Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), 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: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + 25296 x^{8} - 6656 x^{7} - 110848 x^{6} - 227328 x^{5} + 1077248 x^{4} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Root | \(-1.14149 - 2.58786i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.5.c.a.31.3 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.40825 | + | 2.09376i | −0.852063 | + | 0.523440i | ||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 7.23235 | − | 14.2721i | 0.452022 | − | 0.892007i | ||||
\(5\) | −11.1803 | −0.447214 | ||||||||
\(6\) | −10.8795 | − | 17.7098i | −0.302208 | − | 0.491939i | ||||
\(7\) | − | 61.3317i | − | 1.25167i | −0.779956 | − | 0.625834i | \(-0.784759\pi\) | ||
0.779956 | − | 0.625834i | \(-0.215241\pi\) | |||||||
\(8\) | 5.23271 | + | 63.7857i | 0.0817612 | + | 0.996652i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 38.1054 | − | 23.4089i | 0.381054 | − | 0.234089i | ||||
\(11\) | − | 74.1525i | − | 0.612831i | −0.951898 | − | 0.306415i | \(-0.900870\pi\) | ||
0.951898 | − | 0.306415i | \(-0.0991297\pi\) | |||||||
\(12\) | 74.1601 | + | 37.5804i | 0.515000 | + | 0.260975i | ||||
\(13\) | 181.358 | 1.07313 | 0.536563 | − | 0.843861i | \(-0.319723\pi\) | ||||
0.536563 | + | 0.843861i | \(0.319723\pi\) | |||||||
\(14\) | 128.414 | + | 209.034i | 0.655173 | + | 1.06650i | ||||
\(15\) | − | 58.0948i | − | 0.258199i | ||||||
\(16\) | −151.386 | − | 206.442i | −0.591353 | − | 0.806413i | ||||
\(17\) | 516.182 | 1.78610 | 0.893048 | − | 0.449962i | \(-0.148562\pi\) | ||||
0.893048 | + | 0.449962i | \(0.148562\pi\) | |||||||
\(18\) | 92.0228 | − | 56.5315i | 0.284021 | − | 0.174480i | ||||
\(19\) | − | 407.870i | − | 1.12983i | −0.825147 | − | 0.564917i | \(-0.808908\pi\) | ||
0.825147 | − | 0.564917i | \(-0.191092\pi\) | |||||||
\(20\) | −80.8601 | + | 159.567i | −0.202150 | + | 0.398918i | ||||
\(21\) | 318.689 | 0.722651 | ||||||||
\(22\) | 155.258 | + | 252.730i | 0.320780 | + | 0.522170i | ||||
\(23\) | 7.48405i | 0.0141475i | 0.999975 | + | 0.00707377i | \(0.00225167\pi\) | ||||
−0.999975 | + | 0.00707377i | \(0.997748\pi\) | |||||||
\(24\) | −331.440 | + | 27.1900i | −0.575417 | + | 0.0472048i | ||||
\(25\) | 125.000 | 0.200000 | ||||||||
\(26\) | −618.114 | + | 379.720i | −0.914370 | + | 0.561716i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | −875.333 | − | 443.572i | −1.11650 | − | 0.565781i | ||||
\(29\) | −1473.47 | −1.75205 | −0.876023 | − | 0.482270i | \(-0.839812\pi\) | ||||
−0.876023 | + | 0.482270i | \(0.839812\pi\) | |||||||
\(30\) | 121.636 | + | 198.001i | 0.135152 | + | 0.220002i | ||||
\(31\) | − | 1041.01i | − | 1.08326i | −0.840617 | − | 0.541630i | \(-0.817808\pi\) | ||
0.840617 | − | 0.541630i | \(-0.182192\pi\) | |||||||
\(32\) | 948.202 | + | 386.639i | 0.925978 | + | 0.377577i | ||||
\(33\) | 385.308 | 0.353818 | ||||||||
\(34\) | −1759.28 | + | 1080.76i | −1.52187 | + | 0.934913i | ||||
\(35\) | 685.709i | 0.559763i | ||||||||
\(36\) | −195.273 | + | 385.347i | −0.150674 | + | 0.297336i | ||||
\(37\) | −667.800 | −0.487802 | −0.243901 | − | 0.969800i | \(-0.578427\pi\) | ||||
−0.243901 | + | 0.969800i | \(0.578427\pi\) | |||||||
\(38\) | 853.982 | + | 1390.12i | 0.591400 | + | 0.962690i | ||||
\(39\) | 942.365i | 0.619569i | ||||||||
\(40\) | −58.5035 | − | 713.146i | −0.0365647 | − | 0.445716i | ||||
\(41\) | 1215.10 | 0.722842 | 0.361421 | − | 0.932403i | \(-0.382292\pi\) | ||||
0.361421 | + | 0.932403i | \(0.382292\pi\) | |||||||
\(42\) | −1086.17 | + | 667.258i | −0.615744 | + | 0.378264i | ||||
\(43\) | − | 987.639i | − | 0.534148i | −0.963676 | − | 0.267074i | \(-0.913943\pi\) | ||
0.963676 | − | 0.267074i | \(-0.0860568\pi\) | |||||||
\(44\) | −1058.31 | − | 536.297i | −0.546649 | − | 0.277013i | ||||
\(45\) | 301.869 | 0.149071 | ||||||||
\(46\) | −15.6698 | − | 25.5075i | −0.00740539 | − | 0.0120546i | ||||
\(47\) | − | 2943.18i | − | 1.33236i | −0.745792 | − | 0.666178i | \(-0.767929\pi\) | ||
0.745792 | − | 0.666178i | \(-0.232071\pi\) | |||||||
\(48\) | 1072.70 | − | 786.626i | 0.465583 | − | 0.341418i | ||||
\(49\) | −1360.58 | −0.566672 | ||||||||
\(50\) | −426.031 | + | 261.720i | −0.170413 | + | 0.104688i | ||||
\(51\) | 2682.16i | 1.03120i | ||||||||
\(52\) | 1311.64 | − | 2588.36i | 0.485076 | − | 0.957235i | ||||
\(53\) | −2287.61 | −0.814384 | −0.407192 | − | 0.913343i | \(-0.633492\pi\) | ||||
−0.407192 | + | 0.913343i | \(0.633492\pi\) | |||||||
\(54\) | 293.746 | + | 478.164i | 0.100736 | + | 0.163980i | ||||
\(55\) | 829.051i | 0.274066i | ||||||||
\(56\) | 3912.09 | − | 320.931i | 1.24748 | − | 0.102338i | ||||
\(57\) | 2119.36 | 0.652310 | ||||||||
\(58\) | 5021.96 | − | 3085.09i | 1.49285 | − | 0.917090i | ||||
\(59\) | 390.685i | 0.112234i | 0.998424 | + | 0.0561168i | \(0.0178719\pi\) | ||||
−0.998424 | + | 0.0561168i | \(0.982128\pi\) | |||||||
\(60\) | −829.135 | − | 420.161i | −0.230315 | − | 0.116711i | ||||
\(61\) | 4108.86 | 1.10424 | 0.552118 | − | 0.833766i | \(-0.313820\pi\) | ||||
0.552118 | + | 0.833766i | \(0.313820\pi\) | |||||||
\(62\) | 2179.63 | + | 3548.03i | 0.567021 | + | 0.923005i | ||||
\(63\) | 1655.96i | 0.417223i | ||||||||
\(64\) | −4041.24 | + | 667.545i | −0.986630 | + | 0.162975i | ||||
\(65\) | −2027.65 | −0.479916 | ||||||||
\(66\) | −1313.23 | + | 806.742i | −0.301475 | + | 0.185202i | ||||
\(67\) | 6166.96i | 1.37379i | 0.726755 | + | 0.686897i | \(0.241028\pi\) | ||||
−0.726755 | + | 0.686897i | \(0.758972\pi\) | |||||||
\(68\) | 3733.20 | − | 7367.00i | 0.807354 | − | 1.59321i | ||||
\(69\) | −38.8883 | −0.00816809 | ||||||||
\(70\) | −1435.71 | − | 2337.07i | −0.293002 | − | 0.476953i | ||||
\(71\) | − | 4462.68i | − | 0.885276i | −0.896700 | − | 0.442638i | \(-0.854043\pi\) | ||
0.896700 | − | 0.442638i | \(-0.145957\pi\) | |||||||
\(72\) | −141.283 | − | 1722.21i | −0.0272537 | − | 0.332217i | ||||
\(73\) | 3369.06 | 0.632213 | 0.316106 | − | 0.948724i | \(-0.397624\pi\) | ||||
0.316106 | + | 0.948724i | \(0.397624\pi\) | |||||||
\(74\) | 2276.03 | − | 1398.21i | 0.415638 | − | 0.255335i | ||||
\(75\) | 649.519i | 0.115470i | ||||||||
\(76\) | −5821.17 | − | 2949.86i | −1.00782 | − | 0.510710i | ||||
\(77\) | −4547.90 | −0.767061 | ||||||||
\(78\) | −1973.08 | − | 3211.81i | −0.324307 | − | 0.527912i | ||||
\(79\) | 7060.25i | 1.13127i | 0.824656 | + | 0.565635i | \(0.191369\pi\) | ||||
−0.824656 | + | 0.565635i | \(0.808631\pi\) | |||||||
\(80\) | 1692.55 | + | 2308.09i | 0.264461 | + | 0.360639i | ||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −4141.36 | + | 2544.12i | −0.615907 | + | 0.378364i | ||||
\(83\) | 4972.33i | 0.721777i | 0.932609 | + | 0.360889i | \(0.117527\pi\) | ||||
−0.932609 | + | 0.360889i | \(0.882473\pi\) | |||||||
\(84\) | 2304.87 | − | 4548.36i | 0.326654 | − | 0.644609i | ||||
\(85\) | −5771.09 | −0.798766 | ||||||||
\(86\) | 2067.88 | + | 3366.12i | 0.279594 | + | 0.455127i | ||||
\(87\) | − | 7656.38i | − | 1.01154i | ||||||
\(88\) | 4729.87 | − | 388.019i | 0.610779 | − | 0.0501058i | ||||
\(89\) | −12370.7 | −1.56175 | −0.780877 | − | 0.624685i | \(-0.785227\pi\) | ||||
−0.780877 | + | 0.624685i | \(0.785227\pi\) | |||||||
\(90\) | −1028.85 | + | 632.041i | −0.127018 | + | 0.0780298i | ||||
\(91\) | − | 11123.0i | − | 1.34320i | ||||||
\(92\) | 106.813 | + | 54.1273i | 0.0126197 | + | 0.00639500i | ||||
\(93\) | 5409.26 | 0.625420 | ||||||||
\(94\) | 6162.30 | + | 10031.1i | 0.697408 | + | 1.13525i | ||||
\(95\) | 4560.13i | 0.505277i | ||||||||
\(96\) | −2009.03 | + | 4927.00i | −0.217994 | + | 0.534614i | ||||
\(97\) | 2516.32 | 0.267438 | 0.133719 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133719 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(98\) | 4637.19 | − | 2848.72i | 0.482840 | − | 0.296619i | ||||
\(99\) | 2002.12i | 0.204277i | ||||||||
\(100\) | 904.043 | − | 1784.01i | 0.0904043 | − | 0.178401i | ||||
\(101\) | −2974.94 | −0.291632 | −0.145816 | − | 0.989312i | \(-0.546581\pi\) | ||||
−0.145816 | + | 0.989312i | \(0.546581\pi\) | |||||||
\(102\) | −5615.79 | − | 9141.47i | −0.539773 | − | 0.878649i | ||||
\(103\) | 17963.5i | 1.69323i | 0.532202 | + | 0.846617i | \(0.321365\pi\) | ||||
−0.532202 | + | 0.846617i | \(0.678635\pi\) | |||||||
\(104\) | 948.995 | + | 11568.1i | 0.0877399 | + | 1.06953i | ||||
\(105\) | −3563.05 | −0.323179 | ||||||||
\(106\) | 7796.73 | − | 4789.69i | 0.693906 | − | 0.426281i | ||||
\(107\) | 1200.48i | 0.104854i | 0.998625 | + | 0.0524272i | \(0.0166958\pi\) | ||||
−0.998625 | + | 0.0524272i | \(0.983304\pi\) | |||||||
\(108\) | −2002.32 | − | 1014.67i | −0.171667 | − | 0.0869916i | ||||
\(109\) | 16500.9 | 1.38884 | 0.694422 | − | 0.719568i | \(-0.255660\pi\) | ||||
0.694422 | + | 0.719568i | \(0.255660\pi\) | |||||||
\(110\) | −1735.83 | − | 2825.61i | −0.143457 | − | 0.233522i | ||||
\(111\) | − | 3469.99i | − | 0.281632i | ||||||
\(112\) | −12661.4 | + | 9284.78i | −1.00936 | + | 0.740177i | ||||
\(113\) | −6037.80 | −0.472849 | −0.236424 | − | 0.971650i | \(-0.575976\pi\) | ||||
−0.236424 | + | 0.971650i | \(0.575976\pi\) | |||||||
