Properties

Label 252.4.x.a.41.13
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.13
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0939923 + 5.19530i) q^{3} +(7.82452 - 13.5525i) q^{5} +(-13.7444 + 12.4134i) q^{7} +(-26.9823 + 0.976636i) q^{9} +O(q^{10})\) \(q+(0.0939923 + 5.19530i) q^{3} +(7.82452 - 13.5525i) q^{5} +(-13.7444 + 12.4134i) q^{7} +(-26.9823 + 0.976636i) q^{9} +(34.2206 - 19.7573i) q^{11} +(55.5318 + 32.0613i) q^{13} +(71.1446 + 39.3769i) q^{15} +56.6997 q^{17} +117.055i q^{19} +(-65.7832 - 70.2394i) q^{21} +(-6.59593 - 3.80816i) q^{23} +(-59.9462 - 103.830i) q^{25} +(-7.61005 - 140.090i) q^{27} +(39.8226 - 22.9916i) q^{29} +(251.963 + 145.471i) q^{31} +(105.861 + 175.929i) q^{33} +(60.6891 + 283.399i) q^{35} -335.540 q^{37} +(-161.349 + 291.518i) q^{39} +(97.3000 - 168.529i) q^{41} +(152.264 + 263.729i) q^{43} +(-197.888 + 373.319i) q^{45} +(318.029 + 550.842i) q^{47} +(34.8151 - 341.229i) q^{49} +(5.32933 + 294.572i) q^{51} +274.953i q^{53} -618.365i q^{55} +(-608.134 + 11.0022i) q^{57} +(-258.871 + 448.377i) q^{59} +(142.340 - 82.1801i) q^{61} +(358.732 - 348.366i) q^{63} +(869.019 - 501.728i) q^{65} +(368.103 - 637.573i) q^{67} +(19.1646 - 34.6258i) q^{69} -599.619i q^{71} +214.435i q^{73} +(533.793 - 321.198i) q^{75} +(-225.086 + 696.345i) q^{77} +(-454.345 - 786.949i) q^{79} +(727.092 - 52.7039i) q^{81} +(-389.923 - 675.366i) q^{83} +(443.648 - 768.420i) q^{85} +(123.191 + 204.729i) q^{87} -443.089 q^{89} +(-1161.24 + 248.676i) q^{91} +(-732.084 + 1322.70i) q^{93} +(1586.38 + 915.896i) q^{95} +(337.707 - 194.975i) q^{97} +(-904.056 + 566.518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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
\(3\) 0.0939923 + 5.19530i 0.0180888 + 0.999836i
\(4\) 0 0
\(5\) 7.82452 13.5525i 0.699846 1.21217i −0.268673 0.963231i \(-0.586585\pi\)
0.968519 0.248938i \(-0.0800814\pi\)
\(6\) 0 0
\(7\) −13.7444 + 12.4134i −0.742126 + 0.670260i
\(8\) 0 0
\(9\) −26.9823 + 0.976636i −0.999346 + 0.0361717i
\(10\) 0 0
\(11\) 34.2206 19.7573i 0.937991 0.541549i 0.0486610 0.998815i \(-0.484505\pi\)
0.889330 + 0.457266i \(0.151171\pi\)
\(12\) 0 0
\(13\) 55.5318 + 32.0613i 1.18475 + 0.684015i 0.957109 0.289730i \(-0.0935654\pi\)
0.227641 + 0.973745i \(0.426899\pi\)
\(14\) 0 0
\(15\) 71.1446 + 39.3769i 1.22463 + 0.677805i
\(16\) 0 0
\(17\) 56.6997 0.808923 0.404462 0.914555i \(-0.367459\pi\)
0.404462 + 0.914555i \(0.367459\pi\)
\(18\) 0 0
\(19\) 117.055i 1.41338i 0.707525 + 0.706689i \(0.249812\pi\)
−0.707525 + 0.706689i \(0.750188\pi\)
\(20\) 0 0
\(21\) −65.7832 70.2394i −0.683575 0.729880i
\(22\) 0 0
\(23\) −6.59593 3.80816i −0.0597976 0.0345242i 0.469803 0.882771i \(-0.344325\pi\)
−0.529601 + 0.848247i \(0.677658\pi\)
\(24\) 0 0
\(25\) −59.9462 103.830i −0.479569 0.830638i
\(26\) 0 0
\(27\) −7.61005 140.090i −0.0542428 0.998528i
\(28\) 0 0
\(29\) 39.8226 22.9916i 0.254995 0.147222i −0.367054 0.930200i \(-0.619634\pi\)
0.622049 + 0.782978i \(0.286300\pi\)
\(30\) 0 0
\(31\) 251.963 + 145.471i 1.45980 + 0.842819i 0.999001 0.0446836i \(-0.0142280\pi\)
0.460803 + 0.887502i \(0.347561\pi\)
\(32\) 0 0
\(33\) 105.861 + 175.929i 0.558428 + 0.928042i
\(34\) 0 0
\(35\) 60.6891 + 283.399i 0.293095 + 1.36866i
\(36\) 0 0
\(37\) −335.540 −1.49088 −0.745438 0.666575i \(-0.767759\pi\)
−0.745438 + 0.666575i \(0.767759\pi\)
\(38\) 0 0
\(39\) −161.349 + 291.518i −0.662473 + 1.19693i
\(40\) 0 0
\(41\) 97.3000 168.529i 0.370627 0.641945i −0.619035 0.785363i \(-0.712476\pi\)
0.989662 + 0.143419i \(0.0458095\pi\)
\(42\) 0 0
\(43\) 152.264 + 263.729i 0.540000 + 0.935308i 0.998903 + 0.0468214i \(0.0149092\pi\)
−0.458903 + 0.888486i \(0.651757\pi\)
\(44\) 0 0
\(45\) −197.888 + 373.319i −0.655542 + 1.23669i
\(46\) 0 0
\(47\) 318.029 + 550.842i 0.987006 + 1.70954i 0.632659 + 0.774431i \(0.281964\pi\)
0.354347 + 0.935114i \(0.384703\pi\)
\(48\) 0 0
\(49\) 34.8151 341.229i 0.101502 0.994835i
\(50\) 0 0
\(51\) 5.32933 + 294.572i 0.0146325 + 0.808791i
\(52\) 0 0
\(53\) 274.953i 0.712597i 0.934372 + 0.356299i \(0.115961\pi\)
−0.934372 + 0.356299i \(0.884039\pi\)
\(54\) 0 0
\(55\) 618.365i 1.51600i
\(56\) 0 0
\(57\) −608.134 + 11.0022i −1.41315 + 0.0255663i
\(58\) 0 0
