Properties

Label 108.6.h.a.35.6
Level 108
Weight 6
Character 108.35
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.6
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.63825 - 3.23831i) q^{2} +(11.0267 + 30.0402i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(181.157 + 104.591i) q^{7} +(46.1351 - 175.042i) q^{8} +O(q^{10})\) \(q+(-4.63825 - 3.23831i) q^{2} +(11.0267 + 30.0402i) q^{4} +(-61.0162 + 35.2277i) q^{5} +(181.157 + 104.591i) q^{7} +(46.1351 - 175.042i) q^{8} +(397.087 + 34.1946i) q^{10} +(-75.3585 + 130.525i) q^{11} +(-210.949 - 365.375i) q^{13} +(-501.553 - 1071.76i) q^{14} +(-780.825 + 662.486i) q^{16} +662.619i q^{17} -624.161i q^{19} +(-1731.05 - 1444.49i) q^{20} +(772.212 - 361.372i) q^{22} +(-1186.88 - 2055.74i) q^{23} +(919.485 - 1592.59i) q^{25} +(-204.763 + 2377.82i) q^{26} +(-1144.38 + 6595.28i) q^{28} +(3944.46 + 2277.34i) q^{29} +(-8615.25 + 4974.02i) q^{31} +(5767.00 - 544.220i) q^{32} +(2145.77 - 3073.39i) q^{34} -14738.0 q^{35} -5944.72 q^{37} +(-2021.23 + 2895.01i) q^{38} +(3351.33 + 12305.6i) q^{40} +(-10531.7 + 6080.46i) q^{41} +(-15161.2 - 8753.33i) q^{43} +(-4751.94 - 824.530i) q^{44} +(-1152.08 + 13378.5i) q^{46} +(-9291.01 + 16092.5i) q^{47} +(13475.1 + 23339.5i) q^{49} +(-9422.12 + 4409.27i) q^{50} +(8649.87 - 10365.8i) q^{52} -32790.2i q^{53} -10618.8i q^{55} +(26665.5 - 26884.7i) q^{56} +(-10920.7 - 23336.3i) q^{58} +(-1808.33 - 3132.12i) q^{59} +(7916.16 - 13711.2i) q^{61} +(56067.1 + 4828.15i) q^{62} +(-28511.1 - 16151.1i) q^{64} +(25742.7 + 14862.5i) q^{65} +(41652.4 - 24048.0i) q^{67} +(-19905.2 + 7306.48i) q^{68} +(68358.6 + 47726.3i) q^{70} -32192.2 q^{71} -34777.5 q^{73} +(27573.1 + 19250.9i) q^{74} +(18749.9 - 6882.42i) q^{76} +(-27303.5 + 15763.7i) q^{77} +(-73506.0 - 42438.7i) q^{79} +(24305.1 - 67929.1i) q^{80} +(68538.9 + 5902.15i) q^{82} +(7548.53 - 13074.4i) q^{83} +(-23342.6 - 40430.5i) q^{85} +(41975.4 + 89696.8i) q^{86} +(19370.6 + 19212.6i) q^{88} +40174.5i q^{89} -88253.7i q^{91} +(48667.5 - 58322.2i) q^{92} +(95206.5 - 44553.8i) q^{94} +(21987.8 + 38083.9i) q^{95} +(4298.65 - 7445.49i) q^{97} +(13079.9 - 151891. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.63825 3.23831i −0.819934 0.572458i
\(3\) 0 0
\(4\) 11.0267 + 30.0402i 0.344583 + 0.938756i
\(5\) −61.0162 + 35.2277i −1.09149 + 0.630173i −0.933973 0.357343i \(-0.883683\pi\)
−0.157518 + 0.987516i \(0.550349\pi\)
\(6\) 0 0
\(7\) 181.157 + 104.591i 1.39737 + 0.806770i 0.994116 0.108320i \(-0.0345472\pi\)
0.403250 + 0.915090i \(0.367880\pi\)
\(8\) 46.1351 175.042i 0.254863 0.966977i
\(9\) 0 0
\(10\) 397.087 + 34.1946i 1.25570 + 0.108133i
\(11\) −75.3585 + 130.525i −0.187781 + 0.325246i −0.944510 0.328483i \(-0.893463\pi\)
0.756729 + 0.653728i \(0.226796\pi\)
\(12\) 0 0
\(13\) −210.949 365.375i −0.346194 0.599626i 0.639376 0.768895i \(-0.279193\pi\)
−0.985570 + 0.169268i \(0.945860\pi\)
\(14\) −501.553 1071.76i −0.683906 1.46143i
\(15\) 0 0
\(16\) −780.825 + 662.486i −0.762525 + 0.646959i
\(17\) 662.619i 0.556086i 0.960569 + 0.278043i \(0.0896857\pi\)
−0.960569 + 0.278043i \(0.910314\pi\)
\(18\) 0 0
\(19\) 624.161i 0.396655i −0.980136 0.198327i \(-0.936449\pi\)
0.980136 0.198327i \(-0.0635509\pi\)
\(20\) −1731.05 1444.49i −0.967688 0.807496i
\(21\) 0 0
\(22\) 772.212 361.372i 0.340157 0.159183i
\(23\) −1186.88 2055.74i −0.467830 0.810306i 0.531494 0.847062i \(-0.321631\pi\)
−0.999324 + 0.0367563i \(0.988297\pi\)
\(24\) 0 0
\(25\) 919.485 1592.59i 0.294235 0.509630i
\(26\) −204.763 + 2377.82i −0.0594044 + 0.689836i
\(27\) 0 0
\(28\) −1144.38 + 6595.28i −0.275850 + 1.58978i
\(29\) 3944.46 + 2277.34i 0.870950 + 0.502843i 0.867664 0.497152i \(-0.165621\pi\)
0.00328601 + 0.999995i \(0.498954\pi\)
\(30\) 0 0
\(31\) −8615.25 + 4974.02i −1.61014 + 0.929615i −0.620804 + 0.783966i \(0.713194\pi\)
−0.989336 + 0.145649i \(0.953473\pi\)
\(32\) 5767.00 544.220i 0.995577 0.0939506i
\(33\) 0 0
\(34\) 2145.77 3073.39i 0.318336 0.455953i
\(35\) −14738.0 −2.03362
\(36\) 0 0
\(37\) −5944.72 −0.713883 −0.356941 0.934127i \(-0.616180\pi\)
−0.356941 + 0.934127i \(0.616180\pi\)
\(38\) −2021.23 + 2895.01i −0.227068 + 0.325231i
\(39\) 0 0
\(40\) 3351.33 + 12305.6i 0.331182 + 1.21605i
\(41\) −10531.7 + 6080.46i −0.978447 + 0.564907i −0.901801 0.432151i \(-0.857755\pi\)
−0.0766464 + 0.997058i \(0.524421\pi\)
\(42\) 0 0
\(43\) −15161.2 8753.33i −1.25044 0.721941i −0.279243 0.960221i \(-0.590083\pi\)
−0.971197 + 0.238279i \(0.923417\pi\)
\(44\) −4751.94 824.530i −0.370032 0.0642059i
\(45\) 0 0
\(46\) −1152.08 + 13378.5i −0.0802762 + 0.932210i
\(47\) −9291.01 + 16092.5i −0.613505 + 1.06262i 0.377139 + 0.926156i \(0.376908\pi\)
−0.990645 + 0.136466i \(0.956426\pi\)
\(48\) 0 0
\(49\) 13475.1 + 23339.5i 0.801755 + 1.38868i
\(50\) −9422.12 + 4409.27i −0.532995 + 0.249426i
\(51\) 0 0
\(52\) 8649.87 10365.8i 0.443610 0.531613i
