Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(8,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.g (of order \(4\), 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: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.9 | ||
Character | \(\chi\) | \(=\) | 35.8 |
Dual form | 35.5.g.a.22.9 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.18640 | − | 3.18640i | 0.796599 | − | 0.796599i | −0.185959 | − | 0.982558i | \(-0.559539\pi\) |
0.982558 | + | 0.185959i | \(0.0595390\pi\) | |||||||
\(3\) | 5.77081 | + | 5.77081i | 0.641201 | + | 0.641201i | 0.950851 | − | 0.309650i | \(-0.100212\pi\) |
−0.309650 | + | 0.950851i | \(0.600212\pi\) | |||||||
\(4\) | − | 4.30624i | − | 0.269140i | ||||||
\(5\) | 16.7353 | − | 18.5723i | 0.669413 | − | 0.742890i | ||||
\(6\) | 36.7762 | 1.02156 | ||||||||
\(7\) | −13.0958 | + | 13.0958i | −0.267261 | + | 0.267261i | ||||
\(8\) | 37.2610 | + | 37.2610i | 0.582202 | + | 0.582202i | ||||
\(9\) | − | 14.3955i | − | 0.177722i | ||||||
\(10\) | −5.85321 | − | 112.504i | −0.0585321 | − | 1.12504i | ||||
\(11\) | −82.8733 | −0.684903 | −0.342452 | − | 0.939535i | \(-0.611257\pi\) | ||||
−0.342452 | + | 0.939535i | \(0.611257\pi\) | |||||||
\(12\) | 24.8505 | − | 24.8505i | 0.172573 | − | 0.172573i | ||||
\(13\) | −138.646 | − | 138.646i | −0.820391 | − | 0.820391i | 0.165773 | − | 0.986164i | \(-0.446988\pi\) |
−0.986164 | + | 0.165773i | \(0.946988\pi\) | |||||||
\(14\) | 83.4568i | 0.425800i | ||||||||
\(15\) | 203.753 | − | 10.6006i | 0.905571 | − | 0.0471138i | ||||
\(16\) | 306.356 | 1.19670 | ||||||||
\(17\) | −322.389 | + | 322.389i | −1.11553 | + | 1.11553i | −0.123144 | + | 0.992389i | \(0.539298\pi\) |
−0.992389 | + | 0.123144i | \(0.960702\pi\) | |||||||
\(18\) | −45.8698 | − | 45.8698i | −0.141573 | − | 0.141573i | ||||
\(19\) | 318.965i | 0.883559i | 0.897124 | + | 0.441780i | \(0.145653\pi\) | ||||
−0.897124 | + | 0.441780i | \(0.854347\pi\) | |||||||
\(20\) | −79.9766 | − | 72.0663i | −0.199941 | − | 0.180166i | ||||
\(21\) | −151.147 | −0.342736 | ||||||||
\(22\) | −264.067 | + | 264.067i | −0.545593 | + | 0.545593i | ||||
\(23\) | 138.083 | + | 138.083i | 0.261026 | + | 0.261026i | 0.825471 | − | 0.564445i | \(-0.190910\pi\) |
−0.564445 | + | 0.825471i | \(0.690910\pi\) | |||||||
\(24\) | 430.052i | 0.746618i | ||||||||
\(25\) | −64.8578 | − | 621.626i | −0.103772 | − | 0.994601i | ||||
\(26\) | −883.563 | −1.30705 | ||||||||
\(27\) | 550.509 | − | 550.509i | 0.755157 | − | 0.755157i | ||||
\(28\) | 56.3936 | + | 56.3936i | 0.0719306 | + | 0.0719306i | ||||
\(29\) | − | 109.237i | − | 0.129889i | −0.997889 | − | 0.0649446i | \(-0.979313\pi\) | ||
0.997889 | − | 0.0649446i | \(-0.0206871\pi\) | |||||||
\(30\) | 615.461 | − | 683.017i | 0.683846 | − | 0.758907i | ||||
\(31\) | −1063.42 | −1.10657 | −0.553287 | − | 0.832990i | \(-0.686627\pi\) | ||||
−0.553287 | + | 0.832990i | \(0.686627\pi\) | |||||||
\(32\) | 379.997 | − | 379.997i | 0.371090 | − | 0.371090i | ||||
\(33\) | −478.246 | − | 478.246i | −0.439161 | − | 0.439161i | ||||
\(34\) | 2054.52i | 1.77726i | ||||||||
\(35\) | 24.0562 | + | 462.381i | 0.0196377 | + | 0.377454i | ||||
\(36\) | −61.9904 | −0.0478321 | ||||||||
\(37\) | 1791.23 | − | 1791.23i | 1.30842 | − | 1.30842i | 0.385871 | − | 0.922553i | \(-0.373901\pi\) |
0.922553 | − | 0.385871i | \(-0.126099\pi\) | |||||||
\(38\) | 1016.35 | + | 1016.35i | 0.703842 | + | 0.703842i | ||||
\(39\) | − | 1600.20i | − | 1.05207i | ||||||
\(40\) | 1315.59 | − | 68.4460i | 0.822247 | − | 0.0427788i | ||||
\(41\) | −345.340 | −0.205437 | −0.102719 | − | 0.994710i | \(-0.532754\pi\) | ||||
−0.102719 | + | 0.994710i | \(0.532754\pi\) | |||||||
\(42\) | −481.613 | + | 481.613i | −0.273023 | + | 0.273023i | ||||
\(43\) | 1214.03 | + | 1214.03i | 0.656587 | + | 0.656587i | 0.954571 | − | 0.297984i | \(-0.0963141\pi\) |
−0.297984 | + | 0.954571i | \(0.596314\pi\) | |||||||
\(44\) | 356.872i | 0.184335i | ||||||||
\(45\) | −267.357 | − | 240.913i | −0.132028 | − | 0.118970i | ||||
\(46\) | 879.973 | 0.415866 | ||||||||
\(47\) | 1368.18 | − | 1368.18i | 0.619365 | − | 0.619365i | −0.326004 | − | 0.945368i | \(-0.605702\pi\) |
0.945368 | + | 0.326004i | \(0.105702\pi\) | |||||||
\(48\) | 1767.92 | + | 1767.92i | 0.767328 | + | 0.767328i | ||||
\(49\) | − | 343.000i | − | 0.142857i | ||||||
\(50\) | −2187.41 | − | 1774.08i | −0.874963 | − | 0.709633i | ||||
\(51\) | −3720.89 | −1.43056 | ||||||||
\(52\) | −597.043 | + | 597.043i | −0.220800 | + | 0.220800i | ||||
\(53\) | −102.370 | − | 102.370i | −0.0364435 | − | 0.0364435i | 0.688650 | − | 0.725094i | \(-0.258204\pi\) |
−0.725094 | + | 0.688650i | \(0.758204\pi\) | |||||||
\(54\) | − | 3508.28i | − | 1.20311i | ||||||
\(55\) | −1386.91 | + | 1539.14i | −0.458483 | + | 0.508808i | ||||
\(56\) | −975.924 | −0.311200 | ||||||||
\(57\) | −1840.69 | + | 1840.69i | −0.566539 | + | 0.566539i | ||||
\(58\) | −348.072 | − | 348.072i | −0.103470 | − | 0.103470i | ||||
\(59\) | 2476.36i | 0.711393i | 0.934602 | + | 0.355696i | \(0.115756\pi\) | ||||
−0.934602 | + | 0.355696i | \(0.884244\pi\) | |||||||
\(60\) | −45.6487 | − | 877.410i | −0.0126802 | − | 0.243725i | ||||
\(61\) | −1037.52 | −0.278827 | −0.139414 | − | 0.990234i | \(-0.544522\pi\) | ||||
−0.139414 | + | 0.990234i | \(0.544522\pi\) | |||||||
\(62\) | −3388.47 | + | 3388.47i | −0.881496 | + | 0.881496i | ||||
\(63\) | 188.521 | + | 188.521i | 0.0474983 | + | 0.0474983i | ||||
\(64\) | 2480.06i | 0.605483i | ||||||||
\(65\) | −4895.26 | + | 254.684i | −1.15864 | + | 0.0602802i | ||||
\(66\) | −3047.76 | −0.699670 | ||||||||
\(67\) | 3421.35 | − | 3421.35i | 0.762162 | − | 0.762162i | −0.214550 | − | 0.976713i | \(-0.568829\pi\) |
0.976713 | + | 0.214550i | \(0.0688286\pi\) | |||||||
\(68\) | 1388.28 | + | 1388.28i | 0.300234 | + | 0.300234i | ||||
\(69\) | 1593.70i | 0.334740i | ||||||||
\(70\) | 1549.98 | + | 1396.68i | 0.316323 | + | 0.285036i | ||||
\(71\) | 5349.25 | 1.06115 | 0.530574 | − | 0.847638i | \(-0.321976\pi\) | ||||
0.530574 | + | 0.847638i | \(0.321976\pi\) | |||||||
\(72\) | 536.390 | − | 536.390i | 0.103470 | − | 0.103470i | ||||
\(73\) | 6030.77 | + | 6030.77i | 1.13169 | + | 1.13169i | 0.989896 | + | 0.141793i | \(0.0452867\pi\) |
0.141793 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(74\) | − | 11415.1i | − | 2.08458i | ||||||
\(75\) | 3213.00 | − | 3961.57i | 0.571200 | − | 0.704278i | ||||
\(76\) | 1373.54 | 0.237801 | ||||||||
\(77\) | 1085.29 | − | 1085.29i | 0.183048 | − | 0.183048i | ||||
\(78\) | −5098.87 | − | 5098.87i | −0.838079 | − | 0.838079i | ||||
\(79\) | 9397.35i | 1.50574i | 0.658167 | + | 0.752872i | \(0.271332\pi\) | ||||
−0.658167 | + | 0.752872i | \(0.728668\pi\) | |||||||
\(80\) | 5126.97 | − | 5689.73i | 0.801089 | − | 0.889020i | ||||
\(81\) | 5187.73 | 0.790693 | ||||||||
\(82\) | −1100.39 | + | 1100.39i | −0.163651 | + | 0.163651i | ||||
\(83\) | −6842.12 | − | 6842.12i | −0.993195 | − | 0.993195i | 0.00678239 | − | 0.999977i | \(-0.497841\pi\) |
−0.999977 | + | 0.00678239i | \(0.997841\pi\) | |||||||
\(84\) | 650.874i | 0.0922440i | ||||||||
\(85\) | 592.208 | + | 11382.8i | 0.0819665 | + | 1.57547i | ||||
\(86\) | 7736.76 | 1.04607 | ||||||||
\(87\) | 630.385 | − | 630.385i | 0.0832851 | − | 0.0832851i | ||||
\(88\) | −3087.94 | − | 3087.94i | −0.398752 | − | 0.398752i | ||||
\(89\) | 2332.31i | 0.294446i | 0.989103 | + | 0.147223i | \(0.0470335\pi\) | ||||
−0.989103 | + | 0.147223i | \(0.952967\pi\) | |||||||
\(90\) | −1619.55 | + | 84.2598i | −0.199945 | + | 0.0104024i | ||||
\(91\) | 3631.36 | 0.438517 | ||||||||
\(92\) | 594.617 | − | 594.617i | 0.0702525 | − | 0.0702525i | ||||
\(93\) | −6136.78 | − | 6136.78i | −0.709537 | − | 0.709537i | ||||
\(94\) | − | 8719.11i | − | 0.986771i | ||||||
\(95\) | 5923.90 | + | 5337.98i | 0.656388 | + | 0.591466i | ||||
\(96\) | 4385.78 | 0.475887 | ||||||||
\(97\) | −3869.74 | + | 3869.74i | −0.411280 | + | 0.411280i | −0.882184 | − | 0.470904i | \(-0.843928\pi\) |
0.470904 | + | 0.882184i | \(0.343928\pi\) | |||||||
\(98\) | −1092.93 | − | 1092.93i | −0.113800 | − | 0.113800i | ||||
\(99\) | 1193.00i | 0.121723i | ||||||||
\(100\) | −2676.87 | + | 279.293i | −0.267687 | + | 0.0279293i | ||||
\(101\) | −9543.11 | −0.935507 | −0.467754 | − | 0.883859i | \(-0.654937\pi\) | ||||
−0.467754 | + | 0.883859i | \(0.654937\pi\) | |||||||
\(102\) | −11856.2 | + | 11856.2i | −1.13958 | + | 1.13958i | ||||
\(103\) | −3983.11 | − | 3983.11i | −0.375446 | − | 0.375446i | 0.494010 | − | 0.869456i | \(-0.335531\pi\) |
−0.869456 | + | 0.494010i | \(0.835531\pi\) | |||||||
\(104\) | − | 10332.2i | − | 0.955267i | ||||||
\(105\) | −2529.49 | + | 2807.14i | −0.229432 | + | 0.254616i | ||||
\(106\) | −652.381 | −0.0580617 | ||||||||
\(107\) | 7833.17 | − | 7833.17i | 0.684179 | − | 0.684179i | −0.276760 | − | 0.960939i | \(-0.589261\pi\) |
0.960939 | + | 0.276760i | \(0.0892607\pi\) | |||||||
\(108\) | −2370.62 | − | 2370.62i | −0.203243 | − | 0.203243i | ||||
\(109\) | 6238.31i | 0.525066i | 0.964923 | + | 0.262533i | \(0.0845579\pi\) | ||||
−0.964923 | + | 0.262533i | \(0.915442\pi\) | |||||||
\(110\) | 485.075 | + | 9323.57i | 0.0400888 | + | 0.770543i | ||||
\(111\) | 20673.7 | 1.67793 | ||||||||
\(112\) | −4011.98 | + | 4011.98i | −0.319832 | + | 0.319832i | ||||
\(113\) | −10577.0 | − | 10577.0i | −0.828335 | − | 0.828335i | 0.158952 | − | 0.987286i | \(-0.449189\pi\) |
