Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.03639 | −1.43995 | −0.719974 | − | 0.694001i | \(-0.755846\pi\) | ||||
−0.719974 | + | 0.694001i | \(0.755846\pi\) | |||||||
\(3\) | −1.20777 | −0.697306 | −0.348653 | − | 0.937252i | \(-0.613361\pi\) | ||||
−0.348653 | + | 0.937252i | \(0.613361\pi\) | |||||||
\(4\) | 2.14690 | 1.07345 | ||||||||
\(5\) | 3.16451 | 1.41521 | 0.707607 | − | 0.706606i | \(-0.249775\pi\) | ||||
0.707607 | + | 0.706606i | \(0.249775\pi\) | |||||||
\(6\) | 2.45949 | 1.00408 | ||||||||
\(7\) | 3.67207 | 1.38791 | 0.693957 | − | 0.720017i | \(-0.255866\pi\) | ||||
0.693957 | + | 0.720017i | \(0.255866\pi\) | |||||||
\(8\) | −0.299141 | −0.105762 | ||||||||
\(9\) | −1.54130 | −0.513765 | ||||||||
\(10\) | −6.44419 | −2.03783 | ||||||||
\(11\) | 0.325684 | 0.0981976 | 0.0490988 | − | 0.998794i | \(-0.484365\pi\) | ||||
0.0490988 | + | 0.998794i | \(0.484365\pi\) | |||||||
\(12\) | −2.59296 | −0.748522 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −7.47779 | −1.99852 | ||||||||
\(15\) | −3.82200 | −0.986836 | ||||||||
\(16\) | −3.68463 | −0.921157 | ||||||||
\(17\) | −5.38625 | −1.30636 | −0.653179 | − | 0.757203i | \(-0.726565\pi\) | ||||
−0.653179 | + | 0.757203i | \(0.726565\pi\) | |||||||
\(18\) | 3.13868 | 0.739795 | ||||||||
\(19\) | 2.98579 | 0.684988 | 0.342494 | − | 0.939520i | \(-0.388728\pi\) | ||||
0.342494 | + | 0.939520i | \(0.388728\pi\) | |||||||
\(20\) | 6.79389 | 1.51916 | ||||||||
\(21\) | −4.43502 | −0.967800 | ||||||||
\(22\) | −0.663222 | −0.141399 | ||||||||
\(23\) | −4.80284 | −1.00146 | −0.500730 | − | 0.865603i | \(-0.666935\pi\) | ||||
−0.500730 | + | 0.865603i | \(0.666935\pi\) | |||||||
\(24\) | 0.361293 | 0.0737486 | ||||||||
\(25\) | 5.01415 | 1.00283 | ||||||||
\(26\) | −2.03639 | −0.399370 | ||||||||
\(27\) | 5.48483 | 1.05556 | ||||||||
\(28\) | 7.88357 | 1.48985 | ||||||||
\(29\) | −8.51496 | −1.58119 | −0.790594 | − | 0.612340i | \(-0.790228\pi\) | ||||
−0.790594 | + | 0.612340i | \(0.790228\pi\) | |||||||
\(30\) | 7.78310 | 1.42099 | ||||||||
\(31\) | 3.30196 | 0.593050 | 0.296525 | − | 0.955025i | \(-0.404172\pi\) | ||||
0.296525 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(32\) | 8.10163 | 1.43218 | ||||||||
\(33\) | −0.393351 | −0.0684737 | ||||||||
\(34\) | 10.9685 | 1.88109 | ||||||||
\(35\) | 11.6203 | 1.96419 | ||||||||
\(36\) | −3.30900 | −0.551500 | ||||||||
\(37\) | 6.47891 | 1.06513 | 0.532564 | − | 0.846390i | \(-0.321229\pi\) | ||||
0.532564 | + | 0.846390i | \(0.321229\pi\) | |||||||
\(38\) | −6.08025 | −0.986346 | ||||||||
\(39\) | −1.20777 | −0.193398 | ||||||||
\(40\) | −0.946636 | −0.149676 | ||||||||
\(41\) | 1.14589 | 0.178958 | 0.0894791 | − | 0.995989i | \(-0.471480\pi\) | ||||
0.0894791 | + | 0.995989i | \(0.471480\pi\) | |||||||
\(42\) | 9.03144 | 1.39358 | ||||||||
\(43\) | −3.87638 | −0.591142 | −0.295571 | − | 0.955321i | \(-0.595510\pi\) | ||||
−0.295571 | + | 0.955321i | \(0.595510\pi\) | |||||||
\(44\) | 0.699211 | 0.105410 | ||||||||
\(45\) | −4.87745 | −0.727087 | ||||||||
\(46\) | 9.78047 | 1.44205 | ||||||||
\(47\) | −7.55277 | −1.10169 | −0.550843 | − | 0.834609i | \(-0.685694\pi\) | ||||
−0.550843 | + | 0.834609i | \(0.685694\pi\) | |||||||
\(48\) | 4.45018 | 0.642328 | ||||||||
\(49\) | 6.48413 | 0.926304 | ||||||||
\(50\) | −10.2108 | −1.44402 | ||||||||
\(51\) | 6.50535 | 0.910931 | ||||||||
\(52\) | 2.14690 | 0.297721 | ||||||||
\(53\) | −1.66269 | −0.228388 | −0.114194 | − | 0.993458i | \(-0.536429\pi\) | ||||
−0.114194 | + | 0.993458i | \(0.536429\pi\) | |||||||
\(54\) | −11.1693 | −1.51995 | ||||||||
\(55\) | 1.03063 | 0.138971 | ||||||||
\(56\) | −1.09847 | −0.146789 | ||||||||
\(57\) | −3.60615 | −0.477646 | ||||||||
\(58\) | 17.3398 | 2.27683 | ||||||||
\(59\) | −7.23942 | −0.942493 | −0.471246 | − | 0.882002i | \(-0.656196\pi\) | ||||
−0.471246 | + | 0.882002i | \(0.656196\pi\) | |||||||
\(60\) | −8.20544 | −1.05932 | ||||||||
\(61\) | 7.34531 | 0.940470 | 0.470235 | − | 0.882541i | \(-0.344169\pi\) | ||||
0.470235 | + | 0.882541i | \(0.344169\pi\) | |||||||
\(62\) | −6.72410 | −0.853961 | ||||||||
\(63\) | −5.65975 | −0.713061 | ||||||||
\(64\) | −9.12885 | −1.14111 | ||||||||
\(65\) | 3.16451 | 0.392510 | ||||||||
\(66\) | 0.801018 | 0.0985985 | ||||||||
\(67\) | −10.4604 | −1.27794 | −0.638972 | − | 0.769230i | \(-0.720640\pi\) | ||||
−0.638972 | + | 0.769230i | \(0.720640\pi\) | |||||||
\(68\) | −11.5637 | −1.40231 | ||||||||
\(69\) | 5.80072 | 0.698324 | ||||||||
\(70\) | −23.6636 | −2.82834 | ||||||||
\(71\) | −9.22106 | −1.09434 | −0.547169 | − | 0.837022i | \(-0.684295\pi\) | ||||
−0.547169 | + | 0.837022i | \(0.684295\pi\) | |||||||
\(72\) | 0.461064 | 0.0543370 | ||||||||
\(73\) | −3.96706 | −0.464309 | −0.232154 | − | 0.972679i | \(-0.574577\pi\) | ||||
−0.232154 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(74\) | −13.1936 | −1.53373 | ||||||||
\(75\) | −6.05593 | −0.699278 | ||||||||
\(76\) | 6.41019 | 0.735299 | ||||||||
\(77\) | 1.19594 | 0.136290 | ||||||||
\(78\) | 2.45949 | 0.278483 | ||||||||
\(79\) | −14.9799 | −1.68537 | −0.842684 | − | 0.538408i | \(-0.819026\pi\) | ||||
−0.842684 | + | 0.538408i | \(0.819026\pi\) | |||||||
\(80\) | −11.6601 | −1.30363 | ||||||||
\(81\) | −2.00052 | −0.222280 | ||||||||
\(82\) | −2.33349 | −0.257690 | ||||||||
\(83\) | −4.17697 | −0.458482 | −0.229241 | − | 0.973370i | \(-0.573624\pi\) | ||||
−0.229241 | + | 0.973370i | \(0.573624\pi\) | |||||||
\(84\) | −9.52152 | −1.03888 | ||||||||
\(85\) | −17.0449 | −1.84878 | ||||||||
\(86\) | 7.89383 | 0.851213 | ||||||||
\(87\) | 10.2841 | 1.10257 | ||||||||
\(88\) | −0.0974256 | −0.0103856 | ||||||||
\(89\) | −0.223120 | −0.0236507 | −0.0118254 | − | 0.999930i | \(-0.503764\pi\) | ||||
−0.0118254 | + | 0.999930i | \(0.503764\pi\) | |||||||
\(90\) | 9.93240 | 1.04697 | ||||||||
\(91\) | 3.67207 | 0.384938 | ||||||||
\(92\) | −10.3112 | −1.07502 | ||||||||
\(93\) | −3.98801 | −0.413537 | ||||||||
\(94\) | 15.3804 | 1.58637 | ||||||||
\(95\) | 9.44858 | 0.969404 | ||||||||
\(96\) | −9.78489 | −0.998667 | ||||||||
\(97\) | −8.90776 | −0.904446 | −0.452223 | − | 0.891905i | \(-0.649369\pi\) | ||||
−0.452223 | + | 0.891905i | \(0.649369\pi\) | |||||||
\(98\) | −13.2042 | −1.33383 | ||||||||
\(99\) | −0.501976 | −0.0504505 | ||||||||
\(100\) | 10.7649 | 1.07649 | ||||||||
\(101\) | 2.18936 | 0.217849 | 0.108925 | − | 0.994050i | \(-0.465259\pi\) | ||||
0.108925 | + | 0.994050i | \(0.465259\pi\) | |||||||
\(102\) | −13.2474 | −1.31169 | ||||||||
\(103\) | 9.61468 | 0.947362 | 0.473681 | − | 0.880696i | \(-0.342925\pi\) | ||||
0.473681 | + | 0.880696i | \(0.342925\pi\) | |||||||
\(104\) | −0.299141 | −0.0293332 | ||||||||
\(105\) | −14.0347 | −1.36964 | ||||||||
\(106\) | 3.38589 | 0.328867 | ||||||||
\(107\) | −1.10814 | −0.107128 | −0.0535639 | − | 0.998564i | \(-0.517058\pi\) | ||||
−0.0535639 | + | 0.998564i | \(0.517058\pi\) | |||||||
\(108\) | 11.7754 | 1.13309 | ||||||||
\(109\) | −0.760592 | −0.0728515 | −0.0364258 | − | 0.999336i | \(-0.511597\pi\) | ||||
−0.0364258 | + | 0.999336i | \(0.511597\pi\) | |||||||
\(110\) | −2.09877 | −0.200110 | ||||||||