\(59\) −258.871 + 448.377i −0.571222 + 0.989385i 0.425219 + 0.905090i \(0.360197\pi\)
−0.996441 + 0.0842947i \(0.973136\pi\)
\(60\) 0 0
\(61\) 142.340 82.1801i 0.298767 0.172493i −0.343122 0.939291i \(-0.611484\pi\)
0.641889 + 0.766798i \(0.278151\pi\)
\(62\) 0 0
\(63\) 358.732 348.366i 0.717396 0.696666i
\(64\) 0 0
\(65\) 869.019 501.728i 1.65828 0.957411i
\(66\) 0 0
\(67\) 368.103 637.573i 0.671208 1.16257i −0.306353 0.951918i \(-0.599109\pi\)
0.977562 0.210649i \(-0.0675578\pi\)
\(68\) 0 0
\(69\) 19.1646 34.6258i 0.0334369 0.0604123i
\(70\) 0 0
\(71\) 599.619i 1.00228i −0.865367 0.501139i \(-0.832915\pi\)
0.865367 0.501139i \(-0.167085\pi\)
\(72\) 0 0
\(73\) 214.435i 0.343804i 0.985114 + 0.171902i \(0.0549913\pi\)
−0.985114 + 0.171902i \(0.945009\pi\)
\(74\) 0 0
\(75\) 533.793 321.198i 0.821827 0.494516i
\(76\) 0 0
\(77\) −225.086 + 696.345i −0.333128 + 1.03060i
\(78\) 0 0
\(79\) −454.345 786.949i −0.647061 1.12074i −0.983821 0.179152i \(-0.942665\pi\)
0.336761 0.941590i \(-0.390669\pi\)
\(80\) 0 0
\(81\) 727.092 52.7039i 0.997383 0.0722961i
\(82\) 0 0
\(83\) −389.923 675.366i −0.515658 0.893146i −0.999835 0.0181755i \(-0.994214\pi\)
0.484177 0.874970i \(-0.339119\pi\)
\(84\) 0 0
\(85\) 443.648 768.420i 0.566122 0.980552i
\(86\) 0 0
\(87\) 123.191 + 204.729i 0.151810 + 0.252290i
\(88\) 0 0
\(89\) −443.089 −0.527723 −0.263862 0.964561i \(-0.584996\pi\)
−0.263862 + 0.964561i \(0.584996\pi\)
\(90\) 0 0
\(91\) −1161.24 + 248.676i −1.33770 + 0.286465i
\(92\) 0 0
\(93\) −732.084 + 1322.70i −0.816275 + 1.47481i
\(94\) 0 0
\(95\) 1586.38 + 915.896i 1.71325 + 0.989146i
\(96\) 0 0
\(97\) 337.707 194.975i 0.353495 0.204090i −0.312729 0.949842i \(-0.601243\pi\)
0.666223 + 0.745752i \(0.267910\pi\)
\(98\) 0 0
\(99\) −904.056 + 566.518i −0.917788 + 0.575124i
\(100\) 0 0
\(101\) −701.270 1214.63i −0.690881 1.19664i −0.971550 0.236836i \(-0.923890\pi\)
0.280669 0.959805i \(-0.409444\pi\)
\(102\) 0 0
\(103\) −919.911 531.111i −0.880015 0.508077i −0.00935152 0.999956i \(-0.502977\pi\)
−0.870663 + 0.491879i \(0.836310\pi\)
\(104\) 0 0
\(105\) −1466.64 + 341.935i −1.36314 + 0.317805i
\(106\) 0 0
\(107\) 216.811i 0.195887i 0.995192 + 0.0979433i \(0.0312264\pi\)
−0.995192 + 0.0979433i \(0.968774\pi\)
\(108\) 0 0
\(109\) −947.744 −0.832820 −0.416410 0.909177i \(-0.636712\pi\)
−0.416410 + 0.909177i \(0.636712\pi\)
\(110\) 0 0
\(111\) −31.5381 1743.23i −0.0269682 1.49063i
\(112\) 0 0
\(113\) 1219.08 + 703.838i 1.01488 + 0.585942i 0.912617 0.408815i \(-0.134058\pi\)
0.102265 + 0.994757i \(0.467391\pi\)
\(114\) 0 0
\(115\) −103.220 + 59.5940i −0.0836983 + 0.0483232i
\(116\) 0 0
\(117\) −1529.69 810.854i −1.20872 0.640713i
\(118\) 0 0
\(119\) −779.301 + 703.836i −0.600323 + 0.542189i
\(120\) 0 0
\(121\) 115.200 199.532i 0.0865514 0.149911i
\(122\) 0 0
\(123\) 884.702 + 489.662i 0.648544 + 0.358954i
\(124\) 0 0
\(125\) 79.9306 0.0571937
\(126\) 0 0
\(127\) 1271.11 0.888131 0.444066 0.895994i \(-0.353536\pi\)
0.444066 + 0.895994i \(0.353536\pi\)
\(128\) 0 0
\(129\) −1355.84 + 815.845i −0.925387 + 0.556830i
\(130\) 0 0
\(131\) 537.201 930.459i 0.358286 0.620569i −0.629389 0.777091i \(-0.716695\pi\)
0.987675 + 0.156521i \(0.0500280\pi\)
\(132\) 0 0
\(133\) −1453.05 1608.84i −0.947331 1.04890i
\(134\) 0 0
\(135\) −1958.10 992.998i −1.24835 0.633064i
\(136\) 0 0
\(137\) 1303.13 752.364i 0.812658 0.469188i −0.0352200 0.999380i \(-0.511213\pi\)
0.847878 + 0.530191i \(0.177880\pi\)
\(138\) 0 0
\(139\) 738.300 + 426.257i 0.450516 + 0.260106i 0.708048 0.706164i \(-0.249576\pi\)
−0.257532 + 0.966270i \(0.582909\pi\)
\(140\) 0 0
\(141\) −2831.90 + 1704.03i −1.69141 + 1.01777i
\(142\) 0 0
\(143\) 2533.77 1.48171
\(144\) 0 0
\(145\) 719.592i 0.412130i
\(146\) 0 0
\(147\) 1776.06 + 148.802i 0.996509 + 0.0834897i
\(148\) 0 0
\(149\) −669.901 386.768i −0.368325 0.212653i 0.304401 0.952544i \(-0.401544\pi\)
−0.672727 + 0.739891i \(0.734877\pi\)
\(150\) 0 0
\(151\) −1258.88 2180.44i −0.678451 1.17511i −0.975447 0.220232i \(-0.929318\pi\)
0.296997 0.954878i \(-0.404015\pi\)
\(152\) 0 0
\(153\) −1529.89 + 55.3750i −0.808394 + 0.0292601i
\(154\) 0 0
\(155\) 3942.98 2276.48i 2.04328 1.17969i
\(156\) 0 0
\(157\) −63.2586 36.5224i −0.0321566 0.0185656i 0.483836 0.875159i \(-0.339243\pi\)
