Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.79590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −0.154802 | −0.0893752 | −0.0446876 | − | 0.999001i | \(-0.514229\pi\) | ||||
−0.0446876 | + | 0.999001i | \(0.514229\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.154802 | 0.0631978 | ||||||||
\(7\) | −4.41535 | −1.66885 | −0.834423 | − | 0.551125i | \(-0.814199\pi\) | ||||
−0.834423 | + | 0.551125i | \(0.814199\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.97604 | −0.992012 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.07208 | −0.926267 | −0.463133 | − | 0.886289i | \(-0.653275\pi\) | ||||
−0.463133 | + | 0.886289i | \(0.653275\pi\) | |||||||
\(12\) | −0.154802 | −0.0446876 | ||||||||
\(13\) | 6.08938 | 1.68889 | 0.844446 | − | 0.535641i | \(-0.179930\pi\) | ||||
0.844446 | + | 0.535641i | \(0.179930\pi\) | |||||||
\(14\) | 4.41535 | 1.18005 | ||||||||
\(15\) | 0.154802 | 0.0399698 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.99132 | 1.69565 | 0.847823 | − | 0.530280i | \(-0.177913\pi\) | ||||
0.847823 | + | 0.530280i | \(0.177913\pi\) | |||||||
\(18\) | 2.97604 | 0.701458 | ||||||||
\(19\) | −0.745971 | −0.171138 | −0.0855688 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855688 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.683507 | 0.149153 | ||||||||
\(22\) | 3.07208 | 0.654969 | ||||||||
\(23\) | −2.22179 | −0.463274 | −0.231637 | − | 0.972802i | \(-0.574408\pi\) | ||||
−0.231637 | + | 0.972802i | \(0.574408\pi\) | |||||||
\(24\) | 0.154802 | 0.0315989 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.08938 | −1.19423 | ||||||||
\(27\) | 0.925104 | 0.178036 | ||||||||
\(28\) | −4.41535 | −0.834423 | ||||||||
\(29\) | 2.48268 | 0.461023 | 0.230511 | − | 0.973070i | \(-0.425960\pi\) | ||||
0.230511 | + | 0.973070i | \(0.425960\pi\) | |||||||
\(30\) | −0.154802 | −0.0282629 | ||||||||
\(31\) | 2.52786 | 0.454017 | 0.227009 | − | 0.973893i | \(-0.427105\pi\) | ||||
0.227009 | + | 0.973893i | \(0.427105\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.475565 | 0.0827852 | ||||||||
\(34\) | −6.99132 | −1.19900 | ||||||||
\(35\) | 4.41535 | 0.746330 | ||||||||
\(36\) | −2.97604 | −0.496006 | ||||||||
\(37\) | −3.01023 | −0.494878 | −0.247439 | − | 0.968903i | \(-0.579589\pi\) | ||||
−0.247439 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(38\) | 0.745971 | 0.121013 | ||||||||
\(39\) | −0.942651 | −0.150945 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.07906 | 0.949389 | 0.474694 | − | 0.880151i | \(-0.342559\pi\) | ||||
0.474694 | + | 0.880151i | \(0.342559\pi\) | |||||||
\(42\) | −0.683507 | −0.105467 | ||||||||
\(43\) | 1.67837 | 0.255948 | 0.127974 | − | 0.991777i | \(-0.459153\pi\) | ||||
0.127974 | + | 0.991777i | \(0.459153\pi\) | |||||||
\(44\) | −3.07208 | −0.463133 | ||||||||
\(45\) | 2.97604 | 0.443641 | ||||||||
\(46\) | 2.22179 | 0.327584 | ||||||||
\(47\) | 2.53479 | 0.369737 | 0.184868 | − | 0.982763i | \(-0.440814\pi\) | ||||
0.184868 | + | 0.982763i | \(0.440814\pi\) | |||||||
\(48\) | −0.154802 | −0.0223438 | ||||||||
\(49\) | 12.4953 | 1.78504 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.08227 | −0.151549 | ||||||||
\(52\) | 6.08938 | 0.844446 | ||||||||
\(53\) | −0.745448 | −0.102395 | −0.0511976 | − | 0.998689i | \(-0.516304\pi\) | ||||
−0.0511976 | + | 0.998689i | \(0.516304\pi\) | |||||||
\(54\) | −0.925104 | −0.125891 | ||||||||
\(55\) | 3.07208 | 0.414239 | ||||||||
\(56\) | 4.41535 | 0.590026 | ||||||||
\(57\) | 0.115478 | 0.0152954 | ||||||||
\(58\) | −2.48268 | −0.325992 | ||||||||
\(59\) | −3.79594 | −0.494189 | −0.247095 | − | 0.968991i | \(-0.579476\pi\) | ||||
−0.247095 | + | 0.968991i | \(0.579476\pi\) | |||||||
\(60\) | 0.154802 | 0.0199849 | ||||||||
\(61\) | 4.16103 | 0.532766 | 0.266383 | − | 0.963867i | \(-0.414171\pi\) | ||||
0.266383 | + | 0.963867i | \(0.414171\pi\) | |||||||
\(62\) | −2.52786 | −0.321039 | ||||||||
\(63\) | 13.1402 | 1.65551 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.08938 | −0.755295 | ||||||||
\(66\) | −0.475565 | −0.0585380 | ||||||||
\(67\) | −13.0017 | −1.58841 | −0.794203 | − | 0.607653i | \(-0.792111\pi\) | ||||
−0.794203 | + | 0.607653i | \(0.792111\pi\) | |||||||
\(68\) | 6.99132 | 0.847823 | ||||||||
\(69\) | 0.343938 | 0.0414052 | ||||||||
\(70\) | −4.41535 | −0.527735 | ||||||||
\(71\) | 8.13964 | 0.965998 | 0.482999 | − | 0.875621i | \(-0.339548\pi\) | ||||
0.482999 | + | 0.875621i | \(0.339548\pi\) | |||||||
\(72\) | 2.97604 | 0.350729 | ||||||||
\(73\) | 1.02853 | 0.120380 | 0.0601902 | − | 0.998187i | \(-0.480829\pi\) | ||||
0.0601902 | + | 0.998187i | \(0.480829\pi\) | |||||||
\(74\) | 3.01023 | 0.349932 | ||||||||
\(75\) | −0.154802 | −0.0178750 | ||||||||
\(76\) | −0.745971 | −0.0855688 | ||||||||
\(77\) | 13.5643 | 1.54580 | ||||||||
\(78\) | 0.942651 | 0.106734 | ||||||||
\(79\) | −7.95012 | −0.894459 | −0.447229 | − | 0.894419i | \(-0.647589\pi\) | ||||
−0.447229 | + | 0.894419i | \(0.647589\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.78490 | 0.976100 | ||||||||
\(82\) | −6.07906 | −0.671319 | ||||||||
\(83\) | −6.71915 | −0.737522 | −0.368761 | − | 0.929524i | \(-0.620218\pi\) | ||||
−0.368761 | + | 0.929524i | \(0.620218\pi\) | |||||||
\(84\) | 0.683507 | 0.0745767 | ||||||||
\(85\) | −6.99132 | −0.758316 | ||||||||
\(86\) | −1.67837 | −0.180983 | ||||||||
\(87\) | −0.384325 | −0.0412040 | ||||||||
\(88\) | 3.07208 | 0.327485 | ||||||||
\(89\) | 8.62004 | 0.913722 | 0.456861 | − | 0.889538i | \(-0.348974\pi\) | ||||
0.456861 | + | 0.889538i | \(0.348974\pi\) | |||||||
\(90\) | −2.97604 | −0.313702 | ||||||||
\(91\) | −26.8868 | −2.81850 | ||||||||
\(92\) | −2.22179 | −0.231637 | ||||||||
\(93\) | −0.391319 | −0.0405779 | ||||||||
\(94\) | −2.53479 | −0.261443 | ||||||||
\(95\) | 0.745971 | 0.0765350 | ||||||||
\(96\) | 0.154802 | 0.0157994 | ||||||||
\(97\) | −16.4913 | −1.67444 | −0.837218 | − | 0.546870i | \(-0.815819\pi\) | ||||
−0.837218 | + | 0.546870i | \(0.815819\pi\) | |||||||
\(98\) | −12.4953 | −1.26222 | ||||||||
\(99\) | 9.14262 | 0.918868 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.6975 | −1.16394 | −0.581970 | − | 0.813210i | \(-0.697718\pi\) | ||||
−0.581970 | + | 0.813210i | \(0.697718\pi\) | |||||||
\(102\) | 1.08227 | 0.107161 | ||||||||
\(103\) | 2.10592 | 0.207503 | 0.103751 | − | 0.994603i | \(-0.466915\pi\) | ||||
0.103751 | + | 0.994603i | \(0.466915\pi\) | |||||||
\(104\) | −6.08938 | −0.597113 | ||||||||
\(105\) | −0.683507 | −0.0667034 | ||||||||
\(106\) | 0.745448 | 0.0724043 | ||||||||
\(107\) | −11.0502 | −1.06826 | −0.534130 | − | 0.845402i | \(-0.679361\pi\) | ||||
−0.534130 | + | 0.845402i | \(0.679361\pi\) | |||||||
\(108\) | 0.925104 | 0.0890182 | ||||||||
\(109\) | −3.08659 | −0.295642 | −0.147821 | − | 0.989014i | \(-0.547226\pi\) | ||||
−0.147821 | + | 0.989014i | \(0.547226\pi\) | |||||||
\(110\) | −3.07208 | −0.292911 | ||||||||
\(111\) | 0.465990 | 0.0442299 | ||||||||
\(112\) | −4.41535 | −0.417211 | ||||||||
\(113\) | 12.8891 | 1.21250 | 0.606250 | − | 0.795274i | \(-0.292673\pi\) | ||||
0.606250 | + | 0.795274i | \(0.292673\pi\) | |||||||
