Properties

Label 169.4.e.f.23.3
Level $169$
Weight $4$
Character 169.23
Analytic conductor $9.971$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.3
Root \(1.35234 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.4.e.f.147.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35234 - 0.780776i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-2.78078 + 4.81645i) q^{4} +3.56155i q^{5} +(-11.7446 - 6.78078i) q^{6} +(23.5360 + 13.5885i) q^{7} +21.1771i q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})\) \(q+(1.35234 - 0.780776i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-2.78078 + 4.81645i) q^{4} +3.56155i q^{5} +(-11.7446 - 6.78078i) q^{6} +(23.5360 + 13.5885i) q^{7} +21.1771i q^{8} +(-24.2116 + 41.9358i) q^{9} +(2.78078 + 4.81645i) q^{10} +(13.2167 - 7.63068i) q^{11} +48.3002 q^{12} +42.4384 q^{14} +(26.7869 - 15.4654i) q^{15} +(-5.71165 - 9.89286i) q^{16} +(22.2732 - 38.5783i) q^{17} +75.6155i q^{18} +(20.7584 + 11.9848i) q^{19} +(-17.1540 - 9.90388i) q^{20} -236.024i q^{21} +(11.9157 - 20.6386i) q^{22} +(61.3693 + 106.295i) q^{23} +(159.276 - 91.9579i) q^{24} +112.315 q^{25} +186.054 q^{27} +(-130.897 + 75.5734i) q^{28} +(109.955 + 190.447i) q^{29} +(24.1501 - 41.8292i) q^{30} -27.0928i q^{31} +(-162.167 - 93.6274i) q^{32} +(-114.783 - 66.2699i) q^{33} -69.5616i q^{34} +(-48.3963 + 83.8249i) q^{35} +(-134.654 - 233.228i) q^{36} +(81.5729 - 47.0961i) q^{37} +37.4299 q^{38} -75.4233 q^{40} +(138.871 - 80.1771i) q^{41} +(-184.282 - 319.185i) q^{42} +(-75.6510 + 131.031i) q^{43} +84.8769i q^{44} +(-149.357 - 86.2311i) q^{45} +(165.985 + 95.8314i) q^{46} +466.948i q^{47} +(-49.6037 + 85.9161i) q^{48} +(197.797 + 342.594i) q^{49} +(151.889 - 87.6932i) q^{50} -386.870 q^{51} -120.847 q^{53} +(251.609 - 145.267i) q^{54} +(27.1771 + 47.0721i) q^{55} +(-287.766 + 498.425i) q^{56} -208.169i q^{57} +(297.393 + 171.700i) q^{58} +(380.733 + 219.816i) q^{59} +172.024i q^{60} +(68.6525 - 118.910i) q^{61} +(-21.1534 - 36.6388i) q^{62} +(-1139.69 + 658.002i) q^{63} -201.022 q^{64} -206.968 q^{66} +(-443.648 + 256.140i) q^{67} +(123.874 + 214.555i) q^{68} +(532.972 - 923.134i) q^{69} +151.147i q^{70} +(355.693 + 205.359i) q^{71} +(-888.078 - 512.732i) q^{72} -308.004i q^{73} +(73.5431 - 127.380i) q^{74} +(-487.710 - 844.739i) q^{75} +(-115.449 + 66.6543i) q^{76} +414.759 q^{77} -586.462 q^{79} +(35.2339 - 20.3423i) q^{80} +(-154.193 - 267.070i) q^{81} +(125.201 - 216.854i) q^{82} -1354.20i q^{83} +(1136.80 + 656.329i) q^{84} +(137.399 + 79.3272i) q^{85} +236.266i q^{86} +(954.918 - 1653.97i) q^{87} +(161.596 + 279.892i) q^{88} +(380.949 - 219.941i) q^{89} -269.309 q^{90} -682.617 q^{92} +(-203.769 + 117.646i) q^{93} +(364.582 + 631.474i) q^{94} +(-42.6847 + 73.9320i) q^{95} +1626.24i q^{96} +(-1308.80 - 755.634i) q^{97} +(534.979 + 308.870i) q^{98} +739.006i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35234 0.780776i 0.478126 0.276046i −0.241509 0.970399i \(-0.577642\pi\)
0.719635 + 0.694352i \(0.244309\pi\)
\(3\) −4.34233 7.52113i −0.835682 1.44744i −0.893474 0.449114i \(-0.851740\pi\)
0.0577926 0.998329i \(-0.481594\pi\)
\(4\) −2.78078 + 4.81645i −0.347597 + 0.602056i
\(5\) 3.56155i 0.318555i 0.987234 + 0.159277i \(0.0509165\pi\)
−0.987234 + 0.159277i \(0.949084\pi\)
\(6\) −11.7446 6.78078i −0.799122 0.461373i
\(7\) 23.5360 + 13.5885i 1.27083 + 0.733712i 0.975144 0.221574i \(-0.0711194\pi\)
0.295683 + 0.955286i \(0.404453\pi\)
\(8\) 21.1771i 0.935904i
\(9\) −24.2116 + 41.9358i −0.896728 + 1.55318i
\(10\) 2.78078 + 4.81645i 0.0879359 + 0.152309i
\(11\) 13.2167 7.63068i 0.362272 0.209158i −0.307805 0.951450i \(-0.599594\pi\)
0.670077 + 0.742292i \(0.266261\pi\)
\(12\) 48.3002 1.16192
\(13\) 0 0
\(14\) 42.4384 0.810154
\(15\) 26.7869 15.4654i 0.461090 0.266211i
\(16\) −5.71165 9.89286i −0.0892445 0.154576i
\(17\) 22.2732 38.5783i 0.317767 0.550389i −0.662255 0.749279i \(-0.730400\pi\)
0.980022 + 0.198890i \(0.0637336\pi\)
\(18\) 75.6155i 0.990153i
\(19\) 20.7584 + 11.9848i 0.250647 + 0.144711i 0.620061 0.784554i \(-0.287108\pi\)
−0.369413 + 0.929265i \(0.620441\pi\)
\(20\) −17.1540 9.90388i −0.191788 0.110729i
\(21\) 236.024i 2.45260i
\(22\) 11.9157 20.6386i 0.115474 0.200008i
\(23\) 61.3693 + 106.295i 0.556365 + 0.963652i 0.997796 + 0.0663568i \(0.0211376\pi\)
−0.441431 + 0.897295i \(0.645529\pi\)
\(24\) 159.276 91.9579i 1.35467 0.782117i
\(25\) 112.315 0.898523
\(26\) 0 0
\(27\) 186.054 1.32615
\(28\) −130.897 + 75.5734i −0.883471 + 0.510072i
\(29\) 109.955 + 190.447i 0.704071 + 1.21949i 0.967026 + 0.254678i \(0.0819694\pi\)
−0.262955 + 0.964808i \(0.584697\pi\)
\(30\) 24.1501 41.8292i 0.146973 0.254564i
\(31\) 27.0928i 0.156968i −0.996915 0.0784840i \(-0.974992\pi\)
0.996915 0.0784840i \(-0.0250080\pi\)
\(32\) −162.167 93.6274i −0.895856 0.517223i
\(33\) −114.783 66.2699i −0.605488 0.349579i
\(34\) 69.5616i 0.350874i
\(35\) −48.3963 + 83.8249i −0.233728 + 0.404828i
\(36\) −134.654 233.228i −0.623400 1.07976i
\(37\) 81.5729 47.0961i 0.362446 0.209258i −0.307707 0.951481i \(-0.599562\pi\)
0.670153 + 0.742223i \(0.266228\pi\)
\(38\) 37.4299 0.159788
\(39\) 0 0
\(40\) −75.4233 −0.298137
\(41\) 138.871 80.1771i 0.528975 0.305404i −0.211624 0.977351i \(-0.567875\pi\)
0.740599 + 0.671947i \(0.234542\pi\)
\(42\) −184.282 319.185i −0.677031 1.17265i
