Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(4,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.c (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: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 4.3 | ||
Root | \(1.11783i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.4 |
Dual form | 17.4.c.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11783i | 0.748767i | 0.927274 | + | 0.374384i | \(0.122146\pi\) | ||||
−0.927274 | + | 0.374384i | \(0.877854\pi\) | |||||||
\(3\) | −5.92758 | + | 5.92758i | −1.14076 | + | 1.14076i | −0.152453 | + | 0.988311i | \(0.548717\pi\) |
−0.988311 | + | 0.152453i | \(0.951283\pi\) | |||||||
\(4\) | 3.51478 | 0.439347 | ||||||||
\(5\) | 10.1567 | − | 10.1567i | 0.908443 | − | 0.908443i | −0.0877040 | − | 0.996147i | \(-0.527953\pi\) |
0.996147 | + | 0.0877040i | \(0.0279530\pi\) | |||||||
\(6\) | −12.5536 | − | 12.5536i | −0.854167 | − | 0.854167i | ||||
\(7\) | 3.21600 | + | 3.21600i | 0.173648 | + | 0.173648i | 0.788580 | − | 0.614932i | \(-0.210817\pi\) |
−0.614932 | + | 0.788580i | \(0.710817\pi\) | |||||||
\(8\) | 24.3864i | 1.07774i | ||||||||
\(9\) | − | 43.2725i | − | 1.60269i | ||||||
\(10\) | 21.5102 | + | 21.5102i | 0.680212 | + | 0.680212i | ||||
\(11\) | −34.0053 | − | 34.0053i | −0.932090 | − | 0.932090i | 0.0657467 | − | 0.997836i | \(-0.479057\pi\) |
−0.997836 | + | 0.0657467i | \(0.979057\pi\) | |||||||
\(12\) | −20.8341 | + | 20.8341i | −0.501192 | + | 0.501192i | ||||
\(13\) | 49.5377 | 1.05687 | 0.528434 | − | 0.848974i | \(-0.322779\pi\) | ||||
0.528434 | + | 0.848974i | \(0.322779\pi\) | |||||||
\(14\) | −6.81095 | + | 6.81095i | −0.130022 | + | 0.130022i | ||||
\(15\) | 120.409i | 2.07264i | ||||||||
\(16\) | −23.5281 | −0.367627 | ||||||||
\(17\) | −51.7393 | − | 47.2869i | −0.738154 | − | 0.674632i | ||||
\(18\) | 91.6440 | 1.20004 | ||||||||
\(19\) | 31.1112i | 0.375653i | 0.982202 | + | 0.187826i | \(0.0601443\pi\) | ||||
−0.982202 | + | 0.187826i | \(0.939856\pi\) | |||||||
\(20\) | 35.6985 | − | 35.6985i | 0.399122 | − | 0.399122i | ||||
\(21\) | −38.1262 | −0.396182 | ||||||||
\(22\) | 72.0176 | − | 72.0176i | 0.697918 | − | 0.697918i | ||||
\(23\) | −29.6163 | − | 29.6163i | −0.268497 | − | 0.268497i | 0.559998 | − | 0.828494i | \(-0.310802\pi\) |
−0.828494 | + | 0.559998i | \(0.810802\pi\) | |||||||
\(24\) | −144.552 | − | 144.552i | −1.22944 | − | 1.22944i | ||||
\(25\) | − | 81.3170i | − | 0.650536i | ||||||
\(26\) | 104.913i | 0.791349i | ||||||||
\(27\) | 96.4567 | + | 96.4567i | 0.687522 | + | 0.687522i | ||||
\(28\) | 11.3035 | + | 11.3035i | 0.0762916 | + | 0.0762916i | ||||
\(29\) | −85.8152 | + | 85.8152i | −0.549499 | + | 0.549499i | −0.926296 | − | 0.376797i | \(-0.877025\pi\) |
0.376797 | + | 0.926296i | \(0.377025\pi\) | |||||||
\(30\) | −255.007 | −1.55192 | ||||||||
\(31\) | 118.742 | − | 118.742i | 0.687957 | − | 0.687957i | −0.273823 | − | 0.961780i | \(-0.588288\pi\) |
0.961780 | + | 0.273823i | \(0.0882882\pi\) | |||||||
\(32\) | 145.263i | 0.802470i | ||||||||
\(33\) | 403.139 | 2.12659 | ||||||||
\(34\) | 100.146 | − | 109.575i | 0.505143 | − | 0.552706i | ||||
\(35\) | 65.3279 | 0.315498 | ||||||||
\(36\) | − | 152.093i | − | 0.704136i | ||||||
\(37\) | −251.954 | + | 251.954i | −1.11949 | + | 1.11949i | −0.127669 | + | 0.991817i | \(0.540750\pi\) |
−0.991817 | + | 0.127669i | \(0.959250\pi\) | |||||||
\(38\) | −65.8884 | −0.281277 | ||||||||
\(39\) | −293.639 | + | 293.639i | −1.20564 | + | 1.20564i | ||||
\(40\) | 247.685 | + | 247.685i | 0.979062 | + | 0.979062i | ||||
\(41\) | −44.8038 | − | 44.8038i | −0.170663 | − | 0.170663i | 0.616608 | − | 0.787270i | \(-0.288506\pi\) |
−0.787270 | + | 0.616608i | \(0.788506\pi\) | |||||||
\(42\) | − | 80.7450i | − | 0.296648i | ||||||
\(43\) | 87.7863i | 0.311332i | 0.987810 | + | 0.155666i | \(0.0497524\pi\) | ||||
−0.987810 | + | 0.155666i | \(0.950248\pi\) | |||||||
\(44\) | −119.521 | − | 119.521i | −0.409511 | − | 0.409511i | ||||
\(45\) | −439.506 | − | 439.506i | −1.45595 | − | 1.45595i | ||||
\(46\) | 62.7224 | − | 62.7224i | 0.201041 | − | 0.201041i | ||||
\(47\) | 281.901 | 0.874884 | 0.437442 | − | 0.899247i | \(-0.355885\pi\) | ||||
0.437442 | + | 0.899247i | \(0.355885\pi\) | |||||||
\(48\) | 139.465 | − | 139.465i | 0.419375 | − | 0.419375i | ||||
\(49\) | − | 322.315i | − | 0.939693i | ||||||
\(50\) | 172.216 | 0.487100 | ||||||||
\(51\) | 586.986 | − | 26.3920i | 1.61166 | − | 0.0724630i | ||||
\(52\) | 174.114 | 0.464332 | ||||||||
\(53\) | − | 5.63254i | − | 0.0145979i | −0.999973 | − | 0.00729895i | \(-0.997677\pi\) | ||
0.999973 | − | 0.00729895i | \(-0.00232335\pi\) | |||||||
\(54\) | −204.279 | + | 204.279i | −0.514794 | + | 0.514794i | ||||
\(55\) | −690.763 | −1.69350 | ||||||||
\(56\) | −78.4266 | + | 78.4266i | −0.187146 | + | 0.187146i | ||||
\(57\) | −184.414 | − | 184.414i | −0.428531 | − | 0.428531i | ||||
\(58\) | −181.742 | − | 181.742i | −0.411447 | − | 0.411447i | ||||
\(59\) | 134.352i | 0.296460i | 0.988953 | + | 0.148230i | \(0.0473576\pi\) | ||||
−0.988953 | + | 0.148230i | \(0.952642\pi\) | |||||||
\(60\) | 423.212i | 0.910608i | ||||||||
\(61\) | 422.875 | + | 422.875i | 0.887599 | + | 0.887599i | 0.994292 | − | 0.106693i | \(-0.0340261\pi\) |
−0.106693 | + | 0.994292i | \(0.534026\pi\) | |||||||
\(62\) | 251.476 | + | 251.476i | 0.515120 | + | 0.515120i | ||||
\(63\) | 139.164 | − | 139.164i | 0.278303 | − | 0.278303i | ||||
\(64\) | −495.867 | −0.968490 | ||||||||
\(65\) | 503.140 | − | 503.140i | 0.960105 | − | 0.960105i | ||||
\(66\) | 853.781i | 1.59232i | ||||||||
\(67\) | −951.761 | −1.73546 | −0.867732 | − | 0.497032i | \(-0.834423\pi\) | ||||
−0.867732 | + | 0.497032i | \(0.834423\pi\) | |||||||
\(68\) | −181.852 | − | 166.203i | −0.324306 | − | 0.296398i | ||||
\(69\) | 351.106 | 0.612582 | ||||||||
\(70\) | 138.354i | 0.236235i | ||||||||
\(71\) | 234.945 | − | 234.945i | 0.392717 | − | 0.392717i | −0.482938 | − | 0.875655i | \(-0.660430\pi\) |
0.875655 | + | 0.482938i | \(0.160430\pi\) | |||||||
\(72\) | 1055.26 | 1.72727 | ||||||||
\(73\) | 18.7588 | − | 18.7588i | 0.0300761 | − | 0.0300761i | −0.691909 | − | 0.721985i | \(-0.743230\pi\) |
0.721985 | + | 0.691909i | \(0.243230\pi\) | |||||||
\(74\) | −533.597 | − | 533.597i | −0.838235 | − | 0.838235i | ||||
\(75\) | 482.013 | + | 482.013i | 0.742108 | + | 0.742108i | ||||
\(76\) | 109.349i | 0.165042i | ||||||||
\(77\) | − | 218.722i | − | 0.323710i | ||||||
\(78\) | −621.879 | − | 621.879i | −0.902743 | − | 0.902743i | ||||
\(79\) | 23.4362 | + | 23.4362i | 0.0333769 | + | 0.0333769i | 0.723598 | − | 0.690221i | \(-0.242487\pi\) |
−0.690221 | + | 0.723598i | \(0.742487\pi\) | |||||||
\(80\) | −238.968 | + | 238.968i | −0.333968 | + | 0.333968i | ||||
\(81\) | 24.8476 | 0.0340845 | ||||||||
\(82\) | 94.8869 | − | 94.8869i | 0.127787 | − | 0.127787i | ||||
\(83\) | 283.887i | 0.375430i | 0.982224 | + | 0.187715i | \(0.0601081\pi\) | ||||
−0.982224 | + | 0.187715i | \(0.939892\pi\) | |||||||
\(84\) | −134.005 | −0.174062 | ||||||||
\(85\) | −1005.78 | + | 45.2217i | −1.28344 | + | 0.0577056i | ||||
\(86\) | −185.917 | −0.233115 | ||||||||
\(87\) | − | 1017.35i | − | 1.25370i | ||||||
\(88\) | 829.267 | − | 829.267i | 1.00455 | − | 1.00455i | ||||
\(89\) | −191.442 | −0.228009 | −0.114005 | − | 0.993480i | \(-0.536368\pi\) | ||||
−0.114005 | + | 0.993480i | \(0.536368\pi\) | |||||||
\(90\) | 930.800 | − | 930.800i | 1.09017 | − | 1.09017i | ||||
\(91\) | 159.313 | + | 159.313i | 0.183523 | + | 0.183523i | ||||
\(92\) | −104.095 | − | 104.095i | −0.117963 | − | 0.117963i | ||||
\(93\) | 1407.70i | 1.56959i | ||||||||
\(94\) | 597.020i | 0.655085i | ||||||||
\(95\) | 315.987 | + | 315.987i | 0.341259 | + | 0.341259i | ||||
\(96\) | −861.056 | − | 861.056i | −0.915428 | − | 0.915428i | ||||
\(97\) | 203.024 | − | 203.024i | 0.212515 | − | 0.212515i | −0.592820 | − | 0.805335i | \(-0.701985\pi\) |
0.805335 | + | 0.592820i | \(0.201985\pi\) | |||||||
\(98\) | 682.609 | 0.703612 | ||||||||
\(99\) | −1471.50 | + | 1471.50i | −1.49385 | + | 1.49385i | ||||
\(100\) | − | 285.811i | − | 0.285811i | ||||||
\(101\) | 154.062 | 0.151780 | 0.0758899 | − | 0.997116i | \(-0.475820\pi\) | ||||
0.0758899 | + | 0.997116i | \(0.475820\pi\) | |||||||
\(102\) | 55.8938 | + | 1243.14i | 0.0542580 | + | 1.20676i | ||||
\(103\) | 765.082 | 0.731900 | 0.365950 | − | 0.930634i | \(-0.380744\pi\) | ||||
0.365950 | + | 0.930634i | \(0.380744\pi\) | |||||||
\(104\) | 1208.05i | 1.13903i | ||||||||
\(105\) | −387.236 | + | 387.236i | −0.359909 | + | 0.359909i | ||||
\(106\) | 11.9288 | 0.0109304 | ||||||||
\(107\) | −279.648 | + | 279.648i | −0.252660 | + | 0.252660i | −0.822060 | − | 0.569400i | \(-0.807175\pi\) |
0.569400 | + | 0.822060i | \(0.307175\pi\) | |||||||
\(108\) | 339.024 | + | 339.024i | 0.302061 | + | 0.302061i | ||||
\(109\) | 620.769 | + | 620.769i | 0.545495 | + | 0.545495i | 0.925134 | − | 0.379640i | \(-0.123952\pi\) |
−0.379640 | + | 0.925134i | \(0.623952\pi\) | |||||||
\(110\) | − | 1462.92i | − | 1.26804i | ||||||
\(111\) | − | 2986.96i | − | 2.55414i | ||||||
\(112\) | −75.6664 | − | 75.6664i | −0.0638375 | − | 0.0638375i | ||||
