Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [30,4,Mod(17,30)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("30.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 30 = 2 \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 30.e (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: | \(1.77005730017\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 1577x^{8} + 284056x^{4} + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(2.67233 - 2.67233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 30.17 |
Dual form | 30.4.e.a.23.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/30\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | + | 1.41421i | −0.500000 | + | 0.500000i | ||||
\(3\) | −4.79094 | − | 2.01170i | −0.922016 | − | 0.387151i | ||||
\(4\) | − | 4.00000i | − | 0.500000i | ||||||
\(5\) | −10.8454 | − | 2.71609i | −0.970043 | − | 0.242935i | ||||
\(6\) | 9.62038 | − | 3.93044i | 0.654584 | − | 0.267433i | ||||
\(7\) | −16.1789 | − | 16.1789i | −0.873576 | − | 0.873576i | 0.119284 | − | 0.992860i | \(-0.461940\pi\) |
−0.992860 | + | 0.119284i | \(0.961940\pi\) | |||||||
\(8\) | 5.65685 | + | 5.65685i | 0.250000 | + | 0.250000i | ||||
\(9\) | 18.9062 | + | 19.2758i | 0.700228 | + | 0.713919i | ||||
\(10\) | 19.1789 | − | 11.4966i | 0.606489 | − | 0.363554i | ||||
\(11\) | 12.7562i | 0.349649i | 0.984600 | + | 0.174824i | \(0.0559358\pi\) | ||||
−0.984600 | + | 0.174824i | \(0.944064\pi\) | |||||||
\(12\) | −8.04679 | + | 19.1637i | −0.193576 | + | 0.461008i | ||||
\(13\) | −34.2057 | + | 34.2057i | −0.729765 | + | 0.729765i | −0.970573 | − | 0.240808i | \(-0.922588\pi\) |
0.240808 | + | 0.970573i | \(0.422588\pi\) | |||||||
\(14\) | 45.7607 | 0.873576 | ||||||||
\(15\) | 46.4957 | + | 34.8303i | 0.800343 | + | 0.599543i | ||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | 26.9917 | − | 26.9917i | 0.385085 | − | 0.385085i | −0.487845 | − | 0.872930i | \(-0.662217\pi\) |
0.872930 | + | 0.487845i | \(0.162217\pi\) | |||||||
\(18\) | −53.9975 | − | 0.522794i | −0.707074 | − | 0.00684577i | ||||
\(19\) | − | 136.755i | − | 1.65125i | −0.564216 | − | 0.825627i | \(-0.690821\pi\) | ||
0.564216 | − | 0.825627i | \(-0.309179\pi\) | |||||||
\(20\) | −10.8644 | + | 43.3816i | −0.121467 | + | 0.485021i | ||||
\(21\) | 44.9649 | + | 110.059i | 0.467245 | + | 1.14366i | ||||
\(22\) | −18.0400 | − | 18.0400i | −0.174824 | − | 0.174824i | ||||
\(23\) | −72.2934 | − | 72.2934i | −0.655401 | − | 0.655401i | 0.298887 | − | 0.954288i | \(-0.403384\pi\) |
−0.954288 | + | 0.298887i | \(0.903384\pi\) | |||||||
\(24\) | −15.7218 | − | 38.4815i | −0.133716 | − | 0.327292i | ||||
\(25\) | 110.246 | + | 58.9143i | 0.881965 | + | 0.471314i | ||||
\(26\) | − | 96.7483i | − | 0.729765i | ||||||
\(27\) | −51.8011 | − | 130.383i | −0.369227 | − | 0.929339i | ||||
\(28\) | −64.7154 | + | 64.7154i | −0.436788 | + | 0.436788i | ||||
\(29\) | −206.570 | −1.32272 | −0.661362 | − | 0.750066i | \(-0.730021\pi\) | ||||
−0.661362 | + | 0.750066i | \(0.730021\pi\) | |||||||
\(30\) | −115.012 | + | 16.4974i | −0.699943 | + | 0.100400i | ||||
\(31\) | 6.41137 | 0.0371457 | 0.0185728 | − | 0.999828i | \(-0.494088\pi\) | ||||
0.0185728 | + | 0.999828i | \(0.494088\pi\) | |||||||
\(32\) | 22.6274 | − | 22.6274i | 0.125000 | − | 0.125000i | ||||
\(33\) | 25.6616 | − | 61.1141i | 0.135367 | − | 0.322382i | ||||
\(34\) | 76.3440i | 0.385085i | ||||||||
\(35\) | 131.523 | + | 219.410i | 0.635184 | + | 1.05963i | ||||
\(36\) | 77.1033 | − | 75.6246i | 0.356960 | − | 0.350114i | ||||
\(37\) | 148.178 | + | 148.178i | 0.658388 | + | 0.658388i | 0.954999 | − | 0.296610i | \(-0.0958562\pi\) |
−0.296610 | + | 0.954999i | \(0.595856\pi\) | |||||||
\(38\) | 193.401 | + | 193.401i | 0.825627 | + | 0.825627i | ||||
\(39\) | 232.689 | − | 95.0658i | 0.955385 | − | 0.390326i | ||||
\(40\) | −45.9863 | − | 76.7154i | −0.181777 | − | 0.303244i | ||||
\(41\) | − | 20.5652i | − | 0.0783354i | −0.999233 | − | 0.0391677i | \(-0.987529\pi\) | ||
0.999233 | − | 0.0391677i | \(-0.0124706\pi\) | |||||||
\(42\) | −219.237 | − | 92.0567i | −0.805451 | − | 0.338206i | ||||
\(43\) | −162.284 | + | 162.284i | −0.575537 | + | 0.575537i | −0.933670 | − | 0.358133i | \(-0.883413\pi\) |
0.358133 | + | 0.933670i | \(0.383413\pi\) | |||||||
\(44\) | 51.0248 | 0.174824 | ||||||||
\(45\) | −152.690 | − | 260.405i | −0.505815 | − | 0.862642i | ||||
\(46\) | 204.477 | 0.655401 | ||||||||
\(47\) | 191.575 | − | 191.575i | 0.594556 | − | 0.594556i | −0.344303 | − | 0.938859i | \(-0.611885\pi\) |
0.938859 | + | 0.344303i | \(0.111885\pi\) | |||||||
\(48\) | 76.6550 | + | 32.1871i | 0.230504 | + | 0.0967878i | ||||
\(49\) | 180.511i | 0.526271i | ||||||||
\(50\) | −239.228 | + | 72.5935i | −0.676640 | + | 0.205326i | ||||
\(51\) | −183.615 | + | 75.0164i | −0.504141 | + | 0.205969i | ||||
\(52\) | 136.823 | + | 136.823i | 0.364883 | + | 0.364883i | ||||
\(53\) | 12.0238 | + | 12.0238i | 0.0311622 | + | 0.0311622i | 0.722516 | − | 0.691354i | \(-0.242985\pi\) |
−0.691354 | + | 0.722516i | \(0.742985\pi\) | |||||||
\(54\) | 257.647 | + | 111.131i | 0.649283 | + | 0.280056i | ||||
\(55\) | 34.6470 | − | 138.346i | 0.0849419 | − | 0.339174i | ||||
\(56\) | − | 183.043i | − | 0.436788i | ||||||
\(57\) | −275.110 | + | 655.187i | −0.639285 | + | 1.52248i | ||||
\(58\) | 292.134 | − | 292.134i | 0.661362 | − | 0.661362i | ||||
\(59\) | −627.311 | −1.38422 | −0.692110 | − | 0.721792i | \(-0.743319\pi\) | ||||
−0.692110 | + | 0.721792i | \(0.743319\pi\) | |||||||
\(60\) | 139.321 | − | 185.983i | 0.299772 | − | 0.400171i | ||||
\(61\) | −543.776 | −1.14137 | −0.570684 | − | 0.821170i | \(-0.693322\pi\) | ||||
−0.570684 | + | 0.821170i | \(0.693322\pi\) | |||||||
\(62\) | −9.06704 | + | 9.06704i | −0.0185728 | + | 0.0185728i | ||||
\(63\) | 5.98086 | − | 617.741i | 0.0119606 | − | 1.23537i | ||||
\(64\) | 64.0000i | 0.125000i | ||||||||
\(65\) | 463.880 | − | 278.069i | 0.885189 | − | 0.530618i | ||||
\(66\) | 50.1375 | + | 122.719i | 0.0935075 | + | 0.228874i | ||||
\(67\) | −120.548 | − | 120.548i | −0.219810 | − | 0.219810i | 0.588608 | − | 0.808419i | \(-0.299676\pi\) |
−0.808419 | + | 0.588608i | \(0.799676\pi\) | |||||||
\(68\) | −107.967 | − | 107.967i | −0.192543 | − | 0.192543i | ||||
\(69\) | 200.921 | + | 491.786i | 0.350551 | + | 0.858029i | ||||
\(70\) | −496.294 | − | 124.290i | −0.847406 | − | 0.212222i | ||||
\(71\) | 149.269i | 0.249507i | 0.992188 | + | 0.124753i | \(0.0398140\pi\) | ||||
−0.992188 | + | 0.124753i | \(0.960186\pi\) | |||||||
\(72\) | −2.09118 | + | 215.990i | −0.00342288 | + | 0.353537i | ||||
\(73\) | 771.809 | − | 771.809i | 1.23744 | − | 1.23744i | 0.276402 | − | 0.961042i | \(-0.410858\pi\) |
0.961042 | − | 0.276402i | \(-0.0891422\pi\) | |||||||
\(74\) | −419.112 | −0.658388 | ||||||||
\(75\) | −409.662 | − | 504.035i | −0.630717 | − | 0.776013i | ||||
\(76\) | −547.022 | −0.825627 | ||||||||
\(77\) | 206.381 | − | 206.381i | 0.305445 | − | 0.305445i | ||||
\(78\) | −194.628 | + | 463.515i | −0.282530 | + | 0.672855i | ||||
\(79\) | − | 97.9422i | − | 0.139486i | −0.997565 | − | 0.0697428i | \(-0.977782\pi\) | ||
0.997565 | − | 0.0697428i | \(-0.0222178\pi\) | |||||||
\(80\) | 173.526 | + | 43.4575i | 0.242511 | + | 0.0607337i | ||||
\(81\) | −14.1148 | + | 728.863i | −0.0193619 | + | 0.999813i | ||||
\(82\) | 29.0836 | + | 29.0836i | 0.0391677 | + | 0.0391677i | ||||
\(83\) | 735.158 | + | 735.158i | 0.972218 | + | 0.972218i | 0.999624 | − | 0.0274067i | \(-0.00872490\pi\) |
−0.0274067 | + | 0.999624i | \(0.508725\pi\) | |||||||
\(84\) | 440.235 | − | 179.860i | 0.571829 | − | 0.233623i | ||||
\(85\) | −366.048 | + | 219.424i | −0.467100 | + | 0.279998i | ||||
\(86\) | − | 459.009i | − | 0.575537i | ||||||
\(87\) | 989.662 | + | 415.556i | 1.21957 | + | 0.512095i | ||||
\(88\) | −72.1599 | + | 72.1599i | −0.0874122 | + | 0.0874122i | ||||
\(89\) | 492.823 | 0.586956 | 0.293478 | − | 0.955966i | \(-0.405187\pi\) | ||||
0.293478 | + | 0.955966i | \(0.405187\pi\) | |||||||
\(90\) | 584.205 | + | 152.332i | 0.684228 | + | 0.178413i | ||||
\(91\) | 1106.82 | 1.27501 | ||||||||
\(92\) | −289.174 | + | 289.174i | −0.327700 | + | 0.327700i | ||||
\(93\) | −30.7164 | − | 12.8977i | −0.0342489 | − | 0.0143810i | ||||
\(94\) | 541.857i | 0.594556i | ||||||||
\(95\) | −371.441 | + | 1483.17i | −0.401147 | + | 1.60179i | ||||
\(96\) | −153.926 | + | 62.8870i | −0.163646 | + | 0.0668581i | ||||
\(97\) | −811.978 | − | 811.978i | −0.849937 | − | 0.849937i | 0.140188 | − | 0.990125i | \(-0.455229\pi\) |
−0.990125 | + | 0.140188i | \(0.955229\pi\) | |||||||
\(98\) | −255.281 | − | 255.281i | −0.263135 | − | 0.263135i | ||||
\(99\) | −245.886 | + | 241.171i | −0.249621 | + | 0.244834i | ||||
\(100\) | 235.657 | − | 440.983i | 0.235657 | − | 0.440983i | ||||
\(101\) | − | 1221.28i | − | 1.20319i | −0.798801 | − | 0.601596i | \(-0.794532\pi\) | ||
0.798801 | − | 0.601596i | \(-0.205468\pi\) | |||||||
\(102\) | 153.581 | − | 365.760i | 0.149086 | − | 0.355055i | ||||
\(103\) | −1013.81 | + | 1013.81i | −0.969841 | + | 0.969841i | −0.999558 | − | 0.0297171i | \(-0.990539\pi\) |
0.0297171 | + | 0.999558i | \(0.490539\pi\) | |||||||
\(104\) | −386.993 | −0.364883 | ||||||||
\(105\) | −188.733 | − | 1315.76i | −0.175414 | − | 1.22291i | ||||
\(106\) | −34.0085 | −0.0311622 | ||||||||
\(107\) | 104.272 | − | 104.272i | 0.0942090 | − | 0.0942090i | −0.658432 | − | 0.752641i | \(-0.728780\pi\) |
0.752641 | + | 0.658432i | \(0.228780\pi\) | |||||||
\(108\) | −521.531 | + | 207.204i | −0.464670 | + | 0.184613i | ||||
\(109\) | − | 728.726i | − | 0.640360i | −0.947357 | − | 0.320180i | \(-0.896257\pi\) | ||
0.947357 | − | 0.320180i | \(-0.103743\pi\) | |||||||
\(110\) | 146.653 | + | 244.649i | 0.127116 | + | 0.212058i | ||||
\(111\) | −411.823 | − | 1008.00i | −0.352149 | − | 0.861941i | ||||
\(112\) | 258.862 | + | 258.862i | 0.218394 | + | 0.218394i | ||||
