Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (of order \(2\), degree \(1\), 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: | \(5.29266605383\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} + \cdots + 92\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.10 | ||
Root | \(0.456001 - 15.5879i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.6.d.b.32.9 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.58998 | 0.634624 | 0.317312 | − | 0.948321i | \(-0.397220\pi\) | ||||
0.317312 | + | 0.948321i | \(0.397220\pi\) | |||||||
\(3\) | 0.133977 | + | 15.5879i | 0.00859463 | + | 0.999963i | ||||
\(4\) | −19.1121 | −0.597252 | ||||||||
\(5\) | 11.8803i | 0.212521i | 0.994338 | + | 0.106261i | \(0.0338877\pi\) | ||||
−0.994338 | + | 0.106261i | \(0.966112\pi\) | |||||||
\(6\) | 0.480974 | + | 55.9601i | 0.00545436 | + | 0.634601i | ||||
\(7\) | 150.804i | 1.16324i | 0.813461 | + | 0.581619i | \(0.197580\pi\) | ||||
−0.813461 | + | 0.581619i | \(0.802420\pi\) | |||||||
\(8\) | −183.491 | −1.01365 | ||||||||
\(9\) | −242.964 | + | 4.17684i | −0.999852 | + | 0.0171886i | ||||
\(10\) | 42.6500i | 0.134871i | ||||||||
\(11\) | 352.626 | − | 191.588i | 0.878683 | − | 0.477405i | ||||
\(12\) | −2.56058 | − | 297.917i | −0.00513316 | − | 0.597230i | ||||
\(13\) | 778.957i | 1.27837i | 0.769055 | + | 0.639183i | \(0.220727\pi\) | ||||
−0.769055 | + | 0.639183i | \(0.779273\pi\) | |||||||
\(14\) | 541.384i | 0.738219i | ||||||||
\(15\) | −185.188 | + | 1.59169i | −0.212513 | + | 0.00182654i | ||||
\(16\) | −47.1432 | −0.0460383 | ||||||||
\(17\) | 1255.02 | 1.05324 | 0.526622 | − | 0.850100i | \(-0.323458\pi\) | ||||
0.526622 | + | 0.850100i | \(0.323458\pi\) | |||||||
\(18\) | −872.236 | + | 14.9947i | −0.634531 | + | 0.0109083i | ||||
\(19\) | − | 1214.37i | − | 0.771736i | −0.922554 | − | 0.385868i | \(-0.873902\pi\) | ||
0.922554 | − | 0.385868i | \(-0.126098\pi\) | |||||||
\(20\) | − | 227.057i | − | 0.126929i | ||||||
\(21\) | −2350.72 | + | 20.2043i | −1.16319 | + | 0.00999759i | ||||
\(22\) | 1265.92 | − | 687.798i | 0.557634 | − | 0.302973i | ||||
\(23\) | 880.210i | 0.346950i | 0.984838 | + | 0.173475i | \(0.0554996\pi\) | ||||
−0.984838 | + | 0.173475i | \(0.944500\pi\) | |||||||
\(24\) | −24.5836 | − | 2860.24i | −0.00871199 | − | 1.01362i | ||||
\(25\) | 2983.86 | 0.954835 | ||||||||
\(26\) | 2796.44i | 0.811282i | ||||||||
\(27\) | −97.6596 | − | 3786.74i | −0.0257813 | − | 0.999668i | ||||
\(28\) | − | 2882.18i | − | 0.694746i | ||||||
\(29\) | 3201.27 | 0.706851 | 0.353425 | − | 0.935463i | \(-0.385017\pi\) | ||||
0.353425 | + | 0.935463i | \(0.385017\pi\) | |||||||
\(30\) | −664.823 | + | 5.71411i | −0.134866 | + | 0.00115917i | ||||
\(31\) | −6446.10 | −1.20474 | −0.602369 | − | 0.798218i | \(-0.705777\pi\) | ||||
−0.602369 | + | 0.798218i | \(0.705777\pi\) | |||||||
\(32\) | 5702.47 | 0.984438 | ||||||||
\(33\) | 3033.70 | + | 5471.02i | 0.484940 | + | 0.874548i | ||||
\(34\) | 4505.50 | 0.668414 | ||||||||
\(35\) | −1791.60 | −0.247212 | ||||||||
\(36\) | 4643.54 | − | 79.8279i | 0.597164 | − | 0.0102659i | ||||
\(37\) | −9311.53 | −1.11819 | −0.559096 | − | 0.829103i | \(-0.688852\pi\) | ||||
−0.559096 | + | 0.829103i | \(0.688852\pi\) | |||||||
\(38\) | − | 4359.58i | − | 0.489762i | ||||||
\(39\) | −12142.3 | + | 104.362i | −1.27832 | + | 0.0109871i | ||||
\(40\) | − | 2179.93i | − | 0.215423i | ||||||
\(41\) | 5398.38 | 0.501538 | 0.250769 | − | 0.968047i | \(-0.419317\pi\) | ||||
0.250769 | + | 0.968047i | \(0.419317\pi\) | |||||||
\(42\) | −8439.03 | + | 72.5330i | −0.738192 | + | 0.00634472i | ||||
\(43\) | 20867.6i | 1.72108i | 0.509379 | + | 0.860542i | \(0.329875\pi\) | ||||
−0.509379 | + | 0.860542i | \(0.670125\pi\) | |||||||
\(44\) | −6739.40 | + | 3661.65i | −0.524795 | + | 0.285131i | ||||
\(45\) | −49.6220 | − | 2886.48i | −0.00365294 | − | 0.212490i | ||||
\(46\) | 3159.93i | 0.220183i | ||||||||
\(47\) | 11289.4i | 0.745465i | 0.927939 | + | 0.372732i | \(0.121579\pi\) | ||||
−0.927939 | + | 0.372732i | \(0.878421\pi\) | |||||||
\(48\) | −6.31611 | − | 734.863i | −0.000395682 | − | 0.0460366i | ||||
\(49\) | −5934.91 | −0.353122 | ||||||||
\(50\) | 10712.0 | 0.605961 | ||||||||
\(51\) | 168.144 | + | 19563.1i | 0.00905223 | + | 1.05320i | ||||
\(52\) | − | 14887.5i | − | 0.763506i | ||||||
\(53\) | 23978.4i | 1.17255i | 0.810113 | + | 0.586274i | \(0.199406\pi\) | ||||
−0.810113 | + | 0.586274i | \(0.800594\pi\) | |||||||
\(54\) | −350.596 | − | 13594.3i | −0.0163615 | − | 0.634413i | ||||
\(55\) | 2276.12 | + | 4189.29i | 0.101459 | + | 0.186739i | ||||
\(56\) | − | 27671.2i | − | 1.17912i | ||||||
\(57\) | 18929.5 | − | 162.698i | 0.771707 | − | 0.00663278i | ||||
\(58\) | 11492.5 | 0.448585 | ||||||||
\(59\) | − | 22954.8i | − | 0.858507i | −0.903184 | − | 0.429254i | \(-0.858777\pi\) | ||
0.903184 | − | 0.429254i | \(-0.141223\pi\) | |||||||
\(60\) | 3539.33 | − | 30.4204i | 0.126924 | − | 0.00109090i | ||||
\(61\) | − | 27244.5i | − | 0.937462i | −0.883341 | − | 0.468731i | \(-0.844711\pi\) | ||
0.883341 | − | 0.468731i | \(-0.155289\pi\) | |||||||
\(62\) | −23141.4 | −0.764557 | ||||||||
\(63\) | −629.884 | − | 36640.0i | −0.0199945 | − | 1.16307i | ||||
\(64\) | 21980.3 | 0.670787 | ||||||||
\(65\) | −9254.23 | −0.271680 | ||||||||
\(66\) | 10890.9 | + | 19640.8i | 0.307755 | + | 0.555009i | ||||
\(67\) | 20257.5 | 0.551312 | 0.275656 | − | 0.961256i | \(-0.411105\pi\) | ||||
0.275656 | + | 0.961256i | \(0.411105\pi\) | |||||||
\(68\) | −23986.0 | −0.629051 | ||||||||
\(69\) | −13720.6 | + | 117.928i | −0.346937 | + | 0.00298191i | ||||
\(70\) | −6431.79 | −0.156887 | ||||||||
\(71\) | − | 56465.7i | − | 1.32935i | −0.747133 | − | 0.664674i | \(-0.768570\pi\) | ||
0.747133 | − | 0.664674i | \(-0.231430\pi\) | |||||||
\(72\) | 44581.8 | − | 766.412i | 1.01351 | − | 0.0174233i | ||||
\(73\) | − | 12025.4i | − | 0.264116i | −0.991242 | − | 0.132058i | \(-0.957842\pi\) | ||
0.991242 | − | 0.132058i | \(-0.0421585\pi\) | |||||||
\(74\) | −33428.2 | −0.709632 | ||||||||
\(75\) | 399.768 | + | 46512.0i | 0.00820645 | + | 0.954800i | ||||
\(76\) | 23209.2i | 0.460921i | ||||||||
\(77\) | 28892.3 | + | 53177.5i | 0.555336 | + | 1.02212i | ||||
\(78\) | −43590.5 | + | 374.658i | −0.811252 | + | 0.00697267i | ||||
\(79\) | − | 11065.5i | − | 0.199481i | −0.995013 | − | 0.0997407i | \(-0.968199\pi\) | ||
0.995013 | − | 0.0997407i | \(-0.0318013\pi\) | |||||||
\(80\) | − | 560.075i | − | 0.00978411i | ||||||
\(81\) | 59014.1 | − | 2029.64i | 0.999409 | − | 0.0343722i | ||||
\(82\) | 19380.1 | 0.318288 | ||||||||
\(83\) | −51574.3 | −0.821747 | −0.410873 | − | 0.911692i | \(-0.634776\pi\) | ||||
−0.410873 | + | 0.911692i | \(0.634776\pi\) | |||||||
\(84\) | 44927.1 | − | 386.146i | 0.694720 | − | 0.00597108i | ||||
\(85\) | 14910.0i | 0.223836i | ||||||||
\(86\) | 74914.4i | 1.09224i | ||||||||
\(87\) | 428.897 | + | 49901.1i | 0.00607512 | + | 0.706825i | ||||
\(88\) | −64703.7 | + | 35154.8i | −0.890682 | + | 0.483924i | ||||
\(89\) | − | 84147.7i | − | 1.12608i | −0.826431 | − | 0.563038i | \(-0.809633\pi\) | ||
0.826431 | − | 0.563038i | \(-0.190367\pi\) | |||||||
\(90\) | −178.142 | − | 10362.4i | −0.00231825 | − | 0.134851i | ||||
\(91\) | −117470. | −1.48704 | ||||||||
\(92\) | − | 16822.6i | − | 0.207216i | ||||||
\(93\) | −863.629 | − | 100481.i | −0.0103543 | − | 1.20469i | ||||
\(94\) | 40528.8i | 0.473090i | ||||||||
\(95\) | 14427.1 | 0.164010 | ||||||||
\(96\) | 764.000 | + | 88889.5i | 0.00846088 | + | 0.984402i | ||||
\(97\) | 99342.9 | 1.07203 | 0.536016 | − | 0.844208i | \(-0.319929\pi\) | ||||
0.536016 | + | 0.844208i | \(0.319929\pi\) | |||||||
\(98\) | −21306.2 | −0.224100 | ||||||||
\(99\) | −84875.2 | + | 48021.9i | −0.870347 | + | 0.492438i | ||||
\(100\) | −57027.7 | −0.570277 | ||||||||
\(101\) | −8413.56 | −0.0820685 | −0.0410343 | − | 0.999158i | \(-0.513065\pi\) | ||||
−0.0410343 | + | 0.999158i | \(0.513065\pi\) | |||||||
\(102\) | 603.633 | + | 70231.1i | 0.00574477 | + | 0.668389i | ||||
\(103\) | 11603.9 | 0.107773 | 0.0538864 | − | 0.998547i | \(-0.482839\pi\) | ||||
0.0538864 | + | 0.998547i | \(0.482839\pi\) | |||||||
\(104\) | − | 142932.i | − | 1.29582i | ||||||
\(105\) | −240.033 | − | 27927.2i | −0.00212470 | − | 0.247203i | ||||
\(106\) | 86082.0i | 0.744128i | ||||||||
\(107\) | 181478. | 1.53238 | 0.766188 | − | 0.642616i | \(-0.222151\pi\) | ||||
0.766188 | + | 0.642616i | \(0.222151\pi\) | |||||||
\(108\) | 1866.48 | + | 72372.3i | 0.0153980 | + | 0.597053i | ||||
\(109\) | − | 153350.i | − | 1.23628i | −0.786067 | − | 0.618141i | \(-0.787886\pi\) | ||
0.786067 | − | 0.618141i | \(-0.212114\pi\) | |||||||
\(110\) | 8171.23 | + | 15039.5i | 0.0643881 | + | 0.118509i | ||||
\(111\) | −1247.53 | − | 145147.i | −0.00961045 | − | 1.11815i | ||||
\(112\) | − | 7109.40i | − | 0.0535535i | ||||||
\(113\) | 209395.i | 1.54266i | 0.636435 | + | 0.771330i | \(0.280408\pi\) | ||||
