Properties

Label 108.5.k.a.5.1
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.89497 - 1.37096i) q^{3} +(-1.59659 - 4.38660i) q^{5} +(12.9775 + 73.5989i) q^{7} +(77.2410 + 24.3892i) q^{9} +O(q^{10})\) \(q+(-8.89497 - 1.37096i) q^{3} +(-1.59659 - 4.38660i) q^{5} +(12.9775 + 73.5989i) q^{7} +(77.2410 + 24.3892i) q^{9} +(54.6352 - 150.109i) q^{11} +(-161.958 - 135.899i) q^{13} +(8.18781 + 41.2076i) q^{15} +(-295.081 - 170.365i) q^{17} +(-169.557 - 293.681i) q^{19} +(-14.5334 - 672.451i) q^{21} +(946.685 + 166.926i) q^{23} +(462.085 - 387.735i) q^{25} +(-653.619 - 322.835i) q^{27} +(-502.780 - 599.189i) q^{29} +(226.590 - 1285.06i) q^{31} +(-691.772 + 1260.31i) q^{33} +(302.129 - 174.434i) q^{35} +(-611.487 + 1059.13i) q^{37} +(1254.30 + 1430.85i) q^{39} +(-11.6088 + 13.8349i) q^{41} +(-1615.74 - 588.079i) q^{43} +(-16.3366 - 377.765i) q^{45} +(3753.45 - 661.834i) q^{47} +(-2992.18 + 1089.06i) q^{49} +(2391.18 + 1919.94i) q^{51} +850.088i q^{53} -745.699 q^{55} +(1105.58 + 2844.73i) q^{57} +(-1077.21 - 2959.61i) q^{59} +(-630.093 - 3573.43i) q^{61} +(-792.627 + 6001.36i) q^{63} +(-337.554 + 927.421i) q^{65} +(3089.43 + 2592.34i) q^{67} +(-8191.89 - 2782.67i) q^{69} +(3906.92 + 2255.66i) q^{71} +(-2203.63 - 3816.80i) q^{73} +(-4641.80 + 2815.39i) q^{75} +(11756.9 + 2073.06i) q^{77} +(-6846.72 + 5745.08i) q^{79} +(5371.33 + 3767.69i) q^{81} +(-715.401 - 852.581i) q^{83} +(-276.200 + 1566.41i) q^{85} +(3650.75 + 6019.06i) q^{87} +(4214.90 - 2433.47i) q^{89} +(7900.21 - 13683.6i) q^{91} +(-3777.27 + 11119.9i) q^{93} +(-1017.55 + 1212.67i) q^{95} +(-12919.2 - 4702.22i) q^{97} +(7881.12 - 10262.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −8.89497 1.37096i −0.988330 0.152328i
\(4\) 0 0
\(5\) −1.59659 4.38660i −0.0638637 0.175464i 0.903656 0.428258i \(-0.140873\pi\)
−0.967520 + 0.252794i \(0.918650\pi\)
\(6\) 0 0
\(7\) 12.9775 + 73.5989i 0.264846 + 1.50202i 0.769473 + 0.638680i \(0.220519\pi\)
−0.504626 + 0.863338i \(0.668370\pi\)
\(8\) 0 0
\(9\) 77.2410 + 24.3892i 0.953592 + 0.301101i
\(10\) 0 0
\(11\) 54.6352 150.109i 0.451531 1.24057i −0.480116 0.877205i \(-0.659405\pi\)
0.931647 0.363366i \(-0.118372\pi\)
\(12\) 0 0
\(13\) −161.958 135.899i −0.958332 0.804136i 0.0223489 0.999750i \(-0.492886\pi\)
−0.980681 + 0.195614i \(0.937330\pi\)
\(14\) 0 0
\(15\) 8.18781 + 41.2076i 0.0363903 + 0.183145i
\(16\) 0 0
\(17\) −295.081 170.365i −1.02104 0.589499i −0.106637 0.994298i \(-0.534008\pi\)
−0.914406 + 0.404799i \(0.867342\pi\)
\(18\) 0 0
\(19\) −169.557 293.681i −0.469686 0.813520i 0.529713 0.848177i \(-0.322299\pi\)
−0.999399 + 0.0346569i \(0.988966\pi\)
\(20\) 0 0
\(21\) −14.5334 672.451i −0.0329555 1.52483i
\(22\) 0 0
\(23\) 946.685 + 166.926i 1.78958 + 0.315550i 0.967318 0.253566i \(-0.0816035\pi\)
0.822257 + 0.569116i \(0.192715\pi\)
\(24\) 0 0
\(25\) 462.085 387.735i 0.739335 0.620376i
\(26\) 0 0
\(27\) −653.619 322.835i −0.896597 0.442847i
\(28\) 0 0
\(29\) −502.780 599.189i −0.597835 0.712472i 0.379256 0.925292i \(-0.376180\pi\)
−0.977092 + 0.212819i \(0.931735\pi\)
\(30\) 0 0
\(31\) 226.590 1285.06i 0.235786 1.33721i −0.605166 0.796099i \(-0.706893\pi\)
0.840952 0.541110i \(-0.181996\pi\)
\(32\) 0 0
\(33\) −691.772 + 1260.31i −0.635236 + 1.15731i
\(34\) 0 0
\(35\) 302.129 174.434i 0.246636 0.142395i
\(36\) 0 0
\(37\) −611.487 + 1059.13i −0.446667 + 0.773650i −0.998167 0.0605250i \(-0.980723\pi\)
0.551500 + 0.834175i \(0.314056\pi\)
\(38\) 0 0
\(39\) 1254.30 + 1430.85i 0.824655 + 0.940733i
\(40\) 0 0
\(41\) −11.6088 + 13.8349i −0.00690590 + 0.00823013i −0.769486 0.638663i \(-0.779488\pi\)
0.762580 + 0.646893i \(0.223932\pi\)
\(42\) 0 0
\(43\) −1615.74 588.079i −0.873843 0.318053i −0.134120 0.990965i \(-0.542821\pi\)
−0.739722 + 0.672912i \(0.765043\pi\)
\(44\) 0 0
\(45\) −16.3366 377.765i −0.00806744 0.186551i
\(46\) 0 0
\(47\) 3753.45 661.834i 1.69916 0.299608i 0.761760 0.647860i \(-0.224336\pi\)
0.937401 + 0.348252i \(0.113225\pi\)
\(48\) 0 0
\(49\) −2992.18 + 1089.06i −1.24622 + 0.453587i
\(50\) 0 0
\(51\) 2391.18 + 1919.94i 0.919330 + 0.738154i
\(52\) 0 0
\(53\) 850.088i 0.302630i 0.988486 + 0.151315i \(0.0483508\pi\)
−0.988486 + 0.151315i \(0.951649\pi\)
\(54\) 0 0
\(55\) −745.699 −0.246512
\(56\) 0 0
\(57\) 1105.58 + 2844.73i 0.340282 + 0.875572i
\(58\) 0 0
