Properties

Label 108.4.i.a.13.7
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.7
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.66172 + 4.46265i) q^{3} +(-12.8040 - 10.7439i) q^{5} +(-20.8033 - 7.57178i) q^{7} +(-12.8305 + 23.7566i) q^{9} +O(q^{10})\) \(q+(2.66172 + 4.46265i) q^{3} +(-12.8040 - 10.7439i) q^{5} +(-20.8033 - 7.57178i) q^{7} +(-12.8305 + 23.7566i) q^{9} +(-41.5462 + 34.8614i) q^{11} +(12.2534 - 69.4923i) q^{13} +(13.8654 - 85.7371i) q^{15} +(17.7250 - 30.7006i) q^{17} +(37.9595 + 65.7479i) q^{19} +(-21.5823 - 112.992i) q^{21} +(-161.185 + 58.6666i) q^{23} +(26.8068 + 152.029i) q^{25} +(-140.169 + 5.97534i) q^{27} +(-25.1440 - 142.599i) q^{29} +(160.113 - 58.2764i) q^{31} +(-266.158 - 92.6149i) q^{33} +(185.016 + 320.457i) q^{35} +(-180.731 + 313.036i) q^{37} +(342.735 - 130.286i) q^{39} +(-24.4277 + 138.536i) q^{41} +(269.808 - 226.396i) q^{43} +(419.521 - 166.332i) q^{45} +(-74.2539 - 27.0262i) q^{47} +(112.692 + 94.5596i) q^{49} +(184.185 - 2.61583i) q^{51} -195.786 q^{53} +906.505 q^{55} +(-192.372 + 344.402i) q^{57} +(-199.404 - 167.320i) q^{59} +(347.480 + 126.472i) q^{61} +(446.797 - 397.066i) q^{63} +(-903.509 + 758.134i) q^{65} +(-13.6574 + 77.4549i) q^{67} +(-690.838 - 563.159i) q^{69} +(-365.521 + 633.100i) q^{71} +(-361.799 - 626.655i) q^{73} +(-607.100 + 524.287i) q^{75} +(1128.26 - 410.653i) q^{77} +(52.6510 + 298.599i) q^{79} +(-399.756 - 609.620i) q^{81} +(8.20364 + 46.5252i) q^{83} +(-556.794 + 202.656i) q^{85} +(569.442 - 491.766i) q^{87} +(-340.199 - 589.241i) q^{89} +(-781.091 + 1352.89i) q^{91} +(686.243 + 559.413i) q^{93} +(220.351 - 1249.67i) q^{95} +(426.854 - 358.173i) q^{97} +(-295.130 - 1434.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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
\(3\) 2.66172 + 4.46265i 0.512248 + 0.858838i
\(4\) 0 0
\(5\) −12.8040 10.7439i −1.14523 0.960961i −0.145631 0.989339i \(-0.546521\pi\)
−0.999597 + 0.0283783i \(0.990966\pi\)
\(6\) 0 0
\(7\) −20.8033 7.57178i −1.12327 0.408838i −0.287427 0.957803i \(-0.592800\pi\)
−0.835845 + 0.548965i \(0.815022\pi\)
\(8\) 0 0
\(9\) −12.8305 + 23.7566i −0.475204 + 0.879875i
\(10\) 0 0
\(11\) −41.5462 + 34.8614i −1.13879 + 0.955554i −0.999398 0.0346836i \(-0.988958\pi\)
−0.139387 + 0.990238i \(0.544513\pi\)
\(12\) 0 0
\(13\) 12.2534 69.4923i 0.261421 1.48259i −0.517615 0.855613i \(-0.673180\pi\)
0.779036 0.626979i \(-0.215709\pi\)
\(14\) 0 0
\(15\) 13.8654 85.7371i 0.238669 1.47582i
\(16\) 0 0
\(17\) 17.7250 30.7006i 0.252879 0.437999i −0.711439 0.702748i \(-0.751956\pi\)
0.964317 + 0.264750i \(0.0852893\pi\)
\(18\) 0 0
\(19\) 37.9595 + 65.7479i 0.458343 + 0.793873i 0.998874 0.0474510i \(-0.0151098\pi\)
−0.540531 + 0.841324i \(0.681776\pi\)
\(20\) 0 0
\(21\) −21.5823 112.992i −0.224269 1.17413i
\(22\) 0 0
\(23\) −161.185 + 58.6666i −1.46128 + 0.531862i −0.945717 0.324991i \(-0.894639\pi\)
−0.515562 + 0.856853i \(0.672417\pi\)
\(24\) 0 0
\(25\) 26.8068 + 152.029i 0.214454 + 1.21623i
\(26\) 0 0
\(27\) −140.169 + 5.97534i −0.999093 + 0.0425909i
\(28\) 0 0
\(29\) −25.1440 142.599i −0.161004 0.913100i −0.953089 0.302689i \(-0.902116\pi\)
0.792085 0.610411i \(-0.208996\pi\)
\(30\) 0 0
\(31\) 160.113 58.2764i 0.927650 0.337637i 0.166372 0.986063i \(-0.446795\pi\)
0.761278 + 0.648426i \(0.224572\pi\)
\(32\) 0 0
\(33\) −266.158 92.6149i −1.40401 0.488551i
\(34\) 0 0
\(35\) 185.016 + 320.457i 0.893526 + 1.54763i
\(36\) 0 0
\(37\) −180.731 + 313.036i −0.803029 + 1.39089i 0.114585 + 0.993413i \(0.463446\pi\)
−0.917614 + 0.397473i \(0.869887\pi\)
\(38\) 0 0
\(39\) 342.735 130.286i 1.40722 0.534936i
\(40\) 0 0
\(41\) −24.4277 + 138.536i −0.0930479 + 0.527701i 0.902280 + 0.431150i \(0.141892\pi\)
−0.995328 + 0.0965508i \(0.969219\pi\)
\(42\) 0 0
\(43\) 269.808 226.396i 0.956870 0.802909i −0.0235712 0.999722i \(-0.507504\pi\)
0.980441 + 0.196813i \(0.0630592\pi\)
\(44\) 0 0
\(45\) 419.521 166.332i 1.38974 0.551006i
\(46\) 0 0
\(47\) −74.2539 27.0262i −0.230448 0.0838761i 0.224215 0.974540i \(-0.428018\pi\)
−0.454663 + 0.890663i \(0.650240\pi\)
\(48\) 0 0
\(49\) 112.692 + 94.5596i 0.328547 + 0.275684i
\(50\) 0 0
\(51\) 184.185 2.61583i 0.505706 0.00718216i
\(52\) 0 0
\(53\) −195.786 −0.507420 −0.253710 0.967280i \(-0.581651\pi\)
−0.253710 + 0.967280i \(0.581651\pi\)
