Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18299 | −1.54361 | −0.771805 | − | 0.635860i | \(-0.780646\pi\) | ||||
−0.771805 | + | 0.635860i | \(0.780646\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.76546 | 1.38273 | ||||||||
\(5\) | 2.14752 | 0.960402 | 0.480201 | − | 0.877158i | \(-0.340564\pi\) | ||||
0.480201 | + | 0.877158i | \(0.340564\pi\) | |||||||
\(6\) | 2.18299 | 0.891203 | ||||||||
\(7\) | 0.603238 | 0.228002 | 0.114001 | − | 0.993481i | \(-0.463633\pi\) | ||||
0.114001 | + | 0.993481i | \(0.463633\pi\) | |||||||
\(8\) | −1.67100 | −0.590786 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.68803 | −1.48249 | ||||||||
\(11\) | −1.05632 | −0.318492 | −0.159246 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159246 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(12\) | −2.76546 | −0.798320 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.31686 | −0.351947 | ||||||||
\(15\) | −2.14752 | −0.554489 | ||||||||
\(16\) | −1.88315 | −0.470787 | ||||||||
\(17\) | 5.27690 | 1.27984 | 0.639918 | − | 0.768443i | \(-0.278968\pi\) | ||||
0.639918 | + | 0.768443i | \(0.278968\pi\) | |||||||
\(18\) | −2.18299 | −0.514537 | ||||||||
\(19\) | 6.92975 | 1.58979 | 0.794897 | − | 0.606744i | \(-0.207525\pi\) | ||||
0.794897 | + | 0.606744i | \(0.207525\pi\) | |||||||
\(20\) | 5.93890 | 1.32798 | ||||||||
\(21\) | −0.603238 | −0.131637 | ||||||||
\(22\) | 2.30593 | 0.491627 | ||||||||
\(23\) | −3.16152 | −0.659222 | −0.329611 | − | 0.944117i | \(-0.606918\pi\) | ||||
−0.329611 | + | 0.944117i | \(0.606918\pi\) | |||||||
\(24\) | 1.67100 | 0.341091 | ||||||||
\(25\) | −0.388137 | −0.0776275 | ||||||||
\(26\) | −2.18299 | −0.428120 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.66823 | 0.315266 | ||||||||
\(29\) | 6.31547 | 1.17275 | 0.586377 | − | 0.810038i | \(-0.300554\pi\) | ||||
0.586377 | + | 0.810038i | \(0.300554\pi\) | |||||||
\(30\) | 4.68803 | 0.855914 | ||||||||
\(31\) | 1.92623 | 0.345962 | 0.172981 | − | 0.984925i | \(-0.444660\pi\) | ||||
0.172981 | + | 0.984925i | \(0.444660\pi\) | |||||||
\(32\) | 7.45289 | 1.31750 | ||||||||
\(33\) | 1.05632 | 0.183881 | ||||||||
\(34\) | −11.5194 | −1.97557 | ||||||||
\(35\) | 1.29547 | 0.218974 | ||||||||
\(36\) | 2.76546 | 0.460910 | ||||||||
\(37\) | −7.58967 | −1.24773 | −0.623867 | − | 0.781530i | \(-0.714439\pi\) | ||||
−0.623867 | + | 0.781530i | \(0.714439\pi\) | |||||||
\(38\) | −15.1276 | −2.45402 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −3.58851 | −0.567392 | ||||||||
\(41\) | −6.70449 | −1.04707 | −0.523533 | − | 0.852006i | \(-0.675386\pi\) | ||||
−0.523533 | + | 0.852006i | \(0.675386\pi\) | |||||||
\(42\) | 1.31686 | 0.203197 | ||||||||
\(43\) | 3.27034 | 0.498721 | 0.249361 | − | 0.968411i | \(-0.419780\pi\) | ||||
0.249361 | + | 0.968411i | \(0.419780\pi\) | |||||||
\(44\) | −2.92120 | −0.440388 | ||||||||
\(45\) | 2.14752 | 0.320134 | ||||||||
\(46\) | 6.90157 | 1.01758 | ||||||||
\(47\) | 0.617887 | 0.0901281 | 0.0450641 | − | 0.998984i | \(-0.485651\pi\) | ||||
0.0450641 | + | 0.998984i | \(0.485651\pi\) | |||||||
\(48\) | 1.88315 | 0.271809 | ||||||||
\(49\) | −6.63610 | −0.948015 | ||||||||
\(50\) | 0.847301 | 0.119827 | ||||||||
\(51\) | −5.27690 | −0.738913 | ||||||||
\(52\) | 2.76546 | 0.383500 | ||||||||
\(53\) | 14.2897 | 1.96284 | 0.981421 | − | 0.191867i | \(-0.0614542\pi\) | ||||
0.981421 | + | 0.191867i | \(0.0614542\pi\) | |||||||
\(54\) | 2.18299 | 0.297068 | ||||||||
\(55\) | −2.26847 | −0.305880 | ||||||||
\(56\) | −1.00801 | −0.134701 | ||||||||
\(57\) | −6.92975 | −0.917868 | ||||||||
\(58\) | −13.7866 | −1.81027 | ||||||||
\(59\) | 8.58769 | 1.11802 | 0.559011 | − | 0.829160i | \(-0.311181\pi\) | ||||
0.559011 | + | 0.829160i | \(0.311181\pi\) | |||||||
\(60\) | −5.93890 | −0.766708 | ||||||||
\(61\) | 2.25155 | 0.288282 | 0.144141 | − | 0.989557i | \(-0.453958\pi\) | ||||
0.144141 | + | 0.989557i | \(0.453958\pi\) | |||||||
\(62\) | −4.20495 | −0.534030 | ||||||||
\(63\) | 0.603238 | 0.0760008 | ||||||||
\(64\) | −12.5033 | −1.56291 | ||||||||
\(65\) | 2.14752 | 0.266368 | ||||||||
\(66\) | −2.30593 | −0.283841 | ||||||||
\(67\) | 6.67280 | 0.815213 | 0.407606 | − | 0.913158i | \(-0.366364\pi\) | ||||
0.407606 | + | 0.913158i | \(0.366364\pi\) | |||||||
\(68\) | 14.5931 | 1.76967 | ||||||||
\(69\) | 3.16152 | 0.380602 | ||||||||
\(70\) | −2.82800 | −0.338011 | ||||||||
\(71\) | 2.12217 | 0.251855 | 0.125927 | − | 0.992039i | \(-0.459809\pi\) | ||||
0.125927 | + | 0.992039i | \(0.459809\pi\) | |||||||
\(72\) | −1.67100 | −0.196929 | ||||||||
\(73\) | 11.5346 | 1.35002 | 0.675010 | − | 0.737808i | \(-0.264139\pi\) | ||||
0.675010 | + | 0.737808i | \(0.264139\pi\) | |||||||
\(74\) | 16.5682 | 1.92601 | ||||||||
\(75\) | 0.388137 | 0.0448182 | ||||||||
\(76\) | 19.1640 | 2.19826 | ||||||||
\(77\) | −0.637210 | −0.0726169 | ||||||||
\(78\) | 2.18299 | 0.247175 | ||||||||
\(79\) | 3.02621 | 0.340475 | 0.170237 | − | 0.985403i | \(-0.445547\pi\) | ||||
0.170237 | + | 0.985403i | \(0.445547\pi\) | |||||||
\(80\) | −4.04411 | −0.452145 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.6359 | 1.61626 | ||||||||
\(83\) | 6.20971 | 0.681604 | 0.340802 | − | 0.940135i | \(-0.389301\pi\) | ||||
0.340802 | + | 0.940135i | \(0.389301\pi\) | |||||||
\(84\) | −1.66823 | −0.182019 | ||||||||
\(85\) | 11.3323 | 1.22916 | ||||||||
\(86\) | −7.13912 | −0.769831 | ||||||||
\(87\) | −6.31547 | −0.677090 | ||||||||
\(88\) | 1.76510 | 0.188160 | ||||||||
\(89\) | −6.13977 | −0.650815 | −0.325407 | − | 0.945574i | \(-0.605501\pi\) | ||||
−0.325407 | + | 0.945574i | \(0.605501\pi\) | |||||||
\(90\) | −4.68803 | −0.494162 | ||||||||
\(91\) | 0.603238 | 0.0632365 | ||||||||
\(92\) | −8.74305 | −0.911526 | ||||||||
\(93\) | −1.92623 | −0.199741 | ||||||||
\(94\) | −1.34884 | −0.139123 | ||||||||
\(95\) | 14.8818 | 1.52684 | ||||||||
\(96\) | −7.45289 | −0.760658 | ||||||||
\(97\) | −5.90264 | −0.599323 | −0.299661 | − | 0.954046i | \(-0.596874\pi\) | ||||
−0.299661 | + | 0.954046i | \(0.596874\pi\) | |||||||
\(98\) | 14.4866 | 1.46336 | ||||||||
\(99\) | −1.05632 | −0.106164 | ||||||||
\(100\) | −1.07338 | −0.107338 | ||||||||
\(101\) | 7.67214 | 0.763407 | 0.381703 | − | 0.924285i | \(-0.375338\pi\) | ||||
0.381703 | + | 0.924285i | \(0.375338\pi\) | |||||||
\(102\) | 11.5194 | 1.14059 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.67100 | −0.163855 | ||||||||
\(105\) | −1.29547 | −0.126425 | ||||||||
\(106\) | −31.1943 | −3.02986 | ||||||||
\(107\) | 14.0593 | 1.35916 | 0.679582 | − | 0.733599i | \(-0.262161\pi\) | ||||
0.679582 | + | 0.733599i | \(0.262161\pi\) | |||||||
\(108\) | −2.76546 | −0.266107 | ||||||||
\(109\) | −14.1233 | −1.35276 | −0.676381 | − | 0.736552i | \(-0.736453\pi\) | ||||
−0.676381 | + | 0.736552i | \(0.736453\pi\) | |||||||
\(110\) | 4.95205 | 0.472159 | ||||||||
\(111\) | 7.58967 | 0.720380 | ||||||||
\(112\) | −1.13599 | −0.107341 | ||||||||
\(113\) | −19.9292 | −1.87478 | −0.937392 | − | 0.348276i | \(-0.886767\pi\) | ||||
−0.937392 | + | 0.348276i | \(0.886767\pi\) | |||||||
\(114\) | 15.1276 | 1.41683 | ||||||||
