Properties

Label 108.6.h.a.71.12
Level 108
Weight 6
Character 108.71
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 71.12
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.72594 + 5.38713i) q^{2} +(-26.0423 - 18.5957i) q^{4} +(20.1454 + 11.6310i) q^{5} +(-156.832 + 90.5473i) q^{7} +(145.125 - 108.198i) q^{8} +O(q^{10})\) \(q+(-1.72594 + 5.38713i) q^{2} +(-26.0423 - 18.5957i) q^{4} +(20.1454 + 11.6310i) q^{5} +(-156.832 + 90.5473i) q^{7} +(145.125 - 108.198i) q^{8} +(-97.4272 + 88.4515i) q^{10} +(-41.2642 - 71.4718i) q^{11} +(-70.1922 + 121.577i) q^{13} +(-217.106 - 1001.16i) q^{14} +(332.398 + 968.549i) q^{16} -901.814i q^{17} -2363.52i q^{19} +(-308.346 - 677.515i) q^{20} +(456.247 - 98.9396i) q^{22} +(-160.190 + 277.458i) q^{23} +(-1291.94 - 2237.71i) q^{25} +(-533.800 - 587.968i) q^{26} +(5768.06 + 558.359i) q^{28} +(7037.98 - 4063.38i) q^{29} +(1533.72 + 885.495i) q^{31} +(-5791.40 + 119.010i) q^{32} +(4858.19 + 1556.48i) q^{34} -4212.61 q^{35} +13713.9 q^{37} +(12732.6 + 4079.30i) q^{38} +(4182.05 - 491.747i) q^{40} +(4374.37 + 2525.55i) q^{41} +(-17261.6 + 9966.01i) q^{43} +(-254.456 + 2628.62i) q^{44} +(-1218.22 - 1341.84i) q^{46} +(-6620.98 - 11467.9i) q^{47} +(7994.11 - 13846.2i) q^{49} +(14284.6 - 3097.70i) q^{50} +(4088.77 - 1860.85i) q^{52} -25022.9i q^{53} -1919.77i q^{55} +(-12963.3 + 30109.6i) q^{56} +(9742.80 + 44927.6i) q^{58} +(20189.4 - 34969.0i) q^{59} +(-8934.10 - 15474.3i) q^{61} +(-7417.39 + 6734.04i) q^{62} +(9354.49 - 31404.4i) q^{64} +(-2828.10 + 1632.81i) q^{65} +(-29089.1 - 16794.6i) q^{67} +(-16769.9 + 23485.3i) q^{68} +(7270.71 - 22693.8i) q^{70} -55855.2 q^{71} -69860.7 q^{73} +(-23669.4 + 73878.5i) q^{74} +(-43951.5 + 61551.5i) q^{76} +(12943.1 + 7472.73i) q^{77} +(-33076.3 + 19096.6i) q^{79} +(-4568.86 + 23377.9i) q^{80} +(-21155.4 + 19206.4i) q^{82} +(11121.7 + 19263.4i) q^{83} +(10489.0 - 18167.4i) q^{85} +(-23895.6 - 110191. i) q^{86} +(-13721.6 - 5907.63i) q^{88} +98921.0i q^{89} -25422.9i q^{91} +(9331.24 - 4246.77i) q^{92} +(73206.3 - 15875.2i) q^{94} +(27490.1 - 47614.2i) q^{95} +(-20762.4 - 35961.6i) q^{97} +(60793.9 + 66963.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.72594 + 5.38713i −0.305106 + 0.952318i
\(3\) 0 0
\(4\) −26.0423 18.5957i −0.813820 0.581116i
\(5\) 20.1454 + 11.6310i 0.360372 + 0.208061i 0.669244 0.743043i \(-0.266618\pi\)
−0.308872 + 0.951104i \(0.599951\pi\)
\(6\) 0 0
\(7\) −156.832 + 90.5473i −1.20974 + 0.698442i −0.962702 0.270565i \(-0.912790\pi\)
−0.247035 + 0.969007i \(0.579456\pi\)
\(8\) 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 \(-0.199454\pi\)
−0.912847 + 0.408302i \(0.866121\pi\)
\(12\) 0 0
\(13\) −70.1922 + 121.577i −0.115194 + 0.199522i −0.917857 0.396910i \(-0.870082\pi\)
0.802663 + 0.596433i \(0.203416\pi\)
\(14\) −217.106 1001.16i −0.296041 1.36515i
\(15\) 0 0
\(16\) 332.398 + 968.549i 0.324607 + 0.945849i
\(17\) 901.814i 0.756824i −0.925637 0.378412i \(-0.876470\pi\)
0.925637 0.378412i \(-0.123530\pi\)
\(18\) 0 0
\(19\) 2363.52i 1.50202i −0.660290 0.751011i \(-0.729567\pi\)
0.660290 0.751011i \(-0.270433\pi\)
\(20\) −308.346 677.515i −0.172371 0.378742i
\(21\) 0 0
\(22\) 456.247 98.9396i 0.200976 0.0435826i
\(23\) −160.190 + 277.458i −0.0631417 + 0.109365i −0.895868 0.444320i \(-0.853445\pi\)
0.832726 + 0.553685i \(0.186779\pi\)
\(24\) 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 0.556198 0.831050i \(-0.312260\pi\)
0.997809 0.0661569i \(-0.0210738\pi\)
\(30\) 0 0
\(31\) 1533.72 + 885.495i 0.286644 + 0.165494i 0.636427 0.771337i \(-0.280412\pi\)
−0.349784 + 0.936831i \(0.613745\pi\)
\(32\) −5791.40 + 119.010i −0.999789 + 0.0205452i
\(33\) 0 0
\(34\) 4858.19 + 1556.48i 0.720737 + 0.230912i
\(35\) −4212.61 −0.581274
\(36\) 0 0
\(37\) 13713.9 1.64686 0.823429 0.567419i \(-0.192058\pi\)
0.823429 + 0.567419i \(0.192058\pi\)
\(38\) 12732.6 + 4079.30i 1.43040 + 0.458276i
\(39\) 0 0
\(40\) 4182.05 491.747i 0.413275 0.0485950i