\(111\) | −7.82503 | −0.742719 | ||||||||
\(112\) | −13.5302 | −1.27849 | ||||||||
\(113\) | −0.375624 | −0.0353358 | −0.0176679 | − | 0.999844i | \(-0.505624\pi\) | ||||
−0.0176679 | + | 0.999844i | \(0.505624\pi\) | |||||||
\(114\) | 7.34353 | 0.687785 | ||||||||
\(115\) | −15.1986 | −1.41728 | ||||||||
\(116\) | −18.2807 | −1.69732 | ||||||||
\(117\) | −1.54130 | −0.142493 | ||||||||
\(118\) | 14.7423 | 1.35714 | ||||||||
\(119\) | −19.7787 | −1.81311 | ||||||||
\(120\) | 1.14332 | 0.104370 | ||||||||
\(121\) | −10.8939 | −0.990357 | ||||||||
\(122\) | −14.9579 | −1.35423 | ||||||||
\(123\) | −1.38397 | −0.124788 | ||||||||
\(124\) | 7.08898 | 0.636609 | ||||||||
\(125\) | 0.0447683 | 0.00400419 | ||||||||
\(126\) | 11.5255 | 1.02677 | ||||||||
\(127\) | −21.4785 | −1.90591 | −0.952956 | − | 0.303107i | \(-0.901976\pi\) | ||||
−0.952956 | + | 0.303107i | \(0.901976\pi\) | |||||||
\(128\) | 2.38667 | 0.210954 | ||||||||
\(129\) | 4.68176 | 0.412206 | ||||||||
\(130\) | −6.44419 | −0.565193 | ||||||||
\(131\) | −9.49902 | −0.829934 | −0.414967 | − | 0.909837i | \(-0.636207\pi\) | ||||
−0.414967 | + | 0.909837i | \(0.636207\pi\) | |||||||
\(132\) | −0.844485 | −0.0735030 | ||||||||
\(133\) | 10.9640 | 0.950704 | ||||||||
\(134\) | 21.3015 | 1.84017 | ||||||||
\(135\) | 17.3568 | 1.49384 | ||||||||
\(136\) | 1.61125 | 0.138163 | ||||||||
\(137\) | 9.39725 | 0.802862 | 0.401431 | − | 0.915889i | \(-0.368513\pi\) | ||||
0.401431 | + | 0.915889i | \(0.368513\pi\) | |||||||
\(138\) | −11.8125 | −1.00555 | ||||||||
\(139\) | 17.3835 | 1.47445 | 0.737226 | − | 0.675646i | \(-0.236135\pi\) | ||||
0.737226 | + | 0.675646i | \(0.236135\pi\) | |||||||
\(140\) | 24.9477 | 2.10846 | ||||||||
\(141\) | 9.12200 | 0.768211 | ||||||||
\(142\) | 18.7777 | 1.57579 | ||||||||
\(143\) | 0.325684 | 0.0272351 | ||||||||
\(144\) | 5.67910 | 0.473258 | ||||||||
\(145\) | −26.9457 | −2.23772 | ||||||||
\(146\) | 8.07849 | 0.668580 | ||||||||
\(147\) | −7.83133 | −0.645917 | ||||||||
\(148\) | 13.9096 | 1.14336 | ||||||||
\(149\) | 2.72607 | 0.223329 | 0.111664 | − | 0.993746i | \(-0.464382\pi\) | ||||
0.111664 | + | 0.993746i | \(0.464382\pi\) | |||||||
\(150\) | 12.3323 | 1.00692 | ||||||||
\(151\) | 10.7122 | 0.871743 | 0.435871 | − | 0.900009i | \(-0.356440\pi\) | ||||
0.435871 | + | 0.900009i | \(0.356440\pi\) | |||||||
\(152\) | −0.893173 | −0.0724459 | ||||||||
\(153\) | 8.30180 | 0.671161 | ||||||||
\(154\) | −2.43540 | −0.196250 | ||||||||
\(155\) | 10.4491 | 0.839292 | ||||||||
\(156\) | −2.59296 | −0.207603 | ||||||||
\(157\) | −16.4675 | −1.31425 | −0.657126 | − | 0.753781i | \(-0.728228\pi\) | ||||
−0.657126 | + | 0.753781i | \(0.728228\pi\) | |||||||
\(158\) | 30.5049 | 2.42684 | ||||||||
\(159\) | 2.00814 | 0.159256 | ||||||||
\(160\) | 25.6377 | 2.02684 | ||||||||
\(161\) | −17.6364 | −1.38994 | ||||||||
\(162\) | 4.07385 | 0.320072 | ||||||||
\(163\) | 21.6294 | 1.69414 | 0.847072 | − | 0.531478i | \(-0.178363\pi\) | ||||
0.847072 | + | 0.531478i | \(0.178363\pi\) | |||||||
\(164\) | 2.46011 | 0.192102 | ||||||||
\(165\) | −1.24477 | −0.0969049 | ||||||||
\(166\) | 8.50595 | 0.660190 | ||||||||
\(167\) | −23.8419 | −1.84495 | −0.922473 | − | 0.386062i | \(-0.873835\pi\) | ||||
−0.922473 | + | 0.386062i | \(0.873835\pi\) | |||||||
\(168\) | 1.32669 | 0.102357 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 34.7101 | 2.66214 | ||||||||
\(171\) | −4.60199 | −0.351923 | ||||||||
\(172\) | −8.32218 | −0.634560 | ||||||||
\(173\) | 8.88297 | 0.675360 | 0.337680 | − | 0.941261i | \(-0.390358\pi\) | ||||
0.337680 | + | 0.941261i | \(0.390358\pi\) | |||||||
\(174\) | −20.9425 | −1.58764 | ||||||||
\(175\) | 18.4123 | 1.39184 | ||||||||
\(176\) | −1.20003 | −0.0904553 | ||||||||
\(177\) | 8.74355 | 0.657205 | ||||||||
\(178\) | 0.454361 | 0.0340558 | ||||||||
\(179\) | 14.2881 | 1.06794 | 0.533972 | − | 0.845502i | \(-0.320699\pi\) | ||||
0.533972 | + | 0.845502i | \(0.320699\pi\) | |||||||
\(180\) | −10.4714 | −0.780491 | ||||||||
\(181\) | −19.5901 | −1.45612 | −0.728059 | − | 0.685515i | \(-0.759577\pi\) | ||||
−0.728059 | + | 0.685515i | \(0.759577\pi\) | |||||||
\(182\) | −7.47779 | −0.554290 | ||||||||
\(183\) | −8.87143 | −0.655795 | ||||||||
\(184\) | 1.43673 | 0.105917 | ||||||||
\(185\) | 20.5026 | 1.50738 | ||||||||
\(186\) | 8.12115 | 0.595472 | ||||||||
\(187\) | −1.75422 | −0.128281 | ||||||||
\(188\) | −16.2150 | −1.18260 | ||||||||
\(189\) | 20.1407 | 1.46502 | ||||||||
\(190\) | −19.2410 | −1.39589 | ||||||||
\(191\) | −19.4316 | −1.40602 | −0.703011 | − | 0.711179i | \(-0.748162\pi\) | ||||
−0.703011 | + | 0.711179i | \(0.748162\pi\) | |||||||
\(192\) | 11.0255 | 0.795700 | ||||||||
\(193\) | −23.9115 | −1.72119 | −0.860593 | − | 0.509293i | \(-0.829907\pi\) | ||||
−0.860593 | + | 0.509293i | \(0.829907\pi\) | |||||||
\(194\) | 18.1397 | 1.30235 | ||||||||
\(195\) | −3.82200 | −0.273699 | ||||||||
\(196\) | 13.9208 | 0.994340 | ||||||||
\(197\) | −7.53785 | −0.537050 | −0.268525 | − | 0.963273i | \(-0.586536\pi\) | ||||
−0.268525 | + | 0.963273i | \(0.586536\pi\) | |||||||
\(198\) | 1.02222 | 0.0726460 | ||||||||
\(199\) | 8.15967 | 0.578424 | 0.289212 | − | 0.957265i | \(-0.406607\pi\) | ||||
0.289212 | + | 0.957265i | \(0.406607\pi\) | |||||||
\(200\) | −1.49994 | −0.106062 | ||||||||
\(201\) | 12.6338 | 0.891118 | ||||||||
\(202\) | −4.45840 | −0.313692 | ||||||||
\(203\) | −31.2676 | −2.19455 | ||||||||
\(204\) | 13.9663 | 0.977837 | ||||||||
\(205\) | 3.62619 | 0.253264 | ||||||||
\(206\) | −19.5793 | −1.36415 | ||||||||
\(207\) | 7.40259 | 0.514516 | ||||||||
\(208\) | −3.68463 | −0.255483 | ||||||||
\(209\) | 0.972426 | 0.0672641 | ||||||||
\(210\) | 28.5801 | 1.97221 | ||||||||
\(211\) | 1.82738 | 0.125802 | 0.0629009 | − | 0.998020i | \(-0.479965\pi\) | ||||
0.0629009 | + | 0.998020i | \(0.479965\pi\) | |||||||
\(212\) | −3.56962 | −0.245163 | ||||||||
\(213\) | 11.1369 | 0.763088 | ||||||||
\(214\) | 2.25661 | 0.154258 | ||||||||
\(215\) | −12.2668 | −0.836592 | ||||||||
\(216\) | −1.64074 | −0.111638 | ||||||||
\(217\) | 12.1251 | 0.823102 | ||||||||
\(218\) | 1.54887 | 0.104902 | ||||||||
\(219\) | 4.79129 | 0.323765 | ||||||||
\(220\) | 2.21266 | 0.149178 | ||||||||
\(221\) | −5.38625 | −0.362319 | ||||||||
\(222\) | 15.9348 | 1.06948 | ||||||||
\(223\) | 20.6252 | 1.38116 | 0.690582 | − | 0.723254i | \(-0.257354\pi\) | ||||
0.690582 | + | 0.723254i | \(0.257354\pi\) | |||||||
\(224\) | 29.7498 | 1.98774 | ||||||||
\(225\) | −7.72828 | −0.515219 | ||||||||
\(226\) | 0.764919 | 0.0508816 | ||||||||
\(227\) | 18.5219 | 1.22934 | 0.614671 | − | 0.788784i | \(-0.289289\pi\) | ||||
0.614671 | + | 0.788784i | \(0.289289\pi\) | |||||||
\(228\) | −7.74202 | −0.512728 | ||||||||
\(229\) | −16.1829 | −1.06940 | −0.534698 | − | 0.845043i | \(-0.679574\pi\) | ||||
−0.534698 | + | 0.845043i | \(0.679574\pi\) | |||||||
\(230\) | 30.9504 | 2.04081 | ||||||||
\(231\) | −1.44442 | −0.0950356 | ||||||||
\(232\) | 2.54717 | 0.167230 | ||||||||
\(233\) | 14.2178 | 0.931437 | 0.465718 | − | 0.884933i | \(-0.345796\pi\) | ||||
0.465718 | + | 0.884933i | \(0.345796\pi\) | |||||||
