Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (of order \(4\), degree \(2\), 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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.8 | ||
Root | \(-1.75570 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.j.737.8 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.967383 | + | 2.01598i | 0.432627 | + | 0.901573i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.545849 | − | 0.545849i | 0.206311 | − | 0.206311i | −0.596386 | − | 0.802698i | \(-0.703397\pi\) |
0.802698 | + | 0.596386i | \(0.203397\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.741469 | + | 2.10956i | −0.234473 | + | 0.667100i | ||||
\(11\) | − | 0.823770i | − | 0.248376i | −0.992259 | − | 0.124188i | \(-0.960367\pi\) | ||
0.992259 | − | 0.124188i | \(-0.0396326\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.43352 | + | 3.43352i | 0.952286 | + | 0.952286i | 0.998912 | − | 0.0466260i | \(-0.0148469\pi\) |
−0.0466260 | + | 0.998912i | \(0.514847\pi\) | |||||||
\(14\) | 0.771946 | 0.206311 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.823770 | − | 0.823770i | −0.199793 | − | 0.199793i | 0.600118 | − | 0.799911i | \(-0.295120\pi\) |
−0.799911 | + | 0.600118i | \(0.795120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.38410i | 0.776365i | 0.921583 | + | 0.388182i | \(0.126897\pi\) | ||||
−0.921583 | + | 0.388182i | \(0.873103\pi\) | |||||||
\(20\) | −2.01598 | + | 0.967383i | −0.450787 | + | 0.216313i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.582493 | − | 0.582493i | 0.124188 | − | 0.124188i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.12834 | + | 3.90045i | −0.625668 | + | 0.780089i | ||||
\(26\) | 4.85573i | 0.952286i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.545849 | + | 0.545849i | 0.103156 | + | 0.103156i | ||||
\(29\) | 9.51219 | 1.76637 | 0.883185 | − | 0.469025i | \(-0.155395\pi\) | ||||
0.883185 | + | 0.469025i | \(0.155395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.25668 | −1.12373 | −0.561867 | − | 0.827228i | \(-0.689917\pi\) | ||||
−0.561867 | + | 0.827228i | \(0.689917\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.16499i | − | 0.199793i | ||||||
\(35\) | 1.62846 | + | 0.572375i | 0.275261 | + | 0.0967490i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.43100 | + | 2.43100i | −0.399653 | + | 0.399653i | −0.878111 | − | 0.478458i | \(-0.841196\pi\) |
0.478458 | + | 0.878111i | \(0.341196\pi\) | |||||||
\(38\) | −2.39292 | + | 2.39292i | −0.388182 | + | 0.388182i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.10956 | − | 0.741469i | −0.333550 | − | 0.117237i | ||||
\(41\) | 0.0889676i | 0.0138944i | 0.999976 | + | 0.00694720i | \(0.00221138\pi\) | ||||
−0.999976 | + | 0.00694720i | \(0.997789\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12834 | + | 1.12834i | 0.172070 | + | 0.172070i | 0.787888 | − | 0.615818i | \(-0.211174\pi\) |
−0.615818 | + | 0.787888i | \(0.711174\pi\) | |||||||
\(44\) | 0.823770 | 0.124188 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 1.57664 | + | 1.57664i | 0.229977 | + | 0.229977i | 0.812683 | − | 0.582706i | \(-0.198006\pi\) |
−0.582706 | + | 0.812683i | \(0.698006\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.40410i | 0.914871i | ||||||||
\(50\) | −4.97010 | + | 0.545960i | −0.702879 | + | 0.0772104i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.43352 | + | 3.43352i | −0.476143 | + | 0.476143i | ||||
\(53\) | 3.37555 | − | 3.37555i | 0.463667 | − | 0.463667i | −0.436188 | − | 0.899855i | \(-0.643672\pi\) |
0.899855 | + | 0.436188i | \(0.143672\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.66070 | − | 0.796900i | 0.223929 | − | 0.107454i | ||||
\(56\) | 0.771946i | 0.103156i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.72613 | + | 6.72613i | 0.883185 | + | 0.883185i | ||||
\(59\) | −13.3268 | −1.73500 | −0.867502 | − | 0.497434i | \(-0.834276\pi\) | ||||
−0.867502 | + | 0.497434i | \(0.834276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.2076 | 1.94713 | 0.973567 | − | 0.228401i | \(-0.0733498\pi\) | ||||
0.973567 | + | 0.228401i | \(0.0733498\pi\) | |||||||
\(62\) | −4.42414 | − | 4.42414i | −0.561867 | − | 0.561867i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −3.60037 | + | 10.2434i | −0.446571 | + | 1.27054i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.25575 | + | 6.25575i | −0.764262 | + | 0.764262i | −0.977090 | − | 0.212828i | \(-0.931733\pi\) |
0.212828 | + | 0.977090i | \(0.431733\pi\) | |||||||
\(68\) | 0.823770 | − | 0.823770i | 0.0998967 | − | 0.0998967i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.746768 | + | 1.55623i | 0.0892558 | + | 0.186005i | ||||
\(71\) | − | 0.428017i | − | 0.0507963i | −0.999677 | − | 0.0253981i | \(-0.991915\pi\) | ||
0.999677 | − | 0.0253981i | \(-0.00808535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.35876 | − | 7.35876i | −0.861278 | − | 0.861278i | 0.130209 | − | 0.991487i | \(-0.458435\pi\) |
−0.991487 | + | 0.130209i | \(0.958435\pi\) | |||||||
\(74\) | −3.43795 | −0.399653 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.38410 | −0.388182 | ||||||||
\(77\) | −0.449653 | − | 0.449653i | −0.0512428 | − | 0.0512428i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.82787i | 0.205651i | 0.994699 | + | 0.102826i | \(0.0327884\pi\) | ||||
−0.994699 | + | 0.102826i | \(0.967212\pi\) | |||||||
\(80\) | −0.967383 | − | 2.01598i | −0.108157 | − | 0.225393i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.0629096 | + | 0.0629096i | −0.00694720 | + | 0.00694720i | ||||
\(83\) | 3.05325 | − | 3.05325i | 0.335138 | − | 0.335138i | −0.519396 | − | 0.854534i | \(-0.673843\pi\) |
0.854534 | + | 0.519396i | \(0.173843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.863802 | − | 2.45760i | 0.0936924 | − | 0.266564i | ||||
\(86\) | 1.59572i | 0.172070i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.582493 | + | 0.582493i | 0.0620940 | + | 0.0620940i | ||||
\(89\) | −5.58696 | −0.592217 | −0.296108 | − | 0.955154i | \(-0.595689\pi\) | ||||
−0.296108 | + | 0.955154i | \(0.595689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.74836 | 0.392935 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.22971i | 0.229977i | ||||||||
\(95\) | −6.82227 | + | 3.27372i | −0.699950 | + | 0.335876i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.10678 | + | 9.10678i | −0.924653 | + | 0.924653i | −0.997354 | − | 0.0727005i | \(-0.976838\pi\) |
0.0727005 | + | 0.997354i | \(0.476838\pi\) | |||||||
\(98\) | −4.52838 | + | 4.52838i | −0.457436 | + | 0.457436i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.90045 | − | 3.12834i | −0.390045 | − | 0.312834i | ||||
\(101\) | 0.235403i | 0.0234235i | 0.999931 | + | 0.0117118i | \(0.00372805\pi\) | ||||
−0.999931 | + | 0.0117118i | \(0.996272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9841 | + | 12.9841i | 1.27936 | + | 1.27936i | 0.941027 | + | 0.338331i | \(0.109862\pi\) |
0.338331 | + | 0.941027i | \(0.390138\pi\) | |||||||
\(104\) | −4.85573 | −0.476143 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.77374 | 0.463667 | ||||||||
\(107\) | −8.07141 | − | 8.07141i | −0.780292 | − | 0.780292i | 0.199588 | − | 0.979880i | \(-0.436040\pi\) |
−0.979880 | + | 0.199588i | \(0.936040\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.689192i | − | 0.0660127i | −0.999455 | − | 0.0330063i | \(-0.989492\pi\) | ||
0.999455 | − | 0.0330063i | \(-0.0105082\pi\) | |||||||
\(110\) | 1.73779 | + | 0.610800i | 0.165692 | + | 0.0582375i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.545849 | + | 0.545849i | −0.0515778 | + | 0.0515778i | ||||
\(113\) | 5.98479 | − | 5.98479i | 0.563002 | − | 0.563002i | −0.367157 | − | 0.930159i | \(-0.619669\pi\) |
0.930159 | + | 0.367157i | \(0.119669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.10956 | + | 0.741469i | 0.196717 | + | 0.0691424i | ||||
\(116\) | 9.51219i | 0.883185i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.42348 | − | 9.42348i | −0.867502 | − | 0.867502i | ||||
