Properties

Label 441.4.e.c.361.1
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.c.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -21.0000 q^{8} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -21.0000 q^{8} +(4.50000 - 7.79423i) q^{10} +(-7.50000 + 12.9904i) q^{11} +64.0000 q^{13} +(35.5000 + 61.4878i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-8.00000 - 13.8564i) q^{19} -3.00000 q^{20} +45.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(58.0000 - 100.459i) q^{25} +(-96.0000 - 166.277i) q^{26} +297.000 q^{29} +(-126.500 + 219.104i) q^{31} +(22.5000 - 38.9711i) q^{32} +252.000 q^{34} +(158.000 + 273.664i) q^{37} +(-24.0000 + 41.5692i) q^{38} +(-31.5000 - 54.5596i) q^{40} +360.000 q^{41} +26.0000 q^{43} +(-7.50000 - 12.9904i) q^{44} +(-126.000 + 218.238i) q^{46} +(15.0000 + 25.9808i) q^{47} -348.000 q^{50} +(-32.0000 + 55.4256i) q^{52} +(181.500 - 314.367i) q^{53} -45.0000 q^{55} +(-445.500 - 771.629i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-59.0000 - 102.191i) q^{61} +759.000 q^{62} +433.000 q^{64} +(96.0000 + 166.277i) q^{65} +(185.000 - 320.429i) q^{67} +(-42.0000 - 72.7461i) q^{68} +342.000 q^{71} +(181.000 - 313.501i) q^{73} +(474.000 - 820.992i) q^{74} +16.0000 q^{76} +(-233.500 - 404.434i) q^{79} +(-106.500 + 184.463i) q^{80} +(-540.000 - 935.307i) q^{82} +477.000 q^{83} -252.000 q^{85} +(-39.0000 - 67.5500i) q^{86} +(157.500 - 272.798i) q^{88} +(-453.000 - 784.619i) q^{89} +84.0000 q^{92} +(45.0000 - 77.9423i) q^{94} +(24.0000 - 41.5692i) q^{95} -503.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} - q^{4} + 3q^{5} - 42q^{8} + O(q^{10}) \) \( 2q - 3q^{2} - q^{4} + 3q^{5} - 42q^{8} + 9q^{10} - 15q^{11} + 128q^{13} + 71q^{16} - 84q^{17} - 16q^{19} - 6q^{20} + 90q^{22} - 84q^{23} + 116q^{25} - 192q^{26} + 594q^{29} - 253q^{31} + 45q^{32} + 504q^{34} + 316q^{37} - 48q^{38} - 63q^{40} + 720q^{41} + 52q^{43} - 15q^{44} - 252q^{46} + 30q^{47} - 696q^{50} - 64q^{52} + 363q^{53} - 90q^{55} - 891q^{58} + 15q^{59} - 118q^{61} + 1518q^{62} + 866q^{64} + 192q^{65} + 370q^{67} - 84q^{68} + 684q^{71} + 362q^{73} + 948q^{74} + 32q^{76} - 467q^{79} - 213q^{80} - 1080q^{82} + 954q^{83} - 504q^{85} - 78q^{86} + 315q^{88} - 906q^{89} + 168q^{92} + 90q^{94} + 48q^{95} - 1006q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 2.59808i −0.530330 0.918559i −0.999374 0.0353837i \(-0.988735\pi\)
0.469044 0.883175i \(-0.344599\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(5\) 1.50000 + 2.59808i 0.134164 + 0.232379i 0.925278 0.379290i \(-0.123832\pi\)
−0.791114 + 0.611669i \(0.790498\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −21.0000 −0.928078
\(9\) 0 0
\(10\) 4.50000 7.79423i 0.142302 0.246475i
\(11\) −7.50000 + 12.9904i −0.205576 + 0.356068i −0.950316 0.311287i \(-0.899240\pi\)
0.744740 + 0.667355i \(0.232573\pi\)
\(12\) 0 0
\(13\) 64.0000 1.36542 0.682708 0.730691i \(-0.260802\pi\)
0.682708 + 0.730691i \(0.260802\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) −42.0000 + 72.7461i −0.599206 + 1.03785i 0.393733 + 0.919225i \(0.371183\pi\)
−0.992939 + 0.118630i \(0.962150\pi\)
\(18\) 0 0
\(19\) −8.00000 13.8564i −0.0965961 0.167309i 0.813678 0.581317i \(-0.197462\pi\)
−0.910274 + 0.414007i \(0.864129\pi\)
\(20\) −3.00000 −0.0335410
\(21\) 0 0
\(22\) 45.0000 0.436092
\(23\) −42.0000 72.7461i −0.380765 0.659505i 0.610406 0.792088i \(-0.291006\pi\)
−0.991172 + 0.132583i \(0.957673\pi\)
\(24\) 0 0
\(25\) 58.0000 100.459i 0.464000 0.803672i
\(26\) −96.0000 166.277i −0.724121 1.25421i
\(27\) 0 0
\(28\) 0 0
\(29\) 297.000 1.90178 0.950888 0.309535i \(-0.100173\pi\)
0.950888 + 0.309535i \(0.100173\pi\)
\(30\) 0 0
\(31\) −126.500 + 219.104i −0.732906 + 1.26943i 0.222731 + 0.974880i \(0.428503\pi\)
−0.955636 + 0.294550i \(0.904830\pi\)
\(32\) 22.5000 38.9711i 0.124296 0.215287i
\(33\) 0 0
\(34\) 252.000 1.27111
\(35\) 0 0
\(36\) 0 0
\(37\) 158.000 + 273.664i 0.702028 + 1.21595i 0.967753 + 0.251900i \(0.0810553\pi\)
−0.265725 + 0.964049i \(0.585611\pi\)
\(38\) −24.0000 + 41.5692i −0.102456 + 0.177458i
\(39\) 0 0
\(40\) −31.5000 54.5596i −0.124515 0.215666i
\(41\) 360.000 1.37128 0.685641 0.727940i \(-0.259522\pi\)
0.685641 + 0.727940i \(0.259522\pi\)
\(42\) 0 0
\(43\) 26.0000 0.0922084 0.0461042 0.998937i \(-0.485319\pi\)
0.0461042 + 0.998937i \(0.485319\pi\)
\(44\) −7.50000 12.9904i −0.0256970 0.0445085i
\(45\) 0 0
\(46\) −126.000 + 218.238i −0.403863 + 0.699511i
