Properties

Label 169.4.e.f.147.4
Level $169$
Weight $4$
Character 169.147
Analytic conductor $9.971$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 147.4
Root \(2.21837 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 169.147
Dual form 169.4.e.f.23.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.21837 + 1.28078i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-0.719224 - 1.24573i) q^{4} -0.561553i q^{5} +(8.17394 - 4.71922i) q^{6} +(15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})\) \(q+(2.21837 + 1.28078i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-0.719224 - 1.24573i) q^{4} -0.561553i q^{5} +(8.17394 - 4.71922i) q^{6} +(15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 + 11.6249i) q^{9} +(0.719224 - 1.24573i) q^{10} +(-56.0653 - 32.3693i) q^{11} -5.30019 q^{12} +46.5616 q^{14} +(-1.79192 - 1.03457i) q^{15} +(25.2116 - 43.6679i) q^{16} +(-12.7732 - 22.1238i) q^{17} +34.3845i q^{18} +(93.5045 - 53.9848i) q^{19} +(-0.699544 + 0.403882i) q^{20} -66.9763i q^{21} +(-82.9157 - 143.614i) q^{22} +(36.6307 - 63.4462i) q^{23} +(-77.1493 - 44.5421i) q^{24} +124.685 q^{25} +148.946 q^{27} +(-22.6438 - 13.0734i) q^{28} +(-87.9545 + 152.342i) q^{29} +(-2.65009 - 4.59010i) q^{30} +113.093i q^{31} +(-55.6462 + 32.1274i) q^{32} +(-206.581 + 119.270i) q^{33} -65.4384i q^{34} +(-5.10370 - 8.83986i) q^{35} +(9.65435 - 16.7218i) q^{36} +(-99.4264 - 57.4039i) q^{37} +276.570 q^{38} -13.5767 q^{40} +(-60.3151 - 34.8229i) q^{41} +(85.7817 - 148.578i) q^{42} +(219.151 + 379.581i) q^{43} +93.1231i q^{44} +(6.52800 - 3.76894i) q^{45} +(162.521 - 93.8314i) q^{46} -31.9479i q^{47} +(-92.8963 - 160.901i) q^{48} +(-6.29686 + 10.9065i) q^{49} +(276.597 + 159.693i) q^{50} -94.1298 q^{51} +2.84658 q^{53} +(330.417 + 190.767i) q^{54} +(-18.1771 + 31.4836i) q^{55} +(-219.734 - 380.591i) q^{56} -397.831i q^{57} +(-390.231 + 225.300i) q^{58} +(62.0356 - 35.8163i) q^{59} +2.97633i q^{60} +(460.348 + 797.345i) q^{61} +(-144.847 + 250.882i) q^{62} +(211.307 + 121.998i) q^{63} -567.978 q^{64} -611.032 q^{66} +(-384.758 - 222.140i) q^{67} +(-18.3736 + 31.8240i) q^{68} +(-134.972 - 233.778i) q^{69} -26.1468i q^{70} +(469.142 - 270.859i) q^{71} +(281.056 - 162.268i) q^{72} +764.004i q^{73} +(-147.043 - 254.686i) q^{74} +(229.710 - 397.870i) q^{75} +(-134.501 - 77.6543i) q^{76} -1176.76 q^{77} -421.538 q^{79} +(-24.5218 - 14.1577i) q^{80} +(93.1932 - 161.415i) q^{81} +(-89.2007 - 154.500i) q^{82} -603.797i q^{83} +(-83.4346 + 48.1710i) q^{84} +(-12.4237 + 7.17283i) q^{85} +1122.73i q^{86} +(324.082 + 561.327i) q^{87} +(-782.596 + 1355.50i) q^{88} +(1004.49 + 579.941i) q^{89} +19.3087 q^{90} -105.383 q^{92} +(360.880 + 208.354i) q^{93} +(40.9181 - 70.8722i) q^{94} +(-30.3153 - 52.5077i) q^{95} +236.757i q^{96} +(-505.126 + 291.634i) q^{97} +(-27.9375 + 16.1298i) q^{98} -869.006i 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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.21837 + 1.28078i 0.784312 + 0.452823i 0.837956 0.545737i \(-0.183750\pi\)
−0.0536442 + 0.998560i \(0.517084\pi\)
\(3\) 1.84233 3.19101i 0.354556 0.614110i −0.632486 0.774572i \(-0.717965\pi\)
0.987042 + 0.160462i \(0.0512985\pi\)
\(4\) −0.719224 1.24573i −0.0899029 0.155716i
\(5\) 0.561553i 0.0502268i −0.999685 0.0251134i \(-0.992005\pi\)
0.999685 0.0251134i \(-0.00799469\pi\)
\(6\) 8.17394 4.71922i 0.556166 0.321102i
\(7\) 15.7418 9.08854i 0.849978 0.490735i −0.0106654 0.999943i \(-0.503395\pi\)
0.860643 + 0.509208i \(0.170062\pi\)
\(8\) 24.1771i 1.06849i
\(9\) 6.71165 + 11.6249i 0.248579 + 0.430552i
\(10\) 0.719224 1.24573i 0.0227438 0.0393935i
\(11\) −56.0653 32.3693i −1.53676 0.887247i −0.999026 0.0441305i \(-0.985948\pi\)
−0.537731 0.843116i \(-0.680718\pi\)
\(12\) −5.30019 −0.127503
\(13\) 0 0
\(14\) 46.5616 0.888864
\(15\) −1.79192 1.03457i −0.0308448 0.0178082i
\(16\) 25.2116 43.6679i 0.393932 0.682310i
\(17\) −12.7732 22.1238i −0.182233 0.315636i 0.760408 0.649446i \(-0.224999\pi\)
−0.942641 + 0.333810i \(0.891666\pi\)
\(18\) 34.3845i 0.450250i
\(19\) 93.5045 53.9848i 1.12902 0.651841i 0.185333 0.982676i \(-0.440664\pi\)
0.943689 + 0.330835i \(0.107330\pi\)
\(20\) −0.699544 + 0.403882i −0.00782114 + 0.00451554i
\(21\) 66.9763i 0.695973i
\(22\) −82.9157 143.614i −0.803531 1.39176i
\(23\) 36.6307 63.4462i 0.332088 0.575193i −0.650833 0.759221i \(-0.725580\pi\)
0.982921 + 0.184027i \(0.0589135\pi\)
\(24\) −77.1493 44.5421i −0.656168 0.378839i
\(25\) 124.685 0.997477
\(26\) 0 0
\(27\) 148.946 1.06165
\(28\) −22.6438 13.0734i −0.152831 0.0882371i
\(29\) −87.9545 + 152.342i −0.563198 + 0.975488i 0.434017 + 0.900905i \(0.357096\pi\)
−0.997215 + 0.0745830i \(0.976237\pi\)
\(30\) −2.65009 4.59010i −0.0161280 0.0279344i
\(31\) 113.093i 0.655228i 0.944812 + 0.327614i \(0.106245\pi\)
−0.944812 + 0.327614i \(0.893755\pi\)
\(32\) −55.6462 + 32.1274i −0.307405 + 0.177480i
\(33\) −206.581 + 119.270i −1.08973 + 0.629158i
\(34\) 65.4384i 0.330077i
\(35\) −5.10370 8.83986i −0.0246481 0.0426917i
\(36\) 9.65435 16.7218i 0.0446961 0.0774158i
\(37\) −99.4264 57.4039i −0.441773 0.255058i 0.262576 0.964911i \(-0.415428\pi\)
−0.704349 + 0.709853i \(0.748761\pi\)
\(38\) 276.570 1.18067
\(39\) 0 0
\(40\) −13.5767 −0.0536666
\(41\) −60.3151 34.8229i −0.229747 0.132645i 0.380708 0.924695i \(-0.375680\pi\)
−0.610455 + 0.792051i \(0.709014\pi\)
\(42\) 85.7817 148.578i 0.315153 0.545860i