\(43\) −75.6510 + 131.031i −0.268295 + 0.464700i −0.968422 0.249318i \(-0.919793\pi\)
0.700127 + 0.714018i \(0.253127\pi\)
\(44\) 84.8769i 0.290811i
\(45\) −149.357 86.2311i −0.494773 0.285657i
\(46\) 165.985 + 95.8314i 0.532025 + 0.307165i
\(47\) 466.948i 1.44918i 0.689181 + 0.724589i \(0.257970\pi\)
−0.689181 + 0.724589i \(0.742030\pi\)
\(48\) −49.6037 + 85.9161i −0.149160 + 0.258353i
\(49\) 197.797 + 342.594i 0.576667 + 0.998817i
\(50\) 151.889 87.6932i 0.429607 0.248034i
\(51\) −386.870 −1.06221
\(52\) 0 0
\(53\) −120.847 −0.313199 −0.156600 0.987662i \(-0.550053\pi\)
−0.156600 + 0.987662i \(0.550053\pi\)
\(54\) 251.609 145.267i 0.634068 0.366079i
\(55\) 27.1771 + 47.0721i 0.0666283 + 0.115404i
\(56\) −287.766 + 498.425i −0.686684 + 1.18937i
\(57\) 208.169i 0.483730i
\(58\) 297.393 + 171.700i 0.673269 + 0.388712i
\(59\) 380.733 + 219.816i 0.840122 + 0.485045i 0.857306 0.514808i \(-0.172137\pi\)
−0.0171836 + 0.999852i \(0.505470\pi\)
\(60\) 172.024i 0.370136i
\(61\) 68.6525 118.910i 0.144099 0.249587i −0.784937 0.619575i \(-0.787305\pi\)
0.929037 + 0.369988i \(0.120638\pi\)
\(62\) −21.1534 36.6388i −0.0433304 0.0750505i
\(63\) −1139.69 + 658.002i −2.27917 + 1.31588i
\(64\) −201.022 −0.392621
\(65\) 0 0
\(66\) −206.968 −0.386000
\(67\) −443.648 + 256.140i −0.808958 + 0.467052i −0.846594 0.532239i \(-0.821351\pi\)
0.0376358 + 0.999292i \(0.488017\pi\)
\(68\) 123.874 + 214.555i 0.220910 + 0.382627i
\(69\) 532.972 923.134i 0.929887 1.61061i
\(70\) 151.147i 0.258078i
\(71\) 355.693 + 205.359i 0.594549 + 0.343263i 0.766894 0.641774i \(-0.221801\pi\)
−0.172345 + 0.985037i \(0.555134\pi\)
\(72\) −888.078 512.732i −1.45362 0.839251i
\(73\) 308.004i 0.493823i −0.969038 0.246912i \(-0.920584\pi\)
0.969038 0.246912i \(-0.0794158\pi\)
\(74\) 73.5431 127.380i 0.115530 0.200104i
\(75\) −487.710 844.739i −0.750879 1.30056i
\(76\) −115.449 + 66.6543i −0.174248 + 0.100602i
\(77\) 414.759 0.613847
\(78\) 0 0
\(79\) −586.462 −0.835217 −0.417608 0.908627i \(-0.637132\pi\)
−0.417608 + 0.908627i \(0.637132\pi\)
\(80\) 35.2339 20.3423i 0.0492409 0.0284293i
\(81\) −154.193 267.070i −0.211513 0.366352i
\(82\) 125.201 216.854i 0.168611 0.292043i
\(83\) 1354.20i 1.79088i −0.445182 0.895440i \(-0.646861\pi\)
0.445182 0.895440i \(-0.353139\pi\)
\(84\) 1136.80 + 656.329i 1.47660 + 0.852516i
\(85\) 137.399 + 79.3272i 0.175329 + 0.101226i
\(86\) 236.266i 0.296247i
\(87\) 954.918 1653.97i 1.17676 2.03820i
\(88\) 161.596 + 279.892i 0.195752 + 0.339052i
\(89\) 380.949 219.941i 0.453714 0.261952i −0.255683 0.966761i \(-0.582300\pi\)
0.709398 + 0.704809i \(0.248967\pi\)
\(90\) −269.309 −0.315418
\(91\) 0 0
\(92\) −682.617 −0.773563
\(93\) −203.769 + 117.646i −0.227202 + 0.131175i
\(94\) 364.582 + 631.474i 0.400040 + 0.692889i
\(95\) −42.6847 + 73.9320i −0.0460985 + 0.0798449i
\(96\) 1626.24i 1.72894i
\(97\) −1308.80 755.634i −1.36998 0.790959i −0.379056 0.925374i \(-0.623751\pi\)
−0.990925 + 0.134414i \(0.957085\pi\)
\(98\) 534.979 + 308.870i 0.551439 + 0.318374i
\(99\) 739.006i 0.750231i
\(100\) −312.324 + 540.961i −0.312324 + 0.540961i
\(101\) 168.130 + 291.209i 0.165639 + 0.286895i 0.936882 0.349646i \(-0.113698\pi\)
−0.771243 + 0.636541i \(0.780365\pi\)
\(102\) −523.182 + 302.059i −0.507870 + 0.293219i
\(103\) −322.712 −0.308716 −0.154358 0.988015i \(-0.549331\pi\)
−0.154358 + 0.988015i \(0.549331\pi\)
\(104\) 0 0
\(105\) 840.611 0.781288
\(106\) −163.426 + 94.3542i −0.149749 + 0.0864574i
\(107\) −717.309 1242.42i −0.648083 1.12251i −0.983580 0.180471i \(-0.942238\pi\)
0.335498 0.942041i \(-0.391096\pi\)
\(108\) −517.375 + 896.119i −0.460967 + 0.798417i
\(109\) 849.147i 0.746179i −0.927795 0.373089i \(-0.878298\pi\)
0.927795 0.373089i \(-0.121702\pi\)
\(110\) 73.5055 + 42.4384i 0.0637134 + 0.0367850i
\(111\) −708.433 409.014i −0.605779 0.349747i
\(112\) 310.452i 0.261919i
\(113\) −807.263 + 1398.22i −0.672044 + 1.16401i 0.305280 + 0.952263i \(0.401250\pi\)
−0.977324 + 0.211751i \(0.932083\pi\)
\(114\) −162.533 281.516i −0.133532 0.231284i
\(115\) −378.574 + 218.570i −0.306976 + 0.177233i
\(116\) −1223.04 −0.978931
\(117\) 0 0
\(118\) 686.509 0.535579
\(119\) 1048.45 605.321i 0.807654 0.466300i
\(120\) 327.513 + 567.269i 0.249147 + 0.431536i
\(121\) −549.045 + 950.974i −0.412506 + 0.714481i
\(122\) 214.409i 0.159112i
\(123\) −1206.05 696.311i −0.884109 0.510441i
\(124\) 130.491 + 75.3390i 0.0945035 + 0.0545616i
\(125\) 845.211i 0.604784i
\(126\) −1027.50 + 1779.69i −0.726487 + 1.25831i
\(127\) 432.587 + 749.263i 0.302251 + 0.523514i 0.976646 0.214857i \(-0.0689285\pi\)
−0.674394 + 0.738371i \(0.735595\pi\)
\(128\) 1025.49 592.066i 0.708134 0.408842i
\(129\) 1314.01 0.896836
\(130\) 0 0
\(131\) −281.400 −0.187680 −0.0938400 0.995587i \(-0.529914\pi\)
−0.0938400 + 0.995587i \(0.529914\pi\)
\(132\) 638.371 368.563i 0.420932 0.243025i
\(133\) 325.713 + 564.152i 0.212353 + 0.367806i
\(134\) −399.976 + 692.779i −0.257856 + 0.446620i
\(135\) 662.641i 0.422452i
\(136\) 816.976 + 471.681i 0.515111 + 0.297400i
\(137\) 2287.55 + 1320.72i 1.42656 + 0.823624i 0.996847 0.0793428i \(-0.0252822\pi\)
0.429711 + 0.902967i \(0.358616\pi\)
\(138\) 1664.53i 1.02677i
\(139\) 999.318 1730.87i 0.609791 1.05619i −0.381483 0.924376i \(-0.624587\pi\)
0.991274 0.131814i \(-0.0420801\pi\)
\(140\) −269.159 466.196i −0.162486 0.281434i
