Properties

Label 13.4.e.b.10.1
Level 13
Weight 4
Character 13.10
Analytic conductor 0.767
Analytic rank 0
Dimension 2
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 13.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.767024830075\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 13.10
Dual form 13.4.e.b.4.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-2.50000 + 4.33013i) q^{4} +1.73205i q^{5} +(-3.00000 - 1.73205i) q^{6} +(-12.0000 - 6.92820i) q^{7} +22.5167i q^{8} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-2.50000 + 4.33013i) q^{4} +1.73205i q^{5} +(-3.00000 - 1.73205i) q^{6} +(-12.0000 - 6.92820i) q^{7} +22.5167i q^{8} +(11.5000 - 19.9186i) q^{9} +(1.50000 + 2.59808i) q^{10} +(12.0000 - 6.92820i) q^{11} +10.0000 q^{12} +(45.5000 - 11.2583i) q^{13} -24.0000 q^{14} +(3.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-58.5000 + 101.325i) q^{17} -39.8372i q^{18} +(-99.0000 - 57.1577i) q^{19} +(-7.50000 - 4.33013i) q^{20} +27.7128i q^{21} +(12.0000 - 20.7846i) q^{22} +(39.0000 + 67.5500i) q^{23} +(39.0000 - 22.5167i) q^{24} +122.000 q^{25} +(58.5000 - 56.2917i) q^{26} -100.000 q^{27} +(60.0000 - 34.6410i) q^{28} +(70.5000 + 122.110i) q^{29} +(3.00000 - 5.19615i) q^{30} -155.885i q^{31} +(-157.500 - 90.9327i) q^{32} +(-24.0000 - 13.8564i) q^{33} +202.650i q^{34} +(12.0000 - 20.7846i) q^{35} +(57.5000 + 99.5929i) q^{36} +(-124.500 + 71.8801i) q^{37} -198.000 q^{38} +(-65.0000 - 67.5500i) q^{39} -39.0000 q^{40} +(235.500 - 135.966i) q^{41} +(24.0000 + 41.5692i) q^{42} +(-52.0000 + 90.0666i) q^{43} +69.2820i q^{44} +(34.5000 + 19.9186i) q^{45} +(117.000 + 67.5500i) q^{46} -301.377i q^{47} +(-1.00000 + 1.73205i) q^{48} +(-75.5000 - 130.770i) q^{49} +(183.000 - 105.655i) q^{50} +234.000 q^{51} +(-65.0000 + 225.167i) q^{52} +93.0000 q^{53} +(-150.000 + 86.6025i) q^{54} +(12.0000 + 20.7846i) q^{55} +(156.000 - 270.200i) q^{56} +228.631i q^{57} +(211.500 + 122.110i) q^{58} +(-246.000 - 142.028i) q^{59} +17.3205i q^{60} +(-72.5000 + 125.574i) q^{61} +(-135.000 - 233.827i) q^{62} +(-276.000 + 159.349i) q^{63} -307.000 q^{64} +(19.5000 + 78.8083i) q^{65} -48.0000 q^{66} +(-681.000 + 393.176i) q^{67} +(-292.500 - 506.625i) q^{68} +(78.0000 - 135.100i) q^{69} -41.5692i q^{70} +(915.000 + 528.275i) q^{71} +(448.500 + 258.942i) q^{72} -458.993i q^{73} +(-124.500 + 215.640i) q^{74} +(-122.000 - 211.310i) q^{75} +(495.000 - 285.788i) q^{76} -192.000 q^{77} +(-156.000 - 45.0333i) q^{78} +1276.00 q^{79} +(1.50000 - 0.866025i) q^{80} +(-210.500 - 364.597i) q^{81} +(235.500 - 407.898i) q^{82} +789.815i q^{83} +(-120.000 - 69.2820i) q^{84} +(-175.500 - 101.325i) q^{85} +180.133i q^{86} +(141.000 - 244.219i) q^{87} +(156.000 + 270.200i) q^{88} +(-846.000 + 488.438i) q^{89} +69.0000 q^{90} +(-624.000 - 180.133i) q^{91} -390.000 q^{92} +(-270.000 + 155.885i) q^{93} +(-261.000 - 452.065i) q^{94} +(99.0000 - 171.473i) q^{95} +363.731i q^{96} +(174.000 + 100.459i) q^{97} +(-226.500 - 130.770i) q^{98} -318.697i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} - 2q^{3} - 5q^{4} - 6q^{6} - 24q^{7} + 23q^{9} + O(q^{10}) \) \( 2q + 3q^{2} - 2q^{3} - 5q^{4} - 6q^{6} - 24q^{7} + 23q^{9} + 3q^{10} + 24q^{11} + 20q^{12} + 91q^{13} - 48q^{14} + 6q^{15} - q^{16} - 117q^{17} - 198q^{19} - 15q^{20} + 24q^{22} + 78q^{23} + 78q^{24} + 244q^{25} + 117q^{26} - 200q^{27} + 120q^{28} + 141q^{29} + 6q^{30} - 315q^{32} - 48q^{33} + 24q^{35} + 115q^{36} - 249q^{37} - 396q^{38} - 130q^{39} - 78q^{40} + 471q^{41} + 48q^{42} - 104q^{43} + 69q^{45} + 234q^{46} - 2q^{48} - 151q^{49} + 366q^{50} + 468q^{51} - 130q^{52} + 186q^{53} - 300q^{54} + 24q^{55} + 312q^{56} + 423q^{58} - 492q^{59} - 145q^{61} - 270q^{62} - 552q^{63} - 614q^{64} + 39q^{65} - 96q^{66} - 1362q^{67} - 585q^{68} + 156q^{69} + 1830q^{71} + 897q^{72} - 249q^{74} - 244q^{75} + 990q^{76} - 384q^{77} - 312q^{78} + 2552q^{79} + 3q^{80} - 421q^{81} + 471q^{82} - 240q^{84} - 351q^{85} + 282q^{87} + 312q^{88} - 1692q^{89} + 138q^{90} - 1248q^{91} - 780q^{92} - 540q^{93} - 522q^{94} + 198q^{95} + 348q^{97} - 453q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 0.530330 0.306186i −0.210821 0.977525i \(-0.567614\pi\)
0.741151 + 0.671339i \(0.234280\pi\)
\(3\) −1.00000 1.73205i −0.192450 0.333333i 0.753612 0.657320i \(-0.228310\pi\)
−0.946062 + 0.323987i \(0.894977\pi\)
\(4\) −2.50000 + 4.33013i −0.312500 + 0.541266i
\(5\) 1.73205i 0.154919i 0.996995 + 0.0774597i \(0.0246809\pi\)
−0.996995 + 0.0774597i \(0.975319\pi\)
\(6\) −3.00000 1.73205i −0.204124 0.117851i
\(7\) −12.0000 6.92820i −0.647939 0.374088i 0.139727 0.990190i \(-0.455377\pi\)
−0.787666 + 0.616102i \(0.788711\pi\)
\(8\) 22.5167i 0.995105i
\(9\) 11.5000 19.9186i 0.425926 0.737725i
\(10\) 1.50000 + 2.59808i 0.0474342 + 0.0821584i
\(11\) 12.0000 6.92820i 0.328921 0.189903i −0.326441 0.945218i \(-0.605849\pi\)
0.655362 + 0.755315i \(0.272516\pi\)
\(12\) 10.0000 0.240563
\(13\) 45.5000 11.2583i 0.970725 0.240192i
\(14\) −24.0000 −0.458162
\(15\) 3.00000 1.73205i 0.0516398 0.0298142i
\(16\) −0.500000 0.866025i −0.00781250 0.0135316i
\(17\) −58.5000 + 101.325i −0.834608 + 1.44558i 0.0597414 + 0.998214i \(0.480972\pi\)
−0.894349 + 0.447369i \(0.852361\pi\)
