Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.5 | ||
Root | \(-0.384890 + 1.68874i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.b.881.11 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||
\(3\) | 1.17770 | − | 1.27005i | 0.679944 | − | 0.733264i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.27005 | − | 1.17770i | −0.518496 | − | 0.480793i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.226058 | − | 2.99147i | −0.0753527 | − | 0.997157i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | 4.95532i | 1.49409i | 0.664776 | + | 0.747043i | \(0.268527\pi\) | ||||
−0.664776 | + | 0.747043i | \(0.731473\pi\) | |||||||
\(12\) | −1.17770 | + | 1.27005i | −0.339972 | + | 0.366632i | ||||
\(13\) | 6.37523i | 1.76817i | 0.467325 | + | 0.884086i | \(0.345218\pi\) | ||||
−0.467325 | + | 0.884086i | \(0.654782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.17770 | + | 1.27005i | −0.304080 | + | 0.327926i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.62755 | 0.879809 | 0.439905 | − | 0.898044i | \(-0.355012\pi\) | ||||
0.439905 | + | 0.898044i | \(0.355012\pi\) | |||||||
\(18\) | −2.99147 | + | 0.226058i | −0.705096 | + | 0.0532824i | ||||
\(19\) | 4.20710i | 0.965174i | 0.875848 | + | 0.482587i | \(0.160303\pi\) | ||||
−0.875848 | + | 0.482587i | \(0.839697\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.95532 | 1.05648 | ||||||||
\(23\) | 1.91676i | 0.399672i | 0.979829 | + | 0.199836i | \(0.0640409\pi\) | ||||
−0.979829 | + | 0.199836i | \(0.935959\pi\) | |||||||
\(24\) | 1.27005 | + | 1.17770i | 0.259248 | + | 0.240396i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.37523 | 1.25029 | ||||||||
\(27\) | −4.06555 | − | 3.23594i | −0.782415 | − | 0.622757i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.800269i | 0.148606i | 0.997236 | + | 0.0743031i | \(0.0236732\pi\) | ||||
−0.997236 | + | 0.0743031i | \(0.976327\pi\) | |||||||
\(30\) | 1.27005 | + | 1.17770i | 0.231878 | + | 0.215017i | ||||
\(31\) | 5.03641i | 0.904566i | 0.891875 | + | 0.452283i | \(0.149390\pi\) | ||||
−0.891875 | + | 0.452283i | \(0.850610\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 6.29351 | + | 5.83587i | 1.09556 | + | 1.01589i | ||||
\(34\) | − | 3.62755i | − | 0.622119i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.226058 | + | 2.99147i | 0.0376763 | + | 0.498578i | ||||
\(37\) | 5.82789 | 0.958099 | 0.479050 | − | 0.877788i | \(-0.340981\pi\) | ||||
0.479050 | + | 0.877788i | \(0.340981\pi\) | |||||||
\(38\) | 4.20710 | 0.682481 | ||||||||
\(39\) | 8.09687 | + | 7.50809i | 1.29654 | + | 1.20226i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | −7.45163 | −1.16375 | −0.581874 | − | 0.813279i | \(-0.697680\pi\) | ||||
−0.581874 | + | 0.813279i | \(0.697680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.64827 | −0.708854 | −0.354427 | − | 0.935084i | \(-0.615324\pi\) | ||||
−0.354427 | + | 0.935084i | \(0.615324\pi\) | |||||||
\(44\) | − | 4.95532i | − | 0.747043i | ||||||
\(45\) | 0.226058 | + | 2.99147i | 0.0336987 | + | 0.445942i | ||||
\(46\) | 1.91676 | 0.282611 | ||||||||
\(47\) | 0.607779 | 0.0886537 | 0.0443269 | − | 0.999017i | \(-0.485886\pi\) | ||||
0.0443269 | + | 0.999017i | \(0.485886\pi\) | |||||||
\(48\) | 1.17770 | − | 1.27005i | 0.169986 | − | 0.183316i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 4.27215 | − | 4.60717i | 0.598221 | − | 0.645133i | ||||
\(52\) | − | 6.37523i | − | 0.884086i | ||||||
\(53\) | − | 14.3065i | − | 1.96515i | −0.185860 | − | 0.982576i | \(-0.559507\pi\) | ||
0.185860 | − | 0.982576i | \(-0.440493\pi\) | |||||||
\(54\) | −3.23594 | + | 4.06555i | −0.440356 | + | 0.553251i | ||||
\(55\) | − | 4.95532i | − | 0.668175i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.34323 | + | 4.95469i | 0.707727 | + | 0.656264i | ||||
\(58\) | 0.800269 | 0.105080 | ||||||||
\(59\) | −1.75132 | −0.228002 | −0.114001 | − | 0.993481i | \(-0.536367\pi\) | ||||
−0.114001 | + | 0.993481i | \(0.536367\pi\) | |||||||
\(60\) | 1.17770 | − | 1.27005i | 0.152040 | − | 0.163963i | ||||
\(61\) | − | 3.42307i | − | 0.438279i | −0.975693 | − | 0.219140i | \(-0.929675\pi\) | ||
0.975693 | − | 0.219140i | \(-0.0703251\pi\) | |||||||
\(62\) | 5.03641 | 0.639624 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 6.37523i | − | 0.790750i | ||||||
\(66\) | 5.83587 | − | 6.29351i | 0.718346 | − | 0.774678i | ||||
\(67\) | 7.98294 | 0.975272 | 0.487636 | − | 0.873047i | \(-0.337859\pi\) | ||||
0.487636 | + | 0.873047i | \(0.337859\pi\) | |||||||
\(68\) | −3.62755 | −0.439905 | ||||||||
\(69\) | 2.43438 | + | 2.25736i | 0.293065 | + | 0.271754i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.48759i | − | 0.295222i | −0.989045 | − | 0.147611i | \(-0.952842\pi\) | ||
0.989045 | − | 0.147611i | \(-0.0471584\pi\) | |||||||
\(72\) | 2.99147 | − | 0.226058i | 0.352548 | − | 0.0266412i | ||||
\(73\) | 15.0933i | 1.76654i | 0.468866 | + | 0.883270i | \(0.344663\pi\) | ||||
−0.468866 | + | 0.883270i | \(0.655337\pi\) | |||||||
\(74\) | − | 5.82789i | − | 0.677478i | ||||||
\(75\) | 1.17770 | − | 1.27005i | 0.135989 | − | 0.146653i | ||||
\(76\) | − | 4.20710i | − | 0.482587i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.50809 | − | 8.09687i | 0.850124 | − | 0.916790i | ||||
\(79\) | 2.66807 | 0.300182 | 0.150091 | − | 0.988672i | \(-0.452043\pi\) | ||||
0.150091 | + | 0.988672i | \(0.452043\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −8.89780 | + | 1.35249i | −0.988644 | + | 0.150277i | ||||
\(82\) | 7.45163i | 0.822895i | ||||||||
\(83\) | −7.27215 | −0.798222 | −0.399111 | − | 0.916903i | \(-0.630681\pi\) | ||||
−0.399111 | + | 0.916903i | \(0.630681\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.62755 | −0.393463 | ||||||||
\(86\) | 4.64827i | 0.501236i | ||||||||
\(87\) | 1.01638 | + | 0.942474i | 0.108968 | + | 0.101044i | ||||
\(88\) | −4.95532 | −0.528239 | ||||||||
\(89\) | 1.88495 | 0.199804 | 0.0999021 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999021 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(90\) | 2.99147 | − | 0.226058i | 0.315329 | − | 0.0238286i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1.91676i | − | 0.199836i | ||||||
\(93\) | 6.39649 | + | 5.93136i | 0.663286 | + | 0.615054i | ||||
\(94\) | − | 0.607779i | − | 0.0626876i | ||||||
\(95\) | − | 4.20710i | − | 0.431639i | ||||||
\(96\) | −1.27005 | − | 1.17770i | −0.129624 | − | 0.120198i | ||||
\(97\) | 17.6562i | 1.79271i | 0.443334 | + | 0.896356i | \(0.353795\pi\) | ||||
−0.443334 | + | 0.896356i | \(0.646205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.8237 | − | 1.12019i | 1.48984 | − | 0.112583i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 1.14842 | 0.114272 | 0.0571361 | − | 0.998366i | \(-0.481803\pi\) | ||||
0.0571361 | + | 0.998366i | \(0.481803\pi\) | |||||||
\(102\) | −4.60717 | − | 4.27215i | −0.456178 | − | 0.423006i | ||||
\(103\) | 7.28364i | 0.717678i | 0.933399 | + | 0.358839i | \(0.116827\pi\) | ||||
−0.933399 | + | 0.358839i | \(0.883173\pi\) | |||||||
\(104\) | −6.37523 | −0.625143 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.3065 | −1.38957 | ||||||||
\(107\) | − | 2.68637i | − | 0.259701i | −0.991534 | − | 0.129850i | \(-0.958550\pi\) | ||
0.991534 | − | 0.129850i | \(-0.0414497\pi\) | |||||||
\(108\) | 4.06555 | + | 3.23594i | 0.391208 | + | 0.311379i | ||||
\(109\) | 9.02343 | 0.864288 | 0.432144 | − | 0.901805i | \(-0.357757\pi\) | ||||
0.432144 | + | 0.901805i | \(0.357757\pi\) | |||||||
\(110\) | −4.95532 | −0.472471 | ||||||||
\(111\) | 6.86349 | − | 7.40171i | 0.651454 | − | 0.702540i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.4267i | − | 1.16901i | −0.811391 | − | 0.584504i | \(-0.801289\pi\) | ||
0.811391 | − | 0.584504i | \(-0.198711\pi\) | |||||||
\(114\) | 4.95469 | − | 5.34323i | 0.464049 | − | 0.500439i | ||||
\(115\) | − | 1.91676i | − | 0.178739i | ||||||
\(116\) | − | 0.800269i | − | 0.0743031i | ||||||
\(117\) | 19.0713 | − | 1.44117i | 1.76314 | − | 0.133236i | ||||
\(118\) | 1.75132i | 0.161222i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.27005 | − | 1.17770i | −0.115939 | − | 0.107509i | ||||
\(121\) | −13.5552 | −1.23229 | ||||||||
\(122\) | −3.42307 | −0.309910 | ||||||||
