Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.16 | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.l.508.16 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.514418 | − | 0.890998i | 0.363748 | − | 0.630030i | −0.624826 | − | 0.780764i | \(-0.714830\pi\) |
0.988574 | + | 0.150733i | \(0.0481635\pi\) | |||||||
\(3\) | −1.33163 | − | 2.30645i | −0.768817 | − | 1.33163i | −0.938205 | − | 0.346080i | \(-0.887513\pi\) |
0.169388 | − | 0.985549i | \(-0.445821\pi\) | |||||||
\(4\) | 0.470749 | + | 0.815361i | 0.235374 | + | 0.407680i | ||||
\(5\) | −0.745563 | + | 1.29135i | −0.333426 | + | 0.577510i | −0.983181 | − | 0.182633i | \(-0.941538\pi\) |
0.649755 | + | 0.760143i | \(0.274871\pi\) | |||||||
\(6\) | −2.74006 | −1.11862 | ||||||||
\(7\) | −1.93668 | − | 1.80257i | −0.731997 | − | 0.681308i | ||||
\(8\) | 3.02632 | 1.06996 | ||||||||
\(9\) | −2.04647 | + | 3.54460i | −0.682158 | + | 1.18153i | ||||
\(10\) | 0.767061 | + | 1.32859i | 0.242566 | + | 0.420137i | ||||
\(11\) | −2.02066 | − | 3.49989i | −0.609252 | − | 1.05526i | −0.991364 | − | 0.131140i | \(-0.958136\pi\) |
0.382112 | − | 0.924116i | \(-0.375197\pi\) | |||||||
\(12\) | 1.25373 | − | 2.17152i | 0.361920 | − | 0.626863i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.60235 | + | 0.798305i | −0.695507 | + | 0.213356i | ||||
\(15\) | 3.97125 | 1.02537 | ||||||||
\(16\) | 0.615293 | − | 1.06572i | 0.153823 | − | 0.266430i | ||||
\(17\) | −1.84438 | − | 3.19455i | −0.447327 | − | 0.774793i | 0.550884 | − | 0.834582i | \(-0.314291\pi\) |
−0.998211 | + | 0.0597888i | \(0.980957\pi\) | |||||||
\(18\) | 2.10549 | + | 3.64681i | 0.496268 | + | 0.859561i | ||||
\(19\) | 2.64218 | − | 4.57640i | 0.606159 | − | 1.04990i | −0.385708 | − | 0.922621i | \(-0.626043\pi\) |
0.991867 | − | 0.127277i | \(-0.0406237\pi\) | |||||||
\(20\) | −1.40389 | −0.313920 | ||||||||
\(21\) | −1.57860 | + | 6.86722i | −0.344478 | + | 1.49855i | ||||
\(22\) | −4.15786 | −0.886458 | ||||||||
\(23\) | −3.63585 | + | 6.29747i | −0.758127 | + | 1.31311i | 0.185678 | + | 0.982611i | \(0.440552\pi\) |
−0.943805 | + | 0.330503i | \(0.892781\pi\) | |||||||
\(24\) | −4.02993 | − | 6.98005i | −0.822607 | − | 1.42480i | ||||
\(25\) | 1.38827 | + | 2.40456i | 0.277654 | + | 0.480912i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.91081 | 0.560185 | ||||||||
\(28\) | 0.558054 | − | 2.42765i | 0.105462 | − | 0.458783i | ||||
\(29\) | −7.56677 | −1.40511 | −0.702557 | − | 0.711627i | \(-0.747959\pi\) | ||||
−0.702557 | + | 0.711627i | \(0.747959\pi\) | |||||||
\(30\) | 2.04288 | − | 3.53838i | 0.372978 | − | 0.646016i | ||||
\(31\) | 0.838616 | + | 1.45253i | 0.150620 | + | 0.260881i | 0.931456 | − | 0.363855i | \(-0.118540\pi\) |
−0.780836 | + | 0.624737i | \(0.785206\pi\) | |||||||
\(32\) | 2.39328 | + | 4.14528i | 0.423076 | + | 0.732790i | ||||
\(33\) | −5.38154 | + | 9.32111i | −0.936807 | + | 1.62260i | ||||
\(34\) | −3.79512 | −0.650858 | ||||||||
\(35\) | 3.77167 | − | 1.15701i | 0.637529 | − | 0.195570i | ||||
\(36\) | −3.85350 | −0.642250 | ||||||||
\(37\) | −3.51064 | + | 6.08060i | −0.577145 | + | 0.999645i | 0.418659 | + | 0.908143i | \(0.362500\pi\) |
−0.995805 | + | 0.0915020i | \(0.970833\pi\) | |||||||
\(38\) | −2.71837 | − | 4.70836i | −0.440978 | − | 0.763797i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.25631 | + | 3.90804i | −0.356754 | + | 0.617916i | ||||
\(41\) | 0.409255 | 0.0639148 | 0.0319574 | − | 0.999489i | \(-0.489826\pi\) | ||||
0.0319574 | + | 0.999489i | \(0.489826\pi\) | |||||||
\(42\) | 5.30662 | + | 4.93914i | 0.818829 | + | 0.762126i | ||||
\(43\) | −6.43516 | −0.981353 | −0.490677 | − | 0.871342i | \(-0.663250\pi\) | ||||
−0.490677 | + | 0.871342i | \(0.663250\pi\) | |||||||
\(44\) | 1.90245 | − | 3.29514i | 0.286805 | − | 0.496760i | ||||
\(45\) | −3.05155 | − | 5.28544i | −0.454898 | − | 0.787907i | ||||
\(46\) | 3.74069 | + | 6.47906i | 0.551535 | + | 0.955286i | ||||
\(47\) | −2.56942 | + | 4.45036i | −0.374788 | + | 0.649152i | −0.990295 | − | 0.138979i | \(-0.955618\pi\) |
0.615507 | + | 0.788131i | \(0.288951\pi\) | |||||||
\(48\) | −3.27737 | −0.473048 | ||||||||
\(49\) | 0.501479 | + | 6.98201i | 0.0716398 | + | 0.997431i | ||||
\(50\) | 2.85661 | 0.403985 | ||||||||
\(51\) | −4.91205 | + | 8.50792i | −0.687825 | + | 1.19135i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.790945 | + | 1.36996i | 0.108645 | + | 0.188178i | 0.915221 | − | 0.402951i | \(-0.132016\pi\) |
−0.806577 | + | 0.591129i | \(0.798682\pi\) | |||||||
\(54\) | 1.49737 | − | 2.59352i | 0.203766 | − | 0.352934i | ||||
\(55\) | 6.02612 | 0.812562 | ||||||||
\(56\) | −5.86102 | − | 5.45515i | −0.783211 | − | 0.728975i | ||||
\(57\) | −14.0736 | −1.86410 | ||||||||
\(58\) | −3.89248 | + | 6.74198i | −0.511108 | + | 0.885265i | ||||
\(59\) | −3.82320 | − | 6.62197i | −0.497738 | − | 0.862108i | 0.502259 | − | 0.864718i | \(-0.332503\pi\) |
−0.999997 | + | 0.00260987i | \(0.999169\pi\) | |||||||
\(60\) | 1.86946 | + | 3.23800i | 0.241347 | + | 0.418025i | ||||
\(61\) | −5.64467 | + | 9.77685i | −0.722726 | + | 1.25180i | 0.237178 | + | 0.971466i | \(0.423778\pi\) |
−0.959903 | + | 0.280331i | \(0.909556\pi\) | |||||||
\(62\) | 1.72560 | 0.219151 | ||||||||
\(63\) | 10.3528 | − | 3.17585i | 1.30433 | − | 0.400119i | ||||
\(64\) | 7.38576 | 0.923220 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.53672 | + | 9.58989i | 0.681524 | + | 1.18043i | ||||
\(67\) | −6.57883 | − | 11.3949i | −0.803732 | − | 1.39210i | −0.917144 | − | 0.398557i | \(-0.869511\pi\) |
0.113412 | − | 0.993548i | \(-0.463822\pi\) | |||||||
\(68\) | 1.73648 | − | 3.00766i | 0.210579 | − | 0.364733i | ||||
\(69\) | 19.3664 | 2.33144 | ||||||||
\(70\) | 0.909322 | − | 3.95574i | 0.108685 | − | 0.472801i | ||||
\(71\) | 8.71275 | 1.03401 | 0.517007 | − | 0.855981i | \(-0.327046\pi\) | ||||
0.517007 | + | 0.855981i | \(0.327046\pi\) | |||||||
\(72\) | −6.19328 | + | 10.7271i | −0.729885 | + | 1.26420i | ||||
\(73\) | −7.59569 | − | 13.1561i | −0.889008 | − | 1.53981i | −0.841049 | − | 0.540958i | \(-0.818062\pi\) |
−0.0479588 | − | 0.998849i | \(-0.515272\pi\) | |||||||
\(74\) | 3.61187 | + | 6.25594i | 0.419871 | + | 0.727238i | ||||
\(75\) | 3.69733 | − | 6.40396i | 0.426931 | − | 0.739466i | ||||
\(76\) | 4.97522 | 0.570697 | ||||||||
\(77\) | −2.39542 | + | 10.4206i | −0.272983 | + | 1.18753i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.376918 | − | 0.652842i | 0.0424066 | − | 0.0734505i | −0.844043 | − | 0.536275i | \(-0.819831\pi\) |
0.886450 | + | 0.462825i | \(0.153164\pi\) | |||||||
\(80\) | 0.917480 | + | 1.58912i | 0.102577 | + | 0.177669i | ||||
\(81\) | 2.26331 | + | 3.92016i | 0.251479 | + | 0.435574i | ||||
\(82\) | 0.210528 | − | 0.364645i | 0.0232489 | − | 0.0402683i | ||||
\(83\) | −3.96146 | −0.434827 | −0.217413 | − | 0.976080i | \(-0.569762\pi\) | ||||
−0.217413 | + | 0.976080i | \(0.569762\pi\) | |||||||
\(84\) | −6.34238 | + | 1.94561i | −0.692011 | + | 0.212283i | ||||
\(85\) | 5.50039 | 0.596601 | ||||||||
\(86\) | −3.31036 | + | 5.73372i | −0.356966 | + | 0.618282i | ||||
\(87\) | 10.0761 | + | 17.4524i | 1.08028 | + | 1.87109i | ||||
\(88\) | −6.11516 | − | 10.5918i | −0.651878 | − | 1.12909i | ||||
\(89\) | 1.84657 | − | 3.19835i | 0.195736 | − | 0.339024i | −0.751406 | − | 0.659840i | \(-0.770624\pi\) |
0.947141 | + | 0.320816i | \(0.103957\pi\) | |||||||
\(90\) | −6.27909 | −0.661874 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.84629 | −0.713775 | ||||||||
\(93\) | 2.23345 | − | 3.86845i | 0.231598 | − | 0.401140i | ||||
\(94\) | 2.64351 | + | 4.57869i | 0.272657 | + | 0.472256i | ||||
\(95\) | 3.93983 | + | 6.82398i | 0.404218 | + | 0.700126i | ||||
\(96\) | 6.37393 | − | 11.0400i | 0.650536 | − | 1.12676i | ||||
\(97\) | 8.43912 | 0.856863 | 0.428432 | − | 0.903574i | \(-0.359066\pi\) | ||||
0.428432 | + | 0.903574i | \(0.359066\pi\) | |||||||
\(98\) | 6.47893 | + | 3.14486i | 0.654471 | + | 0.317678i | ||||
\(99\) | 16.5409 | 1.66243 | ||||||||
\(100\) | −1.30706 | + | 2.26389i | −0.130706 | + | 0.226389i | ||||
\(101\) | −4.23795 | − | 7.34035i | −0.421692 | − | 0.730392i | 0.574413 | − | 0.818566i | \(-0.305230\pi\) |
−0.996105 | + | 0.0881733i | \(0.971897\pi\) | |||||||
\(102\) | 5.05369 | + | 8.75325i | 0.500390 | + | 0.866701i | ||||
\(103\) | 7.95466 | − | 13.7779i | 0.783796 | − | 1.35757i | −0.145920 | − | 0.989296i | \(-0.546614\pi\) |
0.929716 | − | 0.368277i | \(-0.120052\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.69106 | − | 7.15847i | −0.750570 | − | 0.698595i | ||||
\(106\) | 1.62750 | 0.158077 | ||||||||
\(107\) | −3.57356 | + | 6.18958i | −0.345469 | + | 0.598369i | −0.985439 | − | 0.170031i | \(-0.945613\pi\) |
0.639970 | + | 0.768400i | \(0.278947\pi\) | |||||||
\(108\) | 1.37026 | + | 2.37336i | 0.131853 | + | 0.228376i | ||||
\(109\) | 0.556225 | + | 0.963411i | 0.0532767 | + | 0.0922780i | 0.891434 | − | 0.453151i | \(-0.149700\pi\) |
−0.838157 | + | 0.545429i | \(0.816367\pi\) | |||||||
\(110\) | 3.09994 | − | 5.36926i | 0.295568 | − | 0.511939i | ||||
\(111\) | 18.6995 | 1.77488 | ||||||||
\(112\) | −3.11266 | + | 0.954851i | −0.294119 | + | 0.0902249i | ||||
\(113\) | −13.0433 | −1.22701 | −0.613504 | − | 0.789692i | \(-0.710240\pi\) | ||||
−0.613504 | + | 0.789692i | \(0.710240\pi\) | |||||||
\(114\) | −7.23973 | + | 12.5396i | −0.678063 | + | 1.17444i | ||||
