Properties

Label 169.4.c.j.22.2
Level $169$
Weight $4$
Character 169.22
Analytic conductor $9.971$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 22.2
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 169.22
Dual form 169.4.c.j.146.2

$q$-expansion

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28078 2.21837i 0.452823 0.784312i −0.545737 0.837956i \(-0.683750\pi\)
0.998560 + 0.0536442i \(0.0170837\pi\)
\(3\) 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
\(5\) −0.561553 −0.0502268 −0.0251134 0.999685i \(-0.507995\pi\)
−0.0251134 + 0.999685i \(0.507995\pi\)
\(6\) −4.71922 8.17394i −0.321102 0.556166i
\(7\) 9.08854 + 15.7418i 0.490735 + 0.849978i 0.999943 0.0106654i \(-0.00339497\pi\)
−0.509208 + 0.860643i \(0.670062\pi\)
\(8\) 24.1771 1.06849
\(9\) 6.71165 + 11.6249i 0.248579 + 0.430552i
\(10\) −0.719224 + 1.24573i −0.0227438 + 0.0393935i
\(11\) 32.3693 56.0653i 0.887247 1.53676i 0.0441305 0.999026i \(-0.485948\pi\)
0.843116 0.537731i \(-0.180718\pi\)
\(12\) 5.30019 0.127503
\(13\) 0 0
\(14\) 46.5616 0.888864
\(15\) −1.03457 + 1.79192i −0.0178082 + 0.0308448i
\(16\) 25.2116 43.6679i 0.393932 0.682310i
\(17\) 12.7732 + 22.1238i 0.182233 + 0.315636i 0.942641 0.333810i \(-0.108334\pi\)
−0.760408 + 0.649446i \(0.775001\pi\)
\(18\) 34.3845 0.450250
\(19\) −53.9848 93.5045i −0.651841 1.12902i −0.982676 0.185333i \(-0.940664\pi\)
0.330835 0.943689i \(-0.392670\pi\)
\(20\) −0.403882 0.699544i −0.00451554 0.00782114i
\(21\) 66.9763 0.695973
\(22\) −82.9157 143.614i −0.803531 1.39176i
\(23\) −36.6307 + 63.4462i −0.332088 + 0.575193i −0.982921 0.184027i \(-0.941086\pi\)
0.650833 + 0.759221i \(0.274420\pi\)
\(24\) 44.5421 77.1493i 0.378839 0.656168i
\(25\) −124.685 −0.997477
\(26\) 0 0
\(27\) 148.946 1.06165
\(28\) −13.0734 + 22.6438i −0.0882371 + 0.152831i
\(29\) −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
\(31\) 113.093 0.655228 0.327614 0.944812i \(-0.393755\pi\)
0.327614 + 0.944812i \(0.393755\pi\)
\(32\) 32.1274 + 55.6462i 0.177480 + 0.307405i
\(33\) −119.270 206.581i −0.629158 1.08973i
\(34\) 65.4384 0.330077
\(35\) −5.10370 8.83986i −0.0246481 0.0426917i
\(36\) −9.65435 + 16.7218i −0.0446961 + 0.0774158i
\(37\) 57.4039 99.4264i 0.255058 0.441773i −0.709853 0.704349i \(-0.751239\pi\)
0.964911 + 0.262576i \(0.0845722\pi\)
\(38\) −276.570 −1.18067
\(39\) 0 0
\(40\) −13.5767 −0.0536666
\(41\) −34.8229 + 60.3151i −0.132645 + 0.229747i −0.924695 0.380708i \(-0.875680\pi\)
0.792051 + 0.610455i \(0.209014\pi\)
\(42\) 85.7817 148.578i 0.315153 0.545860i
\(43\) −219.151 379.581i −0.777214 1.34617i −0.933541 0.358469i \(-0.883299\pi\)
0.156327 0.987705i \(-0.450035\pi\)
\(44\) 93.1231 0.319064
\(45\) −3.76894 6.52800i −0.0124854 0.0216253i
\(46\) 93.8314 + 162.521i 0.300754 + 0.520921i
\(47\) 31.9479 0.0991506 0.0495753 0.998770i \(-0.484213\pi\)
0.0495753 + 0.998770i \(0.484213\pi\)
\(48\) −92.8963 160.901i −0.279342 0.483835i
\(49\) 6.29686 10.9065i 0.0183582 0.0317973i
\(50\) −159.693 + 276.597i −0.451680 + 0.782334i
\(51\) 94.1298 0.258447
\(52\) 0 0
\(53\) 2.84658 0.00737752 0.00368876 0.999993i \(-0.498826\pi\)
0.00368876 + 0.999993i \(0.498826\pi\)
\(54\) 190.767 330.417i 0.480741 0.832669i
\(55\) −18.1771 + 31.4836i −0.0445636 + 0.0771864i
\(56\) 219.734 + 380.591i 0.524344 + 0.908190i
\(57\) −397.831 −0.924457
\(58\) 225.300 + 390.231i 0.510058 + 0.883446i
\(59\) 35.8163 + 62.0356i 0.0790319 + 0.136887i 0.902832 0.429992i \(-0.141484\pi\)
−0.823801 + 0.566880i \(0.808150\pi\)
\(60\) −2.97633 −0.00640405
\(61\) 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
\(63\) −121.998 + 211.307i −0.243973 + 0.422574i
\(64\) 567.978 1.10933
\(65\) 0 0
\(66\) −611.032 −1.13959
\(67\) −222.140 + 384.758i −0.405056 + 0.701577i −0.994328 0.106357i \(-0.966081\pi\)
0.589272 + 0.807935i \(0.299415\pi\)
\(68\) −18.3736 + 31.8240i −0.0327665 + 0.0567533i
\(69\) 134.972 + 233.778i 0.235488 + 0.407877i
\(70\) −26.1468 −0.0446448
\(71\) −270.859 469.142i −0.452748 0.784182i 0.545808 0.837910i \(-0.316223\pi\)
−0.998556 + 0.0537283i \(0.982890\pi\)
\(72\) 162.268 + 281.056i 0.265604 + 0.460039i
\(73\) −764.004 −1.22493 −0.612465 0.790498i \(-0.709822\pi\)
−0.612465 + 0.790498i \(0.709822\pi\)
\(74\) −147.043 254.686i −0.230992 0.400090i
\(75\) −229.710 + 397.870i −0.353662 + 0.612561i
\(76\) 77.6543 134.501i 0.117205 0.203005i
\(77\) 1176.76 1.74161
\(78\) 0 0
\(79\) −421.538 −0.600338 −0.300169 0.953886i \(-0.597043\pi\)
−0.300169 + 0.953886i \(0.597043\pi\)
\(80\) −14.1577 + 24.5218i −0.0197859 + 0.0342703i
\(81\) 93.1932 161.415i 0.127837 0.221420i
\(82\) 89.2007 + 154.500i 0.120129 + 0.208069i
\(83\) −603.797 −0.798498 −0.399249 0.916842i \(-0.630729\pi\)
−0.399249 + 0.916842i \(0.630729\pi\)