\(114\) | −7223.30 | + | 4437.42i | −0.555809 | + | 0.341445i | ||||
\(115\) | − | 83.6742i | − | 0.00632697i | ||||||
\(116\) | −10656.6 | + | 21029.5i | −0.791962 | + | 1.56284i | ||||
\(117\) | −4896.67 | −0.357708 | ||||||||
\(118\) | −818.000 | − | 1331.55i | −0.0587475 | − | 0.0956300i | ||||
\(119\) | − | 31658.3i | − | 2.23560i | ||||||
\(120\) | 3705.62 | − | 303.993i | 0.257334 | − | 0.0211106i | ||||
\(121\) | 9142.40 | 0.624438 | ||||||||
\(122\) | −14004.0 | + | 8602.97i | −0.940878 | + | 0.578001i | ||||
\(123\) | 6313.83i | 0.417333i | ||||||||
\(124\) | −14857.4 | − | 7528.96i | −0.966275 | − | 0.489657i | ||||
\(125\) | −1397.54 | −0.0894427 | ||||||||
\(126\) | −3467.17 | − | 5643.91i | −0.218391 | − | 0.355500i | ||||
\(127\) | − | 17483.7i | − | 1.08399i | −0.840382 | − | 0.541995i | \(-0.817669\pi\) | ||
0.840382 | − | 0.541995i | \(-0.182331\pi\) | |||||||
\(128\) | 12375.9 | − | 10736.5i | 0.755363 | − | 0.655306i | ||||
\(129\) | 5131.92 | 0.308390 | ||||||||
\(130\) | 6910.72 | − | 4245.40i | 0.408919 | − | 0.251207i | ||||
\(131\) | − | 10698.3i | − | 0.623408i | −0.950179 | − | 0.311704i | \(-0.899100\pi\) | ||
0.950179 | − | 0.311704i | \(-0.100900\pi\) | |||||||
\(132\) | 2786.68 | − | 5499.16i | 0.159933 | − | 0.315608i | ||||
\(133\) | −25015.4 | −1.41418 | ||||||||
\(134\) | −12912.1 | − | 21018.6i | −0.719099 | − | 1.17056i | ||||
\(135\) | 1568.56i | 0.0860663i | ||||||||
\(136\) | 2701.03 | + | 32925.0i | 0.146033 | + | 1.78012i | ||||
\(137\) | 31259.4 | 1.66548 | 0.832740 | − | 0.553665i | \(-0.186771\pi\) | ||||
0.832740 | + | 0.553665i | \(0.186771\pi\) | |||||||
\(138\) | 132.541 | − | 81.4227i | 0.00695972 | − | 0.00427550i | ||||
\(139\) | 22483.1i | 1.16366i | 0.813310 | + | 0.581831i | \(0.197663\pi\) | ||||
−0.813310 | + | 0.581831i | \(0.802337\pi\) | |||||||
\(140\) | 9786.52 | + | 4959.29i | 0.499312 | + | 0.253025i | ||||
\(141\) | 15293.2 | 0.769236 | ||||||||
\(142\) | 9343.77 | + | 15209.9i | 0.463389 | + | 0.754311i | ||||
\(143\) | − | 13448.2i | − | 0.657644i | ||||||
\(144\) | 4087.43 | + | 5573.93i | 0.197118 | + | 0.268804i | ||||
\(145\) | 16473.9 | 0.783539 | ||||||||
\(146\) | −11482.6 | + | 7054.01i | −0.538685 | + | 0.330925i | ||||
\(147\) | − | 7069.78i | − | 0.327168i | ||||||
\(148\) | −4829.76 | + | 9530.92i | −0.220497 | + | 0.435122i | ||||
\(149\) | 19244.0 | 0.866808 | 0.433404 | − | 0.901200i | \(-0.357312\pi\) | ||||
0.433404 | + | 0.901200i | \(0.357312\pi\) | |||||||
\(150\) | −1359.94 | − | 2213.72i | −0.0604416 | − | 0.0983877i | ||||
\(151\) | − | 42406.7i | − | 1.85986i | −0.367735 | − | 0.929931i | \(-0.619867\pi\) | ||
0.367735 | − | 0.929931i | \(-0.380133\pi\) | |||||||
\(152\) | 26016.3 | − | 2134.27i | 1.12605 | − | 0.0923766i | ||||
\(153\) | −13936.9 | −0.595365 | ||||||||
\(154\) | 15500.4 | − | 9522.21i | 0.653584 | − | 0.401510i | ||||
\(155\) | 11638.9i | 0.484448i | ||||||||
\(156\) | 13449.5 | + | 6815.51i | 0.552660 | + | 0.280059i | ||||
\(157\) | 13979.2 | 0.567129 | 0.283565 | − | 0.958953i | \(-0.408483\pi\) | ||||
0.283565 | + | 0.958953i | \(0.408483\pi\) | |||||||
\(158\) | −14782.5 | − | 24063.1i | −0.592151 | − | 0.963913i | ||||
\(159\) | − | 11886.7i | − | 0.470185i | ||||||
\(160\) | −10601.2 | − | 4322.75i | −0.414110 | − | 0.168857i | ||||
\(161\) | 459.010 | 0.0177080 | ||||||||
\(162\) | −2484.61 | + | 1526.35i | −0.0946736 | + | 0.0581600i | ||||
\(163\) | 31094.2i | 1.17032i | 0.810919 | + | 0.585159i | \(0.198968\pi\) | ||||
−0.810919 | + | 0.585159i | \(0.801032\pi\) | |||||||
\(164\) | 8788.00 | − | 17342.0i | 0.326740 | − | 0.644780i | ||||
\(165\) | −4307.87 | −0.158232 | ||||||||
\(166\) | −10410.9 | − | 16946.9i | −0.377807 | − | 0.615000i | ||||
\(167\) | 30204.9i | 1.08304i | 0.840687 | + | 0.541521i | \(0.182151\pi\) | ||||
−0.840687 | + | 0.541521i | \(0.817849\pi\) | |||||||
\(168\) | 1667.61 | + | 20327.8i | 0.0590847 | + | 0.720231i | ||||
\(169\) | 4329.78 | 0.151598 | ||||||||
\(170\) | 19669.3 | − | 12083.3i | 0.680599 | − | 0.418106i | ||||
\(171\) | 11012.5i | 0.376612i | ||||||||
\(172\) | −14095.7 | − | 7142.95i | −0.476463 | − | 0.241446i | ||||
\(173\) | −22061.5 | −0.737128 | −0.368564 | − | 0.929602i | \(-0.620150\pi\) | ||||
−0.368564 | + | 0.929602i | \(0.620150\pi\) | |||||||
\(174\) | 16030.6 | + | 26094.8i | 0.529482 | + | 0.861899i | ||||
\(175\) | − | 7666.46i | − | 0.250334i | ||||||
\(176\) | −15308.2 | + | 11225.7i | −0.494195 | + | 0.362399i | ||||
\(177\) | −2030.06 | −0.0647981 | ||||||||
\(178\) | 42162.3 | − | 25901.2i | 1.33071 | − | 0.817484i | ||||
\(179\) | − | 4300.24i | − | 0.134210i | −0.997746 | − | 0.0671052i | \(-0.978624\pi\) | ||
0.997746 | − | 0.0671052i | \(-0.0213763\pi\) | |||||||
\(180\) | 2183.22 | − | 4308.31i | 0.0673834 | − | 0.132973i | ||||
\(181\) | −32288.1 | −0.985566 | −0.492783 | − | 0.870152i | \(-0.664020\pi\) | ||||
−0.492783 | + | 0.870152i | \(0.664020\pi\) | |||||||
\(182\) | 23288.9 | + | 37910.0i | 0.703082 | + | 1.14449i | ||||
\(183\) | 21350.3i | 0.637531i | ||||||||
\(184\) | −477.376 | + | 39.1619i | −0.0141002 | + | 0.00115672i | ||||
\(185\) | 7466.24 | 0.218152 | ||||||||
\(186\) | −18436.1 | + | 11325.7i | −0.532897 | + | 0.327370i | ||||
\(187\) | − | 38276.2i | − | 1.09457i | ||||||
\(188\) | −42005.3 | − | 21286.1i | −1.18847 | − | 0.602254i | ||||
\(189\) | −8604.60 | −0.240884 | ||||||||
\(190\) | −9547.81 | − | 15542.1i | −0.264482 | − | 0.430528i | ||||
\(191\) | 23139.2i | 0.634279i | 0.948379 | + | 0.317140i | \(0.102722\pi\) | ||||
−0.948379 | + | 0.317140i | \(0.897278\pi\) | |||||||
\(192\) | −3468.66 | − | 20998.9i | −0.0940936 | − | 0.569631i | ||||
\(193\) | −64774.6 | −1.73896 | −0.869481 | − | 0.493966i | \(-0.835547\pi\) | ||||
−0.869481 | + | 0.493966i | \(0.835547\pi\) | |||||||
\(194\) | −8576.25 | + | 5268.57i | −0.227874 | + | 0.139988i | ||||
\(195\) | − | 10536.0i | − | 0.277080i | ||||||
\(196\) | −9840.18 | + | 19418.3i | −0.256148 | + | 0.505475i | ||||
\(197\) | 317.341 | 0.00817699 | 0.00408850 | − | 0.999992i | \(-0.498699\pi\) | ||||
0.00408850 | + | 0.999992i | \(0.498699\pi\) | |||||||
\(198\) | −4191.95 | − | 6823.72i | −0.106927 | − | 0.174057i | ||||
\(199\) | − | 18051.2i | − | 0.455828i | −0.973681 | − | 0.227914i | \(-0.926810\pi\) | ||
0.973681 | − | 0.227914i | \(-0.0731905\pi\) | |||||||
\(200\) | 654.089 | + | 7973.22i | 0.0163522 | + | 0.199330i | ||||
\(201\) | −32044.5 | −0.793161 | ||||||||
\(202\) | 10139.3 | − | 6228.80i | 0.248489 | − | 0.152652i | ||||
\(203\) | 90370.5i | 2.19298i | ||||||||
\(204\) | 38280.1 | + | 19398.3i | 0.919840 | + | 0.466126i | ||||
\(205\) | −13585.2 | −0.323265 | ||||||||
\(206\) | −37611.3 | − | 61224.2i | −0.886306 | − | 1.44274i | ||||
\(207\) | − | 202.069i | − | 0.00471585i | ||||||
\(208\) | −27455.1 | − | 37439.9i | −0.634596 | − | 0.865382i | ||||
\(209\) | −30244.6 | −0.692398 | ||||||||
\(210\) | 12143.8 | − | 7460.17i | 0.275369 | − | 0.169165i | ||||
\(211\) | 62848.8i | 1.41167i | 0.708378 | + | 0.705833i | \(0.249427\pi\) | ||||
−0.708378 | + | 0.705833i | \(0.750573\pi\) | |||||||
\(212\) | −16544.8 | + | 32649.0i | −0.368119 | + | 0.726436i | ||||
\(213\) | 23188.8 | 0.511115 | ||||||||
\(214\) | −2513.51 | − | 4091.53i | −0.0548850 | − | 0.0893426i | ||||
\(215\) | 11042.1i | 0.238878i | ||||||||
\(216\) | 8948.89 | − | 734.129i | 0.191806 | − | 0.0157349i | ||||
\(217\) | −63847.1 | −1.35588 | ||||||||
\(218\) | −56239.1 | + | 34548.8i | −1.18338 | + | 0.726976i | ||||
\(219\) | 17506.2i | 0.365008i | ||||||||
\(220\) | 11832.3 | + | 5995.98i | 0.244469 | + | 0.123884i | ||||
\(221\) | 93613.7 | 1.91670 | ||||||||
\(222\) | 7265.33 | + | 11826.6i | 0.147418 | + | 0.239968i | ||||
\(223\) | − | 60726.4i | − | 1.22115i | −0.791960 | − | 0.610573i | \(-0.790939\pi\) | ||
0.791960 | − | 0.610573i | \(-0.209061\pi\) | |||||||
\(224\) | 23713.2 | − | 58154.8i | 0.472601 | − | 1.15902i | ||||
\(225\) | −3375.00 | −0.0666667 | ||||||||
\(226\) | 20578.4 | − | 12641.7i | 0.402897 | − | 0.247508i | ||||
\(227\) | 98629.1i | 1.91405i | 0.290006 | + | 0.957025i | \(0.406343\pi\) | ||||
−0.290006 | + | 0.957025i | \(0.593657\pi\) | |||||||
\(228\) | 15327.9 | − | 30247.7i | 0.294858 | − | 0.581865i | ||||
\(229\) | 56329.9 | 1.07416 | 0.537079 | − | 0.843532i | \(-0.319528\pi\) | ||||
0.537079 | + | 0.843532i | \(0.319528\pi\) | |||||||
\(230\) | 175.194 | + | 285.183i | 0.00331179 | + | 0.00539098i | ||||
\(231\) | − | 23631.6i | − | 0.442863i | ||||||
\(232\) | −7710.25 | − | 93986.4i | −0.143249 | − | 1.74618i | ||||
\(233\) | 52509.1 | 0.967215 | 0.483608 | − | 0.875285i | \(-0.339326\pi\) | ||||
0.483608 | + | 0.875285i | \(0.339326\pi\) | |||||||
\(234\) | 16689.1 | − | 10252.4i | 0.304790 | − | 0.187239i | ||||
\(235\) | 32905.7i | 0.595848i | ||||||||
\(236\) | 5575.90 | + | 2825.57i | 0.100113 | + | 0.0507320i | ||||
\(237\) | −36686.2 | −0.653139 | ||||||||
\(238\) | 66284.9 | + | 107899.i | 1.17020 | + | 1.90487i | ||||
\(239\) | − | 51142.5i | − | 0.895336i | −0.894200 | − | 0.447668i | \(-0.852255\pi\) | ||
