567 | + | 20.6567i | −0.737740 | + | 0.737740i | ||||
\(29\) | 14.8012i | 0.510385i | 0.966890 | + | 0.255193i | \(0.0821389\pi\) | ||||
−0.966890 | + | 0.255193i | \(0.917861\pi\) | |||||||
\(30\) | 4.59083 | + | 33.2721i | 0.153028 | + | 1.10907i | ||||
\(31\) | −8.07276 | −0.260412 | −0.130206 | − | 0.991487i | \(-0.541564\pi\) | ||||
−0.130206 | + | 0.991487i | \(0.541564\pi\) | |||||||
\(32\) | −92.0962 | − | 92.0962i | −2.87801 | − | 2.87801i | ||||
\(33\) | −13.3902 | + | 13.3902i | −0.405765 | + | 0.405765i | ||||
\(34\) | − | 30.2222i | − | 0.888888i | ||||||
\(35\) | 7.98780 | − | 10.5449i | 0.228223 | − | 0.301283i | ||||
\(36\) | 33.1244 | 0.920123 | ||||||||
\(37\) | −34.6319 | − | 34.6319i | −0.935998 | − | 0.935998i | 0.0620735 | − | 0.998072i | \(-0.480229\pi\) |
−0.998072 | + | 0.0620735i | \(0.980229\pi\) | |||||||
\(38\) | −33.2701 | + | 33.2701i | −0.875528 | + | 0.875528i | ||||
\(39\) | 19.8537i | 0.509069i | ||||||||
\(40\) | 108.844 | + | 82.4493i | 2.72109 | + | 2.06123i | ||||
\(41\) | 32.0975 | 0.782866 | 0.391433 | − | 0.920207i | \(-0.371979\pi\) | ||||
0.391433 | + | 0.920207i | \(0.371979\pi\) | |||||||
\(42\) | −12.5672 | − | 12.5672i | −0.299220 | − | 0.299220i | ||||
\(43\) | −13.0663 | + | 13.0663i | −0.303868 | + | 0.303868i | −0.842525 | − | 0.538657i | \(-0.818932\pi\) |
0.538657 | + | 0.842525i | \(0.318932\pi\) | |||||||
\(44\) | 120.717i | 2.74358i | ||||||||
\(45\) | −14.8592 | + | 2.05025i | −0.330205 | + | 0.0455611i | ||||
\(46\) | 133.395 | 2.89990 | ||||||||
\(47\) | −54.1653 | − | 54.1653i | −1.15245 | − | 1.15245i | −0.986059 | − | 0.166394i | \(-0.946788\pi\) |
−0.166394 | − | 0.986059i | \(-0.553212\pi\) | |||||||
\(48\) | 75.6259 | − | 75.6259i | 1.57554 | − | 1.57554i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | −84.5643 | − | 47.4321i | −1.69129 | − | 0.948642i | ||||
\(51\) | 13.4971 | 0.264649 | ||||||||
\(52\) | 89.4937 | + | 89.4937i | 1.72103 | + | 1.72103i | ||||
\(53\) | 6.76541 | − | 6.76541i | 0.127649 | − | 0.127649i | −0.640396 | − | 0.768045i | \(-0.721230\pi\) |
0.768045 | + | 0.640396i | \(0.221230\pi\) | |||||||
\(54\) | 20.1524i | 0.373193i | ||||||||
\(55\) | −7.47185 | − | 54.1524i | −0.135852 | − | 0.984589i | ||||
\(56\) | −72.2534 | −1.29024 | ||||||||
\(57\) | −14.8583 | − | 14.8583i | −0.260672 | − | 0.260672i | ||||
\(58\) | −40.5907 | + | 40.5907i | −0.699839 | + | 0.699839i | ||||
\(59\) | − | 44.4162i | − | 0.752816i | −0.926454 | − | 0.376408i | \(-0.877159\pi\) | ||
0.926454 | − | 0.376408i | \(-0.122841\pi\) | |||||||
\(60\) | −57.7385 | + | 76.2222i | −0.962309 | + | 1.27037i | ||||
\(61\) | −84.4444 | −1.38433 | −0.692167 | − | 0.721737i | \(-0.743344\pi\) | ||||
−0.692167 | + | 0.721737i | \(0.743344\pi\) | |||||||
\(62\) | −22.1387 | − | 22.1387i | −0.357076 | − | 0.357076i | ||||
\(63\) | 5.61249 | − | 5.61249i | 0.0890871 | − | 0.0890871i | ||||
\(64\) | − | 258.136i | − | 4.03337i | ||||||
\(65\) | −45.6850 | − | 34.6066i | −0.702847 | − | 0.532409i | ||||
\(66\) | −73.4427 | −1.11277 | ||||||||
\(67\) | 0.661895 | + | 0.661895i | 0.00987903 | + | 0.00987903i | 0.712029 | − | 0.702150i | \(-0.247776\pi\) |
−0.702150 | + | 0.712029i | \(0.747776\pi\) | |||||||
\(68\) | 60.8405 | − | 60.8405i | 0.894713 | − | 0.894713i | ||||
\(69\) | 59.5739i | 0.863390i | ||||||||
\(70\) | 50.8240 | − | 7.01261i | 0.726058 | − | 0.100180i | ||||
\(71\) | 103.429 | 1.45675 | 0.728373 | − | 0.685181i | \(-0.240277\pi\) | ||||
0.728373 | + | 0.685181i | \(0.240277\pi\) | |||||||
\(72\) | 57.9316 | + | 57.9316i | 0.804605 | + | 0.804605i | ||||
\(73\) | −55.1974 | + | 55.1974i | −0.756129 | + | 0.756129i | −0.975616 | − | 0.219486i | \(-0.929562\pi\) |
0.219486 | + | 0.975616i | \(0.429562\pi\) | |||||||
\(74\) | − | 189.949i | − | 2.56688i | ||||||
\(75\) | 21.1830 | − | 37.7661i | 0.282440 | − | 0.503548i | ||||
\(76\) | −133.952 | −1.76253 | ||||||||
\(77\) | 20.4539 | + | 20.4539i | 0.265635 | + | 0.265635i | ||||
\(78\) | −54.4467 | + | 54.4467i | −0.698034 | + | 0.698034i | ||||
\(79\) | 68.8001i | 0.870887i | 0.900216 | + | 0.435444i | \(0.143408\pi\) | ||||
−0.900216 | + | 0.435444i | \(0.856592\pi\) | |||||||
\(80\) | 42.1998 | + | 305.844i | 0.527497 | + | 3.82305i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 88.0241 | + | 88.0241i | 1.07346 | + | 1.07346i | ||||
\(83\) | −71.4410 | + | 71.4410i | −0.860735 | + | 0.860735i | −0.991423 | − | 0.130688i | \(-0.958281\pi\) |
0.130688 | + | 0.991423i | \(0.458281\pi\) | |||||||
\(84\) | − | 50.5984i | − | 0.602362i | ||||||
\(85\) | −23.5266 | + | 31.0581i | −0.276783 | + | 0.365389i | ||||
\(86\) | −71.6660 | −0.833326 | ||||||||
\(87\) | −18.1277 | − | 18.1277i | −0.208364 | − | 0.208364i | ||||
\(88\) | −211.124 | + | 211.124i | −2.39913 | + | 2.39913i | ||||
\(89\) | 41.6575i | 0.468062i | 0.972229 | + | 0.234031i | \(0.0751917\pi\) | ||||
−0.972229 | + | 0.234031i | \(0.924808\pi\) | |||||||
\(90\) | −46.3725 | − | 35.1273i | −0.515250 | − | 0.390303i | ||||
\(91\) | 30.3270 | 0.333264 | ||||||||
\(92\) | 268.539 | + | 268.539i | 2.91890 | + | 2.91890i | ||||
\(93\) | 9.88708 | − | 9.88708i | 0.106313 | − | 0.106313i | ||||
\(94\) | − | 297.086i | − | 3.16048i | ||||||
\(95\) | 60.0895 | − | 8.29103i | 0.632521 | − | 0.0872740i | ||||
\(96\) | 225.589 | 2.34988 | ||||||||
\(97\) | 25.2508 | + | 25.2508i | 0.260318 | + | 0.260318i | 0.825183 | − | 0.564865i | \(-0.191072\pi\) |
−0.564865 | + | 0.825183i | \(0.691072\pi\) | |||||||
\(98\) | −19.1968 | + | 19.1968i | −0.195885 | + | 0.195885i | ||||
\(99\) | − | 32.7993i | − | 0.331306i | ||||||
\(100\) | −74.7510 | − | 265.723i | −0.747510 | − | 2.65723i | ||||
\(101\) | 53.7274 | 0.531955 | 0.265977 | − | 0.963979i | \(-0.414305\pi\) | ||||
0.265977 | + | 0.963979i | \(0.414305\pi\) | |||||||
\(102\) | 37.0145 | + | 37.0145i | 0.362887 | + | 0.362887i | ||||
\(103\) | 39.6796 | − | 39.6796i | 0.385239 | − | 0.385239i | −0.487746 | − | 0.872985i | \(-0.662181\pi\) |
0.872985 | + | 0.487746i | \(0.162181\pi\) | |||||||
\(104\) | 313.032i | 3.00993i | ||||||||
\(105\) | 3.13181 | + | 22.6978i | 0.0298267 | + | 0.216170i | ||||
\(106\) | 37.1069 | 0.350065 | ||||||||
\(107\) | −68.3716 | − | 68.3716i | −0.638987 | − | 0.638987i | 0.311318 | − | 0.950306i | \(-0.399229\pi\) |
−0.950306 | + | 0.311318i | \(0.899229\pi\) | |||||||
\(108\) | −40.5690 | + | 40.5690i | −0.375639 | + | 0.375639i | ||||
\(109\) | 135.475i | 1.24289i | 0.783458 | + | 0.621445i | \(0.213454\pi\) | ||||
−0.783458 | + | 0.621445i | \(0.786546\pi\) | |||||||
\(110\) | 128.017 | − | 168.998i | 1.16379 | − | 1.53635i | ||||
\(111\) | 84.8306 | 0.764239 | ||||||||
\(112\) | −115.520 | − | 115.520i | −1.03143 | − | 1.03143i | ||||
\(113\) | 6.34998 | − | 6.34998i | 0.0561945 | − | 0.0561945i | −0.678451 | − | 0.734646i | \(-0.737348\pi\) |
0.734646 | + | 0.678451i | \(0.237348\pi\) | |||||||
\(114\) | − | 81.4947i | − | 0.714866i | ||||||
\(115\) | −137.085 | − | 103.842i | −1.19204 | − | 0.902975i | ||||
\(116\) | −163.427 | −1.40885 | ||||||||
\(117\) | −24.3157 | − | 24.3157i | −0.207826 | − | 0.207826i | ||||
\(118\) | 121.807 | − | 121.807i | 1.03226 | − | 1.03226i | ||||
\(119\) | − | 20.6172i | − | 0.173254i | ||||||
\(120\) | −234.285 | + | 32.3262i | −1.95237 | + | 0.269385i | ||||
\(121\) | −1.46766 | −0.0121294 | ||||||||
\(122\) | −231.580 | − | 231.580i | −1.89820 | − | 1.89820i | ||||
\(123\) | −39.3113 | + | 39.3113i | −0.319604 | + | 0.319604i | ||||
\(124\) | − | 89.1352i | − | 0.718833i | ||||||
\(125\) | 49.9794 | + | 114.573i | 0.399835 | + | 0.916587i | ||||
\(126\) | 30.7833 | 0.244312 | ||||||||
\(127\) | 20.2819 | + | 20.2819i | 0.159700 | + | 0.159700i | 0.782434 | − | 0.622734i | \(-0.213978\pi\) |
−0.622734 | + | 0.782434i | \(0.713978\pi\) | |||||||
\(128\) | 339.525 | − | 339.525i | 2.65254 | − | 2.65254i | ||||
\(129\) | − | 32.0058i | − | 0.248107i | ||||||
\(130\) | −30.3816 | − | 220.191i | −0.233705 | − | 1.69378i | ||||
\(131\) | 77.7144 | 0.593240 | 0.296620 | − | 0.954996i | \(-0.404141\pi\) | ||||
0.296620 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(132\) | −147.848 | − | 147.848i | −1.12006 | − | 1.12006i | ||||
\(133\) | −22.6964 | + | 22.6964i | −0.170650 | + | 0.170650i | ||||
\(134\) | 3.63036i | 0.0270922i | ||||||||
\(135\) | 15.6877 | − | 20.7098i | 0.116205 | − | 0.153406i | ||||
\(136\) | 212.809 | 1.56477 | ||||||||
\(137\) | 146.870 | + | 146.870i | 1.07205 | + | 1.07205i | 0.997195 | + | 0.0748506i | \(0.0238480\pi\) |
0.0748506 | + | 0.997195i | \(0.476152\pi\) | |||||||
\(138\) | −163.375 | + | 163.375i | −1.18388 | + | 1.18388i | ||||
\(139\) | 146.322i | 1.05268i | 0.850275 | + | 0.526339i | \(0.176436\pi\) | ||||
−0.850275 | + | 0.526339i | \(0.823564\pi\) | |||||||
\(140\) | 116.431 | + | 88.1971i | 0.831653 | + | 0.629979i | ||||
\(141\) | 132.677 | 0.940974 | ||||||||
\(142\) | 283.643 | + | 283.643i | 1.99749 | + | 1.99749i | ||||
\(143\) | 88.6152 | − | 88.6152i | 0.619686 | − | 0.619686i | ||||
