Properties

Label 169.4.c.j.146.2
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 146.2
Root \(1.28078 + 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.4.c.j.22.2

$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28078 + 2.21837i 0.452823 + 0.784312i 0.998560 0.0536442i \(-0.0170837\pi\)
−0.545737 + 0.837956i \(0.683750\pi\)
\(3\) 1.84233 + 3.19101i 0.354556 + 0.614110i 0.987042 0.160462i \(-0.0512985\pi\)
−0.632486 + 0.774572i \(0.717965\pi\)
\(4\) 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 −0.509208 0.860643i \(-0.670062\pi\)
0.999943 + 0.0106654i \(0.00339497\pi\)
\(8\) 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 0.843116 + 0.537731i \(0.180718\pi\)
0.0441305 + 0.999026i \(0.485948\pi\)
\(12\) 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 −0.760408 0.649446i \(-0.775001\pi\)
0.942641 + 0.333810i \(0.108334\pi\)
\(18\) 34.3845 0.450250
\(19\) −53.9848 + 93.5045i −0.651841 + 1.12902i 0.330835 + 0.943689i \(0.392670\pi\)
−0.982676 + 0.185333i \(0.940664\pi\)
\(20\) −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 0.650833 0.759221i \(-0.274420\pi\)
−0.982921 + 0.184027i \(0.941086\pi\)
\(24\) 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 −0.997215 0.0745830i \(-0.976237\pi\)
0.434017 0.900905i \(-0.357096\pi\)
\(30\) 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 0.964911 0.262576i \(-0.0845722\pi\)
−0.709853 + 0.704349i \(0.751239\pi\)
\(38\) −276.570 −1.18067
\(39\) 0 0
\(40\) −13.5767 −0.0536666
\(41\) −34.8229 60.3151i −0.132645 0.229747i 0.792051 0.610455i \(-0.209014\pi\)
−0.924695 + 0.380708i \(0.875680\pi\)
\(42\) 85.7817 + 148.578i 0.315153 + 0.545860i
\(43\) −219.151 + 379.581i −0.777214 + 1.34617i 0.156327 + 0.987705i \(0.450035\pi\)
−0.933541 + 0.358469i \(0.883299\pi\)
\(44\) 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 −0.823801 0.566880i \(-0.808150\pi\)
0.902832 + 0.429992i \(0.141484\pi\)
\(60\) −2.97633 −0.00640405
\(61\) 460.348 797.345i 0.966253 1.67360i 0.260044 0.965597i \(-0.416263\pi\)
0.706209 0.708003i \(-0.250404\pi\)
\(62\) 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 0.589272 0.807935i \(-0.299415\pi\)
−0.994328 + 0.106357i \(0.966081\pi\)
\(68\) −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 −0.998556 0.0537283i \(-0.982890\pi\)
0.545808 + 0.837910i \(0.316223\pi\)
\(72\) 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 −0.971604 0.236613i \(-0.923963\pi\)
0.280889 0.959740i \(-0.409371\pi\)
\(90\) −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 −0.672053 0.740503i \(-0.734587\pi\)
0.977321 + 0.211763i \(0.0679206\pi\)
\(98\) −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 0.544590 0.838702i \(-0.316685\pi\)
−0.998633 + 0.0522775i \(0.983352\pi\)
\(102\) 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 0.604769 0.796401i \(-0.293266\pi\)
−0.992088 + 0.125545i \(0.959932\pi\)
\(108\) 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 −0.968089 0.250607i \(-0.919370\pi\)
0.701077 + 0.713086i \(0.252703\pi\)
\(114\) −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 0.946326 0.323212i \(-0.104763\pi\)
−0.753073 + 0.657937i \(0.771430\pi\)
\(128\) 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 0.433221 + 0.901288i \(0.357377\pi\)
−0.997149 + 0.0754639i \(0.975956\pi\)
\(138\) 691.474 0.426537
\(139\) −746.818 + 1293.53i −0.455714 + 0.789320i −0.998729 0.0504032i \(-0.983949\pi\)
0.543015 + 0.839723i \(0.317283\pi\)