\(59\) −1077.21 2959.61i −0.309455 0.850220i −0.992763 0.120090i \(-0.961682\pi\)
0.683308 0.730130i \(-0.260540\pi\)
\(60\) 0 0
\(61\) −630.093 3573.43i −0.169334 0.960342i −0.944482 0.328562i \(-0.893436\pi\)
0.775148 0.631780i \(-0.217675\pi\)
\(62\) 0 0
\(63\) −792.627 + 6001.36i −0.199704 + 1.51206i
\(64\) 0 0
\(65\) −337.554 + 927.421i −0.0798944 + 0.219508i
\(66\) 0 0
\(67\) 3089.43 + 2592.34i 0.688223 + 0.577488i 0.918396 0.395662i \(-0.129485\pi\)
−0.230173 + 0.973150i \(0.573929\pi\)
\(68\) 0 0
\(69\) −8191.89 2782.67i −1.72062 0.584471i
\(70\) 0 0
\(71\) 3906.92 + 2255.66i 0.775029 + 0.447463i 0.834666 0.550757i \(-0.185661\pi\)
−0.0596365 + 0.998220i \(0.518994\pi\)
\(72\) 0 0
\(73\) −2203.63 3816.80i −0.413517 0.716232i 0.581755 0.813364i \(-0.302366\pi\)
−0.995271 + 0.0971321i \(0.969033\pi\)
\(74\) 0 0
\(75\) −4641.80 + 2815.39i −0.825208 + 0.500514i
\(76\) 0 0
\(77\) 11756.9 + 2073.06i 1.98295 + 0.349647i
\(78\) 0 0
\(79\) −6846.72 + 5745.08i −1.09706 + 0.920538i −0.997224 0.0744659i \(-0.976275\pi\)
−0.0998315 + 0.995004i \(0.531830\pi\)
\(80\) 0 0
\(81\) 5371.33 + 3767.69i 0.818676 + 0.574256i
\(82\) 0 0
\(83\) −715.401 852.581i −0.103847 0.123760i 0.711618 0.702567i \(-0.247963\pi\)
−0.815464 + 0.578807i \(0.803518\pi\)
\(84\) 0 0
\(85\) −276.200 + 1566.41i −0.0382284 + 0.216804i
\(86\) 0 0
\(87\) 3650.75 + 6019.06i 0.482329 + 0.795225i
\(88\) 0 0
\(89\) 4214.90 2433.47i 0.532117 0.307218i −0.209761 0.977753i \(-0.567269\pi\)
0.741878 + 0.670535i \(0.233935\pi\)
\(90\) 0 0
\(91\) 7900.21 13683.6i 0.954016 1.65240i
\(92\) 0 0
\(93\) −3777.27 + 11119.9i −0.436729 + 1.28569i
\(94\) 0 0
\(95\) −1017.55 + 1212.67i −0.112748 + 0.134367i
\(96\) 0 0
\(97\) −12919.2 4702.22i −1.37307 0.499757i −0.453001 0.891510i \(-0.649647\pi\)
−0.920071 + 0.391753i \(0.871869\pi\)
\(98\) 0 0
\(99\) 7881.12 10262.1i 0.804114 1.04704i
\(100\) 0 0
\(101\) −7328.44 + 1292.20i −0.718404 + 0.126674i −0.520887 0.853625i \(-0.674399\pi\)
−0.197517 + 0.980299i \(0.563288\pi\)
\(102\) 0 0
\(103\) −4986.77 + 1815.04i −0.470051 + 0.171085i −0.566176 0.824285i \(-0.691578\pi\)
0.0961244 + 0.995369i \(0.469355\pi\)
\(104\) 0 0
\(105\) −2926.57 + 1137.38i −0.265449 + 0.103164i
\(106\) 0 0
\(107\) 3224.64i 0.281652i −0.990034 0.140826i \(-0.955024\pi\)
0.990034 0.140826i \(-0.0449759\pi\)
\(108\) 0 0
\(109\) 2220.09 0.186861 0.0934304 0.995626i \(-0.470217\pi\)
0.0934304 + 0.995626i \(0.470217\pi\)
\(110\) 0 0
\(111\) 6891.18 8582.58i 0.559303 0.696582i
\(112\) 0 0
\(113\) −4324.96 11882.7i −0.338708 0.930593i −0.985762 0.168148i \(-0.946221\pi\)
0.647054 0.762444i \(-0.276001\pi\)
\(114\) 0 0
\(115\) −779.232 4419.25i −0.0589212 0.334158i
\(116\) 0 0
\(117\) −9195.33 14447.0i −0.671731 1.05537i
\(118\) 0 0
\(119\) 8709.29 23928.6i 0.615019 1.68975i
\(120\) 0 0
\(121\) −8332.07 6991.44i −0.569092 0.477525i
\(122\) 0 0
\(123\) 122.227 107.145i 0.00807899 0.00708212i
\(124\) 0 0
\(125\) −4965.30 2866.72i −0.317779 0.183470i
\(126\) 0 0
\(127\) 2750.24 + 4763.56i 0.170516 + 0.295342i 0.938600 0.345007i \(-0.112123\pi\)
−0.768085 + 0.640348i \(0.778790\pi\)
\(128\) 0 0
\(129\) 13565.7 + 7446.05i 0.815196 + 0.447452i
\(130\) 0 0
\(131\) 23651.6 + 4170.42i 1.37822 + 0.243017i 0.813163 0.582035i \(-0.197744\pi\)
0.565056 + 0.825053i \(0.308855\pi\)
\(132\) 0 0
\(133\) 19414.1 16290.4i 1.09753 0.920934i
\(134\) 0 0
\(135\) −372.586 + 3382.61i −0.0204437 + 0.185603i
\(136\) 0 0
\(137\) −6566.41 7825.54i −0.349854 0.416940i 0.562205 0.826998i \(-0.309953\pi\)
−0.912060 + 0.410058i \(0.865509\pi\)
\(138\) 0 0
\(139\) −4736.20 + 26860.3i −0.245132 + 1.39021i 0.575053 + 0.818116i \(0.304981\pi\)
−0.820185 + 0.572098i \(0.806130\pi\)
\(140\) 0 0
\(141\) −34294.1 + 741.184i −1.72497 + 0.0372810i
\(142\) 0 0
\(143\) −29248.3 + 16886.5i −1.43030 + 0.825787i
\(144\) 0 0
\(145\) −1825.67 + 3162.16i −0.0868334 + 0.150400i
\(146\) 0 0
\(147\) 28108.4 5585.04i 1.30077 0.258459i
\(148\) 0 0
\(149\) −5860.70 + 6984.51i −0.263984 + 0.314603i −0.881712 0.471788i \(-0.843609\pi\)
0.617728 + 0.786392i \(0.288053\pi\)
\(150\) 0 0
\(151\) −10348.1 3766.40i −0.453844 0.165186i 0.104976 0.994475i \(-0.466523\pi\)
−0.558820 + 0.829289i \(0.688746\pi\)
\(152\) 0 0
\(153\) −18637.3 20356.0i −0.796159 0.869579i
