Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(5.29266605383\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
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 | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62772 | 0.641296 | 0.320648 | − | 0.947198i | \(-0.396099\pi\) | ||||
0.320648 | + | 0.947198i | \(0.396099\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −18.8397 | −0.588739 | ||||||||
\(5\) | 57.7228 | 1.03258 | 0.516289 | − | 0.856415i | \(-0.327313\pi\) | ||||
0.516289 | + | 0.856415i | \(0.327313\pi\) | |||||||
\(6\) | 32.6495 | 0.370252 | ||||||||
\(7\) | 251.081 | 1.93673 | 0.968366 | − | 0.249534i | \(-0.0802775\pi\) | ||||
0.968366 | + | 0.249534i | \(0.0802775\pi\) | |||||||
\(8\) | −184.432 | −1.01885 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 209.402 | 0.662188 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −169.557 | −0.339909 | ||||||||
\(13\) | −277.549 | −0.455492 | −0.227746 | − | 0.973721i | \(-0.573136\pi\) | ||||
−0.227746 | + | 0.973721i | \(0.573136\pi\) | |||||||
\(14\) | 910.853 | 1.24202 | ||||||||
\(15\) | 519.505 | 0.596159 | ||||||||
\(16\) | −66.1983 | −0.0646468 | ||||||||
\(17\) | 704.489 | 0.591224 | 0.295612 | − | 0.955308i | \(-0.404477\pi\) | ||||
0.295612 | + | 0.955308i | \(0.404477\pi\) | |||||||
\(18\) | 293.845 | 0.213765 | ||||||||
\(19\) | −2861.18 | −1.81828 | −0.909142 | − | 0.416486i | \(-0.863261\pi\) | ||||
−0.909142 | + | 0.416486i | \(0.863261\pi\) | |||||||
\(20\) | −1087.48 | −0.607919 | ||||||||
\(21\) | 2259.73 | 1.11817 | ||||||||
\(22\) | −438.954 | −0.193358 | ||||||||
\(23\) | −1066.85 | −0.420518 | −0.210259 | − | 0.977646i | \(-0.567431\pi\) | ||||
−0.210259 | + | 0.977646i | \(0.567431\pi\) | |||||||
\(24\) | −1659.89 | −0.588235 | ||||||||
\(25\) | 206.923 | 0.0662154 | ||||||||
\(26\) | −1006.87 | −0.292105 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −4730.29 | −1.14023 | ||||||||
\(29\) | −3937.44 | −0.869399 | −0.434700 | − | 0.900575i | \(-0.643145\pi\) | ||||
−0.434700 | + | 0.900575i | \(0.643145\pi\) | |||||||
\(30\) | 1884.62 | 0.382314 | ||||||||
\(31\) | −644.350 | −0.120425 | −0.0602126 | − | 0.998186i | \(-0.519178\pi\) | ||||
−0.0602126 | + | 0.998186i | \(0.519178\pi\) | |||||||
\(32\) | 5661.67 | 0.977395 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 2555.69 | 0.379149 | ||||||||
\(35\) | 14493.1 | 1.99982 | ||||||||
\(36\) | −1526.01 | −0.196246 | ||||||||
\(37\) | −9042.34 | −1.08587 | −0.542934 | − | 0.839776i | \(-0.682686\pi\) | ||||
−0.542934 | + | 0.839776i | \(0.682686\pi\) | |||||||
\(38\) | −10379.6 | −1.16606 | ||||||||
\(39\) | −2497.94 | −0.262979 | ||||||||
\(40\) | −10645.9 | −1.05204 | ||||||||
\(41\) | 18219.0 | 1.69264 | 0.846322 | − | 0.532672i | \(-0.178812\pi\) | ||||
0.846322 | + | 0.532672i | \(0.178812\pi\) | |||||||
\(42\) | 8197.68 | 0.717080 | ||||||||
\(43\) | −4054.54 | −0.334403 | −0.167202 | − | 0.985923i | \(-0.553473\pi\) | ||||
−0.167202 | + | 0.985923i | \(0.553473\pi\) | |||||||
\(44\) | 2279.60 | 0.177512 | ||||||||
\(45\) | 4675.55 | 0.344192 | ||||||||
\(46\) | −3870.24 | −0.269677 | ||||||||
\(47\) | 20750.8 | 1.37022 | 0.685110 | − | 0.728439i | \(-0.259754\pi\) | ||||
0.685110 | + | 0.728439i | \(0.259754\pi\) | |||||||
\(48\) | −595.785 | −0.0373238 | ||||||||
\(49\) | 46234.9 | 2.75093 | ||||||||
\(50\) | 750.659 | 0.0424637 | ||||||||
\(51\) | 6340.40 | 0.341343 | ||||||||
\(52\) | 5228.92 | 0.268166 | ||||||||
\(53\) | −26485.9 | −1.29517 | −0.647583 | − | 0.761995i | \(-0.724220\pi\) | ||||
−0.647583 | + | 0.761995i | \(0.724220\pi\) | |||||||
\(54\) | 2644.61 | 0.123417 | ||||||||
\(55\) | −6984.46 | −0.311334 | ||||||||
\(56\) | −46307.4 | −1.97324 | ||||||||
\(57\) | −25750.7 | −1.04979 | ||||||||
\(58\) | −14283.9 | −0.557542 | ||||||||
\(59\) | 4293.12 | 0.160562 | 0.0802810 | − | 0.996772i | \(-0.474418\pi\) | ||||
0.0802810 | + | 0.996772i | \(0.474418\pi\) | |||||||
\(60\) | −9787.30 | −0.350982 | ||||||||
\(61\) | −6831.76 | −0.235076 | −0.117538 | − | 0.993068i | \(-0.537500\pi\) | ||||
−0.117538 | + | 0.993068i | \(0.537500\pi\) | |||||||
\(62\) | −2337.52 | −0.0772282 | ||||||||
\(63\) | 20337.6 | 0.645577 | ||||||||
\(64\) | 22657.3 | 0.691446 | ||||||||
\(65\) | −16020.9 | −0.470331 | ||||||||
\(66\) | −3950.59 | −0.111635 | ||||||||
\(67\) | −56749.5 | −1.54445 | −0.772227 | − | 0.635347i | \(-0.780857\pi\) | ||||
−0.772227 | + | 0.635347i | \(0.780857\pi\) | |||||||
\(68\) | −13272.3 | −0.348077 | ||||||||
\(69\) | −9601.68 | −0.242786 | ||||||||
\(70\) | 52577.0 | 1.28248 | ||||||||
\(71\) | 3187.09 | 0.0750323 | 0.0375161 | − | 0.999296i | \(-0.488055\pi\) | ||||
0.0375161 | + | 0.999296i | \(0.488055\pi\) | |||||||
\(72\) | −14939.0 | −0.339617 | ||||||||
\(73\) | −7397.14 | −0.162464 | −0.0812319 | − | 0.996695i | \(-0.525885\pi\) | ||||
−0.0812319 | + | 0.996695i | \(0.525885\pi\) | |||||||
\(74\) | −32803.1 | −0.696362 | ||||||||
\(75\) | 1862.31 | 0.0382295 | ||||||||
\(76\) | 53903.7 | 1.07050 | ||||||||
\(77\) | −30380.9 | −0.583947 | ||||||||
\(78\) | −9061.82 | −0.168647 | ||||||||
\(79\) | 24393.7 | 0.439754 | 0.219877 | − | 0.975528i | \(-0.429434\pi\) | ||||
0.219877 | + | 0.975528i | \(0.429434\pi\) | |||||||
\(80\) | −3821.15 | −0.0667528 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 66093.5 | 1.08549 | ||||||||
\(83\) | 102795. | 1.63786 | 0.818932 | − | 0.573890i | \(-0.194566\pi\) | ||||
0.818932 | + | 0.573890i | \(0.194566\pi\) | |||||||
\(84\) | −42572.6 | −0.658312 | ||||||||
\(85\) | 40665.1 | 0.610484 | ||||||||
\(86\) | −14708.7 | −0.214451 | ||||||||
\(87\) | −35437.0 | −0.501948 | ||||||||
\(88\) | 22316.3 | 0.307196 | ||||||||
\(89\) | 49599.4 | 0.663745 | 0.331873 | − | 0.943324i | \(-0.392320\pi\) | ||||
0.331873 | + | 0.943324i | \(0.392320\pi\) | |||||||
\(90\) | 16961.6 | 0.220729 | ||||||||
\(91\) | −69687.4 | −0.882166 | ||||||||
\(92\) | 20099.1 | 0.247576 | ||||||||
\(93\) | −5799.15 | −0.0695275 | ||||||||
\(94\) | 75278.1 | 0.878717 | ||||||||
\(95\) | −165156. | −1.87752 | ||||||||
\(96\) | 50955.1 | 0.564299 | ||||||||
\(97\) | −92279.5 | −0.995808 | −0.497904 | − | 0.867232i | \(-0.665897\pi\) | ||||
−0.497904 | + | 0.867232i | \(0.665897\pi\) | |||||||
\(98\) | 167727. | 1.76416 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −3898.36 | −0.0389836 | ||||||||
\(101\) | −35546.1 | −0.346728 | −0.173364 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173364 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(102\) | 23001.2 | 0.218902 | ||||||||
\(103\) | −59876.8 | −0.556116 | −0.278058 | − | 0.960564i | \(-0.589691\pi\) | ||||
−0.278058 | + | 0.960564i | \(0.589691\pi\) | |||||||
\(104\) | 51188.9 | 0.464079 | ||||||||
\(105\) | 130438. | 1.15460 | ||||||||
\(106\) | −96083.5 | −0.830586 | ||||||||
\(107\) | 89253.8 | 0.753646 | 0.376823 | − | 0.926285i | \(-0.377017\pi\) | ||||
0.376823 | + | 0.926285i | \(0.377017\pi\) | |||||||
\(108\) | −13734.1 | −0.113303 | ||||||||
\(109\) | 22796.0 | 0.183777 | 0.0918887 | − | 0.995769i | \(-0.470710\pi\) | ||||
0.0918887 | + | 0.995769i | \(0.470710\pi\) | |||||||
\(110\) | −25337.7 | −0.199657 | ||||||||
\(111\) | −81381.1 | −0.626926 | ||||||||
\(112\) | −16621.2 | −0.125203 | ||||||||
\(113\) | −166064. | −1.22343 | −0.611717 | − | 0.791077i | \(-0.709521\pi\) | ||||