\(140\) 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 0.185143 + 0.982712i \(0.440725\pi\)
−0.943625 + 0.331018i \(0.892608\pi\)
\(150\) 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 −0.625917 0.779890i \(-0.715275\pi\)
0.988363 + 0.152115i \(0.0486084\pi\)
\(164\) −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 0.926465 0.376381i \(-0.122832\pi\)
−0.789188 + 0.614152i \(0.789498\pi\)
\(168\) 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 0.359262 0.933237i \(-0.383028\pi\)
0.628576 0.777748i \(-0.283638\pi\)
\(174\) 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 0.881682 0.471844i \(-0.156412\pi\)
−0.849470 + 0.527637i \(0.823078\pi\)
\(180\) 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 −0.923008 0.384781i \(-0.874277\pi\)
0.794734 + 0.606958i \(0.207610\pi\)
\(192\) 1046.40 + 1812.42i 0.393321 + 0.681252i
\(193\) 660.840 + 1144.61i 0.246468 + 0.426895i 0.962543 0.271128i \(-0.0873967\pi\)
−0.716075 + 0.698023i \(0.754063\pi\)
\(194\) 1494.07 0.552929
\(195\) 0 0
\(196\) 18.1154 0.00660183
\(197\) 633.683 + 1097.57i 0.229178 + 0.396948i 0.957565 0.288218i \(-0.0930629\pi\)
−0.728387 + 0.685166i \(0.759730\pi\)
\(198\) 1113.00 + 1927.78i 0.399483 + 0.691925i
\(199\) −1198.12 + 2075.21i −0.426796 + 0.739233i −0.996586 0.0825573i \(-0.973691\pi\)
0.569790 + 0.821790i \(0.307025\pi\)
\(200\) −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 0.873397 0.487010i \(-0.161912\pi\)
−0.858461 + 0.512879i \(0.828579\pi\)
\(212\) 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 0.943742 0.330682i \(-0.107279\pi\)
−0.758250 + 0.651964i \(0.773945\pi\)
\(224\) −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 −0.517118 0.855914i \(-0.672995\pi\)
0.999802 + 0.0198797i \(0.00632833\pi\)
\(228\) −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 0.305034 + 0.952341i \(0.401332\pi\)
−0.977269 + 0.212003i \(0.932001\pi\)
\(242\) −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 −0.817293 0.576223i \(-0.804526\pi\)
0.907670 + 0.419685i \(0.137859\pi\)
\(252\) −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 0.777782 0.628534i \(-0.216345\pi\)
−0.933217 + 0.359312i \(0.883011\pi\)
\(258\) −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 −0.990803 0.135315i \(-0.956795\pi\)
0.378215 0.925718i \(-0.376538\pi\)
\(264\) −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 0.226497 + 0.974012i \(0.427273\pi\)
−0.956768 + 0.290854i \(0.906061\pi\)
\(270\) −107.125 185.547i −0.0241461 0.0418223i
\(271\) −1964.97 3403.42i −0.440455 0.762890i 0.557269 0.830332i \(-0.311849\pi\)
−0.997723 + 0.0674426i \(0.978516\pi\)
\(272\) 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 −0.347635 0.937630i \(-0.613015\pi\)
0.985829 0.167754i \(-0.0536516\pi\)
\(278\) −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 0.969938 0.243353i \(-0.0782474\pi\)
−0.695719 + 0.718314i \(0.744914\pi\)
\(284\) 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 0.451028 + 0.892510i \(0.351057\pi\)
−0.998450 + 0.0556531i \(0.982276\pi\)
\(294\) −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 −0.991741 0.128257i \(-0.959062\pi\)
0.606944 + 0.794745i \(0.292395\pi\)
\(332\) −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 −0.954748 0.297415i \(-0.903876\pi\)
0.734943 + 0.678129i \(0.237209\pi\)
\(348\) −466.175 807.440i −0.0718093 0.124377i
\(349\) 3782.84 + 6552.07i 0.580202 + 1.00494i 0.995455 + 0.0952339i \(0.0303599\pi\)
