Properties

Label 108.6.h.a.35.2
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 35.2
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.52836 + 1.19885i) q^{2} +(29.1255 - 13.2554i) q^{4} +(20.1454 - 11.6310i) q^{5} +(156.832 + 90.5473i) q^{7} +(-145.125 + 108.198i) q^{8} +O(q^{10})\) \(q+(-5.52836 + 1.19885i) q^{2} +(29.1255 - 13.2554i) q^{4} +(20.1454 - 11.6310i) q^{5} +(156.832 + 90.5473i) q^{7} +(-145.125 + 108.198i) q^{8} +(-97.4272 + 88.4515i) q^{10} +(41.2642 - 71.4718i) q^{11} +(-70.1922 - 121.577i) q^{13} +(-975.579 - 312.559i) q^{14} +(672.589 - 772.140i) q^{16} +901.814i q^{17} -2363.52i q^{19} +(432.572 - 605.793i) q^{20} +(-142.439 + 444.591i) q^{22} +(160.190 + 277.458i) q^{23} +(-1291.94 + 2237.71i) q^{25} +(533.800 + 587.968i) q^{26} +(5768.06 + 558.359i) q^{28} +(7037.98 + 4063.38i) q^{29} +(-1533.72 + 885.495i) q^{31} +(-2792.63 + 5075.00i) q^{32} +(-1081.14 - 4985.55i) q^{34} +4212.61 q^{35} +13713.9 q^{37} +(2833.52 + 13066.4i) q^{38} +(-1665.16 + 3867.63i) q^{40} +(4374.37 - 2525.55i) q^{41} +(17261.6 + 9966.01i) q^{43} +(254.456 - 2628.62i) q^{44} +(-1218.22 - 1341.84i) q^{46} +(6620.98 - 11467.9i) q^{47} +(7994.11 + 13846.2i) q^{49} +(4459.63 - 13919.7i) q^{50} +(-3655.93 - 2610.55i) q^{52} +25022.9i q^{53} -1919.77i q^{55} +(-32557.3 + 3828.26i) q^{56} +(-43779.9 - 14026.3i) q^{58} +(-20189.4 - 34969.0i) q^{59} +(-8934.10 + 15474.3i) q^{61} +(7417.39 - 6734.04i) q^{62} +(9354.49 - 31404.4i) q^{64} +(-2828.10 - 1632.81i) q^{65} +(29089.1 - 16794.6i) q^{67} +(11953.9 + 26265.8i) q^{68} +(-23288.8 + 5050.30i) q^{70} +55855.2 q^{71} -69860.7 q^{73} +(-75815.3 + 16441.0i) q^{74} +(-31329.4 - 68838.8i) q^{76} +(12943.1 - 7472.73i) q^{77} +(33076.3 + 19096.6i) q^{79} +(4568.86 - 23377.9i) q^{80} +(-21155.4 + 19206.4i) q^{82} +(-11121.7 + 19263.4i) q^{83} +(10489.0 + 18167.4i) q^{85} +(-107376. - 34401.5i) q^{86} +(1744.62 + 14837.0i) q^{88} -98921.0i q^{89} -25422.9i q^{91} +(8343.43 + 5957.71i) q^{92} +(-22854.8 + 71336.1i) q^{94} +(-27490.1 - 47614.2i) q^{95} +(-20762.4 + 35961.6i) q^{97} +(-60793.9 - 66963.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.52836 + 1.19885i −0.977285 + 0.211929i
\(3\) 0 0
\(4\) 29.1255 13.2554i 0.910172 0.414231i
\(5\) 20.1454 11.6310i 0.360372 0.208061i −0.308872 0.951104i \(-0.599951\pi\)
0.669244 + 0.743043i \(0.266618\pi\)
\(6\) 0 0
\(7\) 156.832 + 90.5473i 1.20974 + 0.698442i 0.962702 0.270565i \(-0.0872104\pi\)
0.247035 + 0.969007i \(0.420544\pi\)
\(8\) −145.125 + 108.198i −0.801710 + 0.597714i
\(9\) 0 0
\(10\) −97.4272 + 88.4515i −0.308092 + 0.279708i
\(11\) 41.2642 71.4718i 0.102823 0.178095i −0.810023 0.586398i \(-0.800546\pi\)
0.912847 + 0.408302i \(0.133879\pi\)
\(12\) 0 0
\(13\) −70.1922 121.577i −0.115194 0.199522i 0.802663 0.596433i \(-0.203416\pi\)
−0.917857 + 0.396910i \(0.870082\pi\)
\(14\) −975.579 312.559i −1.33028 0.426198i
\(15\) 0 0
\(16\) 672.589 772.140i 0.656825 0.754043i
\(17\) 901.814i 0.756824i 0.925637 + 0.378412i \(0.123530\pi\)
−0.925637 + 0.378412i \(0.876470\pi\)
\(18\) 0 0
\(19\) 2363.52i 1.50202i −0.660290 0.751011i \(-0.729567\pi\)
0.660290 0.751011i \(-0.270433\pi\)
\(20\) 432.572 605.793i 0.241815 0.338648i
\(21\) 0 0
\(22\) −142.439 + 444.591i −0.0627441 + 0.195841i
\(23\) 160.190 + 277.458i 0.0631417 + 0.109365i 0.895868 0.444320i \(-0.146555\pi\)
−0.832726 + 0.553685i \(0.813221\pi\)
\(24\) 0 0
\(25\) −1291.94 + 2237.71i −0.413421 + 0.716067i
\(26\) 533.800 + 587.968i 0.154862 + 0.170577i
\(27\) 0 0
\(28\) 5768.06 + 558.359i 1.39038 + 0.134592i
\(29\) 7037.98 + 4063.38i 1.55401 + 0.897207i 0.997809 + 0.0661569i \(0.0210738\pi\)
0.556198 + 0.831050i \(0.312260\pi\)
\(30\) 0 0
\(31\) −1533.72 + 885.495i −0.286644 + 0.165494i −0.636427 0.771337i \(-0.719588\pi\)
0.349784 + 0.936831i \(0.386255\pi\)
\(32\) −2792.63 + 5075.00i −0.482102 + 0.876115i
\(33\) 0 0
\(34\) −1081.14 4985.55i −0.160393 0.739633i
\(35\) 4212.61 0.581274
\(36\) 0 0
\(37\) 13713.9 1.64686 0.823429 0.567419i \(-0.192058\pi\)
0.823429 + 0.567419i \(0.192058\pi\)
\(38\) 2833.52 + 13066.4i 0.318323 + 1.46790i
\(39\) 0 0
\(40\) −1665.16 + 3867.63i −0.164553 + 0.382204i
\(41\) 4374.37 2525.55i 0.406402 0.234637i −0.282840 0.959167i \(-0.591277\pi\)
0.689243 + 0.724530i \(0.257943\pi\)
\(42\) 0 0
\(43\) 17261.6 + 9966.01i 1.42367 + 0.821959i 0.996611 0.0822625i \(-0.0262146\pi\)
0.427064 + 0.904221i \(0.359548\pi\)
\(44\) 254.456 2628.62i 0.0198144 0.204690i
\(45\) 0 0
\(46\) −1218.22 1341.84i −0.0848851 0.0934989i
\(47\) 6620.98 11467.9i 0.437197 0.757248i −0.560275 0.828307i \(-0.689304\pi\)
0.997472 + 0.0710587i \(0.0226378\pi\)
\(48\) 0 0
\(49\) 7994.11 + 13846.2i 0.475642 + 0.823836i
\(50\) 4459.63 13919.7i 0.252275 0.787417i
\(51\) 0 0
\(52\) −3655.93 2610.55i −0.187495 0.133883i
\(53\) 25022.9i 1.22362i 0.791003 + 0.611812i \(0.209559\pi\)
