Properties

Label 169.4.c.j.146.1
Level $169$
Weight $4$
Character 169.146
Analytic conductor $9.971$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.1
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.4.c.j.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.780776 - 1.35234i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(2.78078 - 4.81645i) q^{4} +3.56155 q^{5} +(-6.78078 + 11.7446i) q^{6} +(-13.5885 + 23.5360i) q^{7} -21.1771 q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})\) \(q+(-0.780776 - 1.35234i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(2.78078 - 4.81645i) q^{4} +3.56155 q^{5} +(-6.78078 + 11.7446i) q^{6} +(-13.5885 + 23.5360i) q^{7} -21.1771 q^{8} +(-24.2116 + 41.9358i) q^{9} +(-2.78078 - 4.81645i) q^{10} +(7.63068 + 13.2167i) q^{11} -48.3002 q^{12} +42.4384 q^{14} +(-15.4654 - 26.7869i) q^{15} +(-5.71165 - 9.89286i) q^{16} +(-22.2732 + 38.5783i) q^{17} +75.6155 q^{18} +(11.9848 - 20.7584i) q^{19} +(9.90388 - 17.1540i) q^{20} +236.024 q^{21} +(11.9157 - 20.6386i) q^{22} +(-61.3693 - 106.295i) q^{23} +(91.9579 + 159.276i) q^{24} -112.315 q^{25} +186.054 q^{27} +(75.5734 + 130.897i) q^{28} +(109.955 + 190.447i) q^{29} +(-24.1501 + 41.8292i) q^{30} -27.0928 q^{31} +(-93.6274 + 162.167i) q^{32} +(66.2699 - 114.783i) q^{33} +69.5616 q^{34} +(-48.3963 + 83.8249i) q^{35} +(134.654 + 233.228i) q^{36} +(47.0961 + 81.5729i) q^{37} -37.4299 q^{38} -75.4233 q^{40} +(-80.1771 - 138.871i) q^{41} +(-184.282 - 319.185i) q^{42} +(75.6510 - 131.031i) q^{43} +84.8769 q^{44} +(-86.2311 + 149.357i) q^{45} +(-95.8314 + 165.985i) q^{46} -466.948 q^{47} +(-49.6037 + 85.9161i) q^{48} +(-197.797 - 342.594i) q^{49} +(87.6932 + 151.889i) q^{50} +386.870 q^{51} -120.847 q^{53} +(-145.267 - 251.609i) q^{54} +(27.1771 + 47.0721i) q^{55} +(287.766 - 498.425i) q^{56} -208.169 q^{57} +(171.700 - 297.393i) q^{58} +(-219.816 + 380.733i) q^{59} -172.024 q^{60} +(68.6525 - 118.910i) q^{61} +(21.1534 + 36.6388i) q^{62} +(-658.002 - 1139.69i) q^{63} +201.022 q^{64} -206.968 q^{66} +(256.140 + 443.648i) q^{67} +(123.874 + 214.555i) q^{68} +(-532.972 + 923.134i) q^{69} +151.147 q^{70} +(205.359 - 355.693i) q^{71} +(512.732 - 888.078i) q^{72} +308.004 q^{73} +(73.5431 - 127.380i) q^{74} +(487.710 + 844.739i) q^{75} +(-66.6543 - 115.449i) q^{76} -414.759 q^{77} -586.462 q^{79} +(-20.3423 - 35.2339i) q^{80} +(-154.193 - 267.070i) q^{81} +(-125.201 + 216.854i) q^{82} -1354.20 q^{83} +(656.329 - 1136.80i) q^{84} +(-79.3272 + 137.399i) q^{85} -236.266 q^{86} +(954.918 - 1653.97i) q^{87} +(-161.596 - 279.892i) q^{88} +(219.941 + 380.949i) q^{89} +269.309 q^{90} -682.617 q^{92} +(117.646 + 203.769i) q^{93} +(364.582 + 631.474i) q^{94} +(42.6847 - 73.9320i) q^{95} +1626.24 q^{96} +(-755.634 + 1308.80i) q^{97} +(-308.870 + 534.979i) q^{98} -739.006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9} - 7 q^{10} + 80 q^{11} - 86 q^{12} + 178 q^{14} - 33 q^{15} + 39 q^{16} - 19 q^{17} + 220 q^{18} - 84 q^{19} + 19 q^{20} + 606 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 474 q^{25} + 670 q^{27} + 125 q^{28} + 44 q^{29} - 43 q^{30} + 172 q^{31} - 123 q^{32} - 106 q^{33} + 270 q^{34} - 107 q^{35} + 250 q^{36} + 209 q^{37} - 628 q^{38} - 178 q^{40} - 230 q^{41} - 197 q^{42} - 287 q^{43} + 356 q^{44} - 180 q^{45} - 4 q^{46} - 870 q^{47} - 285 q^{48} - 383 q^{49} - 144 q^{50} + 962 q^{51} - 236 q^{53} + 91 q^{54} + 18 q^{55} + 1015 q^{56} - 1212 q^{57} + 794 q^{58} - 368 q^{59} - 350 q^{60} + 1058 q^{61} + 332 q^{62} - 1560 q^{63} + 1538 q^{64} - 1636 q^{66} + 68 q^{67} + 211 q^{68} - 796 q^{69} + 250 q^{70} - 131 q^{71} + 1350 q^{72} - 912 q^{73} - 147 q^{74} + 516 q^{75} + 22 q^{76} + 1524 q^{77} - 2016 q^{79} - 69 q^{80} - 122 q^{81} - 72 q^{82} - 3916 q^{83} + 1409 q^{84} - 173 q^{85} - 2718 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 500 q^{90} - 1576 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 3726 q^{96} - 928 q^{97} - 650 q^{98} + 260 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.780776 1.35234i −0.276046 0.478126i 0.694352 0.719635i \(-0.255691\pi\)
−0.970399 + 0.241509i \(0.922358\pi\)
\(3\) −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
\(5\) 3.56155 0.318555 0.159277 0.987234i \(-0.449084\pi\)
0.159277 + 0.987234i \(0.449084\pi\)
\(6\) −6.78078 + 11.7446i −0.461373 + 0.799122i
\(7\) −13.5885 + 23.5360i −0.733712 + 1.27083i 0.221574 + 0.975144i \(0.428881\pi\)
−0.955286 + 0.295683i \(0.904453\pi\)
\(8\) −21.1771 −0.935904
\(9\) −24.2116 + 41.9358i −0.896728 + 1.55318i
\(10\) −2.78078 4.81645i −0.0879359 0.152309i
\(11\) 7.63068 + 13.2167i 0.209158 + 0.362272i 0.951450 0.307805i \(-0.0995944\pi\)
−0.742292 + 0.670077i \(0.766261\pi\)
\(12\) −48.3002 −1.16192
\(13\) 0 0
\(14\) 42.4384 0.810154
\(15\) −15.4654 26.7869i −0.266211 0.461090i
\(16\) −5.71165 9.89286i −0.0892445 0.154576i
\(17\) −22.2732 + 38.5783i −0.317767 + 0.550389i −0.980022 0.198890i \(-0.936266\pi\)
0.662255 + 0.749279i \(0.269600\pi\)
\(18\) 75.6155 0.990153
\(19\) 11.9848 20.7584i 0.144711 0.250647i −0.784554 0.620061i \(-0.787108\pi\)
0.929265 + 0.369413i \(0.120441\pi\)
\(20\) 9.90388 17.1540i 0.110729 0.191788i
\(21\) 236.024 2.45260