\(119\) | −0.899307 | −0.0824393 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3214 | 0.938309 | ||||||||
\(122\) | 10.7534 | + | 10.7534i | 0.973567 | + | 0.973567i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 6.25668i | − | 0.561867i | ||||||
\(125\) | −10.8895 | − | 2.53345i | −0.973988 | − | 0.226598i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3994 | + | 11.3994i | −1.01153 | + | 1.01153i | −0.0116001 | + | 0.999933i | \(0.503693\pi\) |
−0.999933 | + | 0.0116001i | \(0.996307\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.78904 | + | 4.69735i | −0.858556 | + | 0.411985i | ||||
\(131\) | − | 13.5764i | − | 1.18618i | −0.805137 | − | 0.593088i | \(-0.797908\pi\) | ||
0.805137 | − | 0.593088i | \(-0.202092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.84720 | + | 1.84720i | 0.160173 | + | 0.160173i | ||||
\(134\) | −8.84697 | −0.764262 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.16499 | 0.0998967 | ||||||||
\(137\) | 1.83112 | + | 1.83112i | 0.156443 | + | 0.156443i | 0.780988 | − | 0.624545i | \(-0.214716\pi\) |
−0.624545 | + | 0.780988i | \(0.714716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.9152i | − | 1.09545i | −0.836657 | − | 0.547727i | \(-0.815493\pi\) | ||
0.836657 | − | 0.547727i | \(-0.184507\pi\) | |||||||
\(140\) | −0.572375 | + | 1.62846i | −0.0483745 | + | 0.137630i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.302654 | − | 0.302654i | 0.0253981 | − | 0.0253981i | ||||
\(143\) | 2.82843 | − | 2.82843i | 0.236525 | − | 0.236525i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.20193 | + | 19.1764i | 0.764178 | + | 1.59251i | ||||
\(146\) | − | 10.4069i | − | 0.861278i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.43100 | − | 2.43100i | −0.199827 | − | 0.199827i | ||||
\(149\) | 11.8391 | 0.969900 | 0.484950 | − | 0.874542i | \(-0.338838\pi\) | ||||
0.484950 | + | 0.874542i | \(0.338838\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.05321 | −0.492604 | −0.246302 | − | 0.969193i | \(-0.579215\pi\) | ||||
−0.246302 | + | 0.969193i | \(0.579215\pi\) | |||||||
\(152\) | −2.39292 | − | 2.39292i | −0.194091 | − | 0.194091i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 0.635906i | − | 0.0512428i | ||||||
\(155\) | −6.05261 | − | 12.6133i | −0.486157 | − | 1.01313i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.88326 | − | 9.88326i | 0.788770 | − | 0.788770i | −0.192522 | − | 0.981293i | \(-0.561667\pi\) |
0.981293 | + | 0.192522i | \(0.0616668\pi\) | |||||||
\(158\) | −1.29250 | + | 1.29250i | −0.102826 | + | 0.102826i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.741469 | − | 2.10956i | 0.0586183 | − | 0.166775i | ||||
\(161\) | − | 0.771946i | − | 0.0608379i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3875 | + | 10.3875i | 0.813615 | + | 0.813615i | 0.985174 | − | 0.171558i | \(-0.0548802\pi\) |
−0.171558 | + | 0.985174i | \(0.554880\pi\) | |||||||
\(164\) | −0.0889676 | −0.00694720 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.31795 | 0.335138 | ||||||||
\(167\) | −12.0791 | − | 12.0791i | −0.934710 | − | 0.934710i | 0.0632853 | − | 0.997995i | \(-0.479842\pi\) |
−0.997995 | + | 0.0632853i | \(0.979842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5781i | 0.813699i | ||||||||
\(170\) | 2.34859 | − | 1.12699i | 0.180128 | − | 0.0864360i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.12834 | + | 1.12834i | −0.0860352 | + | 0.0860352i | ||||
\(173\) | 6.80191 | − | 6.80191i | 0.517140 | − | 0.517140i | −0.399565 | − | 0.916705i | \(-0.630839\pi\) |
0.916705 | + | 0.399565i | \(0.130839\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.421452 | + | 3.83665i | 0.0318588 | + | 0.290024i | ||||
\(176\) | 0.823770i | 0.0620940i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.95058 | − | 3.95058i | −0.296108 | − | 0.296108i | ||||
\(179\) | −8.62964 | −0.645010 | −0.322505 | − | 0.946568i | \(-0.604525\pi\) | ||||
−0.322505 | + | 0.946568i | \(0.604525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4075 | −1.36822 | −0.684111 | − | 0.729378i | \(-0.739810\pi\) | ||||
−0.684111 | + | 0.729378i | \(0.739810\pi\) | |||||||
\(182\) | 2.65049 | + | 2.65049i | 0.196468 | + | 0.196468i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | −7.25254 | − | 2.54913i | −0.533217 | − | 0.187416i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.678596 | + | 0.678596i | −0.0496239 | + | 0.0496239i | ||||
\(188\) | −1.57664 | + | 1.57664i | −0.114988 | + | 0.114988i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.13894 | − | 2.50920i | −0.517913 | − | 0.182037i | ||||
\(191\) | 6.86973i | 0.497076i | 0.968622 | + | 0.248538i | \(0.0799501\pi\) | ||||
−0.968622 | + | 0.248538i | \(0.920050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.83501 | + | 7.83501i | 0.563977 | + | 0.563977i | 0.930435 | − | 0.366458i | \(-0.119430\pi\) |
−0.366458 | + | 0.930435i | \(0.619430\pi\) | |||||||
\(194\) | −12.8789 | −0.924653 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.40410 | −0.457436 | ||||||||
\(197\) | 14.0985 | + | 14.0985i | 1.00447 | + | 1.00447i | 0.999990 | + | 0.00448323i | \(0.00142706\pi\) |
0.00448323 | + | 0.999990i | \(0.498573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17.8854i | − | 1.26787i | −0.773388 | − | 0.633933i | \(-0.781440\pi\) | ||
0.773388 | − | 0.633933i | \(-0.218560\pi\) | |||||||
\(200\) | −0.545960 | − | 4.97010i | −0.0386052 | − | 0.351439i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.166455 | + | 0.166455i | −0.0117118 | + | 0.0117118i | ||||
\(203\) | 5.19222 | − | 5.19222i | 0.364422 | − | 0.364422i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.179357 | + | 0.0860657i | −0.0125268 | + | 0.00601109i | ||||
\(206\) | 18.3622i | 1.27936i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.43352 | − | 3.43352i | −0.238072 | − | 0.238072i | ||||
\(209\) | 2.78772 | 0.192830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.68986 | 0.598235 | 0.299117 | − | 0.954216i | \(-0.403308\pi\) | ||||
0.299117 | + | 0.954216i | \(0.403308\pi\) | |||||||
\(212\) | 3.37555 | + | 3.37555i | 0.231834 | + | 0.231834i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 11.4147i | − | 0.780292i | ||||||
\(215\) | −1.18317 | + | 3.36625i | −0.0806918 | + | 0.229576i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.41520 | + | 3.41520i | −0.231839 | + | 0.231839i | ||||
\(218\) | 0.487333 | − | 0.487333i | 0.0330063 | − | 0.0330063i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.796900 | + | 1.66070i | 0.0537270 | + | 0.111964i | ||||
\(221\) | − | 5.65685i | − | 0.380521i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.43171 | + | 2.43171i | 0.162839 | + | 0.162839i | 0.783823 | − | 0.620984i | \(-0.213267\pi\) |
−0.620984 | + | 0.783823i | \(0.713267\pi\) | |||||||
\(224\) | −0.771946 | −0.0515778 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.46377 | 0.563002 | ||||||||
\(227\) | 15.5944 | + | 15.5944i | 1.03504 | + | 1.03504i | 0.999363 | + | 0.0356765i | \(0.0113586\pi\) |
0.0356765 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.17054i | − | 0.0773513i | −0.999252 | − | 0.0386756i | \(-0.987686\pi\) | ||
0.999252 | − | 0.0386756i | \(-0.0123139\pi\) | |||||||
\(230\) | 0.967383 | + | 2.01598i | 0.0637873 | + | 0.132930i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.72613 | + | 6.72613i | −0.441592 | + | 0.441592i | ||||
\(233\) | −0.391179 | + | 0.391179i | −0.0256270 | + | 0.0256270i | −0.719804 | − | 0.694177i | \(-0.755768\pi\) |
0.694177 | + | 0.719804i | \(0.255768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.65326 | + | 4.70369i | −0.107847 | + | 0.306835i | ||||
\(236\) | − | 13.3268i | − | 0.867502i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.635906 | − | 0.635906i | −0.0412197 | − | 0.0412197i | ||||
\(239\) | 4.90654 | 0.317378 | 0.158689 | − | 0.987329i | \(-0.449273\pi\) | ||||
0.158689 | + | 0.987329i | \(0.449273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.4617 | 1.64013 | 0.820065 | − | 0.572270i | \(-0.193937\pi\) | ||||
0.820065 | + | 0.572270i | \(0.193937\pi\) | |||||||
