Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,6,Mod(9,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.9");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.c (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.24537347738\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{130})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 130x^{2} + 16900 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(-5.70088 + 9.87421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.11 |
Dual form | 14.6.c.b.9.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 3.46410i | 0.353553 | + | 0.612372i | ||||
\(3\) | 14.9018 | − | 25.8106i | 0.955948 | − | 1.65575i | 0.223764 | − | 0.974643i | \(-0.428165\pi\) |
0.732184 | − | 0.681107i | \(-0.238501\pi\) | |||||||
\(4\) | −8.00000 | + | 13.8564i | −0.250000 | + | 0.433013i | ||||
\(5\) | 10.5000 | + | 18.1865i | 0.187830 | + | 0.325331i | 0.944526 | − | 0.328436i | \(-0.106521\pi\) |
−0.756697 | + | 0.653766i | \(0.773188\pi\) | |||||||
\(6\) | 119.214 | 1.35191 | ||||||||
\(7\) | −10.4105 | + | 129.223i | −0.0803022 | + | 0.996771i | ||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −322.625 | − | 558.802i | −1.32767 | − | 2.29960i | ||||
\(10\) | −42.0000 | + | 72.7461i | −0.132816 | + | 0.230043i | ||||
\(11\) | −165.937 | + | 287.411i | −0.413486 | + | 0.716179i | −0.995268 | − | 0.0971656i | \(-0.969022\pi\) |
0.581782 | + | 0.813345i | \(0.302356\pi\) | |||||||
\(12\) | 238.428 | + | 412.970i | 0.477974 | + | 0.827875i | ||||
\(13\) | 66.8211 | 0.109662 | 0.0548308 | − | 0.998496i | \(-0.482538\pi\) | ||||
0.0548308 | + | 0.998496i | \(0.482538\pi\) | |||||||
\(14\) | −468.463 | + | 222.383i | −0.638786 | + | 0.303237i | ||||
\(15\) | 625.874 | 0.718222 | ||||||||
\(16\) | −128.000 | − | 221.703i | −0.125000 | − | 0.216506i | ||||
\(17\) | −120.268 | + | 208.311i | −0.100932 | + | 0.174820i | −0.912069 | − | 0.410037i | \(-0.865516\pi\) |
0.811137 | + | 0.584856i | \(0.198849\pi\) | |||||||
\(18\) | 1290.50 | − | 2235.21i | 0.938807 | − | 1.62606i | ||||
\(19\) | −220.989 | − | 382.765i | −0.140439 | − | 0.243247i | 0.787223 | − | 0.616668i | \(-0.211518\pi\) |
−0.927662 | + | 0.373421i | \(0.878185\pi\) | |||||||
\(20\) | −336.000 | −0.187830 | ||||||||
\(21\) | 3180.19 | + | 2194.35i | 1.57364 | + | 1.08582i | ||||
\(22\) | −1327.49 | −0.584758 | ||||||||
\(23\) | 535.684 | + | 927.832i | 0.211149 | + | 0.365721i | 0.952074 | − | 0.305866i | \(-0.0989461\pi\) |
−0.740925 | + | 0.671587i | \(0.765613\pi\) | |||||||
\(24\) | −953.712 | + | 1651.88i | −0.337979 | + | 0.585396i | ||||
\(25\) | 1342.00 | − | 2324.41i | 0.429440 | − | 0.743812i | ||||
\(26\) | 133.642 | + | 231.475i | 0.0387713 | + | 0.0671538i | ||||
\(27\) | −11988.4 | −3.16485 | ||||||||
\(28\) | −1707.28 | − | 1178.04i | −0.411539 | − | 0.283965i | ||||
\(29\) | 1791.75 | 0.395623 | 0.197812 | − | 0.980240i | \(-0.436617\pi\) | ||||
0.197812 | + | 0.980240i | \(0.436617\pi\) | |||||||
\(30\) | 1251.75 | + | 2168.09i | 0.253930 | + | 0.439819i | ||||
\(31\) | 2844.37 | − | 4926.59i | 0.531596 | − | 0.920751i | −0.467724 | − | 0.883875i | \(-0.654926\pi\) |
0.999320 | − | 0.0368765i | \(-0.0117408\pi\) | |||||||
\(32\) | 512.000 | − | 886.810i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 4945.50 | + | 8565.86i | 0.790543 | + | 1.36926i | ||||
\(34\) | −962.147 | −0.142740 | ||||||||
\(35\) | −2459.43 | + | 1167.51i | −0.339363 | + | 0.161098i | ||||
\(36\) | 10324.0 | 1.32767 | ||||||||
\(37\) | −5605.36 | − | 9708.77i | −0.673131 | − | 1.16590i | −0.977012 | − | 0.213187i | \(-0.931616\pi\) |
0.303881 | − | 0.952710i | \(-0.401718\pi\) | |||||||
\(38\) | 883.958 | − | 1531.06i | 0.0993053 | − | 0.172002i | ||||
\(39\) | 995.751 | − | 1724.69i | 0.104831 | − | 0.181572i | ||||
\(40\) | −672.000 | − | 1163.94i | −0.0664078 | − | 0.115022i | ||||
\(41\) | 12077.9 | 1.12210 | 0.561048 | − | 0.827783i | \(-0.310398\pi\) | ||||
0.561048 | + | 0.827783i | \(0.310398\pi\) | |||||||
\(42\) | −1241.08 | + | 15405.2i | −0.108562 | + | 1.34755i | ||||
\(43\) | −9921.98 | −0.818328 | −0.409164 | − | 0.912461i | \(-0.634180\pi\) | ||||
−0.409164 | + | 0.912461i | \(0.634180\pi\) | |||||||
\(44\) | −2654.99 | − | 4598.58i | −0.206743 | − | 0.358090i | ||||
\(45\) | 6775.12 | − | 11734.8i | 0.498753 | − | 0.863865i | ||||
\(46\) | −2142.74 | + | 3711.33i | −0.149305 | + | 0.258604i | ||||
\(47\) | 8434.62 | + | 14609.2i | 0.556956 | + | 0.964676i | 0.997748 | + | 0.0670671i | \(0.0213642\pi\) |
−0.440792 | + | 0.897609i | \(0.645303\pi\) | |||||||
\(48\) | −7629.70 | −0.477974 | ||||||||
\(49\) | −16590.2 | − | 2690.56i | −0.987103 | − | 0.160086i | ||||
\(50\) | 10736.0 | 0.607320 | ||||||||
\(51\) | 3584.42 | + | 6208.40i | 0.192972 | + | 0.334237i | ||||
\(52\) | −534.568 | + | 925.900i | −0.0274154 | + | 0.0474849i | ||||
\(53\) | −2649.38 | + | 4588.87i | −0.129555 | + | 0.224396i | −0.923504 | − | 0.383588i | \(-0.874688\pi\) |
0.793949 | + | 0.607984i | \(0.208022\pi\) | |||||||
\(54\) | −23976.9 | − | 41529.2i | −1.11894 | − | 1.93807i | ||||
\(55\) | −6969.35 | −0.310660 | ||||||||
\(56\) | 666.274 | − | 8270.28i | 0.0283911 | − | 0.352412i | ||||
\(57\) | −13172.5 | −0.537009 | ||||||||
\(58\) | 3583.49 | + | 6206.79i | 0.139874 | + | 0.242269i | ||||
\(59\) | −20692.4 | + | 35840.3i | −0.773892 | + | 1.34042i | 0.161522 | + | 0.986869i | \(0.448360\pi\) |
−0.935415 | + | 0.353552i | \(0.884974\pi\) | |||||||
\(60\) | −5006.99 | + | 8672.36i | −0.179555 | + | 0.310999i | ||||
\(61\) | 10761.6 | + | 18639.7i | 0.370300 | + | 0.641379i | 0.989612 | − | 0.143766i | \(-0.0459214\pi\) |
−0.619311 | + | 0.785146i | \(0.712588\pi\) | |||||||
\(62\) | 22754.9 | 0.751790 | ||||||||
\(63\) | 75568.9 | − | 35873.1i | 2.39879 | − | 1.13872i | ||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 701.621 | + | 1215.24i | 0.0205977 | + | 0.0356763i | ||||
\(66\) | −19782.0 | + | 34263.4i | −0.558998 | + | 0.968213i | ||||
\(67\) | 13309.4 | − | 23052.5i | 0.362219 | − | 0.627381i | −0.626107 | − | 0.779737i | \(-0.715353\pi\) |
0.988326 | + | 0.152356i | \(0.0486860\pi\) | |||||||
\(68\) | −1924.29 | − | 3332.98i | −0.0504661 | − | 0.0874098i | ||||
\(69\) | 31930.5 | 0.807390 | ||||||||
\(70\) | −8963.24 | − | 6184.70i | −0.218635 | − | 0.150860i | ||||
\(71\) | −58096.5 | −1.36774 | −0.683870 | − | 0.729603i | \(-0.739705\pi\) | ||||
−0.683870 | + | 0.729603i | \(0.739705\pi\) | |||||||
\(72\) | 20648.0 | + | 35763.3i | 0.469403 | + | 0.813030i | ||||
\(73\) | 19993.8 | − | 34630.2i | 0.439124 | − | 0.760585i | −0.558498 | − | 0.829506i | \(-0.688622\pi\) |
0.997622 | + | 0.0689204i | \(0.0219555\pi\) | |||||||
\(74\) | 22421.5 | − | 38835.1i | 0.475975 | − | 0.824413i | ||||
\(75\) | −39996.3 | − | 69275.6i | −0.821045 | − | 1.42209i | ||||
\(76\) | 7071.66 | 0.140439 | ||||||||
\(77\) | −35412.7 | − | 24435.0i | −0.680663 | − | 0.469662i | ||||
\(78\) | 7966.01 | 0.148253 | ||||||||
\(79\) | 21974.9 | + | 38061.7i | 0.396150 | + | 0.686151i | 0.993247 | − | 0.116017i | \(-0.0370128\pi\) |
−0.597098 | + | 0.802169i | \(0.703679\pi\) | |||||||
\(80\) | 2688.00 | − | 4655.75i | 0.0469574 | − | 0.0813327i | ||||
\(81\) | −100251. | + | 173640.i | −1.69776 | + | 2.94060i | ||||
\(82\) | 24155.7 | + | 41838.9i | 0.396721 | + | 0.687141i | ||||
\(83\) | 22421.4 | 0.357246 | 0.178623 | − | 0.983918i | \(-0.442836\pi\) | ||||
0.178623 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(84\) | −55847.4 | + | 26511.2i | −0.863584 | + | 0.409950i | ||||
\(85\) | −5051.27 | −0.0758322 | ||||||||
\(86\) | −19844.0 | − | 34370.7i | −0.289322 | − | 0.501121i | ||||
\(87\) | 26700.2 | − | 46246.1i | 0.378195 | − | 0.655053i | ||||
\(88\) | 10620.0 | − | 18394.3i | 0.146189 | − | 0.253208i | ||||
\(89\) | −12031.0 | − | 20838.3i | −0.161001 | − | 0.278861i | 0.774227 | − | 0.632908i | \(-0.218139\pi\) |
−0.935228 | + | 0.354047i | \(0.884805\pi\) | |||||||
\(90\) | 54200.9 | 0.705343 | ||||||||
\(91\) | −695.642 | + | 8634.83i | −0.00880608 | + | 0.109308i | ||||
\(92\) | −17141.9 | −0.211149 | ||||||||
\(93\) | −84772.2 | − | 146830.i | −1.01636 | − | 1.76038i | ||||
\(94\) | −33738.5 | + | 58436.8i | −0.393827 | + | 0.682129i | ||||
\(95\) | 4640.78 | − | 8038.06i | 0.0527572 | − | 0.0913782i | ||||
\(96\) | −15259.4 | − | 26430.0i | −0.168989 | − | 0.292698i | ||||
\(97\) | 71896.4 | 0.775850 | 0.387925 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(98\) | −23860.1 | − | 62851.4i | −0.250962 | − | 0.661074i | ||||
\(99\) | 214141. | 2.19590 | ||||||||
\(100\) | 21472.0 | + | 37190.6i | 0.214720 | + | 0.371906i | ||||
\(101\) | 7932.73 | − | 13739.9i | 0.0773783 | − | 0.134023i | −0.824740 | − | 0.565512i | \(-0.808678\pi\) |
0.902118 | + | 0.431489i | \(0.142012\pi\) | |||||||
\(102\) | −14337.7 | + | 24833.6i | −0.136452 | + | 0.236341i | ||||
\(103\) | 80286.8 | + | 139061.i | 0.745677 | + | 1.29155i | 0.949878 | + | 0.312622i | \(0.101207\pi\) |
−0.204200 | + | 0.978929i | \(0.565459\pi\) | |||||||
\(104\) | −4276.55 | −0.0387713 | ||||||||
\(105\) | −6515.67 | + | 80877.4i | −0.0576748 | + | 0.715902i | ||||
\(106\) | −21195.1 | −0.183219 | ||||||||
\(107\) | 102523. | + | 177576.i | 0.865693 | + | 1.49942i | 0.866357 | + | 0.499425i | \(0.166455\pi\) |
−0.000664234 | 1.00000i | \(0.500211\pi\) | ||||||||
\(108\) | 95907.5 | − | 166117.i | 0.791212 | − | 1.37042i | ||||
\(109\) | 56272.1 | − | 97466.2i | 0.453657 | − | 0.785756i | −0.544953 | − | 0.838466i | \(-0.683453\pi\) |
0.998610 | + | 0.0527102i | \(0.0167860\pi\) | |||||||
\(110\) | −13938.7 | − | 24142.5i | −0.109835 | − | 0.190240i | ||||
\(111\) | −334119. | −2.57391 | ||||||||
\(112\) | 29981.6 | − | 14232.5i | 0.225845 | − | 0.107210i | ||||
\(113\) | −118332. | −0.871782 | −0.435891 | − | 0.900000i | \(-0.643567\pi\) | ||||
−0.435891 | + | 0.900000i | \(0.643567\pi\) | |||||||
\(114\) | −26345.0 | − | 45631.0i | −0.189861 | − | 0.328850i | ||||
\(115\) | −11249.4 | + | 19484.5i | −0.0793202 | + | 0.137387i | ||||
