Properties

Label 378.4.g.e.109.1
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(1.39378 - 2.41410i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.e.163.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-8.97703 - 15.5487i) q^{5} +(13.2278 + 12.9624i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-8.97703 - 15.5487i) q^{5} +(13.2278 + 12.9624i) q^{7} -8.00000 q^{8} +(17.9541 - 31.0973i) q^{10} +(-19.8381 + 34.3607i) q^{11} +28.4065 q^{13} +(-9.22380 + 35.8737i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(7.38252 - 12.7869i) q^{17} +(-33.9153 - 58.7430i) q^{19} +71.8162 q^{20} -79.3526 q^{22} +(-88.8684 - 153.925i) q^{23} +(-98.6740 + 170.908i) q^{25} +(28.4065 + 49.2016i) q^{26} +(-71.3589 + 19.8976i) q^{28} -209.301 q^{29} +(-143.931 + 249.296i) q^{31} +(16.0000 - 27.7128i) q^{32} +29.5301 q^{34} +(82.8023 - 322.039i) q^{35} +(-183.917 - 318.554i) q^{37} +(67.8305 - 117.486i) q^{38} +(71.8162 + 124.389i) q^{40} -294.638 q^{41} -348.661 q^{43} +(-79.3526 - 137.443i) q^{44} +(177.737 - 307.849i) q^{46} +(-119.010 - 206.132i) q^{47} +(6.95004 + 342.930i) q^{49} -394.696 q^{50} +(-56.8131 + 98.4031i) q^{52} +(-183.607 + 318.017i) q^{53} +712.350 q^{55} +(-105.822 - 103.700i) q^{56} +(-209.301 - 362.520i) q^{58} +(127.872 - 221.481i) q^{59} +(149.170 + 258.371i) q^{61} -575.724 q^{62} +64.0000 q^{64} +(-255.006 - 441.684i) q^{65} +(499.195 - 864.631i) q^{67} +(29.5301 + 51.1476i) q^{68} +(640.590 - 178.621i) q^{70} +659.220 q^{71} +(-319.532 + 553.446i) q^{73} +(367.835 - 637.109i) q^{74} +271.322 q^{76} +(-707.814 + 197.366i) q^{77} +(338.790 + 586.802i) q^{79} +(-143.632 + 248.779i) q^{80} +(-294.638 - 510.328i) q^{82} +830.441 q^{83} -265.092 q^{85} +(-348.661 - 603.899i) q^{86} +(158.705 - 274.885i) q^{88} +(-231.740 - 401.385i) q^{89} +(375.756 + 368.218i) q^{91} +710.948 q^{92} +(238.021 - 412.264i) q^{94} +(-608.916 + 1054.67i) q^{95} +373.154 q^{97} +(-587.021 + 354.967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8} + 8 q^{10} - 56 q^{11} - 18 q^{13} + 22 q^{14} - 64 q^{16} + 118 q^{17} + 37 q^{19} + 32 q^{20} - 224 q^{22} - 200 q^{23} - 104 q^{25} - 18 q^{26} - 56 q^{28} + 524 q^{29} + 276 q^{31} + 128 q^{32} + 472 q^{34} - 290 q^{35} - 185 q^{37} - 74 q^{38} + 32 q^{40} - 60 q^{41} - 1556 q^{43} - 224 q^{44} + 400 q^{46} - 30 q^{47} - 1159 q^{49} - 416 q^{50} + 36 q^{52} - 480 q^{53} + 1456 q^{55} - 200 q^{56} + 524 q^{58} + 296 q^{59} + 474 q^{61} + 1104 q^{62} + 512 q^{64} - 1542 q^{65} + 1319 q^{67} + 472 q^{68} - 32 q^{70} + 1852 q^{71} - 1423 q^{73} + 370 q^{74} - 296 q^{76} - 1228 q^{77} + 765 q^{79} - 64 q^{80} - 60 q^{82} + 1660 q^{83} - 584 q^{85} - 1556 q^{86} + 448 q^{88} + 864 q^{89} - 738 q^{91} + 1600 q^{92} + 60 q^{94} - 1766 q^{95} + 1088 q^{97} - 2704 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −8.97703 15.5487i −0.802930 1.39072i −0.917680 0.397321i \(-0.869940\pi\)
0.114750 0.993394i \(-0.463393\pi\)
\(6\) 0 0
\(7\) 13.2278 + 12.9624i 0.714235 + 0.699906i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 17.9541 31.0973i 0.567757 0.983384i
\(11\) −19.8381 + 34.3607i −0.543766 + 0.941830i 0.454918 + 0.890534i \(0.349669\pi\)
−0.998683 + 0.0512966i \(0.983665\pi\)
\(12\) 0 0
\(13\) 28.4065 0.606043 0.303021 0.952984i \(-0.402005\pi\)
0.303021 + 0.952984i \(0.402005\pi\)
\(14\) −9.22380 + 35.8737i −0.176083 + 0.684832i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 7.38252 12.7869i 0.105325 0.182428i −0.808546 0.588433i \(-0.799745\pi\)
0.913871 + 0.406005i \(0.133078\pi\)
\(18\) 0 0
\(19\) −33.9153 58.7430i −0.409510 0.709293i 0.585325 0.810799i \(-0.300967\pi\)
−0.994835 + 0.101506i \(0.967634\pi\)
\(20\) 71.8162 0.802930
\(21\) 0 0
\(22\) −79.3526 −0.769001
\(23\) −88.8684 153.925i −0.805667 1.39546i −0.915840 0.401544i \(-0.868474\pi\)
0.110172 0.993913i \(-0.464860\pi\)
\(24\) 0 0
\(25\) −98.6740 + 170.908i −0.789392 + 1.36727i
\(26\) 28.4065 + 49.2016i 0.214268 + 0.371124i
\(27\) 0 0
\(28\) −71.3589 + 19.8976i −0.481627 + 0.134296i
\(29\) −209.301 −1.34021 −0.670107 0.742264i \(-0.733752\pi\)
−0.670107 + 0.742264i \(0.733752\pi\)
\(30\) 0 0
\(31\) −143.931 + 249.296i −0.833895 + 1.44435i 0.0610314 + 0.998136i \(0.480561\pi\)
−0.894927 + 0.446213i \(0.852772\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 29.5301 0.148952
\(35\) 82.8023 322.039i 0.399890 1.55527i
\(36\) 0 0
\(37\) −183.917 318.554i −0.817185 1.41541i −0.907748 0.419515i \(-0.862200\pi\)
0.0905633 0.995891i \(-0.471133\pi\)
\(38\) 67.8305 117.486i 0.289567 0.501546i
\(39\) 0 0
\(40\) 71.8162 + 124.389i 0.283879 + 0.491692i
\(41\) −294.638 −1.12231 −0.561156 0.827710i \(-0.689643\pi\)
