Properties

Label 336.4.q.e.193.1
Level $336$
Weight $4$
Character 336.193
Analytic conductor $19.825$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.e.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(1.50000 + 2.59808i) q^{5} +(3.50000 + 18.1865i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(1.50000 + 2.59808i) q^{5} +(3.50000 + 18.1865i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-7.50000 + 12.9904i) q^{11} -64.0000 q^{13} +9.00000 q^{15} +(-42.0000 + 72.7461i) q^{17} +(-8.00000 - 13.8564i) q^{19} +(52.5000 + 18.1865i) q^{21} +(-42.0000 - 72.7461i) q^{23} +(58.0000 - 100.459i) q^{25} -27.0000 q^{27} -297.000 q^{29} +(-126.500 + 219.104i) q^{31} +(22.5000 + 38.9711i) q^{33} +(-42.0000 + 36.3731i) q^{35} +(158.000 + 273.664i) q^{37} +(-96.0000 + 166.277i) q^{39} +360.000 q^{41} -26.0000 q^{43} +(13.5000 - 23.3827i) q^{45} +(-15.0000 - 25.9808i) q^{47} +(-318.500 + 127.306i) q^{49} +(126.000 + 218.238i) q^{51} +(-181.500 + 314.367i) q^{53} -45.0000 q^{55} -48.0000 q^{57} +(-7.50000 + 12.9904i) q^{59} +(59.0000 + 102.191i) q^{61} +(126.000 - 109.119i) q^{63} +(-96.0000 - 166.277i) q^{65} +(-185.000 + 320.429i) q^{67} -252.000 q^{69} +342.000 q^{71} +(-181.000 + 313.501i) q^{73} +(-174.000 - 301.377i) q^{75} +(-262.500 - 90.9327i) q^{77} +(233.500 + 404.434i) q^{79} +(-40.5000 + 70.1481i) q^{81} -477.000 q^{83} -252.000 q^{85} +(-445.500 + 771.629i) q^{87} +(-453.000 - 784.619i) q^{89} +(-224.000 - 1163.94i) q^{91} +(379.500 + 657.313i) q^{93} +(24.0000 - 41.5692i) q^{95} +503.000 q^{97} +135.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + 3q^{5} + 7q^{7} - 9q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + 3q^{5} + 7q^{7} - 9q^{9} - 15q^{11} - 128q^{13} + 18q^{15} - 84q^{17} - 16q^{19} + 105q^{21} - 84q^{23} + 116q^{25} - 54q^{27} - 594q^{29} - 253q^{31} + 45q^{33} - 84q^{35} + 316q^{37} - 192q^{39} + 720q^{41} - 52q^{43} + 27q^{45} - 30q^{47} - 637q^{49} + 252q^{51} - 363q^{53} - 90q^{55} - 96q^{57} - 15q^{59} + 118q^{61} + 252q^{63} - 192q^{65} - 370q^{67} - 504q^{69} + 684q^{71} - 362q^{73} - 348q^{75} - 525q^{77} + 467q^{79} - 81q^{81} - 954q^{83} - 504q^{85} - 891q^{87} - 906q^{89} - 448q^{91} + 759q^{93} + 48q^{95} + 1006q^{97} + 270q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 0 0
\(5\) 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
\(7\) 3.50000 + 18.1865i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) −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 \(-0.739198\pi\)
−0.682708 + 0.730691i \(0.739198\pi\)
\(14\) 0 0
\(15\) 9.00000 0.154919
\(16\) 0 0
\(17\) −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 \(0.864129\pi\)
\(20\) 0 0
\(21\) 52.5000 + 18.1865i 0.545545 + 0.188982i
\(22\) 0 0
\(23\) −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
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −297.000 −1.90178 −0.950888 0.309535i \(-0.899827\pi\)
−0.950888 + 0.309535i \(0.899827\pi\)
\(30\) 0 0
\(31\) −126.500 + 219.104i −0.732906 + 1.26943i 0.222731 + 0.974880i \(0.428503\pi\)
−0.955636 + 0.294550i \(0.904830\pi\)
\(32\) 0 0
\(33\) 22.5000 + 38.9711i 0.118689 + 0.205576i
\(34\) 0 0
\(35\) −42.0000 + 36.3731i −0.202837 + 0.175662i
\(36\) 0 0
\(37\) 158.000 + 273.664i 0.702028 + 1.21595i 0.967753 + 0.251900i \(0.0810553\pi\)
−0.265725 + 0.964049i \(0.585611\pi\)
\(38\) 0 0
\(39\) −96.0000 + 166.277i −0.394162 + 0.682708i
\(40\) 0 0
\(41\) 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 \(-0.514681\pi\)
−0.0461042 + 0.998937i \(0.514681\pi\)
\(44\) 0 0
\(45\) 13.5000 23.3827i 0.0447214 0.0774597i