−0.791003 + 0.611812i \(0.790441\pi\)
\(54\) 0 0
\(55\) 1919.77i 0.0855742i
\(56\) −32557.3 + 3828.26i −1.38733 + 0.163129i
\(57\) 0 0
\(58\) −43779.9 14026.3i −1.70885 0.547487i
\(59\) −20189.4 34969.0i −0.755079 1.30784i −0.945335 0.326101i \(-0.894265\pi\)
0.190256 0.981735i \(1.56093\pi\)
\(60\) 0 0
\(61\) −8934.10 + 15474.3i −0.307416 + 0.532460i −0.977796 0.209558i \(-0.932798\pi\)
0.670381 + 0.742017i \(0.266131\pi\)
\(62\) 7417.39 6734.04i 0.245060 0.222483i
\(63\) 0 0
\(64\) 9354.49 31404.4i 0.285476 0.958386i
\(65\) −2828.10 1632.81i −0.0830256 0.0479348i
\(66\) 0 0
\(67\) 29089.1 16794.6i 0.791668 0.457070i −0.0488814 0.998805i \(-0.515566\pi\)
0.840549 + 0.541735i \(0.182232\pi\)
\(68\) 11953.9 + 26265.8i 0.313500 + 0.688840i
\(69\) 0 0
\(70\) −23288.8 + 5050.30i −0.568070 + 0.123189i
\(71\) 55855.2 1.31498 0.657488 0.753465i \(-0.271619\pi\)
0.657488 + 0.753465i \(0.271619\pi\)
\(72\) 0 0
\(73\) −69860.7 −1.53435 −0.767177 0.641435i \(-0.778339\pi\)
−0.767177 + 0.641435i \(0.778339\pi\)
\(74\) −75815.3 + 16441.0i −1.60945 + 0.349018i
\(75\) 0 0
\(76\) −31329.4 68838.8i −0.622184 1.36710i
\(77\) 12943.1 7472.73i 0.248779 0.143632i
\(78\) 0 0
\(79\) 33076.3 + 19096.6i 0.596278 + 0.344261i 0.767576 0.640958i \(-0.221463\pi\)
−0.171298 + 0.985219i \(0.554796\pi\)
\(80\) 4568.86 23377.9i 0.0798148 0.408396i
\(81\) 0 0
\(82\) −21155.4 + 19206.4i −0.347445 + 0.315435i
\(83\) −11121.7 + 19263.4i −0.177205 + 0.306929i −0.940922 0.338623i \(-0.890039\pi\)
0.763717 + 0.645551i \(0.223372\pi\)
\(84\) 0 0
\(85\) 10489.0 + 18167.4i 0.157465 + 0.272738i
\(86\) −107376. 34401.5i −1.56553 0.501570i
\(87\) 0 0
\(88\) 1744.62 + 14837.0i 0.0240156 + 0.204240i
\(89\) 98921.0i 1.32377i −0.749604 0.661886i \(-0.769756\pi\)
0.749604 0.661886i \(-0.230244\pi\)
\(90\) 0 0
\(91\) 25422.9i 0.321826i
\(92\) 8343.43 + 5957.71i 0.102772 + 0.0733854i
\(93\) 0 0
\(94\) −22854.8 + 71336.1i −0.266783 + 0.832702i
\(95\) −27490.1 47614.2i −0.312512 0.541287i
\(96\) 0 0
\(97\) −20762.4 + 35961.6i −0.224052 + 0.388069i −0.956035 0.293254i \(-0.905262\pi\)
0.731983 + 0.681323i \(0.238595\pi\)
\(98\) −60793.9 66963.0i −0.639433 0.704320i
\(99\) 0 0
\(100\) −7966.74 + 82299.6i −0.0796674 + 0.822996i
\(101\) 100768. + 58178.3i 0.982920 + 0.567489i 0.903150 0.429324i \(-0.141248\pi\)
0.0797694 + 0.996813i \(0.474582\pi\)
\(102\) 0 0
\(103\) −34298.4 + 19802.2i −0.318552 + 0.183916i −0.650747 0.759295i \(-0.725544\pi\)
0.332195 + 0.943211i \(0.392211\pi\)
\(104\) 23340.9 + 10049.1i 0.211609 + 0.0911057i
\(105\) 0 0
\(106\) −29998.8 138336.i −0.259322 1.19583i
\(107\) 82118.9 0.693400 0.346700 0.937976i \(-0.387302\pi\)
0.346700 + 0.937976i \(0.387302\pi\)
\(108\) 0 0
\(109\) −48617.2 −0.391944 −0.195972 0.980610i \(-0.562786\pi\)
−0.195972 + 0.980610i \(0.562786\pi\)
\(110\) 2301.52 + 10613.2i 0.0181357 + 0.0836303i
\(111\) 0 0
\(112\) 175399. 60195.4i 1.32124 0.453439i
\(113\) −14619.7 + 8440.70i −0.107707 + 0.0621845i −0.552886 0.833257i \(-0.686473\pi\)
0.445179 + 0.895442i \(0.353140\pi\)
\(114\) 0 0
\(115\) 6454.20 + 3726.33i 0.0455090 + 0.0262747i
\(116\) 258846. + 25056.8i 1.78606 + 0.172894i
\(117\) 0 0
\(118\) 153537. + 169117.i 1.01510 + 1.11810i
\(119\) −81656.8 + 141434.i −0.528597 + 0.915557i
\(120\) 0 0
\(121\) 77120.0 + 133576.i 0.478855 + 0.829401i
\(122\) 30839.5 96258.2i 0.187589 0.585515i
\(123\) 0 0
\(124\) −32932.8 + 46120.6i −0.192342 + 0.269364i
\(125\) 132800.i 0.760189i
\(126\) 0 0
\(127\) 45880.3i 0.252416i −0.992004 0.126208i \(-0.959719\pi\)
0.992004 0.126208i \(-0.0402807\pi\)
\(128\) −14065.7 + 184829.i −0.0758815 + 0.997117i
\(129\) 0 0
\(130\) 17592.3 + 5636.25i 0.0912984 + 0.0292504i
\(131\) −11973.3 20738.4i −0.0609588 0.105584i 0.833935 0.551862i \(-0.186082\pi\)
−0.894894 + 0.446278i \(0.852749\pi\)
\(132\) 0 0
\(133\) 214011. 370677.i 1.04907 1.81705i
\(134\) −140681. + 127720.i −0.676819 + 0.614465i
\(135\) 0 0
\(136\) −97574.3 130876.i −0.452364 0.606753i
\(137\) −179077. 103390.i −0.815152 0.470628i 0.0335896 0.999436i \(-0.489306\pi\)
−0.848742 + 0.528807i \(0.822639\pi\)
\(138\) 0 0
\(139\) −150292. + 86771.1i −0.659780 + 0.380924i −0.792193 0.610271i \(-0.791061\pi\)
0.132413 + 0.991195i \(0.457727\pi\)
\(140\) 122694. 55839.7i 0.529059 0.240782i
\(141\) 0 0
\(142\) −308788. + 66962.3i −1.28511 + 0.278682i
\(143\) −11585.7 −0.0473787
\(144\) 0 0
\(145\) 189044. 0.746695
\(146\) 386215. 83752.8i 1.49950 0.325175i
\(147\) 0 0
\(148\) 399424. 181783.i 1.49892 0.682180i
\(149\) −195995. + 113158.i −0.723234 + 0.417559i −0.815942 0.578134i \(-0.803781\pi\)
0.0927081 + 0.995693i \(0.470448\pi\)
\(150\) 0 0
\(151\) −48433.2 27962.9i −0.172862 0.0998021i 0.411072 0.911603i \(-0.365154\pi\)
−0.583935 + 0.811801i \(0.698488\pi\)
\(152\) 255728. + 343006.i 0.897779 + 1.20418i
\(153\) 0 0
\(154\) −62595.6 + 56828.9i −0.212688 + 0.193093i