\(234\) | 3.13868 | 0.205182 | ||||||||
\(235\) | −23.9009 | −1.55912 | ||||||||
\(236\) | −15.5423 | −1.01172 | ||||||||
\(237\) | 18.0922 | 1.17522 | ||||||||
\(238\) | 40.2773 | 2.61079 | ||||||||
\(239\) | −11.6325 | −0.752444 | −0.376222 | − | 0.926529i | \(-0.622777\pi\) | ||||
−0.376222 | + | 0.926529i | \(0.622777\pi\) | |||||||
\(240\) | 14.0826 | 0.909031 | ||||||||
\(241\) | 6.93142 | 0.446492 | 0.223246 | − | 0.974762i | \(-0.428335\pi\) | ||||
0.223246 | + | 0.974762i | \(0.428335\pi\) | |||||||
\(242\) | 22.1843 | 1.42606 | ||||||||
\(243\) | −14.0383 | −0.900559 | ||||||||
\(244\) | 15.7696 | 1.00955 | ||||||||
\(245\) | 20.5191 | 1.31092 | ||||||||
\(246\) | 2.81831 | 0.179689 | ||||||||
\(247\) | 2.98579 | 0.189981 | ||||||||
\(248\) | −0.987752 | −0.0627223 | ||||||||
\(249\) | 5.04481 | 0.319702 | ||||||||
\(250\) | −0.0911658 | −0.00576583 | ||||||||
\(251\) | −2.80608 | −0.177118 | −0.0885591 | − | 0.996071i | \(-0.528226\pi\) | ||||
−0.0885591 | + | 0.996071i | \(0.528226\pi\) | |||||||
\(252\) | −12.1509 | −0.765435 | ||||||||
\(253\) | −1.56421 | −0.0983410 | ||||||||
\(254\) | 43.7388 | 2.74441 | ||||||||
\(255\) | 20.5863 | 1.28916 | ||||||||
\(256\) | 13.3975 | 0.837344 | ||||||||
\(257\) | −17.7374 | −1.10643 | −0.553215 | − | 0.833039i | \(-0.686599\pi\) | ||||
−0.553215 | + | 0.833039i | \(0.686599\pi\) | |||||||
\(258\) | −9.53391 | −0.593556 | ||||||||
\(259\) | 23.7911 | 1.47830 | ||||||||
\(260\) | 6.79389 | 0.421339 | ||||||||
\(261\) | 13.1241 | 0.812359 | ||||||||
\(262\) | 19.3437 | 1.19506 | ||||||||
\(263\) | 4.00485 | 0.246950 | 0.123475 | − | 0.992348i | \(-0.460596\pi\) | ||||
0.123475 | + | 0.992348i | \(0.460596\pi\) | |||||||
\(264\) | 0.117668 | 0.00724194 | ||||||||
\(265\) | −5.26160 | −0.323218 | ||||||||
\(266\) | −22.3271 | −1.36896 | ||||||||
\(267\) | 0.269478 | 0.0164918 | ||||||||
\(268\) | −22.4575 | −1.37181 | ||||||||
\(269\) | 4.66055 | 0.284159 | 0.142079 | − | 0.989855i | \(-0.454621\pi\) | ||||
0.142079 | + | 0.989855i | \(0.454621\pi\) | |||||||
\(270\) | −35.3453 | −2.15105 | ||||||||
\(271\) | −1.74512 | −0.106008 | −0.0530041 | − | 0.998594i | \(-0.516880\pi\) | ||||
−0.0530041 | + | 0.998594i | \(0.516880\pi\) | |||||||
\(272\) | 19.8463 | 1.20336 | ||||||||
\(273\) | −4.43502 | −0.268419 | ||||||||
\(274\) | −19.1365 | −1.15608 | ||||||||
\(275\) | 1.63303 | 0.0984754 | ||||||||
\(276\) | 12.4535 | 0.749615 | ||||||||
\(277\) | −12.3319 | −0.740951 | −0.370476 | − | 0.928842i | \(-0.620805\pi\) | ||||
−0.370476 | + | 0.928842i | \(0.620805\pi\) | |||||||
\(278\) | −35.3997 | −2.12313 | ||||||||
\(279\) | −5.08930 | −0.304688 | ||||||||
\(280\) | −3.47612 | −0.207738 | ||||||||
\(281\) | 20.4775 | 1.22159 | 0.610793 | − | 0.791790i | \(-0.290851\pi\) | ||||
0.610793 | + | 0.791790i | \(0.290851\pi\) | |||||||
\(282\) | −18.5760 | −1.10618 | ||||||||
\(283\) | 1.37089 | 0.0814911 | 0.0407456 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407456 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(284\) | −19.7967 | −1.17472 | ||||||||
\(285\) | −11.4117 | −0.675971 | ||||||||
\(286\) | −0.663222 | −0.0392171 | ||||||||
\(287\) | 4.20780 | 0.248378 | ||||||||
\(288\) | −12.4870 | −0.735804 | ||||||||
\(289\) | 12.0117 | 0.706572 | ||||||||
\(290\) | 54.8721 | 3.22220 | ||||||||
\(291\) | 10.7585 | 0.630675 | ||||||||
\(292\) | −8.51686 | −0.498412 | ||||||||
\(293\) | 12.4523 | 0.727472 | 0.363736 | − | 0.931502i | \(-0.381501\pi\) | ||||
0.363736 | + | 0.931502i | \(0.381501\pi\) | |||||||
\(294\) | 15.9477 | 0.930087 | ||||||||
\(295\) | −22.9093 | −1.33383 | ||||||||
\(296\) | −1.93811 | −0.112650 | ||||||||
\(297\) | 1.78633 | 0.103653 | ||||||||
\(298\) | −5.55136 | −0.321581 | ||||||||
\(299\) | −4.80284 | −0.277755 | ||||||||
\(300\) | −13.0015 | −0.750640 | ||||||||
\(301\) | −14.2343 | −0.820454 | ||||||||
\(302\) | −21.8142 | −1.25526 | ||||||||
\(303\) | −2.64424 | −0.151908 | ||||||||
\(304\) | −11.0015 | −0.630981 | ||||||||
\(305\) | 23.2443 | 1.33097 | ||||||||
\(306\) | −16.9057 | −0.966437 | ||||||||
\(307\) | 18.2623 | 1.04228 | 0.521142 | − | 0.853470i | \(-0.325506\pi\) | ||||
0.521142 | + | 0.853470i | \(0.325506\pi\) | |||||||
\(308\) | 2.56756 | 0.146300 | ||||||||
\(309\) | −11.6123 | −0.660601 | ||||||||
\(310\) | −21.2785 | −1.20854 | ||||||||
\(311\) | 16.1164 | 0.913878 | 0.456939 | − | 0.889498i | \(-0.348946\pi\) | ||||
0.456939 | + | 0.889498i | \(0.348946\pi\) | |||||||
\(312\) | 0.361293 | 0.0204542 | ||||||||
\(313\) | 24.7079 | 1.39657 | 0.698287 | − | 0.715818i | \(-0.253946\pi\) | ||||
0.698287 | + | 0.715818i | \(0.253946\pi\) | |||||||
\(314\) | 33.5343 | 1.89245 | ||||||||
\(315\) | −17.9104 | −1.00913 | ||||||||
\(316\) | −32.1603 | −1.80916 | ||||||||
\(317\) | −7.78108 | −0.437029 | −0.218514 | − | 0.975834i | \(-0.570121\pi\) | ||||
−0.218514 | + | 0.975834i | \(0.570121\pi\) | |||||||
\(318\) | −4.08937 | −0.229321 | ||||||||
\(319\) | −2.77319 | −0.155269 | ||||||||
\(320\) | −28.8884 | −1.61491 | ||||||||
\(321\) | 1.33838 | 0.0747008 | ||||||||
\(322\) | 35.9146 | 2.00144 | ||||||||
\(323\) | −16.0822 | −0.894839 | ||||||||
\(324\) | −4.29492 | −0.238607 | ||||||||
\(325\) | 5.01415 | 0.278135 | ||||||||
\(326\) | −44.0459 | −2.43948 | ||||||||
\(327\) | 0.918620 | 0.0507998 | ||||||||
\(328\) | −0.342783 | −0.0189270 | ||||||||
\(329\) | −27.7343 | −1.52904 | ||||||||
\(330\) | 2.53483 | 0.139538 | ||||||||
\(331\) | −6.47813 | −0.356070 | −0.178035 | − | 0.984024i | \(-0.556974\pi\) | ||||
−0.178035 | + | 0.984024i | \(0.556974\pi\) | |||||||
\(332\) | −8.96752 | −0.492157 | ||||||||
\(333\) | −9.98592 | −0.547225 | ||||||||
\(334\) | 48.5516 | 2.65662 | ||||||||
\(335\) | −33.1022 | −1.80856 | ||||||||
\(336\) | 16.3414 | 0.891495 | ||||||||
\(337\) | 6.73009 | 0.366611 | 0.183306 | − | 0.983056i | \(-0.441320\pi\) | ||||
0.183306 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(338\) | −2.03639 | −0.110765 | ||||||||
\(339\) | 0.453667 | 0.0246398 | ||||||||
\(340\) | −36.5936 | −1.98457 | ||||||||
\(341\) | 1.07540 | 0.0582361 | ||||||||
\(342\) | 9.37145 | 0.506750 | ||||||||
\(343\) | −1.89431 | −0.102283 | ||||||||
\(344\) | 1.15958 | 0.0625205 | ||||||||
\(345\) | 18.3564 | 0.988278 | ||||||||
\(346\) | −18.0892 | −0.972482 | ||||||||
\(347\) | 31.7021 | 1.70186 | 0.850930 | − | 0.525279i | \(-0.176039\pi\) | ||||
0.850930 | + | 0.525279i | \(0.176039\pi\) | |||||||
\(348\) | 22.0789 | 1.18355 | ||||||||
\(349\) | −7.86184 | −0.420835 | −0.210417 | − | 0.977612i | \(-0.567482\pi\) | ||||
−0.210417 | + | 0.977612i | \(0.567482\pi\) | |||||||
\(350\) | −37.4947 | −2.00418 | ||||||||
\(351\) | 5.48483 | 0.292759 | ||||||||
\(352\) | 2.63858 | 0.140637 | ||||||||
\(353\) | −9.13306 | −0.486104 | −0.243052 | − | 0.970013i | \(-0.578149\pi\) | ||||
−0.243052 | + | 0.970013i | \(0.578149\pi\) | |||||||
\(354\) | −17.8053 | −0.946341 | ||||||||
\(355\) | −29.1802 | −1.54872 | ||||||||
\(356\) | −0.479017 | −0.0253878 | ||||||||
\(357\) | 23.8881 | 1.26429 | ||||||||
\(358\) | −29.0962 | −1.53778 | ||||||||
\(359\) | −19.0364 | −1.00470 | −0.502352 | − | 0.864663i | \(-0.667532\pi\) | ||||