\(114\) | −0.115478 | −0.0108155 | ||||||||
\(115\) | 2.22179 | 0.207183 | ||||||||
\(116\) | 2.48268 | 0.230511 | ||||||||
\(117\) | −18.1222 | −1.67540 | ||||||||
\(118\) | 3.79594 | 0.349444 | ||||||||
\(119\) | −30.8691 | −2.82977 | ||||||||
\(120\) | −0.154802 | −0.0141315 | ||||||||
\(121\) | −1.56233 | −0.142030 | ||||||||
\(122\) | −4.16103 | −0.376722 | ||||||||
\(123\) | −0.941052 | −0.0848518 | ||||||||
\(124\) | 2.52786 | 0.227009 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −13.1402 | −1.17063 | ||||||||
\(127\) | −11.2095 | −0.994681 | −0.497340 | − | 0.867556i | \(-0.665690\pi\) | ||||
−0.497340 | + | 0.867556i | \(0.665690\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.259815 | −0.0228754 | ||||||||
\(130\) | 6.08938 | 0.534074 | ||||||||
\(131\) | 6.16032 | 0.538230 | 0.269115 | − | 0.963108i | \(-0.413269\pi\) | ||||
0.269115 | + | 0.963108i | \(0.413269\pi\) | |||||||
\(132\) | 0.475565 | 0.0413926 | ||||||||
\(133\) | 3.29372 | 0.285602 | ||||||||
\(134\) | 13.0017 | 1.12317 | ||||||||
\(135\) | −0.925104 | −0.0796203 | ||||||||
\(136\) | −6.99132 | −0.599501 | ||||||||
\(137\) | −16.4405 | −1.40460 | −0.702302 | − | 0.711879i | \(-0.747844\pi\) | ||||
−0.702302 | + | 0.711879i | \(0.747844\pi\) | |||||||
\(138\) | −0.343938 | −0.0292779 | ||||||||
\(139\) | 5.10643 | 0.433122 | 0.216561 | − | 0.976269i | \(-0.430516\pi\) | ||||
0.216561 | + | 0.976269i | \(0.430516\pi\) | |||||||
\(140\) | 4.41535 | 0.373165 | ||||||||
\(141\) | −0.392391 | −0.0330453 | ||||||||
\(142\) | −8.13964 | −0.683063 | ||||||||
\(143\) | −18.7071 | −1.56436 | ||||||||
\(144\) | −2.97604 | −0.248003 | ||||||||
\(145\) | −2.48268 | −0.206176 | ||||||||
\(146\) | −1.02853 | −0.0851217 | ||||||||
\(147\) | −1.93430 | −0.159539 | ||||||||
\(148\) | −3.01023 | −0.247439 | ||||||||
\(149\) | 8.47553 | 0.694342 | 0.347171 | − | 0.937802i | \(-0.387142\pi\) | ||||
0.347171 | + | 0.937802i | \(0.387142\pi\) | |||||||
\(150\) | 0.154802 | 0.0126396 | ||||||||
\(151\) | −20.8152 | −1.69391 | −0.846957 | − | 0.531661i | \(-0.821568\pi\) | ||||
−0.846957 | + | 0.531661i | \(0.821568\pi\) | |||||||
\(152\) | 0.745971 | 0.0605063 | ||||||||
\(153\) | −20.8064 | −1.68210 | ||||||||
\(154\) | −13.5643 | −1.09304 | ||||||||
\(155\) | −2.52786 | −0.203043 | ||||||||
\(156\) | −0.942651 | −0.0754725 | ||||||||
\(157\) | 6.57637 | 0.524851 | 0.262426 | − | 0.964952i | \(-0.415478\pi\) | ||||
0.262426 | + | 0.964952i | \(0.415478\pi\) | |||||||
\(158\) | 7.95012 | 0.632478 | ||||||||
\(159\) | 0.115397 | 0.00915159 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 9.80996 | 0.773133 | ||||||||
\(162\) | −8.78490 | −0.690207 | ||||||||
\(163\) | −7.48490 | −0.586263 | −0.293131 | − | 0.956072i | \(-0.594697\pi\) | ||||
−0.293131 | + | 0.956072i | \(0.594697\pi\) | |||||||
\(164\) | 6.07906 | 0.474694 | ||||||||
\(165\) | −0.475565 | −0.0370227 | ||||||||
\(166\) | 6.71915 | 0.521507 | ||||||||
\(167\) | −8.85429 | −0.685166 | −0.342583 | − | 0.939488i | \(-0.611302\pi\) | ||||
−0.342583 | + | 0.939488i | \(0.611302\pi\) | |||||||
\(168\) | −0.683507 | −0.0527337 | ||||||||
\(169\) | 24.0806 | 1.85235 | ||||||||
\(170\) | 6.99132 | 0.536210 | ||||||||
\(171\) | 2.22004 | 0.169770 | ||||||||
\(172\) | 1.67837 | 0.127974 | ||||||||
\(173\) | −12.4239 | −0.944571 | −0.472285 | − | 0.881446i | \(-0.656571\pi\) | ||||
−0.472285 | + | 0.881446i | \(0.656571\pi\) | |||||||
\(174\) | 0.384325 | 0.0291356 | ||||||||
\(175\) | −4.41535 | −0.333769 | ||||||||
\(176\) | −3.07208 | −0.231567 | ||||||||
\(177\) | 0.587620 | 0.0441682 | ||||||||
\(178\) | −8.62004 | −0.646099 | ||||||||
\(179\) | 4.44563 | 0.332282 | 0.166141 | − | 0.986102i | \(-0.446869\pi\) | ||||
0.166141 | + | 0.986102i | \(0.446869\pi\) | |||||||
\(180\) | 2.97604 | 0.221821 | ||||||||
\(181\) | −16.4715 | −1.22431 | −0.612157 | − | 0.790736i | \(-0.709698\pi\) | ||||
−0.612157 | + | 0.790736i | \(0.709698\pi\) | |||||||
\(182\) | 26.8868 | 1.99298 | ||||||||
\(183\) | −0.644138 | −0.0476160 | ||||||||
\(184\) | 2.22179 | 0.163792 | ||||||||
\(185\) | 3.01023 | 0.221316 | ||||||||
\(186\) | 0.391319 | 0.0286929 | ||||||||
\(187\) | −21.4779 | −1.57062 | ||||||||
\(188\) | 2.53479 | 0.184868 | ||||||||
\(189\) | −4.08466 | −0.297115 | ||||||||
\(190\) | −0.745971 | −0.0541184 | ||||||||
\(191\) | 5.80047 | 0.419707 | 0.209853 | − | 0.977733i | \(-0.432701\pi\) | ||||
0.209853 | + | 0.977733i | \(0.432701\pi\) | |||||||
\(192\) | −0.154802 | −0.0111719 | ||||||||
\(193\) | 17.6844 | 1.27295 | 0.636475 | − | 0.771297i | \(-0.280392\pi\) | ||||
0.636475 | + | 0.771297i | \(0.280392\pi\) | |||||||
\(194\) | 16.4913 | 1.18400 | ||||||||
\(195\) | 0.942651 | 0.0675046 | ||||||||
\(196\) | 12.4953 | 0.892522 | ||||||||
\(197\) | 0.207977 | 0.0148178 | 0.00740888 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740888 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(198\) | −9.14262 | −0.649738 | ||||||||
\(199\) | 20.8974 | 1.48138 | 0.740688 | − | 0.671849i | \(-0.234500\pi\) | ||||
0.740688 | + | 0.671849i | \(0.234500\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 2.01269 | 0.141964 | ||||||||
\(202\) | 11.6975 | 0.823030 | ||||||||
\(203\) | −10.9619 | −0.769375 | ||||||||
\(204\) | −1.08227 | −0.0757743 | ||||||||
\(205\) | −6.07906 | −0.424580 | ||||||||
\(206\) | −2.10592 | −0.146727 | ||||||||
\(207\) | 6.61212 | 0.459574 | ||||||||
\(208\) | 6.08938 | 0.422223 | ||||||||
\(209\) | 2.29168 | 0.158519 | ||||||||
\(210\) | 0.683507 | 0.0471664 | ||||||||
\(211\) | 18.2355 | 1.25538 | 0.627691 | − | 0.778463i | \(-0.284000\pi\) | ||||
0.627691 | + | 0.778463i | \(0.284000\pi\) | |||||||
\(212\) | −0.745448 | −0.0511976 | ||||||||
\(213\) | −1.26004 | −0.0863362 | ||||||||
\(214\) | 11.0502 | 0.755374 | ||||||||
\(215\) | −1.67837 | −0.114464 | ||||||||
\(216\) | −0.925104 | −0.0629454 | ||||||||
\(217\) | −11.1614 | −0.757685 | ||||||||
\(218\) | 3.08659 | 0.209050 | ||||||||
\(219\) | −0.159219 | −0.0107590 | ||||||||
\(220\) | 3.07208 | 0.207120 | ||||||||
\(221\) | 42.5729 | 2.86376 | ||||||||
\(222\) | −0.465990 | −0.0312752 | ||||||||
\(223\) | −0.115780 | −0.00775320 | −0.00387660 | − | 0.999992i | \(-0.501234\pi\) | ||||
−0.00387660 | + | 0.999992i | \(0.501234\pi\) | |||||||
\(224\) | 4.41535 | 0.295013 | ||||||||
\(225\) | −2.97604 | −0.198402 | ||||||||
\(226\) | −12.8891 | −0.857367 | ||||||||
\(227\) | −29.4485 | −1.95457 | −0.977284 | − | 0.211935i | \(-0.932024\pi\) | ||||
−0.977284 | + | 0.211935i | \(0.932024\pi\) | |||||||
\(228\) | 0.115478 | 0.00764772 | ||||||||
\(229\) | −6.16106 | −0.407134 | −0.203567 | − | 0.979061i | \(-0.565254\pi\) | ||||
−0.203567 | + | 0.979061i | \(0.565254\pi\) | |||||||
\(230\) | −2.22179 | −0.146500 | ||||||||
\(231\) | −2.09979 | −0.138156 | ||||||||
\(232\) | −2.48268 | −0.162996 | ||||||||
\(233\) | 8.87040 | 0.581119 | 0.290560 | − | 0.956857i | \(-0.406159\pi\) | ||||
0.290560 | + | 0.956857i | \(0.406159\pi\) | |||||||
\(234\) | 18.1222 | 1.18469 | ||||||||
\(235\) | −2.53479 | −0.165351 | ||||||||
\(236\) | −3.79594 | −0.247095 | ||||||||
\(237\) | 1.23070 | 0.0799424 | ||||||||
