Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.26119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.26119 | −1.88285 | −0.941425 | − | 0.337221i | \(-0.890513\pi\) | ||||
−0.941425 | + | 0.337221i | \(0.890513\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.57113 | −0.702630 | −0.351315 | − | 0.936257i | \(-0.614265\pi\) | ||||
−0.351315 | + | 0.936257i | \(0.614265\pi\) | |||||||
\(6\) | 3.26119 | 1.33138 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.63538 | 2.54513 | ||||||||
\(10\) | 1.57113 | 0.496834 | ||||||||
\(11\) | 3.36723 | 1.01526 | 0.507628 | − | 0.861576i | \(-0.330522\pi\) | ||||
0.507628 | + | 0.861576i | \(0.330522\pi\) | |||||||
\(12\) | −3.26119 | −0.941425 | ||||||||
\(13\) | 4.38488 | 1.21615 | 0.608073 | − | 0.793881i | \(-0.291943\pi\) | ||||
0.608073 | + | 0.793881i | \(0.291943\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 5.12375 | 1.32295 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.97133 | 1.69080 | 0.845398 | − | 0.534137i | \(-0.179363\pi\) | ||||
0.845398 | + | 0.534137i | \(0.179363\pi\) | |||||||
\(18\) | −7.63538 | −1.79968 | ||||||||
\(19\) | 1.24277 | 0.285112 | 0.142556 | − | 0.989787i | \(-0.454468\pi\) | ||||
0.142556 | + | 0.989787i | \(0.454468\pi\) | |||||||
\(20\) | −1.57113 | −0.351315 | ||||||||
\(21\) | −3.26119 | −0.711651 | ||||||||
\(22\) | −3.36723 | −0.717895 | ||||||||
\(23\) | −5.34535 | −1.11458 | −0.557291 | − | 0.830317i | \(-0.688159\pi\) | ||||
−0.557291 | + | 0.830317i | \(0.688159\pi\) | |||||||
\(24\) | 3.26119 | 0.665688 | ||||||||
\(25\) | −2.53156 | −0.506311 | ||||||||
\(26\) | −4.38488 | −0.859946 | ||||||||
\(27\) | −15.1169 | −2.90924 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.714285 | 0.132639 | 0.0663197 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663197 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(30\) | −5.12375 | −0.935465 | ||||||||
\(31\) | −8.61163 | −1.54669 | −0.773347 | − | 0.633982i | \(-0.781419\pi\) | ||||
−0.773347 | + | 0.633982i | \(0.781419\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −10.9812 | −1.91158 | ||||||||
\(34\) | −6.97133 | −1.19557 | ||||||||
\(35\) | −1.57113 | −0.265569 | ||||||||
\(36\) | 7.63538 | 1.27256 | ||||||||
\(37\) | 3.84539 | 0.632179 | 0.316089 | − | 0.948729i | \(-0.397630\pi\) | ||||
0.316089 | + | 0.948729i | \(0.397630\pi\) | |||||||
\(38\) | −1.24277 | −0.201605 | ||||||||
\(39\) | −14.2999 | −2.28982 | ||||||||
\(40\) | 1.57113 | 0.248417 | ||||||||
\(41\) | −2.93275 | −0.458019 | −0.229009 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229009 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(42\) | 3.26119 | 0.503213 | ||||||||
\(43\) | −9.05346 | −1.38064 | −0.690319 | − | 0.723505i | \(-0.742530\pi\) | ||||
−0.690319 | + | 0.723505i | \(0.742530\pi\) | |||||||
\(44\) | 3.36723 | 0.507628 | ||||||||
\(45\) | −11.9962 | −1.78828 | ||||||||
\(46\) | 5.34535 | 0.788128 | ||||||||
\(47\) | 5.79002 | 0.844561 | 0.422280 | − | 0.906465i | \(-0.361230\pi\) | ||||
0.422280 | + | 0.906465i | \(0.361230\pi\) | |||||||
\(48\) | −3.26119 | −0.470713 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.53156 | 0.358016 | ||||||||
\(51\) | −22.7349 | −3.18352 | ||||||||
\(52\) | 4.38488 | 0.608073 | ||||||||
\(53\) | −10.6069 | −1.45696 | −0.728482 | − | 0.685065i | \(-0.759774\pi\) | ||||
−0.728482 | + | 0.685065i | \(0.759774\pi\) | |||||||
\(54\) | 15.1169 | 2.05715 | ||||||||
\(55\) | −5.29034 | −0.713350 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −4.05293 | −0.536823 | ||||||||
\(58\) | −0.714285 | −0.0937902 | ||||||||
\(59\) | −11.6527 | −1.51705 | −0.758523 | − | 0.651646i | \(-0.774079\pi\) | ||||
−0.758523 | + | 0.651646i | \(0.774079\pi\) | |||||||
\(60\) | 5.12375 | 0.661474 | ||||||||
\(61\) | 9.51910 | 1.21880 | 0.609398 | − | 0.792865i | \(-0.291411\pi\) | ||||
0.609398 | + | 0.792865i | \(0.291411\pi\) | |||||||
\(62\) | 8.61163 | 1.09368 | ||||||||
\(63\) | 7.63538 | 0.961968 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.88921 | −0.854501 | ||||||||
\(66\) | 10.9812 | 1.35169 | ||||||||
\(67\) | 9.67742 | 1.18229 | 0.591143 | − | 0.806567i | \(-0.298677\pi\) | ||||
0.591143 | + | 0.806567i | \(0.298677\pi\) | |||||||
\(68\) | 6.97133 | 0.845398 | ||||||||
\(69\) | 17.4322 | 2.09859 | ||||||||
\(70\) | 1.57113 | 0.187786 | ||||||||
\(71\) | −8.28126 | −0.982805 | −0.491402 | − | 0.870933i | \(-0.663516\pi\) | ||||
−0.491402 | + | 0.870933i | \(0.663516\pi\) | |||||||
\(72\) | −7.63538 | −0.899838 | ||||||||
\(73\) | 7.58502 | 0.887759 | 0.443880 | − | 0.896086i | \(-0.353602\pi\) | ||||
0.443880 | + | 0.896086i | \(0.353602\pi\) | |||||||
\(74\) | −3.84539 | −0.447018 | ||||||||
\(75\) | 8.25589 | 0.953309 | ||||||||
\(76\) | 1.24277 | 0.142556 | ||||||||
\(77\) | 3.36723 | 0.383731 | ||||||||
\(78\) | 14.2999 | 1.61915 | ||||||||
\(79\) | −11.6261 | −1.30803 | −0.654017 | − | 0.756479i | \(-0.726918\pi\) | ||||
−0.654017 | + | 0.756479i | \(0.726918\pi\) | |||||||
\(80\) | −1.57113 | −0.175657 | ||||||||
\(81\) | 26.3929 | 2.93254 | ||||||||
\(82\) | 2.93275 | 0.323868 | ||||||||
\(83\) | 15.1640 | 1.66446 | 0.832231 | − | 0.554430i | \(-0.187064\pi\) | ||||
0.832231 | + | 0.554430i | \(0.187064\pi\) | |||||||
\(84\) | −3.26119 | −0.355825 | ||||||||
\(85\) | −10.9529 | −1.18800 | ||||||||
\(86\) | 9.05346 | 0.976259 | ||||||||
\(87\) | −2.32942 | −0.249740 | ||||||||
\(88\) | −3.36723 | −0.358947 | ||||||||
\(89\) | −3.09589 | −0.328164 | −0.164082 | − | 0.986447i | \(-0.552466\pi\) | ||||
−0.164082 | + | 0.986447i | \(0.552466\pi\) | |||||||
\(90\) | 11.9962 | 1.26451 | ||||||||
\(91\) | 4.38488 | 0.459660 | ||||||||
\(92\) | −5.34535 | −0.557291 | ||||||||
\(93\) | 28.0842 | 2.91220 | ||||||||
\(94\) | −5.79002 | −0.597195 | ||||||||
\(95\) | −1.95256 | −0.200328 | ||||||||
\(96\) | 3.26119 | 0.332844 | ||||||||
\(97\) | 12.5883 | 1.27815 | 0.639076 | − | 0.769144i | \(-0.279317\pi\) | ||||
0.639076 | + | 0.769144i | \(0.279317\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 25.7100 | 2.58396 | ||||||||
\(100\) | −2.53156 | −0.253156 | ||||||||
\(101\) | −14.2268 | −1.41562 | −0.707808 | − | 0.706405i | \(-0.750316\pi\) | ||||
−0.707808 | + | 0.706405i | \(0.750316\pi\) | |||||||
\(102\) | 22.7349 | 2.25109 | ||||||||
\(103\) | −13.2806 | −1.30858 | −0.654290 | − | 0.756244i | \(-0.727032\pi\) | ||||
−0.654290 | + | 0.756244i | \(0.727032\pi\) | |||||||
\(104\) | −4.38488 | −0.429973 | ||||||||
\(105\) | 5.12375 | 0.500027 | ||||||||
\(106\) | 10.6069 | 1.03023 | ||||||||
\(107\) | −2.18528 | −0.211259 | −0.105630 | − | 0.994406i | \(-0.533686\pi\) | ||||
−0.105630 | + | 0.994406i | \(0.533686\pi\) | |||||||
\(108\) | −15.1169 | −1.45462 | ||||||||
\(109\) | −4.48445 | −0.429532 | −0.214766 | − | 0.976666i | \(-0.568899\pi\) | ||||
−0.214766 | + | 0.976666i | \(0.568899\pi\) | |||||||
\(110\) | 5.29034 | 0.504414 | ||||||||
\(111\) | −12.5406 | −1.19030 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −13.9140 | −1.30892 | −0.654459 | − | 0.756097i | \(-0.727104\pi\) | ||||