\(46\) 0 0
\(47\) −15.0000 25.9808i −0.0465527 0.0806316i 0.841810 0.539774i \(-0.181490\pi\)
−0.888363 + 0.459142i \(0.848157\pi\)
\(48\) 0 0
\(49\) −318.500 + 127.306i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) 126.000 + 218.238i 0.345952 + 0.599206i
\(52\) 0 0
\(53\) −181.500 + 314.367i −0.470395 + 0.814748i −0.999427 0.0338538i \(-0.989222\pi\)
0.529032 + 0.848602i \(0.322555\pi\)
\(54\) 0 0
\(55\) −45.0000 −0.110324
\(56\) 0 0
\(57\) −48.0000 −0.111540
\(58\) 0 0
\(59\) −7.50000 + 12.9904i −0.0165494 + 0.0286645i −0.874182 0.485599i \(-0.838601\pi\)
0.857632 + 0.514264i \(0.171935\pi\)
\(60\) 0 0
\(61\) 59.0000 + 102.191i 0.123839 + 0.214495i 0.921279 0.388903i \(-0.127146\pi\)
−0.797440 + 0.603399i \(0.793813\pi\)
\(62\) 0 0
\(63\) 126.000 109.119i 0.251976 0.218218i
\(64\) 0 0
\(65\) −96.0000 166.277i −0.183190 0.317294i
\(66\) 0 0
\(67\) −185.000 + 320.429i −0.337334 + 0.584279i −0.983930 0.178553i \(-0.942858\pi\)
0.646597 + 0.762832i \(0.276192\pi\)
\(68\) 0 0
\(69\) −252.000 −0.439670
\(70\) 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 −0.973856 0.227165i \(-0.927054\pi\)
0.683658 + 0.729802i \(0.260388\pi\)
\(74\) 0 0
\(75\) −174.000 301.377i −0.267891 0.464000i
\(76\) 0 0
\(77\) −262.500 90.9327i −0.388502 0.134581i
\(78\) 0 0
\(79\) 233.500 + 404.434i 0.332542 + 0.575979i 0.983010 0.183555i \(-0.0587604\pi\)
−0.650468 + 0.759534i \(0.725427\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −477.000 −0.630814 −0.315407 0.948957i \(-0.602141\pi\)
−0.315407 + 0.948957i \(0.602141\pi\)
\(84\) 0 0
\(85\) −252.000 −0.321568
\(86\) 0 0
\(87\) −445.500 + 771.629i −0.548996 + 0.950888i
\(88\) 0 0
\(89\) −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
\(91\) −224.000 1163.94i −0.258039 1.34081i
\(92\) 0 0
\(93\) 379.500 + 657.313i 0.423143 + 0.732906i
\(94\) 0 0
\(95\) 24.0000 41.5692i 0.0259195 0.0448938i
\(96\) 0 0
\(97\) 503.000 0.526515 0.263257 0.964726i \(-0.415203\pi\)
0.263257 + 0.964726i \(0.415203\pi\)
\(98\) 0 0
\(99\) 135.000 0.137051
\(100\) 0 0
\(101\) 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 \(0.521471\pi\)
\(104\) 0 0
\(105\) 31.5000 + 163.679i 0.0292770 + 0.152128i
\(106\) 0 0
\(107\) −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 \(0.114689\pi\)
\(110\) 0 0
\(111\) 948.000 0.810632
\(112\) 0 0
\(113\) −648.000 −0.539458 −0.269729 0.962936i \(-0.586934\pi\)
−0.269729 + 0.962936i \(0.586934\pi\)
\(114\) 0 0
\(115\) 126.000 218.238i 0.102170 0.176964i
\(116\) 0 0
\(117\) 288.000 + 498.831i 0.227569 + 0.394162i
\(118\) 0 0
\(119\) −1470.00 509.223i −1.13239 0.392272i
\(120\) 0 0
\(121\) 553.000 + 957.824i 0.415477 + 0.719627i
\(122\) 0 0
\(123\) 540.000 935.307i 0.395855 0.685641i
\(124\) 0 0
\(125\) 723.000 0.517337
\(126\) 0 0
\(127\) −377.000 −0.263412 −0.131706 0.991289i \(-0.542046\pi\)
−0.131706 + 0.991289i \(0.542046\pi\)
\(128\) 0 0
\(129\) −39.0000 + 67.5500i −0.0266183 + 0.0461042i
\(130\) 0 0
\(131\) −325.500 563.783i −0.217092 0.376015i 0.736826 0.676083i \(-0.236324\pi\)
−0.953918 + 0.300068i \(0.902991\pi\)
\(132\) 0 0
\(133\) 224.000 193.990i 0.146040 0.126474i
\(134\) 0 0
\(135\) −40.5000 70.1481i −0.0258199 0.0447214i
\(136\) 0 0
\(137\) 885.000 1532.86i 0.551903 0.955923i −0.446235 0.894916i \(-0.647235\pi\)
0.998137 0.0610074i \(-0.0194313\pi\)
\(138\) 0 0
\(139\) 1558.00 0.950704 0.475352 0.879796i \(-0.342321\pi\)
0.475352 + 0.879796i \(0.342321\pi\)
\(140\) 0 0
\(141\) −90.0000 −0.0537544
\(142\) 0 0
\(143\) 480.000 831.384i 0.280697 0.486181i
\(144\) 0 0
