Properties

Label 108.5.k.a.65.5
Level 108
Weight 5
Character 108.65
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 65.5
Character \(\chi\) \(=\) 108.65
Dual form 108.5.k.a.5.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.33607 - 8.69153i) q^{3} +(15.1037 - 41.4971i) q^{5} +(8.53787 - 48.4207i) q^{7} +(-70.0855 + 40.6081i) q^{9} +O(q^{10})\) \(q+(-2.33607 - 8.69153i) q^{3} +(15.1037 - 41.4971i) q^{5} +(8.53787 - 48.4207i) q^{7} +(-70.0855 + 40.6081i) q^{9} +(43.7103 + 120.093i) q^{11} +(6.33166 - 5.31289i) q^{13} +(-395.957 - 34.3341i) q^{15} +(51.3995 - 29.6755i) q^{17} +(195.065 - 337.863i) q^{19} +(-440.795 + 38.9071i) q^{21} +(-956.638 + 168.681i) q^{23} +(-1015.11 - 851.777i) q^{25} +(516.672 + 514.287i) q^{27} +(342.577 - 408.267i) q^{29} +(267.572 + 1517.48i) q^{31} +(941.682 - 660.456i) q^{33} +(-1880.36 - 1085.63i) q^{35} +(157.509 + 272.813i) q^{37} +(-60.9684 - 42.6205i) q^{39} +(-1523.53 - 1815.67i) q^{41} +(2059.19 - 749.486i) q^{43} +(626.568 + 3521.68i) q^{45} +(1944.70 + 342.903i) q^{47} +(-15.4624 - 5.62784i) q^{49} +(-377.999 - 377.416i) q^{51} -2837.46i q^{53} +5643.70 q^{55} +(-3392.23 - 906.144i) q^{57} +(-1440.52 + 3957.81i) q^{59} +(-170.879 + 969.103i) q^{61} +(1367.89 + 3740.29i) q^{63} +(-124.838 - 342.990i) q^{65} +(3050.44 - 2559.62i) q^{67} +(3700.88 + 7920.60i) q^{69} +(-2358.33 + 1361.58i) q^{71} +(4483.19 - 7765.12i) q^{73} +(-5031.88 + 10812.7i) q^{75} +(6188.18 - 1091.14i) q^{77} +(2155.80 + 1808.93i) q^{79} +(3262.96 - 5692.08i) q^{81} +(-1372.40 + 1635.57i) q^{83} +(-455.124 - 2581.14i) q^{85} +(-4348.75 - 2023.77i) q^{87} +(-925.164 - 534.144i) q^{89} +(-203.195 - 351.944i) q^{91} +(12564.1 - 5870.55i) q^{93} +(-11074.1 - 13197.6i) q^{95} +(15343.7 - 5584.66i) q^{97} +(-7940.21 - 6641.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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
\(3\) −2.33607 8.69153i −0.259564 0.965726i
\(4\) 0 0
\(5\) 15.1037 41.4971i 0.604148 1.65988i −0.138629 0.990344i \(-0.544270\pi\)
0.742777 0.669539i \(-0.233508\pi\)
\(6\) 0 0
\(7\) 8.53787 48.4207i 0.174242 0.988177i −0.764773 0.644300i \(-0.777149\pi\)
0.939015 0.343876i \(-0.111740\pi\)
\(8\) 0 0
\(9\) −70.0855 + 40.6081i −0.865253 + 0.501335i
\(10\) 0 0
\(11\) 43.7103 + 120.093i 0.361242 + 0.992504i 0.978591 + 0.205815i \(0.0659845\pi\)
−0.617349 + 0.786689i \(0.711793\pi\)
\(12\) 0 0
\(13\) 6.33166 5.31289i 0.0374654 0.0314372i −0.623863 0.781534i \(-0.714438\pi\)
0.661328 + 0.750097i \(0.269993\pi\)
\(14\) 0 0
\(15\) −395.957 34.3341i −1.75981 0.152596i
\(16\) 0 0
\(17\) 51.3995 29.6755i 0.177853 0.102683i −0.408431 0.912789i \(-0.633924\pi\)
0.586283 + 0.810106i \(0.300590\pi\)
\(18\) 0 0
\(19\) 195.065 337.863i 0.540347 0.935909i −0.458537 0.888675i \(-0.651626\pi\)
0.998884 0.0472332i \(-0.0150404\pi\)
\(20\) 0 0
\(21\) −440.795 + 38.9071i −0.999535 + 0.0882246i
\(22\) 0 0
\(23\) −956.638 + 168.681i −1.80839 + 0.318868i −0.973003 0.230793i \(-0.925868\pi\)
−0.835388 + 0.549661i \(0.814757\pi\)
\(24\) 0 0
\(25\) −1015.11 851.777i −1.62417 1.36284i
\(26\) 0 0
\(27\) 516.672 + 514.287i 0.708741 + 0.705469i
\(28\) 0 0
\(29\) 342.577 408.267i 0.407344 0.485454i −0.522900 0.852394i \(-0.675150\pi\)
0.930245 + 0.366940i \(0.119594\pi\)
\(30\) 0 0
\(31\) 267.572 + 1517.48i 0.278431 + 1.57906i 0.727848 + 0.685739i \(0.240521\pi\)
−0.449417 + 0.893322i \(0.648368\pi\)
\(32\) 0 0
\(33\) 941.682 660.456i 0.864722 0.606479i
\(34\) 0 0
\(35\) −1880.36 1085.63i −1.53499 0.886227i
\(36\) 0 0
\(37\) 157.509 + 272.813i 0.115054 + 0.199279i 0.917801 0.397040i \(-0.129963\pi\)
−0.802747 + 0.596319i \(0.796629\pi\)
\(38\) 0 0
\(39\) −60.9684 42.6205i −0.0400844 0.0280214i
\(40\) 0 0
\(41\) −1523.53 1815.67i −0.906323 1.08011i −0.996450 0.0841836i \(-0.973172\pi\)
0.0901271 0.995930i \(-0.471273\pi\)
\(42\) 0 0
\(43\) 2059.19 749.486i 1.11368 0.405346i 0.281338 0.959609i \(-0.409222\pi\)
0.832342 + 0.554262i \(0.187000\pi\)
\(44\) 0 0
\(45\) 626.568 + 3521.68i 0.309416 + 1.73910i
\(46\) 0 0
\(47\) 1944.70 + 342.903i 0.880352 + 0.155230i 0.595513 0.803345i \(-0.296949\pi\)
0.284839 + 0.958575i \(0.408060\pi\)
\(48\) 0 0
\(49\) −15.4624 5.62784i −0.00643997 0.00234396i
\(50\) 0 0
\(51\) −377.999 377.416i −0.145328 0.145104i
\(52\) 0 0
\(53\) 2837.46i 1.01013i −0.863081 0.505065i \(-0.831469\pi\)
