Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.8 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.27 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.676225 | − | 2.13137i | −0.302417 | − | 0.953176i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.23231i | − | 1.59966i | −0.600225 | − | 0.799831i | \(-0.704922\pi\) | ||
0.600225 | − | 0.799831i | \(-0.295078\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.39022 | −0.419167 | −0.209584 | − | 0.977791i | \(-0.567211\pi\) | ||||
−0.209584 | + | 0.977791i | \(0.567211\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.36038i | − | 1.76405i | −0.471201 | − | 0.882026i | \(-0.656179\pi\) | ||
0.471201 | − | 0.882026i | \(-0.343821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.13137 | + | 0.676225i | −0.550316 | + | 0.174601i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.10855i | 0.996469i | 0.867042 | + | 0.498234i | \(0.166018\pi\) | ||||
−0.867042 | + | 0.498234i | \(0.833982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.15323 | −1.18223 | −0.591116 | − | 0.806587i | \(-0.701312\pi\) | ||||
−0.591116 | + | 0.806587i | \(0.701312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.23231 | −0.923566 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.91335i | 0.398962i | 0.979902 | + | 0.199481i | \(0.0639256\pi\) | ||||
−0.979902 | + | 0.199481i | \(0.936074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.08544 | + | 2.88257i | −0.817088 | + | 0.576513i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.40553 | −1.00378 | −0.501891 | − | 0.864931i | \(-0.667362\pi\) | ||||
−0.501891 | + | 0.864931i | \(0.667362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.479723 | 0.0861608 | 0.0430804 | − | 0.999072i | \(-0.486283\pi\) | ||||
0.0430804 | + | 0.999072i | \(0.486283\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.39022i | 0.242006i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.02060 | + | 2.86199i | −1.52476 | + | 0.483765i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.52485i | − | 0.415083i | −0.978226 | − | 0.207541i | \(-0.933454\pi\) | ||
0.978226 | − | 0.207541i | \(-0.0665462\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.36038 | −1.01848 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14785 | 0.647785 | 0.323893 | − | 0.946094i | \(-0.395008\pi\) | ||||
0.323893 | + | 0.946094i | \(0.395008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.604550i | − | 0.0921930i | −0.998937 | − | 0.0460965i | \(-0.985322\pi\) | ||
0.998937 | − | 0.0460965i | \(-0.0146782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.676225 | + | 2.13137i | 0.100806 | + | 0.317725i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.216591i | 0.0315931i | 0.999875 | + | 0.0157965i | \(0.00502841\pi\) | ||||
−0.999875 | + | 0.0157965i | \(0.994972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.9124 | −1.55892 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.10855 | 0.575312 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.89586i | − | 0.397777i | −0.980022 | − | 0.198889i | \(-0.936267\pi\) | ||
0.980022 | − | 0.198889i | \(-0.0637332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.940102 | + | 2.96307i | 0.126763 | + | 0.399540i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.15323i | 0.682562i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.893364 | −0.116306 | −0.0581530 | − | 0.998308i | \(-0.518521\pi\) | ||||
−0.0581530 | + | 0.998308i | \(0.518521\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.90540 | 0.371998 | 0.185999 | − | 0.982550i | \(-0.440448\pi\) | ||||
0.185999 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.23231i | 0.533221i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.5563 | + | 4.30105i | −1.68145 | + | 0.533479i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.91335 | 0.230341 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.26764 | 0.981188 | 0.490594 | − | 0.871388i | \(-0.336780\pi\) | ||||
0.490594 | + | 0.871388i | \(0.336780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.6582i | − | 1.48153i | −0.671764 | − | 0.740765i | \(-0.734463\pi\) | ||
0.671764 | − | 0.740765i | \(-0.265537\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.88257 | + | 4.08544i | 0.332850 | + | 0.471746i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.88384i | 0.670526i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7111 | 1.54262 | 0.771308 | − | 0.636462i | \(-0.219603\pi\) | ||||
0.771308 | + | 0.636462i | \(0.219603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0898i | 1.32703i | 0.748163 | + | 0.663514i | \(0.230936\pi\) | ||||
−0.748163 | + | 0.663514i | \(0.769064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.75681 | − | 2.77830i | 0.949810 | − | 0.301349i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.40553i | 0.579534i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.0123 | 1.80330 | 0.901648 | − | 0.432471i | \(-0.142358\pi\) | ||||
0.901648 | + | 0.432471i | \(0.142358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.9191 | −2.82189 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.479723i | − | 0.0497449i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.48474 | + | 10.9834i | 0.357527 | + | 1.12687i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.636187i | 0.0645950i | 0.999478 | + | 0.0322975i | \(0.0102824\pi\) | ||||
−0.999478 | + | 0.0322975i | \(0.989718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.39022 | 0.139722 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.71282 | −0.170432 | −0.0852162 | − | 0.996362i | \(-0.527158\pi\) | ||||
−0.0852162 | + | 0.996362i | \(0.527158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.41050i | 0.631645i | 0.948818 | + | 0.315823i | \(0.102280\pi\) | ||||
−0.948818 | + | 0.315823i | \(0.897720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.86199 | + | 9.02060i | 0.279302 | + | 0.880320i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.9246i | − | 1.82951i | −0.404008 | − | 0.914755i | \(-0.632383\pi\) | ||
0.404008 | − | 0.914755i | \(-0.367617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.89694 | 0.469042 | 0.234521 | − | 0.972111i | \(-0.424648\pi\) | ||||
0.234521 | + | 0.972111i | \(0.424648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.52485 | −0.239648 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.88818i | − | 0.271697i | −0.990730 | − | 0.135848i | \(-0.956624\pi\) | ||