\(115\) | −6.78943 | −0.633118 | ||||||||
\(116\) | 17.4652 | 1.62160 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −18.7469 | −1.72579 | ||||||||
\(119\) | 3.18322 | 0.291806 | ||||||||
\(120\) | 3.58851 | 0.327584 | ||||||||
\(121\) | −9.88419 | −0.898563 | ||||||||
\(122\) | −4.91512 | −0.444994 | ||||||||
\(123\) | 6.70449 | 0.604523 | ||||||||
\(124\) | 5.32692 | 0.478372 | ||||||||
\(125\) | −11.5712 | −1.03496 | ||||||||
\(126\) | −1.31686 | −0.117316 | ||||||||
\(127\) | −7.73839 | −0.686671 | −0.343336 | − | 0.939213i | \(-0.611557\pi\) | ||||
−0.343336 | + | 0.939213i | \(0.611557\pi\) | |||||||
\(128\) | 12.3889 | 1.09503 | ||||||||
\(129\) | −3.27034 | −0.287937 | ||||||||
\(130\) | −4.68803 | −0.411168 | ||||||||
\(131\) | 5.61500 | 0.490585 | 0.245293 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245293 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(132\) | 2.92120 | 0.254258 | ||||||||
\(133\) | 4.18029 | 0.362477 | ||||||||
\(134\) | −14.5667 | −1.25837 | ||||||||
\(135\) | −2.14752 | −0.184830 | ||||||||
\(136\) | −8.81767 | −0.756109 | ||||||||
\(137\) | −11.3859 | −0.972766 | −0.486383 | − | 0.873746i | \(-0.661684\pi\) | ||||
−0.486383 | + | 0.873746i | \(0.661684\pi\) | |||||||
\(138\) | −6.90157 | −0.587501 | ||||||||
\(139\) | 12.3445 | 1.04704 | 0.523522 | − | 0.852012i | \(-0.324618\pi\) | ||||
0.523522 | + | 0.852012i | \(0.324618\pi\) | |||||||
\(140\) | 3.58257 | 0.302782 | ||||||||
\(141\) | −0.617887 | −0.0520355 | ||||||||
\(142\) | −4.63267 | −0.388765 | ||||||||
\(143\) | −1.05632 | −0.0883337 | ||||||||
\(144\) | −1.88315 | −0.156929 | ||||||||
\(145\) | 13.5626 | 1.12632 | ||||||||
\(146\) | −25.1799 | −2.08391 | ||||||||
\(147\) | 6.63610 | 0.547337 | ||||||||
\(148\) | −20.9889 | −1.72528 | ||||||||
\(149\) | 5.16781 | 0.423364 | 0.211682 | − | 0.977339i | \(-0.432106\pi\) | ||||
0.211682 | + | 0.977339i | \(0.432106\pi\) | |||||||
\(150\) | −0.847301 | −0.0691819 | ||||||||
\(151\) | −9.03652 | −0.735382 | −0.367691 | − | 0.929948i | \(-0.619852\pi\) | ||||
−0.367691 | + | 0.929948i | \(0.619852\pi\) | |||||||
\(152\) | −11.5796 | −0.939228 | ||||||||
\(153\) | 5.27690 | 0.426612 | ||||||||
\(154\) | 1.39103 | 0.112092 | ||||||||
\(155\) | 4.13663 | 0.332262 | ||||||||
\(156\) | −2.76546 | −0.221414 | ||||||||
\(157\) | −7.10949 | −0.567399 | −0.283700 | − | 0.958913i | \(-0.591562\pi\) | ||||
−0.283700 | + | 0.958913i | \(0.591562\pi\) | |||||||
\(158\) | −6.60619 | −0.525560 | ||||||||
\(159\) | −14.2897 | −1.13325 | ||||||||
\(160\) | 16.0053 | 1.26533 | ||||||||
\(161\) | −1.90715 | −0.150304 | ||||||||
\(162\) | −2.18299 | −0.171512 | ||||||||
\(163\) | −2.59103 | −0.202945 | −0.101472 | − | 0.994838i | \(-0.532355\pi\) | ||||
−0.101472 | + | 0.994838i | \(0.532355\pi\) | |||||||
\(164\) | −18.5410 | −1.44781 | ||||||||
\(165\) | 2.26847 | 0.176600 | ||||||||
\(166\) | −13.5558 | −1.05213 | ||||||||
\(167\) | 14.1263 | 1.09312 | 0.546562 | − | 0.837418i | \(-0.315936\pi\) | ||||
0.546562 | + | 0.837418i | \(0.315936\pi\) | |||||||
\(168\) | 1.00801 | 0.0777695 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −24.7383 | −1.89734 | ||||||||
\(171\) | 6.92975 | 0.529931 | ||||||||
\(172\) | 9.04398 | 0.689597 | ||||||||
\(173\) | 20.8676 | 1.58654 | 0.793269 | − | 0.608872i | \(-0.208378\pi\) | ||||
0.793269 | + | 0.608872i | \(0.208378\pi\) | |||||||
\(174\) | 13.7866 | 1.04516 | ||||||||
\(175\) | −0.234139 | −0.0176993 | ||||||||
\(176\) | 1.98920 | 0.149942 | ||||||||
\(177\) | −8.58769 | −0.645490 | ||||||||
\(178\) | 13.4031 | 1.00460 | ||||||||
\(179\) | 3.05765 | 0.228540 | 0.114270 | − | 0.993450i | \(-0.463547\pi\) | ||||
0.114270 | + | 0.993450i | \(0.463547\pi\) | |||||||
\(180\) | 5.93890 | 0.442659 | ||||||||
\(181\) | −18.0793 | −1.34382 | −0.671912 | − | 0.740631i | \(-0.734527\pi\) | ||||
−0.671912 | + | 0.740631i | \(0.734527\pi\) | |||||||
\(182\) | −1.31686 | −0.0976125 | ||||||||
\(183\) | −2.25155 | −0.166440 | ||||||||
\(184\) | 5.28288 | 0.389459 | ||||||||
\(185\) | −16.2990 | −1.19833 | ||||||||
\(186\) | 4.20495 | 0.308322 | ||||||||
\(187\) | −5.57408 | −0.407617 | ||||||||
\(188\) | 1.70874 | 0.124623 | ||||||||
\(189\) | −0.603238 | −0.0438791 | ||||||||
\(190\) | −32.4869 | −2.35685 | ||||||||
\(191\) | −11.8236 | −0.855525 | −0.427763 | − | 0.903891i | \(-0.640698\pi\) | ||||
−0.427763 | + | 0.903891i | \(0.640698\pi\) | |||||||
\(192\) | 12.5033 | 0.902349 | ||||||||
\(193\) | 7.57274 | 0.545098 | 0.272549 | − | 0.962142i | \(-0.412133\pi\) | ||||
0.272549 | + | 0.962142i | \(0.412133\pi\) | |||||||
\(194\) | 12.8854 | 0.925120 | ||||||||
\(195\) | −2.14752 | −0.153787 | ||||||||
\(196\) | −18.3519 | −1.31085 | ||||||||
\(197\) | −20.4137 | −1.45442 | −0.727208 | − | 0.686418i | \(-0.759182\pi\) | ||||
−0.727208 | + | 0.686418i | \(0.759182\pi\) | |||||||
\(198\) | 2.30593 | 0.163876 | ||||||||
\(199\) | −20.4533 | −1.44990 | −0.724948 | − | 0.688803i | \(-0.758136\pi\) | ||||
−0.724948 | + | 0.688803i | \(0.758136\pi\) | |||||||
\(200\) | 0.648576 | 0.0458612 | ||||||||
\(201\) | −6.67280 | −0.470663 | ||||||||
\(202\) | −16.7482 | −1.17840 | ||||||||
\(203\) | 3.80973 | 0.267391 | ||||||||
\(204\) | −14.5931 | −1.02172 | ||||||||
\(205\) | −14.3981 | −1.00560 | ||||||||
\(206\) | 2.18299 | 0.152096 | ||||||||
\(207\) | −3.16152 | −0.219741 | ||||||||
\(208\) | −1.88315 | −0.130573 | ||||||||
\(209\) | −7.32001 | −0.506336 | ||||||||
\(210\) | 2.82800 | 0.195150 | ||||||||
\(211\) | −10.0266 | −0.690263 | −0.345132 | − | 0.938554i | \(-0.612166\pi\) | ||||
−0.345132 | + | 0.938554i | \(0.612166\pi\) | |||||||
\(212\) | 39.5176 | 2.71408 | ||||||||
\(213\) | −2.12217 | −0.145408 | ||||||||
\(214\) | −30.6914 | −2.09802 | ||||||||
\(215\) | 7.02313 | 0.478973 | ||||||||
\(216\) | 1.67100 | 0.113697 | ||||||||
\(217\) | 1.16198 | 0.0788801 | ||||||||
\(218\) | 30.8310 | 2.08814 | ||||||||
\(219\) | −11.5346 | −0.779435 | ||||||||
\(220\) | −6.27336 | −0.422950 | ||||||||
\(221\) | 5.27690 | 0.354963 | ||||||||
\(222\) | −16.5682 | −1.11199 | ||||||||
\(223\) | −7.81693 | −0.523460 | −0.261730 | − | 0.965141i | \(-0.584293\pi\) | ||||
−0.261730 | + | 0.965141i | \(0.584293\pi\) | |||||||
\(224\) | 4.49587 | 0.300393 | ||||||||
\(225\) | −0.388137 | −0.0258758 | ||||||||
\(226\) | 43.5054 | 2.89393 | ||||||||
\(227\) | 17.4432 | 1.15774 | 0.578872 | − | 0.815418i | \(-0.303493\pi\) | ||||
0.578872 | + | 0.815418i | \(0.303493\pi\) | |||||||
\(228\) | −19.1640 | −1.26916 | ||||||||
\(229\) | 8.39787 | 0.554947 | 0.277473 | − | 0.960733i | \(-0.410503\pi\) | ||||
0.277473 | + | 0.960733i | \(0.410503\pi\) | |||||||
\(230\) | 14.8213 | 0.977287 | ||||||||
\(231\) | 0.637210 | 0.0419254 | ||||||||
\(232\) | −10.5531 | −0.692847 | ||||||||
\(233\) | 27.1373 | 1.77782 | 0.888911 | − | 0.458080i | \(-0.151463\pi\) | ||||
0.888911 | + | 0.458080i | \(0.151463\pi\) | |||||||
\(234\) | −2.18299 | −0.142707 | ||||||||
\(235\) | 1.32693 | 0.0865593 | ||||||||
\(236\) | 23.7489 | 1.54592 | ||||||||
\(237\) | −3.02621 | −0.196573 | ||||||||
\(238\) | −6.94896 | −0.450434 | ||||||||
