Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.11 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.5.b.a.39.12 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32469 | − | 3.25512i | −0.581172 | − | 0.813781i | ||||
\(3\) | − | 7.75287i | − | 0.861430i | −0.902488 | − | 0.430715i | \(-0.858261\pi\) | ||
0.902488 | − | 0.430715i | \(-0.141739\pi\) | |||||||
\(4\) | −5.19165 | + | 15.1343i | −0.324478 | + | 0.945893i | ||||
\(5\) | 27.0702 | 1.08281 | 0.541403 | − | 0.840763i | \(-0.317893\pi\) | ||||
0.541403 | + | 0.840763i | \(0.317893\pi\) | |||||||
\(6\) | −25.2365 | + | 18.0230i | −0.701015 | + | 0.500639i | ||||
\(7\) | 95.4821i | 1.94861i | 0.225223 | + | 0.974307i | \(0.427689\pi\) | ||||
−0.225223 | + | 0.974307i | \(0.572311\pi\) | |||||||
\(8\) | 61.3329 | − | 18.2830i | 0.958327 | − | 0.285673i | ||||
\(9\) | 20.8930 | 0.257938 | ||||||||
\(10\) | −62.9297 | − | 88.1167i | −0.629297 | − | 0.881167i | ||||
\(11\) | 138.578i | 1.14528i | 0.819809 | + | 0.572638i | \(0.194080\pi\) | ||||
−0.819809 | + | 0.572638i | \(0.805920\pi\) | |||||||
\(12\) | 117.334 | + | 40.2502i | 0.814821 | + | 0.279515i | ||||
\(13\) | −68.1130 | −0.403035 | −0.201518 | − | 0.979485i | \(-0.564587\pi\) | ||||
−0.201518 | + | 0.979485i | \(0.564587\pi\) | |||||||
\(14\) | 310.806 | − | 221.966i | 1.58574 | − | 1.13248i | ||||
\(15\) | − | 209.872i | − | 0.932762i | ||||||
\(16\) | −202.094 | − | 157.144i | −0.789428 | − | 0.613843i | ||||
\(17\) | 261.853 | 0.906067 | 0.453033 | − | 0.891494i | \(-0.350342\pi\) | ||||
0.453033 | + | 0.891494i | \(0.350342\pi\) | |||||||
\(18\) | −48.5697 | − | 68.0093i | −0.149906 | − | 0.209905i | ||||
\(19\) | − | 82.8191i | − | 0.229416i | ||||||
\(20\) | −140.539 | + | 409.688i | −0.351347 | + | 1.02422i | ||||
\(21\) | 740.260 | 1.67860 | ||||||||
\(22\) | 451.090 | − | 322.151i | 0.932003 | − | 0.665602i | ||||
\(23\) | − | 46.0152i | − | 0.0869852i | −0.999054 | − | 0.0434926i | \(-0.986152\pi\) | ||
0.999054 | − | 0.0434926i | \(-0.0138485\pi\) | |||||||
\(24\) | −141.746 | − | 475.506i | −0.246087 | − | 0.825532i | ||||
\(25\) | 107.794 | 0.172471 | ||||||||
\(26\) | 158.341 | + | 221.716i | 0.234233 | + | 0.327982i | ||||
\(27\) | − | 789.963i | − | 1.08363i | ||||||
\(28\) | −1445.05 | − | 495.710i | −1.84318 | − | 0.632283i | ||||
\(29\) | 508.504 | 0.604642 | 0.302321 | − | 0.953206i | \(-0.402239\pi\) | ||||
0.302321 | + | 0.953206i | \(0.402239\pi\) | |||||||
\(30\) | −683.158 | + | 487.886i | −0.759064 | + | 0.542095i | ||||
\(31\) | 995.645i | 1.03605i | 0.855365 | + | 0.518026i | \(0.173333\pi\) | ||||
−0.855365 | + | 0.518026i | \(0.826667\pi\) | |||||||
\(32\) | −41.7183 | + | 1023.15i | −0.0407405 | + | 0.999170i | ||||
\(33\) | 1074.38 | 0.986575 | ||||||||
\(34\) | −608.727 | − | 852.365i | −0.526581 | − | 0.737340i | ||||
\(35\) | 2584.72i | 2.10997i | ||||||||
\(36\) | −108.469 | + | 316.201i | −0.0836953 | + | 0.243982i | ||||
\(37\) | 1035.44 | 0.756346 | 0.378173 | − | 0.925735i | \(-0.376552\pi\) | ||||
0.378173 | + | 0.925735i | \(0.376552\pi\) | |||||||
\(38\) | −269.586 | + | 192.529i | −0.186694 | + | 0.133330i | ||||
\(39\) | 528.071i | 0.347187i | ||||||||
\(40\) | 1660.29 | − | 494.925i | 1.03768 | − | 0.309328i | ||||
\(41\) | −1768.23 | −1.05189 | −0.525947 | − | 0.850517i | \(-0.676289\pi\) | ||||
−0.525947 | + | 0.850517i | \(0.676289\pi\) | |||||||
\(42\) | −1720.87 | − | 2409.64i | −0.975552 | − | 1.36601i | ||||
\(43\) | − | 249.767i | − | 0.135082i | −0.997716 | − | 0.0675411i | \(-0.978485\pi\) | ||
0.997716 | − | 0.0675411i | \(-0.0215154\pi\) | |||||||
\(44\) | −2097.28 | − | 719.450i | −1.08331 | − | 0.371617i | ||||
\(45\) | 565.577 | 0.279297 | ||||||||
\(46\) | −149.785 | + | 106.971i | −0.0707869 | + | 0.0505534i | ||||
\(47\) | 345.338i | 0.156332i | 0.996940 | + | 0.0781661i | \(0.0249065\pi\) | ||||
−0.996940 | + | 0.0781661i | \(0.975094\pi\) | |||||||
\(48\) | −1218.32 | + | 1566.81i | −0.528783 | + | 0.680037i | ||||
\(49\) | −6715.83 | −2.79710 | ||||||||
\(50\) | −250.588 | − | 350.883i | −0.100235 | − | 0.140353i | ||||
\(51\) | − | 2030.11i | − | 0.780513i | ||||||
\(52\) | 353.619 | − | 1030.84i | 0.130776 | − | 0.381228i | ||||
\(53\) | 2136.43 | 0.760567 | 0.380284 | − | 0.924870i | \(-0.375826\pi\) | ||||
0.380284 | + | 0.924870i | \(0.375826\pi\) | |||||||
\(54\) | −2571.43 | + | 1836.42i | −0.881834 | + | 0.629773i | ||||
\(55\) | 3751.34i | 1.24011i | ||||||||
\(56\) | 1745.70 | + | 5856.20i | 0.556666 | + | 1.86741i | ||||
\(57\) | −642.086 | −0.197626 | ||||||||
\(58\) | −1182.11 | − | 1655.24i | −0.351401 | − | 0.492046i | ||||
\(59\) | − | 5022.76i | − | 1.44291i | −0.692462 | − | 0.721454i | \(-0.743474\pi\) | ||
0.692462 | − | 0.721454i | \(-0.256526\pi\) | |||||||
\(60\) | 3176.26 | + | 1089.58i | 0.882294 | + | 0.302661i | ||||
\(61\) | 6478.12 | 1.74096 | 0.870481 | − | 0.492201i | \(-0.163808\pi\) | ||||
0.870481 | + | 0.492201i | \(0.163808\pi\) | |||||||
\(62\) | 3240.95 | − | 2314.57i | 0.843119 | − | 0.602124i | ||||
\(63\) | 1994.91i | 0.502622i | ||||||||
\(64\) | 3427.46 | − | 2242.71i | 0.836782 | − | 0.547536i | ||||
\(65\) | −1843.83 | −0.436409 | ||||||||
\(66\) | −2497.60 | − | 3497.24i | −0.573370 | − | 0.802856i | ||||
\(67\) | 3188.74i | 0.710346i | 0.934801 | + | 0.355173i | \(0.115578\pi\) | ||||
−0.934801 | + | 0.355173i | \(0.884422\pi\) | |||||||
\(68\) | −1359.45 | + | 3962.96i | −0.293999 | + | 0.857042i | ||||
\(69\) | −356.750 | −0.0749317 | ||||||||
\(70\) | 8413.57 | − | 6008.66i | 1.71706 | − | 1.22626i | ||||
\(71\) | 824.209i | 0.163501i | 0.996653 | + | 0.0817505i | \(0.0260511\pi\) | ||||
−0.996653 | + | 0.0817505i | \(0.973949\pi\) | |||||||
\(72\) | 1281.43 | − | 381.988i | 0.247189 | − | 0.0736859i | ||||
\(73\) | 6551.48 | 1.22940 | 0.614701 | − | 0.788760i | \(-0.289277\pi\) | ||||
0.614701 | + | 0.788760i | \(0.289277\pi\) | |||||||
\(74\) | −2407.07 | − | 3370.48i | −0.439567 | − | 0.615500i | ||||
\(75\) | − | 835.715i | − | 0.148571i | ||||||
\(76\) | 1253.41 | + | 429.968i | 0.217003 | + | 0.0744404i | ||||
\(77\) | −13231.8 | −2.23170 | ||||||||
\(78\) | 1718.94 | − | 1227.60i | 0.282534 | − | 0.201775i | ||||
\(79\) | − | 11180.3i | − | 1.79142i | −0.444635 | − | 0.895712i | \(-0.646667\pi\) | ||
0.444635 | − | 0.895712i | \(-0.353333\pi\) | |||||||
\(80\) | −5470.71 | − | 4253.91i | −0.854798 | − | 0.664674i | ||||
\(81\) | −4432.15 | −0.675530 | ||||||||
\(82\) | 4110.59 | + | 5755.82i | 0.611332 | + | 0.856012i | ||||
\(83\) | − | 1997.06i | − | 0.289891i | −0.989440 | − | 0.144945i | \(-0.953699\pi\) | ||
0.989440 | − | 0.144945i | \(-0.0463007\pi\) | |||||||
\(84\) | −3843.17 | + | 11203.3i | −0.544667 | + | 1.58777i | ||||
\(85\) | 7088.41 | 0.981095 | ||||||||
\(86\) | −813.023 | + | 580.631i | −0.109927 | + | 0.0785060i | ||||
\(87\) | − | 3942.36i | − | 0.520857i | ||||||
\(88\) | 2533.63 | + | 8499.42i | 0.327174 | + | 1.09755i | ||||
\(89\) | 8875.25 | 1.12047 | 0.560235 | − | 0.828333i | \(-0.310711\pi\) | ||||
0.560235 | + | 0.828333i | \(0.310711\pi\) | |||||||
\(90\) | −1314.79 | − | 1841.02i | −0.162320 | − | 0.227287i | ||||
\(91\) | − | 6503.57i | − | 0.785360i | ||||||
\(92\) | 696.407 | + | 238.895i | 0.0822787 | + | 0.0282248i | ||||
\(93\) | 7719.11 | 0.892486 | ||||||||
\(94\) | 1124.12 | − | 802.803i | 0.127220 | − | 0.0908559i | ||||
\(95\) | − | 2241.93i | − | 0.248413i | ||||||
\(96\) | 7932.35 | + | 323.436i | 0.860715 | + | 0.0350951i | ||||
\(97\) | −14573.4 | −1.54888 | −0.774440 | − | 0.632647i | \(-0.781968\pi\) | ||||
−0.774440 | + | 0.632647i | \(0.781968\pi\) | |||||||
\(98\) | 15612.2 | + | 21860.9i | 1.62560 | + | 2.27622i | ||||
\(99\) | 2895.32i | 0.295410i | ||||||||
\(100\) | −559.630 | + | 1631.39i | −0.0559630 | + | 0.163139i | ||||
\(101\) | −18606.9 | −1.82403 | −0.912015 | − | 0.410157i | \(-0.865474\pi\) | ||||
−0.912015 | + | 0.410157i | \(0.865474\pi\) | |||||||
\(102\) | −6608.27 | + | 4719.38i | −0.635167 | + | 0.453612i | ||||
\(103\) | − | 11364.5i | − | 1.07121i | −0.844467 | − | 0.535607i | \(-0.820083\pi\) | ||
0.844467 | − | 0.535607i | \(-0.179917\pi\) | |||||||
\(104\) | −4177.57 | + | 1245.31i | −0.386240 | + | 0.115136i | ||||
\(105\) | 20039.0 | 1.81759 | ||||||||
\(106\) | −4966.54 | − | 6954.35i | −0.442020 | − | 0.618935i | ||||
\(107\) | 19962.5i | 1.74360i | 0.489863 | + | 0.871799i | \(0.337047\pi\) | ||||
−0.489863 | + | 0.871799i | \(0.662953\pi\) | |||||||
\(108\) | 11955.5 | + | 4101.21i | 1.02499 | + | 0.351613i | ||||
\(109\) | −6277.28 | −0.528346 | −0.264173 | − | 0.964475i | \(-0.585099\pi\) | ||||
−0.264173 | + | 0.964475i | \(0.585099\pi\) | |||||||
\(110\) | 12211.1 | − | 8720.69i | 1.00918 | − | 0.720719i | ||||
\(111\) | − | 8027.62i | − | 0.651539i | ||||||
\(112\) | 15004.4 | − | 19296.3i | 1.19614 | − | 1.53829i | ||||
\(113\) | −19344.5 | −1.51495 | −0.757477 | − | 0.652861i | \(-0.773568\pi\) | ||||
−0.757477 | + | 0.652861i | \(0.773568\pi\) | |||||||