−0.611717 | + | 0.791077i | \(0.709521\pi\) | |||||||
\(114\) | −93416.1 | −0.673224 | ||||||||
\(115\) | −61581.7 | −0.434218 | ||||||||
\(116\) | 74180.1 | 0.511850 | ||||||||
\(117\) | −22481.5 | −0.151831 | ||||||||
\(118\) | 15574.2 | 0.102968 | ||||||||
\(119\) | 176884. | 1.14504 | ||||||||
\(120\) | −95813.4 | −0.607398 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −24783.7 | −0.150753 | ||||||||
\(123\) | 163971. | 0.977248 | ||||||||
\(124\) | 12139.3 | 0.0708991 | ||||||||
\(125\) | −168440. | −0.964205 | ||||||||
\(126\) | 73779.1 | 0.414006 | ||||||||
\(127\) | 159190. | 0.875802 | 0.437901 | − | 0.899023i | \(-0.355722\pi\) | ||||
0.437901 | + | 0.899023i | \(0.355722\pi\) | |||||||
\(128\) | −98979.2 | −0.533973 | ||||||||
\(129\) | −36490.9 | −0.193068 | ||||||||
\(130\) | −58119.3 | −0.301621 | ||||||||
\(131\) | 232174. | 1.18205 | 0.591025 | − | 0.806654i | \(-0.298724\pi\) | ||||
0.591025 | + | 0.806654i | \(0.298724\pi\) | |||||||
\(132\) | 20516.4 | 0.102486 | ||||||||
\(133\) | −718390. | −3.52153 | ||||||||
\(134\) | −205871. | −0.990452 | ||||||||
\(135\) | 42079.9 | 0.198720 | ||||||||
\(136\) | −129930. | −0.602369 | ||||||||
\(137\) | 68205.4 | 0.310468 | 0.155234 | − | 0.987878i | \(-0.450387\pi\) | ||||
0.155234 | + | 0.987878i | \(0.450387\pi\) | |||||||
\(138\) | −34832.2 | −0.155698 | ||||||||
\(139\) | 298162. | 1.30893 | 0.654464 | − | 0.756093i | \(-0.272894\pi\) | ||||
0.654464 | + | 0.756093i | \(0.272894\pi\) | |||||||
\(140\) | −273046. | −1.17738 | ||||||||
\(141\) | 186757. | 0.791097 | ||||||||
\(142\) | 11561.9 | 0.0481179 | ||||||||
\(143\) | 33583.4 | 0.137336 | ||||||||
\(144\) | −5362.06 | −0.0215489 | ||||||||
\(145\) | −227280. | −0.897722 | ||||||||
\(146\) | −26834.7 | −0.104187 | ||||||||
\(147\) | 416114. | 1.58825 | ||||||||
\(148\) | 170355. | 0.639293 | ||||||||
\(149\) | 83131.5 | 0.306761 | 0.153380 | − | 0.988167i | \(-0.450984\pi\) | ||||
0.153380 | + | 0.988167i | \(0.450984\pi\) | |||||||
\(150\) | 6755.93 | 0.0245164 | ||||||||
\(151\) | 167598. | 0.598171 | 0.299085 | − | 0.954226i | \(-0.403318\pi\) | ||||
0.299085 | + | 0.954226i | \(0.403318\pi\) | |||||||
\(152\) | 527694. | 1.85256 | ||||||||
\(153\) | 57063.6 | 0.197075 | ||||||||
\(154\) | −110213. | −0.374483 | ||||||||
\(155\) | −37193.7 | −0.124348 | ||||||||
\(156\) | 47060.3 | 0.154826 | ||||||||
\(157\) | −63259.7 | −0.204823 | −0.102411 | − | 0.994742i | \(-0.532656\pi\) | ||||
−0.102411 | + | 0.994742i | \(0.532656\pi\) | |||||||
\(158\) | 88493.4 | 0.282012 | ||||||||
\(159\) | −238373. | −0.747765 | ||||||||
\(160\) | 326808. | 1.00924 | ||||||||
\(161\) | −267867. | −0.814431 | ||||||||
\(162\) | 23801.5 | 0.0712551 | ||||||||
\(163\) | 237727. | 0.700825 | 0.350412 | − | 0.936596i | \(-0.386041\pi\) | ||||
0.350412 | + | 0.936596i | \(0.386041\pi\) | |||||||
\(164\) | −343240. | −0.996526 | ||||||||
\(165\) | −62860.1 | −0.179749 | ||||||||
\(166\) | 372912. | 1.05036 | ||||||||
\(167\) | 487880. | 1.35370 | 0.676849 | − | 0.736122i | \(-0.263345\pi\) | ||||
0.676849 | + | 0.736122i | \(0.263345\pi\) | |||||||
\(168\) | −416767. | −1.13925 | ||||||||
\(169\) | −294260. | −0.792527 | ||||||||
\(170\) | 147521. | 0.391501 | ||||||||
\(171\) | −231756. | −0.606095 | ||||||||
\(172\) | 76386.1 | 0.196876 | ||||||||
\(173\) | 325942. | 0.827991 | 0.413996 | − | 0.910279i | \(-0.364133\pi\) | ||||
0.413996 | + | 0.910279i | \(0.364133\pi\) | |||||||
\(174\) | −128555. | −0.321897 | ||||||||
\(175\) | 51954.6 | 0.128242 | ||||||||
\(176\) | 8009.99 | 0.0194917 | ||||||||
\(177\) | 38638.1 | 0.0927005 | ||||||||
\(178\) | 179933. | 0.425657 | ||||||||
\(179\) | 462906. | 1.07984 | 0.539921 | − | 0.841716i | \(-0.318454\pi\) | ||||
0.539921 | + | 0.841716i | \(0.318454\pi\) | |||||||
\(180\) | −88085.7 | −0.202640 | ||||||||
\(181\) | 23901.3 | 0.0542281 | 0.0271141 | − | 0.999632i | \(-0.491368\pi\) | ||||
0.0271141 | + | 0.999632i | \(0.491368\pi\) | |||||||
\(182\) | −252806. | −0.565730 | ||||||||
\(183\) | −61485.8 | −0.135721 | ||||||||
\(184\) | 196762. | 0.428446 | ||||||||
\(185\) | −521950. | −1.12124 | ||||||||
\(186\) | −21037.7 | −0.0445877 | ||||||||
\(187\) | −85243.1 | −0.178261 | ||||||||
\(188\) | −390938. | −0.806703 | ||||||||
\(189\) | 183038. | 0.372724 | ||||||||
\(190\) | −599138. | −1.20405 | ||||||||
\(191\) | −565986. | −1.12259 | −0.561297 | − | 0.827615i | \(-0.689697\pi\) | ||||
−0.561297 | + | 0.827615i | \(0.689697\pi\) | |||||||
\(192\) | 203916. | 0.399207 | ||||||||
\(193\) | 91762.3 | 0.177325 | 0.0886627 | − | 0.996062i | \(-0.471741\pi\) | ||||
0.0886627 | + | 0.996062i | \(0.471741\pi\) | |||||||
\(194\) | −334764. | −0.638608 | ||||||||
\(195\) | −144188. | −0.271546 | ||||||||
\(196\) | −871049. | −1.61958 | ||||||||
\(197\) | 485247. | 0.890836 | 0.445418 | − | 0.895323i | \(-0.353055\pi\) | ||||
0.445418 | + | 0.895323i | \(0.353055\pi\) | |||||||
\(198\) | −35555.3 | −0.0644527 | ||||||||
\(199\) | 692632. | 1.23985 | 0.619926 | − | 0.784660i | \(-0.287162\pi\) | ||||
0.619926 | + | 0.784660i | \(0.287162\pi\) | |||||||
\(200\) | −38163.2 | −0.0674637 | ||||||||
\(201\) | −510745. | −0.891690 | ||||||||
\(202\) | −128951. | −0.222355 | ||||||||
\(203\) | −988619. | −1.68379 | ||||||||
\(204\) | −119451. | −0.200962 | ||||||||
\(205\) | 1.05165e6 | 1.74778 | ||||||||
\(206\) | −217216. | −0.356635 | ||||||||
\(207\) | −86415.1 | −0.140173 | ||||||||
\(208\) | 18373.3 | 0.0294461 | ||||||||
\(209\) | 346203. | 0.548233 | ||||||||
\(210\) | 473193. | 0.740440 | ||||||||
\(211\) | −441020. | −0.681949 | −0.340975 | − | 0.940073i | \(-0.610757\pi\) | ||||
−0.340975 | + | 0.940073i | \(0.610757\pi\) | |||||||
\(212\) | 498986. | 0.762516 | ||||||||
\(213\) | 28683.8 | 0.0433199 | ||||||||
\(214\) | 323788. | 0.483310 | ||||||||
\(215\) | −234039. | −0.345297 | ||||||||
\(216\) | −134451. | −0.196078 | ||||||||
\(217\) | −161784. | −0.233231 | ||||||||
\(218\) | 82697.4 | 0.117856 | ||||||||
\(219\) | −66574.2 | −0.0937985 | ||||||||
\(220\) | 131585. | 0.183294 | ||||||||
\(221\) | −195530. | −0.269298 | ||||||||
\(222\) | −295228. | −0.402045 | ||||||||
\(223\) | 1.13133e6 | 1.52345 | 0.761726 | − | 0.647899i | \(-0.224352\pi\) | ||||
0.761726 | + | 0.647899i | \(0.224352\pi\) | |||||||
\(224\) | 1.42154e6 | 1.89295 | ||||||||
\(225\) | 16760.8 | 0.0220718 | ||||||||
\(226\) | −602435. | −0.784583 | ||||||||
\(227\) | −820354. | −1.05666 | −0.528332 | − | 0.849038i | \(-0.677182\pi\) | ||||
−0.528332 | + | 0.849038i | \(0.677182\pi\) | |||||||
\(228\) | 485133. | 0.618051 | ||||||||
\(229\) | −1.00301e6 | −1.26392 | −0.631958 | − | 0.775003i | \(-0.717748\pi\) | ||||
−0.631958 | + | 0.775003i | \(0.717748\pi\) | |||||||
\(230\) | −223401. | −0.278462 | ||||||||
\(231\) | −273428. | −0.337142 | ||||||||
\(232\) | 726191. | 0.885790 | ||||||||
\(233\) | 734.569 | 0.000886427 0 | 0.000443214 | − | 1.00000i | \(-0.499859\pi\) | ||||
0.000443214 | 1.00000i | \(0.499859\pi\) | ||||||||
\(234\) | −81556.4 | −0.0973685 | ||||||||
\(235\) | 1.19780e6 | 1.41486 | ||||||||
\(236\) | −80880.9 | −0.0945291 | ||||||||
\(237\) | 219543. | 0.253892 | ||||||||
\(238\) | 641685. | 0.734311 | ||||||||
\(239\) | −1.06403e6 | −1.20492 | −0.602460 | − | 0.798149i | \(-0.705813\pi\) | ||||
−0.602460 | + | 0.798149i | \(0.705813\pi\) | |||||||