−0.654459 | + | 0.756097i | \(0.727104\pi\) | |||||||
\(114\) | 4.05293 | 0.379591 | ||||||||
\(115\) | 8.39823 | 0.783139 | ||||||||
\(116\) | 0.714285 | 0.0663197 | ||||||||
\(117\) | 33.4802 | 3.09525 | ||||||||
\(118\) | 11.6527 | 1.07271 | ||||||||
\(119\) | 6.97133 | 0.639061 | ||||||||
\(120\) | −5.12375 | −0.467732 | ||||||||
\(121\) | 0.338206 | 0.0307460 | ||||||||
\(122\) | −9.51910 | −0.861819 | ||||||||
\(123\) | 9.56427 | 0.862381 | ||||||||
\(124\) | −8.61163 | −0.773347 | ||||||||
\(125\) | 11.8330 | 1.05838 | ||||||||
\(126\) | −7.63538 | −0.680214 | ||||||||
\(127\) | −7.03075 | −0.623878 | −0.311939 | − | 0.950102i | \(-0.600979\pi\) | ||||
−0.311939 | + | 0.950102i | \(0.600979\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 29.5251 | 2.59954 | ||||||||
\(130\) | 6.88921 | 0.604223 | ||||||||
\(131\) | 4.17590 | 0.364850 | 0.182425 | − | 0.983220i | \(-0.441605\pi\) | ||||
0.182425 | + | 0.983220i | \(0.441605\pi\) | |||||||
\(132\) | −10.9812 | −0.955788 | ||||||||
\(133\) | 1.24277 | 0.107762 | ||||||||
\(134\) | −9.67742 | −0.836002 | ||||||||
\(135\) | 23.7505 | 2.04412 | ||||||||
\(136\) | −6.97133 | −0.597787 | ||||||||
\(137\) | −3.71306 | −0.317228 | −0.158614 | − | 0.987341i | \(-0.550703\pi\) | ||||
−0.158614 | + | 0.987341i | \(0.550703\pi\) | |||||||
\(138\) | −17.4322 | −1.48393 | ||||||||
\(139\) | 3.63187 | 0.308052 | 0.154026 | − | 0.988067i | \(-0.450776\pi\) | ||||
0.154026 | + | 0.988067i | \(0.450776\pi\) | |||||||
\(140\) | −1.57113 | −0.132785 | ||||||||
\(141\) | −18.8824 | −1.59018 | ||||||||
\(142\) | 8.28126 | 0.694948 | ||||||||
\(143\) | 14.7649 | 1.23470 | ||||||||
\(144\) | 7.63538 | 0.636282 | ||||||||
\(145\) | −1.12223 | −0.0931964 | ||||||||
\(146\) | −7.58502 | −0.627741 | ||||||||
\(147\) | −3.26119 | −0.268979 | ||||||||
\(148\) | 3.84539 | 0.316089 | ||||||||
\(149\) | −19.7410 | −1.61725 | −0.808623 | − | 0.588327i | \(-0.799787\pi\) | ||||
−0.808623 | + | 0.588327i | \(0.799787\pi\) | |||||||
\(150\) | −8.25589 | −0.674091 | ||||||||
\(151\) | −6.27958 | −0.511025 | −0.255512 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255512 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(152\) | −1.24277 | −0.100802 | ||||||||
\(153\) | 53.2288 | 4.30329 | ||||||||
\(154\) | −3.36723 | −0.271339 | ||||||||
\(155\) | 13.5300 | 1.08675 | ||||||||
\(156\) | −14.2999 | −1.14491 | ||||||||
\(157\) | −11.6640 | −0.930885 | −0.465442 | − | 0.885078i | \(-0.654105\pi\) | ||||
−0.465442 | + | 0.885078i | \(0.654105\pi\) | |||||||
\(158\) | 11.6261 | 0.924920 | ||||||||
\(159\) | 34.5910 | 2.74325 | ||||||||
\(160\) | 1.57113 | 0.124209 | ||||||||
\(161\) | −5.34535 | −0.421272 | ||||||||
\(162\) | −26.3929 | −2.07362 | ||||||||
\(163\) | 7.11424 | 0.557230 | 0.278615 | − | 0.960403i | \(-0.410125\pi\) | ||||
0.278615 | + | 0.960403i | \(0.410125\pi\) | |||||||
\(164\) | −2.93275 | −0.229009 | ||||||||
\(165\) | 17.2528 | 1.34313 | ||||||||
\(166\) | −15.1640 | −1.17695 | ||||||||
\(167\) | 14.9273 | 1.15511 | 0.577553 | − | 0.816353i | \(-0.304008\pi\) | ||||
0.577553 | + | 0.816353i | \(0.304008\pi\) | |||||||
\(168\) | 3.26119 | 0.251607 | ||||||||
\(169\) | 6.22716 | 0.479013 | ||||||||
\(170\) | 10.9529 | 0.840045 | ||||||||
\(171\) | 9.48906 | 0.725646 | ||||||||
\(172\) | −9.05346 | −0.690319 | ||||||||
\(173\) | 2.92196 | 0.222153 | 0.111076 | − | 0.993812i | \(-0.464570\pi\) | ||||
0.111076 | + | 0.993812i | \(0.464570\pi\) | |||||||
\(174\) | 2.32942 | 0.176593 | ||||||||
\(175\) | −2.53156 | −0.191368 | ||||||||
\(176\) | 3.36723 | 0.253814 | ||||||||
\(177\) | 38.0016 | 2.85637 | ||||||||
\(178\) | 3.09589 | 0.232047 | ||||||||
\(179\) | −19.3029 | −1.44276 | −0.721381 | − | 0.692538i | \(-0.756493\pi\) | ||||
−0.721381 | + | 0.692538i | \(0.756493\pi\) | |||||||
\(180\) | −11.9962 | −0.894141 | ||||||||
\(181\) | −21.4000 | −1.59065 | −0.795324 | − | 0.606184i | \(-0.792699\pi\) | ||||
−0.795324 | + | 0.606184i | \(0.792699\pi\) | |||||||
\(182\) | −4.38488 | −0.325029 | ||||||||
\(183\) | −31.0436 | −2.29481 | ||||||||
\(184\) | 5.34535 | 0.394064 | ||||||||
\(185\) | −6.04161 | −0.444188 | ||||||||
\(186\) | −28.0842 | −2.05923 | ||||||||
\(187\) | 23.4740 | 1.71659 | ||||||||
\(188\) | 5.79002 | 0.422280 | ||||||||
\(189\) | −15.1169 | −1.09959 | ||||||||
\(190\) | 1.95256 | 0.141653 | ||||||||
\(191\) | −0.683469 | −0.0494541 | −0.0247270 | − | 0.999694i | \(-0.507872\pi\) | ||||
−0.0247270 | + | 0.999694i | \(0.507872\pi\) | |||||||
\(192\) | −3.26119 | −0.235356 | ||||||||
\(193\) | −8.49410 | −0.611419 | −0.305709 | − | 0.952125i | \(-0.598894\pi\) | ||||
−0.305709 | + | 0.952125i | \(0.598894\pi\) | |||||||
\(194\) | −12.5883 | −0.903789 | ||||||||
\(195\) | 22.4670 | 1.60890 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.62907 | −0.258560 | −0.129280 | − | 0.991608i | \(-0.541267\pi\) | ||||
−0.129280 | + | 0.991608i | \(0.541267\pi\) | |||||||
\(198\) | −25.7100 | −1.82713 | ||||||||
\(199\) | 4.16886 | 0.295522 | 0.147761 | − | 0.989023i | \(-0.452793\pi\) | ||||
0.147761 | + | 0.989023i | \(0.452793\pi\) | |||||||
\(200\) | 2.53156 | 0.179008 | ||||||||
\(201\) | −31.5599 | −2.22607 | ||||||||
\(202\) | 14.2268 | 1.00099 | ||||||||
\(203\) | 0.714285 | 0.0501330 | ||||||||
\(204\) | −22.7349 | −1.59176 | ||||||||
\(205\) | 4.60773 | 0.321818 | ||||||||
\(206\) | 13.2806 | 0.925305 | ||||||||
\(207\) | −40.8138 | −2.83675 | ||||||||
\(208\) | 4.38488 | 0.304037 | ||||||||
\(209\) | 4.18470 | 0.289462 | ||||||||
\(210\) | −5.12375 | −0.353573 | ||||||||
\(211\) | 1.29992 | 0.0894904 | 0.0447452 | − | 0.998998i | \(-0.485752\pi\) | ||||
0.0447452 | + | 0.998998i | \(0.485752\pi\) | |||||||
\(212\) | −10.6069 | −0.728482 | ||||||||
\(213\) | 27.0068 | 1.85048 | ||||||||
\(214\) | 2.18528 | 0.149383 | ||||||||
\(215\) | 14.2241 | 0.970078 | ||||||||
\(216\) | 15.1169 | 1.02857 | ||||||||
\(217\) | −8.61163 | −0.584596 | ||||||||
\(218\) | 4.48445 | 0.303725 | ||||||||
\(219\) | −24.7362 | −1.67152 | ||||||||
\(220\) | −5.29034 | −0.356675 | ||||||||
\(221\) | 30.5684 | 2.05626 | ||||||||
\(222\) | 12.5406 | 0.841668 | ||||||||
\(223\) | −1.72546 | −0.115545 | −0.0577726 | − | 0.998330i | \(-0.518400\pi\) | ||||
−0.0577726 | + | 0.998330i | \(0.518400\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −19.3294 | −1.28863 | ||||||||
\(226\) | 13.9140 | 0.925545 | ||||||||
\(227\) | −6.83743 | −0.453816 | −0.226908 | − | 0.973916i | \(-0.572862\pi\) | ||||
−0.226908 | + | 0.973916i | \(0.572862\pi\) | |||||||
\(228\) | −4.05293 | −0.268412 | ||||||||
\(229\) | 13.3205 | 0.880246 | 0.440123 | − | 0.897937i | \(-0.354935\pi\) | ||||
0.440123 | + | 0.897937i | \(0.354935\pi\) | |||||||
\(230\) | −8.39823 | −0.553763 | ||||||||
\(231\) | −10.9812 | −0.722508 | ||||||||
\(232\) | −0.714285 | −0.0468951 | ||||||||
\(233\) | −10.5460 | −0.690890 | −0.345445 | − | 0.938439i | \(-0.612272\pi\) | ||||
−0.345445 | + | 0.938439i | \(0.612272\pi\) | |||||||
\(234\) | −33.4802 | −2.18867 | ||||||||
\(235\) | −9.09686 | −0.593414 | ||||||||
\(236\) | −11.6527 | −0.758523 | ||||||||