\(54\) 0 0
\(55\) 906.505 2.22242
\(56\) 0 0
\(57\) −192.372 + 344.402i −0.447023 + 0.800302i
\(58\) 0 0
\(59\) −199.404 167.320i −0.440003 0.369207i 0.395707 0.918377i \(-0.370499\pi\)
−0.835711 + 0.549170i \(0.814944\pi\)
\(60\) 0 0
\(61\) 347.480 + 126.472i 0.729348 + 0.265461i 0.679889 0.733315i \(-0.262028\pi\)
0.0494591 + 0.998776i \(0.484250\pi\)
\(62\) 0 0
\(63\) 446.797 397.066i 0.893510 0.794058i
\(64\) 0 0
\(65\) −903.509 + 758.134i −1.72410 + 1.44669i
\(66\) 0 0
\(67\) −13.6574 + 77.4549i −0.0249032 + 0.141233i −0.994724 0.102585i \(-0.967289\pi\)
0.969821 + 0.243818i \(0.0783999\pi\)
\(68\) 0 0
\(69\) −690.838 563.159i −1.20532 0.982556i
\(70\) 0 0
\(71\) −365.521 + 633.100i −0.610976 + 1.05824i 0.380100 + 0.924945i \(0.375890\pi\)
−0.991076 + 0.133297i \(0.957444\pi\)
\(72\) 0 0
\(73\) −361.799 626.655i −0.580074 1.00472i −0.995470 0.0950773i \(-0.969690\pi\)
0.415396 0.909641i \(-0.363643\pi\)
\(74\) 0 0
\(75\) −607.100 + 524.287i −0.934691 + 0.807193i
\(76\) 0 0
\(77\) 1128.26 410.653i 1.66983 0.607769i
\(78\) 0 0
\(79\) 52.6510 + 298.599i 0.0749836 + 0.425253i 0.999072 + 0.0430739i \(0.0137151\pi\)
−0.924088 + 0.382179i \(0.875174\pi\)
\(80\) 0 0
\(81\) −399.756 609.620i −0.548362 0.836241i
\(82\) 0 0
\(83\) 8.20364 + 46.5252i 0.0108490 + 0.0615277i 0.989752 0.142800i \(-0.0456104\pi\)
−0.978903 + 0.204327i \(0.934499\pi\)
\(84\) 0 0
\(85\) −556.794 + 202.656i −0.710503 + 0.258602i
\(86\) 0 0
\(87\) 569.442 491.766i 0.701730 0.606010i
\(88\) 0 0
\(89\) −340.199 589.241i −0.405180 0.701792i 0.589163 0.808014i \(-0.299458\pi\)
−0.994342 + 0.106223i \(0.966124\pi\)
\(90\) 0 0
\(91\) −781.091 + 1352.89i −0.899786 + 1.55848i
\(92\) 0 0
\(93\) 686.243 + 559.413i 0.765162 + 0.623747i
\(94\) 0 0
\(95\) 220.351 1249.67i 0.237974 1.34962i
\(96\) 0 0
\(97\) 426.854 358.173i 0.446809 0.374917i −0.391441 0.920203i \(-0.628023\pi\)
0.838250 + 0.545286i \(0.183579\pi\)
\(98\) 0 0
\(99\) −295.130 1434.29i −0.299613 1.45607i
\(100\) 0 0
\(101\) 42.5638 + 15.4920i 0.0419332 + 0.0152624i 0.362902 0.931827i \(-0.381786\pi\)
−0.320968 + 0.947090i \(0.604008\pi\)
\(102\) 0 0
\(103\) −1512.45 1269.10i −1.44686 1.21406i −0.934833 0.355087i \(-0.884451\pi\)
−0.512025 0.858971i \(-0.671104\pi\)
\(104\) 0 0
\(105\) −937.628 + 1678.63i −0.871458 + 1.56017i
\(106\) 0 0
\(107\) 1552.11 1.40232 0.701160 0.713004i \(-0.252666\pi\)
0.701160 + 0.713004i \(0.252666\pi\)
\(108\) 0 0
\(109\) −1881.98 −1.65377 −0.826887 0.562368i \(-0.809891\pi\)
−0.826887 + 0.562368i \(0.809891\pi\)
\(110\) 0 0
\(111\) −1878.03 + 26.6722i −1.60590 + 0.0228073i
\(112\) 0 0
\(113\) −801.214 672.299i −0.667008 0.559686i 0.245170 0.969480i \(-0.421156\pi\)
−0.912178 + 0.409794i \(0.865601\pi\)
\(114\) 0 0
\(115\) 2694.13 + 980.582i 2.18460 + 0.795128i
\(116\) 0 0
\(117\) 1493.69 + 1182.72i 1.18027 + 0.934552i
\(118\) 0 0
\(119\) −601.195 + 504.463i −0.463122 + 0.388605i
\(120\) 0 0
\(121\) 279.643 1585.93i 0.210100 1.19153i
\(122\) 0 0
\(123\) −683.259 + 259.732i −0.500873 + 0.190401i
\(124\) 0 0
\(125\) 245.487 425.196i 0.175656 0.304246i
\(126\) 0 0
\(127\) −445.810 772.165i −0.311490 0.539517i 0.667195 0.744883i \(-0.267495\pi\)
−0.978685 + 0.205366i \(0.934161\pi\)
\(128\) 0 0
\(129\) 1728.48 + 601.458i 1.17972 + 0.410507i
\(130\) 0 0
\(131\) 395.806 144.062i 0.263983 0.0960819i −0.206638 0.978417i \(-0.566252\pi\)
0.470621 + 0.882336i \(0.344030\pi\)
\(132\) 0 0
\(133\) −291.855 1655.19i −0.190279 1.07912i
\(134\) 0 0
\(135\) 1858.93 + 1429.45i 1.18512 + 0.911312i
\(136\) 0 0
\(137\) 29.8041 + 169.027i 0.0185864 + 0.105409i 0.992690 0.120695i \(-0.0385123\pi\)
−0.974103 + 0.226104i \(0.927401\pi\)
\(138\) 0 0
\(139\) 354.692 129.097i 0.216436 0.0787761i −0.231527 0.972829i \(-0.574372\pi\)
0.447962 + 0.894052i \(0.352150\pi\)
\(140\) 0 0
\(141\) −77.0344 403.305i −0.0460104 0.240883i
\(142\) 0 0
\(143\) 1913.52 + 3314.31i 1.11900 + 1.93816i
\(144\) 0 0
\(145\) −1210.12 + 2095.98i −0.693066 + 1.20043i
\(146\) 0 0
\(147\) −122.033 + 754.595i −0.0684701 + 0.423387i
\(148\) 0 0
\(149\) 177.014 1003.90i 0.0973257 0.551962i −0.896684 0.442671i \(-0.854031\pi\)
0.994010 0.109291i \(-0.0348579\pi\)
\(150\) 0 0
\(151\) −810.985 + 680.498i −0.437067 + 0.366742i −0.834610 0.550841i \(-0.814307\pi\)
0.397544 + 0.917583i \(0.369863\pi\)
