Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (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: | \(8.60787333789\) |
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: | \( x^{16} - 32x^{14} + 512x^{12} - 2272x^{10} - 1087x^{8} + 72448x^{6} + 819200x^{4} + 1310720x^{2} + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.1 | ||
Root | \(2.98338 - 1.23576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.c.1077.16 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.84776i | − | 1.06680i | −0.845862 | − | 0.533402i | \(-0.820913\pi\) | ||
0.845862 | − | 0.533402i | \(-0.179087\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 3.23688i | − | 1.44758i | −0.690022 | − | 0.723789i | \(-0.742399\pi\) | ||
0.690022 | − | 0.723789i | \(-0.257601\pi\) | |||||||
\(6\) | −1.84776 | −0.754344 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.414214 | −0.138071 | ||||||||
\(10\) | −3.23688 | −1.02359 | ||||||||
\(11\) | 3.28338 | − | 0.468406i | 0.989977 | − | 0.141230i | ||||
\(12\) | 1.84776i | 0.533402i | ||||||||
\(13\) | −6.10838 | −1.69416 | −0.847079 | − | 0.531467i | \(-0.821641\pi\) | ||||
−0.847079 | + | 0.531467i | \(0.821641\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.98098 | −1.54428 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −8.13155 | −1.97219 | −0.986095 | − | 0.166182i | \(-0.946856\pi\) | ||||
−0.986095 | + | 0.166182i | \(0.946856\pi\) | |||||||
\(18\) | 0.414214i | 0.0976311i | ||||||||
\(19\) | 6.61537 | 1.51767 | 0.758835 | − | 0.651282i | \(-0.225769\pi\) | ||||
0.758835 | + | 0.651282i | \(0.225769\pi\) | |||||||
\(20\) | 3.23688i | 0.723789i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.468406 | − | 3.28338i | −0.0998645 | − | 0.700019i | ||||
\(23\) | −5.30583 | −1.10634 | −0.553171 | − | 0.833068i | \(-0.686582\pi\) | ||||
−0.553171 | + | 0.833068i | \(0.686582\pi\) | |||||||
\(24\) | 1.84776 | 0.377172 | ||||||||
\(25\) | −5.47740 | −1.09548 | ||||||||
\(26\) | 6.10838i | 1.19795i | ||||||||
\(27\) | − | 4.77791i | − | 0.919509i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.32485i | − | 0.246019i | −0.992406 | − | 0.123009i | \(-0.960745\pi\) | ||
0.992406 | − | 0.123009i | \(-0.0392545\pi\) | |||||||
\(30\) | 5.98098i | 1.09197i | ||||||||
\(31\) | − | 2.35476i | − | 0.422927i | −0.977386 | − | 0.211464i | \(-0.932177\pi\) | ||
0.977386 | − | 0.211464i | \(-0.0678230\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −0.865501 | − | 6.06690i | −0.150664 | − | 1.05611i | ||||
\(34\) | 8.13155i | 1.39455i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.414214 | 0.0690356 | ||||||||
\(37\) | 5.28681 | 0.869146 | 0.434573 | − | 0.900637i | \(-0.356899\pi\) | ||||
0.434573 | + | 0.900637i | \(0.356899\pi\) | |||||||
\(38\) | − | 6.61537i | − | 1.07316i | ||||||
\(39\) | 11.2868i | 1.80734i | ||||||||
\(40\) | 3.23688 | 0.511796 | ||||||||
\(41\) | 1.22400 | 0.191157 | 0.0955786 | − | 0.995422i | \(-0.469530\pi\) | ||||
0.0955786 | + | 0.995422i | \(0.469530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73834i | 0.570091i | 0.958514 | + | 0.285045i | \(0.0920087\pi\) | ||||
−0.958514 | + | 0.285045i | \(0.907991\pi\) | |||||||
\(44\) | −3.28338 | + | 0.468406i | −0.494988 | + | 0.0706148i | ||||
\(45\) | 1.34076i | 0.199869i | ||||||||
\(46\) | 5.30583i | 0.782302i | ||||||||
\(47\) | − | 1.70615i | − | 0.248867i | −0.992228 | − | 0.124434i | \(-0.960289\pi\) | ||
0.992228 | − | 0.124434i | \(-0.0397114\pi\) | |||||||
\(48\) | − | 1.84776i | − | 0.266701i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.47740i | 0.774622i | ||||||||
\(51\) | 15.0251i | 2.10394i | ||||||||
\(52\) | 6.10838 | 0.847079 | ||||||||
\(53\) | −3.98098 | −0.546829 | −0.273415 | − | 0.961896i | \(-0.588153\pi\) | ||||
−0.273415 | + | 0.961896i | \(0.588153\pi\) | |||||||
\(54\) | −4.77791 | −0.650191 | ||||||||
\(55\) | −1.51617 | − | 10.6279i | −0.204441 | − | 1.43307i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.2236i | − | 1.61906i | ||||||
\(58\) | −1.32485 | −0.173962 | ||||||||
\(59\) | 9.03853i | 1.17672i | 0.808601 | + | 0.588358i | \(0.200225\pi\) | ||||
−0.808601 | + | 0.588358i | \(0.799775\pi\) | |||||||
\(60\) | 5.98098 | 0.772141 | ||||||||
\(61\) | 8.55638 | 1.09553 | 0.547766 | − | 0.836631i | \(-0.315478\pi\) | ||||
0.547766 | + | 0.836631i | \(0.315478\pi\) | |||||||
\(62\) | −2.35476 | −0.299055 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 19.7721i | 2.45243i | ||||||||
\(66\) | −6.06690 | + | 0.865501i | −0.746784 | + | 0.106536i | ||||
\(67\) | 2.35103 | 0.287223 | 0.143612 | − | 0.989634i | \(-0.454128\pi\) | ||||
0.143612 | + | 0.989634i | \(0.454128\pi\) | |||||||
\(68\) | 8.13155 | 0.986095 | ||||||||
\(69\) | 9.80389i | 1.18025i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.17945 | −0.852044 | −0.426022 | − | 0.904713i | \(-0.640085\pi\) | ||||
−0.426022 | + | 0.904713i | \(0.640085\pi\) | |||||||
\(72\) | − | 0.414214i | − | 0.0488155i | ||||||
\(73\) | 10.9927 | 1.28660 | 0.643302 | − | 0.765613i | \(-0.277564\pi\) | ||||
0.643302 | + | 0.765613i | \(0.277564\pi\) | |||||||
\(74\) | − | 5.28681i | − | 0.614579i | ||||||
\(75\) | 10.1209i | 1.16866i | ||||||||
\(76\) | −6.61537 | −0.758835 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.2868 | 1.27798 | ||||||||
\(79\) | − | 8.48528i | − | 0.954669i | −0.878722 | − | 0.477334i | \(-0.841603\pi\) | ||
0.878722 | − | 0.477334i | \(-0.158397\pi\) | |||||||
\(80\) | − | 3.23688i | − | 0.361894i | ||||||
\(81\) | −10.0711 | −1.11901 | ||||||||
\(82\) | − | 1.22400i | − | 0.135169i | ||||||
\(83\) | −5.60138 | −0.614831 | −0.307415 | − | 0.951575i | \(-0.599464\pi\) | ||||
−0.307415 | + | 0.951575i | \(0.599464\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.3209i | 2.85490i | ||||||||
\(86\) | 3.73834 | 0.403115 | ||||||||
\(87\) | −2.44801 | −0.262454 | ||||||||
\(88\) | 0.468406 | + | 3.28338i | 0.0499322 | + | 0.350010i | ||||
\(89\) | 4.66115i | 0.494081i | 0.969005 | + | 0.247041i | \(0.0794581\pi\) | ||||
−0.969005 | + | 0.247041i | \(0.920542\pi\) | |||||||
\(90\) | 1.34076 | 0.141329 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.30583 | 0.553171 | ||||||||
\(93\) | −4.35103 | −0.451180 | ||||||||
\(94\) | −1.70615 | −0.175976 | ||||||||
\(95\) | − | 21.4132i | − | 2.19695i | ||||||
\(96\) | −1.84776 | −0.188586 | ||||||||
\(97\) | − | 3.82683i | − | 0.388556i | −0.980946 | − | 0.194278i | \(-0.937764\pi\) | ||
0.980946 | − | 0.194278i | \(-0.0622364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.36002 | + | 0.194020i | −0.136687 | + | 0.0194997i | ||||
\(100\) | 5.47740 | 0.547740 | ||||||||
\(101\) | −3.66037 | −0.364220 | −0.182110 | − | 0.983278i | \(-0.558293\pi\) | ||||
−0.182110 | + | 0.983278i | \(0.558293\pi\) | |||||||
\(102\) | 15.0251 | 1.48771 | ||||||||
\(103\) | − | 14.5715i | − | 1.43577i | −0.696160 | − | 0.717887i | \(-0.745110\pi\) | ||
0.696160 | − | 0.717887i | \(-0.254890\pi\) | |||||||
\(104\) | − | 6.10838i | − | 0.598975i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.98098i | 0.386667i | ||||||||
\(107\) | − | 7.87362i | − | 0.761172i | −0.924746 | − | 0.380586i | \(-0.875722\pi\) | ||
0.924746 | − | 0.380586i | \(-0.124278\pi\) | |||||||
\(108\) | 4.77791i | 0.459755i | ||||||||
\(109\) | − | 6.00000i | − | 0.574696i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) | ||
0.957826 | − | 0.287348i | \(-0.0927736\pi\) | |||||||
\(110\) | −10.6279 | + | 1.51617i | −1.01333 | + | 0.144562i | ||||