\(238\) | 30.8691 | 2.00095 | ||||||||
\(239\) | 7.53613 | 0.487472 | 0.243736 | − | 0.969842i | \(-0.421627\pi\) | ||||
0.243736 | + | 0.969842i | \(0.421627\pi\) | |||||||
\(240\) | 0.154802 | 0.00999245 | ||||||||
\(241\) | −25.3180 | −1.63088 | −0.815439 | − | 0.578844i | \(-0.803504\pi\) | ||||
−0.815439 | + | 0.578844i | \(0.803504\pi\) | |||||||
\(242\) | 1.56233 | 0.100430 | ||||||||
\(243\) | −4.13524 | −0.265276 | ||||||||
\(244\) | 4.16103 | 0.266383 | ||||||||
\(245\) | −12.4953 | −0.798296 | ||||||||
\(246\) | 0.941052 | 0.0599993 | ||||||||
\(247\) | −4.54251 | −0.289033 | ||||||||
\(248\) | −2.52786 | −0.160519 | ||||||||
\(249\) | 1.04014 | 0.0659162 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 18.4613 | 1.16527 | 0.582633 | − | 0.812735i | \(-0.302022\pi\) | ||||
0.582633 | + | 0.812735i | \(0.302022\pi\) | |||||||
\(252\) | 13.1402 | 0.827757 | ||||||||
\(253\) | 6.82550 | 0.429116 | ||||||||
\(254\) | 11.2095 | 0.703345 | ||||||||
\(255\) | 1.08227 | 0.0677746 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.3938 | −1.77116 | −0.885578 | − | 0.464491i | \(-0.846237\pi\) | ||||
−0.885578 | + | 0.464491i | \(0.846237\pi\) | |||||||
\(258\) | 0.259815 | 0.0161754 | ||||||||
\(259\) | 13.2912 | 0.825876 | ||||||||
\(260\) | −6.08938 | −0.377648 | ||||||||
\(261\) | −7.38855 | −0.457340 | ||||||||
\(262\) | −6.16032 | −0.380586 | ||||||||
\(263\) | 15.6425 | 0.964559 | 0.482280 | − | 0.876017i | \(-0.339809\pi\) | ||||
0.482280 | + | 0.876017i | \(0.339809\pi\) | |||||||
\(264\) | −0.475565 | −0.0292690 | ||||||||
\(265\) | 0.745448 | 0.0457925 | ||||||||
\(266\) | −3.29372 | −0.201951 | ||||||||
\(267\) | −1.33440 | −0.0816641 | ||||||||
\(268\) | −13.0017 | −0.794203 | ||||||||
\(269\) | 12.6077 | 0.768704 | 0.384352 | − | 0.923187i | \(-0.374425\pi\) | ||||
0.384352 | + | 0.923187i | \(0.374425\pi\) | |||||||
\(270\) | 0.925104 | 0.0563001 | ||||||||
\(271\) | −25.6235 | −1.55651 | −0.778257 | − | 0.627946i | \(-0.783896\pi\) | ||||
−0.778257 | + | 0.627946i | \(0.783896\pi\) | |||||||
\(272\) | 6.99132 | 0.423911 | ||||||||
\(273\) | 4.16213 | 0.251904 | ||||||||
\(274\) | 16.4405 | 0.993205 | ||||||||
\(275\) | −3.07208 | −0.185253 | ||||||||
\(276\) | 0.343938 | 0.0207026 | ||||||||
\(277\) | 29.5108 | 1.77313 | 0.886565 | − | 0.462604i | \(-0.153085\pi\) | ||||
0.886565 | + | 0.462604i | \(0.153085\pi\) | |||||||
\(278\) | −5.10643 | −0.306263 | ||||||||
\(279\) | −7.52301 | −0.450391 | ||||||||
\(280\) | −4.41535 | −0.263868 | ||||||||
\(281\) | −11.9491 | −0.712824 | −0.356412 | − | 0.934329i | \(-0.616000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(282\) | 0.392391 | 0.0233666 | ||||||||
\(283\) | −29.0019 | −1.72398 | −0.861991 | − | 0.506923i | \(-0.830783\pi\) | ||||
−0.861991 | + | 0.506923i | \(0.830783\pi\) | |||||||
\(284\) | 8.13964 | 0.482999 | ||||||||
\(285\) | −0.115478 | −0.00684033 | ||||||||
\(286\) | 18.7071 | 1.10617 | ||||||||
\(287\) | −26.8412 | −1.58438 | ||||||||
\(288\) | 2.97604 | 0.175365 | ||||||||
\(289\) | 31.8786 | 1.87521 | ||||||||
\(290\) | 2.48268 | 0.145788 | ||||||||
\(291\) | 2.55289 | 0.149653 | ||||||||
\(292\) | 1.02853 | 0.0601902 | ||||||||
\(293\) | −7.99449 | −0.467043 | −0.233521 | − | 0.972352i | \(-0.575025\pi\) | ||||
−0.233521 | + | 0.972352i | \(0.575025\pi\) | |||||||
\(294\) | 1.93430 | 0.112811 | ||||||||
\(295\) | 3.79594 | 0.221008 | ||||||||
\(296\) | 3.01023 | 0.174966 | ||||||||
\(297\) | −2.84199 | −0.164909 | ||||||||
\(298\) | −8.47553 | −0.490974 | ||||||||
\(299\) | −13.5293 | −0.782420 | ||||||||
\(300\) | −0.154802 | −0.00893752 | ||||||||
\(301\) | −7.41058 | −0.427138 | ||||||||
\(302\) | 20.8152 | 1.19778 | ||||||||
\(303\) | 1.81079 | 0.104027 | ||||||||
\(304\) | −0.745971 | −0.0427844 | ||||||||
\(305\) | −4.16103 | −0.238260 | ||||||||
\(306\) | 20.8064 | 1.18942 | ||||||||
\(307\) | 24.2347 | 1.38315 | 0.691574 | − | 0.722306i | \(-0.256918\pi\) | ||||
0.691574 | + | 0.722306i | \(0.256918\pi\) | |||||||
\(308\) | 13.5643 | 0.772898 | ||||||||
\(309\) | −0.326002 | −0.0185456 | ||||||||
\(310\) | 2.52786 | 0.143573 | ||||||||
\(311\) | 25.0016 | 1.41771 | 0.708854 | − | 0.705355i | \(-0.249212\pi\) | ||||
0.708854 | + | 0.705355i | \(0.249212\pi\) | |||||||
\(312\) | 0.942651 | 0.0533671 | ||||||||
\(313\) | −22.7439 | −1.28556 | −0.642780 | − | 0.766051i | \(-0.722219\pi\) | ||||
−0.642780 | + | 0.766051i | \(0.722219\pi\) | |||||||
\(314\) | −6.57637 | −0.371126 | ||||||||
\(315\) | −13.1402 | −0.740369 | ||||||||
\(316\) | −7.95012 | −0.447229 | ||||||||
\(317\) | −5.43701 | −0.305373 | −0.152686 | − | 0.988275i | \(-0.548792\pi\) | ||||
−0.152686 | + | 0.988275i | \(0.548792\pi\) | |||||||
\(318\) | −0.115397 | −0.00647115 | ||||||||
\(319\) | −7.62700 | −0.427030 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 1.71059 | 0.0954760 | ||||||||
\(322\) | −9.80996 | −0.546688 | ||||||||
\(323\) | −5.21533 | −0.290188 | ||||||||
\(324\) | 8.78490 | 0.488050 | ||||||||
\(325\) | 6.08938 | 0.337778 | ||||||||
\(326\) | 7.48490 | 0.414551 | ||||||||
\(327\) | 0.477811 | 0.0264230 | ||||||||
\(328\) | −6.07906 | −0.335660 | ||||||||
\(329\) | −11.1920 | −0.617034 | ||||||||
\(330\) | 0.475565 | 0.0261790 | ||||||||
\(331\) | 19.8682 | 1.09206 | 0.546028 | − | 0.837767i | \(-0.316139\pi\) | ||||
0.546028 | + | 0.837767i | \(0.316139\pi\) | |||||||
\(332\) | −6.71915 | −0.368761 | ||||||||
\(333\) | 8.95855 | 0.490925 | ||||||||
\(334\) | 8.85429 | 0.484485 | ||||||||
\(335\) | 13.0017 | 0.710356 | ||||||||
\(336\) | 0.683507 | 0.0372883 | ||||||||
\(337\) | −9.36919 | −0.510372 | −0.255186 | − | 0.966892i | \(-0.582137\pi\) | ||||
−0.255186 | + | 0.966892i | \(0.582137\pi\) | |||||||
\(338\) | −24.0806 | −1.30981 | ||||||||
\(339\) | −1.99526 | −0.108367 | ||||||||
\(340\) | −6.99132 | −0.379158 | ||||||||
\(341\) | −7.76579 | −0.420541 | ||||||||
\(342\) | −2.22004 | −0.120046 | ||||||||
\(343\) | −24.2637 | −1.31012 | ||||||||
\(344\) | −1.67837 | −0.0904915 | ||||||||
\(345\) | −0.343938 | −0.0185170 | ||||||||
\(346\) | 12.4239 | 0.667912 | ||||||||
\(347\) | −8.04989 | −0.432141 | −0.216070 | − | 0.976378i | \(-0.569324\pi\) | ||||
−0.216070 | + | 0.976378i | \(0.569324\pi\) | |||||||
\(348\) | −0.384325 | −0.0206020 | ||||||||
\(349\) | −14.1691 | −0.758456 | −0.379228 | − | 0.925303i | \(-0.623810\pi\) | ||||
−0.379228 | + | 0.925303i | \(0.623810\pi\) | |||||||
\(350\) | 4.41535 | 0.236010 | ||||||||
\(351\) | 5.63332 | 0.300684 | ||||||||
\(352\) | 3.07208 | 0.163742 | ||||||||
\(353\) | 29.1375 | 1.55083 | 0.775417 | − | 0.631449i | \(-0.217539\pi\) | ||||
0.775417 | + | 0.631449i | \(0.217539\pi\) | |||||||
\(354\) | −0.587620 | −0.0312317 | ||||||||
\(355\) | −8.13964 | −0.432007 | ||||||||
\(356\) | 8.62004 | 0.456861 | ||||||||
\(357\) | 4.77862 | 0.252911 | ||||||||
\(358\) | −4.44563 | −0.234959 | ||||||||
\(359\) | −1.74842 | −0.0922780 | −0.0461390 | − | 0.998935i | \(-0.514692\pi\) | ||||
−0.0461390 | + | 0.998935i | \(0.514692\pi\) | |||||||
\(360\) | −2.97604 | −0.156851 | ||||||||
\(361\) | −18.4435 | −0.970712 | ||||||||