\(237\) | 37.9149 | 2.46283 | ||||||||
\(238\) | −6.97133 | −0.451884 | ||||||||
\(239\) | 22.1887 | 1.43527 | 0.717634 | − | 0.696421i | \(-0.245225\pi\) | ||||
0.717634 | + | 0.696421i | \(0.245225\pi\) | |||||||
\(240\) | 5.12375 | 0.330737 | ||||||||
\(241\) | 0.311904 | 0.0200915 | 0.0100458 | − | 0.999950i | \(-0.496802\pi\) | ||||
0.0100458 | + | 0.999950i | \(0.496802\pi\) | |||||||
\(242\) | −0.338206 | −0.0217407 | ||||||||
\(243\) | −40.7217 | −2.61230 | ||||||||
\(244\) | 9.51910 | 0.609398 | ||||||||
\(245\) | −1.57113 | −0.100376 | ||||||||
\(246\) | −9.56427 | −0.609796 | ||||||||
\(247\) | 5.44942 | 0.346738 | ||||||||
\(248\) | 8.61163 | 0.546839 | ||||||||
\(249\) | −49.4526 | −3.13393 | ||||||||
\(250\) | −11.8330 | −0.748387 | ||||||||
\(251\) | −15.1712 | −0.957599 | −0.478800 | − | 0.877924i | \(-0.658928\pi\) | ||||
−0.478800 | + | 0.877924i | \(0.658928\pi\) | |||||||
\(252\) | 7.63538 | 0.480984 | ||||||||
\(253\) | −17.9990 | −1.13159 | ||||||||
\(254\) | 7.03075 | 0.441149 | ||||||||
\(255\) | 35.7194 | 2.23683 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.6673 | −1.35157 | −0.675783 | − | 0.737101i | \(-0.736194\pi\) | ||||
−0.675783 | + | 0.737101i | \(0.736194\pi\) | |||||||
\(258\) | −29.5251 | −1.83815 | ||||||||
\(259\) | 3.84539 | 0.238941 | ||||||||
\(260\) | −6.88921 | −0.427250 | ||||||||
\(261\) | 5.45384 | 0.337584 | ||||||||
\(262\) | −4.17590 | −0.257988 | ||||||||
\(263\) | −23.4746 | −1.44750 | −0.723751 | − | 0.690061i | \(-0.757584\pi\) | ||||
−0.723751 | + | 0.690061i | \(0.757584\pi\) | |||||||
\(264\) | 10.9812 | 0.675844 | ||||||||
\(265\) | 16.6647 | 1.02371 | ||||||||
\(266\) | −1.24277 | −0.0761994 | ||||||||
\(267\) | 10.0963 | 0.617884 | ||||||||
\(268\) | 9.67742 | 0.591143 | ||||||||
\(269\) | −11.9068 | −0.725970 | −0.362985 | − | 0.931795i | \(-0.618242\pi\) | ||||
−0.362985 | + | 0.931795i | \(0.618242\pi\) | |||||||
\(270\) | −23.7505 | −1.44541 | ||||||||
\(271\) | 6.70377 | 0.407225 | 0.203613 | − | 0.979052i | \(-0.434732\pi\) | ||||
0.203613 | + | 0.979052i | \(0.434732\pi\) | |||||||
\(272\) | 6.97133 | 0.422699 | ||||||||
\(273\) | −14.2999 | −0.865472 | ||||||||
\(274\) | 3.71306 | 0.224314 | ||||||||
\(275\) | −8.52432 | −0.514036 | ||||||||
\(276\) | 17.4322 | 1.04930 | ||||||||
\(277\) | 24.7887 | 1.48941 | 0.744705 | − | 0.667394i | \(-0.232590\pi\) | ||||
0.744705 | + | 0.667394i | \(0.232590\pi\) | |||||||
\(278\) | −3.63187 | −0.217825 | ||||||||
\(279\) | −65.7531 | −3.93654 | ||||||||
\(280\) | 1.57113 | 0.0938929 | ||||||||
\(281\) | −1.12004 | −0.0668159 | −0.0334080 | − | 0.999442i | \(-0.510636\pi\) | ||||
−0.0334080 | + | 0.999442i | \(0.510636\pi\) | |||||||
\(282\) | 18.8824 | 1.12443 | ||||||||
\(283\) | −15.1845 | −0.902625 | −0.451313 | − | 0.892366i | \(-0.649044\pi\) | ||||
−0.451313 | + | 0.892366i | \(0.649044\pi\) | |||||||
\(284\) | −8.28126 | −0.491402 | ||||||||
\(285\) | 6.36767 | 0.377188 | ||||||||
\(286\) | −14.7649 | −0.873065 | ||||||||
\(287\) | −2.93275 | −0.173115 | ||||||||
\(288\) | −7.63538 | −0.449919 | ||||||||
\(289\) | 31.5994 | 1.85879 | ||||||||
\(290\) | 1.12223 | 0.0658998 | ||||||||
\(291\) | −41.0530 | −2.40657 | ||||||||
\(292\) | 7.58502 | 0.443880 | ||||||||
\(293\) | 2.36549 | 0.138194 | 0.0690968 | − | 0.997610i | \(-0.477988\pi\) | ||||
0.0690968 | + | 0.997610i | \(0.477988\pi\) | |||||||
\(294\) | 3.26119 | 0.190197 | ||||||||
\(295\) | 18.3078 | 1.06592 | ||||||||
\(296\) | −3.84539 | −0.223509 | ||||||||
\(297\) | −50.9019 | −2.95363 | ||||||||
\(298\) | 19.7410 | 1.14357 | ||||||||
\(299\) | −23.4387 | −1.35550 | ||||||||
\(300\) | 8.25589 | 0.476654 | ||||||||
\(301\) | −9.05346 | −0.521832 | ||||||||
\(302\) | 6.27958 | 0.361349 | ||||||||
\(303\) | 46.3962 | 2.66539 | ||||||||
\(304\) | 1.24277 | 0.0712780 | ||||||||
\(305\) | −14.9557 | −0.856362 | ||||||||
\(306\) | −53.2288 | −3.04289 | ||||||||
\(307\) | 31.5770 | 1.80220 | 0.901098 | − | 0.433616i | \(-0.142763\pi\) | ||||
0.901098 | + | 0.433616i | \(0.142763\pi\) | |||||||
\(308\) | 3.36723 | 0.191865 | ||||||||
\(309\) | 43.3107 | 2.46386 | ||||||||
\(310\) | −13.5300 | −0.768451 | ||||||||
\(311\) | −31.4236 | −1.78187 | −0.890935 | − | 0.454130i | \(-0.849950\pi\) | ||||
−0.890935 | + | 0.454130i | \(0.849950\pi\) | |||||||
\(312\) | 14.2999 | 0.809575 | ||||||||
\(313\) | 14.6221 | 0.826490 | 0.413245 | − | 0.910620i | \(-0.364395\pi\) | ||||
0.413245 | + | 0.910620i | \(0.364395\pi\) | |||||||
\(314\) | 11.6640 | 0.658235 | ||||||||
\(315\) | −11.9962 | −0.675907 | ||||||||
\(316\) | −11.6261 | −0.654017 | ||||||||
\(317\) | 18.6590 | 1.04800 | 0.523998 | − | 0.851719i | \(-0.324440\pi\) | ||||
0.523998 | + | 0.851719i | \(0.324440\pi\) | |||||||
\(318\) | −34.5910 | −1.93977 | ||||||||
\(319\) | 2.40516 | 0.134663 | ||||||||
\(320\) | −1.57113 | −0.0878287 | ||||||||
\(321\) | 7.12663 | 0.397770 | ||||||||
\(322\) | 5.34535 | 0.297885 | ||||||||
\(323\) | 8.66379 | 0.482066 | ||||||||
\(324\) | 26.3929 | 1.46627 | ||||||||
\(325\) | −11.1006 | −0.615749 | ||||||||
\(326\) | −7.11424 | −0.394021 | ||||||||
\(327\) | 14.6246 | 0.808745 | ||||||||
\(328\) | 2.93275 | 0.161934 | ||||||||
\(329\) | 5.79002 | 0.319214 | ||||||||
\(330\) | −17.2528 | −0.949737 | ||||||||
\(331\) | 16.6382 | 0.914520 | 0.457260 | − | 0.889333i | \(-0.348831\pi\) | ||||
0.457260 | + | 0.889333i | \(0.348831\pi\) | |||||||
\(332\) | 15.1640 | 0.832231 | ||||||||
\(333\) | 29.3611 | 1.60898 | ||||||||
\(334\) | −14.9273 | −0.816783 | ||||||||
\(335\) | −15.2045 | −0.830709 | ||||||||
\(336\) | −3.26119 | −0.177913 | ||||||||
\(337\) | 34.5642 | 1.88283 | 0.941417 | − | 0.337244i | \(-0.109495\pi\) | ||||
0.941417 | + | 0.337244i | \(0.109495\pi\) | |||||||
\(338\) | −6.22716 | −0.338713 | ||||||||
\(339\) | 45.3762 | 2.46450 | ||||||||
\(340\) | −10.9529 | −0.594002 | ||||||||
\(341\) | −28.9973 | −1.57029 | ||||||||
\(342\) | −9.48906 | −0.513109 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.05346 | 0.488130 | ||||||||
\(345\) | −27.3882 | −1.47453 | ||||||||
\(346\) | −2.92196 | −0.157086 | ||||||||
\(347\) | 2.49822 | 0.134112 | 0.0670558 | − | 0.997749i | \(-0.478639\pi\) | ||||
0.0670558 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(348\) | −2.32942 | −0.124870 | ||||||||
\(349\) | 3.46239 | 0.185337 | 0.0926686 | − | 0.995697i | \(-0.470460\pi\) | ||||
0.0926686 | + | 0.995697i | \(0.470460\pi\) | |||||||
\(350\) | 2.53156 | 0.135317 | ||||||||
\(351\) | −66.2857 | −3.53807 | ||||||||
\(352\) | −3.36723 | −0.179474 | ||||||||
\(353\) | 6.79546 | 0.361686 | 0.180843 | − | 0.983512i | \(-0.442117\pi\) | ||||
0.180843 | + | 0.983512i | \(0.442117\pi\) | |||||||
\(354\) | −38.0016 | −2.01976 | ||||||||
\(355\) | 13.0109 | 0.690548 | ||||||||
\(356\) | −3.09589 | −0.164082 | ||||||||
\(357\) | −22.7349 | −1.20326 | ||||||||
\(358\) | 19.3029 | 1.02019 | ||||||||
\(359\) | 30.4002 | 1.60446 | 0.802231 | − | 0.597013i | \(-0.203646\pi\) | ||||
0.802231 | + | 0.597013i | \(0.203646\pi\) | |||||||
\(360\) | 11.9962 | 0.632253 | ||||||||
\(361\) | −17.4555 | −0.918711 | ||||||||