\(123\) | −8.77576 | + | 9.46395i | −0.791284 | + | 0.853335i | ||||
\(124\) | − | 5.03641i | − | 0.452283i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.06679 | 0.715812 | 0.357906 | − | 0.933758i | \(-0.383491\pi\) | ||||
0.357906 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −5.47425 | + | 5.90354i | −0.481981 | + | 0.519777i | ||||
\(130\) | −6.37523 | −0.559145 | ||||||||
\(131\) | 3.38301 | 0.295575 | 0.147788 | − | 0.989019i | \(-0.452785\pi\) | ||||
0.147788 | + | 0.989019i | \(0.452785\pi\) | |||||||
\(132\) | −6.29351 | − | 5.83587i | −0.547780 | − | 0.507947i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 7.98294i | − | 0.689621i | ||||||
\(135\) | 4.06555 | + | 3.23594i | 0.349907 | + | 0.278506i | ||||
\(136\) | 3.62755i | 0.311060i | ||||||||
\(137\) | 14.8274i | 1.26679i | 0.773829 | + | 0.633395i | \(0.218339\pi\) | ||||
−0.773829 | + | 0.633395i | \(0.781661\pi\) | |||||||
\(138\) | 2.25736 | − | 2.43438i | 0.192159 | − | 0.207228i | ||||
\(139\) | 7.24669i | 0.614656i | 0.951604 | + | 0.307328i | \(0.0994349\pi\) | ||||
−0.951604 | + | 0.307328i | \(0.900565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.715780 | − | 0.771911i | 0.0602796 | − | 0.0650066i | ||||
\(142\) | −2.48759 | −0.208754 | ||||||||
\(143\) | −31.5913 | −2.64180 | ||||||||
\(144\) | −0.226058 | − | 2.99147i | −0.0188382 | − | 0.249289i | ||||
\(145\) | − | 0.800269i | − | 0.0664587i | ||||||
\(146\) | 15.0933 | 1.24913 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.82789 | −0.479050 | ||||||||
\(149\) | − | 6.59303i | − | 0.540122i | −0.962843 | − | 0.270061i | \(-0.912956\pi\) | ||
0.962843 | − | 0.270061i | \(-0.0870439\pi\) | |||||||
\(150\) | −1.27005 | − | 1.17770i | −0.103699 | − | 0.0961586i | ||||
\(151\) | 11.7743 | 0.958183 | 0.479091 | − | 0.877765i | \(-0.340966\pi\) | ||||
0.479091 | + | 0.877765i | \(0.340966\pi\) | |||||||
\(152\) | −4.20710 | −0.341241 | ||||||||
\(153\) | −0.820036 | − | 10.8517i | −0.0662960 | − | 0.877308i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.03641i | − | 0.404534i | ||||||
\(156\) | −8.09687 | − | 7.50809i | −0.648268 | − | 0.601129i | ||||
\(157\) | 1.54479i | 0.123288i | 0.998098 | + | 0.0616440i | \(0.0196343\pi\) | ||||
−0.998098 | + | 0.0616440i | \(0.980366\pi\) | |||||||
\(158\) | − | 2.66807i | − | 0.212261i | ||||||
\(159\) | −18.1700 | − | 16.8488i | −1.44098 | − | 1.33619i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.35249 | + | 8.89780i | 0.106262 | + | 0.699077i | ||||
\(163\) | −3.37759 | −0.264553 | −0.132277 | − | 0.991213i | \(-0.542229\pi\) | ||||
−0.132277 | + | 0.991213i | \(0.542229\pi\) | |||||||
\(164\) | 7.45163 | 0.581874 | ||||||||
\(165\) | −6.29351 | − | 5.83587i | −0.489949 | − | 0.454322i | ||||
\(166\) | 7.27215i | 0.564428i | ||||||||
\(167\) | 12.7685 | 0.988053 | 0.494027 | − | 0.869447i | \(-0.335525\pi\) | ||||
0.494027 | + | 0.869447i | \(0.335525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.6436 | −2.12643 | ||||||||
\(170\) | 3.62755i | 0.278220i | ||||||||
\(171\) | 12.5854 | − | 0.951048i | 0.962430 | − | 0.0727285i | ||||
\(172\) | 4.64827 | 0.354427 | ||||||||
\(173\) | −0.247556 | −0.0188214 | −0.00941068 | − | 0.999956i | \(-0.502996\pi\) | ||||
−0.00941068 | + | 0.999956i | \(0.502996\pi\) | |||||||
\(174\) | 0.942474 | − | 1.01638i | 0.0714488 | − | 0.0770517i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.95532i | 0.373521i | ||||||||
\(177\) | −2.06252 | + | 2.22426i | −0.155029 | + | 0.167186i | ||||
\(178\) | − | 1.88495i | − | 0.141283i | ||||||
\(179\) | − | 19.5963i | − | 1.46470i | −0.680930 | − | 0.732348i | \(-0.738424\pi\) | ||
0.680930 | − | 0.732348i | \(-0.261576\pi\) | |||||||
\(180\) | −0.226058 | − | 2.99147i | −0.0168494 | − | 0.222971i | ||||
\(181\) | − | 14.8103i | − | 1.10084i | −0.834887 | − | 0.550422i | \(-0.814467\pi\) | ||
0.834887 | − | 0.550422i | \(-0.185533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.34748 | − | 4.03134i | −0.321375 | − | 0.298005i | ||||
\(184\) | −1.91676 | −0.141305 | ||||||||
\(185\) | −5.82789 | −0.428475 | ||||||||
\(186\) | 5.93136 | − | 6.39649i | 0.434909 | − | 0.469014i | ||||
\(187\) | 17.9757i | 1.31451i | ||||||||
\(188\) | −0.607779 | −0.0443269 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.20710 | −0.305215 | ||||||||
\(191\) | 0.535503i | 0.0387476i | 0.999812 | + | 0.0193738i | \(0.00616726\pi\) | ||||
−0.999812 | + | 0.0193738i | \(0.993833\pi\) | |||||||
\(192\) | −1.17770 | + | 1.27005i | −0.0849930 | + | 0.0916580i | ||||
\(193\) | −5.53544 | −0.398450 | −0.199225 | − | 0.979954i | \(-0.563842\pi\) | ||||
−0.199225 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(194\) | 17.6562 | 1.26764 | ||||||||
\(195\) | −8.09687 | − | 7.50809i | −0.579829 | − | 0.537666i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.666454i | 0.0474829i | 0.999718 | + | 0.0237414i | \(0.00755785\pi\) | ||||
−0.999718 | + | 0.0237414i | \(0.992442\pi\) | |||||||
\(198\) | −1.12019 | − | 14.8237i | −0.0796085 | − | 1.05347i | ||||
\(199\) | − | 9.02198i | − | 0.639551i | −0.947493 | − | 0.319775i | \(-0.896393\pi\) | ||
0.947493 | − | 0.319775i | \(-0.103607\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 9.40149 | − | 10.1387i | 0.663130 | − | 0.715132i | ||||
\(202\) | − | 1.14842i | − | 0.0808026i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.27215 | + | 4.60717i | −0.299110 | + | 0.322566i | ||||
\(205\) | 7.45163 | 0.520444 | ||||||||
\(206\) | 7.28364 | 0.507475 | ||||||||
\(207\) | 5.73392 | − | 0.433299i | 0.398535 | − | 0.0301163i | ||||
\(208\) | 6.37523i | 0.442043i | ||||||||
\(209\) | −20.8475 | −1.44205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4386 | 0.787467 | 0.393733 | − | 0.919225i | \(-0.371183\pi\) | ||||
0.393733 | + | 0.919225i | \(0.371183\pi\) | |||||||
\(212\) | 14.3065i | 0.982576i | ||||||||
\(213\) | −3.15936 | − | 2.92963i | −0.216476 | − | 0.200735i | ||||
\(214\) | −2.68637 | −0.183636 | ||||||||
\(215\) | 4.64827 | 0.317009 | ||||||||
\(216\) | 3.23594 | − | 4.06555i | 0.220178 | − | 0.276625i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 9.02343i | − | 0.611144i | ||||||
\(219\) | 19.1693 | + | 17.7754i | 1.29534 | + | 1.20115i | ||||
\(220\) | 4.95532i | 0.334088i | ||||||||
\(221\) | 23.1265i | 1.55565i | ||||||||
\(222\) | −7.40171 | − | 6.86349i | −0.496771 | − | 0.460647i | ||||
\(223\) | 5.23397i | 0.350493i | 0.984525 | + | 0.175246i | \(0.0560722\pi\) | ||||
−0.984525 | + | 0.175246i | \(0.943928\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.226058 | − | 2.99147i | −0.0150705 | − | 0.199431i | ||||
\(226\) | −12.4267 | −0.826613 | ||||||||
\(227\) | 13.4623 | 0.893527 | 0.446763 | − | 0.894652i | \(-0.352577\pi\) | ||||
0.446763 | + | 0.894652i | \(0.352577\pi\) | |||||||
\(228\) | −5.34323 | − | 4.95469i | −0.353864 | − | 0.328132i | ||||
\(229\) | − | 16.5216i | − | 1.09178i | −0.837857 | − | 0.545890i | \(-0.816192\pi\) | ||
0.837857 | − | 0.545890i | \(-0.183808\pi\) | |||||||
\(230\) | −1.91676 | −0.126387 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.800269 | −0.0525402 | ||||||||
\(233\) | 18.6359i | 1.22088i | 0.792063 | + | 0.610440i | \(0.209007\pi\) | ||||
−0.792063 | + | 0.610440i | \(0.790993\pi\) | |||||||
\(234\) | −1.44117 | − | 19.0713i | −0.0942124 | − | 1.24673i | ||||
\(235\) | −0.607779 | −0.0396471 | ||||||||
\(236\) | 1.75132 | 0.114001 | ||||||||
\(237\) | 3.14218 | − | 3.38859i | 0.204107 | − | 0.220113i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.8065i | 1.60460i | 0.596922 | + | 0.802299i | \(0.296390\pi\) | ||||
−0.596922 | + | 0.802299i | \(0.703610\pi\) | |||||||
\(240\) | −1.17770 | + | 1.27005i | −0.0760200 | + | 0.0819814i | ||||
\(241\) | − | 22.3364i | − | 1.43882i | −0.694588 | − | 0.719408i | \(-0.744413\pi\) | ||
0.694588 | − | 0.719408i | \(-0.255587\pi\) | |||||||
\(242\) | 13.5552i | 0.871362i | ||||||||
\(243\) | −8.76118 | + | 12.8935i | −0.562030 | + | 0.827117i | ||||
\(244\) | 3.42307i | 0.219140i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.46395 | + | 8.77576i | 0.603399 | + | 0.559522i | ||||
\(247\) | −26.8212 | −1.70659 | ||||||||
\(248\) | −5.03641 | −0.319812 | ||||||||