\(362\) | 16.4715 | 0.865721 | ||||||||
\(363\) | 0.241853 | 0.0126940 | ||||||||
\(364\) | −26.8868 | −1.40925 | ||||||||
\(365\) | −1.02853 | −0.0538357 | ||||||||
\(366\) | 0.644138 | 0.0336696 | ||||||||
\(367\) | −13.1991 | −0.688986 | −0.344493 | − | 0.938789i | \(-0.611949\pi\) | ||||
−0.344493 | + | 0.938789i | \(0.611949\pi\) | |||||||
\(368\) | −2.22179 | −0.115819 | ||||||||
\(369\) | −18.0915 | −0.941805 | ||||||||
\(370\) | −3.01023 | −0.156494 | ||||||||
\(371\) | 3.29141 | 0.170882 | ||||||||
\(372\) | −0.391319 | −0.0202889 | ||||||||
\(373\) | −35.7076 | −1.84887 | −0.924434 | − | 0.381341i | \(-0.875462\pi\) | ||||
−0.924434 | + | 0.381341i | \(0.875462\pi\) | |||||||
\(374\) | 21.4779 | 1.11060 | ||||||||
\(375\) | 0.154802 | 0.00799396 | ||||||||
\(376\) | −2.53479 | −0.130722 | ||||||||
\(377\) | 15.1180 | 0.778617 | ||||||||
\(378\) | 4.08466 | 0.210092 | ||||||||
\(379\) | 20.2654 | 1.04096 | 0.520481 | − | 0.853873i | \(-0.325753\pi\) | ||||
0.520481 | + | 0.853873i | \(0.325753\pi\) | |||||||
\(380\) | 0.745971 | 0.0382675 | ||||||||
\(381\) | 1.73525 | 0.0888998 | ||||||||
\(382\) | −5.80047 | −0.296778 | ||||||||
\(383\) | −35.0482 | −1.79088 | −0.895439 | − | 0.445183i | \(-0.853139\pi\) | ||||
−0.895439 | + | 0.445183i | \(0.853139\pi\) | |||||||
\(384\) | 0.154802 | 0.00789972 | ||||||||
\(385\) | −13.5643 | −0.691301 | ||||||||
\(386\) | −17.6844 | −0.900111 | ||||||||
\(387\) | −4.99488 | −0.253904 | ||||||||
\(388\) | −16.4913 | −0.837218 | ||||||||
\(389\) | −16.6478 | −0.844078 | −0.422039 | − | 0.906578i | \(-0.638686\pi\) | ||||
−0.422039 | + | 0.906578i | \(0.638686\pi\) | |||||||
\(390\) | −0.942651 | −0.0477330 | ||||||||
\(391\) | −15.5332 | −0.785549 | ||||||||
\(392\) | −12.4953 | −0.631109 | ||||||||
\(393\) | −0.953633 | −0.0481044 | ||||||||
\(394\) | −0.207977 | −0.0104777 | ||||||||
\(395\) | 7.95012 | 0.400014 | ||||||||
\(396\) | 9.14262 | 0.459434 | ||||||||
\(397\) | 3.46731 | 0.174019 | 0.0870095 | − | 0.996207i | \(-0.472269\pi\) | ||||
0.0870095 | + | 0.996207i | \(0.472269\pi\) | |||||||
\(398\) | −20.8974 | −1.04749 | ||||||||
\(399\) | −0.509876 | −0.0255257 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −2.01269 | −0.100384 | ||||||||
\(403\) | 15.3931 | 0.766786 | ||||||||
\(404\) | −11.6975 | −0.581970 | ||||||||
\(405\) | −8.78490 | −0.436525 | ||||||||
\(406\) | 10.9619 | 0.544031 | ||||||||
\(407\) | 9.24766 | 0.458389 | ||||||||
\(408\) | 1.08227 | 0.0535805 | ||||||||
\(409\) | −39.8306 | −1.96949 | −0.984747 | − | 0.173990i | \(-0.944334\pi\) | ||||
−0.984747 | + | 0.173990i | \(0.944334\pi\) | |||||||
\(410\) | 6.07906 | 0.300223 | ||||||||
\(411\) | 2.54502 | 0.125537 | ||||||||
\(412\) | 2.10592 | 0.103751 | ||||||||
\(413\) | 16.7604 | 0.824725 | ||||||||
\(414\) | −6.61212 | −0.324968 | ||||||||
\(415\) | 6.71915 | 0.329830 | ||||||||
\(416\) | −6.08938 | −0.298557 | ||||||||
\(417\) | −0.790487 | −0.0387103 | ||||||||
\(418\) | −2.29168 | −0.112090 | ||||||||
\(419\) | 25.3727 | 1.23954 | 0.619768 | − | 0.784785i | \(-0.287227\pi\) | ||||
0.619768 | + | 0.784785i | \(0.287227\pi\) | |||||||
\(420\) | −0.683507 | −0.0333517 | ||||||||
\(421\) | −21.5568 | −1.05062 | −0.525308 | − | 0.850912i | \(-0.676050\pi\) | ||||
−0.525308 | + | 0.850912i | \(0.676050\pi\) | |||||||
\(422\) | −18.2355 | −0.887689 | ||||||||
\(423\) | −7.54362 | −0.366783 | ||||||||
\(424\) | 0.745448 | 0.0362022 | ||||||||
\(425\) | 6.99132 | 0.339129 | ||||||||
\(426\) | 1.26004 | 0.0610489 | ||||||||
\(427\) | −18.3724 | −0.889103 | ||||||||
\(428\) | −11.0502 | −0.534130 | ||||||||
\(429\) | 2.89590 | 0.139815 | ||||||||
\(430\) | 1.67837 | 0.0809380 | ||||||||
\(431\) | −3.17088 | −0.152736 | −0.0763679 | − | 0.997080i | \(-0.524332\pi\) | ||||
−0.0763679 | + | 0.997080i | \(0.524332\pi\) | |||||||
\(432\) | 0.925104 | 0.0445091 | ||||||||
\(433\) | −13.6613 | −0.656520 | −0.328260 | − | 0.944587i | \(-0.606462\pi\) | ||||
−0.328260 | + | 0.944587i | \(0.606462\pi\) | |||||||
\(434\) | 11.1614 | 0.535764 | ||||||||
\(435\) | 0.384325 | 0.0184270 | ||||||||
\(436\) | −3.08659 | −0.147821 | ||||||||
\(437\) | 1.65739 | 0.0792836 | ||||||||
\(438\) | 0.159219 | 0.00760777 | ||||||||
\(439\) | −12.4747 | −0.595386 | −0.297693 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297693 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(440\) | −3.07208 | −0.146456 | ||||||||
\(441\) | −37.1865 | −1.77079 | ||||||||
\(442\) | −42.5729 | −2.02498 | ||||||||
\(443\) | −14.6634 | −0.696677 | −0.348338 | − | 0.937369i | \(-0.613254\pi\) | ||||
−0.348338 | + | 0.937369i | \(0.613254\pi\) | |||||||
\(444\) | 0.465990 | 0.0221149 | ||||||||
\(445\) | −8.62004 | −0.408629 | ||||||||
\(446\) | 0.115780 | 0.00548234 | ||||||||
\(447\) | −1.31203 | −0.0620570 | ||||||||
\(448\) | −4.41535 | −0.208606 | ||||||||
\(449\) | −10.8612 | −0.512573 | −0.256286 | − | 0.966601i | \(-0.582499\pi\) | ||||
−0.256286 | + | 0.966601i | \(0.582499\pi\) | |||||||
\(450\) | 2.97604 | 0.140292 | ||||||||
\(451\) | −18.6753 | −0.879387 | ||||||||
\(452\) | 12.8891 | 0.606250 | ||||||||
\(453\) | 3.22224 | 0.151394 | ||||||||
\(454\) | 29.4485 | 1.38209 | ||||||||
\(455\) | 26.8868 | 1.26047 | ||||||||
\(456\) | −0.115478 | −0.00540776 | ||||||||
\(457\) | −18.3430 | −0.858050 | −0.429025 | − | 0.903293i | \(-0.641143\pi\) | ||||
−0.429025 | + | 0.903293i | \(0.641143\pi\) | |||||||
\(458\) | 6.16106 | 0.287888 | ||||||||
\(459\) | 6.46770 | 0.301887 | ||||||||
\(460\) | 2.22179 | 0.103591 | ||||||||
\(461\) | 38.6901 | 1.80198 | 0.900988 | − | 0.433844i | \(-0.142843\pi\) | ||||
0.900988 | + | 0.433844i | \(0.142843\pi\) | |||||||
\(462\) | 2.09979 | 0.0976909 | ||||||||
\(463\) | 23.1873 | 1.07760 | 0.538802 | − | 0.842433i | \(-0.318877\pi\) | ||||
0.538802 | + | 0.842433i | \(0.318877\pi\) | |||||||
\(464\) | 2.48268 | 0.115256 | ||||||||
\(465\) | 0.391319 | 0.0181470 | ||||||||
\(466\) | −8.87040 | −0.410913 | ||||||||
\(467\) | 22.1349 | 1.02428 | 0.512140 | − | 0.858902i | \(-0.328853\pi\) | ||||
0.512140 | + | 0.858902i | \(0.328853\pi\) | |||||||
\(468\) | −18.1222 | −0.837700 | ||||||||
\(469\) | 57.4069 | 2.65080 | ||||||||
\(470\) | 2.53479 | 0.116921 | ||||||||
\(471\) | −1.01804 | −0.0469087 | ||||||||
\(472\) | 3.79594 | 0.174722 | ||||||||
\(473\) | −5.15607 | −0.237077 | ||||||||
\(474\) | −1.23070 | −0.0565278 | ||||||||
\(475\) | −0.745971 | −0.0342275 | ||||||||
\(476\) | −30.8691 | −1.41488 | ||||||||
\(477\) | 2.21848 | 0.101577 | ||||||||
\(478\) | −7.53613 | −0.344695 | ||||||||
\(479\) | 16.5196 | 0.754799 | 0.377399 | − | 0.926051i | \(-0.376818\pi\) | ||||
0.377399 | + | 0.926051i | \(0.376818\pi\) | |||||||
\(480\) | −0.154802 | −0.00706573 | ||||||||
\(481\) | −18.3304 | −0.835796 | ||||||||
\(482\) | 25.3180 | 1.15320 | ||||||||
\(483\) | −1.51861 | −0.0690989 | ||||||||
\(484\) | −1.56233 | −0.0710151 | ||||||||
\(485\) | 16.4913 | 0.748830 | ||||||||
\(486\) | 4.13524 | 0.187578 | ||||||||
\(487\) | 29.4405 | 1.33407 | 0.667037 | − | 0.745024i | \(-0.267562\pi\) | ||||
0.667037 | + | 0.745024i | \(0.267562\pi\) | |||||||