\(116\) | −14334.0 | + | 24827.2i | −0.0989058 | + | 0.171310i | ||||
\(117\) | −21558.1 | − | 37339.7i | −0.145595 | − | 0.252178i | ||||
\(118\) | −165539. | −1.09445 | ||||||||
\(119\) | −25666.5 | − | 17710.1i | −0.166150 | − | 0.114645i | ||||
\(120\) | −40055.9 | −0.253930 | ||||||||
\(121\) | 25455.4 | + | 44090.1i | 0.158058 | + | 0.273765i | ||||
\(122\) | −43046.6 | + | 74558.9i | −0.261842 | + | 0.453524i | ||||
\(123\) | 179981. | − | 311737.i | 1.07267 | − | 1.85791i | ||||
\(124\) | 45509.9 | + | 78825.5i | 0.265798 | + | 0.460376i | ||||
\(125\) | 121989. | 0.698306 | ||||||||
\(126\) | 275406. | + | 190032.i | 1.54542 | + | 1.06635i | ||||
\(127\) | −245195. | −1.34897 | −0.674485 | − | 0.738289i | \(-0.735634\pi\) | ||||
−0.674485 | + | 0.738289i | \(0.735634\pi\) | |||||||
\(128\) | 8192.00 | + | 14189.0i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −147855. | + | 256092.i | −0.782279 | + | 1.35495i | ||||
\(130\) | −2806.48 | + | 4860.97i | −0.0145648 | + | 0.0252270i | ||||
\(131\) | −34996.9 | − | 60616.3i | −0.178177 | − | 0.308611i | 0.763079 | − | 0.646305i | \(-0.223687\pi\) |
−0.941256 | + | 0.337694i | \(0.890353\pi\) | |||||||
\(132\) | −158256. | −0.790543 | ||||||||
\(133\) | 51762.7 | − | 24572.2i | 0.253739 | − | 0.120452i | ||||
\(134\) | 106475. | 0.512254 | ||||||||
\(135\) | −125879. | − | 218028.i | −0.594453 | − | 1.02962i | ||||
\(136\) | 7697.18 | − | 13331.9i | 0.0356849 | − | 0.0618080i | ||||
\(137\) | 93831.9 | − | 162522.i | 0.427119 | − | 0.739792i | −0.569496 | − | 0.821994i | \(-0.692862\pi\) |
0.996616 | + | 0.0822015i | \(0.0261951\pi\) | |||||||
\(138\) | 63861.1 | + | 110611.i | 0.285456 | + | 0.494424i | ||||
\(139\) | −78272.7 | −0.343616 | −0.171808 | − | 0.985130i | \(-0.554961\pi\) | ||||
−0.171808 | + | 0.985130i | \(0.554961\pi\) | |||||||
\(140\) | 3497.94 | − | 43419.0i | 0.0150831 | − | 0.187223i | ||||
\(141\) | 502763. | 2.12968 | ||||||||
\(142\) | −116193. | − | 201252.i | −0.483569 | − | 0.837567i | ||||
\(143\) | −11088.1 | + | 19205.1i | −0.0453436 | + | 0.0785374i | ||||
\(144\) | −82591.9 | + | 143053.i | −0.331918 | + | 0.574899i | ||||
\(145\) | 18813.3 | + | 32585.7i | 0.0743098 | + | 0.128708i | ||||
\(146\) | 159950. | 0.621015 | ||||||||
\(147\) | −316669. | + | 388110.i | −1.20868 | + | 1.48136i | ||||
\(148\) | 179372. | 0.673131 | ||||||||
\(149\) | 46083.2 | + | 79818.5i | 0.170050 | + | 0.294536i | 0.938437 | − | 0.345450i | \(-0.112274\pi\) |
−0.768387 | + | 0.639985i | \(0.778940\pi\) | |||||||
\(150\) | 159985. | − | 277103.i | 0.580566 | − | 1.00557i | ||||
\(151\) | −26708.0 | + | 46259.6i | −0.0953232 | + | 0.165105i | −0.909743 | − | 0.415171i | \(-0.863722\pi\) |
0.814420 | + | 0.580276i | \(0.197055\pi\) | |||||||
\(152\) | 14143.3 | + | 24497.0i | 0.0496527 | + | 0.0860009i | ||||
\(153\) | 155206. | 0.536019 | ||||||||
\(154\) | 13819.9 | − | 171543.i | 0.0469574 | − | 0.582869i | ||||
\(155\) | 119463. | 0.399398 | ||||||||
\(156\) | 15932.0 | + | 27595.1i | 0.0524154 | + | 0.0907862i | ||||
\(157\) | 140250. | − | 242921.i | 0.454103 | − | 0.786530i | −0.544533 | − | 0.838739i | \(-0.683293\pi\) |
0.998636 | + | 0.0522096i | \(0.0166264\pi\) | |||||||
\(158\) | −87899.6 | + | 152247.i | −0.280120 | + | 0.485182i | ||||
\(159\) | 78960.9 | + | 136764.i | 0.247696 | + | 0.429023i | ||||
\(160\) | 21504.0 | 0.0664078 | ||||||||
\(161\) | −125474. | + | 59563.6i | −0.381496 | + | 0.181099i | ||||
\(162\) | −802008. | −2.40099 | ||||||||
\(163\) | −313405. | − | 542833.i | −0.923925 | − | 1.60028i | −0.793281 | − | 0.608855i | \(-0.791629\pi\) |
−0.130643 | − | 0.991429i | \(-0.541704\pi\) | |||||||
\(164\) | −96622.8 | + | 167356.i | −0.280524 | + | 0.485882i | ||||
\(165\) | −103856. | + | 179883.i | −0.296975 | + | 0.514375i | ||||
\(166\) | 44842.8 | + | 77670.0i | 0.126306 | + | 0.218768i | ||||
\(167\) | 293997. | 0.815741 | 0.407870 | − | 0.913040i | \(-0.366272\pi\) | ||||
0.407870 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(168\) | −203532. | − | 140439.i | −0.556365 | − | 0.383896i | ||||
\(169\) | −366828. | −0.987974 | ||||||||
\(170\) | −10102.5 | − | 17498.1i | −0.0268107 | − | 0.0464375i | ||||
\(171\) | −142593. | + | 246979.i | −0.372914 | + | 0.645906i | ||||
\(172\) | 79375.8 | − | 137483.i | 0.204582 | − | 0.354346i | ||||
\(173\) | −357093. | − | 618504.i | −0.907124 | − | 1.57118i | −0.818041 | − | 0.575160i | \(-0.804940\pi\) |
−0.0890831 | − | 0.996024i | \(-0.528394\pi\) | |||||||
\(174\) | 213601. | 0.534849 | ||||||||
\(175\) | 286397. | + | 197616.i | 0.706925 | + | 0.487783i | ||||
\(176\) | 84959.7 | 0.206743 | ||||||||
\(177\) | 616706. | + | 1.06817e6i | 1.47960 | + | 2.56275i | ||||
\(178\) | 48124.1 | − | 83353.3i | 0.113845 | − | 0.197185i | ||||
\(179\) | −290025. | + | 502338.i | −0.676554 | + | 1.17183i | 0.299458 | + | 0.954110i | \(0.403194\pi\) |
−0.976012 | + | 0.217717i | \(0.930139\pi\) | |||||||
\(180\) | 108402. | + | 187758.i | 0.249376 | + | 0.431933i | ||||
\(181\) | −308046. | −0.698907 | −0.349454 | − | 0.936954i | \(-0.613633\pi\) | ||||
−0.349454 | + | 0.936954i | \(0.613633\pi\) | |||||||
\(182\) | −31303.2 | + | 14859.9i | −0.0700503 | + | 0.0332535i | ||||
\(183\) | 641470. | 1.41595 | ||||||||
\(184\) | −34283.8 | − | 59381.3i | −0.0746525 | − | 0.129302i | ||||
\(185\) | 117713. | − | 203884.i | 0.252868 | − | 0.437980i | ||||
\(186\) | 339089. | − | 587319.i | 0.718672 | − | 1.24478i | ||||
\(187\) | −39913.9 | − | 69132.9i | −0.0834681 | − | 0.144571i | ||||
\(188\) | −269908. | −0.556956 | ||||||||
\(189\) | 124806. | − | 1.54918e6i | 0.254144 | − | 3.15463i | ||||
\(190\) | 37126.2 | 0.0746100 | ||||||||
\(191\) | 101395. | + | 175621.i | 0.201109 | + | 0.348331i | 0.948886 | − | 0.315619i | \(-0.102212\pi\) |
−0.747777 | + | 0.663950i | \(0.768879\pi\) | |||||||
\(192\) | 61037.6 | − | 105720.i | 0.119493 | − | 0.206969i | ||||
\(193\) | −302994. | + | 524801.i | −0.585519 | + | 1.01415i | 0.409292 | + | 0.912403i | \(0.365776\pi\) |
−0.994811 | + | 0.101744i | \(0.967558\pi\) | |||||||
\(194\) | 143793. | + | 249057.i | 0.274305 | + | 0.475109i | ||||
\(195\) | 41821.5 | 0.0787614 | ||||||||
\(196\) | 170003. | − | 208357.i | 0.316095 | − | 0.387407i | ||||
\(197\) | −310.819 | −0.000570614 | −0.000285307 | − | 1.00000i | \(-0.500091\pi\) | ||||
−0.000285307 | 1.00000i | \(0.500091\pi\) | ||||||||
\(198\) | 428282. | + | 741807.i | 0.776367 | + | 1.34471i | ||||
\(199\) | 204833. | − | 354782.i | 0.366664 | − | 0.635080i | −0.622378 | − | 0.782717i | \(-0.713833\pi\) |
0.989042 | + | 0.147637i | \(0.0471667\pi\) | |||||||
\(200\) | −85888.0 | + | 148762.i | −0.151830 | + | 0.262977i | ||||
\(201\) | −396666. | − | 687046.i | −0.692524 | − | 1.19949i | ||||
\(202\) | 63461.9 | 0.109429 | ||||||||
\(203\) | −18653.0 | + | 231535.i | −0.0317694 | + | 0.394346i | ||||
\(204\) | −114701. | −0.192972 | ||||||||
\(205\) | 126817. | + | 219654.i | 0.210763 | + | 0.365052i | ||||
\(206\) | −321147. | + | 556243.i | −0.527274 | + | 0.913265i | ||||
\(207\) | 345650. | − | 598683.i | 0.560674 | − | 0.971116i | ||||
\(208\) | −8553.09 | − | 14814.4i | −0.0137077 | − | 0.0237425i | ||||
\(209\) | 146681. | 0.232278 | ||||||||
\(210\) | −293199. | + | 139184.i | −0.458790 | + | 0.217791i | ||||
\(211\) | −441339. | −0.682442 | −0.341221 | − | 0.939983i | \(-0.610840\pi\) | ||||
−0.341221 | + | 0.939983i | \(0.610840\pi\) | |||||||
\(212\) | −42390.1 | − | 73421.9i | −0.0647777 | − | 0.112198i | ||||
\(213\) | −865739. | + | 1.49950e6i | −1.30749 | + | 2.26464i | ||||
\(214\) | −410094. | + | 710304.i | −0.612137 | + | 1.06025i | ||||
\(215\) | −104181. | − | 180446.i | −0.153706 | − | 0.266227i | ||||
\(216\) | 767260. | 1.11894 | ||||||||
\(217\) | 607018. | + | 418847.i | 0.875089 | + | 0.603817i | ||||
\(218\) | 450177. | 0.641567 | ||||||||
\(219\) | −595884. | − | 1.03210e6i | −0.839560 | − | 1.45416i | ||||
\(220\) | 55754.8 | − | 96570.1i | 0.0776650 | − | 0.134520i | ||||
\(221\) | −8036.46 | + | 13919.6i | −0.0110684 | + | 0.0191710i | ||||
\(222\) | −668238. | − | 1.15742e6i | −0.910015 | − | 1.57619i | ||||
\(223\) | 265133. | 0.357028 | 0.178514 | − | 0.983937i | \(-0.442871\pi\) | ||||
0.178514 | + | 0.983937i | \(0.442871\pi\) | |||||||
\(224\) | 109266. | + | 75394.4i | 0.145501 | + | 0.100397i | ||||
\(225\) | −1.73185e6 | −2.28062 | ||||||||
\(226\) | −236665. | − | 409916.i | −0.308221 | − | 0.533855i | ||||
\(227\) | 715220. | − | 1.23880e6i | 0.921244 | − | 1.59564i | 0.123751 | − | 0.992313i | \(-0.460508\pi\) |
0.797493 | − | 0.603328i | \(-0.206159\pi\) | |||||||
\(228\) | 105380. | − | 182524.i | 0.134252 | − | 0.232532i | ||||
\(229\) | 629025. | + | 1.08950e6i | 0.792646 | + | 1.37290i | 0.924323 | + | 0.381610i | \(0.124630\pi\) |
−0.131678 | + | 0.991293i | \(0.542036\pi\) | |||||||
\(230\) | −89994.9 | −0.112176 | ||||||||
\(231\) | −1.15839e6 | + | 549898.i | −1.42832 | + | 0.678035i | ||||
\(232\) | −114672. | −0.139874 | ||||||||
\(233\) | −112362. | − | 194616.i | −0.135590 | − | 0.234849i | 0.790233 | − | 0.612807i | \(-0.209960\pi\) |
−0.925823 | + | 0.377958i | \(0.876626\pi\) | |||||||
\(234\) | 86232.4 | − | 149359.i | 0.102951 | − | 0.178317i | ||||
\(235\) | −177127. | + | 306793.i | −0.209226 | + | 0.362390i | ||||
\(236\) | −331078. | − | 573444.i | −0.386946 | − | 0.670211i | ||||
\(237\) | 1.30986e6 | 1.51479 | ||||||||
\(238\) | 10016.5 | − | 124332.i | 0.0114623 | − | 0.142279i | ||||
\(239\) | 1.28193e6 | 1.45167 | 0.725837 | − | 0.687867i | \(-0.241453\pi\) | ||||
0.725837 | + | 0.687867i | \(0.241453\pi\) | |||||||
\(240\) | −80111.8 | − | 138758.i | −0.0897777 | − | 0.155500i | ||||
\(241\) | 288062. | − | 498939.i | 0.319480 | − | 0.553356i | −0.660899 | − | 0.750475i | \(-0.729825\pi\) |
0.980380 | + | 0.197118i | \(0.0631583\pi\) | |||||||
\(242\) | −101822. | + | 176360.i | −0.111764 | + | 0.193581i | ||||
\(243\) | 1.53124e6 | + | 2.65218e6i | 1.66351 | + | 2.88129i | ||||