\(41\) 4374.37 + 2525.55i 0.406402 + 0.234637i 0.689243 0.724530i \(-0.257943\pi\)
−0.282840 + 0.959167i \(0.591277\pi\)
\(42\) 0 0
\(43\) −17261.6 + 9966.01i −1.42367 + 0.821959i −0.996611 0.0822625i \(-0.973785\pi\)
−0.427064 + 0.904221i \(0.640452\pi\)
\(44\) −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 \(-0.310696\pi\)
−0.997472 + 0.0710587i \(0.977362\pi\)
\(48\) 0 0
\(49\) 7994.11 13846.2i 0.475642 0.823836i
\(50\) 14284.6 3097.70i 0.808061 0.175232i
\(51\) 0 0
\(52\) 4088.77 1860.85i 0.209693 0.0954340i
\(53\) 25022.9i 1.22362i −0.791003 0.611812i \(-0.790441\pi\)
0.791003 0.611812i \(-0.209559\pi\)
\(54\) 0 0
\(55\) 1919.77i 0.0855742i
\(56\) −12963.3 + 30109.6i −0.552389 + 1.28302i
\(57\) 0 0
\(58\) 9742.80 + 44927.6i 0.380289 + 1.75365i
\(59\) 20189.4 34969.0i 0.755079 1.30784i −0.190256 0.981735i \(-0.560932\pi\)
0.945335 0.326101i \(-0.105735\pi\)
\(60\) 0 0
\(61\) −8934.10 15474.3i −0.307416 0.532460i 0.670381 0.742017i \(-0.266131\pi\)
−0.977796 + 0.209558i \(0.932798\pi\)
\(62\) −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 \(-0.484434\pi\)
−0.840549 + 0.541735i \(0.817768\pi\)
\(68\) −16769.9 + 23485.3i −0.439803 + 0.615919i
\(69\) 0 0
\(70\) 7270.71 22693.8i 0.177350 0.553558i
\(71\) −55855.2 −1.31498 −0.657488 0.753465i \(-0.728381\pi\)
−0.657488 + 0.753465i \(0.728381\pi\)
\(72\) 0 0
\(73\) −69860.7 −1.53435 −0.767177 0.641435i \(-0.778339\pi\)
−0.767177 + 0.641435i \(0.778339\pi\)
\(74\) −23669.4 + 73878.5i −0.502467 + 1.56833i
\(75\) 0 0
\(76\) −43951.5 + 61551.5i −0.872849 + 1.22238i
\(77\) 12943.1 + 7472.73i 0.248779 + 0.143632i
\(78\) 0 0
\(79\) −33076.3 + 19096.6i −0.596278 + 0.344261i −0.767576 0.640958i \(-0.778537\pi\)
0.171298 + 0.985219i \(0.445204\pi\)
\(80\) −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 \(-0.109961\pi\)
−0.763717 + 0.645551i \(0.776628\pi\)
\(84\) 0 0
\(85\) 10489.0 18167.4i 0.157465 0.272738i
\(86\) −23895.6 110191.i −0.348395 1.60658i
\(87\) 0 0
\(88\) −13721.6 5907.63i −0.188885 0.0813218i
\(89\) 98921.0i 1.32377i 0.749604 + 0.661886i \(0.230244\pi\)
−0.749604 + 0.661886i \(0.769756\pi\)
\(90\) 0 0
\(91\) 25422.9i 0.321826i
\(92\) 9331.24 4246.77i 0.114940 0.0523105i
\(93\) 0 0
\(94\) 73206.3 15875.2i 0.854533 0.185310i
\(95\) 27490.1 47614.2i 0.312512 0.541287i
\(96\) 0 0
\(97\) −20762.4 35961.6i −0.224052 0.388069i 0.731983 0.681323i \(-0.238595\pi\)
−0.956035 + 0.293254i \(0.905262\pi\)
\(98\) 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 0.0797694 0.996813i \(-0.474582\pi\)
0.903150 + 0.429324i \(0.141248\pi\)
\(102\) 0 0
\(103\) 34298.4 + 19802.2i 0.318552 + 0.183916i 0.650747 0.759295i \(-0.274456\pi\)
−0.332195 + 0.943211i \(0.607789\pi\)
\(104\) 2967.67 + 25238.4i 0.0269049 + 0.228812i
\(105\) 0 0
\(106\) 134802. + 43188.1i 1.16528 + 0.373335i
\(107\) −82118.9 −0.693400 −0.346700 0.937976i \(-0.612698\pi\)
−0.346700 + 0.937976i \(0.612698\pi\)
\(108\) 0 0
\(109\) −48617.2 −0.391944 −0.195972 0.980610i \(-0.562786\pi\)
−0.195972 + 0.980610i \(0.562786\pi\)
\(110\) 10342.0 + 3313.41i 0.0814938 + 0.0261092i
\(111\) 0 0
\(112\) −139830. 121802.i −1.05331 0.917509i
\(113\) −14619.7 8440.70i −0.107707 0.0621845i 0.445179 0.895442i \(-0.353140\pi\)
−0.552886 + 0.833257i \(0.686473\pi\)
\(114\) 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
\(122\) 98781.8 21421.4i 0.600865 0.130301i
\(123\) 0 0
\(124\) −23475.2 51580.9i −0.137105 0.301256i
\(125\) 132800.i 0.760189i
\(126\) 0 0
\(127\) 45880.3i 0.252416i −0.992004 0.126208i \(-0.959719\pi\)
0.992004 0.126208i \(-0.0402807\pi\)
\(128\) 153034. + 104596.i 0.825588 + 0.564274i
\(129\) 0 0
\(130\) −3914.99 18053.5i −0.0203176 0.0936920i
\(131\) 11973.3 20738.4i 0.0609588 0.105584i −0.833935 0.551862i \(-0.813918\pi\)
0.894894 + 0.446278i \(0.147251\pi\)
\(132\) 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 −0.848742 0.528807i \(-0.822639\pi\)
0.0335896 + 0.999436i \(0.489306\pi\)
\(138\) 0 0
\(139\) 150292. + 86771.1i 0.659780 + 0.380924i 0.792193 0.610271i \(-0.208939\pi\)
