Properties

Label 252.4.x.a.41.12
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 41.12
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0939923 - 5.19530i) q^{3} +(-7.82452 + 13.5525i) q^{5} +(17.6225 - 5.69627i) q^{7} +(-26.9823 + 0.976636i) q^{9} +O(q^{10})\) \(q+(-0.0939923 - 5.19530i) q^{3} +(-7.82452 + 13.5525i) q^{5} +(17.6225 - 5.69627i) q^{7} +(-26.9823 + 0.976636i) q^{9} +(34.2206 - 19.7573i) q^{11} +(-55.5318 - 32.0613i) q^{13} +(71.1446 + 39.3769i) q^{15} -56.6997 q^{17} -117.055i q^{19} +(-31.2502 - 91.0188i) q^{21} +(-6.59593 - 3.80816i) q^{23} +(-59.9462 - 103.830i) q^{25} +(7.61005 + 140.090i) q^{27} +(39.8226 - 22.9916i) q^{29} +(-251.963 - 145.471i) q^{31} +(-105.861 - 175.929i) q^{33} +(-60.6891 + 283.399i) q^{35} -335.540 q^{37} +(-161.349 + 291.518i) q^{39} +(-97.3000 + 168.529i) q^{41} +(152.264 + 263.729i) q^{43} +(197.888 - 373.319i) q^{45} +(-318.029 - 550.842i) q^{47} +(278.105 - 200.765i) q^{49} +(5.32933 + 294.572i) q^{51} +274.953i q^{53} +618.365i q^{55} +(-608.134 + 11.0022i) q^{57} +(258.871 - 448.377i) q^{59} +(-142.340 + 82.1801i) q^{61} +(-469.933 + 170.909i) q^{63} +(869.019 - 501.728i) q^{65} +(368.103 - 637.573i) q^{67} +(-19.1646 + 34.6258i) q^{69} -599.619i q^{71} -214.435i q^{73} +(-533.793 + 321.198i) q^{75} +(490.510 - 543.102i) q^{77} +(-454.345 - 786.949i) q^{79} +(727.092 - 52.7039i) q^{81} +(389.923 + 675.366i) q^{83} +(443.648 - 768.420i) q^{85} +(-123.191 - 204.729i) q^{87} +443.089 q^{89} +(-1161.24 - 248.676i) q^{91} +(-732.084 + 1322.70i) q^{93} +(1586.38 + 915.896i) q^{95} +(-337.707 + 194.975i) q^{97} +(-904.056 + 566.518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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 \(0.413415\pi\)
−0.968519 + 0.248938i \(0.919919\pi\)
\(6\) 0 0
\(7\) 17.6225 5.69627i 0.951526 0.307570i
\(8\) 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 −0.227641 0.973745i \(-0.573101\pi\)
−0.957109 + 0.289730i \(0.906435\pi\)
\(14\) 0 0
\(15\) 71.1446 + 39.3769i 1.22463 + 0.677805i
\(16\) 0 0
\(17\) −56.6997 −0.808923 −0.404462 0.914555i \(-0.632541\pi\)
−0.404462 + 0.914555i \(0.632541\pi\)
\(18\) 0 0
\(19\) 117.055i 1.41338i −0.707525 0.706689i \(-0.750188\pi\)
0.707525 0.706689i \(-0.249812\pi\)
\(20\) 0 0
\(21\) −31.2502 91.0188i −0.324731 0.945806i
\(22\) 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 −0.460803 0.887502i \(-0.652439\pi\)
−0.999001 + 0.0446836i \(0.985772\pi\)
\(32\) 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 −0.989662 0.143419i \(-0.954190\pi\)
0.619035 + 0.785363i \(0.287524\pi\)
\(42\) 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 \(-0.718036\pi\)
−0.354347 0.935114i \(-0.615297\pi\)
\(48\) 0 0
\(49\) 278.105 200.765i 0.810802 0.585321i
\(50\) 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 \(-0.639803\pi\)
0.996441 0.0842947i \(-0.0268637\pi\)
\(60\) 0 0
\(61\) −142.340 + 82.1801i −0.298767 + 0.172493i −0.641889 0.766798i \(-0.721849\pi\)
0.343122 + 0.939291i \(0.388516\pi\)
\(62\) 0 0
\(63\) −469.933 + 170.909i −0.939778 + 0.341787i
\(64\) 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 \(-0.945009\pi\)
0.985114 0.171902i \(-0.0549913\pi\)
\(74\) 0 0
\(75\) −533.793 + 321.198i −0.821827 + 0.494516i
\(76\) 0 0
\(77\) 490.510 543.102i 0.725958 0.803796i
\(78\) 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 \(0.00578575\pi\)
−0.484177 + 0.874970i \(0.660881\pi\)
\(84\) 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 \(-0.415004\pi\)
0.263862 + 0.964561i \(0.415004\pi\)
\(90\) 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 −0.666223 0.745752i \(-0.732090\pi\)
0.312729 + 0.949842i \(0.398757\pi\)
