Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (of order \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Relative dimension: | \(38\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.21 | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.5.g.a.7.21 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.168936 | + | 3.99643i | 0.0422340 | + | 0.999108i | ||||
\(3\) | 14.2858 | + | 8.24790i | 1.58731 | + | 0.916433i | 0.993748 | + | 0.111644i | \(0.0356117\pi\) |
0.593561 | + | 0.804789i | \(0.297722\pi\) | |||||||
\(4\) | −15.9429 | + | 1.35028i | −0.996433 | + | 0.0843926i | ||||
\(5\) | 15.0446 | − | 26.0580i | 0.601784 | − | 1.04232i | −0.390766 | − | 0.920490i | \(-0.627790\pi\) |
0.992551 | − | 0.121831i | \(-0.0388767\pi\) | |||||||
\(6\) | −30.5488 | + | 58.4855i | −0.848577 | + | 1.62460i | ||||
\(7\) | 53.2660i | 1.08706i | 0.839390 | + | 0.543530i | \(0.182913\pi\) | ||||
−0.839390 | + | 0.543530i | \(0.817087\pi\) | |||||||
\(8\) | −8.08964 | − | 63.4867i | −0.126401 | − | 0.991979i | ||||
\(9\) | 95.5557 | + | 165.507i | 1.17970 | + | 2.04330i | ||||
\(10\) | 106.681 | + | 55.7226i | 1.06681 | + | 0.557226i | ||||
\(11\) | 194.395i | 1.60657i | 0.595594 | + | 0.803285i | \(0.296917\pi\) | ||||
−0.595594 | + | 0.803285i | \(0.703083\pi\) | |||||||
\(12\) | −238.894 | − | 112.206i | −1.65899 | − | 0.779207i | ||||
\(13\) | −106.699 | − | 184.807i | −0.631353 | − | 1.09353i | −0.987275 | − | 0.159020i | \(-0.949167\pi\) |
0.355923 | − | 0.934515i | \(-0.384167\pi\) | |||||||
\(14\) | −212.874 | + | 8.99853i | −1.08609 | + | 0.0459109i | ||||
\(15\) | 429.848 | − | 248.173i | 1.91044 | − | 1.10299i | ||||
\(16\) | 252.353 | − | 43.0549i | 0.985756 | − | 0.168183i | ||||
\(17\) | 42.2299 | − | 73.1443i | 0.146124 | − | 0.253094i | −0.783668 | − | 0.621180i | \(-0.786653\pi\) |
0.929792 | + | 0.368086i | \(0.119987\pi\) | |||||||
\(18\) | −645.296 | + | 409.842i | −1.99165 | + | 1.26494i | ||||
\(19\) | −83.7690 | − | 351.146i | −0.232047 | − | 0.972705i | ||||
\(20\) | −204.669 | + | 435.756i | −0.511673 | + | 1.08939i | ||||
\(21\) | −439.332 | + | 760.946i | −0.996218 | + | 1.72550i | ||||
\(22\) | −776.887 | + | 32.8403i | −1.60514 | + | 0.0678519i | ||||
\(23\) | 268.937 | − | 155.271i | 0.508388 | − | 0.293518i | −0.223783 | − | 0.974639i | \(-0.571841\pi\) |
0.732171 | + | 0.681121i | \(0.238507\pi\) | |||||||
\(24\) | 408.065 | − | 973.679i | 0.708446 | − | 1.69042i | ||||
\(25\) | −140.181 | − | 242.800i | −0.224289 | − | 0.388480i | ||||
\(26\) | 720.545 | − | 457.634i | 1.06589 | − | 0.676974i | ||||
\(27\) | 1816.38i | 2.49160i | ||||||||
\(28\) | −71.9240 | − | 849.215i | −0.0917398 | − | 1.08318i | ||||
\(29\) | −77.1824 | − | 133.684i | −0.0917745 | − | 0.158958i | 0.816483 | − | 0.577369i | \(-0.195921\pi\) |
−0.908258 | + | 0.418411i | \(0.862587\pi\) | |||||||
\(30\) | 1064.42 | + | 1675.93i | 1.18269 | + | 1.86215i | ||||
\(31\) | − | 1187.59i | − | 1.23579i | −0.786262 | − | 0.617894i | \(-0.787986\pi\) | ||
0.786262 | − | 0.617894i | \(-0.212014\pi\) | |||||||
\(32\) | 214.697 | + | 1001.24i | 0.209665 | + | 0.977773i | ||||
\(33\) | −1603.35 | + | 2777.09i | −1.47232 | + | 2.55012i | ||||
\(34\) | 299.450 | + | 156.412i | 0.259040 | + | 0.135305i | ||||
\(35\) | 1388.01 | + | 801.366i | 1.13307 | + | 0.654176i | ||||
\(36\) | −1746.92 | − | 2509.64i | −1.34793 | − | 1.93645i | ||||
\(37\) | 759.983 | 0.555137 | 0.277569 | − | 0.960706i | \(-0.410471\pi\) | ||||
0.277569 | + | 0.960706i | \(0.410471\pi\) | |||||||
\(38\) | 1389.18 | − | 394.098i | 0.962036 | − | 0.272921i | ||||
\(39\) | − | 3520.16i | − | 2.31437i | ||||||
\(40\) | −1776.04 | − | 744.332i | −1.11003 | − | 0.465208i | ||||
\(41\) | 627.053 | − | 1086.09i | 0.373024 | − | 0.646096i | −0.617005 | − | 0.786959i | \(-0.711654\pi\) |
0.990029 | + | 0.140863i | \(0.0449877\pi\) | |||||||
\(42\) | −3115.29 | − | 1627.21i | −1.76604 | − | 0.922455i | ||||
\(43\) | 479.506 | + | 276.843i | 0.259333 | + | 0.149726i | 0.624030 | − | 0.781400i | \(-0.285494\pi\) |
−0.364697 | + | 0.931126i | \(0.618828\pi\) | |||||||
\(44\) | −262.488 | − | 3099.23i | −0.135583 | − | 1.60084i | ||||
\(45\) | 5750.39 | 2.83970 | ||||||||
\(46\) | 665.962 | + | 1048.56i | 0.314727 | + | 0.495538i | ||||
\(47\) | −713.038 | + | 411.673i | −0.322788 | + | 0.186362i | −0.652634 | − | 0.757673i | \(-0.726336\pi\) |
0.329847 | + | 0.944034i | \(0.393003\pi\) | |||||||
\(48\) | 3960.18 | + | 1466.31i | 1.71883 | + | 0.636421i | ||||
\(49\) | −436.263 | −0.181701 | ||||||||
\(50\) | 946.652 | − | 601.240i | 0.378661 | − | 0.240496i | ||||
\(51\) | 1206.57 | − | 696.615i | 0.463888 | − | 0.267826i | ||||
\(52\) | 1950.63 | + | 2802.30i | 0.721387 | + | 1.03635i | ||||
\(53\) | −1691.81 | − | 2930.29i | −0.602280 | − | 1.04318i | −0.992475 | − | 0.122448i | \(-0.960926\pi\) |
0.390195 | − | 0.920732i | \(-0.372408\pi\) | |||||||
\(54\) | −7259.02 | + | 306.851i | −2.48938 | + | 0.105230i | ||||
\(55\) | 5065.55 | + | 2924.60i | 1.67456 | + | 0.966809i | ||||
\(56\) | 3381.68 | − | 430.902i | 1.07834 | − | 0.137405i | ||||
\(57\) | 1699.51 | − | 5707.32i | 0.523088 | − | 1.75664i | ||||
\(58\) | 521.219 | − | 331.038i | 0.154940 | − | 0.0984061i | ||||
\(59\) | −1685.78 | − | 973.284i | −0.484279 | − | 0.279599i | 0.237919 | − | 0.971285i | \(-0.423535\pi\) |
−0.722198 | + | 0.691686i | \(0.756868\pi\) | |||||||
\(60\) | −6517.93 | + | 4537.02i | −1.81054 | + | 1.26028i | ||||
\(61\) | 2603.90 | + | 4510.09i | 0.699785 | + | 1.21206i | 0.968541 | + | 0.248855i | \(0.0800543\pi\) |
−0.268756 | + | 0.963208i | \(0.586612\pi\) | |||||||
\(62\) | 4746.13 | − | 200.627i | 1.23469 | − | 0.0521922i | ||||
\(63\) | −8815.91 | + | 5089.87i | −2.22119 | + | 1.28241i | ||||
\(64\) | −3965.12 | + | 1027.17i | −0.968046 | + | 0.250774i | ||||
\(65\) | −6420.96 | −1.51975 | ||||||||
\(66\) | −11369.3 | − | 5938.53i | −2.61003 | − | 1.36330i | ||||
\(67\) | 83.3014 | − | 48.0941i | 0.0185568 | − | 0.0107138i | −0.490693 | − | 0.871333i | \(-0.663256\pi\) |
0.509250 | + | 0.860619i | \(0.329923\pi\) | |||||||
\(68\) | −574.502 | + | 1223.16i | −0.124244 | + | 0.264523i | ||||
\(69\) | 5122.63 | 1.07596 | ||||||||
\(70\) | −2968.12 | + | 5682.45i | −0.605739 | + | 1.15968i | ||||
\(71\) | 2686.05 | + | 1550.79i | 0.532841 | + | 0.307636i | 0.742173 | − | 0.670209i | \(-0.233795\pi\) |
−0.209331 | + | 0.977845i | \(0.567129\pi\) | |||||||
\(72\) | 9734.50 | − | 7405.41i | 1.87780 | − | 1.42851i | ||||
\(73\) | −1120.62 | + | 1940.97i | −0.210287 | + | 0.364227i | −0.951804 | − | 0.306706i | \(-0.900773\pi\) |
0.741518 | + | 0.670933i | \(0.234106\pi\) | |||||||
\(74\) | 128.388 | + | 3037.22i | 0.0234457 | + | 0.554642i | ||||
\(75\) | − | 4624.78i | − | 0.822184i | ||||||
\(76\) | 1809.67 | + | 5485.19i | 0.313308 | + | 0.949651i | ||||
\(77\) | −10354.6 | −1.74644 | ||||||||
\(78\) | 14068.1 | − | 594.681i | 2.31231 | − | 0.0977451i | ||||
\(79\) | −2842.98 | − | 1641.39i | −0.455532 | − | 0.263002i | 0.254632 | − | 0.967038i | \(-0.418046\pi\) |
−0.710164 | + | 0.704036i | \(0.751379\pi\) | |||||||
\(80\) | 2674.64 | − | 7223.58i | 0.417912 | − | 1.12868i | ||||
\(81\) | −7241.27 | + | 12542.3i | −1.10368 | + | 1.91164i | ||||
\(82\) | 4446.41 | + | 2322.49i | 0.661274 | + | 0.345404i | ||||
\(83\) | 246.025i | 0.0357128i | 0.999841 | + | 0.0178564i | \(0.00568416\pi\) | ||||
−0.999841 | + | 0.0178564i | \(0.994316\pi\) | |||||||
\(84\) | 5976.75 | − | 12724.9i | 0.847045 | − | 1.80342i | ||||
\(85\) | −1270.66 | − | 2200.85i | −0.175870 | − | 0.304616i | ||||
\(86\) | −1025.38 | + | 1963.08i | −0.138640 | + | 0.265425i | ||||
\(87\) | − | 2546.37i | − | 0.336421i | ||||||
\(88\) | 12341.5 | − | 1572.59i | 1.59369 | − | 0.203072i | ||||
\(89\) | −5246.93 | − | 9087.94i | −0.662407 | − | 1.14732i | −0.979981 | − | 0.199089i | \(-0.936202\pi\) |
0.317574 | − | 0.948233i | \(-0.397132\pi\) | |||||||
\(90\) | 971.448 | + | 22981.1i | 0.119932 | + | 2.83717i | ||||
\(91\) | 9843.95 | − | 5683.40i | 1.18874 | − | 0.686319i | ||||
\(92\) | −4077.98 | + | 2838.61i | −0.481803 | + | 0.335375i | ||||
\(93\) | 9795.14 | − | 16965.7i | 1.13252 | − | 1.96158i | ||||
\(94\) | −1765.68 | − | 2780.06i | −0.199828 | − | 0.314629i | ||||
\(95\) | −10410.5 | − | 3100.00i | −1.15351 | − | 0.343491i | ||||
\(96\) | −5191.01 | + | 16074.3i | −0.563260 | + | 1.74417i | ||||
\(97\) | −4910.66 | + | 8505.51i | −0.521911 | + | 0.903976i | 0.477764 | + | 0.878488i | \(0.341447\pi\) |
−0.999675 | + | 0.0254879i | \(0.991886\pi\) | |||||||
\(98\) | −73.7005 | − | 1743.50i | −0.00767394 | − | 0.181538i | ||||
\(99\) | −32173.8 | + | 18575.6i | −3.28271 | + | 1.89527i | ||||
\(100\) | 2562.74 | + | 3681.66i | 0.256274 | + | 0.368166i | ||||
\(101\) | −2503.09 | − | 4335.48i | −0.245377 | − | 0.425005i | 0.716861 | − | 0.697217i | \(-0.245578\pi\) |
−0.962238 | + | 0.272211i | \(0.912245\pi\) | |||||||
\(102\) | 2987.81 | + | 4704.30i | 0.287179 | + | 0.452163i | ||||
\(103\) | − | 7464.82i | − | 0.703631i | −0.936069 | − | 0.351815i | \(-0.885565\pi\) | ||
0.936069 | − | 0.351815i | \(-0.114435\pi\) | |||||||
\(104\) | −10869.7 | + | 8268.96i | −1.00496 | + | 0.764512i | ||||
\(105\) | 13219.2 | + | 22896.3i | 1.19902 | + | 2.07676i | ||||
\(106\) | 11424.9 | − | 7256.21i | 1.01681 | − | 0.645801i | ||||
\(107\) | 5548.20i | 0.484601i | 0.970201 | + | 0.242301i | \(0.0779020\pi\) | ||||
−0.970201 | + | 0.242301i | \(0.922098\pi\) | |||||||
\(108\) | −2452.62 | − | 28958.3i | −0.210272 | − | 2.48271i | ||||
\(109\) | 265.661 | − | 460.139i | 0.0223602 | − | 0.0387290i | −0.854629 | − | 0.519239i | \(-0.826215\pi\) |
0.876989 | + | 0.480511i | \(0.159549\pi\) | |||||||
\(110\) | −10832.2 | + | 20738.2i | −0.895223 | + | 1.71390i | ||||
\(111\) | 10857.0 | + | 6268.26i | 0.881175 | + | 0.508746i | ||||
\(112\) | 2293.36 | + | 13441.9i | 0.182825 | + | 1.07158i | ||||
\(113\) | 9653.14 | 0.755983 | 0.377991 | − | 0.925809i | \(-0.376615\pi\) | ||||
0.377991 | + | 0.925809i | \(0.376615\pi\) | |||||||
\(114\) | 23096.0 | + | 5827.82i | 1.77716 | + | 0.448432i | ||||