−0.132413 + 0.991195i \(0.542273\pi\)
\(140\) 109706. + 78336.5i 0.473052 + 0.337788i
\(141\) 0 0
\(142\) 96402.9 300899.i 0.401207 1.25228i
\(143\) 11585.7 0.0473787
\(144\) 0 0
\(145\) 189044. 0.746695
\(146\) 120575. 376348.i 0.468141 1.46119i
\(147\) 0 0
\(148\) −357141. 255020.i −1.34025 0.957017i
\(149\) −195995. 113158.i −0.723234 0.417559i 0.0927081 0.995693i \(-0.470448\pi\)
−0.815942 + 0.578134i \(0.803781\pi\)
\(150\) 0 0
\(151\) 48433.2 27962.9i 0.172862 0.0998021i −0.411072 0.911603i \(-0.634846\pi\)
0.583935 + 0.811801i \(0.301512\pi\)
\(152\) −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 −0.954191 0.299200i \(-0.903280\pi\)
0.736210 + 0.676754i \(0.236614\pi\)
\(158\) −45788.1 211146.i −0.145918 0.672883i
\(159\) 0 0
\(160\) −118054. 64962.0i −0.364571 0.200613i
\(161\) 58019.2i 0.176403i
\(162\) 0 0
\(163\) 93835.4i 0.276629i −0.990388 0.138314i \(-0.955832\pi\)
0.990388 0.138314i \(-0.0441685\pi\)
\(164\) −66954.2 147116.i −0.194387 0.427119i
\(165\) 0 0
\(166\) −122970. + 26666.6i −0.346360 + 0.0751100i
\(167\) 67439.6 116809.i 0.187121 0.324104i −0.757168 0.653220i \(-0.773418\pi\)
0.944289 + 0.329116i \(0.106751\pi\)
\(168\) 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 −0.710684 0.703511i \(-0.751614\pi\)
0.253917 + 0.967226i \(0.418281\pi\)
\(174\) 0 0
\(175\) 405237. + 233964.i 1.00026 + 0.577501i
\(176\) 55507.8 63723.5i 0.135074 0.155067i
\(177\) 0 0
\(178\) −532900. 170732.i −1.26065 0.403891i
\(179\) 525249. 1.22527 0.612636 0.790365i \(-0.290109\pi\)
0.612636 + 0.790365i \(0.290109\pi\)
\(180\) 0 0
\(181\) −825837. −1.87369 −0.936846 0.349743i \(-0.886269\pi\)
−0.936846 + 0.349743i \(0.886269\pi\)
\(182\) 136956. + 43878.4i 0.306481 + 0.0981910i
\(183\) 0 0
\(184\) 6772.70 + 57598.3i 0.0147475 + 0.125419i
\(185\) 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 \(-0.0453778\pi\)
−0.617970 + 0.786202i \(0.712045\pi\)
\(192\) 0 0
\(193\) 238572. 413219.i 0.461027 0.798522i −0.537985 0.842954i \(-0.680814\pi\)
0.999012 + 0.0444321i \(0.0141478\pi\)
\(194\) 229564. 49782.2i 0.437925 0.0949664i
\(195\) 0 0
\(196\) −465665. + 211930.i −0.865832 + 0.394051i
\(197\) 443928.i 0.814979i 0.913210 + 0.407490i \(0.133596\pi\)
−0.913210 + 0.407490i \(0.866404\pi\)
\(198\) 0 0
\(199\) 601252.i 1.07628i −0.842857 0.538138i \(-0.819128\pi\)
0.842857 0.538138i \(-0.180872\pi\)
\(200\) −429608. 184962.i −0.759447 0.326970i
\(201\) 0 0
\(202\) 139495. + 643261.i 0.240535 + 1.10920i
\(203\) −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 \(-0.233598\pi\)
−0.208725 + 0.977974i \(0.566931\pi\)
\(212\) −465319. + 651653.i −0.711068 + 0.995811i
\(213\) 0 0
\(214\) 141732. 442385.i 0.211560 0.660337i
\(215\) −463657. −0.684070
\(216\) 0 0
\(217\) −320716. −0.462351
\(218\) 83910.4 261907.i 0.119584 0.373255i
\(219\) 0 0
\(220\) −35699.5 + 49995.2i −0.0497286 + 0.0696420i
\(221\) 109639. + 63300.4i 0.151003 + 0.0871817i
\(222\) 0 0
\(223\) −290097. + 167488.i −0.390644 + 0.225538i −0.682439 0.730942i \(-0.739081\pi\)
0.291795 + 0.956481i \(0.405747\pi\)
\(224\) 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 −0.998442 0.0558079i \(-0.982227\pi\)
0.450890 0.892580i \(1.64889\pi\)
\(228\) 0 0
\(229\) −204162. + 353618.i −0.257268 + 0.445601i −0.965509 0.260370i \(-0.916156\pi\)
0.708241 + 0.705971i \(0.249489\pi\)
\(230\) −8934.66 41201.0i −0.0111367 0.0513557i
\(231\) 0 0
\(232\) 581738. 1.35119e6i 0.709590 1.64815i
\(233\) 677571.i 0.817645i 0.912614 + 0.408823i \(0.134061\pi\)
−0.912614 + 0.408823i \(0.865939\pi\)
\(234\) 0 0
\(235\) 308033.i 0.363855i
\(236\) −1.17605e6 + 535236.i −1.37450 + 0.625554i
\(237\) 0 0
\(238\) −902856. + 195789.i −1.03318 + 0.224051i
\(239\) 660239. 1.14357e6i 0.747664 1.29499i −0.201275 0.979535i \(-0.564509\pi\)
0.948940 0.315458i \(-0.102158\pi\)
\(240\) 0 0
\(241\) −418674. 725165.i −0.464337 0.804256i 0.534834 0.844957i \(-0.320374\pi\)