\(242\) | 7.29833 | + | 7.29833i | 0.469155 | + | 0.469155i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.2076i | 0.973567i | ||||||||
\(245\) | −12.9105 | + | 6.19521i | −0.824823 | + | 0.395798i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.6194 | + | 11.6194i | −0.739322 | + | 0.739322i | ||||
\(248\) | 4.42414 | − | 4.42414i | 0.280933 | − | 0.280933i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.90864 | − | 9.49147i | −0.373695 | − | 0.600293i | ||||
\(251\) | 6.16290i | 0.388999i | 0.980903 | + | 0.194500i | \(0.0623083\pi\) | ||||
−0.980903 | + | 0.194500i | \(0.937692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.582493 | − | 0.582493i | −0.0366210 | − | 0.0366210i | ||||
\(254\) | −16.1212 | −1.01153 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.598408 | − | 0.598408i | −0.0373277 | − | 0.0373277i | 0.688197 | − | 0.725524i | \(-0.258403\pi\) |
−0.725524 | + | 0.688197i | \(0.758403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.65391i | 0.164906i | ||||||||
\(260\) | −10.2434 | − | 3.60037i | −0.635270 | − | 0.223286i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.59997 | − | 9.59997i | 0.593088 | − | 0.593088i | ||||
\(263\) | 6.40765 | − | 6.40765i | 0.395112 | − | 0.395112i | −0.481393 | − | 0.876505i | \(-0.659869\pi\) |
0.876505 | + | 0.481393i | \(0.159869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0705 | + | 3.53959i | 0.618624 | + | 0.217435i | ||||
\(266\) | 2.61234i | 0.160173i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.25575 | − | 6.25575i | −0.382131 | − | 0.382131i | ||||
\(269\) | −21.4121 | −1.30552 | −0.652760 | − | 0.757565i | \(-0.726389\pi\) | ||||
−0.652760 | + | 0.757565i | \(0.726389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.2617 | 1.47380 | 0.736898 | − | 0.676004i | \(-0.236290\pi\) | ||||
0.736898 | + | 0.676004i | \(0.236290\pi\) | |||||||
\(272\) | 0.823770 | + | 0.823770i | 0.0499484 | + | 0.0499484i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.58959i | 0.156443i | ||||||||
\(275\) | 3.21307 | + | 2.57703i | 0.193755 | + | 0.155401i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0367 | − | 13.0367i | 0.783301 | − | 0.783301i | −0.197085 | − | 0.980386i | \(-0.563148\pi\) |
0.980386 | + | 0.197085i | \(0.0631476\pi\) | |||||||
\(278\) | 9.13243 | − | 9.13243i | 0.547727 | − | 0.547727i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.55623 | + | 0.746768i | −0.0930024 | + | 0.0446279i | ||||
\(281\) | − | 6.37847i | − | 0.380507i | −0.981735 | − | 0.190254i | \(-0.939069\pi\) | ||
0.981735 | − | 0.190254i | \(-0.0609311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.26980 | − | 5.26980i | −0.313257 | − | 0.313257i | 0.532913 | − | 0.846170i | \(-0.321097\pi\) |
−0.846170 | + | 0.532913i | \(0.821097\pi\) | |||||||
\(284\) | 0.428017 | 0.0253981 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 0.0485629 | + | 0.0485629i | 0.00286657 | + | 0.00286657i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.6428i | − | 0.920165i | ||||||
\(290\) | −7.05300 | + | 20.0665i | −0.414166 | + | 1.17834i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.35876 | − | 7.35876i | 0.430639 | − | 0.430639i | ||||
\(293\) | 17.2056 | − | 17.2056i | 1.00516 | − | 1.00516i | 0.00517573 | − | 0.999987i | \(-0.498353\pi\) |
0.999987 | − | 0.00517573i | \(-0.00164749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.8921 | − | 26.8666i | −0.750609 | − | 1.56423i | ||||
\(296\) | − | 3.43795i | − | 0.199827i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.37154 | + | 8.37154i | 0.484950 | + | 0.484950i | ||||
\(299\) | 4.85573 | 0.280814 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.23181 | 0.0710002 | ||||||||
\(302\) | −4.28027 | − | 4.28027i | −0.246302 | − | 0.246302i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 3.38410i | − | 0.194091i | ||||||
\(305\) | 14.7116 | + | 30.6582i | 0.842382 | + | 1.75548i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.42881 | − | 4.42881i | 0.252766 | − | 0.252766i | −0.569338 | − | 0.822104i | \(-0.692800\pi\) |
0.822104 | + | 0.569338i | \(0.192800\pi\) | |||||||
\(308\) | 0.449653 | − | 0.449653i | 0.0256214 | − | 0.0256214i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.63914 | − | 13.1988i | 0.263485 | − | 0.749643i | ||||
\(311\) | − | 33.7161i | − | 1.91186i | −0.293591 | − | 0.955931i | \(-0.594851\pi\) | ||
0.293591 | − | 0.955931i | \(-0.405149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4623 | − | 11.4623i | −0.647888 | − | 0.647888i | 0.304594 | − | 0.952482i | \(-0.401479\pi\) |
−0.952482 | + | 0.304594i | \(0.901479\pi\) | |||||||
\(314\) | 13.9770 | 0.788770 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.82787 | −0.102826 | ||||||||
\(317\) | 5.06949 | + | 5.06949i | 0.284731 | + | 0.284731i | 0.834992 | − | 0.550261i | \(-0.185472\pi\) |
−0.550261 | + | 0.834992i | \(0.685472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.83585i | − | 0.438723i | ||||||
\(320\) | 2.01598 | − | 0.967383i | 0.112697 | − | 0.0540783i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.545849 | − | 0.545849i | 0.0304190 | − | 0.0304190i | ||||
\(323\) | 2.78772 | − | 2.78772i | 0.155113 | − | 0.155113i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.1335 | + | 2.65103i | −1.33868 | + | 0.147053i | ||||
\(326\) | 14.6902i | 0.813615i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.0629096 | − | 0.0629096i | −0.00347360 | − | 0.00347360i | ||||
\(329\) | 1.72121 | 0.0948936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5511 | 0.744836 | 0.372418 | − | 0.928065i | \(-0.378529\pi\) | ||||
0.372418 | + | 0.928065i | \(0.378529\pi\) | |||||||
\(332\) | 3.05325 | + | 3.05325i | 0.167569 | + | 0.167569i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 17.0825i | − | 0.934710i | ||||||
\(335\) | −18.6632 | − | 6.55976i | −1.01968 | − | 0.358398i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7603 | + | 11.7603i | −0.640622 | + | 0.640622i | −0.950708 | − | 0.310086i | \(-0.899642\pi\) |
0.310086 | + | 0.950708i | \(0.399642\pi\) | |||||||
\(338\) | −7.47984 | + | 7.47984i | −0.406849 | + | 0.406849i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.45760 | + | 0.863802i | 0.133282 | + | 0.0468462i | ||||
\(341\) | 5.15406i | 0.279108i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.31661 | + | 7.31661i | 0.395060 | + | 0.395060i | ||||
\(344\) | −1.59572 | −0.0860352 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.61935 | 0.517140 | ||||||||
\(347\) | −14.7814 | − | 14.7814i | −0.793509 | − | 0.793509i | 0.188554 | − | 0.982063i | \(-0.439620\pi\) |
−0.982063 | + | 0.188554i | \(0.939620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.3329i | − | 0.767223i | −0.923495 | − | 0.383612i | \(-0.874680\pi\) | ||
0.923495 | − | 0.383612i | \(-0.125320\pi\) | |||||||
\(350\) | −2.41491 | + | 3.01094i | −0.129082 | + | 0.160941i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.582493 | + | 0.582493i | −0.0310470 | + | 0.0310470i | ||||
\(353\) | −1.89228 | + | 1.89228i | −0.100716 | + | 0.100716i | −0.755669 | − | 0.654953i | \(-0.772688\pi\) |
0.654953 | + | 0.755669i | \(0.272688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.862873 | − | 0.414056i | 0.0457966 | − | 0.0219758i | ||||
\(356\) | − | 5.58696i | − | 0.296108i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.10208 | − | 6.10208i | −0.322505 | − | 0.322505i | ||||
\(359\) | 18.9501 | 1.00015 | 0.500074 | − | 0.865983i | \(-0.333306\pi\) | ||||
0.500074 | + | 0.865983i | \(0.333306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.54789 | 0.397257 | ||||||||
\(362\) | −13.0161 | − | 13.0161i | −0.684111 | − | 0.684111i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.74836i | 0.196468i | ||||||||
\(365\) | 7.71637 | − | 21.9538i | 0.403893 | − | 1.14912i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.190323 | − | 0.190323i | 0.00993477 | − | 0.00993477i | −0.702122 | − | 0.712057i | \(-0.747764\pi\) |
0.712057 | + | 0.702122i | \(0.247764\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.32581 | − | 6.93083i | −0.172901 | − | 0.360317i | ||||