−0.561156 + 0.827710i \(0.689643\pi\)
\(42\) 0 0
\(43\) −348.661 −1.23652 −0.618259 0.785974i \(-0.712162\pi\)
−0.618259 + 0.785974i \(0.712162\pi\)
\(44\) −79.3526 137.443i −0.271883 0.470915i
\(45\) 0 0
\(46\) 177.737 307.849i 0.569693 0.986737i
\(47\) −119.010 206.132i −0.369350 0.639733i 0.620114 0.784512i \(-0.287086\pi\)
−0.989464 + 0.144779i \(0.953753\pi\)
\(48\) 0 0
\(49\) 6.95004 + 342.930i 0.0202625 + 0.999795i
\(50\) −394.696 −1.11637
\(51\) 0 0
\(52\) −56.8131 + 98.4031i −0.151511 + 0.262424i
\(53\) −183.607 + 318.017i −0.475856 + 0.824206i −0.999617 0.0276585i \(-0.991195\pi\)
0.523762 + 0.851865i \(0.324528\pi\)
\(54\) 0 0
\(55\) 712.350 1.74642
\(56\) −105.822 103.700i −0.252520 0.247454i
\(57\) 0 0
\(58\) −209.301 362.520i −0.473837 0.820711i
\(59\) 127.872 221.481i 0.282162 0.488719i −0.689755 0.724043i \(-0.742282\pi\)
0.971917 + 0.235324i \(0.0756151\pi\)
\(60\) 0 0
\(61\) 149.170 + 258.371i 0.313104 + 0.542311i 0.979033 0.203704i \(-0.0652980\pi\)
−0.665929 + 0.746015i \(0.731965\pi\)
\(62\) −575.724 −1.17931
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −255.006 441.684i −0.486610 0.842833i
\(66\) 0 0
\(67\) 499.195 864.631i 0.910245 1.57659i 0.0965267 0.995330i \(-0.469227\pi\)
0.813718 0.581260i \(-0.197440\pi\)
\(68\) 29.5301 + 51.1476i 0.0526625 + 0.0912140i
\(69\) 0 0
\(70\) 640.590 178.621i 1.09379 0.304990i
\(71\) 659.220 1.10190 0.550951 0.834538i \(-0.314265\pi\)
0.550951 + 0.834538i \(0.314265\pi\)
\(72\) 0 0
\(73\) −319.532 + 553.446i −0.512307 + 0.887341i 0.487591 + 0.873072i \(0.337876\pi\)
−0.999898 + 0.0142693i \(0.995458\pi\)
\(74\) 367.835 637.109i 0.577837 1.00084i
\(75\) 0 0
\(76\) 271.322 0.409510
\(77\) −707.814 + 197.366i −1.04757 + 0.292103i
\(78\) 0 0
\(79\) 338.790 + 586.802i 0.482492 + 0.835700i 0.999798 0.0201001i \(-0.00639848\pi\)
−0.517306 + 0.855800i \(0.673065\pi\)
\(80\) −143.632 + 248.779i −0.200732 + 0.347679i
\(81\) 0 0
\(82\) −294.638 510.328i −0.396797 0.687273i
\(83\) 830.441 1.09823 0.549113 0.835748i \(-0.314966\pi\)
0.549113 + 0.835748i \(0.314966\pi\)
\(84\) 0 0
\(85\) −265.092 −0.338274
\(86\) −348.661 603.899i −0.437175 0.757210i
\(87\) 0 0
\(88\) 158.705 274.885i 0.192250 0.332987i
\(89\) −231.740 401.385i −0.276004 0.478053i 0.694384 0.719605i \(-0.255677\pi\)
−0.970388 + 0.241552i \(0.922344\pi\)
\(90\) 0 0
\(91\) 375.756 + 368.218i 0.432857 + 0.424173i
\(92\) 710.948 0.805667
\(93\) 0 0
\(94\) 238.021 412.264i 0.261170 0.452360i
\(95\) −608.916 + 1054.67i −0.657616 + 1.13902i
\(96\) 0 0
\(97\) 373.154 0.390598 0.195299 0.980744i \(-0.437432\pi\)
0.195299 + 0.980744i \(0.437432\pi\)
\(98\) −587.021 + 354.967i −0.605083 + 0.365889i
\(99\) 0 0
\(100\) −394.696 683.634i −0.394696 0.683634i
\(101\) −138.026 + 239.068i −0.135981 + 0.235526i −0.925972 0.377593i \(-0.876752\pi\)
0.789991 + 0.613119i \(0.210085\pi\)
\(102\) 0 0
\(103\) 44.3595 + 76.8329i 0.0424356 + 0.0735007i 0.886463 0.462799i \(-0.153155\pi\)
−0.844027 + 0.536300i \(0.819822\pi\)
\(104\) −227.252 −0.214268
\(105\) 0 0
\(106\) −734.428 −0.672962
\(107\) −344.439 596.585i −0.311197 0.539010i 0.667424 0.744678i \(-0.267397\pi\)
−0.978622 + 0.205668i \(0.934063\pi\)
\(108\) 0 0
\(109\) −292.449 + 506.537i −0.256987 + 0.445114i −0.965433 0.260650i \(-0.916063\pi\)
0.708447 + 0.705765i \(0.249396\pi\)
\(110\) 712.350 + 1233.83i 0.617454 + 1.06946i
\(111\) 0 0
\(112\) 73.7904 286.990i 0.0622548 0.242125i
\(113\) −1397.04 −1.16303 −0.581517 0.813534i \(-0.697541\pi\)
−0.581517 + 0.813534i \(0.697541\pi\)
\(114\) 0 0
\(115\) −1595.55 + 2763.57i −1.29379 + 2.24091i
\(116\) 418.602 725.040i 0.335054 0.580330i
\(117\) 0 0
\(118\) 511.489 0.399037
\(119\) 263.404 73.4472i 0.202909 0.0565789i
\(120\) 0 0
\(121\) −121.604 210.624i −0.0913627 0.158245i
\(122\) −298.341 + 516.742i −0.221398 + 0.383472i
\(123\) 0 0
\(124\) −575.724 997.183i −0.416948 0.722175i
\(125\) 1298.94 0.929446
\(126\) 0 0
\(127\) −988.221 −0.690476 −0.345238 0.938515i \(-0.612202\pi\)
−0.345238 + 0.938515i \(0.612202\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 510.012 883.368i 0.344085 0.595973i
\(131\) −565.462 979.409i −0.377135 0.653217i 0.613509 0.789688i \(-0.289757\pi\)
−0.990644 + 0.136471i \(0.956424\pi\)
\(132\) 0 0
\(133\) 312.828 1216.67i 0.203952 0.793220i
\(134\) 1996.78 1.28728
\(135\) 0 0
\(136\) −59.0601 + 102.295i −0.0372380 + 0.0644981i
\(137\) 451.777 782.501i 0.281737 0.487983i −0.690076 0.723737i \(-0.742423\pi\)
0.971813 + 0.235755i \(0.0757561\pi\)
\(138\) 0 0
\(139\) −1220.74 −0.744903 −0.372451 0.928052i \(-0.621483\pi\)
−0.372451 + 0.928052i \(0.621483\pi\)
\(140\) 949.971 + 930.914i 0.573480 + 0.561976i
\(141\) 0 0