\(84\) 48.1710 + 83.4346i 0.0625700 + 0.108374i
\(85\) −7.17283 12.4237i −0.00915297 0.0158534i
\(86\) −1122.73 −1.40776
\(87\) 324.082 + 561.327i 0.399371 + 0.691731i
\(88\) 782.596 1355.50i 0.948011 1.64200i
\(89\) −579.941 + 1004.49i −0.690715 + 1.19635i 0.280889 + 0.959740i \(0.409371\pi\)
−0.971604 + 0.236613i \(0.923963\pi\)
\(90\) −19.3087 −0.0226146
\(91\) 0 0
\(92\) −105.383 −0.119423
\(93\) 208.354 360.880i 0.232315 0.402382i
\(94\) 40.9181 70.8722i 0.0448977 0.0777650i
\(95\) 30.3153 + 52.5077i 0.0327399 + 0.0567071i
\(96\) 236.757 0.251707
\(97\) 291.634 + 505.126i 0.305268 + 0.528740i 0.977321 0.211763i \(-0.0679206\pi\)
−0.672053 + 0.740503i \(0.734587\pi\)
\(98\) −16.1298 27.9375i −0.0166260 0.0287971i
\(99\) 869.006 0.882206
\(100\) −89.6761 155.324i −0.0896761 0.155324i
\(101\) −460.870 + 798.251i −0.454043 + 0.786425i −0.998633 0.0522775i \(-0.983352\pi\)
0.544590 + 0.838702i \(0.316685\pi\)
\(102\) 120.559 208.815i 0.117031 0.202703i
\(103\) −930.712 −0.890347 −0.445174 0.895444i \(-0.646858\pi\)
−0.445174 + 0.895444i \(0.646858\pi\)
\(104\) 0 0
\(105\) −37.6107 −0.0349565
\(106\) 3.64584 6.31478i 0.00334071 0.00578628i
\(107\) −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
\(109\) −671.853 −0.590384 −0.295192 0.955438i \(-0.595384\pi\)
−0.295192 + 0.955438i \(0.595384\pi\)
\(110\) 46.5616 + 80.6470i 0.0403588 + 0.0699035i
\(111\) −211.514 366.352i −0.180865 0.313267i
\(112\) 916.548 0.773265
\(113\) −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
\(115\) 20.5701 35.6284i 0.0166797 0.0288901i
\(116\) −253.036 −0.202533
\(117\) 0 0
\(118\) 183.491 0.143150
\(119\) −232.179 + 402.147i −0.178856 + 0.309788i
\(120\) −25.0128 + 43.3234i −0.0190279 + 0.0329572i
\(121\) −1430.05 2476.91i −1.07441 1.86094i
\(122\) 2358.41 1.75017
\(123\) 128.311 + 222.240i 0.0940599 + 0.162917i
\(124\) 81.3390 + 140.883i 0.0589069 + 0.102030i
\(125\) 140.211 0.100327
\(126\) 312.505 + 541.274i 0.220953 + 0.382703i
\(127\) 276.587 479.063i 0.193253 0.334724i −0.753073 0.657937i \(-0.771430\pi\)
0.946326 + 0.323212i \(0.104763\pi\)
\(128\) 470.434 814.816i 0.324851 0.562658i
\(129\) −1614.99 −1.10227
\(130\) 0 0
\(131\) 2056.40 1.37152 0.685758 0.727830i \(-0.259471\pi\)
0.685758 + 0.727830i \(0.259471\pi\)
\(132\) 171.563 297.157i 0.113126 0.195941i
\(133\) 981.287 1699.64i 0.639762 1.10810i
\(134\) 569.024 + 985.578i 0.366837 + 0.635380i
\(135\) −83.6411 −0.0533235
\(136\) 308.819 + 534.890i 0.194713 + 0.337253i
\(137\) −904.283 1566.26i −0.563928 0.976752i −0.997149 0.0754639i \(-0.975956\pi\)
0.433221 0.901288i \(-0.357377\pi\)
\(138\) 691.474 0.426537
\(139\) −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
\(141\) 58.8585 101.946i 0.0351545 0.0608894i
\(142\) −1387.64 −0.820058
\(143\) 0 0
\(144\) 676.847 0.391694
\(145\) 49.3911 85.5479i 0.0282876 0.0489956i
\(146\) −978.518 + 1694.84i −0.554676 + 0.960727i
\(147\) −23.2018 40.1867i −0.0130180 0.0225479i
\(148\) 165.145 0.0917218
\(149\) −1379.51 2389.38i −0.758482 1.31373i −0.943625 0.331018i \(-0.892608\pi\)
0.185143 0.982712i \(-0.440725\pi\)
\(150\) 588.415 + 1019.16i 0.320292 + 0.554763i
\(151\) 976.355 0.526190 0.263095 0.964770i \(-0.415257\pi\)
0.263095 + 0.964770i \(0.415257\pi\)
\(152\) −1305.20 2260.67i −0.696483 1.20634i
\(153\) −171.458 + 296.975i −0.0905986 + 0.156921i
\(154\) 1507.17 2610.49i 0.788642 1.36597i
\(155\) −63.5076 −0.0329100
\(156\) 0 0
\(157\) −564.875 −0.287146 −0.143573 0.989640i \(-0.545859\pi\)
−0.143573 + 0.989640i \(0.545859\pi\)
\(158\) −539.896 + 935.127i −0.271847 + 0.470853i
\(159\) 5.24435 9.08347i 0.00261575 0.00453061i
\(160\) −18.0412 31.2483i −0.00891427 0.0154400i
\(161\) −1331.68 −0.651869
\(162\) −238.719 413.474i −0.115775 0.200528i
\(163\) 754.266 + 1306.43i 0.362446 + 0.627775i 0.988363 0.152115i \(-0.0486084\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(164\) −100.182 −0.0477005
\(165\) 66.9763 + 116.006i 0.0316006 + 0.0547339i
\(166\) −773.329 + 1339.45i −0.361578 + 0.626272i
\(167\) 296.260 513.138i 0.137277 0.237771i −0.789188 0.614152i \(-0.789498\pi\)
0.926465 + 0.376381i \(0.122832\pi\)
\(168\) 1619.29 0.743638
\(169\) 0 0
\(170\) −36.7471 −0.0165787
\(171\) 724.654 1255.14i 0.324068 0.561303i
\(172\) 315.237 546.007i 0.139748 0.242050i
\(173\) 2247.78 + 3893.28i 0.987838 + 1.71099i 0.628576 + 0.777748i \(0.283638\pi\)
0.359262 + 0.933237i \(0.383028\pi\)
\(174\) 1660.31 0.723377
\(175\) −1133.20 1962.76i −0.489497 0.847834i
\(176\) −1632.17 2827.00i −0.699030 1.21076i
\(177\) 263.941 0.112085
\(178\) 1485.55 + 2573.05i 0.625543 + 1.08347i
\(179\) 77.1425 133.615i 0.0322117 0.0557924i −0.849470 0.527637i \(-0.823078\pi\)
0.881682 + 0.471844i \(0.156412\pi\)
\(180\) 5.42143 9.39019i 0.00224494 0.00388835i