0.863081 0.505065i \(-0.168531\pi\)
\(54\) 0 0
\(55\) 5643.70 1.86568
\(56\) 0 0
\(57\) −3392.23 906.144i −1.04409 0.278899i
\(58\) 0 0
\(59\) −1440.52 + 3957.81i −0.413825 + 1.13697i 0.541315 + 0.840820i \(0.317927\pi\)
−0.955140 + 0.296154i \(0.904296\pi\)
\(60\) 0 0
\(61\) −170.879 + 969.103i −0.0459229 + 0.260442i −0.999122 0.0419026i \(-0.986658\pi\)
0.953199 + 0.302344i \(0.0977692\pi\)
\(62\) 0 0
\(63\) 1367.89 + 3740.29i 0.344644 + 0.942377i
\(64\) 0 0
\(65\) −124.838 342.990i −0.0295475 0.0811810i
\(66\) 0 0
\(67\) 3050.44 2559.62i 0.679536 0.570199i −0.236334 0.971672i \(-0.575946\pi\)
0.915871 + 0.401473i \(0.131502\pi\)
\(68\) 0 0
\(69\) 3700.88 + 7920.60i 0.777332 + 1.66364i
\(70\) 0 0
\(71\) −2358.33 + 1361.58i −0.467830 + 0.270102i −0.715331 0.698786i \(-0.753724\pi\)
0.247501 + 0.968888i \(0.420391\pi\)
\(72\) 0 0
\(73\) 4483.19 7765.12i 0.841282 1.45714i −0.0475290 0.998870i \(-0.515135\pi\)
0.888811 0.458274i \(-0.151532\pi\)
\(74\) 0 0
\(75\) −5031.88 + 10812.7i −0.894556 + 1.92225i
\(76\) 0 0
\(77\) 6188.18 1091.14i 1.04371 0.184035i
\(78\) 0 0
\(79\) 2155.80 + 1808.93i 0.345426 + 0.289847i 0.798950 0.601397i \(-0.205389\pi\)
−0.453524 + 0.891244i \(0.649834\pi\)
\(80\) 0 0
\(81\) 3262.96 5692.08i 0.497327 0.867563i
\(82\) 0 0
\(83\) −1372.40 + 1635.57i −0.199217 + 0.237417i −0.856399 0.516314i \(-0.827304\pi\)
0.657182 + 0.753732i \(0.271748\pi\)
\(84\) 0 0
\(85\) −455.124 2581.14i −0.0629930 0.357251i
\(86\) 0 0
\(87\) −4348.75 2023.77i −0.574548 0.267377i
\(88\) 0 0
\(89\) −925.164 534.144i −0.116799 0.0674339i 0.440462 0.897771i \(-0.354814\pi\)
−0.557261 + 0.830337i \(0.688148\pi\)
\(90\) 0 0
\(91\) −203.195 351.944i −0.0245375 0.0425001i
\(92\) 0 0
\(93\) 12564.1 5870.55i 1.45267 0.678755i
\(94\) 0 0
\(95\) −11074.1 13197.6i −1.22705 1.46234i
\(96\) 0 0
\(97\) 15343.7 5584.66i 1.63075 0.593544i 0.645363 0.763876i \(-0.276706\pi\)
0.985387 + 0.170332i \(0.0544841\pi\)
\(98\) 0 0
\(99\) −7940.21 6641.79i −0.810143 0.677664i
\(100\) 0 0
\(101\) −15575.1 2746.31i −1.52682 0.269219i −0.653710 0.756745i \(-0.726788\pi\)
−0.873109 + 0.487526i \(0.837900\pi\)
\(102\) 0 0
\(103\) −10316.3 3754.83i −0.972412 0.353929i −0.193526 0.981095i \(-0.561992\pi\)
−0.778885 + 0.627166i \(0.784215\pi\)
\(104\) 0 0
\(105\) −5043.10 + 18879.3i −0.457424 + 1.71241i
\(106\) 0 0
\(107\) 3099.49i 0.270721i 0.990796 + 0.135361i \(0.0432193\pi\)
−0.990796 + 0.135361i \(0.956781\pi\)
\(108\) 0 0
\(109\) −2838.56 −0.238916 −0.119458 0.992839i \(-0.538116\pi\)
−0.119458 + 0.992839i \(0.538116\pi\)
\(110\) 0 0
\(111\) 2003.22 2006.31i 0.162585 0.162836i
\(112\) 0 0
\(113\) 7212.14 19815.2i 0.564816 1.55182i −0.247673 0.968844i \(-0.579666\pi\)
0.812489 0.582976i \(-0.198112\pi\)
\(114\) 0 0
\(115\) −7449.01 + 42245.4i −0.563252 + 3.19436i
\(116\) 0 0
\(117\) −228.011 + 629.473i −0.0166565 + 0.0459839i
\(118\) 0 0
\(119\) −998.065 2742.16i −0.0704799 0.193642i
\(120\) 0 0
\(121\) −1296.09 + 1087.55i −0.0885246 + 0.0742810i
\(122\) 0 0
\(123\) −12221.9 + 17483.3i −0.807845 + 1.15562i
\(124\) 0 0
\(125\) −26775.7 + 15458.9i −1.71364 + 0.989372i
\(126\) 0 0
\(127\) −5070.21 + 8781.86i −0.314354 + 0.544476i −0.979300 0.202415i \(-0.935121\pi\)
0.664946 + 0.746891i \(0.268454\pi\)
\(128\) 0 0
\(129\) −11324.6 16146.7i −0.680525 0.970297i
\(130\) 0 0
\(131\) 7455.32 1314.57i 0.434434 0.0766024i 0.0478455 0.998855i \(-0.484764\pi\)
0.386589 + 0.922252i \(0.373653\pi\)
\(132\) 0 0
\(133\) −14694.1 12329.8i −0.830692 0.697033i
\(134\) 0 0
\(135\) 29145.1 13672.7i 1.59918 0.750219i
\(136\) 0 0
\(137\) 2071.34 2468.52i 0.110359 0.131521i −0.708037 0.706175i \(-0.750419\pi\)
0.818396 + 0.574654i \(0.194863\pi\)
\(138\) 0 0
\(139\) −5631.07 31935.4i −0.291448 1.65289i −0.681298 0.732007i \(-0.738584\pi\)
0.389849 0.920879i \(-0.372527\pi\)
\(140\) 0 0
\(141\) −1562.61 17703.5i −0.0785980 0.890471i
\(142\) 0 0
\(143\) 914.800 + 528.160i 0.0447357 + 0.0258282i
\(144\) 0 0
\(145\) −11767.7 20382.3i −0.559701 0.969430i
\(146\) 0 0
\(147\) −12.7933 + 147.539i −0.000592037 + 0.00682765i
\(148\) 0 0
\(149\) 3566.54 + 4250.44i 0.160648 + 0.191453i 0.840364 0.542023i \(-0.182341\pi\)
−0.679716 + 0.733476i \(0.737897\pi\)
\(150\) 0 0
\(151\) 40345.3 14684.5i 1.76945 0.644029i 0.769469 0.638684i \(-0.220521\pi\)