\(141\) 3511.98 2027.64i 2.09760 1.21105i
\(142\) 641.359 0.379026
\(143\) 0 0
\(144\) 553.153 0.320112
\(145\) −678.286 + 391.609i −0.388473 + 0.224285i
\(146\) −240.482 416.527i −0.136318 0.236110i
\(147\) 1717.80 2975.31i 0.963820 1.66939i
\(148\) 523.855i 0.290950i
\(149\) −1518.13 876.491i −0.834696 0.481912i 0.0207617 0.999784i \(-0.493391\pi\)
−0.855458 + 0.517872i \(0.826724\pi\)
\(150\) −1319.10 761.585i −0.718029 0.414554i
\(151\) 2794.64i 1.50613i −0.657949 0.753063i \(-0.728576\pi\)
0.657949 0.753063i \(-0.271424\pi\)
\(152\) −253.804 + 439.601i −0.135436 + 0.234582i
\(153\) 1078.54 + 1868.09i 0.569901 + 0.987098i
\(154\) 560.898 323.834i 0.293496 0.169450i
\(155\) 96.4924 0.0500030
\(156\) 0 0
\(157\) 3244.87 1.64949 0.824743 0.565508i \(-0.191320\pi\)
0.824743 + 0.565508i \(0.191320\pi\)
\(158\) −793.099 + 457.896i −0.399339 + 0.230558i
\(159\) 524.756 + 908.903i 0.261735 + 0.453338i
\(160\) 333.459 577.568i 0.164764 0.285380i
\(161\) 3335.68i 1.63285i
\(162\) −417.045 240.781i −0.202260 0.116775i
\(163\) −2841.83 1640.73i −1.36558 0.788418i −0.375221 0.926936i \(-0.622433\pi\)
−0.990360 + 0.138517i \(0.955766\pi\)
\(164\) 891.818i 0.424630i
\(165\) 236.024 408.805i 0.111360 0.192881i
\(166\) −1057.33 1831.35i −0.494366 0.856266i
\(167\) −2707.65 + 1563.26i −1.25463 + 0.724364i −0.972026 0.234872i \(-0.924533\pi\)
−0.282608 + 0.959235i \(0.591200\pi\)
\(168\) 4998.29 2.29540
\(169\) 0 0
\(170\) 247.747 0.111773
\(171\) −1005.19 + 580.346i −0.449524 + 0.259533i
\(172\) −420.737 728.738i −0.186517 0.323057i
\(173\) 48.7849 84.4980i 0.0214396 0.0371345i −0.855107 0.518452i \(-0.826508\pi\)
0.876546 + 0.481318i \(0.159842\pi\)
\(174\) 2982.31i 1.29936i
\(175\) 2643.46 + 1526.20i 1.14187 + 0.659257i
\(176\) −150.979 87.1675i −0.0646616 0.0373324i
\(177\) 3818.06i 1.62137i
\(178\) 343.450 594.873i 0.144622 0.250492i
\(179\) −17.3575 30.0640i −0.00724782 0.0125536i 0.862379 0.506264i \(-0.168974\pi\)
−0.869627 + 0.493710i \(0.835640\pi\)
\(180\) 830.654 479.579i 0.343963 0.198587i
\(181\) 1229.35 0.504843 0.252422 0.967617i \(-0.418773\pi\)
0.252422 + 0.967617i \(0.418773\pi\)
\(182\) 0 0
\(183\) −1192.45 −0.481684
\(184\) −2251.01 + 1299.62i −0.901885 + 0.520704i
\(185\) 167.735 + 290.526i 0.0666602 + 0.115459i
\(186\) −183.710 + 318.195i −0.0724209 + 0.125437i
\(187\) 679.839i 0.265854i
\(188\) −2249.03 1298.48i −0.872486 0.503730i
\(189\) 4378.97 + 2528.20i 1.68531 + 0.973014i
\(190\) 133.309i 0.0509012i
\(191\) −2140.40 + 3707.28i −0.810858 + 1.40445i 0.101407 + 0.994845i \(0.467666\pi\)
−0.912265 + 0.409602i \(0.865668\pi\)
\(192\) 872.903 + 1511.91i 0.328106 + 0.568296i
\(193\) 409.041 236.160i 0.152557 0.0880786i −0.421778 0.906699i \(-0.638594\pi\)
0.574335 + 0.818620i \(0.305261\pi\)
\(194\) −2359.93 −0.873365
\(195\) 0 0
\(196\) −2200.12 −0.801791
\(197\) 3883.58 2242.18i 1.40453 0.810908i 0.409681 0.912229i \(-0.365640\pi\)
0.994854 + 0.101321i \(0.0323068\pi\)
\(198\) 576.998 + 999.390i 0.207098 + 0.358705i
\(199\) −183.120 + 317.173i −0.0652314 + 0.112984i −0.896797 0.442443i \(-0.854112\pi\)
0.831565 + 0.555427i \(0.187445\pi\)
\(200\) 2378.51i 0.840931i
\(201\) 3852.93 + 2224.49i 1.35206 + 0.780614i
\(202\) 454.739 + 262.543i 0.158393 + 0.0914480i
\(203\) 5976.49i 2.06634i
\(204\) 1075.80 1863.34i 0.369221 0.639509i
\(205\) 285.555 + 494.596i 0.0972879 + 0.168508i
\(206\) −436.418 + 251.966i −0.147605 + 0.0852199i
\(207\) −5943.41 −1.99563
\(208\) 0 0
\(209\) 365.810 0.121070
\(210\) 1136.80 656.329i 0.373554 0.215671i
\(211\) −1061.28 1838.19i −0.346262 0.599744i 0.639320 0.768941i \(-0.279216\pi\)
−0.985582 + 0.169197i \(0.945883\pi\)
\(212\) 336.047 582.051i 0.108867 0.188563i
\(213\) 3566.95i 1.14743i
\(214\) −1940.10 1120.12i −0.619730 0.357801i
\(215\) −466.675 269.435i −0.148033 0.0854666i
\(216\) 3940.08i 1.24115i
\(217\) 368.152 637.657i 0.115169 0.199479i
\(218\) −662.994 1148.34i −0.205980 0.356768i
\(219\) −2316.54 + 1337.45i −0.714781 + 0.412679i
\(220\) −302.294 −0.0926392
\(221\) 0 0
\(222\) −1277.39 −0.386185
\(223\) 5132.43 2963.21i 1.54122 0.889826i 0.542461 0.840081i \(-0.317493\pi\)
0.998762 0.0497449i \(-0.0158408\pi\)
\(224\) −2544.52 4407.24i −0.758986 1.31460i
\(225\) −2719.34 + 4710.03i −0.805730 + 1.39557i
\(226\) 2521.17i 0.742060i
\(227\) −775.665 447.830i −0.226796 0.130941i 0.382297 0.924039i \(-0.375133\pi\)
−0.609093 + 0.793099i \(0.708466\pi\)
\(228\) 1002.63 + 578.870i 0.291232 + 0.168143i
\(229\) 627.717i 0.181138i 0.995890 + 0.0905692i \(0.0288686\pi\)
−0.995890 + 0.0905692i \(0.971131\pi\)
\(230\) −341.309 + 591.164i −0.0978488 + 0.169479i
\(231\) −1801.02 3119.46i −0.512981 0.888509i
\(232\) −4033.11 + 2328.52i −1.14132 + 0.658942i
\(233\) −2303.72 −0.647734 −0.323867 0.946103i \(-0.604983\pi\)
−0.323867 + 0.946103i \(0.604983\pi\)
\(234\) 0 0
\(235\) −1663.06 −0.461643
\(236\) −2117.47 + 1222.52i −0.584048 + 0.337200i
\(237\) 2546.61 + 4410.86i 0.697976 + 1.20893i
\(238\) 945.240 1637.20i 0.257440 0.445900i
\(239\) 544.622i 0.147400i −0.997280 0.0737001i \(-0.976519\pi\)
0.997280 0.0737001i \(-0.0234808\pi\)
\(240\) −305.995 176.666i −0.0822995 0.0475156i
\(241\) −4699.14 2713.05i −1.25601 0.725157i −0.283713 0.958909i \(-0.591566\pi\)
−0.972296 + 0.233752i \(0.924900\pi\)
\(242\) 1714.73i 0.455483i
\(243\) 1172.61 2031.03i 0.309561 0.536175i