\(144\) | 185.245i | 1.28642i | ||||||||
\(145\) | 73.3113 | − | 10.1154i | 0.505595 | − | 0.0697611i | ||||
\(146\) | −302.746 | −2.07361 | ||||||||
\(147\) | −8.57321 | − | 8.57321i | −0.0583212 | − | 0.0583212i | ||||
\(148\) | 382.388 | − | 382.388i | 2.58370 | − | 2.58370i | ||||
\(149\) | − | 143.223i | − | 0.961228i | −0.876932 | − | 0.480614i | \(-0.840414\pi\) | ||
0.876932 | − | 0.480614i | \(-0.159586\pi\) | |||||||
\(150\) | 161.662 | − | 45.4774i | 1.07775 | − | 0.303183i | ||||
\(151\) | 204.429 | 1.35384 | 0.676919 | − | 0.736058i | \(-0.263315\pi\) | ||||
0.676919 | + | 0.736058i | \(0.263315\pi\) | |||||||
\(152\) | −234.270 | − | 234.270i | −1.54125 | − | 1.54125i | ||||
\(153\) | −16.5305 | + | 16.5305i | −0.108043 | + | 0.108043i | ||||
\(154\) | 112.186i | 0.728478i | ||||||||
\(155\) | 5.51706 | + | 39.9850i | 0.0355939 | + | 0.257968i | ||||
\(156\) | −219.214 | −1.40522 | ||||||||
\(157\) | −168.925 | − | 168.925i | −1.07595 | − | 1.07595i | −0.996868 | − | 0.0790870i | \(-0.974800\pi\) |
−0.0790870 | − | 0.996868i | \(-0.525200\pi\) | |||||||
\(158\) | −188.677 | + | 188.677i | −1.19416 | + | 1.19416i | ||||
\(159\) | 16.5718i | 0.104225i | ||||||||
\(160\) | −393.219 | + | 519.100i | −2.45762 | + | 3.24437i | ||||
\(161\) | 91.0007 | 0.565222 | ||||||||
\(162\) | −24.6816 | − | 24.6816i | −0.152355 | − | 0.152355i | ||||
\(163\) | 167.373 | − | 167.373i | 1.02683 | − | 1.02683i | 0.0271997 | − | 0.999630i | \(-0.491341\pi\) |
0.999630 | − | 0.0271997i | \(-0.00865900\pi\) | |||||||
\(164\) | 354.404i | 2.16100i | ||||||||
\(165\) | 75.4740 | + | 57.1717i | 0.457418 | + | 0.346495i | ||||
\(166\) | −391.839 | −2.36048 | ||||||||
\(167\) | 80.3381 | + | 80.3381i | 0.481066 | + | 0.481066i | 0.905472 | − | 0.424406i | \(-0.139517\pi\) |
−0.424406 | + | 0.905472i | \(0.639517\pi\) | |||||||
\(168\) | 88.4919 | − | 88.4919i | 0.526738 | − | 0.526738i | ||||
\(169\) | 37.6105i | 0.222547i | ||||||||
\(170\) | −149.693 | + | 20.6543i | −0.880545 | + | 0.121496i | ||||
\(171\) | 36.3953 | 0.212838 | ||||||||
\(172\) | −144.271 | − | 144.271i | −0.838787 | − | 0.838787i | ||||
\(173\) | −76.0306 | + | 76.0306i | −0.439483 | + | 0.439483i | −0.891838 | − | 0.452355i | \(-0.850584\pi\) |
0.452355 | + | 0.891838i | \(0.350584\pi\) | |||||||
\(174\) | − | 99.4265i | − | 0.571417i | ||||||
\(175\) | −57.6887 | − | 32.3576i | −0.329650 | − | 0.184901i | ||||
\(176\) | −675.099 | −3.83579 | ||||||||
\(177\) | 54.3985 | + | 54.3985i | 0.307336 | + | 0.307336i | ||||
\(178\) | −114.241 | + | 114.241i | −0.641806 | + | 0.641806i | ||||
\(179\) | − | 72.8033i | − | 0.406722i | −0.979104 | − | 0.203361i | \(-0.934813\pi\) | ||
0.979104 | − | 0.203361i | \(-0.0651865\pi\) | |||||||
\(180\) | −22.6378 | − | 164.068i | −0.125765 | − | 0.911488i | ||||
\(181\) | 116.021 | 0.641000 | 0.320500 | − | 0.947249i | \(-0.396149\pi\) | ||||
0.320500 | + | 0.947249i | \(0.396149\pi\) | |||||||
\(182\) | 83.1686 | + | 83.1686i | 0.456971 | + | 0.456971i | ||||
\(183\) | 103.423 | − | 103.423i | 0.565152 | − | 0.565152i | ||||
\(184\) | 939.301i | 5.10489i | ||||||||
\(185\) | −147.866 | + | 195.203i | −0.799278 | + | 1.05515i | ||||
\(186\) | 54.2286 | 0.291551 | ||||||||
\(187\) | −60.2432 | − | 60.2432i | −0.322156 | − | 0.322156i | ||||
\(188\) | 598.065 | − | 598.065i | 3.18120 | − | 3.18120i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 187.526 | + | 142.052i | 0.986981 | + | 0.747641i | ||||
\(191\) | −134.337 | −0.703336 | −0.351668 | − | 0.936125i | \(-0.614385\pi\) | ||||
−0.351668 | + | 0.936125i | \(0.614385\pi\) | |||||||
\(192\) | 316.150 | + | 316.150i | 1.64662 | + | 1.64662i | ||||
\(193\) | −5.00682 | + | 5.00682i | −0.0259421 | + | 0.0259421i | −0.719959 | − | 0.694017i | \(-0.755839\pi\) |
0.694017 | + | 0.719959i | \(0.255839\pi\) | |||||||
\(194\) | 138.495i | 0.713894i | ||||||||
\(195\) | 98.3367 | − | 13.5683i | 0.504291 | − | 0.0695811i | ||||
\(196\) | −77.2903 | −0.394338 | ||||||||
\(197\) | −207.221 | − | 207.221i | −1.05188 | − | 1.05188i | −0.998578 | − | 0.0533056i | \(-0.983024\pi\) |
−0.0533056 | − | 0.998578i | \(-0.516976\pi\) | |||||||
\(198\) | 89.9486 | − | 89.9486i | 0.454286 | − | 0.454286i | ||||
\(199\) | 115.701i | 0.581414i | 0.956812 | + | 0.290707i | \(0.0938905\pi\) | ||||
−0.956812 | + | 0.290707i | \(0.906109\pi\) | |||||||
\(200\) | 333.992 | − | 595.457i | 1.66996 | − | 2.97729i | ||||
\(201\) | −1.62130 | −0.00806619 | ||||||||
\(202\) | 147.342 | + | 147.342i | 0.729416 | + | 0.729416i | ||||
\(203\) | −27.6905 | + | 27.6905i | −0.136406 | + | 0.136406i | ||||
\(204\) | 149.028i | 0.730530i | ||||||||
\(205\) | −21.9360 | − | 158.981i | −0.107005 | − | 0.775519i | ||||
\(206\) | 217.634 | 1.05648 | ||||||||
\(207\) | −72.9629 | − | 72.9629i | −0.352478 | − | 0.352478i | ||||
\(208\) | −500.484 | + | 500.484i | −2.40617 | + | 2.40617i | ||||
\(209\) | 132.637i | 0.634629i | ||||||||
\(210\) | −53.6578 | + | 70.8351i | −0.255513 | + | 0.337310i | ||||
\(211\) | 66.2124 | 0.313803 | 0.156901 | − | 0.987614i | \(-0.449850\pi\) | ||||
0.156901 | + | 0.987614i | \(0.449850\pi\) | |||||||
\(212\) | 74.7001 | + | 74.7001i | 0.352359 | + | 0.352359i | ||||
\(213\) | −126.674 | + | 126.674i | −0.594714 | + | 0.594714i | ||||
\(214\) | − | 375.004i | − | 1.75236i | ||||||
\(215\) | 73.6482 | + | 55.7887i | 0.342550 | + | 0.259482i | ||||
\(216\) | −141.903 | −0.656957 | ||||||||
\(217\) | −15.1028 | − | 15.1028i | −0.0695980 | − | 0.0695980i | ||||
\(218\) | −371.526 | + | 371.526i | −1.70425 | + | 1.70425i | ||||
\(219\) | − | 135.206i | − | 0.617377i | ||||||
\(220\) | 597.922 | − | 82.5002i | 2.71783 | − | 0.375001i | ||||
\(221\) | −89.3225 | −0.404174 | ||||||||
\(222\) | 232.639 | + | 232.639i | 1.04792 | + | 1.04792i | ||||
\(223\) | −51.3641 | + | 51.3641i | −0.230332 | + | 0.230332i | −0.812831 | − | 0.582499i | \(-0.802075\pi\) |
0.582499 | + | 0.812831i | \(0.302075\pi\) | |||||||
\(224\) | − | 344.593i | − | 1.53836i | ||||||
\(225\) | 20.3101 | + | 72.1977i | 0.0902670 | + | 0.320878i | ||||
\(226\) | 34.8283 | 0.154108 | ||||||||
\(227\) | −106.842 | − | 106.842i | −0.470670 | − | 0.470670i | 0.431461 | − | 0.902132i | \(-0.357998\pi\) |
−0.902132 | + | 0.431461i | \(0.857998\pi\) | |||||||
\(228\) | 164.058 | − | 164.058i | 0.719551 | − | 0.719551i | ||||
\(229\) | − | 88.3402i | − | 0.385765i | −0.981222 | − | 0.192883i | \(-0.938216\pi\) | ||
0.981222 | − | 0.192883i | \(-0.0617836\pi\) | |||||||
\(230\) | −91.1646 | − | 660.717i | −0.396368 | − | 2.87268i | ||||
\(231\) | −50.1017 | −0.216890 | ||||||||
\(232\) | −285.818 | − | 285.818i | −1.23198 | − | 1.23198i | ||||
\(233\) | −260.550 | + | 260.550i | −1.11824 | + | 1.11824i | −0.126242 | + | 0.991999i | \(0.540292\pi\) |
−0.991999 | + | 0.126242i | \(0.959708\pi\) | |||||||
\(234\) | − | 133.367i | − | 0.569942i | ||||||
\(235\) | −231.267 | + | 305.302i | −0.984116 | + | 1.29916i | ||||
\(236\) | 490.420 | 2.07805 | ||||||||
\(237\) | −84.2626 | − | 84.2626i | −0.355538 | − | 0.355538i | ||||
\(238\) | 56.5405 | − | 56.5405i | 0.237565 | − | 0.237565i | ||||
\(239\) | 166.308i | 0.695851i | 0.937522 | + | 0.347925i | \(0.113114\pi\) | ||||
−0.937522 | + | 0.347925i | \(0.886886\pi\) | |||||||
\(240\) | −426.265 | − | 322.897i | −1.77610 | − | 1.34540i | ||||
\(241\) | −309.962 | −1.28615 | −0.643075 | − | 0.765804i | \(-0.722342\pi\) | ||||
−0.643075 | + | 0.765804i | \(0.722342\pi\) | |||||||
\(242\) | −4.02490 | − | 4.02490i | −0.0166318 | − | 0.0166318i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 932.391i | − | 3.82127i | ||||||
\(245\) | 34.6715 | − | 4.78391i | 0.141516 | − | 0.0195262i | ||||
\(246\) | −215.614 | −0.876480 | ||||||||
\(247\) | 98.3306 | + | 98.3306i | 0.398100 | + | 0.398100i | ||||
\(248\) | 155.889 | − | 155.889i | 0.628586 | − | 0.628586i | ||||
\(249\) | − | 174.994i | − | 0.702787i | ||||||
\(250\) | −177.142 | + | 451.269i | −0.708569 | + | 1.80508i | ||||
\(251\) | −403.709 | −1.60840 | −0.804201 | − | 0.594358i | \(-0.797406\pi\) | ||||
−0.804201 | + | 0.594358i | \(0.797406\pi\) | |||||||
\(252\) | 61.9701 | + | 61.9701i | 0.245913 | + | 0.245913i | ||||
\(253\) | 265.903 | − | 265.903i | 1.05100 | − | 1.05100i | ||||
\(254\) | 111.242i | 0.437960i | ||||||||
\(255\) | −9.22415 | − | 66.8522i | −0.0361731 | − | 0.262166i | ||||
\(256\) | 829.683 | 3.24095 | ||||||||
\(257\) | 109.310 | + | 109.310i | 0.425332 | + | 0.425332i | 0.887035 | − | 0.461703i | \(-0.152761\pi\) |
−0.461703 | + | 0.887035i | \(0.652761\pi\) | |||||||
\(258\) | 87.7726 | − | 87.7726i | 0.340204 | − | 0.340204i | ||||
\(259\) | − | 129.581i | − | 0.500312i | ||||||
\(260\) | 382.107 | − | 504.430i | 1.46964 | − | 1.94012i | ||||
\(261\) | 44.4035 | 0.170128 | ||||||||
\(262\) | 213.124 | + | 213.124i | 0.813449 | + | 0.813449i | ||||
\(263\) | 207.442 | − | 207.442i | 0.788754 | − | 0.788754i | −0.192536 | − | 0.981290i | \(-0.561671\pi\) |
