Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3135,2,Mod(1,3135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3135, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3135.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3135 = 3 \cdot 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3135.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: | \(25.0331010337\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.20413244.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 11x^{3} + 7x^{2} - 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.31008\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31008 | −0.926363 | −0.463182 | − | 0.886263i | \(-0.653292\pi\) | ||||
−0.463182 | + | 0.886263i | \(0.653292\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.283703 | −0.141852 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.31008 | −0.534836 | ||||||||
\(7\) | −0.0459382 | −0.0173630 | −0.00868150 | − | 0.999962i | \(-0.502763\pi\) | ||||
−0.00868150 | + | 0.999962i | \(0.502763\pi\) | |||||||
\(8\) | 2.99182 | 1.05777 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.31008 | 0.414282 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.283703 | −0.0818980 | ||||||||
\(13\) | −0.670359 | −0.185924 | −0.0929620 | − | 0.995670i | \(-0.529634\pi\) | ||||
−0.0929620 | + | 0.995670i | \(0.529634\pi\) | |||||||
\(14\) | 0.0601825 | 0.0160844 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −3.35211 | −0.838027 | ||||||||
\(17\) | −7.26175 | −1.76123 | −0.880617 | − | 0.473829i | \(-0.842872\pi\) | ||||
−0.880617 | + | 0.473829i | \(0.842872\pi\) | |||||||
\(18\) | −1.31008 | −0.308788 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.283703 | 0.0634380 | ||||||||
\(21\) | −0.0459382 | −0.0100245 | ||||||||
\(22\) | −1.31008 | −0.279309 | ||||||||
\(23\) | 8.99941 | 1.87651 | 0.938254 | − | 0.345948i | \(-0.112443\pi\) | ||||
0.938254 | + | 0.345948i | \(0.112443\pi\) | |||||||
\(24\) | 2.99182 | 0.610703 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.878220 | 0.172233 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.0130328 | 0.00246297 | ||||||||
\(29\) | −5.76592 | −1.07070 | −0.535352 | − | 0.844629i | \(-0.679821\pi\) | ||||
−0.535352 | + | 0.844629i | \(0.679821\pi\) | |||||||
\(30\) | 1.31008 | 0.239186 | ||||||||
\(31\) | 3.47642 | 0.624384 | 0.312192 | − | 0.950019i | \(-0.398937\pi\) | ||||
0.312192 | + | 0.950019i | \(0.398937\pi\) | |||||||
\(32\) | −1.59213 | −0.281452 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 9.51344 | 1.63154 | ||||||||
\(35\) | 0.0459382 | 0.00776497 | ||||||||
\(36\) | −0.283703 | −0.0472839 | ||||||||
\(37\) | 0.401213 | 0.0659590 | 0.0329795 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329795 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(38\) | 1.31008 | 0.212522 | ||||||||
\(39\) | −0.670359 | −0.107343 | ||||||||
\(40\) | −2.99182 | −0.473049 | ||||||||
\(41\) | 7.75821 | 1.21163 | 0.605815 | − | 0.795606i | \(-0.292847\pi\) | ||||
0.605815 | + | 0.795606i | \(0.292847\pi\) | |||||||
\(42\) | 0.0601825 | 0.00928635 | ||||||||
\(43\) | −7.81186 | −1.19130 | −0.595649 | − | 0.803245i | \(-0.703105\pi\) | ||||
−0.595649 | + | 0.803245i | \(0.703105\pi\) | |||||||
\(44\) | −0.283703 | −0.0427699 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −11.7899 | −1.73833 | ||||||||
\(47\) | −3.18756 | −0.464953 | −0.232476 | − | 0.972602i | \(-0.574683\pi\) | ||||
−0.232476 | + | 0.972602i | \(0.574683\pi\) | |||||||
\(48\) | −3.35211 | −0.483835 | ||||||||
\(49\) | −6.99789 | −0.999699 | ||||||||
\(50\) | −1.31008 | −0.185273 | ||||||||
\(51\) | −7.26175 | −1.01685 | ||||||||
\(52\) | 0.190183 | 0.0263736 | ||||||||
\(53\) | −3.31513 | −0.455368 | −0.227684 | − | 0.973735i | \(-0.573115\pi\) | ||||
−0.227684 | + | 0.973735i | \(0.573115\pi\) | |||||||
\(54\) | −1.31008 | −0.178279 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −0.137439 | −0.0183660 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 7.55379 | 0.991861 | ||||||||
\(59\) | 5.14894 | 0.670335 | 0.335167 | − | 0.942159i | \(-0.391207\pi\) | ||||
0.335167 | + | 0.942159i | \(0.391207\pi\) | |||||||
\(60\) | 0.283703 | 0.0366259 | ||||||||
\(61\) | −4.01303 | −0.513816 | −0.256908 | − | 0.966436i | \(-0.582704\pi\) | ||||
−0.256908 | + | 0.966436i | \(0.582704\pi\) | |||||||
\(62\) | −4.55437 | −0.578406 | ||||||||
\(63\) | −0.0459382 | −0.00578767 | ||||||||
\(64\) | 8.79003 | 1.09875 | ||||||||
\(65\) | 0.670359 | 0.0831478 | ||||||||
\(66\) | −1.31008 | −0.161259 | ||||||||
\(67\) | −1.48182 | −0.181033 | −0.0905165 | − | 0.995895i | \(-0.528852\pi\) | ||||
−0.0905165 | + | 0.995895i | \(0.528852\pi\) | |||||||
\(68\) | 2.06018 | 0.249834 | ||||||||
\(69\) | 8.99941 | 1.08340 | ||||||||
\(70\) | −0.0601825 | −0.00719318 | ||||||||
\(71\) | −12.6022 | −1.49561 | −0.747803 | − | 0.663921i | \(-0.768891\pi\) | ||||
−0.747803 | + | 0.663921i | \(0.768891\pi\) | |||||||
\(72\) | 2.99182 | 0.352590 | ||||||||
\(73\) | 3.55938 | 0.416594 | 0.208297 | − | 0.978066i | \(-0.433208\pi\) | ||||
0.208297 | + | 0.978066i | \(0.433208\pi\) | |||||||
\(74\) | −0.525619 | −0.0611019 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.283703 | 0.0325430 | ||||||||
\(77\) | −0.0459382 | −0.00523514 | ||||||||
\(78\) | 0.878220 | 0.0994389 | ||||||||
\(79\) | −13.4225 | −1.51015 | −0.755077 | − | 0.655636i | \(-0.772401\pi\) | ||||
−0.755077 | + | 0.655636i | \(0.772401\pi\) | |||||||
\(80\) | 3.35211 | 0.374777 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.1638 | −1.12241 | ||||||||
\(83\) | 13.0039 | 1.42736 | 0.713681 | − | 0.700471i | \(-0.247027\pi\) | ||||
0.713681 | + | 0.700471i | \(0.247027\pi\) | |||||||
\(84\) | 0.0130328 | 0.00142200 | ||||||||
\(85\) | 7.26175 | 0.787648 | ||||||||
\(86\) | 10.2341 | 1.10357 | ||||||||
\(87\) | −5.76592 | −0.618171 | ||||||||
\(88\) | 2.99182 | 0.318929 | ||||||||
\(89\) | 1.94409 | 0.206073 | 0.103036 | − | 0.994678i | \(-0.467144\pi\) | ||||
0.103036 | + | 0.994678i | \(0.467144\pi\) | |||||||
\(90\) | 1.31008 | 0.138094 | ||||||||
\(91\) | 0.0307951 | 0.00322820 | ||||||||
\(92\) | −2.55316 | −0.266186 | ||||||||
\(93\) | 3.47642 | 0.360488 | ||||||||
\(94\) | 4.17594 | 0.430715 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | −1.59213 | −0.162497 | ||||||||
\(97\) | 6.31493 | 0.641184 | 0.320592 | − | 0.947217i | \(-0.396118\pi\) | ||||
0.320592 | + | 0.947217i | \(0.396118\pi\) | |||||||
\(98\) | 9.16776 | 0.926084 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.283703 | −0.0283703 | ||||||||
\(101\) | 9.90601 | 0.985685 | 0.492843 | − | 0.870118i | \(-0.335958\pi\) | ||||
0.492843 | + | 0.870118i | \(0.335958\pi\) | |||||||
\(102\) | 9.51344 | 0.941971 | ||||||||
\(103\) | −9.43048 | −0.929213 | −0.464607 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464607 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(104\) | −2.00559 | −0.196665 | ||||||||
\(105\) | 0.0459382 | 0.00448311 | ||||||||
\(106\) | 4.34307 | 0.421836 | ||||||||
\(107\) | −15.7919 | −1.52667 | −0.763333 | − | 0.646006i | \(-0.776438\pi\) | ||||
−0.763333 | + | 0.646006i | \(0.776438\pi\) | |||||||
\(108\) | −0.283703 | −0.0272993 | ||||||||