\(115\) | − | 9343.96i | − | 0.706538i | ||||||
\(116\) | 1411.02 | + | 2027.09i | 0.104862 | + | 0.150646i | ||||
\(117\) | 20391.3 | − | 35318.8i | 1.48961 | − | 2.58009i | ||||
\(118\) | 3604.87 | − | 6901.51i | 0.258896 | − | 0.495656i | ||||
\(119\) | 3896.10 | + | 2249.41i | 0.275129 | + | 0.158846i | ||||
\(120\) | −19233.0 | − | 25282.0i | −1.33562 | − | 1.75569i | ||||
\(121\) | −23148.4 | −1.58107 | ||||||||
\(122\) | −17584.4 | + | 11168.2i | −1.18143 | + | 0.750351i | ||||
\(123\) | 17915.9 | − | 10343.7i | 1.18421 | − | 0.683703i | ||||
\(124\) | 1603.58 | + | 18933.7i | 0.104291 | + | 1.23138i | ||||
\(125\) | 10369.9 | 0.663674 | ||||||||
\(126\) | −21830.6 | − | 34372.3i | −1.37507 | − | 2.16505i | ||||
\(127\) | −11183.2 | + | 6456.64i | −0.693361 | + | 0.400312i | −0.804870 | − | 0.593451i | \(-0.797765\pi\) |
0.111509 | + | 0.993763i | \(0.464432\pi\) | |||||||
\(128\) | −4774.86 | − | 15672.8i | −0.291434 | − | 0.956591i | ||||
\(129\) | 4566.74 | + | 7909.83i | 0.274427 | + | 0.475322i | ||||
\(130\) | −1084.73 | − | 25660.9i | −0.0641852 | − | 1.51840i | ||||
\(131\) | −14502.8 | − | 8373.21i | −0.845104 | − | 0.487921i | 0.0138919 | − | 0.999904i | \(-0.495578\pi\) |
−0.858996 | + | 0.511983i | \(0.828911\pi\) | |||||||
\(132\) | 21812.3 | − | 46439.8i | 1.25185 | − | 2.66528i | ||||
\(133\) | 18704.1 | − | 4462.04i | 1.05739 | − | 0.252249i | ||||
\(134\) | 206.277 | + | 324.784i | 0.0114879 | + | 0.0180877i | ||||
\(135\) | 47331.2 | + | 27326.7i | 2.59705 | + | 1.49941i | ||||
\(136\) | −4985.31 | − | 2089.32i | −0.269535 | − | 0.112961i | ||||
\(137\) | −17091.6 | − | 29603.5i | −0.910627 | − | 1.57725i | −0.813180 | − | 0.582012i | \(-0.802266\pi\) |
−0.0974473 | − | 0.995241i | \(-0.531068\pi\) | |||||||
\(138\) | 865.397 | + | 20472.3i | 0.0454420 | + | 1.07500i | ||||
\(139\) | −22815.1 | + | 13172.3i | −1.18085 | + | 0.681762i | −0.956210 | − | 0.292681i | \(-0.905453\pi\) |
−0.224636 | + | 0.974443i | \(0.572119\pi\) | |||||||
\(140\) | −23210.9 | − | 10901.9i | −1.18423 | − | 0.556220i | ||||
\(141\) | −13581.7 | −0.683152 | ||||||||
\(142\) | −5743.87 | + | 10996.6i | −0.284858 | + | 0.545359i | ||||
\(143\) | 35925.7 | − | 20741.7i | 1.75684 | − | 1.01431i | ||||
\(144\) | 31239.7 | + | 37652.2i | 1.50654 | + | 1.81579i | ||||
\(145\) | −4644.72 | −0.220914 | ||||||||
\(146\) | −7946.25 | − | 4150.57i | −0.372783 | − | 0.194716i | ||||
\(147\) | −6232.36 | − | 3598.25i | −0.288415 | − | 0.166516i | ||||
\(148\) | −12116.4 | + | 1026.19i | −0.553157 | + | 0.0468495i | ||||
\(149\) | −15769.4 | + | 27313.5i | −0.710303 | + | 1.23028i | 0.254440 | + | 0.967089i | \(0.418109\pi\) |
−0.964743 | + | 0.263193i | \(0.915224\pi\) | |||||||
\(150\) | 18482.6 | − | 781.292i | 0.821450 | − | 0.0347241i | ||||
\(151\) | 1155.94i | 0.0506971i | 0.999679 | + | 0.0253485i | \(0.00806956\pi\) | ||||
−0.999679 | + | 0.0253485i | \(0.991930\pi\) | |||||||
\(152\) | −21615.5 | + | 8158.86i | −0.935572 | + | 0.353136i | ||||
\(153\) | 16141.2 | 0.689530 | ||||||||
\(154\) | −1749.27 | − | 41381.6i | −0.0737591 | − | 1.74488i | ||||
\(155\) | −30946.3 | − | 17866.9i | −1.28809 | − | 0.743678i | ||||
\(156\) | 4753.20 | + | 56121.6i | 0.195316 | + | 2.30611i | ||||
\(157\) | −4740.85 | + | 8211.39i | −0.192334 | + | 0.333133i | −0.946023 | − | 0.324098i | \(-0.894939\pi\) |
0.753689 | + | 0.657231i | \(0.228272\pi\) | |||||||
\(158\) | 6079.43 | − | 11639.1i | 0.243528 | − | 0.466233i | ||||
\(159\) | − | 55815.4i | − | 2.20780i | ||||||
\(160\) | 29320.4 | + | 9468.67i | 1.14533 | + | 0.369870i | ||||
\(161\) | 8270.65 | + | 14325.2i | 0.319072 | + | 0.552648i | ||||
\(162\) | −51347.6 | − | 26820.4i | −1.95654 | − | 1.02196i | ||||
\(163\) | 42001.7i | 1.58086i | 0.612555 | + | 0.790428i | \(0.290142\pi\) | ||||
−0.612555 | + | 0.790428i | \(0.709858\pi\) | |||||||
\(164\) | −8530.53 | + | 18162.1i | −0.317167 | + | 0.675272i | ||||
\(165\) | 48243.6 | + | 83560.3i | 1.77203 | + | 3.06925i | ||||
\(166\) | −983.223 | + | 41.5625i | −0.0356809 | + | 0.00150829i | ||||
\(167\) | −6692.13 | + | 3863.70i | −0.239956 | + | 0.138539i | −0.615156 | − | 0.788405i | \(-0.710907\pi\) |
0.375201 | + | 0.926944i | \(0.377574\pi\) | |||||||
\(168\) | 51864.0 | + | 21736.0i | 1.83758 | + | 0.770124i | ||||
\(169\) | −8488.69 | + | 14702.8i | −0.297213 | + | 0.514787i | ||||
\(170\) | 8580.90 | − | 5449.92i | 0.296917 | − | 0.188579i | ||||
\(171\) | 50112.7 | − | 47418.4i | 1.71378 | − | 1.62164i | ||||
\(172\) | −8018.54 | − | 3766.22i | −0.271043 | − | 0.127306i | ||||
\(173\) | −9497.83 | + | 16450.7i | −0.317345 | + | 0.549658i | −0.979933 | − | 0.199326i | \(-0.936125\pi\) |
0.662588 | + | 0.748984i | \(0.269458\pi\) | |||||||
\(174\) | 10176.4 | − | 430.173i | 0.336121 | − | 0.0142084i | ||||
\(175\) | 12933.0 | − | 7466.86i | 0.422301 | − | 0.243816i | ||||
\(176\) | 8369.65 | + | 49056.3i | 0.270198 | + | 1.58369i | ||||
\(177\) | −16055.1 | − | 27808.2i | −0.512467 | − | 0.887620i | ||||
\(178\) | 35432.9 | − | 22504.3i | 1.11832 | − | 0.710272i | ||||
\(179\) | 40567.3i | 1.26611i | 0.774108 | + | 0.633053i | \(0.218199\pi\) | ||||
−0.774108 | + | 0.633053i | \(0.781801\pi\) | |||||||
\(180\) | −91678.1 | + | 7764.65i | −2.82957 | + | 0.239650i | ||||
\(181\) | −9119.13 | − | 15794.8i | −0.278353 | − | 0.482122i | 0.692622 | − | 0.721300i | \(-0.256455\pi\) |
−0.970976 | + | 0.239178i | \(0.923122\pi\) | |||||||
\(182\) | 24376.3 | + | 38380.5i | 0.735911 | + | 1.15869i | ||||
\(183\) | 85906.8i | 2.56523i | ||||||||
\(184\) | −12033.2 | − | 15817.8i | −0.355424 | − | 0.467209i | ||||
\(185\) | 11433.6 | − | 19803.7i | 0.334073 | − | 0.578631i | ||||
\(186\) | 69456.9 | + | 36279.5i | 2.00766 | + | 1.04866i | ||||
\(187\) | 14218.9 | + | 8209.28i | 0.406614 | + | 0.234759i | ||||
\(188\) | 10812.0 | − | 7526.07i | 0.305909 | − | 0.212938i | ||||
\(189\) | −96751.0 | −2.70852 | ||||||||
\(190\) | 10630.3 | − | 42128.4i | 0.294467 | − | 1.16699i | ||||
\(191\) | − | 2920.43i | − | 0.0800536i | −0.999199 | − | 0.0400268i | \(-0.987256\pi\) | ||
0.999199 | − | 0.0400268i | \(-0.0127443\pi\) | |||||||
\(192\) | −65116.8 | − | 18030.0i | −1.76641 | − | 0.489094i | ||||
\(193\) | −10098.9 | + | 17491.7i | −0.271118 | + | 0.469590i | −0.969148 | − | 0.246478i | \(-0.920727\pi\) |
0.698031 | + | 0.716068i | \(0.254060\pi\) | |||||||
\(194\) | −34821.3 | − | 18188.2i | −0.925212 | − | 0.483267i | ||||
\(195\) | −91728.4 | − | 52959.4i | −2.41232 | − | 1.39275i | ||||
\(196\) | 6955.31 | − | 589.078i | 0.181052 | − | 0.0153342i | ||||
\(197\) | −50485.5 | −1.30087 | −0.650436 | − | 0.759561i | \(-0.725414\pi\) | ||||
−0.650436 | + | 0.759561i | \(0.725414\pi\) | |||||||
\(198\) | −79671.2 | − | 125442.i | −2.03222 | − | 3.19973i | ||||
\(199\) | 57910.2 | − | 33434.5i | 1.46234 | − | 0.844283i | 0.463222 | − | 0.886242i | \(-0.346693\pi\) |
0.999119 | + | 0.0419593i | \(0.0133600\pi\) | |||||||
\(200\) | −14280.6 | + | 10863.8i | −0.357014 | + | 0.271594i | ||||
\(201\) | 1586.70 | 0.0392738 | ||||||||
\(202\) | 16903.6 | − | 10735.8i | 0.414263 | − | 0.263108i | ||||
\(203\) | 7120.80 | − | 4111.19i | 0.172797 | − | 0.0997645i | ||||
\(204\) | −18295.7 | + | 12735.3i | −0.439631 | + | 0.306019i | ||||
\(205\) | −18867.5 | − | 32679.5i | −0.448960 | − | 0.777621i | ||||
\(206\) | 29832.6 | − | 1261.08i | 0.703003 | − | 0.0297171i | ||||
\(207\) | 51396.9 | + | 29674.0i | 1.19949 | + | 0.692526i | ||||
\(208\) | −34882.6 | − | 42042.9i | −0.806274 | − | 0.971776i | ||||
\(209\) | 68261.1 | − | 16284.3i | 1.56272 | − | 0.372800i | ||||
\(210\) | −89270.2 | + | 56697.5i | −2.02427 | + | 1.28566i | ||||
\(211\) | 53514.5 | + | 30896.6i | 1.20200 | + | 0.693978i | 0.961001 | − | 0.276546i | \(-0.0891899\pi\) |
0.241004 | + | 0.970524i | \(0.422523\pi\) | |||||||
\(212\) | 30929.0 | + | 44433.0i | 0.688168 | + | 0.988631i | ||||
\(213\) | 25581.6 | + | 44308.6i | 0.563856 | + | 0.976627i | ||||
\(214\) | −22173.0 | + | 937.290i | −0.484169 | + | 0.0204666i | ||||
\(215\) | 14428.0 | − | 8329.99i | 0.312125 | − | 0.180205i | ||||
\(216\) | 115316. | − | 14693.8i | 2.47161 | − | 0.314940i | ||||
\(217\) | 63258.2 | 1.34338 | ||||||||
\(218\) | 1883.79 | + | 983.963i | 0.0396388 | + | 0.0207046i | ||||
\(219\) | −32017.8 | + | 18485.5i | −0.667580 | + | 0.385427i | ||||
\(220\) | −84708.7 | − | 39786.7i | −1.75018 | − | 0.822040i | ||||
\(221\) | −18023.5 | −0.369023 | ||||||||
\(222\) | −23216.6 | + | 44448.0i | −0.471077 | + | 0.901875i | ||||
\(223\) | 48124.1 | + | 27784.5i | 0.967727 | + | 0.558718i | 0.898543 | − | 0.438886i | \(-0.144627\pi\) |
0.0691846 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(224\) | −53332.0 | + | 11436.1i | −1.06290 | + | 0.227919i | ||||
\(225\) | 26790.1 | − | 46401.9i | 0.529188 | − | 0.916580i | ||||
\(226\) | 1630.76 | + | 38578.1i | 0.0319281 | + | 0.755308i | ||||
\(227\) | − | 53723.4i | − | 1.04259i | −0.853378 | − | 0.521293i | \(-0.825450\pi\) | ||
0.853378 | − | 0.521293i | \(-0.174550\pi\) | |||||||
\(228\) | −19388.7 | + | 93286.1i | −0.372975 | + | 1.79452i | ||||
\(229\) | 90851.6 | 1.73245 | 0.866227 | − | 0.499651i | \(-0.166538\pi\) | ||||
0.866227 | + | 0.499651i | \(0.166538\pi\) | |||||||
\(230\) | 37342.5 | − | 1578.53i | 0.705907 | − | 0.0298399i | ||||
\(231\) | −147924. | − | 85404.0i | −2.77214 | − | 1.60050i | ||||
\(232\) | −7862.76 | + | 5981.51i | −0.146083 | + | 0.111131i | ||||
\(233\) | 31995.1 | − | 55417.2i | 0.589348 | − | 1.02078i | −0.404970 | − | 0.914330i | \(-0.632718\pi\) |
0.994318 | − | 0.106451i | \(-0.0339486\pi\) | |||||||
\(234\) | 144594. | + | 75525.9i | 2.64070 | + | 1.37932i | ||||
\(235\) | 24773.8i | 0.448598i | ||||||||
\(236\) | 28190.4 | + | 13240.7i | 0.506148 | + | 0.237732i | ||||
\(237\) | −27076.1 | − | 46897.2i | −0.482047 | − | 0.834930i | ||||
\(238\) | −8331.44 | + | 15950.5i | −0.147084 | + | 0.281592i | ||||
\(239\) | 42916.5i | 0.751326i | 0.926756 | + | 0.375663i | \(0.122585\pi\) | ||||
−0.926756 | + | 0.375663i | \(0.877415\pi\) | |||||||