\(113\) | 1446.78 | + | 1446.78i | 1.20444 | + | 1.20444i | 0.972801 | + | 0.231641i | \(0.0744095\pi\) |
0.231641 | + | 0.972801i | \(0.425590\pi\) | |||||||
\(114\) | 390.559 | − | 390.559i | 0.320870 | − | 0.320870i | ||||
\(115\) | −601.607 | −0.487827 | ||||||||
\(116\) | −301.621 | + | 301.621i | −0.241421 | + | 0.241421i | ||||
\(117\) | − | 2143.62i | − | 1.69383i | ||||||
\(118\) | −284.535 | −0.221980 | ||||||||
\(119\) | −14.3189 | − | 318.468i | −0.0110304 | − | 0.245327i | ||||
\(120\) | −2936.35 | −2.23376 | ||||||||
\(121\) | 981.722i | 0.737582i | ||||||||
\(122\) | −895.578 | + | 895.578i | −0.664605 | + | 0.664605i | ||||
\(123\) | 531.156 | 0.389372 | ||||||||
\(124\) | 417.351 | − | 417.351i | 0.302252 | − | 0.302252i | ||||
\(125\) | 443.675 | + | 443.675i | 0.317468 | + | 0.317468i | ||||
\(126\) | 294.727 | + | 294.727i | 0.208384 | + | 0.208384i | ||||
\(127\) | − | 2106.13i | − | 1.47156i | −0.677218 | − | 0.735782i | \(-0.736815\pi\) | ||
0.677218 | − | 0.735782i | \(-0.263185\pi\) | |||||||
\(128\) | 111.936i | 0.0772959i | ||||||||
\(129\) | −520.361 | − | 520.361i | −0.355157 | − | 0.355157i | ||||
\(130\) | 1065.57 | + | 1065.57i | 0.718895 | + | 0.718895i | ||||
\(131\) | −983.275 | + | 983.275i | −0.655795 | + | 0.655795i | −0.954382 | − | 0.298587i | \(-0.903485\pi\) |
0.298587 | + | 0.954382i | \(0.403485\pi\) | |||||||
\(132\) | 1416.94 | 0.934311 | ||||||||
\(133\) | −100.054 | + | 100.054i | −0.0652313 | + | 0.0652313i | ||||
\(134\) | − | 2015.67i | − | 1.29946i | ||||||
\(135\) | 1959.36 | 1.24915 | ||||||||
\(136\) | 1153.16 | − | 1261.73i | 0.727076 | − | 0.795535i | ||||
\(137\) | −2309.58 | −1.44030 | −0.720149 | − | 0.693820i | \(-0.755926\pi\) | ||||
−0.720149 | + | 0.693820i | \(0.755926\pi\) | |||||||
\(138\) | 743.584i | 0.458682i | ||||||||
\(139\) | 1751.57 | − | 1751.57i | 1.06882 | − | 1.06882i | 0.0713691 | − | 0.997450i | \(-0.477263\pi\) |
0.997450 | − | 0.0713691i | \(-0.0227368\pi\) | |||||||
\(140\) | 229.613 | 0.138613 | ||||||||
\(141\) | −1670.99 | + | 1670.99i | −0.998036 | + | 0.998036i | ||||
\(142\) | 497.576 | + | 497.576i | 0.294054 | + | 0.294054i | ||||
\(143\) | −1684.55 | − | 1684.55i | −0.985097 | − | 0.985097i | ||||
\(144\) | 1018.12i | 0.589190i | ||||||||
\(145\) | 1743.20i | 0.998377i | ||||||||
\(146\) | 39.7281 | + | 39.7281i | 0.0225200 | + | 0.0225200i | ||||
\(147\) | 1910.55 | + | 1910.55i | 1.07197 | + | 1.07197i | ||||
\(148\) | −885.563 | + | 885.563i | −0.491843 | + | 0.491843i | ||||
\(149\) | 1521.60 | 0.836607 | 0.418304 | − | 0.908307i | \(-0.362625\pi\) | ||||
0.418304 | + | 0.908307i | \(0.362625\pi\) | |||||||
\(150\) | −1020.82 | + | 1020.82i | −0.555666 | + | 0.555666i | ||||
\(151\) | − | 397.910i | − | 0.214447i | −0.994235 | − | 0.107223i | \(-0.965804\pi\) | ||
0.994235 | − | 0.107223i | \(-0.0341960\pi\) | |||||||
\(152\) | −758.691 | −0.404855 | ||||||||
\(153\) | −2046.22 | + | 2238.89i | −1.08122 | + | 1.18303i | ||||
\(154\) | 463.217 | 0.242384 | ||||||||
\(155\) | − | 2412.05i | − | 1.24994i | ||||||
\(156\) | −1032.08 | + | 1032.08i | −0.529694 | + | 0.529694i | ||||
\(157\) | −1068.19 | −0.543001 | −0.271501 | − | 0.962438i | \(-0.587520\pi\) | ||||
−0.271501 | + | 0.962438i | \(0.587520\pi\) | |||||||
\(158\) | −49.6339 | + | 49.6339i | −0.0249915 | + | 0.0249915i | ||||
\(159\) | 33.3873 | + | 33.3873i | 0.0166528 | + | 0.0166528i | ||||
\(160\) | 1475.39 | + | 1475.39i | 0.728997 | + | 0.728997i | ||||
\(161\) | − | 190.492i | − | 0.0932476i | ||||||
\(162\) | 52.6231i | 0.0255214i | ||||||||
\(163\) | −597.803 | − | 597.803i | −0.287261 | − | 0.287261i | 0.548735 | − | 0.835996i | \(-0.315110\pi\) |
−0.835996 | + | 0.548735i | \(0.815110\pi\) | |||||||
\(164\) | −157.475 | − | 157.475i | −0.0749802 | − | 0.0749802i | ||||
\(165\) | 4094.56 | − | 4094.56i | 1.93188 | − | 1.93188i | ||||
\(166\) | −601.226 | −0.281109 | ||||||||
\(167\) | −1848.05 | + | 1848.05i | −0.856327 | + | 0.856327i | −0.990903 | − | 0.134576i | \(-0.957033\pi\) |
0.134576 | + | 0.990903i | \(0.457033\pi\) | |||||||
\(168\) | − | 929.761i | − | 0.426980i | ||||||
\(169\) | 256.987 | 0.116972 | ||||||||
\(170\) | −95.7720 | − | 2130.07i | −0.0432081 | − | 0.960994i | ||||
\(171\) | 1346.26 | 0.602054 | ||||||||
\(172\) | 308.549i | 0.136783i | ||||||||
\(173\) | 2181.30 | − | 2181.30i | 0.958620 | − | 0.958620i | −0.0405576 | − | 0.999177i | \(-0.512913\pi\) |
0.999177 | + | 0.0405576i | \(0.0129134\pi\) | |||||||
\(174\) | 2154.59 | 0.938728 | ||||||||
\(175\) | 261.515 | − | 261.515i | 0.112964 | − | 0.112964i | ||||
\(176\) | 800.081 | + | 800.081i | 0.342661 | + | 0.342661i | ||||
\(177\) | −796.383 | − | 796.383i | −0.338191 | − | 0.338191i | ||||
\(178\) | − | 405.443i | − | 0.170726i | ||||||
\(179\) | − | 918.935i | − | 0.383712i | −0.981423 | − | 0.191856i | \(-0.938549\pi\) | ||
0.981423 | − | 0.191856i | \(-0.0614506\pi\) | |||||||
\(180\) | −1544.77 | − | 1544.77i | −0.639667 | − | 0.639667i | ||||
\(181\) | −1526.40 | − | 1526.40i | −0.626833 | − | 0.626833i | 0.320437 | − | 0.947270i | \(-0.396170\pi\) |
−0.947270 | + | 0.320437i | \(0.896170\pi\) | |||||||
\(182\) | −337.399 | + | 337.399i | −0.137416 | + | 0.137416i | ||||
\(183\) | −5013.25 | −2.02508 | ||||||||
\(184\) | 722.234 | − | 722.234i | 0.289368 | − | 0.289368i | ||||
\(185\) | 5118.04i | 2.03398i | ||||||||
\(186\) | −2981.29 | −1.17526 | ||||||||
\(187\) | 151.405 | + | 3367.41i | 0.0592077 | + | 1.31684i | ||||
\(188\) | 990.821 | 0.384378 | ||||||||
\(189\) | 620.409i | 0.238773i | ||||||||
\(190\) | −669.209 | + | 669.209i | −0.255524 | + | 0.255524i | ||||
\(191\) | 1349.67 | 0.511302 | 0.255651 | − | 0.966769i | \(-0.417710\pi\) | ||||
0.255651 | + | 0.966769i | \(0.417710\pi\) | |||||||
\(192\) | 2939.29 | − | 2939.29i | 1.10482 | − | 1.10482i | ||||
\(193\) | −2481.32 | − | 2481.32i | −0.925436 | − | 0.925436i | 0.0719705 | − | 0.997407i | \(-0.477071\pi\) |
−0.997407 | + | 0.0719705i | \(0.977071\pi\) | |||||||
\(194\) | 429.971 | + | 429.971i | 0.159124 | + | 0.159124i | ||||
\(195\) | 5964.81i | 2.19051i | ||||||||
\(196\) | − | 1132.86i | − | 0.412852i | ||||||
\(197\) | 2509.24 | + | 2509.24i | 0.907492 | + | 0.907492i | 0.996069 | − | 0.0885772i | \(-0.0282320\pi\) |
−0.0885772 | + | 0.996069i | \(0.528232\pi\) | |||||||
\(198\) | −3116.38 | − | 3116.38i | −1.11854 | − | 1.11854i | ||||
\(199\) | −2172.17 | + | 2172.17i | −0.773774 | + | 0.773774i | −0.978764 | − | 0.204990i | \(-0.934284\pi\) |
0.204990 | + | 0.978764i | \(0.434284\pi\) | |||||||
\(200\) | 1983.03 | 0.701106 | ||||||||
\(201\) | 5641.64 | − | 5641.64i | 1.97976 | − | 1.97976i | ||||
\(202\) | 326.278i | 0.113648i | ||||||||
\(203\) | −551.963 | −0.190838 | ||||||||
\(204\) | 2063.12 | − | 92.7619i | 0.708077 | − | 0.0318364i | ||||
\(205\) | −910.116 | −0.310075 | ||||||||
\(206\) | 1620.32i | 0.548023i | ||||||||
\(207\) | −1281.57 | + | 1281.57i | −0.430316 | + | 0.430316i | ||||
\(208\) | −1165.53 | −0.388533 | ||||||||
\(209\) | 1057.95 | − | 1057.95i | 0.350142 | − | 0.350142i | ||||
\(210\) | −820.103 | − | 820.103i | −0.269488 | − | 0.269488i | ||||
\(211\) | 4258.19 | + | 4258.19i | 1.38932 | + | 1.38932i | 0.826757 | + | 0.562559i | \(0.190183\pi\) |
0.562559 | + | 0.826757i | \(0.309817\pi\) | |||||||
\(212\) | − | 19.7971i | − | 0.00641354i | ||||||
\(213\) | 2785.32i | 0.895995i | ||||||||
\(214\) | −592.249 | − | 592.249i | −0.189184 | − | 0.189184i | ||||
\(215\) | 891.619 | + | 891.619i | 0.282827 | + | 0.282827i | ||||
\(216\) | −2352.23 | + | 2352.23i | −0.740968 | + | 0.740968i | ||||
\(217\) | 763.748 | 0.238924 | ||||||||
\(218\) | −1314.69 | + | 1314.69i | −0.408449 | + | 0.408449i | ||||
\(219\) | 222.389i | 0.0686194i | ||||||||
\(220\) | −2427.88 | −0.744035 | ||||||||
\(221\) | −2563.05 | − | 2342.48i | −0.780132 | − | 0.712998i | ||||
\(222\) | 6325.88 | 1.91246 | ||||||||
\(223\) | − | 3581.06i | − | 1.07536i | −0.843149 | − | 0.537680i | \(-0.819301\pi\) | ||
0.843149 | − | 0.537680i | \(-0.180699\pi\) | |||||||
\(224\) | −467.164 | + | 467.164i | −0.139347 | + | 0.139347i | ||||
\(225\) | −3518.79 | −1.04260 | ||||||||
\(226\) | −3064.05 | + | 3064.05i | −0.901847 | + | 0.901847i | ||||
\(227\) | −3001.23 | − | 3001.23i | −0.877528 | − | 0.877528i | 0.115751 | − | 0.993278i | \(-0.463073\pi\) |
−0.993278 | + | 0.115751i | \(0.963073\pi\) | |||||||
\(228\) | −648.176 | − | 648.176i | −0.188274 | − | 0.188274i | ||||
\(229\) | − | 5146.73i | − | 1.48518i | −0.669748 | − | 0.742589i | \(-0.733598\pi\) | ||
0.669748 | − | 0.742589i | \(-0.266402\pi\) | |||||||
\(230\) | − | 1274.10i | − | 0.365269i | ||||||
\(231\) | 1296.49 | + | 1296.49i | 0.369277 | + | 0.369277i | ||||
\(232\) | −2092.72 | − | 2092.72i | −0.592215 | − | 0.592215i | ||||
\(233\) | 2013.38 | − | 2013.38i | 0.566098 | − | 0.566098i | −0.364935 | − | 0.931033i | \(-0.618909\pi\) |
0.931033 | + | 0.364935i | \(0.118909\pi\) | |||||||
\(234\) | 4539.84 | 1.26828 | ||||||||
\(235\) | 2863.19 | − | 2863.19i | 0.794782 | − | 0.794782i | ||||
\(236\) | 472.218i | 0.130249i | ||||||||
\(237\) | −277.840 | −0.0761504 | ||||||||
\(238\) | 674.463 | − | 30.3251i | 0.183693 | − | 0.00825917i | ||||
