Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.10 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.c.2155.15 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.66749i | 1.19294i | 0.802635 | + | 0.596470i | \(0.203430\pi\) | ||||
−0.802635 | + | 0.596470i | \(0.796570\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.66749 | 0.843536 | ||||||||
\(11\) | −2.85384 | − | 1.68986i | −0.860464 | − | 0.509511i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.50184 | 0.693885 | 0.346943 | − | 0.937886i | \(-0.387220\pi\) | ||||
0.346943 | + | 0.937886i | \(0.387220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.66749 | 0.688744 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.53541 | 0.614927 | 0.307464 | − | 0.951560i | \(-0.400520\pi\) | ||||
0.307464 | + | 0.951560i | \(0.400520\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.39472 | −0.319972 | −0.159986 | − | 0.987119i | \(-0.551145\pi\) | ||||
−0.159986 | + | 0.987119i | \(0.551145\pi\) | |||||||
\(20\) | − | 2.66749i | − | 0.596470i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.68986 | + | 2.85384i | −0.360279 | + | 0.608440i | ||||
\(23\) | −3.15503 | −0.657869 | −0.328935 | − | 0.944353i | \(-0.606690\pi\) | ||||
−0.328935 | + | 0.944353i | \(0.606690\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.11553 | −0.423105 | ||||||||
\(26\) | − | 2.50184i | − | 0.490651i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.51317i | 1.20947i | 0.796428 | + | 0.604733i | \(0.206720\pi\) | ||||
−0.796428 | + | 0.604733i | \(0.793280\pi\) | |||||||
\(30\) | − | 2.66749i | − | 0.487016i | ||||||
\(31\) | − | 4.05080i | − | 0.727546i | −0.931488 | − | 0.363773i | \(-0.881488\pi\) | ||
0.931488 | − | 0.363773i | \(-0.118512\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −1.68986 | + | 2.85384i | −0.294166 | + | 0.496789i | ||||
\(34\) | − | 2.53541i | − | 0.434819i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.54945 | 0.419127 | 0.209564 | − | 0.977795i | \(-0.432796\pi\) | ||||
0.209564 | + | 0.977795i | \(0.432796\pi\) | |||||||
\(38\) | 1.39472i | 0.226254i | ||||||||
\(39\) | − | 2.50184i | − | 0.400615i | ||||||
\(40\) | −2.66749 | −0.421768 | ||||||||
\(41\) | −2.65301 | −0.414331 | −0.207166 | − | 0.978306i | \(-0.566424\pi\) | ||||
−0.207166 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.62214i | 0.857368i | 0.903454 | + | 0.428684i | \(0.141023\pi\) | ||||
−0.903454 | + | 0.428684i | \(0.858977\pi\) | |||||||
\(44\) | 2.85384 | + | 1.68986i | 0.430232 | + | 0.254755i | ||||
\(45\) | − | 2.66749i | − | 0.397647i | ||||||
\(46\) | 3.15503i | 0.465184i | ||||||||
\(47\) | 2.76266i | 0.402975i | 0.979491 | + | 0.201488i | \(0.0645776\pi\) | ||||
−0.979491 | + | 0.201488i | \(0.935422\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.11553i | 0.299181i | ||||||||
\(51\) | − | 2.53541i | − | 0.355028i | ||||||
\(52\) | −2.50184 | −0.346943 | ||||||||
\(53\) | −6.88010 | −0.945054 | −0.472527 | − | 0.881316i | \(-0.656658\pi\) | ||||
−0.472527 | + | 0.881316i | \(0.656658\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.50768 | − | 7.61259i | 0.607816 | − | 1.02648i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.39472i | 0.184736i | ||||||||
\(58\) | 6.51317 | 0.855221 | ||||||||
\(59\) | − | 4.91595i | − | 0.640002i | −0.947417 | − | 0.320001i | \(-0.896317\pi\) | ||
0.947417 | − | 0.320001i | \(-0.103683\pi\) | |||||||
\(60\) | −2.66749 | −0.344372 | ||||||||
\(61\) | −5.35288 | −0.685366 | −0.342683 | − | 0.939451i | \(-0.611336\pi\) | ||||
−0.342683 | + | 0.939451i | \(0.611336\pi\) | |||||||
\(62\) | −4.05080 | −0.514453 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.67364i | 0.827763i | ||||||||
\(66\) | 2.85384 | + | 1.68986i | 0.351283 | + | 0.208007i | ||||
\(67\) | 7.33059 | 0.895575 | 0.447787 | − | 0.894140i | \(-0.352212\pi\) | ||||
0.447787 | + | 0.894140i | \(0.352212\pi\) | |||||||
\(68\) | −2.53541 | −0.307464 | ||||||||
\(69\) | 3.15503i | 0.379821i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.05096 | −0.718116 | −0.359058 | − | 0.933315i | \(-0.616902\pi\) | ||||
−0.359058 | + | 0.933315i | \(0.616902\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −9.63838 | −1.12809 | −0.564043 | − | 0.825745i | \(-0.690755\pi\) | ||||
−0.564043 | + | 0.825745i | \(0.690755\pi\) | |||||||
\(74\) | − | 2.54945i | − | 0.296368i | ||||||
\(75\) | 2.11553i | 0.244280i | ||||||||
\(76\) | 1.39472 | 0.159986 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.50184 | −0.283277 | ||||||||
\(79\) | 8.30093i | 0.933928i | 0.884276 | + | 0.466964i | \(0.154652\pi\) | ||||
−0.884276 | + | 0.466964i | \(0.845348\pi\) | |||||||
\(80\) | 2.66749i | 0.298235i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.65301i | 0.292976i | ||||||||
\(83\) | −14.4528 | −1.58640 | −0.793200 | − | 0.608961i | \(-0.791587\pi\) | ||||
−0.793200 | + | 0.608961i | \(0.791587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.76319i | 0.733571i | ||||||||
\(86\) | 5.62214 | 0.606251 | ||||||||
\(87\) | 6.51317 | 0.698285 | ||||||||
\(88\) | 1.68986 | − | 2.85384i | 0.180139 | − | 0.304220i | ||||
\(89\) | 11.2019i | 1.18740i | 0.804686 | + | 0.593701i | \(0.202334\pi\) | ||||
−0.804686 | + | 0.593701i | \(0.797666\pi\) | |||||||
\(90\) | −2.66749 | −0.281179 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.15503 | 0.328935 | ||||||||
\(93\) | −4.05080 | −0.420049 | ||||||||
\(94\) | 2.76266 | 0.284947 | ||||||||
\(95\) | − | 3.72042i | − | 0.381707i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.03611i | 0.409805i | 0.978782 | + | 0.204903i | \(0.0656877\pi\) | ||||
−0.978782 | + | 0.204903i | \(0.934312\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.85384 | + | 1.68986i | 0.286821 | + | 0.169837i | ||||
\(100\) | 2.11553 | 0.211553 | ||||||||
\(101\) | 7.27104 | 0.723496 | 0.361748 | − | 0.932276i | \(-0.382180\pi\) | ||||
0.361748 | + | 0.932276i | \(0.382180\pi\) | |||||||
\(102\) | −2.53541 | −0.251043 | ||||||||
\(103\) | 4.71286i | 0.464371i | 0.972671 | + | 0.232186i | \(0.0745877\pi\) | ||||
−0.972671 | + | 0.232186i | \(0.925412\pi\) | |||||||
\(104\) | 2.50184i | 0.245325i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.88010i | 0.668254i | ||||||||
\(107\) | 19.6228i | 1.89701i | 0.316761 | + | 0.948505i | \(0.397405\pi\) | ||||
−0.316761 | + | 0.948505i | \(0.602595\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 15.1803i | 1.45401i | 0.686633 | + | 0.727004i | \(0.259088\pi\) | ||||
−0.686633 | + | 0.727004i | \(0.740912\pi\) | |||||||
\(110\) | −7.61259 | − | 4.50768i | −0.725832 | − | 0.429791i | ||||
\(111\) | − | 2.54945i | − | 0.241983i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.06642 | −0.382536 | −0.191268 | − | 0.981538i | \(-0.561260\pi\) | ||||
−0.191268 | + | 0.981538i | \(0.561260\pi\) | |||||||
\(114\) | 1.39472 | 0.130628 | ||||||||
\(115\) | − | 8.41603i | − | 0.784798i | ||||||
\(116\) | − | 6.51317i | − | 0.604733i | ||||||
\(117\) | −2.50184 | −0.231295 | ||||||||
\(118\) | −4.91595 | −0.452550 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.66749i | 0.243508i | ||||||||
\(121\) | 5.28877 | + | 9.64515i | 0.480797 | + | 0.876832i | ||||
\(122\) | 5.35288i | 0.484627i | ||||||||
\(123\) | 2.65301i | 0.239214i | ||||||||
\(124\) | 4.05080i | 0.363773i | ||||||||