\(114\) | 1492.65 | + | 2090.07i | 0.114854 | + | 0.160824i | ||||
\(115\) | − | 1245.64i | − | 0.0941882i | ||||||
\(116\) | −2639.97 | + | 7695.84i | −0.196193 | + | 0.571927i | ||||
\(117\) | −1423.08 | −0.103958 | ||||||||
\(118\) | −16349.7 | + | 11676.4i | −1.17421 | + | 0.838578i | ||||
\(119\) | 25002.3i | 1.76557i | ||||||||
\(120\) | −3837.09 | − | 12872.0i | −0.266465 | − | 0.893892i | ||||
\(121\) | −4562.96 | −0.311656 | ||||||||
\(122\) | −15059.6 | − | 21087.1i | −1.01180 | − | 1.41676i | ||||
\(123\) | 13708.9i | 0.906134i | ||||||||
\(124\) | −15068.4 | − | 5169.04i | −0.979994 | − | 0.336176i | ||||
\(125\) | −14000.8 | −0.896054 | ||||||||
\(126\) | 6493.67 | − | 4637.54i | 0.409024 | − | 0.292110i | ||||
\(127\) | 715.835i | 0.0443819i | 0.999754 | + | 0.0221909i | \(0.00706418\pi\) | ||||
−0.999754 | + | 0.0221909i | \(0.992936\pi\) | |||||||
\(128\) | −15268.1 | − | 5943.21i | −0.931888 | − | 0.362745i | ||||
\(129\) | −1936.41 | −0.116364 | ||||||||
\(130\) | 4286.33 | + | 6001.89i | 0.253629 | + | 0.355142i | ||||
\(131\) | − | 4998.11i | − | 0.291248i | −0.989340 | − | 0.145624i | \(-0.953481\pi\) | ||
0.989340 | − | 0.145624i | \(-0.0465190\pi\) | |||||||
\(132\) | −5577.81 | + | 16260.0i | −0.320122 | + | 0.933194i | ||||
\(133\) | 7907.74 | 0.447043 | ||||||||
\(134\) | 10379.7 | − | 7412.83i | 0.578066 | − | 0.412833i | ||||
\(135\) | − | 21384.4i | − | 1.17336i | ||||||
\(136\) | 16060.2 | − | 4787.48i | 0.868308 | − | 0.258838i | ||||
\(137\) | 11383.7 | 0.606516 | 0.303258 | − | 0.952908i | \(-0.401926\pi\) | ||||
0.303258 | + | 0.952908i | \(0.401926\pi\) | |||||||
\(138\) | 829.332 | + | 1161.26i | 0.0435482 | + | 0.0609780i | ||||
\(139\) | − | 32382.6i | − | 1.67603i | −0.545644 | − | 0.838017i | \(-0.683715\pi\) | ||
0.545644 | − | 0.838017i | \(-0.316285\pi\) | |||||||
\(140\) | −39117.9 | − | 13418.9i | −1.99581 | − | 0.684640i | ||||
\(141\) | 2677.36 | 0.134669 | ||||||||
\(142\) | 2682.90 | − | 1916.03i | 0.133054 | − | 0.0950222i | ||||
\(143\) | − | 9438.98i | − | 0.461586i | ||||||
\(144\) | −4222.34 | − | 3283.21i | −0.203624 | − | 0.158334i | ||||
\(145\) | 13765.3 | 0.654710 | ||||||||
\(146\) | −15230.2 | − | 21325.9i | −0.714494 | − | 1.00046i | ||||
\(147\) | 52067.0i | 2.40950i | ||||||||
\(148\) | −5375.63 | + | 15670.6i | −0.245418 | + | 0.715423i | ||||
\(149\) | 21304.2 | 0.959604 | 0.479802 | − | 0.877377i | \(-0.340709\pi\) | ||||
0.479802 | + | 0.877377i | \(0.340709\pi\) | |||||||
\(150\) | −2720.35 | + | 1942.78i | −0.120905 | + | 0.0863456i | ||||
\(151\) | − | 5913.44i | − | 0.259350i | −0.991557 | − | 0.129675i | \(-0.958607\pi\) | ||
0.991557 | − | 0.129675i | \(-0.0413934\pi\) | |||||||
\(152\) | −1514.19 | − | 5079.54i | −0.0655378 | − | 0.219855i | ||||
\(153\) | 5470.90 | 0.233709 | ||||||||
\(154\) | 30759.7 | + | 43071.0i | 1.29700 | + | 1.81611i | ||||
\(155\) | 26952.3i | 1.12184i | ||||||||
\(156\) | −7991.98 | − | 2741.56i | −0.328402 | − | 0.112655i | ||||
\(157\) | −4806.24 | −0.194987 | −0.0974936 | − | 0.995236i | \(-0.531083\pi\) | ||||
−0.0974936 | + | 0.995236i | \(0.531083\pi\) | |||||||
\(158\) | −36393.2 | + | 25990.7i | −1.45783 | + | 1.04113i | ||||
\(159\) | − | 16563.5i | − | 0.655175i | ||||||
\(160\) | −1129.32 | + | 27696.8i | −0.0441141 | + | 1.08191i | ||||
\(161\) | 4393.63 | 0.169501 | ||||||||
\(162\) | 10303.4 | + | 14427.2i | 0.392599 | + | 0.549733i | ||||
\(163\) | 39375.3i | 1.48200i | 0.671504 | + | 0.741001i | \(0.265649\pi\) | ||||
−0.671504 | + | 0.741001i | \(0.734351\pi\) | |||||||
\(164\) | 9180.06 | − | 26761.0i | 0.341317 | − | 0.994980i | ||||
\(165\) | 29083.7 | 1.06827 | ||||||||
\(166\) | −6500.67 | + | 4642.54i | −0.235908 | + | 0.168477i | ||||
\(167\) | 18655.2i | 0.668910i | 0.942412 | + | 0.334455i | \(0.108552\pi\) | ||||
−0.942412 | + | 0.334455i | \(0.891448\pi\) | |||||||
\(168\) | 45402.4 | − | 13534.2i | 1.60864 | − | 0.479529i | ||||
\(169\) | −23921.6 | −0.837563 | ||||||||
\(170\) | −16478.3 | − | 23073.7i | −0.570185 | − | 0.798396i | ||||
\(171\) | − | 1730.34i | − | 0.0591751i | ||||||
\(172\) | 3780.05 | + | 1296.70i | 0.127773 | + | 0.0438312i | ||||
\(173\) | 11613.0 | 0.388017 | 0.194008 | − | 0.981000i | \(-0.437851\pi\) | ||||
0.194008 | + | 0.981000i | \(0.437851\pi\) | |||||||
\(174\) | −12832.9 | + | 9164.77i | −0.423863 | + | 0.302707i | ||||
\(175\) | 10292.4i | 0.336079i | ||||||||
\(176\) | 21776.7 | − | 28005.8i | 0.703020 | − | 0.904112i | ||||
\(177\) | −38940.8 | −1.24296 | ||||||||
\(178\) | −20632.2 | − | 28890.0i | −0.651186 | − | 0.911818i | ||||
\(179\) | − | 32946.4i | − | 1.02826i | −0.857713 | − | 0.514128i | \(-0.828116\pi\) | ||
0.857713 | − | 0.514128i | \(-0.171884\pi\) | |||||||
\(180\) | −2936.28 | + | 8559.61i | −0.0906258 | + | 0.264185i | ||||
\(181\) | 15644.6 | 0.477538 | 0.238769 | − | 0.971076i | \(-0.423256\pi\) | ||||
0.238769 | + | 0.971076i | \(0.423256\pi\) | |||||||
\(182\) | −21169.9 | + | 15118.8i | −0.639111 | + | 0.456429i | ||||
\(183\) | − | 50224.0i | − | 1.49972i | ||||||
\(184\) | −841.298 | − | 2822.25i | −0.0248493 | − | 0.0833603i | ||||
\(185\) | 28029.5 | 0.818977 | ||||||||
\(186\) | −17944.5 | − | 25126.7i | −0.518688 | − | 0.726288i | ||||
\(187\) | 36287.2i | 1.03770i | ||||||||
\(188\) | −5226.45 | − | 1792.87i | −0.147874 | − | 0.0507264i | ||||
\(189\) | 75427.3 | 2.11157 | ||||||||
\(190\) | −7297.75 | + | 5211.78i | −0.202154 | + | 0.144371i | ||||
\(191\) | − | 38399.7i | − | 1.05259i | −0.850301 | − | 0.526297i | \(-0.823580\pi\) | ||
0.850301 | − | 0.526297i | \(-0.176420\pi\) | |||||||
\(192\) | −17387.4 | − | 26572.7i | −0.471664 | − | 0.720829i | ||||
\(193\) | 23655.4 | 0.635062 | 0.317531 | − | 0.948248i | \(-0.397146\pi\) | ||||
0.317531 | + | 0.948248i | \(0.397146\pi\) | |||||||
\(194\) | 33878.6 | + | 47438.2i | 0.900166 | + | 1.26045i | ||||
\(195\) | 14295.0i | 0.375936i | ||||||||
\(196\) | 34866.3 | − | 101639.i | 0.907597 | − | 2.64576i | ||||
\(197\) | 32656.2 | 0.841460 | 0.420730 | − | 0.907186i | \(-0.361774\pi\) | ||||
0.420730 | + | 0.907186i | \(0.361774\pi\) | |||||||
\(198\) | 9424.61 | − | 6730.71i | 0.240399 | − | 0.171684i | ||||
\(199\) | − | 17582.4i | − | 0.443989i | −0.975048 | − | 0.221995i | \(-0.928743\pi\) | ||
0.975048 | − | 0.221995i | \(-0.0712568\pi\) | |||||||
\(200\) | 6611.34 | − | 1970.81i | 0.165283 | − | 0.0492702i | ||||
\(201\) | 24721.9 | 0.611913 | ||||||||
\(202\) | 43255.3 | + | 60567.8i | 1.06008 | + | 1.48436i | ||||
\(203\) | 48553.0i | 1.17821i | ||||||||
\(204\) | 30724.3 | + | 10539.6i | 0.738282 | + | 0.253259i | ||||
\(205\) | −47866.4 | −1.13900 | ||||||||
\(206\) | −36992.9 | + | 26418.9i | −0.871733 | + | 0.622559i | ||||
\(207\) | − | 961.395i | − | 0.0224368i | ||||||
\(208\) | 13765.2 | + | 10703.5i | 0.318167 | + | 0.247401i | ||||
\(209\) | 11476.9 | 0.262744 | ||||||||
\(210\) | −46584.4 | − | 65229.3i | −1.05633 | − | 1.47912i | ||||
\(211\) | − | 8226.23i | − | 0.184772i | −0.995723 | − | 0.0923860i | \(-0.970551\pi\) | ||
0.995723 | − | 0.0923860i | \(-0.0294494\pi\) | |||||||
\(212\) | −11091.6 | + | 32333.4i | −0.246787 | + | 0.719415i | ||||
\(213\) | 6389.98 | 0.140845 | ||||||||
\(214\) | 64980.3 | − | 46406.5i | 1.41891 | − | 1.01333i | ||||
\(215\) | − | 6761.24i | − | 0.146268i | ||||||
\(216\) | −14442.9 | − | 48450.8i | −0.309562 | − | 1.03847i | ||||
\(217\) | −95066.3 | −2.01886 | ||||||||
\(218\) | 14592.7 | + | 20433.3i | 0.307060 | + | 0.429958i | ||||
\(219\) | − | 50792.8i | − | 1.05904i | ||||||
\(220\) | −56773.9 | − | 19475.6i | −1.17301 | − | 0.402389i | ||||
\(221\) | −17835.6 | −0.365177 | ||||||||
\(222\) | −26130.9 | + | 18661.7i | −0.530210 | + | 0.378656i | ||||
\(223\) | − | 48097.4i | − | 0.967189i | −0.875292 | − | 0.483595i | \(-0.839331\pi\) | ||
0.875292 | − | 0.483595i | \(-0.160669\pi\) | |||||||
\(224\) | −97692.5 | − | 3983.35i | −1.94700 | − | 0.0793875i | ||||
\(225\) | 2252.14 | 0.0444868 | ||||||||
\(226\) | 44969.8 | + | 62968.6i | 0.880449 | + | 1.23284i | ||||
\(227\) | 31760.4i | 0.616359i | 0.951328 | + | 0.308180i | \(0.0997198\pi\) | ||||
−0.951328 | + | 0.308180i | \(0.900280\pi\) | |||||||
\(228\) | 3333.48 | − | 9717.51i | 0.0641252 | − | 0.186933i | ||||
\(229\) | −54243.4 | −1.03437 | −0.517185 | − | 0.855874i | \(-0.673020\pi\) | ||||
−0.517185 | + | 0.855874i | \(0.673020\pi\) | |||||||
\(230\) | −4054.71 | + | 2895.72i | −0.0766485 | + | 0.0547396i | ||||
\(231\) | 102584.i | 1.92245i | ||||||||
\(232\) | 31188.0 | − | 9297.00i | 0.579445 | − | 0.172730i | ||||
\(233\) | 108192. | 1.99289 | 0.996447 | − | 0.0842239i | \(-0.0268411\pi\) | ||||
0.996447 | + | 0.0842239i | \(0.0268411\pi\) | |||||||
\(234\) | 3308.23 | + | 4632.31i | 0.0604176 | + | 0.0845992i | ||||
\(235\) | 9348.36i | 0.169278i | ||||||||
\(236\) | 76016.0 | + | 26076.4i | 1.36484 | + | 0.468192i | ||||
\(237\) | −86679.2 | −1.54319 | ||||||||
\(238\) | 81385.6 | − | 58122.6i | 1.43679 | − | 1.02610i | ||||