\(239\) | 3984.47 | 1.07839 | 0.539193 | − | 0.842182i | \(-0.318729\pi\) | ||||
0.539193 | + | 0.842182i | \(0.318729\pi\) | |||||||
\(240\) | − | 2833.00i | − | 0.761957i | ||||||
\(241\) | −1268.92 | + | 1268.92i | −0.339163 | + | 0.339163i | −0.856052 | − | 0.516890i | \(-0.827090\pi\) |
0.516890 | + | 0.856052i | \(0.327090\pi\) | |||||||
\(242\) | −2079.12 | −0.552278 | ||||||||
\(243\) | −2751.62 | + | 2751.62i | −0.726404 | + | 0.726404i | ||||
\(244\) | 1486.31 | + | 1486.31i | 0.389964 | + | 0.389964i | ||||
\(245\) | −3273.65 | − | 3273.65i | −0.853657 | − | 0.853657i | ||||
\(246\) | 1124.90i | 0.291549i | ||||||||
\(247\) | 1541.18i | 0.397016i | ||||||||
\(248\) | 2895.69 | + | 2895.69i | 0.741436 | + | 0.741436i | ||||
\(249\) | −1682.76 | − | 1682.76i | −0.428277 | − | 0.428277i | ||||
\(250\) | −939.631 | + | 939.631i | −0.237710 | + | 0.237710i | ||||
\(251\) | −4658.75 | −1.17154 | −0.585772 | − | 0.810476i | \(-0.699209\pi\) | ||||
−0.585772 | + | 0.810476i | \(0.699209\pi\) | |||||||
\(252\) | 489.132 | − | 489.132i | 0.122272 | − | 0.122272i | ||||
\(253\) | 2014.22i | 0.500526i | ||||||||
\(254\) | 4460.43 | 1.10186 | ||||||||
\(255\) | 5693.78 | − | 6229.89i | 1.39827 | − | 1.52993i | ||||
\(256\) | −4204.00 | −1.02637 | ||||||||
\(257\) | 6235.43i | 1.51345i | 0.653736 | + | 0.756723i | \(0.273201\pi\) | ||||
−0.653736 | + | 0.756723i | \(0.726799\pi\) | |||||||
\(258\) | 1102.04 | − | 1102.04i | 0.265930 | − | 0.265930i | ||||
\(259\) | −1620.57 | −0.388792 | ||||||||
\(260\) | 1768.42 | − | 1768.42i | 0.421819 | − | 0.421819i | ||||
\(261\) | 3713.44 | + | 3713.44i | 0.880674 | + | 0.880674i | ||||
\(262\) | −2082.41 | − | 2082.41i | −0.491038 | − | 0.491038i | ||||
\(263\) | − | 149.037i | − | 0.0349430i | −0.999847 | − | 0.0174715i | \(-0.994438\pi\) | ||
0.999847 | − | 0.0174715i | \(-0.00556163\pi\) | |||||||
\(264\) | 9831.10i | 2.29190i | ||||||||
\(265\) | −57.2080 | − | 57.2080i | −0.0132613 | − | 0.0132613i | ||||
\(266\) | −211.897 | − | 211.897i | −0.0488430 | − | 0.0488430i | ||||
\(267\) | 1134.79 | − | 1134.79i | 0.260105 | − | 0.260105i | ||||
\(268\) | −3345.23 | −0.762472 | ||||||||
\(269\) | −2199.13 | + | 2199.13i | −0.498450 | + | 0.498450i | −0.910955 | − | 0.412505i | \(-0.864654\pi\) |
0.412505 | + | 0.910955i | \(0.364654\pi\) | |||||||
\(270\) | 4149.60i | 0.935322i | ||||||||
\(271\) | 4725.42 | 1.05922 | 0.529610 | − | 0.848241i | \(-0.322338\pi\) | ||||
0.529610 | + | 0.848241i | \(0.322338\pi\) | |||||||
\(272\) | 1217.33 | + | 1112.57i | 0.271365 | + | 0.248013i | ||||
\(273\) | −1888.69 | −0.418713 | ||||||||
\(274\) | − | 4891.31i | − | 1.07845i | ||||||
\(275\) | −2765.21 | + | 2765.21i | −0.606358 | + | 0.606358i | ||||
\(276\) | 1234.06 | 0.269136 | ||||||||
\(277\) | −636.499 | + | 636.499i | −0.138063 | + | 0.138063i | −0.772761 | − | 0.634698i | \(-0.781125\pi\) |
0.634698 | + | 0.772761i | \(0.281125\pi\) | |||||||
\(278\) | 3709.53 | + | 3709.53i | 0.800297 | + | 0.800297i | ||||
\(279\) | −5138.26 | − | 5138.26i | −1.10258 | − | 1.10258i | ||||
\(280\) | 1593.11i | 0.340024i | ||||||||
\(281\) | − | 9165.72i | − | 1.94584i | −0.231143 | − | 0.972920i | \(-0.574246\pi\) | ||
0.231143 | − | 0.972920i | \(-0.425754\pi\) | |||||||
\(282\) | −3538.89 | − | 3538.89i | −0.747297 | − | 0.747297i | ||||
\(283\) | 2504.08 | + | 2504.08i | 0.525979 | + | 0.525979i | 0.919371 | − | 0.393392i | \(-0.128698\pi\) |
−0.393392 | + | 0.919371i | \(0.628698\pi\) | |||||||
\(284\) | 825.781 | − | 825.781i | 0.172539 | − | 0.172539i | ||||
\(285\) | −3746.08 | −0.778592 | ||||||||
\(286\) | 3567.59 | − | 3567.59i | 0.737608 | − | 0.737608i | ||||
\(287\) | − | 288.178i | − | 0.0592704i | ||||||
\(288\) | 6285.87 | 1.28611 | ||||||||
\(289\) | 440.904 | + | 4893.18i | 0.0897423 | + | 0.995965i | ||||
\(290\) | −3691.80 | −0.747552 | ||||||||
\(291\) | 2406.88i | 0.484859i | ||||||||
\(292\) | 65.9331 | − | 65.9331i | 0.0132138 | − | 0.0132138i | ||||
\(293\) | 1268.29 | 0.252882 | 0.126441 | − | 0.991974i | \(-0.459645\pi\) | ||||
0.126441 | + | 0.991974i | \(0.459645\pi\) | |||||||
\(294\) | −4046.22 | + | 4046.22i | −0.802655 | + | 0.802655i | ||||
\(295\) | 1364.57 | + | 1364.57i | 0.269317 | + | 0.269317i | ||||
\(296\) | −6144.25 | − | 6144.25i | −1.20651 | − | 1.20651i | ||||
\(297\) | − | 6560.08i | − | 1.28166i | ||||||
\(298\) | 3222.50i | 0.626424i | ||||||||
\(299\) | −1467.12 | − | 1467.12i | −0.283766 | − | 0.283766i | ||||
\(300\) | 1694.17 | + | 1694.17i | 0.326043 | + | 0.326043i | ||||
\(301\) | −282.321 | + | 282.321i | −0.0540621 | + | 0.0540621i | ||||
\(302\) | 842.708 | 0.160571 | ||||||||
\(303\) | −913.217 | + | 913.217i | −0.173145 | + | 0.173145i | ||||
\(304\) | − | 731.988i | − | 0.138100i | ||||||
\(305\) | 8590.02 | 1.61267 | ||||||||
\(306\) | −4741.59 | − | 4333.56i | −0.885813 | − | 0.809585i | ||||
\(307\) | 9924.22 | 1.84497 | 0.922484 | − | 0.386034i | \(-0.126155\pi\) | ||||
0.922484 | + | 0.386034i | \(0.126155\pi\) | |||||||
\(308\) | − | 768.760i | − | 0.142221i | ||||||
\(309\) | −4535.09 | + | 4535.09i | −0.834926 | + | 0.834926i | ||||
\(310\) | 5108.32 | 0.935914 | ||||||||
\(311\) | 1031.43 | − | 1031.43i | 0.188062 | − | 0.188062i | −0.606796 | − | 0.794858i | \(-0.707546\pi\) |
0.794858 | + | 0.606796i | \(0.207546\pi\) | |||||||
\(312\) | −7160.80 | − | 7160.80i | −1.29936 | − | 1.29936i | ||||
\(313\) | 564.173 | + | 564.173i | 0.101882 | + | 0.101882i | 0.756210 | − | 0.654329i | \(-0.227049\pi\) |
−0.654329 | + | 0.756210i | \(0.727049\pi\) | |||||||
\(314\) | − | 2262.26i | − | 0.406582i | ||||||
\(315\) | − | 2826.90i | − | 0.505644i | ||||||
\(316\) | 82.3730 | + | 82.3730i | 0.0146641 | + | 0.0146641i | ||||
\(317\) | −2724.15 | − | 2724.15i | −0.482661 | − | 0.482661i | 0.423319 | − | 0.905981i | \(-0.360865\pi\) |
−0.905981 | + | 0.423319i | \(0.860865\pi\) | |||||||
\(318\) | −70.7088 | + | 70.7088i | −0.0124690 | + | 0.0124690i | ||||
\(319\) | 5836.34 | 1.02436 | ||||||||
\(320\) | −5036.37 | + | 5036.37i | −0.879817 | + | 0.879817i | ||||
\(321\) | − | 3315.28i | − | 0.576451i | ||||||
\(322\) | 403.430 | 0.0698208 | ||||||||
\(323\) | 1471.15 | − | 1609.67i | 0.253428 | − | 0.277290i | ||||
\(324\) | 87.3338 | 0.0149749 | ||||||||
\(325\) | − | 4028.26i | − | 0.687531i | ||||||
\(326\) | 1266.05 | − | 1266.05i | 0.215092 | − | 0.215092i | ||||
\(327\) | −7359.32 | −1.24456 | ||||||||
\(328\) | 1092.60 | − | 1092.60i | 0.183929 | − | 0.183929i | ||||
\(329\) | 906.595 | + | 906.595i | 0.151922 | + | 0.151922i | ||||
\(330\) | 8671.59 | + | 8671.59i | 1.44653 | + | 1.44653i | ||||
\(331\) | 8470.40i | 1.40657i | 0.710907 | + | 0.703286i | \(0.248285\pi\) | ||||
−0.710907 | + | 0.703286i | \(0.751715\pi\) | |||||||
\(332\) | 997.800i | 0.164944i | ||||||||
\(333\) | 10902.7 | + | 10902.7i | 1.79418 | + | 1.79418i | ||||
\(334\) | −3913.87 | − | 3913.87i | −0.641190 | − | 0.641190i | ||||
\(335\) | −9666.75 | + | 9666.75i | −1.57657 | + | 1.57657i | ||||
\(336\) | 897.038 | 0.145647 | ||||||||
\(337\) | −1359.69 | + | 1359.69i | −0.219784 | + | 0.219784i | −0.808407 | − | 0.588624i | \(-0.799670\pi\) |
0.588624 | + | 0.808407i | \(0.299670\pi\) | |||||||
\(338\) | 544.256i | 0.0875848i | ||||||||
\(339\) | −17151.9 | −2.74797 | ||||||||
\(340\) | −3535.09 | + | 158.944i | −0.563874 | + | 0.0253528i | ||||
\(341\) | −8075.71 | −1.28248 | ||||||||
\(342\) | 2851.16i | 0.450798i | ||||||||
\(343\) | 2139.65 | − | 2139.65i | 0.336823 | − | 0.336823i | ||||
\(344\) | −2140.79 | −0.335534 | ||||||||
\(345\) | 3566.08 | − | 3566.08i | 0.556496 | − | 0.556496i | ||||
\(346\) | 4619.63 | + | 4619.63i | 0.717783 | + | 0.717783i | ||||
\(347\) | 1813.08 | + | 1813.08i | 0.280493 | + | 0.280493i | 0.833306 | − | 0.552812i | \(-0.186445\pi\) |
−0.552812 | + | 0.833306i | \(0.686445\pi\) | |||||||
\(348\) | − | 3575.77i | − | 0.550809i | ||||||
\(349\) | 283.156i | 0.0434298i | 0.999764 | + | 0.0217149i | \(0.00691260\pi\) | ||||
−0.999764 | + | 0.0217149i | \(0.993087\pi\) | |||||||
\(350\) | 553.846 | + | 553.846i | 0.0845838 | + | 0.0845838i | ||||
\(351\) | 4778.25 | + | 4778.25i | 0.726621 | + | 0.726621i | ||||
\(352\) | 4939.70 | − | 4939.70i | 0.747974 | − | 0.747974i | ||||
\(353\) | 10695.1 | 1.61259 | 0.806295 | − | 0.591514i | \(-0.201470\pi\) | ||||
0.806295 | + | 0.591514i | \(0.201470\pi\) | |||||||
\(354\) | 1686.61 | − | 1686.61i | 0.253226 | − | 0.253226i | ||||
\(355\) | − | 4772.54i | − | 0.713521i | ||||||
\(356\) | −672.877 | −0.100175 | ||||||||
\(357\) | 1972.62 | + | 1802.87i | 0.292443 | + | 0.267277i | ||||
\(358\) | 1946.15 | 0.287311 | ||||||||
\(359\) | 8702.38i | 1.27937i | 0.768637 | + | 0.639685i | \(0.220935\pi\) | ||||
−0.768637 | + | 0.639685i | \(0.779065\pi\) | |||||||
\(360\) | 10718.0 | − | 10718.0i | 1.56913 | − | 1.56913i | ||||
\(361\) | 5891.09 | 0.858885 | ||||||||
\(362\) | 3232.67 | − | 3232.67i | 0.469352 | − | 0.469352i | ||||
\(363\) | −5819.24 | − | 5819.24i | −0.841407 | − | 0.841407i | ||||
\(364\) | 559.951 | + | 559.951i | 0.0806303 | + | 0.0806303i | ||||
\(365\) | − | 381.055i | − | 0.0546448i | ||||||