−0.636435 | + | 0.771330i | \(0.719592\pi\) | |||||||
\(114\) | 67956.6 | − | 584.083i | 0.489744 | − | 0.00420933i | ||||
\(115\) | −10457.1 | −0.0737341 | ||||||||
\(116\) | −61182.9 | −0.422168 | ||||||||
\(117\) | −3253.57 | − | 189259.i | −0.0219733 | − | 1.27818i | ||||
\(118\) | − | 82407.3i | − | 0.544830i | ||||||
\(119\) | 189262.i | 1.22517i | ||||||||
\(120\) | 33980.5 | − | 292.060i | 0.215415 | − | 0.00185148i | ||||
\(121\) | 87638.8 | − | 135118.i | 0.544168 | − | 0.838976i | ||||
\(122\) | − | 97807.0i | − | 0.594936i | ||||||
\(123\) | 723.259 | + | 84149.3i | 0.00431053 | + | 0.501519i | ||||
\(124\) | 123198. | 0.719532 | ||||||||
\(125\) | 72575.0i | 0.415443i | ||||||||
\(126\) | −2261.27 | − | 131537.i | −0.0126890 | − | 0.738110i | ||||
\(127\) | 117065.i | 0.644046i | 0.946732 | + | 0.322023i | \(0.104363\pi\) | ||||
−0.946732 | + | 0.322023i | \(0.895637\pi\) | |||||||
\(128\) | −103570. | −0.558740 | ||||||||
\(129\) | −325282. | + | 2795.78i | −1.72102 | + | 0.0147921i | ||||
\(130\) | −33222.5 | −0.172414 | ||||||||
\(131\) | 176896. | 0.900614 | 0.450307 | − | 0.892874i | \(-0.351314\pi\) | ||||
0.450307 | + | 0.892874i | \(0.351314\pi\) | |||||||
\(132\) | −57980.3 | − | 104562.i | −0.289631 | − | 0.522325i | ||||
\(133\) | 183133. | 0.897712 | ||||||||
\(134\) | 72723.8 | 0.349876 | ||||||||
\(135\) | 44987.5 | − | 1160.22i | 0.212450 | − | 0.00547908i | ||||
\(136\) | −230285. | −1.06763 | ||||||||
\(137\) | − | 347712.i | − | 1.58277i | −0.611318 | − | 0.791385i | \(-0.709360\pi\) | ||
0.611318 | − | 0.791385i | \(-0.290640\pi\) | |||||||
\(138\) | −49256.7 | + | 423.359i | −0.220175 | + | 0.00189239i | ||||
\(139\) | 8720.60i | 0.0382833i | 0.999817 | + | 0.0191417i | \(0.00609335\pi\) | ||||
−0.999817 | + | 0.0191417i | \(0.993907\pi\) | |||||||
\(140\) | 34241.1 | 0.147648 | ||||||||
\(141\) | −175978. | + | 1512.52i | −0.745437 | + | 0.00640699i | ||||
\(142\) | − | 202711.i | − | 0.843637i | ||||||
\(143\) | 149239. | + | 274680.i | 0.610299 | + | 1.12328i | ||||
\(144\) | 11454.1 | − | 196.909i | 0.0460315 | − | 0.000791335i | ||||
\(145\) | 38032.0i | 0.150221i | ||||||||
\(146\) | − | 43171.1i | − | 0.167614i | ||||||
\(147\) | −795.142 | − | 92512.7i | −0.00303495 | − | 0.353109i | ||||
\(148\) | 177962. | 0.667843 | ||||||||
\(149\) | 354108. | 1.30668 | 0.653342 | − | 0.757063i | \(-0.273366\pi\) | ||||
0.653342 | + | 0.757063i | \(0.273366\pi\) | |||||||
\(150\) | 1435.16 | + | 166977.i | 0.00520801 | + | 0.605939i | ||||
\(151\) | 493279.i | 1.76056i | 0.474457 | + | 0.880278i | \(0.342644\pi\) | ||||
−0.474457 | + | 0.880278i | \(0.657356\pi\) | |||||||
\(152\) | 222827.i | 0.782274i | ||||||||
\(153\) | −304925. | + | 5242.02i | −1.05309 | + | 0.0181038i | ||||
\(154\) | 103723. | + | 190906.i | 0.352430 | + | 0.648661i | ||||
\(155\) | − | 76581.5i | − | 0.256032i | ||||||
\(156\) | 232064. | − | 1994.58i | 0.763478 | − | 0.00656205i | ||||
\(157\) | −94457.3 | −0.305834 | −0.152917 | − | 0.988239i | \(-0.548867\pi\) | ||||
−0.152917 | + | 0.988239i | \(0.548867\pi\) | |||||||
\(158\) | − | 39724.8i | − | 0.126596i | ||||||
\(159\) | −373773. | + | 3212.56i | −1.17251 | + | 0.0100776i | ||||
\(160\) | 67747.0i | 0.209214i | ||||||||
\(161\) | −132739. | −0.403585 | ||||||||
\(162\) | 211859. | − | 7286.37i | 0.634249 | − | 0.0218134i | ||||
\(163\) | −296304. | −0.873510 | −0.436755 | − | 0.899580i | \(-0.643872\pi\) | ||||
−0.436755 | + | 0.899580i | \(0.643872\pi\) | |||||||
\(164\) | −103174. | −0.299544 | ||||||||
\(165\) | −64997.3 | + | 36041.2i | −0.185860 | + | 0.103060i | ||||
\(166\) | −185151. | −0.521501 | ||||||||
\(167\) | −571023. | −1.58439 | −0.792196 | − | 0.610267i | \(-0.791062\pi\) | ||||
−0.792196 | + | 0.610267i | \(0.791062\pi\) | |||||||
\(168\) | 431336. | − | 3707.31i | 1.17908 | − | 0.0101341i | ||||
\(169\) | −235481. | −0.634219 | ||||||||
\(170\) | 53526.6i | 0.142052i | ||||||||
\(171\) | 5072.24 | + | 295049.i | 0.0132651 | + | 0.771622i | ||||
\(172\) | − | 398824.i | − | 1.02792i | ||||||
\(173\) | −12657.7 | −0.0321545 | −0.0160772 | − | 0.999871i | \(-0.505118\pi\) | ||||
−0.0160772 | + | 0.999871i | \(0.505118\pi\) | |||||||
\(174\) | 1539.73 | + | 179144.i | 0.00385542 | + | 0.448568i | ||||
\(175\) | 449979.i | 1.11070i | ||||||||
\(176\) | −16623.9 | + | 9032.09i | −0.0404531 | + | 0.0219789i | ||||
\(177\) | 357817. | − | 3075.42i | 0.858476 | − | 0.00737855i | ||||
\(178\) | − | 302089.i | − | 0.714635i | ||||||
\(179\) | − | 46770.9i | − | 0.109105i | −0.998511 | − | 0.0545523i | \(-0.982627\pi\) | ||
0.998511 | − | 0.0545523i | \(-0.0173732\pi\) | |||||||
\(180\) | 948.379 | + | 55166.6i | 0.00218173 | + | 0.126910i | ||||
\(181\) | 118107. | 0.267965 | 0.133983 | − | 0.990984i | \(-0.457223\pi\) | ||||
0.133983 | + | 0.990984i | \(0.457223\pi\) | |||||||
\(182\) | −421715. | −0.943714 | ||||||||
\(183\) | 424683. | − | 3650.13i | 0.937427 | − | 0.00805714i | ||||
\(184\) | − | 161511.i | − | 0.351688i | ||||||
\(185\) | − | 110624.i | − | 0.237639i | ||||||
\(186\) | −3100.41 | − | 360725.i | −0.00657108 | − | 0.764528i | ||||
\(187\) | 442553. | − | 240447.i | 0.925467 | − | 0.502824i | ||||
\(188\) | − | 215764.i | − | 0.445230i | ||||||
\(189\) | 571056. | − | 14727.5i | 1.16285 | − | 0.0299898i | ||||
\(190\) | 51793.0 | 0.104085 | ||||||||
\(191\) | − | 540991.i | − | 1.07302i | −0.843895 | − | 0.536509i | \(-0.819743\pi\) | ||
0.843895 | − | 0.536509i | \(-0.180257\pi\) | |||||||
\(192\) | 2944.86 | + | 342627.i | 0.00576516 | + | 0.670762i | ||||
\(193\) | − | 610969.i | − | 1.18066i | −0.807161 | − | 0.590331i | \(-0.798997\pi\) | ||
0.807161 | − | 0.590331i | \(-0.201003\pi\) | |||||||
\(194\) | 356639. | 0.680337 | ||||||||
\(195\) | −1239.85 | − | 144254.i | −0.00233498 | − | 0.271670i | ||||
\(196\) | 113428. | 0.210903 | ||||||||
\(197\) | 365903. | 0.671739 | 0.335869 | − | 0.941909i | \(-0.390970\pi\) | ||||
0.335869 | + | 0.941909i | \(0.390970\pi\) | |||||||
\(198\) | −304700. | + | 172398.i | −0.552344 | + | 0.312513i | ||||
\(199\) | −218381. | −0.390915 | −0.195457 | − | 0.980712i | \(-0.562619\pi\) | ||||
−0.195457 | + | 0.980712i | \(0.562619\pi\) | |||||||
\(200\) | −547512. | −0.967873 | ||||||||
\(201\) | 2714.03 | + | 315771.i | 0.00473833 | + | 0.551292i | ||||
\(202\) | −30204.5 | −0.0520827 | ||||||||
\(203\) | 482765.i | 0.822235i | ||||||||
\(204\) | −3213.58 | − | 373891.i | −0.00540646 | − | 0.629028i | ||||
\(205\) | 64134.3i | 0.106587i | ||||||||
\(206\) | 41657.6 | 0.0683953 | ||||||||
\(207\) | −3676.49 | − | 213859.i | −0.00596359 | − | 0.346899i | ||||
\(208\) | − | 36722.5i | − | 0.0588538i | ||||||
\(209\) | −232660. | − | 428220.i | −0.368431 | − | 0.678111i | ||||
\(210\) | −861.713 | − | 100258.i | −0.00134839 | − | 0.156881i | ||||
\(211\) | 697135.i | 1.07798i | 0.842312 | + | 0.538990i | \(0.181194\pi\) | ||||
−0.842312 | + | 0.538990i | \(0.818806\pi\) | |||||||
\(212\) | − | 458277.i | − | 0.700307i | ||||||
\(213\) | 880181. | − | 7565.11i | 1.32930 | − | 0.0114253i | ||||
\(214\) | 651503. | 0.972483 | ||||||||
\(215\) | −247914. | −0.365767 | ||||||||
\(216\) | 17919.7 | + | 694833.i | 0.0261334 | + | 1.01332i | ||||
\(217\) | − | 972099.i | − | 1.40140i | ||||||
\(218\) | − | 550523.i | − | 0.784575i | ||||||
\(219\) | 187451. | − | 1611.13i | 0.264106 | − | 0.00226998i | ||||
\(220\) | −43501.4 | − | 80066.1i | −0.0605964 | − | 0.111530i | ||||
\(221\) | 977607.i | 1.34643i | ||||||||
\(222\) | −4478.61 | − | 521075.i | −0.00609903 | − | 0.709606i | ||||
\(223\) | −1.13148e6 | −1.52365 | −0.761826 | − | 0.647781i | \(-0.775697\pi\) | ||||
−0.761826 | + | 0.647781i | \(0.775697\pi\) | |||||||
\(224\) | 859957.i | 1.14514i | ||||||||
\(225\) | −724971. | + | 12463.1i | −0.954694 | + | 0.0164123i | ||||
\(226\) | 751724.i | 0.979010i | ||||||||
\(227\) | −1.33675e6 | −1.72181 | −0.860904 | − | 0.508767i | \(-0.830101\pi\) | ||||
−0.860904 | + | 0.508767i | \(0.830101\pi\) | |||||||
\(228\) | −361782. | + | 3109.50i | −0.460904 | + | 0.00396144i | ||||
\(229\) | 936509. | 1.18011 | 0.590056 | − | 0.807362i | \(-0.299106\pi\) | ||||
0.590056 | + | 0.807362i | \(0.299106\pi\) | |||||||
\(230\) | −37540.9 | −0.0467935 | ||||||||
\(231\) | −825053. | + | 457495.i | −1.01731 | + | 0.564100i | ||||
\(232\) | −587405. | −0.716503 | ||||||||
\(233\) | 675682. | 0.815366 | 0.407683 | − | 0.913124i | \(-0.366337\pi\) | ||||
0.407683 | + | 0.913124i | \(0.366337\pi\) | |||||||
\(234\) | −11680.3 | − | 679434.i | −0.0139448 | − | 0.811162i | ||||
\(235\) | −134122. | −0.158427 | ||||||||
\(236\) | 438714.i | 0.512745i | ||||||||
\(237\) | 172487. | − | 1482.52i | 0.199474 | − | 0.00171447i | ||||
\(238\) | 679448.i | 0.777524i | ||||||||
\(239\) | 596353. | 0.675319 | 0.337659 | − | 0.941268i | \(-0.390365\pi\) | ||||
0.337659 | + | 0.941268i | \(0.390365\pi\) | |||||||
\(240\) | 8730.38 | − | 75.0372i | 0.00978374 | − | 8.40908e-5i | ||||