0.999986 0.00534447i \(-0.00170121\pi\)
\(152\) 0 0
\(153\) −2397.29 + 4167.06i −0.102409 + 0.178011i
\(154\) 0 0
\(155\) 67012.2 + 11816.1i 2.78927 + 0.491824i
\(156\) 0 0
\(157\) −417.986 152.134i −0.0169575 0.00617203i 0.333527 0.942740i \(-0.391761\pi\)
−0.350485 + 0.936568i \(0.613983\pi\)
\(158\) 0 0
\(159\) −24661.8 + 6628.51i −0.975509 + 0.262193i
\(160\) 0 0
\(161\) 47761.2i 1.84257i
\(162\) 0 0
\(163\) −697.311 −0.0262453 −0.0131226 0.999914i \(-0.504177\pi\)
−0.0131226 + 0.999914i \(0.504177\pi\)
\(164\) 0 0
\(165\) −13184.1 49052.4i −0.484264 1.80174i
\(166\) 0 0
\(167\) 3648.98 10025.5i 0.130839 0.359479i −0.856923 0.515445i \(-0.827627\pi\)
0.987762 + 0.155966i \(0.0498490\pi\)
\(168\) 0 0
\(169\) −4947.70 + 28059.8i −0.173233 + 0.982452i
\(170\) 0 0
\(171\) 48.7322 + 31600.5i 0.00166657 + 1.08069i
\(172\) 0 0
\(173\) 18317.0 + 50325.5i 0.612015 + 1.68150i 0.725727 + 0.687983i \(0.241504\pi\)
−0.113712 + 0.993514i \(0.536274\pi\)
\(174\) 0 0
\(175\) −49910.4 + 41879.8i −1.62973 + 1.36750i
\(176\) 0 0
\(177\) 37764.6 + 3274.63i 1.20542 + 0.104524i
\(178\) 0 0
\(179\) 6224.26 3593.58i 0.194259 0.112156i −0.399716 0.916639i \(-0.630891\pi\)
0.593975 + 0.804484i \(0.297558\pi\)
\(180\) 0 0
\(181\) 22245.3 38530.1i 0.679019 1.17610i −0.296258 0.955108i \(-0.595739\pi\)
0.975277 0.220987i \(-0.0709279\pi\)
\(182\) 0 0
\(183\) 8822.18 778.696i 0.263435 0.0232523i
\(184\) 0 0
\(185\) 13699.9 2415.67i 0.400290 0.0705820i
\(186\) 0 0
\(187\) 5810.51 + 4875.59i 0.166162 + 0.139426i
\(188\) 0 0
\(189\) 29313.4 20626.7i 0.820621 0.577438i
\(190\) 0 0
\(191\) 10413.0 12409.7i 0.285436 0.340170i −0.604206 0.796828i \(-0.706509\pi\)
0.889642 + 0.456659i \(0.150954\pi\)
\(192\) 0 0
\(193\) 7032.75 + 39884.7i 0.188804 + 1.07076i 0.920970 + 0.389633i \(0.127398\pi\)
−0.732167 + 0.681126i \(0.761491\pi\)
\(194\) 0 0
\(195\) −2689.47 + 1886.28i −0.0707291 + 0.0496064i
\(196\) 0 0
\(197\) −1269.74 733.085i −0.0327177 0.0188896i 0.483552 0.875316i \(-0.339346\pi\)
−0.516270 + 0.856426i \(0.672680\pi\)
\(198\) 0 0
\(199\) 25177.4 + 43608.5i 0.635776 + 1.10120i 0.986350 + 0.164661i \(0.0526531\pi\)
−0.350574 + 0.936535i \(0.614014\pi\)
\(200\) 0 0
\(201\) −29373.1 20533.5i −0.727039 0.508243i
\(202\) 0 0
\(203\) −16843.7 20073.5i −0.408738 0.487115i
\(204\) 0 0
\(205\) −98356.0 + 35798.7i −2.34042 + 0.851842i
\(206\) 0 0
\(207\) 60196.7 50669.4i 1.40486 1.18251i
\(208\) 0 0
\(209\) 49101.4 + 8657.89i 1.12409 + 0.198207i
\(210\) 0 0
\(211\) −62282.9 22669.1i −1.39895 0.509178i −0.471087 0.882087i \(-0.656138\pi\)
−0.927868 + 0.372909i \(0.878360\pi\)
\(212\) 0 0
\(213\) 17343.5 + 17316.8i 0.382276 + 0.381687i
\(214\) 0 0
\(215\) 96770.6i 2.09347i
\(216\) 0 0
\(217\) 75761.8 1.60891
\(218\) 0 0
\(219\) −77963.9 20825.9i −1.62557 0.434226i
\(220\) 0 0
\(221\) 167.781 460.975i 0.00343525 0.00943828i
\(222\) 0 0
\(223\) −8376.59 + 47506.0i −0.168445 + 0.955297i 0.776997 + 0.629505i \(0.216742\pi\)
−0.945441 + 0.325793i \(0.894369\pi\)
\(224\) 0 0
\(225\) 105733. + 18475.6i 2.08856 + 0.364950i
\(226\) 0 0
\(227\) 28224.9 + 77547.3i 0.547748 + 1.50493i 0.836743 + 0.547595i \(0.184457\pi\)
−0.288995 + 0.957331i \(0.593321\pi\)
\(228\) 0 0
\(229\) −51383.6 + 43116.0i −0.979837 + 0.822181i −0.984065 0.177810i \(-0.943099\pi\)
0.00422786 + 0.999991i \(0.498654\pi\)
\(230\) 0 0
\(231\) −23939.7 51235.7i −0.448637 0.960172i
\(232\) 0 0
\(233\) −74125.1 + 42796.1i −1.36538 + 0.788302i −0.990334 0.138704i \(-0.955706\pi\)
−0.375046 + 0.927006i \(0.622373\pi\)
\(234\) 0 0
\(235\) 43601.6 75520.2i 0.789527 1.36750i
\(236\) 0 0
\(237\) 10686.3 22963.0i 0.190252 0.408820i
\(238\) 0 0
\(239\) −41173.0 + 7259.90i −0.720802 + 0.127097i −0.522003 0.852943i \(-0.674815\pi\)
−0.198799 + 0.980040i \(0.563704\pi\)
\(240\) 0 0
\(241\) 14342.0 + 12034.4i 0.246931 + 0.207200i 0.757850 0.652429i \(-0.226250\pi\)
−0.510918 + 0.859629i \(0.670695\pi\)
\(242\) 0 0
\(243\) −57095.5 15063.0i −0.966916 0.255093i
\(244\) 0 0
\(245\) −467.078 + 556.642i −0.00778139 + 0.00927350i
\(246\) 0 0
\(247\) −559.943 3175.59i −0.00917804 0.0520512i
\(248\) 0 0
\(249\) 17421.6 + 8107.50i 0.280990 + 0.130764i
\(250\) 0 0
\(251\) 10300.5 + 5946.97i 0.163497 + 0.0943949i 0.579516 0.814961i \(-0.303242\pi\)
−0.416019 + 0.909356i \(0.636575\pi\)
\(252\) 0 0