\(249\) | −8.56439 | + | 9.23600i | −0.542746 | + | 0.585308i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | 2.72107 | 0.171752 | 0.0858762 | − | 0.996306i | \(-0.472631\pi\) | ||||
0.0858762 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.49815 | −0.597144 | ||||||||
\(254\) | − | 8.06679i | − | 0.506156i | ||||||
\(255\) | −4.27215 | + | 4.60717i | −0.267533 | + | 0.288512i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.5038 | −0.717586 | −0.358793 | − | 0.933417i | \(-0.616812\pi\) | ||||
−0.358793 | + | 0.933417i | \(0.616812\pi\) | |||||||
\(258\) | 5.90354 | + | 5.47425i | 0.367538 | + | 0.340812i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.37523i | 0.395375i | ||||||||
\(261\) | 2.39398 | − | 0.180907i | 0.148184 | − | 0.0111979i | ||||
\(262\) | − | 3.38301i | − | 0.209003i | ||||||
\(263\) | 12.7855i | 0.788390i | 0.919027 | + | 0.394195i | \(0.128977\pi\) | ||||
−0.919027 | + | 0.394195i | \(0.871023\pi\) | |||||||
\(264\) | −5.83587 | + | 6.29351i | −0.359173 | + | 0.387339i | ||||
\(265\) | 14.3065i | 0.878843i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.21990 | − | 2.39398i | 0.135856 | − | 0.146509i | ||||
\(268\) | −7.98294 | −0.487636 | ||||||||
\(269\) | 11.6915 | 0.712844 | 0.356422 | − | 0.934325i | \(-0.383997\pi\) | ||||
0.356422 | + | 0.934325i | \(0.383997\pi\) | |||||||
\(270\) | 3.23594 | − | 4.06555i | 0.196933 | − | 0.247421i | ||||
\(271\) | − | 22.0698i | − | 1.34065i | −0.742069 | − | 0.670323i | \(-0.766155\pi\) | ||
0.742069 | − | 0.670323i | \(-0.233845\pi\) | |||||||
\(272\) | 3.62755 | 0.219952 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.8274 | 0.895756 | ||||||||
\(275\) | 4.95532i | 0.298817i | ||||||||
\(276\) | −2.43438 | − | 2.25736i | −0.146532 | − | 0.135877i | ||||
\(277\) | −7.80656 | −0.469051 | −0.234525 | − | 0.972110i | \(-0.575354\pi\) | ||||
−0.234525 | + | 0.972110i | \(0.575354\pi\) | |||||||
\(278\) | 7.24669 | 0.434627 | ||||||||
\(279\) | 15.0663 | − | 1.13852i | 0.901994 | − | 0.0681615i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.0892i | 1.37738i | 0.725054 | + | 0.688692i | \(0.241815\pi\) | ||||
−0.725054 | + | 0.688692i | \(0.758185\pi\) | |||||||
\(282\) | −0.771911 | − | 0.715780i | −0.0459666 | − | 0.0426241i | ||||
\(283\) | 24.7505i | 1.47126i | 0.677382 | + | 0.735631i | \(0.263114\pi\) | ||||
−0.677382 | + | 0.735631i | \(0.736886\pi\) | |||||||
\(284\) | 2.48759i | 0.147611i | ||||||||
\(285\) | −5.34323 | − | 4.95469i | −0.316505 | − | 0.293490i | ||||
\(286\) | 31.5913i | 1.86803i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.99147 | + | 0.226058i | −0.176274 | + | 0.0133206i | ||||
\(289\) | −3.84090 | −0.225935 | ||||||||
\(290\) | −0.800269 | −0.0469934 | ||||||||
\(291\) | 22.4242 | + | 20.7936i | 1.31453 | + | 1.21894i | ||||
\(292\) | − | 15.0933i | − | 0.883270i | ||||||
\(293\) | 25.3384 | 1.48029 | 0.740143 | − | 0.672449i | \(-0.234758\pi\) | ||||
0.740143 | + | 0.672449i | \(0.234758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.75132 | 0.101966 | ||||||||
\(296\) | 5.82789i | 0.338739i | ||||||||
\(297\) | 16.0351 | − | 20.1461i | 0.930453 | − | 1.16900i | ||||
\(298\) | −6.59303 | −0.381924 | ||||||||
\(299\) | −12.2198 | −0.706688 | ||||||||
\(300\) | −1.17770 | + | 1.27005i | −0.0679944 | + | 0.0733264i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 11.7743i | − | 0.677538i | ||||||
\(303\) | 1.35249 | − | 1.45855i | 0.0776986 | − | 0.0837917i | ||||
\(304\) | 4.20710i | 0.241293i | ||||||||
\(305\) | 3.42307i | 0.196005i | ||||||||
\(306\) | −10.8517 | + | 0.820036i | −0.620350 | + | 0.0468784i | ||||
\(307\) | 13.1396i | 0.749919i | 0.927041 | + | 0.374960i | \(0.122343\pi\) | ||||
−0.927041 | + | 0.374960i | \(0.877657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.25059 | + | 8.57792i | 0.526248 | + | 0.487981i | ||||
\(310\) | −5.03641 | −0.286049 | ||||||||
\(311\) | −7.60664 | −0.431333 | −0.215667 | − | 0.976467i | \(-0.569192\pi\) | ||||
−0.215667 | + | 0.976467i | \(0.569192\pi\) | |||||||
\(312\) | −7.50809 | + | 8.09687i | −0.425062 | + | 0.458395i | ||||
\(313\) | − | 12.4254i | − | 0.702328i | −0.936314 | − | 0.351164i | \(-0.885786\pi\) | ||
0.936314 | − | 0.351164i | \(-0.114214\pi\) | |||||||
\(314\) | 1.54479 | 0.0871777 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.66807 | −0.150091 | ||||||||
\(317\) | − | 27.7358i | − | 1.55780i | −0.627150 | − | 0.778898i | \(-0.715779\pi\) | ||
0.627150 | − | 0.778898i | \(-0.284221\pi\) | |||||||
\(318\) | −16.8488 | + | 18.1700i | −0.944831 | + | 1.01892i | ||||
\(319\) | −3.96559 | −0.222030 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.41182 | − | 3.16373i | −0.190429 | − | 0.176582i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.2614i | 0.849169i | ||||||||
\(324\) | 8.89780 | − | 1.35249i | 0.494322 | − | 0.0751385i | ||||
\(325\) | 6.37523i | 0.353634i | ||||||||
\(326\) | 3.37759i | 0.187067i | ||||||||
\(327\) | 10.6269 | − | 11.4602i | 0.587667 | − | 0.633751i | ||||
\(328\) | − | 7.45163i | − | 0.411447i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.83587 | + | 6.29351i | −0.321254 | + | 0.346446i | ||||
\(331\) | 11.7892 | 0.647995 | 0.323997 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323997 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(332\) | 7.27215 | 0.399111 | ||||||||
\(333\) | −1.31744 | − | 17.4340i | −0.0721953 | − | 0.955375i | ||||
\(334\) | − | 12.7685i | − | 0.698659i | ||||||
\(335\) | −7.98294 | −0.436155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.58238 | −0.304092 | −0.152046 | − | 0.988373i | \(-0.548586\pi\) | ||||
−0.152046 | + | 0.988373i | \(0.548586\pi\) | |||||||
\(338\) | 27.6436i | 1.50361i | ||||||||
\(339\) | −15.7826 | − | 14.6349i | −0.857191 | − | 0.794859i | ||||
\(340\) | 3.62755 | 0.196731 | ||||||||
\(341\) | −24.9570 | −1.35150 | ||||||||
\(342\) | −0.951048 | − | 12.5854i | −0.0514268 | − | 0.680541i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4.64827i | − | 0.250618i | ||||||
\(345\) | −2.43438 | − | 2.25736i | −0.131063 | − | 0.121532i | ||||
\(346\) | 0.247556i | 0.0133087i | ||||||||
\(347\) | − | 31.9093i | − | 1.71298i | −0.516165 | − | 0.856489i | \(-0.672641\pi\) | ||
0.516165 | − | 0.856489i | \(-0.327359\pi\) | |||||||
\(348\) | −1.01638 | − | 0.942474i | −0.0544838 | − | 0.0505219i | ||||
\(349\) | − | 1.64353i | − | 0.0879759i | −0.999032 | − | 0.0439879i | \(-0.985994\pi\) | ||
0.999032 | − | 0.0439879i | \(-0.0140063\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.6299 | − | 25.9188i | 1.10114 | − | 1.38344i | ||||
\(352\) | 4.95532 | 0.264120 | ||||||||
\(353\) | −14.6008 | −0.777120 | −0.388560 | − | 0.921423i | \(-0.627027\pi\) | ||||
−0.388560 | + | 0.921423i | \(0.627027\pi\) | |||||||
\(354\) | 2.22426 | + | 2.06252i | 0.118218 | + | 0.109622i | ||||
\(355\) | 2.48759i | 0.132028i | ||||||||
\(356\) | −1.88495 | −0.0999021 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.5963 | −1.03570 | ||||||||
\(359\) | − | 0.506001i | − | 0.0267057i | −0.999911 | − | 0.0133528i | \(-0.995750\pi\) | ||
0.999911 | − | 0.0133528i | \(-0.00425047\pi\) | |||||||
\(360\) | −2.99147 | + | 0.226058i | −0.157664 | + | 0.0119143i | ||||
\(361\) | 1.30035 | 0.0684392 | ||||||||
\(362\) | −14.8103 | −0.778414 | ||||||||
\(363\) | −15.9639 | + | 17.2158i | −0.837889 | + | 0.903595i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15.0933i | − | 0.790020i | ||||||
\(366\) | −4.03134 | + | 4.34748i | −0.210722 | + | 0.227246i | ||||
\(367\) | − | 1.35732i | − | 0.0708515i | −0.999372 | − | 0.0354258i | \(-0.988721\pi\) | ||
0.999372 | − | 0.0354258i | \(-0.0112787\pi\) | |||||||
\(368\) | 1.91676i | 0.0999179i | ||||||||
\(369\) | 1.68450 | + | 22.2913i | 0.0876916 | + | 1.16044i | ||||
\(370\) | 5.82789i | 0.302978i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.39649 | − | 5.93136i | −0.331643 | − | 0.307527i | ||||
\(373\) | −34.1095 | −1.76612 | −0.883062 | − | 0.469257i | \(-0.844522\pi\) | ||||
−0.883062 | + | 0.469257i | \(0.844522\pi\) | |||||||
\(374\) | 17.9757 | 0.929499 | ||||||||
\(375\) | −1.17770 | + | 1.27005i | −0.0608160 | + | 0.0655851i | ||||
\(376\) | 0.607779i | 0.0313438i | ||||||||