\(142\) 659.220 + 1141.80i 0.389581 + 0.674775i
\(143\) −563.533 + 976.068i −0.329545 + 0.570789i
\(144\) 0 0
\(145\) 1878.90 + 3254.35i 1.07610 + 1.86386i
\(146\) −1278.13 −0.724511
\(147\) 0 0
\(148\) 1471.34 0.817185
\(149\) 1003.09 + 1737.41i 0.551520 + 0.955261i 0.998165 + 0.0605494i \(0.0192853\pi\)
−0.446645 + 0.894711i \(0.647381\pi\)
\(150\) 0 0
\(151\) 1138.85 1972.55i 0.613765 1.06307i −0.376835 0.926280i \(-0.622988\pi\)
0.990600 0.136791i \(-0.0436790\pi\)
\(152\) 271.322 + 469.944i 0.144784 + 0.250773i
\(153\) 0 0
\(154\) −1049.66 1028.60i −0.549247 0.538229i
\(155\) 5168.29 2.67824
\(156\) 0 0
\(157\) 150.782 261.163i 0.0766481 0.132758i −0.825154 0.564908i \(-0.808912\pi\)
0.901802 + 0.432150i \(0.142245\pi\)
\(158\) −677.580 + 1173.60i −0.341173 + 0.590929i
\(159\) 0 0
\(160\) −574.530 −0.283879
\(161\) 819.705 3188.04i 0.401253 1.56058i
\(162\) 0 0
\(163\) −1052.33 1822.70i −0.505676 0.875857i −0.999978 0.00656657i \(-0.997910\pi\)
0.494302 0.869290i \(-0.335424\pi\)
\(164\) 589.277 1020.66i 0.280578 0.485975i
\(165\) 0 0
\(166\) 830.441 + 1438.37i 0.388281 + 0.672523i
\(167\) 1229.42 0.569674 0.284837 0.958576i \(-0.408061\pi\)
0.284837 + 0.958576i \(0.408061\pi\)
\(168\) 0 0
\(169\) −1390.07 −0.632712
\(170\) −265.092 459.153i −0.119598 0.207150i
\(171\) 0 0
\(172\) 697.322 1207.80i 0.309130 0.535428i
\(173\) 1110.79 + 1923.95i 0.488162 + 0.845521i 0.999907 0.0136163i \(-0.00433433\pi\)
−0.511746 + 0.859137i \(0.671001\pi\)
\(174\) 0 0
\(175\) −3520.63 + 981.688i −1.52077 + 0.424049i
\(176\) 634.821 0.271883
\(177\) 0 0
\(178\) 463.479 802.770i 0.195164 0.338034i
\(179\) −2152.54 + 3728.31i −0.898818 + 1.55680i −0.0698117 + 0.997560i \(0.522240\pi\)
−0.829007 + 0.559239i \(0.811093\pi\)
\(180\) 0 0
\(181\) 3415.77 1.40272 0.701360 0.712808i \(-0.252577\pi\)
0.701360 + 0.712808i \(0.252577\pi\)
\(182\) −262.016 + 1019.05i −0.106714 + 0.415037i
\(183\) 0 0
\(184\) 710.948 + 1231.40i 0.284846 + 0.493369i
\(185\) −3302.06 + 5719.34i −1.31228 + 2.27294i
\(186\) 0 0
\(187\) 292.911 + 507.336i 0.114544 + 0.198396i
\(188\) 952.083 0.369350
\(189\) 0 0
\(190\) −2435.67 −0.930009
\(191\) 468.636 + 811.700i 0.177535 + 0.307500i 0.941036 0.338307i \(-0.109854\pi\)
−0.763500 + 0.645807i \(0.776521\pi\)
\(192\) 0 0
\(193\) −1371.32 + 2375.20i −0.511450 + 0.885858i 0.488462 + 0.872585i \(0.337558\pi\)
−0.999912 + 0.0132725i \(0.995775\pi\)
\(194\) 373.154 + 646.321i 0.138097 + 0.239191i
\(195\) 0 0
\(196\) −1201.84 661.784i −0.437989 0.241175i
\(197\) 1790.49 0.647548 0.323774 0.946134i \(-0.395048\pi\)
0.323774 + 0.946134i \(0.395048\pi\)
\(198\) 0 0
\(199\) 1910.81 3309.62i 0.680672 1.17896i −0.294104 0.955773i \(-0.595021\pi\)
0.974776 0.223185i \(-0.0716454\pi\)
\(200\) 789.392 1367.27i 0.279092 0.483402i
\(201\) 0 0
\(202\) −552.103 −0.192306
\(203\) −2768.59 2713.05i −0.957228 0.938025i
\(204\) 0 0
\(205\) 2644.98 + 4581.23i 0.901137 + 1.56082i
\(206\) −88.7190 + 153.666i −0.0300065 + 0.0519728i
\(207\) 0 0
\(208\) −227.252 393.613i −0.0757553 0.131212i
\(209\) 2691.26 0.890711
\(210\) 0 0
\(211\) −66.8406 −0.0218080 −0.0109040 0.999941i \(-0.503471\pi\)
−0.0109040 + 0.999941i \(0.503471\pi\)
\(212\) −734.428 1272.07i −0.237928 0.412103i
\(213\) 0 0
\(214\) 688.877 1193.17i 0.220050 0.381138i
\(215\) 3129.94 + 5421.21i 0.992838 + 1.71965i
\(216\) 0 0
\(217\) −5135.37 + 1431.94i −1.60651 + 0.447956i
\(218\) −1169.80 −0.363434
\(219\) 0 0
\(220\) −1424.70 + 2467.65i −0.436606 + 0.756223i
\(221\) 209.712 363.231i 0.0638314 0.110559i
\(222\) 0 0
\(223\) −5993.39 −1.79976 −0.899882 0.436134i \(-0.856348\pi\)
−0.899882 + 0.436134i \(0.856348\pi\)
\(224\) 570.871 159.181i 0.170281 0.0474809i
\(225\) 0 0
\(226\) −1397.04 2419.75i −0.411195 0.712210i
\(227\) 1535.08 2658.83i 0.448840 0.777414i −0.549470 0.835513i \(-0.685171\pi\)
0.998311 + 0.0580988i \(0.0185038\pi\)
\(228\) 0 0
\(229\) −65.7688 113.915i −0.0189787 0.0328721i 0.856380 0.516346i \(-0.172708\pi\)
−0.875359 + 0.483474i \(0.839375\pi\)
\(230\) −6382.20 −1.82969
\(231\) 0 0
\(232\) 1674.41 0.473837
\(233\) −248.293 430.056i −0.0698121 0.120918i 0.829006 0.559239i \(-0.188907\pi\)
−0.898818 + 0.438321i \(0.855573\pi\)
\(234\) 0 0
\(235\) −2136.72 + 3700.91i −0.593124 + 1.02732i
\(236\) 511.489 + 885.925i 0.141081 + 0.244359i
\(237\) 0 0
\(238\) 390.618 + 382.782i 0.106387 + 0.104252i
\(239\) −1827.43 −0.494588 −0.247294 0.968941i \(-0.579541\pi\)
−0.247294 + 0.968941i \(0.579541\pi\)
\(240\) 0 0
\(241\) 3097.90 5365.72i 0.828022 1.43418i −0.0715663 0.997436i \(-0.522800\pi\)
0.899588 0.436740i \(-0.143867\pi\)
\(242\) 243.207 421.248i 0.0646032 0.111896i
\(243\) 0 0
\(244\) −1193.36 −0.313104