\(43\) 219.151 + 379.581i 0.777214 + 1.34617i 0.933541 + 0.358469i \(0.116701\pi\)
−0.156327 + 0.987705i \(0.549965\pi\)
\(44\) 93.1231i 0.319064i
\(45\) 6.52800 3.76894i 0.0216253 0.0124854i
\(46\) 162.521 93.8314i 0.520921 0.300754i
\(47\) 31.9479i 0.0991506i −0.998770 0.0495753i \(-0.984213\pi\)
0.998770 0.0495753i \(-0.0157868\pi\)
\(48\) −92.8963 160.901i −0.279342 0.483835i
\(49\) −6.29686 + 10.9065i −0.0183582 + 0.0317973i
\(50\) 276.597 + 159.693i 0.782334 + 0.451680i
\(51\) −94.1298 −0.258447
\(52\) 0 0
\(53\) 2.84658 0.00737752 0.00368876 0.999993i \(-0.498826\pi\)
0.00368876 + 0.999993i \(0.498826\pi\)
\(54\) 330.417 + 190.767i 0.832669 + 0.480741i
\(55\) −18.1771 + 31.4836i −0.0445636 + 0.0771864i
\(56\) −219.734 380.591i −0.524344 0.908190i
\(57\) 397.831i 0.924457i
\(58\) −390.231 + 225.300i −0.883446 + 0.510058i
\(59\) 62.0356 35.8163i 0.136887 0.0790319i −0.429992 0.902832i \(-0.641484\pi\)
0.566880 + 0.823801i \(0.308150\pi\)
\(60\) 2.97633i 0.00640405i
\(61\) 460.348 + 797.345i 0.966253 + 1.67360i 0.706209 + 0.708003i \(0.250404\pi\)
0.260044 + 0.965597i \(0.416263\pi\)
\(62\) −144.847 + 250.882i −0.296702 + 0.513903i
\(63\) 211.307 + 121.998i 0.422574 + 0.243973i
\(64\) −567.978 −1.10933
\(65\) 0 0
\(66\) −611.032 −1.13959
\(67\) −384.758 222.140i −0.701577 0.405056i 0.106357 0.994328i \(-0.466081\pi\)
−0.807935 + 0.589272i \(0.799415\pi\)
\(68\) −18.3736 + 31.8240i −0.0327665 + 0.0567533i
\(69\) −134.972 233.778i −0.235488 0.407877i
\(70\) 26.1468i 0.0446448i
\(71\) 469.142 270.859i 0.784182 0.452748i −0.0537283 0.998556i \(-0.517110\pi\)
0.837910 + 0.545808i \(0.183777\pi\)
\(72\) 281.056 162.268i 0.460039 0.265604i
\(73\) 764.004i 1.22493i 0.790498 + 0.612465i \(0.209822\pi\)
−0.790498 + 0.612465i \(0.790178\pi\)
\(74\) −147.043 254.686i −0.230992 0.400090i
\(75\) 229.710 397.870i 0.353662 0.612561i
\(76\) −134.501 77.6543i −0.203005 0.117205i
\(77\) −1176.76 −1.74161
\(78\) 0 0
\(79\) −421.538 −0.600338 −0.300169 0.953886i \(-0.597043\pi\)
−0.300169 + 0.953886i \(0.597043\pi\)
\(80\) −24.5218 14.1577i −0.0342703 0.0197859i
\(81\) 93.1932 161.415i 0.127837 0.221420i
\(82\) −89.2007 154.500i −0.120129 0.208069i
\(83\) 603.797i 0.798498i −0.916842 0.399249i \(-0.869271\pi\)
0.916842 0.399249i \(-0.130729\pi\)
\(84\) −83.4346 + 48.1710i −0.108374 + 0.0625700i
\(85\) −12.4237 + 7.17283i −0.0158534 + 0.00915297i
\(86\) 1122.73i 1.40776i
\(87\) 324.082 + 561.327i 0.399371 + 0.691731i
\(88\) −782.596 + 1355.50i −0.948011 + 1.64200i
\(89\) 1004.49 + 579.941i 1.19635 + 0.690715i 0.959740 0.280889i \(-0.0906292\pi\)
0.236613 + 0.971604i \(0.423963\pi\)
\(90\) 19.3087 0.0226146
\(91\) 0 0
\(92\) −105.383 −0.119423
\(93\) 360.880 + 208.354i 0.402382 + 0.232315i
\(94\) 40.9181 70.8722i 0.0448977 0.0777650i
\(95\) −30.3153 52.5077i −0.0327399 0.0567071i
\(96\) 236.757i 0.251707i
\(97\) −505.126 + 291.634i −0.528740 + 0.305268i −0.740503 0.672053i \(-0.765413\pi\)
0.211763 + 0.977321i \(0.432079\pi\)
\(98\) −27.9375 + 16.1298i −0.0287971 + 0.0166260i
\(99\) 869.006i 0.882206i
\(100\) −89.6761 155.324i −0.0896761 0.155324i
\(101\) 460.870 798.251i 0.454043 0.786425i −0.544590 0.838702i \(-0.683315\pi\)
0.998633 + 0.0522775i \(0.0166480\pi\)
\(102\) −208.815 120.559i −0.202703 0.117031i
\(103\) 930.712 0.890347 0.445174 0.895444i \(-0.353142\pi\)
0.445174 + 0.895444i \(0.353142\pi\)
\(104\) 0 0
\(105\) −37.6107 −0.0349565
\(106\) 6.31478 + 3.64584i 0.00578628 + 0.00334071i
\(107\) −428.691 + 742.515i −0.387319 + 0.670857i −0.992088 0.125545i \(-0.959932\pi\)
0.604769 + 0.796401i \(0.293266\pi\)
\(108\) −107.125 185.547i −0.0954459 0.165317i
\(109\) 671.853i 0.590384i −0.955438 0.295192i \(-0.904616\pi\)
0.955438 0.295192i \(-0.0953836\pi\)
\(110\) −80.6470 + 46.5616i −0.0699035 + 0.0403588i
\(111\) −366.352 + 211.514i −0.313267 + 0.180865i
\(112\) 916.548i 0.773265i
\(113\) −320.737 555.532i −0.267012 0.462479i 0.701077 0.713086i \(-0.252703\pi\)
−0.968089 + 0.250607i \(0.919370\pi\)
\(114\) 509.533 882.537i 0.418615 0.725063i
\(115\) −35.6284 20.5701i −0.0288901 0.0166797i
\(116\) 253.036 0.202533
\(117\) 0 0
\(118\) 183.491 0.143150
\(119\) −402.147 232.179i −0.309788 0.178856i
\(120\) −25.0128 + 43.3234i −0.0190279 + 0.0329572i
\(121\) 1430.05 + 2476.91i 1.07441 + 1.86094i
\(122\) 2358.41i 1.75017i
\(123\) −222.240 + 128.311i −0.162917 + 0.0940599i
\(124\) 140.883 81.3390i 0.102030 0.0589069i
\(125\) 140.211i 0.100327i
\(126\) 312.505 + 541.274i 0.220953 + 0.382703i
\(127\) −276.587 + 479.063i −0.193253 + 0.334724i −0.946326 0.323212i \(-0.895237\pi\)
0.753073 + 0.657937i \(0.228570\pi\)
\(128\) −814.816 470.434i −0.562658 0.324851i
\(129\) 1614.99 1.10227
\(130\) 0 0
\(131\) 2056.40 1.37152 0.685758 0.727830i \(-0.259471\pi\)
0.685758 + 0.727830i \(0.259471\pi\)
\(132\) 297.157 + 171.563i 0.195941 + 0.113126i
\(133\) 981.287 1699.64i 0.639762 1.10810i
\(134\) −569.024 985.578i −0.366837 0.635380i
\(135\) 83.6411i 0.0533235i
\(136\) −534.890 + 308.819i −0.337253 + 0.194713i
\(137\) −1566.26 + 904.283i −0.976752 + 0.563928i −0.901288 0.433221i \(-0.857377\pi\)
−0.0754639 + 0.997149i \(0.524044\pi\)
\(138\) 691.474i 0.426537i
\(139\) −746.818 1293.53i −0.455714 0.789320i 0.543015 0.839723i \(-0.317283\pi\)
−0.998729 + 0.0504032i \(0.983949\pi\)
\(140\) −7.34140 + 12.7157i −0.00443187 + 0.00767622i