\(18\) 39.8372i 0.521651i
\(19\) −99.0000 57.1577i −1.19538 0.690151i −0.235856 0.971788i \(-0.575789\pi\)
−0.959521 + 0.281637i \(0.909123\pi\)
\(20\) −7.50000 4.33013i −0.0838525 0.0484123i
\(21\) 27.7128i 0.287973i
\(22\) 12.0000 20.7846i 0.116291 0.201422i
\(23\) 39.0000 + 67.5500i 0.353568 + 0.612398i 0.986872 0.161506i \(-0.0516350\pi\)
−0.633304 + 0.773903i \(0.718302\pi\)
\(24\) 39.0000 22.5167i 0.331702 0.191508i
\(25\) 122.000 0.976000
\(26\) 58.5000 56.2917i 0.441261 0.424604i
\(27\) −100.000 −0.712778
\(28\) 60.0000 34.6410i 0.404962 0.233805i
\(29\) 70.5000 + 122.110i 0.451432 + 0.781903i 0.998475 0.0552014i \(-0.0175801\pi\)
−0.547043 + 0.837104i \(0.684247\pi\)
\(30\) 3.00000 5.19615i 0.0182574 0.0316228i
\(31\) 155.885i 0.903151i −0.892233 0.451576i \(-0.850862\pi\)
0.892233 0.451576i \(-0.149138\pi\)
\(32\) −157.500 90.9327i −0.870073 0.502337i
\(33\) −24.0000 13.8564i −0.126602 0.0730937i
\(34\) 202.650i 1.02218i
\(35\) 12.0000 20.7846i 0.0579534 0.100378i
\(36\) 57.5000 + 99.5929i 0.266204 + 0.461078i
\(37\) −124.500 + 71.8801i −0.553180 + 0.319379i −0.750404 0.660980i \(-0.770141\pi\)
0.197223 + 0.980359i \(0.436808\pi\)
\(38\) −198.000 −0.845259
\(39\) −65.0000 67.5500i −0.266880 0.277350i
\(40\) −39.0000 −0.154161
\(41\) 235.500 135.966i 0.897047 0.517910i 0.0208059 0.999784i \(-0.493377\pi\)
0.876241 + 0.481873i \(0.160043\pi\)
\(42\) 24.0000 + 41.5692i 0.0881733 + 0.152721i
\(43\) −52.0000 + 90.0666i −0.184417 + 0.319419i −0.943380 0.331714i \(-0.892373\pi\)
0.758963 + 0.651134i \(0.225706\pi\)
\(44\) 69.2820i 0.237379i
\(45\) 34.5000 + 19.9186i 0.114288 + 0.0659842i
\(46\) 117.000 + 67.5500i 0.375015 + 0.216515i
\(47\) 301.377i 0.935326i −0.883907 0.467663i \(-0.845096\pi\)
0.883907 0.467663i \(-0.154904\pi\)
\(48\) −1.00000 + 1.73205i −0.00300703 + 0.00520833i
\(49\) −75.5000 130.770i −0.220117 0.381253i
\(50\) 183.000 105.655i 0.517602 0.298838i
\(51\) 234.000 0.642481
\(52\) −65.0000 + 225.167i −0.173344 + 0.600481i
\(53\) 93.0000 0.241029 0.120514 0.992712i \(-0.461546\pi\)
0.120514 + 0.992712i \(0.461546\pi\)
\(54\) −150.000 + 86.6025i −0.378008 + 0.218243i
\(55\) 12.0000 + 20.7846i 0.0294196 + 0.0509563i
\(56\) 156.000 270.200i 0.372257 0.644768i
\(57\) 228.631i 0.531279i
\(58\) 211.500 + 122.110i 0.478816 + 0.276444i
\(59\) −246.000 142.028i −0.542822 0.313398i 0.203400 0.979096i \(-0.434801\pi\)
−0.746222 + 0.665698i \(0.768134\pi\)
\(60\) 17.3205i 0.0372678i
\(61\) −72.5000 + 125.574i −0.152175 + 0.263575i −0.932027 0.362389i \(-0.881961\pi\)
0.779852 + 0.625964i \(0.215294\pi\)