\(181\) 1071.35 0.439959 0.219979 0.975505i \(-0.429401\pi\)
0.219979 + 0.975505i \(0.429401\pi\)
\(182\) 0 0
\(183\) 3392.45 1.37037
\(184\) −885.623 + 1533.94i −0.354831 + 0.614586i
\(185\) −32.2353 + 55.8332i −0.0128107 + 0.0221889i
\(186\) −533.710 924.413i −0.210395 0.364415i
\(187\) 1653.84 0.646742
\(188\) 22.9777 + 39.7985i 0.00891393 + 0.0154394i
\(189\) 1353.70 + 2344.68i 0.520991 + 0.902383i
\(190\) 155.309 0.0593015
\(191\) −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
\(193\) 660.840 1144.61i 0.246468 0.426895i −0.716075 0.698023i \(-0.754063\pi\)
0.962543 + 0.271128i \(0.0873967\pi\)
\(194\) 1494.07 0.552929
\(195\) 0 0
\(196\) 18.1154 0.00660183
\(197\) 633.683 1097.57i 0.229178 0.396948i −0.728387 0.685166i \(-0.759730\pi\)
0.957565 + 0.288218i \(0.0930629\pi\)
\(198\) 1113.00 1927.78i 0.399483 0.691925i
\(199\) −1198.12 2075.21i −0.426796 0.739233i 0.569790 0.821790i \(-0.307025\pi\)
−0.996586 + 0.0825573i \(0.973691\pi\)
\(200\) −3014.51 −1.06579
\(201\) 818.510 + 1417.70i 0.287230 + 0.497497i
\(202\) 1180.54 + 2044.76i 0.411202 + 0.712222i
\(203\) −3197.51 −1.10552
\(204\) 67.7003 + 117.260i 0.0232352 + 0.0402445i
\(205\) 19.5549 33.8701i 0.00666231 0.0115395i
\(206\) −1192.03 + 2064.66i −0.403170 + 0.698310i
\(207\) −983.409 −0.330201
\(208\) 0 0
\(209\) −6989.81 −2.31337
\(210\) −48.1710 + 83.4346i −0.0158291 + 0.0274168i
\(211\) 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
\(213\) −1996.05 −0.642099
\(214\) 1098.12 + 1901.99i 0.350774 + 0.607558i
\(215\) 123.065 + 213.155i 0.0390370 + 0.0676141i
\(216\) 3601.08 1.13436
\(217\) 1027.85 + 1780.29i 0.321543 + 0.556929i
\(218\) −860.494 + 1490.42i −0.267339 + 0.463045i
\(219\) −1407.55 + 2437.94i −0.434307 + 0.752241i
\(220\) −52.2935 −0.0160256
\(221\) 0 0
\(222\) −1083.61 −0.327599
\(223\) 617.709 1069.90i 0.185493 0.321282i −0.758250 0.651964i \(-0.773945\pi\)
0.943742 + 0.330682i \(0.107279\pi\)
\(224\) −583.982 + 1011.49i −0.174192 + 0.301709i
\(225\) −836.839 1449.45i −0.247952 0.429466i
\(226\) −1643.17 −0.483637
\(227\) 1650.83 + 2859.32i 0.482685 + 0.836035i 0.999802 0.0198797i \(-0.00632833\pi\)
−0.517118 + 0.855914i \(0.672995\pi\)
\(228\) −286.130 495.591i −0.0831114 0.143953i
\(229\) −211.283 −0.0609694 −0.0304847 0.999535i \(-0.509705\pi\)
−0.0304847 + 0.999535i \(0.509705\pi\)
\(230\) −52.6913 91.2640i −0.0151059 0.0261642i
\(231\) 2167.98 3755.05i 0.617500 1.06954i
\(232\) −2126.48 + 3683.18i −0.601769 + 1.04230i
\(233\) −256.724 −0.0721827 −0.0360913 0.999348i \(-0.511491\pi\)
−0.0360913 + 0.999348i \(0.511491\pi\)
\(234\) 0 0
\(235\) −17.9404 −0.00498002
\(236\) −51.5198 + 89.2349i −0.0142104 + 0.0246131i
\(237\) −776.612 + 1345.13i −0.212854 + 0.368674i
\(238\) 594.740 + 1030.12i 0.161980 + 0.280558i
\(239\) 3549.62 0.960694 0.480347 0.877078i \(-0.340511\pi\)
0.480347 + 0.877078i \(0.340511\pi\)
\(240\) 52.1662 + 90.3545i 0.0140305 + 0.0243015i
\(241\) −2515.05 4356.19i −0.672235 1.16434i −0.977269 0.212003i \(-0.932001\pi\)
0.305034 0.952341i \(-0.401332\pi\)
\(242\) −7326.27 −1.94608
\(243\) 1667.39 + 2888.00i 0.440176 + 0.762408i
\(244\) −662.186 + 1146.94i −0.173738 + 0.300923i
\(245\) −3.53602 + 6.12457i −0.000922074 + 0.00159708i
\(246\) 657.349 0.170370
\(247\) 0 0
\(248\) 2734.25 0.700102
\(249\) −1112.39 + 1926.72i −0.283113 + 0.490366i
\(250\) 179.579 311.040i 0.0454303 0.0786876i
\(251\) 359.392 + 622.485i 0.0903770 + 0.156538i 0.907670 0.419685i \(-0.137859\pi\)
−0.817293 + 0.576223i \(0.804526\pi\)
\(252\) −350.976 −0.0877357
\(253\) 2371.42 + 4107.42i 0.589288 + 1.02068i
\(254\) −708.492 1227.14i −0.175019 0.303141i
\(255\) −52.8588 −0.0129810
\(256\) 1066.87 + 1847.87i 0.260466 + 0.451141i
\(257\) −640.397 + 1109.20i −0.155435 + 0.269222i −0.933217 0.359312i \(-0.883011\pi\)
0.777782 + 0.628534i \(0.216345\pi\)
\(258\) −2068.45 + 3582.65i −0.499131 + 0.864520i
\(259\) 2086.87 0.500663
\(260\) 0 0
\(261\) −2361.28 −0.559998
\(262\) 2633.79 4561.86i 0.621054 1.07570i
\(263\) −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
\(265\) −1.59851 −0.000370549
\(266\) −2513.62 4353.71i −0.579398 1.00355i
\(267\) 2136.89 + 3701.19i 0.489795 + 0.848350i
\(268\) −639.074 −0.145663
\(269\) −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
\(271\) −1964.97 + 3403.42i −0.440455 + 0.762890i −0.997723 0.0674426i \(-0.978516\pi\)
0.557269 + 0.830332i \(0.311849\pi\)
\(272\) 1288.13 0.287149
\(273\) 0 0
\(274\) −4632.74 −1.02144
\(275\) −4035.96 + 6990.48i −0.885009 + 1.53288i
\(276\) −194.149 + 336.277i −0.0423421 + 0.0733387i
\(277\) 2942.20 + 5096.04i 0.638194 + 1.10538i 0.985829 + 0.167754i \(0.0536516\pi\)
−0.347635 + 0.937630i \(0.613015\pi\)
\(278\) −3826.03 −0.825431
\(279\) 759.039 + 1314.69i 0.162876 + 0.282110i