\(240\) | 97788.6 | − | 81134.3i | 1.69772 | − | 1.40858i | ||||
\(241\) | −40610.6 | − | 70339.6i | −0.699206 | − | 1.21106i | −0.968742 | − | 0.248070i | \(-0.920204\pi\) |
0.269536 | − | 0.962990i | \(-0.413130\pi\) | |||||||
\(242\) | −3910.60 | − | 92511.2i | −0.0667749 | − | 1.57966i | ||||
\(243\) | −79479.3 | + | 45887.4i | −1.34599 | + | 0.777107i | ||||
\(244\) | −47603.7 | − | 68388.0i | −0.799578 | − | 1.14868i | ||||
\(245\) | −6563.41 | + | 11368.2i | −0.109345 | + | 0.189390i | ||||
\(246\) | 44364.7 | + | 69852.2i | 0.733107 | + | 1.15428i | ||||
\(247\) | −55956.4 | + | 52948.0i | −0.917183 | + | 0.867871i | ||||
\(248\) | −75396.3 | + | 9607.19i | −1.22588 | + | 0.156204i | ||||
\(249\) | −2029.19 | + | 3514.66i | −0.0327284 | + | 0.0566872i | ||||
\(250\) | 1751.85 | + | 41442.6i | 0.0280296 | + | 0.663082i | ||||
\(251\) | −79590.2 | + | 45951.4i | −1.26332 | + | 0.729376i | −0.973715 | − | 0.227771i | \(-0.926856\pi\) |
−0.289602 | + | 0.957147i | \(0.593523\pi\) | |||||||
\(252\) | 133679. | − | 93051.3i | 2.10504 | − | 1.46528i | ||||
\(253\) | 30183.9 | + | 52280.0i | 0.471557 | + | 0.816761i | ||||
\(254\) | −27692.8 | − | 43602.2i | −0.429239 | − | 0.675836i | ||||
\(255\) | − | 41921.2i | − | 0.644694i | ||||||
\(256\) | 61828.6 | − | 21730.1i | 0.943429 | − | 0.331575i | ||||
\(257\) | 24263.0 | + | 42024.8i | 0.367349 | + | 0.636267i | 0.989150 | − | 0.146908i | \(-0.0469321\pi\) |
−0.621801 | + | 0.783175i | \(0.713599\pi\) | |||||||
\(258\) | −30839.6 | + | 19586.9i | −0.463308 | + | 0.294257i | ||||
\(259\) | 40481.2i | 0.603468i | ||||||||
\(260\) | 102369. | − | 8670.10i | 1.51433 | − | 0.128256i | ||||
\(261\) | 14750.4 | − | 25548.5i | 0.216533 | − | 0.375046i | ||||
\(262\) | 31012.9 | − | 59374.1i | 0.451794 | − | 0.864957i | ||||
\(263\) | −69499.1 | − | 40125.3i | −1.00477 | − | 0.580106i | −0.0951155 | − | 0.995466i | \(-0.530322\pi\) |
−0.909657 | + | 0.415361i | \(0.863655\pi\) | |||||||
\(264\) | 189278. | + | 79325.8i | 2.71577 | + | 1.13817i | ||||
\(265\) | −101810. | −1.44977 | ||||||||
\(266\) | 20992.0 | + | 73996.0i | 0.296682 | + | 1.04579i | ||||
\(267\) | − | 173104.i | − | 2.42821i | ||||||
\(268\) | −1263.13 | + | 879.241i | −0.0175864 | + | 0.0122416i | ||||
\(269\) | −33999.8 | + | 58889.4i | −0.469864 | + | 0.813828i | −0.999406 | − | 0.0344557i | \(-0.989030\pi\) |
0.529543 | + | 0.848283i | \(0.322364\pi\) | |||||||
\(270\) | −101213. | + | 193772.i | −1.38838 | + | 2.65806i | ||||
\(271\) | 22378.4 | + | 12920.2i | 0.304713 | + | 0.175926i | 0.644558 | − | 0.764555i | \(-0.277041\pi\) |
−0.339845 | + | 0.940481i | \(0.610375\pi\) | |||||||
\(272\) | 7507.64 | − | 20276.4i | 0.101476 | − | 0.274065i | ||||
\(273\) | 187505. | 2.51586 | ||||||||
\(274\) | 115421. | − | 73306.3i | 1.53739 | − | 0.976429i | ||||
\(275\) | 47199.1 | − | 27250.4i | 0.624121 | − | 0.360336i | ||||
\(276\) | −81669.8 | + | 6917.00i | −1.07212 | + | 0.0908028i | ||||
\(277\) | −44987.2 | −0.586313 | −0.293156 | − | 0.956065i | \(-0.594706\pi\) | ||||
−0.293156 | + | 0.956065i | \(0.594706\pi\) | |||||||
\(278\) | −56496.6 | − | 88953.8i | −0.731026 | − | 1.15100i | ||||
\(279\) | 196555. | − | 113481.i | 2.52509 | − | 1.45786i | ||||
\(280\) | 39647.6 | − | 94602.7i | 0.505709 | − | 1.20667i | ||||
\(281\) | −15405.6 | − | 26683.3i | −0.195104 | − | 0.337930i | 0.751830 | − | 0.659356i | \(-0.229171\pi\) |
−0.946935 | + | 0.321426i | \(0.895838\pi\) | |||||||
\(282\) | −2294.44 | − | 54278.5i | −0.0288522 | − | 0.682542i | ||||
\(283\) | −66834.1 | − | 38586.7i | −0.834498 | − | 0.481798i | 0.0208920 | − | 0.999782i | \(-0.493349\pi\) |
−0.855390 | + | 0.517984i | \(0.826683\pi\) | |||||||
\(284\) | −44917.5 | − | 21097.2i | −0.556903 | − | 0.261571i | ||||
\(285\) | −123153. | − | 130150.i | −1.51620 | − | 1.60234i | ||||
\(286\) | 88961.8 | + | 140070.i | 1.08761 | + | 1.71244i | ||||
\(287\) | 57851.5 | + | 33400.6i | 0.702346 | + | 0.405499i | ||||
\(288\) | −145197. | + | 131208.i | −1.75054 | + | 1.58189i | ||||
\(289\) | 38193.8 | + | 66153.6i | 0.457296 | + | 0.792059i | ||||
\(290\) | −784.659 | − | 18562.3i | −0.00933007 | − | 0.220717i | ||||
\(291\) | −140305. | + | 81005.2i | −1.65687 | + | 0.956593i | ||||
\(292\) | 15245.1 | − | 32457.8i | 0.178798 | − | 0.380674i | ||||
\(293\) | −36372.6 | −0.423681 | −0.211841 | − | 0.977304i | \(-0.567946\pi\) | ||||
−0.211841 | + | 0.977304i | \(0.567946\pi\) | |||||||
\(294\) | 13327.3 | − | 25515.1i | 0.154187 | − | 0.295190i | ||||
\(295\) | −50723.7 | + | 29285.3i | −0.582864 | + | 0.336517i | ||||
\(296\) | −6147.99 | − | 48248.8i | −0.0701697 | − | 0.550685i | ||||
\(297\) | −353094. | −4.00293 | ||||||||
\(298\) | −111820. | − | 58407.3i | −1.25918 | − | 0.657710i | ||||
\(299\) | −57390.4 | − | 33134.4i | −0.641944 | − | 0.370626i | ||||
\(300\) | 6244.76 | + | 73732.6i | 0.0693862 | + | 0.819251i | ||||
\(301\) | −14746.3 | + | 25541.3i | −0.162761 | + | 0.281910i | ||||
\(302\) | −4619.65 | + | 195.280i | −0.0506519 | + | 0.00214114i | ||||
\(303\) | − | 82580.9i | − | 0.899486i | ||||||
\(304\) | −36258.0 | − | 85006.3i | −0.392334 | − | 0.919823i | ||||
\(305\) | 156699. | 1.68448 | ||||||||
\(306\) | 2726.83 | + | 64507.3i | 0.0291216 | + | 0.688915i | ||||
\(307\) | 99628.1 | + | 57520.3i | 1.05707 | + | 0.610301i | 0.924621 | − | 0.380888i | \(-0.124382\pi\) |
0.132452 | + | 0.991189i | \(0.457715\pi\) | |||||||
\(308\) | 165083. | − | 13981.7i | 1.74021 | − | 0.147387i | ||||
\(309\) | 61569.1 | − | 106641.i | 0.644830 | − | 1.11688i | ||||
\(310\) | 66175.7 | − | 126693.i | 0.688613 | − | 1.31835i | ||||
\(311\) | 66028.7i | 0.682672i | 0.939941 | + | 0.341336i | \(0.110879\pi\) | ||||
−0.939941 | + | 0.341336i | \(0.889121\pi\) | |||||||
\(312\) | −223483. | + | 28476.8i | −2.29581 | + | 0.292538i | ||||
\(313\) | 79425.4 | + | 137569.i | 0.810719 | + | 1.40421i | 0.912361 | + | 0.409386i | \(0.134257\pi\) |
−0.101642 | + | 0.994821i | \(0.532410\pi\) | |||||||
\(314\) | −33617.2 | − | 17559.3i | −0.340959 | − | 0.178093i | ||||
\(315\) | 306300.i | 3.08693i | ||||||||
\(316\) | 47541.7 | + | 22329.8i | 0.476103 | + | 0.223620i | ||||
\(317\) | −37599.4 | − | 65124.1i | −0.374165 | − | 0.648072i | 0.616037 | − | 0.787717i | \(-0.288737\pi\) |
−0.990202 | + | 0.139645i | \(0.955404\pi\) | |||||||
\(318\) | 223062. | − | 9429.22i | 2.20583 | − | 0.0932441i | ||||
\(319\) | 25987.5 | − | 15003.9i | 0.255378 | − | 0.147442i | ||||
\(320\) | −32887.6 | + | 118776.i | −0.321168 | + | 1.15993i | ||||
\(321\) | −45761.0 | + | 79260.3i | −0.444105 | + | 0.769212i | ||||
\(322\) | −55852.4 | + | 35473.1i | −0.538679 | + | 0.342127i | ||||
\(323\) | −29221.9 | − | 8701.64i | −0.280094 | − | 0.0834057i | ||||
\(324\) | 98511.5 | − | 209738.i | 0.938419 | − | 1.99796i | ||||
\(325\) | −29914.2 | + | 51812.8i | −0.283211 | + | 0.490536i | ||||
\(326\) | −167857. | + | 7095.60i | −1.57944 | + | 0.0667658i | ||||
\(327\) | 7590.36 | − | 4382.30i | 0.0709851 | − | 0.0409832i | ||||
\(328\) | −74024.7 | − | 31023.5i | −0.688064 | − | 0.288365i | ||||
\(329\) | −21928.1 | − | 37980.7i | −0.202586 | − | 0.350890i | ||||
\(330\) | −325793. | + | 206919.i | −2.99167 | + | 1.90008i | ||||
\(331\) | − | 21998.0i | − | 0.200783i | −0.994948 | − | 0.100391i | \(-0.967990\pi\) | ||
0.994948 | − | 0.100391i | \(-0.0320095\pi\) | |||||||
\(332\) | −332.203 | − | 3922.36i | −0.00301389 | − | 0.0355854i | ||||
\(333\) | 72620.7 | + | 125783.i | 0.654896 | + | 1.13431i | ||||
\(334\) | −16571.6 | − | 26091.9i | −0.148549 | − | 0.233891i | ||||
\(335\) | − | 2894.23i | − | 0.0257895i | ||||||
\(336\) | −78104.6 | + | 210943.i | −0.691828 | + | 1.86847i | ||||
\(337\) | 33356.2 | − | 57774.7i | 0.293709 | − | 0.508719i | −0.680975 | − | 0.732307i | \(-0.738444\pi\) |
0.974684 | + | 0.223588i | \(0.0717770\pi\) | |||||||
\(338\) | −60192.9 | − | 31440.6i | −0.526880 | − | 0.275206i | ||||
\(339\) | 137903. | + | 79618.1i | 1.19998 | + | 0.692808i | ||||
\(340\) | 23229.9 | + | 33372.3i | 0.200950 | + | 0.288688i | ||||
\(341\) | 230862. | 1.98538 | ||||||||
\(342\) | 197970. | + | 192261.i | 1.69257 | + | 1.64376i | ||||
\(343\) | 104654.i | 0.889541i | ||||||||
\(344\) | 13696.8 | − | 32681.8i | 0.115745 | − | 0.276178i | ||||
\(345\) | 77068.0 | − | 133486.i | 0.647495 | − | 1.12149i | ||||
\(346\) | −67348.7 | − | 35178.3i | −0.562570 | − | 0.293848i | ||||
\(347\) | −16518.2 | − | 9536.79i | −0.137184 | − | 0.0792033i | 0.429837 | − | 0.902906i | \(-0.358571\pi\) |
−0.567021 | + | 0.823703i | \(0.691904\pi\) | |||||||
\(348\) | 3438.32 | + | 40596.6i | 0.0283914 | + | 0.335221i | ||||
\(349\) | −184902. | −1.51807 | −0.759033 | − | 0.651052i | \(-0.774328\pi\) | ||||
−0.759033 | + | 0.651052i | \(0.774328\pi\) | |||||||
\(350\) | 32025.6 | + | 50424.3i | 0.261434 | + | 0.411627i | ||||
\(351\) | 335680. | − | 193805.i | 2.72465 | − | 1.57308i | ||||
\(352\) | −194636. | + | 41736.1i | −1.57086 | + | 0.336842i | ||||
\(353\) | 125283. | 1.00541 | 0.502705 | − | 0.864458i | \(-0.332338\pi\) | ||||
0.502705 | + | 0.864458i | \(0.332338\pi\) | |||||||
\(354\) | 108421. | − | 68860.9i | 0.865184 | − | 0.549498i | ||||
\(355\) | 80821.2 | − | 46662.2i | 0.641311 | − | 0.370261i | ||||
\(356\) | 95922.6 | + | 137804.i | 0.756869 | + | 1.08733i | ||||
\(357\) | 37105.9 | + | 64269.3i | 0.291143 | + | 0.504275i | ||||
\(358\) | −162124. | + | 6853.28i | −1.26498 | + | 0.0534727i | ||||
\(359\) | −87431.9 | − | 50478.8i | −0.678392 | − | 0.391670i | 0.120857 | − | 0.992670i | \(-0.461436\pi\) |
−0.799249 | + | 0.601000i | \(0.794769\pi\) | |||||||
\(360\) | −46518.6 | − | 365073.i | −0.358940 | − | 2.81692i | ||||
\(361\) | −116287. | + | 58830.4i | −0.892308 | + | 0.451427i | ||||
\(362\) | 61582.3 | − | 39112.3i | 0.469936 | − | 0.298467i | ||||
\(363\) | −330694. | − | 190926.i | −2.50965 | − | 1.44895i | ||||
\(364\) | −149267. | + | 103902.i | −1.12658 | + | 0.784191i | ||||
\(365\) | 33718.5 | + | 58402.1i | 0.253094 | + | 0.438372i | ||||
\(366\) | −343321. | + | 14512.8i | −2.56294 | + | 0.108340i | ||||