\(253\) −62072.4 107513.i −0.969744 1.67965i
\(254\) 0 0
\(255\) −21370.8 + 9985.46i −0.328656 + 0.153563i
\(256\) 0 0
\(257\) 31637.2 + 37703.7i 0.478996 + 0.570845i 0.950383 0.311081i \(-0.100691\pi\)
−0.471387 + 0.881926i \(0.656247\pi\)
\(258\) 0 0
\(259\) 14554.6 5297.44i 0.216970 0.0789708i
\(260\) 0 0
\(261\) −7430.70 + 42525.0i −0.109081 + 0.624257i
\(262\) 0 0
\(263\) 1880.97 + 331.666i 0.0271939 + 0.00479501i 0.187229 0.982316i \(-0.440050\pi\)
−0.160035 + 0.987111i \(0.551161\pi\)
\(264\) 0 0
\(265\) −117746. 42856.1i −1.67670 0.610268i
\(266\) 0 0
\(267\) −2481.28 + 9288.89i −0.0348059 + 0.130299i
\(268\) 0 0
\(269\) 34061.9i 0.470721i 0.971908 + 0.235361i \(0.0756271\pi\)
−0.971908 + 0.235361i \(0.924373\pi\)
\(270\) 0 0
\(271\) −4544.07 −0.0618737 −0.0309369 0.999521i \(-0.509849\pi\)
−0.0309369 + 0.999521i \(0.509849\pi\)
\(272\) 0 0
\(273\) −2584.25 + 2588.24i −0.0346745 + 0.0347280i
\(274\) 0 0
\(275\) 57921.8 159139.i 0.765908 2.10431i
\(276\) 0 0
\(277\) 9712.10 55080.0i 0.126577 0.717852i −0.853782 0.520630i \(-0.825697\pi\)
0.980359 0.197222i \(-0.0631918\pi\)
\(278\) 0 0
\(279\) −80374.9 95487.6i −1.03255 1.22670i
\(280\) 0 0
\(281\) −11916.1 32739.2i −0.150911 0.414625i 0.841083 0.540906i \(-0.181918\pi\)
−0.991995 + 0.126280i \(0.959696\pi\)
\(282\) 0 0
\(283\) 77800.4 65282.3i 0.971424 0.815121i −0.0113496 0.999936i \(-0.503613\pi\)
0.982773 + 0.184814i \(0.0591683\pi\)
\(284\) 0 0
\(285\) −88837.6 + 127082.i −1.09372 + 1.56456i
\(286\) 0 0
\(287\) −100924. + 58268.3i −1.22526 + 0.707406i
\(288\) 0 0
\(289\) −39999.2 + 69280.7i −0.478912 + 0.829500i
\(290\) 0 0
\(291\) −84383.3 120314.i −0.996484 1.42079i
\(292\) 0 0
\(293\) −81181.4 + 14314.5i −0.945630 + 0.166740i −0.625141 0.780512i \(-0.714959\pi\)
−0.320490 + 0.947252i \(0.603847\pi\)
\(294\) 0 0
\(295\) 142480. + 119555.i 1.63723 + 1.37380i
\(296\) 0 0
\(297\) −39178.4 + 84528.3i −0.444154 + 0.958273i
\(298\) 0 0
\(299\) −5160.92 + 6150.55i −0.0577278 + 0.0687973i
\(300\) 0 0
\(301\) −18709.5 106107.i −0.206504 1.17114i
\(302\) 0 0
\(303\) 12514.9 + 141787.i 0.136315 + 1.54437i
\(304\) 0 0
\(305\) 37634.0 + 21728.0i 0.404558 + 0.233572i
\(306\) 0 0
\(307\) 39583.0 + 68559.8i 0.419983 + 0.727433i 0.995937 0.0900495i \(-0.0287025\pi\)
−0.575954 + 0.817482i \(0.695369\pi\)
\(308\) 0 0
\(309\) −8535.57 + 98436.2i −0.0893955 + 1.03095i
\(310\) 0 0
\(311\) 8502.04 + 10132.3i 0.0879027 + 0.104758i 0.808203 0.588904i \(-0.200440\pi\)
−0.720300 + 0.693662i \(0.755996\pi\)
\(312\) 0 0
\(313\) 18431.7 6708.58i 0.188138 0.0684766i −0.246233 0.969211i \(-0.579193\pi\)
0.434371 + 0.900734i \(0.356971\pi\)
\(314\) 0 0
\(315\) 175871. 271.217i 1.77245 0.00273335i
\(316\) 0 0
\(317\) 6921.15 + 1220.39i 0.0688747 + 0.0121445i 0.207979 0.978133i \(-0.433311\pi\)
−0.139105 + 0.990278i \(0.544422\pi\)
\(318\) 0 0
\(319\) 64004.1 + 23295.6i 0.628965 + 0.228925i
\(320\) 0 0
\(321\) 26939.3 7240.63i 0.261443 0.0702694i
\(322\) 0 0
\(323\) 23154.6i 0.221939i
\(324\) 0 0
\(325\) −10952.7 −0.103694
\(326\) 0 0
\(327\) 6631.09 + 24671.4i 0.0620139 + 0.230727i
\(328\) 0 0
\(329\) 33207.2 91235.9i 0.306789 0.842896i
\(330\) 0 0
\(331\) −329.445 + 1868.37i −0.00300695 + 0.0170533i −0.986274 0.165115i \(-0.947200\pi\)
0.983267 + 0.182168i \(0.0583116\pi\)
\(332\) 0 0
\(333\) −22117.5 12724.1i −0.199457 0.114747i
\(334\) 0 0
\(335\) −60143.9 165244.i −0.535923 1.47244i
\(336\) 0 0
\(337\) 96024.8 80574.4i 0.845519 0.709475i −0.113279 0.993563i \(-0.536135\pi\)
0.958798 + 0.284088i \(0.0916909\pi\)
\(338\) 0 0
\(339\) −189072. 16394.8i −1.64524 0.142662i
\(340\) 0 0
\(341\) −170543. + 98462.9i −1.46664 + 0.846767i
\(342\) 0 0
\(343\) 58621.2 101535.i 0.498272 0.863032i
\(344\) 0 0
\(345\) 384579. 33945.1i 3.23108 0.285193i
\(346\) 0 0
\(347\) 191137. 33702.5i 1.58739 0.279901i 0.690898 0.722952i \(-0.257215\pi\)
0.896496 + 0.443051i \(0.146104\pi\)
\(348\) 0 0
\(349\) 153791. + 129046.i 1.26264 + 1.05948i 0.995395 + 0.0958560i \(0.0305588\pi\)
0.267248 + 0.963628i \(0.413886\pi\)
\(350\) 0 0
\(351\) 6003.74 + 511.268i 0.0487313 + 0.00414987i
\(352\) 0 0
\(353\) −226.590 + 270.039i −0.00181841 + 0.00216709i −0.766953 0.641703i \(-0.778228\pi\)
0.765134 + 0.643871i \(0.222672\pi\)
\(354\) 0 0
\(355\) 20882.2 + 118429.i 0.165699 + 0.939725i
\(356\) 0 0
\(357\) −21502.0 + 15080.6i −0.168711 + 0.118327i