−0.515992 + 0.856593i \(0.672577\pi\)
\(158\) 0 0
\(159\) −1428.46 + 25.8434i −0.712480 + 0.0128900i
\(160\) 0 0
\(161\) 137.929 29.5371i 0.0675176 0.0144587i
\(162\) 0 0
\(163\) 1604.80 0.771151 0.385576 0.922676i \(-0.374003\pi\)
0.385576 + 0.922676i \(0.374003\pi\)
\(164\) 0 0
\(165\) 3212.59 58.1215i 1.51576 0.0274227i
\(166\) 0 0
\(167\) −666.547 + 1154.49i −0.308856 + 0.534954i −0.978112 0.208077i \(-0.933279\pi\)
0.669257 + 0.743031i \(0.266613\pi\)
\(168\) 0 0
\(169\) 957.352 + 1658.18i 0.435754 + 0.754749i
\(170\) 0 0
\(171\) −114.320 3158.41i −0.0511243 1.41245i
\(172\) 0 0
\(173\) −1234.93 2138.96i −0.542717 0.940014i −0.998747 0.0500494i \(-0.984062\pi\)
0.456029 0.889965i \(-0.349271\pi\)
\(174\) 0 0
\(175\) 2112.80 + 682.939i 0.912645 + 0.295002i
\(176\) 0 0
\(177\) −2353.79 1302.77i −0.999556 0.553232i
\(178\) 0 0
\(179\) 4348.42i 1.81573i 0.419261 + 0.907866i \(0.362289\pi\)
−0.419261 + 0.907866i \(0.637711\pi\)
\(180\) 0 0
\(181\) 1523.82i 0.625770i 0.949791 + 0.312885i \(0.101295\pi\)
−0.949791 + 0.312885i \(0.898705\pi\)
\(182\) 0 0
\(183\) 440.329 + 731.776i 0.177869 + 0.295598i
\(184\) 0 0
\(185\) −2625.44 + 4547.39i −1.04338 + 1.80719i
\(186\) 0 0
\(187\) 1940.30 1120.23i 0.758763 0.438072i
\(188\) 0 0
\(189\) 1843.58 + 1830.98i 0.709529 + 0.704677i
\(190\) 0 0
\(191\) −3370.81 + 1946.14i −1.27698 + 0.737266i −0.976292 0.216456i \(-0.930550\pi\)
−0.300690 + 0.953722i \(0.597217\pi\)
\(192\) 0 0
\(193\) −189.809 + 328.758i −0.0707914 + 0.122614i −0.899248 0.437438i \(-0.855886\pi\)
0.828457 + 0.560053i \(0.189219\pi\)
\(194\) 0 0
\(195\) 2688.31 + 4467.66i 0.987251 + 1.64070i
\(196\) 0 0
\(197\) 2916.71i 1.05486i −0.849599 0.527429i \(-0.823156\pi\)
0.849599 0.527429i \(-0.176844\pi\)
\(198\) 0 0
\(199\) 2913.59i 1.03789i −0.854809 0.518943i \(-0.826326\pi\)
0.854809 0.518943i \(-0.173674\pi\)
\(200\) 0 0
\(201\) 3346.99 + 1852.48i 1.17452 + 0.650069i
\(202\) 0 0
\(203\) −261.932 + 810.338i −0.0905618 + 0.280170i
\(204\) 0 0
\(205\) −1522.65 2637.31i −0.518764 0.898525i
\(206\) 0 0
\(207\) 181.693 + 96.3112i 0.0610073 + 0.0323386i
\(208\) 0 0
\(209\) 2312.68 + 4005.68i 0.765413 + 1.32573i
\(210\) 0 0
\(211\) −587.128 + 1016.93i −0.191562 + 0.331795i −0.945768 0.324843i \(-0.894689\pi\)
0.754206 + 0.656638i \(0.228022\pi\)
\(212\) 0 0
\(213\) 3115.20 56.3596i 1.00211 0.0181300i
\(214\) 0 0
\(215\) 4765.56 1.51167
\(216\) 0 0
\(217\) −5268.87 + 1128.31i −1.64827 + 0.352972i
\(218\) 0 0
\(219\) −1114.05 + 20.1552i −0.343748 + 0.00621901i
\(220\) 0 0
\(221\) 3148.63 + 1817.86i 0.958371 + 0.553316i
\(222\) 0 0
\(223\) −1611.22 + 930.237i −0.483834 + 0.279342i −0.722013 0.691879i \(-0.756783\pi\)
0.238179 + 0.971221i \(0.423450\pi\)
\(224\) 0 0
\(225\) 1718.89 + 2743.02i 0.509301 + 0.812748i
\(226\) 0 0
\(227\) −1240.21 2148.11i −0.362624 0.628083i 0.625768 0.780009i \(-0.284786\pi\)
−0.988392 + 0.151926i \(0.951452\pi\)
\(228\) 0 0
\(229\) −2878.54 1661.92i −0.830651 0.479577i 0.0234243 0.999726i \(-0.492543\pi\)
−0.854076 + 0.520149i \(0.825876\pi\)
\(230\) 0 0
\(231\) −3638.88 1103.94i −1.03645 0.314432i
\(232\) 0 0
\(233\) 2378.25i 0.668689i −0.942451 0.334344i \(-0.891485\pi\)
0.942451 0.334344i \(-0.108515\pi\)
\(234\) 0 0
\(235\) 9953.69 2.76301
\(236\) 0 0
\(237\) 4045.73 2434.43i 1.10885 0.667228i
\(238\) 0 0
\(239\) −5257.58 3035.47i −1.42295 0.821539i −0.426398 0.904536i \(-0.640218\pi\)
−0.996550 + 0.0829961i \(0.973551\pi\)
\(240\) 0 0
\(241\) −3105.01 + 1792.68i −0.829923 + 0.479156i −0.853826 0.520558i \(-0.825724\pi\)
0.0239031 + 0.999714i \(0.492391\pi\)
\(242\) 0 0
\(243\) 342.154 + 3772.51i 0.0903258 + 0.995912i
\(244\) 0 0
\(245\) −4352.08 3141.78i −1.13487 0.819269i
\(246\) 0 0
\(247\) −3752.92 + 6500.25i −0.966772 + 1.67450i
\(248\) 0 0
\(249\) 3472.08 2089.25i 0.883672 0.531729i
\(250\) 0 0
\(251\) −4359.22 −1.09622 −0.548111 0.836406i \(-0.684653\pi\)
−0.548111 + 0.836406i \(0.684653\pi\)
\(252\) 0 0
\(253\) −300.955 −0.0747862
\(254\) 0 0
\(255\) 4033.88 + 2232.66i 0.990632 + 0.548292i
\(256\) 0 0
\(257\) −1621.40 + 2808.35i −0.393541 + 0.681634i −0.992914 0.118837i \(-0.962084\pi\)
0.599372 + 0.800470i \(0.295417\pi\)
\(258\) 0 0