\(109\) | 19.4517 | 1.86314 | 0.931570 | − | 0.363563i | \(-0.118440\pi\) | ||||
0.931570 | + | 0.363563i | \(0.118440\pi\) | |||||||
\(110\) | 1.31008 | 0.124911 | ||||||||
\(111\) | 0.401213 | 0.0380814 | ||||||||
\(112\) | 0.153990 | 0.0145507 | ||||||||
\(113\) | 7.24273 | 0.681338 | 0.340669 | − | 0.940183i | \(-0.389346\pi\) | ||||
0.340669 | + | 0.940183i | \(0.389346\pi\) | |||||||
\(114\) | 1.31008 | 0.122700 | ||||||||
\(115\) | −8.99941 | −0.839200 | ||||||||
\(116\) | 1.63581 | 0.151881 | ||||||||
\(117\) | −0.670359 | −0.0619747 | ||||||||
\(118\) | −6.74549 | −0.620973 | ||||||||
\(119\) | 0.333592 | 0.0305803 | ||||||||
\(120\) | −2.99182 | −0.273115 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.25737 | 0.475980 | ||||||||
\(123\) | 7.75821 | 0.699535 | ||||||||
\(124\) | −0.986272 | −0.0885698 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.0601825 | 0.00536148 | ||||||||
\(127\) | −11.0073 | −0.976744 | −0.488372 | − | 0.872635i | \(-0.662409\pi\) | ||||
−0.488372 | + | 0.872635i | \(0.662409\pi\) | |||||||
\(128\) | −8.33133 | −0.736392 | ||||||||
\(129\) | −7.81186 | −0.687796 | ||||||||
\(130\) | −0.878220 | −0.0770250 | ||||||||
\(131\) | −2.34467 | −0.204855 | −0.102427 | − | 0.994740i | \(-0.532661\pi\) | ||||
−0.102427 | + | 0.994740i | \(0.532661\pi\) | |||||||
\(132\) | −0.283703 | −0.0246932 | ||||||||
\(133\) | 0.0459382 | 0.00398334 | ||||||||
\(134\) | 1.94130 | 0.167702 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −21.7259 | −1.86298 | ||||||||
\(137\) | 9.57007 | 0.817626 | 0.408813 | − | 0.912618i | \(-0.365943\pi\) | ||||
0.408813 | + | 0.912618i | \(0.365943\pi\) | |||||||
\(138\) | −11.7899 | −1.00362 | ||||||||
\(139\) | −20.3810 | −1.72870 | −0.864349 | − | 0.502893i | \(-0.832269\pi\) | ||||
−0.864349 | + | 0.502893i | \(0.832269\pi\) | |||||||
\(140\) | −0.0130328 | −0.00110147 | ||||||||
\(141\) | −3.18756 | −0.268441 | ||||||||
\(142\) | 16.5098 | 1.38547 | ||||||||
\(143\) | −0.670359 | −0.0560582 | ||||||||
\(144\) | −3.35211 | −0.279342 | ||||||||
\(145\) | 5.76592 | 0.478834 | ||||||||
\(146\) | −4.66306 | −0.385917 | ||||||||
\(147\) | −6.99789 | −0.577176 | ||||||||
\(148\) | −0.113825 | −0.00935638 | ||||||||
\(149\) | −15.8754 | −1.30056 | −0.650282 | − | 0.759693i | \(-0.725349\pi\) | ||||
−0.650282 | + | 0.759693i | \(0.725349\pi\) | |||||||
\(150\) | −1.31008 | −0.106967 | ||||||||
\(151\) | −1.61303 | −0.131267 | −0.0656333 | − | 0.997844i | \(-0.520907\pi\) | ||||
−0.0656333 | + | 0.997844i | \(0.520907\pi\) | |||||||
\(152\) | −2.99182 | −0.242669 | ||||||||
\(153\) | −7.26175 | −0.587078 | ||||||||
\(154\) | 0.0601825 | 0.00484964 | ||||||||
\(155\) | −3.47642 | −0.279233 | ||||||||
\(156\) | 0.190183 | 0.0152268 | ||||||||
\(157\) | −21.1965 | −1.69167 | −0.845833 | − | 0.533448i | \(-0.820896\pi\) | ||||
−0.845833 | + | 0.533448i | \(0.820896\pi\) | |||||||
\(158\) | 17.5845 | 1.39895 | ||||||||
\(159\) | −3.31513 | −0.262907 | ||||||||
\(160\) | 1.59213 | 0.125869 | ||||||||
\(161\) | −0.413417 | −0.0325818 | ||||||||
\(162\) | −1.31008 | −0.102929 | ||||||||
\(163\) | −15.4960 | −1.21374 | −0.606871 | − | 0.794800i | \(-0.707576\pi\) | ||||
−0.606871 | + | 0.794800i | \(0.707576\pi\) | |||||||
\(164\) | −2.20103 | −0.171872 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −17.0361 | −1.32225 | ||||||||
\(167\) | −11.8791 | −0.919231 | −0.459615 | − | 0.888118i | \(-0.652013\pi\) | ||||
−0.459615 | + | 0.888118i | \(0.652013\pi\) | |||||||
\(168\) | −0.137439 | −0.0106036 | ||||||||
\(169\) | −12.5506 | −0.965432 | ||||||||
\(170\) | −9.51344 | −0.729648 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 2.21625 | 0.168987 | ||||||||
\(173\) | 6.40058 | 0.486627 | 0.243314 | − | 0.969948i | \(-0.421766\pi\) | ||||
0.243314 | + | 0.969948i | \(0.421766\pi\) | |||||||
\(174\) | 7.55379 | 0.572651 | ||||||||
\(175\) | −0.0459382 | −0.00347260 | ||||||||
\(176\) | −3.35211 | −0.252675 | ||||||||
\(177\) | 5.14894 | 0.387018 | ||||||||
\(178\) | −2.54690 | −0.190898 | ||||||||
\(179\) | −1.92995 | −0.144251 | −0.0721257 | − | 0.997396i | \(-0.522978\pi\) | ||||
−0.0721257 | + | 0.997396i | \(0.522978\pi\) | |||||||
\(180\) | 0.283703 | 0.0211460 | ||||||||
\(181\) | −1.53419 | −0.114035 | −0.0570177 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570177 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(182\) | −0.0403438 | −0.00299048 | ||||||||
\(183\) | −4.01303 | −0.296652 | ||||||||
\(184\) | 26.9247 | 1.98491 | ||||||||
\(185\) | −0.401213 | −0.0294977 | ||||||||
\(186\) | −4.55437 | −0.333943 | ||||||||
\(187\) | −7.26175 | −0.531032 | ||||||||
\(188\) | 0.904320 | 0.0659543 | ||||||||
\(189\) | −0.0459382 | −0.00334151 | ||||||||
\(190\) | −1.31008 | −0.0950428 | ||||||||
\(191\) | 24.5650 | 1.77746 | 0.888730 | − | 0.458431i | \(-0.151588\pi\) | ||||
0.888730 | + | 0.458431i | \(0.151588\pi\) | |||||||
\(192\) | 8.79003 | 0.634366 | ||||||||
\(193\) | −21.8972 | −1.57620 | −0.788099 | − | 0.615548i | \(-0.788935\pi\) | ||||
−0.788099 | + | 0.615548i | \(0.788935\pi\) | |||||||
\(194\) | −8.27303 | −0.593969 | ||||||||
\(195\) | 0.670359 | 0.0480054 | ||||||||
\(196\) | 1.98532 | 0.141809 | ||||||||
\(197\) | 12.1614 | 0.866463 | 0.433231 | − | 0.901283i | \(-0.357373\pi\) | ||||
0.433231 | + | 0.901283i | \(0.357373\pi\) | |||||||
\(198\) | −1.31008 | −0.0931030 | ||||||||
\(199\) | −23.4031 | −1.65900 | −0.829501 | − | 0.558506i | \(-0.811375\pi\) | ||||
−0.829501 | + | 0.558506i | \(0.811375\pi\) | |||||||
\(200\) | 2.99182 | 0.211554 | ||||||||
\(201\) | −1.48182 | −0.104520 | ||||||||
\(202\) | −12.9776 | −0.913102 | ||||||||
\(203\) | 0.264876 | 0.0185906 | ||||||||
\(204\) | 2.06018 | 0.144242 | ||||||||
\(205\) | −7.75821 | −0.541857 | ||||||||
\(206\) | 12.3546 | 0.860789 | ||||||||
\(207\) | 8.99941 | 0.625503 | ||||||||
\(208\) | 2.24711 | 0.155809 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | −0.0601825 | −0.00415298 | ||||||||
\(211\) | −3.86320 | −0.265954 | −0.132977 | − | 0.991119i | \(-0.542454\pi\) | ||||
−0.132977 | + | 0.991119i | \(0.542454\pi\) | |||||||
\(212\) | 0.940513 | 0.0645947 | ||||||||
\(213\) | −12.6022 | −0.863488 | ||||||||
\(214\) | 20.6886 | 1.41425 | ||||||||
\(215\) | 7.81186 | 0.532764 | ||||||||
\(216\) | 2.99182 | 0.203568 | ||||||||
\(217\) | −0.159700 | −0.0108412 | ||||||||
\(218\) | −25.4833 | −1.72594 | ||||||||
\(219\) | 3.55938 | 0.240521 | ||||||||
\(220\) | 0.283703 | 0.0191273 | ||||||||
\(221\) | 4.86798 | 0.327456 | ||||||||
\(222\) | −0.525619 | −0.0352772 | ||||||||
\(223\) | −13.6672 | −0.915223 | −0.457612 | − | 0.889152i | \(-0.651295\pi\) | ||||
−0.457612 | + | 0.889152i | \(0.651295\pi\) | |||||||
\(224\) | 0.0731397 | 0.00488685 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −9.48852 | −0.631167 | ||||||||
\(227\) | 6.58470 | 0.437042 | 0.218521 | − | 0.975832i | \(-0.429877\pi\) | ||||
0.218521 | + | 0.975832i | \(0.429877\pi\) | |||||||
\(228\) | 0.283703 | 0.0187887 | ||||||||
\(229\) | 12.5156 | 0.827051 | 0.413526 | − | 0.910492i | \(-0.364297\pi\) | ||||
0.413526 | + | 0.910492i | \(0.364297\pi\) | |||||||
\(230\) | 11.7899 | 0.777404 | ||||||||
\(231\) | −0.0459382 | −0.00302251 | ||||||||
\(232\) | −17.2506 | −1.13256 | ||||||||