\(241\) | 1.24321e6i | 1.37880i | 0.724381 | + | 0.689400i | \(0.242126\pi\) | ||||
−0.724381 | + | 0.689400i | \(0.757874\pi\) | |||||||
\(242\) | 314621. | − | 485070.i | 0.345342 | − | 0.532435i | ||||
\(243\) | 39544.4 | + | 919633.i | 0.0429604 | + | 0.999077i | ||||
\(244\) | 520698.i | 0.559901i | ||||||||
\(245\) | − | 70508.5i | − | 0.0750458i | ||||||
\(246\) | 2596.48 | + | 302094.i | 0.00273557 | + | 0.318276i | ||||
\(247\) | 945945. | 0.986560 | ||||||||
\(248\) | 1.18280e6 | 1.22119 | ||||||||
\(249\) | −6909.77 | − | 803934.i | −0.00706261 | − | 0.821716i | ||||
\(250\) | 260543.i | 0.263651i | ||||||||
\(251\) | − | 1.76567e6i | − | 1.76899i | −0.466551 | − | 0.884494i | \(-0.654504\pi\) | ||
0.466551 | − | 0.884494i | \(-0.345496\pi\) | |||||||
\(252\) | 12038.4 | + | 700266.i | 0.0119417 | + | 0.694643i | ||||
\(253\) | 168638. | + | 310385.i | 0.165636 | + | 0.304859i | ||||
\(254\) | 420260.i | 0.408727i | ||||||||
\(255\) | −232415. | + | 1997.60i | −0.223828 | + | 0.00192379i | ||||
\(256\) | −1.07519e6 | −1.02538 | ||||||||
\(257\) | 347788.i | 0.328459i | 0.986422 | + | 0.164230i | \(0.0525138\pi\) | ||||
−0.986422 | + | 0.164230i | \(0.947486\pi\) | |||||||
\(258\) | −1.16776e6 | + | 10036.8i | −1.09220 | + | 0.00938742i | ||||
\(259\) | − | 1.40422e6i | − | 1.30072i | ||||||
\(260\) | 176867. | 0.162261 | ||||||||
\(261\) | −777794. | + | 13371.2i | −0.706746 | + | 0.0121498i | ||||
\(262\) | 635051. | 0.571552 | ||||||||
\(263\) | −985521. | −0.878570 | −0.439285 | − | 0.898348i | \(-0.644768\pi\) | ||||
−0.439285 | + | 0.898348i | \(0.644768\pi\) | |||||||
\(264\) | −556657. | − | 1.00388e6i | −0.491562 | − | 0.886490i | ||||
\(265\) | −284871. | −0.249191 | ||||||||
\(266\) | 657443. | 0.569710 | ||||||||
\(267\) | 1.31169e6 | − | 11273.9i | 1.12603 | − | 0.00967820i | ||||
\(268\) | −387162. | −0.329272 | ||||||||
\(269\) | 1.36787e6i | 1.15257i | 0.817250 | + | 0.576283i | \(0.195497\pi\) | ||||
−0.817250 | + | 0.576283i | \(0.804503\pi\) | |||||||
\(270\) | 161504. | − | 4165.18i | 0.134826 | − | 0.00347716i | ||||
\(271\) | − | 346976.i | − | 0.286996i | −0.989651 | − | 0.143498i | \(-0.954165\pi\) | ||
0.989651 | − | 0.143498i | \(-0.0458351\pi\) | |||||||
\(272\) | −59165.7 | −0.0484895 | ||||||||
\(273\) | −15738.3 | − | 1.83111e6i | −0.0127806 | − | 1.48699i | ||||
\(274\) | − | 1.24828e6i | − | 1.00446i | ||||||
\(275\) | 1.05219e6 | − | 571672.i | 0.838997 | − | 0.455843i | ||||
\(276\) | 262229. | − | 2253.85i | 0.207209 | − | 0.00178095i | ||||
\(277\) | − | 1.92307e6i | − | 1.50590i | −0.658079 | − | 0.752949i | \(-0.728631\pi\) | ||
0.658079 | − | 0.752949i | \(-0.271369\pi\) | |||||||
\(278\) | 31306.8i | 0.0242955i | ||||||||
\(279\) | 1.56617e6 | − | 26924.3i | 1.20456 | − | 0.0207078i | ||||
\(280\) | 328742. | 0.250588 | ||||||||
\(281\) | −1.51815e6 | −1.14696 | −0.573482 | − | 0.819218i | \(-0.694408\pi\) | ||||
−0.573482 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(282\) | −631758. | + | 5429.93i | −0.473073 | + | 0.00406603i | ||||
\(283\) | − | 195988.i | − | 0.145466i | −0.997351 | − | 0.0727332i | \(-0.976828\pi\) | ||
0.997351 | − | 0.0727332i | \(-0.0231721\pi\) | |||||||
\(284\) | 1.07918e6i | 0.793956i | ||||||||
\(285\) | 1932.90 | + | 224888.i | 0.00140961 | + | 0.164004i | ||||
\(286\) | 535765. | + | 986096.i | 0.387310 | + | 0.712860i | ||||
\(287\) | 814098.i | 0.583408i | ||||||||
\(288\) | −1.38550e6 | + | 23818.3i | −0.984293 | + | 0.0169211i | ||||
\(289\) | 155220. | 0.109321 | ||||||||
\(290\) | 136534.i | 0.0953337i | ||||||||
\(291\) | 13309.7 | + | 1.54855e6i | 0.00921371 | + | 1.07199i | ||||
\(292\) | 229831.i | 0.157744i | ||||||||
\(293\) | 2.75485e6 | 1.87469 | 0.937345 | − | 0.348403i | \(-0.113276\pi\) | ||||
0.937345 | + | 0.348403i | \(0.113276\pi\) | |||||||
\(294\) | −2854.54 | − | 332119.i | −0.00192605 | − | 0.224091i | ||||
\(295\) | 272710. | 0.182451 | ||||||||
\(296\) | 1.70858e6 | 1.13346 | ||||||||
\(297\) | −759932. | − | 1.31659e6i | −0.499900 | − | 0.866083i | ||||
\(298\) | 1.27124e6 | 0.829254 | ||||||||
\(299\) | −685646. | −0.443529 | ||||||||
\(300\) | −7640.40 | − | 888941.i | −0.00490132 | − | 0.570256i | ||||
\(301\) | −3.14693e6 | −2.00203 | ||||||||
\(302\) | 1.77086e6i | 1.11729i | ||||||||
\(303\) | −1127.22 | − | 131150.i | −0.000705348 | − | 0.0820655i | ||||
\(304\) | 57249.5i | 0.0355294i | ||||||||
\(305\) | 323672. | 0.199230 | ||||||||
\(306\) | −1.09467e6 | + | 18818.7i | −0.668315 | + | 0.0114891i | ||||
\(307\) | − | 684538.i | − | 0.414526i | −0.978285 | − | 0.207263i | \(-0.933544\pi\) | ||
0.978285 | − | 0.207263i | \(-0.0664556\pi\) | |||||||
\(308\) | −552192. | − | 1.01633e6i | −0.331675 | − | 0.610461i | ||||
\(309\) | 1554.65 | + | 180880.i | 0.000926268 | + | 0.107769i | ||||
\(310\) | − | 274926.i | − | 0.162484i | ||||||
\(311\) | 414984.i | 0.243294i | 0.992573 | + | 0.121647i | \(0.0388175\pi\) | ||||
−0.992573 | + | 0.121647i | \(0.961182\pi\) | |||||||
\(312\) | 2.22800e6 | − | 19149.6i | 1.29577 | − | 0.0111371i | ||||
\(313\) | 1.28268e6 | 0.740043 | 0.370022 | − | 0.929023i | \(-0.379350\pi\) | ||||
0.370022 | + | 0.929023i | \(0.379350\pi\) | |||||||
\(314\) | −339099. | −0.194090 | ||||||||
\(315\) | 435294. | − | 7483.21i | 0.247176 | − | 0.00424924i | ||||
\(316\) | 211484.i | 0.119141i | ||||||||
\(317\) | − | 2.70836e6i | − | 1.51376i | −0.653553 | − | 0.756881i | \(-0.726722\pi\) | ||
0.653553 | − | 0.756881i | \(-0.273278\pi\) | |||||||
\(318\) | −1.34184e6 | + | 11533.0i | −0.744101 | + | 0.00639550i | ||||
\(319\) | 1.12885e6 | − | 613326.i | 0.621098 | − | 0.337454i | ||||
\(320\) | 261133.i | 0.142556i | ||||||||
\(321\) | 24313.9 | + | 2.82886e6i | 0.0131702 | + | 1.53232i | ||||
\(322\) | −476532. | −0.256125 | ||||||||
\(323\) | − | 1.52407e6i | − | 0.812825i | ||||||
\(324\) | −1.12788e6 | + | 38790.6i | −0.596899 | + | 0.0205288i | ||||
\(325\) | 2.32430e6i | 1.22063i | ||||||||
\(326\) | −1.06372e6 | −0.554351 | ||||||||
\(327\) | 2.39040e6 | − | 20545.4i | 1.23624 | − | 0.0106254i | ||||
\(328\) | −990555. | −0.508386 | ||||||||
\(329\) | −1.70249e6 | −0.867153 | ||||||||
\(330\) | −233339. | + | 129387.i | −0.117951 | + | 0.0654043i | ||||
\(331\) | −1.10525e6 | −0.554486 | −0.277243 | − | 0.960800i | \(-0.589421\pi\) | ||||
−0.277243 | + | 0.960800i | \(0.589421\pi\) | |||||||
\(332\) | 985691. | 0.490790 | ||||||||
\(333\) | 2.26237e6 | − | 38892.7i | 1.11803 | − | 0.0192202i | ||||
\(334\) | −2.04996e6 | −1.00549 | ||||||||
\(335\) | 240664.i | 0.117165i | ||||||||
\(336\) | 110820. | − | 952.496i | 0.0535515 | − | 0.000460272i | ||||
\(337\) | 1.20295e6i | 0.576996i | 0.957480 | + | 0.288498i | \(0.0931559\pi\) | ||||
−0.957480 | + | 0.288498i | \(0.906844\pi\) | |||||||
\(338\) | −845371. | −0.402491 | ||||||||
\(339\) | −3.26403e6 | + | 28054.1i | −1.54260 | + | 0.0132586i | ||||
\(340\) | − | 284961.i | − | 0.133687i | ||||||
\(341\) | −2.27306e6 | + | 1.23500e6i | −1.05858 | + | 0.575149i | ||||
\(342\) | 18209.2 | + | 1.05922e6i | 0.00841834 | + | 0.489690i | ||||
\(343\) | 1.63956e6i | 0.752473i | ||||||||
\(344\) | − | 3.82903e6i | − | 1.74459i | ||||||
\(345\) | −1401.02 | − | 163005.i | −0.000633718 | − | 0.0737314i | ||||
\(346\) | −45441.0 | −0.0204060 | ||||||||
\(347\) | 1.61441e6 | 0.719765 | 0.359882 | − | 0.932998i | \(-0.382817\pi\) | ||||
0.359882 | + | 0.932998i | \(0.382817\pi\) | |||||||
\(348\) | −8197.10 | − | 953712.i | −0.00362838 | − | 0.422152i | ||||
\(349\) | 3.17188e6i | 1.39397i | 0.717085 | + | 0.696986i | \(0.245476\pi\) | ||||
−0.717085 | + | 0.696986i | \(0.754524\pi\) | |||||||
\(350\) | 1.61541e6i | 0.704877i | ||||||||
\(351\) | 2.94970e6 | − | 76072.6i | 1.27794 | − | 0.0329580i | ||||
\(352\) | 2.01084e6 | − | 1.09253e6i | 0.865009 | − | 0.469976i | ||||
\(353\) | 675430.i | 0.288499i | 0.989541 | + | 0.144249i | \(0.0460767\pi\) | ||||
−0.989541 | + | 0.144249i | \(0.953923\pi\) | |||||||
\(354\) | 1.28456e6 | − | 11040.7i | 0.544810 | − | 0.00468261i | ||||
\(355\) | 670829. | 0.282515 | ||||||||
\(356\) | 1.60824e6i | 0.672551i | ||||||||
\(357\) | −2.95020e6 | + | 25356.8i | −1.22513 | + | 0.0105299i | ||||
\(358\) | − | 167906.i | − | 0.0692404i | ||||||
\(359\) | −2.48053e6 | −1.01580 | −0.507900 | − | 0.861416i | \(-0.669578\pi\) | ||||
−0.507900 | + | 0.861416i | \(0.669578\pi\) | |||||||
\(360\) | 9105.20 | + | 529644.i | 0.00370282 | + | 0.215391i | ||||
\(361\) | 1.00139e6 | 0.404424 | ||||||||
\(362\) | 424001. | 0.170057 | ||||||||
\(363\) | 2.11794e6 | + | 1.34800e6i | 0.843622 | + | 0.536937i | ||||
\(364\) | 2.24509e6 | 0.888139 | ||||||||
\(365\) | 142866. | 0.0561301 | ||||||||
\(366\) | 1.52460e6 | − | 13103.9i | 0.594914 | − | 0.00511326i | ||||
\(367\) | −2.46844e6 | −0.956659 | −0.478329 | − | 0.878181i | \(-0.658757\pi\) | ||||
−0.478329 | + | 0.878181i | \(0.658757\pi\) | |||||||