\(111\) | − | 9.76874i | − | 0.927208i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5216 | 1.27200 | 0.636001 | − | 0.771688i | \(-0.280587\pi\) | ||||
0.636001 | + | 0.771688i | \(0.280587\pi\) | |||||||
\(114\) | −12.2236 | −1.14485 | ||||||||
\(115\) | 17.1743i | 1.60152i | ||||||||
\(116\) | 1.32485i | 0.123009i | ||||||||
\(117\) | 2.53017 | 0.233914 | ||||||||
\(118\) | 9.03853 | 0.832064 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 5.98098i | − | 0.545986i | ||||||
\(121\) | 10.5612 | − | 3.07591i | 0.960108 | − | 0.279628i | ||||
\(122\) | − | 8.55638i | − | 0.774658i | ||||||
\(123\) | − | 2.26166i | − | 0.203927i | ||||||
\(124\) | 2.35476i | 0.211464i | ||||||||
\(125\) | 1.54529i | 0.138215i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.63710i | − | 0.766419i | −0.923661 | − | 0.383209i | \(-0.874819\pi\) | ||
0.923661 | − | 0.383209i | \(-0.125181\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 6.90755 | 0.608175 | ||||||||
\(130\) | 19.7721 | 1.73413 | ||||||||
\(131\) | −6.20218 | −0.541887 | −0.270944 | − | 0.962595i | \(-0.587336\pi\) | ||||
−0.270944 | + | 0.962595i | \(0.587336\pi\) | |||||||
\(132\) | 0.865501 | + | 6.06690i | 0.0753322 | + | 0.528056i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.35103i | − | 0.203098i | ||||||
\(135\) | −15.4655 | −1.33106 | ||||||||
\(136\) | − | 8.13155i | − | 0.697275i | ||||||
\(137\) | −9.02514 | −0.771070 | −0.385535 | − | 0.922693i | \(-0.625983\pi\) | ||||
−0.385535 | + | 0.922693i | \(0.625983\pi\) | |||||||
\(138\) | 9.80389 | 0.834563 | ||||||||
\(139\) | −8.34638 | −0.707930 | −0.353965 | − | 0.935259i | \(-0.615167\pi\) | ||||
−0.353965 | + | 0.935259i | \(0.615167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.15255 | −0.265493 | ||||||||
\(142\) | 7.17945i | 0.602486i | ||||||||
\(143\) | −20.0561 | + | 2.86120i | −1.67718 | + | 0.239265i | ||||
\(144\) | −0.414214 | −0.0345178 | ||||||||
\(145\) | −4.28839 | −0.356131 | ||||||||
\(146\) | − | 10.9927i | − | 0.909766i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.28681 | −0.434573 | ||||||||
\(149\) | − | 21.2488i | − | 1.74077i | −0.492375 | − | 0.870383i | \(-0.663871\pi\) | ||
0.492375 | − | 0.870383i | \(-0.336129\pi\) | |||||||
\(150\) | 10.1209 | 0.826370 | ||||||||
\(151\) | 16.6751i | 1.35700i | 0.734598 | + | 0.678502i | \(0.237371\pi\) | ||||
−0.734598 | + | 0.678502i | \(0.762629\pi\) | |||||||
\(152\) | 6.61537i | 0.536578i | ||||||||
\(153\) | 3.36820 | 0.272303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.62207 | −0.612220 | ||||||||
\(156\) | − | 11.2868i | − | 0.903668i | ||||||
\(157\) | 12.5095i | 0.998365i | 0.866497 | + | 0.499183i | \(0.166366\pi\) | ||||
−0.866497 | + | 0.499183i | \(0.833634\pi\) | |||||||
\(158\) | −8.48528 | −0.675053 | ||||||||
\(159\) | 7.35589i | 0.583360i | ||||||||
\(160\) | −3.23688 | −0.255898 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.0711i | 0.791258i | ||||||||
\(163\) | 8.39592 | 0.657619 | 0.328810 | − | 0.944396i | \(-0.393353\pi\) | ||||
0.328810 | + | 0.944396i | \(0.393353\pi\) | |||||||
\(164\) | −1.22400 | −0.0955786 | ||||||||
\(165\) | −19.6378 | + | 2.80152i | −1.52880 | + | 0.218098i | ||||
\(166\) | 5.60138i | 0.434751i | ||||||||
\(167\) | 4.04635 | 0.313116 | 0.156558 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156558 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.3123 | 1.87017 | ||||||||
\(170\) | 26.3209 | 2.01872 | ||||||||
\(171\) | −2.74018 | −0.209547 | ||||||||
\(172\) | − | 3.73834i | − | 0.285045i | ||||||
\(173\) | 3.07603 | 0.233866 | 0.116933 | − | 0.993140i | \(-0.462694\pi\) | ||||
0.116933 | + | 0.993140i | \(0.462694\pi\) | |||||||
\(174\) | 2.44801i | 0.185583i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.28338 | − | 0.468406i | 0.247494 | − | 0.0353074i | ||||
\(177\) | 16.7010 | 1.25533 | ||||||||
\(178\) | 4.66115 | 0.349368 | ||||||||
\(179\) | −11.4655 | −0.856974 | −0.428487 | − | 0.903548i | \(-0.640953\pi\) | ||||
−0.428487 | + | 0.903548i | \(0.640953\pi\) | |||||||
\(180\) | − | 1.34076i | − | 0.0999344i | ||||||
\(181\) | 13.2743i | 0.986670i | 0.869839 | + | 0.493335i | \(0.164222\pi\) | ||||
−0.869839 | + | 0.493335i | \(0.835778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 15.8101i | − | 1.16872i | ||||||
\(184\) | − | 5.30583i | − | 0.391151i | ||||||
\(185\) | − | 17.1128i | − | 1.25816i | ||||||
\(186\) | 4.35103i | 0.319033i | ||||||||
\(187\) | −26.6990 | + | 3.80886i | −1.95242 | + | 0.278532i | ||||
\(188\) | 1.70615i | 0.124434i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.4132 | −1.55348 | ||||||||
\(191\) | −12.2147 | −0.883825 | −0.441913 | − | 0.897058i | \(-0.645700\pi\) | ||||
−0.441913 | + | 0.897058i | \(0.645700\pi\) | |||||||
\(192\) | 1.84776i | 0.133351i | ||||||||
\(193\) | 5.06319i | 0.364456i | 0.983256 | + | 0.182228i | \(0.0583309\pi\) | ||||
−0.983256 | + | 0.182228i | \(0.941669\pi\) | |||||||
\(194\) | −3.82683 | −0.274751 | ||||||||
\(195\) | 36.5341 | 2.61626 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.0883i | − | 1.43123i | −0.698493 | − | 0.715617i | \(-0.746146\pi\) | ||
0.698493 | − | 0.715617i | \(-0.253854\pi\) | |||||||
\(198\) | 0.194020 | + | 1.36002i | 0.0137884 | + | 0.0966525i | ||||
\(199\) | − | 14.8196i | − | 1.05053i | −0.850938 | − | 0.525266i | \(-0.823966\pi\) | ||
0.850938 | − | 0.525266i | \(-0.176034\pi\) | |||||||
\(200\) | − | 5.47740i | − | 0.387311i | ||||||
\(201\) | − | 4.34413i | − | 0.306411i | ||||||
\(202\) | 3.66037i | 0.257543i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 15.0251i | − | 1.05197i | ||||||
\(205\) | − | 3.96195i | − | 0.276715i | ||||||
\(206\) | −14.5715 | −1.01525 | ||||||||
\(207\) | 2.19775 | 0.152754 | ||||||||
\(208\) | −6.10838 | −0.423540 | ||||||||
\(209\) | 21.7208 | − | 3.09868i | 1.50246 | − | 0.214340i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.19848i | − | 0.633249i | −0.948551 | − | 0.316625i | \(-0.897450\pi\) | ||
0.948551 | − | 0.316625i | \(-0.102550\pi\) | |||||||
\(212\) | 3.98098 | 0.273415 | ||||||||
\(213\) | 13.2659i | 0.908964i | ||||||||
\(214\) | −7.87362 | −0.538230 | ||||||||
\(215\) | 12.1006 | 0.825251 | ||||||||
\(216\) | 4.77791 | 0.325096 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | − | 20.3119i | − | 1.37255i | ||||||
\(220\) | 1.51617 | + | 10.6279i | 0.102220 | + | 0.716534i | ||||
\(221\) | 49.6706 | 3.34120 | ||||||||
\(222\) | −9.76874 | −0.655635 | ||||||||
\(223\) | 10.8760i | 0.728310i | 0.931338 | + | 0.364155i | \(0.118642\pi\) | ||||
−0.931338 | + | 0.364155i | \(0.881358\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.26881 | 0.151254 | ||||||||
\(226\) | − | 13.5216i | − | 0.899441i | ||||||
\(227\) | 23.4793 | 1.55837 | 0.779187 | − | 0.626791i | \(-0.215632\pi\) | ||||
0.779187 | + | 0.626791i | \(0.215632\pi\) | |||||||
\(228\) | 12.2236i | 0.809529i | ||||||||
\(229\) | − | 22.8301i | − | 1.50866i | −0.656498 | − | 0.754328i | \(-0.727963\pi\) | ||
0.656498 | − | 0.754328i | \(-0.272037\pi\) | |||||||
\(230\) | 17.1743 | 1.13244 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.32485 | 0.0869808 | ||||||||
\(233\) | − | 14.7089i | − | 0.963612i | −0.876278 | − | 0.481806i | \(-0.839981\pi\) | ||
0.876278 | − | 0.481806i | \(-0.160019\pi\) | |||||||
\(234\) | − | 2.53017i | − | 0.165403i | ||||||
\(235\) | −5.52260 | −0.360255 | ||||||||
\(236\) | − | 9.03853i | − | 0.588358i | ||||||
\(237\) | −15.6788 | −1.01844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.4218i | 1.45035i | 0.688567 | + | 0.725173i | \(0.258240\pi\) | ||||