\(233\) | −26.0657 | −1.70762 | −0.853811 | − | 0.520584i | \(-0.825714\pi\) | ||||
−0.853811 | + | 0.520584i | \(0.825714\pi\) | |||||||
\(234\) | 0.878220 | 0.0574111 | ||||||||
\(235\) | 3.18756 | 0.207933 | ||||||||
\(236\) | −1.46077 | −0.0950880 | ||||||||
\(237\) | −13.4225 | −0.871888 | ||||||||
\(238\) | −0.437030 | −0.0283285 | ||||||||
\(239\) | 18.4855 | 1.19573 | 0.597863 | − | 0.801598i | \(-0.296017\pi\) | ||||
0.597863 | + | 0.801598i | \(0.296017\pi\) | |||||||
\(240\) | 3.35211 | 0.216378 | ||||||||
\(241\) | −27.7704 | −1.78885 | −0.894425 | − | 0.447218i | \(-0.852415\pi\) | ||||
−0.894425 | + | 0.447218i | \(0.852415\pi\) | |||||||
\(242\) | −1.31008 | −0.0842148 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.13851 | 0.0728856 | ||||||||
\(245\) | 6.99789 | 0.447079 | ||||||||
\(246\) | −10.1638 | −0.648023 | ||||||||
\(247\) | 0.670359 | 0.0426539 | ||||||||
\(248\) | 10.4008 | 0.660454 | ||||||||
\(249\) | 13.0039 | 0.824087 | ||||||||
\(250\) | 1.31008 | 0.0828564 | ||||||||
\(251\) | −20.7247 | −1.30813 | −0.654065 | − | 0.756438i | \(-0.726938\pi\) | ||||
−0.654065 | + | 0.756438i | \(0.726938\pi\) | |||||||
\(252\) | 0.0130328 | 0.000820989 0 | ||||||||
\(253\) | 8.99941 | 0.565788 | ||||||||
\(254\) | 14.4205 | 0.904820 | ||||||||
\(255\) | 7.26175 | 0.454749 | ||||||||
\(256\) | −6.66539 | −0.416587 | ||||||||
\(257\) | −29.2153 | −1.82240 | −0.911201 | − | 0.411961i | \(-0.864844\pi\) | ||||
−0.911201 | + | 0.411961i | \(0.864844\pi\) | |||||||
\(258\) | 10.2341 | 0.637148 | ||||||||
\(259\) | −0.0184310 | −0.00114525 | ||||||||
\(260\) | −0.190183 | −0.0117946 | ||||||||
\(261\) | −5.76592 | −0.356901 | ||||||||
\(262\) | 3.07169 | 0.189770 | ||||||||
\(263\) | −4.20016 | −0.258993 | −0.129496 | − | 0.991580i | \(-0.541336\pi\) | ||||
−0.129496 | + | 0.991580i | \(0.541336\pi\) | |||||||
\(264\) | 2.99182 | 0.184134 | ||||||||
\(265\) | 3.31513 | 0.203647 | ||||||||
\(266\) | −0.0601825 | −0.00369002 | ||||||||
\(267\) | 1.94409 | 0.118976 | ||||||||
\(268\) | 0.420397 | 0.0256798 | ||||||||
\(269\) | 1.37742 | 0.0839830 | 0.0419915 | − | 0.999118i | \(-0.486630\pi\) | ||||
0.0419915 | + | 0.999118i | \(0.486630\pi\) | |||||||
\(270\) | 1.31008 | 0.0797286 | ||||||||
\(271\) | 2.44349 | 0.148431 | 0.0742156 | − | 0.997242i | \(-0.476355\pi\) | ||||
0.0742156 | + | 0.997242i | \(0.476355\pi\) | |||||||
\(272\) | 24.3422 | 1.47596 | ||||||||
\(273\) | 0.0307951 | 0.00186380 | ||||||||
\(274\) | −12.5375 | −0.757419 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −2.55316 | −0.153682 | ||||||||
\(277\) | −12.7285 | −0.764784 | −0.382392 | − | 0.924000i | \(-0.624900\pi\) | ||||
−0.382392 | + | 0.924000i | \(0.624900\pi\) | |||||||
\(278\) | 26.7007 | 1.60140 | ||||||||
\(279\) | 3.47642 | 0.208128 | ||||||||
\(280\) | 0.137439 | 0.00821354 | ||||||||
\(281\) | 4.08159 | 0.243487 | 0.121743 | − | 0.992562i | \(-0.461151\pi\) | ||||
0.121743 | + | 0.992562i | \(0.461151\pi\) | |||||||
\(282\) | 4.17594 | 0.248674 | ||||||||
\(283\) | 5.84982 | 0.347736 | 0.173868 | − | 0.984769i | \(-0.444373\pi\) | ||||
0.173868 | + | 0.984769i | \(0.444373\pi\) | |||||||
\(284\) | 3.57528 | 0.212154 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0.878220 | 0.0519303 | ||||||||
\(287\) | −0.356398 | −0.0210375 | ||||||||
\(288\) | −1.59213 | −0.0938174 | ||||||||
\(289\) | 35.7331 | 2.10195 | ||||||||
\(290\) | −7.55379 | −0.443574 | ||||||||
\(291\) | 6.31493 | 0.370188 | ||||||||
\(292\) | −1.00981 | −0.0590945 | ||||||||
\(293\) | −2.77452 | −0.162089 | −0.0810445 | − | 0.996710i | \(-0.525826\pi\) | ||||
−0.0810445 | + | 0.996710i | \(0.525826\pi\) | |||||||
\(294\) | 9.16776 | 0.534675 | ||||||||
\(295\) | −5.14894 | −0.299783 | ||||||||
\(296\) | 1.20036 | 0.0697693 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 20.7980 | 1.20479 | ||||||||
\(299\) | −6.03284 | −0.348888 | ||||||||
\(300\) | −0.283703 | −0.0163796 | ||||||||
\(301\) | 0.358862 | 0.0206845 | ||||||||
\(302\) | 2.11319 | 0.121601 | ||||||||
\(303\) | 9.90601 | 0.569086 | ||||||||
\(304\) | 3.35211 | 0.192256 | ||||||||
\(305\) | 4.01303 | 0.229786 | ||||||||
\(306\) | 9.51344 | 0.543847 | ||||||||
\(307\) | −12.6532 | −0.722154 | −0.361077 | − | 0.932536i | \(-0.617591\pi\) | ||||
−0.361077 | + | 0.932536i | \(0.617591\pi\) | |||||||
\(308\) | 0.0130328 | 0.000742613 0 | ||||||||
\(309\) | −9.43048 | −0.536481 | ||||||||
\(310\) | 4.55437 | 0.258671 | ||||||||
\(311\) | −15.3789 | −0.872056 | −0.436028 | − | 0.899933i | \(-0.643615\pi\) | ||||
−0.436028 | + | 0.899933i | \(0.643615\pi\) | |||||||
\(312\) | −2.00559 | −0.113544 | ||||||||
\(313\) | 13.9974 | 0.791180 | 0.395590 | − | 0.918427i | \(-0.370540\pi\) | ||||
0.395590 | + | 0.918427i | \(0.370540\pi\) | |||||||
\(314\) | 27.7690 | 1.56710 | ||||||||
\(315\) | 0.0459382 | 0.00258832 | ||||||||
\(316\) | 3.80802 | 0.214218 | ||||||||
\(317\) | 13.2141 | 0.742181 | 0.371090 | − | 0.928597i | \(-0.378984\pi\) | ||||
0.371090 | + | 0.928597i | \(0.378984\pi\) | |||||||
\(318\) | 4.34307 | 0.243547 | ||||||||
\(319\) | −5.76592 | −0.322830 | ||||||||
\(320\) | −8.79003 | −0.491378 | ||||||||
\(321\) | −15.7919 | −0.881421 | ||||||||
\(322\) | 0.541607 | 0.0301826 | ||||||||
\(323\) | 7.26175 | 0.404055 | ||||||||
\(324\) | −0.283703 | −0.0157613 | ||||||||
\(325\) | −0.670359 | −0.0371848 | ||||||||
\(326\) | 20.3010 | 1.12437 | ||||||||
\(327\) | 19.4517 | 1.07568 | ||||||||
\(328\) | 23.2112 | 1.28162 | ||||||||
\(329\) | 0.146431 | 0.00807298 | ||||||||
\(330\) | 1.31008 | 0.0721173 | ||||||||
\(331\) | 17.2209 | 0.946545 | 0.473273 | − | 0.880916i | \(-0.343073\pi\) | ||||
0.473273 | + | 0.880916i | \(0.343073\pi\) | |||||||
\(332\) | −3.68924 | −0.202473 | ||||||||
\(333\) | 0.401213 | 0.0219863 | ||||||||
\(334\) | 15.5625 | 0.851541 | ||||||||
\(335\) | 1.48182 | 0.0809605 | ||||||||
\(336\) | 0.153990 | 0.00840082 | ||||||||
\(337\) | −5.51617 | −0.300485 | −0.150242 | − | 0.988649i | \(-0.548005\pi\) | ||||
−0.150242 | + | 0.988649i | \(0.548005\pi\) | |||||||
\(338\) | 16.4423 | 0.894341 | ||||||||
\(339\) | 7.24273 | 0.393371 | ||||||||
\(340\) | −2.06018 | −0.111729 | ||||||||
\(341\) | 3.47642 | 0.188259 | ||||||||
\(342\) | 1.31008 | 0.0708408 | ||||||||
\(343\) | 0.643037 | 0.0347208 | ||||||||
\(344\) | −23.3717 | −1.26012 | ||||||||
\(345\) | −8.99941 | −0.484512 | ||||||||
\(346\) | −8.38524 | −0.450793 | ||||||||
\(347\) | −14.0377 | −0.753584 | −0.376792 | − | 0.926298i | \(-0.622973\pi\) | ||||
−0.376792 | + | 0.926298i | \(0.622973\pi\) | |||||||
\(348\) | 1.63581 | 0.0876886 | ||||||||
\(349\) | 1.11525 | 0.0596978 | 0.0298489 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298489 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(350\) | 0.0601825 | 0.00321689 | ||||||||
\(351\) | −0.670359 | −0.0357811 | ||||||||
\(352\) | −1.59213 | −0.0848610 | ||||||||
\(353\) | −28.6187 | −1.52322 | −0.761609 | − | 0.648037i | \(-0.775590\pi\) | ||||
−0.761609 | + | 0.648037i | \(0.775590\pi\) | |||||||
\(354\) | −6.74549 | −0.358519 | ||||||||
\(355\) | 12.6022 | 0.668855 | ||||||||
\(356\) | −0.551544 | −0.0292318 | ||||||||
\(357\) | 0.333592 | 0.0176555 | ||||||||
\(358\) | 2.52838 | 0.133629 | ||||||||