0.894200 | − | 0.447668i | \(-0.147745\pi\) | |||||||
\(240\) | −11993.2 | + | 8794.75i | −0.208215 | + | 0.152687i | ||||
\(241\) | 7.06147 | 0.000121580 | 6.07899e−5 | − | 1.00000i | \(-0.499981\pi\) | ||||
6.07899e−5 | 1.00000i | \(0.499981\pi\) | ||||||||
\(242\) | −31159.6 | + | 19142.0i | −0.532061 | + | 0.326856i | ||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | 29716.7 | − | 58642.1i | 0.499139 | − | 0.984986i | ||||
\(245\) | 15211.7 | 0.253423 | ||||||||
\(246\) | −13219.6 | − | 21519.1i | −0.218449 | − | 0.355594i | ||||
\(247\) | − | 73970.6i | − | 1.21245i | ||||||
\(248\) | 66401.7 | − | 5447.32i | 1.07963 | − | 0.0885685i | ||||
\(249\) | −25837.0 | −0.416718 | ||||||||
\(250\) | 4763.18 | − | 2926.12i | 0.0762108 | − | 0.0468179i | ||||
\(251\) | − | 60466.9i | − | 0.959776i | −0.877330 | − | 0.479888i | \(-0.840677\pi\) | ||
0.877330 | − | 0.479888i | \(-0.159323\pi\) | |||||||
\(252\) | 23634.0 | + | 11976.4i | 0.372165 | + | 0.188594i | ||||
\(253\) | 554.961 | 0.00867005 | ||||||||
\(254\) | 36606.6 | + | 59588.7i | 0.567403 | + | 0.923627i | ||||
\(255\) | − | 29987.4i | − | 0.461168i | ||||||
\(256\) | −19700.4 | + | 62504.9i | −0.300604 | + | 0.953749i | ||||
\(257\) | 38335.4 | 0.580408 | 0.290204 | − | 0.956965i | \(-0.406277\pi\) | ||||
0.290204 | + | 0.956965i | \(0.406277\pi\) | |||||||
\(258\) | −17490.9 | + | 10745.0i | −0.262768 | + | 0.161424i | ||||
\(259\) | 40957.3i | 0.610566i | ||||||||
\(260\) | −14664.6 | + | 28938.8i | −0.216932 | + | 0.428089i | ||||
\(261\) | 39783.7 | 0.584015 | ||||||||
\(262\) | 22399.7 | + | 36462.5i | 0.326316 | + | 0.531183i | ||||
\(263\) | − | 38851.9i | − | 0.561696i | −0.959752 | − | 0.280848i | \(-0.909384\pi\) | ||
0.959752 | − | 0.280848i | \(-0.0906156\pi\) | |||||||
\(264\) | 2016.21 | + | 24577.1i | 0.0289286 | + | 0.352634i | ||||
\(265\) | 25576.2 | 0.364204 | ||||||||
\(266\) | 85258.7 | − | 52376.2i | 1.20497 | − | 0.740237i | ||||
\(267\) | − | 64279.8i | − | 0.901679i | ||||||
\(268\) | 88015.6 | + | 44601.6i | 1.22543 | + | 0.620985i | ||||
\(269\) | −18724.5 | −0.258765 | −0.129382 | − | 0.991595i | \(-0.541299\pi\) | ||||
−0.129382 | + | 0.991595i | \(0.541299\pi\) | |||||||
\(270\) | −3284.18 | − | 5346.04i | −0.0450505 | − | 0.0733339i | ||||
\(271\) | 25639.5i | 0.349117i | 0.984647 | + | 0.174559i | \(0.0558499\pi\) | ||||
−0.984647 | + | 0.174559i | \(0.944150\pi\) | |||||||
\(272\) | −78142.8 | − | 106561.i | −1.05621 | − | 1.44033i | ||||
\(273\) | 57796.8 | 0.775495 | ||||||||
\(274\) | −106540. | + | 65449.6i | −1.41909 | + | 0.871778i | ||||
\(275\) | − | 9269.07i | − | 0.122566i | ||||||
\(276\) | −281.253 | + | 555.018i | −0.00369215 | + | 0.00728599i | ||||
\(277\) | −69695.7 | −0.908335 | −0.454168 | − | 0.890916i | \(-0.650063\pi\) | ||||
−0.454168 | + | 0.890916i | \(0.650063\pi\) | |||||||
\(278\) | −47074.2 | − | 76628.1i | −0.609107 | − | 0.991513i | ||||
\(279\) | 28107.3i | 0.361086i | ||||||||
\(280\) | −43738.5 | + | 3588.12i | −0.557889 | + | 0.0457668i | ||||
\(281\) | −69900.0 | −0.885248 | −0.442624 | − | 0.896707i | \(-0.645952\pi\) | ||||
−0.442624 | + | 0.896707i | \(0.645952\pi\) | |||||||
\(282\) | −52123.0 | + | 32020.3i | −0.655438 | + | 0.402649i | ||||
\(283\) | − | 107624.i | − | 1.34381i | −0.740637 | − | 0.671905i | \(-0.765476\pi\) | ||
0.740637 | − | 0.671905i | \(-0.234524\pi\) | |||||||
\(284\) | −63691.8 | − | 32275.6i | −0.789673 | − | 0.400164i | ||||
\(285\) | −23695.1 | −0.291722 | ||||||||
\(286\) | 28157.2 | + | 45834.7i | 0.344237 | + | 0.560354i | ||||
\(287\) | − | 74524.0i | − | 0.904758i | ||||||
\(288\) | −25601.4 | − | 10439.2i | −0.308659 | − | 0.125859i | ||||
\(289\) | 182922. | 2.19014 | ||||||||
\(290\) | −56147.2 | + | 34492.4i | −0.667624 | + | 0.410135i | ||||
\(291\) | 13075.2i | 0.154405i | ||||||||
\(292\) | 24366.2 | − | 48083.6i | 0.285774 | − | 0.563938i | ||||
\(293\) | 21779.0 | 0.253689 | 0.126845 | − | 0.991923i | \(-0.459515\pi\) | ||||
0.126845 | + | 0.991923i | \(0.459515\pi\) | |||||||
\(294\) | 14802.4 | + | 24095.6i | 0.171253 | + | 0.278768i | ||||
\(295\) | − | 4367.99i | − | 0.0501924i | ||||||
\(296\) | −3494.41 | − | 42596.1i | −0.0398832 | − | 0.486168i | ||||
\(297\) | −10403.3 | −0.117939 | ||||||||
\(298\) | −65588.4 | + | 40292.3i | −0.738574 | + | 0.453722i | ||||
\(299\) | 1357.29i | 0.0151821i | ||||||||
\(300\) | 9270.01 | + | 4697.55i | 0.103000 | + | 0.0521950i | ||||
\(301\) | −60573.6 | −0.668575 | ||||||||
\(302\) | 88789.4 | + | 144533.i | 0.973525 | + | 1.58472i | ||||
\(303\) | − | 15458.2i | − | 0.168374i | ||||||
\(304\) | −84201.5 | + | 61746.0i | −0.911113 | + | 0.668131i | ||||
\(305\) | −45938.5 | −0.493829 | ||||||||
\(306\) | 47500.5 | − | 29180.5i | 0.507288 | − | 0.311638i | ||||
\(307\) | 129208.i | 1.37092i | 0.728111 | + | 0.685460i | \(0.240399\pi\) | ||||
−0.728111 | + | 0.685460i | \(0.759601\pi\) | |||||||
\(308\) | −32892.0 | + | 64908.2i | −0.346728 | + | 0.684223i | ||||
\(309\) | −93341.2 | −0.977590 | ||||||||
\(310\) | −24369.0 | − | 39668.2i | −0.253580 | − | 0.412780i | ||||
\(311\) | 39962.2i | 0.413170i | 0.978429 | + | 0.206585i | \(0.0662351\pi\) | ||||
−0.978429 | + | 0.206585i | \(0.933765\pi\) | |||||||
\(312\) | −60109.4 | + | 4931.12i | −0.617495 | + | 0.0506567i | ||||
\(313\) | 99259.1 | 1.01317 | 0.506584 | − | 0.862191i | \(-0.330908\pi\) | ||||
0.506584 | + | 0.862191i | \(0.330908\pi\) | |||||||
\(314\) | −47644.5 | + | 29269.0i | −0.483230 | + | 0.296858i | ||||
\(315\) | − | 18514.2i | − | 0.186588i | ||||||
\(316\) | 100765. | + | 51062.2i | 1.00910 | + | 0.511358i | ||||
\(317\) | 92350.2 | 0.919008 | 0.459504 | − | 0.888176i | \(-0.348027\pi\) | ||||
0.459504 | + | 0.888176i | \(0.348027\pi\) | |||||||
\(318\) | 24888.0 | + | 40513.0i | 0.246114 | + | 0.400627i | ||||
\(319\) | 109262.i | 1.07371i | ||||||||
\(320\) | 45182.4 | − | 7463.38i | 0.441234 | − | 0.0728846i | ||||
\(321\) | −6237.87 | −0.0605378 | ||||||||
\(322\) | −1564.42 | + | 961.056i | −0.0150883 | + | 0.00926908i | ||||
\(323\) | − | 210535.i | − | 2.01799i | ||||||
\(324\) | 5272.38 | − | 10404.4i | 0.0502246 | − | 0.0991119i | ||||
\(325\) | 22669.8 | 0.214625 | ||||||||
\(326\) | −65103.7 | − | 105977.i | −0.612591 | − | 0.997184i | ||||
\(327\) | 85741.0i | 0.801850i | ||||||||
\(328\) | 6358.25 | + | 77505.8i | 0.0591004 | + | 0.720422i | ||||
\(329\) | −180510. | −1.66767 | ||||||||
\(330\) | 14682.3 | − | 9019.65i | 0.134824 | − | 0.0828251i | ||||
\(331\) | 37376.0i | 0.341143i | 0.985345 | + | 0.170572i | \(0.0545614\pi\) | ||||
−0.985345 | + | 0.170572i | \(0.945439\pi\) | |||||||
\(332\) | 70965.6 | + | 35961.6i | 0.643831 | + | 0.326259i | ||||
\(333\) | 18030.6 | 0.162601 | ||||||||
\(334\) | −63241.9 | − | 102946.i | −0.566907 | − | 0.922819i | ||||
\(335\) | − | 68948.7i | − | 0.614380i | ||||||
\(336\) | −48245.2 | − | 65790.7i | −0.427342 | − | 0.582755i | ||||
\(337\) | 119047. | 1.04824 | 0.524118 | − | 0.851645i | \(-0.324395\pi\) | ||||
0.524118 | + | 0.851645i | \(0.324395\pi\) | |||||||
\(338\) | −14757.0 | + | 9065.51i | −0.129171 | + | 0.0793522i | ||||
\(339\) | − | 31373.4i | − | 0.272999i | ||||||
\(340\) | −41738.5 | + | 82365.6i | −0.361060 | + | 0.712505i | ||||
\(341\) | −77193.7 | −0.663855 | ||||||||
\(342\) | −23057.5 | − | 37533.4i | −0.197133 | − | 0.320897i | ||||
\(343\) | − | 63810.8i | − | 0.542383i | ||||||
\(344\) | 62997.3 | − | 5168.03i | 0.532359 | − | 0.0436725i | ||||
\(345\) | 434.784 | 0.00365288 | ||||||||
\(346\) | 75191.1 | − | 46191.5i | 0.628079 | − | 0.385842i | ||||
\(347\) | 84780.6i | 0.704105i | 0.935980 | + | 0.352052i | \(0.114516\pi\) | ||||
−0.935980 | + | 0.352052i | \(0.885484\pi\) | |||||||
\(348\) | −109273. | − | 55373.6i | −0.902304 | − | 0.457240i | ||||
\(349\) | −171629. | −1.40909 | −0.704545 | − | 0.709659i | \(-0.748849\pi\) | ||||
−0.704545 | + | 0.709659i | \(0.748849\pi\) | |||||||
\(350\) | 16051.7 | + | 26129.2i | 0.131035 | + | 0.213300i | ||||
\(351\) | − | 25443.8i | − | 0.206523i | ||||||
\(352\) | 28670.2 | − | 70311.6i | 0.231391 | − | 0.567468i | ||||
\(353\) | 195140. | 1.56602 | 0.783010 | − | 0.622009i | \(-0.213683\pi\) | ||||
0.783010 | + | 0.622009i | \(0.213683\pi\) | |||||||
\(354\) | 6918.95 | − | 4250.45i | 0.0552120 | − | 0.0339179i | ||||
\(355\) | 49894.3i | 0.395908i | ||||||||
\(356\) | −89468.9 | + | 176555.i | −0.705947 | + | 1.39310i | ||||
\(357\) | 164501. | 1.29072 | ||||||||
\(358\) | 9003.66 | + | 14656.3i | 0.0702511 | + | 0.114356i | ||||
\(359\) | − | 50318.4i | − | 0.390426i | −0.980761 | − | 0.195213i | \(-0.937460\pi\) | ||
0.980761 | − | 0.195213i | \(-0.0625398\pi\) | |||||||
\(360\) | 1579.59 | + | 19254.9i | 0.0121882 | + | 0.148572i | ||||
\(361\) | −36037.2 | −0.276527 | ||||||||
\(362\) | 110046. | − | 67603.6i | 0.839764 | − | 0.515884i | ||||
\(363\) | 47505.3i | 0.360520i | ||||||||
\(364\) | −158749. | − | 80445.4i | −1.19814 | − | 0.607154i | ||||
\(365\) | −37667.3 | −0.282734 | ||||||||
\(366\) | −44702.3 | − | 72767.1i | −0.333709 | − | 0.543216i | ||||
\(367\) | 50718.2i | 0.376558i | 0.982116 | + | 0.188279i | \(0.0602909\pi\) | ||||