−0.688567 | + | 0.725173i | \(0.741760\pi\) | |||||||
\(240\) | −5.98098 | −0.386070 | ||||||||
\(241\) | −15.4687 | −0.996430 | −0.498215 | − | 0.867054i | \(-0.666011\pi\) | ||||
−0.498215 | + | 0.867054i | \(0.666011\pi\) | |||||||
\(242\) | −3.07591 | − | 10.5612i | −0.197727 | − | 0.678899i | ||||
\(243\) | 4.27518i | 0.274253i | ||||||||
\(244\) | −8.55638 | −0.547766 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.26166 | −0.144198 | ||||||||
\(247\) | −40.4092 | −2.57118 | ||||||||
\(248\) | 2.35476 | 0.149527 | ||||||||
\(249\) | 10.3500i | 0.655904i | ||||||||
\(250\) | 1.54529 | 0.0977329 | ||||||||
\(251\) | − | 4.87408i | − | 0.307649i | −0.988098 | − | 0.153825i | \(-0.950841\pi\) | ||
0.988098 | − | 0.153825i | \(-0.0491590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.4211 | + | 2.48528i | −1.09525 | + | 0.156248i | ||||
\(254\) | −8.63710 | −0.541940 | ||||||||
\(255\) | 48.6346 | 3.04562 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 19.7743i | − | 1.23348i | −0.787165 | − | 0.616742i | \(-0.788452\pi\) | ||
0.787165 | − | 0.616742i | \(-0.211548\pi\) | |||||||
\(258\) | − | 6.90755i | − | 0.430045i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 19.7721i | − | 1.22621i | ||||||
\(261\) | 0.548772i | 0.0339681i | ||||||||
\(262\) | 6.20218i | 0.383172i | ||||||||
\(263\) | − | 8.48528i | − | 0.523225i | −0.965173 | − | 0.261612i | \(-0.915746\pi\) | ||
0.965173 | − | 0.261612i | \(-0.0842542\pi\) | |||||||
\(264\) | 6.06690 | − | 0.865501i | 0.373392 | − | 0.0532679i | ||||
\(265\) | 12.8860i | 0.791578i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.61269 | 0.527088 | ||||||||
\(268\) | −2.35103 | −0.143612 | ||||||||
\(269\) | − | 7.39943i | − | 0.451151i | −0.974226 | − | 0.225575i | \(-0.927574\pi\) | ||
0.974226 | − | 0.225575i | \(-0.0724262\pi\) | |||||||
\(270\) | 15.4655i | 0.941202i | ||||||||
\(271\) | −14.3609 | −0.872365 | −0.436183 | − | 0.899858i | \(-0.643670\pi\) | ||||
−0.436183 | + | 0.899858i | \(0.643670\pi\) | |||||||
\(272\) | −8.13155 | −0.493048 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.02514i | 0.545229i | ||||||||
\(275\) | −17.9844 | + | 2.56565i | −1.08450 | + | 0.154714i | ||||
\(276\) | − | 9.80389i | − | 0.590125i | ||||||
\(277\) | − | 2.18987i | − | 0.131576i | −0.997834 | − | 0.0657882i | \(-0.979044\pi\) | ||
0.997834 | − | 0.0657882i | \(-0.0209562\pi\) | |||||||
\(278\) | 8.34638i | 0.500582i | ||||||||
\(279\) | 0.975373i | 0.0583940i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.7003i | 1.53315i | 0.642154 | + | 0.766575i | \(0.278041\pi\) | ||||
−0.642154 | + | 0.766575i | \(0.721959\pi\) | |||||||
\(282\) | 3.15255i | 0.187732i | ||||||||
\(283\) | −15.5577 | −0.924811 | −0.462406 | − | 0.886668i | \(-0.653014\pi\) | ||||
−0.462406 | + | 0.886668i | \(0.653014\pi\) | |||||||
\(284\) | 7.17945 | 0.426022 | ||||||||
\(285\) | −39.5664 | −2.34371 | ||||||||
\(286\) | 2.86120 | + | 20.0561i | 0.169186 | + | 1.18594i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.414214i | 0.0244078i | ||||||||
\(289\) | 49.1221 | 2.88953 | ||||||||
\(290\) | 4.28839i | 0.251823i | ||||||||
\(291\) | −7.07107 | −0.414513 | ||||||||
\(292\) | −10.9927 | −0.643302 | ||||||||
\(293\) | 3.11451 | 0.181952 | 0.0909759 | − | 0.995853i | \(-0.471001\pi\) | ||||
0.0909759 | + | 0.995853i | \(0.471001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.2566 | 1.70339 | ||||||||
\(296\) | 5.28681i | 0.307289i | ||||||||
\(297\) | −2.23800 | − | 15.6877i | −0.129862 | − | 0.910293i | ||||
\(298\) | −21.2488 | −1.23091 | ||||||||
\(299\) | 32.4100 | 1.87432 | ||||||||
\(300\) | − | 10.1209i | − | 0.584332i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 16.6751 | 0.959547 | ||||||||
\(303\) | 6.76348i | 0.388552i | ||||||||
\(304\) | 6.61537 | 0.379418 | ||||||||
\(305\) | − | 27.6960i | − | 1.58587i | ||||||
\(306\) | − | 3.36820i | − | 0.192547i | ||||||
\(307\) | −8.93072 | −0.509703 | −0.254852 | − | 0.966980i | \(-0.582027\pi\) | ||||
−0.254852 | + | 0.966980i | \(0.582027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.9246 | −1.53169 | ||||||||
\(310\) | 7.62207i | 0.432905i | ||||||||
\(311\) | − | 19.1346i | − | 1.08502i | −0.840048 | − | 0.542512i | \(-0.817473\pi\) | ||
0.840048 | − | 0.542512i | \(-0.182527\pi\) | |||||||
\(312\) | −11.2868 | −0.638990 | ||||||||
\(313\) | − | 1.17856i | − | 0.0666161i | −0.999445 | − | 0.0333080i | \(-0.989396\pi\) | ||
0.999445 | − | 0.0333080i | \(-0.0106042\pi\) | |||||||
\(314\) | 12.5095 | 0.705951 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | −9.09694 | −0.510935 | −0.255468 | − | 0.966818i | \(-0.582229\pi\) | ||||
−0.255468 | + | 0.966818i | \(0.582229\pi\) | |||||||
\(318\) | 7.35589 | 0.412498 | ||||||||
\(319\) | −0.620568 | − | 4.34999i | −0.0347452 | − | 0.243553i | ||||
\(320\) | 3.23688i | 0.180947i | ||||||||
\(321\) | −14.5486 | −0.812021 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −53.7932 | −2.99314 | ||||||||
\(324\) | 10.0711 | 0.559504 | ||||||||
\(325\) | 33.4580 | 1.85592 | ||||||||
\(326\) | − | 8.39592i | − | 0.465007i | ||||||
\(327\) | −11.0866 | −0.613088 | ||||||||
\(328\) | 1.22400i | 0.0675843i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.80152 | + | 19.6378i | 0.154219 | + | 1.08103i | ||||
\(331\) | 2.72973 | 0.150039 | 0.0750197 | − | 0.997182i | \(-0.476098\pi\) | ||||
0.0750197 | + | 0.997182i | \(0.476098\pi\) | |||||||
\(332\) | 5.60138 | 0.307415 | ||||||||
\(333\) | −2.18987 | −0.120004 | ||||||||
\(334\) | − | 4.04635i | − | 0.221406i | ||||||
\(335\) | − | 7.60999i | − | 0.415778i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.3209i | − | 1.10695i | −0.832867 | − | 0.553474i | \(-0.813302\pi\) | ||
0.832867 | − | 0.553474i | \(-0.186698\pi\) | |||||||
\(338\) | − | 24.3123i | − | 1.32241i | ||||||
\(339\) | − | 24.9846i | − | 1.35698i | ||||||
\(340\) | − | 26.3209i | − | 1.42745i | ||||||
\(341\) | −1.10298 | − | 7.73157i | −0.0597298 | − | 0.418688i | ||||
\(342\) | 2.74018i | 0.148172i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.73834 | −0.201558 | ||||||||
\(345\) | 31.7340 | 1.70850 | ||||||||
\(346\) | − | 3.07603i | − | 0.165368i | ||||||
\(347\) | − | 24.4383i | − | 1.31192i | −0.754797 | − | 0.655959i | \(-0.772264\pi\) | ||
0.754797 | − | 0.655959i | \(-0.227736\pi\) | |||||||
\(348\) | 2.44801 | 0.131227 | ||||||||
\(349\) | 3.07603 | 0.164656 | 0.0823280 | − | 0.996605i | \(-0.473764\pi\) | ||||
0.0823280 | + | 0.996605i | \(0.473764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.1853i | 1.55779i | ||||||||
\(352\) | −0.468406 | − | 3.28338i | −0.0249661 | − | 0.175005i | ||||
\(353\) | 33.7399i | 1.79579i | 0.440206 | + | 0.897897i | \(0.354905\pi\) | ||||
−0.440206 | + | 0.897897i | \(0.645095\pi\) | |||||||
\(354\) | − | 16.7010i | − | 0.887649i | ||||||
\(355\) | 23.2390i | 1.23340i | ||||||||
\(356\) | − | 4.66115i | − | 0.247041i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.4655i | 0.605972i | ||||||||
\(359\) | − | 29.8985i | − | 1.57798i | −0.614406 | − | 0.788990i | \(-0.710604\pi\) | ||
0.614406 | − | 0.788990i | \(-0.289396\pi\) | |||||||
\(360\) | −1.34076 | −0.0706643 | ||||||||
\(361\) | 24.7632 | 1.30333 | ||||||||
\(362\) | 13.2743 | 0.697681 | ||||||||
\(363\) | −5.68354 | − | 19.5145i | −0.298309 | − | 1.02425i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 35.5822i | − | 1.86246i | ||||||
\(366\) | −15.8101 | −0.826409 | ||||||||