−0.999171 + 0.0407014i \(0.987041\pi\)
\(242\) 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
\(248\) 318390. 37437.9i 0.328723 0.0386529i
\(249\) 0 0
\(250\) 715408. + 229204.i 0.723942 + 0.231938i
\(251\) 1.41641e6 1.41907 0.709534 0.704671i \(-0.248905\pi\)
0.709534 + 0.704671i \(0.248905\pi\)
\(252\) 0 0
\(253\) 26440.5 0.0259698
\(254\) 247163. + 79186.7i 0.240380 + 0.0770137i
\(255\) 0 0
\(256\) −827599. + 643888.i −0.789260 + 0.614059i
\(257\) −887077. 512154.i −0.837777 0.483691i 0.0187311 0.999825i \(-0.494037\pi\)
−0.856508 + 0.516134i \(0.827371\pi\)
\(258\) 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 −0.947660 0.319283i \(-0.896558\pi\)
0.197323 0.980339i \(1.56322\pi\)
\(264\) 0 0
\(265\) 291040. 504097.i 0.254588 0.440960i
\(266\) −2.36626e6 + 513135.i −2.05049 + 0.444660i
\(267\) 0 0
\(268\) 445238. + 978302.i 0.378665 + 0.832024i
\(269\) 2.11837e6i 1.78493i −0.451117 0.892465i \(-0.648974\pi\)
0.451117 0.892465i \(-0.351026\pi\)
\(270\) 0 0
\(271\) 596748.i 0.493592i −0.969067 0.246796i \(-0.920622\pi\)
0.969067 0.246796i \(-0.0793778\pi\)
\(272\) 873451. 299761.i 0.715841 0.245671i
\(273\) 0 0
\(274\) −247900. 1.14316e6i −0.199480 0.919876i
\(275\) −106622. + 184675.i −0.0850188 + 0.147257i
\(276\) 0 0
\(277\) 532237. + 921861.i 0.416779 + 0.721882i 0.995613 0.0935631i \(-0.0298257\pi\)
−0.578835 + 0.815445i \(0.696492\pi\)
\(278\) −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 −0.124492 0.992221i \(-0.539730\pi\)
0.797043 + 0.603923i \(0.206397\pi\)
\(282\) 0 0
\(283\) −958119. 553170.i −0.711137 0.410575i 0.100345 0.994953i \(-0.468005\pi\)
−0.811482 + 0.584377i \(0.801339\pi\)
\(284\) 1.45460e6 + 1.03867e6i 1.07015 + 0.764154i
\(285\) 0 0
\(286\) −19996.3 + 62413.7i −0.0144555 + 0.0451196i
\(287\) −914725. −0.655520
\(288\) 0 0
\(289\) 606588. 0.427218
\(290\) −326279. + 1.01840e6i −0.227821 + 0.711091i
\(291\) 0 0
\(292\) 1.81933e6 + 1.29911e6i 1.24869 + 0.891639i
\(293\) 989169. + 571097.i 0.673134 + 0.388634i 0.797263 0.603632i \(-0.206280\pi\)
−0.124129 + 0.992266i \(0.539614\pi\)
\(294\) 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
\(302\) 67046.9 + 309178.i 0.0423020 + 0.195070i
\(303\) 0 0
\(304\) 2.28919e6 785631.i 1.42069 0.487567i
\(305\) 415648.i 0.255845i
\(306\) 0 0
\(307\) 1.32248e6i 0.800836i 0.916333 + 0.400418i \(0.131135\pi\)
−0.916333 + 0.400418i \(0.868865\pi\)
\(308\) −198108. 435294.i −0.118994 0.261460i
\(309\) 0 0
\(310\) −227750. + 49388.7i −0.134603 + 0.0291893i
\(311\) −139474. + 241576.i −0.0817698 + 0.141629i −0.904010 0.427511i \(-0.859391\pi\)
0.822240 + 0.569140i \(0.192724\pi\)
\(312\) 0 0
\(313\) 68921.8 + 119376.i 0.0397645 + 0.0688742i 0.885223 0.465167i \(-0.154006\pi\)
−0.845458 + 0.534042i \(0.820673\pi\)
\(314\) −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 −0.149653 0.988739i \(-0.547816\pi\)
0.781446 + 0.623973i \(0.214482\pi\)
\(318\) 0 0
\(319\) −580834. 335345.i −0.319577 0.184508i
\(320\) 553713. 523853.i 0.302280 0.285979i
\(321\) 0 0
\(322\) 312557. + 100138.i 0.167992 + 0.0538217i
\(323\) −2.13146e6 −1.13677
\(324\) 0 0
\(325\) 362737. 0.190495
\(326\) 505503. + 161954.i 0.263439 + 0.0844012i
\(327\) 0 0
\(328\) 908089. 106778.i 0.466062 0.0548020i
\(329\) 2.07677e6 + 1.19902e6i 1.05779 + 0.610714i
\(330\) 0 0
\(331\) 552755. 319133.i 0.277308 0.160104i −0.354896 0.934906i \(-0.615484\pi\)
0.632204 + 0.774802i \(0.282150\pi\)
\(332\) 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 −0.959484 0.281763i \(-0.909081\pi\)
0.723756 + 0.690056i \(0.242414\pi\)
\(338\) −1.94369e6 + 421499.i −0.925412 + 0.200680i
\(339\) 0 0
\(340\) −610993. + 278071.i −0.286641 + 0.130454i
\(341\) 146157.i 0.0680666i
\(342\) 0 0
\(343\) 148276.i 0.0680511i
\(344\) −1.42679e6 + 3.31399e6i −0.650077 + 1.50992i
\(345\) 0 0
\(346\) −248912. 1.14783e6i −0.111778 0.515449i
\(347\) −675607. + 1.17018e6i −0.301211 + 0.521712i −0.976410 0.215923i \(-0.930724\pi\)
0.675200 + 0.737635i \(0.264057\pi\)