\(280\) −123.392 213.722i −0.0263361 0.0456155i
\(281\) −3529.79 −0.749358 −0.374679 0.927155i \(-0.622247\pi\)
−0.374679 + 0.927155i \(0.622247\pi\)
\(282\) −150.769 261.140i −0.0318375 0.0551442i
\(283\) 1305.50 2261.19i 0.274219 0.474961i −0.695719 0.718314i \(-0.744914\pi\)
0.969938 + 0.243353i \(0.0782474\pi\)
\(284\) 389.617 674.836i 0.0814067 0.141001i
\(285\) 223.403 0.0464325
\(286\) 0 0
\(287\) −1265.96 −0.260373
\(288\) −431.255 + 746.955i −0.0882359 + 0.152829i
\(289\) 2130.19 3689.60i 0.433582 0.750987i
\(290\) −126.518 219.136i −0.0256186 0.0443727i
\(291\) 2149.15 0.432939
\(292\) −549.490 951.744i −0.110125 0.190742i
\(293\) −2745.51 4755.37i −0.547422 0.948163i −0.998450 0.0556531i \(-0.982276\pi\)
0.451028 0.892510i \(-0.351057\pi\)
\(294\) −118.865 −0.0235795
\(295\) −20.1127 34.8363i −0.00396952 0.00687541i
\(296\) 1387.86 2403.84i 0.272526 0.472028i
\(297\) 4821.28 8350.70i 0.941950 1.63150i
\(298\) −7067.37 −1.37383
\(299\) 0 0
\(300\) −660.852 −0.127181
\(301\) 3983.53 6899.67i 0.762813 1.32123i
\(302\) 1250.49 2165.92i 0.238271 0.412697i
\(303\) 1698.15 + 2941.28i 0.321967 + 0.557664i
\(304\) −5444.19 −1.02712
\(305\) −258.509 447.751i −0.0485318 0.0840596i
\(306\) 439.200 + 760.716i 0.0820502 + 0.142115i
\(307\) 7307.59 1.35852 0.679261 0.733897i \(-0.262300\pi\)
0.679261 + 0.733897i \(0.262300\pi\)
\(308\) 846.353 + 1465.93i 0.156576 + 0.271198i
\(309\) −1714.68 + 2969.91i −0.315678 + 0.546771i
\(310\) −81.3390 + 140.883i −0.0149024 + 0.0258117i
\(311\) 7904.92 1.44131 0.720654 0.693295i \(-0.243842\pi\)
0.720654 + 0.693295i \(0.243842\pi\)
\(312\) 0 0
\(313\) 10002.4 1.80629 0.903145 0.429336i \(-0.141252\pi\)
0.903145 + 0.429336i \(0.141252\pi\)
\(314\) −723.478 + 1253.10i −0.130026 + 0.225212i
\(315\) 68.5084 118.660i 0.0122540 0.0212246i
\(316\) −303.180 525.123i −0.0539722 0.0934825i
\(317\) 6230.81 1.10397 0.551983 0.833856i \(-0.313871\pi\)
0.551983 + 0.833856i \(0.313871\pi\)
\(318\) −13.4337 23.2678i −0.00236894 0.00410312i
\(319\) 5694.06 + 9862.40i 0.999392 + 1.73100i
\(320\) −318.950 −0.0557182
\(321\) 1579.58 + 2735.91i 0.274653 + 0.475713i
\(322\) −1705.58 + 2954.15i −0.295181 + 0.511269i
\(323\) 1379.12 2388.70i 0.237573 0.411489i
\(324\) 268.107 0.0459717
\(325\) 0 0
\(326\) 3864.19 0.656495
\(327\) −1237.77 + 2143.89i −0.209324 + 0.362561i
\(328\) −841.917 + 1458.24i −0.141729 + 0.245482i
\(329\) 290.360 + 502.918i 0.0486567 + 0.0842758i
\(330\) 343.127 0.0572379
\(331\) −2317.25 4013.60i −0.384797 0.666488i 0.606944 0.794745i \(-0.292395\pi\)
−0.991741 + 0.128257i \(0.959062\pi\)
\(332\) −434.265 752.170i −0.0717874 0.124339i
\(333\) 1541.10 0.253609
\(334\) −758.886 1314.43i −0.124325 0.215337i
\(335\) 124.743 216.062i 0.0203447 0.0352380i
\(336\) 1688.58 2924.71i 0.274166 0.474870i
\(337\) 3029.82 0.489747 0.244874 0.969555i \(-0.421254\pi\)
0.244874 + 0.969555i \(0.421254\pi\)
\(338\) 0 0
\(339\) −2363.61 −0.378684
\(340\) 10.3177 17.8708i 0.00164576 0.00285054i
\(341\) 3660.74 6340.58i 0.581349 1.00693i
\(342\) −1856.24 3215.10i −0.293491 0.508342i
\(343\) 6463.66 1.01751
\(344\) −5298.43 9177.15i −0.830443 1.43837i
\(345\) −75.7937 131.278i −0.0118278 0.0204864i
\(346\) 11515.6 1.78926
\(347\) −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
\(349\) 3782.84 6552.07i 0.580202 1.00494i −0.415252 0.909706i \(-0.636307\pi\)
0.995455 0.0952339i \(-0.0303599\pi\)
\(350\) −5805.51 −0.886622
\(351\) 0 0
\(352\) 4159.76 0.629875
\(353\) −1169.72 + 2026.01i −0.176368 + 0.305478i −0.940634 0.339423i \(-0.889768\pi\)
0.764266 + 0.644901i \(0.223101\pi\)
\(354\) 338.050 585.520i 0.0507547 0.0879097i
\(355\) 152.102 + 263.448i 0.0227401 + 0.0393870i
\(356\) −1668.43 −0.248389
\(357\) 855.502 + 1481.77i 0.126829 + 0.219674i
\(358\) −197.605 342.261i −0.0291724 0.0505281i
\(359\) 2531.68 0.372192 0.186096 0.982532i \(-0.440417\pi\)
0.186096 + 0.982532i \(0.440417\pi\)
\(360\) −91.1221 157.828i −0.0133404 0.0231063i
\(361\) −2399.23 + 4155.58i −0.349793 + 0.605858i
\(362\) 1372.16 2376.64i 0.199223 0.345065i
\(363\) −10538.5 −1.52376
\(364\) 0 0
\(365\) 429.028 0.0615243
\(366\) 4344.97 7525.70i 0.620533 1.07479i
\(367\) −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
\(369\) −934.876 −0.131891
\(370\) 82.5725 + 143.020i 0.0116020 + 0.0200952i
\(371\) 25.8713 + 44.8104i 0.00362041 + 0.00627073i
\(372\) 599.413 0.0835433
\(373\) −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
\(375\) 258.315 447.415i 0.0355716 0.0616117i
\(376\) 772.407 0.105941
\(377\) 0 0
\(378\) 6935.16 0.943667
\(379\) −932.867 + 1615.77i −0.126433 + 0.218989i −0.922292 0.386493i \(-0.873686\pi\)
0.795859 + 0.605482i \(0.207020\pi\)
\(380\) −43.6070 + 75.5296i −0.00588682 + 0.0101963i