\(244\) | −344373. | −0.370300 | ||||||||
\(245\) | −125266. | − | 329970.i | −0.133326 | − | 0.351204i | ||||
\(246\) | 1.43985e6 | 1.51698 | ||||||||
\(247\) | −14766.7 | − | 25576.8i | −0.0154008 | − | 0.0266749i | ||||
\(248\) | −182040. | + | 315302.i | −0.187948 | + | 0.325535i | ||||
\(249\) | 334118. | − | 578709.i | 0.341509 | − | 0.591510i | ||||
\(250\) | 243978. | + | 422582.i | 0.246888 | + | 0.427623i | ||||
\(251\) | −609040. | −0.610185 | −0.305092 | − | 0.952323i | \(-0.598687\pi\) | ||||
−0.305092 | + | 0.952323i | \(0.598687\pi\) | |||||||
\(252\) | −107478. | + | 1.33410e6i | −0.106615 | + | 1.32339i | ||||
\(253\) | −355559. | −0.349229 | ||||||||
\(254\) | −490390. | − | 849380.i | −0.476933 | − | 0.826072i | ||||
\(255\) | −75272.8 | + | 130376.i | −0.0724916 | + | 0.125559i | ||||
\(256\) | −32768.0 | + | 56755.8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −515335. | − | 892586.i | −0.486695 | − | 0.842980i | 0.513188 | − | 0.858276i | \(-0.328464\pi\) |
−0.999883 | + | 0.0152961i | \(0.995131\pi\) | |||||||
\(258\) | −1.18284e6 | −1.10631 | ||||||||
\(259\) | 1.31295e6 | − | 623269.i | 1.21619 | − | 0.577333i | ||||
\(260\) | −22451.9 | −0.0205977 | ||||||||
\(261\) | −578062. | − | 1.00123e6i | −0.525258 | − | 0.909774i | ||||
\(262\) | 139987. | − | 242465.i | 0.125990 | − | 0.218221i | ||||
\(263\) | 455293. | − | 788590.i | 0.405883 | − | 0.703011i | −0.588540 | − | 0.808468i | \(-0.700297\pi\) |
0.994424 | + | 0.105457i | \(0.0336306\pi\) | |||||||
\(264\) | −316512. | − | 548215.i | −0.279499 | − | 0.484107i | ||||
\(265\) | −111274. | −0.0973374 | ||||||||
\(266\) | 188646. | + | 130167.i | 0.163472 | + | 0.112797i | ||||
\(267\) | −717133. | −0.615633 | ||||||||
\(268\) | 212950. | + | 368840.i | 0.181109 | + | 0.313691i | ||||
\(269\) | −710499. | + | 1.23062e6i | −0.598663 | + | 1.03692i | 0.394355 | + | 0.918958i | \(0.370968\pi\) |
−0.993019 | + | 0.117957i | \(0.962365\pi\) | |||||||
\(270\) | 503514. | − | 872112.i | 0.420342 | − | 0.728053i | ||||
\(271\) | 148765. | + | 257668.i | 0.123049 | + | 0.213127i | 0.920969 | − | 0.389637i | \(-0.127400\pi\) |
−0.797920 | + | 0.602764i | \(0.794066\pi\) | |||||||
\(272\) | 61577.4 | 0.0504661 | ||||||||
\(273\) | 212504. | + | 146629.i | 0.172568 | + | 0.119073i | ||||
\(274\) | 750655. | 0.604038 | ||||||||
\(275\) | 445374. | + | 771411.i | 0.355135 | + | 0.615112i | ||||
\(276\) | −255444. | + | 442442.i | −0.201848 | + | 0.349610i | ||||
\(277\) | −424806. | + | 735785.i | −0.332653 | + | 0.576171i | −0.983031 | − | 0.183439i | \(-0.941277\pi\) |
0.650378 | + | 0.759610i | \(0.274610\pi\) | |||||||
\(278\) | −156545. | − | 271144.i | −0.121487 | − | 0.210421i | ||||
\(279\) | −3.67065e6 | −2.82314 | ||||||||
\(280\) | 157404. | − | 74720.7i | 0.119983 | − | 0.0569569i | ||||
\(281\) | −7680.49 | −0.00580261 | −0.00290130 | − | 0.999996i | \(-0.500924\pi\) | ||||
−0.00290130 | + | 0.999996i | \(0.500924\pi\) | |||||||
\(282\) | 1.00553e6 | + | 1.74162e6i | 0.752957 | + | 1.30416i | ||||
\(283\) | 492684. | − | 853353.i | 0.365681 | − | 0.633378i | −0.623204 | − | 0.782059i | \(-0.714170\pi\) |
0.988885 | + | 0.148681i | \(0.0475029\pi\) | |||||||
\(284\) | 464772. | − | 805008.i | 0.341935 | − | 0.592249i | ||||
\(285\) | −138311. | − | 239563.i | −0.100866 | − | 0.174706i | ||||
\(286\) | −88704.6 | −0.0641255 | ||||||||
\(287\) | −125737. | + | 1.56074e6i | −0.0901068 | + | 1.11847i | ||||
\(288\) | −660735. | −0.469403 | ||||||||
\(289\) | 681000. | + | 1.17953e6i | 0.479625 | + | 0.830736i | ||||
\(290\) | −75253.4 | + | 130343.i | −0.0525450 | + | 0.0910105i | ||||
\(291\) | 1.07138e6 | − | 1.85569e6i | 0.741673 | − | 1.28461i | ||||
\(292\) | 319900. | + | 554083.i | 0.219562 | + | 0.380293i | ||||
\(293\) | −2.16934e6 | −1.47625 | −0.738124 | − | 0.674665i | \(-0.764288\pi\) | ||||
−0.738124 | + | 0.674665i | \(0.764288\pi\) | |||||||
\(294\) | −1.97779e6 | − | 320753.i | −1.33448 | − | 0.216422i | ||||
\(295\) | −869080. | −0.581440 | ||||||||
\(296\) | 358743. | + | 621362.i | 0.237988 | + | 0.412207i | ||||
\(297\) | 1.98932e6 | − | 3.44561e6i | 1.30862 | − | 2.26660i | ||||
\(298\) | −184333. | + | 319274.i | −0.120244 | + | 0.208268i | ||||
\(299\) | 35795.0 | + | 61998.7i | 0.0231550 | + | 0.0401056i | ||||
\(300\) | 1.27988e6 | 0.821045 | ||||||||
\(301\) | 103293. | − | 1.28215e6i | 0.0657135 | − | 0.815685i | ||||
\(302\) | −213664. | −0.134807 | ||||||||
\(303\) | −236423. | − | 409497.i | −0.147939 | − | 0.256238i | ||||
\(304\) | −56573.3 | + | 97987.8i | −0.0351097 | + | 0.0608118i | ||||
\(305\) | −225995. | + | 391434.i | −0.139107 | + | 0.240940i | ||||
\(306\) | 310412. | + | 537650.i | 0.189511 | + | 0.328243i | ||||
\(307\) | −1.39093e6 | −0.842287 | −0.421143 | − | 0.906994i | \(-0.638371\pi\) | ||||
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(308\) | 621882. | − | 295212.i | 0.373535 | − | 0.177320i | ||||
\(309\) | 4.78566e6 | 2.85132 | ||||||||
\(310\) | 238927. | + | 413834.i | 0.141209 | + | 0.244580i | ||||
\(311\) | −1.01897e6 | + | 1.76491e6i | −0.597394 | + | 1.03472i | 0.395810 | + | 0.918332i | \(0.370464\pi\) |
−0.993204 | + | 0.116385i | \(0.962869\pi\) | |||||||
\(312\) | −63728.1 | + | 110380.i | −0.0370633 | + | 0.0641955i | ||||
\(313\) | 584789. | + | 1.01288e6i | 0.337395 | + | 0.584385i | 0.983942 | − | 0.178489i | \(-0.0571210\pi\) |
−0.646547 | + | 0.762874i | \(0.723788\pi\) | |||||||
\(314\) | 1.12200e6 | 0.642199 | ||||||||
\(315\) | 1.44588e6 | + | 997668.i | 0.821025 | + | 0.566513i | ||||
\(316\) | −703197. | −0.396150 | ||||||||
\(317\) | −400568. | − | 693805.i | −0.223887 | − | 0.387783i | 0.732098 | − | 0.681199i | \(-0.238541\pi\) |
−0.955985 | + | 0.293416i | \(0.905208\pi\) | |||||||
\(318\) | −315844. | + | 547057.i | −0.175148 | + | 0.303365i | ||||
\(319\) | −297317. | + | 514968.i | −0.163585 | + | 0.283337i | ||||
\(320\) | 43008.0 | + | 74492.0i | 0.0234787 | + | 0.0406663i | ||||
\(321\) | 6.11112e6 | 3.31023 | ||||||||
\(322\) | −457283. | − | 315528.i | −0.245779 | − | 0.169589i | ||||
\(323\) | 106312. | 0.0566992 | ||||||||
\(324\) | −1.60402e6 | − | 2.77824e6i | −0.848879 | − | 1.47030i | ||||
\(325\) | 89673.9 | − | 155320.i | 0.0470931 | − | 0.0815677i | ||||
\(326\) | 1.25362e6 | − | 2.17133e6i | 0.653313 | − | 1.13157i | ||||
\(327\) | −1.67711e6 | − | 2.90483e6i | −0.867344 | − | 1.50228i | ||||
\(328\) | −772983. | −0.396721 | ||||||||
\(329\) | −1.97565e6 | + | 937859.i | −1.00629 | + | 0.477692i | ||||
\(330\) | −830844. | −0.419986 | ||||||||
\(331\) | −1.32476e6 | − | 2.29454e6i | −0.664608 | − | 1.15114i | −0.979391 | − | 0.201972i | \(-0.935265\pi\) |
0.314783 | − | 0.949164i | \(-0.398068\pi\) | |||||||
\(332\) | −179371. | + | 310680.i | −0.0893115 | + | 0.154692i | ||||
\(333\) | −3.61686e6 | + | 6.26458e6i | −1.78740 | + | 3.09586i | ||||
\(334\) | 587994. | + | 1.01844e6i | 0.288408 | + | 0.499537i | ||||
\(335\) | 558994. | 0.272142 | ||||||||
\(336\) | 79429.2 | − | 985934.i | 0.0383824 | − | 0.476430i | ||||
\(337\) | −3.40056e6 | −1.63108 | −0.815541 | − | 0.578699i | \(-0.803560\pi\) | ||||
−0.815541 | + | 0.578699i | \(0.803560\pi\) | |||||||
\(338\) | −733656. | − | 1.27073e6i | −0.349302 | − | 0.605008i | ||||
\(339\) | −1.76336e6 | + | 3.05423e6i | −0.833378 | + | 1.44345i | ||||
\(340\) | 40410.2 | − | 69992.5i | 0.0189580 | − | 0.0328363i | ||||
\(341\) | 943971. | + | 1.63501e6i | 0.439615 | + | 0.761436i | ||||
\(342\) | −1.14075e6 | −0.527380 | ||||||||
\(343\) | 520396. | − | 2.11583e6i | 0.238835 | − | 0.971060i | ||||
\(344\) | 635007. | 0.289322 | ||||||||
\(345\) | 335271. | + | 580706.i | 0.151652 | + | 0.262669i | ||||
\(346\) | 1.42837e6 | − | 2.47402e6i | 0.641433 | − | 1.11100i | ||||
\(347\) | 308855. | − | 534952.i | 0.137699 | − | 0.238501i | −0.788926 | − | 0.614488i | \(-0.789363\pi\) |
0.926625 | + | 0.375986i | \(0.122696\pi\) | |||||||
\(348\) | 427203. | + | 739937.i | 0.189098 | + | 0.327527i | ||||
\(349\) | 2.70539e6 | 1.18896 | 0.594479 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(350\) | −111767. | + | 1.38734e6i | −0.0487691 | + | 0.605359i | ||||
\(351\) | −801080. | −0.347063 | ||||||||
\(352\) | 169919. | + | 294309.i | 0.0730947 | + | 0.126604i | ||||
\(353\) | 1.59032e6 | − | 2.75452e6i | 0.679279 | − | 1.17655i | −0.295919 | − | 0.955213i | \(-0.595626\pi\) |
0.975198 | − | 0.221333i | \(-0.0710407\pi\) | |||||||
\(354\) | −2.46682e6 | + | 4.27266e6i | −1.04624 | + | 1.81213i | ||||
\(355\) | −610013. | − | 1.05657e6i | −0.256902 | − | 0.444968i | ||||
\(356\) | 384993. | 0.161001 | ||||||||
\(357\) | −839585. | + | 398557.i | −0.348653 | + | 0.165509i | ||||
\(358\) | −2.32020e6 | −0.956792 | ||||||||
\(359\) | 2.22985e6 | + | 3.86222e6i | 0.913145 | + | 1.58161i | 0.809595 | + | 0.586989i | \(0.199687\pi\) |
0.103550 | + | 0.994624i | \(0.466980\pi\) | |||||||
\(360\) | −433607. | + | 751030.i | −0.176336 | + | 0.305423i | ||||
\(361\) | 1.14038e6 | − | 1.97519e6i | 0.460554 | − | 0.797703i | ||||
\(362\) | −616093. | − | 1.06710e6i | −0.247101 | − | 0.427992i | ||||
\(363\) | 1.51732e6 | 0.604382 | ||||||||
\(364\) | −114083. | − | 78717.7i | −0.0451300 | − | 0.0311400i | ||||
\(365\) | 839738. | 0.329922 | ||||||||
\(366\) | 1.28294e6 | + | 2.22212e6i | 0.500615 | + | 0.867090i | ||||
\(367\) | −230623. | + | 399451.i | −0.0893795 | + | 0.154810i | −0.907249 | − | 0.420594i | \(-0.861822\pi\) |
0.817869 | + | 0.575404i | \(0.195155\pi\) | |||||||
\(368\) | 137135. | − | 237525.i | 0.0527873 | − | 0.0914302i | ||||
\(369\) | −3.89661e6 | − | 6.74913e6i | −1.48978 | − | 2.58037i | ||||
\(370\) | 941701. | 0.357609 | ||||||||
\(371\) | −565406. | − | 390134.i | −0.213268 | − | 0.147156i | ||||
\(372\) | 2.71271e6 | 1.01636 | ||||||||
\(373\) | −1.70977e6 | − | 2.96141e6i | −0.636305 | − | 1.10211i | −0.986237 | − | 0.165338i | \(-0.947129\pi\) |
0.349932 | − | 0.936775i | \(-0.386205\pi\) | |||||||