\(366\) | − | 10617.2i | − | 1.51632i | ||||||
\(367\) | −8429.92 | − | 8429.92i | −1.19901 | − | 1.19901i | −0.974462 | − | 0.224552i | \(-0.927908\pi\) |
−0.224552 | − | 0.974462i | \(-0.572092\pi\) | |||||||
\(368\) | 696.815 | + | 696.815i | 0.0987065 | + | 0.0987065i | ||||
\(369\) | −1938.77 | + | 1938.77i | −0.273519 | + | 0.273519i | ||||
\(370\) | −10839.2 | −1.52298 | ||||||||
\(371\) | 18.1142 | − | 18.1142i | 0.00253489 | − | 0.00253489i | ||||
\(372\) | 4947.77i | 0.689597i | ||||||||
\(373\) | −11054.6 | −1.53454 | −0.767270 | − | 0.641324i | \(-0.778385\pi\) | ||||
−0.767270 | + | 0.641324i | \(0.778385\pi\) | |||||||
\(374\) | −7131.63 | + | 320.651i | −0.986010 | + | 0.0443328i | ||||
\(375\) | −5259.85 | −0.724313 | ||||||||
\(376\) | 6874.56i | 0.942894i | ||||||||
\(377\) | −4251.09 | + | 4251.09i | −0.580749 | + | 0.580749i | ||||
\(378\) | −1313.92 | −0.178786 | ||||||||
\(379\) | 8166.04 | − | 8166.04i | 1.10676 | − | 1.10676i | 0.113185 | − | 0.993574i | \(-0.463895\pi\) |
0.993574 | − | 0.113185i | \(-0.0361051\pi\) | |||||||
\(380\) | 1110.63 | + | 1110.63i | 0.149931 | + | 0.149931i | ||||
\(381\) | 12484.3 | + | 12484.3i | 1.67871 | + | 1.67871i | ||||
\(382\) | 2858.38i | 0.382847i | ||||||||
\(383\) | − | 10238.7i | − | 1.36599i | −0.730423 | − | 0.682995i | \(-0.760677\pi\) | ||
0.730423 | − | 0.682995i | \(-0.239323\pi\) | |||||||
\(384\) | −663.513 | − | 663.513i | −0.0881764 | − | 0.0881764i | ||||
\(385\) | −2221.49 | − | 2221.49i | −0.294072 | − | 0.294072i | ||||
\(386\) | 5255.02 | − | 5255.02i | 0.692937 | − | 0.692937i | ||||
\(387\) | 3798.73 | 0.498968 | ||||||||
\(388\) | 713.584 | − | 713.584i | 0.0933678 | − | 0.0933678i | ||||
\(389\) | 4378.48i | 0.570688i | 0.958425 | + | 0.285344i | \(0.0921079\pi\) | ||||
−0.958425 | + | 0.285344i | \(0.907892\pi\) | |||||||
\(390\) | −12632.5 | −1.64018 | ||||||||
\(391\) | 131.863 | + | 2932.79i | 0.0170553 | + | 0.379328i | ||||
\(392\) | 7860.09 | 1.01274 | ||||||||
\(393\) | − | 11656.9i | − | 1.49621i | ||||||
\(394\) | −5314.15 | + | 5314.15i | −0.679501 | + | 0.679501i | ||||
\(395\) | 476.068 | 0.0606420 | ||||||||
\(396\) | −5171.98 | + | 5171.98i | −0.656317 | + | 0.656317i | ||||
\(397\) | −7110.57 | − | 7110.57i | −0.898915 | − | 0.898915i | 0.0964253 | − | 0.995340i | \(-0.469259\pi\) |
−0.995340 | + | 0.0964253i | \(0.969259\pi\) | |||||||
\(398\) | −4600.30 | − | 4600.30i | −0.579377 | − | 0.579377i | ||||
\(399\) | − | 1186.15i | − | 0.148827i | ||||||
\(400\) | 1913.23i | 0.239154i | ||||||||
\(401\) | −5809.87 | − | 5809.87i | −0.723519 | − | 0.723519i | 0.245801 | − | 0.969320i | \(-0.420949\pi\) |
−0.969320 | + | 0.245801i | \(0.920949\pi\) | |||||||
\(402\) | 11948.1 | + | 11948.1i | 1.48238 | + | 1.48238i | ||||
\(403\) | 5882.20 | − | 5882.20i | 0.727080 | − | 0.727080i | ||||
\(404\) | 541.495 | 0.0666841 | ||||||||
\(405\) | 252.370 | − | 252.370i | 0.0309638 | − | 0.0309638i | ||||
\(406\) | − | 1168.97i | − | 0.142894i | ||||||
\(407\) | 17135.6 | 2.08692 | ||||||||
\(408\) | 643.605 | + | 14314.5i | 0.0780960 | + | 1.73694i | ||||
\(409\) | −5402.57 | −0.653154 | −0.326577 | − | 0.945171i | \(-0.605895\pi\) | ||||
−0.326577 | + | 0.945171i | \(0.605895\pi\) | |||||||
\(410\) | − | 1927.48i | − | 0.232174i | ||||||
\(411\) | 13690.2 | − | 13690.2i | 1.64304 | − | 1.64304i | ||||
\(412\) | 2689.09 | 0.321558 | ||||||||
\(413\) | −432.076 | + | 432.076i | −0.0514796 | + | 0.0514796i | ||||
\(414\) | −2714.15 | − | 2714.15i | −0.322206 | − | 0.322206i | ||||
\(415\) | 2883.36 | + | 2883.36i | 0.341056 | + | 0.341056i | ||||
\(416\) | 7195.98i | 0.848105i | ||||||||
\(417\) | 20765.1i | 2.43854i | ||||||||
\(418\) | 2240.56 | + | 2240.56i | 0.262175 | + | 0.262175i | ||||
\(419\) | −4458.44 | − | 4458.44i | −0.519831 | − | 0.519831i | 0.397689 | − | 0.917520i | \(-0.369812\pi\) |
−0.917520 | + | 0.397689i | \(0.869812\pi\) | |||||||
\(420\) | −1361.05 | + | 1361.05i | −0.158125 | + | 0.158125i | ||||
\(421\) | −6492.45 | −0.751598 | −0.375799 | − | 0.926701i | \(-0.622632\pi\) | ||||
−0.375799 | + | 0.926701i | \(0.622632\pi\) | |||||||
\(422\) | −9018.13 | + | 9018.13i | −1.04027 | + | 1.04027i | ||||
\(423\) | − | 12198.6i | − | 1.40216i | ||||||
\(424\) | 137.357 | 0.0157327 | ||||||||
\(425\) | −3845.22 | + | 4207.28i | −0.438872 | + | 0.480195i | ||||
\(426\) | −5898.84 | −0.670892 | ||||||||
\(427\) | 2719.93i | 0.308259i | ||||||||
\(428\) | −982.902 | + | 982.902i | −0.111006 | + | 0.111006i | ||||
\(429\) | 19970.6 | 2.24753 | ||||||||
\(430\) | −1888.30 | + | 1888.30i | −0.211772 | + | 0.211772i | ||||
\(431\) | 9530.02 | + | 9530.02i | 1.06507 | + | 1.06507i | 0.997730 | + | 0.0673390i | \(0.0214509\pi\) |
0.0673390 | + | 0.997730i | \(0.478549\pi\) | |||||||
\(432\) | −2269.44 | − | 2269.44i | −0.252751 | − | 0.252751i | ||||
\(433\) | 13237.8i | 1.46921i | 0.678495 | + | 0.734605i | \(0.262633\pi\) | ||||
−0.678495 | + | 0.734605i | \(0.737367\pi\) | |||||||
\(434\) | 1617.49i | 0.178899i | ||||||||
\(435\) | −10332.9 | − | 10332.9i | −1.13891 | − | 1.13891i | ||||
\(436\) | 2181.87 | + | 2181.87i | 0.239662 | + | 0.239662i | ||||
\(437\) | 921.399 | − | 921.399i | 0.100862 | − | 0.100862i | ||||
\(438\) | −470.983 | −0.0513800 | ||||||||
\(439\) | −7247.17 | + | 7247.17i | −0.787901 | + | 0.787901i | −0.981150 | − | 0.193248i | \(-0.938098\pi\) |
0.193248 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(440\) | − | 16845.2i | − | 1.82515i | ||||||
\(441\) | −13947.4 | −1.50603 | ||||||||
\(442\) | 4960.99 | − | 5428.11i | 0.533870 | − | 0.584137i | ||||
\(443\) | −8163.30 | −0.875508 | −0.437754 | − | 0.899095i | \(-0.644226\pi\) | ||||
−0.437754 | + | 0.899095i | \(0.644226\pi\) | |||||||
\(444\) | − | 10498.5i | − | 1.12215i | ||||||
\(445\) | −1944.42 | + | 1944.42i | −0.207133 | + | 0.207133i | ||||
\(446\) | 7584.09 | 0.805195 | ||||||||
\(447\) | −9019.42 | + | 9019.42i | −0.954372 | + | 0.954372i | ||||
\(448\) | −1594.71 | − | 1594.71i | −0.168176 | − | 0.168176i | ||||
\(449\) | −3099.02 | − | 3099.02i | −0.325727 | − | 0.325727i | 0.525232 | − | 0.850959i | \(-0.323979\pi\) |
−0.850959 | + | 0.525232i | \(0.823979\pi\) | |||||||
\(450\) | − | 7452.21i | − | 0.780668i | ||||||
\(451\) | 3047.13i | 0.318146i | ||||||||
\(452\) | 5085.13 | + | 5085.13i | 0.529169 | + | 0.529169i | ||||
\(453\) | 2358.65 | + | 2358.65i | 0.244633 | + | 0.244633i | ||||
\(454\) | 6356.11 | − | 6356.11i | 0.657064 | − | 0.657064i | ||||
\(455\) | 3236.19 | 0.333440 | ||||||||
\(456\) | 4497.20 | − | 4497.20i | 0.461844 | − | 0.461844i | ||||
\(457\) | − | 10463.4i | − | 1.07102i | −0.844530 | − | 0.535509i | \(-0.820120\pi\) | ||
0.844530 | − | 0.535509i | \(-0.179880\pi\) | |||||||
\(458\) | 10899.9 | 1.11205 | ||||||||
\(459\) | −429.464 | − | 9551.73i | −0.0436724 | − | 0.971322i | ||||
\(460\) | −2114.52 | −0.214326 | ||||||||
\(461\) | − | 7540.64i | − | 0.761828i | −0.924610 | − | 0.380914i | \(-0.875609\pi\) | ||
0.924610 | − | 0.380914i | \(-0.124391\pi\) | |||||||
\(462\) | −2745.76 | + | 2745.76i | −0.276503 | + | 0.276503i | ||||
\(463\) | −12962.0 | −1.30107 | −0.650536 | − | 0.759475i | \(-0.725456\pi\) | ||||
−0.650536 | + | 0.759475i | \(0.725456\pi\) | |||||||
\(464\) | 2019.07 | − | 2019.07i | 0.202011 | − | 0.202011i | ||||
\(465\) | 14297.6 | + | 14297.6i | 1.42589 | + | 1.42589i | ||||
\(466\) | 4264.00 | + | 4264.00i | 0.423876 | + | 0.423876i | ||||
\(467\) | − | 12536.8i | − | 1.24226i | −0.783707 | − | 0.621130i | \(-0.786674\pi\) | ||
0.783707 | − | 0.621130i | \(-0.213326\pi\) | |||||||
\(468\) | − | 7534.36i | − | 0.744179i | ||||||
\(469\) | −3060.86 | − | 3060.86i | −0.301359 | − | 0.301359i | ||||
\(470\) | 6063.76 | + | 6063.76i | 0.595107 | + | 0.595107i | ||||
\(471\) | 6331.81 | − | 6331.81i | 0.619436 | − | 0.619436i | ||||
\(472\) | −3276.36 | −0.319506 | ||||||||
\(473\) | 2985.20 | − | 2985.20i | 0.290190 | − | 0.290190i | ||||
\(474\) | − | 588.419i | − | 0.0570189i | ||||||
\(475\) | 2529.87 | 0.244376 | ||||||||
\(476\) | −50.3278 | − | 1119.34i | −0.00484616 | − | 0.107784i | ||||
\(477\) | −243.734 | −0.0233958 | ||||||||
\(478\) | 8438.46i | 0.807460i | ||||||||
\(479\) | 741.437 | − | 741.437i | 0.0707246 | − | 0.0707246i | −0.670860 | − | 0.741584i | \(-0.734075\pi\) |
0.741584 | + | 0.670860i | \(0.234075\pi\) | |||||||
\(480\) | −17491.0 | −1.66323 | ||||||||
\(481\) | −12481.2 | + | 12481.2i | −1.18315 | + | 1.18315i | ||||
\(482\) | −2687.36 | − | 2687.36i | −0.253954 | − | 0.253954i | ||||
\(483\) | 1129.16 | + | 1129.16i | 0.106374 | + | 0.106374i | ||||
\(484\) | 3450.54i | 0.324055i | ||||||||
\(485\) | − | 4124.10i | − | 0.386115i | ||||||
\(486\) | −5827.47 | − | 5827.47i | −0.543908 | − | 0.543908i | ||||
\(487\) | 639.001 | + | 639.001i | 0.0594577 | + | 0.0594577i | 0.736210 | − | 0.676753i | \(-0.236613\pi\) |
−0.676753 | + | 0.736210i | \(0.736613\pi\) | |||||||
\(488\) | −10312.4 | + | 10312.4i | −0.956598 | + | 0.956598i | ||||
\(489\) | 7087.06 | 0.655394 | ||||||||
\(490\) | 6933.05 | − | 6933.05i | 0.639191 | − | 0.639191i | ||||
\(491\) | 14922.5i | 1.37158i | 0.727800 | + | 0.685789i | \(0.240543\pi\) | ||||