\(240\) | −34390.4 | −0.0385397 | ||||||||
\(241\) | −661636. | −0.733798 | −0.366899 | − | 0.930261i | \(-0.619581\pi\) | ||||
−0.366899 | + | 0.930261i | \(0.619581\pi\) | |||||||
\(242\) | 53113.4 | 0.0582996 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 128708. | 0.138398 | ||||||||
\(245\) | 2.66881e6 | 2.84055 | ||||||||
\(246\) | 594841. | 0.626705 | ||||||||
\(247\) | 794118. | 0.828214 | ||||||||
\(248\) | 118839. | 0.122696 | ||||||||
\(249\) | 925158. | 0.945622 | ||||||||
\(250\) | −611051. | −0.618341 | ||||||||
\(251\) | 1.34864e6 | 1.35118 | 0.675590 | − | 0.737277i | \(-0.263889\pi\) | ||||
0.675590 | + | 0.737277i | \(0.263889\pi\) | |||||||
\(252\) | −383153. | −0.380077 | ||||||||
\(253\) | 129089. | 0.126791 | ||||||||
\(254\) | 577496. | 0.561648 | ||||||||
\(255\) | 365986. | 0.352463 | ||||||||
\(256\) | −1.08410e6 | −1.03388 | ||||||||
\(257\) | −1.65015e6 | −1.55844 | −0.779220 | − | 0.626751i | \(-0.784384\pi\) | ||||
−0.779220 | + | 0.626751i | \(0.784384\pi\) | |||||||
\(258\) | −132379. | −0.123814 | ||||||||
\(259\) | −2.27036e6 | −2.10303 | ||||||||
\(260\) | 301828. | 0.276902 | ||||||||
\(261\) | −318933. | −0.289800 | ||||||||
\(262\) | 842262. | 0.758044 | ||||||||
\(263\) | −868163. | −0.773948 | −0.386974 | − | 0.922091i | \(-0.626480\pi\) | ||||
−0.386974 | + | 0.922091i | \(0.626480\pi\) | |||||||
\(264\) | 200846. | 0.177359 | ||||||||
\(265\) | −1.52884e6 | −1.33736 | ||||||||
\(266\) | −2.60612e6 | −2.25834 | ||||||||
\(267\) | 446395. | 0.383213 | ||||||||
\(268\) | 1.06914e6 | 0.909280 | ||||||||
\(269\) | 271547. | 0.228804 | 0.114402 | − | 0.993435i | \(-0.463505\pi\) | ||||
0.114402 | + | 0.993435i | \(0.463505\pi\) | |||||||
\(270\) | 152654. | 0.127438 | ||||||||
\(271\) | −752770. | −0.622643 | −0.311322 | − | 0.950305i | \(-0.600772\pi\) | ||||
−0.311322 | + | 0.950305i | \(0.600772\pi\) | |||||||
\(272\) | −46635.9 | −0.0382207 | ||||||||
\(273\) | −627186. | −0.509319 | ||||||||
\(274\) | 247430. | 0.199102 | ||||||||
\(275\) | −25037.7 | −0.0199647 | ||||||||
\(276\) | 180892. | 0.142938 | ||||||||
\(277\) | 811445. | 0.635418 | 0.317709 | − | 0.948188i | \(-0.397086\pi\) | ||||
0.317709 | + | 0.948188i | \(0.397086\pi\) | |||||||
\(278\) | 1.08165e6 | 0.839411 | ||||||||
\(279\) | −52192.3 | −0.0401417 | ||||||||
\(280\) | −2.67300e6 | −2.03753 | ||||||||
\(281\) | −1.72395e6 | −1.30244 | −0.651221 | − | 0.758888i | \(-0.725743\pi\) | ||||
−0.651221 | + | 0.758888i | \(0.725743\pi\) | |||||||
\(282\) | 677503. | 0.507327 | ||||||||
\(283\) | 272979. | 0.202611 | 0.101305 | − | 0.994855i | \(-0.467698\pi\) | ||||
0.101305 | + | 0.994855i | \(0.467698\pi\) | |||||||
\(284\) | −60043.6 | −0.0441744 | ||||||||
\(285\) | −1.48640e6 | −1.08399 | ||||||||
\(286\) | 121831. | 0.0880731 | ||||||||
\(287\) | 4.57446e6 | 3.27820 | ||||||||
\(288\) | 458596. | 0.325798 | ||||||||
\(289\) | −923553. | −0.650455 | ||||||||
\(290\) | −824509. | −0.575706 | ||||||||
\(291\) | −830515. | −0.574930 | ||||||||
\(292\) | 139360. | 0.0956488 | ||||||||
\(293\) | −713441. | −0.485500 | −0.242750 | − | 0.970089i | \(-0.578049\pi\) | ||||
−0.242750 | + | 0.970089i | \(0.578049\pi\) | |||||||
\(294\) | 1.50954e6 | 1.01854 | ||||||||
\(295\) | 247811. | 0.165793 | ||||||||
\(296\) | 1.66770e6 | 1.10634 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 301578. | 0.196725 | ||||||||
\(299\) | 296104. | 0.191543 | ||||||||
\(300\) | −35085.3 | −0.0225072 | ||||||||
\(301\) | −1.01802e6 | −0.647649 | ||||||||
\(302\) | 607997. | 0.383605 | ||||||||
\(303\) | −319915. | −0.200184 | ||||||||
\(304\) | 189405. | 0.117546 | ||||||||
\(305\) | −394348. | −0.242734 | ||||||||
\(306\) | 207011. | 0.126383 | ||||||||
\(307\) | −2.67734e6 | −1.62128 | −0.810640 | − | 0.585545i | \(-0.800881\pi\) | ||||
−0.810640 | + | 0.585545i | \(0.800881\pi\) | |||||||
\(308\) | 572365. | 0.343792 | ||||||||
\(309\) | −538891. | −0.321074 | ||||||||
\(310\) | −134928. | −0.0797441 | ||||||||
\(311\) | −1.28078e6 | −0.750886 | −0.375443 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375443 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(312\) | 460700. | 0.267936 | ||||||||
\(313\) | 1.36808e6 | 0.789313 | 0.394656 | − | 0.918829i | \(-0.370864\pi\) | ||||
0.394656 | + | 0.918829i | \(0.370864\pi\) | |||||||
\(314\) | −229488. | −0.131352 | ||||||||
\(315\) | 1.17394e6 | 0.666608 | ||||||||
\(316\) | −459569. | −0.258900 | ||||||||
\(317\) | −7686.28 | −0.00429604 | −0.00214802 | − | 0.999998i | \(-0.500684\pi\) | ||||
−0.00214802 | + | 0.999998i | \(0.500684\pi\) | |||||||
\(318\) | −864752. | −0.479539 | ||||||||
\(319\) | 476431. | 0.262134 | ||||||||
\(320\) | 1.30784e6 | 0.713971 | ||||||||
\(321\) | 803284. | 0.435117 | ||||||||
\(322\) | −971746. | −0.522292 | ||||||||
\(323\) | −2.01567e6 | −1.07501 | ||||||||
\(324\) | −123607. | −0.0654155 | ||||||||
\(325\) | −57431.3 | −0.0301606 | ||||||||
\(326\) | 862406. | 0.449436 | ||||||||
\(327\) | 205164. | 0.106104 | ||||||||
\(328\) | −3.36017e6 | −1.72455 | ||||||||
\(329\) | 5.21014e6 | 2.65375 | ||||||||
\(330\) | −228039. | −0.115272 | ||||||||
\(331\) | 958347. | 0.480787 | 0.240393 | − | 0.970676i | \(-0.422724\pi\) | ||||
0.240393 | + | 0.970676i | \(0.422724\pi\) | |||||||
\(332\) | −1.93663e6 | −0.964275 | ||||||||
\(333\) | −732430. | −0.361956 | ||||||||
\(334\) | 1.76989e6 | 0.868121 | ||||||||
\(335\) | −3.27574e6 | −1.59477 | ||||||||
\(336\) | −149590. | −0.0722862 | ||||||||
\(337\) | 4.08768e6 | 1.96066 | 0.980330 | − | 0.197365i | \(-0.0632384\pi\) | ||||
0.980330 | + | 0.197365i | \(0.0632384\pi\) | |||||||
\(338\) | −1.06749e6 | −0.508244 | ||||||||
\(339\) | −1.49458e6 | −0.706350 | ||||||||
\(340\) | −766116. | −0.359416 | ||||||||
\(341\) | 77966.3 | 0.0363096 | ||||||||
\(342\) | −840745. | −0.388686 | ||||||||
\(343\) | 7.38880e6 | 3.39108 | ||||||||
\(344\) | 747787. | 0.340707 | ||||||||
\(345\) | −554236. | −0.250696 | ||||||||
\(346\) | 1.18243e6 | 0.530988 | ||||||||
\(347\) | 84250.2 | 0.0375619 | 0.0187809 | − | 0.999824i | \(-0.494021\pi\) | ||||
0.0187809 | + | 0.999824i | \(0.494021\pi\) | |||||||
\(348\) | 667621. | 0.295517 | ||||||||
\(349\) | 1.11859e6 | 0.491597 | 0.245798 | − | 0.969321i | \(-0.420950\pi\) | ||||
0.245798 | + | 0.969321i | \(0.420950\pi\) | |||||||
\(350\) | 188477. | 0.0822408 | ||||||||
\(351\) | −202333. | −0.0876595 | ||||||||
\(352\) | −685063. | −0.294696 | ||||||||
\(353\) | −3.73570e6 | −1.59564 | −0.797820 | − | 0.602896i | \(-0.794013\pi\) | ||||
−0.797820 | + | 0.602896i | \(0.794013\pi\) | |||||||
\(354\) | 140168. | 0.0594485 | ||||||||
\(355\) | 183968. | 0.0774766 | ||||||||
\(356\) | −934436. | −0.390773 | ||||||||
\(357\) | 1.59196e6 | 0.661090 | ||||||||
\(358\) | 1.67929e6 | 0.692499 | ||||||||
\(359\) | 1.45342e6 | 0.595189 | 0.297595 | − | 0.954692i | \(-0.403816\pi\) | ||||
0.297595 | + | 0.954692i | \(0.403816\pi\) | |||||||
\(360\) | −862321. | −0.350681 | ||||||||
\(361\) | 5.71027e6 | 2.30616 | ||||||||
\(362\) | 86707.1 | 0.0347763 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 1.31289e6 | 0.519366 | ||||||||
\(365\) | −426984. | −0.167756 | ||||||||
\(366\) | −223053. | −0.0870374 | ||||||||
\(367\) | 25363.4 | 0.00982975 | 0.00491487 | − | 0.999988i | \(-0.498436\pi\) | ||||
0.00491487 | + | 0.999988i | \(0.498436\pi\) | |||||||