\(371\) | − | 3.68508i | − | 0.191320i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.01623 | − | 7.01623i | −0.363287 | − | 0.363287i | 0.501735 | − | 0.865021i | \(-0.332695\pi\) |
−0.865021 | + | 0.501735i | \(0.832695\pi\) | |||||||
\(374\) | −0.959680 | −0.0496239 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.22971 | −0.114988 | ||||||||
\(377\) | 32.6603 | + | 32.6603i | 1.68209 | + | 1.68209i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 29.6158i | − | 1.52126i | −0.649184 | − | 0.760631i | \(-0.724890\pi\) | ||
0.649184 | − | 0.760631i | \(-0.275110\pi\) | |||||||
\(380\) | −3.27372 | − | 6.82227i | −0.167938 | − | 0.349975i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.85763 | + | 4.85763i | −0.248538 | + | 0.248538i | ||||
\(383\) | 7.39104 | − | 7.39104i | 0.377665 | − | 0.377665i | −0.492594 | − | 0.870259i | \(-0.663951\pi\) |
0.870259 | + | 0.492594i | \(0.163951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.471505 | − | 1.34148i | 0.0240301 | − | 0.0683681i | ||||
\(386\) | 11.0804i | 0.563977i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.10678 | − | 9.10678i | −0.462327 | − | 0.462327i | ||||
\(389\) | 14.7314 | 0.746911 | 0.373455 | − | 0.927648i | \(-0.378173\pi\) | ||||
0.373455 | + | 0.927648i | \(0.378173\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.16499 | −0.0589159 | ||||||||
\(392\) | −4.52838 | − | 4.52838i | −0.228718 | − | 0.228718i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.9382i | 1.00447i | ||||||||
\(395\) | −3.68494 | + | 1.76825i | −0.185410 | + | 0.0889702i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.42637 | + | 6.42637i | −0.322530 | + | 0.322530i | −0.849737 | − | 0.527207i | \(-0.823239\pi\) |
0.527207 | + | 0.849737i | \(0.323239\pi\) | |||||||
\(398\) | 12.6469 | − | 12.6469i | 0.633933 | − | 0.633933i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.12834 | − | 3.90045i | 0.156417 | − | 0.195022i | ||||
\(401\) | − | 1.21263i | − | 0.0605558i | −0.999542 | − | 0.0302779i | \(-0.990361\pi\) | ||
0.999542 | − | 0.0302779i | \(-0.00963923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.4824 | − | 21.4824i | −1.07012 | − | 1.07012i | ||||
\(404\) | −0.235403 | −0.0117118 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.34290 | 0.364422 | ||||||||
\(407\) | 2.00258 | + | 2.00258i | 0.0992642 | + | 0.0992642i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.2113i | − | 0.851044i | −0.904948 | − | 0.425522i | \(-0.860091\pi\) | ||
0.904948 | − | 0.425522i | \(-0.139909\pi\) | |||||||
\(410\) | −0.187682 | − | 0.0659668i | −0.00926896 | − | 0.00325787i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.9841 | + | 12.9841i | −0.639679 | + | 0.639679i | ||||
\(413\) | −7.27442 | + | 7.27442i | −0.357951 | + | 0.357951i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.10896 | + | 3.20163i | 0.447141 | + | 0.157162i | ||||
\(416\) | − | 4.85573i | − | 0.238072i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.97121 | + | 1.97121i | 0.0964152 | + | 0.0964152i | ||||
\(419\) | 10.0536 | 0.491150 | 0.245575 | − | 0.969378i | \(-0.421023\pi\) | ||||
0.245575 | + | 0.969378i | \(0.421023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.81796 | −0.186076 | −0.0930379 | − | 0.995663i | \(-0.529658\pi\) | ||||
−0.0930379 | + | 0.995663i | \(0.529658\pi\) | |||||||
\(422\) | 6.14466 | + | 6.14466i | 0.299117 | + | 0.299117i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.77374i | 0.231834i | ||||||||
\(425\) | 5.79010 | − | 0.636036i | 0.280861 | − | 0.0308523i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.30105 | − | 8.30105i | 0.401716 | − | 0.401716i | ||||
\(428\) | 8.07141 | − | 8.07141i | 0.390146 | − | 0.390146i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.21693 | + | 1.54367i | −0.155134 | + | 0.0744423i | ||||
\(431\) | − | 35.8552i | − | 1.72708i | −0.504278 | − | 0.863541i | \(-0.668241\pi\) | ||
0.504278 | − | 0.863541i | \(-0.331759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.52198 | + | 4.52198i | 0.217313 | + | 0.217313i | 0.807365 | − | 0.590052i | \(-0.200893\pi\) |
−0.590052 | + | 0.807365i | \(0.700893\pi\) | |||||||
\(434\) | −4.82982 | −0.231839 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.689192 | 0.0330063 | ||||||||
\(437\) | 2.39292 | + | 2.39292i | 0.114469 | + | 0.114469i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.3661i | − | 1.68793i | −0.536396 | − | 0.843966i | \(-0.680215\pi\) | ||
0.536396 | − | 0.843966i | \(-0.319785\pi\) | |||||||
\(440\) | −0.610800 | + | 1.73779i | −0.0291187 | + | 0.0828458i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | − | 4.00000i | 0.190261 | − | 0.190261i | ||||
\(443\) | −17.5186 | + | 17.5186i | −0.832336 | + | 0.832336i | −0.987836 | − | 0.155500i | \(-0.950301\pi\) |
0.155500 | + | 0.987836i | \(0.450301\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.40473 | − | 11.2632i | −0.256209 | − | 0.533927i | ||||
\(446\) | 3.43895i | 0.162839i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.545849 | − | 0.545849i | −0.0257889 | − | 0.0257889i | ||||
\(449\) | −4.05598 | −0.191413 | −0.0957067 | − | 0.995410i | \(-0.530511\pi\) | ||||
−0.0957067 | + | 0.995410i | \(0.530511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0732888 | 0.00345104 | ||||||||
\(452\) | 5.98479 | + | 5.98479i | 0.281501 | + | 0.281501i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.0539i | 1.03504i | ||||||||
\(455\) | 3.62610 | + | 7.55662i | 0.169994 | + | 0.354260i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.1765 | + | 24.1765i | −1.13093 | + | 1.13093i | −0.140908 | + | 0.990023i | \(0.545002\pi\) |
−0.990023 | + | 0.140908i | \(0.954998\pi\) | |||||||
\(458\) | 0.827695 | − | 0.827695i | 0.0386756 | − | 0.0386756i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.741469 | + | 2.10956i | −0.0345712 | + | 0.0983585i | ||||
\(461\) | − | 10.8730i | − | 0.506407i | −0.967413 | − | 0.253204i | \(-0.918516\pi\) | ||
0.967413 | − | 0.253204i | \(-0.0814843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2413 | + | 20.2413i | 0.940694 | + | 0.940694i | 0.998337 | − | 0.0576437i | \(-0.0183587\pi\) |
−0.0576437 | + | 0.998337i | \(0.518359\pi\) | |||||||
\(464\) | −9.51219 | −0.441592 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.553211 | −0.0256270 | ||||||||
\(467\) | −3.11096 | − | 3.11096i | −0.143958 | − | 0.143958i | 0.631455 | − | 0.775413i | \(-0.282458\pi\) |
−0.775413 | + | 0.631455i | \(0.782458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.82939i | 0.315352i | ||||||||
\(470\) | −4.49504 | + | 2.15698i | −0.207341 | + | 0.0994940i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.42348 | − | 9.42348i | 0.433751 | − | 0.433751i | ||||
\(473\) | 0.929493 | − | 0.929493i | 0.0427382 | − | 0.0427382i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.1995 | − | 10.5866i | −0.605634 | − | 0.485747i | ||||
\(476\) | − | 0.899307i | − | 0.0412197i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.46945 | + | 3.46945i | 0.158689 | + | 0.158689i | ||||
\(479\) | 39.1662 | 1.78955 | 0.894774 | − | 0.446520i | \(-0.147337\pi\) | ||||
0.894774 | + | 0.446520i | \(0.147337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.6937 | −0.761169 | ||||||||
\(482\) | 18.0041 | + | 18.0041i | 0.820065 | + | 0.820065i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.3214i | 0.469155i | ||||||||
\(485\) | −27.1688 | − | 9.54933i | −1.23367 | − | 0.433613i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.07985 | + | 4.07985i | −0.184876 | + | 0.184876i | −0.793476 | − | 0.608601i | \(-0.791731\pi\) |
0.608601 | + | 0.793476i | \(0.291731\pi\) | |||||||
\(488\) | −10.7534 | + | 10.7534i | −0.486784 | + | 0.486784i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.5098 | − | 4.74844i | −0.610311 | − | 0.214513i | ||||
\(491\) | − | 34.5406i | − | 1.55879i | −0.626530 | − | 0.779397i | \(-0.715525\pi\) | ||
0.626530 | − | 0.779397i | \(-0.284475\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.83585 | − | 7.83585i | −0.352909 | − | 0.352909i | ||||