−0.727800 | + | 0.685789i | \(0.759457\pi\) | |||||||
\(492\) | 1866.90 | 0.171069 | ||||||||
\(493\) | 8497.94 | − | 382.083i | 0.776325 | − | 0.0349050i | ||||
\(494\) | −3263.96 | −0.297273 | ||||||||
\(495\) | 29891.1i | 2.71415i | ||||||||
\(496\) | −2793.77 | + | 2793.77i | −0.252911 | + | 0.252911i | ||||
\(497\) | 1511.17 | 0.136389 | ||||||||
\(498\) | 3563.82 | − | 3563.82i | 0.320680 | − | 0.320680i | ||||
\(499\) | −1858.57 | − | 1858.57i | −0.166735 | − | 0.166735i | 0.618807 | − | 0.785543i | \(-0.287616\pi\) |
−0.785543 | + | 0.618807i | \(0.787616\pi\) | |||||||
\(500\) | 1559.42 | + | 1559.42i | 0.139479 | + | 0.139479i | ||||
\(501\) | − | 21909.0i | − | 1.95373i | ||||||
\(502\) | − | 9866.45i | − | 0.877214i | ||||||
\(503\) | 4596.21 | + | 4596.21i | 0.407426 | + | 0.407426i | 0.880840 | − | 0.473414i | \(-0.156979\pi\) |
−0.473414 | + | 0.880840i | \(0.656979\pi\) | |||||||
\(504\) | 3393.72 | + | 3393.72i | 0.299937 | + | 0.299937i | ||||
\(505\) | 1564.76 | − | 1564.76i | 0.137883 | − | 0.137883i | ||||
\(506\) | −4265.79 | −0.374777 | ||||||||
\(507\) | −1523.31 | + | 1523.31i | −0.133437 | + | 0.133437i | ||||
\(508\) | − | 7402.58i | − | 0.646528i | ||||||
\(509\) | −1931.57 | −0.168203 | −0.0841013 | − | 0.996457i | \(-0.526802\pi\) | ||||
−0.0841013 | + | 0.996457i | \(0.526802\pi\) | |||||||
\(510\) | 13193.9 | + | 12058.5i | 1.14556 | + | 1.04698i | ||||
\(511\) | 120.657 | 0.0104453 | ||||||||
\(512\) | − | 8007.88i | − | 0.691214i | ||||||
\(513\) | −3000.89 | + | 3000.89i | −0.258270 | + | 0.258270i | ||||
\(514\) | −13205.6 | −1.13322 | ||||||||
\(515\) | 7770.70 | − | 7770.70i | 0.664889 | − | 0.664889i | ||||
\(516\) | −1828.95 | − | 1828.95i | −0.156037 | − | 0.156037i | ||||
\(517\) | −9586.14 | − | 9586.14i | −0.815470 | − | 0.815470i | ||||
\(518\) | − | 3432.10i | − | 0.291115i | ||||||
\(519\) | 25859.7i | 2.18712i | ||||||||
\(520\) | 12269.8 | + | 12269.8i | 1.03474 | + | 1.03474i | ||||
\(521\) | 3738.53 | + | 3738.53i | 0.314372 | + | 0.314372i | 0.846601 | − | 0.532229i | \(-0.178645\pi\) |
−0.532229 | + | 0.846601i | \(0.678645\pi\) | |||||||
\(522\) | −7864.44 | + | 7864.44i | −0.659420 | + | 0.659420i | ||||
\(523\) | 8406.61 | 0.702859 | 0.351430 | − | 0.936214i | \(-0.385696\pi\) | ||||
0.351430 | + | 0.936214i | \(0.385696\pi\) | |||||||
\(524\) | −3455.99 | + | 3455.99i | −0.288122 | + | 0.288122i | ||||
\(525\) | 3100.31i | 0.257731i | ||||||||
\(526\) | 315.635 | 0.0261642 | ||||||||
\(527\) | −11758.5 | + | 528.686i | −0.971936 | + | 0.0437001i | ||||
\(528\) | −9485.09 | −0.781791 | ||||||||
\(529\) | − | 10412.8i | − | 0.855819i | ||||||
\(530\) | 121.157 | − | 121.157i | 0.00992966 | − | 0.00992966i | ||||
\(531\) | 5813.75 | 0.475132 | ||||||||
\(532\) | −351.667 | + | 351.667i | −0.0286592 | + | 0.0286592i | ||||
\(533\) | −2219.48 | − | 2219.48i | −0.180368 | − | 0.180368i | ||||
\(534\) | 2403.30 | + | 2403.30i | 0.194758 | + | 0.194758i | ||||
\(535\) | 5680.61i | 0.459054i | ||||||||
\(536\) | − | 23210.0i | − | 1.87037i | ||||||
\(537\) | 5447.06 | + | 5447.06i | 0.437725 | + | 0.437725i | ||||
\(538\) | −4657.39 | − | 4657.39i | −0.373223 | − | 0.373223i | ||||
\(539\) | −10960.4 | + | 10960.4i | −0.875878 | + | 0.875878i | ||||
\(540\) | 6886.72 | 0.548810 | ||||||||
\(541\) | −8004.01 | + | 8004.01i | −0.636080 | + | 0.636080i | −0.949586 | − | 0.313506i | \(-0.898496\pi\) |
0.313506 | + | 0.949586i | \(0.398496\pi\) | |||||||
\(542\) | 10007.6i | 0.793110i | ||||||||
\(543\) | 18095.8 | 1.43014 | ||||||||
\(544\) | 6869.01 | − | 7515.78i | 0.541372 | − | 0.592346i | ||||
\(545\) | 12609.9 | 0.991101 | ||||||||
\(546\) | − | 3999.93i | − | 0.313518i | ||||||
\(547\) | 849.665 | − | 849.665i | 0.0664151 | − | 0.0664151i | −0.673119 | − | 0.739534i | \(-0.735046\pi\) |
0.739534 | + | 0.673119i | \(0.235046\pi\) | |||||||
\(548\) | −8117.66 | −0.632791 | ||||||||
\(549\) | 18298.8 | − | 18298.8i | 1.42254 | − | 1.42254i | ||||
\(550\) | −5856.25 | − | 5856.25i | −0.454021 | − | 0.454021i | ||||
\(551\) | −2669.82 | − | 2669.82i | −0.206421 | − | 0.206421i | ||||
\(552\) | 8562.21i | 0.660202i | ||||||||
\(553\) | 150.742i | 0.0115916i | ||||||||
\(554\) | −1348.00 | − | 1348.00i | −0.103377 | − | 0.103377i | ||||
\(555\) | −30337.6 | − | 30337.6i | −2.32029 | − | 2.32029i | ||||
\(556\) | 6156.36 | − | 6156.36i | 0.469583 | − | 0.469583i | ||||
\(557\) | −5277.38 | −0.401454 | −0.200727 | − | 0.979647i | \(-0.564330\pi\) | ||||
−0.200727 | + | 0.979647i | \(0.564330\pi\) | |||||||
\(558\) | 10882.0 | − | 10882.0i | 0.825575 | − | 0.825575i | ||||
\(559\) | 4348.73i | 0.329037i | ||||||||
\(560\) | −1537.04 | −0.115985 | ||||||||
\(561\) | −20858.1 | − | 19063.2i | −1.56975 | − | 1.43467i | ||||
\(562\) | 19411.5 | 1.45698 | ||||||||
\(563\) | 2341.00i | 0.175243i | 0.996154 | + | 0.0876213i | \(0.0279265\pi\) | ||||
−0.996154 | + | 0.0876213i | \(0.972073\pi\) | |||||||
\(564\) | −5873.18 | + | 5873.18i | −0.438485 | + | 0.438485i | ||||
\(565\) | 29389.1 | 2.18833 | ||||||||
\(566\) | −5303.23 | + | 5303.23i | −0.393836 | + | 0.393836i | ||||
\(567\) | 79.9099 | + | 79.9099i | 0.00591869 | + | 0.00591869i | ||||
\(568\) | 5729.47 | + | 5729.47i | 0.423245 | + | 0.423245i | ||||
\(569\) | 3732.25i | 0.274981i | 0.990503 | + | 0.137490i | \(0.0439036\pi\) | ||||
−0.990503 | + | 0.137490i | \(0.956096\pi\) | |||||||
\(570\) | − | 7933.58i | − | 0.582985i | ||||||
\(571\) | −3185.66 | − | 3185.66i | −0.233478 | − | 0.233478i | 0.580665 | − | 0.814143i | \(-0.302793\pi\) |
−0.814143 | + | 0.580665i | \(0.802793\pi\) | |||||||
\(572\) | −5920.81 | − | 5920.81i | −0.432800 | − | 0.432800i | ||||
\(573\) | −8000.29 | + | 8000.29i | −0.583275 | + | 0.583275i | ||||
\(574\) | 610.313 | 0.0443797 | ||||||||
\(575\) | −2408.31 | + | 2408.31i | −0.174667 | + | 0.174667i | ||||
\(576\) | 21457.4i | 1.55218i | ||||||||
\(577\) | −15292.7 | −1.10337 | −0.551685 | − | 0.834053i | \(-0.686015\pi\) | ||||
−0.551685 | + | 0.834053i | \(0.686015\pi\) | |||||||
\(578\) | −10362.9 | + | 933.761i | −0.745746 | + | 0.0671961i | ||||
\(579\) | 29416.4 | 2.11141 | ||||||||
\(580\) | 6126.95i | 0.438634i | ||||||||
\(581\) | −912.981 | + | 912.981i | −0.0651925 | + | 0.0651925i | ||||
\(582\) | −5097.37 | −0.363046 | ||||||||
\(583\) | −191.536 | + | 191.536i | −0.0136065 | + | 0.0136065i | ||||
\(584\) | 457.460 | + | 457.460i | 0.0324141 | + | 0.0324141i | ||||
\(585\) | −21772.1 | − | 21772.1i | −1.53875 | − | 1.53875i | ||||
\(586\) | 2686.03i | 0.189350i | ||||||||
\(587\) | 11208.5i | 0.788116i | 0.919086 | + | 0.394058i | \(0.128929\pi\) | ||||
−0.919086 | + | 0.394058i | \(0.871071\pi\) | |||||||
\(588\) | 6715.15 | + | 6715.15i | 0.470966 | + | 0.470966i | ||||
\(589\) | 3694.21 | + | 3694.21i | 0.258433 | + | 0.258433i | ||||
\(590\) | −2889.94 | + | 2889.94i | −0.201656 | + | 0.201656i | ||||
\(591\) | −29747.5 | −2.07047 | ||||||||
\(592\) | 5928.00 | − | 5928.00i | 0.411553 | − | 0.411553i | ||||
\(593\) | 10220.6i | 0.707774i | 0.935288 | + | 0.353887i | \(0.115140\pi\) | ||||
−0.935288 | + | 0.353887i | \(0.884860\pi\) | |||||||
\(594\) | 13893.2 | 0.959669 | ||||||||
\(595\) | −3380.02 | − | 3089.15i | −0.232886 | − | 0.212845i | ||||
\(596\) | 5348.09 | 0.367561 | ||||||||
\(597\) | − | 25751.4i | − | 1.76539i | ||||||
\(598\) | 3107.12 | − | 3107.12i | 0.212474 | − | 0.212474i | ||||
\(599\) | 9068.76 | 0.618597 | 0.309298 | − | 0.950965i | \(-0.399906\pi\) | ||||
0.309298 | + | 0.950965i | \(0.399906\pi\) | |||||||
\(600\) | −11754.6 | + | 11754.6i | −0.799797 | + | 0.799797i | ||||
\(601\) | 10107.0 | + | 10107.0i | 0.685980 | + | 0.685980i | 0.961341 | − | 0.275361i | \(-0.0887974\pi\) |
−0.275361 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(602\) | −597.908 | − | 597.908i | −0.0404800 | − | 0.0404800i | ||||
\(603\) | 41185.1i | 2.78140i | ||||||||
\(604\) | − | 1398.57i | − | 0.0942167i | ||||||
\(605\) | 9971.05 | + | 9971.05i | 0.670051 | + | 0.670051i | ||||
\(606\) | −1934.04 | − | 1934.04i | −0.129645 | − | 0.129645i | ||||
\(607\) | 9231.72 | − | 9231.72i | 0.617304 | − | 0.617304i | −0.327535 | − | 0.944839i | \(-0.606218\pi\) |
0.944839 | + | 0.327535i | \(0.106218\pi\) | |||||||
\(608\) | −4519.30 | −0.301450 | ||||||||
\(609\) | 3271.81 | − | 3271.81i | 0.217702 | − | 0.217702i | ||||
\(610\) | 18192.2i | 1.20751i | ||||||||
\(611\) | 13964.8 | 0.924638 | ||||||||
\(612\) | −7192.02 | + | 7869.20i | −0.475033 | + | 0.519760i | ||||
\(613\) | −15590.7 | −1.02725 | −0.513623 | − | 0.858016i | \(-0.671697\pi\) | ||||
−0.513623 | + | 0.858016i | \(0.671697\pi\) | |||||||
\(614\) | 21017.9i | 1.38145i | ||||||||
\(615\) | 5394.79 | − | 5394.79i | 0.353722 | − | 0.353722i | ||||
\(616\) | 5333.84 | 0.348874 | ||||||||
\(617\) | 18303.2 | − | 18303.2i | 1.19426 | − | 1.19426i | 0.218400 | − | 0.975859i | \(-0.429916\pi\) |
0.975859 | − | 0.218400i | \(-0.0700837\pi\) | |||||||
\(618\) | −9604.56 | − | 9604.56i | −0.625165 | − | 0.625165i | ||||
\(619\) | −317.054 | − | 317.054i | −0.0205872 | − | 0.0205872i | 0.696738 | − | 0.717325i | \(-0.254634\pi\) |
−0.717325 | + | 0.696738i | \(0.754634\pi\) | |||||||