0.990730 | − | 0.135848i | \(-0.0433760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.07806 | − | 1.29386i | 0.380281 | − | 0.120653i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.36038i | 0.588017i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.3886 | 1.59401 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.06729 | −0.824299 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.14785i | − | 0.373999i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.90648 | + | 6.75830i | 0.796620 | + | 0.604481i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.09910i | 0.275001i | 0.990502 | + | 0.137500i | \(0.0439068\pi\) | ||||
−0.990502 | + | 0.137500i | \(0.956093\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.604550 | −0.0532276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.52174 | 0.220326 | 0.110163 | − | 0.993914i | \(-0.464863\pi\) | ||||
0.110163 | + | 0.993914i | \(0.464863\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.8101i | 1.89117i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.13137 | − | 0.676225i | 0.183439 | − | 0.0582002i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.3830i | − | 0.887077i | −0.896255 | − | 0.443538i | \(-0.853723\pi\) | ||
0.896255 | − | 0.443538i | \(-0.146277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.7427 | −1.25046 | −0.625230 | − | 0.780440i | \(-0.714995\pi\) | ||||
−0.625230 | + | 0.780440i | \(0.714995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.216591 | 0.0182403 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.84233i | 0.739433i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.65536 | + | 11.5212i | 0.303561 | + | 0.956781i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9124i | 0.900044i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.09056 | −0.662804 | −0.331402 | − | 0.943490i | \(-0.607522\pi\) | ||||
−0.331402 | + | 0.943490i | \(0.607522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.26776 | 0.591442 | 0.295721 | − | 0.955274i | \(-0.404440\pi\) | ||||
0.295721 | + | 0.955274i | \(0.404440\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.10855i | − | 0.332156i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.324401 | − | 1.02246i | −0.0260565 | − | 0.0821263i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.9836i | 1.59486i | 0.603410 | + | 0.797431i | \(0.293808\pi\) | ||||
−0.603410 | + | 0.797431i | \(0.706192\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.89586 | −0.229657 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.09791 | 0.638205 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.3663i | − | 1.04693i | −0.852048 | − | 0.523464i | \(-0.824639\pi\) | ||
0.852048 | − | 0.523464i | \(-0.175361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.96307 | − | 0.940102i | 0.230674 | − | 0.0731868i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4531i | 0.808886i | 0.914563 | + | 0.404443i | \(0.132535\pi\) | ||||
−0.914563 | + | 0.404443i | \(0.867465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.4544 | −2.11188 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.15323 | 0.394077 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 17.7535i | − | 1.34977i | −0.737922 | − | 0.674886i | \(-0.764193\pi\) | ||
0.737922 | − | 0.674886i | \(-0.235807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.1999 | + | 17.2908i | 0.922227 | + | 1.30707i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.893364i | 0.0671493i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.2777 | −1.21665 | −0.608327 | − | 0.793687i | \(-0.708159\pi\) | ||||
−0.608327 | + | 0.793687i | \(0.708159\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6664 | −1.31314 | −0.656568 | − | 0.754267i | \(-0.727993\pi\) | ||||
−0.656568 | + | 0.754267i | \(0.727993\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.90540i | − | 0.214773i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.38138 | + | 1.70737i | −0.395647 | + | 0.125528i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.71178i | − | 0.417687i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.23231 | 0.307855 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0200 | 1.44859 | 0.724297 | − | 0.689488i | \(-0.242164\pi\) | ||||
0.724297 | + | 0.689488i | \(0.242164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15297i | 0.0829923i | 0.999139 | + | 0.0414962i | \(0.0132124\pi\) | ||||
−0.999139 | + | 0.0414962i | \(0.986788\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.30105 | + | 13.5563i | 0.308004 | + | 0.970786i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.53115i | − | 0.251584i | −0.992057 | − | 0.125792i | \(-0.959853\pi\) | ||
0.992057 | − | 0.125792i | \(-0.0401472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.63461 | −0.257651 | −0.128825 | − | 0.991667i | \(-0.541121\pi\) | ||||
−0.128825 | + | 0.991667i | \(0.541121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.8779i | 1.60571i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.80488 | − | 8.84058i | −0.195901 | − | 0.617453i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.91335i | − | 0.132987i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.16412 | 0.495553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9563 | 1.37385 | 0.686925 | − | 0.726728i | \(-0.258960\pi\) | ||||
0.686925 | + | 0.726728i | \(0.258960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.26764i | − | 0.566489i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.28852 | + | 0.408812i | −0.0878761 | + | 0.0278807i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.03034i | − | 0.137828i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.6582 | −0.855361 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.1319 | 1.75782 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2283i | 1.42155i | 0.703417 | + | 0.710777i | \(0.251657\pi\) | ||||
−0.703417 | + | 0.710777i | \(0.748343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.08544 | − | 2.88257i | 0.272363 | − | 0.192171i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.5637i | − | 0.767507i | −0.923436 | − | 0.383754i | \(-0.874631\pi\) | ||
0.923436 | − | 0.383754i | \(-0.125369\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9167 | −0.853560 | −0.426780 | − | 0.904355i | \(-0.640352\pi\) | ||||
−0.426780 | + | 0.904355i | \(0.640352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.88384 | 0.387128 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9294i | 1.04357i | 0.853078 | + | 0.521784i | \(0.174733\pi\) | ||||
−0.853078 | + | 0.521784i | \(0.825267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.461635 | − | 0.146464i | 0.0301138 | − | 0.00955429i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.7111i | − | 0.890629i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.80764 | −0.634403 | −0.317202 | − | 0.948358i | \(-0.602743\pi\) | ||||
−0.317202 | + | 0.948358i | \(0.602743\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.9392 | −1.21998 | −0.609989 | − | 0.792410i | \(-0.708826\pi\) | ||||