−0.987286 | + | 0.158952i | \(0.949189\pi\) | |||||||
\(114\) | 11730.3i | 0.902609i | ||||||||
\(115\) | 4875.37 | − | 253.649i | 0.368648 | − | 0.0191795i | ||||
\(116\) | −470.400 | −0.0349584 | ||||||||
\(117\) | −1995.88 | + | 1995.88i | −0.145802 | + | 0.145802i | ||||
\(118\) | 7890.66 | + | 7890.66i | 0.566695 | + | 0.566695i | ||||
\(119\) | − | 8443.88i | − | 0.596277i | ||||||
\(120\) | 7987.03 | + | 7197.06i | 0.554655 | + | 0.499796i | ||||
\(121\) | −7773.01 | −0.530907 | ||||||||
\(122\) | −3305.93 | + | 3305.93i | −0.222113 | + | 0.222113i | ||||
\(123\) | −1992.89 | − | 1992.89i | −0.131726 | − | 0.131726i | ||||
\(124\) | 4579.33i | 0.297823i | ||||||||
\(125\) | −12630.4 | − | 9198.55i | −0.808346 | − | 0.588707i | ||||
\(126\) | 1201.40 | 0.0756741 | ||||||||
\(127\) | 13759.2 | − | 13759.2i | 0.853070 | − | 0.853070i | −0.137440 | − | 0.990510i | \(-0.543888\pi\) |
0.990510 | + | 0.137440i | \(0.0438875\pi\) | |||||||
\(128\) | 13982.4 | + | 13982.4i | 0.853418 | + | 0.853418i | ||||
\(129\) | 14011.9i | 0.842009i | ||||||||
\(130\) | −14786.7 | + | 16409.8i | −0.874953 | + | 0.970992i | ||||
\(131\) | −15675.4 | −0.913432 | −0.456716 | − | 0.889613i | \(-0.650974\pi\) | ||||
−0.456716 | + | 0.889613i | \(0.650974\pi\) | |||||||
\(132\) | −2059.44 | + | 2059.44i | −0.118196 | + | 0.118196i | ||||
\(133\) | −4177.10 | − | 4177.10i | −0.236141 | − | 0.236141i | ||||
\(134\) | − | 21803.5i | − | 1.21428i | ||||||
\(135\) | −1011.25 | − | 19437.2i | −0.0554870 | − | 1.06651i | ||||
\(136\) | −24025.0 | −1.29893 | ||||||||
\(137\) | −23960.0 | + | 23960.0i | −1.27657 | + | 1.27657i | −0.334003 | + | 0.942572i | \(0.608399\pi\) |
−0.942572 | + | 0.334003i | \(0.891601\pi\) | |||||||
\(138\) | 5078.16 | + | 5078.16i | 0.266654 | + | 0.266654i | ||||
\(139\) | − | 19971.2i | − | 1.03365i | −0.856091 | − | 0.516826i | \(-0.827113\pi\) | ||
0.856091 | − | 0.516826i | \(-0.172887\pi\) | |||||||
\(140\) | 1991.12 | − | 103.591i | 0.101588 | − | 0.00528528i | ||||
\(141\) | 15791.0 | 0.794275 | ||||||||
\(142\) | 17044.8 | − | 17044.8i | 0.845310 | − | 0.845310i | ||||
\(143\) | 11490.1 | + | 11490.1i | 0.561889 | + | 0.561889i | ||||
\(144\) | − | 4410.15i | − | 0.212681i | ||||||
\(145\) | −2028.78 | − | 1828.11i | −0.0964935 | − | 0.0869496i | ||||
\(146\) | 38432.8 | 1.80300 | ||||||||
\(147\) | 1979.39 | − | 1979.39i | 0.0916002 | − | 0.0916002i | ||||
\(148\) | −7713.47 | − | 7713.47i | −0.352149 | − | 0.352149i | ||||
\(149\) | − | 6819.69i | − | 0.307179i | −0.988135 | − | 0.153590i | \(-0.950917\pi\) | ||
0.988135 | − | 0.153590i | \(-0.0490834\pi\) | |||||||
\(150\) | −2385.22 | − | 22861.0i | −0.106010 | − | 1.01604i | ||||
\(151\) | 30817.2 | 1.35157 | 0.675786 | − | 0.737098i | \(-0.263804\pi\) | ||||
0.675786 | + | 0.737098i | \(0.263804\pi\) | |||||||
\(152\) | −11884.9 | + | 11884.9i | −0.514410 | + | 0.514410i | ||||
\(153\) | 4640.95 | + | 4640.95i | 0.198255 | + | 0.198255i | ||||
\(154\) | − | 6916.34i | − | 0.291632i | ||||||
\(155\) | −17796.6 | + | 19750.1i | −0.740755 | + | 0.822064i | ||||
\(156\) | −6890.84 | −0.283154 | ||||||||
\(157\) | 28933.5 | − | 28933.5i | 1.17382 | − | 1.17382i | 0.192527 | − | 0.981292i | \(-0.438332\pi\) |
0.981292 | − | 0.192527i | \(-0.0616682\pi\) | |||||||
\(158\) | 29943.7 | + | 29943.7i | 1.19947 | + | 1.19947i | ||||
\(159\) | − | 1181.51i | − | 0.0467352i | ||||||
\(160\) | −698.029 | − | 13416.8i | −0.0272668 | − | 0.524092i | ||||
\(161\) | −3616.61 | −0.139524 | ||||||||
\(162\) | 16530.2 | − | 16530.2i | 0.629865 | − | 0.629865i | ||||
\(163\) | −10644.9 | − | 10644.9i | −0.400652 | − | 0.400652i | 0.477811 | − | 0.878463i | \(-0.341430\pi\) |
−0.878463 | + | 0.477811i | \(0.841430\pi\) | |||||||
\(164\) | 1487.11i | 0.0552913i | ||||||||
\(165\) | −16885.7 | + | 878.508i | −0.620228 | + | 0.0322684i | ||||
\(166\) | −43603.4 | −1.58236 | ||||||||
\(167\) | −5465.46 | + | 5465.46i | −0.195972 | + | 0.195972i | −0.798271 | − | 0.602299i | \(-0.794252\pi\) |
0.602299 | + | 0.798271i | \(0.294252\pi\) | |||||||
\(168\) | −5631.87 | − | 5631.87i | −0.199542 | − | 0.199542i | ||||
\(169\) | 9884.48i | 0.346083i | ||||||||
\(170\) | 38157.0 | + | 34383.0i | 1.32031 | + | 1.18972i | ||||
\(171\) | 4591.66 | 0.157028 | ||||||||
\(172\) | 5227.90 | − | 5227.90i | 0.176714 | − | 0.176714i | ||||
\(173\) | 30524.7 | + | 30524.7i | 1.01990 | + | 1.01990i | 0.999798 | + | 0.0201068i | \(0.00640061\pi\) |
0.0201068 | + | 0.999798i | \(0.493599\pi\) | |||||||
\(174\) | − | 4017.31i | − | 0.132690i | ||||||
\(175\) | 8990.05 | + | 7291.32i | 0.293553 | + | 0.238084i | ||||
\(176\) | −25388.7 | −0.819626 | ||||||||
\(177\) | −14290.6 | + | 14290.6i | −0.456146 | + | 0.456146i | ||||
\(178\) | 7431.65 | + | 7431.65i | 0.234555 | + | 0.234555i | ||||
\(179\) | 46636.5i | 1.45553i | 0.685829 | + | 0.727763i | \(0.259440\pi\) | ||||
−0.685829 | + | 0.727763i | \(0.740560\pi\) | |||||||
\(180\) | −1037.43 | + | 1151.30i | −0.0320195 | + | 0.0355340i | ||||
\(181\) | −31065.2 | −0.948238 | −0.474119 | − | 0.880461i | \(-0.657233\pi\) | ||||
−0.474119 | + | 0.880461i | \(0.657233\pi\) | |||||||
\(182\) | 11571.0 | − | 11571.0i | 0.349323 | − | 0.349323i | ||||
\(183\) | −5987.30 | − | 5987.30i | −0.178784 | − | 0.178784i | ||||
\(184\) | 10290.2i | 0.303940i | ||||||||
\(185\) | −3290.38 | − | 63244.1i | −0.0961396 | − | 1.84789i | ||||
\(186\) | −39108.4 | −1.13043 | ||||||||
\(187\) | 26717.4 | − | 26717.4i | 0.764032 | − | 0.764032i | ||||
\(188\) | −5891.69 | − | 5891.69i | −0.166696 | − | 0.166696i | ||||
\(189\) | 14418.7i | 0.403648i | ||||||||
\(190\) | 35884.8 | − | 1866.97i | 0.994039 | − | 0.0517165i | ||||
\(191\) | −65488.4 | −1.79514 | −0.897569 | − | 0.440874i | \(-0.854668\pi\) | ||||
−0.897569 | + | 0.440874i | \(0.854668\pi\) | |||||||
\(192\) | −14311.9 | + | 14311.9i | −0.388236 | + | 0.388236i | ||||
\(193\) | −43523.1 | − | 43523.1i | −1.16844 | − | 1.16844i | −0.982576 | − | 0.185860i | \(-0.940493\pi\) |
−0.185860 | − | 0.982576i | \(-0.559507\pi\) | |||||||
\(194\) | 24661.0i | 0.655251i | ||||||||
\(195\) | −29719.3 | − | 26779.9i | −0.781574 | − | 0.704270i | ||||
\(196\) | −1477.04 | −0.0384485 | ||||||||
\(197\) | −27866.9 | + | 27866.9i | −0.718052 | + | 0.718052i | −0.968206 | − | 0.250154i | \(-0.919519\pi\) |
0.250154 | + | 0.968206i | \(0.419519\pi\) | |||||||
\(198\) | 3801.38 | + | 3801.38i | 0.0969641 | + | 0.0969641i | ||||
\(199\) | 23306.9i | 0.588542i | 0.955722 | + | 0.294271i | \(0.0950769\pi\) | ||||
−0.955722 | + | 0.294271i | \(0.904923\pi\) | |||||||
\(200\) | 20745.7 | − | 25579.0i | 0.518643 | − | 0.639476i | ||||
\(201\) | 39487.9 | 0.977399 | ||||||||
\(202\) | −30408.1 | + | 30408.1i | −0.745224 | + | 0.745224i | ||||
\(203\) | 1430.54 | + | 1430.54i | 0.0347144 | + | 0.0347144i | ||||
\(204\) | 16023.0i | 0.385021i | ||||||||
\(205\) | −5779.37 | + | 6413.74i | −0.137522 | + | 0.152617i | ||||
\(206\) | −25383.5 | −0.598160 | ||||||||
\(207\) | 1987.77 | − | 1987.77i | 0.0463901 | − | 0.0463901i | ||||
\(208\) | −42475.1 | − | 42475.1i | −0.981765 | − | 0.981765i | ||||
\(209\) | − | 26433.7i | − | 0.605153i | ||||||
\(210\) | 884.693 | + | 17004.6i | 0.0200611 | + | 0.385592i | ||||
\(211\) | 1800.55 | 0.0404426 | 0.0202213 | − | 0.999796i | \(-0.493563\pi\) | ||||
0.0202213 | + | 0.999796i | \(0.493563\pi\) | |||||||
\(212\) | −440.829 | + | 440.829i | −0.00980840 | + | 0.00980840i | ||||
\(213\) | 30869.5 | + | 30869.5i | 0.680410 | + | 0.680410i | ||||
\(214\) | − | 49919.1i | − | 1.09003i | ||||||
\(215\) | 42864.5 | − | 2230.10i | 0.927301 | − | 0.0482444i | ||||
\(216\) | 41025.0 | 0.879308 | ||||||||
\(217\) | 13926.3 | − | 13926.3i | 0.295745 | − | 0.295745i | ||||
\(218\) | 19877.7 | + | 19877.7i | 0.418267 | + | 0.418267i | ||||
\(219\) | 69604.9i | 1.45128i | ||||||||
\(220\) | 6627.92 | + | 5972.37i | 0.136941 | + | 0.123396i | ||||
\(221\) | 89395.9 | 1.83035 | ||||||||
\(222\) | 65874.7 | − | 65874.7i | 1.33663 | − | 1.33663i | ||||
\(223\) | 30912.7 | + | 30912.7i | 0.621623 | + | 0.621623i | 0.945946 | − | 0.324323i | \(-0.105136\pi\) |
−0.324323 | + | 0.945946i | \(0.605136\pi\) | |||||||
\(224\) | 9952.72i | 0.198356i | ||||||||
\(225\) | −8948.61 | + | 933.660i | −0.176763 | + | 0.0184427i | ||||
\(226\) | −67405.0 | −1.31970 | ||||||||
\(227\) | 2474.87 | − | 2474.87i | 0.0480288 | − | 0.0480288i | −0.682684 | − | 0.730713i | \(-0.739188\pi\) |
0.730713 | + | 0.682684i | \(0.239188\pi\) | |||||||
\(228\) | 7926.43 | + | 7926.43i | 0.152478 | + | 0.152478i | ||||
\(229\) | 45124.3i | 0.860477i | 0.902715 | + | 0.430239i | \(0.141571\pi\) | ||||
−0.902715 | + | 0.430239i | \(0.858429\pi\) | |||||||
\(230\) | 14726.6 | − | 16343.1i | 0.278386 | − | 0.308943i | ||||
\(231\) | 12526.0 | 0.234741 | ||||||||
\(232\) | 4070.27 | − | 4070.27i | 0.0756219 | − | 0.0756219i | ||||
\(233\) | −17537.4 | − | 17537.4i | −0.323038 | − | 0.323038i | 0.526894 | − | 0.849931i | \(-0.323357\pi\) |
−0.849931 | + | 0.526894i | \(0.823357\pi\) | |||||||
\(234\) | 12719.3i | 0.232291i | ||||||||
\(235\) | −2513.25 | − | 48307.0i | −0.0455093 | − | 0.874731i | ||||
\(236\) | 10663.8 | 0.191464 | ||||||||
\(237\) | −54230.3 | + | 54230.3i | −0.965485 | + | 0.965485i | ||||
\(238\) | −26905.5 | − | 26905.5i | −0.474994 | − | 0.474994i | ||||