\(245\) 5269.71 3186.55i 1.37416 0.830944i
\(246\) 0 0
\(247\) −963.415 1668.68i −0.248181 0.429862i
\(248\) 1151.45 1994.37i 0.294827 0.510654i
\(249\) 0 0
\(250\) 1298.94 + 2249.83i 0.328609 + 0.569167i
\(251\) −2249.36 −0.565652 −0.282826 0.959171i \(-0.591272\pi\)
−0.282826 + 0.959171i \(0.591272\pi\)
\(252\) 0 0
\(253\) 7051.94 1.75238
\(254\) −988.221 1711.65i −0.244120 0.422828i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1183.64 + 2050.13i 0.287291 + 0.497602i 0.973162 0.230121i \(-0.0739121\pi\)
−0.685871 + 0.727723i \(0.740579\pi\)
\(258\) 0 0
\(259\) 1696.42 6597.80i 0.406990 1.58289i
\(260\) 2040.05 0.486610
\(261\) 0 0
\(262\) 1130.92 1958.82i 0.266675 0.461894i
\(263\) −802.307 + 1389.64i −0.188108 + 0.325813i −0.944619 0.328168i \(-0.893569\pi\)
0.756511 + 0.653980i \(0.226902\pi\)
\(264\) 0 0
\(265\) 6592.98 1.52831
\(266\) 2420.15 674.832i 0.557854 0.155551i
\(267\) 0 0
\(268\) 1996.78 + 3458.53i 0.455122 + 0.788295i
\(269\) −197.727 + 342.474i −0.0448166 + 0.0776246i −0.887564 0.460685i \(-0.847604\pi\)
0.842747 + 0.538310i \(0.180937\pi\)
\(270\) 0 0
\(271\) 1722.52 + 2983.49i 0.386109 + 0.668761i 0.991922 0.126846i \(-0.0404854\pi\)
−0.605813 + 0.795607i \(0.707152\pi\)
\(272\) −236.241 −0.0526625
\(273\) 0 0
\(274\) 1807.11 0.398436
\(275\) −3915.02 6781.01i −0.858489 1.48695i
\(276\) 0 0
\(277\) 3826.62 6627.90i 0.830034 1.43766i −0.0679770 0.997687i \(-0.521654\pi\)
0.898011 0.439974i \(-0.145012\pi\)
\(278\) −1220.74 2114.38i −0.263363 0.456158i
\(279\) 0 0
\(280\) −662.418 + 2576.31i −0.141382 + 0.549872i
\(281\) 3291.80 0.698835 0.349417 0.936967i \(-0.386380\pi\)
0.349417 + 0.936967i \(0.386380\pi\)
\(282\) 0 0
\(283\) 2728.08 4725.16i 0.573029 0.992516i −0.423224 0.906025i \(-0.639102\pi\)
0.996253 0.0864903i \(-0.0275651\pi\)
\(284\) −1318.44 + 2283.61i −0.275476 + 0.477138i
\(285\) 0 0
\(286\) −2254.13 −0.466048
\(287\) −3897.42 3819.23i −0.801594 0.785513i
\(288\) 0 0
\(289\) 2347.50 + 4065.98i 0.477813 + 0.827597i
\(290\) −3757.80 + 6508.70i −0.760916 + 1.31795i
\(291\) 0 0
\(292\) −1278.13 2213.78i −0.256153 0.443671i
\(293\) −4614.48 −0.920072 −0.460036 0.887900i \(-0.652163\pi\)
−0.460036 + 0.887900i \(0.652163\pi\)
\(294\) 0 0
\(295\) −4591.65 −0.906225
\(296\) 1471.34 + 2548.44i 0.288919 + 0.500422i
\(297\) 0 0
\(298\) −2006.18 + 3474.81i −0.389983 + 0.675471i
\(299\) −2524.44 4372.47i −0.488269 0.845707i
\(300\) 0 0
\(301\) −4612.02 4519.50i −0.883165 0.865447i
\(302\) 4555.41 0.867994
\(303\) 0 0
\(304\) −542.644 + 939.887i −0.102378 + 0.177323i
\(305\) 2678.21 4638.80i 0.502800 0.870876i
\(306\) 0 0
\(307\) 7520.35 1.39808 0.699038 0.715085i \(-0.253612\pi\)
0.699038 + 0.715085i \(0.253612\pi\)
\(308\) 731.932 2846.67i 0.135408 0.526636i
\(309\) 0 0
\(310\) 5168.29 + 8951.73i 0.946900 + 1.64008i
\(311\) −4683.36 + 8111.81i −0.853919 + 1.47903i 0.0237254 + 0.999719i \(0.492447\pi\)
−0.877644 + 0.479312i \(0.840886\pi\)
\(312\) 0 0
\(313\) 1402.09 + 2428.49i 0.253197 + 0.438550i 0.964404 0.264432i \(-0.0851846\pi\)
−0.711207 + 0.702982i \(0.751851\pi\)
\(314\) 603.130 0.108397
\(315\) 0 0
\(316\) −2710.32 −0.482492
\(317\) −4383.08 7591.72i −0.776588 1.34509i −0.933898 0.357540i \(-0.883615\pi\)
0.157310 0.987549i \(-0.449718\pi\)
\(318\) 0 0
\(319\) 4152.14 7191.72i 0.728763 1.26225i
\(320\) −574.530 995.115i −0.100366 0.173839i
\(321\) 0 0
\(322\) 6341.55 1768.27i 1.09752 0.306030i
\(323\) −1001.52 −0.172527
\(324\) 0 0
\(325\) −2802.99 + 4854.92i −0.478405 + 0.828622i
\(326\) 2104.67 3645.39i 0.357567 0.619324i
\(327\) 0 0
\(328\) 2357.11 0.396797
\(329\) 1097.73 4269.34i 0.183951 0.715430i
\(330\) 0 0
\(331\) −3337.31 5780.40i −0.554185 0.959877i −0.997966 0.0637421i \(-0.979697\pi\)
0.443781 0.896135i \(-0.353637\pi\)
\(332\) −1660.88 + 2876.73i −0.274556 + 0.475546i
\(333\) 0 0
\(334\) 1229.42 + 2129.42i 0.201410 + 0.348853i
\(335\) −17925.2 −2.92345
\(336\) 0 0
\(337\) −3025.35 −0.489024 −0.244512 0.969646i \(-0.578628\pi\)
−0.244512 + 0.969646i \(0.578628\pi\)
\(338\) −1390.07 2407.67i −0.223698 0.387456i
\(339\) 0 0
\(340\) 530.184 918.306i 0.0845685 0.146477i
\(341\) −5710.64 9891.12i −0.906888 1.57078i
\(342\) 0 0
\(343\) −4353.27 + 4626.30i −0.685290 + 0.728270i
\(344\) 2789.29 0.437175
\(345\) 0 0
\(346\) −2221.58 + 3847.90i −0.345182 + 0.597873i
\(347\) 4438.95 7688.48i 0.686730 1.18945i −0.286160 0.958182i \(-0.592379\pi\)
0.972890 0.231269i \(-0.0742877\pi\)
\(348\) 0 0
\(349\) −7994.22 −1.22613 −0.613067 0.790031i \(-0.710064\pi\)
−0.613067 + 0.790031i \(0.710064\pi\)
\(350\) −5220.97 5116.23i −0.797350 0.781354i
\(351\) 0 0
\(352\) 634.821 + 1099.54i 0.0961251 + 0.166494i
