Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,3,Mod(73,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.73");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.u (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: | \(3.26976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.73 |
Dual form | 120.3.u.a.97.1 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.67423 | + | 4.22474i | −0.534847 | + | 0.844949i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.44949 | + | 5.44949i | −0.778499 | + | 0.778499i | −0.979575 | − | 0.201077i | \(-0.935556\pi\) |
0.201077 | + | 0.979575i | \(0.435556\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.44949 | −0.586317 | −0.293159 | − | 0.956064i | \(-0.594706\pi\) | ||||
−0.293159 | + | 0.956064i | \(0.594706\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4495 | + | 14.4495i | 1.11150 | + | 1.11150i | 0.992948 | + | 0.118551i | \(0.0378250\pi\) |
0.118551 | + | 0.992948i | \(0.462175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.44949 | − | 1.89898i | 0.563299 | − | 0.126599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.1464 | + | 23.1464i | −1.36155 | + | 1.36155i | −0.489617 | + | 0.871938i | \(0.662863\pi\) |
−0.871938 | + | 0.489617i | \(0.837137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 16.6969i | − | 0.878786i | −0.898295 | − | 0.439393i | \(-0.855194\pi\) | ||
0.898295 | − | 0.439393i | \(-0.144806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.3485 | 0.635641 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.65153 | − | 6.65153i | −0.289197 | − | 0.289197i | 0.547566 | − | 0.836763i | \(-0.315555\pi\) |
−0.836763 | + | 0.547566i | \(0.815555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.6969 | − | 22.5959i | −0.427878 | − | 0.903837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0454077i | 0.00156578i | 1.00000 | 0.000782891i | \(0.000249202\pi\) | |||||
−1.00000 | 0.000782891i | \(0.999751\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.49490 | 0.144997 | 0.0724983 | − | 0.997369i | \(-0.476903\pi\) | ||||
0.0724983 | + | 0.997369i | \(0.476903\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.89898 | + | 7.89898i | 0.239363 | + | 0.239363i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.44949 | − | 37.5959i | −0.241414 | − | 1.07417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.3485 | − | 35.3485i | 0.955364 | − | 0.955364i | −0.0436815 | − | 0.999046i | \(-0.513909\pi\) |
0.999046 | + | 0.0436815i | \(0.0139087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 35.3939i | − | 0.907535i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.2929 | 0.494948 | 0.247474 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247474 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.2929 | + | 32.2929i | 0.750997 | + | 0.750997i | 0.974665 | − | 0.223669i | \(-0.0718033\pi\) |
−0.223669 | + | 0.974665i | \(0.571803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.6742 | − | 8.02270i | −0.281650 | − | 0.178282i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −50.5403 | + | 50.5403i | −1.07533 | + | 1.07533i | −0.0784040 | + | 0.996922i | \(0.524982\pi\) |
−0.996922 | + | 0.0784040i | \(0.975018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 10.3939i | − | 0.212120i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 56.6969 | 1.11170 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.50510 | − | 5.50510i | −0.103870 | − | 0.103870i | 0.653262 | − | 0.757132i | \(-0.273400\pi\) |
−0.757132 | + | 0.653262i | \(0.773400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.2474 | − | 27.2474i | 0.313590 | − | 0.495408i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −20.4495 | + | 20.4495i | −0.358763 | + | 0.358763i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 55.4393i | − | 0.939649i | −0.882760 | − | 0.469824i | \(-0.844317\pi\) | ||
0.882760 | − | 0.469824i | \(-0.155683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.8888 | 0.785062 | 0.392531 | − | 0.919739i | \(-0.371600\pi\) | ||||
0.392531 | + | 0.919739i | \(0.371600\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.3485 | − | 16.3485i | −0.259500 | − | 0.259500i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −99.6867 | + | 22.4041i | −1.53364 | + | 0.344678i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −85.2827 | + | 85.2827i | −1.27288 | + | 1.27288i | −0.328303 | + | 0.944573i | \(0.606477\pi\) |
−0.944573 | + | 0.328303i | \(0.893523\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.2929i | 0.236128i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.4041 | 0.681748 | 0.340874 | − | 0.940109i | \(-0.389277\pi\) | ||||
0.340874 | + | 0.940109i | \(0.389277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.9898 | − | 21.9898i | −0.301230 | − | 0.301230i | 0.540265 | − | 0.841495i | \(-0.318324\pi\) |
−0.841495 | + | 0.540265i | \(0.818324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.5732 | + | 40.7753i | −0.194310 | + | 0.543670i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 35.1464 | − | 35.1464i | 0.456447 | − | 0.456447i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 126.697i | 1.60376i | 0.597486 | + | 0.801879i | \(0.296166\pi\) | ||||
−0.597486 | + | 0.801879i | \(0.703834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 94.9444 | + | 94.9444i | 1.14391 | + | 1.14391i | 0.987729 | + | 0.156180i | \(0.0499179\pi\) |
0.156180 | + | 0.987729i | \(0.450082\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −35.8888 | − | 159.687i | −0.422221 | − | 1.87867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0556128 | − | 0.0556128i | 0.000639228 | − | 0.000639228i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 71.7980i | 0.806719i | 0.915042 | + | 0.403359i | \(0.132158\pi\) | ||||
−0.915042 | + | 0.403359i | \(0.867842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −157.485 | −1.73060 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.50510 | − | 5.50510i | −0.0591947 | − | 0.0591947i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 70.5403 | + | 44.6515i | 0.742530 | + | 0.470016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −37.0000 | + | 37.0000i | −0.381443 | + | 0.381443i | −0.871622 | − | 0.490179i | \(-0.836932\pi\) |
0.490179 | + | 0.871622i | \(0.336932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 19.3485i | − | 0.195439i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 94.3383 | 0.934042 | 0.467021 | − | 0.884246i | \(-0.345327\pi\) | ||||
0.467021 | + | 0.884246i | \(0.345327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 72.6413 | + | 72.6413i | 0.705256 | + | 0.705256i | 0.965534 | − | 0.260278i | \(-0.0838142\pi\) |
−0.260278 | + | 0.965534i | \(0.583814\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −35.6969 | + | 56.3939i | −0.339971 | + | 0.537085i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.0556 | + | 13.0556i | −0.122015 | + | 0.122015i | −0.765478 | − | 0.643463i | \(-0.777497\pi\) |
0.643463 | + | 0.765478i | \(0.277497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 69.2827i | 0.635621i | 0.948154 | + | 0.317810i | \(0.102948\pi\) | ||||
−0.948154 | + | 0.317810i | \(0.897052\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −86.5857 | −0.780051 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −102.136 | − | 102.136i | −0.903860 | − | 0.903860i | 0.0919072 | − | 0.995768i | \(-0.470704\pi\) |