−0.502352 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(360\) | 1.45904 | 0.0768984 | ||||||||
\(361\) | −10.0850 | −0.530792 | ||||||||
\(362\) | 39.8931 | 2.09673 | ||||||||
\(363\) | 13.1573 | 0.690582 | ||||||||
\(364\) | 7.88357 | 0.413211 | ||||||||
\(365\) | −12.5538 | −0.657096 | ||||||||
\(366\) | 18.0657 | 0.944311 | ||||||||
\(367\) | −34.4748 | −1.79957 | −0.899786 | − | 0.436332i | \(-0.856277\pi\) | ||||
−0.899786 | + | 0.436332i | \(0.856277\pi\) | |||||||
\(368\) | 17.6967 | 0.922502 | ||||||||
\(369\) | −1.76616 | −0.0919424 | ||||||||
\(370\) | −41.7514 | −2.17055 | ||||||||
\(371\) | −6.10552 | −0.316983 | ||||||||
\(372\) | −8.56184 | −0.443911 | ||||||||
\(373\) | 20.8863 | 1.08145 | 0.540725 | − | 0.841199i | \(-0.318150\pi\) | ||||
0.540725 | + | 0.841199i | \(0.318150\pi\) | |||||||
\(374\) | 3.57228 | 0.184718 | ||||||||
\(375\) | −0.0540697 | −0.00279215 | ||||||||
\(376\) | 2.25934 | 0.116517 | ||||||||
\(377\) | −8.51496 | −0.438543 | ||||||||
\(378\) | −41.0144 | −2.10955 | ||||||||
\(379\) | 27.5913 | 1.41727 | 0.708635 | − | 0.705576i | \(-0.249312\pi\) | ||||
0.708635 | + | 0.705576i | \(0.249312\pi\) | |||||||
\(380\) | 20.2851 | 1.04061 | ||||||||
\(381\) | 25.9411 | 1.32900 | ||||||||
\(382\) | 39.5704 | 2.02460 | ||||||||
\(383\) | 1.49392 | 0.0763359 | 0.0381680 | − | 0.999271i | \(-0.487848\pi\) | ||||
0.0381680 | + | 0.999271i | \(0.487848\pi\) | |||||||
\(384\) | −2.88255 | −0.147099 | ||||||||
\(385\) | 3.78456 | 0.192879 | ||||||||
\(386\) | 48.6932 | 2.47842 | ||||||||
\(387\) | 5.97464 | 0.303708 | ||||||||
\(388\) | −19.1240 | −0.970876 | ||||||||
\(389\) | 23.5649 | 1.19479 | 0.597393 | − | 0.801948i | \(-0.296203\pi\) | ||||
0.597393 | + | 0.801948i | \(0.296203\pi\) | |||||||
\(390\) | 7.78310 | 0.394112 | ||||||||
\(391\) | 25.8693 | 1.30827 | ||||||||
\(392\) | −1.93967 | −0.0979681 | ||||||||
\(393\) | 11.4726 | 0.578717 | ||||||||
\(394\) | 15.3500 | 0.773324 | ||||||||
\(395\) | −47.4040 | −2.38516 | ||||||||
\(396\) | −1.07769 | −0.0541560 | ||||||||
\(397\) | −18.8816 | −0.947638 | −0.473819 | − | 0.880622i | \(-0.657125\pi\) | ||||
−0.473819 | + | 0.880622i | \(0.657125\pi\) | |||||||
\(398\) | −16.6163 | −0.832900 | ||||||||
\(399\) | −13.2420 | −0.662931 | ||||||||
\(400\) | −18.4753 | −0.923763 | ||||||||
\(401\) | 13.6578 | 0.682038 | 0.341019 | − | 0.940056i | \(-0.389228\pi\) | ||||
0.341019 | + | 0.940056i | \(0.389228\pi\) | |||||||
\(402\) | −25.7273 | −1.28316 | ||||||||
\(403\) | 3.30196 | 0.164482 | ||||||||
\(404\) | 4.70033 | 0.233850 | ||||||||
\(405\) | −6.33069 | −0.314574 | ||||||||
\(406\) | 63.6731 | 3.16004 | ||||||||
\(407\) | 2.11008 | 0.104593 | ||||||||
\(408\) | −1.94602 | −0.0963421 | ||||||||
\(409\) | 4.14536 | 0.204975 | 0.102487 | − | 0.994734i | \(-0.467320\pi\) | ||||
0.102487 | + | 0.994734i | \(0.467320\pi\) | |||||||
\(410\) | −7.38435 | −0.364687 | ||||||||
\(411\) | −11.3497 | −0.559840 | ||||||||
\(412\) | 20.6417 | 1.01694 | ||||||||
\(413\) | −26.5837 | −1.30810 | ||||||||
\(414\) | −15.0746 | −0.740875 | ||||||||
\(415\) | −13.2181 | −0.648850 | ||||||||
\(416\) | 8.10163 | 0.397215 | ||||||||
\(417\) | −20.9953 | −1.02814 | ||||||||
\(418\) | −1.98024 | −0.0968568 | ||||||||
\(419\) | −3.77620 | −0.184480 | −0.0922398 | − | 0.995737i | \(-0.529403\pi\) | ||||
−0.0922398 | + | 0.995737i | \(0.529403\pi\) | |||||||
\(420\) | −30.1310 | −1.47024 | ||||||||
\(421\) | 12.9866 | 0.632930 | 0.316465 | − | 0.948604i | \(-0.397504\pi\) | ||||
0.316465 | + | 0.948604i | \(0.397504\pi\) | |||||||
\(422\) | −3.72125 | −0.181148 | ||||||||
\(423\) | 11.6411 | 0.566007 | ||||||||
\(424\) | 0.497379 | 0.0241548 | ||||||||
\(425\) | −27.0075 | −1.31005 | ||||||||
\(426\) | −22.6791 | −1.09881 | ||||||||
\(427\) | 26.9725 | 1.30529 | ||||||||
\(428\) | −2.37906 | −0.114996 | ||||||||
\(429\) | −0.393351 | −0.0189912 | ||||||||
\(430\) | 24.9801 | 1.20465 | ||||||||
\(431\) | −23.6577 | −1.13955 | −0.569776 | − | 0.821800i | \(-0.692970\pi\) | ||||
−0.569776 | + | 0.821800i | \(0.692970\pi\) | |||||||
\(432\) | −20.2096 | −0.972333 | ||||||||
\(433\) | 1.49669 | 0.0719265 | 0.0359633 | − | 0.999353i | \(-0.488550\pi\) | ||||
0.0359633 | + | 0.999353i | \(0.488550\pi\) | |||||||
\(434\) | −24.6914 | −1.18522 | ||||||||
\(435\) | 32.5442 | 1.56037 | ||||||||
\(436\) | −1.63291 | −0.0782024 | ||||||||
\(437\) | −14.3403 | −0.685988 | ||||||||
\(438\) | −9.75694 | −0.466205 | ||||||||
\(439\) | −30.6552 | −1.46310 | −0.731548 | − | 0.681790i | \(-0.761202\pi\) | ||||
−0.731548 | + | 0.681790i | \(0.761202\pi\) | |||||||
\(440\) | −0.308305 | −0.0146978 | ||||||||
\(441\) | −9.99396 | −0.475903 | ||||||||
\(442\) | 10.9685 | 0.521720 | ||||||||
\(443\) | 6.73875 | 0.320168 | 0.160084 | − | 0.987103i | \(-0.448824\pi\) | ||||
0.160084 | + | 0.987103i | \(0.448824\pi\) | |||||||
\(444\) | −16.7995 | −0.797271 | ||||||||
\(445\) | −0.706067 | −0.0334708 | ||||||||
\(446\) | −42.0010 | −1.98880 | ||||||||
\(447\) | −3.29247 | −0.155728 | ||||||||
\(448\) | −33.5218 | −1.58376 | ||||||||
\(449\) | −16.9851 | −0.801578 | −0.400789 | − | 0.916170i | \(-0.631264\pi\) | ||||
−0.400789 | + | 0.916170i | \(0.631264\pi\) | |||||||
\(450\) | 15.7378 | 0.741888 | ||||||||
\(451\) | 0.373199 | 0.0175733 | ||||||||
\(452\) | −0.806427 | −0.0379311 | ||||||||
\(453\) | −12.9378 | −0.607871 | ||||||||
\(454\) | −37.7179 | −1.77019 | ||||||||
\(455\) | 11.6203 | 0.544769 | ||||||||
\(456\) | 1.07875 | 0.0505169 | ||||||||
\(457\) | 7.20357 | 0.336969 | 0.168484 | − | 0.985704i | \(-0.446113\pi\) | ||||
0.168484 | + | 0.985704i | \(0.446113\pi\) | |||||||
\(458\) | 32.9547 | 1.53987 | ||||||||
\(459\) | −29.5427 | −1.37894 | ||||||||
\(460\) | −32.6299 | −1.52138 | ||||||||
\(461\) | 11.3545 | 0.528830 | 0.264415 | − | 0.964409i | \(-0.414821\pi\) | ||||
0.264415 | + | 0.964409i | \(0.414821\pi\) | |||||||
\(462\) | 2.94140 | 0.136846 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | 31.3744 | 1.45652 | ||||||||
\(465\) | −12.6201 | −0.585243 | ||||||||
\(466\) | −28.9530 | −1.34122 | ||||||||
\(467\) | 10.4290 | 0.482598 | 0.241299 | − | 0.970451i | \(-0.422427\pi\) | ||||
0.241299 | + | 0.970451i | \(0.422427\pi\) | |||||||
\(468\) | −3.30900 | −0.152959 | ||||||||
\(469\) | −38.4115 | −1.77368 | ||||||||
\(470\) | 48.6715 | 2.24505 | ||||||||
\(471\) | 19.8890 | 0.916434 | ||||||||
\(472\) | 2.16561 | 0.0996802 | ||||||||
\(473\) | −1.26248 | −0.0580487 | ||||||||
\(474\) | −36.8429 | −1.69225 | ||||||||
\(475\) | 14.9712 | 0.686926 | ||||||||
\(476\) | −42.4629 | −1.94628 | ||||||||
\(477\) | 2.56270 | 0.117338 | ||||||||
\(478\) | 23.6884 | 1.08348 | ||||||||
\(479\) | −5.63936 | −0.257669 | −0.128835 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128835 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(480\) | −30.9644 | −1.41333 | ||||||||
\(481\) | 6.47891 | 0.295413 | ||||||||
\(482\) | −14.1151 | −0.642925 | ||||||||
\(483\) | 21.3007 | 0.969214 | ||||||||
\(484\) | −23.3881 | −1.06310 | ||||||||
\(485\) | −28.1887 | −1.27998 | ||||||||
\(486\) | 28.5876 | 1.29676 | ||||||||