\(367\) | 3.55525i | 0.185583i | 0.995686 | + | 0.0927914i | \(0.0295790\pi\) | ||||
−0.995686 | + | 0.0927914i | \(0.970421\pi\) | |||||||
\(368\) | −5.30583 | −0.276585 | ||||||||
\(369\) | −0.506999 | −0.0263933 | ||||||||
\(370\) | −17.1128 | −0.889650 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.35103 | 0.225590 | ||||||||
\(373\) | 21.0969i | 1.09236i | 0.837668 | + | 0.546179i | \(0.183918\pi\) | ||||
−0.837668 | + | 0.546179i | \(0.816082\pi\) | |||||||
\(374\) | 3.80886 | + | 26.6990i | 0.196952 | + | 1.38057i | ||||
\(375\) | 2.85533 | 0.147449 | ||||||||
\(376\) | 1.70615 | 0.0879879 | ||||||||
\(377\) | 8.09269i | 0.416795i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.61063 | 0.442298 | 0.221149 | − | 0.975240i | \(-0.429019\pi\) | ||||
0.221149 | + | 0.975240i | \(0.429019\pi\) | |||||||
\(380\) | 21.4132i | 1.09847i | ||||||||
\(381\) | −15.9593 | −0.817619 | ||||||||
\(382\) | 12.2147i | 0.624959i | ||||||||
\(383\) | 34.2290i | 1.74902i | 0.485007 | + | 0.874510i | \(0.338817\pi\) | ||||
−0.485007 | + | 0.874510i | \(0.661183\pi\) | |||||||
\(384\) | 1.84776 | 0.0942931 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.06319 | 0.257709 | ||||||||
\(387\) | − | 1.54847i | − | 0.0787131i | ||||||
\(388\) | 3.82683i | 0.194278i | ||||||||
\(389\) | 22.8252 | 1.15728 | 0.578641 | − | 0.815582i | \(-0.303583\pi\) | ||||
0.578641 | + | 0.815582i | \(0.303583\pi\) | |||||||
\(390\) | − | 36.5341i | − | 1.84997i | ||||||
\(391\) | 43.1446 | 2.18192 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.4601i | 0.578088i | ||||||||
\(394\) | −20.0883 | −1.01204 | ||||||||
\(395\) | −27.4659 | −1.38196 | ||||||||
\(396\) | 1.36002 | − | 0.194020i | 0.0683436 | − | 0.00974987i | ||||
\(397\) | 12.6414i | 0.634451i | 0.948350 | + | 0.317226i | \(0.102751\pi\) | ||||
−0.948350 | + | 0.317226i | \(0.897249\pi\) | |||||||
\(398\) | −14.8196 | −0.742839 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.47740 | −0.273870 | ||||||||
\(401\) | −5.21750 | −0.260549 | −0.130275 | − | 0.991478i | \(-0.541586\pi\) | ||||
−0.130275 | + | 0.991478i | \(0.541586\pi\) | |||||||
\(402\) | −4.34413 | −0.216665 | ||||||||
\(403\) | 14.3837i | 0.716505i | ||||||||
\(404\) | 3.66037 | 0.182110 | ||||||||
\(405\) | 32.5989i | 1.61985i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.3586 | − | 2.47637i | 0.860434 | − | 0.122749i | ||||
\(408\) | −15.0251 | −0.743855 | ||||||||
\(409\) | 20.3483 | 1.00616 | 0.503079 | − | 0.864240i | \(-0.332200\pi\) | ||||
0.503079 | + | 0.864240i | \(0.332200\pi\) | |||||||
\(410\) | −3.96195 | −0.195667 | ||||||||
\(411\) | 16.6763i | 0.822581i | ||||||||
\(412\) | 14.5715i | 0.717887i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 2.19775i | − | 0.108013i | ||||||
\(415\) | 18.1310i | 0.890015i | ||||||||
\(416\) | 6.10838i | 0.299488i | ||||||||
\(417\) | 15.4221i | 0.755223i | ||||||||
\(418\) | −3.09868 | − | 21.7208i | −0.151561 | − | 1.06240i | ||||
\(419\) | 20.3391i | 0.993631i | 0.867856 | + | 0.496816i | \(0.165497\pi\) | ||||
−0.867856 | + | 0.496816i | \(0.834503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.3327 | −0.747272 | −0.373636 | − | 0.927575i | \(-0.621889\pi\) | ||||
−0.373636 | + | 0.927575i | \(0.621889\pi\) | |||||||
\(422\) | −9.19848 | −0.447775 | ||||||||
\(423\) | 0.706710i | 0.0343614i | ||||||||
\(424\) | − | 3.98098i | − | 0.193333i | ||||||
\(425\) | 44.5398 | 2.16050 | ||||||||
\(426\) | 13.2659 | 0.642735 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.87362i | 0.380586i | ||||||||
\(429\) | 5.28681 | + | 37.0589i | 0.255249 | + | 1.78922i | ||||
\(430\) | − | 12.1006i | − | 0.583540i | ||||||
\(431\) | 2.16904i | 0.104479i | 0.998635 | + | 0.0522394i | \(0.0166359\pi\) | ||||
−0.998635 | + | 0.0522394i | \(0.983364\pi\) | |||||||
\(432\) | − | 4.77791i | − | 0.229877i | ||||||
\(433\) | − | 38.4356i | − | 1.84710i | −0.383479 | − | 0.923550i | \(-0.625274\pi\) | ||
0.383479 | − | 0.923550i | \(-0.374726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.92391i | 0.379922i | ||||||||
\(436\) | 6.00000i | 0.287348i | ||||||||
\(437\) | −35.1000 | −1.67906 | ||||||||
\(438\) | −20.3119 | −0.970542 | ||||||||
\(439\) | 5.72240 | 0.273115 | 0.136558 | − | 0.990632i | \(-0.456396\pi\) | ||||
0.136558 | + | 0.990632i | \(0.456396\pi\) | |||||||
\(440\) | 10.6279 | − | 1.51617i | 0.506666 | − | 0.0722808i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 49.6706i | − | 2.36259i | ||||||
\(443\) | 7.18733 | 0.341480 | 0.170740 | − | 0.985316i | \(-0.445384\pi\) | ||||
0.170740 | + | 0.985316i | \(0.445384\pi\) | |||||||
\(444\) | 9.76874i | 0.463604i | ||||||||
\(445\) | 15.0876 | 0.715221 | ||||||||
\(446\) | 10.8760 | 0.514993 | ||||||||
\(447\) | −39.2626 | −1.85706 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.63068 | 0.407307 | 0.203654 | − | 0.979043i | \(-0.434718\pi\) | ||||
0.203654 | + | 0.979043i | \(0.434718\pi\) | |||||||
\(450\) | − | 2.26881i | − | 0.106953i | ||||||
\(451\) | 4.01887 | − | 0.573330i | 0.189241 | − | 0.0269971i | ||||
\(452\) | −13.5216 | −0.636001 | ||||||||
\(453\) | 30.8117 | 1.44766 | ||||||||
\(454\) | − | 23.4793i | − | 1.10194i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.2236 | 0.572423 | ||||||||
\(457\) | 28.5018i | 1.33326i | 0.745389 | + | 0.666629i | \(0.232264\pi\) | ||||
−0.745389 | + | 0.666629i | \(0.767736\pi\) | |||||||
\(458\) | −22.8301 | −1.06678 | ||||||||
\(459\) | 38.8518i | 1.81345i | ||||||||
\(460\) | − | 17.1743i | − | 0.800758i | ||||||
\(461\) | 35.6022 | 1.65816 | 0.829080 | − | 0.559129i | \(-0.188865\pi\) | ||||
0.829080 | + | 0.559129i | \(0.188865\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2369 | 1.49818 | 0.749088 | − | 0.662471i | \(-0.230492\pi\) | ||||
0.749088 | + | 0.662471i | \(0.230492\pi\) | |||||||
\(464\) | − | 1.32485i | − | 0.0615047i | ||||||
\(465\) | 14.0838i | 0.653118i | ||||||||
\(466\) | −14.7089 | −0.681377 | ||||||||
\(467\) | 25.8620i | 1.19675i | 0.801215 | + | 0.598376i | \(0.204187\pi\) | ||||
−0.801215 | + | 0.598376i | \(0.795813\pi\) | |||||||
\(468\) | −2.53017 | −0.116957 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.52260i | 0.254738i | ||||||||
\(471\) | 23.1145 | 1.06506 | ||||||||
\(472\) | −9.03853 | −0.416032 | ||||||||
\(473\) | 1.75106 | + | 12.2744i | 0.0805138 | + | 0.564377i | ||||
\(474\) | 15.6788i | 0.720149i | ||||||||
\(475\) | −36.2351 | −1.66258 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.64897 | 0.0755014 | ||||||||
\(478\) | 22.4218 | 1.02555 | ||||||||
\(479\) | 12.5206 | 0.572079 | 0.286040 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286040 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(480\) | 5.98098i | 0.272993i | ||||||||
\(481\) | −32.2938 | −1.47247 | ||||||||
\(482\) | 15.4687i | 0.704582i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5612 | + | 3.07591i | −0.480054 | + | 0.139814i | ||||
\(485\) | −12.3870 | −0.562465 | ||||||||
\(486\) | 4.27518 | 0.193926 | ||||||||
\(487\) | 20.7085 | 0.938390 | 0.469195 | − | 0.883094i | \(-0.344544\pi\) | ||||
0.469195 | + | 0.883094i | \(0.344544\pi\) | |||||||
\(488\) | 8.55638i | 0.387329i | ||||||||
\(489\) | − | 15.5136i | − | 0.701551i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.6712i | − | 1.06826i | −0.845401 | − | 0.534132i | \(-0.820638\pi\) | ||
0.845401 | − | 0.534132i | \(-0.179362\pi\) | |||||||
\(492\) | 2.26166i | 0.101964i | ||||||||
\(493\) | 10.7731i | 0.485196i | ||||||||
\(494\) | 40.4092i | 1.81810i | ||||||||