\(22\) 11.9157 20.6386i 0.115474 0.200008i
\(23\) −61.3693 106.295i −0.556365 0.963652i −0.997796 0.0663568i \(-0.978862\pi\)
0.441431 0.897295i \(-0.354471\pi\)
\(24\) 91.9579 + 159.276i 0.782117 + 1.35467i
\(25\) −112.315 −0.898523
\(26\) 0 0
\(27\) 186.054 1.32615
\(28\) 75.5734 + 130.897i 0.510072 + 0.883471i
\(29\) 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
\(31\) −27.0928 −0.156968 −0.0784840 0.996915i \(-0.525008\pi\)
−0.0784840 + 0.996915i \(0.525008\pi\)
\(32\) −93.6274 + 162.167i −0.517223 + 0.895856i
\(33\) 66.2699 114.783i 0.349579 0.605488i
\(34\) 69.5616 0.350874
\(35\) −48.3963 + 83.8249i −0.233728 + 0.404828i
\(36\) 134.654 + 233.228i 0.623400 + 1.07976i
\(37\) 47.0961 + 81.5729i 0.209258 + 0.362446i 0.951481 0.307707i \(-0.0995617\pi\)
−0.742223 + 0.670153i \(0.766228\pi\)
\(38\) −37.4299 −0.159788
\(39\) 0 0
\(40\) −75.4233 −0.298137
\(41\) −80.1771 138.871i −0.305404 0.528975i 0.671947 0.740599i \(-0.265458\pi\)
−0.977351 + 0.211624i \(0.932125\pi\)
\(42\) −184.282 319.185i −0.677031 1.17265i
\(43\) 75.6510 131.031i 0.268295 0.464700i −0.700127 0.714018i \(-0.746873\pi\)
0.968422 + 0.249318i \(0.0802066\pi\)
\(44\) 84.8769 0.290811
\(45\) −86.2311 + 149.357i −0.285657 + 0.494773i
\(46\) −95.8314 + 165.985i −0.307165 + 0.532025i
\(47\) −466.948 −1.44918 −0.724589 0.689181i \(-0.757970\pi\)
−0.724589 + 0.689181i \(0.757970\pi\)
\(48\) −49.6037 + 85.9161i −0.149160 + 0.258353i
\(49\) −197.797 342.594i −0.576667 0.998817i
\(50\) 87.6932 + 151.889i 0.248034 + 0.429607i
\(51\) 386.870 1.06221
\(52\) 0 0
\(53\) −120.847 −0.313199 −0.156600 0.987662i \(-0.550053\pi\)
−0.156600 + 0.987662i \(0.550053\pi\)
\(54\) −145.267 251.609i −0.366079 0.634068i
\(55\) 27.1771 + 47.0721i 0.0666283 + 0.115404i
\(56\) 287.766 498.425i 0.686684 1.18937i
\(57\) −208.169 −0.483730
\(58\) 171.700 297.393i 0.388712 0.673269i
\(59\) −219.816 + 380.733i −0.485045 + 0.840122i −0.999852 0.0171836i \(-0.994530\pi\)
0.514808 + 0.857306i \(0.327863\pi\)
\(60\) −172.024 −0.370136
\(61\) 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
\(63\) −658.002 1139.69i −1.31588 2.27917i
\(64\) 201.022 0.392621
\(65\) 0 0
\(66\) −206.968 −0.386000
\(67\) 256.140 + 443.648i 0.467052 + 0.808958i 0.999292 0.0376358i \(-0.0119827\pi\)
−0.532239 + 0.846594i \(0.678649\pi\)
\(68\) 123.874 + 214.555i 0.220910 + 0.382627i
\(69\) −532.972 + 923.134i −0.929887 + 1.61061i
\(70\) 151.147 0.258078
\(71\) 205.359 355.693i 0.343263 0.594549i −0.641774 0.766894i \(-0.721801\pi\)
0.985037 + 0.172345i \(0.0551345\pi\)
\(72\) 512.732 888.078i 0.839251 1.45362i
\(73\) 308.004 0.493823 0.246912 0.969038i \(-0.420584\pi\)
0.246912 + 0.969038i \(0.420584\pi\)
\(74\) 73.5431 127.380i 0.115530 0.200104i
\(75\) 487.710 + 844.739i 0.750879 + 1.30056i
\(76\) −66.6543 115.449i −0.100602 0.174248i
\(77\) −414.759 −0.613847
\(78\) 0 0
\(79\) −586.462 −0.835217 −0.417608 0.908627i \(-0.637132\pi\)
−0.417608 + 0.908627i \(0.637132\pi\)
\(80\) −20.3423 35.2339i −0.0284293 0.0492409i
\(81\) −154.193 267.070i −0.211513 0.366352i
\(82\) −125.201 + 216.854i −0.168611 + 0.292043i
\(83\) −1354.20 −1.79088 −0.895440 0.445182i \(-0.853139\pi\)
−0.895440 + 0.445182i \(0.853139\pi\)
\(84\) 656.329 1136.80i 0.852516 1.47660i
\(85\) −79.3272 + 137.399i −0.101226 + 0.175329i
\(86\) −236.266 −0.296247
\(87\) 954.918 1653.97i 1.17676 2.03820i
\(88\) −161.596 279.892i −0.195752 0.339052i
\(89\) 219.941 + 380.949i 0.261952 + 0.453714i 0.966761 0.255683i \(-0.0823005\pi\)
−0.704809 + 0.709398i \(0.748967\pi\)
\(90\) 269.309 0.315418
\(91\) 0 0
\(92\) −682.617 −0.773563
\(93\) 117.646 + 203.769i 0.131175 + 0.227202i
\(94\) 364.582 + 631.474i 0.400040 + 0.692889i
\(95\) 42.6847 73.9320i 0.0460985 0.0798449i
\(96\) 1626.24 1.72894
\(97\) −755.634 + 1308.80i −0.790959 + 1.36998i 0.134414 + 0.990925i \(0.457085\pi\)
−0.925374 + 0.379056i \(0.876249\pi\)
\(98\) −308.870 + 534.979i −0.318374 + 0.551439i
\(99\) −739.006 −0.750231
\(100\) −312.324 + 540.961i −0.312324 + 0.540961i
\(101\) −168.130 291.209i −0.165639 0.286895i 0.771243 0.636541i \(-0.219635\pi\)
−0.936882 + 0.349646i \(0.886302\pi\)
\(102\) −302.059 523.182i −0.293219 0.507870i
\(103\) 322.712 0.308716 0.154358 0.988015i \(-0.450669\pi\)
0.154358 + 0.988015i \(0.450669\pi\)
\(104\) 0 0
\(105\) 840.611 0.781288
\(106\) 94.3542 + 163.426i 0.0864574 + 0.149749i
\(107\) −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
\(109\) −849.147 −0.746179 −0.373089 0.927795i \(-0.621702\pi\)
−0.373089 + 0.927795i \(0.621702\pi\)
\(110\) 42.4384 73.5055i 0.0367850 0.0637134i
\(111\) 409.014 708.433i 0.349747 0.605779i
\(112\) 310.452 0.261919
\(113\) −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
\(115\) −218.570 378.574i −0.177233 0.306976i
\(116\) 1223.04 0.978931
\(117\) 0 0
\(118\) 686.509 0.535579
\(119\) −605.321 1048.45i −0.466300 0.807654i
\(120\) 327.513 + 567.269i 0.249147 + 0.431536i
\(121\) 549.045 950.974i 0.412506 0.714481i
\(122\) −214.409 −0.159112
\(123\) −696.311 + 1206.05i −0.510441 + 0.884109i
\(124\) −75.3390 + 130.491i −0.0545616 + 0.0945035i
\(125\) −845.211 −0.604784
\(126\) −1027.50 + 1779.69i −0.726487 + 1.25831i