\(359\) | 11.3401 | 0.598505 | 0.299253 | − | 0.954174i | \(-0.403263\pi\) | ||||
0.299253 | + | 0.954174i | \(0.403263\pi\) | |||||||
\(360\) | −2.99182 | −0.157683 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 2.00990 | 0.105638 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −0.00873665 | −0.000457925 0 | ||||||||
\(365\) | −3.55938 | −0.186307 | ||||||||
\(366\) | 5.25737 | 0.274807 | ||||||||
\(367\) | 14.6528 | 0.764872 | 0.382436 | − | 0.923982i | \(-0.375085\pi\) | ||||
0.382436 | + | 0.923982i | \(0.375085\pi\) | |||||||
\(368\) | −30.1670 | −1.57256 | ||||||||
\(369\) | 7.75821 | 0.403877 | ||||||||
\(370\) | 0.525619 | 0.0273256 | ||||||||
\(371\) | 0.152291 | 0.00790656 | ||||||||
\(372\) | −0.986272 | −0.0511358 | ||||||||
\(373\) | −28.2032 | −1.46031 | −0.730154 | − | 0.683282i | \(-0.760552\pi\) | ||||
−0.730154 | + | 0.683282i | \(0.760552\pi\) | |||||||
\(374\) | 9.51344 | 0.491928 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −9.53660 | −0.491813 | ||||||||
\(377\) | 3.86523 | 0.199070 | ||||||||
\(378\) | 0.0601825 | 0.00309545 | ||||||||
\(379\) | −13.7448 | −0.706023 | −0.353011 | − | 0.935619i | \(-0.614842\pi\) | ||||
−0.353011 | + | 0.935619i | \(0.614842\pi\) | |||||||
\(380\) | −0.283703 | −0.0145537 | ||||||||
\(381\) | −11.0073 | −0.563924 | ||||||||
\(382\) | −32.1820 | −1.64657 | ||||||||
\(383\) | −19.9867 | −1.02127 | −0.510637 | − | 0.859796i | \(-0.670591\pi\) | ||||
−0.510637 | + | 0.859796i | \(0.670591\pi\) | |||||||
\(384\) | −8.33133 | −0.425156 | ||||||||
\(385\) | 0.0459382 | 0.00234123 | ||||||||
\(386\) | 28.6870 | 1.46013 | ||||||||
\(387\) | −7.81186 | −0.397099 | ||||||||
\(388\) | −1.79157 | −0.0909530 | ||||||||
\(389\) | 19.4723 | 0.987284 | 0.493642 | − | 0.869665i | \(-0.335665\pi\) | ||||
0.493642 | + | 0.869665i | \(0.335665\pi\) | |||||||
\(390\) | −0.878220 | −0.0444704 | ||||||||
\(391\) | −65.3515 | −3.30497 | ||||||||
\(392\) | −20.9364 | −1.05745 | ||||||||
\(393\) | −2.34467 | −0.118273 | ||||||||
\(394\) | −15.9323 | −0.802659 | ||||||||
\(395\) | 13.4225 | 0.675362 | ||||||||
\(396\) | −0.283703 | −0.0142566 | ||||||||
\(397\) | −18.9970 | −0.953431 | −0.476716 | − | 0.879058i | \(-0.658173\pi\) | ||||
−0.476716 | + | 0.879058i | \(0.658173\pi\) | |||||||
\(398\) | 30.6598 | 1.53684 | ||||||||
\(399\) | 0.0459382 | 0.00229979 | ||||||||
\(400\) | −3.35211 | −0.167605 | ||||||||
\(401\) | −5.48110 | −0.273713 | −0.136856 | − | 0.990591i | \(-0.543700\pi\) | ||||
−0.136856 | + | 0.990591i | \(0.543700\pi\) | |||||||
\(402\) | 1.94130 | 0.0968230 | ||||||||
\(403\) | −2.33045 | −0.116088 | ||||||||
\(404\) | −2.81037 | −0.139821 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −0.347007 | −0.0172217 | ||||||||
\(407\) | 0.401213 | 0.0198874 | ||||||||
\(408\) | −21.7259 | −1.07559 | ||||||||
\(409\) | 15.1666 | 0.749938 | 0.374969 | − | 0.927037i | \(-0.377653\pi\) | ||||
0.374969 | + | 0.927037i | \(0.377653\pi\) | |||||||
\(410\) | 10.1638 | 0.501956 | ||||||||
\(411\) | 9.57007 | 0.472057 | ||||||||
\(412\) | 2.67546 | 0.131810 | ||||||||
\(413\) | −0.236533 | −0.0116390 | ||||||||
\(414\) | −11.7899 | −0.579442 | ||||||||
\(415\) | −13.0039 | −0.638335 | ||||||||
\(416\) | 1.06730 | 0.0523287 | ||||||||
\(417\) | −20.3810 | −0.998064 | ||||||||
\(418\) | 1.31008 | 0.0640779 | ||||||||
\(419\) | 10.3184 | 0.504089 | 0.252045 | − | 0.967716i | \(-0.418897\pi\) | ||||
0.252045 | + | 0.967716i | \(0.418897\pi\) | |||||||
\(420\) | −0.0130328 | −0.000635936 0 | ||||||||
\(421\) | 16.3990 | 0.799240 | 0.399620 | − | 0.916681i | \(-0.369142\pi\) | ||||
0.399620 | + | 0.916681i | \(0.369142\pi\) | |||||||
\(422\) | 5.06109 | 0.246370 | ||||||||
\(423\) | −3.18756 | −0.154984 | ||||||||
\(424\) | −9.91828 | −0.481674 | ||||||||
\(425\) | −7.26175 | −0.352247 | ||||||||
\(426\) | 16.5098 | 0.799904 | ||||||||
\(427\) | 0.184351 | 0.00892139 | ||||||||
\(428\) | 4.48023 | 0.216560 | ||||||||
\(429\) | −0.670359 | −0.0323652 | ||||||||
\(430\) | −10.2341 | −0.493533 | ||||||||
\(431\) | −15.4812 | −0.745702 | −0.372851 | − | 0.927891i | \(-0.621620\pi\) | ||||
−0.372851 | + | 0.927891i | \(0.621620\pi\) | |||||||
\(432\) | −3.35211 | −0.161278 | ||||||||
\(433\) | −4.34940 | −0.209019 | −0.104509 | − | 0.994524i | \(-0.533327\pi\) | ||||
−0.104509 | + | 0.994524i | \(0.533327\pi\) | |||||||
\(434\) | 0.209220 | 0.0100429 | ||||||||
\(435\) | 5.76592 | 0.276455 | ||||||||
\(436\) | −5.51852 | −0.264289 | ||||||||
\(437\) | −8.99941 | −0.430500 | ||||||||
\(438\) | −4.66306 | −0.222810 | ||||||||
\(439\) | −14.2170 | −0.678541 | −0.339270 | − | 0.940689i | \(-0.610180\pi\) | ||||
−0.339270 | + | 0.940689i | \(0.610180\pi\) | |||||||
\(440\) | −2.99182 | −0.142630 | ||||||||
\(441\) | −6.99789 | −0.333233 | ||||||||
\(442\) | −6.37742 | −0.303343 | ||||||||
\(443\) | 27.0252 | 1.28400 | 0.642002 | − | 0.766703i | \(-0.278104\pi\) | ||||
0.642002 | + | 0.766703i | \(0.278104\pi\) | |||||||
\(444\) | −0.113825 | −0.00540191 | ||||||||
\(445\) | −1.94409 | −0.0921586 | ||||||||
\(446\) | 17.9051 | 0.847829 | ||||||||
\(447\) | −15.8754 | −0.750881 | ||||||||
\(448\) | −0.403798 | −0.0190777 | ||||||||
\(449\) | 29.5700 | 1.39550 | 0.697748 | − | 0.716344i | \(-0.254186\pi\) | ||||
0.697748 | + | 0.716344i | \(0.254186\pi\) | |||||||
\(450\) | −1.31008 | −0.0617575 | ||||||||
\(451\) | 7.75821 | 0.365320 | ||||||||
\(452\) | −2.05478 | −0.0966489 | ||||||||
\(453\) | −1.61303 | −0.0757868 | ||||||||
\(454\) | −8.62645 | −0.404859 | ||||||||
\(455\) | −0.0307951 | −0.00144369 | ||||||||
\(456\) | −2.99182 | −0.140105 | ||||||||
\(457\) | −40.0064 | −1.87142 | −0.935709 | − | 0.352772i | \(-0.885239\pi\) | ||||
−0.935709 | + | 0.352772i | \(0.885239\pi\) | |||||||
\(458\) | −16.3963 | −0.766150 | ||||||||
\(459\) | −7.26175 | −0.338950 | ||||||||
\(460\) | 2.55316 | 0.119042 | ||||||||
\(461\) | −8.87332 | −0.413272 | −0.206636 | − | 0.978418i | \(-0.566252\pi\) | ||||
−0.206636 | + | 0.978418i | \(0.566252\pi\) | |||||||
\(462\) | 0.0601825 | 0.00279994 | ||||||||
\(463\) | −14.3604 | −0.667383 | −0.333692 | − | 0.942682i | \(-0.608294\pi\) | ||||
−0.333692 | + | 0.942682i | \(0.608294\pi\) | |||||||
\(464\) | 19.3280 | 0.897279 | ||||||||
\(465\) | −3.47642 | −0.161215 | ||||||||
\(466\) | 34.1480 | 1.58188 | ||||||||
\(467\) | 18.2237 | 0.843290 | 0.421645 | − | 0.906761i | \(-0.361453\pi\) | ||||
0.421645 | + | 0.906761i | \(0.361453\pi\) | |||||||
\(468\) | 0.190183 | 0.00879121 | ||||||||
\(469\) | 0.0680721 | 0.00314328 | ||||||||
\(470\) | −4.17594 | −0.192622 | ||||||||
\(471\) | −21.1965 | −0.976684 | ||||||||
\(472\) | 15.4047 | 0.709059 | ||||||||
\(473\) | −7.81186 | −0.359190 | ||||||||
\(474\) | 17.5845 | 0.807685 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −0.0946410 | −0.00433786 | ||||||||
\(477\) | −3.31513 | −0.151789 | ||||||||
\(478\) | −24.2174 | −1.10768 | ||||||||
\(479\) | 29.5781 | 1.35146 | 0.675729 | − | 0.737150i | \(-0.263829\pi\) | ||||
0.675729 | + | 0.737150i | \(0.263829\pi\) | |||||||
\(480\) | 1.59213 | 0.0726707 | ||||||||
\(481\) | −0.268956 | −0.0122634 | ||||||||
\(482\) | 36.3813 | 1.65712 | ||||||||
\(483\) | −0.413417 | −0.0188111 | ||||||||
\(484\) | −0.283703 | −0.0128956 | ||||||||