\(495\) | 0.628020 | + | 4.40223i | 0.0282274 | + | 0.197865i | ||||
\(496\) | − | 2.35476i | − | 0.105732i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.3500 | 0.463794 | ||||||||
\(499\) | 11.6124 | 0.519842 | 0.259921 | − | 0.965630i | \(-0.416304\pi\) | ||||
0.259921 | + | 0.965630i | \(0.416304\pi\) | |||||||
\(500\) | − | 1.54529i | − | 0.0691076i | ||||||
\(501\) | − | 7.47667i | − | 0.334033i | ||||||
\(502\) | −4.87408 | −0.217541 | ||||||||
\(503\) | −11.7871 | −0.525561 | −0.262780 | − | 0.964856i | \(-0.584639\pi\) | ||||
−0.262780 | + | 0.964856i | \(0.584639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8482i | 0.527237i | ||||||||
\(506\) | 2.48528 | + | 17.4211i | 0.110484 | + | 0.774461i | ||||
\(507\) | − | 44.9232i | − | 1.99511i | ||||||
\(508\) | 8.63710i | 0.383209i | ||||||||
\(509\) | − | 0.905073i | − | 0.0401167i | −0.999799 | − | 0.0200583i | \(-0.993615\pi\) | ||
0.999799 | − | 0.0200583i | \(-0.00638519\pi\) | |||||||
\(510\) | − | 48.6346i | − | 2.15358i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 31.6077i | − | 1.39551i | ||||||
\(514\) | −19.7743 | −0.872205 | ||||||||
\(515\) | −47.1662 | −2.07839 | ||||||||
\(516\) | −6.90755 | −0.304088 | ||||||||
\(517\) | −0.799170 | − | 5.60193i | −0.0351474 | − | 0.246373i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.68376i | − | 0.249489i | ||||||
\(520\) | −19.7721 | −0.867063 | ||||||||
\(521\) | − | 8.06821i | − | 0.353475i | −0.984258 | − | 0.176737i | \(-0.943446\pi\) | ||
0.984258 | − | 0.176737i | \(-0.0565543\pi\) | |||||||
\(522\) | 0.548772 | 0.0240191 | ||||||||
\(523\) | −17.8346 | −0.779852 | −0.389926 | − | 0.920846i | \(-0.627499\pi\) | ||||
−0.389926 | + | 0.920846i | \(0.627499\pi\) | |||||||
\(524\) | 6.20218 | 0.270944 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.48528 | −0.369976 | ||||||||
\(527\) | 19.1478i | 0.834093i | ||||||||
\(528\) | −0.865501 | − | 6.06690i | −0.0376661 | − | 0.264028i | ||||
\(529\) | 5.15182 | 0.223992 | ||||||||
\(530\) | 12.8860 | 0.559730 | ||||||||
\(531\) | − | 3.74388i | − | 0.162471i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.47667 | −0.323851 | ||||||||
\(534\) | − | 8.61269i | − | 0.372707i | ||||||
\(535\) | −25.4860 | −1.10186 | ||||||||
\(536\) | 2.35103i | 0.101549i | ||||||||
\(537\) | 21.1855i | 0.914223i | ||||||||
\(538\) | −7.39943 | −0.319012 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 15.4655 | 0.665530 | ||||||||
\(541\) | 1.47667i | 0.0634871i | 0.999496 | + | 0.0317436i | \(0.0101060\pi\) | ||||
−0.999496 | + | 0.0317436i | \(0.989894\pi\) | |||||||
\(542\) | 14.3609i | 0.616855i | ||||||||
\(543\) | 24.5277 | 1.05258 | ||||||||
\(544\) | 8.13155i | 0.348637i | ||||||||
\(545\) | −19.4213 | −0.831917 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.3374i | − | 0.698536i | −0.937023 | − | 0.349268i | \(-0.886430\pi\) | ||
0.937023 | − | 0.349268i | \(-0.113570\pi\) | |||||||
\(548\) | 9.02514 | 0.385535 | ||||||||
\(549\) | −3.54417 | −0.151261 | ||||||||
\(550\) | 2.56565 | + | 17.9844i | 0.109400 | + | 0.766857i | ||||
\(551\) | − | 8.76439i | − | 0.373376i | ||||||
\(552\) | −9.80389 | −0.417281 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.18987 | −0.0930385 | ||||||||
\(555\) | −31.6203 | −1.34221 | ||||||||
\(556\) | 8.34638 | 0.353965 | ||||||||
\(557\) | 17.3497i | 0.735130i | 0.929998 | + | 0.367565i | \(0.119808\pi\) | ||||
−0.929998 | + | 0.367565i | \(0.880192\pi\) | |||||||
\(558\) | 0.975373 | 0.0412908 | ||||||||
\(559\) | − | 22.8352i | − | 0.965824i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.03786 | + | 49.3333i | 0.297139 | + | 2.08285i | ||||
\(562\) | 25.7003 | 1.08410 | ||||||||
\(563\) | −8.93072 | −0.376385 | −0.188192 | − | 0.982132i | \(-0.560263\pi\) | ||||
−0.188192 | + | 0.982132i | \(0.560263\pi\) | |||||||
\(564\) | 3.15255 | 0.132746 | ||||||||
\(565\) | − | 43.7677i | − | 1.84132i | ||||||
\(566\) | 15.5577i | 0.653940i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 7.17945i | − | 0.301243i | ||||||
\(569\) | 9.65831i | 0.404898i | 0.979293 | + | 0.202449i | \(0.0648900\pi\) | ||||
−0.979293 | + | 0.202449i | \(0.935110\pi\) | |||||||
\(570\) | 39.5664i | 1.65725i | ||||||||
\(571\) | 11.9282i | 0.499180i | 0.968352 | + | 0.249590i | \(0.0802958\pi\) | ||||
−0.968352 | + | 0.249590i | \(0.919704\pi\) | |||||||
\(572\) | 20.0561 | − | 2.86120i | 0.838589 | − | 0.119633i | ||||
\(573\) | 22.5698i | 0.942868i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.0622 | 1.21198 | ||||||||
\(576\) | 0.414214 | 0.0172589 | ||||||||
\(577\) | 37.5475i | 1.56312i | 0.623828 | + | 0.781561i | \(0.285576\pi\) | ||||
−0.623828 | + | 0.781561i | \(0.714424\pi\) | |||||||
\(578\) | − | 49.1221i | − | 2.04321i | ||||||
\(579\) | 9.35555 | 0.388803 | ||||||||
\(580\) | 4.28839 | 0.178066 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.07107i | 0.293105i | ||||||||
\(583\) | −13.0711 | + | 1.86471i | −0.541348 | + | 0.0772285i | ||||
\(584\) | 10.9927i | 0.454883i | ||||||||
\(585\) | − | 8.18987i | − | 0.338609i | ||||||
\(586\) | − | 3.11451i | − | 0.128659i | ||||||
\(587\) | 29.1914i | 1.20486i | 0.798173 | + | 0.602429i | \(0.205800\pi\) | ||||
−0.798173 | + | 0.602429i | \(0.794200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 15.5776i | − | 0.641864i | ||||||
\(590\) | − | 29.2566i | − | 1.20448i | ||||||
\(591\) | −37.1184 | −1.52685 | ||||||||
\(592\) | 5.28681 | 0.217286 | ||||||||
\(593\) | 28.6899 | 1.17815 | 0.589076 | − | 0.808078i | \(-0.299492\pi\) | ||||
0.589076 | + | 0.808078i | \(0.299492\pi\) | |||||||
\(594\) | −15.6877 | + | 2.23800i | −0.643674 | + | 0.0918263i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.2488i | 0.870383i | ||||||||
\(597\) | −27.3830 | −1.12071 | ||||||||
\(598\) | − | 32.4100i | − | 1.32534i | ||||||
\(599\) | −10.6561 | −0.435397 | −0.217699 | − | 0.976016i | \(-0.569855\pi\) | ||||
−0.217699 | + | 0.976016i | \(0.569855\pi\) | |||||||
\(600\) | −10.1209 | −0.413185 | ||||||||
\(601\) | −43.5354 | −1.77585 | −0.887923 | − | 0.459992i | \(-0.847852\pi\) | ||||
−0.887923 | + | 0.459992i | \(0.847852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.973827 | −0.0396573 | ||||||||
\(604\) | − | 16.6751i | − | 0.678502i | ||||||
\(605\) | −9.95636 | − | 34.1853i | −0.404784 | − | 1.38983i | ||||
\(606\) | 6.76348 | 0.274748 | ||||||||
\(607\) | 27.3497 | 1.11009 | 0.555044 | − | 0.831821i | \(-0.312701\pi\) | ||||
0.555044 | + | 0.831821i | \(0.312701\pi\) | |||||||
\(608\) | − | 6.61537i | − | 0.268289i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27.6960 | −1.12138 | ||||||||
\(611\) | 10.4218i | 0.421621i | ||||||||
\(612\) | −3.36820 | −0.136151 | ||||||||
\(613\) | 27.8604i | 1.12527i | 0.826705 | + | 0.562636i | \(0.190213\pi\) | ||||
−0.826705 | + | 0.562636i | \(0.809787\pi\) | |||||||
\(614\) | 8.93072i | 0.360414i | ||||||||
\(615\) | −7.32074 | −0.295201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.0263 | 1.28933 | 0.644665 | − | 0.764465i | \(-0.276997\pi\) | ||||
0.644665 | + | 0.764465i | \(0.276997\pi\) | |||||||
\(618\) | 26.9246i | 1.08307i | ||||||||
\(619\) | − | 20.0009i | − | 0.803906i | −0.915660 | − | 0.401953i | \(-0.868332\pi\) | ||
0.915660 | − | 0.401953i | \(-0.131668\pi\) | |||||||
\(620\) | 7.62207 | 0.306110 | ||||||||
\(621\) | 25.3508i | 1.01729i | ||||||||
\(622\) | −19.1346 | −0.767227 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.2868i | 0.451834i | ||||||||
\(625\) | −22.3851 | −0.895403 | ||||||||
\(626\) | −1.17856 | −0.0471047 | ||||||||