\(113\) | −124.657 | − | 124.657i | −0.103777 | − | 0.103777i | 0.653312 | − | 0.757089i | \(-0.273379\pi\) |
−0.757089 | + | 0.653312i | \(0.773379\pi\) | |||||||
\(114\) | −537.509 | − | 1315.64i | −0.441599 | − | 1.08088i | ||||
\(115\) | 587.696 | + | 980.407i | 0.476547 | + | 0.794986i | ||||
\(116\) | 826.279i | 0.661362i | ||||||||
\(117\) | −1306.04 | − | 12.6449i | −1.03200 | − | 0.00999161i | ||||
\(118\) | 887.152 | − | 887.152i | 0.692110 | − | 0.692110i | ||||
\(119\) | −873.390 | −0.672802 | ||||||||
\(120\) | 65.9895 | + | 460.049i | 0.0501999 | + | 0.349971i | ||||
\(121\) | 1168.28 | 0.877746 | ||||||||
\(122\) | 769.015 | − | 769.015i | 0.570684 | − | 0.570684i | ||||
\(123\) | −41.3710 | + | 98.5267i | −0.0303276 | + | 0.0722265i | ||||
\(124\) | − | 25.6455i | − | 0.0185728i | ||||||
\(125\) | −1035.64 | − | 938.387i | −0.741045 | − | 0.671455i | ||||
\(126\) | 865.159 | + | 882.076i | 0.611702 | + | 0.623663i | ||||
\(127\) | 292.476 | + | 292.476i | 0.204355 | + | 0.204355i | 0.801863 | − | 0.597508i | \(-0.203842\pi\) |
−0.597508 | + | 0.801863i | \(0.703842\pi\) | |||||||
\(128\) | −90.5097 | − | 90.5097i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 1103.96 | − | 451.026i | 0.753474 | − | 0.307835i | ||||
\(130\) | −262.777 | + | 1049.27i | −0.177285 | + | 0.707903i | ||||
\(131\) | − | 464.976i | − | 0.310115i | −0.987905 | − | 0.155058i | \(-0.950444\pi\) | ||
0.987905 | − | 0.155058i | \(-0.0495563\pi\) | |||||||
\(132\) | −244.457 | − | 102.646i | −0.161191 | − | 0.0676835i | ||||
\(133\) | −2212.55 | + | 2212.55i | −1.44250 | + | 1.44250i | ||||
\(134\) | 340.962 | 0.219810 | ||||||||
\(135\) | 207.672 | + | 1554.75i | 0.132397 | + | 0.991197i | ||||
\(136\) | 305.376 | 0.192543 | ||||||||
\(137\) | −102.116 | + | 102.116i | −0.0636815 | + | 0.0636815i | −0.738230 | − | 0.674549i | \(-0.764338\pi\) |
0.674549 | + | 0.738230i | \(0.264338\pi\) | |||||||
\(138\) | −979.635 | − | 411.345i | −0.604290 | − | 0.253739i | ||||
\(139\) | − | 336.335i | − | 0.205234i | −0.994721 | − | 0.102617i | \(-0.967278\pi\) | ||
0.994721 | − | 0.102617i | \(-0.0327216\pi\) | |||||||
\(140\) | 877.638 | − | 526.092i | 0.529814 | − | 0.317592i | ||||
\(141\) | −1303.22 | + | 532.434i | −0.778373 | + | 0.318007i | ||||
\(142\) | −211.098 | − | 211.098i | −0.124753 | − | 0.124753i | ||||
\(143\) | −436.334 | − | 436.334i | −0.255162 | − | 0.255162i | ||||
\(144\) | −302.498 | − | 308.413i | −0.175057 | − | 0.178480i | ||||
\(145\) | 2240.33 | + | 561.063i | 1.28310 | + | 0.321336i | ||||
\(146\) | 2183.01i | 1.23744i | ||||||||
\(147\) | 363.133 | − | 864.816i | 0.203746 | − | 0.485230i | ||||
\(148\) | 592.713 | − | 592.713i | 0.329194 | − | 0.329194i | ||||
\(149\) | 3241.32 | 1.78214 | 0.891071 | − | 0.453864i | \(-0.149955\pi\) | ||||
0.891071 | + | 0.453864i | \(0.149955\pi\) | |||||||
\(150\) | 1292.16 | + | 133.464i | 0.703365 | + | 0.0726484i | ||||
\(151\) | −224.154 | −0.120804 | −0.0604019 | − | 0.998174i | \(-0.519238\pi\) | ||||
−0.0604019 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(152\) | 773.605 | − | 773.605i | 0.412814 | − | 0.412814i | ||||
\(153\) | 1030.60 | + | 9.97806i | 0.544567 | + | 0.00527241i | ||||
\(154\) | 583.733i | 0.305445i | ||||||||
\(155\) | −69.5339 | − | 17.4139i | −0.0360329 | − | 0.00902397i | ||||
\(156\) | −380.263 | − | 930.755i | −0.195163 | − | 0.477693i | ||||
\(157\) | −1006.73 | − | 1006.73i | −0.511759 | − | 0.511759i | 0.403306 | − | 0.915065i | \(-0.367861\pi\) |
−0.915065 | + | 0.403306i | \(0.867861\pi\) | |||||||
\(158\) | 138.511 | + | 138.511i | 0.0697428 | + | 0.0697428i | ||||
\(159\) | −33.4171 | − | 81.7936i | −0.0166676 | − | 0.0407966i | ||||
\(160\) | −306.862 | + | 183.945i | −0.151622 | + | 0.0908885i | ||||
\(161\) | 2339.25i | 1.14509i | ||||||||
\(162\) | −1010.81 | − | 1050.73i | −0.490225 | − | 0.509587i | ||||
\(163\) | 694.457 | − | 694.457i | 0.333706 | − | 0.333706i | −0.520286 | − | 0.853992i | \(-0.674175\pi\) |
0.853992 | + | 0.520286i | \(0.174175\pi\) | |||||||
\(164\) | −82.2609 | −0.0391677 | ||||||||
\(165\) | −444.302 | + | 593.108i | −0.209630 | + | 0.279839i | ||||
\(166\) | −2079.34 | −0.972218 | ||||||||
\(167\) | −1875.50 | + | 1875.50i | −0.869044 | + | 0.869044i | −0.992367 | − | 0.123322i | \(-0.960645\pi\) |
0.123322 | + | 0.992367i | \(0.460645\pi\) | |||||||
\(168\) | −368.227 | + | 876.947i | −0.169103 | + | 0.402726i | ||||
\(169\) | − | 143.057i | − | 0.0651149i | ||||||
\(170\) | 207.358 | − | 827.982i | 0.0935506 | − | 0.373549i | ||||
\(171\) | 2636.07 | − | 2585.52i | 1.17886 | − | 1.15625i | ||||
\(172\) | 649.136 | + | 649.136i | 0.287768 | + | 0.287768i | ||||
\(173\) | −2100.72 | − | 2100.72i | −0.923208 | − | 0.923208i | 0.0740463 | − | 0.997255i | \(-0.476409\pi\) |
−0.997255 | + | 0.0740463i | \(0.976409\pi\) | |||||||
\(174\) | −1987.28 | + | 811.910i | −0.865834 | + | 0.353740i | ||||
\(175\) | −830.483 | − | 2736.81i | −0.358735 | − | 1.18219i | ||||
\(176\) | − | 204.099i | − | 0.0874122i | ||||||
\(177\) | 3005.41 | + | 1261.96i | 1.27627 | + | 0.535902i | ||||
\(178\) | −696.957 | + | 696.957i | −0.293478 | + | 0.293478i | ||||
\(179\) | −1272.12 | −0.531190 | −0.265595 | − | 0.964085i | \(-0.585568\pi\) | ||||
−0.265595 | + | 0.964085i | \(0.585568\pi\) | |||||||
\(180\) | −1041.62 | + | 610.760i | −0.431321 | + | 0.252908i | ||||
\(181\) | 62.7280 | 0.0257599 | 0.0128799 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128799 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(182\) | −1565.28 | + | 1565.28i | −0.637506 | + | 0.637506i | ||||
\(183\) | 2605.20 | + | 1093.91i | 1.05236 | + | 0.441882i | ||||
\(184\) | − | 817.907i | − | 0.327700i | ||||||
\(185\) | −1204.59 | − | 2009.52i | −0.478719 | − | 0.798610i | ||||
\(186\) | 61.6798 | − | 25.1995i | 0.0243149 | − | 0.00993396i | ||||
\(187\) | 344.311 | + | 344.311i | 0.134645 | + | 0.134645i | ||||
\(188\) | −766.301 | − | 766.301i | −0.297278 | − | 0.297278i | ||||
\(189\) | −1271.36 | + | 2947.53i | −0.489301 | + | 1.13440i | ||||
\(190\) | −1572.22 | − | 2622.81i | −0.600320 | − | 1.00147i | ||||
\(191\) | − | 2039.90i | − | 0.772785i | −0.922335 | − | 0.386392i | \(-0.873721\pi\) | ||
0.922335 | − | 0.386392i | \(-0.126279\pi\) | |||||||
\(192\) | 128.749 | − | 306.620i | 0.0483939 | − | 0.115252i | ||||
\(193\) | 1274.49 | − | 1274.49i | 0.475335 | − | 0.475335i | −0.428301 | − | 0.903636i | \(-0.640888\pi\) |
0.903636 | + | 0.428301i | \(0.140888\pi\) | |||||||
\(194\) | 2296.62 | 0.849937 | ||||||||
\(195\) | −2781.81 | + | 399.023i | −1.02159 | + | 0.146537i | ||||
\(196\) | 722.043 | 0.263135 | ||||||||
\(197\) | −1983.65 | + | 1983.65i | −0.717407 | + | 0.717407i | −0.968073 | − | 0.250667i | \(-0.919350\pi\) |
0.250667 | + | 0.968073i | \(0.419350\pi\) | |||||||
\(198\) | 6.66887 | − | 688.802i | 0.00239362 | − | 0.247228i | ||||
\(199\) | − | 1815.35i | − | 0.646666i | −0.946285 | − | 0.323333i | \(-0.895197\pi\) | ||
0.946285 | − | 0.323333i | \(-0.104803\pi\) | |||||||
\(200\) | 290.374 | + | 956.913i | 0.102663 | + | 0.338320i | ||||
\(201\) | 335.032 | + | 820.045i | 0.117569 | + | 0.287769i | ||||
\(202\) | 1727.16 | + | 1727.16i | 0.601596 | + | 0.601596i | ||||
\(203\) | 3342.06 | + | 3342.06i | 1.15550 | + | 1.15550i | ||||
\(204\) | 300.066 | + | 734.459i | 0.102984 | + | 0.252070i | ||||
\(205\) | −55.8571 | + | 223.038i | −0.0190304 | + | 0.0759886i | ||||
\(206\) | − | 2867.49i | − | 0.969841i | ||||||
\(207\) | 26.7248 | − | 2760.31i | 0.00897345 | − | 0.926833i | ||||
\(208\) | 547.291 | − | 547.291i | 0.182441 | − | 0.182441i | ||||
\(209\) | 1744.48 | 0.577360 | ||||||||
\(210\) | 2127.68 | + | 1593.86i | 0.699160 | + | 0.523746i | ||||
\(211\) | −3581.87 | −1.16865 | −0.584327 | − | 0.811518i | \(-0.698642\pi\) | ||||
−0.584327 | + | 0.811518i | \(0.698642\pi\) | |||||||
\(212\) | 48.0952 | − | 48.0952i | 0.0155811 | − | 0.0155811i | ||||
\(213\) | 300.284 | − | 715.139i | 0.0965969 | − | 0.230049i | ||||
\(214\) | 294.926i | 0.0942090i | ||||||||
\(215\) | 2200.82 | − | 1319.26i | 0.698113 | − | 0.418477i | ||||
\(216\) | 444.525 | − | 1030.59i | 0.140028 | − | 0.324642i | ||||
\(217\) | −103.729 | − | 103.729i | −0.0324496 | − | 0.0324496i | ||||
\(218\) | 1030.57 | + | 1030.57i | 0.320180 | + | 0.320180i | ||||
\(219\) | −5250.34 | + | 2145.04i | −1.62002 | + | 0.661866i | ||||
\(220\) | −553.385 | − | 138.588i | −0.169587 | − | 0.0424709i | ||||
\(221\) | 1846.54i | 0.562044i | ||||||||
\(222\) | 2007.94 | + | 843.126i | 0.607045 | + | 0.254896i | ||||
\(223\) | −285.691 | + | 285.691i | −0.0857906 | + | 0.0857906i | −0.748700 | − | 0.662909i | \(-0.769322\pi\) |
0.662909 | + | 0.748700i | \(0.269322\pi\) | |||||||
\(224\) | −732.171 | −0.218394 | ||||||||
\(225\) | 948.700 | + | 3238.92i | 0.281096 | + | 0.959680i | ||||
\(226\) | 352.584 | 0.103777 | ||||||||
\(227\) | 4779.51 | − | 4779.51i | 1.39748 | − | 1.39748i | 0.590270 | − | 0.807206i | \(-0.299021\pi\) |
0.807206 | − | 0.590270i | \(-0.200979\pi\) | |||||||
\(228\) | 2620.75 | + | 1100.44i | 0.761242 | + | 0.319643i | ||||
\(229\) | 5062.03i | 1.46074i | 0.683054 | + | 0.730368i | \(0.260651\pi\) | ||||
−0.683054 | + | 0.730368i | \(0.739349\pi\) | |||||||
\(230\) | −2217.63 | − | 555.378i | −0.635767 | − | 0.159220i | ||||
\(231\) | −1403.93 | + | 573.582i | −0.399879 | + | 0.163372i | ||||
\(232\) | −1168.53 | − | 1168.53i | −0.330681 | − | 0.330681i | ||||
\(233\) | −1012.79 | − | 1012.79i | −0.284765 | − | 0.284765i | 0.550241 | − | 0.835006i | \(-0.314536\pi\) |
−0.835006 | + | 0.550241i | \(0.814536\pi\) | |||||||
\(234\) | 1864.90 | − | 1829.14i | 0.520994 | − | 0.511002i | ||||
\(235\) | −2598.05 | + | 1557.38i | −0.721183 | + | 0.432306i | ||||
\(236\) | 2509.25i | 0.692110i | ||||||||
\(237\) | −197.030 | + | 469.235i | −0.0540020 | + | 0.128608i | ||||
\(238\) | 1235.16 | − | 1235.16i | 0.336401 | − | 0.336401i | ||||