\(115\) | −5.42151 | − | 9.39032i | −0.505558 | − | 0.875652i | ||||
\(116\) | −3.56205 | − | 6.16965i | −0.330728 | − | 0.572838i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.86688 | −0.724205 | ||||||||
\(119\) | −2.18644 | + | 9.51145i | −0.200430 | + | 0.871914i | ||||
\(120\) | 12.0183 | 1.09711 | ||||||||
\(121\) | −2.66614 | + | 4.61790i | −0.242377 | + | 0.419809i | ||||
\(122\) | 5.80744 | + | 10.0588i | 0.525780 | + | 0.910678i | ||||
\(123\) | −0.544975 | − | 0.943925i | −0.0491388 | − | 0.0851109i | ||||
\(124\) | −0.789555 | + | 1.36755i | −0.0709041 | + | 0.122810i | ||||
\(125\) | −11.5958 | −1.03716 | ||||||||
\(126\) | 2.49597 | − | 10.8580i | 0.222359 | − | 0.967307i | ||||
\(127\) | 11.4482 | 1.01587 | 0.507933 | − | 0.861396i | \(-0.330410\pi\) | ||||
0.507933 | + | 0.861396i | \(0.330410\pi\) | |||||||
\(128\) | −0.987197 | + | 1.70988i | −0.0872567 | + | 0.151133i | ||||
\(129\) | 8.56925 | + | 14.8424i | 0.754481 | + | 1.30680i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.894228 | + | 1.54885i | −0.0781290 | + | 0.135323i | −0.902443 | − | 0.430810i | \(-0.858228\pi\) |
0.824314 | + | 0.566133i | \(0.191561\pi\) | |||||||
\(132\) | −10.1334 | −0.882001 | ||||||||
\(133\) | −13.3664 | + | 4.10031i | −1.15901 | + | 0.355542i | ||||
\(134\) | −13.5371 | −1.16942 | ||||||||
\(135\) | −2.17019 | + | 3.75888i | −0.186780 | + | 0.323513i | ||||
\(136\) | −5.58167 | − | 9.66773i | −0.478624 | − | 0.829001i | ||||
\(137\) | −3.17735 | − | 5.50333i | −0.271459 | − | 0.470181i | 0.697776 | − | 0.716316i | \(-0.254173\pi\) |
−0.969236 | + | 0.246134i | \(0.920840\pi\) | |||||||
\(138\) | 9.96243 | − | 17.2554i | 0.848058 | − | 1.46888i | ||||
\(139\) | 10.6138 | 0.900250 | 0.450125 | − | 0.892966i | \(-0.351380\pi\) | ||||
0.450125 | + | 0.892966i | \(0.351380\pi\) | |||||||
\(140\) | 2.71889 | + | 2.53061i | 0.229788 | + | 0.213876i | ||||
\(141\) | 13.6861 | 1.15257 | ||||||||
\(142\) | 4.48199 | − | 7.76304i | 0.376121 | − | 0.651460i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.51836 | + | 4.36194i | 0.209864 | + | 0.363495i | ||||
\(145\) | 5.64150 | − | 9.77137i | 0.468501 | − | 0.811468i | ||||
\(146\) | −15.6294 | −1.29350 | ||||||||
\(147\) | 15.4359 | − | 10.4541i | 1.27313 | − | 0.862239i | ||||
\(148\) | −6.61052 | −0.543381 | ||||||||
\(149\) | −2.40270 | + | 4.16160i | −0.196837 | + | 0.340931i | −0.947501 | − | 0.319752i | \(-0.896400\pi\) |
0.750664 | + | 0.660684i | \(0.229734\pi\) | |||||||
\(150\) | −3.80394 | − | 6.58862i | −0.310591 | − | 0.537959i | ||||
\(151\) | −2.06539 | − | 3.57735i | −0.168079 | − | 0.291121i | 0.769666 | − | 0.638447i | \(-0.220423\pi\) |
−0.937744 | + | 0.347326i | \(0.887090\pi\) | |||||||
\(152\) | 7.99609 | − | 13.8496i | 0.648568 | − | 1.12335i | ||||
\(153\) | 15.0979 | 1.22059 | ||||||||
\(154\) | 8.05245 | + | 7.49483i | 0.648885 | + | 0.603950i | ||||
\(155\) | −2.50096 | −0.200882 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.97959 | − | 5.16081i | −0.237797 | − | 0.411877i | 0.722285 | − | 0.691596i | \(-0.243092\pi\) |
−0.960082 | + | 0.279719i | \(0.909759\pi\) | |||||||
\(158\) | −0.387787 | − | 0.671667i | −0.0308507 | − | 0.0534349i | ||||
\(159\) | 2.10649 | − | 3.64855i | 0.167056 | − | 0.289349i | ||||
\(160\) | −7.13737 | −0.564258 | ||||||||
\(161\) | 18.3931 | − | 5.64234i | 1.44958 | − | 0.444678i | ||||
\(162\) | 4.65714 | 0.365900 | ||||||||
\(163\) | 4.43410 | − | 7.68008i | 0.347305 | − | 0.601551i | −0.638464 | − | 0.769651i | \(-0.720430\pi\) |
0.985770 | + | 0.168101i | \(0.0537634\pi\) | |||||||
\(164\) | 0.192656 | + | 0.333690i | 0.0150439 | + | 0.0260568i | ||||
\(165\) | −8.02456 | − | 13.8989i | −0.624711 | − | 1.08203i | ||||
\(166\) | −2.03785 | + | 3.52965i | −0.158167 | + | 0.273954i | ||||
\(167\) | −11.9219 | −0.922547 | −0.461274 | − | 0.887258i | \(-0.652607\pi\) | ||||
−0.461274 | + | 0.887258i | \(0.652607\pi\) | |||||||
\(168\) | −4.77733 | + | 20.7824i | −0.368579 | + | 1.60340i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.82950 | − | 4.90084i | 0.217013 | − | 0.375877i | ||||
\(171\) | 10.8143 | + | 18.7310i | 0.826992 | + | 1.43239i | ||||
\(172\) | −3.02935 | − | 5.24698i | −0.230985 | − | 0.400079i | ||||
\(173\) | 4.41559 | − | 7.64803i | 0.335711 | − | 0.581469i | −0.647910 | − | 0.761717i | \(-0.724357\pi\) |
0.983621 | + | 0.180248i | \(0.0576900\pi\) | |||||||
\(174\) | 20.7334 | 1.57179 | ||||||||
\(175\) | 1.64574 | − | 7.15932i | 0.124406 | − | 0.541194i | ||||
\(176\) | −4.97320 | −0.374869 | ||||||||
\(177\) | −10.1822 | + | 17.6360i | −0.765339 | + | 1.32561i | ||||
\(178\) | −1.89981 | − | 3.29057i | −0.142397 | − | 0.246639i | ||||
\(179\) | 9.05271 | + | 15.6798i | 0.676632 | + | 1.17196i | 0.975989 | + | 0.217819i | \(0.0698943\pi\) |
−0.299358 | + | 0.954141i | \(0.596772\pi\) | |||||||
\(180\) | 2.87303 | − | 4.97623i | 0.214143 | − | 0.370906i | ||||
\(181\) | −21.3354 | −1.58585 | −0.792923 | − | 0.609322i | \(-0.791442\pi\) | ||||
−0.792923 | + | 0.609322i | \(0.791442\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.0664 | 2.22257 | ||||||||
\(184\) | −11.0032 | + | 19.0582i | −0.811169 | + | 1.40499i | ||||
\(185\) | −5.23480 | − | 9.06695i | −0.384870 | − | 0.666615i | ||||
\(186\) | −2.29785 | − | 3.98000i | −0.168487 | − | 0.291828i | ||||
\(187\) | −7.45372 | + | 12.9102i | −0.545070 | + | 0.944089i | ||||
\(188\) | −4.83820 | −0.352862 | ||||||||
\(189\) | −5.63731 | − | 5.24693i | −0.410054 | − | 0.381658i | ||||
\(190\) | 8.10687 | 0.588134 | ||||||||
\(191\) | 8.11444 | − | 14.0546i | 0.587140 | − | 1.01696i | −0.407465 | − | 0.913221i | \(-0.633587\pi\) |
0.994605 | − | 0.103736i | \(-0.0330797\pi\) | |||||||
\(192\) | −9.83510 | − | 17.0349i | −0.709787 | − | 1.22939i | ||||
\(193\) | −1.02587 | − | 1.77685i | −0.0738434 | − | 0.127901i | 0.826739 | − | 0.562585i | \(-0.190193\pi\) |
−0.900583 | + | 0.434685i | \(0.856860\pi\) | |||||||
\(194\) | 4.34123 | − | 7.51924i | 0.311682 | − | 0.539850i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.45679 | + | 3.69566i | −0.389771 | + | 0.263976i | ||||
\(197\) | 2.49922 | 0.178062 | 0.0890309 | − | 0.996029i | \(-0.471623\pi\) | ||||
0.0890309 | + | 0.996029i | \(0.471623\pi\) | |||||||
\(198\) | 8.50895 | − | 14.7379i | 0.604704 | − | 1.04738i | ||||
\(199\) | 7.87329 | + | 13.6369i | 0.558123 | + | 0.966697i | 0.997653 | + | 0.0684695i | \(0.0218116\pi\) |
−0.439530 | + | 0.898228i | \(0.644855\pi\) | |||||||
\(200\) | 4.20135 | + | 7.27696i | 0.297080 | + | 0.514558i | ||||
\(201\) | −17.5211 | + | 30.3475i | −1.23585 | + | 2.14055i | ||||
\(202\) | −8.72032 | −0.613559 | ||||||||
\(203\) | 14.6544 | + | 13.6396i | 1.02854 | + | 0.957315i | ||||
\(204\) | −9.24937 | −0.647585 | ||||||||
\(205\) | −0.305125 | + | 0.528492i | −0.0213109 | + | 0.0369115i | ||||
\(206\) | −8.18403 | − | 14.1752i | −0.570209 | − | 0.987630i | ||||
\(207\) | −14.8813 | − | 25.7752i | −1.03432 | − | 1.79150i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.3558 | −1.47721 | ||||||||
\(210\) | −10.3346 | + | 3.17027i | −0.713155 | + | 0.218770i | ||||
\(211\) | 7.75205 | 0.533673 | 0.266837 | − | 0.963742i | \(-0.414022\pi\) | ||||
0.266837 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(212\) | −0.744673 | + | 1.28981i | −0.0511443 | + | 0.0885846i | ||||
\(213\) | −11.6022 | − | 20.0955i | −0.794967 | − | 1.37692i | ||||
\(214\) | 3.67660 | + | 6.36806i | 0.251327 | + | 0.435312i | ||||
\(215\) | 4.79782 | − | 8.31006i | 0.327208 | − | 0.566742i | ||||
\(216\) | 8.80902 | 0.599378 | ||||||||
\(217\) | 0.994147 | − | 4.32475i | 0.0674871 | − | 0.293583i | ||||
\(218\) | 1.14453 | 0.0775173 | ||||||||
\(219\) | −20.2293 | + | 35.0382i | −1.36697 | + | 2.36766i | ||||
\(220\) | 2.83679 | + | 4.91346i | 0.191256 | + | 0.331266i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.61934 | − | 16.6612i | 0.645608 | − | 1.11823i | ||||
\(223\) | −4.75374 | −0.318334 | −0.159167 | − | 0.987252i | \(-0.550881\pi\) | ||||
−0.159167 | + | 0.987252i | \(0.550881\pi\) | |||||||
\(224\) | 2.83714 | − | 12.3422i | 0.189565 | − | 0.824645i | ||||
\(225\) | −11.3643 | −0.757617 | ||||||||
\(226\) | −6.70969 | + | 11.6215i | −0.446322 | + | 0.773052i | ||||
\(227\) | −6.29498 | − | 10.9032i | −0.417813 | − | 0.723673i | 0.577906 | − | 0.816103i | \(-0.303870\pi\) |
−0.995719 | + | 0.0924301i | \(0.970537\pi\) | |||||||
\(228\) | −6.62515 | − | 11.4751i | −0.438761 | − | 0.759957i | ||||
\(229\) | 2.62874 | − | 4.55311i | 0.173712 | − | 0.300878i | −0.766003 | − | 0.642837i | \(-0.777757\pi\) |
0.939715 | + | 0.341959i | \(0.111090\pi\) | |||||||
\(230\) | −11.1557 | −0.735583 | ||||||||
\(231\) | 27.2243 | − | 8.35141i | 1.79123 | − | 0.549483i | ||||
\(232\) | −22.8995 | −1.50342 | ||||||||
\(233\) | 4.22816 | − | 7.32340i | 0.276996 | − | 0.479772i | −0.693641 | − | 0.720321i | \(-0.743994\pi\) |
0.970637 | + | 0.240550i | \(0.0773277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.83133 | − | 6.63605i | −0.249928 | − | 0.432888i | ||||
\(236\) | 3.59953 | − | 6.23457i | 0.234310 | − | 0.405836i | ||||
\(237\) | −2.00766 | −0.130412 | ||||||||
\(238\) | 7.34994 | + | 6.84097i | 0.476426 | + | 0.443434i | ||||
\(239\) | −6.55677 | −0.424122 | −0.212061 | − | 0.977256i | \(-0.568018\pi\) | ||||
−0.212061 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(240\) | 2.44349 | − | 4.23224i | 0.157726 | − | 0.273190i | ||||