\(353\) −5726.13 + 9917.96i −0.863375 + 1.49541i 0.00527653 + 0.999986i \(0.498320\pi\)
−0.868652 + 0.495423i \(0.835013\pi\)
\(354\) 0 0
\(355\) −5917.84 10250.0i −0.884750 1.53243i
\(356\) 1853.92 0.276004
\(357\) 0 0
\(358\) −8610.16 −1.27112
\(359\) 3639.69 + 6304.12i 0.535084 + 0.926793i 0.999159 + 0.0409973i \(0.0130535\pi\)
−0.464075 + 0.885796i \(0.653613\pi\)
\(360\) 0 0
\(361\) 1129.01 1955.50i 0.164603 0.285100i
\(362\) 3415.77 + 5916.29i 0.495936 + 0.858987i
\(363\) 0 0
\(364\) −2027.06 + 565.222i −0.291887 + 0.0813892i
\(365\) 11473.8 1.64539
\(366\) 0 0
\(367\) 1050.66 1819.80i 0.149439 0.258837i −0.781581 0.623804i \(-0.785586\pi\)
0.931020 + 0.364967i \(0.118920\pi\)
\(368\) −1421.90 + 2462.79i −0.201417 + 0.348864i
\(369\) 0 0
\(370\) −13208.3 −1.85585
\(371\) −6550.99 + 1826.67i −0.916740 + 0.255622i
\(372\) 0 0
\(373\) −1979.37 3428.37i −0.274767 0.475910i 0.695310 0.718710i \(-0.255267\pi\)
−0.970076 + 0.242801i \(0.921934\pi\)
\(374\) −585.822 + 1014.67i −0.0809950 + 0.140287i
\(375\) 0 0
\(376\) 952.083 + 1649.06i 0.130585 + 0.226180i
\(377\) −5945.52 −0.812227
\(378\) 0 0
\(379\) −3876.03 −0.525325 −0.262662 0.964888i \(-0.584601\pi\)
−0.262662 + 0.964888i \(0.584601\pi\)
\(380\) −2435.67 4218.70i −0.328808 0.569512i
\(381\) 0 0
\(382\) −937.271 + 1623.40i −0.125537 + 0.217436i
\(383\) 3281.16 + 5683.14i 0.437753 + 0.758211i 0.997516 0.0704423i \(-0.0224411\pi\)
−0.559763 + 0.828653i \(0.689108\pi\)
\(384\) 0 0
\(385\) 9422.83 + 9233.80i 1.24736 + 1.22233i
\(386\) −5485.29 −0.723300
\(387\) 0 0
\(388\) −746.307 + 1292.64i −0.0976495 + 0.169134i
\(389\) −4275.65 + 7405.64i −0.557286 + 0.965247i 0.440436 + 0.897784i \(0.354824\pi\)
−0.997722 + 0.0674631i \(0.978510\pi\)
\(390\) 0 0
\(391\) −2624.29 −0.339427
\(392\) −55.6003 2743.44i −0.00716388 0.353481i
\(393\) 0 0
\(394\) 1790.49 + 3101.22i 0.228943 + 0.396541i
\(395\) 6082.65 10535.5i 0.774814 1.34202i
\(396\) 0 0
\(397\) 1246.36 + 2158.76i 0.157564 + 0.272910i 0.933990 0.357300i \(-0.116302\pi\)
−0.776425 + 0.630209i \(0.782969\pi\)
\(398\) 7643.24 0.962616
\(399\) 0 0
\(400\) 3157.57 0.394696
\(401\) −5375.99 9311.49i −0.669487 1.15959i −0.978048 0.208381i \(-0.933181\pi\)
0.308561 0.951205i \(-0.400153\pi\)
\(402\) 0 0
\(403\) −4088.58 + 7081.63i −0.505376 + 0.875337i
\(404\) −552.103 956.271i −0.0679905 0.117763i
\(405\) 0 0
\(406\) 1930.55 7508.40i 0.235989 0.917822i
\(407\) 14594.3 1.77743
\(408\) 0 0
\(409\) −6071.96 + 10516.9i −0.734081 + 1.27147i 0.221044 + 0.975264i \(0.429054\pi\)
−0.955125 + 0.296202i \(0.904280\pi\)
\(410\) −5289.95 + 9162.46i −0.637200 + 1.10366i
\(411\) 0 0
\(412\) −354.876 −0.0424356
\(413\) 4562.41 1272.18i 0.543587 0.151573i
\(414\) 0 0
\(415\) −7454.89 12912.2i −0.881798 1.52732i
\(416\) 454.505 787.225i 0.0535671 0.0927810i
\(417\) 0 0
\(418\) 2691.26 + 4661.40i 0.314914 + 0.545447i
\(419\) 14733.1 1.71780 0.858902 0.512140i \(-0.171147\pi\)
0.858902 + 0.512140i \(0.171147\pi\)
\(420\) 0 0
\(421\) 8152.89 0.943818 0.471909 0.881647i \(-0.343565\pi\)
0.471909 + 0.881647i \(0.343565\pi\)
\(422\) −66.8406 115.771i −0.00771030 0.0133546i
\(423\) 0 0
\(424\) 1468.86 2544.13i 0.168240 0.291401i
\(425\) 1456.93 + 2523.47i 0.166285 + 0.288015i
\(426\) 0 0
\(427\) −1375.92 + 5351.29i −0.155938 + 0.606481i
\(428\) 2755.51 0.311197
\(429\) 0 0
\(430\) −6259.88 + 10842.4i −0.702042 + 1.21597i
\(431\) −6721.50 + 11642.0i −0.751191 + 1.30110i 0.196055 + 0.980593i \(0.437187\pi\)
−0.947246 + 0.320508i \(0.896146\pi\)
\(432\) 0 0
\(433\) 10303.9 1.14359 0.571796 0.820396i \(-0.306247\pi\)
0.571796 + 0.820396i \(0.306247\pi\)
\(434\) −7615.56 7462.79i −0.842301 0.825404i
\(435\) 0 0
\(436\) −1169.80 2026.15i −0.128493 0.222557i
\(437\) −6027.99 + 10440.8i −0.659858 + 1.14291i
\(438\) 0 0
\(439\) −1049.70 1818.14i −0.114122 0.197665i 0.803306 0.595566i \(-0.203072\pi\)
−0.917428 + 0.397901i \(0.869739\pi\)
\(440\) −5698.80 −0.617454
\(441\) 0 0
\(442\) 838.847 0.0902712
\(443\) −3171.89 5493.87i −0.340182 0.589213i 0.644284 0.764786i \(-0.277156\pi\)
−0.984466 + 0.175573i \(0.943822\pi\)
\(444\) 0 0
\(445\) −4160.67 + 7206.48i −0.443224 + 0.767686i
\(446\) −5993.39 10380.9i −0.636313 1.10213i
\(447\) 0 0
\(448\) 846.580 + 829.596i 0.0892793 + 0.0874883i
\(449\) 12278.8 1.29058 0.645290 0.763938i \(-0.276737\pi\)
0.645290 + 0.763938i \(0.276737\pi\)
\(450\) 0 0
\(451\) 5845.08 10124.0i 0.610275 1.05703i
\(452\) 2794.09 4839.51i 0.290759 0.503609i
\(453\) 0 0
\(454\) 6140.32 0.634756
\(455\) 2352.13 9148.01i 0.242350 0.942562i
\(456\) 0 0
\(457\) −5848.66 10130.2i −0.598663 1.03691i −0.993019 0.117957i \(-0.962366\pi\)
0.394356 0.918958i \(-0.370968\pi\)