\(127\) −432.587 749.263i −0.302251 0.523514i 0.674394 0.738371i \(-0.264405\pi\)
−0.976646 + 0.214857i \(0.931071\pi\)
\(128\) 592.066 + 1025.49i 0.408842 + 0.708134i
\(129\) −1314.01 −0.896836
\(130\) 0 0
\(131\) −281.400 −0.187680 −0.0938400 0.995587i \(-0.529914\pi\)
−0.0938400 + 0.995587i \(0.529914\pi\)
\(132\) −368.563 638.371i −0.243025 0.420932i
\(133\) 325.713 + 564.152i 0.212353 + 0.367806i
\(134\) 399.976 692.779i 0.257856 0.446620i
\(135\) 662.641 0.422452
\(136\) 471.681 816.976i 0.297400 0.515111i
\(137\) −1320.72 + 2287.55i −0.823624 + 1.42656i 0.0793428 + 0.996847i \(0.474718\pi\)
−0.902967 + 0.429711i \(0.858616\pi\)
\(138\) 1664.53 1.02677
\(139\) 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
\(141\) 2027.64 + 3511.98i 1.21105 + 2.09760i
\(142\) −641.359 −0.379026
\(143\) 0 0
\(144\) 553.153 0.320112
\(145\) 391.609 + 678.286i 0.224285 + 0.388473i
\(146\) −240.482 416.527i −0.136318 0.236110i
\(147\) −1717.80 + 2975.31i −0.963820 + 1.66939i
\(148\) 523.855 0.290950
\(149\) −876.491 + 1518.13i −0.481912 + 0.834696i −0.999784 0.0207617i \(-0.993391\pi\)
0.517872 + 0.855458i \(0.326724\pi\)
\(150\) 761.585 1319.10i 0.414554 0.718029i
\(151\) 2794.64 1.50613 0.753063 0.657949i \(-0.228576\pi\)
0.753063 + 0.657949i \(0.228576\pi\)
\(152\) −253.804 + 439.601i −0.135436 + 0.234582i
\(153\) −1078.54 1868.09i −0.569901 0.987098i
\(154\) 323.834 + 560.898i 0.169450 + 0.293496i
\(155\) −96.4924 −0.0500030
\(156\) 0 0
\(157\) 3244.87 1.64949 0.824743 0.565508i \(-0.191320\pi\)
0.824743 + 0.565508i \(0.191320\pi\)
\(158\) 457.896 + 793.099i 0.230558 + 0.399339i
\(159\) 524.756 + 908.903i 0.261735 + 0.453338i
\(160\) −333.459 + 577.568i −0.164764 + 0.285380i
\(161\) 3335.68 1.63285
\(162\) −240.781 + 417.045i −0.116775 + 0.202260i
\(163\) 1640.73 2841.83i 0.788418 1.36558i −0.138517 0.990360i \(-0.544234\pi\)
0.926936 0.375221i \(-0.122433\pi\)
\(164\) −891.818 −0.424630
\(165\) 236.024 408.805i 0.111360 0.192881i
\(166\) 1057.33 + 1831.35i 0.494366 + 0.856266i
\(167\) −1563.26 2707.65i −0.724364 1.25463i −0.959235 0.282608i \(-0.908800\pi\)
0.234872 0.972026i \(-0.424533\pi\)
\(168\) −4998.29 −2.29540
\(169\) 0 0
\(170\) 247.747 0.111773
\(171\) 580.346 + 1005.19i 0.259533 + 0.449524i
\(172\) −420.737 728.738i −0.186517 0.323057i
\(173\) −48.7849 + 84.4980i −0.0214396 + 0.0371345i −0.876546 0.481318i \(-0.840158\pi\)
0.855107 + 0.518452i \(0.173492\pi\)
\(174\) −2982.31 −1.29936
\(175\) 1526.20 2643.46i 0.659257 1.14187i
\(176\) 87.1675 150.979i 0.0373324 0.0646616i
\(177\) 3818.06 1.62137
\(178\) 343.450 594.873i 0.144622 0.250492i
\(179\) 17.3575 + 30.0640i 0.00724782 + 0.0125536i 0.869627 0.493710i \(-0.164360\pi\)
−0.862379 + 0.506264i \(0.831026\pi\)
\(180\) 479.579 + 830.654i 0.198587 + 0.343963i
\(181\) −1229.35 −0.504843 −0.252422 0.967617i \(-0.581227\pi\)
−0.252422 + 0.967617i \(0.581227\pi\)
\(182\) 0 0
\(183\) −1192.45 −0.481684
\(184\) 1299.62 + 2251.01i 0.520704 + 0.901885i
\(185\) 167.735 + 290.526i 0.0666602 + 0.115459i
\(186\) 183.710 318.195i 0.0724209 0.125437i
\(187\) −679.839 −0.265854
\(188\) −1298.48 + 2249.03i −0.503730 + 0.872486i
\(189\) −2528.20 + 4378.97i −0.973014 + 1.68531i
\(190\) −133.309 −0.0509012
\(191\) −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
\(193\) 236.160 + 409.041i 0.0880786 + 0.152557i 0.906699 0.421778i \(-0.138594\pi\)
−0.818620 + 0.574335i \(0.805261\pi\)
\(194\) 2359.93 0.873365
\(195\) 0 0
\(196\) −2200.12 −0.801791
\(197\) −2242.18 3883.58i −0.810908 1.40453i −0.912229 0.409681i \(-0.865640\pi\)
0.101321 0.994854i \(-0.467693\pi\)
\(198\) 576.998 + 999.390i 0.207098 + 0.358705i
\(199\) 183.120 317.173i 0.0652314 0.112984i −0.831565 0.555427i \(-0.812555\pi\)
0.896797 + 0.442443i \(0.145888\pi\)
\(200\) 2378.51 0.840931
\(201\) 2224.49 3852.93i 0.780614 1.35206i
\(202\) −262.543 + 454.739i −0.0914480 + 0.158393i
\(203\) −5976.49 −2.06634
\(204\) 1075.80 1863.34i 0.369221 0.639509i
\(205\) −285.555 494.596i −0.0972879 0.168508i
\(206\) −251.966 436.418i −0.0852199 0.147605i
\(207\) 5943.41 1.99563
\(208\) 0 0
\(209\) 365.810 0.121070
\(210\) −656.329 1136.80i −0.215671 0.373554i
\(211\) −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
\(213\) −3566.95 −1.14743
\(214\) −1120.12 + 1940.10i −0.357801 + 0.619730i
\(215\) 269.435 466.675i 0.0854666 0.148033i
\(216\) −3940.08 −1.24115
\(217\) 368.152 637.657i 0.115169 0.199479i
\(218\) 662.994 + 1148.34i 0.205980 + 0.356768i
\(219\) −1337.45 2316.54i −0.412679 0.714781i
\(220\) 302.294 0.0926392
\(221\) 0 0
\(222\) −1277.39 −0.386185
\(223\) −2963.21 5132.43i −0.889826 1.54122i −0.840081 0.542461i \(-0.817493\pi\)
−0.0497449 0.998762i \(-0.515841\pi\)
\(224\) −2544.52 4407.24i −0.758986 1.31460i
\(225\) 2719.34 4710.03i 0.805730 1.39557i
\(226\) 2521.17 0.742060
\(227\) −447.830 + 775.665i −0.130941 + 0.226796i −0.924039 0.382297i \(-0.875133\pi\)
0.793099 + 0.609093i \(0.208466\pi\)
\(228\) −578.870 + 1002.63i −0.168143 + 0.291232i
\(229\) −627.717 −0.181138 −0.0905692 0.995890i \(-0.528869\pi\)
−0.0905692 + 0.995890i \(0.528869\pi\)
\(230\) −341.309 + 591.164i −0.0978488 + 0.169479i
\(231\) 1801.02 + 3119.46i 0.512981 + 0.888509i