\(241\) | −5.79652 | − | 10.0399i | −0.373387 | − | 0.646725i | 0.616698 | − | 0.787200i | \(-0.288470\pi\) |
−0.990084 | + | 0.140476i | \(0.955137\pi\) | |||||||
\(242\) | 2.74302 | + | 4.75106i | 0.176328 | + | 0.305409i | ||||
\(243\) | 10.3940 | − | 18.0029i | 0.666774 | − | 1.15489i | ||||
\(244\) | −10.6289 | −0.680445 | ||||||||
\(245\) | −9.39013 | − | 4.55794i | −0.599913 | − | 0.291196i | ||||
\(246\) | −1.12138 | −0.0714966 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.53792 | + | 4.39580i | 0.161158 | + | 0.279134i | ||||
\(249\) | 5.27520 | + | 9.13691i | 0.334302 | + | 0.579028i | ||||
\(250\) | −5.96509 | + | 10.3318i | −0.377265 | + | 0.653443i | ||||
\(251\) | −19.3214 | −1.21956 | −0.609778 | − | 0.792572i | \(-0.708741\pi\) | ||||
−0.609778 | + | 0.792572i | \(0.708741\pi\) | |||||||
\(252\) | 7.46301 | + | 6.94621i | 0.470125 | + | 0.437570i | ||||
\(253\) | 29.3873 | 1.84756 | ||||||||
\(254\) | 5.88918 | − | 10.2004i | 0.369520 | − | 0.640027i | ||||
\(255\) | −7.32449 | − | 12.6864i | −0.458677 | − | 0.794452i | ||||
\(256\) | 8.40142 | + | 14.5517i | 0.525089 | + | 0.909481i | ||||
\(257\) | 8.65652 | − | 14.9935i | 0.539979 | − | 0.935271i | −0.458925 | − | 0.888475i | \(-0.651765\pi\) |
0.998904 | − | 0.0467965i | \(-0.0149012\pi\) | |||||||
\(258\) | 17.6327 | 1.09776 | ||||||||
\(259\) | 17.7597 | − | 5.44803i | 1.10353 | − | 0.338524i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.4852 | − | 26.8212i | 0.958510 | − | 1.66019i | ||||
\(262\) | 0.920013 | + | 1.59351i | 0.0568386 | + | 0.0984473i | ||||
\(263\) | −12.6968 | − | 21.9916i | −0.782921 | − | 1.35606i | −0.930233 | − | 0.366969i | \(-0.880395\pi\) |
0.147312 | − | 0.989090i | \(-0.452938\pi\) | |||||||
\(264\) | −16.2863 | + | 28.2086i | −1.00235 | + | 1.73612i | ||||
\(265\) | −2.35880 | −0.144900 | ||||||||
\(266\) | −3.22253 | + | 14.0187i | −0.197586 | + | 0.859539i | ||||
\(267\) | −9.83577 | −0.601939 | ||||||||
\(268\) | 6.19395 | − | 10.7282i | 0.378356 | − | 0.655332i | ||||
\(269\) | −5.84420 | − | 10.1225i | −0.356327 | − | 0.617177i | 0.631017 | − | 0.775769i | \(-0.282638\pi\) |
−0.987344 | + | 0.158592i | \(0.949305\pi\) | |||||||
\(270\) | 2.23277 | + | 3.86727i | 0.135882 | + | 0.235354i | ||||
\(271\) | −1.70695 | + | 2.95653i | −0.103690 | + | 0.179596i | −0.913202 | − | 0.407507i | \(-0.866398\pi\) |
0.809512 | + | 0.587103i | \(0.199732\pi\) | |||||||
\(272\) | −4.53933 | −0.275237 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.53794 | −0.394971 | ||||||||
\(275\) | 5.61046 | − | 9.71759i | 0.338323 | − | 0.585993i | ||||
\(276\) | 9.11672 | + | 15.7906i | 0.548762 | + | 0.950483i | ||||
\(277\) | −0.957821 | − | 1.65899i | −0.0575499 | − | 0.0996793i | 0.835815 | − | 0.549011i | \(-0.184995\pi\) |
−0.893365 | + | 0.449332i | \(0.851662\pi\) | |||||||
\(278\) | 5.45992 | − | 9.45686i | 0.327464 | − | 0.567185i | ||||
\(279\) | −6.86483 | −0.410986 | ||||||||
\(280\) | 11.4143 | − | 3.50148i | 0.682134 | − | 0.209254i | ||||
\(281\) | −14.8090 | −0.883432 | −0.441716 | − | 0.897155i | \(-0.645630\pi\) | ||||
−0.441716 | + | 0.897155i | \(0.645630\pi\) | |||||||
\(282\) | 7.04035 | − | 12.1942i | 0.419247 | − | 0.726157i | ||||
\(283\) | −16.7797 | − | 29.0633i | −0.997449 | − | 1.72763i | −0.560548 | − | 0.828122i | \(-0.689409\pi\) |
−0.436901 | − | 0.899510i | \(-0.643924\pi\) | |||||||
\(284\) | 4.10152 | + | 7.10404i | 0.243380 | + | 0.421547i | ||||
\(285\) | 10.4928 | − | 18.1740i | 0.621539 | − | 1.07654i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.792596 | − | 0.737710i | −0.0467855 | − | 0.0435457i | ||||
\(288\) | −19.5912 | −1.15442 | ||||||||
\(289\) | 1.69655 | − | 2.93852i | 0.0997972 | − | 0.172854i | ||||
\(290\) | −5.80418 | − | 10.0531i | −0.340833 | − | 0.590340i | ||||
\(291\) | −11.2378 | − | 19.4644i | −0.658771 | − | 1.14102i | ||||
\(292\) | 7.15132 | − | 12.3865i | 0.418500 | − | 0.724863i | ||||
\(293\) | 5.03064 | 0.293893 | 0.146946 | − | 0.989144i | \(-0.453056\pi\) | ||||
0.146946 | + | 0.989144i | \(0.453056\pi\) | |||||||
\(294\) | −1.37408 | − | 19.1311i | −0.0801380 | − | 1.11575i | ||||
\(295\) | 11.4017 | 0.663835 | ||||||||
\(296\) | −10.6243 | + | 18.4018i | −0.617525 | + | 1.06959i | ||||
\(297\) | −5.88175 | − | 10.1875i | −0.341294 | − | 0.591139i | ||||
\(298\) | 2.47198 | + | 4.28160i | 0.143198 | + | 0.248026i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.96205 | 0.401954 | ||||||||
\(301\) | 12.4629 | + | 11.5998i | 0.718348 | + | 0.668603i | ||||
\(302\) | −4.24989 | −0.244553 | ||||||||
\(303\) | −11.2868 | + | 19.5493i | −0.648408 | + | 1.12308i | ||||
\(304\) | −3.25144 | − | 5.63166i | −0.186483 | − | 0.322998i | ||||
\(305\) | −8.41691 | − | 14.5785i | −0.481951 | − | 0.834763i | ||||
\(306\) | 7.76661 | − | 13.4522i | 0.443988 | − | 0.769009i | ||||
\(307\) | 14.1518 | 0.807688 | 0.403844 | − | 0.914828i | \(-0.367674\pi\) | ||||
0.403844 | + | 0.914828i | \(0.367674\pi\) | |||||||
\(308\) | −9.62415 | + | 2.95234i | −0.548387 | + | 0.168225i | ||||
\(309\) | −42.3706 | −2.41038 | ||||||||
\(310\) | −1.28654 | + | 2.22835i | −0.0730706 | + | 0.126562i | ||||
\(311\) | 4.34767 | + | 7.53038i | 0.246534 | + | 0.427009i | 0.962562 | − | 0.271063i | \(-0.0873751\pi\) |
−0.716028 | + | 0.698072i | \(0.754042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.4388 | + | 18.0806i | −0.590038 | + | 1.02198i | 0.404188 | + | 0.914676i | \(0.367554\pi\) |
−0.994227 | + | 0.107300i | \(0.965779\pi\) | |||||||
\(314\) | −6.13102 | −0.345994 | ||||||||
\(315\) | −3.61749 | + | 15.7369i | −0.203823 | + | 0.886671i | ||||
\(316\) | 0.709736 | 0.0399258 | ||||||||
\(317\) | −8.74509 | + | 15.1469i | −0.491173 | + | 0.850737i | −0.999948 | − | 0.0101626i | \(-0.996765\pi\) |
0.508775 | + | 0.860899i | \(0.330098\pi\) | |||||||
\(318\) | −2.16723 | − | 3.75376i | −0.121532 | − | 0.210500i | ||||
\(319\) | 15.2899 | + | 26.4829i | 0.856069 | + | 1.48276i | ||||
\(320\) | −5.50655 | + | 9.53762i | −0.307825 | + | 0.533169i | ||||
\(321\) | 19.0346 | 1.06241 | ||||||||
\(322\) | 4.43444 | − | 19.2907i | 0.247122 | − | 1.07503i | ||||
\(323\) | −19.4927 | −1.08460 | ||||||||
\(324\) | −2.13090 | + | 3.69082i | −0.118383 | + | 0.205046i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.56196 | − | 7.90154i | −0.252663 | − | 0.437626i | ||||
\(327\) | 1.48137 | − | 2.56581i | 0.0819201 | − | 0.141890i | ||||
\(328\) | 1.23853 | 0.0683866 | ||||||||
\(329\) | 12.9982 | − | 3.98738i | 0.716616 | − | 0.219832i | ||||
\(330\) | −16.5119 | −0.908950 | ||||||||
\(331\) | −2.28944 | + | 3.96542i | −0.125839 | + | 0.217959i | −0.922061 | − | 0.387046i | \(-0.873496\pi\) |
0.796222 | + | 0.605005i | \(0.206829\pi\) | |||||||
\(332\) | −1.86485 | − | 3.23002i | −0.102347 | − | 0.177270i | ||||
\(333\) | −14.3689 | − | 24.8876i | −0.787409 | − | 1.36383i | ||||
\(334\) | −6.13286 | + | 10.6224i | −0.335575 | + | 0.581233i | ||||
\(335\) | 19.6197 | 1.07194 | ||||||||
\(336\) | 6.34723 | + | 5.90769i | 0.346270 | + | 0.322291i | ||||
\(337\) | 23.5671 | 1.28378 | 0.641891 | − | 0.766796i | \(-0.278150\pi\) | ||||
0.641891 | + | 0.766796i | \(0.278150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3688 | + | 30.0836i | 0.943344 | + | 1.63392i | ||||
\(340\) | 2.58930 | + | 4.48481i | 0.140425 | + | 0.243223i | ||||
\(341\) | 3.38912 | − | 5.87013i | 0.183531 | − | 0.317885i | ||||
\(342\) | 22.2523 | 1.20327 | ||||||||
\(343\) | 11.6144 | − | 14.4259i | 0.627117 | − | 0.778925i | ||||
\(344\) | −19.4748 | −1.05001 | ||||||||
\(345\) | −14.4389 | + | 25.0089i | −0.777363 | + | 1.34643i | ||||
\(346\) | −4.54292 | − | 7.86857i | −0.244229 | − | 0.423017i | ||||
\(347\) | −13.4942 | − | 23.3727i | −0.724408 | − | 1.25471i | −0.959217 | − | 0.282669i | \(-0.908780\pi\) |
0.234810 | − | 0.972041i | \(-0.424553\pi\) | |||||||
\(348\) | −9.48666 | + | 16.4314i | −0.508538 | + | 0.880814i | ||||
\(349\) | 24.7255 | 1.32352 | 0.661762 | − | 0.749714i | \(-0.269809\pi\) | ||||
0.661762 | + | 0.749714i | \(0.269809\pi\) | |||||||
\(350\) | −5.53234 | − | 5.14924i | −0.295716 | − | 0.275238i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.67202 | − | 16.7524i | 0.515520 | − | 0.892908i | ||||
\(353\) | −0.722951 | − | 1.25219i | −0.0384788 | − | 0.0666473i | 0.846145 | − | 0.532953i | \(-0.178918\pi\) |
−0.884623 | + | 0.466306i | \(0.845585\pi\) | |||||||
\(354\) | 10.4758 | + | 18.1446i | 0.556781 | + | 0.964373i | ||||
\(355\) | −6.49590 | + | 11.2512i | −0.344767 | + | 0.597154i | ||||
\(356\) | 3.47708 | 0.184285 | ||||||||
\(357\) | 24.8492 | − | 7.62283i | 1.31516 | − | 0.403443i | ||||
\(358\) | 18.6275 | 0.984494 | ||||||||
\(359\) | 8.27465 | − | 14.3321i | 0.436719 | − | 0.756420i | −0.560715 | − | 0.828009i | \(-0.689474\pi\) |
0.997434 | + | 0.0715889i | \(0.0228070\pi\) | |||||||
\(360\) | −9.23496 | − | 15.9954i | −0.486725 | − | 0.843033i | ||||
\(361\) | −4.46228 | − | 7.72890i | −0.234857 | − | 0.406784i | ||||
\(362\) | −10.9753 | + | 19.0098i | −0.576848 | + | 0.999131i | ||||
\(363\) | 14.2013 | 0.745373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.6523 | 1.18567 | ||||||||
\(366\) | 15.4667 | − | 26.7891i | 0.808458 | − | 1.40029i | ||||
\(367\) | 16.3799 | + | 28.3708i | 0.855023 | + | 1.48094i | 0.876624 | + | 0.481176i | \(0.159790\pi\) |