\(152\) 0 0
\(153\) 501.921 + 814.990i 0.265215 + 0.430641i
\(154\) 0 0
\(155\) −2676.21 974.060i −1.38683 0.504764i
\(156\) 0 0
\(157\) −682.838 572.969i −0.347111 0.291261i 0.452518 0.891755i \(-0.350526\pi\)
−0.799629 + 0.600495i \(0.794970\pi\)
\(158\) 0 0
\(159\) −521.127 873.725i −0.259925 0.435792i
\(160\) 0 0
\(161\) 3797.39 1.85886
\(162\) 0 0
\(163\) 1261.47 0.606173 0.303086 0.952963i \(-0.401983\pi\)
0.303086 + 0.952963i \(0.401983\pi\)
\(164\) 0 0
\(165\) 2412.86 + 4045.41i 1.13843 + 1.90870i
\(166\) 0 0
\(167\) −1362.74 1143.48i −0.631450 0.529850i 0.269929 0.962880i \(-0.413000\pi\)
−0.901379 + 0.433030i \(0.857444\pi\)
\(168\) 0 0
\(169\) −2614.53 951.612i −1.19005 0.433141i
\(170\) 0 0
\(171\) −2048.99 + 58.2122i −0.916316 + 0.0260327i
\(172\) 0 0
\(173\) 2778.70 2331.60i 1.22116 1.02467i 0.222395 0.974957i \(-0.428613\pi\)
0.998763 0.0497167i \(-0.0158319\pi\)
\(174\) 0 0
\(175\) 593.459 3365.68i 0.256350 1.45384i
\(176\) 0 0
\(177\) 215.933 1335.23i 0.0916978 0.567017i
\(178\) 0 0
\(179\) 975.147 1689.00i 0.407184 0.705263i −0.587389 0.809305i \(-0.699844\pi\)
0.994573 + 0.104042i \(0.0331775\pi\)
\(180\) 0 0
\(181\) 1929.16 + 3341.40i 0.792226 + 1.37218i 0.924585 + 0.380975i \(0.124411\pi\)
−0.132359 + 0.991202i \(0.542255\pi\)
\(182\) 0 0
\(183\) 360.491 + 1887.31i 0.145619 + 0.762373i
\(184\) 0 0
\(185\) 5677.31 2066.37i 2.25624 0.821204i
\(186\) 0 0
\(187\) 333.859 + 1893.41i 0.130557 + 0.740426i
\(188\) 0 0
\(189\) 2961.22 + 937.020i 1.13967 + 0.360625i
\(190\) 0 0
\(191\) 236.098 + 1338.98i 0.0894421 + 0.507251i 0.996309 + 0.0858348i \(0.0273557\pi\)
−0.906867 + 0.421416i \(0.861533\pi\)
\(192\) 0 0
\(193\) −1975.24 + 718.930i −0.736690 + 0.268133i −0.682994 0.730424i \(-0.739322\pi\)
−0.0536961 + 0.998557i \(0.517100\pi\)
\(194\) 0 0
\(195\) −5788.17 2014.11i −2.12564 0.739657i
\(196\) 0 0
\(197\) 744.973 + 1290.33i 0.269427 + 0.466661i 0.968714 0.248180i \(-0.0798323\pi\)
−0.699287 + 0.714841i \(0.746499\pi\)
\(198\) 0 0
\(199\) −537.438 + 930.870i −0.191447 + 0.331596i −0.945730 0.324953i \(-0.894651\pi\)
0.754283 + 0.656549i \(0.227985\pi\)
\(200\) 0 0
\(201\) −382.006 + 145.215i −0.134053 + 0.0509586i
\(202\) 0 0
\(203\) −556.647 + 3156.90i −0.192458 + 1.09148i
\(204\) 0 0
\(205\) 1801.19 1511.38i 0.613661 0.514923i
\(206\) 0 0
\(207\) 674.367 4581.94i 0.226434 1.53849i
\(208\) 0 0
\(209\) −3869.13 1408.25i −1.28054 0.466080i
\(210\) 0 0
\(211\) −2250.23 1888.17i −0.734180 0.616051i 0.197087 0.980386i \(-0.436852\pi\)
−0.931268 + 0.364335i \(0.881296\pi\)
\(212\) 0 0
\(213\) −3798.22 + 53.9432i −1.22183 + 0.0173527i
\(214\) 0 0
\(215\) −5887.01 −1.86740
\(216\) 0 0
\(217\) −3772.13 −1.18004
\(218\) 0 0
\(219\) 1833.54 3282.56i 0.565748 1.01285i
\(220\) 0 0
\(221\) −1916.26 1607.93i −0.583266 0.489418i
\(222\) 0 0
\(223\) 26.0168 + 9.46936i 0.00781263 + 0.00284357i 0.345924 0.938263i \(-0.387566\pi\)
−0.338111 + 0.941106i \(0.609788\pi\)
\(224\) 0 0
\(225\) −3955.64 1313.77i −1.17204 0.389265i
\(226\) 0 0
\(227\) −2720.48 + 2282.76i −0.795440 + 0.667453i −0.947085 0.320982i \(-0.895987\pi\)
0.151646 + 0.988435i \(0.451543\pi\)
\(228\) 0 0
\(229\) −449.344 + 2548.36i −0.129666 + 0.735372i 0.848761 + 0.528777i \(0.177349\pi\)
−0.978427 + 0.206595i \(0.933762\pi\)
\(230\) 0 0
\(231\) 4835.71 + 3941.99i 1.37734 + 1.12279i
\(232\) 0 0
\(233\) −2151.96 + 3727.31i −0.605064 + 1.04800i 0.386978 + 0.922089i \(0.373519\pi\)
−0.992041 + 0.125912i \(0.959814\pi\)
\(234\) 0 0
\(235\) 660.384 + 1143.82i 0.183314 + 0.317509i
\(236\) 0 0
\(237\) −1192.40 + 1029.75i −0.326813 + 0.282234i
\(238\) 0 0
\(239\) −1776.21 + 646.488i −0.480726 + 0.174970i −0.571005 0.820947i \(-0.693446\pi\)
0.0902790 + 0.995917i \(0.471224\pi\)
\(240\) 0 0
\(241\) 294.365 + 1669.43i 0.0786793 + 0.446212i 0.998542 + 0.0539728i \(0.0171884\pi\)
−0.919863 + 0.392239i \(0.871700\pi\)
\(242\) 0 0
\(243\) 1656.48 3406.61i 0.437298 0.899316i
\(244\) 0 0
\(245\) −426.974 2421.49i −0.111340 0.631442i
\(246\) 0 0
\(247\) 5034.10 1832.26i 1.29681 0.472001i
\(248\) 0 0
\(249\) −185.790 + 160.447i −0.0472850 + 0.0408350i
\(250\) 0 0
\(251\) −81.6710 141.458i −0.0205380 0.0355728i 0.855574 0.517681i \(-0.173205\pi\)
−0.876112 + 0.482108i \(0.839871\pi\)
\(252\) 0 0
\(253\) 4651.42 8056.50i 1.15586 2.00201i