\(458\) 131.538 227.830i 0.0134200 0.0232441i
\(459\) 0 0
\(460\) −6382.20 11054.3i −0.646894 1.12045i
\(461\) −13465.2 −1.36039 −0.680194 0.733033i \(-0.738104\pi\)
−0.680194 + 0.733033i \(0.738104\pi\)
\(462\) 0 0
\(463\) 7792.30 0.782157 0.391079 0.920357i \(-0.372102\pi\)
0.391079 + 0.920357i \(0.372102\pi\)
\(464\) 1674.41 + 2900.16i 0.167527 + 0.290165i
\(465\) 0 0
\(466\) 496.586 860.112i 0.0493646 0.0855020i
\(467\) 7086.38 + 12274.0i 0.702181 + 1.21621i 0.967699 + 0.252108i \(0.0811238\pi\)
−0.265518 + 0.964106i \(0.585543\pi\)
\(468\) 0 0
\(469\) 17811.0 4966.39i 1.75359 0.488969i
\(470\) −8546.88 −0.838804
\(471\) 0 0
\(472\) −1022.98 + 1771.85i −0.0997593 + 0.172788i
\(473\) 6916.79 11980.2i 0.672377 1.16459i
\(474\) 0 0
\(475\) 13386.2 1.29306
\(476\) −272.379 + 1059.35i −0.0262279 + 0.102007i
\(477\) 0 0
\(478\) −1827.43 3165.20i −0.174863 0.302872i
\(479\) −2984.18 + 5168.75i −0.284657 + 0.493040i −0.972526 0.232795i \(-0.925213\pi\)
0.687869 + 0.725835i \(0.258546\pi\)
\(480\) 0 0
\(481\) −5224.46 9049.03i −0.495249 0.857797i
\(482\) 12391.6 1.17100
\(483\) 0 0
\(484\) 972.830 0.0913627
\(485\) −3349.81 5802.04i −0.313623 0.543211i
\(486\) 0 0
\(487\) −1845.34 + 3196.22i −0.171705 + 0.297401i −0.939016 0.343874i \(-0.888261\pi\)
0.767311 + 0.641275i \(0.221594\pi\)
\(488\) −1193.36 2066.97i −0.110699 0.191736i
\(489\) 0 0
\(490\) 10789.0 + 5940.85i 0.994686 + 0.547715i
\(491\) 11918.0 1.09542 0.547708 0.836669i \(-0.315500\pi\)
0.547708 + 0.836669i \(0.315500\pi\)
\(492\) 0 0
\(493\) −1545.17 + 2676.31i −0.141158 + 0.244493i
\(494\) 1926.83 3337.37i 0.175490 0.303958i
\(495\) 0 0
\(496\) 4605.79 0.416948
\(497\) 8720.04 + 8545.11i 0.787017 + 0.771228i
\(498\) 0 0
\(499\) −6982.72 12094.4i −0.626432 1.08501i −0.988262 0.152768i \(-0.951181\pi\)
0.361830 0.932244i \(-0.382152\pi\)
\(500\) −2597.88 + 4499.66i −0.232362 + 0.402462i
\(501\) 0 0
\(502\) −2249.36 3896.01i −0.199988 0.346390i
\(503\) −8268.76 −0.732974 −0.366487 0.930423i \(-0.619440\pi\)
−0.366487 + 0.930423i \(0.619440\pi\)
\(504\) 0 0
\(505\) 4956.25 0.436733
\(506\) 7051.94 + 12214.3i 0.619559 + 1.07311i
\(507\) 0 0
\(508\) 1976.44 3423.30i 0.172619 0.298985i
\(509\) 10568.7 + 18305.6i 0.920336 + 1.59407i 0.798895 + 0.601470i \(0.205418\pi\)
0.121441 + 0.992599i \(0.461248\pi\)
\(510\) 0 0
\(511\) −11400.7 + 3178.96i −0.986963 + 0.275203i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −2367.29 + 4100.27i −0.203145 + 0.351858i
\(515\) 796.433 1379.46i 0.0681457 0.118032i
\(516\) 0 0
\(517\) 9443.78 0.803360
\(518\) 13124.1 3659.52i 1.11321 0.310405i
\(519\) 0 0
\(520\) 2040.05 + 3533.47i 0.172043 + 0.297986i
\(521\) −8634.33 + 14955.1i −0.726060 + 1.25757i 0.232477 + 0.972602i \(0.425317\pi\)
−0.958536 + 0.284970i \(0.908016\pi\)
\(522\) 0 0
\(523\) 1000.71 + 1733.28i 0.0836674 + 0.144916i 0.904823 0.425789i \(-0.140003\pi\)
−0.821155 + 0.570705i \(0.806670\pi\)
\(524\) 4523.70 0.377135
\(525\) 0 0
\(526\) −3209.23 −0.266025
\(527\) 2125.14 + 3680.86i 0.175660 + 0.304252i
\(528\) 0 0
\(529\) −9711.70 + 16821.2i −0.798200 + 1.38252i
\(530\) 6592.98 + 11419.4i 0.540341 + 0.935898i
\(531\) 0 0
\(532\) 3589.00 + 3517.00i 0.292486 + 0.286619i
\(533\) −8369.65 −0.680169
\(534\) 0 0
\(535\) −6184.07 + 10711.1i −0.499739 + 0.865574i
\(536\) −3993.56 + 6917.05i −0.321820 + 0.557409i
\(537\) 0 0
\(538\) −790.910 −0.0633802
\(539\) −11921.2 6564.28i −0.952655 0.524570i
\(540\) 0 0
\(541\) −206.979 358.499i −0.0164487 0.0284899i 0.857684 0.514177i \(-0.171903\pi\)
−0.874133 + 0.485687i \(0.838569\pi\)
\(542\) −3445.04 + 5966.99i −0.273021 + 0.472886i
\(543\) 0 0
\(544\) −236.241 409.181i −0.0186190 0.0322490i
\(545\) 10501.3 0.825369
\(546\) 0 0
\(547\) −17009.5 −1.32957 −0.664786 0.747034i \(-0.731477\pi\)
−0.664786 + 0.747034i \(0.731477\pi\)
\(548\) 1807.11 + 3130.01i 0.140868 + 0.243991i
\(549\) 0 0
\(550\) 7830.04 13562.0i 0.607043 1.05143i
\(551\) 7098.50 + 12295.0i 0.548832 + 0.950604i
\(552\) 0 0
\(553\) −3124.93 + 12153.6i −0.240299 + 0.934585i
\(554\) 15306.5 1.17384
\(555\) 0 0
\(556\) 2441.47 4228.75i 0.186226 0.322552i
\(557\) −4146.02 + 7181.13i −0.315391 + 0.546273i −0.979521 0.201344i \(-0.935469\pi\)
0.664130 + 0.747617i \(0.268802\pi\)
\(558\) 0 0
\(559\) −9904.25 −0.749383
\(560\) −5124.72 + 1428.97i −0.386713 + 0.107830i
\(561\) 0 0
\(562\) 3291.80 + 5701.57i 0.247075 + 0.427947i
\(563\) 7875.43 13640.6i 0.589538 1.02111i −0.404755 0.914425i \(-0.632643\pi\)
0.994293 0.106685i \(-0.0340235\pi\)
\(564\) 0 0
\(565\) 12541.3 + 21722.2i 0.933835 + 1.61745i
\(566\) 10912.3 0.810386
\(567\) 0 0
\(568\) −5273.76 −0.389581
\(569\) −8339.46 14444.4i −0.614426 1.06422i −0.990485 0.137622i \(-0.956054\pi\)