\(368\) | − | 41495.9i | − | 0.0159730i | ||||||
\(369\) | −1.31161e6 | + | 22548.1i | −0.501464 | + | 0.00862075i | ||||
\(370\) | − | 397136.i | − | 0.150812i | ||||||
\(371\) | −3.61605e6 | −1.36395 | ||||||||
\(372\) | 16505.7 | + | 1.92040e6i | 0.00618411 | + | 0.719506i | ||||
\(373\) | − | 2.16792e6i | − | 0.806809i | −0.915022 | − | 0.403405i | \(-0.867827\pi\) | ||
0.915022 | − | 0.403405i | \(-0.132173\pi\) | |||||||
\(374\) | 1.58875e6 | − | 863201.i | 0.587324 | − | 0.319104i | ||||
\(375\) | −1.13129e6 | + | 9723.38i | −0.415428 | + | 0.00357058i | ||||
\(376\) | − | 2.07151e6i | − | 0.755644i | ||||||
\(377\) | 2.49365e6i | 0.903614i | ||||||||
\(378\) | 2.05008e6 | − | 52871.3i | 0.737974 | − | 0.0190323i | ||||
\(379\) | 3.73283e6 | 1.33487 | 0.667437 | − | 0.744666i | \(-0.267391\pi\) | ||||
0.667437 | + | 0.744666i | \(0.267391\pi\) | |||||||
\(380\) | −275732. | −0.0979553 | ||||||||
\(381\) | −1.82479e6 | + | 15684.0i | −0.644022 | + | 0.00553534i | ||||
\(382\) | − | 1.94215e6i | − | 0.680963i | ||||||
\(383\) | − | 2.18000e6i | − | 0.759382i | −0.925113 | − | 0.379691i | \(-0.876030\pi\) | ||
0.925113 | − | 0.379691i | \(-0.123970\pi\) | |||||||
\(384\) | −13876.0 | − | 1.61444e6i | −0.00480217 | − | 0.558720i | ||||
\(385\) | −631763. | + | 343249.i | −0.217221 | + | 0.118021i | ||||
\(386\) | − | 2.19336e6i | − | 0.749277i | ||||||
\(387\) | −87160.7 | − | 5.07009e6i | −0.0295831 | − | 1.72083i | ||||
\(388\) | −1.89865e6 | −0.640273 | ||||||||
\(389\) | − | 2.48481e6i | − | 0.832567i | −0.909235 | − | 0.416284i | \(-0.863332\pi\) | ||
0.909235 | − | 0.416284i | \(-0.136668\pi\) | |||||||
\(390\) | −4451.05 | − | 517868.i | −0.00148184 | − | 0.172408i | ||||
\(391\) | 1.10468e6i | 0.365423i | ||||||||
\(392\) | 1.08900e6 | 0.357943 | ||||||||
\(393\) | 23699.9 | + | 2.75743e6i | 0.00774045 | + | 0.900581i | ||||
\(394\) | 1.31358e6 | 0.426302 | ||||||||
\(395\) | 131461. | 0.0423940 | ||||||||
\(396\) | 1.62214e6 | − | 917798.i | 0.519817 | − | 0.294110i | ||||
\(397\) | −54162.3 | −0.0172473 | −0.00862364 | − | 0.999963i | \(-0.502745\pi\) | ||||
−0.00862364 | + | 0.999963i | \(0.502745\pi\) | |||||||
\(398\) | −783983. | −0.248084 | ||||||||
\(399\) | 24535.6 | + | 2.85465e6i | 0.00771550 | + | 0.897679i | ||||
\(400\) | −140669. | −0.0439590 | ||||||||
\(401\) | − | 3.15932e6i | − | 0.981144i | −0.871401 | − | 0.490572i | \(-0.836788\pi\) | ||
0.871401 | − | 0.490572i | \(-0.163212\pi\) | |||||||
\(402\) | 9743.32 | + | 1.13361e6i | 0.00300706 | + | 0.349863i | ||||
\(403\) | − | 5.02123e6i | − | 1.54010i | ||||||
\(404\) | 160801. | 0.0490156 | ||||||||
\(405\) | 24112.7 | + | 701105.i | 0.00730481 | + | 0.212395i | ||||
\(406\) | 1.73312e6i | 0.521811i | ||||||||
\(407\) | −3.28348e6 | + | 1.78398e6i | −0.982537 | + | 0.533831i | ||||
\(408\) | −30852.9 | − | 3.58966e6i | −0.00917584 | − | 1.06759i | ||||
\(409\) | 3.24246e6i | 0.958444i | 0.877694 | + | 0.479222i | \(0.159081\pi\) | ||||
−0.877694 | + | 0.479222i | \(0.840919\pi\) | |||||||
\(410\) | 230241.i | 0.0676429i | ||||||||
\(411\) | 5.42009e6 | − | 46585.4i | 1.58271 | − | 0.0136033i | ||||
\(412\) | −221774. | −0.0643675 | ||||||||
\(413\) | 3.46168e6 | 0.998648 | ||||||||
\(414\) | −13198.5 | − | 767751.i | −0.00378464 | − | 0.220150i | ||||
\(415\) | − | 612717.i | − | 0.174638i | ||||||
\(416\) | 4.44198e6i | 1.25847i | ||||||||
\(417\) | −135936. | + | 1168.36i | −0.0382819 | + | 0.000329031i | ||||
\(418\) | −835244. | − | 1.53730e6i | −0.233815 | − | 0.430346i | ||||
\(419\) | − | 540226.i | − | 0.150328i | −0.997171 | − | 0.0751642i | \(-0.976052\pi\) | ||
0.997171 | − | 0.0751642i | \(-0.0239481\pi\) | |||||||
\(420\) | 4587.52 | + | 533746.i | 0.00126898 | + | 0.147643i | ||||
\(421\) | −3.05118e6 | −0.839003 | −0.419501 | − | 0.907755i | \(-0.637795\pi\) | ||||
−0.419501 | + | 0.907755i | \(0.637795\pi\) | |||||||
\(422\) | 2.50270e6i | 0.684112i | ||||||||
\(423\) | −47154.1 | − | 2.74293e6i | −0.0128135 | − | 0.745355i | ||||
\(424\) | − | 4.39983e6i | − | 1.18856i | ||||||
\(425\) | 3.74480e6 | 1.00567 | ||||||||
\(426\) | 3.15983e6 | − | 27158.6i | 0.843606 | − | 0.00725075i | ||||
\(427\) | 4.10858e6 | 1.09049 | ||||||||
\(428\) | −3.46843e6 | −0.915215 | ||||||||
\(429\) | −4.26169e6 | + | 2.36312e6i | −1.11799 | + | 0.619930i | ||||
\(430\) | −890004. | −0.232124 | ||||||||
\(431\) | 2.10023e6 | 0.544596 | 0.272298 | − | 0.962213i | \(-0.412216\pi\) | ||||
0.272298 | + | 0.962213i | \(0.412216\pi\) | |||||||
\(432\) | 4603.99 | + | 178519.i | 0.00118693 | + | 0.0460230i | ||||
\(433\) | −3.92143e6 | −1.00514 | −0.502568 | − | 0.864538i | \(-0.667611\pi\) | ||||
−0.502568 | + | 0.864538i | \(0.667611\pi\) | |||||||
\(434\) | − | 3.48981e6i | − | 0.889361i | ||||||
\(435\) | −592839. | + | 5095.42i | −0.150215 | + | 0.00129109i | ||||
\(436\) | 2.93084e6i | 0.738372i | ||||||||
\(437\) | 1.06890e6 | 0.267754 | ||||||||
\(438\) | 672946. | − | 5783.93i | 0.167608 | − | 0.00144058i | ||||
\(439\) | 1.31281e6i | 0.325118i | 0.986699 | + | 0.162559i | \(0.0519748\pi\) | ||||
−0.986699 | + | 0.162559i | \(0.948025\pi\) | |||||||
\(440\) | −417649. | − | 768699.i | −0.102844 | − | 0.189289i | ||||
\(441\) | 1.44197e6 | − | 24789.2i | 0.353069 | − | 0.00606967i | ||||
\(442\) | 3.50959e6i | 0.854477i | ||||||||
\(443\) | 6.39479e6i | 1.54816i | 0.633086 | + | 0.774082i | \(0.281788\pi\) | ||||
−0.633086 | + | 0.774082i | \(0.718212\pi\) | |||||||
\(444\) | 23842.9 | + | 2.77406e6i | 0.00573986 | + | 0.667818i | ||||
\(445\) | 999699. | 0.239315 | ||||||||
\(446\) | −4.06200e6 | −0.966947 | ||||||||
\(447\) | 47442.4 | + | 5.51980e6i | 0.0112305 | + | 1.30664i | ||||
\(448\) | 3.31473e6i | 0.780284i | ||||||||
\(449\) | 4.54884e6i | 1.06484i | 0.846480 | + | 0.532420i | \(0.178717\pi\) | ||||
−0.846480 | + | 0.532420i | \(0.821283\pi\) | |||||||
\(450\) | −2.60263e6 | + | 44742.2i | −0.605872 | + | 0.0104156i | ||||
\(451\) | 1.90361e6 | − | 1.03427e6i | 0.440693 | − | 0.239437i | ||||
\(452\) | − | 4.00197e6i | − | 0.921357i | ||||||
\(453\) | −7.68917e6 | + | 66088.0i | −1.76049 | + | 0.0151313i | ||||
\(454\) | −4.79889e6 | −1.09270 | ||||||||
\(455\) | − | 1.39558e6i | − | 0.316028i | ||||||
\(456\) | −3.47340e6 | + | 29853.7i | −0.782245 | + | 0.00672335i | ||||
\(457\) | 2.25014e6i | 0.503987i | 0.967729 | + | 0.251993i | \(0.0810861\pi\) | ||||
−0.967729 | + | 0.251993i | \(0.918914\pi\) | |||||||
\(458\) | 3.36205e6 | 0.748928 | ||||||||
\(459\) | −122565. | − | 4.75243e6i | −0.0271540 | − | 1.05289i | ||||
\(460\) | 199858. | 0.0440379 | ||||||||
\(461\) | 3.13541e6 | 0.687136 | 0.343568 | − | 0.939128i | \(-0.388364\pi\) | ||||
0.343568 | + | 0.939128i | \(0.388364\pi\) | |||||||
\(462\) | −2.96192e6 | + | 1.64240e6i | −0.645608 | + | 0.357992i | ||||
\(463\) | −5.47459e6 | −1.18686 | −0.593429 | − | 0.804886i | \(-0.702226\pi\) | ||||
−0.593429 | + | 0.804886i | \(0.702226\pi\) | |||||||
\(464\) | −150918. | −0.0325422 | ||||||||
\(465\) | 1.19374e6 | − | 10260.2i | 0.256023 | − | 0.00220050i | ||||
\(466\) | 2.42568e6 | 0.517451 | ||||||||
\(467\) | − | 8.52104e6i | − | 1.80801i | −0.427524 | − | 0.904004i | \(-0.640614\pi\) | ||
0.427524 | − | 0.904004i | \(-0.359386\pi\) | |||||||
\(468\) | 62182.5 | + | 3.61712e6i | 0.0131236 | + | 0.763393i | ||||
\(469\) | 3.05491e6i | 0.641307i | ||||||||
\(470\) | −481494. | −0.100542 | ||||||||
\(471\) | −12655.1 | − | 1.47239e6i | −0.00262853 | − | 0.305823i | ||||
\(472\) | 4.21201e6i | 0.870230i | ||||||||
\(473\) | 3.99800e6 | + | 7.35847e6i | 0.821655 | + | 1.51229i | ||||
\(474\) | 619226. | − | 5322.21i | 0.126591 | − | 0.00108804i | ||||
\(475\) | − | 3.62352e6i | − | 0.736880i | ||||||
\(476\) | − | 3.61720e6i | − | 0.731736i | ||||||
\(477\) | −100154. | − | 5.82590e6i | −0.0201545 | − | 1.17238i | ||||
\(478\) | 2.14089e6 | 0.428574 | ||||||||
\(479\) | 8568.59 | 0.00170636 | 0.000853180 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000853180 | 1.00000i | \(0.499728\pi\) | ||||||||
\(480\) | −1.05603e6 | + | 9076.54i | −0.209206 | + | 0.00179811i | ||||
\(481\) | − | 7.25328e6i | − | 1.42946i | ||||||
\(482\) | 4.46309e6i | 0.875020i | ||||||||
\(483\) | −17784.0 | − | 2.06913e6i | −0.00346866 | − | 0.403570i | ||||
\(484\) | −1.67496e6 | + | 2.58238e6i | −0.325006 | + | 0.501080i | ||||
\(485\) | 1.18022e6i | 0.227829i | ||||||||
\(486\) | 141963. | + | 3.30146e6i | 0.0272637 | + | 0.634038i | ||||
\(487\) | 440964. | 0.0842520 | 0.0421260 | − | 0.999112i | \(-0.486587\pi\) | ||||
0.0421260 | + | 0.999112i | \(0.486587\pi\) | |||||||
\(488\) | 4.99912e6i | 0.950263i | ||||||||
\(489\) | −39697.9 | − | 4.61875e6i | −0.00750750 | − | 0.873478i | ||||
\(490\) | − | 253124.i | − | 0.0476259i | ||||||
\(491\) | −179754. | −0.0336493 | −0.0168246 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168246 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(492\) | −13823.0 | − | 1.60827e6i | −0.00257447 | − | 0.299533i | ||||