\(232\) −2328.52 4033.11i −0.658942 1.14132i
\(233\) 2303.72 0.647734 0.323867 0.946103i \(-0.395017\pi\)
0.323867 + 0.946103i \(0.395017\pi\)
\(234\) 0 0
\(235\) −1663.06 −0.461643
\(236\) 1222.52 + 2117.47i 0.337200 + 0.584048i
\(237\) 2546.61 + 4410.86i 0.697976 + 1.20893i
\(238\) −945.240 + 1637.20i −0.257440 + 0.445900i
\(239\) −544.622 −0.147400 −0.0737001 0.997280i \(-0.523481\pi\)
−0.0737001 + 0.997280i \(0.523481\pi\)
\(240\) −176.666 + 305.995i −0.0475156 + 0.0822995i
\(241\) 2713.05 4699.14i 0.725157 1.25601i −0.233752 0.972296i \(-0.575100\pi\)
0.958909 0.283713i \(-0.0915662\pi\)
\(242\) −1714.73 −0.455483
\(243\) 1172.61 2031.03i 0.309561 0.536175i
\(244\) −381.814 661.322i −0.100177 0.173511i
\(245\) −704.464 1220.17i −0.183700 0.318178i
\(246\) 2174.65 0.563621
\(247\) 0 0
\(248\) 573.746 0.146907
\(249\) 5880.39 + 10185.1i 1.49661 + 2.59220i
\(250\) 659.921 + 1143.02i 0.166948 + 0.289163i
\(251\) 2610.61 4521.71i 0.656494 1.13708i −0.325022 0.945706i \(-0.605372\pi\)
0.981517 0.191375i \(-0.0612948\pi\)
\(252\) −7319.02 −1.82958
\(253\) 936.580 1622.20i 0.232736 0.403111i
\(254\) −675.508 + 1170.01i −0.166871 + 0.289028i
\(255\) 1377.86 0.338372
\(256\) 1728.63 2994.07i 0.422029 0.730975i
\(257\) −329.103 570.023i −0.0798789 0.138354i 0.823319 0.567579i \(-0.192120\pi\)
−0.903198 + 0.429225i \(0.858787\pi\)
\(258\) 1025.95 + 1776.99i 0.247568 + 0.428801i
\(259\) −2559.87 −0.614141
\(260\) 0 0
\(261\) −10648.7 −2.52544
\(262\) 219.711 + 380.550i 0.0518083 + 0.0897346i
\(263\) −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
\(265\) −430.401 −0.0997711
\(266\) 508.618 880.953i 0.117238 0.203063i
\(267\) 1910.11 3308.42i 0.437817 0.758321i
\(268\) 2849.07 0.649384
\(269\) 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
\(271\) 494.466 + 856.441i 0.110836 + 0.191974i 0.916108 0.400932i \(-0.131314\pi\)
−0.805271 + 0.592907i \(0.797980\pi\)
\(272\) 508.867 0.113436
\(273\) 0 0
\(274\) 4124.74 0.909433
\(275\) −857.043 1484.44i −0.187933 0.325510i
\(276\) 2964.15 + 5134.06i 0.646452 + 1.11969i
\(277\) −4071.20 + 7051.53i −0.883086 + 1.52955i −0.0351939 + 0.999381i \(0.511205\pi\)
−0.847892 + 0.530169i \(0.822128\pi\)
\(278\) −3120.97 −0.673322
\(279\) 655.961 1136.16i 0.140758 0.243799i
\(280\) 1024.89 1775.17i 0.218747 0.378880i
\(281\) −1534.21 −0.325705 −0.162853 0.986650i \(-0.552070\pi\)
−0.162853 + 0.986650i \(0.552070\pi\)
\(282\) 3166.27 5484.14i 0.668612 1.15807i
\(283\) 3482.50 + 6031.87i 0.731495 + 1.26699i 0.956244 + 0.292570i \(0.0945105\pi\)
−0.224749 + 0.974417i \(0.572156\pi\)
\(284\) −1142.12 1978.20i −0.238634 0.413327i
\(285\) −741.403 −0.154095
\(286\) 0 0
\(287\) 4357.96 0.896314
\(288\) −4533.75 7852.68i −0.927616 1.60668i
\(289\) 1464.31 + 2536.26i 0.298048 + 0.516234i
\(290\) 611.518 1059.18i 0.123826 0.214473i
\(291\) 13124.9 2.64396
\(292\) 856.490 1483.48i 0.171652 0.297309i
\(293\) 320.015 554.281i 0.0638070 0.110517i −0.832357 0.554240i \(-0.813009\pi\)
0.896164 + 0.443723i \(0.146342\pi\)
\(294\) 5364.87 1.06424
\(295\) −782.887 + 1356.00i −0.154513 + 0.267625i
\(296\) −997.358 1727.48i −0.195846 0.339214i
\(297\) 1419.72 + 2459.03i 0.277375 + 0.480428i
\(298\) 2737.37 0.532120
\(299\) 0 0
\(300\) 5424.85 1.04401
\(301\) 2055.97 + 3561.05i 0.393702 + 0.681912i
\(302\) −2181.99 3779.32i −0.415760 0.720118i
\(303\) −1460.15 + 2529.05i −0.276843 + 0.479506i
\(304\) −273.813 −0.0516587
\(305\) 244.509 423.503i 0.0459035 0.0795072i
\(306\) −1684.20 + 2917.12i −0.314638 + 0.544969i
\(307\) 100.406 0.0186660 0.00933299 0.999956i \(-0.497029\pi\)
0.00933299 + 0.999956i \(0.497029\pi\)
\(308\) −1153.35 + 1997.67i −0.213371 + 0.369570i
\(309\) −1401.32 2427.16i −0.257988 0.446849i
\(310\) 75.3390 + 130.491i 0.0138031 + 0.0239077i
\(311\) −3878.92 −0.707245 −0.353623 0.935388i \(-0.615050\pi\)
−0.353623 + 0.935388i \(0.615050\pi\)
\(312\) 0 0
\(313\) −3789.39 −0.684311 −0.342155 0.939643i \(-0.611157\pi\)
−0.342155 + 0.939643i \(0.611157\pi\)
\(314\) −2533.52 4388.19i −0.455334 0.788662i
\(315\) −2343.51 4059.08i −0.419180 0.726041i
\(316\) −1630.82 + 2824.66i −0.290319 + 0.502847i
\(317\) −4406.81 −0.780791 −0.390396 0.920647i \(-0.627662\pi\)
−0.390396 + 0.920647i \(0.627662\pi\)
\(318\) 819.434 1419.30i 0.144502 0.250284i
\(319\) −1678.06 + 2906.48i −0.294524 + 0.510130i
\(320\) 715.950 0.125071
\(321\) −6229.58 + 10790.0i −1.08318 + 1.87613i
\(322\) −2604.42 4510.99i −0.450741 0.780706i
\(323\) 533.882 + 924.710i 0.0919690 + 0.159295i
\(324\) −1715.11 −0.294086
\(325\) 0 0
\(326\) −5124.19 −0.870559
\(327\) 3687.27 + 6386.55i 0.623568 + 1.08005i
\(328\) 1697.92 + 2940.88i 0.285829 + 0.495070i
\(329\) 6345.14 10990.1i 1.06328 1.84165i
\(330\) −737.127 −0.122962
\(331\) −2065.75 + 3577.98i −0.343032 + 0.594149i −0.984994 0.172587i \(-0.944787\pi\)
0.641962 + 0.766736i \(0.278121\pi\)
\(332\) −3765.73 + 6522.44i −0.622505 + 1.07821i
\(333\) −4561.10 −0.750591
\(334\) −2441.11 + 4228.13i −0.399916 + 0.692674i
\(335\) 912.257 + 1580.07i 0.148782 + 0.257698i
\(336\) −1348.08 2334.95i −0.218881 0.379113i
\(337\) −4560.82 −0.737221 −0.368611 0.929584i \(-0.620166\pi\)