\(47\) 15.0000 + 25.9808i 0.0465527 + 0.0806316i 0.888363 0.459142i \(-0.151843\pi\)
−0.841810 + 0.539774i \(0.818510\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −348.000 −0.984293
\(51\) 0 0
\(52\) −32.0000 + 55.4256i −0.0853385 + 0.147811i
\(53\) 181.500 314.367i 0.470395 0.814748i −0.529032 0.848602i \(-0.677445\pi\)
0.999427 + 0.0338538i \(0.0107781\pi\)
\(54\) 0 0
\(55\) −45.0000 −0.110324
\(56\) 0 0
\(57\) 0 0
\(58\) −445.500 771.629i −1.00857 1.74689i
\(59\) 7.50000 12.9904i 0.0165494 0.0286645i −0.857632 0.514264i \(-0.828065\pi\)
0.874182 + 0.485599i \(0.161399\pi\)
\(60\) 0 0
\(61\) −59.0000 102.191i −0.123839 0.214495i 0.797440 0.603399i \(-0.206187\pi\)
−0.921279 + 0.388903i \(0.872854\pi\)
\(62\) 759.000 1.55473
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) 96.0000 + 166.277i 0.183190 + 0.317294i
\(66\) 0 0
\(67\) 185.000 320.429i 0.337334 0.584279i −0.646597 0.762832i \(-0.723808\pi\)
0.983930 + 0.178553i \(0.0571417\pi\)
\(68\) −42.0000 72.7461i −0.0749007 0.129732i
\(69\) 0 0
\(70\) 0 0
\(71\) 342.000 0.571661 0.285831 0.958280i \(-0.407731\pi\)
0.285831 + 0.958280i \(0.407731\pi\)
\(72\) 0 0
\(73\) 181.000 313.501i 0.290198 0.502638i −0.683658 0.729802i \(-0.739612\pi\)
0.973856 + 0.227165i \(0.0729455\pi\)
\(74\) 474.000 820.992i 0.744613 1.28971i
\(75\) 0 0
\(76\) 16.0000 0.0241490
\(77\) 0 0
\(78\) 0 0
\(79\) −233.500 404.434i −0.332542 0.575979i 0.650468 0.759534i \(-0.274573\pi\)
−0.983010 + 0.183555i \(0.941240\pi\)
\(80\) −106.500 + 184.463i −0.148838 + 0.257795i
\(81\) 0 0
\(82\) −540.000 935.307i −0.727232 1.25960i
\(83\) 477.000 0.630814 0.315407 0.948957i \(-0.397859\pi\)
0.315407 + 0.948957i \(0.397859\pi\)
\(84\) 0 0
\(85\) −252.000 −0.321568
\(86\) −39.0000 67.5500i −0.0489009 0.0846989i
\(87\) 0 0
\(88\) 157.500 272.798i 0.190790 0.330459i
\(89\) −453.000 784.619i −0.539527 0.934488i −0.998929 0.0462600i \(-0.985270\pi\)
0.459402 0.888228i \(-0.348064\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 84.0000 0.0951914
\(93\) 0 0
\(94\) 45.0000 77.9423i 0.0493765 0.0855227i
\(95\) 24.0000 41.5692i 0.0259195 0.0448938i
\(96\) 0 0
\(97\) −503.000 −0.526515 −0.263257 0.964726i \(-0.584797\pi\)
−0.263257 + 0.964726i \(0.584797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 58.0000 + 100.459i 0.0580000 + 0.100459i
\(101\) 543.000 940.504i 0.534956 0.926570i −0.464210 0.885725i \(-0.653662\pi\)
0.999165 0.0408451i \(-0.0130050\pi\)
\(102\) 0 0
\(103\) 868.000 + 1503.42i 0.830355 + 1.43822i 0.897757 + 0.440491i \(0.145196\pi\)
−0.0674017 + 0.997726i \(0.521471\pi\)
\(104\) −1344.00 −1.26721
\(105\) 0 0
\(106\) −1089.00 −0.997859
\(107\) −676.500 1171.73i −0.611212 1.05865i −0.991036 0.133592i \(-0.957349\pi\)
0.379824 0.925059i \(-0.375985\pi\)
\(108\) 0 0
\(109\) 185.000 320.429i 0.162567 0.281574i −0.773222 0.634136i \(-0.781356\pi\)
0.935789 + 0.352562i \(0.114689\pi\)
\(110\) 67.5000 + 116.913i 0.0585079 + 0.101339i
\(111\) 0 0
\(112\) 0 0
\(113\) 648.000 0.539458 0.269729 0.962936i \(-0.413066\pi\)
0.269729 + 0.962936i \(0.413066\pi\)
\(114\) 0 0
\(115\) 126.000 218.238i 0.102170 0.176964i
\(116\) −148.500 + 257.210i −0.118861 + 0.205873i
\(117\) 0 0
\(118\) −45.0000 −0.0351067
\(119\) 0 0
\(120\) 0 0
\(121\) 553.000 + 957.824i 0.415477 + 0.719627i
\(122\) −177.000 + 306.573i −0.131351 + 0.227507i
\(123\) 0 0
\(124\) −126.500 219.104i −0.0916132 0.158679i
\(125\) 723.000 0.517337
\(126\) 0 0
\(127\) 377.000 0.263412 0.131706 0.991289i \(-0.457954\pi\)
0.131706 + 0.991289i \(0.457954\pi\)
\(128\) −829.500 1436.74i −0.572798 0.992115i
\(129\) 0 0
\(130\) 288.000 498.831i 0.194302 0.336541i
\(131\) 325.500 + 563.783i 0.217092 + 0.376015i 0.953918 0.300068i \(-0.0970095\pi\)
−0.736826 + 0.676083i \(0.763676\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1110.00 −0.715593
\(135\) 0 0
\(136\) 882.000 1527.67i 0.556109 0.963210i
\(137\) −885.000 + 1532.86i −0.551903 + 0.955923i 0.446235 + 0.894916i \(0.352765\pi\)
−0.998137 + 0.0610074i \(0.980569\pi\)
\(138\) 0 0
\(139\) 1558.00 0.950704 0.475352 0.879796i \(-0.342321\pi\)
0.475352 + 0.879796i \(0.342321\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −513.000 888.542i −0.303169 0.525104i
\(143\) −480.000 + 831.384i −0.280697 + 0.486181i
\(144\) 0 0
\(145\) 445.500 + 771.629i 0.255150 + 0.441933i
\(146\) −1086.00 −0.615603
\(147\) 0 0
\(148\) −316.000 −0.175507