\(239\) | −1140.60 | −0.308701 | −0.154350 | − | 0.988016i | \(-0.549328\pi\) | ||||
−0.154350 | + | 0.988016i | \(0.549328\pi\) | |||||||
\(240\) | −743.931 | − | 557.285i | −0.200086 | − | 0.149886i | ||||
\(241\) | 894.509 | 0.239089 | 0.119544 | − | 0.992829i | \(-0.461857\pi\) | ||||
0.119544 | + | 0.992829i | \(0.461857\pi\) | |||||||
\(242\) | −1652.20 | + | 1652.20i | −0.438873 | + | 0.438873i | ||||
\(243\) | 1533.88 | − | 3463.54i | 0.404931 | − | 0.914347i | ||||
\(244\) | 2175.10i | 0.570684i | ||||||||
\(245\) | 490.284 | − | 1957.71i | 0.127849 | − | 0.510505i | ||||
\(246\) | −80.8304 | − | 197.845i | −0.0209494 | − | 0.0512771i | ||||
\(247\) | 4677.81 | + | 4677.81i | 1.20503 | + | 1.20503i | ||||
\(248\) | 36.2682 | + | 36.2682i | 0.00928641 | + | 0.00928641i | ||||
\(249\) | −2043.18 | − | 5001.01i | −0.520005 | − | 1.27280i | ||||
\(250\) | 2791.70 | − | 137.540i | 0.706250 | − | 0.0347952i | ||||
\(251\) | 4198.52i | 1.05581i | 0.849304 | + | 0.527905i | \(0.177022\pi\) | ||||
−0.849304 | + | 0.527905i | \(0.822978\pi\) | |||||||
\(252\) | −2470.96 | − | 23.9235i | −0.617683 | − | 0.00598030i | ||||
\(253\) | 922.189 | − | 922.189i | 0.229160 | − | 0.229160i | ||||
\(254\) | −827.246 | −0.204355 | ||||||||
\(255\) | 2195.13 | − | 314.869i | 0.539075 | − | 0.0773249i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3004.70 | + | 3004.70i | −0.729291 | + | 0.729291i | −0.970479 | − | 0.241188i | \(-0.922463\pi\) |
0.241188 | + | 0.970479i | \(0.422463\pi\) | |||||||
\(258\) | −923.386 | + | 2199.08i | −0.222820 | + | 0.530654i | ||||
\(259\) | − | 4794.71i | − | 1.15030i | ||||||
\(260\) | −1112.27 | − | 1855.52i | −0.265309 | − | 0.442594i | ||||
\(261\) | −3905.44 | − | 3981.80i | −0.926209 | − | 0.944319i | ||||
\(262\) | 657.575 | + | 657.575i | 0.155058 | + | 0.155058i | ||||
\(263\) | −3594.55 | − | 3594.55i | −0.842773 | − | 0.842773i | 0.146446 | − | 0.989219i | \(-0.453217\pi\) |
−0.989219 | + | 0.146446i | \(0.953217\pi\) | |||||||
\(264\) | 490.878 | − | 200.550i | 0.114437 | − | 0.0467537i | ||||
\(265\) | −97.7453 | − | 163.061i | −0.0226583 | − | 0.0377991i | ||||
\(266\) | − | 6258.03i | − | 1.44250i | ||||||
\(267\) | −2361.08 | − | 991.410i | −0.541183 | − | 0.227241i | ||||
\(268\) | −482.193 | + | 482.193i | −0.109905 | + | 0.109905i | ||||
\(269\) | 2096.25 | 0.475132 | 0.237566 | − | 0.971371i | \(-0.423650\pi\) | ||||
0.237566 | + | 0.971371i | \(0.423650\pi\) | |||||||
\(270\) | −2492.44 | − | 1905.06i | −0.561797 | − | 0.429400i | ||||
\(271\) | −588.893 | −0.132002 | −0.0660012 | − | 0.997820i | \(-0.521024\pi\) | ||||
−0.0660012 | + | 0.997820i | \(0.521024\pi\) | |||||||
\(272\) | −431.867 | + | 431.867i | −0.0962713 | + | 0.0962713i | ||||
\(273\) | −5302.69 | − | 2226.58i | −1.17558 | − | 0.493622i | ||||
\(274\) | − | 288.828i | − | 0.0636815i | ||||||
\(275\) | −751.522 | + | 1406.32i | −0.164795 | + | 0.308378i | ||||
\(276\) | 1967.14 | − | 803.683i | 0.429015 | − | 0.175276i | ||||
\(277\) | −1492.04 | − | 1492.04i | −0.323639 | − | 0.323639i | 0.526522 | − | 0.850161i | \(-0.323496\pi\) |
−0.850161 | + | 0.526522i | \(0.823496\pi\) | |||||||
\(278\) | 475.649 | + | 475.649i | 0.102617 | + | 0.102617i | ||||
\(279\) | 121.214 | + | 123.584i | 0.0260104 | + | 0.0265190i | ||||
\(280\) | −497.162 | + | 1985.17i | −0.106111 | + | 0.423703i | ||||
\(281\) | 5169.08i | 1.09737i | 0.836028 | + | 0.548686i | \(0.184872\pi\) | ||||
−0.836028 | + | 0.548686i | \(0.815128\pi\) | |||||||
\(282\) | 1090.05 | − | 2596.00i | 0.230183 | − | 0.548190i | ||||
\(283\) | −892.521 | + | 892.521i | −0.187473 | + | 0.187473i | −0.794603 | − | 0.607130i | \(-0.792321\pi\) |
0.607130 | + | 0.794603i | \(0.292321\pi\) | |||||||
\(284\) | 597.077 | 0.124753 | ||||||||
\(285\) | 4763.23 | − | 6358.54i | 0.989998 | − | 1.32157i | ||||
\(286\) | 1234.14 | 0.255162 | ||||||||
\(287\) | −332.722 | + | 332.722i | −0.0684319 | + | 0.0684319i | ||||
\(288\) | 863.960 | + | 8.36471i | 0.176768 | + | 0.00171144i | ||||
\(289\) | 3455.90i | 0.703419i | ||||||||
\(290\) | −3961.77 | + | 2374.85i | −0.802218 | + | 0.480882i | ||||
\(291\) | 2256.68 | + | 5523.59i | 0.454602 | + | 1.11271i | ||||
\(292\) | −3087.24 | − | 3087.24i | −0.618722 | − | 0.618722i | ||||
\(293\) | 3323.48 | + | 3323.48i | 0.662661 | + | 0.662661i | 0.956006 | − | 0.293346i | \(-0.0947687\pi\) |
−0.293346 | + | 0.956006i | \(0.594769\pi\) | |||||||
\(294\) | 709.487 | + | 1736.58i | 0.140742 | + | 0.344488i | ||||
\(295\) | 6803.45 | + | 1703.84i | 1.34275 | + | 0.336275i | ||||
\(296\) | 1676.45i | 0.329194i | ||||||||
\(297\) | 1663.19 | − | 660.785i | 0.324943 | − | 0.129100i | ||||
\(298\) | −4583.92 | + | 4583.92i | −0.891071 | + | 0.891071i | ||||
\(299\) | 4945.69 | 0.956578 | ||||||||
\(300\) | −2016.14 | + | 1638.65i | −0.388007 | + | 0.315358i | ||||
\(301\) | 5251.14 | 1.00555 | ||||||||
\(302\) | 317.001 | − | 317.001i | 0.0604019 | − | 0.0604019i | ||||
\(303\) | −2456.85 | + | 5851.09i | −0.465817 | + | 1.10936i | ||||
\(304\) | 2188.09i | 0.412814i | ||||||||
\(305\) | 5897.47 | + | 1476.95i | 1.10717 | + | 0.277278i | ||||
\(306\) | −1471.59 | + | 1443.37i | −0.274920 | + | 0.269647i | ||||
\(307\) | −2558.00 | − | 2558.00i | −0.475547 | − | 0.475547i | 0.428157 | − | 0.903704i | \(-0.359163\pi\) |
−0.903704 | + | 0.428157i | \(0.859163\pi\) | |||||||
\(308\) | −825.523 | − | 825.523i | −0.152722 | − | 0.152722i | ||||
\(309\) | 6896.58 | − | 2817.62i | 1.26968 | − | 0.518734i | ||||
\(310\) | 122.963 | − | 73.7088i | 0.0225284 | − | 0.0135044i | ||||
\(311\) | − | 8102.38i | − | 1.47731i | −0.674083 | − | 0.738655i | \(-0.735461\pi\) | ||
0.674083 | − | 0.738655i | \(-0.264539\pi\) | |||||||
\(312\) | 1854.06 | + | 778.513i | 0.336428 | + | 0.141265i | ||||
\(313\) | 106.246 | − | 106.246i | 0.0191865 | − | 0.0191865i | −0.697448 | − | 0.716635i | \(-0.745681\pi\) |
0.716635 | + | 0.697448i | \(0.245681\pi\) | |||||||
\(314\) | 2847.47 | 0.511759 | ||||||||
\(315\) | −1742.71 | + | 6683.40i | −0.311716 | + | 1.19545i | ||||
\(316\) | −391.769 | −0.0697428 | ||||||||
\(317\) | 1174.48 | − | 1174.48i | 0.208093 | − | 0.208093i | −0.595364 | − | 0.803456i | \(-0.702992\pi\) |
0.803456 | + | 0.595364i | \(0.202992\pi\) | |||||||
\(318\) | 162.932 | + | 68.4147i | 0.0287321 | + | 0.0120645i | ||||
\(319\) | − | 2635.04i | − | 0.462489i | ||||||
\(320\) | 173.830 | − | 694.106i | 0.0303669 | − | 0.121255i | ||||
\(321\) | −709.325 | + | 289.797i | −0.123335 | + | 0.0503891i | ||||
\(322\) | −3308.20 | − | 3308.20i | −0.572543 | − | 0.572543i | ||||
\(323\) | −3691.26 | − | 3691.26i | −0.635874 | − | 0.635874i | ||||
\(324\) | 2915.45 | + | 56.4592i | 0.499906 | + | 0.00968093i | ||||
\(325\) | −5786.23 | + | 1755.83i | −0.987577 | + | 0.299679i | ||||
\(326\) | 1964.22i | 0.333706i | ||||||||
\(327\) | −1465.98 | + | 3491.28i | −0.247916 | + | 0.590423i | ||||
\(328\) | 116.335 | − | 116.335i | 0.0195838 | − | 0.0195838i | ||||
\(329\) | −6198.94 | −1.03878 | ||||||||
\(330\) | −210.444 | − | 1467.12i | −0.0351047 | − | 0.244734i | ||||
\(331\) | 2832.47 | 0.470352 | 0.235176 | − | 0.971953i | \(-0.424433\pi\) | ||||
0.235176 | + | 0.971953i | \(0.424433\pi\) | |||||||
\(332\) | 2940.63 | − | 2940.63i | 0.486109 | − | 0.486109i | ||||
\(333\) | −54.7773 | + | 5657.74i | −0.00901435 | + | 0.931058i | ||||
\(334\) | − | 5304.71i | − | 0.869044i | ||||||
\(335\) | 979.974 | + | 1634.81i | 0.159826 | + | 0.266625i | ||||
\(336\) | −719.439 | − | 1760.94i | −0.116811 | − | 0.285914i | ||||
\(337\) | −4789.86 | − | 4789.86i | −0.774244 | − | 0.774244i | 0.204601 | − | 0.978845i | \(-0.434410\pi\) |
−0.978845 | + | 0.204601i | \(0.934410\pi\) | |||||||
\(338\) | 202.314 | + | 202.314i | 0.0325575 | + | 0.0325575i | ||||
\(339\) | 346.453 | + | 847.998i | 0.0555066 | + | 0.135861i | ||||
\(340\) | 877.696 | + | 1464.19i | 0.139999 | + | 0.233550i | ||||
\(341\) | 81.7846i | 0.0129879i | ||||||||
\(342\) | −71.4950 | + | 7384.45i | −0.0113041 | + | 1.16756i | ||||
\(343\) | −2628.89 | + | 2628.89i | −0.413839 | + | 0.413839i | ||||
\(344\) | −1836.03 | −0.287768 | ||||||||
\(345\) | −843.332 | − | 5879.33i | −0.131604 | − | 0.917486i | ||||
\(346\) | 5941.74 | 0.923208 | ||||||||
\(347\) | 2124.17 | − | 2124.17i | 0.328621 | − | 0.328621i | −0.523441 | − | 0.852062i | \(-0.675352\pi\) |
0.852062 | + | 0.523441i | \(0.175352\pi\) | |||||||
\(348\) | 1662.22 | − | 3958.65i | 0.256047 | − | 0.609787i | ||||
\(349\) | − | 9235.10i | − | 1.41646i | −0.705983 | − | 0.708229i | \(-0.749495\pi\) | ||
0.705983 | − | 0.708229i | \(-0.250505\pi\) | |||||||
\(350\) | 5044.92 | + | 2695.96i | 0.770464 | + | 0.411729i | ||||
\(351\) | 6231.72 | + | 2687.94i | 0.947649 | + | 0.408751i | ||||
\(352\) | 288.640 | + | 288.640i | 0.0437061 | + | 0.0437061i | ||||
\(353\) | −986.773 | − | 986.773i | −0.148784 | − | 0.148784i | 0.628791 | − | 0.777574i | \(-0.283550\pi\) |
−0.777574 | + | 0.628791i | \(0.783550\pi\) | |||||||
\(354\) | −6034.97 | + | 2465.61i | −0.906088 | + | 0.370185i | ||||
\(355\) | 405.429 | − | 1618.88i | 0.0606139 | − | 0.242032i | ||||
\(356\) | − | 1971.29i | − | 0.293478i | ||||||
\(357\) | 4184.35 | + | 1757.00i | 0.620335 | + | 0.260476i | ||||
\(358\) | 1799.06 | − | 1799.06i | 0.265595 | − | 0.265595i | ||||
\(359\) | −10701.5 | −1.57327 | −0.786635 | − | 0.617419i | \(-0.788178\pi\) | ||||
−0.786635 | + | 0.617419i | \(0.788178\pi\) | |||||||
\(360\) | 609.328 | − | 2336.82i | 0.0892067 | − | 0.342114i | ||||
\(361\) | −11843.0 | −1.72664 | ||||||||
\(362\) | −88.7108 | + | 88.7108i | −0.0128799 | + | 0.0128799i | ||||
\(363\) | −5597.15 | − | 2350.22i | −0.809296 | − | 0.339820i | ||||
\(364\) | − | 4427.27i | − | 0.637506i | ||||||
\(365\) | −10466.9 | + | 6274.28i | −1.50099 | + | 0.899755i | ||||
\(366\) | −5231.33 | + | 2137.28i | −0.747120 | + | 0.305239i | ||||
