Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(0\) |
Dimension: | \(140\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54565 | −1.80005 | −0.900025 | − | 0.435838i | \(-0.856452\pi\) | ||||
−0.900025 | + | 0.435838i | \(0.856452\pi\) | |||||||
\(3\) | 1.89511 | 1.09414 | 0.547072 | − | 0.837086i | \(-0.315742\pi\) | ||||
0.547072 | + | 0.837086i | \(0.315742\pi\) | |||||||
\(4\) | 4.48036 | 2.24018 | ||||||||
\(5\) | 0.316502 | 0.141544 | 0.0707721 | − | 0.997493i | \(-0.477454\pi\) | ||||
0.0707721 | + | 0.997493i | \(0.477454\pi\) | |||||||
\(6\) | −4.82430 | −1.96951 | ||||||||
\(7\) | 4.66425 | 1.76292 | 0.881460 | − | 0.472259i | \(-0.156561\pi\) | ||||
0.881460 | + | 0.472259i | \(0.156561\pi\) | |||||||
\(8\) | −6.31414 | −2.23238 | ||||||||
\(9\) | 0.591450 | 0.197150 | ||||||||
\(10\) | −0.805706 | −0.254787 | ||||||||
\(11\) | −5.53509 | −1.66889 | −0.834446 | − | 0.551090i | \(-0.814212\pi\) | ||||
−0.834446 | + | 0.551090i | \(0.814212\pi\) | |||||||
\(12\) | 8.49078 | 2.45108 | ||||||||
\(13\) | 3.33573 | 0.925164 | 0.462582 | − | 0.886576i | \(-0.346923\pi\) | ||||
0.462582 | + | 0.886576i | \(0.346923\pi\) | |||||||
\(14\) | −11.8736 | −3.17334 | ||||||||
\(15\) | 0.599808 | 0.154870 | ||||||||
\(16\) | 7.11290 | 1.77822 | ||||||||
\(17\) | 4.94232 | 1.19869 | 0.599345 | − | 0.800491i | \(-0.295428\pi\) | ||||
0.599345 | + | 0.800491i | \(0.295428\pi\) | |||||||
\(18\) | −1.50563 | −0.354880 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.41804 | 0.317084 | ||||||||
\(21\) | 8.83927 | 1.92889 | ||||||||
\(22\) | 14.0904 | 3.00409 | ||||||||
\(23\) | −4.57605 | −0.954172 | −0.477086 | − | 0.878857i | \(-0.658307\pi\) | ||||
−0.477086 | + | 0.878857i | \(0.658307\pi\) | |||||||
\(24\) | −11.9660 | −2.44255 | ||||||||
\(25\) | −4.89983 | −0.979965 | ||||||||
\(26\) | −8.49161 | −1.66534 | ||||||||
\(27\) | −4.56447 | −0.878433 | ||||||||
\(28\) | 20.8975 | 3.94926 | ||||||||
\(29\) | −7.40314 | −1.37473 | −0.687364 | − | 0.726313i | \(-0.741232\pi\) | ||||
−0.687364 | + | 0.726313i | \(0.741232\pi\) | |||||||
\(30\) | −1.52690 | −0.278773 | ||||||||
\(31\) | 9.17278 | 1.64748 | 0.823740 | − | 0.566968i | \(-0.191884\pi\) | ||||
0.823740 | + | 0.566968i | \(0.191884\pi\) | |||||||
\(32\) | −5.47871 | −0.968508 | ||||||||
\(33\) | −10.4896 | −1.82601 | ||||||||
\(34\) | −12.5814 | −2.15770 | ||||||||
\(35\) | 1.47625 | 0.249531 | ||||||||
\(36\) | 2.64991 | 0.441651 | ||||||||
\(37\) | −1.44497 | −0.237551 | −0.118776 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118776 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(38\) | 2.54565 | 0.412960 | ||||||||
\(39\) | 6.32158 | 1.01226 | ||||||||
\(40\) | −1.99844 | −0.315981 | ||||||||
\(41\) | 2.63740 | 0.411893 | 0.205947 | − | 0.978563i | \(-0.433973\pi\) | ||||
0.205947 | + | 0.978563i | \(0.433973\pi\) | |||||||
\(42\) | −22.5017 | −3.47209 | ||||||||
\(43\) | 7.90393 | 1.20534 | 0.602669 | − | 0.797991i | \(-0.294104\pi\) | ||||
0.602669 | + | 0.797991i | \(0.294104\pi\) | |||||||
\(44\) | −24.7992 | −3.73862 | ||||||||
\(45\) | 0.187195 | 0.0279054 | ||||||||
\(46\) | 11.6490 | 1.71756 | ||||||||
\(47\) | 7.76536 | 1.13269 | 0.566347 | − | 0.824167i | \(-0.308356\pi\) | ||||
0.566347 | + | 0.824167i | \(0.308356\pi\) | |||||||
\(48\) | 13.4797 | 1.94563 | ||||||||
\(49\) | 14.7552 | 2.10789 | ||||||||
\(50\) | 12.4733 | 1.76399 | ||||||||
\(51\) | 9.36625 | 1.31154 | ||||||||
\(52\) | 14.9453 | 2.07253 | ||||||||
\(53\) | −0.605101 | −0.0831170 | −0.0415585 | − | 0.999136i | \(-0.513232\pi\) | ||||
−0.0415585 | + | 0.999136i | \(0.513232\pi\) | |||||||
\(54\) | 11.6196 | 1.58122 | ||||||||
\(55\) | −1.75187 | −0.236222 | ||||||||
\(56\) | −29.4507 | −3.93551 | ||||||||
\(57\) | −1.89511 | −0.251014 | ||||||||
\(58\) | 18.8458 | 2.47458 | ||||||||
\(59\) | 3.69609 | 0.481190 | 0.240595 | − | 0.970626i | \(-0.422657\pi\) | ||||
0.240595 | + | 0.970626i | \(0.422657\pi\) | |||||||
\(60\) | 2.68735 | 0.346936 | ||||||||
\(61\) | −6.99411 | −0.895504 | −0.447752 | − | 0.894158i | \(-0.647775\pi\) | ||||
−0.447752 | + | 0.894158i | \(0.647775\pi\) | |||||||
\(62\) | −23.3507 | −2.96555 | ||||||||
\(63\) | 2.75867 | 0.347560 | ||||||||
\(64\) | −0.278896 | −0.0348620 | ||||||||
\(65\) | 1.05577 | 0.130952 | ||||||||
\(66\) | 26.7029 | 3.28690 | ||||||||
\(67\) | −8.29778 | −1.01374 | −0.506868 | − | 0.862024i | \(-0.669197\pi\) | ||||
−0.506868 | + | 0.862024i | \(0.669197\pi\) | |||||||
\(68\) | 22.1434 | 2.68528 | ||||||||
\(69\) | −8.67212 | −1.04400 | ||||||||
\(70\) | −3.75801 | −0.449168 | ||||||||
\(71\) | 9.96718 | 1.18289 | 0.591443 | − | 0.806347i | \(-0.298558\pi\) | ||||
0.591443 | + | 0.806347i | \(0.298558\pi\) | |||||||
\(72\) | −3.73450 | −0.440115 | ||||||||
\(73\) | 0.947379 | 0.110882 | 0.0554412 | − | 0.998462i | \(-0.482343\pi\) | ||||
0.0554412 | + | 0.998462i | \(0.482343\pi\) | |||||||
\(74\) | 3.67839 | 0.427604 | ||||||||
\(75\) | −9.28572 | −1.07222 | ||||||||
\(76\) | −4.48036 | −0.513932 | ||||||||
\(77\) | −25.8170 | −2.94212 | ||||||||
\(78\) | −16.0925 | −1.82212 | ||||||||
\(79\) | 11.6227 | 1.30766 | 0.653828 | − | 0.756643i | \(-0.273162\pi\) | ||||
0.653828 | + | 0.756643i | \(0.273162\pi\) | |||||||
\(80\) | 2.25125 | 0.251697 | ||||||||
\(81\) | −10.4245 | −1.15828 | ||||||||
\(82\) | −6.71392 | −0.741429 | ||||||||
\(83\) | 11.7301 | 1.28754 | 0.643770 | − | 0.765219i | \(-0.277369\pi\) | ||||
0.643770 | + | 0.765219i | \(0.277369\pi\) | |||||||
\(84\) | 39.6031 | 4.32105 | ||||||||
\(85\) | 1.56426 | 0.169667 | ||||||||
\(86\) | −20.1207 | −2.16967 | ||||||||
\(87\) | −14.0298 | −1.50415 | ||||||||
\(88\) | 34.9493 | 3.72561 | ||||||||
\(89\) | −9.66359 | −1.02434 | −0.512169 | − | 0.858884i | \(-0.671158\pi\) | ||||
−0.512169 | + | 0.858884i | \(0.671158\pi\) | |||||||
\(90\) | −0.476535 | −0.0502312 | ||||||||
\(91\) | 15.5587 | 1.63099 | ||||||||
\(92\) | −20.5023 | −2.13752 | ||||||||
\(93\) | 17.3834 | 1.80258 | ||||||||
\(94\) | −19.7679 | −2.03891 | ||||||||
\(95\) | −0.316502 | −0.0324725 | ||||||||
\(96\) | −10.3828 | −1.05969 | ||||||||
\(97\) | −1.85979 | −0.188833 | −0.0944166 | − | 0.995533i | \(-0.530099\pi\) | ||||
−0.0944166 | + | 0.995533i | \(0.530099\pi\) | |||||||
\(98\) | −37.5616 | −3.79430 | ||||||||
\(99\) | −3.27373 | −0.329022 | ||||||||
\(100\) | −21.9530 | −2.19530 | ||||||||
\(101\) | 5.45710 | 0.543002 | 0.271501 | − | 0.962438i | \(-0.412480\pi\) | ||||
0.271501 | + | 0.962438i | \(0.412480\pi\) | |||||||
\(102\) | −23.8433 | −2.36083 | ||||||||
\(103\) | 13.0148 | 1.28238 | 0.641192 | − | 0.767380i | \(-0.278440\pi\) | ||||
0.641192 | + | 0.767380i | \(0.278440\pi\) | |||||||
\(104\) | −21.0622 | −2.06532 | ||||||||
\(105\) | 2.79765 | 0.273023 | ||||||||
\(106\) | 1.54038 | 0.149615 | ||||||||
\(107\) | 1.91919 | 0.185535 | 0.0927675 | − | 0.995688i | \(-0.470429\pi\) | ||||
0.0927675 | + | 0.995688i | \(0.470429\pi\) | |||||||
\(108\) | −20.4505 | −1.96785 | ||||||||
\(109\) | 14.1159 | 1.35206 | 0.676029 | − | 0.736875i | \(-0.263700\pi\) | ||||
0.676029 | + | 0.736875i | \(0.263700\pi\) | |||||||