\(155\) −20598.3 + 35677.3i −0.0688656 + 0.119279i
\(156\) 0 0
\(157\) −67323.6 116608.i −0.217981 0.377554i 0.736210 0.676754i \(-0.236614\pi\)
−0.954191 + 0.299200i \(0.903280\pi\)
\(158\) −205752. 65919.2i −0.655693 0.210073i
\(159\) 0 0
\(160\) 2768.41 + 134719.i 0.00854930 + 0.416034i
\(161\) 58019.2i 0.176403i
\(162\) 0 0
\(163\) 93835.4i 0.276629i −0.990388 0.138314i \(-0.955832\pi\)
0.990388 0.138314i \(-0.0441685\pi\)
\(164\) 93928.7 131542.i 0.272702 0.381904i
\(165\) 0 0
\(166\) 38390.9 119828.i 0.108133 0.337512i
\(167\) −67439.6 116809.i −0.187121 0.324104i 0.757168 0.653220i \(-0.226582\pi\)
−0.944289 + 0.329116i \(0.893249\pi\)
\(168\) 0 0
\(169\) 175793. 304482.i 0.473461 0.820058i
\(170\) −79766.8 87861.3i −0.211690 0.233171i
\(171\) 0 0
\(172\) 634857. + 61455.3i 1.63627 + 0.158394i
\(173\) −179808. 103812.i −0.456767 0.263715i 0.253917 0.967226i \(-0.418281\pi\)
−0.710684 + 0.703511i \(0.751614\pi\)
\(174\) 0 0
\(175\) −405237. + 233964.i −1.00026 + 0.577501i
\(176\) −27432.3 79932.9i −0.0667545 0.194511i
\(177\) 0 0
\(178\) 118592. + 546871.i 0.280546 + 1.29370i
\(179\) −525249. −1.22527 −0.612636 0.790365i \(-0.709891\pi\)
−0.612636 + 0.790365i \(0.709891\pi\)
\(180\) 0 0
\(181\) −825837. −1.87369 −0.936846 0.349743i \(-0.886269\pi\)
−0.936846 + 0.349743i \(0.886269\pi\)
\(182\) 30478.3 + 140547.i 0.0682044 + 0.314516i
\(183\) 0 0
\(184\) −53267.9 22933.8i −0.115990 0.0499380i
\(185\) 276272. 159506.i 0.593482 0.342647i
\(186\) 0 0
\(187\) 64454.3 + 37212.7i 0.134787 + 0.0778192i
\(188\) 40828.2 421771.i 0.0842492 0.870327i
\(189\) 0 0
\(190\) 209057. + 230272.i 0.420128 + 0.462761i
\(191\) −187497. + 324754.i −0.371886 + 0.644126i −0.989856 0.142076i \(-0.954622\pi\)
0.617970 + 0.786202i \(0.287955\pi\)
\(192\) 0 0
\(193\) 238572. + 413219.i 0.461027 + 0.798522i 0.999012 0.0444321i \(-0.0141478\pi\)
−0.537985 + 0.842954i \(0.680814\pi\)
\(194\) 71669.4 223700.i 0.136719 0.426737i
\(195\) 0 0
\(196\) 416369. + 297313.i 0.774174 + 0.552807i
\(197\) 443928.i 0.814979i −0.913210 0.407490i \(-0.866404\pi\)
0.913210 0.407490i \(-0.133596\pi\)
\(198\) 0 0
\(199\) 601252.i 1.07628i −0.842857 0.538138i \(-0.819128\pi\)
0.842857 0.538138i \(-0.180872\pi\)
\(200\) −54622.1 464532.i −0.0965592 0.821185i
\(201\) 0 0
\(202\) −626827. 200825.i −1.08086 0.346289i
\(203\) 735856. + 1.27454e6i 1.25329 + 2.17077i
\(204\) 0 0
\(205\) 58749.1 101756.i 0.0976374 0.169113i
\(206\) 165874. 150592.i 0.272339 0.247249i
\(207\) 0 0
\(208\) −141085. 27572.9i −0.226111 0.0441899i
\(209\) −168925. 97529.1i −0.267503 0.154443i
\(210\) 0 0
\(211\) −345252. + 199331.i −0.533863 + 0.308226i −0.742588 0.669748i \(-0.766402\pi\)
0.208725 + 0.977974i \(0.433069\pi\)
\(212\) 331688. + 728805.i 0.506863 + 1.11371i
\(213\) 0 0
\(214\) −453983. + 98448.5i −0.677649 + 0.146952i
\(215\) 463657. 0.684070
\(216\) 0 0
\(217\) −320716. −0.462351
\(218\) 268773. 58284.9i 0.383041 0.0830644i
\(219\) 0 0
\(220\) −25447.3 55914.3i −0.0354475 0.0778872i
\(221\) 109639. 63300.4i 0.151003 0.0871817i
\(222\) 0 0
\(223\) 290097. + 167488.i 0.390644 + 0.225538i 0.682439 0.730942i \(-0.260919\pi\)
−0.291795 + 0.956481i \(0.594253\pi\)
\(224\) −897503. + 543060.i −1.19513 + 0.723149i
\(225\) 0 0
\(226\) 70703.9 64190.1i 0.0920815 0.0835982i
\(227\) 425099. 736293.i 0.547552 0.948388i −0.450890 0.892580i \(-0.648893\pi\)
0.998442 0.0558079i \(-0.0177734\pi\)
\(228\) 0 0
\(229\) −204162. 353618.i −0.257268 0.445601i 0.708241 0.705971i \(-0.249489\pi\)
−0.965509 + 0.260370i \(0.916156\pi\)
\(230\) −40148.5 12862.9i −0.0500437 0.0160331i
\(231\) 0 0
\(232\) −1.46104e6 + 171796.i −1.78214 + 0.209553i
\(233\) 677571.i 0.817645i −0.912614 0.408823i \(-0.865939\pi\)
0.912614 0.408823i \(-0.134061\pi\)
\(234\) 0 0
\(235\) 308033.i 0.363855i
\(236\) −1.05155e6 750872.i −1.22900 0.877578i
\(237\) 0 0
\(238\) 281870. 879791.i 0.322557 1.00679i
\(239\) −660239. 1.14357e6i −0.747664 1.29499i −0.948940 0.315458i \(-0.897842\pi\)
0.201275 0.979535i \(1.56451\pi\)
\(240\) 0 0
\(241\) −418674. + 725165.i −0.464337 + 0.804256i −0.999171 0.0407014i \(-0.987041\pi\)
0.534834 + 0.844957i \(0.320374\pi\)
\(242\) −586485. 645999.i −0.643752 0.709077i
\(243\) 0 0
\(244\) −55092.0 + 569122.i −0.0592399 + 0.611971i
\(245\) 322089. + 185958.i 0.342816 + 0.197925i
\(246\) 0 0
\(247\) −287349. + 165901.i −0.299687 + 0.173024i
\(248\) 126773. 294453.i 0.130887 0.304009i
\(249\) 0 0
\(250\) −159207. 734164.i −0.161106 0.742921i
\(251\) −1.41641e6 −1.41907 −0.709534 0.704671i \(-0.751095\pi\)
−0.709534 + 0.704671i \(0.751095\pi\)
\(252\) 0 0
\(253\) 26440.5 0.0259698
\(254\) 55003.8 + 253643.i 0.0534944 + 0.246682i
\(255\) 0 0
\(256\) −143823. 1.03867e6i −0.137161 0.990549i
\(257\) −887077. + 512154.i −0.837777 + 0.483691i −0.856508 0.516134i \(-0.827371\pi\)
0.0187311 + 0.999825i \(0.494037\pi\)