−0.982116 | + | 0.188279i | \(0.939709\pi\) | |||||||
\(368\) | 1545.02 | − | 1132.98i | 0.0114088 | − | 0.00836619i | ||||
\(369\) | −32807.6 | −0.240947 | ||||||||
\(370\) | −25446.8 | + | 15632.5i | −0.185879 | + | 0.114189i | ||||
\(371\) | 140303.i | 1.01934i | ||||||||
\(372\) | 39121.6 | − | 77201.5i | 0.282703 | − | 0.557879i | ||||
\(373\) | −119570. | −0.859417 | −0.429709 | − | 0.902968i | \(-0.641384\pi\) | ||||
−0.429709 | + | 0.902968i | \(0.641384\pi\) | |||||||
\(374\) | 80141.1 | + | 130455.i | 0.572944 | + | 0.932646i | ||||
\(375\) | − | 7261.84i | − | 0.0516398i | ||||||
\(376\) | 187733. | − | 15400.8i | 1.32790 | − | 0.108935i | ||||
\(377\) | −267226. | −1.88016 | ||||||||
\(378\) | 29326.6 | − | 18016.0i | 0.205248 | − | 0.126088i | ||||
\(379\) | 104060.i | 0.724447i | 0.932091 | + | 0.362223i | \(0.117982\pi\) | ||||
−0.932091 | + | 0.362223i | \(0.882018\pi\) | |||||||
\(380\) | 65082.7 | + | 32980.4i | 0.450711 | + | 0.228396i | ||||
\(381\) | 90847.8 | 0.625842 | ||||||||
\(382\) | −48447.8 | − | 78864.0i | −0.332007 | − | 0.540446i | ||||
\(383\) | 72442.8i | 0.493853i | 0.969034 | + | 0.246926i | \(0.0794206\pi\) | ||||
−0.969034 | + | 0.246926i | \(0.920579\pi\) | |||||||
\(384\) | 55788.7 | + | 64306.9i | 0.378341 | + | 0.436109i | ||||
\(385\) | 50847.1 | 0.343040 | ||||||||
\(386\) | 220768. | − | 135622.i | 1.48171 | − | 0.910242i | ||||
\(387\) | 26666.3i | 0.178049i | ||||||||
\(388\) | 18198.9 | − | 35913.2i | 0.120888 | − | 0.238556i | ||||
\(389\) | −162511. | −1.07395 | −0.536975 | − | 0.843598i | \(-0.680433\pi\) | ||||
−0.536975 | + | 0.843598i | \(0.680433\pi\) | |||||||
\(390\) | 22059.8 | + | 35909.2i | 0.145035 | + | 0.236089i | ||||
\(391\) | 3863.13i | 0.0252689i | ||||||||
\(392\) | −7119.52 | − | 86785.5i | −0.0463317 | − | 0.564775i | ||||
\(393\) | 55590.0 | 0.359925 | ||||||||
\(394\) | −1081.58 | + | 664.435i | −0.00696731 | + | 0.00428016i | ||||
\(395\) | − | 78936.0i | − | 0.505919i | ||||||
\(396\) | 28574.5 | + | 14480.0i | 0.182216 | + | 0.0923376i | ||||
\(397\) | 53291.6 | 0.338125 | 0.169063 | − | 0.985605i | \(-0.445926\pi\) | ||||
0.169063 | + | 0.985605i | \(0.445926\pi\) | |||||||
\(398\) | 37794.9 | + | 61523.1i | 0.238598 | + | 0.388394i | ||||
\(399\) | − | 129984.i | − | 0.816476i | ||||||
\(400\) | −18923.3 | − | 25805.2i | −0.118271 | − | 0.161283i | ||||
\(401\) | −33793.7 | −0.210159 | −0.105079 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105079 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(402\) | 109216. | − | 67093.4i | 0.675823 | − | 0.415172i | ||||
\(403\) | − | 188796.i | − | 1.16247i | ||||||
\(404\) | −21515.8 | + | 42458.6i | −0.131824 | + | 0.260138i | ||||
\(405\) | −8150.47 | −0.0496904 | ||||||||
\(406\) | −189214. | − | 308005.i | −1.14789 | − | 1.86856i | ||||
\(407\) | 49519.1i | 0.298940i | ||||||||
\(408\) | −171083. | + | 14035.0i | −1.02775 | + | 0.0843123i | ||||
\(409\) | 192978. | 1.15361 | 0.576807 | − | 0.816881i | \(-0.304299\pi\) | ||||
0.576807 | + | 0.816881i | \(0.304299\pi\) | |||||||
\(410\) | 46301.8 | − | 28444.1i | 0.275442 | − | 0.169210i | ||||
\(411\) | 162429.i | 0.961565i | ||||||||
\(412\) | 256377. | + | 129918.i | 1.51038 | + | 0.765379i | ||||
\(413\) | 23961.4 | 0.140479 | ||||||||
\(414\) | 423.085 | + | 688.703i | 0.00246846 | + | 0.00401820i | ||||
\(415\) | − | 55592.3i | − | 0.322789i | ||||||
\(416\) | 171964. | + | 70120.1i | 0.993691 | + | 0.405187i | ||||
\(417\) | −116826. | −0.671840 | ||||||||
\(418\) | 103081. | − | 63325.0i | 0.589966 | − | 0.362428i | ||||
\(419\) | 207731.i | 1.18324i | 0.806216 | + | 0.591621i | \(0.201512\pi\) | ||||
−0.806216 | + | 0.591621i | \(0.798488\pi\) | |||||||
\(420\) | −25769.2 | + | 50852.3i | −0.146084 | + | 0.288278i | ||||
\(421\) | −135957. | −0.767075 | −0.383538 | − | 0.923525i | \(-0.625294\pi\) | ||||
−0.383538 | + | 0.923525i | \(0.625294\pi\) | |||||||
\(422\) | −131590. | − | 214204.i | −0.738922 | − | 1.20283i | ||||
\(423\) | 79465.8i | 0.444119i | ||||||||
\(424\) | −11970.4 | − | 145917.i | −0.0665850 | − | 0.811658i | ||||
\(425\) | 64522.7 | 0.357219 | ||||||||
\(426\) | −79033.1 | + | 48551.7i | −0.435502 | + | 0.267538i | ||||
\(427\) | − | 252004.i | − | 1.38214i | ||||||
\(428\) | 17133.4 | + | 8682.28i | 0.0935309 | + | 0.0473965i | ||||
\(429\) | 69878.7 | 0.379691 | ||||||||
\(430\) | −23119.6 | − | 37634.4i | −0.125038 | − | 0.203539i | ||||
\(431\) | 151994.i | 0.818222i | 0.912485 | + | 0.409111i | \(0.134161\pi\) | ||||
−0.912485 | + | 0.409111i | \(0.865839\pi\) | |||||||
\(432\) | −28963.0 | + | 21238.9i | −0.155194 | + | 0.113806i | ||||
\(433\) | −36457.2 | −0.194450 | −0.0972249 | − | 0.995262i | \(-0.530997\pi\) | ||||
−0.0972249 | + | 0.995262i | \(0.530997\pi\) | |||||||
\(434\) | 217607. | − | 133680.i | 1.15530 | − | 0.709722i | ||||
\(435\) | 85600.9i | 0.452376i | ||||||||
\(436\) | 119340. | − | 235502.i | 0.627788 | − | 1.23886i | ||||
\(437\) | 3052.52 | 0.0159844 | ||||||||
\(438\) | −36653.7 | − | 59665.4i | −0.191060 | − | 0.311010i | ||||
\(439\) | 118065.i | 0.612620i | 0.951932 | + | 0.306310i | \(0.0990944\pi\) | ||||
−0.951932 | + | 0.306310i | \(0.900906\pi\) | |||||||
\(440\) | −52881.6 | + | 4338.18i | −0.273149 | + | 0.0224080i | ||||
\(441\) | 36735.6 | 0.188891 | ||||||||
\(442\) | −319059. | + | 196005.i | −1.63315 | + | 1.00328i | ||||
\(443\) | − | 113592.i | − | 0.578817i | −0.957206 | − | 0.289409i | \(-0.906541\pi\) | ||
0.957206 | − | 0.289409i | \(-0.0934587\pi\) | |||||||
\(444\) | −49524.1 | − | 25096.2i | −0.251218 | − | 0.127304i | ||||
\(445\) | 138308. | 0.698438 | ||||||||
\(446\) | 127146. | + | 206971.i | 0.639196 | + | 1.04049i | ||||
\(447\) | 99994.7i | 0.500452i | ||||||||
\(448\) | 40941.7 | + | 247856.i | 0.203990 | + | 1.23493i | ||||
\(449\) | −1745.18 | −0.00865662 | −0.00432831 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432831 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(450\) | 11502.8 | − | 7066.44i | 0.0568042 | − | 0.0348960i | ||||
\(451\) | − | 90102.5i | − | 0.442980i | ||||||
\(452\) | −43667.5 | + | 86172.2i | −0.213738 | + | 0.421784i | ||||
\(453\) | 220352. | 1.07379 | ||||||||
\(454\) | −206506. | − | 336153.i | −1.00189 | − | 1.63089i | ||||
\(455\) | 124359.i | 0.600696i | ||||||||
\(456\) | 11090.0 | + | 135185.i | 0.0533337 | + | 0.650126i | ||||
\(457\) | −74606.1 | −0.357225 | −0.178613 | − | 0.983919i | \(-0.557161\pi\) | ||||
−0.178613 | + | 0.983919i | \(0.557161\pi\) | |||||||
\(458\) | −191987. | + | 117941.i | −0.915250 | + | 0.562257i | ||||
\(459\) | − | 72418.3i | − | 0.343734i | ||||||
\(460\) | −1194.21 | − | 605.161i | −0.00564371 | − | 0.00285993i | ||||
\(461\) | 17305.9 | 0.0814314 | 0.0407157 | − | 0.999171i | \(-0.487036\pi\) | ||||
0.0407157 | + | 0.999171i | \(0.487036\pi\) | |||||||
\(462\) | 49478.9 | + | 80542.4i | 0.231812 | + | 0.377347i | ||||
\(463\) | 124639.i | 0.581422i | 0.956811 | + | 0.290711i | \(0.0938918\pi\) | ||||
−0.956811 | + | 0.290711i | \(0.906108\pi\) | |||||||
\(464\) | 223063. | + | 304186.i | 1.03608 | + | 1.41287i | ||||
\(465\) | −60477.3 | −0.279696 | ||||||||
\(466\) | −178964. | + | 109941.i | −0.824128 | + | 0.506279i | ||||
\(467\) | − | 208541.i | − | 0.956219i | −0.878300 | − | 0.478110i | \(-0.841322\pi\) | ||
0.878300 | − | 0.478110i | \(-0.158678\pi\) | |||||||
\(468\) | −35414.4 | + | 69885.8i | −0.161692 | + | 0.319078i | ||||
\(469\) | 378230. | 1.71953 | ||||||||
\(470\) | −68896.6 | − | 112151.i | −0.311891 | − | 0.507700i | ||||
\(471\) | 72637.9i | 0.327432i | ||||||||
\(472\) | −24920.1 | + | 2044.34i | −0.111858 | + | 0.00917634i | ||||
\(473\) | −73235.9 | −0.327342 | ||||||||
\(474\) | 125036. | − | 76812.0i | 0.556515 | − | 0.341879i | ||||
\(475\) | − | 50983.8i | − | 0.225967i | ||||||
\(476\) | −451831. | − | 228964.i | −1.99417 | − | 1.01054i | ||||
\(477\) | 61765.3 | 0.271461 | ||||||||
\(478\) | 107080. | + | 174306.i | 0.468654 | + | 0.762882i | ||||
\(479\) | − | 399291.i | − | 1.74028i | −0.492805 | − | 0.870140i | \(-0.664028\pi\) | ||
0.492805 | − | 0.870140i | \(-0.335972\pi\) | |||||||
\(480\) | 22461.7 | − | 55085.5i | 0.0974899 | − | 0.239087i | ||||
\(481\) | −121111. | −0.523472 | ||||||||
\(482\) | −24.0673 | + | 14.7850i | −0.000103594 | + | 6.36397e-5i | ||||
\(483\) | 2385.08i | 0.0102237i | ||||||||
\(484\) | 66121.0 | − | 130481.i | 0.282260 | − | 0.557003i | ||||
\(485\) | −28133.3 | −0.119602 | ||||||||
\(486\) | −7931.15 | − | 12910.4i | −0.0335787 | − | 0.0546598i | ||||
\(487\) | 432403.i | 1.82318i | 0.411097 | + | 0.911592i | \(0.365146\pi\) | ||||
−0.411097 | + | 0.911592i | \(0.634854\pi\) | |||||||
\(488\) | 21500.5 | + | 262087.i | 0.0902836 | + | 1.10054i | ||||
\(489\) | −161570. | −0.675683 | ||||||||
\(490\) | −51845.4 | + | 31849.7i | −0.215933 | + | 0.132652i | ||||
\(491\) | − | 266902.i | − | 1.10710i | −0.832814 | − | 0.553552i | \(-0.813272\pi\) | ||
0.832814 | − | 0.553552i | \(-0.186728\pi\) | |||||||
\(492\) | 90111.7 | + | 45663.8i | 0.372264 | + | 0.188643i | ||||
\(493\) | −760578. | −3.12932 | ||||||||