\(53\) 32790.2i 1.60345i −0.597696 0.801723i \(-0.703917\pi\)
0.597696 0.801723i \(-0.296083\pi\)
\(54\) 0 0
\(55\) 10618.8i 0.473337i
\(56\) 26665.5 26884.7i 1.13626 1.14561i
\(57\) 0 0
\(58\) −10920.7 23336.3i −0.426265 0.910880i
\(59\) −1808.33 3132.12i −0.0676312 0.117141i 0.830227 0.557426i \(-0.188211\pi\)
−0.897858 + 0.440285i \(0.854877\pi\)
\(60\) 0 0
\(61\) 7916.16 13711.2i 0.272389 0.471792i −0.697084 0.716990i \(-0.745520\pi\)
0.969473 + 0.245198i \(0.0788528\pi\)
\(62\) 56067.1 + 4828.15i 1.85237 + 0.159515i
\(63\) 0 0
\(64\) −28511.1 16151.1i −0.870090 0.492893i
\(65\) 25742.7 + 14862.5i 0.755736 + 0.436324i
\(66\) 0 0
\(67\) 41652.4 24048.0i 1.13358 0.654474i 0.188749 0.982025i \(-0.439557\pi\)
0.944833 + 0.327552i \(0.106224\pi\)
\(68\) −19905.2 + 7306.48i −0.522028 + 0.191618i
\(69\) 0 0
\(70\) 68358.6 + 47726.3i 1.66743 + 1.16416i
\(71\) −32192.2 −0.757887 −0.378944 0.925420i \(-0.623713\pi\)
−0.378944 + 0.925420i \(0.623713\pi\)
\(72\) 0 0
\(73\) −34777.5 −0.763820 −0.381910 0.924200i \(-0.624734\pi\)
−0.381910 + 0.924200i \(0.624734\pi\)
\(74\) 27573.1 + 19250.9i 0.585337 + 0.408668i
\(75\) 0 0
\(76\) 18749.9 6882.42i 0.372362 0.136681i
\(77\) −27303.5 + 15763.7i −0.524797 + 0.302991i
\(78\) 0 0
\(79\) −73506.0 42438.7i −1.32512 0.765058i −0.340579 0.940216i \(-0.610623\pi\)
−0.984540 + 0.175158i \(0.943956\pi\)
\(80\) 24305.1 67929.1i 0.424593 1.18667i
\(81\) 0 0
\(82\) 68538.9 + 5902.15i 1.12565 + 0.0969338i
\(83\) 7548.53 13074.4i 0.120273 0.208318i −0.799602 0.600530i \(-0.794956\pi\)
0.919875 + 0.392211i \(0.128290\pi\)
\(84\) 0 0
\(85\) −23342.6 40430.5i −0.350430 0.606962i
\(86\) 41975.4 + 89696.8i 0.611996 + 1.30777i
\(87\) 0 0
\(88\) 19370.6 + 19212.6i 0.266647 + 0.264473i
\(89\) 40174.5i 0.537620i 0.963193 + 0.268810i \(0.0866303\pi\)
−0.963193 + 0.268810i \(0.913370\pi\)
\(90\) 0 0
\(91\) 88253.7i 1.11720i
\(92\) 48667.5 58322.2i 0.599473 0.718396i
\(93\) 0 0
\(94\) 95206.5 44553.8i 1.11134 0.520074i
\(95\) 21987.8 + 38083.9i 0.249961 + 0.432945i
\(96\) 0 0
\(97\) 4298.65 7445.49i 0.0463877 0.0803459i −0.841899 0.539635i \(-0.818562\pi\)
0.888287 + 0.459289i \(0.151896\pi\)
\(98\) 13079.9 151891.i 0.137575 1.59760i
\(99\) 0 0
\(100\) 57980.7 + 10060.5i 0.579807 + 0.100605i
\(101\) 5537.77 + 3197.23i 0.0540171 + 0.0311868i 0.526765 0.850011i \(-0.323405\pi\)
−0.472748 + 0.881198i \(0.656738\pi\)
\(102\) 0 0
\(103\) −74198.4 + 42838.4i −0.689130 + 0.397869i −0.803286 0.595593i \(-0.796917\pi\)
0.114156 + 0.993463i \(0.463584\pi\)
\(104\) −73688.0 + 20068.3i −0.668057 + 0.181940i
\(105\) 0 0
\(106\) −106185. + 152089.i −0.917905 + 1.31472i
\(107\) 10199.1 0.0861200 0.0430600 0.999072i \(-0.486289\pi\)
0.0430600 + 0.999072i \(0.486289\pi\)
\(108\) 0 0
\(109\) 30565.5 0.246414 0.123207 0.992381i \(-0.460682\pi\)
0.123207 + 0.992381i \(0.460682\pi\)
\(110\) −34387.1 + 49252.8i −0.270966 + 0.388105i
\(111\) 0 0
\(112\) −210742. + 38346.7i −1.58747 + 0.288857i
\(113\) 55820.3 32227.9i 0.411241 0.237430i −0.280082 0.959976i \(-0.590362\pi\)
0.691323 + 0.722546i \(0.257028\pi\)
\(114\) 0 0
\(115\) 144838. + 83622.4i 1.02126 + 0.589628i
\(116\) −24917.3 + 143604.i −0.171932 + 0.990880i
\(117\) 0 0
\(118\) −1755.30 + 20383.5i −0.0116050 + 0.134764i
\(119\) −69304.0 + 120038.i −0.448633 + 0.777055i
\(120\) 0 0
\(121\) 69167.7 + 119802.i 0.429477 + 0.743876i
\(122\) −81118.2 + 37960.9i −0.493422 + 0.230907i
\(123\) 0 0
\(124\) −244418. 203957.i −1.42751 1.19120i
\(125\) 90607.8i 0.518670i
\(126\) 0 0
\(127\) 142174.i 0.782189i 0.920350 + 0.391095i \(0.127904\pi\)
−0.920350 + 0.391095i \(0.872096\pi\)
\(128\) 79939.2 + 167241.i 0.431256 + 0.902230i
\(129\) 0 0
\(130\) −71271.3 152299.i −0.369876 0.790384i
\(131\) −44178.9 76520.1i −0.224925 0.389581i 0.731372 0.681978i \(-0.238880\pi\)
−0.956297 + 0.292398i \(0.905547\pi\)
\(132\) 0 0
\(133\) 65281.7 113071.i 0.320009 0.554272i
\(134\) −271069. 23342.8i −1.30412 0.112303i
\(135\) 0 0
\(136\) 115986. + 30570.0i 0.537722 + 0.141725i
\(137\) 88390.4 + 51032.2i 0.402350 + 0.232297i 0.687497 0.726187i \(-0.258709\pi\)
−0.285148 + 0.958484i \(0.592043\pi\)
\(138\) 0 0
\(139\) −78817.2 + 45505.1i −0.346006 + 0.199767i −0.662925 0.748686i \(-0.730685\pi\)
0.316919 + 0.948453i \(0.397352\pi\)
\(140\) −162511. 442733.i −0.700751 1.90907i
\(141\) 0 0
\(142\) 149315. + 104248.i 0.621418 + 0.433859i
\(143\) 63587.4 0.260034
\(144\) 0 0
\(145\) −320902. −1.26751
\(146\) 161307. + 112620.i 0.626282 + 0.437255i
\(147\) 0 0
\(148\) −65550.4 178580.i −0.245992 0.670162i
\(149\) −398601. + 230133.i −1.47087 + 0.849205i −0.999465 0.0327141i \(-0.989585\pi\)
−0.471401 + 0.881919i \(0.656252\pi\)
\(150\) 0 0
\(151\) 157479. + 90920.8i 0.562059 + 0.324505i 0.753971 0.656907i \(-0.228136\pi\)
−0.191913 + 0.981412i \(0.561469\pi\)
\(152\) −109254. 28795.7i −0.383556 0.101092i
\(153\) 0 0
