Properties

Label 147.4.e.h.79.1
Level $147$
Weight $4$
Character 147.79
Analytic conductor $8.673$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
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 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.4.e.h.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +9.00000 q^{6} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(4.50000 + 7.79423i) q^{10} +(7.50000 + 12.9904i) q^{11} +(1.50000 - 2.59808i) q^{12} +64.0000 q^{13} -9.00000 q^{15} +(35.5000 - 61.4878i) q^{16} +(42.0000 + 72.7461i) q^{17} +(13.5000 + 23.3827i) q^{18} +(-8.00000 + 13.8564i) q^{19} +3.00000 q^{20} +45.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(31.5000 + 54.5596i) q^{24} +(58.0000 + 100.459i) q^{25} +(96.0000 - 166.277i) q^{26} -27.0000 q^{27} -297.000 q^{29} +(-13.5000 + 23.3827i) q^{30} +(-126.500 - 219.104i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(-22.5000 + 38.9711i) q^{33} +252.000 q^{34} +9.00000 q^{36} +(158.000 - 273.664i) q^{37} +(24.0000 + 41.5692i) q^{38} +(96.0000 + 166.277i) q^{39} +(-31.5000 + 54.5596i) q^{40} -360.000 q^{41} +26.0000 q^{43} +(7.50000 - 12.9904i) q^{44} +(-13.5000 - 23.3827i) q^{45} +(-126.000 - 218.238i) q^{46} +(-15.0000 + 25.9808i) q^{47} +213.000 q^{48} +348.000 q^{50} +(-126.000 + 218.238i) q^{51} +(-32.0000 - 55.4256i) q^{52} +(-181.500 - 314.367i) q^{53} +(-40.5000 + 70.1481i) q^{54} -45.0000 q^{55} -48.0000 q^{57} +(-445.500 + 771.629i) q^{58} +(-7.50000 - 12.9904i) q^{59} +(4.50000 + 7.79423i) q^{60} +(-59.0000 + 102.191i) q^{61} -759.000 q^{62} +433.000 q^{64} +(-96.0000 + 166.277i) q^{65} +(67.5000 + 116.913i) q^{66} +(185.000 + 320.429i) q^{67} +(42.0000 - 72.7461i) q^{68} +252.000 q^{69} -342.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(181.000 + 313.501i) q^{73} +(-474.000 - 820.992i) q^{74} +(-174.000 + 301.377i) q^{75} +16.0000 q^{76} +576.000 q^{78} +(-233.500 + 404.434i) q^{79} +(106.500 + 184.463i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-540.000 + 935.307i) q^{82} -477.000 q^{83} -252.000 q^{85} +(39.0000 - 67.5500i) q^{86} +(-445.500 - 771.629i) q^{87} +(157.500 + 272.798i) q^{88} +(453.000 - 784.619i) q^{89} -81.0000 q^{90} -84.0000 q^{92} +(379.500 - 657.313i) q^{93} +(45.0000 + 77.9423i) q^{94} +(-24.0000 - 41.5692i) q^{95} +(67.5000 - 116.913i) q^{96} -503.000 q^{97} -135.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} + 3q^{3} - q^{4} - 3q^{5} + 18q^{6} + 42q^{8} - 9q^{9} + O(q^{10}) \) \( 2q + 3q^{2} + 3q^{3} - q^{4} - 3q^{5} + 18q^{6} + 42q^{8} - 9q^{9} + 9q^{10} + 15q^{11} + 3q^{12} + 128q^{13} - 18q^{15} + 71q^{16} + 84q^{17} + 27q^{18} - 16q^{19} + 6q^{20} + 90q^{22} + 84q^{23} + 63q^{24} + 116q^{25} + 192q^{26} - 54q^{27} - 594q^{29} - 27q^{30} - 253q^{31} - 45q^{32} - 45q^{33} + 504q^{34} + 18q^{36} + 316q^{37} + 48q^{38} + 192q^{39} - 63q^{40} - 720q^{41} + 52q^{43} + 15q^{44} - 27q^{45} - 252q^{46} - 30q^{47} + 426q^{48} + 696q^{50} - 252q^{51} - 64q^{52} - 363q^{53} - 81q^{54} - 90q^{55} - 96q^{57} - 891q^{58} - 15q^{59} + 9q^{60} - 118q^{61} - 1518q^{62} + 866q^{64} - 192q^{65} + 135q^{66} + 370q^{67} + 84q^{68} + 504q^{69} - 684q^{71} - 189q^{72} + 362q^{73} - 948q^{74} - 348q^{75} + 32q^{76} + 1152q^{78} - 467q^{79} + 213q^{80} - 81q^{81} - 1080q^{82} - 954q^{83} - 504q^{85} + 78q^{86} - 891q^{87} + 315q^{88} + 906q^{89} - 162q^{90} - 168q^{92} + 759q^{93} + 90q^{94} - 48q^{95} + 135q^{96} - 1006q^{97} - 270q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 2.59808i 0.530330 0.918559i −0.469044 0.883175i \(-0.655401\pi\)
0.999374 0.0353837i \(-0.0112653\pi\)
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.0625000 0.108253i
\(5\) −1.50000 + 2.59808i −0.134164 + 0.232379i −0.925278 0.379290i \(-0.876168\pi\)
0.791114 + 0.611669i \(0.209502\pi\)
\(6\) 9.00000 0.612372
\(7\) 0 0
\(8\) 21.0000 0.928078
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 4.50000 + 7.79423i 0.142302 + 0.246475i
\(11\) 7.50000 + 12.9904i 0.205576 + 0.356068i 0.950316 0.311287i \(-0.100760\pi\)
−0.744740 + 0.667355i \(0.767427\pi\)
\(12\) 1.50000 2.59808i 0.0360844 0.0625000i
\(13\) 64.0000 1.36542 0.682708 0.730691i \(-0.260802\pi\)
0.682708 + 0.730691i \(0.260802\pi\)
\(14\) 0 0
\(15\) −9.00000 −0.154919
\(16\) 35.5000 61.4878i 0.554688 0.960747i
\(17\) 42.0000 + 72.7461i 0.599206 + 1.03785i 0.992939 + 0.118630i \(0.0378502\pi\)
−0.393733 + 0.919225i \(0.628817\pi\)
\(18\) 13.5000 + 23.3827i 0.176777 + 0.306186i
\(19\) −8.00000 + 13.8564i −0.0965961 + 0.167309i −0.910274 0.414007i \(-0.864129\pi\)
0.813678 + 0.581317i \(0.197462\pi\)
\(20\) 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 \(-0.708994\pi\)
0.991172 + 0.132583i \(0.0423272\pi\)
\(24\) 31.5000 + 54.5596i 0.267913 + 0.464039i
\(25\) 58.0000 + 100.459i 0.464000 + 0.803672i