\(348\) 0 0
\(349\) −376947. 652891.i −0.165660 0.286931i 0.771230 0.636557i \(-0.219642\pi\)
−0.936889 + 0.349626i \(0.886309\pi\)
\(350\) −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 −0.580961 0.813931i \(-0.697323\pi\)
0.414404 + 0.910093i \(0.363990\pi\)
\(354\) 0 0
\(355\) −1.12523e6 649650.i −0.473881 0.273595i
\(356\) 1.83951e6 2.57612e6i 0.769266 1.07731i
\(357\) 0 0
\(358\) −906549. + 2.82958e6i −0.373838 + 1.16685i
\(359\) 3.02244e6 1.23772 0.618860 0.785502i \(-0.287595\pi\)
0.618860 + 0.785502i \(0.287595\pi\)
\(360\) 0 0
\(361\) −3.11015e6 −1.25607
\(362\) 1.42535e6 4.44889e6i 0.571675 1.78435i
\(363\) 0 0
\(364\) −472756. + 662068.i −0.187018 + 0.261908i
\(365\) −1.40737e6 812547.i −0.552939 0.319239i
\(366\) 0 0
\(367\) 2.33704e6 1.34929e6i 0.905735 0.522927i 0.0266788 0.999644i \(-0.491507\pi\)
0.879057 + 0.476718i \(0.158174\pi\)
\(368\) −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 −0.985080 0.172096i \(-0.944946\pi\)
0.641579 + 0.767057i \(0.278279\pi\)
\(374\) −89225.1 411450.i −0.0329844 0.152103i
\(375\) 0 0
\(376\) −2.20167e6 947899.i −0.803123 0.345774i
\(377\) 1.14087e6i 0.413412i
\(378\) 0 0
\(379\) 1.35806e6i 0.485649i 0.970070 + 0.242824i \(0.0780739\pi\)
−0.970070 + 0.242824i \(0.921926\pi\)
\(380\) −1.60132e6 + 728783.i −0.568879 + 0.258904i
\(381\) 0 0
\(382\) −2.07310e6 + 449562.i −0.726877 + 0.157627i
\(383\) 1.84507e6 3.19575e6i 0.642710 1.11321i −0.342115 0.939658i \(-0.611143\pi\)
0.984825 0.173548i \(-0.0555233\pi\)
\(384\) 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 −0.896679 0.442681i \(-0.854027\pi\)
−0.0649663 + 0.997887i \(0.520694\pi\)
\(390\) 0 0
\(391\) 250215. + 144462.i 0.0827698 + 0.0477872i
\(392\) −337984. 2.87438e6i −0.111092 0.944775i
\(393\) 0 0
\(394\) −2.39149e6 766193.i −0.776120 0.248655i
\(395\) −888447. −0.286509
\(396\) 0 0
\(397\) −119467. −0.0380427 −0.0190214 0.999819i \(-0.506055\pi\)
−0.0190214 + 0.999819i \(0.506055\pi\)
\(398\) 3.23902e6 + 1.03773e6i 1.02496 + 0.328379i
\(399\) 0 0
\(400\) 1.73789e6 1.99512e6i 0.543091 0.623475i
\(401\) −4.09522e6 2.36438e6i −1.27179 0.734271i −0.296469 0.955043i \(-0.595809\pi\)
−0.975325 + 0.220772i \(0.929142\pi\)
\(402\) 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 −0.124422 + 0.992229i \(0.539708\pi\)
−0.797085 + 0.603867i \(0.793626\pi\)
\(410\) −649572. + 140863.i −0.190839 + 0.0413845i
\(411\) 0 0
\(412\) −524971. 1.15350e6i −0.152367 0.334790i
\(413\) 7.31236e6i 2.10952i
\(414\) 0 0
\(415\) 517425.i 0.147478i
\(416\) 392042. 712451.i 0.111071 0.201847i
\(417\) 0 0
\(418\) −233846. 1.07835e6i −0.0654621 0.301870i
\(419\) −347632. + 602117.i −0.0967353 + 0.167551i −0.910332 0.413880i \(-0.864173\pi\)
0.813596 + 0.581430i \(0.197507\pi\)
\(420\) 0 0
\(421\) −585766. 1.01458e6i −0.161071 0.278984i 0.774182 0.632963i \(-0.218162\pi\)
−0.935253 + 0.353979i \(0.884828\pi\)
\(422\) −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
\(428\) 2.13856e6 + 1.52706e6i 0.564303 + 0.402946i
\(429\) 0 0
\(430\) 800245. 2.49778e6i 0.208714 0.651453i
\(431\) −2.98148e6 −0.773104 −0.386552 0.922268i \(-0.626334\pi\)
−0.386552 + 0.922268i \(0.626334\pi\)
\(432\) 0 0
\(433\) 5.90562e6 1.51372 0.756861 0.653576i \(-0.226732\pi\)
0.756861 + 0.653576i \(0.226732\pi\)
\(434\) 553538. 1.72774e6i 0.141066 0.440305i
\(435\) 0 0
\(436\) 1.26610e6 + 904072.i 0.318972 + 0.227765i
\(437\) 655778. + 378614.i 0.164268 + 0.0948403i
\(438\) 0 0
\(439\) 2.85286e6 1.64710e6i 0.706512 0.407905i −0.103256 0.994655i \(-0.532926\pi\)
0.809768 + 0.586750i \(0.199593\pi\)
\(440\) −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 0.953174 + 0.302423i \(0.0977956\pi\)
−0.214681 + 0.976684i \(0.568871\pi\)
\(444\) 0 0
\(445\) −1.15055e6 + 1.99280e6i −0.275425 + 0.477051i
\(446\) −401586. 1.85186e6i −0.0955965 0.440831i
\(447\) 0 0
\(448\) 1.37649e6 + 5.77225e6i 0.324026 + 1.35878i
\(449\) 5.38289e6i 1.26008i −0.776561 0.630042i \(-0.783038\pi\)