0.376059 0.926596i \(-0.377279\pi\)
\(570\) 0 0
\(571\) 2338.21 4049.89i 0.171368 0.296817i −0.767531 0.641012i \(-0.778515\pi\)
0.938898 + 0.344195i \(0.111848\pi\)
\(572\) −2254.13 3904.27i −0.164773 0.285395i
\(573\) 0 0
\(574\) 2717.68 10569.8i 0.197620 0.768595i
\(575\) 35076.0 2.54395
\(576\) 0 0
\(577\) 4491.29 7779.13i 0.324046 0.561265i −0.657273 0.753653i \(-0.728290\pi\)
0.981319 + 0.192388i \(0.0616233\pi\)
\(578\) −4694.99 + 8131.97i −0.337865 + 0.585199i
\(579\) 0 0
\(580\) −15031.2 −1.07610
\(581\) 10984.9 + 10764.5i 0.784391 + 0.768655i
\(582\) 0 0
\(583\) −7284.84 12617.7i −0.517508 0.896351i
\(584\) 2556.26 4427.56i 0.181128 0.313723i
\(585\) 0 0
\(586\) −4614.48 7992.52i −0.325294 0.563427i
\(587\) −3547.35 −0.249429 −0.124714 0.992193i \(-0.539801\pi\)
−0.124714 + 0.992193i \(0.539801\pi\)
\(588\) 0 0
\(589\) 19525.8 1.36595
\(590\) −4591.65 7952.98i −0.320399 0.554947i
\(591\) 0 0
\(592\) −2942.68 + 5096.87i −0.204296 + 0.353851i
\(593\) 3489.19 + 6043.45i 0.241625 + 0.418507i 0.961177 0.275931i \(-0.0889862\pi\)
−0.719552 + 0.694438i \(0.755653\pi\)
\(594\) 0 0
\(595\) −3506.59 3436.24i −0.241607 0.236760i
\(596\) −8024.73 −0.551520
\(597\) 0 0
\(598\) 5048.89 8744.93i 0.345258 0.598005i
\(599\) 3375.23 5846.06i 0.230230 0.398771i −0.727645 0.685953i \(-0.759385\pi\)
0.957876 + 0.287183i \(0.0927187\pi\)
\(600\) 0 0
\(601\) 27765.5 1.88449 0.942243 0.334929i \(-0.108712\pi\)
0.942243 + 0.334929i \(0.108712\pi\)
\(602\) 3215.98 12507.8i 0.217730 0.846808i
\(603\) 0 0
\(604\) 4555.41 + 7890.20i 0.306882 + 0.531536i
\(605\) −2183.28 + 3781.55i −0.146716 + 0.254119i
\(606\) 0 0
\(607\) −7448.52 12901.2i −0.498066 0.862675i 0.501932 0.864907i \(-0.332623\pi\)
−0.999998 + 0.00223201i \(0.999290\pi\)
\(608\) −2170.58 −0.144784
\(609\) 0 0
\(610\) 10712.9 0.711067
\(611\) −3380.67 5855.50i −0.223842 0.387706i
\(612\) 0 0
\(613\) −9490.34 + 16437.7i −0.625304 + 1.08306i 0.363179 + 0.931720i \(0.381691\pi\)
−0.988482 + 0.151338i \(0.951642\pi\)
\(614\) 7520.35 + 13025.6i 0.494294 + 0.856143i
\(615\) 0 0
\(616\) 5662.51 1578.93i 0.370372 0.103274i
\(617\) −18594.0 −1.21324 −0.606618 0.794993i \(-0.707474\pi\)
−0.606618 + 0.794993i \(0.707474\pi\)
\(618\) 0 0
\(619\) 8274.89 14332.5i 0.537311 0.930651i −0.461736 0.887017i \(-0.652773\pi\)
0.999048 0.0436334i \(-0.0138933\pi\)
\(620\) −10336.6 + 17903.5i −0.669559 + 1.15971i
\(621\) 0 0
\(622\) −18733.4 −1.20762
\(623\) 2137.52 8313.35i 0.137461 0.534619i
\(624\) 0 0
\(625\) 673.628 + 1166.76i 0.0431122 + 0.0746725i
\(626\) −2804.17 + 4856.97i −0.179037 + 0.310102i
\(627\) 0 0
\(628\) 603.130 + 1044.65i 0.0383240 + 0.0663792i
\(629\) −5431.10 −0.344280
\(630\) 0 0
\(631\) −4468.32 −0.281904 −0.140952 0.990016i \(-0.545016\pi\)
−0.140952 + 0.990016i \(0.545016\pi\)
\(632\) −2710.32 4694.41i −0.170587 0.295465i
\(633\) 0 0
\(634\) 8766.16 15183.4i 0.549131 0.951122i
\(635\) 8871.29 + 15365.5i 0.554404 + 0.960255i
\(636\) 0 0
\(637\) 197.426 + 9741.44i 0.0122799 + 0.605918i
\(638\) 16608.6 1.03063
\(639\) 0 0
\(640\) 1149.06 1990.23i 0.0709696 0.122923i
\(641\) −9245.29 + 16013.3i −0.569683 + 0.986721i 0.426914 + 0.904292i \(0.359601\pi\)
−0.996597 + 0.0824282i \(0.973732\pi\)
\(642\) 0 0
\(643\) −8584.51 −0.526501 −0.263250 0.964728i \(-0.584795\pi\)
−0.263250 + 0.964728i \(0.584795\pi\)
\(644\) 9404.28 + 9215.62i 0.575436 + 0.563892i
\(645\) 0 0
\(646\) −1001.52 1734.68i −0.0609973 0.105650i
\(647\) 9936.10 17209.8i 0.603753 1.04573i −0.388494 0.921451i \(-0.627005\pi\)
0.992247 0.124280i \(-0.0396621\pi\)
\(648\) 0 0
\(649\) 5073.50 + 8787.56i 0.306860 + 0.531497i
\(650\) −11211.9 −0.676567
\(651\) 0 0
\(652\) 8418.68 0.505676
\(653\) −9867.12 17090.4i −0.591318 1.02419i −0.994055 0.108877i \(-0.965275\pi\)
0.402738 0.915315i \(-0.368059\pi\)
\(654\) 0 0
\(655\) −10152.3 + 17584.4i −0.605626 + 1.04897i
\(656\) 2357.11 + 4082.63i 0.140289 + 0.242988i
\(657\) 0 0
\(658\) 8492.45 2368.02i 0.503146 0.140296i
\(659\) 1670.68 0.0987564 0.0493782 0.998780i \(-0.484276\pi\)
0.0493782 + 0.998780i \(0.484276\pi\)
\(660\) 0 0
\(661\) 2828.16 4898.51i 0.166418 0.288245i −0.770740 0.637150i \(-0.780113\pi\)
0.937158 + 0.348905i \(0.113446\pi\)
\(662\) 6674.63 11560.8i 0.391868 0.678736i
\(663\) 0 0
\(664\) −6643.53 −0.388281
\(665\) −21725.8 + 6057.99i −1.26690 + 0.353261i
\(666\) 0 0
\(667\) 18600.3 + 32216.6i 1.07977 + 1.87021i
\(668\) −2458.84 + 4258.84i −0.142418 + 0.246676i
\(669\) 0 0
\(670\) −17925.2 31047.3i −1.03360 1.79024i
\(671\) −11837.1 −0.681020
\(672\) 0 0
\(673\) 342.738 0.0196309 0.00981544 0.999952i \(-0.496876\pi\)
0.00981544 + 0.999952i \(0.496876\pi\)