\(367\) | 1004.85 | + | 1004.85i | 0.142923 | + | 0.142923i | 0.774948 | − | 0.632025i | \(-0.217776\pi\) |
−0.632025 | + | 0.774948i | \(0.717776\pi\) | |||||||
\(368\) | 1156.69 | + | 1156.69i | 0.163850 | + | 0.163850i | ||||
\(369\) | 396.412 | − | 388.809i | 0.0559251 | − | 0.0548526i | ||||
\(370\) | 4545.44 | + | 1138.35i | 0.638665 | + | 0.159945i | ||||
\(371\) | − | 389.063i | − | 0.0544451i | ||||||
\(372\) | −51.5909 | + | 122.866i | −0.00719049 | + | 0.0171244i | ||||
\(373\) | 8677.69 | − | 8677.69i | 1.20460 | − | 1.20460i | 0.231842 | − | 0.972754i | \(-0.425525\pi\) |
0.972754 | − | 0.231842i | \(-0.0744751\pi\) | |||||||
\(374\) | −973.860 | −0.134645 | ||||||||
\(375\) | 3073.95 | + | 6579.15i | 0.423301 | + | 0.905989i | ||||
\(376\) | 2167.43 | 0.297278 | ||||||||
\(377\) | 7065.86 | − | 7065.86i | 0.965279 | − | 0.965279i | ||||
\(378\) | −2370.45 | − | 5966.41i | −0.322548 | − | 0.811849i | ||||
\(379\) | 14693.0i | 1.99137i | 0.0927715 | + | 0.995687i | \(0.470427\pi\) | ||||
−0.0927715 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(380\) | 5932.67 | + | 1485.76i | 0.800894 | + | 0.200574i | ||||
\(381\) | −812.860 | − | 1989.61i | −0.109302 | − | 0.267534i | ||||
\(382\) | 2884.85 | + | 2884.85i | 0.386392 | + | 0.386392i | ||||
\(383\) | 1850.91 | + | 1850.91i | 0.246937 | + | 0.246937i | 0.819713 | − | 0.572775i | \(-0.194133\pi\) |
−0.572775 | + | 0.819713i | \(0.694133\pi\) | |||||||
\(384\) | 251.548 | + | 615.704i | 0.0334291 | + | 0.0818230i | ||||
\(385\) | −2798.83 | + | 1677.73i | −0.370498 | + | 0.222091i | ||||
\(386\) | 3604.80i | 0.475335i | ||||||||
\(387\) | −6196.33 | − | 59.9918i | −0.813894 | − | 0.00787999i | ||||
\(388\) | −3247.91 | + | 3247.91i | −0.424969 | + | 0.424969i | ||||
\(389\) | −9296.60 | −1.21171 | −0.605856 | − | 0.795574i | \(-0.707169\pi\) | ||||
−0.605856 | + | 0.795574i | \(0.707169\pi\) | |||||||
\(390\) | 3369.77 | − | 4498.38i | 0.437526 | − | 0.584062i | ||||
\(391\) | −3902.64 | −0.504770 | ||||||||
\(392\) | −1021.12 | + | 1021.12i | −0.131568 | + | 0.131568i | ||||
\(393\) | −935.390 | + | 2227.67i | −0.120062 | + | 0.285931i | ||||
\(394\) | − | 5610.60i | − | 0.717407i | ||||||
\(395\) | −266.020 | + | 1062.22i | −0.0338859 | + | 0.135307i | ||||
\(396\) | 964.682 | + | 983.545i | 0.122417 | + | 0.124811i | ||||
\(397\) | 848.145 | + | 848.145i | 0.107222 | + | 0.107222i | 0.758683 | − | 0.651460i | \(-0.225843\pi\) |
−0.651460 | + | 0.758683i | \(0.725843\pi\) | |||||||
\(398\) | 2567.29 | + | 2567.29i | 0.323333 | + | 0.323333i | ||||
\(399\) | 15051.1 | − | 6149.20i | 1.88847 | − | 0.771541i | ||||
\(400\) | −1763.93 | − | 942.628i | −0.220491 | − | 0.117829i | ||||
\(401\) | − | 8527.15i | − | 1.06191i | −0.847400 | − | 0.530954i | \(-0.821834\pi\) | ||
0.847400 | − | 0.530954i | \(-0.178166\pi\) | |||||||
\(402\) | −1633.53 | − | 685.911i | −0.202669 | − | 0.0850999i | ||||
\(403\) | −219.305 | + | 219.305i | −0.0271076 | + | 0.0271076i | ||||
\(404\) | −4885.14 | −0.601596 | ||||||||
\(405\) | 2132.74 | − | 7866.48i | 0.261671 | − | 0.965157i | ||||
\(406\) | −9452.78 | −1.15550 | ||||||||
\(407\) | −1890.19 | + | 1890.19i | −0.230205 | + | 0.230205i | ||||
\(408\) | −1463.04 | − | 614.324i | −0.177527 | − | 0.0745431i | ||||
\(409\) | 7604.85i | 0.919403i | 0.888073 | + | 0.459702i | \(0.152044\pi\) | ||||
−0.888073 | + | 0.459702i | \(0.847956\pi\) | |||||||
\(410\) | −236.430 | − | 394.418i | −0.0284791 | − | 0.0475095i | ||||
\(411\) | 694.658 | − | 283.805i | 0.0833697 | − | 0.0340610i | ||||
\(412\) | 4055.24 | + | 4055.24i | 0.484921 | + | 0.484921i | ||||
\(413\) | 10149.2 | + | 10149.2i | 1.20922 | + | 1.20922i | ||||
\(414\) | 3865.87 | + | 3941.46i | 0.458930 | + | 0.467903i | ||||
\(415\) | −5976.33 | − | 9969.84i | −0.706907 | − | 1.17928i | ||||
\(416\) | 1547.97i | 0.182441i | ||||||||
\(417\) | −676.603 | + | 1611.36i | −0.0794566 | + | 0.189229i | ||||
\(418\) | −2467.07 | + | 2467.07i | −0.288680 | + | 0.288680i | ||||
\(419\) | 13904.7 | 1.62122 | 0.810609 | − | 0.585588i | \(-0.199136\pi\) | ||||
0.810609 | + | 0.585588i | \(0.199136\pi\) | |||||||
\(420\) | −5263.05 | + | 754.931i | −0.611453 | + | 0.0877068i | ||||
\(421\) | 15613.5 | 1.80749 | 0.903745 | − | 0.428071i | \(-0.140807\pi\) | ||||
0.903745 | + | 0.428071i | \(0.140807\pi\) | |||||||
\(422\) | 5065.53 | − | 5065.53i | 0.584327 | − | 0.584327i | ||||
\(423\) | 7314.73 | + | 70.8200i | 0.840790 | + | 0.00814039i | ||||
\(424\) | 136.034i | 0.0155811i | ||||||||
\(425\) | 4565.91 | − | 1385.52i | 0.521128 | − | 0.158136i | ||||
\(426\) | 586.693 | + | 1436.03i | 0.0667263 | + | 0.163323i | ||||
\(427\) | 8797.68 | + | 8797.68i | 0.997071 | + | 0.997071i | ||||
\(428\) | −417.088 | − | 417.088i | −0.0471045 | − | 0.0471045i | ||||
\(429\) | 1212.68 | + | 2968.22i | 0.136477 | + | 0.334049i | ||||
\(430\) | −1246.71 | + | 4978.14i | −0.139818 | + | 0.558295i | ||||
\(431\) | − | 1687.62i | − | 0.188607i | −0.995544 | − | 0.0943034i | \(-0.969938\pi\) | ||
0.995544 | − | 0.0943034i | \(-0.0300624\pi\) | |||||||
\(432\) | 828.817 | + | 2086.12i | 0.0923067 | + | 0.232335i | ||||
\(433\) | 3605.54 | − | 3605.54i | 0.400164 | − | 0.400164i | −0.478127 | − | 0.878291i | \(-0.658684\pi\) |
0.878291 | + | 0.478127i | \(0.158684\pi\) | |||||||
\(434\) | 293.389 | 0.0324496 | ||||||||
\(435\) | −9604.60 | − | 7194.88i | −1.05863 | − | 0.793031i | ||||
\(436\) | −2914.90 | −0.320180 | ||||||||
\(437\) | −9886.52 | + | 9886.52i | −1.08223 | + | 1.08223i | ||||
\(438\) | 4391.55 | − | 10458.6i | 0.479078 | − | 1.14094i | ||||
\(439\) | 8014.92i | 0.871369i | 0.900099 | + | 0.435685i | \(0.143494\pi\) | ||||
−0.900099 | + | 0.435685i | \(0.856506\pi\) | |||||||
\(440\) | 978.597 | − | 586.611i | 0.106029 | − | 0.0635581i | ||||
\(441\) | −3479.50 | + | 3412.77i | −0.375715 | + | 0.368509i | ||||
\(442\) | −2611.40 | − | 2611.40i | −0.281022 | − | 0.281022i | ||||
\(443\) | 4788.70 | + | 4788.70i | 0.513584 | + | 0.513584i | 0.915623 | − | 0.402039i | \(-0.131698\pi\) |
−0.402039 | + | 0.915623i | \(0.631698\pi\) | |||||||
\(444\) | −4032.01 | + | 1647.29i | −0.430970 | + | 0.176074i | ||||
\(445\) | −5344.86 | − | 1338.55i | −0.569373 | − | 0.142592i | ||||
\(446\) | − | 808.057i | − | 0.0857906i | ||||||
\(447\) | −15528.9 | − | 6520.55i | −1.64316 | − | 0.689958i | ||||
\(448\) | 1035.45 | − | 1035.45i | 0.109197 | − | 0.109197i | ||||
\(449\) | −6437.16 | −0.676588 | −0.338294 | − | 0.941040i | \(-0.609850\pi\) | ||||
−0.338294 | + | 0.941040i | \(0.609850\pi\) | |||||||
\(450\) | −5922.19 | − | 3238.86i | −0.620388 | − | 0.339292i | ||||
\(451\) | 262.334 | 0.0273899 | ||||||||
\(452\) | −498.629 | + | 498.629i | −0.0518884 | + | 0.0518884i | ||||
\(453\) | 1073.91 | + | 450.929i | 0.111383 | + | 0.0467693i | ||||
\(454\) | 13518.5i | 1.39748i | ||||||||
\(455\) | −12003.9 | − | 3006.22i | −1.23682 | − | 0.309745i | ||||
\(456\) | −5262.55 | + | 2150.04i | −0.540442 | + | 0.220800i | ||||
\(457\) | 7433.15 | + | 7433.15i | 0.760850 | + | 0.760850i | 0.976476 | − | 0.215626i | \(-0.0691793\pi\) |
−0.215626 | + | 0.976476i | \(0.569179\pi\) | |||||||
\(458\) | −7158.79 | − | 7158.79i | −0.730368 | − | 0.730368i | ||||
\(459\) | −4917.45 | − | 2121.05i | −0.500059 | − | 0.215691i | ||||
\(460\) | 3921.63 | − | 2350.78i | 0.397493 | − | 0.238274i | ||||
\(461\) | − | 15742.8i | − | 1.59049i | −0.606291 | − | 0.795243i | \(-0.707343\pi\) | ||
0.606291 | − | 0.795243i | \(-0.292657\pi\) | |||||||
\(462\) | 1174.29 | − | 2796.63i | 0.118253 | − | 0.281625i | ||||
\(463\) | 4385.12 | − | 4385.12i | 0.440160 | − | 0.440160i | −0.451906 | − | 0.892066i | \(-0.649256\pi\) |
0.892066 | + | 0.451906i | \(0.149256\pi\) | |||||||
\(464\) | 3305.11 | 0.330681 | ||||||||
\(465\) | 298.101 | + | 223.310i | 0.0297292 | + | 0.0222704i | ||||
\(466\) | 2864.61 | 0.284765 | ||||||||
\(467\) | 405.352 | − | 405.352i | 0.0401659 | − | 0.0401659i | −0.686739 | − | 0.726904i | \(-0.740958\pi\) |
0.726904 | + | 0.686739i | \(0.240958\pi\) | |||||||
\(468\) | −50.5795 | + | 5224.16i | −0.00499581 | + | 0.515998i | ||||
\(469\) | 3900.66i | 0.384042i | ||||||||
\(470\) | 1471.73 | − | 5876.66i | 0.144438 | − | 0.576745i | ||||
\(471\) | 2797.96 | + | 6848.44i | 0.273722 | + | 0.669978i | ||||
\(472\) | −3548.61 | − | 3548.61i | −0.346055 | − | 0.346055i | ||||
\(473\) | −2070.13 | − | 2070.13i | −0.201236 | − | 0.201236i | ||||
\(474\) | −384.956 | − | 942.241i | −0.0373030 | − | 0.0913049i | ||||
\(475\) | 8056.85 | − | 15076.7i | 0.778260 | − | 1.45635i | ||||
\(476\) | 3493.56i | 0.336401i | ||||||||
\(477\) | −4.44486 | + | 459.093i | −0.000426659 | + | 0.0440680i | ||||
\(478\) | 1613.06 | − | 1613.06i | 0.154350 | − | 0.154350i | ||||
\(479\) | 834.821 | 0.0796324 | 0.0398162 | − | 0.999207i | \(-0.487323\pi\) | ||||
0.0398162 | + | 0.999207i | \(0.487323\pi\) | |||||||
\(480\) | 1840.20 | − | 263.958i | 0.174986 | − | 0.0250999i | ||||
\(481\) | −10137.1 | −0.960938 | ||||||||
\(482\) | −1265.03 | + | 1265.03i | −0.119544 | + | 0.119544i | ||||
\(483\) | 4705.86 | − | 11207.2i | 0.443321 | − | 1.05579i | ||||
\(484\) | − | 4673.12i | − | 0.438873i | ||||||
\(485\) | 6600.83 | + | 11011.6i | 0.617996 | + | 1.03095i | ||||
\(486\) | 2728.96 | + | 7067.42i | 0.254708 | + | 0.659639i | ||||
\(487\) | 1123.69 | + | 1123.69i | 0.104557 | + | 0.104557i | 0.757450 | − | 0.652893i | \(-0.226445\pi\) |
−0.652893 | + | 0.757450i | \(0.726445\pi\) | |||||||
\(488\) | −3076.06 | − | 3076.06i | −0.285342 | − | 0.285342i | ||||
\(489\) | −4724.14 | + | 1930.06i | −0.436877 | + | 0.178488i | ||||
\(490\) | 2075.26 | + | 3461.99i | 0.191328 | + | 0.319177i | ||||
\(491\) | − | 2933.72i | − | 0.269647i | −0.990870 | − | 0.134824i | \(-0.956953\pi\) | ||
0.990870 | − | 0.134824i | \(-0.0430468\pi\) | |||||||
\(492\) | 394.107 | + | 165.484i | 0.0361132 | + | 0.0151638i | ||||
\(493\) | −5575.67 | + | 5575.67i | −0.509362 | + | 0.509362i | ||||