\(125\) | 7.69432i | 0.688201i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.01581i | 0.711288i | 0.934621 | + | 0.355644i | \(0.115738\pi\) | ||||
−0.934621 | + | 0.355644i | \(0.884262\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 5.62214 | 0.495002 | ||||||||
\(130\) | 6.67364 | 0.585317 | ||||||||
\(131\) | 14.5316 | 1.26963 | 0.634815 | − | 0.772664i | \(-0.281076\pi\) | ||||
0.634815 | + | 0.772664i | \(0.281076\pi\) | |||||||
\(132\) | 1.68986 | − | 2.85384i | 0.147083 | − | 0.248395i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 7.33059i | − | 0.633267i | ||||||
\(135\) | −2.66749 | −0.229581 | ||||||||
\(136\) | 2.53541i | 0.217410i | ||||||||
\(137\) | −10.1601 | −0.868040 | −0.434020 | − | 0.900903i | \(-0.642905\pi\) | ||||
−0.434020 | + | 0.900903i | \(0.642905\pi\) | |||||||
\(138\) | 3.15503 | 0.268574 | ||||||||
\(139\) | −2.15019 | −0.182377 | −0.0911885 | − | 0.995834i | \(-0.529067\pi\) | ||||
−0.0911885 | + | 0.995834i | \(0.529067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.76266 | 0.232658 | ||||||||
\(142\) | 6.05096i | 0.507785i | ||||||||
\(143\) | −7.13984 | − | 4.22775i | −0.597063 | − | 0.353542i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −17.3739 | −1.44282 | ||||||||
\(146\) | 9.63838i | 0.797678i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.54945 | −0.209564 | ||||||||
\(149\) | 18.1396i | 1.48606i | 0.669260 | + | 0.743028i | \(0.266611\pi\) | ||||
−0.669260 | + | 0.743028i | \(0.733389\pi\) | |||||||
\(150\) | 2.11553 | 0.172732 | ||||||||
\(151\) | − | 1.69350i | − | 0.137815i | −0.997623 | − | 0.0689075i | \(-0.978049\pi\) | ||
0.997623 | − | 0.0689075i | \(-0.0219513\pi\) | |||||||
\(152\) | − | 1.39472i | − | 0.113127i | ||||||
\(153\) | −2.53541 | −0.204976 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8055 | 0.867918 | ||||||||
\(156\) | 2.50184i | 0.200307i | ||||||||
\(157\) | − | 6.48100i | − | 0.517240i | −0.965979 | − | 0.258620i | \(-0.916732\pi\) | ||
0.965979 | − | 0.258620i | \(-0.0832677\pi\) | |||||||
\(158\) | 8.30093 | 0.660387 | ||||||||
\(159\) | 6.88010i | 0.545627i | ||||||||
\(160\) | 2.66749 | 0.210884 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 1.86138 | 0.145795 | 0.0728973 | − | 0.997339i | \(-0.476775\pi\) | ||||
0.0728973 | + | 0.997339i | \(0.476775\pi\) | |||||||
\(164\) | 2.65301 | 0.207166 | ||||||||
\(165\) | −7.61259 | − | 4.50768i | −0.592640 | − | 0.350923i | ||||
\(166\) | 14.4528i | 1.12175i | ||||||||
\(167\) | −10.4965 | −0.812240 | −0.406120 | − | 0.913820i | \(-0.633118\pi\) | ||||
−0.406120 | + | 0.913820i | \(0.633118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.74080 | −0.518523 | ||||||||
\(170\) | 6.76319 | 0.518713 | ||||||||
\(171\) | 1.39472 | 0.106657 | ||||||||
\(172\) | − | 5.62214i | − | 0.428684i | ||||||
\(173\) | 7.72136 | 0.587044 | 0.293522 | − | 0.955952i | \(-0.405173\pi\) | ||||
0.293522 | + | 0.955952i | \(0.405173\pi\) | |||||||
\(174\) | − | 6.51317i | − | 0.493762i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.85384 | − | 1.68986i | −0.215116 | − | 0.127378i | ||||
\(177\) | −4.91595 | −0.369505 | ||||||||
\(178\) | 11.2019 | 0.839620 | ||||||||
\(179\) | −20.4836 | −1.53102 | −0.765509 | − | 0.643426i | \(-0.777513\pi\) | ||||
−0.765509 | + | 0.643426i | \(0.777513\pi\) | |||||||
\(180\) | 2.66749i | 0.198823i | ||||||||
\(181\) | 22.7331i | 1.68974i | 0.534975 | + | 0.844868i | \(0.320321\pi\) | ||||
−0.534975 | + | 0.844868i | \(0.679679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.35288i | 0.395696i | ||||||||
\(184\) | − | 3.15503i | − | 0.232592i | ||||||
\(185\) | 6.80065i | 0.499994i | ||||||||
\(186\) | 4.05080i | 0.297019i | ||||||||
\(187\) | −7.23565 | − | 4.28448i | −0.529123 | − | 0.313312i | ||||
\(188\) | − | 2.76266i | − | 0.201488i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.72042 | −0.269908 | ||||||||
\(191\) | 21.7595 | 1.57446 | 0.787231 | − | 0.616659i | \(-0.211514\pi\) | ||||
0.787231 | + | 0.616659i | \(0.211514\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 7.69156i | 0.553650i | 0.960920 | + | 0.276825i | \(0.0892823\pi\) | ||||
−0.960920 | + | 0.276825i | \(0.910718\pi\) | |||||||
\(194\) | 4.03611 | 0.289776 | ||||||||
\(195\) | 6.67364 | 0.477909 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.1678i | − | 1.50815i | −0.656791 | − | 0.754073i | \(-0.728087\pi\) | ||
0.656791 | − | 0.754073i | \(-0.271913\pi\) | |||||||
\(198\) | 1.68986 | − | 2.85384i | 0.120093 | − | 0.202813i | ||||
\(199\) | − | 23.2150i | − | 1.64566i | −0.568284 | − | 0.822832i | \(-0.692393\pi\) | ||
0.568284 | − | 0.822832i | \(-0.307607\pi\) | |||||||
\(200\) | − | 2.11553i | − | 0.149590i | ||||||
\(201\) | − | 7.33059i | − | 0.517060i | ||||||
\(202\) | − | 7.27104i | − | 0.511589i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.53541i | 0.177514i | ||||||||
\(205\) | − | 7.07690i | − | 0.494272i | ||||||
\(206\) | 4.71286 | 0.328360 | ||||||||
\(207\) | 3.15503 | 0.219290 | ||||||||
\(208\) | 2.50184 | 0.173471 | ||||||||
\(209\) | 3.98032 | + | 2.35688i | 0.275324 | + | 0.163029i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.1204i | − | 0.972087i | −0.873935 | − | 0.486044i | \(-0.838440\pi\) | ||
0.873935 | − | 0.486044i | \(-0.161560\pi\) | |||||||
\(212\) | 6.88010 | 0.472527 | ||||||||
\(213\) | 6.05096i | 0.414605i | ||||||||
\(214\) | 19.6228 | 1.34139 | ||||||||
\(215\) | −14.9970 | −1.02279 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.1803 | 1.02814 | ||||||||
\(219\) | 9.63838i | 0.651301i | ||||||||
\(220\) | −4.50768 | + | 7.61259i | −0.303908 | + | 0.513241i | ||||
\(221\) | 6.34319 | 0.426689 | ||||||||
\(222\) | −2.54945 | −0.171108 | ||||||||
\(223\) | − | 12.4044i | − | 0.830658i | −0.909671 | − | 0.415329i | \(-0.863666\pi\) | ||
0.909671 | − | 0.415329i | \(-0.136334\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.11553 | 0.141035 | ||||||||
\(226\) | 4.06642i | 0.270494i | ||||||||
\(227\) | −15.2148 | −1.00985 | −0.504923 | − | 0.863165i | \(-0.668479\pi\) | ||||
−0.504923 | + | 0.863165i | \(0.668479\pi\) | |||||||
\(228\) | − | 1.39472i | − | 0.0923679i | ||||||
\(229\) | − | 19.2052i | − | 1.26911i | −0.772876 | − | 0.634557i | \(-0.781183\pi\) | ||
0.772876 | − | 0.634557i | \(-0.218817\pi\) | |||||||
\(230\) | −8.41603 | −0.554936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.51317 | −0.427611 | ||||||||
\(233\) | 11.5244i | 0.754988i | 0.926012 | + | 0.377494i | \(0.123214\pi\) | ||||
−0.926012 | + | 0.377494i | \(0.876786\pi\) | |||||||
\(234\) | 2.50184i | 0.163550i | ||||||||
\(235\) | −7.36938 | −0.480725 | ||||||||
\(236\) | 4.91595i | 0.320001i | ||||||||
\(237\) | 8.30093 | 0.539203 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3520i | − | 0.669613i | −0.942287 | − | 0.334807i | \(-0.891329\pi\) | ||
0.942287 | − | 0.334807i | \(-0.108671\pi\) | |||||||
\(240\) | 2.66749 | 0.172186 | ||||||||
\(241\) | 25.1255 | 1.61848 | 0.809238 | − | 0.587481i | \(-0.199880\pi\) | ||||
0.809238 | + | 0.587481i | \(0.199880\pi\) | |||||||
\(242\) | 9.64515 | − | 5.28877i | 0.620014 | − | 0.339975i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 5.35288 | 0.342683 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.65301 | 0.169150 | ||||||||
\(247\) | −3.48938 | −0.222024 | ||||||||