\(377\) | −5.10190 | −0.262761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.53951 | −0.0790795 | −0.0395398 | − | 0.999218i | \(-0.512589\pi\) | ||||
−0.0395398 | + | 0.999218i | \(0.512589\pi\) | |||||||
\(380\) | 4.20710i | 0.215819i | ||||||||
\(381\) | 9.50024 | − | 10.2452i | 0.486712 | − | 0.524879i | ||||
\(382\) | 0.535503 | 0.0273987 | ||||||||
\(383\) | −32.5261 | −1.66201 | −0.831004 | − | 0.556267i | \(-0.812233\pi\) | ||||
−0.831004 | + | 0.556267i | \(0.812233\pi\) | |||||||
\(384\) | 1.27005 | + | 1.17770i | 0.0648120 | + | 0.0600991i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.53544i | 0.281747i | ||||||||
\(387\) | 1.05078 | + | 13.9052i | 0.0534141 | + | 0.706839i | ||||
\(388\) | − | 17.6562i | − | 0.896356i | ||||||
\(389\) | − | 7.10169i | − | 0.360070i | −0.983660 | − | 0.180035i | \(-0.942379\pi\) | ||
0.983660 | − | 0.180035i | \(-0.0576211\pi\) | |||||||
\(390\) | −7.50809 | + | 8.09687i | −0.380187 | + | 0.410001i | ||||
\(391\) | 6.95313i | 0.351635i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.98417 | − | 4.29660i | 0.200975 | − | 0.216735i | ||||
\(394\) | 0.666454 | 0.0335755 | ||||||||
\(395\) | −2.66807 | −0.134245 | ||||||||
\(396\) | −14.8237 | + | 1.12019i | −0.744919 | + | 0.0562917i | ||||
\(397\) | − | 13.0239i | − | 0.653650i | −0.945085 | − | 0.326825i | \(-0.894021\pi\) | ||
0.945085 | − | 0.326825i | \(-0.105979\pi\) | |||||||
\(398\) | −9.02198 | −0.452231 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − | 23.4030i | − | 1.16869i | −0.811506 | − | 0.584345i | \(-0.801352\pi\) | ||
0.811506 | − | 0.584345i | \(-0.198648\pi\) | |||||||
\(402\) | −10.1387 | − | 9.40149i | −0.505674 | − | 0.468904i | ||||
\(403\) | −32.1083 | −1.59943 | ||||||||
\(404\) | −1.14842 | −0.0571361 | ||||||||
\(405\) | 8.89780 | − | 1.35249i | 0.442135 | − | 0.0672059i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.8791i | 1.43148i | ||||||||
\(408\) | 4.60717 | + | 4.27215i | 0.228089 | + | 0.211503i | ||||
\(409\) | 13.1994i | 0.652670i | 0.945254 | + | 0.326335i | \(0.105814\pi\) | ||||
−0.945254 | + | 0.326335i | \(0.894186\pi\) | |||||||
\(410\) | − | 7.45163i | − | 0.368010i | ||||||
\(411\) | 18.8316 | + | 17.4622i | 0.928892 | + | 0.861346i | ||||
\(412\) | − | 7.28364i | − | 0.358839i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.433299 | − | 5.73392i | −0.0212955 | − | 0.281807i | ||||
\(415\) | 7.27215 | 0.356976 | ||||||||
\(416\) | 6.37523 | 0.312571 | ||||||||
\(417\) | 9.20366 | + | 8.53440i | 0.450705 | + | 0.417932i | ||||
\(418\) | 20.8475i | 1.01969i | ||||||||
\(419\) | 27.9492 | 1.36541 | 0.682704 | − | 0.730695i | \(-0.260804\pi\) | ||||
0.682704 | + | 0.730695i | \(0.260804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.6795 | 1.20281 | 0.601403 | − | 0.798946i | \(-0.294609\pi\) | ||||
0.601403 | + | 0.798946i | \(0.294609\pi\) | |||||||
\(422\) | − | 11.4386i | − | 0.556823i | ||||||
\(423\) | −0.137393 | − | 1.81815i | −0.00668030 | − | 0.0884017i | ||||
\(424\) | 14.3065 | 0.694786 | ||||||||
\(425\) | 3.62755 | 0.175962 | ||||||||
\(426\) | −2.92963 | + | 3.15936i | −0.141941 | + | 0.153072i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.68637i | 0.129850i | ||||||||
\(429\) | −37.2050 | + | 40.1226i | −1.79628 | + | 1.93714i | ||||
\(430\) | − | 4.64827i | − | 0.224159i | ||||||
\(431\) | 3.34445i | 0.161097i | 0.996751 | + | 0.0805483i | \(0.0256671\pi\) | ||||
−0.996751 | + | 0.0805483i | \(0.974333\pi\) | |||||||
\(432\) | −4.06555 | − | 3.23594i | −0.195604 | − | 0.155689i | ||||
\(433\) | 14.6756i | 0.705264i | 0.935762 | + | 0.352632i | \(0.114713\pi\) | ||||
−0.935762 | + | 0.352632i | \(0.885287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.01638 | − | 0.942474i | −0.0487318 | − | 0.0451882i | ||||
\(436\) | −9.02343 | −0.432144 | ||||||||
\(437\) | −8.06398 | −0.385753 | ||||||||
\(438\) | 17.7754 | − | 19.1693i | 0.849339 | − | 0.915944i | ||||
\(439\) | 6.58702i | 0.314381i | 0.987568 | + | 0.157191i | \(0.0502437\pi\) | ||||
−0.987568 | + | 0.157191i | \(0.949756\pi\) | |||||||
\(440\) | 4.95532 | 0.236236 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.1265 | 1.10001 | ||||||||
\(443\) | 40.7210i | 1.93471i | 0.253417 | + | 0.967357i | \(0.418445\pi\) | ||||
−0.253417 | + | 0.967357i | \(0.581555\pi\) | |||||||
\(444\) | −6.86349 | + | 7.40171i | −0.325727 | + | 0.351270i | ||||
\(445\) | −1.88495 | −0.0893551 | ||||||||
\(446\) | 5.23397 | 0.247836 | ||||||||
\(447\) | −8.37348 | − | 7.76459i | −0.396052 | − | 0.367253i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18.3485i | − | 0.865919i | −0.901413 | − | 0.432960i | \(-0.857469\pi\) | ||
0.901413 | − | 0.432960i | \(-0.142531\pi\) | |||||||
\(450\) | −2.99147 | + | 0.226058i | −0.141019 | + | 0.0106565i | ||||
\(451\) | − | 36.9252i | − | 1.73874i | ||||||
\(452\) | 12.4267i | 0.584504i | ||||||||
\(453\) | 13.8666 | − | 14.9540i | 0.651511 | − | 0.702601i | ||||
\(454\) | − | 13.4623i | − | 0.631819i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.95469 | + | 5.34323i | −0.232024 | + | 0.250219i | ||||
\(457\) | −8.64332 | −0.404317 | −0.202159 | − | 0.979353i | \(-0.564796\pi\) | ||||
−0.202159 | + | 0.979353i | \(0.564796\pi\) | |||||||
\(458\) | −16.5216 | −0.772005 | ||||||||
\(459\) | −14.7480 | − | 11.7385i | −0.688376 | − | 0.547908i | ||||
\(460\) | 1.91676i | 0.0893693i | ||||||||
\(461\) | −24.7864 | −1.15442 | −0.577210 | − | 0.816596i | \(-0.695859\pi\) | ||||
−0.577210 | + | 0.816596i | \(0.695859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9797 | −0.835589 | −0.417794 | − | 0.908542i | \(-0.637197\pi\) | ||||
−0.417794 | + | 0.908542i | \(0.637197\pi\) | |||||||
\(464\) | 0.800269i | 0.0371515i | ||||||||
\(465\) | −6.39649 | − | 5.93136i | −0.296630 | − | 0.275060i | ||||
\(466\) | 18.6359 | 0.863292 | ||||||||
\(467\) | 1.27342 | 0.0589271 | 0.0294635 | − | 0.999566i | \(-0.490620\pi\) | ||||
0.0294635 | + | 0.999566i | \(0.490620\pi\) | |||||||
\(468\) | −19.0713 | + | 1.44117i | −0.881572 | + | 0.0666182i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.607779i | 0.0280348i | ||||||||
\(471\) | 1.96197 | + | 1.81930i | 0.0904026 | + | 0.0838289i | ||||
\(472\) | − | 1.75132i | − | 0.0806109i | ||||||
\(473\) | − | 23.0337i | − | 1.05909i | ||||||
\(474\) | −3.38859 | − | 3.14218i | −0.155643 | − | 0.144325i | ||||
\(475\) | 4.20710i | 0.193035i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −42.7976 | + | 3.23411i | −1.95957 | + | 0.148080i | ||||
\(478\) | 24.8065 | 1.13462 | ||||||||
\(479\) | −14.2267 | −0.650033 | −0.325017 | − | 0.945708i | \(-0.605370\pi\) | ||||
−0.325017 | + | 0.945708i | \(0.605370\pi\) | |||||||
\(480\) | 1.27005 | + | 1.17770i | 0.0579696 | + | 0.0537543i | ||||
\(481\) | 37.1541i | 1.69408i | ||||||||
\(482\) | −22.3364 | −1.01740 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.5552 | 0.616146 | ||||||||
\(485\) | − | 17.6562i | − | 0.801726i | ||||||
\(486\) | 12.8935 | + | 8.76118i | 0.584860 | + | 0.397415i | ||||
\(487\) | 39.8951 | 1.80782 | 0.903910 | − | 0.427723i | \(-0.140684\pi\) | ||||
0.903910 | + | 0.427723i | \(0.140684\pi\) | |||||||
\(488\) | 3.42307 | 0.154955 | ||||||||
\(489\) | −3.97778 | + | 4.28971i | −0.179881 | + | 0.193988i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.9778i | 0.721069i | 0.932746 | + | 0.360535i | \(0.117406\pi\) | ||||
−0.932746 | + | 0.360535i | \(0.882594\pi\) | |||||||
\(492\) | 8.77576 | − | 9.46395i | 0.395642 | − | 0.426668i | ||||
\(493\) | 2.90301i | 0.130745i | ||||||||
\(494\) | 26.8212i | 1.20674i | ||||||||
\(495\) | −14.8237 | + | 1.12019i | −0.666276 | + | 0.0503488i | ||||
\(496\) | 5.03641i | 0.226141i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.23600 | + | 8.56439i | 0.413875 | + | 0.383780i | ||||
\(499\) | −13.8063 | −0.618053 | −0.309027 | − | 0.951053i | \(-0.600003\pi\) | ||||
−0.309027 | + | 0.951053i | \(0.600003\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 15.0374 | − | 16.2166i | 0.671821 | − | 0.724504i | ||||
\(502\) | − | 2.72107i | − | 0.121447i | ||||||
\(503\) | 2.11183 | 0.0941620 | 0.0470810 | − | 0.998891i | \(-0.485008\pi\) | ||||
0.0470810 | + | 0.998891i | \(0.485008\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.14842 | −0.0511041 | ||||||||