\(98\) 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 \(0.0761103\pi\)
−0.280669 + 0.959805i \(0.590556\pi\)
\(102\) 0 0
\(103\) 919.911 + 531.111i 0.880015 + 0.508077i 0.870663 0.491879i \(-0.163690\pi\)
0.00935152 + 0.999956i \(0.497023\pi\)
\(104\) 0 0
\(105\) 1478.05 + 288.661i 1.37374 + 0.268290i
\(106\) 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
\(119\) −999.190 + 322.977i −0.769711 + 0.248800i
\(120\) 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 −0.987675 0.156521i \(-0.949972\pi\)
0.629389 + 0.777091i \(0.283305\pi\)
\(132\) 0 0
\(133\) −666.774 2062.79i −0.434712 1.34486i
\(134\) 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 0.257532 0.966270i \(-0.417091\pi\)
−0.708048 + 0.706164i \(0.750424\pi\)
\(140\) 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
\(147\) −1069.17 1425.97i −0.599891 0.800081i
\(148\) 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 0.515992 0.856593i \(-0.327423\pi\)
−0.483836 + 0.875159i \(0.660757\pi\)
\(158\) 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 −0.669257 0.743031i \(-0.733387\pi\)
0.978112 + 0.208077i \(0.0667206\pi\)
\(168\) 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 \(0.0159379\pi\)
−0.456029 + 0.889965i \(0.650729\pi\)
\(174\) 0 0
\(175\) −1647.84 1488.27i −0.711801 0.642873i
\(176\) 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 \(-0.898705\pi\)
0.949791 0.312885i \(-0.101295\pi\)
\(182\) 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
\(189\) 932.096 + 2425.38i 0.358730 + 0.933441i
\(190\) 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 \(0.173674\pi\)
−0.854809 + 0.518943i \(0.826326\pi\)
\(200\) 0 0
\(201\) −3346.99 1852.48i −1.17452 0.650069i
\(202\) 0 0
\(203\) 570.807 632.009i 0.197354 0.218514i
\(204\) 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 −0.238179 0.971221i \(-0.576550\pi\)
0.722013 + 0.691879i \(0.243217\pi\)
\(224\) 0 0
\(225\) 1718.89 + 2743.02i 0.509301 + 0.812748i
\(226\) 0 0
\(227\) 1240.21 + 2148.11i 0.362624 + 0.628083i 0.988392 0.151926i \(-0.0485477\pi\)
−0.625768 + 0.780009i \(0.715214\pi\)
\(228\) 0 0
\(229\) 2878.54 + 1661.92i 0.830651 + 0.479577i 0.854076 0.520149i \(-0.174124\pi\)
−0.0234243 + 0.999726i \(0.507457\pi\)
\(230\) 0 0
\(231\) −2867.69 2497.30i −0.816796 0.711300i
\(232\) 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 −0.0239031 0.999714i \(-0.507609\pi\)
0.853826 + 0.520558i \(0.174276\pi\)
\(242\) 0 0
\(243\) −342.154 3772.51i −0.0903258 0.995912i
\(244\) 0 0
\(245\) 544.823 + 5339.90i 0.142071 + 1.39246i
\(246\) 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 \(-0.315347\pi\)
0.548111 + 0.836406i \(0.315347\pi\)
\(252\) 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 −0.599372 0.800470i \(-0.704583\pi\)
0.992914 + 0.118837i \(0.0379165\pi\)
\(258\) 0 0
\(259\) −5913.05 + 1911.32i −1.41861 + 0.458548i
\(260\) 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 \(-0.855048\pi\)
−0.898095 + 0.439802i \(0.855048\pi\)
\(270\) 0 0
\(271\) 6601.56i 1.47976i −0.672737 0.739882i \(-0.734881\pi\)
0.672737 0.739882i \(-0.265119\pi\)
\(272\) 0 0
\(273\) −1182.80 + 6056.36i −0.262221 + 1.34266i
\(274\) 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 0.349490 0.936940i \(-0.386355\pi\)
−0.636669 + 0.771137i \(0.719688\pi\)
\(284\) 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 −0.749251 0.662286i \(-0.769586\pi\)
0.948182 + 0.317728i \(0.102920\pi\)
\(294\) 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
\(301\) 4185.54 + 3780.22i 0.801496 + 0.723882i
\(302\) 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 \(-0.949085\pi\)
0.987235 0.159272i \(-0.0509146\pi\)