\(154\) 0 0
\(155\) −5998.81 + 1057.75i −0.249690 + 0.0440272i
\(156\) 0 0
\(157\) 27245.9 9916.68i 1.10535 0.402316i 0.276066 0.961139i \(-0.410969\pi\)
0.829287 + 0.558823i \(0.188747\pi\)
\(158\) 0 0
\(159\) 1165.43 7561.50i 0.0460991 0.299098i
\(160\) 0 0
\(161\) 71841.2i 2.77155i
\(162\) 0 0
\(163\) 28656.2 1.07856 0.539279 0.842127i \(-0.318697\pi\)
0.539279 + 0.842127i \(0.318697\pi\)
\(164\) 0 0
\(165\) 6632.97 + 1022.32i 0.243635 + 0.0375508i
\(166\) 0 0
\(167\) 13011.4 + 35748.5i 0.466542 + 1.28181i 0.920483 + 0.390782i \(0.127795\pi\)
−0.453941 + 0.891032i \(0.649982\pi\)
\(168\) 0 0
\(169\) 2802.33 + 15892.8i 0.0981173 + 0.556451i
\(170\) 0 0
\(171\) −5934.07 26819.5i −0.202937 0.917189i
\(172\) 0 0
\(173\) 3685.17 10124.9i 0.123130 0.338298i −0.862778 0.505582i \(-0.831278\pi\)
0.985909 + 0.167285i \(0.0534999\pi\)
\(174\) 0 0
\(175\) 34533.5 + 28977.1i 1.12763 + 0.946191i
\(176\) 0 0
\(177\) 5524.26 + 27802.5i 0.176331 + 0.887436i
\(178\) 0 0
\(179\) −40319.4 23278.4i −1.25837 0.726519i −0.285611 0.958346i \(-0.592196\pi\)
−0.972757 + 0.231827i \(0.925530\pi\)
\(180\) 0 0
\(181\) 4651.64 + 8056.88i 0.141987 + 0.245929i 0.928245 0.371970i \(-0.121317\pi\)
−0.786258 + 0.617899i \(0.787984\pi\)
\(182\) 0 0
\(183\) 705.637 + 32649.4i 0.0210707 + 0.974929i
\(184\) 0 0
\(185\) 5622.27 + 991.357i 0.164274 + 0.0289659i
\(186\) 0 0
\(187\) −41695.2 + 34986.4i −1.19235 + 1.00050i
\(188\) 0 0
\(189\) 15278.0 52295.2i 0.427703 1.46399i
\(190\) 0 0
\(191\) −40513.7 48282.4i −1.11054 1.32349i −0.941167 0.337943i \(-0.890269\pi\)
−0.169377 0.985551i \(-0.554175\pi\)
\(192\) 0 0
\(193\) −8351.64 + 47364.5i −0.224211 + 1.27156i 0.639976 + 0.768395i \(0.278944\pi\)
−0.864187 + 0.503170i \(0.832167\pi\)
\(194\) 0 0
\(195\) 4273.98 7786.61i 0.112399 0.204776i
\(196\) 0 0
\(197\) −21887.7 + 12636.9i −0.563985 + 0.325617i −0.754743 0.656020i \(-0.772239\pi\)
0.190758 + 0.981637i \(0.438905\pi\)
\(198\) 0 0
\(199\) 6646.68 11512.4i 0.167841 0.290709i −0.769819 0.638262i \(-0.779654\pi\)
0.937661 + 0.347552i \(0.112987\pi\)
\(200\) 0 0
\(201\) −23926.4 27294.3i −0.592224 0.675585i
\(202\) 0 0
\(203\) 37574.9 44780.0i 0.911812 1.08666i
\(204\) 0 0
\(205\) 79.2226 + 28.8347i 0.00188513 + 0.000686131i
\(206\) 0 0
\(207\) 69051.7 + 35982.4i 1.61151 + 0.839750i
\(208\) 0 0
\(209\) −53347.9 + 9406.67i −1.22131 + 0.215349i
\(210\) 0 0
\(211\) −28402.4 + 10337.6i −0.637954 + 0.232196i −0.640690 0.767800i \(-0.721352\pi\)
0.00273545 + 0.999996i \(0.499129\pi\)
\(212\) 0 0
\(213\) −31659.5 25420.3i −0.697823 0.560300i
\(214\) 0 0
\(215\) 8026.51i 0.173640i
\(216\) 0 0
\(217\) 97519.4 2.07096
\(218\) 0 0
\(219\) 14368.6 + 36971.4i 0.299589 + 0.770864i
\(220\) 0 0
\(221\) 24638.4 + 67693.3i 0.504460 + 1.38599i
\(222\) 0 0
\(223\) −9815.65 55667.3i −0.197383 1.11941i −0.908984 0.416830i \(-0.863141\pi\)
0.711602 0.702583i \(-0.247970\pi\)
\(224\) 0 0
\(225\) 45148.4 18679.1i 0.891820 0.368971i
\(226\) 0 0
\(227\) −22493.6 + 61800.7i −0.436523 + 1.19934i 0.505216 + 0.862993i \(0.331413\pi\)
−0.941739 + 0.336344i \(0.890809\pi\)
\(228\) 0 0
\(229\) 42755.1 + 35875.8i 0.815299 + 0.684117i 0.951866 0.306514i \(-0.0991625\pi\)
−0.136567 + 0.990631i \(0.543607\pi\)
\(230\) 0 0
\(231\) −101735. 34557.9i −1.90654 0.647625i
\(232\) 0 0
\(233\) 6779.35 + 3914.06i 0.124875 + 0.0720968i 0.561136 0.827723i \(-0.310364\pi\)
−0.436261 + 0.899820i \(0.643698\pi\)
\(234\) 0 0
\(235\) −8895.93 15408.2i −0.161085 0.279008i
\(236\) 0 0
\(237\) 68777.6 41715.8i 1.22448 0.742683i
\(238\) 0 0
\(239\) −71682.9 12639.6i −1.25493 0.221278i −0.493627 0.869674i \(-0.664329\pi\)
−0.761303 + 0.648396i \(0.775440\pi\)
\(240\) 0 0
\(241\) −4923.27 + 4131.12i −0.0847656 + 0.0711268i −0.684186 0.729308i \(-0.739842\pi\)
0.599420 + 0.800435i \(0.295398\pi\)
\(242\) 0 0
\(243\) −42612.5 40877.4i −0.721646 0.692262i
\(244\) 0 0
\(245\) 9554.58 + 11386.7i 0.159177 + 0.189699i
\(246\) 0 0
\(247\) −12449.8 + 70606.5i −0.204066 + 1.15731i
\(248\) 0 0
\(249\) 5194.62 + 8564.47i 0.0837828 + 0.138134i
\(250\) 0 0
\(251\) 8404.40 4852.28i 0.133401 0.0770191i −0.431814 0.901963i \(-0.642126\pi\)
0.565215 + 0.824943i \(0.308793\pi\)
\(252\) 0 0
\(253\) 76779.5 132986.i 1.19951 2.07761i
\(254\) 0 0
\(255\) 4604.27 13554.5i 0.0708077 0.208451i