−0.368611 + 0.929584i \(0.620166\pi\)
\(338\) 0 0
\(339\) 14021.6 2.24646
\(340\) 441.182 + 764.150i 0.0703720 + 0.121888i
\(341\) −206.737 358.078i −0.0328311 0.0568652i
\(342\) 906.240 1569.65i 0.143286 0.248179i
\(343\) 1429.34 0.225007
\(344\) −1602.07 + 2774.86i −0.251098 + 0.434914i
\(345\) −1898.21 + 3287.79i −0.296220 + 0.513069i
\(346\) 152.360 0.0236733
\(347\) −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
\(349\) 2939.66 + 5091.64i 0.450878 + 0.780944i 0.998441 0.0558207i \(-0.0177775\pi\)
−0.547563 + 0.836765i \(0.684444\pi\)
\(350\) −4766.49 −0.727942
\(351\) 0 0
\(352\) −2857.76 −0.432725
\(353\) −4571.28 7917.69i −0.689249 1.19381i −0.972081 0.234644i \(-0.924607\pi\)
0.282833 0.959169i \(-0.408726\pi\)
\(354\) −2981.05 5163.33i −0.447574 0.775220i
\(355\) 731.398 1266.82i 0.109348 0.189397i
\(356\) 2446.43 0.364215
\(357\) −5257.00 + 9105.39i −0.779356 + 1.34988i
\(358\) 27.1046 46.9466i 0.00400146 0.00693074i
\(359\) 2754.32 0.404924 0.202462 0.979290i \(-0.435106\pi\)
0.202462 + 0.979290i \(0.435106\pi\)
\(360\) 1826.12 3162.94i 0.267347 0.463059i
\(361\) 3142.23 + 5442.50i 0.458117 + 0.793483i
\(362\) 959.845 + 1662.50i 0.139360 + 0.241379i
\(363\) −9536.54 −1.37889
\(364\) 0 0
\(365\) 1096.97 0.157310
\(366\) 931.034 + 1612.60i 0.132967 + 0.230306i
\(367\) −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
\(369\) 7764.88 1.09546
\(370\) 261.928 453.672i 0.0368026 0.0637440i
\(371\) 1642.13 2844.25i 0.229798 0.398022i
\(372\) 1308.59 0.182385
\(373\) 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
\(375\) 3670.18 + 6356.95i 0.505407 + 0.875390i
\(376\) 9888.59 1.35629
\(377\) 0 0
\(378\) 7895.84 1.07439
\(379\) −1712.13 2965.50i −0.232049 0.401920i 0.726362 0.687312i \(-0.241209\pi\)
−0.958411 + 0.285392i \(0.907876\pi\)
\(380\) −237.393 411.177i −0.0320474 0.0555077i
\(381\) −3756.87 + 6507.09i −0.505171 + 0.874983i
\(382\) 6684.69 0.895336
\(383\) −191.493 + 331.675i −0.0255478 + 0.0442501i −0.878517 0.477712i \(-0.841466\pi\)
0.852969 + 0.521962i \(0.174800\pi\)
\(384\) 5141.89 8906.01i 0.683323 1.18355i
\(385\) −1477.19 −0.195544
\(386\) 368.776 638.739i 0.0486275 0.0842253i
\(387\) 3663.27 + 6344.97i 0.481175 + 0.833419i
\(388\) 4202.50 + 7278.94i 0.549870 + 0.952403i
\(389\) 8588.34 1.11940 0.559699 0.828696i \(-0.310917\pi\)
0.559699 + 0.828696i \(0.310917\pi\)
\(390\) 0 0
\(391\) 5467.56 0.707178
\(392\) 4188.76 + 7255.15i 0.539705 + 0.934796i
\(393\) 1221.93 + 2116.45i 0.156841 + 0.271656i
\(394\) −3501.29 + 6064.41i −0.447696 + 0.775433i
\(395\) −2088.72 −0.266063
\(396\) −2055.01 + 3559.38i −0.260778 + 0.451681i
\(397\) −3619.58 + 6269.30i −0.457586 + 0.792562i −0.998833 0.0483020i \(-0.984619\pi\)
0.541247 + 0.840864i \(0.317952\pi\)
\(398\) −571.904 −0.0720275
\(399\) 2828.71 4899.46i 0.354918 0.614737i
\(400\) 641.505 + 1111.12i 0.0801882 + 0.138890i
\(401\) 2134.81 + 3697.60i 0.265854 + 0.460472i 0.967787 0.251770i \(-0.0810128\pi\)
−0.701933 + 0.712243i \(0.747679\pi\)
\(402\) −6947.32 −0.861942
\(403\) 0 0
\(404\) −1870.12 −0.230302
\(405\) −549.167 951.185i −0.0673786 0.116703i
\(406\) 4666.30 + 8082.27i 0.570405 + 0.987971i
\(407\) −718.751 + 1244.91i −0.0875360 + 0.151617i
\(408\) −8192.78 −0.994125
\(409\) 6781.26 11745.5i 0.819834 1.41999i −0.0859711 0.996298i \(-0.527399\pi\)
0.905805 0.423696i \(-0.139267\pi\)
\(410\) −445.909 + 772.337i −0.0537119 + 0.0930317i
\(411\) 22939.9 2.75315
\(412\) 897.390 1554.33i 0.107309 0.185864i
\(413\) −5973.96 10347.2i −0.711767 1.23282i
\(414\) −4640.47 8037.54i −0.550886 0.954163i
\(415\) −4823.06 −0.570494
\(416\) 0 0
\(417\) −17357.5 −2.03837
\(418\) −285.616 494.701i −0.0334209 0.0578867i
\(419\) 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
\(421\) −15848.4 −1.83469 −0.917343 0.398099i \(-0.869670\pi\)
−0.917343 + 0.398099i \(0.869670\pi\)
\(422\) −1657.24 + 2870.42i −0.191169 + 0.331114i
\(423\) 11305.6 19581.8i 1.29952 2.25083i
\(424\) 2559.18 0.293124
\(425\) 2501.62 4332.94i 0.285521 0.494537i
\(426\) 2784.99 + 4823.75i 0.316745 + 0.548618i
\(427\) 1865.77 + 3231.62i 0.211455 + 0.366250i
\(428\) −7978.70 −0.901087
\(429\) 0 0
\(430\) −841.474 −0.0943709
\(431\) 5347.36 + 9261.90i 0.597618 + 1.03510i 0.993172 + 0.116662i \(0.0372193\pi\)
−0.395554 + 0.918443i \(0.629447\pi\)
\(432\) −1062.67 1840.61i −0.118352 0.204991i
\(433\) 8039.50 13924.8i 0.892272 1.54546i 0.0551273 0.998479i \(-0.482444\pi\)
0.837145 0.546981i \(-0.184223\pi\)
\(434\) −1149.78 −0.127168
\(435\) 3400.99 5890.69i 0.374862 0.649280i
\(436\) −2361.29 + 4089.87i −0.259370 + 0.449241i
\(437\) −2942.01 −0.322049
\(438\) −2088.50 + 3617.40i −0.227837 + 0.394625i
\(439\) −3017.90 5227.16i −0.328101 0.568288i 0.654034 0.756465i \(-0.273075\pi\)
−0.982135 + 0.188177i \(0.939742\pi\)
\(440\) −575.531 996.849i −0.0623577 0.108007i
\(441\) 19156.0 2.06845
\(442\) 0 0
\(443\) 10201.3 1.09409 0.547043 0.837105i \(-0.315753\pi\)
0.547043 + 0.837105i \(0.315753\pi\)
\(444\) −2274.75 3939.98i −0.243142 0.421134i
\(445\) 783.332 + 1356.77i 0.0834461 + 0.144533i
\(446\) −4627.21 + 8014.56i −0.491266 + 0.850897i
\(447\) 15224.0 1.61090
\(448\) −2731.59 + 4731.26i −0.288071 + 0.498953i