0.981290 | + | 0.192536i | \(0.0616713\pi\) | |||||||
\(264\) | − | 517.145i | − | 1.95888i | ||||||
\(265\) | −38.1332 | − | 28.8860i | −0.143899 | − | 0.109004i | ||||
\(266\) | −124.485 | −0.467989 | ||||||||
\(267\) | −51.0198 | − | 51.0198i | −0.191086 | − | 0.191086i | ||||
\(268\) | −7.30830 | + | 7.30830i | −0.0272698 | + | 0.0272698i | ||||
\(269\) | − | 31.5174i | − | 0.117165i | −0.998283 | − | 0.0585825i | \(-0.981342\pi\) | ||
0.998283 | − | 0.0585825i | \(-0.0186581\pi\) | |||||||
\(270\) | 99.8164 | − | 13.7725i | 0.369690 | − | 0.0510092i | ||||
\(271\) | −92.6505 | −0.341884 | −0.170942 | − | 0.985281i | \(-0.554681\pi\) | ||||
−0.170942 | + | 0.985281i | \(0.554681\pi\) | |||||||
\(272\) | 340.244 | + | 340.244i | 1.25090 | + | 1.25090i | ||||
\(273\) | −37.1428 | + | 37.1428i | −0.136054 | + | 0.136054i | ||||
\(274\) | 805.553i | 2.93997i | ||||||||
\(275\) | −263.114 | + | 74.0172i | −0.956779 | + | 0.269154i | ||||
\(276\) | −657.784 | −2.38328 | ||||||||
\(277\) | −29.1214 | − | 29.1214i | −0.105131 | − | 0.105131i | 0.652585 | − | 0.757716i | \(-0.273685\pi\) |
−0.757716 | + | 0.652585i | \(0.773685\pi\) | |||||||
\(278\) | −401.274 | + | 401.274i | −1.44343 | + | 1.44343i | ||||
\(279\) | 24.2183i | 0.0868039i | ||||||||
\(280\) | 49.3791 | + | 357.876i | 0.176354 | + | 1.27813i | ||||
\(281\) | −186.605 | −0.664075 | −0.332038 | − | 0.943266i | \(-0.607736\pi\) | ||||
−0.332038 | + | 0.943266i | \(0.607736\pi\) | |||||||
\(282\) | 363.854 | + | 363.854i | 1.29026 | + | 1.29026i | ||||
\(283\) | 199.836 | − | 199.836i | 0.706135 | − | 0.706135i | −0.259585 | − | 0.965720i | \(-0.583586\pi\) |
0.965720 | + | 0.259585i | \(0.0835859\pi\) | |||||||
\(284\) | 1142.01i | 4.02115i | ||||||||
\(285\) | −63.4399 | + | 83.7487i | −0.222596 | + | 0.293855i | ||||
\(286\) | 486.036 | 1.69943 | ||||||||
\(287\) | 60.0489 | + | 60.0489i | 0.209230 | + | 0.209230i | ||||
\(288\) | −276.289 | + | 276.289i | −0.959336 | + | 0.959336i | ||||
\(289\) | − | 228.276i | − | 0.789882i | ||||||
\(290\) | 228.789 | + | 173.308i | 0.788928 | + | 0.597615i | ||||
\(291\) | −61.8516 | −0.212548 | ||||||||
\(292\) | −609.461 | − | 609.461i | −2.08720 | − | 2.08720i | ||||
\(293\) | −118.656 | + | 118.656i | −0.404969 | + | 0.404969i | −0.879980 | − | 0.475011i | \(-0.842444\pi\) |
0.475011 | + | 0.879980i | \(0.342444\pi\) | |||||||
\(294\) | − | 47.0223i | − | 0.159940i | ||||||
\(295\) | −219.996 | + | 30.3547i | −0.745751 | + | 0.102897i | ||||
\(296\) | 1337.52 | 4.51865 | ||||||||
\(297\) | 40.1707 | + | 40.1707i | 0.135255 | + | 0.135255i | ||||
\(298\) | 392.774 | − | 392.774i | 1.31803 | − | 1.31803i | ||||
\(299\) | − | 394.254i | − | 1.31857i | ||||||
\(300\) | 416.994 | + | 233.892i | 1.38998 | + | 0.779639i | ||||
\(301\) | −48.8897 | −0.162424 | ||||||||
\(302\) | 560.626 | + | 560.626i | 1.85638 | + | 1.85638i | ||||
\(303\) | −65.8024 | + | 65.8024i | −0.217170 | + | 0.217170i | ||||
\(304\) | − | 749.115i | − | 2.46419i | ||||||
\(305\) | 57.7107 | + | 418.259i | 0.189215 | + | 1.37134i | ||||
\(306\) | −90.6665 | −0.296296 | ||||||||
\(307\) | 315.593 | + | 315.593i | 1.02799 | + | 1.02799i | 0.999597 | + | 0.0283934i | \(0.00903913\pi\) |
0.0283934 | + | 0.999597i | \(0.490961\pi\) | |||||||
\(308\) | −225.842 | + | 225.842i | −0.733252 | + | 0.733252i | ||||
\(309\) | 97.1948i | 0.314546i | ||||||||
\(310\) | −94.5248 | + | 124.785i | −0.304919 | + | 0.402531i | ||||
\(311\) | 569.702 | 1.83184 | 0.915919 | − | 0.401362i | \(-0.131463\pi\) | ||||
0.915919 | + | 0.401362i | \(0.131463\pi\) | |||||||
\(312\) | −383.385 | − | 383.385i | −1.22880 | − | 1.22880i | ||||
\(313\) | 222.379 | − | 222.379i | 0.710475 | − | 0.710475i | −0.256160 | − | 0.966634i | \(-0.582457\pi\) |
0.966634 | + | 0.256160i | \(0.0824574\pi\) | |||||||
\(314\) | − | 926.518i | − | 2.95069i | ||||||
\(315\) | −31.6347 | − | 23.9634i | −0.100428 | − | 0.0760743i | ||||
\(316\) | −759.655 | −2.40397 | ||||||||
\(317\) | −183.394 | − | 183.394i | −0.578530 | − | 0.578530i | 0.355968 | − | 0.934498i | \(-0.384151\pi\) |
−0.934498 | + | 0.355968i | \(0.884151\pi\) | |||||||
\(318\) | −45.4464 | + | 45.4464i | −0.142913 | + | 0.142913i | ||||
\(319\) | 161.822i | 0.507281i | ||||||||
\(320\) | −1278.56 | + | 176.414i | −3.99551 | + | 0.551294i | ||||
\(321\) | 167.476 | 0.521731 | ||||||||
\(322\) | 249.560 | + | 249.560i | 0.775031 | + | 0.775031i | ||||
\(323\) | 66.8481 | − | 66.8481i | 0.206960 | − | 0.206960i | ||||
\(324\) | − | 99.3733i | − | 0.306708i | ||||||
\(325\) | −140.187 | + | 249.932i | −0.431344 | + | 0.769022i | ||||
\(326\) | 918.008 | 2.81597 | ||||||||
\(327\) | −165.922 | − | 165.922i | −0.507408 | − | 0.507408i | ||||
\(328\) | −619.819 | + | 619.819i | −1.88969 | + | 1.88969i | ||||
\(329\) | − | 202.668i | − | 0.616012i | ||||||
\(330\) | 50.1919 | + | 363.767i | 0.152097 | + | 1.10232i | ||||
\(331\) | −215.246 | −0.650291 | −0.325146 | − | 0.945664i | \(-0.605413\pi\) | ||||
−0.325146 | + | 0.945664i | \(0.605413\pi\) | |||||||
\(332\) | −788.814 | − | 788.814i | −2.37595 | − | 2.37595i | ||||
\(333\) | −103.896 | + | 103.896i | −0.311999 | + | 0.311999i | ||||
\(334\) | 440.638i | 1.31927i | ||||||||
\(335\) | 2.82606 | − | 3.73076i | 0.00843601 | − | 0.0111366i | ||||
\(336\) | 282.966 | 0.842161 | ||||||||
\(337\) | −401.198 | − | 401.198i | −1.19050 | − | 1.19050i | −0.976927 | − | 0.213571i | \(-0.931490\pi\) |
−0.213571 | − | 0.976927i | \(-0.568510\pi\) | |||||||
\(338\) | −103.143 | + | 103.143i | −0.305157 | + | 0.305157i | ||||
\(339\) | 15.5542i | 0.0458827i | ||||||||
\(340\) | −342.927 | − | 259.768i | −1.00861 | − | 0.764024i | ||||
\(341\) | −88.2602 | −0.258828 | ||||||||
\(342\) | 99.8102 | + | 99.8102i | 0.291843 | + | 0.291843i | ||||
\(343\) | −13.0958 | + | 13.0958i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 504.635i | − | 1.46696i | ||||||
\(345\) | 295.074 | − | 40.7138i | 0.855287 | − | 0.118011i | ||||
\(346\) | −417.012 | −1.20524 | ||||||||
\(347\) | −122.535 | − | 122.535i | −0.353126 | − | 0.353126i | 0.508145 | − | 0.861271i | \(-0.330331\pi\) |
−0.861271 | + | 0.508145i | \(0.830331\pi\) | |||||||
\(348\) | 200.156 | − | 200.156i | 0.575161 | − | 0.575161i | ||||
\(349\) | 18.8032i | 0.0538774i | 0.999637 | + | 0.0269387i | \(0.00857589\pi\) | ||||
−0.999637 | + | 0.0269387i | \(0.991424\pi\) | |||||||
\(350\) | −69.4679 | − | 246.943i | −0.198480 | − | 0.705550i | ||||
\(351\) | 59.5610 | 0.169690 | ||||||||
\(352\) | −1006.90 | − | 1006.90i | −2.86050 | − | 2.86050i | ||||
\(353\) | 242.291 | − | 242.291i | 0.686377 | − | 0.686377i | −0.275052 | − | 0.961429i | \(-0.588695\pi\) |
0.961429 | + | 0.275052i | \(0.0886951\pi\) | |||||||
\(354\) | 298.364i | 0.842837i | ||||||||
\(355\) | −70.6850 | − | 512.291i | −0.199113 | − | 1.44307i | ||||
\(356\) | −459.961 | −1.29202 | ||||||||
\(357\) | 25.2508 | + | 25.2508i | 0.0707305 | + | 0.0707305i | ||||
\(358\) | 199.655 | − | 199.655i | 0.557697 | − | 0.557697i | ||||
\(359\) | 228.420i | 0.636268i | 0.948046 | + | 0.318134i | \(0.103056\pi\) | ||||
−0.948046 | + | 0.318134i | \(0.896944\pi\) | |||||||
\(360\) | 247.348 | − | 326.531i | 0.687078 | − | 0.907030i | ||||
\(361\) | 213.821 | 0.592301 | ||||||||
\(362\) | 318.176 | + | 318.176i | 0.878938 | + | 0.878938i | ||||
\(363\) | 1.79750 | − | 1.79750i | 0.00495180 | − | 0.00495180i | ||||
\(364\) | 334.855i | 0.919931i | ||||||||
\(365\) | 311.120 | + | 235.674i | 0.852383 | + | 0.645682i | ||||
\(366\) | 567.253 | 1.54987 | ||||||||
\(367\) | 490.375 | + | 490.375i | 1.33617 | + | 1.33617i | 0.899735 | + | 0.436437i | \(0.143760\pi\) |
0.436437 | + | 0.899735i | \(0.356240\pi\) | |||||||
\(368\) | −1501.78 | + | 1501.78i | −4.08092 | + | 4.08092i | ||||
\(369\) | − | 96.2925i | − | 0.260955i | ||||||
\(370\) | −940.831 | + | 129.814i | −2.54279 | + | 0.350849i | ||||
\(371\) | 25.3138 | 0.0682314 | ||||||||
\(372\) | 109.168 | + | 109.168i | 0.293462 | + | 0.293462i | ||||
\(373\) | 282.198 | − | 282.198i | 0.756562 | − | 0.756562i | −0.219133 | − | 0.975695i | \(-0.570323\pi\) |
0.975695 | + | 0.219133i | \(0.0703229\pi\) | |||||||
\(374\) | − | 330.422i | − | 0.883480i | ||||||
\(375\) | −201.535 | − | 79.1111i | −0.537427 | − | 0.210963i | ||||
\(376\) | 2091.92 | 5.56362 | ||||||||
\(377\) | 119.967 | + | 119.967i | 0.318215 | + | 0.318215i | ||||
\(378\) | −37.7017 | + | 37.7017i | −0.0997400 | + | 0.0997400i | ||||
\(379\) | 389.970i | 1.02895i | 0.857507 | + | 0.514473i | \(0.172012\pi\) | ||||
−0.857507 | + | 0.514473i | \(0.827988\pi\) | |||||||
\(380\) | 91.5453 | + | 663.476i | 0.240909 | + | 1.74599i | ||||
\(381\) | −49.6802 | −0.130394 | ||||||||
\(382\) | −368.406 | − | 368.406i | −0.964412 | − | 0.964412i | ||||
\(383\) | 330.663 | − | 330.663i | 0.863350 | − | 0.863350i | −0.128376 | − | 0.991726i | \(-0.540976\pi\) |
0.991726 | + | 0.128376i | \(0.0409764\pi\) | |||||||
\(384\) | 831.663i | 2.16579i | ||||||||
\(385\) | 87.3313 | − | 115.288i | 0.226834 | − | 0.299450i | ||||