\(145\) −445.500 771.629i −0.255150 0.441933i
\(146\) 0 0
\(147\) −147.000 + 1018.45i −0.0824786 + 0.571429i
\(148\) 0 0
\(149\) −1227.00 2125.23i −0.674629 1.16849i −0.976577 0.215168i \(-0.930970\pi\)
0.301948 0.953324i \(-0.402363\pi\)
\(150\) 0 0
\(151\) 629.500 1090.33i 0.339258 0.587612i −0.645035 0.764153i \(-0.723157\pi\)
0.984293 + 0.176540i \(0.0564906\pi\)
\(152\) 0 0
\(153\) 756.000 0.399470
\(154\) 0 0
\(155\) −759.000 −0.393318
\(156\) 0 0
\(157\) 98.0000 169.741i 0.0498169 0.0862854i −0.840042 0.542522i \(-0.817470\pi\)
0.889859 + 0.456236i \(0.150803\pi\)
\(158\) 0 0
\(159\) 544.500 + 943.102i 0.271583 + 0.470395i
\(160\) 0 0
\(161\) 1176.00 1018.45i 0.575663 0.498539i
\(162\) 0 0
\(163\) −626.000 1084.26i −0.300810 0.521019i 0.675509 0.737351i \(-0.263924\pi\)
−0.976320 + 0.216332i \(0.930590\pi\)
\(164\) 0 0
\(165\) −67.5000 + 116.913i −0.0318477 + 0.0551618i
\(166\) 0 0
\(167\) 2646.00 1.22607 0.613035 0.790056i \(-0.289949\pi\)
0.613035 + 0.790056i \(0.289949\pi\)
\(168\) 0 0
\(169\) 1899.00 0.864360
\(170\) 0 0
\(171\) −72.0000 + 124.708i −0.0321987 + 0.0557698i
\(172\) 0 0
\(173\) 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
\(175\) 2030.00 + 703.213i 0.876878 + 0.303759i
\(176\) 0 0
\(177\) 22.5000 + 38.9711i 0.00955482 + 0.0165494i
\(178\) 0 0
\(179\) 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 \(-0.410459\pi\)
0.277606 + 0.960695i \(0.410459\pi\)
\(182\) 0 0
\(183\) 354.000 0.142997
\(184\) 0 0
\(185\) −474.000 + 820.992i −0.188374 + 0.326273i
\(186\) 0 0
\(187\) −630.000 1091.19i −0.246365 0.426716i
\(188\) 0 0
\(189\) −94.5000 491.036i −0.0363696 0.188982i
\(190\) 0 0
\(191\) 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 \(0.256476\pi\)
\(194\) 0 0
\(195\) −576.000 −0.211529
\(196\) 0 0
\(197\) −4086.00 −1.47774 −0.738872 0.673846i \(-0.764641\pi\)
−0.738872 + 0.673846i \(0.764641\pi\)
\(198\) 0 0
\(199\) −1778.00 + 3079.59i −0.633362 + 1.09702i 0.353497 + 0.935436i \(0.384992\pi\)
−0.986860 + 0.161580i \(0.948341\pi\)
\(200\) 0 0
\(201\) 555.000 + 961.288i 0.194760 + 0.337334i
\(202\) 0 0
\(203\) −1039.50 5401.40i −0.359402 1.86751i
\(204\) 0 0
\(205\) 540.000 + 935.307i 0.183977 + 0.318657i
\(206\) 0 0
\(207\) −378.000 + 654.715i −0.126922 + 0.219835i
\(208\) 0 0
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) −1250.00 −0.407837 −0.203918 0.978988i \(-0.565368\pi\)
−0.203918 + 0.978988i \(0.565368\pi\)
\(212\) 0 0
\(213\) 513.000 888.542i 0.165024 0.285831i
\(214\) 0 0
\(215\) −39.0000 67.5500i −0.0123711 0.0214273i
\(216\) 0 0
\(217\) −4427.50 1533.73i −1.38506 0.479799i
\(218\) 0 0
\(219\) 543.000 + 940.504i 0.167546 + 0.290198i
\(220\) 0 0
\(221\) 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
\(225\) −1044.00 −0.309333
\(226\) 0 0
\(227\) 1927.50 3338.53i 0.563580 0.976149i −0.433600 0.901105i \(-0.642757\pi\)
0.997180 0.0750439i \(-0.0239097\pi\)
\(228\) 0 0
\(229\) 1094.00 + 1894.86i 0.315692 + 0.546795i 0.979584 0.201033i \(-0.0644299\pi\)
−0.663892 + 0.747828i \(0.731097\pi\)
\(230\) 0 0
\(231\) −630.000 + 545.596i −0.179441 + 0.155401i
\(232\) 0 0
\(233\) −426.000 737.854i −0.119778 0.207461i 0.799902 0.600131i \(-0.204885\pi\)
−0.919679 + 0.392670i \(0.871551\pi\)
\(234\) 0 0
\(235\) 45.0000 77.9423i 0.0124914 0.0216357i
\(236\) 0 0
\(237\) 1401.00 0.383986
\(238\) 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 −0.914029 0.405650i \(-0.867045\pi\)
0.808317 + 0.588747i \(0.200379\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −808.500 636.529i −0.210829 0.165985i
\(246\) 0 0
\(247\) 512.000 + 886.810i 0.131894 + 0.228447i