0.776561 0.630042i \(-0.216962\pi\)
\(450\) 0 0
\(451\) 416859.i 0.0965046i
\(452\) 223770. + 491679.i 0.0515175 + 0.113197i
\(453\) 0 0
\(454\) 4.70020e6 1.01926e6i 1.07023 0.232085i
\(455\) 295692. 512154.i 0.0669594 0.115977i
\(456\) 0 0
\(457\) −231952. 401752.i −0.0519526 0.0899846i 0.838880 0.544317i \(-0.183211\pi\)
−0.890832 + 0.454332i \(0.849878\pi\)
\(458\) −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 −0.840417 0.541940i \(-0.817690\pi\)
0.0491256 + 0.998793i \(0.484357\pi\)
\(462\) 0 0
\(463\) 5.46488e6 + 3.15515e6i 1.18475 + 0.684018i 0.957110 0.289726i \(-0.0935643\pi\)
0.227644 + 0.973744i \(0.426898\pi\)
\(464\) 6.27499e6 + 5.46597e6i 1.35306 + 1.17862i
\(465\) 0 0
\(466\) −3.65016e6 1.16945e6i −0.778658 0.249469i
\(467\) 763795. 0.162063 0.0810316 0.996712i \(-0.474179\pi\)
0.0810316 + 0.996712i \(0.474179\pi\)
\(468\) 0 0
\(469\) 6.08282e6 1.27695
\(470\) 1.65941e6 + 531648.i 0.346506 + 0.111014i
\(471\) 0 0
\(472\) −853588. 7.25932e6i −0.176357 1.49983i
\(473\) 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 \(-0.0381172\pi\)
−0.599877 + 0.800092i \(0.704784\pi\)
\(480\) 0 0
\(481\) −962608. + 1.66729e6i −0.189709 + 0.328585i
\(482\) 4.62916e6 1.00386e6i 0.907580 0.196813i
\(483\) 0 0
\(484\) −4.49232e6 + 2.04451e6i −0.871680 + 0.396713i
\(485\) 965947.i 0.186466i
\(486\) 0 0
\(487\) 1.97847e6i 0.378012i −0.981976 0.189006i \(-0.939473\pi\)
0.981976 0.189006i \(-0.0605266\pi\)
\(488\) −2.97085e6 1.27906e6i −0.564717 0.243131i
\(489\) 0 0
\(490\) 445874. + 2.05609e6i 0.0838923 + 0.386858i
\(491\) 547411. 948143.i 0.102473 0.177488i −0.810230 0.586112i \(-0.800658\pi\)
0.912703 + 0.408624i \(0.133991\pi\)
\(492\) 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 −0.983841 0.179045i \(-0.942699\pi\)
−0.646978 0.762508i \(1.27603\pi\)
\(500\) −2.46950e6 + 3.45840e6i −0.441758 + 0.618657i
\(501\) 0 0
\(502\) −2.44463e6 + 7.63035e6i −0.432967 + 1.35140i
\(503\) −639826. −0.112757 −0.0563783 0.998409i \(-0.517955\pi\)
−0.0563783 + 0.998409i \(0.517955\pi\)
\(504\) 0 0
\(505\) 2.70668e6 0.472289
\(506\) −45634.8 + 142438.i −0.00792355 + 0.0247315i
\(507\) 0 0
\(508\) −853177. + 1.19483e6i −0.146683 + 0.205421i
\(509\) 2.75241e6 + 1.58911e6i 0.470890 + 0.271868i 0.716612 0.697472i \(-0.245692\pi\)
−0.245722 + 0.969340i \(0.579025\pi\)
\(510\) 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
\(518\) −2.97737e6 1.37297e7i −0.487537 2.24821i
\(519\) 0 0
\(520\) −233762. + 542955.i −0.0379111 + 0.0880553i
\(521\) 1.76213e6i 0.284408i −0.989837 0.142204i \(-0.954581\pi\)
0.989837 0.142204i \(-0.0454190\pi\)
\(522\) 0 0
\(523\) 8.86393e6i 1.41701i 0.705708 + 0.708503i \(0.250629\pi\)
−0.705708 + 0.708503i \(0.749371\pi\)
\(524\) −697458. + 317422.i −0.110966 + 0.0505020i
\(525\) 0 0
\(526\) 9.30619e6 2.01810e6i 1.46659 0.318037i
\(527\) 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
\(536\) −6.03869e6 + 710060.i −0.907885 + 0.106754i
\(537\) 0 0
\(538\) 1.14119e7 + 3.65618e6i 1.69982 + 0.544593i
\(539\) −1.31948e6 −0.195629
\(540\) 0 0
\(541\) −6.03815e6 −0.886974 −0.443487 0.896281i \(-0.646259\pi\)
−0.443487 + 0.896281i \(0.646259\pi\)
\(542\) 3.21476e6 + 1.02995e6i 0.470057 + 0.150598i
\(543\) 0 0
\(544\) 107325. + 5.22276e6i 0.0155491 + 0.756664i
\(545\) −979414. 565465.i −0.141246 0.0815482i
\(546\) 0 0
\(547\) 544056. 314111.i 0.0777455 0.0448864i −0.460623 0.887596i \(-0.652374\pi\)
0.538369 + 0.842709i \(0.319041\pi\)
\(548\) 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
\(554\) −5.88479e6 + 1.27615e6i −0.814623 + 0.176655i
\(555\) 0 0
\(556\) −2.30037e6 5.05451e6i −0.315581 0.693413i
\(557\) 2.33240e6i 0.318541i −0.987235 0.159270i \(-0.949086\pi\)
0.987235 0.159270i \(-0.0509142\pi\)
\(558\) 0 0
\(559\) 2.79815e6i 0.378740i
\(560\) −1.40026e6 4.08012e6i −0.188686 0.549797i
\(561\) 0 0
\(562\) 1.23233e6 + 5.68272e6i 0.164583 + 0.758955i
\(563\) −4.06546e6 + 7.04158e6i −0.540553 + 0.936266i 0.458319 + 0.888788i \(0.348452\pi\)