\(506\) | 9.49815i | 0.422244i | ||||||||
\(507\) | −32.5558 | + | 35.1088i | −1.44585 | + | 1.55923i | ||||
\(508\) | −8.06679 | −0.357906 | ||||||||
\(509\) | 16.1911 | 0.717659 | 0.358830 | − | 0.933403i | \(-0.383176\pi\) | ||||
0.358830 | + | 0.933403i | \(0.383176\pi\) | |||||||
\(510\) | 4.60717 | + | 4.27215i | 0.204009 | + | 0.189174i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 13.6139 | − | 17.1041i | 0.601069 | − | 0.755167i | ||||
\(514\) | 11.5038i | 0.507410i | ||||||||
\(515\) | − | 7.28364i | − | 0.320955i | ||||||
\(516\) | 5.47425 | − | 5.90354i | 0.240991 | − | 0.259889i | ||||
\(517\) | 3.01174i | 0.132456i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.291546 | + | 0.314409i | −0.0127975 | + | 0.0138010i | ||||
\(520\) | 6.37523 | 0.279572 | ||||||||
\(521\) | 24.9352 | 1.09243 | 0.546216 | − | 0.837645i | \(-0.316068\pi\) | ||||
0.546216 | + | 0.837645i | \(0.316068\pi\) | |||||||
\(522\) | −0.180907 | − | 2.39398i | −0.00791809 | − | 0.104782i | ||||
\(523\) | − | 19.7186i | − | 0.862233i | −0.902296 | − | 0.431116i | \(-0.858120\pi\) | ||
0.902296 | − | 0.431116i | \(-0.141880\pi\) | |||||||
\(524\) | −3.38301 | −0.147788 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.7855 | 0.557476 | ||||||||
\(527\) | 18.2698i | 0.795845i | ||||||||
\(528\) | 6.29351 | + | 5.83587i | 0.273890 | + | 0.253974i | ||||
\(529\) | 19.3260 | 0.840263 | ||||||||
\(530\) | 14.3065 | 0.621436 | ||||||||
\(531\) | 0.395899 | + | 5.23901i | 0.0171806 | + | 0.227354i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 47.5059i | − | 2.05771i | ||||||
\(534\) | −2.39398 | − | 2.21990i | −0.103598 | − | 0.0960644i | ||||
\(535\) | 2.68637i | 0.116142i | ||||||||
\(536\) | 7.98294i | 0.344811i | ||||||||
\(537\) | −24.8883 | − | 23.0785i | −1.07401 | − | 0.995912i | ||||
\(538\) | − | 11.6915i | − | 0.504057i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.06555 | − | 3.23594i | −0.174953 | − | 0.139253i | ||||
\(541\) | −8.55845 | −0.367957 | −0.183978 | − | 0.982930i | \(-0.558898\pi\) | ||||
−0.183978 | + | 0.982930i | \(0.558898\pi\) | |||||||
\(542\) | −22.0698 | −0.947980 | ||||||||
\(543\) | −18.8099 | − | 17.4421i | −0.807210 | − | 0.748512i | ||||
\(544\) | − | 3.62755i | − | 0.155530i | ||||||
\(545\) | −9.02343 | −0.386521 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.5472 | −1.43437 | −0.717187 | − | 0.696881i | \(-0.754570\pi\) | ||||
−0.717187 | + | 0.696881i | \(0.754570\pi\) | |||||||
\(548\) | − | 14.8274i | − | 0.633395i | ||||||
\(549\) | −10.2400 | + | 0.773813i | −0.437033 | + | 0.0330255i | ||||
\(550\) | 4.95532 | 0.211296 | ||||||||
\(551\) | −3.36681 | −0.143431 | ||||||||
\(552\) | −2.25736 | + | 2.43438i | −0.0960796 | + | 0.103614i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.80656i | 0.331669i | ||||||||
\(555\) | −6.86349 | + | 7.40171i | −0.291339 | + | 0.314185i | ||||
\(556\) | − | 7.24669i | − | 0.307328i | ||||||
\(557\) | 5.35028i | 0.226699i | 0.993555 | + | 0.113349i | \(0.0361580\pi\) | ||||
−0.993555 | + | 0.113349i | \(0.963842\pi\) | |||||||
\(558\) | −1.13852 | − | 15.0663i | −0.0481974 | − | 0.637806i | ||||
\(559\) | − | 29.6338i | − | 1.25338i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.8300 | + | 21.1699i | 0.963883 | + | 0.893793i | ||||
\(562\) | 23.0892 | 0.973958 | ||||||||
\(563\) | 29.3370 | 1.23641 | 0.618205 | − | 0.786017i | \(-0.287860\pi\) | ||||
0.618205 | + | 0.786017i | \(0.287860\pi\) | |||||||
\(564\) | −0.715780 | + | 0.771911i | −0.0301398 | + | 0.0325033i | ||||
\(565\) | 12.4267i | 0.522796i | ||||||||
\(566\) | 24.7505 | 1.04034 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.48759 | 0.104377 | ||||||||
\(569\) | − | 42.2121i | − | 1.76962i | −0.465949 | − | 0.884812i | \(-0.654287\pi\) | ||
0.465949 | − | 0.884812i | \(-0.345713\pi\) | |||||||
\(570\) | −4.95469 | + | 5.34323i | −0.207529 | + | 0.223803i | ||||
\(571\) | −31.3580 | −1.31229 | −0.656145 | − | 0.754635i | \(-0.727814\pi\) | ||||
−0.656145 | + | 0.754635i | \(0.727814\pi\) | |||||||
\(572\) | 31.5913 | 1.32090 | ||||||||
\(573\) | 0.680116 | + | 0.630661i | 0.0284123 | + | 0.0263462i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.91676i | 0.0799343i | ||||||||
\(576\) | 0.226058 | + | 2.99147i | 0.00941909 | + | 0.124645i | ||||
\(577\) | − | 32.0769i | − | 1.33538i | −0.744440 | − | 0.667689i | \(-0.767283\pi\) | ||
0.744440 | − | 0.667689i | \(-0.232717\pi\) | |||||||
\(578\) | 3.84090i | 0.159760i | ||||||||
\(579\) | −6.51908 | + | 7.03029i | −0.270924 | + | 0.292169i | ||||
\(580\) | 0.800269i | 0.0332293i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.7936 | − | 22.4242i | 0.861924 | − | 0.929515i | ||||
\(583\) | 70.8934 | 2.93611 | ||||||||
\(584\) | −15.0933 | −0.624566 | ||||||||
\(585\) | −19.0713 | + | 1.44117i | −0.788502 | + | 0.0595852i | ||||
\(586\) | − | 25.3384i | − | 1.04672i | ||||||
\(587\) | −1.93731 | −0.0799612 | −0.0399806 | − | 0.999200i | \(-0.512730\pi\) | ||||
−0.0399806 | + | 0.999200i | \(0.512730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1887 | −0.873063 | ||||||||
\(590\) | − | 1.75132i | − | 0.0721006i | ||||||
\(591\) | 0.846431 | + | 0.784881i | 0.0348175 | + | 0.0322857i | ||||
\(592\) | 5.82789 | 0.239525 | ||||||||
\(593\) | −11.2615 | −0.462454 | −0.231227 | − | 0.972900i | \(-0.574274\pi\) | ||||
−0.231227 | + | 0.972900i | \(0.574274\pi\) | |||||||
\(594\) | −20.1461 | − | 16.0351i | −0.826604 | − | 0.657929i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.59303i | 0.270061i | ||||||||
\(597\) | −11.4584 | − | 10.6252i | −0.468960 | − | 0.434859i | ||||
\(598\) | 12.2198i | 0.499704i | ||||||||
\(599\) | 44.3460i | 1.81193i | 0.423356 | + | 0.905963i | \(0.360852\pi\) | ||||
−0.423356 | + | 0.905963i | \(0.639148\pi\) | |||||||
\(600\) | 1.27005 | + | 1.17770i | 0.0518496 | + | 0.0480793i | ||||
\(601\) | − | 17.7126i | − | 0.722514i | −0.932466 | − | 0.361257i | \(-0.882348\pi\) | ||
0.932466 | − | 0.361257i | \(-0.117652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.80461 | − | 23.8807i | −0.0734893 | − | 0.972499i | ||||
\(604\) | −11.7743 | −0.479091 | ||||||||
\(605\) | 13.5552 | 0.551098 | ||||||||
\(606\) | −1.45855 | − | 1.35249i | −0.0592497 | − | 0.0549412i | ||||
\(607\) | 18.3499i | 0.744801i | 0.928072 | + | 0.372400i | \(0.121465\pi\) | ||||
−0.928072 | + | 0.372400i | \(0.878535\pi\) | |||||||
\(608\) | 4.20710 | 0.170620 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.42307 | 0.138596 | ||||||||
\(611\) | 3.87473i | 0.156755i | ||||||||
\(612\) | 0.820036 | + | 10.8517i | 0.0331480 | + | 0.438654i | ||||
\(613\) | 0.631673 | 0.0255130 | 0.0127565 | − | 0.999919i | \(-0.495939\pi\) | ||||
0.0127565 | + | 0.999919i | \(0.495939\pi\) | |||||||
\(614\) | 13.1396 | 0.530273 | ||||||||
\(615\) | 8.77576 | − | 9.46395i | 0.353873 | − | 0.381623i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5902i | 0.627638i | 0.949483 | + | 0.313819i | \(0.101608\pi\) | ||||
−0.949483 | + | 0.313819i | \(0.898392\pi\) | |||||||
\(618\) | 8.57792 | − | 9.25059i | 0.345054 | − | 0.372113i | ||||
\(619\) | 12.6859i | 0.509890i | 0.966956 | + | 0.254945i | \(0.0820573\pi\) | ||||
−0.966956 | + | 0.254945i | \(0.917943\pi\) | |||||||
\(620\) | 5.03641i | 0.202267i | ||||||||
\(621\) | 6.20252 | − | 7.79267i | 0.248898 | − | 0.312709i | ||||
\(622\) | 7.60664i | 0.304999i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.09687 | + | 7.50809i | 0.324134 | + | 0.300564i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.4254 | −0.496621 | ||||||||
\(627\) | −24.5521 | + | 26.4774i | −0.980515 | + | 1.05741i | ||||
\(628\) | − | 1.54479i | − | 0.0616440i | ||||||
\(629\) | 21.1409 | 0.842945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.96052 | −0.237284 | −0.118642 | − | 0.992937i | \(-0.537854\pi\) | ||||
−0.118642 | + | 0.992937i | \(0.537854\pi\) | |||||||
\(632\) | 2.66807i | 0.106130i | ||||||||
\(633\) | 13.4712 | − | 14.5276i | 0.535433 | − | 0.577421i | ||||
\(634\) | −27.7358 | −1.10153 | ||||||||
\(635\) | −8.06679 | −0.320121 | ||||||||
\(636\) | 18.1700 | + | 16.8488i | 0.720488 | + | 0.668097i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.96559i | 0.156999i | ||||||||