\(620\) | − | 8477.82i | − | 0.549157i | ||||||
\(621\) | − | 5713.38i | − | 0.369195i | ||||||
\(622\) | 2184.40 | + | 2184.40i | 0.140814 | + | 0.140814i | ||||
\(623\) | −615.678 | − | 615.678i | −0.0395933 | − | 0.0395933i | ||||
\(624\) | 6908.77 | − | 6908.77i | 0.443225 | − | 0.443225i | ||||
\(625\) | 19177.2 | 1.22734 | ||||||||
\(626\) | −1194.83 | + | 1194.83i | −0.0762857 | + | 0.0762857i | ||||
\(627\) | 12542.1i | 0.798859i | ||||||||
\(628\) | −3754.47 | −0.238566 | ||||||||
\(629\) | 24950.0 | − | 1121.80i | 1.58159 | − | 0.0711114i | ||||
\(630\) | 5986.91 | 0.378610 | ||||||||
\(631\) | − | 6811.18i | − | 0.429713i | −0.976646 | − | 0.214856i | \(-0.931072\pi\) | ||
0.976646 | − | 0.214856i | \(-0.0689284\pi\) | |||||||
\(632\) | −571.524 | + | 571.524i | −0.0359715 | + | 0.0359715i | ||||
\(633\) | −50481.5 | −3.16976 | ||||||||
\(634\) | 5769.30 | − | 5769.30i | 0.361401 | − | 0.361401i | ||||
\(635\) | −21391.3 | − | 21391.3i | −1.33683 | − | 1.33683i | ||||
\(636\) | 117.349 | + | 117.349i | 0.00731634 | + | 0.00731634i | ||||
\(637\) | − | 15966.7i | − | 0.993132i | ||||||
\(638\) | 12360.4i | 0.767011i | ||||||||
\(639\) | −10166.7 | − | 10166.7i | −0.629402 | − | 0.629402i | ||||
\(640\) | 1136.90 | + | 1136.90i | 0.0702189 | + | 0.0702189i | ||||
\(641\) | −9965.73 | + | 9965.73i | −0.614076 | + | 0.614076i | −0.944006 | − | 0.329930i | \(-0.892975\pi\) |
0.329930 | + | 0.944006i | \(0.392975\pi\) | |||||||
\(642\) | 7021.21 | 0.431628 | ||||||||
\(643\) | 6116.96 | − | 6116.96i | 0.375162 | − | 0.375162i | −0.494191 | − | 0.869353i | \(-0.664536\pi\) |
0.869353 | + | 0.494191i | \(0.164536\pi\) | |||||||
\(644\) | − | 669.537i | − | 0.0409681i | ||||||
\(645\) | −10570.3 | −0.645279 | ||||||||
\(646\) | 3409.02 | + | 3115.66i | 0.207626 | + | 0.189758i | ||||
\(647\) | −10310.7 | −0.626515 | −0.313258 | − | 0.949668i | \(-0.601420\pi\) | ||||
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(648\) | 605.943i | 0.0367341i | ||||||||
\(649\) | 4568.68 | − | 4568.68i | 0.276327 | − | 0.276327i | ||||
\(650\) | 8531.18 | 0.514801 | ||||||||
\(651\) | −4527.18 | + | 4527.18i | −0.272556 | + | 0.272556i | ||||
\(652\) | −2101.15 | − | 2101.15i | −0.126207 | − | 0.126207i | ||||
\(653\) | −6074.29 | − | 6074.29i | −0.364020 | − | 0.364020i | 0.501270 | − | 0.865291i | \(-0.332866\pi\) |
−0.865291 | + | 0.501270i | \(0.832866\pi\) | |||||||
\(654\) | − | 15585.8i | − | 0.931887i | ||||||
\(655\) | 19973.6i | 1.19150i | ||||||||
\(656\) | 1054.15 | + | 1054.15i | 0.0627402 | + | 0.0627402i | ||||
\(657\) | −811.741 | − | 811.741i | −0.0482025 | − | 0.0482025i | ||||
\(658\) | −1920.02 | + | 1920.02i | −0.113754 | + | 0.113754i | ||||
\(659\) | −4635.27 | −0.273998 | −0.136999 | − | 0.990571i | \(-0.543746\pi\) | ||||
−0.136999 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(660\) | 14391.5 | − | 14391.5i | 0.848768 | − | 0.848768i | ||||
\(661\) | 27861.5i | 1.63946i | 0.572747 | + | 0.819732i | \(0.305878\pi\) | ||||
−0.572747 | + | 0.819732i | \(0.694122\pi\) | |||||||
\(662\) | −17938.9 | −1.05320 | ||||||||
\(663\) | 29077.9 | − | 1307.40i | 1.70331 | − | 0.0765839i | ||||
\(664\) | −6922.98 | −0.404614 | ||||||||
\(665\) | 2032.43i | 0.118518i | ||||||||
\(666\) | −23090.1 | + | 23090.1i | −1.34343 | + | 1.34343i | ||||
\(667\) | 5083.05 | 0.295077 | ||||||||
\(668\) | −6495.50 | + | 6495.50i | −0.376225 | + | 0.376225i | ||||
\(669\) | 21227.0 | + | 21227.0i | 1.22673 | + | 1.22673i | ||||
\(670\) | −20472.6 | − | 20472.6i | −1.18048 | − | 1.18048i | ||||
\(671\) | − | 28760.0i | − | 1.65464i | ||||||
\(672\) | − | 5538.31i | − | 0.317924i | ||||||
\(673\) | −5996.35 | − | 5996.35i | −0.343451 | − | 0.343451i | 0.514212 | − | 0.857663i | \(-0.328084\pi\) |
−0.857663 | + | 0.514212i | \(0.828084\pi\) | |||||||
\(674\) | −2879.60 | − | 2879.60i | −0.164567 | − | 0.164567i | ||||
\(675\) | 7843.56 | − | 7843.56i | 0.447258 | − | 0.447258i | ||||
\(676\) | 903.253 | 0.0513913 | ||||||||
\(677\) | 7979.46 | − | 7979.46i | 0.452992 | − | 0.452992i | −0.443355 | − | 0.896346i | \(-0.646212\pi\) |
0.896346 | + | 0.443355i | \(0.146212\pi\) | |||||||
\(678\) | − | 36324.8i | − | 2.05759i | ||||||
\(679\) | 1305.85 | 0.0738054 | ||||||||
\(680\) | −1102.79 | − | 24527.3i | −0.0621914 | − | 1.38320i | ||||
\(681\) | 35580.1 | 2.00210 | ||||||||
\(682\) | − | 17103.0i | − | 0.960276i | ||||||
\(683\) | 1637.44 | − | 1637.44i | 0.0917350 | − | 0.0917350i | −0.659750 | − | 0.751485i | \(-0.729338\pi\) |
0.751485 | + | 0.659750i | \(0.229338\pi\) | |||||||
\(684\) | 4731.81 | 0.264511 | ||||||||
\(685\) | −23457.7 | + | 23457.7i | −1.30843 | + | 1.30843i | ||||
\(686\) | 4531.43 | + | 4531.43i | 0.252202 | + | 0.252202i | ||||
\(687\) | 30507.7 | + | 30507.7i | 1.69424 | + | 1.69424i | ||||
\(688\) | − | 2065.45i | − | 0.114454i | ||||||
\(689\) | − | 279.023i | − | 0.0154281i | ||||||
\(690\) | 7552.36 | + | 7552.36i | 0.416686 | + | 0.416686i | ||||
\(691\) | 5780.78 | + | 5780.78i | 0.318251 | + | 0.318251i | 0.848095 | − | 0.529844i | \(-0.177750\pi\) |
−0.529844 | + | 0.848095i | \(0.677750\pi\) | |||||||
\(692\) | 7666.79 | − | 7666.79i | 0.421167 | − | 0.421167i | ||||
\(693\) | −9464.66 | −0.518806 | ||||||||
\(694\) | −3839.80 | + | 3839.80i | −0.210024 | + | 0.210024i | ||||
\(695\) | − | 35580.2i | − | 1.94192i | ||||||
\(696\) | 24809.6 | 1.35116 | ||||||||
\(697\) | 199.484 | + | 4436.74i | 0.0108407 | + | 0.241110i | ||||
\(698\) | −599.677 | −0.0325188 | ||||||||
\(699\) | 23868.9i | 1.29157i | ||||||||
\(700\) | 919.168 | − | 919.168i | 0.0496304 | − | 0.0496304i | ||||
\(701\) | −22583.3 | −1.21677 | −0.608387 | − | 0.793640i | \(-0.708183\pi\) | ||||
−0.608387 | + | 0.793640i | \(0.708183\pi\) | |||||||
\(702\) | −10119.5 | + | 10119.5i | −0.544070 | + | 0.544070i | ||||
\(703\) | −7838.60 | − | 7838.60i | −0.420538 | − | 0.420538i | ||||
\(704\) | 16862.1 | + | 16862.1i | 0.902719 | + | 0.902719i | ||||
\(705\) | 33943.6i | 1.81332i | ||||||||
\(706\) | 22650.5i | 1.20745i | ||||||||
\(707\) | 495.464 | + | 495.464i | 0.0263562 | + | 0.0263562i | ||||
\(708\) | −2799.11 | − | 2799.11i | −0.148583 | − | 0.148583i | ||||
\(709\) | −16352.3 | + | 16352.3i | −0.866183 | + | 0.866183i | −0.992048 | − | 0.125864i | \(-0.959830\pi\) |
0.125864 | + | 0.992048i | \(0.459830\pi\) | |||||||
\(710\) | 10107.4 | 0.534262 | ||||||||
\(711\) | 1014.14 | − | 1014.14i | 0.0534927 | − | 0.0534927i | ||||
\(712\) | − | 4668.58i | − | 0.245734i | ||||||
\(713\) | −7033.38 | −0.369428 | ||||||||
\(714\) | −3818.18 | + | 4177.69i | −0.200129 | + | 0.218972i | ||||
\(715\) | −34218.8 | −1.78981 | ||||||||
\(716\) | − | 3229.85i | − | 0.168583i | ||||||
\(717\) | −23618.3 | + | 23618.3i | −1.23018 | + | 1.23018i | ||||
\(718\) | −18430.2 | −0.957951 | ||||||||
\(719\) | −24637.7 | + | 24637.7i | −1.27793 | + | 1.27793i | −0.336108 | + | 0.941823i | \(0.609111\pi\) |
−0.941823 | + | 0.336108i | \(0.890889\pi\) | |||||||
\(720\) | 10340.7 | + | 10340.7i | 0.535245 | + | 0.535245i | ||||
\(721\) | 2460.50 | + | 2460.50i | 0.127093 | + | 0.127093i | ||||
\(722\) | 12476.4i | 0.643105i | ||||||||
\(723\) | − | 15043.2i | − | 0.773809i | ||||||
\(724\) | −5364.97 | − | 5364.97i | −0.275397 | − | 0.275397i | ||||
\(725\) | 6978.23 | + | 6978.23i | 0.357469 | + | 0.357469i | ||||
\(726\) | 12324.2 | − | 12324.2i | 0.630019 | − | 0.630019i | ||||
\(727\) | 11782.3 | 0.601077 | 0.300538 | − | 0.953770i | \(-0.402834\pi\) | ||||
0.300538 | + | 0.953770i | \(0.402834\pi\) | |||||||
\(728\) | −3885.08 | + | 3885.08i | −0.197789 | + | 0.197789i | ||||
\(729\) | − | 31950.0i | − | 1.62323i | ||||||
\(730\) | 807.012 | 0.0409162 | ||||||||
\(731\) | 4151.14 | − | 4542.00i | 0.210035 | − | 0.229811i | ||||
\(732\) | −17620.5 | −0.889715 | ||||||||
\(733\) | − | 20099.0i | − | 1.01279i | −0.862302 | − | 0.506394i | \(-0.830978\pi\) | ||
0.862302 | − | 0.506394i | \(-0.169022\pi\) | |||||||
\(734\) | 17853.2 | − | 17853.2i | 0.897783 | − | 0.897783i | ||||
\(735\) | 38809.7 | 1.94764 | ||||||||
\(736\) | 4302.13 | − | 4302.13i | 0.215460 | − | 0.215460i | ||||
\(737\) | 32364.9 | + | 32364.9i | 1.61761 | + | 1.61761i | ||||
\(738\) | −4106.00 | − | 4106.00i | −0.204802 | − | 0.204802i | ||||
\(739\) | − | 12538.4i | − | 0.624132i | −0.950060 | − | 0.312066i | \(-0.898979\pi\) | ||
0.950060 | − | 0.312066i | \(-0.101021\pi\) | |||||||
\(740\) | 17988.8i | 0.893623i | ||||||||
\(741\) | −9135.48 | − | 9135.48i | −0.452902 | − | 0.452902i | ||||
\(742\) | 38.3629 | + | 38.3629i | 0.00189804 | + | 0.00189804i | ||||
\(743\) | 2329.69 | − | 2329.69i | 0.115031 | − | 0.115031i | −0.647248 | − | 0.762279i | \(-0.724080\pi\) |
0.762279 | + | 0.647248i | \(0.224080\pi\) | |||||||
\(744\) | −34328.8 | −1.69161 | ||||||||
\(745\) | 15454.5 | − | 15454.5i | 0.760010 | − | 0.760010i | ||||
\(746\) | − | 23411.7i | − | 1.14901i | ||||||
\(747\) | 12284.5 | 0.601696 | ||||||||
\(748\) | 532.156 | + | 11835.7i | 0.0260127 | + | 0.578552i | ||||
\(749\) | −1798.70 | −0.0877477 | ||||||||
\(750\) | − | 11139.5i | − | 0.542342i | ||||||
\(751\) | −5128.04 | + | 5128.04i | −0.249168 | + | 0.249168i | −0.820629 | − | 0.571461i | \(-0.806377\pi\) |