\(248\) 0 0
\(249\) −715.500 + 1239.28i −0.182100 + 0.315407i
\(250\) 0 0
\(251\) −5265.00 −1.32400 −0.662000 0.749504i \(-0.730292\pi\)
−0.662000 + 0.749504i \(0.730292\pi\)
\(252\) 0 0
\(253\) 1260.00 0.313105
\(254\) 0 0
\(255\) −378.000 + 654.715i −0.0928285 + 0.160784i
\(256\) 0 0
\(257\) 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
\(259\) −4424.00 + 3831.30i −1.06137 + 0.919171i
\(260\) 0 0
\(261\) 1336.50 + 2314.89i 0.316963 + 0.548996i
\(262\) 0 0
\(263\) −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
\(267\) −2718.00 −0.622992
\(268\) 0 0
\(269\) −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 \(0.636036\pi\)
\(272\) 0 0
\(273\) −3360.00 1163.94i −0.744895 0.258039i
\(274\) 0 0
\(275\) 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 \(-0.0141298\pi\)
\(278\) 0 0
\(279\) 2277.00 0.488604
\(280\) 0 0
\(281\) −774.000 −0.164317 −0.0821583 0.996619i \(-0.526181\pi\)
−0.0821583 + 0.996619i \(0.526181\pi\)
\(282\) 0 0
\(283\) 1849.00 3202.56i 0.388380 0.672695i −0.603852 0.797097i \(-0.706368\pi\)
0.992232 + 0.124402i \(0.0397013\pi\)
\(284\) 0 0
\(285\) −72.0000 124.708i −0.0149646 0.0259195i
\(286\) 0 0
\(287\) 1260.00 + 6547.15i 0.259148 + 1.34657i
\(288\) 0 0
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) 0 0
\(291\) 754.500 1306.83i 0.151992 0.263257i
\(292\) 0 0
\(293\) −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
\(296\) 0 0
\(297\) 202.500 350.740i 0.0395631 0.0685253i
\(298\) 0 0
\(299\) 2688.00 + 4655.75i 0.519903 + 0.900499i
\(300\) 0 0
\(301\) −91.0000 472.850i −0.0174258 0.0905469i
\(302\) 0 0
\(303\) −1629.00 2821.51i −0.308857 0.534956i
\(304\) 0 0
\(305\) −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
\(309\) 5208.00 0.958812
\(310\) 0 0
\(311\) −660.000 + 1143.15i −0.120338 + 0.208432i −0.919901 0.392151i \(-0.871731\pi\)
0.799563 + 0.600582i \(0.205065\pi\)
\(312\) 0 0
\(313\) 4251.50 + 7363.81i 0.767760 + 1.32980i 0.938775 + 0.344531i \(0.111962\pi\)
−0.171014 + 0.985269i \(0.554704\pi\)
\(314\) 0 0
\(315\) 472.500 + 163.679i 0.0845154 + 0.0292770i
\(316\) 0 0
\(317\) 1288.50 + 2231.75i 0.228295 + 0.395418i 0.957303 0.289087i \(-0.0933517\pi\)
−0.729008 + 0.684505i \(0.760018\pi\)
\(318\) 0 0
\(319\) 2227.50 3858.14i 0.390959 0.677162i
\(320\) 0 0
\(321\) −4059.00 −0.705767
\(322\) 0 0
\(323\) 1344.00 0.231524
\(324\) 0 0
\(325\) −3712.00 + 6429.37i −0.633553 + 1.09735i
\(326\) 0 0
\(327\) −555.000 961.288i −0.0938580 0.162567i
\(328\) 0 0
\(329\) 420.000 363.731i 0.0703810 0.0609517i
\(330\) 0 0
\(331\) −242.000 419.156i −0.0401859 0.0696040i 0.845233 0.534398i \(-0.179462\pi\)
−0.885419 + 0.464794i \(0.846128\pi\)
\(332\) 0 0
\(333\) 1422.00 2462.98i 0.234009 0.405316i
\(334\) 0 0
\(335\) −1110.00 −0.181032
\(336\) 0 0
\(337\) −8359.00 −1.35117 −0.675584 0.737283i \(-0.736109\pi\)
−0.675584 + 0.737283i \(0.736109\pi\)
\(338\) 0 0
\(339\) −972.000 + 1683.55i −0.155728 + 0.269729i
\(340\) 0 0
\(341\) −1897.50 3286.57i −0.301335 0.521928i
\(342\) 0 0
\(343\) −3430.00 5346.84i −0.539949 0.841698i
\(344\) 0 0
\(345\) −378.000 654.715i −0.0589879 0.102170i
\(346\) 0 0
\(347\) −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 \(-0.546990\pi\)
−0.147089 + 0.989123i \(0.546990\pi\)
\(350\) 0 0
\(351\) 1728.00 0.262774
\(352\) 0 0
\(353\) 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
\(356\) 0 0
\(357\) −3528.00 + 3055.34i −0.523030 + 0.452957i
\(358\) 0 0
\(359\) −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
\(362\) 0 0
\(363\) 3318.00 0.479752