\(258\) 0 0
\(259\) 2.15078e6 + 1.24176e6i 1.99227 + 1.15023i
\(260\) −104013. 10068.7i −0.0954236 0.00923718i
\(261\) 0 0
\(262\) 91055.1 + 100295.i 0.0819504 + 0.0902664i
\(263\) 841677. 1.45783e6i 0.750337 1.29962i −0.197323 0.980339i \(-0.563225\pi\)
0.947660 0.319283i \(-0.103442\pi\)
\(264\) 0 0
\(265\) 291040. + 504097.i 0.254588 + 0.440960i
\(266\) −738740. + 2.30581e6i −0.640158 + 1.99811i
\(267\) 0 0
\(268\) 624615. 874738.i 0.531221 0.743945i
\(269\) 2.11837e6i 1.78493i 0.451117 + 0.892465i \(0.351026\pi\)
−0.451117 + 0.892465i \(0.648974\pi\)
\(270\) 0 0
\(271\) 596748.i 0.493592i −0.969067 0.246796i \(-0.920622\pi\)
0.969067 0.246796i \(-0.0793778\pi\)
\(272\) 696327. + 606551.i 0.570677 + 0.497101i
\(273\) 0 0
\(274\) 1.11395e6 + 356891.i 0.896376 + 0.287183i
\(275\) 106622. + 184675.i 0.0850188 + 0.147257i
\(276\) 0 0
\(277\) 532237. 921861.i 0.416779 0.721882i −0.578835 0.815445i \(-0.696492\pi\)
0.995613 + 0.0935631i \(0.0298257\pi\)
\(278\) 726842. 659880.i 0.564064 0.512098i
\(279\) 0 0
\(280\) −611354. + 455795.i −0.466013 + 0.347435i
\(281\) 890207. + 513961.i 0.672551 + 0.388298i 0.797043 0.603923i \(-0.206397\pi\)
−0.124492 + 0.992221i \(0.539730\pi\)
\(282\) 0 0
\(283\) 958119. 553170.i 0.711137 0.410575i −0.100345 0.994953i \(-0.531995\pi\)
0.811482 + 0.584377i \(0.198661\pi\)
\(284\) 1.62681e6 740383.i 1.19685 0.544704i
\(285\) 0 0
\(286\) 64050.0 13889.6i 0.0463025 0.0100409i
\(287\) 914725. 0.655520
\(288\) 0 0
\(289\) 606588. 0.427218
\(290\) −1.04510e6 + 226636.i −0.729733 + 0.158247i
\(291\) 0 0
\(292\) −2.03473e6 + 926031.i −1.39653 + 0.635577i
\(293\) 989169. 571097.i 0.673134 0.388634i −0.124129 0.992266i \(-0.539614\pi\)
0.797263 + 0.603632i \(0.206280\pi\)
\(294\) 0 0
\(295\) −813446. 469643.i −0.544219 0.314205i
\(296\) −1.99023e6 + 1.48381e6i −1.32030 + 0.984350i
\(297\) 0 0
\(298\) 947869. 860545.i 0.618312 0.561349i
\(299\) 22488.2 38950.7i 0.0145471 0.0251964i
\(300\) 0 0
\(301\) 1.80479e6 + 3.12599e6i 1.14818 + 1.98871i
\(302\) 301279. + 96524.6i 0.190087 + 0.0609005i
\(303\) 0 0
\(304\) −1.82497e6 1.58968e6i −1.13259 0.986566i
\(305\) 415648.i 0.255845i
\(306\) 0 0
\(307\) 1.32248e6i 0.800836i 0.916333 + 0.400418i \(0.131135\pi\)
−0.916333 + 0.400418i \(0.868865\pi\)
\(308\) 277922. 389213.i 0.166934 0.233782i
\(309\) 0 0
\(310\) 71102.9 221931.i 0.0420226 0.131164i
\(311\) 139474. + 241576.i 0.0817698 + 0.141629i 0.904010 0.427511i \(-0.140609\pi\)
−0.822240 + 0.569140i \(0.807276\pi\)
\(312\) 0 0
\(313\) 68921.8 119376.i 0.0397645 0.0688742i −0.845458 0.534042i \(-0.820673\pi\)
0.885223 + 0.465167i \(0.154006\pi\)
\(314\) 511985. + 563939.i 0.293044 + 0.322781i
\(315\) 0 0
\(316\) 1.21650e6 + 117759.i 0.685319 + 0.0663401i
\(317\) 1.13038e6 + 652623.i 0.631793 + 0.364766i 0.781446 0.623973i \(-0.214482\pi\)
−0.149653 + 0.988739i \(0.547816\pi\)
\(318\) 0 0
\(319\) 580834. 335345.i 0.319577 0.184508i
\(320\) −176813. 741456.i −0.0965250 0.404772i
\(321\) 0 0
\(322\) −69556.5 320751.i −0.0373851 0.172396i
\(323\) 2.13146e6 1.13677
\(324\) 0 0
\(325\) 362737. 0.190495
\(326\) 112495. + 518756.i 0.0586258 + 0.270345i
\(327\) 0 0
\(328\) −361572. + 839817.i −0.185571 + 0.431023i
\(329\) 2.07677e6 1.19902e6i 1.05779 0.610714i
\(330\) 0 0
\(331\) −552755. 319133.i −0.277308 0.160104i 0.354896 0.934906i \(-0.384516\pi\)
−0.632204 + 0.774802i \(0.717850\pi\)
\(332\) −68582.0 + 708478.i −0.0341479 + 0.352762i
\(333\) 0 0
\(334\) 512867. + 564910.i 0.251558 + 0.277085i
\(335\) 390674. 676668.i 0.190197 0.329430i
\(336\) 0 0
\(337\) −491457. 851229.i −0.235728 0.408293i 0.723756 0.690056i \(-0.242414\pi\)
−0.959484 + 0.281763i \(0.909081\pi\)
\(338\) −606815. + 1.89403e6i −0.288912 + 0.901770i
\(339\) 0 0
\(340\) 546313. + 390100.i 0.256297 + 0.183012i
\(341\) 146157.i 0.0680666i
\(342\) 0 0
\(343\) 148276.i 0.0680511i
\(344\) −3.58339e6 + 421354.i −1.63267 + 0.191978i
\(345\) 0 0
\(346\) 1.11850e6 + 358348.i 0.502281 + 0.160922i
\(347\) 675607. + 1.17018e6i 0.301211 + 0.521712i 0.976410 0.215923i \(-0.0692760\pi\)
−0.675200 + 0.737635i \(0.735943\pi\)
\(348\) 0 0
\(349\) −376947. + 652891.i −0.165660 + 0.286931i −0.936889 0.349626i \(-0.886309\pi\)
0.771230 + 0.636557i \(0.219642\pi\)
\(350\) 1.95981e6 1.77925e6i 0.855151 0.776368i
\(351\) 0 0
\(352\) 247483. + 409010.i 0.106461 + 0.175945i
\(353\) −389941. 225133.i −0.166557 0.0961616i 0.414404 0.910093i \(-0.363990\pi\)
−0.580961 + 0.813931i \(0.697323\pi\)
\(354\) 0 0
\(355\) 1.12523e6 649650.i 0.473881 0.273595i
\(356\) −1.31124e6 2.88112e6i −0.548347 1.20486i
\(357\) 0 0
\(358\) 2.90377e6 629697.i 1.19744 0.259671i
\(359\) −3.02244e6 −1.23772 −0.618860 0.785502i \(-0.712405\pi\)
−0.618860 + 0.785502i \(0.712405\pi\)
\(360\) 0 0
\(361\) −3.11015e6 −1.25607
\(362\) 4.56552e6 990058.i 1.83113 0.397090i
\(363\) 0 0
\(364\) −336990. 740453.i −0.133310 0.292917i