\(627\) | −5.72561 | − | 40.1348i | −0.228659 | − | 1.60283i | ||||
\(628\) | − | 12.5095i | − | 0.499183i | ||||||
\(629\) | −42.9899 | −1.71412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.3751 | 1.01017 | 0.505084 | − | 0.863070i | \(-0.331461\pi\) | ||||
0.505084 | + | 0.863070i | \(0.331461\pi\) | |||||||
\(632\) | 8.48528 | 0.337526 | ||||||||
\(633\) | −16.9966 | −0.675553 | ||||||||
\(634\) | 9.09694i | 0.361286i | ||||||||
\(635\) | −27.9573 | −1.10945 | ||||||||
\(636\) | − | 7.35589i | − | 0.291680i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.34999 | + | 0.620568i | −0.172218 | + | 0.0245685i | ||||
\(639\) | 2.97383 | 0.117643 | ||||||||
\(640\) | 3.23688 | 0.127949 | ||||||||
\(641\) | 29.3371 | 1.15875 | 0.579373 | − | 0.815063i | \(-0.303298\pi\) | ||||
0.579373 | + | 0.815063i | \(0.303298\pi\) | |||||||
\(642\) | 14.5486i | 0.574186i | ||||||||
\(643\) | − | 7.53612i | − | 0.297196i | −0.988898 | − | 0.148598i | \(-0.952524\pi\) | ||
0.988898 | − | 0.148598i | \(-0.0474760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 22.3589i | − | 0.880381i | ||||||
\(646\) | 53.7932i | 2.11647i | ||||||||
\(647\) | − | 29.0558i | − | 1.14230i | −0.820845 | − | 0.571151i | \(-0.806497\pi\) | ||
0.820845 | − | 0.571151i | \(-0.193503\pi\) | |||||||
\(648\) | − | 10.0711i | − | 0.395629i | ||||||
\(649\) | 4.23370 | + | 29.6769i | 0.166187 | + | 1.16492i | ||||
\(650\) | − | 33.4580i | − | 1.31233i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.39592 | −0.328810 | ||||||||
\(653\) | 29.5840 | 1.15771 | 0.578856 | − | 0.815430i | \(-0.303499\pi\) | ||||
0.578856 | + | 0.815430i | \(0.303499\pi\) | |||||||
\(654\) | 11.0866i | 0.433519i | ||||||||
\(655\) | 20.0757i | 0.784424i | ||||||||
\(656\) | 1.22400 | 0.0477893 | ||||||||
\(657\) | −4.55335 | −0.177643 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.39725i | 0.210247i | 0.994459 | + | 0.105124i | \(0.0335238\pi\) | ||||
−0.994459 | + | 0.105124i | \(0.966476\pi\) | |||||||
\(660\) | 19.6378 | − | 2.80152i | 0.764402 | − | 0.109049i | ||||
\(661\) | 29.4503i | 1.14548i | 0.819736 | + | 0.572742i | \(0.194120\pi\) | ||||
−0.819736 | + | 0.572742i | \(0.805880\pi\) | |||||||
\(662\) | − | 2.72973i | − | 0.106094i | ||||||
\(663\) | − | 91.7792i | − | 3.56441i | ||||||
\(664\) | − | 5.60138i | − | 0.217376i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.18987i | 0.0848556i | ||||||||
\(667\) | 7.02944i | 0.272181i | ||||||||
\(668\) | −4.04635 | −0.156558 | ||||||||
\(669\) | 20.0962 | 0.776964 | ||||||||
\(670\) | −7.60999 | −0.294000 | ||||||||
\(671\) | 28.0939 | − | 4.00786i | 1.08455 | − | 0.154722i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.21501i | 0.201024i | 0.994936 | + | 0.100512i | \(0.0320481\pi\) | ||||
−0.994936 | + | 0.100512i | \(0.967952\pi\) | |||||||
\(674\) | −20.3209 | −0.782730 | ||||||||
\(675\) | 26.1705i | 1.00730i | ||||||||
\(676\) | −24.3123 | −0.935087 | ||||||||
\(677\) | 9.73471 | 0.374135 | 0.187068 | − | 0.982347i | \(-0.440102\pi\) | ||||
0.187068 | + | 0.982347i | \(0.440102\pi\) | |||||||
\(678\) | −24.9846 | −0.959528 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −26.3209 | −1.00936 | ||||||||
\(681\) | − | 43.3840i | − | 1.66248i | ||||||
\(682\) | −7.73157 | + | 1.10298i | −0.296057 | + | 0.0422354i | ||||
\(683\) | −17.5015 | −0.669677 | −0.334838 | − | 0.942276i | \(-0.608682\pi\) | ||||
−0.334838 | + | 0.942276i | \(0.608682\pi\) | |||||||
\(684\) | 2.74018 | 0.104773 | ||||||||
\(685\) | 29.2133i | 1.11618i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42.1845 | −1.60944 | ||||||||
\(688\) | 3.73834i | 0.142523i | ||||||||
\(689\) | 24.3173 | 0.926415 | ||||||||
\(690\) | − | 31.7340i | − | 1.20809i | ||||||
\(691\) | 46.2750i | 1.76038i | 0.474617 | + | 0.880192i | \(0.342587\pi\) | ||||
−0.474617 | + | 0.880192i | \(0.657413\pi\) | |||||||
\(692\) | −3.07603 | −0.116933 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.4383 | −0.927666 | ||||||||
\(695\) | 27.0162i | 1.02478i | ||||||||
\(696\) | − | 2.44801i | − | 0.0927915i | ||||||
\(697\) | −9.95304 | −0.376998 | ||||||||
\(698\) | − | 3.07603i | − | 0.116429i | ||||||
\(699\) | −27.1785 | −1.02799 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7883i | 1.08732i | 0.839306 | + | 0.543660i | \(0.182962\pi\) | ||||
−0.839306 | + | 0.543660i | \(0.817038\pi\) | |||||||
\(702\) | 29.1853 | 1.10153 | ||||||||
\(703\) | 34.9742 | 1.31908 | ||||||||
\(704\) | −3.28338 | + | 0.468406i | −0.123747 | + | 0.0176537i | ||||
\(705\) | 10.2044i | 0.384321i | ||||||||
\(706\) | 33.7399 | 1.26982 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16.7010 | −0.627663 | ||||||||
\(709\) | 2.50285 | 0.0939964 | 0.0469982 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469982 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(710\) | 23.2390 | 0.872146 | ||||||||
\(711\) | 3.51472i | 0.131812i | ||||||||
\(712\) | −4.66115 | −0.174684 | ||||||||
\(713\) | 12.4939i | 0.467902i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.26136 | + | 64.9193i | 0.346355 | + | 2.42784i | ||||
\(716\) | 11.4655 | 0.428487 | ||||||||
\(717\) | 41.4301 | 1.54723 | ||||||||
\(718\) | −29.8985 | −1.11580 | ||||||||
\(719\) | 2.13580i | 0.0796520i | 0.999207 | + | 0.0398260i | \(0.0126804\pi\) | ||||
−0.999207 | + | 0.0398260i | \(0.987320\pi\) | |||||||
\(720\) | 1.34076i | 0.0499672i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 24.7632i | − | 0.921590i | ||||||
\(723\) | 28.5825i | 1.06300i | ||||||||
\(724\) | − | 13.2743i | − | 0.493335i | ||||||
\(725\) | 7.25675i | 0.269509i | ||||||||
\(726\) | −19.5145 | + | 5.68354i | −0.724252 | + | 0.210936i | ||||
\(727\) | − | 35.5296i | − | 1.31772i | −0.752266 | − | 0.658859i | \(-0.771039\pi\) | ||
0.752266 | − | 0.658859i | \(-0.228961\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.3137 | −0.826434 | ||||||||
\(730\) | −35.5822 | −1.31696 | ||||||||
\(731\) | − | 30.3985i | − | 1.12433i | ||||||
\(732\) | 15.8101i | 0.584359i | ||||||||
\(733\) | −2.34256 | −0.0865244 | −0.0432622 | − | 0.999064i | \(-0.513775\pi\) | ||||
−0.0432622 | + | 0.999064i | \(0.513775\pi\) | |||||||
\(734\) | 3.55525 | 0.131227 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.30583i | 0.195575i | ||||||||
\(737\) | 7.71931 | − | 1.10123i | 0.284345 | − | 0.0405645i | ||||
\(738\) | 0.506999i | 0.0186629i | ||||||||
\(739\) | − | 13.7129i | − | 0.504437i | −0.967670 | − | 0.252218i | \(-0.918840\pi\) | ||
0.967670 | − | 0.252218i | \(-0.0811602\pi\) | |||||||
\(740\) | 17.1128i | 0.629078i | ||||||||
\(741\) | 74.6664i | 2.74294i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.2193i | − | 1.62225i | −0.584873 | − | 0.811125i | \(-0.698856\pi\) | ||
0.584873 | − | 0.811125i | \(-0.301144\pi\) | |||||||
\(744\) | − | 4.35103i | − | 0.159516i | ||||||
\(745\) | −68.7797 | −2.51989 | ||||||||
\(746\) | 21.0969 | 0.772414 | ||||||||
\(747\) | 2.32017 | 0.0848904 | ||||||||
\(748\) | 26.6990 | − | 3.80886i | 0.976211 | − | 0.139266i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 2.85533i | − | 0.104262i | ||||||
\(751\) | 9.66328 | 0.352618 | 0.176309 | − | 0.984335i | \(-0.443584\pi\) | ||||
0.176309 | + | 0.984335i | \(0.443584\pi\) | |||||||
\(752\) | − | 1.70615i | − | 0.0622168i | ||||||
\(753\) | −9.00612 | −0.328201 | ||||||||
\(754\) | 8.09269 | 0.294718 | ||||||||
\(755\) | 53.9755 | 1.96437 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.0384 | −1.05542 | −0.527710 | − | 0.849425i | \(-0.676949\pi\) | ||||