\(154\) 177688. + 15301.4i 0.603748 + 0.0519911i
\(155\) 350447. 606991.i 1.17164 2.02933i
\(156\) 0 0
\(157\) 181731. + 314767.i 0.588408 + 1.01915i 0.994441 + 0.105295i \(0.0335786\pi\)
−0.406033 + 0.913859i \(0.633088\pi\)
\(158\) 203509. + 434877.i 0.648547 + 1.38587i
\(159\) 0 0
\(160\) −332709. + 236364.i −1.02746 + 0.729932i
\(161\) 496549.i 1.50972i
\(162\) 0 0
\(163\) 342002.i 1.00823i 0.863636 + 0.504115i \(0.168181\pi\)
−0.863636 + 0.504115i \(0.831819\pi\)
\(164\) −298787. 249326.i −0.867466 0.723866i
\(165\) 0 0
\(166\) −77351.0 + 36198.0i −0.217869 + 0.101956i
\(167\) −8208.18 14217.0i −0.0227749 0.0394472i 0.854413 0.519594i \(-0.173917\pi\)
−0.877188 + 0.480147i \(0.840583\pi\)
\(168\) 0 0
\(169\) 96647.2 167398.i 0.260299 0.450851i
\(170\) −22658.0 + 263117.i −0.0601312 + 0.698276i
\(171\) 0 0
\(172\) 95773.9 551965.i 0.246846 1.42263i
\(173\) 60123.0 + 34712.1i 0.152730 + 0.0881790i 0.574418 0.818562i \(-0.305229\pi\)
−0.421687 + 0.906741i \(0.638562\pi\)
\(174\) 0 0
\(175\) 333142. 192340.i 0.822308 0.474760i
\(176\) −27629.1 151841.i −0.0672333 0.369494i
\(177\) 0 0
\(178\) 130097. 186339.i 0.307765 0.440813i
\(179\) 146989. 0.342888 0.171444 0.985194i \(-0.445157\pi\)
0.171444 + 0.985194i \(0.445157\pi\)
\(180\) 0 0
\(181\) 238346. 0.540768 0.270384 0.962752i \(-0.412849\pi\)
0.270384 + 0.962752i \(0.412849\pi\)
\(182\) −285793. + 409343.i −0.639548 + 0.916027i
\(183\) 0 0
\(184\) −414597. + 112912.i −0.902780 + 0.245865i
\(185\) 362724. 209419.i 0.779197 0.449869i
\(186\) 0 0
\(187\) −86488.2 49934.0i −0.180864 0.104422i
\(188\) −585871. 101657.i −1.20895 0.209770i
\(189\) 0 0
\(190\) 21343.0 247846.i 0.0428914 0.498079i
\(191\) −223937. + 387870.i −0.444162 + 0.769312i −0.997993 0.0633172i \(-0.979832\pi\)
0.553831 + 0.832629i \(0.313165\pi\)
\(192\) 0 0
\(193\) −29922.0 51826.4i −0.0578226 0.100152i 0.835665 0.549239i \(-0.185082\pi\)
−0.893488 + 0.449088i \(0.851749\pi\)
\(194\) −44049.0 + 20613.6i −0.0840295 + 0.0393233i
\(195\) 0 0
\(196\) −552539. + 662152.i −1.02736 + 1.23117i
\(197\) 834312.i 1.53166i 0.643042 + 0.765831i \(0.277672\pi\)
−0.643042 + 0.765831i \(0.722328\pi\)
\(198\) 0 0
\(199\) 413079.i 0.739435i 0.929144 + 0.369718i \(0.120546\pi\)
−0.929144 + 0.369718i \(0.879454\pi\)
\(200\) −236350. 234423.i −0.417811 0.414404i
\(201\) 0 0
\(202\) −15331.9 32762.6i −0.0264373 0.0564936i
\(203\) 476378. + 825112.i 0.811357 + 1.40531i
\(204\) 0 0
\(205\) 428402. 742013.i 0.711978 1.23318i
\(206\) 482875. + 41582.2i 0.792805 + 0.0682714i
\(207\) 0 0
\(208\) 406771. + 145543.i 0.651915 + 0.233256i
\(209\) 81468.5 + 47035.9i 0.129010 + 0.0744841i
\(210\) 0 0
\(211\) 416461. 240444.i 0.643973 0.371798i −0.142170 0.989842i \(-0.545408\pi\)
0.786143 + 0.618044i \(0.212075\pi\)
\(212\) 985023. 361567.i 1.50524 0.552521i
\(213\) 0 0
\(214\) −47306.1 33028.0i −0.0706127 0.0493001i
\(215\) 1.23344e6 1.81979
\(216\) 0 0
\(217\) −2.08095e6 −2.99994
\(218\) −141770. 98980.7i −0.202043 0.141062i
\(219\) 0 0
\(220\) 318992. 117090.i 0.444348 0.163104i
\(221\) 242105. 139779.i 0.333443 0.192514i
\(222\) 0 0
\(223\) 202627. + 116987.i 0.272858 + 0.157534i 0.630186 0.776445i \(-0.282979\pi\)
−0.357328 + 0.933979i \(0.616312\pi\)
\(224\) 1.10165e6 + 504587.i 1.46698 + 0.671918i
\(225\) 0 0
\(226\) −363272. 31282.8i −0.473109 0.0407412i
\(227\) −60951.8 + 105572.i −0.0785094 + 0.135982i −0.902607 0.430466i \(-0.858349\pi\)
0.824098 + 0.566448i \(0.191683\pi\)
\(228\) 0 0
\(229\) 460471. + 797559.i 0.580248 + 1.00502i 0.995450 + 0.0952893i \(0.0303776\pi\)
−0.415202 + 0.909729i \(0.636289\pi\)
\(230\) −401000. 856892.i −0.499833 1.06809i
\(231\) 0 0
\(232\) 580607. 585380.i 0.708210 0.714033i
\(233\) 564143.i 0.680768i 0.940287 + 0.340384i \(0.110557\pi\)
−0.940287 + 0.340384i \(0.889443\pi\)
\(234\) 0 0
\(235\) 1.30920e6i 1.54646i
\(236\) 74149.5 88859.4i 0.0866619 0.103854i
\(237\) 0 0
\(238\) 710170. 332338.i 0.812681 0.380310i
\(239\) −812725. 1.40768e6i −0.920341 1.59408i −0.798887 0.601481i \(-0.794578\pi\)
−0.121454 0.992597i \(1.46124\pi\)
\(240\) 0 0
\(241\) 595736. 1.03184e6i 0.660710 1.14438i −0.319719 0.947512i \(-0.603589\pi\)
0.980429 0.196871i \(-0.0630781\pi\)
\(242\) 67139.3 779658.i 0.0736950 0.855787i
\(243\) 0 0
\(244\) 499175. + 86614.1i 0.536758 + 0.0931352i
\(245\) −1.64440e6 949394.i −1.75022 1.01049i
\(246\) 0 0
\(247\) −228053. + 131666.i −0.237845 + 0.137320i
\(248\) 473195. + 1.73750e6i 0.488552 + 1.79389i
\(249\) 0 0
\(250\) −293416. + 420262.i −0.296917 + 0.425275i
\(251\) −1.48383e6 −1.48662 −0.743311 0.668946i \(-0.766746\pi\)
−0.743311 + 0.668946i \(0.766746\pi\)
\(252\) 0 0
\(253\) 357767. 0.351398
\(254\) 460405. 659440.i 0.447771 0.641344i
\(255\) 0 0
\(256\) 170800. 1.03457e6i 0.162887 0.986645i
\(257\) 1.18845e6 686154.i 1.12240 0.648020i 0.180390 0.983595i \(-0.442264\pi\)