\(256\) 0 0
\(257\) 41364.9 49296.7i 0.626276 0.746366i −0.355860 0.934539i \(-0.615812\pi\)
0.982136 + 0.188173i \(0.0602565\pi\)
\(258\) 0 0
\(259\) −85886.1 31260.0i −1.28033 0.466004i
\(260\) 0 0
\(261\) −24221.4 58544.4i −0.355565 0.859417i
\(262\) 0 0
\(263\) 43081.5 7596.43i 0.622844 0.109824i 0.146685 0.989183i \(-0.453140\pi\)
0.476159 + 0.879359i \(0.342029\pi\)
\(264\) 0 0
\(265\) 3729.00 1357.24i 0.0531007 0.0193271i
\(266\) 0 0
\(267\) −40827.6 + 15867.2i −0.572706 + 0.222576i
\(268\) 0 0
\(269\) 60652.2i 0.838189i 0.907943 + 0.419094i \(0.137652\pi\)
−0.907943 + 0.419094i \(0.862348\pi\)
\(270\) 0 0
\(271\) −31866.2 −0.433902 −0.216951 0.976183i \(-0.569611\pi\)
−0.216951 + 0.976183i \(0.569611\pi\)
\(272\) 0 0
\(273\) −89031.6 + 110884.i −1.19459 + 1.48780i
\(274\) 0 0
\(275\) −32956.4 90547.1i −0.435788 1.19732i
\(276\) 0 0
\(277\) −8963.47 50834.4i −0.116820 0.662518i −0.985833 0.167729i \(-0.946357\pi\)
0.869013 0.494789i \(-0.164755\pi\)
\(278\) 0 0
\(279\) 48843.6 93732.8i 0.627479 1.20416i
\(280\) 0 0
\(281\) 45325.4 124530.i 0.574022 1.57711i −0.224067 0.974574i \(-0.571934\pi\)
0.798089 0.602539i \(-0.205844\pi\)
\(282\) 0 0
\(283\) 30812.7 + 25854.9i 0.384730 + 0.322827i 0.814556 0.580085i \(-0.196981\pi\)
−0.429826 + 0.902912i \(0.641425\pi\)
\(284\) 0 0
\(285\) 10713.6 9391.61i 0.131900 0.115625i
\(286\) 0 0
\(287\) −1168.88 674.855i −0.0141908 0.00819307i
\(288\) 0 0
\(289\) 16288.2 + 28212.0i 0.195019 + 0.337783i
\(290\) 0 0
\(291\) 108470. + 59537.8i 1.28092 + 0.703083i
\(292\) 0 0
\(293\) 109933. + 19384.2i 1.28054 + 0.225794i 0.772210 0.635368i \(-0.219152\pi\)
0.508331 + 0.861162i \(0.330263\pi\)
\(294\) 0 0
\(295\) −11262.8 + 9450.60i −0.129420 + 0.108596i
\(296\) 0 0
\(297\) −84171.2 + 80476.0i −0.954224 + 0.912334i
\(298\) 0 0
\(299\) −130638. 155689.i −1.46126 1.74146i
\(300\) 0 0
\(301\) 22313.8 126548.i 0.246287 1.39676i
\(302\) 0 0
\(303\) 66957.8 1447.13i 0.729316 0.0157624i
\(304\) 0 0
\(305\) −14669.2 + 8469.28i −0.157691 + 0.0910431i
\(306\) 0 0
\(307\) −45164.5 + 78227.2i −0.479204 + 0.830006i −0.999716 0.0238487i \(-0.992408\pi\)
0.520511 + 0.853855i \(0.325741\pi\)
\(308\) 0 0
\(309\) 46845.5 9308.05i 0.490627 0.0974859i
\(310\) 0 0
\(311\) 38249.6 45584.1i 0.395463 0.471295i −0.531168 0.847267i \(-0.678247\pi\)
0.926631 + 0.375972i \(0.122691\pi\)
\(312\) 0 0
\(313\) −90164.7 32817.3i −0.920339 0.334976i −0.161966 0.986796i \(-0.551783\pi\)
−0.758373 + 0.651820i \(0.774006\pi\)
\(314\) 0 0
\(315\) 27591.1 6104.79i 0.278066 0.0615247i
\(316\) 0 0
\(317\) 84008.5 14813.0i 0.835997 0.147409i 0.260768 0.965401i \(-0.416024\pi\)
0.575229 + 0.817993i \(0.304913\pi\)
\(318\) 0 0
\(319\) −117413. + 42734.9i −1.15381 + 0.419954i
\(320\) 0 0
\(321\) −4420.84 + 28683.1i −0.0429037 + 0.278366i
\(322\) 0 0
\(323\) 115546.i 1.10752i
\(324\) 0 0
\(325\) −127531. −1.20740
\(326\) 0 0
\(327\) −19747.7 3043.65i −0.184680 0.0284642i
\(328\) 0 0
\(329\) 97420.4 + 267660.i 0.900033 + 2.47282i
\(330\) 0 0
\(331\) 11786.7 + 66845.7i 0.107581 + 0.610123i 0.990158 + 0.139955i \(0.0446957\pi\)
−0.882577 + 0.470168i \(0.844193\pi\)
\(332\) 0 0
\(333\) −73063.1 + 66894.3i −0.658885 + 0.603255i
\(334\) 0 0
\(335\) 6439.01 17691.0i 0.0573759 0.157639i
\(336\) 0 0
\(337\) 15610.7 + 13098.9i 0.137456 + 0.115339i 0.708923 0.705286i \(-0.249181\pi\)
−0.571468 + 0.820625i \(0.693626\pi\)
\(338\) 0 0
\(339\) 22179.7 + 111626.i 0.193000 + 0.971328i
\(340\) 0 0
\(341\) −180519. 104223.i −1.55244 0.896301i
\(342\) 0 0
\(343\) −29266.2 50690.6i −0.248759 0.430863i
\(344\) 0 0
\(345\) 872.657 + 40377.3i 0.00733172 + 0.339234i
\(346\) 0 0
\(347\) 117734. + 20759.6i 0.977781 + 0.172409i 0.639630 0.768683i \(-0.279088\pi\)
0.338151 + 0.941092i \(0.390199\pi\)
\(348\) 0 0
\(349\) 69392.2 58227.0i 0.569718 0.478050i −0.311835 0.950136i \(-0.600943\pi\)
0.881552 + 0.472087i \(0.156499\pi\)
\(350\) 0 0
\(351\) 61986.0 + 141112.i 0.503129 + 1.14538i
\(352\) 0 0
\(353\) 126461. + 150710.i 1.01486 + 1.20947i 0.977667 + 0.210158i \(0.0673980\pi\)
0.0371955 + 0.999308i \(0.488158\pi\)
\(354\) 0 0
\(355\) 3656.93 20739.5i 0.0290175 0.164567i
\(356\) 0 0
\(357\) −110274. + 200904.i −0.865239 + 1.57635i
\(358\) 0 0
\(359\) 188927. 109077.i 1.46590 0.846338i 0.466627 0.884454i \(-0.345469\pi\)