\(639\) | −7.44155 | + | 0.562340i | −0.294383 | + | 0.0222458i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 12.9407i | − | 0.511128i | −0.966792 | − | 0.255564i | \(-0.917739\pi\) | ||
0.966792 | − | 0.255564i | \(-0.0822611\pi\) | |||||||
\(642\) | −3.16373 | + | 3.41182i | −0.124862 | + | 0.134654i | ||||
\(643\) | − | 27.7420i | − | 1.09404i | −0.837120 | − | 0.547019i | \(-0.815763\pi\) | ||
0.837120 | − | 0.547019i | \(-0.184237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.47425 | − | 5.90354i | 0.215549 | − | 0.232452i | ||||
\(646\) | 15.2614 | 0.600453 | ||||||||
\(647\) | 46.7712 | 1.83876 | 0.919382 | − | 0.393365i | \(-0.128689\pi\) | ||||
0.919382 | + | 0.393365i | \(0.128689\pi\) | |||||||
\(648\) | −1.35249 | − | 8.89780i | −0.0531309 | − | 0.349538i | ||||
\(649\) | − | 8.67834i | − | 0.340654i | ||||||
\(650\) | 6.37523 | 0.250057 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.37759 | 0.132277 | ||||||||
\(653\) | − | 31.5984i | − | 1.23654i | −0.785965 | − | 0.618271i | \(-0.787833\pi\) | ||
0.785965 | − | 0.618271i | \(-0.212167\pi\) | |||||||
\(654\) | −11.4602 | − | 10.6269i | −0.448130 | − | 0.415544i | ||||
\(655\) | −3.38301 | −0.132185 | ||||||||
\(656\) | −7.45163 | −0.290937 | ||||||||
\(657\) | 45.1512 | − | 3.41197i | 1.76152 | − | 0.133113i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 29.8627i | − | 1.16329i | −0.813444 | − | 0.581643i | \(-0.802410\pi\) | ||
0.813444 | − | 0.581643i | \(-0.197590\pi\) | |||||||
\(660\) | 6.29351 | + | 5.83587i | 0.244975 | + | 0.227161i | ||||
\(661\) | − | 13.8572i | − | 0.538983i | −0.963003 | − | 0.269492i | \(-0.913144\pi\) | ||
0.963003 | − | 0.269492i | \(-0.0868556\pi\) | |||||||
\(662\) | − | 11.7892i | − | 0.458202i | ||||||
\(663\) | 29.3718 | + | 27.2360i | 1.14071 | + | 1.05776i | ||||
\(664\) | − | 7.27215i | − | 0.282214i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.4340 | + | 1.31744i | −0.675552 | + | 0.0510498i | ||||
\(667\) | −1.53392 | −0.0593937 | ||||||||
\(668\) | −12.7685 | −0.494027 | ||||||||
\(669\) | 6.64741 | + | 6.16403i | 0.257004 | + | 0.238315i | ||||
\(670\) | 7.98294i | 0.308408i | ||||||||
\(671\) | 16.9624 | 0.654827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.1836 | 0.816568 | 0.408284 | − | 0.912855i | \(-0.366127\pi\) | ||||
0.408284 | + | 0.912855i | \(0.366127\pi\) | |||||||
\(674\) | 5.58238i | 0.215025i | ||||||||
\(675\) | −4.06555 | − | 3.23594i | −0.156483 | − | 0.124551i | ||||
\(676\) | 27.6436 | 1.06322 | ||||||||
\(677\) | 48.3365 | 1.85772 | 0.928860 | − | 0.370430i | \(-0.120790\pi\) | ||||
0.928860 | + | 0.370430i | \(0.120790\pi\) | |||||||
\(678\) | −14.6349 | + | 15.7826i | −0.562050 | + | 0.606126i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 3.62755i | − | 0.139110i | ||||||
\(681\) | 15.8546 | − | 17.0978i | 0.607548 | − | 0.655191i | ||||
\(682\) | 24.9570i | 0.955654i | ||||||||
\(683\) | − | 26.3276i | − | 1.00740i | −0.863879 | − | 0.503699i | \(-0.831972\pi\) | ||
0.863879 | − | 0.503699i | \(-0.168028\pi\) | |||||||
\(684\) | −12.5854 | + | 0.951048i | −0.481215 | + | 0.0363642i | ||||
\(685\) | − | 14.8274i | − | 0.566526i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.9833 | − | 19.4575i | −0.800563 | − | 0.742349i | ||||
\(688\) | −4.64827 | −0.177214 | ||||||||
\(689\) | 91.2074 | 3.47473 | ||||||||
\(690\) | −2.25736 | + | 2.43438i | −0.0859362 | + | 0.0926753i | ||||
\(691\) | 19.1148i | 0.727163i | 0.931562 | + | 0.363581i | \(0.118446\pi\) | ||||
−0.931562 | + | 0.363581i | \(0.881554\pi\) | |||||||
\(692\) | 0.247556 | 0.00941068 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.9093 | −1.21126 | ||||||||
\(695\) | − | 7.24669i | − | 0.274883i | ||||||
\(696\) | −0.942474 | + | 1.01638i | −0.0357244 | + | 0.0385258i | ||||
\(697\) | −27.0311 | −1.02388 | ||||||||
\(698\) | −1.64353 | −0.0622084 | ||||||||
\(699\) | 23.6686 | + | 21.9475i | 0.895227 | + | 0.830130i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 36.3536i | − | 1.37306i | −0.727103 | − | 0.686528i | \(-0.759134\pi\) | ||
0.727103 | − | 0.686528i | \(-0.240866\pi\) | |||||||
\(702\) | −25.9188 | − | 20.6299i | −0.978243 | − | 0.778625i | ||||
\(703\) | 24.5185i | 0.924732i | ||||||||
\(704\) | − | 4.95532i | − | 0.186761i | ||||||
\(705\) | −0.715780 | + | 0.771911i | −0.0269578 | + | 0.0290718i | ||||
\(706\) | 14.6008i | 0.549507i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.06252 | − | 2.22426i | 0.0775143 | − | 0.0835928i | ||||
\(709\) | 5.09212 | 0.191239 | 0.0956193 | − | 0.995418i | \(-0.469517\pi\) | ||||
0.0956193 | + | 0.995418i | \(0.469517\pi\) | |||||||
\(710\) | 2.48759 | 0.0933575 | ||||||||
\(711\) | −0.603140 | − | 7.98147i | −0.0226195 | − | 0.299328i | ||||
\(712\) | 1.88495i | 0.0706414i | ||||||||
\(713\) | −9.65357 | −0.361529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.5913 | 1.18145 | ||||||||
\(716\) | 19.5963i | 0.732348i | ||||||||
\(717\) | 31.5055 | + | 29.2145i | 1.17659 | + | 1.09104i | ||||
\(718\) | −0.506001 | −0.0188838 | ||||||||
\(719\) | 41.1644 | 1.53517 | 0.767587 | − | 0.640945i | \(-0.221457\pi\) | ||||
0.767587 | + | 0.640945i | \(0.221457\pi\) | |||||||
\(720\) | 0.226058 | + | 2.99147i | 0.00842469 | + | 0.111486i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.30035i | − | 0.0483938i | ||||||
\(723\) | −28.3684 | − | 26.3055i | −1.05503 | − | 0.978314i | ||||
\(724\) | 14.8103i | 0.550422i | ||||||||
\(725\) | 0.800269i | 0.0297212i | ||||||||
\(726\) | 17.2158 | + | 15.9639i | 0.638938 | + | 0.592477i | ||||
\(727\) | − | 46.1288i | − | 1.71082i | −0.517948 | − | 0.855412i | \(-0.673304\pi\) | ||
0.517948 | − | 0.855412i | \(-0.326696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.05736 | + | 26.3118i | 0.224347 | + | 0.974509i | ||||
\(730\) | −15.0933 | −0.558629 | ||||||||
\(731\) | −16.8618 | −0.623657 | ||||||||
\(732\) | 4.34748 | + | 4.03134i | 0.160687 | + | 0.149003i | ||||
\(733\) | 9.99727i | 0.369258i | 0.982808 | + | 0.184629i | \(0.0591083\pi\) | ||||
−0.982808 | + | 0.184629i | \(0.940892\pi\) | |||||||
\(734\) | −1.35732 | −0.0500996 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.91676 | 0.0706526 | ||||||||
\(737\) | 39.5580i | 1.45714i | ||||||||
\(738\) | 22.2913 | − | 1.68450i | 0.820555 | − | 0.0620073i | ||||
\(739\) | 0.836051 | 0.0307547 | 0.0153773 | − | 0.999882i | \(-0.495105\pi\) | ||||
0.0153773 | + | 0.999882i | \(0.495105\pi\) | |||||||
\(740\) | 5.82789 | 0.214237 | ||||||||
\(741\) | −31.5873 | + | 34.0643i | −1.16039 | + | 1.25138i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.3336i | 1.95662i | 0.207146 | + | 0.978310i | \(0.433582\pi\) | ||||
−0.207146 | + | 0.978310i | \(0.566418\pi\) | |||||||
\(744\) | −5.93136 | + | 6.39649i | −0.217454 | + | 0.234507i | ||||
\(745\) | 6.59303i | 0.241550i | ||||||||
\(746\) | 34.1095i | 1.24884i | ||||||||
\(747\) | 1.64393 | + | 21.7544i | 0.0601482 | + | 0.795953i | ||||
\(748\) | − | 17.9757i | − | 0.657255i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.27005 | + | 1.17770i | 0.0463757 | + | 0.0430034i | ||||
\(751\) | 33.7319 | 1.23090 | 0.615448 | − | 0.788178i | \(-0.288975\pi\) | ||||
0.615448 | + | 0.788178i | \(0.288975\pi\) | |||||||
\(752\) | 0.607779 | 0.0221634 | ||||||||
\(753\) | 3.20460 | − | 3.45590i | 0.116782 | − | 0.125940i | ||||
\(754\) | 5.10190i | 0.185800i | ||||||||
\(755\) | −11.7743 | −0.428512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1033 | 1.34854 | 0.674272 | − | 0.738483i | \(-0.264458\pi\) | ||||
0.674272 | + | 0.738483i | \(0.264458\pi\) | |||||||
\(758\) | 1.53951i | 0.0559177i | ||||||||
\(759\) | −11.1859 | + | 12.0631i | −0.406024 | + | 0.437864i | ||||
\(760\) | 4.20710 | 0.152607 | ||||||||
\(761\) | 17.9104 | 0.649251 | 0.324625 | − | 0.945843i | \(-0.394762\pi\) | ||||
0.324625 | + | 0.945843i | \(0.394762\pi\) | |||||||
\(762\) | −10.2452 | − | 9.50024i | −0.371146 | − | 0.344157i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 0.535503i | − | 0.0193738i | ||||||
\(765\) | 0.820036 | + | 10.8517i | 0.0296485 | + | 0.392344i | ||||
\(766\) | 32.5261i | 1.17522i | ||||||||
\(767\) | − | 11.1650i | − | 0.403147i | ||||||