\(364\) 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 \(0.869154\pi\)
\(368\) 0 0
\(369\) −1620.00 2805.92i −0.228547 0.395855i
\(370\) 0 0
\(371\) −6352.50 2200.57i −0.888963 0.307946i
\(372\) 0 0
\(373\) −604.000 1046.16i −0.0838443 0.145223i 0.821054 0.570851i \(-0.193387\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(374\) 0 0
\(375\) 1084.50 1878.41i 0.149342 0.258668i
\(376\) 0 0
\(377\) 19008.0 2.59672
\(378\) 0 0
\(379\) −7640.00 −1.03546 −0.517731 0.855543i \(-0.673223\pi\)
−0.517731 + 0.855543i \(0.673223\pi\)
\(380\) 0 0
\(381\) −565.500 + 979.475i −0.0760405 + 0.131706i
\(382\) 0 0
\(383\) 6375.00 + 11041.8i 0.850515 + 1.47314i 0.880744 + 0.473592i \(0.157043\pi\)
−0.0302291 + 0.999543i \(0.509624\pi\)
\(384\) 0 0
\(385\) −157.500 818.394i −0.0208492 0.108336i
\(386\) 0 0
\(387\) 117.000 + 202.650i 0.0153681 + 0.0266183i
\(388\) 0 0
\(389\) −1563.00 + 2707.20i −0.203720 + 0.352854i −0.949724 0.313087i \(-0.898637\pi\)
0.746004 + 0.665942i \(0.231970\pi\)
\(390\) 0 0
\(391\) 7056.00 0.912627
\(392\) 0 0
\(393\) −1953.00 −0.250676
\(394\) 0 0
\(395\) −700.500 + 1213.30i −0.0892303 + 0.154551i
\(396\) 0 0
\(397\) 2966.00 + 5137.26i 0.374960 + 0.649450i 0.990321 0.138795i \(-0.0443230\pi\)
−0.615361 + 0.788246i \(0.710990\pi\)
\(398\) 0 0
\(399\) −168.000 872.954i −0.0210790 0.109530i
\(400\) 0 0
\(401\) −804.000 1392.57i −0.100124 0.173420i 0.811611 0.584198i \(-0.198591\pi\)
−0.911736 + 0.410777i \(0.865257\pi\)
\(402\) 0 0
\(403\) 8096.00 14022.7i 1.00072 1.73330i
\(404\) 0 0
\(405\) −243.000 −0.0298142
\(406\) 0 0
\(407\) −4740.00 −0.577280
\(408\) 0 0
\(409\) 2232.50 3866.80i 0.269902 0.467484i −0.698934 0.715186i \(-0.746342\pi\)
0.968836 + 0.247702i \(0.0796753\pi\)
\(410\) 0 0
\(411\) −2655.00 4598.59i −0.318641 0.551903i
\(412\) 0 0
\(413\) −262.500 90.9327i −0.0312755 0.0108342i
\(414\) 0 0
\(415\) −715.500 1239.28i −0.0846326 0.146588i
\(416\) 0 0
\(417\) 2337.00 4047.80i 0.274445 0.475352i
\(418\) 0 0
\(419\) 1584.00 0.184686 0.0923430 0.995727i \(-0.470564\pi\)
0.0923430 + 0.995727i \(0.470564\pi\)
\(420\) 0 0
\(421\) −1330.00 −0.153967 −0.0769837 0.997032i \(-0.524529\pi\)
−0.0769837 + 0.997032i \(0.524529\pi\)
\(422\) 0 0
\(423\) −135.000 + 233.827i −0.0155176 + 0.0268772i
\(424\) 0 0
\(425\) 4872.00 + 8438.55i 0.556063 + 0.963129i
\(426\) 0 0
\(427\) −1652.00 + 1430.67i −0.187227 + 0.162143i
\(428\) 0 0
\(429\) −1440.00 2494.15i −0.162060 0.280697i
\(430\) 0 0
\(431\) 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 \(-0.491273\pi\)
0.0274135 + 0.999624i \(0.491273\pi\)
\(434\) 0 0
\(435\) −2673.00 −0.294622
\(436\) 0 0
\(437\) −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 \(-0.502701\pi\)
\(440\) 0 0
\(441\) 2425.50 + 1909.59i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 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
\(446\) 0 0
\(447\) −7362.00 −0.778995
\(448\) 0 0
\(449\) 864.000 0.0908122 0.0454061 0.998969i \(-0.485542\pi\)
0.0454061 + 0.998969i \(0.485542\pi\)
\(450\) 0 0
\(451\) −2700.00 + 4676.54i −0.281903 + 0.488269i
\(452\) 0 0
\(453\) −1888.50 3270.98i −0.195871 0.339258i
\(454\) 0 0
\(455\) 2688.00 2327.88i 0.276957 0.239852i
\(456\) 0 0
\(457\) −1259.50 2181.52i −0.128921 0.223298i 0.794338 0.607476i \(-0.207818\pi\)
−0.923259 + 0.384179i \(0.874485\pi\)
\(458\) 0 0
\(459\) 1134.00 1964.15i 0.115317 0.199735i
\(460\) 0 0
\(461\) −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 \(-0.430172\pi\)
0.217614 + 0.976035i \(0.430172\pi\)
\(464\) 0 0
\(465\) −1138.50 + 1971.94i −0.113541 + 0.196659i
\(466\) 0 0