−0.415252 + 0.909706i \(0.636307\pi\)
\(350\) −5805.51 −0.886622
\(351\) 0 0
\(352\) 4159.76 0.629875
\(353\) −1169.72 2026.01i −0.176368 0.305478i 0.764266 0.644901i \(-0.223101\pi\)
−0.940634 + 0.339423i \(0.889768\pi\)
\(354\) 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 0.531531 0.847039i \(-0.321617\pi\)
−0.999323 + 0.0368000i \(0.988284\pi\)
\(368\) 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 −0.949003 0.315268i \(-0.897905\pi\)
0.747532 + 0.664226i \(0.231239\pi\)
\(374\) 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 0.795859 0.605482i \(-0.207020\pi\)
−0.922292 + 0.386493i \(0.873686\pi\)
\(380\) −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 −0.237021 0.971504i \(-0.576171\pi\)
0.959858 0.280486i \(-0.0904955\pi\)
\(384\) −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 0.346680 + 0.937983i \(0.387309\pi\)
−0.985657 + 0.168758i \(0.946024\pi\)
\(398\) −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 0.923594 0.383373i \(-0.125237\pi\)
−0.793807 + 0.608169i \(0.791904\pi\)
\(402\) 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 0.407229 + 0.913326i \(0.366495\pi\)
−0.994578 + 0.103992i \(0.966838\pi\)
\(410\) −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 −0.931866 0.362802i \(-0.881820\pi\)
0.151737 0.988421i \(-0.451513\pi\)
\(420\) −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 0.969155 0.246452i \(-0.0792647\pi\)
−0.698011 + 0.716087i \(0.745931\pi\)
\(432\) 3755.17 + 6504.15i 0.418220 + 0.724378i
\(433\) 4104.00 7108.33i 0.455486 0.788925i −0.543230 0.839584i \(-0.682799\pi\)
0.998716 + 0.0506587i \(0.0161321\pi\)
\(434\) 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 0.935851 0.352397i \(-0.114633\pi\)
−0.773110 + 0.634272i \(0.781300\pi\)
\(440\) −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 −0.880402 0.474229i \(-0.842727\pi\)
0.850895 + 0.525336i \(0.176060\pi\)
\(450\) −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 0.966998 + 0.254783i \(0.0820040\pi\)
−0.262851 + 0.964837i \(0.584663\pi\)
\(458\) −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 −0.385145 0.922856i \(-0.625849\pi\)
0.991789 0.127882i \(-0.0408179\pi\)
\(462\) −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 −0.969402 0.245480i \(-0.921054\pi\)
0.272109 0.962267i \(-0.412279\pi\)
\(480\) −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 −0.998738 0.0502150i \(-0.984009\pi\)
0.542857 + 0.839825i \(0.317343\pi\)
\(488\) 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 0.999997 0.00232091i \(-0.000738769\pi\)
−0.502009 + 0.864863i \(0.667405\pi\)
\(492\) −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 −0.188183 0.982134i \(-0.560260\pi\)
0.944644 0.328096i \(-0.106407\pi\)
\(504\) −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 0.843132 0.537707i \(-0.180709\pi\)
−0.887234 + 0.461320i \(0.847376\pi\)
\(510\) −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 0.975565 + 0.219709i \(0.0705109\pi\)
−0.297509 + 0.954719i \(0.596156\pi\)
\(524\) 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 0.856211 0.516626i \(-0.172812\pi\)
−0.875517 + 0.483188i \(0.839479\pi\)
\(558\) 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 −0.794367 0.607438i \(-0.792197\pi\)
0.923240 + 0.384223i \(0.125531\pi\)
\(564\) 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 −0.847879 0.530190i \(-0.822121\pi\)