\(487\) | −32.3977 | −1.46808 | −0.734040 | − | 0.679107i | \(-0.762367\pi\) | ||||
−0.734040 | + | 0.679107i | \(0.762367\pi\) | |||||||
\(488\) | −2.19728 | −0.0994663 | ||||||||
\(489\) | −26.1233 | −1.18134 | ||||||||
\(490\) | −41.7850 | −1.88765 | ||||||||
\(491\) | −6.11571 | −0.275998 | −0.137999 | − | 0.990432i | \(-0.544067\pi\) | ||||
−0.137999 | + | 0.990432i | \(0.544067\pi\) | |||||||
\(492\) | −2.97124 | −0.133954 | ||||||||
\(493\) | 45.8637 | 2.06560 | ||||||||
\(494\) | −6.08025 | −0.273563 | ||||||||
\(495\) | −1.58851 | −0.0713982 | ||||||||
\(496\) | −12.1665 | −0.546292 | ||||||||
\(497\) | −33.8604 | −1.51885 | ||||||||
\(498\) | −10.2732 | −0.460354 | ||||||||
\(499\) | 21.7925 | 0.975568 | 0.487784 | − | 0.872964i | \(-0.337805\pi\) | ||||
0.487784 | + | 0.872964i | \(0.337805\pi\) | |||||||
\(500\) | 0.0961128 | 0.00429830 | ||||||||
\(501\) | 28.7956 | 1.28649 | ||||||||
\(502\) | 5.71429 | 0.255041 | ||||||||
\(503\) | 5.60934 | 0.250108 | 0.125054 | − | 0.992150i | \(-0.460090\pi\) | ||||
0.125054 | + | 0.992150i | \(0.460090\pi\) | |||||||
\(504\) | 1.69306 | 0.0754150 | ||||||||
\(505\) | 6.92826 | 0.308304 | ||||||||
\(506\) | 3.18535 | 0.141606 | ||||||||
\(507\) | −1.20777 | −0.0536389 | ||||||||
\(508\) | −46.1122 | −2.04590 | ||||||||
\(509\) | −42.5667 | −1.88674 | −0.943368 | − | 0.331749i | \(-0.892361\pi\) | ||||
−0.943368 | + | 0.331749i | \(0.892361\pi\) | |||||||
\(510\) | −41.9217 | −1.85632 | ||||||||
\(511\) | −14.5673 | −0.644420 | ||||||||
\(512\) | −32.0559 | −1.41669 | ||||||||
\(513\) | 16.3766 | 0.723043 | ||||||||
\(514\) | 36.1203 | 1.59320 | ||||||||
\(515\) | 30.4258 | 1.34072 | ||||||||
\(516\) | 10.0513 | 0.442482 | ||||||||
\(517\) | −2.45982 | −0.108183 | ||||||||
\(518\) | −48.4479 | −2.12868 | ||||||||
\(519\) | −10.7286 | −0.470932 | ||||||||
\(520\) | −0.946636 | −0.0415127 | ||||||||
\(521\) | 10.7733 | 0.471988 | 0.235994 | − | 0.971754i | \(-0.424165\pi\) | ||||
0.235994 | + | 0.971754i | \(0.424165\pi\) | |||||||
\(522\) | −26.7258 | −1.16975 | ||||||||
\(523\) | −12.9543 | −0.566450 | −0.283225 | − | 0.959053i | \(-0.591404\pi\) | ||||
−0.283225 | + | 0.959053i | \(0.591404\pi\) | |||||||
\(524\) | −20.3934 | −0.890891 | ||||||||
\(525\) | −22.2378 | −0.970538 | ||||||||
\(526\) | −8.15545 | −0.355594 | ||||||||
\(527\) | −17.7852 | −0.774736 | ||||||||
\(528\) | 1.44935 | 0.0630750 | ||||||||
\(529\) | 0.0672478 | 0.00292382 | ||||||||
\(530\) | 10.7147 | 0.465417 | ||||||||
\(531\) | 11.1581 | 0.484220 | ||||||||
\(532\) | 23.5387 | 1.02053 | ||||||||
\(533\) | 1.14589 | 0.0496341 | ||||||||
\(534\) | −0.548763 | −0.0237473 | ||||||||
\(535\) | −3.50672 | −0.151609 | ||||||||
\(536\) | 3.12914 | 0.135158 | ||||||||
\(537\) | −17.2567 | −0.744683 | ||||||||
\(538\) | −9.49072 | −0.409174 | ||||||||
\(539\) | 2.11178 | 0.0909608 | ||||||||
\(540\) | 37.2633 | 1.60356 | ||||||||
\(541\) | −5.89003 | −0.253232 | −0.126616 | − | 0.991952i | \(-0.540412\pi\) | ||||
−0.126616 | + | 0.991952i | \(0.540412\pi\) | |||||||
\(542\) | 3.55374 | 0.152646 | ||||||||
\(543\) | 23.6603 | 1.01536 | ||||||||
\(544\) | −43.6374 | −1.87094 | ||||||||
\(545\) | −2.40691 | −0.103100 | ||||||||
\(546\) | 9.03144 | 0.386510 | ||||||||
\(547\) | 18.2027 | 0.778293 | 0.389146 | − | 0.921176i | \(-0.372770\pi\) | ||||
0.389146 | + | 0.921176i | \(0.372770\pi\) | |||||||
\(548\) | 20.1749 | 0.861831 | ||||||||
\(549\) | −11.3213 | −0.483181 | ||||||||
\(550\) | −3.32549 | −0.141799 | ||||||||
\(551\) | −25.4239 | −1.08309 | ||||||||
\(552\) | −1.73523 | −0.0738564 | ||||||||
\(553\) | −55.0072 | −2.33915 | ||||||||
\(554\) | 25.1126 | 1.06693 | ||||||||
\(555\) | −24.7624 | −1.05111 | ||||||||
\(556\) | 37.3207 | 1.58275 | ||||||||
\(557\) | 29.2708 | 1.24024 | 0.620121 | − | 0.784506i | \(-0.287083\pi\) | ||||
0.620121 | + | 0.784506i | \(0.287083\pi\) | |||||||
\(558\) | 10.3638 | 0.438735 | ||||||||
\(559\) | −3.87638 | −0.163953 | ||||||||
\(560\) | −42.8166 | −1.80933 | ||||||||
\(561\) | 2.11869 | 0.0894512 | ||||||||
\(562\) | −41.7003 | −1.75902 | ||||||||
\(563\) | −22.9899 | −0.968910 | −0.484455 | − | 0.874816i | \(-0.660982\pi\) | ||||
−0.484455 | + | 0.874816i | \(0.660982\pi\) | |||||||
\(564\) | 19.5840 | 0.824635 | ||||||||
\(565\) | −1.18867 | −0.0500076 | ||||||||
\(566\) | −2.79168 | −0.117343 | ||||||||
\(567\) | −7.34607 | −0.308506 | ||||||||
\(568\) | 2.75840 | 0.115740 | ||||||||
\(569\) | −15.3968 | −0.645466 | −0.322733 | − | 0.946490i | \(-0.604602\pi\) | ||||
−0.322733 | + | 0.946490i | \(0.604602\pi\) | |||||||
\(570\) | 23.2387 | 0.973362 | ||||||||
\(571\) | 1.66828 | 0.0698154 | 0.0349077 | − | 0.999391i | \(-0.488886\pi\) | ||||
0.0349077 | + | 0.999391i | \(0.488886\pi\) | |||||||
\(572\) | 0.699211 | 0.0292355 | ||||||||
\(573\) | 23.4689 | 0.980427 | ||||||||
\(574\) | −8.56873 | −0.357652 | ||||||||
\(575\) | −24.0821 | −1.00429 | ||||||||
\(576\) | 14.0703 | 0.586261 | ||||||||
\(577\) | 10.8345 | 0.451047 | 0.225523 | − | 0.974238i | \(-0.427591\pi\) | ||||
0.225523 | + | 0.974238i | \(0.427591\pi\) | |||||||
\(578\) | −24.4606 | −1.01743 | ||||||||
\(579\) | 28.8795 | 1.20019 | ||||||||
\(580\) | −57.8497 | −2.40208 | ||||||||
\(581\) | −15.3381 | −0.636333 | ||||||||
\(582\) | −21.9086 | −0.908139 | ||||||||
\(583\) | −0.541512 | −0.0224271 | ||||||||
\(584\) | 1.18671 | 0.0491064 | ||||||||
\(585\) | −4.87745 | −0.201658 | ||||||||
\(586\) | −25.3578 | −1.04752 | ||||||||
\(587\) | −35.2224 | −1.45378 | −0.726892 | − | 0.686751i | \(-0.759036\pi\) | ||||
−0.726892 | + | 0.686751i | \(0.759036\pi\) | |||||||
\(588\) | −16.8131 | −0.693359 | ||||||||
\(589\) | 9.85897 | 0.406232 | ||||||||
\(590\) | 46.6523 | 1.92064 | ||||||||
\(591\) | 9.10398 | 0.374488 | ||||||||
\(592\) | −23.8724 | −0.981149 | ||||||||
\(593\) | −33.5346 | −1.37710 | −0.688551 | − | 0.725188i | \(-0.741753\pi\) | ||||
−0.688551 | + | 0.725188i | \(0.741753\pi\) | |||||||
\(594\) | −3.63766 | −0.149255 | ||||||||
\(595\) | −62.5900 | −2.56594 | ||||||||
\(596\) | 5.85260 | 0.239732 | ||||||||
\(597\) | −9.85500 | −0.403338 | ||||||||
\(598\) | 9.78047 | 0.399953 | ||||||||
\(599\) | 23.3052 | 0.952223 | 0.476112 | − | 0.879385i | \(-0.342046\pi\) | ||||
0.476112 | + | 0.879385i | \(0.342046\pi\) | |||||||
\(600\) | 1.81158 | 0.0739573 | ||||||||
\(601\) | 34.3096 | 1.39952 | 0.699759 | − | 0.714379i | \(-0.253291\pi\) | ||||
0.699759 | + | 0.714379i | \(0.253291\pi\) | |||||||
\(602\) | 28.9867 | 1.18141 | ||||||||
\(603\) | 16.1226 | 0.656563 | ||||||||
\(604\) | 22.9979 | 0.935771 | ||||||||
\(605\) | −34.4740 | −1.40157 | ||||||||
\(606\) | 5.38471 | 0.218739 | ||||||||
\(607\) | 3.25199 | 0.131994 | 0.0659972 | − | 0.997820i | \(-0.478977\pi\) | ||||
0.0659972 | + | 0.997820i | \(0.478977\pi\) | |||||||
\(608\) | 24.1898 | 0.981025 | ||||||||
\(609\) | 37.7640 | 1.53027 | ||||||||
\(610\) | −47.3346 | −1.91652 | ||||||||
\(611\) | −7.55277 | −0.305552 | ||||||||
\(612\) | 17.8231 | 0.720457 | ||||||||
\(613\) | 40.9545 | 1.65414 | 0.827069 | − | 0.562101i | \(-0.190007\pi\) | ||||
0.827069 | + | 0.562101i | \(0.190007\pi\) | |||||||