−0.0216008 | + | 0.999767i | \(0.506876\pi\) | |||||||
\(368\) | 4.47423 | + | 7.74959i | 0.233235 | + | 0.403975i | ||||
\(369\) | −0.837529 | + | 1.45064i | −0.0436000 | + | 0.0755175i | ||||
\(370\) | −10.7715 | −0.559984 | ||||||||
\(371\) | 0.937635 | − | 4.07891i | 0.0486796 | − | 0.211766i | ||||
\(372\) | 4.20558 | 0.218049 | ||||||||
\(373\) | −8.01284 | + | 13.8786i | −0.414889 | + | 0.718609i | −0.995417 | − | 0.0956314i | \(-0.969513\pi\) |
0.580528 | + | 0.814241i | \(0.302846\pi\) | |||||||
\(374\) | 7.66865 | + | 13.2825i | 0.396536 | + | 0.686821i | ||||
\(375\) | 15.4413 | + | 26.7451i | 0.797386 | + | 1.38111i | ||||
\(376\) | −7.77588 | + | 13.4682i | −0.401010 | + | 0.694570i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7.57494 | + | 2.32371i | −0.389613 | + | 0.119519i | ||||
\(379\) | 4.97761 | 0.255682 | 0.127841 | − | 0.991795i | \(-0.459195\pi\) | ||||
0.127841 | + | 0.991795i | \(0.459195\pi\) | |||||||
\(380\) | −3.70934 | + | 6.42477i | −0.190285 | + | 0.329584i | ||||
\(381\) | −15.2448 | − | 26.4048i | −0.781015 | − | 1.35276i | ||||
\(382\) | −8.34842 | − | 14.4599i | −0.427143 | − | 0.739833i | ||||
\(383\) | −11.1258 | + | 19.2704i | −0.568501 | + | 0.984672i | 0.428214 | + | 0.903677i | \(0.359143\pi\) |
−0.996715 | + | 0.0809945i | \(0.974190\pi\) | |||||||
\(384\) | 5.25832 | 0.268338 | ||||||||
\(385\) | −11.6707 | − | 10.8625i | −0.594793 | − | 0.553605i | ||||
\(386\) | −2.11089 | −0.107442 | ||||||||
\(387\) | 13.1694 | − | 22.8101i | 0.669438 | − | 1.15950i | ||||
\(388\) | 3.97271 | + | 6.88093i | 0.201684 | + | 0.349326i | ||||
\(389\) | −0.509272 | − | 0.882086i | −0.0258211 | − | 0.0447235i | 0.852826 | − | 0.522195i | \(-0.174887\pi\) |
−0.878647 | + | 0.477472i | \(0.841553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.8235 | 1.35652 | ||||||||
\(392\) | 1.51763 | + | 21.1298i | 0.0766521 | + | 1.06722i | ||||
\(393\) | 4.76312 | 0.240268 | ||||||||
\(394\) | 1.28564 | − | 2.22680i | 0.0647697 | − | 0.112184i | ||||
\(395\) | 0.562033 | + | 0.973469i | 0.0282789 | + | 0.0489806i | ||||
\(396\) | 7.78662 | + | 13.4868i | 0.391292 | + | 0.677738i | ||||
\(397\) | −10.7037 | + | 18.5394i | −0.537205 | + | 0.930467i | 0.461848 | + | 0.886959i | \(0.347187\pi\) |
−0.999053 | + | 0.0435075i | \(0.986147\pi\) | |||||||
\(398\) | 16.2006 | 0.812065 | ||||||||
\(399\) | 27.2562 | + | 25.3687i | 1.36452 | + | 1.27003i | ||||
\(400\) | 3.41678 | 0.170839 | ||||||||
\(401\) | −0.802610 | + | 1.39016i | −0.0400804 | + | 0.0694214i | −0.885370 | − | 0.464888i | \(-0.846095\pi\) |
0.845289 | + | 0.534309i | \(0.179428\pi\) | |||||||
\(402\) | 18.0264 | + | 31.2226i | 0.899073 | + | 1.55724i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.99002 | − | 6.91093i | 0.198511 | − | 0.343831i | ||||
\(405\) | −6.74975 | −0.335398 | ||||||||
\(406\) | 19.6914 | − | 6.04060i | 0.977267 | − | 0.299790i | ||||
\(407\) | 28.3752 | 1.40651 | ||||||||
\(408\) | −14.8654 | + | 25.7477i | −0.735948 | + | 1.27470i | ||||
\(409\) | 17.8585 | + | 30.9319i | 0.883047 | + | 1.52948i | 0.847936 | + | 0.530099i | \(0.177845\pi\) |
0.0351113 | + | 0.999383i | \(0.488821\pi\) | |||||||
\(410\) | 0.313923 | + | 0.543731i | 0.0155036 | + | 0.0268530i | ||||
\(411\) | −8.46211 | + | 14.6568i | −0.417405 | + | 0.722966i | ||||
\(412\) | 14.9786 | 0.737942 | ||||||||
\(413\) | −4.53225 | + | 19.7162i | −0.223018 | + | 0.970173i | ||||
\(414\) | −30.6209 | −1.50494 | ||||||||
\(415\) | 2.95352 | − | 5.11564i | 0.144982 | − | 0.251117i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.1336 | − | 24.4802i | −0.692127 | − | 1.19880i | ||||
\(418\) | −10.9858 | + | 19.0280i | −0.537334 | + | 0.930690i | ||||
\(419\) | 12.3317 | 0.602443 | 0.301221 | − | 0.953554i | \(-0.402606\pi\) | ||||
0.301221 | + | 0.953554i | \(0.402606\pi\) | |||||||
\(420\) | 2.21618 | − | 9.64083i | 0.108138 | − | 0.470424i | ||||
\(421\) | 12.8739 | 0.627436 | 0.313718 | − | 0.949516i | \(-0.398425\pi\) | ||||
0.313718 | + | 0.949516i | \(0.398425\pi\) | |||||||
\(422\) | 3.98779 | − | 6.90706i | 0.194123 | − | 0.336230i | ||||
\(423\) | −10.5165 | − | 18.2151i | −0.511330 | − | 0.885649i | ||||
\(424\) | 2.39365 | + | 4.14592i | 0.116246 | + | 0.201344i | ||||
\(425\) | 5.12099 | − | 8.86982i | 0.248405 | − | 0.430249i | ||||
\(426\) | −23.8734 | −1.15667 | ||||||||
\(427\) | 28.5554 | − | 8.75975i | 1.38189 | − | 0.423914i | ||||
\(428\) | −6.72899 | −0.325258 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.93617 | − | 8.54969i | −0.238043 | − | 0.412303i | ||||
\(431\) | 8.31088 | + | 14.3949i | 0.400321 | + | 0.693376i | 0.993765 | − | 0.111499i | \(-0.0355653\pi\) |
−0.593444 | + | 0.804876i | \(0.702232\pi\) | |||||||
\(432\) | 1.79100 | − | 3.10210i | 0.0861695 | − | 0.149250i | ||||
\(433\) | 7.34167 | 0.352818 | 0.176409 | − | 0.984317i | \(-0.443552\pi\) | ||||
0.176409 | + | 0.984317i | \(0.443552\pi\) | |||||||
\(434\) | −3.34193 | − | 3.11051i | −0.160418 | − | 0.149309i | ||||
\(435\) | −30.0496 | −1.44077 | ||||||||
\(436\) | −0.523685 | + | 0.907049i | −0.0250800 | + | 0.0434398i | ||||
\(437\) | 19.2132 | + | 33.2782i | 0.919090 | + | 1.59191i | ||||
\(438\) | 20.8126 | + | 36.0485i | 0.994465 | + | 1.72246i | ||||
\(439\) | 0.855908 | − | 1.48248i | 0.0408503 | − | 0.0707547i | −0.844877 | − | 0.534960i | \(-0.820327\pi\) |
0.885728 | + | 0.464205i | \(0.153660\pi\) | |||||||
\(440\) | 18.2369 | 0.869412 | ||||||||
\(441\) | −25.7747 | − | 12.5110i | −1.22737 | − | 0.595761i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.60251 | + | 6.23972i | −0.171160 | + | 0.296458i | −0.938826 | − | 0.344392i | \(-0.888085\pi\) |
0.767666 | + | 0.640851i | \(0.221418\pi\) | |||||||
\(444\) | 8.80276 | + | 15.2468i | 0.417760 | + | 0.723582i | ||||
\(445\) | 2.75346 | + | 4.76914i | 0.130527 | + | 0.226079i | ||||
\(446\) | −2.44541 | + | 4.23557i | −0.115793 | + | 0.200560i | ||||
\(447\) | 12.7980 | 0.605326 | ||||||||
\(448\) | −14.3039 | − | 13.3134i | −0.675794 | − | 0.628997i | ||||
\(449\) | −7.17254 | −0.338493 | −0.169247 | − | 0.985574i | \(-0.554133\pi\) | ||||
−0.169247 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(450\) | −5.84597 | + | 10.1255i | −0.275582 | + | 0.477322i | ||||
\(451\) | −0.826965 | − | 1.43235i | −0.0389403 | − | 0.0674465i | ||||
\(452\) | −6.14010 | − | 10.6350i | −0.288806 | − | 0.500227i | ||||
\(453\) | −5.50066 | + | 9.52742i | −0.258444 | + | 0.447637i | ||||
\(454\) | −12.9530 | −0.607915 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −42.5913 | −1.99452 | ||||||||
\(457\) | 18.0487 | − | 31.2612i | 0.844282 | − | 1.46234i | −0.0419612 | − | 0.999119i | \(-0.513361\pi\) |
0.886243 | − | 0.463220i | \(-0.153306\pi\) | |||||||
\(458\) | −2.70454 | − | 4.68440i | −0.126375 | − | 0.218888i | ||||
\(459\) | −5.36862 | − | 9.29873i | −0.250586 | − | 0.434027i | ||||
\(460\) | 5.10434 | − | 8.84097i | 0.237991 | − | 0.412212i | ||||
\(461\) | 21.0255 | 0.979257 | 0.489628 | − | 0.871931i | \(-0.337132\pi\) | ||||
0.489628 | + | 0.871931i | \(0.337132\pi\) | |||||||
\(462\) | 6.56357 | − | 28.5529i | 0.305365 | − | 1.32840i | ||||
\(463\) | −25.7348 | −1.19600 | −0.597999 | − | 0.801497i | \(-0.704037\pi\) | ||||
−0.597999 | + | 0.801497i | \(0.704037\pi\) | |||||||
\(464\) | −4.65579 | + | 8.06406i | −0.216139 | + | 0.374365i | ||||
\(465\) | 3.33036 | + | 5.76835i | 0.154442 | + | 0.267501i | ||||
\(466\) | −4.35009 | − | 7.53457i | −0.201514 | − | 0.349032i | ||||
\(467\) | −13.3702 | + | 23.1578i | −0.618697 | + | 1.07162i | 0.371026 | + | 0.928622i | \(0.379006\pi\) |
−0.989724 | + | 0.142993i | \(0.954327\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.79895 | + | 33.9270i | −0.360122 | + | 1.56661i | ||||
\(470\) | −7.88361 | −0.363644 | ||||||||
\(471\) | −7.93543 | + | 13.7446i | −0.365645 | + | 0.633316i | ||||
\(472\) | −11.5702 | − | 20.0402i | −0.532562 | − | 0.922425i | ||||
\(473\) | 13.0033 | + | 22.5224i | 0.597892 | + | 1.03558i | ||||
\(474\) | −1.03278 | + | 1.78882i | −0.0474370 | + | 0.0821634i | ||||
\(475\) | 14.6723 | 0.673211 | ||||||||
\(476\) | −8.78453 | + | 2.69477i | −0.402638 | + | 0.123515i | ||||
\(477\) | −6.47460 | −0.296451 | ||||||||
\(478\) | −3.37292 | + | 5.84207i | −0.154274 | + | 0.267210i | ||||
\(479\) | −15.5003 | − | 26.8474i | −0.708228 | − | 1.22669i | −0.965514 | − | 0.260352i | \(-0.916162\pi\) |
0.257286 | − | 0.966335i | \(-0.417172\pi\) | |||||||
\(480\) | 9.50433 | + | 16.4620i | 0.433811 | + | 0.751383i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11.9273 | −0.543275 | ||||||||
\(483\) | −37.5066 | − | 34.9093i | −1.70661 | − | 1.58843i | ||||
\(484\) | −5.02034 | −0.228197 | ||||||||
\(485\) | −6.29190 | + | 10.8979i | −0.285700 | + | 0.494847i | ||||
\(486\) | −10.6937 | − | 18.5220i | −0.485076 | − | 0.840176i | ||||
\(487\) | −4.30696 | − | 7.45988i | −0.195167 | − | 0.338039i | 0.751788 | − | 0.659405i | \(-0.229192\pi\) |
−0.946955 | + | 0.321365i | \(0.895858\pi\) | |||||||
\(488\) | −17.0826 | + | 29.5879i | −0.773291 | + | 1.33938i | ||||
\(489\) | −23.6183 | −1.06806 | ||||||||
\(490\) | −8.89156 | + | 6.02189i | −0.401680 | + | 0.272041i | ||||
\(491\) | −0.762083 | −0.0343923 | −0.0171962 | − | 0.999852i | \(-0.505474\pi\) | ||||
−0.0171962 | + | 0.999852i | \(0.505474\pi\) | |||||||
\(492\) | 0.513093 | − | 0.888703i | 0.0231320 | − | 0.0400658i | ||||