\(110\) | 4.45965 | 0.425211 | ||||||||
\(111\) | −2.73838 | −0.259915 | ||||||||
\(112\) | 33.1763 | 3.13487 | ||||||||
\(113\) | −16.5722 | −1.55898 | −0.779488 | − | 0.626417i | \(-0.784521\pi\) | ||||
−0.779488 | + | 0.626417i | \(0.784521\pi\) | |||||||
\(114\) | 4.82430 | 0.451837 | ||||||||
\(115\) | −1.44833 | −0.135057 | ||||||||
\(116\) | −33.1687 | −3.07964 | ||||||||
\(117\) | 1.97292 | 0.182396 | ||||||||
\(118\) | −9.40898 | −0.866167 | ||||||||
\(119\) | 23.0522 | 2.11319 | ||||||||
\(120\) | −3.78727 | −0.345729 | ||||||||
\(121\) | 19.6372 | 1.78520 | ||||||||
\(122\) | 17.8046 | 1.61195 | ||||||||
\(123\) | 4.99818 | 0.450670 | ||||||||
\(124\) | 41.0973 | 3.69065 | ||||||||
\(125\) | −3.13332 | −0.280253 | ||||||||
\(126\) | −7.02262 | −0.625625 | ||||||||
\(127\) | 19.1078 | 1.69554 | 0.847771 | − | 0.530362i | \(-0.177944\pi\) | ||||
0.847771 | + | 0.530362i | \(0.177944\pi\) | |||||||
\(128\) | 11.6674 | 1.03126 | ||||||||
\(129\) | 14.9788 | 1.31881 | ||||||||
\(130\) | −2.68761 | −0.235719 | ||||||||
\(131\) | 18.4194 | 1.60931 | 0.804654 | − | 0.593744i | \(-0.202351\pi\) | ||||
0.804654 | + | 0.593744i | \(0.202351\pi\) | |||||||
\(132\) | −46.9972 | −4.09058 | ||||||||
\(133\) | −4.66425 | −0.404441 | ||||||||
\(134\) | 21.1233 | 1.82477 | ||||||||
\(135\) | −1.44467 | −0.124337 | ||||||||
\(136\) | −31.2065 | −2.67594 | ||||||||
\(137\) | 22.9348 | 1.95945 | 0.979725 | − | 0.200345i | \(-0.0642062\pi\) | ||||
0.979725 | + | 0.200345i | \(0.0642062\pi\) | |||||||
\(138\) | 22.0762 | 1.87925 | ||||||||
\(139\) | −2.12317 | −0.180085 | −0.0900426 | − | 0.995938i | \(-0.528700\pi\) | ||||
−0.0900426 | + | 0.995938i | \(0.528700\pi\) | |||||||
\(140\) | 6.61411 | 0.558994 | ||||||||
\(141\) | 14.7162 | 1.23933 | ||||||||
\(142\) | −25.3730 | −2.12925 | ||||||||
\(143\) | −18.4635 | −1.54400 | ||||||||
\(144\) | 4.20692 | 0.350577 | ||||||||
\(145\) | −2.34311 | −0.194585 | ||||||||
\(146\) | −2.41170 | −0.199594 | ||||||||
\(147\) | 27.9628 | 2.30633 | ||||||||
\(148\) | −6.47397 | −0.532157 | ||||||||
\(149\) | 24.4012 | 1.99903 | 0.999513 | − | 0.0311948i | \(-0.00993122\pi\) | ||||
0.999513 | + | 0.0311948i | \(0.00993122\pi\) | |||||||
\(150\) | 23.6382 | 1.93005 | ||||||||
\(151\) | −4.75068 | −0.386605 | −0.193302 | − | 0.981139i | \(-0.561920\pi\) | ||||
−0.193302 | + | 0.981139i | \(0.561920\pi\) | |||||||
\(152\) | 6.31414 | 0.512144 | ||||||||
\(153\) | 2.92314 | 0.236322 | ||||||||
\(154\) | 65.7212 | 5.29597 | ||||||||
\(155\) | 2.90321 | 0.233191 | ||||||||
\(156\) | 28.3229 | 2.26765 | ||||||||
\(157\) | −16.1839 | −1.29161 | −0.645807 | − | 0.763501i | \(-0.723479\pi\) | ||||
−0.645807 | + | 0.763501i | \(0.723479\pi\) | |||||||
\(158\) | −29.5874 | −2.35385 | ||||||||
\(159\) | −1.14673 | −0.0909419 | ||||||||
\(160\) | −1.73402 | −0.137087 | ||||||||
\(161\) | −21.3438 | −1.68213 | ||||||||
\(162\) | 26.5373 | 2.08497 | ||||||||
\(163\) | 23.6260 | 1.85053 | 0.925266 | − | 0.379318i | \(-0.123841\pi\) | ||||
0.925266 | + | 0.379318i | \(0.123841\pi\) | |||||||
\(164\) | 11.8165 | 0.922715 | ||||||||
\(165\) | −3.31999 | −0.258461 | ||||||||
\(166\) | −29.8607 | −2.31764 | ||||||||
\(167\) | −16.2965 | −1.26106 | −0.630531 | − | 0.776164i | \(-0.717163\pi\) | ||||
−0.630531 | + | 0.776164i | \(0.717163\pi\) | |||||||
\(168\) | −55.8124 | −4.30602 | ||||||||
\(169\) | −1.87293 | −0.144072 | ||||||||
\(170\) | −3.98206 | −0.305410 | ||||||||
\(171\) | −0.591450 | −0.0452293 | ||||||||
\(172\) | 35.4124 | 2.70017 | ||||||||
\(173\) | 17.1955 | 1.30735 | 0.653676 | − | 0.756775i | \(-0.273226\pi\) | ||||
0.653676 | + | 0.756775i | \(0.273226\pi\) | |||||||
\(174\) | 35.7150 | 2.70755 | ||||||||
\(175\) | −22.8540 | −1.72760 | ||||||||
\(176\) | −39.3705 | −2.96766 | ||||||||
\(177\) | 7.00451 | 0.526491 | ||||||||
\(178\) | 24.6002 | 1.84386 | ||||||||
\(179\) | 16.2993 | 1.21827 | 0.609135 | − | 0.793066i | \(-0.291517\pi\) | ||||
0.609135 | + | 0.793066i | \(0.291517\pi\) | |||||||
\(180\) | 0.838702 | 0.0625132 | ||||||||
\(181\) | 13.7710 | 1.02359 | 0.511796 | − | 0.859107i | \(-0.328981\pi\) | ||||
0.511796 | + | 0.859107i | \(0.328981\pi\) | |||||||
\(182\) | −39.6070 | −2.93586 | ||||||||
\(183\) | −13.2546 | −0.979810 | ||||||||
\(184\) | 28.8938 | 2.13008 | ||||||||
\(185\) | −0.457336 | −0.0336240 | ||||||||
\(186\) | −44.2523 | −3.24473 | ||||||||
\(187\) | −27.3562 | −2.00048 | ||||||||
\(188\) | 34.7916 | 2.53744 | ||||||||
\(189\) | −21.2898 | −1.54861 | ||||||||
\(190\) | 0.805706 | 0.0584520 | ||||||||
\(191\) | −10.5101 | −0.760487 | −0.380244 | − | 0.924886i | \(-0.624160\pi\) | ||||
−0.380244 | + | 0.924886i | \(0.624160\pi\) | |||||||
\(192\) | −0.528540 | −0.0381441 | ||||||||
\(193\) | −17.1093 | −1.23155 | −0.615776 | − | 0.787921i | \(-0.711157\pi\) | ||||
−0.615776 | + | 0.787921i | \(0.711157\pi\) | |||||||
\(194\) | 4.73439 | 0.339909 | ||||||||
\(195\) | 2.00079 | 0.143280 | ||||||||
\(196\) | 66.1086 | 4.72204 | ||||||||
\(197\) | 14.6514 | 1.04387 | 0.521934 | − | 0.852986i | \(-0.325211\pi\) | ||||
0.521934 | + | 0.852986i | \(0.325211\pi\) | |||||||
\(198\) | 8.33378 | 0.592256 | ||||||||
\(199\) | 14.4925 | 1.02734 | 0.513672 | − | 0.857987i | \(-0.328285\pi\) | ||||
0.513672 | + | 0.857987i | \(0.328285\pi\) | |||||||
\(200\) | 30.9382 | 2.18766 | ||||||||
\(201\) | −15.7252 | −1.10917 | ||||||||
\(202\) | −13.8919 | −0.977430 | ||||||||
\(203\) | −34.5301 | −2.42354 | ||||||||
\(204\) | 41.9642 | 2.93808 | ||||||||
\(205\) | 0.834745 | 0.0583011 | ||||||||
\(206\) | −33.1311 | −2.30836 | ||||||||
\(207\) | −2.70650 | −0.188115 | ||||||||
\(208\) | 23.7267 | 1.64515 | ||||||||
\(209\) | 5.53509 | 0.382870 | ||||||||
\(210\) | −7.12185 | −0.491455 | ||||||||
\(211\) | 3.62012 | 0.249219 | 0.124610 | − | 0.992206i | \(-0.460232\pi\) | ||||
0.124610 | + | 0.992206i | \(0.460232\pi\) | |||||||
\(212\) | −2.71107 | −0.186197 | ||||||||
\(213\) | 18.8889 | 1.29425 | ||||||||
\(214\) | −4.88559 | −0.333972 | ||||||||
\(215\) | 2.50161 | 0.170609 | ||||||||
\(216\) | 28.8207 | 1.96100 | ||||||||
\(217\) | 42.7841 | 2.90437 | ||||||||
\(218\) | −35.9342 | −2.43377 | ||||||||
\(219\) | 1.79539 | 0.121321 | ||||||||
\(220\) | −7.84900 | −0.529180 | ||||||||
\(221\) | 16.4862 | 1.10898 | ||||||||
\(222\) | 6.97096 | 0.467860 | ||||||||
\(223\) | −6.09079 | −0.407869 | −0.203935 | − | 0.978985i | \(-0.565373\pi\) | ||||
−0.203935 | + | 0.978985i | \(0.565373\pi\) | |||||||
\(224\) | −25.5540 | −1.70740 | ||||||||
\(225\) | −2.89800 | −0.193200 | ||||||||
\(226\) | 42.1870 | 2.80624 | ||||||||
\(227\) | −1.66290 | −0.110370 | −0.0551852 | − | 0.998476i | \(-0.517575\pi\) | ||||
−0.0551852 | + | 0.998476i | \(0.517575\pi\) | |||||||
\(228\) | −8.49078 | −0.562316 | ||||||||
\(229\) | −14.3276 | −0.946794 | −0.473397 | − | 0.880849i | \(-0.656972\pi\) | ||||
−0.473397 | + | 0.880849i | \(0.656972\pi\) | |||||||
\(230\) | 3.68695 | 0.243110 | ||||||||
\(231\) | −48.9261 | −3.21910 | ||||||||
\(232\) | 46.7444 | 3.06892 | ||||||||
\(233\) | −3.40222 | −0.222887 | −0.111443 | − | 0.993771i | \(-0.535547\pi\) | ||||