\(259\) 4611.78 4165.19i 1.10642 0.999275i
\(260\) 0 0
\(261\) −1052.05 + 659.258i −0.249503 + 0.156349i
\(262\) 0 0
\(263\) −302.312 + 174.540i −0.0708796 + 0.0409223i −0.535021 0.844839i \(-0.679696\pi\)
0.464141 + 0.885761i \(0.346363\pi\)
\(264\) 0 0
\(265\) 3726.28 + 2151.37i 0.863788 + 0.498708i
\(266\) 0 0
\(267\) −41.6470 2301.98i −0.00954589 0.527637i
\(268\) 0 0
\(269\) 7924.66 1.79619 0.898095 0.439802i \(-0.144952\pi\)
0.898095 + 0.439802i \(0.144952\pi\)
\(270\) 0 0
\(271\) 6601.56i 1.47976i 0.672737 + 0.739882i \(0.265119\pi\)
−0.672737 + 0.739882i \(0.734881\pi\)
\(272\) 0 0
\(273\) −1401.09 6009.61i −0.310616 1.33230i
\(274\) 0 0
\(275\) −4102.79 2368.75i −0.899663 0.519421i
\(276\) 0 0
\(277\) 2868.51 + 4968.41i 0.622210 + 1.07770i 0.989073 + 0.147424i \(0.0470983\pi\)
−0.366863 + 0.930275i \(0.619568\pi\)
\(278\) 0 0
\(279\) −6940.63 3679.07i −1.48934 0.789463i
\(280\) 0 0
\(281\) −640.561 + 369.828i −0.135988 + 0.0785128i −0.566451 0.824096i \(-0.691684\pi\)
0.430462 + 0.902608i \(0.358350\pi\)
\(282\) 0 0
\(283\) 1367.20 + 789.355i 0.287179 + 0.165803i 0.636669 0.771137i \(-0.280312\pi\)
−0.349490 + 0.936940i \(0.613645\pi\)
\(284\) 0 0
\(285\) −4609.25 + 8327.80i −0.957994 + 1.73086i
\(286\) 0 0
\(287\) 754.685 + 3524.14i 0.155218 + 0.724820i
\(288\) 0 0
\(289\) −1698.15 −0.345643
\(290\) 0 0
\(291\) 1044.70 + 1736.17i 0.210451 + 0.349745i
\(292\) 0 0
\(293\) −997.708 + 1728.08i −0.198931 + 0.344558i −0.948182 0.317728i \(-0.897080\pi\)
0.749251 + 0.662286i \(0.230414\pi\)
\(294\) 0 0
\(295\) 4051.08 + 7016.67i 0.799535 + 1.38483i
\(296\) 0 0
\(297\) −3028.21 4643.60i −0.591631 0.907235i
\(298\) 0 0
\(299\) −244.189 422.948i −0.0472301 0.0818050i
\(300\) 0 0
\(301\) −5366.54 1734.67i −1.02765 0.332175i
\(302\) 0 0
\(303\) 6244.48 3757.47i 1.18395 0.712413i
\(304\) 0 0
\(305\) 2572.08i 0.482875i
\(306\) 0 0
\(307\) 1713.47i 0.318543i 0.987235 + 0.159272i \(0.0509146\pi\)
−0.987235 + 0.159272i \(0.949085\pi\)
\(308\) 0 0
\(309\) 2672.82 4829.14i 0.492075 0.889061i
\(310\) 0 0
\(311\) 3264.75 5654.71i 0.595263 1.03103i −0.398246 0.917278i \(-0.630381\pi\)
0.993510 0.113748i \(-0.0362855\pi\)
\(312\) 0 0
\(313\) 377.873 218.165i 0.0682384 0.0393975i −0.465493 0.885052i \(-0.654123\pi\)
0.533731 + 0.845654i \(0.320789\pi\)
\(314\) 0 0
\(315\) −1914.31 7587.49i −0.342410 1.35716i
\(316\) 0 0
\(317\) 1201.15 693.486i 0.212818 0.122871i −0.389802 0.920899i \(-0.627457\pi\)
0.602621 + 0.798028i \(0.294123\pi\)
\(318\) 0 0
\(319\) 908.501 1573.57i 0.159456 0.276185i
\(320\) 0 0
\(321\) −1126.40 + 20.3785i −0.195855 + 0.00354336i
\(322\) 0 0
\(323\) 6636.96i 1.14331i
\(324\) 0 0
\(325\) 7687.80i 1.31213i
\(326\) 0 0
\(327\) −89.0806 4923.82i −0.0150647 0.832684i
\(328\) 0 0
\(329\) −11208.9 3623.16i −1.87832 0.607146i
\(330\) 0 0
\(331\) 233.117 + 403.771i 0.0387108 + 0.0670491i 0.884732 0.466101i \(-0.154342\pi\)
−0.846021 + 0.533150i \(0.821008\pi\)
\(332\) 0 0
\(333\) 9053.64 327.700i 1.48990 0.0539275i
\(334\) 0 0
\(335\) −5760.46 9977.41i −0.939485 1.62724i
\(336\) 0 0
\(337\) 784.235 1358.34i 0.126766 0.219565i −0.795656 0.605749i \(-0.792874\pi\)
0.922422 + 0.386184i \(0.126207\pi\)
\(338\) 0 0
\(339\) −3542.07 + 6399.66i −0.567489 + 1.02532i
\(340\) 0 0
\(341\) 11496.4 1.82571
\(342\) 0 0
\(343\) 3757.29 + 5122.14i 0.591472 + 0.806326i
\(344\) 0 0
\(345\) −319.311 530.657i −0.0498293 0.0828105i
\(346\) 0 0
\(347\) −4674.58 2698.87i −0.723184 0.417530i 0.0927396 0.995690i \(-0.470438\pi\)
−0.815923 + 0.578160i \(0.803771\pi\)
\(348\) 0 0
\(349\) −2247.57 + 1297.64i −0.344727 + 0.199029i −0.662361 0.749185i \(-0.730445\pi\)
0.317633 + 0.948214i \(0.397112\pi\)
\(350\) 0 0
\(351\) 4068.85 8023.41i 0.618744 1.22011i
\(352\) 0 0
\(353\) −2303.43 3989.65i −0.347306 0.601551i 0.638464 0.769652i \(-0.279570\pi\)
−0.985770 + 0.168100i \(0.946237\pi\)
\(354\) 0 0
\(355\) −8126.32 4691.73i −1.21493 0.701440i
\(356\) 0 0
\(357\) −3729.89 3982.55i −0.552960 0.590417i
\(358\) 0 0
\(359\) 2973.15i 0.437095i 0.975826 + 0.218547i \(0.0701319\pi\)
−0.975826 + 0.218547i \(0.929868\pi\)
\(360\) 0 0
\(361\) −6842.78 −0.997635
\(362\) 0 0
\(363\) 1047.46 + 579.744i 0.151452 + 0.0838255i
\(364\) 0 0