\(467\) 9318.00 + 16139.2i 0.923310 + 1.59922i 0.794257 + 0.607581i \(0.207860\pi\)
0.129052 + 0.991638i \(0.458806\pi\)
\(468\) 0 0
\(469\) −6475.00 2243.01i −0.637500 0.220837i
\(470\) 0 0
\(471\) −294.000 509.223i −0.0287618 0.0498169i
\(472\) 0 0
\(473\) 195.000 337.750i 0.0189558 0.0328325i
\(474\) 0 0
\(475\) −1856.00 −0.179282
\(476\) 0 0
\(477\) 3267.00 0.313597
\(478\) 0 0
\(479\) 7539.00 13057.9i 0.719135 1.24558i −0.242208 0.970224i \(-0.577872\pi\)
0.961343 0.275354i \(-0.0887951\pi\)
\(480\) 0 0
\(481\) −10112.0 17514.5i −0.958560 1.66028i
\(482\) 0 0
\(483\) −882.000 4583.01i −0.0830898 0.431747i
\(484\) 0 0
\(485\) 754.500 + 1306.83i 0.0706393 + 0.122351i
\(486\) 0 0
\(487\) 3110.50 5387.54i 0.289425 0.501300i −0.684247 0.729250i \(-0.739869\pi\)
0.973673 + 0.227950i \(0.0732024\pi\)
\(488\) 0 0
\(489\) −3756.00 −0.347346
\(490\) 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
\(494\) 0 0
\(495\) 202.500 + 350.740i 0.0183873 + 0.0318477i
\(496\) 0 0
\(497\) 1197.00 + 6219.79i 0.108034 + 0.561360i
\(498\) 0 0
\(499\) 2137.00 + 3701.39i 0.191714 + 0.332058i 0.945818 0.324696i \(-0.105262\pi\)
−0.754104 + 0.656755i \(0.771929\pi\)
\(500\) 0 0
\(501\) 3969.00 6874.51i 0.353936 0.613035i
\(502\) 0 0
\(503\) 2520.00 0.223382 0.111691 0.993743i \(-0.464373\pi\)
0.111691 + 0.993743i \(0.464373\pi\)
\(504\) 0 0
\(505\) 3258.00 0.287087
\(506\) 0 0
\(507\) 2848.50 4933.75i 0.249519 0.432180i
\(508\) 0 0
\(509\) 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
\(511\) −6335.00 2194.51i −0.548423 0.189979i
\(512\) 0 0
\(513\) 216.000 + 374.123i 0.0185899 + 0.0321987i
\(514\) 0 0
\(515\) −2604.00 + 4510.26i −0.222808 + 0.385914i
\(516\) 0 0
\(517\) 450.000 0.0382804
\(518\) 0 0
\(519\) 2358.00 0.199431
\(520\) 0 0
\(521\) 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 \(0.723772\pi\)
\(524\) 0 0
\(525\) 4872.00 4219.28i 0.405012 0.350751i
\(526\) 0 0
\(527\) −10626.0 18404.8i −0.878322 1.52130i
\(528\) 0 0
\(529\) 2555.50 4426.26i 0.210035 0.363792i
\(530\) 0 0
\(531\) 135.000 0.0110330
\(532\) 0 0
\(533\) −23040.0 −1.87237
\(534\) 0 0
\(535\) 2029.50 3515.20i 0.164005 0.284066i
\(536\) 0 0
\(537\) −4338.00 7513.64i −0.348601 0.603794i
\(538\) 0 0
\(539\) 735.000 5092.23i 0.0587360 0.406935i
\(540\) 0 0
\(541\) 11429.0 + 19795.6i 0.908264 + 1.57316i 0.816474 + 0.577382i \(0.195926\pi\)
0.0917903 + 0.995778i \(0.470741\pi\)
\(542\) 0 0
\(543\) 2028.00 3512.60i 0.160276 0.277606i
\(544\) 0 0
\(545\) 1110.00 0.0872425
\(546\) 0 0
\(547\) 24724.0 1.93258 0.966291 0.257454i \(-0.0828835\pi\)
0.966291 + 0.257454i \(0.0828835\pi\)
\(548\) 0 0
\(549\) 531.000 919.719i 0.0412796 0.0714985i
\(550\) 0 0
\(551\) 2376.00 + 4115.35i 0.183704 + 0.318185i
\(552\) 0 0
\(553\) −6538.00 + 5662.07i −0.502756 + 0.435399i
\(554\) 0 0
\(555\) 1422.00 + 2462.98i 0.108758 + 0.188374i
\(556\) 0 0
\(557\) 4921.50 8524.29i 0.374382 0.648448i −0.615853 0.787861i \(-0.711188\pi\)
0.990234 + 0.139413i \(0.0445216\pi\)
\(558\) 0 0
\(559\) 1664.00 0.125903
\(560\) 0 0
\(561\) −3780.00 −0.284477
\(562\) 0 0
\(563\) −6685.50 + 11579.6i −0.500462 + 0.866826i 0.499538 + 0.866292i \(0.333503\pi\)
−1.00000 0.000533812i \(0.999830\pi\)
\(564\) 0 0
\(565\) −972.000 1683.55i −0.0723758 0.125359i
\(566\) 0 0
\(567\) −1417.50 491.036i −0.104990 0.0363696i
\(568\) 0 0
\(569\) 2616.00 + 4531.04i 0.192739 + 0.333834i 0.946157 0.323708i \(-0.104930\pi\)
−0.753418 + 0.657542i \(0.771596\pi\)
\(570\) 0 0
\(571\) −7199.00 + 12469.0i −0.527616 + 0.913858i 0.471866 + 0.881670i \(0.343581\pi\)
−0.999482 + 0.0321874i \(0.989753\pi\)