−0.527710 | + | 0.849425i | \(0.676949\pi\) | |||||||
\(758\) | − | 8.61063i | − | 0.312752i | ||||||
\(759\) | 4.59220 | + | 32.1899i | 0.166686 | + | 1.16842i | ||||
\(760\) | 21.4132 | 0.776738 | ||||||||
\(761\) | −21.3623 | −0.774383 | −0.387191 | − | 0.921999i | \(-0.626555\pi\) | ||||
−0.387191 | + | 0.921999i | \(0.626555\pi\) | |||||||
\(762\) | 15.9593i | 0.578144i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.2147 | 0.441913 | ||||||||
\(765\) | − | 10.9025i | − | 0.394179i | ||||||
\(766\) | 34.2290 | 1.23674 | ||||||||
\(767\) | − | 55.2107i | − | 1.99354i | ||||||
\(768\) | − | 1.84776i | − | 0.0666753i | ||||||
\(769\) | 15.7726 | 0.568773 | 0.284387 | − | 0.958710i | \(-0.408210\pi\) | ||||
0.284387 | + | 0.958710i | \(0.408210\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.5381 | −1.31589 | ||||||||
\(772\) | − | 5.06319i | − | 0.182228i | ||||||
\(773\) | 6.71948i | 0.241683i | 0.992672 | + | 0.120841i | \(0.0385592\pi\) | ||||
−0.992672 | + | 0.120841i | \(0.961441\pi\) | |||||||
\(774\) | −1.54847 | −0.0556586 | ||||||||
\(775\) | 12.8980i | 0.463308i | ||||||||
\(776\) | 3.82683 | 0.137375 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 22.8252i | − | 0.818322i | ||||||
\(779\) | 8.09724 | 0.290114 | ||||||||
\(780\) | −36.5341 | −1.30813 | ||||||||
\(781\) | −23.5729 | + | 3.36290i | −0.843504 | + | 0.120334i | ||||
\(782\) | − | 43.1446i | − | 1.54285i | ||||||
\(783\) | −6.33002 | −0.226217 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.4917 | 1.44521 | ||||||||
\(786\) | 11.4601 | 0.408770 | ||||||||
\(787\) | 47.0796 | 1.67821 | 0.839103 | − | 0.543973i | \(-0.183081\pi\) | ||||
0.839103 | + | 0.543973i | \(0.183081\pi\) | |||||||
\(788\) | 20.0883i | 0.715617i | ||||||||
\(789\) | −15.6788 | −0.558178 | ||||||||
\(790\) | 27.4659i | 0.977191i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.194020 | − | 1.36002i | −0.00689420 | − | 0.0483263i | ||||
\(793\) | −52.2656 | −1.85601 | ||||||||
\(794\) | 12.6414 | 0.448625 | ||||||||
\(795\) | 23.8101 | 0.844458 | ||||||||
\(796\) | 14.8196i | 0.525266i | ||||||||
\(797\) | 0.354303i | 0.0125501i | 0.999980 | + | 0.00627504i | \(0.00199742\pi\) | ||||
−0.999980 | + | 0.00627504i | \(0.998003\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8736i | 0.490814i | ||||||||
\(800\) | 5.47740i | 0.193655i | ||||||||
\(801\) | − | 1.93071i | − | 0.0682184i | ||||||
\(802\) | 5.21750i | 0.184236i | ||||||||
\(803\) | 36.0934 | − | 5.14907i | 1.27371 | − | 0.181707i | ||||
\(804\) | 4.34413i | 0.153206i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.3837 | 0.506646 | ||||||||
\(807\) | −13.6724 | −0.481290 | ||||||||
\(808\) | − | 3.66037i | − | 0.128771i | ||||||
\(809\) | − | 45.4724i | − | 1.59872i | −0.600850 | − | 0.799362i | \(-0.705171\pi\) | ||
0.600850 | − | 0.799362i | \(-0.294829\pi\) | |||||||
\(810\) | 32.5989 | 1.14541 | ||||||||
\(811\) | 18.9483 | 0.665366 | 0.332683 | − | 0.943039i | \(-0.392046\pi\) | ||||
0.332683 | + | 0.943039i | \(0.392046\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.5356i | 0.930643i | ||||||||
\(814\) | −2.47637 | − | 17.3586i | −0.0867968 | − | 0.608419i | ||||
\(815\) | − | 27.1766i | − | 0.951955i | ||||||
\(816\) | 15.0251i | 0.525985i | ||||||||
\(817\) | 24.7305i | 0.865210i | ||||||||
\(818\) | − | 20.3483i | − | 0.711462i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.96195i | 0.138357i | ||||||||
\(821\) | 26.0757i | 0.910049i | 0.890479 | + | 0.455025i | \(0.150370\pi\) | ||||
−0.890479 | + | 0.455025i | \(0.849630\pi\) | |||||||
\(822\) | 16.6763 | 0.581652 | ||||||||
\(823\) | −41.5696 | −1.44903 | −0.724513 | − | 0.689261i | \(-0.757935\pi\) | ||||
−0.724513 | + | 0.689261i | \(0.757935\pi\) | |||||||
\(824\) | 14.5715 | 0.507623 | ||||||||
\(825\) | 4.74070 | + | 33.2308i | 0.165050 | + | 1.15695i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 51.2279i | − | 1.78137i | −0.454621 | − | 0.890685i | \(-0.650225\pi\) | ||
0.454621 | − | 0.890685i | \(-0.349775\pi\) | |||||||
\(828\) | −2.19775 | −0.0763770 | ||||||||
\(829\) | 4.30662i | 0.149575i | 0.997199 | + | 0.0747875i | \(0.0238279\pi\) | ||||
−0.997199 | + | 0.0747875i | \(0.976172\pi\) | |||||||
\(830\) | 18.1310 | 0.629336 | ||||||||
\(831\) | −4.04635 | −0.140366 | ||||||||
\(832\) | 6.10838 | 0.211770 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.4221 | 0.534023 | ||||||||
\(835\) | − | 13.0975i | − | 0.453259i | ||||||
\(836\) | −21.7208 | + | 3.09868i | −0.751230 | + | 0.107170i | ||||
\(837\) | −11.2508 | −0.388885 | ||||||||
\(838\) | 20.3391 | 0.702603 | ||||||||
\(839\) | − | 32.0881i | − | 1.10781i | −0.832581 | − | 0.553903i | \(-0.813138\pi\) | ||
0.832581 | − | 0.553903i | \(-0.186862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2448 | 0.939475 | ||||||||
\(842\) | 15.3327i | 0.528401i | ||||||||
\(843\) | 47.4879 | 1.63557 | ||||||||
\(844\) | 9.19848i | 0.316625i | ||||||||
\(845\) | − | 78.6959i | − | 2.70722i | ||||||
\(846\) | 0.706710 | 0.0242972 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.98098 | −0.136707 | ||||||||
\(849\) | 28.7469i | 0.986593i | ||||||||
\(850\) | − | 44.5398i | − | 1.52770i | ||||||
\(851\) | −28.0509 | −0.961572 | ||||||||
\(852\) | − | 13.2659i | − | 0.454482i | ||||||
\(853\) | 46.8146 | 1.60290 | 0.801451 | − | 0.598060i | \(-0.204062\pi\) | ||||
0.801451 | + | 0.598060i | \(0.204062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.86963i | 0.303335i | ||||||||
\(856\) | 7.87362 | 0.269115 | ||||||||
\(857\) | 42.5146 | 1.45227 | 0.726135 | − | 0.687552i | \(-0.241315\pi\) | ||||
0.726135 | + | 0.687552i | \(0.241315\pi\) | |||||||
\(858\) | 37.0589 | − | 5.28681i | 1.26517 | − | 0.180489i | ||||
\(859\) | − | 23.4563i | − | 0.800320i | −0.916445 | − | 0.400160i | \(-0.868955\pi\) | ||
0.916445 | − | 0.400160i | \(-0.131045\pi\) | |||||||
\(860\) | −12.1006 | −0.412625 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.16904 | 0.0738777 | ||||||||
\(863\) | 13.6411 | 0.464348 | 0.232174 | − | 0.972674i | \(-0.425416\pi\) | ||||
0.232174 | + | 0.972674i | \(0.425416\pi\) | |||||||
\(864\) | −4.77791 | −0.162548 | ||||||||
\(865\) | − | 9.95673i | − | 0.338539i | ||||||
\(866\) | −38.4356 | −1.30610 | ||||||||
\(867\) | − | 90.7658i | − | 3.08257i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.97456 | − | 27.8604i | −0.134828 | − | 0.945100i | ||||
\(870\) | 7.92391 | 0.268646 | ||||||||
\(871\) | −14.3609 | −0.486602 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | 1.58513i | 0.0536484i | ||||||||
\(874\) | 35.1000i | 1.18728i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.3119i | 0.686277i | ||||||||
\(877\) | − | 15.1178i | − | 0.510491i | −0.966876 | − | 0.255245i | \(-0.917844\pi\) | ||
0.966876 | − | 0.255245i | \(-0.0821563\pi\) | |||||||
\(878\) | − | 5.72240i | − | 0.193122i | ||||||
\(879\) | − | 5.75487i | − | 0.194107i | ||||||
\(880\) | −1.51617 | − | 10.6279i | −0.0511102 | − | 0.358267i | ||||
\(881\) | − | 4.23924i | − | 0.142824i | −0.997447 | − | 0.0714118i | \(-0.977250\pi\) | ||
0.997447 | − | 0.0714118i | \(-0.0227504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9457 | 0.435658 | 0.217829 | − | 0.975987i | \(-0.430102\pi\) | ||||
0.217829 | + | 0.975987i | \(0.430102\pi\) | |||||||
\(884\) | −49.6706 | −1.67060 | ||||||||
\(885\) | − | 54.0592i | − | 1.81718i | ||||||
\(886\) | − | 7.18733i | − | 0.241463i | ||||||
\(887\) | 22.6413 | 0.760219 | 0.380109 | − | 0.924942i | \(-0.375886\pi\) | ||||