\(365\) 2906.12 + 1677.85i 0.416749 + 0.240610i
\(366\) 0 0
\(367\) −8243.22 + 4759.22i −1.17246 + 0.676919i −0.954258 0.298984i \(-0.903352\pi\)
−0.218201 + 0.975904i \(0.570019\pi\)
\(368\) 0 0
\(369\) −2460.79 + 4642.32i −0.347164 + 0.654931i
\(370\) 0 0
\(371\) −3413.10 3779.05i −0.477626 0.528837i
\(372\) 0 0
\(373\) 972.449 1684.33i 0.134991 0.233811i −0.790603 0.612329i \(-0.790233\pi\)
0.925594 + 0.378518i \(0.123566\pi\)
\(374\) 0 0
\(375\) 7.51285 + 415.263i 0.00103457 + 0.0571843i
\(376\) 0 0
\(377\) 2948.56 0.402807
\(378\) 0 0
\(379\) 4140.33 0.561147 0.280573 0.959833i \(-0.409475\pi\)
0.280573 + 0.959833i \(0.409475\pi\)
\(380\) 0 0
\(381\) 119.474 + 6603.80i 0.0160652 + 0.887986i
\(382\) 0 0
\(383\) 549.242 951.316i 0.0732767 0.126919i −0.827059 0.562115i \(-0.809988\pi\)
0.900336 + 0.435196i \(0.143321\pi\)
\(384\) 0 0
\(385\) 7676.01 + 8499.03i 1.01612 + 1.12507i
\(386\) 0 0
\(387\) −4366.00 6967.31i −0.573479 0.915163i
\(388\) 0 0
\(389\) 7971.13 4602.13i 1.03895 0.599839i 0.119416 0.992844i \(-0.461898\pi\)
0.919536 + 0.393005i \(0.128564\pi\)
\(390\) 0 0
\(391\) −373.987 215.921i −0.0483717 0.0279274i
\(392\) 0 0
\(393\) 4884.51 + 2703.46i 0.626949 + 0.347002i
\(394\) 0 0
\(395\) −14220.1 −1.81137
\(396\) 0 0
\(397\) 13251.6i 1.67526i −0.546237 0.837630i \(-0.683940\pi\)
0.546237 0.837630i \(-0.316060\pi\)
\(398\) 0 0
\(399\) 8221.84 7700.23i 1.03160 0.966149i
\(400\) 0 0
\(401\) −10109.5 5836.72i −1.25896 0.726862i −0.286090 0.958203i \(-0.592356\pi\)
−0.972873 + 0.231340i \(0.925689\pi\)
\(402\) 0 0
\(403\) 9327.98 + 16156.5i 1.15300 + 1.99706i
\(404\) 0 0
\(405\) 4974.88 10266.3i 0.610380 1.25959i
\(406\) 0 0
\(407\) −11482.4 + 6629.35i −1.39843 + 0.807382i
\(408\) 0 0
\(409\) 9968.20 + 5755.14i 1.20512 + 0.695779i 0.961690 0.274139i \(-0.0883927\pi\)
0.243434 + 0.969917i \(0.421726\pi\)
\(410\) 0 0
\(411\) 4031.24 + 6699.45i 0.483812 + 0.804038i
\(412\) 0 0
\(413\) −2007.87 9376.12i −0.239227 1.11712i
\(414\) 0 0
\(415\) −12203.8 −1.44352
\(416\) 0 0
\(417\) −2145.14 + 3875.75i −0.251914 + 0.455148i
\(418\) 0 0
\(419\) −7814.88 + 13535.8i −0.911174 + 1.57820i −0.0987667 + 0.995111i \(0.531490\pi\)
−0.812408 + 0.583090i \(0.801844\pi\)
\(420\) 0 0
\(421\) −3771.44 6532.33i −0.436600 0.756214i 0.560824 0.827935i \(-0.310484\pi\)
−0.997425 + 0.0717208i \(0.977151\pi\)
\(422\) 0 0
\(423\) −9119.13 14552.4i −1.04820 1.67272i
\(424\) 0 0
\(425\) −3398.93 5887.12i −0.387935 0.671922i
\(426\) 0 0
\(427\) −936.240 + 2896.44i −0.106107 + 0.328263i
\(428\) 0 0
\(429\) 238.155 + 13163.7i 0.0268024 + 1.48147i
\(430\) 0 0
\(431\) 13115.9i 1.46582i −0.680324 0.732911i \(-0.738161\pi\)
0.680324 0.732911i \(-0.261839\pi\)
\(432\) 0 0
\(433\) 1126.39i 0.125013i −0.998045 0.0625065i \(-0.980091\pi\)
0.998045 0.0625065i \(-0.0199094\pi\)
\(434\) 0 0
\(435\) 3738.50 67.6360i 0.412062 0.00745494i
\(436\) 0 0
\(437\) 445.763 772.083i 0.0487957 0.0845166i
\(438\) 0 0
\(439\) −11682.3 + 6744.81i −1.27009 + 0.733285i −0.975004 0.222187i \(-0.928680\pi\)
−0.295083 + 0.955472i \(0.595347\pi\)
\(440\) 0 0
\(441\) −606.136 + 9241.14i −0.0654504 + 0.997856i
\(442\) 0 0
\(443\) −7184.54 + 4147.99i −0.770536 + 0.444869i −0.833066 0.553174i \(-0.813417\pi\)
0.0625295 + 0.998043i \(0.480083\pi\)
\(444\) 0 0
\(445\) −3466.96 + 6004.95i −0.369325 + 0.639690i
\(446\) 0 0
\(447\) 1946.41 3516.69i 0.205955 0.372112i
\(448\) 0 0
\(449\) 14603.8i 1.53496i 0.641075 + 0.767478i \(0.278489\pi\)
−0.641075 + 0.767478i \(0.721511\pi\)
\(450\) 0 0
\(451\) 7689.53i 0.802851i
\(452\) 0 0
\(453\) 11209.7 6745.20i 1.16265 0.699596i
\(454\) 0 0
\(455\) −5715.96 + 17683.4i −0.588941 + 1.82200i
\(456\) 0 0
\(457\) 327.533 + 567.304i 0.0335259 + 0.0580686i 0.882302 0.470685i \(-0.155993\pi\)
−0.848776 + 0.528753i \(0.822660\pi\)
\(458\) 0 0
\(459\) −431.488 7943.03i −0.0438782 0.807732i
\(460\) 0 0
\(461\) −6136.84 10629.3i −0.620002 1.07387i −0.989485 0.144637i \(-0.953798\pi\)
0.369483 0.929238i \(-0.379535\pi\)
\(462\) 0 0
\(463\) 4612.44 7988.98i 0.462977 0.801900i −0.536131 0.844135i \(-0.680115\pi\)
0.999108 + 0.0422354i \(0.0134479\pi\)
\(464\) 0 0
\(465\) 12197.6 + 20271.0i 1.21645 + 2.02160i
\(466\) 0 0
\(467\) 14189.7 1.40605 0.703023 0.711167i \(-0.251833\pi\)