\(239\) | 2954.27i | 0.0517195i | 0.999666 | + | 0.0258598i | \(0.00823233\pi\) | ||||
−0.999666 | + | 0.0258598i | \(0.991768\pi\) | |||||||
\(240\) | −32980.0 | + | 42413.7i | −0.572570 | + | 0.736349i | ||||
\(241\) | −42725.9 | −0.735627 | −0.367813 | − | 0.929900i | \(-0.619893\pi\) | ||||
−0.367813 | + | 0.929900i | \(0.619893\pi\) | |||||||
\(242\) | 10607.4 | + | 14853.0i | 0.181126 | + | 0.253620i | ||||
\(243\) | − | 29625.1i | − | 0.501704i | ||||||
\(244\) | −33632.1 | + | 98041.8i | −0.564904 | + | 1.64676i | ||||
\(245\) | −181799. | −3.02872 | ||||||||
\(246\) | 44624.1 | − | 31868.9i | 0.737394 | − | 0.526620i | ||||
\(247\) | 5641.05i | 0.0924626i | ||||||||
\(248\) | 18203.4 | + | 61065.9i | 0.295972 | + | 0.992876i | ||||
\(249\) | −15482.9 | −0.249721 | ||||||||
\(250\) | 32547.6 | + | 45574.5i | 0.520762 | + | 0.729192i | ||||
\(251\) | − | 23355.5i | − | 0.370717i | −0.982671 | − | 0.185359i | \(-0.940655\pi\) | ||
0.982671 | − | 0.185359i | \(-0.0593446\pi\) | |||||||
\(252\) | −30191.5 | − | 10356.9i | −0.475427 | − | 0.163090i | ||||
\(253\) | 6376.71 | 0.0996221 | ||||||||
\(254\) | 2330.13 | − | 1664.09i | 0.0361171 | − | 0.0257935i | ||||
\(255\) | − | 54955.6i | − | 0.845145i | ||||||
\(256\) | 16147.6 | + | 63515.5i | 0.246393 | + | 0.969170i | ||||
\(257\) | −72635.4 | −1.09972 | −0.549860 | − | 0.835257i | \(-0.685319\pi\) | ||||
−0.549860 | + | 0.835257i | \(0.685319\pi\) | |||||||
\(258\) | 4501.55 | + | 6303.26i | 0.0676275 | + | 0.0946947i | ||||
\(259\) | 98865.8i | 1.47383i | ||||||||
\(260\) | 9572.52 | − | 27905.1i | 0.141605 | − | 0.412797i | ||||
\(261\) | 10624.2 | 0.155960 | ||||||||
\(262\) | −16269.5 | + | 11619.0i | −0.237012 | + | 0.169265i | ||||
\(263\) | 26045.0i | 0.376542i | 0.982117 | + | 0.188271i | \(0.0602884\pi\) | ||||
−0.982117 | + | 0.188271i | \(0.939712\pi\) | |||||||
\(264\) | 65894.9 | − | 19642.9i | 0.945462 | − | 0.281837i | ||||
\(265\) | 57833.6 | 0.823547 | ||||||||
\(266\) | −18383.0 | − | 25740.7i | −0.259809 | − | 0.363795i | ||||
\(267\) | − | 68808.7i | − | 0.965207i | ||||||
\(268\) | −48259.3 | − | 16554.8i | −0.671911 | − | 0.230492i | ||||
\(269\) | −1823.60 | −0.0252014 | −0.0126007 | − | 0.999921i | \(-0.504011\pi\) | ||||
−0.0126007 | + | 0.999921i | \(0.504011\pi\) | |||||||
\(270\) | −69609.0 | + | 49712.2i | −0.954856 | + | 0.681923i | ||||
\(271\) | − | 51451.6i | − | 0.700585i | −0.936640 | − | 0.350292i | \(-0.886082\pi\) | ||
0.936640 | − | 0.350292i | \(-0.113918\pi\) | |||||||
\(272\) | −52918.9 | − | 41148.6i | −0.715274 | − | 0.556183i | ||||
\(273\) | −50421.3 | −0.676533 | ||||||||
\(274\) | −26463.6 | − | 37055.4i | −0.352490 | − | 0.493571i | ||||
\(275\) | 14937.9i | 0.197526i | ||||||||
\(276\) | 1852.12 | − | 5399.16i | 0.0243137 | − | 0.0708774i | ||||
\(277\) | 72997.4 | 0.951367 | 0.475683 | − | 0.879617i | \(-0.342201\pi\) | ||||
0.475683 | + | 0.879617i | \(0.342201\pi\) | |||||||
\(278\) | −105410. | + | 75279.6i | −1.36392 | + | 0.974064i | ||||
\(279\) | 20802.0i | 0.267237i | ||||||||
\(280\) | 47256.5 | + | 158528.i | 0.602761 | + | 2.02204i | ||||
\(281\) | 66784.4 | 0.845790 | 0.422895 | − | 0.906179i | \(-0.361014\pi\) | ||||
0.422895 | + | 0.906179i | \(0.361014\pi\) | |||||||
\(282\) | −6224.03 | − | 8715.14i | −0.0782660 | − | 0.109591i | ||||
\(283\) | − | 152009.i | − | 1.89800i | −0.315277 | − | 0.949000i | \(-0.602098\pi\) | ||
0.315277 | − | 0.949000i | \(-0.397902\pi\) | |||||||
\(284\) | −12473.8 | − | 4279.00i | −0.154654 | − | 0.0530525i | ||||
\(285\) | −17381.4 | −0.213990 | ||||||||
\(286\) | −30725.0 | + | 21942.7i | −0.375630 | + | 0.268261i | ||||
\(287\) | − | 168835.i | − | 2.04974i | ||||||
\(288\) | −871.619 | + | 21376.7i | −0.0105085 | + | 0.257724i | ||||
\(289\) | −14953.9 | −0.179043 | ||||||||
\(290\) | −32000.0 | − | 44807.7i | −0.380499 | − | 0.532791i | ||||
\(291\) | 112986.i | 1.33425i | ||||||||
\(292\) | −34013.0 | + | 99152.1i | −0.398914 | + | 1.16288i | ||||
\(293\) | −33912.7 | −0.395027 | −0.197514 | − | 0.980300i | \(-0.563287\pi\) | ||||
−0.197514 | + | 0.980300i | \(0.563287\pi\) | |||||||
\(294\) | 169484. | − | 121039.i | 1.96081 | − | 1.40034i | ||||
\(295\) | − | 135967.i | − | 1.56239i | ||||||
\(296\) | 63506.5 | − | 18931.0i | 0.724827 | − | 0.216067i | ||||
\(297\) | 109472. | 1.24105 | ||||||||
\(298\) | −49525.5 | − | 69347.7i | −0.557695 | − | 0.780907i | ||||
\(299\) | 3134.23i | 0.0350581i | ||||||||
\(300\) | 12647.9 | + | 4338.74i | 0.140533 | + | 0.0482082i | ||||
\(301\) | 23848.3 | 0.263223 | ||||||||
\(302\) | −19249.0 | + | 13746.9i | −0.211054 | + | 0.150727i | ||||
\(303\) | 144257.i | 1.57127i | ||||||||
\(304\) | −13014.5 | + | 16737.2i | −0.140825 | + | 0.181107i | ||||
\(305\) | 175364. | 1.88513 | ||||||||
\(306\) | −12718.1 | − | 17808.4i | −0.135825 | − | 0.190188i | ||||
\(307\) | 38139.5i | 0.404667i | 0.979317 | + | 0.202334i | \(0.0648525\pi\) | ||||
−0.979317 | + | 0.202334i | \(0.935147\pi\) | |||||||
\(308\) | 68694.6 | − | 200253.i | 0.724138 | − | 2.11095i | ||||
\(309\) | −88107.5 | −0.922776 | ||||||||
\(310\) | 87733.0 | − | 62655.7i | 0.912935 | − | 0.651984i | ||||
\(311\) | − | 69149.4i | − | 0.714937i | −0.933925 | − | 0.357468i | \(-0.883640\pi\) | ||
0.933925 | − | 0.357468i | \(-0.116360\pi\) | |||||||
\(312\) | 9654.75 | + | 32388.1i | 0.0991817 | + | 0.332718i | ||||
\(313\) | −114540. | −1.16915 | −0.584575 | − | 0.811340i | \(-0.698739\pi\) | ||||
−0.584575 | + | 0.811340i | \(0.698739\pi\) | |||||||
\(314\) | 11173.0 | + | 15644.9i | 0.113321 | + | 0.158677i | ||||
\(315\) | 54002.5i | 0.544243i | ||||||||
\(316\) | 169206. | + | 58044.1i | 1.69450 | + | 0.581278i | ||||
\(317\) | −58663.2 | −0.583778 | −0.291889 | − | 0.956452i | \(-0.594284\pi\) | ||||
−0.291889 | + | 0.956452i | \(0.594284\pi\) | |||||||
\(318\) | −53916.2 | + | 38504.9i | −0.533169 | + | 0.380770i | ||||
\(319\) | 70467.6i | 0.692482i | ||||||||
\(320\) | 92781.9 | − | 60710.4i | 0.906074 | − | 0.592875i | ||||
\(321\) | 154766. | 1.50199 | ||||||||
\(322\) | −10213.8 | − | 14301.8i | −0.0985090 | − | 0.137936i | ||||
\(323\) | − | 21686.4i | − | 0.207866i | ||||||
\(324\) | 23010.2 | − | 67077.5i | 0.219195 | − | 0.638979i | ||||
\(325\) | −7342.18 | −0.0695118 | ||||||||
\(326\) | 128172. | − | 91535.3i | 1.20603 | − | 0.861298i | ||||
\(327\) | 48666.9i | 0.455133i | ||||||||
\(328\) | −108451. | + | 32328.7i | −1.00806 | + | 0.300497i | ||||
\(329\) | −32973.6 | −0.304631 | ||||||||
\(330\) | −67610.4 | − | 94670.9i | −0.620849 | − | 0.869338i | ||||
\(331\) | 110676.i | 1.01018i | 0.863067 | + | 0.505090i | \(0.168541\pi\) | ||||
−0.863067 | + | 0.505090i | \(0.831459\pi\) | |||||||
\(332\) | 30224.1 | + | 10368.0i | 0.274206 | + | 0.0940633i | ||||
\(333\) | 21633.4 | 0.195091 | ||||||||
\(334\) | 60725.1 | − | 43367.6i | 0.544346 | − | 0.388752i | ||||
\(335\) | 86319.8i | 0.769167i | ||||||||
\(336\) | −149602. | − | 116327.i | −1.32513 | − | 1.03039i | ||||
\(337\) | −52549.8 | −0.462712 | −0.231356 | − | 0.972869i | \(-0.574316\pi\) | ||||
−0.231356 | + | 0.972869i | \(0.574316\pi\) | |||||||
\(338\) | 55610.3 | + | 77867.8i | 0.486768 | + | 0.681592i | ||||
\(339\) | 149975.i | 1.30503i | ||||||||
\(340\) | −36800.6 | + | 107278.i | −0.318344 | + | 0.928011i | ||||
\(341\) | −137975. | −1.18656 | ||||||||
\(342\) | −5632.46 | + | 4022.50i | −0.0481555 | + | 0.0343909i | ||||
\(343\) | − | 411989.i | − | 3.50185i | ||||||
\(344\) | −4566.50 | − | 15319.0i | −0.0385893 | − | 0.129453i | ||||
\(345\) | −9657.28 | −0.0811366 | ||||||||
\(346\) | −26996.5 | − | 37801.6i | −0.225504 | − | 0.315761i | ||||
\(347\) | 58173.0i | 0.483128i | 0.970385 | + | 0.241564i | \(0.0776604\pi\) | ||||
−0.970385 | + | 0.241564i | \(0.922340\pi\) | |||||||
\(348\) | 59664.9 | + | 20467.4i | 0.492675 | + | 0.169007i | ||||
\(349\) | 93243.7 | 0.765542 | 0.382771 | − | 0.923843i | \(-0.374970\pi\) | ||||
0.382771 | + | 0.923843i | \(0.374970\pi\) | |||||||
\(350\) | 33503.1 | − | 23926.7i | 0.273495 | − | 0.195320i | ||||
\(351\) | 53806.7i | 0.436739i | ||||||||
\(352\) | −141786. | − | 5781.25i | −1.14432 | − | 0.0466591i | ||||
\(353\) | 204758. | 1.64320 | 0.821601 | − | 0.570063i | \(-0.193081\pi\) | ||||
0.821601 | + | 0.570063i | \(0.193081\pi\) | |||||||
\(354\) | 90525.3 | + | 126757.i | 0.722376 | + | 1.01150i | ||||
\(355\) | 22311.5i | 0.177040i | ||||||||
\(356\) | −46077.2 | + | 134321.i | −0.363568 | + | 1.05985i | ||||
\(357\) | 193840. | 1.52092 | ||||||||
\(358\) | −107244. | + | 76590.0i | −0.836775 | + | 0.597594i | ||||
\(359\) | 34342.6i | 0.266468i | 0.991085 | + | 0.133234i | \(0.0425362\pi\) | ||||
−0.991085 | + | 0.133234i | \(0.957464\pi\) | |||||||
\(360\) | 34688.5 | − | 10340.5i | 0.267658 | − | 0.0797876i | ||||
\(361\) | −6859.00 | −0.0526316 | ||||||||
\(362\) | −36368.9 | − | 50925.2i | −0.277532 | − | 0.388611i | ||||
\(363\) | 35376.0i | 0.268470i | ||||||||
\(364\) | 98426.9 | + | 33764.3i | 0.742867 | + | 0.254832i | ||||