\(493\) | 4.01766e6 | 0.744486 | ||||||||
\(494\) | 3.39592e6 | 0.626095 | ||||||||
\(495\) | −570514. | − | 1.00834e6i | −0.104653 | − | 0.184967i | ||||
\(496\) | 303890. | 0.0554641 | ||||||||
\(497\) | 8.51527e6 | 1.54635 | ||||||||
\(498\) | −24805.9 | − | 2.88610e6i | −0.00448210 | − | 0.521481i | ||||
\(499\) | 4.77108e6 | 0.857759 | 0.428879 | − | 0.903362i | \(-0.358908\pi\) | ||||
0.428879 | + | 0.903362i | \(0.358908\pi\) | |||||||
\(500\) | − | 1.38706e6i | − | 0.248124i | ||||||
\(501\) | −76504.0 | − | 8.90105e6i | −0.0136173 | − | 1.58433i | ||||
\(502\) | − | 6.33871e6i | − | 1.12264i | ||||||
\(503\) | 270590. | 0.0476860 | 0.0238430 | − | 0.999716i | \(-0.492410\pi\) | ||||
0.0238430 | + | 0.999716i | \(0.492410\pi\) | |||||||
\(504\) | 115578. | + | 6.72312e6i | 0.0202675 | + | 1.17895i | ||||
\(505\) | − | 99955.6i | − | 0.0174413i | ||||||
\(506\) | 605407. | + | 1.11427e6i | 0.105116 | + | 0.193471i | ||||
\(507\) | −31549.0 | − | 3.67065e6i | −0.00545087 | − | 0.634195i | ||||
\(508\) | − | 2.23735e6i | − | 0.384658i | ||||||
\(509\) | 3.74567e6i | 0.640819i | 0.947279 | + | 0.320410i | \(0.103821\pi\) | ||||
−0.947279 | + | 0.320410i | \(0.896179\pi\) | |||||||
\(510\) | −834366. | + | 7171.33i | −0.142047 | + | 0.00122088i | ||||
\(511\) | 1.81349e6 | 0.307229 | ||||||||
\(512\) | −545645. | −0.0919888 | ||||||||
\(513\) | −4.59852e6 | + | 118595.i | −0.771479 | + | 0.0198964i | ||||
\(514\) | 1.24855e6i | 0.208448i | ||||||||
\(515\) | 137857.i | 0.0229040i | ||||||||
\(516\) | 6.21682e6 | − | 53433.2i | 1.02788 | − | 0.00883460i | ||||
\(517\) | 2.16292e6 | + | 3.98094e6i | 0.355889 | + | 0.655027i | ||||
\(518\) | − | 5.04111e6i | − | 0.825471i | ||||||
\(519\) | −1695.85 | − | 197307.i | −0.000276356 | − | 0.0321533i | ||||
\(520\) | 1.69807e6 | 0.275389 | ||||||||
\(521\) | − | 6.27808e6i | − | 1.01329i | −0.862156 | − | 0.506644i | \(-0.830886\pi\) | ||
0.862156 | − | 0.506644i | \(-0.169114\pi\) | |||||||
\(522\) | −2.79226e6 | + | 48002.3i | −0.448518 | + | 0.00771055i | ||||
\(523\) | − | 5.76389e6i | − | 0.921428i | −0.887549 | − | 0.460714i | \(-0.847593\pi\) | ||
0.887549 | − | 0.460714i | \(-0.152407\pi\) | |||||||
\(524\) | −3.38084e6 | −0.537894 | ||||||||
\(525\) | −7.01421e6 | + | 60286.8i | −1.11066 | + | 0.00954605i | ||||
\(526\) | −3.53800e6 | −0.557562 | ||||||||
\(527\) | −8.08999e6 | −1.26888 | ||||||||
\(528\) | −143018. | − | 257921.i | −0.0223258 | − | 0.0402627i | ||||
\(529\) | 5.66157e6 | 0.879626 | ||||||||
\(530\) | −1.02268e6 | −0.158143 | ||||||||
\(531\) | 95878.5 | + | 5.57720e6i | 0.0147566 | + | 0.858380i | ||||
\(532\) | −3.50005e6 | −0.536160 | ||||||||
\(533\) | 4.20510e6i | 0.641149i | ||||||||
\(534\) | 4.70892e6 | − | 40472.9i | 0.714609 | − | 0.00614202i | ||||
\(535\) | 2.15601e6i | 0.325662i | ||||||||
\(536\) | −3.71706e6 | −0.558841 | ||||||||
\(537\) | 729059. | − | 6266.22i | 0.109101 | − | 0.000937713i | ||||
\(538\) | 4.91064e6i | 0.731446i | ||||||||
\(539\) | −2.09280e6 | + | 1.13706e6i | −0.310282 | + | 0.168582i | ||||
\(540\) | −859804. | + | 22174.3i | −0.126886 | + | 0.00327239i | ||||
\(541\) | − | 7.90557e6i | − | 1.16129i | −0.814157 | − | 0.580644i | \(-0.802801\pi\) | ||
0.814157 | − | 0.580644i | \(-0.197199\pi\) | |||||||
\(542\) | − | 1.24564e6i | − | 0.182135i | ||||||
\(543\) | 15823.6 | + | 1.84104e6i | 0.00230306 | + | 0.267955i | ||||
\(544\) | 7.15672e6 | 1.03685 | ||||||||
\(545\) | 1.82184e6 | 0.262736 | ||||||||
\(546\) | −56500.1 | − | 6.57364e6i | −0.00811087 | − | 0.943679i | ||||
\(547\) | 721261.i | 0.103068i | 0.998671 | + | 0.0515341i | \(0.0164111\pi\) | ||||
−0.998671 | + | 0.0515341i | \(0.983589\pi\) | |||||||
\(548\) | 6.64549e6i | 0.945312i | ||||||||
\(549\) | 113796. | + | 6.61943e6i | 0.0161137 | + | 0.937323i | ||||
\(550\) | 3.77732e6 | − | 2.05229e6i | 0.532448 | − | 0.289289i | ||||
\(551\) | − | 3.88754e6i | − | 0.545502i | ||||||
\(552\) | 2.51761e6 | − | 21638.7i | 0.351675 | − | 0.00302262i | ||||
\(553\) | 1.66872e6 | 0.232044 | ||||||||
\(554\) | − | 6.90377e6i | − | 0.955679i | ||||||
\(555\) | 1.72439e6 | − | 14821.0i | 0.237631 | − | 0.00204242i | ||||
\(556\) | − | 166669.i | − | 0.0228648i | ||||||
\(557\) | −8.49710e6 | −1.16047 | −0.580233 | − | 0.814450i | \(-0.697039\pi\) | ||||
−0.580233 | + | 0.814450i | \(0.697039\pi\) | |||||||
\(558\) | 5.62252e6 | − | 96657.6i | 0.764444 | − | 0.0131417i | ||||
\(559\) | −1.62550e7 | −2.20018 | ||||||||
\(560\) | 84461.7 | 0.0113812 | ||||||||
\(561\) | 3.80736e6 | + | 6.86624e6i | 0.510759 | + | 0.921111i | ||||
\(562\) | −5.45013e6 | −0.727891 | ||||||||
\(563\) | −1.78249e6 | −0.237005 | −0.118502 | − | 0.992954i | \(-0.537809\pi\) | ||||
−0.118502 | + | 0.992954i | \(0.537809\pi\) | |||||||
\(564\) | 3.36331e6 | − | 28907.4i | 0.445214 | − | 0.00382659i | ||||
\(565\) | −2.48767e6 | −0.327848 | ||||||||
\(566\) | − | 703591.i | − | 0.0923165i | ||||||
\(567\) | 306079. | + | 8.89958e6i | 0.0399830 | + | 1.16255i | ||||
\(568\) | 1.03610e7i | 1.34750i | ||||||||
\(569\) | 1.16476e7 | 1.50819 | 0.754094 | − | 0.656767i | \(-0.228076\pi\) | ||||
0.754094 | + | 0.656767i | \(0.228076\pi\) | |||||||
\(570\) | 6939.07 | + | 807344.i | 0.000894570 | + | 0.104081i | ||||
\(571\) | − | 7.50760e6i | − | 0.963632i | −0.876272 | − | 0.481816i | \(-0.839977\pi\) | ||
0.876272 | − | 0.481816i | \(-0.160023\pi\) | |||||||
\(572\) | −2.85227e6 | − | 5.24971e6i | −0.364502 | − | 0.670880i | ||||
\(573\) | 8.43291e6 | − | 72480.4i | 1.07298 | − | 0.00922219i | ||||
\(574\) | 2.92260e6i | 0.370245i | ||||||||
\(575\) | 2.62642e6i | 0.331280i | ||||||||
\(576\) | −5.34043e6 | + | 91808.2i | −0.670688 | + | 0.0115299i | ||||
\(577\) | −1.53192e7 | −1.91557 | −0.957784 | − | 0.287488i | \(-0.907180\pi\) | ||||
−0.957784 | + | 0.287488i | \(0.907180\pi\) | |||||||
\(578\) | 557237. | 0.0693778 | ||||||||
\(579\) | 9.52371e6 | − | 81855.7i | 1.18062 | − | 0.0101474i | ||||
\(580\) | − | 726871.i | − | 0.0897196i | ||||||
\(581\) | − | 7.77762e6i | − | 0.955887i | ||||||
\(582\) | 47781.4 | + | 5.55924e6i | 0.00584725 | + | 0.680312i | ||||
\(583\) | 4.59399e6 | + | 8.45541e6i | 0.559781 | + | 1.03030i | ||||
\(584\) | 2.20656e6i | 0.267722i | ||||||||
\(585\) | 2.24845e6 | − | 38653.4i | 0.271639 | − | 0.00466980i | ||||
\(586\) | 9.88986e6 | 1.18972 | ||||||||
\(587\) | 2.66999e6i | 0.319826i | 0.987131 | + | 0.159913i | \(0.0511214\pi\) | ||||
−0.987131 | + | 0.159913i | \(0.948879\pi\) | |||||||
\(588\) | 15196.8 | + | 1.76811e6i | 0.00181263 | + | 0.210895i | ||||
\(589\) | 7.82798e6i | 0.929740i | ||||||||
\(590\) | 979022. | 0.115788 | ||||||||
\(591\) | 49022.6 | + | 5.70365e6i | 0.00577334 | + | 0.671714i | ||||
\(592\) | 438975. | 0.0514797 | ||||||||
\(593\) | −814291. | −0.0950918 | −0.0475459 | − | 0.998869i | \(-0.515140\pi\) | ||||
−0.0475459 | + | 0.998869i | \(0.515140\pi\) | |||||||
\(594\) | −2.72814e6 | − | 4.72653e6i | −0.317249 | − | 0.549637i | ||||
\(595\) | −2.24849e6 | −0.260375 | ||||||||
\(596\) | −6.76774e6 | −0.780419 | ||||||||
\(597\) | −29258.0 | − | 3.40410e6i | −0.00335977 | − | 0.390900i | ||||
\(598\) | −2.46145e6 | −0.281474 | ||||||||
\(599\) | 1.21744e6i | 0.138637i | 0.997595 | + | 0.0693187i | \(0.0220825\pi\) | ||||
−0.997595 | + | 0.0693187i | \(0.977917\pi\) | |||||||
\(600\) | −73354.0 | − | 8.53455e6i | −0.00831851 | − | 0.967837i | ||||
\(601\) | 3.13293e6i | 0.353806i | 0.984228 | + | 0.176903i | \(0.0566078\pi\) | ||||
−0.984228 | + | 0.176903i | \(0.943392\pi\) | |||||||
\(602\) | −1.12974e7 | −1.27054 | ||||||||
\(603\) | −4.92183e6 | + | 84612.0i | −0.551231 | + | 0.00947630i | ||||
\(604\) | − | 9.42757e6i | − | 1.05150i | ||||||
\(605\) | 1.60524e6 | + | 1.04117e6i | 0.178300 | + | 0.115647i | ||||
\(606\) | −4046.71 | − | 470824.i | −0.000447631 | − | 0.0520808i | ||||
\(607\) | 1.32997e7i | 1.46511i | 0.680707 | + | 0.732556i | \(0.261673\pi\) | ||||
−0.680707 | + | 0.732556i | \(0.738327\pi\) | |||||||
\(608\) | − | 6.92494e6i | − | 0.759726i | ||||||
\(609\) | −7.52529e6 | + | 64679.5i | −0.822205 | + | 0.00706681i | ||||
\(610\) | 1.16198e6 | 0.126436 | ||||||||
\(611\) | −8.79398e6 | −0.952977 | ||||||||
\(612\) | 5.82775e6 | − | 100186.i | 0.628959 | − | 0.0108125i | ||||
\(613\) | − | 2.10731e6i | − | 0.226504i | −0.993566 | − | 0.113252i | \(-0.963873\pi\) | ||
0.993566 | − | 0.113252i | \(-0.0361268\pi\) | |||||||
\(614\) | − | 2.45748e6i | − | 0.263068i | ||||||
\(615\) | −999718. | + | 8592.52i | −0.106583 | + | 0.000916079i | ||||
\(616\) | −5.30149e6 | − | 9.75759e6i | −0.562919 | − | 1.03607i | ||||
\(617\) | 4.13947e6i | 0.437756i | 0.975752 | + | 0.218878i | \(0.0702397\pi\) | ||||
−0.975752 | + | 0.218878i | \(0.929760\pi\) | |||||||
\(618\) | 5581.16 | + | 649354.i | 0.000587832 | + | 0.0683928i | ||||
\(619\) | −5.30546e6 | −0.556540 | −0.278270 | − | 0.960503i | \(-0.589761\pi\) | ||||