\(381\) −1019.13 1765.18i −0.137038 0.237357i
\(382\) −1734.69 −0.232342
\(383\) 5417.99 + 9384.24i 0.722837 + 1.25199i 0.959858 + 0.280486i \(0.0904955\pi\)
−0.237021 + 0.971504i \(0.576171\pi\)
\(384\) −1733.39 3002.32i −0.230356 0.398988i
\(385\) −660.813 −0.0874757
\(386\) −1692.78 2931.97i −0.223213 0.386616i
\(387\) 2941.73 5095.22i 0.386399 0.669263i
\(388\) −419.501 + 726.597i −0.0548890 + 0.0950705i
\(389\) −9520.34 −1.24088 −0.620438 0.784256i \(-0.713045\pi\)
−0.620438 + 0.784256i \(0.713045\pi\)
\(390\) 0 0
\(391\) −1871.56 −0.242069
\(392\) 152.240 263.687i 0.0196155 0.0339750i
\(393\) 3788.57 6561.99i 0.486280 0.842261i
\(394\) −1623.21 2811.49i −0.207554 0.359494i
\(395\) 236.716 0.0301531
\(396\) 625.009 + 1082.55i 0.0793129 + 0.137374i
\(397\) −5054.42 8754.51i −0.638978 1.10674i −0.985657 0.168758i \(-0.946024\pi\)
0.346680 0.937983i \(-0.387309\pi\)
\(398\) −6138.10 −0.773053
\(399\) −3615.71 6262.59i −0.453664 0.785768i
\(400\) −3143.51 + 5444.71i −0.392938 + 0.680589i
\(401\) 1042.19 1805.12i 0.129787 0.224797i −0.793807 0.608169i \(-0.791904\pi\)
0.923594 + 0.383373i \(0.125237\pi\)
\(402\) 4193.32 0.520258
\(403\) 0 0
\(404\) −1325.88 −0.163279
\(405\) −52.3329 + 90.6432i −0.00642084 + 0.0111212i
\(406\) −4095.30 + 7093.27i −0.500607 + 0.867076i
\(407\) −3716.25 6436.73i −0.452599 0.783924i
\(408\) 2275.78 0.276147
\(409\) −4858.26 8414.76i −0.587349 1.01732i −0.994578 0.103992i \(-0.966838\pi\)
0.407229 0.913326i \(-0.366495\pi\)
\(410\) −50.0909 86.7600i −0.00603369 0.0104507i
\(411\) −6663.95 −0.799777
\(412\) −669.390 1159.42i −0.0800449 0.138642i
\(413\) −651.035 + 1127.63i −0.0775674 + 0.134351i
\(414\) −1259.53 + 2181.56i −0.149523 + 0.258981i
\(415\) 339.064 0.0401060
\(416\) 0 0
\(417\) −5503.54 −0.646305
\(418\) −8952.38 + 15506.0i −1.04755 + 1.81441i
\(419\) −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
\(421\) 9463.37 1.09553 0.547763 0.836633i \(-0.315479\pi\)
0.547763 + 0.836633i \(0.315479\pi\)
\(422\) −117.260 203.100i −0.0135264 0.0234284i
\(423\) 214.423 + 371.391i 0.0246468 + 0.0426895i
\(424\) 68.8221 0.00788278
\(425\) −1592.62 2758.50i −0.181773 0.314840i
\(426\) −2556.49 + 4427.97i −0.290757 + 0.503606i
\(427\) −8367.77 + 14493.4i −0.948349 + 1.64259i
\(428\) −1233.30 −0.139285
\(429\) 0 0
\(430\) 630.474 0.0707074
\(431\) 2426.14 4202.20i 0.271144 0.469635i −0.698011 0.716087i \(-0.745931\pi\)
0.969155 + 0.246452i \(0.0792647\pi\)
\(432\) 3755.17 6504.15i 0.418220 0.724378i
\(433\) 4104.00 + 7108.33i 0.455486 + 0.788925i 0.998716 0.0506587i \(-0.0161321\pi\)
−0.543230 + 0.839584i \(0.682799\pi\)
\(434\) 5265.78 0.582409
\(435\) −181.989 315.215i −0.0200591 0.0347434i
\(436\) −483.213 836.949i −0.0530773 0.0919325i
\(437\) 7910.01 0.865874
\(438\) 3605.50 + 6244.92i 0.393328 + 0.681264i
\(439\) 1496.90 2592.71i 0.162741 0.281875i −0.773110 0.634272i \(-0.781300\pi\)
0.935851 + 0.352397i \(0.114633\pi\)
\(440\) −439.469 + 761.182i −0.0476156 + 0.0824726i
\(441\) 169.049 0.0182539
\(442\) 0 0
\(443\) 9743.67 1.04500 0.522501 0.852639i \(-0.324999\pi\)
0.522501 + 0.852639i \(0.324999\pi\)
\(444\) 304.251 526.979i 0.0325206 0.0563273i
\(445\) 325.668 564.073i 0.0346924 0.0600890i
\(446\) −1582.29 2740.61i −0.167990 0.290968i
\(447\) −10166.0 −1.07570
\(448\) 5162.09 + 8941.01i 0.544388 + 0.942908i
\(449\) −280.729 486.237i −0.0295065 0.0511068i 0.850895 0.525336i \(-0.176060\pi\)
−0.880402 + 0.474229i \(0.842727\pi\)
\(450\) −4287.22 −0.449114
\(451\) 2254.39 + 3904.71i 0.235377 + 0.407685i
\(452\) 461.363 799.104i 0.0480104 0.0831564i
\(453\) 1798.77 3115.56i 0.186564 0.323138i
\(454\) 8457.38 0.874283
\(455\) 0 0
\(456\) −9618.40 −0.987770
\(457\) 6879.20 11915.1i 0.704148 1.21962i −0.262851 0.964837i \(-0.584663\pi\)
0.966998 0.254783i \(-0.0820040\pi\)
\(458\) −270.606 + 468.704i −0.0276083 + 0.0478190i
\(459\) 1902.52 + 3295.26i 0.193468 + 0.335097i
\(460\) 59.1779 0.00599823
\(461\) 6004.62 + 10400.3i 0.606644 + 1.05074i 0.991789 + 0.127882i \(0.0408179\pi\)
−0.385145 + 0.922856i \(0.625849\pi\)
\(462\) −5553.39 9618.75i −0.559236 0.968625i
\(463\) −13635.7 −1.36870 −0.684348 0.729156i \(-0.739913\pi\)
−0.684348 + 0.729156i \(0.739913\pi\)
\(464\) 4434.96 + 7681.57i 0.443724 + 0.768552i
\(465\) −117.002 + 202.653i −0.0116685 + 0.0202104i
\(466\) −328.806 + 569.509i −0.0326860 + 0.0566138i
\(467\) 8821.95 0.874157 0.437079 0.899423i \(-0.356013\pi\)
0.437079 + 0.899423i \(0.356013\pi\)
\(468\) 0 0
\(469\) −8075.72 −0.795100
\(470\) −22.9777 + 39.7985i −0.00225507 + 0.00390589i
\(471\) −1040.69 + 1802.52i −0.101809 + 0.176339i
\(472\) 865.933 + 1499.84i 0.0844445 + 0.146262i
\(473\) −28375.1 −2.75832
\(474\) 1989.33 + 3445.62i 0.192770 + 0.333888i