\(248\) | 4.05080 | 0.257226 | ||||||||
\(249\) | 14.4528i | 0.915909i | ||||||||
\(250\) | 7.69432 | 0.486631 | ||||||||
\(251\) | 7.97557i | 0.503414i | 0.967804 | + | 0.251707i | \(0.0809918\pi\) | ||||
−0.967804 | + | 0.251707i | \(0.919008\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00394 | + | 5.33155i | 0.566073 | + | 0.335192i | ||||
\(254\) | 8.01581 | 0.502957 | ||||||||
\(255\) | 6.76319 | 0.423528 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 7.57023i | − | 0.472218i | −0.971727 | − | 0.236109i | \(-0.924128\pi\) | ||
0.971727 | − | 0.236109i | \(-0.0758722\pi\) | |||||||
\(258\) | − | 5.62214i | − | 0.350019i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 6.67364i | − | 0.413882i | ||||||
\(261\) | − | 6.51317i | − | 0.403155i | ||||||
\(262\) | − | 14.5316i | − | 0.897764i | ||||||
\(263\) | 26.3900i | 1.62728i | 0.581369 | + | 0.813640i | \(0.302517\pi\) | ||||
−0.581369 | + | 0.813640i | \(0.697483\pi\) | |||||||
\(264\) | −2.85384 | − | 1.68986i | −0.175642 | − | 0.104003i | ||||
\(265\) | − | 18.3526i | − | 1.12739i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.2019 | 0.685547 | ||||||||
\(268\) | −7.33059 | −0.447787 | ||||||||
\(269\) | 5.00096i | 0.304914i | 0.988310 | + | 0.152457i | \(0.0487185\pi\) | ||||
−0.988310 | + | 0.152457i | \(0.951282\pi\) | |||||||
\(270\) | 2.66749i | 0.162339i | ||||||||
\(271\) | −28.1218 | −1.70828 | −0.854140 | − | 0.520044i | \(-0.825916\pi\) | ||||
−0.854140 | + | 0.520044i | \(0.825916\pi\) | |||||||
\(272\) | 2.53541 | 0.153732 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.1601i | 0.613797i | ||||||||
\(275\) | 6.03737 | + | 3.57494i | 0.364067 | + | 0.215577i | ||||
\(276\) | − | 3.15503i | − | 0.189910i | ||||||
\(277\) | 4.15631i | 0.249728i | 0.992174 | + | 0.124864i | \(0.0398495\pi\) | ||||
−0.992174 | + | 0.124864i | \(0.960150\pi\) | |||||||
\(278\) | 2.15019i | 0.128960i | ||||||||
\(279\) | 4.05080i | 0.242515i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.6193i | 1.82660i | 0.407291 | + | 0.913299i | \(0.366474\pi\) | ||||
−0.407291 | + | 0.913299i | \(0.633526\pi\) | |||||||
\(282\) | − | 2.76266i | − | 0.164514i | ||||||
\(283\) | 5.38804 | 0.320286 | 0.160143 | − | 0.987094i | \(-0.448805\pi\) | ||||
0.160143 | + | 0.987094i | \(0.448805\pi\) | |||||||
\(284\) | 6.05096 | 0.359058 | ||||||||
\(285\) | −3.72042 | −0.220379 | ||||||||
\(286\) | −4.22775 | + | 7.13984i | −0.249992 | + | 0.422188i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −10.5717 | −0.621864 | ||||||||
\(290\) | 17.3739i | 1.02023i | ||||||||
\(291\) | 4.03611 | 0.236601 | ||||||||
\(292\) | 9.63838 | 0.564043 | ||||||||
\(293\) | −4.27517 | −0.249758 | −0.124879 | − | 0.992172i | \(-0.539854\pi\) | ||||
−0.124879 | + | 0.992172i | \(0.539854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.1133 | 0.763484 | ||||||||
\(296\) | 2.54945i | 0.148184i | ||||||||
\(297\) | 1.68986 | − | 2.85384i | 0.0980554 | − | 0.165596i | ||||
\(298\) | 18.1396 | 1.05080 | ||||||||
\(299\) | −7.89338 | −0.456486 | ||||||||
\(300\) | − | 2.11553i | − | 0.122140i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.69350 | −0.0974500 | ||||||||
\(303\) | − | 7.27104i | − | 0.417710i | ||||||
\(304\) | −1.39472 | −0.0799929 | ||||||||
\(305\) | − | 14.2788i | − | 0.817600i | ||||||
\(306\) | 2.53541i | 0.144940i | ||||||||
\(307\) | 4.80816 | 0.274416 | 0.137208 | − | 0.990542i | \(-0.456187\pi\) | ||||
0.137208 | + | 0.990542i | \(0.456187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.71286 | 0.268105 | ||||||||
\(310\) | − | 10.8055i | − | 0.613711i | ||||||
\(311\) | − | 28.8146i | − | 1.63393i | −0.576690 | − | 0.816963i | \(-0.695656\pi\) | ||
0.576690 | − | 0.816963i | \(-0.304344\pi\) | |||||||
\(312\) | 2.50184 | 0.141639 | ||||||||
\(313\) | − | 21.6235i | − | 1.22223i | −0.791541 | − | 0.611117i | \(-0.790721\pi\) | ||
0.791541 | − | 0.611117i | \(-0.209279\pi\) | |||||||
\(314\) | −6.48100 | −0.365744 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.30093i | − | 0.466964i | ||||||
\(317\) | 8.45799 | 0.475048 | 0.237524 | − | 0.971382i | \(-0.423664\pi\) | ||||
0.237524 | + | 0.971382i | \(0.423664\pi\) | |||||||
\(318\) | 6.88010 | 0.385817 | ||||||||
\(319\) | 11.0063 | − | 18.5875i | 0.616236 | − | 1.04070i | ||||
\(320\) | − | 2.66749i | − | 0.149117i | ||||||
\(321\) | 19.6228 | 1.09524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.53620 | −0.196759 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −5.29271 | −0.293587 | ||||||||
\(326\) | − | 1.86138i | − | 0.103092i | ||||||
\(327\) | 15.1803 | 0.839472 | ||||||||
\(328\) | − | 2.65301i | − | 0.146488i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.50768 | + | 7.61259i | −0.248140 | + | 0.419060i | ||||
\(331\) | 2.57208 | 0.141374 | 0.0706872 | − | 0.997499i | \(-0.477481\pi\) | ||||
0.0706872 | + | 0.997499i | \(0.477481\pi\) | |||||||
\(332\) | 14.4528 | 0.793200 | ||||||||
\(333\) | −2.54945 | −0.139709 | ||||||||
\(334\) | 10.4965i | 0.574340i | ||||||||
\(335\) | 19.5543i | 1.06837i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2962i | 0.833235i | 0.909082 | + | 0.416617i | \(0.136785\pi\) | ||||
−0.909082 | + | 0.416617i | \(0.863215\pi\) | |||||||
\(338\) | 6.74080i | 0.366651i | ||||||||
\(339\) | 4.06642i | 0.220857i | ||||||||
\(340\) | − | 6.76319i | − | 0.366786i | ||||||
\(341\) | −6.84528 | + | 11.5603i | −0.370693 | + | 0.626027i | ||||
\(342\) | − | 1.39472i | − | 0.0754181i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.62214 | −0.303125 | ||||||||
\(345\) | −8.41603 | −0.453104 | ||||||||
\(346\) | − | 7.72136i | − | 0.415103i | ||||||
\(347\) | 10.6965i | 0.574220i | 0.957898 | + | 0.287110i | \(0.0926945\pi\) | ||||
−0.957898 | + | 0.287110i | \(0.907305\pi\) | |||||||
\(348\) | −6.51317 | −0.349143 | ||||||||
\(349\) | 25.2258 | 1.35030 | 0.675152 | − | 0.737679i | \(-0.264078\pi\) | ||||
0.675152 | + | 0.737679i | \(0.264078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.50184i | 0.133538i | ||||||||
\(352\) | −1.68986 | + | 2.85384i | −0.0900696 | + | 0.152110i | ||||
\(353\) | 28.3189i | 1.50726i | 0.657297 | + | 0.753631i | \(0.271700\pi\) | ||||
−0.657297 | + | 0.753631i | \(0.728300\pi\) | |||||||
\(354\) | 4.91595i | 0.261280i | ||||||||
\(355\) | − | 16.1409i | − | 0.856670i | ||||||
\(356\) | − | 11.2019i | − | 0.593701i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.4836i | 1.08259i | ||||||||
\(359\) | − | 10.0681i | − | 0.531374i | −0.964059 | − | 0.265687i | \(-0.914401\pi\) | ||
0.964059 | − | 0.265687i | \(-0.0855988\pi\) | |||||||
\(360\) | 2.66749 | 0.140589 | ||||||||
\(361\) | −17.0547 | −0.897618 | ||||||||
\(362\) | 22.7331 | 1.19482 | ||||||||
\(363\) | 9.64515 | − | 5.28877i | 0.506239 | − | 0.277589i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 25.7103i | − | 1.34574i | ||||||
\(366\) | 5.35288 | 0.279800 | ||||||||
\(367\) | − | 24.5516i | − | 1.28158i | −0.767716 | − | 0.640791i | \(-0.778607\pi\) | ||
0.767716 | − | 0.640791i | \(-0.221393\pi\) | |||||||
\(368\) | −3.15503 | −0.164467 | ||||||||
\(369\) | 2.65301 | 0.138110 | ||||||||
\(370\) | 6.80065 | 0.353549 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.05080 | 0.210024 | ||||||||
\(373\) | 1.27622i | 0.0660802i | 0.999454 | + | 0.0330401i | \(0.0105189\pi\) | ||||