\(386\) | −27.4614 | −0.0711435 | ||||||||
\(387\) | 39.1989 | + | 39.1989i | 0.101289 | + | 0.101289i | ||||
\(388\) | −278.806 | + | 278.806i | −0.718572 | + | 0.718572i | ||||
\(389\) | − | 491.789i | − | 1.26424i | −0.774871 | − | 0.632119i | \(-0.782185\pi\) | ||
0.774871 | − | 0.632119i | \(-0.217815\pi\) | |||||||
\(390\) | 306.888 | + | 232.469i | 0.786892 | + | 0.596073i | ||||
\(391\) | −268.025 | −0.685487 | ||||||||
\(392\) | −135.174 | − | 135.174i | −0.344831 | − | 0.344831i | ||||
\(393\) | −95.1803 | + | 95.1803i | −0.242189 | + | 0.242189i | ||||
\(394\) | − | 1136.56i | − | 2.88468i | ||||||
\(395\) | 340.772 | − | 47.0191i | 0.862714 | − | 0.119036i | ||||
\(396\) | 362.152 | 0.914526 | ||||||||
\(397\) | 546.007 | + | 546.007i | 1.37533 | + | 1.37533i | 0.852333 | + | 0.523000i | \(0.175187\pi\) |
0.523000 | + | 0.852333i | \(0.324813\pi\) | |||||||
\(398\) | −317.299 | + | 317.299i | −0.797234 | + | 0.797234i | ||||
\(399\) | − | 55.5947i | − | 0.139335i | ||||||
\(400\) | 1486.03 | − | 418.037i | 3.71507 | − | 1.04509i | ||||
\(401\) | −631.914 | −1.57585 | −0.787923 | − | 0.615774i | \(-0.788843\pi\) | ||||
−0.787923 | + | 0.615774i | \(0.788843\pi\) | |||||||
\(402\) | −4.44626 | − | 4.44626i | −0.0110603 | − | 0.0110603i | ||||
\(403\) | −65.4316 | + | 65.4316i | −0.162361 | + | 0.162361i | ||||
\(404\) | 593.230i | 1.46839i | ||||||||
\(405\) | 6.15075 | + | 44.5777i | 0.0151870 | + | 0.110068i | ||||
\(406\) | −151.876 | −0.374080 | ||||||||
\(407\) | −378.634 | − | 378.634i | −0.930304 | − | 0.930304i | ||||
\(408\) | −260.636 | + | 260.636i | −0.638815 | + | 0.638815i | ||||
\(409\) | 72.2476i | 0.176645i | 0.996092 | + | 0.0883223i | \(0.0281505\pi\) | ||||
−0.996092 | + | 0.0883223i | \(0.971849\pi\) | |||||||
\(410\) | 375.833 | − | 496.147i | 0.916665 | − | 1.21011i | ||||
\(411\) | −359.757 | −0.875321 | ||||||||
\(412\) | 438.121 | + | 438.121i | 1.06340 | + | 1.06340i | ||||
\(413\) | 83.0950 | − | 83.0950i | 0.201199 | − | 0.201199i | ||||
\(414\) | − | 400.186i | − | 0.966633i | ||||||
\(415\) | 402.677 | + | 305.029i | 0.970305 | + | 0.735009i | ||||
\(416\) | −1492.92 | −3.58876 | ||||||||
\(417\) | −179.207 | − | 179.207i | −0.429754 | − | 0.429754i | ||||
\(418\) | −363.744 | + | 363.744i | −0.870202 | + | 0.870202i | ||||
\(419\) | − | 334.155i | − | 0.797506i | −0.917058 | − | 0.398753i | \(-0.869443\pi\) | ||
0.917058 | − | 0.398753i | \(-0.130557\pi\) | |||||||
\(420\) | −250.618 | + | 34.5798i | −0.596709 | + | 0.0823328i | ||||
\(421\) | 316.485 | 0.751746 | 0.375873 | − | 0.926671i | \(-0.377343\pi\) | ||||
0.375873 | + | 0.926671i | \(0.377343\pi\) | |||||||
\(422\) | 181.581 | + | 181.581i | 0.430286 | + | 0.430286i | ||||
\(423\) | −162.496 | + | 162.496i | −0.384151 | + | 0.384151i | ||||
\(424\) | 261.287i | 0.616243i | ||||||||
\(425\) | 169.911 | + | 95.3033i | 0.399791 | + | 0.224243i | ||||
\(426\) | −694.781 | −1.63094 | ||||||||
\(427\) | −157.981 | − | 157.981i | −0.369979 | − | 0.369979i | ||||
\(428\) | 754.924 | − | 754.924i | 1.76384 | − | 1.76384i | ||||
\(429\) | 217.062i | 0.505972i | ||||||||
\(430\) | 48.9777 | + | 354.967i | 0.113902 | + | 0.825505i | ||||
\(431\) | −431.234 | −1.00054 | −0.500272 | − | 0.865869i | \(-0.666766\pi\) | ||||
−0.500272 | + | 0.865869i | \(0.666766\pi\) | |||||||
\(432\) | −226.878 | − | 226.878i | −0.525180 | − | 0.525180i | ||||
\(433\) | −13.1404 | + | 13.1404i | −0.0303474 | + | 0.0303474i | −0.722118 | − | 0.691770i | \(-0.756831\pi\) |
0.691770 | + | 0.722118i | \(0.256831\pi\) | |||||||
\(434\) | − | 82.8355i | − | 0.190865i | ||||||
\(435\) | −77.3989 | + | 102.176i | −0.177929 | + | 0.234888i | ||||
\(436\) | −1495.84 | −3.43084 | ||||||||
\(437\) | 295.056 | + | 295.056i | 0.675185 | + | 0.675185i | ||||
\(438\) | 370.787 | − | 370.787i | 0.846546 | − | 0.846546i | ||||
\(439\) | 426.469i | 0.971457i | 0.874110 | + | 0.485728i | \(0.161446\pi\) | ||||
−0.874110 | + | 0.485728i | \(0.838554\pi\) | |||||||
\(440\) | 1190.00 | + | 901.425i | 2.70454 | + | 2.04869i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −244.958 | − | 244.958i | −0.554203 | − | 0.554203i | ||||
\(443\) | 334.181 | − | 334.181i | 0.754360 | − | 0.754360i | −0.220930 | − | 0.975290i | \(-0.570909\pi\) |
0.975290 | + | 0.220930i | \(0.0709093\pi\) | |||||||
\(444\) | 936.655i | 2.10958i | ||||||||
\(445\) | 206.333 | − | 28.4694i | 0.463669 | − | 0.0639762i | ||||
\(446\) | −281.721 | −0.631662 | ||||||||
\(447\) | 175.412 | + | 175.412i | 0.392420 | + | 0.392420i | ||||
\(448\) | 482.927 | − | 482.927i | 1.07796 | − | 1.07796i | ||||
\(449\) | − | 463.309i | − | 1.03187i | −0.856628 | − | 0.515935i | \(-0.827445\pi\) | ||
0.856628 | − | 0.515935i | \(-0.172555\pi\) | |||||||
\(450\) | −142.296 | + | 253.693i | −0.316214 | + | 0.563762i | ||||
\(451\) | 350.925 | 0.778104 | ||||||||
\(452\) | 70.1132 | + | 70.1132i | 0.155118 | + | 0.155118i | ||||
\(453\) | −250.374 | + | 250.374i | −0.552702 | + | 0.552702i | ||||
\(454\) | − | 586.007i | − | 1.29076i | ||||||
\(455\) | −20.7260 | − | 150.212i | −0.0455516 | − | 0.330136i | ||||
\(456\) | 573.843 | 1.25843 | ||||||||
\(457\) | 356.971 | + | 356.971i | 0.781119 | + | 0.781119i | 0.980020 | − | 0.198901i | \(-0.0637372\pi\) |
−0.198901 | + | 0.980020i | \(0.563737\pi\) | |||||||
\(458\) | 242.264 | − | 242.264i | 0.528960 | − | 0.528960i | ||||
\(459\) | − | 40.4914i | − | 0.0882165i | ||||||
\(460\) | 1146.57 | − | 1513.62i | 2.49255 | − | 3.29048i | ||||
\(461\) | −126.296 | −0.273960 | −0.136980 | − | 0.990574i | \(-0.543740\pi\) | ||||
−0.136980 | + | 0.990574i | \(0.543740\pi\) | |||||||
\(462\) | −137.399 | − | 137.399i | −0.297400 | − | 0.297400i | ||||
\(463\) | −40.0934 | + | 40.0934i | −0.0865947 | + | 0.0865947i | −0.749077 | − | 0.662483i | \(-0.769503\pi\) |
0.662483 | + | 0.749077i | \(0.269503\pi\) | |||||||
\(464\) | − | 913.947i | − | 1.96971i | ||||||
\(465\) | −55.7284 | − | 42.2144i | −0.119846 | − | 0.0907837i | ||||
\(466\) | −1429.06 | −3.06666 | ||||||||
\(467\) | 494.819 | + | 494.819i | 1.05957 | + | 1.05957i | 0.998110 | + | 0.0614589i | \(0.0195753\pi\) |
0.0614589 | + | 0.998110i | \(0.480425\pi\) | |||||||
\(468\) | 268.481 | − | 268.481i | 0.573678 | − | 0.573678i | ||||
\(469\) | 2.47658i | 0.00528056i | ||||||||
\(470\) | −1471.49 | + | 203.033i | −3.13082 | + | 0.431985i | ||||
\(471\) | 413.780 | 0.878513 | ||||||||
\(472\) | 857.699 | + | 857.699i | 1.81716 | + | 1.81716i | ||||
\(473\) | −142.855 | + | 142.855i | −0.302019 | + | 0.302019i | ||||
\(474\) | − | 462.163i | − | 0.975027i | ||||||
\(475\) | −82.1322 | − | 291.961i | −0.172910 | − | 0.614655i | ||||
\(476\) | 227.644 | 0.478244 | ||||||||
\(477\) | −20.2962 | − | 20.2962i | −0.0425497 | − | 0.0425497i | ||||
\(478\) | −456.083 | + | 456.083i | −0.954149 | + | 0.954149i | ||||
\(479\) | 854.008i | 1.78290i | 0.453121 | + | 0.891449i | \(0.350311\pi\) | ||||
−0.453121 | + | 0.891449i | \(0.649689\pi\) | |||||||
\(480\) | −154.171 | − | 1117.36i | −0.321190 | − | 2.32783i | ||||
\(481\) | −561.399 | −1.16715 | ||||||||
\(482\) | −850.039 | − | 850.039i | −1.76357 | − | 1.76357i | ||||
\(483\) | −111.453 | + | 111.453i | −0.230751 | + | 0.230751i | ||||
\(484\) | − | 16.2051i | − | 0.0334816i | ||||||
\(485\) | 107.812 | − | 142.326i | 0.222293 | − | 0.293455i | ||||
\(486\) | 60.4572 | 0.124398 | ||||||||
\(487\) | 401.669 | + | 401.669i | 0.824782 | + | 0.824782i | 0.986790 | − | 0.162007i | \(-0.0517968\pi\) |
−0.162007 | + | 0.986790i | \(0.551797\pi\) | |||||||
\(488\) | 1630.66 | − | 1630.66i | 3.34153 | − | 3.34153i | ||||
\(489\) | 409.979i | 0.838403i | ||||||||
\(490\) | 108.202 | + | 81.9637i | 0.220821 | + | 0.167273i | ||||
\(491\) | −250.314 | −0.509805 | −0.254903 | − | 0.966967i | \(-0.582043\pi\) | ||||
−0.254903 | + | 0.966967i | \(0.582043\pi\) | |||||||
\(492\) | −434.054 | − | 434.054i | −0.882224 | − | 0.882224i | ||||
\(493\) | 81.5571 | − | 81.5571i | 0.165430 | − | 0.165430i | ||||
\(494\) | 539.323i | 1.09175i | ||||||||
\(495\) | −162.457 | + | 22.4155i | −0.328196 | + | 0.0452839i | ||||
\(496\) | 498.480 | 1.00500 | ||||||||
\(497\) | 193.498 | + | 193.498i | 0.389332 | + | 0.389332i | ||||
\(498\) | 479.903 | − | 479.903i | 0.963661 | − | 0.963661i | ||||
\(499\) | 293.789i | 0.588756i | 0.955689 | + | 0.294378i | \(0.0951125\pi\) | ||||
−0.955689 | + | 0.294378i | \(0.904888\pi\) | |||||||
\(500\) | −1265.06 | + | 551.847i | −2.53012 | + | 1.10369i | ||||
\(501\) | −196.787 | −0.392789 | ||||||||
\(502\) | −1107.13 | − | 1107.13i | −2.20544 | − | 2.20544i | ||||
\(503\) | −301.845 | + | 301.845i | −0.600090 | + | 0.600090i | −0.940336 | − | 0.340246i | \(-0.889490\pi\) |
0.340246 | + | 0.940336i | \(0.389490\pi\) | |||||||
\(504\) | 216.760i | 0.430079i | ||||||||
\(505\) | −36.7182 | − | 266.116i | −0.0727093 | − | 0.526962i | ||||
\(506\) | 1458.42 | 2.88226 | ||||||||
\(507\) | −46.0633 | − | 46.0633i | −0.0908546 | − | 0.0908546i | ||||