\(494\) | −13230.9 | −1.20503 | ||||||||
\(495\) | 3321.78 | − | 1947.74i | 0.301622 | − | 0.176858i | ||||
\(496\) | −102.582 | −0.00928641 | ||||||||
\(497\) | 2415.00 | − | 2415.00i | 0.217963 | − | 0.217963i | ||||
\(498\) | 9961.99 | + | 4183.00i | 0.896401 | + | 0.376395i | ||||
\(499\) | − | 19512.5i | − | 1.75050i | −0.483668 | − | 0.875252i | \(-0.660696\pi\) | ||
0.483668 | − | 0.875252i | \(-0.339304\pi\) | |||||||
\(500\) | −3753.55 | + | 4142.57i | −0.335727 | + | 0.370523i | ||||
\(501\) | 12758.3 | − | 5212.46i | 1.13772 | − | 0.464821i | ||||
\(502\) | −5937.60 | − | 5937.60i | −0.527905 | − | 0.527905i | ||||
\(503\) | −8770.75 | − | 8770.75i | −0.777472 | − | 0.777472i | 0.201928 | − | 0.979400i | \(-0.435279\pi\) |
−0.979400 | + | 0.201928i | \(0.935279\pi\) | |||||||
\(504\) | 3528.30 | − | 3460.64i | 0.311831 | − | 0.305851i | ||||
\(505\) | −3317.12 | + | 13245.3i | −0.292297 | + | 1.16715i | ||||
\(506\) | 2608.34i | 0.229160i | ||||||||
\(507\) | −287.788 | + | 685.379i | −0.0252093 | + | 0.0600370i | ||||
\(508\) | 1169.90 | − | 1169.90i | 0.102177 | − | 0.102177i | ||||
\(509\) | 16213.8 | 1.41192 | 0.705959 | − | 0.708253i | \(-0.250516\pi\) | ||||
0.705959 | + | 0.708253i | \(0.250516\pi\) | |||||||
\(510\) | −2659.09 | + | 3549.67i | −0.230875 | + | 0.308200i | ||||
\(511\) | −24974.0 | −2.16200 | ||||||||
\(512\) | −362.039 | + | 362.039i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −17830.5 | + | 7084.08i | −1.53458 | + | 0.609687i | ||||
\(514\) | − | 8498.56i | − | 0.729291i | ||||||
\(515\) | 13748.8 | − | 8241.58i | 1.17640 | − | 0.705179i | ||||
\(516\) | −1804.11 | − | 4415.84i | −0.153917 | − | 0.376737i | ||||
\(517\) | 2443.77 | + | 2443.77i | 0.207886 | + | 0.207886i | ||||
\(518\) | 6780.75 | + | 6780.75i | 0.575152 | + | 0.575152i | ||||
\(519\) | 5838.42 | + | 14290.5i | 0.493792 | + | 1.20863i | ||||
\(520\) | 4197.10 | + | 1051.11i | 0.353952 | + | 0.0886427i | ||||
\(521\) | 17031.0i | 1.43213i | 0.698032 | + | 0.716067i | \(0.254059\pi\) | ||||
−0.698032 | + | 0.716067i | \(0.745941\pi\) | |||||||
\(522\) | 11154.2 | + | 107.993i | 0.935264 | + | 0.00905507i | ||||
\(523\) | −6159.97 | + | 6159.97i | −0.515023 | + | 0.515023i | −0.916061 | − | 0.401039i | \(-0.868649\pi\) |
0.401039 | + | 0.916061i | \(0.368649\pi\) | |||||||
\(524\) | −1859.90 | −0.155058 | ||||||||
\(525\) | −1526.85 | + | 14782.6i | −0.126928 | + | 1.22889i | ||||
\(526\) | 10166.9 | 0.842773 | ||||||||
\(527\) | 173.054 | − | 173.054i | 0.0143042 | − | 0.0143042i | ||||
\(528\) | −410.586 | + | 977.826i | −0.0338418 | + | 0.0805955i | ||||
\(529\) | − | 1714.32i | − | 0.140899i | ||||||
\(530\) | 368.836 | + | 92.3702i | 0.0302287 | + | 0.00757039i | ||||
\(531\) | −11860.0 | − | 12091.9i | −0.969269 | − | 0.988221i | ||||
\(532\) | 8850.19 | + | 8850.19i | 0.721248 | + | 0.721248i | ||||
\(533\) | 703.448 | + | 703.448i | 0.0571664 | + | 0.0571664i | ||||
\(534\) | 4741.14 | − | 1937.01i | 0.384212 | − | 0.156971i | ||||
\(535\) | −1414.09 | + | 847.660i | −0.114273 | + | 0.0685001i | ||||
\(536\) | − | 1363.85i | − | 0.109905i | ||||||
\(537\) | 6094.67 | + | 2559.13i | 0.489766 | + | 0.205651i | ||||
\(538\) | −2964.54 | + | 2964.54i | −0.237566 | + | 0.237566i | ||||
\(539\) | −2302.63 | −0.184010 | ||||||||
\(540\) | 6219.00 | − | 830.688i | 0.495598 | − | 0.0661984i | ||||
\(541\) | 17947.7 | 1.42630 | 0.713152 | − | 0.701010i | \(-0.247267\pi\) | ||||
0.713152 | + | 0.701010i | \(0.247267\pi\) | |||||||
\(542\) | 832.820 | − | 832.820i | 0.0660012 | − | 0.0660012i | ||||
\(543\) | −300.526 | − | 126.190i | −0.0237510 | − | 0.00997297i | ||||
\(544\) | − | 1221.50i | − | 0.0962713i | ||||||
\(545\) | −1979.29 | + | 7903.33i | −0.155566 | + | 0.621177i | ||||
\(546\) | 10648.0 | − | 4350.28i | 0.834602 | − | 0.340979i | ||||
\(547\) | −6743.17 | − | 6743.17i | −0.527088 | − | 0.527088i | 0.392615 | − | 0.919703i | \(-0.371571\pi\) |
−0.919703 | + | 0.392615i | \(0.871571\pi\) | |||||||
\(548\) | 408.464 | + | 408.464i | 0.0318407 | + | 0.0318407i | ||||
\(549\) | −10280.7 | − | 10481.7i | −0.799217 | − | 0.814844i | ||||
\(550\) | −926.018 | − | 3051.64i | −0.0717919 | − | 0.236586i | ||||
\(551\) | 28249.5i | 2.18416i | ||||||||
\(552\) | −1645.38 | + | 3918.54i | −0.126870 | + | 0.302145i | ||||
\(553\) | −1584.59 | + | 1584.59i | −0.121851 | + | 0.121851i | ||||
\(554\) | 4220.13 | 0.323639 | ||||||||
\(555\) | 1728.56 | + | 12050.8i | 0.132204 | + | 0.921668i | ||||
\(556\) | −1345.34 | −0.102617 | ||||||||
\(557\) | 14440.2 | − | 14440.2i | 1.09847 | − | 1.09847i | 0.103884 | − | 0.994589i | \(-0.466873\pi\) |
0.994589 | − | 0.103884i | \(-0.0331270\pi\) | |||||||
\(558\) | −346.198 | − | 3.35183i | −0.0262647 | − | 0.000254291i | ||||
\(559\) | − | 11102.1i | − | 0.840014i | ||||||
\(560\) | −2104.37 | − | 3510.55i | −0.158796 | − | 0.264907i | ||||
\(561\) | −956.924 | − | 2342.22i | −0.0720167 | − | 0.176272i | ||||
\(562\) | −7310.19 | − | 7310.19i | −0.548686 | − | 0.548686i | ||||
\(563\) | 13865.7 | + | 13865.7i | 1.03796 | + | 1.03796i | 0.999251 | + | 0.0387094i | \(0.0123247\pi\) |
0.0387094 | + | 0.999251i | \(0.487675\pi\) | |||||||
\(564\) | 2129.74 | + | 5212.87i | 0.159004 | + | 0.389187i | ||||
\(565\) | 1013.38 | + | 1690.54i | 0.0754569 | + | 0.125879i | ||||
\(566\) | − | 2524.43i | − | 0.187473i | ||||||
\(567\) | 12020.5 | − | 11563.8i | 0.890326 | − | 0.856498i | ||||
\(568\) | −844.394 | + | 844.394i | −0.0623767 | + | 0.0623767i | ||||
\(569\) | −18660.0 | −1.37481 | −0.687405 | − | 0.726274i | \(-0.741250\pi\) | ||||
−0.687405 | + | 0.726274i | \(0.741250\pi\) | |||||||
\(570\) | 2256.10 | + | 15728.6i | 0.165786 | + | 1.15578i | ||||
\(571\) | 6653.04 | 0.487602 | 0.243801 | − | 0.969825i | \(-0.421606\pi\) | ||||
0.243801 | + | 0.969825i | \(0.421606\pi\) | |||||||
\(572\) | −1745.34 | + | 1745.34i | −0.127581 | + | 0.127581i | ||||
\(573\) | −4103.66 | + | 9773.03i | −0.299185 | + | 0.712520i | ||||
\(574\) | − | 941.080i | − | 0.0684319i | ||||||
\(575\) | −3710.92 | − | 12229.2i | −0.269141 | − | 0.886941i | ||||
\(576\) | −1233.65 | + | 1209.99i | −0.0892399 | + | 0.0875285i | ||||
\(577\) | −18037.4 | − | 18037.4i | −1.30140 | − | 1.30140i | −0.927451 | − | 0.373944i | \(-0.878005\pi\) |
−0.373944 | − | 0.927451i | \(-0.621995\pi\) | |||||||
\(578\) | −4887.38 | − | 4887.38i | −0.351709 | − | 0.351709i | ||||
\(579\) | −8669.87 | + | 3542.11i | −0.622293 | + | 0.254240i | ||||
\(580\) | 2244.25 | − | 8961.33i | 0.160668 | − | 0.641550i | ||||
\(581\) | − | 23788.0i | − | 1.69861i | ||||||
\(582\) | −11003.0 | − | 4620.11i | −0.783656 | − | 0.329054i | ||||
\(583\) | −153.378 | + | 153.378i | −0.0108958 | + | 0.0108958i | ||||
\(584\) | 8732.02 | 0.618722 | ||||||||
\(585\) | 14130.2 | + | 3684.47i | 0.998652 | + | 0.260400i | ||||
\(586\) | −9400.21 | −0.662661 | ||||||||
\(587\) | −14567.2 | + | 14567.2i | −1.02428 | + | 1.02428i | −0.0245838 | + | 0.999698i | \(0.507826\pi\) |
−0.999698 | + | 0.0245838i | \(0.992174\pi\) | |||||||
\(588\) | −3459.26 | − | 1452.53i | −0.242615 | − | 0.101873i | ||||
\(589\) | − | 876.789i | − | 0.0613369i | ||||||
\(590\) | −12031.1 | + | 7211.94i | −0.839514 | + | 0.503239i | ||||
\(591\) | 13494.0 | − | 5513.04i | 0.939205 | − | 0.383716i | ||||
\(592\) | −2370.85 | − | 2370.85i | −0.164597 | − | 0.164597i | ||||
\(593\) | −20017.5 | − | 20017.5i | −1.38621 | − | 1.38621i | −0.833128 | − | 0.553080i | \(-0.813453\pi\) |
−0.553080 | − | 0.833128i | \(-0.686547\pi\) | |||||||
\(594\) | −1417.61 | + | 3286.59i | −0.0979214 | + | 0.227021i | ||||
\(595\) | 9472.27 | + | 2372.21i | 0.652647 | + | 0.163447i | ||||
\(596\) | − | 12965.3i | − | 0.891071i | ||||||
\(597\) | −3651.93 | + | 8697.21i | −0.250357 | + | 0.596236i | ||||
\(598\) | −6994.26 | + | 6994.26i | −0.478289 | + | 0.478289i | ||||
\(599\) | 19821.1 | 1.35203 | 0.676017 | − | 0.736886i | \(-0.263705\pi\) | ||||
0.676017 | + | 0.736886i | \(0.263705\pi\) | |||||||
\(600\) | 533.855 | − | 5168.66i | 0.0363242 | − | 0.351682i | ||||
\(601\) | 9850.79 | 0.668589 | 0.334294 | − | 0.942469i | \(-0.391502\pi\) | ||||
0.334294 | + | 0.942469i | \(0.391502\pi\) | |||||||
\(602\) | −7426.24 | + | 7426.24i | −0.502775 | + | 0.502775i | ||||
\(603\) | 44.5632 | − | 4602.77i | 0.00300954 | − | 0.310844i | ||||
\(604\) | 896.614i | 0.0604019i | ||||||||
\(605\) | −12670.5 | − | 3173.16i | −0.851451 | − | 0.213235i | ||||
\(606\) | −4800.18 | − | 11749.2i | −0.321772 | − | 0.787589i | ||||
\(607\) | 403.095 | + | 403.095i | 0.0269540 | + | 0.0269540i | 0.720455 | − | 0.693501i | \(-0.243933\pi\) |
−0.693501 | + | 0.720455i | \(0.743933\pi\) | |||||||
\(608\) | −3094.42 | − | 3094.42i | −0.206407 | − | 0.206407i | ||||
\(609\) | −9288.39 | − | 22734.8i | −0.618037 | − | 1.51274i | ||||
\(610\) | −10429.0 | + | 6251.57i | −0.692226 | + | 0.414948i | ||||
\(611\) | 13105.9i | 0.867773i | ||||||||
\(612\) | 39.9122 | − | 4122.39i | 0.00263620 | − | 0.272284i | ||||
\(613\) | 4616.26 | − | 4616.26i | 0.304158 | − | 0.304158i | −0.538480 | − | 0.842638i | \(-0.681001\pi\) |
0.842638 | + | 0.538480i | \(0.181001\pi\) | |||||||
\(614\) | 7235.13 | 0.475547 | ||||||||
\(615\) | 716.293 | − | 956.195i | 0.0469654 | − | 0.0626951i | ||||
\(616\) | 2334.93 | 0.152722 | ||||||||
\(617\) | 14556.9 | − | 14556.9i | 0.949818 | − | 0.949818i | −0.0489818 | − | 0.998800i | \(-0.515598\pi\) |
0.998800 | + | 0.0489818i | \(0.0155976\pi\) | |||||||
\(618\) | −5768.51 | + | 13738.0i | −0.375475 | + | 0.894209i | ||||
\(619\) | 12601.3i | 0.818236i | 0.912482 | + | 0.409118i | \(0.134163\pi\) | ||||
−0.912482 | + | 0.409118i | \(0.865837\pi\) | |||||||
\(620\) | −69.6555 | + | 278.135i | −0.00451199 | + | 0.0180164i | ||||
\(621\) | −5680.93 | + | 13170.7i | −0.367098 | + | 0.851081i | ||||
\(622\) | 11458.5 | + | 11458.5i | 0.738655 | + | 0.738655i | ||||