0.942014 + 0.335575i \(0.108931\pi\)
\(258\) 0 0
\(259\) −1.07693e6 621764.i −0.997556 0.575939i
\(260\) −162617. + 937199.i −0.149188 + 0.859802i
\(261\) 0 0
\(262\) −42883.3 + 497984.i −0.0385954 + 0.448190i
\(263\) −85328.1 + 147793.i −0.0760681 + 0.131754i −0.901550 0.432674i \(-0.857570\pi\)
0.825482 + 0.564428i \(0.190903\pi\)
\(264\) 0 0
\(265\) 1.15512e6 + 2.00073e6i 1.01045 + 1.75015i
\(266\) −668952. + 313050.i −0.579684 + 0.271275i
\(267\) 0 0
\(268\) 1.18169e6 + 986076.i 1.00500 + 0.838636i
\(269\) 28534.0i 0.0240427i 0.999928 + 0.0120213i \(0.00382660\pi\)
−0.999928 + 0.0120213i \(0.996173\pi\)
\(270\) 0 0
\(271\) 485769.i 0.401797i −0.979612 0.200899i \(-0.935614\pi\)
0.979612 0.200899i \(-0.0643862\pi\)
\(272\) −438976. 517390.i −0.359765 0.424029i
\(273\) 0 0
\(274\) −244718. 522936.i −0.196920 0.420796i
\(275\) 138582. + 240031.i 0.110503 + 0.191397i
\(276\) 0 0
\(277\) −696662. + 1.20665e6i −0.545535 + 0.944894i 0.453038 + 0.891491i \(0.350340\pi\)
−0.998573 + 0.0534030i \(0.982993\pi\)
\(278\) 512934. + 44170.7i 0.398061 + 0.0342785i
\(279\) 0 0
\(280\) −679940. + 2.57977e6i −0.518293 + 1.96646i
\(281\) −691310. 399128.i −0.522285 0.301541i 0.215584 0.976485i \(-0.430834\pi\)
−0.737869 + 0.674944i \(0.764168\pi\)
\(282\) 0 0
\(283\) −1.50272e6 + 867593.i −1.11535 + 0.643947i −0.940209 0.340597i \(-0.889371\pi\)
−0.175139 + 0.984544i \(0.556038\pi\)
\(284\) −354973. 967059.i −0.261155 0.711471i
\(285\) 0 0
\(286\) −294934. 205916.i −0.213211 0.148859i
\(287\) −2.54385e6 −1.82300
\(288\) 0 0
\(289\) 980793. 0.690769
\(290\) 1.48842e6 + 1.03918e6i 1.03928 + 0.725597i
\(291\) 0 0
\(292\) −383480. 1.04472e6i −0.263200 0.717040i
\(293\) 376330. 217274.i 0.256094 0.147856i −0.366457 0.930435i \(-0.619429\pi\)
0.622551 + 0.782579i \(0.286096\pi\)
\(294\) 0 0
\(295\) 220675. + 127407.i 0.147638 + 0.0852387i
\(296\) −274260. + 1.04057e6i −0.181942 + 0.690308i
\(297\) 0 0
\(298\) 2.59405e6 + 223384.i 1.69215 + 0.145717i
\(299\) −500745. + 867315.i −0.323920 + 0.561047i
\(300\) 0 0
\(301\) −1.83104e6 3.17145e6i −1.16488 2.01763i
\(302\) −435999. 931681.i −0.275086 0.587827i
\(303\) 0 0
\(304\) 413498. + 487361.i 0.256620 + 0.302459i
\(305\) 1.11547e6i 0.686609i
\(306\) 0 0
\(307\) 48971.1i 0.0296547i 0.999890 + 0.0148274i \(0.00471987\pi\)
−0.999890 + 0.0148274i \(0.995280\pi\)
\(308\) −774610. 646380.i −0.465271 0.388250i
\(309\) 0 0
\(310\) −3.59109e6 + 1.68052e6i −2.12237 + 0.993206i
\(311\) 36344.9 + 62951.1i 0.0213080 + 0.0369065i 0.876483 0.481433i \(-0.159884\pi\)
−0.855175 + 0.518340i \(0.826550\pi\)
\(312\) 0 0
\(313\) −319768. + 553854.i −0.184490 + 0.319547i −0.943405 0.331644i \(-0.892397\pi\)
0.758914 + 0.651191i \(0.225730\pi\)
\(314\) 176401. 2.04847e6i 0.100967 1.17248i
\(315\) 0 0
\(316\) 464340. 2.67609e6i 0.261588 1.50759i
\(317\) 2.43119e6 + 1.40365e6i 1.35885 + 0.784531i 0.989469 0.144748i \(-0.0462373\pi\)
0.369379 + 0.929279i \(0.379571\pi\)
\(318\) 0 0
\(319\) −594498. + 343234.i −0.327095 + 0.188848i
\(320\) 2.30861e6 18902.0i 1.26030 0.0103189i
\(321\) 0 0
\(322\) −1.60798e6 + 2.30312e6i −0.864254 + 1.23787i
\(323\) 413581. 0.220574
\(324\) 0 0
\(325\) −775859. −0.407450
\(326\) 1.10751e6 1.58629e6i 0.577170 0.826683i
\(327\) 0 0
\(328\) 578454. + 2.12400e6i 0.296882 + 1.09011i
\(329\) −3.36626e6 + 1.94351e6i −1.71458 + 0.989915i
\(330\) 0 0
\(331\) −2.68009e6 1.54735e6i −1.34456 0.776280i −0.357084 0.934072i \(-0.616229\pi\)
−0.987472 + 0.157793i \(0.949562\pi\)
\(332\) 475994. + 82591.7i 0.237004 + 0.0411236i
\(333\) 0 0
\(334\) −7967.47 + 92522.6i −0.00390800 + 0.0453818i
\(335\) −1.69431e6 + 2.93464e6i −0.824863 + 1.42870i
\(336\) 0 0
\(337\) 66234.5 + 114721.i 0.0317694 + 0.0550263i 0.881473 0.472234i \(-0.156552\pi\)
−0.849704 + 0.527261i \(0.823219\pi\)
\(338\) −990360. + 463459.i −0.471521 + 0.220658i
\(339\) 0 0
\(340\) 957149. 1.14703e6i 0.449037 0.538117i
\(341\) 1.49934e6i 0.698255i
\(342\) 0 0
\(343\) 2.12177e6i 0.973786i
\(344\) −2.23166e6 + 2.25001e6i −1.01679 + 1.02515i
\(345\) 0 0
\(346\) −166457. 355700.i −0.0747501 0.159733i
\(347\) −840739. 1.45620e6i −0.374833 0.649229i 0.615469 0.788161i \(-0.288967\pi\)
−0.990302 + 0.138932i \(0.955633\pi\)
\(348\) 0 0
\(349\) −8603.35 + 14901.4i −0.00378097 + 0.00654884i −0.867910 0.496722i \(-0.834537\pi\)
0.864129 + 0.503271i \(0.167870\pi\)
\(350\) −2.16805e6 186699.i −0.946019 0.0814653i
\(351\) 0 0
\(352\) −363558. + 793748.i −0.156393 + 0.341449i
\(353\) 1.66268e6 + 959951.i 0.710187 + 0.410027i 0.811130 0.584865i \(-0.198853\pi\)
−0.100943 + 0.994892i \(0.532186\pi\)
\(354\) 0 0
\(355\) 1.96425e6 1.13406e6i 0.827227 0.477600i
\(356\) −1.20685e6 + 442991.i −0.504694 + 0.185255i
\(357\) 0 0
\(358\) −681772. 475997.i −0.281146 0.196289i
\(359\) 207171. 0.0848386 0.0424193 0.999100i \(-0.486493\pi\)
0.0424193 + 0.999100i \(0.486493\pi\)
\(360\) 0 0