\(494\) | 154877. | + | 252110.i | 0.634647 | + | 1.03309i | ||||
\(495\) | − | 22384.4i | − | 0.0913554i | ||||||
\(496\) | −214908. | + | 157595.i | −0.873554 | + | 0.640589i | ||||
\(497\) | −273704. | −1.10807 | ||||||||
\(498\) | 88058.8 | − | 54096.4i | 0.355070 | − | 0.218127i | ||||
\(499\) | 21287.2i | 0.0854905i | 0.999086 | + | 0.0427452i | \(0.0136104\pi\) | ||||
−0.999086 | + | 0.0427452i | \(0.986390\pi\) | |||||||
\(500\) | −10107.5 | + | 19945.9i | −0.0404300 | + | 0.0797835i | ||||
\(501\) | −156949. | −0.625294 | ||||||||
\(502\) | 126603. | + | 206086.i | 0.502385 | + | 0.817790i | ||||
\(503\) | 267207.i | 1.05612i | 0.849208 | + | 0.528058i | \(0.177080\pi\) | ||||
−0.849208 | + | 0.528058i | \(0.822920\pi\) | |||||||
\(504\) | −105626. | + | 8665.15i | −0.415826 | + | 0.0341126i | ||||
\(505\) | 33260.8 | 0.130422 | ||||||||
\(506\) | −1891.45 | + | 1161.96i | −0.00738743 | + | 0.00453825i | ||||
\(507\) | 22498.2i | 0.0875249i | ||||||||
\(508\) | −249529. | − | 126448.i | −0.966926 | − | 0.489987i | ||||
\(509\) | 449991. | 1.73687 | 0.868437 | − | 0.495800i | \(-0.165125\pi\) | ||||
0.868437 | + | 0.495800i | \(0.165125\pi\) | |||||||
\(510\) | 62786.5 | + | 102205.i | 0.241394 | + | 0.392944i | ||||
\(511\) | − | 206630.i | − | 0.791320i | ||||||
\(512\) | −63726.5 | − | 254280.i | −0.243097 | − | 0.970002i | ||||
\(513\) | −57222.6 | −0.217437 | ||||||||
\(514\) | −130657. | + | 80265.0i | −0.494544 | + | 0.303809i | ||||
\(515\) | − | 200838.i | − | 0.757238i | ||||||
\(516\) | 37115.8 | − | 73243.4i | 0.139399 | − | 0.275086i | ||||
\(517\) | −218244. | −0.816509 | ||||||||
\(518\) | −85754.8 | − | 139593.i | −0.319594 | − | 0.520240i | ||||
\(519\) | − | 114635.i | − | 0.425581i | ||||||
\(520\) | −10610.1 | − | 129335.i | −0.0392385 | − | 0.478309i | ||||
\(521\) | 147922. | 0.544951 | 0.272475 | − | 0.962163i | \(-0.412158\pi\) | ||||
0.272475 | + | 0.962163i | \(0.412158\pi\) | |||||||
\(522\) | −135593. | + | 83297.5i | −0.497618 | + | 0.305697i | ||||
\(523\) | − | 329638.i | − | 1.20513i | −0.798070 | − | 0.602565i | \(-0.794145\pi\) | ||
0.798070 | − | 0.602565i | \(-0.205855\pi\) | |||||||
\(524\) | −152687. | − | 77373.8i | −0.556084 | − | 0.281794i | ||||
\(525\) | 39836.1 | 0.144530 | ||||||||
\(526\) | 81346.6 | + | 132417.i | 0.294014 | + | 0.478600i | ||||
\(527\) | − | 537351.i | − | 1.93480i | ||||||
\(528\) | −58330.4 | − | 79543.6i | −0.209231 | − | 0.285323i | ||||
\(529\) | 279785. | 0.999800 | ||||||||
\(530\) | −87170.1 | + | 53550.4i | −0.310324 | + | 0.190639i | ||||
\(531\) | − | 10548.5i | − | 0.0374112i | ||||||
\(532\) | −180920. | + | 357022.i | −0.639239 | + | 1.26146i | ||||
\(533\) | 220368. | 0.775700 | ||||||||
\(534\) | 134586. | + | 219082.i | 0.471975 | + | 0.768287i | ||||
\(535\) | − | 13421.8i | − | 0.0468923i | ||||||
\(536\) | −393364. | + | 32270.0i | −1.36919 | + | 0.112323i | ||||
\(537\) | 22344.7 | 0.0774865 | ||||||||
\(538\) | 63817.7 | − | 39204.6i | 0.220484 | − | 0.135448i | ||||
\(539\) | 100890.i | 0.347274i | ||||||||
\(540\) | 22386.6 | + | 11344.4i | 0.0767717 | + | 0.0389038i | ||||
\(541\) | 412276. | 1.40862 | 0.704309 | − | 0.709894i | \(-0.251257\pi\) | ||||
0.704309 | + | 0.709894i | \(0.251257\pi\) | |||||||
\(542\) | −53683.0 | − | 87385.9i | −0.182742 | − | 0.297470i | ||||
\(543\) | − | 167774.i | − | 0.569017i | ||||||
\(544\) | 489444. | + | 199576.i | 1.65389 | + | 0.674388i | ||||
\(545\) | −184485. | −0.621110 | ||||||||
\(546\) | −196986. | + | 121013.i | −0.660770 | + | 0.405925i | ||||
\(547\) | 37918.1i | 0.126728i | 0.997990 | + | 0.0633638i | \(0.0201829\pi\) | ||||
−0.997990 | + | 0.0633638i | \(0.979817\pi\) | |||||||
\(548\) | 226079. | − | 446137.i | 0.752833 | − | 1.48562i | ||||
\(549\) | −110939. | −0.368079 | ||||||||
\(550\) | 19407.2 | + | 31591.3i | 0.0641560 | + | 0.104434i | ||||
\(551\) | 600985.i | 1.97952i | ||||||||
\(552\) | −203.491 | − | 2480.52i | −0.000667832 | − | 0.00814074i | ||||
\(553\) | 433017. | 1.41597 | ||||||||
\(554\) | 237540. | − | 145926.i | 0.773959 | − | 0.475459i | ||||
\(555\) | 38795.7i | 0.125950i | ||||||||
\(556\) | 320881. | + | 162606.i | 1.03799 | + | 0.526000i | ||||
\(557\) | 229026. | 0.738200 | 0.369100 | − | 0.929390i | \(-0.379666\pi\) | ||||
0.369100 | + | 0.929390i | \(0.379666\pi\) | |||||||
\(558\) | −58850.0 | − | 95796.8i | −0.189007 | − | 0.307668i | ||||
\(559\) | − | 179116.i | − | 0.573207i | ||||||
\(560\) | 141559. | − | 103807.i | 0.451400 | − | 0.331017i | ||||
\(561\) | 198889. | 0.631953 | ||||||||
\(562\) | 238237. | − | 146354.i | 0.754286 | − | 0.463374i | ||||
\(563\) | 529561.i | 1.67070i | 0.549717 | + | 0.835351i | \(0.314735\pi\) | ||||
−0.549717 | + | 0.835351i | \(0.685265\pi\) | |||||||
\(564\) | 110606. | − | 218266.i | 0.347712 | − | 0.686164i | ||||
\(565\) | 67504.7 | 0.211464 | ||||||||
\(566\) | 225340. | + | 366811.i | 0.703403 | + | 1.14501i | ||||
\(567\) | − | 44710.8i | − | 0.139074i | ||||||
\(568\) | 284655. | − | 23351.9i | 0.882312 | − | 0.0723812i | ||||
\(569\) | 273177. | 0.843760 | 0.421880 | − | 0.906652i | \(-0.361370\pi\) | ||||
0.421880 | + | 0.906652i | \(0.361370\pi\) | |||||||
\(570\) | 80758.9 | − | 49611.9i | 0.248566 | − | 0.152699i | ||||
\(571\) | − | 465596.i | − | 1.42803i | −0.700132 | − | 0.714014i | \(-0.746875\pi\) | ||
0.700132 | − | 0.714014i | \(-0.253125\pi\) | |||||||
\(572\) | −191934. | − | 97261.8i | −0.586623 | − | 0.297269i | ||||
\(573\) | −120235. | −0.366201 | ||||||||
\(574\) | 156035. | + | 253996.i | 0.473586 | + | 0.770910i | ||||
\(575\) | 935.506i | 0.00282951i | ||||||||
\(576\) | 109113. | − | 18023.7i | 0.328877 | − | 0.0543249i | ||||
\(577\) | 292168. | 0.877570 | 0.438785 | − | 0.898592i | \(-0.355409\pi\) | ||||
0.438785 | + | 0.898592i | \(0.355409\pi\) | |||||||
\(578\) | −623446. | + | 382996.i | −1.86613 | + | 1.14641i | ||||
\(579\) | − | 336579.i | − | 1.00399i | ||||||
\(580\) | 119145. | − | 235117.i | 0.354176 | − | 0.698922i | ||||
\(581\) | 304961. | 0.903426 | ||||||||
\(582\) | −27376.3 | − | 44563.5i | −0.0808218 | − | 0.131563i | ||||
\(583\) | 169632.i | 0.499080i | ||||||||
\(584\) | 17629.3 | + | 214898.i | 0.0516905 | + | 0.630096i | ||||
\(585\) | 54746.4 | 0.159972 | ||||||||
\(586\) | −74228.2 | + | 45599.9i | −0.216159 | + | 0.132791i | ||||
\(587\) | − | 184222.i | − | 0.534644i | −0.963607 | − | 0.267322i | \(-0.913861\pi\) | ||
0.963607 | − | 0.267322i | \(-0.0861387\pi\) | |||||||
\(588\) | −100901. | − | 51131.1i | −0.291836 | − | 0.147887i | ||||
\(589\) | −424598. | −1.22390 | ||||||||
\(590\) | 9145.52 | + | 14887.2i | 0.0262727 | + | 0.0427670i | ||||
\(591\) | 1648.95i | 0.00472099i | ||||||||
\(592\) | 101096. | + | 137862.i | 0.288463 | + | 0.393370i | ||||
\(593\) | −385641. | −1.09666 | −0.548332 | − | 0.836261i | \(-0.684737\pi\) | ||||
−0.548332 | + | 0.836261i | \(0.684737\pi\) | |||||||
\(594\) | 35457.1 | − | 21782.0i | 0.100492 | − | 0.0617342i | ||||
\(595\) | 353951.i | 0.999790i | ||||||||
\(596\) | 139179. | − | 274652.i | 0.391816 | − | 0.773198i | ||||
\(597\) | 93797.0 | 0.263172 | ||||||||
\(598\) | −2841.85 | − | 4626.00i | −0.00794691 | − | 0.0129361i | ||||
\(599\) | 316862.i | 0.883115i | 0.897233 | + | 0.441557i | \(0.145574\pi\) | ||||
−0.897233 | + | 0.441557i | \(0.854426\pi\) | |||||||
\(600\) | −41430.0 | + | 3398.75i | −0.115083 | + | 0.00944096i | ||||
\(601\) | −388882. | −1.07663 | −0.538317 | − | 0.842742i | \(-0.680940\pi\) | ||||
−0.538317 | + | 0.842742i | \(0.680940\pi\) | |||||||
\(602\) | 206450. | − | 126827.i | 0.569668 | − | 0.349959i | ||||
\(603\) | − | 166508.i | − | 0.457931i | ||||||
\(604\) | −605233. | − | 306700.i | −1.65901 | − | 0.840698i | ||||
\(605\) | −102215. | −0.279257 | ||||||||
\(606\) | 32365.8 | + | 52685.5i | 0.0881335 | + | 0.143465i | ||||
\(607\) | 235572.i | 0.639362i | 0.947525 | + | 0.319681i | \(0.103576\pi\) | ||||
−0.947525 | + | 0.319681i | \(0.896424\pi\) | |||||||
\(608\) | 157698. | − | 386743.i | 0.426599 | − | 1.04620i | ||||
\(609\) | −469579. | −1.26612 | ||||||||
\(610\) | 156570. | − | 96184.1i | 0.420774 | − | 0.258490i | ||||
\(611\) | − | 533769.i | − | 1.42979i | ||||||
\(612\) | −100797. | + | 198909.i | −0.269118 | + | 0.531070i | ||||
\(613\) | −74819.9 | −0.199111 | −0.0995557 | − | 0.995032i | \(-0.531742\pi\) | ||||
−0.0995557 | + | 0.995032i | \(0.531742\pi\) | |||||||
\(614\) | −270530. | − | 440372.i | −0.717594 | − | 1.16811i | ||||
\(615\) | − | 70590.8i | − | 0.186637i | ||||||
\(616\) | −23797.9 | − | 290091.i | −0.0627158 | − | 0.764493i | ||||
\(617\) | 476184. | 1.25085 | 0.625424 | − | 0.780285i | \(-0.284926\pi\) | ||||
0.625424 | + | 0.780285i | \(0.284926\pi\) | |||||||
\(618\) | 318130. | − | 195434.i | 0.832968 | − | 0.511709i | ||||
\(619\) | − | 95751.1i | − | 0.249898i | −0.992163 | − | 0.124949i | \(-0.960123\pi\) | ||
0.992163 | − | 0.124949i | \(-0.0398767\pi\) | |||||||
\(620\) | 166111. | + | 84176.3i | 0.432131 | + | 0.218981i | ||||
\(621\) | 1049.98 | 0.00272270 | ||||||||
\(622\) | −83671.3 | − | 136201.i | −0.216270 | − | 0.352047i | ||||