\(623\) | −7973.31 | − | 7973.31i | −0.512751 | − | 0.512751i | ||||
\(624\) | −3723.02 | + | 1521.05i | −0.238846 | + | 0.0975815i | ||||
\(625\) | 8683.22 | + | 12990.1i | 0.555726 | + | 0.831366i | ||||
\(626\) | 300.509i | 0.0191865i | ||||||||
\(627\) | −8357.69 | − | 3509.36i | −0.532335 | − | 0.223525i | ||||
\(628\) | −4026.94 | + | 4026.94i | −0.255879 | + | 0.255879i | ||||
\(629\) | 7999.17 | 0.507071 | ||||||||
\(630\) | −6987.20 | − | 11916.3i | −0.441868 | − | 0.753583i | ||||
\(631\) | 20754.9 | 1.30942 | 0.654708 | − | 0.755882i | \(-0.272792\pi\) | ||||
0.654708 | + | 0.755882i | \(0.272792\pi\) | |||||||
\(632\) | 554.045 | − | 554.045i | 0.0348714 | − | 0.0348714i | ||||
\(633\) | 17160.5 | + | 7205.64i | 1.07752 | + | 0.452446i | ||||
\(634\) | 3321.93i | 0.208093i | ||||||||
\(635\) | −2377.63 | − | 3966.41i | −0.148588 | − | 0.247877i | ||||
\(636\) | −327.174 | + | 133.668i | −0.0203983 | + | 0.00833379i | ||||
\(637\) | −6174.50 | − | 6174.50i | −0.384054 | − | 0.384054i | ||||
\(638\) | 3726.51 | + | 3726.51i | 0.231245 | + | 0.231245i | ||||
\(639\) | −2877.29 | + | 2822.11i | −0.178128 | + | 0.174712i | ||||
\(640\) | 735.781 | + | 1227.45i | 0.0454442 | + | 0.0758111i | ||||
\(641\) | 28695.5i | 1.76818i | 0.467313 | + | 0.884092i | \(0.345222\pi\) | ||||
−0.467313 | + | 0.884092i | \(0.654778\pi\) | |||||||
\(642\) | 593.301 | − | 1412.97i | 0.0364731 | − | 0.0868622i | ||||
\(643\) | −7444.99 | + | 7444.99i | −0.456612 | + | 0.456612i | −0.897542 | − | 0.440930i | \(-0.854649\pi\) |
0.440930 | + | 0.897542i | \(0.354649\pi\) | |||||||
\(644\) | 9357.00 | 0.572543 | ||||||||
\(645\) | −13197.9 | + | 1893.11i | −0.805686 | + | 0.115568i | ||||
\(646\) | 10440.5 | 0.635874 | ||||||||
\(647\) | −15997.5 | + | 15997.5i | −0.972065 | + | 0.972065i | −0.999620 | − | 0.0275552i | \(-0.991228\pi\) |
0.0275552 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(648\) | −4202.92 | + | 4043.23i | −0.254794 | + | 0.245113i | ||||
\(649\) | − | 8002.11i | − | 0.483991i | ||||||
\(650\) | 5699.86 | − | 10666.1i | 0.343949 | − | 0.643628i | ||||
\(651\) | 288.287 | + | 705.627i | 0.0173561 | + | 0.0424819i | ||||
\(652\) | −2777.83 | − | 2777.83i | −0.166853 | − | 0.166853i | ||||
\(653\) | 4592.90 | + | 4592.90i | 0.275243 | + | 0.275243i | 0.831207 | − | 0.555963i | \(-0.187651\pi\) |
−0.555963 | + | 0.831207i | \(0.687651\pi\) | |||||||
\(654\) | −2864.21 | − | 7010.62i | −0.171253 | − | 0.419170i | ||||
\(655\) | −1262.92 | + | 5042.85i | −0.0753378 | + | 0.300825i | ||||
\(656\) | 329.044i | 0.0195838i | ||||||||
\(657\) | 29469.2 | + | 285.316i | 1.74993 | + | 0.0169425i | ||||
\(658\) | 8766.63 | − | 8766.63i | 0.519390 | − | 0.519390i | ||||
\(659\) | 12460.6 | 0.736565 | 0.368282 | − | 0.929714i | \(-0.379946\pi\) | ||||
0.368282 | + | 0.929714i | \(0.379946\pi\) | |||||||
\(660\) | 2372.43 | + | 1777.21i | 0.139919 | + | 0.104815i | ||||
\(661\) | −21945.5 | −1.29135 | −0.645675 | − | 0.763612i | \(-0.723424\pi\) | ||||
−0.645675 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(662\) | −4005.71 | + | 4005.71i | −0.235176 | + | 0.235176i | ||||
\(663\) | 3714.68 | − | 8846.65i | 0.217596 | − | 0.518213i | ||||
\(664\) | 8317.36i | 0.486109i | ||||||||
\(665\) | 30005.4 | − | 17986.5i | 1.74972 | − | 1.04885i | ||||
\(666\) | −7923.79 | − | 8078.72i | −0.461022 | − | 0.470036i | ||||
\(667\) | 14933.6 | + | 14933.6i | 0.866915 | + | 0.866915i | ||||
\(668\) | 7501.99 | + | 7501.99i | 0.434522 | + | 0.434522i | ||||
\(669\) | 1943.45 | − | 794.005i | 0.112314 | − | 0.0458864i | ||||
\(670\) | −3697.87 | − | 926.084i | −0.213225 | − | 0.0533996i | ||||
\(671\) | − | 6936.51i | − | 0.399078i | ||||||
\(672\) | 3507.79 | + | 1472.91i | 0.201363 | + | 0.0845515i | ||||
\(673\) | 5271.96 | − | 5271.96i | 0.301960 | − | 0.301960i | −0.539820 | − | 0.841780i | \(-0.681508\pi\) |
0.841780 | + | 0.539820i | \(0.181508\pi\) | |||||||
\(674\) | 13547.8 | 0.774244 | ||||||||
\(675\) | 1970.56 | − | 17426.0i | 0.112366 | − | 0.993667i | ||||
\(676\) | −572.230 | −0.0325575 | ||||||||
\(677\) | −6270.55 | + | 6270.55i | −0.355977 | + | 0.355977i | −0.862328 | − | 0.506350i | \(-0.830994\pi\) |
0.506350 | + | 0.862328i | \(0.330994\pi\) | |||||||
\(678\) | −1689.21 | − | 709.293i | −0.0956839 | − | 0.0401773i | ||||
\(679\) | 26273.8i | 1.48497i | ||||||||
\(680\) | −3311.93 | − | 829.430i | −0.186775 | − | 0.0467753i | ||||
\(681\) | −32513.2 | + | 13283.4i | −1.82953 | + | 0.747461i | ||||
\(682\) | −115.661 | − | 115.661i | −0.00649397 | − | 0.00649397i | ||||
\(683\) | −16616.6 | − | 16616.6i | −0.930917 | − | 0.930917i | 0.0668461 | − | 0.997763i | \(-0.478706\pi\) |
−0.997763 | + | 0.0668461i | \(0.978706\pi\) | |||||||
\(684\) | −10342.1 | − | 10544.3i | −0.578127 | − | 0.589431i | ||||
\(685\) | 1384.85 | − | 830.133i | 0.0772442 | − | 0.0463033i | ||||
\(686\) | − | 7435.62i | − | 0.413839i | ||||||
\(687\) | 10183.3 | − | 24251.9i | 0.565526 | − | 1.34682i | ||||
\(688\) | 2596.55 | − | 2596.55i | 0.143884 | − | 0.143884i | ||||
\(689\) | −822.565 | −0.0454822 | ||||||||
\(690\) | 9507.29 | + | 7121.98i | 0.524545 | + | 0.392941i | ||||
\(691\) | −35477.3 | −1.95314 | −0.976571 | − | 0.215197i | \(-0.930961\pi\) | ||||
−0.976571 | + | 0.215197i | \(0.930961\pi\) | |||||||
\(692\) | −8402.89 | + | 8402.89i | −0.461604 | + | 0.461604i | ||||
\(693\) | 7880.02 | + | 76.2931i | 0.431944 | + | 0.00418201i | ||||
\(694\) | 6008.07i | 0.328621i | ||||||||
\(695\) | −913.516 | + | 3647.68i | −0.0498585 | + | 0.199086i | ||||
\(696\) | 3247.64 | + | 7949.11i | 0.176870 | + | 0.432917i | ||||
\(697\) | −555.091 | − | 555.091i | −0.0301658 | − | 0.0301658i | ||||
\(698\) | 13060.4 | + | 13060.4i | 0.708229 | + | 0.708229i | ||||
\(699\) | 2814.79 | + | 6889.65i | 0.152311 | + | 0.372805i | ||||
\(700\) | −10947.3 | + | 3321.93i | −0.591096 | + | 0.179368i | ||||
\(701\) | − | 6316.02i | − | 0.340304i | −0.985418 | − | 0.170152i | \(-0.945574\pi\) | ||
0.985418 | − | 0.170152i | \(-0.0544258\pi\) | |||||||
\(702\) | −12614.3 | + | 5011.66i | −0.678200 | + | 0.269449i | ||||
\(703\) | 20264.2 | − | 20264.2i | 1.08717 | − | 1.08717i | ||||
\(704\) | −816.397 | −0.0437061 | ||||||||
\(705\) | 15580.1 | − | 2234.80i | 0.832310 | − | 0.119387i | ||||
\(706\) | 2791.01 | 0.148784 | ||||||||
\(707\) | −19759.0 | + | 19759.0i | −1.05108 | + | 1.05108i | ||||
\(708\) | 5047.84 | − | 12021.6i | 0.267951 | − | 0.638137i | ||||
\(709\) | 4327.74i | 0.229241i | 0.993409 | + | 0.114620i | \(0.0365652\pi\) | ||||
−0.993409 | + | 0.114620i | \(0.963435\pi\) | |||||||
\(710\) | 1716.09 | + | 2862.81i | 0.0907092 | + | 0.151323i | ||||
\(711\) | 1887.92 | − | 1851.71i | 0.0995814 | − | 0.0976716i | ||||
\(712\) | 2787.83 | + | 2787.83i | 0.146739 | + | 0.146739i | ||||
\(713\) | −463.500 | − | 463.500i | −0.0243453 | − | 0.0243453i | ||||
\(714\) | −8402.34 | + | 3432.80i | −0.440406 | + | 0.179929i | ||||
\(715\) | 3547.10 | + | 5917.35i | 0.185530 | + | 0.309505i | ||||
\(716\) | 5088.50i | 0.265595i | ||||||||
\(717\) | 5464.55 | + | 2294.55i | 0.284627 | + | 0.119514i | ||||
\(718\) | 15134.2 | − | 15134.2i | 0.786635 | − | 0.786635i | ||||
\(719\) | −26854.1 | −1.39289 | −0.696447 | − | 0.717609i | \(-0.745237\pi\) | ||||
−0.696447 | + | 0.717609i | \(0.745237\pi\) | |||||||
\(720\) | 2443.04 | + | 4166.48i | 0.126454 | + | 0.215660i | ||||
\(721\) | 32804.6 | 1.69446 | ||||||||
\(722\) | 16748.6 | − | 16748.6i | 0.863321 | − | 0.863321i | ||||
\(723\) | −4285.53 | − | 1799.48i | −0.220444 | − | 0.0925635i | ||||
\(724\) | − | 250.912i | − | 0.0128799i | ||||||
\(725\) | −22773.4 | − | 12169.9i | −1.16660 | − | 0.623419i | ||||
\(726\) | 11239.3 | − | 4591.85i | 0.574558 | − | 0.234738i | ||||
\(727\) | 15761.3 | + | 15761.3i | 0.804065 | + | 0.804065i | 0.983728 | − | 0.179663i | \(-0.0575007\pi\) |
−0.179663 | + | 0.983728i | \(0.557501\pi\) | |||||||
\(728\) | 6261.11 | + | 6261.11i | 0.318753 | + | 0.318753i | ||||
\(729\) | −14316.3 | + | 13507.9i | −0.727343 | + | 0.686274i | ||||
\(730\) | 5929.25 | − | 23675.6i | 0.300618 | − | 1.20037i | ||||
\(731\) | 8760.65i | 0.443262i | ||||||||
\(732\) | 4375.65 | − | 10420.8i | 0.220941 | − | 0.526179i | ||||
\(733\) | −16481.2 | + | 16481.2i | −0.830487 | + | 0.830487i | −0.987583 | − | 0.157096i | \(-0.949787\pi\) |
0.157096 | + | 0.987583i | \(0.449787\pi\) | |||||||
\(734\) | −2842.14 | −0.142923 | ||||||||
\(735\) | −6287.25 | + | 8392.98i | −0.315522 | + | 0.421197i | ||||
\(736\) | −3271.63 | −0.163850 | ||||||||
\(737\) | 1537.74 | − | 1537.74i | 0.0768565 | − | 0.0768565i | ||||
\(738\) | −10.7514 | + | 1110.47i | −0.000536266 | + | 0.0553889i | ||||
\(739\) | − | 18693.3i | − | 0.930505i | −0.885178 | − | 0.465253i | \(-0.845963\pi\) | ||
0.885178 | − | 0.465253i | \(-0.154037\pi\) | |||||||
\(740\) | −8038.08 | + | 4818.35i | −0.399305 | + | 0.239360i | ||||
\(741\) | −13000.8 | − | 31821.4i | −0.644528 | − | 1.57758i | ||||
\(742\) | 550.218 | + | 550.218i | 0.0272226 | + | 0.0272226i | ||||
\(743\) | 2518.82 | + | 2518.82i | 0.124369 | + | 0.124369i | 0.766552 | − | 0.642182i | \(-0.221971\pi\) |
−0.642182 | + | 0.766552i | \(0.721971\pi\) | |||||||
\(744\) | −100.798 | − | 246.719i | −0.00496698 | − | 0.0121575i | ||||
\(745\) | −35153.4 | − | 8803.72i | −1.72875 | − | 0.432944i | ||||
\(746\) | 24544.2i | 1.20460i | ||||||||
\(747\) | −271.767 | + | 28069.8i | −0.0133112 | + | 1.37486i | ||||
\(748\) | 1377.25 | − | 1377.25i | 0.0673223 | − | 0.0673223i | ||||
\(749\) | −3374.01 | −0.164597 | ||||||||
\(750\) | −13651.5 | − | 4957.11i | −0.664645 | − | 0.241344i | ||||
\(751\) | −2523.97 | −0.122638 | −0.0613190 | − | 0.998118i | \(-0.519531\pi\) | ||||
−0.0613190 | + | 0.998118i | \(0.519531\pi\) | |||||||
\(752\) | −3065.21 | + | 3065.21i | −0.148639 | + | 0.148639i | ||||
\(753\) | 8446.15 | − | 20114.8i | 0.408758 | − | 0.973474i | ||||