\(614\) | −37.1892 | −1.50083 | ||||||||
\(615\) | −4.37960 | −0.176602 | ||||||||
\(616\) | −0.357754 | −0.0144143 | ||||||||
\(617\) | 2.51153 | 0.101110 | 0.0505552 | − | 0.998721i | \(-0.483901\pi\) | ||||
0.0505552 | + | 0.998721i | \(0.483901\pi\) | |||||||
\(618\) | 23.6472 | 0.951231 | ||||||||
\(619\) | 44.6593 | 1.79501 | 0.897505 | − | 0.441005i | \(-0.145378\pi\) | ||||
0.897505 | + | 0.441005i | \(0.145378\pi\) | |||||||
\(620\) | 22.4332 | 0.900937 | ||||||||
\(621\) | −26.3428 | −1.05710 | ||||||||
\(622\) | −32.8194 | −1.31594 | ||||||||
\(623\) | −0.819315 | −0.0328251 | ||||||||
\(624\) | 4.45018 | 0.178150 | ||||||||
\(625\) | −24.9291 | −0.997163 | ||||||||
\(626\) | −50.3150 | −2.01099 | ||||||||
\(627\) | −1.17447 | −0.0469036 | ||||||||
\(628\) | −35.3541 | −1.41078 | ||||||||
\(629\) | −34.8971 | −1.39144 | ||||||||
\(630\) | 36.4725 | 1.45310 | ||||||||
\(631\) | 0.155159 | 0.00617678 | 0.00308839 | − | 0.999995i | \(-0.499017\pi\) | ||||
0.00308839 | + | 0.999995i | \(0.499017\pi\) | |||||||
\(632\) | 4.48110 | 0.178248 | ||||||||
\(633\) | −2.20705 | −0.0877222 | ||||||||
\(634\) | 15.8453 | 0.629299 | ||||||||
\(635\) | −67.9692 | −2.69727 | ||||||||
\(636\) | 4.31128 | 0.170953 | ||||||||
\(637\) | 6.48413 | 0.256911 | ||||||||
\(638\) | 5.64731 | 0.223579 | ||||||||
\(639\) | 14.2124 | 0.562233 | ||||||||
\(640\) | 7.55266 | 0.298545 | ||||||||
\(641\) | −20.0369 | −0.791410 | −0.395705 | − | 0.918378i | \(-0.629500\pi\) | ||||
−0.395705 | + | 0.918378i | \(0.629500\pi\) | |||||||
\(642\) | −2.72546 | −0.107565 | ||||||||
\(643\) | 34.1066 | 1.34503 | 0.672516 | − | 0.740082i | \(-0.265213\pi\) | ||||
0.672516 | + | 0.740082i | \(0.265213\pi\) | |||||||
\(644\) | −37.8635 | −1.49203 | ||||||||
\(645\) | 14.8155 | 0.583360 | ||||||||
\(646\) | 32.7497 | 1.28852 | ||||||||
\(647\) | −1.07534 | −0.0422760 | −0.0211380 | − | 0.999777i | \(-0.506729\pi\) | ||||
−0.0211380 | + | 0.999777i | \(0.506729\pi\) | |||||||
\(648\) | 0.598439 | 0.0235089 | ||||||||
\(649\) | −2.35777 | −0.0925505 | ||||||||
\(650\) | −10.2108 | −0.400500 | ||||||||
\(651\) | −14.6443 | −0.573954 | ||||||||
\(652\) | 46.4361 | 1.81858 | ||||||||
\(653\) | −39.5979 | −1.54959 | −0.774793 | − | 0.632215i | \(-0.782146\pi\) | ||||
−0.774793 | + | 0.632215i | \(0.782146\pi\) | |||||||
\(654\) | −1.87067 | −0.0731490 | ||||||||
\(655\) | −30.0598 | −1.17453 | ||||||||
\(656\) | −4.22218 | −0.164848 | ||||||||
\(657\) | 6.11440 | 0.238546 | ||||||||
\(658\) | 56.4780 | 2.20174 | ||||||||
\(659\) | −8.20392 | −0.319579 | −0.159790 | − | 0.987151i | \(-0.551082\pi\) | ||||
−0.159790 | + | 0.987151i | \(0.551082\pi\) | |||||||
\(660\) | −2.67239 | −0.104022 | ||||||||
\(661\) | −45.5675 | −1.77237 | −0.886186 | − | 0.463330i | \(-0.846655\pi\) | ||||
−0.886186 | + | 0.463330i | \(0.846655\pi\) | |||||||
\(662\) | 13.1920 | 0.512722 | ||||||||
\(663\) | 6.50535 | 0.252647 | ||||||||
\(664\) | 1.24950 | 0.0484901 | ||||||||
\(665\) | 34.6959 | 1.34545 | ||||||||
\(666\) | 20.3353 | 0.787975 | ||||||||
\(667\) | 40.8960 | 1.58350 | ||||||||
\(668\) | −51.1862 | −1.98045 | ||||||||
\(669\) | −24.9104 | −0.963093 | ||||||||
\(670\) | 67.4090 | 2.60424 | ||||||||
\(671\) | 2.39225 | 0.0923519 | ||||||||
\(672\) | −35.9309 | −1.38606 | ||||||||
\(673\) | 4.58451 | 0.176720 | 0.0883600 | − | 0.996089i | \(-0.471837\pi\) | ||||
0.0883600 | + | 0.996089i | \(0.471837\pi\) | |||||||
\(674\) | −13.7051 | −0.527901 | ||||||||
\(675\) | 27.5018 | 1.05854 | ||||||||
\(676\) | 2.14690 | 0.0825730 | ||||||||
\(677\) | −23.2884 | −0.895048 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(678\) | −0.923845 | −0.0354800 | ||||||||
\(679\) | −32.7099 | −1.25529 | ||||||||
\(680\) | 5.09882 | 0.195531 | ||||||||
\(681\) | −22.3702 | −0.857227 | ||||||||
\(682\) | −2.18993 | −0.0838569 | ||||||||
\(683\) | 24.8311 | 0.950134 | 0.475067 | − | 0.879950i | \(-0.342424\pi\) | ||||
0.475067 | + | 0.879950i | \(0.342424\pi\) | |||||||
\(684\) | −9.87999 | −0.377771 | ||||||||
\(685\) | 29.7377 | 1.13622 | ||||||||
\(686\) | 3.85756 | 0.147282 | ||||||||
\(687\) | 19.5452 | 0.745695 | ||||||||
\(688\) | 14.2830 | 0.544534 | ||||||||
\(689\) | −1.66269 | −0.0633434 | ||||||||
\(690\) | −37.3809 | −1.42307 | ||||||||
\(691\) | 14.6146 | 0.555967 | 0.277984 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277984 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(692\) | 19.0708 | 0.724964 | ||||||||
\(693\) | −1.84329 | −0.0700209 | ||||||||
\(694\) | −64.5580 | −2.45059 | ||||||||
\(695\) | 55.0104 | 2.08666 | ||||||||
\(696\) | −3.07640 | −0.116610 | ||||||||
\(697\) | −6.17206 | −0.233783 | ||||||||
\(698\) | 16.0098 | 0.605980 | ||||||||
\(699\) | −17.1718 | −0.649496 | ||||||||
\(700\) | 39.5294 | 1.49407 | ||||||||
\(701\) | −50.0742 | −1.89127 | −0.945637 | − | 0.325223i | \(-0.894561\pi\) | ||||
−0.945637 | + | 0.325223i | \(0.894561\pi\) | |||||||
\(702\) | −11.1693 | −0.421557 | ||||||||
\(703\) | 19.3447 | 0.729599 | ||||||||
\(704\) | −2.97313 | −0.112054 | ||||||||
\(705\) | 28.8667 | 1.08718 | ||||||||
\(706\) | 18.5985 | 0.699964 | ||||||||
\(707\) | 8.03949 | 0.302356 | ||||||||
\(708\) | 18.7715 | 0.705476 | ||||||||
\(709\) | −18.1534 | −0.681766 | −0.340883 | − | 0.940106i | \(-0.610726\pi\) | ||||
−0.340883 | + | 0.940106i | \(0.610726\pi\) | |||||||
\(710\) | 59.4223 | 2.23008 | ||||||||
\(711\) | 23.0884 | 0.865883 | ||||||||
\(712\) | 0.0667444 | 0.00250135 | ||||||||
\(713\) | −15.8588 | −0.593916 | ||||||||
\(714\) | −48.6456 | −1.82052 | ||||||||
\(715\) | 1.03063 | 0.0385435 | ||||||||
\(716\) | 30.6751 | 1.14638 | ||||||||
\(717\) | 14.0494 | 0.524684 | ||||||||
\(718\) | 38.7656 | 1.44672 | ||||||||
\(719\) | −29.9414 | −1.11663 | −0.558313 | − | 0.829631i | \(-0.688551\pi\) | ||||
−0.558313 | + | 0.829631i | \(0.688551\pi\) | |||||||
\(720\) | 17.9716 | 0.669761 | ||||||||
\(721\) | 35.3058 | 1.31486 | ||||||||
\(722\) | 20.5371 | 0.764313 | ||||||||
\(723\) | −8.37155 | −0.311341 | ||||||||
\(724\) | −42.0578 | −1.56307 | ||||||||
\(725\) | −42.6953 | −1.58566 | ||||||||
\(726\) | −26.7935 | −0.994401 | ||||||||
\(727\) | 18.1382 | 0.672710 | 0.336355 | − | 0.941735i | \(-0.390806\pi\) | ||||
0.336355 | + | 0.941735i | \(0.390806\pi\) | |||||||
\(728\) | −1.09847 | −0.0407119 | ||||||||
\(729\) | 22.9566 | 0.850245 | ||||||||
\(730\) | 25.5645 | 0.946184 | ||||||||
\(731\) | 20.8791 | 0.772243 | ||||||||
\(732\) | −19.0461 | −0.703962 | ||||||||
\(733\) | −20.5141 | −0.757705 | −0.378852 | − | 0.925457i | \(-0.623681\pi\) | ||||
−0.378852 | + | 0.925457i | \(0.623681\pi\) | |||||||
\(734\) | 70.2043 | 2.59129 | ||||||||
\(735\) | −24.7823 | −0.914111 | ||||||||
\(736\) | −38.9108 | −1.43427 | ||||||||
\(737\) | −3.40680 | −0.125491 | ||||||||
\(738\) | 3.59659 | 0.132392 | ||||||||
\(739\) | −29.4397 | −1.08296 | −0.541479 | − | 0.840715i | \(-0.682135\pi\) | ||||
−0.541479 | + | 0.840715i | \(0.682135\pi\) | |||||||
\(740\) | 44.0170 | 1.61810 | ||||||||
\(741\) | −3.60615 | −0.132475 | ||||||||
\(742\) | 12.4332 | 0.456439 | ||||||||