\(768\) | 1.17770 | − | 1.27005i | 0.0424965 | − | 0.0458290i | ||||
\(769\) | − | 0.619084i | − | 0.0223247i | −0.999938 | − | 0.0111624i | \(-0.996447\pi\) | ||
0.999938 | − | 0.0111624i | \(-0.00355317\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5480 | + | 14.6104i | −0.487918 | + | 0.526180i | ||||
\(772\) | 5.53544 | 0.199225 | ||||||||
\(773\) | −48.9365 | −1.76012 | −0.880062 | − | 0.474859i | \(-0.842499\pi\) | ||||
−0.880062 | + | 0.474859i | \(0.842499\pi\) | |||||||
\(774\) | 13.9052 | − | 1.05078i | 0.499811 | − | 0.0377695i | ||||
\(775\) | 5.03641i | 0.180913i | ||||||||
\(776\) | −17.6562 | −0.633820 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.10169 | −0.254608 | ||||||||
\(779\) | − | 31.3497i | − | 1.12322i | ||||||
\(780\) | 8.09687 | + | 7.50809i | 0.289914 | + | 0.268833i | ||||
\(781\) | 12.3268 | 0.441088 | ||||||||
\(782\) | 6.95313 | 0.248643 | ||||||||
\(783\) | 2.58962 | − | 3.25353i | 0.0925456 | − | 0.116272i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.54479i | − | 0.0551360i | ||||||
\(786\) | −4.29660 | − | 3.98417i | −0.153255 | − | 0.142111i | ||||
\(787\) | − | 0.0672107i | − | 0.00239580i | −0.999999 | − | 0.00119790i | \(-0.999619\pi\) | ||
0.999999 | − | 0.00119790i | \(-0.000381304\pi\) | |||||||
\(788\) | − | 0.666454i | − | 0.0237414i | ||||||
\(789\) | 16.2383 | + | 15.0575i | 0.578098 | + | 0.536061i | ||||
\(790\) | 2.66807i | 0.0949258i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.12019 | + | 14.8237i | 0.0398042 | + | 0.526737i | ||||
\(793\) | 21.8229 | 0.774953 | ||||||||
\(794\) | −13.0239 | −0.462200 | ||||||||
\(795\) | 18.1700 | + | 16.8488i | 0.644424 | + | 0.597564i | ||||
\(796\) | 9.02198i | 0.319775i | ||||||||
\(797\) | 7.61311 | 0.269670 | 0.134835 | − | 0.990868i | \(-0.456950\pi\) | ||||
0.134835 | + | 0.990868i | \(0.456950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.20475 | 0.0779984 | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −0.426108 | − | 5.63877i | −0.0150558 | − | 0.199236i | ||||
\(802\) | −23.4030 | −0.826388 | ||||||||
\(803\) | −74.7922 | −2.63936 | ||||||||
\(804\) | −9.40149 | + | 10.1387i | −0.331565 | + | 0.357566i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.1083i | 1.13097i | ||||||||
\(807\) | 13.7691 | − | 14.8488i | 0.484694 | − | 0.522703i | ||||
\(808\) | 1.14842i | 0.0404013i | ||||||||
\(809\) | − | 19.5941i | − | 0.688891i | −0.938806 | − | 0.344445i | \(-0.888067\pi\) | ||
0.938806 | − | 0.344445i | \(-0.111933\pi\) | |||||||
\(810\) | −1.35249 | − | 8.89780i | −0.0475217 | − | 0.312637i | ||||
\(811\) | − | 38.1099i | − | 1.33822i | −0.743164 | − | 0.669110i | \(-0.766676\pi\) | ||
0.743164 | − | 0.669110i | \(-0.233324\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.0298 | − | 25.9916i | −0.983048 | − | 0.911564i | ||||
\(814\) | 28.8791 | 1.01221 | ||||||||
\(815\) | 3.37759 | 0.118312 | ||||||||
\(816\) | 4.27215 | − | 4.60717i | 0.149555 | − | 0.161283i | ||||
\(817\) | − | 19.5557i | − | 0.684168i | ||||||
\(818\) | 13.1994 | 0.461508 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.45163 | −0.260222 | ||||||||
\(821\) | − | 37.4185i | − | 1.30592i | −0.757394 | − | 0.652958i | \(-0.773528\pi\) | ||
0.757394 | − | 0.652958i | \(-0.226472\pi\) | |||||||
\(822\) | 17.4622 | − | 18.8316i | 0.609064 | − | 0.656826i | ||||
\(823\) | 34.3864 | 1.19864 | 0.599318 | − | 0.800511i | \(-0.295439\pi\) | ||||
0.599318 | + | 0.800511i | \(0.295439\pi\) | |||||||
\(824\) | −7.28364 | −0.253737 | ||||||||
\(825\) | 6.29351 | + | 5.83587i | 0.219112 | + | 0.203179i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.15552i | 0.144502i | 0.997386 | + | 0.0722508i | \(0.0230182\pi\) | ||||
−0.997386 | + | 0.0722508i | \(0.976982\pi\) | |||||||
\(828\) | −5.73392 | + | 0.433299i | −0.199268 | + | 0.0150582i | ||||
\(829\) | − | 28.1053i | − | 0.976137i | −0.872805 | − | 0.488068i | \(-0.837702\pi\) | ||
0.872805 | − | 0.488068i | \(-0.162298\pi\) | |||||||
\(830\) | − | 7.27215i | − | 0.252420i | ||||||
\(831\) | −9.19376 | + | 9.91472i | −0.318928 | + | 0.343938i | ||||
\(832\) | − | 6.37523i | − | 0.221021i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.53440 | − | 9.20366i | 0.295522 | − | 0.318697i | ||||
\(835\) | −12.7685 | −0.441871 | ||||||||
\(836\) | 20.8475 | 0.721026 | ||||||||
\(837\) | 16.2975 | − | 20.4758i | 0.563325 | − | 0.707746i | ||||
\(838\) | − | 27.9492i | − | 0.965489i | ||||||
\(839\) | −23.6646 | −0.816992 | −0.408496 | − | 0.912760i | \(-0.633947\pi\) | ||||
−0.408496 | + | 0.912760i | \(0.633947\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.3596 | 0.977916 | ||||||||
\(842\) | − | 24.6795i | − | 0.850512i | ||||||
\(843\) | 29.3244 | + | 27.1920i | 1.00999 | + | 0.936544i | ||||
\(844\) | −11.4386 | −0.393733 | ||||||||
\(845\) | 27.6436 | 0.950968 | ||||||||
\(846\) | −1.81815 | + | 0.137393i | −0.0625094 | + | 0.00472368i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 14.3065i | − | 0.491288i | ||||||
\(849\) | 31.4343 | + | 29.1486i | 1.07882 | + | 1.00038i | ||||
\(850\) | − | 3.62755i | − | 0.124424i | ||||||
\(851\) | 11.1707i | 0.382925i | ||||||||
\(852\) | 3.15936 | + | 2.92963i | 0.108238 | + | 0.100367i | ||||
\(853\) | − | 23.7742i | − | 0.814012i | −0.913426 | − | 0.407006i | \(-0.866573\pi\) | ||
0.913426 | − | 0.407006i | \(-0.133427\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.5854 | + | 0.951048i | −0.430412 | + | 0.0325252i | ||||
\(856\) | 2.68637 | 0.0918181 | ||||||||
\(857\) | −22.3621 | −0.763875 | −0.381938 | − | 0.924188i | \(-0.624743\pi\) | ||||
−0.381938 | + | 0.924188i | \(0.624743\pi\) | |||||||
\(858\) | 40.1226 | + | 37.2050i | 1.36976 | + | 1.27016i | ||||
\(859\) | 42.9236i | 1.46453i | 0.681018 | + | 0.732267i | \(0.261538\pi\) | ||||
−0.681018 | + | 0.732267i | \(0.738462\pi\) | |||||||
\(860\) | −4.64827 | −0.158505 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.34445 | 0.113912 | ||||||||
\(863\) | − | 23.5198i | − | 0.800623i | −0.916379 | − | 0.400312i | \(-0.868902\pi\) | ||
0.916379 | − | 0.400312i | \(-0.131098\pi\) | |||||||
\(864\) | −3.23594 | + | 4.06555i | −0.110089 | + | 0.138313i | ||||
\(865\) | 0.247556 | 0.00841717 | ||||||||
\(866\) | 14.6756 | 0.498697 | ||||||||
\(867\) | −4.52342 | + | 4.87814i | −0.153623 | + | 0.165670i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.2212i | 0.448497i | ||||||||
\(870\) | −0.942474 | + | 1.01638i | −0.0319529 | + | 0.0344586i | ||||
\(871\) | 50.8931i | 1.72445i | ||||||||
\(872\) | 9.02343i | 0.305572i | ||||||||
\(873\) | 52.8179 | − | 3.99132i | 1.78762 | − | 0.135086i | ||||
\(874\) | 8.06398i | 0.272768i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.1693 | − | 17.7754i | −0.647670 | − | 0.600574i | ||||
\(877\) | 8.18713 | 0.276460 | 0.138230 | − | 0.990400i | \(-0.455859\pi\) | ||||
0.138230 | + | 0.990400i | \(0.455859\pi\) | |||||||
\(878\) | 6.58702 | 0.222301 | ||||||||
\(879\) | 29.8410 | − | 32.1811i | 1.00651 | − | 1.08544i | ||||
\(880\) | − | 4.95532i | − | 0.167044i | ||||||
\(881\) | −26.6496 | −0.897847 | −0.448923 | − | 0.893570i | \(-0.648192\pi\) | ||||
−0.448923 | + | 0.893570i | \(0.648192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.41249 | −0.182145 | −0.0910724 | − | 0.995844i | \(-0.529029\pi\) | ||||
−0.0910724 | + | 0.995844i | \(0.529029\pi\) | |||||||
\(884\) | − | 23.1265i | − | 0.777827i | ||||||
\(885\) | 2.06252 | − | 2.22426i | 0.0693309 | − | 0.0747677i | ||||
\(886\) | 40.7210 | 1.36805 | ||||||||
\(887\) | −24.0998 | −0.809194 | −0.404597 | − | 0.914495i | \(-0.632588\pi\) | ||||
−0.404597 | + | 0.914495i | \(0.632588\pi\) | |||||||
\(888\) | 7.40171 | + | 6.86349i | 0.248385 | + | 0.230324i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.88495i | 0.0631836i | ||||||||
\(891\) | −6.70203 | − | 44.0914i | −0.224527 | − | 1.47712i | ||||
\(892\) | − | 5.23397i | − | 0.175246i | ||||||
\(893\) | 2.55699i | 0.0855663i | ||||||||
\(894\) | −7.76459 | + | 8.37348i | −0.259687 | + | 0.280051i | ||||
\(895\) | 19.5963i | 0.655032i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.3912 | + | 15.5197i | −0.480508 | + | 0.518189i | ||||
\(898\) | −18.3485 | −0.612297 | ||||||||
\(899\) | −4.03048 | −0.134424 | ||||||||