−0.995768 | + | 0.0919072i | \(0.970704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 45.8888 | − | 10.3133i | 0.399033 | − | 0.0896806i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −43.3485 | + | 43.3485i | −0.370500 | + | 0.370500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 252.272i | − | 2.11994i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −79.4041 | −0.656232 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.8536 | − | 24.8536i | −0.202062 | − | 0.202062i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 124.068 | + | 15.2350i | 0.992545 | + | 0.121880i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 119.944 | − | 119.944i | 0.944444 | − | 0.944444i | −0.0540920 | − | 0.998536i | \(-0.517226\pi\) |
0.998536 | + | 0.0540920i | \(0.0172264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 79.1010i | − | 0.613186i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 121.146 | 0.924782 | 0.462391 | − | 0.886676i | \(-0.346992\pi\) | ||||
0.462391 | + | 0.886676i | \(0.346992\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.9898 | + | 90.9898i | 0.684134 | + | 0.684134i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.69694 | + | 25.3485i | 0.0421995 | + | 0.187766i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 119.530 | − | 119.530i | 0.872482 | − | 0.872482i | −0.120260 | − | 0.992742i | \(-0.538373\pi\) |
0.992742 | + | 0.120260i | \(0.0383728\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 140.788i | − | 1.01286i | −0.862281 | − | 0.506431i | \(-0.830965\pi\) | ||
0.862281 | − | 0.506431i | \(-0.169035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 123.798 | 0.878000 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −93.1918 | − | 93.1918i | −0.651691 | − | 0.651691i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.191836 | − | 0.121431i | −0.00132301 | − | 0.000837454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7298 | + | 12.7298i | −0.0865976 | + | 0.0865976i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 53.5301i | 0.359262i | 0.983734 | + | 0.179631i | \(0.0574904\pi\) | ||||
−0.983734 | + | 0.179631i | \(0.942510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −232.606 | −1.54044 | −0.770219 | − | 0.637780i | \(-0.779853\pi\) | ||||
−0.770219 | + | 0.637780i | \(0.779853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −69.4393 | − | 69.4393i | −0.453852 | − | 0.453852i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0204 | + | 18.9898i | −0.0775510 | + | 0.122515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 128.631 | − | 128.631i | 0.819306 | − | 0.819306i | −0.166701 | − | 0.986007i | \(-0.553311\pi\) |
0.986007 | + | 0.166701i | \(0.0533115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.4847i | 0.0848094i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72.4949 | 0.450279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −117.576 | − | 117.576i | −0.721322 | − | 0.721322i | 0.247552 | − | 0.968875i | \(-0.420374\pi\) |
−0.968875 | + | 0.247552i | \(0.920374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −54.4949 | + | 12.2474i | −0.330272 | + | 0.0742270i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −33.6617 | + | 33.6617i | −0.201567 | + | 0.201567i | −0.800671 | − | 0.599104i | \(-0.795524\pi\) |
0.599104 | + | 0.800671i | \(0.295524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 248.576i | 1.47086i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 50.0908 | 0.292929 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 28.2474 | + | 28.2474i | 0.163280 | + | 0.163280i | 0.784018 | − | 0.620738i | \(-0.213167\pi\) |
−0.620738 | + | 0.784018i | \(0.713167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 181.429 | + | 64.8434i | 1.03674 | + | 0.370534i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −67.8990 | + | 67.8990i | −0.383610 | + | 0.383610i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 45.2372i | 0.252722i | 0.991984 | + | 0.126361i | \(0.0403298\pi\) | ||||
−0.991984 | + | 0.126361i | \(0.959670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −260.656 | −1.44009 | −0.720045 | − | 0.693928i | \(-0.755879\pi\) | ||||
−0.720045 | + | 0.693928i | \(0.755879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −58.6515 | − | 58.6515i | −0.320500 | − | 0.320500i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 54.8082 | + | 243.868i | 0.296260 | + | 1.31821i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 149.283 | − | 149.283i | 0.798303 | − | 0.798303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 40.0454i | 0.211880i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −51.8684 | −0.271562 | −0.135781 | − | 0.990739i | \(-0.543354\pi\) | ||||
−0.135781 | + | 0.990739i | \(0.543354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6163 | + | 16.6163i | 0.0860950 | + | 0.0860950i | 0.748843 | − | 0.662748i | \(-0.230610\pi\) |
−0.662748 | + | 0.748843i | \(0.730610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 149.530 | + | 94.6515i | 0.766821 | + | 0.485392i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 86.0908 | − | 86.0908i | 0.437009 | − | 0.437009i | −0.453995 | − | 0.891004i | \(-0.650002\pi\) |
0.891004 | + | 0.453995i | \(0.150002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 28.5653i | − | 0.143544i | −0.997421 | − | 0.0717721i | \(-0.977135\pi\) | ||
0.997421 | − | 0.0717721i | \(-0.0228654\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 208.899 | 1.03930 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.247449 | − | 0.247449i | −0.00121896 | − | 0.00121896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −54.2679 | + | 85.7321i | −0.264721 | + | 0.418206i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.9546 | − | 19.9546i | 0.0963990 | − | 0.0963990i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 107.687i | 0.515248i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −197.151 | −0.934365 | −0.467183 | − | 0.884161i | \(-0.654731\pi\) | ||||
−0.467183 | + | 0.884161i | \(0.654731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −59.2827 | − | 59.2827i | −0.278322 | − | 0.278322i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −222.788 | + | 50.0704i | −1.03622 | + | 0.232886i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.4949 | + | 24.4949i | −0.112880 | + | 0.112880i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 53.8638i | 0.245953i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −668.908 | −3.02673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 287.338 | + | 287.338i | 1.28851 | + | 1.28851i | 0.935690 | + | 0.352822i | \(0.114778\pi\) |
0.352822 | + | 0.935690i | \(0.385222\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 67.7878 | − | 32.0908i | 0.301279 | − | 0.142626i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −234.384 | + | 234.384i | −1.03253 | + | 1.03253i | −0.0330743 | + | 0.999453i | \(0.510530\pi\) |
−0.999453 | + | 0.0330743i | \(0.989470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 284.969i | 1.24441i | 0.782855 | + | 0.622204i | \(0.213763\pi\) | ||||
−0.782855 | + | 0.622204i | \(0.786237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −86.0908 | −0.372688 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −241.530 | − | 241.530i | −1.03661 | − | 1.03661i | −0.999304 | − | 0.0373060i | \(-0.988122\pi\) |
−0.0373060 | − | 0.999304i | \(-0.511878\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −78.3633 | − | 348.677i | −0.333461 | − | 1.48373i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 155.171 | − | 155.171i | 0.654732 | − | 0.654732i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 327.737i | 1.37128i | 0.727939 | + | 0.685642i | \(0.240478\pi\) | ||||
−0.727939 | + | 0.685642i | \(0.759522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 269.131 | 1.11672 | 0.558362 | − | 0.829597i | \(-0.311430\pi\) | ||||