\(365\) | 177350. | 1.33121 | ||||||||
\(366\) | −163485. | + | 116755.i | −1.22044 | + | 0.871594i | ||||
\(367\) | − | 149381.i | − | 1.10908i | −0.832157 | − | 0.554540i | \(-0.812894\pi\) | ||
0.832157 | − | 0.554540i | \(-0.187106\pi\) | |||||||
\(368\) | −7231.01 | + | 9299.37i | −0.0533953 | + | 0.0686686i | ||||
\(369\) | −36943.7 | −0.271324 | ||||||||
\(370\) | −65159.8 | − | 91239.4i | −0.475966 | − | 0.666468i | ||||
\(371\) | 203991.i | 1.48205i | ||||||||
\(372\) | −40074.9 | + | 116823.i | −0.289592 | + | 0.844196i | ||||
\(373\) | 46484.3 | 0.334110 | 0.167055 | − | 0.985948i | \(-0.446574\pi\) | ||||
0.167055 | + | 0.985948i | \(0.446574\pi\) | |||||||
\(374\) | 118119. | − | 84356.4i | 0.844457 | − | 0.603080i | ||||
\(375\) | 108547.i | 0.771888i | ||||||||
\(376\) | 6313.83 | + | 21180.6i | 0.0446598 | + | 0.149817i | ||||
\(377\) | −34635.7 | −0.243692 | ||||||||
\(378\) | −175345. | − | 245525.i | −1.22718 | − | 1.71835i | ||||
\(379\) | 30244.9i | 0.210559i | 0.994443 | + | 0.105279i | \(0.0335737\pi\) | ||||
−0.994443 | + | 0.105279i | \(0.966426\pi\) | |||||||
\(380\) | 33930.0 | + | 11639.3i | 0.234972 | + | 0.0806046i | ||||
\(381\) | 5549.78 | 0.0382319 | ||||||||
\(382\) | −124996. | + | 89267.2i | −0.856580 | + | 0.611738i | ||||
\(383\) | 243104.i | 1.65728i | 0.559785 | + | 0.828638i | \(0.310884\pi\) | ||||
−0.559785 | + | 0.828638i | \(0.689116\pi\) | |||||||
\(384\) | −46077.0 | + | 118371.i | −0.312479 | + | 0.802757i | ||||
\(385\) | −358186. | −2.41650 | ||||||||
\(386\) | −54991.5 | − | 77001.4i | −0.369080 | − | 0.516802i | ||||
\(387\) | − | 5218.38i | − | 0.0348429i | ||||||
\(388\) | 75660.1 | − | 220558.i | 0.502578 | − | 1.46508i | ||||
\(389\) | 142045. | 0.938700 | 0.469350 | − | 0.883012i | \(-0.344488\pi\) | ||||
0.469350 | + | 0.883012i | \(0.344488\pi\) | |||||||
\(390\) | 46531.9 | − | 33231.4i | 0.305930 | − | 0.218484i | ||||
\(391\) | − | 12049.2i | − | 0.0788144i | ||||||
\(392\) | −411902. | + | 122786.i | −2.68054 | + | 0.799054i | ||||
\(393\) | −38749.7 | −0.250890 | ||||||||
\(394\) | −75915.6 | − | 106300.i | −0.489033 | − | 0.684764i | ||||
\(395\) | − | 302652.i | − | 1.93977i | ||||||
\(396\) | −43818.6 | − | 15031.5i | −0.279427 | − | 0.0958542i | ||||
\(397\) | 106459. | 0.675464 | 0.337732 | − | 0.941242i | \(-0.390340\pi\) | ||||
0.337732 | + | 0.941242i | \(0.390340\pi\) | |||||||
\(398\) | −57233.0 | + | 40873.7i | −0.361310 | + | 0.258034i | ||||
\(399\) | − | 61307.7i | − | 0.385096i | ||||||
\(400\) | −21784.5 | − | 16939.2i | −0.136153 | − | 0.105870i | ||||
\(401\) | 10549.6 | 0.0656063 | 0.0328031 | − | 0.999462i | \(-0.489557\pi\) | ||||
0.0328031 | + | 0.999462i | \(0.489557\pi\) | |||||||
\(402\) | −57470.7 | − | 80472.8i | −0.355627 | − | 0.497963i | ||||
\(403\) | − | 67816.4i | − | 0.417565i | ||||||
\(404\) | 96600.7 | − | 281603.i | 0.591858 | − | 1.72534i | ||||
\(405\) | −119979. | −0.731468 | ||||||||
\(406\) | 158046. | − | 112871.i | 0.958808 | − | 0.684745i | ||||
\(407\) | 143489.i | 0.866225i | ||||||||
\(408\) | −37116.7 | − | 124513.i | −0.222971 | − | 0.747987i | ||||
\(409\) | −2759.57 | −0.0164966 | −0.00824830 | − | 0.999966i | \(-0.502626\pi\) | ||||
−0.00824830 | + | 0.999966i | \(0.502626\pi\) | |||||||
\(410\) | 111275. | + | 155811.i | 0.661954 | + | 0.926895i | ||||
\(411\) | − | 88256.4i | − | 0.522472i | ||||||
\(412\) | 171994. | + | 59000.5i | 1.01325 | + | 0.347585i | ||||
\(413\) | 479584. | 2.81167 | ||||||||
\(414\) | −3129.46 | + | 2234.94i | −0.0182586 | + | 0.0130396i | ||||
\(415\) | − | 54060.7i | − | 0.313896i | ||||||
\(416\) | 2841.55 | − | 69689.8i | 0.0164199 | − | 0.402701i | ||||
\(417\) | −251058. | −1.44379 | ||||||||
\(418\) | −26680.3 | − | 37358.8i | −0.152700 | − | 0.213816i | ||||
\(419\) | − | 36994.3i | − | 0.210720i | −0.994434 | − | 0.105360i | \(-0.966400\pi\) | ||
0.994434 | − | 0.105360i | \(-0.0335996\pi\) | |||||||
\(420\) | −104035. | + | 303276.i | −0.589770 | + | 1.71925i | ||||
\(421\) | −197130. | −1.11221 | −0.556107 | − | 0.831111i | \(-0.687705\pi\) | ||||
−0.556107 | + | 0.831111i | \(0.687705\pi\) | |||||||
\(422\) | −26777.4 | + | 19123.4i | −0.150364 | + | 0.107384i | ||||
\(423\) | 7215.14i | 0.0403241i | ||||||||
\(424\) | 131034. | − | 39060.5i | 0.728872 | − | 0.217273i | ||||
\(425\) | 28226.3 | 0.156270 | ||||||||
\(426\) | −14854.7 | − | 20800.2i | −0.0818550 | − | 0.114617i | ||||
\(427\) | 618545.i | 3.39247i | ||||||||
\(428\) | −302118. | − | 103638.i | −1.64926 | − | 0.565760i | ||||
\(429\) | −73179.2 | −0.397624 | ||||||||
\(430\) | −22008.7 | + | 15717.8i | −0.119030 | + | 0.0850069i | ||||
\(431\) | − | 179901.i | − | 0.968455i | −0.874942 | − | 0.484227i | \(-0.839101\pi\) | ||
0.874942 | − | 0.484227i | \(-0.160899\pi\) | |||||||
\(432\) | −124138. | + | 159646.i | −0.665176 | + | 0.855444i | ||||
\(433\) | −79092.9 | −0.421853 | −0.210927 | − | 0.977502i | \(-0.567648\pi\) | ||||
−0.210927 | + | 0.977502i | \(0.567648\pi\) | |||||||
\(434\) | 221000. | + | 309453.i | 1.17331 | + | 1.64291i | ||||
\(435\) | − | 106720.i | − | 0.563987i | ||||||
\(436\) | 32589.4 | − | 95002.2i | 0.171437 | − | 0.499759i | ||||
\(437\) | −3810.94 | −0.0199558 | ||||||||
\(438\) | −165337. | + | 118077.i | −0.861830 | + | 0.615487i | ||||
\(439\) | − | 178466.i | − | 0.926035i | −0.886349 | − | 0.463017i | \(-0.846767\pi\) | ||
0.886349 | − | 0.463017i | \(-0.153233\pi\) | |||||||
\(440\) | 68585.9 | + | 230081.i | 0.354266 | + | 1.18843i | ||||
\(441\) | −140314. | −0.721478 | ||||||||
\(442\) | 41462.2 | + | 58057.1i | 0.212231 | + | 0.297174i | ||||
\(443\) | 308460.i | 1.57178i | 0.618366 | + | 0.785890i | \(0.287795\pi\) | ||||
−0.618366 | + | 0.785890i | \(0.712205\pi\) | |||||||
\(444\) | 121492. | + | 41676.6i | 0.616287 | + | 0.211410i | ||||
\(445\) | 240255. | 1.21325 | ||||||||
\(446\) | −156563. | + | 111811.i | −0.787080 | + | 0.562103i | ||||
\(447\) | − | 165168.i | − | 0.826632i | ||||||
\(448\) | 214138. | + | 327261.i | 1.06694 | + | 1.63057i | ||||
\(449\) | 26812.0 | 0.132995 | 0.0664977 | − | 0.997787i | \(-0.478817\pi\) | ||||
0.0664977 | + | 0.997787i | \(0.478817\pi\) | |||||||
\(450\) | −5235.53 | − | 7331.00i | −0.0258545 | − | 0.0362025i | ||||
\(451\) | − | 245039.i | − | 1.20471i | ||||||
\(452\) | 100430. | − | 292765.i | 0.491570 | − | 1.43299i | ||||
\(453\) | −45846.2 | −0.223412 | ||||||||
\(454\) | 103384. | − | 73833.0i | 0.501581 | − | 0.358211i | ||||
\(455\) | − | 176053.i | − | 0.850394i | ||||||
\(456\) | −39381.0 | + | 11739.3i | −0.189390 | + | 0.0564562i | ||||
\(457\) | −305012. | −1.46044 | −0.730222 | − | 0.683209i | \(-0.760584\pi\) | ||||
−0.730222 | + | 0.683209i | \(0.760584\pi\) | |||||||
\(458\) | 126099. | + | 176569.i | 0.601147 | + | 0.841750i | ||||
\(459\) | − | 206854.i | − | 0.981837i | ||||||
\(460\) | 18851.9 | + | 6466.92i | 0.0890920 | + | 0.0305620i | ||||
\(461\) | 48637.0 | 0.228858 | 0.114429 | − | 0.993431i | \(-0.463496\pi\) | ||||
0.114429 | + | 0.993431i | \(0.463496\pi\) | |||||||
\(462\) | 333924. | − | 238476.i | 1.56446 | − | 1.11728i | ||||
\(463\) | 9810.69i | 0.0457654i | 0.999738 | + | 0.0228827i | \(0.00728443\pi\) | ||||
−0.999738 | + | 0.0228827i | \(0.992716\pi\) | |||||||
\(464\) | −102765. | − | 79908.3i | −0.477321 | − | 0.371155i | ||||
\(465\) | 208958. | 0.966390 | ||||||||
\(466\) | −251513. | − | 352179.i | −1.15821 | − | 1.62178i | ||||
\(467\) | 139743.i | 0.640761i | 0.947289 | + | 0.320381i | \(0.103811\pi\) | ||||
−0.947289 | + | 0.320381i | \(0.896189\pi\) | |||||||
\(468\) | 7388.15 | − | 21537.4i | 0.0337322 | − | 0.0983333i | ||||
\(469\) | −304468. | −1.38419 | ||||||||
\(470\) | 30430.1 | − | 21732.0i | 0.137755 | − | 0.0983794i | ||||
\(471\) | 37262.2i | 0.167968i | ||||||||
\(472\) | −91831.4 | − | 308061.i | −0.412199 | − | 1.38278i | ||||
\(473\) | 34612.3 | 0.154706 | ||||||||
\(474\) | 201502. | + | 282152.i | 0.896857 | + | 1.25582i | ||||
\(475\) | − | 8927.42i | − | 0.0395675i | ||||||
\(476\) | −378392. | − | 129803.i | −1.67004 | − | 0.572890i | ||||
\(477\) | 44636.5 | 0.196179 | ||||||||
\(478\) | 9616.51 | − | 6867.76i | 0.0420883 | − | 0.0300579i | ||||
\(479\) | 19255.8i | 0.0839248i | 0.999119 | + | 0.0419624i | \(0.0133610\pi\) | ||||
−0.999119 | + | 0.0419624i | \(0.986639\pi\) | |||||||
\(480\) | 214730. | + | 8755.48i | 0.931988 | + | 0.0380012i | ||||
\(481\) | −70526.8 | −0.304834 | ||||||||
\(482\) | 99324.5 | + | 139078.i | 0.427526 | + | 0.598639i | ||||
\(483\) | − | 34063.2i | − | 0.146013i | ||||||
\(484\) | 23689.3 | − | 69057.1i | 0.101126 | − | 0.294793i | ||||
\(485\) | −394505. | −1.67714 | ||||||||
\(486\) | −96433.4 | + | 68869.2i | −0.408277 | + | 0.291576i | ||||
\(487\) | − | 421633.i | − | 1.77778i | −0.458124 | − | 0.888888i | \(-0.651479\pi\) | ||
0.458124 | − | 0.888888i | \(-0.348521\pi\) | |||||||
\(488\) | 397322. | − | 118440.i | 1.66841 | − | 0.497345i | ||||
\(489\) | 305272. | 1.27664 | ||||||||