\(485\) | −6.31493 | −0.286746 | ||||||||
\(486\) | −1.31008 | −0.0594262 | ||||||||
\(487\) | −41.1765 | −1.86588 | −0.932942 | − | 0.360026i | \(-0.882768\pi\) | ||||
−0.932942 | + | 0.360026i | \(0.882768\pi\) | |||||||
\(488\) | −12.0063 | −0.543499 | ||||||||
\(489\) | −15.4960 | −0.700755 | ||||||||
\(490\) | −9.16776 | −0.414157 | ||||||||
\(491\) | 29.3336 | 1.32381 | 0.661904 | − | 0.749588i | \(-0.269749\pi\) | ||||
0.661904 | + | 0.749588i | \(0.269749\pi\) | |||||||
\(492\) | −2.20103 | −0.0992301 | ||||||||
\(493\) | 41.8707 | 1.88576 | ||||||||
\(494\) | −0.878220 | −0.0395130 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −11.6533 | −0.523250 | ||||||||
\(497\) | 0.578922 | 0.0259682 | ||||||||
\(498\) | −17.0361 | −0.763404 | ||||||||
\(499\) | 19.6484 | 0.879584 | 0.439792 | − | 0.898100i | \(-0.355052\pi\) | ||||
0.439792 | + | 0.898100i | \(0.355052\pi\) | |||||||
\(500\) | 0.283703 | 0.0126876 | ||||||||
\(501\) | −11.8791 | −0.530718 | ||||||||
\(502\) | 27.1509 | 1.21180 | ||||||||
\(503\) | 14.7316 | 0.656850 | 0.328425 | − | 0.944530i | \(-0.393482\pi\) | ||||
0.328425 | + | 0.944530i | \(0.393482\pi\) | |||||||
\(504\) | −0.137439 | −0.00612201 | ||||||||
\(505\) | −9.90601 | −0.440812 | ||||||||
\(506\) | −11.7899 | −0.524125 | ||||||||
\(507\) | −12.5506 | −0.557393 | ||||||||
\(508\) | 3.12282 | 0.138553 | ||||||||
\(509\) | −15.6584 | −0.694044 | −0.347022 | − | 0.937857i | \(-0.612807\pi\) | ||||
−0.347022 | + | 0.937857i | \(0.612807\pi\) | |||||||
\(510\) | −9.51344 | −0.421262 | ||||||||
\(511\) | −0.163511 | −0.00723332 | ||||||||
\(512\) | 25.3948 | 1.12230 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 38.2743 | 1.68821 | ||||||||
\(515\) | 9.43048 | 0.415557 | ||||||||
\(516\) | 2.21625 | 0.0975649 | ||||||||
\(517\) | −3.18756 | −0.140189 | ||||||||
\(518\) | 0.0241460 | 0.00106091 | ||||||||
\(519\) | 6.40058 | 0.280954 | ||||||||
\(520\) | 2.00559 | 0.0879511 | ||||||||
\(521\) | 11.5177 | 0.504598 | 0.252299 | − | 0.967649i | \(-0.418813\pi\) | ||||
0.252299 | + | 0.967649i | \(0.418813\pi\) | |||||||
\(522\) | 7.55379 | 0.330620 | ||||||||
\(523\) | 30.8368 | 1.34840 | 0.674199 | − | 0.738550i | \(-0.264489\pi\) | ||||
0.674199 | + | 0.738550i | \(0.264489\pi\) | |||||||
\(524\) | 0.665190 | 0.0290589 | ||||||||
\(525\) | −0.0459382 | −0.00200491 | ||||||||
\(526\) | 5.50252 | 0.239921 | ||||||||
\(527\) | −25.2449 | −1.09969 | ||||||||
\(528\) | −3.35211 | −0.145882 | ||||||||
\(529\) | 57.9895 | 2.52128 | ||||||||
\(530\) | −4.34307 | −0.188651 | ||||||||
\(531\) | 5.14894 | 0.223445 | ||||||||
\(532\) | −0.0130328 | −0.000565044 0 | ||||||||
\(533\) | −5.20079 | −0.225271 | ||||||||
\(534\) | −2.54690 | −0.110215 | ||||||||
\(535\) | 15.7919 | 0.682745 | ||||||||
\(536\) | −4.43334 | −0.191491 | ||||||||
\(537\) | −1.92995 | −0.0832836 | ||||||||
\(538\) | −1.80453 | −0.0777987 | ||||||||
\(539\) | −6.99789 | −0.301420 | ||||||||
\(540\) | 0.283703 | 0.0122086 | ||||||||
\(541\) | −12.7813 | −0.549510 | −0.274755 | − | 0.961514i | \(-0.588597\pi\) | ||||
−0.274755 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(542\) | −3.20115 | −0.137501 | ||||||||
\(543\) | −1.53419 | −0.0658383 | ||||||||
\(544\) | 11.5617 | 0.495703 | ||||||||
\(545\) | −19.4517 | −0.833221 | ||||||||
\(546\) | −0.0403438 | −0.00172656 | ||||||||
\(547\) | 45.8536 | 1.96056 | 0.980279 | − | 0.197621i | \(-0.0633214\pi\) | ||||
0.980279 | + | 0.197621i | \(0.0633214\pi\) | |||||||
\(548\) | −2.71506 | −0.115982 | ||||||||
\(549\) | −4.01303 | −0.171272 | ||||||||
\(550\) | −1.31008 | −0.0558618 | ||||||||
\(551\) | 5.76592 | 0.245636 | ||||||||
\(552\) | 26.9247 | 1.14599 | ||||||||
\(553\) | 0.616607 | 0.0262208 | ||||||||
\(554\) | 16.6753 | 0.708468 | ||||||||
\(555\) | −0.401213 | −0.0170305 | ||||||||
\(556\) | 5.78216 | 0.245218 | ||||||||
\(557\) | −0.119732 | −0.00507322 | −0.00253661 | − | 0.999997i | \(-0.500807\pi\) | ||||
−0.00253661 | + | 0.999997i | \(0.500807\pi\) | |||||||
\(558\) | −4.55437 | −0.192802 | ||||||||
\(559\) | 5.23675 | 0.221491 | ||||||||
\(560\) | −0.153990 | −0.00650725 | ||||||||
\(561\) | −7.26175 | −0.306592 | ||||||||
\(562\) | −5.34718 | −0.225557 | ||||||||
\(563\) | −43.9151 | −1.85080 | −0.925400 | − | 0.378992i | \(-0.876271\pi\) | ||||
−0.925400 | + | 0.378992i | \(0.876271\pi\) | |||||||
\(564\) | 0.904320 | 0.0380787 | ||||||||
\(565\) | −7.24273 | −0.304704 | ||||||||
\(566\) | −7.66371 | −0.322130 | ||||||||
\(567\) | −0.0459382 | −0.00192922 | ||||||||
\(568\) | −37.7035 | −1.58201 | ||||||||
\(569\) | −3.35766 | −0.140760 | −0.0703802 | − | 0.997520i | \(-0.522421\pi\) | ||||
−0.0703802 | + | 0.997520i | \(0.522421\pi\) | |||||||
\(570\) | −1.31008 | −0.0548730 | ||||||||
\(571\) | −15.4088 | −0.644840 | −0.322420 | − | 0.946597i | \(-0.604496\pi\) | ||||
−0.322420 | + | 0.946597i | \(0.604496\pi\) | |||||||
\(572\) | 0.190183 | 0.00795195 | ||||||||
\(573\) | 24.5650 | 1.02622 | ||||||||
\(574\) | 0.466908 | 0.0194884 | ||||||||
\(575\) | 8.99941 | 0.375302 | ||||||||
\(576\) | 8.79003 | 0.366251 | ||||||||
\(577\) | 25.3587 | 1.05570 | 0.527849 | − | 0.849338i | \(-0.322999\pi\) | ||||
0.527849 | + | 0.849338i | \(0.322999\pi\) | |||||||
\(578\) | −46.8130 | −1.94716 | ||||||||
\(579\) | −21.8972 | −0.910018 | ||||||||
\(580\) | −1.63581 | −0.0679233 | ||||||||
\(581\) | −0.597375 | −0.0247833 | ||||||||
\(582\) | −8.27303 | −0.342928 | ||||||||
\(583\) | −3.31513 | −0.137299 | ||||||||
\(584\) | 10.6490 | 0.440660 | ||||||||
\(585\) | 0.670359 | 0.0277159 | ||||||||
\(586\) | 3.63482 | 0.150153 | ||||||||
\(587\) | 14.2122 | 0.586601 | 0.293301 | − | 0.956020i | \(-0.405246\pi\) | ||||
0.293301 | + | 0.956020i | \(0.405246\pi\) | |||||||
\(588\) | 1.98532 | 0.0818734 | ||||||||
\(589\) | −3.47642 | −0.143243 | ||||||||
\(590\) | 6.74549 | 0.277708 | ||||||||
\(591\) | 12.1614 | 0.500252 | ||||||||
\(592\) | −1.34491 | −0.0552754 | ||||||||
\(593\) | −16.3696 | −0.672218 | −0.336109 | − | 0.941823i | \(-0.609111\pi\) | ||||
−0.336109 | + | 0.941823i | \(0.609111\pi\) | |||||||
\(594\) | −1.31008 | −0.0537530 | ||||||||
\(595\) | −0.333592 | −0.0136759 | ||||||||
\(596\) | 4.50390 | 0.184487 | ||||||||
\(597\) | −23.4031 | −0.957825 | ||||||||
\(598\) | 7.90347 | 0.323197 | ||||||||
\(599\) | 36.2534 | 1.48127 | 0.740637 | − | 0.671905i | \(-0.234524\pi\) | ||||
0.740637 | + | 0.671905i | \(0.234524\pi\) | |||||||
\(600\) | 2.99182 | 0.122141 | ||||||||
\(601\) | 13.0869 | 0.533828 | 0.266914 | − | 0.963720i | \(-0.413996\pi\) | ||||
0.266914 | + | 0.963720i | \(0.413996\pi\) | |||||||
\(602\) | −0.470137 | −0.0191613 | ||||||||
\(603\) | −1.48182 | −0.0603444 | ||||||||
\(604\) | 0.457622 | 0.0186204 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −12.9776 | −0.527180 | ||||||||
\(607\) | 42.8327 | 1.73853 | 0.869263 | − | 0.494351i | \(-0.164594\pi\) | ||||
0.869263 | + | 0.494351i | \(0.164594\pi\) | |||||||
\(608\) | 1.59213 | 0.0645696 | ||||||||
\(609\) | 0.264876 | 0.0107333 | ||||||||
\(610\) | −5.25737 | −0.212865 | ||||||||
\(611\) | 2.13681 | 0.0864459 | ||||||||
\(612\) | 2.06018 | 0.0832779 | ||||||||
\(613\) | −12.8152 | −0.517602 | −0.258801 | − | 0.965931i | \(-0.583327\pi\) | ||||