\(367\) | 87592.5 | − | 50571.5i | 0.650331 | − | 0.375469i | −0.138252 | − | 0.990397i | \(-0.544148\pi\) |
0.788583 | + | 0.614928i | \(0.210815\pi\) | |||||||
\(368\) | 61182.0 | − | 50762.2i | 0.451781 | − | 0.374839i | ||||
\(369\) | 239674. | 1.76022 | ||||||||
\(370\) | 81075.5 | + | 42348.2i | 0.592224 | + | 0.309337i | ||||
\(371\) | 156085. | − | 90115.6i | 1.13400 | − | 0.654715i | ||||
\(372\) | −133255. | + | 283709.i | −0.962934 | + | 2.05016i | ||||
\(373\) | 61611.7 | 0.442839 | 0.221419 | − | 0.975179i | \(-0.428931\pi\) | ||||
0.221419 | + | 0.975179i | \(0.428931\pi\) | |||||||
\(374\) | −30405.7 | + | 58211.6i | −0.217376 | + | 0.416166i | ||||
\(375\) | 148142. | + | 85530.0i | 1.05346 | + | 0.608213i | ||||
\(376\) | 31904.0 | + | 41938.1i | 0.225667 | + | 0.296643i | ||||
\(377\) | −16470.5 | + | 28527.8i | −0.115884 | + | 0.200717i | ||||
\(378\) | −16344.7 | − | 386659.i | −0.114392 | − | 2.70610i | ||||
\(379\) | 132679.i | 0.923685i | 0.886962 | + | 0.461843i | \(0.152812\pi\) | ||||
−0.886962 | + | 0.461843i | \(0.847188\pi\) | |||||||
\(380\) | 170159. | + | 35366.1i | 1.17839 | + | 0.244918i | ||||
\(381\) | −213015. | −1.46744 | ||||||||
\(382\) | 11671.3 | − | 493.366i | 0.0799822 | − | 0.00338098i | ||||
\(383\) | 17590.8 | + | 10156.1i | 0.119919 | + | 0.0692353i | 0.558760 | − | 0.829330i | \(-0.311277\pi\) |
−0.438841 | + | 0.898565i | \(0.644611\pi\) | |||||||
\(384\) | 61055.0 | − | 263281.i | 0.414056 | − | 1.78549i | ||||
\(385\) | −155782. | + | 269822.i | −1.05098 | + | 1.82035i | ||||
\(386\) | −71610.6 | − | 37404.4i | −0.480621 | − | 0.251043i | ||||
\(387\) | 105816.i | 0.706526i | ||||||||
\(388\) | 66805.4 | − | 142233.i | 0.443760 | − | 0.944796i | ||||
\(389\) | −56468.0 | − | 97805.5i | −0.373167 | − | 0.646345i | 0.616884 | − | 0.787054i | \(-0.288395\pi\) |
−0.990051 | + | 0.140710i | \(0.955062\pi\) | |||||||
\(390\) | 196152. | − | 375533.i | 1.28963 | − | 2.46899i | ||||
\(391\) | − | 26228.3i | − | 0.171560i | ||||||
\(392\) | 3529.21 | + | 27696.9i | 0.0229671 | + | 0.180243i | ||||
\(393\) | −138123. | − | 239236.i | −0.894294 | − | 1.54896i | ||||
\(394\) | −8528.82 | − | 201762.i | −0.0549410 | − | 1.29971i | ||||
\(395\) | −85543.0 | + | 49388.3i | −0.548264 | + | 0.316541i | ||||
\(396\) | 487862. | − | 339592.i | 3.11105 | − | 2.16555i | ||||
\(397\) | 14009.0 | − | 24264.3i | 0.0888845 | − | 0.153953i | −0.818155 | − | 0.574997i | \(-0.805003\pi\) |
0.907040 | + | 0.421045i | \(0.138336\pi\) | |||||||
\(398\) | 143402. | + | 225786.i | 0.905290 | + | 1.42538i | ||||
\(399\) | 304006. | + | 90526.3i | 1.90957 | + | 0.568629i | ||||
\(400\) | −45828.8 | − | 55236.0i | −0.286430 | − | 0.345225i | ||||
\(401\) | −121470. | + | 210392.i | −0.755406 | + | 1.30840i | 0.189766 | + | 0.981829i | \(0.439227\pi\) |
−0.945172 | + | 0.326572i | \(0.894106\pi\) | |||||||
\(402\) | 268.051 | + | 6341.14i | 0.00165869 | + | 0.0392388i | ||||
\(403\) | −219476. | + | 126714.i | −1.35138 | + | 0.780218i | ||||
\(404\) | 45760.7 | + | 65740.3i | 0.280369 | + | 0.402781i | ||||
\(405\) | 217884. | + | 377387.i | 1.32836 | + | 2.30079i | ||||
\(406\) | 17633.1 | + | 27763.2i | 0.106973 | + | 0.168430i | ||||
\(407\) | 147737.i | 0.891868i | ||||||||
\(408\) | −53986.5 | − | 70965.9i | −0.324314 | − | 0.426314i | ||||
\(409\) | −141071. | − | 244343.i | −0.843320 | − | 1.46067i | −0.887073 | − | 0.461630i | \(-0.847265\pi\) |
0.0437531 | − | 0.999042i | \(-0.486068\pi\) | |||||||
\(410\) | 127414. | − | 80923.5i | 0.757966 | − | 0.481401i | ||||
\(411\) | − | 563878.i | − | 3.33812i | ||||||
\(412\) | 10079.6 | + | 119011.i | 0.0593812 | + | 0.701120i | ||||
\(413\) | 51842.9 | − | 89794.5i | 0.303941 | − | 0.526441i | ||||
\(414\) | −109907. | + | 210417.i | −0.641249 | + | 1.22767i | ||||
\(415\) | 6410.93 | + | 3701.35i | 0.0372242 | + | 0.0214914i | ||||
\(416\) | 162129. | − | 146509.i | 0.936856 | − | 0.846596i | ||||
\(417\) | −434576. | −2.49916 | ||||||||
\(418\) | 76610.8 | + | 270050.i | 0.438467 | + | 1.54558i | ||||
\(419\) | − | 289972.i | − | 1.65169i | −0.563897 | − | 0.825845i | \(-0.690699\pi\) | ||
0.563897 | − | 0.825845i | \(-0.309301\pi\) | |||||||
\(420\) | −241669. | − | 347184.i | −1.37000 | − | 1.96816i | ||||
\(421\) | 104292. | − | 180638.i | 0.588417 | − | 1.01917i | −0.406023 | − | 0.913863i | \(-0.633085\pi\) |
0.994440 | − | 0.105305i | \(-0.0335820\pi\) | |||||||
\(422\) | −114436. | + | 219086.i | −0.642593 | + | 1.23024i | ||||
\(423\) | −136270. | − | 78675.4i | −0.761585 | − | 0.439702i | ||||
\(424\) | −172348. | + | 131112.i | −0.958684 | + | 0.729308i | ||||
\(425\) | −23679.2 | −0.131096 | ||||||||
\(426\) | −172755. | + | 109720.i | −0.951942 | + | 0.604600i | ||||
\(427\) | −240234. | + | 138699.i | −1.31759 | + | 0.760709i | ||||
\(428\) | −7491.63 | − | 88454.5i | −0.0408967 | − | 0.482872i | ||||
\(429\) | 684301. | 3.71820 | ||||||||
\(430\) | 35727.6 | + | 56253.1i | 0.193227 | + | 0.304235i | ||||
\(431\) | −269770. | + | 155752.i | −1.45224 | + | 0.838453i | −0.998609 | − | 0.0527340i | \(-0.983206\pi\) |
−0.453635 | + | 0.891187i | \(0.649873\pi\) | |||||||
\(432\) | 78203.8 | + | 458369.i | 0.419045 | + | 2.45611i | ||||
\(433\) | 163396. | + | 283010.i | 0.871495 | + | 1.50947i | 0.860450 | + | 0.509535i | \(0.170183\pi\) |
0.0110458 | + | 0.999939i | \(0.496484\pi\) | |||||||
\(434\) | 10686.6 | + | 252807.i | 0.0567361 | + | 1.34218i | ||||
\(435\) | −66353.4 | − | 38309.2i | −0.350659 | − | 0.202453i | ||||
\(436\) | −3614.10 | + | 7694.68i | −0.0190120 | + | 0.0404778i | ||||
\(437\) | −77051.4 | − | 81429.4i | −0.403476 | − | 0.426401i | ||||
\(438\) | −79284.9 | − | 124834.i | −0.413278 | − | 0.650706i | ||||
\(439\) | 250279. | + | 144499.i | 1.29866 | + | 0.749782i | 0.980173 | − | 0.198145i | \(-0.0634917\pi\) |
0.318488 | + | 0.947927i | \(0.396825\pi\) | |||||||
\(440\) | 144695. | − | 345254.i | 0.747389 | − | 1.78334i | ||||
\(441\) | −41687.4 | − | 72204.7i | −0.214352 | − | 0.371269i | ||||
\(442\) | −3044.81 | − | 72029.6i | −0.0155853 | − | 0.368694i | ||||
\(443\) | 321746. | − | 185760.i | 1.63948 | − | 0.946552i | 0.658463 | − | 0.752613i | \(-0.271207\pi\) |
0.981013 | − | 0.193940i | \(-0.0621266\pi\) | |||||||
\(444\) | −181555. | − | 85274.5i | −0.920966 | − | 0.432567i | ||||
\(445\) | −315752. | −1.59450 | ||||||||
\(446\) | −102909. | + | 197018.i | −0.517348 | + | 0.990461i | ||||
\(447\) | −450558. | + | 260130.i | −2.25494 | + | 1.30189i | ||||
\(448\) | −54713.1 | − | 211206.i | −0.272606 | − | 1.05232i | ||||
\(449\) | 276103. | 1.36955 | 0.684775 | − | 0.728754i | \(-0.259900\pi\) | ||||
0.684775 | + | 0.728754i | \(0.259900\pi\) | |||||||
\(450\) | 189968. | + | 99225.9i | 0.938112 | + | 0.490005i | ||||
\(451\) | 211130. | + | 121896.i | 1.03800 | + | 0.599289i | ||||
\(452\) | −153899. | + | 13034.5i | −0.753286 | + | 0.0637993i | ||||
\(453\) | −9534.11 | + | 16513.6i | −0.0464605 | + | 0.0804719i | ||||
\(454\) | 214702. | − | 9075.81i | 1.04166 | − | 0.0440325i | ||||
\(455\) | − | 342018.i | − | 1.65206i | ||||||
\(456\) | −376087. | − | 61726.4i | −1.80867 | − | 0.296853i | ||||
\(457\) | 143615. | 0.687652 | 0.343826 | − | 0.939033i | \(-0.388277\pi\) | ||||
0.343826 | + | 0.939033i | \(0.388277\pi\) | |||||||
\(458\) | 15348.1 | + | 363082.i | 0.0731684 | + | 1.73091i | ||||
\(459\) | 132857. | + | 76705.3i | 0.630610 | + | 0.364083i | ||||
\(460\) | 12617.0 | + | 148970.i | 0.0596265 | + | 0.704017i | ||||
\(461\) | 60841.9 | − | 105381.i | 0.286286 | − | 0.495863i | −0.686634 | − | 0.727003i | \(-0.740912\pi\) |
0.972920 | + | 0.231141i | \(0.0742458\pi\) | |||||||
\(462\) | 316322. | − | 605596.i | 1.48199 | − | 2.83726i | ||||
\(463\) | − | 108755.i | − | 0.507326i | −0.967293 | − | 0.253663i | \(-0.918365\pi\) | ||
0.967293 | − | 0.253663i | \(-0.0816354\pi\) | |||||||
\(464\) | −25233.0 | − | 30412.5i | −0.117201 | − | 0.141259i | ||||
\(465\) | −294728. | − | 510484.i | −1.36306 | − | 2.36089i | ||||
\(466\) | 226876. | + | 118504.i | 1.04476 | + | 0.545711i | ||||
\(467\) | − | 214011.i | − | 0.981300i | −0.871357 | − | 0.490650i | \(-0.836759\pi\) | ||
0.871357 | − | 0.490650i | \(-0.163241\pi\) | |||||||
\(468\) | −277407. | + | 590619.i | −1.26656 | + | 2.69659i | ||||
\(469\) | 2561.78 | + | 4437.13i | 0.0116465 | + | 0.0201724i | ||||
\(470\) | −99006.9 | + | 4185.19i | −0.448198 | + | 0.0189461i | ||||
\(471\) | −135453. | + | 78204.1i | −0.610588 | + | 0.352523i | ||||
\(472\) | −48153.2 | + | 114898.i | −0.216143 | + | 0.515737i | ||||
\(473\) | −53816.9 | + | 93213.6i | −0.240545 | + | 0.416636i | ||||
\(474\) | 182847. | − | 116130.i | 0.813826 | − | 0.516879i | ||||
\(475\) | −73515.5 | + | 69563.0i | −0.325831 | + | 0.308313i | ||||
\(476\) | −65152.6 | − | 30601.4i | −0.287553 | − | 0.135060i | ||||
\(477\) | 323323. | − | 560012.i | 1.42102 | − | 2.46128i | ||||
\(478\) | −171513. | + | 7250.14i | −0.750656 | + | 0.0317315i | ||||
\(479\) | −27949.8 | + | 16136.8i | −0.121817 | + | 0.0703311i | −0.559670 | − | 0.828715i | \(-0.689072\pi\) |
0.437853 | + | 0.899046i | \(0.355739\pi\) | |||||||
\(480\) | 340768. | + | 377099.i | 1.47903 | + | 1.63671i | ||||
\(481\) | −81089.1 | − | 140451.i | −0.350488 | − | 0.607062i | ||||
\(482\) | 274247. | − | 174180.i | 1.18045 | − | 0.749730i | ||||
\(483\) | 272862.i | 1.16963i | ||||||||
\(484\) | 369054. | − | 31256.9i | 1.57543 | − | 0.133431i | ||||
\(485\) | 147758. | + | 255924.i | 0.628155 | + | 1.08800i | ||||
\(486\) | −196813. | − | 309881.i | −0.833260 | − | 1.31197i | ||||
\(487\) | − | 468356.i | − | 1.97478i | −0.158317 | − | 0.987388i | \(-0.550607\pi\) | ||
0.158317 | − | 0.987388i | \(-0.449393\pi\) | |||||||
\(488\) | 265266. | − | 201798.i | 1.11389 | − | 0.847378i | ||||
\(489\) | −346426. | + | 600028.i | −1.44875 | + | 2.50931i | ||||
\(490\) | −46540.8 | − | 24309.7i | −0.193839 | − | 0.101248i | ||||
\(491\) | 166109. | + | 95903.2i | 0.689018 | + | 0.397805i | 0.803244 | − | 0.595650i | \(-0.203105\pi\) |