\(358\) 0 0
\(359\) 14162.8 + 8176.91i 0.109891 + 0.0634454i 0.553938 0.832558i \(-0.313124\pi\)
−0.444047 + 0.896003i \(0.646458\pi\)
\(360\) 0 0
\(361\) −10940.5 18949.4i −0.0839501 0.145406i
\(362\) 0 0
\(363\) 12480.2 + 8724.41i 0.0947128 + 0.0662099i
\(364\) 0 0
\(365\) −254517. 303321.i −1.91043 2.27676i
\(366\) 0 0
\(367\) −61422.1 + 22355.8i −0.456029 + 0.165981i −0.559813 0.828619i \(-0.689127\pi\)
0.103784 + 0.994600i \(0.466905\pi\)
\(368\) 0 0
\(369\) 180508. + 65384.6i 1.32570 + 0.480201i
\(370\) 0 0
\(371\) −137391. 24225.8i −0.998187 0.176007i
\(372\) 0 0
\(373\) 126454. + 46025.4i 0.908896 + 0.330811i 0.753812 0.657090i \(-0.228213\pi\)
0.155084 + 0.987901i \(0.450435\pi\)
\(374\) 0 0
\(375\) 196912. + 196608.i 1.40026 + 1.39810i
\(376\) 0 0
\(377\) 4405.08i 0.0309935i
\(378\) 0 0
\(379\) −34222.9 −0.238253 −0.119126 0.992879i \(-0.538009\pi\)
−0.119126 + 0.992879i \(0.538009\pi\)
\(380\) 0 0
\(381\) 88172.2 + 23552.8i 0.607410 + 0.162253i
\(382\) 0 0
\(383\) −45187.3 + 124151.i −0.308048 + 0.846356i 0.684989 + 0.728554i \(0.259807\pi\)
−0.993037 + 0.117802i \(0.962415\pi\)
\(384\) 0 0
\(385\) 48185.1 273271.i 0.325081 1.84363i
\(386\) 0 0
\(387\) −113885. + 136148.i −0.760401 + 0.909054i
\(388\) 0 0
\(389\) 78137.1 + 214680.i 0.516366 + 1.41871i 0.874496 + 0.485033i \(0.161192\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(390\) 0 0
\(391\) −44165.0 + 37058.9i −0.288885 + 0.242403i
\(392\) 0 0
\(393\) −28841.9 61727.2i −0.186740 0.399661i
\(394\) 0 0
\(395\) 107626. 62137.9i 0.689800 0.398256i
\(396\) 0 0
\(397\) −59361.6 + 102817.i −0.376638 + 0.652357i −0.990571 0.137002i \(-0.956253\pi\)
0.613932 + 0.789359i \(0.289587\pi\)
\(398\) 0 0
\(399\) −72838.5 + 156518.i −0.457526 + 0.983145i
\(400\) 0 0
\(401\) −29720.7 + 5240.56i −0.184829 + 0.0325903i −0.265296 0.964167i \(-0.585470\pi\)
0.0804674 + 0.996757i \(0.474359\pi\)
\(402\) 0 0
\(403\) 9756.37 + 8186.57i 0.0600728 + 0.0504071i
\(404\) 0 0
\(405\) −186922. 221375.i −1.13959 1.34964i
\(406\) 0 0
\(407\) −25878.2 + 30840.5i −0.156223 + 0.186180i
\(408\) 0 0
\(409\) −30526.3 173123.i −0.182485 1.03493i −0.929144 0.369718i \(-0.879454\pi\)
0.746659 0.665207i \(-0.231657\pi\)
\(410\) 0 0
\(411\) −26294.0 12236.4i −0.155659 0.0724388i
\(412\) 0 0
\(413\) 179341. + 103542.i 1.05143 + 0.607041i
\(414\) 0 0
\(415\) 47142.9 + 81653.9i 0.273729 + 0.474112i
\(416\) 0 0
\(417\) −264413. + 123546.i −1.52058 + 0.710488i
\(418\) 0 0
\(419\) 113503. + 135267.i 0.646514 + 0.770486i 0.985384 0.170348i \(-0.0544891\pi\)
−0.338870 + 0.940833i \(0.610045\pi\)
\(420\) 0 0
\(421\) −56524.7 + 20573.3i −0.318914 + 0.116075i −0.496517 0.868027i \(-0.665388\pi\)
0.177603 + 0.984102i \(0.443166\pi\)
\(422\) 0 0
\(423\) −150220. + 54938.0i −0.839550 + 0.307038i
\(424\) 0 0
\(425\) −77452.9 13657.0i −0.428805 0.0756099i
\(426\) 0 0
\(427\) 45465.7 + 16548.1i 0.249361 + 0.0907598i
\(428\) 0 0
\(429\) 2453.48 9184.83i 0.0133312 0.0499065i
\(430\) 0 0
\(431\) 340028.i 1.83046i −0.402932 0.915230i \(-0.632009\pi\)
0.402932 0.915230i \(-0.367991\pi\)
\(432\) 0 0
\(433\) 207455. 1.10649 0.553246 0.833018i \(-0.313389\pi\)
0.553246 + 0.833018i \(0.313389\pi\)
\(434\) 0 0
\(435\) −149663. + 149894.i −0.790926 + 0.792147i
\(436\) 0 0
\(437\) −129616. + 356117.i −0.678727 + 1.86479i
\(438\) 0 0
\(439\) 31086.7 176301.i 0.161304 0.914801i −0.791490 0.611183i \(-0.790694\pi\)
0.952794 0.303618i \(-0.0981948\pi\)
\(440\) 0 0
\(441\) 1312.22 233.468i 0.00674731 0.00120046i
\(442\) 0 0
\(443\) −91577.4 251607.i −0.466639 1.28208i −0.920408 0.390960i \(-0.872143\pi\)
0.453769 0.891119i \(-0.350079\pi\)
\(444\) 0 0
\(445\) −36138.8 + 30324.0i −0.182496 + 0.153132i
\(446\) 0 0
\(447\) 28611.2 40928.1i 0.143193 0.204836i
\(448\) 0 0
\(449\) −67183.1 + 38788.2i −0.333248 + 0.192401i −0.657282 0.753645i \(-0.728294\pi\)
0.324034 + 0.946045i \(0.394961\pi\)
\(450\) 0 0
\(451\) 151456. 262329.i 0.744616 1.28971i
\(452\) 0 0
\(453\) −221881. 316359.i −1.08124 1.54164i
\(454\) 0 0
\(455\) −17673.6 + 3116.34i −0.0853695 + 0.0150530i
\(456\) 0 0
\(457\) −109698. 92047.6i −0.525250 0.440737i 0.341207 0.939988i \(-0.389164\pi\)
−0.866458 + 0.499251i \(0.833609\pi\)
\(458\) 0 0
\(459\) 41818.4 + 11101.6i 0.198492 + 0.0526938i
\(460\) 0 0