\(244\) 381.814 + 661.322i 0.100177 + 0.173511i
\(245\) −1220.17 + 704.464i −0.318178 + 0.183700i
\(246\) −2174.65 −0.563621
\(247\) 0 0
\(248\) 573.746 0.146907
\(249\) −10185.1 + 5880.39i −2.59220 + 1.49661i
\(250\) 659.921 + 1143.02i 0.166948 + 0.289163i
\(251\) −2610.61 + 4521.71i −0.656494 + 1.13708i 0.325022 + 0.945706i \(0.394628\pi\)
−0.981517 + 0.191375i \(0.938705\pi\)
\(252\) 7319.02i 1.82958i
\(253\) 1622.20 + 936.580i 0.403111 + 0.232736i
\(254\) 1170.01 + 675.508i 0.289028 + 0.166871i
\(255\) 1377.86i 0.338372i
\(256\) 1728.63 2994.07i 0.422029 0.730975i
\(257\) 329.103 + 570.023i 0.0798789 + 0.138354i 0.903198 0.429225i \(-0.141213\pi\)
−0.823319 + 0.567579i \(0.807880\pi\)
\(258\) 1776.99 1025.95i 0.428801 0.247568i
\(259\) 2559.87 0.614141
\(260\) 0 0
\(261\) −10648.7 −2.52544
\(262\) −380.550 + 219.711i −0.0897346 + 0.0518083i
\(263\) −1623.23 2811.51i −0.380580 0.659184i 0.610565 0.791966i \(-0.290942\pi\)
−0.991145 + 0.132782i \(0.957609\pi\)
\(264\) 1403.40 2430.76i 0.327172 0.566679i
\(265\) 430.401i 0.0997711i
\(266\) 880.953 + 508.618i 0.203063 + 0.117238i
\(267\) −3308.42 1910.11i −0.758321 0.437817i
\(268\) 2849.07i 0.649384i
\(269\) 1292.90 2239.37i 0.293047 0.507572i −0.681482 0.731835i \(-0.738664\pi\)
0.974529 + 0.224263i \(0.0719976\pi\)
\(270\) 517.375 + 896.119i 0.116616 + 0.201985i
\(271\) 856.441 494.466i 0.191974 0.110836i −0.400932 0.916108i \(-0.631314\pi\)
0.592907 + 0.805271i \(0.297980\pi\)
\(272\) −508.867 −0.113436
\(273\) 0 0
\(274\) 4124.74 0.909433
\(275\) 1484.44 857.043i 0.325510 0.187933i
\(276\) 2964.15 + 5134.06i 0.646452 + 1.11969i
\(277\) 4071.20 7051.53i 0.883086 1.52955i 0.0351939 0.999381i \(-0.488795\pi\)
0.847892 0.530169i \(-0.177872\pi\)
\(278\) 3120.97i 0.673322i
\(279\) 1136.16 + 655.961i 0.243799 + 0.140758i
\(280\) −1775.17 1024.89i −0.378880 0.218747i
\(281\) 1534.21i 0.325705i 0.986650 + 0.162853i \(0.0520695\pi\)
−0.986650 + 0.162853i \(0.947930\pi\)
\(282\) 3166.27 5484.14i 0.668612 1.15807i
\(283\) −3482.50 6031.87i −0.731495 1.26699i −0.956244 0.292570i \(-0.905490\pi\)
0.224749 0.974417i \(-0.427844\pi\)
\(284\) −1978.20 + 1142.12i −0.413327 + 0.238634i
\(285\) 741.403 0.154095
\(286\) 0 0
\(287\) 4357.96 0.896314
\(288\) 7852.68 4533.75i 1.60668 0.927616i
\(289\) 1464.31 + 2536.26i 0.298048 + 0.516234i
\(290\) −611.518 + 1059.18i −0.123826 + 0.214473i
\(291\) 13124.9i 2.64396i
\(292\) 1483.48 + 856.490i 0.297309 + 0.171652i
\(293\) −554.281 320.015i −0.110517 0.0638070i 0.443723 0.896164i \(-0.353658\pi\)
−0.554240 + 0.832357i \(0.686991\pi\)
\(294\) 5364.87i 1.06424i
\(295\) −782.887 + 1356.00i −0.154513 + 0.267625i
\(296\) 997.358 + 1727.48i 0.195846 + 0.339214i
\(297\) 2459.03 1419.72i 0.480428 0.277375i
\(298\) −2737.37 −0.532120
\(299\) 0 0
\(300\) 5424.85 1.04401
\(301\) −3561.05 + 2055.97i −0.681912 + 0.393702i
\(302\) −2181.99 3779.32i −0.415760 0.720118i
\(303\) 1460.15 2529.05i 0.276843 0.479506i
\(304\) 273.813i 0.0516587i
\(305\) 423.503 + 244.509i 0.0795072 + 0.0459035i
\(306\) 2917.12 + 1684.20i 0.544969 + 0.314638i
\(307\) 100.406i 0.0186660i −0.999956 0.00933299i \(-0.997029\pi\)
0.999956 0.00933299i \(-0.00297083\pi\)
\(308\) −1153.35 + 1997.67i −0.213371 + 0.369570i
\(309\) 1401.32 + 2427.16i 0.257988 + 0.446849i
\(310\) 130.491 75.3390i 0.0239077 0.0138031i
\(311\) 3878.92 0.707245 0.353623 0.935388i \(-0.384950\pi\)
0.353623 + 0.935388i \(0.384950\pi\)
\(312\) 0 0
\(313\) −3789.39 −0.684311 −0.342155 0.939643i \(-0.611157\pi\)
−0.342155 + 0.939643i \(0.611157\pi\)
\(314\) 4388.19 2533.52i 0.788662 0.455334i
\(315\) −2343.51 4059.08i −0.419180 0.726041i
\(316\) 1630.82 2824.66i 0.290319 0.502847i
\(317\) 4406.81i 0.780791i −0.920647 0.390396i \(-0.872338\pi\)
0.920647 0.390396i \(-0.127662\pi\)
\(318\) 1419.30 + 819.434i 0.250284 + 0.144502i
\(319\) 2906.48 + 1678.06i 0.510130 + 0.294524i
\(320\) 715.950i 0.125071i
\(321\) −6229.58 + 10790.0i −1.08318 + 1.87613i
\(322\) 2604.42 + 4510.99i 0.450741 + 0.780706i
\(323\) 924.710 533.882i 0.159295 0.0919690i
\(324\) 1715.11 0.294086
\(325\) 0 0
\(326\) −5124.19 −0.870559
\(327\) −6386.55 + 3687.27i −1.08005 + 0.623568i
\(328\) 1697.92 + 2940.88i 0.285829 + 0.495070i
\(329\) −6345.14 + 10990.1i −1.06328 + 1.84165i
\(330\) 737.127i 0.122962i
\(331\) −3577.98 2065.75i −0.594149 0.343032i 0.172587 0.984994i \(-0.444787\pi\)
−0.766736 + 0.641962i \(0.778121\pi\)
\(332\) 6522.44 + 3765.73i 1.07821 + 0.622505i
\(333\) 4561.10i 0.750591i
\(334\) −2441.11 + 4228.13i −0.399916 + 0.692674i
\(335\) −912.257 1580.07i −0.148782 0.257698i
\(336\) −2334.95 + 1348.08i −0.379113 + 0.218881i
\(337\) 4560.82 0.737221 0.368611 0.929584i \(-0.379834\pi\)
0.368611 + 0.929584i \(0.379834\pi\)
\(338\) 0 0
\(339\) 14021.6 2.24646
\(340\) −764.150 + 441.182i −0.121888 + 0.0703720i
\(341\) −206.737 358.078i −0.0328311 0.0568652i
\(342\) −906.240 + 1569.65i −0.143286 + 0.248179i
\(343\) 1429.34i 0.225007i
\(344\) −2774.86 1602.07i −0.434914 0.251098i
\(345\) 3287.79 + 1898.21i 0.513069 + 0.296220i
\(346\) 152.360i 0.0236733i
\(347\) −5034.70 + 8720.36i −0.778896 + 1.34909i 0.153683 + 0.988120i \(0.450887\pi\)
−0.932579 + 0.360967i \(0.882447\pi\)
\(348\) 5310.82 + 9198.62i 0.818075 + 1.41695i
\(349\) 5091.64 2939.66i 0.780944 0.450878i −0.0558207 0.998441i \(-0.517778\pi\)