\(361\) 2.08652e6 0.842665
\(362\) −1.10551e6 771839.i −0.443394 0.309567i
\(363\) 0 0
\(364\) 2.65116e6 973145.i 1.04877 0.384967i
\(365\) 2.12199e6 1.22513e6i 0.833703 0.481338i
\(366\) 0 0
\(367\) 1.53243e6 + 884750.i 0.593904 + 0.342891i 0.766640 0.642078i \(-0.221927\pi\)
−0.172736 + 0.984968i \(0.555261\pi\)
\(368\) 2.28865e6 + 818881.i 0.880967 + 0.315211i
\(369\) 0 0
\(370\) −2.36057e6 203277.i −0.896421 0.0771942i
\(371\) 3.42956e6 5.94017e6i 1.29361 2.24060i
\(372\) 0 0
\(373\) 171024. + 296222.i 0.0636481 + 0.110242i 0.896093 0.443865i \(-0.146393\pi\)
−0.832445 + 0.554107i \(0.813060\pi\)
\(374\) 239452. + 511682.i 0.0885196 + 0.189156i
\(375\) 0 0
\(376\) 2.38822e6 + 2.36874e6i 0.871172 + 0.864068i
\(377\) 1.92161e6i 0.696326i
\(378\) 0 0
\(379\) 1.91370e6i 0.684345i −0.939637 0.342172i \(-0.888837\pi\)
0.939637 0.342172i \(-0.111163\pi\)
\(380\) −901597. + 1.08046e6i −0.320297 + 0.383838i
\(381\) 0 0
\(382\) 2.29472e6 1.07386e6i 0.804583 0.376521i
\(383\) 1.50852e6 + 2.61283e6i 0.525477 + 0.910153i 0.999560 + 0.0296726i \(0.00944646\pi\)
−0.474083 + 0.880480i \(0.657220\pi\)
\(384\) 0 0
\(385\) 1.11064e6 1.92368e6i 0.381874 0.661425i
\(386\) −29044.5 + 337280.i −0.00992192 + 0.115219i
\(387\) 0 0
\(388\) 271064. + 47033.4i 0.0914096 + 0.0158609i
\(389\) −2.16211e6 1.24829e6i −0.724442 0.418257i 0.0919434 0.995764i \(-0.470692\pi\)
−0.816385 + 0.577507i \(0.804025\pi\)
\(390\) 0 0
\(391\) 1.36217e6 786451.i 0.450599 0.260154i
\(392\) 4.70706e6 1.28193e6i 1.54716 0.421356i
\(393\) 0 0
\(394\) 2.70176e6 3.86975e6i 0.876812 1.25586i
\(395\) 5.98008e6 1.92848
\(396\) 0 0
\(397\) −160060. −0.0509692 −0.0254846 0.999675i \(-0.508113\pi\)
−0.0254846 + 0.999675i \(0.508113\pi\)
\(398\) 1.33768e6 1.91596e6i 0.423296 0.606288i
\(399\) 0 0
\(400\) 337115. + 1.85268e6i 0.105349 + 0.578964i
\(401\) −2.51150e6 + 1.45002e6i −0.779960 + 0.450310i −0.836416 0.548095i \(-0.815353\pi\)
0.0564561 + 0.998405i \(0.482020\pi\)
\(402\) 0 0
\(403\) 3.63476e6 + 2.09853e6i 1.11484 + 0.643655i
\(404\) −34982.3 + 201610.i −0.0106634 + 0.0614553i
\(405\) 0 0
\(406\) 462408. 5.36973e6i 0.139223 1.61673i
\(407\) 447985. 775933.i 0.134053 0.232187i
\(408\) 0 0
\(409\) −565751. 979909.i −0.167231 0.289653i 0.770214 0.637785i \(-0.220149\pi\)
−0.937445 + 0.348133i \(0.886816\pi\)
\(410\) −4.38990e6 + 2.05434e6i −1.28972 + 0.603550i
\(411\) 0 0
\(412\) −2.10504e6 1.75657e6i −0.610965 0.509826i
\(413\) 756540.i 0.218251i
\(414\) 0 0
\(415\) 1.06367e6i 0.303170i
\(416\) −1.41539e6 1.99231e6i −0.400998 0.564449i
\(417\) 0 0
\(418\) −225554. 481984.i −0.0631408 0.134925i
\(419\) 257000. + 445137.i 0.0715152 + 0.123868i 0.899566 0.436786i \(-0.143883\pi\)
−0.828050 + 0.560654i \(0.810550\pi\)
\(420\) 0 0
\(421\) −3.24121e6 + 5.61394e6i −0.891255 + 1.54370i −0.0528829 + 0.998601i \(0.516841\pi\)
−0.838372 + 0.545098i \(0.816492\pi\)
\(422\) −2.71028e6 233392.i −0.740854 0.0637978i
\(423\) 0 0
\(424\) −5.73965e6 1.51278e6i −1.55050 0.408658i
\(425\) 1.05528e6 + 609268.i 0.283398 + 0.163620i
\(426\) 0 0
\(427\) 2.86814e6 1.65592e6i 0.761255 0.439511i
\(428\) 112463. + 306384.i 0.0296755 + 0.0808457i
\(429\) 0 0
\(430\) −5.72100e6 3.99426e6i −1.49211 1.04175i
\(431\) −680530. −0.176463 −0.0882316 0.996100i \(-0.528122\pi\)
−0.0882316 + 0.996100i \(0.528122\pi\)
\(432\) 0 0
\(433\) −1.78685e6 −0.458003 −0.229002 0.973426i \(-0.573546\pi\)
−0.229002 + 0.973426i \(0.573546\pi\)
\(434\) 9.65197e6 + 6.73877e6i 2.45975 + 1.71734i
\(435\) 0 0
\(436\) 337036. + 918193.i 0.0849102 + 0.231323i
\(437\) −1.28311e6 + 740806.i −0.321412 + 0.185567i
\(438\) 0 0
\(439\) 5.72585e6 + 3.30582e6i 1.41801 + 0.818687i 0.996124 0.0879624i \(-0.0280355\pi\)
0.421884 + 0.906650i \(0.361369\pi\)
\(440\) −1.85874e6 489901.i −0.457706 0.120636i
\(441\) 0 0
\(442\) −1.57559e6 135680.i −0.383608 0.0330339i
\(443\) 1.27077e6 2.20104e6i 0.307650 0.532866i −0.670198 0.742183i \(-0.733791\pi\)
0.977848 + 0.209317i \(0.0671240\pi\)
\(444\) 0 0
\(445\) −1.41526e6 2.45129e6i −0.338793 0.586807i
\(446\) −560996. 1.19879e6i −0.133543 0.285367i
\(447\) 0 0
\(448\) −3.47573e6 5.90790e6i −0.818183 1.39071i
\(449\) 4.29742e6i 1.00599i −0.864290 0.502993i \(-0.832232\pi\)
0.864290 0.502993i \(-0.167768\pi\)
\(450\) 0 0
\(451\) 1.83286e6i 0.424314i
\(452\) 1.58364e6 + 1.32149e6i 0.364595 + 0.304240i
\(453\) 0 0
\(454\) 624583. 292286.i 0.142217 0.0665532i
\(455\) 3.10898e6 + 5.38491e6i 0.704027 + 1.21941i
\(456\) 0 0
\(457\) 795252. 1.37742e6i 0.178121 0.308514i −0.763116 0.646261i \(-0.776332\pi\)
0.941237 + 0.337747i \(0.109665\pi\)
\(458\) 446967. 5.19042e6i 0.0995662 1.15622i
\(459\) 0 0
\(460\) −914948. + 5.27304e6i −0.201605 + 1.16189i
\(461\) 3.92509e6 + 2.26615e6i 0.860195 + 0.496634i 0.864078 0.503359i \(-0.167903\pi\)
−0.00388260 + 0.999992i \(0.501236\pi\)
\(462\) 0 0