\(149\) 1227.00 + 2125.23i 0.674629 + 1.16849i 0.976577 + 0.215168i \(0.0690298\pi\)
−0.301948 + 0.953324i \(0.597637\pi\)
\(150\) 0 0
\(151\) −629.500 + 1090.33i −0.339258 + 0.587612i −0.984293 0.176540i \(-0.943509\pi\)
0.645035 + 0.764153i \(0.276843\pi\)
\(152\) 168.000 + 290.985i 0.0896487 + 0.155276i
\(153\) 0 0
\(154\) 0 0
\(155\) −759.000 −0.393318
\(156\) 0 0
\(157\) −98.0000 + 169.741i −0.0498169 + 0.0862854i −0.889859 0.456236i \(-0.849197\pi\)
0.840042 + 0.542522i \(0.182530\pi\)
\(158\) −700.500 + 1213.30i −0.352714 + 0.610918i
\(159\) 0 0
\(160\) 135.000 0.0667043
\(161\) 0 0
\(162\) 0 0
\(163\) 626.000 + 1084.26i 0.300810 + 0.521019i 0.976320 0.216332i \(-0.0694095\pi\)
−0.675509 + 0.737351i \(0.736076\pi\)
\(164\) −180.000 + 311.769i −0.0857051 + 0.148446i
\(165\) 0 0
\(166\) −715.500 1239.28i −0.334540 0.579440i
\(167\) −2646.00 −1.22607 −0.613035 0.790056i \(-0.710051\pi\)
−0.613035 + 0.790056i \(0.710051\pi\)
\(168\) 0 0
\(169\) 1899.00 0.864360
\(170\) 378.000 + 654.715i 0.170537 + 0.295379i
\(171\) 0 0
\(172\) −13.0000 + 22.5167i −0.00576303 + 0.00998186i
\(173\) 393.000 + 680.696i 0.172712 + 0.299147i 0.939367 0.342913i \(-0.111414\pi\)
−0.766655 + 0.642059i \(0.778080\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1065.00 −0.456122
\(177\) 0 0
\(178\) −1359.00 + 2353.86i −0.572255 + 0.991174i
\(179\) 1446.00 2504.55i 0.603794 1.04580i −0.388447 0.921471i \(-0.626988\pi\)
0.992241 0.124331i \(-0.0396784\pi\)
\(180\) 0 0
\(181\) −1352.00 −0.555212 −0.277606 0.960695i \(-0.589541\pi\)
−0.277606 + 0.960695i \(0.589541\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 882.000 + 1527.67i 0.353380 + 0.612072i
\(185\) −474.000 + 820.992i −0.188374 + 0.326273i
\(186\) 0 0
\(187\) −630.000 1091.19i −0.246365 0.426716i
\(188\) −30.0000 −0.0116382
\(189\) 0 0
\(190\) −144.000 −0.0549835
\(191\) 1956.00 + 3387.89i 0.741001 + 1.28345i 0.952040 + 0.305974i \(0.0989820\pi\)
−0.211039 + 0.977478i \(0.567685\pi\)
\(192\) 0 0
\(193\) −746.500 + 1292.98i −0.278416 + 0.482230i −0.970991 0.239115i \(-0.923143\pi\)
0.692575 + 0.721345i \(0.256476\pi\)
\(194\) 754.500 + 1306.83i 0.279227 + 0.483635i
\(195\) 0 0
\(196\) 0 0
\(197\) 4086.00 1.47774 0.738872 0.673846i \(-0.235359\pi\)
0.738872 + 0.673846i \(0.235359\pi\)
\(198\) 0 0
\(199\) −1778.00 + 3079.59i −0.633362 + 1.09702i 0.353497 + 0.935436i \(0.384992\pi\)
−0.986860 + 0.161580i \(0.948341\pi\)
\(200\) −1218.00 + 2109.64i −0.430628 + 0.745870i
\(201\) 0 0
\(202\) −3258.00 −1.13481
\(203\) 0 0
\(204\) 0 0
\(205\) 540.000 + 935.307i 0.183977 + 0.318657i
\(206\) 2604.00 4510.26i 0.880725 1.52546i
\(207\) 0 0
\(208\) 2272.00 + 3935.22i 0.757379 + 1.31182i
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) 1250.00 0.407837 0.203918 0.978988i \(-0.434632\pi\)
0.203918 + 0.978988i \(0.434632\pi\)
\(212\) 181.500 + 314.367i 0.0587994 + 0.101844i
\(213\) 0 0
\(214\) −2029.50 + 3515.20i −0.648289 + 1.12287i
\(215\) 39.0000 + 67.5500i 0.0123711 + 0.0214273i
\(216\) 0 0
\(217\) 0 0
\(218\) −1110.00 −0.344856
\(219\) 0 0
\(220\) 22.5000 38.9711i 0.00689523 0.0119429i
\(221\) −2688.00 + 4655.75i −0.818165 + 1.41710i
\(222\) 0 0
\(223\) −425.000 −0.127624 −0.0638119 0.997962i \(-0.520326\pi\)
−0.0638119 + 0.997962i \(0.520326\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −972.000 1683.55i −0.286091 0.495523i
\(227\) −1927.50 + 3338.53i −0.563580 + 0.976149i 0.433600 + 0.901105i \(0.357243\pi\)
−0.997180 + 0.0750439i \(0.976090\pi\)
\(228\) 0 0
\(229\) −1094.00 1894.86i −0.315692 0.546795i 0.663892 0.747828i \(-0.268903\pi\)
−0.979584 + 0.201033i \(0.935570\pi\)
\(230\) −756.000 −0.216735
\(231\) 0 0
\(232\) −6237.00 −1.76500
\(233\) 426.000 + 737.854i 0.119778 + 0.207461i 0.919679 0.392670i \(-0.128449\pi\)
−0.799902 + 0.600131i \(0.795115\pi\)
\(234\) 0 0
\(235\) −45.0000 + 77.9423i −0.0124914 + 0.0216357i
\(236\) 7.50000 + 12.9904i 0.00206868 + 0.00358306i
\(237\) 0 0
\(238\) 0 0
\(239\) −5508.00 −1.49072 −0.745362 0.666660i \(-0.767723\pi\)
−0.745362 + 0.666660i \(0.767723\pi\)
\(240\) 0 0
\(241\) 395.500 685.026i 0.105711 0.183097i −0.808317 0.588747i \(-0.799621\pi\)
0.914029 + 0.405650i \(0.132955\pi\)
\(242\) 1659.00 2873.47i 0.440680 0.763280i
\(243\) 0 0
\(244\) 118.000 0.0309597
\(245\) 0 0
\(246\) 0 0
\(247\) −512.000 886.810i −0.131894 0.228447i
\(248\) 2656.50 4601.19i 0.680193 1.17813i
\(249\) 0 0