−0.111443 | + | 0.993771i | \(0.535547\pi\) | |||||||
\(234\) | −5.02236 | −0.328322 | ||||||||
\(235\) | 2.45776 | 0.160326 | ||||||||
\(236\) | 16.5598 | 1.07795 | ||||||||
\(237\) | 22.0263 | 1.43076 | ||||||||
\(238\) | −58.6830 | −3.80385 | ||||||||
\(239\) | 25.5476 | 1.65254 | 0.826269 | − | 0.563275i | \(-0.190459\pi\) | ||||
0.826269 | + | 0.563275i | \(0.190459\pi\) | |||||||
\(240\) | 4.26637 | 0.275393 | ||||||||
\(241\) | 10.5789 | 0.681449 | 0.340725 | − | 0.940163i | \(-0.389328\pi\) | ||||
0.340725 | + | 0.940163i | \(0.389328\pi\) | |||||||
\(242\) | −49.9895 | −3.21345 | ||||||||
\(243\) | −6.06225 | −0.388894 | ||||||||
\(244\) | −31.3361 | −2.00609 | ||||||||
\(245\) | 4.67006 | 0.298359 | ||||||||
\(246\) | −12.7236 | −0.811229 | ||||||||
\(247\) | −3.33573 | −0.212247 | ||||||||
\(248\) | −57.9182 | −3.67781 | ||||||||
\(249\) | 22.2298 | 1.40875 | ||||||||
\(250\) | 7.97635 | 0.504469 | ||||||||
\(251\) | −15.0680 | −0.951084 | −0.475542 | − | 0.879693i | \(-0.657748\pi\) | ||||
−0.475542 | + | 0.879693i | \(0.657748\pi\) | |||||||
\(252\) | 12.3598 | 0.778596 | ||||||||
\(253\) | 25.3288 | 1.59241 | ||||||||
\(254\) | −48.6418 | −3.05206 | ||||||||
\(255\) | 2.96444 | 0.185641 | ||||||||
\(256\) | −29.1434 | −1.82146 | ||||||||
\(257\) | −18.1833 | −1.13424 | −0.567122 | − | 0.823634i | \(-0.691943\pi\) | ||||
−0.567122 | + | 0.823634i | \(0.691943\pi\) | |||||||
\(258\) | −38.1309 | −2.37393 | ||||||||
\(259\) | −6.73969 | −0.418784 | ||||||||
\(260\) | 4.73021 | 0.293355 | ||||||||
\(261\) | −4.37859 | −0.271028 | ||||||||
\(262\) | −46.8894 | −2.89683 | ||||||||
\(263\) | −5.88636 | −0.362968 | −0.181484 | − | 0.983394i | \(-0.558090\pi\) | ||||
−0.181484 | + | 0.983394i | \(0.558090\pi\) | |||||||
\(264\) | 66.2329 | 4.07635 | ||||||||
\(265\) | −0.191516 | −0.0117647 | ||||||||
\(266\) | 11.8736 | 0.728015 | ||||||||
\(267\) | −18.3136 | −1.12077 | ||||||||
\(268\) | −37.1770 | −2.27095 | ||||||||
\(269\) | 9.28943 | 0.566387 | 0.283193 | − | 0.959063i | \(-0.408606\pi\) | ||||
0.283193 | + | 0.959063i | \(0.408606\pi\) | |||||||
\(270\) | 3.67762 | 0.223813 | ||||||||
\(271\) | 4.10786 | 0.249535 | 0.124767 | − | 0.992186i | \(-0.460182\pi\) | ||||
0.124767 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(272\) | 35.1542 | 2.13154 | ||||||||
\(273\) | 29.4854 | 1.78454 | ||||||||
\(274\) | −58.3840 | −3.52711 | ||||||||
\(275\) | 27.1210 | 1.63546 | ||||||||
\(276\) | −38.8542 | −2.33875 | ||||||||
\(277\) | −16.9305 | −1.01725 | −0.508627 | − | 0.860987i | \(-0.669847\pi\) | ||||
−0.508627 | + | 0.860987i | \(0.669847\pi\) | |||||||
\(278\) | 5.40486 | 0.324162 | ||||||||
\(279\) | 5.42524 | 0.324801 | ||||||||
\(280\) | −9.32122 | −0.557049 | ||||||||
\(281\) | 7.66355 | 0.457169 | 0.228585 | − | 0.973524i | \(-0.426590\pi\) | ||||
0.228585 | + | 0.973524i | \(0.426590\pi\) | |||||||
\(282\) | −37.4624 | −2.23086 | ||||||||
\(283\) | 0.896363 | 0.0532832 | 0.0266416 | − | 0.999645i | \(-0.491519\pi\) | ||||
0.0266416 | + | 0.999645i | \(0.491519\pi\) | |||||||
\(284\) | 44.6565 | 2.64988 | ||||||||
\(285\) | −0.599808 | −0.0355295 | ||||||||
\(286\) | 47.0018 | 2.77927 | ||||||||
\(287\) | 12.3015 | 0.726135 | ||||||||
\(288\) | −3.24038 | −0.190941 | ||||||||
\(289\) | 7.42655 | 0.436856 | ||||||||
\(290\) | 5.96475 | 0.350262 | ||||||||
\(291\) | −3.52451 | −0.206611 | ||||||||
\(292\) | 4.24460 | 0.248396 | ||||||||
\(293\) | −30.2868 | −1.76937 | −0.884687 | − | 0.466186i | \(-0.845628\pi\) | ||||
−0.884687 | + | 0.466186i | \(0.845628\pi\) | |||||||
\(294\) | −71.1835 | −4.15151 | ||||||||
\(295\) | 1.16982 | 0.0681097 | ||||||||
\(296\) | 9.12373 | 0.530306 | ||||||||
\(297\) | 25.2648 | 1.46601 | ||||||||
\(298\) | −62.1171 | −3.59835 | ||||||||
\(299\) | −15.2644 | −0.882765 | ||||||||
\(300\) | −41.6034 | −2.40197 | ||||||||
\(301\) | 36.8659 | 2.12491 | ||||||||
\(302\) | 12.0936 | 0.695908 | ||||||||
\(303\) | 10.3418 | 0.594122 | ||||||||
\(304\) | −7.11290 | −0.407953 | ||||||||
\(305\) | −2.21365 | −0.126753 | ||||||||
\(306\) | −7.44130 | −0.425391 | ||||||||
\(307\) | −24.5666 | −1.40209 | −0.701045 | − | 0.713117i | \(-0.747283\pi\) | ||||
−0.701045 | + | 0.713117i | \(0.747283\pi\) | |||||||
\(308\) | −115.670 | −6.59088 | ||||||||
\(309\) | 24.6645 | 1.40311 | ||||||||
\(310\) | −7.39056 | −0.419756 | ||||||||
\(311\) | 15.4303 | 0.874975 | 0.437487 | − | 0.899225i | \(-0.355868\pi\) | ||||
0.437487 | + | 0.899225i | \(0.355868\pi\) | |||||||
\(312\) | −39.9153 | −2.25976 | ||||||||
\(313\) | 13.4409 | 0.759726 | 0.379863 | − | 0.925043i | \(-0.375971\pi\) | ||||
0.379863 | + | 0.925043i | \(0.375971\pi\) | |||||||
\(314\) | 41.1985 | 2.32497 | ||||||||
\(315\) | 0.873125 | 0.0491950 | ||||||||
\(316\) | 52.0739 | 2.92939 | ||||||||
\(317\) | 1.00000 | 0.0561656 | ||||||||
\(318\) | 2.91919 | 0.163700 | ||||||||
\(319\) | 40.9770 | 2.29427 | ||||||||
\(320\) | −0.0882713 | −0.00493452 | ||||||||
\(321\) | 3.63708 | 0.203002 | ||||||||
\(322\) | 54.3340 | 3.02791 | ||||||||
\(323\) | −4.94232 | −0.274998 | ||||||||
\(324\) | −46.7057 | −2.59476 | ||||||||
\(325\) | −16.3445 | −0.906629 | ||||||||
\(326\) | −60.1437 | −3.33105 | ||||||||
\(327\) | 26.7512 | 1.47934 | ||||||||
\(328\) | −16.6529 | −0.919505 | ||||||||
\(329\) | 36.2196 | 1.99685 | ||||||||
\(330\) | 8.45154 | 0.465242 | ||||||||
\(331\) | −31.5538 | −1.73436 | −0.867178 | − | 0.497998i | \(-0.834069\pi\) | ||||
−0.867178 | + | 0.497998i | \(0.834069\pi\) | |||||||
\(332\) | 52.5549 | 2.88432 | ||||||||
\(333\) | −0.854626 | −0.0468332 | ||||||||
\(334\) | 41.4853 | 2.26997 | ||||||||
\(335\) | −2.62627 | −0.143488 | ||||||||
\(336\) | 62.8728 | 3.42999 | ||||||||
\(337\) | 6.16200 | 0.335665 | 0.167833 | − | 0.985815i | \(-0.446323\pi\) | ||||
0.167833 | + | 0.985815i | \(0.446323\pi\) | |||||||
\(338\) | 4.76783 | 0.259336 | ||||||||
\(339\) | −31.4061 | −1.70574 | ||||||||
\(340\) | 7.00843 | 0.380086 | ||||||||
\(341\) | −50.7722 | −2.74947 | ||||||||
\(342\) | 1.50563 | 0.0814150 | ||||||||
\(343\) | 36.1722 | 1.95311 | ||||||||
\(344\) | −49.9065 | −2.69078 | ||||||||
\(345\) | −2.74475 | −0.147772 | ||||||||
\(346\) | −43.7739 | −2.35330 | ||||||||
\(347\) | −3.58728 | −0.192575 | −0.0962875 | − | 0.995354i | \(-0.530697\pi\) | ||||
−0.0962875 | + | 0.995354i | \(0.530697\pi\) | |||||||
\(348\) | −62.8584 | −3.36957 | ||||||||
\(349\) | −12.7690 | −0.683511 | −0.341756 | − | 0.939789i | \(-0.611022\pi\) | ||||
−0.341756 | + | 0.939789i | \(0.611022\pi\) | |||||||
\(350\) | 58.1784 | 3.10977 | ||||||||
\(351\) | −15.2258 | −0.812695 | ||||||||
\(352\) | 30.3251 | 1.61633 | ||||||||
\(353\) | −17.7649 | −0.945530 | −0.472765 | − | 0.881189i | \(-0.656744\pi\) | ||||
−0.472765 | + | 0.881189i | \(0.656744\pi\) | |||||||
\(354\) | −17.8311 | −0.947711 | ||||||||
\(355\) | 3.15463 | 0.167431 | ||||||||
\(356\) | −43.2964 | −2.29470 | ||||||||
\(357\) | 43.6865 | 2.31214 | ||||||||
\(358\) | −41.4925 | −2.19295 | ||||||||
\(359\) | −17.9441 | −0.947052 | −0.473526 | − | 0.880780i | \(-0.657019\pi\) | ||||
−0.473526 | + | 0.880780i | \(0.657019\pi\) | |||||||