\(362\) | 21.4000 | 1.12476 | ||||||||
\(363\) | −1.10295 | −0.0578901 | ||||||||
\(364\) | 4.38488 | 0.229830 | ||||||||
\(365\) | −11.9170 | −0.623766 | ||||||||
\(366\) | 31.0436 | 1.62268 | ||||||||
\(367\) | −2.07915 | −0.108531 | −0.0542654 | − | 0.998527i | \(-0.517282\pi\) | ||||
−0.0542654 | + | 0.998527i | \(0.517282\pi\) | |||||||
\(368\) | −5.34535 | −0.278645 | ||||||||
\(369\) | −22.3927 | −1.16572 | ||||||||
\(370\) | 6.04161 | 0.314088 | ||||||||
\(371\) | −10.6069 | −0.550681 | ||||||||
\(372\) | 28.0842 | 1.45610 | ||||||||
\(373\) | 5.48030 | 0.283759 | 0.141880 | − | 0.989884i | \(-0.454685\pi\) | ||||
0.141880 | + | 0.989884i | \(0.454685\pi\) | |||||||
\(374\) | −23.4740 | −1.21381 | ||||||||
\(375\) | −38.5898 | −1.99277 | ||||||||
\(376\) | −5.79002 | −0.298597 | ||||||||
\(377\) | 3.13205 | 0.161309 | ||||||||
\(378\) | 15.1169 | 0.777528 | ||||||||
\(379\) | −1.62719 | −0.0835829 | −0.0417914 | − | 0.999126i | \(-0.513307\pi\) | ||||
−0.0417914 | + | 0.999126i | \(0.513307\pi\) | |||||||
\(380\) | −1.95256 | −0.100164 | ||||||||
\(381\) | 22.9286 | 1.17467 | ||||||||
\(382\) | 0.683469 | 0.0349693 | ||||||||
\(383\) | −13.2210 | −0.675559 | −0.337780 | − | 0.941225i | \(-0.609676\pi\) | ||||
−0.337780 | + | 0.941225i | \(0.609676\pi\) | |||||||
\(384\) | 3.26119 | 0.166422 | ||||||||
\(385\) | −5.29034 | −0.269621 | ||||||||
\(386\) | 8.49410 | 0.432338 | ||||||||
\(387\) | −69.1266 | −3.51390 | ||||||||
\(388\) | 12.5883 | 0.639076 | ||||||||
\(389\) | −3.02357 | −0.153301 | −0.0766505 | − | 0.997058i | \(-0.524423\pi\) | ||||
−0.0766505 | + | 0.997058i | \(0.524423\pi\) | |||||||
\(390\) | −22.4670 | −1.13766 | ||||||||
\(391\) | −37.2642 | −1.88453 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −13.6184 | −0.686959 | ||||||||
\(394\) | 3.62907 | 0.182830 | ||||||||
\(395\) | 18.2660 | 0.919064 | ||||||||
\(396\) | 25.7100 | 1.29198 | ||||||||
\(397\) | −13.4729 | −0.676186 | −0.338093 | − | 0.941113i | \(-0.609782\pi\) | ||||
−0.338093 | + | 0.941113i | \(0.609782\pi\) | |||||||
\(398\) | −4.16886 | −0.208966 | ||||||||
\(399\) | −4.05293 | −0.202900 | ||||||||
\(400\) | −2.53156 | −0.126578 | ||||||||
\(401\) | −19.2938 | −0.963489 | −0.481744 | − | 0.876312i | \(-0.659997\pi\) | ||||
−0.481744 | + | 0.876312i | \(0.659997\pi\) | |||||||
\(402\) | 31.5599 | 1.57407 | ||||||||
\(403\) | −37.7610 | −1.88101 | ||||||||
\(404\) | −14.2268 | −0.707808 | ||||||||
\(405\) | −41.4666 | −2.06049 | ||||||||
\(406\) | −0.714285 | −0.0354494 | ||||||||
\(407\) | 12.9483 | 0.641824 | ||||||||
\(408\) | 22.7349 | 1.12554 | ||||||||
\(409\) | 10.3677 | 0.512649 | 0.256324 | − | 0.966591i | \(-0.417488\pi\) | ||||
0.256324 | + | 0.966591i | \(0.417488\pi\) | |||||||
\(410\) | −4.60773 | −0.227560 | ||||||||
\(411\) | 12.1090 | 0.597294 | ||||||||
\(412\) | −13.2806 | −0.654290 | ||||||||
\(413\) | −11.6527 | −0.573390 | ||||||||
\(414\) | 40.8138 | 2.00589 | ||||||||
\(415\) | −23.8245 | −1.16950 | ||||||||
\(416\) | −4.38488 | −0.214986 | ||||||||
\(417\) | −11.8442 | −0.580015 | ||||||||
\(418\) | −4.18470 | −0.204680 | ||||||||
\(419\) | 23.9351 | 1.16931 | 0.584653 | − | 0.811283i | \(-0.301231\pi\) | ||||
0.584653 | + | 0.811283i | \(0.301231\pi\) | |||||||
\(420\) | 5.12375 | 0.250014 | ||||||||
\(421\) | 32.5135 | 1.58461 | 0.792305 | − | 0.610125i | \(-0.208881\pi\) | ||||
0.792305 | + | 0.610125i | \(0.208881\pi\) | |||||||
\(422\) | −1.29992 | −0.0632793 | ||||||||
\(423\) | 44.2090 | 2.14951 | ||||||||
\(424\) | 10.6069 | 0.515114 | ||||||||
\(425\) | −17.6483 | −0.856069 | ||||||||
\(426\) | −27.0068 | −1.30848 | ||||||||
\(427\) | 9.51910 | 0.460662 | ||||||||
\(428\) | −2.18528 | −0.105630 | ||||||||
\(429\) | −48.1511 | −2.32476 | ||||||||
\(430\) | −14.2241 | −0.685949 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | −15.1169 | −0.727311 | ||||||||
\(433\) | 21.3318 | 1.02514 | 0.512570 | − | 0.858645i | \(-0.328693\pi\) | ||||
0.512570 | + | 0.858645i | \(0.328693\pi\) | |||||||
\(434\) | 8.61163 | 0.413372 | ||||||||
\(435\) | 3.65982 | 0.175475 | ||||||||
\(436\) | −4.48445 | −0.214766 | ||||||||
\(437\) | −6.64306 | −0.317781 | ||||||||
\(438\) | 24.7362 | 1.18194 | ||||||||
\(439\) | −30.9592 | −1.47760 | −0.738801 | − | 0.673924i | \(-0.764608\pi\) | ||||
−0.738801 | + | 0.673924i | \(0.764608\pi\) | |||||||
\(440\) | 5.29034 | 0.252207 | ||||||||
\(441\) | 7.63538 | 0.363590 | ||||||||
\(442\) | −30.5684 | −1.45399 | ||||||||
\(443\) | −18.0899 | −0.859478 | −0.429739 | − | 0.902953i | \(-0.641394\pi\) | ||||
−0.429739 | + | 0.902953i | \(0.641394\pi\) | |||||||
\(444\) | −12.5406 | −0.595149 | ||||||||
\(445\) | 4.86404 | 0.230578 | ||||||||
\(446\) | 1.72546 | 0.0817027 | ||||||||
\(447\) | 64.3792 | 3.04503 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −24.9108 | −1.17561 | −0.587807 | − | 0.809001i | \(-0.700009\pi\) | ||||
−0.587807 | + | 0.809001i | \(0.700009\pi\) | |||||||
\(450\) | 19.3294 | 0.911197 | ||||||||
\(451\) | −9.87524 | −0.465007 | ||||||||
\(452\) | −13.9140 | −0.654459 | ||||||||
\(453\) | 20.4789 | 0.962183 | ||||||||
\(454\) | 6.83743 | 0.320897 | ||||||||
\(455\) | −6.88921 | −0.322971 | ||||||||
\(456\) | 4.05293 | 0.189796 | ||||||||
\(457\) | 4.95753 | 0.231904 | 0.115952 | − | 0.993255i | \(-0.463008\pi\) | ||||
0.115952 | + | 0.993255i | \(0.463008\pi\) | |||||||
\(458\) | −13.3205 | −0.622428 | ||||||||
\(459\) | −105.385 | −4.91894 | ||||||||
\(460\) | 8.39823 | 0.391569 | ||||||||
\(461\) | 26.9228 | 1.25392 | 0.626960 | − | 0.779052i | \(-0.284299\pi\) | ||||
0.626960 | + | 0.779052i | \(0.284299\pi\) | |||||||
\(462\) | 10.9812 | 0.510890 | ||||||||
\(463\) | −7.07952 | −0.329013 | −0.164506 | − | 0.986376i | \(-0.552603\pi\) | ||||
−0.164506 | + | 0.986376i | \(0.552603\pi\) | |||||||
\(464\) | 0.714285 | 0.0331598 | ||||||||
\(465\) | −44.1239 | −2.04620 | ||||||||
\(466\) | 10.5460 | 0.488533 | ||||||||
\(467\) | 2.70233 | 0.125049 | 0.0625246 | − | 0.998043i | \(-0.480085\pi\) | ||||
0.0625246 | + | 0.998043i | \(0.480085\pi\) | |||||||
\(468\) | 33.4802 | 1.54762 | ||||||||
\(469\) | 9.67742 | 0.446862 | ||||||||
\(470\) | 9.09686 | 0.419607 | ||||||||
\(471\) | 38.0384 | 1.75272 | ||||||||
\(472\) | 11.6527 | 0.536357 | ||||||||
\(473\) | −30.4850 | −1.40170 | ||||||||
\(474\) | −37.9149 | −1.74149 | ||||||||
\(475\) | −3.14615 | −0.144355 | ||||||||
\(476\) | 6.97133 | 0.319530 | ||||||||
\(477\) | −80.9874 | −3.70816 | ||||||||
\(478\) | −22.1887 | −1.01489 | ||||||||
\(479\) | −18.1714 | −0.830274 | −0.415137 | − | 0.909759i | \(-0.636266\pi\) | ||||
−0.415137 | + | 0.909759i | \(0.636266\pi\) | |||||||
\(480\) | −5.12375 | −0.233866 | ||||||||
\(481\) | 16.8616 | 0.768822 | ||||||||
\(482\) | −0.311904 | −0.0142068 | ||||||||
\(483\) | 17.4322 | 0.793193 | ||||||||
\(484\) | 0.338206 | 0.0153730 | ||||||||
\(485\) | −19.7779 | −0.898067 | ||||||||
\(486\) | 40.7217 | 1.84718 | ||||||||
\(487\) | −16.1307 | −0.730953 | −0.365476 | − | 0.930821i | \(-0.619094\pi\) | ||||
−0.365476 | + | 0.930821i | \(0.619094\pi\) | |||||||