\(368\) | 70623.8 | 0.0271851 | ||||||||
\(369\) | 1.47574e6 | 0.564214 | ||||||||
\(370\) | −1.89349e6 | −0.719048 | ||||||||
\(371\) | −6.65013e6 | −2.50839 | ||||||||
\(372\) | 109254. | 0.0409336 | ||||||||
\(373\) | −1.72695e6 | −0.642699 | −0.321350 | − | 0.946961i | \(-0.604136\pi\) | ||||
−0.321350 | + | 0.946961i | \(0.604136\pi\) | |||||||
\(374\) | −309238. | −0.114318 | ||||||||
\(375\) | −1.51596e6 | −0.556684 | ||||||||
\(376\) | −3.82711e6 | −1.39605 | ||||||||
\(377\) | 1.09283e6 | 0.396005 | ||||||||
\(378\) | 664012. | 0.239027 | ||||||||
\(379\) | −4.29401e6 | −1.53555 | −0.767777 | − | 0.640718i | \(-0.778637\pi\) | ||||
−0.767777 | + | 0.640718i | \(0.778637\pi\) | |||||||
\(380\) | 3.11147e6 | 1.10537 | ||||||||
\(381\) | 1.43271e6 | 0.505644 | ||||||||
\(382\) | −2.05324e6 | −0.719915 | ||||||||
\(383\) | 1.29297e6 | 0.450392 | 0.225196 | − | 0.974313i | \(-0.427698\pi\) | ||||
0.225196 | + | 0.974313i | \(0.427698\pi\) | |||||||
\(384\) | −890813. | −0.308289 | ||||||||
\(385\) | −1.75367e6 | −0.602970 | ||||||||
\(386\) | 332888. | 0.113718 | ||||||||
\(387\) | −328418. | −0.111468 | ||||||||
\(388\) | 1.73851e6 | 0.586272 | ||||||||
\(389\) | 1.55257e6 | 0.520209 | 0.260104 | − | 0.965581i | \(-0.416243\pi\) | ||||
0.260104 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(390\) | −523074. | −0.174141 | ||||||||
\(391\) | −751586. | −0.248620 | ||||||||
\(392\) | −8.52719e6 | −2.80279 | ||||||||
\(393\) | 2.08957e6 | 0.682456 | ||||||||
\(394\) | 1.76034e6 | 0.571290 | ||||||||
\(395\) | 1.40807e6 | 0.454080 | ||||||||
\(396\) | 184647. | 0.0591705 | ||||||||
\(397\) | 819569. | 0.260981 | 0.130491 | − | 0.991450i | \(-0.458345\pi\) | ||||
0.130491 | + | 0.991450i | \(0.458345\pi\) | |||||||
\(398\) | 2.51268e6 | 0.795113 | ||||||||
\(399\) | −6.46551e6 | −2.03316 | ||||||||
\(400\) | −13698.0 | −0.00428061 | ||||||||
\(401\) | 1.38956e6 | 0.431536 | 0.215768 | − | 0.976445i | \(-0.430774\pi\) | ||||
0.215768 | + | 0.976445i | \(0.430774\pi\) | |||||||
\(402\) | −1.85284e6 | −0.571838 | ||||||||
\(403\) | 178839. | 0.0548528 | ||||||||
\(404\) | 669677. | 0.204132 | ||||||||
\(405\) | 378719. | 0.114731 | ||||||||
\(406\) | −3.58643e6 | −1.07981 | ||||||||
\(407\) | 1.09412e6 | 0.327401 | ||||||||
\(408\) | −1.16937e6 | −0.347778 | ||||||||
\(409\) | −3.53091e6 | −1.04371 | −0.521854 | − | 0.853035i | \(-0.674759\pi\) | ||||
−0.521854 | + | 0.853035i | \(0.674759\pi\) | |||||||
\(410\) | 3.81510e6 | 1.12085 | ||||||||
\(411\) | 613849. | 0.179249 | ||||||||
\(412\) | 1.12806e6 | 0.327407 | ||||||||
\(413\) | 1.07792e6 | 0.310966 | ||||||||
\(414\) | −313490. | −0.0898923 | ||||||||
\(415\) | 5.93363e6 | 1.69122 | ||||||||
\(416\) | −1.57139e6 | −0.445196 | ||||||||
\(417\) | 2.68346e6 | 0.755710 | ||||||||
\(418\) | 1.25593e6 | 0.351580 | ||||||||
\(419\) | −6.69977e6 | −1.86434 | −0.932170 | − | 0.362021i | \(-0.882087\pi\) | ||||
−0.932170 | + | 0.362021i | \(0.882087\pi\) | |||||||
\(420\) | −2.45741e6 | −0.679758 | ||||||||
\(421\) | −5.01124e6 | −1.37797 | −0.688986 | − | 0.724775i | \(-0.741944\pi\) | ||||
−0.688986 | + | 0.724775i | \(0.741944\pi\) | |||||||
\(422\) | −1.59990e6 | −0.437331 | ||||||||
\(423\) | 1.68082e6 | 0.456740 | ||||||||
\(424\) | 4.88485e6 | 1.31958 | ||||||||
\(425\) | 145775. | 0.0391481 | ||||||||
\(426\) | 104057. | 0.0277809 | ||||||||
\(427\) | −1.71533e6 | −0.455279 | ||||||||
\(428\) | −1.68151e6 | −0.443701 | ||||||||
\(429\) | 302251. | 0.0792910 | ||||||||
\(430\) | −849029. | −0.221438 | ||||||||
\(431\) | −1.14741e6 | −0.297526 | −0.148763 | − | 0.988873i | \(-0.547529\pi\) | ||||
−0.148763 | + | 0.988873i | \(0.547529\pi\) | |||||||
\(432\) | −48258.6 | −0.0124413 | ||||||||
\(433\) | −1.13393e6 | −0.290649 | −0.145324 | − | 0.989384i | \(-0.546423\pi\) | ||||
−0.145324 | + | 0.989384i | \(0.546423\pi\) | |||||||
\(434\) | −586908. | −0.149570 | ||||||||
\(435\) | −2.04552e6 | −0.518300 | ||||||||
\(436\) | −429469. | −0.108197 | ||||||||
\(437\) | 3.05246e6 | 0.764622 | ||||||||
\(438\) | −241513. | −0.0601526 | ||||||||
\(439\) | 7.44692e6 | 1.84423 | 0.922115 | − | 0.386915i | \(-0.126459\pi\) | ||||
0.922115 | + | 0.386915i | \(0.126459\pi\) | |||||||
\(440\) | 1.28816e6 | 0.317203 | ||||||||
\(441\) | 3.74503e6 | 0.916977 | ||||||||
\(442\) | −709328. | −0.172700 | ||||||||
\(443\) | 6.72521e6 | 1.62816 | 0.814079 | − | 0.580754i | \(-0.197242\pi\) | ||||
0.814079 | + | 0.580754i | \(0.197242\pi\) | |||||||
\(444\) | 1.53319e6 | 0.369096 | ||||||||
\(445\) | 2.86302e6 | 0.685368 | ||||||||
\(446\) | 4.10416e6 | 0.976984 | ||||||||
\(447\) | 748183. | 0.177108 | ||||||||
\(448\) | 5.68883e6 | 1.33915 | ||||||||
\(449\) | 2.17793e6 | 0.509834 | 0.254917 | − | 0.966963i | \(-0.417952\pi\) | ||||
0.254917 | + | 0.966963i | \(0.417952\pi\) | |||||||
\(450\) | 60803.4 | 0.0141546 | ||||||||
\(451\) | −2.20450e6 | −0.510351 | ||||||||
\(452\) | 3.12860e6 | 0.720284 | ||||||||
\(453\) | 1.50838e6 | 0.345354 | ||||||||
\(454\) | −2.97601e6 | −0.677634 | ||||||||
\(455\) | −4.02255e6 | −0.910905 | ||||||||
\(456\) | 4.74924e6 | 1.06958 | ||||||||
\(457\) | −3.72380e6 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(458\) | −3.63865e6 | −0.810544 | ||||||||
\(459\) | 513572. | 0.113781 | ||||||||
\(460\) | 1.16018e6 | 0.255641 | ||||||||
\(461\) | 4.74202e6 | 1.03923 | 0.519615 | − | 0.854401i | \(-0.326076\pi\) | ||||
0.519615 | + | 0.854401i | \(0.326076\pi\) | |||||||
\(462\) | −991919. | −0.216208 | ||||||||
\(463\) | −4.82803e6 | −1.04669 | −0.523344 | − | 0.852121i | \(-0.675316\pi\) | ||||
−0.523344 | + | 0.852121i | \(0.675316\pi\) | |||||||
\(464\) | 260652. | 0.0562039 | ||||||||
\(465\) | −334743. | −0.0717925 | ||||||||
\(466\) | 2664.81 | 0.000568462 0 | ||||||||
\(467\) | 7.56254e6 | 1.60463 | 0.802316 | − | 0.596900i | \(-0.203601\pi\) | ||||
0.802316 | + | 0.596900i | \(0.203601\pi\) | |||||||
\(468\) | 423543. | 0.0893887 | ||||||||
\(469\) | −1.42487e7 | −2.99119 | ||||||||
\(470\) | 4.34526e6 | 0.907343 | ||||||||
\(471\) | −569337. | −0.118254 | ||||||||
\(472\) | −791788. | −0.163589 | ||||||||
\(473\) | 490599. | 0.100826 | ||||||||
\(474\) | 796441. | 0.162820 | ||||||||
\(475\) | −592045. | −0.120398 | ||||||||
\(476\) | −3.33243e6 | −0.674131 | ||||||||
\(477\) | −2.14536e6 | −0.431722 | ||||||||
\(478\) | −3.85999e6 | −0.772710 | ||||||||
\(479\) | −1.71897e6 | −0.342319 | −0.171159 | − | 0.985243i | \(-0.554751\pi\) | ||||
−0.171159 | + | 0.985243i | \(0.554751\pi\) | |||||||
\(480\) | 2.94127e6 | 0.582682 | ||||||||
\(481\) | 2.50969e6 | 0.494604 | ||||||||
\(482\) | −2.40023e6 | −0.470582 | ||||||||
\(483\) | −2.41080e6 | −0.470212 | ||||||||
\(484\) | −275831. | −0.0535218 | ||||||||
\(485\) | −5.32663e6 | −1.02825 | ||||||||
\(486\) | 214213. | 0.0411392 | ||||||||
\(487\) | −3.08125e6 | −0.588715 | −0.294357 | − | 0.955695i | \(-0.595106\pi\) | ||||
−0.294357 | + | 0.955695i | \(0.595106\pi\) | |||||||
\(488\) | 1.25999e6 | 0.239508 | ||||||||
\(489\) | 2.13954e6 | 0.404621 | ||||||||
\(490\) | 9.68168e6 | 1.82163 | ||||||||
\(491\) | −1.05909e6 | −0.198258 | −0.0991290 | − | 0.995075i | \(-0.531606\pi\) | ||||
−0.0991290 | + | 0.995075i | \(0.531606\pi\) | |||||||
\(492\) | −3.08916e6 | −0.575344 | ||||||||
\(493\) | −2.77388e6 | −0.514009 | ||||||||
\(494\) | 2.88084e6 | 0.531131 | ||||||||