\(374\) | 159656. | − | 276532.i | 0.0590208 | − | 0.102227i | ||||
\(375\) | 1.81785e6 | − | 3.14861e6i | 0.667544 | − | 1.15622i | ||||
\(376\) | −539816. | − | 934988.i | −0.196914 | − | 0.341065i | ||||
\(377\) | 119726. | 0.0433847 | ||||||||
\(378\) | 5.61614e6 | − | 2.66603e6i | 2.02166 | − | 0.959699i | ||||
\(379\) | 16355.6 | 0.00584882 | 0.00292441 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292441 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(380\) | 74252.5 | + | 128609.i | 0.0263786 | + | 0.0456891i | ||||
\(381\) | −3.65383e6 | + | 6.32863e6i | −1.28954 | + | 2.23356i | ||||
\(382\) | −405579. | + | 702483.i | −0.142206 | + | 0.246308i | ||||
\(383\) | 1.71822e6 | + | 2.97604e6i | 0.598523 | + | 1.03667i | 0.993039 | + | 0.117784i | \(0.0375789\pi\) |
−0.394516 | + | 0.918889i | \(0.629088\pi\) | |||||||
\(384\) | 488301. | 0.168989 | ||||||||
\(385\) | 72554.6 | − | 900601.i | 0.0249467 | − | 0.309657i | ||||
\(386\) | −2.42395e6 | −0.828048 | ||||||||
\(387\) | 3.20107e6 | + | 5.54442e6i | 1.08647 | + | 1.88182i | ||||
\(388\) | −575171. | + | 996226.i | −0.193963 | + | 0.335953i | ||||
\(389\) | 2.40526e6 | − | 4.16604e6i | 0.805914 | − | 1.39588i | −0.109759 | − | 0.993958i | \(-0.535008\pi\) |
0.915673 | − | 0.401925i | \(-0.131659\pi\) | |||||||
\(390\) | 83643.1 | + | 144874.i | 0.0278464 | + | 0.0482313i | ||||
\(391\) | −257704. | −0.0852469 | ||||||||
\(392\) | 1.06178e6 | + | 172196.i | 0.348994 | + | 0.0565989i | ||||
\(393\) | −2.08606e6 | −0.681310 | ||||||||
\(394\) | −621.638 | − | 1076.71i | −0.000201742 | − | 0.000349428i | ||||
\(395\) | −461473. | + | 799295.i | −0.148817 | + | 0.257759i | ||||
\(396\) | −1.71313e6 | + | 2.96723e6i | −0.548975 | + | 0.950852i | ||||
\(397\) | 1.64924e6 | + | 2.85657e6i | 0.525180 | + | 0.909638i | 0.999570 | + | 0.0293232i | \(0.00933522\pi\) |
−0.474390 | + | 0.880315i | \(0.657331\pi\) | |||||||
\(398\) | 1.63867e6 | 0.518540 | ||||||||
\(399\) | 137133. | − | 1.70219e6i | 0.0431230 | − | 0.535275i | ||||
\(400\) | −687104. | −0.214720 | ||||||||
\(401\) | −68082.0 | − | 117921.i | −0.0211432 | − | 0.0366211i | 0.855260 | − | 0.518199i | \(-0.173397\pi\) |
−0.876403 | + | 0.481578i | \(0.840064\pi\) | |||||||
\(402\) | 1.58666e6 | − | 2.74818e6i | 0.489689 | − | 0.848166i | ||||
\(403\) | 190064. | − | 329200.i | 0.0582957 | − | 0.100971i | ||||
\(404\) | 126924. | + | 219838.i | 0.0386892 | + | 0.0670116i | ||||
\(405\) | −4.21054e6 | −1.27556 | ||||||||
\(406\) | −839368. | + | 398454.i | −0.252719 | + | 0.119967i | ||||
\(407\) | 3.72054e6 | 1.11332 | ||||||||
\(408\) | −229403. | − | 397338.i | −0.0682258 | − | 0.118171i | ||||
\(409\) | −1.37435e6 | + | 2.38044e6i | −0.406245 | + | 0.703637i | −0.994466 | − | 0.105064i | \(-0.966495\pi\) |
0.588220 | + | 0.808701i | \(0.299829\pi\) | |||||||
\(410\) | −507270. | + | 878617.i | −0.149032 | + | 0.258131i | ||||
\(411\) | −2.79652e6 | − | 4.84372e6i | −0.816608 | − | 1.41441i | ||||
\(412\) | −2.56918e6 | −0.745677 | ||||||||
\(413\) | −4.41597e6 | − | 3.04705e6i | −1.27395 | − | 0.879032i | ||||
\(414\) | 2.76520e6 | 0.792913 | ||||||||
\(415\) | 235425. | + | 407767.i | 0.0671014 | + | 0.116223i | ||||
\(416\) | 34212.4 | − | 59257.6i | 0.00969282 | − | 0.0167884i | ||||
\(417\) | −1.16640e6 | + | 2.02026e6i | −0.328479 | + | 0.568942i | ||||
\(418\) | 293362. | + | 508118.i | 0.0821228 | + | 0.142241i | ||||
\(419\) | −1.87219e6 | −0.520973 | −0.260486 | − | 0.965478i | \(-0.583883\pi\) | ||||
−0.260486 | + | 0.965478i | \(0.583883\pi\) | |||||||
\(420\) | −1.06854e6 | − | 737303.i | −0.295576 | − | 0.203949i | ||||
\(421\) | 655225. | 0.180171 | 0.0900856 | − | 0.995934i | \(-0.471286\pi\) | ||||
0.0900856 | + | 0.995934i | \(0.471286\pi\) | |||||||
\(422\) | −882677. | − | 1.52884e6i | −0.241280 | − | 0.417909i | ||||
\(423\) | 5.44243e6 | − | 9.42657e6i | 1.47891 | − | 2.56155i | ||||
\(424\) | 169561. | − | 293688.i | 0.0458047 | − | 0.0793361i | ||||
\(425\) | 322800. | + | 559107.i | 0.0866886 | + | 0.150149i | ||||
\(426\) | −6.92591e6 | −1.84907 | ||||||||
\(427\) | −2.52072e6 | + | 1.19660e6i | −0.669044 | + | 0.317600i | ||||
\(428\) | −3.28075e6 | −0.865693 | ||||||||
\(429\) | 330464. | + | 572380.i | 0.0866923 | + | 0.150155i | ||||
\(430\) | 416723. | − | 721786.i | 0.108687 | − | 0.188251i | ||||
\(431\) | −3.18845e6 | + | 5.52256e6i | −0.826773 | + | 1.43201i | 0.0737832 | + | 0.997274i | \(0.476493\pi\) |
−0.900556 | + | 0.434739i | \(0.856841\pi\) | |||||||
\(432\) | 1.53452e6 | + | 2.65787e6i | 0.395606 | + | 0.685210i | ||||
\(433\) | 4.80003e6 | 1.23034 | 0.615168 | − | 0.788396i | \(-0.289088\pi\) | ||||
0.615168 | + | 0.788396i | \(0.289088\pi\) | |||||||
\(434\) | −236891. | + | 2.94047e6i | −0.0603704 | + | 0.749362i | ||||
\(435\) | 1.12141e6 | 0.284145 | ||||||||
\(436\) | 900354. | + | 1.55946e6i | 0.226828 | + | 0.392878i | ||||
\(437\) | 236761. | − | 410082.i | 0.0593071 | − | 0.102723i | ||||
\(438\) | 2.38354e6 | − | 4.12841e6i | 0.593658 | − | 1.02825i | ||||
\(439\) | 2.79754e6 | + | 4.84548e6i | 0.692811 | + | 1.19998i | 0.970913 | + | 0.239432i | \(0.0769612\pi\) |
−0.278102 | + | 0.960551i | \(0.589705\pi\) | |||||||
\(440\) | 446038. | 0.109835 | ||||||||
\(441\) | 3.84893e6 | + | 1.01387e7i | 0.942417 | + | 2.48248i | ||||
\(442\) | −64291.7 | −0.0156531 | ||||||||
\(443\) | −2.07005e6 | − | 3.58543e6i | −0.501154 | − | 0.868024i | −0.999999 | − | 0.00133297i | \(-0.999576\pi\) |
0.498845 | − | 0.866691i | \(-0.333758\pi\) | |||||||
\(444\) | 2.67295e6 | − | 4.62969e6i | 0.643478 | − | 1.11454i | ||||
\(445\) | 252651. | − | 437605.i | 0.0604814 | − | 0.104757i | ||||
\(446\) | 530267. | + | 918449.i | 0.126228 | + | 0.218634i | ||||
\(447\) | 2.74688e6 | 0.650237 | ||||||||
\(448\) | −42641.5 | + | 529298.i | −0.0100378 | + | 0.124596i | ||||
\(449\) | −305966. | −0.0716239 | −0.0358119 | − | 0.999359i | \(-0.511402\pi\) | ||||
−0.0358119 | + | 0.999359i | \(0.511402\pi\) | |||||||
\(450\) | −3.46370e6 | − | 5.99930e6i | −0.806322 | − | 1.39659i | ||||
\(451\) | −2.00416e6 | + | 3.47131e6i | −0.463971 | + | 0.803622i | ||||
\(452\) | 946660. | − | 1.63966e6i | 0.217945 | − | 0.377493i | ||||
\(453\) | 795992. | + | 1.37870e6i | 0.182248 | + | 0.315663i | ||||
\(454\) | 5.72176e6 | 1.30284 | ||||||||
\(455\) | −164342. | + | 78014.4i | −0.0372151 | + | 0.0176663i | ||||
\(456\) | 843041. | 0.189861 | ||||||||
\(457\) | −446304. | − | 773021.i | −0.0999632 | − | 0.173141i | 0.811706 | − | 0.584066i | \(-0.198539\pi\) |
−0.911669 | + | 0.410925i | \(0.865206\pi\) | |||||||
\(458\) | −2.51610e6 | + | 4.35801e6i | −0.560485 | + | 0.970789i | ||||
\(459\) | 1.44183e6 | − | 2.49732e6i | 0.319435 | − | 0.553278i | ||||
\(460\) | −179990. | − | 311752.i | −0.0396601 | − | 0.0686933i | ||||
\(461\) | −3.01465e6 | −0.660670 | −0.330335 | − | 0.943864i | \(-0.607162\pi\) | ||||
−0.330335 | + | 0.943864i | \(0.607162\pi\) | |||||||
\(462\) | −4.22169e6 | − | 2.91299e6i | −0.920198 | − | 0.634943i | ||||
\(463\) | 3.45497e6 | 0.749017 | 0.374508 | − | 0.927224i | \(-0.377812\pi\) | ||||
0.374508 | + | 0.927224i | \(0.377812\pi\) | |||||||
\(464\) | −229344. | − | 397235.i | −0.0494529 | − | 0.0856549i | ||||
\(465\) | 1.78022e6 | − | 3.08342e6i | 0.381804 | − | 0.661303i | ||||
\(466\) | 449446. | − | 778464.i | 0.0958767 | − | 0.166063i | ||||
\(467\) | −1.41888e6 | − | 2.45757e6i | −0.301060 | − | 0.521451i | 0.675316 | − | 0.737528i | \(-0.264007\pi\) |
−0.976376 | + | 0.216077i | \(0.930674\pi\) | |||||||
\(468\) | 689860. | 0.145595 | ||||||||
\(469\) | 2.84036e6 | + | 1.95987e6i | 0.596268 | + | 0.411429i | ||||
\(470\) | −1.41702e6 | −0.295890 | ||||||||
\(471\) | −4.17995e6 | − | 7.23989e6i | −0.868198 | − | 1.50376i | ||||
\(472\) | 1.32431e6 | − | 2.29378e6i | 0.273612 | − | 0.473910i | ||||
\(473\) | 1.64642e6 | − | 2.85169e6i | 0.338367 | − | 0.586069i | ||||
\(474\) | 2.61972e6 | + | 4.53748e6i | 0.535561 | + | 0.927618i | ||||
\(475\) | −1.18627e6 | −0.241240 | ||||||||
\(476\) | 450731. | − | 213965.i | 0.0911800 | − | 0.0432839i | ||||
\(477\) | 3.41903e6 | 0.688028 | ||||||||
\(478\) | 2.56386e6 | + | 4.44073e6i | 0.513244 | + | 0.888965i | ||||
\(479\) | 2.35221e6 | − | 4.07415e6i | 0.468422 | − | 0.811331i | −0.530926 | − | 0.847418i | \(-0.678156\pi\) |
0.999349 | + | 0.0360866i | \(0.0114892\pi\) | |||||||
\(480\) | 320447. | − | 555031.i | 0.0634824 | − | 0.109955i | ||||
\(481\) | −374556. | − | 648750.i | −0.0738167 | − | 0.127854i | ||||
\(482\) | 2.30450e6 | 0.451813 | ||||||||
\(483\) | −332414. | + | 4.12616e6i | −0.0648352 | + | 0.804783i | ||||
\(484\) | −814574. | −0.158058 | ||||||||
\(485\) | 754912. | + | 1.30755e6i | 0.145728 | + | 0.252408i | ||||
\(486\) | −6.12494e6 | + | 1.06087e7i | −1.17628 | + | 2.03738i | ||||
\(487\) | −2.08317e6 | + | 3.60816e6i | −0.398018 | + | 0.689387i | −0.993481 | − | 0.113995i | \(-0.963635\pi\) |
0.595463 | + | 0.803383i | \(0.296969\pi\) | |||||||
\(488\) | −688745. | − | 1.19294e6i | −0.130921 | − | 0.226762i | ||||
\(489\) | −1.86811e7 | −3.53290 | ||||||||
\(490\) | 892518. | − | 1.09387e6i | 0.167929 | − | 0.205815i | ||||
\(491\) | 1.57876e6 | 0.295537 | 0.147768 | − | 0.989022i | \(-0.452791\pi\) | ||||
0.147768 | + | 0.989022i | \(0.452791\pi\) | |||||||
\(492\) | 2.87970e6 | + | 4.98779e6i | 0.536333 | + | 0.928956i | ||||
\(493\) | −215491. | + | 373241.i | −0.0399311 | + | 0.0691627i | ||||
\(494\) | 59067.0 | − | 102307.i | 0.0108900 | − | 0.0188620i | ||||
\(495\) | 2.24848e6 | + | 3.89449e6i | 0.412455 | + | 0.714393i | ||||
\(496\) | −1.45632e6 | −0.265798 | ||||||||
\(497\) | 604815. | − | 7.50741e6i | 0.109833 | − | 1.36332i | ||||
\(498\) | 2.67294e6 | 0.482966 | ||||||||
\(499\) | −778559. | − | 1.34850e6i | −0.139972 | − | 0.242438i | 0.787514 | − | 0.616297i | \(-0.211368\pi\) |
−0.927486 | + | 0.373859i | \(0.878034\pi\) | |||||||
\(500\) | −975912. | + | 1.69033e6i | −0.174576 | + | 0.302375i | ||||
\(501\) | 4.38107e6 | − | 7.58824e6i | 0.779806 | − | 1.35066i | ||||