\(490\) | 422625. | + | 591777.i | 1.76021 | + | 2.46471i | ||||
\(491\) | 26607.2i | 0.110366i | 0.998476 | + | 0.0551830i | \(0.0175742\pi\) | ||||
−0.998476 | + | 0.0551830i | \(0.982426\pi\) | |||||||
\(492\) | −207474. | − | 71171.8i | −0.857106 | − | 0.294021i | ||||
\(493\) | 133153. | 0.547846 | ||||||||
\(494\) | 18362.3 | − | 13113.7i | 0.0752443 | − | 0.0537367i | ||||
\(495\) | 78376.7i | 0.319872i | ||||||||
\(496\) | 156460. | − | 201213.i | 0.635973 | − | 0.817888i | ||||
\(497\) | −78697.2 | −0.318600 | ||||||||
\(498\) | 35993.0 | + | 50398.9i | 0.145131 | + | 0.203218i | ||||
\(499\) | 307129.i | 1.23344i | 0.787181 | + | 0.616722i | \(0.211540\pi\) | ||||
−0.787181 | + | 0.616722i | \(0.788460\pi\) | |||||||
\(500\) | 72687.5 | − | 211893.i | 0.290750 | − | 0.847572i | ||||
\(501\) | 144632. | 0.576219 | ||||||||
\(502\) | −76025.2 | + | 54294.4i | −0.301682 | + | 0.215450i | ||||
\(503\) | 60713.0i | 0.239964i | 0.992776 | + | 0.119982i | \(0.0382836\pi\) | ||||
−0.992776 | + | 0.119982i | \(0.961716\pi\) | |||||||
\(504\) | 36473.0 | + | 122354.i | 0.143585 | + | 0.481676i | ||||
\(505\) | −503693. | −1.97507 | ||||||||
\(506\) | −14823.9 | − | 20757.0i | −0.0578976 | − | 0.0810705i | ||||
\(507\) | 185461.i | 0.721502i | ||||||||
\(508\) | −10833.7 | − | 3716.37i | −0.0419805 | − | 0.0144010i | ||||
\(509\) | −50488.9 | −0.194877 | −0.0974385 | − | 0.995242i | \(-0.531065\pi\) | ||||
−0.0974385 | + | 0.995242i | \(0.531065\pi\) | |||||||
\(510\) | −178887. | + | 127755.i | −0.687763 | + | 0.491175i | ||||
\(511\) | 625550.i | 2.39563i | ||||||||
\(512\) | 169213. | − | 200216.i | 0.645495 | − | 0.763764i | ||||
\(513\) | −65424.0 | −0.248601 | ||||||||
\(514\) | 168855. | + | 236437.i | 0.639127 | + | 0.894931i | ||||
\(515\) | − | 307639.i | − | 1.15992i | ||||||
\(516\) | 10053.2 | − | 29306.2i | 0.0377576 | − | 0.110068i | ||||
\(517\) | −47856.4 | −0.179044 | ||||||||
\(518\) | 321820. | − | 229832.i | 1.19937 | − | 0.856547i | ||||
\(519\) | − | 90033.7i | − | 0.334249i | ||||||
\(520\) | −113087. | + | 33710.8i | −0.418223 | + | 0.124670i | ||||
\(521\) | 346352. | 1.27598 | 0.637988 | − | 0.770046i | \(-0.279767\pi\) | ||||
0.637988 | + | 0.770046i | \(0.279767\pi\) | |||||||
\(522\) | −24697.9 | − | 34583.0i | −0.0906397 | − | 0.126917i | ||||
\(523\) | − | 218022.i | − | 0.797072i | −0.917153 | − | 0.398536i | \(-0.869518\pi\) | ||
0.917153 | − | 0.398536i | \(-0.130482\pi\) | |||||||
\(524\) | 75642.8 | + | 25948.4i | 0.275490 | + | 0.0945037i | ||||
\(525\) | 79795.8 | 0.289508 | ||||||||
\(526\) | 84779.8 | − | 60546.6i | 0.306423 | − | 0.218836i | ||||
\(527\) | 260713.i | 0.938732i | ||||||||
\(528\) | −217125. | − | 168832.i | −0.778830 | − | 0.605602i | ||||
\(529\) | 277724. | 0.992434 | ||||||||
\(530\) | −134445. | − | 188256.i | −0.478623 | − | 0.670187i | ||||
\(531\) | − | 104941.i | − | 0.372181i | ||||||
\(532\) | −41054.2 | + | 119678.i | −0.145056 | + | 0.422855i | ||||
\(533\) | 120440. | 0.423951 | ||||||||
\(534\) | −223981. | + | 159959.i | −0.785467 | + | 0.560951i | ||||
\(535\) | 540387.i | 1.88798i | ||||||||
\(536\) | 58299.9 | + | 195575.i | 0.202926 | + | 0.680744i | ||||
\(537\) | −255429. | −0.885771 | ||||||||
\(538\) | 4239.29 | + | 5936.03i | 0.0146463 | + | 0.0205084i | ||||
\(539\) | − | 930669.i | − | 3.20345i | ||||||
\(540\) | 323638. | + | 111021.i | 1.10987 | + | 0.380729i | ||||
\(541\) | −206688. | −0.706187 | −0.353094 | − | 0.935588i | \(-0.614870\pi\) | ||||
−0.353094 | + | 0.935588i | \(0.614870\pi\) | |||||||
\(542\) | −167481. | + | 119609.i | −0.570122 | + | 0.407160i | ||||
\(543\) | − | 121291.i | − | 0.411366i | ||||||
\(544\) | −10924.1 | + | 267915.i | −0.0369136 | + | 0.905314i | ||||
\(545\) | −169927. | −0.572097 | ||||||||
\(546\) | 117214. | + | 164128.i | 0.393182 | + | 0.550550i | ||||
\(547\) | − | 393318.i | − | 1.31453i | −0.753662 | − | 0.657263i | \(-0.771714\pi\) | ||
0.753662 | − | 0.657263i | \(-0.228286\pi\) | |||||||
\(548\) | −59100.2 | + | 172284.i | −0.196801 | + | 0.573700i | ||||
\(549\) | 135347. | 0.449061 | ||||||||
\(550\) | 48624.8 | − | 34726.1i | 0.160743 | − | 0.114797i | ||||
\(551\) | − | 42113.8i | − | 0.138714i | ||||||
\(552\) | −21880.5 | + | 6522.47i | −0.0718091 | + | 0.0214059i | ||||
\(553\) | 1.06752e6 | 3.49079 | ||||||||
\(554\) | −169696. | − | 237616.i | −0.552908 | − | 0.774204i | ||||
\(555\) | − | 217309.i | − | 0.705491i | ||||||
\(556\) | 490088. | + | 168119.i | 1.58535 | + | 0.543836i | ||||
\(557\) | −179469. | −0.578469 | −0.289234 | − | 0.957258i | \(-0.593401\pi\) | ||||
−0.289234 | + | 0.957258i | \(0.593401\pi\) | |||||||
\(558\) | 67713.1 | − | 48358.2i | 0.217472 | − | 0.155311i | ||||
\(559\) | 17012.4i | 0.0544429i | ||||||||
\(560\) | 406172. | − | 522355.i | 1.29519 | − | 1.66567i | ||||
\(561\) | 281330. | 0.893903 | ||||||||
\(562\) | −155253. | − | 217391.i | −0.491549 | − | 0.688287i | ||||
\(563\) | 216106.i | 0.681791i | 0.940101 | + | 0.340895i | \(0.110730\pi\) | ||||
−0.940101 | + | 0.340895i | \(0.889270\pi\) | |||||||
\(564\) | −13899.9 | + | 40520.0i | −0.0436973 | + | 0.127383i | ||||
\(565\) | −523658. | −1.64040 | ||||||||
\(566\) | −494808. | + | 353373.i | −1.54456 | + | 1.10306i | ||||
\(567\) | − | 423191.i | − | 1.31635i | ||||||
\(568\) | 15069.0 | + | 50551.1i | 0.0467078 | + | 0.156687i | ||||
\(569\) | −359240. | −1.10959 | −0.554793 | − | 0.831989i | \(-0.687202\pi\) | ||||
−0.554793 | + | 0.831989i | \(0.687202\pi\) | |||||||
\(570\) | 40406.3 | + | 56578.5i | 0.124365 | + | 0.174141i | ||||
\(571\) | − | 338881.i | − | 1.03938i | −0.854355 | − | 0.519691i | \(-0.826047\pi\) | ||
0.854355 | − | 0.519691i | \(-0.173953\pi\) | |||||||
\(572\) | 142852. | + | 49003.9i | 0.436611 | + | 0.149775i | ||||
\(573\) | −297708. | −0.906736 | ||||||||
\(574\) | −549578. | + | 392488.i | −1.66804 | + | 1.19125i | ||||
\(575\) | − | 4960.17i | − | 0.0150024i | ||||||
\(576\) | 71609.9 | − | 46856.8i | 0.215838 | − | 0.141230i | ||||
\(577\) | −173684. | −0.521685 | −0.260842 | − | 0.965381i | \(-0.584000\pi\) | ||||
−0.260842 | + | 0.965381i | \(0.584000\pi\) | |||||||
\(578\) | 34763.1 | + | 48676.7i | 0.104055 | + | 0.145702i | ||||
\(579\) | − | 183398.i | − | 0.547062i | ||||||
\(580\) | −71464.5 | + | 208328.i | −0.212439 | + | 0.619286i | ||||
\(581\) | 190683. | 0.564886 | ||||||||
\(582\) | 367783. | − | 262657.i | 1.08579 | − | 0.775430i | ||||
\(583\) | 296063.i | 0.871059i | ||||||||
\(584\) | 401822. | − | 119781.i | 1.17817 | − | 0.351207i | ||||
\(585\) | −38523.1 | −0.112567 | ||||||||
\(586\) | 78836.4 | + | 110390.i | 0.229579 | + | 0.321465i | ||||
\(587\) | 11640.3i | 0.0337823i | 0.999857 | + | 0.0168911i | \(0.00537687\pi\) | ||||
−0.999857 | + | 0.0168911i | \(0.994623\pi\) | |||||||
\(588\) | −787997. | − | 270314.i | −2.27913 | − | 0.781831i | ||||
\(589\) | 82458.4 | 0.237686 | ||||||||
\(590\) | −442590. | + | 316081.i | −1.27144 | + | 0.908018i | ||||
\(591\) | − | 253180.i | − | 0.724859i | ||||||
\(592\) | −209255. | − | 162713.i | −0.597081 | − | 0.464278i | ||||
\(593\) | 36753.2 | 0.104517 | 0.0522583 | − | 0.998634i | \(-0.483358\pi\) | ||||
0.0522583 | + | 0.998634i | \(0.483358\pi\) | |||||||
\(594\) | −254488. | − | 356344.i | −0.721264 | − | 1.00994i | ||||
\(595\) | 676817.i | 1.91178i | ||||||||
\(596\) | −110604. | + | 322423.i | −0.311371 | + | 0.907683i | ||||
\(597\) | −136314. | −0.382466 | ||||||||
\(598\) | 10202.3 | − | 7286.11i | 0.0285296 | − | 0.0203748i | ||||
\(599\) | − | 311824.i | − | 0.869073i | −0.900654 | − | 0.434536i | \(-0.856912\pi\) | ||
0.900654 | − | 0.434536i | \(-0.143088\pi\) | |||||||
\(600\) | −15279.4 | − | 51256.8i | −0.0424428 | − | 0.142380i | ||||
\(601\) | 200210. | 0.554289 | 0.277145 | − | 0.960828i | \(-0.410612\pi\) | ||||
0.277145 | + | 0.960828i | \(0.410612\pi\) | |||||||
\(602\) | −55439.8 | − | 77629.1i | −0.152978 | − | 0.214206i | ||||
\(603\) | 66622.3i | 0.183225i | ||||||||
\(604\) | 89495.8 | + | 30700.5i | 0.245318 | + | 0.0841535i | ||||
\(605\) | −123520. | −0.337463 | ||||||||
\(606\) | 469575. | − | 335353.i | 1.27867 | − | 0.913181i | ||||
\(607\) | 307693.i | 0.835103i | 0.908653 | + | 0.417551i | \(0.137112\pi\) | ||||
−0.908653 | + | 0.417551i | \(0.862888\pi\) | |||||||
\(608\) | 84736.3 | + | 3455.07i | 0.229225 | + | 0.00934651i | ||||
\(609\) | 376425. | 1.01495 | ||||||||
\(610\) | −407666. | − | 570831.i | −1.09558 | − | 1.53408i | ||||
\(611\) | − | 23522.0i | − | 0.0630074i | ||||||
\(612\) | −28403.0 | + | 82798.2i | −0.0758335 | + | 0.221064i | ||||
\(613\) | −274260. | −0.729862 | −0.364931 | − | 0.931034i | \(-0.618907\pi\) | ||||
−0.364931 | + | 0.931034i | \(0.618907\pi\) | |||||||
\(614\) | 124149. | − | 88662.4i | 0.329310 | − | 0.235181i | ||||
\(615\) | 371102.i | 0.981168i | ||||||||
\(616\) | −811542. | + | 241917.i | −2.13870 | + | 0.637536i | ||||
\(617\) | −409116. | −1.07467 | −0.537336 | − | 0.843368i | \(-0.680569\pi\) | ||||