\(461\) 126706. 151002.i 0.596204 0.710529i −0.380581 0.924747i \(-0.624276\pi\)
0.976786 + 0.214219i \(0.0687205\pi\)
\(462\) 0 0
\(463\) 16939.0 + 96065.6i 0.0790177 + 0.448132i 0.998488 + 0.0549721i \(0.0175070\pi\)
−0.919470 + 0.393160i \(0.871382\pi\)
\(464\) 0 0
\(465\) −53845.8 610042.i −0.249027 2.82133i
\(466\) 0 0
\(467\) 35247.4 + 20350.1i 0.161619 + 0.0933108i 0.578628 0.815592i \(-0.303588\pi\)
−0.417009 + 0.908902i \(0.636922\pi\)
\(468\) 0 0
\(469\) −97894.3 169558.i −0.445053 0.770855i
\(470\) 0 0
\(471\) −345.835 + 3988.33i −0.00155893 + 0.0179783i
\(472\) 0 0
\(473\) 180016. + 214535.i 0.804616 + 0.958904i
\(474\) 0 0
\(475\) −485796. + 176815.i −2.15311 + 0.783669i
\(476\) 0 0
\(477\) 115224. + 198865.i 0.506413 + 0.874018i
\(478\) 0 0
\(479\) 172260. + 30374.0i 0.750779 + 0.132383i 0.535927 0.844264i \(-0.319962\pi\)
0.214852 + 0.976647i \(0.431073\pi\)
\(480\) 0 0
\(481\) 2446.72 + 890.534i 0.0105753 + 0.00384911i
\(482\) 0 0
\(483\) 415118. 111574.i 1.77942 0.478264i
\(484\) 0 0
\(485\) 721068.i 3.06544i
\(486\) 0 0
\(487\) −126602. −0.533804 −0.266902 0.963724i \(-0.586000\pi\)
−0.266902 + 0.963724i \(0.586000\pi\)
\(488\) 0 0
\(489\) 1628.97 + 6060.70i 0.00681232 + 0.0253458i
\(490\) 0 0
\(491\) −50828.3 + 139650.i −0.210835 + 0.579264i −0.999361 0.0357367i \(-0.988622\pi\)
0.788526 + 0.615001i \(0.210844\pi\)
\(492\) 0 0
\(493\) 5492.73 31150.8i 0.0225993 0.128167i
\(494\) 0 0
\(495\) −395541. + 229180.i −1.61429 + 0.935333i
\(496\) 0 0
\(497\) 45793.6 + 125817.i 0.185393 + 0.509362i
\(498\) 0 0
\(499\) −241396. + 202555.i −0.969457 + 0.813471i −0.982466 0.186444i \(-0.940304\pi\)
0.0130085 + 0.999915i \(0.495859\pi\)
\(500\) 0 0
\(501\) −95661.2 8294.95i −0.381119 0.0330475i
\(502\) 0 0
\(503\) −246833. + 142509.i −0.975589 + 0.563256i −0.900935 0.433953i \(-0.857118\pi\)
−0.0746533 + 0.997210i \(0.523785\pi\)
\(504\) 0 0
\(505\) −349205. + 604841.i −1.36930 + 2.37169i
\(506\) 0 0
\(507\) 255441. 22546.7i 0.993745 0.0877135i
\(508\) 0 0
\(509\) −270821. + 47753.0i −1.04531 + 0.184317i −0.669832 0.742513i \(-0.733634\pi\)
−0.375481 + 0.926830i \(0.622523\pi\)
\(510\) 0 0
\(511\) −337715. 283377.i −1.29333 1.08523i
\(512\) 0 0
\(513\) 274543. 74244.8i 1.04322 0.282118i
\(514\) 0 0
\(515\) −311629. + 371385.i −1.17496 + 1.40026i
\(516\) 0 0
\(517\) 43823.1 + 248533.i 0.163954 + 0.929829i
\(518\) 0 0
\(519\) 394616. 276767.i 1.46501 1.02749i
\(520\) 0 0
\(521\) 312798. + 180594.i 1.15236 + 0.665315i 0.949461 0.313884i \(-0.101630\pi\)
0.202899 + 0.979200i \(0.434964\pi\)
\(522\) 0 0
\(523\) 164895. + 285607.i 0.602845 + 1.04416i 0.992388 + 0.123149i \(0.0392994\pi\)
−0.389544 + 0.921008i \(0.627367\pi\)
\(524\) 0 0
\(525\) 480594. + 335964.i 1.74365 + 1.21892i
\(526\) 0 0
\(527\) 58785.0 + 70057.2i 0.211663 + 0.252250i
\(528\) 0 0
\(529\) 623739. 227023.i 2.22891 0.811255i
\(530\) 0 0
\(531\) −59759.3 335882.i −0.211942 1.19124i
\(532\) 0 0
\(533\) −19292.9 3401.86i −0.0679116 0.0119746i
\(534\) 0 0
\(535\) 128620. + 46813.7i 0.449366 + 0.163556i
\(536\) 0 0
\(537\) −45774.0 45703.5i −0.158734 0.158490i
\(538\) 0 0
\(539\) 2102.92i 0.00723843i
\(540\) 0 0
\(541\) −458131. −1.56529 −0.782645 0.622468i \(-0.786130\pi\)
−0.782645 + 0.622468i \(0.786130\pi\)
\(542\) 0 0
\(543\) −386852. 103337.i −1.31203 0.350474i
\(544\) 0 0
\(545\) −42872.8 + 117792.i −0.144341 + 0.396573i
\(546\) 0 0
\(547\) −100576. + 570394.i −0.336139 + 1.90634i 0.0795459 + 0.996831i \(0.474653\pi\)
−0.415685 + 0.909509i \(0.636458\pi\)
\(548\) 0 0
\(549\) −27377.3 74859.2i −0.0908335 0.248371i
\(550\) 0 0
\(551\) −71113.5 195383.i −0.234233 0.643551i
\(552\) 0 0
\(553\) 105996. 88940.9i 0.346607 0.290838i
\(554\) 0 0
\(555\) −52999.9 113430.i −0.172064 0.368250i
\(556\) 0 0
\(557\) 254413. 146885.i 0.820027 0.473443i −0.0303989 0.999538i \(-0.509678\pi\)
0.850426 + 0.526095i \(0.176344\pi\)
\(558\) 0 0
\(559\) 9056.18 15685.8i 0.0289815 0.0501975i
\(560\) 0 0
\(561\) 28802.6 61892.0i 0.0915179 0.196657i
\(562\) 0 0
\(563\) 353649. 62357.8i 1.11572 0.196732i 0.414760 0.909931i \(-0.363866\pi\)
0.700961 + 0.713199i \(0.252755\pi\)
\(564\) 0 0
\(565\) −713342. 598565.i −2.23461 1.87506i
\(566\) 0 0
\(567\) −247756. 206593.i −0.770651 0.642613i
\(568\) 0 0
\(569\) 311809. 371600.i 0.963085 1.14776i −0.0258884 0.999665i \(-0.508241\pi\)