\(360\) | −1.18198 | −0.0622957 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −35.0562 | −1.84252 | ||||||||
\(363\) | 37.2147 | 1.95327 | ||||||||
\(364\) | 69.7083 | 3.65371 | ||||||||
\(365\) | 0.299848 | 0.0156947 | ||||||||
\(366\) | 33.7417 | 1.76371 | ||||||||
\(367\) | 1.52729 | 0.0797241 | 0.0398621 | − | 0.999205i | \(-0.487308\pi\) | ||||
0.0398621 | + | 0.999205i | \(0.487308\pi\) | |||||||
\(368\) | −32.5489 | −1.69673 | ||||||||
\(369\) | 1.55989 | 0.0812048 | ||||||||
\(370\) | 1.16422 | 0.0605249 | ||||||||
\(371\) | −2.82234 | −0.146529 | ||||||||
\(372\) | 77.8841 | 4.03810 | ||||||||
\(373\) | −7.61685 | −0.394385 | −0.197193 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197193 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(374\) | 69.6394 | 3.60097 | ||||||||
\(375\) | −5.93799 | −0.306637 | ||||||||
\(376\) | −49.0316 | −2.52861 | ||||||||
\(377\) | −24.6948 | −1.27185 | ||||||||
\(378\) | 54.1965 | 2.78757 | ||||||||
\(379\) | 3.63609 | 0.186773 | 0.0933866 | − | 0.995630i | \(-0.470231\pi\) | ||||
0.0933866 | + | 0.995630i | \(0.470231\pi\) | |||||||
\(380\) | −1.41804 | −0.0727441 | ||||||||
\(381\) | 36.2114 | 1.85517 | ||||||||
\(382\) | 26.7552 | 1.36891 | ||||||||
\(383\) | 5.26058 | 0.268803 | 0.134402 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134402 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(384\) | 22.1110 | 1.12835 | ||||||||
\(385\) | −8.17115 | −0.416440 | ||||||||
\(386\) | 43.5543 | 2.21686 | ||||||||
\(387\) | 4.67478 | 0.237632 | ||||||||
\(388\) | −8.33253 | −0.423020 | ||||||||
\(389\) | 4.14762 | 0.210293 | 0.105146 | − | 0.994457i | \(-0.466469\pi\) | ||||
0.105146 | + | 0.994457i | \(0.466469\pi\) | |||||||
\(390\) | −5.09333 | −0.257911 | ||||||||
\(391\) | −22.6163 | −1.14376 | ||||||||
\(392\) | −93.1664 | −4.70561 | ||||||||
\(393\) | 34.9068 | 1.76081 | ||||||||
\(394\) | −37.2973 | −1.87901 | ||||||||
\(395\) | 3.67861 | 0.185091 | ||||||||
\(396\) | −14.6675 | −0.737068 | ||||||||
\(397\) | −6.47950 | −0.325197 | −0.162598 | − | 0.986692i | \(-0.551987\pi\) | ||||
−0.162598 | + | 0.986692i | \(0.551987\pi\) | |||||||
\(398\) | −36.8928 | −1.84927 | ||||||||
\(399\) | −8.83927 | −0.442517 | ||||||||
\(400\) | −34.8520 | −1.74260 | ||||||||
\(401\) | −35.9748 | −1.79650 | −0.898249 | − | 0.439488i | \(-0.855160\pi\) | ||||
−0.898249 | + | 0.439488i | \(0.855160\pi\) | |||||||
\(402\) | 40.0310 | 1.99657 | ||||||||
\(403\) | 30.5979 | 1.52419 | ||||||||
\(404\) | 24.4498 | 1.21642 | ||||||||
\(405\) | −3.29939 | −0.163948 | ||||||||
\(406\) | 87.9016 | 4.36248 | ||||||||
\(407\) | 7.99802 | 0.396447 | ||||||||
\(408\) | −59.1398 | −2.92786 | ||||||||
\(409\) | 0.173147 | 0.00856155 | 0.00428077 | − | 0.999991i | \(-0.498637\pi\) | ||||
0.00428077 | + | 0.999991i | \(0.498637\pi\) | |||||||
\(410\) | −2.12497 | −0.104945 | ||||||||
\(411\) | 43.4640 | 2.14392 | ||||||||
\(412\) | 58.3109 | 2.87277 | ||||||||
\(413\) | 17.2395 | 0.848300 | ||||||||
\(414\) | 6.88982 | 0.338616 | ||||||||
\(415\) | 3.71259 | 0.182244 | ||||||||
\(416\) | −18.2755 | −0.896029 | ||||||||
\(417\) | −4.02365 | −0.197039 | ||||||||
\(418\) | −14.0904 | −0.689185 | ||||||||
\(419\) | −29.8459 | −1.45807 | −0.729033 | − | 0.684479i | \(-0.760030\pi\) | ||||
−0.729033 | + | 0.684479i | \(0.760030\pi\) | |||||||
\(420\) | 12.5345 | 0.611620 | ||||||||
\(421\) | 21.2863 | 1.03743 | 0.518716 | − | 0.854946i | \(-0.326410\pi\) | ||||
0.518716 | + | 0.854946i | \(0.326410\pi\) | |||||||
\(422\) | −9.21558 | −0.448607 | ||||||||
\(423\) | 4.59282 | 0.223311 | ||||||||
\(424\) | 3.82069 | 0.185549 | ||||||||
\(425\) | −24.2165 | −1.17467 | ||||||||
\(426\) | −48.0847 | −2.32971 | ||||||||
\(427\) | −32.6223 | −1.57870 | ||||||||
\(428\) | 8.59865 | 0.415632 | ||||||||
\(429\) | −34.9905 | −1.68936 | ||||||||
\(430\) | −6.36824 | −0.307104 | ||||||||
\(431\) | −2.30301 | −0.110932 | −0.0554660 | − | 0.998461i | \(-0.517664\pi\) | ||||
−0.0554660 | + | 0.998461i | \(0.517664\pi\) | |||||||
\(432\) | −32.4666 | −1.56205 | ||||||||
\(433\) | 11.5598 | 0.555530 | 0.277765 | − | 0.960649i | \(-0.410406\pi\) | ||||
0.277765 | + | 0.960649i | \(0.410406\pi\) | |||||||
\(434\) | −108.914 | −5.22802 | ||||||||
\(435\) | −4.44046 | −0.212904 | ||||||||
\(436\) | 63.2443 | 3.02885 | ||||||||
\(437\) | 4.57605 | 0.218902 | ||||||||
\(438\) | −4.57044 | −0.218384 | ||||||||
\(439\) | −20.3669 | −0.972058 | −0.486029 | − | 0.873943i | \(-0.661555\pi\) | ||||
−0.486029 | + | 0.873943i | \(0.661555\pi\) | |||||||
\(440\) | 11.0615 | 0.527338 | ||||||||
\(441\) | 8.72696 | 0.415570 | ||||||||
\(442\) | −41.9683 | −1.99623 | ||||||||
\(443\) | −4.23451 | −0.201188 | −0.100594 | − | 0.994928i | \(-0.532074\pi\) | ||||
−0.100594 | + | 0.994928i | \(0.532074\pi\) | |||||||
\(444\) | −12.2689 | −0.582257 | ||||||||
\(445\) | −3.05855 | −0.144989 | ||||||||
\(446\) | 15.5050 | 0.734185 | ||||||||
\(447\) | 46.2431 | 2.18722 | ||||||||
\(448\) | −1.30084 | −0.0614590 | ||||||||
\(449\) | −20.8798 | −0.985380 | −0.492690 | − | 0.870205i | \(-0.663986\pi\) | ||||
−0.492690 | + | 0.870205i | \(0.663986\pi\) | |||||||
\(450\) | 7.37731 | 0.347770 | ||||||||
\(451\) | −14.5983 | −0.687406 | ||||||||
\(452\) | −74.2492 | −3.49239 | ||||||||
\(453\) | −9.00307 | −0.423001 | ||||||||
\(454\) | 4.23316 | 0.198672 | ||||||||
\(455\) | 4.92435 | 0.230857 | ||||||||
\(456\) | 11.9660 | 0.560359 | ||||||||
\(457\) | −14.7038 | −0.687816 | −0.343908 | − | 0.939003i | \(-0.611751\pi\) | ||||
−0.343908 | + | 0.939003i | \(0.611751\pi\) | |||||||
\(458\) | 36.4731 | 1.70428 | ||||||||
\(459\) | −22.5591 | −1.05297 | ||||||||
\(460\) | −6.48904 | −0.302553 | ||||||||
\(461\) | 3.93563 | 0.183300 | 0.0916502 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916502 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(462\) | 124.549 | 5.79455 | ||||||||
\(463\) | −12.1457 | −0.564458 | −0.282229 | − | 0.959347i | \(-0.591074\pi\) | ||||
−0.282229 | + | 0.959347i | \(0.591074\pi\) | |||||||
\(464\) | −52.6578 | −2.44458 | ||||||||
\(465\) | 5.50190 | 0.255145 | ||||||||
\(466\) | 8.66088 | 0.401207 | ||||||||
\(467\) | −2.48781 | −0.115122 | −0.0575610 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575610 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(468\) | 8.83937 | 0.408600 | ||||||||
\(469\) | −38.7029 | −1.78713 | ||||||||
\(470\) | −6.25660 | −0.288595 | ||||||||
\(471\) | −30.6702 | −1.41321 | ||||||||
\(472\) | −23.3376 | −1.07420 | ||||||||
\(473\) | −43.7489 | −2.01158 | ||||||||
\(474\) | −56.0714 | −2.57545 | ||||||||
\(475\) | 4.89983 | 0.224819 | ||||||||
\(476\) | 103.282 | 4.73393 | ||||||||
\(477\) | −0.357887 | −0.0163865 | ||||||||
\(478\) | −65.0355 | −2.97465 | ||||||||
\(479\) | 4.28565 | 0.195816 | 0.0979082 | − | 0.995195i | \(-0.468785\pi\) | ||||
0.0979082 | + | 0.995195i | \(0.468785\pi\) | |||||||
\(480\) | −3.28617 | −0.149992 | ||||||||
\(481\) | −4.82002 | −0.219774 | ||||||||
\(482\) | −26.9303 | −1.22664 | ||||||||
\(483\) | −40.4489 | −1.84049 | ||||||||
\(484\) | 87.9817 | 3.99917 | ||||||||