\(239\) | − | 64631.3i | − | 1.13148i | −0.824584 | − | 0.565740i | \(-0.808591\pi\) | ||
0.824584 | − | 0.565740i | \(-0.191409\pi\) | |||||||
\(240\) | 62421.1 | − | 3247.56i | 1.08370 | − | 0.0563813i | ||||
\(241\) | 103691. | 1.78529 | 0.892644 | − | 0.450763i | \(-0.148848\pi\) | ||||
0.892644 | + | 0.450763i | \(0.148848\pi\) | |||||||
\(242\) | −24767.9 | + | 24767.9i | −0.422920 | + | 0.422920i | ||||
\(243\) | −14653.8 | − | 14653.8i | −0.248164 | − | 0.248164i | ||||
\(244\) | 4467.79i | 0.0750434i | ||||||||
\(245\) | −6370.29 | − | 5740.22i | −0.106127 | − | 0.0956304i | ||||
\(246\) | −12700.3 | −0.209866 | ||||||||
\(247\) | 44223.2 | − | 44223.2i | 0.724864 | − | 0.724864i | ||||
\(248\) | −39624.0 | − | 39624.0i | −0.644250 | − | 0.644250i | ||||
\(249\) | − | 78969.1i | − | 1.27367i | ||||||
\(250\) | −69555.7 | + | 10935.3i | −1.11289 | + | 0.174964i | ||||
\(251\) | −22110.1 | −0.350949 | −0.175475 | − | 0.984484i | \(-0.556146\pi\) | ||||
−0.175475 | + | 0.984484i | \(0.556146\pi\) | |||||||
\(252\) | 811.815 | − | 811.815i | 0.0127837 | − | 0.0127837i | ||||
\(253\) | −11443.4 | − | 11443.4i | −0.178778 | − | 0.178778i | ||||
\(254\) | − | 87684.3i | − | 1.35911i | ||||||
\(255\) | −62270.3 | + | 69105.3i | −0.957636 | + | 1.06275i | ||||
\(256\) | 49425.9 | 0.754180 | ||||||||
\(257\) | 6050.54 | − | 6050.54i | 0.0916068 | − | 0.0916068i | −0.659818 | − | 0.751425i | \(-0.729367\pi\) |
0.751425 | + | 0.659818i | \(0.229367\pi\) | |||||||
\(258\) | 44647.4 | + | 44647.4i | 0.670744 | + | 0.670744i | ||||
\(259\) | 46915.2i | 0.699382i | ||||||||
\(260\) | 1096.73 | + | 21080.1i | 0.0162238 | + | 0.311836i | ||||
\(261\) | −1572.52 | −0.0230842 | ||||||||
\(262\) | −49948.1 | + | 49948.1i | −0.727639 | + | 0.727639i | ||||
\(263\) | 58737.2 | + | 58737.2i | 0.849183 | + | 0.849183i | 0.990031 | − | 0.140848i | \(-0.0449829\pi\) |
−0.140848 | + | 0.990031i | \(0.544983\pi\) | |||||||
\(264\) | − | 35639.8i | − | 0.511361i | ||||||
\(265\) | −3614.43 | + | 188.047i | −0.0514693 | + | 0.00267778i | ||||
\(266\) | −26619.8 | −0.376220 | ||||||||
\(267\) | −13459.3 | + | 13459.3i | −0.188799 | + | 0.188799i | ||||
\(268\) | −14733.1 | − | 14733.1i | −0.205128 | − | 0.205128i | ||||
\(269\) | − | 43293.1i | − | 0.598293i | −0.954207 | − | 0.299147i | \(-0.903298\pi\) | ||
0.954207 | − | 0.299147i | \(-0.0967020\pi\) | |||||||
\(270\) | −65156.7 | − | 58712.2i | −0.893782 | − | 0.805380i | ||||
\(271\) | −69048.3 | −0.940187 | −0.470093 | − | 0.882617i | \(-0.655780\pi\) | ||||
−0.470093 | + | 0.882617i | \(0.655780\pi\) | |||||||
\(272\) | −98765.8 | + | 98765.8i | −1.33496 | + | 1.33496i | ||||
\(273\) | 20955.9 | + | 20955.9i | 0.281178 | + | 0.281178i | ||||
\(274\) | 152692.i | 2.03384i | ||||||||
\(275\) | 5374.98 | + | 51516.2i | 0.0710741 | + | 0.681206i | ||||
\(276\) | 6862.85 | 0.0900920 | ||||||||
\(277\) | 13133.8 | − | 13133.8i | 0.171171 | − | 0.171171i | −0.616323 | − | 0.787494i | \(-0.711378\pi\) |
0.787494 | + | 0.616323i | \(0.211378\pi\) | |||||||
\(278\) | −63636.1 | − | 63636.1i | −0.823406 | − | 0.823406i | ||||
\(279\) | 15308.4i | 0.196663i | ||||||||
\(280\) | −16332.4 | + | 18125.1i | −0.208322 | + | 0.231188i | ||||
\(281\) | −75278.8 | −0.953367 | −0.476683 | − | 0.879075i | \(-0.658161\pi\) | ||||
−0.476683 | + | 0.879075i | \(0.658161\pi\) | |||||||
\(282\) | 50316.3 | − | 50316.3i | 0.632718 | − | 0.632718i | ||||
\(283\) | 19793.7 | + | 19793.7i | 0.247147 | + | 0.247147i | 0.819799 | − | 0.572652i | \(-0.194085\pi\) |
−0.572652 | + | 0.819799i | \(0.694085\pi\) | |||||||
\(284\) | − | 23035.1i | − | 0.285597i | ||||||
\(285\) | 3381.22 | + | 64990.2i | 0.0416279 | + | 0.800125i | ||||
\(286\) | 73223.8 | 0.895200 | ||||||||
\(287\) | 4522.50 | − | 4522.50i | 0.0549054 | − | 0.0549054i | ||||
\(288\) | −5470.24 | − | 5470.24i | −0.0659510 | − | 0.0659510i | ||||
\(289\) | − | 124348.i | − | 1.48883i | ||||||
\(290\) | −12289.6 | + | 639.386i | −0.146131 | + | 0.00760269i | ||||
\(291\) | −44663.0 | −0.527427 | ||||||||
\(292\) | 25969.9 | − | 25969.9i | 0.304583 | − | 0.304583i | ||||
\(293\) | 94611.0 | + | 94611.0i | 1.10206 | + | 1.10206i | 0.994162 | + | 0.107901i | \(0.0344130\pi\) |
0.107901 | + | 0.994162i | \(0.465587\pi\) | |||||||
\(294\) | − | 12614.2i | − | 0.145937i | ||||||
\(295\) | 45991.6 | + | 41442.6i | 0.528487 | + | 0.476215i | ||||
\(296\) | 133486. | 1.52354 | ||||||||
\(297\) | −45622.5 | + | 45622.5i | −0.517209 | + | 0.517209i | ||||
\(298\) | −21730.2 | − | 21730.2i | −0.244699 | − | 0.244699i | ||||
\(299\) | − | 38289.3i | − | 0.428287i | ||||||
\(300\) | −17059.4 | − | 13835.9i | −0.189549 | − | 0.153733i | ||||
\(301\) | −31797.4 | −0.350961 | ||||||||
\(302\) | 98195.8 | − | 98195.8i | 1.07666 | − | 1.07666i | ||||
\(303\) | −55071.5 | − | 55071.5i | −0.599848 | − | 0.599848i | ||||
\(304\) | 97716.9i | 1.05736i | ||||||||
\(305\) | −17363.2 | + | 19269.0i | −0.186650 | + | 0.207138i | ||||
\(306\) | 29575.8 | 0.315859 | ||||||||
\(307\) | −30023.7 | + | 30023.7i | −0.318557 | + | 0.318557i | −0.848213 | − | 0.529655i | \(-0.822321\pi\) |
0.529655 | + | 0.848213i | \(0.322321\pi\) | |||||||
\(308\) | −4673.53 | − | 4673.53i | −0.0492655 | − | 0.0492655i | ||||
\(309\) | − | 45971.5i | − | 0.481473i | ||||||
\(310\) | 6224.41 | + | 119639.i | 0.0647701 | + | 1.24494i | ||||
\(311\) | −26989.1 | −0.279040 | −0.139520 | − | 0.990219i | \(-0.544556\pi\) | ||||
−0.139520 | + | 0.990219i | \(0.544556\pi\) | |||||||
\(312\) | 59625.0 | − | 59625.0i | 0.612519 | − | 0.612519i | ||||
\(313\) | 2185.91 | + | 2185.91i | 0.0223122 | + | 0.0223122i | 0.718175 | − | 0.695863i | \(-0.244978\pi\) |
−0.695863 | + | 0.718175i | \(0.744978\pi\) | |||||||
\(314\) | − | 184387.i | − | 1.87013i | ||||||
\(315\) | 6656.21 | − | 346.300i | 0.0670820 | − | 0.00349005i | ||||
\(316\) | 40467.2 | 0.405256 | ||||||||
\(317\) | −10009.8 | + | 10009.8i | −0.0996105 | + | 0.0996105i | −0.755156 | − | 0.655545i | \(-0.772439\pi\) |
0.655545 | + | 0.755156i | \(0.272439\pi\) | |||||||
\(318\) | −3764.77 | − | 3764.77i | −0.0372292 | − | 0.0372292i | ||||
\(319\) | 9052.82i | 0.0889616i | ||||||||
\(320\) | 46060.3 | + | 41504.6i | 0.449808 | + | 0.405318i | ||||
\(321\) | 90407.4 | 0.877393 | ||||||||
\(322\) | −11524.0 | + | 11524.0i | −0.111145 | + | 0.111145i | ||||
\(323\) | −102831. | − | 102831.i | −0.985639 | − | 0.985639i | ||||
\(324\) | − | 22339.6i | − | 0.212807i | ||||||
\(325\) | −77193.7 | + | 95178.3i | −0.730828 | + | 0.901096i | ||||
\(326\) | −67837.8 | −0.638317 | ||||||||
\(327\) | −36000.1 | + | 36000.1i | −0.336673 | + | 0.336673i | ||||
\(328\) | −12867.7 | − | 12867.7i | −0.119606 | − | 0.119606i | ||||
\(329\) | 35834.7i | 0.331064i | ||||||||
\(330\) | −51005.3 | + | 56603.9i | −0.468368 | + | 0.519778i | ||||
\(331\) | 27160.9 | 0.247907 | 0.123953 | − | 0.992288i | \(-0.460443\pi\) | ||||
0.123953 | + | 0.992288i | \(0.460443\pi\) | |||||||
\(332\) | −29463.8 | + | 29463.8i | −0.267308 | + | 0.267308i | ||||
\(333\) | −25785.7 | − | 25785.7i | −0.232536 | − | 0.232536i | ||||
\(334\) | 34830.2i | 0.312222i | ||||||||
\(335\) | −6284.80 | − | 120800.i | −0.0560018 | − | 1.07640i | ||||
\(336\) | −46304.7 | −0.410154 | ||||||||
\(337\) | 132874. | − | 132874.i | 1.16999 | − | 1.16999i | 0.187774 | − | 0.982212i | \(-0.439873\pi\) |
0.982212 | − | 0.187774i | \(-0.0601273\pi\) | |||||||
\(338\) | 31495.9 | + | 31495.9i | 0.275689 | + | 0.275689i | ||||
\(339\) | − | 122076.i | − | 1.06226i | ||||||
\(340\) | 49016.9 | − | 2550.19i | 0.424022 | − | 0.0220604i | ||||
\(341\) | 88129.0 | 0.757897 | ||||||||
\(342\) | 14630.8 | − | 14630.8i | 0.125088 | − | 0.125088i | ||||
\(343\) | 4491.86 | + | 4491.86i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 90471.8i | 0.764534i | ||||||||
\(345\) | 29598.6 | + | 26671.1i | 0.248675 | + | 0.224080i | ||||
\(346\) | 194528. | 1.62491 | ||||||||
\(347\) | −15311.9 | + | 15311.9i | −0.127165 | + | 0.127165i | −0.767825 | − | 0.640660i | \(-0.778661\pi\) |
0.640660 | + | 0.767825i | \(0.278661\pi\) | |||||||
\(348\) | −2714.59 | − | 2714.59i | −0.0224153 | − | 0.0224153i | ||||
\(349\) | 37132.2i | 0.304859i | 0.988314 | + | 0.152430i | \(0.0487098\pi\) | ||||
−0.988314 | + | 0.152430i | \(0.951290\pi\) | |||||||
\(350\) | 51878.9 | − | 5412.82i | 0.423501 | − | 0.0441863i | ||||
\(351\) | −152652. | −1.23905 | ||||||||
\(352\) | −31491.6 | + | 31491.6i | −0.254161 | + | 0.254161i | ||||
\(353\) | −161388. | − | 161388.i | −1.29515 | − | 1.29515i | −0.931556 | − | 0.363597i | \(-0.881548\pi\) |
−0.363597 | − | 0.931556i | \(-0.618452\pi\) | |||||||
\(354\) | 91070.9i | 0.726730i | ||||||||
\(355\) | 89521.5 | − | 99347.7i | 0.710347 | − | 0.788317i | ||||
\(356\) | 10043.5 | 0.0792471 | ||||||||
\(357\) | 48728.0 | − | 48728.0i | 0.382334 | − | 0.382334i | ||||
\(358\) | 148602. | + | 148602.i | 1.15947 | + | 1.15947i | ||||
\(359\) | 125942.i | 0.977196i | 0.872509 | + | 0.488598i | \(0.162492\pi\) | ||||
−0.872509 | + | 0.488598i | \(0.837508\pi\) | |||||||
\(360\) | −985.315 | − | 18938.6i | −0.00760274 | − | 0.146132i | ||||
\(361\) | 28582.4 | 0.219323 | ||||||||
\(362\) | −98986.1 | + | 98986.1i | −0.755365 | + | 0.755365i | ||||
\(363\) | −44856.6 | − | 44856.6i | −0.340418 | − | 0.340418i | ||||