−0.998872 + 0.0474781i \(0.984882\pi\)
\(564\) 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 −0.0735725 0.997290i \(-0.523440\pi\)
0.826892 + 0.562361i \(0.190107\pi\)
\(570\) 0 0
\(571\) −1.04309e7 6.02229e6i −1.33885 0.772985i −0.352213 0.935920i \(-0.614571\pi\)
−0.986637 + 0.162935i \(0.947904\pi\)
\(572\) −301718. 215445.i −0.0385577 0.0275325i
\(573\) 0 0
\(574\) 1.57876e6 4.92774e6i 0.200003 0.624264i
\(575\) 827826. 0.104417
\(576\) 0 0
\(577\) −906368. −0.113335 −0.0566676 0.998393i \(-0.518048\pi\)
−0.0566676 + 0.998393i \(0.518048\pi\)
\(578\) −1.04694e6 + 3.26777e6i −0.130347 + 0.406847i
\(579\) 0 0
\(580\) −4.92313e6 3.51541e6i −0.607675 0.433916i
\(581\) −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 0.996184 + 0.0872766i \(0.0278164\pi\)
−0.422508 + 0.906359i \(0.638850\pi\)
\(588\) 0 0
\(589\) 2.09289e6 3.62499e6i 0.248575 0.430545i
\(590\) 1.12607e6 + 5.19271e6i 0.133179 + 0.614136i
\(591\) 0 0
\(592\) 4.55847e6 + 1.32826e7i 0.534582 + 1.55768i
\(593\) 6.46951e6i 0.755501i 0.925907 + 0.377750i \(0.123302\pi\)
−0.925907 + 0.377750i \(0.876698\pi\)
\(594\) 0 0
\(595\) 3.79899e6i 0.439922i
\(596\) 2.99990e6 + 6.59154e6i 0.345932 + 0.760101i
\(597\) 0 0
\(598\) 248646. 53920.2i 0.0284334 0.00616593i
\(599\) 2.38231e6 4.12628e6i 0.271288 0.469885i −0.697904 0.716192i \(-0.745884\pi\)
0.969192 + 0.246306i \(0.0792169\pi\)
\(600\) 0 0
\(601\) −7.09387e6 1.22869e7i −0.801119 1.38758i −0.918880 0.394537i \(-0.870905\pi\)
0.117761 0.993042i \(-0.462428\pi\)
\(602\) 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 \(-0.479031\pi\)
−0.831233 + 0.555924i \(0.812364\pi\)
\(608\) 281284. + 1.36881e7i 0.0308593 + 1.50170i
\(609\) 0 0
\(610\) 2.23915e6 + 717385.i 0.243646 + 0.0780598i
\(611\) 1.85897e6 0.201450
\(612\) 0 0
\(613\) 4.92638e6 0.529513 0.264757 0.964315i \(-0.414708\pi\)
0.264757 + 0.964315i \(0.414708\pi\)
\(614\) −7.12437e6 2.28252e6i −0.762651 0.244340i
\(615\) 0 0
\(616\) 2.68691e6 315940.i 0.285299 0.0335470i
\(617\) −1.81236e6 1.04636e6i −0.191660 0.110655i 0.401100 0.916034i \(-0.368628\pi\)
−0.592759 + 0.805380i \(0.701961\pi\)
\(618\) 0 0
\(619\) −7.46071e6 + 4.30745e6i −0.782625 + 0.451849i −0.837360 0.546652i \(-0.815902\pi\)
0.0547347 + 0.998501i \(0.482569\pi\)
\(620\) 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
\(626\) −762049. + 165254.i −0.0777225 + 0.0168545i
\(627\) 0 0
\(628\) 3.92167e6 1.78480e6i 0.396800 0.180589i
\(629\) 1.23674e7i 1.24638i
\(630\) 0 0
\(631\) 1.15818e7i 1.15798i 0.815334 + 0.578991i \(0.196554\pi\)
−0.815334 + 0.578991i \(0.803446\pi\)
\(632\) −2.73398e6 + 6.35017e6i −0.272272 + 0.632401i
\(633\) 0 0
\(634\) 1.56480e6 + 7.21587e6i 0.154609 + 0.712960i
\(635\) 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 −0.998675 0.0514611i \(-0.983612\pi\)
−0.454771 + 0.890608i \(0.650279\pi\)
\(642\) 0 0
\(643\) 8.37838e6 + 4.83726e6i 0.799158 + 0.461394i 0.843177 0.537637i \(-0.180683\pi\)
−0.0440186 + 0.999031i \(0.514016\pi\)
\(644\) −1.07891e6 + 1.51095e6i −0.102511 + 0.143561i
\(645\) 0 0
\(646\) 3.67878e6 1.14824e7i 0.346834 1.08256i
\(647\) 1.26182e7 1.18505 0.592525 0.805552i \(-0.298131\pi\)
0.592525 + 0.805552i \(0.298131\pi\)
\(648\) 0 0
\(649\) −3.33239e6 −0.310559
\(650\) −626063. + 1.95411e6i −0.0581212 + 0.181412i
\(651\) 0 0
\(652\) −1.74494e6 + 2.44368e6i −0.160754 + 0.225126i
\(653\) 1.65281e7 + 9.54250e6i 1.51684 + 0.875748i 0.999804 + 0.0197840i \(0.00629786\pi\)
0.517036 + 0.855964i \(0.327035\pi\)
\(654\) 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 \(-0.325403\pi\)
−0.999690 + 0.0249112i \(0.992070\pi\)
\(660\) 0 0
\(661\) 1.35400e6 2.34520e6i 0.120535 0.208774i −0.799443 0.600741i \(-0.794872\pi\)
0.919979 + 0.391968i \(0.128206\pi\)
\(662\) 765188. + 3.52857e6i 0.0678615 + 0.312934i
\(663\) 0 0
\(664\) 3.69829e6 + 1.59225e6i 0.325523 + 0.140149i
\(665\) 9.95660e6i 0.873086i
\(666\) 0 0
\(667\) 2.60366e6i 0.226605i