−0.114226 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(492\) | −271665. | + | 189101.i | −1.12228 | + | 0.781202i | ||||
\(493\) | −13037.6 | −0.0536419 | ||||||||
\(494\) | −221056. | − | 214681.i | −0.905833 | − | 0.879711i | ||||
\(495\) | 1.11785e6i | 4.56218i | ||||||||
\(496\) | −51131.6 | − | 299693.i | −0.207839 | − | 1.21818i | ||||
\(497\) | −82604.5 | + | 143075.i | −0.334419 | + | 0.579231i | ||||
\(498\) | −14388.9 | − | 7515.77i | −0.0580189 | − | 0.0303050i | ||||
\(499\) | 37633.6 | + | 21727.8i | 0.151138 | + | 0.0872598i | 0.573662 | − | 0.819092i | \(-0.305522\pi\) |
−0.422524 | + | 0.906352i | \(0.638856\pi\) | |||||||
\(500\) | −165327. | + | 14002.3i | −0.661307 | + | 0.0560092i | ||||
\(501\) | −127470. | −0.507845 | ||||||||
\(502\) | −197087. | − | 310314.i | −0.782080 | − | 1.23138i | ||||
\(503\) | 249928. | − | 144296.i | 0.987824 | − | 0.570320i | 0.0832007 | − | 0.996533i | \(-0.473486\pi\) |
0.904623 | + | 0.426212i | \(0.140152\pi\) | |||||||
\(504\) | 394456. | + | 518517.i | 1.55288 | + | 2.04128i | ||||
\(505\) | −150632. | −0.590656 | ||||||||
\(506\) | −203834. | + | 129460.i | −0.796116 | + | 0.505631i | ||||
\(507\) | −242535. | + | 140028.i | −0.943536 | + | 0.544751i | ||||
\(508\) | 169575. | − | 118038.i | 0.657104 | − | 0.457399i | ||||
\(509\) | −133723. | − | 231614.i | −0.516142 | − | 0.893984i | −0.999824 | − | 0.0187406i | \(-0.994034\pi\) |
0.483682 | − | 0.875244i | \(-0.339299\pi\) | |||||||
\(510\) | 167535. | − | 7082.00i | 0.644119 | − | 0.0272280i | ||||
\(511\) | −103387. | − | 59690.7i | −0.395937 | − | 0.228594i | ||||
\(512\) | 97287.9 | + | 243423.i | 0.371124 | + | 0.928583i | ||||
\(513\) | 637814. | − | 152156.i | 2.42359 | − | 0.578168i | ||||
\(514\) | −163850. | + | 104065.i | −0.620185 | + | 0.393893i | ||||
\(515\) | −194518. | − | 112305.i | −0.733409 | − | 0.423434i | ||||
\(516\) | −83487.8 | − | 119939.i | −0.313562 | − | 0.450467i | ||||
\(517\) | −80027.2 | − | 138611.i | −0.299403 | − | 0.518581i | ||||
\(518\) | −161780. | + | 6838.73i | −0.602929 | + | 0.0254868i | ||||
\(519\) | −271368. | + | 156674.i | −1.00745 | + | 0.581652i | ||||
\(520\) | 51943.2 | + | 407645.i | 0.192098 | + | 1.50756i | ||||
\(521\) | 433092. | 1.59553 | 0.797765 | − | 0.602969i | \(-0.206016\pi\) | ||||
0.797765 | + | 0.602969i | \(0.206016\pi\) | |||||||
\(522\) | 104595. | + | 54633.0i | 0.383856 | + | 0.200500i | ||||
\(523\) | −193325. | + | 111616.i | −0.706780 | + | 0.408059i | −0.809868 | − | 0.586613i | \(-0.800461\pi\) |
0.103088 | + | 0.994672i | \(0.467128\pi\) | |||||||
\(524\) | 242524. | + | 113911.i | 0.883266 | + | 0.414860i | ||||
\(525\) | 246344. | 0.893764 | ||||||||
\(526\) | 148617. | − | 284527.i | 0.537152 | − | 1.02838i | ||||
\(527\) | −86865.5 | − | 50151.8i | −0.312771 | − | 0.180578i | ||||
\(528\) | −285044. | + | 769839.i | −1.02246 | + | 2.76142i | ||||
\(529\) | −91702.4 | + | 158833.i | −0.327695 | + | 0.567584i | ||||
\(530\) | −17199.4 | − | 406877.i | −0.0612296 | − | 1.44848i | ||||
\(531\) | − | 372011.i | − | 1.31937i | ||||||
\(532\) | −292174. | + | 96393.8i | −1.03233 | + | 0.340585i | ||||
\(533\) | −267623. | −0.942038 | ||||||||
\(534\) | 691800. | − | 29243.6i | 2.42604 | − | 0.102553i | ||||
\(535\) | 144575. | + | 83470.5i | 0.505110 | + | 0.291625i | ||||
\(536\) | −3727.21 | − | 4899.47i | −0.0129734 | − | 0.0170537i | ||||
\(537\) | −334595. | + | 579536.i | −1.16030 | + | 2.00970i | ||||
\(538\) | −241091. | − | 125929.i | −0.832946 | − | 0.435073i | ||||
\(539\) | − | 84807.4i | − | 0.291915i | ||||||
\(540\) | −791496. | − | 371756.i | −2.71432 | − | 1.27489i | ||||
\(541\) | −282363. | − | 489067.i | −0.964746 | − | 1.67099i | −0.710295 | − | 0.703904i | \(-0.751438\pi\) |
−0.254452 | − | 0.967085i | \(-0.581895\pi\) | |||||||
\(542\) | −47854.1 | + | 91616.4i | −0.162900 | + | 0.311871i | ||||
\(543\) | − | 300855.i | − | 1.02037i | ||||||
\(544\) | 82301.6 | + | 26578.3i | 0.278106 | + | 0.0898111i | ||||
\(545\) | −7993.54 | − | 13845.2i | −0.0269120 | − | 0.0466130i | ||||
\(546\) | 31676.3 | + | 749349.i | 0.106255 | + | 2.51362i | ||||
\(547\) | 65738.7 | − | 37954.2i | 0.219708 | − | 0.126849i | −0.386107 | − | 0.922454i | \(-0.626180\pi\) |
0.605815 | + | 0.795605i | \(0.292847\pi\) | |||||||
\(548\) | 312462. | + | 448887.i | 1.04049 | + | 1.49478i | ||||
\(549\) | −497635. | + | 861929.i | −1.65107 | + | 2.85974i | ||||
\(550\) | 116878. | + | 184024.i | 0.386374 | + | 0.608345i | ||||
\(551\) | −40477.1 | + | 38300.9i | −0.133323 | + | 0.126155i | ||||
\(552\) | −41440.3 | − | 325219.i | −0.136002 | − | 1.06733i | ||||
\(553\) | 87430.4 | − | 151434.i | 0.285899 | − | 0.495191i | ||||
\(554\) | −7599.95 | − | 179788.i | −0.0247623 | − | 0.585790i | ||||
\(555\) | 326677. | − | 188607.i | 1.06055 | − | 0.612311i | ||||
\(556\) | 345954. | − | 240812.i | 1.11910 | − | 0.778985i | ||||
\(557\) | −168806. | − | 292381.i | −0.544100 | − | 0.942408i | −0.998663 | − | 0.0516937i | \(-0.983538\pi\) |
0.454563 | − | 0.890714i | \(-0.349795\pi\) | |||||||
\(558\) | 486725. | + | 766348.i | 1.56320 | + | 2.46126i | ||||
\(559\) | − | 118155.i | − | 0.378119i | ||||||
\(560\) | 384771. | + | 142467.i | 1.22695 | + | 0.454295i | ||||
\(561\) | 135419. | + | 234552.i | 0.430281 | + | 0.745269i | ||||
\(562\) | 104035. | − | 66075.3i | 0.329389 | − | 0.209202i | ||||
\(563\) | 436011.i | 1.37556i | 0.725917 | + | 0.687782i | \(0.241416\pi\) | ||||
−0.725917 | + | 0.687782i | \(0.758584\pi\) | |||||||
\(564\) | 216533. | − | 18339.2i | 0.680715 | − | 0.0576530i | ||||
\(565\) | 145228. | − | 251542.i | 0.454939 | − | 0.787977i | ||||
\(566\) | 142918. | − | 273617.i | 0.446124 | − | 0.854102i | ||||
\(567\) | −668075. | − | 385713.i | −2.07807 | − | 1.19977i | ||||
\(568\) | 76725.5 | − | 183074.i | 0.237817 | − | 0.567453i | ||||
\(569\) | −280075. | −0.865067 | −0.432534 | − | 0.901618i | \(-0.642380\pi\) | ||||
−0.432534 | + | 0.901618i | \(0.642380\pi\) | |||||||
\(570\) | 499332. | − | 514159.i | 1.53688 | − | 1.58252i | ||||
\(571\) | 307405.i | 0.942841i | 0.881909 | + | 0.471420i | \(0.156258\pi\) | ||||
−0.881909 | + | 0.471420i | \(0.843742\pi\) | |||||||
\(572\) | −544753. | + | 379193.i | −1.66497 | + | 1.15896i | ||||
\(573\) | 24087.5 | − | 41720.7i | 0.0733638 | − | 0.127070i | ||||
\(574\) | −123710. | + | 236842.i | −0.375475 | + | 0.718845i | ||||
\(575\) | −75399.5 | − | 43531.9i | −0.228052 | − | 0.131666i | ||||
\(576\) | −548893. | − | 558104.i | −1.65441 | − | 1.68217i | ||||
\(577\) | 145917. | 0.438284 | 0.219142 | − | 0.975693i | \(-0.429674\pi\) | ||||
0.219142 | + | 0.975693i | \(0.429674\pi\) | |||||||
\(578\) | −257926. | + | 163815.i | −0.772039 | + | 0.490339i | ||||
\(579\) | −288540. | + | 166589.i | −0.860695 | + | 0.496923i | ||||
\(580\) | 74050.3 | − | 6271.67i | 0.220126 | − | 0.0186435i | ||||
\(581\) | −13104.8 | −0.0388219 | ||||||||
\(582\) | −347434. | − | 547035.i | −1.02572 | − | 1.61499i | ||||
\(583\) | 569634. | − | 328879.i | 1.67594 | − | 0.967606i | ||||
\(584\) | 132291. | + | 55442.5i | 0.387886 | + | 0.162561i | ||||
\(585\) | −613559. | − | 1.06272e6i | −1.79285 | − | 3.10531i | ||||
\(586\) | −6144.64 | − | 145361.i | −0.0178937 | − | 0.423303i | ||||
\(587\) | 210426. | + | 121489.i | 0.610692 | + | 0.352583i | 0.773236 | − | 0.634118i | \(-0.218637\pi\) |
−0.162544 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(588\) | 104221. | + | 48951.2i | 0.301439 | + | 0.141582i | ||||
\(589\) | −417019. | + | 99483.4i | −1.20206 | + | 0.286761i | ||||
\(590\) | −125606. | − | 197766.i | −0.360833 | − | 0.568131i | ||||
\(591\) | −721225. | − | 416400.i | −2.06489 | − | 1.19216i | ||||
\(592\) | 191784. | − | 32721.0i | 0.547230 | − | 0.0933647i | ||||
\(593\) | −227189. | − | 393503.i | −0.646068 | − | 1.11902i | −0.984054 | − | 0.177871i | \(-0.943079\pi\) |
0.337986 | − | 0.941151i | \(-0.390254\pi\) | |||||||
\(594\) | −59650.3 | − | 1.41112e6i | −0.169060 | − | 3.99936i | ||||
\(595\) | 117231. | − | 67683.1i | 0.331137 | − | 0.191182i | ||||
\(596\) | 214530. | − | 456750.i | 0.603943 | − | 1.28584i | ||||
\(597\) | 1.10306e6 | 3.09492 | ||||||||
\(598\) | 122724. | − | 234954.i | 0.343184 | − | 0.657024i | ||||
\(599\) | 181088. | − | 104551.i | 0.504702 | − | 0.291390i | −0.225951 | − | 0.974139i | \(-0.572549\pi\) |
0.730653 | + | 0.682749i | \(0.239216\pi\) | |||||||
\(600\) | −293612. | + | 37412.8i | −0.815589 | + | 0.103925i | ||||
\(601\) | 644658. | 1.78476 | 0.892381 | − | 0.451283i | \(-0.149034\pi\) | ||||
0.892381 | + | 0.451283i | \(0.149034\pi\) | |||||||
\(602\) | −104565. | − | 54617.7i | −0.288533 | − | 0.150710i | ||||
\(603\) | 15919.9 | + | 9191.33i | 0.0437829 | + | 0.0252781i | ||||
\(604\) | −1560.85 | − | 18429.1i | −0.00427846 | − | 0.0505162i | ||||
\(605\) | −348259. | + | 603203.i | −0.951463 | + | 1.64798i | ||||
\(606\) | 330029. | − | 13950.9i | 0.898684 | − | 0.0379889i | ||||
\(607\) | − | 168054.i | − | 0.456112i | −0.973648 | − | 0.228056i | \(-0.926763\pi\) | ||
0.973648 | − | 0.228056i | \(-0.0732370\pi\) | |||||||
\(608\) | 333597. | − | 159263.i | 0.902432 | − | 0.430832i | ||||
\(609\) | 135635. | 0.365710 | ||||||||
\(610\) | 26472.0 | + | 626236.i | 0.0711423 | + | 1.68298i | ||||
\(611\) | 152160. | + | 87849.8i | 0.407586 | + | 0.235320i | ||||
\(612\) | −257338. | + | 21795.2i | −0.687071 | + | 0.0581912i | ||||
\(613\) | −19651.3 | + | 34037.0i | −0.0522961 | + | 0.0905795i | −0.890988 | − | 0.454026i | \(-0.849987\pi\) |
0.838692 | + | 0.544606i | \(0.183321\pi\) | |||||||
\(614\) | −213045. | + | 407874.i | −0.565112 | + | 1.08191i | ||||
\(615\) | − | 622470.i | − | 1.64577i | ||||||
\(616\) | 83765.3 | + | 657382.i | 0.220751 | + | 1.73243i | ||||
\(617\) | 278877. | + | 483028.i | 0.732557 | + | 1.26883i | 0.955787 | + | 0.294061i | \(0.0950068\pi\) |
−0.223229 | + | 0.974766i | \(0.571660\pi\) | |||||||
\(618\) | 436584. | + | 228041.i | 1.14312 | + | 0.597085i | ||||
\(619\) | 19071.0i | 0.0497727i | 0.999690 | + | 0.0248864i | \(0.00792240\pi\) | ||||