\(141\) −101.946 58.8585i −0.0608894 0.0351545i
\(142\) 1387.64 0.820058
\(143\) 0 0
\(144\) 676.847 0.391694
\(145\) 85.5479 + 49.3911i 0.0489956 + 0.0282876i
\(146\) −978.518 + 1694.84i −0.554676 + 0.960727i
\(147\) 23.2018 + 40.1867i 0.0130180 + 0.0225479i
\(148\) 165.145i 0.0917218i
\(149\) 2389.38 1379.51i 1.31373 0.758482i 0.331018 0.943625i \(-0.392608\pi\)
0.982712 + 0.185143i \(0.0592747\pi\)
\(150\) 1019.16 588.415i 0.554763 0.320292i
\(151\) 976.355i 0.526190i −0.964770 0.263095i \(-0.915257\pi\)
0.964770 0.263095i \(-0.0847432\pi\)
\(152\) −1305.20 2260.67i −0.696483 1.20634i
\(153\) 171.458 296.975i 0.0905986 0.156921i
\(154\) −2610.49 1507.17i −1.36597 0.788642i
\(155\) 63.5076 0.0329100
\(156\) 0 0
\(157\) −564.875 −0.287146 −0.143573 0.989640i \(-0.545859\pi\)
−0.143573 + 0.989640i \(0.545859\pi\)
\(158\) −935.127 539.896i −0.470853 0.271847i
\(159\) 5.24435 9.08347i 0.00261575 0.00453061i
\(160\) 18.0412 + 31.2483i 0.00891427 + 0.0154400i
\(161\) 1331.68i 0.651869i
\(162\) 413.474 238.719i 0.200528 0.115775i
\(163\) 1306.43 754.266i 0.627775 0.362446i −0.152115 0.988363i \(-0.548608\pi\)
0.779890 + 0.625917i \(0.215275\pi\)
\(164\) 100.182i 0.0477005i
\(165\) 66.9763 + 116.006i 0.0316006 + 0.0547339i
\(166\) 773.329 1339.45i 0.361578 0.626272i
\(167\) −513.138 296.260i −0.237771 0.137277i 0.376381 0.926465i \(-0.377168\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(168\) −1619.29 −0.743638
\(169\) 0 0
\(170\) −36.7471 −0.0165787
\(171\) 1255.14 + 724.654i 0.561303 + 0.324068i
\(172\) 315.237 546.007i 0.139748 0.242050i
\(173\) −2247.78 3893.28i −0.987838 1.71099i −0.628576 0.777748i \(-0.716362\pi\)
−0.359262 0.933237i \(-0.616972\pi\)
\(174\) 1660.31i 0.723377i
\(175\) 1962.76 1133.20i 0.847834 0.489497i
\(176\) −2827.00 + 1632.17i −1.21076 + 0.699030i
\(177\) 263.941i 0.112085i
\(178\) 1485.55 + 2573.05i 0.625543 + 1.08347i
\(179\) −77.1425 + 133.615i −0.0322117 + 0.0557924i −0.881682 0.471844i \(-0.843588\pi\)
0.849470 + 0.527637i \(0.176922\pi\)
\(180\) −9.39019 5.42143i −0.00388835 0.00224494i
\(181\) −1071.35 −0.439959 −0.219979 0.975505i \(-0.570599\pi\)
−0.219979 + 0.975505i \(0.570599\pi\)
\(182\) 0 0
\(183\) 3392.45 1.37037
\(184\) −1533.94 885.623i −0.614586 0.354831i
\(185\) −32.2353 + 55.8332i −0.0128107 + 0.0221889i
\(186\) 533.710 + 924.413i 0.210395 + 0.364415i
\(187\) 1653.84i 0.646742i
\(188\) −39.7985 + 22.9777i −0.0154394 + 0.00891393i
\(189\) 2344.68 1353.70i 0.902383 0.520991i
\(190\) 155.309i 0.0593015i
\(191\) −338.601 586.475i −0.128274 0.222177i 0.794734 0.606958i \(-0.207610\pi\)
−0.923008 + 0.384781i \(0.874277\pi\)
\(192\) −1046.40 + 1812.42i −0.393321 + 0.681252i
\(193\) −1144.61 660.840i −0.426895 0.246468i 0.271128 0.962543i \(-0.412603\pi\)
−0.698023 + 0.716075i \(0.745937\pi\)
\(194\) −1494.07 −0.552929
\(195\) 0 0
\(196\) 18.1154 0.00660183
\(197\) 1097.57 + 633.683i 0.396948 + 0.229178i 0.685166 0.728387i \(-0.259730\pi\)
−0.288218 + 0.957565i \(0.593063\pi\)
\(198\) 1113.00 1927.78i 0.399483 0.691925i
\(199\) 1198.12 + 2075.21i 0.426796 + 0.739233i 0.996586 0.0825573i \(-0.0263088\pi\)
−0.569790 + 0.821790i \(0.692975\pi\)
\(200\) 3014.51i 1.06579i
\(201\) −1417.70 + 818.510i −0.497497 + 0.287230i
\(202\) 2044.76 1180.54i 0.712222 0.411202i
\(203\) 3197.51i 1.10552i
\(204\) 67.7003 + 117.260i 0.0232352 + 0.0402445i
\(205\) −19.5549 + 33.8701i −0.00666231 + 0.0115395i
\(206\) 2064.66 + 1192.03i 0.698310 + 0.403170i
\(207\) 983.409 0.330201
\(208\) 0 0
\(209\) −6989.81 −2.31337
\(210\) −83.4346 48.1710i −0.0274168 0.0158291i
\(211\) 45.7769 79.2880i 0.0149356 0.0258692i −0.858461 0.512879i \(-0.828579\pi\)
0.873397 + 0.487010i \(0.161912\pi\)
\(212\) −2.04733 3.54608i −0.000663261 0.00114880i
\(213\) 1996.05i 0.642099i
\(214\) −1901.99 + 1098.12i −0.607558 + 0.350774i
\(215\) 213.155 123.065i 0.0676141 0.0390370i
\(216\) 3601.08i 1.13436i
\(217\) 1027.85 + 1780.29i 0.321543 + 0.556929i
\(218\) 860.494 1490.42i 0.267339 0.463045i
\(219\) 2437.94 + 1407.55i 0.752241 + 0.434307i
\(220\) 52.2935 0.0160256
\(221\) 0 0
\(222\) −1083.61 −0.327599
\(223\) 1069.90 + 617.709i 0.321282 + 0.185493i 0.651964 0.758250i \(-0.273945\pi\)
−0.330682 + 0.943742i \(0.607279\pi\)
\(224\) −583.982 + 1011.49i −0.174192 + 0.301709i
\(225\) 836.839 + 1449.45i 0.247952 + 0.429466i
\(226\) 1643.17i 0.483637i
\(227\) −2859.32 + 1650.83i −0.836035 + 0.482685i −0.855914 0.517118i \(-0.827005\pi\)
0.0198797 + 0.999802i \(0.493672\pi\)
\(228\) −495.591 + 286.130i −0.143953 + 0.0831114i
\(229\) 211.283i 0.0609694i 0.999535 + 0.0304847i \(0.00970508\pi\)
−0.999535 + 0.0304847i \(0.990295\pi\)
\(230\) −52.6913 91.2640i −0.0151059 0.0261642i
\(231\) −2167.98 + 3755.05i −0.617500 + 1.06954i
\(232\) 3683.18 + 2126.48i 1.04230 + 0.601769i
\(233\) 256.724 0.0721827 0.0360913 0.999348i \(-0.488509\pi\)
0.0360913 + 0.999348i \(0.488509\pi\)
\(234\) 0 0
\(235\) −17.9404 −0.00498002
\(236\) −89.2349 51.5198i −0.0246131 0.0142104i
\(237\) −776.612 + 1345.13i −0.212854 + 0.368674i
\(238\) −594.740 1030.12i −0.161980 0.280558i
\(239\) 3549.62i 0.960694i 0.877078 + 0.480347i \(0.159489\pi\)
−0.877078 + 0.480347i \(0.840511\pi\)
\(240\) −90.3545 + 52.1662i −0.0243015 + 0.0140305i
\(241\) −4356.19 + 2515.05i −1.16434 + 0.672235i −0.952341 0.305034i \(-0.901332\pi\)
−0.212003 + 0.977269i \(0.567999\pi\)
\(242\) 7326.27i 1.94608i