\(475\) 6731.08 + 11658.6i 0.650196 + 1.12617i
\(476\) −667.956 −0.0643187
\(477\) 19.1053 + 33.0913i 0.00183390 + 0.00317641i
\(478\) 4546.27 7874.37i 0.435024 0.753484i
\(479\) −7310.02 + 12661.3i −0.697293 + 1.20775i 0.272109 + 0.962267i \(0.412279\pi\)
−0.969402 + 0.245480i \(0.921054\pi\)
\(480\) −132.951 −0.0126424
\(481\) 0 0
\(482\) −12884.9 −1.21761
\(483\) −2453.39 + 4249.39i −0.231124 + 0.400319i
\(484\) 2057.04 3562.91i 0.193186 0.334608i
\(485\) −163.768 283.655i −0.0153326 0.0265569i
\(486\) 8542.20 0.797288
\(487\) −4899.43 8486.06i −0.455882 0.789610i 0.542857 0.839825i \(-0.317343\pi\)
−0.998738 + 0.0502150i \(0.984009\pi\)
\(488\) 11129.9 + 19277.5i 1.03243 + 1.78822i
\(489\) 5558.43 0.514030
\(490\) 9.05771 + 15.6884i 0.000835072 + 0.00144639i
\(491\) 5418.03 9384.31i 0.497989 0.862542i −0.502009 0.864863i \(-0.667405\pi\)
0.999997 + 0.00232091i \(0.000738769\pi\)
\(492\) −184.568 + 319.681i −0.0169125 + 0.0292934i
\(493\) −4493.84 −0.410532
\(494\) 0 0
\(495\) −487.993 −0.0443104
\(496\) 2851.26 4938.52i 0.258115 0.447069i
\(497\) 4923.43 8527.63i 0.444358 0.769651i
\(498\) 2849.45 + 4935.40i 0.256400 + 0.444098i
\(499\) −2589.96 −0.232349 −0.116175 0.993229i \(-0.537063\pi\)
−0.116175 + 0.993229i \(0.537063\pi\)
\(500\) 100.843 + 174.665i 0.00901969 + 0.0156226i
\(501\) −1091.62 1890.74i −0.0973451 0.168607i
\(502\) 1841.20 0.163699
\(503\) 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
\(505\) 258.803 448.260i 0.0228051 0.0394996i
\(506\) 12149.0 1.06737
\(507\) 0 0
\(508\) 795.712 0.0694961
\(509\) −506.447 + 877.192i −0.0441019 + 0.0763867i −0.887234 0.461320i \(-0.847376\pi\)
0.843132 + 0.537707i \(0.180709\pi\)
\(510\) −67.7003 + 117.260i −0.00587808 + 0.0101811i
\(511\) −6943.68 12026.8i −0.601116 1.04116i
\(512\) 12992.6 1.12148
\(513\) −8040.83 13927.1i −0.692030 1.19863i
\(514\) 1640.41 + 2841.28i 0.140769 + 0.243820i
\(515\) 522.644 0.0447193
\(516\) −1161.54 2011.85i −0.0990969 0.171641i
\(517\) 1034.13 1791.17i 0.0879711 0.152370i
\(518\) 2672.81 4629.45i 0.226712 0.392676i
\(519\) 16564.6 1.40098
\(520\) 0 0
\(521\) −14367.7 −1.20818 −0.604089 0.796917i \(-0.706463\pi\)
−0.604089 + 0.796917i \(0.706463\pi\)
\(522\) −3024.27 + 5238.19i −0.253580 + 0.439213i
\(523\) 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
\(525\) −8350.92 −0.694217
\(526\) 6692.76 + 11592.2i 0.554787 + 0.960919i
\(527\) 1444.56 + 2502.05i 0.119404 + 0.206814i
\(528\) −12028.0 −0.991382
\(529\) 3399.89 + 5888.78i 0.279435 + 0.483996i
\(530\) −2.04733 + 3.54608i −0.000167793 + 0.000290626i
\(531\) −480.772 + 832.722i −0.0392914 + 0.0680547i
\(532\) 2823.06 0.230066
\(533\) 0 0
\(534\) 10947.5 0.887161
\(535\) 240.733 416.961i 0.0194538 0.0336950i
\(536\) −5370.70 + 9302.32i −0.432796 + 0.749625i
\(537\) −284.244 492.325i −0.0228418 0.0395631i
\(538\) −16506.1 −1.32273
\(539\) −407.650 706.071i −0.0325765 0.0564242i
\(540\) −60.1566 104.194i −0.00479394 0.00830335i
\(541\) −17592.2 −1.39806 −0.699029 0.715094i \(-0.746384\pi\)
−0.699029 + 0.715094i \(0.746384\pi\)
\(542\) 5033.36 + 8718.04i 0.398896 + 0.690908i
\(543\) 1973.77 3418.67i 0.155990 0.270183i
\(544\) −820.738 + 1421.56i −0.0646854 + 0.112038i
\(545\) 377.281 0.0296531
\(546\) 0 0
\(547\) 10504.6 0.821103 0.410552 0.911837i \(-0.365336\pi\)
0.410552 + 0.911837i \(0.365336\pi\)
\(548\) 1300.76 2252.99i 0.101398 0.175626i
\(549\) −6179.38 + 10703.0i −0.480382 + 0.832045i
\(550\) 10338.3 + 17906.5i 0.801504 + 1.38825i
\(551\) 18992.8 1.46846
\(552\) 3263.22 + 5652.06i 0.251616 + 0.435811i
\(553\) −3831.16 6635.77i −0.294607 0.510274i
\(554\) 15073.2 1.15596
\(555\) 118.776 + 205.726i 0.00908426 + 0.0157344i
\(556\) 1074.26 1860.67i 0.0819401 0.141924i
\(557\) −253.779 + 439.558i −0.0193051 + 0.0334375i −0.875517 0.483188i \(-0.839479\pi\)
0.856211 + 0.516626i \(0.172812\pi\)
\(558\) 3888.64 0.295016
\(559\) 0 0
\(560\) −514.690 −0.0388386
\(561\) 3046.92 5277.41i 0.229306 0.397170i
\(562\) −4520.87 + 7830.38i −0.339327 + 0.587731i
\(563\) 1721.57 + 2981.85i 0.128873 + 0.223215i 0.923240 0.384223i \(-0.125531\pi\)
−0.794367 + 0.607438i \(0.792197\pi\)
\(564\) 169.330 0.0126420
\(565\) 180.111 + 311.961i 0.0134112 + 0.0232288i
\(566\) −3344.11 5792.16i −0.248345 0.430146i
\(567\) 3387.96 0.250936
\(568\) −6548.59 11342.5i −0.483755 0.837888i
\(569\) −11986.1 + 20760.5i −0.883098 + 1.52957i −0.0352188 + 0.999380i \(0.511213\pi\)
−0.847879 + 0.530190i \(0.822121\pi\)
\(570\) 286.130 495.591i 0.0210257 0.0364176i
\(571\) −7458.32 −0.546622 −0.273311 0.961926i \(-0.588119\pi\)
−0.273311 + 0.961926i \(0.588119\pi\)
\(572\) 0 0
\(573\) −2495.26 −0.181922
\(574\) −1621.41 + 2808.36i −0.117903 + 0.204214i
\(575\) 4567.28 7910.77i 0.331250 0.573742i