−0.258801 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(614\) | 16.5766 | 0.668977 | ||||||||
\(615\) | −7.75821 | −0.312841 | ||||||||
\(616\) | −0.137439 | −0.00553757 | ||||||||
\(617\) | −36.1671 | −1.45603 | −0.728017 | − | 0.685559i | \(-0.759558\pi\) | ||||
−0.728017 | + | 0.685559i | \(0.759558\pi\) | |||||||
\(618\) | 12.3546 | 0.496977 | ||||||||
\(619\) | 38.1619 | 1.53386 | 0.766928 | − | 0.641733i | \(-0.221784\pi\) | ||||
0.766928 | + | 0.641733i | \(0.221784\pi\) | |||||||
\(620\) | 0.986272 | 0.0396096 | ||||||||
\(621\) | 8.99941 | 0.361134 | ||||||||
\(622\) | 20.1475 | 0.807841 | ||||||||
\(623\) | −0.0893078 | −0.00357804 | ||||||||
\(624\) | 2.24711 | 0.0899565 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.3376 | −0.732919 | ||||||||
\(627\) | −1.00000 | −0.0399362 | ||||||||
\(628\) | 6.01352 | 0.239965 | ||||||||
\(629\) | −2.91351 | −0.116169 | ||||||||
\(630\) | −0.0601825 | −0.00239773 | ||||||||
\(631\) | 30.1987 | 1.20219 | 0.601095 | − | 0.799177i | \(-0.294731\pi\) | ||||
0.601095 | + | 0.799177i | \(0.294731\pi\) | |||||||
\(632\) | −40.1579 | −1.59740 | ||||||||
\(633\) | −3.86320 | −0.153549 | ||||||||
\(634\) | −17.3115 | −0.687529 | ||||||||
\(635\) | 11.0073 | 0.436813 | ||||||||
\(636\) | 0.940513 | 0.0372938 | ||||||||
\(637\) | 4.69110 | 0.185868 | ||||||||
\(638\) | 7.55379 | 0.299057 | ||||||||
\(639\) | −12.6022 | −0.498535 | ||||||||
\(640\) | 8.33133 | 0.329325 | ||||||||
\(641\) | −8.69574 | −0.343461 | −0.171731 | − | 0.985144i | \(-0.554936\pi\) | ||||
−0.171731 | + | 0.985144i | \(0.554936\pi\) | |||||||
\(642\) | 20.6886 | 0.816515 | ||||||||
\(643\) | −38.9210 | −1.53489 | −0.767447 | − | 0.641112i | \(-0.778473\pi\) | ||||
−0.767447 | + | 0.641112i | \(0.778473\pi\) | |||||||
\(644\) | 0.117288 | 0.00462178 | ||||||||
\(645\) | 7.81186 | 0.307592 | ||||||||
\(646\) | −9.51344 | −0.374301 | ||||||||
\(647\) | −18.5600 | −0.729670 | −0.364835 | − | 0.931072i | \(-0.618875\pi\) | ||||
−0.364835 | + | 0.931072i | \(0.618875\pi\) | |||||||
\(648\) | 2.99182 | 0.117530 | ||||||||
\(649\) | 5.14894 | 0.202113 | ||||||||
\(650\) | 0.878220 | 0.0344466 | ||||||||
\(651\) | −0.159700 | −0.00625915 | ||||||||
\(652\) | 4.39627 | 0.172171 | ||||||||
\(653\) | 8.12148 | 0.317818 | 0.158909 | − | 0.987293i | \(-0.449202\pi\) | ||||
0.158909 | + | 0.987293i | \(0.449202\pi\) | |||||||
\(654\) | −25.4833 | −0.996474 | ||||||||
\(655\) | 2.34467 | 0.0916138 | ||||||||
\(656\) | −26.0064 | −1.01538 | ||||||||
\(657\) | 3.55938 | 0.138865 | ||||||||
\(658\) | −0.191835 | −0.00747851 | ||||||||
\(659\) | −12.7803 | −0.497852 | −0.248926 | − | 0.968523i | \(-0.580078\pi\) | ||||
−0.248926 | + | 0.968523i | \(0.580078\pi\) | |||||||
\(660\) | 0.283703 | 0.0110431 | ||||||||
\(661\) | 48.7774 | 1.89722 | 0.948610 | − | 0.316446i | \(-0.102490\pi\) | ||||
0.948610 | + | 0.316446i | \(0.102490\pi\) | |||||||
\(662\) | −22.5606 | −0.876844 | ||||||||
\(663\) | 4.86798 | 0.189057 | ||||||||
\(664\) | 38.9053 | 1.50982 | ||||||||
\(665\) | −0.0459382 | −0.00178141 | ||||||||
\(666\) | −0.525619 | −0.0203673 | ||||||||
\(667\) | −51.8899 | −2.00918 | ||||||||
\(668\) | 3.37013 | 0.130394 | ||||||||
\(669\) | −13.6672 | −0.528405 | ||||||||
\(670\) | −1.94130 | −0.0749988 | ||||||||
\(671\) | −4.01303 | −0.154921 | ||||||||
\(672\) | 0.0731397 | 0.00282143 | ||||||||
\(673\) | −26.4225 | −1.01851 | −0.509255 | − | 0.860615i | \(-0.670079\pi\) | ||||
−0.509255 | + | 0.860615i | \(0.670079\pi\) | |||||||
\(674\) | 7.22660 | 0.278358 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 3.56065 | 0.136948 | ||||||||
\(677\) | 3.80976 | 0.146421 | 0.0732104 | − | 0.997317i | \(-0.476676\pi\) | ||||
0.0732104 | + | 0.997317i | \(0.476676\pi\) | |||||||
\(678\) | −9.48852 | −0.364404 | ||||||||
\(679\) | −0.290096 | −0.0111329 | ||||||||
\(680\) | 21.7259 | 0.833150 | ||||||||
\(681\) | 6.58470 | 0.252326 | ||||||||
\(682\) | −4.55437 | −0.174396 | ||||||||
\(683\) | 25.8187 | 0.987924 | 0.493962 | − | 0.869484i | \(-0.335548\pi\) | ||||
0.493962 | + | 0.869484i | \(0.335548\pi\) | |||||||
\(684\) | 0.283703 | 0.0108477 | ||||||||
\(685\) | −9.57007 | −0.365654 | ||||||||
\(686\) | −0.842427 | −0.0321640 | ||||||||
\(687\) | 12.5156 | 0.477498 | ||||||||
\(688\) | 26.1862 | 0.998339 | ||||||||
\(689\) | 2.22233 | 0.0846639 | ||||||||
\(690\) | 11.7899 | 0.448834 | ||||||||
\(691\) | 27.0739 | 1.02994 | 0.514969 | − | 0.857209i | \(-0.327803\pi\) | ||||
0.514969 | + | 0.857209i | \(0.327803\pi\) | |||||||
\(692\) | −1.81586 | −0.0690288 | ||||||||
\(693\) | −0.0459382 | −0.00174505 | ||||||||
\(694\) | 18.3905 | 0.698093 | ||||||||
\(695\) | 20.3810 | 0.773097 | ||||||||
\(696\) | −17.2506 | −0.653883 | ||||||||
\(697\) | −56.3382 | −2.13396 | ||||||||
\(698\) | −1.46106 | −0.0553018 | ||||||||
\(699\) | −26.0657 | −0.985896 | ||||||||
\(700\) | 0.0130328 | 0.000492594 0 | ||||||||
\(701\) | 32.3535 | 1.22198 | 0.610988 | − | 0.791640i | \(-0.290772\pi\) | ||||
0.610988 | + | 0.791640i | \(0.290772\pi\) | |||||||
\(702\) | 0.878220 | 0.0331463 | ||||||||
\(703\) | −0.401213 | −0.0151320 | ||||||||
\(704\) | 8.79003 | 0.331287 | ||||||||
\(705\) | 3.18756 | 0.120050 | ||||||||
\(706\) | 37.4926 | 1.41105 | ||||||||
\(707\) | −0.455064 | −0.0171144 | ||||||||
\(708\) | −1.46077 | −0.0548991 | ||||||||
\(709\) | 7.78682 | 0.292440 | 0.146220 | − | 0.989252i | \(-0.453289\pi\) | ||||
0.146220 | + | 0.989252i | \(0.453289\pi\) | |||||||
\(710\) | −16.5098 | −0.619603 | ||||||||
\(711\) | −13.4225 | −0.503385 | ||||||||
\(712\) | 5.81637 | 0.217978 | ||||||||
\(713\) | 31.2858 | 1.17166 | ||||||||
\(714\) | −0.437030 | −0.0163554 | ||||||||
\(715\) | 0.670359 | 0.0250700 | ||||||||
\(716\) | 0.547534 | 0.0204623 | ||||||||
\(717\) | 18.4855 | 0.690353 | ||||||||
\(718\) | −14.8563 | −0.554433 | ||||||||
\(719\) | 11.1846 | 0.417116 | 0.208558 | − | 0.978010i | \(-0.433123\pi\) | ||||
0.208558 | + | 0.978010i | \(0.433123\pi\) | |||||||
\(720\) | 3.35211 | 0.124926 | ||||||||
\(721\) | 0.433219 | 0.0161339 | ||||||||
\(722\) | −1.31008 | −0.0487559 | ||||||||
\(723\) | −27.7704 | −1.03279 | ||||||||
\(724\) | 0.435254 | 0.0161761 | ||||||||
\(725\) | −5.76592 | −0.214141 | ||||||||
\(726\) | −1.31008 | −0.0486214 | ||||||||
\(727\) | −33.5929 | −1.24589 | −0.622945 | − | 0.782265i | \(-0.714064\pi\) | ||||
−0.622945 | + | 0.782265i | \(0.714064\pi\) | |||||||
\(728\) | 0.0921333 | 0.00341469 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.66306 | 0.172588 | ||||||||
\(731\) | 56.7278 | 2.09815 | ||||||||
\(732\) | 1.13851 | 0.0420805 | ||||||||
\(733\) | −35.2861 | −1.30332 | −0.651660 | − | 0.758511i | \(-0.725927\pi\) | ||||
−0.651660 | + | 0.758511i | \(0.725927\pi\) | |||||||
\(734\) | −19.1963 | −0.708549 | ||||||||
\(735\) | 6.99789 | 0.258121 | ||||||||
\(736\) | −14.3283 | −0.528147 | ||||||||
\(737\) | −1.48182 | −0.0545835 | ||||||||
\(738\) | −10.1638 | −0.374136 | ||||||||
\(739\) | 51.0315 | 1.87722 | 0.938612 | − | 0.344974i | \(-0.112112\pi\) | ||||
0.938612 | + | 0.344974i | \(0.112112\pi\) | |||||||
\(740\) | 0.113825 | 0.00418430 | ||||||||
\(741\) | 0.670359 | 0.0246262 | ||||||||
\(742\) | −0.199513 | −0.00732434 | ||||||||