0.703023 + 0.711167i \(0.251833\pi\)
\(468\) 0 0
\(469\) 2855.11 + 13332.5i 0.281102 + 1.31266i
\(470\) 0 0
\(471\) 183.799 332.080i 0.0179809 0.0324872i
\(472\) 0 0
\(473\) 10421.1 + 6016.63i 1.01303 + 0.584873i
\(474\) 0 0
\(475\) 12153.8 7016.97i 1.17401 0.677812i
\(476\) 0 0
\(477\) −268.529 7418.86i −0.0257759 0.712131i
\(478\) 0 0
\(479\) 5260.23 + 9110.99i 0.501766 + 0.869085i 0.999998 + 0.00204079i \(0.000649604\pi\)
−0.498232 + 0.867044i \(0.666017\pi\)
\(480\) 0 0
\(481\) −18633.1 10757.8i −1.76631 1.01978i
\(482\) 0 0
\(483\) 166.419 + 713.807i 0.0156776 + 0.0672450i
\(484\) 0 0
\(485\) 6102.35i 0.571327i
\(486\) 0 0
\(487\) 19692.0 1.83230 0.916149 0.400838i \(-0.131281\pi\)
0.916149 + 0.400838i \(0.131281\pi\)
\(488\) 0 0
\(489\) 150.839 + 8337.42i 0.0139492 + 0.771025i
\(490\) 0 0
\(491\) −585.724 338.168i −0.0538358 0.0310821i 0.472841 0.881148i \(-0.343229\pi\)
−0.526676 + 0.850066i \(0.676562\pi\)
\(492\) 0 0
\(493\) 2257.93 1303.61i 0.206272 0.119091i
\(494\) 0 0
\(495\) 603.917 + 16684.9i 0.0548365 + 1.51501i
\(496\) 0 0
\(497\) 7443.31 + 8241.38i 0.671787 + 0.743816i
\(498\) 0 0
\(499\) 3095.81 5362.10i 0.277730 0.481043i −0.693090 0.720851i \(-0.743751\pi\)
0.970820 + 0.239808i \(0.0770845\pi\)
\(500\) 0 0
\(501\) −6060.59 3354.40i −0.540453 0.299129i
\(502\) 0 0
\(503\) 9490.52 0.841275 0.420638 0.907229i \(-0.361806\pi\)
0.420638 + 0.907229i \(0.361806\pi\)
\(504\) 0 0
\(505\) −21948.4 −1.93404
\(506\) 0 0
\(507\) −8524.78 + 5129.59i −0.746743 + 0.449336i
\(508\) 0 0
\(509\) 6484.87 11232.1i 0.564709 0.978104i −0.432368 0.901697i \(-0.642322\pi\)
0.997077 0.0764070i \(-0.0243448\pi\)
\(510\) 0 0
\(511\) −2661.87 2947.27i −0.230438 0.255146i
\(512\) 0 0
\(513\) 16398.1 890.792i 1.41130 0.0766655i
\(514\) 0 0
\(515\) −14395.7 + 8311.37i −1.23175 + 0.711151i
\(516\) 0 0
\(517\) 21766.3 + 12566.8i 1.85161 + 1.06902i
\(518\) 0 0
\(519\) 10996.5 6616.89i 0.930043 0.559632i
\(520\) 0 0
\(521\) 20707.4 1.74128 0.870642 0.491917i \(-0.163704\pi\)
0.870642 + 0.491917i \(0.163704\pi\)
\(522\) 0 0
\(523\) 10537.8i 0.881043i −0.897742 0.440522i \(-0.854794\pi\)
0.897742 0.440522i \(-0.145206\pi\)
\(524\) 0 0
\(525\) −3349.49 + 11040.8i −0.278445 + 0.917832i
\(526\) 0 0
\(527\) 14286.2 + 8248.16i 1.18087 + 0.681775i
\(528\) 0 0
\(529\) −6054.50 10486.7i −0.497616 0.861896i
\(530\) 0 0
\(531\) 6547.03 12351.1i 0.535060 1.00940i
\(532\) 0 0
\(533\) 10806.5 6239.13i 0.878200 0.507029i
\(534\) 0 0
\(535\) 2938.32 + 1696.44i 0.237448 + 0.137090i
\(536\) 0 0
\(537\) −22591.3 + 408.718i −1.81543 + 0.0328444i
\(538\) 0 0
\(539\) −5550.35 12364.9i −0.443545 0.988115i
\(540\) 0 0
\(541\) 11394.7 0.905542 0.452771 0.891627i \(-0.350436\pi\)
0.452771 + 0.891627i \(0.350436\pi\)
\(542\) 0 0
\(543\) −7916.68 + 143.227i −0.625667 + 0.0113194i
\(544\) 0 0
\(545\) −7415.64 + 12844.3i −0.582846 + 1.00952i
\(546\) 0 0
\(547\) −11353.1 19664.1i −0.887426 1.53707i −0.842908 0.538058i \(-0.819158\pi\)
−0.0445177 0.999009i \(-0.514175\pi\)
\(548\) 0 0
\(549\) −3760.41 + 2356.43i −0.292332 + 0.183187i
\(550\) 0 0
\(551\) 2691.27 + 4661.41i 0.208080 + 0.360404i
\(552\) 0 0
\(553\) 16013.4 + 5176.14i 1.23139 + 0.398033i
\(554\) 0 0
\(555\) −23871.8 13212.5i −1.82577 1.01052i
\(556\) 0 0
\(557\) 6229.16i 0.473857i 0.971527 + 0.236928i \(0.0761407\pi\)
−0.971527 + 0.236928i \(0.923859\pi\)
\(558\) 0 0
\(559\) 19527.1i 1.47747i
\(560\) 0 0
\(561\) 6002.31 + 9975.14i 0.451725 + 0.750714i
\(562\) 0 0
\(563\) 1558.81 2699.94i 0.116689 0.202112i −0.801764 0.597640i \(-0.796105\pi\)
0.918454 + 0.395528i \(0.129438\pi\)
\(564\) 0 0
\(565\) 19077.5 11014.4i 1.42052 0.820139i
\(566\) 0 0
\(567\) −9339.19 + 9750.07i −0.691727 + 0.722159i
\(568\) 0 0
\(569\) 10879.4 6281.22i 0.801561 0.462781i −0.0424558 0.999098i \(-0.513518\pi\)
0.844017 + 0.536317i \(0.180185\pi\)
\(570\) 0 0
\(571\) 3644.80 6312.98i 0.267128 0.462679i −0.700991 0.713170i \(-0.747259\pi\)
0.968119 + 0.250491i \(0.0805920\pi\)
\(572\) 0 0
\(573\) −10427.6 17329.5i −0.760244 1.26344i
\(574\) 0 0
\(575\) 913.138i 0.0662269i
\(576\) 0 0
\(577\) 5616.75i 0.405248i 0.979257 + 0.202624i \(0.0649470\pi\)
−0.979257 + 0.202624i \(0.935053\pi\)
\(578\) 0 0