\(576\) 3812.07 + 6602.70i 0.275757 + 0.477626i
\(577\) −5669.57 −0.409059 −0.204530 0.978860i \(-0.565566\pi\)
−0.204530 + 0.978860i \(0.565566\pi\)
\(578\) −5456.60 9451.10i −0.392672 0.680128i
\(579\) −2434.97 4217.49i −0.174774 0.302717i
\(580\) 142.093 0.0101726
\(581\) −5487.64 9504.87i −0.391851 0.678706i
\(582\) 2752.58 4767.60i 0.196045 0.339559i
\(583\) 92.1420 159.595i 0.00654568 0.0113375i
\(584\) −18471.4 −1.30882
\(585\) 0 0
\(586\) −14065.6 −0.991541
\(587\) 508.696 881.087i 0.0357685 0.0619529i −0.847587 0.530657i \(-0.821945\pi\)
0.883355 + 0.468704i \(0.155279\pi\)
\(588\) 33.3746 57.8064i 0.00234072 0.00405425i
\(589\) −6105.30 10574.7i −0.427104 0.739766i
\(590\) −103.040 −0.00718996
\(591\) −2334.91 4044.18i −0.162513 0.281481i
\(592\) −2894.49 5013.41i −0.200951 0.348057i
\(593\) 10198.2 0.706221 0.353111 0.935582i \(-0.385124\pi\)
0.353111 + 0.935582i \(0.385124\pi\)
\(594\) −12350.0 21390.8i −0.853073 1.47757i
\(595\) 130.381 225.827i 0.00898336 0.0155596i
\(596\) 1984.35 3437.00i 0.136380 0.236216i
\(597\) −8829.33 −0.605294
\(598\) 0 0
\(599\) 12516.3 0.853763 0.426881 0.904308i \(-0.359612\pi\)
0.426881 + 0.904308i \(0.359612\pi\)
\(600\) −5553.72 + 9619.33i −0.377883 + 0.654512i
\(601\) −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
\(603\) −5963.70 −0.402754
\(604\) 702.218 + 1216.28i 0.0473060 + 0.0819364i
\(605\) 803.046 + 1390.92i 0.0539644 + 0.0934691i
\(606\) 8699.80 0.583177
\(607\) −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
\(609\) −5890.87 + 10203.3i −0.391971 + 0.678913i
\(610\) −1324.37 −0.0879053
\(611\) 0 0
\(612\) −493.268 −0.0325803
\(613\) −11542.7 + 19992.5i −0.760530 + 1.31728i 0.182047 + 0.983290i \(0.441728\pi\)
−0.942578 + 0.333987i \(0.891606\pi\)
\(614\) 9359.39 16210.9i 0.615170 1.06551i
\(615\) −72.0532 124.800i −0.00472433 0.00818278i
\(616\) 28450.6 1.86089
\(617\) 1524.62 + 2640.72i 0.0994796 + 0.172304i 0.911469 0.411368i \(-0.134949\pi\)
−0.811990 + 0.583672i \(0.801616\pi\)
\(618\) 4392.24 + 7607.58i 0.285893 + 0.495181i
\(619\) −7296.58 −0.473787 −0.236894 0.971536i \(-0.576129\pi\)
−0.236894 + 0.971536i \(0.576129\pi\)
\(620\) −45.6761 79.1134i −0.00295871 0.00512463i
\(621\) −5455.99 + 9450.06i −0.352563 + 0.610657i
\(622\) 10124.4 17536.0i 0.652657 1.13044i
\(623\) −21083.3 −1.35583
\(624\) 0 0
\(625\) 15506.8 0.992438
\(626\) 12810.8 22189.0i 0.817929 1.41670i
\(627\) −12877.5 + 22304.5i −0.820222 + 1.42067i
\(628\) −406.271 703.683i −0.0258153 0.0447134i
\(629\) 2932.92 0.185920
\(630\) −175.488 303.954i −0.0110978 0.0192219i
\(631\) −11914.8 20637.0i −0.751694 1.30197i −0.947001 0.321230i \(-0.895904\pi\)
0.195307 0.980742i \(-0.437430\pi\)
\(632\) −10191.6 −0.641453
\(633\) −168.672 292.149i −0.0105910 0.0183442i
\(634\) 7980.27 13822.2i 0.499901 0.865853i
\(635\) −155.318 + 269.019i −0.00970648 + 0.0168121i
\(636\) 15.0874 0.000940653
\(637\) 0 0
\(638\) 29171.3 1.81019
\(639\) 3635.82 6297.43i 0.225088 0.389863i
\(640\) −264.174 + 457.562i −0.0163162 + 0.0282605i
\(641\) −6702.63 11609.3i −0.413008 0.715351i 0.582209 0.813039i \(-0.302188\pi\)
−0.995217 + 0.0976883i \(0.968855\pi\)
\(642\) 8092.36 0.497477
\(643\) 2625.76 + 4547.94i 0.161042 + 0.278932i 0.935243 0.354008i \(-0.115181\pi\)
−0.774201 + 0.632940i \(0.781848\pi\)
\(644\) −957.774 1658.91i −0.0586049 0.101507i
\(645\) 906.904 0.0553633
\(646\) −3532.68 6118.79i −0.215157 0.372663i
\(647\) −10805.7 + 18716.1i −0.656595 + 1.13726i 0.324897 + 0.945749i \(0.394670\pi\)
−0.981492 + 0.191506i \(0.938663\pi\)
\(648\) 2253.14 3902.55i 0.136592 0.236584i
\(649\) 4637.39 0.280483
\(650\) 0 0
\(651\) 7574.54 0.456021
\(652\) −1084.97 + 1879.23i −0.0651699 + 0.112878i
\(653\) 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
\(655\) −1154.78 −0.0688869
\(656\) 1755.89 + 3041.28i 0.104506 + 0.181009i
\(657\) −5127.72 8881.48i −0.304492 0.527396i
\(658\) 1487.54 0.0881314
\(659\) 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
\(661\) 13490.6 23366.3i 0.793831 1.37495i −0.129748 0.991547i \(-0.541417\pi\)
0.923579 0.383408i \(-0.125250\pi\)
\(662\) −11871.5 −0.696980
\(663\) 0 0
\(664\) −14598.1 −0.853185
\(665\) −551.044 + 954.437i −0.0321332 + 0.0556564i
\(666\) 1973.80 3418.73i 0.114840 0.198908i
\(667\) −6443.67 11160.8i −0.374063 0.647896i
\(668\) 852.310 0.0493665
\(669\) −2276.05 3942.23i −0.131535 0.227826i
\(670\) −319.537 553.454i −0.0184251 0.0319131i
\(671\) 59604.5 3.42922
\(672\) 2151.77 + 3726.98i 0.123521 + 0.213945i
\(673\) −5574.62 + 9655.53i −0.319296 + 0.553036i −0.980341 0.197309i \(-0.936780\pi\)
0.661046 + 0.750346i \(0.270113\pi\)
\(674\) 3880.52 6721.26i 0.221769 0.384115i
\(675\) −18571.3 −1.05898
\(676\) 0 0
\(677\) 3314.33 0.188154 0.0940769 0.995565i \(-0.470010\pi\)