\(254\) 0 0
\(255\) −2386.41 1945.36i −0.586051 0.477739i
\(256\) 0 0
\(257\) −312.000 + 1769.44i −0.0757277 + 0.429473i 0.923247 + 0.384206i \(0.125525\pi\)
−0.998975 + 0.0452667i \(0.985586\pi\)
\(258\) 0 0
\(259\) 6130.05 5143.72i 1.47067 1.23404i
\(260\) 0 0
\(261\) 3710.27 + 1232.28i 0.879924 + 0.292245i
\(262\) 0 0
\(263\) 3362.81 + 1223.96i 0.788440 + 0.286969i 0.704687 0.709518i \(-0.251087\pi\)
0.0837527 + 0.996487i \(0.473309\pi\)
\(264\) 0 0
\(265\) 2506.85 + 2103.50i 0.581112 + 0.487611i
\(266\) 0 0
\(267\) 1724.07 3086.58i 0.395173 0.707475i
\(268\) 0 0
\(269\) 1080.51 0.244908 0.122454 0.992474i \(-0.460924\pi\)
0.122454 + 0.992474i \(0.460924\pi\)
\(270\) 0 0
\(271\) −7858.41 −1.76149 −0.880746 0.473590i \(-0.842958\pi\)
−0.880746 + 0.473590i \(0.842958\pi\)
\(272\) 0 0
\(273\) −8116.51 + 115.273i −1.79939 + 0.0255554i
\(274\) 0 0
\(275\) −6413.65 5381.70i −1.40639 1.18010i
\(276\) 0 0
\(277\) 5715.93 + 2080.43i 1.23984 + 0.451267i 0.876958 0.480567i \(-0.159569\pi\)
0.362887 + 0.931833i \(0.381791\pi\)
\(278\) 0 0
\(279\) −669.882 + 4551.46i −0.143745 + 0.976663i
\(280\) 0 0
\(281\) −4250.20 + 3566.34i −0.902297 + 0.757117i −0.970638 0.240545i \(-0.922674\pi\)
0.0683411 + 0.997662i \(0.478229\pi\)
\(282\) 0 0
\(283\) −975.267 + 5531.01i −0.204854 + 1.16178i 0.692816 + 0.721114i \(0.256370\pi\)
−0.897670 + 0.440669i \(0.854741\pi\)
\(284\) 0 0
\(285\) 6163.36 2342.92i 1.28100 0.486957i
\(286\) 0 0
\(287\) 1557.14 2697.05i 0.320262 0.554710i
\(288\) 0 0
\(289\) 1828.15 + 3166.45i 0.372105 + 0.644504i
\(290\) 0 0
\(291\) 2734.57 + 951.546i 0.550870 + 0.191686i
\(292\) 0 0
\(293\) 5648.62 2055.93i 1.12626 0.409927i 0.289330 0.957229i \(-0.406567\pi\)
0.836935 + 0.547302i \(0.184345\pi\)
\(294\) 0 0
\(295\) 755.515 + 4284.74i 0.149111 + 0.845652i
\(296\) 0 0
\(297\) 5615.17 5134.73i 1.09705 1.00319i
\(298\) 0 0
\(299\) 2101.82 + 11920.0i 0.406525 + 2.30552i
\(300\) 0 0
\(301\) −7327.12 + 2666.86i −1.40308 + 0.510681i
\(302\) 0 0
\(303\) 44.1576 + 231.183i 0.00837224 + 0.0438320i
\(304\) 0 0
\(305\) −3090.34 5352.63i −0.580172 1.00489i
\(306\) 0 0
\(307\) 959.723 1662.29i 0.178418 0.309029i −0.762921 0.646492i \(-0.776235\pi\)
0.941339 + 0.337463i \(0.109569\pi\)
\(308\) 0 0
\(309\) 1637.82 10127.5i 0.301529 1.86451i
\(310\) 0 0
\(311\) −1333.89 + 7564.89i −0.243210 + 1.37931i 0.581404 + 0.813615i \(0.302504\pi\)
−0.824614 + 0.565696i \(0.808608\pi\)
\(312\) 0 0
\(313\) −6883.88 + 5776.26i −1.24313 + 1.04311i −0.245858 + 0.969306i \(0.579070\pi\)
−0.997273 + 0.0738052i \(0.976486\pi\)
\(314\) 0 0
\(315\) −9986.83 + 283.728i −1.78633 + 0.0507500i
\(316\) 0 0
\(317\) 3964.88 + 1443.10i 0.702491 + 0.255686i 0.668474 0.743735i \(-0.266948\pi\)
0.0340172 + 0.999421i \(0.489170\pi\)
\(318\) 0 0
\(319\) 6015.82 + 5047.87i 1.05587 + 0.885976i
\(320\) 0 0
\(321\) 4131.28 + 6926.53i 0.718335 + 1.20436i
\(322\) 0 0
\(323\) 2691.33 0.463621
\(324\) 0 0
\(325\) 10893.3 1.85924
\(326\) 0 0
\(327\) −5009.31 8398.64i −0.847142 1.42032i
\(328\) 0 0
\(329\) 1340.09 + 1124.47i 0.224564 + 0.188431i
\(330\) 0 0
\(331\) 4463.91 + 1624.73i 0.741265 + 0.269798i 0.684925 0.728613i \(-0.259835\pi\)
0.0563398 + 0.998412i \(0.482057\pi\)
\(332\) 0 0
\(333\) −5117.80 8309.98i −0.842204 1.36752i
\(334\) 0 0
\(335\) 1007.04 845.003i 0.164239 0.137813i
\(336\) 0 0
\(337\) 1170.70 6639.39i 0.189235 1.07321i −0.731156 0.682210i \(-0.761019\pi\)
0.920392 0.390997i \(-0.127870\pi\)
\(338\) 0 0
\(339\) 867.628 5365.01i 0.139006 0.859550i
\(340\) 0 0
\(341\) −4620.49 + 8002.92i −0.733764 + 1.27092i
\(342\) 0 0
\(343\) 2168.36 + 3755.71i 0.341343 + 0.591223i
\(344\) 0 0
\(345\) 2795.01 + 14633.0i 0.436169 + 2.28352i
\(346\) 0 0
\(347\) 5429.26 1976.09i 0.839936 0.305712i 0.114006 0.993480i \(-0.463632\pi\)
0.725930 + 0.687768i \(0.241409\pi\)
\(348\) 0 0
\(349\) −980.754 5562.13i −0.150426 0.853106i −0.962849 0.270039i \(-0.912963\pi\)
0.812424 0.583067i \(-0.198148\pi\)
\(350\) 0 0
\(351\) −1302.30 + 9813.87i −0.198039 + 1.49238i
\(352\) 0 0
\(353\) −1941.90 11013.0i −0.292795 1.66052i −0.676030 0.736874i \(-0.736301\pi\)
0.383235 0.923651i \(-0.374810\pi\)
\(354\) 0 0
\(355\) 11482.1 4179.14i 1.71664 0.624805i
\(356\) 0 0
\(357\) −3851.45 1340.19i −0.570982 0.198684i
\(358\) 0 0