\(239\) | 17.3407 | 1.12168 | 0.560839 | − | 0.827925i | \(-0.310479\pi\) | ||||
0.560839 | + | 0.827925i | \(0.310479\pi\) | |||||||
\(240\) | 4.04411 | 0.261046 | ||||||||
\(241\) | −11.9353 | −0.768822 | −0.384411 | − | 0.923162i | \(-0.625595\pi\) | ||||
−0.384411 | + | 0.923162i | \(0.625595\pi\) | |||||||
\(242\) | 21.5771 | 1.38703 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.22658 | 0.398616 | ||||||||
\(245\) | −14.2512 | −0.910476 | ||||||||
\(246\) | −14.6359 | −0.933148 | ||||||||
\(247\) | 6.92975 | 0.440929 | ||||||||
\(248\) | −3.21873 | −0.204389 | ||||||||
\(249\) | −6.20971 | −0.393524 | ||||||||
\(250\) | 25.2598 | 1.59757 | ||||||||
\(251\) | 14.6678 | 0.925823 | 0.462911 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462911 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(252\) | 1.66823 | 0.105089 | ||||||||
\(253\) | 3.33956 | 0.209957 | ||||||||
\(254\) | 16.8929 | 1.05995 | ||||||||
\(255\) | −11.3323 | −0.709654 | ||||||||
\(256\) | −2.03821 | −0.127388 | ||||||||
\(257\) | −12.1143 | −0.755669 | −0.377835 | − | 0.925873i | \(-0.623331\pi\) | ||||
−0.377835 | + | 0.925873i | \(0.623331\pi\) | |||||||
\(258\) | 7.13912 | 0.444462 | ||||||||
\(259\) | −4.57838 | −0.284487 | ||||||||
\(260\) | 5.93890 | 0.368315 | ||||||||
\(261\) | 6.31547 | 0.390918 | ||||||||
\(262\) | −12.2575 | −0.757272 | ||||||||
\(263\) | 14.7217 | 0.907779 | 0.453889 | − | 0.891058i | \(-0.350036\pi\) | ||||
0.453889 | + | 0.891058i | \(0.350036\pi\) | |||||||
\(264\) | −1.76510 | −0.108634 | ||||||||
\(265\) | 30.6875 | 1.88512 | ||||||||
\(266\) | −9.12554 | −0.559523 | ||||||||
\(267\) | 6.13977 | 0.375748 | ||||||||
\(268\) | 18.4534 | 1.12722 | ||||||||
\(269\) | 26.8565 | 1.63747 | 0.818733 | − | 0.574174i | \(-0.194677\pi\) | ||||
0.818733 | + | 0.574174i | \(0.194677\pi\) | |||||||
\(270\) | 4.68803 | 0.285305 | ||||||||
\(271\) | 18.3421 | 1.11420 | 0.557101 | − | 0.830445i | \(-0.311914\pi\) | ||||
0.557101 | + | 0.830445i | \(0.311914\pi\) | |||||||
\(272\) | −9.93718 | −0.602530 | ||||||||
\(273\) | −0.603238 | −0.0365096 | ||||||||
\(274\) | 24.8554 | 1.50157 | ||||||||
\(275\) | 0.409996 | 0.0247237 | ||||||||
\(276\) | 8.74305 | 0.526270 | ||||||||
\(277\) | −21.2918 | −1.27930 | −0.639651 | − | 0.768666i | \(-0.720921\pi\) | ||||
−0.639651 | + | 0.768666i | \(0.720921\pi\) | |||||||
\(278\) | −26.9479 | −1.61623 | ||||||||
\(279\) | 1.92623 | 0.115321 | ||||||||
\(280\) | −2.16472 | −0.129367 | ||||||||
\(281\) | −32.8578 | −1.96013 | −0.980067 | − | 0.198668i | \(-0.936339\pi\) | ||||
−0.980067 | + | 0.198668i | \(0.936339\pi\) | |||||||
\(282\) | 1.34884 | 0.0803225 | ||||||||
\(283\) | −14.5898 | −0.867276 | −0.433638 | − | 0.901087i | \(-0.642770\pi\) | ||||
−0.433638 | + | 0.901087i | \(0.642770\pi\) | |||||||
\(284\) | 5.86876 | 0.348247 | ||||||||
\(285\) | −14.8818 | −0.881522 | ||||||||
\(286\) | 2.30593 | 0.136353 | ||||||||
\(287\) | −4.04440 | −0.238733 | ||||||||
\(288\) | 7.45289 | 0.439166 | ||||||||
\(289\) | 10.8456 | 0.637979 | ||||||||
\(290\) | −29.6071 | −1.73859 | ||||||||
\(291\) | 5.90264 | 0.346019 | ||||||||
\(292\) | 31.8984 | 1.86671 | ||||||||
\(293\) | 22.6706 | 1.32443 | 0.662215 | − | 0.749314i | \(-0.269617\pi\) | ||||
0.662215 | + | 0.749314i | \(0.269617\pi\) | |||||||
\(294\) | −14.4866 | −0.844874 | ||||||||
\(295\) | 18.4423 | 1.07375 | ||||||||
\(296\) | 12.6823 | 0.737144 | ||||||||
\(297\) | 1.05632 | 0.0612937 | ||||||||
\(298\) | −11.2813 | −0.653508 | ||||||||
\(299\) | −3.16152 | −0.182835 | ||||||||
\(300\) | 1.07338 | 0.0619716 | ||||||||
\(301\) | 1.97279 | 0.113710 | ||||||||
\(302\) | 19.7267 | 1.13514 | ||||||||
\(303\) | −7.67214 | −0.440753 | ||||||||
\(304\) | −13.0497 | −0.748454 | ||||||||
\(305\) | 4.83526 | 0.276866 | ||||||||
\(306\) | −11.5194 | −0.658522 | ||||||||
\(307\) | 18.6881 | 1.06659 | 0.533293 | − | 0.845930i | \(-0.320954\pi\) | ||||
0.533293 | + | 0.845930i | \(0.320954\pi\) | |||||||
\(308\) | −1.76218 | −0.100410 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −9.03024 | −0.512883 | ||||||||
\(311\) | −10.0778 | −0.571460 | −0.285730 | − | 0.958310i | \(-0.592236\pi\) | ||||
−0.285730 | + | 0.958310i | \(0.592236\pi\) | |||||||
\(312\) | 1.67100 | 0.0946015 | ||||||||
\(313\) | 3.34692 | 0.189179 | 0.0945895 | − | 0.995516i | \(-0.469846\pi\) | ||||
0.0945895 | + | 0.995516i | \(0.469846\pi\) | |||||||
\(314\) | 15.5200 | 0.875843 | ||||||||
\(315\) | 1.29547 | 0.0729914 | ||||||||
\(316\) | 8.36886 | 0.470785 | ||||||||
\(317\) | −1.89021 | −0.106165 | −0.0530824 | − | 0.998590i | \(-0.516905\pi\) | ||||
−0.0530824 | + | 0.998590i | \(0.516905\pi\) | |||||||
\(318\) | 31.1943 | 1.74929 | ||||||||
\(319\) | −6.67114 | −0.373512 | ||||||||
\(320\) | −26.8512 | −1.50103 | ||||||||
\(321\) | −14.0593 | −0.784714 | ||||||||
\(322\) | 4.16329 | 0.232011 | ||||||||
\(323\) | 36.5676 | 2.03467 | ||||||||
\(324\) | 2.76546 | 0.153637 | ||||||||
\(325\) | −0.388137 | −0.0215300 | ||||||||
\(326\) | 5.65620 | 0.313268 | ||||||||
\(327\) | 14.1233 | 0.781018 | ||||||||
\(328\) | 11.2032 | 0.618592 | ||||||||
\(329\) | 0.372733 | 0.0205494 | ||||||||
\(330\) | −4.95205 | −0.272601 | ||||||||
\(331\) | −22.6947 | −1.24741 | −0.623706 | − | 0.781659i | \(-0.714374\pi\) | ||||
−0.623706 | + | 0.781659i | \(0.714374\pi\) | |||||||
\(332\) | 17.1727 | 0.942475 | ||||||||
\(333\) | −7.58967 | −0.415911 | ||||||||
\(334\) | −30.8376 | −1.68736 | ||||||||
\(335\) | 14.3300 | 0.782932 | ||||||||
\(336\) | 1.13599 | 0.0619731 | ||||||||
\(337\) | 34.4444 | 1.87631 | 0.938153 | − | 0.346220i | \(-0.112535\pi\) | ||||
0.938153 | + | 0.346220i | \(0.112535\pi\) | |||||||
\(338\) | −2.18299 | −0.118739 | ||||||||
\(339\) | 19.9292 | 1.08241 | ||||||||
\(340\) | 31.3389 | 1.69959 | ||||||||
\(341\) | −2.03471 | −0.110186 | ||||||||
\(342\) | −15.1276 | −0.818007 | ||||||||
\(343\) | −8.22581 | −0.444152 | ||||||||
\(344\) | −5.46472 | −0.294638 | ||||||||
\(345\) | 6.78943 | 0.365531 | ||||||||
\(346\) | −45.5539 | −2.44899 | ||||||||
\(347\) | −19.0816 | −1.02435 | −0.512176 | − | 0.858881i | \(-0.671160\pi\) | ||||
−0.512176 | + | 0.858881i | \(0.671160\pi\) | |||||||
\(348\) | −17.4652 | −0.936232 | ||||||||
\(349\) | 21.9421 | 1.17453 | 0.587267 | − | 0.809393i | \(-0.300204\pi\) | ||||
0.587267 | + | 0.809393i | \(0.300204\pi\) | |||||||
\(350\) | 0.511124 | 0.0273207 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −7.87262 | −0.419612 | ||||||||
\(353\) | −5.60304 | −0.298220 | −0.149110 | − | 0.988821i | \(-0.547641\pi\) | ||||
−0.149110 | + | 0.988821i | \(0.547641\pi\) | |||||||
\(354\) | 18.7469 | 0.996384 | ||||||||
\(355\) | 4.55740 | 0.241882 | ||||||||
\(356\) | −16.9793 | −0.899901 | ||||||||
\(357\) | −3.18322 | −0.168474 | ||||||||
\(358\) | −6.67484 | −0.352776 | ||||||||
\(359\) | 13.9845 | 0.738075 | 0.369038 | − | 0.929414i | \(-0.379687\pi\) | ||||
0.369038 | + | 0.929414i | \(0.379687\pi\) | |||||||
\(360\) | −3.58851 | −0.189131 | ||||||||
\(361\) | 29.0214 | 1.52744 | ||||||||
\(362\) | 39.4670 | 2.07434 | ||||||||
\(363\) | 9.88419 | 0.518786 | ||||||||