0.999273 + 0.0381164i \(0.0121358\pi\)
\(360\) 0 0
\(361\) 7661.62 13270.3i 0.0587904 0.101828i
\(362\) 0 0
\(363\) 64528.6 + 73611.5i 0.489710 + 0.558641i
\(364\) 0 0
\(365\) −13224.5 + 15760.3i −0.0992643 + 0.118299i
\(366\) 0 0
\(367\) 138372. + 50363.4i 1.02735 + 0.373924i 0.800070 0.599906i \(-0.204795\pi\)
0.227277 + 0.973830i \(0.427018\pi\)
\(368\) 0 0
\(369\) −1234.10 + 785.487i −0.00906352 + 0.00576881i
\(370\) 0 0
\(371\) −62565.5 + 11032.0i −0.454556 + 0.0801504i
\(372\) 0 0
\(373\) −71253.4 + 25934.1i −0.512139 + 0.186403i −0.585146 0.810928i \(-0.698963\pi\)
0.0730067 + 0.997331i \(0.476741\pi\)
\(374\) 0 0
\(375\) 40236.0 + 32306.6i 0.286123 + 0.229736i
\(376\) 0 0
\(377\) 165371.i 1.16353i
\(378\) 0 0
\(379\) 138702. 0.965616 0.482808 0.875726i \(-0.339617\pi\)
0.482808 + 0.875726i \(0.339617\pi\)
\(380\) 0 0
\(381\) −17932.7 46142.2i −0.123537 0.317869i
\(382\) 0 0
\(383\) −65429.9 179767.i −0.446045 1.22550i −0.935455 0.353445i \(-0.885010\pi\)
0.489411 0.872053i \(-0.337212\pi\)
\(384\) 0 0
\(385\) −9677.29 54882.6i −0.0652878 0.370266i
\(386\) 0 0
\(387\) −110458. 84830.3i −0.737523 0.566408i
\(388\) 0 0
\(389\) 64370.0 176855.i 0.425387 1.16874i −0.523196 0.852212i \(-0.675260\pi\)
0.948583 0.316529i \(-0.102517\pi\)
\(390\) 0 0
\(391\) −250911. 210539.i −1.64122 1.37714i
\(392\) 0 0
\(393\) −204663. 69521.1i −1.32512 0.450123i
\(394\) 0 0
\(395\) 36132.8 + 20861.3i 0.231584 + 0.133705i
\(396\) 0 0
\(397\) −46197.3 80016.0i −0.293113 0.507687i 0.681431 0.731882i \(-0.261358\pi\)
−0.974544 + 0.224195i \(0.928025\pi\)
\(398\) 0 0
\(399\) −195022. + 118287.i −1.22500 + 0.743002i
\(400\) 0 0
\(401\) 692.633 + 122.130i 0.00430739 + 0.000759510i 0.175801 0.984426i \(-0.443748\pi\)
−0.171494 + 0.985185i \(0.554859\pi\)
\(402\) 0 0
\(403\) −211336. + 177332.i −1.30126 + 1.09189i
\(404\) 0 0
\(405\) 7951.54 29577.4i 0.0484776 0.180322i
\(406\) 0 0
\(407\) 125576. + 149655.i 0.758084 + 0.903449i
\(408\) 0 0
\(409\) −22043.3 + 125014.i −0.131774 + 0.747327i 0.845278 + 0.534326i \(0.179435\pi\)
−0.977052 + 0.213000i \(0.931676\pi\)
\(410\) 0 0
\(411\) 47679.6 + 78610.2i 0.282260 + 0.465367i
\(412\) 0 0
\(413\) 203845. 117690.i 1.19509 0.689984i
\(414\) 0 0
\(415\) −2597.73 + 4499.40i −0.0150834 + 0.0261251i
\(416\) 0 0
\(417\) 78952.7 232429.i 0.454041 1.33665i
\(418\) 0 0
\(419\) −55961.7 + 66692.5i −0.318759 + 0.379882i −0.901503 0.432774i \(-0.857535\pi\)
0.582743 + 0.812656i \(0.301979\pi\)
\(420\) 0 0
\(421\) 49871.4 + 18151.7i 0.281376 + 0.102413i 0.478853 0.877895i \(-0.341053\pi\)
−0.197477 + 0.980308i \(0.563275\pi\)
\(422\) 0 0
\(423\) 306061. + 40422.9i 1.71052 + 0.225916i
\(424\) 0 0
\(425\) −202409. + 35690.2i −1.12060 + 0.197593i
\(426\) 0 0
\(427\) 254824. 92748.2i 1.39760 0.508686i
\(428\) 0 0
\(429\) 283313. 110107.i 1.53940 0.598274i
\(430\) 0 0
\(431\) 133930.i 0.720980i −0.932763 0.360490i \(-0.882609\pi\)
0.932763 0.360490i \(-0.117391\pi\)
\(432\) 0 0
\(433\) −42018.9 −0.224114 −0.112057 0.993702i \(-0.535744\pi\)
−0.112057 + 0.993702i \(0.535744\pi\)
\(434\) 0 0
\(435\) 20574.5 25624.4i 0.108730 0.135417i
\(436\) 0 0
\(437\) −111494. 306327.i −0.583832 1.60406i
\(438\) 0 0
\(439\) −39764.9 225518.i −0.206334 1.17018i −0.895327 0.445410i \(-0.853058\pi\)
0.688993 0.724768i \(-0.258053\pi\)
\(440\) 0 0
\(441\) −257680. + 11143.4i −1.32496 + 0.0572984i
\(442\) 0 0
\(443\) −80393.0 + 220878.i −0.409648 + 1.12550i 0.547728 + 0.836656i \(0.315493\pi\)
−0.957377 + 0.288843i \(0.906730\pi\)
\(444\) 0 0
\(445\) −17404.2 14603.8i −0.0878888 0.0737474i
\(446\) 0 0
\(447\) 61706.2 54092.3i 0.308826 0.270720i
\(448\) 0 0
\(449\) −143947. 83107.7i −0.714018 0.412239i 0.0985287 0.995134i \(-0.468586\pi\)
−0.812547 + 0.582895i \(0.801920\pi\)
\(450\) 0 0
\(451\) 1442.49 + 2498.46i 0.00709184 + 0.0122834i
\(452\) 0 0
\(453\) 86882.5 + 47688.8i 0.423385 + 0.232391i
\(454\) 0 0
\(455\) −72637.8 12808.0i −0.350865 0.0618669i
\(456\) 0 0
\(457\) 101420. 85101.3i 0.485613 0.407478i −0.366838 0.930285i \(-0.619560\pi\)
0.852451 + 0.522807i \(0.175115\pi\)
\(458\) 0 0
\(459\) 137871. + 206617.i 0.654406 + 0.980709i
\(460\) 0 0
\(461\) −42494.6 50643.1i −0.199955 0.238297i 0.656744 0.754113i \(-0.271933\pi\)
−0.856699 + 0.515816i \(0.827489\pi\)