\(243\) 1667.39 + 2888.00i 0.440176 + 0.762408i
\(244\) 662.186 1146.94i 0.173738 0.300923i
\(245\) 6.12457 + 3.53602i 0.00159708 + 0.000922074i
\(246\) −657.349 −0.170370
\(247\) 0 0
\(248\) 2734.25 0.700102
\(249\) −1926.72 1112.39i −0.490366 0.283113i
\(250\) 179.579 311.040i 0.0454303 0.0786876i
\(251\) −359.392 622.485i −0.0903770 0.156538i 0.817293 0.576223i \(-0.195474\pi\)
−0.907670 + 0.419685i \(0.862141\pi\)
\(252\) 350.976i 0.0877357i
\(253\) −4107.42 + 2371.42i −1.02068 + 0.589288i
\(254\) −1227.14 + 708.492i −0.303141 + 0.175019i
\(255\) 52.8588i 0.0129810i
\(256\) 1066.87 + 1847.87i 0.260466 + 0.451141i
\(257\) 640.397 1109.20i 0.155435 0.269222i −0.777782 0.628534i \(-0.783655\pi\)
0.933217 + 0.359312i \(0.116989\pi\)
\(258\) 3582.65 + 2068.45i 0.864520 + 0.499131i
\(259\) −2086.87 −0.500663
\(260\) 0 0
\(261\) −2361.28 −0.559998
\(262\) 4561.86 + 2633.79i 1.07570 + 0.621054i
\(263\) −2612.77 + 4525.46i −0.612587 + 1.06103i 0.378215 + 0.925718i \(0.376538\pi\)
−0.990803 + 0.135315i \(0.956795\pi\)
\(264\) 2883.60 + 4994.54i 0.672247 + 1.16437i
\(265\) 1.59851i 0.000370549i
\(266\) 4353.71 2513.62i 1.00355 0.579398i
\(267\) 3701.19 2136.89i 0.848350 0.489795i
\(268\) 639.074i 0.145663i
\(269\) −3221.90 5580.50i −0.730270 1.26487i −0.956768 0.290854i \(-0.906061\pi\)
0.226497 0.974012i \(-0.427273\pi\)
\(270\) 107.125 185.547i 0.0241461 0.0418223i
\(271\) 3403.42 + 1964.97i 0.762890 + 0.440455i 0.830332 0.557269i \(-0.188151\pi\)
−0.0674426 + 0.997723i \(0.521484\pi\)
\(272\) −1288.13 −0.287149
\(273\) 0 0
\(274\) −4632.74 −1.02144
\(275\) −6990.48 4035.96i −1.53288 0.885009i
\(276\) −194.149 + 336.277i −0.0423421 + 0.0733387i
\(277\) −2942.20 5096.04i −0.638194 1.10538i −0.985829 0.167754i \(-0.946348\pi\)
0.347635 0.937630i \(-0.386985\pi\)
\(278\) 3826.03i 0.825431i
\(279\) −1314.69 + 759.039i −0.282110 + 0.162876i
\(280\) −213.722 + 123.392i −0.0456155 + 0.0263361i
\(281\) 3529.79i 0.749358i 0.927155 + 0.374679i \(0.122247\pi\)
−0.927155 + 0.374679i \(0.877753\pi\)
\(282\) −150.769 261.140i −0.0318375 0.0551442i
\(283\) −1305.50 + 2261.19i −0.274219 + 0.474961i −0.969938 0.243353i \(-0.921753\pi\)
0.695719 + 0.718314i \(0.255086\pi\)
\(284\) −674.836 389.617i −0.141001 0.0814067i
\(285\) −223.403 −0.0464325
\(286\) 0 0
\(287\) −1265.96 −0.260373
\(288\) −746.955 431.255i −0.152829 0.0882359i
\(289\) 2130.19 3689.60i 0.433582 0.750987i
\(290\) 126.518 + 219.136i 0.0256186 + 0.0443727i
\(291\) 2149.15i 0.432939i
\(292\) 951.744 549.490i 0.190742 0.110125i
\(293\) −4755.37 + 2745.51i −0.948163 + 0.547422i −0.892510 0.451028i \(-0.851057\pi\)
−0.0556531 + 0.998450i \(0.517724\pi\)
\(294\) 118.865i 0.0235795i
\(295\) −20.1127 34.8363i −0.00396952 0.00687541i
\(296\) −1387.86 + 2403.84i −0.272526 + 0.472028i
\(297\) −8350.70 4821.28i −1.63150 0.941950i
\(298\) 7067.37 1.37383
\(299\) 0 0
\(300\) −660.852 −0.127181
\(301\) 6899.67 + 3983.53i 1.32123 + 0.762813i
\(302\) 1250.49 2165.92i 0.238271 0.412697i
\(303\) −1698.15 2941.28i −0.321967 0.557664i
\(304\) 5444.19i 1.02712i
\(305\) 447.751 258.509i 0.0840596 0.0485318i
\(306\) 760.716 439.200i 0.142115 0.0820502i
\(307\) 7307.59i 1.35852i −0.733897 0.679261i \(-0.762300\pi\)
0.733897 0.679261i \(-0.237700\pi\)
\(308\) 846.353 + 1465.93i 0.156576 + 0.271198i
\(309\) 1714.68 2969.91i 0.315678 0.546771i
\(310\) 140.883 + 81.3390i 0.0258117 + 0.0149024i
\(311\) −7904.92 −1.44131 −0.720654 0.693295i \(-0.756158\pi\)
−0.720654 + 0.693295i \(0.756158\pi\)
\(312\) 0 0
\(313\) 10002.4 1.80629 0.903145 0.429336i \(-0.141252\pi\)
0.903145 + 0.429336i \(0.141252\pi\)
\(314\) −1253.10 723.478i −0.225212 0.130026i
\(315\) 68.5084 118.660i 0.0122540 0.0212246i
\(316\) 303.180 + 525.123i 0.0539722 + 0.0934825i
\(317\) 6230.81i 1.10397i 0.833856 + 0.551983i \(0.186129\pi\)
−0.833856 + 0.551983i \(0.813871\pi\)
\(318\) 23.2678 13.4337i 0.00410312 0.00236894i
\(319\) 9862.40 5694.06i 1.73100 0.999392i
\(320\) 318.950i 0.0557182i
\(321\) 1579.58 + 2735.91i 0.274653 + 0.475713i
\(322\) 1705.58 2954.15i 0.295181 0.511269i
\(323\) −2388.70 1379.12i −0.411489 0.237573i
\(324\) −268.107 −0.0459717
\(325\) 0 0
\(326\) 3864.19 0.656495
\(327\) −2143.89 1237.77i −0.362561 0.209324i
\(328\) −841.917 + 1458.24i −0.141729 + 0.245482i
\(329\) −290.360 502.918i −0.0486567 0.0842758i
\(330\) 343.127i 0.0572379i
\(331\) 4013.60 2317.25i 0.666488 0.384797i −0.128257 0.991741i \(-0.540938\pi\)
0.794745 + 0.606944i \(0.207605\pi\)
\(332\) −752.170 + 434.265i −0.124339 + 0.0717874i
\(333\) 1541.10i 0.253609i
\(334\) −758.886 1314.43i −0.124325 0.215337i
\(335\) −124.743 + 216.062i −0.0203447 + 0.0352380i
\(336\) −2924.71 1688.58i −0.474870 0.274166i
\(337\) −3029.82 −0.489747 −0.244874 0.969555i \(-0.578746\pi\)
−0.244874 + 0.969555i \(0.578746\pi\)
\(338\) 0 0
\(339\) −2363.61 −0.378684
\(340\) 17.8708 + 10.3177i 0.00285054 + 0.00164576i
\(341\) 3660.74 6340.58i 0.581349 1.00693i
\(342\) 1856.24 + 3215.10i 0.293491 + 0.508342i
\(343\) 6463.66i 1.01751i
\(344\) 9177.15 5298.43i 1.43837 0.830443i
\(345\) −131.278 + 75.7937i −0.0204864 + 0.0118278i
\(346\) 11515.6i 1.78926i
\(347\) −1420.80 2460.90i −0.219805 0.380714i 0.734943 0.678129i \(-0.237209\pi\)
−0.954748 + 0.297415i \(0.903876\pi\)
\(348\) 466.175 807.440i 0.0718093 0.124377i
\(349\) −6552.07 3782.84i −1.00494 0.580202i −0.0952339 0.995455i \(-0.530360\pi\)