0.558362 | + | 0.829597i | \(0.311430\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 43.9115 | + | 27.7957i | 0.179231 | + | 0.113452i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 241.262 | − | 241.262i | 0.976770 | − | 0.976770i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 232.565i | − | 0.933997i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 186.136 | 0.741579 | 0.370789 | − | 0.928717i | \(-0.379087\pi\) | ||||
0.370789 | + | 0.928717i | \(0.379087\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.8990 | + | 42.8990i | 0.169561 | + | 0.169561i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −151.621 | + | 239.530i | −0.594592 | + | 0.939334i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 138.268 | − | 138.268i | 0.538007 | − | 0.538007i | −0.384936 | − | 0.922943i | \(-0.625776\pi\) |
0.922943 | + | 0.384936i | \(0.125776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 385.262i | 1.48750i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.136223 | −0.000521927 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −163.146 | − | 163.146i | −0.620329 | − | 0.620329i | 0.325287 | − | 0.945615i | \(-0.394539\pi\) |
−0.945615 | + | 0.325287i | \(0.894539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.9796 | − | 8.53572i | 0.143319 | − | 0.0322103i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 87.9342 | − | 87.9342i | 0.329342 | − | 0.329342i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 108.227i | − | 0.402331i | −0.979557 | − | 0.201165i | \(-0.935527\pi\) | ||
0.979557 | − | 0.201165i | \(-0.0644729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 324.384 | 1.19699 | 0.598494 | − | 0.801127i | \(-0.295766\pi\) | ||||
0.598494 | + | 0.801127i | \(0.295766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 192.879 | + | 192.879i | 0.706515 | + | 0.706515i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 68.9898 | + | 145.732i | 0.250872 | + | 0.529935i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −165.864 | + | 165.864i | −0.598786 | + | 0.598786i | −0.939990 | − | 0.341203i | \(-0.889166\pi\) |
0.341203 | + | 0.939990i | \(0.389166\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.4847i | 0.0483322i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 300.434 | 1.06916 | 0.534579 | − | 0.845118i | \(-0.320470\pi\) | ||||
0.534579 | + | 0.845118i | \(0.320470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −352.161 | − | 352.161i | −1.24439 | − | 1.24439i | −0.958163 | − | 0.286223i | \(-0.907600\pi\) |
−0.286223 | − | 0.958163i | \(-0.592400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.7071 | − | 141.081i | −0.111253 | − | 0.495020i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −110.586 | + | 110.586i | −0.385316 | + | 0.385316i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 782.514i | − | 2.70766i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 90.6311 | 0.311447 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −109.414 | − | 109.414i | −0.373428 | − | 0.373428i | 0.495296 | − | 0.868724i | \(-0.335059\pi\) |
−0.868724 | + | 0.495296i | \(0.835059\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 234.217 | + | 148.258i | 0.793955 | + | 0.502568i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.6969 | + | 23.6969i | −0.0797877 | + | 0.0797877i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 192.222i | − | 0.642884i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −351.959 | −1.16930 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −115.540 | − | 115.540i | −0.381321 | − | 0.381321i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −128.066 | + | 202.318i | −0.419888 | + | 0.663337i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 110.627 | − | 110.627i | 0.360347 | − | 0.360347i | −0.503594 | − | 0.863941i | \(-0.667989\pi\) |
0.863941 | + | 0.503594i | \(0.167989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 177.934i | − | 0.575839i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.38367 | 0.00766454 | 0.00383227 | − | 0.999993i | \(-0.498780\pi\) | ||||
0.00383227 | + | 0.999993i | \(0.498780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 132.959 | + | 132.959i | 0.424790 | + | 0.424790i | 0.886849 | − | 0.462059i | \(-0.152889\pi\) |
−0.462059 | + | 0.886849i | \(0.652889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 112.788 | − | 25.3485i | 0.358056 | − | 0.0804713i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −37.1464 | + | 37.1464i | −0.117181 | + | 0.117181i | −0.763266 | − | 0.646085i | \(-0.776405\pi\) |
0.646085 | + | 0.763266i | \(0.276405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.292856i | − | 0.000918045i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.9796 | 0.0996249 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 386.474 | + | 386.474i | 1.19652 | + | 1.19652i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 171.934 | − | 481.065i | 0.529028 | − | 1.48020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 84.8536 | − | 84.8536i | 0.259491 | − | 0.259491i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 550.838i | − | 1.67428i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.6459 | 0.0653955 | 0.0326978 | − | 0.999465i | \(-0.489590\pi\) | ||||
0.0326978 | + | 0.999465i | \(0.489590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 106.045 | + | 106.045i | 0.318455 | + | 0.318455i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −132.232 | − | 588.363i | −0.394721 | − | 1.75631i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −136.757 | + | 136.757i | −0.405808 | + | 0.405808i | −0.880274 | − | 0.474466i | \(-0.842641\pi\) |
0.474466 | + | 0.880274i | \(0.342641\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 250.182i | 0.737999i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.9898 | −0.0850141 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −210.384 | − | 210.384i | −0.613363 | − | 0.613363i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −68.8332 | − | 43.5709i | −0.199516 | − | 0.126293i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.8480 | − | 33.8480i | 0.0975445 | − | 0.0975445i | −0.656650 | − | 0.754195i | \(-0.728027\pi\) |
0.754195 | + | 0.656650i | \(0.228027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 241.283i | 0.691354i | 0.938354 | + | 0.345677i | \(0.112351\pi\) | ||||
−0.938354 | + | 0.345677i | \(0.887649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 106.182 | 0.302512 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 126.833 | + | 126.833i | 0.359301 | + | 0.359301i | 0.863555 | − | 0.504254i | \(-0.168233\pi\) |
−0.504254 | + | 0.863555i | \(0.668233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −129.444 | + | 204.495i | −0.364631 | + | 0.576042i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −308.969 | + | 308.969i | −0.865460 | + | 0.865460i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.1112i | 0.0615912i | 0.999526 | + | 0.0307956i | \(0.00980409\pi\) | ||||
−0.999526 | + | 0.0307956i | \(0.990196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 82.2122 | 0.227735 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 97.2497 | + | 97.2497i | 0.267906 | + | 0.267906i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 151.707 | − | 34.0954i | 0.415636 | − | 0.0934121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −213.944 | + | 213.944i | −0.582955 | + | 0.582955i | −0.935714 | − | 0.352759i | \(-0.885243\pi\) |
0.352759 | + | 0.935714i | \(0.385243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 60.8786i | 0.164983i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 60.0000 | 0.161725 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 210.025 | + | 210.025i | 0.563070 | + | 0.563070i | 0.930178 | − | 0.367108i | \(-0.119652\pi\) |