\(579\) −1725.84 955.213i −0.123875 0.0685618i
\(580\) 0 0
\(581\) 13742.8 + 4442.21i 0.981323 + 0.317201i
\(582\) 0 0
\(583\) 5432.31 + 9409.04i 0.385906 + 0.668410i
\(584\) 0 0
\(585\) −22958.1 + 14386.5i −1.62257 + 1.01677i
\(586\) 0 0
\(587\) −897.050 1553.74i −0.0630753 0.109250i 0.832763 0.553629i \(-0.186758\pi\)
−0.895839 + 0.444380i \(0.853424\pi\)
\(588\) 0 0
\(589\) −17028.1 + 29493.5i −1.19122 + 2.06325i
\(590\) 0 0
\(591\) 15153.2 274.148i 1.05469 0.0190811i
\(592\) 0 0
\(593\) 16863.9 1.16782 0.583912 0.811817i \(-0.301521\pi\)
0.583912 + 0.811817i \(0.301521\pi\)
\(594\) 0 0
\(595\) 3441.05 + 16068.6i 0.237091 + 1.10714i
\(596\) 0 0
\(597\) 15137.0 273.855i 1.03772 0.0187741i
\(598\) 0 0
\(599\) −12704.3 7334.84i −0.866585 0.500323i −0.000372774 1.00000i \(-0.500119\pi\)
−0.866212 + 0.499677i \(0.833452\pi\)
\(600\) 0 0
\(601\) −854.824 + 493.533i −0.0580183 + 0.0334969i −0.528729 0.848791i \(-0.677331\pi\)
0.470710 + 0.882288i \(0.343998\pi\)
\(602\) 0 0
\(603\) −9309.60 + 17562.7i −0.628717 + 1.18608i
\(604\) 0 0
\(605\) −1802.77 3122.48i −0.121145 0.209830i
\(606\) 0 0
\(607\) −12623.0 7287.87i −0.844069 0.487323i 0.0145763 0.999894i \(-0.495360\pi\)
−0.858645 + 0.512570i \(0.828693\pi\)
\(608\) 0 0
\(609\) −4234.57 1284.65i −0.281763 0.0854790i
\(610\) 0 0
\(611\) 40785.7i 2.70051i
\(612\) 0 0
\(613\) −20361.1 −1.34156 −0.670780 0.741656i \(-0.734041\pi\)
−0.670780 + 0.741656i \(0.734041\pi\)
\(614\) 0 0
\(615\) 13558.5 8158.52i 0.888994 0.534932i
\(616\) 0 0
\(617\) −3623.21 2091.86i −0.236410 0.136491i 0.377116 0.926166i \(-0.376916\pi\)
−0.613526 + 0.789675i \(0.710249\pi\)
\(618\) 0 0
\(619\) −24006.3 + 13860.0i −1.55879 + 0.899970i −0.561421 + 0.827530i \(0.689745\pi\)
−0.997373 + 0.0724400i \(0.976921\pi\)
\(620\) 0 0
\(621\) −483.288 + 953.001i −0.0312298 + 0.0615823i
\(622\) 0 0
\(623\) 6089.98 5500.24i 0.391637 0.353712i
\(624\) 0 0
\(625\) 8118.69 14062.0i 0.519596 0.899967i
\(626\) 0 0
\(627\) −20593.3 + 12391.6i −1.31167 + 0.789269i
\(628\) 0 0
\(629\) −19025.0 −1.20600
\(630\) 0 0
\(631\) 6437.94 0.406165 0.203083 0.979162i \(-0.434904\pi\)
0.203083 + 0.979162i \(0.434904\pi\)
\(632\) 0 0
\(633\) −5338.47 2954.72i −0.335206 0.185529i
\(634\) 0 0
\(635\) 9945.81 17226.7i 0.621555 1.07657i
\(636\) 0 0
\(637\) 12873.6 17832.8i 0.800737 1.10920i
\(638\) 0 0
\(639\) 585.610 + 16179.1i 0.0362541 + 1.00162i
\(640\) 0 0
\(641\) 25430.0 14682.0i 1.56696 0.904687i 0.570444 0.821336i \(-0.306771\pi\)
0.996520 0.0833510i \(-0.0265622\pi\)
\(642\) 0 0
\(643\) 951.096 + 549.116i 0.0583321 + 0.0336781i 0.528882 0.848695i \(-0.322611\pi\)
−0.470550 + 0.882373i \(0.655945\pi\)
\(644\) 0 0
\(645\) 447.926 + 24758.5i 0.0273443 + 1.51142i
\(646\) 0 0
\(647\) −8485.25 −0.515595 −0.257797 0.966199i \(-0.582997\pi\)
−0.257797 + 0.966199i \(0.582997\pi\)
\(648\) 0 0
\(649\) 20458.3i 1.23738i
\(650\) 0 0
\(651\) −6357.16 27267.3i −0.382729 1.64161i
\(652\) 0 0
\(653\) 2743.06 + 1583.71i 0.164386 + 0.0949085i 0.579936 0.814662i \(-0.303077\pi\)
−0.415550 + 0.909570i \(0.636411\pi\)
\(654\) 0 0
\(655\) −8406.67 14560.8i −0.501490 0.868606i
\(656\) 0 0
\(657\) −209.425 5785.95i −0.0124360 0.343579i
\(658\) 0 0
\(659\) 13457.9 7769.91i 0.795516 0.459291i −0.0463851 0.998924i \(-0.514770\pi\)
0.841901 + 0.539632i \(0.181437\pi\)
\(660\) 0 0
\(661\) −9109.85 5259.57i −0.536054 0.309491i 0.207424 0.978251i \(-0.433492\pi\)
−0.743478 + 0.668760i \(0.766825\pi\)
\(662\) 0 0
\(663\) −9148.41 + 16529.0i −0.535890 + 0.968223i
\(664\) 0 0
\(665\) −33173.1 + 7103.94i −1.93443 + 0.414254i
\(666\) 0 0
\(667\) −350.222 −0.0203308
\(668\) 0 0
\(669\) −4984.30 8283.32i −0.288048 0.478702i
\(670\) 0 0
\(671\) 3247.31 5624.51i 0.186827 0.323594i
\(672\) 0 0
\(673\) −14642.5 25361.6i −0.838674 1.45263i −0.891004 0.453996i \(-0.849998\pi\)
0.0523297 0.998630i \(-0.483335\pi\)
\(674\) 0 0
\(675\) −14089.3 + 9187.98i −0.803402 + 0.523919i
\(676\) 0 0
\(677\) 2923.06 + 5062.89i 0.165941 + 0.287419i 0.936989 0.349358i \(-0.113600\pi\)
−0.771048 + 0.636777i \(0.780267\pi\)
\(678\) 0 0
\(679\) −2221.26 + 6871.91i −0.125544 + 0.388394i
\(680\) 0 0
\(681\) 11043.5 6645.17i 0.621421 0.373926i
\(682\) 0 0