\(493\) | 13.9560 | + | 24.1725i | 0.628546 | + | 1.08867i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.3323 | + | 21.3602i | −0.554296 | + | 0.960068i | ||||
\(496\) | 2.06398 | 0.0926754 | ||||||||
\(497\) | −16.8738 | − | 15.7053i | −0.756895 | − | 0.704481i | ||||
\(498\) | 10.8546 | 0.486407 | ||||||||
\(499\) | 15.7076 | − | 27.2064i | 0.703169 | − | 1.21792i | −0.264179 | − | 0.964474i | \(-0.585101\pi\) |
0.967348 | − | 0.253451i | \(-0.0815657\pi\) | |||||||
\(500\) | −5.45871 | − | 9.45477i | −0.244121 | − | 0.422830i | ||||
\(501\) | 15.8756 | + | 27.4973i | 0.709270 | + | 1.22849i | ||||
\(502\) | −9.93927 | + | 17.2153i | −0.443611 | + | 0.768357i | ||||
\(503\) | −32.0350 | −1.42837 | −0.714185 | − | 0.699957i | \(-0.753202\pi\) | ||||
−0.714185 | + | 0.699957i | \(0.753202\pi\) | |||||||
\(504\) | 31.3307 | − | 9.61112i | 1.39558 | − | 0.428113i | ||||
\(505\) | 12.6386 | 0.562412 | ||||||||
\(506\) | 15.1173 | − | 26.1840i | 0.672047 | − | 1.16402i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.38924 | + | 9.33445i | 0.239109 | + | 0.414149i | ||||
\(509\) | −5.28329 | + | 9.15092i | −0.234178 | + | 0.405607i | −0.959033 | − | 0.283293i | \(-0.908573\pi\) |
0.724856 | + | 0.688901i | \(0.241906\pi\) | |||||||
\(510\) | −15.0714 | −0.667372 | ||||||||
\(511\) | −9.00440 | + | 39.1710i | −0.398331 | + | 1.73282i | ||||
\(512\) | 13.3386 | 0.589487 | ||||||||
\(513\) | 7.69089 | − | 13.3210i | 0.339561 | − | 0.588137i | ||||
\(514\) | −8.90614 | − | 15.4259i | −0.392833 | − | 0.680407i | ||||
\(515\) | 11.8614 | + | 20.5445i | 0.522675 | + | 0.905300i | ||||
\(516\) | −8.06793 | + | 13.9741i | −0.355171 | + | 0.615174i | ||||
\(517\) | 20.7677 | 0.913362 | ||||||||
\(518\) | 4.28173 | − | 18.6264i | 0.188128 | − | 0.818398i | ||||
\(519\) | −23.5197 | −1.03240 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3947 | − | 18.0041i | −0.455398 | − | 0.788773i | 0.543313 | − | 0.839530i | \(-0.317170\pi\) |
−0.998711 | + | 0.0507575i | \(0.983836\pi\) | |||||||
\(522\) | −15.9317 | − | 27.5946i | −0.697313 | − | 1.20778i | ||||
\(523\) | 3.03097 | − | 5.24979i | 0.132535 | − | 0.229557i | −0.792118 | − | 0.610368i | \(-0.791022\pi\) |
0.924653 | + | 0.380811i | \(0.124355\pi\) | |||||||
\(524\) | −1.68383 | −0.0735583 | ||||||||
\(525\) | −18.7041 | + | 5.73774i | −0.816316 | + | 0.250416i | ||||
\(526\) | −26.1259 | −1.13915 | ||||||||
\(527\) | 3.09345 | − | 5.35801i | 0.134753 | − | 0.233399i | ||||
\(528\) | 6.62246 | + | 11.4704i | 0.288205 | + | 0.499187i | ||||
\(529\) | −14.9388 | − | 25.8747i | −0.649513 | − | 1.12499i | ||||
\(530\) | −1.21341 | + | 2.10168i | −0.0527070 | + | 0.0912912i | ||||
\(531\) | 31.2963 | 1.35814 | ||||||||
\(532\) | −9.63542 | − | 8.96819i | −0.417749 | − | 0.388820i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.05970 | + | 8.76365i | −0.218954 | + | 0.379240i | ||||
\(535\) | −5.32862 | − | 9.22944i | −0.230376 | − | 0.399023i | ||||
\(536\) | −19.9096 | − | 34.4845i | −0.859965 | − | 1.48950i | ||||
\(537\) | 24.1097 | − | 41.7593i | 1.04041 | − | 1.80205i | ||||
\(538\) | −12.0254 | −0.518454 | ||||||||
\(539\) | 23.4229 | − | 15.8634i | 1.00890 | − | 0.683285i | ||||
\(540\) | −4.08646 | −0.175853 | ||||||||
\(541\) | 16.5689 | − | 28.6982i | 0.712353 | − | 1.23383i | −0.251618 | − | 0.967827i | \(-0.580963\pi\) |
0.963972 | − | 0.266005i | \(-0.0857039\pi\) | |||||||
\(542\) | 1.75617 | + | 3.04178i | 0.0754342 | + | 0.130656i | ||||
\(543\) | 28.4108 | + | 49.2089i | 1.21922 | + | 2.11176i | ||||
\(544\) | 8.82822 | − | 15.2909i | 0.378507 | − | 0.655593i | ||||
\(545\) | −1.65880 | −0.0710554 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.8568 | 1.02004 | 0.510021 | − | 0.860162i | \(-0.329637\pi\) | ||||
0.510021 | + | 0.860162i | \(0.329637\pi\) | |||||||
\(548\) | 2.99147 | − | 5.18137i | 0.127789 | − | 0.221337i | ||||
\(549\) | −23.1033 | − | 40.0162i | −0.986027 | − | 1.70785i | ||||
\(550\) | −5.77224 | − | 9.99781i | −0.246129 | − | 0.426308i | ||||
\(551\) | −19.9928 | + | 34.6286i | −0.851723 | + | 1.47523i | ||||
\(552\) | 58.6089 | 2.49456 | ||||||||
\(553\) | −1.90676 | + | 0.584925i | −0.0810839 | + | 0.0248736i | ||||
\(554\) | −1.97088 | −0.0837347 | ||||||||
\(555\) | −13.9416 | + | 24.1476i | −0.591790 | + | 1.02501i | ||||
\(556\) | 4.99643 | + | 8.65407i | 0.211896 | + | 0.367014i | ||||
\(557\) | −16.8012 | − | 29.1005i | −0.711888 | − | 1.23303i | −0.964147 | − | 0.265367i | \(-0.914507\pi\) |
0.252259 | − | 0.967660i | \(-0.418827\pi\) | |||||||
\(558\) | −3.53139 | + | 6.11654i | −0.149496 | + | 0.258934i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.08764 | − | 4.73145i | 0.0459610 | − | 0.199940i | ||||
\(561\) | 39.7024 | 1.67624 | ||||||||
\(562\) | −7.61802 | + | 13.1948i | −0.321347 | + | 0.556589i | ||||
\(563\) | −15.8125 | − | 27.3881i | −0.666418 | − | 1.15427i | −0.978899 | − | 0.204345i | \(-0.934493\pi\) |
0.312481 | − | 0.949924i | \(-0.398840\pi\) | |||||||
\(564\) | 6.44269 | + | 11.1591i | 0.271286 | + | 0.469882i | ||||
\(565\) | 9.72457 | − | 16.8435i | 0.409116 | − | 0.708610i | ||||
\(566\) | −34.5271 | −1.45128 | ||||||||
\(567\) | 2.68306 | − | 11.6719i | 0.112678 | − | 0.490173i | ||||
\(568\) | 26.3675 | 1.10636 | ||||||||
\(569\) | −8.40268 | + | 14.5539i | −0.352259 | + | 0.610130i | −0.986645 | − | 0.162886i | \(-0.947920\pi\) |
0.634386 | + | 0.773016i | \(0.281253\pi\) | |||||||
\(570\) | −10.7954 | − | 18.6981i | −0.452167 | − | 0.783177i | ||||
\(571\) | −7.03033 | − | 12.1769i | −0.294210 | − | 0.509587i | 0.680591 | − | 0.732664i | \(-0.261723\pi\) |
−0.974801 | + | 0.223077i | \(0.928390\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −43.2217 | −1.80561 | ||||||||
\(574\) | −1.06502 | + | 0.326710i | −0.0444532 | + | 0.0136366i | ||||
\(575\) | −20.1902 | −0.841989 | ||||||||
\(576\) | −15.1148 | + | 26.1795i | −0.629782 | + | 1.09081i | ||||
\(577\) | 7.10639 | + | 12.3086i | 0.295843 | + | 0.512415i | 0.975181 | − | 0.221411i | \(-0.0710662\pi\) |
−0.679338 | + | 0.733826i | \(0.737733\pi\) | |||||||
\(578\) | −1.74547 | − | 3.02325i | −0.0726021 | − | 0.125751i | ||||
\(579\) | −2.73215 | + | 4.73222i | −0.113544 | + | 0.196664i | ||||
\(580\) | 10.6229 | 0.441093 | ||||||||
\(581\) | 7.67209 | + | 7.14081i | 0.318292 | + | 0.296251i | ||||
\(582\) | −23.1237 | −0.958507 | ||||||||
\(583\) | 3.19646 | − | 5.53644i | 0.132384 | − | 0.229296i | ||||
\(584\) | −22.9870 | − | 39.8146i | −0.951207 | − | 1.64754i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.58785 | − | 4.48228i | 0.106903 | − | 0.185161i | ||||
\(587\) | −17.9188 | −0.739590 | −0.369795 | − | 0.929113i | \(-0.620572\pi\) | ||||
−0.369795 | + | 0.929113i | \(0.620572\pi\) | |||||||
\(588\) | 15.7903 | + | 7.66456i | 0.651180 | + | 0.316081i | ||||
\(589\) | 8.86312 | 0.365198 | ||||||||
\(590\) | 5.86526 | − | 10.1589i | 0.241469 | − | 0.418236i | ||||
\(591\) | −3.32803 | − | 5.76432i | −0.136897 | − | 0.237112i | ||||
\(592\) | 4.32015 | + | 7.48271i | 0.177557 | + | 0.307538i | ||||
\(593\) | 2.65203 | − | 4.59345i | 0.108906 | − | 0.188630i | −0.806421 | − | 0.591341i | \(-0.798599\pi\) |
0.915327 | + | 0.402711i | \(0.131932\pi\) | |||||||
\(594\) | −12.1027 | −0.496580 | ||||||||
\(595\) | −10.6525 | − | 9.91485i | −0.436711 | − | 0.406469i | ||||
\(596\) | −4.52427 | −0.185321 | ||||||||
\(597\) | 20.9686 | − | 36.3187i | 0.858188 | − | 1.48643i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.96219 | + | 17.2550i | 0.407044 | + | 0.705021i | 0.994557 | − | 0.104194i | \(-0.0332262\pi\) |
−0.587513 | + | 0.809215i | \(0.699893\pi\) | |||||||
\(600\) | 11.1893 | − | 19.3804i | 0.456801 | − | 0.791202i | ||||
\(601\) | 3.44445 | 0.140502 | 0.0702509 | − | 0.997529i | \(-0.477620\pi\) | ||||
0.0702509 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(602\) | 16.7465 | − | 5.13723i | 0.682538 | − | 0.209378i | ||||
\(603\) | 53.8536 | 2.19309 | ||||||||
\(604\) | 1.94456 | − | 3.36807i | 0.0791229 | − | 0.137045i | ||||
\(605\) | −3.97555 | − | 6.88586i | −0.161629 | − | 0.279950i | ||||
\(606\) | 11.6122 | + | 20.1130i | 0.471715 | + | 0.817034i | ||||
\(607\) | −11.6226 | + | 20.1309i | −0.471745 | + | 0.817087i | −0.999477 | − | 0.0323240i | \(-0.989709\pi\) |
0.527732 | + | 0.849411i | \(0.323042\pi\) | |||||||
\(608\) | 25.2940 | 1.02581 | ||||||||
\(609\) | 11.9449 | − | 51.9627i | 0.484031 | − | 2.10563i | ||||
\(610\) | −17.3192 | −0.701235 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.10731 | + | 12.3102i | 0.287296 | + | 0.497611i | ||||
\(613\) | −4.23118 | − | 7.32862i | −0.170896 | − | 0.296000i | 0.767838 | − | 0.640645i | \(-0.221333\pi\) |
−0.938733 | + | 0.344645i | \(0.887999\pi\) | |||||||
\(614\) | 7.27996 | − | 12.6093i | 0.293795 | − | 0.508868i | ||||
\(615\) | 1.62525 | 0.0655366 | ||||||||
\(616\) | −7.24929 | + | 31.5359i | −0.292082 | + | 1.27062i | ||||
\(617\) | −14.9847 | −0.603262 | −0.301631 | − | 0.953425i | \(-0.597531\pi\) | ||||
−0.301631 | + | 0.953425i | \(0.597531\pi\) | |||||||
\(618\) | −21.7962 | + | 37.7521i | −0.876772 | + | 1.51861i | ||||
\(619\) | 15.8131 | + | 27.3890i | 0.635580 | + | 1.10086i | 0.986392 | + | 0.164411i | \(0.0525724\pi\) |
−0.350812 | + | 0.936446i | \(0.614094\pi\) | |||||||
\(620\) | −1.17733 | − | 2.03919i | −0.0472825 | − | 0.0818958i | ||||