−0.537336 | + | 0.843368i | \(0.680569\pi\) | |||||||
\(618\) | 204823. | + | 286801.i | 0.536291 | + | 0.750937i | ||||
\(619\) | − | 17549.2i | − | 0.0458012i | −0.999738 | − | 0.0229006i | \(-0.992710\pi\) | ||
0.999738 | − | 0.0229006i | \(-0.00729012\pi\) | |||||||
\(620\) | −407904. | − | 139927.i | −1.06114 | − | 0.364014i | ||||
\(621\) | −36350.3 | −0.0942594 | ||||||||
\(622\) | −225090. | + | 160751.i | −0.581802 | + | 0.415501i | ||||
\(623\) | 847427.i | 2.18337i | ||||||||
\(624\) | 82983.1 | − | 106720.i | 0.213118 | − | 0.274079i | ||||
\(625\) | −446377. | −1.14272 | ||||||||
\(626\) | 266271. | + | 372843.i | 0.679477 | + | 0.951431i | ||||
\(627\) | − | 88979.2i | − | 0.226336i | ||||||
\(628\) | 24952.3 | − | 72739.0i | 0.0632691 | − | 0.184437i | ||||
\(629\) | 271133. | 0.685300 | ||||||||
\(630\) | 175785. | − | 125539.i | 0.442894 | − | 0.316299i | ||||
\(631\) | 494018.i | 1.24075i | 0.784305 | + | 0.620375i | \(0.213020\pi\) | ||||
−0.784305 | + | 0.620375i | \(0.786980\pi\) | |||||||
\(632\) | −204409. | − | 685719.i | −0.511761 | − | 1.71677i | ||||
\(633\) | −63776.9 | −0.159168 | ||||||||
\(634\) | 136374. | + | 190956.i | 0.339275 | + | 0.475067i | ||||
\(635\) | 19377.8i | 0.0480570i | ||||||||
\(636\) | 250677. | + | 85991.8i | 0.619726 | + | 0.212590i | ||||
\(637\) | 457435. | 1.12733 | ||||||||
\(638\) | 229381. | − | 163815.i | 0.563528 | − | 0.402451i | ||||
\(639\) | 17220.2i | 0.0421732i | ||||||||
\(640\) | −413309. | − | 160884.i | −1.00906 | − | 0.392783i | ||||
\(641\) | −541057. | −1.31682 | −0.658411 | − | 0.752659i | \(-0.728771\pi\) | ||||
−0.658411 | + | 0.752659i | \(0.728771\pi\) | |||||||
\(642\) | −359784. | − | 503784.i | −0.872914 | − | 1.22229i | ||||
\(643\) | 19642.5i | 0.0475088i | 0.999718 | + | 0.0237544i | \(0.00756197\pi\) | ||||
−0.999718 | + | 0.0237544i | \(0.992438\pi\) | |||||||
\(644\) | −22810.2 | + | 66494.4i | −0.0549993 | + | 0.160330i | ||||
\(645\) | −52419.0 | −0.126000 | ||||||||
\(646\) | −70592.1 | + | 50414.2i | −0.169157 | + | 0.120806i | ||||
\(647\) | 645080.i | 1.54101i | 0.637435 | + | 0.770504i | \(0.279995\pi\) | ||||
−0.637435 | + | 0.770504i | \(0.720005\pi\) | |||||||
\(648\) | −271837. | + | 81033.2i | −0.647379 | + | 0.192980i | ||||
\(649\) | 696046. | 1.65253 | ||||||||
\(650\) | 17068.3 | + | 23899.7i | 0.0403983 | + | 0.0565673i | ||||
\(651\) | 737037.i | 1.73911i | ||||||||
\(652\) | −595918. | − | 204423.i | −1.40182 | − | 0.480877i | ||||
\(653\) | −49027.0 | −0.114977 | −0.0574883 | − | 0.998346i | \(-0.518309\pi\) | ||||
−0.0574883 | + | 0.998346i | \(0.518309\pi\) | |||||||
\(654\) | 158417. | − | 113135.i | 0.370379 | − | 0.264511i | ||||
\(655\) | − | 135300.i | − | 0.315365i | ||||||
\(656\) | 357349. | + | 277867.i | 0.830395 | + | 0.645699i | ||||
\(657\) | 136880. | 0.317110 | ||||||||
\(658\) | 76653.3 | + | 107333.i | 0.177043 | + | 0.247903i | ||||
\(659\) | 66084.5i | 0.152170i | 0.997101 | + | 0.0760850i | \(0.0242420\pi\) | ||||
−0.997101 | + | 0.0760850i | \(0.975758\pi\) | |||||||
\(660\) | −150992. | + | 440160.i | −0.346630 | + | 1.01047i | ||||
\(661\) | 585427. | 1.33989 | 0.669946 | − | 0.742410i | \(-0.266317\pi\) | ||||
0.669946 | + | 0.742410i | \(0.266317\pi\) | |||||||
\(662\) | 360265. | − | 257288.i | 0.822065 | − | 0.587088i | ||||
\(663\) | 138277.i | 0.314574i | ||||||||
\(664\) | −36512.3 | − | 122486.i | −0.0828139 | − | 0.277810i | ||||
\(665\) | 214064. | 0.484061 | ||||||||
\(666\) | −50290.9 | − | 70419.4i | −0.113381 | − | 0.158761i | ||||
\(667\) | − | 23398.9i | − | 0.0525949i | ||||||
\(668\) | −282334. | − | 96851.4i | −0.632717 | − | 0.217047i | ||||
\(669\) | −372893. | −0.833166 | ||||||||
\(670\) | 280981. | − | 200667.i | 0.625933 | − | 0.447018i | ||||
\(671\) | 897727.i | 1.99388i | ||||||||
\(672\) | −30882.4 | + | 757397.i | −0.0683868 | + | 1.67720i | ||||
\(673\) | 793279. | 1.75144 | 0.875721 | − | 0.482817i | \(-0.160386\pi\) | ||||
0.875721 | + | 0.482817i | \(0.160386\pi\) | |||||||
\(674\) | 122162. | + | 171056.i | 0.268915 | + | 0.376546i | ||||
\(675\) | − | 85153.5i | − | 0.186894i | ||||||
\(676\) | 124193. | − | 362037.i | 0.271771 | − | 0.792245i | ||||
\(677\) | 672510. | 1.46731 | 0.733654 | − | 0.679523i | \(-0.237813\pi\) | ||||
0.733654 | + | 0.679523i | \(0.237813\pi\) | |||||||
\(678\) | 488187. | − | 348645.i | 1.06201 | − | 0.758446i | ||||
\(679\) | − | 1.39150e6i | − | 3.01817i | ||||||
\(680\) | 434753. | − | 129598.i | 0.940210 | − | 0.280272i | ||||
\(681\) | 246234. | 0.530950 | ||||||||
\(682\) | 320749. | + | 449125.i | 0.689598 | + | 0.965603i | ||||
\(683\) | 197889.i | 0.424210i | 0.977247 | + | 0.212105i | \(0.0680319\pi\) | ||||
−0.977247 | + | 0.212105i | \(0.931968\pi\) | |||||||
\(684\) | 26187.4 | + | 8983.31i | 0.0559733 | + | 0.0192010i | ||||
\(685\) | 308159. | 0.656740 | ||||||||
\(686\) | −1.34108e6 | + | 957746.i | −2.84974 | + | 2.03518i | ||||
\(687\) | 420542.i | 0.891037i | ||||||||
\(688\) | −39249.4 | + | 50476.3i | −0.0829194 | + | 0.106638i | ||||
\(689\) | −145519. | −0.306535 | ||||||||
\(690\) | 22450.2 | + | 31435.6i | 0.0471543 | + | 0.0660274i | ||||
\(691\) | 174133.i | 0.364690i | 0.983235 | + | 0.182345i | \(0.0583688\pi\) | ||||
−0.983235 | + | 0.182345i | \(0.941631\pi\) | |||||||
\(692\) | −60290.4 | + | 175754.i | −0.125903 | + | 0.367022i | ||||
\(693\) | −276451. | −0.575641 | ||||||||
\(694\) | 189360. | − | 135234.i | 0.393161 | − | 0.280781i | ||||
\(695\) | − | 876604.i | − | 1.81482i | ||||||
\(696\) | −72078.4 | − | 241797.i | −0.148794 | − | 0.499151i | ||||
\(697\) | −463018. | −0.953087 | ||||||||
\(698\) | −216763. | − | 303520.i | −0.444911 | − | 0.622983i | ||||
\(699\) | − | 838800.i | − | 1.71674i | ||||||
\(700\) | −155768. | − | 53434.6i | −0.317895 | − | 0.109050i | ||||
\(701\) | −669508. | −1.36245 | −0.681224 | − | 0.732075i | \(-0.738552\pi\) | ||||
−0.681224 | + | 0.732075i | \(0.738552\pi\) | |||||||
\(702\) | 175148. | − | 125084.i | 0.355410 | − | 0.253821i | ||||
\(703\) | − | 85754.0i | − | 0.173518i | ||||||
\(704\) | 310791. | + | 474972.i | 0.627079 | + | 0.958346i | ||||
\(705\) | 72476.6 | 0.145821 | ||||||||
\(706\) | −475998. | − | 666512.i | −0.954983 | − | 1.33721i | ||||
\(707\) | − | 1.77663e6i | − | 3.55433i | ||||||
\(708\) | 202167. | − | 589342.i | 0.403315 | − | 1.17571i | ||||
\(709\) | −94715.2 | −0.188420 | −0.0942101 | − | 0.995552i | \(-0.530033\pi\) | ||||
−0.0942101 | + | 0.995552i | \(0.530033\pi\) | |||||||
\(710\) | 72626.6 | − | 51867.2i | 0.144072 | − | 0.102891i | ||||
\(711\) | − | 233589.i | − | 0.462077i | ||||||
\(712\) | 544345. | − | 162267.i | 1.07378 | − | 0.320088i | ||||
\(713\) | 45814.8 | 0.0901212 | ||||||||
\(714\) | −450617. | − | 630972.i | −0.883916 | − | 1.23769i | ||||
\(715\) | − | 255515.i | − | 0.499809i | ||||||
\(716\) | 498620. | + | 171046.i | 0.972621 | + | 0.333647i | ||||
\(717\) | 22904.1 | 0.0445527 | ||||||||
\(718\) | 111790. | − | 79835.9i | 0.216846 | − | 0.154864i | ||||
\(719\) | − | 374829.i | − | 0.725063i | −0.931972 | − | 0.362531i | \(-0.881913\pi\) | ||
0.931972 | − | 0.362531i | \(-0.118087\pi\) | |||||||
\(720\) | −114299. | − | 88877.0i | −0.220485 | − | 0.171445i | ||||
\(721\) | 1.08511e6 | 2.08738 | ||||||||
\(722\) | 15945.0 | + | 22326.9i | 0.0305880 | + | 0.0428306i | ||||
\(723\) | 331249.i | 0.633691i | ||||||||
\(724\) | −81221.4 | + | 236770.i | −0.154951 | + | 0.451700i | ||||
\(725\) | 54813.8 | 0.104283 | ||||||||
\(726\) | 115153. | − | 82238.2i | 0.218476 | − | 0.156027i | ||||
\(727\) | 294599.i | 0.557394i | 0.960379 | + | 0.278697i | \(0.0899025\pi\) | ||||
−0.960379 | + | 0.278697i | \(0.910097\pi\) | |||||||
\(728\) | −118905. | − | 398883.i | −0.224356 | − | 0.752632i | ||||
\(729\) | −588684. | −1.10771 | ||||||||
\(730\) | −412283. | − | 577295.i | −0.773659 | − | 1.08331i | ||||
\(731\) | − | 65402.3i | − | 0.122394i | ||||||
\(732\) | 760105. | + | 260746.i | 1.41857 | + | 0.486626i | ||||
\(733\) | 733723. | 1.36560 | 0.682801 | − | 0.730604i | \(-0.260761\pi\) | ||||
0.682801 | + | 0.730604i | \(0.260761\pi\) | |||||||
\(734\) | −486253. | + | 347264.i | −0.902547 | + | 0.644566i | ||||
\(735\) | 1.40946e6i | 2.60903i | ||||||||
\(736\) | 47080.4 | + | 1919.67i | 0.0869130 | + | 0.00354382i | ||||
\(737\) | −441890. | −0.813541 | ||||||||
\(738\) | 85882.6 | + | 120256.i | 0.157686 | + | 0.220798i | ||||
\(739\) | − | 204061.i | − | 0.373655i | −0.982393 | − | 0.186828i | \(-0.940179\pi\) | ||
0.982393 | − | 0.186828i | \(-0.0598206\pi\) | |||||||
\(740\) | −145519. | + | 424206.i | −0.265740 | + | 0.774665i | ||||
\(741\) | 43734.4 | 0.0796501 | ||||||||
\(742\) | 664016. | − | 474216.i | 1.20607 | − | 0.861327i | ||||
\(743\) | 159993.i | 0.289816i | 0.989445 | + | 0.144908i | \(0.0462886\pi\) | ||||
−0.989445 | + | 0.144908i | \(0.953711\pi\) | |||||||
\(744\) | 473436. | − | 141129.i | 0.855294 | − | 0.254959i | ||||
\(745\) | 576707. | 1.03907 | ||||||||