\(623\) | 758713.i | 1.95480i | ||||||||
\(624\) | 194543. | − | 142661.i | 0.499628 | − | 0.366384i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | −338300. | + | 207825.i | −0.863283 | + | 0.530332i | ||||
\(627\) | − | 157156.i | − | 0.399756i | ||||||
\(628\) | 101102. | − | 199512.i | 0.256355 | − | 0.505883i | ||||
\(629\) | −344706. | −0.871260 | ||||||||
\(630\) | 38764.2 | + | 63100.9i | 0.0976674 | + | 0.158984i | ||||
\(631\) | 363696.i | 0.913439i | 0.889611 | + | 0.456720i | \(0.150976\pi\) | ||||
−0.889611 | + | 0.456720i | \(0.849024\pi\) | |||||||
\(632\) | −450343. | + | 36944.3i | −1.12748 | + | 0.0924939i | ||||
\(633\) | −326572. | −0.815026 | ||||||||
\(634\) | −314753. | + | 193359.i | −0.783053 | + | 0.481045i | ||||
\(635\) | 195473.i | 0.484775i | ||||||||
\(636\) | −169649. | − | 85969.1i | −0.419408 | − | 0.212534i | ||||
\(637\) | −246752. | −0.608110 | ||||||||
\(638\) | −228767. | − | 372391.i | −0.562021 | − | 0.914866i | ||||
\(639\) | 120492.i | 0.295092i | ||||||||
\(640\) | −138366. | + | 120038.i | −0.337809 | + | 0.293062i | ||||
\(641\) | 11650.4 | 0.0283547 | 0.0141773 | − | 0.999899i | \(-0.495487\pi\) | ||||
0.0141773 | + | 0.999899i | \(0.495487\pi\) | |||||||
\(642\) | 21260.2 | − | 13060.6i | 0.0515820 | − | 0.0316879i | ||||
\(643\) | 477647.i | 1.15527i | 0.816294 | + | 0.577637i | \(0.196025\pi\) | ||||
−0.816294 | + | 0.577637i | \(0.803975\pi\) | |||||||
\(644\) | 3319.72 | − | 6551.04i | 0.00800441 | − | 0.0157957i | ||||
\(645\) | −57376.6 | −0.137916 | ||||||||
\(646\) | 440810. | + | 717557.i | 1.05630 | + | 1.71946i | ||||
\(647\) | 184457.i | 0.440642i | 0.975427 | + | 0.220321i | \(0.0707105\pi\) | ||||
−0.975427 | + | 0.220321i | \(0.929289\pi\) | |||||||
\(648\) | 3814.65 | + | 46499.8i | 0.00908457 | + | 0.110739i | ||||
\(649\) | 28970.3 | 0.0687802 | ||||||||
\(650\) | −77264.3 | + | 47465.0i | −0.182874 | + | 0.112343i | ||||
\(651\) | − | 331759.i | − | 0.782818i | ||||||
\(652\) | 443779. | + | 224884.i | 1.04393 | + | 0.529009i | ||||
\(653\) | 105463. | 0.247329 | 0.123664 | − | 0.992324i | \(-0.460535\pi\) | ||||
0.123664 | + | 0.992324i | \(0.460535\pi\) | |||||||
\(654\) | −179521. | − | 292227.i | −0.419720 | − | 0.683226i | ||||
\(655\) | 119611.i | 0.278796i | ||||||||
\(656\) | −183949. | − | 250847.i | −0.427455 | − | 0.582909i | ||||
\(657\) | −90964.7 | −0.210738 | ||||||||
\(658\) | 615223. | − | 377944.i | 1.42096 | − | 0.872924i | ||||
\(659\) | 434371.i | 1.00021i | 0.865966 | + | 0.500103i | \(0.166705\pi\) | ||||
−0.865966 | + | 0.500103i | \(0.833295\pi\) | |||||||
\(660\) | −31156.0 | + | 61482.5i | −0.0715244 | + | 0.141144i | ||||
\(661\) | −474718. | −1.08651 | −0.543254 | − | 0.839568i | \(-0.682808\pi\) | ||||
−0.543254 | + | 0.839568i | \(0.682808\pi\) | |||||||
\(662\) | −78256.3 | − | 127387.i | −0.178568 | − | 0.290675i | ||||
\(663\) | 486431.i | 1.10661i | ||||||||
\(664\) | −317163. | + | 26018.8i | −0.719361 | + | 0.0590134i | ||||
\(665\) | 279681. | 0.632439 | ||||||||
\(666\) | −61452.8 | + | 37751.8i | −0.138546 | + | 0.0851116i | ||||
\(667\) | − | 11027.5i | − | 0.0247871i | ||||||
\(668\) | 431088. | + | 218453.i | 0.966080 | + | 0.489558i | ||||
\(669\) | 315544. | 0.705029 | ||||||||
\(670\) | 144362. | + | 234995.i | 0.321591 | + | 0.523490i | ||||
\(671\) | − | 304683.i | − | 0.676710i | ||||||
\(672\) | 302181. | + | 123217.i | 0.669159 | + | 0.272856i | ||||
\(673\) | −701401. | −1.54859 | −0.774295 | − | 0.632825i | \(-0.781895\pi\) | ||||
−0.774295 | + | 0.632825i | \(0.781895\pi\) | |||||||
\(674\) | −405743. | + | 249256.i | −0.893164 | + | 0.548689i | ||||
\(675\) | − | 17537.0i | − | 0.0384900i | ||||||
\(676\) | 31314.4 | − | 61795.1i | 0.0685254 | − | 0.135226i | ||||
\(677\) | −284255. | −0.620199 | −0.310100 | − | 0.950704i | \(-0.600362\pi\) | ||||
−0.310100 | + | 0.950704i | \(0.600362\pi\) | |||||||
\(678\) | 65688.2 | + | 106928.i | 0.142899 | + | 0.232613i | ||||
\(679\) | − | 154330.i | − | 0.334743i | ||||||
\(680\) | −30198.4 | − | 368113.i | −0.0653080 | − | 0.796092i | ||||
\(681\) | −512492. | −1.10508 | ||||||||
\(682\) | 263096. | − | 161625.i | 0.565646 | − | 0.347488i | ||||
\(683\) | − | 659478.i | − | 1.41371i | −0.707361 | − | 0.706853i | \(-0.750114\pi\) | ||
0.707361 | − | 0.706853i | \(-0.249886\pi\) | |||||||
\(684\) | 157172. | + | 79646.2i | 0.335940 | + | 0.170237i | ||||
\(685\) | −349491. | −0.744825 | ||||||||
\(686\) | 133604. | + | 217483.i | 0.283905 | + | 0.462144i | ||||
\(687\) | 292699.i | 0.620166i | ||||||||
\(688\) | −203890. | + | 149515.i | −0.430744 | + | 0.315870i | ||||
\(689\) | −414876. | −0.873936 | ||||||||
\(690\) | −1481.85 | + | 910.333i | −0.00311248 | + | 0.00191206i | ||||
\(691\) | − | 163007.i | − | 0.341390i | −0.985324 | − | 0.170695i | \(-0.945399\pi\) | ||
0.985324 | − | 0.170695i | \(-0.0546012\pi\) | |||||||
\(692\) | −159556. | + | 314864.i | −0.333198 | + | 0.657523i | ||||
\(693\) | 122793. | 0.255687 | ||||||||
\(694\) | −177510. | − | 288953.i | −0.368556 | − | 0.599941i | ||||
\(695\) | − | 251369.i | − | 0.520405i | ||||||
\(696\) | 488367. | − | 40063.6i | 1.00816 | − | 0.0827050i | ||||
\(697\) | 627211. | 1.29106 | ||||||||
\(698\) | 584953. | − | 359349.i | 1.20063 | − | 0.737574i | ||||
\(699\) | 272846.i | 0.558422i | ||||||||
\(700\) | −109417. | − | 55446.5i | −0.223299 | − | 0.113156i | ||||
\(701\) | 270195. | 0.549847 | 0.274924 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(702\) | 53273.3 | + | 86719.0i | 0.108102 | + | 0.175971i | ||||
\(703\) | 272376.i | 0.551135i | ||||||||
\(704\) | 49500.2 | + | 299668.i | 0.0998760 | + | 0.604638i | ||||
\(705\) | −170983. | −0.344013 | ||||||||
\(706\) | −665087. | + | 408577.i | −1.33435 | + | 0.819717i | ||||
\(707\) | 182458.i | 0.365026i | ||||||||
\(708\) | −14682.1 | + | 28973.2i | −0.0292901 | + | 0.0578003i | ||||
\(709\) | 40040.3 | 0.0796534 | 0.0398267 | − | 0.999207i | \(-0.487319\pi\) | ||||
0.0398267 | + | 0.999207i | \(0.487319\pi\) | |||||||
\(710\) | −104467. | − | 170052.i | −0.207234 | − | 0.337338i | ||||
\(711\) | − | 190627.i | − | 0.377090i | ||||||
\(712\) | −64732.1 | − | 789071.i | −0.127691 | − | 1.55653i | ||||
\(713\) | 7790.99 | 0.0153255 | ||||||||
\(714\) | −560662. | + | 344426.i | −1.09978 | + | 0.675616i | ||||
\(715\) | 150355.i | 0.294107i | ||||||||
\(716\) | −61373.5 | − | 31100.8i | −0.119717 | − | 0.0606660i | ||||
\(717\) | 265744. | 0.516922 | ||||||||
\(718\) | 105355. | + | 171498.i | 0.204364 | + | 0.332667i | ||||
\(719\) | 388789.i | 0.752066i | 0.926606 | + | 0.376033i | \(0.122712\pi\) | ||||
−0.926606 | + | 0.376033i | \(0.877288\pi\) | |||||||
\(720\) | −45698.9 | − | 62318.4i | −0.0881537 | − | 0.120213i | ||||
\(721\) | 1.10173e6 | 2.11937 | ||||||||
\(722\) | 122824. | − | 75453.3i | 0.235618 | − | 0.144745i | ||||
\(723\) | 36.6925i | 7.01941e-5i | ||||||||
\(724\) | −233519. | + | 460820.i | −0.445497 | + | 0.879132i | ||||
\(725\) | −184184. | −0.350409 | ||||||||
\(726\) | −99464.7 | − | 161910.i | −0.188710 | − | 0.307185i | ||||
\(727\) | − | 569739.i | − | 1.07797i | −0.842315 | − | 0.538985i | \(-0.818808\pi\) | ||
0.842315 | − | 0.538985i | \(-0.181192\pi\) | |||||||
\(728\) | 709489. | − | 58203.5i | 1.33870 | − | 0.109821i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 128379. | − | 78866.2i | 0.240907 | − | 0.147994i | ||||
\(731\) | − | 509801.i | − | 0.954039i | ||||||
\(732\) | 304714. | + | 154413.i | 0.568682 | + | 0.288178i | ||||
\(733\) | 119853. | 0.223070 | 0.111535 | − | 0.993760i | \(-0.464423\pi\) | ||||
0.111535 | + | 0.993760i | \(0.464423\pi\) | |||||||
\(734\) | −106192. | − | 172860.i | −0.197105 | − | 0.320851i | ||||
\(735\) | 79042.5i | 0.146314i | ||||||||
\(736\) | −2893.62 | + | 7096.39i | −0.00534178 | + | 0.0131003i | ||||
\(737\) | 457296. | 0.841904 | ||||||||
\(738\) | 111817. | − | 68691.3i | 0.205302 | − | 0.126121i | ||||
\(739\) | 543414.i | 0.995044i | 0.867451 | + | 0.497522i | \(0.165757\pi\) | ||||
−0.867451 | + | 0.497522i | \(0.834243\pi\) | |||||||
\(740\) | 53998.4 | − | 106559.i | 0.0986092 | − | 0.194593i | ||||
\(741\) | 384363. | 0.700011 | ||||||||
\(742\) | −293760. | − | 478187.i | −0.533562 | − | 0.868540i | ||||
\(743\) | − | 33513.7i | − | 0.0607078i | −0.999539 | − | 0.0303539i | \(-0.990337\pi\) | ||
0.999539 | − | 0.0303539i | \(-0.00966343\pi\) | |||||||
\(744\) | 28305.1 | + | 345033.i | 0.0511351 | + | 0.623326i | ||||
\(745\) | −215154. | −0.387648 | ||||||||
\(746\) | 407524. | − | 250351.i | 0.732277 | − | 0.449853i | ||||
\(747\) | − | 134253.i | − | 0.240592i | ||||||
\(748\) | −546282. | − | 276827.i | −0.976368 | − | 0.494771i | ||||
\(749\) | 73627.4 | 0.131243 | ||||||||
\(750\) | 15204.6 | + | 24750.2i | 0.0270303 | + | 0.0440003i | ||||
\(751\) | − | 483614.i | − | 0.857471i | −0.903430 | − | 0.428735i | \(-0.858959\pi\) | ||
0.903430 | − | 0.428735i | \(-0.141041\pi\) | |||||||
\(752\) | −607594. | + | 445557.i | −1.07443 | + | 0.787893i | ||||
\(753\) | 314195. | 0.554127 | ||||||||
\(754\) | 910773. | − | 559506.i | 1.60202 | − | 0.984153i | ||||