−0.999454 | + | 0.0330401i | \(0.989481\pi\) | |||||||
\(374\) | −4.28448 | + | 7.23565i | −0.221545 | + | 0.374146i | ||||
\(375\) | 7.69432 | 0.397333 | ||||||||
\(376\) | −2.76266 | −0.142473 | ||||||||
\(377\) | 16.2949i | 0.839230i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.0451 | 1.95425 | 0.977124 | − | 0.212672i | \(-0.0682166\pi\) | ||||
0.977124 | + | 0.212672i | \(0.0682166\pi\) | |||||||
\(380\) | 3.72042i | 0.190854i | ||||||||
\(381\) | 8.01581 | 0.410662 | ||||||||
\(382\) | − | 21.7595i | − | 1.11331i | ||||||
\(383\) | − | 11.2055i | − | 0.572574i | −0.958144 | − | 0.286287i | \(-0.907579\pi\) | ||
0.958144 | − | 0.286287i | \(-0.0924211\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.69156 | 0.391490 | ||||||||
\(387\) | − | 5.62214i | − | 0.285789i | ||||||
\(388\) | − | 4.03611i | − | 0.204903i | ||||||
\(389\) | 7.21388 | 0.365758 | 0.182879 | − | 0.983135i | \(-0.441458\pi\) | ||||
0.182879 | + | 0.983135i | \(0.441458\pi\) | |||||||
\(390\) | − | 6.67364i | − | 0.337933i | ||||||
\(391\) | −7.99930 | −0.404542 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.5316i | − | 0.733021i | ||||||
\(394\) | −21.1678 | −1.06642 | ||||||||
\(395\) | −22.1427 | −1.11412 | ||||||||
\(396\) | −2.85384 | − | 1.68986i | −0.143411 | − | 0.0849185i | ||||
\(397\) | − | 19.4918i | − | 0.978264i | −0.872210 | − | 0.489132i | \(-0.837314\pi\) | ||
0.872210 | − | 0.489132i | \(-0.162686\pi\) | |||||||
\(398\) | −23.2150 | −1.16366 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.11553 | −0.105776 | ||||||||
\(401\) | −13.0461 | −0.651492 | −0.325746 | − | 0.945457i | \(-0.605615\pi\) | ||||
−0.325746 | + | 0.945457i | \(0.605615\pi\) | |||||||
\(402\) | −7.33059 | −0.365617 | ||||||||
\(403\) | − | 10.1345i | − | 0.504833i | ||||||
\(404\) | −7.27104 | −0.361748 | ||||||||
\(405\) | 2.66749i | 0.132549i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.27572 | − | 4.30821i | −0.360644 | − | 0.213550i | ||||
\(408\) | 2.53541 | 0.125522 | ||||||||
\(409\) | 33.8668 | 1.67461 | 0.837303 | − | 0.546739i | \(-0.184131\pi\) | ||||
0.837303 | + | 0.546739i | \(0.184131\pi\) | |||||||
\(410\) | −7.07690 | −0.349503 | ||||||||
\(411\) | 10.1601i | 0.501163i | ||||||||
\(412\) | − | 4.71286i | − | 0.232186i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 3.15503i | − | 0.155061i | ||||||
\(415\) | − | 38.5528i | − | 1.89248i | ||||||
\(416\) | − | 2.50184i | − | 0.122663i | ||||||
\(417\) | 2.15019i | 0.105295i | ||||||||
\(418\) | 2.35688 | − | 3.98032i | 0.115279 | − | 0.194684i | ||||
\(419\) | 12.9005i | 0.630233i | 0.949053 | + | 0.315116i | \(0.102044\pi\) | ||||
−0.949053 | + | 0.315116i | \(0.897956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.05921 | −0.344045 | −0.172022 | − | 0.985093i | \(-0.555030\pi\) | ||||
−0.172022 | + | 0.985093i | \(0.555030\pi\) | |||||||
\(422\) | −14.1204 | −0.687369 | ||||||||
\(423\) | − | 2.76266i | − | 0.134325i | ||||||
\(424\) | − | 6.88010i | − | 0.334127i | ||||||
\(425\) | −5.36373 | −0.260179 | ||||||||
\(426\) | 6.05096 | 0.293170 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 19.6228i | − | 0.948505i | ||||||
\(429\) | −4.22775 | + | 7.13984i | −0.204118 | + | 0.344715i | ||||
\(430\) | 14.9970i | 0.723221i | ||||||||
\(431\) | − | 3.54328i | − | 0.170674i | −0.996352 | − | 0.0853368i | \(-0.972803\pi\) | ||
0.996352 | − | 0.0853368i | \(-0.0271966\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 16.2125i | 0.779121i | 0.921001 | + | 0.389561i | \(0.127373\pi\) | ||||
−0.921001 | + | 0.389561i | \(0.872627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.3739i | 0.833012i | ||||||||
\(436\) | − | 15.1803i | − | 0.727004i | ||||||
\(437\) | 4.40040 | 0.210500 | ||||||||
\(438\) | 9.63838 | 0.460539 | ||||||||
\(439\) | 24.8095 | 1.18409 | 0.592047 | − | 0.805903i | \(-0.298320\pi\) | ||||
0.592047 | + | 0.805903i | \(0.298320\pi\) | |||||||
\(440\) | 7.61259 | + | 4.50768i | 0.362916 | + | 0.214895i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 6.34319i | − | 0.301715i | ||||||
\(443\) | −36.3380 | −1.72647 | −0.863235 | − | 0.504803i | \(-0.831565\pi\) | ||||
−0.863235 | + | 0.504803i | \(0.831565\pi\) | |||||||
\(444\) | 2.54945i | 0.120992i | ||||||||
\(445\) | −29.8811 | −1.41650 | ||||||||
\(446\) | −12.4044 | −0.587364 | ||||||||
\(447\) | 18.1396 | 0.857975 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.6858 | −1.30657 | −0.653287 | − | 0.757110i | \(-0.726611\pi\) | ||||
−0.653287 | + | 0.757110i | \(0.726611\pi\) | |||||||
\(450\) | − | 2.11553i | − | 0.0997269i | ||||||
\(451\) | 7.57127 | + | 4.48321i | 0.356517 | + | 0.211106i | ||||
\(452\) | 4.06642 | 0.191268 | ||||||||
\(453\) | −1.69350 | −0.0795676 | ||||||||
\(454\) | 15.2148i | 0.714068i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.39472 | −0.0653140 | ||||||||
\(457\) | − | 20.5828i | − | 0.962821i | −0.876495 | − | 0.481411i | \(-0.840125\pi\) | ||
0.876495 | − | 0.481411i | \(-0.159875\pi\) | |||||||
\(458\) | −19.2052 | −0.897399 | ||||||||
\(459\) | 2.53541i | 0.118343i | ||||||||
\(460\) | 8.41603i | 0.392399i | ||||||||
\(461\) | −21.4634 | −0.999648 | −0.499824 | − | 0.866127i | \(-0.666602\pi\) | ||||
−0.499824 | + | 0.866127i | \(0.666602\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.62818 | −0.261563 | −0.130782 | − | 0.991411i | \(-0.541749\pi\) | ||||
−0.130782 | + | 0.991411i | \(0.541749\pi\) | |||||||
\(464\) | 6.51317i | 0.302366i | ||||||||
\(465\) | − | 10.8055i | − | 0.501093i | ||||||
\(466\) | 11.5244 | 0.533857 | ||||||||
\(467\) | 14.8084i | 0.685251i | 0.939472 | + | 0.342626i | \(0.111316\pi\) | ||||
−0.939472 | + | 0.342626i | \(0.888684\pi\) | |||||||
\(468\) | 2.50184 | 0.115648 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.36938i | 0.339924i | ||||||||
\(471\) | −6.48100 | −0.298629 | ||||||||
\(472\) | 4.91595 | 0.226275 | ||||||||
\(473\) | 9.50061 | − | 16.0447i | 0.436838 | − | 0.737735i | ||||
\(474\) | − | 8.30093i | − | 0.381274i | ||||||
\(475\) | 2.95058 | 0.135382 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.88010 | 0.315018 | ||||||||
\(478\) | −10.3520 | −0.473488 | ||||||||
\(479\) | −27.8523 | −1.27261 | −0.636303 | − | 0.771439i | \(-0.719537\pi\) | ||||
−0.636303 | + | 0.771439i | \(0.719537\pi\) | |||||||
\(480\) | − | 2.66749i | − | 0.121754i | ||||||
\(481\) | 6.37832 | 0.290826 | ||||||||
\(482\) | − | 25.1255i | − | 1.14443i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.28877 | − | 9.64515i | −0.240399 | − | 0.438416i | ||||
\(485\) | −10.7663 | −0.488873 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −19.4540 | −0.881544 | −0.440772 | − | 0.897619i | \(-0.645295\pi\) | ||||
−0.440772 | + | 0.897619i | \(0.645295\pi\) | |||||||
\(488\) | − | 5.35288i | − | 0.242313i | ||||||
\(489\) | − | 1.86138i | − | 0.0841745i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 41.7607i | − | 1.88463i | −0.334724 | − | 0.942316i | \(-0.608643\pi\) | ||
0.334724 | − | 0.942316i | \(-0.391357\pi\) | |||||||
\(492\) | − | 2.65301i | − | 0.119607i | ||||||
\(493\) | 16.5136i | 0.743733i | ||||||||
\(494\) | 3.48938i | 0.156994i | ||||||||
\(495\) | −4.50768 | + | 7.61259i | −0.202605 | + | 0.342161i | ||||