−0.909706 + 0.415252i \(0.863693\pi\)
\(350\) 5805.51 0.886622
\(351\) 0 0
\(352\) 4159.76 0.629875
\(353\) −2026.01 1169.72i −0.305478 0.176368i 0.339423 0.940634i \(-0.389768\pi\)
−0.644901 + 0.764266i \(0.723101\pi\)
\(354\) 338.050 585.520i 0.0507547 0.0879097i
\(355\) −152.102 263.448i −0.0227401 0.0393870i
\(356\) 1668.43i 0.248389i
\(357\) −1481.77 + 855.502i −0.219674 + 0.126829i
\(358\) −342.261 + 197.605i −0.0505281 + 0.0291724i
\(359\) 2531.68i 0.372192i −0.982532 0.186096i \(-0.940417\pi\)
0.982532 0.186096i \(-0.0595835\pi\)
\(360\) −91.1221 157.828i −0.0133404 0.0231063i
\(361\) 2399.23 4155.58i 0.349793 0.605858i
\(362\) −2376.64 1372.16i −0.345065 0.199223i
\(363\) 10538.5 1.52376
\(364\) 0 0
\(365\) 429.028 0.0615243
\(366\) 7525.70 + 4344.97i 1.07479 + 0.620533i
\(367\) −3288.91 + 5696.55i −0.467792 + 0.810239i −0.999323 0.0368000i \(-0.988284\pi\)
0.531531 + 0.847039i \(0.321617\pi\)
\(368\) −1847.04 3199.17i −0.261640 0.453174i
\(369\) 934.876i 0.131891i
\(370\) −143.020 + 82.5725i −0.0200952 + 0.0116020i
\(371\) 44.8104 25.8713i 0.00627073 0.00362041i
\(372\) 599.413i 0.0835433i
\(373\) −1451.36 2513.83i −0.201471 0.348958i 0.747532 0.664226i \(-0.231239\pi\)
−0.949003 + 0.315268i \(0.897905\pi\)
\(374\) −2118.20 + 3668.83i −0.292859 + 0.507247i
\(375\) −447.415 258.315i −0.0616117 0.0355716i
\(376\) −772.407 −0.105941
\(377\) 0 0
\(378\) 6935.16 0.943667
\(379\) −1615.77 932.867i −0.218989 0.126433i 0.386493 0.922292i \(-0.373686\pi\)
−0.605482 + 0.795859i \(0.707020\pi\)
\(380\) −43.6070 + 75.5296i −0.00588682 + 0.0101963i
\(381\) 1019.13 + 1765.18i 0.137038 + 0.237357i
\(382\) 1734.69i 0.232342i
\(383\) −9384.24 + 5417.99i −1.25199 + 0.722837i −0.971504 0.237021i \(-0.923829\pi\)
−0.280486 + 0.959858i \(0.590496\pi\)
\(384\) −3002.32 + 1733.39i −0.398988 + 0.230356i
\(385\) 660.813i 0.0874757i
\(386\) −1692.78 2931.97i −0.223213 0.386616i
\(387\) −2941.73 + 5095.22i −0.386399 + 0.669263i
\(388\) 726.597 + 419.501i 0.0950705 + 0.0548890i
\(389\) 9520.34 1.24088 0.620438 0.784256i \(-0.286955\pi\)
0.620438 + 0.784256i \(0.286955\pi\)
\(390\) 0 0
\(391\) −1871.56 −0.242069
\(392\) 263.687 + 152.240i 0.0339750 + 0.0196155i
\(393\) 3788.57 6561.99i 0.486280 0.842261i
\(394\) 1623.21 + 2811.49i 0.207554 + 0.359494i
\(395\) 236.716i 0.0301531i
\(396\) −1082.55 + 625.009i −0.137374 + 0.0793129i
\(397\) −8754.51 + 5054.42i −1.10674 + 0.638978i −0.937983 0.346680i \(-0.887309\pi\)
−0.168758 + 0.985657i \(0.553976\pi\)
\(398\) 6138.10i 0.773053i
\(399\) −3615.71 6262.59i −0.453664 0.785768i
\(400\) 3143.51 5444.71i 0.392938 0.680589i
\(401\) −1805.12 1042.19i −0.224797 0.129787i 0.383373 0.923594i \(-0.374763\pi\)
−0.608169 + 0.793807i \(0.708096\pi\)
\(402\) −4193.32 −0.520258
\(403\) 0 0
\(404\) −1325.88 −0.163279
\(405\) −90.6432 52.3329i −0.0111212 0.00642084i
\(406\) −4095.30 + 7093.27i −0.500607 + 0.867076i
\(407\) 3716.25 + 6436.73i 0.452599 + 0.783924i
\(408\) 2275.78i 0.276147i
\(409\) 8414.76 4858.26i 1.01732 0.587349i 0.103992 0.994578i \(-0.466838\pi\)
0.913326 + 0.407229i \(0.133505\pi\)
\(410\) −86.7600 + 50.0909i −0.0104507 + 0.00603369i
\(411\) 6663.95i 0.799777i
\(412\) −669.390 1159.42i −0.0800449 0.138642i
\(413\) 651.035 1127.63i 0.0775674 0.134351i
\(414\) 2181.56 + 1259.53i 0.258981 + 0.149523i
\(415\) −339.064 −0.0401060
\(416\) 0 0
\(417\) −5503.54 −0.646305
\(418\) −15506.0 8952.38i −1.81441 1.04755i
\(419\) −6690.94 + 11589.1i −0.780129 + 1.35122i 0.151737 + 0.988421i \(0.451513\pi\)
−0.931866 + 0.362802i \(0.881820\pi\)
\(420\) 27.0505 + 46.8529i 0.00314269 + 0.00544330i
\(421\) 9463.37i 1.09553i 0.836633 + 0.547763i \(0.184521\pi\)
−0.836633 + 0.547763i \(0.815479\pi\)
\(422\) 203.100 117.260i 0.0234284 0.0135264i
\(423\) 371.391 214.423i 0.0426895 0.0246468i
\(424\) 68.8221i 0.00788278i
\(425\) −1592.62 2758.50i −0.181773 0.314840i
\(426\) 2556.49 4427.97i 0.290757 0.503606i
\(427\) 14493.4 + 8367.77i 1.64259 + 0.948349i
\(428\) 1233.30 0.139285
\(429\) 0 0
\(430\) 630.474 0.0707074
\(431\) 4202.20 + 2426.14i 0.469635 + 0.271144i 0.716087 0.698011i \(-0.245931\pi\)
−0.246452 + 0.969155i \(0.579265\pi\)
\(432\) 3755.17 6504.15i 0.418220 0.724378i
\(433\) −4104.00 7108.33i −0.455486 0.788925i 0.543230 0.839584i \(-0.317201\pi\)
−0.998716 + 0.0506587i \(0.983868\pi\)
\(434\) 5265.78i 0.582409i
\(435\) 315.215 181.989i 0.0347434 0.0200591i
\(436\) −836.949 + 483.213i −0.0919325 + 0.0530773i
\(437\) 7910.01i 0.865874i
\(438\) 3605.50 + 6244.92i 0.393328 + 0.681264i
\(439\) −1496.90 + 2592.71i −0.162741 + 0.281875i −0.935851 0.352397i \(-0.885367\pi\)
0.773110 + 0.634272i \(0.218700\pi\)
\(440\) 761.182 + 439.469i 0.0824726 + 0.0476156i
\(441\) −169.049 −0.0182539
\(442\) 0 0
\(443\) 9743.67 1.04500 0.522501 0.852639i \(-0.324999\pi\)
0.522501 + 0.852639i \(0.324999\pi\)
\(444\) 526.979 + 304.251i 0.0563273 + 0.0325206i
\(445\) 325.668 564.073i 0.0346924 0.0600890i
\(446\) 1582.29 + 2740.61i 0.167990 + 0.290968i
\(447\) 10166.0i 1.07570i
\(448\) −8941.01 + 5162.09i −0.942908 + 0.544388i
\(449\) −486.237 + 280.729i −0.0511068 + 0.0295065i −0.525336 0.850895i \(-0.676060\pi\)
0.474229 + 0.880402i \(0.342727\pi\)
\(450\) 4287.22i 0.449114i
\(451\) 2254.39 + 3904.71i 0.235377 + 0.407685i
\(452\) −461.363 + 799.104i −0.0480104 + 0.0831564i
\(453\) −3115.56 1798.77i −0.323138 0.186564i