0.836765 + 0.547563i \(0.184444\pi\)
\(350\) 4766.49 0.727942
\(351\) 0 0
\(352\) −2857.76 −0.432725
\(353\) 7917.69 4571.28i 1.19381 0.689249i 0.234644 0.972081i \(-0.424607\pi\)
0.959169 + 0.282833i \(0.0912741\pi\)
\(354\) −2981.05 5163.33i −0.447574 0.775220i
\(355\) −731.398 + 1266.82i −0.109348 + 0.189397i
\(356\) 2446.43i 0.364215i
\(357\) −9105.39 5257.00i −1.34988 0.779356i
\(358\) −46.9466 27.1046i −0.00693074 0.00400146i
\(359\) 2754.32i 0.404924i −0.979290 0.202462i \(-0.935106\pi\)
0.979290 0.202462i \(-0.0648942\pi\)
\(360\) 1826.12 3162.94i 0.267347 0.463059i
\(361\) −3142.23 5442.50i −0.458117 0.793483i
\(362\) 1662.50 959.845i 0.241379 0.139360i
\(363\) 9536.54 1.37889
\(364\) 0 0
\(365\) 1096.97 0.157310
\(366\) −1612.60 + 931.034i −0.230306 + 0.132967i
\(367\) −1520.09 2632.88i −0.216208 0.374483i 0.737438 0.675415i \(-0.236036\pi\)
−0.953646 + 0.300932i \(0.902702\pi\)
\(368\) 701.040 1214.24i 0.0993049 0.172001i
\(369\) 7764.88i 1.09546i
\(370\) 453.672 + 261.928i 0.0637440 + 0.0368026i
\(371\) −2844.25 1642.13i −0.398022 0.229798i
\(372\) 1308.59i 0.182385i
\(373\) 2692.36 4663.31i 0.373740 0.647337i −0.616397 0.787435i \(-0.711408\pi\)
0.990138 + 0.140098i \(0.0447418\pi\)
\(374\) −530.802 919.376i −0.0733880 0.127112i
\(375\) 6356.95 3670.18i 0.875390 0.505407i
\(376\) −9888.59 −1.35629
\(377\) 0 0
\(378\) 7895.84 1.07439
\(379\) 2965.50 1712.13i 0.401920 0.232049i −0.285392 0.958411i \(-0.592124\pi\)
0.687312 + 0.726362i \(0.258791\pi\)
\(380\) −237.393 411.177i −0.0320474 0.0555077i
\(381\) 3756.87 6507.09i 0.505171 0.874983i
\(382\) 6684.69i 0.895336i
\(383\) −331.675 191.493i −0.0442501 0.0255478i 0.477712 0.878517i \(-0.341466\pi\)
−0.521962 + 0.852969i \(0.674800\pi\)
\(384\) −8906.01 5141.89i −1.18355 0.683323i
\(385\) 1477.19i 0.195544i
\(386\) 368.776 638.739i 0.0486275 0.0842253i
\(387\) −3663.27 6344.97i −0.481175 0.833419i
\(388\) 7278.94 4202.50i 0.952403 0.549870i
\(389\) −8588.34 −1.11940 −0.559699 0.828696i \(-0.689083\pi\)
−0.559699 + 0.828696i \(0.689083\pi\)
\(390\) 0 0
\(391\) 5467.56 0.707178
\(392\) −7255.15 + 4188.76i −0.934796 + 0.539705i
\(393\) 1221.93 + 2116.45i 0.156841 + 0.271656i
\(394\) 3501.29 6064.41i 0.447696 0.775433i
\(395\) 2088.72i 0.266063i
\(396\) −3559.38 2055.01i −0.451681 0.260778i
\(397\) 6269.30 + 3619.58i 0.792562 + 0.457586i 0.840864 0.541247i \(-0.182048\pi\)
−0.0483020 + 0.998833i \(0.515381\pi\)
\(398\) 571.904i 0.0720275i
\(399\) 2828.71 4899.46i 0.354918 0.614737i
\(400\) −641.505 1111.12i −0.0801882 0.138890i
\(401\) 3697.60 2134.81i 0.460472 0.265854i −0.251770 0.967787i \(-0.581013\pi\)
0.712243 + 0.701933i \(0.247679\pi\)
\(402\) 6947.32 0.861942
\(403\) 0 0
\(404\) −1870.12 −0.230302
\(405\) 951.185 549.167i 0.116703 0.0673786i
\(406\) 4666.30 + 8082.27i 0.570405 + 0.987971i
\(407\) 718.751 1244.91i 0.0875360 0.151617i
\(408\) 8192.78i 0.994125i
\(409\) 11745.5 + 6781.26i 1.41999 + 0.819834i 0.996298 0.0859711i \(-0.0273993\pi\)
0.423696 + 0.905805i \(0.360733\pi\)
\(410\) 772.337 + 445.909i 0.0930317 + 0.0537119i
\(411\) 22939.9i 2.75315i
\(412\) 897.390 1554.33i 0.107309 0.185864i
\(413\) 5973.96 + 10347.2i 0.711767 + 1.23282i
\(414\) −8037.54 + 4640.47i −0.954163 + 0.550886i
\(415\) 4823.06 0.570494
\(416\) 0 0
\(417\) −17357.5 −2.03837
\(418\) 494.701 285.616i 0.0578867 0.0334209i
\(419\) 7288.44 + 12624.0i 0.849794 + 1.47189i 0.881392 + 0.472386i \(0.156607\pi\)
−0.0315973 + 0.999501i \(0.510059\pi\)
\(420\) −2337.55 + 4048.76i −0.271573 + 0.470379i
\(421\) 15848.4i 1.83469i −0.398099 0.917343i \(-0.630330\pi\)
0.398099 0.917343i \(-0.369670\pi\)
\(422\) −2870.42 1657.24i −0.331114 0.191169i
\(423\) −19581.8 11305.6i −2.25083 1.29952i
\(424\) 2559.18i 0.293124i
\(425\) 2501.62 4332.94i 0.285521 0.494537i
\(426\) −2784.99 4823.75i −0.316745 0.548618i
\(427\) 3231.62 1865.77i 0.366250 0.211455i
\(428\) 7978.70 0.901087
\(429\) 0 0
\(430\) −841.474 −0.0943709
\(431\) −9261.90 + 5347.36i −1.03510 + 0.597618i −0.918443 0.395554i \(-0.870553\pi\)
−0.116662 + 0.993172i \(0.537219\pi\)
\(432\) −1062.67 1840.61i −0.118352 0.204991i
\(433\) −8039.50 + 13924.8i −0.892272 + 1.54546i −0.0551273 + 0.998479i \(0.517556\pi\)
−0.837145 + 0.546981i \(0.815777\pi\)
\(434\) 1149.78i 0.127168i
\(435\) 5890.69 + 3400.99i 0.649280 + 0.374862i
\(436\) 4089.87 + 2361.29i 0.449241 + 0.259370i
\(437\) 2942.01i 0.322049i
\(438\) −2088.50 + 3617.40i −0.227837 + 0.394625i
\(439\) 3017.90 + 5227.16i 0.328101 + 0.568288i 0.982135 0.188177i \(-0.0602579\pi\)
−0.654034 + 0.756465i \(0.726925\pi\)
\(440\) −996.849 + 575.531i −0.108007 + 0.0623577i
\(441\) −19156.0 −2.06845
\(442\) 0 0
\(443\) 10201.3 1.09409 0.547043 0.837105i \(-0.315753\pi\)
0.547043 + 0.837105i \(0.315753\pi\)
\(444\) 3939.98 2274.75i 0.421134 0.243142i
\(445\) 783.332 + 1356.77i 0.0834461 + 0.144533i
\(446\) 4627.21 8014.56i 0.491266 0.850897i
\(447\) 15224.0i 1.61090i
\(448\) −4731.26 2731.59i −0.498953 0.288071i
\(449\) 5042.47 + 2911.27i 0.529997 + 0.305994i 0.741015 0.671488i \(-0.234345\pi\)
−0.211018 + 0.977482i \(0.567678\pi\)
\(450\) 8492.78i 0.889675i
\(451\) 1223.61 2119.36i 0.127755 0.221279i
\(452\) −4489.64 7776.28i −0.467201 0.809216i
\(453\) −21018.9 + 12135.3i −2.18003 + 1.25864i
\(454\) −1398.62 −0.144583
\(455\) 0 0