\(462\) 0 0
\(463\) −25053.8 + 142087.i −0.116872 + 0.662817i 0.868934 + 0.494929i \(0.164806\pi\)
−0.985806 + 0.167888i \(0.946305\pi\)
\(464\) 0 0
\(465\) 54809.4 1184.57i 0.253483 0.00547842i
\(466\) 0 0
\(467\) 324271. 187218.i 1.48687 0.858446i 0.486985 0.873411i \(-0.338097\pi\)
0.999888 + 0.0149642i \(0.00476345\pi\)
\(468\) 0 0
\(469\) −150701. + 261021.i −0.685124 + 1.18667i
\(470\) 0 0
\(471\) −255946. + 50855.7i −1.15374 + 0.229244i
\(472\) 0 0
\(473\) −176552. + 210407.i −0.789134 + 0.940453i
\(474\) 0 0
\(475\) −192220. 69962.3i −0.851944 0.310082i
\(476\) 0 0
\(477\) −20733.0 + 65661.6i −0.0911223 + 0.288586i
\(478\) 0 0
\(479\) 376454. 66379.1i 1.64075 0.289308i 0.724306 0.689479i \(-0.242160\pi\)
0.916440 + 0.400171i \(0.131049\pi\)
\(480\) 0 0
\(481\) 242970. 88433.7i 1.05018 0.382233i
\(482\) 0 0
\(483\) 98491.1 639026.i 0.422185 2.73920i
\(484\) 0 0
\(485\) 64179.1i 0.272841i
\(486\) 0 0
\(487\) −170794. −0.720135 −0.360068 0.932926i \(-0.617246\pi\)
−0.360068 + 0.932926i \(0.617246\pi\)
\(488\) 0 0
\(489\) −254896. 39286.4i −1.06597 0.164295i
\(490\) 0 0
\(491\) −93039.5 255624.i −0.385926 1.06032i −0.968818 0.247774i \(-0.920301\pi\)
0.582892 0.812550i \(-0.301921\pi\)
\(492\) 0 0
\(493\) 46279.8 + 262466.i 0.190413 + 1.07989i
\(494\) 0 0
\(495\) −57598.5 18187.0i −0.235072 0.0742252i
\(496\) 0 0
\(497\) −115312. + 316818.i −0.466834 + 1.28262i
\(498\) 0 0
\(499\) 310696. + 260705.i 1.24777 + 1.04700i 0.996875 + 0.0789903i \(0.0251696\pi\)
0.250896 + 0.968014i \(0.419275\pi\)
\(500\) 0 0
\(501\) −66726.3 335820.i −0.265841 1.33792i
\(502\) 0 0
\(503\) −258998. 149532.i −1.02367 0.591016i −0.108505 0.994096i \(-0.534606\pi\)
−0.915165 + 0.403080i \(0.867940\pi\)
\(504\) 0 0
\(505\) 17368.9 + 30083.8i 0.0681067 + 0.117964i
\(506\) 0 0
\(507\) −3138.31 145208.i −0.0122090 0.564903i
\(508\) 0 0
\(509\) −75484.0 13309.9i −0.291353 0.0513734i 0.0260613 0.999660i \(-0.491703\pi\)
−0.317414 + 0.948287i \(0.602815\pi\)
\(510\) 0 0
\(511\) 252315. 211717.i 0.966275 0.810801i
\(512\) 0 0
\(513\) 16015.0 + 246694.i 0.0608545 + 0.937398i
\(514\) 0 0
\(515\) 15923.7 + 18977.1i 0.0600384 + 0.0715510i
\(516\) 0 0
\(517\) 105723. 599586.i 0.395539 2.24321i
\(518\) 0 0
\(519\) −46660.2 + 85008.6i −0.173226 + 0.315593i
\(520\) 0 0
\(521\) −147819. + 85343.1i −0.544570 + 0.314408i −0.746929 0.664904i \(-0.768473\pi\)
0.202359 + 0.979311i \(0.435139\pi\)
\(522\) 0 0
\(523\) 150342. 260400.i 0.549639 0.952003i −0.448660 0.893702i \(-0.648099\pi\)
0.998299 0.0583002i \(-0.0185680\pi\)
\(524\) 0 0
\(525\) −267449. 305094.i −0.970335 1.10692i
\(526\) 0 0
\(527\) −285792. + 340594.i −1.02903 + 1.22635i
\(528\) 0 0
\(529\) 605384. + 220342.i 2.16331 + 0.787382i
\(530\) 0 0
\(531\) −11022.2 254876.i −0.0390912 0.903940i
\(532\) 0 0
\(533\) 3760.29 663.040i 0.0132363 0.00233392i
\(534\) 0 0
\(535\) −14145.2 + 5148.44i −0.0494199 + 0.0179874i
\(536\) 0 0
\(537\) 326726. + 262337.i 1.13301 + 0.909726i
\(538\) 0 0
\(539\) 508654.i 1.75083i
\(540\) 0 0
\(541\) −45127.6 −0.154187 −0.0770935 0.997024i \(-0.524564\pi\)
−0.0770935 + 0.997024i \(0.524564\pi\)
\(542\) 0 0
\(543\) −30330.6 78042.9i −0.102868 0.264688i
\(544\) 0 0
\(545\) −3544.59 9738.67i −0.0119336 0.0327874i
\(546\) 0 0
\(547\) 101751. + 577057.i 0.340066 + 1.92861i 0.369939 + 0.929056i \(0.379379\pi\)
−0.0298729 + 0.999554i \(0.509510\pi\)
\(548\) 0 0
\(549\) 38484.3 291383.i 0.127685 0.966761i
\(550\) 0 0
\(551\) −90720.7 + 249253.i −0.298816 + 0.820989i
\(552\) 0 0
\(553\) −511685. 429354.i −1.67322 1.40399i
\(554\) 0 0
\(555\) −48650.8 16526.0i −0.157944 0.0536514i
\(556\) 0 0
\(557\) −102333. 59082.0i −0.329841 0.190434i 0.325929 0.945394i \(-0.394323\pi\)
−0.655771 + 0.754960i \(0.727656\pi\)
\(558\) 0 0
\(559\) 181762. + 314821.i 0.581674 + 1.00749i
\(560\) 0 0
\(561\) 418843. 254041.i 1.33084 0.807195i
\(562\) 0 0
\(563\) −364046. 64191.1i −1.14852 0.202515i −0.433191 0.901302i \(-0.642613\pi\)
−0.715330 + 0.698787i \(0.753724\pi\)
\(564\) 0 0
\(565\) −45219.7 + 37943.8i −0.141655 + 0.118862i
\(566\) 0 0
\(567\) −207592. + 444219.i −0.645719 + 1.38176i
\(568\) 0 0
\(569\) 34692.3 + 41344.7i 0.107154 + 0.127701i 0.816956 0.576700i \(-0.195660\pi\)
−0.709802 + 0.704402i \(0.751215\pi\)
\(570\) 0 0