\(621\) | −10.5833 | + | 18.3307i | −0.424691 | + | 0.735587i | ||||
\(622\) | 8.94607 | 0.358705 | ||||||||
\(623\) | −9.34146 | + | 2.86562i | −0.374258 | + | 0.114809i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.70404 | − | 2.95148i | 0.0681616 | − | 0.118059i | ||||
\(626\) | 10.7398 | + | 18.6020i | 0.429251 | + | 0.743484i | ||||
\(627\) | 28.4381 | + | 49.2562i | 1.13571 | + | 1.96710i | ||||
\(628\) | 2.80528 | − | 4.85889i | 0.111943 | − | 0.193891i | ||||
\(629\) | 25.8998 | 1.03269 | ||||||||
\(630\) | 12.1606 | + | 11.3185i | 0.484490 | + | 0.450940i | ||||
\(631\) | −26.9817 | −1.07412 | −0.537062 | − | 0.843543i | \(-0.680466\pi\) | ||||
−0.537062 | + | 0.843543i | \(0.680466\pi\) | |||||||
\(632\) | 1.14067 | − | 1.97571i | 0.0453736 | − | 0.0785894i | ||||
\(633\) | −10.3229 | − | 17.8797i | −0.410297 | − | 0.710655i | ||||
\(634\) | 8.99726 | + | 15.5837i | 0.357327 | + | 0.618908i | ||||
\(635\) | −8.53538 | + | 14.7837i | −0.338716 | + | 0.586674i | ||||
\(636\) | 3.96651 | 0.157283 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31.4616 | 1.24557 | ||||||||
\(639\) | −17.8304 | + | 30.8832i | −0.705361 | + | 1.22172i | ||||
\(640\) | −1.47204 | − | 2.54964i | −0.0581873 | − | 0.100783i | ||||
\(641\) | 17.5165 | + | 30.3395i | 0.691861 | + | 1.19834i | 0.971227 | + | 0.238154i | \(0.0765422\pi\) |
−0.279367 | + | 0.960184i | \(0.590124\pi\) | |||||||
\(642\) | 9.79174 | − | 16.9598i | 0.386449 | − | 0.669349i | ||||
\(643\) | −38.2944 | −1.51019 | −0.755093 | − | 0.655618i | \(-0.772408\pi\) | ||||
−0.755093 | + | 0.655618i | \(0.772408\pi\) | |||||||
\(644\) | 13.2591 | + | 12.3409i | 0.522481 | + | 0.486300i | ||||
\(645\) | −25.5557 | −1.00625 | ||||||||
\(646\) | −10.0274 | + | 17.3680i | −0.394523 | + | 0.683334i | ||||
\(647\) | 7.43216 | + | 12.8729i | 0.292188 | + | 0.506085i | 0.974327 | − | 0.225138i | \(-0.0722832\pi\) |
−0.682138 | + | 0.731223i | \(0.738950\pi\) | |||||||
\(648\) | 6.84949 | + | 11.8637i | 0.269073 | + | 0.466048i | ||||
\(649\) | −15.4508 | + | 26.7615i | −0.606496 | + | 1.05048i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.2986 | + | 3.46601i | −0.442829 | + | 0.135844i | ||||
\(652\) | 8.34939 | 0.326987 | ||||||||
\(653\) | 13.1693 | − | 22.8099i | 0.515354 | − | 0.892620i | −0.484487 | − | 0.874799i | \(-0.660994\pi\) |
0.999841 | − | 0.0178215i | \(-0.00567306\pi\) | |||||||
\(654\) | −1.52409 | − | 2.63980i | −0.0595966 | − | 0.103224i | ||||
\(655\) | −1.33341 | − | 2.30953i | −0.0521005 | − | 0.0902407i | ||||
\(656\) | 0.251812 | − | 0.436151i | 0.00983159 | − | 0.0170288i | ||||
\(657\) | 62.1775 | 2.42578 | ||||||||
\(658\) | 3.13378 | − | 13.6326i | 0.122167 | − | 0.531453i | ||||
\(659\) | 3.18074 | 0.123904 | 0.0619521 | − | 0.998079i | \(-0.480267\pi\) | ||||
0.0619521 | + | 0.998079i | \(0.480267\pi\) | |||||||
\(660\) | 7.55510 | − | 13.0858i | 0.294082 | − | 0.509365i | ||||
\(661\) | −0.545429 | − | 0.944712i | −0.0212147 | − | 0.0367450i | 0.855223 | − | 0.518260i | \(-0.173420\pi\) |
−0.876438 | + | 0.481515i | \(0.840087\pi\) | |||||||
\(662\) | 2.35545 | + | 4.07977i | 0.0915473 | + | 0.158565i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.9886 | −0.465249 | ||||||||
\(665\) | 4.67051 | − | 20.3177i | 0.181115 | − | 0.787887i | ||||
\(666\) | −29.5664 | −1.14567 | ||||||||
\(667\) | 27.5116 | − | 47.6516i | 1.06526 | − | 1.84508i | ||||
\(668\) | −5.61224 | − | 9.72068i | −0.217144 | − | 0.376104i | ||||
\(669\) | 6.33022 | + | 10.9643i | 0.244740 | + | 0.423903i | ||||
\(670\) | 10.0927 | − | 17.4811i | 0.389916 | − | 0.675355i | ||||
\(671\) | 45.6239 | 1.76129 | ||||||||
\(672\) | −32.2446 | + | 9.89146i | −1.24386 | + | 0.381571i | ||||
\(673\) | −3.63442 | −0.140096 | −0.0700482 | − | 0.997544i | \(-0.522315\pi\) | ||||
−0.0700482 | + | 0.997544i | \(0.522315\pi\) | |||||||
\(674\) | 12.1233 | − | 20.9982i | 0.466973 | − | 0.808822i | ||||
\(675\) | 4.04099 | + | 6.99920i | 0.155538 | + | 0.269399i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.09468 | − | 3.62810i | 0.0805052 | − | 0.139439i | −0.822962 | − | 0.568097i | \(-0.807680\pi\) |
0.903467 | + | 0.428658i | \(0.141013\pi\) | |||||||
\(678\) | 35.7393 | 1.37256 | ||||||||
\(679\) | −16.3439 | − | 15.2121i | −0.627221 | − | 0.583787i | ||||
\(680\) | 16.6459 | 0.638342 | ||||||||
\(681\) | −16.7652 | + | 29.0381i | −0.642443 | + | 1.11274i | ||||
\(682\) | −3.48685 | − | 6.03939i | −0.133518 | − | 0.231260i | ||||
\(683\) | −18.7579 | − | 32.4896i | −0.717750 | − | 1.24318i | −0.961889 | − | 0.273439i | \(-0.911839\pi\) |
0.244140 | − | 0.969740i | \(-0.421494\pi\) | |||||||
\(684\) | −10.1817 | + | 17.6352i | −0.389306 | + | 0.674297i | ||||
\(685\) | 9.47565 | 0.362046 | ||||||||
\(686\) | −6.87880 | − | 17.7693i | −0.262634 | − | 0.678435i | ||||
\(687\) | −14.0020 | −0.534211 | ||||||||
\(688\) | −3.95951 | + | 6.85808i | −0.150955 | + | 0.261462i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 14.8552 | + | 25.7300i | 0.565529 | + | 0.979525i | ||||
\(691\) | −7.56277 | + | 13.0991i | −0.287701 | + | 0.498313i | −0.973261 | − | 0.229704i | \(-0.926224\pi\) |
0.685559 | + | 0.728017i | \(0.259558\pi\) | |||||||
\(692\) | 8.31454 | 0.316071 | ||||||||
\(693\) | −32.0345 | − | 29.8162i | −1.21689 | − | 1.13262i | ||||
\(694\) | −27.7667 | −1.05401 | ||||||||
\(695\) | −7.91324 | + | 13.7061i | −0.300166 | + | 0.519903i | ||||
\(696\) | 30.4936 | + | 52.8165i | 1.15586 | + | 2.00200i | ||||
\(697\) | −0.754819 | − | 1.30739i | −0.0285908 | − | 0.0495208i | ||||
\(698\) | 12.7192 | − | 22.0303i | 0.481430 | − | 0.833861i | ||||
\(699\) | −22.5214 | −0.851837 | ||||||||
\(700\) | 6.61216 | − | 2.02837i | 0.249916 | − | 0.0766652i | ||||
\(701\) | −38.7255 | −1.46264 | −0.731320 | − | 0.682034i | \(-0.761096\pi\) | ||||
−0.731320 | + | 0.682034i | \(0.761096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5515 | + | 32.1322i | 0.699684 | + | 1.21189i | ||||
\(704\) | −14.9241 | − | 25.8493i | −0.562474 | − | 0.974233i | ||||
\(705\) | −10.2038 | + | 17.6735i | −0.384298 | + | 0.665623i | ||||
\(706\) | −1.48760 | −0.0559864 | ||||||||
\(707\) | −5.02393 | + | 21.8551i | −0.188944 | + | 0.821947i | ||||
\(708\) | −19.1730 | −0.720565 | ||||||||
\(709\) | −2.21513 | + | 3.83671i | −0.0831908 | + | 0.144091i | −0.904619 | − | 0.426222i | \(-0.859844\pi\) |
0.821428 | + | 0.570312i | \(0.193178\pi\) | |||||||
\(710\) | 6.68322 | + | 11.5757i | 0.250817 | + | 0.434427i | ||||
\(711\) | 1.54271 | + | 2.67205i | 0.0578561 | + | 0.100210i | ||||
\(712\) | 5.58830 | − | 9.67921i | 0.209430 | − | 0.362744i | ||||
\(713\) | −12.1963 | −0.456756 | ||||||||
\(714\) | 5.99096 | − | 26.0619i | 0.224206 | − | 0.975342i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.52311 | + | 14.7625i | −0.318523 | + | 0.551699i | ||||
\(717\) | 8.73119 | + | 15.1229i | 0.326072 | + | 0.564774i | ||||
\(718\) | −8.51325 | − | 14.7454i | −0.317712 | − | 0.550293i | ||||
\(719\) | 17.2330 | − | 29.8484i | 0.642681 | − | 1.11316i | −0.342151 | − | 0.939645i | \(-0.611155\pi\) |
0.984832 | − | 0.173511i | \(-0.0555113\pi\) | |||||||
\(720\) | −7.51040 | −0.279896 | ||||||||
\(721\) | −40.2412 | + | 12.3445i | −1.49866 | + | 0.459734i | ||||
\(722\) | −9.18191 | −0.341715 | ||||||||
\(723\) | −15.4376 | + | 26.7388i | −0.574132 | + | 0.994425i | ||||
\(724\) | −10.0436 | − | 17.3960i | −0.373267 | − | 0.646518i | ||||
\(725\) | −10.5047 | − | 18.1947i | −0.390136 | − | 0.675736i | ||||
\(726\) | 7.30538 | − | 12.6533i | 0.271128 | − | 0.469608i | ||||
\(727\) | 0.889602 | 0.0329935 | 0.0164968 | − | 0.999864i | \(-0.494749\pi\) | ||||
0.0164968 | + | 0.999864i | \(0.494749\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.7839 | −1.54755 | ||||||||
\(730\) | 11.6527 | − | 20.1831i | 0.431287 | − | 0.747010i | ||||
\(731\) | 11.8689 | + | 20.5575i | 0.438986 | + | 0.760346i | ||||
\(732\) | 14.1537 | + | 24.5150i | 0.523137 | + | 0.906100i | ||||
\(733\) | −2.79094 | + | 4.83404i | −0.103086 | + | 0.178550i | −0.912954 | − | 0.408061i | \(-0.866205\pi\) |
0.809869 | + | 0.586611i | \(0.199538\pi\) | |||||||
\(734\) | 33.7044 | 1.24405 | ||||||||
\(735\) | 1.99150 | + | 27.7273i | 0.0734576 | + | 1.02274i | ||||
\(736\) | −34.8064 | −1.28298 | ||||||||
\(737\) | −26.5872 | + | 46.0503i | −0.979351 | + | 1.69629i | ||||
\(738\) | 0.861680 | + | 1.49247i | 0.0317189 | + | 0.0549387i | ||||
\(739\) | 12.6439 | + | 21.8998i | 0.465112 | + | 0.805598i | 0.999207 | − | 0.0398267i | \(-0.0126806\pi\) |
−0.534094 | + | 0.845425i | \(0.679347\pi\) | |||||||
\(740\) | 4.92856 | − | 8.53651i | 0.181177 | − | 0.313808i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.15196 | − | 2.93369i | −0.115712 | − | 0.107699i | ||||
\(743\) | 12.7921 | 0.469298 | 0.234649 | − | 0.972080i | \(-0.424606\pi\) | ||||
0.234649 | + | 0.972080i | \(0.424606\pi\) | |||||||
\(744\) | 6.75913 | − | 11.7072i | 0.247802 | − | 0.429205i | ||||
\(745\) | −3.58273 | − | 6.20547i | −0.131261 | − | 0.227351i | ||||
\(746\) | 8.24389 | + | 14.2788i | 0.301830 | + | 0.522786i | ||||
\(747\) | 8.10703 | − | 14.0418i | 0.296621 | − | 0.513762i | ||||
\(748\) | −14.0353 | −0.513182 | ||||||||
\(749\) | 18.0780 | − | 5.54566i | 0.660556 | − | 0.202634i | ||||
\(750\) | 31.7731 | 1.16019 | ||||||||
\(751\) | −18.0839 | + | 31.3222i | −0.659890 | + | 1.14296i | 0.320754 | + | 0.947163i | \(0.396064\pi\) |