−0.0352188 0.999380i \(-0.511213\pi\)
\(570\) 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 0.883355 0.468704i \(-0.155279\pi\)
−0.847587 + 0.530657i \(0.821945\pi\)
\(588\) 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 0.655142 0.755505i \(-0.272609\pi\)
−0.981858 + 0.189617i \(0.939275\pi\)
\(602\) −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 −0.955690 0.294373i \(-0.904889\pi\)
0.732780 + 0.680466i \(0.238222\pi\)
\(608\) 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 −0.942578 0.333987i \(-0.891606\pi\)
0.182047 0.983290i \(-0.441728\pi\)
\(614\) 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 −0.811990 0.583672i \(-0.801616\pi\)
0.911469 + 0.411368i \(0.134949\pi\)
\(618\) 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 0.195307 + 0.980742i \(0.437430\pi\)
−0.947001 + 0.321230i \(0.895904\pi\)
\(632\) −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 −0.995217 0.0976883i \(-0.968855\pi\)
0.582209 + 0.813039i \(0.302188\pi\)
\(642\) 8092.36 0.497477
\(643\) 2625.76 4547.94i 0.161042 0.278932i −0.774201 0.632940i \(-0.781848\pi\)
0.935243 + 0.354008i \(0.115181\pi\)
\(644\) −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 −0.981492 0.191506i \(-0.938663\pi\)
0.324897 0.945749i \(-0.394670\pi\)
\(648\) 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 0.983813 + 0.179201i \(0.0573512\pi\)
−0.336714 + 0.941607i \(0.609316\pi\)
\(654\) 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 −0.508072 0.861315i \(-0.669642\pi\)
0.999956 + 0.00934609i \(0.00297500\pi\)
\(660\) −96.3419 166.869i −0.00568198 0.00984147i
\(661\) 13490.6 + 23366.3i 0.793831 + 1.37495i 0.923579 + 0.383408i \(0.125250\pi\)
−0.129748 + 0.991547i \(0.541417\pi\)
\(662\) −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 0.661046 0.750346i \(-0.270113\pi\)
−0.980341 + 0.197309i \(0.936780\pi\)
\(674\) 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 −0.286552 0.958065i \(-0.592509\pi\)
0.972984 0.230872i \(-0.0741577\pi\)
\(684\) 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 −0.993001 0.118105i \(-0.962318\pi\)
0.394219 0.919017i \(-0.371015\pi\)
\(692\) −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 −0.929889 0.367840i \(-0.880097\pi\)
0.783503 + 0.621388i \(0.213431\pi\)
\(710\) 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 −0.812872 0.582443i \(-0.802097\pi\)
0.910846 + 0.412746i \(0.135430\pi\)
\(720\) −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 0.960452 + 0.278445i \(0.0898190\pi\)
−0.239086 + 0.970998i \(0.576848\pi\)
\(740\) −92.7376 −0.00460689
\(741\) 0 0
\(742\) 132.541 0.00655761
\(743\) −9572.69 16580.4i −0.472662 0.818674i 0.526849 0.849959i \(-0.323373\pi\)
−0.999511 + 0.0312847i \(0.990040\pi\)
\(744\) 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 0.989499 + 0.144538i \(0.0461695\pi\)
−0.369576 + 0.929200i \(0.620497\pi\)
\(752\) 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 0.995285 0.0969925i \(-0.0309223\pi\)
−0.581641 + 0.813446i \(0.697589\pi\)
\(758\) 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 −0.892579 0.450892i \(-0.851106\pi\)
0.836773 + 0.547550i \(0.184439\pi\)
\(762\) −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 0.770703 0.637195i \(-0.219905\pi\)
−0.937178 + 0.348851i \(0.886572\pi\)
\(770\) −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 −0.687253 0.726418i \(-0.741184\pi\)
0.972723 + 0.231969i \(0.0745169\pi\)
\(774\) −7535.39