\(359\) −4436.64 7684.48i −0.652247 1.12973i −0.982576 0.185860i \(-0.940493\pi\)
0.330329 0.943866i \(-0.392840\pi\)
\(360\) 0 0
\(361\) 547.646 948.551i 0.0798434 0.138293i
\(362\) 0 0
\(363\) 7821.80 2973.36i 1.13096 0.429920i
\(364\) 0 0
\(365\) −2100.20 + 11910.8i −0.301177 + 1.70806i
\(366\) 0 0
\(367\) −4478.44 + 3757.85i −0.636982 + 0.534491i −0.903090 0.429452i \(-0.858707\pi\)
0.266108 + 0.963943i \(0.414262\pi\)
\(368\) 0 0
\(369\) −2977.74 2357.81i −0.420094 0.332636i
\(370\) 0 0
\(371\) 4072.99 + 1482.45i 0.569971 + 0.207452i
\(372\) 0 0
\(373\) 663.209 + 556.499i 0.0920635 + 0.0772504i 0.687658 0.726035i \(-0.258639\pi\)
−0.595594 + 0.803285i \(0.703083\pi\)
\(374\) 0 0
\(375\) 2550.92 36.2288i 0.351277 0.00498892i
\(376\) 0 0
\(377\) −10217.6 −1.39584
\(378\) 0 0
\(379\) −1536.47 −0.208240 −0.104120 0.994565i \(-0.533203\pi\)
−0.104120 + 0.994565i \(0.533203\pi\)
\(380\) 0 0
\(381\) 2259.28 4044.78i 0.303797 0.543886i
\(382\) 0 0
\(383\) −999.899 839.015i −0.133401 0.111936i 0.573646 0.819103i \(-0.305528\pi\)
−0.707047 + 0.707167i \(0.749973\pi\)
\(384\) 0 0
\(385\) −18858.3 6863.85i −2.49638 0.908609i
\(386\) 0 0
\(387\) 1916.63 + 9314.52i 0.251751 + 1.22347i
\(388\) 0 0
\(389\) 8814.64 7396.36i 1.14889 0.964037i 0.149201 0.988807i \(-0.452330\pi\)
0.999693 + 0.0247702i \(0.00788542\pi\)
\(390\) 0 0
\(391\) −1055.90 + 5988.33i −0.136571 + 0.774535i
\(392\) 0 0
\(393\) 1696.42 + 1382.89i 0.217744 + 0.177501i
\(394\) 0 0
\(395\) 2533.96 4388.95i 0.322778 0.559068i
\(396\) 0 0
\(397\) −7192.58 12457.9i −0.909283 1.57492i −0.815062 0.579373i \(-0.803297\pi\)
−0.0942206 0.995551i \(-0.530036\pi\)
\(398\) 0 0
\(399\) 6609.71 5708.10i 0.829322 0.716197i
\(400\) 0 0
\(401\) −11581.1 + 4215.16i −1.44222 + 0.524926i −0.940407 0.340050i \(-0.889556\pi\)
−0.501814 + 0.864976i \(0.667334\pi\)
\(402\) 0 0
\(403\) −2087.84 11840.7i −0.258071 1.46359i
\(404\) 0 0
\(405\) −1431.19 + 12100.5i −0.175596 + 1.48464i
\(406\) 0 0
\(407\) −3404.17 19306.0i −0.414590 2.35126i
\(408\) 0 0
\(409\) −8895.19 + 3237.58i −1.07540 + 0.391414i −0.818194 0.574943i \(-0.805024\pi\)
−0.257207 + 0.966356i \(0.582802\pi\)
\(410\) 0 0
\(411\) −674.980 + 582.908i −0.0810080 + 0.0699580i
\(412\) 0 0
\(413\) 2881.35 + 4990.65i 0.343298 + 0.594609i
\(414\) 0 0
\(415\) 394.820 683.849i 0.0467011 0.0808888i
\(416\) 0 0
\(417\) 1520.20 + 1239.24i 0.178525 + 0.145530i
\(418\) 0 0
\(419\) −2393.77 + 13575.7i −0.279101 + 1.58286i 0.446526 + 0.894771i \(0.352661\pi\)
−0.725627 + 0.688089i \(0.758450\pi\)
\(420\) 0 0
\(421\) −6924.37 + 5810.23i −0.801598 + 0.672621i −0.948587 0.316517i \(-0.897486\pi\)
0.146988 + 0.989138i \(0.453042\pi\)
\(422\) 0 0
\(423\) 1594.77 1417.26i 0.183310 0.162907i
\(424\) 0 0
\(425\) 5142.52 + 1871.72i 0.586939 + 0.213628i
\(426\) 0 0
\(427\) −6271.10 5262.08i −0.710726 0.596370i
\(428\) 0 0
\(429\) −9697.36 + 17361.1i −1.09136 + 1.95385i
\(430\) 0 0
\(431\) 7656.71 0.855709 0.427855 0.903848i \(-0.359269\pi\)
0.427855 + 0.903848i \(0.359269\pi\)
\(432\) 0 0
\(433\) 15823.7 1.75620 0.878102 0.478473i \(-0.158810\pi\)
0.878102 + 0.478473i \(0.158810\pi\)
\(434\) 0 0
\(435\) −12574.6 + 178.588i −1.38599 + 0.0196842i
\(436\) 0 0
\(437\) −9975.71 8370.62i −1.09200 0.916295i
\(438\) 0 0
\(439\) −8402.95 3058.42i −0.913556 0.332507i −0.157884 0.987458i \(-0.550467\pi\)
−0.755672 + 0.654951i \(0.772689\pi\)
\(440\) 0 0
\(441\) −3692.31 + 1463.93i −0.398695 + 0.158074i
\(442\) 0 0
\(443\) −25.8250 + 21.6698i −0.00276972 + 0.00232407i −0.644171 0.764881i \(-0.722798\pi\)
0.641402 + 0.767205i \(0.278353\pi\)
\(444\) 0 0
\(445\) −1974.81 + 11199.7i −0.210371 + 1.19307i
\(446\) 0 0
\(447\) 4951.20 1882.13i 0.523900 0.199154i
\(448\) 0 0
\(449\) 6809.18 11793.8i 0.715691 1.23961i −0.247002 0.969015i \(-0.579445\pi\)
0.962693 0.270597i \(-0.0872212\pi\)
\(450\) 0 0
\(451\) −3814.69 6607.24i −0.398285 0.689851i
\(452\) 0 0
\(453\) −5195.44 1807.85i −0.538859 0.187506i
\(454\) 0 0
\(455\) 24536.4 8930.51i 2.52809 0.920151i
\(456\) 0 0
\(457\) −1345.77 7632.27i −0.137752 0.781230i −0.972904 0.231211i \(-0.925731\pi\)
0.835152 0.550020i \(-0.185380\pi\)
\(458\) 0 0
\(459\) −2301.04 + 4409.17i −0.233994 + 0.448372i
\(460\) 0 0
\(461\) −612.250 3472.24i −0.0618553 0.350799i −0.999990 0.00452774i \(-0.998559\pi\)