\(502\) | −1.21808e6 | − | 2.10978e6i | −0.215733 | − | 0.373660i | ||||
\(503\) | −1.19459e6 | −0.210523 | −0.105261 | − | 0.994445i | \(-0.533568\pi\) | ||||
−0.105261 | + | 0.994445i | \(0.533568\pi\) | |||||||
\(504\) | −4.83641e6 | + | 2.29588e6i | −0.848099 | + | 0.402599i | ||||
\(505\) | 333175. | 0.0581358 | ||||||||
\(506\) | −711118. | − | 1.23169e6i | −0.123471 | − | 0.213858i | ||||
\(507\) | −5.46638e6 | + | 9.46805e6i | −0.944452 | + | 1.63584i | ||||
\(508\) | 1.96156e6 | − | 3.39752e6i | 0.337242 | − | 0.584121i | ||||
\(509\) | −1.58428e6 | − | 2.74406e6i | −0.271043 | − | 0.469461i | 0.698086 | − | 0.716014i | \(-0.254035\pi\) |
−0.969129 | + | 0.246553i | \(0.920702\pi\) | |||||||
\(510\) | −602183. | −0.102519 | ||||||||
\(511\) | 4.26688e6 | + | 2.94418e6i | 0.722867 | + | 0.498783i | ||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 2.64932e6 | + | 4.58875e6i | 0.444468 | + | 0.769841i | ||||
\(514\) | 2.06134e6 | − | 3.57034e6i | 0.344145 | − | 0.596077i | ||||
\(515\) | −1.68602e6 | + | 2.92028e6i | −0.280121 | + | 0.485183i | ||||
\(516\) | −2.36568e6 | − | 4.09747e6i | −0.391139 | − | 0.677473i | ||||
\(517\) | −5.59846e6 | −0.921175 | ||||||||
\(518\) | 4.78497e6 | + | 3.30166e6i | 0.783529 | + | 0.540640i | ||||
\(519\) | −2.12853e7 | −3.46865 | ||||||||
\(520\) | −44903.7 | − | 77775.6i | −0.00728239 | − | 0.0126135i | ||||
\(521\) | 503289. | − | 871722.i | 0.0812312 | − | 0.140697i | −0.822548 | − | 0.568696i | \(-0.807448\pi\) |
0.903779 | + | 0.427999i | \(0.140781\pi\) | |||||||
\(522\) | 2.31225e6 | − | 4.00493e6i | 0.371414 | − | 0.643307i | ||||
\(523\) | −4.39493e6 | − | 7.61224e6i | −0.702583 | − | 1.21691i | −0.967557 | − | 0.252653i | \(-0.918697\pi\) |
0.264974 | − | 0.964255i | \(-0.414637\pi\) | |||||||
\(524\) | 1.11990e6 | 0.178177 | ||||||||
\(525\) | 9.36840e6 | − | 4.44725e6i | 1.48343 | − | 0.704196i | ||||
\(526\) | 3.64234e6 | 0.574006 | ||||||||
\(527\) | 684175. | + | 1.18503e6i | 0.107310 | + | 0.185867i | ||||
\(528\) | 1.26605e6 | − | 2.19286e6i | 0.197636 | − | 0.342315i | ||||
\(529\) | 2.64426e6 | − | 4.57999e6i | 0.410832 | − | 0.711582i | ||||
\(530\) | −222548. | − | 385465.i | −0.0344140 | − | 0.0596067i | ||||
\(531\) | 2.67035e7 | 4.10990 | ||||||||
\(532\) | −73619.7 | + | 913823.i | −0.0112776 | + | 0.139985i | ||||
\(533\) | 807055. | 0.123051 | ||||||||
\(534\) | −1.43427e6 | − | 2.48422e6i | −0.217659 | − | 0.376996i | ||||
\(535\) | −2.15299e6 | + | 3.72909e6i | −0.325206 | + | 0.563273i | ||||
\(536\) | −851800. | + | 1.47536e6i | −0.128064 | + | 0.221813i | ||||
\(537\) | 8.64376e6 | + | 1.49714e7i | 1.29350 | + | 2.24041i | ||||
\(538\) | −5.68399e6 | −0.846638 | ||||||||
\(539\) | 3.52623e6 | − | 4.32176e6i | 0.522804 | − | 0.640749i | ||||
\(540\) | 4.02811e6 | 0.594453 | ||||||||
\(541\) | 1.77432e6 | + | 3.07321e6i | 0.260639 | + | 0.451439i | 0.966412 | − | 0.256999i | \(-0.0827336\pi\) |
−0.705773 | + | 0.708438i | \(0.749400\pi\) | |||||||
\(542\) | −595059. | + | 1.03067e6i | −0.0870086 | + | 0.150703i | ||||
\(543\) | −4.59043e6 | + | 7.95086e6i | −0.668119 | + | 1.15722i | ||||
\(544\) | 123155. | + | 213310.i | 0.0178424 | + | 0.0309040i | ||||
\(545\) | 2.36343e6 | 0.340841 | ||||||||
\(546\) | −82930.3 | + | 1.02939e6i | −0.0119051 | + | 0.147774i | ||||
\(547\) | 4.68179e6 | 0.669027 | 0.334513 | − | 0.942391i | \(-0.391428\pi\) | ||||
0.334513 | + | 0.942391i | \(0.391428\pi\) | |||||||
\(548\) | 1.50131e6 | + | 2.60035e6i | 0.213560 | + | 0.369896i | ||||
\(549\) | 6.94394e6 | − | 1.20273e7i | 0.983276 | − | 1.70308i | ||||
\(550\) | −1.78150e6 | + | 3.08564e6i | −0.251118 | + | 0.434950i | ||||
\(551\) | −395957. | − | 685818.i | −0.0555609 | − | 0.0962343i | ||||
\(552\) | −2.04355e6 | −0.285456 | ||||||||
\(553\) | −5.14722e6 | + | 2.44342e6i | −0.715747 | + | 0.339771i | ||||
\(554\) | −3.39845e6 | −0.470442 | ||||||||
\(555\) | −3.50825e6 | − | 6.07647e6i | −0.483457 | − | 0.837372i | ||||
\(556\) | 626181. | − | 1.08458e6i | 0.0859040 | − | 0.148790i | ||||
\(557\) | −2.89754e6 | + | 5.01868e6i | −0.395723 | + | 0.685412i | −0.993193 | − | 0.116479i | \(-0.962839\pi\) |
0.597470 | + | 0.801891i | \(0.296173\pi\) | |||||||
\(558\) | −7.34130e6 | − | 1.27155e7i | −0.998132 | − | 1.72881i | ||||
\(559\) | −662997. | −0.0897392 | ||||||||
\(560\) | 573647. | + | 395821.i | 0.0772992 | + | 0.0533370i | ||||
\(561\) | −2.37915e6 | −0.319165 | ||||||||
\(562\) | −15361.0 | − | 26606.0i | −0.00205153 | − | 0.00355336i | ||||
\(563\) | 3.79852e6 | − | 6.57922e6i | 0.505060 | − | 0.874789i | −0.494923 | − | 0.868937i | \(-0.664804\pi\) |
0.999983 | − | 0.00585257i | \(-0.00186294\pi\) | |||||||
\(564\) | −4.02210e6 | + | 6.96648e6i | −0.532421 | + | 0.922180i | ||||
\(565\) | −1.24249e6 | − | 2.15206e6i | −0.163747 | − | 0.283617i | ||||
\(566\) | 3.94147e6 | 0.517151 | ||||||||
\(567\) | −2.13946e7 | − | 1.47624e7i | −2.79477 | − | 1.92841i | ||||
\(568\) | 3.71817e6 | 0.483569 | ||||||||
\(569\) | 4.90850e6 | + | 8.50176e6i | 0.635576 | + | 1.10085i | 0.986393 | + | 0.164406i | \(0.0525708\pi\) |
−0.350816 | + | 0.936444i | \(0.614096\pi\) | |||||||
\(570\) | 553246. | − | 958250.i | 0.0713232 | − | 0.123535i | ||||
\(571\) | −2.62944e6 | + | 4.55432e6i | −0.337499 | + | 0.584566i | −0.983962 | − | 0.178380i | \(-0.942914\pi\) |
0.646462 | + | 0.762946i | \(0.276248\pi\) | |||||||
\(572\) | −177409. | − | 307282.i | −0.0226718 | − | 0.0392687i | ||||
\(573\) | 6.04384e6 | 0.769000 | ||||||||
\(574\) | −5.65803e6 | + | 2.68591e6i | −0.716779 | + | 0.340261i | ||||
\(575\) | 2.87555e6 | 0.362703 | ||||||||
\(576\) | −1.32147e6 | − | 2.28885e6i | −0.165959 | − | 0.287450i | ||||
\(577\) | −4.31734e6 | + | 7.47785e6i | −0.539855 | + | 0.935056i | 0.459057 | + | 0.888407i | \(0.348187\pi\) |
−0.998911 | + | 0.0466486i | \(0.985146\pi\) | |||||||
\(578\) | −2.72400e6 | + | 4.71810e6i | −0.339146 | + | 0.587419i | ||||
\(579\) | 9.03028e6 | + | 1.56409e7i | 1.11945 | + | 1.93895i | ||||
\(580\) | −602027. | −0.0743098 | ||||||||
\(581\) | −233418. | + | 2.89736e6i | −0.0286876 | + | 0.356092i | ||||
\(582\) | 8.57106e6 | 1.04888 | ||||||||
\(583\) | −879261. | − | 1.52292e6i | −0.107139 | − | 0.185570i | ||||
\(584\) | −1.27960e6 | + | 2.21633e6i | −0.155254 | + | 0.268908i | ||||
\(585\) | 452720. | − | 784135.i | 0.0546941 | − | 0.0947329i | ||||
\(586\) | −4.33869e6 | − | 7.51483e6i | −0.521932 | − | 0.904014i | ||||
\(587\) | −3.32014e6 | −0.397705 | −0.198852 | − | 0.980029i | \(-0.563721\pi\) | ||||
−0.198852 | + | 0.980029i | \(0.563721\pi\) | |||||||
\(588\) | −2.84446e6 | − | 7.49277e6i | −0.339279 | − | 0.893715i | ||||
\(589\) | −2.51430e6 | −0.298627 | ||||||||
\(590\) | −1.73816e6 | − | 3.01058e6i | −0.205570 | − | 0.356058i | ||||
\(591\) | −4631.75 | + | 8022.43i | −0.000545477 | + | 0.000944794i | ||||
\(592\) | −1.43497e6 | + | 2.48545e6i | −0.168283 | + | 0.291474i | ||||
\(593\) | 3.20001e6 | + | 5.54257e6i | 0.373692 | + | 0.647254i | 0.990130 | − | 0.140149i | \(-0.0447583\pi\) |
−0.616438 | + | 0.787403i | \(0.711425\pi\) | |||||||
\(594\) | 1.59146e7 | 1.85067 | ||||||||
\(595\) | 52586.4 | − | 652741.i | 0.00608949 | − | 0.0755873i | ||||
\(596\) | −1.47466e6 | −0.170050 | ||||||||
\(597\) | −6.10475e6 | − | 1.05737e7i | −0.701022 | − | 1.21421i | ||||
\(598\) | −143180. | + | 247995.i | −0.0163730 | + | 0.0283589i | ||||
\(599\) | −3.74931e6 | + | 6.49400e6i | −0.426957 | + | 0.739512i | −0.996601 | − | 0.0823800i | \(-0.973748\pi\) |
0.569644 | + | 0.821892i | \(0.307081\pi\) | |||||||
\(600\) | 2.55976e6 | + | 4.43364e6i | 0.290283 | + | 0.502785i | ||||
\(601\) | −227052. | −0.0256412 | −0.0128206 | − | 0.999918i | \(-0.504081\pi\) | ||||
−0.0128206 | + | 0.999918i | \(0.504081\pi\) | |||||||
\(602\) | 4.64808e6 | − | 2.20648e6i | 0.522736 | − | 0.248147i | ||||
\(603\) | −1.71757e7 | −1.92363 | ||||||||
\(604\) | −427328. | − | 740153.i | −0.0476616 | − | 0.0825523i | ||||
\(605\) | −534564. | + | 925892.i | −0.0593761 | + | 0.102842i | ||||
\(606\) | 945693. | − | 1.63799e6i | 0.104609 | − | 0.181188i | ||||
\(607\) | −8.15183e6 | − | 1.41194e7i | −0.898015 | − | 1.55541i | −0.830029 | − | 0.557721i | \(-0.811676\pi\) |
−0.0679862 | − | 0.997686i | \(-0.521657\pi\) | |||||||
\(608\) | −452586. | −0.0496527 | ||||||||
\(609\) | 5.69810e6 | + | 3.93173e6i | 0.622568 | + | 0.429576i | ||||
\(610\) | −1.80796e6 | −0.196727 | ||||||||
\(611\) | 563610. | + | 976202.i | 0.0610767 | + | 0.105788i | ||||
\(612\) | −1.24165e6 | + | 2.15060e6i | −0.134005 | + | 0.232103i | ||||
\(613\) | 5.20312e6 | − | 9.01207e6i | 0.559259 | − | 0.968664i | −0.438300 | − | 0.898829i | \(-0.644419\pi\) |
0.997559 | − | 0.0698355i | \(-0.0222474\pi\) | |||||||
\(614\) | −2.78186e6 | − | 4.81833e6i | −0.297793 | − | 0.515793i | ||||
\(615\) | 7.55921e6 | 0.805914 | ||||||||
\(616\) | 2.26641e6 | + | 1.56384e6i | 0.240651 | + | 0.166050i | ||||
\(617\) | 4.74140e6 | 0.501411 | 0.250705 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250705 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(618\) | 9.57131e6 | + | 1.65780e7i | 1.00809 | + | 1.74607i | ||||
\(619\) | 5.42668e6 | − | 9.39929e6i | 0.569256 | − | 0.985981i | −0.427383 | − | 0.904070i | \(-0.640565\pi\) |
0.996640 | − | 0.0819103i | \(-0.0261021\pi\) | |||||||
\(620\) | −955708. | + | 1.65533e6i | −0.0998495 | + | 0.172944i | ||||
\(621\) | −6.42202e6 | − | 1.11233e7i | −0.668255 | − | 1.15745i | ||||
\(622\) | −8.15177e6 | −0.844843 | ||||||||
\(623\) | 2.81804e6 | − | 1.33775e6i | 0.290889 | − | 0.138087i | ||||
\(624\) | −509824. | −0.0524154 | ||||||||
\(625\) | −2.91287e6 | − | 5.04523e6i | −0.298277 | − | 0.516632i | ||||
\(626\) | −2.33915e6 | + | 4.05154e6i | −0.238574 | + | 0.413222i | ||||
\(627\) | 2.18581e6 | − | 3.78593e6i | 0.222046 | − | 0.384595i | ||||
\(628\) | 2.24400e6 | + | 3.88673e6i | 0.227052 | + | 0.393265i | ||||
\(629\) | 2.69659e6 | 0.271762 | ||||||||