\(488\) | −4.16103 | −0.188361 | ||||||||
\(489\) | 1.15868 | 0.0523974 | ||||||||
\(490\) | 12.4953 | 0.564481 | ||||||||
\(491\) | 17.5779 | 0.793280 | 0.396640 | − | 0.917974i | \(-0.370176\pi\) | ||||
0.396640 | + | 0.917974i | \(0.370176\pi\) | |||||||
\(492\) | −0.941052 | −0.0424259 | ||||||||
\(493\) | 17.3572 | 0.781731 | ||||||||
\(494\) | 4.54251 | 0.204377 | ||||||||
\(495\) | −9.14262 | −0.410930 | ||||||||
\(496\) | 2.52786 | 0.113504 | ||||||||
\(497\) | −35.9394 | −1.61210 | ||||||||
\(498\) | −1.04014 | −0.0466098 | ||||||||
\(499\) | −35.8606 | −1.60534 | −0.802672 | − | 0.596421i | \(-0.796589\pi\) | ||||
−0.802672 | + | 0.596421i | \(0.796589\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 1.37067 | 0.0612368 | ||||||||
\(502\) | −18.4613 | −0.823968 | ||||||||
\(503\) | −6.35538 | −0.283372 | −0.141686 | − | 0.989912i | \(-0.545252\pi\) | ||||
−0.141686 | + | 0.989912i | \(0.545252\pi\) | |||||||
\(504\) | −13.1402 | −0.585313 | ||||||||
\(505\) | 11.6975 | 0.520530 | ||||||||
\(506\) | −6.82550 | −0.303431 | ||||||||
\(507\) | −3.72773 | −0.165554 | ||||||||
\(508\) | −11.2095 | −0.497340 | ||||||||
\(509\) | −8.02027 | −0.355492 | −0.177746 | − | 0.984076i | \(-0.556881\pi\) | ||||
−0.177746 | + | 0.984076i | \(0.556881\pi\) | |||||||
\(510\) | −1.08227 | −0.0479239 | ||||||||
\(511\) | −4.54132 | −0.200896 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.690101 | −0.0304687 | ||||||||
\(514\) | 28.3938 | 1.25240 | ||||||||
\(515\) | −2.10592 | −0.0927981 | ||||||||
\(516\) | −0.259815 | −0.0114377 | ||||||||
\(517\) | −7.78707 | −0.342475 | ||||||||
\(518\) | −13.2912 | −0.583982 | ||||||||
\(519\) | 1.92325 | 0.0844212 | ||||||||
\(520\) | 6.08938 | 0.267037 | ||||||||
\(521\) | −33.1875 | −1.45397 | −0.726986 | − | 0.686652i | \(-0.759080\pi\) | ||||
−0.726986 | + | 0.686652i | \(0.759080\pi\) | |||||||
\(522\) | 7.38855 | 0.323388 | ||||||||
\(523\) | −34.9210 | −1.52699 | −0.763494 | − | 0.645815i | \(-0.776518\pi\) | ||||
−0.763494 | + | 0.645815i | \(0.776518\pi\) | |||||||
\(524\) | 6.16032 | 0.269115 | ||||||||
\(525\) | 0.683507 | 0.0298307 | ||||||||
\(526\) | −15.6425 | −0.682047 | ||||||||
\(527\) | 17.6731 | 0.769852 | ||||||||
\(528\) | 0.475565 | 0.0206963 | ||||||||
\(529\) | −18.0637 | −0.785377 | ||||||||
\(530\) | −0.745448 | −0.0323802 | ||||||||
\(531\) | 11.2969 | 0.490242 | ||||||||
\(532\) | 3.29372 | 0.142801 | ||||||||
\(533\) | 37.0177 | 1.60341 | ||||||||
\(534\) | 1.33440 | 0.0577452 | ||||||||
\(535\) | 11.0502 | 0.477741 | ||||||||
\(536\) | 13.0017 | 0.561586 | ||||||||
\(537\) | −0.688193 | −0.0296977 | ||||||||
\(538\) | −12.6077 | −0.543556 | ||||||||
\(539\) | −38.3866 | −1.65343 | ||||||||
\(540\) | −0.925104 | −0.0398102 | ||||||||
\(541\) | 5.86367 | 0.252099 | 0.126049 | − | 0.992024i | \(-0.459770\pi\) | ||||
0.126049 | + | 0.992024i | \(0.459770\pi\) | |||||||
\(542\) | 25.6235 | 1.10062 | ||||||||
\(543\) | 2.54982 | 0.109423 | ||||||||
\(544\) | −6.99132 | −0.299751 | ||||||||
\(545\) | 3.08659 | 0.132215 | ||||||||
\(546\) | −4.16213 | −0.178123 | ||||||||
\(547\) | 11.9297 | 0.510079 | 0.255039 | − | 0.966931i | \(-0.417912\pi\) | ||||
0.255039 | + | 0.966931i | \(0.417912\pi\) | |||||||
\(548\) | −16.4405 | −0.702302 | ||||||||
\(549\) | −12.3834 | −0.528510 | ||||||||
\(550\) | 3.07208 | 0.130994 | ||||||||
\(551\) | −1.85201 | −0.0788983 | ||||||||
\(552\) | −0.343938 | −0.0146390 | ||||||||
\(553\) | 35.1026 | 1.49271 | ||||||||
\(554\) | −29.5108 | −1.25379 | ||||||||
\(555\) | −0.465990 | −0.0197802 | ||||||||
\(556\) | 5.10643 | 0.216561 | ||||||||
\(557\) | 22.5121 | 0.953868 | 0.476934 | − | 0.878939i | \(-0.341748\pi\) | ||||
0.476934 | + | 0.878939i | \(0.341748\pi\) | |||||||
\(558\) | 7.52301 | 0.318474 | ||||||||
\(559\) | 10.2202 | 0.432269 | ||||||||
\(560\) | 4.41535 | 0.186583 | ||||||||
\(561\) | 3.32483 | 0.140374 | ||||||||
\(562\) | 11.9491 | 0.504042 | ||||||||
\(563\) | −5.22004 | −0.219998 | −0.109999 | − | 0.993932i | \(-0.535085\pi\) | ||||
−0.109999 | + | 0.993932i | \(0.535085\pi\) | |||||||
\(564\) | −0.392391 | −0.0165226 | ||||||||
\(565\) | −12.8891 | −0.542247 | ||||||||
\(566\) | 29.0019 | 1.21904 | ||||||||
\(567\) | −38.7884 | −1.62896 | ||||||||
\(568\) | −8.13964 | −0.341532 | ||||||||
\(569\) | −14.6065 | −0.612335 | −0.306168 | − | 0.951978i | \(-0.599047\pi\) | ||||
−0.306168 | + | 0.951978i | \(0.599047\pi\) | |||||||
\(570\) | 0.115478 | 0.00483685 | ||||||||
\(571\) | 2.78927 | 0.116727 | 0.0583636 | − | 0.998295i | \(-0.481412\pi\) | ||||
0.0583636 | + | 0.998295i | \(0.481412\pi\) | |||||||
\(572\) | −18.7071 | −0.782182 | ||||||||
\(573\) | −0.897926 | −0.0375114 | ||||||||
\(574\) | 26.8412 | 1.12033 | ||||||||
\(575\) | −2.22179 | −0.0926549 | ||||||||
\(576\) | −2.97604 | −0.124002 | ||||||||
\(577\) | −22.3981 | −0.932447 | −0.466223 | − | 0.884667i | \(-0.654386\pi\) | ||||
−0.466223 | + | 0.884667i | \(0.654386\pi\) | |||||||
\(578\) | −31.8786 | −1.32598 | ||||||||
\(579\) | −2.73758 | −0.113770 | ||||||||
\(580\) | −2.48268 | −0.103088 | ||||||||
\(581\) | 29.6674 | 1.23081 | ||||||||
\(582\) | −2.55289 | −0.105821 | ||||||||
\(583\) | 2.29008 | 0.0948452 | ||||||||
\(584\) | −1.02853 | −0.0425609 | ||||||||
\(585\) | 18.1222 | 0.749262 | ||||||||
\(586\) | 7.99449 | 0.330249 | ||||||||
\(587\) | 17.3786 | 0.717292 | 0.358646 | − | 0.933474i | \(-0.383239\pi\) | ||||
0.358646 | + | 0.933474i | \(0.383239\pi\) | |||||||
\(588\) | −1.93430 | −0.0797694 | ||||||||
\(589\) | −1.88571 | −0.0776994 | ||||||||
\(590\) | −3.79594 | −0.156276 | ||||||||
\(591\) | −0.0321954 | −0.00132434 | ||||||||
\(592\) | −3.01023 | −0.123720 | ||||||||
\(593\) | 30.3699 | 1.24714 | 0.623570 | − | 0.781767i | \(-0.285681\pi\) | ||||
0.623570 | + | 0.781767i | \(0.285681\pi\) | |||||||
\(594\) | 2.84199 | 0.116608 | ||||||||
\(595\) | 30.8691 | 1.26551 | ||||||||
\(596\) | 8.47553 | 0.347171 | ||||||||
\(597\) | −3.23497 | −0.132398 | ||||||||
\(598\) | 13.5293 | 0.553255 | ||||||||
\(599\) | 38.9697 | 1.59226 | 0.796129 | − | 0.605127i | \(-0.206878\pi\) | ||||
0.796129 | + | 0.605127i | \(0.206878\pi\) | |||||||
\(600\) | 0.154802 | 0.00631978 | ||||||||
\(601\) | −17.3389 | −0.707270 | −0.353635 | − | 0.935383i | \(-0.615055\pi\) | ||||
−0.353635 | + | 0.935383i | \(0.615055\pi\) | |||||||
\(602\) | 7.41058 | 0.302033 | ||||||||
\(603\) | 38.6934 | 1.57572 | ||||||||
\(604\) | −20.8152 | −0.846957 | ||||||||
\(605\) | 1.56233 | 0.0635178 | ||||||||
\(606\) | −1.81079 | −0.0735585 | ||||||||
\(607\) | 16.2869 | 0.661066 | 0.330533 | − | 0.943794i | \(-0.392772\pi\) | ||||
0.330533 | + | 0.943794i | \(0.392772\pi\) | |||||||
\(608\) | 0.745971 | 0.0302531 | ||||||||
\(609\) | 1.69693 | 0.0687631 | ||||||||
\(610\) | 4.16103 | 0.168475 | ||||||||
\(611\) | 15.4353 | 0.624445 | ||||||||
\(612\) | −20.8064 | −0.841050 | ||||||||
\(613\) | 8.14183 | 0.328845 | 0.164423 | − | 0.986390i | \(-0.447424\pi\) | ||||
0.164423 | + | 0.986390i | \(0.447424\pi\) | |||||||
\(614\) | −24.2347 | −0.978033 | ||||||||
\(615\) | 0.941052 | 0.0379469 | ||||||||
\(616\) | −13.5643 | −0.546521 | ||||||||