−0.609989 | + | 0.792410i | \(0.708826\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.37927 | + | 23.2584i | 0.471444 | + | 1.48593i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.7765i | 2.08552i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0898 | 0.766160 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4401 | −0.848334 | −0.424167 | − | 0.905584i | \(-0.639433\pi\) | ||||
−0.424167 | + | 0.905584i | \(0.639433\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.65998i | − | 0.167232i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.77830 | − | 8.75681i | −0.173984 | − | 0.548373i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.47817i | − | 0.404097i | −0.979376 | − | 0.202049i | \(-0.935240\pi\) | ||
0.979376 | − | 0.202049i | \(-0.0647599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6860 | −0.663993 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.40553 | 0.334594 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.0096i | 1.29551i | 0.761850 | + | 0.647753i | \(0.224291\pi\) | ||||
−0.761850 | + | 0.647753i | \(0.775709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.17214 | + | 1.95825i | −0.379151 | + | 0.120295i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 17.0123i | − | 1.04113i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.6527 | −0.893393 | −0.446697 | − | 0.894686i | \(-0.647400\pi\) | ||||
−0.446697 | + | 0.894686i | \(0.647400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3153 | −0.930337 | −0.465169 | − | 0.885222i | \(-0.654006\pi\) | ||||
−0.465169 | + | 0.885222i | \(0.654006\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.9191i | 1.62922i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.67966 | − | 4.00740i | 0.342496 | − | 0.241655i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.6763i | − | 0.881815i | −0.897553 | − | 0.440907i | \(-0.854657\pi\) | ||
0.897553 | − | 0.440907i | \(-0.145343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.479723 | −0.0287203 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9400 | 1.01056 | 0.505278 | − | 0.862957i | \(-0.331390\pi\) | ||||
0.505278 | + | 0.862957i | \(0.331390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.7694i | 1.05628i | 0.849158 | + | 0.528139i | \(0.177110\pi\) | ||||
−0.849158 | + | 0.528139i | \(0.822890\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.9834 | − | 3.48474i | 0.650602 | − | 0.206418i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 17.5550i | − | 1.03624i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.119848 | 0.00704986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.636187 | 0.0372939 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.4037i | − | 0.724630i | −0.932056 | − | 0.362315i | \(-0.881986\pi\) | ||
0.932056 | − | 0.362315i | \(-0.118014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.604115 | + | 1.90408i | 0.0351729 | + | 0.110860i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.39022i | − | 0.0806687i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.1697 | 0.703790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.55864 | −0.147478 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.71282i | 0.0983992i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.96470 | − | 6.19246i | −0.112499 | − | 0.354579i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.43370i | 0.138899i | 0.997585 | + | 0.0694494i | \(0.0221242\pi\) | ||||
−0.997585 | + | 0.0694494i | \(0.977876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.41050 | 0.364681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.6408 | −0.886909 | −0.443455 | − | 0.896297i | \(-0.646247\pi\) | ||||
−0.443455 | + | 0.896297i | \(0.646247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 34.9072i | − | 1.97307i | −0.163538 | − | 0.986537i | \(-0.552290\pi\) | ||
0.163538 | − | 0.986537i | \(-0.447710\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.02060 | − | 2.86199i | 0.508253 | − | 0.161255i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.84170i | − | 0.552765i | −0.961048 | − | 0.276382i | \(-0.910864\pi\) | ||
0.961048 | − | 0.276382i | \(-0.0891356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.51488 | 0.420752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.9246 | −1.05627 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 21.1723i | − | 1.17806i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.3342 | + | 25.9849i | 1.01700 | + | 1.44139i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.89694i | − | 0.270802i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.916682 | 0.0505383 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.9414 | 0.931182 | 0.465591 | − | 0.885000i | \(-0.345842\pi\) | ||||
0.465591 | + | 0.885000i | \(0.345842\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.52485i | 0.138361i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.13137 | + | 0.676225i | −0.116449 | + | 0.0369461i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6820i | 1.50793i | 0.656913 | + | 0.753966i | \(0.271862\pi\) | ||||
−0.656913 | + | 0.753966i | \(0.728138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.88818 | −0.156864 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.666920 | −0.0361158 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5587i | 0.894086i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.29386 | − | 4.07806i | −0.0696590 | − | 0.219555i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.2355i | 1.62312i | 0.584266 | + | 0.811562i | \(0.301382\pi\) | ||||
−0.584266 | + | 0.811562i | \(0.698618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.3093 | −0.819486 | −0.409743 | − | 0.912201i | \(-0.634382\pi\) | ||||
−0.409743 | + | 0.912201i | \(0.634382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.36038 | 0.339492 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 15.8352i | − | 0.842824i | −0.906869 | − | 0.421412i | \(-0.861535\pi\) | ||
0.906869 | − | 0.421412i | \(-0.138465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.59079 | − | 17.6214i | −0.296728 | − | 0.935245i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 17.3886i | − | 0.920305i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.6388 | 0.561496 | 0.280748 | − | 0.959782i | \(-0.409417\pi\) | ||||
0.280748 | + | 0.959782i | \(0.409417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.55578 | 0.397673 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.06729i | 0.475909i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.9792 | + | 8.55979i | −1.41216 | + | 0.448040i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 21.5187i | − | 1.12327i | −0.827386 | − | 0.561633i | \(-0.810173\pi\) | ||