\(571\) −36084.4 + 204645.i −0.110674 + 0.627665i 0.878127 + 0.478428i \(0.158793\pi\)
−0.988801 + 0.149238i \(0.952318\pi\)
\(572\) 0 0
\(573\) 294175. + 485013.i 0.895977 + 1.47722i
\(574\) 0 0
\(575\) 502172. 289929.i 1.51886 0.876912i
\(576\) 0 0
\(577\) −328925. + 569715.i −0.987974 + 1.71122i −0.360081 + 0.932921i \(0.617251\pi\)
−0.627893 + 0.778300i \(0.716083\pi\)
\(578\) 0 0
\(579\) 139222. 409856.i 0.415290 1.22257i
\(580\) 0 0
\(581\) 53464.9 63717.0i 0.158386 0.188757i
\(582\) 0 0
\(583\) 127606. + 46444.7i 0.375434 + 0.136647i
\(584\) 0 0
\(585\) −48692.1 + 63402.3i −0.142281 + 0.185265i
\(586\) 0 0
\(587\) −339150. + 59801.2i −0.984272 + 0.173554i −0.642547 0.766246i \(-0.722122\pi\)
−0.341725 + 0.939800i \(0.611011\pi\)
\(588\) 0 0
\(589\) −415817. + 151345.i −1.19859 + 0.436252i
\(590\) 0 0
\(591\) 212015. 82397.5i 0.607004 0.235906i
\(592\) 0 0
\(593\) 222202.i 0.631886i −0.948778 0.315943i \(-0.897679\pi\)
0.948778 0.315943i \(-0.102321\pi\)
\(594\) 0 0
\(595\) −118870. −0.335768
\(596\) 0 0
\(597\) −74904.9 + 93290.0i −0.210166 + 0.261750i
\(598\) 0 0
\(599\) 215568. + 592269.i 0.600801 + 1.65069i 0.749655 + 0.661829i \(0.230220\pi\)
−0.148853 + 0.988859i \(0.547558\pi\)
\(600\) 0 0
\(601\) 50236.9 + 284908.i 0.139083 + 0.788778i 0.971929 + 0.235274i \(0.0755987\pi\)
−0.832846 + 0.553505i \(0.813290\pi\)
\(602\) 0 0
\(603\) 175406. + 275584.i 0.482402 + 0.757913i
\(604\) 0 0
\(605\) −17365.7 + 47712.0i −0.0474441 + 0.130352i
\(606\) 0 0
\(607\) 319799. + 268343.i 0.867959 + 0.728304i 0.963667 0.267105i \(-0.0860671\pi\)
−0.0957082 + 0.995409i \(0.530512\pi\)
\(608\) 0 0
\(609\) −395619. + 346803.i −1.06670 + 0.935079i
\(610\) 0 0
\(611\) −697844. 402900.i −1.86929 1.07923i
\(612\) 0 0
\(613\) 309732. + 536471.i 0.824261 + 1.42766i 0.902483 + 0.430726i \(0.141742\pi\)
−0.0782216 + 0.996936i \(0.524924\pi\)
\(614\) 0 0
\(615\) −665.151 365.094i −0.00175861 0.000965283i
\(616\) 0 0
\(617\) −209190. 36885.8i −0.549502 0.0968921i −0.107998 0.994151i \(-0.534444\pi\)
−0.441505 + 0.897259i \(0.645555\pi\)
\(618\) 0 0
\(619\) 423509. 355367.i 1.10530 0.927460i 0.107534 0.994201i \(-0.465705\pi\)
0.997770 + 0.0667411i \(0.0212601\pi\)
\(620\) 0 0
\(621\) −564882. 414730.i −1.46479 1.07543i
\(622\) 0 0
\(623\) 233800. + 278632.i 0.602376 + 0.717884i
\(624\) 0 0
\(625\) 60818.7 344920.i 0.155696 0.882995i
\(626\) 0 0
\(627\) 487424. 10534.5i 1.23986 0.0267965i
\(628\) 0 0
\(629\) 360877. 208352.i 0.912133 0.526620i
\(630\) 0 0
\(631\) −86024.6 + 148999.i −0.216055 + 0.374218i −0.953598 0.301082i \(-0.902652\pi\)
0.737544 + 0.675300i \(0.235986\pi\)
\(632\) 0 0
\(633\) 266811. 53014.4i 0.665879 0.132308i
\(634\) 0 0
\(635\) 16504.8 19669.7i 0.0409321 0.0487810i
\(636\) 0 0
\(637\) 632610. + 230251.i 1.55904 + 0.567444i
\(638\) 0 0
\(639\) 246761. + 269516.i 0.604330 + 0.660060i
\(640\) 0 0
\(641\) 220023. 38796.0i 0.535491 0.0944216i 0.100638 0.994923i \(-0.467911\pi\)
0.434853 + 0.900502i \(0.356800\pi\)
\(642\) 0 0
\(643\) 249787. 90915.0i 0.604154 0.219894i −0.0217893 0.999763i \(-0.506936\pi\)
0.625943 + 0.779868i \(0.284714\pi\)
\(644\) 0 0
\(645\) 11004.0 71395.6i 0.0264503 0.171614i
\(646\) 0 0
\(647\) 182160.i 0.435155i 0.976043 + 0.217577i \(0.0698155\pi\)
−0.976043 + 0.217577i \(0.930185\pi\)
\(648\) 0 0
\(649\) −503119. −1.19449
\(650\) 0 0
\(651\) −867432. 133695.i −2.04679 0.315466i
\(652\) 0 0
\(653\) 65152.7 + 179006.i 0.152794 + 0.419798i 0.992347 0.123480i \(-0.0394054\pi\)
−0.839553 + 0.543278i \(0.817183\pi\)
\(654\) 0 0
\(655\) −19468.0 110409.i −0.0453774 0.257348i
\(656\) 0 0
\(657\) −77121.8 348558.i −0.178668 0.807504i
\(658\) 0 0
\(659\) −116401. + 319808.i −0.268030 + 0.736407i 0.730536 + 0.682875i \(0.239270\pi\)
−0.998566 + 0.0535329i \(0.982952\pi\)
\(660\) 0 0
\(661\) −252525. 211893.i −0.577964 0.484969i 0.306314 0.951931i \(-0.400904\pi\)
−0.884278 + 0.466961i \(0.845349\pi\)
\(662\) 0 0
\(663\) −126353. 635908.i −0.287447 1.44666i
\(664\) 0 0
\(665\) −102456. 59153.0i −0.231683 0.133762i
\(666\) 0 0
\(667\) −375954. 651171.i −0.845050 1.46367i
\(668\) 0 0
\(669\) 10992.5 + 508616.i 0.0245609 + 1.13642i
\(670\) 0 0
\(671\) −570830. 100653.i −1.26783 0.223553i
\(672\) 0 0
\(673\) −139865. + 117361.i −0.308801 + 0.259115i −0.783996 0.620765i \(-0.786822\pi\)