0.938134 0.346271i \(-0.112552\pi\)
\(462\) 0 0
\(463\) 430.400 156.653i 0.0432017 0.0157241i −0.320329 0.947306i \(-0.603793\pi\)
0.363531 + 0.931582i \(0.381571\pi\)
\(464\) 0 0
\(465\) −2776.42 14535.7i −0.276889 1.44962i
\(466\) 0 0
\(467\) 2690.34 + 4659.80i 0.266582 + 0.461734i 0.967977 0.251039i \(-0.0807722\pi\)
−0.701395 + 0.712773i \(0.747439\pi\)
\(468\) 0 0
\(469\) 870.590 1507.91i 0.0857145 0.148462i
\(470\) 0 0
\(471\) 739.440 4572.35i 0.0723388 0.447310i
\(472\) 0 0
\(473\) −3317.03 + 18811.8i −0.322446 + 1.82868i
\(474\) 0 0
\(475\) −8978.00 + 7533.44i −0.867240 + 0.727701i
\(476\) 0 0
\(477\) 2512.04 4651.22i 0.241128 0.446467i
\(478\) 0 0
\(479\) 8832.30 + 3214.70i 0.842502 + 0.306646i 0.726979 0.686659i \(-0.240924\pi\)
0.115522 + 0.993305i \(0.463146\pi\)
\(480\) 0 0
\(481\) 19539.0 + 16395.2i 1.85219 + 1.55417i
\(482\) 0 0
\(483\) 10107.6 + 16946.4i 0.952196 + 1.59646i
\(484\) 0 0
\(485\) −9313.63 −0.871979
\(486\) 0 0
\(487\) −8531.94 −0.793879 −0.396939 0.917845i \(-0.629928\pi\)
−0.396939 + 0.917845i \(0.629928\pi\)
\(488\) 0 0
\(489\) 3357.68 + 5629.51i 0.310511 + 0.520604i
\(490\) 0 0
\(491\) −13067.3 10964.8i −1.20106 1.00781i −0.999599 0.0283132i \(-0.990986\pi\)
−0.201462 0.979496i \(-0.564569\pi\)
\(492\) 0 0
\(493\) −4823.53 1755.62i −0.440651 0.160384i
\(494\) 0 0
\(495\) −11630.9 + 21535.5i −1.05610 + 1.95545i
\(496\) 0 0
\(497\) 12397.7 10402.9i 1.11894 0.938904i
\(498\) 0 0
\(499\) 678.059 3845.46i 0.0608299 0.344983i −0.939169 0.343455i \(-0.888403\pi\)
0.999999 0.00152782i \(-0.000486322\pi\)
\(500\) 0 0
\(501\) 1475.70 9125.06i 0.131596 0.813728i
\(502\) 0 0
\(503\) 8186.51 14179.5i 0.725683 1.25692i −0.233010 0.972474i \(-0.574857\pi\)
0.958692 0.284445i \(-0.0918093\pi\)
\(504\) 0 0
\(505\) −378.545 655.660i −0.0333565 0.0577752i
\(506\) 0 0
\(507\) −2712.43 14200.7i −0.237600 1.24393i
\(508\) 0 0
\(509\) 13457.6 4898.15i 1.17190 0.426536i 0.318564 0.947901i \(-0.396799\pi\)
0.853333 + 0.521366i \(0.174577\pi\)
\(510\) 0 0
\(511\) 2781.73 + 15776.0i 0.240815 + 1.36573i
\(512\) 0 0
\(513\) −5713.61 8988.98i −0.491739 0.773632i
\(514\) 0 0
\(515\) 5730.48 + 32499.2i 0.490321 + 2.78075i
\(516\) 0 0
\(517\) 4027.14 1465.76i 0.342579 0.124688i
\(518\) 0 0
\(519\) 17801.2 + 6194.28i 1.50556 + 0.523890i
\(520\) 0 0
\(521\) −6002.38 10396.4i −0.504739 0.874234i −0.999985 0.00548128i \(-0.998255\pi\)
0.495246 0.868753i \(-0.335078\pi\)
\(522\) 0 0
\(523\) −1823.72 + 3158.77i −0.152477 + 0.264099i −0.932138 0.362104i \(-0.882058\pi\)
0.779660 + 0.626203i \(0.215392\pi\)
\(524\) 0 0
\(525\) 16599.5 6310.08i 1.37992 0.524561i
\(526\) 0 0
\(527\) 1048.88 5948.51i 0.0866983 0.491691i
\(528\) 0 0
\(529\) 13218.4 11091.6i 1.08641 0.911610i
\(530\) 0 0
\(531\) 6533.41 2590.37i 0.533947 0.211700i
\(532\) 0 0
\(533\) 9327.89 + 3395.07i 0.758041 + 0.275904i
\(534\) 0 0
\(535\) −19873.3 16675.7i −1.60598 1.34757i
\(536\) 0 0
\(537\) 10133.0 143.911i 0.814286 0.0115647i
\(538\) 0 0
\(539\) −7978.38 −0.637576
\(540\) 0 0
\(541\) 7624.55 0.605924 0.302962 0.953003i \(-0.402024\pi\)
0.302962 + 0.953003i \(0.402024\pi\)
\(542\) 0 0
\(543\) −9776.61 + 17503.0i −0.772661 + 1.38329i
\(544\) 0 0
\(545\) 24097.0 + 20219.8i 1.89395 + 1.58921i
\(546\) 0 0
\(547\) 3960.55 + 1441.52i 0.309582 + 0.112678i 0.492139 0.870517i \(-0.336215\pi\)
−0.182557 + 0.983195i \(0.558437\pi\)
\(548\) 0 0
\(549\) −7462.90 + 6632.25i −0.580162 + 0.515587i
\(550\) 0 0
\(551\) 8421.10 7066.14i 0.651090 0.546330i
\(552\) 0 0
\(553\) 1165.61 6610.50i 0.0896324 0.508331i
\(554\) 0 0
\(555\) 24332.9 + 19835.8i 1.86103 + 1.51708i
\(556\) 0 0
\(557\) −8126.05 + 14074.7i −0.618154 + 1.07067i 0.371669 + 0.928365i \(0.378786\pi\)
−0.989822 + 0.142308i \(0.954548\pi\)
\(558\) 0 0
\(559\) −12426.7 21523.7i −0.940241 1.62855i
\(560\) 0 0
\(561\) −7560.98 + 6529.61i −0.569028 + 0.491409i
\(562\) 0 0
\(563\) −13643.5 + 4965.82i −1.02132 + 0.371731i −0.797770 0.602962i \(-0.793987\pi\)
−0.223551 + 0.974692i \(0.571765\pi\)
\(564\) 0 0
\(565\) 3035.70 + 17216.3i 0.226040 + 1.28194i
\(566\) 0 0
\(567\) 3700.33 + 15709.0i 0.274073 + 1.16352i
\(568\) 0 0
\(569\) 669.121 + 3794.77i 0.0492988 + 0.279587i 0.999485 0.0320961i \(-0.0102183\pi\)
−0.950186 + 0.311683i \(0.899107\pi\)
\(570\) 0 0