−0.278270 | + | 0.960503i | \(0.589761\pi\) | |||||||
\(620\) | 1.46363e6i | 0.152916i | ||||||||
\(621\) | 3.33312e6 | − | 85961.0i | 0.346835 | − | 0.00894484i | ||||
\(622\) | 1.48978e6i | 0.154400i | ||||||||
\(623\) | 1.26898e7 | 1.30989 | ||||||||
\(624\) | 572426. | − | 4919.97i | 0.0588516 | − | 0.000505826i | ||||
\(625\) | 8.46235e6 | 0.866544 | ||||||||
\(626\) | 4.60479e6 | 0.469649 | ||||||||
\(627\) | 6.64387e6 | − | 3.68405e6i | 0.674920 | − | 0.374245i | ||||
\(628\) | 1.80527e6 | 0.182660 | ||||||||
\(629\) | −1.16862e7 | −1.17773 | ||||||||
\(630\) | 1.56270e6 | − | 26864.5i | 0.156864 | − | 0.00269667i | ||||
\(631\) | 8.10190e6 | 0.810053 | 0.405027 | − | 0.914305i | \(-0.367262\pi\) | ||||
0.405027 | + | 0.914305i | \(0.367262\pi\) | |||||||
\(632\) | 2.03042e6i | 0.202205i | ||||||||
\(633\) | −1.08669e7 | + | 93400.0i | −1.07794 | + | 0.00926483i | ||||
\(634\) | − | 9.72293e6i | − | 0.960670i | ||||||
\(635\) | −1.39076e6 | −0.136873 | ||||||||
\(636\) | 7.14357e6 | − | 61398.6i | 0.700281 | − | 0.00601888i | ||||
\(637\) | − | 4.62304e6i | − | 0.451418i | ||||||
\(638\) | 4.05255e6 | − | 2.20183e6i | 0.394164 | − | 0.214157i | ||||
\(639\) | 235848. | + | 1.37191e7i | 0.0228497 | + | 1.32915i | ||||
\(640\) | − | 1.23044e6i | − | 0.118744i | ||||||
\(641\) | − | 1.82583e6i | − | 0.175515i | −0.996142 | − | 0.0877576i | \(-0.972030\pi\) | ||
0.996142 | − | 0.0877576i | \(-0.0279701\pi\) | |||||||
\(642\) | 87286.5 | + | 1.01556e7i | 0.00835813 | + | 0.972447i | ||||
\(643\) | −3.69890e6 | −0.352813 | −0.176407 | − | 0.984317i | \(-0.556447\pi\) | ||||
−0.176407 | + | 0.984317i | \(0.556447\pi\) | |||||||
\(644\) | 2.53692e6 | 0.241042 | ||||||||
\(645\) | −33214.7 | − | 3.86445e6i | −0.00314363 | − | 0.365753i | ||||
\(646\) | − | 5.47136e6i | − | 0.515839i | ||||||
\(647\) | − | 1.07732e7i | − | 1.01178i | −0.862599 | − | 0.505888i | \(-0.831165\pi\) | ||
0.862599 | − | 0.505888i | \(-0.168835\pi\) | |||||||
\(648\) | −1.08286e7 | + | 372421.i | −1.01306 | + | 0.0348415i | ||||
\(649\) | −4.39788e6 | − | 8.09446e6i | −0.409856 | − | 0.754356i | ||||
\(650\) | 8.34418e6i | 0.774640i | ||||||||
\(651\) | 1.51530e7 | − | 130239.i | 1.40135 | − | 0.0120445i | ||||
\(652\) | 5.66297e6 | 0.521706 | ||||||||
\(653\) | 1.06326e7i | 0.975791i | 0.872902 | + | 0.487896i | \(0.162235\pi\) | ||||
−0.872902 | + | 0.487896i | \(0.837765\pi\) | |||||||
\(654\) | 8.58149e6 | − | 73757.4i | 0.784546 | − | 0.00674313i | ||||
\(655\) | 2.10157e6i | 0.191400i | ||||||||
\(656\) | −254497. | −0.0230899 | ||||||||
\(657\) | 50228.3 | + | 2.92175e6i | 0.00453978 | + | 0.264077i | ||||
\(658\) | −6.11191e6 | −0.550316 | ||||||||
\(659\) | 6.09424e6 | 0.546645 | 0.273323 | − | 0.961922i | \(-0.411877\pi\) | ||||
0.273323 | + | 0.961922i | \(0.411877\pi\) | |||||||
\(660\) | 1.24223e6 | − | 688822.i | 0.111005 | − | 0.0615527i | ||||
\(661\) | 1.01212e7 | 0.901004 | 0.450502 | − | 0.892775i | \(-0.351245\pi\) | ||||
0.450502 | + | 0.892775i | \(0.351245\pi\) | |||||||
\(662\) | −3.96782e6 | −0.351890 | ||||||||
\(663\) | −1.52388e7 | + | 130977.i | −1.34638 | + | 0.0115721i | ||||
\(664\) | 9.46342e6 | 0.832968 | ||||||||
\(665\) | 2.17567e6i | 0.190783i | ||||||||
\(666\) | 8.12185e6 | − | 139624.i | 0.709528 | − | 0.0121976i | ||||
\(667\) | 2.81779e6i | 0.245242i | ||||||||
\(668\) | 1.09134e7 | 0.946281 | ||||||||
\(669\) | −151593. | − | 1.76374e7i | −0.0130952 | − | 1.52360i | ||||
\(670\) | 863980.i | 0.0743561i | ||||||||
\(671\) | −5.21972e6 | − | 9.60710e6i | −0.447549 | − | 0.823732i | ||||
\(672\) | −1.34049e7 | + | 115214.i | −1.14509 | + | 0.00984201i | ||||
\(673\) | − | 1.28100e7i | − | 1.09022i | −0.838366 | − | 0.545108i | \(-0.816489\pi\) | ||
0.838366 | − | 0.545108i | \(-0.183511\pi\) | |||||||
\(674\) | 4.31857e6i | 0.366176i | ||||||||
\(675\) | −291403. | − | 1.12991e7i | −0.0246169 | − | 0.954517i | ||||
\(676\) | 4.50053e6 | 0.378788 | ||||||||
\(677\) | 1.11938e7 | 0.938656 | 0.469328 | − | 0.883024i | \(-0.344496\pi\) | ||||
0.469328 | + | 0.883024i | \(0.344496\pi\) | |||||||
\(678\) | −1.17178e7 | + | 100714.i | −0.978974 | + | 0.00841423i | ||||
\(679\) | 1.49813e7i | 1.24703i | ||||||||
\(680\) | − | 2.73585e6i | − | 0.226893i | ||||||
\(681\) | −179093. | − | 2.08371e7i | −0.0147983 | − | 1.72174i | ||||
\(682\) | −8.16024e6 | + | 4.43361e6i | −0.671803 | + | 0.365003i | ||||
\(683\) | − | 577600.i | − | 0.0473779i | −0.999719 | − | 0.0236889i | \(-0.992459\pi\) | ||
0.999719 | − | 0.0236889i | \(-0.00754113\pi\) | |||||||
\(684\) | −96941.0 | − | 5.63900e6i | −0.00792259 | − | 0.460853i | ||||
\(685\) | 4.13091e6 | 0.336372 | ||||||||
\(686\) | 5.88597e6i | 0.477538i | ||||||||
\(687\) | 125471. | + | 1.45982e7i | 0.0101426 | + | 1.18007i | ||||
\(688\) | − | 983768.i | − | 0.0792358i | ||||||
\(689\) | −1.86782e7 | −1.49895 | ||||||||
\(690\) | −5029.62 | − | 585184.i | −0.000402173 | − | 0.0467918i | ||||
\(691\) | 7.05063e6 | 0.561737 | 0.280868 | − | 0.959746i | \(-0.409378\pi\) | ||||
0.280868 | + | 0.959746i | \(0.409378\pi\) | |||||||
\(692\) | 241916. | 0.0192043 | ||||||||
\(693\) | −7.24191e6 | − | 1.27995e7i | −0.572823 | − | 1.01242i | ||||
\(694\) | 5.79570e6 | 0.456780 | ||||||||
\(695\) | −103603. | −0.00813601 | ||||||||
\(696\) | −78698.8 | − | 9.15640e6i | −0.00615808 | − | 0.716476i | ||||
\(697\) | 6.77508e6 | 0.528241 | ||||||||
\(698\) | 1.13870e7i | 0.884648i | ||||||||
\(699\) | 90525.8 | + | 1.05324e7i | 0.00700777 | + | 0.815336i | ||||
\(700\) | − | 8.60002e6i | − | 0.663367i | ||||||
\(701\) | 5.52192e6 | 0.424419 | 0.212209 | − | 0.977224i | \(-0.431934\pi\) | ||||
0.212209 | + | 0.977224i | \(0.431934\pi\) | |||||||
\(702\) | 1.05894e7 | − | 273099.i | 0.811012 | − | 0.0209159i | ||||
\(703\) | 1.13077e7i | 0.862949i | ||||||||
\(704\) | 7.75083e6 | − | 4.21118e6i | 0.589409 | − | 0.320237i | ||||
\(705\) | −17969.2 | − | 2.09067e6i | −0.00136162 | − | 0.158421i | ||||
\(706\) | 2.42478e6i | 0.183088i | ||||||||
\(707\) | − | 1.26880e6i | − | 0.0954652i | ||||||
\(708\) | −6.83862e6 | + | 58777.6i | −0.512726 | + | 0.00440685i | ||||
\(709\) | −9.02213e6 | −0.674052 | −0.337026 | − | 0.941495i | \(-0.609421\pi\) | ||||
−0.337026 | + | 0.941495i | \(0.609421\pi\) | |||||||
\(710\) | 2.40826e6 | 0.179291 | ||||||||
\(711\) | 46218.7 | + | 2.68851e6i | 0.00342881 | + | 0.199452i | ||||
\(712\) | 1.54404e7i | 1.14145i | ||||||||
\(713\) | − | 5.67392e6i | − | 0.417984i | ||||||
\(714\) | −1.05912e7 | + | 91030.4i | −0.777495 | + | 0.00668253i | ||||
\(715\) | −3.26328e6 | + | 1.77300e6i | −0.238720 | + | 0.129701i | ||||
\(716\) | 893888.i | 0.0651629i | ||||||||
\(717\) | 79897.6 | + | 9.29588e6i | 0.00580411 | + | 0.675294i | ||||
\(718\) | −8.90505e6 | −0.644652 | ||||||||
\(719\) | − | 1.01462e7i | − | 0.731949i | −0.930625 | − | 0.365974i | \(-0.880736\pi\) | ||
0.930625 | − | 0.365974i | \(-0.119264\pi\) | |||||||
\(720\) | 2339.34 | + | 136078.i | 0.000168175 | + | 0.00978266i | ||||
\(721\) | 1.74991e6i | 0.125365i | ||||||||
\(722\) | 3.59498e6 | 0.256657 | ||||||||
\(723\) | −1.93790e7 | + | 166561.i | −1.37875 | + | 0.0118503i | ||||
\(724\) | −2.25726e6 | −0.160043 | ||||||||
\(725\) | 9.55215e6 | 0.674926 | ||||||||
\(726\) | 7.60337e6 | + | 4.83929e6i | 0.535383 | + | 0.340754i | ||||
\(727\) | −1.92374e7 | −1.34993 | −0.674965 | − | 0.737850i | \(-0.735841\pi\) | ||||
−0.674965 | + | 0.737850i | \(0.735841\pi\) | |||||||
\(728\) | 2.15547e7 | 1.50735 | ||||||||
\(729\) | −1.43298e7 | + | 739622.i | −0.998671 | + | 0.0515456i | ||||
\(730\) | 512885. | 0.0356215 | ||||||||
\(731\) | 2.61893e7i | 1.81272i | ||||||||
\(732\) | −8.11658e6 | + | 69761.5i | −0.559880 | + | 0.00481214i | ||||
\(733\) | − | 1.22590e7i | − | 0.842743i | −0.906888 | − | 0.421371i | \(-0.861549\pi\) | ||
0.906888 | − | 0.421371i | \(-0.138451\pi\) | |||||||
\(734\) | −8.86164e6 | −0.607119 | ||||||||
\(735\) | 1.09908e6 | − | 9446.52i | 0.0750430 | − | 0.000644990i | ||||
\(736\) | 5.01938e6i | 0.341551i | ||||||||
\(737\) | 7.14330e6 | − | 3.88109e6i | 0.484429 | − | 0.263200i | ||||
\(738\) | −4.70866e6 | + | 80947.3i | −0.318241 | + | 0.00547094i | ||||
\(739\) | 1.89627e6i | 0.127729i | 0.997959 | + | 0.0638645i | \(0.0203425\pi\) | ||||
−0.997959 | + | 0.0638645i | \(0.979657\pi\) | |||||||
\(740\) | 2.11425e6i | 0.141931i | ||||||||
\(741\) | 126735. | + | 1.47453e7i | 0.00847912 | + | 0.986524i | ||||
\(742\) | −1.29815e7 | −0.865598 | ||||||||
\(743\) | 6.60277e6 | 0.438787 | 0.219394 | − | 0.975636i | \(-0.429592\pi\) | ||||
0.219394 | + | 0.975636i | \(0.429592\pi\) | |||||||
\(744\) | 158468. | + | 1.84374e7i | 0.0104957 | + | 1.22114i | ||||
\(745\) | 4.20691e6i | 0.277698i | ||||||||
\(746\) | − | 7.78278e6i | − | 0.512021i | ||||||
\(747\) | 1.25307e7 | − | 215417.i | 0.821625 | − | 0.0141247i | ||||
\(748\) | −8.45809e6 | + | 4.59544e6i | −0.552737 | + | 0.300313i | ||||
\(749\) | 2.73677e7i | 1.78252i | ||||||||