\(250\) −1084.50 1878.41i −0.274359 0.475204i
\(251\) 5265.00 1.32400 0.662000 0.749504i \(-0.269708\pi\)
0.662000 + 0.749504i \(0.269708\pi\)
\(252\) 0 0
\(253\) 1260.00 0.313105
\(254\) −565.500 979.475i −0.139695 0.241959i
\(255\) 0 0
\(256\) −756.500 + 1310.30i −0.184692 + 0.319897i
\(257\) 3435.00 + 5949.59i 0.833733 + 1.44407i 0.895058 + 0.445950i \(0.147134\pi\)
−0.0613246 + 0.998118i \(0.519532\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −192.000 −0.0457974
\(261\) 0 0
\(262\) 976.500 1691.35i 0.230261 0.398824i
\(263\) −111.000 + 192.258i −0.0260249 + 0.0450765i −0.878745 0.477292i \(-0.841618\pi\)
0.852720 + 0.522369i \(0.174952\pi\)
\(264\) 0 0
\(265\) 1089.00 0.252441
\(266\) 0 0
\(267\) 0 0
\(268\) 185.000 + 320.429i 0.0421667 + 0.0730349i
\(269\) −3925.50 + 6799.17i −0.889747 + 1.54109i −0.0495729 + 0.998771i \(0.515786\pi\)
−0.840174 + 0.542317i \(0.817547\pi\)
\(270\) 0 0
\(271\) 2591.50 + 4488.61i 0.580895 + 1.00614i 0.995374 + 0.0960800i \(0.0306305\pi\)
−0.414479 + 0.910059i \(0.636036\pi\)
\(272\) −5964.00 −1.32949
\(273\) 0 0
\(274\) 5310.00 1.17076
\(275\) 870.000 + 1506.88i 0.190774 + 0.330431i
\(276\) 0 0
\(277\) 2480.00 4295.49i 0.537938 0.931736i −0.461077 0.887360i \(-0.652537\pi\)
0.999015 0.0443755i \(-0.0141298\pi\)
\(278\) −2337.00 4047.80i −0.504187 0.873277i
\(279\) 0 0
\(280\) 0 0
\(281\) 774.000 0.164317 0.0821583 0.996619i \(-0.473819\pi\)
0.0821583 + 0.996619i \(0.473819\pi\)
\(282\) 0 0
\(283\) 1849.00 3202.56i 0.388380 0.672695i −0.603852 0.797097i \(-0.706368\pi\)
0.992232 + 0.124402i \(0.0397013\pi\)
\(284\) −171.000 + 296.181i −0.0357288 + 0.0618841i
\(285\) 0 0
\(286\) 2880.00 0.595447
\(287\) 0 0
\(288\) 0 0
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) 1336.50 2314.89i 0.270628 0.468741i
\(291\) 0 0
\(292\) 181.000 + 313.501i 0.0362747 + 0.0628297i
\(293\) −6273.00 −1.25076 −0.625380 0.780321i \(-0.715056\pi\)
−0.625380 + 0.780321i \(0.715056\pi\)
\(294\) 0 0
\(295\) 45.0000 0.00888136
\(296\) −3318.00 5746.94i −0.651537 1.12849i
\(297\) 0 0
\(298\) 3681.00 6375.68i 0.715552 1.23937i
\(299\) −2688.00 4655.75i −0.519903 0.900499i
\(300\) 0 0
\(301\) 0 0
\(302\) 3777.00 0.719675
\(303\) 0 0
\(304\) 568.000 983.805i 0.107161 0.185609i
\(305\) 177.000 306.573i 0.0332295 0.0575551i
\(306\) 0 0
\(307\) 1684.00 0.313065 0.156533 0.987673i \(-0.449968\pi\)
0.156533 + 0.987673i \(0.449968\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1138.50 + 1971.94i 0.208589 + 0.361286i
\(311\) 660.000 1143.15i 0.120338 0.208432i −0.799563 0.600582i \(-0.794935\pi\)
0.919901 + 0.392151i \(0.128269\pi\)
\(312\) 0 0
\(313\) −4251.50 7363.81i −0.767760 1.32980i −0.938775 0.344531i \(-0.888038\pi\)
0.171014 0.985269i \(-0.445296\pi\)
\(314\) 588.000 0.105678
\(315\) 0 0
\(316\) 467.000 0.0831355
\(317\) −1288.50 2231.75i −0.228295 0.395418i 0.729008 0.684505i \(-0.239982\pi\)
−0.957303 + 0.289087i \(0.906648\pi\)
\(318\) 0 0
\(319\) −2227.50 + 3858.14i −0.390959 + 0.677162i
\(320\) 649.500 + 1124.97i 0.113463 + 0.196524i
\(321\) 0 0
\(322\) 0 0
\(323\) 1344.00 0.231524
\(324\) 0 0
\(325\) 3712.00 6429.37i 0.633553 1.09735i
\(326\) 1878.00 3252.79i 0.319058 0.552624i
\(327\) 0 0
\(328\) −7560.00 −1.27266
\(329\) 0 0
\(330\) 0 0
\(331\) 242.000 + 419.156i 0.0401859 + 0.0696040i 0.885419 0.464794i \(-0.153872\pi\)
−0.845233 + 0.534398i \(0.820538\pi\)
\(332\) −238.500 + 413.094i −0.0394259 + 0.0682876i
\(333\) 0 0
\(334\) 3969.00 + 6874.51i 0.650222 + 1.12622i
\(335\) 1110.00 0.181032
\(336\) 0 0
\(337\) −8359.00 −1.35117 −0.675584 0.737283i \(-0.736109\pi\)
−0.675584 + 0.737283i \(0.736109\pi\)
\(338\) −2848.50 4933.75i −0.458396 0.793966i
\(339\) 0 0
\(340\) 126.000 218.238i 0.0200980 0.0348107i
\(341\) −1897.50 3286.57i −0.301335 0.521928i
\(342\) 0 0
\(343\) 0 0
\(344\) −546.000 −0.0855766
\(345\) 0 0
\(346\) 1179.00 2042.09i 0.183189 0.317293i
\(347\) −930.000 + 1610.81i −0.143876 + 0.249201i −0.928953 0.370197i \(-0.879290\pi\)
0.785077 + 0.619398i \(0.212623\pi\)
\(348\) 0 0
\(349\) 1918.00 0.294178 0.147089 0.989123i \(-0.453010\pi\)
0.147089 + 0.989123i \(0.453010\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 337.500 + 584.567i 0.0511046 + 0.0885157i
\(353\) 1524.00 2639.65i 0.229786 0.398000i −0.727959 0.685621i \(-0.759531\pi\)
0.957744 + 0.287620i \(0.0928642\pi\)
\(354\) 0 0
\(355\) 513.000 + 888.542i 0.0766964 + 0.132842i