\(494\) | −16.4322 | −0.739322 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.25668 | 0.280933 | ||||||||
\(497\) | −0.233632 | − | 0.233632i | −0.0104798 | − | 0.0104798i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.67978i | 0.343794i | 0.985115 | + | 0.171897i | \(0.0549896\pi\) | ||||
−0.985115 | + | 0.171897i | \(0.945010\pi\) | |||||||
\(500\) | 2.53345 | − | 10.8895i | 0.113299 | − | 0.486994i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.35783 | + | 4.35783i | −0.194500 | + | 0.194500i | ||||
\(503\) | −7.02025 | + | 7.02025i | −0.313018 | + | 0.313018i | −0.846077 | − | 0.533060i | \(-0.821042\pi\) |
0.533060 | + | 0.846077i | \(0.321042\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.474568 | + | 0.227725i | −0.0211180 | + | 0.0101336i | ||||
\(506\) | − | 0.823770i | − | 0.0366210i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.3994 | − | 11.3994i | −0.505766 | − | 0.505766i | ||||
\(509\) | 29.8928 | 1.32497 | 0.662487 | − | 0.749074i | \(-0.269501\pi\) | ||||
0.662487 | + | 0.749074i | \(0.269501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.03354 | −0.355383 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 0.846277i | − | 0.0373277i | ||||||
\(515\) | −13.6150 | + | 38.7362i | −0.599951 | + | 1.70692i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.29879 | − | 1.29879i | 0.0571207 | − | 0.0571207i | ||||
\(518\) | −1.87660 | + | 1.87660i | −0.0824530 | + | 0.0824530i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.69735 | − | 9.78904i | −0.205992 | − | 0.429278i | ||||
\(521\) | − | 7.33613i | − | 0.321402i | −0.987003 | − | 0.160701i | \(-0.948625\pi\) | ||
0.987003 | − | 0.160701i | \(-0.0513755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.119339 | − | 0.119339i | −0.00521834 | − | 0.00521834i | 0.704493 | − | 0.709711i | \(-0.251175\pi\) |
−0.709711 | + | 0.704493i | \(0.751175\pi\) | |||||||
\(524\) | 13.5764 | 0.593088 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.06178 | 0.395112 | ||||||||
\(527\) | 5.15406 | + | 5.15406i | 0.224515 | + | 0.224515i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | 4.61804 | + | 9.62377i | 0.200595 | + | 0.418030i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.84720 | + | 1.84720i | −0.0800865 | + | 0.0800865i | ||||
\(533\) | −0.305472 | + | 0.305472i | −0.0132315 | + | 0.0132315i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.46365 | − | 24.0799i | 0.365915 | − | 1.04107i | ||||
\(536\) | − | 8.84697i | − | 0.382131i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.1407 | − | 15.1407i | −0.652760 | − | 0.652760i | ||||
\(539\) | 5.27550 | 0.227232 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.8485 | −1.11132 | −0.555658 | − | 0.831411i | \(-0.687533\pi\) | ||||
−0.555658 | + | 0.831411i | \(0.687533\pi\) | |||||||
\(542\) | 17.1556 | + | 17.1556i | 0.736898 | + | 0.736898i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.16499i | 0.0499484i | ||||||||
\(545\) | 1.38940 | − | 0.666713i | 0.0595152 | − | 0.0285588i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.355526 | − | 0.355526i | 0.0152012 | − | 0.0152012i | −0.699465 | − | 0.714667i | \(-0.746578\pi\) |
0.714667 | + | 0.699465i | \(0.246578\pi\) | |||||||
\(548\) | −1.83112 | + | 1.83112i | −0.0782215 | + | 0.0782215i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.449745 | + | 4.09422i | 0.0191772 | + | 0.174578i | ||||
\(551\) | 32.1902i | 1.37135i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.997739 | + | 0.997739i | 0.0424282 | + | 0.0424282i | ||||
\(554\) | 18.4367 | 0.783301 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.9152 | 0.547727 | ||||||||
\(557\) | 28.7593 | + | 28.7593i | 1.21857 | + | 1.21857i | 0.968133 | + | 0.250438i | \(0.0805745\pi\) |
0.250438 | + | 0.968133i | \(0.419426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.74836i | 0.327721i | ||||||||
\(560\) | −1.62846 | − | 0.572375i | −0.0688152 | − | 0.0241872i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.51026 | − | 4.51026i | 0.190254 | − | 0.190254i | ||||
\(563\) | 2.05030 | − | 2.05030i | 0.0864099 | − | 0.0864099i | −0.662581 | − | 0.748991i | \(-0.730539\pi\) |
0.748991 | + | 0.662581i | \(0.230539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.8548 | + | 6.27563i | 0.751157 | + | 0.264018i | ||||
\(566\) | − | 7.45263i | − | 0.313257i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.302654 | + | 0.302654i | 0.0126991 | + | 0.0126991i | ||||
\(569\) | 17.8381 | 0.747813 | 0.373907 | − | 0.927466i | \(-0.378018\pi\) | ||||
0.373907 | + | 0.927466i | \(0.378018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.3891 | 1.06250 | 0.531251 | − | 0.847214i | \(-0.321722\pi\) | ||||
0.531251 | + | 0.847214i | \(0.321722\pi\) | |||||||
\(572\) | 2.82843 | + | 2.82843i | 0.118262 | + | 0.118262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0686782i | 0.00286657i | ||||||||
\(575\) | 0.545960 | + | 4.97010i | 0.0227681 | + | 0.207268i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.7672 | + | 22.7672i | −0.947812 | + | 0.947812i | −0.998704 | − | 0.0508924i | \(-0.983793\pi\) |
0.0508924 | + | 0.998704i | \(0.483793\pi\) | |||||||
\(578\) | 11.0611 | − | 11.0611i | 0.460083 | − | 0.460083i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.1764 | + | 9.20193i | −0.796256 | + | 0.382089i | ||||
\(581\) | − | 3.33323i | − | 0.138286i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.78067 | − | 2.78067i | −0.115164 | − | 0.115164i | ||||
\(584\) | 10.4069 | 0.430639 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.3324 | 1.00516 | ||||||||
\(587\) | 6.18537 | + | 6.18537i | 0.255298 | + | 0.255298i | 0.823138 | − | 0.567841i | \(-0.192221\pi\) |
−0.567841 | + | 0.823138i | \(0.692221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21.1732i | − | 0.872427i | ||||||
\(590\) | 9.88143 | − | 28.1136i | 0.406812 | − | 1.15742i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.43100 | − | 2.43100i | 0.0999133 | − | 0.0999133i | ||||
\(593\) | 32.3700 | − | 32.3700i | 1.32927 | − | 1.32927i | 0.423273 | − | 0.906002i | \(-0.360881\pi\) |
0.906002 | − | 0.423273i | \(-0.139119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.869974 | − | 1.81298i | −0.0356655 | − | 0.0743251i | ||||
\(596\) | 11.8391i | 0.484950i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.43352 | + | 3.43352i | 0.140407 | + | 0.140407i | ||||
\(599\) | −35.6565 | −1.45688 | −0.728442 | − | 0.685108i | \(-0.759755\pi\) | ||||
−0.728442 | + | 0.685108i | \(0.759755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.3509 | −0.544594 | −0.272297 | − | 0.962213i | \(-0.587783\pi\) | ||||
−0.272297 | + | 0.962213i | \(0.587783\pi\) | |||||||
\(602\) | 0.871019 | + | 0.871019i | 0.0355001 | + | 0.0355001i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 6.05321i | − | 0.246302i | ||||||
\(605\) | 9.98475 | + | 20.8077i | 0.405938 | + | 0.845955i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1614 | − | 10.1614i | 0.412439 | − | 0.412439i | −0.470148 | − | 0.882587i | \(-0.655800\pi\) |
0.882587 | + | 0.470148i | \(0.155800\pi\) | |||||||
\(608\) | 2.39292 | − | 2.39292i | 0.0970456 | − | 0.0970456i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.2760 | + | 32.0813i | −0.456551 | + | 1.29893i | ||||
\(611\) | 10.8268i | 0.438007i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.45520 | − | 7.45520i | −0.301113 | − | 0.301113i | 0.540336 | − | 0.841449i | \(-0.318297\pi\) |
−0.841449 | + | 0.540336i | \(0.818297\pi\) | |||||||
\(614\) | 6.26329 | 0.252766 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.635906 | 0.0256214 | ||||||||
\(617\) | −6.27790 | − | 6.27790i | −0.252739 | − | 0.252739i | 0.569354 | − | 0.822093i | \(-0.307193\pi\) |
−0.822093 | + | 0.569354i | \(0.807193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.0408i | − | 1.20744i | −0.797196 | − | 0.603720i | \(-0.793684\pi\) | ||
0.797196 | − | 0.603720i | \(-0.206316\pi\) | |||||||
\(620\) | 12.6133 | − | 6.05261i | 0.506564 | − | 0.243079i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.8409 | − | 23.8409i | 0.955931 | − | 0.955931i | ||||