\(456\) 4408.40 0.452724
\(457\) −4002.42 + 2310.80i −0.409684 + 0.236531i −0.690654 0.723186i \(-0.742677\pi\)
0.280970 + 0.959717i \(0.409344\pi\)
\(458\) 490.106 + 848.889i 0.0500026 + 0.0866070i
\(459\) 4144.02 7177.65i 0.421408 0.729900i
\(460\) 2431.18i 0.246422i
\(461\) 4440.78 + 2563.88i 0.448650 + 0.259028i 0.707260 0.706954i \(-0.249931\pi\)
−0.258610 + 0.965982i \(0.583264\pi\)
\(462\) −4871.20 2812.39i −0.490539 0.283213i
\(463\) 6486.27i 0.651064i 0.945531 + 0.325532i \(0.105543\pi\)
−0.945531 + 0.325532i \(0.894457\pi\)
\(464\) 1256.04 2175.53i 0.125669 0.217665i
\(465\) −419.002 725.733i −0.0417866 0.0723764i
\(466\) −3115.43 + 1798.69i −0.309698 + 0.178804i
\(467\) −12978.0 −1.28598 −0.642990 0.765875i \(-0.722306\pi\)
−0.642990 + 0.765875i \(0.722306\pi\)
\(468\) 0 0
\(469\) −13922.3 −1.37073
\(470\) −2249.03 + 1298.48i −0.220723 + 0.127435i
\(471\) −14090.3 24405.1i −1.37844 2.38754i
\(472\) −4655.07 + 8062.81i −0.453955 + 0.786273i
\(473\) 2309.08i 0.224464i
\(474\) 6887.79 + 3976.67i 0.667440 + 0.385347i
\(475\) 2331.48 + 1346.08i 0.225212 + 0.130026i
\(476\) 6733.04i 0.648337i
\(477\) 2925.89 5067.80i 0.280854 0.486454i
\(478\) −425.228 736.516i −0.0406893 0.0704759i
\(479\) −5030.71 + 2904.48i −0.479873 + 0.277055i −0.720363 0.693597i \(-0.756025\pi\)
0.240491 + 0.970651i \(0.422692\pi\)
\(480\) −5791.95 −0.550761
\(481\) 0 0
\(482\) −8473.14 −0.800707
\(483\) 25088.1 14484.6i 2.36345 1.36454i
\(484\) −3053.54 5288.89i −0.286772 0.496703i
\(485\) 2691.23 4661.35i 0.251964 0.436414i
\(486\) 3662.20i 0.341812i
\(487\) −4665.40 2693.57i −0.434106 0.250631i 0.266989 0.963700i \(-0.413971\pi\)
−0.701094 + 0.713069i \(0.747305\pi\)
\(488\) 2518.16 + 1453.86i 0.233589 + 0.134863i
\(489\) 28498.4i 2.63547i
\(490\) −1100.06 + 1905.36i −0.101419 + 0.175664i
\(491\) 7629.53 + 13214.7i 0.701255 + 1.21461i 0.968026 + 0.250849i \(0.0807097\pi\)
−0.266772 + 0.963760i \(0.585957\pi\)
\(492\) 6707.48 3872.57i 0.614628 0.354855i
\(493\) 9796.16 0.894922
\(494\) 0 0
\(495\) −2632.01 −0.238990
\(496\) −268.025 + 154.744i −0.0242635 + 0.0140085i
\(497\) 5581.07 + 9666.69i 0.503712 + 0.872456i
\(498\) −9182.55 + 15904.6i −0.826264 + 1.43113i
\(499\) 1856.04i 0.166509i −0.996528 0.0832544i \(-0.973469\pi\)
0.996528 0.0832544i \(-0.0265314\pi\)
\(500\) −4070.91 2350.34i −0.364114 0.210221i
\(501\) 23515.0 + 13576.4i 2.09695 + 1.21067i
\(502\) 8153.20i 0.724891i
\(503\) −524.732 + 908.862i −0.0465142 + 0.0805649i −0.888345 0.459176i \(-0.848145\pi\)
0.841831 + 0.539741i \(0.181478\pi\)
\(504\) −13934.6 24135.4i −1.23154 2.13308i
\(505\) −1037.16 + 598.803i −0.0913919 + 0.0527651i
\(506\) 2925.04 0.256984
\(507\) 0 0
\(508\) −4811.71 −0.420246
\(509\) 477.272 275.553i 0.0415613 0.0239954i −0.479075 0.877774i \(-0.659028\pi\)
0.520637 + 0.853778i \(0.325695\pi\)
\(510\) −1075.80 1863.34i −0.0934063 0.161784i
\(511\) 4185.32 7249.19i 0.362324 0.627564i
\(512\) 4074.36i 0.351686i
\(513\) 3862.18 + 2229.83i 0.332396 + 0.191909i
\(514\) 890.121 + 513.911i 0.0763843 + 0.0441005i
\(515\) 1149.36i 0.0983431i
\(516\) −3653.96 + 6328.84i −0.311738 + 0.539945i
\(517\) 3563.13 + 6171.52i 0.303107 + 0.524997i
\(518\) 3461.83 1998.69i 0.293637 0.169531i
\(519\) −847.361 −0.0716667
\(520\) 0 0
\(521\) −8995.30 −0.756413 −0.378206 0.925721i \(-0.623459\pi\)
−0.378206 + 0.925721i \(0.623459\pi\)
\(522\) −14400.7 + 8314.27i −1.20748 + 0.697137i
\(523\) −1331.96 2307.02i −0.111362 0.192885i 0.804958 0.593332i \(-0.202188\pi\)
−0.916320 + 0.400448i \(0.868855\pi\)
\(524\) 782.512 1355.35i 0.0652370 0.112994i
\(525\) 26509.1i 2.20372i
\(526\) −4390.32 2534.76i −0.363930 0.210115i
\(527\) −1045.19 603.443i −0.0863935 0.0498793i
\(528\) 1514.04i 0.124792i
\(529\) −1448.89 + 2509.54i −0.119083 + 0.206258i
\(530\) −336.047 582.051i −0.0275414 0.0477032i
\(531\) −18436.3 + 10644.2i −1.50672 + 0.869906i
\(532\) −3622.94 −0.295253
\(533\) 0 0
\(534\) −5965.49 −0.483431
\(535\) 4424.93 2554.73i 0.357582 0.206450i
\(536\) −5424.30 9395.16i −0.437116 0.757107i
\(537\) −150.744 + 261.096i −0.0121137 + 0.0209816i
\(538\) 4037.86i 0.323577i
\(539\) 5228.46 + 3018.65i 0.417821 + 0.241229i
\(540\) −3191.57 1842.66i −0.254340 0.146843i
\(541\) 6169.23i 0.490270i −0.969489 0.245135i \(-0.921168\pi\)
0.969489 0.245135i \(-0.0788322\pi\)
\(542\) 772.135 1337.38i 0.0611920 0.105988i
\(543\) −5338.23 9246.08i −0.421888 0.730732i
\(544\) −7223.97 + 4170.76i −0.569348 + 0.328713i
\(545\) 3024.28 0.237699
\(546\) 0 0
\(547\) 5140.42 0.401807 0.200904 0.979611i \(-0.435612\pi\)
0.200904 + 0.979611i \(0.435612\pi\)
\(548\) −12722.3 + 7345.24i −0.991735 + 0.572578i
\(549\) 3324.38 + 5757.99i 0.258435 + 0.447623i
\(550\) 1338.32 2318.03i 0.103756 0.179711i
\(551\) 5271.15i 0.407547i
\(552\) 19549.3 + 11286.8i 1.50738 + 0.870285i
\(553\) −13803.0 7969.16i −1.06142 0.612809i
\(554\) 12714.8i 0.975090i
\(555\) 1456.72 2523.12i 0.111413 0.192974i
\(556\) 5557.76 + 9626.32i 0.423923 + 0.734257i
\(557\) 2406.30 1389.28i 0.183049 0.105683i −0.405675 0.914017i \(-0.632964\pi\)
0.588724 + 0.808334i \(0.299630\pi\)
\(558\) 2048.64 0.155422
\(559\) 0 0
\(560\) 1105.69 0.0834356
\(561\) −5113.16 + 2952.08i −0.384809 + 0.222170i
\(562\) 1197.87 + 2074.78i 0.0899097 + 0.155728i
\(563\) 2453.07 4248.85i 0.183632 0.318059i −0.759483 0.650527i \(-0.774548\pi\)