\(449\) −2911.27 + 5042.47i −0.305994 + 0.529997i −0.977482 0.211018i \(-0.932322\pi\)
0.671488 + 0.741015i \(0.265655\pi\)
\(450\) −8492.78 −0.889675
\(451\) 1223.61 2119.36i 0.127755 0.221279i
\(452\) 4489.64 + 7776.28i 0.467201 + 0.809216i
\(453\) −12135.3 21018.9i −1.25864 2.18003i
\(454\) 1398.62 0.144583
\(455\) 0 0
\(456\) 4408.40 0.452724
\(457\) 2310.80 + 4002.42i 0.236531 + 0.409684i 0.959717 0.280970i \(-0.0906562\pi\)
−0.723186 + 0.690654i \(0.757323\pi\)
\(458\) 490.106 + 848.889i 0.0500026 + 0.0866070i
\(459\) −4144.02 + 7177.65i −0.421408 + 0.729900i
\(460\) −2431.18 −0.246422
\(461\) 2563.88 4440.78i 0.259028 0.448650i −0.706954 0.707260i \(-0.749931\pi\)
0.965982 + 0.258610i \(0.0832644\pi\)
\(462\) 2812.39 4871.20i 0.283213 0.490539i
\(463\) −6486.27 −0.651064 −0.325532 0.945531i \(-0.605543\pi\)
−0.325532 + 0.945531i \(0.605543\pi\)
\(464\) 1256.04 2175.53i 0.125669 0.217665i
\(465\) 419.002 + 725.733i 0.0417866 + 0.0723764i
\(466\) −1798.69 3115.43i −0.178804 0.309698i
\(467\) 12978.0 1.28598 0.642990 0.765875i \(-0.277694\pi\)
0.642990 + 0.765875i \(0.277694\pi\)
\(468\) 0 0
\(469\) −13922.3 −1.37073
\(470\) 1298.48 + 2249.03i 0.127435 + 0.220723i
\(471\) −14090.3 24405.1i −1.37844 2.38754i
\(472\) 4655.07 8062.81i 0.453955 0.786273i
\(473\) 2309.08 0.224464
\(474\) 3976.67 6887.79i 0.385347 0.667440i
\(475\) −1346.08 + 2331.48i −0.130026 + 0.225212i
\(476\) −6733.04 −0.648337
\(477\) 2925.89 5067.80i 0.280854 0.486454i
\(478\) 425.228 + 736.516i 0.0406893 + 0.0704759i
\(479\) −2904.48 5030.71i −0.277055 0.479873i 0.693597 0.720363i \(-0.256025\pi\)
−0.970651 + 0.240491i \(0.922692\pi\)
\(480\) 5791.95 0.550761
\(481\) 0 0
\(482\) −8473.14 −0.800707
\(483\) −14484.6 25088.1i −1.36454 2.36345i
\(484\) −3053.54 5288.89i −0.286772 0.496703i
\(485\) −2691.23 + 4661.35i −0.251964 + 0.436414i
\(486\) −3662.20 −0.341812
\(487\) −2693.57 + 4665.40i −0.250631 + 0.434106i −0.963700 0.266989i \(-0.913971\pi\)
0.713069 + 0.701094i \(0.247305\pi\)
\(488\) −1453.86 + 2518.16i −0.134863 + 0.233589i
\(489\) −28498.4 −2.63547
\(490\) −1100.06 + 1905.36i −0.101419 + 0.175664i
\(491\) −7629.53 13214.7i −0.701255 1.21461i −0.968026 0.250849i \(-0.919290\pi\)
0.266772 0.963760i \(-0.414043\pi\)
\(492\) 3872.57 + 6707.48i 0.354855 + 0.614628i
\(493\) −9796.16 −0.894922
\(494\) 0 0
\(495\) −2632.01 −0.238990
\(496\) 154.744 + 268.025i 0.0140085 + 0.0242635i
\(497\) 5581.07 + 9666.69i 0.503712 + 0.872456i
\(498\) 9182.55 15904.6i 0.826264 1.43113i
\(499\) −1856.04 −0.166509 −0.0832544 0.996528i \(-0.526531\pi\)
−0.0832544 + 0.996528i \(0.526531\pi\)
\(500\) −2350.34 + 4070.91i −0.210221 + 0.364114i
\(501\) −13576.4 + 23515.0i −1.21067 + 2.09695i
\(502\) −8153.20 −0.724891
\(503\) −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
\(505\) −598.803 1037.16i −0.0527651 0.0913919i
\(506\) −2925.04 −0.256984
\(507\) 0 0
\(508\) −4811.71 −0.420246
\(509\) −275.553 477.272i −0.0239954 0.0415613i 0.853778 0.520637i \(-0.174305\pi\)
−0.877774 + 0.479075i \(0.840972\pi\)
\(510\) −1075.80 1863.34i −0.0934063 0.161784i
\(511\) −4185.32 + 7249.19i −0.362324 + 0.627564i
\(512\) 4074.36 0.351686
\(513\) 2229.83 3862.18i 0.191909 0.332396i
\(514\) −513.911 + 890.121i −0.0441005 + 0.0763843i
\(515\) 1149.36 0.0983431
\(516\) −3653.96 + 6328.84i −0.311738 + 0.539945i
\(517\) −3563.13 6171.52i −0.303107 0.524997i
\(518\) 1998.69 + 3461.83i 0.169531 + 0.293637i
\(519\) 847.361 0.0716667
\(520\) 0 0
\(521\) −8995.30 −0.756413 −0.378206 0.925721i \(-0.623459\pi\)
−0.378206 + 0.925721i \(0.623459\pi\)
\(522\) 8314.27 + 14400.7i 0.697137 + 1.20748i
\(523\) −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
\(525\) −26509.1 −2.20372
\(526\) −2534.76 + 4390.32i −0.210115 + 0.363930i
\(527\) 603.443 1045.19i 0.0498793 0.0863935i
\(528\) −1514.04 −0.124792
\(529\) −1448.89 + 2509.54i −0.119083 + 0.206258i
\(530\) 336.047 + 582.051i 0.0275414 + 0.0477032i
\(531\) −10644.2 18436.3i −0.869906 1.50672i
\(532\) 3622.94 0.295253
\(533\) 0 0
\(534\) −5965.49 −0.483431
\(535\) −2554.73 4424.93i −0.206450 0.357582i
\(536\) −5424.30 9395.16i −0.437116 0.757107i
\(537\) 150.744 261.096i 0.0121137 0.0209816i
\(538\) −4037.86 −0.323577
\(539\) 3018.65 5228.46i 0.241229 0.417821i
\(540\) 1842.66 3191.57i 0.146843 0.254340i
\(541\) 6169.23 0.490270 0.245135 0.969489i \(-0.421168\pi\)
0.245135 + 0.969489i \(0.421168\pi\)
\(542\) 772.135 1337.38i 0.0611920 0.105988i
\(543\) 5338.23 + 9246.08i 0.421888 + 0.730732i
\(544\) −4170.76 7223.97i −0.328713 0.569348i
\(545\) −3024.28 −0.237699
\(546\) 0 0
\(547\) 5140.42 0.401807 0.200904 0.979611i \(-0.435612\pi\)
0.200904 + 0.979611i \(0.435612\pi\)
\(548\) 7345.24 + 12722.3i 0.572578 + 0.991735i
\(549\) 3324.38 + 5757.99i 0.258435 + 0.447623i
\(550\) −1338.32 + 2318.03i −0.103756 + 0.179711i
\(551\) 5271.15 0.407547
\(552\) 11286.8 19549.3i 0.870285 1.50738i
\(553\) 7969.16 13803.0i 0.612809 1.06142i
\(554\) 12714.8 0.975090
\(555\) 1456.72 2523.12i 0.111413 0.192974i
\(556\) −5557.76 9626.32i −0.423923 0.734257i
\(557\) 1389.28 + 2406.30i 0.105683 + 0.183049i 0.914017 0.405675i \(-0.132964\pi\)
−0.808334 + 0.588724i \(0.799630\pi\)