\(26\) 96.0000 166.277i 0.724121 1.25421i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −297.000 −1.90178 −0.950888 0.309535i \(-0.899827\pi\)
−0.950888 + 0.309535i \(0.899827\pi\)
\(30\) −13.5000 + 23.3827i −0.0821584 + 0.142302i
\(31\) −126.500 219.104i −0.732906 1.26943i −0.955636 0.294550i \(-0.904830\pi\)
0.222731 0.974880i \(-0.428503\pi\)
\(32\) −22.5000 38.9711i −0.124296 0.215287i
\(33\) −22.5000 + 38.9711i −0.118689 + 0.205576i
\(34\) 252.000 1.27111
\(35\) 0 0
\(36\) 9.00000 0.0416667
\(37\) 158.000 273.664i 0.702028 1.21595i −0.265725 0.964049i \(-0.585611\pi\)
0.967753 0.251900i \(-0.0810553\pi\)
\(38\) 24.0000 + 41.5692i 0.102456 + 0.177458i
\(39\) 96.0000 + 166.277i 0.394162 + 0.682708i
\(40\) −31.5000 + 54.5596i −0.124515 + 0.215666i
\(41\) −360.000 −1.37128 −0.685641 0.727940i \(-0.740478\pi\)
−0.685641 + 0.727940i \(0.740478\pi\)
\(42\) 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
\(45\) −13.5000 23.3827i −0.0447214 0.0774597i
\(46\) −126.000 218.238i −0.403863 0.699511i
\(47\) −15.0000 + 25.9808i −0.0465527 + 0.0806316i −0.888363 0.459142i \(-0.848157\pi\)
0.841810 + 0.539774i \(0.181490\pi\)
\(48\) 213.000 0.640498
\(49\) 0 0
\(50\) 348.000 0.984293
\(51\) −126.000 + 218.238i −0.345952 + 0.599206i
\(52\) −32.0000 55.4256i −0.0853385 0.147811i
\(53\) −181.500 314.367i −0.470395 0.814748i 0.529032 0.848602i \(-0.322555\pi\)
−0.999427 + 0.0338538i \(0.989222\pi\)
\(54\) −40.5000 + 70.1481i −0.102062 + 0.176777i
\(55\) −45.0000 −0.110324
\(56\) 0 0
\(57\) −48.0000 −0.111540
\(58\) −445.500 + 771.629i −1.00857 + 1.74689i
\(59\) −7.50000 12.9904i −0.0165494 0.0286645i 0.857632 0.514264i \(-0.171935\pi\)
−0.874182 + 0.485599i \(0.838601\pi\)
\(60\) 4.50000 + 7.79423i 0.00968246 + 0.0167705i
\(61\) −59.0000 + 102.191i −0.123839 + 0.214495i −0.921279 0.388903i \(-0.872854\pi\)
0.797440 + 0.603399i \(0.206187\pi\)
\(62\) −759.000 −1.55473
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) −96.0000 + 166.277i −0.183190 + 0.317294i
\(66\) 67.5000 + 116.913i 0.125889 + 0.218046i
\(67\) 185.000 + 320.429i 0.337334 + 0.584279i 0.983930 0.178553i \(-0.0571417\pi\)
−0.646597 + 0.762832i \(0.723808\pi\)
\(68\) 42.0000 72.7461i 0.0749007 0.129732i
\(69\) 252.000 0.439670
\(70\) 0 0
\(71\) −342.000 −0.571661 −0.285831 0.958280i \(-0.592269\pi\)
−0.285831 + 0.958280i \(0.592269\pi\)
\(72\) −94.5000 + 163.679i −0.154680 + 0.267913i
\(73\) 181.000 + 313.501i 0.290198 + 0.502638i 0.973856 0.227165i \(-0.0729455\pi\)
−0.683658 + 0.729802i \(0.739612\pi\)
\(74\) −474.000 820.992i −0.744613 1.28971i
\(75\) −174.000 + 301.377i −0.267891 + 0.464000i
\(76\) 16.0000 0.0241490
\(77\) 0 0
\(78\) 576.000 0.836143
\(79\) −233.500 + 404.434i −0.332542 + 0.575979i −0.983010 0.183555i \(-0.941240\pi\)
0.650468 + 0.759534i \(0.274573\pi\)
\(80\) 106.500 + 184.463i 0.148838 + 0.257795i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −540.000 + 935.307i −0.727232 + 1.25960i
\(83\) −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
\(86\) 39.0000 67.5500i 0.0489009 0.0846989i
\(87\) −445.500 771.629i −0.548996 0.950888i
\(88\) 157.500 + 272.798i 0.190790 + 0.330459i
\(89\) 453.000 784.619i 0.539527 0.934488i −0.459402 0.888228i \(-0.651936\pi\)
0.998929 0.0462600i \(-0.0147303\pi\)
\(90\) −81.0000 −0.0948683
\(91\) 0 0
\(92\) −84.0000 −0.0951914
\(93\) 379.500 657.313i 0.423143 0.732906i
\(94\) 45.0000 + 77.9423i 0.0493765 + 0.0855227i
\(95\) −24.0000 41.5692i −0.0259195 0.0448938i
\(96\) 67.5000 116.913i 0.0717624 0.124296i
\(97\) −503.000 −0.526515 −0.263257 0.964726i \(-0.584797\pi\)
−0.263257 + 0.964726i \(0.584797\pi\)
\(98\) 0 0
\(99\) −135.000 −0.137051
\(100\) 58.0000 100.459i 0.0580000 0.100459i
\(101\) −543.000 940.504i −0.534956 0.926570i −0.999165 0.0408451i \(-0.986995\pi\)
0.464210 0.885725i \(-0.346338\pi\)
\(102\) 378.000 + 654.715i 0.366937 + 0.635554i
\(103\) 868.000 1503.42i 0.830355 1.43822i −0.0674017 0.997726i \(-0.521471\pi\)
0.897757 0.440491i \(-0.145196\pi\)
\(104\) 1344.00 1.26721
\(105\) 0 0
\(106\) −1089.00 −0.997859
\(107\) 676.500 1171.73i 0.611212 1.05865i −0.379824 0.925059i \(-0.624015\pi\)
0.991036 0.133592i \(-0.0426512\pi\)
\(108\) 13.5000 + 23.3827i 0.0120281 + 0.0208333i
\(109\) 185.000 + 320.429i 0.162567 + 0.281574i 0.935789 0.352562i \(-0.114689\pi\)
−0.773222 + 0.634136i \(0.781356\pi\)
\(110\) −67.5000 + 116.913i −0.0585079 + 0.101339i
\(111\) 948.000 0.810632
\(112\) 0 0
\(113\) −648.000 −0.539458 −0.269729 0.962936i \(-0.586934\pi\)
−0.269729 + 0.962936i \(0.586934\pi\)
\(114\) −72.0000 + 124.708i −0.0591528 + 0.102456i
\(115\) 126.000 + 218.238i 0.102170 + 0.176964i
\(116\) 148.500 + 257.210i 0.118861 + 0.205873i
\(117\) −288.000 + 498.831i −0.227569 + 0.394162i
\(118\) −45.0000 −0.0351067
\(119\) 0 0
\(120\) −189.000 −0.143777