\(496\) | − | 4.05080i | − | 0.181886i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.4528 | 0.647645 | ||||||||
\(499\) | 13.9993 | 0.626694 | 0.313347 | − | 0.949639i | \(-0.398550\pi\) | ||||
0.313347 | + | 0.949639i | \(0.398550\pi\) | |||||||
\(500\) | − | 7.69432i | − | 0.344100i | ||||||
\(501\) | 10.4965i | 0.468947i | ||||||||
\(502\) | 7.97557 | 0.355967 | ||||||||
\(503\) | 14.9827 | 0.668044 | 0.334022 | − | 0.942565i | \(-0.391594\pi\) | ||||
0.334022 | + | 0.942565i | \(0.391594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.3955i | 0.863087i | ||||||||
\(506\) | 5.33155 | − | 9.00394i | 0.237016 | − | 0.400274i | ||||
\(507\) | 6.74080i | 0.299370i | ||||||||
\(508\) | − | 8.01581i | − | 0.355644i | ||||||
\(509\) | − | 1.76581i | − | 0.0782680i | −0.999234 | − | 0.0391340i | \(-0.987540\pi\) | ||
0.999234 | − | 0.0391340i | \(-0.0124599\pi\) | |||||||
\(510\) | − | 6.76319i | − | 0.299479i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 1.39472i | − | 0.0615786i | ||||||
\(514\) | −7.57023 | −0.333908 | ||||||||
\(515\) | −12.5715 | −0.553967 | ||||||||
\(516\) | −5.62214 | −0.247501 | ||||||||
\(517\) | 4.66850 | − | 7.88418i | 0.205320 | − | 0.346746i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.72136i | − | 0.338930i | ||||||
\(520\) | −6.67364 | −0.292659 | ||||||||
\(521\) | 37.9681i | 1.66341i | 0.555217 | + | 0.831706i | \(0.312635\pi\) | ||||
−0.555217 | + | 0.831706i | \(0.687365\pi\) | |||||||
\(522\) | −6.51317 | −0.285074 | ||||||||
\(523\) | 23.9395 | 1.04680 | 0.523400 | − | 0.852087i | \(-0.324663\pi\) | ||||
0.523400 | + | 0.852087i | \(0.324663\pi\) | |||||||
\(524\) | −14.5316 | −0.634815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.3900 | 1.15066 | ||||||||
\(527\) | − | 10.2704i | − | 0.447388i | ||||||
\(528\) | −1.68986 | + | 2.85384i | −0.0735416 | + | 0.124197i | ||||
\(529\) | −13.0458 | −0.567208 | ||||||||
\(530\) | −18.3526 | −0.797187 | ||||||||
\(531\) | 4.91595i | 0.213334i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.63741 | −0.287498 | ||||||||
\(534\) | − | 11.2019i | − | 0.484755i | ||||||
\(535\) | −52.3438 | −2.26302 | ||||||||
\(536\) | 7.33059i | 0.316633i | ||||||||
\(537\) | 20.4836i | 0.883933i | ||||||||
\(538\) | 5.00096 | 0.215607 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.66749 | 0.114791 | ||||||||
\(541\) | − | 23.9757i | − | 1.03079i | −0.856951 | − | 0.515397i | \(-0.827644\pi\) | ||
0.856951 | − | 0.515397i | \(-0.172356\pi\) | |||||||
\(542\) | 28.1218i | 1.20794i | ||||||||
\(543\) | 22.7331 | 0.975569 | ||||||||
\(544\) | − | 2.53541i | − | 0.108705i | ||||||
\(545\) | −40.4933 | −1.73454 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.5789i | − | 0.922645i | −0.887232 | − | 0.461323i | \(-0.847375\pi\) | ||
0.887232 | − | 0.461323i | \(-0.152625\pi\) | |||||||
\(548\) | 10.1601 | 0.434020 | ||||||||
\(549\) | 5.35288 | 0.228455 | ||||||||
\(550\) | 3.57494 | − | 6.03737i | 0.152436 | − | 0.257434i | ||||
\(551\) | − | 9.08408i | − | 0.386995i | ||||||
\(552\) | −3.15503 | −0.134287 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.15631 | 0.176585 | ||||||||
\(555\) | 6.80065 | 0.288672 | ||||||||
\(556\) | 2.15019 | 0.0911885 | ||||||||
\(557\) | − | 3.24887i | − | 0.137659i | −0.997628 | − | 0.0688295i | \(-0.978074\pi\) | ||
0.997628 | − | 0.0688295i | \(-0.0219264\pi\) | |||||||
\(558\) | 4.05080 | 0.171484 | ||||||||
\(559\) | 14.0657i | 0.594915i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.28448 | + | 7.23565i | −0.180891 | + | 0.305489i | ||||
\(562\) | 30.6193 | 1.29160 | ||||||||
\(563\) | −12.2902 | −0.517969 | −0.258984 | − | 0.965881i | \(-0.583388\pi\) | ||||
−0.258984 | + | 0.965881i | \(0.583388\pi\) | |||||||
\(564\) | −2.76266 | −0.116329 | ||||||||
\(565\) | − | 10.8471i | − | 0.456343i | ||||||
\(566\) | − | 5.38804i | − | 0.226476i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.05096i | − | 0.253892i | ||||||
\(569\) | 45.2479i | 1.89689i | 0.316938 | + | 0.948446i | \(0.397345\pi\) | ||||
−0.316938 | + | 0.948446i | \(0.602655\pi\) | |||||||
\(570\) | 3.72042i | 0.155831i | ||||||||
\(571\) | − | 2.89745i | − | 0.121254i | −0.998160 | − | 0.0606272i | \(-0.980690\pi\) | ||
0.998160 | − | 0.0606272i | \(-0.0193101\pi\) | |||||||
\(572\) | 7.13984 | + | 4.22775i | 0.298532 | + | 0.176771i | ||||
\(573\) | − | 21.7595i | − | 0.909016i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.67455 | 0.278348 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 1.99114i | − | 0.0828922i | −0.999141 | − | 0.0414461i | \(-0.986804\pi\) | ||
0.999141 | − | 0.0414461i | \(-0.0131965\pi\) | |||||||
\(578\) | 10.5717i | 0.439725i | ||||||||
\(579\) | 7.69156 | 0.319650 | ||||||||
\(580\) | 17.3739 | 0.721410 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 4.03611i | − | 0.167302i | ||||||
\(583\) | 19.6347 | + | 11.6264i | 0.813185 | + | 0.481515i | ||||
\(584\) | − | 9.63838i | − | 0.398839i | ||||||
\(585\) | − | 6.67364i | − | 0.275921i | ||||||
\(586\) | 4.27517i | 0.176606i | ||||||||
\(587\) | 37.4423i | 1.54541i | 0.634766 | + | 0.772705i | \(0.281097\pi\) | ||||
−0.634766 | + | 0.772705i | \(0.718903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.64976i | 0.232794i | ||||||||
\(590\) | − | 13.1133i | − | 0.539864i | ||||||
\(591\) | −21.1678 | −0.870728 | ||||||||
\(592\) | 2.54945 | 0.104782 | ||||||||
\(593\) | 42.0052 | 1.72495 | 0.862473 | − | 0.506103i | \(-0.168914\pi\) | ||||
0.862473 | + | 0.506103i | \(0.168914\pi\) | |||||||
\(594\) | −2.85384 | − | 1.68986i | −0.117094 | − | 0.0693356i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.1396i | − | 0.743028i | ||||||
\(597\) | −23.2150 | −0.950125 | ||||||||
\(598\) | 7.89338i | 0.322784i | ||||||||
\(599\) | −20.5239 | −0.838585 | −0.419292 | − | 0.907851i | \(-0.637722\pi\) | ||||
−0.419292 | + | 0.907851i | \(0.637722\pi\) | |||||||
\(600\) | −2.11553 | −0.0863660 | ||||||||
\(601\) | −9.51509 | −0.388128 | −0.194064 | − | 0.980989i | \(-0.562167\pi\) | ||||
−0.194064 | + | 0.980989i | \(0.562167\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.33059 | −0.298525 | ||||||||
\(604\) | 1.69350i | 0.0689075i | ||||||||
\(605\) | −25.7284 | + | 14.1078i | −1.04601 | + | 0.573562i | ||||
\(606\) | −7.27104 | −0.295366 | ||||||||
\(607\) | 1.47149 | 0.0597258 | 0.0298629 | − | 0.999554i | \(-0.490493\pi\) | ||||
0.0298629 | + | 0.999554i | \(0.490493\pi\) | |||||||
\(608\) | 1.39472i | 0.0565635i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2788 | −0.578131 | ||||||||
\(611\) | 6.91173i | 0.279619i | ||||||||
\(612\) | 2.53541 | 0.102488 | ||||||||
\(613\) | − | 11.0599i | − | 0.446705i | −0.974738 | − | 0.223353i | \(-0.928300\pi\) | ||
0.974738 | − | 0.223353i | \(-0.0717002\pi\) | |||||||
\(614\) | − | 4.80816i | − | 0.194041i | ||||||
\(615\) | −7.07690 | −0.285368 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.9204 | −1.16429 | −0.582146 | − | 0.813085i | \(-0.697787\pi\) | ||||
−0.582146 | + | 0.813085i | \(0.697787\pi\) | |||||||
\(618\) | − | 4.71286i | − | 0.189579i | ||||||
\(619\) | − | 13.0186i | − | 0.523261i | −0.965168 | − | 0.261630i | \(-0.915740\pi\) | ||
0.965168 | − | 0.261630i | \(-0.0842601\pi\) | |||||||
\(620\) | −10.8055 | −0.433959 | ||||||||
\(621\) | − | 3.15503i | − | 0.126607i | ||||||