\(746\) | −108062. | − | 151312.i | −0.194175 | − | 0.271892i | ||||
\(747\) | − | 41724.5i | − | 0.0747739i | ||||||
\(748\) | −549181. | − | 188390.i | −0.981550 | − | 0.336710i | ||||
\(749\) | −1.90606e6 | −3.39760 | ||||||||
\(750\) | 353333. | − | 252337.i | 0.628148 | − | 0.448600i | ||||
\(751\) | 658168.i | 1.16696i | 0.812127 | + | 0.583481i | \(0.198310\pi\) | ||||
−0.812127 | + | 0.583481i | \(0.801690\pi\) | |||||||
\(752\) | 54267.8 | − | 69790.6i | 0.0959635 | − | 0.123413i | ||||
\(753\) | −181073. | −0.319347 | ||||||||
\(754\) | 80517.2 | + | 112743.i | 0.141627 | + | 0.198312i | ||||
\(755\) | − | 160078.i | − | 0.280826i | ||||||
\(756\) | −391592. | + | 1.14154e6i | −0.685158 | + | 1.99732i | ||||
\(757\) | 588857. | 1.02759 | 0.513793 | − | 0.857914i | \(-0.328240\pi\) | ||||
0.513793 | + | 0.857914i | \(0.328240\pi\) | |||||||
\(758\) | 98450.7 | − | 70309.8i | 0.171349 | − | 0.122371i | ||||
\(759\) | − | 49437.8i | − | 0.0858174i | ||||||
\(760\) | −40989.3 | − | 137504.i | −0.0709648 | − | 0.238061i | ||||
\(761\) | 500664. | 0.864524 | 0.432262 | − | 0.901748i | \(-0.357716\pi\) | ||||
0.432262 | + | 0.901748i | \(0.357716\pi\) | |||||||
\(762\) | −12901.5 | − | 18065.2i | −0.0222193 | − | 0.0311124i | ||||
\(763\) | − | 599368.i | − | 1.02954i | ||||||
\(764\) | 581152. | + | 199358.i | 0.995641 | + | 0.341544i | ||||
\(765\) | 148098. | 0.253062 | ||||||||
\(766\) | 791333. | − | 565141.i | 1.34866 | − | 0.963162i | ||||
\(767\) | 342115.i | 0.581543i | ||||||||
\(768\) | 492428. | − | 125190.i | 0.834872 | − | 0.212250i | ||||
\(769\) | −685037. | −1.15841 | −0.579204 | − | 0.815183i | \(-0.696637\pi\) | ||||
−0.579204 | + | 0.815183i | \(0.696637\pi\) | |||||||
\(770\) | 832670. | + | 1.16594e6i | 1.40440 | + | 1.96650i | ||||
\(771\) | 563133.i | 0.947332i | ||||||||
\(772\) | −122811. | + | 358008.i | −0.206064 | + | 0.600701i | ||||
\(773\) | 1.01843e6 | 1.70440 | 0.852200 | − | 0.523216i | \(-0.175268\pi\) | ||||
0.852200 | + | 0.523216i | \(0.175268\pi\) | |||||||
\(774\) | −16986.5 | + | 12131.1i | −0.0283545 | + | 0.0202497i | ||||
\(775\) | 107325.i | 0.178689i | ||||||||
\(776\) | −893830. | + | 266446.i | −1.48433 | + | 0.442473i | ||||
\(777\) | 766494. | 1.26960 | ||||||||
\(778\) | −330210. | − | 462374.i | −0.545546 | − | 0.763896i | ||||
\(779\) | 146444.i | 0.241321i | ||||||||
\(780\) | −216344. | − | 74214.5i | −0.355595 | − | 0.121983i | ||||
\(781\) | −114217. | −0.187254 | ||||||||
\(782\) | −39221.7 | + | 28010.7i | −0.0641377 | + | 0.0458047i | ||||
\(783\) | − | 401699.i | − | 0.655206i | ||||||
\(784\) | 1.35723e6 | + | 1.05535e6i | 2.20811 | + | 1.71698i | ||||
\(785\) | −130106. | −0.211134 | ||||||||
\(786\) | 90081.0 | + | 126135.i | 0.145810 | + | 0.204169i | ||||
\(787\) | 35708.8i | 0.0576535i | 0.999584 | + | 0.0288267i | \(0.00917711\pi\) | ||||
−0.999584 | + | 0.0288267i | \(0.990823\pi\) | |||||||
\(788\) | −169540. | + | 494229.i | −0.273035 | + | 0.795932i | ||||
\(789\) | 201924. | 0.324365 | ||||||||
\(790\) | −985169. | + | 703571.i | −1.57854 | + | 1.12734i | ||||
\(791\) | − | 1.84705e6i | − | 2.95206i | ||||||
\(792\) | 52935.2 | + | 177578.i | 0.0843906 | + | 0.283100i | ||||
\(793\) | −441244. | −0.701669 | ||||||||
\(794\) | −247484. | − | 346538.i | −0.392561 | − | 0.549679i | ||||
\(795\) | − | 448377.i | − | 0.709428i | ||||||
\(796\) | 266098. | + | 91281.8i | 0.419967 | + | 0.144065i | ||||
\(797\) | −50303.0 | −0.0791912 | −0.0395956 | − | 0.999216i | \(-0.512607\pi\) | ||||
−0.0395956 | + | 0.999216i | \(0.512607\pi\) | |||||||
\(798\) | −199564. | + | 142521.i | −0.313384 | + | 0.223807i | ||||
\(799\) | 90427.9i | 0.141647i | ||||||||
\(800\) | −4496.99 | + | 110290.i | −0.00702654 | + | 0.172328i | ||||
\(801\) | 185431. | 0.289012 | ||||||||
\(802\) | −24524.4 | − | 34340.1i | −0.0381285 | − | 0.0533891i | ||||
\(803\) | 907894.i | 1.40800i | ||||||||
\(804\) | −128347. | + | 374148.i | −0.198552 | + | 0.578804i | ||||
\(805\) | 118936. | 0.183536 | ||||||||
\(806\) | −220751. | + | 157652.i | −0.339807 | + | 0.242677i | ||||
\(807\) | 14138.1i | 0.0217092i | ||||||||
\(808\) | −1.14122e6 | + | 340191.i | −1.74802 | + | 0.521075i | ||||
\(809\) | −1.23431e6 | −1.88594 | −0.942972 | − | 0.332873i | \(-0.891982\pi\) | ||||
−0.942972 | + | 0.332873i | \(0.891982\pi\) | |||||||
\(810\) | 278914. | + | 390547.i | 0.425109 | + | 0.595255i | ||||
\(811\) | − | 645223.i | − | 0.980998i | −0.871442 | − | 0.490499i | \(-0.836815\pi\) | ||
0.871442 | − | 0.490499i | \(-0.163185\pi\) | |||||||
\(812\) | −734815. | − | 252070.i | −1.11446 | − | 0.382305i | ||||
\(813\) | −398898. | −0.603505 | ||||||||
\(814\) | 467075. | − | 333568.i | 0.704917 | − | 0.503426i | ||||
\(815\) | 1.06590e6i | 1.60472i | ||||||||
\(816\) | −319020. | + | 410273.i | −0.479113 | + | 0.616159i | ||||
\(817\) | −20685.5 | −0.0309900 | ||||||||
\(818\) | 6415.14 | + | 8982.74i | 0.00958737 | + | 0.0134246i | ||||
\(819\) | − | 135879.i | − | 0.202574i | ||||||
\(820\) | 248506. | − | 724424.i | 0.369580 | − | 1.07737i | ||||
\(821\) | −275509. | −0.408742 | −0.204371 | − | 0.978894i | \(-0.565515\pi\) | ||||
−0.204371 | + | 0.978894i | \(0.565515\pi\) | |||||||
\(822\) | −287285. | + | 205169.i | −0.425177 | + | 0.303646i | ||||
\(823\) | 327870.i | 0.484063i | 0.970268 | + | 0.242031i | \(0.0778137\pi\) | ||||
−0.970268 | + | 0.242031i | \(0.922186\pi\) | |||||||
\(824\) | −207778. | − | 697019.i | −0.306016 | − | 1.02657i | ||||
\(825\) | 115812. | 0.170155 | ||||||||
\(826\) | −1.11488e6 | − | 1.56110e6i | −1.63406 | − | 2.28808i | ||||
\(827\) | 459333.i | 0.671609i | 0.941932 | + | 0.335804i | \(0.109008\pi\) | ||||
−0.941932 | + | 0.335804i | \(0.890992\pi\) | |||||||
\(828\) | 14550.0 | + | 4991.23i | 0.0212228 | + | 0.00728026i | ||||
\(829\) | −1.21143e6 | −1.76274 | −0.881369 | − | 0.472429i | \(-0.843377\pi\) | ||||
−0.881369 | + | 0.472429i | \(0.843377\pi\) | |||||||
\(830\) | −175974. | + | 125674.i | −0.255442 | + | 0.182428i | ||||
\(831\) | − | 565940.i | − | 0.819536i | ||||||
\(832\) | −233454. | + | 152757.i | −0.337253 | + | 0.220676i | ||||
\(833\) | −1.75856e6 | −2.53436 | ||||||||
\(834\) | 583633. | + | 817226.i | 0.839088 | + | 1.17493i | ||||
\(835\) | 505000.i | 0.724300i | ||||||||
\(836\) | −59584.2 | + | 173695.i | −0.0852548 | + | 0.248528i | ||||
\(837\) | 786523. | 1.12269 | ||||||||
\(838\) | −120421. | + | 86000.2i | −0.171480 | + | 0.122465i | ||||
\(839\) | 302017.i | 0.429050i | 0.976719 | + | 0.214525i | \(0.0688203\pi\) | ||||
−0.976719 | + | 0.214525i | \(0.931180\pi\) | |||||||
\(840\) | 1.22905e6 | − | 366374.i | 1.74185 | − | 0.519237i | ||||
\(841\) | −448705. | −0.634408 | ||||||||
\(842\) | 458265. | + | 641682.i | 0.646387 | + | 0.905098i | ||||
\(843\) | − | 517771.i | − | 0.728589i | ||||||
\(844\) | 124498. | + | 42707.7i | 0.174775 | + | 0.0599545i | ||||
\(845\) | −647562. | −0.906919 | ||||||||
\(846\) | 23486.2 | − | 16773.0i | 0.0328149 | − | 0.0234352i | ||||
\(847\) | − | 435681.i | − | 0.607297i | ||||||
\(848\) | −431759. | − | 335727.i | −0.600413 | − | 0.466869i | ||||
\(849\) | −1.17851e6 | −1.63499 | ||||||||
\(850\) | −65617.3 | − | 91880.0i | −0.0908197 | − | 0.127169i | ||||
\(851\) | − | 47645.9i | − | 0.0657910i | ||||||
\(852\) | −33174.6 | + | 96707.9i | −0.0457010 | + | 0.133224i | ||||
\(853\) | −359597. | −0.494217 | −0.247109 | − | 0.968988i | \(-0.579480\pi\) | ||||
−0.247109 | + | 0.968988i | \(0.579480\pi\) | |||||||
\(854\) | 2.01344e6 | − | 1.43792e6i | 2.76072 | − | 1.97161i | ||||
\(855\) | − | 46840.6i | − | 0.0640752i | ||||||
\(856\) | 364975. | + | 1.22436e6i | 0.498098 | + | 1.67094i | ||||
\(857\) | 132686. | 0.180661 | 0.0903304 | − | 0.995912i | \(-0.471208\pi\) | ||||
0.0903304 | + | 0.995912i | \(0.471208\pi\) | |||||||
\(858\) | 170119. | + | 238207.i | 0.231088 | + | 0.323579i | ||||
\(859\) | 621274.i | 0.841971i | 0.907067 | + | 0.420986i | \(0.138316\pi\) | ||||
−0.907067 | + | 0.420986i | \(0.861684\pi\) | |||||||
\(860\) | 102327. | + | 35102.0i | 0.138354 | + | 0.0474608i | ||||
\(861\) | −1.30895e6 | −1.76571 | ||||||||
\(862\) | −585600. | + | 418214.i | −0.788110 | + | 0.562839i | ||||
\(863\) | − | 151855.i | − | 0.203896i | −0.994790 | − | 0.101948i | \(-0.967492\pi\) | ||
0.994790 | − | 0.101948i | \(-0.0325075\pi\) | |||||||
\(864\) | 808251. | + | 32955.9i | 1.08273 | + | 0.0441474i | ||||
\(865\) | 314365. | 0.420147 | ||||||||
\(866\) | 183866. | + | 257457.i | 0.245169 | + | 0.343296i | ||||
\(867\) | 115935.i | 0.154233i | ||||||||
\(868\) | 493551. | − | 1.43876e6i | 0.655077 | − | 1.90963i | ||||
\(869\) | 1.54934e6 | 2.05167 | ||||||||
\(870\) | −347388. | + | 248092.i | −0.458962 | + | 0.327774i | ||||
\(871\) | − | 217195.i | − | 0.286294i | ||||||
\(872\) | −385004. | + | 114768.i | −0.506328 | + | 0.150934i | ||||
\(873\) | −304482. | −0.399515 | ||||||||
\(874\) | 8859.24 | + | 12405.1i | 0.0115977 | + | 0.0162396i | ||||