0.827386 | − | 0.561633i | \(-0.189827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.14785 | −0.215928 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.2562 | −0.636309 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.9322i | 1.49805i | 0.662540 | + | 0.749027i | \(0.269479\pi\) | ||||
−0.662540 | + | 0.749027i | \(0.730521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.75830 | − | 8.90648i | 0.348997 | − | 0.459929i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.3812i | 1.77072i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.3578 | −0.942976 | −0.471488 | − | 0.881873i | \(-0.656283\pi\) | ||||
−0.471488 | + | 0.881873i | \(0.656283\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.09910 | 0.158772 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.14772i | 0.314134i | 0.987588 | + | 0.157067i | \(0.0502039\pi\) | ||||
−0.987588 | + | 0.157067i | \(0.949796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.5406 | − | 3.97880i | 0.639129 | − | 0.202778i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.604550i | 0.0307310i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.1069 | −0.512439 | −0.256219 | − | 0.966619i | \(-0.582477\pi\) | ||||
−0.256219 | + | 0.966619i | \(0.582477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.86111 | −0.397553 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.52174i | − | 0.127205i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.27177 | − | 29.2233i | −0.466513 | − | 1.47038i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.09727i | 0.356202i | 0.984012 | + | 0.178101i | \(0.0569953\pi\) | ||||
−0.984012 | + | 0.178101i | \(0.943005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.8101 | 1.09187 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.82791 | 0.241094 | 0.120547 | − | 0.992708i | \(-0.461535\pi\) | ||||
0.120547 | + | 0.992708i | \(0.461535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.05122i | − | 0.151992i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.676225 | − | 2.13137i | −0.0336019 | − | 0.105908i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.51010i | 0.173989i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.0608 | −1.68420 | −0.842098 | − | 0.539324i | \(-0.818680\pi\) | ||||
−0.842098 | + | 0.539324i | \(0.818680\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3830 | −0.512154 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.78099i | 0.186050i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.7678 | − | 8.17543i | 1.26489 | − | 0.401316i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.7427i | 0.721954i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.2974 | −1.48013 | −0.740063 | − | 0.672538i | \(-0.765204\pi\) | ||||
−0.740063 | + | 0.672538i | \(0.765204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6514 | −0.665327 | −0.332663 | − | 0.943046i | \(-0.607947\pi\) | ||||
−0.332663 | + | 0.943046i | \(0.607947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.216591i | − | 0.0105310i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8432 | − | 16.7852i | −0.574477 | − | 0.814203i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 12.2965i | − | 0.595071i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.84233 | 0.426912 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.97781 | −0.239773 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.9998i | − | 1.44170i | −0.693093 | − | 0.720848i | \(-0.743752\pi\) | ||
0.693093 | − | 0.720848i | \(-0.256248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.5212 | − | 3.65536i | 0.552398 | − | 0.175261i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.85996i | − | 0.471666i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.68934 | −0.223810 | −0.111905 | − | 0.993719i | \(-0.535695\pi\) | ||||
−0.111905 | + | 0.993719i | \(0.535695\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.9124 | 0.519640 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.5335i | 1.16562i | 0.812608 | + | 0.582811i | \(0.198047\pi\) | ||||
−0.812608 | + | 0.582811i | \(0.801953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.5041 | − | 36.2594i | −0.545347 | − | 1.71886i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.09056i | 0.382670i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.8758 | −0.796417 | −0.398208 | − | 0.917295i | \(-0.630368\pi\) | ||||
−0.398208 | + | 0.917295i | \(0.630368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.76642 | −0.271530 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.26776i | − | 0.341469i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.2034 | + | 57.3744i | 0.853387 | + | 2.68976i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4653i | 1.47188i | 0.677045 | + | 0.735942i | \(0.263260\pi\) | ||||
−0.677045 | + | 0.735942i | \(0.736740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.10855 | −0.191771 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7846 | 1.57350 | 0.786752 | − | 0.617270i | \(-0.211761\pi\) | ||||
0.786752 | + | 0.617270i | \(0.211761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.4179i | − | 0.995373i | −0.867357 | − | 0.497687i | \(-0.834183\pi\) | ||
0.867357 | − | 0.497687i | \(-0.165817\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.02246 | + | 0.324401i | −0.0474157 | + | 0.0150437i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.8173i | 1.24096i | 0.784224 | + | 0.620478i | \(0.213062\pi\) | ||||
−0.784224 | + | 0.620478i | \(0.786938\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.23231 | −0.195430 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.9836 | 0.920794 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.840457i | 0.0386443i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.0532 | − | 14.8545i | 0.965988 | − | 0.681572i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.89586i | 0.132592i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9878 | −0.776194 | −0.388097 | − | 0.921619i | \(-0.626867\pi\) | ||||
−0.388097 | + | 0.921619i | \(0.626867\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0590 | −0.732228 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 8.09791i | − | 0.368468i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35595 | − | 0.430205i | 0.0615704 | − | 0.0195346i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 39.5253i | − | 1.79106i | −0.444999 | − | 0.895531i | \(-0.646796\pi\) | ||
0.444999 | − | 0.895531i | \(-0.353204\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.3663 | −0.604445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0417 | −0.859339 | −0.429669 | − | 0.902986i | \(-0.641370\pi\) | ||||