\(365\) −1.40737e6 + 812547.i −0.552939 + 0.319239i
\(366\) 0 0
\(367\) −2.33704e6 1.34929e6i −0.905735 0.522927i −0.0266788 0.999644i \(-0.508493\pi\)
−0.879057 + 0.476718i \(0.841826\pi\)
\(368\) 321978. + 62925.8i 0.123939 + 0.0242220i
\(369\) 0 0
\(370\) −1.33611e6 + 1.21301e6i −0.507384 + 0.460640i
\(371\) −2.26576e6 + 3.92440e6i −0.854630 + 1.48026i
\(372\) 0 0
\(373\) −922996. 1.59868e6i −0.343501 0.594961i 0.641579 0.767057i \(-0.278279\pi\)
−0.985080 + 0.172096i \(0.944946\pi\)
\(374\) −400939. 128454.i −0.148217 0.0474863i
\(375\) 0 0
\(376\) 279929. + 2.38065e6i 0.102112 + 0.868412i
\(377\) 1.14087e6i 0.413412i
\(378\) 0 0
\(379\) 1.35806e6i 0.485649i 0.970070 + 0.242824i \(0.0780739\pi\)
−0.970070 + 0.242824i \(0.921926\pi\)
\(380\) −1.43181e6 1.02240e6i −0.508657 0.363212i
\(381\) 0 0
\(382\) 647216. 2.02014e6i 0.226930 0.708308i
\(383\) −1.84507e6 3.19575e6i −0.642710 1.11321i −0.984825 0.173548i \(-0.944477\pi\)
0.342115 0.939658i \(1.61114\pi\)
\(384\) 0 0
\(385\) 173830. 301082.i 0.0597686 0.103522i
\(386\) −1.81430e6 1.99841e6i −0.619785 0.682678i
\(387\) 0 0
\(388\) −128031. + 1.32261e6i −0.0431754 + 0.446019i
\(389\) −2.87005e6 1.65702e6i −0.961645 0.555206i −0.0649663 0.997887i \(-0.520694\pi\)
−0.896679 + 0.442681i \(0.854027\pi\)
\(390\) 0 0
\(391\) −250215. + 144462.i −0.0827698 + 0.0477872i
\(392\) −2.65827e6 1.14448e6i −0.873745 0.376179i
\(393\) 0 0
\(394\) 532204. + 2.45419e6i 0.172718 + 0.796467i
\(395\) 888447. 0.286509
\(396\) 0 0
\(397\) −119467. −0.0380427 −0.0190214 0.999819i \(-0.506055\pi\)
−0.0190214 + 0.999819i \(0.506055\pi\)
\(398\) 720813. + 3.32394e6i 0.228095 + 1.05183i
\(399\) 0 0
\(400\) 858877. + 2.50262e6i 0.268399 + 0.782068i
\(401\) −4.09522e6 + 2.36438e6i −1.27179 + 0.734271i −0.975325 0.220772i \(-0.929142\pi\)
−0.296469 + 0.955043i \(0.595809\pi\)
\(402\) 0 0
\(403\) 215311. + 124310.i 0.0660394 + 0.0381279i
\(404\) 3.70609e6 + 358756.i 1.12970 + 0.109357i
\(405\) 0 0
\(406\) −5.59606e6 6.16393e6i −1.68487 1.85585i
\(407\) 565893. 980156.i 0.169336 0.293298i
\(408\) 0 0
\(409\) −3.11750e6 5.39967e6i −0.921507 1.59610i −0.797085 0.603867i \(-0.793626\pi\)
−0.124422 0.992229i \(-0.539708\pi\)
\(410\) −202795. + 632977.i −0.0595796 + 0.185964i
\(411\) 0 0
\(412\) −736471. + 1.03139e6i −0.213753 + 0.299349i
\(413\) 7.31236e6i 2.10952i
\(414\) 0 0
\(415\) 517425.i 0.147478i
\(416\) 813022. 16707.2i 0.230340 0.00473337i
\(417\) 0 0
\(418\) 1.05080e6 + 336659.i 0.294158 + 0.0942430i
\(419\) 347632. + 602117.i 0.0967353 + 0.167551i 0.910332 0.413880i \(-0.135827\pi\)
−0.813596 + 0.581430i \(0.802493\pi\)
\(420\) 0 0
\(421\) −585766. + 1.01458e6i −0.161071 + 0.278984i −0.935253 0.353979i \(-0.884828\pi\)
0.774182 + 0.632963i \(0.218162\pi\)
\(422\) 1.66971e6 1.51588e6i 0.456414 0.414366i
\(423\) 0 0
\(424\) −2.70742e6 3.63145e6i −0.731377 0.980991i
\(425\) −2.01800e6 1.16509e6i −0.541936 0.312887i
\(426\) 0 0
\(427\) −2.80231e6 + 1.61792e6i −0.743784 + 0.429424i
\(428\) 2.39175e6 1.08852e6i 0.631113 0.287228i
\(429\) 0 0
\(430\) −2.56326e6 + 555857.i −0.668531 + 0.144975i
\(431\) 2.98148e6 0.773104 0.386552 0.922268i \(-0.373666\pi\)
0.386552 + 0.922268i \(0.373666\pi\)
\(432\) 0 0
\(433\) 5.90562e6 1.51372 0.756861 0.653576i \(-0.226732\pi\)
0.756861 + 0.653576i \(0.226732\pi\)
\(434\) 1.77304e6 384492.i 0.451849 0.0979858i
\(435\) 0 0
\(436\) −1.41600e6 + 644440.i −0.356736 + 0.162355i
\(437\) 655778. 378614.i 0.164268 0.0948403i
\(438\) 0 0
\(439\) −2.85286e6 1.64710e6i −0.706512 0.407905i 0.103256 0.994655i \(-0.467074\pi\)
−0.809768 + 0.586750i \(0.800407\pi\)
\(440\) 207715. + 278607.i 0.0511489 + 0.0686056i
\(441\) 0 0
\(442\) −530238. + 481389.i −0.129097 + 0.117203i
\(443\) −3.05039e6 + 5.28344e6i −0.738493 + 1.27911i 0.214681 + 0.976684i \(0.431129\pi\)
−0.953174 + 0.302423i \(0.902204\pi\)
\(444\) 0 0
\(445\) −1.15055e6 1.99280e6i −0.275425 0.477051i
\(446\) −1.80455e6 578148.i −0.429569 0.137626i
\(447\) 0 0
\(448\) 4.31067e6 4.07820e6i 1.01473 0.960006i
\(449\) 5.38289e6i 1.26008i 0.776561 + 0.630042i \(0.216962\pi\)
−0.776561 + 0.630042i \(0.783038\pi\)
\(450\) 0 0
\(451\) 416859.i 0.0965046i
\(452\) −313922. + 439630.i −0.0722729 + 0.101214i
\(453\) 0 0
\(454\) −1.46739e6 + 4.58012e6i −0.334123 + 1.04289i
\(455\) −295692. 512154.i −0.0669594 0.115977i
\(456\) 0 0
\(457\) −231952. + 401752.i −0.0519526 + 0.0899846i −0.890832 0.454332i \(-0.849878\pi\)
0.838880 + 0.544317i \(0.183211\pi\)
\(458\) 1.55262e6 + 1.71017e6i 0.345860 + 0.380956i
\(459\) 0 0
\(460\) 237376. + 22978.4i 0.0523048 + 0.00506320i
\(461\) −3.61068e6 2.08463e6i −0.791291 0.456852i 0.0491256 0.998793i \(-0.484357\pi\)
−0.840417 + 0.541940i \(0.817690\pi\)
\(462\) 0 0
\(463\) −5.46488e6 + 3.15515e6i −1.18475 + 0.684018i −0.957110 0.289726i \(-0.906436\pi\)
−0.227644 + 0.973744i \(0.573102\pi\)