\(508\) | −223.942 | + | 223.942i | −0.440830 | + | 0.440830i | ||||
\(509\) | − | 495.550i | − | 0.973575i | −0.873520 | − | 0.486787i | \(-0.838169\pi\) | ||
0.873520 | − | 0.486787i | \(-0.161831\pi\) | |||||||
\(510\) | 158.039 | − | 208.632i | 0.309881 | − | 0.409082i | ||||
\(511\) | −206.530 | −0.404168 | ||||||||
\(512\) | 917.219 | + | 917.219i | 1.79144 | + | 1.79144i | ||||
\(513\) | −44.5749 | + | 44.5749i | −0.0868906 | + | 0.0868906i | ||||
\(514\) | 599.544i | 1.16643i | ||||||||
\(515\) | −223.654 | − | 169.418i | −0.434279 | − | 0.328968i | ||||
\(516\) | 353.391 | 0.684867 | ||||||||
\(517\) | −592.194 | − | 592.194i | −1.14544 | − | 1.14544i | ||||
\(518\) | 355.362 | − | 355.362i | 0.686027 | − | 0.686027i | ||||
\(519\) | − | 186.236i | − | 0.358837i | ||||||
\(520\) | 1550.47 | − | 213.931i | 2.98168 | − | 0.411407i | ||||
\(521\) | 375.437 | 0.720609 | 0.360304 | − | 0.932835i | \(-0.382673\pi\) | ||||
0.360304 | + | 0.932835i | \(0.382673\pi\) | |||||||
\(522\) | 121.772 | + | 121.772i | 0.233280 | + | 0.233280i | ||||
\(523\) | −671.097 | + | 671.097i | −1.28317 | + | 1.28317i | −0.344314 | + | 0.938855i | \(0.611889\pi\) |
−0.938855 | + | 0.344314i | \(0.888111\pi\) | |||||||
\(524\) | 858.082i | 1.63756i | ||||||||
\(525\) | 110.284 | − | 31.0241i | 0.210064 | − | 0.0590936i | ||||
\(526\) | 1137.78 | 2.16308 | ||||||||
\(527\) | 44.4824 | + | 44.4824i | 0.0844068 | + | 0.0844068i | ||||
\(528\) | 826.825 | − | 826.825i | 1.56596 | − | 1.56596i | ||||
\(529\) | − | 654.018i | − | 1.23633i | ||||||
\(530\) | −25.3594 | − | 183.793i | −0.0478480 | − | 0.346779i | ||||
\(531\) | −133.248 | −0.250939 | ||||||||
\(532\) | −250.602 | − | 250.602i | −0.471057 | − | 0.471057i | ||||
\(533\) | 260.158 | − | 260.158i | 0.488101 | − | 0.488101i | ||||
\(534\) | − | 279.833i | − | 0.524032i | ||||||
\(535\) | −291.924 | + | 385.376i | −0.545651 | + | 0.720329i | ||||
\(536\) | −25.5631 | −0.0476923 | ||||||||
\(537\) | 89.1654 | + | 89.1654i | 0.166044 | + | 0.166044i | ||||
\(538\) | 86.4331 | − | 86.4331i | 0.160656 | − | 0.160656i | ||||
\(539\) | 76.5316i | 0.141988i | ||||||||
\(540\) | 228.667 | + | 173.216i | 0.423457 | + | 0.320770i | ||||
\(541\) | 557.721 | 1.03091 | 0.515454 | − | 0.856917i | \(-0.327623\pi\) | ||||
0.515454 | + | 0.856917i | \(0.327623\pi\) | |||||||
\(542\) | −254.084 | − | 254.084i | −0.468790 | − | 0.468790i | ||||
\(543\) | −142.096 | + | 142.096i | −0.261687 | + | 0.261687i | ||||
\(544\) | 1014.93i | 1.86569i | ||||||||
\(545\) | 671.018 | − | 92.5858i | 1.23123 | − | 0.169882i | ||||
\(546\) | −203.721 | −0.373115 | ||||||||
\(547\) | −656.108 | − | 656.108i | −1.19947 | − | 1.19947i | −0.974326 | − | 0.225141i | \(-0.927716\pi\) |
−0.225141 | − | 0.974326i | \(-0.572284\pi\) | |||||||
\(548\) | −1621.66 | + | 1621.66i | −2.95924 | + | 2.95924i | ||||
\(549\) | 253.333i | 0.461445i | ||||||||
\(550\) | −924.548 | − | 518.579i | −1.68100 | − | 0.942871i | ||||
\(551\) | −179.564 | −0.325888 | ||||||||
\(552\) | −1150.40 | − | 1150.40i | −2.08406 | − | 2.08406i | ||||
\(553\) | −128.713 | + | 128.713i | −0.232754 | + | 0.232754i | ||||
\(554\) | − | 159.725i | − | 0.288312i | ||||||
\(555\) | −57.9746 | − | 420.172i | −0.104459 | − | 0.757067i | ||||
\(556\) | −1615.61 | −2.90578 | ||||||||
\(557\) | 77.0795 | + | 77.0795i | 0.138383 | + | 0.138383i | 0.772905 | − | 0.634522i | \(-0.218803\pi\) |
−0.634522 | + | 0.772905i | \(0.718803\pi\) | |||||||
\(558\) | −66.4162 | + | 66.4162i | −0.119025 | + | 0.119025i | ||||
\(559\) | 211.811i | 0.378910i | ||||||||
\(560\) | −493.233 | + | 651.130i | −0.880773 | + | 1.16273i | ||||
\(561\) | 147.565 | 0.263040 | ||||||||
\(562\) | −511.745 | − | 511.745i | −0.910579 | − | 0.910579i | ||||
\(563\) | 100.072 | − | 100.072i | 0.177747 | − | 0.177747i | −0.612626 | − | 0.790373i | \(-0.709887\pi\) |
0.790373 | + | 0.612626i | \(0.209887\pi\) | |||||||
\(564\) | 1464.95i | 2.59744i | ||||||||
\(565\) | −35.7916 | − | 27.1123i | −0.0633480 | − | 0.0479863i | ||||
\(566\) | 1096.06 | 1.93650 | ||||||||
\(567\) | −16.8375 | − | 16.8375i | −0.0296957 | − | 0.0296957i | ||||
\(568\) | −1997.27 | + | 1997.27i | −3.51631 | + | 3.51631i | ||||
\(569\) | 73.3966i | 0.128992i | 0.997918 | + | 0.0644961i | \(0.0205440\pi\) | ||||
−0.997918 | + | 0.0644961i | \(0.979456\pi\) | |||||||
\(570\) | −403.649 | + | 55.6948i | −0.708157 | + | 0.0977102i | ||||
\(571\) | −131.618 | −0.230504 | −0.115252 | − | 0.993336i | \(-0.536768\pi\) | ||||
−0.115252 | + | 0.993336i | \(0.536768\pi\) | |||||||
\(572\) | 978.442 | + | 978.442i | 1.71056 | + | 1.71056i | ||||
\(573\) | 164.529 | − | 164.529i | 0.287136 | − | 0.287136i | ||||
\(574\) | 329.356i | 0.573791i | ||||||||
\(575\) | −420.652 | + | 749.959i | −0.731568 | + | 1.30428i | ||||
\(576\) | −774.407 | −1.34446 | ||||||||
\(577\) | −614.754 | − | 614.754i | −1.06543 | − | 1.06543i | −0.997704 | − | 0.0677285i | \(-0.978425\pi\) |
−0.0677285 | − | 0.997704i | \(-0.521575\pi\) | |||||||
\(578\) | 626.023 | − | 626.023i | 1.08308 | − | 1.08308i | ||||
\(579\) | − | 12.2642i | − | 0.0211816i | ||||||
\(580\) | 111.689 | + | 809.465i | 0.192566 | + | 1.39563i | ||||
\(581\) | −267.308 | −0.460082 | ||||||||
\(582\) | −169.622 | − | 169.622i | −0.291446 | − | 0.291446i | ||||
\(583\) | 73.9668 | − | 73.9668i | 0.126873 | − | 0.126873i | ||||
\(584\) | − | 2131.78i | − | 3.65031i | ||||||
\(585\) | −103.820 | + | 137.055i | −0.177470 | + | 0.234282i | ||||
\(586\) | −650.803 | −1.11059 | ||||||||
\(587\) | −328.506 | − | 328.506i | −0.559636 | − | 0.559636i | 0.369568 | − | 0.929204i | \(-0.379506\pi\) |
−0.929204 | + | 0.369568i | \(0.879506\pi\) | |||||||
\(588\) | 94.6609 | − | 94.6609i | 0.160988 | − | 0.160988i | ||||
\(589\) | − | 97.9368i | − | 0.166276i | ||||||
\(590\) | −686.562 | − | 520.073i | −1.16366 | − | 0.881480i | ||||
\(591\) | 507.586 | 0.858860 | ||||||||
\(592\) | 2138.46 | + | 2138.46i | 3.61227 | + | 3.61227i | ||||
\(593\) | −46.4495 | + | 46.4495i | −0.0783298 | + | 0.0783298i | −0.745186 | − | 0.666856i | \(-0.767639\pi\) |
0.666856 | + | 0.745186i | \(0.267639\pi\) | |||||||
\(594\) | 220.328i | 0.370923i | ||||||||
\(595\) | −102.118 | + | 14.0901i | −0.171628 | + | 0.0236809i | ||||
\(596\) | 1581.39 | 2.65334 | ||||||||
\(597\) | −141.705 | − | 141.705i | −0.237361 | − | 0.237361i | ||||
\(598\) | 1081.20 | − | 1081.20i | 1.80803 | − | 1.80803i | ||||
\(599\) | 256.090i | 0.427529i | 0.976885 | + | 0.213764i | \(0.0685724\pi\) | ||||
−0.976885 | + | 0.213764i | \(0.931428\pi\) | |||||||
\(600\) | 320.228 | + | 1138.34i | 0.533714 | + | 1.89723i | ||||
\(601\) | 433.545 | 0.721372 | 0.360686 | − | 0.932687i | \(-0.382543\pi\) | ||||
0.360686 | + | 0.932687i | \(0.382543\pi\) | |||||||
\(602\) | −134.075 | − | 134.075i | −0.222716 | − | 0.222716i | ||||
\(603\) | 1.98568 | − | 1.98568i | 0.00329301 | − | 0.00329301i | ||||
\(604\) | 2257.20i | 3.73709i | ||||||||
\(605\) | 1.00302 | + | 7.26941i | 0.00165788 | + | 0.0120156i | ||||
\(606\) | −360.913 | −0.595565 | ||||||||
\(607\) | 788.344 | + | 788.344i | 1.29875 | + | 1.29875i | 0.929215 | + | 0.369540i | \(0.120485\pi\) |
0.369540 | + | 0.929215i | \(0.379515\pi\) | |||||||
\(608\) | 1117.29 | − | 1117.29i | 1.83765 | − | 1.83765i | ||||
\(609\) | − | 67.8275i | − | 0.111375i | ||||||
\(610\) | −988.767 | + | 1305.30i | −1.62093 | + | 2.13983i | ||||
\(611\) | −878.045 | −1.43706 | ||||||||
\(612\) | −182.521 | − | 182.521i | −0.298238 | − | 0.298238i | ||||
\(613\) | 143.879 | − | 143.879i | 0.234712 | − | 0.234712i | −0.579944 | − | 0.814656i | \(-0.696926\pi\) |
0.814656 | + | 0.579944i | \(0.196926\pi\) | |||||||
\(614\) | 1730.96i | 2.81916i | ||||||||
\(615\) | 221.577 | + | 167.846i | 0.360289 | + | 0.272920i | ||||
\(616\) | −789.952 | −1.28239 | ||||||||
\(617\) | −280.216 | − | 280.216i | −0.454159 | − | 0.454159i | 0.442573 | − | 0.896732i | \(-0.354066\pi\) |
−0.896732 | + | 0.442573i | \(0.854066\pi\) | |||||||
\(618\) | −266.547 | + | 266.547i | −0.431305 | + | 0.431305i | ||||
\(619\) | − | 438.884i | − | 0.709020i | −0.935052 | − | 0.354510i | \(-0.884648\pi\) | ||
0.935052 | − | 0.354510i | \(-0.115352\pi\) | |||||||
\(620\) | −441.493 | + | 60.9165i | −0.712086 | + | 0.0982524i | ||||
\(621\) | 178.722 | 0.287797 | ||||||||
\(622\) | 1562.35 | + | 1562.35i | 2.51181 | + | 2.51181i | ||||
\(623\) | −77.9341 | + | 77.9341i | −0.125095 | + | 0.125095i | ||||
\(624\) | − | 1225.93i | − | 1.96463i | ||||||
\(625\) | 533.334 | − | 325.853i | 0.853334 | − | 0.521365i | ||||
\(626\) | 1219.70 | 1.94840 | ||||||||
\(627\) | −162.447 | − | 162.447i | −0.259086 | − | 0.259086i | ||||
\(628\) | 1865.18 | − | 1865.18i | 2.97003 | − | 2.97003i | ||||
\(629\) | 381.656i | 0.606766i | ||||||||
\(630\) | −21.0378 | − | 152.472i | −0.0333934 | − | 0.242019i | ||||
\(631\) | 601.250 | 0.952852 | 0.476426 | − | 0.879215i | \(-0.341932\pi\) | ||||
0.476426 | + | 0.879215i | \(0.341932\pi\) | |||||||