\(488\) | −9.51910 | −0.430909 | ||||||||
\(489\) | −23.2009 | −1.04918 | ||||||||
\(490\) | 1.57113 | 0.0709763 | ||||||||
\(491\) | −18.1349 | −0.818417 | −0.409208 | − | 0.912441i | \(-0.634195\pi\) | ||||
−0.409208 | + | 0.912441i | \(0.634195\pi\) | |||||||
\(492\) | 9.56427 | 0.431191 | ||||||||
\(493\) | 4.97951 | 0.224266 | ||||||||
\(494\) | −5.44942 | −0.245181 | ||||||||
\(495\) | −40.3938 | −1.81557 | ||||||||
\(496\) | −8.61163 | −0.386674 | ||||||||
\(497\) | −8.28126 | −0.371465 | ||||||||
\(498\) | 49.4526 | 2.21602 | ||||||||
\(499\) | −32.7814 | −1.46750 | −0.733748 | − | 0.679422i | \(-0.762231\pi\) | ||||
−0.733748 | + | 0.679422i | \(0.762231\pi\) | |||||||
\(500\) | 11.8330 | 0.529190 | ||||||||
\(501\) | −48.6807 | −2.17489 | ||||||||
\(502\) | 15.1712 | 0.677125 | ||||||||
\(503\) | −34.4754 | −1.53718 | −0.768592 | − | 0.639739i | \(-0.779042\pi\) | ||||
−0.768592 | + | 0.639739i | \(0.779042\pi\) | |||||||
\(504\) | −7.63538 | −0.340107 | ||||||||
\(505\) | 22.3521 | 0.994654 | ||||||||
\(506\) | 17.9990 | 0.800153 | ||||||||
\(507\) | −20.3080 | −0.901909 | ||||||||
\(508\) | −7.03075 | −0.311939 | ||||||||
\(509\) | 12.2201 | 0.541646 | 0.270823 | − | 0.962629i | \(-0.412704\pi\) | ||||
0.270823 | + | 0.962629i | \(0.412704\pi\) | |||||||
\(510\) | −35.7194 | −1.58168 | ||||||||
\(511\) | 7.58502 | 0.335542 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −18.7869 | −0.829460 | ||||||||
\(514\) | 21.6673 | 0.955702 | ||||||||
\(515\) | 20.8656 | 0.919447 | ||||||||
\(516\) | 29.5251 | 1.29977 | ||||||||
\(517\) | 19.4963 | 0.857446 | ||||||||
\(518\) | −3.84539 | −0.168957 | ||||||||
\(519\) | −9.52908 | −0.418280 | ||||||||
\(520\) | 6.88921 | 0.302112 | ||||||||
\(521\) | −36.7535 | −1.61020 | −0.805101 | − | 0.593138i | \(-0.797889\pi\) | ||||
−0.805101 | + | 0.593138i | \(0.797889\pi\) | |||||||
\(522\) | −5.45384 | −0.238708 | ||||||||
\(523\) | −37.4162 | −1.63610 | −0.818049 | − | 0.575149i | \(-0.804944\pi\) | ||||
−0.818049 | + | 0.575149i | \(0.804944\pi\) | |||||||
\(524\) | 4.17590 | 0.182425 | ||||||||
\(525\) | 8.25589 | 0.360317 | ||||||||
\(526\) | 23.4746 | 1.02354 | ||||||||
\(527\) | −60.0345 | −2.61515 | ||||||||
\(528\) | −10.9812 | −0.477894 | ||||||||
\(529\) | 5.57273 | 0.242293 | ||||||||
\(530\) | −16.6647 | −0.723870 | ||||||||
\(531\) | −88.9725 | −3.86108 | ||||||||
\(532\) | 1.24277 | 0.0538811 | ||||||||
\(533\) | −12.8598 | −0.557018 | ||||||||
\(534\) | −10.0963 | −0.436910 | ||||||||
\(535\) | 3.43336 | 0.148437 | ||||||||
\(536\) | −9.67742 | −0.418001 | ||||||||
\(537\) | 62.9503 | 2.71651 | ||||||||
\(538\) | 11.9068 | 0.513339 | ||||||||
\(539\) | 3.36723 | 0.145037 | ||||||||
\(540\) | 23.7505 | 1.02206 | ||||||||
\(541\) | 3.29851 | 0.141814 | 0.0709071 | − | 0.997483i | \(-0.477411\pi\) | ||||
0.0709071 | + | 0.997483i | \(0.477411\pi\) | |||||||
\(542\) | −6.70377 | −0.287952 | ||||||||
\(543\) | 69.7895 | 2.99495 | ||||||||
\(544\) | −6.97133 | −0.298893 | ||||||||
\(545\) | 7.04564 | 0.301802 | ||||||||
\(546\) | 14.2999 | 0.611981 | ||||||||
\(547\) | 44.4439 | 1.90028 | 0.950141 | − | 0.311819i | \(-0.100938\pi\) | ||||
0.950141 | + | 0.311819i | \(0.100938\pi\) | |||||||
\(548\) | −3.71306 | −0.158614 | ||||||||
\(549\) | 72.6820 | 3.10199 | ||||||||
\(550\) | 8.52432 | 0.363478 | ||||||||
\(551\) | 0.887695 | 0.0378171 | ||||||||
\(552\) | −17.4322 | −0.741964 | ||||||||
\(553\) | −11.6261 | −0.494391 | ||||||||
\(554\) | −24.7887 | −1.05317 | ||||||||
\(555\) | 19.7028 | 0.836339 | ||||||||
\(556\) | 3.63187 | 0.154026 | ||||||||
\(557\) | 26.6439 | 1.12894 | 0.564470 | − | 0.825454i | \(-0.309081\pi\) | ||||
0.564470 | + | 0.825454i | \(0.309081\pi\) | |||||||
\(558\) | 65.7531 | 2.78355 | ||||||||
\(559\) | −39.6983 | −1.67906 | ||||||||
\(560\) | −1.57113 | −0.0663923 | ||||||||
\(561\) | −76.5534 | −3.23209 | ||||||||
\(562\) | 1.12004 | 0.0472460 | ||||||||
\(563\) | 19.9398 | 0.840360 | 0.420180 | − | 0.907441i | \(-0.361967\pi\) | ||||
0.420180 | + | 0.907441i | \(0.361967\pi\) | |||||||
\(564\) | −18.8824 | −0.795091 | ||||||||
\(565\) | 21.8607 | 0.919685 | ||||||||
\(566\) | 15.1845 | 0.638253 | ||||||||
\(567\) | 26.3929 | 1.10840 | ||||||||
\(568\) | 8.28126 | 0.347474 | ||||||||
\(569\) | 1.28540 | 0.0538868 | 0.0269434 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269434 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(570\) | −6.36767 | −0.266712 | ||||||||
\(571\) | 32.1980 | 1.34745 | 0.673723 | − | 0.738984i | \(-0.264694\pi\) | ||||
0.673723 | + | 0.738984i | \(0.264694\pi\) | |||||||
\(572\) | 14.7649 | 0.617350 | ||||||||
\(573\) | 2.22893 | 0.0931147 | ||||||||
\(574\) | 2.93275 | 0.122411 | ||||||||
\(575\) | 13.5320 | 0.564325 | ||||||||
\(576\) | 7.63538 | 0.318141 | ||||||||
\(577\) | −13.4500 | −0.559931 | −0.279966 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279966 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(578\) | −31.5994 | −1.31436 | ||||||||
\(579\) | 27.7009 | 1.15121 | ||||||||
\(580\) | −1.12223 | −0.0465982 | ||||||||
\(581\) | 15.1640 | 0.629107 | ||||||||
\(582\) | 41.0530 | 1.70170 | ||||||||
\(583\) | −35.7157 | −1.47919 | ||||||||
\(584\) | −7.58502 | −0.313870 | ||||||||
\(585\) | −52.6017 | −2.17481 | ||||||||
\(586\) | −2.36549 | −0.0977176 | ||||||||
\(587\) | 14.3519 | 0.592368 | 0.296184 | − | 0.955131i | \(-0.404286\pi\) | ||||
0.296184 | + | 0.955131i | \(0.404286\pi\) | |||||||
\(588\) | −3.26119 | −0.134489 | ||||||||
\(589\) | −10.7023 | −0.440981 | ||||||||
\(590\) | −18.3078 | −0.753721 | ||||||||
\(591\) | 11.8351 | 0.486830 | ||||||||
\(592\) | 3.84539 | 0.158045 | ||||||||
\(593\) | −34.3015 | −1.40859 | −0.704296 | − | 0.709906i | \(-0.748737\pi\) | ||||
−0.704296 | + | 0.709906i | \(0.748737\pi\) | |||||||
\(594\) | 50.9019 | 2.08853 | ||||||||
\(595\) | −10.9529 | −0.449023 | ||||||||
\(596\) | −19.7410 | −0.808623 | ||||||||
\(597\) | −13.5954 | −0.556424 | ||||||||
\(598\) | 23.4387 | 0.958480 | ||||||||
\(599\) | −46.2196 | −1.88848 | −0.944240 | − | 0.329258i | \(-0.893201\pi\) | ||||
−0.944240 | + | 0.329258i | \(0.893201\pi\) | |||||||
\(600\) | −8.25589 | −0.337045 | ||||||||
\(601\) | 31.6371 | 1.29051 | 0.645253 | − | 0.763969i | \(-0.276752\pi\) | ||||
0.645253 | + | 0.763969i | \(0.276752\pi\) | |||||||
\(602\) | 9.05346 | 0.368991 | ||||||||
\(603\) | 73.8908 | 3.00907 | ||||||||
\(604\) | −6.27958 | −0.255512 | ||||||||
\(605\) | −0.531365 | −0.0216031 | ||||||||
\(606\) | −46.3962 | −1.88472 | ||||||||
\(607\) | −6.66317 | −0.270450 | −0.135225 | − | 0.990815i | \(-0.543176\pi\) | ||||
−0.135225 | + | 0.990815i | \(0.543176\pi\) | |||||||
\(608\) | −1.24277 | −0.0504012 | ||||||||
\(609\) | −2.32942 | −0.0943929 | ||||||||
\(610\) | 14.9557 | 0.605540 | ||||||||
\(611\) | 25.3885 | 1.02711 | ||||||||
\(612\) | 53.2288 | 2.15165 | ||||||||
\(613\) | −20.7301 | −0.837281 | −0.418641 | − | 0.908152i | \(-0.637493\pi\) | ||||
−0.418641 | + | 0.908152i | \(0.637493\pi\) | |||||||
\(614\) | −31.5770 | −1.27434 | ||||||||
\(615\) | −15.0267 | −0.605935 | ||||||||