\(622\) | −28.8146 | −1.15536 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 2.50184i | − | 0.100154i | ||||||
\(625\) | −31.1022 | −1.24409 | ||||||||
\(626\) | −21.6235 | −0.864249 | ||||||||
\(627\) | 2.35688 | − | 3.98032i | 0.0941249 | − | 0.158959i | ||||
\(628\) | 6.48100i | 0.258620i | ||||||||
\(629\) | 6.46391 | 0.257733 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.4603 | −1.33204 | −0.666018 | − | 0.745936i | \(-0.732002\pi\) | ||||
−0.666018 | + | 0.745936i | \(0.732002\pi\) | |||||||
\(632\) | −8.30093 | −0.330193 | ||||||||
\(633\) | −14.1204 | −0.561235 | ||||||||
\(634\) | − | 8.45799i | − | 0.335910i | ||||||
\(635\) | −21.3821 | −0.848524 | ||||||||
\(636\) | − | 6.88010i | − | 0.272814i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.5875 | − | 11.0063i | −0.735887 | − | 0.435745i | ||||
\(639\) | 6.05096 | 0.239372 | ||||||||
\(640\) | −2.66749 | −0.105442 | ||||||||
\(641\) | 39.6896 | 1.56765 | 0.783823 | − | 0.620984i | \(-0.213267\pi\) | ||||
0.783823 | + | 0.620984i | \(0.213267\pi\) | |||||||
\(642\) | − | 19.6228i | − | 0.774451i | ||||||
\(643\) | − | 1.46168i | − | 0.0576432i | −0.999585 | − | 0.0288216i | \(-0.990825\pi\) | ||
0.999585 | − | 0.0288216i | \(-0.00917547\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.9970i | 0.590507i | ||||||||
\(646\) | 3.53620i | 0.139130i | ||||||||
\(647\) | − | 0.0217615i | − | 0.000855533i | −1.00000 | 0.000427766i | \(-0.999864\pi\) | |||
1.00000 | 0.000427766i | \(-0.000136162\pi\) | ||||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −8.30724 | + | 14.0293i | −0.326088 | + | 0.550699i | ||||
\(650\) | 5.29271i | 0.207597i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.86138 | −0.0728973 | ||||||||
\(653\) | 22.9725 | 0.898985 | 0.449493 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449493 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(654\) | − | 15.1803i | − | 0.593596i | ||||||
\(655\) | 38.7629i | 1.51459i | ||||||||
\(656\) | −2.65301 | −0.103583 | ||||||||
\(657\) | 9.63838 | 0.376029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.84925i | 0.110991i | 0.998459 | + | 0.0554956i | \(0.0176739\pi\) | ||||
−0.998459 | + | 0.0554956i | \(0.982326\pi\) | |||||||
\(660\) | 7.61259 | + | 4.50768i | 0.296320 | + | 0.175461i | ||||
\(661\) | 44.2307i | 1.72038i | 0.509977 | + | 0.860188i | \(0.329654\pi\) | ||||
−0.509977 | + | 0.860188i | \(0.670346\pi\) | |||||||
\(662\) | − | 2.57208i | − | 0.0999668i | ||||||
\(663\) | − | 6.34319i | − | 0.246349i | ||||||
\(664\) | − | 14.4528i | − | 0.560877i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.54945i | 0.0987893i | ||||||||
\(667\) | − | 20.5493i | − | 0.795670i | ||||||
\(668\) | 10.4965 | 0.406120 | ||||||||
\(669\) | −12.4044 | −0.479581 | ||||||||
\(670\) | 19.5543 | 0.755449 | ||||||||
\(671\) | 15.2762 | + | 9.04560i | 0.589733 | + | 0.349201i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.2881i | − | 0.820597i | −0.911951 | − | 0.410299i | \(-0.865424\pi\) | ||
0.911951 | − | 0.410299i | \(-0.134576\pi\) | |||||||
\(674\) | 15.2962 | 0.589186 | ||||||||
\(675\) | − | 2.11553i | − | 0.0814267i | ||||||
\(676\) | 6.74080 | 0.259262 | ||||||||
\(677\) | 27.2776 | 1.04836 | 0.524182 | − | 0.851606i | \(-0.324371\pi\) | ||||
0.524182 | + | 0.851606i | \(0.324371\pi\) | |||||||
\(678\) | 4.06642 | 0.156170 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.76319 | −0.259357 | ||||||||
\(681\) | 15.2148i | 0.583034i | ||||||||
\(682\) | 11.5603 | + | 6.84528i | 0.442668 | + | 0.262119i | ||||
\(683\) | 25.2966 | 0.967947 | 0.483973 | − | 0.875083i | \(-0.339193\pi\) | ||||
0.483973 | + | 0.875083i | \(0.339193\pi\) | |||||||
\(684\) | −1.39472 | −0.0533286 | ||||||||
\(685\) | − | 27.1021i | − | 1.03552i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.2052 | −0.732723 | ||||||||
\(688\) | 5.62214i | 0.214342i | ||||||||
\(689\) | −17.2129 | −0.655759 | ||||||||
\(690\) | 8.41603i | 0.320393i | ||||||||
\(691\) | 18.3503i | 0.698077i | 0.937108 | + | 0.349039i | \(0.113492\pi\) | ||||
−0.937108 | + | 0.349039i | \(0.886508\pi\) | |||||||
\(692\) | −7.72136 | −0.293522 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.6965 | 0.406035 | ||||||||
\(695\) | − | 5.73563i | − | 0.217565i | ||||||
\(696\) | 6.51317i | 0.246881i | ||||||||
\(697\) | −6.72648 | −0.254783 | ||||||||
\(698\) | − | 25.2258i | − | 0.954809i | ||||||
\(699\) | 11.5244 | 0.435892 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.1203i | − | 0.986550i | −0.869873 | − | 0.493275i | \(-0.835800\pi\) | ||
0.869873 | − | 0.493275i | \(-0.164200\pi\) | |||||||
\(702\) | 2.50184 | 0.0944258 | ||||||||
\(703\) | −3.55578 | −0.134109 | ||||||||
\(704\) | 2.85384 | + | 1.68986i | 0.107558 | + | 0.0636889i | ||||
\(705\) | 7.36938i | 0.277547i | ||||||||
\(706\) | 28.3189 | 1.06580 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.91595 | 0.184753 | ||||||||
\(709\) | −16.9144 | −0.635232 | −0.317616 | − | 0.948219i | \(-0.602882\pi\) | ||||
−0.317616 | + | 0.948219i | \(0.602882\pi\) | |||||||
\(710\) | −16.1409 | −0.605757 | ||||||||
\(711\) | − | 8.30093i | − | 0.311309i | ||||||
\(712\) | −11.2019 | −0.419810 | ||||||||
\(713\) | 12.7804i | 0.478630i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.2775 | − | 19.0455i | 0.421754 | − | 0.712261i | ||||
\(716\) | 20.4836 | 0.765509 | ||||||||
\(717\) | −10.3520 | −0.386602 | ||||||||
\(718\) | −10.0681 | −0.375738 | ||||||||
\(719\) | − | 2.96473i | − | 0.110566i | −0.998471 | − | 0.0552829i | \(-0.982394\pi\) | ||
0.998471 | − | 0.0552829i | \(-0.0176061\pi\) | |||||||
\(720\) | − | 2.66749i | − | 0.0994116i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0547i | 0.634712i | ||||||||
\(723\) | − | 25.1255i | − | 0.934427i | ||||||
\(724\) | − | 22.7331i | − | 0.844868i | ||||||
\(725\) | − | 13.7788i | − | 0.511731i | ||||||
\(726\) | −5.28877 | − | 9.64515i | −0.196285 | − | 0.357965i | ||||
\(727\) | − | 35.7180i | − | 1.32471i | −0.749191 | − | 0.662354i | \(-0.769557\pi\) | ||
0.749191 | − | 0.662354i | \(-0.230443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −25.7103 | −0.951582 | ||||||||
\(731\) | 14.2544i | 0.527219i | ||||||||
\(732\) | − | 5.35288i | − | 0.197848i | ||||||
\(733\) | −3.01235 | −0.111264 | −0.0556318 | − | 0.998451i | \(-0.517717\pi\) | ||||
−0.0556318 | + | 0.998451i | \(0.517717\pi\) | |||||||
\(734\) | −24.5516 | −0.906215 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.15503i | 0.116296i | ||||||||
\(737\) | −20.9203 | − | 12.3876i | −0.770610 | − | 0.456305i | ||||
\(738\) | − | 2.65301i | − | 0.0976588i | ||||||
\(739\) | 32.7689i | 1.20542i | 0.797959 | + | 0.602711i | \(0.205913\pi\) | ||||
−0.797959 | + | 0.602711i | \(0.794087\pi\) | |||||||
\(740\) | − | 6.80065i | − | 0.249997i | ||||||
\(741\) | 3.48938i | 0.128185i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.6910i | 1.78630i | 0.449759 | + | 0.893150i | \(0.351510\pi\) | ||||
−0.449759 | + | 0.893150i | \(0.648490\pi\) | |||||||
\(744\) | − | 4.05080i | − | 0.148510i | ||||||
\(745\) | −48.3874 | −1.77278 | ||||||||
\(746\) | 1.27622 | 0.0467257 | ||||||||
\(747\) | 14.4528 | 0.528800 | ||||||||
\(748\) | 7.23565 | + | 4.28448i | 0.264561 | + | 0.156656i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 7.69432i | − | 0.280957i | ||||||