\(572\) 0 0
\(573\) 11736.0 0.855634
\(574\) 0 0
\(575\) −9744.00 −0.706701
\(576\) 0 0
\(577\) −9935.50 + 17208.8i −0.716846 + 1.24161i 0.245397 + 0.969423i \(0.421082\pi\)
−0.962243 + 0.272191i \(0.912252\pi\)
\(578\) 0 0
\(579\) 2239.50 + 3878.93i 0.160743 + 0.278416i
\(580\) 0 0
\(581\) −1669.50 8674.98i −0.119213 0.619447i
\(582\) 0 0
\(583\) −2722.50 4715.51i −0.193404 0.334985i
\(584\) 0 0
\(585\) −864.000 + 1496.49i −0.0610633 + 0.105765i
\(586\) 0 0
\(587\) 16137.0 1.13466 0.567330 0.823491i \(-0.307976\pi\)
0.567330 + 0.823491i \(0.307976\pi\)
\(588\) 0 0
\(589\) 4048.00 0.283183
\(590\) 0 0
\(591\) −6129.00 + 10615.7i −0.426588 + 0.738872i
\(592\) 0 0
\(593\) 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
\(595\) −882.000 4583.01i −0.0607705 0.315773i
\(596\) 0 0
\(597\) 5334.00 + 9238.76i 0.365672 + 0.633362i
\(598\) 0 0
\(599\) −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 \(-0.375954\pi\)
0.379911 + 0.925023i \(0.375954\pi\)
\(602\) 0 0
\(603\) 3330.00 0.224889
\(604\) 0 0
\(605\) −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 \(0.930298\pi\)
\(608\) 0 0
\(609\) −15592.5 5401.40i −1.03750 0.359402i
\(610\) 0 0
\(611\) 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 \(0.0284288\pi\)
\(614\) 0 0
\(615\) 3240.00 0.212438
\(616\) 0 0
\(617\) 12762.0 0.832705 0.416352 0.909203i \(-0.363308\pi\)
0.416352 + 0.909203i \(0.363308\pi\)
\(618\) 0 0
\(619\) 6421.00 11121.5i 0.416933 0.722150i −0.578696 0.815543i \(-0.696438\pi\)
0.995629 + 0.0933936i \(0.0297715\pi\)
\(620\) 0 0
\(621\) 1134.00 + 1964.15i 0.0732783 + 0.126922i
\(622\) 0 0
\(623\) 12684.0 10984.7i 0.815688 0.706407i
\(624\) 0 0
\(625\) −6165.50 10679.0i −0.394592 0.683453i
\(626\) 0 0
\(627\) 360.000 623.538i 0.0229298 0.0397157i
\(628\) 0 0
\(629\) −26544.0 −1.68264
\(630\) 0 0
\(631\) −21365.0 −1.34790 −0.673952 0.738775i \(-0.735404\pi\)
−0.673952 + 0.738775i \(0.735404\pi\)
\(632\) 0 0
\(633\) −1875.00 + 3247.60i −0.117732 + 0.203918i
\(634\) 0 0
\(635\) −565.500 979.475i −0.0353404 0.0612114i
\(636\) 0 0
\(637\) 20384.0 8147.57i 1.26789 0.506779i
\(638\) 0 0
\(639\) −1539.00 2665.63i −0.0952768 0.165024i
\(640\) 0 0
\(641\) −4137.00 + 7165.49i −0.254917 + 0.441529i −0.964873 0.262717i \(-0.915381\pi\)
0.709956 + 0.704246i \(0.248715\pi\)
\(642\) 0 0
\(643\) −27998.0 −1.71716 −0.858580 0.512680i \(-0.828653\pi\)
−0.858580 + 0.512680i \(0.828653\pi\)
\(644\) 0 0
\(645\) −234.000 −0.0142849
\(646\) 0 0
\(647\) −8733.00 + 15126.0i −0.530649 + 0.919110i 0.468712 + 0.883351i \(0.344718\pi\)
−0.999360 + 0.0357592i \(0.988615\pi\)
\(648\) 0 0
\(649\) −112.500 194.856i −0.00680433 0.0117854i
\(650\) 0 0
\(651\) −10626.0 + 9202.39i −0.639732 + 0.554024i
\(652\) 0 0
\(653\) −1078.50 1868.02i −0.0646324 0.111947i 0.831898 0.554928i \(-0.187254\pi\)
−0.896531 + 0.442981i \(0.853921\pi\)
\(654\) 0 0
\(655\) 976.500 1691.35i 0.0582519 0.100895i
\(656\) 0 0
\(657\) 3258.00 0.193465
\(658\) 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 \(0.466806\pi\)
−0.913368 + 0.407135i \(0.866528\pi\)
\(662\) 0 0
\(663\) −8064.00 13967.3i −0.472368 0.818165i
\(664\) 0 0
\(665\) 840.000 + 290.985i 0.0489832 + 0.0169683i
\(666\) 0 0
\(667\) 12474.0 + 21605.6i 0.724131 + 1.25423i
\(668\) 0 0
\(669\) −637.500 + 1104.18i −0.0368418 + 0.0638119i
\(670\) 0 0
\(671\) −1770.00 −0.101833
\(672\) 0 0
\(673\) −19123.0 −1.09530 −0.547650 0.836707i \(-0.684478\pi\)
−0.547650 + 0.836707i \(0.684478\pi\)
\(674\) 0 0
\(675\) −1566.00 + 2712.39i −0.0892968 + 0.154667i
\(676\) 0 0