0.988973 0.148095i \(-0.0473141\pi\)
\(570\) 0 0
\(571\) −9613.31 54519.8i −0.0294850 0.167218i 0.966510 0.256630i \(-0.0826122\pi\)
−0.995995 + 0.0894125i \(0.971501\pi\)
\(572\) 0 0
\(573\) −132185. 61514.9i −0.402600 0.187358i
\(574\) 0 0
\(575\) 1.11477e6 + 643613.i 3.37170 + 1.94665i
\(576\) 0 0
\(577\) 60962.7 + 105591.i 0.183110 + 0.317156i 0.942938 0.332968i \(-0.108050\pi\)
−0.759828 + 0.650124i \(0.774717\pi\)
\(578\) 0 0
\(579\) 330230. 154299.i 0.985053 0.460263i
\(580\) 0 0
\(581\) 67477.9 + 80417.0i 0.199898 + 0.238230i
\(582\) 0 0
\(583\) 340759. 124026.i 1.00256 0.364901i
\(584\) 0 0
\(585\) 22677.5 + 18969.2i 0.0662649 + 0.0554289i
\(586\) 0 0
\(587\) −365201. 64394.8i −1.05988 0.186885i −0.383576 0.923509i \(-0.625308\pi\)
−0.676302 + 0.736624i \(0.736419\pi\)
\(588\) 0 0
\(589\) 564894. + 205604.i 1.62831 + 0.592655i
\(590\) 0 0
\(591\) −3405.43 + 12748.5i −0.00974982 + 0.0364994i
\(592\) 0 0
\(593\) 172744.i 0.491240i 0.969366 + 0.245620i \(0.0789916\pi\)
−0.969366 + 0.245620i \(0.921008\pi\)
\(594\) 0 0
\(595\) −128866. −0.364003
\(596\) 0 0
\(597\) 320208. 320702.i 0.898429 0.899816i
\(598\) 0 0
\(599\) −118262. + 324923.i −0.329605 + 0.905581i 0.658607 + 0.752487i \(0.271146\pi\)
−0.988212 + 0.153094i \(0.951076\pi\)
\(600\) 0 0
\(601\) 13755.4 78010.7i 0.0380824 0.215976i −0.959828 0.280589i \(-0.909470\pi\)
0.997910 + 0.0646132i \(0.0205813\pi\)
\(602\) 0 0
\(603\) −109850. + 303265.i −0.302111 + 0.834042i
\(604\) 0 0
\(605\) 25554.3 + 70209.9i 0.0698157 + 0.191817i
\(606\) 0 0
\(607\) 410746. 344657.i 1.11480 0.935426i 0.116468 0.993194i \(-0.462843\pi\)
0.998330 + 0.0577680i \(0.0183984\pi\)
\(608\) 0 0
\(609\) −135122. + 193291.i −0.364326 + 0.521166i
\(610\) 0 0
\(611\) 14135.0 8160.83i 0.0378628 0.0218601i
\(612\) 0 0
\(613\) −199705. + 345899.i −0.531457 + 0.920511i 0.467869 + 0.883798i \(0.345022\pi\)
−0.999326 + 0.0367129i \(0.988311\pi\)
\(614\) 0 0
\(615\) 540912. + 771236.i 1.43013 + 2.03909i
\(616\) 0 0
\(617\) 299092. 52738.1i 0.785661 0.138533i 0.233595 0.972334i \(-0.424951\pi\)
0.552065 + 0.833801i \(0.313840\pi\)
\(618\) 0 0
\(619\) 148396. + 124519.i 0.387293 + 0.324978i 0.815558 0.578676i \(-0.196430\pi\)
−0.428264 + 0.903654i \(0.640875\pi\)
\(620\) 0 0
\(621\) −581019. 404834.i −1.50663 1.04977i
\(622\) 0 0
\(623\) −33762.5 + 40236.6i −0.0869878 + 0.103668i
\(624\) 0 0
\(625\) 93272.8 + 528976.i 0.238778 + 1.35418i
\(626\) 0 0
\(627\) −39454.0 446992.i −0.100359 1.13701i
\(628\) 0 0
\(629\) 16191.8 + 9348.31i 0.0409254 + 0.0236283i
\(630\) 0 0
\(631\) −147768. 255942.i −0.371126 0.642809i 0.618613 0.785696i \(-0.287695\pi\)
−0.989739 + 0.142887i \(0.954362\pi\)
\(632\) 0 0
\(633\) −51532.0 + 594290.i −0.128608 + 1.48317i
\(634\) 0 0
\(635\) 287843. + 343037.i 0.713851 + 0.850735i
\(636\) 0 0
\(637\) −127.802 + 46.5163i −0.000314964 + 0.000114637i
\(638\) 0 0
\(639\) 109994. 191195.i 0.269380 0.468246i
\(640\) 0 0
\(641\) 178986. + 31560.0i 0.435614 + 0.0768105i 0.387155 0.922015i \(-0.373458\pi\)
0.0484592 + 0.998825i \(0.484569\pi\)
\(642\) 0 0
\(643\) −416371. 151547.i −1.00707 0.366543i −0.214761 0.976667i \(-0.568897\pi\)
−0.792306 + 0.610124i \(0.791120\pi\)
\(644\) 0 0
\(645\) −841085. + 226063.i −2.02172 + 0.543388i
\(646\) 0 0
\(647\) 242796.i 0.580005i −0.957026 0.290003i \(-0.906344\pi\)
0.957026 0.290003i \(-0.0936562\pi\)
\(648\) 0 0
\(649\) −538271. −1.27794
\(650\) 0 0
\(651\) −176985. 658486.i −0.417614 1.55376i
\(652\) 0 0
\(653\) 286708. 787724.i 0.672378 1.84734i 0.163412 0.986558i \(-0.447750\pi\)
0.508967 0.860786i \(-0.330028\pi\)
\(654\) 0 0
\(655\) 58052.0 329229.i 0.135311 0.767389i
\(656\) 0 0
\(657\) 1120.01 + 726276.i 0.00259473 + 1.68256i
\(658\) 0 0
\(659\) 37338.0 + 102585.i 0.0859766 + 0.236219i 0.975229 0.221198i \(-0.0709968\pi\)
−0.889252 + 0.457417i \(0.848775\pi\)
\(660\) 0 0
\(661\) 480727. 403378.i 1.10026 0.923229i 0.102819 0.994700i \(-0.467214\pi\)
0.997443 + 0.0714712i \(0.0227694\pi\)
\(662\) 0 0
\(663\) −4398.53 381.404i −0.0100065 0.000867677i
\(664\) 0 0
\(665\) −733587. + 423537.i −1.65885 + 0.957740i
\(666\) 0 0
\(667\) −258855. + 448350.i −0.581842 + 1.00778i
\(668\) 0 0
\(669\) 432468. 38172.1i 0.966278 0.0852892i
\(670\) 0 0
\(671\) −123852. + 21838.4i −0.275079 + 0.0485038i
\(672\) 0 0