\(751\) | −1.97476 | −0.0720600 | −0.0360300 | − | 0.999351i | \(-0.511471\pi\) | ||||
−0.0360300 | + | 0.999351i | \(0.511471\pi\) | |||||||
\(752\) | 2.76266i | 0.100744i | ||||||||
\(753\) | 7.97557 | 0.290646 | ||||||||
\(754\) | 16.2949 | 0.593425 | ||||||||
\(755\) | 4.51740 | 0.164405 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.7224 | −1.62546 | −0.812731 | − | 0.582639i | \(-0.802020\pi\) | ||||
−0.812731 | + | 0.582639i | \(0.802020\pi\) | |||||||
\(758\) | − | 38.0451i | − | 1.38186i | ||||||
\(759\) | 5.33155 | − | 9.00394i | 0.193523 | − | 0.326822i | ||||
\(760\) | 3.72042 | 0.134954 | ||||||||
\(761\) | −35.3144 | −1.28014 | −0.640072 | − | 0.768315i | \(-0.721096\pi\) | ||||
−0.640072 | + | 0.768315i | \(0.721096\pi\) | |||||||
\(762\) | − | 8.01581i | − | 0.290382i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21.7595 | −0.787231 | ||||||||
\(765\) | − | 6.76319i | − | 0.244524i | ||||||
\(766\) | −11.2055 | −0.404871 | ||||||||
\(767\) | − | 12.2989i | − | 0.444088i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 9.12167 | 0.328936 | 0.164468 | − | 0.986382i | \(-0.447409\pi\) | ||||
0.164468 | + | 0.986382i | \(0.447409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.57023 | −0.272635 | ||||||||
\(772\) | − | 7.69156i | − | 0.276825i | ||||||
\(773\) | − | 29.4632i | − | 1.05972i | −0.848086 | − | 0.529859i | \(-0.822245\pi\) | ||
0.848086 | − | 0.529859i | \(-0.177755\pi\) | |||||||
\(774\) | −5.62214 | −0.202084 | ||||||||
\(775\) | 8.56958i | 0.307829i | ||||||||
\(776\) | −4.03611 | −0.144888 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 7.21388i | − | 0.258630i | ||||||
\(779\) | 3.70022 | 0.132574 | ||||||||
\(780\) | −6.67364 | −0.238955 | ||||||||
\(781\) | 17.2684 | + | 10.2252i | 0.617913 | + | 0.365888i | ||||
\(782\) | 7.99930i | 0.286054i | ||||||||
\(783\) | −6.51317 | −0.232762 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.2880 | 0.617036 | ||||||||
\(786\) | −14.5316 | −0.518324 | ||||||||
\(787\) | −4.31295 | −0.153740 | −0.0768700 | − | 0.997041i | \(-0.524493\pi\) | ||||
−0.0768700 | + | 0.997041i | \(0.524493\pi\) | |||||||
\(788\) | 21.1678i | 0.754073i | ||||||||
\(789\) | 26.3900 | 0.939511 | ||||||||
\(790\) | 22.1427i | 0.787801i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.68986 | + | 2.85384i | −0.0600464 | + | 0.101407i | ||||
\(793\) | −13.3920 | −0.475565 | ||||||||
\(794\) | −19.4918 | −0.691737 | ||||||||
\(795\) | −18.3526 | −0.650900 | ||||||||
\(796\) | 23.2150i | 0.822832i | ||||||||
\(797\) | − | 37.1341i | − | 1.31536i | −0.753299 | − | 0.657679i | \(-0.771538\pi\) | ||
0.753299 | − | 0.657679i | \(-0.228462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.00448i | 0.247801i | ||||||||
\(800\) | 2.11553i | 0.0747952i | ||||||||
\(801\) | − | 11.2019i | − | 0.395801i | ||||||
\(802\) | 13.0461i | 0.460674i | ||||||||
\(803\) | 27.5064 | + | 16.2875i | 0.970678 | + | 0.574772i | ||||
\(804\) | 7.33059i | 0.258530i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.1345 | −0.356971 | ||||||||
\(807\) | 5.00096 | 0.176042 | ||||||||
\(808\) | 7.27104i | 0.255794i | ||||||||
\(809\) | − | 2.82043i | − | 0.0991610i | −0.998770 | − | 0.0495805i | \(-0.984212\pi\) | ||
0.998770 | − | 0.0495805i | \(-0.0157884\pi\) | |||||||
\(810\) | 2.66749 | 0.0937262 | ||||||||
\(811\) | 26.7441 | 0.939114 | 0.469557 | − | 0.882902i | \(-0.344414\pi\) | ||||
0.469557 | + | 0.882902i | \(0.344414\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.1218i | 0.986275i | ||||||||
\(814\) | −4.30821 | + | 7.27572i | −0.151003 | + | 0.255014i | ||||
\(815\) | 4.96522i | 0.173924i | ||||||||
\(816\) | − | 2.53541i | − | 0.0887571i | ||||||
\(817\) | − | 7.84134i | − | 0.274334i | ||||||
\(818\) | − | 33.8668i | − | 1.18413i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.07690i | 0.247136i | ||||||||
\(821\) | − | 47.3792i | − | 1.65355i | −0.562535 | − | 0.826773i | \(-0.690174\pi\) | ||
0.562535 | − | 0.826773i | \(-0.309826\pi\) | |||||||
\(822\) | 10.1601 | 0.354376 | ||||||||
\(823\) | 17.9168 | 0.624542 | 0.312271 | − | 0.949993i | \(-0.398910\pi\) | ||||
0.312271 | + | 0.949993i | \(0.398910\pi\) | |||||||
\(824\) | −4.71286 | −0.164180 | ||||||||
\(825\) | 3.57494 | − | 6.03737i | 0.124463 | − | 0.210194i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 54.3119i | − | 1.88861i | −0.329072 | − | 0.944305i | \(-0.606736\pi\) | ||
0.329072 | − | 0.944305i | \(-0.393264\pi\) | |||||||
\(828\) | −3.15503 | −0.109645 | ||||||||
\(829\) | 5.77320i | 0.200512i | 0.994962 | + | 0.100256i | \(0.0319661\pi\) | ||||
−0.994962 | + | 0.100256i | \(0.968034\pi\) | |||||||
\(830\) | −38.5528 | −1.33819 | ||||||||
\(831\) | 4.15631 | 0.144181 | ||||||||
\(832\) | −2.50184 | −0.0867356 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.15019 | 0.0744551 | ||||||||
\(835\) | − | 27.9992i | − | 0.968953i | ||||||
\(836\) | −3.98032 | − | 2.35688i | −0.137662 | − | 0.0815145i | ||||
\(837\) | 4.05080 | 0.140016 | ||||||||
\(838\) | 12.9005 | 0.445642 | ||||||||
\(839\) | 36.9556i | 1.27585i | 0.770099 | + | 0.637925i | \(0.220207\pi\) | ||||
−0.770099 | + | 0.637925i | \(0.779793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4214 | −0.462807 | ||||||||
\(842\) | 7.05921i | 0.243276i | ||||||||
\(843\) | 30.6193 | 1.05459 | ||||||||
\(844\) | 14.1204i | 0.486044i | ||||||||
\(845\) | − | 17.9811i | − | 0.618567i | ||||||
\(846\) | −2.76266 | −0.0949822 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.88010 | −0.236263 | ||||||||
\(849\) | − | 5.38804i | − | 0.184917i | ||||||
\(850\) | 5.36373i | 0.183974i | ||||||||
\(851\) | −8.04360 | −0.275731 | ||||||||
\(852\) | − | 6.05096i | − | 0.207302i | ||||||
\(853\) | −30.9159 | −1.05854 | −0.529269 | − | 0.848454i | \(-0.677534\pi\) | ||||
−0.529269 | + | 0.848454i | \(0.677534\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.72042i | 0.127236i | ||||||||
\(856\) | −19.6228 | −0.670695 | ||||||||
\(857\) | −19.5344 | −0.667284 | −0.333642 | − | 0.942700i | \(-0.608278\pi\) | ||||
−0.333642 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(858\) | 7.13984 | + | 4.22775i | 0.243750 | + | 0.144333i | ||||
\(859\) | − | 23.0367i | − | 0.786002i | −0.919538 | − | 0.393001i | \(-0.871437\pi\) | ||
0.919538 | − | 0.393001i | \(-0.128563\pi\) | |||||||
\(860\) | 14.9970 | 0.511394 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.54328 | −0.120685 | ||||||||
\(863\) | 17.4076 | 0.592562 | 0.296281 | − | 0.955101i | \(-0.404253\pi\) | ||||
0.296281 | + | 0.955101i | \(0.404253\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 20.5967i | 0.700308i | ||||||||
\(866\) | 16.2125 | 0.550922 | ||||||||
\(867\) | 10.5717i | 0.359034i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.0274 | − | 23.6895i | 0.475846 | − | 0.803611i | ||||
\(870\) | 17.3739 | 0.589029 | ||||||||
\(871\) | 18.3400 | 0.621426 | ||||||||
\(872\) | −15.1803 | −0.514070 | ||||||||
\(873\) | − | 4.03611i | − | 0.136602i | ||||||
\(874\) | − | 4.40040i | − | 0.148846i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 9.63838i | − | 0.325651i | ||||||
\(877\) | 7.81136i | 0.263771i | 0.991265 | + | 0.131885i | \(0.0421031\pi\) | ||||
−0.991265 | + | 0.131885i | \(0.957897\pi\) | |||||||
\(878\) | − | 24.8095i | − | 0.837281i | ||||||
\(879\) | 4.27517i | 0.144198i | ||||||||