\(558\) −2048.64 −0.155422
\(559\) 0 0
\(560\) 1105.69 0.0834356
\(561\) 2952.08 + 5113.16i 0.222170 + 0.384809i
\(562\) 1197.87 + 2074.78i 0.0899097 + 0.155728i
\(563\) −2453.07 + 4248.85i −0.183632 + 0.318059i −0.943115 0.332468i \(-0.892119\pi\)
0.759483 + 0.650527i \(0.225452\pi\)
\(564\) 22553.7 1.68383
\(565\) −2875.11 + 4979.84i −0.214083 + 0.370802i
\(566\) 5438.11 9419.08i 0.403853 0.699494i
\(567\) 8381.04 0.620759
\(568\) −4348.91 + 7532.54i −0.321261 + 0.556440i
\(569\) 4681.58 + 8108.73i 0.344924 + 0.597426i 0.985340 0.170602i \(-0.0545713\pi\)
−0.640416 + 0.768028i \(0.721238\pi\)
\(570\) 578.870 + 1002.63i 0.0425372 + 0.0736766i
\(571\) 7199.32 0.527640 0.263820 0.964572i \(-0.415018\pi\)
0.263820 + 0.964572i \(0.415018\pi\)
\(572\) 0 0
\(573\) 37177.3 2.71048
\(574\) −3402.59 5893.46i −0.247424 0.428551i
\(575\) 6892.72 + 11938.5i 0.499906 + 0.865863i
\(576\) −4867.07 + 8430.01i −0.352074 + 0.609810i
\(577\) 11449.6 0.826086 0.413043 0.910711i \(-0.364466\pi\)
0.413043 + 0.910711i \(0.364466\pi\)
\(578\) 2286.60 3960.50i 0.164550 0.285009i
\(579\) 2050.97 3552.38i 0.147211 0.254978i
\(580\) 4355.91 0.311843
\(581\) 18401.6 31872.6i 1.31399 2.27590i
\(582\) −10247.6 17749.3i −0.729855 1.26415i
\(583\) −922.142 1597.20i −0.0655081 0.113463i
\(584\) −6522.62 −0.462171
\(585\) 0 0
\(586\) −999.439 −0.0704547
\(587\) −2719.70 4710.65i −0.191233 0.331226i 0.754426 0.656385i \(-0.227915\pi\)
−0.945659 + 0.325160i \(0.894582\pi\)
\(588\) 9553.63 + 16547.4i 0.670042 + 1.16055i
\(589\) −324.703 + 562.402i −0.0227150 + 0.0393436i
\(590\) 2445.04 0.170611
\(591\) −19472.6 + 33727.5i −1.35532 + 2.34749i
\(592\) 537.993 931.831i 0.0373503 0.0646926i
\(593\) 28405.8 1.96709 0.983547 0.180651i \(-0.0578204\pi\)
0.983547 + 0.180651i \(0.0578204\pi\)
\(594\) 2216.97 3839.90i 0.153137 0.265241i
\(595\) −2155.88 3734.10i −0.148542 0.257282i
\(596\) 4874.65 + 8443.14i 0.335022 + 0.580276i
\(597\) −3180.67 −0.218051
\(598\) 0 0
\(599\) −10482.3 −0.715020 −0.357510 0.933909i \(-0.616374\pi\)
−0.357510 + 0.933909i \(0.616374\pi\)
\(600\) −10328.3 17889.1i −0.702750 1.21720i
\(601\) −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
\(603\) −24806.3 −1.67527
\(604\) 7771.28 13460.3i 0.523525 0.906772i
\(605\) 1955.45 3386.95i 0.131406 0.227602i
\(606\) 4560.20 0.305686
\(607\) −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
\(609\) 25951.9 + 44950.0i 1.72680 + 2.99091i
\(610\) −763.629 −0.0506859
\(611\) 0 0
\(612\) −11996.7 −0.792384
\(613\) 7192.70 + 12458.1i 0.473916 + 0.820846i 0.999554 0.0298622i \(-0.00950685\pi\)
−0.525638 + 0.850708i \(0.676174\pi\)
\(614\) −78.3944 135.783i −0.00515267 0.00892469i
\(615\) −2479.95 + 4295.39i −0.162603 + 0.281637i
\(616\) 8783.39 0.574502
\(617\) 11028.4 19101.7i 0.719588 1.24636i −0.241575 0.970382i \(-0.577664\pi\)
0.961163 0.275981i \(-0.0890027\pi\)
\(618\) −2188.24 + 3790.14i −0.142433 + 0.246702i
\(619\) −13621.4 −0.884477 −0.442238 0.896898i \(-0.645815\pi\)
−0.442238 + 0.896898i \(0.645815\pi\)
\(620\) −268.324 + 464.751i −0.0173809 + 0.0301046i
\(621\) −11418.0 19776.6i −0.737824 1.27795i
\(622\) 3028.57 + 5245.63i 0.195232 + 0.338152i
\(623\) −11954.7 −0.768789
\(624\) 0 0
\(625\) 11029.2 0.705866
\(626\) 2958.67 + 5124.57i 0.188901 + 0.327187i
\(627\) −1588.47 2751.31i −0.101176 0.175242i
\(628\) 9023.27 15628.8i 0.573356 0.993082i
\(629\) −4195.92 −0.265982
\(630\) −3659.51 + 6338.46i −0.231426 + 0.400842i
\(631\) −9368.74 + 16227.1i −0.591068 + 1.02376i 0.403021 + 0.915191i \(0.367960\pi\)
−0.994089 + 0.108569i \(0.965373\pi\)
\(632\) 12419.6 0.781683
\(633\) −9216.83 + 15964.0i −0.578730 + 1.00239i
\(634\) 3440.73 + 5959.52i 0.215534 + 0.373317i
\(635\) −1540.68 2668.54i −0.0962836 0.166768i
\(636\) 5836.91 0.363913
\(637\) 0 0
\(638\) 5240.75 0.325209
\(639\) 9944.18 + 17223.8i 0.615627 + 1.06630i
\(640\) 2108.67 + 3652.33i 0.130239 + 0.225580i
\(641\) −14899.4 + 25806.5i −0.918081 + 1.59016i −0.115753 + 0.993278i \(0.536928\pi\)
−0.802327 + 0.596884i \(0.796405\pi\)
\(642\) 19455.6 1.19603
\(643\) −11491.8 + 19904.3i −0.704807 + 1.22076i 0.261955 + 0.965080i \(0.415633\pi\)
−0.966761 + 0.255681i \(0.917700\pi\)
\(644\) 9275.77 16066.1i 0.567573 0.983064i
\(645\) −4679.90 −0.285692
\(646\) 833.684 1443.98i 0.0507753 0.0879455i
\(647\) 12452.7 + 21568.7i 0.756672 + 1.31059i 0.944539 + 0.328400i \(0.106509\pi\)
−0.187866 + 0.982195i \(0.560157\pi\)
\(648\) 3265.36 + 5655.77i 0.197956 + 0.342870i
\(649\) −6709.39 −0.405804
\(650\) 0 0
\(651\) −6394.54 −0.384980
\(652\) −9125.03 15805.0i −0.548104 0.949344i
\(653\) −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
\(655\) −1002.22 −0.0597864
\(656\) −915.886 + 1586.36i −0.0545112 + 0.0944162i
\(657\) −7457.28 + 12916.4i −0.442825 + 0.766996i
\(658\) −19816.5 −1.17406
\(659\) −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
\(661\) −6374.56 11041.1i −0.375101 0.649694i 0.615241 0.788339i \(-0.289059\pi\)
−0.990342 + 0.138645i \(0.955725\pi\)
\(662\) 6451.54 0.378771
\(663\) 0 0
\(664\) 28678.1 1.67609
\(665\) 1160.04 + 2009.26i 0.0676460 + 0.117166i
\(666\) 3561.20 + 6168.18i 0.207198 + 0.358877i
\(667\) 13495.7 23375.2i 0.783440 1.35696i