\(364\) | 1.66823 | 0.0874390 | ||||||||
\(365\) | 24.7708 | 1.29656 | ||||||||
\(366\) | 4.91512 | 0.256918 | ||||||||
\(367\) | −7.73232 | −0.403624 | −0.201812 | − | 0.979424i | \(-0.564683\pi\) | ||||
−0.201812 | + | 0.979424i | \(0.564683\pi\) | |||||||
\(368\) | 5.95360 | 0.310353 | ||||||||
\(369\) | −6.70449 | −0.349022 | ||||||||
\(370\) | 35.5806 | 1.84975 | ||||||||
\(371\) | 8.62009 | 0.447533 | ||||||||
\(372\) | −5.32692 | −0.276188 | ||||||||
\(373\) | −24.1629 | −1.25111 | −0.625555 | − | 0.780180i | \(-0.715127\pi\) | ||||
−0.625555 | + | 0.780180i | \(0.715127\pi\) | |||||||
\(374\) | 12.1682 | 0.629201 | ||||||||
\(375\) | 11.5712 | 0.597532 | ||||||||
\(376\) | −1.03249 | −0.0532465 | ||||||||
\(377\) | 6.31547 | 0.325263 | ||||||||
\(378\) | 1.31686 | 0.0677322 | ||||||||
\(379\) | 8.27854 | 0.425240 | 0.212620 | − | 0.977135i | \(-0.431800\pi\) | ||||
0.212620 | + | 0.977135i | \(0.431800\pi\) | |||||||
\(380\) | 41.1551 | 2.11121 | ||||||||
\(381\) | 7.73839 | 0.396450 | ||||||||
\(382\) | 25.8108 | 1.32060 | ||||||||
\(383\) | 14.0812 | 0.719516 | 0.359758 | − | 0.933046i | \(-0.382859\pi\) | ||||
0.359758 | + | 0.933046i | \(0.382859\pi\) | |||||||
\(384\) | −12.3889 | −0.632217 | ||||||||
\(385\) | −1.36843 | −0.0697414 | ||||||||
\(386\) | −16.5313 | −0.841418 | ||||||||
\(387\) | 3.27034 | 0.166240 | ||||||||
\(388\) | −16.3235 | −0.828702 | ||||||||
\(389\) | −1.09755 | −0.0556480 | −0.0278240 | − | 0.999613i | \(-0.508858\pi\) | ||||
−0.0278240 | + | 0.999613i | \(0.508858\pi\) | |||||||
\(390\) | 4.68803 | 0.237388 | ||||||||
\(391\) | −16.6830 | −0.843695 | ||||||||
\(392\) | 11.0889 | 0.560074 | ||||||||
\(393\) | −5.61500 | −0.283240 | ||||||||
\(394\) | 44.5629 | 2.24505 | ||||||||
\(395\) | 6.49885 | 0.326993 | ||||||||
\(396\) | −2.92120 | −0.146796 | ||||||||
\(397\) | 30.4637 | 1.52893 | 0.764464 | − | 0.644667i | \(-0.223004\pi\) | ||||
0.764464 | + | 0.644667i | \(0.223004\pi\) | |||||||
\(398\) | 44.6494 | 2.23807 | ||||||||
\(399\) | −4.18029 | −0.209276 | ||||||||
\(400\) | 0.730920 | 0.0365460 | ||||||||
\(401\) | 6.94279 | 0.346706 | 0.173353 | − | 0.984860i | \(-0.444540\pi\) | ||||
0.173353 | + | 0.984860i | \(0.444540\pi\) | |||||||
\(402\) | 14.5667 | 0.726520 | ||||||||
\(403\) | 1.92623 | 0.0959525 | ||||||||
\(404\) | 21.2170 | 1.05559 | ||||||||
\(405\) | 2.14752 | 0.106711 | ||||||||
\(406\) | −8.31662 | −0.412747 | ||||||||
\(407\) | 8.01710 | 0.397393 | ||||||||
\(408\) | 8.81767 | 0.436540 | ||||||||
\(409\) | −0.773582 | −0.0382512 | −0.0191256 | − | 0.999817i | \(-0.506088\pi\) | ||||
−0.0191256 | + | 0.999817i | \(0.506088\pi\) | |||||||
\(410\) | 31.4309 | 1.55226 | ||||||||
\(411\) | 11.3859 | 0.561627 | ||||||||
\(412\) | −2.76546 | −0.136244 | ||||||||
\(413\) | 5.18042 | 0.254912 | ||||||||
\(414\) | 6.90157 | 0.339194 | ||||||||
\(415\) | 13.3355 | 0.654614 | ||||||||
\(416\) | 7.45289 | 0.365408 | ||||||||
\(417\) | −12.3445 | −0.604511 | ||||||||
\(418\) | 15.9795 | 0.781585 | ||||||||
\(419\) | 27.6118 | 1.34892 | 0.674462 | − | 0.738310i | \(-0.264376\pi\) | ||||
0.674462 | + | 0.738310i | \(0.264376\pi\) | |||||||
\(420\) | −3.58257 | −0.174811 | ||||||||
\(421\) | 26.8931 | 1.31069 | 0.655344 | − | 0.755330i | \(-0.272524\pi\) | ||||
0.655344 | + | 0.755330i | \(0.272524\pi\) | |||||||
\(422\) | 21.8881 | 1.06550 | ||||||||
\(423\) | 0.617887 | 0.0300427 | ||||||||
\(424\) | −23.8780 | −1.15962 | ||||||||
\(425\) | −2.04816 | −0.0993504 | ||||||||
\(426\) | 4.63267 | 0.224454 | ||||||||
\(427\) | 1.35822 | 0.0657289 | ||||||||
\(428\) | 38.8805 | 1.87936 | ||||||||
\(429\) | 1.05632 | 0.0509995 | ||||||||
\(430\) | −15.3314 | −0.739348 | ||||||||
\(431\) | 20.8097 | 1.00237 | 0.501185 | − | 0.865340i | \(-0.332898\pi\) | ||||
0.501185 | + | 0.865340i | \(0.332898\pi\) | |||||||
\(432\) | 1.88315 | 0.0906030 | ||||||||
\(433\) | 4.03399 | 0.193861 | 0.0969305 | − | 0.995291i | \(-0.469098\pi\) | ||||
0.0969305 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(434\) | −2.53659 | −0.121760 | ||||||||
\(435\) | −13.5626 | −0.650278 | ||||||||
\(436\) | −39.0573 | −1.87051 | ||||||||
\(437\) | −21.9085 | −1.04803 | ||||||||
\(438\) | 25.1799 | 1.20314 | ||||||||
\(439\) | −8.85604 | −0.422676 | −0.211338 | − | 0.977413i | \(-0.567782\pi\) | ||||
−0.211338 | + | 0.977413i | \(0.567782\pi\) | |||||||
\(440\) | 3.79060 | 0.180710 | ||||||||
\(441\) | −6.63610 | −0.316005 | ||||||||
\(442\) | −11.5194 | −0.547923 | ||||||||
\(443\) | 35.3295 | 1.67855 | 0.839277 | − | 0.543704i | \(-0.182979\pi\) | ||||
0.839277 | + | 0.543704i | \(0.182979\pi\) | |||||||
\(444\) | 20.9889 | 0.996091 | ||||||||
\(445\) | −13.1853 | −0.625044 | ||||||||
\(446\) | 17.0643 | 0.808018 | ||||||||
\(447\) | −5.16781 | −0.244429 | ||||||||
\(448\) | −7.54248 | −0.356348 | ||||||||
\(449\) | −13.7652 | −0.649619 | −0.324810 | − | 0.945779i | \(-0.605300\pi\) | ||||
−0.324810 | + | 0.945779i | \(0.605300\pi\) | |||||||
\(450\) | 0.847301 | 0.0399422 | ||||||||
\(451\) | 7.08207 | 0.333481 | ||||||||
\(452\) | −55.1135 | −2.59232 | ||||||||
\(453\) | 9.03652 | 0.424573 | ||||||||
\(454\) | −38.0783 | −1.78710 | ||||||||
\(455\) | 1.29547 | 0.0607325 | ||||||||
\(456\) | 11.5796 | 0.542264 | ||||||||
\(457\) | −5.99230 | −0.280308 | −0.140154 | − | 0.990130i | \(-0.544760\pi\) | ||||
−0.140154 | + | 0.990130i | \(0.544760\pi\) | |||||||
\(458\) | −18.3325 | −0.856621 | ||||||||
\(459\) | −5.27690 | −0.246304 | ||||||||
\(460\) | −18.7759 | −0.875431 | ||||||||
\(461\) | −30.2105 | −1.40704 | −0.703521 | − | 0.710675i | \(-0.748390\pi\) | ||||
−0.703521 | + | 0.710675i | \(0.748390\pi\) | |||||||
\(462\) | −1.39103 | −0.0647164 | ||||||||
\(463\) | −3.79915 | −0.176561 | −0.0882807 | − | 0.996096i | \(-0.528137\pi\) | ||||
−0.0882807 | + | 0.996096i | \(0.528137\pi\) | |||||||
\(464\) | −11.8930 | −0.552117 | ||||||||
\(465\) | −4.13663 | −0.191832 | ||||||||
\(466\) | −59.2405 | −2.74426 | ||||||||
\(467\) | 0.327390 | 0.0151498 | 0.00757489 | − | 0.999971i | \(-0.497589\pi\) | ||||
0.00757489 | + | 0.999971i | \(0.497589\pi\) | |||||||
\(468\) | 2.76546 | 0.127833 | ||||||||
\(469\) | 4.02529 | 0.185871 | ||||||||
\(470\) | −2.89668 | −0.133614 | ||||||||
\(471\) | 7.10949 | 0.327588 | ||||||||
\(472\) | −14.3500 | −0.660512 | ||||||||
\(473\) | −3.45451 | −0.158839 | ||||||||
\(474\) | 6.60619 | 0.303432 | ||||||||
\(475\) | −2.68970 | −0.123412 | ||||||||
\(476\) | 8.80308 | 0.403489 | ||||||||
\(477\) | 14.2897 | 0.654281 | ||||||||
\(478\) | −37.8547 | −1.73143 | ||||||||
\(479\) | 28.1466 | 1.28605 | 0.643024 | − | 0.765846i | \(-0.277679\pi\) | ||||
0.643024 | + | 0.765846i | \(0.277679\pi\) | |||||||
\(480\) | −16.0053 | −0.730537 | ||||||||
\(481\) | −7.58967 | −0.346059 | ||||||||
\(482\) | 26.0548 | 1.18676 | ||||||||
\(483\) | 1.90715 | 0.0867782 | ||||||||
\(484\) | −27.3344 | −1.24247 | ||||||||
\(485\) | −12.6761 | −0.575591 | ||||||||
\(486\) | 2.18299 | 0.0990226 | ||||||||
\(487\) | 34.7053 | 1.57265 | 0.786323 | − | 0.617815i | \(-0.211982\pi\) | ||||
0.786323 | + | 0.617815i | \(0.211982\pi\) | |||||||