\(571\) −9021.71 + 3283.63i −0.661203 + 0.240658i −0.650756 0.759287i \(-0.725548\pi\)
−0.0104473 + 0.999945i \(0.503326\pi\)
\(572\) 0 0
\(573\) −5346.96 + 4617.60i −0.389830 + 0.336654i
\(574\) 0 0
\(575\) −13239.9 22932.1i −0.960245 1.66319i
\(576\) 0 0
\(577\) −2519.05 + 4363.13i −0.181750 + 0.314800i −0.942476 0.334273i \(-0.891509\pi\)
0.760727 + 0.649072i \(0.224843\pi\)
\(578\) 0 0
\(579\) −8465.88 6901.24i −0.607651 0.495346i
\(580\) 0 0
\(581\) 181.615 1029.99i 0.0129685 0.0735478i
\(582\) 0 0
\(583\) 8134.16 6825.37i 0.577843 0.484868i
\(584\) 0 0
\(585\) −6418.23 31191.6i −0.453609 2.20447i
\(586\) 0 0
\(587\) −26587.6 9677.08i −1.86948 0.680436i −0.969806 0.243878i \(-0.921580\pi\)
−0.899676 0.436558i \(-0.856197\pi\)
\(588\) 0 0
\(589\) 9909.36 + 8314.94i 0.693223 + 0.581683i
\(590\) 0 0
\(591\) −3775.39 + 6759.05i −0.262773 + 0.470440i
\(592\) 0 0
\(593\) −6418.01 −0.444446 −0.222223 0.974996i \(-0.571331\pi\)
−0.222223 + 0.974996i \(0.571331\pi\)
\(594\) 0 0
\(595\) 13117.6 0.903815
\(596\) 0 0
\(597\) −5584.65 + 79.3146i −0.382855 + 0.00543740i
\(598\) 0 0
\(599\) −19148.7 16067.6i −1.30616 1.09600i −0.989045 0.147617i \(-0.952840\pi\)
−0.317120 0.948385i \(-0.602716\pi\)
\(600\) 0 0
\(601\) 4731.73 + 1722.21i 0.321150 + 0.116889i 0.497565 0.867427i \(-0.334228\pi\)
−0.176415 + 0.984316i \(0.556450\pi\)
\(602\) 0 0
\(603\) −1664.84 1318.24i −0.112434 0.0890264i
\(604\) 0 0
\(605\) −20619.6 + 17301.9i −1.38563 + 1.16268i
\(606\) 0 0
\(607\) −2916.95 + 16542.9i −0.195050 + 1.10618i 0.717297 + 0.696768i \(0.245379\pi\)
−0.912347 + 0.409417i \(0.865732\pi\)
\(608\) 0 0
\(609\) −15569.8 + 5918.66i −1.03599 + 0.393820i
\(610\) 0 0
\(611\) −2787.97 + 4828.91i −0.184598 + 0.319733i
\(612\) 0 0
\(613\) −6512.11 11279.3i −0.429073 0.743176i 0.567718 0.823223i \(-0.307826\pi\)
−0.996791 + 0.0800468i \(0.974493\pi\)
\(614\) 0 0
\(615\) 11539.0 + 4015.22i 0.756582 + 0.263267i
\(616\) 0 0
\(617\) 19391.5 7057.92i 1.26527 0.460520i 0.379735 0.925095i \(-0.376015\pi\)
0.885534 + 0.464575i \(0.153793\pi\)
\(618\) 0 0
\(619\) −905.701 5136.48i −0.0588097 0.333526i 0.941181 0.337904i \(-0.109718\pi\)
−0.999990 + 0.00437732i \(0.998607\pi\)
\(620\) 0 0
\(621\) 22242.6 9186.36i 1.43730 0.593617i
\(622\) 0 0
\(623\) 2615.65 + 14834.1i 0.168208 + 0.953956i
\(624\) 0 0
\(625\) 10421.6 3793.13i 0.666979 0.242761i
\(626\) 0 0
\(627\) −4014.02 21015.0i −0.255669 1.33853i
\(628\) 0 0
\(629\) 6406.92 + 11097.1i 0.406138 + 0.703451i
\(630\) 0 0
\(631\) −2190.76 + 3794.50i −0.138213 + 0.239393i −0.926820 0.375505i \(-0.877469\pi\)
0.788607 + 0.614898i \(0.210803\pi\)
\(632\) 0 0
\(633\) 2436.75 15067.7i 0.153005 0.946112i
\(634\) 0 0
\(635\) −2587.87 + 14676.6i −0.161727 + 0.917199i
\(636\) 0 0
\(637\) 7952.02 6672.53i 0.494616 0.415032i
\(638\) 0 0
\(639\) −10350.5 16806.5i −0.640783 1.04046i
\(640\) 0 0
\(641\) −4363.85 1588.31i −0.268895 0.0978697i 0.204054 0.978960i \(-0.434588\pi\)
−0.472949 + 0.881090i \(0.656810\pi\)
\(642\) 0 0
\(643\) 7650.57 + 6419.59i 0.469221 + 0.393723i 0.846510 0.532372i \(-0.178699\pi\)
−0.377289 + 0.926095i \(0.623144\pi\)
\(644\) 0 0
\(645\) −15669.6 26271.7i −0.956571 1.60379i
\(646\) 0 0
\(647\) 27979.8 1.70016 0.850078 0.526658i \(-0.176555\pi\)
0.850078 + 0.526658i \(0.176555\pi\)
\(648\) 0 0
\(649\) 14117.5 0.853866
\(650\) 0 0
\(651\) −10040.4 16833.7i −0.604474 1.01346i
\(652\) 0 0
\(653\) −17499.4 14683.7i −1.04871 0.879968i −0.0557484 0.998445i \(-0.517754\pi\)
−0.992957 + 0.118477i \(0.962199\pi\)
\(654\) 0 0
\(655\) −6615.70 2407.92i −0.394652 0.143641i
\(656\) 0 0
\(657\) 19529.3 554.831i 1.15968 0.0329468i
\(658\) 0 0
\(659\) 21442.2 17992.2i 1.26748 1.06354i 0.272638 0.962117i \(-0.412104\pi\)
0.994843 0.101427i \(-0.0323407\pi\)
\(660\) 0 0
\(661\) −5005.68 + 28388.6i −0.294551 + 1.67048i 0.374469 + 0.927239i \(0.377825\pi\)
−0.669021 + 0.743244i \(0.733286\pi\)
\(662\) 0 0
\(663\) 2075.10 12831.5i 0.121554 0.751634i
\(664\) 0 0
\(665\) −14046.2 + 24328.8i −0.819083 + 1.41869i
\(666\) 0 0
\(667\) 12418.6 + 21509.7i 0.720915 + 1.24866i
\(668\) 0 0
\(669\) 26.9911 + 141.309i 0.00155984 + 0.00816639i
\(670\) 0 0
\(671\) −18845.4 + 6859.18i −1.08423 + 0.394629i
\(672\) 0 0
\(673\) −3476.92 19718.6i −0.199146 1.12941i −0.906390 0.422443i \(-0.861173\pi\)