\(463\) −6.33289e6 + 3.65630e6i −1.37293 + 0.792664i −0.991296 0.131648i \(-0.957973\pi\)
−0.381637 + 0.924312i \(0.624640\pi\)
\(464\) −4.58864e6 + 834951.i −0.989440 + 0.180039i
\(465\) 0 0
\(466\) 1.82687e6 2.61663e6i 0.389711 0.558185i
\(467\) 5.59542e6 1.18724 0.593622 0.804744i \(-0.297697\pi\)
0.593622 + 0.804744i \(0.297697\pi\)
\(468\) 0 0
\(469\) 1.00608e7 2.11204
\(470\) −4.23961e6 + 6.07241e6i −0.885282 + 1.26799i
\(471\) 0 0
\(472\) −631678. + 172032.i −0.130509 + 0.0355431i
\(473\) 2.28505e6 1.31928e6i 0.469617 0.271133i
\(474\) 0 0
\(475\) −994036. 573907.i −0.202147 0.116710i
\(476\) −4.37016e6 758285.i −0.884056 0.153396i
\(477\) 0 0
\(478\) −788891. + 9.16103e6i −0.157924 + 1.83390i
\(479\) −3.79751e6 + 6.57748e6i −0.756241 + 1.30985i 0.188515 + 0.982070i \(0.439633\pi\)
−0.944755 + 0.327777i \(0.893701\pi\)
\(480\) 0 0
\(481\) 1.25403e6 + 2.17205e6i 0.247142 + 0.428063i
\(482\) −6.10460e6 + 2.85677e6i −1.19685 + 0.560090i
\(483\) 0 0
\(484\) −2.83618e6 + 3.39883e6i −0.550327 + 0.659501i
\(485\) 605727.i 0.116929i
\(486\) 0 0
\(487\) 9.63136e6i 1.84020i 0.391682 + 0.920101i \(0.371893\pi\)
−0.391682 + 0.920101i \(0.628107\pi\)
\(488\) −2.03482e6 2.01822e6i −0.386790 0.383636i
\(489\) 0 0
\(490\) 4.55269e6 + 9.72860e6i 0.856600 + 1.83046i
\(491\) −3.74298e6 6.48304e6i −0.700671 1.21360i −0.968231 0.250056i \(-0.919551\pi\)
0.267560 0.963541i \(1.58622\pi\)
\(492\) 0 0
\(493\) −1.50901e6 + 2.61368e6i −0.279624 + 0.484323i
\(494\) 1.48414e6 + 127805.i 0.273627 + 0.0235630i
\(495\) 0 0
\(496\) 3.43179e6 9.59132e6i 0.626348 1.75055i
\(497\) −5.83184e6 3.36702e6i −1.05905 0.611441i
\(498\) 0 0
\(499\) −983698. + 567938.i −0.176852 + 0.102106i −0.585813 0.810446i \(-0.699225\pi\)
0.408961 + 0.912552i \(0.365891\pi\)
\(500\) 2.72188e6 999103.i 0.486904 0.178725i
\(501\) 0 0
\(502\) 6.88239e6 + 4.80512e6i 1.21893 + 0.851029i
\(503\) −9.15158e6 −1.61278 −0.806391 0.591382i \(-0.798583\pi\)
−0.806391 + 0.591382i \(0.798583\pi\)
\(504\) 0 0
\(505\) −450525. −0.0786123
\(506\) −1.65941e6 1.15856e6i −0.288123 0.201160i
\(507\) 0 0
\(508\) −4.27094e6 + 1.56771e6i −0.734285 + 0.269530i
\(509\) −659417. + 380714.i −0.112815 + 0.0651336i −0.555346 0.831620i \(-0.687414\pi\)
0.442531 + 0.896753i \(0.354081\pi\)
\(510\) 0 0
\(511\) −6.30019e6 3.63741e6i −1.06734 0.616227i
\(512\) −4.14248e6 + 4.24550e6i −0.698370 + 0.715737i
\(513\) 0 0
\(514\) −7.73432e6 666032.i −1.29126 0.111195i
\(515\) 3.01820e6 5.22768e6i 0.501453 0.868542i
\(516\) 0 0
\(517\) −1.40031e6 2.42541e6i −0.230409 0.399080i
\(518\) 2.98159e6 + 6.37133e6i 0.488229 + 1.04329i
\(519\) 0 0
\(520\) 3.78920e6 3.82035e6i 0.614525 0.619577i
\(521\) 8.50821e6i 1.37323i 0.727020 + 0.686616i \(0.240905\pi\)
−0.727020 + 0.686616i \(0.759095\pi\)
\(522\) 0 0
\(523\) 8.02433e6i 1.28279i −0.767212 0.641394i \(-0.778356\pi\)
0.767212 0.641394i \(-0.221644\pi\)
\(524\) 1.81153e6 2.17091e6i 0.288216 0.345392i
\(525\) 0 0
\(526\) 874371. 409179.i 0.137794 0.0644836i
\(527\) −3.29588e6 5.70863e6i −0.516945 0.895376i
\(528\) 0 0
\(529\) 400790. 694188.i 0.0622698 0.107854i
\(530\) 1.12125e6 1.30205e7i 0.173385 2.01344i
\(531\) 0 0
\(532\) 4.11652e6 + 714275.i 0.630596 + 0.109417i
\(533\) 4.44330e6 + 2.56534e6i 0.677466 + 0.391135i
\(534\) 0 0
\(535\) −622313. + 359292.i −0.0939992 + 0.0542705i
\(536\) −2.28777e6 8.40036e6i −0.343954 1.26295i
\(537\) 0 0
\(538\) 92402.1 132348.i 0.0137634 0.0197134i
\(539\) −4.06185e6 −0.602216
\(540\) 0 0
\(541\) −7.93678e6 −1.16587 −0.582937 0.812518i \(-0.698096\pi\)
−0.582937 + 0.812518i \(0.698096\pi\)
\(542\) −1.57307e6 + 2.25312e6i −0.230012 + 0.329447i
\(543\) 0 0
\(544\) 360610. + 3.82132e6i 0.0522446 + 0.553626i
\(545\) −1.86499e6 + 1.07675e6i −0.268959 + 0.155283i
\(546\) 0 0
\(547\) −5.32459e6 3.07415e6i −0.760883 0.439296i 0.0687298 0.997635i \(-0.478105\pi\)
−0.829613 + 0.558339i \(0.811439\pi\)
\(548\) −558366. + 3.21798e6i −0.0794268 + 0.457754i
\(549\) 0 0
\(550\) 134518. 1.56210e6i 0.0189615 0.220192i
\(551\) 1.42143e6 2.46198e6i 0.199455 0.345466i
\(552\) 0 0
\(553\) −8.87742e6 1.53761e7i −1.23445 2.13813i
\(554\) 7.13881e6 3.34075e6i 0.988215 0.462455i
\(555\) 0 0
\(556\) −2.23607e6 1.86591e6i −0.306760 0.255979i
\(557\) 6.19751e6i 0.846407i 0.906035 + 0.423203i \(0.139094\pi\)
−0.906035 + 0.423203i \(0.860906\pi\)
\(558\) 0 0
\(559\) 7.38604e6i 0.999728i
\(560\) 1.15078e7 9.76374e6i 1.55068 1.31567i
\(561\) 0 0
\(562\) 1.91397e6 + 4.08993e6i 0.255619 + 0.546230i
\(563\) 744431. + 1.28939e6i 0.0989814 + 0.171441i 0.911263 0.411824i \(-0.135108\pi\)
−0.812282 + 0.583265i \(0.801775\pi\)
\(564\) 0 0
\(565\) −2.27063e6 + 3.93284e6i −0.299244 + 0.518305i
\(566\) 9.77950e6 + 842150.i 1.28315 + 0.110497i
\(567\) 0 0
\(568\) −1.48519e6 + 5.63497e6i −0.193157 + 0.732860i
\(569\) −149856. 86519.3i −0.0194041 0.0112029i 0.490267 0.871573i \(-0.336899\pi\)