\(488\) | −3.76233 | −0.170313 | ||||||||
\(489\) | 2.59103 | 0.117170 | ||||||||
\(490\) | 31.1103 | 1.40542 | ||||||||
\(491\) | −30.6696 | −1.38410 | −0.692049 | − | 0.721851i | \(-0.743292\pi\) | ||||
−0.692049 | + | 0.721851i | \(0.743292\pi\) | |||||||
\(492\) | 18.5410 | 0.835893 | ||||||||
\(493\) | 33.3261 | 1.50093 | ||||||||
\(494\) | −15.1276 | −0.680623 | ||||||||
\(495\) | −2.26847 | −0.101960 | ||||||||
\(496\) | −3.62738 | −0.162874 | ||||||||
\(497\) | 1.28017 | 0.0574235 | ||||||||
\(498\) | 13.5558 | 0.607448 | ||||||||
\(499\) | −11.0663 | −0.495394 | −0.247697 | − | 0.968838i | \(-0.579674\pi\) | ||||
−0.247697 | + | 0.968838i | \(0.579674\pi\) | |||||||
\(500\) | −31.9996 | −1.43106 | ||||||||
\(501\) | −14.1263 | −0.631116 | ||||||||
\(502\) | −32.0197 | −1.42911 | ||||||||
\(503\) | 5.48152 | 0.244409 | 0.122204 | − | 0.992505i | \(-0.461004\pi\) | ||||
0.122204 | + | 0.992505i | \(0.461004\pi\) | |||||||
\(504\) | −1.00801 | −0.0449002 | ||||||||
\(505\) | 16.4761 | 0.733177 | ||||||||
\(506\) | −7.29024 | −0.324091 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −21.4002 | −0.949481 | ||||||||
\(509\) | −7.49438 | −0.332183 | −0.166091 | − | 0.986110i | \(-0.553115\pi\) | ||||
−0.166091 | + | 0.986110i | \(0.553115\pi\) | |||||||
\(510\) | 24.7383 | 1.09543 | ||||||||
\(511\) | 6.95810 | 0.307808 | ||||||||
\(512\) | −20.3284 | −0.898395 | ||||||||
\(513\) | −6.92975 | −0.305956 | ||||||||
\(514\) | 26.4454 | 1.16646 | ||||||||
\(515\) | −2.14752 | −0.0946312 | ||||||||
\(516\) | −9.04398 | −0.398139 | ||||||||
\(517\) | −0.652685 | −0.0287050 | ||||||||
\(518\) | 9.99457 | 0.439136 | ||||||||
\(519\) | −20.8676 | −0.915988 | ||||||||
\(520\) | −3.58851 | −0.157366 | ||||||||
\(521\) | −28.3150 | −1.24050 | −0.620251 | − | 0.784403i | \(-0.712969\pi\) | ||||
−0.620251 | + | 0.784403i | \(0.712969\pi\) | |||||||
\(522\) | −13.7866 | −0.603425 | ||||||||
\(523\) | 33.1848 | 1.45107 | 0.725535 | − | 0.688186i | \(-0.241593\pi\) | ||||
0.725535 | + | 0.688186i | \(0.241593\pi\) | |||||||
\(524\) | 15.5281 | 0.678347 | ||||||||
\(525\) | 0.234139 | 0.0102187 | ||||||||
\(526\) | −32.1374 | −1.40126 | ||||||||
\(527\) | 10.1645 | 0.442774 | ||||||||
\(528\) | −1.98920 | −0.0865689 | ||||||||
\(529\) | −13.0048 | −0.565427 | ||||||||
\(530\) | −66.9906 | −2.90989 | ||||||||
\(531\) | 8.58769 | 0.372674 | ||||||||
\(532\) | 11.5604 | 0.501208 | ||||||||
\(533\) | −6.70449 | −0.290404 | ||||||||
\(534\) | −13.4031 | −0.580008 | ||||||||
\(535\) | 30.1927 | 1.30534 | ||||||||
\(536\) | −11.1502 | −0.481616 | ||||||||
\(537\) | −3.05765 | −0.131948 | ||||||||
\(538\) | −58.6275 | −2.52761 | ||||||||
\(539\) | 7.00983 | 0.301935 | ||||||||
\(540\) | −5.93890 | −0.255569 | ||||||||
\(541\) | 5.17839 | 0.222636 | 0.111318 | − | 0.993785i | \(-0.464493\pi\) | ||||
0.111318 | + | 0.993785i | \(0.464493\pi\) | |||||||
\(542\) | −40.0406 | −1.71989 | ||||||||
\(543\) | 18.0793 | 0.775858 | ||||||||
\(544\) | 39.3281 | 1.68618 | ||||||||
\(545\) | −30.3300 | −1.29920 | ||||||||
\(546\) | 1.31686 | 0.0563566 | ||||||||
\(547\) | 19.9967 | 0.854997 | 0.427498 | − | 0.904016i | \(-0.359395\pi\) | ||||
0.427498 | + | 0.904016i | \(0.359395\pi\) | |||||||
\(548\) | −31.4874 | −1.34507 | ||||||||
\(549\) | 2.25155 | 0.0960939 | ||||||||
\(550\) | −0.895019 | −0.0381637 | ||||||||
\(551\) | 43.7646 | 1.86444 | ||||||||
\(552\) | −5.28288 | −0.224854 | ||||||||
\(553\) | 1.82552 | 0.0776291 | ||||||||
\(554\) | 46.4799 | 1.97474 | ||||||||
\(555\) | 16.2990 | 0.691854 | ||||||||
\(556\) | 34.1381 | 1.44778 | ||||||||
\(557\) | −28.0503 | −1.18853 | −0.594265 | − | 0.804269i | \(-0.702557\pi\) | ||||
−0.594265 | + | 0.804269i | \(0.702557\pi\) | |||||||
\(558\) | −4.20495 | −0.178010 | ||||||||
\(559\) | 3.27034 | 0.138320 | ||||||||
\(560\) | −2.43956 | −0.103090 | ||||||||
\(561\) | 5.57408 | 0.235338 | ||||||||
\(562\) | 71.7284 | 3.02568 | ||||||||
\(563\) | −35.5708 | −1.49913 | −0.749565 | − | 0.661930i | \(-0.769737\pi\) | ||||
−0.749565 | + | 0.661930i | \(0.769737\pi\) | |||||||
\(564\) | −1.70874 | −0.0719511 | ||||||||
\(565\) | −42.7985 | −1.80055 | ||||||||
\(566\) | 31.8495 | 1.33873 | ||||||||
\(567\) | 0.603238 | 0.0253336 | ||||||||
\(568\) | −3.54613 | −0.148792 | ||||||||
\(569\) | −12.8128 | −0.537142 | −0.268571 | − | 0.963260i | \(-0.586551\pi\) | ||||
−0.268571 | + | 0.963260i | \(0.586551\pi\) | |||||||
\(570\) | 32.4869 | 1.36073 | ||||||||
\(571\) | −2.65151 | −0.110962 | −0.0554811 | − | 0.998460i | \(-0.517669\pi\) | ||||
−0.0554811 | + | 0.998460i | \(0.517669\pi\) | |||||||
\(572\) | −2.92120 | −0.122142 | ||||||||
\(573\) | 11.8236 | 0.493938 | ||||||||
\(574\) | 8.82890 | 0.368511 | ||||||||
\(575\) | 1.22710 | 0.0511737 | ||||||||
\(576\) | −12.5033 | −0.520972 | ||||||||
\(577\) | 33.7490 | 1.40499 | 0.702495 | − | 0.711689i | \(-0.252069\pi\) | ||||
0.702495 | + | 0.711689i | \(0.252069\pi\) | |||||||
\(578\) | −23.6760 | −0.984790 | ||||||||
\(579\) | −7.57274 | −0.314712 | ||||||||
\(580\) | 37.5069 | 1.55739 | ||||||||
\(581\) | 3.74593 | 0.155407 | ||||||||
\(582\) | −12.8854 | −0.534118 | ||||||||
\(583\) | −15.0945 | −0.625149 | ||||||||
\(584\) | −19.2742 | −0.797574 | ||||||||
\(585\) | 2.14752 | 0.0887892 | ||||||||
\(586\) | −49.4897 | −2.04440 | ||||||||
\(587\) | 3.72873 | 0.153901 | 0.0769505 | − | 0.997035i | \(-0.475482\pi\) | ||||
0.0769505 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(588\) | 18.3519 | 0.756819 | ||||||||
\(589\) | 13.3483 | 0.550008 | ||||||||
\(590\) | −40.2593 | −1.65745 | ||||||||
\(591\) | 20.4137 | 0.839707 | ||||||||
\(592\) | 14.2925 | 0.587417 | ||||||||
\(593\) | 32.6347 | 1.34015 | 0.670074 | − | 0.742294i | \(-0.266262\pi\) | ||||
0.670074 | + | 0.742294i | \(0.266262\pi\) | |||||||
\(594\) | −2.30593 | −0.0946136 | ||||||||
\(595\) | 6.83605 | 0.280251 | ||||||||
\(596\) | 14.2914 | 0.585398 | ||||||||
\(597\) | 20.4533 | 0.837098 | ||||||||
\(598\) | 6.90157 | 0.282226 | ||||||||
\(599\) | −37.1180 | −1.51660 | −0.758300 | − | 0.651905i | \(-0.773970\pi\) | ||||
−0.758300 | + | 0.651905i | \(0.773970\pi\) | |||||||
\(600\) | −0.648576 | −0.0264780 | ||||||||
\(601\) | −1.54003 | −0.0628192 | −0.0314096 | − | 0.999507i | \(-0.510000\pi\) | ||||
−0.0314096 | + | 0.999507i | \(0.510000\pi\) | |||||||
\(602\) | −4.30659 | −0.175523 | ||||||||
\(603\) | 6.67280 | 0.271738 | ||||||||
\(604\) | −24.9901 | −1.01683 | ||||||||
\(605\) | −21.2266 | −0.862982 | ||||||||
\(606\) | 16.7482 | 0.680351 | ||||||||
\(607\) | 33.7817 | 1.37116 | 0.685578 | − | 0.727999i | \(-0.259550\pi\) | ||||
0.685578 | + | 0.727999i | \(0.259550\pi\) | |||||||
\(608\) | 51.6467 | 2.09455 | ||||||||
\(609\) | −3.80973 | −0.154378 | ||||||||
\(610\) | −10.5553 | −0.427374 | ||||||||
\(611\) | 0.617887 | 0.0249970 | ||||||||
\(612\) | 14.5931 | 0.589889 | ||||||||
\(613\) | 32.0731 | 1.29542 | 0.647710 | − | 0.761887i | \(-0.275727\pi\) | ||||
0.647710 | + | 0.761887i | \(0.275727\pi\) | |||||||
\(614\) | −40.7960 | −1.64639 | ||||||||
\(615\) | 14.3981 | 0.580586 | ||||||||