\(616\) | −3.36723 | −0.135669 | ||||||||
\(617\) | 24.1935 | 0.973993 | 0.486996 | − | 0.873404i | \(-0.338092\pi\) | ||||
0.486996 | + | 0.873404i | \(0.338092\pi\) | |||||||
\(618\) | −43.3107 | −1.74221 | ||||||||
\(619\) | −4.78915 | −0.192492 | −0.0962461 | − | 0.995358i | \(-0.530684\pi\) | ||||
−0.0962461 | + | 0.995358i | \(0.530684\pi\) | |||||||
\(620\) | 13.5300 | 0.543377 | ||||||||
\(621\) | 80.8049 | 3.24259 | ||||||||
\(622\) | 31.4236 | 1.25997 | ||||||||
\(623\) | −3.09589 | −0.124034 | ||||||||
\(624\) | −14.2999 | −0.572456 | ||||||||
\(625\) | −5.93344 | −0.237338 | ||||||||
\(626\) | −14.6221 | −0.584416 | ||||||||
\(627\) | −13.6471 | −0.545014 | ||||||||
\(628\) | −11.6640 | −0.465442 | ||||||||
\(629\) | 26.8075 | 1.06889 | ||||||||
\(630\) | 11.9962 | 0.477939 | ||||||||
\(631\) | −24.7116 | −0.983752 | −0.491876 | − | 0.870665i | \(-0.663689\pi\) | ||||
−0.491876 | + | 0.870665i | \(0.663689\pi\) | |||||||
\(632\) | 11.6261 | 0.462460 | ||||||||
\(633\) | −4.23930 | −0.168497 | ||||||||
\(634\) | −18.6590 | −0.741045 | ||||||||
\(635\) | 11.0462 | 0.438356 | ||||||||
\(636\) | 34.5910 | 1.37162 | ||||||||
\(637\) | 4.38488 | 0.173735 | ||||||||
\(638\) | −2.40516 | −0.0952211 | ||||||||
\(639\) | −63.2306 | −2.50136 | ||||||||
\(640\) | 1.57113 | 0.0621043 | ||||||||
\(641\) | −33.2427 | −1.31301 | −0.656505 | − | 0.754322i | \(-0.727966\pi\) | ||||
−0.656505 | + | 0.754322i | \(0.727966\pi\) | |||||||
\(642\) | −7.12663 | −0.281266 | ||||||||
\(643\) | 17.2791 | 0.681422 | 0.340711 | − | 0.940168i | \(-0.389332\pi\) | ||||
0.340711 | + | 0.940168i | \(0.389332\pi\) | |||||||
\(644\) | −5.34535 | −0.210636 | ||||||||
\(645\) | −46.3877 | −1.82651 | ||||||||
\(646\) | −8.66379 | −0.340872 | ||||||||
\(647\) | −47.6101 | −1.87175 | −0.935873 | − | 0.352336i | \(-0.885387\pi\) | ||||
−0.935873 | + | 0.352336i | \(0.885387\pi\) | |||||||
\(648\) | −26.3929 | −1.03681 | ||||||||
\(649\) | −39.2371 | −1.54019 | ||||||||
\(650\) | 11.1006 | 0.435400 | ||||||||
\(651\) | 28.0842 | 1.10071 | ||||||||
\(652\) | 7.11424 | 0.278615 | ||||||||
\(653\) | 1.35550 | 0.0530447 | 0.0265223 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265223 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(654\) | −14.6246 | −0.571869 | ||||||||
\(655\) | −6.56088 | −0.256355 | ||||||||
\(656\) | −2.93275 | −0.114505 | ||||||||
\(657\) | 57.9145 | 2.25946 | ||||||||
\(658\) | −5.79002 | −0.225718 | ||||||||
\(659\) | −20.8063 | −0.810499 | −0.405250 | − | 0.914206i | \(-0.632815\pi\) | ||||
−0.405250 | + | 0.914206i | \(0.632815\pi\) | |||||||
\(660\) | 17.2528 | 0.671565 | ||||||||
\(661\) | 40.5697 | 1.57798 | 0.788989 | − | 0.614407i | \(-0.210605\pi\) | ||||
0.788989 | + | 0.614407i | \(0.210605\pi\) | |||||||
\(662\) | −16.6382 | −0.646663 | ||||||||
\(663\) | −99.6896 | −3.87162 | ||||||||
\(664\) | −15.1640 | −0.588476 | ||||||||
\(665\) | −1.95256 | −0.0757170 | ||||||||
\(666\) | −29.3611 | −1.13772 | ||||||||
\(667\) | −3.81810 | −0.147837 | ||||||||
\(668\) | 14.9273 | 0.577553 | ||||||||
\(669\) | 5.62705 | 0.217554 | ||||||||
\(670\) | 15.2045 | 0.587400 | ||||||||
\(671\) | 32.0530 | 1.23739 | ||||||||
\(672\) | 3.26119 | 0.125803 | ||||||||
\(673\) | −14.7209 | −0.567450 | −0.283725 | − | 0.958906i | \(-0.591570\pi\) | ||||
−0.283725 | + | 0.958906i | \(0.591570\pi\) | |||||||
\(674\) | −34.5642 | −1.33137 | ||||||||
\(675\) | 38.2692 | 1.47298 | ||||||||
\(676\) | 6.22716 | 0.239506 | ||||||||
\(677\) | 15.6906 | 0.603038 | 0.301519 | − | 0.953460i | \(-0.402506\pi\) | ||||
0.301519 | + | 0.953460i | \(0.402506\pi\) | |||||||
\(678\) | −45.3762 | −1.74266 | ||||||||
\(679\) | 12.5883 | 0.483096 | ||||||||
\(680\) | 10.9529 | 0.420023 | ||||||||
\(681\) | 22.2982 | 0.854468 | ||||||||
\(682\) | 28.9973 | 1.11036 | ||||||||
\(683\) | 36.9372 | 1.41336 | 0.706681 | − | 0.707532i | \(-0.250191\pi\) | ||||
0.706681 | + | 0.707532i | \(0.250191\pi\) | |||||||
\(684\) | 9.48906 | 0.362823 | ||||||||
\(685\) | 5.83370 | 0.222894 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −43.4409 | −1.65737 | ||||||||
\(688\) | −9.05346 | −0.345160 | ||||||||
\(689\) | −46.5098 | −1.77188 | ||||||||
\(690\) | 27.3882 | 1.04265 | ||||||||
\(691\) | 16.1687 | 0.615088 | 0.307544 | − | 0.951534i | \(-0.400493\pi\) | ||||
0.307544 | + | 0.951534i | \(0.400493\pi\) | |||||||
\(692\) | 2.92196 | 0.111076 | ||||||||
\(693\) | 25.7100 | 0.976644 | ||||||||
\(694\) | −2.49822 | −0.0948313 | ||||||||
\(695\) | −5.70614 | −0.216446 | ||||||||
\(696\) | 2.32942 | 0.0882965 | ||||||||
\(697\) | −20.4452 | −0.774417 | ||||||||
\(698\) | −3.46239 | −0.131053 | ||||||||
\(699\) | 34.3925 | 1.30084 | ||||||||
\(700\) | −2.53156 | −0.0956838 | ||||||||
\(701\) | 42.3903 | 1.60106 | 0.800530 | − | 0.599292i | \(-0.204551\pi\) | ||||
0.800530 | + | 0.599292i | \(0.204551\pi\) | |||||||
\(702\) | 66.2857 | 2.50179 | ||||||||
\(703\) | 4.77896 | 0.180242 | ||||||||
\(704\) | 3.36723 | 0.126907 | ||||||||
\(705\) | 29.6666 | 1.11731 | ||||||||
\(706\) | −6.79546 | −0.255751 | ||||||||
\(707\) | −14.2268 | −0.535052 | ||||||||
\(708\) | 38.0016 | 1.42819 | ||||||||
\(709\) | 13.8289 | 0.519356 | 0.259678 | − | 0.965695i | \(-0.416384\pi\) | ||||
0.259678 | + | 0.965695i | \(0.416384\pi\) | |||||||
\(710\) | −13.0109 | −0.488291 | ||||||||
\(711\) | −88.7695 | −3.32911 | ||||||||
\(712\) | 3.09589 | 0.116023 | ||||||||
\(713\) | 46.0322 | 1.72392 | ||||||||
\(714\) | 22.7349 | 0.850831 | ||||||||
\(715\) | −23.1975 | −0.867538 | ||||||||
\(716\) | −19.3029 | −0.721381 | ||||||||
\(717\) | −72.3616 | −2.70240 | ||||||||
\(718\) | −30.4002 | −1.13453 | ||||||||
\(719\) | 0.806829 | 0.0300896 | 0.0150448 | − | 0.999887i | \(-0.495211\pi\) | ||||
0.0150448 | + | 0.999887i | \(0.495211\pi\) | |||||||
\(720\) | −11.9962 | −0.447071 | ||||||||
\(721\) | −13.2806 | −0.494596 | ||||||||
\(722\) | 17.4555 | 0.649627 | ||||||||
\(723\) | −1.01718 | −0.0378293 | ||||||||
\(724\) | −21.4000 | −0.795324 | ||||||||
\(725\) | −1.80825 | −0.0671568 | ||||||||
\(726\) | 1.10295 | 0.0409345 | ||||||||
\(727\) | −24.9063 | −0.923725 | −0.461863 | − | 0.886952i | \(-0.652819\pi\) | ||||
−0.461863 | + | 0.886952i | \(0.652819\pi\) | |||||||
\(728\) | −4.38488 | −0.162514 | ||||||||
\(729\) | 53.6227 | 1.98603 | ||||||||
\(730\) | 11.9170 | 0.441069 | ||||||||
\(731\) | −63.1146 | −2.33438 | ||||||||
\(732\) | −31.0436 | −1.14741 | ||||||||
\(733\) | −16.3177 | −0.602708 | −0.301354 | − | 0.953512i | \(-0.597439\pi\) | ||||
−0.301354 | + | 0.953512i | \(0.597439\pi\) | |||||||
\(734\) | 2.07915 | 0.0767429 | ||||||||
\(735\) | 5.12375 | 0.188992 | ||||||||
\(736\) | 5.34535 | 0.197032 | ||||||||
\(737\) | 32.5861 | 1.20032 | ||||||||
\(738\) | 22.3927 | 0.824286 | ||||||||
\(739\) | −8.66294 | −0.318671 | −0.159336 | − | 0.987224i | \(-0.550935\pi\) | ||||
−0.159336 | + | 0.987224i | \(0.550935\pi\) | |||||||
\(740\) | −6.04161 | −0.222094 | ||||||||
\(741\) | −17.7716 | −0.652856 | ||||||||
\(742\) | 10.6069 | 0.389390 | ||||||||
\(743\) | −45.8861 | −1.68340 | −0.841699 | − | 0.539947i | \(-0.818444\pi\) | ||||