\(617\) | 25.3130 | 1.01906 | 0.509531 | − | 0.860452i | \(-0.329819\pi\) | ||||
0.509531 | + | 0.860452i | \(0.329819\pi\) | |||||||
\(618\) | 0.326002 | 0.0131137 | ||||||||
\(619\) | 27.8255 | 1.11840 | 0.559201 | − | 0.829032i | \(-0.311108\pi\) | ||||
0.559201 | + | 0.829032i | \(0.311108\pi\) | |||||||
\(620\) | −2.52786 | −0.101521 | ||||||||
\(621\) | −2.05538 | −0.0824797 | ||||||||
\(622\) | −25.0016 | −1.00247 | ||||||||
\(623\) | −38.0605 | −1.52486 | ||||||||
\(624\) | −0.942651 | −0.0377362 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.7439 | 0.909028 | ||||||||
\(627\) | −0.354758 | −0.0141677 | ||||||||
\(628\) | 6.57637 | 0.262426 | ||||||||
\(629\) | −21.0455 | −0.839138 | ||||||||
\(630\) | 13.1402 | 0.523520 | ||||||||
\(631\) | −13.7708 | −0.548205 | −0.274103 | − | 0.961700i | \(-0.588381\pi\) | ||||
−0.274103 | + | 0.961700i | \(0.588381\pi\) | |||||||
\(632\) | 7.95012 | 0.316239 | ||||||||
\(633\) | −2.82289 | −0.112200 | ||||||||
\(634\) | 5.43701 | 0.215931 | ||||||||
\(635\) | 11.2095 | 0.444835 | ||||||||
\(636\) | 0.115397 | 0.00457579 | ||||||||
\(637\) | 76.0888 | 3.01475 | ||||||||
\(638\) | 7.62700 | 0.301956 | ||||||||
\(639\) | −24.2239 | −0.958281 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 7.82313 | 0.308995 | 0.154497 | − | 0.987993i | \(-0.450624\pi\) | ||||
0.154497 | + | 0.987993i | \(0.450624\pi\) | |||||||
\(642\) | −1.71059 | −0.0675117 | ||||||||
\(643\) | −19.4985 | −0.768948 | −0.384474 | − | 0.923136i | \(-0.625617\pi\) | ||||
−0.384474 | + | 0.923136i | \(0.625617\pi\) | |||||||
\(644\) | 9.80996 | 0.386567 | ||||||||
\(645\) | 0.259815 | 0.0102302 | ||||||||
\(646\) | 5.21533 | 0.205194 | ||||||||
\(647\) | −20.7712 | −0.816599 | −0.408300 | − | 0.912848i | \(-0.633878\pi\) | ||||
−0.408300 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(648\) | −8.78490 | −0.345103 | ||||||||
\(649\) | 11.6614 | 0.457751 | ||||||||
\(650\) | −6.08938 | −0.238845 | ||||||||
\(651\) | 1.72781 | 0.0677182 | ||||||||
\(652\) | −7.48490 | −0.293131 | ||||||||
\(653\) | −14.9981 | −0.586920 | −0.293460 | − | 0.955971i | \(-0.594807\pi\) | ||||
−0.293460 | + | 0.955971i | \(0.594807\pi\) | |||||||
\(654\) | −0.477811 | −0.0186839 | ||||||||
\(655\) | −6.16032 | −0.240704 | ||||||||
\(656\) | 6.07906 | 0.237347 | ||||||||
\(657\) | −3.06094 | −0.119419 | ||||||||
\(658\) | 11.1920 | 0.436309 | ||||||||
\(659\) | −48.6747 | −1.89610 | −0.948048 | − | 0.318127i | \(-0.896946\pi\) | ||||
−0.948048 | + | 0.318127i | \(0.896946\pi\) | |||||||
\(660\) | −0.475565 | −0.0185113 | ||||||||
\(661\) | −23.0823 | −0.897797 | −0.448898 | − | 0.893583i | \(-0.648184\pi\) | ||||
−0.448898 | + | 0.893583i | \(0.648184\pi\) | |||||||
\(662\) | −19.8682 | −0.772200 | ||||||||
\(663\) | −6.59038 | −0.255949 | ||||||||
\(664\) | 6.71915 | 0.260753 | ||||||||
\(665\) | −3.29372 | −0.127725 | ||||||||
\(666\) | −8.95855 | −0.347137 | ||||||||
\(667\) | −5.51599 | −0.213580 | ||||||||
\(668\) | −8.85429 | −0.342583 | ||||||||
\(669\) | 0.0179230 | 0.000692944 0 | ||||||||
\(670\) | −13.0017 | −0.502298 | ||||||||
\(671\) | −12.7830 | −0.493483 | ||||||||
\(672\) | −0.683507 | −0.0263668 | ||||||||
\(673\) | 24.1094 | 0.929349 | 0.464675 | − | 0.885482i | \(-0.346171\pi\) | ||||
0.464675 | + | 0.885482i | \(0.346171\pi\) | |||||||
\(674\) | 9.36919 | 0.360888 | ||||||||
\(675\) | 0.925104 | 0.0356073 | ||||||||
\(676\) | 24.0806 | 0.926177 | ||||||||
\(677\) | −32.1416 | −1.23530 | −0.617651 | − | 0.786452i | \(-0.711916\pi\) | ||||
−0.617651 | + | 0.786452i | \(0.711916\pi\) | |||||||
\(678\) | 1.99526 | 0.0766274 | ||||||||
\(679\) | 72.8147 | 2.79437 | ||||||||
\(680\) | 6.99132 | 0.268105 | ||||||||
\(681\) | 4.55870 | 0.174690 | ||||||||
\(682\) | 7.76579 | 0.297367 | ||||||||
\(683\) | −24.7150 | −0.945692 | −0.472846 | − | 0.881145i | \(-0.656773\pi\) | ||||
−0.472846 | + | 0.881145i | \(0.656773\pi\) | |||||||
\(684\) | 2.22004 | 0.0848852 | ||||||||
\(685\) | 16.4405 | 0.628158 | ||||||||
\(686\) | 24.2637 | 0.926394 | ||||||||
\(687\) | 0.953747 | 0.0363877 | ||||||||
\(688\) | 1.67837 | 0.0639871 | ||||||||
\(689\) | −4.53932 | −0.172934 | ||||||||
\(690\) | 0.343938 | 0.0130935 | ||||||||
\(691\) | 8.28709 | 0.315256 | 0.157628 | − | 0.987499i | \(-0.449615\pi\) | ||||
0.157628 | + | 0.987499i | \(0.449615\pi\) | |||||||
\(692\) | −12.4239 | −0.472285 | ||||||||
\(693\) | −40.3679 | −1.53345 | ||||||||
\(694\) | 8.04989 | 0.305570 | ||||||||
\(695\) | −5.10643 | −0.193698 | ||||||||
\(696\) | 0.384325 | 0.0145678 | ||||||||
\(697\) | 42.5006 | 1.60983 | ||||||||
\(698\) | 14.1691 | 0.536309 | ||||||||
\(699\) | −1.37316 | −0.0519376 | ||||||||
\(700\) | −4.41535 | −0.166885 | ||||||||
\(701\) | −34.6270 | −1.30785 | −0.653923 | − | 0.756561i | \(-0.726878\pi\) | ||||
−0.653923 | + | 0.756561i | \(0.726878\pi\) | |||||||
\(702\) | −5.63332 | −0.212616 | ||||||||
\(703\) | 2.24554 | 0.0846923 | ||||||||
\(704\) | −3.07208 | −0.115783 | ||||||||
\(705\) | 0.392391 | 0.0147783 | ||||||||
\(706\) | −29.1375 | −1.09661 | ||||||||
\(707\) | 51.6484 | 1.94244 | ||||||||
\(708\) | 0.587620 | 0.0220841 | ||||||||
\(709\) | 31.5726 | 1.18574 | 0.592868 | − | 0.805300i | \(-0.297996\pi\) | ||||
0.592868 | + | 0.805300i | \(0.297996\pi\) | |||||||
\(710\) | 8.13964 | 0.305475 | ||||||||
\(711\) | 23.6599 | 0.887314 | ||||||||
\(712\) | −8.62004 | −0.323050 | ||||||||
\(713\) | −5.61637 | −0.210335 | ||||||||
\(714\) | −4.77862 | −0.178835 | ||||||||
\(715\) | 18.7071 | 0.699605 | ||||||||
\(716\) | 4.44563 | 0.166141 | ||||||||
\(717\) | −1.16661 | −0.0435679 | ||||||||
\(718\) | 1.74842 | 0.0652504 | ||||||||
\(719\) | −13.7600 | −0.513163 | −0.256581 | − | 0.966523i | \(-0.582596\pi\) | ||||
−0.256581 | + | 0.966523i | \(0.582596\pi\) | |||||||
\(720\) | 2.97604 | 0.110910 | ||||||||
\(721\) | −9.29839 | −0.346290 | ||||||||
\(722\) | 18.4435 | 0.686397 | ||||||||
\(723\) | 3.91929 | 0.145760 | ||||||||
\(724\) | −16.4715 | −0.612157 | ||||||||
\(725\) | 2.48268 | 0.0922045 | ||||||||
\(726\) | −0.241853 | −0.00897599 | ||||||||
\(727\) | 5.15813 | 0.191304 | 0.0956522 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956522 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(728\) | 26.8868 | 0.996490 | ||||||||
\(729\) | −25.7146 | −0.952391 | ||||||||
\(730\) | 1.02853 | 0.0380676 | ||||||||
\(731\) | 11.7340 | 0.433998 | ||||||||
\(732\) | −0.644138 | −0.0238080 | ||||||||
\(733\) | 3.56423 | 0.131648 | 0.0658239 | − | 0.997831i | \(-0.479032\pi\) | ||||
0.0658239 | + | 0.997831i | \(0.479032\pi\) | |||||||
\(734\) | 13.1991 | 0.487187 | ||||||||
\(735\) | 1.93430 | 0.0713479 | ||||||||
\(736\) | 2.22179 | 0.0818961 | ||||||||
\(737\) | 39.9421 | 1.47129 | ||||||||
\(738\) | 18.0915 | 0.665957 | ||||||||
\(739\) | −24.8946 | −0.915763 | −0.457882 | − | 0.889013i | \(-0.651392\pi\) | ||||
−0.457882 | + | 0.889013i | \(0.651392\pi\) | |||||||
\(740\) | 3.01023 | 0.110658 | ||||||||
\(741\) | 0.703191 | 0.0258324 | ||||||||
\(742\) | −3.29141 | −0.120832 | ||||||||
\(743\) | 2.95294 | 0.108333 | 0.0541664 | − | 0.998532i | \(-0.482750\pi\) | ||||