\(616\) | 1.06478 | 0.0429010 | ||||||||
\(617\) | 42.7972 | 1.72295 | 0.861475 | − | 0.507799i | \(-0.169541\pi\) | ||||
0.861475 | + | 0.507799i | \(0.169541\pi\) | |||||||
\(618\) | −2.18299 | −0.0878129 | ||||||||
\(619\) | −38.6834 | −1.55482 | −0.777409 | − | 0.628995i | \(-0.783467\pi\) | ||||
−0.777409 | + | 0.628995i | \(0.783467\pi\) | |||||||
\(620\) | 11.4397 | 0.459429 | ||||||||
\(621\) | 3.16152 | 0.126867 | ||||||||
\(622\) | 21.9998 | 0.882112 | ||||||||
\(623\) | −3.70374 | −0.148387 | ||||||||
\(624\) | 1.88315 | 0.0753863 | ||||||||
\(625\) | −22.9087 | −0.916346 | ||||||||
\(626\) | −7.30630 | −0.292018 | ||||||||
\(627\) | 7.32001 | 0.292333 | ||||||||
\(628\) | −19.6610 | −0.784560 | ||||||||
\(629\) | −40.0499 | −1.59689 | ||||||||
\(630\) | −2.82800 | −0.112670 | ||||||||
\(631\) | 32.0582 | 1.27622 | 0.638109 | − | 0.769946i | \(-0.279717\pi\) | ||||
0.638109 | + | 0.769946i | \(0.279717\pi\) | |||||||
\(632\) | −5.05678 | −0.201148 | ||||||||
\(633\) | 10.0266 | 0.398524 | ||||||||
\(634\) | 4.12632 | 0.163877 | ||||||||
\(635\) | −16.6184 | −0.659481 | ||||||||
\(636\) | −39.5176 | −1.56698 | ||||||||
\(637\) | −6.63610 | −0.262932 | ||||||||
\(638\) | 14.5631 | 0.576557 | ||||||||
\(639\) | 2.12217 | 0.0839516 | ||||||||
\(640\) | 26.6054 | 1.05167 | ||||||||
\(641\) | −1.75709 | −0.0694010 | −0.0347005 | − | 0.999398i | \(-0.511048\pi\) | ||||
−0.0347005 | + | 0.999398i | \(0.511048\pi\) | |||||||
\(642\) | 30.6914 | 1.21129 | ||||||||
\(643\) | 13.5640 | 0.534913 | 0.267457 | − | 0.963570i | \(-0.413817\pi\) | ||||
0.267457 | + | 0.963570i | \(0.413817\pi\) | |||||||
\(644\) | −5.27414 | −0.207830 | ||||||||
\(645\) | −7.02313 | −0.276535 | ||||||||
\(646\) | −79.8268 | −3.14074 | ||||||||
\(647\) | 10.4286 | 0.409991 | 0.204996 | − | 0.978763i | \(-0.434282\pi\) | ||||
0.204996 | + | 0.978763i | \(0.434282\pi\) | |||||||
\(648\) | −1.67100 | −0.0656429 | ||||||||
\(649\) | −9.07132 | −0.356080 | ||||||||
\(650\) | 0.847301 | 0.0332339 | ||||||||
\(651\) | −1.16198 | −0.0455414 | ||||||||
\(652\) | −7.16538 | −0.280618 | ||||||||
\(653\) | 16.4692 | 0.644491 | 0.322246 | − | 0.946656i | \(-0.395562\pi\) | ||||
0.322246 | + | 0.946656i | \(0.395562\pi\) | |||||||
\(654\) | −30.8310 | −1.20559 | ||||||||
\(655\) | 12.0584 | 0.471159 | ||||||||
\(656\) | 12.6255 | 0.492945 | ||||||||
\(657\) | 11.5346 | 0.450007 | ||||||||
\(658\) | −0.813674 | −0.0317203 | ||||||||
\(659\) | −39.2008 | −1.52704 | −0.763522 | − | 0.645781i | \(-0.776532\pi\) | ||||
−0.763522 | + | 0.645781i | \(0.776532\pi\) | |||||||
\(660\) | 6.27336 | 0.244190 | ||||||||
\(661\) | 9.94678 | 0.386885 | 0.193442 | − | 0.981112i | \(-0.438035\pi\) | ||||
0.193442 | + | 0.981112i | \(0.438035\pi\) | |||||||
\(662\) | 49.5423 | 1.92552 | ||||||||
\(663\) | −5.27690 | −0.204938 | ||||||||
\(664\) | −10.3764 | −0.402682 | ||||||||
\(665\) | 8.97727 | 0.348124 | ||||||||
\(666\) | 16.5682 | 0.642005 | ||||||||
\(667\) | −19.9665 | −0.773105 | ||||||||
\(668\) | 39.0657 | 1.51150 | ||||||||
\(669\) | 7.81693 | 0.302220 | ||||||||
\(670\) | −31.2823 | −1.20854 | ||||||||
\(671\) | −2.37835 | −0.0918153 | ||||||||
\(672\) | −4.49587 | −0.173432 | ||||||||
\(673\) | 23.5980 | 0.909637 | 0.454819 | − | 0.890584i | \(-0.349704\pi\) | ||||
0.454819 | + | 0.890584i | \(0.349704\pi\) | |||||||
\(674\) | −75.1919 | −2.89628 | ||||||||
\(675\) | 0.388137 | 0.0149394 | ||||||||
\(676\) | 2.76546 | 0.106364 | ||||||||
\(677\) | 1.96251 | 0.0754254 | 0.0377127 | − | 0.999289i | \(-0.487993\pi\) | ||||
0.0377127 | + | 0.999289i | \(0.487993\pi\) | |||||||
\(678\) | −43.5054 | −1.67081 | ||||||||
\(679\) | −3.56070 | −0.136647 | ||||||||
\(680\) | −18.9362 | −0.726169 | ||||||||
\(681\) | −17.4432 | −0.668424 | ||||||||
\(682\) | 4.44176 | 0.170084 | ||||||||
\(683\) | −11.7025 | −0.447785 | −0.223893 | − | 0.974614i | \(-0.571877\pi\) | ||||
−0.223893 | + | 0.974614i | \(0.571877\pi\) | |||||||
\(684\) | 19.1640 | 0.732752 | ||||||||
\(685\) | −24.4516 | −0.934247 | ||||||||
\(686\) | 17.9569 | 0.685598 | ||||||||
\(687\) | −8.39787 | −0.320399 | ||||||||
\(688\) | −6.15853 | −0.234792 | ||||||||
\(689\) | 14.2897 | 0.544394 | ||||||||
\(690\) | −14.8213 | −0.564237 | ||||||||
\(691\) | 23.7265 | 0.902598 | 0.451299 | − | 0.892373i | \(-0.350961\pi\) | ||||
0.451299 | + | 0.892373i | \(0.350961\pi\) | |||||||
\(692\) | 57.7086 | 2.19375 | ||||||||
\(693\) | −0.637210 | −0.0242056 | ||||||||
\(694\) | 41.6549 | 1.58120 | ||||||||
\(695\) | 26.5100 | 1.00558 | ||||||||
\(696\) | 10.5531 | 0.400015 | ||||||||
\(697\) | −35.3789 | −1.34007 | ||||||||
\(698\) | −47.8995 | −1.81302 | ||||||||
\(699\) | −27.1373 | −1.02643 | ||||||||
\(700\) | −0.647503 | −0.0244733 | ||||||||
\(701\) | 28.7248 | 1.08492 | 0.542460 | − | 0.840082i | \(-0.317493\pi\) | ||||
0.542460 | + | 0.840082i | \(0.317493\pi\) | |||||||
\(702\) | 2.18299 | 0.0823918 | ||||||||
\(703\) | −52.5945 | −1.98364 | ||||||||
\(704\) | 13.2075 | 0.497775 | ||||||||
\(705\) | −1.32693 | −0.0499750 | ||||||||
\(706\) | 12.2314 | 0.460335 | ||||||||
\(707\) | 4.62813 | 0.174059 | ||||||||
\(708\) | −23.7489 | −0.892539 | ||||||||
\(709\) | 8.87649 | 0.333364 | 0.166682 | − | 0.986011i | \(-0.446695\pi\) | ||||
0.166682 | + | 0.986011i | \(0.446695\pi\) | |||||||
\(710\) | −9.94878 | −0.373371 | ||||||||
\(711\) | 3.02621 | 0.113492 | ||||||||
\(712\) | 10.2595 | 0.384492 | ||||||||
\(713\) | −6.08981 | −0.228065 | ||||||||
\(714\) | 6.94896 | 0.260058 | ||||||||
\(715\) | −2.26847 | −0.0848358 | ||||||||
\(716\) | 8.45582 | 0.316009 | ||||||||
\(717\) | −17.3407 | −0.647601 | ||||||||
\(718\) | −30.5281 | −1.13930 | ||||||||
\(719\) | 46.4119 | 1.73087 | 0.865437 | − | 0.501018i | \(-0.167041\pi\) | ||||
0.865437 | + | 0.501018i | \(0.167041\pi\) | |||||||
\(720\) | −4.04411 | −0.150715 | ||||||||
\(721\) | −0.603238 | −0.0224658 | ||||||||
\(722\) | −63.3536 | −2.35778 | ||||||||
\(723\) | 11.9353 | 0.443880 | ||||||||
\(724\) | −49.9976 | −1.85815 | ||||||||
\(725\) | −2.45127 | −0.0910379 | ||||||||
\(726\) | −21.5771 | −0.800803 | ||||||||
\(727\) | −1.13202 | −0.0419844 | −0.0209922 | − | 0.999780i | \(-0.506683\pi\) | ||||
−0.0209922 | + | 0.999780i | \(0.506683\pi\) | |||||||
\(728\) | −1.00801 | −0.0373593 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −54.0745 | −2.00139 | ||||||||
\(731\) | 17.2572 | 0.638281 | ||||||||
\(732\) | −6.22658 | −0.230141 | ||||||||
\(733\) | 44.7170 | 1.65166 | 0.825829 | − | 0.563920i | \(-0.190707\pi\) | ||||
0.825829 | + | 0.563920i | \(0.190707\pi\) | |||||||
\(734\) | 16.8796 | 0.623038 | ||||||||
\(735\) | 14.2512 | 0.525663 | ||||||||
\(736\) | −23.5624 | −0.868523 | ||||||||
\(737\) | −7.04860 | −0.259638 | ||||||||
\(738\) | 14.6359 | 0.538753 | ||||||||
\(739\) | 35.9114 | 1.32102 | 0.660512 | − | 0.750816i | \(-0.270339\pi\) | ||||
0.660512 | + | 0.750816i | \(0.270339\pi\) | |||||||
\(740\) | −45.0743 | −1.65696 | ||||||||
\(741\) | −6.92975 | −0.254571 | ||||||||
\(742\) | −18.8176 | −0.690816 | ||||||||
\(743\) | −5.46113 | −0.200349 | −0.100175 | − | 0.994970i | \(-0.531940\pi\) | ||||