\(495\) | −565741. | −0.103778 | ||||||||
\(496\) | 42654.9 | 0.00778510 | ||||||||
\(497\) | 800218. | 0.145317 | ||||||||
\(498\) | 3.35621e6 | 0.606423 | ||||||||
\(499\) | 2.26415e6 | 0.407056 | 0.203528 | − | 0.979069i | \(-0.434759\pi\) | ||||
0.203528 | + | 0.979069i | \(0.434759\pi\) | |||||||
\(500\) | 3.17334e6 | 0.567665 | ||||||||
\(501\) | 4.39092e6 | 0.781558 | ||||||||
\(502\) | 4.89250e6 | 0.866507 | ||||||||
\(503\) | −7.65222e6 | −1.34855 | −0.674276 | − | 0.738480i | \(-0.735544\pi\) | ||||
−0.674276 | + | 0.738480i | \(0.735544\pi\) | |||||||
\(504\) | −3.75090e6 | −0.657748 | ||||||||
\(505\) | −2.05182e6 | −0.358023 | ||||||||
\(506\) | 468299. | 0.0813106 | ||||||||
\(507\) | −2.64834e6 | −0.457566 | ||||||||
\(508\) | −2.99908e6 | −0.515619 | ||||||||
\(509\) | 489107. | 0.0836777 | 0.0418388 | − | 0.999124i | \(-0.486678\pi\) | ||||
0.0418388 | + | 0.999124i | \(0.486678\pi\) | |||||||
\(510\) | 1.32769e6 | 0.226033 | ||||||||
\(511\) | −1.85728e6 | −0.314649 | ||||||||
\(512\) | −765484. | −0.129051 | ||||||||
\(513\) | −2.08580e6 | −0.349929 | ||||||||
\(514\) | −5.98627e6 | −0.999421 | ||||||||
\(515\) | −3.45626e6 | −0.574233 | ||||||||
\(516\) | 687475. | 0.113667 | ||||||||
\(517\) | −2.51085e6 | −0.413137 | ||||||||
\(518\) | −8.23624e6 | −1.34867 | ||||||||
\(519\) | 2.93348e6 | 0.478041 | ||||||||
\(520\) | 2.95477e6 | 0.479198 | ||||||||
\(521\) | 1.36556e6 | 0.220402 | 0.110201 | − | 0.993909i | \(-0.464851\pi\) | ||||
0.110201 | + | 0.993909i | \(0.464851\pi\) | |||||||
\(522\) | −1.15700e6 | −0.185847 | ||||||||
\(523\) | −5.63994e6 | −0.901613 | −0.450807 | − | 0.892622i | \(-0.648864\pi\) | ||||
−0.450807 | + | 0.892622i | \(0.648864\pi\) | |||||||
\(524\) | −4.37408e6 | −0.695919 | ||||||||
\(525\) | 467591. | 0.0740403 | ||||||||
\(526\) | −3.14945e6 | −0.496330 | ||||||||
\(527\) | −453937. | −0.0711982 | ||||||||
\(528\) | 72089.9 | 0.0112536 | ||||||||
\(529\) | −5.29817e6 | −0.823164 | ||||||||
\(530\) | −5.54621e6 | −0.857644 | ||||||||
\(531\) | 347742. | 0.0535207 | ||||||||
\(532\) | 1.35342e7 | 2.07326 | ||||||||
\(533\) | −5.05667e6 | −0.770986 | ||||||||
\(534\) | 1.61939e6 | 0.245753 | ||||||||
\(535\) | 5.15198e6 | 0.778197 | ||||||||
\(536\) | 1.04664e7 | 1.57357 | ||||||||
\(537\) | 4.16615e6 | 0.623447 | ||||||||
\(538\) | 985095. | 0.146731 | ||||||||
\(539\) | −5.59442e6 | −0.829437 | ||||||||
\(540\) | −792771. | −0.116994 | ||||||||
\(541\) | 8.24934e6 | 1.21179 | 0.605893 | − | 0.795546i | \(-0.292816\pi\) | ||||
0.605893 | + | 0.795546i | \(0.292816\pi\) | |||||||
\(542\) | −2.73084e6 | −0.399299 | ||||||||
\(543\) | 215111. | 0.0313086 | ||||||||
\(544\) | 3.98859e6 | 0.577859 | ||||||||
\(545\) | 1.31585e6 | 0.189764 | ||||||||
\(546\) | −2.27526e6 | −0.326624 | ||||||||
\(547\) | −4.74537e6 | −0.678112 | −0.339056 | − | 0.940766i | \(-0.610108\pi\) | ||||
−0.339056 | + | 0.940766i | \(0.610108\pi\) | |||||||
\(548\) | −1.28497e6 | −0.182785 | ||||||||
\(549\) | −553372. | −0.0783586 | ||||||||
\(550\) | −90829.7 | −0.0128033 | ||||||||
\(551\) | 1.12657e7 | 1.58082 | ||||||||
\(552\) | 1.77086e6 | 0.247363 | ||||||||
\(553\) | 6.12480e6 | 0.851685 | ||||||||
\(554\) | 2.94369e6 | 0.407491 | ||||||||
\(555\) | −4.69755e6 | −0.647349 | ||||||||
\(556\) | −5.61728e6 | −0.770617 | ||||||||
\(557\) | 2.99690e6 | 0.409293 | 0.204647 | − | 0.978836i | \(-0.434395\pi\) | ||||
0.204647 | + | 0.978836i | \(0.434395\pi\) | |||||||
\(558\) | −189339. | −0.0257427 | ||||||||
\(559\) | 1.12533e6 | 0.152318 | ||||||||
\(560\) | −959420. | −0.129282 | ||||||||
\(561\) | −767188. | −0.102919 | ||||||||
\(562\) | −6.25400e6 | −0.835251 | ||||||||
\(563\) | −3.89491e6 | −0.517876 | −0.258938 | − | 0.965894i | \(-0.583373\pi\) | ||||
−0.258938 | + | 0.965894i | \(0.583373\pi\) | |||||||
\(564\) | −3.51844e6 | −0.465750 | ||||||||
\(565\) | −9.58571e6 | −1.26329 | ||||||||
\(566\) | 990290. | 0.129934 | ||||||||
\(567\) | 1.64735e6 | 0.215192 | ||||||||
\(568\) | −587801. | −0.0764468 | ||||||||
\(569\) | 2.08127e6 | 0.269493 | 0.134747 | − | 0.990880i | \(-0.456978\pi\) | ||||
0.134747 | + | 0.990880i | \(0.456978\pi\) | |||||||
\(570\) | −5.39224e6 | −0.695156 | ||||||||
\(571\) | 1.28958e7 | 1.65523 | 0.827615 | − | 0.561297i | \(-0.189697\pi\) | ||||
0.827615 | + | 0.561297i | \(0.189697\pi\) | |||||||
\(572\) | −632700. | −0.0808551 | ||||||||
\(573\) | −5.09387e6 | −0.648129 | ||||||||
\(574\) | 1.65948e7 | 2.10229 | ||||||||
\(575\) | −220757. | −0.0278448 | ||||||||
\(576\) | 1.83524e6 | 0.230482 | ||||||||
\(577\) | 1.26163e6 | 0.157759 | 0.0788795 | − | 0.996884i | \(-0.474866\pi\) | ||||
0.0788795 | + | 0.996884i | \(0.474866\pi\) | |||||||
\(578\) | −3.35039e6 | −0.417134 | ||||||||
\(579\) | 825861. | 0.102379 | ||||||||
\(580\) | 4.28188e6 | 0.528524 | ||||||||
\(581\) | 2.58100e7 | 3.17210 | ||||||||
\(582\) | −3.01288e6 | −0.368701 | ||||||||
\(583\) | 3.20480e6 | 0.390508 | ||||||||
\(584\) | 1.36427e6 | 0.165527 | ||||||||
\(585\) | −1.29769e6 | −0.156777 | ||||||||
\(586\) | −2.58816e6 | −0.311349 | ||||||||
\(587\) | −1.25673e7 | −1.50538 | −0.752689 | − | 0.658376i | \(-0.771244\pi\) | ||||
−0.752689 | + | 0.658376i | \(0.771244\pi\) | |||||||
\(588\) | −7.83945e6 | −0.935065 | ||||||||
\(589\) | 1.84360e6 | 0.218967 | ||||||||
\(590\) | 898988. | 0.106322 | ||||||||
\(591\) | 4.36723e6 | 0.514324 | ||||||||
\(592\) | 598588. | 0.0701978 | ||||||||
\(593\) | −4.32620e6 | −0.505207 | −0.252604 | − | 0.967570i | \(-0.581287\pi\) | ||||
−0.252604 | + | 0.967570i | \(0.581287\pi\) | |||||||
\(594\) | −319997. | −0.0372118 | ||||||||
\(595\) | 1.02102e7 | 1.18234 | ||||||||
\(596\) | −1.56617e6 | −0.180602 | ||||||||
\(597\) | 6.23369e6 | 0.715829 | ||||||||
\(598\) | 1.07418e6 | 0.122836 | ||||||||
\(599\) | 1.45262e7 | 1.65419 | 0.827097 | − | 0.562060i | \(-0.189991\pi\) | ||||
0.827097 | + | 0.562060i | \(0.189991\pi\) | |||||||
\(600\) | −343469. | −0.0389502 | ||||||||
\(601\) | −380688. | −0.0429915 | −0.0214958 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214958 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(602\) | −3.69309e6 | −0.415335 | ||||||||
\(603\) | −4.59671e6 | −0.514818 | ||||||||
\(604\) | −3.15748e6 | −0.352167 | ||||||||
\(605\) | 845120. | 0.0938706 | ||||||||
\(606\) | −1.16056e6 | −0.128377 | ||||||||
\(607\) | −4.99233e6 | −0.549961 | −0.274980 | − | 0.961450i | \(-0.588671\pi\) | ||||
−0.274980 | + | 0.961450i | \(0.588671\pi\) | |||||||
\(608\) | −1.61991e7 | −1.77718 | ||||||||
\(609\) | −8.89757e6 | −0.972139 | ||||||||
\(610\) | −1.43058e6 | −0.155664 | ||||||||
\(611\) | −5.75936e6 | −0.624125 | ||||||||
\(612\) | −1.07506e6 | −0.116026 | ||||||||
\(613\) | 2.99353e6 | 0.321760 | 0.160880 | − | 0.986974i | \(-0.448567\pi\) | ||||
0.160880 | + | 0.986974i | \(0.448567\pi\) | |||||||
\(614\) | −9.71265e6 | −1.03972 | ||||||||
\(615\) | 9.46488e6 | 1.00908 | ||||||||
\(616\) | 5.60320e6 | 0.594955 | ||||||||
\(617\) | 6.27781e6 | 0.663889 | 0.331945 | − | 0.943299i | \(-0.392295\pi\) | ||||
0.331945 | + | 0.943299i | \(0.392295\pi\) | |||||||
\(618\) | −1.95494e6 | −0.205903 | ||||||||
\(619\) | 3.96477e6 | 0.415902 | 0.207951 | − | 0.978139i | \(-0.433320\pi\) | ||||
0.207951 | + | 0.978139i | \(0.433320\pi\) | |||||||
\(620\) | 700716. | 0.0732088 | ||||||||