\(632\) | −1328.57 | − | 1328.57i | −2.10216 | − | 2.10216i | ||||
\(633\) | −81.0933 | + | 81.0933i | −0.128109 | + | 0.128109i | ||||
\(634\) | − | 1005.88i | − | 1.58656i | ||||||
\(635\) | 86.5966 | − | 114.319i | 0.136373 | − | 0.180029i | ||||
\(636\) | −182.977 | −0.287700 | ||||||||
\(637\) | 56.7366 | + | 56.7366i | 0.0890685 | + | 0.0890685i | ||||
\(638\) | −443.781 | + | 443.781i | −0.695582 | + | 0.695582i | ||||
\(639\) | − | 310.287i | − | 0.485582i | ||||||
\(640\) | −1913.73 | − | 1449.66i | −2.99020 | − | 2.26509i | ||||
\(641\) | 803.007 | 1.25274 | 0.626371 | − | 0.779525i | \(-0.284540\pi\) | ||||
0.626371 | + | 0.779525i | \(0.284540\pi\) | |||||||
\(642\) | 459.285 | + | 459.285i | 0.715397 | + | 0.715397i | ||||
\(643\) | −164.070 | + | 164.070i | −0.255163 | + | 0.255163i | −0.823084 | − | 0.567920i | \(-0.807748\pi\) |
0.567920 | + | 0.823084i | \(0.307748\pi\) | |||||||
\(644\) | 1004.78i | 1.56022i | ||||||||
\(645\) | −158.527 | + | 21.8733i | −0.245778 | + | 0.0339121i | ||||
\(646\) | 366.648 | 0.567566 | ||||||||
\(647\) | 495.936 | + | 495.936i | 0.766517 | + | 0.766517i | 0.977491 | − | 0.210975i | \(-0.0676638\pi\) |
−0.210975 | + | 0.977491i | \(0.567664\pi\) | |||||||
\(648\) | 173.795 | − | 173.795i | 0.268202 | − | 0.268202i | ||||
\(649\) | − | 485.606i | − | 0.748237i | ||||||
\(650\) | −1069.86 | + | 300.965i | −1.64594 | + | 0.463023i | ||||
\(651\) | 36.9941 | 0.0568265 | ||||||||
\(652\) | 1848.05 | + | 1848.05i | 2.83443 | + | 2.83443i | ||||
\(653\) | −812.931 | + | 812.931i | −1.24492 | + | 1.24492i | −0.286982 | + | 0.957936i | \(0.592652\pi\) |
−0.957936 | + | 0.286982i | \(0.907348\pi\) | |||||||
\(654\) | − | 910.050i | − | 1.39151i | ||||||
\(655\) | −53.1113 | − | 384.925i | −0.0810859 | − | 0.587672i | ||||
\(656\) | −1981.97 | −3.02129 | ||||||||
\(657\) | 165.592 | + | 165.592i | 0.252043 | + | 0.252043i | ||||
\(658\) | 555.796 | − | 555.796i | 0.844675 | − | 0.844675i | ||||
\(659\) | 135.081i | 0.204979i | 0.994734 | + | 0.102490i | \(0.0326808\pi\) | ||||
−0.994734 | + | 0.102490i | \(0.967319\pi\) | |||||||
\(660\) | −631.260 | + | 833.344i | −0.956455 | + | 1.26264i | ||||
\(661\) | −128.892 | −0.194996 | −0.0974980 | − | 0.995236i | \(-0.531084\pi\) | ||||
−0.0974980 | + | 0.995236i | \(0.531084\pi\) | |||||||
\(662\) | −590.291 | − | 590.291i | −0.891678 | − | 0.891678i | ||||
\(663\) | 109.397 | − | 109.397i | 0.165003 | − | 0.165003i | ||||
\(664\) | − | 2759.13i | − | 4.15531i | ||||||
\(665\) | 127.928 | + | 96.9060i | 0.192373 | + | 0.145723i | ||||
\(666\) | −569.847 | −0.855626 | ||||||||
\(667\) | 359.979 | + | 359.979i | 0.539698 | + | 0.539698i | ||||
\(668\) | −887.051 | + | 887.051i | −1.32792 | + | 1.32792i | ||||
\(669\) | − | 125.816i | − | 0.188065i | ||||||
\(670\) | 17.9814 | − | 2.48104i | 0.0268379 | − | 0.00370305i | ||||
\(671\) | −923.237 | −1.37591 | ||||||||
\(672\) | 422.038 | + | 422.038i | 0.628033 | + | 0.628033i | ||||
\(673\) | −217.545 | + | 217.545i | −0.323246 | + | 0.323246i | −0.850011 | − | 0.526765i | \(-0.823405\pi\) |
0.526765 | + | 0.850011i | \(0.323405\pi\) | |||||||
\(674\) | − | 2200.49i | − | 3.26482i | ||||||
\(675\) | −113.298 | − | 63.5491i | −0.167849 | − | 0.0941468i | ||||
\(676\) | −415.276 | −0.614313 | ||||||||
\(677\) | −601.143 | − | 601.143i | −0.887952 | − | 0.887952i | 0.106374 | − | 0.994326i | \(-0.466076\pi\) |
−0.994326 | + | 0.106374i | \(0.966076\pi\) | |||||||
\(678\) | −42.6558 | + | 42.6558i | −0.0629142 | + | 0.0629142i | ||||
\(679\) | 94.4798i | 0.139146i | ||||||||
\(680\) | −145.437 | − | 1054.06i | −0.213878 | − | 1.55008i | ||||
\(681\) | 261.709 | 0.384301 | ||||||||
\(682\) | −242.045 | − | 242.045i | −0.354904 | − | 0.354904i | ||||
\(683\) | −16.6370 | + | 16.6370i | −0.0243587 | + | 0.0243587i | −0.719181 | − | 0.694823i | \(-0.755483\pi\) |
0.694823 | + | 0.719181i | \(0.255483\pi\) | |||||||
\(684\) | 401.857i | 0.587511i | ||||||||
\(685\) | 627.086 | − | 827.833i | 0.915453 | − | 1.20851i | ||||
\(686\) | −71.8278 | −0.104705 | ||||||||
\(687\) | 108.194 | + | 108.194i | 0.157488 | + | 0.157488i | ||||
\(688\) | 806.823 | − | 806.823i | 1.17271 | − | 1.17271i | ||||
\(689\) | − | 109.670i | − | 0.159173i | ||||||
\(690\) | 920.863 | + | 697.557i | 1.33458 | + | 1.01095i | ||||
\(691\) | 333.673 | 0.482884 | 0.241442 | − | 0.970415i | \(-0.422380\pi\) | ||||
0.241442 | + | 0.970415i | \(0.422380\pi\) | |||||||
\(692\) | −839.490 | − | 839.490i | −1.21314 | − | 1.21314i | ||||
\(693\) | 61.3618 | − | 61.3618i | 0.0885451 | − | 0.0885451i | ||||
\(694\) | − | 672.077i | − | 0.968411i | ||||||
\(695\) | 724.745 | − | 99.9990i | 1.04280 | − | 0.143883i | ||||
\(696\) | 700.109 | 1.00590 | ||||||||
\(697\) | −176.863 | − | 176.863i | −0.253749 | − | 0.253749i | ||||
\(698\) | −51.5659 | + | 51.5659i | −0.0738766 | + | 0.0738766i | ||||
\(699\) | − | 638.215i | − | 0.913040i | ||||||
\(700\) | 357.276 | − | 636.968i | 0.510394 | − | 0.909955i | ||||
\(701\) | 978.544 | 1.39593 | 0.697963 | − | 0.716134i | \(-0.254090\pi\) | ||||
0.697963 | + | 0.716134i | \(0.254090\pi\) | |||||||
\(702\) | 163.340 | + | 163.340i | 0.232678 | + | 0.232678i | ||||
\(703\) | 420.146 | − | 420.146i | 0.597647 | − | 0.597647i | ||||
\(704\) | − | 2822.22i | − | 4.00883i | ||||||
\(705\) | −90.6739 | − | 657.161i | −0.128615 | − | 0.932143i | ||||
\(706\) | 1328.92 | 1.88232 | ||||||||
\(707\) | 100.515 | + | 100.515i | 0.142171 | + | 0.142171i | ||||
\(708\) | −600.639 | + | 600.639i | −0.848361 | + | 0.848361i | ||||
\(709\) | 775.664i | 1.09402i | 0.837125 | + | 0.547012i | \(0.184235\pi\) | ||||
−0.837125 | + | 0.547012i | \(0.815765\pi\) | |||||||
\(710\) | 1211.06 | − | 1598.75i | 1.70572 | − | 2.25176i | ||||
\(711\) | 206.400 | 0.290296 | ||||||||
\(712\) | −804.428 | − | 804.428i | −1.12982 | − | 1.12982i | ||||
\(713\) | −196.337 | + | 196.337i | −0.275368 | + | 0.275368i | ||||
\(714\) | 138.495i | 0.193971i | ||||||||
\(715\) | −499.478 | − | 378.356i | −0.698571 | − | 0.529170i | ||||
\(716\) | 803.856 | 1.12270 | ||||||||
\(717\) | −203.685 | − | 203.685i | −0.284080 | − | 0.284080i | ||||
\(718\) | −626.419 | + | 626.419i | −0.872450 | + | 0.872450i | ||||
\(719\) | − | 195.183i | − | 0.271464i | −0.990746 | − | 0.135732i | \(-0.956661\pi\) | ||
0.990746 | − | 0.135732i | \(-0.0433386\pi\) | |||||||
\(720\) | 917.532 | − | 126.599i | 1.27435 | − | 0.175832i | ||||
\(721\) | 148.467 | 0.205919 | ||||||||
\(722\) | 586.381 | + | 586.381i | 0.812162 | + | 0.812162i | ||||
\(723\) | 379.624 | − | 379.624i | 0.525068 | − | 0.525068i | ||||
\(724\) | 1281.04i | 1.76940i | ||||||||
\(725\) | −100.204 | − | 356.203i | −0.138213 | − | 0.491315i | ||||
\(726\) | 9.85894 | 0.0135798 | ||||||||
\(727\) | −127.418 | − | 127.418i | −0.175265 | − | 0.175265i | 0.614023 | − | 0.789288i | \(-0.289550\pi\) |
−0.789288 | + | 0.614023i | \(0.789550\pi\) | |||||||
\(728\) | −585.630 | + | 585.630i | −0.804437 | + | 0.804437i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 206.902 | + | 1499.53i | 0.283427 | + | 2.05414i | ||||
\(731\) | 143.995 | 0.196984 | ||||||||
\(732\) | 1141.94 | + | 1141.94i | 1.56003 | + | 1.56003i | ||||
\(733\) | −657.079 | + | 657.079i | −0.896425 | + | 0.896425i | −0.995118 | − | 0.0986932i | \(-0.968534\pi\) |
0.0986932 | + | 0.995118i | \(0.468534\pi\) | |||||||
\(734\) | 2689.61i | 3.66431i | ||||||||
\(735\) | −36.6047 | + | 48.3228i | −0.0498023 | + | 0.0657454i | ||||
\(736\) | −4479.74 | −6.08660 | ||||||||
\(737\) | 7.23655 | + | 7.23655i | 0.00981893 | + | 0.00981893i | ||||
\(738\) | 264.072 | − | 264.072i | 0.357821 | − | 0.357821i | ||||
\(739\) | 1191.53i | 1.61235i | 0.591676 | + | 0.806176i | \(0.298466\pi\) | ||||
−0.591676 | + | 0.806176i | \(0.701534\pi\) | |||||||
\(740\) | −2155.32 | − | 1632.66i | −2.91260 | − | 2.20630i | ||||
\(741\) | −240.860 | −0.325047 | ||||||||
\(742\) | 69.4206 | + | 69.4206i | 0.0935588 | + | 0.0935588i | ||||
\(743\) | 115.268 | − | 115.268i | 0.155138 | − | 0.155138i | −0.625270 | − | 0.780408i | \(-0.715011\pi\) |
0.780408 | + | 0.625270i | \(0.215011\pi\) | |||||||
\(744\) | 381.849i | 0.513238i | ||||||||
\(745\) | −709.394 | + | 97.8809i | −0.952207 | + | 0.131384i | ||||
\(746\) | 1547.79 | 2.07479 | ||||||||
\(747\) | 214.323 | + | 214.323i | 0.286912 | + | 0.286912i | ||||
\(748\) | 665.174 | − | 665.174i | 0.889270 | − | 0.889270i | ||||
\(749\) | − | 255.823i | − | 0.341553i | ||||||
\(750\) | −335.735 | − | 769.643i | −0.447647 | − | 1.02619i | ||||
\(751\) | −627.744 | −0.835878 | −0.417939 | − | 0.908475i | \(-0.637247\pi\) | ||||
−0.417939 | + | 0.908475i | \(0.637247\pi\) | |||||||
\(752\) | 3344.62 | + | 3344.62i | 4.44763 | + | 4.44763i | ||||
\(753\) | 494.440 | − | 494.440i | 0.656627 | − | 0.656627i | ||||
\(754\) | 657.994i | 0.872671i | ||||||||
\(755\) | −139.710 | − | 1012.55i | −0.185047 | − | 1.34113i | ||||
\(756\) | −151.795 | −0.200787 | ||||||||