\(485\) | −0.588628 | −0.0267282 | ||||||||
\(486\) | 15.4324 | 0.700028 | ||||||||
\(487\) | −4.93276 | −0.223525 | −0.111762 | − | 0.993735i | \(-0.535650\pi\) | ||||
−0.111762 | + | 0.993735i | \(0.535650\pi\) | |||||||
\(488\) | 44.1618 | 1.99911 | ||||||||
\(489\) | 44.7740 | 2.02475 | ||||||||
\(490\) | −11.8884 | −0.537061 | ||||||||
\(491\) | −1.80599 | −0.0815031 | −0.0407515 | − | 0.999169i | \(-0.512975\pi\) | ||||
−0.0407515 | + | 0.999169i | \(0.512975\pi\) | |||||||
\(492\) | 22.3936 | 1.00958 | ||||||||
\(493\) | −36.5887 | −1.64787 | ||||||||
\(494\) | 8.49161 | 0.382056 | ||||||||
\(495\) | −1.03614 | −0.0465712 | ||||||||
\(496\) | 65.2451 | 2.92959 | ||||||||
\(497\) | 46.4894 | 2.08533 | ||||||||
\(498\) | −56.5893 | −2.53583 | ||||||||
\(499\) | −36.8886 | −1.65136 | −0.825680 | − | 0.564139i | \(-0.809208\pi\) | ||||
−0.825680 | + | 0.564139i | \(0.809208\pi\) | |||||||
\(500\) | −14.0384 | −0.627816 | ||||||||
\(501\) | −30.8837 | −1.37978 | ||||||||
\(502\) | 38.3579 | 1.71200 | ||||||||
\(503\) | 18.1362 | 0.808653 | 0.404327 | − | 0.914615i | \(-0.367506\pi\) | ||||
0.404327 | + | 0.914615i | \(0.367506\pi\) | |||||||
\(504\) | −17.4186 | −0.775887 | ||||||||
\(505\) | 1.72719 | 0.0768587 | ||||||||
\(506\) | −64.4784 | −2.86642 | ||||||||
\(507\) | −3.54941 | −0.157635 | ||||||||
\(508\) | 85.6097 | 3.79832 | ||||||||
\(509\) | 32.5396 | 1.44229 | 0.721146 | − | 0.692783i | \(-0.243616\pi\) | ||||
0.721146 | + | 0.692783i | \(0.243616\pi\) | |||||||
\(510\) | −7.54645 | −0.334162 | ||||||||
\(511\) | 4.41881 | 0.195477 | ||||||||
\(512\) | 50.8541 | 2.24746 | ||||||||
\(513\) | 4.56447 | 0.201526 | ||||||||
\(514\) | 46.2884 | 2.04169 | ||||||||
\(515\) | 4.11921 | 0.181514 | ||||||||
\(516\) | 67.1105 | 2.95438 | ||||||||
\(517\) | −42.9820 | −1.89034 | ||||||||
\(518\) | 17.1569 | 0.753832 | ||||||||
\(519\) | 32.5874 | 1.43043 | ||||||||
\(520\) | −6.66625 | −0.292334 | ||||||||
\(521\) | 29.8223 | 1.30654 | 0.653270 | − | 0.757125i | \(-0.273397\pi\) | ||||
0.653270 | + | 0.757125i | \(0.273397\pi\) | |||||||
\(522\) | 11.1464 | 0.487863 | ||||||||
\(523\) | −28.5264 | −1.24737 | −0.623687 | − | 0.781674i | \(-0.714366\pi\) | ||||
−0.623687 | + | 0.781674i | \(0.714366\pi\) | |||||||
\(524\) | 82.5254 | 3.60514 | ||||||||
\(525\) | −43.3109 | −1.89024 | ||||||||
\(526\) | 14.9846 | 0.653361 | ||||||||
\(527\) | 45.3348 | 1.97482 | ||||||||
\(528\) | −74.6115 | −3.24705 | ||||||||
\(529\) | −2.05981 | −0.0895567 | ||||||||
\(530\) | 0.487533 | 0.0211771 | ||||||||
\(531\) | 2.18605 | 0.0948667 | ||||||||
\(532\) | −20.8975 | −0.906022 | ||||||||
\(533\) | 8.79766 | 0.381069 | ||||||||
\(534\) | 46.6201 | 2.01745 | ||||||||
\(535\) | 0.607428 | 0.0262614 | ||||||||
\(536\) | 52.3933 | 2.26305 | ||||||||
\(537\) | 30.8891 | 1.33296 | ||||||||
\(538\) | −23.6477 | −1.01952 | ||||||||
\(539\) | −81.6713 | −3.51783 | ||||||||
\(540\) | −6.47262 | −0.278537 | ||||||||
\(541\) | 37.8510 | 1.62734 | 0.813670 | − | 0.581327i | \(-0.197466\pi\) | ||||
0.813670 | + | 0.581327i | \(0.197466\pi\) | |||||||
\(542\) | −10.4572 | −0.449175 | ||||||||
\(543\) | 26.0976 | 1.11996 | ||||||||
\(544\) | −27.0775 | −1.16094 | ||||||||
\(545\) | 4.46771 | 0.191376 | ||||||||
\(546\) | −75.0596 | −3.21226 | ||||||||
\(547\) | −10.8761 | −0.465028 | −0.232514 | − | 0.972593i | \(-0.574695\pi\) | ||||
−0.232514 | + | 0.972593i | \(0.574695\pi\) | |||||||
\(548\) | 102.756 | 4.38952 | ||||||||
\(549\) | −4.13667 | −0.176549 | ||||||||
\(550\) | −69.0406 | −2.94390 | ||||||||
\(551\) | 7.40314 | 0.315384 | ||||||||
\(552\) | 54.7570 | 2.33061 | ||||||||
\(553\) | 54.2112 | 2.30529 | ||||||||
\(554\) | 43.0991 | 1.83111 | ||||||||
\(555\) | −0.866703 | −0.0367895 | ||||||||
\(556\) | −9.51257 | −0.403423 | ||||||||
\(557\) | 12.3233 | 0.522153 | 0.261077 | − | 0.965318i | \(-0.415922\pi\) | ||||
0.261077 | + | 0.965318i | \(0.415922\pi\) | |||||||
\(558\) | −13.8108 | −0.584657 | ||||||||
\(559\) | 26.3653 | 1.11514 | ||||||||
\(560\) | 10.5004 | 0.443722 | ||||||||
\(561\) | −51.8430 | −2.18882 | ||||||||
\(562\) | −19.5088 | −0.822927 | ||||||||
\(563\) | −27.3809 | −1.15397 | −0.576983 | − | 0.816756i | \(-0.695770\pi\) | ||||
−0.576983 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(564\) | 65.9340 | 2.77632 | ||||||||
\(565\) | −5.24513 | −0.220664 | ||||||||
\(566\) | −2.28183 | −0.0959125 | ||||||||
\(567\) | −48.6226 | −2.04196 | ||||||||
\(568\) | −62.9341 | −2.64066 | ||||||||
\(569\) | 33.0975 | 1.38752 | 0.693760 | − | 0.720206i | \(-0.255953\pi\) | ||||
0.693760 | + | 0.720206i | \(0.255953\pi\) | |||||||
\(570\) | 1.52690 | 0.0639549 | ||||||||
\(571\) | 15.8545 | 0.663489 | 0.331745 | − | 0.943369i | \(-0.392363\pi\) | ||||
0.331745 | + | 0.943369i | \(0.392363\pi\) | |||||||
\(572\) | −82.7233 | −3.45883 | ||||||||
\(573\) | −19.9179 | −0.832082 | ||||||||
\(574\) | −31.3154 | −1.30708 | ||||||||
\(575\) | 22.4218 | 0.935055 | ||||||||
\(576\) | −0.164953 | −0.00687305 | ||||||||
\(577\) | −3.96527 | −0.165076 | −0.0825381 | − | 0.996588i | \(-0.526303\pi\) | ||||
−0.0825381 | + | 0.996588i | \(0.526303\pi\) | |||||||
\(578\) | −18.9054 | −0.786362 | ||||||||
\(579\) | −32.4240 | −1.34749 | ||||||||
\(580\) | −10.4980 | −0.435905 | ||||||||
\(581\) | 54.7119 | 2.26983 | ||||||||
\(582\) | 8.97219 | 0.371909 | ||||||||
\(583\) | 3.34929 | 0.138713 | ||||||||
\(584\) | −5.98188 | −0.247532 | ||||||||
\(585\) | 0.624432 | 0.0258171 | ||||||||
\(586\) | 77.0998 | 3.18496 | ||||||||
\(587\) | 12.9203 | 0.533279 | 0.266640 | − | 0.963796i | \(-0.414087\pi\) | ||||
0.266640 | + | 0.963796i | \(0.414087\pi\) | |||||||
\(588\) | 125.283 | 5.16659 | ||||||||
\(589\) | −9.17278 | −0.377958 | ||||||||
\(590\) | −2.97796 | −0.122601 | ||||||||
\(591\) | 27.7660 | 1.14214 | ||||||||
\(592\) | −10.2779 | −0.422419 | ||||||||
\(593\) | 32.6578 | 1.34109 | 0.670547 | − | 0.741867i | \(-0.266059\pi\) | ||||
0.670547 | + | 0.741867i | \(0.266059\pi\) | |||||||
\(594\) | −64.3154 | −2.63889 | ||||||||
\(595\) | 7.29608 | 0.299110 | ||||||||
\(596\) | 109.326 | 4.47818 | ||||||||
\(597\) | 27.4649 | 1.12406 | ||||||||
\(598\) | 38.8580 | 1.58902 | ||||||||
\(599\) | −44.6873 | −1.82587 | −0.912937 | − | 0.408101i | \(-0.866191\pi\) | ||||
−0.912937 | + | 0.408101i | \(0.866191\pi\) | |||||||
\(600\) | 58.6313 | 2.39361 | ||||||||
\(601\) | −32.2859 | −1.31697 | −0.658484 | − | 0.752595i | \(-0.728802\pi\) | ||||
−0.658484 | + | 0.752595i | \(0.728802\pi\) | |||||||
\(602\) | −93.8478 | −3.82495 | ||||||||
\(603\) | −4.90772 | −0.199858 | ||||||||
\(604\) | −21.2847 | −0.866064 | ||||||||
\(605\) | 6.21522 | 0.252685 | ||||||||
\(606\) | −26.3267 | −1.06945 | ||||||||
\(607\) | −29.4296 | −1.19451 | −0.597255 | − | 0.802052i | \(-0.703742\pi\) | ||||
−0.597255 | + | 0.802052i | \(0.703742\pi\) | |||||||
\(608\) | 5.47871 | 0.222191 | ||||||||
\(609\) | −65.4383 | −2.65170 | ||||||||
\(610\) | 5.63520 | 0.228163 | ||||||||
\(611\) | 25.9031 | 1.04793 | ||||||||
\(612\) | 13.0967 | 0.529403 | ||||||||