−0.367108 | + | 0.930178i | \(0.619652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −133.293 | − | 170.611i | −0.355448 | − | 0.454962i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.656118 | + | 0.656118i | −0.00174037 | + | 0.00174037i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 124.343i | 0.328081i | 0.986454 | + | 0.164041i | \(0.0524528\pi\) | ||||
−0.986454 | + | 0.164041i | \(0.947547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −293.803 | −0.771135 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 418.540 | + | 418.540i | 1.09279 | + | 1.09279i | 0.995229 | + | 0.0975654i | \(0.0311055\pi\) |
0.0975654 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 54.4949 | + | 242.474i | 0.141545 | + | 0.629804i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −96.8786 | + | 96.8786i | −0.250332 | + | 0.250332i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 369.884i | 0.950859i | 0.879754 | + | 0.475430i | \(0.157707\pi\) | ||||
−0.879754 | + | 0.475430i | \(0.842293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 307.918 | 0.787515 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −148.373 | − | 148.373i | −0.377541 | − | 0.377541i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −535.262 | − | 338.817i | −1.35509 | − | 0.857765i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −373.984 | + | 373.984i | −0.942026 | + | 0.942026i | −0.998409 | − | 0.0563835i | \(-0.982043\pi\) |
0.0563835 | + | 0.998409i | \(0.482043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 222.879i | − | 0.558593i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 113.151 | 0.282172 | 0.141086 | − | 0.989997i | \(-0.454941\pi\) | ||||
0.141086 | + | 0.989997i | \(0.454941\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 64.9490 | + | 64.9490i | 0.161164 | + | 0.161164i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.0681 | − | 38.0227i | 0.0594274 | − | 0.0938832i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −227.980 | + | 227.980i | −0.560146 | + | 0.560146i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 90.3837i | − | 0.220987i | −0.993877 | − | 0.110493i | \(-0.964757\pi\) | ||
0.993877 | − | 0.110493i | \(-0.0352431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −292.788 | −0.712379 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 302.116 | + | 302.116i | 0.731515 | + | 0.731515i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −655.019 | + | 147.212i | −1.57836 | + | 0.354728i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −172.429 | + | 172.429i | −0.413499 | + | 0.413499i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 334.772i | − | 0.798978i | −0.916738 | − | 0.399489i | \(-0.869188\pi\) | ||
0.916738 | − | 0.399489i | \(-0.130812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 57.2735 | 0.136042 | 0.0680208 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680208 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −151.621 | − | 151.621i | −0.358442 | − | 0.358442i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 770.611 | + | 275.419i | 1.81320 | + | 0.648044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −260.969 | + | 260.969i | −0.611170 | + | 0.611170i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 228.272i | 0.532104i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 442.656 | 1.02704 | 0.513522 | − | 0.858076i | \(-0.328340\pi\) | ||||
0.513522 | + | 0.858076i | \(0.328340\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.8684 | − | 14.8684i | −0.0343380 | − | 0.0343380i | 0.689729 | − | 0.724067i | \(-0.257730\pi\) |
−0.724067 | + | 0.689729i | \(0.757730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0862283 | + | 0.383672i | 0.000198226 | + | 0.000882004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −111.060 | + | 111.060i | −0.254142 | + | 0.254142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 233.818i | − | 0.532616i | −0.963888 | − | 0.266308i | \(-0.914196\pi\) | ||
0.963888 | − | 0.266308i | \(-0.0858038\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.1816 | 0.0707066 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −246.747 | − | 246.747i | −0.556991 | − | 0.556991i | 0.371459 | − | 0.928449i | \(-0.378858\pi\) |
−0.928449 | + | 0.371459i | \(0.878858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −303.328 | − | 192.005i | −0.681636 | − | 0.431471i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 65.5607 | − | 65.5607i | 0.146668 | − | 0.146668i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 282.758i | 0.629751i | 0.949133 | + | 0.314875i | \(0.101963\pi\) | ||||
−0.949133 | + | 0.314875i | \(0.898037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −130.879 | −0.290196 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 284.883 | + | 284.883i | 0.628881 | + | 0.628881i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 421.151 | − | 665.333i | 0.925607 | − | 1.46227i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −298.171 | + | 298.171i | −0.652454 | + | 0.652454i | −0.953583 | − | 0.301129i | \(-0.902636\pi\) |
0.301129 | + | 0.953583i | \(0.402636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 170.091i | 0.370568i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −264.318 | −0.573358 | −0.286679 | − | 0.958027i | \(-0.592551\pi\) | ||||
−0.286679 | + | 0.958027i | \(0.592551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 135.116 | + | 135.116i | 0.291827 | + | 0.291827i | 0.837802 | − | 0.545975i | \(-0.183841\pi\) |
−0.545975 | + | 0.837802i | \(0.683841\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.9796 | − | 8.53572i | 0.0816765 | − | 0.0183564i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 558.631 | − | 558.631i | 1.19621 | − | 1.19621i | 0.220920 | − | 0.975292i | \(-0.429094\pi\) |
0.975292 | − | 0.220920i | \(-0.0709061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 929.494i | − | 1.98186i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −315.081 | −0.668961 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −208.272 | − | 208.272i | −0.440322 | − | 0.440322i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −377.283 | + | 178.606i | −0.794279 | + | 0.376013i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.5153 | − | 16.5153i | 0.0346233 | − | 0.0346233i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 456.141i | 0.952277i | 0.879370 | + | 0.476139i | \(0.157964\pi\) | ||||
−0.879370 | + | 0.476139i | \(0.842036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1021.53 | 2.12377 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −88.7878 | − | 88.7878i | −0.183826 | − | 0.183826i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −57.3689 | − | 255.262i | −0.118286 | − | 0.526314i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9444 | − | 11.9444i | 0.0245265 | − | 0.0245265i | −0.694737 | − | 0.719264i | \(-0.744479\pi\) |
0.719264 | + | 0.694737i | \(0.244479\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 288.000i | 0.588957i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 822.468 | 1.67509 | 0.837544 | − | 0.546370i | \(-0.183991\pi\) | ||||
0.837544 | + | 0.546370i | \(0.183991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.05103 | − | 1.05103i | −0.00213190 | − | 0.00213190i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 81.7423 | + | 51.7423i | 0.165136 | + | 0.104530i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −263.778 | + | 263.778i | −0.530740 | + | 0.530740i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 312.474i | − | 0.626201i | −0.949720 | − | 0.313101i | \(-0.898632\pi\) | ||
0.949720 | − | 0.313101i | \(-0.101368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 82.4541 | 0.164579 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −371.530 | − | 371.530i | −0.738628 | − | 0.738628i | 0.233684 | − | 0.972313i | \(-0.424922\pi\) |