\(875\) | − | 1.33683e6i | − | 1.74606i | ||||||
\(876\) | 768713. | + | 263699.i | 1.00174 | + | 0.343637i | ||||
\(877\) | 76093.6 | 0.0989347 | 0.0494674 | − | 0.998776i | \(-0.484248\pi\) | ||||
0.0494674 | + | 0.998776i | \(0.484248\pi\) | |||||||
\(878\) | −580930. | + | 414878.i | −0.753589 | + | 0.538185i | ||||
\(879\) | 262921.i | 0.340288i | ||||||||
\(880\) | 589500. | − | 758121.i | 0.761235 | − | 0.978979i | ||||
\(881\) | 1.05655e6 | 1.36125 | 0.680624 | − | 0.732633i | \(-0.261709\pi\) | ||||
0.680624 | + | 0.732633i | \(0.261709\pi\) | |||||||
\(882\) | 326186. | + | 456739.i | 0.419303 | + | 0.587125i | ||||
\(883\) | 1.42282e6i | 1.82485i | 0.409242 | + | 0.912426i | \(0.365793\pi\) | ||||
−0.409242 | + | 0.912426i | \(0.634207\pi\) | |||||||
\(884\) | 92596.2 | − | 269929.i | 0.118492 | − | 0.345418i | ||||
\(885\) | −1.05414e6 | −1.34589 | ||||||||
\(886\) | 1.00408e6 | − | 717074.i | 1.27908 | − | 0.913474i | ||||
\(887\) | 527731.i | 0.670757i | 0.942083 | + | 0.335378i | \(0.108864\pi\) | ||||
−0.942083 | + | 0.335378i | \(0.891136\pi\) | |||||||
\(888\) | −146769. | − | 492357.i | −0.186127 | − | 0.624388i | ||||
\(889\) | −68349.5 | −0.0864832 | ||||||||
\(890\) | −558517. | − | 782058.i | −0.705109 | − | 0.987322i | ||||
\(891\) | − | 614200.i | − | 0.773668i | ||||||
\(892\) | 727919. | + | 249705.i | 0.914858 | + | 0.313832i | ||||
\(893\) | 28600.6 | 0.0358651 | ||||||||
\(894\) | −537644. | + | 383965.i | −0.672697 | + | 0.480415i | ||||
\(895\) | − | 891864.i | − | 1.11340i | ||||||
\(896\) | 567470. | − | 1.45783e6i | 0.706850 | − | 1.81589i | ||||
\(897\) | 24299.3 | 0.0302001 | ||||||||
\(898\) | −62329.6 | − | 87276.4i | −0.0772932 | − | 0.108229i | ||||
\(899\) | 506289.i | 0.626440i | ||||||||
\(900\) | −11692.3 | + | 34084.6i | −0.0144350 | + | 0.0420797i | ||||
\(901\) | 559432. | 0.689125 | ||||||||
\(902\) | −797632. | + | 569639.i | −0.980369 | + | 0.700143i | ||||
\(903\) | − | 184893.i | − | 0.226748i | ||||||
\(904\) | −1.18645e6 | + | 353676.i | −1.45182 | + | 0.432781i | ||||
\(905\) | 423503. | 0.517082 | ||||||||
\(906\) | 106578. | + | 149235.i | 0.129841 | + | 0.181808i | ||||
\(907\) | − | 559308.i | − | 0.679887i | −0.940446 | − | 0.339944i | \(-0.889592\pi\) | ||
0.940446 | − | 0.339944i | \(-0.110408\pi\) | |||||||
\(908\) | −480671. | − | 164889.i | −0.583010 | − | 0.199995i | ||||
\(909\) | −388754. | −0.470487 | ||||||||
\(910\) | −573073. | + | 409268.i | −0.692034 | + | 0.494225i | ||||
\(911\) | − | 1.29307e6i | − | 1.55807i | −0.626983 | − | 0.779033i | \(-0.715710\pi\) | ||
0.626983 | − | 0.779033i | \(-0.284290\pi\) | |||||||
\(912\) | 129761. | + | 100900.i | 0.156011 | + | 0.121311i | ||||
\(913\) | 276749. | 0.332005 | ||||||||
\(914\) | 709059. | + | 992853.i | 0.848770 | + | 1.18848i | ||||
\(915\) | − | 1.35957e6i | − | 1.62390i | ||||||
\(916\) | 281613. | − | 820935.i | 0.335630 | − | 0.978403i | ||||
\(917\) | 477230. | 0.567530 | ||||||||
\(918\) | −673337. | + | 480872.i | −0.799000 | + | 0.570616i | ||||
\(919\) | 987271.i | 1.16897i | 0.811403 | + | 0.584487i | \(0.198704\pi\) | ||||
−0.811403 | + | 0.584487i | \(0.801296\pi\) | |||||||
\(920\) | −22774.1 | − | 76398.7i | −0.0269070 | − | 0.0902631i | ||||
\(921\) | 295690. | 0.348593 | ||||||||
\(922\) | −113066. | − | 158320.i | −0.133006 | − | 0.186240i | ||||
\(923\) | − | 56139.3i | − | 0.0658967i | ||||||
\(924\) | −1.55254e6 | − | 532581.i | −1.81844 | − | 0.623794i | ||||
\(925\) | 111614. | 0.130448 | ||||||||
\(926\) | 31935.0 | − | 22806.8i | 0.0372430 | − | 0.0265976i | ||||
\(927\) | − | 237439.i | − | 0.276307i | ||||||
\(928\) | −21213.9 | + | 520276.i | −0.0246334 | + | 0.604140i | ||||
\(929\) | 472888. | 0.547933 | 0.273966 | − | 0.961739i | \(-0.411664\pi\) | ||||
0.273966 | + | 0.961739i | \(0.411664\pi\) | |||||||
\(930\) | −485761. | − | 680183.i | −0.561639 | − | 0.786429i | ||||
\(931\) | 556199.i | 0.641698i | ||||||||
\(932\) | −561696. | + | 1.63741e6i | −0.646650 | + | 1.88506i | ||||
\(933\) | −536106. | −0.615868 | ||||||||
\(934\) | 454881. | − | 324859.i | 0.521439 | − | 0.372392i | ||||
\(935\) | 982300.i | 1.12362i | ||||||||
\(936\) | −87281.9 | + | 26018.3i | −0.0996260 | + | 0.0296980i | ||||
\(937\) | 183381. | 0.208869 | 0.104435 | − | 0.994532i | \(-0.466697\pi\) | ||||
0.104435 | + | 0.994532i | \(0.466697\pi\) | |||||||
\(938\) | 707793. | + | 991080.i | 0.804452 | + | 1.12643i | ||||
\(939\) | 888017.i | 1.00714i | ||||||||
\(940\) | −141481. | − | 48533.4i | −0.160119 | − | 0.0549269i | ||||
\(941\) | 1.15706e6 | 1.30670 | 0.653351 | − | 0.757055i | \(-0.273363\pi\) | ||||
0.653351 | + | 0.757055i | \(0.273363\pi\) | |||||||
\(942\) | 121293. | − | 86622.9i | 0.136689 | − | 0.0976182i | ||||
\(943\) | 81365.7i | 0.0914993i | ||||||||
\(944\) | −789297. | + | 1.01507e6i | −0.885720 | + | 1.13907i | ||||
\(945\) | 2.04183e6 | 2.28642 | ||||||||
\(946\) | −80462.8 | − | 112667.i | −0.0899110 | − | 0.125897i | ||||
\(947\) | − | 330922.i | − | 0.369000i | −0.982833 | − | 0.184500i | \(-0.940933\pi\) | ||
0.982833 | − | 0.184500i | \(-0.0590665\pi\) | |||||||
\(948\) | 450008. | − | 1.31183e6i | 0.500730 | − | 1.45969i | ||||
\(949\) | −446241. | −0.495492 | ||||||||
\(950\) | −29059.8 | + | 20753.5i | −0.0321993 | + | 0.0229955i | ||||
\(951\) | 454808.i | 0.502884i | ||||||||
\(952\) | 457118. | + | 1.53346e6i | 0.504376 | + | 1.69200i | ||||
\(953\) | −1.14501e6 | −1.26073 | −0.630366 | − | 0.776298i | \(-0.717095\pi\) | ||||
−0.630366 | + | 0.776298i | \(0.717095\pi\) | |||||||
\(954\) | −103766. | − | 145297.i | −0.114014 | − | 0.159647i | ||||
\(955\) | − | 1.03949e6i | − | 1.13976i | ||||||
\(956\) | −44710.8 | − | 15337.5i | −0.0489211 | − | 0.0167819i | ||||
\(957\) | 546326. | 0.596524 | ||||||||
\(958\) | 62680.0 | − | 44763.7i | 0.0682964 | − | 0.0487748i | ||||
\(959\) | 1.08694e6i | 1.18187i | ||||||||
\(960\) | −470680. | − | 719326.i | −0.510721 | − | 0.780519i | ||||
\(961\) | −67788.8 | −0.0734025 | ||||||||
\(962\) | 163953. | + | 229573.i | 0.177161 | + | 0.248068i | ||||
\(963\) | 417076.i | 0.449741i | ||||||||
\(964\) | 221818. | − | 646627.i | 0.238695 | − | 0.695824i | ||||
\(965\) | 640357. | 0.687650 | ||||||||
\(966\) | −110880. | + | 79186.4i | −0.118823 | + | 0.0848587i | ||||
\(967\) | − | 1.36604e6i | − | 1.46087i | −0.682982 | − | 0.730436i | \(-0.739317\pi\) | ||
0.682982 | − | 0.730436i | \(-0.260683\pi\) | |||||||
\(968\) | −279860. | + | 83424.7i | −0.298668 | + | 0.0890316i | ||||
\(969\) | −168132. | −0.179062 | ||||||||
\(970\) | 917101. | + | 1.28416e6i | 0.974706 | + | 1.36482i | ||||
\(971\) | − | 52205.0i | − | 0.0553699i | −0.999617 | − | 0.0276850i | \(-0.991186\pi\) | ||
0.999617 | − | 0.0276850i | \(-0.00881352\pi\) | |||||||
\(972\) | 448355. | + | 153803.i | 0.474559 | + | 0.162792i | ||||
\(973\) | 3.09196e6 | 3.26594 | ||||||||
\(974\) | −1.37247e6 | + | 980166.i | −1.44672 | + | 1.03319i | ||||
\(975\) | 56923.0i | 0.0598795i | ||||||||
\(976\) | −1.30919e6 | − | 1.01800e6i | −1.37436 | − | 1.06868i | ||||
\(977\) | −833646. | −0.873358 | −0.436679 | − | 0.899617i | \(-0.643845\pi\) | ||||
−0.436679 | + | 0.899617i | \(0.643845\pi\) | |||||||
\(978\) | −709662. | − | 993697.i | −0.741948 | − | 1.03891i | ||||
\(979\) | 1.22992e6i | 1.28325i | ||||||||
\(980\) | 943835. | − | 2.75139e6i | 0.982752 | − | 2.86484i | ||||
\(981\) | −131151. | −0.136281 | ||||||||
\(982\) | 86609.6 | − | 61853.4i | 0.0898138 | − | 0.0641417i | ||||
\(983\) | 809453.i | 0.837692i | 0.908057 | + | 0.418846i | \(0.137565\pi\) | ||||
−0.908057 | + | 0.418846i | \(0.862435\pi\) | |||||||
\(984\) | 250640. | + | 840807.i | 0.258858 | + | 0.868373i | ||||
\(985\) | 884010. | 0.911139 | ||||||||
\(986\) | −309540. | − | 433431.i | −0.318393 | − | 0.445826i | ||||
\(987\) | 255640.i | 0.262419i | ||||||||
\(988\) | −85373.3 | − | 29286.4i | −0.0874598 | − | 0.0300021i | ||||
\(989\) | −11493.1 | −0.0117502 | ||||||||
\(990\) | 255126. | − | 182201.i | 0.260306 | − | 0.185901i | ||||
\(991\) | 241862.i | 0.246275i | 0.992390 | + | 0.123137i | \(0.0392956\pi\) | ||||
−0.992390 | + | 0.123137i | \(0.960704\pi\) | |||||||
\(992\) | −1.01869e6 | − | 41536.6i | −1.03519 | − | 0.0422092i | ||||
\(993\) | 858059. | 0.870199 | ||||||||
\(994\) | 182946. | + | 256169.i | 0.185162 | + | 0.259271i | ||||
\(995\) | − | 475959.i | − | 0.480755i | ||||||
\(996\) | 80382.0 | − | 234323.i | 0.0810289 | − | 0.236209i | ||||
\(997\) | 483196. | 0.486108 | 0.243054 | − | 0.970013i | \(-0.421851\pi\) | ||||
0.243054 | + | 0.970013i | \(0.421851\pi\) | |||||||
\(998\) | 999742. | − | 713979.i | 1.00375 | − | 0.716843i | ||||
\(999\) | − | 817958.i | − | 0.819596i |
(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 | 76.5.b.a.39.11 | ✓ | 36 | |
4.3 | odd | 2 | inner | 76.5.b.a.39.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.b.a.39.11 | ✓ | 36 | 1.1 | even | 1 | trivial | |
76.5.b.a.39.12 | yes | 36 | 4.3 | odd | 2 | inner |