\(364\) | − | 15637.5i | − | 0.118023i | ||||||
\(365\) | 212932. | − | 11078.1i | 1.59829 | − | 0.0831536i | ||||
\(366\) | −38155.8 | −0.284839 | ||||||||
\(367\) | −9247.64 | + | 9247.64i | −0.0686592 | + | 0.0686592i | −0.740603 | − | 0.671943i | \(-0.765460\pi\) |
0.671943 | + | 0.740603i | \(0.265460\pi\) | |||||||
\(368\) | 42302.5 | + | 42302.5i | 0.312371 | + | 0.312371i | ||||
\(369\) | 4971.34i | 0.0365107i | ||||||||
\(370\) | −212005. | − | 191036.i | −1.54861 | − | 1.39544i | ||||
\(371\) | 2681.23 | 0.0194799 | ||||||||
\(372\) | −26426.4 | + | 26426.4i | −0.190965 | + | 0.190965i | ||||
\(373\) | −24882.0 | − | 24882.0i | −0.178841 | − | 0.178841i | 0.612009 | − | 0.790851i | \(-0.290362\pi\) |
−0.790851 | + | 0.612009i | \(0.790362\pi\) | |||||||
\(374\) | − | 170265.i | − | 1.21725i | ||||||
\(375\) | −19804.6 | − | 125971.i | −0.140833 | − | 0.895792i | ||||
\(376\) | 101959. | 0.721191 | ||||||||
\(377\) | −15145.3 | + | 15145.3i | −0.106560 | + | 0.106560i | ||||
\(378\) | 45943.8 | + | 45943.8i | 0.321546 | + | 0.321546i | ||||
\(379\) | 95296.2i | 0.663433i | 0.943379 | + | 0.331717i | \(0.107628\pi\) | ||||
−0.943379 | + | 0.331717i | \(0.892372\pi\) | |||||||
\(380\) | 22986.6 | − | 25509.7i | 0.159187 | − | 0.176660i | ||||
\(381\) | 158803. | 1.09398 | ||||||||
\(382\) | −208672. | + | 208672.i | −1.43000 | + | 1.43000i | ||||
\(383\) | 53485.3 | + | 53485.3i | 0.364617 | + | 0.364617i | 0.865509 | − | 0.500893i | \(-0.166995\pi\) |
−0.500893 | + | 0.865509i | \(0.666995\pi\) | |||||||
\(384\) | 161379.i | 1.09442i | ||||||||
\(385\) | −1993.61 | − | 38319.1i | −0.0134499 | − | 0.258520i | ||||
\(386\) | −277364. | −1.86155 | ||||||||
\(387\) | 17476.6 | − | 17476.6i | 0.116690 | − | 0.116690i | ||||
\(388\) | 16664.0 | + | 16664.0i | 0.110692 | + | 0.110692i | ||||
\(389\) | 90635.5i | 0.598962i | 0.954102 | + | 0.299481i | \(0.0968135\pi\) | ||||
−0.954102 | + | 0.299481i | \(0.903187\pi\) | |||||||
\(390\) | −180029. | + | 9366.30i | −1.18362 | + | 0.0615799i | ||||
\(391\) | −89032.7 | −0.582366 | ||||||||
\(392\) | 12780.5 | − | 12780.5i | 0.0831718 | − | 0.0831718i | ||||
\(393\) | −90459.8 | − | 90459.8i | −0.585694 | − | 0.585694i | ||||
\(394\) | 177590.i | 1.14400i | ||||||||
\(395\) | 174530. | + | 157268.i | 1.11860 | + | 1.00796i | ||||
\(396\) | 5137.35 | 0.0327604 | ||||||||
\(397\) | −80322.1 | + | 80322.1i | −0.509629 | + | 0.509629i | −0.914412 | − | 0.404784i | \(-0.867347\pi\) |
0.404784 | + | 0.914412i | \(0.367347\pi\) | |||||||
\(398\) | 74264.9 | + | 74264.9i | 0.468832 | + | 0.468832i | ||||
\(399\) | − | 48210.5i | − | 0.302828i | ||||||
\(400\) | −19869.6 | − | 190439.i | −0.124185 | − | 1.19024i | ||||
\(401\) | −218532. | −1.35902 | −0.679512 | − | 0.733664i | \(-0.737808\pi\) | ||||
−0.679512 | + | 0.733664i | \(0.737808\pi\) | |||||||
\(402\) | 125824. | − | 125824.i | 0.778595 | − | 0.778595i | ||||
\(403\) | 147439. | + | 147439.i | 0.907824 | + | 0.907824i | ||||
\(404\) | 41094.9i | 0.251782i | ||||||||
\(405\) | 86818.4 | − | 96347.9i | 0.529300 | − | 0.587398i | ||||
\(406\) | 9116.56 | 0.0553069 | ||||||||
\(407\) | −148445. | + | 148445.i | −0.896144 | + | 0.896144i | ||||
\(408\) | −138644. | − | 138644.i | −0.832876 | − | 0.832876i | ||||
\(409\) | − | 148940.i | − | 0.890358i | −0.895442 | − | 0.445179i | \(-0.853140\pi\) | ||
0.895442 | − | 0.445179i | \(-0.146860\pi\) | |||||||
\(410\) | 2021.34 | + | 38852.1i | 0.0120247 | + | 0.231125i | ||||
\(411\) | −276538. | −1.63708 | ||||||||
\(412\) | −17152.2 | + | 17152.2i | −0.101048 | + | 0.101048i | ||||
\(413\) | −32429.9 | − | 32429.9i | −0.190128 | − | 0.190128i | ||||
\(414\) | − | 12667.7i | − | 0.0739087i | ||||||
\(415\) | −241579. | + | 12568.5i | −1.40269 | + | 0.0729774i | ||||
\(416\) | −105370. | −0.608878 | ||||||||
\(417\) | 115250. | − | 115250.i | 0.662779 | − | 0.662779i | ||||
\(418\) | −84228.2 | − | 84228.2i | −0.482064 | − | 0.482064i | ||||
\(419\) | 23757.3i | 0.135322i | 0.997708 | + | 0.0676611i | \(0.0215536\pi\) | ||||
−0.997708 | + | 0.0676611i | \(0.978446\pi\) | |||||||
\(420\) | 12088.2 | + | 10892.6i | 0.0685272 | + | 0.0617493i | ||||
\(421\) | 210054. | 1.18513 | 0.592566 | − | 0.805522i | \(-0.298115\pi\) | ||||
0.592566 | + | 0.805522i | \(0.298115\pi\) | |||||||
\(422\) | 5737.25 | − | 5737.25i | 0.0322165 | − | 0.0322165i | ||||
\(423\) | −19695.6 | − | 19695.6i | −0.110075 | − | 0.110075i | ||||
\(424\) | − | 7628.79i | − | 0.0424350i | ||||||
\(425\) | 221315. | + | 179496.i | 1.22527 | + | 0.993748i | ||||
\(426\) | 196725. | 1.08403 | ||||||||
\(427\) | 13587.1 | − | 13587.1i | 0.0745197 | − | 0.0745197i | ||||
\(428\) | −33731.5 | − | 33731.5i | −0.184140 | − | 0.184140i | ||||
\(429\) | 132614.i | 0.720567i | ||||||||
\(430\) | 129477. | − | 143689.i | 0.700255 | − | 0.777118i | ||||
\(431\) | −214415. | −1.15425 | −0.577125 | − | 0.816656i | \(-0.695826\pi\) | ||||
−0.577125 | + | 0.816656i | \(0.695826\pi\) | |||||||
\(432\) | 168652. | − | 168652.i | 0.903699 | − | 0.903699i | ||||
\(433\) | −9412.58 | − | 9412.58i | −0.0502034 | − | 0.0502034i | 0.681559 | − | 0.731763i | \(-0.261302\pi\) |
−0.731763 | + | 0.681559i | \(0.761302\pi\) | |||||||
\(434\) | − | 88749.5i | − | 0.471180i | ||||||
\(435\) | −1157.98 | − | 22257.4i | −0.00611958 | − | 0.117624i | ||||
\(436\) | 26863.7 | 0.141316 | ||||||||
\(437\) | −44043.6 | + | 44043.6i | −0.230632 | + | 0.230632i | ||||
\(438\) | 221789. | + | 221789.i | 1.15609 | + | 1.15609i | ||||
\(439\) | − | 202275.i | − | 1.04957i | −0.851234 | − | 0.524787i | \(-0.824145\pi\) | ||
0.851234 | − | 0.524787i | \(-0.175855\pi\) | |||||||
\(440\) | −109028. | + | 5672.35i | −0.563159 | + | 0.0292993i | ||||
\(441\) | −4937.66 | −0.0253889 | ||||||||
\(442\) | 284851. | − | 284851.i | 1.45805 | − | 1.45805i | ||||
\(443\) | 102659. | + | 102659.i | 0.523103 | + | 0.523103i | 0.918507 | − | 0.395404i | \(-0.129395\pi\) |
−0.395404 | + | 0.918507i | \(0.629395\pi\) | |||||||
\(444\) | − | 89025.9i | − | 0.451597i | ||||||
\(445\) | 43316.2 | + | 39031.9i | 0.218741 | + | 0.197106i | ||||
\(446\) | 197000. | 0.990369 | ||||||||
\(447\) | 39355.1 | − | 39355.1i | 0.196964 | − | 0.196964i | ||||
\(448\) | −32478.4 | − | 32478.4i | −0.161822 | − | 0.161822i | ||||
\(449\) | − | 209359.i | − | 1.03848i | −0.854628 | − | 0.519241i | \(-0.826215\pi\) | ||
0.854628 | − | 0.519241i | \(-0.173785\pi\) | |||||||
\(450\) | −25538.8 | + | 31488.8i | −0.126118 | + | 0.155500i | ||||
\(451\) | 28619.4 | 0.140705 | ||||||||
\(452\) | −45547.1 | + | 45547.1i | −0.222938 | + | 0.222938i | ||||
\(453\) | 177840. | + | 177840.i | 0.866629 | + | 0.866629i | ||||
\(454\) | − | 15771.9i | − | 0.0765193i | ||||||
\(455\) | 60772.0 | − | 67442.6i | 0.293549 | − | 0.325770i | ||||
\(456\) | −137171. | −0.659681 | ||||||||
\(457\) | 63047.3 | − | 63047.3i | 0.301880 | − | 0.301880i | −0.539869 | − | 0.841749i | \(-0.681526\pi\) |
0.841749 | + | 0.539869i | \(0.181526\pi\) | |||||||
\(458\) | 143784. | + | 143784.i | 0.685455 | + | 0.685455i | ||||
\(459\) | 354956.i | 1.68480i | ||||||||
\(460\) | −1092.27 | − | 20994.5i | −0.00516198 | − | 0.0992179i | ||||
\(461\) | −65395.3 | −0.307712 | −0.153856 | − | 0.988093i | \(-0.549169\pi\) | ||||
−0.153856 | + | 0.988093i | \(0.549169\pi\) | |||||||
\(462\) | 39912.9 | − | 39912.9i | 0.186995 | − | 0.186995i | ||||
\(463\) | 268394. | + | 268394.i | 1.25202 | + | 1.25202i | 0.954814 | + | 0.297203i | \(0.0960539\pi\) |
0.297203 | + | 0.954814i | \(0.403946\pi\) | |||||||
\(464\) | − | 33465.4i | − | 0.155439i | ||||||
\(465\) | −216675. | + | 11272.9i | −1.00208 | + | 0.0521350i | ||||
\(466\) | −111762. | −0.514663 | ||||||||
\(467\) | 119388. | − | 119388.i | 0.547429 | − | 0.547429i | −0.378268 | − | 0.925696i | \(-0.623480\pi\) |
0.925696 | + | 0.378268i | \(0.123480\pi\) | |||||||
\(468\) | 8594.73 | + | 8594.73i | 0.0392411 | + | 0.0392411i | ||||
\(469\) | 89610.6i | 0.407393i | ||||||||
\(470\) | −161934. | − | 145917.i | −0.733062 | − | 0.660557i | ||||
\(471\) | 333939. | 1.50531 | ||||||||
\(472\) | −92271.5 | + | 92271.5i | −0.414175 | + | 0.414175i | ||||
\(473\) | −100611. | − | 100611.i | −0.449699 | − | 0.449699i | ||||
\(474\) | 345598.i | 1.53821i | ||||||||
\(475\) | 198277. | − | 20687.4i | 0.878789 | − | 0.0916891i | ||||
\(476\) | −36361.4 | −0.160482 | ||||||||
\(477\) | −1473.66 | + | 1473.66i | −0.00647682 | + | 0.00647682i | ||||
\(478\) | −205941. | − | 205941.i | −0.901336 | − | 0.901336i | ||||
\(479\) | 58396.0i | 0.254514i | 0.991870 | + | 0.127257i | \(0.0406173\pi\) | ||||
−0.991870 | + | 0.127257i | \(0.959383\pi\) | |||||||
\(480\) | 73397.4 | − | 81453.8i | 0.318565 | − | 0.353532i | ||||
\(481\) | −496695. | −2.14684 | ||||||||
\(482\) | 330401. | − | 330401.i | 1.42216 | − | 1.42216i | ||||
\(483\) | −20870.8 | − | 20870.8i | −0.0894631 | − | 0.0894631i | ||||
\(484\) | 33472.4i | 0.142888i | ||||||||
\(485\) | 7108.46 | + | 136631.i | 0.0302198 | + | 0.580853i | ||||
\(486\) | −93385.8 | −0.395374 | ||||||||
\(487\) | −136786. | + | 136786.i | −0.576746 | + | 0.576746i | −0.934005 | − | 0.357259i | \(-0.883711\pi\) |
0.357259 | + | 0.934005i | \(0.383711\pi\) | |||||||
\(488\) | −38658.8 | − | 38658.8i | −0.162334 | − | 0.162334i | ||||
\(489\) | − | 122860.i | − | 0.513796i | ||||||
\(490\) | −38588.9 | + | 2007.65i | −0.160720 | + | 0.00836172i | ||||