\(356\) 906.000 0.134882
\(357\) 0 0
\(358\) −8676.00 −1.28084
\(359\) −15.0000 25.9808i −0.00220521 0.00381953i 0.864921 0.501909i \(-0.167369\pi\)
−0.867126 + 0.498089i \(0.834035\pi\)
\(360\) 0 0
\(361\) 3301.50 5718.37i 0.481338 0.833703i
\(362\) 2028.00 + 3512.60i 0.294446 + 0.509995i
\(363\) 0 0
\(364\) 0 0
\(365\) 1086.00 0.155737
\(366\) 0 0
\(367\) −5655.50 + 9795.61i −0.804400 + 1.39326i 0.112296 + 0.993675i \(0.464180\pi\)
−0.916696 + 0.399586i \(0.869154\pi\)
\(368\) 2982.00 5164.98i 0.422412 0.731638i
\(369\) 0 0
\(370\) 2844.00 0.399601
\(371\) 0 0
\(372\) 0 0
\(373\) −604.000 1046.16i −0.0838443 0.145223i 0.821054 0.570851i \(-0.193387\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(374\) −1890.00 + 3273.58i −0.261309 + 0.452600i
\(375\) 0 0
\(376\) −315.000 545.596i −0.0432045 0.0748324i
\(377\) 19008.0 2.59672
\(378\) 0 0
\(379\) 7640.00 1.03546 0.517731 0.855543i \(-0.326777\pi\)
0.517731 + 0.855543i \(0.326777\pi\)
\(380\) 24.0000 + 41.5692i 0.00323993 + 0.00561173i
\(381\) 0 0
\(382\) 5868.00 10163.7i 0.785950 1.36131i
\(383\) −6375.00 11041.8i −0.850515 1.47314i −0.880744 0.473592i \(-0.842957\pi\)
0.0302291 0.999543i \(-0.490376\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4479.00 0.590609
\(387\) 0 0
\(388\) 251.500 435.611i 0.0329072 0.0569969i
\(389\) 1563.00 2707.20i 0.203720 0.352854i −0.746004 0.665942i \(-0.768030\pi\)
0.949724 + 0.313087i \(0.101363\pi\)
\(390\) 0 0
\(391\) 7056.00 0.912627
\(392\) 0 0
\(393\) 0 0
\(394\) −6129.00 10615.7i −0.783692 1.35739i
\(395\) 700.500 1213.30i 0.0892303 0.154551i
\(396\) 0 0
\(397\) −2966.00 5137.26i −0.374960 0.649450i 0.615361 0.788246i \(-0.289010\pi\)
−0.990321 + 0.138795i \(0.955677\pi\)
\(398\) 10668.0 1.34356
\(399\) 0 0
\(400\) 8236.00 1.02950
\(401\) 804.000 + 1392.57i 0.100124 + 0.173420i 0.911736 0.410777i \(-0.134743\pi\)
−0.811611 + 0.584198i \(0.801409\pi\)
\(402\) 0 0
\(403\) −8096.00 + 14022.7i −1.00072 + 1.73330i
\(404\) 543.000 + 940.504i 0.0668695 + 0.115821i
\(405\) 0 0
\(406\) 0 0
\(407\) −4740.00 −0.577280
\(408\) 0 0
\(409\) −2232.50 + 3866.80i −0.269902 + 0.467484i −0.968836 0.247702i \(-0.920325\pi\)
0.698934 + 0.715186i \(0.253658\pi\)
\(410\) 1620.00 2805.92i 0.195137 0.337987i
\(411\) 0 0
\(412\) −1736.00 −0.207589
\(413\) 0 0
\(414\) 0 0
\(415\) 715.500 + 1239.28i 0.0846326 + 0.146588i
\(416\) 1440.00 2494.15i 0.169716 0.293957i
\(417\) 0 0
\(418\) −360.000 623.538i −0.0421248 0.0729623i
\(419\) −1584.00 −0.184686 −0.0923430 0.995727i \(-0.529436\pi\)
−0.0923430 + 0.995727i \(0.529436\pi\)
\(420\) 0 0
\(421\) −1330.00 −0.153967 −0.0769837 0.997032i \(-0.524529\pi\)
−0.0769837 + 0.997032i \(0.524529\pi\)
\(422\) −1875.00 3247.60i −0.216288 0.374622i
\(423\) 0 0
\(424\) −3811.50 + 6601.71i −0.436563 + 0.756150i
\(425\) 4872.00 + 8438.55i 0.556063 + 0.963129i
\(426\) 0 0
\(427\) 0 0
\(428\) 1353.00 0.152803
\(429\) 0 0
\(430\) 117.000 202.650i 0.0131215 0.0227271i
\(431\) 4794.00 8303.45i 0.535775 0.927989i −0.463351 0.886175i \(-0.653353\pi\)
0.999125 0.0418139i \(-0.0133137\pi\)
\(432\) 0 0
\(433\) −494.000 −0.0548271 −0.0274135 0.999624i \(-0.508727\pi\)
−0.0274135 + 0.999624i \(0.508727\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 185.000 + 320.429i 0.0203209 + 0.0351968i
\(437\) −672.000 + 1163.94i −0.0735609 + 0.127411i
\(438\) 0 0
\(439\) −8004.50 13864.2i −0.870237 1.50729i −0.861752 0.507330i \(-0.830632\pi\)
−0.00848508 0.999964i \(-0.502701\pi\)
\(440\) 945.000 0.102389
\(441\) 0 0
\(442\) 16128.0 1.73559
\(443\) 3886.50 + 6731.62i 0.416824 + 0.721961i 0.995618 0.0935130i \(-0.0298097\pi\)
−0.578794 + 0.815474i \(0.696476\pi\)
\(444\) 0 0
\(445\) 1359.00 2353.86i 0.144770 0.250749i
\(446\) 637.500 + 1104.18i 0.0676827 + 0.117230i
\(447\) 0 0
\(448\) 0 0
\(449\) −864.000 −0.0908122 −0.0454061 0.998969i \(-0.514458\pi\)
−0.0454061 + 0.998969i \(0.514458\pi\)
\(450\) 0 0
\(451\) −2700.00 + 4676.54i −0.281903 + 0.488269i
\(452\) −324.000 + 561.184i −0.0337161 + 0.0583980i
\(453\) 0 0
\(454\) 11565.0 1.19553
\(455\) 0 0
\(456\) 0 0
\(457\) −1259.50 2181.52i −0.128921 0.223298i 0.794338 0.607476i \(-0.207818\pi\)
−0.923259 + 0.384179i \(0.874485\pi\)
\(458\) −3282.00 + 5684.59i −0.334842 + 0.579964i
\(459\) 0 0
\(460\) 126.000 + 218.238i 0.0127713 + 0.0221205i
\(461\) −342.000 −0.0345521 −0.0172761 0.999851i \(-0.505499\pi\)
−0.0172761 + 0.999851i \(0.505499\pi\)
\(462\) 0 0