\(121\) 553.000 957.824i 0.415477 0.719627i
\(122\) 177.000 + 306.573i 0.131351 + 0.227507i
\(123\) −540.000 935.307i −0.395855 0.685641i
\(124\) −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
\(129\) 39.0000 + 67.5500i 0.0266183 + 0.0461042i
\(130\) 288.000 + 498.831i 0.194302 + 0.336541i
\(131\) −325.500 + 563.783i −0.217092 + 0.376015i −0.953918 0.300068i \(-0.902991\pi\)
0.736826 + 0.676083i \(0.236324\pi\)
\(132\) 45.0000 0.0296723
\(133\) 0 0
\(134\) 1110.00 0.715593
\(135\) 40.5000 70.1481i 0.0258199 0.0447214i
\(136\) 882.000 + 1527.67i 0.556109 + 0.963210i
\(137\) 885.000 + 1532.86i 0.551903 + 0.955923i 0.998137 + 0.0610074i \(0.0194313\pi\)
−0.446235 + 0.894916i \(0.647235\pi\)
\(138\) 378.000 654.715i 0.233170 0.403863i
\(139\) 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
\(142\) −513.000 + 888.542i −0.303169 + 0.525104i
\(143\) 480.000 + 831.384i 0.280697 + 0.486181i
\(144\) 319.500 + 553.390i 0.184896 + 0.320249i
\(145\) 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 0.301948 + 0.953324i \(0.402363\pi\)
−0.976577 + 0.215168i \(0.930970\pi\)
\(150\) 522.000 + 904.131i 0.284141 + 0.492146i
\(151\) −629.500 1090.33i −0.339258 0.587612i 0.645035 0.764153i \(-0.276843\pi\)
−0.984293 + 0.176540i \(0.943509\pi\)
\(152\) −168.000 + 290.985i −0.0896487 + 0.155276i
\(153\) −756.000 −0.399470
\(154\) 0 0
\(155\) 759.000 0.393318
\(156\) 96.0000 166.277i 0.0492702 0.0853385i
\(157\) −98.0000 169.741i −0.0498169 0.0862854i 0.840042 0.542522i \(-0.182530\pi\)
−0.889859 + 0.456236i \(0.849197\pi\)
\(158\) 700.500 + 1213.30i 0.352714 + 0.610918i
\(159\) 544.500 943.102i 0.271583 0.470395i
\(160\) 135.000 0.0667043
\(161\) 0 0
\(162\) −243.000 −0.117851
\(163\) 626.000 1084.26i 0.300810 0.521019i −0.675509 0.737351i \(-0.736076\pi\)
0.976320 + 0.216332i \(0.0694095\pi\)
\(164\) 180.000 + 311.769i 0.0857051 + 0.148446i
\(165\) −67.5000 116.913i −0.0318477 0.0551618i
\(166\) −715.500 + 1239.28i −0.334540 + 0.579440i
\(167\) 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
\(170\) −378.000 + 654.715i −0.170537 + 0.295379i
\(171\) −72.0000 124.708i −0.0321987 0.0557698i
\(172\) −13.0000 22.5167i −0.00576303 0.00998186i
\(173\) −393.000 + 680.696i −0.172712 + 0.299147i −0.939367 0.342913i \(-0.888586\pi\)
0.766655 + 0.642059i \(0.221920\pi\)
\(174\) −2673.00 −1.16460
\(175\) 0 0
\(176\) 1065.00 0.456122
\(177\) 22.5000 38.9711i 0.00955482 0.0165494i
\(178\) −1359.00 2353.86i −0.572255 0.991174i
\(179\) −1446.00 2504.55i −0.603794 1.04580i −0.992241 0.124331i \(-0.960322\pi\)
0.388447 0.921471i \(-0.373012\pi\)
\(180\) −13.5000 + 23.3827i −0.00559017 + 0.00968246i
\(181\) −1352.00 −0.555212 −0.277606 0.960695i \(-0.589541\pi\)
−0.277606 + 0.960695i \(0.589541\pi\)
\(182\) 0 0
\(183\) −354.000 −0.142997
\(184\) 882.000 1527.67i 0.353380 0.612072i
\(185\) 474.000 + 820.992i 0.188374 + 0.326273i
\(186\) −1138.50 1971.94i −0.448811 0.777364i
\(187\) −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 0.211039 + 0.977478i \(0.432315\pi\)
−0.952040 + 0.305974i \(0.901018\pi\)
\(192\) 649.500 + 1124.97i 0.244133 + 0.422852i
\(193\) −746.500 1292.98i −0.278416 0.482230i 0.692575 0.721345i \(-0.256476\pi\)
−0.970991 + 0.239115i \(0.923143\pi\)
\(194\) −754.500 + 1306.83i −0.279227 + 0.483635i
\(195\) −576.000 −0.211529
\(196\) 0 0
\(197\) −4086.00 −1.47774 −0.738872 0.673846i \(-0.764641\pi\)
−0.738872 + 0.673846i \(0.764641\pi\)
\(198\) −202.500 + 350.740i −0.0726821 + 0.125889i
\(199\) −1778.00 3079.59i −0.633362 1.09702i −0.986860 0.161580i \(-0.948341\pi\)
0.353497 0.935436i \(-0.384992\pi\)
\(200\) 1218.00 + 2109.64i 0.430628 + 0.745870i
\(201\) −555.000 + 961.288i −0.194760 + 0.337334i
\(202\) −3258.00 −1.13481
\(203\) 0 0
\(204\) 252.000 0.0864879
\(205\) 540.000 935.307i 0.183977 0.318657i
\(206\) −2604.00 4510.26i −0.880725 1.52546i
\(207\) 378.000 + 654.715i 0.126922 + 0.219835i
\(208\) 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
\(213\) −513.000 888.542i −0.165024 0.285831i
\(214\) −2029.50 3515.20i −0.648289 1.12287i
\(215\) −39.0000 + 67.5500i −0.0123711 + 0.0214273i
\(216\) −567.000 −0.178609
\(217\) 0 0
\(218\) 1110.00 0.344856
\(219\) −543.000 + 940.504i −0.167546 + 0.290198i
\(220\) 22.5000 + 38.9711i 0.00689523 + 0.0119429i
\(221\) 2688.00 + 4655.75i 0.818165 + 1.41710i
\(222\) 1422.00 2462.98i 0.429903 0.744613i
\(223\) −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
\(226\) −972.000 + 1683.55i −0.286091 + 0.495523i
\(227\) 1927.50 + 3338.53i 0.563580 + 0.976149i 0.997180 + 0.0750439i \(0.0239097\pi\)
−0.433600 + 0.901105i \(0.642757\pi\)
\(228\) 24.0000 + 41.5692i 0.00697122 + 0.0120745i
\(229\) −1094.00 + 1894.86i −0.315692 + 0.546795i −0.979584 0.201033i \(-0.935570\pi\)
0.663892 + 0.747828i \(0.268903\pi\)
\(230\) 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 \(-0.871551\pi\)
0.799902 + 0.600131i \(0.204885\pi\)
\(234\) 864.000 + 1496.49i 0.241374 + 0.418072i
\(235\) −45.0000 77.9423i −0.0124914 0.0216357i
\(236\) −7.50000 + 12.9904i −0.00206868 + 0.00358306i
\(237\) −1401.00 −0.383986
\(238\) 0 0
\(239\) 5508.00 1.49072 0.745362 0.666660i \(-0.232277\pi\)
0.745362 + 0.666660i \(0.232277\pi\)
\(240\) −319.500 + 553.390i −0.0859318 + 0.148838i
\(241\) 395.500 + 685.026i 0.105711 + 0.183097i 0.914029 0.405650i \(-0.132955\pi\)
−0.808317 + 0.588747i \(0.799621\pi\)
\(242\) −1659.00 2873.47i −0.440680 0.763280i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 118.000 0.0309597
\(245\) 0 0
\(246\) −3240.00 −0.839735
\(247\) −512.000 + 886.810i −0.131894 + 0.228447i
\(248\) −2656.50 4601.19i −0.680193 1.17813i
\(249\) −715.500 1239.28i −0.182100 0.315407i
\(250\) −1084.50 + 1878.41i −0.274359 + 0.475204i
\(251\) −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
\(254\) 565.500 979.475i 0.139695 0.241959i
\(255\) −378.000 654.715i −0.0928285 0.160784i
\(256\) −756.500 1310.30i −0.184692 0.319897i
\(257\) −3435.00 + 5949.59i −0.833733 + 1.44407i 0.0613246 + 0.998118i \(0.480468\pi\)
−0.895058 + 0.445950i \(0.852866\pi\)
\(258\) 234.000 0.0564659
\(259\) 0 0
\(260\) 192.000 0.0457974
\(261\) 1336.50 2314.89i 0.316963 0.548996i
\(262\) 976.500 + 1691.35i 0.230261 + 0.398824i
\(263\) 111.000 + 192.258i 0.0260249 + 0.0450765i 0.878745 0.477292i \(-0.158382\pi\)
−0.852720 + 0.522369i \(0.825048\pi\)
\(264\) −472.500 + 818.394i −0.110153 + 0.190790i
\(265\) 1089.00 0.252441
\(266\) 0 0
\(267\) 2718.00 0.622992
\(268\) 185.000 320.429i 0.0421667 0.0730349i
\(269\) 3925.50 + 6799.17i 0.889747 + 1.54109i 0.840174 + 0.542317i \(0.182453\pi\)
0.0495729 + 0.998771i \(0.484214\pi\)
\(270\) −121.500 210.444i −0.0273861 0.0474342i
\(271\) 2591.50 4488.61i 0.580895 1.00614i −0.414479 0.910059i \(-0.636036\pi\)
0.995374 0.0960800i \(-0.0306305\pi\)
\(272\) 5964.00 1.32949
\(273\) 0 0
\(274\) 5310.00 1.17076
\(275\) −870.000 + 1506.88i −0.190774 + 0.330431i
\(276\) −126.000 218.238i −0.0274794 0.0475957i
\(277\) 2480.00 + 4295.49i 0.537938 + 0.931736i 0.999015 + 0.0443755i \(0.0141298\pi\)
−0.461077 + 0.887360i \(0.652537\pi\)
\(278\) 2337.00 4047.80i 0.504187 0.873277i
\(279\) 2277.00 0.488604
\(280\) 0 0
\(281\) −774.000 −0.164317 −0.0821583 0.996619i \(-0.526181\pi\)
−0.0821583 + 0.996619i \(0.526181\pi\)
\(282\) −135.000 + 233.827i −0.0285076 + 0.0493765i
\(283\) 1849.00 + 3202.56i 0.388380 + 0.672695i 0.992232 0.124402i \(-0.0397013\pi\)
−0.603852 + 0.797097i \(0.706368\pi\)
\(284\) 171.000 + 296.181i 0.0357288 + 0.0618841i
\(285\) 72.0000 124.708i 0.0149646 0.0259195i
\(286\) 2880.00 0.595447
\(287\) 0 0
\(288\) 405.000 0.0828641
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) −1336.50 2314.89i −0.270628 0.468741i
\(291\) −754.500 1306.83i −0.151992 0.263257i
\(292\) 181.000 313.501i 0.0362747 0.0628297i
\(293\) 6273.00 1.25076 0.625380 0.780321i \(-0.284944\pi\)
0.625380 + 0.780321i \(0.284944\pi\)
\(294\) 0 0
\(295\) 45.0000 0.00888136
\(296\) 3318.00 5746.94i 0.651537 1.12849i
\(297\) −202.500 350.740i −0.0395631 0.0685253i
\(298\) 3681.00 + 6375.68i 0.715552 + 1.23937i
\(299\) 2688.00 4655.75i 0.519903 0.900499i
\(300\) 348.000 0.0669726
\(301\) 0 0
\(302\) −3777.00 −0.719675
\(303\) 1629.00 2821.51i 0.308857 0.534956i
\(304\) 568.000 + 983.805i 0.107161 + 0.185609i
\(305\) −177.000 306.573i −0.0332295 0.0575551i
\(306\) −1134.00 + 1964.15i −0.211851 + 0.366937i
\(307\) 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
\(310\) 1138.50 1971.94i 0.208589 0.361286i
\(311\) −660.000 1143.15i −0.120338 0.208432i 0.799563 0.600582i \(-0.205065\pi\)
−0.919901 + 0.392151i \(0.871731\pi\)
\(312\) 2016.00 + 3491.81i 0.365813 + 0.633606i
\(313\) −4251.50 + 7363.81i −0.767760 + 1.32980i 0.171014 + 0.985269i \(0.445296\pi\)
−0.938775 + 0.344531i \(0.888038\pi\)
\(314\) −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 \(-0.760018\pi\)
0.957303 + 0.289087i \(0.0933517\pi\)
\(318\) −1633.50 2829.30i −0.288057 0.498929i
\(319\) −2227.50 3858.14i −0.390959 0.677162i
\(320\) −649.500 + 1124.97i −0.113463 + 0.196524i
\(321\) 4059.00 0.705767
\(322\) 0 0
\(323\) −1344.00 −0.231524
\(324\) −40.5000 + 70.1481i −0.00694444 + 0.0120281i
\(325\) 3712.00 + 6429.37i 0.633553 + 1.09735i
\(326\) −1878.00 3252.79i −0.319058 0.552624i
\(327\) −555.000 + 961.288i −0.0938580 + 0.162567i
\(328\) −7560.00 −1.27266
\(329\) 0 0
\(330\) −405.000 −0.0675591
\(331\) 242.000 419.156i 0.0401859 0.0696040i −0.845233 0.534398i \(-0.820538\pi\)
0.885419 + 0.464794i \(0.153872\pi\)
\(332\) 238.500 + 413.094i 0.0394259 + 0.0682876i
\(333\) 1422.00 + 2462.98i 0.234009 + 0.405316i
\(334\) 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
\(339\) −972.000 1683.55i −0.155728 0.269729i
\(340\) 126.000 + 218.238i 0.0200980 + 0.0348107i
\(341\) 1897.50 3286.57i 0.301335 0.521928i
\(342\) −432.000 −0.0683038
\(343\) 0 0
\(344\) 546.000 0.0855766
\(345\) −378.000 + 654.715i −0.0589879 + 0.102170i
\(346\) 1179.00 + 2042.09i 0.183189 + 0.317293i
\(347\) 930.000 + 1610.81i 0.143876 + 0.249201i 0.928953 0.370197i \(-0.120710\pi\)
−0.785077 + 0.619398i \(0.787377\pi\)
\(348\) −445.500 + 771.629i −0.0686244 + 0.118861i
\(349\) 1918.00 0.294178 0.147089 0.989123i \(-0.453010\pi\)
0.147089 + 0.989123i \(0.453010\pi\)
\(350\) 0 0
\(351\) −1728.00 −0.262774
\(352\) 337.500 584.567i 0.0511046 0.0885157i
\(353\) −1524.00 2639.65i −0.229786 0.398000i 0.727959 0.685621i \(-0.240469\pi\)
−0.957744 + 0.287620i \(0.907136\pi\)
\(354\) −67.5000 116.913i −0.0101344 0.0175533i
\(355\) 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 \(-0.832631\pi\)
0.867126 + 0.498089i \(0.165965\pi\)
\(360\) −283.500 491.036i −0.0415049 0.0718886i
\(361\) 3301.50 + 5718.37i 0.481338 + 0.833703i
\(362\) −2028.00 + 3512.60i −0.294446 + 0.509995i
\(363\) 3318.00 0.479752
\(364\) 0 0
\(365\) −1086.00 −0.155737
\(366\) −531.000 + 919.719i −0.0758356 + 0.131351i
\(367\) −5655.50 9795.61i −0.804400 1.39326i −0.916696 0.399586i \(-0.869154\pi\)
0.112296 0.993675i \(-0.464180\pi\)
\(368\) −2982.00 5164.98i −0.422412 0.731638i
\(369\) 1620.00 2805.92i 0.228547 0.395855i
\(370\) 2844.00 0.399601
\(371\) 0 0
\(372\) −759.000 −0.105786
\(373\) −604.000 + 1046.16i −0.0838443 + 0.145223i −0.904898 0.425628i \(-0.860053\pi\)
0.821054 + 0.570851i \(0.193387\pi\)
\(374\) 1890.00 + 3273.58i 0.261309 + 0.452600i
\(375\) −1084.50 1878.41i −0.149342 0.258668i
\(376\) −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
\(381\) 565.500 + 979.475i 0.0760405 + 0.131706i
\(382\) 5868.00 + 10163.7i 0.785950 + 1.36131i
\(383\) 6375.00 11041.8i 0.850515 1.47314i −0.0302291 0.999543i \(-0.509624\pi\)
0.880744 0.473592i \(-0.157043\pi\)
\(384\) 4977.00 0.661410
\(385\) 0 0
\(386\) −4479.00 −0.590609
\(387\) −117.000 + 202.650i −0.0153681 + 0.0266183i
\(388\) 251.500 + 435.611i 0.0329072 + 0.0569969i
\(389\) −1563.00 2707.20i −0.203720 0.352854i 0.746004 0.665942i \(-0.231970\pi\)
−0.949724 + 0.313087i \(0.898637\pi\)
\(390\) −864.000 + 1496.49i −0.112180 + 0.194302i
\(391\) 7056.00 0.912627
\(392\) 0 0
\(393\) −1953.00 −0.250676
\(394\) −6129.00 + 10615.7i −0.783692 + 1.35739i
\(395\) −700.500 1213.30i −0.0892303 0.154551i
\(396\) 67.5000 + 116.913i 0.00856566 + 0.0148362i
\(397\) −2966.00 + 5137.26i −0.374960 + 0.649450i −0.990321 0.138795i \(-0.955677\pi\)
0.615361 + 0.788246i \(0.289010\pi\)
\(398\) −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 \(-0.865257\pi\)
0.811611 + 0.584198i \(0.198591\pi\)
\(402\) 1665.00 + 2883.86i 0.206574 + 0.357796i
\(403\) −8096.00 14022.7i −1.00072 1.73330i
\(404\) −543.000 + 940.504i −0.0668695 + 0.115821i
\(405\) 243.000 0.0298142
\(406\) 0 0
\(407\) 4740.00 0.577280
\(408\) −2646.00 + 4583.01i −0.321070 + 0.556109i
\(409\) −2232.50 3866.80i −0.269902 0.467484i 0.698934 0.715186i \(-0.253658\pi\)
−0.968836 + 0.247702i \(0.920325\pi\)
\(410\) −1620.00 2805.92i −0.195137 0.337987i
\(411\) −2655.00 + 4598.59i −0.318641 + 0.551903i
\(412\) −1736.00 −0.207589
\(413\) 0 0
\(414\) 2268.00 0.269242
\(415\) 715.500 1239.28i 0.0846326 0.146588i
\(416\) −1440.00 2494.15i −0.169716 0.293957i
\(417\) 2337.00 + 4047.80i 0.274445 + 0.475352i
\(418\) −360.000 + 623.538i −0.0421248 + 0.0729623i
\(419\) 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 \(0.524529\pi\)
\(422\) 1875.00 3247.60i 0.216288 0.374622i
\(423\) −135.000 233.827i −0.0155176 0.0268772i
\(424\) −3811.50 6601.71i −0.436563 0.756150i
\(425\) −4872.00 + 8438.55i −0.556063 + 0.963129i
\(426\) −3078.00 −0.350069
\(427\) 0 0
\(428\) −1353.00 −0.152803
\(429\) −1440.00 + 2494.15i −0.162060 + 0.280697i
\(430\) 117.000 + 202.650i 0.0131215 + 0.0227271i
\(431\) −4794.00 8303.45i −0.535775 0.927989i −0.999125 0.0418139i \(-0.986686\pi\)
0.463351 0.886175i \(-0.346647\pi\)
\(432\) −958.500 + 1660.17i −0.106750 + 0.184896i
\(433\) −494.000 −0.0548271 −0.0274135 0.999624i \(-0.508727\pi\)
−0.0274135 + 0.999624i \(0.508727\pi\)
\(434\) 0 0
\(435\) 2673.00 0.294622
\(436\) 185.000 320.429i 0.0203209 0.0351968i
\(437\) 672.000 + 1163.94i 0.0735609 + 0.127411i
\(438\) 1629.00 + 2821.51i 0.177709 + 0.307801i
\(439\) −8004.50 + 13864.2i −0.870237 + 1.50729i −0.00848508 + 0.999964i \(0.502701\pi\)
−0.861752 + 0.507330i \(0.830632\pi\)
\(440\) −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 \(-0.970190\pi\)
0.578794 + 0.815474i \(0.303524\pi\)
\(444\) −474.000 820.992i −0.0506645 0.0877535i
\(445\) 1359.00 + 2353.86i 0.144770 + 0.250749i
\(446\) −637.500 + 1104.18i −0.0676827 + 0.117230i
\(447\) −7362.00 −0.778995
\(448\) 0 0
\(449\) 864.000 0.0908122 0.0454061 0.998969i \(-0.485542\pi\)
0.0454061 + 0.998969i \(0.485542\pi\)
\(450\) −1566.00 + 2712.39i −0.164049 + 0.284141i
\(451\) −2700.00 4676.54i −0.281903 0.488269i
\(452\) 324.000 + 561.184i 0.0337161 + 0.0583980i
\(453\) 1888.50 3270.98i 0.195871 0.339258i
\(454\) 11565.0 1.19553
\(455\) 0 0
\(456\) −1008.00 −0.103517
\(457\) −1259.50 + 2181.52i −0.128921 + 0.223298i −0.923259 0.384179i \(-0.874485\pi\)
0.794338 + 0.607476i \(0.207818\pi\)
\(458\) 3282.00 + 5684.59i 0.334842 + 0.579964i
\(459\) −1134.00 1964.15i −0.115317 0.199735i
\(460\) 126.000 218.238i 0.0127713 0.0221205i
\(461\) 342.000 0.0345521 0.0172761 0.999851i \(-0.494501\pi\)
0.0172761 + 0.999851i \(0.494501\pi\)
\(462\) 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
\(465\) 1138.50 + 1971.94i 0.113541 + 0.196659i
\(466\) 1278.00 + 2213.56i 0.127043 + 0.220046i
\(467\) 9318.00 16139.2i 0.923310 1.59922i 0.129052 0.991638i \(-0.458806\pi\)
0.794257 0.607581i \(-0.207860\pi\)
\(468\) 576.000 0.0568923
\(469\) 0 0
\(470\) −270.000 −0.0264982
\(471\) 294.000 509.223i 0.0287618 0.0498169i
\(472\) −157.500 272.798i −0.0153592 0.0266029i
\(473\) 195.000 + 337.750i 0.0189558 + 0.0328325i
\(474\) −2101.50 + 3639.90i −0.203639 + 0.352714i
\(475\) −1856.00 −0.179282
\(476\) 0 0
\(477\) 3267.00 0.313597
\(478\) 8262.00 14310.2i 0.790575 1.36932i
\(479\) 7539.00 + 13057.9i 0.719135 + 1.24558i 0.961343 + 0.275354i \(0.0887951\pi\)
−0.242208 + 0.970224i \(0.577872\pi\)
\(480\) 202.500 + 350.740i 0.0192559 + 0.0333521i
\(481\) 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
\(486\) −364.500 631.333i −0.0340207 0.0589256i
\(487\) −3110.50 5387.54i −0.289425 0.501300i 0.684247 0.729250i \(-0.260131\pi\)
−0.973673 + 0.227950i \(0.926798\pi\)
\(488\) −1239.00 + 2146.01i −0.114932 + 0.199068i
\(489\) 3756.00 0.347346
\(490\) 0 0
\(491\) −7371.00 −0.677492 −0.338746 0.940878i \(-0.610003\pi\)
−0.338746 + 0.940878i \(0.610003\pi\)
\(492\) −540.000 + 935.307i −0.0494819 + 0.0857051i
\(493\) −12474.0 21605.6i −1.13956 1.97377i
\(494\) 1536.00 + 2660.43i 0.139895 + 0.242304i
\(495\) 202.500 350.740i 0.0183873 0.0318477i
\(496\) −17963.0 −1.62613
\(497\) 0 0
\(498\) −4293.00 −0.386293
\(499\) −2137.00 + 3701.39i −0.191714 + 0.332058i −0.945818 0.324696i \(-0.894738\pi\)
0.754104 + 0.656755i \(0.228071\pi\)
\(500\) 361.500 + 626.136i 0.0323335 + 0.0560033i
\(501\) 3969.00 + 6874.51i 0.353936 + 0.613035i
\(502\) −7897.50 + 13678.9i −0.702157 + 1.21617i
\(503\) 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
\(506\) 1890.00 3273.58i 0.166049 0.287605i
\(507\) 2848.50 + 4933.75i 0.249519 + 0.432180i
\(508\) −188.500 326.492i −0.0164633 0.0285152i
\(509\) −7138.50 + 12364.2i −0.621628 + 1.07669i 0.367555 + 0.930002i \(0.380195\pi\)
−0.989183 + 0.146689i \(0.953138\pi\)
\(510\) −2268.00 −0.196919
\(511\) 0 0
\(512\) 8733.00 0.753804
\(513\) 216.000 374.123i 0.0185899 0.0321987i
\(514\) 10305.0 + 17848.8i 0.884308 + 1.53167i
\(515\) 2604.00 + 4510.26i 0.222808 + 0.385914i
\(516\) 39.0000 67.5500i 0.00332729 0.00576303i
\(517\) −450.000 −0.0382804
\(518\) 0 0
\(519\) −2358.00 −0.199431
\(520\) −2016.00 + 3491.81i −0.170014 + 0.294473i
\(521\) −3153.00 5461.16i −0.265135 0.459228i 0.702464 0.711719i \(-0.252083\pi\)
−0.967599 + 0.252492i \(0.918750\pi\)
\(522\) −4009.50 6944.66i −0.336190 0.582298i
\(523\) 4036.00 6990.56i 0.337442 0.584466i −0.646509 0.762906i \(-0.723772\pi\)
0.983951 + 0.178440i \(0.0571051\pi\)
\(524\) 651.000 0.0542730
\(525\) 0 0
\(526\) 666.000 0.0552072
\(527\) 10626.0 18404.8i 0.878322 1.52130i
\(528\) 1597.50 + 2766.95i 0.131671 + 0.228061i
\(529\) 2555.50 + 4426.26i 0.210035 + 0.363792i
\(530\) 1633.50 2829.30i 0.133877 0.231881i
\(531\) 135.000 0.0110330
\(532\) 0 0
\(533\) −23040.0 −1.87237
\(534\) 4077.00 7061.57i 0.330391 0.572255i
\(535\) 2029.50 + 3515.20i 0.164005 + 0.284066i
\(536\) 3885.00 + 6729.02i 0.313072 + 0.542256i
\(537\) 4338.00 7513.64i 0.348601 0.603794i
\(538\) 23553.0 1.88744
\(539\) 0 0
\(540\) −81.0000 −0.00645497
\(541\) 11429.0 19795.6i 0.908264 1.57316i 0.0917903 0.995778i \(-0.470741\pi\)
0.816474 0.577382i \(-0.195926\pi\)
\(542\) −7774.50 13465.8i −0.616132 1.06717i
\(543\) −2028.00 3512.60i −0.160276 0.277606i
\(544\) 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
\(549\) −531.000 919.719i −0.0412796 0.0714985i
\(550\) 2610.00 + 4520.65i 0.202347 + 0.350475i
\(551\) 2376.00 4115.35i 0.183704 0.318185i
\(552\) 5292.00 0.408048
\(553\) 0 0
\(554\) 14880.0 1.14114
\(555\) −1422.00 + 2462.98i −0.108758 + 0.188374i
\(556\) −779.000 1349.27i −0.0594190 0.102917i
\(557\) 4921.50 + 8524.29i 0.374382 + 0.648448i 0.990234 0.139413i \(-0.0445216\pi\)
−0.615853 + 0.787861i \(0.711188\pi\)