−0.100175 | + | 0.994970i | \(0.531940\pi\) | |||||||
\(744\) | 3.21873 | 0.118004 | ||||||||
\(745\) | 11.0980 | 0.406600 | ||||||||
\(746\) | 52.7475 | 1.93122 | ||||||||
\(747\) | 6.20971 | 0.227201 | ||||||||
\(748\) | −15.4149 | −0.563624 | ||||||||
\(749\) | 8.48111 | 0.309893 | ||||||||
\(750\) | −25.2598 | −0.922356 | ||||||||
\(751\) | −6.65506 | −0.242847 | −0.121423 | − | 0.992601i | \(-0.538746\pi\) | ||||
−0.121423 | + | 0.992601i | \(0.538746\pi\) | |||||||
\(752\) | −1.16357 | −0.0424312 | ||||||||
\(753\) | −14.6678 | −0.534524 | ||||||||
\(754\) | −13.7866 | −0.502080 | ||||||||
\(755\) | −19.4062 | −0.706262 | ||||||||
\(756\) | −1.66823 | −0.0606730 | ||||||||
\(757\) | −37.9946 | −1.38094 | −0.690468 | − | 0.723363i | \(-0.742595\pi\) | ||||
−0.690468 | + | 0.723363i | \(0.742595\pi\) | |||||||
\(758\) | −18.0720 | −0.656404 | ||||||||
\(759\) | −3.33956 | −0.121218 | ||||||||
\(760\) | −24.8674 | −0.902037 | ||||||||
\(761\) | 47.7901 | 1.73239 | 0.866196 | − | 0.499705i | \(-0.166558\pi\) | ||||
0.866196 | + | 0.499705i | \(0.166558\pi\) | |||||||
\(762\) | −16.8929 | −0.611964 | ||||||||
\(763\) | −8.51968 | −0.308433 | ||||||||
\(764\) | −32.6977 | −1.18296 | ||||||||
\(765\) | 11.3323 | 0.409719 | ||||||||
\(766\) | −30.7392 | −1.11065 | ||||||||
\(767\) | 8.58769 | 0.310083 | ||||||||
\(768\) | 2.03821 | 0.0735475 | ||||||||
\(769\) | −33.6790 | −1.21449 | −0.607247 | − | 0.794513i | \(-0.707726\pi\) | ||||
−0.607247 | + | 0.794513i | \(0.707726\pi\) | |||||||
\(770\) | 2.98726 | 0.107653 | ||||||||
\(771\) | 12.1143 | 0.436286 | ||||||||
\(772\) | 20.9421 | 0.753724 | ||||||||
\(773\) | −4.76372 | −0.171339 | −0.0856696 | − | 0.996324i | \(-0.527303\pi\) | ||||
−0.0856696 | + | 0.996324i | \(0.527303\pi\) | |||||||
\(774\) | −7.13912 | −0.256610 | ||||||||
\(775\) | −0.747643 | −0.0268561 | ||||||||
\(776\) | 9.86329 | 0.354072 | ||||||||
\(777\) | 4.57838 | 0.164248 | ||||||||
\(778\) | 2.39595 | 0.0858988 | ||||||||
\(779\) | −46.4604 | −1.66462 | ||||||||
\(780\) | −5.93890 | −0.212647 | ||||||||
\(781\) | −2.24168 | −0.0802136 | ||||||||
\(782\) | 36.4189 | 1.30234 | ||||||||
\(783\) | −6.31547 | −0.225697 | ||||||||
\(784\) | 12.4968 | 0.446313 | ||||||||
\(785\) | −15.2678 | −0.544931 | ||||||||
\(786\) | 12.2575 | 0.437211 | ||||||||
\(787\) | −7.39989 | −0.263778 | −0.131889 | − | 0.991265i | \(-0.542104\pi\) | ||||
−0.131889 | + | 0.991265i | \(0.542104\pi\) | |||||||
\(788\) | −56.4533 | −2.01106 | ||||||||
\(789\) | −14.7217 | −0.524106 | ||||||||
\(790\) | −14.1870 | −0.504749 | ||||||||
\(791\) | −12.0221 | −0.427455 | ||||||||
\(792\) | 1.76510 | 0.0627201 | ||||||||
\(793\) | 2.25155 | 0.0799550 | ||||||||
\(794\) | −66.5020 | −2.36007 | ||||||||
\(795\) | −30.6875 | −1.08837 | ||||||||
\(796\) | −56.5628 | −2.00482 | ||||||||
\(797\) | 22.3261 | 0.790832 | 0.395416 | − | 0.918502i | \(-0.370600\pi\) | ||||
0.395416 | + | 0.918502i | \(0.370600\pi\) | |||||||
\(798\) | 9.12554 | 0.323041 | ||||||||
\(799\) | 3.26053 | 0.115349 | ||||||||
\(800\) | −2.89275 | −0.102274 | ||||||||
\(801\) | −6.13977 | −0.216938 | ||||||||
\(802\) | −15.1561 | −0.535179 | ||||||||
\(803\) | −12.1842 | −0.429970 | ||||||||
\(804\) | −18.4534 | −0.650800 | ||||||||
\(805\) | −4.09564 | −0.144352 | ||||||||
\(806\) | −4.20495 | −0.148113 | ||||||||
\(807\) | −26.8565 | −0.945392 | ||||||||
\(808\) | −12.8201 | −0.451010 | ||||||||
\(809\) | 40.3047 | 1.41704 | 0.708519 | − | 0.705691i | \(-0.249363\pi\) | ||||
0.708519 | + | 0.705691i | \(0.249363\pi\) | |||||||
\(810\) | −4.68803 | −0.164721 | ||||||||
\(811\) | 9.23529 | 0.324295 | 0.162147 | − | 0.986767i | \(-0.448158\pi\) | ||||
0.162147 | + | 0.986767i | \(0.448158\pi\) | |||||||
\(812\) | 10.5357 | 0.369729 | ||||||||
\(813\) | −18.3421 | −0.643284 | ||||||||
\(814\) | −17.5013 | −0.613419 | ||||||||
\(815\) | −5.56429 | −0.194909 | ||||||||
\(816\) | 9.93718 | 0.347871 | ||||||||
\(817\) | 22.6626 | 0.792864 | ||||||||
\(818\) | 1.68873 | 0.0590449 | ||||||||
\(819\) | 0.603238 | 0.0210788 | ||||||||
\(820\) | −39.8173 | −1.39048 | ||||||||
\(821\) | −13.1297 | −0.458230 | −0.229115 | − | 0.973399i | \(-0.573583\pi\) | ||||
−0.229115 | + | 0.973399i | \(0.573583\pi\) | |||||||
\(822\) | −24.8554 | −0.866933 | ||||||||
\(823\) | 3.44974 | 0.120250 | 0.0601251 | − | 0.998191i | \(-0.480850\pi\) | ||||
0.0601251 | + | 0.998191i | \(0.480850\pi\) | |||||||
\(824\) | 1.67100 | 0.0582119 | ||||||||
\(825\) | −0.409996 | −0.0142742 | ||||||||
\(826\) | −11.3088 | −0.393484 | ||||||||
\(827\) | 39.2823 | 1.36598 | 0.682990 | − | 0.730427i | \(-0.260679\pi\) | ||||
0.682990 | + | 0.730427i | \(0.260679\pi\) | |||||||
\(828\) | −8.74305 | −0.303842 | ||||||||
\(829\) | −9.59393 | −0.333211 | −0.166605 | − | 0.986024i | \(-0.553281\pi\) | ||||
−0.166605 | + | 0.986024i | \(0.553281\pi\) | |||||||
\(830\) | −29.1113 | −1.01047 | ||||||||
\(831\) | 21.2918 | 0.738605 | ||||||||
\(832\) | −12.5033 | −0.433475 | ||||||||
\(833\) | −35.0180 | −1.21330 | ||||||||
\(834\) | 26.9479 | 0.933129 | ||||||||
\(835\) | 30.3365 | 1.04984 | ||||||||
\(836\) | −20.2432 | −0.700126 | ||||||||
\(837\) | −1.92623 | −0.0665803 | ||||||||
\(838\) | −60.2763 | −2.08221 | ||||||||
\(839\) | −32.9251 | −1.13670 | −0.568351 | − | 0.822786i | \(-0.692418\pi\) | ||||
−0.568351 | + | 0.822786i | \(0.692418\pi\) | |||||||
\(840\) | 2.16472 | 0.0746900 | ||||||||
\(841\) | 10.8852 | 0.375351 | ||||||||
\(842\) | −58.7074 | −2.02319 | ||||||||
\(843\) | 32.8578 | 1.13168 | ||||||||
\(844\) | −27.7283 | −0.954448 | ||||||||
\(845\) | 2.14752 | 0.0738771 | ||||||||
\(846\) | −1.34884 | −0.0463742 | ||||||||
\(847\) | −5.96252 | −0.204875 | ||||||||
\(848\) | −26.9096 | −0.924081 | ||||||||
\(849\) | 14.5898 | 0.500722 | ||||||||
\(850\) | 4.47112 | 0.153358 | ||||||||
\(851\) | 23.9949 | 0.822534 | ||||||||
\(852\) | −5.86876 | −0.201061 | ||||||||
\(853\) | 3.45990 | 0.118465 | 0.0592323 | − | 0.998244i | \(-0.481135\pi\) | ||||
0.0592323 | + | 0.998244i | \(0.481135\pi\) | |||||||
\(854\) | −2.96499 | −0.101460 | ||||||||
\(855\) | 14.8818 | 0.508947 | ||||||||
\(856\) | −23.4930 | −0.802976 | ||||||||
\(857\) | −33.5096 | −1.14467 | −0.572333 | − | 0.820021i | \(-0.693962\pi\) | ||||
−0.572333 | + | 0.820021i | \(0.693962\pi\) | |||||||
\(858\) | −2.30593 | −0.0787233 | ||||||||
\(859\) | −32.1134 | −1.09569 | −0.547847 | − | 0.836579i | \(-0.684552\pi\) | ||||
−0.547847 | + | 0.836579i | \(0.684552\pi\) | |||||||
\(860\) | 19.4222 | 0.662291 | ||||||||
\(861\) | 4.04440 | 0.137833 | ||||||||
\(862\) | −45.4275 | −1.54727 | ||||||||
\(863\) | −55.9802 | −1.90559 | −0.952793 | − | 0.303620i | \(-0.901805\pi\) | ||||
−0.952793 | + | 0.303620i | \(0.901805\pi\) | |||||||
\(864\) | −7.45289 | −0.253553 | ||||||||
\(865\) | 44.8138 | 1.52371 | ||||||||
\(866\) | −8.80617 | −0.299246 | ||||||||
\(867\) | −10.8456 | −0.368337 | ||||||||
\(868\) | 3.21340 | 0.109070 | ||||||||
\(869\) | −3.19663 | −0.108438 | ||||||||
\(870\) | 29.6071 | 1.00378 | ||||||||
\(871\) | 6.67280 | 0.226099 | ||||||||
\(872\) | 23.5999 | 0.799194 | ||||||||