\(880\) | 4.50768 | − | 7.61259i | 0.151954 | − | 0.256621i | ||||
\(881\) | − | 27.9273i | − | 0.940895i | −0.882428 | − | 0.470448i | \(-0.844092\pi\) | ||
0.882428 | − | 0.470448i | \(-0.155908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.2909 | 1.05302 | 0.526511 | − | 0.850168i | \(-0.323500\pi\) | ||||
0.526511 | + | 0.850168i | \(0.323500\pi\) | |||||||
\(884\) | −6.34319 | −0.213344 | ||||||||
\(885\) | − | 13.1133i | − | 0.440797i | ||||||
\(886\) | 36.3380i | 1.22080i | ||||||||
\(887\) | 44.7264 | 1.50177 | 0.750883 | − | 0.660435i | \(-0.229628\pi\) | ||||
0.750883 | + | 0.660435i | \(0.229628\pi\) | |||||||
\(888\) | 2.54945 | 0.0855540 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 29.8811i | 1.00162i | ||||||||
\(891\) | −2.85384 | − | 1.68986i | −0.0956071 | − | 0.0566123i | ||||
\(892\) | 12.4044i | 0.415329i | ||||||||
\(893\) | − | 3.85315i | − | 0.128941i | ||||||
\(894\) | − | 18.1396i | − | 0.606680i | ||||||
\(895\) | − | 54.6399i | − | 1.82641i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.89338i | 0.263552i | ||||||||
\(898\) | 27.6858i | 0.923887i | ||||||||
\(899\) | 26.3836 | 0.879942 | ||||||||
\(900\) | −2.11553 | −0.0705176 | ||||||||
\(901\) | −17.4439 | −0.581139 | ||||||||
\(902\) | 4.48321 | − | 7.57127i | 0.149275 | − | 0.252096i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 4.06642i | − | 0.135247i | ||||||
\(905\) | −60.6403 | −2.01575 | ||||||||
\(906\) | 1.69350i | 0.0562628i | ||||||||
\(907\) | −30.2825 | −1.00552 | −0.502758 | − | 0.864427i | \(-0.667681\pi\) | ||||
−0.502758 | + | 0.864427i | \(0.667681\pi\) | |||||||
\(908\) | 15.2148 | 0.504923 | ||||||||
\(909\) | −7.27104 | −0.241165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.7787 | −0.887217 | −0.443609 | − | 0.896221i | \(-0.646302\pi\) | ||||
−0.443609 | + | 0.896221i | \(0.646302\pi\) | |||||||
\(912\) | 1.39472i | 0.0461839i | ||||||||
\(913\) | 41.2459 | + | 24.4232i | 1.36504 | + | 0.808288i | ||||
\(914\) | −20.5828 | −0.680818 | ||||||||
\(915\) | −14.2788 | −0.472042 | ||||||||
\(916\) | 19.2052i | 0.634557i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.53541 | 0.0836810 | ||||||||
\(919\) | − | 18.0347i | − | 0.594909i | −0.954736 | − | 0.297455i | \(-0.903862\pi\) | ||
0.954736 | − | 0.297455i | \(-0.0961377\pi\) | |||||||
\(920\) | 8.41603 | 0.277468 | ||||||||
\(921\) | − | 4.80816i | − | 0.158434i | ||||||
\(922\) | 21.4634i | 0.706858i | ||||||||
\(923\) | −15.1385 | −0.498290 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.39344 | −0.177335 | ||||||||
\(926\) | 5.62818i | 0.184953i | ||||||||
\(927\) | − | 4.71286i | − | 0.154790i | ||||||
\(928\) | 6.51317 | 0.213805 | ||||||||
\(929\) | − | 19.9369i | − | 0.654108i | −0.945006 | − | 0.327054i | \(-0.893944\pi\) | ||
0.945006 | − | 0.327054i | \(-0.106056\pi\) | |||||||
\(930\) | −10.8055 | −0.354326 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 11.5244i | − | 0.377494i | ||||||
\(933\) | −28.8146 | −0.943348 | ||||||||
\(934\) | 14.8084 | 0.484546 | ||||||||
\(935\) | 11.4288 | − | 19.3010i | 0.373762 | − | 0.631212i | ||||
\(936\) | − | 2.50184i | − | 0.0817752i | ||||||
\(937\) | 34.1520 | 1.11570 | 0.557849 | − | 0.829943i | \(-0.311627\pi\) | ||||
0.557849 | + | 0.829943i | \(0.311627\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.6235 | −0.705657 | ||||||||
\(940\) | 7.36938 | 0.240363 | ||||||||
\(941\) | 16.9067 | 0.551142 | 0.275571 | − | 0.961281i | \(-0.411133\pi\) | ||||
0.275571 | + | 0.961281i | \(0.411133\pi\) | |||||||
\(942\) | 6.48100i | 0.211162i | ||||||||
\(943\) | 8.37034 | 0.272576 | ||||||||
\(944\) | − | 4.91595i | − | 0.160000i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0447 | − | 9.50061i | −0.521657 | − | 0.308891i | ||||
\(947\) | 27.4767 | 0.892872 | 0.446436 | − | 0.894815i | \(-0.352693\pi\) | ||||
0.446436 | + | 0.894815i | \(0.352693\pi\) | |||||||
\(948\) | −8.30093 | −0.269602 | ||||||||
\(949\) | −24.1137 | −0.782763 | ||||||||
\(950\) | − | 2.95058i | − | 0.0957293i | ||||||
\(951\) | − | 8.45799i | − | 0.274269i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21.4315i | − | 0.694234i | −0.937822 | − | 0.347117i | \(-0.887161\pi\) | ||
0.937822 | − | 0.347117i | \(-0.112839\pi\) | |||||||
\(954\) | − | 6.88010i | − | 0.222751i | ||||||
\(955\) | 58.0433i | 1.87824i | ||||||||
\(956\) | 10.3520i | 0.334807i | ||||||||
\(957\) | −18.5875 | − | 11.0063i | −0.600850 | − | 0.355784i | ||||
\(958\) | 27.8523i | 0.899868i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.66749 | −0.0860930 | ||||||||
\(961\) | 14.5910 | 0.470677 | ||||||||
\(962\) | − | 6.37832i | − | 0.205645i | ||||||
\(963\) | − | 19.6228i | − | 0.632337i | ||||||
\(964\) | −25.1255 | −0.809238 | ||||||||
\(965\) | −20.5172 | −0.660472 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.7348i | 1.69584i | 0.530126 | + | 0.847919i | \(0.322145\pi\) | ||||
−0.530126 | + | 0.847919i | \(0.677855\pi\) | |||||||
\(968\) | −9.64515 | + | 5.28877i | −0.310007 | + | 0.169988i | ||||
\(969\) | 3.53620i | 0.113599i | ||||||||
\(970\) | 10.7663i | 0.345685i | ||||||||
\(971\) | 33.9902i | 1.09080i | 0.838177 | + | 0.545398i | \(0.183622\pi\) | ||||
−0.838177 | + | 0.545398i | \(0.816378\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.4540i | 0.623346i | ||||||||
\(975\) | 5.29271i | 0.169502i | ||||||||
\(976\) | −5.35288 | −0.171342 | ||||||||
\(977\) | 8.79178 | 0.281274 | 0.140637 | − | 0.990061i | \(-0.455085\pi\) | ||||
0.140637 | + | 0.990061i | \(0.455085\pi\) | |||||||
\(978\) | −1.86138 | −0.0595204 | ||||||||
\(979\) | 18.9296 | − | 31.9685i | 0.604994 | − | 1.02172i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 15.1803i | − | 0.484669i | ||||||
\(982\) | −41.7607 | −1.33264 | ||||||||
\(983\) | − | 25.6832i | − | 0.819167i | −0.912273 | − | 0.409583i | \(-0.865674\pi\) | ||
0.912273 | − | 0.409583i | \(-0.134326\pi\) | |||||||
\(984\) | −2.65301 | −0.0845750 | ||||||||
\(985\) | 56.4651 | 1.79913 | ||||||||
\(986\) | 16.5136 | 0.525899 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.48938 | 0.111012 | ||||||||
\(989\) | − | 17.7380i | − | 0.564036i | ||||||
\(990\) | 7.61259 | + | 4.50768i | 0.241944 | + | 0.143264i | ||||
\(991\) | 22.4094 | 0.711858 | 0.355929 | − | 0.934513i | \(-0.384165\pi\) | ||||
0.355929 | + | 0.934513i | \(0.384165\pi\) | |||||||
\(992\) | −4.05080 | −0.128613 | ||||||||
\(993\) | − | 2.57208i | − | 0.0816226i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61.9258 | 1.96318 | ||||||||
\(996\) | − | 14.4528i | − | 0.457954i | ||||||
\(997\) | 19.6542 | 0.622454 | 0.311227 | − | 0.950336i | \(-0.399260\pi\) | ||||
0.311227 | + | 0.950336i | \(0.399260\pi\) | |||||||
\(998\) | − | 13.9993i | − | 0.443140i | ||||||
\(999\) | 2.54945i | 0.0806611i |
(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 | 3234.2.e.c.2155.10 | ✓ | 24 | |
7.6 | odd | 2 | 3234.2.e.d.2155.3 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.d.2155.22 | yes | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.c.2155.15 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.10 | ✓ | 24 | 1.1 | even | 1 | trivial | |
3234.2.e.c.2155.15 | yes | 24 | 77.76 | even | 2 | inner | |
3234.2.e.d.2155.3 | yes | 24 | 7.6 | odd | 2 | ||
3234.2.e.d.2155.22 | yes | 24 | 11.10 | odd | 2 |