−0.429669 | + | 0.902986i | \(0.641370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 22.2089i | − | 1.00024i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.940102 | − | 2.96307i | −0.0422544 | − | 0.133180i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 34.9912i | − | 1.56957i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3317 | −0.910170 | −0.455085 | − | 0.890448i | \(-0.650391\pi\) | ||||
−0.455085 | + | 0.890448i | \(0.650391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4531 | 0.467011 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.9475i | 1.46906i | 0.678578 | + | 0.734528i | \(0.262596\pi\) | ||||
−0.678578 | + | 0.734528i | \(0.737404\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.15825 | + | 3.65065i | 0.0515416 | + | 0.162452i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.4544i | 1.21929i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.7348 | 1.58392 | 0.791959 | − | 0.610574i | \(-0.209061\pi\) | ||||
0.791959 | + | 0.610574i | \(0.209061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.5734 | −2.36995 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.15323i | − | 0.227521i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.6631 | − | 4.33494i | 0.602069 | − | 0.191020i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.301110i | − | 0.0132428i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.7535 | −0.779292 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 44.8076 | 1.96305 | 0.981527 | − | 0.191322i | \(-0.0612774\pi\) | ||||
0.981527 | + | 0.191322i | \(0.0612774\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8543i | 0.605806i | 0.953021 | + | 0.302903i | \(0.0979558\pi\) | ||||
−0.953021 | + | 0.302903i | \(0.902044\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.2908 | − | 12.1999i | 0.754634 | − | 0.532448i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.97096i | 0.0858565i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.3391 | 0.840829 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.893364 | 0.0387687 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 26.3819i | − | 1.14273i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.3353 | + | 12.7973i | −1.74385 | + | 0.553275i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.2777i | 0.702435i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.1707 | 0.653449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.29139 | 0.141508 | 0.0707540 | − | 0.997494i | \(-0.477459\pi\) | ||||
0.0707540 | + | 0.997494i | \(0.477459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.6664i | 0.758140i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.31143 | − | 10.4372i | −0.141846 | − | 0.447079i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.38046i | 0.315566i | 0.987474 | + | 0.157783i | \(0.0504346\pi\) | ||||
−0.987474 | + | 0.157783i | \(0.949565\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.90540 | −0.123999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.8559 | 1.18670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 58.0295i | − | 2.46766i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.70737 | + | 5.38138i | 0.0724737 | + | 0.228427i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.83073i | 0.0775705i | 0.999248 | + | 0.0387852i | \(0.0123488\pi\) | ||||
−0.999248 | + | 0.0387852i | \(0.987651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.84517 | −0.162633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.71178 | −0.241152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4344i | 0.819063i | 0.912296 | + | 0.409532i | \(0.134308\pi\) | ||||
−0.912296 | + | 0.409532i | \(0.865692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.15576 | + | 1.95306i | −0.258975 | + | 0.0821657i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.23231i | − | 0.177740i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5151 | −0.608506 | −0.304253 | − | 0.952591i | \(-0.598407\pi\) | ||||
−0.304253 | + | 0.952591i | \(0.598407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3594 | −0.517225 | −0.258613 | − | 0.965981i | \(-0.583265\pi\) | ||||
−0.258613 | + | 0.965981i | \(0.583265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 20.0200i | − | 0.836346i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.51537 | − | 7.81690i | −0.230007 | − | 0.325987i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.1837i | − | 1.33983i | −0.742439 | − | 0.669913i | \(-0.766331\pi\) | ||
0.742439 | − | 0.669913i | \(-0.233669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.15297 | 0.0479157 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.1678 | 2.12280 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.02588i | 0.166735i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.5563 | − | 4.30105i | 0.560484 | − | 0.177826i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.8765i | 1.52206i | 0.648718 | + | 0.761029i | \(0.275305\pi\) | ||||
−0.648718 | + | 0.761029i | \(0.724695\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.47212 | −0.101862 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.53115 | −0.145252 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.4549i | − | 1.29170i | −0.763465 | − | 0.645849i | \(-0.776504\pi\) | ||
0.763465 | − | 0.645849i | \(-0.223496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7586 | − | 37.0616i | −0.482057 | − | 1.51938i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.63461i | 0.148755i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.68221 | 0.354746 | 0.177373 | − | 0.984144i | \(-0.443240\pi\) | ||||
0.177373 | + | 0.984144i | \(0.443240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1262 | 0.453848 | 0.226924 | − | 0.973913i | \(-0.427133\pi\) | ||||
0.226924 | + | 0.973913i | \(0.427133\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.13153 | + | 19.3257i | 0.249282 | + | 0.785702i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.8119i | 1.12885i | 0.825485 | + | 0.564424i | \(0.190902\pi\) | ||||
−0.825485 | + | 0.564424i | \(0.809098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.8779 | 0.927059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.37760 | 0.0557319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27.6331i | − | 1.11609i | −0.829811 | − | 0.558045i | \(-0.811552\pi\) | ||
0.829811 | − | 0.558045i | \(-0.188448\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.84058 | + | 2.80488i | −0.356487 | + | 0.113104i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.6017i | − | 0.708618i | −0.935128 | − | 0.354309i | \(-0.884716\pi\) | ||
0.935128 | − | 0.354309i | \(-0.115284\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8586 | −0.677604 | −0.338802 | − | 0.940858i | \(-0.610022\pi\) | ||||