\(308\) 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 \(0.369619\pi\)
−0.993510 + 0.113748i \(0.963714\pi\)
\(312\) 0 0
\(313\) −377.873 + 218.165i −0.0682384 + 0.0393975i −0.533731 0.845654i \(-0.679211\pi\)
0.465493 + 0.885052i \(0.345877\pi\)
\(314\) 0 0
\(315\) 1360.76 7706.03i 0.243396 1.37837i
\(316\) 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
\(329\) −8742.21 7895.64i −1.46497 1.32310i
\(330\) 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 −0.317633 0.948214i \(-0.602888\pi\)
0.662361 + 0.749185i \(0.269555\pi\)
\(350\) 0 0
\(351\) 4068.85 8023.41i 0.618744 1.22011i
\(352\) 0 0
\(353\) 2303.43 + 3989.65i 0.347306 + 0.601551i 0.985770 0.168100i \(-0.0537632\pi\)
−0.638464 + 0.769652i \(0.720430\pi\)
\(354\) 0 0
\(355\) 8126.32 + 4691.73i 1.21493 + 0.701440i
\(356\) 0 0
\(357\) 1771.88 + 5160.74i 0.262683 + 0.765085i
\(358\) 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 0.218201 0.975904i \(-0.429981\pi\)
0.954258 + 0.298984i \(0.0966479\pi\)
\(368\) 0 0
\(369\) 2460.79 4642.32i 0.347164 0.654931i
\(370\) 0 0
\(371\) 1566.20 + 4845.35i 0.219173 + 0.678054i
\(372\) 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 −0.900336 0.435196i \(-0.856679\pi\)
0.827059 + 0.562115i \(0.190012\pi\)
\(384\) 0 0
\(385\) 3522.37 + 10897.1i 0.466277 + 1.44252i
\(386\) 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 \(0.316060\pi\)
−0.546237 + 0.837630i \(0.683940\pi\)
\(398\) 0 0
\(399\) −10654.2 + 3657.98i −1.33678 + 0.458968i
\(400\) 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 −0.243434 0.969917i \(-0.578274\pi\)
−0.961690 + 0.274139i \(0.911607\pi\)
\(410\) 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 \(-0.468510\pi\)
0.812408 0.583090i \(-0.198156\pi\)
\(420\) 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
\(427\) −2040.27 + 2259.03i −0.231231 + 0.256023i
\(428\) 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 \(0.0199094\pi\)
−0.998045 + 0.0625065i \(0.980091\pi\)
\(434\) 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 0.295083 0.955472i \(-0.404653\pi\)
0.975004 + 0.222187i \(0.0713195\pi\)
\(440\) 0 0
\(441\) −7307.85 + 5688.72i −0.789099 + 0.614266i
\(442\) 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
\(455\) 12456.3 13791.9i 1.28343 1.42104i
\(456\) 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 \(0.0462015\pi\)
−0.369483 + 0.929238i \(0.620465\pi\)
\(462\) 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 \(-0.748167\pi\)
−0.703023 + 0.711167i \(0.748167\pi\)
\(468\) 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 \(-0.999350\pi\)
0.498232 0.867044i \(-0.333983\pi\)
\(480\) 0 0
\(481\) 18633.1 + 10757.8i 1.76631 + 1.01978i
\(482\) 0 0
\(483\) −140.490 + 719.359i −0.0132350 + 0.0677681i
\(484\) 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
\(497\) −3415.59 10566.8i −0.308270 0.953693i
\(498\) 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 \(-0.638194\pi\)
−0.420638 + 0.907229i \(0.638194\pi\)
\(504\) 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 \(0.357678\pi\)
−0.997077 + 0.0764070i \(0.975655\pi\)
\(510\) 0 0
\(511\) −1221.48 3778.88i −0.105744 0.327138i
\(512\) 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 \(-0.836296\pi\)
−0.870642 + 0.491917i \(0.836296\pi\)
\(522\) 0 0
\(523\) 10537.8i 0.881043i 0.897742 + 0.440522i \(0.145206\pi\)
−0.897742 + 0.440522i \(0.854794\pi\)
\(524\) 0 0
\(525\) −7577.13 + 8700.93i −0.629892 + 0.723314i
\(526\) 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
\(553\) −12489.4 11279.9i −0.960401 0.867399i
\(554\) 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 −0.918454 0.395528i \(-0.870562\pi\)
0.801764 + 0.597640i \(0.203895\pi\)