0.571461 | + | 0.820629i | \(0.306377\pi\) | |||||||
\(752\) | −6632.61 | −0.321631 | ||||||||
\(753\) | 27615.1 | − | 27615.1i | 1.33646 | − | 1.33646i | ||||
\(754\) | −9003.10 | − | 9003.10i | −0.434846 | − | 0.434846i | ||||
\(755\) | −4041.46 | − | 4041.46i | −0.194813 | − | 0.194813i | ||||
\(756\) | 2180.60i | 0.104904i | ||||||||
\(757\) | − | 26725.2i | − | 1.28315i | −0.767061 | − | 0.641574i | \(-0.778282\pi\) | ||
0.767061 | − | 0.641574i | \(-0.221718\pi\) | |||||||
\(758\) | 17294.3 | + | 17294.3i | 0.828705 | + | 0.828705i | ||||
\(759\) | −11939.5 | − | 11939.5i | −0.570982 | − | 0.570982i | ||||
\(760\) | −7705.79 | + | 7705.79i | −0.367787 | + | 0.367787i | ||||
\(761\) | 1638.39 | 0.0780443 | 0.0390222 | − | 0.999238i | \(-0.487576\pi\) | ||||
0.0390222 | + | 0.999238i | \(0.487576\pi\) | |||||||
\(762\) | −26439.6 | + | 26439.6i | −1.25696 | + | 1.25696i | ||||
\(763\) | 3992.79i | 0.189448i | ||||||||
\(764\) | 4743.79 | 0.224639 | ||||||||
\(765\) | 1956.85 | + | 43522.6i | 0.0924840 | + | 2.05694i | ||||
\(766\) | 21683.9 | 1.02281 | ||||||||
\(767\) | 6655.50i | 0.313319i | ||||||||
\(768\) | 24919.5 | − | 24919.5i | 1.17084 | − | 1.17084i | ||||
\(769\) | 9542.58 | 0.447483 | 0.223741 | − | 0.974649i | \(-0.428173\pi\) | ||||
0.223741 | + | 0.974649i | \(0.428173\pi\) | |||||||
\(770\) | 4704.76 | − | 4704.76i | 0.220192 | − | 0.220192i | ||||
\(771\) | −36961.0 | − | 36961.0i | −1.72648 | − | 1.72648i | ||||
\(772\) | −8721.28 | − | 8721.28i | −0.406588 | − | 0.406588i | ||||
\(773\) | − | 10640.1i | − | 0.495080i | −0.968878 | − | 0.247540i | \(-0.920378\pi\) | ||
0.968878 | − | 0.247540i | \(-0.0796222\pi\) | |||||||
\(774\) | 8045.09i | 0.373611i | ||||||||
\(775\) | −9655.73 | − | 9655.73i | −0.447541 | − | 0.447541i | ||||
\(776\) | 4951.02 | + | 4951.02i | 0.229035 | + | 0.229035i | ||||
\(777\) | 9606.06 | − | 9606.06i | 0.443520 | − | 0.443520i | ||||
\(778\) | −9272.90 | −0.427313 | ||||||||
\(779\) | 1393.90 | − | 1393.90i | 0.0641100 | − | 0.0641100i | ||||
\(780\) | 20965.0i | 0.962393i | ||||||||
\(781\) | −15978.8 | −0.732095 | ||||||||
\(782\) | −6211.15 | + | 279.265i | −0.284029 | + | 0.0127705i | ||||
\(783\) | −16554.9 | −0.755586 | ||||||||
\(784\) | 7583.45i | 0.345456i | ||||||||
\(785\) | −10849.3 | + | 10849.3i | −0.493285 | + | 0.493285i | ||||
\(786\) | 24687.4 | 1.12032 | ||||||||
\(787\) | −3081.73 | + | 3081.73i | −0.139583 | + | 0.139583i | −0.773446 | − | 0.633863i | \(-0.781468\pi\) |
0.633863 | + | 0.773446i | \(0.281468\pi\) | |||||||
\(788\) | 8819.42 | + | 8819.42i | 0.398704 | + | 0.398704i | ||||
\(789\) | 883.429 | + | 883.429i | 0.0398617 | + | 0.0398617i | ||||
\(790\) | 1008.23i | 0.0454068i | ||||||||
\(791\) | 9305.71i | 0.418297i | ||||||||
\(792\) | −35884.5 | − | 35884.5i | −1.60997 | − | 1.60997i | ||||
\(793\) | 20948.3 | + | 20948.3i | 0.938076 | + | 0.938076i | ||||
\(794\) | 15059.0 | − | 15059.0i | 0.673078 | − | 0.673078i | ||||
\(795\) | 678.210 | 0.0302561 | ||||||||
\(796\) | −7634.70 | + | 7634.70i | −0.339956 | + | 0.339956i | ||||
\(797\) | 19901.9i | 0.884517i | 0.896888 | + | 0.442259i | \(0.145823\pi\) | ||||
−0.896888 | + | 0.442259i | \(0.854177\pi\) | |||||||
\(798\) | 2512.08 | 0.111437 | ||||||||
\(799\) | −14585.4 | − | 13330.2i | −0.645799 | − | 0.590225i | ||||
\(800\) | 11812.3 | 0.522035 | ||||||||
\(801\) | 8284.18i | 0.365427i | ||||||||
\(802\) | 12304.3 | − | 12304.3i | 0.541747 | − | 0.541747i | ||||
\(803\) | −1275.80 | −0.0560672 | ||||||||
\(804\) | 19829.1 | − | 19829.1i | 0.869800 | − | 0.869800i | ||||
\(805\) | −1934.77 | − | 1934.77i | −0.0847101 | − | 0.0847101i | ||||
\(806\) | 12457.5 | + | 12457.5i | 0.544414 | + | 0.544414i | ||||
\(807\) | − | 26071.0i | − | 1.13723i | ||||||
\(808\) | 3757.02i | 0.163579i | ||||||||
\(809\) | −19895.7 | − | 19895.7i | −0.864641 | − | 0.864641i | 0.127232 | − | 0.991873i | \(-0.459391\pi\) |
−0.991873 | + | 0.127232i | \(0.959391\pi\) | |||||||
\(810\) | 534.477 | + | 534.477i | 0.0231847 | + | 0.0231847i | ||||
\(811\) | −151.038 | + | 151.038i | −0.00653964 | + | 0.00653964i | −0.710369 | − | 0.703829i | \(-0.751472\pi\) |
0.703829 | + | 0.710369i | \(0.251472\pi\) | |||||||
\(812\) | −1940.03 | −0.0838444 | ||||||||
\(813\) | −28010.3 | + | 28010.3i | −1.20832 | + | 1.20832i | ||||
\(814\) | 36290.3i | 1.56262i | ||||||||
\(815\) | −12143.4 | −0.521921 | ||||||||
\(816\) | −13810.7 | + | 620.953i | −0.592488 | + | 0.0266393i | ||||
\(817\) | −2731.14 | −0.116953 | ||||||||
\(818\) | − | 11441.8i | − | 0.489061i | ||||||
\(819\) | 6893.89 | − | 6893.89i | 0.294129 | − | 0.294129i | ||||
\(820\) | −3198.86 | −0.136230 | ||||||||
\(821\) | 7369.47 | − | 7369.47i | 0.313272 | − | 0.313272i | −0.532904 | − | 0.846176i | \(-0.678899\pi\) |
0.846176 | + | 0.532904i | \(0.178899\pi\) | |||||||
\(822\) | 28993.6 | + | 28993.6i | 1.23025 | + | 1.23025i | ||||
\(823\) | 17736.3 | + | 17736.3i | 0.751215 | + | 0.751215i | 0.974706 | − | 0.223491i | \(-0.0717453\pi\) |
−0.223491 | + | 0.974706i | \(0.571745\pi\) | |||||||
\(824\) | 18657.6i | 0.788796i | ||||||||
\(825\) | − | 32782.0i | − | 1.38342i | ||||||
\(826\) | −915.066 | − | 915.066i | −0.0385462 | − | 0.0385462i | ||||
\(827\) | 19714.3 | + | 19714.3i | 0.828939 | + | 0.828939i | 0.987370 | − | 0.158431i | \(-0.0506437\pi\) |
−0.158431 | + | 0.987370i | \(0.550644\pi\) | |||||||
\(828\) | −4504.44 | + | 4504.44i | −0.189058 | + | 0.189058i | ||||
\(829\) | 28128.7 | 1.17847 | 0.589235 | − | 0.807962i | \(-0.299429\pi\) | ||||
0.589235 | + | 0.807962i | \(0.299429\pi\) | |||||||
\(830\) | −6106.47 | + | 6106.47i | −0.255372 | + | 0.255372i | ||||
\(831\) | − | 7545.80i | − | 0.314995i | ||||||
\(832\) | −24564.1 | −1.02357 | ||||||||
\(833\) | −15241.3 | + | 16676.3i | −0.633947 | + | 0.693638i | ||||
\(834\) | −43977.0 | −1.82590 | ||||||||
\(835\) | 37540.2i | 1.55585i | ||||||||
\(836\) | 3718.45 | − | 3718.45i | 0.153834 | − | 0.153834i | ||||
\(837\) | 22906.9 | 0.945971 | ||||||||
\(838\) | 9442.25 | − | 9442.25i | 0.389233 | − | 0.389233i | ||||
\(839\) | −27739.1 | − | 27739.1i | −1.14143 | − | 1.14143i | −0.988189 | − | 0.153240i | \(-0.951029\pi\) |
−0.153240 | − | 0.988189i | \(-0.548971\pi\) | |||||||
\(840\) | −9443.30 | − | 9443.30i | −0.387887 | − | 0.387887i | ||||
\(841\) | 9660.52i | 0.396101i | ||||||||
\(842\) | − | 13749.9i | − | 0.562772i | ||||||
\(843\) | 54330.6 | + | 54330.6i | 2.21974 | + | 2.21974i | ||||
\(844\) | 14966.6 | + | 14966.6i | 0.610392 | + | 0.610392i | ||||
\(845\) | 2610.14 | − | 2610.14i | 0.106262 | − | 0.106262i | ||||
\(846\) | 25834.6 | 1.04989 | ||||||||
\(847\) | −3157.22 | + | 3157.22i | −0.128079 | + | 0.128079i | ||||
\(848\) | 132.523i | 0.00536657i | ||||||||
\(849\) | −29686.3 | −1.20004 | ||||||||
\(850\) | −8910.32 | − | 8143.55i | −0.359555 | − | 0.328613i | ||||
\(851\) | 14923.9 | 0.601156 | ||||||||
\(852\) | 9789.78i | 0.393653i | ||||||||
\(853\) | 27355.5 | − | 27355.5i | 1.09805 | − | 1.09805i | 0.103407 | − | 0.994639i | \(-0.467026\pi\) |
0.994639 | − | 0.103407i | \(-0.0329744\pi\) | |||||||
\(854\) | −5760.36 | −0.230814 | ||||||||
\(855\) | 13673.6 | − | 13673.6i | 0.546931 | − | 0.546931i | ||||
\(856\) | −6819.62 | − | 6819.62i | −0.272301 | − | 0.272301i | ||||
\(857\) | 6659.46 | + | 6659.46i | 0.265441 | + | 0.265441i | 0.827260 | − | 0.561819i | \(-0.189898\pi\) |
−0.561819 | + | 0.827260i | \(0.689898\pi\) | |||||||
\(858\) | 42294.4i | 1.68287i | ||||||||
\(859\) | − | 43890.4i | − | 1.74333i | −0.490101 | − | 0.871666i | \(-0.663040\pi\) | ||
0.490101 | − | 0.871666i | \(-0.336960\pi\) | |||||||
\(860\) | 3133.84 | + | 3133.84i | 0.124259 | + | 0.124259i | ||||
\(861\) | 1708.20 | + | 1708.20i | 0.0676135 | + | 0.0676135i | ||||
\(862\) | −20183.0 | + | 20183.0i | −0.797489 | + | 0.797489i | ||||
\(863\) | −6822.88 | −0.269123 | −0.134562 | − | 0.990905i | \(-0.542963\pi\) | ||||
−0.134562 | + | 0.990905i | \(0.542963\pi\) | |||||||
\(864\) | −14011.5 | + | 14011.5i | −0.551716 | + | 0.551716i | ||||
\(865\) | − | 44309.6i | − | 1.74170i | ||||||
\(866\) | −28035.5 | −1.10010 | ||||||||
\(867\) | −31618.2 | − | 26391.2i | −1.23854 | − | 1.03379i | ||||
\(868\) | 2684.40 | 0.104971 | ||||||||
\(869\) | − | 1593.91i | − | 0.0622206i | ||||||
\(870\) | 21883.5 | − | 21883.5i | 0.852781 | − | 0.852781i | ||||
\(871\) | −47148.1 | −1.83416 | ||||||||
\(872\) | −15138.3 | + | 15138.3i | −0.587899 | + | 0.587899i | ||||
\(873\) | −8785.35 | − | 8785.35i | −0.340594 | − | 0.340594i | ||||
\(874\) | 1951.37 | + | 1951.37i | 0.0755218 | + | 0.0755218i | ||||
\(875\) | 2853.72i | 0.110255i | ||||||||
\(876\) | 781.648i | 0.0301478i | ||||||||
\(877\) | 24429.3 | + | 24429.3i | 0.940613 | + | 0.940613i | 0.998333 | − | 0.0577194i | \(-0.0183829\pi\) |
−0.0577194 | + | 0.998333i | \(0.518383\pi\) | |||||||
\(878\) | −15348.3 | − | 15348.3i | −0.589955 | − | 0.589955i | ||||
\(879\) | −7517.91 | + | 7517.91i | −0.288479 | + | 0.288479i | ||||
\(880\) | 16252.4 | 0.622576 | ||||||||
\(881\) | 21645.5 | − | 21645.5i | 0.827760 | − | 0.827760i | −0.159446 | − | 0.987207i | \(-0.550971\pi\) |