−0.338802 | + | 0.940858i | \(0.610022\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.91335 | −0.0767803 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 72.0012i | − | 2.88467i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.38163 | − | 23.5531i | 0.335265 | − | 0.942124i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 7.16412i | − | 0.286108i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.3735 | 0.413617 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.7361 | 1.66149 | 0.830744 | − | 0.556654i | \(-0.187915\pi\) | ||||
0.830744 | + | 0.556654i | \(0.187915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 19.9563i | − | 0.793192i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.60532 | − | 2.09569i | 0.262124 | − | 0.0831649i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 69.4073i | 2.75002i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.26764 | −0.327063 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2358 | 0.483286 | 0.241643 | − | 0.970365i | \(-0.422314\pi\) | ||||
0.241643 | + | 0.970365i | \(0.422314\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.694878i | − | 0.0274033i | −0.999906 | − | 0.0137017i | \(-0.995638\pi\) | ||
0.999906 | − | 0.0137017i | \(-0.00436151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.408812 | + | 1.28852i | 0.0160969 | + | 0.0507353i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.15047i | 0.0845437i | 0.999106 | + | 0.0422719i | \(0.0134596\pi\) | ||||
−0.999106 | + | 0.0422719i | \(0.986540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.24197 | 0.0487517 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.03034 | −0.0795751 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.3611i | 1.38379i | 0.722000 | + | 0.691893i | \(0.243223\pi\) | ||||
−0.722000 | + | 0.691893i | \(0.756777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.70526 | − | 5.37475i | −0.0666302 | − | 0.210009i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.6582i | 0.493843i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.37707 | −0.209461 | −0.104730 | − | 0.994501i | \(-0.533398\pi\) | ||||
−0.104730 | + | 0.994501i | \(0.533398\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.5561 | 0.449481 | 0.224741 | − | 0.974419i | \(-0.427846\pi\) | ||||
0.224741 | + | 0.974419i | \(0.427846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 26.1319i | − | 1.01488i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 46.4852 | − | 14.7485i | 1.80262 | − | 0.571923i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.3427i | − | 0.400471i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.2283 | 0.820735 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.03914 | −0.155929 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.1408i | − | 0.583634i | −0.956474 | − | 0.291817i | \(-0.905740\pi\) | ||
0.956474 | − | 0.291817i | \(-0.0942598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.88257 | − | 4.08544i | −0.110950 | − | 0.157249i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 40.1536i | − | 1.54323i | −0.636092 | − | 0.771613i | \(-0.719450\pi\) | ||
0.636092 | − | 0.771613i | \(-0.280550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.69254 | 0.103330 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.5637 | −0.443121 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.1608i | 1.49844i | 0.662319 | + | 0.749222i | \(0.269573\pi\) | ||||
−0.662319 | + | 0.749222i | \(0.730427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.1299 | + | 7.02122i | −0.845540 | + | 0.268267i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.9167i | 0.492803i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.4188 | −0.701699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7016 | 1.39620 | 0.698098 | − | 0.716002i | \(-0.254030\pi\) | ||||
0.698098 | + | 0.716002i | \(0.254030\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 5.88384i | − | 0.223509i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.96939 | + | 31.4221i | 0.378161 | + | 1.19191i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.0416i | 0.645498i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9294 | 0.602504 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.1254 | −1.47775 | −0.738873 | − | 0.673844i | \(-0.764642\pi\) | ||||
−0.738873 | + | 0.673844i | \(0.764642\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.0111i | 0.490724i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.146464 | − | 0.461635i | −0.00551617 | − | 0.0173862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.24920i | 0.272634i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.88538 | 0.221030 | 0.110515 | − | 0.993874i | \(-0.464750\pi\) | ||||
0.110515 | + | 0.993874i | \(0.464750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.7111 | −0.514205 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.917880i | 0.0343749i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8462 | − | 5.97940i | 0.704809 | − | 0.223617i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.80764i | 0.366273i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.40620 | −0.313498 | −0.156749 | − | 0.987638i | \(-0.550101\pi\) | ||||
−0.156749 | + | 0.987638i | \(0.550101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.1312 | 1.01042 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9392i | 0.704355i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.0840 | − | 15.5818i | 0.820178 | − | 0.578694i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.9152i | 0.664439i | 0.943202 | + | 0.332220i | \(0.107797\pi\) | ||||
−0.943202 | + | 0.332220i | \(0.892203\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.48382 | 0.0918674 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.1553i | 0.818325i | 0.912462 | + | 0.409162i | \(0.134179\pi\) | ||||
−0.912462 | + | 0.409162i | \(0.865821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.2584 | − | 7.37927i | 0.857900 | − | 0.272189i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.39022i | 0.0512094i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3616 | 0.859371 | 0.429686 | − | 0.902979i | \(-0.358624\pi\) | ||||
0.429686 | + | 0.902979i | \(0.358624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.7765 | 1.20407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.2885i | − | 0.487508i | −0.969837 | − | 0.243754i | \(-0.921621\pi\) | ||
0.969837 | − | 0.243754i | \(-0.0783789\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.47104 | + | 17.2439i | 0.200443 | + | 0.631769i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 12.0898i | − | 0.442343i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −80.0948 | −2.92660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.4870 | −1.29494 | −0.647470 | − | 0.762091i | \(-0.724173\pi\) | ||||