\(464\) 7.87117e6 2.70132e6i 1.69724 0.582480i
\(465\) 0 0
\(466\) 812308. + 3.74585e6i 0.173283 + 0.799072i
\(467\) −763795. −0.162063 −0.0810316 0.996712i \(-0.525821\pi\)
−0.0810316 + 0.996712i \(0.525821\pi\)
\(468\) 0 0
\(469\) 6.08282e6 1.27695
\(470\) 369287. + 1.70292e6i 0.0771115 + 0.355590i
\(471\) 0 0
\(472\) 6.71355e6 + 2.89043e6i 1.38707 + 0.597183i
\(473\) 1.42458e6 822480.i 0.292774 0.169033i
\(474\) 0 0
\(475\) 5.28888e6 + 3.05354e6i 1.07555 + 0.620968i
\(476\) −503536. + 5.20172e6i −0.101862 + 1.05228i
\(477\) 0 0
\(478\) 5.02101e6 + 5.53052e6i 1.00513 + 1.10712i
\(479\) −1.97328e6 + 3.41782e6i −0.392962 + 0.680629i −0.992839 0.119463i \(-0.961883\pi\)
0.599877 + 0.800092i \(0.295216\pi\)
\(480\) 0 0
\(481\) −962608. 1.66729e6i −0.189709 0.328585i
\(482\) 1.44521e6 4.51090e6i 0.283344 0.884394i
\(483\) 0 0
\(484\) 4.01676e6 + 2.86821e6i 0.779403 + 0.556541i
\(485\) 965947.i 0.186466i
\(486\) 0 0
\(487\) 1.97847e6i 0.378012i −0.981976 0.189006i \(-0.939473\pi\)
0.981976 0.189006i \(-0.0605266\pi\)
\(488\) −377726. 3.21236e6i −0.0718004 0.610625i
\(489\) 0 0
\(490\) −2.00356e6 641907.i −0.376975 0.120776i
\(491\) −547411. 948143.i −0.102473 0.177488i 0.810230 0.586112i \(-0.199342\pi\)
−0.912703 + 0.408624i \(0.866009\pi\)
\(492\) 0 0
\(493\) −3.66441e6 + 6.34695e6i −0.679027 + 1.17611i
\(494\) 1.38968e6 1.26165e6i 0.256210 0.232606i
\(495\) 0 0
\(496\) −347839. + 1.77982e6i −0.0634855 + 0.324842i
\(497\) 8.75991e6 + 5.05754e6i 1.59078 + 0.918435i
\(498\) 0 0
\(499\) 9.07104e6 5.23717e6i 1.63082 0.941554i 0.646978 0.762508i \(-0.276032\pi\)
0.983841 0.179045i \(-0.0573009\pi\)
\(500\) 1.76031e6 + 3.86785e6i 0.314894 + 0.691903i
\(501\) 0 0
\(502\) 7.83040e6 1.69806e6i 1.38683 0.300742i
\(503\) 639826. 0.112757 0.0563783 0.998409i \(-0.482045\pi\)
0.0563783 + 0.998409i \(0.482045\pi\)
\(504\) 0 0
\(505\) 2.70668e6 0.472289
\(506\) −146173. + 31698.3i −0.0253799 + 0.00550377i
\(507\) 0 0
\(508\) −608161. 1.33629e6i −0.104559 0.229742i
\(509\) 2.75241e6 1.58911e6i 0.470890 0.271868i −0.245722 0.969340i \(-0.579025\pi\)
0.716612 + 0.697472i \(0.245692\pi\)
\(510\) 0 0
\(511\) −1.09564e7 6.32570e6i −1.85617 1.07166i
\(512\) 2.04032e6 + 5.56969e6i 0.343971 + 0.938980i
\(513\) 0 0
\(514\) 4.29008e6 3.89485e6i 0.716238 0.650253i
\(515\) −460636. + 797845.i −0.0765315 + 0.132556i
\(516\) 0 0
\(517\) −546419. 946426.i −0.0899083 0.155726i
\(518\) −1.33790e7 4.28639e6i −2.19078 0.701888i
\(519\) 0 0
\(520\) 587094. 69033.6i 0.0952137 0.0111957i
\(521\) 1.76213e6i 0.284408i 0.989837 + 0.142204i \(0.0454190\pi\)
−0.989837 + 0.142204i \(0.954581\pi\)
\(522\) 0 0
\(523\) 8.86393e6i 1.41701i 0.705708 + 0.708503i \(0.250629\pi\)
−0.705708 + 0.708503i \(0.749371\pi\)
\(524\) −623624. 445305.i −0.0992190 0.0708483i
\(525\) 0 0
\(526\) −2.90537e6 + 9.06844e6i −0.457865 + 1.42912i
\(527\) −798552. 1.38313e6i −0.125250 0.216939i
\(528\) 0 0
\(529\) 3.16685e6 5.48514e6i 0.492026 0.852214i
\(530\) −2.21331e6 2.43791e6i −0.342258 0.376989i
\(531\) 0 0
\(532\) 1.31969e6 1.36330e7i 0.202160 2.08839i
\(533\) −614094. 354547.i −0.0936304 0.0540575i
\(534\) 0 0
\(535\) 1.65432e6 955121.i 0.249882 0.144269i
\(536\) −2.40441e6 + 5.58469e6i −0.361491 + 0.839628i
\(537\) 0 0
\(538\) −2.53962e6 1.17111e7i −0.378279 1.74438i
\(539\) 1.31948e6 0.195629
\(540\) 0 0
\(541\) −6.03815e6 −0.886974 −0.443487 0.896281i \(-0.646259\pi\)
−0.443487 + 0.896281i \(0.646259\pi\)
\(542\) 715414. + 3.29904e6i 0.104607 + 0.482380i
\(543\) 0 0
\(544\) −4.57671e6 2.51844e6i −0.663065 0.364866i
\(545\) −979414. + 565465.i −0.141246 + 0.0815482i
\(546\) 0 0
\(547\) −544056. 314111.i −0.0777455 0.0448864i 0.460623 0.887596i \(-0.347626\pi\)
−0.538369 + 0.842709i \(0.680959\pi\)
\(548\) −6.58619e6 637555.i −0.936878 0.0906914i
\(549\) 0 0
\(550\) −810842. 893124.i −0.114296 0.125894i
\(551\) 9.60390e6 1.66344e7i 1.34762 2.33415i
\(552\) 0 0
\(553\) 3.45829e6 + 5.98993e6i 0.480893 + 0.832931i
\(554\) −1.83722e6 + 5.73445e6i −0.254323 + 0.793812i
\(555\) 0 0
\(556\) −3.22714e6 + 4.51943e6i −0.442722 + 0.620007i
\(557\) 2.33240e6i 0.318541i 0.987235 + 0.159270i \(0.0509142\pi\)
−0.987235 + 0.159270i \(0.949086\pi\)
\(558\) 0 0
\(559\) 2.79815e6i 0.378740i
\(560\) 2.83335e6 3.25272e6i 0.381795 0.438305i
\(561\) 0 0
\(562\) −5.53755e6 1.77413e6i −0.739566 0.236944i
\(563\) 4.06546e6 + 7.04158e6i 0.540553 + 0.936266i 0.998872 + 0.0474781i \(0.0151184\pi\)
−0.458319 + 0.888788i \(0.651548\pi\)
\(564\) 0 0
\(565\) −196347. + 340083.i −0.0258763 + 0.0448191i
\(566\) −4.63366e6 + 4.20677e6i −0.607971 + 0.551960i
\(567\) 0 0
\(568\) −8.10599e6 + 6.04341e6i −1.05423 + 0.785980i
\(569\) 5.81782e6 + 3.35892e6i 0.753320 + 0.434929i 0.826892 0.562361i \(-0.190107\pi\)
−0.0735725 + 0.997290i \(0.523440\pi\)
\(570\) 0 0
\(571\) 1.04309e7 6.02229e6i 1.33885 0.772985i 0.352213 0.935920i \(-0.385429\pi\)