\(750\) | −4.06131e6 | + | 34906.7i | −0.263641 | + | 0.00226598i | ||||
\(751\) | 3.98388e6 | 0.257754 | 0.128877 | − | 0.991661i | \(-0.458863\pi\) | ||||
0.128877 | + | 0.991661i | \(0.458863\pi\) | |||||||
\(752\) | − | 532220.i | − | 0.0343199i | ||||||
\(753\) | 2.75230e7 | − | 236559.i | 1.76892 | − | 0.0152038i | ||||
\(754\) | 8.95216e6i | 0.573455i | ||||||||
\(755\) | −5.86029e6 | −0.374155 | ||||||||
\(756\) | −1.09141e7 | + | 281473.i | −0.694515 | + | 0.0179115i | ||||
\(757\) | 1.21560e7 | 0.770994 | 0.385497 | − | 0.922709i | \(-0.374030\pi\) | ||||
0.385497 | + | 0.922709i | \(0.374030\pi\) | |||||||
\(758\) | 1.34008e7 | 0.847143 | ||||||||
\(759\) | −4.81565e6 | + | 2.67029e6i | −0.303424 | + | 0.168250i | ||||
\(760\) | −2.64725e6 | −0.166250 | ||||||||
\(761\) | −1.46323e7 | −0.915904 | −0.457952 | − | 0.888977i | \(-0.651417\pi\) | ||||
−0.457952 | + | 0.888977i | \(0.651417\pi\) | |||||||
\(762\) | −6.55096e6 | + | 56305.2i | −0.408712 | + | 0.00351286i | ||||
\(763\) | 2.31258e7 | 1.43809 | ||||||||
\(764\) | 1.03395e7i | 0.640862i | ||||||||
\(765\) | −62276.6 | − | 3.62260e6i | −0.00384744 | − | 0.223803i | ||||
\(766\) | − | 7.82616e6i | − | 0.481922i | ||||||
\(767\) | 1.78808e7 | 1.09749 | ||||||||
\(768\) | −144050. | − | 1.67599e7i | −0.00881273 | − | 1.02534i | ||||
\(769\) | 6.23273e6i | 0.380069i | 0.981777 | + | 0.190034i | \(0.0608600\pi\) | ||||
−0.981777 | + | 0.190034i | \(0.939140\pi\) | |||||||
\(770\) | −2.26802e6 | + | 1.23226e6i | −0.137854 | + | 0.0748987i | ||||
\(771\) | −5.42128e6 | + | 46595.6i | −0.328447 | + | 0.00282299i | ||||
\(772\) | 1.16769e7i | 0.705153i | ||||||||
\(773\) | − | 2.38906e7i | − | 1.43806i | −0.694978 | − | 0.719031i | \(-0.744586\pi\) | ||
0.694978 | − | 0.719031i | \(-0.255414\pi\) | |||||||
\(774\) | −312905. | − | 1.82015e7i | −0.0187741 | − | 1.09208i | ||||
\(775\) | −1.92343e7 | −1.15033 | ||||||||
\(776\) | −1.82285e7 | −1.08667 | ||||||||
\(777\) | 2.18888e7 | − | 188133.i | 1.30068 | − | 0.0111792i | ||||
\(778\) | − | 8.92041e6i | − | 0.528367i | ||||||
\(779\) | − | 6.55565e6i | − | 0.387055i | ||||||
\(780\) | 23696.2 | + | 2.75699e6i | 0.00139457 | + | 0.162255i | ||||
\(781\) | −1.08182e7 | − | 1.99113e7i | −0.634638 | − | 1.16808i | ||||
\(782\) | 3.96578e6i | 0.231906i | ||||||||
\(783\) | −312635. | − | 1.21224e7i | −0.0182236 | − | 0.706616i | ||||
\(784\) | 279791. | 0.0162571 | ||||||||
\(785\) | − | 1.12218e6i | − | 0.0649962i | ||||||
\(786\) | 85082.3 | + | 9.89911e6i | 0.00491228 | + | 0.571531i | ||||
\(787\) | − | 2.81984e7i | − | 1.62288i | −0.584433 | − | 0.811442i | \(-0.698683\pi\) | ||
0.584433 | − | 0.811442i | \(-0.301317\pi\) | |||||||
\(788\) | −6.99316e6 | −0.401197 | ||||||||
\(789\) | −132037. | − | 1.53622e7i | −0.00755098 | − | 0.878537i | ||||
\(790\) | 471942. | 0.0269043 | ||||||||
\(791\) | −3.15777e7 | −1.79448 | ||||||||
\(792\) | 1.55738e7 | − | 8.81160e6i | 0.882232 | − | 0.499162i | ||||
\(793\) | 2.12223e7 | 1.19842 | ||||||||
\(794\) | −194441. | −0.0109455 | ||||||||
\(795\) | −38166.1 | − | 4.44053e6i | −0.00214171 | − | 0.249182i | ||||
\(796\) | 4.17371e6 | 0.233475 | ||||||||
\(797\) | − | 3.41343e6i | − | 0.190347i | −0.995461 | − | 0.0951733i | \(-0.969659\pi\) | ||
0.995461 | − | 0.0951733i | \(-0.0303405\pi\) | |||||||
\(798\) | 88082.2 | + | 1.02481e7i | 0.00489645 | + | 0.569689i | ||||
\(799\) | 1.41685e7i | 0.785156i | ||||||||
\(800\) | 1.70154e7 | 0.939976 | ||||||||
\(801\) | 351471. | + | 2.04449e7i | 0.0193557 | + | 1.12591i | ||||
\(802\) | − | 1.13419e7i | − | 0.622658i | ||||||
\(803\) | −2.30394e6 | − | 4.24048e6i | −0.126090 | − | 0.232074i | ||||
\(804\) | −51870.8 | − | 6.03503e6i | −0.00282997 | − | 0.329260i | ||||
\(805\) | − | 1.57698e6i | − | 0.0857703i | ||||||
\(806\) | − | 1.80261e7i | − | 0.977383i | ||||||
\(807\) | −2.13223e7 | + | 183264.i | −1.15252 | + | 0.00990587i | ||||
\(808\) | 1.54381e6 | 0.0831892 | ||||||||
\(809\) | −7.67008e6 | −0.412030 | −0.206015 | − | 0.978549i | \(-0.566050\pi\) | ||||
−0.206015 | + | 0.978549i | \(0.566050\pi\) | |||||||
\(810\) | 86564.2 | + | 2.51695e6i | 0.00463581 | + | 0.134791i | ||||
\(811\) | − | 2.38944e7i | − | 1.27569i | −0.770166 | − | 0.637843i | \(-0.779827\pi\) | ||
0.770166 | − | 0.637843i | \(-0.220173\pi\) | |||||||
\(812\) | − | 9.22664e6i | − | 0.491082i | ||||||
\(813\) | 5.40862e6 | − | 46486.8i | 0.286986 | − | 0.00246663i | ||||
\(814\) | −1.17876e7 | + | 6.40445e6i | −0.623542 | + | 0.338782i | ||||
\(815\) | − | 3.52017e6i | − | 0.185639i | ||||||
\(816\) | −7926.85 | − | 922268.i | −0.000416749 | − | 0.0484877i | ||||
\(817\) | 2.53411e7 | 1.32822 | ||||||||
\(818\) | 1.16404e7i | 0.608252i | ||||||||
\(819\) | 2.85410e7 | − | 490653.i | 1.48682 | − | 0.0255602i | ||||
\(820\) | − | 1.22574e6i | − | 0.0636595i | ||||||
\(821\) | 2.14968e7 | 1.11305 | 0.556527 | − | 0.830830i | \(-0.312134\pi\) | ||||
0.556527 | + | 0.830830i | \(0.312134\pi\) | |||||||
\(822\) | 1.94580e7 | − | 167240.i | 1.00443 | − | 0.00863300i | ||||
\(823\) | −1.39033e7 | −0.715512 | −0.357756 | − | 0.933815i | \(-0.616458\pi\) | ||||
−0.357756 | + | 0.933815i | \(0.616458\pi\) | |||||||
\(824\) | −2.12921e6 | −0.109245 | ||||||||
\(825\) | 9.05213e6 | + | 1.63248e7i | 0.463037 | + | 0.835048i | ||||
\(826\) | 1.24274e7 | 0.633766 | ||||||||
\(827\) | −1.82513e7 | −0.927964 | −0.463982 | − | 0.885845i | \(-0.653580\pi\) | ||||
−0.463982 | + | 0.885845i | \(0.653580\pi\) | |||||||
\(828\) | 70265.4 | + | 4.08729e6i | 0.00356177 | + | 0.207186i | ||||
\(829\) | −1.05826e7 | −0.534819 | −0.267410 | − | 0.963583i | \(-0.586168\pi\) | ||||
−0.267410 | + | 0.963583i | \(0.586168\pi\) | |||||||
\(830\) | − | 2.19964e6i | − | 0.110830i | ||||||
\(831\) | 2.99766e7 | − | 257647.i | 1.50584 | − | 0.0129426i | ||||
\(832\) | 1.71217e7i | 0.857511i | ||||||||
\(833\) | −7.44844e6 | −0.371923 | ||||||||
\(834\) | −488006. | + | 4194.39i | −0.0242946 | + | 0.000208811i | ||||
\(835\) | − | 6.78392e6i | − | 0.336717i | ||||||
\(836\) | 4.44661e6 | + | 8.18416e6i | 0.220046 | + | 0.405003i | ||||
\(837\) | 629524. | + | 2.44097e7i | 0.0310598 | + | 1.20434i | ||||
\(838\) | − | 1.93940e6i | − | 0.0954020i | ||||||
\(839\) | 3.34860e6i | 0.164232i | 0.996623 | + | 0.0821160i | \(0.0261678\pi\) | ||||
−0.996623 | + | 0.0821160i | \(0.973832\pi\) | |||||||
\(840\) | 44043.9 | + | 5.12440e6i | 0.00215371 | + | 0.250579i | ||||
\(841\) | −1.02630e7 | −0.500362 | ||||||||
\(842\) | −1.09537e7 | −0.532451 | ||||||||
\(843\) | −203397. | − | 2.36648e7i | −0.00985772 | − | 1.14692i | ||||
\(844\) | − | 1.33237e7i | − | 0.643825i | ||||||
\(845\) | − | 2.79758e6i | − | 0.134785i | ||||||
\(846\) | −169282. | − | 9.84704e6i | −0.00813177 | − | 0.473020i | ||||
\(847\) | 2.03764e7 | + | 1.32163e7i | 0.975929 | + | 0.632997i | ||||
\(848\) | − | 1.13042e6i | − | 0.0539821i | ||||||
\(849\) | 3.05503e6 | − | 26257.8i | 0.145461 | − | 0.00125023i | ||||
\(850\) | 1.34438e7 | 0.638225 | ||||||||
\(851\) | − | 8.19610e6i | − | 0.387957i | ||||||
\(852\) | −1.68221e7 | + | 144585.i | −0.793927 | + | 0.00682376i | ||||
\(853\) | − | 5.72242e6i | − | 0.269282i | −0.990894 | − | 0.134641i | \(-0.957012\pi\) | ||
0.990894 | − | 0.134641i | \(-0.0429881\pi\) | |||||||
\(854\) | 1.47497e7 | 0.692052 | ||||||||
\(855\) | −3.50527e6 | + | 60259.7i | −0.163986 | + | 0.00281911i | ||||
\(856\) | −3.32997e7 | −1.55330 | ||||||||
\(857\) | −1.32490e7 | −0.616215 | −0.308107 | − | 0.951352i | \(-0.599696\pi\) | ||||
−0.308107 | + | 0.951352i | \(0.599696\pi\) | |||||||
\(858\) | −1.52994e7 | + | 8.48355e6i | −0.709505 | + | 0.393423i | ||||
\(859\) | −2.07212e6 | −0.0958145 | −0.0479072 | − | 0.998852i | \(-0.515255\pi\) | ||||
−0.0479072 | + | 0.998852i | \(0.515255\pi\) | |||||||
\(860\) | 4.73814e6 | 0.218455 | ||||||||
\(861\) | −1.26901e7 | + | 109070.i | −0.583386 | + | 0.00501417i | ||||
\(862\) | 7.53979e6 | 0.345614 | ||||||||
\(863\) | 1.16792e6i | 0.0533808i | 0.999644 | + | 0.0266904i | \(0.00849682\pi\) | ||||
−0.999644 | + | 0.0266904i | \(0.991503\pi\) | |||||||
\(864\) | −556901. | − | 2.15938e7i | −0.0253801 | − | 0.984111i | ||||
\(865\) | − | 150378.i | − | 0.00683350i | ||||||
\(866\) | −1.40778e7 | −0.637884 | ||||||||
\(867\) | 20796.0 | + | 2.41956e6i | 0.000939574 | + | 0.109317i | ||||
\(868\) | 1.85788e7i | 0.836987i | ||||||||
\(869\) | −2.12002e6 | − | 3.90197e6i | −0.0952335 | − | 0.175281i | ||||
\(870\) | −2.12828e6 | + | 18292.4i | −0.0953302 | + | 0.000819358i | ||||
\(871\) | 1.57797e7i | 0.704779i | ||||||||
\(872\) | 2.81384e7i | 1.25316i | ||||||||
\(873\) | −2.41368e7 | + | 414939.i | −1.07187 | + | 0.0184267i | ||||
\(874\) | 3.83734e6 | 0.169923 | ||||||||
\(875\) | −1.09446e7 | −0.483259 | ||||||||
\(876\) | −3.58258e6 | + | 30792.1i | −0.157738 | + | 0.00135575i | ||||
\(877\) | 4.06658e6i | 0.178538i | 0.996008 | + | 0.0892690i | \(0.0284531\pi\) | ||||