\(630\) | −564260. | + | 7.00401e6i | −0.0566406 | + | 0.703065i | ||||
\(631\) | 1.58978e7 | 1.58951 | 0.794757 | − | 0.606928i | \(-0.207598\pi\) | ||||
0.794757 | + | 0.606928i | \(0.207598\pi\) | |||||||
\(632\) | −1.40639e6 | − | 2.43595e6i | −0.140060 | − | 0.242591i | ||||
\(633\) | −6.57672e6 | + | 1.13912e7i | −0.652379 | + | 1.12995i | ||||
\(634\) | 1.60227e6 | − | 2.77522e6i | 0.158312 | − | 0.274204i | ||||
\(635\) | −2.57455e6 | − | 4.45925e6i | −0.253377 | − | 0.438861i | ||||
\(636\) | −2.52675e6 | −0.247696 | ||||||||
\(637\) | −1.10858e6 | − | 179786.i | −0.108247 | − | 0.0175553i | ||||
\(638\) | −2.37854e6 | −0.231344 | ||||||||
\(639\) | 1.87433e7 | + | 3.24644e7i | 1.81591 | + | 3.14525i | ||||
\(640\) | −172032. | + | 297968.i | −0.0166020 | + | 0.0287554i | ||||
\(641\) | −5.59139e6 | + | 9.68457e6i | −0.537496 | + | 0.930970i | 0.461543 | + | 0.887118i | \(0.347296\pi\) |
−0.999038 | + | 0.0438515i | \(0.986037\pi\) | |||||||
\(642\) | 1.22222e7 | + | 2.11695e7i | 1.17034 | + | 2.02709i | ||||
\(643\) | 1.55983e6 | 0.148782 | 0.0743909 | − | 0.997229i | \(-0.476299\pi\) | ||||
0.0743909 | + | 0.997229i | \(0.476299\pi\) | |||||||
\(644\) | 178456. | − | 2.21513e6i | 0.0169557 | − | 0.210467i | ||||
\(645\) | −6.20991e6 | −0.587741 | ||||||||
\(646\) | 212624. | + | 368276.i | 0.0200462 | + | 0.0347210i | ||||
\(647\) | 7.74118e6 | − | 1.34081e7i | 0.727020 | − | 1.25924i | −0.231117 | − | 0.972926i | \(-0.574238\pi\) |
0.958137 | − | 0.286310i | \(-0.0924286\pi\) | |||||||
\(648\) | 6.41606e6 | − | 1.11129e7i | 0.600248 | − | 1.03966i | ||||
\(649\) | −6.86726e6 | − | 1.18944e7i | −0.639988 | − | 1.10849i | ||||
\(650\) | 717391. | 0.0665997 | ||||||||
\(651\) | 1.98563e7 | − | 9.42595e6i | 1.83631 | − | 0.871711i | ||||
\(652\) | 1.00290e7 | 0.923925 | ||||||||
\(653\) | −307376. | − | 532391.i | −0.0282090 | − | 0.0488593i | 0.851576 | − | 0.524231i | \(-0.175647\pi\) |
−0.879785 | + | 0.475371i | \(0.842314\pi\) | |||||||
\(654\) | 6.70843e6 | − | 1.16193e7i | 0.613305 | − | 1.06228i | ||||
\(655\) | 734934. | − | 1.27294e6i | 0.0669337 | − | 0.115933i | ||||
\(656\) | −1.54597e6 | − | 2.67769e6i | −0.140262 | − | 0.242941i | ||||
\(657\) | −2.58019e7 | −2.33205 | ||||||||
\(658\) | −7.20015e6 | − | 4.96815e6i | −0.648301 | − | 0.447332i | ||||
\(659\) | −1.32697e7 | −1.19028 | −0.595139 | − | 0.803623i | \(-0.702903\pi\) | ||||
−0.595139 | + | 0.803623i | \(0.702903\pi\) | |||||||
\(660\) | −1.66169e6 | − | 2.87813e6i | −0.148487 | − | 0.257188i | ||||
\(661\) | −2.51792e6 | + | 4.36116e6i | −0.224150 | + | 0.388238i | −0.956064 | − | 0.293158i | \(-0.905294\pi\) |
0.731914 | + | 0.681397i | \(0.238627\pi\) | |||||||
\(662\) | 5.29902e6 | − | 9.17817e6i | 0.469949 | − | 0.813975i | ||||
\(663\) | 239515. | + | 414852.i | 0.0211616 | + | 0.0366530i | ||||
\(664\) | −1.43497e6 | −0.126306 | ||||||||
\(665\) | 990391. | + | 683377.i | 0.0868466 | + | 0.0599247i | ||||
\(666\) | −2.89348e7 | −2.52776 | ||||||||
\(667\) | 959811. | + | 1.66244e6i | 0.0835355 | + | 0.144688i | ||||
\(668\) | −2.35198e6 | + | 4.07375e6i | −0.203935 | + | 0.353226i | ||||
\(669\) | 3.95095e6 | − | 6.84325e6i | 0.341300 | − | 0.591149i | ||||
\(670\) | 1.11799e6 | + | 1.93641e6i | 0.0962166 | + | 0.166652i | ||||
\(671\) | −7.14301e6 | −0.612457 | ||||||||
\(672\) | 3.57423e6 | − | 1.69672e6i | 0.305323 | − | 0.144939i | ||||
\(673\) | 8.28068e6 | 0.704739 | 0.352369 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352369 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(674\) | −6.80112e6 | − | 1.17799e7i | −0.576675 | − | 0.998830i | ||||
\(675\) | −1.60885e7 | + | 2.78661e7i | −1.35911 | + | 2.35405i | ||||
\(676\) | 2.93462e6 | − | 5.08292e6i | 0.246994 | − | 0.427805i | ||||
\(677\) | 7.62563e6 | + | 1.32080e7i | 0.639446 | + | 1.10755i | 0.985554 | + | 0.169359i | \(0.0541698\pi\) |
−0.346108 | + | 0.938195i | \(0.612497\pi\) | |||||||
\(678\) | −1.41069e7 | −1.17857 | ||||||||
\(679\) | −748480. | + | 9.29068e6i | −0.0623025 | + | 0.773345i | ||||
\(680\) | 323282. | 0.0268107 | ||||||||
\(681\) | −2.13161e7 | − | 3.69205e7i | −1.76132 | − | 3.05070i | ||||
\(682\) | −3.77588e6 | + | 6.54002e6i | −0.310855 | + | 0.538416i | ||||
\(683\) | −3.94337e6 | + | 6.83011e6i | −0.323456 | + | 0.560243i | −0.981199 | − | 0.193000i | \(-0.938178\pi\) |
0.657743 | + | 0.753243i | \(0.271511\pi\) | |||||||
\(684\) | −2.28149e6 | − | 3.95166e6i | −0.186457 | − | 0.322953i | ||||
\(685\) | 3.94094e6 | 0.320903 | ||||||||
\(686\) | 8.37025e6 | − | 2.42896e6i | 0.679091 | − | 0.197065i | ||||
\(687\) | 3.74943e7 | 3.03091 | ||||||||
\(688\) | 1.27001e6 | + | 2.19973e6i | 0.102291 | + | 0.177173i | ||||
\(689\) | −177035. | + | 306633.i | −0.0142073 | + | 0.0246077i | ||||
\(690\) | −1.34108e6 | + | 2.32282e6i | −0.107234 | + | 0.185735i | ||||
\(691\) | 830950. | + | 1.43925e6i | 0.0662033 | + | 0.114667i | 0.897227 | − | 0.441569i | \(-0.145578\pi\) |
−0.831024 | + | 0.556237i | \(0.812245\pi\) | |||||||
\(692\) | 1.14270e7 | 0.907124 | ||||||||
\(693\) | −2.22932e6 | + | 2.76720e7i | −0.176336 | + | 2.18881i | ||||
\(694\) | 2.47084e6 | 0.194736 | ||||||||
\(695\) | −821863. | − | 1.42351e6i | −0.0645413 | − | 0.111789i | ||||
\(696\) | −1.70881e6 | + | 2.95975e6i | −0.133712 | + | 0.231596i | ||||
\(697\) | −1.45258e6 | + | 2.51595e6i | −0.113256 | + | 0.196164i | ||||
\(698\) | 5.41078e6 | + | 9.37175e6i | 0.420360 | + | 0.728085i | ||||
\(699\) | −6.69754e6 | −0.518469 | ||||||||
\(700\) | −5.02942e6 | + | 2.38751e6i | −0.387947 | + | 0.184162i | ||||
\(701\) | −1.39364e7 | −1.07117 | −0.535583 | − | 0.844483i | \(-0.679908\pi\) | ||||
−0.535583 | + | 0.844483i | \(0.679908\pi\) | |||||||
\(702\) | −1.60216e6 | − | 2.77502e6i | −0.122705 | − | 0.212532i | ||||
\(703\) | −2.47745e6 | + | 4.29107e6i | −0.189068 | + | 0.327475i | ||||
\(704\) | −679677. | + | 1.17724e6i | −0.0516858 | + | 0.0895224i | ||||
\(705\) | 5.27901e6 | + | 9.14351e6i | 0.400018 | + | 0.692851i | ||||
\(706\) | 1.27226e7 | 0.960646 | ||||||||
\(707\) | 1.69293e6 | + | 1.16813e6i | 0.127377 | + | 0.0878908i | ||||
\(708\) | −1.97346e7 | −1.47960 | ||||||||
\(709\) | 5.09368e6 | + | 8.82252e6i | 0.380554 | + | 0.659139i | 0.991142 | − | 0.132810i | \(-0.0424000\pi\) |
−0.610587 | + | 0.791949i | \(0.709067\pi\) | |||||||
\(710\) | 2.44005e6 | − | 4.22629e6i | 0.181657 | − | 0.314640i | ||||
\(711\) | 1.41793e7 | − | 2.45592e7i | 1.05191 | − | 1.82197i | ||||
\(712\) | 769985. | + | 1.33365e6i | 0.0569223 | + | 0.0985923i | ||||
\(713\) | 6.09473e6 | 0.448984 | ||||||||
\(714\) | −3.05981e6 | − | 2.11129e6i | −0.224620 | − | 0.154990i | ||||
\(715\) | −465699. | −0.0340675 | ||||||||
\(716\) | −4.64040e6 | − | 8.03740e6i | −0.338277 | − | 0.585913i | ||||
\(717\) | 1.91030e7 | − | 3.30874e7i | 1.38773 | − | 2.40361i | ||||
\(718\) | −8.91940e6 | + | 1.54489e7i | −0.645691 | + | 1.11837i | ||||
\(719\) | −6.95844e6 | − | 1.20524e7i | −0.501983 | − | 0.869461i | −0.999997 | − | 0.00229184i | \(-0.999270\pi\) |
0.498014 | − | 0.867169i | \(-0.334063\pi\) | |||||||
\(720\) | −3.46886e6 | −0.249376 | ||||||||
\(721\) | −1.88057e7 | + | 8.92721e6i | −1.34726 | + | 0.639555i | ||||
\(722\) | 9.12301e6 | 0.651321 | ||||||||
\(723\) | −8.58527e6 | − | 1.48701e7i | −0.610813 | − | 1.05796i | ||||
\(724\) | 2.46437e6 | − | 4.26841e6i | 0.174727 | − | 0.302636i | ||||
\(725\) | 2.40452e6 | − | 4.16476e6i | 0.169896 | − | 0.294269i | ||||
\(726\) | 3.03464e6 | + | 5.25616e6i | 0.213681 | + | 0.370107i | ||||
\(727\) | 3.42063e6 | 0.240033 | 0.120016 | − | 0.992772i | \(-0.461705\pi\) | ||||
0.120016 | + | 0.992772i | \(0.461705\pi\) | |||||||
\(728\) | 44521.1 | − | 552629.i | 0.00311342 | − | 0.0386461i | ||||
\(729\) | 4.25504e7 | 2.96541 | ||||||||
\(730\) | 1.67948e6 | + | 2.90894e6i | 0.116645 | + | 0.202035i | ||||
\(731\) | 1.19330e6 | − | 2.06686e6i | 0.0825955 | − | 0.143060i | ||||
\(732\) | −5.13176e6 | + | 8.88846e6i | −0.353988 | + | 0.613125i | ||||
\(733\) | 5.15810e6 | + | 8.93410e6i | 0.354593 | + | 0.614173i | 0.987048 | − | 0.160424i | \(-0.0512861\pi\) |
−0.632455 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(734\) | −1.84499e6 | −0.126402 | ||||||||
\(735\) | −1.03834e7 | − | 1.68395e6i | −0.708959 | − | 0.114977i | ||||
\(736\) | 1.09708e6 | 0.0746525 | ||||||||
\(737\) | 4.41703e6 | + | 7.65052e6i | 0.299545 | + | 0.518827i | ||||
\(738\) | 1.55864e7 | − | 2.69965e7i | 1.05343 | − | 1.82460i | ||||
\(739\) | 5.19448e6 | − | 8.99710e6i | 0.349889 | − | 0.606026i | −0.636340 | − | 0.771409i | \(-0.719553\pi\) |
0.986229 | + | 0.165383i | \(0.0528859\pi\) | |||||||
\(740\) | 1.88340e6 | + | 3.26215e6i | 0.126434 | + | 0.218990i | ||||
\(741\) | −880202. | −0.0588893 | ||||||||
\(742\) | 220652. | − | 2.73889e6i | 0.0147129 | − | 0.182627i | ||||
\(743\) | −1.04738e7 | −0.696035 | −0.348018 | − | 0.937488i | \(-0.613145\pi\) | ||||
−0.348018 | + | 0.937488i | \(0.613145\pi\) | |||||||
\(744\) | 5.42542e6 | + | 9.39710e6i | 0.359336 | + | 0.622388i | ||||
\(745\) | −967748. | + | 1.67619e6i | −0.0638810 | + | 0.110645i | ||||
\(746\) | 6.83908e6 | − | 1.18456e7i | 0.449936 | − | 0.779312i | ||||
\(747\) | −7.23369e6 | − | 1.25291e7i | −0.474306 | − | 0.821522i | ||||
\(748\) | 1.27725e6 | 0.0834681 | ||||||||
\(749\) | −2.40142e7 | + | 1.13997e7i | −1.56410 | + | 0.742490i | ||||
\(750\) | 1.45428e7 | 0.944050 | ||||||||
\(751\) | 4.70223e6 | + | 8.14449e6i | 0.304231 | + | 0.526944i | 0.977090 | − | 0.212827i | \(-0.0682671\pi\) |
−0.672859 | + | 0.739771i | \(0.734934\pi\) | |||||||
\(752\) | 2.15926e6 | − | 3.73995e6i | 0.139239 | − | 0.241169i | ||||
\(753\) | −9.07576e6 | + | 1.57197e7i | −0.583305 | + | 1.01031i | ||||
\(754\) | 239453. | + | 414745.i | 0.0153388 | + | 0.0265676i | ||||
\(755\) | −1.12174e6 | −0.0716181 | ||||||||
\(756\) | 2.04677e7 | + | 1.41228e7i | 1.30246 | + | 0.898705i | ||||
\(757\) | −1.33677e7 | −0.847848 | −0.423924 | − | 0.905698i | \(-0.639348\pi\) | ||||
−0.423924 | + | 0.905698i | \(0.639348\pi\) | |||||||