0.986637 + 0.162935i \(0.0520961\pi\)
\(572\) −337440. + 153573.i −0.0431227 + 0.0196257i
\(573\) 0 0
\(574\) −5.05693e6 + 1.09662e6i −0.640630 + 0.138924i
\(575\) −827826. −0.104417
\(576\) 0 0
\(577\) −906368. −0.113335 −0.0566676 0.998393i \(-0.518048\pi\)
−0.0566676 + 0.998393i \(0.518048\pi\)
\(578\) −3.35344e6 + 727211.i −0.417513 + 0.0905400i
\(579\) 0 0
\(580\) 5.50600e6 2.50585e6i 0.679620 0.309304i
\(581\) −3.48849e6 + 2.01408e6i −0.428743 + 0.247535i
\(582\) 0 0
\(583\) 1.78843e6 + 1.03255e6i 0.217922 + 0.125817i
\(584\) 1.01385e7 7.55877e6i 1.23011 0.917105i
\(585\) 0 0
\(586\) −4.78382e6 + 4.34310e6i −0.575480 + 0.522463i
\(587\) −4.78919e6 + 8.29511e6i −0.573676 + 0.993636i 0.422508 + 0.906359i \(0.361150\pi\)
−0.996184 + 0.0872766i \(0.972184\pi\)
\(588\) 0 0
\(589\) 2.09289e6 + 3.62499e6i 0.248575 + 0.430545i
\(590\) 5.06005e6 + 1.62115e6i 0.598446 + 0.191732i
\(591\) 0 0
\(592\) 9.22382e6 1.05890e7i 1.08170 1.24180i
\(593\) 6.46951e6i 0.755501i −0.925907 0.377750i \(-0.876698\pi\)
0.925907 0.377750i \(-0.123302\pi\)
\(594\) 0 0
\(595\) 3.79899e6i 0.439922i
\(596\) −4.20849e6 + 5.89376e6i −0.485301 + 0.679636i
\(597\) 0 0
\(598\) −77626.7 + 242294.i −0.00887684 + 0.0277070i
\(599\) −2.38231e6 4.12628e6i −0.271288 0.469885i 0.697904 0.716192i \(-0.254116\pi\)
−0.969192 + 0.246306i \(0.920783\pi\)
\(600\) 0 0
\(601\) −7.09387e6 + 1.22869e7i −0.801119 + 1.38758i 0.117761 + 0.993042i \(0.462428\pi\)
−0.918880 + 0.394537i \(0.870905\pi\)
\(602\) −1.37251e7 1.51179e7i −1.54357 1.70020i
\(603\) 0 0
\(604\) −1.78130e6 172433.i −0.198676 0.0192322i
\(605\) 3.10723e6 + 1.79396e6i 0.345132 + 0.199262i
\(606\) 0 0
\(607\) 6.94805e6 4.01146e6i 0.765404 0.441906i −0.0658283 0.997831i \(-0.520969\pi\)
0.831233 + 0.555924i \(0.187636\pi\)
\(608\) 1.19949e7 + 6.60045e6i 1.31594 + 0.724127i
\(609\) 0 0
\(610\) −498302. 2.29785e6i −0.0542210 0.250033i
\(611\) −1.85897e6 −0.201450
\(612\) 0 0
\(613\) 4.92638e6 0.529513 0.264757 0.964315i \(-0.414708\pi\)
0.264757 + 0.964315i \(0.414708\pi\)
\(614\) −1.58546e6 7.31115e6i −0.169721 0.782645i
\(615\) 0 0
\(616\) −1.06984e6 + 2.48490e6i −0.113597 + 0.263850i
\(617\) −1.81236e6 + 1.04636e6i −0.191660 + 0.110655i −0.592759 0.805380i \(-0.701961\pi\)
0.401100 + 0.916034i \(0.368628\pi\)
\(618\) 0 0
\(619\) 7.46071e6 + 4.30745e6i 0.782625 + 0.451849i 0.837360 0.546652i \(-0.184098\pi\)
−0.0547347 + 0.998501i \(0.517431\pi\)
\(620\) −127019. + 1.31216e6i −0.0132706 + 0.137090i
\(621\) 0 0
\(622\) −1.06068e6 1.16831e6i −0.109928 0.121083i
\(623\) 8.95702e6 1.55140e7i 0.924578 1.60142i
\(624\) 0 0
\(625\) −2.49273e6 4.31754e6i −0.255256 0.442116i
\(626\) −237910. + 742581.i −0.0242648 + 0.0757369i
\(627\) 0 0
\(628\) −3.50652e6 2.50386e6i −0.354795 0.253345i
\(629\) 1.23674e7i 1.24638i
\(630\) 0 0
\(631\) 1.15818e7i 1.15798i 0.815334 + 0.578991i \(0.196554\pi\)
−0.815334 + 0.578991i \(0.803446\pi\)
\(632\) −6.86640e6 + 807387.i −0.683812 + 0.0804061i
\(633\) 0 0
\(634\) −7.03152e6 2.25278e6i −0.694746 0.222585i
\(635\) −533632. 924277.i −0.0525179 0.0909637i
\(636\) 0 0
\(637\) 1.12225e6 1.94379e6i 0.109582 0.189802i
\(638\) −2.80903e6 + 2.55024e6i −0.273215 + 0.248044i
\(639\) 0 0
\(640\) 1.86638e6 + 3.88706e6i 0.180115 + 0.375121i
\(641\) −1.51197e7 8.72938e6i −1.45345 0.839147i −0.454771 0.890608i \(-0.650279\pi\)
−0.998675 + 0.0514611i \(0.983612\pi\)
\(642\) 0 0
\(643\) −8.37838e6 + 4.83726e6i −0.799158 + 0.461394i −0.843177 0.537637i \(-0.819317\pi\)
0.0440186 + 0.999031i \(0.485984\pi\)
\(644\) 769067. + 1.68984e6i 0.0730717 + 0.160557i
\(645\) 0 0
\(646\) −1.17835e7 + 2.55531e6i −1.11094 + 0.240914i
\(647\) −1.26182e7 −1.18505 −0.592525 0.805552i \(-0.701869\pi\)
−0.592525 + 0.805552i \(0.701869\pi\)
\(648\) 0 0
\(649\) −3.33239e6 −0.310559
\(650\) −2.00534e6 + 434869.i −0.186168 + 0.0403715i
\(651\) 0 0
\(652\) −1.24382e6 2.73300e6i −0.114588 0.251780i
\(653\) 1.65281e7 9.54250e6i 1.51684 0.875748i 0.517036 0.855964i \(-0.327035\pi\)
0.999804 0.0197840i \(-0.00629786\pi\)
\(654\) 0 0
\(655\) −482415. 278522.i −0.0439357 0.0253663i
\(656\) 992083. 5.07628e6i 0.0900095 0.460560i
\(657\) 0 0
\(658\) −1.00437e7 + 9.11837e6i −0.904332 + 0.821018i
\(659\) 5.33197e6 9.23524e6i 0.478271 0.828390i −0.521419 0.853301i \(-0.674597\pi\)
0.999690 + 0.0249112i \(0.00793029\pi\)
\(660\) 0 0
\(661\) 1.35400e6 + 2.34520e6i 0.120535 + 0.208774i 0.919979 0.391968i \(-0.128206\pi\)
−0.799443 + 0.600741i \(0.794872\pi\)
\(662\) 3.43842e6 + 1.10161e6i 0.304940 + 0.0976974i
\(663\) 0 0
\(664\) −470216. 3.99894e6i −0.0413883 0.351986i
\(665\) 9.95660e6i 0.873086i
\(666\) 0 0
\(667\) 2.60366e6i 0.226605i
\(668\) −3.51256e6 2.50818e6i −0.304566 0.217479i
\(669\) 0 0
\(670\) −1.34856e6 + 4.20922e6i −0.116060 + 0.362256i
\(671\) 737317. + 1.27707e6i 0.0632191 + 0.109499i
\(672\) 0 0