\(621\) | −777736. | −0.0809288 | ||||||||
\(622\) | −4.64631e6 | −0.481540 | ||||||||
\(623\) | 1.24535e7 | 1.28550 | ||||||||
\(624\) | 165359. | 0.0170007 | ||||||||
\(625\) | −1.03694e7 | −1.06183 | ||||||||
\(626\) | 4.96299e6 | 0.506183 | ||||||||
\(627\) | 3.11583e6 | 0.316523 | ||||||||
\(628\) | 1.19179e6 | 0.120587 | ||||||||
\(629\) | −6.37023e6 | −0.641990 | ||||||||
\(630\) | 4.25874e6 | 0.427493 | ||||||||
\(631\) | −9.62587e6 | −0.962425 | −0.481212 | − | 0.876604i | \(-0.659803\pi\) | ||||
−0.481212 | + | 0.876604i | \(0.659803\pi\) | |||||||
\(632\) | −4.49898e6 | −0.448044 | ||||||||
\(633\) | −3.96918e6 | −0.393724 | ||||||||
\(634\) | −27883.7 | −0.00275503 | ||||||||
\(635\) | 9.18888e6 | 0.904333 | ||||||||
\(636\) | 4.49087e6 | 0.440239 | ||||||||
\(637\) | −1.28324e7 | −1.25303 | ||||||||
\(638\) | 1.72836e6 | 0.168105 | ||||||||
\(639\) | 258154. | 0.0250108 | ||||||||
\(640\) | −5.71336e6 | −0.551368 | ||||||||
\(641\) | −2.20090e6 | −0.211571 | −0.105785 | − | 0.994389i | \(-0.533736\pi\) | ||||
−0.105785 | + | 0.994389i | \(0.533736\pi\) | |||||||
\(642\) | 2.91409e6 | 0.279039 | ||||||||
\(643\) | 2.00555e7 | 1.91296 | 0.956482 | − | 0.291791i | \(-0.0942512\pi\) | ||||
0.956482 | + | 0.291791i | \(0.0942512\pi\) | |||||||
\(644\) | 5.04652e6 | 0.479488 | ||||||||
\(645\) | −2.10635e6 | −0.199357 | ||||||||
\(646\) | −7.31229e6 | −0.689401 | ||||||||
\(647\) | 128900. | 0.0121057 | 0.00605287 | − | 0.999982i | \(-0.498073\pi\) | ||||
0.00605287 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(648\) | −1.21006e6 | −0.113206 | ||||||||
\(649\) | −519467. | −0.0484113 | ||||||||
\(650\) | −208345. | −0.0193419 | ||||||||
\(651\) | −1.45606e6 | −0.134656 | ||||||||
\(652\) | −4.47869e6 | −0.412603 | ||||||||
\(653\) | 3.03250e6 | 0.278303 | 0.139151 | − | 0.990271i | \(-0.455563\pi\) | ||||
0.139151 | + | 0.990271i | \(0.455563\pi\) | |||||||
\(654\) | 744277. | 0.0680441 | ||||||||
\(655\) | 1.34017e7 | 1.22056 | ||||||||
\(656\) | −1.20607e6 | −0.109424 | ||||||||
\(657\) | −599168. | −0.0541546 | ||||||||
\(658\) | 1.89009e7 | 1.70184 | ||||||||
\(659\) | −1.59132e7 | −1.42740 | −0.713698 | − | 0.700454i | \(-0.752981\pi\) | ||||
−0.713698 | + | 0.700454i | \(0.752981\pi\) | |||||||
\(660\) | 1.18426e6 | 0.105825 | ||||||||
\(661\) | 6.50892e6 | 0.579436 | 0.289718 | − | 0.957112i | \(-0.406439\pi\) | ||||
0.289718 | + | 0.957112i | \(0.406439\pi\) | |||||||
\(662\) | 3.47661e6 | 0.308327 | ||||||||
\(663\) | −1.75977e6 | −0.155479 | ||||||||
\(664\) | −1.89587e7 | −1.66874 | ||||||||
\(665\) | −4.14675e7 | −3.63625 | ||||||||
\(666\) | −2.65705e6 | −0.232121 | ||||||||
\(667\) | 4.20067e6 | 0.365598 | ||||||||
\(668\) | −9.19149e6 | −0.796975 | ||||||||
\(669\) | 1.01820e7 | 0.879565 | ||||||||
\(670\) | −1.18835e7 | −1.02272 | ||||||||
\(671\) | 826643. | 0.0708780 | ||||||||
\(672\) | 1.27939e7 | 1.09290 | ||||||||
\(673\) | −5.66035e6 | −0.481732 | −0.240866 | − | 0.970558i | \(-0.577431\pi\) | ||||
−0.240866 | + | 0.970558i | \(0.577431\pi\) | |||||||
\(674\) | 1.48290e7 | 1.25736 | ||||||||
\(675\) | 150847. | 0.0127432 | ||||||||
\(676\) | 5.54375e6 | 0.466592 | ||||||||
\(677\) | −1.53601e7 | −1.28802 | −0.644012 | − | 0.765016i | \(-0.722731\pi\) | ||||
−0.644012 | + | 0.765016i | \(0.722731\pi\) | |||||||
\(678\) | −5.42192e6 | −0.452979 | ||||||||
\(679\) | −2.31697e7 | −1.92861 | ||||||||
\(680\) | −7.49994e6 | −0.621993 | ||||||||
\(681\) | −7.38319e6 | −0.610065 | ||||||||
\(682\) | 282840. | 0.0232852 | ||||||||
\(683\) | 1.47069e6 | 0.120634 | 0.0603170 | − | 0.998179i | \(-0.480789\pi\) | ||||
0.0603170 | + | 0.998179i | \(0.480789\pi\) | |||||||
\(684\) | 4.36620e6 | 0.356832 | ||||||||
\(685\) | 3.93701e6 | 0.320583 | ||||||||
\(686\) | 2.68045e7 | 2.17469 | ||||||||
\(687\) | −9.02712e6 | −0.729722 | ||||||||
\(688\) | 268404. | 0.0216181 | ||||||||
\(689\) | 7.35114e6 | 0.589939 | ||||||||
\(690\) | −2.01061e6 | −0.160770 | ||||||||
\(691\) | −3.65617e6 | −0.291294 | −0.145647 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145647 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(692\) | −6.14064e6 | −0.487471 | ||||||||
\(693\) | −2.46085e6 | −0.194649 | ||||||||
\(694\) | 305636. | 0.0240883 | ||||||||
\(695\) | 1.72108e7 | 1.35157 | ||||||||
\(696\) | 6.53571e6 | 0.511411 | ||||||||
\(697\) | 1.28351e7 | 1.00073 | ||||||||
\(698\) | 4.05794e6 | 0.315259 | ||||||||
\(699\) | 6611.12 | 0.000511779 0 | ||||||||
\(700\) | −978806. | −0.0755008 | ||||||||
\(701\) | −5.21232e6 | −0.400623 | −0.200312 | − | 0.979732i | \(-0.564195\pi\) | ||||
−0.200312 | + | 0.979732i | \(0.564195\pi\) | |||||||
\(702\) | −734008. | −0.0562157 | ||||||||
\(703\) | 2.58718e7 | 1.97442 | ||||||||
\(704\) | −2.74153e6 | −0.208479 | ||||||||
\(705\) | 1.07802e7 | 0.816869 | ||||||||
\(706\) | −1.35521e7 | −1.02328 | ||||||||
\(707\) | −8.92498e6 | −0.671519 | ||||||||
\(708\) | −727928. | −0.0545764 | ||||||||
\(709\) | −1.48388e7 | −1.10862 | −0.554311 | − | 0.832310i | \(-0.687018\pi\) | ||||
−0.554311 | + | 0.832310i | \(0.687018\pi\) | |||||||
\(710\) | 667383. | 0.0496854 | ||||||||
\(711\) | 1.97589e6 | 0.146585 | ||||||||
\(712\) | −9.14772e6 | −0.676258 | ||||||||
\(713\) | 687427. | 0.0506410 | ||||||||
\(714\) | 5.77517e6 | 0.423954 | ||||||||
\(715\) | 1.93853e6 | 0.141810 | ||||||||
\(716\) | −8.72099e6 | −0.635745 | ||||||||
\(717\) | −9.57625e6 | −0.695661 | ||||||||
\(718\) | 5.27260e6 | 0.381693 | ||||||||
\(719\) | 1.37497e7 | 0.991906 | 0.495953 | − | 0.868349i | \(-0.334819\pi\) | ||||
0.495953 | + | 0.868349i | \(0.334819\pi\) | |||||||
\(720\) | −309513. | −0.0222509 | ||||||||
\(721\) | −1.50339e7 | −1.07705 | ||||||||
\(722\) | 2.07153e7 | 1.47893 | ||||||||
\(723\) | −5.95473e6 | −0.423659 | ||||||||
\(724\) | −450292. | −0.0319262 | ||||||||
\(725\) | −814748. | −0.0575676 | ||||||||
\(726\) | 478021. | 0.0336593 | ||||||||
\(727\) | −8.20549e6 | −0.575796 | −0.287898 | − | 0.957661i | \(-0.592956\pi\) | ||||
−0.287898 | + | 0.957661i | \(0.592956\pi\) | |||||||
\(728\) | 1.28526e7 | 0.898797 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.54898e6 | −0.107582 | ||||||||
\(731\) | −2.85638e6 | −0.197707 | ||||||||
\(732\) | 1.15837e6 | 0.0799043 | ||||||||
\(733\) | 1.20636e7 | 0.829312 | 0.414656 | − | 0.909978i | \(-0.363902\pi\) | ||||
0.414656 | + | 0.909978i | \(0.363902\pi\) | |||||||
\(734\) | 92011.3 | 0.00630378 | ||||||||
\(735\) | 2.40193e7 | 1.63999 | ||||||||
\(736\) | −6.04017e6 | −0.411012 | ||||||||
\(737\) | 6.86668e6 | 0.465670 | ||||||||
\(738\) | 5.35357e6 | 0.361828 | ||||||||
\(739\) | −1.02319e7 | −0.689203 | −0.344602 | − | 0.938749i | \(-0.611986\pi\) | ||||
−0.344602 | + | 0.938749i | \(0.611986\pi\) | |||||||
\(740\) | 9.83335e6 | 0.660119 | ||||||||
\(741\) | 7.14706e6 | 0.478170 | ||||||||
\(742\) | −2.41248e7 | −1.60862 | ||||||||
\(743\) | 2.41980e7 | 1.60808 | 0.804039 | − | 0.594577i | \(-0.202680\pi\) | ||||
0.804039 | + | 0.594577i | \(0.202680\pi\) | |||||||
\(744\) | 1.06955e6 | 0.0708383 | ||||||||
\(745\) | 4.79858e6 | 0.316754 | ||||||||
\(746\) | −6.26489e6 | −0.412161 | ||||||||
\(747\) | 8.32642e6 | 0.545955 | ||||||||
\(748\) | 1.60595e6 | 0.104949 | ||||||||
\(749\) | 2.24100e7 | 1.45961 | ||||||||
\(750\) | −5.49946e6 | −0.356999 | ||||||||
\(751\) | 1.10121e7 | 0.712476 | 0.356238 | − | 0.934395i | \(-0.384059\pi\) | ||||