\(623\) | −3.04964 | + | 3.04964i | −0.122181 | + | 0.122181i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.42696 | − | 24.4039i | −0.217078 | − | 0.976154i | ||||
\(626\) | − | 16.2101i | − | 0.647888i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.88326 | + | 9.88326i | 0.394385 | + | 0.394385i | ||||
\(629\) | 4.00516 | 0.159696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.75693 | −0.109752 | −0.0548758 | − | 0.998493i | \(-0.517476\pi\) | ||||
−0.0548758 | + | 0.998493i | \(0.517476\pi\) | |||||||
\(632\) | −1.29250 | − | 1.29250i | −0.0514128 | − | 0.0514128i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.16935i | 0.284731i | ||||||||
\(635\) | −34.0085 | − | 11.9534i | −1.34959 | − | 0.474355i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.9886 | + | 21.9886i | −0.871219 | + | 0.871219i | ||||
\(638\) | 5.54078 | − | 5.54078i | 0.219362 | − | 0.219362i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.10956 | + | 0.741469i | 0.0833875 | + | 0.0293092i | ||||
\(641\) | 32.3276i | 1.27686i | 0.769679 | + | 0.638431i | \(0.220416\pi\) | ||||
−0.769679 | + | 0.638431i | \(0.779584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.3690 | + | 22.3690i | 0.882149 | + | 0.882149i | 0.993753 | − | 0.111604i | \(-0.0355987\pi\) |
−0.111604 | + | 0.993753i | \(0.535599\pi\) | |||||||
\(644\) | 0.771946 | 0.0304190 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.94242 | 0.155113 | ||||||||
\(647\) | 28.3388 | + | 28.3388i | 1.11411 | + | 1.11411i | 0.992589 | + | 0.121523i | \(0.0387779\pi\) |
0.121523 | + | 0.992589i | \(0.461222\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.9782i | 0.430933i | ||||||||
\(650\) | −18.9395 | − | 15.1904i | −0.742868 | − | 0.595815i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.3875 | + | 10.3875i | −0.406808 | + | 0.406808i | ||||
\(653\) | 8.22997 | − | 8.22997i | 0.322064 | − | 0.322064i | −0.527495 | − | 0.849558i | \(-0.676869\pi\) |
0.849558 | + | 0.527495i | \(0.176869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.3698 | − | 13.1336i | 1.06942 | − | 0.513172i | ||||
\(656\) | − | 0.0889676i | − | 0.00347360i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.21708 | + | 1.21708i | 0.0474468 | + | 0.0474468i | ||||
\(659\) | −17.5863 | −0.685066 | −0.342533 | − | 0.939506i | \(-0.611285\pi\) | ||||
−0.342533 | + | 0.939506i | \(0.611285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.1567 | −1.83418 | −0.917092 | − | 0.398675i | \(-0.869470\pi\) | ||||
−0.917092 | + | 0.398675i | \(0.869470\pi\) | |||||||
\(662\) | 9.58208 | + | 9.58208i | 0.372418 | + | 0.372418i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.31795i | 0.167569i | ||||||||
\(665\) | −1.93697 | + | 5.51088i | −0.0751125 | + | 0.213703i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.72613 | − | 6.72613i | 0.260437 | − | 0.260437i | ||||
\(668\) | 12.0791 | − | 12.0791i | 0.467355 | − | 0.467355i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.55841 | − | 17.8353i | −0.330640 | − | 0.689038i | ||||
\(671\) | − | 12.5276i | − | 0.483621i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0202 | − | 10.0202i | −0.386251 | − | 0.386251i | 0.487097 | − | 0.873348i | \(-0.338056\pi\) |
−0.873348 | + | 0.487097i | \(0.838056\pi\) | |||||||
\(674\) | −16.6315 | −0.640622 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.5781 | −0.406849 | ||||||||
\(677\) | 17.2224 | + | 17.2224i | 0.661909 | + | 0.661909i | 0.955830 | − | 0.293921i | \(-0.0949601\pi\) |
−0.293921 | + | 0.955830i | \(0.594960\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.94185i | 0.381533i | ||||||||
\(680\) | 1.12699 | + | 2.34859i | 0.0432180 | + | 0.0900642i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.64447 | + | 3.64447i | −0.139554 | + | 0.139554i | ||||
\(683\) | 5.97392 | − | 5.97392i | 0.228586 | − | 0.228586i | −0.583516 | − | 0.812102i | \(-0.698323\pi\) |
0.812102 | + | 0.583516i | \(0.198323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.92010 | + | 5.46289i | −0.0733634 | + | 0.208726i | ||||
\(686\) | 10.3472i | 0.395060i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.12834 | − | 1.12834i | −0.0430176 | − | 0.0430176i | ||||
\(689\) | 23.1800 | 0.883088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.4935 | −1.23611 | −0.618056 | − | 0.786134i | \(-0.712080\pi\) | ||||
−0.618056 | + | 0.786134i | \(0.712080\pi\) | |||||||
\(692\) | 6.80191 | + | 6.80191i | 0.258570 | + | 0.258570i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 20.9041i | − | 0.793509i | ||||||
\(695\) | 26.0368 | − | 12.4939i | 0.987631 | − | 0.473922i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0732888 | − | 0.0732888i | 0.00277601 | − | 0.00277601i | ||||
\(698\) | 10.1349 | − | 10.1349i | 0.383612 | − | 0.383612i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.83665 | + | 0.421452i | −0.145012 | + | 0.0159294i | ||||
\(701\) | 20.7760i | 0.784698i | 0.919816 | + | 0.392349i | \(0.128337\pi\) | ||||
−0.919816 | + | 0.392349i | \(0.871663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.22672 | − | 8.22672i | −0.310277 | − | 0.310277i | ||||
\(704\) | −0.823770 | −0.0310470 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.67609 | −0.100716 | ||||||||
\(707\) | 0.128495 | + | 0.128495i | 0.00483254 | + | 0.00483254i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.1760i | − | 0.682613i | −0.939952 | − | 0.341307i | \(-0.889131\pi\) | ||
0.939952 | − | 0.341307i | \(-0.110869\pi\) | |||||||
\(710\) | 0.902925 | + | 0.317362i | 0.0338862 | + | 0.0119104i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.95058 | − | 3.95058i | 0.148054 | − | 0.148054i | ||||
\(713\) | −4.42414 | + | 4.42414i | −0.165685 | + | 0.165685i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.43822 | + | 2.96588i | 0.315572 | + | 0.110918i | ||||
\(716\) | − | 8.62964i | − | 0.322505i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.3997 | + | 13.3997i | 0.500074 | + | 0.500074i | ||||
\(719\) | −33.5991 | −1.25304 | −0.626518 | − | 0.779407i | \(-0.715520\pi\) | ||||
−0.626518 | + | 0.779407i | \(0.715520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.1747 | 0.527892 | ||||||||
\(722\) | 5.33717 | + | 5.33717i | 0.198629 | + | 0.198629i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 18.4075i | − | 0.684111i | ||||||
\(725\) | −29.7574 | + | 37.1018i | −1.10516 | + | 1.37793i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.35893 | − | 5.35893i | 0.198752 | − | 0.198752i | −0.600713 | − | 0.799465i | \(-0.705117\pi\) |
0.799465 | + | 0.600713i | \(0.205117\pi\) | |||||||
\(728\) | −2.65049 | + | 2.65049i | −0.0982338 | + | 0.0982338i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.9800 | − | 10.0674i | 0.776505 | − | 0.372612i | ||||
\(731\) | − | 1.85899i | − | 0.0687571i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1434 | + | 21.1434i | 0.780949 | + | 0.780949i | 0.979991 | − | 0.199042i | \(-0.0637830\pi\) |
−0.199042 | + | 0.979991i | \(0.563783\pi\) | |||||||
\(734\) | 0.269157 | 0.00993477 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 5.15330 | + | 5.15330i | 0.189824 | + | 0.189824i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.67003i | 0.355718i | 0.984056 | + | 0.177859i | \(0.0569171\pi\) | ||||
−0.984056 | + | 0.177859i | \(0.943083\pi\) | |||||||
\(740\) | 2.54913 | − | 7.25254i | 0.0937080 | − | 0.266609i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.60574 | − | 2.60574i | 0.0956598 | − | 0.0956598i | ||||
\(743\) | −11.5881 | + | 11.5881i | −0.425124 | + | 0.425124i | −0.886964 | − | 0.461839i | \(-0.847190\pi\) |
0.461839 | + | 0.886964i | \(0.347190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4530 | + | 23.8675i | 0.419605 | + | 0.874436i | ||||
\(746\) | − | 9.92244i | − | 0.363287i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.678596 | − | 0.678596i | −0.0248119 | − | 0.0248119i | ||||
\(749\) | −8.81153 | −0.321966 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0545 | 1.09670 | 0.548351 | − | 0.836248i | \(-0.315256\pi\) | ||||