\(900\) | 0.226058 | + | 2.99147i | 0.00753527 | + | 0.0997157i | ||||
\(901\) | − | 51.8976i | − | 1.72896i | ||||||
\(902\) | −36.9252 | −1.22948 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.4267 | 0.413306 | ||||||||
\(905\) | 14.8103i | 0.492312i | ||||||||
\(906\) | −14.9540 | − | 13.8666i | −0.496814 | − | 0.460688i | ||||
\(907\) | −21.6581 | −0.719144 | −0.359572 | − | 0.933117i | \(-0.617077\pi\) | ||||
−0.359572 | + | 0.933117i | \(0.617077\pi\) | |||||||
\(908\) | −13.4623 | −0.446763 | ||||||||
\(909\) | −0.259610 | − | 3.43547i | −0.00861071 | − | 0.113947i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 47.4302i | − | 1.57143i | −0.618587 | − | 0.785716i | \(-0.712295\pi\) | ||
0.618587 | − | 0.785716i | \(-0.287705\pi\) | |||||||
\(912\) | 5.34323 | + | 4.95469i | 0.176932 | + | 0.164066i | ||||
\(913\) | − | 36.0359i | − | 1.19261i | ||||||
\(914\) | 8.64332i | 0.285896i | ||||||||
\(915\) | 4.34748 | + | 4.03134i | 0.143723 | + | 0.133272i | ||||
\(916\) | 16.5216i | 0.545890i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.7385 | + | 14.7480i | −0.387429 | + | 0.486755i | ||||
\(919\) | 10.6442 | 0.351119 | 0.175559 | − | 0.984469i | \(-0.443827\pi\) | ||||
0.175559 | + | 0.984469i | \(0.443827\pi\) | |||||||
\(920\) | 1.91676 | 0.0631936 | ||||||||
\(921\) | 16.6880 | + | 15.4745i | 0.549889 | + | 0.509903i | ||||
\(922\) | 24.7864i | 0.816298i | ||||||||
\(923\) | 15.8590 | 0.522004 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.82789 | 0.191620 | ||||||||
\(926\) | 17.9797i | 0.590850i | ||||||||
\(927\) | 21.7888 | − | 1.64652i | 0.715638 | − | 0.0540790i | ||||
\(928\) | 0.800269 | 0.0262701 | ||||||||
\(929\) | 34.3965 | 1.12851 | 0.564257 | − | 0.825599i | \(-0.309163\pi\) | ||||
0.564257 | + | 0.825599i | \(0.309163\pi\) | |||||||
\(930\) | −5.93136 | + | 6.39649i | −0.194497 | + | 0.209749i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 18.6359i | − | 0.610440i | ||||||
\(933\) | −8.95832 | + | 9.66082i | −0.293282 | + | 0.316281i | ||||
\(934\) | − | 1.27342i | − | 0.0416677i | ||||||
\(935\) | − | 17.9757i | − | 0.587867i | ||||||
\(936\) | 1.44117 | + | 19.0713i | 0.0471062 | + | 0.623366i | ||||
\(937\) | 40.0917i | 1.30974i | 0.755742 | + | 0.654870i | \(0.227277\pi\) | ||||
−0.755742 | + | 0.654870i | \(0.772723\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.7809 | − | 14.6334i | −0.514992 | − | 0.477543i | ||||
\(940\) | 0.607779 | 0.0198236 | ||||||||
\(941\) | −27.2630 | −0.888747 | −0.444374 | − | 0.895842i | \(-0.646574\pi\) | ||||
−0.444374 | + | 0.895842i | \(0.646574\pi\) | |||||||
\(942\) | 1.81930 | − | 1.96197i | 0.0592760 | − | 0.0639243i | ||||
\(943\) | − | 14.2830i | − | 0.465117i | ||||||
\(944\) | −1.75132 | −0.0570005 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.0337 | −0.748889 | ||||||||
\(947\) | 22.7062i | 0.737853i | 0.929459 | + | 0.368926i | \(0.120275\pi\) | ||||
−0.929459 | + | 0.368926i | \(0.879725\pi\) | |||||||
\(948\) | −3.14218 | + | 3.38859i | −0.102053 | + | 0.110056i | ||||
\(949\) | −96.2234 | −3.12354 | ||||||||
\(950\) | 4.20710 | 0.136496 | ||||||||
\(951\) | −35.2258 | − | 32.6644i | −1.14228 | − | 1.05921i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.7288i | 1.25455i | 0.778799 | + | 0.627274i | \(0.215829\pi\) | ||||
−0.778799 | + | 0.627274i | \(0.784171\pi\) | |||||||
\(954\) | 3.23411 | + | 42.7976i | 0.104708 | + | 1.38562i | ||||
\(955\) | − | 0.535503i | − | 0.0173285i | ||||||
\(956\) | − | 24.8065i | − | 0.802299i | ||||||
\(957\) | −4.67026 | + | 5.03650i | −0.150968 | + | 0.162807i | ||||
\(958\) | 14.2267i | 0.459643i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.17770 | − | 1.27005i | 0.0380100 | − | 0.0409907i | ||||
\(961\) | 5.63459 | 0.181761 | ||||||||
\(962\) | 37.1541 | 1.19790 | ||||||||
\(963\) | −8.03619 | + | 0.607275i | −0.258963 | + | 0.0195692i | ||||
\(964\) | 22.3364i | 0.719408i | ||||||||
\(965\) | 5.53544 | 0.178192 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.1631 | 1.25940 | 0.629700 | − | 0.776838i | \(-0.283178\pi\) | ||||
0.629700 | + | 0.776838i | \(0.283178\pi\) | |||||||
\(968\) | − | 13.5552i | − | 0.435681i | ||||||
\(969\) | 19.3828 | + | 17.9734i | 0.622665 | + | 0.577387i | ||||
\(970\) | −17.6562 | −0.566906 | ||||||||
\(971\) | −26.8011 | −0.860087 | −0.430044 | − | 0.902808i | \(-0.641502\pi\) | ||||
−0.430044 | + | 0.902808i | \(0.641502\pi\) | |||||||
\(972\) | 8.76118 | − | 12.8935i | 0.281015 | − | 0.413559i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 39.8951i | − | 1.27832i | ||||||
\(975\) | 8.09687 | + | 7.50809i | 0.259307 | + | 0.240451i | ||||
\(976\) | − | 3.42307i | − | 0.109570i | ||||||
\(977\) | − | 27.8772i | − | 0.891871i | −0.895065 | − | 0.445936i | \(-0.852871\pi\) | ||
0.895065 | − | 0.445936i | \(-0.147129\pi\) | |||||||
\(978\) | 4.28971 | + | 3.97778i | 0.137170 | + | 0.127195i | ||||
\(979\) | 9.34052i | 0.298524i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.03982 | − | 26.9933i | −0.0651264 | − | 0.861831i | ||||
\(982\) | 15.9778 | 0.509873 | ||||||||
\(983\) | 21.8424 | 0.696665 | 0.348332 | − | 0.937371i | \(-0.386748\pi\) | ||||
0.348332 | + | 0.937371i | \(0.386748\pi\) | |||||||
\(984\) | −9.46395 | − | 8.77576i | −0.301700 | − | 0.279761i | ||||
\(985\) | − | 0.666454i | − | 0.0212350i | ||||||
\(986\) | 2.90301 | 0.0924507 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.8212 | 0.853297 | ||||||||
\(989\) | − | 8.90960i | − | 0.283309i | ||||||
\(990\) | 1.12019 | + | 14.8237i | 0.0356020 | + | 0.471128i | ||||
\(991\) | −58.8600 | −1.86975 | −0.934875 | − | 0.354977i | \(-0.884489\pi\) | ||||
−0.934875 | + | 0.354977i | \(0.884489\pi\) | |||||||
\(992\) | 5.03641 | 0.159906 | ||||||||
\(993\) | 13.8841 | − | 14.9729i | 0.440600 | − | 0.475151i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.02198i | 0.286016i | ||||||||
\(996\) | 8.56439 | − | 9.23600i | 0.271373 | − | 0.292654i | ||||
\(997\) | − | 12.0467i | − | 0.381522i | −0.981636 | − | 0.190761i | \(-0.938904\pi\) | ||
0.981636 | − | 0.190761i | \(-0.0610956\pi\) | |||||||
\(998\) | 13.8063i | 0.437030i | ||||||||
\(999\) | −23.6936 | − | 18.8587i | −0.749631 | − | 0.596663i |
(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 | 1470.2.b.b.881.5 | 12 | ||
3.2 | odd | 2 | 1470.2.b.a.881.8 | 12 | |||
7.4 | even | 3 | 210.2.r.a.131.4 | yes | 12 | ||
7.5 | odd | 6 | 210.2.r.b.101.2 | yes | 12 | ||
7.6 | odd | 2 | 1470.2.b.a.881.2 | 12 | |||
21.5 | even | 6 | 210.2.r.a.101.4 | ✓ | 12 | ||
21.11 | odd | 6 | 210.2.r.b.131.2 | yes | 12 | ||
21.20 | even | 2 | inner | 1470.2.b.b.881.11 | 12 | ||
35.4 | even | 6 | 1050.2.s.g.551.3 | 12 | |||
35.12 | even | 12 | 1050.2.u.e.899.1 | 12 | |||
35.18 | odd | 12 | 1050.2.u.g.299.5 | 12 | |||
35.19 | odd | 6 | 1050.2.s.f.101.5 | 12 | |||
35.32 | odd | 12 | 1050.2.u.f.299.2 | 12 | |||
35.33 | even | 12 | 1050.2.u.h.899.6 | 12 | |||
105.32 | even | 12 | 1050.2.u.h.299.6 | 12 | |||
105.47 | odd | 12 | 1050.2.u.g.899.5 | 12 | |||
105.53 | even | 12 | 1050.2.u.e.299.1 | 12 | |||
105.68 | odd | 12 | 1050.2.u.f.899.2 | 12 | |||
105.74 | odd | 6 | 1050.2.s.f.551.5 | 12 | |||
105.89 | even | 6 | 1050.2.s.g.101.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.r.a.101.4 | ✓ | 12 | 21.5 | even | 6 | ||
210.2.r.a.131.4 | yes | 12 | 7.4 | even | 3 | ||
210.2.r.b.101.2 | yes | 12 | 7.5 | odd | 6 | ||
210.2.r.b.131.2 | yes | 12 | 21.11 | odd | 6 | ||
1050.2.s.f.101.5 | 12 | 35.19 | odd | 6 | |||
1050.2.s.f.551.5 | 12 | 105.74 | odd | 6 | |||
1050.2.s.g.101.3 | 12 | 105.89 | even | 6 | |||
1050.2.s.g.551.3 | 12 | 35.4 | even | 6 | |||
1050.2.u.e.299.1 | 12 | 105.53 | even | 12 | |||
1050.2.u.e.899.1 | 12 | 35.12 | even | 12 | |||
1050.2.u.f.299.2 | 12 | 35.32 | odd | 12 | |||
1050.2.u.f.899.2 | 12 | 105.68 | odd | 12 | |||
1050.2.u.g.299.5 | 12 | 35.18 | odd | 12 | |||
1050.2.u.g.899.5 | 12 | 105.47 | odd | 12 | |||
1050.2.u.h.299.6 | 12 | 105.32 | even | 12 | |||
1050.2.u.h.899.6 | 12 | 35.33 | even | 12 | |||
1470.2.b.a.881.2 | 12 | 7.6 | odd | 2 | |||
1470.2.b.a.881.8 | 12 | 3.2 | odd | 2 | |||
1470.2.b.b.881.5 | 12 | 1.1 | even | 1 | trivial | ||
1470.2.b.b.881.11 | 12 | 21.20 | even | 2 | inner |