0.356238 | + | 0.934395i | \(0.384059\pi\) | |||||||
\(752\) | −1.37367e6 | −0.0885803 | ||||||||
\(753\) | 1.21378e7 | 0.780104 | ||||||||
\(754\) | 3.96449e6 | 0.253956 | ||||||||
\(755\) | 9.67420e6 | 0.617657 | ||||||||
\(756\) | −3.44838e6 | −0.219437 | ||||||||
\(757\) | −2.08747e7 | −1.32398 | −0.661989 | − | 0.749513i | \(-0.730288\pi\) | ||||
−0.661989 | + | 0.749513i | \(0.730288\pi\) | |||||||
\(758\) | −1.55775e7 | −0.984744 | ||||||||
\(759\) | 1.16180e6 | 0.0732028 | ||||||||
\(760\) | 3.04600e7 | 1.91291 | ||||||||
\(761\) | 2.85723e7 | 1.78848 | 0.894240 | − | 0.447587i | \(-0.147716\pi\) | ||||
0.894240 | + | 0.447587i | \(0.147716\pi\) | |||||||
\(762\) | 5.19746e6 | 0.324268 | ||||||||
\(763\) | 5.72365e6 | 0.355928 | ||||||||
\(764\) | 1.06630e7 | 0.660915 | ||||||||
\(765\) | 3.29387e6 | 0.203495 | ||||||||
\(766\) | 4.69052e6 | 0.288835 | ||||||||
\(767\) | −1.19155e6 | −0.0731347 | ||||||||
\(768\) | −9.75692e6 | −0.596911 | ||||||||
\(769\) | −3.07246e6 | −0.187357 | −0.0936787 | − | 0.995602i | \(-0.529863\pi\) | ||||
−0.0936787 | + | 0.995602i | \(0.529863\pi\) | |||||||
\(770\) | −6.36182e6 | −0.386682 | ||||||||
\(771\) | −1.48513e7 | −0.899765 | ||||||||
\(772\) | −1.72877e6 | −0.104398 | ||||||||
\(773\) | −3.02076e7 | −1.81831 | −0.909153 | − | 0.416461i | \(-0.863270\pi\) | ||||
−0.909153 | + | 0.416461i | \(0.863270\pi\) | |||||||
\(774\) | −1.19141e6 | −0.0714838 | ||||||||
\(775\) | −133331. | −0.00797401 | ||||||||
\(776\) | 1.70193e7 | 1.01458 | ||||||||
\(777\) | −2.04333e7 | −1.21419 | ||||||||
\(778\) | 5.63229e6 | 0.333608 | ||||||||
\(779\) | −5.21280e7 | −3.07771 | ||||||||
\(780\) | 2.71645e6 | 0.159870 | ||||||||
\(781\) | −385638. | −0.0226231 | ||||||||
\(782\) | −2.72654e6 | −0.159439 | ||||||||
\(783\) | −2.87040e6 | −0.167316 | ||||||||
\(784\) | −3.06067e6 | −0.177839 | ||||||||
\(785\) | −3.65153e6 | −0.211495 | ||||||||
\(786\) | 7.58036e6 | 0.437657 | ||||||||
\(787\) | −2.07854e7 | −1.19625 | −0.598126 | − | 0.801402i | \(-0.704088\pi\) | ||||
−0.598126 | + | 0.801402i | \(0.704088\pi\) | |||||||
\(788\) | −9.14190e6 | −0.524470 | ||||||||
\(789\) | −7.81346e6 | −0.446839 | ||||||||
\(790\) | 5.10809e6 | 0.291200 | ||||||||
\(791\) | −4.16957e7 | −2.36946 | ||||||||
\(792\) | 1.80762e6 | 0.102399 | ||||||||
\(793\) | 1.89615e6 | 0.107075 | ||||||||
\(794\) | 2.97317e6 | 0.167366 | ||||||||
\(795\) | −1.37596e7 | −0.772125 | ||||||||
\(796\) | −1.30490e7 | −0.729950 | ||||||||
\(797\) | −7.95535e6 | −0.443622 | −0.221811 | − | 0.975090i | \(-0.571197\pi\) | ||||
−0.221811 | + | 0.975090i | \(0.571197\pi\) | |||||||
\(798\) | −2.34551e7 | −1.30385 | ||||||||
\(799\) | 1.46187e7 | 0.810106 | ||||||||
\(800\) | 1.17153e6 | 0.0647186 | ||||||||
\(801\) | 4.01755e6 | 0.221248 | ||||||||
\(802\) | 5.04094e6 | 0.276742 | ||||||||
\(803\) | 895054. | 0.0489847 | ||||||||
\(804\) | 9.62226e6 | 0.524973 | ||||||||
\(805\) | −1.54620e7 | −0.840963 | ||||||||
\(806\) | 648776. | 0.0351769 | ||||||||
\(807\) | 2.44392e6 | 0.132100 | ||||||||
\(808\) | 6.55584e6 | 0.353265 | ||||||||
\(809\) | −3.04660e7 | −1.63661 | −0.818303 | − | 0.574787i | \(-0.805085\pi\) | ||||
−0.818303 | + | 0.574787i | \(0.805085\pi\) | |||||||
\(810\) | 1.37389e6 | 0.0735764 | ||||||||
\(811\) | 1.28041e7 | 0.683594 | 0.341797 | − | 0.939774i | \(-0.388964\pi\) | ||||
0.341797 | + | 0.939774i | \(0.388964\pi\) | |||||||
\(812\) | 1.86252e7 | 0.991316 | ||||||||
\(813\) | −6.77493e6 | −0.359483 | ||||||||
\(814\) | 3.96917e6 | 0.209961 | ||||||||
\(815\) | 1.37223e7 | 0.723655 | ||||||||
\(816\) | −419723. | −0.0220667 | ||||||||
\(817\) | 1.16008e7 | 0.608040 | ||||||||
\(818\) | −1.28092e7 | −0.669325 | ||||||||
\(819\) | −5.64468e6 | −0.294055 | ||||||||
\(820\) | −1.98128e7 | −1.02899 | ||||||||
\(821\) | 1.13635e7 | 0.588373 | 0.294186 | − | 0.955748i | \(-0.404951\pi\) | ||||
0.294186 | + | 0.955748i | \(0.404951\pi\) | |||||||
\(822\) | 2.22687e6 | 0.114952 | ||||||||
\(823\) | 8.23741e6 | 0.423927 | 0.211964 | − | 0.977278i | \(-0.432014\pi\) | ||||
0.211964 | + | 0.977278i | \(0.432014\pi\) | |||||||
\(824\) | 1.10432e7 | 0.566600 | ||||||||
\(825\) | −225339. | −0.0115266 | ||||||||
\(826\) | 3.91040e6 | 0.199421 | ||||||||
\(827\) | 2.21035e7 | 1.12382 | 0.561909 | − | 0.827199i | \(-0.310067\pi\) | ||||
0.561909 | + | 0.827199i | \(0.310067\pi\) | |||||||
\(828\) | 1.62803e6 | 0.0825252 | ||||||||
\(829\) | −5.57875e6 | −0.281936 | −0.140968 | − | 0.990014i | \(-0.545021\pi\) | ||||
−0.140968 | + | 0.990014i | \(0.545021\pi\) | |||||||
\(830\) | 2.15256e7 | 1.08457 | ||||||||
\(831\) | 7.30300e6 | 0.366859 | ||||||||
\(832\) | −6.28851e6 | −0.314948 | ||||||||
\(833\) | 3.25720e7 | 1.62641 | ||||||||
\(834\) | 9.73484e6 | 0.484634 | ||||||||
\(835\) | 2.81618e7 | 1.39780 | ||||||||
\(836\) | −6.52235e6 | −0.322766 | ||||||||
\(837\) | −469731. | −0.0231758 | ||||||||
\(838\) | −2.43049e7 | −1.19559 | ||||||||
\(839\) | −2.33576e7 | −1.14558 | −0.572788 | − | 0.819704i | \(-0.694138\pi\) | ||||
−0.572788 | + | 0.819704i | \(0.694138\pi\) | |||||||
\(840\) | −2.40570e7 | −1.17637 | ||||||||
\(841\) | −5.00769e6 | −0.244145 | ||||||||
\(842\) | −1.81794e7 | −0.883688 | ||||||||
\(843\) | −1.55155e7 | −0.751965 | ||||||||
\(844\) | 8.30866e6 | 0.401490 | ||||||||
\(845\) | −1.69855e7 | −0.818345 | ||||||||
\(846\) | 6.09753e6 | 0.292906 | ||||||||
\(847\) | 3.67608e6 | 0.176067 | ||||||||
\(848\) | 1.75332e6 | 0.0837284 | ||||||||
\(849\) | 2.45681e6 | 0.116977 | ||||||||
\(850\) | 528831. | 0.0251055 | ||||||||
\(851\) | 9.64685e6 | 0.456627 | ||||||||
\(852\) | −540393. | −0.0255041 | ||||||||
\(853\) | 8.94855e6 | 0.421095 | 0.210548 | − | 0.977584i | \(-0.432475\pi\) | ||||
0.210548 | + | 0.977584i | \(0.432475\pi\) | |||||||
\(854\) | −6.22273e6 | −0.291969 | ||||||||
\(855\) | −1.33776e7 | −0.625839 | ||||||||
\(856\) | −1.64612e7 | −0.767853 | ||||||||
\(857\) | −2.03190e6 | −0.0945039 | −0.0472520 | − | 0.998883i | \(-0.515046\pi\) | ||||
−0.0472520 | + | 0.998883i | \(0.515046\pi\) | |||||||
\(858\) | 1.09648e6 | 0.0508490 | ||||||||
\(859\) | −1.92359e7 | −0.889467 | −0.444734 | − | 0.895663i | \(-0.646702\pi\) | ||||
−0.444734 | + | 0.895663i | \(0.646702\pi\) | |||||||
\(860\) | 4.40922e6 | 0.203290 | ||||||||
\(861\) | 4.11701e7 | 1.89267 | ||||||||
\(862\) | −4.16247e6 | −0.190802 | ||||||||
\(863\) | 2.00380e7 | 0.915856 | 0.457928 | − | 0.888989i | \(-0.348592\pi\) | ||||
0.457928 | + | 0.888989i | \(0.348592\pi\) | |||||||
\(864\) | 4.12736e6 | 0.188100 | ||||||||
\(865\) | 1.88143e7 | 0.854965 | ||||||||
\(866\) | −4.11360e6 | −0.186392 | ||||||||
\(867\) | −8.31197e6 | −0.375540 | ||||||||
\(868\) | 3.04796e6 | 0.137312 | ||||||||
\(869\) | −2.95164e6 | −0.132591 | ||||||||
\(870\) | −7.42058e6 | −0.332384 | ||||||||
\(871\) | 1.57507e7 | 0.703486 | ||||||||
\(872\) | −4.20431e6 | −0.187242 | ||||||||
\(873\) | −7.47464e6 | −0.331936 | ||||||||
\(874\) | 1.10735e7 | 0.490349 | ||||||||
\(875\) | −4.22921e7 | −1.86741 | ||||||||
\(876\) | 1.25424e6 | 0.0552229 | ||||||||
\(877\) | 1.98487e7 | 0.871430 | 0.435715 | − | 0.900085i | \(-0.356496\pi\) | ||||
0.435715 | + | 0.900085i | \(0.356496\pi\) | |||||||
\(878\) | 2.70153e7 | 1.18270 | ||||||||
\(879\) | −6.42097e6 | −0.280304 | ||||||||
\(880\) | 462359. | 0.0201267 | ||||||||