\(743\) | −7.59972 | −0.278807 | −0.139403 | − | 0.990236i | \(-0.544518\pi\) | ||||
−0.139403 | + | 0.990236i | \(0.544518\pi\) | |||||||
\(744\) | 10.4008 | 0.381313 | ||||||||
\(745\) | 15.8754 | 0.581630 | ||||||||
\(746\) | 36.9484 | 1.35278 | ||||||||
\(747\) | 13.0039 | 0.475787 | ||||||||
\(748\) | 2.06018 | 0.0753277 | ||||||||
\(749\) | 0.725453 | 0.0265075 | ||||||||
\(750\) | 1.31008 | 0.0478372 | ||||||||
\(751\) | 4.60241 | 0.167944 | 0.0839722 | − | 0.996468i | \(-0.473239\pi\) | ||||
0.0839722 | + | 0.996468i | \(0.473239\pi\) | |||||||
\(752\) | 10.6850 | 0.389643 | ||||||||
\(753\) | −20.7247 | −0.755250 | ||||||||
\(754\) | −5.06375 | −0.184411 | ||||||||
\(755\) | 1.61303 | 0.0587042 | ||||||||
\(756\) | 0.0130328 | 0.000473998 0 | ||||||||
\(757\) | 14.3750 | 0.522468 | 0.261234 | − | 0.965275i | \(-0.415871\pi\) | ||||
0.261234 | + | 0.965275i | \(0.415871\pi\) | |||||||
\(758\) | 18.0067 | 0.654034 | ||||||||
\(759\) | 8.99941 | 0.326658 | ||||||||
\(760\) | 2.99182 | 0.108525 | ||||||||
\(761\) | −50.3207 | −1.82412 | −0.912062 | − | 0.410053i | \(-0.865510\pi\) | ||||
−0.912062 | + | 0.410053i | \(0.865510\pi\) | |||||||
\(762\) | 14.4205 | 0.522398 | ||||||||
\(763\) | −0.893578 | −0.0323497 | ||||||||
\(764\) | −6.96916 | −0.252135 | ||||||||
\(765\) | 7.26175 | 0.262549 | ||||||||
\(766\) | 26.1841 | 0.946071 | ||||||||
\(767\) | −3.45163 | −0.124631 | ||||||||
\(768\) | −6.66539 | −0.240517 | ||||||||
\(769\) | 24.8105 | 0.894690 | 0.447345 | − | 0.894361i | \(-0.352370\pi\) | ||||
0.447345 | + | 0.894361i | \(0.352370\pi\) | |||||||
\(770\) | −0.0601825 | −0.00216883 | ||||||||
\(771\) | −29.2153 | −1.05216 | ||||||||
\(772\) | 6.21232 | 0.223586 | ||||||||
\(773\) | −6.44996 | −0.231989 | −0.115994 | − | 0.993250i | \(-0.537005\pi\) | ||||
−0.115994 | + | 0.993250i | \(0.537005\pi\) | |||||||
\(774\) | 10.2341 | 0.367858 | ||||||||
\(775\) | 3.47642 | 0.124877 | ||||||||
\(776\) | 18.8932 | 0.678225 | ||||||||
\(777\) | −0.0184310 | −0.000661208 0 | ||||||||
\(778\) | −25.5102 | −0.914584 | ||||||||
\(779\) | −7.75821 | −0.277967 | ||||||||
\(780\) | −0.190183 | −0.00680964 | ||||||||
\(781\) | −12.6022 | −0.450942 | ||||||||
\(782\) | 85.6154 | 3.06160 | ||||||||
\(783\) | −5.76592 | −0.206057 | ||||||||
\(784\) | 23.4577 | 0.837774 | ||||||||
\(785\) | 21.1965 | 0.756536 | ||||||||
\(786\) | 3.07169 | 0.109564 | ||||||||
\(787\) | −3.35379 | −0.119550 | −0.0597749 | − | 0.998212i | \(-0.519038\pi\) | ||||
−0.0597749 | + | 0.998212i | \(0.519038\pi\) | |||||||
\(788\) | −3.45022 | −0.122909 | ||||||||
\(789\) | −4.20016 | −0.149530 | ||||||||
\(790\) | −17.5845 | −0.625630 | ||||||||
\(791\) | −0.332718 | −0.0118301 | ||||||||
\(792\) | 2.99182 | 0.106310 | ||||||||
\(793\) | 2.69017 | 0.0955308 | ||||||||
\(794\) | 24.8875 | 0.883224 | ||||||||
\(795\) | 3.31513 | 0.117576 | ||||||||
\(796\) | 6.63953 | 0.235332 | ||||||||
\(797\) | −7.51135 | −0.266066 | −0.133033 | − | 0.991112i | \(-0.542472\pi\) | ||||
−0.133033 | + | 0.991112i | \(0.542472\pi\) | |||||||
\(798\) | −0.0601825 | −0.00213044 | ||||||||
\(799\) | 23.1473 | 0.818891 | ||||||||
\(800\) | −1.59213 | −0.0562904 | ||||||||
\(801\) | 1.94409 | 0.0686910 | ||||||||
\(802\) | 7.18065 | 0.253557 | ||||||||
\(803\) | 3.55938 | 0.125608 | ||||||||
\(804\) | 0.420397 | 0.0148263 | ||||||||
\(805\) | 0.413417 | 0.0145710 | ||||||||
\(806\) | 3.05306 | 0.107540 | ||||||||
\(807\) | 1.37742 | 0.0484876 | ||||||||
\(808\) | 29.6370 | 1.04263 | ||||||||
\(809\) | −43.8080 | −1.54021 | −0.770104 | − | 0.637918i | \(-0.779796\pi\) | ||||
−0.770104 | + | 0.637918i | \(0.779796\pi\) | |||||||
\(810\) | 1.31008 | 0.0460313 | ||||||||
\(811\) | −41.4737 | −1.45634 | −0.728170 | − | 0.685396i | \(-0.759629\pi\) | ||||
−0.728170 | + | 0.685396i | \(0.759629\pi\) | |||||||
\(812\) | −0.0751461 | −0.00263711 | ||||||||
\(813\) | 2.44349 | 0.0856968 | ||||||||
\(814\) | −0.525619 | −0.0184229 | ||||||||
\(815\) | 15.4960 | 0.542802 | ||||||||
\(816\) | 24.3422 | 0.852146 | ||||||||
\(817\) | 7.81186 | 0.273302 | ||||||||
\(818\) | −19.8693 | −0.694715 | ||||||||
\(819\) | 0.0307951 | 0.00107607 | ||||||||
\(820\) | 2.20103 | 0.0768633 | ||||||||
\(821\) | −30.9218 | −1.07918 | −0.539590 | − | 0.841928i | \(-0.681421\pi\) | ||||
−0.539590 | + | 0.841928i | \(0.681421\pi\) | |||||||
\(822\) | −12.5375 | −0.437296 | ||||||||
\(823\) | 33.6565 | 1.17319 | 0.586597 | − | 0.809879i | \(-0.300467\pi\) | ||||
0.586597 | + | 0.809879i | \(0.300467\pi\) | |||||||
\(824\) | −28.2143 | −0.982893 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 0.309876 | 0.0107820 | ||||||||
\(827\) | 53.0019 | 1.84306 | 0.921528 | − | 0.388312i | \(-0.126942\pi\) | ||||
0.921528 | + | 0.388312i | \(0.126942\pi\) | |||||||
\(828\) | −2.55316 | −0.0887285 | ||||||||
\(829\) | 48.8099 | 1.69524 | 0.847618 | − | 0.530607i | \(-0.178036\pi\) | ||||
0.847618 | + | 0.530607i | \(0.178036\pi\) | |||||||
\(830\) | 17.0361 | 0.591330 | ||||||||
\(831\) | −12.7285 | −0.441548 | ||||||||
\(832\) | −5.89247 | −0.204285 | ||||||||
\(833\) | 50.8170 | 1.76070 | ||||||||
\(834\) | 26.7007 | 0.924569 | ||||||||
\(835\) | 11.8791 | 0.411092 | ||||||||
\(836\) | 0.283703 | 0.00981208 | ||||||||
\(837\) | 3.47642 | 0.120163 | ||||||||
\(838\) | −13.5179 | −0.466970 | ||||||||
\(839\) | 41.1240 | 1.41976 | 0.709879 | − | 0.704323i | \(-0.248749\pi\) | ||||
0.709879 | + | 0.704323i | \(0.248749\pi\) | |||||||
\(840\) | 0.137439 | 0.00474209 | ||||||||
\(841\) | 4.24582 | 0.146408 | ||||||||
\(842\) | −21.4840 | −0.740387 | ||||||||
\(843\) | 4.08159 | 0.140577 | ||||||||
\(844\) | 1.09600 | 0.0377260 | ||||||||
\(845\) | 12.5506 | 0.431754 | ||||||||
\(846\) | 4.17594 | 0.143572 | ||||||||
\(847\) | −0.0459382 | −0.00157845 | ||||||||
\(848\) | 11.1127 | 0.381611 | ||||||||
\(849\) | 5.84982 | 0.200765 | ||||||||
\(850\) | 9.51344 | 0.326308 | ||||||||
\(851\) | 3.61068 | 0.123772 | ||||||||
\(852\) | 3.57528 | 0.122487 | ||||||||
\(853\) | 1.34400 | 0.0460176 | 0.0230088 | − | 0.999735i | \(-0.492675\pi\) | ||||
0.0230088 | + | 0.999735i | \(0.492675\pi\) | |||||||
\(854\) | −0.241514 | −0.00826445 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | −47.2467 | −1.61486 | ||||||||
\(857\) | 32.6082 | 1.11388 | 0.556938 | − | 0.830554i | \(-0.311976\pi\) | ||||
0.556938 | + | 0.830554i | \(0.311976\pi\) | |||||||
\(858\) | 0.878220 | 0.0299819 | ||||||||
\(859\) | −29.4158 | −1.00365 | −0.501827 | − | 0.864968i | \(-0.667339\pi\) | ||||
−0.501827 | + | 0.864968i | \(0.667339\pi\) | |||||||
\(860\) | −2.21625 | −0.0755734 | ||||||||
\(861\) | −0.356398 | −0.0121460 | ||||||||
\(862\) | 20.2815 | 0.690791 | ||||||||
\(863\) | 24.9710 | 0.850022 | 0.425011 | − | 0.905188i | \(-0.360270\pi\) | ||||
0.425011 | + | 0.905188i | \(0.360270\pi\) | |||||||
\(864\) | −1.59213 | −0.0541655 | ||||||||
\(865\) | −6.40058 | −0.217626 | ||||||||
\(866\) | 5.69804 | 0.193627 | ||||||||
\(867\) | 35.7331 | 1.21356 | ||||||||
\(868\) | 0.0453075 | 0.00153784 | ||||||||
\(869\) | −13.4225 | −0.455329 | ||||||||
\(870\) | −7.55379 | −0.256097 | ||||||||
\(871\) | 0.993351 | 0.0336584 | ||||||||
\(872\) | 58.1962 | 1.97077 | ||||||||
\(873\) | 6.31493 | 0.213728 | ||||||||