\(613\) | 4.49454 | 0.181533 | 0.0907664 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907664 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(614\) | 62.5381 | 2.52383 | ||||||||
\(615\) | 1.58194 | 0.0637898 | ||||||||
\(616\) | 163.012 | 6.56795 | ||||||||
\(617\) | −21.6954 | −0.873422 | −0.436711 | − | 0.899602i | \(-0.643857\pi\) | ||||
−0.436711 | + | 0.899602i | \(0.643857\pi\) | |||||||
\(618\) | −62.7872 | −2.52567 | ||||||||
\(619\) | 2.03464 | 0.0817791 | 0.0408895 | − | 0.999164i | \(-0.486981\pi\) | ||||
0.0408895 | + | 0.999164i | \(0.486981\pi\) | |||||||
\(620\) | 13.0074 | 0.522390 | ||||||||
\(621\) | 20.8872 | 0.838176 | ||||||||
\(622\) | −39.2803 | −1.57500 | ||||||||
\(623\) | −45.0734 | −1.80583 | ||||||||
\(624\) | 44.9647 | 1.80003 | ||||||||
\(625\) | 23.5074 | 0.940297 | ||||||||
\(626\) | −34.2160 | −1.36754 | ||||||||
\(627\) | 10.4896 | 0.418915 | ||||||||
\(628\) | −72.5095 | −2.89345 | ||||||||
\(629\) | −7.14150 | −0.284750 | ||||||||
\(630\) | −2.22268 | −0.0885535 | ||||||||
\(631\) | 12.4420 | 0.495308 | 0.247654 | − | 0.968849i | \(-0.420340\pi\) | ||||
0.247654 | + | 0.968849i | \(0.420340\pi\) | |||||||
\(632\) | −73.3874 | −2.91919 | ||||||||
\(633\) | 6.86053 | 0.272682 | ||||||||
\(634\) | −2.54565 | −0.101101 | ||||||||
\(635\) | 6.04766 | 0.239994 | ||||||||
\(636\) | −5.13778 | −0.203726 | ||||||||
\(637\) | 49.2193 | 1.95014 | ||||||||
\(638\) | −104.313 | −4.12981 | ||||||||
\(639\) | 5.89509 | 0.233206 | ||||||||
\(640\) | 3.69276 | 0.145969 | ||||||||
\(641\) | −18.5946 | −0.734444 | −0.367222 | − | 0.930133i | \(-0.619691\pi\) | ||||
−0.367222 | + | 0.930133i | \(0.619691\pi\) | |||||||
\(642\) | −9.25874 | −0.365413 | ||||||||
\(643\) | −21.5171 | −0.848552 | −0.424276 | − | 0.905533i | \(-0.639471\pi\) | ||||
−0.424276 | + | 0.905533i | \(0.639471\pi\) | |||||||
\(644\) | −95.6279 | −3.76827 | ||||||||
\(645\) | 4.74084 | 0.186670 | ||||||||
\(646\) | 12.5814 | 0.495010 | ||||||||
\(647\) | 44.0666 | 1.73243 | 0.866217 | − | 0.499667i | \(-0.166544\pi\) | ||||
0.866217 | + | 0.499667i | \(0.166544\pi\) | |||||||
\(648\) | 65.8220 | 2.58573 | ||||||||
\(649\) | −20.4582 | −0.803055 | ||||||||
\(650\) | 41.6074 | 1.63198 | ||||||||
\(651\) | 81.0807 | 3.17780 | ||||||||
\(652\) | 105.853 | 4.14553 | ||||||||
\(653\) | 43.0317 | 1.68396 | 0.841981 | − | 0.539507i | \(-0.181389\pi\) | ||||
0.841981 | + | 0.539507i | \(0.181389\pi\) | |||||||
\(654\) | −68.0993 | −2.66289 | ||||||||
\(655\) | 5.82977 | 0.227788 | ||||||||
\(656\) | 18.7596 | 0.732439 | ||||||||
\(657\) | 0.560327 | 0.0218604 | ||||||||
\(658\) | −92.2025 | −3.59443 | ||||||||
\(659\) | −33.2290 | −1.29442 | −0.647209 | − | 0.762313i | \(-0.724064\pi\) | ||||
−0.647209 | + | 0.762313i | \(0.724064\pi\) | |||||||
\(660\) | −14.8747 | −0.578998 | ||||||||
\(661\) | −35.5010 | −1.38083 | −0.690415 | − | 0.723413i | \(-0.742572\pi\) | ||||
−0.690415 | + | 0.723413i | \(0.742572\pi\) | |||||||
\(662\) | 80.3252 | 3.12193 | ||||||||
\(663\) | 31.2433 | 1.21339 | ||||||||
\(664\) | −74.0652 | −2.87429 | ||||||||
\(665\) | −1.47625 | −0.0572463 | ||||||||
\(666\) | 2.17558 | 0.0843021 | ||||||||
\(667\) | 33.8771 | 1.31173 | ||||||||
\(668\) | −73.0142 | −2.82501 | ||||||||
\(669\) | −11.5427 | −0.446268 | ||||||||
\(670\) | 6.68557 | 0.258286 | ||||||||
\(671\) | 38.7130 | 1.49450 | ||||||||
\(672\) | −48.4278 | −1.86814 | ||||||||
\(673\) | −15.6112 | −0.601769 | −0.300885 | − | 0.953661i | \(-0.597282\pi\) | ||||
−0.300885 | + | 0.953661i | \(0.597282\pi\) | |||||||
\(674\) | −15.6863 | −0.604214 | ||||||||
\(675\) | 22.3651 | 0.860834 | ||||||||
\(676\) | −8.39140 | −0.322746 | ||||||||
\(677\) | 2.01484 | 0.0774365 | 0.0387183 | − | 0.999250i | \(-0.487673\pi\) | ||||
0.0387183 | + | 0.999250i | \(0.487673\pi\) | |||||||
\(678\) | 79.9491 | 3.07042 | ||||||||
\(679\) | −8.67453 | −0.332898 | ||||||||
\(680\) | −9.87693 | −0.378763 | ||||||||
\(681\) | −3.15138 | −0.120761 | ||||||||
\(682\) | 129.248 | 4.94918 | ||||||||
\(683\) | −20.7050 | −0.792254 | −0.396127 | − | 0.918196i | \(-0.629646\pi\) | ||||
−0.396127 | + | 0.918196i | \(0.629646\pi\) | |||||||
\(684\) | −2.64991 | −0.101322 | ||||||||
\(685\) | 7.25891 | 0.277349 | ||||||||
\(686\) | −92.0818 | −3.51570 | ||||||||
\(687\) | −27.1524 | −1.03593 | ||||||||
\(688\) | 56.2198 | 2.14336 | ||||||||
\(689\) | −2.01845 | −0.0768968 | ||||||||
\(690\) | 6.98718 | 0.265997 | ||||||||
\(691\) | −38.1194 | −1.45013 | −0.725066 | − | 0.688680i | \(-0.758191\pi\) | ||||
−0.725066 | + | 0.688680i | \(0.758191\pi\) | |||||||
\(692\) | 77.0421 | 2.92870 | ||||||||
\(693\) | −15.2695 | −0.580039 | ||||||||
\(694\) | 9.13197 | 0.346645 | ||||||||
\(695\) | −0.671989 | −0.0254900 | ||||||||
\(696\) | 88.5859 | 3.35784 | ||||||||
\(697\) | 13.0349 | 0.493732 | ||||||||
\(698\) | 32.5056 | 1.23035 | ||||||||
\(699\) | −6.44759 | −0.243870 | ||||||||
\(700\) | −102.394 | −3.87013 | ||||||||
\(701\) | −25.3004 | −0.955583 | −0.477792 | − | 0.878473i | \(-0.658563\pi\) | ||||
−0.477792 | + | 0.878473i | \(0.658563\pi\) | |||||||
\(702\) | 38.7597 | 1.46289 | ||||||||
\(703\) | 1.44497 | 0.0544980 | ||||||||
\(704\) | 1.54372 | 0.0581810 | ||||||||
\(705\) | 4.65772 | 0.175420 | ||||||||
\(706\) | 45.2233 | 1.70200 | ||||||||
\(707\) | 25.4533 | 0.957268 | ||||||||
\(708\) | 31.3827 | 1.17943 | ||||||||
\(709\) | 0.917146 | 0.0344441 | 0.0172221 | − | 0.999852i | \(-0.494518\pi\) | ||||
0.0172221 | + | 0.999852i | \(0.494518\pi\) | |||||||
\(710\) | −8.03061 | −0.301383 | ||||||||
\(711\) | 6.87425 | 0.257804 | ||||||||
\(712\) | 61.0173 | 2.28672 | ||||||||
\(713\) | −41.9751 | −1.57198 | ||||||||
\(714\) | −111.211 | −4.16196 | ||||||||
\(715\) | −5.84375 | −0.218544 | ||||||||
\(716\) | 73.0269 | 2.72914 | ||||||||
\(717\) | 48.4156 | 1.80811 | ||||||||
\(718\) | 45.6794 | 1.70474 | ||||||||
\(719\) | 44.0937 | 1.64442 | 0.822208 | − | 0.569186i | \(-0.192742\pi\) | ||||
0.822208 | + | 0.569186i | \(0.192742\pi\) | |||||||
\(720\) | 1.33150 | 0.0496221 | ||||||||
\(721\) | 60.7041 | 2.26074 | ||||||||
\(722\) | −2.54565 | −0.0947395 | ||||||||
\(723\) | 20.0483 | 0.745603 | ||||||||
\(724\) | 61.6991 | 2.29303 | ||||||||
\(725\) | 36.2741 | 1.34719 | ||||||||
\(726\) | −94.7358 | −3.51597 | ||||||||
\(727\) | 47.8820 | 1.77585 | 0.887923 | − | 0.459992i | \(-0.152148\pi\) | ||||
0.887923 | + | 0.459992i | \(0.152148\pi\) | |||||||
\(728\) | −98.2395 | −3.64100 | ||||||||
\(729\) | 19.7850 | 0.732777 | ||||||||
\(730\) | −0.763309 | −0.0282513 | ||||||||
\(731\) | 39.0638 | 1.44483 | ||||||||
\(732\) | −59.3855 | −2.19495 | ||||||||
\(733\) | 11.0573 | 0.408409 | 0.204205 | − | 0.978928i | \(-0.434539\pi\) | ||||
0.204205 | + | 0.978928i | \(0.434539\pi\) | |||||||
\(734\) | −3.88796 | −0.143507 | ||||||||
\(735\) | 8.85028 | 0.326447 | ||||||||
\(736\) | 25.0708 | 0.924123 | ||||||||
\(737\) | 45.9290 | 1.69182 | ||||||||
\(738\) | −3.97095 | −0.146173 | ||||||||
\(739\) | 16.8623 | 0.620291 | 0.310145 | − | 0.950689i | \(-0.399622\pi\) | ||||
0.310145 | + | 0.950689i | \(0.399622\pi\) | |||||||
\(740\) | −2.04903 | −0.0753238 | ||||||||
\(741\) | −6.32158 | −0.232229 | ||||||||