−0.647470 | + | 0.762091i | \(0.724173\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4401i | 0.489786i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.91464 | − | 15.4903i | −0.178862 | − | 0.563748i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.0646i | − | 1.34714i | −0.739125 | − | 0.673568i | \(-0.764761\pi\) | ||
0.739125 | − | 0.673568i | \(-0.235239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.65998 | −0.0965513 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9718 | 0.687726 | 0.343863 | − | 0.939020i | \(-0.388264\pi\) | ||||
0.343863 | + | 0.939020i | \(0.388264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 20.7254i | − | 0.750309i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.75681 | + | 2.77830i | −0.316603 | + | 0.100450i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.68213i | 0.205170i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.7057 | −0.638483 | −0.319241 | − | 0.947673i | \(-0.603428\pi\) | ||||
−0.319241 | + | 0.947673i | \(0.603428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.47817 | −0.233306 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 28.7012i | − | 1.03231i | −0.856495 | − | 0.516155i | \(-0.827363\pi\) | ||
0.856495 | − | 0.516155i | \(-0.172637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.95988 | + | 1.38283i | −0.0704009 | + | 0.0496728i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.6860i | 0.383356i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.3748 | −0.765832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4938 | −0.411282 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.40553i | − | 0.193178i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.5923 | − | 13.5134i | 1.52018 | − | 0.482313i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.9880i | − | 1.06896i | −0.845182 | − | 0.534478i | \(-0.820508\pi\) | ||
0.845182 | − | 0.534478i | \(-0.179492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0096 | 0.747961 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2237 | −0.434623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.4794i | − | 0.656224i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.95825 | + | 6.17214i | 0.0694521 | + | 0.218903i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.4386i | − | 1.18446i | −0.805770 | − | 0.592228i | \(-0.798248\pi\) | ||
0.805770 | − | 0.592228i | \(-0.201752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.889875 | −0.0314815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.0123 | −0.601099 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.5977i | 0.621008i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.47601 | − | 17.2596i | −0.193004 | − | 0.608321i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.6527i | 0.515801i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.7628 | −1.04640 | −0.523201 | − | 0.852209i | \(-0.675262\pi\) | ||||
−0.523201 | + | 0.852209i | \(0.675262\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.1877 | −1.02492 | −0.512459 | − | 0.858712i | \(-0.671265\pi\) | ||||
−0.512459 | + | 0.858712i | \(0.671265\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.3153i | 0.537130i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.4885 | + | 9.03862i | −0.997907 | + | 0.316609i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.11538i | 0.108994i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.9191 | 0.940629 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.3728 | 1.06002 | 0.530008 | − | 0.847992i | \(-0.322189\pi\) | ||||
0.530008 | + | 0.847992i | \(0.322189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 43.0909i | − | 1.50206i | −0.660271 | − | 0.751028i | \(-0.729558\pi\) | ||
0.660271 | − | 0.751028i | \(-0.270442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00740 | − | 5.67966i | −0.139520 | − | 0.197740i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.1128i | 1.25577i | 0.778308 | + | 0.627883i | \(0.216078\pi\) | ||||
−0.778308 | + | 0.627883i | \(0.783922\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.6499 | −0.717202 | −0.358601 | − | 0.933491i | \(-0.616746\pi\) | ||||
−0.358601 | + | 0.933491i | \(0.616746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.6763 | −0.509116 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 44.8343i | − | 1.55342i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.2794 | − | 7.06865i | 0.771010 | − | 0.244621i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.479723i | 0.0165816i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.7406 | −0.370806 | −0.185403 | − | 0.982663i | \(-0.559359\pi\) | ||||
−0.185403 | + | 0.982663i | \(0.559359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.219775 | 0.00757845 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 16.9400i | − | 0.583445i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.5654 | + | 58.5154i | 0.638668 | + | 2.01299i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.3756i | 1.31860i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.7694 | 0.609843 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.83094 | 0.165602 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.9205i | − | 0.955978i | −0.878366 | − | 0.477989i | \(-0.841366\pi\) | ||
0.878366 | − | 0.477989i | \(-0.158634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.48474 | − | 10.9834i | −0.119176 | − | 0.375625i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 40.7854i | − | 1.39320i | −0.717458 | − | 0.696602i | \(-0.754694\pi\) | ||
0.717458 | − | 0.696602i | \(-0.245306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.7575 | −1.32239 | −0.661195 | − | 0.750214i | \(-0.729950\pi\) | ||||
−0.661195 | + | 0.750214i | \(0.729950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.5550 | −0.598272 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 38.2235i | − | 1.30114i | −0.759445 | − | 0.650572i | \(-0.774529\pi\) | ||
0.759445 | − | 0.650572i | \(-0.225471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.8392 | + | 12.0054i | −1.28657 | + | 0.408194i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 0.119848i | − | 0.00407024i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.0614 | −0.646614 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.36038 | −0.215513 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.636187i | − | 0.0215317i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.6032 | − | 37.6950i | 0.966966 | − | 1.27432i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 30.0536i | − | 1.01484i | −0.861700 | − | 0.507419i | \(-0.830600\pi\) | ||