\(873\) | −5.90264 | −0.199774 | ||||||||
\(874\) | 47.8262 | 1.61774 | ||||||||
\(875\) | −6.98016 | −0.235973 | ||||||||
\(876\) | −31.8984 | −1.07775 | ||||||||
\(877\) | 36.0850 | 1.21850 | 0.609252 | − | 0.792977i | \(-0.291470\pi\) | ||||
0.609252 | + | 0.792977i | \(0.291470\pi\) | |||||||
\(878\) | 19.3327 | 0.652446 | ||||||||
\(879\) | −22.6706 | −0.764660 | ||||||||
\(880\) | 4.27186 | 0.144004 | ||||||||
\(881\) | −35.2781 | −1.18855 | −0.594274 | − | 0.804262i | \(-0.702561\pi\) | ||||
−0.594274 | + | 0.804262i | \(0.702561\pi\) | |||||||
\(882\) | 14.4866 | 0.487788 | ||||||||
\(883\) | 10.7259 | 0.360954 | 0.180477 | − | 0.983579i | \(-0.442236\pi\) | ||||
0.180477 | + | 0.983579i | \(0.442236\pi\) | |||||||
\(884\) | 14.5931 | 0.490817 | ||||||||
\(885\) | −18.4423 | −0.619930 | ||||||||
\(886\) | −77.1240 | −2.59103 | ||||||||
\(887\) | −21.0020 | −0.705179 | −0.352590 | − | 0.935778i | \(-0.614699\pi\) | ||||
−0.352590 | + | 0.935778i | \(0.614699\pi\) | |||||||
\(888\) | −12.6823 | −0.425591 | ||||||||
\(889\) | −4.66809 | −0.156563 | ||||||||
\(890\) | 28.7835 | 0.964824 | ||||||||
\(891\) | −1.05632 | −0.0353879 | ||||||||
\(892\) | −21.6174 | −0.723805 | ||||||||
\(893\) | 4.28181 | 0.143285 | ||||||||
\(894\) | 11.2813 | 0.377303 | ||||||||
\(895\) | 6.56639 | 0.219490 | ||||||||
\(896\) | 7.47344 | 0.249670 | ||||||||
\(897\) | 3.16152 | 0.105560 | ||||||||
\(898\) | 30.0493 | 1.00276 | ||||||||
\(899\) | 12.1651 | 0.405728 | ||||||||
\(900\) | −1.07338 | −0.0357793 | ||||||||
\(901\) | 75.4053 | 2.51211 | ||||||||
\(902\) | −15.4601 | −0.514765 | ||||||||
\(903\) | −1.97279 | −0.0656503 | ||||||||
\(904\) | 33.3017 | 1.10760 | ||||||||
\(905\) | −38.8258 | −1.29061 | ||||||||
\(906\) | −19.7267 | −0.655375 | ||||||||
\(907\) | −52.4356 | −1.74110 | −0.870549 | − | 0.492082i | \(-0.836236\pi\) | ||||
−0.870549 | + | 0.492082i | \(0.836236\pi\) | |||||||
\(908\) | 48.2384 | 1.60085 | ||||||||
\(909\) | 7.67214 | 0.254469 | ||||||||
\(910\) | −2.82800 | −0.0937473 | ||||||||
\(911\) | −9.84115 | −0.326052 | −0.163026 | − | 0.986622i | \(-0.552125\pi\) | ||||
−0.163026 | + | 0.986622i | \(0.552125\pi\) | |||||||
\(912\) | 13.0497 | 0.432120 | ||||||||
\(913\) | −6.55942 | −0.217085 | ||||||||
\(914\) | 13.0812 | 0.432686 | ||||||||
\(915\) | −4.83526 | −0.159849 | ||||||||
\(916\) | 23.2240 | 0.767342 | ||||||||
\(917\) | 3.38718 | 0.111855 | ||||||||
\(918\) | 11.5194 | 0.380198 | ||||||||
\(919\) | −27.0275 | −0.891556 | −0.445778 | − | 0.895144i | \(-0.647073\pi\) | ||||
−0.445778 | + | 0.895144i | \(0.647073\pi\) | |||||||
\(920\) | 11.3451 | 0.374037 | ||||||||
\(921\) | −18.6881 | −0.615794 | ||||||||
\(922\) | 65.9492 | 2.17192 | ||||||||
\(923\) | 2.12217 | 0.0698519 | ||||||||
\(924\) | 1.76218 | 0.0579715 | ||||||||
\(925\) | 2.94584 | 0.0968585 | ||||||||
\(926\) | 8.29351 | 0.272542 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 47.0685 | 1.54510 | ||||||||
\(929\) | 3.35293 | 0.110006 | 0.0550031 | − | 0.998486i | \(-0.482483\pi\) | ||||
0.0550031 | + | 0.998486i | \(0.482483\pi\) | |||||||
\(930\) | 9.03024 | 0.296113 | ||||||||
\(931\) | −45.9865 | −1.50715 | ||||||||
\(932\) | 75.0471 | 2.45825 | ||||||||
\(933\) | 10.0778 | 0.329933 | ||||||||
\(934\) | −0.714689 | −0.0233853 | ||||||||
\(935\) | −11.9705 | −0.391476 | ||||||||
\(936\) | −1.67100 | −0.0546182 | ||||||||
\(937\) | −1.87747 | −0.0613342 | −0.0306671 | − | 0.999530i | \(-0.509763\pi\) | ||||
−0.0306671 | + | 0.999530i | \(0.509763\pi\) | |||||||
\(938\) | −8.78718 | −0.286912 | ||||||||
\(939\) | −3.34692 | −0.109223 | ||||||||
\(940\) | 3.66957 | 0.119688 | ||||||||
\(941\) | 7.46359 | 0.243306 | 0.121653 | − | 0.992573i | \(-0.461180\pi\) | ||||
0.121653 | + | 0.992573i | \(0.461180\pi\) | |||||||
\(942\) | −15.5200 | −0.505668 | ||||||||
\(943\) | 21.1963 | 0.690248 | ||||||||
\(944\) | −16.1719 | −0.526350 | ||||||||
\(945\) | −1.29547 | −0.0421416 | ||||||||
\(946\) | 7.54117 | 0.245185 | ||||||||
\(947\) | −26.2180 | −0.851970 | −0.425985 | − | 0.904730i | \(-0.640072\pi\) | ||||
−0.425985 | + | 0.904730i | \(0.640072\pi\) | |||||||
\(948\) | −8.36886 | −0.271808 | ||||||||
\(949\) | 11.5346 | 0.374428 | ||||||||
\(950\) | 5.87159 | 0.190499 | ||||||||
\(951\) | 1.89021 | 0.0612943 | ||||||||
\(952\) | −5.31915 | −0.172395 | ||||||||
\(953\) | −44.6207 | −1.44541 | −0.722703 | − | 0.691159i | \(-0.757100\pi\) | ||||
−0.722703 | + | 0.691159i | \(0.757100\pi\) | |||||||
\(954\) | −31.1943 | −1.00995 | ||||||||
\(955\) | −25.3915 | −0.821648 | ||||||||
\(956\) | 47.9551 | 1.55098 | ||||||||
\(957\) | 6.67114 | 0.215647 | ||||||||
\(958\) | −61.4437 | −1.98516 | ||||||||
\(959\) | −6.86843 | −0.221793 | ||||||||
\(960\) | 26.8512 | 0.866618 | ||||||||
\(961\) | −27.2896 | −0.880311 | ||||||||
\(962\) | 16.5682 | 0.534180 | ||||||||
\(963\) | 14.0593 | 0.453055 | ||||||||
\(964\) | −33.0067 | −1.06307 | ||||||||
\(965\) | 16.2627 | 0.523513 | ||||||||
\(966\) | −4.16329 | −0.133952 | ||||||||
\(967\) | 53.2215 | 1.71149 | 0.855744 | − | 0.517400i | \(-0.173100\pi\) | ||||
0.855744 | + | 0.517400i | \(0.173100\pi\) | |||||||
\(968\) | 16.5164 | 0.530859 | ||||||||
\(969\) | −36.5676 | −1.17472 | ||||||||
\(970\) | 27.6718 | 0.888488 | ||||||||
\(971\) | 15.3042 | 0.491135 | 0.245568 | − | 0.969379i | \(-0.421026\pi\) | ||||
0.245568 | + | 0.969379i | \(0.421026\pi\) | |||||||
\(972\) | −2.76546 | −0.0887022 | ||||||||
\(973\) | 7.44665 | 0.238729 | ||||||||
\(974\) | −75.7614 | −2.42755 | ||||||||
\(975\) | 0.388137 | 0.0124303 | ||||||||
\(976\) | −4.24001 | −0.135719 | ||||||||
\(977\) | 4.73103 | 0.151359 | 0.0756795 | − | 0.997132i | \(-0.475887\pi\) | ||||
0.0756795 | + | 0.997132i | \(0.475887\pi\) | |||||||
\(978\) | −5.65620 | −0.180865 | ||||||||
\(979\) | 6.48555 | 0.207279 | ||||||||
\(980\) | −39.4111 | −1.25894 | ||||||||
\(981\) | −14.1233 | −0.450921 | ||||||||
\(982\) | 66.9515 | 2.13651 | ||||||||
\(983\) | 2.48434 | 0.0792382 | 0.0396191 | − | 0.999215i | \(-0.487386\pi\) | ||||
0.0396191 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(984\) | −11.2032 | −0.357144 | ||||||||
\(985\) | −43.8389 | −1.39682 | ||||||||
\(986\) | −72.7506 | −2.31685 | ||||||||
\(987\) | −0.372733 | −0.0118642 | ||||||||
\(988\) | 19.1640 | 0.609687 | ||||||||
\(989\) | −10.3392 | −0.328768 | ||||||||
\(990\) | 4.95205 | 0.157386 | ||||||||
\(991\) | 31.9034 | 1.01344 | 0.506722 | − | 0.862109i | \(-0.330857\pi\) | ||||
0.506722 | + | 0.862109i | \(0.330857\pi\) | |||||||
\(992\) | 14.3560 | 0.455804 | ||||||||
\(993\) | 22.6947 | 0.720194 | ||||||||
\(994\) | −2.79460 | −0.0886394 | ||||||||
\(995\) | −43.9240 | −1.39248 | ||||||||
\(996\) | −17.1727 | −0.544138 | ||||||||
\(997\) | −7.36795 | −0.233345 | −0.116673 | − | 0.993170i | \(-0.537223\pi\) | ||||
−0.116673 | + | 0.993170i | \(0.537223\pi\) | |||||||
\(998\) | 24.1576 | 0.764695 | ||||||||
\(999\) | 7.58967 | 0.240127 |
(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 | 4017.2.a.j.1.3 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.3 | ✓ | 25 | 1.1 | even | 1 | trivial |