0.0541664 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(744\) | 0.391319 | 0.0143464 | ||||||||
\(745\) | −8.47553 | −0.310519 | ||||||||
\(746\) | 35.7076 | 1.30735 | ||||||||
\(747\) | 19.9964 | 0.731631 | ||||||||
\(748\) | −21.4779 | −0.785310 | ||||||||
\(749\) | 48.7904 | 1.78276 | ||||||||
\(750\) | −0.154802 | −0.00565258 | ||||||||
\(751\) | −30.8730 | −1.12657 | −0.563286 | − | 0.826262i | \(-0.690463\pi\) | ||||
−0.563286 | + | 0.826262i | \(0.690463\pi\) | |||||||
\(752\) | 2.53479 | 0.0924342 | ||||||||
\(753\) | −2.85785 | −0.104146 | ||||||||
\(754\) | −15.1180 | −0.550565 | ||||||||
\(755\) | 20.8152 | 0.757542 | ||||||||
\(756\) | −4.08466 | −0.148558 | ||||||||
\(757\) | −16.6834 | −0.606368 | −0.303184 | − | 0.952932i | \(-0.598050\pi\) | ||||
−0.303184 | + | 0.952932i | \(0.598050\pi\) | |||||||
\(758\) | −20.2654 | −0.736072 | ||||||||
\(759\) | −1.05660 | −0.0383523 | ||||||||
\(760\) | −0.745971 | −0.0270592 | ||||||||
\(761\) | 4.46462 | 0.161843 | 0.0809213 | − | 0.996720i | \(-0.474214\pi\) | ||||
0.0809213 | + | 0.996720i | \(0.474214\pi\) | |||||||
\(762\) | −1.73525 | −0.0628616 | ||||||||
\(763\) | 13.6284 | 0.493380 | ||||||||
\(764\) | 5.80047 | 0.209853 | ||||||||
\(765\) | 20.8064 | 0.752258 | ||||||||
\(766\) | 35.0482 | 1.26634 | ||||||||
\(767\) | −23.1149 | −0.834632 | ||||||||
\(768\) | −0.154802 | −0.00558595 | ||||||||
\(769\) | 14.1587 | 0.510577 | 0.255289 | − | 0.966865i | \(-0.417830\pi\) | ||||
0.255289 | + | 0.966865i | \(0.417830\pi\) | |||||||
\(770\) | 13.5643 | 0.488824 | ||||||||
\(771\) | 4.39542 | 0.158297 | ||||||||
\(772\) | 17.6844 | 0.636475 | ||||||||
\(773\) | 2.64733 | 0.0952179 | 0.0476090 | − | 0.998866i | \(-0.484840\pi\) | ||||
0.0476090 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(774\) | 4.99488 | 0.179537 | ||||||||
\(775\) | 2.52786 | 0.0908035 | ||||||||
\(776\) | 16.4913 | 0.592002 | ||||||||
\(777\) | −2.05751 | −0.0738128 | ||||||||
\(778\) | 16.6478 | 0.596853 | ||||||||
\(779\) | −4.53480 | −0.162476 | ||||||||
\(780\) | 0.942651 | 0.0337523 | ||||||||
\(781\) | −25.0056 | −0.894771 | ||||||||
\(782\) | 15.5332 | 0.555467 | ||||||||
\(783\) | 2.29674 | 0.0820788 | ||||||||
\(784\) | 12.4953 | 0.446261 | ||||||||
\(785\) | −6.57637 | −0.234721 | ||||||||
\(786\) | 0.953633 | 0.0340149 | ||||||||
\(787\) | −19.8674 | −0.708195 | −0.354097 | − | 0.935209i | \(-0.615212\pi\) | ||||
−0.354097 | + | 0.935209i | \(0.615212\pi\) | |||||||
\(788\) | 0.207977 | 0.00740888 | ||||||||
\(789\) | −2.42150 | −0.0862077 | ||||||||
\(790\) | −7.95012 | −0.282853 | ||||||||
\(791\) | −56.9097 | −2.02348 | ||||||||
\(792\) | −9.14262 | −0.324869 | ||||||||
\(793\) | 25.3381 | 0.899783 | ||||||||
\(794\) | −3.46731 | −0.123050 | ||||||||
\(795\) | −0.115397 | −0.00409271 | ||||||||
\(796\) | 20.8974 | 0.740688 | ||||||||
\(797\) | −24.9638 | −0.884263 | −0.442131 | − | 0.896950i | \(-0.645778\pi\) | ||||
−0.442131 | + | 0.896950i | \(0.645778\pi\) | |||||||
\(798\) | 0.509876 | 0.0180494 | ||||||||
\(799\) | 17.7215 | 0.626942 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −25.6536 | −0.906424 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −3.15973 | −0.111504 | ||||||||
\(804\) | 2.01269 | 0.0709820 | ||||||||
\(805\) | −9.80996 | −0.345756 | ||||||||
\(806\) | −15.3931 | −0.542200 | ||||||||
\(807\) | −1.95170 | −0.0687030 | ||||||||
\(808\) | 11.6975 | 0.411515 | ||||||||
\(809\) | 36.0771 | 1.26840 | 0.634201 | − | 0.773168i | \(-0.281329\pi\) | ||||
0.634201 | + | 0.773168i | \(0.281329\pi\) | |||||||
\(810\) | 8.78490 | 0.308670 | ||||||||
\(811\) | −9.67711 | −0.339809 | −0.169905 | − | 0.985461i | \(-0.554346\pi\) | ||||
−0.169905 | + | 0.985461i | \(0.554346\pi\) | |||||||
\(812\) | −10.9619 | −0.384688 | ||||||||
\(813\) | 3.96657 | 0.139114 | ||||||||
\(814\) | −9.24766 | −0.324130 | ||||||||
\(815\) | 7.48490 | 0.262185 | ||||||||
\(816\) | −1.08227 | −0.0378871 | ||||||||
\(817\) | −1.25201 | −0.0438024 | ||||||||
\(818\) | 39.8306 | 1.39264 | ||||||||
\(819\) | 80.0160 | 2.79598 | ||||||||
\(820\) | −6.07906 | −0.212290 | ||||||||
\(821\) | −54.0490 | −1.88632 | −0.943161 | − | 0.332335i | \(-0.892163\pi\) | ||||
−0.943161 | + | 0.332335i | \(0.892163\pi\) | |||||||
\(822\) | −2.54502 | −0.0887678 | ||||||||
\(823\) | 6.13977 | 0.214019 | 0.107010 | − | 0.994258i | \(-0.465872\pi\) | ||||
0.107010 | + | 0.994258i | \(0.465872\pi\) | |||||||
\(824\) | −2.10592 | −0.0733633 | ||||||||
\(825\) | 0.475565 | 0.0165570 | ||||||||
\(826\) | −16.7604 | −0.583169 | ||||||||
\(827\) | −38.4233 | −1.33611 | −0.668055 | − | 0.744112i | \(-0.732873\pi\) | ||||
−0.668055 | + | 0.744112i | \(0.732873\pi\) | |||||||
\(828\) | 6.61212 | 0.229787 | ||||||||
\(829\) | −37.4537 | −1.30082 | −0.650411 | − | 0.759583i | \(-0.725403\pi\) | ||||
−0.650411 | + | 0.759583i | \(0.725403\pi\) | |||||||
\(830\) | −6.71915 | −0.233225 | ||||||||
\(831\) | −4.56834 | −0.158474 | ||||||||
\(832\) | 6.08938 | 0.211111 | ||||||||
\(833\) | 87.3588 | 3.02680 | ||||||||
\(834\) | 0.790487 | 0.0273723 | ||||||||
\(835\) | 8.85429 | 0.306415 | ||||||||
\(836\) | 2.29168 | 0.0792595 | ||||||||
\(837\) | 2.33854 | 0.0808316 | ||||||||
\(838\) | −25.3727 | −0.876485 | ||||||||
\(839\) | 0.219915 | 0.00759230 | 0.00379615 | − | 0.999993i | \(-0.498792\pi\) | ||||
0.00379615 | + | 0.999993i | \(0.498792\pi\) | |||||||
\(840\) | 0.683507 | 0.0235832 | ||||||||
\(841\) | −22.8363 | −0.787458 | ||||||||
\(842\) | 21.5568 | 0.742898 | ||||||||
\(843\) | 1.84975 | 0.0637087 | ||||||||
\(844\) | 18.2355 | 0.627691 | ||||||||
\(845\) | −24.0806 | −0.828398 | ||||||||
\(846\) | 7.54362 | 0.259355 | ||||||||
\(847\) | 6.89824 | 0.237026 | ||||||||
\(848\) | −0.745448 | −0.0255988 | ||||||||
\(849\) | 4.48956 | 0.154081 | ||||||||
\(850\) | −6.99132 | −0.239800 | ||||||||
\(851\) | 6.68808 | 0.229265 | ||||||||
\(852\) | −1.26004 | −0.0431681 | ||||||||
\(853\) | 1.66005 | 0.0568390 | 0.0284195 | − | 0.999596i | \(-0.490953\pi\) | ||||
0.0284195 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(854\) | 18.3724 | 0.628691 | ||||||||
\(855\) | −2.22004 | −0.0759237 | ||||||||
\(856\) | 11.0502 | 0.377687 | ||||||||
\(857\) | 24.0659 | 0.822074 | 0.411037 | − | 0.911619i | \(-0.365167\pi\) | ||||
0.411037 | + | 0.911619i | \(0.365167\pi\) | |||||||
\(858\) | −2.89590 | −0.0988643 | ||||||||
\(859\) | 11.3191 | 0.386203 | 0.193102 | − | 0.981179i | \(-0.438145\pi\) | ||||
0.193102 | + | 0.981179i | \(0.438145\pi\) | |||||||
\(860\) | −1.67837 | −0.0572318 | ||||||||
\(861\) | 4.15507 | 0.141605 | ||||||||
\(862\) | 3.17088 | 0.108001 | ||||||||
\(863\) | −20.3884 | −0.694029 | −0.347015 | − | 0.937860i | \(-0.612805\pi\) | ||||
−0.347015 | + | 0.937860i | \(0.612805\pi\) | |||||||
\(864\) | −0.925104 | −0.0314727 | ||||||||
\(865\) | 12.4239 | 0.422425 | ||||||||
\(866\) | 13.6613 | 0.464230 | ||||||||
\(867\) | −4.93488 | −0.167597 | ||||||||
\(868\) | −11.1614 | −0.378842 | ||||||||
\(869\) | 24.4234 | 0.828507 | ||||||||
\(870\) | −0.384325 | −0.0130298 | ||||||||
\(871\) | −79.1721 | −2.68264 | ||||||||
\(872\) | 3.08659 | 0.104525 | ||||||||