0.943115 + 0.332468i \(0.107881\pi\)
\(564\) 22553.7i 1.68383i
\(565\) −4979.84 2875.11i −0.370802 0.214083i
\(566\) −9419.08 5438.11i −0.699494 0.403853i
\(567\) 8381.04i 0.620759i
\(568\) −4348.91 + 7532.54i −0.321261 + 0.556440i
\(569\) −4681.58 8108.73i −0.344924 0.597426i 0.640416 0.768028i \(-0.278762\pi\)
−0.985340 + 0.170602i \(0.945429\pi\)
\(570\) 1002.63 578.870i 0.0736766 0.0425372i
\(571\) −7199.32 −0.527640 −0.263820 0.964572i \(-0.584982\pi\)
−0.263820 + 0.964572i \(0.584982\pi\)
\(572\) 0 0
\(573\) 37177.3 2.71048
\(574\) 5893.46 3402.59i 0.428551 0.247424i
\(575\) 6892.72 + 11938.5i 0.499906 + 0.865863i
\(576\) 4867.07 8430.01i 0.352074 0.609810i
\(577\) 11449.6i 0.826086i 0.910711 + 0.413043i \(0.135534\pi\)
−0.910711 + 0.413043i \(0.864466\pi\)
\(578\) 3960.50 + 2286.60i 0.285009 + 0.164550i
\(579\) −3552.38 2050.97i −0.254978 0.147211i
\(580\) 4355.91i 0.311843i
\(581\) 18401.6 31872.6i 1.31399 2.27590i
\(582\) 10247.6 + 17749.3i 0.729855 + 1.26415i
\(583\) −1597.20 + 922.142i −0.113463 + 0.0655081i
\(584\) 6522.62 0.462171
\(585\) 0 0
\(586\) −999.439 −0.0704547
\(587\) 4710.65 2719.70i 0.331226 0.191233i −0.325160 0.945659i \(-0.605418\pi\)
0.656385 + 0.754426i \(0.272085\pi\)
\(588\) 9553.63 + 16547.4i 0.670042 + 1.16055i
\(589\) 324.703 562.402i 0.0227150 0.0393436i
\(590\) 2445.04i 0.170611i
\(591\) −33727.5 19472.6i −2.34749 1.35532i
\(592\) −931.831 537.993i −0.0646926 0.0373503i
\(593\) 28405.8i 1.96709i −0.180651 0.983547i \(-0.557820\pi\)
0.180651 0.983547i \(-0.442180\pi\)
\(594\) 2216.97 3839.90i 0.153137 0.265241i
\(595\) 2155.88 + 3734.10i 0.148542 + 0.257282i
\(596\) 8443.14 4874.65i 0.580276 0.335022i
\(597\) 3180.67 0.218051
\(598\) 0 0
\(599\) −10482.3 −0.715020 −0.357510 0.933909i \(-0.616374\pi\)
−0.357510 + 0.933909i \(0.616374\pi\)
\(600\) 17889.1 10328.3i 1.21720 0.702750i
\(601\) −1599.77 2770.88i −0.108579 0.188064i 0.806616 0.591076i \(-0.201297\pi\)
−0.915195 + 0.403012i \(0.867963\pi\)
\(602\) −3210.51 + 5560.77i −0.217360 + 0.376479i
\(603\) 24806.3i 1.67527i
\(604\) 13460.3 + 7771.28i 0.906772 + 0.523525i
\(605\) −3386.95 1955.45i −0.227602 0.131406i
\(606\) 4560.20i 0.305686i
\(607\) −5671.40 + 9823.15i −0.379234 + 0.656853i −0.990951 0.134224i \(-0.957146\pi\)
0.611717 + 0.791077i \(0.290479\pi\)
\(608\) −2244.22 3887.10i −0.149696 0.259281i
\(609\) 44950.0 25951.9i 2.99091 1.72680i
\(610\) 763.629 0.0506859
\(611\) 0 0
\(612\) −11996.7 −0.792384
\(613\) −12458.1 + 7192.70i −0.820846 + 0.473916i −0.850708 0.525638i \(-0.823826\pi\)
0.0298622 + 0.999554i \(0.490493\pi\)
\(614\) −78.3944 135.783i −0.00515267 0.00892469i
\(615\) 2479.95 4295.39i 0.162603 0.281637i
\(616\) 8783.39i 0.574502i
\(617\) 19101.7 + 11028.4i 1.24636 + 0.719588i 0.970382 0.241575i \(-0.0776640\pi\)
0.275981 + 0.961163i \(0.410997\pi\)
\(618\) 3790.14 + 2188.24i 0.246702 + 0.142433i
\(619\) 13621.4i 0.884477i 0.896898 + 0.442238i \(0.145815\pi\)
−0.896898 + 0.442238i \(0.854185\pi\)
\(620\) −268.324 + 464.751i −0.0173809 + 0.0301046i
\(621\) 11418.0 + 19776.6i 0.737824 + 1.27795i
\(622\) 5245.63 3028.57i 0.338152 0.195232i
\(623\) 11954.7 0.768789
\(624\) 0 0
\(625\) 11029.2 0.705866
\(626\) −5124.57 + 2958.67i −0.327187 + 0.188901i
\(627\) −1588.47 2751.31i −0.101176 0.175242i
\(628\) −9023.27 + 15628.8i −0.573356 + 0.993082i
\(629\) 4195.92i 0.265982i
\(630\) −6338.46 3659.51i −0.400842 0.231426i
\(631\) 16227.1 + 9368.74i 1.02376 + 0.591068i 0.915191 0.403021i \(-0.132040\pi\)
0.108569 + 0.994089i \(0.465373\pi\)
\(632\) 12419.6i 0.781683i
\(633\) −9216.83 + 15964.0i −0.578730 + 1.00239i
\(634\) −3440.73 5959.52i −0.215534 0.373317i
\(635\) −2668.54 + 1540.68i −0.166768 + 0.0962836i
\(636\) −5836.91 −0.363913
\(637\) 0 0
\(638\) 5240.75 0.325209
\(639\) −17223.8 + 9944.18i −1.06630 + 0.615627i
\(640\) 2108.67 + 3652.33i 0.130239 + 0.225580i
\(641\) 14899.4 25806.5i 0.918081 1.59016i 0.115753 0.993278i \(-0.463072\pi\)
0.802327 0.596884i \(-0.203595\pi\)
\(642\) 19455.6i 1.19603i
\(643\) −19904.3 11491.8i −1.22076 0.704807i −0.255681 0.966761i \(-0.582300\pi\)
−0.965080 + 0.261955i \(0.915633\pi\)
\(644\) −16066.1 9275.77i −0.983064 0.567573i
\(645\) 4679.90i 0.285692i
\(646\) 833.684 1443.98i 0.0507753 0.0879455i
\(647\) −12452.7 21568.7i −0.756672 1.31059i −0.944539 0.328400i \(-0.893491\pi\)
0.187866 0.982195i \(-0.439843\pi\)
\(648\) 5655.77 3265.36i 0.342870 0.197956i
\(649\) 6709.39 0.405804
\(650\) 0 0
\(651\) −6394.54 −0.384980
\(652\) 15805.0 9125.03i 0.949344 0.548104i
\(653\) −5038.92 8727.67i −0.301973 0.523033i 0.674610 0.738175i \(-0.264312\pi\)
−0.976583 + 0.215142i \(0.930979\pi\)
\(654\) −5757.87 + 9972.93i −0.344267 + 0.596288i
\(655\) 1002.22i 0.0597864i
\(656\) −1586.36 915.886i −0.0944162 0.0545112i
\(657\) 12916.4 + 7457.28i 0.766996 + 0.442825i
\(658\) 19816.5i 1.17406i
\(659\) −6167.30 + 10682.1i −0.364558 + 0.631433i −0.988705 0.149874i \(-0.952113\pi\)
0.624147 + 0.781307i \(0.285447\pi\)
\(660\) 1312.66 + 2273.59i 0.0774169 + 0.134090i
\(661\) −11041.1 + 6374.56i −0.649694 + 0.375101i −0.788339 0.615241i \(-0.789059\pi\)
0.138645 + 0.990342i \(0.455725\pi\)
\(662\) −6451.54 −0.378771
\(663\) 0 0
\(664\) 28678.1 1.67609
\(665\) −2009.26 + 1160.04i −0.117166 + 0.0676460i
\(666\) 3561.20 + 6168.18i 0.207198 + 0.358877i