\(463\) −4336.00 −0.435229 −0.217614 0.976035i \(-0.569828\pi\)
−0.217614 + 0.976035i \(0.569828\pi\)
\(464\) 10543.5 + 18261.9i 1.05489 + 1.82713i
\(465\) 0 0
\(466\) 1278.00 2213.56i 0.127043 0.220046i
\(467\) −9318.00 16139.2i −0.923310 1.59922i −0.794257 0.607581i \(-0.792140\pi\)
−0.129052 0.991638i \(-0.541194\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 270.000 0.0264982
\(471\) 0 0
\(472\) −157.500 + 272.798i −0.0153592 + 0.0266029i
\(473\) −195.000 + 337.750i −0.0189558 + 0.0328325i
\(474\) 0 0
\(475\) −1856.00 −0.179282
\(476\) 0 0
\(477\) 0 0
\(478\) 8262.00 + 14310.2i 0.790575 + 1.36932i
\(479\) −7539.00 + 13057.9i −0.719135 + 1.24558i 0.242208 + 0.970224i \(0.422128\pi\)
−0.961343 + 0.275354i \(0.911205\pi\)
\(480\) 0 0
\(481\) 10112.0 + 17514.5i 0.958560 + 1.66028i
\(482\) −2373.00 −0.224247
\(483\) 0 0
\(484\) −1106.00 −0.103869
\(485\) −754.500 1306.83i −0.0706393 0.122351i
\(486\) 0 0
\(487\) −3110.50 + 5387.54i −0.289425 + 0.501300i −0.973673 0.227950i \(-0.926798\pi\)
0.684247 + 0.729250i \(0.260131\pi\)
\(488\) 1239.00 + 2146.01i 0.114932 + 0.199068i
\(489\) 0 0
\(490\) 0 0
\(491\) 7371.00 0.677492 0.338746 0.940878i \(-0.389997\pi\)
0.338746 + 0.940878i \(0.389997\pi\)
\(492\) 0 0
\(493\) −12474.0 + 21605.6i −1.13956 + 1.97377i
\(494\) −1536.00 + 2660.43i −0.139895 + 0.242304i
\(495\) 0 0
\(496\) −17963.0 −1.62613
\(497\) 0 0
\(498\) 0 0
\(499\) −2137.00 3701.39i −0.191714 0.332058i 0.754104 0.656755i \(-0.228071\pi\)
−0.945818 + 0.324696i \(0.894738\pi\)
\(500\) −361.500 + 626.136i −0.0323335 + 0.0560033i
\(501\) 0 0
\(502\) −7897.50 13678.9i −0.702157 1.21617i
\(503\) −2520.00 −0.223382 −0.111691 0.993743i \(-0.535627\pi\)
−0.111691 + 0.993743i \(0.535627\pi\)
\(504\) 0 0
\(505\) 3258.00 0.287087
\(506\) −1890.00 3273.58i −0.166049 0.287605i
\(507\) 0 0
\(508\) −188.500 + 326.492i −0.0164633 + 0.0285152i
\(509\) 7138.50 + 12364.2i 0.621628 + 1.07669i 0.989183 + 0.146689i \(0.0468616\pi\)
−0.367555 + 0.930002i \(0.619805\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −8733.00 −0.753804
\(513\) 0 0
\(514\) 10305.0 17848.8i 0.884308 1.53167i
\(515\) −2604.00 + 4510.26i −0.222808 + 0.385914i
\(516\) 0 0
\(517\) −450.000 −0.0382804
\(518\) 0 0
\(519\) 0 0
\(520\) −2016.00 3491.81i −0.170014 0.294473i
\(521\) 3153.00 5461.16i 0.265135 0.459228i −0.702464 0.711719i \(-0.747917\pi\)
0.967599 + 0.252492i \(0.0812501\pi\)
\(522\) 0 0
\(523\) 4036.00 + 6990.56i 0.337442 + 0.584466i 0.983951 0.178440i \(-0.0571051\pi\)
−0.646509 + 0.762906i \(0.723772\pi\)
\(524\) −651.000 −0.0542730
\(525\) 0 0
\(526\) 666.000 0.0552072
\(527\) −10626.0 18404.8i −0.878322 1.52130i
\(528\) 0 0
\(529\) 2555.50 4426.26i 0.210035 0.363792i
\(530\) −1633.50 2829.30i −0.133877 0.231881i
\(531\) 0 0
\(532\) 0 0
\(533\) 23040.0 1.87237
\(534\) 0 0
\(535\) 2029.50 3515.20i 0.164005 0.284066i
\(536\) −3885.00 + 6729.02i −0.313072 + 0.542256i
\(537\) 0 0
\(538\) 23553.0 1.88744
\(539\) 0 0
\(540\) 0 0
\(541\) 11429.0 + 19795.6i 0.908264 + 1.57316i 0.816474 + 0.577382i \(0.195926\pi\)
0.0917903 + 0.995778i \(0.470741\pi\)
\(542\) 7774.50 13465.8i 0.616132 1.06717i
\(543\) 0 0
\(544\) 1890.00 + 3273.58i 0.148958 + 0.258003i
\(545\) 1110.00 0.0872425
\(546\) 0 0
\(547\) −24724.0 −1.93258 −0.966291 0.257454i \(-0.917116\pi\)
−0.966291 + 0.257454i \(0.917116\pi\)
\(548\) −885.000 1532.86i −0.0689878 0.119490i
\(549\) 0 0
\(550\) 2610.00 4520.65i 0.202347 0.350475i
\(551\) −2376.00 4115.35i −0.183704 0.318185i
\(552\) 0 0
\(553\) 0 0
\(554\) −14880.0 −1.14114
\(555\) 0 0
\(556\) −779.000 + 1349.27i −0.0594190 + 0.102917i
\(557\) −4921.50 + 8524.29i −0.374382 + 0.648448i −0.990234 0.139413i \(-0.955478\pi\)
0.615853 + 0.787861i \(0.288812\pi\)
\(558\) 0 0
\(559\) 1664.00 0.125903
\(560\) 0 0
\(561\) 0 0
\(562\) −1161.00 2010.91i −0.0871420 0.150934i
\(563\) 6685.50 11579.6i 0.500462 0.866826i −0.499538 0.866292i \(-0.666497\pi\)
1.00000 0.000533812i \(-0.000169918\pi\)
\(564\) 0 0
\(565\) 972.000 + 1683.55i 0.0723758 + 0.125359i
\(566\) −11094.0 −0.823879
\(567\) 0 0
\(568\) −7182.00 −0.530546
\(569\) −2616.00 4531.04i −0.192739 0.333834i 0.753418 0.657542i \(-0.228404\pi\)
−0.946157 + 0.323708i \(0.895070\pi\)
\(570\) 0 0
\(571\) 7199.00 12469.0i 0.527616 0.913858i −0.471866 0.881670i \(-0.656419\pi\)
0.999482 0.0321874i \(-0.0102474\pi\)
\(572\) −480.000 831.384i −0.0350871 0.0607726i
\(573\) 0 0