−0.972313 | + | 0.233684i | \(0.924922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −252.283 | + | 398.555i | −0.499570 | + | 0.789218i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 304.442 | − | 304.442i | 0.600476 | − | 0.600476i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 171.228i | − | 0.336401i | −0.985753 | − | 0.168200i | \(-0.946204\pi\) | ||
0.985753 | − | 0.168200i | \(-0.0537956\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 239.666 | 0.469014 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −61.3485 | − | 61.3485i | −0.119588 | − | 0.119588i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −501.151 | + | 112.631i | −0.973109 | + | 0.218701i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 325.959 | − | 325.959i | 0.630482 | − | 0.630482i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 69.1918i | − | 0.133318i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −206.313 | −0.395995 | −0.197997 | − | 0.980203i | \(-0.563444\pi\) | ||||
−0.197997 | + | 0.980203i | \(0.563444\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −135.526 | − | 135.526i | −0.259131 | − | 0.259131i | 0.565570 | − | 0.824701i | \(-0.308656\pi\) |
−0.824701 | + | 0.565570i | \(0.808656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −142.788 | − | 301.621i | −0.271977 | − | 0.574516i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −104.041 | + | 104.041i | −0.197421 | + | 0.197421i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 440.514i | − | 0.832730i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 166.318 | 0.313216 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 293.221 | + | 293.221i | 0.550134 | + | 0.550134i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.2429 | − | 90.0704i | −0.0378371 | − | 0.168356i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.4041 | − | 55.4041i | 0.103173 | − | 0.103173i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 67.0352i | 0.124370i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 303.485 | 0.560970 | 0.280485 | − | 0.959858i | \(-0.409505\pi\) | ||||
0.280485 | + | 0.959858i | \(0.409505\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 319.237 | + | 319.237i | 0.587914 | + | 0.587914i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −292.702 | − | 185.278i | −0.537067 | − | 0.339960i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −71.3939 | + | 71.3939i | −0.130519 | + | 0.130519i | −0.769348 | − | 0.638829i | \(-0.779419\pi\) |
0.638829 | + | 0.769348i | \(0.279419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 143.666i | 0.261687i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.758169 | 0.00137599 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −690.434 | − | 690.434i | −1.24852 | − | 1.24852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 231.551 | − | 365.803i | 0.417208 | − | 0.659104i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 753.019 | − | 753.019i | 1.35192 | − | 1.35192i | 0.468407 | − | 0.883513i | \(-0.344828\pi\) |
0.883513 | − | 0.468407i | \(-0.155172\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 933.231i | 1.66946i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −365.666 | −0.651812 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 703.464 | + | 703.464i | 1.24949 | + | 1.24949i | 0.955944 | + | 0.293548i | \(0.0948361\pi\) |
0.293548 | + | 0.955944i | \(0.405164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 704.636 | − | 158.363i | 1.24714 | − | 0.280289i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 49.0454 | − | 49.0454i | 0.0864998 | − | 0.0864998i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 434.504i | − | 0.763628i | −0.924239 | − | 0.381814i | \(-0.875300\pi\) | ||
0.924239 | − | 0.381814i | \(-0.124700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −131.040 | −0.229492 | −0.114746 | − | 0.993395i | \(-0.536605\pi\) | ||||
−0.114746 | + | 0.993395i | \(0.536605\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 63.5255 | + | 63.5255i | 0.110865 | + | 0.110865i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −79.1464 | + | 221.448i | −0.137646 | + | 0.385128i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 290.444 | − | 290.444i | 0.503369 | − | 0.503369i | −0.409114 | − | 0.912483i | \(-0.634162\pi\) |
0.912483 | + | 0.409114i | \(0.134162\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 40.7015i | − | 0.0702962i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1034.80 | −1.78106 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.5051 | + | 35.5051i | 0.0609007 | + | 0.0609007i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −67.2122 | − | 299.060i | −0.114893 | − | 0.511214i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 180.288 | − | 180.288i | 0.307135 | − | 0.307135i | −0.536662 | − | 0.843797i | \(-0.680315\pi\) |
0.843797 | + | 0.536662i | \(0.180315\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 75.0510i | − | 0.127421i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −210.879 | −0.356817 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.0556 | − | 25.0556i | −0.0422523 | − | 0.0422523i | 0.685665 | − | 0.727917i | \(-0.259512\pi\) |
−0.727917 | + | 0.685665i | \(0.759512\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1065.79 | + | 674.636i | 1.79124 | + | 1.13384i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.9852 | + | 34.9852i | −0.0586017 | + | 0.0586017i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 509.807i | − | 0.851097i | −0.904936 | − | 0.425549i | \(-0.860081\pi\) | ||
0.904936 | − | 0.425549i | \(-0.139919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 179.757 | 0.299097 | 0.149548 | − | 0.988754i | \(-0.452218\pi\) | ||||
0.149548 | + | 0.988754i | \(0.452218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −255.848 | − | 255.848i | −0.424292 | − | 0.424292i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 212.345 | − | 335.462i | 0.350984 | − | 0.554483i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.1566 | − | 33.1566i | 0.0546238 | − | 0.0546238i | −0.679267 | − | 0.733891i | \(-0.737702\pi\) |
0.733891 | + | 0.679267i | \(0.237702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.606123i | 0.000995276i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1460.56 | −2.39045 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −261.712 | − | 261.712i | −0.426936 | − | 0.426936i | 0.460647 | − | 0.887583i | \(-0.347617\pi\) |
−0.887583 | + | 0.460647i | \(0.847617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 171.464 | − | 38.5357i | 0.278804 | − | 0.0626597i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −762.075 | + | 762.075i | −1.23513 | + | 1.23513i | −0.273161 | + | 0.961968i | \(0.588069\pi\) |
−0.961968 | + | 0.273161i | \(0.911931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 81.6367i | 0.131885i | 0.997823 | + | 0.0659424i | \(0.0210054\pi\) | ||||
−0.997823 | + | 0.0659424i | \(0.978995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.8786 | −0.0787095 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −391.262 | − | 391.262i | −0.628029 | − | 0.628029i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −396.151 | + | 483.414i | −0.633842 | + | 0.773463i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 131.889 | − | 131.889i | 0.210349 | − | 0.210349i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1636.38i | 2.60156i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.4133 | −0.0260115 | −0.0130057 | − | 0.999915i | \(-0.504140\pi\) | ||||