\(673\) 48577.6 + 40761.5i 0.107252 + 0.0899953i 0.694837 0.719167i \(-0.255477\pi\)
−0.587585 + 0.809163i \(0.699921\pi\)
\(674\) 0 0
\(675\) −86420.0 962146.i −0.189673 2.11171i
\(676\) 0 0
\(677\) −284775. + 339382.i −0.621334 + 0.740477i −0.981299 0.192489i \(-0.938344\pi\)
0.359965 + 0.932966i \(0.382789\pi\)
\(678\) 0 0
\(679\) −139410. 790634.i −0.302381 1.71489i
\(680\) 0 0
\(681\) 608070. 426474.i 1.31117 0.919599i
\(682\) 0 0
\(683\) 37938.6 + 21903.9i 0.0813280 + 0.0469547i 0.540113 0.841593i \(-0.318382\pi\)
−0.458785 + 0.888548i \(0.651715\pi\)
\(684\) 0 0
\(685\) −71151.6 123238.i −0.151636 0.262642i
\(686\) 0 0
\(687\) 494780. + 345880.i 1.04833 + 0.732846i
\(688\) 0 0
\(689\) −15075.1 17965.8i −0.0317557 0.0378450i
\(690\) 0 0
\(691\) 239969. 87341.4i 0.502572 0.182921i −0.0782785 0.996932i \(-0.524942\pi\)
0.580850 + 0.814010i \(0.302720\pi\)
\(692\) 0 0
\(693\) −389392. + 327763.i −0.810813 + 0.682487i
\(694\) 0 0
\(695\) −1.41028e6 248670.i −2.91967 0.514817i
\(696\) 0 0
\(697\) −132190. 48113.1i −0.272102 0.0990370i
\(698\) 0 0
\(699\) 545126. + 544286.i 1.11569 + 1.11397i
\(700\) 0 0
\(701\) 192790.i 0.392328i −0.980571 0.196164i \(-0.937152\pi\)
0.980571 0.196164i \(-0.0628485\pi\)
\(702\) 0 0
\(703\) 122898. 0.248676
\(704\) 0 0
\(705\) −758243. 202544.i −1.52556 0.407513i
\(706\) 0 0
\(707\) −265956. + 730708.i −0.532073 + 1.46186i
\(708\) 0 0
\(709\) −101457. + 575389.i −0.201831 + 1.14464i 0.700518 + 0.713635i \(0.252952\pi\)
−0.902349 + 0.431006i \(0.858159\pi\)
\(710\) 0 0
\(711\) −224548. 39236.9i −0.444191 0.0776167i
\(712\) 0 0
\(713\) −511940. 1.40654e6i −1.00702 2.76678i
\(714\) 0 0
\(715\) 35734.0 29984.3i 0.0698987 0.0586520i
\(716\) 0 0
\(717\) 159283. + 340896.i 0.309835 + 0.663108i
\(718\) 0 0
\(719\) 105460. 60887.3i 0.204000 0.117779i −0.394520 0.918887i \(-0.629089\pi\)
0.598520 + 0.801108i \(0.295756\pi\)
\(720\) 0 0
\(721\) −269891. + 467465.i −0.519179 + 0.899245i
\(722\) 0 0
\(723\) 71093.2 152767.i 0.136004 0.292249i
\(724\) 0 0
\(725\) −695504. + 122636.i −1.32320 + 0.233315i
\(726\) 0 0
\(727\) −31443.0 26383.8i −0.0594916 0.0499194i 0.612557 0.790426i \(-0.290141\pi\)
−0.672049 + 0.740507i \(0.734585\pi\)
\(728\) 0 0
\(729\) 2458.65 + 531435.i 0.00462638 + 0.999989i
\(730\) 0 0
\(731\) 83600.2 99630.8i 0.156449 0.186449i
\(732\) 0 0
\(733\) 96146.6 + 545274.i 0.178948 + 1.01486i 0.933488 + 0.358609i \(0.116749\pi\)
−0.754540 + 0.656254i \(0.772140\pi\)
\(734\) 0 0
\(735\) 5929.20 + 2759.27i 0.0109754 + 0.00510762i
\(736\) 0 0
\(737\) 440728. + 254455.i 0.811402 + 0.468463i
\(738\) 0 0
\(739\) 256927. + 445011.i 0.470459 + 0.814858i 0.999429 0.0337817i \(-0.0107551\pi\)
−0.528970 + 0.848640i \(0.677422\pi\)
\(740\) 0 0
\(741\) −26292.7 + 12285.2i −0.0478849 + 0.0223741i
\(742\) 0 0
\(743\) 17473.4 + 20824.0i 0.0316519 + 0.0377213i 0.781638 0.623732i \(-0.214384\pi\)
−0.749986 + 0.661453i \(0.769940\pi\)
\(744\) 0 0
\(745\) 230249. 83803.8i 0.414844 0.150991i
\(746\) 0 0
\(747\) 29768.3 170360.i 0.0533474 0.305301i
\(748\) 0 0
\(749\) 150079. + 26463.0i 0.267520 + 0.0471711i
\(750\) 0 0
\(751\) −369939. 134647.i −0.655919 0.238735i −0.00744559 0.999972i \(-0.502370\pi\)
−0.648473 + 0.761237i \(0.724592\pi\)
\(752\) 0 0
\(753\) 27625.7 103419.i 0.0487218 0.182395i
\(754\) 0 0
\(755\) 1.89600e6i 3.32618i
\(756\) 0 0
\(757\) 502122. 0.876228 0.438114 0.898919i \(-0.355647\pi\)
0.438114 + 0.898919i \(0.355647\pi\)
\(758\) 0 0
\(759\) −789443. + 790661.i −1.37037 + 1.37248i
\(760\) 0 0
\(761\) 284590. 781906.i 0.491418 1.35016i −0.407965 0.912997i \(-0.633762\pi\)
0.899383 0.437162i \(-0.144016\pi\)
\(762\) 0 0
\(763\) −24235.3 + 137445.i −0.0416292 + 0.236091i
\(764\) 0 0
\(765\) 136713. + 162419.i 0.233607 + 0.277532i
\(766\) 0 0
\(767\) 11906.5 + 32712.8i 0.0202392 + 0.0556067i
\(768\) 0 0
\(769\) −347407. + 291509.i −0.587470 + 0.492946i −0.887391 0.461018i \(-0.847484\pi\)
0.299921 + 0.953964i \(0.403040\pi\)
\(770\) 0 0
\(771\) 253797. 363055.i 0.426950 0.610749i
\(772\) 0 0
\(773\) −175007. + 101041.i −0.292885 + 0.169097i −0.639242 0.769005i \(-0.720752\pi\)
0.346357 + 0.938103i \(0.387419\pi\)
\(774\) 0 0
\(775\) 1.02094e6 1.76832e6i 1.69979 2.94413i
\(776\) 0 0
\(777\) −80043.5 114127.i −0.132582 0.189036i
\(778\) 0 0
\(779\) −910636. + 160570.i −1.50062 + 0.264599i
\(780\) 0 0