0.707244 0.706970i \(-0.249938\pi\)
\(674\) 0 0
\(675\) −4665.90 21149.5i −0.266060 1.20599i
\(676\) 0 0
\(677\) −4675.19 26514.3i −0.265409 1.50521i −0.767867 0.640609i \(-0.778682\pi\)
0.502458 0.864602i \(-0.332429\pi\)
\(678\) 0 0
\(679\) −11592.0 + 4219.14i −0.655169 + 0.238462i
\(680\) 0 0
\(681\) −17428.3 6064.51i −0.980696 0.341252i
\(682\) 0 0
\(683\) 10823.6 + 18747.1i 0.606376 + 1.05027i 0.991832 + 0.127548i \(0.0407108\pi\)
−0.385456 + 0.922726i \(0.625956\pi\)
\(684\) 0 0
\(685\) 1434.39 2484.44i 0.0800079 0.138578i
\(686\) 0 0
\(687\) −12568.5 + 4777.74i −0.697987 + 0.265331i
\(688\) 0 0
\(689\) −2399.04 + 13605.6i −0.132650 + 0.752297i
\(690\) 0 0
\(691\) −10158.7 + 8524.19i −0.559271 + 0.469284i −0.878066 0.478539i \(-0.841166\pi\)
0.318795 + 0.947824i \(0.396722\pi\)
\(692\) 0 0
\(693\) −4720.42 + 32072.5i −0.258750 + 1.75806i
\(694\) 0 0
\(695\) −5928.49 2157.79i −0.323569 0.117769i
\(696\) 0 0
\(697\) 3820.16 + 3205.50i 0.207603 + 0.174199i
\(698\) 0 0
\(699\) −22361.6 + 317.585i −1.21001 + 0.0171848i
\(700\) 0 0
\(701\) −20645.6 −1.11237 −0.556187 0.831057i \(-0.687736\pi\)
−0.556187 + 0.831057i \(0.687736\pi\)
\(702\) 0 0
\(703\) −27441.9 −1.47225
\(704\) 0 0
\(705\) −3346.71 + 5991.59i −0.178786 + 0.320080i
\(706\) 0 0
\(707\) −768.165 644.567i −0.0408626 0.0342878i
\(708\) 0 0
\(709\) 7122.25 + 2592.29i 0.377266 + 0.137314i 0.523691 0.851908i \(-0.324555\pi\)
−0.146425 + 0.989222i \(0.546777\pi\)
\(710\) 0 0
\(711\) −7769.24 2580.36i −0.409802 0.136106i
\(712\) 0 0
\(713\) −22389.0 + 18786.6i −1.17598 + 0.986763i
\(714\) 0 0
\(715\) 11107.7 62995.1i 0.580987 3.29494i
\(716\) 0 0
\(717\) −7612.82 6205.84i −0.396522 0.323238i
\(718\) 0 0
\(719\) −947.326 + 1640.82i −0.0491367 + 0.0851073i −0.889548 0.456842i \(-0.848980\pi\)
0.840411 + 0.541950i \(0.182314\pi\)
\(720\) 0 0
\(721\) 21854.7 + 37853.4i 1.12886 + 1.95525i
\(722\) 0 0
\(723\) −6666.55 + 5757.19i −0.342921 + 0.296144i
\(724\) 0 0
\(725\) 21005.1 7645.22i 1.07601 0.391636i
\(726\) 0 0
\(727\) 3900.92 + 22123.2i 0.199006 + 1.12862i 0.906598 + 0.421996i \(0.138670\pi\)
−0.707592 + 0.706621i \(0.750219\pi\)
\(728\) 0 0
\(729\) 19611.6 1675.11i 0.996372 0.0851046i
\(730\) 0 0
\(731\) −2168.14 12296.1i −0.109701 0.622146i
\(732\) 0 0
\(733\) 4541.24 1652.88i 0.228833 0.0832883i −0.225059 0.974345i \(-0.572257\pi\)
0.453892 + 0.891057i \(0.350035\pi\)
\(734\) 0 0
\(735\) 9669.78 8350.76i 0.485272 0.419078i
\(736\) 0 0
\(737\) −2132.77 3694.07i −0.106597 0.184631i
\(738\) 0 0
\(739\) −3014.98 + 5222.09i −0.150078 + 0.259943i −0.931256 0.364366i \(-0.881286\pi\)
0.781178 + 0.624309i \(0.214619\pi\)
\(740\) 0 0
\(741\) 21576.1 + 17588.5i 1.06966 + 0.871969i
\(742\) 0 0
\(743\) 2481.91 14075.6i 0.122547 0.694999i −0.860187 0.509978i \(-0.829654\pi\)
0.982735 0.185021i \(-0.0592354\pi\)
\(744\) 0 0
\(745\) −13052.2 + 10952.1i −0.641874 + 0.538596i
\(746\) 0 0
\(747\) −1210.54 402.051i −0.0592922 0.0196925i
\(748\) 0 0
\(749\) −32289.0 11752.2i −1.57519 0.573321i
\(750\) 0 0
\(751\) 125.354 + 105.185i 0.00609088 + 0.00511085i 0.645828 0.763483i \(-0.276512\pi\)
−0.639737 + 0.768594i \(0.720957\pi\)
\(752\) 0 0
\(753\) 413.894 740.991i 0.0200307 0.0358608i
\(754\) 0 0
\(755\) 17695.1 0.852966
\(756\) 0 0
\(757\) 1044.73 0.0501604 0.0250802 0.999685i \(-0.492016\pi\)
0.0250802 + 0.999685i \(0.492016\pi\)
\(758\) 0 0
\(759\) 48334.1 686.453i 2.31149 0.0328283i
\(760\) 0 0
\(761\) 10258.8 + 8608.15i 0.488674 + 0.410046i 0.853551 0.521009i \(-0.174444\pi\)
−0.364877 + 0.931056i \(0.618889\pi\)
\(762\) 0 0
\(763\) 39151.5 + 14250.0i 1.85764 + 0.676125i
\(764\) 0 0
\(765\) 2329.52 15827.7i 0.110097 0.748043i
\(766\) 0 0
\(767\) −14070.8 + 11806.8i −0.662409 + 0.555827i
\(768\) 0 0
\(769\) 1313.03 7446.58i 0.0615724 0.349194i −0.938421 0.345495i \(-0.887711\pi\)
0.999993 0.00369990i \(-0.00117772\pi\)
\(770\) 0 0
\(771\) −8726.84 + 3317.40i −0.407639 + 0.154959i
\(772\) 0 0
\(773\) 9922.23 17185.8i 0.461679 0.799652i −0.537366 0.843349i \(-0.680581\pi\)
0.999045 + 0.0436977i \(0.0139138\pi\)
\(774\) 0 0
\(775\) 13151.8 + 22779.6i 0.609583 + 1.05583i
\(776\) 0 0
\(777\) 39271.1 + 13665.1i 1.81318 + 0.630931i
\(778\) 0 0
\(779\) −10035.7 + 3652.71i −0.461576 + 0.168000i
\(780\) 0 0
\(781\) −6884.76 39045.4i −0.315437 1.78893i
\(782\) 0 0