−0.0130057 | + | 0.999915i | \(0.504140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 241.460 | + | 241.460i | 0.381453 | + | 0.381453i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 185.975 | + | 827.494i | 0.292874 | + | 1.30314i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 150.186 | − | 150.186i | 0.235771 | − | 0.235771i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 145.212i | 0.227249i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −546.041 | −0.851858 | −0.425929 | − | 0.904757i | \(-0.640053\pi\) | ||||
−0.425929 | + | 0.904757i | \(0.640053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −142.879 | − | 142.879i | −0.222206 | − | 0.222206i | 0.587221 | − | 0.809427i | \(-0.300222\pi\) |
−0.809427 | + | 0.587221i | \(0.800222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 334.182 | + | 211.535i | 0.518111 | + | 0.327961i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −649.691 | + | 649.691i | −1.00416 | + | 1.00416i | −0.00416838 | + | 0.999991i | \(0.501327\pi\) |
−0.999991 | + | 0.00416838i | \(0.998673\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 357.555i | 0.550932i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 60.0000 | 0.0921659 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −150.904 | − | 150.904i | −0.231093 | − | 0.231093i | 0.582056 | − | 0.813149i | \(-0.302248\pi\) |
−0.813149 | + | 0.582056i | \(0.802248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −323.974 | + | 511.813i | −0.494617 | + | 0.781394i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 65.9694 | − | 65.9694i | 0.100410 | − | 0.100410i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 268.802i | 0.407893i | 0.978982 | + | 0.203947i | \(0.0653769\pi\) | ||||
−0.978982 | + | 0.203947i | \(0.934623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 311.162 | 0.470745 | 0.235372 | − | 0.971905i | \(-0.424369\pi\) | ||||
0.235372 | + | 0.971905i | \(0.424369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 819.242 | + | 819.242i | 1.23566 | + | 1.23566i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −627.737 | + | 141.081i | −0.943965 | + | 0.212151i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.302031 | − | 0.302031i | 0.000452820 | − | 0.000452820i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 703.832i | − | 1.05207i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −308.858 | −0.460295 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −547.756 | − | 547.756i | −0.813902 | − | 0.813902i | 0.171314 | − | 0.985216i | \(-0.445199\pi\) |
−0.985216 | + | 0.171314i | \(0.945199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −122.326 | − | 43.7196i | −0.181223 | − | 0.0647698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 696.257 | − | 696.257i | 1.02844 | − | 1.02844i | 0.0288606 | − | 0.999583i | \(-0.490812\pi\) |
0.999583 | − | 0.0288606i | \(-0.00918789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 403.262i | − | 0.593906i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 574.120 | 0.843055 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −84.0250 | − | 84.0250i | −0.123023 | − | 0.123023i | 0.642915 | − | 0.765938i | \(-0.277725\pi\) |
−0.765938 | + | 0.642915i | \(0.777725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 185.333 | + | 824.636i | 0.270559 | + | 1.20385i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 349.015 | − | 349.015i | 0.508027 | − | 0.508027i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 159.092i | − | 0.230903i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1157.06 | 1.67447 | 0.837236 | − | 0.546842i | \(-0.184170\pi\) | ||||
0.837236 | + | 0.546842i | \(0.184170\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 105.439 | + | 105.439i | 0.152149 | + | 0.152149i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 594.792 | + | 376.499i | 0.855816 | + | 0.541726i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −469.707 | + | 469.707i | −0.673898 | + | 0.673898i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 591.626i | 0.846388i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 843.691 | 1.20355 | 0.601777 | − | 0.798664i | \(-0.294460\pi\) | ||||
0.601777 | + | 0.798664i | \(0.294460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −590.211 | − | 590.211i | −0.839561 | − | 0.839561i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −331.065 | + | 523.015i | −0.469595 | + | 0.741865i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −514.095 | + | 514.095i | −0.727150 | + | 0.727150i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 170.686i | 0.240741i | 0.992729 | + | 0.120371i | \(0.0384083\pi\) | ||||
−0.992729 | + | 0.120371i | \(0.961592\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −380.091 | −0.534586 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.8979 | − | 29.8979i | −0.0419326 | − | 0.0419326i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 642.929 | − | 144.495i | 0.899201 | − | 0.202091i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 401.394 | − | 401.394i | 0.559824 | − | 0.559824i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 605.435i | 0.842051i | 0.907049 | + | 0.421026i | \(0.138330\pi\) | ||||
−0.907049 | + | 0.421026i | \(0.861670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −791.716 | −1.09808 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −329.616 | − | 329.616i | −0.455901 | − | 0.455901i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.02603 | − | 0.485723i | 0.00141521 | − | 0.000669963i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.8025 | + | 50.8025i | −0.0698797 | + | 0.0698797i | −0.741183 | − | 0.671303i | \(-0.765735\pi\) |
0.671303 | + | 0.741183i | \(0.265735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1494.93 | −2.04505 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 516.529 | + | 516.529i | 0.704678 | + | 0.704678i | 0.965411 | − | 0.260733i | \(-0.0839642\pi\) |
−0.260733 | + | 0.965411i | \(0.583964\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.7378 | − | 87.8230i | −0.0268541 | − | 0.119487i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 550.030 | − | 550.030i | 0.746309 | − | 0.746309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 650.109i | − | 0.879715i | −0.898068 | − | 0.439857i | \(-0.855029\pi\) | ||
0.898068 | − | 0.439857i | \(-0.144971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −590.969 | −0.797530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 90.6811 | + | 90.6811i | 0.122047 | + | 0.122047i | 0.765492 | − | 0.643445i | \(-0.222496\pi\) |
−0.643445 | + | 0.765492i | \(0.722496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −226.151 | − | 143.152i | −0.303558 | − | 0.192150i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −284.833 | + | 284.833i | −0.381303 | + | 0.381303i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 142.293i | − | 0.189977i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −300.050 | −0.399534 | −0.199767 | − | 0.979843i | \(-0.564019\pi\) | ||||
−0.199767 | + | 0.979843i | \(0.564019\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −227.969 | − | 227.969i | −0.302748 | − | 0.302748i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 622.043 | − | 982.702i | 0.823898 | − | 1.30159i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 523.176 | − | 523.176i | 0.691118 | − | 0.691118i | −0.271360 | − | 0.962478i | \(-0.587473\pi\) |
0.962478 | + | 0.271360i | \(0.0874735\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 105.081i | − | 0.138446i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −724.130 | −0.951550 | −0.475775 | − | 0.879567i | \(-0.657832\pi\) | ||||