\(491\) | 76816.5 | 0.318633 | 0.159317 | − | 0.987228i | \(-0.449071\pi\) | ||||
0.159317 | + | 0.987228i | \(0.449071\pi\) | |||||||
\(492\) | −8581.85 | + | 8581.85i | −0.0354528 | + | 0.0354528i | ||||
\(493\) | 35216.8 | + | 35216.8i | 0.144896 | + | 0.144896i | ||||
\(494\) | − | 281826.i | − | 1.15485i | ||||||
\(495\) | 22156.8 | + | 19965.3i | 0.0904265 | + | 0.0814827i | ||||
\(496\) | −325785. | −1.32424 | ||||||||
\(497\) | −70052.7 | + | 70052.7i | −0.283604 | + | 0.283604i | ||||
\(498\) | −251627. | − | 251627.i | −1.01461 | − | 1.01461i | ||||
\(499\) | − | 93103.6i | − | 0.373908i | −0.982369 | − | 0.186954i | \(-0.940138\pi\) | ||
0.982369 | − | 0.186954i | \(-0.0598616\pi\) | |||||||
\(500\) | −39611.1 | + | 54389.5i | −0.158445 | + | 0.217558i | ||||
\(501\) | −63080.2 | −0.251315 | ||||||||
\(502\) | −70451.7 | + | 70451.7i | −0.279566 | + | 0.279566i | ||||
\(503\) | 55172.2 | + | 55172.2i | 0.218064 | + | 0.218064i | 0.807682 | − | 0.589618i | \(-0.200722\pi\) |
−0.589618 | + | 0.807682i | \(0.700722\pi\) | |||||||
\(504\) | 14048.9i | 0.0553072i | ||||||||
\(505\) | −159707. | + | 177237.i | −0.626241 | + | 0.694979i | ||||
\(506\) | −72926.3 | −0.284828 | ||||||||
\(507\) | −57041.5 | + | 57041.5i | −0.221909 | + | 0.221909i | ||||
\(508\) | −59250.2 | − | 59250.2i | −0.229595 | − | 0.229595i | ||||
\(509\) | − | 336340.i | − | 1.29820i | −0.760702 | − | 0.649102i | \(-0.775145\pi\) | ||
0.760702 | − | 0.649102i | \(-0.224855\pi\) | |||||||
\(510\) | 21779.1 | + | 418615.i | 0.0837337 | + | 1.60944i | ||||
\(511\) | −157956. | −0.604913 | ||||||||
\(512\) | −66227.7 | + | 66227.7i | −0.252639 | + | 0.252639i | ||||
\(513\) | 175593. | + | 175593.i | 0.667226 | + | 0.667226i | ||||
\(514\) | − | 38558.8i | − | 0.145948i | ||||||
\(515\) | −140634. | + | 7316.72i | −0.530244 | + | 0.0275868i | ||||
\(516\) | 60338.4 | 0.226618 | ||||||||
\(517\) | −113385. | + | 113385.i | −0.424205 | + | 0.424205i | ||||
\(518\) | 149491. | + | 149491.i | 0.557127 | + | 0.557127i | ||||
\(519\) | 352305.i | 1.30793i | ||||||||
\(520\) | −191892. | − | 172912.i | −0.709659 | − | 0.639468i | ||||
\(521\) | 6117.78 | 0.0225382 | 0.0112691 | − | 0.999937i | \(-0.496413\pi\) | ||||
0.0112691 | + | 0.999937i | \(0.496413\pi\) | |||||||
\(522\) | −5010.67 | + | 5010.67i | −0.0183889 | + | 0.0183889i | ||||
\(523\) | −45550.4 | − | 45550.4i | −0.166529 | − | 0.166529i | 0.618923 | − | 0.785452i | \(-0.287569\pi\) |
−0.785452 | + | 0.618923i | \(0.787569\pi\) | |||||||
\(524\) | 67502.0i | 0.245841i | ||||||||
\(525\) | 9803.04 | + | 93956.7i | 0.0355666 | + | 0.340886i | ||||
\(526\) | 374320. | 1.35292 | ||||||||
\(527\) | 342834. | − | 342834.i | 1.23442 | − | 1.23442i | ||||
\(528\) | −146514. | − | 146514.i | −0.525545 | − | 0.525545i | ||||
\(529\) | − | 241707.i | − | 0.863731i | ||||||
\(530\) | −10917.8 | + | 12116.2i | −0.0388673 | + | 0.0431335i | ||||
\(531\) | 35648.4 | 0.126430 | ||||||||
\(532\) | −17987.6 | + | 17987.6i | −0.0635550 | + | 0.0635550i | ||||
\(533\) | 47880.0 | + | 47880.0i | 0.168539 | + | 0.168539i | ||||
\(534\) | 85773.3i | 0.300794i | ||||||||
\(535\) | −14389.0 | − | 276570.i | −0.0502717 | − | 0.966268i | ||||
\(536\) | 254965. | 0.887466 | ||||||||
\(537\) | −269130. | + | 269130.i | −0.933285 | + | 0.933285i | ||||
\(538\) | −137949. | − | 137949.i | −0.476600 | − | 0.476600i | ||||
\(539\) | 28425.5i | 0.0978433i | ||||||||
\(540\) | −83701.0 | + | 4354.68i | −0.287040 | + | 0.0149338i | ||||
\(541\) | 450261. | 1.53840 | 0.769201 | − | 0.639007i | \(-0.220655\pi\) | ||||
0.769201 | + | 0.639007i | \(0.220655\pi\) | |||||||
\(542\) | −220015. | + | 220015.i | −0.748952 | + | 0.748952i | ||||
\(543\) | −179271. | − | 179271.i | −0.608011 | − | 0.608011i | ||||
\(544\) | 245013.i | 0.827927i | ||||||||
\(545\) | 115860. | + | 104400.i | 0.390067 | + | 0.351486i | ||||
\(546\) | 133548. | 0.447972 | ||||||||
\(547\) | −244018. | + | 244018.i | −0.815543 | + | 0.815543i | −0.985459 | − | 0.169916i | \(-0.945650\pi\) |
0.169916 | + | 0.985459i | \(0.445650\pi\) | |||||||
\(548\) | 103178. | + | 103178.i | 0.343577 | + | 0.343577i | ||||
\(549\) | 14935.6i | 0.0495538i | ||||||||
\(550\) | 181278. | + | 147024.i | 0.599265 | + | 0.486030i | ||||
\(551\) | 34842.7 | 0.114765 | ||||||||
\(552\) | −59382.8 | + | 59382.8i | −0.194887 | + | 0.194887i | ||||
\(553\) | −123066. | − | 123066.i | −0.402427 | − | 0.402427i | ||||
\(554\) | − | 83698.7i | − | 0.272709i | ||||||
\(555\) | 345981. | − | 383958.i | 1.12323 | − | 1.24651i | ||||
\(556\) | −86000.7 | −0.278197 | ||||||||
\(557\) | −48553.9 | + | 48553.9i | −0.156500 | + | 0.156500i | −0.781014 | − | 0.624514i | \(-0.785297\pi\) |
0.624514 | + | 0.781014i | \(0.285297\pi\) | |||||||
\(558\) | 48778.8 | + | 48778.8i | 0.156662 | + | 0.156662i | ||||
\(559\) | − | 336641.i | − | 1.07732i | ||||||
\(560\) | 7369.75 | + | 141653.i | 0.0235005 | + | 0.451701i | ||||
\(561\) | 308362. | 0.979796 | ||||||||
\(562\) | −239868. | + | 239868.i | −0.759451 | + | 0.759451i | ||||
\(563\) | 181644. | + | 181644.i | 0.573065 | + | 0.573065i | 0.932984 | − | 0.359919i | \(-0.117196\pi\) |
−0.359919 | + | 0.932984i | \(0.617196\pi\) | |||||||
\(564\) | − | 67999.7i | − | 0.213771i | ||||||
\(565\) | −373448. | + | 19429.3i | −1.16986 | + | 0.0608639i | ||||
\(566\) | 126141. | 0.393753 | ||||||||
\(567\) | −67937.5 | + | 67937.5i | −0.211321 | + | 0.211321i | ||||
\(568\) | 199318. | + | 199318.i | 0.617804 | + | 0.617804i | ||||
\(569\) | − | 18687.2i | − | 0.0577191i | −0.999583 | − | 0.0288595i | \(-0.990812\pi\) | ||
0.999583 | − | 0.0288595i | \(-0.00918755\pi\) | |||||||
\(570\) | 217858. | + | 196311.i | 0.670540 | + | 0.604218i | ||||
\(571\) | 518058. | 1.58893 | 0.794467 | − | 0.607307i | \(-0.207750\pi\) | ||||
0.794467 | + | 0.607307i | \(0.207750\pi\) | |||||||
\(572\) | 49478.9 | − | 49478.9i | 0.151227 | − | 0.151227i | ||||
\(573\) | −377921. | − | 377921.i | −1.15104 | − | 1.15104i | ||||
\(574\) | − | 28820.9i | − | 0.0874751i | ||||||
\(575\) | 76880.1 | − | 94791.6i | 0.232530 | − | 0.286704i | ||||
\(576\) | 35701.7 | 0.107608 | ||||||||
\(577\) | 151903. | − | 151903.i | 0.456262 | − | 0.456262i | −0.441164 | − | 0.897426i | \(-0.645434\pi\) |
0.897426 | + | 0.441164i | \(0.145434\pi\) | |||||||
\(578\) | −396222. | − | 396222.i | −1.18600 | − | 1.18600i | ||||
\(579\) | − | 502327.i | − | 1.49841i | ||||||
\(580\) | −7872.30 | + | 8736.39i | −0.0234016 | + | 0.0259702i | ||||
\(581\) | 179206. | 0.530885 | ||||||||
\(582\) | −142314. | + | 142314.i | −0.420148 | + | 0.420148i | ||||
\(583\) | 8483.72 | + | 8483.72i | 0.0249603 | + | 0.0249603i | ||||
\(584\) | 449425.i | 1.31774i | ||||||||
\(585\) | 3666.30 | + | 70469.7i | 0.0107131 | + | 0.205916i | ||||
\(586\) | 602936. | 1.75580 | ||||||||
\(587\) | 36664.3 | − | 36664.3i | 0.106406 | − | 0.106406i | −0.651899 | − | 0.758306i | \(-0.726028\pi\) |
0.758306 | + | 0.651899i | \(0.226028\pi\) | |||||||
\(588\) | −8523.71 | − | 8523.71i | −0.0246532 | − | 0.0246532i | ||||
\(589\) | − | 339193.i | − | 0.977724i | ||||||
\(590\) | 278600. | − | 14494.6i | 0.800345 | − | 0.0416393i | ||||
\(591\) | −321629. | −0.920831 | ||||||||
\(592\) | 548755. | − | 548755.i | 1.56580 | − | 1.56580i | ||||
\(593\) | −164771. | − | 164771.i | −0.468567 | − | 0.468567i | 0.432883 | − | 0.901450i | \(-0.357496\pi\) |
−0.901450 | + | 0.432883i | \(0.857496\pi\) | |||||||
\(594\) | 290743.i | 0.824017i | ||||||||
\(595\) | −156822. | − | 141311.i | −0.442969 | − | 0.399156i | ||||
\(596\) | −29367.2 | −0.0826741 | ||||||||
\(597\) | −134499. | + | 134499.i | −0.377374 | + | 0.377374i | ||||
\(598\) | −122005. | − | 122005.i | −0.341173 | − | 0.341173i | ||||
\(599\) | − | 452258.i | − | 1.26047i | −0.776405 | − | 0.630235i | \(-0.782959\pi\) | ||
0.776405 | − | 0.630235i | \(-0.217041\pi\) | |||||||
\(600\) | 267331. | − | 27892.2i | 0.742587 | − | 0.0774784i | ||||
\(601\) | −52710.0 | −0.145930 | −0.0729648 | − | 0.997335i | \(-0.523246\pi\) | ||||
−0.0729648 | + | 0.997335i | \(0.523246\pi\) | |||||||
\(602\) | −101319. | + | 101319.i | −0.279575 | + | 0.279575i | ||||
\(603\) | −49252.0 | − | 49252.0i | −0.135453 | − | 0.135453i | ||||
\(604\) | − | 132706.i | − | 0.363762i | ||||||
\(605\) | −130084. | + | 144362.i | −0.355396 | + | 0.394406i | ||||
\(606\) | −350959. | −0.955677 | ||||||||
\(607\) | 89771.2 | − | 89771.2i | 0.243646 | − | 0.243646i | −0.574710 | − | 0.818357i | \(-0.694885\pi\) |
0.818357 | + | 0.574710i | \(0.194885\pi\) | |||||||
\(608\) | 121206. | + | 121206.i | 0.327880 | + | 0.327880i | ||||
\(609\) | 16510.8i | 0.0445178i | ||||||||
\(610\) | 6072.79 | + | 116725.i | 0.0163203 | + | 0.313691i | ||||
\(611\) | −379385. | −1.01624 | ||||||||
\(612\) | 19985.0 | − | 19985.0i | 0.0533583 | − | 0.0533583i | ||||
\(613\) | −101979. | − | 101979.i | −0.271387 | − | 0.271387i | 0.558272 | − | 0.829658i | \(-0.311465\pi\) |
−0.829658 | + | 0.558272i | \(0.811465\pi\) | |||||||
\(614\) | 191335.i | 0.507525i | ||||||||
\(615\) | −70364.1 | + | 3660.81i | −0.186038 | + | 0.00967892i | ||||
\(616\) | 80878.1 | 0.213142 | ||||||||
\(617\) | −265131. | + | 265131.i | −0.696451 | + | 0.696451i | −0.963643 | − | 0.267192i | \(-0.913904\pi\) |
0.267192 | + | 0.963643i | \(0.413904\pi\) | |||||||