\(758\) | 32711.2 | + | 56657.5i | 0.00206787 | + | 0.00358166i | ||||
\(759\) | −5.29845e6 | + | 9.17719e6i | −0.333845 | + | 0.578236i | ||||
\(760\) | −297010. | + | 514436.i | −0.0186525 | + | 0.0323071i | ||||
\(761\) | 1.11312e7 | + | 1.92797e7i | 0.696752 | + | 1.20681i | 0.969586 | + | 0.244749i | \(0.0787057\pi\) |
−0.272834 | + | 0.962061i | \(0.587961\pi\) | |||||||
\(762\) | −2.92307e7 | −1.82369 | ||||||||
\(763\) | 1.20091e7 | + | 8.28634e6i | 0.746789 | + | 0.515289i | ||||
\(764\) | −3.24463e6 | −0.201109 | ||||||||
\(765\) | 1.62966e6 | + | 2.82266e6i | 0.100680 | + | 0.174383i | ||||
\(766\) | −6.87287e6 | + | 1.19042e7i | −0.423220 | + | 0.733038i | ||||
\(767\) | −1.38269e6 | + | 2.39488e6i | −0.0848664 | + | 0.146993i | ||||
\(768\) | 976601. | + | 1.69152e6i | 0.0597467 | + | 0.103484i | ||||
\(769\) | 9.65833e6 | 0.588961 | 0.294480 | − | 0.955658i | \(-0.404853\pi\) | ||||
0.294480 | + | 0.955658i | \(0.404853\pi\) | |||||||
\(770\) | 3.26488e6 | − | 1.54987e6i | 0.198445 | − | 0.0942035i | ||||
\(771\) | −3.07176e7 | −1.86102 | ||||||||
\(772\) | −4.84790e6 | − | 8.39681e6i | −0.292759 | − | 0.507074i | ||||
\(773\) | 2.55476e6 | − | 4.42497e6i | 0.153780 | − | 0.266355i | −0.778834 | − | 0.627230i | \(-0.784189\pi\) |
0.932614 | + | 0.360875i | \(0.117522\pi\) | |||||||
\(774\) | −1.28043e7 | + | 2.21777e7i | −0.768251 | + | 1.33065i | ||||
\(775\) | −7.63428e6 | − | 1.32230e7i | −0.456577 | − | 0.790815i | ||||
\(776\) | −4.60137e6 | −0.274305 | ||||||||
\(777\) | 3.47835e6 | − | 4.31759e7i | 0.206691 | − | 2.56560i | ||||
\(778\) | 1.92421e7 | 1.13973 | ||||||||
\(779\) | −2.66908e6 | − | 4.62298e6i | −0.157586 | − | 0.272947i | ||||
\(780\) | −334572. | + | 579496.i | −0.0196904 | + | 0.0341047i | ||||
\(781\) | 9.64034e6 | − | 1.66976e7i | 0.565542 | − | 0.979548i | ||||
\(782\) | −515407. | − | 892711.i | −0.0301393 | − | 0.0522028i | ||||
\(783\) | −2.14802e7 | −1.25209 | ||||||||
\(784\) | 1.52705e6 | + | 4.02249e6i | 0.0887283 | + | 0.233725i | ||||
\(785\) | 5.89051e6 | 0.341176 | ||||||||
\(786\) | −4.17212e6 | − | 7.22632e6i | −0.240880 | − | 0.417216i | ||||
\(787\) | −1.25796e7 | + | 2.17885e7i | −0.723984 | + | 1.25398i | 0.235406 | + | 0.971897i | \(0.424358\pi\) |
−0.959391 | + | 0.282081i | \(0.908975\pi\) | |||||||
\(788\) | 2486.55 | − | 4306.84i | 0.000142653 | − | 0.000247083i | ||||
\(789\) | −1.35693e7 | − | 2.35028e7i | −0.776007 | − | 1.34408i | ||||
\(790\) | −3.69178e6 | −0.210460 | ||||||||
\(791\) | 1.23190e6 | − | 1.52913e7i | 0.0700060 | − | 0.868966i | ||||
\(792\) | −1.37050e7 | −0.776367 | ||||||||
\(793\) | 719105. | + | 1.24553e6i | 0.0406078 | + | 0.0703347i | ||||
\(794\) | −6.59696e6 | + | 1.14263e7i | −0.371358 | + | 0.643211i | ||||
\(795\) | −1.65818e6 | + | 2.87205e6i | −0.0930495 | + | 0.161166i | ||||
\(796\) | 3.27733e6 | + | 5.67650e6i | 0.183332 | + | 0.317540i | ||||
\(797\) | −3.35976e6 | −0.187354 | −0.0936768 | − | 0.995603i | \(-0.529862\pi\) | ||||
−0.0936768 | + | 0.995603i | \(0.529862\pi\) | |||||||
\(798\) | 6.17084e6 | − | 2.92935e6i | 0.343034 | − | 0.162841i | ||||
\(799\) | −4.05767e6 | −0.224859 | ||||||||
\(800\) | −1.37421e6 | − | 2.38020e6i | −0.0759150 | − | 0.131489i | ||||
\(801\) | −7.76300e6 | + | 1.34459e7i | −0.427512 | + | 0.740473i | ||||
\(802\) | 272328. | − | 471686.i | 0.0149505 | − | 0.0258951i | ||||
\(803\) | 6.63540e6 | + | 1.14929e7i | 0.363144 | + | 0.628983i | ||||
\(804\) | 1.26933e7 | 0.692524 | ||||||||
\(805\) | −2.40073e6 | − | 1.65652e6i | −0.130573 | − | 0.0900964i | ||||
\(806\) | 1.52051e6 | 0.0824426 | ||||||||
\(807\) | 2.11754e7 | + | 3.66768e7i | 1.14458 | + | 1.98247i | ||||
\(808\) | −507695. | + | 879353.i | −0.0273574 | + | 0.0473844i | ||||
\(809\) | 1.48525e7 | − | 2.57253e7i | 0.797862 | − | 1.38194i | −0.123143 | − | 0.992389i | \(-0.539297\pi\) |
0.921006 | − | 0.389549i | \(-0.127369\pi\) | |||||||
\(810\) | −8.42108e6 | − | 1.45857e7i | −0.450978 | − | 0.781117i | ||||
\(811\) | 1.26386e7 | 0.674757 | 0.337379 | − | 0.941369i | \(-0.390460\pi\) | ||||
0.337379 | + | 0.941369i | \(0.390460\pi\) | |||||||
\(812\) | −3.05902e6 | − | 2.11075e6i | −0.162814 | − | 0.112343i | ||||
\(813\) | 8.86743e6 | 0.470513 | ||||||||
\(814\) | 7.44109e6 | + | 1.28883e7i | 0.393619 | + | 0.681767i | ||||
\(815\) | 6.58150e6 | − | 1.13995e7i | 0.347081 | − | 0.601162i | ||||
\(816\) | 917612. | − | 1.58935e6i | 0.0482429 | − | 0.0835592i | ||||
\(817\) | 2.19265e6 | + | 3.79779e6i | 0.114925 | + | 0.199056i | ||||
\(818\) | −1.09948e7 | −0.574517 | ||||||||
\(819\) | 5.04959e6 | − | 2.39708e6i | 0.263055 | − | 0.124874i | ||||
\(820\) | −4.05816e6 | −0.210763 | ||||||||
\(821\) | 1.30880e7 | + | 2.26691e7i | 0.677666 | + | 1.17375i | 0.975682 | + | 0.219190i | \(0.0703416\pi\) |
−0.298017 | + | 0.954561i | \(0.596325\pi\) | |||||||
\(822\) | 1.11861e7 | − | 1.93749e7i | 0.577429 | − | 1.00014i | ||||
\(823\) | 3.64922e6 | − | 6.32063e6i | 0.187802 | − | 0.325283i | −0.756715 | − | 0.653745i | \(-0.773197\pi\) |
0.944517 | + | 0.328462i | \(0.106530\pi\) | |||||||
\(824\) | −5.13835e6 | − | 8.89989e6i | −0.263637 | − | 0.456632i | ||||
\(825\) | 2.65474e7 | 1.35796 | ||||||||
\(826\) | 1.72335e6 | − | 2.13915e7i | 0.0878867 | − | 1.09091i | ||||
\(827\) | 1.18681e7 | 0.603418 | 0.301709 | − | 0.953400i | \(-0.402443\pi\) | ||||
0.301709 | + | 0.953400i | \(0.402443\pi\) | |||||||
\(828\) | 5.53040e6 | + | 9.57893e6i | 0.280337 | + | 0.485558i | ||||
\(829\) | 5.21689e6 | − | 9.03593e6i | 0.263649 | − | 0.456653i | −0.703560 | − | 0.710636i | \(-0.748407\pi\) |
0.967209 | + | 0.253983i | \(0.0817407\pi\) | |||||||
\(830\) | −941698. | + | 1.63107e6i | −0.0474479 | + | 0.0821821i | ||||
\(831\) | 1.26607e7 | + | 2.19290e7i | 0.635997 | + | 1.10158i | ||||
\(832\) | 273699. | 0.0137077 | ||||||||
\(833\) | 2.55576e6 | − | 3.13234e6i | 0.127617 | − | 0.156407i | ||||
\(834\) | −9.33120e6 | −0.464539 | ||||||||
\(835\) | 3.08697e6 | + | 5.34679e6i | 0.153220 | + | 0.265385i | ||||
\(836\) | −1.17345e6 | + | 2.03247e6i | −0.0580696 | + | 0.100579i | ||||
\(837\) | −3.40995e7 | + | 5.90621e7i | −1.68242 | + | 2.91404i | ||||
\(838\) | −3.74438e6 | − | 6.48546e6i | −0.184192 | − | 0.319029i | ||||
\(839\) | −2.91444e7 | −1.42939 | −0.714695 | − | 0.699436i | \(-0.753435\pi\) | ||||
−0.714695 | + | 0.699436i | \(0.753435\pi\) | |||||||
\(840\) | 417003. | − | 5.17615e6i | 0.0203911 | − | 0.253110i | ||||
\(841\) | −1.73008e7 | −0.843482 | ||||||||
\(842\) | 1.31045e6 | + | 2.26977e6i | 0.0637001 | + | 0.110332i | ||||
\(843\) | −114453. | + | 198238.i | −0.00554699 | + | 0.00960767i | ||||
\(844\) | 3.53071e6 | − | 6.11537e6i | 0.170610 | − | 0.295506i | ||||
\(845\) | −3.85169e6 | − | 6.67133e6i | −0.185571 | − | 0.321418i | ||||
\(846\) | 4.35395e7 | 2.09150 | ||||||||
\(847\) | −5.96247e6 | + | 2.83043e6i | −0.285573 | + | 0.135564i | ||||
\(848\) | 1.35648e6 | 0.0647777 | ||||||||
\(849\) | −1.46837e7 | − | 2.54329e7i | −0.699144 | − | 1.21095i | ||||
\(850\) | −1.29120e6 | + | 2.23643e6i | −0.0612981 | + | 0.106171i | ||||
\(851\) | 6.00541e6 | − | 1.04017e7i | 0.284262 | − | 0.492356i | ||||
\(852\) | −1.38518e7 | − | 2.39921e7i | −0.653745 | − | 1.13232i | ||||
\(853\) | 2.63032e7 | 1.23776 | 0.618879 | − | 0.785487i | \(-0.287587\pi\) | ||||
0.618879 | + | 0.785487i | \(0.287587\pi\) | |||||||
\(854\) | −9.18660e6 | − | 6.33881e6i | −0.431032 | − | 0.297415i | ||||
\(855\) | −5.98892e6 | −0.280177 | ||||||||
\(856\) | −6.56150e6 | − | 1.13649e7i | −0.306069 | − | 0.530127i | ||||
\(857\) | −1.71799e6 | + | 2.97565e6i | −0.0799040 | + | 0.138398i | −0.903208 | − | 0.429202i | \(-0.858795\pi\) |
0.823304 | + | 0.567600i | \(0.192128\pi\) | |||||||
\(858\) | −1.32185e6 | + | 2.28952e6i | −0.0613007 | + | 0.106176i | ||||
\(859\) | −5.45696e6 | − | 9.45173e6i | −0.252329 | − | 0.437047i | 0.711837 | − | 0.702344i | \(-0.247863\pi\) |
−0.964167 | + | 0.265297i | \(0.914530\pi\) | |||||||
\(860\) | 3.33378e6 | 0.153706 | ||||||||
\(861\) | 3.84099e7 | + | 2.65031e7i | 1.76577 | + | 1.21840i | ||||
\(862\) | −2.55076e7 | −1.16923 | ||||||||
\(863\) | −1.09529e7 | − | 1.89710e7i | −0.500614 | − | 0.867088i | −1.00000 | 0.000708873i | \(-0.999774\pi\) | |
0.499386 | − | 0.866380i | \(-0.333559\pi\) | |||||||
\(864\) | −6.13808e6 | + | 1.06315e7i | −0.279736 | + | 0.484517i | ||||
\(865\) | 7.49896e6 | − | 1.29886e7i | 0.340770 | − | 0.590230i | ||||
\(866\) | 9.60005e6 | + | 1.66278e7i | 0.434990 | + | 0.753424i | ||||
\(867\) | 4.05923e7 | 1.83399 | ||||||||
\(868\) | −1.06599e7 | + | 5.06032e6i | −0.480233 | + | 0.227970i | ||||
\(869\) | −1.45858e7 | −0.655210 | ||||||||
\(870\) | 2.24282e6 | + | 3.88467e6i | 0.100460 | + | 0.174003i | ||||
\(871\) | 889347. | − | 1.54039e6i | 0.0397215 | − | 0.0687997i | ||||
\(872\) | −3.60142e6 | + | 6.23784e6i | −0.160392 | + | 0.277807i | ||||
\(873\) | −2.31956e7 | − | 4.01759e7i | −1.03008 | − | 1.78414i | ||||
\(874\) | 1.89409e6 | 0.0838729 | ||||||||
\(875\) | −1.26997e6 | + | 1.57638e7i | −0.0560755 | + | 0.696051i | ||||
\(876\) | 1.90683e7 | 0.839560 | ||||||||
\(877\) | −3.23464e6 | − | 5.60256e6i | −0.142012 | − | 0.245973i | 0.786242 | − | 0.617919i | \(-0.212024\pi\) |
−0.928254 | + | 0.371946i | \(0.878691\pi\) | |||||||
\(878\) | −1.11902e7 | + | 1.93819e7i | −0.489891 | + | 0.848516i | ||||
\(879\) | −3.23270e7 | + | 5.59920e7i | −1.41122 | + | 2.44430i | ||||
\(880\) | 892076. | + | 1.54512e6i | 0.0388325 | + | 0.0672599i | ||||
\(881\) | 2.03983e7 | 0.885430 | 0.442715 | − | 0.896662i | \(-0.354015\pi\) | ||||
0.442715 | + | 0.896662i | \(0.354015\pi\) | |||||||
\(882\) | −2.74236e7 | + | 3.36105e7i | −1.18701 | + | 1.45480i | ||||
\(883\) | 1.62381e7 | 0.700862 | 0.350431 | − | 0.936589i | \(-0.386035\pi\) | ||||
0.350431 | + | 0.936589i | \(0.386035\pi\) | |||||||
\(884\) | −128583. | − | 222713.i | −0.00553419 | − | 0.00958550i | ||||
\(885\) | −1.29508e7 | + | 2.24315e7i | −0.555826 | + | 0.962720i | ||||