−0.996008 | + | 0.0892690i | \(0.971547\pi\) | |||||||
\(878\) | 4.71296e6i | 0.206328i | ||||||||
\(879\) | 369087. | + | 4.29423e7i | 0.0161123 | + | 1.87462i | ||||
\(880\) | −107304. | − | 197497.i | −0.00467098 | − | 0.00859713i | ||||
\(881\) | − | 2.68824e7i | − | 1.16689i | −0.812154 | − | 0.583443i | \(-0.801705\pi\) | ||
0.812154 | − | 0.583443i | \(-0.198295\pi\) | |||||||
\(882\) | 5.17664e6 | − | 88992.5i | 0.224066 | − | 0.00385196i | ||||
\(883\) | 3.29324e7 | 1.42142 | 0.710709 | − | 0.703486i | \(-0.248374\pi\) | ||||
0.710709 | + | 0.703486i | \(0.248374\pi\) | |||||||
\(884\) | − | 1.86841e7i | − | 0.804158i | ||||||
\(885\) | 36536.9 | + | 4.25097e6i | 0.00156810 | + | 0.182444i | ||||
\(886\) | 2.29571e7i | 0.982502i | ||||||||
\(887\) | −4.53827e7 | −1.93678 | −0.968392 | − | 0.249435i | \(-0.919755\pi\) | ||||
−0.968392 | + | 0.249435i | \(0.919755\pi\) | |||||||
\(888\) | 228911. | + | 2.66332e7i | 0.00974168 | + | 1.13342i | ||||
\(889\) | −1.76539e7 | −0.749179 | ||||||||
\(890\) | 3.58890e6 | 0.151875 | ||||||||
\(891\) | 2.04210e7 | − | 1.20221e7i | 0.861755 | − | 0.507326i | ||||
\(892\) | 2.16250e7 | 0.910004 | ||||||||
\(893\) | 1.37096e7 | 0.575302 | ||||||||
\(894\) | 170317. | + | 1.98160e7i | 0.00712713 | + | 0.829223i | ||||
\(895\) | 555651. | 0.0231870 | ||||||||
\(896\) | − | 1.56188e7i | − | 0.649948i | ||||||
\(897\) | −91860.8 | − | 1.06878e7i | −0.00381197 | − | 0.443512i | ||||
\(898\) | 1.63302e7i | 0.675774i | ||||||||
\(899\) | −2.06357e7 | −0.851570 | ||||||||
\(900\) | 1.38557e7 | − | 238195.i | 0.570193 | − | 0.00980227i | ||||
\(901\) | 3.00934e7i | 1.23498i | ||||||||
\(902\) | 6.83391e6 | − | 3.71299e6i | 0.279674 | − | 0.151952i | ||||
\(903\) | −421616. | − | 4.90539e7i | −0.0172067 | − | 2.00196i | ||||
\(904\) | − | 3.84221e7i | − | 1.56373i | ||||||
\(905\) | 1.40314e6i | 0.0569483i | ||||||||
\(906\) | −2.76040e7 | + | 237254.i | −1.11725 | + | 0.00960271i | ||||
\(907\) | −3.29518e7 | −1.33003 | −0.665014 | − | 0.746831i | \(-0.731574\pi\) | ||||
−0.665014 | + | 0.746831i | \(0.731574\pi\) | |||||||
\(908\) | 2.55480e7 | 1.02835 | ||||||||
\(909\) | 2.04419e6 | − | 35142.1i | 0.0820564 | − | 0.00141064i | ||||
\(910\) | − | 5.01009e6i | − | 0.200559i | ||||||
\(911\) | 3.28702e7i | 1.31222i | 0.754666 | + | 0.656110i | \(0.227799\pi\) | ||||
−0.754666 | + | 0.656110i | \(0.772201\pi\) | |||||||
\(912\) | −892399. | + | 7670.12i | −0.0355281 | + | 0.000305362i | ||||
\(913\) | −1.81864e7 | + | 9.88103e6i | −0.722055 | + | 0.392306i | ||||
\(914\) | 8.07795e6i | 0.319842i | ||||||||
\(915\) | 43364.6 | + | 5.04536e6i | 0.00171231 | + | 0.199223i | ||||
\(916\) | −1.78986e7 | −0.704824 | ||||||||
\(917\) | 2.66766e7i | 1.04763i | ||||||||
\(918\) | −440005. | − | 1.70611e7i | −0.0172326 | − | 0.668192i | ||||
\(919\) | 1.54186e7i | 0.602220i | 0.953589 | + | 0.301110i | \(0.0973571\pi\) | ||||
−0.953589 | + | 0.301110i | \(0.902643\pi\) | |||||||
\(920\) | 1.91879e6 | 0.0747410 | ||||||||
\(921\) | 1.06705e7 | − | 91712.3i | 0.414510 | − | 0.00356270i | ||||
\(922\) | 1.12561e7 | 0.436073 | ||||||||
\(923\) | 4.39844e7 | 1.69939 | ||||||||
\(924\) | 1.57685e7 | − | 8.74367e6i | 0.607588 | − | 0.336910i | ||||
\(925\) | −2.77843e7 | −1.06769 | ||||||||
\(926\) | −1.96536e7 | −0.753209 | ||||||||
\(927\) | −2.81932e6 | + | 48467.4i | −0.107757 | + | 0.00185247i | ||||
\(928\) | 1.82552e7 | 0.695851 | ||||||||
\(929\) | − | 4.64429e7i | − | 1.76555i | −0.469798 | − | 0.882774i | \(-0.655673\pi\) | ||
0.469798 | − | 0.882774i | \(-0.344327\pi\) | |||||||
\(930\) | 4.28551e6 | − | 36833.8i | 0.162478 | − | 0.00139649i | ||||
\(931\) | 7.20721e6i | 0.272517i | ||||||||
\(932\) | −1.29137e7 | −0.486979 | ||||||||
\(933\) | −6.46873e6 | + | 55598.4i | −0.243285 | + | 0.00209102i | ||||
\(934\) | − | 3.05903e7i | − | 1.14741i | ||||||
\(935\) | 2.85658e6 | + | 5.25765e6i | 0.106861 | + | 0.196681i | ||||
\(936\) | 597002. | + | 3.47273e7i | 0.0222734 | + | 1.29563i | ||||
\(937\) | 273623.i | 0.0101813i | 0.999987 | + | 0.00509066i | \(0.00162041\pi\) | ||||
−0.999987 | + | 0.00509066i | \(0.998380\pi\) | |||||||
\(938\) | 1.09671e7i | 0.406989i | ||||||||
\(939\) | 171849. | + | 1.99942e7i | 0.00636040 | + | 0.740016i | ||||
\(940\) | 2.56334e6 | 0.0946208 | ||||||||
\(941\) | 1.06577e7 | 0.392363 | 0.196182 | − | 0.980568i | \(-0.437146\pi\) | ||||
0.196182 | + | 0.980568i | \(0.437146\pi\) | |||||||
\(942\) | −45431.5 | − | 5.28584e6i | −0.00166813 | − | 0.194083i | ||||
\(943\) | 4.75171e6i | 0.174009i | ||||||||
\(944\) | 1.08216e6i | 0.0395242i | ||||||||
\(945\) | 174967. | + | 6.78431e6i | 0.00637347 | + | 0.247130i | ||||
\(946\) | 1.43527e7 | + | 2.64167e7i | 0.521442 | + | 0.959735i | ||||
\(947\) | − | 2.94592e7i | − | 1.06745i | −0.845659 | − | 0.533723i | \(-0.820792\pi\) | ||
0.845659 | − | 0.533723i | \(-0.179208\pi\) | |||||||
\(948\) | −3.29659e6 | + | 28334.0i | −0.119136 | + | 0.00102397i | ||||
\(949\) | 9.36731e6 | 0.337636 | ||||||||
\(950\) | − | 1.30084e7i | − | 0.467642i | ||||||
\(951\) | 4.22175e7 | − | 362857.i | 1.51371 | − | 0.0130102i | ||||
\(952\) | − | 3.47280e7i | − | 1.24190i | ||||||
\(953\) | −6.69811e6 | −0.238902 | −0.119451 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119451 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(954\) | −359550. | − | 2.09148e7i | −0.0127905 | − | 0.744018i | ||||
\(955\) | 6.42713e6 | 0.228039 | ||||||||
\(956\) | −1.13975e7 | −0.403335 | ||||||||
\(957\) | 9.71170e6 | + | 1.75142e7i | 0.342780 | + | 0.618175i | ||||
\(958\) | 30761.1 | 0.00108290 | ||||||||
\(959\) | 5.24364e7 | 1.84114 | ||||||||
\(960\) | −4.07051e6 | + | 34985.8i | −0.142551 | + | 0.00122522i | ||||
\(961\) | 1.29231e7 | 0.451395 | ||||||||
\(962\) | − | 2.60391e7i | − | 0.907170i | ||||||
\(963\) | −4.40927e7 | + | 758005.i | −1.53215 | + | 0.0263394i | ||||
\(964\) | − | 2.37603e7i | − | 0.823491i | ||||||
\(965\) | 7.25848e6 | 0.250916 | ||||||||
\(966\) | −63844.3 | − | 7.42812e6i | −0.00220130 | − | 0.256116i | ||||
\(967\) | − | 3.37513e7i | − | 1.16071i | −0.814363 | − | 0.580356i | \(-0.802913\pi\) | ||
0.814363 | − | 0.580356i | \(-0.197087\pi\) | |||||||
\(968\) | −1.60810e7 | + | 2.47929e7i | −0.551599 | + | 0.850432i | ||||
\(969\) | 2.37570e7 | − | 204190.i | 0.812795 | − | 0.00698593i | ||||
\(970\) | 4.23697e6i | 0.144586i | ||||||||
\(971\) | 9.80791e6i | 0.333832i | 0.985971 | + | 0.166916i | \(0.0533809\pi\) | ||||
−0.985971 | + | 0.166916i | \(0.946619\pi\) | |||||||
\(972\) | −755774. | − | 1.75761e7i | −0.0256582 | − | 0.596700i | ||||
\(973\) | −1.31510e6 | −0.0445326 | ||||||||
\(974\) | 1.58305e6 | 0.0534684 | ||||||||
\(975\) | −3.62309e7 | + | 311402.i | −1.22058 | + | 0.0104908i | ||||
\(976\) | 1.28439e6i | 0.0431591i | ||||||||
\(977\) | 3.44181e7i | 1.15359i | 0.816890 | + | 0.576793i | \(0.195696\pi\) | ||||
−0.816890 | + | 0.576793i | \(0.804304\pi\) | |||||||
\(978\) | −142514. | − | 1.65812e7i | −0.00476444 | − | 0.554330i | ||||
\(979\) | −1.61217e7 | − | 2.96727e7i | −0.537594 | − | 0.989463i | ||||
\(980\) | 1.34756e6i | 0.0448212i | ||||||||
\(981\) | 640518. | + | 3.72586e7i | 0.0212500 | + | 1.23610i | ||||
\(982\) | −645314. | −0.0213547 | ||||||||
\(983\) | 1.57313e7i | 0.519254i | 0.965709 | + | 0.259627i | \(0.0835995\pi\) | ||||
−0.965709 | + | 0.259627i | \(0.916400\pi\) | |||||||
\(984\) | −132712. | − | 1.54407e7i | −0.00436939 | − | 0.508368i | ||||
\(985\) | 4.34703e6i | 0.142759i | ||||||||
\(986\) | 1.44233e7 | 0.472469 | ||||||||
\(987\) | −228095. | − | 2.65383e7i | −0.00745286 | − | 0.867121i | ||||
\(988\) | −1.80790e7 | −0.589225 | ||||||||
\(989\) | −1.83679e7 | −0.597130 | ||||||||
\(990\) | −2.04813e6 | − | 3.61992e6i | −0.0664156 | − | 0.117385i | ||||
\(991\) | −2.38014e7 | −0.769870 | −0.384935 | − | 0.922944i | \(-0.625776\pi\) | ||||
−0.384935 | + | 0.922944i | \(0.625776\pi\) | |||||||
\(992\) | −3.67587e7 | −1.18599 | ||||||||
\(993\) | −148078. | − | 1.72285e7i | −0.00476560 | − | 0.554466i | ||||
\(994\) | 3.05696e7 | 0.981350 | ||||||||
\(995\) | − | 2.59443e6i | − | 0.0830776i | ||||||
\(996\) | 132060. | + | 1.53648e7i | 0.00421816 | + | 0.490772i | ||||
\(997\) | 7.04150e6i | 0.224351i | 0.993688 | + | 0.112175i | \(0.0357818\pi\) | ||||
−0.993688 | + | 0.112175i | \(0.964218\pi\) | |||||||
\(998\) | 1.71281e7 | 0.544355 | ||||||||
\(999\) | 909360. | + | 3.52603e7i | 0.0288285 | + | 1.11782i |
(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 | 33.6.d.b.32.10 | yes | 16 | |
3.2 | odd | 2 | inner | 33.6.d.b.32.7 | ✓ | 16 | |
11.10 | odd | 2 | inner | 33.6.d.b.32.8 | yes | 16 | |
33.32 | even | 2 | inner | 33.6.d.b.32.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.d.b.32.7 | ✓ | 16 | 3.2 | odd | 2 | inner | |
33.6.d.b.32.8 | yes | 16 | 11.10 | odd | 2 | inner | |
33.6.d.b.32.9 | yes | 16 | 33.32 | even | 2 | inner | |
33.6.d.b.32.10 | yes | 16 | 1.1 | even | 1 | trivial |