−0.475775 | + | 0.879567i | \(0.657832\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −377.555 | − | 377.555i | −0.494830 | − | 0.494830i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 479.060 | − | 107.666i | 0.626222 | − | 0.140740i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 801.069 | − | 801.069i | 1.04442 | − | 1.04442i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.7775i | 0.0179162i | 0.999960 | + | 0.00895809i | \(0.00285149\pi\) | ||||
−0.999960 | + | 0.00895809i | \(0.997149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −338.686 | −0.439281 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −564.207 | − | 564.207i | −0.729892 | − | 0.729892i | 0.240706 | − | 0.970598i | \(-0.422621\pi\) |
−0.970598 | + | 0.240706i | \(0.922621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −48.0816 | − | 101.566i | −0.0620408 | − | 0.131053i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 471.848 | − | 471.848i | 0.607269 | − | 0.607269i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 338.829i | − | 0.434953i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −312.182 | −0.399720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.166838 | + | 0.166838i | 0.000213076 | + | 0.000213076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 199.444 | + | 887.423i | 0.254069 | + | 1.13048i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −212.424 | + | 212.424i | −0.269917 | + | 0.269917i | −0.829067 | − | 0.559150i | \(-0.811128\pi\) |
0.559150 | + | 0.829067i | \(0.311128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 399.626i | 0.506496i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1113.18 | 1.40731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 691.968 | + | 691.968i | 0.872596 | + | 0.872596i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −56.9694 | − | 36.0612i | −0.0716596 | − | 0.0453600i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.6617 | + | 15.6617i | −0.0196509 | + | 0.0196509i | −0.716864 | − | 0.697213i | \(-0.754423\pi\) |
0.697213 | + | 0.716864i | \(0.254423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2339.66i | − | 2.92823i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −215.394 | −0.268906 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 141.823 | + | 141.823i | 0.176616 | + | 0.176616i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −193.868 | + | 306.272i | −0.240830 | + | 0.380463i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −132.551 | + | 132.551i | −0.164251 | + | 0.164251i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 816.788i | 1.00963i | 0.863229 | + | 0.504813i | \(0.168439\pi\) | ||||
−0.863229 | + | 0.504813i | \(0.831561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 830.504 | 1.02405 | 0.512025 | − | 0.858971i | \(-0.328896\pi\) | ||||
0.512025 | + | 0.858971i | \(0.328896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −397.287 | − | 397.287i | −0.488668 | − | 0.488668i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 811.151 | − | 182.302i | 0.995277 | − | 0.223683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 539.192 | − | 539.192i | 0.659966 | − | 0.659966i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 472.454i | − | 0.576867i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 569.217 | 0.693321 | 0.346661 | − | 0.937991i | \(-0.387316\pi\) | ||||
0.346661 | + | 0.937991i | \(0.387316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 497.095 | + | 497.095i | 0.604004 | + | 0.604004i | 0.941373 | − | 0.337369i | \(-0.109537\pi\) |
−0.337369 | + | 0.941373i | \(0.609537\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 93.9898 | − | 262.980i | 0.113927 | − | 0.318763i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 874.070 | − | 874.070i | 1.05692 | − | 1.05692i | 0.0586377 | − | 0.998279i | \(-0.481324\pi\) |
0.998279 | − | 0.0586377i | \(-0.0186757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1548.77i | 1.86824i | 0.356954 | + | 0.934122i | \(0.383815\pi\) | ||||
−0.356954 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 406.282 | 0.488907 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 240.581 | + | 240.581i | 0.288813 | + | 0.288813i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.1929 | − | 232.232i | −0.0625064 | − | 0.278122i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.5153 | − | 16.5153i | 0.0197316 | − | 0.0197316i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 731.523i | − | 0.871899i | −0.899971 | − | 0.435950i | \(-0.856413\pi\) | ||
0.899971 | − | 0.435950i | \(-0.143587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.998 | 0.999998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −367.955 | − | 367.955i | −0.436482 | − | 0.436482i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1050.17 | − | 664.749i | −1.24280 | − | 0.786685i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 432.712 | − | 432.712i | 0.510876 | − | 0.510876i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 862.615i | 1.01604i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −470.243 | −0.552577 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −554.166 | − | 554.166i | −0.649667 | − | 0.649667i | 0.303246 | − | 0.952912i | \(-0.401930\pi\) |
−0.952912 | + | 0.303246i | \(0.901930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −133.955 | + | 211.621i | −0.156672 | + | 0.247510i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 687.206 | − | 687.206i | 0.801874 | − | 0.801874i | −0.181515 | − | 0.983388i | \(-0.558100\pi\) |
0.983388 | + | 0.181515i | \(0.0581000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1285.29i | 1.49627i | 0.663549 | + | 0.748133i | \(0.269049\pi\) | ||||
−0.663549 | + | 0.748133i | \(0.730951\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 270.879 | 0.314609 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −712.985 | − | 712.985i | −0.826171 | − | 0.826171i | 0.160814 | − | 0.986985i | \(-0.448588\pi\) |
−0.986985 | + | 0.160814i | \(0.948588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −194.879 | + | 43.7980i | −0.225293 | + | 0.0506335i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −958.380 | + | 958.380i | −1.10540 | + | 1.10540i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 817.131i | − | 0.940311i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2464.58 | −2.82960 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −111.000 | − | 111.000i | −0.127148 | − | 0.127148i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −759.131 | + | 593.085i | −0.867578 | + | 0.677812i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −474.297 | + | 474.297i | −0.540818 | + | 0.540818i | −0.923769 | − | 0.382951i | \(-0.874908\pi\) |
0.382951 | + | 0.923769i | \(0.374908\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 268.009i | 0.304902i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1652.71 | 1.87594 | 0.937972 | − | 0.346712i | \(-0.112702\pi\) | ||||
0.937972 | + | 0.346712i | \(0.112702\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9286 | + | 18.9286i | 0.0214367 | + | 0.0214367i | 0.717744 | − | 0.696307i | \(-0.245175\pi\) |
−0.696307 | + | 0.717744i | \(0.745175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −105.278 | − | 468.434i | −0.118958 | − | 0.529304i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −382.338 | + | 382.338i | −0.431047 | + | 0.431047i | −0.888984 | − | 0.457938i | \(-0.848588\pi\) |