\(673\) −2.61627e6 + 4.53151e6i −0.222661 + 0.385660i −0.955615 0.294618i \(-0.904808\pi\)
0.732954 + 0.680278i \(0.238141\pi\)
\(674\) 3.73745e6 + 4.11671e6i 0.316903 + 0.349061i
\(675\) 0 0
\(676\) 1.08402e6 1.11984e7i 0.0912372 0.942516i
\(677\) 1.63183e6 + 942135.i 0.136837 + 0.0790026i 0.566855 0.823817i \(-0.308160\pi\)
−0.430019 + 0.902820i \(0.641493\pi\)
\(678\) 0 0
\(679\) −6.51244e6 + 3.75996e6i −0.542087 + 0.312974i
\(680\) −3.48788e6 1.50166e6i −0.289261 0.124537i
\(681\) 0 0
\(682\) −175221. 808009.i −0.0144253 0.0665204i
\(683\) 8.13981e6 0.667671 0.333835 0.942631i \(-0.391657\pi\)
0.333835 + 0.942631i \(0.391657\pi\)
\(684\) 0 0
\(685\) −4.81011e6 −0.391678
\(686\) 177761. + 819722.i 0.0144220 + 0.0665053i
\(687\) 0 0
\(688\) 1.93051e7 6.62536e6i 1.55490 0.533628i
\(689\) 3.04220e6 1.75641e6i 0.244140 0.140954i
\(690\) 0 0
\(691\) 1.22215e7 + 7.05606e6i 0.973706 + 0.562169i 0.900364 0.435138i \(-0.143300\pi\)
0.0733417 + 0.997307i \(0.476634\pi\)
\(692\) −6.61309e6 640158.i −0.524975 0.0508186i
\(693\) 0 0
\(694\) −5.13788e6 5.65925e6i −0.404935 0.446026i
\(695\) −2.01846e6 + 3.49608e6i −0.158511 + 0.274549i
\(696\) 0 0
\(697\) 2.27757e6 + 3.94487e6i 0.177579 + 0.307575i
\(698\) 1.30118e6 4.06132e6i 0.101088 0.315521i
\(699\) 0 0
\(700\) −8.70144e6 + 1.21859e7i −0.671191 + 0.939965i
\(701\) 2.52168e6i 0.193818i −0.995293 0.0969090i \(-0.969104\pi\)
0.995293 0.0969090i \(-0.0308956\pi\)
\(702\) 0 0
\(703\) 3.24131e7i 2.47362i
\(704\) −1.85852e6 1.96446e6i −0.141330 0.149387i
\(705\) 0 0
\(706\) 2.42564e6 + 777132.i 0.183153 + 0.0586790i
\(707\) 1.05358e7 + 1.82485e7i 0.792716 + 1.37302i
\(708\) 0 0
\(709\) 7.59486e6 1.31547e7i 0.567419 0.982799i −0.429401 0.903114i \(-0.641275\pi\)
0.996820 0.0796849i \(-0.0253914\pi\)
\(710\) −5.44182e6 + 4.94048e6i −0.405134 + 0.367810i
\(711\) 0 0
\(712\) 1.07030e7 + 1.43559e7i 0.791237 + 1.06128i
\(713\) −491375. 283695.i −0.0361984 0.0208991i
\(714\) 0 0
\(715\) −233399. + 134753.i −0.0170739 + 0.00985765i
\(716\) −1.52981e7 + 6.96238e6i −1.11521 + 0.507546i
\(717\) 0 0
\(718\) 1.67092e7 3.62347e6i 1.20960 0.262309i
\(719\) −4.45507e6 −0.321390 −0.160695 0.987004i \(-0.551374\pi\)
−0.160695 + 0.987004i \(0.551374\pi\)
\(720\) 0 0
\(721\) −7.17213e6 −0.513819
\(722\) 1.71940e7 3.72862e6i 1.22754 0.266198i
\(723\) 0 0
\(724\) −2.40529e7 + 1.09468e7i −1.70538 + 0.776141i
\(725\) −1.81853e7 + 1.04993e7i −1.28492 + 0.741849i
\(726\) 0 0
\(727\) −1.03556e7 5.97878e6i −0.726670 0.419543i 0.0905324 0.995894i \(-0.471143\pi\)
−0.817203 + 0.576350i \(0.804476\pi\)
\(728\) 2.75070e6 + 3.68949e6i 0.192360 + 0.258011i
\(729\) 0 0
\(730\) 6.80634e6 6.17929e6i 0.472722 0.429172i
\(731\) −8.98749e6 + 1.55668e7i −0.622078 + 1.07747i
\(732\) 0 0
\(733\) −6.24966e6 1.08247e7i −0.429632 0.744144i 0.567209 0.823574i \(-0.308023\pi\)
−0.996840 + 0.0794302i \(0.974690\pi\)
\(734\) 1.45376e7 + 4.65760e6i 0.995985 + 0.319096i
\(735\) 0 0
\(736\) −1.85545e6 + 38128.6i −0.126257 + 0.00259452i
\(737\) 2.77206e6i 0.187990i
\(738\) 0 0
\(739\) 3.34559e6i 0.225352i −0.993632 0.112676i \(-0.964058\pi\)
0.993632 0.112676i \(-0.0359422\pi\)
\(740\) 5.93225e6 8.30778e6i 0.398236 0.557706i
\(741\) 0 0
\(742\) 7.82112e6 2.44118e7i 0.521506 1.62776i
\(743\) −1.84277e6 3.19177e6i −0.122461 0.212109i 0.798276 0.602291i \(-0.205745\pi\)
−0.920738 + 0.390182i \(0.872412\pi\)
\(744\) 0 0
\(745\) −2.63226e6 + 4.55921e6i −0.173755 + 0.300953i
\(746\) 7.01923e6 + 7.73152e6i 0.461788 + 0.508648i
\(747\) 0 0
\(748\) 2.37053e6 + 229472.i 0.154914 + 0.0149960i
\(749\) 1.28789e7 + 7.43564e6i 0.838831 + 0.484299i
\(750\) 0 0
\(751\) −1.11291e7 + 6.42540e6i −0.720048 + 0.415720i −0.814770 0.579784i \(-0.803137\pi\)
0.0947225 + 0.995504i \(0.469804\pi\)
\(752\) −4.40160e6 1.28255e7i −0.283835 0.827045i
\(753\) 0 0
\(754\) 1.36774e6 + 6.30714e6i 0.0876142 + 0.404021i
\(755\) −1.30094e6 −0.0830597
\(756\) 0 0
\(757\) 2.81332e6 0.178435 0.0892175 0.996012i \(-0.471563\pi\)
0.0892175 + 0.996012i \(0.471563\pi\)
\(758\) −1.62812e6 7.50787e6i −0.102923 0.474617i
\(759\) 0 0
\(760\) 9.14124e6 + 3.93564e6i 0.574078 + 0.247162i
\(761\) −2.67932e6 + 1.54691e6i −0.167712 + 0.0968283i −0.581506 0.813542i \(-0.697536\pi\)
0.413795 + 0.910370i \(0.364203\pi\)
\(762\) 0 0
\(763\) −7.62475e6 4.40215e6i −0.474149 0.273750i
\(764\) −1.15620e6 + 1.19440e7i −0.0716635 + 0.740312i
\(765\) 0 0
\(766\) 1.40314e7 + 1.54553e7i 0.864032 + 0.951711i
\(767\) −2.83427e6 + 4.90910e6i −0.173962 + 0.301310i
\(768\) 0 0
\(769\) 602040. + 1.04276e6i 0.0367122 + 0.0635873i 0.883798 0.467869i \(-0.154978\pi\)
−0.847086 + 0.531457i \(0.821645\pi\)
\(770\) −600041. + 1.87289e6i −0.0364715 + 0.113837i
\(771\) 0 0
\(772\) 1.24259e7 + 8.87284e6i 0.750386 + 0.535821i
\(773\) 2.76278e7i 1.66302i 0.555510 + 0.831510i \(0.312523\pi\)
−0.555510 + 0.831510i \(0.687477\pi\)
\(774\) 0 0