\(754\) | 19985.3i | 0.965279i | ||||||||
\(755\) | 2431.04 | + | 608.822i | 0.117185 | + | 0.0293474i | ||||
\(756\) | 11790.1 | + | 5085.44i | 0.567198 | + | 0.244651i | ||||
\(757\) | −23079.0 | − | 23079.0i | −1.10809 | − | 1.10809i | −0.993402 | − | 0.114684i | \(-0.963415\pi\) |
−0.114684 | − | 0.993402i | \(-0.536585\pi\) | |||||||
\(758\) | −20779.1 | − | 20779.1i | −0.995687 | − | 0.995687i | ||||
\(759\) | −6273.31 | + | 2562.99i | −0.300009 | + | 0.122570i | ||||
\(760\) | −10491.3 | + | 6288.88i | −0.500734 | + | 0.300160i | ||||
\(761\) | − | 30848.4i | − | 1.46945i | −0.678364 | − | 0.734726i | \(-0.737311\pi\) | ||
0.678364 | − | 0.734726i | \(-0.262689\pi\) | |||||||
\(762\) | 3963.28 | + | 1664.17i | 0.188418 | + | 0.0791161i | ||||
\(763\) | −11790.0 | + | 11790.0i | −0.559404 | + | 0.559404i | ||||
\(764\) | −8159.59 | −0.386392 | ||||||||
\(765\) | −11150.1 | − | 2907.41i | −0.526973 | − | 0.137409i | ||||
\(766\) | −5235.16 | −0.246937 | ||||||||
\(767\) | 21457.6 | − | 21457.6i | 1.01016 | − | 1.01016i | ||||
\(768\) | −1226.48 | − | 514.994i | −0.0576260 | − | 0.0241970i | ||||
\(769\) | − | 24831.0i | − | 1.16441i | −0.813043 | − | 0.582204i | \(-0.802191\pi\) | ||
0.813043 | − | 0.582204i | \(-0.197809\pi\) | |||||||
\(770\) | 1585.47 | − | 6330.82i | 0.0742032 | − | 0.296295i | ||||
\(771\) | 20439.8 | − | 8350.77i | 0.954764 | − | 0.390072i | ||||
\(772\) | −5097.95 | − | 5097.95i | −0.237667 | − | 0.237667i | ||||
\(773\) | 17900.7 | + | 17900.7i | 0.832913 | + | 0.832913i | 0.987914 | − | 0.155001i | \(-0.0495380\pi\) |
−0.155001 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(774\) | 8847.77 | − | 8678.09i | 0.410887 | − | 0.403007i | ||||
\(775\) | 706.825 | + | 377.721i | 0.0327612 | + | 0.0175073i | ||||
\(776\) | − | 9186.49i | − | 0.424969i | ||||||
\(777\) | −9645.51 | + | 22971.2i | −0.445342 | + | 1.06060i | ||||
\(778\) | 13147.4 | − | 13147.4i | 0.605856 | − | 0.605856i | ||||
\(779\) | −2812.41 | −0.129352 | ||||||||
\(780\) | 1596.09 | + | 11127.2i | 0.0732683 | + | 0.510794i | ||||
\(781\) | −1904.11 | −0.0872398 | ||||||||
\(782\) | 5519.17 | − | 5519.17i | 0.252385 | − | 0.252385i | ||||
\(783\) | 10700.5 | + | 26933.1i | 0.488385 | + | 1.22926i | ||||
\(784\) | − | 2888.17i | − | 0.131568i | ||||||
\(785\) | 8184.06 | + | 13652.8i | 0.372104 | + | 0.620752i | ||||
\(786\) | −1827.56 | − | 4473.24i | −0.0829349 | − | 0.202996i | ||||
\(787\) | −3928.66 | − | 3928.66i | −0.177944 | − | 0.177944i | 0.612515 | − | 0.790459i | \(-0.290158\pi\) |
−0.790459 | + | 0.612515i | \(0.790158\pi\) | |||||||
\(788\) | 7934.59 | + | 7934.59i | 0.358703 | + | 0.358703i | ||||
\(789\) | 9990.11 | + | 24452.4i | 0.450770 | + | 1.10333i | ||||
\(790\) | −1126.00 | − | 1878.42i | −0.0507105 | − | 0.0845964i | ||||
\(791\) | 4033.63i | 0.181314i | ||||||||
\(792\) | −2755.21 | − | 26.6755i | −0.123614 | − | 0.00119681i | ||||
\(793\) | 18600.2 | − | 18600.2i | 0.832930 | − | 0.832930i | ||||
\(794\) | −2398.92 | −0.107222 | ||||||||
\(795\) | 140.263 | + | 977.849i | 0.00625736 | + | 0.0436235i | ||||
\(796\) | −7261.38 | −0.323333 | ||||||||
\(797\) | −10942.0 | + | 10942.0i | −0.486307 | + | 0.486307i | −0.907139 | − | 0.420832i | \(-0.861738\pi\) |
0.420832 | + | 0.907139i | \(0.361738\pi\) | |||||||
\(798\) | −12589.3 | + | 29981.8i | −0.558464 | + | 1.33001i | ||||
\(799\) | − | 10341.9i | − | 0.457909i | ||||||
\(800\) | 3827.65 | − | 1161.50i | 0.169160 | − | 0.0513314i | ||||
\(801\) | 9317.38 | + | 9499.56i | 0.411003 | + | 0.419039i | ||||
\(802\) | 12059.2 | + | 12059.2i | 0.530954 | + | 0.530954i | ||||
\(803\) | 9845.35 | + | 9845.35i | 0.432671 | + | 0.432671i | ||||
\(804\) | 3280.18 | − | 1340.13i | 0.143884 | − | 0.0587845i | ||||
\(805\) | 6353.62 | − | 25370.1i | 0.278181 | − | 1.11078i | ||||
\(806\) | − | 620.289i | − | 0.0271076i | ||||||
\(807\) | −10043.0 | − | 4217.02i | −0.438080 | − | 0.183948i | ||||
\(808\) | 6908.63 | − | 6908.63i | 0.300798 | − | 0.300798i | ||||
\(809\) | 15310.9 | 0.665395 | 0.332697 | − | 0.943034i | \(-0.392041\pi\) | ||||
0.332697 | + | 0.943034i | \(0.392041\pi\) | |||||||
\(810\) | 8108.73 | + | 14141.0i | 0.351743 | + | 0.613414i | ||||
\(811\) | −3667.20 | −0.158783 | −0.0793915 | − | 0.996844i | \(-0.525298\pi\) | ||||
−0.0793915 | + | 0.996844i | \(0.525298\pi\) | |||||||
\(812\) | 13368.2 | − | 13368.2i | 0.577751 | − | 0.577751i | ||||
\(813\) | 2821.35 | + | 1184.67i | 0.121708 | + | 0.0511049i | ||||
\(814\) | − | 5346.27i | − | 0.230205i | ||||||
\(815\) | −9417.88 | + | 5645.46i | −0.404778 | + | 0.242640i | ||||
\(816\) | 2937.83 | − | 1200.26i | 0.126035 | − | 0.0514921i | ||||
\(817\) | 22193.2 | + | 22193.2i | 0.950358 | + | 0.950358i | ||||
\(818\) | −10754.9 | − | 10754.9i | −0.459702 | − | 0.459702i | ||||
\(819\) | 20925.7 | + | 21334.8i | 0.892798 | + | 0.910255i | ||||
\(820\) | 892.153 | + | 223.428i | 0.0379943 | + | 0.00951519i | ||||
\(821\) | − | 7128.41i | − | 0.303025i | −0.988455 | − | 0.151512i | \(-0.951586\pi\) | ||
0.988455 | − | 0.151512i | \(-0.0484143\pi\) | |||||||
\(822\) | −581.034 | + | 1383.76i | −0.0246544 | + | 0.0587153i | ||||
\(823\) | −17408.3 | + | 17408.3i | −0.737321 | + | 0.737321i | −0.972059 | − | 0.234738i | \(-0.924577\pi\) |
0.234738 | + | 0.972059i | \(0.424577\pi\) | |||||||
\(824\) | −11469.9 | −0.484921 | ||||||||
\(825\) | 6429.58 | − | 5225.73i | 0.271332 | − | 0.220529i | ||||
\(826\) | −28706.2 | −1.20922 | ||||||||
\(827\) | 25331.1 | − | 25331.1i | 1.06511 | − | 1.06511i | 0.0673858 | − | 0.997727i | \(-0.478534\pi\) |
0.997727 | − | 0.0673858i | \(-0.0214658\pi\) | |||||||
\(828\) | −11041.2 | − | 106.899i | −0.463417 | − | 0.00448672i | ||||
\(829\) | 37685.9i | 1.57887i | 0.613832 | + | 0.789437i | \(0.289627\pi\) | ||||
−0.613832 | + | 0.789437i | \(0.710373\pi\) | |||||||
\(830\) | 22551.3 | + | 5647.68i | 0.943093 | + | 0.236186i | ||||
\(831\) | 4146.74 | + | 10149.8i | 0.173103 | + | 0.423698i | ||||
\(832\) | −2189.16 | − | 2189.16i | −0.0912207 | − | 0.0912207i | ||||
\(833\) | 4872.29 | + | 4872.29i | 0.202659 | + | 0.202659i | ||||
\(834\) | −1321.94 | − | 3235.67i | −0.0548862 | − | 0.134343i | ||||
\(835\) | 25434.6 | − | 15246.5i | 1.05413 | − | 0.631889i | ||||
\(836\) | − | 6977.92i | − | 0.288680i | ||||||
\(837\) | −332.116 | − | 835.931i | −0.0137152 | − | 0.0345209i | ||||
\(838\) | −19664.2 | + | 19664.2i | −0.810609 | + | 0.810609i | ||||
\(839\) | 10906.1 | 0.448774 | 0.224387 | − | 0.974500i | \(-0.427962\pi\) | ||||
0.224387 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(840\) | 6375.44 | − | 8510.71i | 0.261873 | − | 0.349580i | ||||
\(841\) | 18282.0 | 0.749601 | ||||||||
\(842\) | −22080.8 | + | 22080.8i | −0.903745 | + | 0.903745i | ||||
\(843\) | 10398.6 | − | 24764.7i | 0.424849 | − | 1.01180i | ||||
\(844\) | 14327.5i | 0.584327i | ||||||||
\(845\) | −388.557 | + | 1551.52i | −0.0158187 | + | 0.0631642i | ||||
\(846\) | −10444.7 | + | 10244.4i | −0.424465 | + | 0.416325i | ||||
\(847\) | −18901.4 | − | 18901.4i | −0.766778 | − | 0.766778i | ||||
\(848\) | −192.381 | − | 192.381i | −0.00779055 | − | 0.00779055i | ||||
\(849\) | 6071.49 | − | 2480.53i | 0.245434 | − | 0.100273i | ||||
\(850\) | −4497.75 | + | 8416.60i | −0.181496 | + | 0.339632i | ||||
\(851\) | − | 21424.6i | − | 0.863017i | ||||||
\(852\) | −2860.56 | − | 1201.14i | −0.115025 | − | 0.0482984i | ||||
\(853\) | −14701.8 | + | 14701.8i | −0.590131 | + | 0.590131i | −0.937667 | − | 0.347536i | \(-0.887018\pi\) |
0.347536 | + | 0.937667i | \(0.387018\pi\) | |||||||
\(854\) | −24883.6 | −0.997071 | ||||||||
\(855\) | −35611.8 | + | 20881.2i | −1.42444 | + | 0.835230i | ||||
\(856\) | 1179.70 | 0.0471045 | ||||||||
\(857\) | −14745.6 | + | 14745.6i | −0.587749 | + | 0.587749i | −0.937021 | − | 0.349272i | \(-0.886429\pi\) |
0.349272 | + | 0.937021i | \(0.386429\pi\) | |||||||
\(858\) | −5912.69 | − | 2482.72i | −0.235263 | − | 0.0987862i | ||||
\(859\) | − | 45884.6i | − | 1.82254i | −0.411808 | − | 0.911271i | \(-0.635103\pi\) | ||
0.411808 | − | 0.911271i | \(-0.364897\pi\) | |||||||
\(860\) | −5277.03 | − | 8803.26i | −0.209239 | − | 0.349057i | ||||
\(861\) | 2263.39 | − | 924.714i | 0.0895888 | − | 0.0366018i | ||||
\(862\) | 2386.65 | + | 2386.65i | 0.0943034 | + | 0.0943034i | ||||
\(863\) | 10936.4 | + | 10936.4i | 0.431376 | + | 0.431376i | 0.889096 | − | 0.457720i | \(-0.151334\pi\) |
−0.457720 | + | 0.889096i | \(0.651334\pi\) | |||||||
\(864\) | −4122.35 | − | 1778.10i | −0.162321 | − | 0.0700141i | ||||
\(865\) | 17077.4 | + | 28489.0i | 0.671272 | + | 1.11983i | ||||
\(866\) | 10198.0i | 0.400164i | ||||||||
\(867\) | 6952.22 | − | 16557.0i | 0.272329 | − | 0.648564i | ||||
\(868\) | −414.914 | + | 414.914i | −0.0162248 | + | 0.0162248i | ||||
\(869\) | 1249.37 | 0.0487710 | ||||||||
\(870\) | 23758.1 | − | 3407.86i | 0.925832 | − | 0.132801i | ||||
\(871\) | 8246.86 | 0.320820 | ||||||||
\(872\) | 4122.30 | − | 4122.30i | 0.160090 | − | 0.160090i | ||||
\(873\) | 300.165 | − | 31002.9i | 0.0116370 | − | 1.20194i | ||||
\(874\) | − | 27963.3i | − | 1.08223i | ||||||
\(875\) | 1573.48 | + | 31937.5i | 0.0607925 | + | 1.23393i | ||||
\(876\) | 8580.17 | + | 21001.3i | 0.330933 | + | 0.810011i | ||||
\(877\) | −4986.22 | − | 4986.22i | −0.191987 | − | 0.191987i | 0.604567 | − | 0.796554i | \(-0.293346\pi\) |
−0.796554 | + | 0.604567i | \(0.793346\pi\) | |||||||
\(878\) | −11334.8 | − | 11334.8i | −0.435685 | − | 0.435685i | ||||
\(879\) | −9236.74 | − | 22608.4i | −0.354434 | − | 0.867534i | ||||
\(880\) | −554.352 | + | 2213.54i | −0.0212355 | + | 0.0847936i | ||||
\(881\) | 40395.0i | 1.54477i | 0.635155 | + | 0.772385i | \(0.280936\pi\) | ||||
−0.635155 | + | 0.772385i | \(0.719064\pi\) | |||||||
\(882\) | 94.3701 | − | 9747.13i | 0.00360273 | − | 0.372112i | ||||
\(883\) | −16473.1 | + | 16473.1i | −0.627819 | + | 0.627819i | −0.947519 | − | 0.319700i | \(-0.896418\pi\) |