\(677\) −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
\(679\) 1760.50 + 9147.83i 0.0995019 + 0.517027i
\(680\) 0 0
\(681\) −5782.50 10015.6i −0.325383 0.563580i
\(682\) 0 0
\(683\) −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
\(687\) 6564.00 0.364530
\(688\) 0 0
\(689\) 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 \(0.838941\pi\)
\(692\) 0 0
\(693\) 472.500 + 2455.18i 0.0259001 + 0.134581i
\(694\) 0 0
\(695\) 2337.00 + 4047.80i 0.127550 + 0.220924i
\(696\) 0 0
\(697\) −15120.0 + 26188.6i −0.821680 + 1.42319i
\(698\) 0 0
\(699\) −2556.00 −0.138307
\(700\) 0 0
\(701\) −15561.0 −0.838418 −0.419209 0.907890i \(-0.637693\pi\)
−0.419209 + 0.907890i \(0.637693\pi\)
\(702\) 0 0
\(703\) 2528.00 4378.62i 0.135626 0.234912i
\(704\) 0 0
\(705\) −135.000 233.827i −0.00721191 0.0124914i
\(706\) 0 0
\(707\) 19005.0 + 6583.53i 1.01097 + 0.350211i
\(708\) 0 0
\(709\) −2767.00 4792.58i −0.146568 0.253864i 0.783389 0.621532i \(-0.213489\pi\)
−0.929957 + 0.367668i \(0.880156\pi\)
\(710\) 0 0
\(711\) 2101.50 3639.90i 0.110847 0.191993i
\(712\) 0 0
\(713\) 21252.0 1.11626
\(714\) 0 0
\(715\) 2880.00 0.150638
\(716\) 0 0
\(717\) −8262.00 + 14310.2i −0.430335 + 0.745362i
\(718\) 0 0
\(719\) −10923.0 18919.2i −0.566564 0.981317i −0.996902 0.0786494i \(-0.974939\pi\)
0.430339 0.902667i \(-0.358394\pi\)
\(720\) 0 0
\(721\) −24304.0 + 21047.9i −1.25538 + 1.08719i
\(722\) 0 0
\(723\) 1186.50 + 2055.08i 0.0610324 + 0.105711i
\(724\) 0 0
\(725\) −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
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 1092.00 1891.40i 0.0552518 0.0956990i
\(732\) 0 0
\(733\) −5881.00 10186.2i −0.296343 0.513282i 0.678953 0.734182i \(-0.262434\pi\)
−0.975296 + 0.220900i \(0.929101\pi\)
\(734\) 0 0
\(735\) −2866.50 + 1145.75i −0.143854 + 0.0574989i
\(736\) 0 0
\(737\) −2775.00 4806.44i −0.138695 0.240227i
\(738\) 0 0
\(739\) −11363.0 + 19681.3i −0.565622 + 0.979686i 0.431369 + 0.902175i \(0.358031\pi\)
−0.996992 + 0.0775108i \(0.975303\pi\)
\(740\) 0 0
\(741\) 3072.00 0.152298
\(742\) 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
\(746\) 0 0
\(747\) 2146.50 + 3717.85i 0.105136 + 0.182100i
\(748\) 0 0
\(749\) 18942.0 16404.3i 0.924066 0.800265i
\(750\) 0 0
\(751\) −9993.50 17309.2i −0.485577 0.841043i 0.514286 0.857619i \(-0.328057\pi\)
−0.999863 + 0.0165754i \(0.994724\pi\)
\(752\) 0 0
\(753\) −7897.50 + 13678.9i −0.382206 + 0.662000i
\(754\) 0 0
\(755\) 3777.00 0.182065
\(756\) 0 0
\(757\) 314.000 0.0150760 0.00753799 0.999972i \(-0.497601\pi\)
0.00753799 + 0.999972i \(0.497601\pi\)
\(758\) 0 0
\(759\) 1890.00 3273.58i 0.0903856 0.156552i
\(760\) 0 0
\(761\) 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
\(763\) 6475.00 + 2243.01i 0.307222 + 0.106425i
\(764\) 0 0
\(765\) 1134.00 + 1964.15i 0.0535946 + 0.0928285i
\(766\) 0 0
\(767\) 480.000 831.384i 0.0225969 0.0391389i
\(768\) 0 0
\(769\) 2765.00 0.129660 0.0648299 0.997896i \(-0.479350\pi\)
0.0648299 + 0.997896i \(0.479350\pi\)
\(770\) 0 0
\(771\) 20610.0 0.962712
\(772\) 0 0
\(773\) 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
\(776\) 0 0
\(777\) 3318.00 + 17240.8i 0.153195 + 0.796025i
\(778\) 0 0
\(779\) −2880.00 4988.31i −0.132460 0.229428i
\(780\) 0 0
\(781\) −2565.00 + 4442.71i −0.117520 + 0.203550i
\(782\) 0 0
\(783\) 8019.00 0.365997
\(784\) 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 \(0.304385\pi\)
\(788\) 0 0
\(789\) 333.000 + 576.773i 0.0150255 + 0.0260249i
\(790\) 0 0
\(791\) −2268.00 11784.9i −0.101948 0.529737i
\(792\) 0 0
\(793\) −3776.00 6540.22i −0.169092 &minu