\(873\) | 49.0786 | 1.66106 | ||||||||
\(874\) | −1.65739 | −0.0560620 | ||||||||
\(875\) | 4.41535 | 0.149266 | ||||||||
\(876\) | −0.159219 | −0.00537951 | ||||||||
\(877\) | −8.71953 | −0.294438 | −0.147219 | − | 0.989104i | \(-0.547032\pi\) | ||||
−0.147219 | + | 0.989104i | \(0.547032\pi\) | |||||||
\(878\) | 12.4747 | 0.421001 | ||||||||
\(879\) | 1.23757 | 0.0417421 | ||||||||
\(880\) | 3.07208 | 0.103560 | ||||||||
\(881\) | −22.8663 | −0.770386 | −0.385193 | − | 0.922836i | \(-0.625865\pi\) | ||||
−0.385193 | + | 0.922836i | \(0.625865\pi\) | |||||||
\(882\) | 37.1865 | 1.25213 | ||||||||
\(883\) | 1.05873 | 0.0356292 | 0.0178146 | − | 0.999841i | \(-0.494329\pi\) | ||||
0.0178146 | + | 0.999841i | \(0.494329\pi\) | |||||||
\(884\) | 42.5729 | 1.43188 | ||||||||
\(885\) | −0.587620 | −0.0197526 | ||||||||
\(886\) | 14.6634 | 0.492625 | ||||||||
\(887\) | 53.9716 | 1.81219 | 0.906094 | − | 0.423076i | \(-0.139050\pi\) | ||||
0.906094 | + | 0.423076i | \(0.139050\pi\) | |||||||
\(888\) | −0.465990 | −0.0156376 | ||||||||
\(889\) | 49.4938 | 1.65997 | ||||||||
\(890\) | 8.62004 | 0.288944 | ||||||||
\(891\) | −26.9879 | −0.904129 | ||||||||
\(892\) | −0.115780 | −0.00387660 | ||||||||
\(893\) | −1.89088 | −0.0632759 | ||||||||
\(894\) | 1.31203 | 0.0438809 | ||||||||
\(895\) | −4.44563 | −0.148601 | ||||||||
\(896\) | 4.41535 | 0.147506 | ||||||||
\(897\) | 2.09437 | 0.0699289 | ||||||||
\(898\) | 10.8612 | 0.362444 | ||||||||
\(899\) | 6.27588 | 0.209312 | ||||||||
\(900\) | −2.97604 | −0.0992012 | ||||||||
\(901\) | −5.21167 | −0.173626 | ||||||||
\(902\) | 18.6753 | 0.621821 | ||||||||
\(903\) | 1.14717 | 0.0381756 | ||||||||
\(904\) | −12.8891 | −0.428684 | ||||||||
\(905\) | 16.4715 | 0.547530 | ||||||||
\(906\) | −3.22224 | −0.107052 | ||||||||
\(907\) | −42.0614 | −1.39662 | −0.698312 | − | 0.715793i | \(-0.746065\pi\) | ||||
−0.698312 | + | 0.715793i | \(0.746065\pi\) | |||||||
\(908\) | −29.4485 | −0.977284 | ||||||||
\(909\) | 34.8120 | 1.15464 | ||||||||
\(910\) | −26.8868 | −0.891287 | ||||||||
\(911\) | 17.5017 | 0.579858 | 0.289929 | − | 0.957048i | \(-0.406368\pi\) | ||||
0.289929 | + | 0.957048i | \(0.406368\pi\) | |||||||
\(912\) | 0.115478 | 0.00382386 | ||||||||
\(913\) | 20.6417 | 0.683142 | ||||||||
\(914\) | 18.3430 | 0.606733 | ||||||||
\(915\) | 0.644138 | 0.0212945 | ||||||||
\(916\) | −6.16106 | −0.203567 | ||||||||
\(917\) | −27.2000 | −0.898223 | ||||||||
\(918\) | −6.46770 | −0.213466 | ||||||||
\(919\) | −23.6999 | −0.781786 | −0.390893 | − | 0.920436i | \(-0.627834\pi\) | ||||
−0.390893 | + | 0.920436i | \(0.627834\pi\) | |||||||
\(920\) | −2.22179 | −0.0732501 | ||||||||
\(921\) | −3.75159 | −0.123619 | ||||||||
\(922\) | −38.6901 | −1.27419 | ||||||||
\(923\) | 49.5654 | 1.63146 | ||||||||
\(924\) | −2.09979 | −0.0690779 | ||||||||
\(925\) | −3.01023 | −0.0989757 | ||||||||
\(926\) | −23.1873 | −0.761981 | ||||||||
\(927\) | −6.26731 | −0.205845 | ||||||||
\(928\) | −2.48268 | −0.0814980 | ||||||||
\(929\) | 21.2366 | 0.696751 | 0.348376 | − | 0.937355i | \(-0.386733\pi\) | ||||
0.348376 | + | 0.937355i | \(0.386733\pi\) | |||||||
\(930\) | −0.391319 | −0.0128319 | ||||||||
\(931\) | −9.32114 | −0.305488 | ||||||||
\(932\) | 8.87040 | 0.290560 | ||||||||
\(933\) | −3.87030 | −0.126708 | ||||||||
\(934\) | −22.1349 | −0.724275 | ||||||||
\(935\) | 21.4779 | 0.702402 | ||||||||
\(936\) | 18.1222 | 0.592344 | ||||||||
\(937\) | −38.9094 | −1.27112 | −0.635558 | − | 0.772053i | \(-0.719230\pi\) | ||||
−0.635558 | + | 0.772053i | \(0.719230\pi\) | |||||||
\(938\) | −57.4069 | −1.87440 | ||||||||
\(939\) | 3.52081 | 0.114897 | ||||||||
\(940\) | −2.53479 | −0.0826757 | ||||||||
\(941\) | 43.8295 | 1.42880 | 0.714401 | − | 0.699737i | \(-0.246699\pi\) | ||||
0.714401 | + | 0.699737i | \(0.246699\pi\) | |||||||
\(942\) | 1.01804 | 0.0331694 | ||||||||
\(943\) | −13.5064 | −0.439828 | ||||||||
\(944\) | −3.79594 | −0.123547 | ||||||||
\(945\) | 4.08466 | 0.132874 | ||||||||
\(946\) | 5.15607 | 0.167638 | ||||||||
\(947\) | 5.64650 | 0.183487 | 0.0917433 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917433 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(948\) | 1.23070 | 0.0399712 | ||||||||
\(949\) | 6.26311 | 0.203309 | ||||||||
\(950\) | 0.745971 | 0.0242025 | ||||||||
\(951\) | 0.841662 | 0.0272927 | ||||||||
\(952\) | 30.8691 | 1.00047 | ||||||||
\(953\) | 44.5998 | 1.44473 | 0.722364 | − | 0.691513i | \(-0.243055\pi\) | ||||
0.722364 | + | 0.691513i | \(0.243055\pi\) | |||||||
\(954\) | −2.21848 | −0.0718260 | ||||||||
\(955\) | −5.80047 | −0.187699 | ||||||||
\(956\) | 7.53613 | 0.243736 | ||||||||
\(957\) | 1.18068 | 0.0381659 | ||||||||
\(958\) | −16.5196 | −0.533723 | ||||||||
\(959\) | 72.5904 | 2.34407 | ||||||||
\(960\) | 0.154802 | 0.00499622 | ||||||||
\(961\) | −24.6099 | −0.793868 | ||||||||
\(962\) | 18.3304 | 0.590997 | ||||||||
\(963\) | 32.8857 | 1.05973 | ||||||||
\(964\) | −25.3180 | −0.815439 | ||||||||
\(965\) | −17.6844 | −0.569280 | ||||||||
\(966\) | 1.51861 | 0.0488603 | ||||||||
\(967\) | −1.31598 | −0.0423192 | −0.0211596 | − | 0.999776i | \(-0.506736\pi\) | ||||
−0.0211596 | + | 0.999776i | \(0.506736\pi\) | |||||||
\(968\) | 1.56233 | 0.0502152 | ||||||||
\(969\) | 0.807345 | 0.0259357 | ||||||||
\(970\) | −16.4913 | −0.529503 | ||||||||
\(971\) | 6.26871 | 0.201173 | 0.100586 | − | 0.994928i | \(-0.467928\pi\) | ||||
0.100586 | + | 0.994928i | \(0.467928\pi\) | |||||||
\(972\) | −4.13524 | −0.132638 | ||||||||
\(973\) | −22.5467 | −0.722813 | ||||||||
\(974\) | −29.4405 | −0.943333 | ||||||||
\(975\) | −0.942651 | −0.0301890 | ||||||||
\(976\) | 4.16103 | 0.133191 | ||||||||
\(977\) | 10.8736 | 0.347878 | 0.173939 | − | 0.984756i | \(-0.444350\pi\) | ||||
0.173939 | + | 0.984756i | \(0.444350\pi\) | |||||||
\(978\) | −1.15868 | −0.0370505 | ||||||||
\(979\) | −26.4814 | −0.846351 | ||||||||
\(980\) | −12.4953 | −0.399148 | ||||||||
\(981\) | 9.18580 | 0.293280 | ||||||||
\(982\) | −17.5779 | −0.560933 | ||||||||
\(983\) | −22.8613 | −0.729162 | −0.364581 | − | 0.931172i | \(-0.618788\pi\) | ||||
−0.364581 | + | 0.931172i | \(0.618788\pi\) | |||||||
\(984\) | 0.941052 | 0.0299996 | ||||||||
\(985\) | −0.207977 | −0.00662671 | ||||||||
\(986\) | −17.3572 | −0.552767 | ||||||||
\(987\) | 1.73254 | 0.0551475 | ||||||||
\(988\) | −4.54251 | −0.144516 | ||||||||
\(989\) | −3.72897 | −0.118574 | ||||||||
\(990\) | 9.14262 | 0.290571 | ||||||||
\(991\) | −11.4088 | −0.362413 | −0.181206 | − | 0.983445i | \(-0.558000\pi\) | ||||
−0.181206 | + | 0.983445i | \(0.558000\pi\) | |||||||
\(992\) | −2.52786 | −0.0802597 | ||||||||
\(993\) | −3.07565 | −0.0976027 | ||||||||
\(994\) | 35.9394 | 1.13993 | ||||||||
\(995\) | −20.8974 | −0.662492 | ||||||||
\(996\) | 1.04014 | 0.0329581 | ||||||||
\(997\) | −11.3329 | −0.358917 | −0.179458 | − | 0.983766i | \(-0.557434\pi\) | ||||
−0.179458 | + | 0.983766i | \(0.557434\pi\) | |||||||
\(998\) | 35.8606 | 1.13515 | ||||||||
\(999\) | −2.78478 | −0.0881064 |
(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 | 4010.2.a.k.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial |