Properties

Label 147.4.e.j.67.1
Level $147$
Weight $4$
Character 147.67
Analytic conductor $8.673$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.j.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20711 - 2.09077i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.08579 - 1.88064i) q^{4} +(9.94975 + 17.2335i) q^{5} +7.24264 q^{6} -24.5563 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.20711 - 2.09077i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.08579 - 1.88064i) q^{4} +(9.94975 + 17.2335i) q^{5} +7.24264 q^{6} -24.5563 q^{8} +(-4.50000 - 7.79423i) q^{9} +(24.0208 - 41.6053i) q^{10} +(-11.9706 + 20.7336i) q^{11} +(3.25736 + 5.64191i) q^{12} -87.3553 q^{13} -59.6985 q^{15} +(20.9558 + 36.2966i) q^{16} +(-2.81981 + 4.88405i) q^{17} +(-10.8640 + 18.8169i) q^{18} +(32.4437 + 56.1941i) q^{19} +43.2132 q^{20} +57.7990 q^{22} +(12.7990 + 22.1685i) q^{23} +(36.8345 - 63.7993i) q^{24} +(-135.495 + 234.684i) q^{25} +(105.447 + 182.640i) q^{26} +27.0000 q^{27} +60.3188 q^{29} +(72.0624 + 124.816i) q^{30} +(-61.3553 + 106.271i) q^{31} +(-47.6335 + 82.5037i) q^{32} +(-35.9117 - 62.2009i) q^{33} +13.6152 q^{34} -19.5442 q^{36} +(28.0589 + 48.5994i) q^{37} +(78.3259 - 135.664i) q^{38} +(131.033 - 226.956i) q^{39} +(-244.329 - 423.191i) q^{40} +299.713 q^{41} -501.421 q^{43} +(25.9949 + 45.0246i) q^{44} +(89.5477 - 155.101i) q^{45} +(30.8995 - 53.5195i) q^{46} +(152.777 + 264.617i) q^{47} -125.735 q^{48} +654.227 q^{50} +(-8.45942 - 14.6521i) q^{51} +(-94.8492 + 164.284i) q^{52} +(187.558 - 324.861i) q^{53} +(-32.5919 - 56.4508i) q^{54} -476.416 q^{55} -194.662 q^{57} +(-72.8112 - 126.113i) q^{58} +(-313.806 + 543.528i) q^{59} +(-64.8198 + 112.271i) q^{60} +(1.87868 + 3.25397i) q^{61} +296.250 q^{62} +565.288 q^{64} +(-869.164 - 1505.44i) q^{65} +(-86.6985 + 150.166i) q^{66} +(406.524 - 704.120i) q^{67} +(6.12341 + 10.6061i) q^{68} -76.7939 q^{69} +165.902 q^{71} +(110.504 + 191.398i) q^{72} +(309.550 - 536.156i) q^{73} +(67.7401 - 117.329i) q^{74} +(-406.485 - 704.052i) q^{75} +140.908 q^{76} -632.683 q^{78} +(69.1228 + 119.724i) q^{79} +(-417.011 + 722.284i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-361.785 - 626.631i) q^{82} -621.137 q^{83} -112.225 q^{85} +(605.269 + 1048.36i) q^{86} +(-90.4781 + 156.713i) q^{87} +(293.953 - 509.142i) q^{88} +(142.709 + 247.180i) q^{89} -432.375 q^{90} +55.5879 q^{92} +(-184.066 - 318.812i) q^{93} +(368.836 - 638.842i) q^{94} +(-645.612 + 1118.23i) q^{95} +(-142.901 - 247.511i) q^{96} +603.114 q^{97} +215.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 6q^{3} + 10q^{4} + 20q^{5} + 12q^{6} - 36q^{8} - 18q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 6q^{3} + 10q^{4} + 20q^{5} + 12q^{6} - 36q^{8} - 18q^{9} + 48q^{10} + 20q^{11} + 30q^{12} - 208q^{13} - 120q^{15} - 18q^{16} + 116q^{17} - 18q^{18} + 192q^{19} + 88q^{20} + 152q^{22} - 28q^{23} + 54q^{24} - 146q^{25} + 204q^{26} + 108q^{27} + 592q^{29} + 144q^{30} - 104q^{31} - 18q^{32} + 60q^{33} + 128q^{34} - 180q^{36} + 248q^{37} + 104q^{38} + 312q^{39} - 488q^{40} - 40q^{41} - 1440q^{43} - 292q^{44} + 180q^{45} + 84q^{46} - 96q^{47} + 108q^{48} + 1412q^{50} + 348q^{51} - 320q^{52} - 268q^{53} - 54q^{54} - 944q^{55} - 1152q^{57} - 48q^{58} - 616q^{59} - 132q^{60} + 16q^{61} + 608q^{62} + 236q^{64} - 1740q^{65} - 228q^{66} + 144q^{67} - 940q^{68} + 168q^{69} + 1976q^{71} + 162q^{72} + 104q^{73} + 56q^{74} - 438q^{75} + 2272q^{76} - 1224q^{78} + 944q^{79} - 828q^{80} - 162q^{81} - 856q^{82} - 2032q^{83} - 200q^{85} + 1120q^{86} - 888q^{87} + 876q^{88} - 388q^{89} - 864q^{90} - 728q^{92} - 312q^{93} + 904q^{94} - 1304q^{95} - 54q^{96} - 976q^{97} - 360q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20711 2.09077i −0.426777 0.739199i 0.569808 0.821778i \(-0.307018\pi\)
−0.996585 + 0.0825791i \(0.973684\pi\)
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 1.08579 1.88064i 0.135723 0.235080i
\(5\) 9.94975 + 17.2335i 0.889932 + 1.54141i 0.839954 + 0.542658i \(0.182582\pi\)
0.0499787 + 0.998750i \(0.484085\pi\)
\(6\) 7.24264 0.492799
\(7\) 0 0
\(8\) −24.5563 −1.08525
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 24.0208 41.6053i 0.759605 1.31567i
\(11\) −11.9706 + 20.7336i −0.328115 + 0.568311i −0.982138 0.188163i \(-0.939747\pi\)
0.654023 + 0.756475i \(0.273080\pi\)
\(12\) 3.25736 + 5.64191i 0.0783599 + 0.135723i
\(13\) −87.3553 −1.86369 −0.931847 0.362852i \(-0.881803\pi\)
−0.931847 + 0.362852i \(0.881803\pi\)
\(14\) 0 0
\(15\) −59.6985 −1.02761
\(16\) 20.9558 + 36.2966i 0.327435 + 0.567134i
\(17\) −2.81981 + 4.88405i −0.0402296 + 0.0696797i −0.885439 0.464755i \(-0.846142\pi\)
0.845210 + 0.534435i \(0.179476\pi\)
\(18\) −10.8640 + 18.8169i −0.142259 + 0.246400i
\(19\) 32.4437 + 56.1941i 0.391741 + 0.678516i 0.992679 0.120780i \(-0.0385395\pi\)
−0.600938 + 0.799296i \(0.705206\pi\)
\(20\) 43.2132 0.483138
\(21\) 0 0
\(22\) 57.7990 0.560127
\(23\) 12.7990 + 22.1685i 0.116034 + 0.200976i 0.918192 0.396135i \(-0.129649\pi\)
−0.802159 + 0.597111i \(0.796315\pi\)
\(24\) 36.8345 63.7993i 0.313284 0.542624i
\(25\) −135.495 + 234.684i −1.08396 + 1.87747i
\(26\) 105.447 + 182.640i 0.795381 + 1.37764i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 60.3188 0.386238 0.193119 0.981175i \(-0.438140\pi\)
0.193119 + 0.981175i \(0.438140\pi\)
\(30\) 72.0624 + 124.816i 0.438558 + 0.759605i
\(31\) −61.3553 + 106.271i −0.355476 + 0.615702i −0.987199 0.159492i \(-0.949014\pi\)
0.631724 + 0.775194i \(0.282348\pi\)
\(32\) −47.6335 + 82.5037i −0.263140 + 0.455773i
\(33\) −35.9117 62.2009i −0.189437 0.328115i
\(34\) 13.6152 0.0686762
\(35\) 0 0
\(36\) −19.5442 −0.0904822
\(37\) 28.0589 + 48.5994i 0.124672 + 0.215938i 0.921605 0.388130i \(-0.126879\pi\)
−0.796933 + 0.604068i \(0.793546\pi\)
\(38\) 78.3259 135.664i 0.334372 0.579149i
\(39\) 131.033 226.956i 0.538002 0.931847i
\(40\) −244.329 423.191i −0.965797 1.67281i
\(41\) 299.713 1.14164 0.570820 0.821075i \(-0.306625\pi\)
0.570820 + 0.821075i \(0.306625\pi\)
\(42\) 0 0
\(43\) −501.421 −1.77828 −0.889140 0.457635i \(-0.848697\pi\)
−0.889140 + 0.457635i \(0.848697\pi\)
\(44\) 25.9949 + 45.0246i 0.0890656 + 0.154266i
\(45\) 89.5477 155.101i 0.296644 0.513803i
\(46\) 30.8995 53.5195i 0.0990409 0.171544i
\(47\) 152.777 + 264.617i 0.474144 + 0.821242i 0.999562 0.0296028i \(-0.00942425\pi\)
−0.525418 + 0.850844i \(0.676091\pi\)
\(48\) −125.735 −0.378089
\(49\) 0 0
\(50\) 654.227 1.85043
\(51\) −8.45942 14.6521i −0.0232266 0.0402296i
\(52\) −94.8492 + 164.284i −0.252947 + 0.438116i
\(53\) 187.558 324.861i 0.486097 0.841944i −0.513775 0.857925i \(-0.671754\pi\)
0.999872 + 0.0159802i \(0.00508689\pi\)
\(54\) −32.5919 56.4508i −0.0821332 0.142259i
\(55\) −476.416 −1.16800
\(56\) 0 0
\(57\) −194.662 −0.452344
\(58\) −72.8112 126.113i −0.164838 0.285507i
\(59\) −313.806 + 543.528i −0.692442 + 1.19934i 0.278593 + 0.960409i \(0.410132\pi\)
−0.971035 + 0.238936i \(0.923202\pi\)
\(60\) −64.8198 + 112.271i −0.139470 + 0.241569i
\(61\) 1.87868 + 3.25397i 0.00394328 + 0.00682997i 0.867990 0.496581i \(-0.165411\pi\)
−0.864047 + 0.503411i \(0.832078\pi\)
\(62\) 296.250 0.606835
\(63\) 0 0
\(64\) 565.288 1.10408
\(65\) −869.164 1505.44i −1.65856 2.87271i
\(66\) −86.6985 + 150.166i −0.161695 + 0.280063i
\(67\) 406.524 704.120i 0.741266 1.28391i −0.210653 0.977561i \(-0.567559\pi\)
0.951919 0.306349i \(-0.0991075\pi\)
\(68\) 6.12341 + 10.6061i 0.0109202 + 0.0189143i
\(69\) −76.7939 −0.133984
\(70\) 0 0
\(71\) 165.902 0.277310 0.138655 0.990341i \(-0.455722\pi\)
0.138655 + 0.990341i \(0.455722\pi\)
\(72\) 110.504 + 191.398i 0.180875 + 0.313284i
\(73\) 309.550 536.156i 0.496302 0.859621i −0.503689 0.863885i \(-0.668024\pi\)
0.999991 + 0.00426452i \(0.00135744\pi\)
\(74\) 67.7401 117.329i 0.106414 0.184314i
\(75\) −406.485 704.052i −0.625824 1.08396i
\(76\) 140.908 0.212674
\(77\) 0 0
\(78\) −632.683 −0.918427
\(79\) 69.1228 + 119.724i 0.0984421 + 0.170507i 0.911040 0.412318i \(-0.135281\pi\)
−0.812598 + 0.582825i \(0.801947\pi\)
\(80\) −417.011 + 722.284i −0.582790 + 1.00942i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −361.785 626.631i −0.487226 0.843900i
\(83\) −621.137 −0.821430 −0.410715 0.911764i \(-0.634721\pi\)
−0.410715 + 0.911764i \(0.634721\pi\)
\(84\) 0 0
\(85\) −112.225 −0.143207
\(86\) 605.269 + 1048.36i 0.758928 + 1.31450i
\(87\) −90.4781 + 156.713i −0.111497 + 0.193119i
\(88\) 293.953 509.142i 0.356086 0.616758i
\(89\) 142.709 + 247.180i 0.169968 + 0.294393i 0.938408 0.345528i \(-0.112300\pi\)
−0.768440 + 0.639921i \(0.778967\pi\)
\(90\) −432.375 −0.506403
\(91\) 0 0
\(92\) 55.5879 0.0629939
\(93\) −184.066 318.812i −0.205234 0.355476i
\(94\) 368.836 638.842i 0.404707 0.700974i
\(95\) −645.612 + 1118.23i −0.697247 + 1.20767i
\(96\) −142.901 247.511i −0.151924 0.263140i
\(97\) 603.114 0.631309 0.315654 0.948874i \(-0.397776\pi\)
0.315654 + 0.948874i \(0.397776\pi\)
\(98\) 0 0
\(99\) 215.470 0.218743
\(100\) 294.237 + 509.634i 0.294237 + 0.509634i
\(101\) 228.605 395.955i 0.225218 0.390089i −0.731167 0.682199i \(-0.761024\pi\)
0.956385 + 0.292110i \(0.0943573\pi\)
\(102\) −20.4228 + 35.3734i −0.0198251 + 0.0343381i
\(103\) 393.022 + 680.735i 0.375977 + 0.651211i 0.990473 0.137709i \(-0.0439738\pi\)
−0.614496 + 0.788920i \(0.710640\pi\)
\(104\) 2145.13 2.02257
\(105\) 0 0
\(106\) −905.612 −0.829819
\(107\) 98.2304 + 170.140i 0.0887504 + 0.153720i 0.906983 0.421167i \(-0.138379\pi\)
−0.818233 + 0.574887i \(0.805046\pi\)
\(108\) 29.3162 50.7772i 0.0261200 0.0452411i
\(109\) 153.172 265.301i 0.134598 0.233130i −0.790846 0.612015i \(-0.790359\pi\)
0.925444 + 0.378885i \(0.123692\pi\)
\(110\) 575.085 + 996.077i 0.498475 + 0.863384i
\(111\) −168.353 −0.143958
\(112\) 0 0
\(113\) 1997.63 1.66302 0.831508 0.555512i \(-0.187478\pi\)
0.831508 + 0.555512i \(0.187478\pi\)
\(114\) 234.978 + 406.993i 0.193050 + 0.334372i
\(115\) −254.693 + 441.142i −0.206524 + 0.357710i
\(116\) 65.4933 113.438i 0.0524215 0.0907968i
\(117\) 393.099 + 680.867i 0.310616 + 0.538002i
\(118\) 1515.19 1.18207
\(119\) 0 0
\(120\) 1465.98 1.11521
\(121\) 378.911 + 656.294i 0.284682 + 0.493083i
\(122\) 4.53553 7.85578i 0.00336580 0.00582974i
\(123\) −449.569 + 778.677i −0.329563 + 0.570820i
\(124\) 133.238 + 230.774i 0.0964927 + 0.167130i
\(125\) −2905.13 −2.07874
\(126\) 0 0
\(127\) −2311.40 −1.61499 −0.807494 0.589875i \(-0.799177\pi\)
−0.807494 + 0.589875i \(0.799177\pi\)
\(128\) −301.295 521.859i −0.208055 0.360361i
\(129\) 752.132 1302.73i 0.513345 0.889140i
\(130\) −2098.35 + 3634.44i −1.41567 + 2.45201i
\(131\) −77.5088 134.249i −0.0516945 0.0895374i 0.839020 0.544100i \(-0.183129\pi\)
−0.890715 + 0.454563i \(0.849796\pi\)
\(132\) −155.970 −0.102844
\(133\) 0 0
\(134\) −1962.87 −1.26542
\(135\) 268.643 + 465.304i 0.171268 + 0.296644i
\(136\) 69.2441 119.934i 0.0436591 0.0756197i
\(137\) −258.468 + 447.680i −0.161186 + 0.279181i −0.935294 0.353871i \(-0.884865\pi\)
0.774109 + 0.633053i \(0.218198\pi\)
\(138\) 92.6985 + 160.558i 0.0571813 + 0.0990409i
\(139\) −958.067 −0.584620 −0.292310 0.956324i \(-0.594424\pi\)
−0.292310 + 0.956324i \(0.594424\pi\)
\(140\) 0 0
\(141\) −916.660 −0.547494
\(142\) −200.262 346.864i −0.118349 0.204987i
\(143\) 1045.69 1811.19i 0.611505 1.05916i
\(144\) 188.603 326.669i 0.109145 0.189045i
\(145\) 600.156 + 1039.50i 0.343726 + 0.595351i
\(146\) −1494.64 −0.847241
\(147\) 0 0
\(148\) 121.864 0.0676834
\(149\) 885.313 + 1533.41i 0.486763 + 0.843098i 0.999884 0.0152182i \(-0.00484428\pi\)
−0.513121 + 0.858316i \(0.671511\pi\)
\(150\) −981.341 + 1699.73i −0.534175 + 0.925217i
\(151\) 1270.12 2199.91i 0.684508 1.18560i −0.289083 0.957304i \(-0.593350\pi\)
0.973591 0.228299i \(-0.0733163\pi\)
\(152\) −796.698 1379.92i −0.425136 0.736358i
\(153\) 50.7565 0.0268197
\(154\) 0 0
\(155\) −2441.88 −1.26540
\(156\) −284.548 492.851i −0.146039 0.252947i
\(157\) −541.672 + 938.203i −0.275351 + 0.476922i −0.970224 0.242211i \(-0.922127\pi\)
0.694873 + 0.719133i \(0.255461\pi\)
\(158\) 166.877 289.040i 0.0840256 0.145537i
\(159\) 562.675 + 974.582i 0.280648 + 0.486097i
\(160\) −1895.77 −0.936709
\(161\) 0 0
\(162\) 195.551 0.0948393
\(163\) −1484.36 2570.99i −0.713277 1.23543i −0.963620 0.267275i \(-0.913877\pi\)
0.250343 0.968157i \(-0.419457\pi\)
\(164\) 325.424 563.651i 0.154947 0.268377i
\(165\) 714.624 1237.77i 0.337172 0.584000i
\(166\) 749.779 + 1298.65i 0.350567 + 0.607200i
\(167\) 2091.53 0.969149 0.484574 0.874750i \(-0.338975\pi\)
0.484574 + 0.874750i \(0.338975\pi\)
\(168\) 0 0
\(169\) 5433.96 2.47335
\(170\) 135.468 + 234.638i 0.0611172 + 0.105858i
\(171\) 291.993 505.746i 0.130580 0.226172i
\(172\) −544.437 + 942.992i −0.241354 + 0.418037i
\(173\) −235.074 407.160i −0.103308 0.178935i 0.809738 0.586792i \(-0.199609\pi\)
−0.913046 + 0.407857i \(0.866276\pi\)
\(174\) 436.867 0.190338
\(175\) 0 0
\(176\) −1003.41 −0.429745
\(177\) −941.418 1630.58i −0.399782 0.692442i
\(178\) 344.530 596.744i 0.145077 0.251280i
\(179\) −528.230 + 914.922i −0.220569 + 0.382036i −0.954981 0.296668i \(-0.904125\pi\)
0.734412 + 0.678704i \(0.237458\pi\)
\(180\) −194.459 336.814i −0.0805231 0.139470i
\(181\) 406.470 0.166921 0.0834605 0.996511i \(-0.473403\pi\)
0.0834605 + 0.996511i \(0.473403\pi\)
\(182\) 0 0
\(183\) −11.2721 −0.00455331
\(184\) −314.296 544.377i −0.125925 0.218109i
\(185\) −558.357 + 967.103i −0.221899 + 0.384340i
\(186\) −444.375 + 769.680i −0.175178 + 0.303417i
\(187\) −67.5093 116.930i −0.0263998 0.0457259i
\(188\) 663.531 0.257410
\(189\) 0 0
\(190\) 3117.29 1.19027
\(191\) −89.7048 155.373i −0.0339833 0.0588608i 0.848534 0.529142i \(-0.177486\pi\)
−0.882517 + 0.470281i \(0.844153\pi\)
\(192\) −847.933 + 1468.66i −0.318720 + 0.552040i
\(193\) 1194.18 2068.39i 0.445385 0.771429i −0.552694 0.833384i \(-0.686400\pi\)
0.998079 + 0.0619551i \(0.0197336\pi\)
\(194\) −728.023 1260.97i −0.269428 0.466663i
\(195\) 5214.98 1.91514
\(196\) 0 0
\(197\) −2665.35 −0.963952 −0.481976 0.876184i \(-0.660081\pi\)
−0.481976 + 0.876184i \(0.660081\pi\)
\(198\) −260.095 450.499i −0.0933544 0.161695i
\(199\) −671.153 + 1162.47i −0.239079 + 0.414098i −0.960450 0.278451i \(-0.910179\pi\)
0.721371 + 0.692549i \(0.243512\pi\)
\(200\) 3327.26 5762.99i 1.17636 2.03752i
\(201\) 1219.57 + 2112.36i 0.427970 + 0.741266i
\(202\) −1103.80 −0.384471
\(203\) 0 0
\(204\) −36.7405 −0.0126095
\(205\) 2982.07 + 5165.09i 1.01598 + 1.75973i
\(206\) 948.840 1643.44i 0.320916 0.555844i
\(207\) 115.191 199.517i 0.0386779 0.0669921i
\(208\) −1830.60 3170.70i −0.610239 1.05696i
\(209\) −1553.48 −0.514144
\(210\) 0 0
\(211\) 628.442 0.205042 0.102521 0.994731i \(-0.467309\pi\)
0.102521 + 0.994731i \(0.467309\pi\)
\(212\) −407.297 705.459i −0.131949 0.228543i
\(213\) −248.854 + 431.027i −0.0800525 + 0.138655i
\(214\) 237.149 410.755i 0.0757532 0.131208i
\(215\) −4989.02 8641.23i −1.58255 2.74106i
\(216\) −663.021 −0.208856
\(217\) 0 0
\(218\) −739.578 −0.229773
\(219\) 928.649 + 1608.47i 0.286540 + 0.496302i
\(220\) −517.286 + 895.966i −0.158525 + 0.274573i
\(221\) 246.325 426.647i 0.0749756 0.129862i
\(222\) 203.220 + 351.988i 0.0614381 + 0.106414i
\(223\) 969.970 0.291273 0.145637 0.989338i \(-0.453477\pi\)
0.145637 + 0.989338i \(0.453477\pi\)
\(224\) 0 0
\(225\) 2438.91 0.722640
\(226\) −2411.35 4176.58i −0.709737 1.22930i
\(227\) −2374.32 + 4112.44i −0.694225 + 1.20243i 0.276216 + 0.961096i \(0.410920\pi\)
−0.970441 + 0.241338i \(0.922414\pi\)
\(228\) −211.361 + 366.088i −0.0613936 + 0.106337i
\(229\) −2401.00 4158.65i −0.692848 1.20005i −0.970901 0.239482i \(-0.923022\pi\)
0.278052 0.960566i \(-0.410311\pi\)
\(230\) 1229.77 0.352559
\(231\) 0 0
\(232\) −1481.21 −0.419164
\(233\) 1577.64 + 2732.56i 0.443583 + 0.768309i 0.997952 0.0639623i \(-0.0203737\pi\)
−0.554369 + 0.832271i \(0.687040\pi\)
\(234\) 949.025 1643.76i 0.265127 0.459213i
\(235\) −3040.18 + 5265.74i −0.843912 + 1.46170i
\(236\) 681.453 + 1180.31i 0.187961 + 0.325558i
\(237\) −414.737 −0.113671
\(238\) 0 0
\(239\) 4241.93 1.14806 0.574032 0.818833i \(-0.305378\pi\)
0.574032 + 0.818833i \(0.305378\pi\)
\(240\) −1251.03 2166.85i −0.336474 0.582790i
\(241\) −2171.49 + 3761.14i −0.580407 + 1.00530i 0.415024 + 0.909811i \(0.363773\pi\)
−0.995431 + 0.0954844i \(0.969560\pi\)
\(242\) 914.773 1584.43i 0.242991 0.420873i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 8.15938 0.00214078
\(245\) 0 0
\(246\) 2170.71 0.562600
\(247\) −2834.13 4908.85i −0.730086 1.26455i
\(248\) 1506.66 2609.62i 0.385779 0.668189i
\(249\) 931.706 1613.76i 0.237126 0.410715i
\(250\) 3506.80 + 6073.95i 0.887157 + 1.53660i
\(251\) −3003.01 −0.755172 −0.377586 0.925974i \(-0.623246\pi\)
−0.377586 + 0.925974i \(0.623246\pi\)
\(252\) 0 0
\(253\) −612.844 −0.152289
\(254\) 2790.11 + 4832.61i 0.689239 + 1.19380i
\(255\) 168.338 291.570i 0.0413402 0.0716033i
\(256\) 1533.76 2656.55i 0.374454 0.648573i
\(257\) 2234.42 + 3870.13i 0.542332 + 0.939347i 0.998770 + 0.0495916i \(0.0157920\pi\)
−0.456437 + 0.889756i \(0.650875\pi\)
\(258\) −3631.61 −0.876335
\(259\) 0 0
\(260\) −3774.90 −0.900422
\(261\) −271.434 470.138i −0.0643731 0.111497i
\(262\) −187.123 + 324.106i −0.0441240 + 0.0764250i
\(263\) −3080.07 + 5334.83i −0.722148 + 1.25080i 0.237989 + 0.971268i \(0.423512\pi\)
−0.960137 + 0.279530i \(0.909821\pi\)
\(264\) 881.860 + 1527.43i 0.205586 + 0.356086i
\(265\) 7464.64 1.73037
\(266\) 0 0
\(267\) −856.255 −0.196262
\(268\) −882.796 1529.05i −0.201214 0.348513i
\(269\) 2494.45 4320.52i 0.565388 0.979281i −0.431625 0.902053i \(-0.642060\pi\)
0.997013 0.0772281i \(-0.0246070\pi\)
\(270\) 648.562 1123.34i 0.146186 0.253202i
\(271\) 2216.86 + 3839.72i 0.496918 + 0.860688i 0.999994 0.00355459i \(-0.00113146\pi\)
−0.503075 + 0.864243i \(0.667798\pi\)
\(272\) −236.366 −0.0526903
\(273\) 0 0
\(274\) 1247.99 0.275161
\(275\) −3243.90 5618.60i −0.711326 1.23205i
\(276\) −83.3818 + 144.422i −0.0181848 + 0.0314969i
\(277\) −556.184 + 963.339i −0.120642 + 0.208958i −0.920021 0.391869i \(-0.871829\pi\)
0.799379 + 0.600827i \(0.205162\pi\)
\(278\) 1156.49 + 2003.10i 0.249502 + 0.432151i
\(279\) 1104.40 0.236984
\(280\) 0 0
\(281\) 2813.22 0.597233 0.298616 0.954373i \(-0.403475\pi\)
0.298616 + 0.954373i \(0.403475\pi\)
\(282\) 1106.51 + 1916.53i 0.233658 + 0.404707i
\(283\) 1573.77 2725.85i 0.330569 0.572562i −0.652055 0.758172i \(-0.726093\pi\)
0.982623 + 0.185610i \(0.0594262\pi\)
\(284\) 180.135 312.002i 0.0376374 0.0651899i
\(285\) −1936.84 3354.70i −0.402555 0.697247i
\(286\) −5049.05 −1.04390
\(287\) 0 0
\(288\) 857.403 0.175427
\(289\) 2440.60 + 4227.24i 0.496763 + 0.860419i
\(290\) 1448.91 2509.58i 0.293389 0.508164i
\(291\) −904.671 + 1566.94i −0.182243 + 0.315654i
\(292\) −672.210 1164.30i −0.134720 0.233341i
\(293\) −9143.04 −1.82301 −0.911505 0.411289i \(-0.865079\pi\)
−0.911505 + 0.411289i \(0.865079\pi\)
\(294\) 0 0
\(295\) −12489.2 −2.46491
\(296\) −689.024 1193.42i −0.135300 0.234346i
\(297\) −323.205 + 559.808i −0.0631457 + 0.109372i
\(298\) 2137.33 3701.97i 0.415478 0.719629i
\(299\) −1118.06 1936.54i −0.216251 0.374558i
\(300\) −1765.42 −0.339756
\(301\) 0 0
\(302\) −6132.67 −1.16853
\(303\) 685.814 + 1187.86i 0.130030 + 0.225218i
\(304\) −1359.77 + 2355.19i −0.256540 + 0.444340i
\(305\) −37.3848 + 64.7523i −0.00701851 + 0.0121564i
\(306\) −61.2685 106.120i −0.0114460 0.0198251i
\(307\) 4648.90 0.864257 0.432129 0.901812i \(-0.357763\pi\)
0.432129 + 0.901812i \(0.357763\pi\)
\(308\) 0 0
\(309\) −2358.13 −0.434141
\(310\) 2947.61 + 5105.41i 0.540042 + 0.935380i
\(311\) −3208.59 + 5557.44i −0.585024 + 1.01329i 0.409849 + 0.912154i \(0.365582\pi\)
−0.994872 + 0.101138i \(0.967752\pi\)
\(312\) −3217.69 + 5573.21i −0.583865 + 1.01128i
\(313\) 2934.11 + 5082.02i 0.529858 + 0.917741i 0.999393 + 0.0348275i \(0.0110882\pi\)
−0.469535 + 0.882914i \(0.655578\pi\)
\(314\) 2615.42 0.470054
\(315\) 0 0
\(316\) 300.210 0.0534435
\(317\) 1987.26 + 3442.04i 0.352100 + 0.609855i 0.986617 0.163054i \(-0.0521344\pi\)
−0.634517 + 0.772909i \(0.718801\pi\)
\(318\) 1358.42 2352.85i 0.239548 0.414910i
\(319\) −722.049 + 1250.63i −0.126730 + 0.219504i
\(320\) 5624.48 + 9741.88i 0.982556 + 1.70184i
\(321\) −589.383 −0.102480
\(322\) 0 0
\(323\) −365.939 −0.0630384
\(324\) 87.9487 + 152.332i 0.0150804 + 0.0261200i
\(325\) 11836.2 20500.9i 2.02017 3.49903i
\(326\) −3583.57 + 6206.92i −0.608820 + 1.05451i
\(327\) 459.515 + 795.903i 0.0777102 + 0.134598i
\(328\) −7359.85 −1.23896
\(329\) 0 0
\(330\) −3450.51 −0.575589
\(331\) 4456.41 + 7718.73i 0.740020 + 1.28175i 0.952486 + 0.304583i \(0.0985172\pi\)
−0.212466 + 0.977168i \(0.568149\pi\)
\(332\) −674.422 + 1168.13i −0.111487 + 0.193101i
\(333\) 252.530 437.395i 0.0415572 0.0719792i
\(334\) −2524.71 4372.92i −0.413610 0.716394i
\(335\) 16179.2 2.63871
\(336\) 0 0
\(337\) 3977.06 0.642862 0.321431 0.946933i \(-0.395836\pi\)
0.321431 + 0.946933i \(0.395836\pi\)
\(338\) −6559.36 11361.2i −1.05557 1.82830i
\(339\) −2996.44 + 5189.99i −0.480072 + 0.831508i
\(340\) −121.853 + 211.055i −0.0194365 + 0.0336649i
\(341\) −1468.92 2544.24i −0.233273 0.404042i
\(342\) −1409.87 −0.222915
\(343\) 0 0
\(344\) 12313.1 1.92987
\(345\) −764.080 1323.43i −0.119237 0.206524i
\(346\) −567.518 + 982.971i −0.0881791 + 0.152731i
\(347\) −3413.21 + 5911.86i −0.528043 + 0.914597i 0.471423 + 0.881907i \(0.343741\pi\)
−0.999466 + 0.0326898i \(0.989593\pi\)
\(348\) 196.480 + 340.313i 0.0302656 + 0.0524215i
\(349\) 807.342 0.123828 0.0619141 0.998081i \(-0.480280\pi\)
0.0619141 + 0.998081i \(0.480280\pi\)
\(350\) 0 0
\(351\) −2358.59 −0.358668
\(352\) −1140.40 1975.23i −0.172680 0.299091i
\(353\) −3959.60 + 6858.23i −0.597020 + 1.03407i 0.396238 + 0.918148i \(0.370316\pi\)
−0.993258 + 0.115922i \(0.963018\pi\)
\(354\) −2272.79 + 3936.58i −0.341235 + 0.591036i
\(355\) 1650.69 + 2859.07i 0.246787 + 0.427448i
\(356\) 619.807 0.0922744
\(357\) 0 0
\(358\) 2550.52 0.376534
\(359\) 4409.61 + 7637.66i 0.648273 + 1.12284i 0.983535 + 0.180717i \(0.0578419\pi\)
−0.335262 + 0.942125i \(0.608825\pi\)
\(360\) −2198.97 + 3808.72i −0.321932 + 0.557603i
\(361\) 1324.32 2293.79i 0.193078 0.334420i
\(362\) −490.653 849.836i −0.0712380 0.123388i
\(363\) −2273.47 −0.328722
\(364\) 0 0
\(365\) 12319.8 1.76670
\(366\) 13.6066 + 23.5673i 0.00194325 + 0.00336580i
\(367\) −5580.89 + 9666.39i −0.793788 + 1.37488i 0.129817 + 0.991538i \(0.458561\pi\)
−0.923606 + 0.383344i \(0.874772\pi\)
\(368\) −536.427 + 929.119i −0.0759870 + 0.131613i
\(369\) −1348.71 2336.03i −0.190273 0.329563i
\(370\) 2695.99 0.378805
\(371\) 0 0
\(372\) −799.426 −0.111420
\(373\) −1363.93 2362.39i −0.189334 0.327936i 0.755694 0.654924i \(-0.227300\pi\)
−0.945028 + 0.326988i \(0.893966\pi\)
\(374\) −162.982 + 282.293i −0.0225337 + 0.0390295i
\(375\) 4357.69 7547.74i 0.600080 1.03937i
\(376\) −3751.64 6498.03i −0.514564 0.891250i
\(377\) −5269.17 −0.719830
\(378\) 0 0
\(379\) 4086.49 0.553849 0.276924 0.960892i \(-0.410685\pi\)
0.276924 + 0.960892i \(0.410685\pi\)
\(380\) 1401.99 + 2428.32i 0.189265 + 0.327817i
\(381\) 3467.10 6005.19i 0.466207 0.807494i
\(382\) −216.566 + 375.104i −0.0290066 + 0.0502408i
\(383\) 6516.47 + 11286.9i 0.869389 + 1.50583i 0.862622 + 0.505848i \(0.168820\pi\)
0.00676631 + 0.999977i \(0.497846\pi\)
\(384\) 1807.77 0.240241
\(385\) 0 0
\(386\) −5766.03 −0.760319
\(387\) 2256.40 + 3908.19i 0.296380 + 0.513345i
\(388\) 654.853 1134.24i 0.0856833 0.148408i
\(389\) 97.4957 168.868i 0.0127075 0.0220101i −0.859602 0.510965i \(-0.829288\pi\)
0.872309 + 0.488955i \(0.162622\pi\)
\(390\) −6295.04 10903.3i −0.817338 1.41567i
\(391\) −144.363 −0.0186719
\(392\) 0 0
\(393\) 465.053 0.0596916
\(394\) 3217.37 + 5572.64i 0.411392 + 0.712553i
\(395\) −1375.51 + 2382.45i −0.175214 + 0.303479i
\(396\) 233.955 405.221i 0.0296885 0.0514220i
\(397\) −7091.48 12282.8i −0.896501 1.55279i −0.831936 0.554872i \(-0.812767\pi\)
−0.0645653 0.997913i \(-0.520566\pi\)
\(398\) 3240.61 0.408134
\(399\) 0 0
\(400\) −11357.6 −1.41971
\(401\) −5002.52 8664.63i −0.622978 1.07903i −0.988928 0.148395i \(-0.952589\pi\)
0.365950 0.930634i \(-0.380744\pi\)
\(402\) 2944.31 5099.69i 0.365295 0.632710i
\(403\) 5359.72 9283.30i 0.662498 1.14748i
\(404\) −496.431 859.844i −0.0611346 0.105888i
\(405\) −1611.86 −0.197763
\(406\) 0 0
\(407\) −1343.52 −0.163626
\(408\) 207.732 + 359.803i 0.0252066 + 0.0436591i
\(409\) 2317.47 4013.97i 0.280174 0.485276i −0.691253 0.722613i \(-0.742941\pi\)
0.971428 + 0.237336i \(0.0762744\pi\)
\(410\) 7199.35 12469.6i 0.867196 1.50203i
\(411\) −775.404 1343.04i −0.0930605 0.161186i
\(412\) 1706.95 0.204115
\(413\) 0 0
\(414\) −556.191 −0.0660273
\(415\) −6180.16 10704.3i −0.731017 1.26616i
\(416\) 4161.04 7207.14i 0.490413 0.849420i
\(417\) 1437.10 2489.13i 0.168765 0.292310i
\(418\) 1875.21 + 3247.96i 0.219425 + 0.380055i
\(419\) −4998.31 −0.582777 −0.291388 0.956605i \(-0.594117\pi\)
−0.291388 + 0.956605i \(0.594117\pi\)
\(420\) 0 0
\(421\) −704.160 −0.0815170 −0.0407585 0.999169i \(-0.512977\pi\)
−0.0407585 + 0.999169i \(0.512977\pi\)
\(422\) −758.597 1313.93i −0.0875069 0.151566i
\(423\) 1374.99 2381.55i 0.158048 0.273747i
\(424\) −4605.75 + 7977.39i −0.527535 + 0.913718i
\(425\) −764.139 1323.53i −0.0872145 0.151060i
\(426\) 1201.57 0.136658
\(427\) 0 0
\(428\) 426.629 0.0481820
\(429\) 3137.08 + 5433.58i 0.353053 + 0.611505i
\(430\) −12044.5 + 20861.8i −1.35079 + 2.33964i
\(431\) 5166.39 8948.45i 0.577393 1.00007i −0.418384 0.908270i \(-0.637403\pi\)
0.995777 0.0918037i \(-0.0292632\pi\)
\(432\) 565.808 + 980.008i 0.0630149 + 0.109145i
\(433\) −11106.8 −1.23270 −0.616348 0.787474i \(-0.711389\pi\)
−0.616348 + 0.787474i \(0.711389\pi\)
\(434\) 0 0
\(435\) −3600.94 −0.396901
\(436\) −332.623 576.120i −0.0365362 0.0632825i
\(437\) −830.492 + 1438.45i −0.0909103 + 0.157461i
\(438\) 2241.96 3883.19i 0.244577 0.423620i
\(439\) −3649.64 6321.36i −0.396783 0.687249i 0.596544 0.802581i \(-0.296540\pi\)
−0.993327 + 0.115332i \(0.963207\pi\)
\(440\) 11699.0 1.26757
\(441\) 0 0
\(442\) −1189.36 −0.127991
\(443\) −8044.83 13934.1i −0.862802 1.49442i −0.869213 0.494438i \(-0.835374\pi\)
0.00641088 0.999979i \(-0.497959\pi\)
\(444\) −182.796 + 316.611i −0.0195385 + 0.0338417i
\(445\) −2839.84 + 4918.75i −0.302520 + 0.523980i
\(446\) −1170.86 2027.98i −0.124309 0.215309i
\(447\) −5311.88 −0.562065
\(448\) 0 0
\(449\) 13561.7 1.42543 0.712715 0.701454i \(-0.247466\pi\)
0.712715 + 0.701454i \(0.247466\pi\)
\(450\) −2944.02 5099.20i −0.308406 0.534175i
\(451\) −3587.73 + 6214.13i −0.374589 + 0.648807i
\(452\) 2169.00 3756.81i 0.225710 0.390941i
\(453\) 3810.35 + 6599.73i 0.395201 + 0.684508i
\(454\) 11464.2 1.18512
\(455\) 0 0
\(456\) 4780.19 0.490905
\(457\) −5424.28 9395.14i −0.555224 0.961676i −0.997886 0.0649876i \(-0.979299\pi\)
0.442662 0.896688i \(-0.354034\pi\)
\(458\) −5796.52 + 10039.9i −0.591383 + 1.02431i
\(459\) −76.1347 + 131.869i −0.00774219 + 0.0134099i
\(460\) 553.085 + 957.972i 0.0560603 + 0.0970993i
\(461\) 1758.69 0.177679 0.0888397 0.996046i \(-0.471684\pi\)
0.0888397 + 0.996046i \(0.471684\pi\)
\(462\) 0 0
\(463\) −5411.95 −0.543228 −0.271614 0.962406i \(-0.587557\pi\)
−0.271614 + 0.962406i \(0.587557\pi\)
\(464\) 1264.03 + 2189.37i 0.126468 + 0.219049i
\(465\) 3662.82 6344.19i 0.365289 0.632699i
\(466\) 3808.77 6596.98i 0.378622 0.655792i
\(467\) 4055.67 + 7024.63i 0.401872 + 0.696062i 0.993952 0.109817i \(-0.0350264\pi\)
−0.592080 + 0.805879i \(0.701693\pi\)
\(468\) 1707.29 0.168631
\(469\) 0 0
\(470\) 14679.3 1.44065
\(471\) −1625.02 2814.61i −0.158974 0.275351i
\(472\) 7705.93 13347.1i 0.751471 1.30159i
\(473\) 6002.30 10396.3i 0.583480 1.01062i
\(474\) 500.632 + 867.119i 0.0485122 + 0.0840256i
\(475\) −17583.8 −1.69853
\(476\) 0 0
\(477\) −3376.05 −0.324065
\(478\) −5120.46 8868.90i −0.489967 0.848648i
\(479\) 1047.88 1814.98i 0.0999559 0.173129i −0.811710 0.584060i \(-0.801463\pi\)
0.911666 + 0.410932i \(0.134797\pi\)
\(480\) 2843.65 4925.34i 0.270405 0.468355i
\(481\) −2451.09 4245.42i −0.232350 0.402441i
\(482\) 10484.9 0.990817
\(483\) 0 0
\(484\) 1645.67 0.154552
\(485\) 6000.83 + 10393.7i 0.561822 + 0.973104i
\(486\) −293.327 + 508.057i −0.0273777 + 0.0474196i
\(487\) −4805.04 + 8322.57i −0.447099 + 0.774398i −0.998196 0.0600435i \(-0.980876\pi\)
0.551097 + 0.834441i \(0.314209\pi\)
\(488\) −46.1335 79.9056i −0.00427944 0.00741221i
\(489\) 8906.17 0.823622
\(490\) 0 0
\(491\) −11717.3 −1.07698 −0.538488 0.842633i \(-0.681004\pi\)
−0.538488 + 0.842633i \(0.681004\pi\)
\(492\) 976.272 + 1690.95i 0.0894588 + 0.154947i
\(493\) −170.087 + 294.600i −0.0155382 + 0.0269130i
\(494\) −6842.19 + 11851.0i −0.623167 + 1.07936i
\(495\) 2143.87 + 3713.30i 0.194667 + 0.337172i
\(496\) −5143.01 −0.465581
\(497\) 0 0
\(498\) −4498.67 −0.404800
\(499\) 4597.59 + 7963.26i 0.412458 + 0.714398i 0.995158 0.0982893i \(-0.0313370\pi\)
−0.582700 + 0.812687i \(0.698004\pi\)
\(500\) −3154.35 + 5463.49i −0.282133 + 0.488669i
\(501\) −3137.30 + 5433.97i −0.279769 + 0.484574i
\(502\) 3624.95 + 6278.60i 0.322290 + 0.558222i
\(503\) −16118.8 −1.42883 −0.714414 0.699724i \(-0.753307\pi\)
−0.714414 + 0.699724i \(0.753307\pi\)
\(504\) 0 0
\(505\) 9098.23 0.801715
\(506\) 739.769 + 1281.32i 0.0649935 + 0.112572i
\(507\) −8150.93 + 14117.8i −0.713995 + 1.23668i
\(508\) −2509.69 + 4346.90i −0.219192 + 0.379651i
\(509\) 2459.39 + 4259.79i 0.214166 + 0.370947i 0.953014 0.302925i \(-0.0979632\pi\)
−0.738848 + 0.673872i \(0.764630\pi\)
\(510\) −812.808 −0.0705721
\(511\) 0 0
\(512\) −12226.4 −1.05534
\(513\) 875.979 + 1517.24i 0.0753906 + 0.130580i
\(514\) 5394.37 9343.33i 0.462910 0.801783i
\(515\) −7820.95 + 13546.3i −0.669188 + 1.15907i
\(516\) −1633.31 2828.98i −0.139346 0.241354i
\(517\) −7315.29 −0.622294
\(518\) 0 0
\(519\) 1410.44 0.119290
\(520\) 21343.5 + 36968.0i 1.79995 + 3.11760i
\(521\) 6981.69 12092.6i 0.587089 1.01687i −0.407522 0.913195i \(-0.633607\pi\)
0.994611 0.103673i \(-0.0330596\pi\)
\(522\) −655.301 + 1135.01i −0.0549458 + 0.0951690i
\(523\) −6877.63 11912.4i −0.575024 0.995972i −0.996039 0.0889177i \(-0.971659\pi\)
0.421015 0.907054i \(-0.361674\pi\)
\(524\) −336.632 −0.0280646
\(525\) 0 0
\(526\) 14871.9 1.23278
\(527\) −346.020 599.325i −0.0286013 0.0495389i
\(528\) 1505.12 2606.94i 0.124057 0.214872i
\(529\) 5755.87 9969.46i 0.473072 0.819385i
\(530\) −9010.61 15606.8i −0.738483 1.27909i
\(531\) 5648.51 0.461628
\(532\) 0 0
\(533\) −26181.5 −2.12767
\(534\) 1033.59 + 1790.23i 0.0837601 + 0.145077i
\(535\) −1954.74 + 3385.70i −0.157964 + 0.273601i
\(536\) −9982.74 + 17290.6i −0.804457 + 1.39336i
\(537\) −1584.69 2744.77i −0.127345 0.220569i
\(538\) −12044.3 −0.965178
\(539\) 0 0
\(540\) 1166.76 0.0929800
\(541\) −7231.34 12525.1i −0.574676 0.995368i −0.996077 0.0884937i \(-0.971795\pi\)
0.421401 0.906875i \(-0.361539\pi\)
\(542\) 5351.98 9269.91i 0.424146 0.734643i
\(543\) −609.706 + 1056.04i −0.0481860 + 0.0834605i
\(544\) −268.634 465.289i −0.0211721 0.0366711i
\(545\) 6096.07 0.479132
\(546\) 0 0
\(547\) 13682.5 1.06951 0.534755 0.845007i \(-0.320404\pi\)
0.534755 + 0.845007i \(0.320404\pi\)
\(548\) 561.282 + 972.169i 0.0437533 + 0.0757829i
\(549\) 16.9081 29.2857i 0.00131443 0.00227666i
\(550\) −7831.47 + 13564.5i −0.607155 + 1.05162i
\(551\) 1956.96 + 3389.56i 0.151306 + 0.262069i
\(552\) 1885.78 0.145406
\(553\) 0 0
\(554\) 2685.49 0.205949
\(555\) −1675.07 2901.31i −0.128113 0.221899i
\(556\) −1040.26 + 1801.78i −0.0793466 + 0.137432i
\(557\) 3831.56 6636.46i 0.291470 0.504840i −0.682688 0.730710i \(-0.739189\pi\)
0.974157 + 0.225870i \(0.0725225\pi\)
\(558\) −1333.12 2309.04i −0.101139 0.175178i
\(559\) 43801.8 3.31417
\(560\) 0 0
\(561\) 405.056 0.0304839
\(562\) −3395.85 5881.79i −0.254885 0.441474i
\(563\) 8735.24 15129.9i 0.653902 1.13259i −0.328266 0.944585i \(-0.606464\pi\)
0.982168 0.188006i \(-0.0602023\pi\)
\(564\) −995.297 + 1723.91i −0.0743078 + 0.128705i
\(565\) 19875.9 + 34426.0i 1.47997 + 2.56339i
\(566\) −7598.83 −0.564316
\(567\) 0 0
\(568\) −4073.96 −0.300950
\(569\) 6936.96 + 12015.2i 0.511094 + 0.885240i 0.999917 + 0.0128577i \(0.00409284\pi\)
−0.488824 + 0.872383i \(0.662574\pi\)
\(570\) −4675.94 + 8098.96i −0.343603 + 0.595137i
\(571\) 1888.76 3271.43i 0.138428 0.239764i −0.788474 0.615068i \(-0.789129\pi\)
0.926902 + 0.375305i \(0.122462\pi\)
\(572\) −2270.80 3933.14i −0.165991 0.287505i
\(573\) 538.229 0.0392405
\(574\) 0 0
\(575\) −6936.79 −0.503103
\(576\) −2543.80 4405.99i −0.184013 0.318720i
\(577\) 6940.23 12020.8i 0.500738 0.867303i −0.499262 0.866451i \(-0.666395\pi\)
1.00000 0.000852075i \(-0.000271224\pi\)
\(578\) 5892.12 10205.5i 0.424014 0.734414i
\(579\) 3582.55 + 6205.16i 0.257143 + 0.445385i
\(580\) 2606.57 0.186607
\(581\) 0 0
\(582\) 4368.14 0.311108
\(583\) 4490.36 + 7777.53i 0.318991 + 0.552509i
\(584\) −7601.41 + 13166.0i −0.538611 + 0.932901i
\(585\) −7822.47 + 13548.9i −0.552854 + 0.957571i
\(586\) 11036.6 + 19116.0i 0.778018 + 1.34757i
\(587\) 2395.61 0.168445 0.0842227 0.996447i \(-0.473159\pi\)
0.0842227 + 0.996447i \(0.473159\pi\)
\(588\) 0 0
\(589\) −7962.36 −0.557018
\(590\) 15075.8 + 26112.0i 1.05196 + 1.82206i
\(591\) 3998.03 6924.79i 0.278269 0.481976i
\(592\) −1175.99 + 2036.88i −0.0816437 + 0.141411i
\(593\) 3301.75 + 5718.80i 0.228645 + 0.396025i 0.957407 0.288742i \(-0.0932371\pi\)
−0.728762 + 0.684767i \(0.759904\pi\)
\(594\) 1560.57 0.107796
\(595\) 0 0
\(596\) 3845.04 0.264260
\(597\) −2013.46 3487.41i −0.138033 0.239079i
\(598\) −2699.24 + 4675.21i −0.184582 + 0.319705i
\(599\) −8626.05 + 14940.8i −0.588399 + 1.01914i 0.406044 + 0.913854i \(0.366908\pi\)
−0.994442 + 0.105283i \(0.966425\pi\)
\(600\) 9981.78 + 17289.0i 0.679174 + 1.17636i
\(601\) −12833.1 −0.871005 −0.435503 0.900187i \(-0.643429\pi\)
−0.435503 + 0.900187i \(0.643429\pi\)
\(602\) 0 0
\(603\) −7317.43 −0.494177
\(604\) −2758.15 4777.26i −0.185807 0.321828i
\(605\) −7540.14 + 13059.9i −0.506695 + 0.877621i
\(606\) 1655.70 2867.76i 0.110987 0.192235i
\(607\) 4310.08 + 7465.28i 0.288206 + 0.499187i 0.973381 0.229191i \(-0.0736080\pi\)
−0.685176 + 0.728378i \(0.740275\pi\)
\(608\) −6181.62 −0.412332
\(609\) 0 0
\(610\) 180.510 0.0119813
\(611\) −13345.9 23115.7i −0.883659 1.53054i
\(612\) 55.1107 95.4546i 0.00364006 0.00630477i
\(613\) −2568.37 + 4448.54i −0.169226 + 0.293107i −0.938148 0.346235i \(-0.887460\pi\)
0.768922 + 0.639342i \(0.220793\pi\)
\(614\) −5611.72 9719.79i −0.368845 0.638858i
\(615\) −17892.4 −1.17316
\(616\) 0 0
\(617\) −1759.82 −0.114826 −0.0574131 0.998351i \(-0.518285\pi\)
−0.0574131 + 0.998351i \(0.518285\pi\)
\(618\) 2846.52 + 4930.32i 0.185281 + 0.320916i
\(619\) −1780.12 + 3083.26i −0.115588 + 0.200205i −0.918015 0.396546i \(-0.870209\pi\)
0.802427 + 0.596751i \(0.203542\pi\)
\(620\) −2651.36 + 4592.29i −0.171744 + 0.297469i
\(621\) 345.573 + 598.550i 0.0223307 + 0.0386779i
\(622\) 15492.4 0.998698
\(623\) 0 0
\(624\) 10983.6 0.704643
\(625\) −11968.4 20729.9i −0.765977 1.32671i
\(626\) 7083.56 12269.1i 0.452262 0.783341i
\(627\) 2330.21 4036.05i 0.148421 0.257072i
\(628\) 1176.28 + 2037.38i 0.0747431 + 0.129459i
\(629\) −316.482 −0.0200620
\(630\) 0 0
\(631\) −27321.4 −1.72369 −0.861845 0.507172i \(-0.830691\pi\)
−0.861845 + 0.507172i \(0.830691\pi\)
\(632\) −1697.40 2939.99i −0.106834 0.185042i
\(633\) −942.664 + 1632.74i −0.0591904 + 0.102521i
\(634\) 4797.67 8309.81i 0.300536 0.520544i
\(635\) −22997.8 39833.4i −1.43723 2.48936i
\(636\) 2443.78 0.152362
\(637\) 0 0
\(638\) 3486.36 0.216342
\(639\) −746.561 1293.08i −0.0462183 0.0800525i
\(640\) 5995.63 10384.7i 0.370309 0.641395i
\(641\) 10963.5 18989.4i 0.675558 1.17010i −0.300748 0.953704i \(-0.597236\pi\)
0.976306 0.216397i \(-0.0694305\pi\)
\(642\) 711.448 + 1232.26i 0.0437361 + 0.0757532i
\(643\) 5826.04 0.357320 0.178660 0.983911i \(-0.442824\pi\)
0.178660 + 0.983911i \(0.442824\pi\)
\(644\) 0 0
\(645\) 29934.1 1.82737
\(646\) 441.728 + 765.095i 0.0269033 + 0.0465979i
\(647\) 12105.4 20967.1i 0.735565 1.27404i −0.218910 0.975745i \(-0.570250\pi\)
0.954475 0.298291i \(-0.0964166\pi\)
\(648\) 994.532 1722.58i 0.0602915 0.104428i
\(649\) −7512.87 13012.7i −0.454401 0.787045i
\(650\) −57150.3 −3.44864
\(651\) 0 0
\(652\) −6446.80 −0.387233
\(653\) 12811.7 + 22190.4i 0.767778 + 1.32983i 0.938765 + 0.344557i \(0.111971\pi\)
−0.170988 + 0.985273i \(0.554696\pi\)
\(654\) 1109.37 1921.48i 0.0663298 0.114887i
\(655\) 1542.39 2671.49i 0.0920092 0.159365i
\(656\) 6280.73 + 10878.6i 0.373813 + 0.647463i
\(657\) −5571.90 −0.330868
\(658\) 0 0
\(659\) −23273.7 −1.37574 −0.687871 0.725833i \(-0.741455\pi\)
−0.687871 + 0.725833i \(0.741455\pi\)
\(660\) −1551.86 2687.90i −0.0915243 0.158525i
\(661\) −10018.2 + 17352.1i −0.589508 + 1.02106i 0.404789 + 0.914410i \(0.367345\pi\)
−0.994297 + 0.106647i \(0.965988\pi\)
\(662\) 10758.7 18634.7i 0.631646 1.09404i
\(663\) 738.975 + 1279.94i 0.0432872 + 0.0749756i
\(664\) 15252.9 0.891454
\(665\) 0 0
\(666\) −1219.32 −0.0709426
\(667\) 772.019 + 1337.18i 0.0448166 + 0.0776247i
\(668\) 2270.96 3933.42i 0.131536 0.227827i
\(669\) −1454.95 + 2520.06i −0.0840834 + 0.145637i
\(670\) −19530.1 33827.1i −1.12614 1.95053i
\(671\) −89.9554 −0.00517540
\(672\) 0 0
\(673\) −18127.8 −1.03830 −0.519149 0.854684i \(-0.673751\pi\)
−0.519149 + 0.854684i \(0.673751\pi\)
\(674\) −4800.74 8315.12i −0.274358 0.475203i
\(675\) −3658.36 + 6336.47i −0.208608 + 0.361320i
\(676\) 5900.11 10219.3i 0.335692 0.581435i
\(677\) 6907.73 + 11964.5i 0.392150 + 0.679224i 0.992733 0.120339i \(-0.0383980\pi\)
−0.600583 + 0.799563i \(0.705065\pi\)
\(678\) 14468.1 0.819533
\(679\) 0 0
\(680\) 2755.85 0.155415
\(681\) −7122.96 12337.3i −0.400811 0.694225i
\(682\) −3546.28 + 6142.33i −0.199111 + 0.344871i
\(683\) 2302.11 3987.38i 0.128972 0.223386i −0.794306 0.607517i \(-0.792166\pi\)
0.923279 + 0.384131i \(0.125499\pi\)
\(684\) −634.084 1098.27i −0.0354456 0.0613936i
\(685\) −10286.8 −0.573777
\(686\) 0 0
\(687\) 14406.0 0.800032
\(688\) −10507.7 18199.9i −0.582271 1.00852i
\(689\) −16384.2 + 28378.3i −0.905935 + 1.56913i
\(690\) −1844.65 + 3195.03i −0.101775 + 0.176279i
\(691\) 8956.83 + 15513.7i 0.493103 + 0.854079i 0.999968 0.00794632i \(-0.00252942\pi\)
−0.506866 + 0.862025i \(0.669196\pi\)
\(692\) −1020.96 −0.0560854
\(693\) 0 0
\(694\) 16480.5 0.901426
\(695\) −9532.53 16510.8i −0.520272 0.901138i
\(696\) 2221.81 3848.29i 0.121002 0.209582i
\(697\) −845.132 + 1463.81i −0.0459278 + 0.0795492i
\(698\) −974.548 1687.97i −0.0528470 0.0915336i
\(699\) −9465.86 −0.512206
\(700\) 0 0
\(701\) 11303.7 0.609035 0.304518 0.952507i \(-0.401505\pi\)
0.304518 + 0.952507i \(0.401505\pi\)
\(702\) 2847.07 + 4931.28i 0.153071 + 0.265127i
\(703\) −1820.66 + 3153.48i −0.0976780 + 0.169183i
\(704\) −6766.82 + 11720.5i −0.362264 + 0.627460i
\(705\) −9120.54 15797.2i −0.487233 0.843912i
\(706\) 19118.6 1.01918
\(707\) 0 0
\(708\) −4088.72 −0.217039
\(709\) 8023.15 + 13896.5i 0.424987 + 0.736099i 0.996419 0.0845505i \(-0.0269454\pi\)
−0.571432 + 0.820649i \(0.693612\pi\)
\(710\) 3985.11 6902.42i 0.210646 0.364849i
\(711\) 622.105 1077.52i 0.0328140 0.0568355i
\(712\) −3504.42 6069.83i −0.184457 0.319489i
\(713\) −3141.15 −0.164989
\(714\) 0 0
\(715\) 41617.5 2.17679
\(716\) 1147.09 + 1986.82i 0.0598726 + 0.103702i
\(717\) −6362.89 + 11020.9i −0.331418 + 0.574032i
\(718\) 10645.7 18438.9i 0.553336 0.958406i
\(719\) −12595.2 21815.6i −0.653300 1.13155i −0.982317 0.187225i \(-0.940051\pi\)
0.329017 0.944324i \(-0.393283\pi\)
\(720\) 7506.19 0.388527
\(721\) 0 0
\(722\) −6394.38 −0.329604
\(723\) −6514.48 11283.4i −0.335098 0.580407i
\(724\) 441.340 764.424i 0.0226551 0.0392397i
\(725\) −8172.89 + 14155.9i −0.418667 + 0.725152i
\(726\) 2744.32 + 4753.30i 0.140291 + 0.242991i
\(727\) −11277.2 −0.575307 −0.287653 0.957735i \(-0.592875\pi\)
−0.287653 + 0.957735i \(0.592875\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −14871.3 25757.8i −0.753987 1.30594i
\(731\) 1413.91 2448.96i 0.0715395 0.123910i
\(732\) −12.2391 + 21.1987i −0.000617990 + 0.00107039i
\(733\) 11860.0 + 20542.2i 0.597626 + 1.03512i 0.993171 + 0.116672i \(0.0372226\pi\)
−0.395544 + 0.918447i \(0.629444\pi\)
\(734\) 26946.9 1.35508
\(735\) 0 0
\(736\) −2438.64 −0.122133
\(737\) 9732.64 + 16857.4i 0.486440 + 0.842539i
\(738\) −3256.07 + 5639.67i −0.162409 + 0.281300i
\(739\) −4062.36 + 7036.21i −0.202214 + 0.350245i −0.949242 0.314548i \(-0.898147\pi\)
0.747027 + 0.664793i \(0.231480\pi\)
\(740\) 1212.51 + 2100.14i 0.0602336 + 0.104328i
\(741\) 17004.8 0.843030
\(742\) 0 0
\(743\) 20955.3 1.03469 0.517346 0.855777i \(-0.326920\pi\)
0.517346 + 0.855777i \(0.326920\pi\)
\(744\) 4519.99 + 7828.85i 0.222730 + 0.385779i
\(745\) −17617.3 + 30514.0i −0.866372 + 1.50060i
\(746\) −3292.81 + 5703.32i −0.161607 + 0.279911i
\(747\) 2795.12 + 4841.28i 0.136905 + 0.237126i
\(748\) −293.203 −0.0143323
\(749\) 0 0
\(750\) −21040.8 −1.02440
\(751\) 19104.0 + 33089.2i 0.928251 + 1.60778i 0.786247 + 0.617912i \(0.212021\pi\)
0.142004 + 0.989866i \(0.454645\pi\)
\(752\) −6403.13 + 11090.5i −0.310503 + 0.537807i
\(753\) 4504.51 7802.04i 0.217999 0.377586i
\(754\) 6360.45 + 11016.6i 0.307207 + 0.532097i
\(755\) 50549.4 2.43666
\(756\) 0 0
\(757\) 30958.1 1.48638 0.743191 0.669079i \(-0.233311\pi\)
0.743191 + 0.669079i \(0.233311\pi\)
\(758\) −4932.82 8543.90i −0.236370 0.409404i
\(759\) 919.267 1592.22i 0.0439621 0.0761447i
\(760\) 15853.9 27459.7i 0.756685 1.31062i
\(761\) −20024.7 34683.8i −0.953871 1.65215i −0.736932 0.675967i \(-0.763726\pi\)
−0.216939 0.976185i \(-0.569607\pi\)
\(762\) −16740.6 −0.795865
\(763\) 0 0
\(764\) −389.601 −0.0184493
\(765\) 505.014 + 874.710i 0.0238678 + 0.0413402i
\(766\) 15732.1 27248.9i 0.742070 1.28530i
\(767\) 27412.6 47480.1i 1.29050 2.23521i
\(768\) 4601.29 + 7969.66i 0.216191 + 0.374454i
\(769\) 8002.01 0.375240 0.187620 0.982242i \(-0.439923\pi\)
0.187620 + 0.982242i \(0.439923\pi\)
\(770\) 0 0
\(771\) −13406.5 −0.626231
\(772\) −2593.26 4491.65i −0.120898 0.209402i
\(773\) −6966.68 + 12066.6i −0.324158 + 0.561458i −0.981342 0.192273i \(-0.938414\pi\)
0.657184 + 0.753730i \(0.271748\pi\)
\(774\) 5447.42 9435.21i 0.252976 0.438168i
\(775\) −16626.7 28798.2i −0.770642 1.33479i
\(776\) −14810.3 −0.685126
\(777\) 0 0
\(778\) −470.751 −0.0216931
\(779\) 9723.78 + 16842.1i 0.447228 + 0.774621i
\(780\) 5662.36