\(558\) 3415.50 5915.82i 0.259121 0.448811i
\(559\) 1664.00 0.125903
\(560\) 0 0
\(561\) −3780.00 −0.284477
\(562\) −1161.00 + 2010.91i −0.0871420 + 0.150934i
\(563\) −6685.50 11579.6i −0.500462 0.866826i −1.00000 0.000533812i \(-0.999830\pi\)
0.499538 0.866292i \(-0.333503\pi\)
\(564\) 45.0000 + 77.9423i 0.00335965 + 0.00581908i
\(565\) 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 \(-0.771596\pi\)
0.946157 + 0.323708i \(0.104930\pi\)
\(570\) −216.000 374.123i −0.0158724 0.0274917i
\(571\) 7199.00 + 12469.0i 0.527616 + 0.913858i 0.999482 + 0.0321874i \(0.0102474\pi\)
−0.471866 + 0.881670i \(0.656419\pi\)
\(572\) 480.000 831.384i 0.0350871 0.0607726i
\(573\) −11736.0 −0.855634
\(574\) 0 0
\(575\) 9744.00 0.706701
\(576\) −1948.50 + 3374.90i −0.140951 + 0.244133i
\(577\) 9935.50 + 17208.8i 0.716846 + 1.24161i 0.962243 + 0.272191i \(0.0877484\pi\)
−0.245397 + 0.969423i \(0.578918\pi\)
\(578\) 3214.50 + 5567.68i 0.231325 + 0.400666i
\(579\) 2239.50 3878.93i 0.160743 0.278416i
\(580\) −891.000 −0.0637875
\(581\) 0 0
\(582\) −4527.00 −0.322423
\(583\) 2722.50 4715.51i 0.193404 0.334985i
\(584\) 3801.00 + 6583.53i 0.269326 + 0.466487i
\(585\) −864.000 1496.49i −0.0610633 0.105765i
\(586\) 9409.50 16297.7i 0.663315 1.14890i
\(587\) 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
\(590\) 67.5000 116.913i 0.00471005 0.00815805i
\(591\) −6129.00 10615.7i −0.426588 0.738872i
\(592\) −11218.0 19430.1i −0.778812 1.34894i
\(593\) −10662.0 + 18467.1i −0.738340 + 1.27884i 0.214902 + 0.976636i \(0.431057\pi\)
−0.953242 + 0.302207i \(0.902276\pi\)
\(594\) −1215.00 −0.0839260
\(595\) 0 0
\(596\) 2454.00 0.168657
\(597\) 5334.00 9238.76i 0.365672 0.633362i
\(598\) −8064.00 13967.3i −0.551441 0.955123i
\(599\) 4323.00 + 7487.66i 0.294880 + 0.510747i 0.974957 0.222394i \(-0.0713871\pi\)
−0.680077 + 0.733141i \(0.738054\pi\)
\(600\) −3654.00 + 6328.91i −0.248623 + 0.430628i
\(601\) −11195.0 −0.759823 −0.379911 0.925023i \(-0.624046\pi\)
−0.379911 + 0.925023i \(0.624046\pi\)
\(602\) 0 0
\(603\) −3330.00 −0.224889
\(604\) −629.500 + 1090.33i −0.0424073 + 0.0734515i
\(605\) 1659.00 + 2873.47i 0.111484 + 0.193096i
\(606\) −4887.00 8464.53i −0.327592 0.567406i
\(607\) −4485.50 + 7769.11i −0.299935 + 0.519503i −0.976121 0.217228i \(-0.930298\pi\)
0.676185 + 0.736731i \(0.263632\pi\)
\(608\) 720.000 0.0480261
\(609\) 0 0
\(610\) −1062.00 −0.0704904
\(611\) −960.000 + 1662.77i −0.0635637 + 0.110096i
\(612\) 378.000 + 654.715i 0.0249669 + 0.0432439i
\(613\) 6386.00 + 11060.9i 0.420764 + 0.728784i 0.996014 0.0891932i \(-0.0284288\pi\)
−0.575251 + 0.817977i \(0.695096\pi\)
\(614\) 2526.00 4375.16i 0.166028 0.287569i
\(615\) 3240.00 0.212438
\(616\) 0 0
\(617\) 12762.0 0.832705 0.416352 0.909203i \(-0.363308\pi\)
0.416352 + 0.909203i \(0.363308\pi\)
\(618\) 7812.00 13530.8i 0.508487 0.880725i
\(619\) 6421.00 + 11121.5i 0.416933 + 0.722150i 0.995629 0.0933936i \(-0.0297715\pi\)
−0.578696 + 0.815543i \(0.696438\pi\)
\(620\) −379.500 657.313i −0.0245824 0.0425780i
\(621\) −1134.00 + 1964.15i −0.0732783 + 0.126922i
\(622\) −3960.00 −0.255276
\(623\) 0 0
\(624\) 13632.0 0.874546
\(625\) −6165.50 + 10679.0i −0.394592 + 0.683453i
\(626\) 12754.5 + 22091.4i 0.814333 + 1.41047i
\(627\) −360.000 623.538i −0.0229298 0.0397157i
\(628\) −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
\(633\) 1875.00 + 3247.60i 0.117732 + 0.203918i
\(634\) −3865.50 6695.24i −0.242143 0.419404i
\(635\) −565.500 + 979.475i −0.0353404 + 0.0612114i
\(636\) −1089.00 −0.0678957
\(637\) 0 0
\(638\) −13365.0 −0.829350
\(639\) 1539.00 2665.63i 0.0952768 0.165024i
\(640\) 2488.50 + 4310.21i 0.153698 + 0.266212i
\(641\) −4137.00 7165.49i −0.254917 0.441529i 0.709956 0.704246i \(-0.248715\pi\)
−0.964873 + 0.262717i \(0.915381\pi\)
\(642\) 6088.50 10545.6i 0.374290 0.648289i
\(643\) −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
\(646\) −2016.00 + 3491.81i −0.122784 + 0.212668i
\(647\) −8733.00 15126.0i −0.530649 0.919110i −0.999360 0.0357592i \(-0.988615\pi\)
0.468712 0.883351i \(-0.344718\pi\)
\(648\) −850.500 1473.11i −0.0515599 0.0893043i
\(649\) 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 \(-0.853921\pi\)
0.831898 + 0.554928i \(0.187254\pi\)
\(654\) 1665.00 + 2883.86i 0.0995515 + 0.172428i
\(655\) −976.500 1691.35i −0.0582519 0.100895i
\(656\) −12780.0 + 22135.6i −0.760633 + 1.31745i
\(657\) −3258.00 −0.193465
\(658\) 0 0
\(659\) 19944.0 1.17892 0.589460 0.807798i \(-0.299341\pi\)
0.589460 + 0.807798i \(0.299341\pi\)
\(660\) −67.5000 + 116.913i −0.00398096 + 0.00689523i
\(661\) 13753.0 + 23820.9i 0.809273 + 1.40170i 0.913368 + 0.407135i \(0.133472\pi\)
−0.104095 + 0.994567i \(0.533194\pi\)
\(662\) −726.000 1257.47i −0.0426236 0.0738262i
\(663\) −8064.00 + 13967.3i −0.472368 + 0.818165i
\(664\) −10017.0 −0.585444