−0.841699 | + | 0.539947i | \(0.818444\pi\) | |||||||
\(744\) | −28.0842 | −1.02962 | ||||||||
\(745\) | 31.0156 | 1.13633 | ||||||||
\(746\) | −5.48030 | −0.200648 | ||||||||
\(747\) | 115.783 | 4.23627 | ||||||||
\(748\) | 23.4740 | 0.858296 | ||||||||
\(749\) | −2.18528 | −0.0798485 | ||||||||
\(750\) | 38.5898 | 1.40910 | ||||||||
\(751\) | −25.1720 | −0.918538 | −0.459269 | − | 0.888297i | \(-0.651889\pi\) | ||||
−0.459269 | + | 0.888297i | \(0.651889\pi\) | |||||||
\(752\) | 5.79002 | 0.211140 | ||||||||
\(753\) | 49.4763 | 1.80302 | ||||||||
\(754\) | −3.13205 | −0.114063 | ||||||||
\(755\) | 9.86602 | 0.359061 | ||||||||
\(756\) | −15.1169 | −0.549795 | ||||||||
\(757\) | −53.6092 | −1.94846 | −0.974230 | − | 0.225557i | \(-0.927580\pi\) | ||||
−0.974230 | + | 0.225557i | \(0.927580\pi\) | |||||||
\(758\) | 1.62719 | 0.0591020 | ||||||||
\(759\) | 58.6982 | 2.13061 | ||||||||
\(760\) | 1.95256 | 0.0708267 | ||||||||
\(761\) | −3.15020 | −0.114195 | −0.0570973 | − | 0.998369i | \(-0.518185\pi\) | ||||
−0.0570973 | + | 0.998369i | \(0.518185\pi\) | |||||||
\(762\) | −22.9286 | −0.830617 | ||||||||
\(763\) | −4.48445 | −0.162348 | ||||||||
\(764\) | −0.683469 | −0.0247270 | ||||||||
\(765\) | −83.6292 | −3.02362 | ||||||||
\(766\) | 13.2210 | 0.477693 | ||||||||
\(767\) | −51.0955 | −1.84495 | ||||||||
\(768\) | −3.26119 | −0.117678 | ||||||||
\(769\) | 16.1388 | 0.581981 | 0.290991 | − | 0.956726i | \(-0.406015\pi\) | ||||
0.290991 | + | 0.956726i | \(0.406015\pi\) | |||||||
\(770\) | 5.29034 | 0.190651 | ||||||||
\(771\) | 70.6611 | 2.54480 | ||||||||
\(772\) | −8.49410 | −0.305709 | ||||||||
\(773\) | −4.95524 | −0.178228 | −0.0891139 | − | 0.996021i | \(-0.528403\pi\) | ||||
−0.0891139 | + | 0.996021i | \(0.528403\pi\) | |||||||
\(774\) | 69.1266 | 2.48470 | ||||||||
\(775\) | 21.8008 | 0.783109 | ||||||||
\(776\) | −12.5883 | −0.451895 | ||||||||
\(777\) | −12.5406 | −0.449891 | ||||||||
\(778\) | 3.02357 | 0.108400 | ||||||||
\(779\) | −3.64475 | −0.130587 | ||||||||
\(780\) | 22.4670 | 0.804449 | ||||||||
\(781\) | −27.8849 | −0.997799 | ||||||||
\(782\) | 37.2642 | 1.33256 | ||||||||
\(783\) | −10.7978 | −0.385880 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 18.3256 | 0.654068 | ||||||||
\(786\) | 13.6184 | 0.485753 | ||||||||
\(787\) | 46.0584 | 1.64180 | 0.820901 | − | 0.571070i | \(-0.193471\pi\) | ||||
0.820901 | + | 0.571070i | \(0.193471\pi\) | |||||||
\(788\) | −3.62907 | −0.129280 | ||||||||
\(789\) | 76.5550 | 2.72543 | ||||||||
\(790\) | −18.2660 | −0.649877 | ||||||||
\(791\) | −13.9140 | −0.494725 | ||||||||
\(792\) | −25.7100 | −0.913567 | ||||||||
\(793\) | 41.7401 | 1.48223 | ||||||||
\(794\) | 13.4729 | 0.478136 | ||||||||
\(795\) | −54.3469 | −1.92749 | ||||||||
\(796\) | 4.16886 | 0.147761 | ||||||||
\(797\) | −3.72891 | −0.132085 | −0.0660423 | − | 0.997817i | \(-0.521037\pi\) | ||||
−0.0660423 | + | 0.997817i | \(0.521037\pi\) | |||||||
\(798\) | 4.05293 | 0.143472 | ||||||||
\(799\) | 40.3641 | 1.42798 | ||||||||
\(800\) | 2.53156 | 0.0895040 | ||||||||
\(801\) | −23.6383 | −0.835219 | ||||||||
\(802\) | 19.2938 | 0.681289 | ||||||||
\(803\) | 25.5405 | 0.901304 | ||||||||
\(804\) | −31.5599 | −1.11303 | ||||||||
\(805\) | 8.39823 | 0.295999 | ||||||||
\(806\) | 37.7610 | 1.33007 | ||||||||
\(807\) | 38.8304 | 1.36689 | ||||||||
\(808\) | 14.2268 | 0.500496 | ||||||||
\(809\) | −8.85209 | −0.311223 | −0.155611 | − | 0.987818i | \(-0.549735\pi\) | ||||
−0.155611 | + | 0.987818i | \(0.549735\pi\) | |||||||
\(810\) | 41.4666 | 1.45699 | ||||||||
\(811\) | −4.67052 | −0.164004 | −0.0820020 | − | 0.996632i | \(-0.526131\pi\) | ||||
−0.0820020 | + | 0.996632i | \(0.526131\pi\) | |||||||
\(812\) | 0.714285 | 0.0250665 | ||||||||
\(813\) | −21.8623 | −0.766744 | ||||||||
\(814\) | −12.9483 | −0.453838 | ||||||||
\(815\) | −11.1774 | −0.391527 | ||||||||
\(816\) | −22.7349 | −0.795879 | ||||||||
\(817\) | −11.2514 | −0.393637 | ||||||||
\(818\) | −10.3677 | −0.362497 | ||||||||
\(819\) | 33.4802 | 1.16989 | ||||||||
\(820\) | 4.60773 | 0.160909 | ||||||||
\(821\) | 32.7449 | 1.14280 | 0.571402 | − | 0.820670i | \(-0.306400\pi\) | ||||
0.571402 | + | 0.820670i | \(0.306400\pi\) | |||||||
\(822\) | −12.1090 | −0.422351 | ||||||||
\(823\) | 0.628101 | 0.0218942 | 0.0109471 | − | 0.999940i | \(-0.496515\pi\) | ||||
0.0109471 | + | 0.999940i | \(0.496515\pi\) | |||||||
\(824\) | 13.2806 | 0.462653 | ||||||||
\(825\) | 27.7995 | 0.967853 | ||||||||
\(826\) | 11.6527 | 0.405448 | ||||||||
\(827\) | −24.2206 | −0.842231 | −0.421116 | − | 0.907007i | \(-0.638361\pi\) | ||||
−0.421116 | + | 0.907007i | \(0.638361\pi\) | |||||||
\(828\) | −40.8138 | −1.41838 | ||||||||
\(829\) | −30.1071 | −1.04566 | −0.522831 | − | 0.852436i | \(-0.675124\pi\) | ||||
−0.522831 | + | 0.852436i | \(0.675124\pi\) | |||||||
\(830\) | 23.8245 | 0.826961 | ||||||||
\(831\) | −80.8408 | −2.80434 | ||||||||
\(832\) | 4.38488 | 0.152018 | ||||||||
\(833\) | 6.97133 | 0.241542 | ||||||||
\(834\) | 11.8442 | 0.410133 | ||||||||
\(835\) | −23.4526 | −0.811612 | ||||||||
\(836\) | 4.18470 | 0.144731 | ||||||||
\(837\) | 130.181 | 4.49971 | ||||||||
\(838\) | −23.9351 | −0.826824 | ||||||||
\(839\) | −30.9338 | −1.06795 | −0.533977 | − | 0.845499i | \(-0.679303\pi\) | ||||
−0.533977 | + | 0.845499i | \(0.679303\pi\) | |||||||
\(840\) | −5.12375 | −0.176786 | ||||||||
\(841\) | −28.4898 | −0.982407 | ||||||||
\(842\) | −32.5135 | −1.12049 | ||||||||
\(843\) | 3.65266 | 0.125804 | ||||||||
\(844\) | 1.29992 | 0.0447452 | ||||||||
\(845\) | −9.78367 | −0.336569 | ||||||||
\(846\) | −44.2090 | −1.51994 | ||||||||
\(847\) | 0.338206 | 0.0116209 | ||||||||
\(848\) | −10.6069 | −0.364241 | ||||||||
\(849\) | 49.5196 | 1.69951 | ||||||||
\(850\) | 17.6483 | 0.605332 | ||||||||
\(851\) | −20.5550 | −0.704615 | ||||||||
\(852\) | 27.0068 | 0.925238 | ||||||||
\(853\) | −27.0888 | −0.927504 | −0.463752 | − | 0.885965i | \(-0.653497\pi\) | ||||
−0.463752 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(854\) | −9.51910 | −0.325737 | ||||||||
\(855\) | −14.9085 | −0.509861 | ||||||||
\(856\) | 2.18528 | 0.0746914 | ||||||||
\(857\) | −32.3127 | −1.10378 | −0.551890 | − | 0.833917i | \(-0.686093\pi\) | ||||
−0.551890 | + | 0.833917i | \(0.686093\pi\) | |||||||
\(858\) | 48.1511 | 1.64385 | ||||||||
\(859\) | 45.4196 | 1.54970 | 0.774849 | − | 0.632146i | \(-0.217826\pi\) | ||||
0.774849 | + | 0.632146i | \(0.217826\pi\) | |||||||
\(860\) | 14.2241 | 0.485039 | ||||||||
\(861\) | 9.56427 | 0.325949 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 4.68965 | 0.159638 | 0.0798188 | − | 0.996809i | \(-0.474566\pi\) | ||||
0.0798188 | + | 0.996809i | \(0.474566\pi\) | |||||||
\(864\) | 15.1169 | 0.514287 | ||||||||
\(865\) | −4.59078 | −0.156091 | ||||||||
\(866\) | −21.3318 | −0.724884 | ||||||||
\(867\) | −103.052 | −3.49983 | ||||||||
\(868\) | −8.61163 | −0.292298 | ||||||||
\(869\) | −39.1476 | −1.32799 | ||||||||
\(870\) | −3.65982 | −0.124079 | ||||||||
\(871\) | 42.4343 | 1.43783 | ||||||||