\(454\) −8457.38 −0.874283
\(455\) 0 0
\(456\) −9618.40 −0.987770
\(457\) 11915.1 + 6879.20i 1.21962 + 0.704148i 0.964837 0.262851i \(-0.0846627\pi\)
0.254783 + 0.966998i \(0.417996\pi\)
\(458\) −270.606 + 468.704i −0.0276083 + 0.0478190i
\(459\) −1902.52 3295.26i −0.193468 0.335097i
\(460\) 59.1779i 0.00599823i
\(461\) −10400.3 + 6004.62i −1.05074 + 0.606644i −0.922856 0.385145i \(-0.874151\pi\)
−0.127882 + 0.991789i \(0.540818\pi\)
\(462\) −9618.75 + 5553.39i −0.968625 + 0.559236i
\(463\) 13635.7i 1.36870i 0.729156 + 0.684348i \(0.239913\pi\)
−0.729156 + 0.684348i \(0.760087\pi\)
\(464\) 4434.96 + 7681.57i 0.443724 + 0.768552i
\(465\) 117.002 202.653i 0.0116685 0.0202104i
\(466\) 569.509 + 328.806i 0.0566138 + 0.0326860i
\(467\) −8821.95 −0.874157 −0.437079 0.899423i \(-0.643987\pi\)
−0.437079 + 0.899423i \(0.643987\pi\)
\(468\) 0 0
\(469\) −8075.72 −0.795100
\(470\) −39.7985 22.9777i −0.00390589 0.00225507i
\(471\) −1040.69 + 1802.52i −0.101809 + 0.176339i
\(472\) −865.933 1499.84i −0.0844445 0.146262i
\(473\) 28375.1i 2.75832i
\(474\) −3445.62 + 1989.33i −0.333888 + 0.192770i
\(475\) 11658.6 6731.08i 1.12617 0.650196i
\(476\) 667.956i 0.0643187i
\(477\) 19.1053 + 33.0913i 0.00183390 + 0.00317641i
\(478\) −4546.27 + 7874.37i −0.435024 + 0.753484i
\(479\) 12661.3 + 7310.02i 1.20775 + 0.697293i 0.962267 0.272109i \(-0.0877210\pi\)
0.245480 + 0.969402i \(0.421054\pi\)
\(480\) 132.951 0.0126424
\(481\) 0 0
\(482\) −12884.9 −1.21761
\(483\) −4249.39 2453.39i −0.400319 0.231124i
\(484\) 2057.04 3562.91i 0.193186 0.334608i
\(485\) 163.768 + 283.655i 0.0153326 + 0.0265569i
\(486\) 8542.20i 0.797288i
\(487\) 8486.06 4899.43i 0.789610 0.455882i −0.0502150 0.998738i \(-0.515991\pi\)
0.839825 + 0.542857i \(0.182657\pi\)
\(488\) 19277.5 11129.9i 1.78822 1.03243i
\(489\) 5558.43i 0.514030i
\(490\) 9.05771 + 15.6884i 0.000835072 + 0.00144639i
\(491\) −5418.03 + 9384.31i −0.497989 + 0.862542i −0.999997 0.00232091i \(-0.999261\pi\)
0.502009 + 0.864863i \(0.332595\pi\)
\(492\) 319.681 + 184.568i 0.0292934 + 0.0169125i
\(493\) 4493.84 0.410532
\(494\) 0 0
\(495\) −487.993 −0.0443104
\(496\) 4938.52 + 2851.26i 0.447069 + 0.258115i
\(497\) 4923.43 8527.63i 0.444358 0.769651i
\(498\) −2849.45 4935.40i −0.256400 0.444098i
\(499\) 2589.96i 0.232349i −0.993229 0.116175i \(-0.962937\pi\)
0.993229 0.116175i \(-0.0370633\pi\)
\(500\) −174.665 + 100.843i −0.0156226 + 0.00901969i
\(501\) −1890.74 + 1091.62i −0.168607 + 0.0973451i
\(502\) 1841.20i 0.163699i
\(503\) 8533.73 + 14780.9i 0.756462 + 1.31023i 0.944644 + 0.328096i \(0.106407\pi\)
−0.188183 + 0.982134i \(0.560260\pi\)
\(504\) 2949.56 5108.79i 0.260682 0.451515i
\(505\) −448.260 258.803i −0.0394996 0.0228051i
\(506\) −12149.0 −1.06737
\(507\) 0 0
\(508\) 795.712 0.0694961
\(509\) −877.192 506.447i −0.0763867 0.0441019i 0.461320 0.887234i \(-0.347376\pi\)
−0.537707 + 0.843132i \(0.680709\pi\)
\(510\) −67.7003 + 117.260i −0.00587808 + 0.0101811i
\(511\) 6943.68 + 12026.8i 0.601116 + 1.04116i
\(512\) 12992.6i 1.12148i
\(513\) 13927.1 8040.83i 1.19863 0.692030i
\(514\) 2841.28 1640.41i 0.243820 0.140769i
\(515\) 522.644i 0.0447193i
\(516\) −1161.54 2011.85i −0.0990969 0.171641i
\(517\) −1034.13 + 1791.17i −0.0879711 + 0.152370i
\(518\) −4629.45 2672.81i −0.392676 0.226712i
\(519\) −16564.6 −1.40098
\(520\) 0 0
\(521\) −14367.7 −1.20818 −0.604089 0.796917i \(-0.706463\pi\)
−0.604089 + 0.796917i \(0.706463\pi\)
\(522\) −5238.19 3024.27i −0.439213 0.253580i
\(523\) 8109.96 14046.9i 0.678057 1.17443i −0.297509 0.954719i \(-0.596156\pi\)
0.975565 0.219709i \(-0.0705109\pi\)
\(524\) −1479.01 2561.72i −0.123303 0.213568i
\(525\) 8350.92i 0.694217i
\(526\) −11592.2 + 6692.76i −0.960919 + 0.554787i
\(527\) 2502.05 1444.56i 0.206814 0.119404i
\(528\) 12028.0i 0.991382i
\(529\) 3399.89 + 5888.78i 0.279435 + 0.483996i
\(530\) 2.04733 3.54608i 0.000167793 0.000290626i
\(531\) 832.722 + 480.772i 0.0680547 + 0.0392914i
\(532\) −2823.06 −0.230066
\(533\) 0 0
\(534\) 10947.5 0.887161
\(535\) 416.961 + 240.733i 0.0336950 + 0.0194538i
\(536\) −5370.70 + 9302.32i −0.432796 + 0.749625i
\(537\) 284.244 + 492.325i 0.0228418 + 0.0395631i
\(538\) 16506.1i 1.32273i
\(539\) 706.071 407.650i 0.0564242 0.0325765i
\(540\) −104.194 + 60.1566i −0.00830335 + 0.00479394i
\(541\) 17592.2i 1.39806i 0.715094 + 0.699029i \(0.246384\pi\)
−0.715094 + 0.699029i \(0.753616\pi\)
\(542\) 5033.36 + 8718.04i 0.398896 + 0.690908i
\(543\) −1973.77 + 3418.67i −0.155990 + 0.270183i
\(544\) 1421.56 + 820.738i 0.112038 + 0.0646854i
\(545\) −377.281 −0.0296531
\(546\) 0 0
\(547\) 10504.6 0.821103 0.410552 0.911837i \(-0.365336\pi\)
0.410552 + 0.911837i \(0.365336\pi\)
\(548\) 2252.99 + 1300.76i 0.175626 + 0.101398i
\(549\) −6179.38 + 10703.0i −0.480382 + 0.832045i
\(550\) −10338.3 17906.5i −0.801504 1.38825i
\(551\) 18992.8i 1.46846i
\(552\) −5652.06 + 3263.22i −0.435811 + 0.251616i
\(553\) −6635.77 + 3831.16i −0.510274 + 0.294607i
\(554\) 15073.2i 1.15596i
\(555\) 118.776 + 205.726i 0.00908426 + 0.0157344i
\(556\) −1074.26 + 1860.67i −0.0819401 + 0.141924i
\(557\) 439.558 + 253.779i 0.0334375 + 0.0193051i 0.516626 0.856211i \(-0.327188\pi\)
−0.483188 + 0.875517i \(0.660521\pi\)
\(558\) −3888.64 −0.295016
\(559\) 0 0
\(560\) −514.690 −0.0388386
\(561\) 5277.41 + 3046.92i 0.397170 + 0.229306i
\(562\) −4520.87 + 7830.38i −0.339327 + 0.587731i