\(618\) | −146483. | − | 146483.i | −0.383541 | − | 0.383541i | ||||
\(619\) | 533768.i | 1.39306i | 0.717526 | + | 0.696532i | \(0.245274\pi\) | ||||
−0.717526 | + | 0.696532i | \(0.754726\pi\) | |||||||
\(620\) | 85048.5 | + | 76636.6i | 0.221250 | + | 0.199367i | ||||
\(621\) | 152032. | 0.394231 | ||||||||
\(622\) | −85997.9 | + | 85997.9i | −0.222283 | + | 0.222283i | ||||
\(623\) | −30543.4 | − | 30543.4i | −0.0786940 | − | 0.0786940i | ||||
\(624\) | − | 490231.i | − | 1.25902i | ||||||
\(625\) | −382212. | + | 80634.5i | −0.978463 | + | 0.206424i | ||||
\(626\) | 13930.3 | 0.0355478 | ||||||||
\(627\) | 152544. | − | 152544.i | 0.388025 | − | 0.388025i | ||||
\(628\) | −124594. | − | 124594.i | −0.315921 | − | 0.315921i | ||||
\(629\) | 1.15495e6i | 2.91918i | ||||||||
\(630\) | 20105.9 | − | 22312.8i | 0.0506573 | − | 0.0562176i | ||||
\(631\) | 68287.8 | 0.171508 | 0.0857539 | − | 0.996316i | \(-0.472670\pi\) | ||||
0.0857539 | + | 0.996316i | \(0.472670\pi\) | |||||||
\(632\) | −350154. | + | 350154.i | −0.876648 | + | 0.876648i | ||||
\(633\) | 10390.6 | + | 10390.6i | 0.0259319 | + | 0.0259319i | ||||
\(634\) | 63790.1i | 0.158699i | ||||||||
\(635\) | −25274.7 | − | 485803.i | −0.0626814 | − | 1.20479i | ||||
\(636\) | −5087.88 | −0.0125783 | ||||||||
\(637\) | −47555.6 | + | 47555.6i | −0.117199 | + | 0.117199i | ||||
\(638\) | 28845.9 | + | 28845.9i | 0.0708667 | + | 0.0708667i | ||||
\(639\) | − | 77005.2i | − | 0.188590i | ||||||
\(640\) | 493685. | − | 25684.8i | 1.20528 | − | 0.0627070i | ||||
\(641\) | 222733. | 0.542087 | 0.271043 | − | 0.962567i | \(-0.412631\pi\) | ||||
0.271043 | + | 0.962567i | \(0.412631\pi\) | |||||||
\(642\) | 288074. | − | 288074.i | 0.698930 | − | 0.698930i | ||||
\(643\) | 231245. | + | 231245.i | 0.559308 | + | 0.559308i | 0.929110 | − | 0.369802i | \(-0.120575\pi\) |
−0.369802 | + | 0.929110i | \(0.620575\pi\) | |||||||
\(644\) | 15574.0i | 0.0375515i | ||||||||
\(645\) | 260232. | + | 234493.i | 0.625521 | + | 0.563652i | ||||
\(646\) | −655319. | −1.57032 | ||||||||
\(647\) | 456819. | − | 456819.i | 1.09128 | − | 1.09128i | 0.0958866 | − | 0.995392i | \(-0.469431\pi\) |
0.995392 | − | 0.0958866i | \(-0.0305686\pi\) | |||||||
\(648\) | 193300. | + | 193300.i | 0.460343 | + | 0.460343i | ||||
\(649\) | − | 205224.i | − | 0.487235i | ||||||
\(650\) | 57305.9 | + | 549245.i | 0.135635 | + | 1.29999i | ||||
\(651\) | 160732. | 0.379263 | ||||||||
\(652\) | −45839.5 | + | 45839.5i | −0.107831 | + | 0.107831i | ||||
\(653\) | 103032. | + | 103032.i | 0.241627 | + | 0.241627i | 0.817523 | − | 0.575896i | \(-0.195347\pi\) |
−0.575896 | + | 0.817523i | \(0.695347\pi\) | |||||||
\(654\) | 229421.i | 0.536387i | ||||||||
\(655\) | −262333. | + | 291128.i | −0.611463 | + | 0.678580i | ||||
\(656\) | −105797. | −0.245847 | ||||||||
\(657\) | 86816.0 | − | 86816.0i | 0.201126 | − | 0.201126i | ||||
\(658\) | 114184. | + | 114184.i | 0.263726 | + | 0.263726i | ||||
\(659\) | 121879.i | 0.280645i | 0.990106 | + | 0.140322i | \(0.0448139\pi\) | ||||
−0.990106 | + | 0.140322i | \(0.955186\pi\) | |||||||
\(660\) | 3783.06 | + | 72713.9i | 0.00868472 | + | 0.166928i | ||||
\(661\) | −463772. | −1.06145 | −0.530727 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530727 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(662\) | 86545.3 | − | 86545.3i | 0.197482 | − | 0.197482i | ||||
\(663\) | 515887. | + | 515887.i | 1.17362 | + | 1.17362i | ||||
\(664\) | − | 509888.i | − | 1.15648i | ||||||
\(665\) | −147483. | + | 7673.07i | −0.333503 | + | 0.0173511i | ||||
\(666\) | −164327. | −0.370476 | ||||||||
\(667\) | 15083.7 | − | 15083.7i | 0.0339045 | − | 0.0339045i | ||||
\(668\) | 23535.6 | + | 23535.6i | 0.0527438 | + | 0.0527438i | ||||
\(669\) | 356783.i | 0.797171i | ||||||||
\(670\) | −404941. | − | 364889.i | −0.902074 | − | 0.812852i | ||||
\(671\) | 85982.3 | 0.190970 | ||||||||
\(672\) | −57435.2 | + | 57435.2i | −0.127186 | + | 0.127186i | ||||
\(673\) | −507009. | − | 507009.i | −1.11940 | − | 1.11940i | −0.991829 | − | 0.127572i | \(-0.959282\pi\) |
−0.127572 | − | 0.991829i | \(-0.540718\pi\) | |||||||
\(674\) | − | 846779.i | − | 1.86402i | ||||||
\(675\) | −377916. | − | 306506.i | −0.829444 | − | 0.672715i | ||||
\(676\) | 42564.9 | 0.0931448 | ||||||||
\(677\) | −190567. | + | 190567.i | −0.415786 | + | 0.415786i | −0.883748 | − | 0.467963i | \(-0.844988\pi\) |
0.467963 | + | 0.883748i | \(0.344988\pi\) | |||||||
\(678\) | −388982. | − | 388982.i | −0.846194 | − | 0.846194i | ||||
\(679\) | − | 101355.i | − | 0.219839i | ||||||
\(680\) | −402067. | + | 446199.i | −0.869522 | + | 0.964964i | ||||
\(681\) | 28564.1 | 0.0615922 | ||||||||
\(682\) | 280814. | − | 280814.i | 0.603740 | − | 0.603740i | ||||
\(683\) | −482929. | − | 482929.i | −1.03524 | − | 1.03524i | −0.999356 | − | 0.0358871i | \(-0.988574\pi\) |
−0.0358871 | − | 0.999356i | \(-0.511426\pi\) | |||||||
\(684\) | − | 19772.8i | − | 0.0422625i | ||||||
\(685\) | 44013.1 | + | 845971.i | 0.0937995 | + | 1.80291i | ||||
\(686\) | 28625.7 | 0.0608286 | ||||||||
\(687\) | −260404. | + | 260404.i | −0.551739 | + | 0.551739i | ||||
\(688\) | 371926. | + | 371926.i | 0.785740 | + | 0.785740i | ||||
\(689\) | 28386.3i | 0.0597958i | ||||||||
\(690\) | 179297. | − | 9328.25i | 0.376596 | − | 0.0195930i | ||||
\(691\) | 115996. | 0.242933 | 0.121466 | − | 0.992596i | \(-0.461240\pi\) | ||||
0.121466 | + | 0.992596i | \(0.461240\pi\) | |||||||
\(692\) | 131447. | − | 131447.i | 0.274497 | − | 0.274497i | ||||
\(693\) | −15623.3 | − | 15623.3i | −0.0325317 | − | 0.0325317i | ||||
\(694\) | 97579.3i | 0.202600i | ||||||||
\(695\) | −370910. | − | 334224.i | −0.767890 | − | 0.691940i | ||||
\(696\) | 46977.5 | 0.0969776 | ||||||||
\(697\) | 111334. | − | 111334.i | 0.229172 | − | 0.229172i | ||||
\(698\) | 118318. | + | 118318.i | 0.242851 | + | 0.242851i | ||||
\(699\) | − | 202410.i | − | 0.414264i | ||||||
\(700\) | 31398.2 | − | 38713.3i | 0.0640779 | − | 0.0790067i | ||||
\(701\) | −868.758 | −0.00176792 | −0.000883961 | − | 1.00000i | \(-0.500281\pi\) | ||||
−0.000883961 | 1.00000i | \(0.500281\pi\) | ||||||||
\(702\) | −486410. | + | 486410.i | −0.987024 | + | 0.987024i | ||||
\(703\) | 571340. | + | 571340.i | 1.15607 | + | 1.15607i | ||||
\(704\) | − | 205531.i | − | 0.414697i | ||||||
\(705\) | 264267. | − | 293274.i | 0.531698 | − | 0.590059i | ||||
\(706\) | −1.02849e6 | −2.06344 | ||||||||
\(707\) | 124975. | − | 124975.i | 0.250025 | − | 0.250025i | ||||
\(708\) | 61538.7 | + | 61538.7i | 0.122767 | + | 0.122767i | ||||
\(709\) | 339639.i | 0.675654i | 0.941208 | + | 0.337827i | \(0.109692\pi\) | ||||
−0.941208 | + | 0.337827i | \(0.890308\pi\) | |||||||
\(710\) | −31310.3 | − | 601812.i | −0.0621112 | − | 1.19383i | ||||
\(711\) | 135280. | 0.267604 | ||||||||
\(712\) | −86904.0 | + | 86904.0i | −0.171427 | + | 0.171427i | ||||
\(713\) | −146840. | − | 146840.i | −0.288845 | − | 0.288845i | ||||
\(714\) | − | 310534.i | − | 0.609133i | ||||||
\(715\) | 405686. | − | 21106.5i | 0.793557 | − | 0.0412861i | ||||
\(716\) | 200828. | 0.391740 | ||||||||
\(717\) | 372975. | − | 372975.i | 0.725506 | − | 0.725506i | ||||
\(718\) | 401301. | + | 401301.i | 0.778434 | + | 0.778434i | ||||
\(719\) | 479729.i | 0.927979i | 0.885841 | + | 0.463990i | \(0.153582\pi\) | ||||
−0.885841 | + | 0.463990i | \(0.846418\pi\) | |||||||
\(720\) | −81906.5 | − | 73805.3i | −0.157999 | − | 0.142371i | ||||
\(721\) | 104324. | 0.200684 | ||||||||
\(722\) | 91074.8 | − | 91074.8i | 0.174712 | − | 0.174712i | ||||
\(723\) | 598383. | + | 598383.i | 1.14473 | + | 1.14473i | ||||
\(724\) | 133774.i | 0.255209i | ||||||||
\(725\) | −67904.4 | + | 7084.86i | −0.129188 | + | 0.0134789i | ||||
\(726\) | −285862. | −0.542354 | ||||||||
\(727\) | 253324. | − | 253324.i | 0.479300 | − | 0.479300i | −0.425608 | − | 0.904908i | \(-0.639940\pi\) |
0.904908 | + | 0.425608i | \(0.139940\pi\) | |||||||
\(728\) | 135308. | + | 135308.i | 0.255306 | + | 0.255306i | ||||
\(729\) | − | 589335.i | − | 1.10894i | ||||||
\(730\) | 643186. | − | 713785.i | 1.20695 | − | 1.33944i | ||||
\(731\) | −782780. | −1.46489 | ||||||||
\(732\) | −25782.7 | + | 25782.7i | −0.0481179 | + | 0.0481179i | ||||
\(733\) | −39917.3 | − | 39917.3i | −0.0742939 | − | 0.0742939i | 0.668983 | − | 0.743277i | \(-0.266730\pi\) |
−0.743277 | + | 0.668983i | \(0.766730\pi\) | |||||||
\(734\) | 58933.3i | 0.109388i | ||||||||
\(735\) | −3636.01 | − | 69887.4i | −0.00673055 | − | 0.129367i | ||||
\(736\) | 104942. | 0.193729 | ||||||||
\(737\) | −283538. | + | 283538.i | −0.522008 | + | 0.522008i | ||||
\(738\) | 15840.6 | + | 15840.6i | 0.0290844 | + | 0.0290844i | ||||
\(739\) | 838842.i | 1.53600i | 0.640450 | + | 0.768000i | \(0.278748\pi\) | ||||
−0.640450 | + | 0.768000i | \(0.721252\pi\) | |||||||
\(740\) | −272344. | + | 14169.2i | −0.497341 | + | 0.0258750i | ||||
\(741\) | 510408. | 0.929568 | ||||||||
\(742\) | 8543.46 | − | 8543.46i | 0.0155176 | − | 0.0155176i | ||||
\(743\) | 411846. | + | 411846.i | 0.746031 | + | 0.746031i | 0.973731 | − | 0.227701i | \(-0.0731207\pi\) |
−0.227701 | + | 0.973731i | \(0.573121\pi\) | |||||||
\(744\) | − | 457325.i | − | 0.826188i | ||||||
\(745\) | −126657. | − | 114130.i | −0.228200 | − | 0.205630i | ||||
\(746\) | −158568. | −0.284930 | ||||||||