0.475195 + 0.879880i \(0.342378\pi\)
\(674\) 0 0
\(675\) −427202. + 104254.i −0.937618 + 0.228815i
\(676\) 0 0
\(677\) −15878.7 18923.4i −0.0346447 0.0412879i 0.748444 0.663198i \(-0.230801\pi\)
−0.783089 + 0.621910i \(0.786357\pi\)
\(678\) 0 0
\(679\) 178419. 1.01186e6i 0.386991 2.19474i
\(680\) 0 0
\(681\) 284806. 518877.i 0.614122 1.11885i
\(682\) 0 0
\(683\) 582433. 336268.i 1.24855 0.720849i 0.277727 0.960660i \(-0.410419\pi\)
0.970819 + 0.239811i \(0.0770856\pi\)
\(684\) 0 0
\(685\) −23843.7 + 41298.5i −0.0508150 + 0.0880142i
\(686\) 0 0
\(687\) −331121. 377729.i −0.701574 0.800327i
\(688\) 0 0
\(689\) 115526. 137679.i 0.243356 0.290020i
\(690\) 0 0
\(691\) −422287. 153700.i −0.884406 0.321897i −0.140419 0.990092i \(-0.544845\pi\)
−0.743986 + 0.668195i \(0.767067\pi\)
\(692\) 0 0
\(693\) 857553. + 446866.i 1.78564 + 0.930488i
\(694\) 0 0
\(695\) 125387. 22109.2i 0.259588 0.0457723i
\(696\) 0 0
\(697\) 5782.53 2104.67i 0.0119029 0.00433229i
\(698\) 0 0
\(699\) −54936.1 44109.7i −0.112436 0.0902775i
\(700\) 0 0
\(701\) 819779.i 1.66825i 0.551577 + 0.834124i \(0.314026\pi\)
−0.551577 + 0.834124i \(0.685974\pi\)
\(702\) 0 0
\(703\) 414727. 0.839173
\(704\) 0 0
\(705\) 58005.1 + 149251.i 0.116705 + 0.300290i
\(706\) 0 0
\(707\) −190209. 522595.i −0.380533 1.04551i
\(708\) 0 0
\(709\) −144814. 821282.i −0.288084 1.63380i −0.694058 0.719919i \(-0.744179\pi\)
0.405975 0.913884i \(-0.366932\pi\)
\(710\) 0 0
\(711\) −668965. + 276769.i −1.32332 + 0.547493i
\(712\) 0 0
\(713\) 429020. 1.17872e6i 0.843914 2.31863i
\(714\) 0 0
\(715\) 120772. + 101340.i 0.236240 + 0.198229i
\(716\) 0 0
\(717\) 620289. + 210703.i 1.20658 + 0.409857i
\(718\) 0 0
\(719\) 149544. + 86339.5i 0.289276 + 0.167014i 0.637615 0.770355i \(-0.279921\pi\)
−0.348339 + 0.937369i \(0.613254\pi\)
\(720\) 0 0
\(721\) −198300. 343466.i −0.381463 0.660714i
\(722\) 0 0
\(723\) 49455.9 29996.6i 0.0946111 0.0573846i
\(724\) 0 0
\(725\) −464653. 81930.9i −0.884002 0.155873i
\(726\) 0 0
\(727\) −692985. + 581483.i −1.31116 + 1.10019i −0.323058 + 0.946379i \(0.604711\pi\)
−0.988100 + 0.153813i \(0.950845\pi\)
\(728\) 0 0
\(729\) 322996. + 422023.i 0.607774 + 0.794110i
\(730\) 0 0
\(731\) 376585. + 448797.i 0.704739 + 0.839875i
\(732\) 0 0
\(733\) −89146.5 + 505575.i −0.165919 + 0.940974i 0.782193 + 0.623037i \(0.214101\pi\)
−0.948112 + 0.317937i \(0.897010\pi\)
\(734\) 0 0
\(735\) −69377.0 114383.i −0.128422 0.211733i
\(736\) 0 0
\(737\) 557926. 322119.i 1.02717 0.593036i
\(738\) 0 0
\(739\) 258778. 448217.i 0.473848 0.820729i −0.525704 0.850668i \(-0.676198\pi\)
0.999552 + 0.0299391i \(0.00953133\pi\)
\(740\) 0 0
\(741\) 207539. 610975.i 0.377976 1.11272i
\(742\) 0 0
\(743\) 507847. 605228.i 0.919930 1.09633i −0.0751416 0.997173i \(-0.523941\pi\)
0.995072 0.0991572i \(-0.0316147\pi\)
\(744\) 0 0
\(745\) 39995.4 + 14557.1i 0.0720606 + 0.0262279i
\(746\) 0 0
\(747\) −34464.4 83302.3i −0.0617632 0.149285i
\(748\) 0 0
\(749\) 237330. 41847.6i 0.423047 0.0745946i
\(750\) 0 0
\(751\) −299004. + 108829.i −0.530148 + 0.192958i −0.593205 0.805052i \(-0.702137\pi\)
0.0630562 + 0.998010i \(0.479915\pi\)
\(752\) 0 0
\(753\) −81409.1 + 31638.8i −0.143576 + 0.0557995i
\(754\) 0 0
\(755\) 51406.4i 0.0901827i
\(756\) 0 0
\(757\) −265313. −0.462985 −0.231493 0.972837i \(-0.574361\pi\)
−0.231493 + 0.972837i \(0.574361\pi\)
\(758\) 0 0
\(759\) −865269. + 1.07765e6i −1.50199 + 1.87065i
\(760\) 0 0
\(761\) 40717.9 + 111871.i 0.0703098 + 0.193175i 0.969870 0.243621i \(-0.0783354\pi\)
−0.899561 + 0.436796i \(0.856113\pi\)
\(762\) 0 0
\(763\) 28811.2 + 163396.i 0.0494894 + 0.280668i
\(764\) 0 0
\(765\) −59537.5 + 114255.i −0.101734 + 0.195232i
\(766\) 0 0
\(767\) −227745. + 625726.i −0.387132 + 1.06364i
\(768\) 0 0
\(769\) 155869. + 130789.i 0.263576 + 0.221167i 0.764992 0.644040i \(-0.222743\pi\)
−0.501416 + 0.865206i \(0.667187\pi\)
\(770\) 0 0
\(771\) −435523. + 381784.i −0.732660 + 0.642257i
\(772\) 0 0
\(773\) −861696. 497500.i −1.44210 0.832596i −0.444109 0.895973i \(-0.646480\pi\)
−0.997990 + 0.0633765i \(0.979813\pi\)
\(774\) 0 0
\(775\) −393558. 681663.i −0.655248 1.13492i
\(776\) 0 0
\(777\) 721098. + 395803.i 1.19441 + 0.655597i
\(778\) 0 0
\(779\) 6031.38 + 1063.50i 0.00993898 + 0.00175251i
\(780\) 0 0