\(563\) −1721.57 2981.85i −0.128873 0.223215i 0.794367 0.607438i \(-0.207803\pi\)
−0.923240 + 0.384223i \(0.874469\pi\)
\(564\) 169.330i 0.0126420i
\(565\) −311.961 + 180.111i −0.0232288 + 0.0134112i
\(566\) −5792.16 + 3344.11i −0.430146 + 0.248345i
\(567\) 3387.96i 0.250936i
\(568\) −6548.59 11342.5i −0.483755 0.837888i
\(569\) 11986.1 20760.5i 0.883098 1.52957i 0.0352188 0.999380i \(-0.488787\pi\)
0.847879 0.530190i \(-0.177879\pi\)
\(570\) −495.591 286.130i −0.0364176 0.0210257i
\(571\) 7458.32 0.546622 0.273311 0.961926i \(-0.411881\pi\)
0.273311 + 0.961926i \(0.411881\pi\)
\(572\) 0 0
\(573\) −2495.26 −0.181922
\(574\) −2808.36 1621.41i −0.204214 0.117903i
\(575\) 4567.28 7910.77i 0.331250 0.573742i
\(576\) −3812.07 6602.70i −0.275757 0.477626i
\(577\) 5669.57i 0.409059i −0.978860 0.204530i \(-0.934434\pi\)
0.978860 0.204530i \(-0.0655665\pi\)
\(578\) 9451.10 5456.60i 0.680128 0.392672i
\(579\) −4217.49 + 2434.97i −0.302717 + 0.174774i
\(580\) 142.093i 0.0101726i
\(581\) −5487.64 9504.87i −0.391851 0.678706i
\(582\) −2752.58 + 4767.60i −0.196045 + 0.339559i
\(583\) −159.595 92.1420i −0.0113375 0.00654568i
\(584\) 18471.4 1.30882
\(585\) 0 0
\(586\) −14065.6 −0.991541
\(587\) 881.087 + 508.696i 0.0619529 + 0.0357685i 0.530657 0.847587i \(-0.321945\pi\)
−0.468704 + 0.883355i \(0.655279\pi\)
\(588\) 33.3746 57.8064i 0.00234072 0.00405425i
\(589\) 6105.30 + 10574.7i 0.427104 + 0.739766i
\(590\) 103.040i 0.00718996i
\(591\) 4044.18 2334.91i 0.281481 0.162513i
\(592\) −5013.41 + 2894.49i −0.348057 + 0.200951i
\(593\) 10198.2i 0.706221i −0.935582 0.353111i \(-0.885124\pi\)
0.935582 0.353111i \(-0.114876\pi\)
\(594\) −12350.0 21390.8i −0.853073 1.47757i
\(595\) −130.381 + 225.827i −0.00898336 + 0.0155596i
\(596\) −3437.00 1984.35i −0.236216 0.136380i
\(597\) 8829.33 0.605294
\(598\) 0 0
\(599\) 12516.3 0.853763 0.426881 0.904308i \(-0.359612\pi\)
0.426881 + 0.904308i \(0.359612\pi\)
\(600\) −9619.33 5553.72i −0.654512 0.377883i
\(601\) −4813.73 + 8337.63i −0.326716 + 0.565888i −0.981858 0.189617i \(-0.939275\pi\)
0.655142 + 0.755505i \(0.272609\pi\)
\(602\) 10204.0 + 17673.9i 0.690838 + 1.19657i
\(603\) 5963.70i 0.402754i
\(604\) −1216.28 + 702.218i −0.0819364 + 0.0473060i
\(605\) 1390.92 803.046i 0.0934691 0.0539644i
\(606\) 8699.80i 0.583177i
\(607\) −3333.60 5773.96i −0.222910 0.386092i 0.732780 0.680466i \(-0.238222\pi\)
−0.955690 + 0.294373i \(0.904889\pi\)
\(608\) −3468.78 + 6008.11i −0.231378 + 0.400758i
\(609\) 10203.3 + 5890.87i 0.678913 + 0.391971i
\(610\) 1324.37 0.0879053
\(611\) 0 0
\(612\) −493.268 −0.0325803
\(613\) −19992.5 11542.7i −1.31728 0.760530i −0.333987 0.942578i \(-0.608394\pi\)
−0.983290 + 0.182047i \(0.941728\pi\)
\(614\) 9359.39 16210.9i 0.615170 1.06551i
\(615\) 72.0532 + 124.800i 0.00472433 + 0.00818278i
\(616\) 28450.6i 1.86089i
\(617\) −2640.72 + 1524.62i −0.172304 + 0.0994796i −0.583672 0.811990i \(-0.698384\pi\)
0.411368 + 0.911469i \(0.365051\pi\)
\(618\) 7607.58 4392.24i 0.495181 0.285893i
\(619\) 7296.58i 0.473787i 0.971536 + 0.236894i \(0.0761293\pi\)
−0.971536 + 0.236894i \(0.923871\pi\)
\(620\) −45.6761 79.1134i −0.00295871 0.00512463i
\(621\) 5455.99 9450.06i 0.352563 0.610657i
\(622\) −17536.0 10124.4i −1.13044 0.652657i
\(623\) 21083.3 1.35583
\(624\) 0 0
\(625\) 15506.8 0.992438
\(626\) 22189.0 + 12810.8i 1.41670 + 0.817929i
\(627\) −12877.5 + 22304.5i −0.820222 + 1.42067i
\(628\) 406.271 + 703.683i 0.0258153 + 0.0447134i
\(629\) 2932.92i 0.185920i
\(630\) 303.954 175.488i 0.0192219 0.0110978i
\(631\) −20637.0 + 11914.8i −1.30197 + 0.751694i −0.980742 0.195307i \(-0.937430\pi\)
−0.321230 + 0.947001i \(0.604096\pi\)
\(632\) 10191.6i 0.641453i
\(633\) −168.672 292.149i −0.0105910 0.0183442i
\(634\) −7980.27 + 13822.2i −0.499901 + 0.865853i
\(635\) 269.019 + 155.318i 0.0168121 + 0.00970648i
\(636\) −15.0874 −0.000940653
\(637\) 0 0
\(638\) 29171.3 1.81019
\(639\) 6297.43 + 3635.82i 0.389863 + 0.225088i
\(640\) −264.174 + 457.562i −0.0163162 + 0.0282605i
\(641\) 6702.63 + 11609.3i 0.413008 + 0.715351i 0.995217 0.0976883i \(-0.0311448\pi\)
−0.582209 + 0.813039i \(0.697812\pi\)
\(642\) 8092.36i 0.497477i
\(643\) −4547.94 + 2625.76i −0.278932 + 0.161042i −0.632940 0.774201i \(-0.718152\pi\)
0.354008 + 0.935243i \(0.384819\pi\)
\(644\) −1658.91 + 957.774i −0.101507 + 0.0586049i
\(645\) 906.904i 0.0553633i
\(646\) −3532.68 6118.79i −0.215157 0.372663i
\(647\) 10805.7 18716.1i 0.656595 1.13726i −0.324897 0.945749i \(-0.605330\pi\)
0.981492 0.191506i \(-0.0613370\pi\)
\(648\) −3902.55 2253.14i −0.236584 0.136592i
\(649\) −4637.39 −0.280483
\(650\) 0 0
\(651\) 7574.54 0.456021
\(652\) −1879.23 1084.97i −0.112878 0.0651699i
\(653\) 10797.9 18702.6i 0.647099 1.12081i −0.336714 0.941607i \(-0.609316\pi\)
0.983813 0.179201i \(-0.0573512\pi\)
\(654\) −3170.63 5491.68i −0.189574 0.328351i
\(655\) 1154.78i 0.0688869i
\(656\) −3041.28 + 1755.89i −0.181009 + 0.104506i
\(657\) −8881.48 + 5127.72i −0.527396 + 0.304492i
\(658\) 1487.54i 0.0881314i
\(659\) 8321.30 + 14412.9i 0.491884 + 0.851968i 0.999956 0.00934609i \(-0.00297500\pi\)
−0.508072 + 0.861315i \(0.669642\pi\)
\(660\) 96.3419 166.869i 0.00568198 0.00984147i
\(661\) −23366.3 13490.6i −1.37495 0.793831i −0.383408 0.923579i \(-0.625250\pi\)
−0.991547 + 0.129748i \(0.958583\pi\)
\(662\) 11871.5 0.696980
\(663\) 0 0
\(664\) −14598.1 −0.853185
\(665\) −954.437 551.044i −0.0556564 0.0321332i