\(742\) | 7.18470 | 0.263759 | ||||||||
\(743\) | −22.7239 | −0.833660 | −0.416830 | − | 0.908984i | \(-0.636859\pi\) | ||||
−0.416830 | + | 0.908984i | \(0.636859\pi\) | |||||||
\(744\) | −109.761 | −4.02405 | ||||||||
\(745\) | 7.72305 | 0.282951 | ||||||||
\(746\) | 19.3899 | 0.709914 | ||||||||
\(747\) | 6.93774 | 0.253839 | ||||||||
\(748\) | −122.566 | −4.48144 | ||||||||
\(749\) | 8.95157 | 0.327083 | ||||||||
\(750\) | 15.1161 | 0.551961 | ||||||||
\(751\) | 31.6105 | 1.15348 | 0.576741 | − | 0.816927i | \(-0.304324\pi\) | ||||
0.576741 | + | 0.816927i | \(0.304324\pi\) | |||||||
\(752\) | 55.2342 | 2.01418 | ||||||||
\(753\) | −28.5556 | −1.04062 | ||||||||
\(754\) | 62.8646 | 2.28939 | ||||||||
\(755\) | −1.50360 | −0.0547216 | ||||||||
\(756\) | −95.3861 | −3.46916 | ||||||||
\(757\) | −36.2439 | −1.31731 | −0.658654 | − | 0.752446i | \(-0.728874\pi\) | ||||
−0.658654 | + | 0.752446i | \(0.728874\pi\) | |||||||
\(758\) | −9.25622 | −0.336201 | ||||||||
\(759\) | 48.0009 | 1.74232 | ||||||||
\(760\) | 1.99844 | 0.0724910 | ||||||||
\(761\) | −29.6810 | −1.07594 | −0.537969 | − | 0.842965i | \(-0.680808\pi\) | ||||
−0.537969 | + | 0.842965i | \(0.680808\pi\) | |||||||
\(762\) | −92.1817 | −3.33939 | ||||||||
\(763\) | 65.8400 | 2.38357 | ||||||||
\(764\) | −47.0892 | −1.70363 | ||||||||
\(765\) | 0.925180 | 0.0334499 | ||||||||
\(766\) | −13.3916 | −0.483859 | ||||||||
\(767\) | 12.3292 | 0.445180 | ||||||||
\(768\) | −55.2299 | −1.99294 | ||||||||
\(769\) | 14.3250 | 0.516575 | 0.258287 | − | 0.966068i | \(-0.416842\pi\) | ||||
0.258287 | + | 0.966068i | \(0.416842\pi\) | |||||||
\(770\) | 20.8009 | 0.749613 | ||||||||
\(771\) | −34.4594 | −1.24102 | ||||||||
\(772\) | −76.6557 | −2.75890 | ||||||||
\(773\) | −48.7533 | −1.75353 | −0.876767 | − | 0.480916i | \(-0.840304\pi\) | ||||
−0.876767 | + | 0.480916i | \(0.840304\pi\) | |||||||
\(774\) | −11.9004 | −0.427750 | ||||||||
\(775\) | −44.9450 | −1.61447 | ||||||||
\(776\) | 11.7430 | 0.421548 | ||||||||
\(777\) | −12.7725 | −0.458210 | ||||||||
\(778\) | −10.5584 | −0.378537 | ||||||||
\(779\) | −2.63740 | −0.0944948 | ||||||||
\(780\) | 8.96427 | 0.320973 | ||||||||
\(781\) | −55.1692 | −1.97411 | ||||||||
\(782\) | 57.5733 | 2.05882 | ||||||||
\(783\) | 33.7914 | 1.20761 | ||||||||
\(784\) | 104.952 | 3.74829 | ||||||||
\(785\) | −5.12223 | −0.182820 | ||||||||
\(786\) | −88.8606 | −3.16955 | ||||||||
\(787\) | −20.1129 | −0.716948 | −0.358474 | − | 0.933540i | \(-0.616703\pi\) | ||||
−0.358474 | + | 0.933540i | \(0.616703\pi\) | |||||||
\(788\) | 65.6434 | 2.33845 | ||||||||
\(789\) | −11.1553 | −0.397139 | ||||||||
\(790\) | −9.36448 | −0.333173 | ||||||||
\(791\) | −77.2966 | −2.74835 | ||||||||
\(792\) | 20.6708 | 0.734504 | ||||||||
\(793\) | −23.3304 | −0.828488 | ||||||||
\(794\) | 16.4946 | 0.585370 | ||||||||
\(795\) | −0.362944 | −0.0128723 | ||||||||
\(796\) | 64.9315 | 2.30143 | ||||||||
\(797\) | 31.4974 | 1.11569 | 0.557847 | − | 0.829944i | \(-0.311628\pi\) | ||||
0.557847 | + | 0.829944i | \(0.311628\pi\) | |||||||
\(798\) | 22.5017 | 0.796553 | ||||||||
\(799\) | 38.3789 | 1.35775 | ||||||||
\(800\) | 26.8447 | 0.949104 | ||||||||
\(801\) | −5.71553 | −0.201948 | ||||||||
\(802\) | 91.5795 | 3.23378 | ||||||||
\(803\) | −5.24383 | −0.185051 | ||||||||
\(804\) | −70.4547 | −2.48474 | ||||||||
\(805\) | −6.75537 | −0.238095 | ||||||||
\(806\) | −77.8917 | −2.74362 | ||||||||
\(807\) | 17.6045 | 0.619708 | ||||||||
\(808\) | −34.4569 | −1.21219 | ||||||||
\(809\) | 19.9961 | 0.703026 | 0.351513 | − | 0.936183i | \(-0.385667\pi\) | ||||
0.351513 | + | 0.936183i | \(0.385667\pi\) | |||||||
\(810\) | 8.39911 | 0.295115 | ||||||||
\(811\) | 15.4908 | 0.543956 | 0.271978 | − | 0.962303i | \(-0.412322\pi\) | ||||
0.271978 | + | 0.962303i | \(0.412322\pi\) | |||||||
\(812\) | −154.707 | −5.42915 | ||||||||
\(813\) | 7.78486 | 0.273027 | ||||||||
\(814\) | −20.3602 | −0.713625 | ||||||||
\(815\) | 7.47769 | 0.261932 | ||||||||
\(816\) | 66.6212 | 2.33221 | ||||||||
\(817\) | −7.90393 | −0.276524 | ||||||||
\(818\) | −0.440771 | −0.0154112 | ||||||||
\(819\) | 9.20216 | 0.321550 | ||||||||
\(820\) | 3.73996 | 0.130605 | ||||||||
\(821\) | 27.6540 | 0.965132 | 0.482566 | − | 0.875860i | \(-0.339705\pi\) | ||||
0.482566 | + | 0.875860i | \(0.339705\pi\) | |||||||
\(822\) | −110.644 | −3.85916 | ||||||||
\(823\) | 43.0063 | 1.49911 | 0.749553 | − | 0.661944i | \(-0.230268\pi\) | ||||
0.749553 | + | 0.661944i | \(0.230268\pi\) | |||||||
\(824\) | −82.1771 | −2.86278 | ||||||||
\(825\) | 51.3973 | 1.78942 | ||||||||
\(826\) | −43.8858 | −1.52698 | ||||||||
\(827\) | −44.5986 | −1.55085 | −0.775423 | − | 0.631442i | \(-0.782463\pi\) | ||||
−0.775423 | + | 0.631442i | \(0.782463\pi\) | |||||||
\(828\) | −12.1261 | −0.421411 | ||||||||
\(829\) | 51.1885 | 1.77785 | 0.888925 | − | 0.458052i | \(-0.151453\pi\) | ||||
0.888925 | + | 0.458052i | \(0.151453\pi\) | |||||||
\(830\) | −9.45097 | −0.328048 | ||||||||
\(831\) | −32.0851 | −1.11302 | ||||||||
\(832\) | −0.930321 | −0.0322531 | ||||||||
\(833\) | 72.9249 | 2.52670 | ||||||||
\(834\) | 10.2428 | 0.354680 | ||||||||
\(835\) | −5.15789 | −0.178496 | ||||||||
\(836\) | 24.7992 | 0.857698 | ||||||||
\(837\) | −41.8689 | −1.44720 | ||||||||
\(838\) | 75.9773 | 2.62459 | ||||||||
\(839\) | 37.7700 | 1.30396 | 0.651982 | − | 0.758234i | \(-0.273938\pi\) | ||||
0.651982 | + | 0.758234i | \(0.273938\pi\) | |||||||
\(840\) | −17.6648 | −0.609492 | ||||||||
\(841\) | 25.8065 | 0.889878 | ||||||||
\(842\) | −54.1877 | −1.86743 | ||||||||
\(843\) | 14.5233 | 0.500209 | ||||||||
\(844\) | 16.2194 | 0.558296 | ||||||||
\(845\) | −0.592787 | −0.0203925 | ||||||||
\(846\) | −11.6917 | −0.401970 | ||||||||
\(847\) | 91.5928 | 3.14716 | ||||||||
\(848\) | −4.30402 | −0.147801 | ||||||||
\(849\) | 1.69871 | 0.0582995 | ||||||||
\(850\) | 61.6469 | 2.11447 | ||||||||
\(851\) | 6.61224 | 0.226665 | ||||||||
\(852\) | 84.6291 | 2.89935 | ||||||||
\(853\) | 16.1477 | 0.552888 | 0.276444 | − | 0.961030i | \(-0.410844\pi\) | ||||
0.276444 | + | 0.961030i | \(0.410844\pi\) | |||||||
\(854\) | 83.0450 | 2.84174 | ||||||||
\(855\) | −0.187195 | −0.00640195 | ||||||||
\(856\) | −12.1180 | −0.414185 | ||||||||
\(857\) | 29.1814 | 0.996819 | 0.498409 | − | 0.866942i | \(-0.333918\pi\) | ||||
0.498409 | + | 0.866942i | \(0.333918\pi\) | |||||||
\(858\) | 89.0737 | 3.04093 | ||||||||
\(859\) | 2.05743 | 0.0701984 | 0.0350992 | − | 0.999384i | \(-0.488825\pi\) | ||||
0.0350992 | + | 0.999384i | \(0.488825\pi\) | |||||||
\(860\) | 11.2081 | 0.382194 | ||||||||
\(861\) | 23.3127 | 0.794496 | ||||||||
\(862\) | 5.86267 | 0.199683 | ||||||||
\(863\) | −3.07626 | −0.104717 | −0.0523586 | − | 0.998628i | \(-0.516674\pi\) | ||||
−0.0523586 | + | 0.998628i | \(0.516674\pi\) | |||||||
\(864\) | 25.0074 | 0.850769 | ||||||||
\(865\) | 5.44242 | 0.185048 | ||||||||
\(866\) | −29.4273 | −0.999981 | ||||||||
\(867\) | 14.0741 | 0.477983 | ||||||||
\(868\) | 191.688 | 6.50632 | ||||||||
\(869\) | −64.3327 | −2.18234 | ||||||||
\(870\) | 11.3039 | 0.383237 | ||||||||
\(871\) | −27.6791 | −0.937872 | ||||||||