\(743\) | 10.9248 | 0.400791 | 0.200396 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200396 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(744\) | 1.19298 | 0.0437366 | ||||||||
\(745\) | 8.62670 | 0.316058 | ||||||||
\(746\) | −42.5327 | −1.55723 | ||||||||
\(747\) | 6.43794 | 0.235552 | ||||||||
\(748\) | −3.76613 | −0.137703 | ||||||||
\(749\) | −4.06917 | −0.148684 | ||||||||
\(750\) | 0.110107 | 0.00402054 | ||||||||
\(751\) | 47.3938 | 1.72942 | 0.864712 | − | 0.502268i | \(-0.167501\pi\) | ||||
0.864712 | + | 0.502268i | \(0.167501\pi\) | |||||||
\(752\) | 27.8291 | 1.01482 | ||||||||
\(753\) | 3.38910 | 0.123506 | ||||||||
\(754\) | 17.3398 | 0.631479 | ||||||||
\(755\) | 33.8988 | 1.23370 | ||||||||
\(756\) | 43.2401 | 1.57263 | ||||||||
\(757\) | 20.6881 | 0.751923 | 0.375961 | − | 0.926635i | \(-0.377312\pi\) | ||||
0.375961 | + | 0.926635i | \(0.377312\pi\) | |||||||
\(758\) | −56.1867 | −2.04079 | ||||||||
\(759\) | 1.88920 | 0.0685737 | ||||||||
\(760\) | −2.82646 | −0.102526 | ||||||||
\(761\) | 3.15824 | 0.114486 | 0.0572431 | − | 0.998360i | \(-0.481769\pi\) | ||||
0.0572431 | + | 0.998360i | \(0.481769\pi\) | |||||||
\(762\) | −52.8263 | −1.91370 | ||||||||
\(763\) | −2.79295 | −0.101112 | ||||||||
\(764\) | −41.7177 | −1.50929 | ||||||||
\(765\) | 26.2712 | 0.949836 | ||||||||
\(766\) | −3.04222 | −0.109920 | ||||||||
\(767\) | −7.23942 | −0.261400 | ||||||||
\(768\) | −16.1811 | −0.583884 | ||||||||
\(769\) | 6.44023 | 0.232241 | 0.116120 | − | 0.993235i | \(-0.462954\pi\) | ||||
0.116120 | + | 0.993235i | \(0.462954\pi\) | |||||||
\(770\) | −7.70685 | −0.277736 | ||||||||
\(771\) | 21.4227 | 0.771519 | ||||||||
\(772\) | −51.3355 | −1.84761 | ||||||||
\(773\) | 3.65404 | 0.131427 | 0.0657133 | − | 0.997839i | \(-0.479068\pi\) | ||||
0.0657133 | + | 0.997839i | \(0.479068\pi\) | |||||||
\(774\) | −12.1667 | −0.437324 | ||||||||
\(775\) | 16.5565 | 0.594728 | ||||||||
\(776\) | 2.66467 | 0.0956562 | ||||||||
\(777\) | −28.7341 | −1.03083 | ||||||||
\(778\) | −47.9874 | −1.72043 | ||||||||
\(779\) | 3.42139 | 0.122584 | ||||||||
\(780\) | −8.20544 | −0.293802 | ||||||||
\(781\) | −3.00316 | −0.107461 | ||||||||
\(782\) | −52.6801 | −1.88384 | ||||||||
\(783\) | −46.7031 | −1.66903 | ||||||||
\(784\) | −23.8916 | −0.853271 | ||||||||
\(785\) | −52.1117 | −1.85995 | ||||||||
\(786\) | −23.3628 | −0.833323 | ||||||||
\(787\) | 22.6759 | 0.808308 | 0.404154 | − | 0.914691i | \(-0.367566\pi\) | ||||
0.404154 | + | 0.914691i | \(0.367566\pi\) | |||||||
\(788\) | −16.1830 | −0.576495 | ||||||||
\(789\) | −4.83693 | −0.172199 | ||||||||
\(790\) | 96.5333 | 3.43450 | ||||||||
\(791\) | −1.37932 | −0.0490430 | ||||||||
\(792\) | 0.150162 | 0.00533576 | ||||||||
\(793\) | 7.34531 | 0.260840 | ||||||||
\(794\) | 38.4503 | 1.36455 | ||||||||
\(795\) | 6.35480 | 0.225382 | ||||||||
\(796\) | 17.5180 | 0.620908 | ||||||||
\(797\) | 25.2459 | 0.894256 | 0.447128 | − | 0.894470i | \(-0.352447\pi\) | ||||
0.447128 | + | 0.894470i | \(0.352447\pi\) | |||||||
\(798\) | 26.9660 | 0.954586 | ||||||||
\(799\) | 40.6811 | 1.43920 | ||||||||
\(800\) | 40.6228 | 1.43623 | ||||||||
\(801\) | 0.343894 | 0.0121509 | ||||||||
\(802\) | −27.8126 | −0.982099 | ||||||||
\(803\) | −1.29201 | −0.0455940 | ||||||||
\(804\) | 27.1234 | 0.956569 | ||||||||
\(805\) | −55.8106 | −1.96706 | ||||||||
\(806\) | −6.72410 | −0.236846 | ||||||||
\(807\) | −5.62887 | −0.198146 | ||||||||
\(808\) | −0.654927 | −0.0230403 | ||||||||
\(809\) | −16.1100 | −0.566396 | −0.283198 | − | 0.959061i | \(-0.591395\pi\) | ||||
−0.283198 | + | 0.959061i | \(0.591395\pi\) | |||||||
\(810\) | 12.8918 | 0.452971 | ||||||||
\(811\) | 27.7160 | 0.973239 | 0.486620 | − | 0.873614i | \(-0.338230\pi\) | ||||
0.486620 | + | 0.873614i | \(0.338230\pi\) | |||||||
\(812\) | −67.1283 | −2.35574 | ||||||||
\(813\) | 2.10770 | 0.0739202 | ||||||||
\(814\) | −4.29696 | −0.150608 | ||||||||
\(815\) | 68.4465 | 2.39758 | ||||||||
\(816\) | −23.9698 | −0.839110 | ||||||||
\(817\) | −11.5741 | −0.404925 | ||||||||
\(818\) | −8.44159 | −0.295153 | ||||||||
\(819\) | −5.65975 | −0.197768 | ||||||||
\(820\) | 7.78505 | 0.271866 | ||||||||
\(821\) | −47.9281 | −1.67270 | −0.836352 | − | 0.548193i | \(-0.815316\pi\) | ||||
−0.836352 | + | 0.548193i | \(0.815316\pi\) | |||||||
\(822\) | 23.1125 | 0.806140 | ||||||||
\(823\) | 8.70562 | 0.303459 | 0.151729 | − | 0.988422i | \(-0.451516\pi\) | ||||
0.151729 | + | 0.988422i | \(0.451516\pi\) | |||||||
\(824\) | −2.87614 | −0.100195 | ||||||||
\(825\) | −1.97232 | −0.0686674 | ||||||||
\(826\) | 54.1349 | 1.88359 | ||||||||
\(827\) | 28.2245 | 0.981462 | 0.490731 | − | 0.871311i | \(-0.336730\pi\) | ||||
0.490731 | + | 0.871311i | \(0.336730\pi\) | |||||||
\(828\) | 15.8926 | 0.552306 | ||||||||
\(829\) | −20.4121 | −0.708943 | −0.354472 | − | 0.935067i | \(-0.615339\pi\) | ||||
−0.354472 | + | 0.935067i | \(0.615339\pi\) | |||||||
\(830\) | 26.9172 | 0.934310 | ||||||||
\(831\) | 14.8941 | 0.516669 | ||||||||
\(832\) | −9.12885 | −0.316486 | ||||||||
\(833\) | −34.9252 | −1.21009 | ||||||||
\(834\) | 42.7547 | 1.48047 | ||||||||
\(835\) | −75.4482 | −2.61099 | ||||||||
\(836\) | 2.08770 | 0.0722046 | ||||||||
\(837\) | 18.1107 | 0.625998 | ||||||||
\(838\) | 7.68984 | 0.265641 | ||||||||
\(839\) | 0.349416 | 0.0120632 | 0.00603158 | − | 0.999982i | \(-0.498080\pi\) | ||||
0.00603158 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(840\) | 4.19834 | 0.144857 | ||||||||
\(841\) | 43.5045 | 1.50016 | ||||||||
\(842\) | −26.4459 | −0.911386 | ||||||||
\(843\) | −24.7321 | −0.851819 | ||||||||
\(844\) | 3.92319 | 0.135042 | ||||||||
\(845\) | 3.16451 | 0.108863 | ||||||||
\(846\) | −23.7058 | −0.815021 | ||||||||
\(847\) | −40.0033 | −1.37453 | ||||||||
\(848\) | 6.12639 | 0.210381 | ||||||||
\(849\) | −1.65572 | −0.0568242 | ||||||||
\(850\) | 54.9978 | 1.88641 | ||||||||
\(851\) | −31.1172 | −1.06668 | ||||||||
\(852\) | 23.9098 | 0.819136 | ||||||||
\(853\) | −32.8259 | −1.12394 | −0.561968 | − | 0.827159i | \(-0.689956\pi\) | ||||
−0.561968 | + | 0.827159i | \(0.689956\pi\) | |||||||
\(854\) | −54.9267 | −1.87955 | ||||||||
\(855\) | −14.5630 | −0.498046 | ||||||||
\(856\) | 0.331490 | 0.0113301 | ||||||||
\(857\) | 34.6302 | 1.18295 | 0.591473 | − | 0.806325i | \(-0.298547\pi\) | ||||
0.591473 | + | 0.806325i | \(0.298547\pi\) | |||||||
\(858\) | 0.801018 | 0.0273463 | ||||||||
\(859\) | 48.3834 | 1.65082 | 0.825410 | − | 0.564534i | \(-0.190944\pi\) | ||||
0.825410 | + | 0.564534i | \(0.190944\pi\) | |||||||
\(860\) | −26.3357 | −0.898038 | ||||||||
\(861\) | −5.08205 | −0.173196 | ||||||||
\(862\) | 48.1764 | 1.64089 | ||||||||
\(863\) | 27.8819 | 0.949110 | 0.474555 | − | 0.880226i | \(-0.342609\pi\) | ||||
0.474555 | + | 0.880226i | \(0.342609\pi\) | |||||||
\(864\) | 44.4361 | 1.51175 | ||||||||
\(865\) | 28.1103 | 0.955778 | ||||||||
\(866\) | −3.04786 | −0.103570 | ||||||||
\(867\) | −14.5074 | −0.492696 | ||||||||
\(868\) | 26.0312 | 0.883558 | ||||||||
\(869\) | −4.87872 | −0.165499 | ||||||||
\(870\) | −66.2727 | −2.24686 | ||||||||
\(871\) | −10.4604 | −0.354438 | ||||||||