\(874\) | 11.7899 | 0.398800 | ||||||||
\(875\) | 0.0459382 | 0.00155299 | ||||||||
\(876\) | −1.00981 | −0.0341182 | ||||||||
\(877\) | −13.8555 | −0.467868 | −0.233934 | − | 0.972252i | \(-0.575160\pi\) | ||||
−0.233934 | + | 0.972252i | \(0.575160\pi\) | |||||||
\(878\) | 18.6253 | 0.628575 | ||||||||
\(879\) | −2.77452 | −0.0935821 | ||||||||
\(880\) | 3.35211 | 0.112999 | ||||||||
\(881\) | 23.3533 | 0.786794 | 0.393397 | − | 0.919369i | \(-0.371300\pi\) | ||||
0.393397 | + | 0.919369i | \(0.371300\pi\) | |||||||
\(882\) | 9.16776 | 0.308695 | ||||||||
\(883\) | 39.0324 | 1.31354 | 0.656772 | − | 0.754089i | \(-0.271921\pi\) | ||||
0.656772 | + | 0.754089i | \(0.271921\pi\) | |||||||
\(884\) | −1.38106 | −0.0464501 | ||||||||
\(885\) | −5.14894 | −0.173080 | ||||||||
\(886\) | −35.4050 | −1.18945 | ||||||||
\(887\) | −17.3827 | −0.583655 | −0.291828 | − | 0.956471i | \(-0.594263\pi\) | ||||
−0.291828 | + | 0.956471i | \(0.594263\pi\) | |||||||
\(888\) | 1.20036 | 0.0402813 | ||||||||
\(889\) | 0.505657 | 0.0169592 | ||||||||
\(890\) | 2.54690 | 0.0853723 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 3.87743 | 0.129826 | ||||||||
\(893\) | 3.18756 | 0.106668 | ||||||||
\(894\) | 20.7980 | 0.695588 | ||||||||
\(895\) | 1.92995 | 0.0645112 | ||||||||
\(896\) | 0.382726 | 0.0127860 | ||||||||
\(897\) | −6.03284 | −0.201431 | ||||||||
\(898\) | −38.7389 | −1.29274 | ||||||||
\(899\) | −20.0448 | −0.668530 | ||||||||
\(900\) | −0.283703 | −0.00945677 | ||||||||
\(901\) | 24.0737 | 0.802010 | ||||||||
\(902\) | −10.1638 | −0.338419 | ||||||||
\(903\) | 0.358862 | 0.0119422 | ||||||||
\(904\) | 21.6690 | 0.720699 | ||||||||
\(905\) | 1.53419 | 0.0509981 | ||||||||
\(906\) | 2.11319 | 0.0702061 | ||||||||
\(907\) | −22.7667 | −0.755955 | −0.377978 | − | 0.925815i | \(-0.623380\pi\) | ||||
−0.377978 | + | 0.925815i | \(0.623380\pi\) | |||||||
\(908\) | −1.86810 | −0.0619951 | ||||||||
\(909\) | 9.90601 | 0.328562 | ||||||||
\(910\) | 0.0403438 | 0.00133739 | ||||||||
\(911\) | 12.1324 | 0.401964 | 0.200982 | − | 0.979595i | \(-0.435587\pi\) | ||||
0.200982 | + | 0.979595i | \(0.435587\pi\) | |||||||
\(912\) | 3.35211 | 0.110999 | ||||||||
\(913\) | 13.0039 | 0.430366 | ||||||||
\(914\) | 52.4113 | 1.73361 | ||||||||
\(915\) | 4.01303 | 0.132667 | ||||||||
\(916\) | −3.55070 | −0.117319 | ||||||||
\(917\) | 0.107710 | 0.00355689 | ||||||||
\(918\) | 9.51344 | 0.313990 | ||||||||
\(919\) | −42.1151 | −1.38925 | −0.694625 | − | 0.719372i | \(-0.744430\pi\) | ||||
−0.694625 | + | 0.719372i | \(0.744430\pi\) | |||||||
\(920\) | −26.9247 | −0.887679 | ||||||||
\(921\) | −12.6532 | −0.416936 | ||||||||
\(922\) | 11.6247 | 0.382840 | ||||||||
\(923\) | 8.44799 | 0.278069 | ||||||||
\(924\) | 0.0130328 | 0.000428748 0 | ||||||||
\(925\) | 0.401213 | 0.0131918 | ||||||||
\(926\) | 18.8132 | 0.618239 | ||||||||
\(927\) | −9.43048 | −0.309738 | ||||||||
\(928\) | 9.18012 | 0.301352 | ||||||||
\(929\) | −5.58087 | −0.183102 | −0.0915512 | − | 0.995800i | \(-0.529183\pi\) | ||||
−0.0915512 | + | 0.995800i | \(0.529183\pi\) | |||||||
\(930\) | 4.55437 | 0.149344 | ||||||||
\(931\) | 6.99789 | 0.229347 | ||||||||
\(932\) | 7.39492 | 0.242229 | ||||||||
\(933\) | −15.3789 | −0.503482 | ||||||||
\(934\) | −23.8744 | −0.781193 | ||||||||
\(935\) | 7.26175 | 0.237485 | ||||||||
\(936\) | −2.00559 | −0.0655549 | ||||||||
\(937\) | 31.0344 | 1.01385 | 0.506925 | − | 0.861990i | \(-0.330782\pi\) | ||||
0.506925 | + | 0.861990i | \(0.330782\pi\) | |||||||
\(938\) | −0.0891796 | −0.00291182 | ||||||||
\(939\) | 13.9974 | 0.456788 | ||||||||
\(940\) | −0.904320 | −0.0294957 | ||||||||
\(941\) | 47.5393 | 1.54974 | 0.774868 | − | 0.632123i | \(-0.217816\pi\) | ||||
0.774868 | + | 0.632123i | \(0.217816\pi\) | |||||||
\(942\) | 27.7690 | 0.904764 | ||||||||
\(943\) | 69.8194 | 2.27363 | ||||||||
\(944\) | −17.2598 | −0.561758 | ||||||||
\(945\) | 0.0459382 | 0.00149437 | ||||||||
\(946\) | 10.2341 | 0.332740 | ||||||||
\(947\) | 8.06096 | 0.261946 | 0.130973 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130973 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(948\) | 3.80802 | 0.123679 | ||||||||
\(949\) | −2.38606 | −0.0774549 | ||||||||
\(950\) | 1.31008 | 0.0425045 | ||||||||
\(951\) | 13.2141 | 0.428498 | ||||||||
\(952\) | 0.998047 | 0.0323469 | ||||||||
\(953\) | −35.1400 | −1.13830 | −0.569149 | − | 0.822235i | \(-0.692727\pi\) | ||||
−0.569149 | + | 0.822235i | \(0.692727\pi\) | |||||||
\(954\) | 4.34307 | 0.140612 | ||||||||
\(955\) | −24.5650 | −0.794904 | ||||||||
\(956\) | −5.24439 | −0.169616 | ||||||||
\(957\) | −5.76592 | −0.186386 | ||||||||
\(958\) | −38.7495 | −1.25194 | ||||||||
\(959\) | −0.439632 | −0.0141964 | ||||||||
\(960\) | −8.79003 | −0.283697 | ||||||||
\(961\) | −18.9145 | −0.610145 | ||||||||
\(962\) | 0.352353 | 0.0113603 | ||||||||
\(963\) | −15.7919 | −0.508888 | ||||||||
\(964\) | 7.87856 | 0.253751 | ||||||||
\(965\) | 21.8972 | 0.704897 | ||||||||
\(966\) | 0.541607 | 0.0174259 | ||||||||
\(967\) | −16.0851 | −0.517263 | −0.258632 | − | 0.965976i | \(-0.583272\pi\) | ||||
−0.258632 | + | 0.965976i | \(0.583272\pi\) | |||||||
\(968\) | 2.99182 | 0.0961608 | ||||||||
\(969\) | 7.26175 | 0.233281 | ||||||||
\(970\) | 8.27303 | 0.265631 | ||||||||
\(971\) | −50.2083 | −1.61126 | −0.805631 | − | 0.592418i | \(-0.798173\pi\) | ||||
−0.805631 | + | 0.592418i | \(0.798173\pi\) | |||||||
\(972\) | −0.283703 | −0.00909978 | ||||||||
\(973\) | 0.936268 | 0.0300154 | ||||||||
\(974\) | 53.9443 | 1.72849 | ||||||||
\(975\) | −0.670359 | −0.0214687 | ||||||||
\(976\) | 13.4521 | 0.430592 | ||||||||
\(977\) | 1.00917 | 0.0322861 | 0.0161431 | − | 0.999870i | \(-0.494861\pi\) | ||||
0.0161431 | + | 0.999870i | \(0.494861\pi\) | |||||||
\(978\) | 20.3010 | 0.649153 | ||||||||
\(979\) | 1.94409 | 0.0621333 | ||||||||
\(980\) | −1.98532 | −0.0634188 | ||||||||
\(981\) | 19.4517 | 0.621046 | ||||||||
\(982\) | −38.4293 | −1.22633 | ||||||||
\(983\) | −25.2319 | −0.804772 | −0.402386 | − | 0.915470i | \(-0.631819\pi\) | ||||
−0.402386 | + | 0.915470i | \(0.631819\pi\) | |||||||
\(984\) | 23.2112 | 0.739946 | ||||||||
\(985\) | −12.1614 | −0.387494 | ||||||||
\(986\) | −54.8537 | −1.74690 | ||||||||
\(987\) | 0.146431 | 0.00466093 | ||||||||
\(988\) | −0.190183 | −0.00605052 | ||||||||
\(989\) | −70.3021 | −2.23548 | ||||||||
\(990\) | 1.31008 | 0.0416369 | ||||||||
\(991\) | −30.8482 | −0.979925 | −0.489962 | − | 0.871744i | \(-0.662989\pi\) | ||||
−0.489962 | + | 0.871744i | \(0.662989\pi\) | |||||||
\(992\) | −5.53493 | −0.175734 | ||||||||
\(993\) | 17.2209 | 0.546488 | ||||||||
\(994\) | −0.758431 | −0.0240560 | ||||||||
\(995\) | 23.4031 | 0.741928 | ||||||||
\(996\) | −3.68924 | −0.116898 | ||||||||
\(997\) | −40.1424 | −1.27132 | −0.635662 | − | 0.771967i | \(-0.719273\pi\) | ||||
−0.635662 | + | 0.771967i | \(0.719273\pi\) | |||||||
\(998\) | −25.7409 | −0.814814 | ||||||||
\(999\) | 0.401213 | 0.0126938 |
(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 | 3135.2.a.o.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 9405.2.a.y.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3135.2.a.o.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9405.2.a.y.1.4 | 6 | 3.2 | odd | 2 |