\(747\) | −98495.7 | + | 98495.7i | −0.176513 | + | 0.176513i | ||||
\(748\) | −115052. | − | 115052.i | −0.205631 | − | 0.205631i | ||||
\(749\) | 205163.i | 0.365709i | ||||||||
\(750\) | −464498. | − | 338288.i | −0.825774 | − | 0.601400i | ||||
\(751\) | 223384. | 0.396070 | 0.198035 | − | 0.980195i | \(-0.436544\pi\) | ||||
0.198035 | + | 0.980195i | \(0.436544\pi\) | |||||||
\(752\) | 419149. | − | 419149.i | 0.741196 | − | 0.741196i | ||||
\(753\) | −127593. | − | 127593.i | −0.225029 | − | 0.225029i | ||||
\(754\) | 96517.6i | 0.169771i | ||||||||
\(755\) | 515736. | − | 572345.i | 0.904760 | − | 1.00407i | ||||
\(756\) | 62090.4 | 0.108638 | ||||||||
\(757\) | 571626. | − | 571626.i | 0.997517 | − | 0.997517i | −0.00248013 | − | 0.999997i | \(-0.500789\pi\) |
0.999997 | + | 0.00248013i | \(0.000789451\pi\) | |||||||
\(758\) | 303652. | + | 303652.i | 0.528490 | + | 0.528490i | ||||
\(759\) | − | 132075.i | − | 0.229265i | ||||||
\(760\) | 21831.9 | + | 419628.i | 0.0377976 | + | 0.726504i | ||||
\(761\) | −142806. | −0.246592 | −0.123296 | − | 0.992370i | \(-0.539346\pi\) | ||||
−0.123296 | + | 0.992370i | \(0.539346\pi\) | |||||||
\(762\) | 506009. | − | 506009.i | 0.871462 | − | 0.871462i | ||||
\(763\) | −81695.7 | − | 81695.7i | −0.140330 | − | 0.140330i | ||||
\(764\) | 282009.i | 0.483143i | ||||||||
\(765\) | 163861. | − | 8525.13i | 0.279996 | − | 0.0145673i | ||||
\(766\) | 340851. | 0.580907 | ||||||||
\(767\) | 343337. | − | 343337.i | 0.583620 | − | 0.583620i | ||||
\(768\) | 285228. | + | 285228.i | 0.483581 | + | 0.483581i | ||||
\(769\) | − | 736553.i | − | 1.24552i | −0.782412 | − | 0.622761i | \(-0.786011\pi\) | ||
0.782412 | − | 0.622761i | \(-0.213989\pi\) | |||||||
\(770\) | −128452. | − | 115747.i | −0.216651 | − | 0.195222i | ||||
\(771\) | 69833.0 | 0.117477 | ||||||||
\(772\) | −187421. | + | 187421.i | −0.314473 | + | 0.314473i | ||||
\(773\) | −17851.7 | − | 17851.7i | −0.0298759 | − | 0.0298759i | 0.692011 | − | 0.721887i | \(-0.256725\pi\) |
−0.721887 | + | 0.692011i | \(0.756725\pi\) | |||||||
\(774\) | − | 111375.i | − | 0.185911i | ||||||
\(775\) | 68970.9 | + | 661048.i | 0.114832 | + | 1.10060i | ||||
\(776\) | −288380. | −0.478897 | ||||||||
\(777\) | −270739. | + | 270739.i | −0.448444 | + | 0.448444i | ||||
\(778\) | 288801. | + | 288801.i | 0.477132 | + | 0.477132i | ||||
\(779\) | − | 110151.i | − | 0.181516i | ||||||
\(780\) | −115320. | + | 127979.i | −0.189547 | + | 0.210353i | ||||
\(781\) | −443310. | −0.726785 | ||||||||
\(782\) | −283693. | + | 283693.i | −0.463912 | + | 0.463912i | ||||
\(783\) | −60135.9 | − | 60135.9i | −0.0980868 | − | 0.0980868i | ||||
\(784\) | − | 105080.i | − | 0.170958i | ||||||
\(785\) | −53148.9 | − | 1.02157e6i | −0.0862492 | − | 1.65779i | ||||
\(786\) | −576481. | −0.933126 | ||||||||
\(787\) | −406163. | + | 406163.i | −0.655770 | + | 0.655770i | −0.954376 | − | 0.298607i | \(-0.903478\pi\) |
0.298607 | + | 0.954376i | \(0.403478\pi\) | |||||||
\(788\) | 120001. | + | 120001.i | 0.193256 | + | 0.193256i | ||||
\(789\) | 677922.i | 1.08899i | ||||||||
\(790\) | 1.05724e6 | − | 55004.6i | 1.69402 | − | 0.0881343i | ||||
\(791\) | 277029. | 0.442763 | ||||||||
\(792\) | −44452.4 | + | 44452.4i | −0.0708672 | + | 0.0708672i | ||||
\(793\) | 143847. | + | 143847.i | 0.228747 | + | 0.228747i | ||||
\(794\) | 511876.i | 0.811939i | ||||||||
\(795\) | −21943.4 | − | 19773.0i | −0.0347191 | − | 0.0312852i | ||||
\(796\) | 100365. | 0.158400 | ||||||||
\(797\) | 145600. | − | 145600.i | 0.229216 | − | 0.229216i | −0.583149 | − | 0.812365i | \(-0.698180\pi\) |
0.812365 | + | 0.583149i | \(0.198180\pi\) | |||||||
\(798\) | −153618. | − | 153618.i | −0.241232 | − | 0.241232i | ||||
\(799\) | 882170.i | 1.38184i | ||||||||
\(800\) | −260861. | − | 211570.i | −0.407596 | − | 0.330578i | ||||
\(801\) | 33574.7 | 0.0523296 | ||||||||
\(802\) | −696331. | + | 696331.i | −1.08260 | + | 1.08260i | ||||
\(803\) | −499790. | − | 499790.i | −0.775098 | − | 0.775098i | ||||
\(804\) | − | 170044.i | − | 0.263057i | ||||||
\(805\) | −60525.1 | + | 67168.6i | −0.0933994 | + | 0.103651i | ||||
\(806\) | 939597. | 1.44634 | ||||||||
\(807\) | 249836. | − | 249836.i | 0.383626 | − | 0.383626i | ||||
\(808\) | −355585. | − | 355585.i | −0.544655 | − | 0.544655i | ||||
\(809\) | 446624.i | 0.682409i | 0.939989 | + | 0.341205i | \(0.110835\pi\) | ||||
−0.939989 | + | 0.341205i | \(0.889165\pi\) | |||||||
\(810\) | −30364.9 | − | 583641.i | −0.0462809 | − | 0.889560i | ||||
\(811\) | −1.10605e6 | −1.68164 | −0.840821 | − | 0.541313i | \(-0.817927\pi\) | ||||
−0.840821 | + | 0.541313i | \(0.817927\pi\) | |||||||
\(812\) | 6160.26 | − | 6160.26i | 0.00934302 | − | 0.00934302i | ||||
\(813\) | −398464. | − | 398464.i | −0.602849 | − | 0.602849i | ||||
\(814\) | 946011.i | 1.42773i | ||||||||
\(815\) | −375846. | + | 19554.0i | −0.565842 | + | 0.0294389i | ||||
\(816\) | −1.13992e6 | −1.71196 | ||||||||
\(817\) | −387233. | + | 387233.i | −0.580134 | + | 0.580134i | ||||
\(818\) | −474582. | − | 474582.i | −0.709258 | − | 0.709258i | ||||
\(819\) | − | 52275.3i | − | 0.0779343i | ||||||
\(820\) | 27619.1 | + | 24887.3i | 0.0410754 | + | 0.0370127i | ||||
\(821\) | 551335. | 0.817954 | 0.408977 | − | 0.912545i | \(-0.365886\pi\) | ||||
0.408977 | + | 0.912545i | \(0.365886\pi\) | |||||||
\(822\) | −881158. | + | 881158.i | −1.30410 | + | 1.30410i | ||||
\(823\) | −435505. | − | 435505.i | −0.642975 | − | 0.642975i | 0.308311 | − | 0.951286i | \(-0.400236\pi\) |
−0.951286 | + | 0.308311i | \(0.900236\pi\) | |||||||
\(824\) | − | 296829.i | − | 0.437171i | ||||||
\(825\) | −266272. | + | 328308.i | −0.391217 | + | 0.482363i | ||||
\(826\) | −206669. | −0.302911 | ||||||||
\(827\) | −634581. | + | 634581.i | −0.927847 | + | 0.927847i | −0.997567 | − | 0.0697197i | \(-0.977790\pi\) |
0.0697197 | + | 0.997567i | \(0.477790\pi\) | |||||||
\(828\) | −8559.82 | − | 8559.82i | −0.0124854 | − | 0.0124854i | ||||
\(829\) | − | 471650.i | − | 0.686296i | −0.939281 | − | 0.343148i | \(-0.888507\pi\) | ||
0.939281 | − | 0.343148i | \(-0.111493\pi\) | |||||||
\(830\) | −729717. | + | 809814.i | −1.05925 | + | 1.17552i | ||||
\(831\) | 151585. | 0.219510 | ||||||||
\(832\) | 343851. | − | 343851.i | 0.496733 | − | 0.496733i | ||||
\(833\) | 110579. | + | 110579.i | 0.159362 | + | 0.159362i | ||||
\(834\) | − | 734464.i | − | 1.05594i | ||||||
\(835\) | 10039.7 | + | 192972.i | 0.0143995 | + | 0.276772i | ||||
\(836\) | −113830. | −0.162871 | ||||||||
\(837\) | −585422. | + | 585422.i | −0.835637 | + | 0.835637i | ||||
\(838\) | 75700.1 | + | 75700.1i | 0.107797 | + | 0.107797i | ||||
\(839\) | 476036.i | 0.676263i | 0.941099 | + | 0.338131i | \(0.109795\pi\) | ||||
−0.941099 | + | 0.338131i | \(0.890205\pi\) | |||||||
\(840\) | −198848. | + | 10345.4i | −0.281814 | + | 0.0146618i | ||||
\(841\) | 695348. | 0.983129 | ||||||||
\(842\) | 669316. | − | 669316.i | 0.944076 | − | 0.944076i | ||||
\(843\) | −434420. | − | 434420.i | −0.611300 | − | 0.611300i | ||||
\(844\) | − | 7753.58i | − | 0.0108847i | ||||||
\(845\) | 183577. | + | 165420.i | 0.257102 | + | 0.231673i | ||||
\(846\) | −125516. | −0.175371 | ||||||||
\(847\) | 101794. | − | 101794.i | 0.141891 | − | 0.141891i | ||||
\(848\) | −31361.6 | − | 31361.6i | −0.0436121 | − | 0.0436121i | ||||
\(849\) | 228452.i | 0.316941i | ||||||||
\(850\) | 1.27714e6 | − | 133251.i | 1.76767 | − | 0.184431i | ||||
\(851\) | 494677. | 0.683065 | ||||||||
\(852\) | 132931. | − | 132931.i | 0.183125 | − | 0.183125i | ||||
\(853\) | −305921. | − | 305921.i | −0.420447 | − | 0.420447i | 0.464911 | − | 0.885358i | \(-0.346086\pi\) |
−0.885358 | + | 0.464911i | \(0.846086\pi\) | |||||||
\(854\) | − | 86587.7i | − | 0.118725i | ||||||
\(855\) | 76842.9 | − | 85277.5i | 0.105117 | − | 0.116655i | ||||
\(856\) | 583743. | 0.796661 | ||||||||
\(857\) | 983217. | − | 983217.i | 1.33871 | − | 1.33871i | 0.441407 | − | 0.897307i | \(-0.354480\pi\) |
0.897307 | − | 0.441407i | \(-0.145520\pi\) | |||||||
\(858\) | 422560. | + | 422560.i | 0.574003 | + | 0.574003i | ||||
\(859\) | 621201.i | 0.841871i | 0.907091 | + | 0.420936i | \(0.138298\pi\) | ||||
−0.907091 | + | 0.420936i | \(0.861702\pi\) | |||||||
\(860\) | −9603.32 | − | 184585.i | −0.0129845 | − | 0.249574i | ||||
\(861\) | 52197.0 | 0.0704107 | ||||||||
\(862\) | −683210. | + | 683210.i | −0.919475 | + | 0.919475i | ||||
\(863\) | −377282. | − | 377282.i | −0.506576 | − | 0.506576i | 0.406898 | − | 0.913474i | \(-0.366610\pi\) |
−0.913474 | + | 0.406898i | \(0.866610\pi\) | |||||||
\(864\) | − | 418383.i | − | 0.560463i | ||||||
\(865\) | 1.07775e6 | − | 56072.0i | 1.44041 | − | 0.0749400i | ||||
\(866\) | −59984.4 | −0.0799839 | ||||||||
\(867\) | 717590. | − | 717590.i | 0.954636 | − | 0.954636i | ||||
\(868\) | −59970.0 | − | 59970.0i | −0.0795966 | − | 0.0795966i | ||||
\(869\) | − | 778789.i | − | 1.03129i | ||||||
\(870\) | −74610.6 | − | 67231.1i | −0.0985739 | − | 0.0888242i | ||||
\(871\) | −948713. | −1.25054 | ||||||||
\(872\) | −232446. | + | 232446.i | −0.305695 | + | 0.305695i | ||||
\(873\) | 55706.8 | + | 55706.8i | 0.0730937 | + | 0.0730937i | ||||
\(874\) | 280681.i | 0.367442i | ||||||||
\(875\) | 285868. | − | 44942.9i | 0.373378 | − | 0.0587010i | ||||
\(876\) | 299735. | 0.390597 | ||||||||
\(877\) | 507278. | − | 507278.i | 0.659548 | − | 0.659548i | −0.295725 | − | 0.955273i | \(-0.595561\pi\) |