\(668\) −17388.3 −1.00715
\(669\) −25734.5 + 44573.4i −1.48722 + 2.57594i
\(670\) 1424.54 2467.37i 0.0821413 0.142273i
\(671\) 2095.46 0.120558
\(672\) −22098.3 + 38275.3i −1.26854 + 2.19718i
\(673\) 6809.12 + 11793.7i 0.390004 + 0.675506i 0.992450 0.122654i \(-0.0391404\pi\)
−0.602446 + 0.798160i \(0.705807\pi\)
\(674\) 3560.98 + 6167.80i 0.203507 + 0.352485i
\(675\) −20896.7 −1.19158
\(676\) 0 0
\(677\) 9655.67 0.548150 0.274075 0.961708i \(-0.411628\pi\)
0.274075 + 0.961708i \(0.411628\pi\)
\(678\) −10947.7 18962.0i −0.620126 1.07409i
\(679\) −20535.9 35569.3i −1.16067 2.01034i
\(680\) 1679.92 2909.70i 0.0947381 0.164091i
\(681\) 7778.51 0.437699
\(682\) −322.830 + 559.158i −0.0181258 + 0.0313948i
\(683\) 8158.38 14130.7i 0.457060 0.791650i −0.541744 0.840543i \(-0.682236\pi\)
0.998804 + 0.0488929i \(0.0155693\pi\)
\(684\) 6455.25 0.360852
\(685\) −4703.80 + 8147.23i −0.262369 + 0.454437i
\(686\) −1116.00 1932.97i −0.0621123 0.107582i
\(687\) 2725.75 + 4721.14i 0.151374 + 0.262188i
\(688\) −1728.37 −0.0957753
\(689\) 0 0
\(690\) 5928.30 0.327082
\(691\) 1175.42 + 2035.89i 0.0647106 + 0.112082i 0.896566 0.442911i \(-0.146054\pi\)
−0.831855 + 0.554993i \(0.812721\pi\)
\(692\) 271.320 + 469.940i 0.0149047 + 0.0258157i
\(693\) 10042.0 17393.3i 0.550454 0.953414i
\(694\) 15723.9 0.860045
\(695\) 3559.12 6164.58i 0.194252 0.336455i
\(696\) −20222.4 + 35026.2i −1.10133 + 1.90756i
\(697\) 7143.20 0.388189
\(698\) 4590.44 7950.87i 0.248926 0.431153i
\(699\) −10003.5 17326.6i −0.541299 0.937558i
\(700\) −8488.05 14701.7i −0.458312 0.793819i
\(701\) −8076.90 −0.435179 −0.217589 0.976040i \(-0.569819\pi\)
−0.217589 + 0.976040i \(0.569819\pi\)
\(702\) 0 0
\(703\) 2257.76 0.121128
\(704\) 1533.93 + 2656.85i 0.0821197 + 0.142236i
\(705\) 7221.55 + 12508.1i 0.385786 + 0.668202i
\(706\) −7138.30 + 12363.9i −0.380529 + 0.659095i
\(707\) 9138.55 0.486125
\(708\) 10617.2 18389.5i 0.563584 0.976156i
\(709\) −6812.44 + 11799.5i −0.360856 + 0.625021i −0.988102 0.153801i \(-0.950849\pi\)
0.627246 + 0.778821i \(0.284182\pi\)
\(710\) −2284.23 −0.120741
\(711\) 14199.2 24593.8i 0.748962 1.29724i
\(712\) −4657.71 8067.40i −0.245162 0.424633i
\(713\) 1662.67 + 2879.82i 0.0873315 + 0.151263i
\(714\) 16418.2 0.860553
\(715\) 0 0
\(716\) 193.069 0.0100773
\(717\) 2364.93 + 4096.18i 0.123180 + 0.213354i
\(718\) −2150.51 3724.79i −0.111778 0.193605i
\(719\) −8117.89 + 14060.6i −0.421066 + 0.729307i −0.996044 0.0888616i \(-0.971677\pi\)
0.574978 + 0.818169i \(0.305010\pi\)
\(720\) 1970.09 0.101973
\(721\) −4385.19 + 7595.36i −0.226509 + 0.392325i
\(722\) 4906.75 8498.75i 0.252923 0.438076i
\(723\) −47123.8 −2.42400
\(724\) −3418.54 + 5921.08i −0.175482 + 0.303944i
\(725\) −12349.6 21390.1i −0.632623 1.09574i
\(726\) 7445.91 + 12896.7i 0.380638 + 0.659285i
\(727\) 24181.2 1.23361 0.616803 0.787118i \(-0.288428\pi\)
0.616803 + 0.787118i \(0.288428\pi\)
\(728\) 0 0
\(729\) −28693.9 −1.45780
\(730\) −856.490 1483.48i −0.0434248 0.0752139i
\(731\) 3369.98 + 5836.98i 0.170511 + 0.295333i
\(732\) −3315.93 + 5743.36i −0.167432 + 0.290001i
\(733\) −3053.70 −0.153876 −0.0769379 0.997036i \(-0.524514\pi\)
−0.0769379 + 0.997036i \(0.524514\pi\)
\(734\) −2373.71 + 4111.38i −0.119367 + 0.206749i
\(735\) −6118.03 + 10596.7i −0.307030 + 0.531791i
\(736\) 22983.4 1.15106
\(737\) −3909.05 + 6770.67i −0.195375 + 0.338400i
\(738\) −6062.63 10500.8i −0.302396 0.523766i
\(739\) −4016.81 6957.32i −0.199947 0.346318i 0.748564 0.663062i \(-0.230744\pi\)
−0.948511 + 0.316744i \(0.897410\pi\)
\(740\) 1865.74 0.0926836
\(741\) 0 0
\(742\) −5128.54 −0.253739
\(743\) −8069.81 13977.3i −0.398456 0.690146i 0.595080 0.803667i \(-0.297120\pi\)
−0.993536 + 0.113521i \(0.963787\pi\)
\(744\) −2491.40 4315.22i −0.122767 0.212639i
\(745\) −3121.67 + 5406.89i −0.153515 + 0.265897i
\(746\) −8408.53 −0.412678
\(747\) 32787.5 56789.6i 1.60593 2.78156i
\(748\) −1890.48 + 3274.41i −0.0924102 + 0.160059i
\(749\) 38988.7 1.90202
\(750\) 5731.19 9926.71i 0.279031 0.483296i
\(751\) 9245.56 + 16013.8i 0.449235 + 0.778097i 0.998336 0.0576584i \(-0.0183634\pi\)
−0.549102 + 0.835755i \(0.685030\pi\)
\(752\) 2667.04 + 4619.45i 0.129331 + 0.224008i
\(753\) −45344.5 −2.19448
\(754\) 0 0
\(755\) 9953.28 0.479784
\(756\) 14060.7 + 24353.9i 0.676434 + 1.17162i
\(757\) −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
\(759\) −16267.7 −0.777973
\(760\) −903.936 + 1565.66i −0.0431437 + 0.0747271i
\(761\) 13399.5 23208.7i 0.638282 1.10554i −0.347528 0.937670i \(-0.612979\pi\)
0.985810 0.167867i \(-0.0536879\pi\)
\(762\) 11733.1 0.557803
\(763\) 11538.7 19985.6i 0.547481 0.948264i
\(764\) 11903.9 + 20618.2i 0.563703 + 0.976363i
\(765\) −3841.28 6653.30i −0.181545 0.314445i
\(766\) 598.052 0.0282095
\(767\) 0 0
\(768\) −30025.1 −1.41073
\(769\) −2572.91 4456.41i −0.120652 0.208976i 0.799373 0.600835i \(-0.205165\pi\)
−0.920025 + 0.391860i \(0.871832\pi\)
\(770\) 1153.35 + 1997.67i 0.0539792 + 0.0934947i
\(771\) −2858.15 + 4950.45i −0.133507 + 0.231240i
\(772\) 2626.83 0.122463
\(773\) 6405.28 11094.3i 0.298036 0.516214i −0.677650 0.735384i \(-0.737002\pi\)
0.975687 + 0.219170i \(0.0703351\pi\)
\(774\) 5720.39 9908.01i