0.0940769 + 0.995565i \(0.470010\pi\)
\(678\) −3027.26 + 5243.36i −0.171477 + 0.297006i
\(679\) −5301.06 + 9181.71i −0.299611 + 0.518942i
\(680\) −173.418 300.369i −0.00977982 0.0169391i
\(681\) 12165.5 0.684556
\(682\) −9377.17 16241.7i −0.526496 0.911918i
\(683\) 12252.6 + 21222.2i 0.686433 + 1.18894i 0.972984 + 0.230872i \(0.0741577\pi\)
−0.286552 + 0.958065i \(0.592509\pi\)
\(684\) 2084.75 0.116539
\(685\) 507.803 + 879.540i 0.0283243 + 0.0490591i
\(686\) 8278.50 14338.8i 0.460750 0.798042i
\(687\) −389.253 + 674.206i −0.0216171 + 0.0374419i
\(688\) −22100.6 −1.22468
\(689\) 0 0
\(690\) −388.299 −0.0214236
\(691\) −10876.4 + 18838.5i −0.598782 + 1.03712i 0.394219 + 0.919017i \(0.371015\pi\)
−0.993001 + 0.118105i \(0.962318\pi\)
\(692\) −3233.32 + 5600.27i −0.177619 + 0.307645i
\(693\) 7897.99 + 13679.7i 0.432929 + 0.749855i
\(694\) −7278.90 −0.398132
\(695\) 419.378 + 726.383i 0.0228891 + 0.0396450i
\(696\) 7835.37 + 13571.3i 0.426722 + 0.739105i
\(697\) −1779.20 −0.0966887
\(698\) −9689.94 16783.5i −0.525458 0.910120i
\(699\) −472.971 + 819.209i −0.0255928 + 0.0443281i
\(700\) 1630.05 2823.33i 0.0880145 0.152446i
\(701\) 34250.9 1.84542 0.922709 0.385496i \(-0.125970\pi\)
0.922709 + 0.385496i \(0.125970\pi\)
\(702\) 0 0
\(703\) −12395.8 −0.665028
\(704\) 18385.1 31843.9i 0.984252 1.70477i
\(705\) −33.0522 + 57.2480i −0.00176570 + 0.00305828i
\(706\) 2996.30 + 5189.74i 0.159727 + 0.276655i
\(707\) −16754.6 −0.891259
\(708\) 189.833 + 328.800i 0.0100768 + 0.0174535i
\(709\) −2763.56 4786.62i −0.146386 0.253548i 0.783503 0.621388i \(-0.213431\pi\)
−0.929889 + 0.367840i \(0.880097\pi\)
\(710\) 779.234 0.0411889
\(711\) −2829.21 4900.34i −0.149232 0.258477i
\(712\) −14021.3 + 24285.6i −0.738020 + 1.27829i
\(713\) −4142.67 + 7175.31i −0.217593 + 0.376883i
\(714\) 4382.83 0.229724
\(715\) 0 0
\(716\) 221.931 0.0115837
\(717\) 6539.57 11326.9i 0.340620 0.589972i
\(718\) 3242.51 5616.19i 0.168537 0.291914i
\(719\) 1888.89 + 3271.65i 0.0979745 + 0.169697i 0.910846 0.412746i \(-0.135430\pi\)
−0.812872 + 0.582443i \(0.802097\pi\)
\(720\) −380.085 −0.0196735
\(721\) −8458.81 14651.1i −0.436925 0.756776i
\(722\) 6145.75 + 10644.7i 0.316788 + 0.548693i
\(723\) −18534.2 −0.953380
\(724\) 770.538 + 1334.61i 0.0395536 + 0.0685088i
\(725\) 10966.6 18994.7i 0.561777 0.973027i
\(726\) −13497.4 + 23378.2i −0.689994 + 1.19510i
\(727\) 19076.8 0.973204 0.486602 0.873624i \(-0.338236\pi\)
0.486602 + 0.873624i \(0.338236\pi\)
\(728\) 0 0
\(729\) 17319.9 0.879944
\(730\) 549.490 951.744i 0.0278596 0.0482543i
\(731\) 5598.52 9696.92i 0.283268 0.490634i
\(732\) 2439.93 + 4226.08i 0.123200 + 0.213388i
\(733\) −7997.30 −0.402984 −0.201492 0.979490i \(-0.564579\pi\)
−0.201492 + 0.979490i \(0.564579\pi\)
\(734\) 8424.71 + 14592.0i 0.423653 + 0.733789i
\(735\) 13.0290 + 22.5669i 0.000653855 + 0.00113251i
\(736\) −4707.39 −0.235756
\(737\) 14381.0 + 24908.7i 0.718769 + 1.24494i
\(738\) −1197.37 + 2073.90i −0.0597232 + 0.103444i
\(739\) 14491.8 25100.6i 0.721367 1.24944i −0.239086 0.970998i \(-0.576848\pi\)
0.960452 0.278445i \(-0.0898190\pi\)
\(740\) −92.7376 −0.00460689
\(741\) 0 0
\(742\) 132.541 0.00655761
\(743\) −9572.69 + 16580.4i −0.472662 + 0.818674i −0.999511 0.0312847i \(-0.990040\pi\)
0.526849 + 0.849959i \(0.323373\pi\)
\(744\) 5037.40 8725.02i 0.248226 0.429939i
\(745\) 774.667 + 1341.76i 0.0380961 + 0.0659844i
\(746\) −7435.47 −0.364922
\(747\) −4052.47 7019.09i −0.198490 0.343795i
\(748\) 1189.48 + 2060.24i 0.0581440 + 0.100708i
\(749\) −15584.7 −0.760284
\(750\) −661.688 1146.08i −0.0322152 0.0557984i
\(751\) 12758.4 22098.3i 0.619923 1.07374i −0.369576 0.929200i \(-0.620497\pi\)
0.989499 0.144538i \(-0.0461695\pi\)
\(752\) 805.459 1395.10i 0.0390586 0.0676515i
\(753\) 2648.47 0.128175
\(754\) 0 0
\(755\) −548.275 −0.0264288
\(756\) −1947.23 + 3372.70i −0.0936773 + 0.162254i
\(757\) 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
\(759\) 17475.7 0.835744
\(760\) 732.936 + 1269.48i 0.0349821 + 0.0605908i
\(761\) −1171.53 2029.15i −0.0558053 0.0966576i 0.836773 0.547550i \(-0.184439\pi\)
−0.892579 + 0.450892i \(0.851106\pi\)
\(762\) −5221.11 −0.248216
\(763\) −6106.17 10576.2i −0.289722 0.501814i
\(764\) 487.060 843.613i 0.0230644 0.0399488i
\(765\) 96.2829 166.767i 0.00455048 0.00788166i
\(766\) 27756.9 1.30927
\(767\) 0 0
\(768\) 7862.11 0.369400
\(769\) −3550.09 + 6148.93i −0.166475 + 0.288344i −0.937178 0.348851i \(-0.886572\pi\)
0.770703 + 0.637195i \(0.219905\pi\)
\(770\) −846.353 + 1465.93i −0.0396110 + 0.0686082i
\(771\) 2359.65 + 4087.03i 0.110221 + 0.190909i
\(772\) 1901.17 0.0886328
\(773\) 6135.22 + 10626.5i 0.285470 + 0.494449i 0.972723 0.231969i \(-0.0745169\pi\)
−0.687253 + 0.726418i \(0.741184\pi\)
\(774\)