\(665\) 0 0
\(666\) 8532.00 0.496409
\(667\) −12474.0 + 21605.6i −0.724131 + 1.25423i
\(668\) −1323.00 2291.50i −0.0766294 0.132726i
\(669\) −637.500 1104.18i −0.0368418 0.0638119i
\(670\) −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
\(675\) −1566.00 2712.39i −0.0892968 0.154667i
\(676\) −949.500 1644.58i −0.0540225 0.0935698i
\(677\) 6928.50 12000.5i 0.393329 0.681266i −0.599557 0.800332i \(-0.704657\pi\)
0.992886 + 0.119066i \(0.0379899\pi\)
\(678\) −5832.00 −0.330349
\(679\) 0 0
\(680\) −5292.00 −0.298440
\(681\) −5782.50 + 10015.6i −0.325383 + 0.563580i
\(682\) −5692.50 9859.70i −0.319615 0.553589i
\(683\) 11122.5 + 19264.7i 0.623120 + 1.07927i 0.988901 + 0.148574i \(0.0474683\pi\)
−0.365782 + 0.930701i \(0.619198\pi\)
\(684\) −72.0000 + 124.708i −0.00402484 + 0.00697122i
\(685\) −5310.00 −0.296182
\(686\) 0 0
\(687\) −6564.00 −0.364530
\(688\) 923.000 1598.68i 0.0511469 0.0885890i
\(689\) −11616.0 20119.5i −0.642285 1.11247i
\(690\) 1134.00 + 1964.15i 0.0625661 + 0.108368i
\(691\) −320.000 + 554.256i −0.0176170 + 0.0305136i −0.874700 0.484666i \(-0.838941\pi\)
0.857082 + 0.515179i \(0.172275\pi\)
\(692\) 786.000 0.0431781
\(693\) 0 0
\(694\) 5580.00 0.305207
\(695\) −2337.00 + 4047.80i −0.127550 + 0.220924i
\(696\) −9355.50 16204.2i −0.509511 0.882498i
\(697\) −15120.0 26188.6i −0.821680 1.42319i
\(698\) 2877.00 4983.11i 0.156012 0.270220i
\(699\) −2556.00 −0.138307
\(700\) 0 0
\(701\) −15561.0 −0.838418 −0.419209 0.907890i \(-0.637693\pi\)
−0.419209 + 0.907890i \(0.637693\pi\)
\(702\) −2592.00 + 4489.48i −0.139357 + 0.241374i
\(703\) 2528.00 + 4378.62i 0.135626 + 0.234912i
\(704\) 3247.50 + 5624.83i 0.173856 + 0.301128i
\(705\) 135.000 233.827i 0.00721191 0.0124914i
\(706\) −9144.00 −0.487449
\(707\) 0 0
\(708\) −45.0000 −0.00238871
\(709\) −2767.00 + 4792.58i −0.146568 + 0.253864i −0.929957 0.367668i \(-0.880156\pi\)
0.783389 + 0.621532i \(0.213489\pi\)
\(710\) −1539.00 2665.63i −0.0813488 0.140900i
\(711\) −2101.50 3639.90i −0.110847 0.191993i
\(712\) 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
\(717\) 8262.00 + 14310.2i 0.430335 + 0.745362i
\(718\) −45.0000 77.9423i −0.00233898 0.00405123i
\(719\) −10923.0 + 18919.2i −0.566564 + 0.981317i 0.430339 + 0.902667i \(0.358394\pi\)
−0.996902 + 0.0786494i \(0.974939\pi\)
\(720\) −1917.00 −0.0992255
\(721\) 0 0
\(722\) 19809.0 1.02107
\(723\) −1186.50 + 2055.08i −0.0610324 + 0.105711i
\(724\) 676.000 + 1170.87i 0.0347007 + 0.0601035i
\(725\) −17226.0 29836.3i −0.882424 1.52840i
\(726\) 4977.00 8620.42i 0.254427 0.440680i
\(727\) 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
\(730\) −1629.00 + 2821.51i −0.0825918 + 0.143053i
\(731\) 1092.00 + 1891.40i 0.0552518 + 0.0956990i
\(732\) 177.000 + 306.573i 0.00893731 + 0.0154799i
\(733\) 5881.00 10186.2i 0.296343 0.513282i −0.678953 0.734182i \(-0.737566\pi\)
0.975296 + 0.220900i \(0.0708994\pi\)
\(734\) −33933.0 −1.70639
\(735\) 0 0
\(736\) −3780.00 −0.189311
\(737\) −2775.00 + 4806.44i −0.138695 + 0.240227i
\(738\) −4860.00 8417.77i −0.242411 0.419868i
\(739\) 11363.0 + 19681.3i 0.565622 + 0.979686i 0.996992 + 0.0775108i \(0.0246972\pi\)
−0.431369 + 0.902175i \(0.641969\pi\)
\(740\) 474.000 820.992i 0.0235467 0.0407841i
\(741\) −3072.00 −0.152298
\(742\) 0 0
\(743\) 6678.00 0.329734 0.164867 0.986316i \(-0.447281\pi\)
0.164867 + 0.986316i \(0.447281\pi\)
\(744\) 7969.50 13803.6i 0.392710 0.680193i
\(745\) −3681.00 6375.68i −0.181022 0.313539i
\(746\) 1812.00 + 3138.48i 0.0889303 + 0.154032i
\(747\) 2146.50 3717.85i 0.105136 0.182100i
\(748\) 1260.00 0.0615911
\(749\) 0 0
\(750\) −6507.00 −0.316803
\(751\) 9993.50 17309.2i 0.485577 0.841043i −0.514286 0.857619i \(-0.671943\pi\)
0.999863 + 0.0165754i \(0.00527637\pi\)
\(752\) 1065.00 + 1844.63i 0.0516444 + 0.0894506i
\(753\) −7897.50 13678.9i −0.382206 0.662000i
\(754\) −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
\(759\) 1890.00 + 3273.58i 0.0903856 + 0.156552i
\(760\) −504.000 872.954i −0.0240553 0.0416649i
\(761\) −5748.00 + 9955.83i −0.273804 + 0.474242i −0.969833 0.243772i \(-0.921615\pi\)
0.696029 + 0.718014i \(0.254949\pi\)
\(762\) 3393.00 0.161306
\(763\) 0 0
\(764\) 3912.00 0.185250
\(765\) 1134.00 1964.15i 0.0535946 0.0928285i
\(766\) −19125.0 33125.5i −0.902107 1.56250i
\(767\) −480.000 831.384i −0.0225969 0.0391389i
\(768\) 2269.50 3930.89i 0.106632 0.184692i
\(769\) −2765.00 −0.129660 −0.0648299 0.997896i \(-0.520650\pi\)
−0.0648299 + 0.997896i \(0.520650\pi\)
\(770\) 0 0
\(771\) −20610.0 −0.962712
\(772\) −746.500 + 1292.98i −0.0348020 + 0.0602788i
\(773\) −7023.00 12164.2i −0.326778 0.565997i 0.655092 0.755549i \(-0.272630\pi\)
−0.981871 + 0.189552i \(0.939296\pi\)
\(774\) 351.000 + 607.950i 0.0163003 + 0.0282330i
\(775\) 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