\(872\) | 0.227524 | 0.00770495 | ||||||||
\(873\) | 13.7295 | 0.464672 | ||||||||
\(874\) | 29.2024 | 0.987787 | ||||||||
\(875\) | 0.164392 | 0.00555748 | ||||||||
\(876\) | 10.2864 | 0.347545 | ||||||||
\(877\) | −16.8052 | −0.567471 | −0.283736 | − | 0.958903i | \(-0.591574\pi\) | ||||
−0.283736 | + | 0.958903i | \(0.591574\pi\) | |||||||
\(878\) | 62.4261 | 2.10678 | ||||||||
\(879\) | −15.0395 | −0.507270 | ||||||||
\(880\) | −3.79750 | −0.128014 | ||||||||
\(881\) | 6.95008 | 0.234154 | 0.117077 | − | 0.993123i | \(-0.462648\pi\) | ||||
0.117077 | + | 0.993123i | \(0.462648\pi\) | |||||||
\(882\) | 20.3516 | 0.685275 | ||||||||
\(883\) | 28.0030 | 0.942376 | 0.471188 | − | 0.882033i | \(-0.343825\pi\) | ||||
0.471188 | + | 0.882033i | \(0.343825\pi\) | |||||||
\(884\) | −11.5637 | −0.388930 | ||||||||
\(885\) | 27.6691 | 0.930086 | ||||||||
\(886\) | −13.7227 | −0.461024 | ||||||||
\(887\) | 50.2416 | 1.68695 | 0.843475 | − | 0.537169i | \(-0.180506\pi\) | ||||
0.843475 | + | 0.537169i | \(0.180506\pi\) | |||||||
\(888\) | 2.34079 | 0.0785517 | ||||||||
\(889\) | −78.8708 | −2.64524 | ||||||||
\(890\) | 1.43783 | 0.0481962 | ||||||||
\(891\) | −0.651540 | −0.0218274 | ||||||||
\(892\) | 44.2801 | 1.48261 | ||||||||
\(893\) | −22.5510 | −0.754641 | ||||||||
\(894\) | 6.70475 | 0.224241 | ||||||||
\(895\) | 45.2149 | 1.51137 | ||||||||
\(896\) | 8.76404 | 0.292786 | ||||||||
\(897\) | 5.80072 | 0.193680 | ||||||||
\(898\) | 34.5884 | 1.15423 | ||||||||
\(899\) | −28.1161 | −0.937724 | ||||||||
\(900\) | −16.5918 | −0.553061 | ||||||||
\(901\) | 8.95567 | 0.298357 | ||||||||
\(902\) | −0.759980 | −0.0253046 | ||||||||
\(903\) | 17.1918 | 0.572107 | ||||||||
\(904\) | 0.112365 | 0.00373719 | ||||||||
\(905\) | −61.9930 | −2.06072 | ||||||||
\(906\) | 26.3465 | 0.875302 | ||||||||
\(907\) | 52.1191 | 1.73059 | 0.865293 | − | 0.501267i | \(-0.167133\pi\) | ||||
0.865293 | + | 0.501267i | \(0.167133\pi\) | |||||||
\(908\) | 39.7646 | 1.31964 | ||||||||
\(909\) | −3.37445 | −0.111923 | ||||||||
\(910\) | −23.6636 | −0.784439 | ||||||||
\(911\) | −48.6531 | −1.61195 | −0.805974 | − | 0.591951i | \(-0.798358\pi\) | ||||
−0.805974 | + | 0.591951i | \(0.798358\pi\) | |||||||
\(912\) | 13.2873 | 0.439986 | ||||||||
\(913\) | −1.36037 | −0.0450218 | ||||||||
\(914\) | −14.6693 | −0.485217 | ||||||||
\(915\) | −28.0738 | −0.928090 | ||||||||
\(916\) | −34.7430 | −1.14794 | ||||||||
\(917\) | −34.8811 | −1.15188 | ||||||||
\(918\) | 60.1606 | 1.98559 | ||||||||
\(919\) | −16.4346 | −0.542128 | −0.271064 | − | 0.962561i | \(-0.587376\pi\) | ||||
−0.271064 | + | 0.962561i | \(0.587376\pi\) | |||||||
\(920\) | 4.54654 | 0.149895 | ||||||||
\(921\) | −22.0566 | −0.726791 | ||||||||
\(922\) | −23.1222 | −0.761488 | ||||||||
\(923\) | −9.22106 | −0.303515 | ||||||||
\(924\) | −3.10101 | −0.102016 | ||||||||
\(925\) | 32.4862 | 1.06814 | ||||||||
\(926\) | −2.03639 | −0.0669200 | ||||||||
\(927\) | −14.8191 | −0.486722 | ||||||||
\(928\) | −68.9851 | −2.26455 | ||||||||
\(929\) | −8.18395 | −0.268507 | −0.134253 | − | 0.990947i | \(-0.542864\pi\) | ||||
−0.134253 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(930\) | 25.6995 | 0.842720 | ||||||||
\(931\) | 19.3603 | 0.634507 | ||||||||
\(932\) | 30.5241 | 0.999850 | ||||||||
\(933\) | −19.4649 | −0.637252 | ||||||||
\(934\) | −21.2376 | −0.694915 | ||||||||
\(935\) | −5.55125 | −0.181545 | ||||||||
\(936\) | 0.461064 | 0.0150704 | ||||||||
\(937\) | −40.7435 | −1.33103 | −0.665516 | − | 0.746384i | \(-0.731788\pi\) | ||||
−0.665516 | + | 0.746384i | \(0.731788\pi\) | |||||||
\(938\) | 78.2208 | 2.55400 | ||||||||
\(939\) | −29.8414 | −0.973838 | ||||||||
\(940\) | −51.3127 | −1.67363 | ||||||||
\(941\) | −20.8235 | −0.678826 | −0.339413 | − | 0.940637i | \(-0.610228\pi\) | ||||
−0.339413 | + | 0.940637i | \(0.610228\pi\) | |||||||
\(942\) | −40.5017 | −1.31962 | ||||||||
\(943\) | −5.50353 | −0.179220 | ||||||||
\(944\) | 26.6746 | 0.868183 | ||||||||
\(945\) | 63.7356 | 2.07332 | ||||||||
\(946\) | 2.57090 | 0.0835871 | ||||||||
\(947\) | −4.38750 | −0.142574 | −0.0712872 | − | 0.997456i | \(-0.522711\pi\) | ||||
−0.0712872 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(948\) | 38.8422 | 1.26153 | ||||||||
\(949\) | −3.96706 | −0.128776 | ||||||||
\(950\) | −30.4872 | −0.989137 | ||||||||
\(951\) | 9.39774 | 0.304743 | ||||||||
\(952\) | 5.91663 | 0.191759 | ||||||||
\(953\) | −7.57524 | −0.245386 | −0.122693 | − | 0.992445i | \(-0.539153\pi\) | ||||
−0.122693 | + | 0.992445i | \(0.539153\pi\) | |||||||
\(954\) | −5.21866 | −0.168960 | ||||||||
\(955\) | −61.4916 | −1.98982 | ||||||||
\(956\) | −24.9738 | −0.807710 | ||||||||
\(957\) | 3.34937 | 0.108270 | ||||||||
\(958\) | 11.4840 | 0.371030 | ||||||||
\(959\) | 34.5074 | 1.11430 | ||||||||
\(960\) | 34.8905 | 1.12609 | ||||||||
\(961\) | −20.0970 | −0.648292 | ||||||||
\(962\) | −13.1936 | −0.425379 | ||||||||
\(963\) | 1.70797 | 0.0550385 | ||||||||
\(964\) | 14.8810 | 0.479286 | ||||||||
\(965\) | −75.6682 | −2.43585 | ||||||||
\(966\) | −43.3765 | −1.39562 | ||||||||
\(967\) | −27.7049 | −0.890931 | −0.445466 | − | 0.895299i | \(-0.646962\pi\) | ||||
−0.445466 | + | 0.895299i | \(0.646962\pi\) | |||||||
\(968\) | 3.25882 | 0.104742 | ||||||||
\(969\) | 19.4236 | 0.623976 | ||||||||
\(970\) | 57.4033 | 1.84311 | ||||||||
\(971\) | 7.79820 | 0.250256 | 0.125128 | − | 0.992141i | \(-0.460066\pi\) | ||||
0.125128 | + | 0.992141i | \(0.460066\pi\) | |||||||
\(972\) | −30.1389 | −0.966704 | ||||||||
\(973\) | 63.8336 | 2.04641 | ||||||||
\(974\) | 65.9744 | 2.11396 | ||||||||
\(975\) | −6.05593 | −0.193945 | ||||||||
\(976\) | −27.0647 | −0.866320 | ||||||||
\(977\) | 42.1784 | 1.34941 | 0.674703 | − | 0.738089i | \(-0.264272\pi\) | ||||
0.674703 | + | 0.738089i | \(0.264272\pi\) | |||||||
\(978\) | 53.1973 | 1.70106 | ||||||||
\(979\) | −0.0726668 | −0.00232244 | ||||||||
\(980\) | 44.0524 | 1.40720 | ||||||||
\(981\) | 1.17230 | 0.0374286 | ||||||||
\(982\) | 12.4540 | 0.397423 | ||||||||
\(983\) | 44.9360 | 1.43323 | 0.716617 | − | 0.697467i | \(-0.245689\pi\) | ||||
0.716617 | + | 0.697467i | \(0.245689\pi\) | |||||||
\(984\) | 0.414003 | 0.0131979 | ||||||||
\(985\) | −23.8536 | −0.760040 | ||||||||
\(986\) | −93.3966 | −2.97435 | ||||||||
\(987\) | 33.4967 | 1.06621 | ||||||||
\(988\) | 6.41019 | 0.203935 | ||||||||
\(989\) | 18.6176 | 0.592005 | ||||||||
\(990\) | 3.23483 | 0.102810 | ||||||||
\(991\) | −36.1289 | −1.14767 | −0.573836 | − | 0.818970i | \(-0.694545\pi\) | ||||
−0.573836 | + | 0.818970i | \(0.694545\pi\) | |||||||
\(992\) | 26.7513 | 0.849354 | ||||||||
\(993\) | 7.82408 | 0.248290 | ||||||||
\(994\) | 68.9531 | 2.18706 | ||||||||
\(995\) | 25.8214 | 0.818593 | ||||||||
\(996\) | 10.8307 | 0.343184 | ||||||||
\(997\) | 7.54780 | 0.239041 | 0.119521 | − | 0.992832i | \(-0.461864\pi\) | ||||
0.119521 | + | 0.992832i | \(0.461864\pi\) | |||||||
\(998\) | −44.3782 | −1.40477 | ||||||||
\(999\) | 35.5358 | 1.12430 |
(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 | 6019.2.a.b.1.19 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.b.1.19 | ✓ | 101 | 1.1 | even | 1 | trivial |