\(755\) | 474121.i | 0.831755i | ||||||||
\(756\) | −62231.5 | + | 122806.i | −0.108885 | + | 0.214870i | ||||
\(757\) | −154021. | −0.268774 | −0.134387 | − | 0.990929i | \(-0.542906\pi\) | ||||
−0.134387 | + | 0.990929i | \(0.542906\pi\) | |||||||
\(758\) | −217877. | − | 354663.i | −0.379204 | − | 0.617274i | ||||
\(759\) | 2883.66i | 0.00500566i | ||||||||
\(760\) | −290871. | + | 23861.9i | −0.503586 | + | 0.0413121i | ||||
\(761\) | −242974. | −0.419557 | −0.209779 | − | 0.977749i | \(-0.567274\pi\) | ||||
−0.209779 | + | 0.977749i | \(0.567274\pi\) | |||||||
\(762\) | −309632. | + | 190213.i | −0.533256 | + | 0.327590i | ||||
\(763\) | − | 1.01203e6i | − | 1.73837i | ||||||
\(764\) | 330245. | + | 167350.i | 0.565782 | + | 0.286708i | ||||
\(765\) | 155819. | 0.266255 | ||||||||
\(766\) | −151678. | − | 246903.i | −0.258502 | − | 0.420794i | ||||
\(767\) | 70853.9i | 0.120441i | ||||||||
\(768\) | −324785. | − | 102366.i | −0.550647 | − | 0.173554i | ||||
\(769\) | −86574.7 | −0.146399 | −0.0731995 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731995 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(770\) | −173300. | + | 106462.i | −0.292292 | + | 0.179561i | ||||
\(771\) | 199196.i | 0.335099i | ||||||||
\(772\) | −468473. | + | 924471.i | −0.786049 | + | 1.55117i | ||||
\(773\) | 1.07093e6 | 1.79227 | 0.896133 | − | 0.443785i | \(-0.146365\pi\) | ||||
0.896133 | + | 0.443785i | \(0.146365\pi\) | |||||||
\(774\) | −55832.7 | − | 90885.3i | −0.0931980 | − | 0.151709i | ||||
\(775\) | − | 130127.i | − | 0.216652i | ||||||
\(776\) | 13167.2 | + | 160505.i | 0.0218660 | + | 0.266542i | ||||
\(777\) | −212821. | −0.352510 | ||||||||
\(778\) | 553879. | − | 340259.i | 0.915073 | − | 0.562148i | ||||
\(779\) | − | 495602.i | − | 0.816692i | ||||||
\(780\) | −150370. | − | 76199.7i | −0.247157 | − | 0.125246i | ||||
\(781\) | −330919. | −0.542525 | ||||||||
\(782\) | −8088.46 | − | 13166.5i | −0.0132267 | − | 0.0215307i | ||||
\(783\) | 206722.i | 0.337181i | ||||||||
\(784\) | 205973. | + | 280880.i | 0.335103 | + | 0.456972i | ||||
\(785\) | −156292. | −0.253628 | ||||||||
\(786\) | −189465. | + | 116392.i | −0.306678 | + | 0.188399i | ||||
\(787\) | − | 751269.i | − | 1.21296i | −0.795099 | − | 0.606479i | \(-0.792581\pi\) | ||
0.795099 | − | 0.606479i | \(-0.207419\pi\) | |||||||
\(788\) | 2295.12 | − | 4529.12i | 0.00369618 | − | 0.00729393i | ||||
\(789\) | 201881. | 0.324295 | ||||||||
\(790\) | 165273. | + | 269034.i | 0.264818 | + | 0.431075i | ||||
\(791\) | 370309.i | 0.591849i | ||||||||
\(792\) | −127707. | + | 10476.5i | −0.203593 | + | 0.0167019i | ||||
\(793\) | 745176. | 1.18498 | ||||||||
\(794\) | −181631. | + | 111580.i | −0.288104 | + | 0.176988i | ||||
\(795\) | 132898.i | 0.210273i | ||||||||
\(796\) | −257629. | − | 130553.i | −0.406601 | − | 0.206044i | ||||
\(797\) | −410930. | −0.646921 | −0.323461 | − | 0.946242i | \(-0.604846\pi\) | ||||
−0.323461 | + | 0.946242i | \(0.604846\pi\) | |||||||
\(798\) | 272155. | + | 443017.i | 0.427376 | + | 0.695689i | ||||
\(799\) | − | 1.51921e6i | − | 2.37972i | ||||||
\(800\) | 118525. | + | 48329.8i | 0.185196 | + | 0.0755153i | ||||
\(801\) | 334008. | 0.520585 | ||||||||
\(802\) | 115177. | − | 70755.9i | 0.179068 | − | 0.110005i | ||||
\(803\) | − | 249825.i | − | 0.387440i | ||||||
\(804\) | −231757. | + | 457342.i | −0.358526 | + | 0.707505i | ||||
\(805\) | −5131.88 | −0.00791927 | ||||||||
\(806\) | 395293. | + | 643464.i | 0.608484 | + | 0.990500i | ||||
\(807\) | − | 97295.3i | − | 0.149398i | ||||||
\(808\) | −15567.0 | − | 189758.i | −0.0238442 | − | 0.290655i | ||||
\(809\) | −81222.3 | −0.124102 | −0.0620510 | − | 0.998073i | \(-0.519764\pi\) | ||||
−0.0620510 | + | 0.998073i | \(0.519764\pi\) | |||||||
\(810\) | 27778.8 | − | 17065.1i | 0.0423393 | − | 0.0260099i | ||||
\(811\) | 665948.i | 1.01251i | 0.862384 | + | 0.506254i | \(0.168970\pi\) | ||||
−0.862384 | + | 0.506254i | \(0.831030\pi\) | |||||||
\(812\) | 1.28978e6 | + | 653590.i | 1.95615 | + | 0.991274i | ||||
\(813\) | −133227. | −0.201563 | ||||||||
\(814\) | −103681. | − | 168774.i | −0.156477 | − | 0.254716i | ||||
\(815\) | − | 347643.i | − | 0.523382i | ||||||
\(816\) | 553709. | − | 406042.i | 0.831575 | − | 0.609805i | ||||
\(817\) | −402829. | −0.603499 | ||||||||
\(818\) | −657716. | + | 404049.i | −0.982951 | + | 0.603847i | ||||
\(819\) | 300321.i | 0.447732i | ||||||||
\(820\) | −98252.9 | + | 193889.i | −0.146123 | + | 0.288354i | ||||
\(821\) | 175974. | 0.261074 | 0.130537 | − | 0.991443i | \(-0.458330\pi\) | ||||
0.130537 | + | 0.991443i | \(0.458330\pi\) | |||||||
\(822\) | −340086. | − | 553597.i | −0.503321 | − | 0.819314i | ||||
\(823\) | 825656.i | 1.21899i | 0.792790 | + | 0.609494i | \(0.208627\pi\) | ||||
−0.792790 | + | 0.609494i | \(0.791373\pi\) | |||||||
\(824\) | −1.14582e6 | + | 93998.0i | −1.68757 | + | 0.138441i | ||||
\(825\) | 48163.5 | 0.0707636 | ||||||||
\(826\) | −81666.4 | + | 50169.4i | −0.119697 | + | 0.0735324i | ||||
\(827\) | 184129.i | 0.269222i | 0.990899 | + | 0.134611i | \(0.0429785\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(828\) | −2883.96 | − | 1461.44i | −0.00420657 | − | 0.00213167i | ||||
\(829\) | −713518. | −1.03824 | −0.519118 | − | 0.854703i | \(-0.673739\pi\) | ||||
−0.519118 | + | 0.854703i | \(0.673739\pi\) | |||||||
\(830\) | 116397. | + | 189472.i | 0.168960 | + | 0.275036i | ||||
\(831\) | − | 362149.i | − | 0.524428i | ||||||
\(832\) | −732911. | + | 121065.i | −1.05878 | + | 0.174892i | ||||
\(833\) | −702306. | −1.01213 | ||||||||
\(834\) | 398171. | − | 244605.i | 0.572450 | − | 0.351668i | ||||
\(835\) | − | 337701.i | − | 0.484351i | ||||||
\(836\) | −218740. | + | 431655.i | −0.312979 | + | 0.617624i | ||||
\(837\) | −146050. | −0.208473 | ||||||||
\(838\) | −434939. | − | 708000.i | −0.619356 | − | 1.00820i | ||||
\(839\) | − | 1.30678e6i | − | 1.85643i | −0.372047 | − | 0.928214i | \(-0.621344\pi\) | ||
0.372047 | − | 0.928214i | \(-0.378656\pi\) | |||||||
\(840\) | −18644.4 | − | 227272.i | −0.0264235 | − | 0.322097i | ||||
\(841\) | 1.46383e6 | 2.06966 | ||||||||
\(842\) | 463376. | − | 284662.i | 0.653596 | − | 0.401518i | ||||
\(843\) | − | 363211.i | − | 0.511098i | ||||||
\(844\) | 896985. | + | 454544.i | 1.25922 | + | 0.638104i | ||||
\(845\) | −48408.4 | −0.0677965 | ||||||||
\(846\) | −166382. | − | 270839.i | −0.232469 | − | 0.378417i | ||||
\(847\) | − | 560719.i | − | 0.781589i | ||||||
\(848\) | 346312. | + | 472257.i | 0.481589 | + | 0.656730i | ||||
\(849\) | 559233. | 0.775849 | ||||||||
\(850\) | −219910. | + | 135095.i | −0.304373 | + | 0.186983i | ||||
\(851\) | − | 4997.85i | − | 0.00690120i | ||||||
\(852\) | 167709. | − | 330952.i | 0.231035 | − | 0.455918i | ||||
\(853\) | 590922. | 0.812143 | 0.406071 | − | 0.913841i | \(-0.366898\pi\) | ||||
0.406071 | + | 0.913841i | \(0.366898\pi\) | |||||||
\(854\) | 527635. | + | 858891.i | 0.723465 | + | 1.17767i | ||||
\(855\) | − | 123123.i | − | 0.168426i | ||||||
\(856\) | −76573.4 | + | 6281.76i | −0.104503 | + | 0.00857302i | ||||
\(857\) | −756073. | −1.02944 | −0.514721 | − | 0.857358i | \(-0.672105\pi\) | ||||
−0.514721 | + | 0.857358i | \(0.672105\pi\) | |||||||
\(858\) | −238164. | + | 146309.i | −0.323521 | + | 0.198745i | ||||
\(859\) | 1.02880e6i | 1.39426i | 0.716945 | + | 0.697130i | \(0.245540\pi\) | ||||
−0.716945 | + | 0.697130i | \(0.754460\pi\) | |||||||
\(860\) | 157595. | + | 79860.6i | 0.213081 | + | 0.107978i | ||||
\(861\) | 387238. | 0.522362 | ||||||||
\(862\) | −318238. | − | 518033.i | −0.428290 | − | 0.697176i | ||||
\(863\) | − | 520287.i | − | 0.698589i | −0.937013 | − | 0.349294i | \(-0.886421\pi\) | ||
0.937013 | − | 0.349294i | \(-0.113579\pi\) | |||||||
\(864\) | 54243.9 | − | 133029.i | 0.0726647 | − | 0.178205i | ||||
\(865\) | 246655. | 0.329654 | ||||||||
\(866\) | 124255. | − | 76332.6i | 0.165683 | − | 0.101783i | ||||
\(867\) | 950493.i | 1.26448i | ||||||||
\(868\) | −461764. | + | 911232.i | −0.612887 | + | 1.20946i | ||||
\(869\) | 523536. | 0.693277 | ||||||||
\(870\) | −179228. | − | 291749.i | −0.236792 | − | 0.385453i | ||||
\(871\) | 1.11843e6i | 1.47425i | ||||||||
\(872\) | 86344.3 | + | 1.05252e6i | 0.113554 | + | 1.38419i | ||||
\(873\) | −67940.7 | −0.0891459 | ||||||||
\(874\) | −10403.8 | + | 6391.25i | −0.0136197 | + | 0.00836686i | ||||
\(875\) | 85713.7i | 0.111953i | ||||||||
\(876\) | 249850. | + | 126611.i | 0.325590 | + | 0.164992i | ||||
\(877\) | −132059. | −0.171699 | −0.0858496 | − | 0.996308i | \(-0.527360\pi\) | ||||
−0.0858496 | + | 0.996308i | \(0.527360\pi\) | |||||||
\(878\) | −247199. | − | 402394.i | −0.320670 | − | 0.521990i | ||||
\(879\) | 113167.i | 0.146468i | ||||||||
\(880\) | 171151. | − | 125507.i | 0.221011 | − | 0.162070i | ||||
\(881\) | −485203. | −0.625132 | −0.312566 | − | 0.949896i | \(-0.601189\pi\) | ||||
−0.312566 | + | 0.949896i | \(0.601189\pi\) | |||||||
\(882\) | −125204. | + | 76915.6i | −0.160947 | + | 0.0988729i | ||||
\(883\) | 454909.i | 0.583449i | 0.956502 | + | 0.291725i | \(0.0942291\pi\) | ||||
−0.956502 | + | 0.291725i | \(0.905771\pi\) | |||||||