0.955273 | + | 0.295725i | \(0.0955612\pi\) | |||||||
\(878\) | −644528. | − | 644528.i | −0.836089 | − | 0.836089i | ||||
\(879\) | 1.09196e6i | 1.41329i | ||||||||
\(880\) | −424889. | + | 471526.i | −0.548669 | + | 0.608893i | ||||
\(881\) | 859437. | 1.10729 | 0.553646 | − | 0.832752i | \(-0.313236\pi\) | ||||
0.553646 | + | 0.832752i | \(0.313236\pi\) | |||||||
\(882\) | −15733.3 | + | 15733.3i | −0.0202248 | + | 0.0202248i | ||||
\(883\) | −95336.1 | − | 95336.1i | −0.122275 | − | 0.122275i | 0.643322 | − | 0.765596i | \(-0.277556\pi\) |
−0.765596 | + | 0.643322i | \(0.777556\pi\) | |||||||
\(884\) | − | 384960.i | − | 0.492619i | ||||||
\(885\) | 26250.9 | + | 504566.i | 0.0335164 | + | 0.644216i | ||||
\(886\) | 654221. | 0.833407 | ||||||||
\(887\) | 207677. | − | 207677.i | 0.263962 | − | 0.263962i | −0.562699 | − | 0.826662i | \(-0.690237\pi\) |
0.826662 | + | 0.562699i | \(0.190237\pi\) | |||||||
\(888\) | 770323. | + | 770323.i | 0.976892 | + | 0.976892i | ||||
\(889\) | 360374.i | 0.455985i | ||||||||
\(890\) | 262394. | − | 13651.5i | 0.331263 | − | 0.0172345i | ||||
\(891\) | −429925. | −0.541548 | ||||||||
\(892\) | 133117. | − | 133117.i | 0.167304 | − | 0.167304i | ||||
\(893\) | 436400. | + | 436400.i | 0.547246 | + | 0.547246i | ||||
\(894\) | − | 250802.i | − | 0.313802i | ||||||
\(895\) | 866146. | + | 780477.i | 1.08130 | + | 0.974348i | ||||
\(896\) | −366221. | −0.456171 | ||||||||
\(897\) | 220960. | − | 220960.i | 0.274618 | − | 0.274618i | ||||
\(898\) | −667100. | − | 667100.i | −0.827253 | − | 0.827253i | ||||
\(899\) | 116164.i | 0.143732i | ||||||||
\(900\) | 4020.56 | + | 38534.9i | 0.00496366 | + | 0.0475739i | ||||
\(901\) | 66005.8 | 0.0813078 | ||||||||
\(902\) | 91192.9 | − | 91192.9i | 0.112085 | − | 0.112085i | ||||
\(903\) | −183497. | − | 183497.i | −0.225036 | − | 0.225036i | ||||
\(904\) | − | 788219.i | − | 0.964517i | ||||||
\(905\) | −519886. | + | 576951.i | −0.634763 | + | 0.704437i | ||||
\(906\) | 1.13334e6 | 1.38071 | ||||||||
\(907\) | 230370. | − | 230370.i | 0.280034 | − | 0.280034i | −0.553088 | − | 0.833123i | \(-0.686551\pi\) |
0.833123 | + | 0.553088i | \(0.186551\pi\) | |||||||
\(908\) | −10657.4 | − | 10657.4i | −0.0129265 | − | 0.0129265i | ||||
\(909\) | 137378.i | 0.166260i | ||||||||
\(910\) | −21255.1 | − | 408543.i | −0.0256673 | − | 0.493349i | ||||
\(911\) | −1.25046e6 | −1.50672 | −0.753362 | − | 0.657606i | \(-0.771569\pi\) | ||||
−0.753362 | + | 0.657606i | \(0.771569\pi\) | |||||||
\(912\) | −563905. | + | 563905.i | −0.677980 | + | 0.677980i | ||||
\(913\) | 567029. | + | 567029.i | 0.680242 | + | 0.680242i | ||||
\(914\) | − | 401788.i | − | 0.480955i | ||||||
\(915\) | −211397. | + | 10998.3i | −0.252498 | + | 0.0131366i | ||||
\(916\) | 194316. | 0.231589 | ||||||||
\(917\) | 205282. | − | 205282.i | 0.244125 | − | 0.244125i | ||||
\(918\) | 1.13103e6 | + | 1.13103e6i | 1.34211 | + | 1.34211i | ||||
\(919\) | − | 345006.i | − | 0.408503i | −0.978918 | − | 0.204252i | \(-0.934524\pi\) | ||
0.978918 | − | 0.204252i | \(-0.0654761\pi\) | |||||||
\(920\) | 191112. | + | 172210.i | 0.225794 | + | 0.203461i | ||||
\(921\) | −346522. | −0.408519 | ||||||||
\(922\) | −208375. | + | 208375.i | −0.245123 | + | 0.245123i | ||||
\(923\) | −741653. | − | 741653.i | −0.870557 | − | 0.870557i | ||||
\(924\) | − | 53940.1i | − | 0.0631782i | ||||||
\(925\) | −1.22965e6 | − | 997301.i | −1.43714 | − | 1.16558i | ||||
\(926\) | 1.71042e6 | 1.99471 | ||||||||
\(927\) | −57338.9 | + | 57338.9i | −0.0667251 | + | 0.0667251i | ||||
\(928\) | −41509.6 | − | 41509.6i | −0.0482007 | − | 0.0482007i | ||||
\(929\) | − | 768509.i | − | 0.890466i | −0.895415 | − | 0.445233i | \(-0.853121\pi\) | ||
0.895415 | − | 0.445233i | \(-0.146879\pi\) | |||||||
\(930\) | −654493. | + | 726332.i | −0.756726 | + | 0.839788i | ||||
\(931\) | 109405. | 0.126223 | ||||||||
\(932\) | −75520.2 | + | 75520.2i | −0.0869423 | + | 0.0869423i | ||||
\(933\) | −155749. | − | 155749.i | −0.178921 | − | 0.178921i | ||||
\(934\) | − | 760836.i | − | 0.872162i | ||||||
\(935\) | −49078.2 | − | 943328.i | −0.0561391 | − | 1.07904i | ||||
\(936\) | −148737. | −0.169772 | ||||||||
\(937\) | −616858. | + | 616858.i | −0.702596 | + | 0.702596i | −0.964967 | − | 0.262371i | \(-0.915496\pi\) |
0.262371 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(938\) | 285535. | + | 285535.i | 0.324529 | + | 0.324529i | ||||
\(939\) | 25228.9i | 0.0286132i | ||||||||
\(940\) | −208021. | + | 10822.7i | −0.235425 | + | 0.0122484i | ||||
\(941\) | 1.51049e6 | 1.70584 | 0.852922 | − | 0.522039i | \(-0.174828\pi\) | ||||
0.852922 | + | 0.522039i | \(0.174828\pi\) | |||||||
\(942\) | 1.06406e6 | − | 1.06406e6i | 1.19913 | − | 1.19913i | ||||
\(943\) | −47685.5 | − | 47685.5i | −0.0536244 | − | 0.0536244i | ||||
\(944\) | 758647.i | 0.851326i | ||||||||
\(945\) | 267788. | + | 241302.i | 0.299866 | + | 0.270207i | ||||
\(946\) | −641171. | −0.716459 | ||||||||
\(947\) | −1.17580e6 | + | 1.17580e6i | −1.31109 | + | 1.31109i | −0.390485 | + | 0.920609i | \(0.627693\pi\) |
−0.920609 | + | 0.390485i | \(0.872307\pi\) | |||||||
\(948\) | 233529. | + | 233529.i | 0.259850 | + | 0.259850i | ||||
\(949\) | − | 1.67229e6i | − | 1.85686i | ||||||
\(950\) | 565870. | − | 697706.i | 0.627003 | − | 0.773082i | ||||
\(951\) | −115529. | −0.127741 | ||||||||
\(952\) | 314627. | − | 314627.i | 0.347154 | − | 0.347154i | ||||
\(953\) | −171350. | − | 171350.i | −0.188668 | − | 0.188668i | 0.606452 | − | 0.795120i | \(-0.292592\pi\) |
−0.795120 | + | 0.606452i | \(0.792592\pi\) | |||||||
\(954\) | 9391.36i | 0.0103189i | ||||||||
\(955\) | −1.09597e6 | + | 1.21627e6i | −1.20169 | + | 1.33359i | ||||
\(956\) | −278318. | −0.304526 | ||||||||
\(957\) | −52242.1 | + | 52242.1i | −0.0570423 | + | 0.0570423i | ||||
\(958\) | 186073. | + | 186073.i | 0.202746 | + | 0.202746i | ||||
\(959\) | − | 627552.i | − | 0.682358i | ||||||
\(960\) | 26290.1 | + | 505320.i | 0.0285266 | + | 0.548308i | ||||
\(961\) | 207337. | 0.224507 | ||||||||
\(962\) | −1.58267e6 | + | 1.58267e6i | −1.71017 | + | 1.71017i | ||||
\(963\) | −112762. | − | 112762.i | −0.121594 | − | 0.121594i | ||||
\(964\) | − | 446519.i | − | 0.480492i | ||||||
\(965\) | −1.53670e6 | + | 79949.1i | −1.65019 | + | 0.0858537i | ||||
\(966\) | −133005. | −0.142533 | ||||||||
\(967\) | 330131. | − | 330131.i | 0.353047 | − | 0.353047i | −0.508195 | − | 0.861242i | \(-0.669687\pi\) |
0.861242 | + | 0.508195i | \(0.169687\pi\) | |||||||
\(968\) | −289630. | − | 289630.i | −0.309096 | − | 0.309096i | ||||
\(969\) | − | 1.18683e6i | − | 1.26399i | ||||||
\(970\) | 458011. | + | 412710.i | 0.486780 | + | 0.438634i | ||||
\(971\) | 657629. | 0.697497 | 0.348749 | − | 0.937216i | \(-0.386607\pi\) | ||||
0.348749 | + | 0.937216i | \(0.386607\pi\) | |||||||
\(972\) | −63102.9 | + | 63102.9i | −0.0667908 | + | 0.0667908i | ||||
\(973\) | 261539. | + | 261539.i | 0.276255 | + | 0.276255i | ||||
\(974\) | 871710.i | 0.918870i | ||||||||
\(975\) | −994726. | + | 103785.i | −1.04639 | + | 0.109176i | ||||
\(976\) | −317849. | −0.333673 | ||||||||
\(977\) | 361872. | − | 361872.i | 0.379110 | − | 0.379110i | −0.491671 | − | 0.870781i | \(-0.663614\pi\) |
0.870781 | + | 0.491671i | \(0.163614\pi\) | |||||||
\(978\) | −391479. | − | 391479.i | −0.409290 | − | 0.409290i | ||||
\(979\) | − | 193286.i | − | 0.201667i | ||||||
\(980\) | −24718.7 | + | 27432.0i | −0.0257380 | + | 0.0285631i | ||||
\(981\) | 89803.7 | 0.0933160 | ||||||||
\(982\) | 244768. | − | 244768.i | 0.253823 | − | 0.253823i | ||||
\(983\) | 867909. | + | 867909.i | 0.898188 | + | 0.898188i | 0.995276 | − | 0.0970877i | \(-0.0309527\pi\) |
−0.0970877 | + | 0.995276i | \(0.530953\pi\) | |||||||
\(984\) | − | 148514.i | − | 0.153383i | ||||||
\(985\) | 51189.7 | + | 983912.i | 0.0527606 | + | 1.01411i | ||||
\(986\) | 224429. | 0.230848 | ||||||||
\(987\) | −206795. | + | 206795.i | −0.212279 | + | 0.212279i | ||||
\(988\) | −190436. | − | 190436.i | −0.195090 | − | 0.195090i | ||||
\(989\) | 335273.i | 0.342773i | ||||||||
\(990\) | 134218. | − | 6982.89i | 0.136943 | − | 0.00712467i | ||||
\(991\) | −1.08310e6 | −1.10286 | −0.551432 | − | 0.834220i | \(-0.685918\pi\) | ||||
−0.551432 | + | 0.834220i | \(0.685918\pi\) | |||||||
\(992\) | −404095. | + | 404095.i | −0.410639 | + | 0.410639i | ||||
\(993\) | 156740. | + | 156740.i | 0.158958 | + | 0.158958i | ||||
\(994\) | 446432.i | 0.451837i | ||||||||
\(995\) | 432861. | + | 390048.i | 0.437222 | + | 0.393978i | ||||
\(996\) | −340060. | −0.342797 | ||||||||
\(997\) | 36094.4 | − | 36094.4i | 0.0363119 | − | 0.0363119i | −0.688718 | − | 0.725030i | \(-0.741826\pi\) |
0.725030 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(998\) | −296665. | − | 296665.i | −0.297855 | − | 0.297855i | ||||
\(999\) | − | 1.97218e6i | − | 1.97613i |
(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 | 35.5.g.a.8.9 | ✓ | 24 | |
5.2 | odd | 4 | inner | 35.5.g.a.22.9 | yes | 24 | |
5.3 | odd | 4 | 175.5.g.c.57.4 | 24 | |||
5.4 | even | 2 | 175.5.g.c.43.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.g.a.8.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
35.5.g.a.22.9 | yes | 24 | 5.2 | odd | 4 | inner | |
175.5.g.c.43.4 | 24 | 5.4 | even | 2 | |||
175.5.g.c.57.4 | 24 | 5.3 | odd | 4 |