−0.980644 | + | 0.195800i | \(0.937270\pi\) | |||||||
\(752\) | 3.16189 | + | 5.47656i | 0.115302 | + | 0.199710i | ||||
\(753\) | 25.7290 | + | 44.5638i | 0.937615 | + | 1.62400i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.15950 | 0.224167 | ||||||||
\(756\) | 1.62439 | − | 7.06643i | 0.0590784 | − | 0.257004i | ||||
\(757\) | 27.7793 | 1.00966 | 0.504828 | − | 0.863220i | \(-0.331556\pi\) | ||||
0.504828 | + | 0.863220i | \(0.331556\pi\) | |||||||
\(758\) | 2.56057 | − | 4.43503i | 0.0930040 | − | 0.161088i | ||||
\(759\) | −39.1330 | − | 67.7803i | −1.42044 | − | 2.46027i | ||||
\(760\) | 11.9232 | + | 20.6515i | 0.432499 | + | 0.749110i | ||||
\(761\) | 7.85382 | − | 13.6032i | 0.284701 | − | 0.493116i | −0.687836 | − | 0.725866i | \(-0.741439\pi\) |
0.972537 | + | 0.232750i | \(0.0747724\pi\) | |||||||
\(762\) | −31.3688 | −1.13637 | ||||||||
\(763\) | 0.659384 | − | 2.86846i | 0.0238713 | − | 0.103845i | ||||
\(764\) | 15.2795 | 0.552791 | ||||||||
\(765\) | −11.2564 | + | 19.4967i | −0.406977 | + | 0.704904i | ||||
\(766\) | 11.4466 | + | 19.8261i | 0.413582 | + | 0.716345i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 22.3752 | − | 38.7549i | 0.807394 | − | 1.39845i | ||||
\(769\) | −23.0847 | −0.832455 | −0.416228 | − | 0.909260i | \(-0.636648\pi\) | ||||
−0.416228 | + | 0.909260i | \(0.636648\pi\) | |||||||
\(770\) | −15.6821 | + | 4.81068i | −0.565143 | + | 0.173365i | ||||
\(771\) | −46.1091 | −1.66058 | ||||||||
\(772\) | 0.965850 | − | 1.67290i | 0.0347617 | − | 0.0602090i | ||||
\(773\) | 12.8693 | + | 22.2903i | 0.462876 | + | 0.801725i | 0.999103 | − | 0.0423492i | \(-0.0134842\pi\) |
−0.536227 | + | 0.844074i | \(0.680151\pi\) | |||||||
\(774\) | −13.5491 | − | 23.4678i | −0.487014 | − | 0.843533i | ||||
\(775\) | −2.32846 | + | 4.03300i | −0.0836406 | + | 0.144870i | ||||
\(776\) | 25.5395 | 0.916813 | ||||||||
\(777\) | −36.2150 | − | 33.7071i | −1.29920 | − | 1.20924i | ||||
\(778\) | −1.04791 | −0.0375696 | ||||||||
\(779\) | 1.08133 | − | 1.87291i | 0.0387425 | − | 0.0671040i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.6055 | − | 30.4937i | −0.629975 | − | 1.09115i | ||||
\(782\) | 13.7985 | − | 23.8997i | 0.493433 | − | 0.854650i | ||||
\(783\) | −22.0254 | −0.787124 | ||||||||
\(784\) | 7.74942 | + | 3.76155i | 0.276765 | + | 0.134341i | ||||
\(785\) | 8.88589 | 0.317151 | ||||||||
\(786\) | 2.45023 | − | 4.24393i | 0.0873969 | − | 0.151376i | ||||
\(787\) | −2.23959 | − | 3.87909i | −0.0798328 | − | 0.138274i | 0.823345 | − | 0.567541i | \(-0.192105\pi\) |
−0.903178 | + | 0.429267i | \(0.858772\pi\) | |||||||
\(788\) | 1.17650 | + | 2.03776i | 0.0419112 | + | 0.0725924i | ||||
\(789\) | −33.8150 | + | 58.5693i | −1.20385 | + | 2.08512i | ||||
\(790\) | 1.15648 | 0.0411457 | ||||||||
\(791\) | 25.2607 | + | 23.5114i | 0.898166 | + | 0.835969i | ||||
\(792\) | 50.0581 | 1.77874 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.0124 | + | 19.0740i | 0.390815 | + | 0.676911i | ||||
\(795\) | 3.14104 | + | 5.44045i | 0.111401 | + | 0.192953i | ||||
\(796\) | −7.41269 | + | 12.8391i | −0.262736 | + | 0.455072i | ||||
\(797\) | −20.6676 | −0.732083 | −0.366042 | − | 0.930598i | \(-0.619287\pi\) | ||||
−0.366042 | + | 0.930598i | \(0.619287\pi\) | |||||||
\(798\) | 36.6245 | − | 11.2351i | 1.29650 | − | 0.397717i | ||||
\(799\) | 18.9559 | 0.670611 | ||||||||
\(800\) | −6.64505 | + | 11.5096i | −0.234938 | + | 0.406925i | ||||
\(801\) | 7.55790 | + | 13.0907i | 0.267045 | + | 0.462536i | ||||
\(802\) | 0.825754 | + | 1.43025i | 0.0291584 | + | 0.0505038i | ||||
\(803\) | −30.6966 | + | 53.1681i | −1.08326 | + | 1.87626i | ||||
\(804\) | −32.9922 | −1.16355 | ||||||||
\(805\) | −6.42699 | + | 27.9587i | −0.226521 | + | 0.985416i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.5646 | + | 26.9587i | −0.547901 | + | 0.948992i | ||||
\(808\) | −12.8254 | − | 22.2142i | −0.451196 | − | 0.781494i | ||||
\(809\) | 23.7441 | + | 41.1259i | 0.834797 | + | 1.44591i | 0.894196 | + | 0.447676i | \(0.147748\pi\) |
−0.0593986 | + | 0.998234i | \(0.518918\pi\) | |||||||
\(810\) | −3.47219 | + | 6.01401i | −0.122000 | + | 0.211311i | ||||
\(811\) | −26.3338 | −0.924704 | −0.462352 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462352 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(812\) | −4.22267 | + | 18.3695i | −0.148187 | + | 0.644643i | ||||
\(813\) | 9.09212 | 0.318875 | ||||||||
\(814\) | 14.5967 | − | 25.2823i | 0.511615 | − | 0.886143i | ||||
\(815\) | 6.61180 | + | 11.4520i | 0.231601 | + | 0.401145i | ||||
\(816\) | 6.04471 | + | 10.4697i | 0.211607 | + | 0.366514i | ||||
\(817\) | −17.0029 | + | 29.4499i | −0.594856 | + | 1.03032i | ||||
\(818\) | 36.7470 | 1.28483 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.574549 | −0.0200641 | ||||||||
\(821\) | −5.25414 | + | 9.10043i | −0.183371 | + | 0.317607i | −0.943026 | − | 0.332718i | \(-0.892034\pi\) |
0.759656 | + | 0.650326i | \(0.225368\pi\) | |||||||
\(822\) | 8.70611 | + | 15.0794i | 0.303661 | + | 0.525956i | ||||
\(823\) | 6.16752 | + | 10.6825i | 0.214986 | + | 0.372367i | 0.953268 | − | 0.302125i | \(-0.0976960\pi\) |
−0.738282 | + | 0.674492i | \(0.764363\pi\) | |||||||
\(824\) | 24.0733 | − | 41.6962i | 0.838634 | − | 1.45256i | ||||
\(825\) | −29.8842 | −1.04043 | ||||||||
\(826\) | 15.2357 | + | 14.1806i | 0.530116 | + | 0.493407i | ||||
\(827\) | −29.2074 | −1.01564 | −0.507820 | − | 0.861463i | \(-0.669548\pi\) | ||||
−0.507820 | + | 0.861463i | \(0.669548\pi\) | |||||||
\(828\) | 14.0107 | − | 24.2673i | 0.486907 | − | 0.843348i | ||||
\(829\) | −4.23610 | − | 7.33714i | −0.147126 | − | 0.254830i | 0.783038 | − | 0.621974i | \(-0.213669\pi\) |
−0.930164 | + | 0.367144i | \(0.880336\pi\) | |||||||
\(830\) | −3.03868 | − | 5.26315i | −0.105474 | − | 0.182687i | ||||
\(831\) | −2.55093 | + | 4.41833i | −0.0884906 | + | 0.153270i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.3795 | − | 14.4795i | 0.740756 | − | 0.501684i | ||||
\(834\) | −29.0824 | −1.00704 | ||||||||
\(835\) | 8.88855 | − | 15.3954i | 0.307601 | − | 0.532781i | ||||
\(836\) | −10.0532 | − | 17.4127i | −0.347698 | − | 0.602231i | ||||
\(837\) | 2.44105 | + | 4.22802i | 0.0843750 | + | 0.146142i | ||||
\(838\) | 6.34364 | − | 10.9875i | 0.219138 | − | 0.379557i | ||||
\(839\) | −32.3795 | −1.11786 | −0.558932 | − | 0.829213i | \(-0.688789\pi\) | ||||
−0.558932 | + | 0.829213i | \(0.688789\pi\) | |||||||
\(840\) | −23.2756 | − | 21.6638i | −0.803084 | − | 0.747472i | ||||
\(841\) | 28.2561 | 0.974347 | ||||||||
\(842\) | 6.62257 | − | 11.4706i | 0.228229 | − | 0.395304i | ||||
\(843\) | 19.7201 | + | 34.1563i | 0.679197 | + | 1.17640i | ||||
\(844\) | 3.64927 | + | 6.32072i | 0.125613 | + | 0.217568i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.6395 | −0.743981 | ||||||||
\(847\) | 13.4876 | − | 4.13749i | 0.463438 | − | 0.142166i | ||||
\(848\) | 1.94665 | 0.0668483 | ||||||||
\(849\) | −44.6886 | + | 77.4030i | −1.53371 | + | 2.65646i | ||||
\(850\) | −5.26866 | − | 9.12558i | −0.180714 | − | 0.313005i | ||||
\(851\) | −25.5283 | − | 44.2163i | −0.875099 | − | 1.51572i | ||||
\(852\) | 10.9234 | − | 18.9199i | 0.374230 | − | 0.648185i | ||||
\(853\) | −39.8315 | −1.36381 | −0.681903 | − | 0.731443i | \(-0.738847\pi\) | ||||
−0.681903 | + | 0.731443i | \(0.738847\pi\) | |||||||
\(854\) | 6.88449 | − | 29.9490i | 0.235582 | − | 1.02483i | ||||
\(855\) | −32.2510 | −1.10296 | ||||||||
\(856\) | −10.8147 | + | 18.7316i | −0.369639 | + | 0.640234i | ||||
\(857\) | −1.30280 | − | 2.25652i | −0.0445028 | − | 0.0770811i | 0.842916 | − | 0.538045i | \(-0.180837\pi\) |
−0.887419 | + | 0.460964i | \(0.847504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.2583 | − | 40.2845i | 0.793562 | − | 1.37449i | −0.130186 | − | 0.991490i | \(-0.541557\pi\) |
0.923748 | − | 0.383000i | \(-0.125109\pi\) | |||||||
\(860\) | 9.03427 | 0.308066 | ||||||||
\(861\) | −0.646047 | + | 2.81044i | −0.0220172 | + | 0.0957795i | ||||
\(862\) | 17.1011 | 0.582464 | ||||||||
\(863\) | −7.05102 | + | 12.2127i | −0.240019 | + | 0.415726i | −0.960720 | − | 0.277521i | \(-0.910487\pi\) |
0.720700 | + | 0.693247i | \(0.243820\pi\) | |||||||
\(864\) | 6.96638 | + | 12.0661i | 0.237001 | + | 0.410498i | ||||
\(865\) | 6.58420 | + | 11.4042i | 0.223870 | + | 0.387754i | ||||
\(866\) | 3.77669 | − | 6.54141i | 0.128337 | − | 0.222286i | ||||
\(867\) | −9.03672 | −0.306903 | ||||||||
\(868\) | 3.99422 | − | 1.22528i | 0.135573 | − | 0.0415887i | ||||
\(869\) | −3.04650 | −0.103345 | ||||||||
\(870\) | −15.4580 | + | 26.7741i | −0.524077 | + | 0.907727i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.68331 | + | 2.91559i | 0.0570042 | + | 0.0987342i | ||||
\(873\) | −17.2705 | + | 29.9133i | −0.584516 | + | 1.01241i | ||||
\(874\) | 39.5344 | 1.33727 | ||||||||
\(875\) | 22.4574 | + | 20.9023i | 0.759198 | + | 0.706625i | ||||
\(876\) | −38.0917 | −1.28700 | ||||||||
\(877\) | 5.30523 | − | 9.18893i | 0.179145 | − | 0.310288i | −0.762443 | − | 0.647055i | \(-0.776000\pi\) |
0.941588 | + | 0.336767i | \(0.109334\pi\) | |||||||
\(878\) | −0.880589 | − | 1.52522i | −0.0297184 | − | 0.0514738i | ||||
\(879\) | −6.69894 | − | 11.6029i | −0.225950 | − | 0.391356i | ||||
\(880\) | 3.70783 | − | 6.42215i | 0.124991 | − | 0.216491i | ||||
\(881\) | 33.4123 | 1.12569 | 0.562844 | − | 0.826563i | \(-0.309707\pi\) | ||||