0.457938 | + | 0.888984i | \(0.348588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1307.27i | 1.47050i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 58.0454 | 0.0651464 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 843.868 | + | 843.868i | 0.944981 | + | 0.944981i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −191.116 | − | 120.975i | −0.213537 | − | 0.135168i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −235.423 | + | 235.423i | −0.262456 | + | 0.262456i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.204103i | 0.000227033i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 254.847 | 0.282849 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 431.060 | + | 431.060i | 0.477365 | + | 0.477365i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 697.056 | − | 1101.21i | 0.770227 | − | 1.21680i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 725.485 | − | 725.485i | 0.799873 | − | 0.799873i | −0.183202 | − | 0.983075i | \(-0.558646\pi\) |
0.983075 | + | 0.183202i | \(0.0586464\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 283.015i | 0.311347i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −154.474 | −0.169566 | −0.0847829 | − | 0.996399i | \(-0.527020\pi\) | ||||
−0.0847829 | + | 0.996399i | \(0.527020\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −612.343 | − | 612.343i | −0.670693 | − | 0.670693i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 404.636 | − | 90.9398i | 0.442225 | − | 0.0993878i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −660.186 | + | 660.186i | −0.719941 | + | 0.719941i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 659.079i | − | 0.717169i | −0.933497 | − | 0.358585i | \(-0.883259\pi\) | ||
0.933497 | − | 0.358585i | \(-0.116741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −270.979 | −0.294222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 699.414 | + | 699.414i | 0.757762 | + | 0.757762i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1176.85 | − | 420.611i | −1.27227 | − | 0.454714i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −217.924 | + | 217.924i | −0.235085 | + | 0.235085i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 368.556i | − | 0.396723i | −0.980129 | − | 0.198362i | \(-0.936438\pi\) | ||
0.980129 | − | 0.198362i | \(-0.0635621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −173.546 | −0.186408 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.91939 | − | 2.91939i | −0.00312904 | − | 0.00312904i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 231.464 | + | 1029.90i | 0.247555 | + | 1.10150i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −820.898 | + | 820.898i | −0.876092 | + | 0.876092i | −0.993128 | − | 0.117036i | \(-0.962661\pi\) |
0.117036 | + | 0.993128i | \(0.462661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 325.682i | − | 0.346839i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1758.50 | 1.86875 | 0.934377 | − | 0.356286i | \(-0.115957\pi\) | ||||
0.934377 | + | 0.356286i | \(0.115957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −134.979 | − | 134.979i | −0.143137 | − | 0.143137i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −169.182 | − | 107.091i | −0.179028 | − | 0.113324i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −118.080 | + | 118.080i | −0.124688 | + | 0.124688i | −0.766697 | − | 0.642009i | \(-0.778101\pi\) |
0.642009 | + | 0.766697i | \(0.278101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 635.483i | − | 0.669634i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 90.9898 | 0.0956780 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −217.955 | − | 217.955i | −0.228704 | − | 0.228704i | 0.583447 | − | 0.812151i | \(-0.301703\pi\) |
−0.812151 | + | 0.583447i | \(0.801703\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 138.708 | − | 219.131i | 0.145244 | − | 0.229456i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.358674 | + | 0.358674i | −0.000374790 | + | 0.000374790i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1302.76i | 1.35845i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −940.796 | −0.978976 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.1668 | − | 39.1668i | −0.0406717 | − | 0.0406717i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −114.636 | + | 25.7638i | −0.118793 | + | 0.0266982i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −323.983 | + | 323.983i | −0.335039 | + | 0.335039i | −0.854497 | − | 0.519457i | \(-0.826134\pi\) |
0.519457 | + | 0.854497i | \(0.326134\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 946.665i | − | 0.976951i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 743.743 | 0.765956 | 0.382978 | − | 0.923757i | \(-0.374898\pi\) | ||||
0.382978 | + | 0.923757i | \(0.374898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 767.221 | + | 767.221i | 0.788511 | + | 0.788511i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −799.757 | + | 378.606i | −0.820264 | + | 0.388314i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1050.52 | + | 1050.52i | −1.07525 | + | 1.07525i | −0.0783226 | + | 0.996928i | \(0.524956\pi\) |
−0.996928 | + | 0.0783226i | \(0.975044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 463.060i | − | 0.472993i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −207.848 | −0.211874 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 72.9648 | + | 72.9648i | 0.0742267 | + | 0.0742267i | 0.743245 | − | 0.669019i | \(-0.233285\pi\) |
−0.669019 | + | 0.743245i | \(0.733285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 133.485 | + | 593.939i | 0.135517 | + | 0.602984i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −674.636 | + | 674.636i | −0.683521 | + | 0.683521i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 429.594i | − | 0.434372i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 444.624 | 0.448662 | 0.224331 | − | 0.974513i | \(-0.427980\pi\) | ||||
0.224331 | + | 0.974513i | \(0.427980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.5107 | − | 26.5107i | −0.0266976 | − | 0.0266976i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 120.681 | + | 76.3903i | 0.121288 | + | 0.0767742i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.6424 | − | 12.6424i | 0.0126804 | − | 0.0126804i | −0.700738 | − | 0.713419i | \(-0.747146\pi\) |
0.713419 | + | 0.700738i | \(0.247146\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 259.757i | − | 0.260017i |
(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 | 120.3.u.a.73.1 | ✓ | 4 | |
3.2 | odd | 2 | 360.3.v.b.73.2 | 4 | |||
4.3 | odd | 2 | 240.3.bg.c.193.2 | 4 | |||
5.2 | odd | 4 | inner | 120.3.u.a.97.1 | yes | 4 | |
5.3 | odd | 4 | 600.3.u.e.457.2 | 4 | |||
5.4 | even | 2 | 600.3.u.e.193.2 | 4 | |||
8.3 | odd | 2 | 960.3.bg.d.193.1 | 4 | |||
8.5 | even | 2 | 960.3.bg.c.193.2 | 4 | |||
12.11 | even | 2 | 720.3.bh.g.433.2 | 4 | |||
15.2 | even | 4 | 360.3.v.b.217.2 | 4 | |||
15.8 | even | 4 | 1800.3.v.n.1657.2 | 4 | |||
15.14 | odd | 2 | 1800.3.v.n.793.2 | 4 | |||
20.3 | even | 4 | 1200.3.bg.e.1057.1 | 4 | |||
20.7 | even | 4 | 240.3.bg.c.97.2 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.e.193.1 | 4 | |||
40.27 | even | 4 | 960.3.bg.d.577.1 | 4 | |||
40.37 | odd | 4 | 960.3.bg.c.577.2 | 4 | |||
60.47 | odd | 4 | 720.3.bh.g.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.u.a.73.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
120.3.u.a.97.1 | yes | 4 | 5.2 | odd | 4 | inner | |
240.3.bg.c.97.2 | 4 | 20.7 | even | 4 | |||
240.3.bg.c.193.2 | 4 | 4.3 | odd | 2 | |||
360.3.v.b.73.2 | 4 | 3.2 | odd | 2 | |||
360.3.v.b.217.2 | 4 | 15.2 | even | 4 | |||
600.3.u.e.193.2 | 4 | 5.4 | even | 2 | |||
600.3.u.e.457.2 | 4 | 5.3 | odd | 4 | |||
720.3.bh.g.433.2 | 4 | 12.11 | even | 2 | |||
720.3.bh.g.577.2 | 4 | 60.47 | odd | 4 | |||
960.3.bg.c.193.2 | 4 | 8.5 | even | 2 | |||
960.3.bg.c.577.2 | 4 | 40.37 | odd | 4 | |||
960.3.bg.d.193.1 | 4 | 8.3 | odd | 2 | |||
960.3.bg.d.577.1 | 4 | 40.27 | even | 4 | |||
1200.3.bg.e.193.1 | 4 | 20.19 | odd | 2 | |||
1200.3.bg.e.1057.1 | 4 | 20.3 | even | 4 | |||
1800.3.v.n.793.2 | 4 | 15.14 | odd | 2 | |||
1800.3.v.n.1657.2 | 4 | 15.8 | even | 4 |