\(757\) | 117.159 | + | 117.159i | 0.154767 | + | 0.154767i | 0.780243 | − | 0.625476i | \(-0.215095\pi\) |
−0.625476 | + | 0.780243i | \(0.715095\pi\) | |||||||
\(758\) | −1069.45 | + | 1069.45i | −1.41089 | + | 1.41089i | ||||
\(759\) | 651.327i | 0.858138i | ||||||||
\(760\) | −1000.25 | + | 1320.46i | −1.31612 | + | 1.73745i | ||||
\(761\) | 1272.61 | 1.67229 | 0.836145 | − | 0.548509i | \(-0.184804\pi\) | ||||
0.836145 | + | 0.548509i | \(0.184804\pi\) | |||||||
\(762\) | −136.243 | − | 136.243i | −0.178796 | − | 0.178796i | ||||
\(763\) | −253.451 | + | 253.451i | −0.332176 | + | 0.332176i | ||||
\(764\) | − | 1483.28i | − | 1.94147i | ||||||
\(765\) | 93.1742 | + | 70.5797i | 0.121796 | + | 0.0922610i | ||||
\(766\) | 1813.62 | 2.36765 | ||||||||
\(767\) | −360.003 | − | 360.003i | −0.469365 | − | 0.469365i | ||||
\(768\) | −1016.15 | + | 1016.15i | −1.32311 | + | 1.32311i | ||||
\(769\) | − | 1506.02i | − | 1.95842i | −0.202857 | − | 0.979208i | \(-0.565022\pi\) | ||
0.202857 | − | 0.979208i | \(-0.434978\pi\) | |||||||
\(770\) | 555.663 | − | 76.6694i | 0.721641 | − | 0.0995707i | ||||
\(771\) | −267.754 | −0.347282 | ||||||||
\(772\) | −55.2827 | − | 55.2827i | −0.0716097 | − | 0.0716097i | ||||
\(773\) | −580.116 | + | 580.116i | −0.750474 | + | 0.750474i | −0.974568 | − | 0.224094i | \(-0.928058\pi\) |
0.224094 | + | 0.974568i | \(0.428058\pi\) | |||||||
\(774\) | 214.998i | 0.277775i | ||||||||
\(775\) | 194.278 | − | 54.6528i | 0.250682 | − | 0.0705197i | ||||
\(776\) | −975.212 | −1.25672 | ||||||||
\(777\) | 158.703 | + | 158.703i | 0.204252 | + | 0.204252i | ||||
\(778\) | 1348.68 | − | 1348.68i | 1.73352 | − | 1.73352i | ||||
\(779\) | 389.399i | 0.499870i | ||||||||
\(780\) | 149.814 | + | 1085.78i | 0.192070 | + | 1.39203i | ||||
\(781\) | 1130.80 | 1.44788 | ||||||||
\(782\) | −735.032 | − | 735.032i | −0.939939 | − | 0.939939i | ||||
\(783\) | −54.3830 | + | 54.3830i | −0.0694546 | + | 0.0694546i | ||||
\(784\) | − | 432.238i | − | 0.551324i | ||||||
\(785\) | −721.251 | + | 952.144i | −0.918792 | + | 1.21292i | ||||
\(786\) | −522.044 | −0.664179 | ||||||||
\(787\) | −138.491 | − | 138.491i | −0.175973 | − | 0.175973i | 0.613625 | − | 0.789598i | \(-0.289711\pi\) |
−0.789598 | + | 0.613625i | \(0.789711\pi\) | |||||||
\(788\) | 2288.03 | − | 2288.03i | 2.90359 | − | 2.90359i | ||||
\(789\) | 508.128i | 0.644015i | ||||||||
\(790\) | 1063.48 | + | 805.587i | 1.34617 | + | 1.01973i | ||||
\(791\) | 23.7595 | 0.0300372 | ||||||||
\(792\) | 633.371 | + | 633.371i | 0.799710 | + | 0.799710i | ||||
\(793\) | −684.441 | + | 684.441i | −0.863103 | + | 0.863103i | ||||
\(794\) | 2994.74i | 3.77171i | ||||||||
\(795\) | 82.0814 | − | 11.3254i | 0.103247 | − | 0.0142458i | ||||
\(796\) | −1277.51 | −1.60492 | ||||||||
\(797\) | 1122.40 | + | 1122.40i | 1.40829 | + | 1.40829i | 0.768811 | + | 0.639475i | \(0.220848\pi\) |
0.639475 | + | 0.768811i | \(0.279152\pi\) | |||||||
\(798\) | 152.463 | − | 152.463i | 0.191056 | − | 0.191056i | ||||
\(799\) | 596.921i | 0.747085i | ||||||||
\(800\) | 2839.87 | + | 1592.88i | 3.54984 | + | 1.99110i | ||||
\(801\) | 124.973 | 0.156021 | ||||||||
\(802\) | −1732.96 | − | 1732.96i | −2.16080 | − | 2.16080i | ||||
\(803\) | −603.478 | + | 603.478i | −0.751529 | + | 0.751529i | ||||
\(804\) | − | 17.9016i | − | 0.0222657i | ||||||
\(805\) | −62.1913 | − | 450.733i | −0.0772563 | − | 0.559917i | ||||
\(806\) | −358.879 | −0.445259 | ||||||||
\(807\) | 38.6007 | + | 38.6007i | 0.0478324 | + | 0.0478324i | ||||
\(808\) | −1037.50 | + | 1037.50i | −1.28404 | + | 1.28404i | ||||
\(809\) | 30.2805i | 0.0374295i | 0.999825 | + | 0.0187147i | \(0.00595744\pi\) | ||||
−0.999825 | + | 0.0187147i | \(0.994043\pi\) | |||||||
\(810\) | −105.382 | + | 139.117i | −0.130101 | + | 0.171750i | ||||
\(811\) | −1118.58 | −1.37926 | −0.689629 | − | 0.724163i | \(-0.742226\pi\) | ||||
−0.689629 | + | 0.724163i | \(0.742226\pi\) | |||||||
\(812\) | −305.744 | − | 305.744i | −0.376532 | − | 0.376532i | ||||
\(813\) | 113.473 | − | 113.473i | 0.139573 | − | 0.139573i | ||||
\(814\) | − | 2076.73i | − | 2.55126i | ||||||
\(815\) | −943.398 | − | 714.626i | −1.15754 | − | 0.876842i | ||||
\(816\) | −833.424 | −1.02135 | ||||||||
\(817\) | −158.517 | − | 158.517i | −0.194024 | − | 0.194024i | ||||
\(818\) | −198.132 | + | 198.132i | −0.242215 | + | 0.242215i | ||||
\(819\) | − | 90.9810i | − | 0.111088i | ||||||
\(820\) | 1755.39 | − | 242.205i | 2.14072 | − | 0.295372i | ||||
\(821\) | −923.859 | −1.12528 | −0.562642 | − | 0.826700i | \(-0.690215\pi\) | ||||
−0.562642 | + | 0.826700i | \(0.690215\pi\) | |||||||
\(822\) | −986.597 | − | 986.597i | −1.20024 | − | 1.20024i | ||||
\(823\) | −186.823 | + | 186.823i | −0.227002 | + | 0.227002i | −0.811439 | − | 0.584437i | \(-0.801315\pi\) |
0.584437 | + | 0.811439i | \(0.301315\pi\) | |||||||
\(824\) | 1532.47i | 1.85979i | ||||||||
\(825\) | 231.596 | − | 412.900i | 0.280722 | − | 0.500485i | ||||
\(826\) | 455.759 | 0.551766 | ||||||||
\(827\) | 59.3982 | + | 59.3982i | 0.0718237 | + | 0.0718237i | 0.742106 | − | 0.670282i | \(-0.233827\pi\) |
−0.670282 | + | 0.742106i | \(0.733827\pi\) | |||||||
\(828\) | 805.618 | − | 805.618i | 0.972968 | − | 0.972968i | ||||
\(829\) | − | 1486.79i | − | 1.79347i | −0.442564 | − | 0.896737i | \(-0.645931\pi\) | ||
0.442564 | − | 0.896737i | \(-0.354069\pi\) | |||||||
\(830\) | 267.789 | + | 1940.81i | 0.322638 | + | 2.33832i | ||||
\(831\) | 71.3326 | 0.0858394 | ||||||||
\(832\) | −2092.25 | − | 2092.25i | −2.51472 | − | 2.51472i | ||||
\(833\) | 38.5712 | − | 38.5712i | 0.0463040 | − | 0.0463040i | ||||
\(834\) | − | 982.916i | − | 1.17856i | ||||||
\(835\) | 343.016 | − | 452.825i | 0.410798 | − | 0.542305i | ||||
\(836\) | −1464.51 | −1.75181 | ||||||||
\(837\) | −29.6612 | − | 29.6612i | −0.0354376 | − | 0.0354376i | ||||
\(838\) | 916.386 | − | 916.386i | 1.09354 | − | 1.09354i | ||||
\(839\) | − | 453.536i | − | 0.540568i | −0.962781 | − | 0.270284i | \(-0.912882\pi\) | ||
0.962781 | − | 0.270284i | \(-0.0871176\pi\) | |||||||
\(840\) | −498.784 | − | 377.830i | −0.593790 | − | 0.449798i | ||||
\(841\) | 621.925 | 0.739507 | ||||||||
\(842\) | 867.927 | + | 867.927i | 1.03079 | + | 1.03079i | ||||
\(843\) | 228.544 | − | 228.544i | 0.271108 | − | 0.271108i | ||||
\(844\) | 731.082i | 0.866211i | ||||||||
\(845\) | 186.288 | − | 25.7036i | 0.220459 | − | 0.0304185i | ||||
\(846\) | −891.257 | −1.05349 | ||||||||
\(847\) | −2.74573 | − | 2.74573i | −0.00324172 | − | 0.00324172i | ||||
\(848\) | −417.753 | + | 417.753i | −0.492633 | + | 0.492633i | ||||
\(849\) | 489.497i | 0.576557i | ||||||||
\(850\) | 204.605 | + | 727.323i | 0.240712 | + | 0.855675i | ||||
\(851\) | −1684.56 | −1.97951 | ||||||||
\(852\) | −1398.67 | − | 1398.67i | −1.64163 | − | 1.64163i | ||||
\(853\) | −827.180 | + | 827.180i | −0.969730 | + | 0.969730i | −0.999555 | − | 0.0298251i | \(-0.990505\pi\) |
0.0298251 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(854\) | − | 866.493i | − | 1.01463i | ||||||
\(855\) | −24.8731 | − | 180.268i | −0.0290913 | − | 0.210840i | ||||
\(856\) | 2640.58 | 3.08479 | ||||||||
\(857\) | −264.140 | − | 264.140i | −0.308215 | − | 0.308215i | 0.536002 | − | 0.844217i | \(-0.319934\pi\) |
−0.844217 | + | 0.536002i | \(0.819934\pi\) | |||||||
\(858\) | −595.270 | + | 595.270i | −0.693788 | + | 0.693788i | ||||
\(859\) | − | 710.066i | − | 0.826619i | −0.910591 | − | 0.413310i | \(-0.864373\pi\) | ||
0.910591 | − | 0.413310i | \(-0.135627\pi\) | |||||||
\(860\) | −615.990 | + | 813.184i | −0.716267 | + | 0.945563i | ||||
\(861\) | −147.089 | −0.170835 | ||||||||
\(862\) | −1182.61 | − | 1182.61i | −1.37194 | − | 1.37194i | ||||
\(863\) | 966.508 | − | 966.508i | 1.11994 | − | 1.11994i | 0.128190 | − | 0.991750i | \(-0.459083\pi\) |
0.991750 | − | 0.128190i | \(-0.0409167\pi\) | |||||||
\(864\) | − | 676.766i | − | 0.783294i | ||||||
\(865\) | 428.546 | + | 324.625i | 0.495429 | + | 0.375289i | ||||
\(866\) | −72.0725 | −0.0832246 | ||||||||
\(867\) | 279.580 | + | 279.580i | 0.322468 | + | 0.322468i | ||||
\(868\) | 166.757 | − | 166.757i | 0.192116 | − | 0.192116i | ||||
\(869\) | 752.197i | 0.865590i | ||||||||
\(870\) | −492.467 | + | 67.9497i | −0.566054 | + | 0.0781031i | ||||
\(871\) | 10.7296 | 0.0123187 | ||||||||
\(872\) | −2616.09 | − | 2616.09i | −3.00011 | − | 3.00011i | ||||
\(873\) | 75.7524 | − | 75.7524i | 0.0867725 | − | 0.0867725i | ||||
\(874\) | 1618.32i | 1.85162i | ||||||||
\(875\) | −120.844 | + | 307.850i | −0.138108 | + | 0.351829i | ||||
\(876\) | 1492.87 | 1.70419 | ||||||||
\(877\) | −1016.78 | − | 1016.78i | −1.15939 | − | 1.15939i | −0.984608 | − | 0.174779i | \(-0.944079\pi\) |
−0.174779 | − | 0.984608i | \(-0.555921\pi\) | |||||||
\(878\) | −1169.55 | + | 1169.55i | −1.33206 | + | 1.33206i | ||||
\(879\) | − | 290.646i | − | 0.330656i | ||||||
\(880\) | 461.374 | + | 3343.82i | 0.524288 | + | 3.79979i | ||||
\(881\) | 615.784 | 0.698961 | 0.349480 | − | 0.936944i | \(-0.386358\pi\) | ||||
0.349480 | + | 0.936944i | \(0.386358\pi\) | |||||||