−0.509671 + 0.860370i \(0.670233\pi\)
\(570\) 0 0
\(571\) 5.22869e6 3.01878e6i 0.671123 0.387473i −0.125379 0.992109i \(-0.540015\pi\)
0.796502 + 0.604636i \(0.206681\pi\)
\(572\) 701157. + 1.91018e6i 0.0896035 + 0.244109i
\(573\) 0 0
\(574\) 1.17990e7 + 8.23777e6i 1.49474 + 1.04359i
\(575\) −4.36528e6 −0.550608
\(576\) 0 0
\(577\) 1.58937e7 1.98740 0.993698 0.112090i \(-0.0357546\pi\)
0.993698 + 0.112090i \(0.0357546\pi\)
\(578\) −4.54916e6 3.17611e6i −0.566385 0.395436i
\(579\) 0 0
\(580\) −3.53848e6 9.63995e6i −0.436764 1.18988i
\(581\) 2.73494e6 1.57902e6i 0.336130 0.194065i
\(582\) 0 0
\(583\) 4.27993e6 + 2.47102e6i 0.521514 + 0.301096i
\(584\) −1.60446e6 + 6.08751e6i −0.194669 + 0.738597i
\(585\) 0 0
\(586\) −2.44911e6 210902.i −0.294622 0.0253710i
\(587\) −7.04599e6 + 1.22040e7i −0.844008 + 1.46186i 0.0424722 + 0.999098i \(0.486477\pi\)
−0.886480 + 0.462767i \(0.846857\pi\)
\(588\) 0 0
\(589\) 3.10459e6 + 5.37730e6i 0.368736 + 0.638670i
\(590\) −610962. 1.30556e6i −0.0722576 0.154407i
\(591\) 0 0
\(592\) 4.64178e6 3.93829e6i 0.544353 0.461853i
\(593\) 1.07696e7i 1.25766i −0.777544 0.628828i \(-0.783535\pi\)
0.777544 0.628828i \(-0.216465\pi\)
\(594\) 0 0
\(595\) 9.76569e6i 1.13086i
\(596\) −1.13085e7 9.43646e6i −1.30403 1.08816i
\(597\) 0 0
\(598\) 5.13121e6 2.40125e6i 0.586769 0.274590i
\(599\) 5.44302e6 + 9.42759e6i 0.619831 + 1.07358i 0.989516 + 0.144422i \(0.0461321\pi\)
−0.369685 + 0.929157i \(0.620535\pi\)
\(600\) 0 0
\(601\) −6.66377e6 + 1.15420e7i −0.752548 + 1.30345i 0.194036 + 0.980994i \(0.437842\pi\)
−0.946584 + 0.322457i \(0.895491\pi\)
\(602\) −1.77734e6 + 2.06395e7i −0.199885 + 2.32117i
\(603\) 0 0
\(604\) −994804. + 5.73327e6i −0.110955 + 0.639455i
\(605\) −8.44070e6 4.87324e6i −0.937540 0.541289i
\(606\) 0 0
\(607\) 1.90927e6 1.10232e6i 0.210327 0.121432i −0.391136 0.920333i \(-0.627918\pi\)
0.601463 + 0.798900i \(0.294585\pi\)
\(608\) −339681. 3.59954e6i −0.0372659 0.394900i
\(609\) 0 0
\(610\) 3.61225e6 5.17384e6i 0.393055 0.562974i
\(611\) 7.83973e6 0.849568
\(612\) 0 0
\(613\) 2.50240e6 0.268971 0.134485 0.990916i \(-0.457062\pi\)
0.134485 + 0.990916i \(0.457062\pi\)
\(614\) 158584. 227140.i 0.0169761 0.0243149i
\(615\) 0 0
\(616\) 1.49965e6 + 5.50650e6i 0.159235 + 0.584688i
\(617\) 6.29534e6 3.63461e6i 0.665742 0.384366i −0.128719 0.991681i \(-0.541087\pi\)
0.794461 + 0.607315i \(0.207753\pi\)
\(618\) 0 0
\(619\) −9.08516e6 5.24532e6i −0.953028 0.550231i −0.0590081 0.998258i \(-0.518794\pi\)
−0.894020 + 0.448026i \(0.852127\pi\)
\(620\) 2.20984e7 + 3.83439e6i 2.30877 + 0.400605i
\(621\) 0 0
\(622\) 35279.0 409679.i 0.00365629 0.0424588i
\(623\) −4.20189e6 + 7.27789e6i −0.433735 + 0.751252i
\(624\) 0 0
\(625\) 6.06530e6 + 1.05054e7i 0.621087 + 1.07575i
\(626\) 3.27671e6 1.53340e6i 0.334197 0.156394i
\(627\) 0 0
\(628\) −7.45176e6 + 8.93005e6i −0.753980 + 0.903555i
\(629\) 3.93908e6i 0.396980i
\(630\) 0 0
\(631\) 1.25868e7i 1.25846i −0.777218 0.629231i \(-0.783370\pi\)
0.777218 0.629231i \(-0.216630\pi\)
\(632\) −1.08197e7 + 1.09087e7i −1.07752 + 1.08638i
\(633\) 0 0
\(634\) −6.73101e6 1.43834e7i −0.665054 1.42115i
\(635\) −5.00848e6 8.67494e6i −0.492914 0.853753i
\(636\) 0 0
\(637\) 5.68513e6 9.84693e6i 0.555126 0.961506i
\(638\) 3.86893e6 + 333168.i 0.376304 + 0.0324050i
\(639\) 0 0
\(640\) −1.07691e7 7.38832e6i −1.03927 0.713010i
\(641\) 4.75044e6 + 2.74267e6i 0.456655 + 0.263650i 0.710637 0.703559i \(-0.248407\pi\)
−0.253981 + 0.967209i \(0.581740\pi\)
\(642\) 0 0
\(643\) −1.03225e7 + 5.95970e6i −0.984595 + 0.568456i −0.903654 0.428263i \(-0.859126\pi\)
−0.0809407 + 0.996719i \(0.525792\pi\)
\(644\) 1.49164e7 5.47529e6i 1.41726 0.520226i
\(645\) 0 0
\(646\) −1.91829e6 1.33930e6i −0.180856 0.126269i
\(647\) −1.43126e7 −1.34418 −0.672092 0.740468i \(-0.734604\pi\)
−0.672092 + 0.740468i \(0.734604\pi\)
\(648\) 0 0
\(649\) 545092. 0.0507993
\(650\) 3.59863e6 + 2.51247e6i 0.334082 + 0.233248i
\(651\) 0 0
\(652\) −1.02738e7 + 3.77115e6i −0.946482 + 0.347420i
\(653\) 3.09615e6 1.78757e6i 0.284145 0.164051i −0.351154 0.936318i \(-0.614211\pi\)
0.635298 + 0.772267i \(0.280877\pi\)
\(654\) 0 0
\(655\) 5.39126e6 + 3.11265e6i 0.491006 + 0.283483i
\(656\) 4.19517e6 1.17249e7i 0.380618 1.06377i
\(657\) 0 0
\(658\) 2.19073e7 + 1.88652e6i 1.97253 + 0.169862i
\(659\) 1.66026e6 2.87565e6i 0.148923 0.257942i −0.781907 0.623396i \(-0.785753\pi\)
0.930830 + 0.365453i \(0.119086\pi\)
\(660\) 0 0
\(661\) −4.26668e6 7.39011e6i −0.379828 0.657881i 0.611209 0.791469i \(-0.290683\pi\)
−0.991037 + 0.133588i \(0.957350\pi\)
\(662\) 7.42011e6 + 1.58559e7i 0.658060 + 1.40620i
\(663\) 0 0
\(664\) −1.94032e6 1.92450e6i −0.170786 0.169394i
\(665\) 9.19890e6i 0.806644i
\(666\) 0 0
\(667\) 1.08117e7i 0.940981i
\(668\) 336572. 403341.i 0.0291835 0.0349729i
\(669\) 0 0
\(670\) 1.73619e7 8.12486e6i 1.49421 0.699244i
\(671\) 1.19310e6 + 2.06651e6i 0.102299 + 0.177187i