−0.999690 | + | 0.0248864i | \(0.992078\pi\) | |||||||
\(620\) | 517500. | + | 243064.i | 1.34625 | + | 0.632320i | ||||
\(621\) | 282030. | + | 488491.i | 0.731328 | + | 1.26670i | ||||
\(622\) | −263879. | + | 11154.6i | −0.682063 | + | 0.0288320i | ||||
\(623\) | 484078. | − | 279483.i | 1.24721 | − | 0.720076i | ||||
\(624\) | −151560. | − | 888324.i | −0.389238 | − | 2.28140i | ||||
\(625\) | 243624. | − | 421969.i | 0.623678 | − | 1.08024i | ||||
\(626\) | −536366. | + | 340658.i | −1.36871 | + | 0.869301i | ||||
\(627\) | 1.10947e6 | + | 330377.i | 2.82216 | + | 0.840379i | ||||
\(628\) | 64495.3 | − | 137315.i | 0.163534 | − | 0.348176i | ||||
\(629\) | 32094.0 | − | 55588.4i | 0.0811189 | − | 0.140502i | ||||
\(630\) | −1.22411e6 | + | 51745.1i | −3.08417 | + | 0.130373i | ||||
\(631\) | 288451. | − | 166537.i | 0.724458 | − | 0.418266i | −0.0919330 | − | 0.995765i | \(-0.529305\pi\) |
0.816391 | + | 0.577499i | \(0.195971\pi\) | |||||||
\(632\) | −81208.0 | + | 193769.i | −0.203313 | + | 0.485122i | ||||
\(633\) | 509664. | + | 882764.i | 1.27197 | + | 2.20311i | ||||
\(634\) | 253912. | − | 161265.i | 0.631691 | − | 0.401201i | ||||
\(635\) | 388550.i | 0.963607i | ||||||||
\(636\) | 75366.4 | + | 889860.i | 0.186322 | + | 2.19992i | ||||
\(637\) | 46548.7 | + | 80624.7i | 0.114717 | + | 0.198696i | ||||
\(638\) | 64352.2 | + | 101322.i | 0.158096 | + | 0.248923i | ||||
\(639\) | 592749.i | 1.45167i | ||||||||
\(640\) | −480238. | − | 111368.i | −1.17246 | − | 0.271893i | ||||
\(641\) | 117313. | − | 203191.i | 0.285515 | − | 0.494526i | −0.687219 | − | 0.726450i | \(-0.741169\pi\) |
0.972734 | + | 0.231924i | \(0.0745021\pi\) | |||||||
\(642\) | −324489. | − | 169491.i | −0.787282 | − | 0.411221i | ||||
\(643\) | −221657. | − | 127974.i | −0.536118 | − | 0.309528i | 0.207386 | − | 0.978259i | \(-0.433504\pi\) |
−0.743504 | + | 0.668731i | \(0.766838\pi\) | |||||||
\(644\) | −151201. | − | 217218.i | −0.364573 | − | 0.523749i | ||||
\(645\) | 274820. | 0.660584 | ||||||||
\(646\) | 29838.9 | − | 118253.i | 0.0715019 | − | 0.283366i | ||||
\(647\) | 403074.i | 0.962888i | 0.876477 | + | 0.481444i | \(0.159888\pi\) | ||||
−0.876477 | + | 0.481444i | \(0.840112\pi\) | |||||||
\(648\) | 854845. | + | 358262.i | 2.03581 | + | 0.853200i | ||||
\(649\) | 189202. | − | 327707.i | 0.449195 | − | 0.778029i | ||||
\(650\) | −212120. | − | 110797.i | −0.502059 | − | 0.262241i | ||||
\(651\) | 903693. | + | 521748.i | 2.13235 | + | 1.23111i | ||||
\(652\) | −56714.2 | − | 669630.i | −0.133412 | − | 1.57522i | ||||
\(653\) | −229583. | −0.538411 | −0.269205 | − | 0.963083i | \(-0.586761\pi\) | ||||
−0.269205 | + | 0.963083i | \(0.586761\pi\) | |||||||
\(654\) | 18795.8 | + | 29594.0i | 0.0439447 | + | 0.0691908i | ||||
\(655\) | −436379. | + | 251943.i | −1.01714 | + | 0.587247i | ||||
\(656\) | 111478. | − | 301076.i | 0.259048 | − | 0.699629i | ||||
\(657\) | −428325. | −0.992300 | ||||||||
\(658\) | 148083. | − | 94050.6i | 0.342021 | − | 0.217225i | ||||
\(659\) | −574579. | + | 331734.i | −1.32306 | + | 0.763868i | −0.984215 | − | 0.176974i | \(-0.943369\pi\) |
−0.338843 | + | 0.940843i | \(0.610036\pi\) | |||||||
\(660\) | −881974. | − | 1.26705e6i | −2.02473 | − | 2.90875i | ||||
\(661\) | 159778. | + | 276744.i | 0.365691 | + | 0.633395i | 0.988887 | − | 0.148671i | \(-0.0474995\pi\) |
−0.623196 | + | 0.782066i | \(0.714166\pi\) | |||||||
\(662\) | 87913.4 | − | 3716.25i | 0.200604 | − | 0.00847986i | ||||
\(663\) | −257479. | − | 148656.i | −0.585754 | − | 0.338185i | ||||
\(664\) | 15619.3 | − | 1990.25i | 0.0354263 | − | 0.00451411i | ||||
\(665\) | 165125. | − | 554523.i | 0.373395 | − | 1.25394i | ||||
\(666\) | −490414. | + | 311473.i | −1.10564 | + | 0.702218i | ||||
\(667\) | −41514.4 | − | 23968.4i | −0.0933141 | − | 0.0538749i | ||||
\(668\) | 101475. | − | 70635.0i | 0.227408 | − | 0.158295i | ||||
\(669\) | 458327. | + | 793846.i | 1.02405 | + | 1.77371i | ||||
\(670\) | 11566.6 | − | 488.939i | 0.0257665 | − | 0.00108919i | ||||
\(671\) | −876739. | + | 506185.i | −1.94727 | + | 1.12425i | ||||
\(672\) | −856213. | − | 276504.i | −1.89602 | − | 0.612298i | ||||
\(673\) | 210538. | 0.464838 | 0.232419 | − | 0.972616i | \(-0.425336\pi\) | ||||
0.232419 | + | 0.972616i | \(0.425336\pi\) | |||||||
\(674\) | 236528. | + | 123546.i | 0.520669 | + | 0.271962i | ||||
\(675\) | 441016. | − | 254621.i | 0.967936 | − | 0.558838i | ||||
\(676\) | 115482. | − | 245868.i | 0.252708 | − | 0.538033i | ||||
\(677\) | −201810. | −0.440317 | −0.220158 | − | 0.975464i | \(-0.570657\pi\) | ||||
−0.220158 | + | 0.975464i | \(0.570657\pi\) | |||||||
\(678\) | −294892. | + | 564569.i | −0.641510 | + | 1.22817i | ||||
\(679\) | −453054. | − | 261571.i | −0.982676 | − | 0.567349i | ||||
\(680\) | −129446. | + | 98474.3i | −0.279943 | + | 0.212963i | ||||
\(681\) | 443105. | − | 767481.i | 0.955460 | − | 1.65491i | ||||
\(682\) | 39000.9 | + | 922624.i | 0.0838505 | + | 1.98361i | ||||
\(683\) | − | 382747.i | − | 0.820484i | −0.911977 | − | 0.410242i | \(-0.865444\pi\) | ||
0.911977 | − | 0.410242i | \(-0.134556\pi\) | |||||||
\(684\) | −734914. | + | 823654.i | −1.57081 | + | 1.76049i | ||||
\(685\) | −1.02854e6 | −2.19201 | ||||||||
\(686\) | −418241. | + | 17679.8i | −0.888747 | + | 0.0375689i | ||||
\(687\) | 1.29789e6 | + | 749335.i | 2.74994 | + | 1.58768i | ||||
\(688\) | 132924. | + | 49217.2i | 0.280820 | + | 0.103978i | ||||
\(689\) | −361027. | + | 625316.i | −0.760503 | + | 1.31723i | ||||
\(690\) | 546486. | + | 285447.i | 1.14784 | + | 0.599552i | ||||
\(691\) | 212096.i | 0.444198i | 0.975024 | + | 0.222099i | \(0.0712909\pi\) | ||||
−0.975024 | + | 0.222099i | \(0.928709\pi\) | |||||||
\(692\) | 129210. | − | 275097.i | 0.269826 | − | 0.574479i | ||||
\(693\) | −989445. | − | 1.71377e6i | −2.06028 | − | 3.56850i | ||||
\(694\) | 35322.6 | − | 67625.0i | 0.0733388 | − | 0.140407i | ||||
\(695\) | 792690.i | 1.64110i | ||||||||
\(696\) | −161661. | + | 20599.2i | −0.333723 | + | 0.0425238i | ||||
\(697\) | −52960.7 | − | 91730.7i | −0.109016 | − | 0.188820i | ||||
\(698\) | −31236.6 | − | 738948.i | −0.0641140 | − | 1.51671i | ||||
\(699\) | 914150. | − | 527785.i | 1.87095 | − | 1.08020i | ||||
\(700\) | −196107. | + | 136507.i | −0.400219 | + | 0.278585i | ||||
\(701\) | −87973.4 | + | 152374.i | −0.179026 | + | 0.310082i | −0.941547 | − | 0.336881i | \(-0.890628\pi\) |
0.762521 | + | 0.646963i | \(0.223961\pi\) | |||||||
\(702\) | 831236. | + | 1.30878e6i | 1.68675 | + | 2.65578i | ||||
\(703\) | −63663.0 | − | 266865.i | −0.128818 | − | 0.539985i | ||||
\(704\) | −199676. | − | 770799.i | −0.402885 | − | 1.55523i | ||||
\(705\) | −204332. | + | 353913.i | −0.411110 | + | 0.712064i | ||||
\(706\) | 21164.8 | + | 500685.i | 0.0424624 | + | 1.00451i | ||||
\(707\) | 230933. | − | 133329.i | 0.462006 | − | 0.266740i | ||||
\(708\) | 293514. | + | 421666.i | 0.585548 | + | 0.841205i | ||||
\(709\) | 447334. | + | 774806.i | 0.889897 | + | 1.54135i | 0.839996 | + | 0.542592i | \(0.182557\pi\) |
0.0499006 | + | 0.998754i | \(0.484110\pi\) | |||||||
\(710\) | 200136. | + | 315114.i | 0.397016 | + | 0.625101i | ||||
\(711\) | − | 627378.i | − | 1.24105i | ||||||
\(712\) | −534517. | + | 406628.i | −1.05439 | + | 0.802116i | ||||
\(713\) | −184398. | − | 319387.i | −0.362726 | − | 0.628259i | ||||
\(714\) | −250579. | + | 159149.i | −0.491528 | + | 0.312181i | ||||
\(715\) | − | 1.24820e6i | − | 2.44159i | ||||||
\(716\) | −54777.3 | − | 646761.i | −0.106850 | − | 1.26159i | ||||
\(717\) | −353971. | + | 613096.i | −0.688540 | + | 1.19259i | ||||
\(718\) | 186965. | − | 357943.i | 0.362669 | − | 0.694329i | ||||
\(719\) | 427120. | + | 246598.i | 0.826214 | + | 0.477015i | 0.852555 | − | 0.522638i | \(-0.175052\pi\) |
−0.0263406 | + | 0.999653i | \(0.508385\pi\) | |||||||
\(720\) | 1.45113e6 | − | 247582.i | 2.79925 | − | 0.477589i | ||||
\(721\) | 397621. | 0.764889 | ||||||||
\(722\) | −254756. | − | 454792.i | −0.488710 | − | 0.872447i | ||||
\(723\) | − | 1.33981e6i | − | 2.56310i | ||||||
\(724\) | 166713. | + | 239502.i | 0.318048 | + | 0.456911i | ||||
\(725\) | −21639.0 | + | 37479.8i | −0.0411680 | + | 0.0713051i | ||||
\(726\) | 707157. | − | 1.35385e6i | 1.34166 | − | 2.56860i | ||||
\(727\) | −519947. | − | 300191.i | −0.983762 | − | 0.567975i | −0.0803584 | − | 0.996766i | \(-0.525606\pi\) |
−0.903404 | + | 0.428791i | \(0.858940\pi\) | |||||||
\(728\) | −440454. | − | 578983.i | −0.831071 | − | 1.09245i | ||||
\(729\) | −340812. | −0.641297 | ||||||||
\(730\) | −227704. | + | 144620.i | −0.427292 | + | 0.271383i | ||||
\(731\) | 40498.9 | − | 23382.1i | 0.0757895 | − | 0.0437571i | ||||
\(732\) | −115998. | − | 1.36961e6i | −0.216486 | − | 2.55607i | ||||
\(733\) | 709490. | 1.32050 | 0.660250 | − | 0.751046i | \(-0.270450\pi\) | ||||
0.660250 | + | 0.751046i | \(0.270450\pi\) | |||||||
\(734\) | 216903. | + | 341514.i | 0.402600 | + | 0.633893i | ||||
\(735\) | −187527. | + | 108269.i | −0.347127 | + | 0.200414i | ||||
\(736\) | 213203. | + | 235934.i | 0.393585 | + | 0.435547i | ||||
\(737\) | 9349.26 | + | 16193.4i | 0.0172124 | + | 0.0298128i | ||||
\(738\) | 40489.5 | + | 957840.i | 0.0743413 | + | 1.75865i | ||||
\(739\) | −38501.6 | − | 22228.9i | −0.0705000 | − | 0.0407032i | 0.464336 | − | 0.885659i | \(-0.346293\pi\) |
−0.534836 | + | 0.844956i | \(0.679626\pi\) | |||||||
\(740\) | −155545. | + | 331167.i | −0.284049 | + | 0.604761i | ||||
\(741\) | −1.23609e6 | + | 294880.i | −2.25120 | + | 0.537043i | ||||
\(742\) | 386509. | + | 608559.i | 0.702024 | + | 1.10534i | ||||
\(743\) | −612762. | − | 353778.i | −1.10998 | − | 0.640846i | −0.171154 | − | 0.985244i | \(-0.554749\pi\) |
−0.938823 | + | 0.344399i | \(0.888083\pi\) | |||||||
\(744\) | −1.15633e6 | − | 484615.i | −2.08899 | − | 0.875489i | ||||
\(745\) | 474490. | + | 821841.i | 0.854899 | + | 1.48073i | ||||
\(746\) | 10408.4 | + | 246227.i | 0.0187028 | + | 0.442443i | ||||
\(747\) | −40719.0 | + | 23509.1i | −0.0729719 | + | 0.0421303i | ||||