0.987207 | + | 0.159446i | \(0.0509709\pi\) | |||||||
\(882\) | − | 29538.2i | − | 1.12767i | ||||||
\(883\) | 42598.5 | 1.62350 | 0.811751 | − | 0.584003i | \(-0.198514\pi\) | ||||
0.811751 | + | 0.584003i | \(0.198514\pi\) | |||||||
\(884\) | −9008.54 | − | 8233.31i | −0.342749 | − | 0.313254i | ||||
\(885\) | −16177.2 | −0.614454 | ||||||||
\(886\) | − | 17288.5i | − | 0.655552i | ||||||
\(887\) | 13469.8 | − | 13469.8i | 0.509888 | − | 0.509888i | −0.404604 | − | 0.914492i | \(-0.632591\pi\) |
0.914492 | + | 0.404604i | \(0.132591\pi\) | |||||||
\(888\) | 72841.1 | 2.75269 | ||||||||
\(889\) | 6773.31 | − | 6773.31i | 0.255534 | − | 0.255534i | ||||
\(890\) | −4117.96 | − | 4117.96i | −0.155095 | − | 0.155095i | ||||
\(891\) | −844.950 | − | 844.950i | −0.0317698 | − | 0.0317698i | ||||
\(892\) | − | 12586.6i | − | 0.472457i | ||||||
\(893\) | 8770.30i | 0.328653i | ||||||||
\(894\) | −19101.6 | − | 19101.6i | −0.714602 | − | 0.714602i | ||||
\(895\) | −9333.34 | − | 9333.34i | −0.348580 | − | 0.348580i | ||||
\(896\) | −359.988 | + | 359.988i | −0.0134223 | + | 0.0134223i | ||||
\(897\) | 17393.0 | 0.647419 | ||||||||
\(898\) | 6563.20 | − | 6563.20i | 0.243894 | − | 0.243894i | ||||
\(899\) | 20379.7i | 0.756064i | ||||||||
\(900\) | −12367.8 | −0.458065 | ||||||||
\(901\) | −266.345 | + | 291.423i | −0.00984821 | + | 0.0107755i | ||||
\(902\) | −6453.32 | −0.238217 | ||||||||
\(903\) | − | 3346.96i | − | 0.123344i | ||||||
\(904\) | −35281.8 | + | 35281.8i | −1.29807 | + | 1.29807i | ||||
\(905\) | −31006.4 | −1.13888 | ||||||||
\(906\) | −4995.22 | + | 4995.22i | −0.183174 | + | 0.183174i | ||||
\(907\) | 5931.91 | + | 5931.91i | 0.217162 | + | 0.217162i | 0.807301 | − | 0.590139i | \(-0.200927\pi\) |
−0.590139 | + | 0.807301i | \(0.700927\pi\) | |||||||
\(908\) | −10548.7 | − | 10548.7i | −0.385539 | − | 0.385539i | ||||
\(909\) | − | 6666.66i | − | 0.243255i | ||||||
\(910\) | 6853.72i | 0.249669i | ||||||||
\(911\) | −7401.81 | − | 7401.81i | −0.269191 | − | 0.269191i | 0.559583 | − | 0.828774i | \(-0.310961\pi\) |
−0.828774 | + | 0.559583i | \(0.810961\pi\) | |||||||
\(912\) | 4338.92 | + | 4338.92i | 0.157540 | + | 0.157540i | ||||
\(913\) | 9653.67 | − | 9653.67i | 0.349934 | − | 0.349934i | ||||
\(914\) | 22159.6 | 0.801943 | ||||||||
\(915\) | −50918.1 | + | 50918.1i | −1.83967 | + | 1.83967i | ||||
\(916\) | − | 18089.6i | − | 0.652509i | ||||||
\(917\) | −6324.42 | −0.227754 | ||||||||
\(918\) | 20229.0 | − | 909.532i | 0.727294 | − | 0.0327005i | ||||
\(919\) | −16180.4 | −0.580787 | −0.290394 | − | 0.956907i | \(-0.593786\pi\) | ||||
−0.290394 | + | 0.956907i | \(0.593786\pi\) | |||||||
\(920\) | − | 14671.0i | − | 0.525749i | ||||||
\(921\) | −58826.7 | + | 58826.7i | −2.10467 | + | 2.10467i | ||||
\(922\) | 15969.8 | 0.570432 | ||||||||
\(923\) | 11638.7 | − | 11638.7i | 0.415050 | − | 0.415050i | ||||
\(924\) | 4556.89 | + | 4556.89i | 0.162241 | + | 0.162241i | ||||
\(925\) | 20488.1 | + | 20488.1i | 0.728266 | + | 0.728266i | ||||
\(926\) | − | 27451.4i | − | 0.974201i | ||||||
\(927\) | − | 33107.0i | − | 1.17301i | ||||||
\(928\) | −12465.7 | − | 12465.7i | −0.440956 | − | 0.440956i | ||||
\(929\) | 10051.5 | + | 10051.5i | 0.354982 | + | 0.354982i | 0.861959 | − | 0.506978i | \(-0.169237\pi\) |
−0.506978 | + | 0.861959i | \(0.669237\pi\) | |||||||
\(930\) | −30280.0 | + | 30280.0i | −1.06766 | + | 1.06766i | ||||
\(931\) | 10027.6 | 0.352998 | ||||||||
\(932\) | 7076.58 | − | 7076.58i | 0.248714 | − | 0.248714i | ||||
\(933\) | 12227.8i | 0.429068i | ||||||||
\(934\) | 26550.9 | 0.930164 | ||||||||
\(935\) | 35739.6 | + | 32664.0i | 1.25006 | + | 1.14249i | ||||
\(936\) | 52275.2 | 1.82550 | ||||||||
\(937\) | 49244.5i | 1.71691i | 0.512887 | + | 0.858456i | \(0.328576\pi\) | ||||
−0.512887 | + | 0.858456i | \(0.671424\pi\) | |||||||
\(938\) | 6482.40 | − | 6482.40i | 0.225648 | − | 0.225648i | ||||
\(939\) | −6688.37 | −0.232446 | ||||||||
\(940\) | 10063.5 | − | 10063.5i | 0.349185 | − | 0.349185i | ||||
\(941\) | −11062.8 | − | 11062.8i | −0.383247 | − | 0.383247i | 0.489023 | − | 0.872271i | \(-0.337353\pi\) |
−0.872271 | + | 0.489023i | \(0.837353\pi\) | |||||||
\(942\) | 13409.7 | + | 13409.7i | 0.463814 | + | 0.463814i | ||||
\(943\) | 2653.84i | 0.0916447i | ||||||||
\(944\) | − | 3161.05i | − | 0.108987i | ||||||
\(945\) | 6301.31 | + | 6301.31i | 0.216912 | + | 0.216912i | ||||
\(946\) | 6322.16 | + | 6322.16i | 0.217284 | + | 0.217284i | ||||
\(947\) | 23380.2 | − | 23380.2i | 0.802273 | − | 0.802273i | −0.181177 | − | 0.983450i | \(-0.557991\pi\) |
0.983450 | + | 0.181177i | \(0.0579907\pi\) | |||||||
\(948\) | −976.546 | −0.0334565 | ||||||||
\(949\) | 929.270 | − | 929.270i | 0.0317865 | − | 0.0317865i | ||||
\(950\) | 5357.85i | 0.182981i | ||||||||
\(951\) | 32295.3 | 1.10121 | ||||||||
\(952\) | 7766.29 | − | 349.187i | 0.264398 | − | 0.0118878i | ||||
\(953\) | −47771.2 | −1.62378 | −0.811890 | − | 0.583811i | \(-0.801561\pi\) | ||||
−0.811890 | + | 0.583811i | \(0.801561\pi\) | |||||||
\(954\) | − | 516.188i | − | 0.0175180i | ||||||
\(955\) | 13708.2 | − | 13708.2i | 0.464489 | − | 0.464489i | ||||
\(956\) | 14004.5 | 0.473786 | ||||||||
\(957\) | −34595.4 | + | 34595.4i | −1.16856 | + | 1.16856i | ||||
\(958\) | 1570.24 | + | 1570.24i | 0.0529563 | + | 0.0529563i | ||||
\(959\) | −7427.61 | − | 7427.61i | −0.250104 | − | 0.250104i | ||||
\(960\) | − | 59707.0i | − | 2.00733i | ||||||
\(961\) | 1591.73i | 0.0534300i | ||||||||
\(962\) | −26433.2 | − | 26433.2i | −0.885904 | − | 0.885904i | ||||
\(963\) | 12101.1 | + | 12101.1i | 0.404935 | + | 0.404935i | ||||
\(964\) | −4459.97 | + | 4459.97i | −0.149010 | + | 0.149010i | ||||
\(965\) | −50404.0 | −1.68141 | ||||||||
\(966\) | −2391.37 | + | 2391.37i | −0.0796490 | + | 0.0796490i | ||||
\(967\) | − | 29494.2i | − | 0.980837i | −0.871487 | − | 0.490418i | \(-0.836844\pi\) | ||
0.871487 | − | 0.490418i | \(-0.163156\pi\) | |||||||
\(968\) | −23940.7 | −0.794919 | ||||||||
\(969\) | 821.087 | + | 18261.9i | 0.0272210 | + | 0.605423i | ||||
\(970\) | 8734.16 | 0.289110 | ||||||||
\(971\) | 32058.3i | 1.05953i | 0.848146 | + | 0.529763i | \(0.177719\pi\) | ||||
−0.848146 | + | 0.529763i | \(0.822281\pi\) | |||||||
\(972\) | −9671.32 | + | 9671.32i | −0.319144 | + | 0.319144i | ||||
\(973\) | 11266.1 | 0.371196 | ||||||||
\(974\) | −1353.30 | + | 1353.30i | −0.0445200 | + | 0.0445200i | ||||
\(975\) | 23877.8 | + | 23877.8i | 0.784311 | + | 0.784311i | ||||
\(976\) | −9949.44 | − | 9949.44i | −0.326305 | − | 0.326305i | ||||
\(977\) | 47602.0i | 1.55878i | 0.626542 | + | 0.779388i | \(0.284470\pi\) | ||||
−0.626542 | + | 0.779388i | \(0.715530\pi\) | |||||||
\(978\) | 15009.2i | 0.490738i | ||||||||
\(979\) | 6510.05 | + | 6510.05i | 0.212525 | + | 0.212525i | ||||
\(980\) | −11506.2 | − | 11506.2i | −0.375052 | − | 0.375052i | ||||
\(981\) | 26862.2 | − | 26862.2i | 0.874256 | − | 0.874256i | ||||
\(982\) | −31603.5 | −1.02699 | ||||||||
\(983\) | 20407.1 | − | 20407.1i | 0.662142 | − | 0.662142i | −0.293743 | − | 0.955885i | \(-0.594901\pi\) |
0.955885 | + | 0.293743i | \(0.0949009\pi\) | |||||||
\(984\) | 12953.0i | 0.419640i | ||||||||
\(985\) | 50971.2 | 1.64881 | ||||||||
\(986\) | 809.189 | + | 17997.2i | 0.0261357 | + | 0.581287i | ||||
\(987\) | −10747.8 | −0.346613 | ||||||||
\(988\) | 5416.91i | 0.174428i | ||||||||
\(989\) | 2599.90 | − | 2599.90i | 0.0835916 | − | 0.0835916i | ||||
\(990\) | −63304.3 | −2.03227 | ||||||||
\(991\) | −3326.26 | + | 3326.26i | −0.106622 | + | 0.106622i | −0.758405 | − | 0.651783i | \(-0.774021\pi\) |
0.651783 | + | 0.758405i | \(0.274021\pi\) | |||||||
\(992\) | 17248.7 | + | 17248.7i | 0.552065 | + | 0.552065i | ||||
\(993\) | −50209.0 | − | 50209.0i | −1.60457 | − | 1.60457i | ||||
\(994\) | 3200.41i | 0.102123i | ||||||||
\(995\) | 44124.1i | 1.40586i | ||||||||
\(996\) | −5914.55 | − | 5914.55i | −0.188162 | − | 0.188162i | ||||
\(997\) | −23322.1 | − | 23322.1i | −0.740842 | − | 0.740842i | 0.231898 | − | 0.972740i | \(-0.425506\pi\) |
−0.972740 | + | 0.231898i | \(0.925506\pi\) | |||||||
\(998\) | 3936.14 | − | 3936.14i | 0.124846 | − | 0.124846i | ||||
\(999\) | −48605.3 | −1.53934 |
(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 | 17.4.c.a.4.3 | ✓ | 8 | |
3.2 | odd | 2 | 153.4.f.a.55.2 | 8 | |||
4.3 | odd | 2 | 272.4.o.e.225.4 | 8 | |||
17.2 | even | 8 | 289.4.b.c.288.4 | 8 | |||
17.8 | even | 8 | 289.4.a.f.1.6 | 8 | |||
17.9 | even | 8 | 289.4.a.f.1.5 | 8 | |||
17.13 | even | 4 | inner | 17.4.c.a.13.2 | yes | 8 | |
17.15 | even | 8 | 289.4.b.c.288.3 | 8 | |||
51.47 | odd | 4 | 153.4.f.a.64.3 | 8 | |||
68.47 | odd | 4 | 272.4.o.e.81.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.c.a.4.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
17.4.c.a.13.2 | yes | 8 | 17.13 | even | 4 | inner | |
153.4.f.a.55.2 | 8 | 3.2 | odd | 2 | |||
153.4.f.a.64.3 | 8 | 51.47 | odd | 4 | |||
272.4.o.e.81.4 | 8 | 68.47 | odd | 4 | |||
272.4.o.e.225.4 | 8 | 4.3 | odd | 2 | |||
289.4.a.f.1.5 | 8 | 17.9 | even | 8 | |||
289.4.a.f.1.6 | 8 | 17.8 | even | 8 | |||
289.4.b.c.288.3 | 8 | 17.15 | even | 8 | |||
289.4.b.c.288.4 | 8 | 17.2 | even | 8 |