\(882\) | 57.5903 | + | 57.5903i | 0.0652952 | + | 0.0652952i | ||||
\(883\) | −393.825 | + | 393.825i | −0.446008 | + | 0.446008i | −0.894025 | − | 0.448017i | \(-0.852130\pi\) |
0.448017 | + | 0.894025i | \(0.352130\pi\) | |||||||
\(884\) | − | 986.252i | − | 1.11567i | ||||||
\(885\) | 232.263 | − | 306.616i | 0.262444 | − | 0.346459i | ||||
\(886\) | 1832.92 | 2.06875 | ||||||||
\(887\) | 1046.82 | + | 1046.82i | 1.18018 | + | 1.18018i | 0.979697 | + | 0.200486i | \(0.0642520\pi\) |
0.200486 | + | 0.979697i | \(0.435748\pi\) | |||||||
\(888\) | −1638.12 | + | 1638.12i | −1.84473 | + | 1.84473i | ||||
\(889\) | 75.8878i | 0.0853631i | ||||||||
\(890\) | 643.921 | + | 487.772i | 0.723506 | + | 0.548058i | ||||
\(891\) | −98.3978 | −0.110435 | ||||||||
\(892\) | −567.135 | − | 567.135i | −0.635802 | − | 0.635802i | ||||
\(893\) | 657.120 | − | 657.120i | 0.735857 | − | 0.735857i | ||||
\(894\) | 962.096i | 1.07617i | ||||||||
\(895\) | −360.600 | + | 49.7549i | −0.402905 | + | 0.0555921i | ||||
\(896\) | 1270.39 | 1.41784 | ||||||||
\(897\) | 482.860 | + | 482.860i | 0.538306 | + | 0.538306i | ||||
\(898\) | 1270.58 | − | 1270.58i | 1.41490 | − | 1.41490i | ||||
\(899\) | − | 119.486i | − | 0.132910i | ||||||
\(900\) | −797.169 | + | 224.253i | −0.885743 | + | 0.249170i | ||||
\(901\) | −74.5572 | −0.0827494 | ||||||||
\(902\) | 962.375 | + | 962.375i | 1.06693 | + | 1.06693i | ||||
\(903\) | 59.8774 | − | 59.8774i | 0.0663094 | − | 0.0663094i | ||||
\(904\) | 245.243i | 0.271286i | ||||||||
\(905\) | −79.2906 | − | 574.661i | −0.0876140 | − | 0.634984i | ||||
\(906\) | −1373.25 | −1.51573 | ||||||||
\(907\) | −343.564 | − | 343.564i | −0.378791 | − | 0.378791i | 0.491875 | − | 0.870666i | \(-0.336312\pi\) |
−0.870666 | + | 0.491875i | \(0.836312\pi\) | |||||||
\(908\) | 1179.70 | − | 1179.70i | 1.29922 | − | 1.29922i | ||||
\(909\) | − | 161.182i | − | 0.177318i | ||||||
\(910\) | 355.102 | − | 468.779i | 0.390222 | − | 0.515142i | ||||
\(911\) | 313.466 | 0.344090 | 0.172045 | − | 0.985089i | \(-0.444963\pi\) | ||||
0.172045 | + | 0.985089i | \(0.444963\pi\) | |||||||
\(912\) | 917.475 | + | 917.475i | 1.00600 | + | 1.00600i | ||||
\(913\) | −781.071 | + | 781.071i | −0.855499 | + | 0.855499i | ||||
\(914\) | 1957.91i | 2.14214i | ||||||||
\(915\) | −582.942 | − | 441.580i | −0.637095 | − | 0.482601i | ||||
\(916\) | 975.406 | 1.06485 | ||||||||
\(917\) | 145.390 | + | 145.390i | 0.158550 | + | 0.158550i | ||||
\(918\) | 111.043 | − | 111.043i | 0.120962 | − | 0.120962i | ||||
\(919\) | − | 229.218i | − | 0.249422i | −0.992193 | − | 0.124711i | \(-0.960200\pi\) | ||
0.992193 | − | 0.124711i | \(-0.0398003\pi\) | |||||||
\(920\) | 4652.43 | − | 641.933i | 5.05698 | − | 0.697753i | ||||
\(921\) | −773.042 | −0.839351 | ||||||||
\(922\) | −346.352 | − | 346.352i | −0.375653 | − | 0.375653i | ||||
\(923\) | 838.315 | − | 838.315i | 0.908250 | − | 0.908250i | ||||
\(924\) | − | 553.197i | − | 0.598698i | ||||||
\(925\) | 1067.91 | + | 598.989i | 1.15449 | + | 0.647556i | ||||
\(926\) | −219.904 | −0.237477 | ||||||||
\(927\) | −119.039 | − | 119.039i | −0.128413 | − | 0.128413i | ||||
\(928\) | 1363.13 | − | 1363.13i | 1.46889 | − | 1.46889i | ||||
\(929\) | − | 1037.08i | − | 1.11634i | −0.829728 | − | 0.558168i | \(-0.811505\pi\) | ||
0.829728 | − | 0.558168i | \(-0.188495\pi\) | |||||||
\(930\) | −37.0607 | − | 268.598i | −0.0398502 | − | 0.288815i | ||||
\(931\) | −84.9223 | −0.0912162 | ||||||||
\(932\) | −2876.86 | − | 2876.86i | −3.08676 | − | 3.08676i | ||||
\(933\) | −697.739 | + | 697.739i | −0.747845 | + | 0.747845i | ||||
\(934\) | 2713.98i | 2.90576i | ||||||||
\(935\) | −257.218 | + | 339.560i | −0.275099 | + | 0.363166i | ||||
\(936\) | 939.097 | 1.00331 | ||||||||
\(937\) | −147.149 | − | 147.149i | −0.157043 | − | 0.157043i | 0.624212 | − | 0.781255i | \(-0.285420\pi\) |
−0.781255 | + | 0.624212i | \(0.785420\pi\) | |||||||
\(938\) | −6.79177 | + | 6.79177i | −0.00724070 | + | 0.00724070i | ||||
\(939\) | 544.714i | 0.580100i | ||||||||
\(940\) | −3370.99 | − | 2553.53i | −3.58616 | − | 2.71652i | ||||
\(941\) | −1810.77 | −1.92431 | −0.962154 | − | 0.272505i | \(-0.912148\pi\) | ||||
−0.962154 | + | 0.272505i | \(0.912148\pi\) | |||||||
\(942\) | 1134.75 | + | 1134.75i | 1.20462 | + | 1.20462i | ||||
\(943\) | 780.642 | − | 780.642i | 0.827828 | − | 0.827828i | ||||
\(944\) | 2742.62i | 2.90532i | ||||||||
\(945\) | 68.0935 | − | 9.39542i | 0.0720566 | − | 0.00994224i | ||||
\(946\) | −783.531 | −0.828257 | ||||||||
\(947\) | 147.333 | + | 147.333i | 0.155579 | + | 0.155579i | 0.780604 | − | 0.625026i | \(-0.214911\pi\) |
−0.625026 | + | 0.780604i | \(0.714911\pi\) | |||||||
\(948\) | 930.383 | − | 930.383i | 0.981417 | − | 0.981417i | ||||
\(949\) | 894.776i | 0.942861i | ||||||||
\(950\) | 575.435 | − | 1025.91i | 0.605721 | − | 1.07991i | ||||
\(951\) | 449.222 | 0.472368 | ||||||||
\(952\) | 398.129 | + | 398.129i | 0.418202 | + | 0.418202i | ||||
\(953\) | 85.4967 | − | 85.4967i | 0.0897132 | − | 0.0897132i | −0.660826 | − | 0.750539i | \(-0.729794\pi\) |
0.750539 | + | 0.660826i | \(0.229794\pi\) | |||||||
\(954\) | − | 111.321i | − | 0.116688i | ||||||
\(955\) | 91.8081 | + | 665.382i | 0.0961342 | + | 0.696735i | ||||
\(956\) | −1836.29 | −1.92081 | ||||||||
\(957\) | −198.191 | − | 198.191i | −0.207096 | − | 0.207096i | ||||
\(958\) | −2342.03 | + | 2342.03i | −2.44471 | + | 2.44471i | ||||
\(959\) | 549.538i | 0.573032i | ||||||||
\(960\) | 1349.85 | − | 1781.98i | 1.40610 | − | 1.85623i | ||||
\(961\) | −895.830 | −0.932186 | ||||||||
\(962\) | −1539.58 | − | 1539.58i | −1.60039 | − | 1.60039i | ||||
\(963\) | −205.115 | + | 205.115i | −0.212996 | + | 0.212996i | ||||
\(964\) | − | 3422.44i | − | 3.55025i | ||||||
\(965\) | 28.2209 | + | 21.3774i | 0.0292444 | + | 0.0221528i | ||||
\(966\) | −611.295 | −0.632810 | ||||||||
\(967\) | −322.508 | − | 322.508i | −0.333514 | − | 0.333514i | 0.520406 | − | 0.853919i | \(-0.325781\pi\) |
−0.853919 | + | 0.520406i | \(0.825781\pi\) | |||||||
\(968\) | 28.3412 | − | 28.3412i | 0.0292781 | − | 0.0292781i | ||||
\(969\) | 163.744i | 0.168982i | ||||||||
\(970\) | 685.978 | − | 94.6500i | 0.707194 | − | 0.0975773i | ||||
\(971\) | −1373.43 | −1.41445 | −0.707223 | − | 0.706991i | \(-0.750052\pi\) | ||||
−0.707223 | + | 0.706991i | \(0.750052\pi\) | |||||||
\(972\) | 121.707 | + | 121.707i | 0.125213 | + | 0.125213i | ||||
\(973\) | −273.744 | + | 273.744i | −0.281340 | + | 0.281340i | ||||
\(974\) | 2203.07i | 2.26188i | ||||||||
\(975\) | −134.410 | − | 477.796i | −0.137856 | − | 0.490047i | ||||
\(976\) | 5214.30 | 5.34252 | ||||||||
\(977\) | 40.3145 | + | 40.3145i | 0.0412635 | + | 0.0412635i | 0.727437 | − | 0.686174i | \(-0.240711\pi\) |
−0.686174 | + | 0.727437i | \(0.740711\pi\) | |||||||
\(978\) | −1124.33 | + | 1124.33i | −1.14962 | + | 1.14962i | ||||
\(979\) | 455.445i | 0.465215i | ||||||||
\(980\) | 52.8215 | + | 382.825i | 0.0538995 | + | 0.390638i | ||||
\(981\) | 406.425 | 0.414297 | ||||||||
\(982\) | −686.461 | − | 686.461i | −0.699044 | − | 0.699044i | ||||
\(983\) | 1061.02 | − | 1061.02i | 1.07937 | − | 1.07937i | 0.0828047 | − | 0.996566i | \(-0.473612\pi\) |
0.996566 | − | 0.0828047i | \(-0.0263878\pi\) | |||||||
\(984\) | − | 1518.24i | − | 1.54293i | ||||||
\(985\) | −884.763 | + | 1168.00i | −0.898237 | + | 1.18579i | ||||
\(986\) | 447.324 | 0.453675 | ||||||||
\(987\) | 248.217 | + | 248.217i | 0.251486 | + | 0.251486i | ||||
\(988\) | −1085.72 | + | 1085.72i | −1.09890 | + | 1.09890i | ||||
\(989\) | 635.570i | 0.642640i | ||||||||
\(990\) | −506.994 | − | 384.050i | −0.512115 | − | 0.387929i | ||||
\(991\) | 1624.85 | 1.63960 | 0.819802 | − | 0.572647i | \(-0.194083\pi\) | ||||
0.819802 | + | 0.572647i | \(0.194083\pi\) | |||||||
\(992\) | 743.471 | + | 743.471i | 0.749467 | + | 0.749467i | ||||
\(993\) | 263.622 | − | 263.622i | 0.265480 | − | 0.265480i | ||||
\(994\) | 1061.30i | 1.06770i | ||||||||
\(995\) | 573.078 | − | 79.0722i | 0.575957 | − | 0.0794696i | ||||
\(996\) | 1932.19 | 1.93995 | ||||||||
\(997\) | −273.633 | − | 273.633i | −0.274456 | − | 0.274456i | 0.556435 | − | 0.830891i | \(-0.312169\pi\) |
−0.830891 | + | 0.556435i | \(0.812169\pi\) | |||||||
\(998\) | −805.687 | + | 805.687i | −0.807301 | + | 0.807301i | ||||
\(999\) | − | 254.492i | − | 0.254746i |
(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 | 105.3.l.a.22.12 | ✓ | 24 | |
3.2 | odd | 2 | 315.3.o.b.127.1 | 24 | |||
5.2 | odd | 4 | 525.3.l.e.43.1 | 24 | |||
5.3 | odd | 4 | inner | 105.3.l.a.43.12 | yes | 24 | |
5.4 | even | 2 | 525.3.l.e.232.1 | 24 | |||
15.8 | even | 4 | 315.3.o.b.253.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.12 | ✓ | 24 | 1.1 | even | 1 | trivial | |
105.3.l.a.43.12 | yes | 24 | 5.3 | odd | 4 | inner | |
315.3.o.b.127.1 | 24 | 3.2 | odd | 2 | |||
315.3.o.b.253.1 | 24 | 15.8 | even | 4 | |||
525.3.l.e.43.1 | 24 | 5.2 | odd | 4 | |||
525.3.l.e.232.1 | 24 | 5.4 | even | 2 |