0.548351 | + | 0.836248i | \(0.315256\pi\) | |||||||
\(752\) | −1.57664 | − | 1.57664i | −0.0574942 | − | 0.0574942i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46.1886i | 1.68209i | ||||||||
\(755\) | −5.85577 | − | 12.2032i | −0.213113 | − | 0.444118i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1394 | + | 38.1394i | −1.38620 | + | 1.38620i | −0.553060 | + | 0.833141i | \(0.686540\pi\) |
−0.833141 | + | 0.553060i | \(0.813460\pi\) | |||||||
\(758\) | 20.9415 | − | 20.9415i | 0.760631 | − | 0.760631i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.50920 | − | 7.13894i | 0.0910184 | − | 0.258956i | ||||
\(761\) | 1.74371i | 0.0632093i | 0.999500 | + | 0.0316046i | \(0.0100617\pi\) | ||||
−0.999500 | + | 0.0316046i | \(0.989938\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.376195 | − | 0.376195i | −0.0136192 | − | 0.0136192i | ||||
\(764\) | −6.86973 | −0.248538 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.4525 | 0.377665 | ||||||||
\(767\) | −45.7578 | − | 45.7578i | −1.65222 | − | 1.65222i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.8398i | 0.931808i | 0.884835 | + | 0.465904i | \(0.154271\pi\) | ||||
−0.884835 | + | 0.465904i | \(0.845729\pi\) | |||||||
\(770\) | 1.28197 | − | 0.615164i | 0.0461991 | − | 0.0221690i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.83501 | + | 7.83501i | −0.281988 | + | 0.281988i | ||||
\(773\) | −31.7741 | + | 31.7741i | −1.14284 | + | 1.14284i | −0.154906 | + | 0.987929i | \(0.549507\pi\) |
−0.987929 | + | 0.154906i | \(0.950493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.5730 | − | 24.4039i | 0.703084 | − | 0.876612i | ||||
\(776\) | − | 12.8789i | − | 0.462327i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.4167 | + | 10.4167i | 0.373455 | + | 0.373455i | ||||
\(779\) | −0.301075 | −0.0107871 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.352587 | −0.0126166 | ||||||||
\(782\) | −0.823770 | − | 0.823770i | −0.0294579 | − | 0.0294579i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 6.40410i | − | 0.228718i | ||||||
\(785\) | 29.4853 | + | 10.3636i | 1.05238 | + | 0.369891i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.8573 | + | 34.8573i | −1.24253 | + | 1.24253i | −0.283580 | + | 0.958949i | \(0.591522\pi\) |
−0.958949 | + | 0.283580i | \(0.908478\pi\) | |||||||
\(788\) | −14.0985 | + | 14.0985i | −0.502237 | + | 0.502237i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.85599 | − | 1.35531i | −0.137190 | − | 0.0482197i | ||||
\(791\) | − | 6.53358i | − | 0.232307i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.2156 | + | 52.2156i | 1.85423 | + | 1.85423i | ||||
\(794\) | −9.08826 | −0.322530 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.8854 | 0.633933 | ||||||||
\(797\) | 2.33267 | + | 2.33267i | 0.0826275 | + | 0.0826275i | 0.747213 | − | 0.664585i | \(-0.231392\pi\) |
−0.664585 | + | 0.747213i | \(0.731392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.59758i | − | 0.0918957i | ||||||
\(800\) | 4.97010 | − | 0.545960i | 0.175720 | − | 0.0193026i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.857459 | − | 0.857459i | 0.0302779 | − | 0.0302779i | ||||
\(803\) | −6.06192 | + | 6.06192i | −0.213921 | + | 0.213921i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.55623 | − | 0.746768i | 0.0548498 | − | 0.0263201i | ||||
\(806\) | − | 30.3807i | − | 1.07012i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.166455 | − | 0.166455i | −0.00585588 | − | 0.00585588i | ||||
\(809\) | −21.7674 | −0.765303 | −0.382651 | − | 0.923893i | \(-0.624989\pi\) | ||||
−0.382651 | + | 0.923893i | \(0.624989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.82577 | 0.239685 | 0.119843 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119843 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(812\) | 5.19222 | + | 5.19222i | 0.182211 | + | 0.182211i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.83208i | 0.0992642i | ||||||||
\(815\) | −10.8923 | + | 30.9898i | −0.381542 | + | 1.08553i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.81842 | + | 3.81842i | −0.133589 | + | 0.133589i | ||||
\(818\) | 12.1702 | − | 12.1702i | 0.425522 | − | 0.425522i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0860657 | − | 0.179357i | −0.00300555 | − | 0.00626341i | ||||
\(821\) | − | 8.55784i | − | 0.298671i | −0.988787 | − | 0.149335i | \(-0.952287\pi\) | ||
0.988787 | − | 0.149335i | \(-0.0477134\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.3021 | − | 20.3021i | −0.707687 | − | 0.707687i | 0.258361 | − | 0.966048i | \(-0.416818\pi\) |
−0.966048 | + | 0.258361i | \(0.916818\pi\) | |||||||
\(824\) | −18.3622 | −0.639679 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.2876 | −0.357951 | ||||||||
\(827\) | 17.5394 | + | 17.5394i | 0.609906 | + | 0.609906i | 0.942921 | − | 0.333016i | \(-0.108066\pi\) |
−0.333016 | + | 0.942921i | \(0.608066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.9440i | − | 0.380101i | −0.981774 | − | 0.190050i | \(-0.939135\pi\) | ||
0.981774 | − | 0.190050i | \(-0.0608652\pi\) | |||||||
\(830\) | 4.17711 | + | 8.70490i | 0.144990 | + | 0.302152i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.43352 | − | 3.43352i | 0.119036 | − | 0.119036i | ||||
\(833\) | 5.27550 | − | 5.27550i | 0.182785 | − | 0.182785i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6661 | − | 36.0364i | 0.438329 | − | 1.24709i | ||||
\(836\) | 2.78772i | 0.0964152i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.10896 | + | 7.10896i | 0.245575 | + | 0.245575i | ||||
\(839\) | −50.9037 | −1.75739 | −0.878696 | − | 0.477382i | \(-0.841586\pi\) | ||||
−0.878696 | + | 0.477382i | \(0.841586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.4818 | 2.12006 | ||||||||
\(842\) | −2.69970 | − | 2.69970i | −0.0930379 | − | 0.0930379i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.68986i | 0.299117i | ||||||||
\(845\) | −21.3252 | + | 10.2331i | −0.733609 | + | 0.352028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.63392 | − | 5.63392i | 0.193584 | − | 0.193584i | ||||
\(848\) | −3.37555 | + | 3.37555i | −0.115917 | + | 0.115917i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.54396 | + | 3.64447i | 0.155857 | + | 0.125004i | ||||
\(851\) | 3.43795i | 0.117851i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.76417 | − | 6.76417i | −0.231601 | − | 0.231601i | 0.581760 | − | 0.813361i | \(-0.302364\pi\) |
−0.813361 | + | 0.581760i | \(0.802364\pi\) | |||||||
\(854\) | 11.7395 | 0.401716 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.4147 | 0.390146 | ||||||||
\(857\) | −5.91490 | − | 5.91490i | −0.202049 | − | 0.202049i | 0.598828 | − | 0.800877i | \(-0.295633\pi\) |
−0.800877 | + | 0.598828i | \(0.795633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.86410i | − | 0.165961i | −0.996551 | − | 0.0829804i | \(-0.973556\pi\) | ||
0.996551 | − | 0.0829804i | \(-0.0264439\pi\) | |||||||
\(860\) | −3.36625 | − | 1.18317i | −0.114788 | − | 0.0403459i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.3534 | − | 25.3534i | 0.863541 | − | 0.863541i | ||||
\(863\) | −4.84105 | + | 4.84105i | −0.164791 | + | 0.164791i | −0.784685 | − | 0.619894i | \(-0.787176\pi\) |
0.619894 | + | 0.784685i | \(0.287176\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.2926 | + | 7.13246i | 0.689968 | + | 0.242511i | ||||
\(866\) | 6.39505i | 0.217313i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.41520 | − | 3.41520i | −0.115919 | − | 0.115919i | ||||
\(869\) | 1.50574 | 0.0510788 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.9585 | −1.45559 | ||||||||
\(872\) | 0.487333 | + | 0.487333i | 0.0165032 | + | 0.0165032i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.38410i | 0.114469i | ||||||||
\(875\) | −7.32691 | + | 4.56115i | −0.247695 | + | 0.154195i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.1613 | + | 35.1613i | −1.18731 | + | 1.18731i | −0.209504 | + | 0.977808i | \(0.567185\pi\) |
−0.977808 | + | 0.209504i | \(0.932815\pi\) | |||||||