\(884\) | 677047. | − | 1.33607e6i | 0.866392 | − | 1.70971i | ||||
\(885\) | 22696.7 | 0.0289786 | ||||||||
\(886\) | 237835. | + | 387151.i | 0.302976 | + | 0.493189i | ||||
\(887\) | 372656.i | 0.473654i | 0.971552 | + | 0.236827i | \(0.0761075\pi\) | ||||
−0.971552 | + | 0.236827i | \(0.923893\pi\) | |||||||
\(888\) | 221336. | − | 18157.5i | 0.280689 | − | 0.0230266i | ||||
\(889\) | −1.07230e6 | −1.35679 | ||||||||
\(890\) | −471389. | + | 289584.i | −0.595113 | + | 0.365590i | ||||
\(891\) | − | 54057.2i | − | 0.0680923i | ||||||
\(892\) | −866694. | − | 439194.i | −1.08927 | − | 0.551985i | ||||
\(893\) | −1.20043e6 | −1.50534 | ||||||||
\(894\) | −209365. | − | 340807.i | −0.261956 | − | 0.426416i | ||||
\(895\) | 48078.1i | 0.0600207i | ||||||||
\(896\) | −658490. | − | 759033.i | −0.820226 | − | 0.945464i | ||||
\(897\) | −7052.71 | −0.00876538 | ||||||||
\(898\) | 5948.02 | − | 3653.99i | 0.00737598 | − | 0.00453122i | ||||
\(899\) | 1.53390e6i | 1.89792i | ||||||||
\(900\) | −24409.2 | + | 48168.4i | −0.0301348 | + | 0.0594671i | ||||
\(901\) | −1.18082e6 | −1.45457 | ||||||||
\(902\) | 188653. | + | 307092.i | 0.231873 | + | 0.377447i | ||||
\(903\) | − | 314750.i | − | 0.386002i | ||||||
\(904\) | −31594.1 | − | 385126.i | −0.0386607 | − | 0.471266i | ||||
\(905\) | 360992. | 0.440759 | ||||||||
\(906\) | −751014. | + | 461363.i | −0.914938 | + | 0.562065i | ||||
\(907\) | − | 354962.i | − | 0.431487i | −0.976450 | − | 0.215743i | \(-0.930783\pi\) | ||
0.976450 | − | 0.215743i | \(-0.0692175\pi\) | |||||||
\(908\) | 1.40765e6 | + | 713320.i | 1.70735 | + | 0.865192i | ||||
\(909\) | 80323.3 | 0.0972106 | ||||||||
\(910\) | −260378. | − | 423847.i | −0.314428 | − | 0.511830i | ||||
\(911\) | − | 108935.i | − | 0.131260i | −0.997844 | − | 0.0656298i | \(-0.979094\pi\) | ||
0.997844 | − | 0.0656298i | \(-0.0209056\pi\) | |||||||
\(912\) | −320842. | − | 437524.i | −0.385746 | − | 0.526032i | ||||
\(913\) | 368711. | 0.442328 | ||||||||
\(914\) | 254276. | − | 156207.i | 0.304378 | − | 0.186986i | ||||
\(915\) | − | 238703.i | − | 0.285113i | ||||||
\(916\) | 407398. | − | 803947.i | 0.485543 | − | 0.958157i | ||||
\(917\) | −656145. | −0.780299 | ||||||||
\(918\) | 151626. | + | 246820.i | 0.179924 | + | 0.292883i | ||||
\(919\) | 306482.i | 0.362889i | 0.983401 | + | 0.181444i | \(0.0580772\pi\) | ||||
−0.983401 | + | 0.181444i | \(0.941923\pi\) | |||||||
\(920\) | 5337.22 | − | 437.843i | 0.00630579 | − | 0.000517301i | ||||
\(921\) | −671383. | −0.791500 | ||||||||
\(922\) | −58982.8 | + | 36234.3i | −0.0693846 | + | 0.0426244i | ||||
\(923\) | − | 809343.i | − | 0.950012i | ||||||
\(924\) | −337273. | − | 170912.i | −0.395037 | − | 0.200184i | ||||
\(925\) | −83475.1 | −0.0975603 | ||||||||
\(926\) | −260964. | − | 424800.i | −0.304339 | − | 0.495408i | ||||
\(927\) | − | 485015.i | − | 0.564412i | ||||||
\(928\) | −1.39715e6 | − | 569700.i | −1.62236 | − | 0.661532i | ||||
\(929\) | 230175. | 0.266702 | 0.133351 | − | 0.991069i | \(-0.457426\pi\) | ||||
0.133351 | + | 0.991069i | \(0.457426\pi\) | |||||||
\(930\) | 206122. | − | 126625.i | 0.238319 | − | 0.146404i | ||||
\(931\) | 554940.i | 0.640246i | ||||||||
\(932\) | 379764. | − | 749416.i | 0.437202 | − | 0.862763i | ||||
\(933\) | −207650. | −0.238544 | ||||||||
\(934\) | 436634. | + | 710760.i | 0.500523 | + | 0.814759i | ||||
\(935\) | 427941.i | 0.489509i | ||||||||
\(936\) | −25622.9 | − | 312338.i | −0.0292466 | − | 0.356511i | ||||
\(937\) | 1.06117e6 | 1.20867 | 0.604333 | − | 0.796732i | \(-0.293440\pi\) | ||||
0.604333 | + | 0.796732i | \(0.293440\pi\) | |||||||
\(938\) | −1.28910e6 | + | 791923.i | −1.46515 | + | 0.900073i | ||||
\(939\) | 515765.i | 0.584953i | ||||||||
\(940\) | 469634. | + | 237985.i | 0.531501 | + | 0.269336i | ||||
\(941\) | −1.17032e6 | −1.32168 | −0.660838 | − | 0.750529i | \(-0.729799\pi\) | ||||
−0.660838 | + | 0.750529i | \(0.729799\pi\) | |||||||
\(942\) | −152086. | − | 247568.i | −0.171391 | − | 0.278993i | ||||
\(943\) | 9093.85i | 0.0102264i | ||||||||
\(944\) | 80653.7 | − | 59144.4i | 0.0905066 | − | 0.0663696i | ||||
\(945\) | 96202.4 | 0.107726 | ||||||||
\(946\) | 249606. | − | 153338.i | 0.278916 | − | 0.171344i | ||||
\(947\) | 605186.i | 0.674822i | 0.941357 | + | 0.337411i | \(0.109551\pi\) | ||||
−0.941357 | + | 0.337411i | \(0.890449\pi\) | |||||||
\(948\) | −265327. | + | 523589.i | −0.295233 | + | 0.582604i | ||||
\(949\) | 611007. | 0.678444 | ||||||||
\(950\) | 106748. | + | 173766.i | 0.118280 | + | 0.192538i | ||||
\(951\) | 479866.i | 0.530590i | ||||||||
\(952\) | 2.01935e6 | − | 165659.i | 2.22811 | − | 0.182785i | ||||
\(953\) | −1.26323e6 | −1.39090 | −0.695452 | − | 0.718572i | \(-0.744796\pi\) | ||||
−0.695452 | + | 0.718572i | \(0.744796\pi\) | |||||||
\(954\) | −210512. | + | 129322.i | −0.231302 | + | 0.142094i | ||||
\(955\) | − | 258704.i | − | 0.283658i | ||||||
\(956\) | −729911. | − | 369880.i | −0.798646 | − | 0.404711i | ||||
\(957\) | −567740. | −0.619905 | ||||||||
\(958\) | 836020. | + | 1.36089e6i | 0.910931 | + | 1.48283i | ||||
\(959\) | − | 1.91719e6i | − | 2.08463i | ||||||
\(960\) | 38780.9 | + | 234775.i | 0.0420799 | + | 0.254747i | ||||
\(961\) | −160185. | −0.173451 | ||||||||
\(962\) | 412777. | − | 253577.i | 0.446031 | − | 0.274006i | ||||
\(963\) | − | 32412.9i | − | 0.0349515i | ||||||
\(964\) | 51.0710 | − | 100.782i | 5.49567e−5 | − | 0.000108450i | ||||
\(965\) | 724202. | 0.777688 | ||||||||
\(966\) | −4993.79 | − | 8128.97i | −0.00535151 | − | 0.00871126i | ||||
\(967\) | 1.65602e6i | 1.77098i | 0.464657 | + | 0.885491i | \(0.346177\pi\) | ||||
−0.464657 | + | 0.885491i | \(0.653823\pi\) | |||||||
\(968\) | 47839.6 | + | 583155.i | 0.0510548 | + | 0.622348i | ||||
\(969\) | 1.09397e6 | 1.16509 | ||||||||
\(970\) | 95885.4 | − | 58904.4i | 0.101908 | − | 0.0626043i | ||||
\(971\) | 538842.i | 0.571508i | 0.958303 | + | 0.285754i | \(0.0922441\pi\) | ||||
−0.958303 | + | 0.285754i | \(0.907756\pi\) | |||||||
\(972\) | 54062.7 | + | 27396.1i | 0.0572223 | + | 0.0289972i | ||||
\(973\) | 1.37893e6 | 1.45652 | ||||||||
\(974\) | −905347. | − | 1.47374e6i | −0.954327 | − | 1.55347i | ||||
\(975\) | 117796.i | 0.123914i | ||||||||
\(976\) | −622026. | − | 848241.i | −0.652993 | − | 0.890470i | ||||
\(977\) | 962571. | 1.00843 | 0.504213 | − | 0.863579i | \(-0.331783\pi\) | ||||
0.504213 | + | 0.863579i | \(0.331783\pi\) | |||||||
\(978\) | 550671. | − | 338289.i | 0.575724 | − | 0.353679i | ||||
\(979\) | 917315.i | 0.957091i | ||||||||
\(980\) | 110017. | − | 217104.i | 0.114553 | − | 0.226055i | ||||
\(981\) | −445523. | −0.462948 | ||||||||
\(982\) | 558828. | + | 909669.i | 0.579503 | + | 0.943323i | ||||
\(983\) | 386329.i | 0.399807i | 0.979816 | + | 0.199903i | \(0.0640628\pi\) | ||||
−0.979816 | + | 0.199903i | \(0.935937\pi\) | |||||||
\(984\) | −402732. | + | 33038.5i | −0.415936 | + | 0.0341216i | ||||
\(985\) | −3547.98 | −0.00365686 | ||||||||
\(986\) | 2.59224e6 | − | 1.59247e6i | 2.66638 | − | 1.63801i | ||||
\(987\) | − | 937958.i | − | 0.962828i | ||||||
\(988\) | −1.05572e6 | − | 534981.i | −1.08152 | − | 0.548055i | ||||
\(989\) | 7391.54 | 0.00755688 | ||||||||
\(990\) | 46867.5 | + | 76291.5i | 0.0478191 | + | 0.0778406i | ||||
\(991\) | 18475.3i | 0.0188124i | 0.999956 | + | 0.00940620i | \(0.00299413\pi\) | ||||
−0.999956 | + | 0.00940620i | \(0.997006\pi\) | |||||||
\(992\) | 402495. | − | 987090.i | 0.409014 | − | 1.00307i | ||||
\(993\) | −194211. | −0.196959 | ||||||||
\(994\) | 932851. | − | 573070.i | 0.944147 | − | 0.580009i | ||||
\(995\) | 201819.i | 0.203852i | ||||||||
\(996\) | −186862. | + | 368748.i | −0.188366 | + | 0.371716i | ||||
\(997\) | 177630. | 0.178701 | 0.0893503 | − | 0.996000i | \(-0.471521\pi\) | ||||
0.0893503 | + | 0.996000i | \(0.471521\pi\) | |||||||
\(998\) | −44570.3 | − | 72552.1i | −0.0447491 | − | 0.0728432i | ||||
\(999\) | 93689.8i | 0.0938775i |
(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 | 60.5.c.a.31.4 | yes | 16 | |
3.2 | odd | 2 | 180.5.c.c.91.13 | 16 | |||
4.3 | odd | 2 | inner | 60.5.c.a.31.3 | ✓ | 16 | |
5.2 | odd | 4 | 300.5.f.b.199.11 | 32 | |||
5.3 | odd | 4 | 300.5.f.b.199.22 | 32 | |||
5.4 | even | 2 | 300.5.c.d.151.13 | 16 | |||
8.3 | odd | 2 | 960.5.e.f.511.16 | 16 | |||
8.5 | even | 2 | 960.5.e.f.511.5 | 16 | |||
12.11 | even | 2 | 180.5.c.c.91.14 | 16 | |||
20.3 | even | 4 | 300.5.f.b.199.12 | 32 | |||
20.7 | even | 4 | 300.5.f.b.199.21 | 32 | |||
20.19 | odd | 2 | 300.5.c.d.151.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.c.a.31.3 | ✓ | 16 | 4.3 | odd | 2 | inner | |
60.5.c.a.31.4 | yes | 16 | 1.1 | even | 1 | trivial | |
180.5.c.c.91.13 | 16 | 3.2 | odd | 2 | |||
180.5.c.c.91.14 | 16 | 12.11 | even | 2 | |||
300.5.c.d.151.13 | 16 | 5.4 | even | 2 | |||
300.5.c.d.151.14 | 16 | 20.19 | odd | 2 | |||
300.5.f.b.199.11 | 32 | 5.2 | odd | 4 | |||
300.5.f.b.199.12 | 32 | 20.3 | even | 4 | |||
300.5.f.b.199.21 | 32 | 20.7 | even | 4 | |||
300.5.f.b.199.22 | 32 | 5.3 | odd | 4 | |||
960.5.e.f.511.5 | 16 | 8.5 | even | 2 | |||
960.5.e.f.511.16 | 16 | 8.3 | odd | 2 |