\(672\) 0 0
\(673\) −9.81452e6 + 1.69992e7i −0.835279 + 1.44675i 0.0585245 + 0.998286i \(0.481360\pi\)
−0.893803 + 0.448459i \(0.851973\pi\)
\(674\) 64292.1 746594.i 0.00545140 0.0633046i
\(675\) 0 0
\(676\) 6.09436e6 + 1.05746e6i 0.512934 + 0.0890013i
\(677\) −1.67817e7 9.68890e6i −1.40722 0.812461i −0.412104 0.911137i \(-0.635206\pi\)
−0.995120 + 0.0986755i \(0.968539\pi\)
\(678\) 0 0
\(679\) 1.55746e6 899202.i 0.129641 0.0748484i
\(680\) −8.15393e6 + 2.22065e6i −0.676230 + 0.184166i
\(681\) 0 0
\(682\) −4.85533e6 + 6.95430e6i −0.399722 + 0.572523i
\(683\) 1.79967e7 1.47618 0.738092 0.674700i \(-0.235727\pi\)
0.738092 + 0.674700i \(0.235727\pi\)
\(684\) 0 0
\(685\) −7.19100e6 −0.585548
\(686\) 6.87096e6 9.84131e6i 0.557452 0.798440i
\(687\) 0 0
\(688\) 1.76372e7 3.20927e6i 1.42056 0.258485i
\(689\) −1.19807e7 + 6.91707e6i −0.961468 + 0.555104i
\(690\) 0 0
\(691\) −9.29000e6 5.36359e6i −0.740152 0.427327i 0.0819727 0.996635i \(-0.473878\pi\)
−0.822124 + 0.569308i \(0.807211\pi\)
\(692\) −379800. + 2.18887e6i −0.0301501 + 0.173762i
\(693\) 0 0
\(694\) −816083. + 9.47680e6i −0.0643185 + 0.746901i
\(695\) 3.20608e6 5.55310e6i 0.251775 0.436088i
\(696\) 0 0
\(697\) −4.02903e6 6.97848e6i −0.314137 0.544100i
\(698\) 88159.9 41256.2i 0.00684909 0.00320517i
\(699\) 0 0
\(700\) 9.45137e6 + 7.88679e6i 0.729038 + 0.608352i
\(701\) 3.82293e6i 0.293834i 0.989149 + 0.146917i \(0.0469350\pi\)
−0.989149 + 0.146917i \(0.953065\pi\)
\(702\) 0 0
\(703\) 3.71046e6i 0.283165i
\(704\) 4.25668e6 2.50428e6i 0.323697 0.190437i
\(705\) 0 0
\(706\) −4.60332e6 9.83678e6i −0.347584 0.742748i
\(707\) 668804. + 1.15840e6i 0.0503211 + 0.0871587i
\(708\) 0 0
\(709\) 1.02820e7 1.78090e7i 0.768181 1.33053i −0.170368 0.985381i \(-0.554496\pi\)
0.938549 0.345147i \(-0.112171\pi\)
\(710\) −1.27831e7 1.10080e6i −0.951678 0.0819526i
\(711\) 0 0
\(712\) 7.03220e6 + 1.85345e6i 0.519866 + 0.137019i
\(713\) 2.04506e7 + 1.18072e7i 1.50654 + 0.869804i
\(714\) 0 0
\(715\) −3.87986e6 + 2.24004e6i −0.283825 + 0.163867i
\(716\) 1.62080e6 + 4.41558e6i 0.118154 + 0.321888i
\(717\) 0 0
\(718\) −960912. 670886.i −0.0695621 0.0485666i
\(719\) 482918. 0.0348378 0.0174189 0.999848i \(-0.494455\pi\)
0.0174189 + 0.999848i \(0.494455\pi\)
\(720\) 0 0
\(721\) −1.79221e7 −1.28396
\(722\) −9.67780e6 6.75681e6i −0.690930 0.482390i
\(723\) 0 0
\(724\) 2.62816e6 + 7.15996e6i 0.186340 + 0.507649i
\(725\) 7.25375e6 4.18796e6i 0.512528 0.295908i
\(726\) 0 0
\(727\) 2.15466e7 + 1.24399e7i 1.51197 + 0.872935i 0.999902 + 0.0139889i \(0.00445295\pi\)
0.512066 + 0.858946i \(0.328880\pi\)
\(728\) −1.54481e7 4.07159e6i −1.08030 0.284732i
\(729\) 0 0
\(730\) −1.38097e7 1.18920e6i −0.959127 0.0825941i
\(731\) 5.80012e6 1.00461e7i 0.401461 0.695351i
\(732\) 0 0
\(733\) 5.66177e6 + 9.80648e6i 0.389218 + 0.674145i 0.992344 0.123501i \(-0.0394121\pi\)
−0.603127 + 0.797645i \(0.706079\pi\)
\(734\) −4.24270e6 9.06618e6i −0.290671 0.621133i
\(735\) 0 0
\(736\) −7.96353e6 1.12095e7i −0.541890 0.762769i
\(737\) 7.24889e6i 0.491590i
\(738\) 0 0
\(739\) 2.22042e7i 1.49563i 0.663909 + 0.747814i \(0.268896\pi\)
−0.663909 + 0.747814i \(0.731104\pi\)
\(740\) 1.02906e7 + 8.58711e6i 0.690816 + 0.576458i
\(741\) 0 0
\(742\) −3.51433e7 + 1.64460e7i −2.34333 + 1.09661i
\(743\) −650311. 1.12637e6i −0.0432165 0.0748531i 0.843608 0.536959i \(-0.180427\pi\)
−0.886825 + 0.462106i \(0.847094\pi\)
\(744\) 0 0
\(745\) 1.62141e7 2.80836e7i 1.07029 1.85380i
\(746\) 166009. 1.92778e6i 0.0109215 0.126827i
\(747\) 0 0
\(748\) 546349. 3.14873e6i 0.0357040 0.205770i
\(749\) 1.84765e6 + 1.06674e6i 0.120341 + 0.0694790i
\(750\) 0 0
\(751\) 1.35125e7 7.80146e6i 0.874253 0.504750i 0.00549352 0.999985i \(-0.498251\pi\)
0.868759 + 0.495235i \(0.164918\pi\)
\(752\) −3.40641e6 1.87206e7i −0.219661 1.20719i
\(753\) 0 0
\(754\) −6.22278e6 + 8.91291e6i −0.398617 + 0.570941i
\(755\) −1.28117e7 −0.817976
\(756\) 0 0
\(757\) −1.06995e6 −0.0678613 −0.0339307 0.999424i \(-0.510803\pi\)
−0.0339307 + 0.999424i \(0.510803\pi\)
\(758\) −6.19714e6 + 8.87619e6i −0.391759 + 0.561117i
\(759\) 0 0
\(760\) 7.68068e6 2.09177e6i 0.482354 0.131365i
\(761\) 1.68821e7 9.74690e6i 1.05673 0.610105i 0.132207 0.991222i \(-0.457794\pi\)
0.924527 + 0.381117i \(0.124460\pi\)
\(762\) 0 0
\(763\) 5.53716e6 + 3.19688e6i 0.344331 + 0.198799i
\(764\) −1.41210e7 2.45019e6i −0.875247 0.151868i
\(765\) 0 0
\(766\) 1.46428e6 1.70040e7i 0.0901679 1.04708i
\(767\) −762932. + 1.32144e6i −0.0468271 + 0.0811069i
\(768\) 0 0
\(769\) 6.92454e6 + 1.19937e7i 0.422255 + 0.731368i 0.996160 0.0875545i \(-0.0279052\pi\)
−0.573904 + 0.818922i \(0.694572\pi\)
\(770\) −1.13809e7 + 5.32591e6i −0.691749 + 0.323718i
\(771\) 0 0
\(772\) 1.22693e6 1.47033e6i 0.0740932 0.0887918i
\(773\) 1.41475e7i 0.851588i 0.904820 + 0.425794i \(0.140005\pi\)
−0.904820 + 0.425794i \(0.859995\pi\)
\(774\) 0 0