\(574\) 0 0
\(575\) −9744.00 −0.706701
\(576\) 0 0
\(577\) 9935.50 17208.8i 0.716846 1.24161i −0.245397 0.969423i \(-0.578918\pi\)
0.962243 0.272191i \(-0.0877484\pi\)
\(578\) −3214.50 + 5567.68i −0.231325 + 0.400666i
\(579\) 0 0
\(580\) −891.000 −0.0637875
\(581\) 0 0
\(582\) 0 0
\(583\) 2722.50 + 4715.51i 0.193404 + 0.334985i
\(584\) −3801.00 + 6583.53i −0.269326 + 0.466487i
\(585\) 0 0
\(586\) 9409.50 + 16297.7i 0.663315 + 1.14890i
\(587\) −16137.0 −1.13466 −0.567330 0.823491i \(-0.692024\pi\)
−0.567330 + 0.823491i \(0.692024\pi\)
\(588\) 0 0
\(589\) 4048.00 0.283183
\(590\) −67.5000 116.913i −0.00471005 0.00815805i
\(591\) 0 0
\(592\) −11218.0 + 19430.1i −0.778812 + 1.34894i
\(593\) 10662.0 + 18467.1i 0.738340 + 1.27884i 0.953242 + 0.302207i \(0.0977235\pi\)
−0.214902 + 0.976636i \(0.568943\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2454.00 −0.168657
\(597\) 0 0
\(598\) −8064.00 + 13967.3i −0.551441 + 0.955123i
\(599\) −4323.00 + 7487.66i −0.294880 + 0.510747i −0.974957 0.222394i \(-0.928613\pi\)
0.680077 + 0.733141i \(0.261946\pi\)
\(600\) 0 0
\(601\) −11195.0 −0.759823 −0.379911 0.925023i \(-0.624046\pi\)
−0.379911 + 0.925023i \(0.624046\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −629.500 1090.33i −0.0424073 0.0734515i
\(605\) −1659.00 + 2873.47i −0.111484 + 0.193096i
\(606\) 0 0
\(607\) −4485.50 7769.11i −0.299935 0.519503i 0.676185 0.736731i \(-0.263632\pi\)
−0.976121 + 0.217228i \(0.930298\pi\)
\(608\) −720.000 −0.0480261
\(609\) 0 0
\(610\) −1062.00 −0.0704904
\(611\) 960.000 + 1662.77i 0.0635637 + 0.110096i
\(612\) 0 0
\(613\) 6386.00 11060.9i 0.420764 0.728784i −0.575251 0.817977i \(-0.695096\pi\)
0.996014 + 0.0891932i \(0.0284288\pi\)
\(614\) −2526.00 4375.16i −0.166028 0.287569i
\(615\) 0 0
\(616\) 0 0
\(617\) −12762.0 −0.832705 −0.416352 0.909203i \(-0.636692\pi\)
−0.416352 + 0.909203i \(0.636692\pi\)
\(618\) 0 0
\(619\) 6421.00 11121.5i 0.416933 0.722150i −0.578696 0.815543i \(-0.696438\pi\)
0.995629 + 0.0933936i \(0.0297715\pi\)
\(620\) 379.500 657.313i 0.0245824 0.0425780i
\(621\) 0 0
\(622\) −3960.00 −0.255276
\(623\) 0 0
\(624\) 0 0
\(625\) −6165.50 10679.0i −0.394592 0.683453i
\(626\) −12754.5 + 22091.4i −0.814333 + 1.41047i
\(627\) 0 0
\(628\) −98.0000 169.741i −0.00622711 0.0107857i
\(629\) −26544.0 −1.68264
\(630\) 0 0
\(631\) 21365.0 1.34790 0.673952 0.738775i \(-0.264596\pi\)
0.673952 + 0.738775i \(0.264596\pi\)
\(632\) 4903.50 + 8493.11i 0.308625 + 0.534554i
\(633\) 0 0
\(634\) −3865.50 + 6695.24i −0.242143 + 0.419404i
\(635\) 565.500 + 979.475i 0.0353404 + 0.0612114i
\(636\) 0 0
\(637\) 0 0
\(638\) 13365.0 0.829350
\(639\) 0 0
\(640\) 2488.50 4310.21i 0.153698 0.266212i
\(641\) 4137.00 7165.49i 0.254917 0.441529i −0.709956 0.704246i \(-0.751285\pi\)
0.964873 + 0.262717i \(0.0846186\pi\)
\(642\) 0 0
\(643\) −27998.0 −1.71716 −0.858580 0.512680i \(-0.828653\pi\)
−0.858580 + 0.512680i \(0.828653\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2016.00 3491.81i −0.122784 0.212668i
\(647\) 8733.00 15126.0i 0.530649 0.919110i −0.468712 0.883351i \(-0.655282\pi\)
0.999360 0.0357592i \(-0.0113849\pi\)
\(648\) 0 0
\(649\) 112.500 + 194.856i 0.00680433 + 0.0117854i
\(650\) −22272.0 −1.34397
\(651\) 0 0
\(652\) −1252.00 −0.0752026
\(653\) 1078.50 + 1868.02i 0.0646324 + 0.111947i 0.896531 0.442981i \(-0.146079\pi\)
−0.831898 + 0.554928i \(0.812746\pi\)
\(654\) 0 0
\(655\) −976.500 + 1691.35i −0.0582519 + 0.100895i
\(656\) 12780.0 + 22135.6i 0.760633 + 1.31745i
\(657\) 0 0
\(658\) 0 0
\(659\) −19944.0 −1.17892 −0.589460 0.807798i \(-0.700659\pi\)
−0.589460 + 0.807798i \(0.700659\pi\)
\(660\) 0 0
\(661\) 13753.0 23820.9i 0.809273 1.40170i −0.104095 0.994567i \(-0.533194\pi\)
0.913368 0.407135i \(-0.133472\pi\)
\(662\) 726.000 1257.47i 0.0426236 0.0738262i
\(663\) 0 0
\(664\) −10017.0 −0.585444
\(665\) 0 0
\(666\) 0 0
\(667\) −12474.0 21605.6i −0.724131 1.25423i
\(668\) 1323.00 2291.50i 0.0766294 0.132726i
\(669\) 0 0
\(670\) −1665.00 2883.86i −0.0960068 0.166289i
\(671\) 1770.00 0.101833
\(672\) 0 0
\(673\) −19123.0 −1.09530 −0.547650 0.836707i \(-0.684478\pi\)
−0.547650 + 0.836707i \(0.684478\pi\)
\(674\) 12538.5 + 21717.3i 0.716565 + 1.24113i
\(675\) 0 0
\(676\) −949.500 + 1644.58i −0.0540225 + 0.0935698i
\(677\) −6928.50 12000.5i −0.393329 0.681266i 0.599557 0.800332i \(-0.295343\pi\)
−0.992886 + 0.119066i \(0.962010\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 5292.00 0.298440