\(668\) −3.92842e6 + 1.78788e6i −0.340625 + 0.155023i
\(669\) 0 0
\(670\) 4.31958e6 936723.i 0.371753 0.0806166i
\(671\) −737317. + 1.27707e6i −0.0632191 + 0.109499i
\(672\) 0 0
\(673\) −2.61627e6 4.53151e6i −0.222661 0.385660i 0.732954 0.680278i \(-0.238141\pi\)
−0.955615 + 0.294618i \(0.904808\pi\)
\(674\) −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 −0.430019 0.902820i \(-0.641493\pi\)
0.566855 + 0.823817i \(0.308160\pi\)
\(678\) 0 0
\(679\) 6.51244e6 + 3.75996e6i 0.542087 + 0.312974i
\(680\) −443464. 3.77143e6i −0.0367778 0.312776i
\(681\) 0 0
\(682\) 787366. + 252259.i 0.0648210 + 0.0207675i
\(683\) −8.13981e6 −0.667671 −0.333835 0.942631i \(-0.608343\pi\)
−0.333835 + 0.942631i \(0.608343\pi\)
\(684\) 0 0
\(685\) −4.81011e6 −0.391678
\(686\) 798780. + 255915.i 0.0648063 + 0.0207628i
\(687\) 0 0
\(688\) −1.53903e7 1.34061e7i −1.23958 1.07977i
\(689\) 3.04220e6 + 1.75641e6i 0.244140 + 0.140954i
\(690\) 0 0
\(691\) −1.22215e7 + 7.05606e6i −0.973706 + 0.562169i −0.900364 0.435138i \(-0.856700\pi\)
−0.0733417 + 0.997307i \(0.523366\pi\)
\(692\) 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
\(698\) 4.16779e6 903808.i 0.323793 0.0702163i
\(699\) 0 0
\(700\) −6.20256e6 1.36286e7i −0.478438 1.05125i
\(701\) 2.52168e6i 0.193818i 0.995293 + 0.0969090i \(0.0308956\pi\)
−0.995293 + 0.0969090i \(0.969104\pi\)
\(702\) 0 0
\(703\) 3.24131e7i 2.47362i
\(704\) −2.63053e6 + 627297.i −0.200038 + 0.0477025i
\(705\) 0 0
\(706\) −539802. 2.48923e6i −0.0407590 0.187955i
\(707\) −1.05358e7 + 1.82485e7i −0.792716 + 1.37302i
\(708\) 0 0
\(709\) 7.59486e6 + 1.31547e7i 0.567419 + 0.982799i 0.996820 + 0.0796849i \(0.0253914\pi\)
−0.429401 + 0.903114i \(0.641275\pi\)
\(710\) 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
\(716\) −1.36787e7 9.76739e6i −0.997152 0.712026i
\(717\) 0 0
\(718\) −5.21656e6 + 1.62823e7i −0.377636 + 1.17870i
\(719\) 4.45507e6 0.321390 0.160695 0.987004i \(-0.448626\pi\)
0.160695 + 0.987004i \(0.448626\pi\)
\(720\) 0 0
\(721\) −7.17213e6 −0.513819
\(722\) 5.36794e6 1.67548e7i 0.383234 1.19618i
\(723\) 0 0
\(724\) 2.15067e7 + 1.53570e7i 1.52485 + 1.08883i
\(725\) −1.81853e7 1.04993e7i −1.28492 0.741849i
\(726\) 0 0
\(727\) 1.03556e7 5.97878e6i 0.726670 0.419543i −0.0905324 0.995894i \(-0.528857\pi\)
0.817203 + 0.576350i \(0.195524\pi\)
\(728\) −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 −0.996840 0.0794302i \(-0.974690\pi\)
0.567209 + 0.823574i \(0.308023\pi\)
\(734\) 3.23521e6 + 1.49187e7i 0.221647 + 1.02210i
\(735\) 0 0
\(736\) 894705. 1.62593e6i 0.0608815 0.110639i
\(737\) 2.77206e6i 0.187990i
\(738\) 0 0
\(739\) 3.34559e6i 0.225352i −0.993632 0.112676i \(-0.964058\pi\)
0.993632 0.112676i \(-0.0359422\pi\)
\(740\) −4.22862e6 9.29137e6i −0.283870 0.623735i
\(741\) 0 0
\(742\) −2.50518e7 + 5.43262e6i −1.67044 + 0.362243i
\(743\) 1.84277e6 3.19177e6i 0.122461 0.212109i −0.798276 0.602291i \(-0.794255\pi\)
0.920738 + 0.390182i \(0.127588\pi\)
\(744\) 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 \(-0.196863\pi\)
−0.0947225 + 0.995504i \(0.530196\pi\)
\(752\) 8.90640e6 1.02246e7i 0.574325 0.659331i
\(753\) 0 0
\(754\) −6.14601e6 1.96908e6i −0.393700 0.126135i
\(755\) 1.30094e6 0.0830597
\(756\) 0 0
\(757\) 2.81332e6 0.178435 0.0892175 0.996012i \(-0.471563\pi\)
0.0892175 + 0.996012i \(0.471563\pi\)
\(758\) −7.31606e6 2.34394e6i −0.462492 0.148174i
\(759\) 0 0
\(760\) −1.16226e6 9.88437e6i −0.0729907 0.620747i
\(761\) −2.67932e6 1.54691e6i −0.167712 0.0968283i 0.413795 0.910370i \(-0.364203\pi\)
−0.581506 + 0.813542i \(0.697536\pi\)
\(762\) 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 −0.847086 0.531457i \(-0.821645\pi\)
0.883798 + 0.467869i \(0.154978\pi\)
\(770\) −1.92199e6 + 416794.i −0.116822 + 0.0253334i
\(771\) 0 0
\(772\) −1.38971e7 + 6.32473e6i −0.839227 + 0.381943i
\(773\) 2.76278e7i 1.66302i −0.555510 0.831510i \(-0.687477\pi\)
0.555510 0.831510i \(-0.312523\pi\)
\(774\) 0 0
\(775\) 4.57603e6i 0.273675i