0.380109 | + | 0.924942i | \(0.375886\pi\) | |||||||
\(888\) | 9.76874 | 0.327818 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 15.0876i | − | 0.505738i | ||||||
\(891\) | −33.0672 | + | 4.71735i | −1.10779 | + | 0.158037i | ||||
\(892\) | − | 10.8760i | − | 0.364155i | ||||||
\(893\) | − | 11.2868i | − | 0.377699i | ||||||
\(894\) | 39.2626i | 1.31314i | ||||||||
\(895\) | 37.1126i | 1.24054i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 59.8859i | − | 1.99953i | ||||||
\(898\) | − | 8.63068i | − | 0.288010i | ||||||
\(899\) | −3.11971 | −0.104048 | ||||||||
\(900\) | −2.26881 | −0.0756271 | ||||||||
\(901\) | 32.3715 | 1.07845 | ||||||||
\(902\) | −0.573330 | − | 4.01887i | −0.0190898 | − | 0.133814i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.5216i | 0.449721i | ||||||||
\(905\) | 42.9673 | 1.42828 | ||||||||
\(906\) | − | 30.8117i | − | 1.02365i | ||||||
\(907\) | 48.9120 | 1.62410 | 0.812049 | − | 0.583590i | \(-0.198352\pi\) | ||||
0.812049 | + | 0.583590i | \(0.198352\pi\) | |||||||
\(908\) | −23.4793 | −0.779187 | ||||||||
\(909\) | 1.51617 | 0.0502883 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.4028 | −1.73618 | −0.868091 | − | 0.496406i | \(-0.834653\pi\) | ||||
−0.868091 | + | 0.496406i | \(0.834653\pi\) | |||||||
\(912\) | − | 12.2236i | − | 0.404764i | ||||||
\(913\) | −18.3915 | + | 2.62372i | −0.608668 | + | 0.0868324i | ||||
\(914\) | 28.5018 | 0.942756 | ||||||||
\(915\) | −51.1755 | −1.69181 | ||||||||
\(916\) | 22.8301i | 0.754328i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 38.8518 | 1.28230 | ||||||||
\(919\) | − | 15.5442i | − | 0.512755i | −0.966577 | − | 0.256378i | \(-0.917471\pi\) | ||
0.966577 | − | 0.256378i | \(-0.0825290\pi\) | |||||||
\(920\) | −17.1743 | −0.566221 | ||||||||
\(921\) | 16.5018i | 0.543753i | ||||||||
\(922\) | − | 35.6022i | − | 1.17250i | ||||||
\(923\) | 43.8548 | 1.44350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.9580 | −0.952132 | ||||||||
\(926\) | − | 32.2369i | − | 1.05937i | ||||||
\(927\) | 6.03572i | 0.198239i | ||||||||
\(928\) | −1.32485 | −0.0434904 | ||||||||
\(929\) | − | 27.2257i | − | 0.893248i | −0.894722 | − | 0.446624i | \(-0.852626\pi\) | ||
0.894722 | − | 0.446624i | \(-0.147374\pi\) | |||||||
\(930\) | 14.0838 | 0.461824 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.7089i | 0.481806i | ||||||||
\(933\) | −35.3561 | −1.15751 | ||||||||
\(934\) | 25.8620 | 0.846232 | ||||||||
\(935\) | 12.3288 | + | 86.4214i | 0.403196 | + | 2.82628i | ||||
\(936\) | 2.53017i | 0.0827013i | ||||||||
\(937\) | 28.7613 | 0.939590 | 0.469795 | − | 0.882776i | \(-0.344328\pi\) | ||||
0.469795 | + | 0.882776i | \(0.344328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.17769 | −0.0710663 | ||||||||
\(940\) | 5.52260 | 0.180127 | ||||||||
\(941\) | −35.2984 | −1.15070 | −0.575348 | − | 0.817909i | \(-0.695133\pi\) | ||||
−0.575348 | + | 0.817909i | \(0.695133\pi\) | |||||||
\(942\) | − | 23.1145i | − | 0.753111i | ||||||
\(943\) | −6.49435 | −0.211485 | ||||||||
\(944\) | 9.03853i | 0.294179i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.2744 | − | 1.75106i | 0.399075 | − | 0.0569318i | ||||
\(947\) | 41.0245 | 1.33312 | 0.666559 | − | 0.745452i | \(-0.267766\pi\) | ||||
0.666559 | + | 0.745452i | \(0.267766\pi\) | |||||||
\(948\) | 15.6788 | 0.509222 | ||||||||
\(949\) | −67.1478 | −2.17971 | ||||||||
\(950\) | 36.2351i | 1.17562i | ||||||||
\(951\) | 16.8090i | 0.545068i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.09232i | − | 0.0353838i | −0.999843 | − | 0.0176919i | \(-0.994368\pi\) | ||
0.999843 | − | 0.0176919i | \(-0.00563181\pi\) | |||||||
\(954\) | − | 1.64897i | − | 0.0533875i | ||||||
\(955\) | 39.5376i | 1.27941i | ||||||||
\(956\) | − | 22.4218i | − | 0.725173i | ||||||
\(957\) | −8.03774 | + | 1.14666i | −0.259823 | + | 0.0370663i | ||||
\(958\) | − | 12.5206i | − | 0.404521i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.98098 | 0.193035 | ||||||||
\(961\) | 25.4551 | 0.821133 | ||||||||
\(962\) | 32.2938i | 1.04119i | ||||||||
\(963\) | 3.26136i | 0.105096i | ||||||||
\(964\) | 15.4687 | 0.498215 | ||||||||
\(965\) | 16.3889 | 0.527579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0334i | 1.31955i | 0.751465 | + | 0.659773i | \(0.229348\pi\) | ||||
−0.751465 | + | 0.659773i | \(0.770652\pi\) | |||||||
\(968\) | 3.07591 | + | 10.5612i | 0.0988635 | + | 0.339450i | ||||
\(969\) | 99.3969i | 3.19309i | ||||||||
\(970\) | 12.3870i | 0.397723i | ||||||||
\(971\) | 8.07758i | 0.259222i | 0.991565 | + | 0.129611i | \(0.0413728\pi\) | ||||
−0.991565 | + | 0.129611i | \(0.958627\pi\) | |||||||
\(972\) | − | 4.27518i | − | 0.137126i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 20.7085i | − | 0.663542i | ||||||
\(975\) | − | 61.8224i | − | 1.97990i | ||||||
\(976\) | 8.55638 | 0.273883 | ||||||||
\(977\) | 35.6432 | 1.14033 | 0.570164 | − | 0.821531i | \(-0.306880\pi\) | ||||
0.570164 | + | 0.821531i | \(0.306880\pi\) | |||||||
\(978\) | −15.5136 | −0.496071 | ||||||||
\(979\) | 2.18331 | + | 15.3043i | 0.0697789 | + | 0.489129i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.48528i | 0.0793489i | ||||||||
\(982\) | −23.6712 | −0.755377 | ||||||||
\(983\) | 39.0034i | 1.24402i | 0.783011 | + | 0.622008i | \(0.213683\pi\) | ||||
−0.783011 | + | 0.622008i | \(0.786317\pi\) | |||||||
\(984\) | 2.26166 | 0.0720992 | ||||||||
\(985\) | −65.0235 | −2.07182 | ||||||||
\(986\) | 10.7731 | 0.343085 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40.4092 | 1.28559 | ||||||||
\(989\) | − | 19.8350i | − | 0.630715i | ||||||
\(990\) | 4.40223 | − | 0.628020i | 0.139912 | − | 0.0199598i | ||||
\(991\) | −16.6038 | −0.527436 | −0.263718 | − | 0.964600i | \(-0.584949\pi\) | ||||
−0.263718 | + | 0.964600i | \(0.584949\pi\) | |||||||
\(992\) | −2.35476 | −0.0747636 | ||||||||
\(993\) | − | 5.04388i | − | 0.160063i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47.9692 | −1.52073 | ||||||||
\(996\) | − | 10.3500i | − | 0.327952i | ||||||
\(997\) | 42.3386 | 1.34088 | 0.670439 | − | 0.741965i | \(-0.266106\pi\) | ||||
0.670439 | + | 0.741965i | \(0.266106\pi\) | |||||||
\(998\) | − | 11.6124i | − | 0.367584i | ||||||
\(999\) | − | 25.2599i | − | 0.799187i |
(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 | 1078.2.c.c.1077.1 | ✓ | 16 | |
7.2 | even | 3 | 1078.2.i.d.1011.4 | 32 | |||
7.3 | odd | 6 | 1078.2.i.d.901.16 | 32 | |||
7.4 | even | 3 | 1078.2.i.d.901.15 | 32 | |||
7.5 | odd | 6 | 1078.2.i.d.1011.3 | 32 | |||
7.6 | odd | 2 | inner | 1078.2.c.c.1077.8 | yes | 16 | |
11.10 | odd | 2 | inner | 1078.2.c.c.1077.9 | yes | 16 | |
77.10 | even | 6 | 1078.2.i.d.901.4 | 32 | |||
77.32 | odd | 6 | 1078.2.i.d.901.3 | 32 | |||
77.54 | even | 6 | 1078.2.i.d.1011.15 | 32 | |||
77.65 | odd | 6 | 1078.2.i.d.1011.16 | 32 | |||
77.76 | even | 2 | inner | 1078.2.c.c.1077.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.c.1077.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1078.2.c.c.1077.8 | yes | 16 | 7.6 | odd | 2 | inner | |
1078.2.c.c.1077.9 | yes | 16 | 11.10 | odd | 2 | inner | |
1078.2.c.c.1077.16 | yes | 16 | 77.76 | even | 2 | inner | |
1078.2.i.d.901.3 | 32 | 77.32 | odd | 6 | |||
1078.2.i.d.901.4 | 32 | 77.10 | even | 6 | |||
1078.2.i.d.901.15 | 32 | 7.4 | even | 3 | |||
1078.2.i.d.901.16 | 32 | 7.3 | odd | 6 | |||
1078.2.i.d.1011.3 | 32 | 7.5 | odd | 6 | |||
1078.2.i.d.1011.4 | 32 | 7.2 | even | 3 | |||
1078.2.i.d.1011.15 | 32 | 77.54 | even | 6 | |||
1078.2.i.d.1011.16 | 32 | 77.65 | odd | 6 |