\(872\) | 4.48445 | 0.151863 | ||||||||
\(873\) | 96.1167 | 3.25306 | ||||||||
\(874\) | 6.64306 | 0.224705 | ||||||||
\(875\) | 11.8330 | 0.400030 | ||||||||
\(876\) | −24.7362 | −0.835759 | ||||||||
\(877\) | −33.1684 | −1.12002 | −0.560008 | − | 0.828487i | \(-0.689202\pi\) | ||||
−0.560008 | + | 0.828487i | \(0.689202\pi\) | |||||||
\(878\) | 30.9592 | 1.04482 | ||||||||
\(879\) | −7.71433 | −0.260198 | ||||||||
\(880\) | −5.29034 | −0.178337 | ||||||||
\(881\) | 4.10609 | 0.138338 | 0.0691689 | − | 0.997605i | \(-0.477965\pi\) | ||||
0.0691689 | + | 0.997605i | \(0.477965\pi\) | |||||||
\(882\) | −7.63538 | −0.257097 | ||||||||
\(883\) | −13.8065 | −0.464624 | −0.232312 | − | 0.972641i | \(-0.574629\pi\) | ||||
−0.232312 | + | 0.972641i | \(0.574629\pi\) | |||||||
\(884\) | 30.5684 | 1.02813 | ||||||||
\(885\) | −59.7053 | −2.00697 | ||||||||
\(886\) | 18.0899 | 0.607743 | ||||||||
\(887\) | 54.3458 | 1.82475 | 0.912377 | − | 0.409350i | \(-0.134244\pi\) | ||||
0.912377 | + | 0.409350i | \(0.134244\pi\) | |||||||
\(888\) | 12.5406 | 0.420834 | ||||||||
\(889\) | −7.03075 | −0.235804 | ||||||||
\(890\) | −4.86404 | −0.163043 | ||||||||
\(891\) | 88.8709 | 2.97729 | ||||||||
\(892\) | −1.72546 | −0.0577726 | ||||||||
\(893\) | 7.19569 | 0.240794 | ||||||||
\(894\) | −64.3792 | −2.15316 | ||||||||
\(895\) | 30.3273 | 1.01373 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 76.4381 | 2.55219 | ||||||||
\(898\) | 24.9108 | 0.831285 | ||||||||
\(899\) | −6.15116 | −0.205153 | ||||||||
\(900\) | −19.3294 | −0.644313 | ||||||||
\(901\) | −73.9439 | −2.46343 | ||||||||
\(902\) | 9.87524 | 0.328809 | ||||||||
\(903\) | 29.5251 | 0.982533 | ||||||||
\(904\) | 13.9140 | 0.462772 | ||||||||
\(905\) | 33.6221 | 1.11764 | ||||||||
\(906\) | −20.4789 | −0.680366 | ||||||||
\(907\) | 8.36601 | 0.277789 | 0.138894 | − | 0.990307i | \(-0.455645\pi\) | ||||
0.138894 | + | 0.990307i | \(0.455645\pi\) | |||||||
\(908\) | −6.83743 | −0.226908 | ||||||||
\(909\) | −108.627 | −3.60292 | ||||||||
\(910\) | 6.88921 | 0.228375 | ||||||||
\(911\) | 57.2065 | 1.89534 | 0.947668 | − | 0.319257i | \(-0.103433\pi\) | ||||
0.947668 | + | 0.319257i | \(0.103433\pi\) | |||||||
\(912\) | −4.05293 | −0.134206 | ||||||||
\(913\) | 51.0605 | 1.68986 | ||||||||
\(914\) | −4.95753 | −0.163981 | ||||||||
\(915\) | 48.7735 | 1.61240 | ||||||||
\(916\) | 13.3205 | 0.440123 | ||||||||
\(917\) | 4.17590 | 0.137901 | ||||||||
\(918\) | 105.385 | 3.47821 | ||||||||
\(919\) | −37.3857 | −1.23324 | −0.616619 | − | 0.787261i | \(-0.711498\pi\) | ||||
−0.616619 | + | 0.787261i | \(0.711498\pi\) | |||||||
\(920\) | −8.39823 | −0.276881 | ||||||||
\(921\) | −102.979 | −3.39327 | ||||||||
\(922\) | −26.9228 | −0.886655 | ||||||||
\(923\) | −36.3123 | −1.19523 | ||||||||
\(924\) | −10.9812 | −0.361254 | ||||||||
\(925\) | −9.73483 | −0.320079 | ||||||||
\(926\) | 7.07952 | 0.232647 | ||||||||
\(927\) | −101.403 | −3.33050 | ||||||||
\(928\) | −0.714285 | −0.0234475 | ||||||||
\(929\) | 3.18317 | 0.104437 | 0.0522183 | − | 0.998636i | \(-0.483371\pi\) | ||||
0.0522183 | + | 0.998636i | \(0.483371\pi\) | |||||||
\(930\) | 44.1239 | 1.44688 | ||||||||
\(931\) | 1.24277 | 0.0407303 | ||||||||
\(932\) | −10.5460 | −0.345445 | ||||||||
\(933\) | 102.479 | 3.35500 | ||||||||
\(934\) | −2.70233 | −0.0884231 | ||||||||
\(935\) | −36.8807 | −1.20613 | ||||||||
\(936\) | −33.4802 | −1.09434 | ||||||||
\(937\) | −6.52518 | −0.213168 | −0.106584 | − | 0.994304i | \(-0.533991\pi\) | ||||
−0.106584 | + | 0.994304i | \(0.533991\pi\) | |||||||
\(938\) | −9.67742 | −0.315979 | ||||||||
\(939\) | −47.6855 | −1.55616 | ||||||||
\(940\) | −9.09686 | −0.296707 | ||||||||
\(941\) | −10.2289 | −0.333452 | −0.166726 | − | 0.986003i | \(-0.553320\pi\) | ||||
−0.166726 | + | 0.986003i | \(0.553320\pi\) | |||||||
\(942\) | −38.0384 | −1.23936 | ||||||||
\(943\) | 15.6766 | 0.510500 | ||||||||
\(944\) | −11.6527 | −0.379262 | ||||||||
\(945\) | 23.7505 | 0.772605 | ||||||||
\(946\) | 30.4850 | 0.991154 | ||||||||
\(947\) | 38.0021 | 1.23490 | 0.617451 | − | 0.786610i | \(-0.288165\pi\) | ||||
0.617451 | + | 0.786610i | \(0.288165\pi\) | |||||||
\(948\) | 37.9149 | 1.23142 | ||||||||
\(949\) | 33.2594 | 1.07965 | ||||||||
\(950\) | 3.14615 | 0.102075 | ||||||||
\(951\) | −60.8508 | −1.97322 | ||||||||
\(952\) | −6.97133 | −0.225942 | ||||||||
\(953\) | 3.63754 | 0.117831 | 0.0589157 | − | 0.998263i | \(-0.481236\pi\) | ||||
0.0589157 | + | 0.998263i | \(0.481236\pi\) | |||||||
\(954\) | 80.9874 | 2.62206 | ||||||||
\(955\) | 1.07382 | 0.0347479 | ||||||||
\(956\) | 22.1887 | 0.717634 | ||||||||
\(957\) | −7.84368 | −0.253550 | ||||||||
\(958\) | 18.1714 | 0.587092 | ||||||||
\(959\) | −3.71306 | −0.119901 | ||||||||
\(960\) | 5.12375 | 0.165368 | ||||||||
\(961\) | 43.1602 | 1.39227 | ||||||||
\(962\) | −16.8616 | −0.543639 | ||||||||
\(963\) | −16.6855 | −0.537682 | ||||||||
\(964\) | 0.311904 | 0.0100458 | ||||||||
\(965\) | 13.3453 | 0.429601 | ||||||||
\(966\) | −17.4322 | −0.560872 | ||||||||
\(967\) | 40.4191 | 1.29979 | 0.649896 | − | 0.760023i | \(-0.274813\pi\) | ||||
0.649896 | + | 0.760023i | \(0.274813\pi\) | |||||||
\(968\) | −0.338206 | −0.0108703 | ||||||||
\(969\) | −28.2543 | −0.907659 | ||||||||
\(970\) | 19.7779 | 0.635029 | ||||||||
\(971\) | 36.7845 | 1.18047 | 0.590236 | − | 0.807231i | \(-0.299035\pi\) | ||||
0.590236 | + | 0.807231i | \(0.299035\pi\) | |||||||
\(972\) | −40.7217 | −1.30615 | ||||||||
\(973\) | 3.63187 | 0.116433 | ||||||||
\(974\) | 16.1307 | 0.516862 | ||||||||
\(975\) | 36.2011 | 1.15936 | ||||||||
\(976\) | 9.51910 | 0.304699 | ||||||||
\(977\) | 31.0061 | 0.991972 | 0.495986 | − | 0.868331i | \(-0.334807\pi\) | ||||
0.495986 | + | 0.868331i | \(0.334807\pi\) | |||||||
\(978\) | 23.2009 | 0.741884 | ||||||||
\(979\) | −10.4246 | −0.333171 | ||||||||
\(980\) | −1.57113 | −0.0501878 | ||||||||
\(981\) | −34.2405 | −1.09321 | ||||||||
\(982\) | 18.1349 | 0.578708 | ||||||||
\(983\) | 21.8076 | 0.695554 | 0.347777 | − | 0.937577i | \(-0.386937\pi\) | ||||
0.347777 | + | 0.937577i | \(0.386937\pi\) | |||||||
\(984\) | −9.56427 | −0.304898 | ||||||||
\(985\) | 5.70173 | 0.181672 | ||||||||
\(986\) | −4.97951 | −0.158580 | ||||||||
\(987\) | −18.8824 | −0.601032 | ||||||||
\(988\) | 5.44942 | 0.173369 | ||||||||
\(989\) | 48.3939 | 1.53884 | ||||||||
\(990\) | 40.3938 | 1.28380 | ||||||||
\(991\) | −2.79087 | −0.0886548 | −0.0443274 | − | 0.999017i | \(-0.514114\pi\) | ||||
−0.0443274 | + | 0.999017i | \(0.514114\pi\) | |||||||
\(992\) | 8.61163 | 0.273420 | ||||||||
\(993\) | −54.2605 | −1.72190 | ||||||||
\(994\) | 8.28126 | 0.262666 | ||||||||
\(995\) | −6.54981 | −0.207643 | ||||||||
\(996\) | −49.4526 | −1.56697 | ||||||||
\(997\) | 8.17537 | 0.258916 | 0.129458 | − | 0.991585i | \(-0.458676\pi\) | ||||
0.129458 | + | 0.991585i | \(0.458676\pi\) | |||||||
\(998\) | 32.7814 | 1.03768 | ||||||||
\(999\) | −58.1303 | −1.83916 |
(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 | 6034.2.a.k.1.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.k.1.1 | ✓ | 20 | 1.1 | even | 1 | trivial |