\(748\) | −237775. | − | 111680.i | −0.424975 | − | 0.199606i | ||||
\(749\) | −295530. | −0.526791 | ||||||||
\(750\) | −316788. | + | 606489.i | −0.563179 | + | 1.07820i | ||||
\(751\) | −908763. | + | 524675.i | −1.61128 | + | 0.930272i | −0.622205 | + | 0.782855i | \(0.713763\pi\) |
−0.989074 | + | 0.147418i | \(0.952904\pi\) | |||||||
\(752\) | −162213. | + | 134587.i | −0.286847 | + | 0.237994i | ||||
\(753\) | −1.51601e6 | −2.67370 | ||||||||
\(754\) | −116792. | − | 61003.9i | −0.205432 | − | 0.107304i | ||||
\(755\) | 30121.6 | + | 17390.7i | 0.0528427 | + | 0.0305087i | ||||
\(756\) | 1.54249e6 | − | 130641.i | 2.69886 | − | 0.228579i | ||||
\(757\) | −205034. | + | 355129.i | −0.357795 | + | 0.619719i | −0.987592 | − | 0.157041i | \(-0.949805\pi\) |
0.629797 | + | 0.776760i | \(0.283138\pi\) | |||||||
\(758\) | −530243. | + | 22414.3i | −0.922861 | + | 0.0390109i | ||||
\(759\) | 995815.i | 1.72860i | ||||||||
\(760\) | −112592. | + | 686003.i | −0.194931 | + | 1.18768i | ||||
\(761\) | 688016. | 1.18804 | 0.594018 | − | 0.804452i | \(-0.297541\pi\) | ||||
0.594018 | + | 0.804452i | \(0.297541\pi\) | |||||||
\(762\) | −35985.8 | − | 851299.i | −0.0619758 | − | 1.46613i | ||||
\(763\) | 24509.7 | + | 14150.7i | 0.0421007 | + | 0.0243069i | ||||
\(764\) | 3943.41 | + | 46560.3i | 0.00675593 | + | 0.0797680i | ||||
\(765\) | 242838. | − | 420608.i | 0.414949 | − | 0.718712i | ||||
\(766\) | −37616.2 | + | 72016.1i | −0.0641088 | + | 0.122736i | ||||
\(767\) | 415392.i | 0.706102i | ||||||||
\(768\) | 1.06250e6 | + | 199524.i | 1.80138 | + | 0.338278i | ||||
\(769\) | 393721. | + | 681945.i | 0.665788 | + | 1.15318i | 0.979071 | + | 0.203519i | \(0.0652378\pi\) |
−0.313283 | + | 0.949660i | \(0.601429\pi\) | |||||||
\(770\) | −1.10464e6 | − | 576988.i | −1.86311 | − | 0.973162i | ||||
\(771\) | 800477.i | 1.34660i | ||||||||
\(772\) | 137387. | − | 292506.i | 0.230521 | − | 0.490795i | ||||
\(773\) | −286229. | − | 495763.i | −0.479021 | − | 0.829688i | 0.520690 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240575i | \(0.992342\pi\) | |||||||
\(774\) | −422885. | + | 17876.1i | −0.705895 | + | 0.0298394i | ||||
\(775\) | −288347. | + | 166477.i | −0.480079 | + | 0.277174i | ||||
\(776\) | 579712. | + | 242955.i | 0.962695 | + | 0.403462i | ||||
\(777\) | −333885. | + | 578306.i | −0.553038 | + | 0.957890i | ||||
\(778\) | 381334. | − | 242194.i | 0.630008 | − | 0.400132i | ||||
\(779\) | −433903. | − | 129207.i | −0.715020 | − | 0.212917i | ||||
\(780\) | 1.53393e6 | + | 720469.i | 2.52125 | + | 1.18420i | ||||
\(781\) | −301467. | + | 522155.i | −0.494239 | + | 0.856047i | ||||
\(782\) | 104819. | − | 4430.90i | 0.171407 | − | 0.00724566i | ||||
\(783\) | 242820. | − | 140192.i | 0.396060 | − | 0.228665i | ||||
\(784\) | −110093. | + | 18783.2i | −0.179112 | + | 0.0305590i | ||||
\(785\) | 142648. | + | 247074.i | 0.231488 | + | 0.400948i | ||||
\(786\) | 932755. | − | 592414.i | 1.50981 | − | 0.958915i | ||||
\(787\) | 339633.i | 0.548354i | 0.961679 | + | 0.274177i | \(0.0884054\pi\) | ||||
−0.961679 | + | 0.274177i | \(0.911595\pi\) | |||||||
\(788\) | 804887. | − | 68169.7i | 1.29623 | − | 0.109784i | ||||
\(789\) | −661899. | − | 1.14644e6i | −1.06326 | − | 1.84161i | ||||
\(790\) | −211828. | − | 333523.i | −0.339414 | − | 0.534406i | ||||
\(791\) | 514184.i | 0.821799i | ||||||||
\(792\) | 1.43957e6 | + | 1.89234e6i | 2.29501 | + | 3.01681i | ||||
\(793\) | 555665. | − | 962440.i | 0.883623 | − | 1.53048i | ||||
\(794\) | 99337.2 | + | 51886.9i | 0.157569 | + | 0.0823032i | ||||
\(795\) | −1.45444e6 | − | 839720.i | −2.30124 | − | 1.32862i | ||||
\(796\) | −878111. | + | 611238.i | −1.38587 | + | 0.964682i | ||||
\(797\) | 38837.6 | 0.0611414 | 0.0305707 | − | 0.999533i | \(-0.490268\pi\) | ||||
0.0305707 | + | 0.999533i | \(0.490268\pi\) | |||||||
\(798\) | −310424. | + | 1.23023e6i | −0.487473 | + | 1.93188i | ||||
\(799\) | 69539.5i | 0.108928i | ||||||||
\(800\) | 213005. | − | 192483.i | 0.332820 | − | 0.300755i | ||||
\(801\) | 1.00275e6 | − | 1.73681e6i | 1.56288 | − | 2.70699i | ||||
\(802\) | −861339. | − | 449904.i | −1.33914 | − | 0.699473i | ||||
\(803\) | −377314. | − | 217842.i | −0.585156 | − | 0.337840i | ||||
\(804\) | −25296.7 | + | 2142.49i | −0.0391337 | + | 0.00331442i | ||||
\(805\) | 497715. | 0.768049 | ||||||||
\(806\) | −543483. | − | 855713.i | −0.836596 | − | 1.31722i | ||||
\(807\) | −971427. | + | 560854.i | −1.49164 | + | 0.861197i | ||||
\(808\) | −254996. | + | 193985.i | −0.390581 | + | 0.297130i | ||||
\(809\) | 126031. | 0.192567 | 0.0962835 | − | 0.995354i | \(-0.469304\pi\) | ||||
0.0962835 | + | 0.995354i | \(0.469304\pi\) | |||||||
\(810\) | −1.47139e6 | + | 934514.i | −2.24263 | + | 1.42435i | ||||
\(811\) | 696758. | − | 402273.i | 1.05935 | − | 0.611617i | 0.134099 | − | 0.990968i | \(-0.457186\pi\) |
0.925253 | + | 0.379351i | \(0.123853\pi\) | |||||||
\(812\) | −107975. | + | 75159.5i | −0.163761 | + | 0.113991i | ||||
\(813\) | 213129. | + | 369150.i | 0.322449 | + | 0.558498i | ||||
\(814\) | −590421. | + | 24958.1i | −0.891072 | + | 0.0376671i | ||||
\(815\) | 1.09448e6 | + | 631900.i | 1.64776 | + | 0.951334i | ||||
\(816\) | 274490. | − | 227742.i | 0.412237 | − | 0.342029i | ||||
\(817\) | 57044.6 | − | 191568.i | 0.0854615 | − | 0.286997i | ||||
\(818\) | 952667. | − | 605060.i | 1.42375 | − | 0.904257i | ||||
\(819\) | 1.88129e6 | + | 1.08616e6i | 2.80471 | + | 1.61930i | ||||
\(820\) | 344930. | + | 495531.i | 0.512984 | + | 0.736958i | ||||
\(821\) | −388971. | − | 673717.i | −0.577073 | − | 0.999519i | −0.995813 | − | 0.0914131i | \(-0.970862\pi\) |
0.418740 | − | 0.908106i | \(-0.362472\pi\) | |||||||
\(822\) | 2.25350e6 | − | 95259.2i | 3.33514 | − | 0.140982i | ||||
\(823\) | 137606. | − | 79447.1i | 0.203160 | − | 0.117295i | −0.394968 | − | 0.918695i | \(-0.629244\pi\) |
0.598129 | + | 0.801400i | \(0.295911\pi\) | |||||||
\(824\) | −473916. | + | 60387.7i | −0.697987 | + | 0.0889393i | ||||
\(825\) | 899035. | 1.32090 | ||||||||
\(826\) | 367616. | + | 192017.i | 0.538808 | + | 0.281436i | ||||
\(827\) | 37972.9 | − | 21923.7i | 0.0555217 | − | 0.0320555i | −0.471982 | − | 0.881608i | \(-0.656461\pi\) |
0.527504 | + | 0.849553i | \(0.323128\pi\) | |||||||
\(828\) | −859486. | − | 403690.i | −1.25365 | − | 0.588827i | ||||
\(829\) | 321511. | 0.467828 | 0.233914 | − | 0.972257i | \(-0.424847\pi\) | ||||
0.233914 | + | 0.972257i | \(0.424847\pi\) | |||||||
\(830\) | −13709.2 | + | 26246.1i | −0.0199001 | + | 0.0380986i | ||||
\(831\) | −642677. | − | 371050.i | −0.930659 | − | 0.537316i | ||||
\(832\) | 612901. | + | 623185.i | 0.885408 | + | 0.900265i | ||||
\(833\) | −18423.3 | + | 31910.1i | −0.0265508 | + | 0.0459874i | ||||
\(834\) | −73415.5 | − | 1.73675e6i | −0.105549 | − | 2.49693i | ||||
\(835\) | 232512.i | 0.333481i | ||||||||
\(836\) | −1.06629e6 | + | 351791.i | −1.52568 | + | 0.503352i | ||||
\(837\) | 2.15711e6 | 3.07909 | ||||||||
\(838\) | 1.15885e6 | − | 48986.7i | 1.65022 | − | 0.0697574i | ||||
\(839\) | −720518. | − | 415991.i | −1.02358 | − | 0.590963i | −0.108440 | − | 0.994103i | \(-0.534586\pi\) |
−0.915138 | + | 0.403140i | \(0.867919\pi\) | |||||||
\(840\) | 1.34667e6 | − | 1.02446e6i | 1.90855 | − | 1.45190i | ||||
\(841\) | 341726. | − | 591887.i | 0.483155 | − | 0.836849i | ||||
\(842\) | 739528. | + | 386278.i | 1.04311 | + | 0.544849i | ||||
\(843\) | − | 508256.i | − | 0.715200i | ||||||
\(844\) | −894896. | − | 420322.i | −1.25628 | − | 0.590062i | ||||
\(845\) | 255418. | + | 442397.i | 0.357716 | + | 0.619582i | ||||
\(846\) | 291400. | − | 557884.i | 0.407144 | − | 0.779476i | ||||
\(847\) | − | 1.23302e6i | − | 1.71872i | ||||||
\(848\) | −553096. | − | 666629.i | −0.769146 | − | 0.927027i | ||||
\(849\) | −636519. | − | 1.10248e6i | −0.883071 | − | 1.52952i | ||||
\(850\) | −4000.27 | − | 94632.4i | −0.00553671 | − | 0.130979i | ||||
\(851\) | 204388. | − | 118003.i | 0.282225 | − | 0.162943i | ||||
\(852\) | −467674. | − | 671866.i | −0.644264 | − | 0.925558i | ||||
\(853\) | −99623.0 | + | 172552.i | −0.136918 | + | 0.237149i | −0.926329 | − | 0.376716i | \(-0.877053\pi\) |
0.789410 | + | 0.613866i | \(0.210386\pi\) | |||||||
\(854\) | −594886. | − | 936648.i | −0.815677 | − | 1.28428i | ||||
\(855\) | −481705. | − | 2.01923e6i | −0.658944 | − | 2.76219i | ||||
\(856\) | 352237. | − | 44882.9i | 0.480714 | − | 0.0612539i | ||||
\(857\) | 15810.8 | − | 27385.1i | 0.0215275 | − | 0.0372866i | −0.855061 | − | 0.518527i | \(-0.826480\pi\) |
0.876588 | + | 0.481241i | \(0.159814\pi\) | |||||||
\(858\) | 115603. | + | 2.73476e6i | 0.157034 | + | 3.71488i | ||||
\(859\) | −833297. | + | 481104.i | −1.12931 | + | 0.652008i | −0.943762 | − | 0.330627i | \(-0.892740\pi\) |
−0.185550 | + | 0.982635i | \(0.559407\pi\) | |||||||
\(860\) | −218776. | + | 152286.i | −0.295803 | + | 0.205903i | ||||
\(861\) | 550969. | + | 954307.i | 0.743226 | + | 1.28731i | ||||
\(862\) | −668026. | − | 1.05181e6i | −0.899039 | − | 1.41554i | ||||
\(863\) | 41382.1i | 0.0555637i | 0.999614 | + | 0.0277819i | \(0.00884438\pi\) | ||||
−0.999614 | + | 0.0277819i | \(0.991156\pi\) | |||||||
\(864\) | −1.81863e6 | + | 389971.i | −2.43622 | + | 0.522402i | ||||
\(865\) | 285782. | + | 494989.i | 0.381947 | + | 0.661551i | ||||
\(866\) | −1.10343e6 | + | 700811.i | −1.47132 | + | 0.934469i | ||||
\(867\) | 1.26007e6i | 1.67632i | ||||||||
\(868\) | −1.00852e6 | + | 85416.4i | −1.33858 | + | 0.113371i | ||||
\(869\) | 319079. | − | 552661.i | 0.422531 | − | 0.731845i | ||||
\(870\) | 141890. | − | 271649.i | 0.187463 | − | 0.358896i | ||||
\(871\) | −17776.3 | − | 10263.1i | −0.0234318 | − | 0.0135283i | ||||
\(872\) | −31361.8 | − | 13143.6i | −0.0412447 | − | 0.0172855i | ||||
\(873\) | −1.87697e6 | −2.46279 | ||||||||
\(874\) | 312410. | − | 321687.i | 0.408980 | − | 0.421125i | ||||
\(875\) | 552363.i | 0.721454i | ||||||||
\(876\) | 485496. | − | 337945.i | 0.632671 | − | 0.440391i | ||||
\(877\) | 423044. | − | 732734.i | 0.550030 | − | 0.952680i | −0.448242 | − | 0.893912i | \(-0.647950\pi\) |