\(674\) −3025.35 5240.06i −0.172896 0.299465i
\(675\) 0 0
\(676\) 2780.14 4815.34i 0.158178 0.273972i
\(677\) −9873.37 17101.2i −0.560509 0.970830i −0.997452 0.0713405i \(-0.977272\pi\)
0.436943 0.899489i \(-0.356061\pi\)
\(678\) 0 0
\(679\) 4936.01 + 4836.98i 0.278979 + 0.273382i
\(680\) 2120.74 0.119598
\(681\) 0 0
\(682\) 11421.3 19782.2i 0.641266 1.11071i
\(683\) −1739.93 + 3013.65i −0.0974766 + 0.168834i −0.910640 0.413202i \(-0.864410\pi\)
0.813163 + 0.582036i \(0.197744\pi\)
\(684\) 0 0
\(685\) −16222.5 −0.904860
\(686\) −12366.3 2913.79i −0.688259 0.162171i
\(687\) 0 0
\(688\) 2789.29 + 4831.19i 0.154565 + 0.267714i
\(689\) −5215.64 + 9033.75i −0.288389 + 0.499504i
\(690\) 0 0
\(691\) 1399.18 + 2423.45i 0.0770295 + 0.133419i 0.901967 0.431805i \(-0.142123\pi\)
−0.824938 + 0.565224i \(0.808790\pi\)
\(692\) −8886.34 −0.488162
\(693\) 0 0
\(694\) 17755.8 0.971182
\(695\) 10958.6 + 18980.8i 0.598105 + 1.03595i
\(696\) 0 0
\(697\) −2175.17 + 3767.51i −0.118207 + 0.204741i
\(698\) −7994.22 13846.4i −0.433504 0.750850i
\(699\) 0 0
\(700\) 3640.60 14159.2i 0.196574 0.764525i
\(701\) −4777.03 −0.257384 −0.128692 0.991685i \(-0.541078\pi\)
−0.128692 + 0.991685i \(0.541078\pi\)
\(702\) 0 0
\(703\) −12475.2 + 21607.7i −0.669291 + 1.15925i
\(704\) −1269.64 + 2199.08i −0.0679707 + 0.117729i
\(705\) 0 0
\(706\) −22904.5 −1.22100
\(707\) −4924.68 + 1373.19i −0.261969 + 0.0730469i
\(708\) 0 0
\(709\) −9952.32 17237.9i −0.527175 0.913094i −0.999498 0.0316689i \(-0.989918\pi\)
0.472323 0.881425i \(-0.343416\pi\)
\(710\) 11835.7 20500.0i 0.625613 1.08359i
\(711\) 0 0
\(712\) 1853.92 + 3211.08i 0.0975821 + 0.169017i
\(713\) 51163.7 2.68737
\(714\) 0 0
\(715\) 20235.4 1.05841
\(716\) −8610.16 14913.2i −0.449409 0.778399i
\(717\) 0 0
\(718\) −7279.37 + 12608.2i −0.378362 + 0.655342i
\(719\) −9113.53 15785.1i −0.472708 0.818755i 0.526804 0.849987i \(-0.323390\pi\)
−0.999512 + 0.0312322i \(0.990057\pi\)
\(720\) 0 0
\(721\) −409.163 + 1591.34i −0.0211346 + 0.0821977i
\(722\) 4516.04 0.232783
\(723\) 0 0
\(724\) −6831.54 + 11832.6i −0.350680 + 0.607395i
\(725\) 20652.6 35771.3i 1.05796 1.83243i
\(726\) 0 0
\(727\) −23706.6 −1.20940 −0.604698 0.796455i \(-0.706706\pi\)
−0.604698 + 0.796455i \(0.706706\pi\)
\(728\) −3006.05 2945.75i −0.153038 0.149968i
\(729\) 0 0
\(730\) 11473.8 + 19873.2i 0.581731 + 1.00759i
\(731\) −2574.00 + 4458.29i −0.130236 + 0.225576i
\(732\) 0 0
\(733\) 7052.15 + 12214.7i 0.355358 + 0.615498i 0.987179 0.159616i \(-0.0510257\pi\)
−0.631821 + 0.775114i \(0.717692\pi\)
\(734\) 4202.66 0.211339
\(735\) 0 0
\(736\) −5687.58 −0.284846
\(737\) 19806.2 + 34305.4i 0.989920 + 1.71459i
\(738\) 0 0
\(739\) −12281.0 + 21271.3i −0.611317 + 1.05883i 0.379701 + 0.925109i \(0.376027\pi\)
−0.991019 + 0.133724i \(0.957307\pi\)
\(740\) −13208.3 22877.4i −0.656142 1.13647i
\(741\) 0 0
\(742\) −9714.87 9519.98i −0.480653 0.471010i
\(743\) −24154.7 −1.19267 −0.596333 0.802738i \(-0.703376\pi\)
−0.596333 + 0.802738i \(0.703376\pi\)
\(744\) 0 0
\(745\) 18009.6 31193.5i 0.885663 1.53401i
\(746\) 3958.74 6856.74i 0.194289 0.336519i
\(747\) 0 0
\(748\) −2343.29 −0.114544
\(749\) 3177.03 12356.3i 0.154988 0.602789i
\(750\) 0 0
\(751\) 11784.7 + 20411.7i 0.572608 + 0.991787i 0.996297 + 0.0859790i \(0.0274018\pi\)
−0.423688 + 0.905808i \(0.639265\pi\)
\(752\) −1904.17 + 3298.11i −0.0923375 + 0.159933i
\(753\) 0 0
\(754\) −5945.52 10297.9i −0.287166 0.497386i
\(755\) −40894.0 −1.97124
\(756\) 0 0
\(757\) −13175.7 −0.632603 −0.316302 0.948659i \(-0.602441\pi\)
−0.316302 + 0.948659i \(0.602441\pi\)
\(758\) −3876.03 6713.47i −0.185730 0.321694i
\(759\) 0 0
\(760\) 4871.33 8437.39i 0.232502 0.402706i
\(761\) −16037.4 27777.6i −0.763936 1.32318i −0.940807 0.338942i \(-0.889931\pi\)
0.176872 0.984234i \(-0.443402\pi\)
\(762\) 0 0
\(763\) −10434.4 + 2909.52i −0.495087 + 0.138049i
\(764\) −3749.08 −0.177535
\(765\) 0 0
\(766\) −6562.32 + 11366.3i −0.309538 + 0.536136i
\(767\) 3632.41 6291.52i 0.171002 0.296185i
\(768\) 0 0
\(769\) −25596.8 −1.20032 −0.600159 0.799881i \(-0.704896\pi\)
−0.600159 + 0.799881i \(0.704896\pi\)
\(770\) −6570.58 + 25554.6i −0.307516 + 1.19601i
\(771\) 0 0
\(772\) −5485.29 9500.80i −0.255725 0.442929i
\(773\) 1382.15 2393.96i 0.0643112 0.111390i −0.832077 0.554660i \(-0.812848\pi\)
0.896388 + 0.443270i \(0.146182\pi\)
\(774\) 0 0
\(775\) −28404.5 49198.0i −1.31654 2.28032i
\(776\) −2985.23 −0.138097
\(777\) 0 0
\(778\) −17102.6 −0.788121
\(779\) 9992.73 + 17307.9i 0.459598 + 0.796047i
\(780\) 0 0
\(781\) −13077.7 + 22651.3i −0.599177 + 1.03780i
\(782\) −2624.29 4545.41i −0.120006 0.207856i
\(783\) 0 0
\(784\) 4696.17 2839.74i 0.213929 &mi