\(878\) | 25.0076 | − | 25.0076i | 0.843966 | − | 0.843966i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.66070 | + | 0.796900i | −0.0559822 | + | 0.0268635i | ||||
\(881\) | − | 33.2817i | − | 1.12129i | −0.828057 | − | 0.560644i | \(-0.810553\pi\) | ||
0.828057 | − | 0.560644i | \(-0.189447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.99858 | + | 9.99858i | 0.336479 | + | 0.336479i | 0.855040 | − | 0.518561i | \(-0.173532\pi\) |
−0.518561 | + | 0.855040i | \(0.673532\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.7751 | −0.832336 | ||||||||
\(887\) | −37.4673 | − | 37.4673i | −1.25803 | − | 1.25803i | −0.952032 | − | 0.305997i | \(-0.901010\pi\) |
−0.305997 | − | 0.952032i | \(-0.598990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4447i | 0.417381i | ||||||||
\(890\) | 4.14256 | − | 11.7860i | 0.138859 | − | 0.395068i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.43171 | + | 2.43171i | −0.0814196 | + | 0.0814196i | ||||
\(893\) | −5.33550 | + | 5.33550i | −0.178546 | + | 0.178546i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.34816 | − | 17.3972i | −0.279048 | − | 0.581523i | ||||
\(896\) | − | 0.771946i | − | 0.0257889i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.86801 | − | 2.86801i | −0.0957067 | − | 0.0957067i | ||||
\(899\) | −59.5148 | −1.98493 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.56135 | −0.185275 | ||||||||
\(902\) | 0.0518230 | + | 0.0518230i | 0.00172552 | + | 0.00172552i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.46377i | 0.281501i | ||||||||
\(905\) | −17.8071 | − | 37.1092i | −0.591929 | − | 1.23355i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.0280 | − | 42.0280i | 1.39552 | − | 1.39552i | 0.583157 | − | 0.812359i | \(-0.301817\pi\) |
0.812359 | − | 0.583157i | \(-0.198183\pi\) | |||||||
\(908\) | −15.5944 | + | 15.5944i | −0.517520 | + | 0.517520i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.77930 | + | 7.90738i | −0.0921328 | + | 0.262127i | ||||
\(911\) | − | 35.4560i | − | 1.17471i | −0.809329 | − | 0.587355i | \(-0.800169\pi\) | ||
0.809329 | − | 0.587355i | \(-0.199831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.51518 | − | 2.51518i | −0.0832402 | − | 0.0832402i | ||||
\(914\) | −34.1908 | −1.13093 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.17054 | 0.0386756 | ||||||||
\(917\) | −7.41067 | − | 7.41067i | −0.244722 | − | 0.244722i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6463i | 0.417163i | 0.978005 | + | 0.208581i | \(0.0668846\pi\) | ||||
−0.978005 | + | 0.208581i | \(0.933115\pi\) | |||||||
\(920\) | −2.01598 | + | 0.967383i | −0.0664649 | + | 0.0318937i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.68839 | − | 7.68839i | 0.253204 | − | 0.253204i | ||||
\(923\) | 1.46960 | − | 1.46960i | 0.0483726 | − | 0.0483726i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.87698 | − | 17.0869i | −0.0617148 | − | 0.561815i | ||||
\(926\) | 28.6255i | 0.940694i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.72613 | − | 6.72613i | −0.220796 | − | 0.220796i | ||||
\(929\) | 6.96583 | 0.228541 | 0.114271 | − | 0.993450i | \(-0.463547\pi\) | ||||
0.114271 | + | 0.993450i | \(0.463547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.6721 | −0.710274 | ||||||||
\(932\) | −0.391179 | − | 0.391179i | −0.0128135 | − | 0.0128135i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 4.39957i | − | 0.143958i | ||||||
\(935\) | −2.02450 | − | 0.711573i | −0.0662082 | − | 0.0232709i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.21026 | − | 4.21026i | 0.137543 | − | 0.137543i | −0.634983 | − | 0.772526i | \(-0.718993\pi\) |
0.772526 | + | 0.634983i | \(0.218993\pi\) | |||||||
\(938\) | −4.82911 | + | 4.82911i | −0.157676 | + | 0.157676i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.70369 | − | 1.65326i | −0.153417 | − | 0.0539234i | ||||
\(941\) | − | 2.55988i | − | 0.0834498i | −0.999129 | − | 0.0417249i | \(-0.986715\pi\) | ||
0.999129 | − | 0.0417249i | \(-0.0132853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0629096 | + | 0.0629096i | 0.00204862 | + | 0.00204862i | ||||
\(944\) | 13.3268 | 0.433751 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.31450 | 0.0427382 | ||||||||
\(947\) | −12.5991 | − | 12.5991i | −0.409416 | − | 0.409416i | 0.472119 | − | 0.881535i | \(-0.343489\pi\) |
−0.881535 | + | 0.472119i | \(0.843489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 50.5329i | − | 1.64037i | ||||||
\(950\) | −1.84758 | − | 16.8193i | −0.0599435 | − | 0.545690i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.635906 | − | 0.635906i | 0.0206098 | − | 0.0206098i | ||||
\(953\) | 5.29171 | − | 5.29171i | 0.171415 | − | 0.171415i | −0.616186 | − | 0.787601i | \(-0.711323\pi\) |
0.787601 | + | 0.616186i | \(0.211323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8492 | + | 6.64565i | −0.448150 | + | 0.215048i | ||||
\(956\) | 4.90654i | 0.158689i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.6947 | + | 27.6947i | 0.894774 | + | 0.894774i | ||||
\(959\) | 1.99903 | 0.0645520 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.14608 | 0.262777 | ||||||||
\(962\) | −11.8042 | − | 11.8042i | −0.380584 | − | 0.380584i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.4617i | 0.820065i | ||||||||
\(965\) | −8.21577 | + | 23.3747i | −0.264475 | + | 0.752458i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.0727 | − | 21.0727i | 0.677651 | − | 0.677651i | −0.281817 | − | 0.959468i | \(-0.590937\pi\) |
0.959468 | + | 0.281817i | \(0.0909372\pi\) | |||||||
\(968\) | −7.29833 | + | 7.29833i | −0.234577 | + | 0.234577i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.4589 | − | 25.9637i | −0.400030 | − | 0.833643i | ||||
\(971\) | 34.5438i | 1.10856i | 0.832329 | + | 0.554282i | \(0.187007\pi\) | ||||
−0.832329 | + | 0.554282i | \(0.812993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.04975 | − | 7.04975i | −0.226004 | − | 0.226004i | ||||
\(974\) | −5.76978 | −0.184876 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.2076 | −0.486784 | ||||||||
\(977\) | −29.6333 | − | 29.6333i | −0.948053 | − | 0.948053i | 0.0506632 | − | 0.998716i | \(-0.483866\pi\) |
−0.998716 | + | 0.0506632i | \(0.983866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.60237i | 0.147092i | ||||||||
\(980\) | −6.19521 | − | 12.9105i | −0.197899 | − | 0.412412i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.4239 | − | 24.4239i | 0.779397 | − | 0.779397i | ||||
\(983\) | −40.1893 | + | 40.1893i | −1.28184 | + | 1.28184i | −0.342221 | + | 0.939620i | \(0.611179\pi\) |
−0.939620 | + | 0.342221i | \(0.888821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.7836 | + | 42.0608i | −0.471044 | + | 1.34017i | ||||
\(986\) | − | 11.0816i | − | 0.352909i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.6194 | − | 11.6194i | −0.369661 | − | 0.369661i | ||||
\(989\) | 1.59572 | 0.0507408 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.1900 | −1.34021 | −0.670105 | − | 0.742266i | \(-0.733751\pi\) | ||||
−0.670105 | + | 0.742266i | \(0.733751\pi\) | |||||||
\(992\) | 4.42414 | + | 4.42414i | 0.140467 | + | 0.140467i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 0.330406i | − | 0.0104798i | ||||||
\(995\) | 36.0567 | − | 17.3021i | 1.14307 | − | 0.548512i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.72432 | + | 4.72432i | −0.149621 | + | 0.149621i | −0.777949 | − | 0.628328i | \(-0.783740\pi\) |
0.628328 | + | 0.777949i | \(0.283740\pi\) | |||||||
\(998\) | −5.43042 | + | 5.43042i | −0.171897 | + | 0.171897i | ||||
\(999\) | 0 | 0 |
(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 | 2070.2.j.j.323.8 | yes | 20 | |
3.2 | odd | 2 | inner | 2070.2.j.j.323.3 | ✓ | 20 | |
5.2 | odd | 4 | inner | 2070.2.j.j.737.3 | yes | 20 | |
15.2 | even | 4 | inner | 2070.2.j.j.737.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.j.323.3 | ✓ | 20 | 3.2 | odd | 2 | inner | |
2070.2.j.j.323.8 | yes | 20 | 1.1 | even | 1 | trivial | |
2070.2.j.j.737.3 | yes | 20 | 5.2 | odd | 4 | inner | |
2070.2.j.j.737.8 | yes | 20 | 15.2 | even | 4 | inner |