\(872\) | −89.1297 | −3.01831 | ||||||||
\(873\) | −1.09997 | −0.0372285 | ||||||||
\(874\) | −11.6490 | −0.394034 | ||||||||
\(875\) | −14.6146 | −0.494063 | ||||||||
\(876\) | 8.04399 | 0.271781 | ||||||||
\(877\) | 16.4822 | 0.556565 | 0.278282 | − | 0.960499i | \(-0.410235\pi\) | ||||
0.278282 | + | 0.960499i | \(0.410235\pi\) | |||||||
\(878\) | 51.8470 | 1.74975 | ||||||||
\(879\) | −57.3969 | −1.93595 | ||||||||
\(880\) | −12.4609 | −0.420056 | ||||||||
\(881\) | 50.2810 | 1.69401 | 0.847005 | − | 0.531585i | \(-0.178403\pi\) | ||||
0.847005 | + | 0.531585i | \(0.178403\pi\) | |||||||
\(882\) | −22.2158 | −0.748046 | ||||||||
\(883\) | −20.3725 | −0.685588 | −0.342794 | − | 0.939411i | \(-0.611373\pi\) | ||||
−0.342794 | + | 0.939411i | \(0.611373\pi\) | |||||||
\(884\) | 73.8642 | 2.48432 | ||||||||
\(885\) | 2.21694 | 0.0745218 | ||||||||
\(886\) | 10.7796 | 0.362148 | ||||||||
\(887\) | −3.89311 | −0.130718 | −0.0653590 | − | 0.997862i | \(-0.520819\pi\) | ||||
−0.0653590 | + | 0.997862i | \(0.520819\pi\) | |||||||
\(888\) | 17.2905 | 0.580231 | ||||||||
\(889\) | 89.1234 | 2.98910 | ||||||||
\(890\) | 7.78601 | 0.260988 | ||||||||
\(891\) | 57.7007 | 1.93305 | ||||||||
\(892\) | −27.2889 | −0.913700 | ||||||||
\(893\) | −7.76536 | −0.259858 | ||||||||
\(894\) | −117.719 | −3.93711 | ||||||||
\(895\) | 5.15878 | 0.172439 | ||||||||
\(896\) | 54.4196 | 1.81803 | ||||||||
\(897\) | −28.9278 | −0.965872 | ||||||||
\(898\) | 53.1528 | 1.77373 | ||||||||
\(899\) | −67.9074 | −2.26484 | ||||||||
\(900\) | −12.9841 | −0.432803 | ||||||||
\(901\) | −2.99060 | −0.0996314 | ||||||||
\(902\) | 37.1622 | 1.23736 | ||||||||
\(903\) | 69.8650 | 2.32496 | ||||||||
\(904\) | 104.639 | 3.48024 | ||||||||
\(905\) | 4.35856 | 0.144883 | ||||||||
\(906\) | 22.9187 | 0.761423 | ||||||||
\(907\) | −14.2907 | −0.474515 | −0.237258 | − | 0.971447i | \(-0.576249\pi\) | ||||
−0.237258 | + | 0.971447i | \(0.576249\pi\) | |||||||
\(908\) | −7.45038 | −0.247249 | ||||||||
\(909\) | 3.22760 | 0.107053 | ||||||||
\(910\) | −12.5357 | −0.415554 | ||||||||
\(911\) | −48.5421 | −1.60827 | −0.804135 | − | 0.594447i | \(-0.797371\pi\) | ||||
−0.804135 | + | 0.594447i | \(0.797371\pi\) | |||||||
\(912\) | −13.4797 | −0.446359 | ||||||||
\(913\) | −64.9269 | −2.14877 | ||||||||
\(914\) | 37.4309 | 1.23810 | ||||||||
\(915\) | −4.19512 | −0.138686 | ||||||||
\(916\) | −64.1928 | −2.12099 | ||||||||
\(917\) | 85.9125 | 2.83708 | ||||||||
\(918\) | 57.4277 | 1.89540 | ||||||||
\(919\) | 32.7326 | 1.07975 | 0.539874 | − | 0.841746i | \(-0.318472\pi\) | ||||
0.539874 | + | 0.841746i | \(0.318472\pi\) | |||||||
\(920\) | 9.14495 | 0.301500 | ||||||||
\(921\) | −46.5565 | −1.53409 | ||||||||
\(922\) | −10.0187 | −0.329950 | ||||||||
\(923\) | 33.2478 | 1.09436 | ||||||||
\(924\) | −219.207 | −7.21137 | ||||||||
\(925\) | 7.08009 | 0.232792 | ||||||||
\(926\) | 30.9187 | 1.01605 | ||||||||
\(927\) | 7.69759 | 0.252822 | ||||||||
\(928\) | 40.5596 | 1.33144 | ||||||||
\(929\) | −36.6497 | −1.20244 | −0.601219 | − | 0.799085i | \(-0.705318\pi\) | ||||
−0.601219 | + | 0.799085i | \(0.705318\pi\) | |||||||
\(930\) | −14.0059 | −0.459273 | ||||||||
\(931\) | −14.7552 | −0.483582 | ||||||||
\(932\) | −15.2432 | −0.499306 | ||||||||
\(933\) | 29.2422 | 0.957348 | ||||||||
\(934\) | 6.33309 | 0.207225 | ||||||||
\(935\) | −8.65830 | −0.283157 | ||||||||
\(936\) | −12.4573 | −0.407178 | ||||||||
\(937\) | −49.4702 | −1.61612 | −0.808061 | − | 0.589099i | \(-0.799483\pi\) | ||||
−0.808061 | + | 0.589099i | \(0.799483\pi\) | |||||||
\(938\) | 98.5243 | 3.21693 | ||||||||
\(939\) | 25.4721 | 0.831249 | ||||||||
\(940\) | 11.0116 | 0.359160 | ||||||||
\(941\) | −27.0221 | −0.880894 | −0.440447 | − | 0.897779i | \(-0.645180\pi\) | ||||
−0.440447 | + | 0.897779i | \(0.645180\pi\) | |||||||
\(942\) | 78.0759 | 2.54385 | ||||||||
\(943\) | −12.0689 | −0.393017 | ||||||||
\(944\) | 26.2899 | 0.855664 | ||||||||
\(945\) | −6.73828 | −0.219196 | ||||||||
\(946\) | 111.370 | 3.62094 | ||||||||
\(947\) | 8.37251 | 0.272070 | 0.136035 | − | 0.990704i | \(-0.456564\pi\) | ||||
0.136035 | + | 0.990704i | \(0.456564\pi\) | |||||||
\(948\) | 98.6859 | 3.20517 | ||||||||
\(949\) | 3.16020 | 0.102584 | ||||||||
\(950\) | −12.4733 | −0.404686 | ||||||||
\(951\) | 1.89511 | 0.0614532 | ||||||||
\(952\) | −145.555 | −4.71746 | ||||||||
\(953\) | −22.7311 | −0.736333 | −0.368167 | − | 0.929760i | \(-0.620014\pi\) | ||||
−0.368167 | + | 0.929760i | \(0.620014\pi\) | |||||||
\(954\) | 0.911056 | 0.0294965 | ||||||||
\(955\) | −3.32648 | −0.107643 | ||||||||
\(956\) | 114.463 | 3.70198 | ||||||||
\(957\) | 77.6561 | 2.51026 | ||||||||
\(958\) | −10.9098 | −0.352479 | ||||||||
\(959\) | 106.973 | 3.45435 | ||||||||
\(960\) | −0.167284 | −0.00539907 | ||||||||
\(961\) | 53.1399 | 1.71419 | ||||||||
\(962\) | 12.2701 | 0.395604 | ||||||||
\(963\) | 1.13510 | 0.0365782 | ||||||||
\(964\) | 47.3974 | 1.52657 | ||||||||
\(965\) | −5.41513 | −0.174319 | ||||||||
\(966\) | 102.969 | 3.31297 | ||||||||
\(967\) | 47.9446 | 1.54180 | 0.770898 | − | 0.636959i | \(-0.219808\pi\) | ||||
0.770898 | + | 0.636959i | \(0.219808\pi\) | |||||||
\(968\) | −123.992 | −3.98525 | ||||||||
\(969\) | −9.36625 | −0.300887 | ||||||||
\(970\) | 1.49844 | 0.0481122 | ||||||||
\(971\) | 59.7327 | 1.91691 | 0.958456 | − | 0.285240i | \(-0.0920734\pi\) | ||||
0.958456 | + | 0.285240i | \(0.0920734\pi\) | |||||||
\(972\) | −27.1611 | −0.871191 | ||||||||
\(973\) | −9.90300 | −0.317476 | ||||||||
\(974\) | 12.5571 | 0.402356 | ||||||||
\(975\) | −30.9746 | −0.991982 | ||||||||
\(976\) | −49.7484 | −1.59241 | ||||||||
\(977\) | −38.8945 | −1.24435 | −0.622173 | − | 0.782880i | \(-0.713750\pi\) | ||||
−0.622173 | + | 0.782880i | \(0.713750\pi\) | |||||||
\(978\) | −113.979 | −3.64465 | ||||||||
\(979\) | 53.4888 | 1.70951 | ||||||||
\(980\) | 20.9235 | 0.668378 | ||||||||
\(981\) | 8.34884 | 0.266558 | ||||||||
\(982\) | 4.59742 | 0.146710 | ||||||||
\(983\) | 23.0924 | 0.736532 | 0.368266 | − | 0.929720i | \(-0.379952\pi\) | ||||
0.368266 | + | 0.929720i | \(0.379952\pi\) | |||||||
\(984\) | −31.5592 | −1.00607 | ||||||||
\(985\) | 4.63720 | 0.147753 | ||||||||
\(986\) | 93.1422 | 2.96625 | ||||||||
\(987\) | 68.6401 | 2.18484 | ||||||||
\(988\) | −14.9453 | −0.475472 | ||||||||
\(989\) | −36.1687 | −1.15010 | ||||||||
\(990\) | 2.63766 | 0.0838304 | ||||||||
\(991\) | −15.3479 | −0.487544 | −0.243772 | − | 0.969833i | \(-0.578385\pi\) | ||||
−0.243772 | + | 0.969833i | \(0.578385\pi\) | |||||||
\(992\) | −50.2550 | −1.59560 | ||||||||
\(993\) | −59.7981 | −1.89763 | ||||||||
\(994\) | −118.346 | −3.75370 | ||||||||
\(995\) | 4.58690 | 0.145415 | ||||||||
\(996\) | 99.5973 | 3.15586 | ||||||||
\(997\) | −8.20030 | −0.259706 | −0.129853 | − | 0.991533i | \(-0.541451\pi\) | ||||
−0.129853 | + | 0.991533i | \(0.541451\pi\) | |||||||
\(998\) | 93.9056 | 2.97253 | ||||||||
\(999\) | 6.59552 | 0.208673 |
(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 | 6023.2.a.d.1.11 | ✓ | 140 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.d.1.11 | ✓ | 140 | 1.1 | even | 1 | trivial |