\(564\) 0 0
\(565\) −19077.5 + 11014.4i −1.42052 + 0.820139i
\(566\) 0 0
\(567\) 12513.0 5070.49i 0.926800 0.375556i
\(568\) 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 \(-0.935053\pi\)
0.979257 0.202624i \(-0.0649470\pi\)
\(578\) 0 0
\(579\) 1725.84 + 955.213i 0.123875 + 0.0685618i
\(580\) 0 0
\(581\) 10718.5 + 9680.54i 0.765366 + 0.691250i
\(582\) 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 0.895839 0.444380i \(-0.146576\pi\)
−0.832763 + 0.553629i \(0.813242\pi\)
\(588\) 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 \(-0.698479\pi\)
−0.583912 + 0.811817i \(0.698479\pi\)
\(594\) 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 −0.470710 0.882288i \(-0.656002\pi\)
0.528729 + 0.848791i \(0.322669\pi\)
\(602\) 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 0.858645 0.512570i \(-0.171307\pi\)
−0.0145763 + 0.999894i \(0.504640\pi\)
\(608\) 0 0
\(609\) −3337.13 2906.11i −0.222048 0.193369i
\(610\) 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 \(-0.310255\pi\)
0.997373 0.0724400i \(-0.0230786\pi\)
\(620\) 0 0
\(621\) 483.288 953.001i 0.0312298 0.0615823i
\(622\) 0 0
\(623\) 7808.34 2523.96i 0.502142 0.162312i
\(624\) 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
\(637\) −21880.5 + 2232.43i −1.36097 + 0.138858i
\(638\) 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 0.470550 0.882373i \(-0.344055\pi\)
−0.528882 + 0.848695i \(0.677389\pi\)
\(644\) 0 0
\(645\) 447.926 + 24758.5i 0.0273443 + 1.51142i
\(646\) 0 0
\(647\) 8485.25 0.515595 0.257797 0.966199i \(-0.417003\pi\)
0.257797 + 0.966199i \(0.417003\pi\)
\(648\) 0 0
\(649\) 20458.3i 1.23738i
\(650\) 0 0
\(651\) −5366.70 + 27479.4i −0.323099 + 1.65438i
\(652\) 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 0.743478 0.668760i \(-0.233175\pi\)
−0.207424 + 0.978251i \(0.566508\pi\)
\(662\) 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 0.771048 0.636777i \(-0.219733\pi\)
−0.936989 + 0.349358i \(0.886400\pi\)
\(678\) 0 0
\(679\) −4840.61 + 5359.63i −0.273587 + 0.302921i
\(680\) 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 −0.680538 0.732713i \(-0.738254\pi\)
0.294279 + 0.955720i \(0.404921\pi\)
\(692\) 0 0
\(693\) −12704.7 + 15133.2i −0.696409 + 0.829529i
\(694\) 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
\(707\) 19277.0 + 17410.3i 1.02544 + 0.926140i
\(708\) 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 \(-0.561431\pi\)
−0.191795 + 0.981435i \(0.561431\pi\)
\(720\) 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 −0.439232 0.898374i \(-0.644749\pi\)
0.558398 + 0.829573i \(0.311416\pi\)
\(728\) 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 \(0.124221\pi\)
0.791861 + 0.610701i \(0.209112\pi\)
\(734\) 0 0
\(735\) 27691.2 3332.43i 1.38967 0.167236i
\(736\) 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
\(749\) 1235.01 + 3820.74i 0.0602488 + 0.186391i
\(750\) 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 −0.891665 0.452697i \(-0.850462\pi\)
0.837879 + 0.545856i \(0.183795\pi\)
\(762\) 0 0
\(763\) −16701.6 + 5398.61i −0.792450 + 0.256150i
\(764\) 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 0.335837 0.941920i \(-0.390981\pi\)
−0.647809 + 0.761803i \(0.724314\pi\)
\(770\) 0 0
\(771\) −14742.6 8159.70i −0.688641 0.381147i
\(772\) 0 0
\(773\) −13041.2 −0.606804 −0.303402 0.952863i \(-0.598122\pi\)
−0.303402 + 0.952863i \(0.598122\pi\)
\(774\) 0 0
\(775\) 34881.7i 1.61676i
\(776\) 0 0
\(777\) 10485.7 + 30540.4i 0.484134 + 1.41008i
\(778\) 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 0.310447 0.950591i \(-0.399521\pi\)
−0.668013 + 0.744150i \(0.732855\pi\)
\(788\) 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