\(667\) −13495.7 + 23375.2i −0.783440 + 1.35696i
\(668\) 17388.3i 1.00715i
\(669\) −44573.4 25734.5i −2.57594 1.48722i
\(670\) −2467.37 1424.54i −0.142273 0.0821413i
\(671\) 2095.46i 0.120558i
\(672\) −22098.3 + 38275.3i −1.26854 + 2.19718i
\(673\) −6809.12 11793.7i −0.390004 0.675506i 0.602446 0.798160i \(-0.294193\pi\)
−0.992450 + 0.122654i \(0.960860\pi\)
\(674\) 6167.80 3560.98i 0.352485 0.203507i
\(675\) 20896.7 1.19158
\(676\) 0 0
\(677\) 9655.67 0.548150 0.274075 0.961708i \(-0.411628\pi\)
0.274075 + 0.961708i \(0.411628\pi\)
\(678\) 18962.0 10947.7i 1.07409 0.620126i
\(679\) −20535.9 35569.3i −1.16067 2.01034i
\(680\) −1679.92 + 2909.70i −0.0947381 + 0.164091i
\(681\) 7778.51i 0.437699i
\(682\) −559.158 322.830i −0.0313948 0.0181258i
\(683\) −14130.7 8158.38i −0.791650 0.457060i 0.0488929 0.998804i \(-0.484431\pi\)
−0.840543 + 0.541744i \(0.817764\pi\)
\(684\) 6455.25i 0.360852i
\(685\) −4703.80 + 8147.23i −0.262369 + 0.454437i
\(686\) 1116.00 + 1932.97i 0.0621123 + 0.107582i
\(687\) 4721.14 2725.75i 0.262188 0.151374i
\(688\) 1728.37 0.0957753
\(689\) 0 0
\(690\) 5928.30 0.327082
\(691\) −2035.89 + 1175.42i −0.112082 + 0.0647106i −0.554993 0.831855i \(-0.687279\pi\)
0.442911 + 0.896566i \(0.353946\pi\)
\(692\) 271.320 + 469.940i 0.0149047 + 0.0258157i
\(693\) −10042.0 + 17393.3i −0.550454 + 0.953414i
\(694\) 15723.9i 0.860045i
\(695\) 6164.58 + 3559.12i 0.336455 + 0.194252i
\(696\) 35026.2 + 20222.4i 1.90756 + 1.10133i
\(697\) 7143.20i 0.388189i
\(698\) 4590.44 7950.87i 0.248926 0.431153i
\(699\) 10003.5 + 17326.6i 0.541299 + 0.937558i
\(700\) −14701.7 + 8488.05i −0.793819 + 0.458312i
\(701\) 8076.90 0.435179 0.217589 0.976040i \(-0.430181\pi\)
0.217589 + 0.976040i \(0.430181\pi\)
\(702\) 0 0
\(703\) 2257.76 0.121128
\(704\) −2656.85 + 1533.93i −0.142236 + 0.0821197i
\(705\) 7221.55 + 12508.1i 0.385786 + 0.668202i
\(706\) 7138.30 12363.9i 0.380529 0.659095i
\(707\) 9138.55i 0.486125i
\(708\) 18389.5 + 10617.2i 0.976156 + 0.563584i
\(709\) 11799.5 + 6812.44i 0.625021 + 0.360856i 0.778821 0.627246i \(-0.215818\pi\)
−0.153801 + 0.988102i \(0.549151\pi\)
\(710\) 2284.23i 0.120741i
\(711\) 14199.2 24593.8i 0.748962 1.29724i
\(712\) 4657.71 + 8067.40i 0.245162 + 0.424633i
\(713\) 2879.82 1662.67i 0.151263 0.0873315i
\(714\) −16418.2 −0.860553
\(715\) 0 0
\(716\) 193.069 0.0100773
\(717\) −4096.18 + 2364.93i −0.213354 + 0.123180i
\(718\) −2150.51 3724.79i −0.111778 0.193605i
\(719\) 8117.89 14060.6i 0.421066 0.729307i −0.574978 0.818169i \(-0.694990\pi\)
0.996044 + 0.0888616i \(0.0283229\pi\)
\(720\) 1970.09i 0.101973i
\(721\) −7595.36 4385.19i −0.392325 0.226509i
\(722\) −8498.75 4906.75i −0.438076 0.252923i
\(723\) 47123.8i 2.42400i
\(724\) −3418.54 + 5921.08i −0.175482 + 0.303944i
\(725\) 12349.6 + 21390.1i 0.632623 + 1.09574i
\(726\) 12896.7 7445.91i 0.659285 0.380638i
\(727\) −24181.2 −1.23361 −0.616803 0.787118i \(-0.711572\pi\)
−0.616803 + 0.787118i \(0.711572\pi\)
\(728\) 0 0
\(729\) −28693.9 −1.45780
\(730\) 1483.48 856.490i 0.0752139 0.0434248i
\(731\) 3369.98 + 5836.98i 0.170511 + 0.295333i
\(732\) 3315.93 5743.36i 0.167432 0.290001i
\(733\) 3053.70i 0.153876i −0.997036 0.0769379i \(-0.975486\pi\)
0.997036 0.0769379i \(-0.0245143\pi\)
\(734\) −4111.38 2373.71i −0.206749 0.119367i
\(735\) 10596.7 + 6118.03i 0.531791 + 0.307030i
\(736\) 22983.4i 1.15106i
\(737\) −3909.05 + 6770.67i −0.195375 + 0.338400i
\(738\) 6062.63 + 10500.8i 0.302396 + 0.523766i
\(739\) −6957.32 + 4016.81i −0.346318 + 0.199947i −0.663062 0.748564i \(-0.730744\pi\)
0.316744 + 0.948511i \(0.397410\pi\)
\(740\) −1865.74 −0.0926836
\(741\) 0 0
\(742\) −5128.54 −0.253739
\(743\) 13977.3 8069.81i 0.690146 0.398456i −0.113521 0.993536i \(-0.536213\pi\)
0.803667 + 0.595080i \(0.202880\pi\)
\(744\) −2491.40 4315.22i −0.122767 0.212639i
\(745\) 3121.67 5406.89i 0.153515 0.265897i
\(746\) 8408.53i 0.412678i
\(747\) 56789.6 + 32787.5i 2.78156 + 1.60593i
\(748\) 3274.41 + 1890.48i 0.160059 + 0.0924102i
\(749\) 38988.7i 1.90202i
\(750\) 5731.19 9926.71i 0.279031 0.483296i
\(751\) −9245.56 16013.8i −0.449235 0.778097i 0.549102 0.835755i \(-0.314970\pi\)
−0.998336 + 0.0576584i \(0.981637\pi\)
\(752\) 4619.45 2667.04i 0.224008 0.129331i
\(753\) 45344.5 2.19448
\(754\) 0 0
\(755\) 9953.28 0.479784
\(756\) −24353.9 + 14060.7i −1.17162 + 0.676434i
\(757\) −80.3149 139.109i −0.00385613 0.00667902i 0.864091 0.503336i \(-0.167894\pi\)
−0.867947 + 0.496657i \(0.834561\pi\)
\(758\) 2673.59 4630.79i 0.128112 0.221897i
\(759\) 16267.7i 0.777973i
\(760\) −1565.66 903.936i −0.0747271 0.0431437i
\(761\) −23208.7 13399.5i −1.10554 0.638282i −0.167867 0.985810i \(-0.553688\pi\)
−0.937670 + 0.347528i \(0.887021\pi\)
\(762\) 11733.1i 0.557803i
\(763\) 11538.7 19985.6i 0.547481 0.948264i
\(764\) −11903.9 20618.2i −0.563703 0.976363i
\(765\) −6653.30 + 3841.28i −0.314445 + 0.181545i
\(766\) −598.052 −0.0282095
\(767\) 0 0
\(768\) −30025.1 −1.41073
\(769\) 4456.41 2572.91i 0.208976 0.120652i −0.391860 0.920025i \(-0.628168\pi\)
0.600835 + 0.799373i \(0.294835\pi\)
\(770\) 1153.35 + 1997.67i 0.0539792 + 0.0934947i
\(771\) 2858.15 4950.45i 0.133507 0.231240i
\(772\) 2626.83i 0.122463i
\(773\) 11094.3 + 6405.28i 0.516214 + 0.298036i 0.735384 0.677650i \(-0.237002\pi\)
−0.219170 + 0.975687i \(0.570335\pi\)
\(774\) −9908.01