0.562844 | + | 0.826563i | \(0.309707\pi\) | |||||||
\(882\) | −24.4062 | + | 16.5293i | −0.821800 | + | 0.556571i | ||||
\(883\) | 12.9066 | 0.434341 | 0.217170 | − | 0.976134i | \(-0.430317\pi\) | ||||
0.217170 | + | 0.976134i | \(0.430317\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.1829 | − | 26.2975i | −0.510367 | − | 0.883982i | ||||
\(886\) | 3.70639 | + | 6.41965i | 0.124518 | + | 0.215672i | ||||
\(887\) | 8.75988 | − | 15.1726i | 0.294128 | − | 0.509445i | −0.680654 | − | 0.732605i | \(-0.738304\pi\) |
0.974782 | + | 0.223161i | \(0.0716375\pi\) | |||||||
\(888\) | 56.5906 | 1.89905 | ||||||||
\(889\) | −22.1716 | − | 20.6363i | −0.743612 | − | 0.692118i | ||||
\(890\) | 5.66572 | 0.189915 | ||||||||
\(891\) | 9.14675 | − | 15.8426i | 0.306428 | − | 0.530749i | ||||
\(892\) | −2.23782 | − | 3.87601i | −0.0749276 | − | 0.129778i | ||||
\(893\) | 13.5778 | + | 23.5174i | 0.454362 | + | 0.786979i | ||||
\(894\) | 6.58353 | − | 11.4030i | 0.220186 | − | 0.381374i | ||||
\(895\) | −26.9975 | −0.902426 | ||||||||
\(896\) | 4.99406 | − | 1.53199i | 0.166840 | − | 0.0511803i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.68968 | + | 6.39072i | −0.123126 | + | 0.213261i | ||||
\(899\) | −6.34562 | − | 10.9909i | −0.211638 | − | 0.366568i | ||||
\(900\) | −5.34971 | − | 9.26597i | −0.178324 | − | 0.308866i | ||||
\(901\) | 2.91760 | − | 5.05343i | 0.0971994 | − | 0.168354i | ||||
\(902\) | −1.70162 | −0.0566578 | ||||||||
\(903\) | 10.1585 | − | 44.1917i | 0.338054 | − | 1.47061i | ||||
\(904\) | −39.4731 | −1.31285 | ||||||||
\(905\) | 15.9069 | − | 27.5515i | 0.528762 | − | 0.915842i | ||||
\(906\) | 5.65927 | + | 9.80215i | 0.188017 | + | 0.325655i | ||||
\(907\) | −9.60387 | − | 16.6344i | −0.318891 | − | 0.552336i | 0.661366 | − | 0.750063i | \(-0.269977\pi\) |
−0.980257 | + | 0.197728i | \(0.936644\pi\) | |||||||
\(908\) | 5.92671 | − | 10.2654i | 0.196685 | − | 0.340668i | ||||
\(909\) | 34.6915 | 1.15064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.98108 | 0.198162 | 0.0990811 | − | 0.995079i | \(-0.468410\pi\) | ||||
0.0990811 | + | 0.995079i | \(0.468410\pi\) | |||||||
\(912\) | −8.65942 | + | 14.9986i | −0.286742 | + | 0.496652i | ||||
\(913\) | 8.00477 | + | 13.8647i | 0.264919 | + | 0.458853i | ||||
\(914\) | −18.5691 | − | 32.1627i | −0.614212 | − | 1.06385i | ||||
\(915\) | −22.4164 | + | 38.8264i | −0.741064 | + | 1.28356i | ||||
\(916\) | 4.94991 | 0.163549 | ||||||||
\(917\) | 4.52374 | − | 1.38772i | 0.149387 | − | 0.0458265i | ||||
\(918\) | −11.0469 | −0.364601 | ||||||||
\(919\) | 23.0421 | − | 39.9101i | 0.760090 | − | 1.31651i | −0.182714 | − | 0.983166i | \(-0.558488\pi\) |
0.942804 | − | 0.333348i | \(-0.108178\pi\) | |||||||
\(920\) | −16.4072 | − | 28.4181i | −0.540929 | − | 0.936917i | ||||
\(921\) | −18.8450 | − | 32.6405i | −0.620964 | − | 1.07554i | ||||
\(922\) | 10.8159 | − | 18.7337i | 0.356203 | − | 0.616961i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 19.6252 | + | 18.2662i | 0.645622 | + | 0.600914i | ||||
\(925\) | −19.4949 | −0.640988 | ||||||||
\(926\) | −13.2384 | + | 22.9296i | −0.435042 | + | 0.753515i | ||||
\(927\) | 32.5580 | + | 56.3921i | 1.06935 | + | 1.85216i | ||||
\(928\) | −18.1094 | − | 31.3664i | −0.594471 | − | 1.02965i | ||||
\(929\) | 2.11345 | − | 3.66060i | 0.0693401 | − | 0.120101i | −0.829271 | − | 0.558847i | \(-0.811244\pi\) |
0.898611 | + | 0.438746i | \(0.144577\pi\) | |||||||
\(930\) | 6.85278 | 0.224712 | ||||||||
\(931\) | 33.2775 | + | 16.1528i | 1.09063 | + | 0.529387i | ||||
\(932\) | 7.96161 | 0.260791 | ||||||||
\(933\) | 11.5790 | − | 20.0554i | 0.379078 | − | 0.656583i | ||||
\(934\) | 13.7557 | + | 23.8256i | 0.450100 | + | 0.779596i | ||||
\(935\) | −11.1144 | − | 19.2508i | −0.363481 | − | 0.629567i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.0155 | 1.47059 | 0.735296 | − | 0.677746i | \(-0.237043\pi\) | ||||
0.735296 | + | 0.677746i | \(0.237043\pi\) | |||||||
\(938\) | 26.2170 | + | 24.4015i | 0.856015 | + | 0.796738i | ||||
\(939\) | 55.6027 | 1.81452 | ||||||||
\(940\) | 3.60718 | − | 6.24783i | 0.117653 | − | 0.203782i | ||||
\(941\) | −10.4884 | − | 18.1664i | −0.341911 | − | 0.592207i | 0.642876 | − | 0.765970i | \(-0.277741\pi\) |
−0.984788 | + | 0.173762i | \(0.944408\pi\) | |||||||
\(942\) | 8.16425 | + | 14.1409i | 0.266006 | + | 0.460735i | ||||
\(943\) | −1.48799 | + | 2.57727i | −0.0484555 | + | 0.0839275i | ||||
\(944\) | −9.40956 | −0.306255 | ||||||||
\(945\) | 10.9786 | − | 3.36783i | 0.357134 | − | 0.109556i | ||||
\(946\) | 26.7565 | 0.869928 | ||||||||
\(947\) | 28.2064 | − | 48.8549i | 0.916584 | − | 1.58757i | 0.112019 | − | 0.993706i | \(-0.464268\pi\) |
0.804565 | − | 0.593864i | \(-0.202398\pi\) | |||||||
\(948\) | −0.945105 | − | 1.63697i | −0.0306956 | − | 0.0531663i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.54768 | − | 13.0730i | 0.244879 | − | 0.424143i | ||||
\(951\) | 46.5809 | 1.51049 | ||||||||
\(952\) | −6.61685 | + | 28.7847i | −0.214453 | + | 0.932917i | ||||
\(953\) | −46.8932 | −1.51902 | −0.759510 | − | 0.650495i | \(-0.774561\pi\) | ||||
−0.759510 | + | 0.650495i | \(0.774561\pi\) | |||||||
\(954\) | −3.33065 | + | 5.76885i | −0.107834 | + | 0.186773i | ||||
\(955\) | 12.0997 | + | 20.9572i | 0.391536 | + | 0.678159i | ||||
\(956\) | −3.08659 | − | 5.34613i | −0.0998275 | − | 0.172906i | ||||
\(957\) | 40.7209 | − | 70.5307i | 1.31632 | − | 2.27993i | ||||
\(958\) | −31.8946 | −1.03047 | ||||||||
\(959\) | −3.76662 | + | 16.3856i | −0.121631 | + | 0.529119i | ||||
\(960\) | 29.3307 | 0.946645 | ||||||||
\(961\) | 14.0934 | − | 24.4106i | 0.454627 | − | 0.787438i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6264 | − | 25.3336i | −0.471328 | − | 0.816365i | ||||
\(964\) | 5.45741 | − | 9.45251i | 0.175771 | − | 0.304445i | ||||
\(965\) | 3.05939 | 0.0984852 | ||||||||
\(966\) | −50.3982 | + | 15.4603i | −1.62153 | + | 0.497427i | ||||
\(967\) | 44.8315 | 1.44168 | 0.720842 | − | 0.693100i | \(-0.243755\pi\) | ||||
0.720842 | + | 0.693100i | \(0.243755\pi\) | |||||||
\(968\) | −8.06860 | + | 13.9752i | −0.259334 | + | 0.449181i | ||||
\(969\) | 25.9571 | + | 44.9590i | 0.833862 | + | 1.44429i | ||||
\(970\) | 6.47333 | + | 11.2121i | 0.207846 | + | 0.360000i | ||||
\(971\) | 6.07720 | − | 10.5260i | 0.195027 | − | 0.337796i | −0.751883 | − | 0.659297i | \(-0.770854\pi\) |
0.946909 | + | 0.321501i | \(0.104187\pi\) | |||||||
\(972\) | 19.5718 | 0.627767 | ||||||||
\(973\) | −20.5555 | − | 19.1321i | −0.658980 | − | 0.613347i | ||||
\(974\) | −8.86231 | −0.283967 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.94626 | + | 12.0313i | 0.222344 | + | 0.385111i | ||||
\(977\) | 13.9808 | + | 24.2155i | 0.447286 | + | 0.774723i | 0.998208 | − | 0.0598342i | \(-0.0190572\pi\) |
−0.550922 | + | 0.834557i | \(0.685724\pi\) | |||||||
\(978\) | −12.1497 | + | 21.0439i | −0.388504 | + | 0.672908i | ||||
\(979\) | −14.9251 | −0.477010 | ||||||||
\(980\) | −0.704022 | − | 9.80199i | −0.0224892 | − | 0.313113i | ||||
\(981\) | −4.55320 | −0.145373 | ||||||||
\(982\) | −0.392029 | + | 0.679014i | −0.0125102 | + | 0.0216682i | ||||
\(983\) | −25.0128 | − | 43.3234i | −0.797784 | − | 1.38180i | −0.921056 | − | 0.389430i | \(-0.872672\pi\) |
0.123272 | − | 0.992373i | \(-0.460661\pi\) | |||||||
\(984\) | −1.64927 | − | 2.85662i | −0.0525768 | − | 0.0910656i | ||||
\(985\) | −1.86332 | + | 3.22737i | −0.0593704 | + | 0.102833i | ||||
\(986\) | 28.7168 | 0.914530 | ||||||||
\(987\) | −26.5055 | − | 24.6701i | −0.843681 | − | 0.785257i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.3973 | − | 40.5253i | 0.743990 | − | 1.28863i | ||||
\(990\) | 12.6879 | + | 21.9761i | 0.403248 | + | 0.698446i | ||||
\(991\) | 7.02915 | + | 12.1748i | 0.223288 | + | 0.386747i | 0.955805 | − | 0.294003i | \(-0.0949876\pi\) |
−0.732516 | + | 0.680749i | \(0.761654\pi\) | |||||||
\(992\) | −4.01409 | + | 6.95261i | −0.127447 | + | 0.220745i | ||||
\(993\) | 12.1947 | 0.386988 | ||||||||
\(994\) | −22.6736 | + | 6.95544i | −0.719164 | + | 0.220613i | ||||
\(995\) | −23.4801 | −0.744370 | ||||||||
\(996\) | −4.96659 | + | 8.60238i | −0.157372 | + | 0.272577i | ||||
\(997\) | 3.73683 | + | 6.47237i | 0.118346 | + | 0.204982i | 0.919113 | − | 0.393995i | \(-0.128907\pi\) |
−0.800766 | + | 0.598977i | \(0.795574\pi\) | |||||||
\(998\) | −16.1605 | − | 27.9909i | −0.511553 | − | 0.886036i | ||||
\(999\) | −10.2188 | + | 17.6995i | −0.323308 | + | 0.559986i |
(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 | 1183.2.e.l.170.16 | yes | 48 | |
7.2 | even | 3 | 8281.2.a.cu.1.9 | 24 | |||
7.4 | even | 3 | inner | 1183.2.e.l.508.16 | yes | 48 | |
7.5 | odd | 6 | 8281.2.a.ct.1.9 | 24 | |||
13.12 | even | 2 | 1183.2.e.k.170.9 | ✓ | 48 | ||
91.12 | odd | 6 | 8281.2.a.cw.1.16 | 24 | |||
91.25 | even | 6 | 1183.2.e.k.508.9 | yes | 48 | ||
91.51 | even | 6 | 8281.2.a.cv.1.16 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.e.k.170.9 | ✓ | 48 | 13.12 | even | 2 | ||
1183.2.e.k.508.9 | yes | 48 | 91.25 | even | 6 | ||
1183.2.e.l.170.16 | yes | 48 | 1.1 | even | 1 | trivial | |
1183.2.e.l.508.16 | yes | 48 | 7.4 | even | 3 | inner | |
8281.2.a.ct.1.9 | 24 | 7.5 | odd | 6 | |||
8281.2.a.cu.1.9 | 24 | 7.2 | even | 3 | |||
8281.2.a.cv.1.16 | 24 | 91.51 | even | 6 | |||
8281.2.a.cw.1.16 | 24 | 91.12 | odd | 6 |