\(683\) 7438.18i 0.416712i −0.978053 0.208356i \(-0.933189\pi\)
0.978053 0.208356i \(-0.0668112\pi\)
\(684\) 0 0
\(685\) 23547.5i 1.31344i
\(686\) 0 0
\(687\) 8363.64 15111.1i 0.464473 0.839190i
\(688\) 0 0
\(689\) −8815.33 + 15268.6i −0.487427 + 0.844249i
\(690\) 0 0
\(691\) 7016.10 4050.75i 0.386259 0.223007i −0.294279 0.955720i \(-0.595079\pi\)
0.680538 + 0.732713i \(0.261746\pi\)
\(692\) 0 0
\(693\) 5393.26 19008.8i 0.295632 1.04197i
\(694\) 0 0
\(695\) 11553.7 6670.52i 0.630584 0.364068i
\(696\) 0 0
\(697\) 5516.88 9555.51i 0.299809 0.519284i
\(698\) 0 0
\(699\) 12355.7 223.537i 0.668579 0.0120958i
\(700\) 0 0
\(701\) 80.5954i 0.00434243i 0.999998 + 0.00217122i \(0.000691120\pi\)
−0.999998 + 0.00217122i \(0.999309\pi\)
\(702\) 0 0
\(703\) 39276.5i 2.10717i
\(704\) 0 0
\(705\) 935.570 + 51712.4i 0.0499796 + 2.76256i
\(706\) 0 0
\(707\) 24716.2 + 7989.24i 1.31478 + 0.424988i
\(708\) 0 0
\(709\) −10309.1 17855.8i −0.546071 0.945823i −0.998539 0.0540423i \(-0.982789\pi\)
0.452467 0.891781i \(-0.350544\pi\)
\(710\) 0 0
\(711\) 13027.8 + 20790.0i 0.687177 + 1.09660i
\(712\) 0 0
\(713\) −1107.95 1919.03i −0.0581952 0.100797i
\(714\) 0 0
\(715\) 19825.6 34338.9i 1.03697 1.79609i
\(716\) 0 0
\(717\) 15276.0 27600.0i 0.795666 1.43758i
\(718\) 0 0
\(719\) 7395.39 0.383591 0.191795 0.981435i \(-0.438569\pi\)
0.191795 + 0.981435i \(0.438569\pi\)
\(720\) 0 0
\(721\) 19236.5 4119.44i 0.993626 0.212782i
\(722\) 0 0
\(723\) −9605.36 15963.0i −0.494090 0.821120i
\(724\) 0 0
\(725\) −4774.42 2756.51i −0.244576 0.141206i
\(726\) 0 0
\(727\) −2335.91 + 1348.64i −0.119167 + 0.0688008i −0.558398 0.829573i \(-0.688584\pi\)
0.439232 + 0.898374i \(0.355251\pi\)
\(728\) 0 0
\(729\) −19567.2 + 2132.18i −0.994115 + 0.108326i
\(730\) 0 0
\(731\) 8633.31 + 14953.3i 0.436819 + 0.756592i
\(732\) 0 0
\(733\) −34067.8 19669.0i −1.71667 0.991122i −0.924813 0.380421i \(-0.875779\pi\)
−0.791861 0.610701i \(-0.790888\pi\)
\(734\) 0 0
\(735\) 15913.4 22905.6i 0.798606 1.14951i
\(736\) 0 0
\(737\) 29090.9i 1.45397i
\(738\) 0 0
\(739\) −16780.5 −0.835293 −0.417646 0.908610i \(-0.637145\pi\)
−0.417646 + 0.908610i \(0.637145\pi\)
\(740\) 0 0
\(741\) −34123.5 18886.6i −1.69171 0.936324i
\(742\) 0 0
\(743\) 10852.9 + 6265.91i 0.535873 + 0.309386i 0.743405 0.668842i \(-0.233210\pi\)
−0.207532 + 0.978228i \(0.566543\pi\)
\(744\) 0 0
\(745\) −10483.3 + 6052.54i −0.515542 + 0.297648i
\(746\) 0 0
\(747\) 11180.6 + 17842.1i 0.547627 + 0.873909i
\(748\) 0 0
\(749\) −2691.36 2979.92i −0.131295 0.145373i
\(750\) 0 0
\(751\) −5313.64 + 9203.49i −0.258186 + 0.447190i −0.965756 0.259452i \(-0.916458\pi\)
0.707570 + 0.706643i \(0.249791\pi\)
\(752\) 0 0
\(753\) −409.733 22647.5i −0.0198293 1.09604i
\(754\) 0 0
\(755\) −39400.5 −1.89924
\(756\) 0 0
\(757\) 19420.8 0.932443 0.466221 0.884668i \(-0.345615\pi\)
0.466221 + 0.884668i \(0.345615\pi\)
\(758\) 0 0
\(759\) −28.2875 1563.55i −0.00135279 0.0747739i
\(760\) 0 0
\(761\) 1129.12 1955.70i 0.0537854 0.0931591i −0.837879 0.545856i \(-0.816205\pi\)
0.891665 + 0.452697i \(0.149538\pi\)
\(762\) 0 0
\(763\) 13026.1 11764.7i 0.618058 0.558207i
\(764\) 0 0
\(765\) −11220.2 + 21167.1i −0.530283 + 1.00039i
\(766\) 0 0
\(767\) −28751.1 + 16599.5i −1.35351 + 0.781449i
\(768\) 0 0
\(769\) 6652.81 + 3841.00i 0.311972 + 0.180117i 0.647809 0.761803i \(-0.275686\pi\)
−0.335837 + 0.941920i \(0.609019\pi\)
\(770\) 0 0
\(771\) −14742.6 8159.70i −0.688641 0.381147i
\(772\) 0 0
\(773\) 13041.2 0.606804 0.303402 0.952863i \(-0.401878\pi\)
0.303402 + 0.952863i \(0.401878\pi\)
\(774\) 0 0
\(775\) 34881.7i 1.61676i
\(776\) 0 0
\(777\) 22072.9 + 23568.1i 1.01913 + 1.08816i
\(778\) 0 0
\(779\) 19727.0 + 11389.4i 0.907310 + 0.523836i
\(780\) 0 0
\(781\) −11846.8 20519.3i −0.542783 0.940127i
\(782\) 0 0
\(783\) −3523.93 5403.76i −0.160836 0.246634i
\(784\) 0 0
\(785\) −989.936 + 571.540i −0.0450093 + 0.0259861i
\(786\) 0 0
\(787\) 7894.38 + 4557.83i 0.357566 + 0.206441i 0.668013 0.744150i \(-0.267145\pi\)
−0.310447 + 0.950591i \(0.600479\pi\)
\(788\) 0 0
\(789\) −935.201 1554.19i −0.0421978 0.0701277i
\(790\) 0 0
\(791\) −25492.5 + 5459.16i −1.14590 + 0.245392i
\(792\) 0 0
\(793\) 10539.2 0.471952
\(794\) 0 0
\(795\) −10826.8 + 19561.4i −0.483002 + 0.872668i