0.319700 | + | 0.947519i | \(0.396418\pi\) | |||||||
\(884\) | 7386.16 | 0.281022 | ||||||||
\(885\) | −29167.3 | − | 21849.4i | −1.10785 | − | 0.829899i | ||||
\(886\) | −13544.5 | −0.513584 | ||||||||
\(887\) | 8236.06 | − | 8236.06i | 0.311770 | − | 0.311770i | −0.533825 | − | 0.845595i | \(-0.679246\pi\) |
0.845595 | + | 0.533825i | \(0.179246\pi\) | |||||||
\(888\) | 3372.50 | − | 8031.75i | 0.127448 | − | 0.303522i | ||||
\(889\) | − | 9463.85i | − | 0.357038i | ||||||
\(890\) | 9451.78 | − | 5665.78i | 0.355982 | − | 0.213390i | ||||
\(891\) | −9297.52 | − | 180.051i | −0.349583 | − | 0.00676985i | ||||
\(892\) | 1142.77 | + | 1142.77i | 0.0428953 | + | 0.0428953i | ||||
\(893\) | −26199.0 | − | 26199.0i | −0.981764 | − | 0.981764i | ||||
\(894\) | 31182.7 | − | 12739.8i | 1.16656 | − | 0.476603i | ||||
\(895\) | 13796.7 | + | 3455.21i | 0.515277 | + | 0.129045i | ||||
\(896\) | 2928.69i | 0.109197i | ||||||||
\(897\) | −23694.5 | − | 9949.23i | −0.881980 | − | 0.370340i | ||||
\(898\) | 9103.51 | − | 9103.51i | 0.338294 | − | 0.338294i | ||||
\(899\) | −1324.39 | −0.0491335 | ||||||||
\(900\) | 12955.7 | − | 3794.80i | 0.479840 | − | 0.140548i | ||||
\(901\) | 649.086 | 0.0240002 | ||||||||
\(902\) | −370.997 | + | 370.997i | −0.0136949 | + | 0.0136949i | ||||
\(903\) | −25157.9 | − | 10563.7i | −0.927134 | − | 0.389300i | ||||
\(904\) | − | 1410.34i | − | 0.0518884i | ||||||
\(905\) | −680.311 | − | 170.375i | −0.0249882 | − | 0.00625797i | ||||
\(906\) | −2156.44 | + | 881.022i | −0.0790761 | + | 0.0323068i | ||||
\(907\) | −5461.54 | − | 5461.54i | −0.199942 | − | 0.199942i | 0.600033 | − | 0.799975i | \(-0.295154\pi\) |
−0.799975 | + | 0.600033i | \(0.795154\pi\) | |||||||
\(908\) | −19118.0 | − | 19118.0i | −0.698738 | − | 0.698738i | ||||
\(909\) | 23541.3 | − | 23089.8i | 0.858982 | − | 0.842508i | ||||
\(910\) | 21227.5 | − | 12724.6i | 0.773280 | − | 0.463535i | ||||
\(911\) | − | 1893.10i | − | 0.0688486i | −0.999407 | − | 0.0344243i | \(-0.989040\pi\) | ||
0.999407 | − | 0.0344243i | \(-0.0109598\pi\) | |||||||
\(912\) | 4401.77 | − | 10483.0i | 0.159821 | − | 0.380621i | ||||
\(913\) | −9377.82 | + | 9377.82i | −0.339935 | + | 0.339935i | ||||
\(914\) | −21024.1 | −0.760850 | ||||||||
\(915\) | −25283.2 | − | 18939.9i | −0.913485 | − | 0.684299i | ||||
\(916\) | 20248.1 | 0.730368 | ||||||||
\(917\) | −7522.77 | + | 7522.77i | −0.270909 | + | 0.270909i | ||||
\(918\) | 9953.94 | − | 3954.70i | 0.357875 | − | 0.142184i | ||||
\(919\) | − | 6455.86i | − | 0.231729i | −0.993265 | − | 0.115865i | \(-0.963036\pi\) | ||
0.993265 | − | 0.115865i | \(-0.0369638\pi\) | |||||||
\(920\) | −2221.51 | + | 8870.53i | −0.0796098 | + | 0.317883i | ||||
\(921\) | 7109.31 | + | 17401.2i | 0.254354 | + | 0.622571i | ||||
\(922\) | 22263.6 | + | 22263.6i | 0.795243 | + | 0.795243i | ||||
\(923\) | −5105.85 | − | 5105.85i | −0.182081 | − | 0.182081i | ||||
\(924\) | 2294.33 | + | 5615.73i | 0.0816859 | + | 0.199939i | ||||
\(925\) | 7606.20 | + | 25065.8i | 0.270368 | + | 0.890984i | ||||
\(926\) | 12403.0i | 0.440160i | ||||||||
\(927\) | −38709.3 | − | 374.777i | −1.37150 | − | 0.0132786i | ||||
\(928\) | −4674.14 | + | 4674.14i | −0.165341 | + | 0.165341i | ||||
\(929\) | −14798.5 | −0.522628 | −0.261314 | − | 0.965254i | \(-0.584156\pi\) | ||||
−0.261314 | + | 0.965254i | \(0.584156\pi\) | |||||||
\(930\) | −737.386 | + | 105.771i | −0.0259998 | + | 0.00372941i | ||||
\(931\) | 24685.8 | 0.869007 | ||||||||
\(932\) | −4051.17 | + | 4051.17i | −0.142382 | + | 0.142382i | ||||
\(933\) | −16299.5 | + | 38818.0i | −0.571943 | + | 1.36210i | ||||
\(934\) | 1146.51i | 0.0401659i | ||||||||
\(935\) | −2799.02 | − | 4669.38i | −0.0979012 | − | 0.163321i | ||||
\(936\) | −7316.55 | − | 7459.61i | −0.255501 | − | 0.260497i | ||||
\(937\) | 5568.25 | + | 5568.25i | 0.194137 | + | 0.194137i | 0.797481 | − | 0.603344i | \(-0.206165\pi\) |
−0.603344 | + | 0.797481i | \(0.706165\pi\) | |||||||
\(938\) | −5516.37 | − | 5516.37i | −0.192021 | − | 0.192021i | ||||
\(939\) | −722.754 | + | 295.284i | −0.0251184 | + | 0.0102622i | ||||
\(940\) | 6229.50 | + | 10392.2i | 0.216153 | + | 0.360592i | ||||
\(941\) | − | 26799.4i | − | 0.928413i | −0.885727 | − | 0.464207i | \(-0.846340\pi\) | ||
0.885727 | − | 0.464207i | \(-0.153660\pi\) | |||||||
\(942\) | −13642.1 | − | 5728.25i | −0.471850 | − | 0.198128i | ||||
\(943\) | −1486.73 | + | 1486.73i | −0.0513411 | + | 0.0513411i | ||||
\(944\) | 10037.0 | 0.346055 | ||||||||
\(945\) | 21794.2 | − | 28514.0i | 0.750227 | − | 0.981545i | ||||
\(946\) | 5855.21 | 0.201236 | ||||||||
\(947\) | 20065.7 | − | 20065.7i | 0.688540 | − | 0.688540i | −0.273369 | − | 0.961909i | \(-0.588138\pi\) |
0.961909 | + | 0.273369i | \(0.0881379\pi\) | |||||||
\(948\) | 1876.94 | + | 788.120i | 0.0643039 | + | 0.0270010i | ||||
\(949\) | 52800.5i | 1.80609i | ||||||||
\(950\) | 9927.56 | + | 32715.8i | 0.339045 | + | 1.11730i | ||||
\(951\) | −7989.56 | + | 3264.16i | −0.272428 | + | 0.111302i | ||||
\(952\) | −4940.64 | − | 4940.64i | −0.168201 | − | 0.168201i | ||||
\(953\) | 22947.3 | + | 22947.3i | 0.779996 | + | 0.779996i | 0.979830 | − | 0.199834i | \(-0.0640402\pi\) |
−0.199834 | + | 0.979830i | \(0.564040\pi\) | |||||||
\(954\) | −642.969 | − | 655.541i | −0.0218207 | − | 0.0222473i | ||||
\(955\) | −5540.56 | + | 22123.5i | −0.187736 | + | 0.749634i | ||||
\(956\) | 4562.41i | 0.154350i | ||||||||
\(957\) | −5300.91 | + | 12624.3i | −0.179053 | + | 0.426423i | ||||
\(958\) | −1180.61 | + | 1180.61i | −0.0398162 | + | 0.0398162i | ||||
\(959\) | 3304.24 | 0.111261 | ||||||||
\(960\) | −2229.14 | + | 2975.72i | −0.0749429 | + | 0.100043i | ||||
\(961\) | −29749.9 | −0.998620 | ||||||||
\(962\) | 14336.0 | − | 14336.0i | 0.480469 | − | 0.480469i | ||||
\(963\) | 3981.31 | + | 38.5464i | 0.133225 | + | 0.00128987i | ||||
\(964\) | − | 3578.03i | − | 0.119544i | ||||||
\(965\) | −17284.0 | + | 10360.7i | −0.576571 | + | 0.345620i | ||||
\(966\) | 9194.28 | + | 22504.5i | 0.306233 | + | 0.749554i | ||||
\(967\) | −15372.5 | − | 15372.5i | −0.511218 | − | 0.511218i | 0.403682 | − | 0.914899i | \(-0.367730\pi\) |
−0.914899 | + | 0.403682i | \(0.867730\pi\) | |||||||
\(968\) | 6608.79 | + | 6608.79i | 0.219436 | + | 0.219436i | ||||
\(969\) | 10258.9 | + | 25110.3i | 0.340107 | + | 0.832465i | ||||
\(970\) | −24907.8 | − | 6237.84i | −0.824475 | − | 0.206479i | ||||
\(971\) | − | 50515.3i | − | 1.66953i | −0.550607 | − | 0.834765i | \(-0.685604\pi\) | ||
0.550607 | − | 0.834765i | \(-0.314396\pi\) | |||||||
\(972\) | −13854.2 | − | 6135.50i | −0.457174 | − | 0.202465i | ||||
\(973\) | −5441.51 | + | 5441.51i | −0.179288 | + | 0.179288i | ||||
\(974\) | −3178.29 | −0.104557 | ||||||||
\(975\) | 31253.7 | + | 3228.09i | 1.02658 | + | 0.106033i | ||||
\(976\) | 8700.42 | 0.285342 | ||||||||
\(977\) | 9640.67 | − | 9640.67i | 0.315693 | − | 0.315693i | −0.531417 | − | 0.847110i | \(-0.678340\pi\) |
0.847110 | + | 0.531417i | \(0.178340\pi\) | |||||||
\(978\) | 3951.42 | − | 9410.46i | 0.129195 | − | 0.307682i | ||||
\(979\) | 6286.54i | 0.205229i | ||||||||
\(980\) | −7830.85 | − | 1961.14i | −0.255252 | − | 0.0639247i | ||||
\(981\) | 14046.8 | − | 13777.4i | 0.457166 | − | 0.448398i | ||||
\(982\) | 4148.90 | + | 4148.90i | 0.134824 | + | 0.134824i | ||||
\(983\) | 30440.0 | + | 30440.0i | 0.987677 | + | 0.987677i | 0.999925 | − | 0.0122482i | \(-0.00389882\pi\) |
−0.0122482 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(984\) | −791.381 | + | 323.322i | −0.0256385 | + | 0.0104747i | ||||
\(985\) | 26901.2 | − | 16125.7i | 0.870198 | − | 0.521632i | ||||
\(986\) | − | 15770.4i | − | 0.509362i | ||||||
\(987\) | 29698.7 | + | 12470.4i | 0.957772 | + | 0.402165i | ||||
\(988\) | 18711.2 | − | 18711.2i | 0.602514 | − | 0.602514i | ||||
\(989\) | 23464.1 | 0.754415 | ||||||||
\(990\) | −1943.18 | + | 7452.23i | −0.0623821 | + | 0.239240i | ||||
\(991\) | −6167.34 | −0.197691 | −0.0988455 | − | 0.995103i | \(-0.531515\pi\) | ||||
−0.0988455 | + | 0.995103i | \(0.531515\pi\) | |||||||
\(992\) | 145.073 | − | 145.073i | 0.00464321 | − | 0.00464321i | ||||
\(993\) | −13570.2 | − | 5698.07i | −0.433672 | − | 0.182097i | ||||
\(994\) | 6830.66i | 0.217963i | ||||||||
\(995\) | −4930.65 | + | 19688.2i | −0.157098 | + | 0.627293i | ||||
\(996\) | −20004.0 | + | 8172.72i | −0.636398 | + | 0.260003i | ||||
\(997\) | 6952.37 | + | 6952.37i | 0.220846 | + | 0.220846i | 0.808855 | − | 0.588008i | \(-0.200088\pi\) |
−0.588008 | + | 0.808855i | \(0.700088\pi\) | |||||||
\(998\) | 27594.9 | + | 27594.9i | 0.875252 | + | 0.875252i | ||||
\(999\) | 11644.1 | − | 26995.7i | 0.368772 | − | 0.854961i |
(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 | 30.4.e.a.17.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 30.4.e.a.17.5 | yes | 12 | |
4.3 | odd | 2 | 240.4.v.d.17.6 | 12 | |||
5.2 | odd | 4 | 150.4.e.c.143.2 | 12 | |||
5.3 | odd | 4 | inner | 30.4.e.a.23.5 | yes | 12 | |
5.4 | even | 2 | 150.4.e.c.107.6 | 12 | |||
12.11 | even | 2 | 240.4.v.d.17.4 | 12 | |||
15.2 | even | 4 | 150.4.e.c.143.6 | 12 | |||
15.8 | even | 4 | inner | 30.4.e.a.23.1 | yes | 12 | |
15.14 | odd | 2 | 150.4.e.c.107.2 | 12 | |||
20.3 | even | 4 | 240.4.v.d.113.4 | 12 | |||
60.23 | odd | 4 | 240.4.v.d.113.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.4.e.a.17.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
30.4.e.a.17.5 | yes | 12 | 3.2 | odd | 2 | inner | |
30.4.e.a.23.1 | yes | 12 | 15.8 | even | 4 | inner | |
30.4.e.a.23.5 | yes | 12 | 5.3 | odd | 4 | inner | |
150.4.e.c.107.2 | 12 | 15.14 | odd | 2 | |||
150.4.e.c.107.6 | 12 | 5.4 | even | 2 | |||
150.4.e.c.143.2 | 12 | 5.2 | odd | 4 | |||
150.4.e.c.143.6 | 12 | 15.2 | even | 4 | |||
240.4.v.d.17.4 | 12 | 12.11 | even | 2 | |||
240.4.v.d.17.6 | 12 | 4.3 | odd | 2 | |||
240.4.v.d.113.4 | 12 | 20.3 | even | 4 | |||
240.4.v.d.113.6 | 12 | 60.23 | odd | 4 |