\(666\) 1973.80 3418.73i 0.114840 0.198908i
\(667\) 6443.67 + 11160.8i 0.374063 + 0.647896i
\(668\) 852.310i 0.0493665i
\(669\) 3942.23 2276.05i 0.227826 0.131535i
\(670\) −553.454 + 319.537i −0.0319131 + 0.0184251i
\(671\) 59604.5i 3.42922i
\(672\) 2151.77 + 3726.98i 0.123521 + 0.213945i
\(673\) 5574.62 9655.53i 0.319296 0.553036i −0.661046 0.750346i \(-0.729887\pi\)
0.980341 + 0.197309i \(0.0632204\pi\)
\(674\) −6721.26 3880.52i −0.384115 0.221769i
\(675\) 18571.3 1.05898
\(676\) 0 0
\(677\) 3314.33 0.188154 0.0940769 0.995565i \(-0.470010\pi\)
0.0940769 + 0.995565i \(0.470010\pi\)
\(678\) −5243.36 3027.26i −0.297006 0.171477i
\(679\) −5301.06 + 9181.71i −0.299611 + 0.518942i
\(680\) 173.418 + 300.369i 0.00977982 + 0.0169391i
\(681\) 12165.5i 0.684556i
\(682\) 16241.7 9377.17i 0.911918 0.526496i
\(683\) 21222.2 12252.6i 1.18894 0.686433i 0.230872 0.972984i \(-0.425842\pi\)
0.958065 + 0.286552i \(0.0925090\pi\)
\(684\) 2084.75i 0.116539i
\(685\) 507.803 + 879.540i 0.0283243 + 0.0490591i
\(686\) −8278.50 + 14338.8i −0.460750 + 0.798042i
\(687\) 674.206 + 389.253i 0.0374419 + 0.0216171i
\(688\) 22100.6 1.22468
\(689\) 0 0
\(690\) −388.299 −0.0214236
\(691\) −18838.5 10876.4i −1.03712 0.598782i −0.118105 0.993001i \(-0.537682\pi\)
−0.919017 + 0.394219i \(0.871015\pi\)
\(692\) −3233.32 + 5600.27i −0.177619 + 0.307645i
\(693\) −7897.99 13679.7i −0.432929 0.749855i
\(694\) 7278.90i 0.398132i
\(695\) −726.383 + 419.378i −0.0396450 + 0.0228891i
\(696\) 13571.3 7835.37i 0.739105 0.426722i
\(697\) 1779.20i 0.0966887i
\(698\) −9689.94 16783.5i −0.525458 0.910120i
\(699\) 472.971 819.209i 0.0255928 0.0443281i
\(700\) −2823.33 1630.05i −0.152446 0.0880145i
\(701\) −34250.9 −1.84542 −0.922709 0.385496i \(-0.874030\pi\)
−0.922709 + 0.385496i \(0.874030\pi\)
\(702\) 0 0
\(703\) −12395.8 −0.665028
\(704\) 31843.9 + 18385.1i 1.70477 + 0.984252i
\(705\) −33.0522 + 57.2480i −0.00176570 + 0.00305828i
\(706\) −2996.30 5189.74i −0.159727 0.276655i
\(707\) 16754.6i 0.891259i
\(708\) −328.800 + 189.833i −0.0174535 + 0.0100768i
\(709\) −4786.62 + 2763.56i −0.253548 + 0.146386i −0.621388 0.783503i \(-0.713431\pi\)
0.367840 + 0.929889i \(0.380097\pi\)
\(710\) 779.234i 0.0411889i
\(711\) −2829.21 4900.34i −0.149232 0.258477i
\(712\) 14021.3 24285.6i 0.738020 1.27829i
\(713\) 7175.31 + 4142.67i 0.376883 + 0.217593i
\(714\) −4382.83 −0.229724
\(715\) 0 0
\(716\) 221.931 0.0115837
\(717\) 11326.9 + 6539.57i 0.589972 + 0.340620i
\(718\) 3242.51 5616.19i 0.168537 0.291914i
\(719\) −1888.89 3271.65i −0.0979745 0.169697i 0.812872 0.582443i \(-0.197903\pi\)
−0.910846 + 0.412746i \(0.864570\pi\)
\(720\) 380.085i 0.0196735i
\(721\) 14651.1 8458.81i 0.756776 0.436925i
\(722\) 10644.7 6145.75i 0.548693 0.316788i
\(723\) 18534.2i 0.953380i
\(724\) 770.538 + 1334.61i 0.0395536 + 0.0685088i
\(725\) −10966.6 + 18994.7i −0.561777 + 0.973027i
\(726\) 23378.2 + 13497.4i 1.19510 + 0.689994i
\(727\) −19076.8 −0.973204 −0.486602 0.873624i \(-0.661764\pi\)
−0.486602 + 0.873624i \(0.661764\pi\)
\(728\) 0 0
\(729\) 17319.9 0.879944
\(730\) 951.744 + 549.490i 0.0482543 + 0.0278596i
\(731\) 5598.52 9696.92i 0.283268 0.490634i
\(732\) −2439.93 4226.08i −0.123200 0.213388i
\(733\) 7997.30i 0.402984i −0.979490 0.201492i \(-0.935421\pi\)
0.979490 0.201492i \(-0.0645790\pi\)
\(734\) −14592.0 + 8424.71i −0.733789 + 0.423653i
\(735\) 22.5669 13.0290i 0.00113251 0.000653855i
\(736\) 4707.39i 0.235756i
\(737\) 14381.0 + 24908.7i 0.718769 + 1.24494i
\(738\) 1197.37 2073.90i 0.0597232 0.103444i
\(739\) −25100.6 14491.8i −1.24944 0.721367i −0.278445 0.960452i \(-0.589819\pi\)
−0.970998 + 0.239086i \(0.923152\pi\)
\(740\) 92.7376 0.00460689
\(741\) 0 0
\(742\) 132.541 0.00655761
\(743\) −16580.4 9572.69i −0.818674 0.472662i 0.0312847 0.999511i \(-0.490040\pi\)
−0.849959 + 0.526849i \(0.823373\pi\)
\(744\) 5037.40 8725.02i 0.248226 0.429939i
\(745\) −774.667 1341.76i −0.0380961 0.0659844i
\(746\) 7435.47i 0.364922i
\(747\) 7019.09 4052.47i 0.343795 0.198490i
\(748\) 2060.24 1189.48i 0.100708 0.0581440i
\(749\) 15584.7i 0.760284i
\(750\) −661.688 1146.08i −0.0322152 0.0557984i
\(751\) −12758.4 + 22098.3i −0.619923 + 1.07374i 0.369576 + 0.929200i \(0.379503\pi\)
−0.989499 + 0.144538i \(0.953830\pi\)
\(752\) −1395.10 805.459i −0.0676515 0.0390586i
\(753\) −2648.47 −0.128175
\(754\) 0 0
\(755\) −548.275 −0.0264288
\(756\) −3372.70 1947.23i −0.162254 0.0936773i
\(757\) 8615.31 14922.2i 0.413645 0.716453i −0.581641 0.813446i \(-0.697589\pi\)
0.995285 + 0.0969925i \(0.0309223\pi\)
\(758\) −2389.59 4138.89i −0.114504 0.198326i
\(759\) 17475.7i 0.835744i
\(760\) −1269.48 + 732.936i −0.0605908 + 0.0349821i
\(761\) −2029.15 + 1171.53i −0.0966576 + 0.0558053i −0.547550 0.836773i \(-0.684439\pi\)
0.450892 + 0.892579i \(0.351106\pi\)
\(762\) 5221.11i 0.248216i
\(763\) −6106.17 10576.2i −0.289722 0.501814i
\(764\) −487.060 + 843.613i −0.0230644 + 0.0399488i
\(765\) −166.767 96.2829i −0.00788166 0.00455048i
\(766\) −27756.9 −1.30927
\(767\) 0 0
\(768\) 7862.11 0.369400
\(769\) −6148.93 3550.09i −0.288344 0.166475i 0.348851 0.937178i \(-0.386572\pi\)
−0.637195 + 0.770703i \(0.719905\pi\)
\(770\) −846.353 + 1465.93i −0.0396110 + 0.0686082i
\(771\) −2359.65 4087.03i −0.110221 0.190909i
\(772\) 1901.17i 0.0886328i
\(773\) −10626.5 + 6135.22i −0.494449 + 0.285470i −0.726418 0.687253i \(-0.758816\pi\)
0.231969 +