0.998272 | − | 0.0587676i | \(-0.0187171\pi\) | |||||||
\(878\) | −535198. | + | 1.02463e6i | −0.694265 | + | 1.32917i | ||||
\(879\) | −519611. | − | 299998.i | −0.672513 | − | 0.388276i | ||||
\(880\) | 1.40423e6 | + | 519936.i | 1.81331 | + | 0.671405i | ||||
\(881\) | −422356. | −0.544161 | −0.272080 | − | 0.962275i | \(-0.587712\pi\) | ||||
−0.272080 | + | 0.962275i | \(0.587712\pi\) | |||||||
\(882\) | 281519. | − | 178799.i | 0.361885 | − | 0.229841i | ||||
\(883\) | 166985. | − | 96408.7i | 0.214168 | − | 0.123650i | −0.389079 | − | 0.921204i | \(-0.627207\pi\) |
0.603247 | + | 0.797554i | \(0.293873\pi\) | |||||||
\(884\) | 287347. | − | 24336.8i | 0.367707 | − | 0.0311428i | ||||
\(885\) | −966170. | −1.23358 | ||||||||
\(886\) | 796731. | + | 1.25445e6i | 1.01495 | + | 1.59804i | ||||
\(887\) | 706851. | − | 408100.i | 0.898422 | − | 0.518704i | 0.0217341 | − | 0.999764i | \(-0.493081\pi\) |
0.876688 | + | 0.481060i | \(0.159748\pi\) | |||||||
\(888\) | 310122. | − | 739980.i | 0.393285 | − | 0.938413i | ||||
\(889\) | −343919. | − | 595685.i | −0.435164 | − | 0.753726i | ||||
\(890\) | −53341.8 | − | 1.26188e6i | −0.0673423 | − | 1.59308i | ||||
\(891\) | −2.43815e6 | − | 1.40767e6i | −3.07118 | − | 1.77315i | ||||
\(892\) | −804756. | − | 377984.i | −1.01143 | − | 0.475055i | ||||
\(893\) | 204288. | + | 215895.i | 0.256177 | + | 0.270732i | ||||
\(894\) | −1.11571e6 | − | 1.75668e6i | −1.39596 | − | 2.19795i | ||||
\(895\) | 1.05710e6 | + | 610319.i | 1.31969 | + | 0.761923i | ||||
\(896\) | 834826. | − | 254337.i | 1.03987 | − | 0.316807i | ||||
\(897\) | −546578. | − | 946701.i | −0.679309 | − | 1.17660i | ||||
\(898\) | 46643.7 | + | 1.10343e6i | 0.0578416 | + | 1.36833i | ||||
\(899\) | −158762. | + | 91661.2i | −0.196439 | + | 0.113414i | ||||
\(900\) | −364457. | + | 775955.i | −0.449947 | + | 0.957969i | ||||
\(901\) | −285779. | −0.352031 | ||||||||
\(902\) | −451482. | + | 864359.i | −0.554916 | + | 1.06238i | ||||
\(903\) | −421325. | + | 243252.i | −0.516704 | + | 0.298319i | ||||
\(904\) | −78090.4 | − | 612846.i | −0.0955566 | − | 0.749919i | ||||
\(905\) | −548775. | −0.670035 | ||||||||
\(906\) | −67606.0 | − | 35312.7i | −0.0823624 | − | 0.0430204i | ||||
\(907\) | −1.10359e6 | − | 637160.i | −1.34151 | − | 0.774522i | −0.354482 | − | 0.935063i | \(-0.615343\pi\) |
−0.987029 | + | 0.160541i | \(0.948676\pi\) | |||||||
\(908\) | 72541.7 | + | 856508.i | 0.0879865 | + | 1.03887i | ||||
\(909\) | 478369. | − | 828559.i | 0.578942 | − | 1.00276i | ||||
\(910\) | 1.36685e6 | − | 57779.2i | 1.65059 | − | 0.0697732i | ||||
\(911\) | 796819.i | 0.960114i | 0.877237 | + | 0.480057i | \(0.159384\pi\) | ||||
−0.877237 | + | 0.480057i | \(0.840616\pi\) | |||||||
\(912\) | 183151. | − | 1.51343e6i | 0.220201 | − | 1.81959i | ||||
\(913\) | −47826.1 | −0.0573751 | ||||||||
\(914\) | 24261.8 | + | 573949.i | 0.0290423 | + | 0.687038i | ||||
\(915\) | 2.23856e6 | + | 1.29244e6i | 2.67379 | + | 1.54371i | ||||
\(916\) | −1.44844e6 | + | 122675.i | −1.72627 | + | 0.146206i | ||||
\(917\) | 446007. | − | 772507.i | 0.530400 | − | 0.918679i | ||||
\(918\) | −284103. | + | 543914.i | −0.337125 | + | 0.645424i | ||||
\(919\) | 1.41415e6i | 1.67442i | 0.546881 | + | 0.837211i | \(0.315815\pi\) | ||||
−0.546881 | + | 0.837211i | \(0.684185\pi\) | |||||||
\(920\) | −593217. | + | 75589.2i | −0.700871 | + | 0.0893068i | ||||
\(921\) | 948843. | + | 1.64344e6i | 1.11860 | + | 1.93747i | ||||
\(922\) | 431427. | + | 225348.i | 0.507511 | + | 0.265089i | ||||
\(923\) | − | 661870.i | − | 0.776907i | ||||||
\(924\) | 2.47366e6 | + | 1.16185e6i | 2.89732 | + | 1.36084i | ||||
\(925\) | −106535. | − | 184524.i | −0.124511 | − | 0.215660i | ||||
\(926\) | 434632. | − | 18372.6i | 0.506873 | − | 0.0214264i | ||||
\(927\) | 1.23548e6 | − | 713306.i | 1.43773 | − | 0.830073i | ||||
\(928\) | 117279. | − | 105980.i | 0.136183 | − | 0.123063i | ||||
\(929\) | −472923. | + | 819127.i | −0.547973 | + | 0.949117i | 0.450440 | + | 0.892807i | \(0.351267\pi\) |
−0.998413 | + | 0.0563105i | \(0.982066\pi\) | |||||||
\(930\) | 1.99032e6 | − | 1.26410e6i | 2.30122 | − | 1.46156i | ||||
\(931\) | 36545.3 | + | 153192.i | 0.0421631 | + | 0.176741i | ||||
\(932\) | −435267. | + | 926714.i | −0.501099 | + | 1.06688i | ||||
\(933\) | −544598. | + | 943272.i | −0.625623 | + | 1.08361i | ||||
\(934\) | 855279. | − | 36154.1i | 0.980424 | − | 0.0414442i | ||||
\(935\) | 427835. | − | 247011.i | 0.489388 | − | 0.282548i | ||||
\(936\) | −2.40723e6 | − | 1.00886e6i | −2.74768 | − | 1.15154i | ||||
\(937\) | 162929. | + | 282201.i | 0.185575 | + | 0.321425i | 0.943770 | − | 0.330603i | \(-0.107252\pi\) |
−0.758195 | + | 0.652028i | \(0.773919\pi\) | |||||||
\(938\) | −17299.9 | + | 10987.6i | −0.0196625 | + | 0.0124881i | ||||
\(939\) | 2.62037e6i | 2.97188i | ||||||||
\(940\) | −33451.6 | − | 394967.i | −0.0378583 | − | 0.446998i | ||||
\(941\) | 195615. | + | 338816.i | 0.220914 | + | 0.382635i | 0.955086 | − | 0.296329i | \(-0.0957626\pi\) |
−0.734172 | + | 0.678964i | \(0.762429\pi\) | |||||||
\(942\) | −335420. | − | 528119.i | −0.377996 | − | 0.595155i | ||||
\(943\) | − | 389452.i | − | 0.437956i | ||||||
\(944\) | −467316. | − | 173031.i | −0.524405 | − | 0.194169i | ||||
\(945\) | −1.45558e6 | + | 2.52114e6i | −1.62994 | + | 2.82315i | ||||
\(946\) | −381613. | − | 199328.i | −0.426424 | − | 0.222734i | ||||
\(947\) | −107302. | − | 61951.0i | −0.119649 | − | 0.0690793i | 0.438981 | − | 0.898496i | \(-0.355339\pi\) |
−0.558630 | + | 0.829417i | \(0.688673\pi\) | |||||||
\(948\) | 494996. | + | 711118.i | 0.550789 | + | 0.791270i | ||||
\(949\) | 478273. | 0.531060 | ||||||||
\(950\) | −290423. | − | 282048.i | −0.321799 | − | 0.312519i | ||||
\(951\) | − | 1.24046e6i | − | 1.37159i | ||||||
\(952\) | 111290. | − | 265547.i | 0.122795 | − | 0.293000i | ||||
\(953\) | −529005. | + | 916263.i | −0.582470 | + | 1.00887i | 0.412715 | + | 0.910860i | \(0.364580\pi\) |
−0.995186 | + | 0.0980080i | \(0.968753\pi\) | |||||||
\(954\) | 2.29267e6 | + | 1.19753e6i | 2.51910 | + | 1.31580i | ||||
\(955\) | −76100.8 | − | 43936.8i | −0.0834416 | − | 0.0481750i | ||||
\(956\) | −57949.3 | − | 684214.i | −0.0634064 | − | 0.748646i | ||||
\(957\) | 495002. | 0.540484 | ||||||||
\(958\) | −69211.5 | − | 108974.i | −0.0754132 | − | 0.118738i | ||||
\(959\) | 1.57686e6 | − | 910399.i | 1.71457 | − | 0.989907i | ||||
\(960\) | −1.44948e6 | + | 1.42556e6i | −1.57279 | + | 1.54683i | ||||
\(961\) | −486854. | −0.527171 | ||||||||
\(962\) | 547602. | − | 347794.i | 0.591718 | − | 0.375813i | ||||
\(963\) | −918267. | + | 530162.i | −0.990186 | + | 0.571684i | ||||
\(964\) | 742429. | + | 1.06658e6i | 0.798916 | + | 1.14773i | ||||
\(965\) | 303867. | + | 526313.i | 0.326309 | + | 0.565184i | ||||
\(966\) | −1.09047e6 | + | 46096.2i | −1.16859 | + | 0.0493982i | ||||
\(967\) | −641774. | − | 370528.i | −0.686324 | − | 0.396249i | 0.115910 | − | 0.993260i | \(-0.463022\pi\) |
−0.802233 | + | 0.597011i | \(0.796355\pi\) | |||||||
\(968\) | 187263. | + | 1.46962e6i | 0.199848 | + | 1.56839i | ||||
\(969\) | −345687. | − | 365329.i | −0.368159 | − | 0.389078i | ||||
\(970\) | −997822. | + | 633739.i | −1.06050 | + | 0.673545i | ||||
\(971\) | 1.51680e6 | + | 875726.i | 1.60876 | + | 0.928816i | 0.989649 | + | 0.143511i | \(0.0458391\pi\) |
0.619108 | + | 0.785306i | \(0.287494\pi\) | |||||||
\(972\) | 1.20517e6 | − | 838898.i | 1.27560 | − | 0.887926i | ||||
\(973\) | −701637. | − | 1.21527e6i | −0.741117 | − | 1.28365i | ||||
\(974\) | 1.87175e6 | − | 79122.1i | 1.97301 | − | 0.0834027i | ||||
\(975\) | −854694. | + | 493458.i | −0.899087 | + | 0.519088i | ||||
\(976\) | 851285. | + | 1.02603e6i | 0.893666 | + | 1.07711i | ||||
\(977\) | −616617. | −0.645991 | −0.322996 | − | 0.946400i | \(-0.604690\pi\) | ||||
−0.322996 | + | 0.946400i | \(0.604690\pi\) | |||||||
\(978\) | −2.45649e6 | − | 1.28310e6i | −2.56825 | − | 1.34148i | ||||
\(979\) | 1.76665e6 | − | 1.01998e6i | 1.84325 | − | 1.06420i | ||||
\(980\) | 89289.7 | − | 190104.i | 0.0929714 | − | 0.197943i | ||||
\(981\) | 101542. | 0.105513 | ||||||||
\(982\) | −355209. | + | 680045.i | −0.368350 | + | 0.705204i | ||||
\(983\) | −678866. | − | 391943.i | −0.702549 | − | 0.405617i | 0.105747 | − | 0.994393i | \(-0.466277\pi\) |
−0.808296 | + | 0.588776i | \(0.799610\pi\) | |||||||
\(984\) | −801623. | − | 1.05374e6i | −0.827904 | − | 1.08829i | ||||
\(985\) | −759535. | + | 1.31555e6i | −0.782845 | + | 1.35593i | ||||
\(986\) | −2202.52 | − | 52103.9i | −0.00226551 | − | 0.0535940i | ||||
\(987\) | − | 723445.i | − | 0.742627i | ||||||
\(988\) | 820614. | − | 919702.i | 0.840669 | − | 0.942179i | ||||
\(989\) | 171943. | 0.175789 | ||||||||
\(990\) | −4.46740e6 | + | 188845.i | −4.55811 | + | 0.192679i | ||||
\(991\) | −1.06346e6 | − | 613988.i | −1.08286 | − | 0.625191i | −0.151196 | − | 0.988504i | \(-0.548312\pi\) |
−0.931667 | + | 0.363313i | \(0.881646\pi\) | |||||||
\(992\) | 1.18906e6 | − | 254973.i | 1.20832 | − | 0.259102i | ||||
\(993\) | 181437. | − | 314258.i | 0.184004 | − | 0.318705i | ||||
\(994\) | −585745. | − | 305953.i | −0.592838 | − | 0.309657i | ||||
\(995\) | − | 2.01203e6i | − | 2.03231i | ||||||
\(996\) | 27605.5 | − | 58774.0i | 0.0278276 | − | 0.0592470i | ||||
\(997\) | −401897. | − | 696105.i | −0.404319 | − | 0.700301i | 0.589923 | − | 0.807459i | \(-0.299158\pi\) |
−0.994242 | + | 0.107159i | \(0.965825\pi\) | |||||||
\(998\) | −80475.9 | + | 154071.i | −0.0807988 | + | 0.154689i | ||||
\(999\) | 1.38041e6i | 1.38318i |
(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 | 76.5.g.a.11.21 | yes | 76 | |
4.3 | odd | 2 | inner | 76.5.g.a.11.7 | yes | 76 | |
19.7 | even | 3 | inner | 76.5.g.a.7.7 | ✓ | 76 | |
76.7 | odd | 6 | inner | 76.5.g.a.7.21 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.g.a.7.7 | ✓ | 76 | 19.7 | even | 3 | inner | |
76.5.g.a.7.21 | yes | 76 | 76.7 | odd | 6 | inner | |
76.5.g.a.11.7 | yes | 76 | 4.3 | odd | 2 | inner | |
76.5.g.a.11.21 | yes | 76 | 1.1 | even | 1 | trivial |