0.861700 | − | 0.507419i | \(-0.169400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.4037 | −0.418365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7852 | 0.397054 | 0.198527 | − | 0.980095i | \(-0.436384\pi\) | ||||
0.198527 | + | 0.980095i | \(0.436384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.9106i | − | 1.00657i | −0.864120 | − | 0.503287i | \(-0.832124\pi\) | ||
0.864120 | − | 0.503287i | \(-0.167876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.90408 | − | 0.604115i | 0.0640051 | − | 0.0203071i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.5542i | 1.26095i | 0.776212 | + | 0.630473i | \(0.217139\pi\) | ||||
−0.776212 | + | 0.630473i | \(0.782861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.1164 | 0.439909 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.39022 | −0.0465741 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.11614i | − | 0.0373504i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0074 | + | 34.6938i | 0.367937 | + | 1.15968i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.1697i | − | 0.406333i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.59316 | −0.0864866 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8978 | 0.396372 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.55864i | 0.0851463i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.9465 | + | 37.6537i | 0.397115 | + | 1.25165i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 11.1361i | − | 0.369767i | −0.982760 | − | 0.184883i | \(-0.940809\pi\) | ||
0.982760 | − | 0.184883i | \(-0.0591907\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.71282 | 0.0568108 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0528 | −0.399326 | −0.199663 | − | 0.979865i | \(-0.563985\pi\) | ||||
−0.199663 | + | 0.979865i | \(0.563985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 16.8075i | − | 0.556247i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.19246 | + | 1.96470i | −0.204717 | + | 0.0649511i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 10.6728i | − | 0.352447i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.7133 | 1.57392 | 0.786958 | − | 0.617007i | \(-0.211655\pi\) | ||||
0.786958 | + | 0.617007i | \(0.211655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.43370 | 0.0801932 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 52.5853i | − | 1.73087i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.27805 | + | 10.3151i | 0.239301 | + | 0.339159i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 6.41050i | − | 0.210548i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.7529 | −0.746497 | −0.373249 | − | 0.927731i | \(-0.621756\pi\) | ||||
−0.373249 | + | 0.927731i | \(0.621756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 56.2344 | 1.84301 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.6408i | 0.512057i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.1739 | + | 3.86245i | −0.398129 | + | 0.126316i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.73047i | 0.219875i | 0.993939 | + | 0.109937i | \(0.0350650\pi\) | ||||
−0.993939 | + | 0.109937i | \(0.964935\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.9072 | −1.13915 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4839 | −0.732954 | −0.366477 | − | 0.930427i | \(-0.619436\pi\) | ||||
−0.366477 | + | 0.930427i | \(0.619436\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.93631i | 0.258442i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.86199 | − | 9.02060i | −0.0931007 | − | 0.293440i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 29.8044i | − | 0.968514i | −0.874926 | − | 0.484257i | \(-0.839090\pi\) | ||
0.874926 | − | 0.484257i | \(-0.160910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80.5109 | −2.61349 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.84170 | −0.319139 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4121i | 1.40626i | 0.711063 | + | 0.703128i | \(0.248214\pi\) | ||||
−0.711063 | + | 0.703128i | \(0.751786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5380 | − | 42.6699i | −0.438079 | − | 1.38076i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 7.51488i | − | 0.242922i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.9439 | −1.41902 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7699 | −0.992576 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.9246i | 0.609837i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.45739 | − | 0.779665i | 0.0791063 | − | 0.0250983i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.2974i | 0.749195i | 0.927187 | + | 0.374598i | \(0.122219\pi\) | ||||
−0.927187 | + | 0.374598i | \(0.877781\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.1723 | −0.680152 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.9394 | −1.02498 | −0.512492 | − | 0.858692i | \(-0.671278\pi\) | ||||
−0.512492 | + | 0.858692i | \(0.671278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 62.3957i | 2.00032i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.9849 | − | 18.3342i | 0.832184 | − | 0.587165i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 36.5084i | − | 1.16801i | −0.811751 | − | 0.584004i | \(-0.801485\pi\) | ||
0.811751 | − | 0.584004i | \(-0.198515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.6508 | −0.755882 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.89694 | −0.156347 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 25.4785i | − | 0.812637i | −0.913732 | − | 0.406318i | \(-0.866812\pi\) | ||
0.913732 | − | 0.406318i | \(-0.133188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.52618 | + | 2.38785i | −0.239804 | + | 0.0760833i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 0.916682i | − | 0.0291783i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.15672 | 0.0367815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.65306 | 0.306640 | 0.153320 | − | 0.988177i | \(-0.451004\pi\) | ||||
0.153320 | + | 0.988177i | \(0.451004\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 16.9414i | − | 0.537618i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.45782 | + | 7.74669i | 0.0779180 | + | 0.245587i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 53.2290i | − | 1.68578i | −0.538086 | − | 0.842890i | \(-0.680852\pi\) | ||
0.538086 | − | 0.842890i | \(-0.319148\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.52485 | 0.0798827 |
(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 | 4020.2.g.c.1609.8 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.27 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.8 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.27 | yes | 38 | 5.4 | even | 2 | inner |