\(681\) 0 0
\(682\) −5692.50 + 9859.70i −0.319615 + 0.553589i
\(683\) −11122.5 + 19264.7i −0.623120 + 1.07927i 0.365782 + 0.930701i \(0.380802\pi\)
−0.988901 + 0.148574i \(0.952532\pi\)
\(684\) 0 0
\(685\) −5310.00 −0.296182
\(686\) 0 0
\(687\) 0 0
\(688\) 923.000 + 1598.68i 0.0511469 + 0.0885890i
\(689\) 11616.0 20119.5i 0.642285 1.11247i
\(690\) 0 0
\(691\) −320.000 554.256i −0.0176170 0.0305136i 0.857082 0.515179i \(-0.172275\pi\)
−0.874700 + 0.484666i \(0.838941\pi\)
\(692\) −786.000 −0.0431781
\(693\) 0 0
\(694\) 5580.00 0.305207
\(695\) 2337.00 + 4047.80i 0.127550 + 0.220924i
\(696\) 0 0
\(697\) −15120.0 + 26188.6i −0.821680 + 1.42319i
\(698\) −2877.00 4983.11i −0.156012 0.270220i
\(699\) 0 0
\(700\) 0 0
\(701\) 15561.0 0.838418 0.419209 0.907890i \(-0.362307\pi\)
0.419209 + 0.907890i \(0.362307\pi\)
\(702\) 0 0
\(703\) 2528.00 4378.62i 0.135626 0.234912i
\(704\) −3247.50 + 5624.83i −0.173856 + 0.301128i
\(705\) 0 0
\(706\) −9144.00 −0.487449
\(707\) 0 0
\(708\) 0 0
\(709\) −2767.00 4792.58i −0.146568 0.253864i 0.783389 0.621532i \(-0.213489\pi\)
−0.929957 + 0.367668i \(0.880156\pi\)
\(710\) 1539.00 2665.63i 0.0813488 0.140900i
\(711\) 0 0
\(712\) 9513.00 + 16477.0i 0.500723 + 0.867278i
\(713\) 21252.0 1.11626
\(714\) 0 0
\(715\) −2880.00 −0.150638
\(716\) 1446.00 + 2504.55i 0.0754742 + 0.130725i
\(717\) 0 0
\(718\) −45.0000 + 77.9423i −0.00233898 + 0.00405123i
\(719\) 10923.0 + 18919.2i 0.566564 + 0.981317i 0.996902 + 0.0786494i \(0.0250607\pi\)
−0.430339 + 0.902667i \(0.641606\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −19809.0 −1.02107
\(723\) 0 0
\(724\) 676.000 1170.87i 0.0347007 0.0601035i
\(725\) 17226.0 29836.3i 0.882424 1.52840i
\(726\) 0 0
\(727\) 11089.0 0.565706 0.282853 0.959163i \(-0.408719\pi\)
0.282853 + 0.959163i \(0.408719\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −1629.00 2821.51i −0.0825918 0.143053i
\(731\) −1092.00 + 1891.40i −0.0552518 + 0.0956990i
\(732\) 0 0
\(733\) 5881.00 + 10186.2i 0.296343 + 0.513282i 0.975296 0.220900i \(-0.0708994\pi\)
−0.678953 + 0.734182i \(0.737566\pi\)
\(734\) 33933.0 1.70639
\(735\) 0 0
\(736\) −3780.00 −0.189311
\(737\) 2775.00 + 4806.44i 0.138695 + 0.240227i
\(738\) 0 0
\(739\) 11363.0 19681.3i 0.565622 0.979686i −0.431369 0.902175i \(-0.641969\pi\)
0.996992 0.0775108i \(-0.0246972\pi\)
\(740\) −474.000 820.992i −0.0235467 0.0407841i
\(741\) 0 0
\(742\) 0 0
\(743\) −6678.00 −0.329734 −0.164867 0.986316i \(-0.552719\pi\)
−0.164867 + 0.986316i \(0.552719\pi\)
\(744\) 0 0
\(745\) −3681.00 + 6375.68i −0.181022 + 0.313539i
\(746\) −1812.00 + 3138.48i −0.0889303 + 0.154032i
\(747\) 0 0
\(748\) 1260.00 0.0615911
\(749\) 0 0
\(750\) 0 0
\(751\) 9993.50 + 17309.2i 0.485577 + 0.841043i 0.999863 0.0165754i \(-0.00527637\pi\)
−0.514286 + 0.857619i \(0.671943\pi\)
\(752\) −1065.00 + 1844.63i −0.0516444 + 0.0894506i
\(753\) 0 0
\(754\) −28512.0 49384.2i −1.37712 2.38524i
\(755\) −3777.00 −0.182065
\(756\) 0 0
\(757\) 314.000 0.0150760 0.00753799 0.999972i \(-0.497601\pi\)
0.00753799 + 0.999972i \(0.497601\pi\)
\(758\) −11460.0 19849.3i −0.549137 0.951133i
\(759\) 0 0
\(760\) −504.000 + 872.954i −0.0240553 + 0.0416649i
\(761\) 5748.00 + 9955.83i 0.273804 + 0.474242i 0.969833 0.243772i \(-0.0783847\pi\)
−0.696029 + 0.718014i \(0.745051\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3912.00 −0.185250
\(765\) 0 0
\(766\) −19125.0 + 33125.5i −0.902107 + 1.56250i
\(767\) 480.000 831.384i 0.0225969 0.0391389i
\(768\) 0 0
\(769\) −2765.00 −0.129660 −0.0648299 0.997896i \(-0.520650\pi\)
−0.0648299 + 0.997896i \(0.520650\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −746.500 1292.98i −0.0348020 0.0602788i
\(773\) 7023.00 12164.2i 0.326778 0.565997i −0.655092 0.755549i \(-0.727370\pi\)
0.981871 + 0.189552i \(0.0607036\pi\)
\(774\) 0 0
\(775\) 14674.0 + 25416.1i 0.680136 + 1.17803i
\(776\) 10563.0 0.488646
\(777\) 0 0
\(778\) −9378.00 −0.432156
\(779\) −2880.00 4988.31i −0.132460 0.229428i
\(780\) 0 0
\(781\) −2565.00 + 4442.71i −0.117520 + 0.203550i
\(782\) −10584.0 18332.0i −0.483994 0.838302i
\(783\) 0 0
\(784\) 0 0
\(785\) −588.000 −0.0267345
\(786\) 0 0
\(787\) −9257.00 + 16033.6i −0.419284 + 0.726221i −0.995868 0.0908171i \(-0.971052\pi\)
0.576584 + 0.817038i \(0.304385\pi\)
\(788\) −2043.00 + 3538.58i −0.0923590 + 0.159970i
\(789\) 0 0
\(790\) −4203.00 −0.189286
\(791\)