\(881\) | −2.93546e7 | −1.27420 | −0.637099 | − | 0.770782i | \(-0.719866\pi\) | ||||
−0.637099 | + | 0.770782i | \(0.719866\pi\) | |||||||
\(882\) | 1.35859e7 | 0.588054 | ||||||||
\(883\) | 3.85199e7 | 1.66258 | 0.831291 | − | 0.555838i | \(-0.187602\pi\) | ||||
0.831291 | + | 0.555838i | \(0.187602\pi\) | |||||||
\(884\) | 3.68372e6 | 0.158546 | ||||||||
\(885\) | 2.23030e6 | 0.0957204 | ||||||||
\(886\) | 2.43972e7 | 1.04413 | ||||||||
\(887\) | −2.68797e6 | −0.114714 | −0.0573569 | − | 0.998354i | \(-0.518267\pi\) | ||||
−0.0573569 | + | 0.998354i | \(0.518267\pi\) | |||||||
\(888\) | 1.50093e7 | 0.638745 | ||||||||
\(889\) | 3.99696e7 | 1.69619 | ||||||||
\(890\) | 1.03862e7 | 0.439524 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −2.13139e7 | −0.896916 | ||||||||
\(893\) | −5.93719e7 | −2.49145 | ||||||||
\(894\) | 2.71420e6 | 0.113579 | ||||||||
\(895\) | 2.67202e7 | 1.11502 | ||||||||
\(896\) | −2.48519e7 | −1.03416 | ||||||||
\(897\) | 2.66493e6 | 0.110587 | ||||||||
\(898\) | 7.90093e6 | 0.326955 | ||||||||
\(899\) | 2.53709e6 | 0.104698 | ||||||||
\(900\) | −315767. | −0.0129945 | ||||||||
\(901\) | −1.86590e7 | −0.765733 | ||||||||
\(902\) | −7.99731e6 | −0.327286 | ||||||||
\(903\) | −9.16218e6 | −0.373921 | ||||||||
\(904\) | 3.06276e7 | 1.24650 | ||||||||
\(905\) | 1.37965e6 | 0.0559947 | ||||||||
\(906\) | 5.47197e6 | 0.221474 | ||||||||
\(907\) | −7.78340e6 | −0.314160 | −0.157080 | − | 0.987586i | \(-0.550208\pi\) | ||||
−0.157080 | + | 0.987586i | \(0.550208\pi\) | |||||||
\(908\) | 1.54552e7 | 0.622099 | ||||||||
\(909\) | −2.87924e6 | −0.115576 | ||||||||
\(910\) | −1.45927e7 | −0.584160 | ||||||||
\(911\) | 3.15361e7 | 1.25896 | 0.629481 | − | 0.777016i | \(-0.283268\pi\) | ||||
0.629481 | + | 0.777016i | \(0.283268\pi\) | |||||||
\(912\) | 1.70465e6 | 0.0678653 | ||||||||
\(913\) | −1.24382e7 | −0.493835 | ||||||||
\(914\) | −1.35089e7 | −0.534878 | ||||||||
\(915\) | −3.54913e6 | −0.140142 | ||||||||
\(916\) | 1.88964e7 | 0.744117 | ||||||||
\(917\) | 5.82946e7 | 2.28931 | ||||||||
\(918\) | 1.86310e6 | 0.0729673 | ||||||||
\(919\) | 4.21184e7 | 1.64507 | 0.822533 | − | 0.568717i | \(-0.192560\pi\) | ||||
0.822533 | + | 0.568717i | \(0.192560\pi\) | |||||||
\(920\) | 1.13576e7 | 0.442404 | ||||||||
\(921\) | −2.40961e7 | −0.936047 | ||||||||
\(922\) | 1.72027e7 | 0.666454 | ||||||||
\(923\) | −884572. | −0.0341766 | ||||||||
\(924\) | 5.15128e6 | 0.198489 | ||||||||
\(925\) | −1.87107e6 | −0.0719011 | ||||||||
\(926\) | −1.75147e7 | −0.671237 | ||||||||
\(927\) | −4.85002e6 | −0.185372 | ||||||||
\(928\) | −2.22925e7 | −0.849746 | ||||||||
\(929\) | 9.43595e6 | 0.358712 | 0.179356 | − | 0.983784i | \(-0.442599\pi\) | ||||
0.179356 | + | 0.983784i | \(0.442599\pi\) | |||||||
\(930\) | −1.21435e6 | −0.0460403 | ||||||||
\(931\) | −1.32287e8 | −5.00197 | ||||||||
\(932\) | −13839.0 | −0.000521874 0 | ||||||||
\(933\) | −1.15270e7 | −0.433524 | ||||||||
\(934\) | 2.74348e7 | 1.02904 | ||||||||
\(935\) | −4.92047e6 | −0.184068 | ||||||||
\(936\) | 4.14630e6 | 0.154693 | ||||||||
\(937\) | 2.17869e7 | 0.810674 | 0.405337 | − | 0.914167i | \(-0.367154\pi\) | ||||
0.405337 | + | 0.914167i | \(0.367154\pi\) | |||||||
\(938\) | −5.16904e7 | −1.91824 | ||||||||
\(939\) | 1.23127e7 | 0.455710 | ||||||||
\(940\) | −2.25660e7 | −0.832983 | ||||||||
\(941\) | 2.18678e7 | 0.805065 | 0.402532 | − | 0.915406i | \(-0.368130\pi\) | ||||
0.402532 | + | 0.915406i | \(0.368130\pi\) | |||||||
\(942\) | −2.06540e6 | −0.0758361 | ||||||||
\(943\) | −1.94370e7 | −0.711787 | ||||||||
\(944\) | −284197. | −0.0103798 | ||||||||
\(945\) | 1.05655e7 | 0.384867 | ||||||||
\(946\) | 1.77976e6 | 0.0646595 | ||||||||
\(947\) | 2.42335e7 | 0.878094 | 0.439047 | − | 0.898464i | \(-0.355316\pi\) | ||||
0.439047 | + | 0.898464i | \(0.355316\pi\) | |||||||
\(948\) | −4.13612e6 | −0.149476 | ||||||||
\(949\) | 2.05307e6 | 0.0740010 | ||||||||
\(950\) | −2.14777e6 | −0.0772110 | ||||||||
\(951\) | −69176.5 | −0.00248032 | ||||||||
\(952\) | −3.26231e7 | −1.16663 | ||||||||
\(953\) | 5.56092e7 | 1.98342 | 0.991710 | − | 0.128499i | \(-0.0410159\pi\) | ||||
0.991710 | + | 0.128499i | \(0.0410159\pi\) | |||||||
\(954\) | −7.78277e6 | −0.276862 | ||||||||
\(955\) | −3.26703e7 | −1.15916 | ||||||||
\(956\) | 2.00459e7 | 0.709383 | ||||||||
\(957\) | 4.28788e6 | 0.151343 | ||||||||
\(958\) | −6.23595e6 | −0.219528 | ||||||||
\(959\) | 1.71251e7 | 0.601294 | ||||||||
\(960\) | 1.17706e7 | 0.412212 | ||||||||
\(961\) | −2.82140e7 | −0.985498 | ||||||||
\(962\) | 9.10446e6 | 0.317188 | ||||||||
\(963\) | 7.22956e6 | 0.251215 | ||||||||
\(964\) | 1.24650e7 | 0.432016 | ||||||||
\(965\) | 5.29678e6 | 0.183102 | ||||||||
\(966\) | −8.74571e6 | −0.301545 | ||||||||
\(967\) | −2.09122e7 | −0.719173 | −0.359586 | − | 0.933112i | \(-0.617082\pi\) | ||||
−0.359586 | + | 0.933112i | \(0.617082\pi\) | |||||||
\(968\) | −2.70027e6 | −0.0926229 | ||||||||
\(969\) | −1.81410e7 | −0.620659 | ||||||||
\(970\) | −1.93235e7 | −0.659412 | ||||||||
\(971\) | 1.68184e7 | 0.572448 | 0.286224 | − | 0.958163i | \(-0.407600\pi\) | ||||
0.286224 | + | 0.958163i | \(0.407600\pi\) | |||||||
\(972\) | −1.11246e6 | −0.0377676 | ||||||||
\(973\) | 7.48630e7 | 2.53504 | ||||||||
\(974\) | −1.11779e7 | −0.377541 | ||||||||
\(975\) | −516882. | −0.0174132 | ||||||||
\(976\) | 452251. | 0.0151969 | ||||||||
\(977\) | −3.45472e7 | −1.15792 | −0.578958 | − | 0.815358i | \(-0.696540\pi\) | ||||
−0.578958 | + | 0.815358i | \(0.696540\pi\) | |||||||
\(978\) | 7.76166e6 | 0.259482 | ||||||||
\(979\) | −6.00153e6 | −0.200127 | ||||||||
\(980\) | −5.02794e7 | −1.67234 | ||||||||
\(981\) | 1.84648e6 | 0.0612592 | ||||||||
\(982\) | −3.84210e6 | −0.127142 | ||||||||
\(983\) | −3.40232e7 | −1.12303 | −0.561516 | − | 0.827466i | \(-0.689782\pi\) | ||||
−0.561516 | + | 0.827466i | \(0.689782\pi\) | |||||||
\(984\) | −3.02415e7 | −0.995671 | ||||||||
\(985\) | 2.80099e7 | 0.919857 | ||||||||
\(986\) | −1.00629e7 | −0.329632 | ||||||||
\(987\) | 4.68913e7 | 1.53214 | ||||||||
\(988\) | −1.49609e7 | −0.487602 | ||||||||
\(989\) | 4.32560e6 | 0.140623 | ||||||||
\(990\) | −2.05235e6 | −0.0665524 | ||||||||
\(991\) | −4.47458e7 | −1.44733 | −0.723665 | − | 0.690151i | \(-0.757544\pi\) | ||||
−0.723665 | + | 0.690151i | \(0.757544\pi\) | |||||||
\(992\) | −3.64810e6 | −0.117703 | ||||||||
\(993\) | 8.62512e6 | 0.277583 | ||||||||
\(994\) | 2.90297e6 | 0.0931915 | ||||||||
\(995\) | 3.99807e7 | 1.28024 | ||||||||
\(996\) | −1.74297e7 | −0.556725 | ||||||||
\(997\) | −5.86494e6 | −0.186864 | −0.0934320 | − | 0.995626i | \(-0.529784\pi\) | ||||
−0.0934320 | + | 0.995626i | \(0.529784\pi\) | |||||||
\(998\) | 8.21371e6 | 0.261044 | ||||||||
\(999\) | −6.59187e6 | −0.208975 |
(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 | 33.6.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 99.6.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 528.6.a.o.1.2 | 2 | |||
5.4 | even | 2 | 825.6.a.c.1.2 | 2 | |||
11.10 | odd | 2 | 363.6.a.f.1.2 | 2 | |||
33.32 | even | 2 | 1089.6.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.6.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
363.6.a.f.1.2 | 2 | 11.10 | odd | 2 | |||
528.6.a.o.1.2 | 2 | 4.3 | odd | 2 | |||
825.6.a.c.1.2 | 2 | 5.4 | even | 2 | |||
1089.6.a.p.1.1 | 2 | 33.32 | even | 2 |