\(886\) | 8.28019e6 | − | 1.43417e7i | 0.354369 | − | 0.613786i | ||||
\(887\) | 3.39513e6 | + | 5.88055e6i | 0.144893 | + | 0.250962i | 0.929333 | − | 0.369242i | \(-0.120383\pi\) |
−0.784440 | + | 0.620205i | \(0.787049\pi\) | |||||||
\(888\) | 2.13836e7 | 0.910015 | ||||||||
\(889\) | 2.55261e6 | − | 3.16849e7i | 0.108325 | − | 1.34461i | ||||
\(890\) | 2.02121e6 | 0.0855336 | ||||||||
\(891\) | −3.32706e7 | − | 5.76265e7i | −1.40400 | − | 2.43180i | ||||
\(892\) | −2.12107e6 | + | 3.67380e6i | −0.0892570 | + | 0.154598i | ||||
\(893\) | 3.72792e6 | − | 6.45696e6i | 0.156437 | − | 0.270956i | ||||
\(894\) | 5.49377e6 | + | 9.51548e6i | 0.229893 | + | 0.398187i | ||||
\(895\) | −1.21810e7 | −0.508308 | ||||||||
\(896\) | −1.91883e6 | + | 910881.i | −0.0798482 | + | 0.0379046i | ||||
\(897\) | 2.13363e6 | 0.0885398 | ||||||||
\(898\) | −611933. | − | 1.05990e6i | −0.0253229 | − | 0.0438605i | ||||
\(899\) | 5.09639e6 | − | 8.82721e6i | 0.210312 | − | 0.364271i | ||||
\(900\) | 1.38548e7 | − | 2.39972e7i | 0.570156 | − | 0.987539i | ||||
\(901\) | −637275. | − | 1.10379e6i | −0.0261526 | − | 0.0452976i | ||||
\(902\) | −1.60333e7 | −0.656155 | ||||||||
\(903\) | −3.15538e7 | − | 2.17723e7i | −1.28775 | − | 0.888557i | ||||
\(904\) | 7.57328e6 | 0.308221 | ||||||||
\(905\) | −3.23449e6 | − | 5.60229e6i | −0.131276 | − | 0.227376i | ||||
\(906\) | −3.18397e6 | + | 5.51479e6i | −0.128869 | + | 0.223207i | ||||
\(907\) | −1.71071e7 | + | 2.96304e7i | −0.690492 | + | 1.19597i | 0.281185 | + | 0.959654i | \(0.409273\pi\) |
−0.971677 | + | 0.236313i | \(0.924061\pi\) | |||||||
\(908\) | 1.14435e7 | + | 1.98207e7i | 0.460622 | + | 0.797821i | ||||
\(909\) | −1.02372e7 | −0.410932 | ||||||||
\(910\) | −598933. | − | 413268.i | −0.0239759 | − | 0.0165435i | ||||
\(911\) | −4.47390e6 | −0.178604 | −0.0893019 | − | 0.996005i | \(-0.528464\pi\) | ||||
−0.0893019 | + | 0.996005i | \(0.528464\pi\) | |||||||
\(912\) | 1.68608e6 | + | 2.92038e6i | 0.0671262 | + | 0.116266i | ||||
\(913\) | −3.72053e6 | + | 6.44415e6i | −0.147716 | + | 0.255852i | ||||
\(914\) | 1.78522e6 | − | 3.09208e6i | 0.0706846 | − | 0.122429i | ||||
\(915\) | 6.73543e6 | + | 1.16661e7i | 0.265958 | + | 0.460652i | ||||
\(916\) | −2.01288e7 | −0.792646 | ||||||||
\(917\) | 8.19737e6 | − | 3.89136e6i | 0.321922 | − | 0.152819i | ||||
\(918\) | 1.15346e7 | 0.451749 | ||||||||
\(919\) | 268950. | + | 465835.i | 0.0105047 | + | 0.0181946i | 0.871230 | − | 0.490875i | \(-0.163323\pi\) |
−0.860725 | + | 0.509070i | \(0.829990\pi\) | |||||||
\(920\) | 719960. | − | 1.24701e6i | 0.0280439 | − | 0.0485735i | ||||
\(921\) | −2.07273e7 | + | 3.59008e7i | −0.805182 | + | 1.39462i | ||||
\(922\) | −6.02930e6 | − | 1.04431e7i | −0.233582 | − | 0.404576i | ||||
\(923\) | −3.88207e6 | −0.149989 | ||||||||
\(924\) | 1.64753e6 | − | 2.04503e7i | 0.0634823 | − | 0.787990i | ||||
\(925\) | −3.00896e7 | −1.15628 | ||||||||
\(926\) | 6.90993e6 | + | 1.19684e7i | 0.264817 | + | 0.458677i | ||||
\(927\) | 5.18050e7 | − | 8.97288e7i | 1.98003 | − | 3.42952i | ||||
\(928\) | 917375. | − | 1.58894e6i | 0.0349685 | − | 0.0605672i | ||||
\(929\) | 8.86206e6 | + | 1.53495e7i | 0.336896 | + | 0.583521i | 0.983847 | − | 0.179011i | \(-0.0572897\pi\) |
−0.646951 | + | 0.762531i | \(0.723956\pi\) | |||||||
\(930\) | 1.42417e7 | 0.539952 | ||||||||
\(931\) | 2.63642e6 | + | 6.94475e6i | 0.0996873 | + | 0.262593i | ||||
\(932\) | 3.59557e6 | 0.135590 | ||||||||
\(933\) | 3.03689e7 | + | 5.26005e7i | 1.14216 | + | 1.97827i | ||||
\(934\) | 5.67551e6 | − | 9.83028e6i | 0.212881 | − | 0.368722i | ||||
\(935\) | 838192. | − | 1.45179e6i | 0.0313556 | − | 0.0543094i | ||||
\(936\) | 1.37972e6 | + | 2.38974e6i | 0.0514756 | + | 0.0891583i | ||||
\(937\) | −3.32444e7 | −1.23700 | −0.618499 | − | 0.785786i | \(-0.712259\pi\) | ||||
−0.618499 | + | 0.785786i | \(0.712259\pi\) | |||||||
\(938\) | −1.10846e6 | + | 1.37590e7i | −0.0411352 | + | 0.510600i | ||||
\(939\) | 3.48575e7 | 1.29013 | ||||||||
\(940\) | −2.83403e6 | − | 4.90869e6i | −0.104613 | − | 0.181195i | ||||
\(941\) | −1.39240e7 | + | 2.41170e7i | −0.512613 | + | 0.887871i | 0.487281 | + | 0.873245i | \(0.337989\pi\) |
−0.999893 | + | 0.0146254i | \(0.995344\pi\) | |||||||
\(942\) | 1.67198e7 | − | 2.89595e7i | 0.613909 | − | 1.06332i | ||||
\(943\) | 6.46991e6 | + | 1.12062e7i | 0.236930 | + | 0.410374i | ||||
\(944\) | 1.05945e7 | 0.386946 | ||||||||
\(945\) | 2.94847e7 | − | 1.39966e7i | 1.07403 | − | 0.509852i | ||||
\(946\) | 1.31714e7 | 0.478523 | ||||||||
\(947\) | 1.15284e7 | + | 1.99678e7i | 0.417729 | + | 0.723529i | 0.995711 | − | 0.0925215i | \(-0.0294927\pi\) |
−0.577981 | + | 0.816050i | \(0.696159\pi\) | |||||||
\(948\) | −1.04789e7 | + | 1.81499e7i | −0.378698 | + | 0.655925i | ||||
\(949\) | 1.33600e6 | − | 2.31403e6i | 0.0481551 | − | 0.0834071i | ||||
\(950\) | −2.37254e6 | − | 4.10936e6i | −0.0852914 | − | 0.147729i | ||||
\(951\) | −2.38767e7 | −0.856097 | ||||||||
\(952\) | 1.64266e6 | + | 1.13345e6i | 0.0587429 | + | 0.0405330i | ||||
\(953\) | 2.85536e7 | 1.01843 | 0.509213 | − | 0.860641i | \(-0.329937\pi\) | ||||
0.509213 | + | 0.860641i | \(0.329937\pi\) | |||||||
\(954\) | 6.83805e6 | + | 1.18439e7i | 0.243255 | + | 0.421330i | ||||
\(955\) | −2.12929e6 | + | 3.68804e6i | −0.0755486 | + | 0.130854i | ||||
\(956\) | −1.02554e7 | + | 1.77629e7i | −0.362919 | + | 0.628593i | ||||
\(957\) | 8.86109e6 | + | 1.53479e7i | 0.312757 | + | 0.541711i | ||||
\(958\) | 1.88177e7 | 0.662449 | ||||||||
\(959\) | 2.00247e7 | + | 1.38172e7i | 0.703105 | + | 0.485147i | ||||
\(960\) | 2.56358e6 | 0.0897777 | ||||||||
\(961\) | −1.86629e6 | − | 3.23251e6i | −0.0651884 | − | 0.112910i | ||||
\(962\) | 1.49823e6 | − | 2.59500e6i | 0.0521963 | − | 0.0904066i | ||||
\(963\) | 6.61532e7 | − | 1.14581e8i | 2.29871 | − | 3.98149i | ||||
\(964\) | 4.60900e6 | + | 7.98302e6i | 0.159740 | + | 0.276678i | ||||
\(965\) | −1.27257e7 | −0.439911 | ||||||||
\(966\) | −1.49583e7 | + | 7.10081e6i | −0.515750 | + | 0.244830i | ||||
\(967\) | −3.45310e7 | −1.18753 | −0.593763 | − | 0.804640i | \(-0.702358\pi\) | ||||
−0.593763 | + | 0.804640i | \(0.702358\pi\) | |||||||
\(968\) | −1.62915e6 | − | 2.82177e6i | −0.0558820 | − | 0.0967905i | ||||
\(969\) | 1.58424e6 | − | 2.74398e6i | 0.0542015 | − | 0.0938797i | ||||
\(970\) | −3.01965e6 | + | 5.23019e6i | −0.103045 | + | 0.178479i | ||||
\(971\) | −6.24666e6 | − | 1.08195e7i | −0.212618 | − | 0.368265i | 0.739915 | − | 0.672700i | \(-0.234866\pi\) |
−0.952533 | + | 0.304435i | \(0.901532\pi\) | |||||||
\(972\) | −4.89995e7 | −1.66351 | ||||||||
\(973\) | 814860. | − | 1.01146e7i | 0.0275931 | − | 0.342506i | ||||
\(974\) | −1.66654e7 | −0.562883 | ||||||||
\(975\) | −2.67260e6 | − | 4.62907e6i | −0.0900371 | − | 0.155949i | ||||
\(976\) | 2.75498e6 | − | 4.77177e6i | 0.0925751 | − | 0.160345i | ||||
\(977\) | 1.94720e7 | − | 3.37265e7i | 0.652641 | − | 1.13041i | −0.329839 | − | 0.944037i | \(-0.606994\pi\) |
0.982480 | − | 0.186370i | \(-0.0596723\pi\) | |||||||
\(978\) | −3.73622e7 | − | 6.47133e7i | −1.24907 | − | 2.16345i | ||||
\(979\) | 7.98556e6 | 0.266286 | ||||||||
\(980\) | 5.57432e6 | + | 904029.i | 0.185407 | + | 0.0300689i | ||||
\(981\) | −7.26191e7 | −2.40923 | ||||||||
\(982\) | 3.15751e6 | + | 5.46897e6i | 0.104488 | + | 0.180979i | ||||
\(983\) | −139950. | + | 242401.i | −0.00461945 | + | 0.00800112i | −0.868326 | − | 0.495994i | \(-0.834804\pi\) |
0.863706 | + | 0.503995i | \(0.168137\pi\) | |||||||
\(984\) | −1.15188e7 | + | 1.99511e7i | −0.379245 | + | 0.656871i | ||||
\(985\) | −3263.60 | − | 5652.72i | −0.000107178 | − | 0.000185638i | ||||
\(986\) | −1.72393e6 | −0.0564711 | ||||||||
\(987\) | −5.23402e6 | + | 6.49686e7i | −0.171018 | + | 2.12281i | ||||
\(988\) | 472536. | 0.0154008 | ||||||||
\(989\) | −5.31505e6 | − | 9.20593e6i | −0.172789 | − | 0.299280i | ||||
\(990\) | −8.99393e6 | + | 1.55779e7i | −0.291650 | + | 0.505152i | ||||
\(991\) | −9.81715e6 | + | 1.70038e7i | −0.317542 | + | 0.549999i | −0.979975 | − | 0.199122i | \(-0.936191\pi\) |
0.662432 | + | 0.749122i | \(0.269524\pi\) | |||||||
\(992\) | −2.91263e6 | − | 5.04483e6i | −0.0939738 | − | 0.162767i | ||||
\(993\) | −7.89647e7 | −2.54132 | ||||||||
\(994\) | 2.72161e7 | − | 1.29197e7i | 0.873694 | − | 0.414749i | ||||
\(995\) | 8.60299e6 | 0.275481 | ||||||||
\(996\) | 5.34589e6 | + | 9.25935e6i | 0.170754 | + | 0.295755i | ||||
\(997\) | 1.86687e7 | − | 3.23351e7i | 0.594807 | − | 1.03024i | −0.398767 | − | 0.917052i | \(-0.630562\pi\) |
0.993574 | − | 0.113184i | \(-0.0361050\pi\) | |||||||
\(998\) | 3.11423e6 | − | 5.39401e6i | 0.0989749 | − | 0.171430i | ||||
\(999\) | 6.71995e7 | + | 1.16393e8i | 2.13036 | + | 3.68989i |
(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 | 14.6.c.b.11.2 | yes | 4 | |
3.2 | odd | 2 | 126.6.g.e.109.1 | 4 | |||
4.3 | odd | 2 | 112.6.i.b.81.1 | 4 | |||
7.2 | even | 3 | inner | 14.6.c.b.9.2 | ✓ | 4 | |
7.3 | odd | 6 | 98.6.a.f.1.2 | 2 | |||
7.4 | even | 3 | 98.6.a.c.1.1 | 2 | |||
7.5 | odd | 6 | 98.6.c.f.79.1 | 4 | |||
7.6 | odd | 2 | 98.6.c.f.67.1 | 4 | |||
21.2 | odd | 6 | 126.6.g.e.37.1 | 4 | |||
21.11 | odd | 6 | 882.6.a.bt.1.1 | 2 | |||
21.17 | even | 6 | 882.6.a.bl.1.1 | 2 | |||
28.3 | even | 6 | 784.6.a.r.1.1 | 2 | |||
28.11 | odd | 6 | 784.6.a.bc.1.2 | 2 | |||
28.23 | odd | 6 | 112.6.i.b.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.b.9.2 | ✓ | 4 | 7.2 | even | 3 | inner | |
14.6.c.b.11.2 | yes | 4 | 1.1 | even | 1 | trivial | |
98.6.a.c.1.1 | 2 | 7.4 | even | 3 | |||
98.6.a.f.1.2 | 2 | 7.3 | odd | 6 | |||
98.6.c.f.67.1 | 4 | 7.6 | odd | 2 | |||
98.6.c.f.79.1 | 4 | 7.5 | odd | 6 | |||
112.6.i.b.65.1 | 4 | 28.23 | odd | 6 | |||
112.6.i.b.81.1 | 4 | 4.3 | odd | 2 | |||
126.6.g.e.37.1 | 4 | 21.2 | odd | 6 | |||
126.6.g.e.109.1 | 4 | 3.2 | odd | 2 | |||
784.6.a.r.1.1 | 2 | 28.3 | even | 6 | |||
784.6.a.bc.1.2 | 2 | 28.11 | odd | 6 | |||
882.6.a.bl.1.1 | 2 | 21.17 | even | 6 | |||
882.6.a.bt.1.1 | 2 | 21.11 | odd | 6 |