\(62\) −135.000 233.827i −0.276533 0.478968i
\(63\) −276.000 + 159.349i −0.551948 + 0.318667i
\(64\) −307.000 −0.599609
\(65\) 19.5000 + 78.8083i 0.0372104 + 0.150384i
\(66\) −48.0000 −0.0895211
\(67\) −681.000 + 393.176i −1.24175 + 0.716926i −0.969451 0.245286i \(-0.921118\pi\)
−0.272301 + 0.962212i \(0.587785\pi\)
\(68\) −292.500 506.625i −0.521630 0.903490i
\(69\) 78.0000 135.100i 0.136088 0.235712i
\(70\) 41.5692i 0.0709782i
\(71\) 915.000 + 528.275i 1.52944 + 0.883025i 0.999385 + 0.0350641i \(0.0111635\pi\)
0.530059 + 0.847961i \(0.322170\pi\)
\(72\) 448.500 + 258.942i 0.734114 + 0.423841i
\(73\) 458.993i 0.735906i −0.929844 0.367953i \(-0.880059\pi\)
0.929844 0.367953i \(-0.119941\pi\)
\(74\) −124.500 + 215.640i −0.195579 + 0.338752i
\(75\) −122.000 211.310i −0.187831 0.325333i
\(76\) 495.000 285.788i 0.747110 0.431344i
\(77\) −192.000 −0.284161
\(78\) −156.000 45.0333i −0.226455 0.0653720i
\(79\) 1276.00 1.81723 0.908615 0.417634i \(-0.137141\pi\)
0.908615 + 0.417634i \(0.137141\pi\)
\(80\) 1.50000 0.866025i 0.00209631 0.00121031i
\(81\) −210.500 364.597i −0.288752 0.500133i
\(82\) 235.500 407.898i 0.317154 0.549327i
\(83\) 789.815i 1.04450i 0.852793 + 0.522250i \(0.174907\pi\)
−0.852793 + 0.522250i \(0.825093\pi\)
\(84\) −120.000 69.2820i −0.155870 0.0899915i
\(85\) −175.500 101.325i −0.223949 0.129297i
\(86\) 180.133i 0.225864i
\(87\) 141.000 244.219i 0.173756 0.300955i
\(88\) 156.000 + 270.200i 0.188973 + 0.327311i
\(89\) −846.000 + 488.438i −1.00759 + 0.581734i −0.910486 0.413540i \(-0.864292\pi\)
−0.0971073 + 0.995274i \(0.530959\pi\)
\(90\) 69.0000 0.0808138
\(91\) −624.000 180.133i −0.718824 0.207507i
\(92\) −390.000 −0.441960
\(93\) −270.000 + 155.885i −0.301050 + 0.173812i
\(94\) −261.000 452.065i −0.286384 0.496032i
\(95\) 99.0000 171.473i 0.106918 0.185187i
\(96\) 363.731i 0.386699i
\(97\) 174.000 + 100.459i 0.182134 + 0.105155i 0.588295 0.808646i \(-0.299799\pi\)
−0.406161 + 0.913802i \(0.633133\pi\)
\(98\) −226.500 130.770i −0.233469 0.134793i
\(99\) 318.697i 0.323538i
\(100\) −305.000 + 528.275i −0.305000 + 0.528275i
\(101\) −214.500 371.525i −0.211322 0.366021i 0.740806 0.671719i \(-0.234444\pi\)
−0.952129 + 0.305698i \(0.901110\pi\)
\(102\) 351.000 202.650i 0.340727 0.196719i
\(103\) 182.000 0.174107 0.0870534 0.996204i \(-0.472255\pi\)
0.0870534 + 0.996204i \(0.472255\pi\)
\(104\) 253.500 + 1024.51i 0.239017 + 0.965974i
\(105\) −48.0000 −0.0446126
\(106\) 139.500 80.5404i 0.127825 0.0737997i
\(107\) 753.000 + 1304.23i 0.680330 + 1.17837i 0.974880 + 0.222729i \(0.0714967\pi\)
−0.294551 + 0.955636i \(0.595170\pi\)
\(108\) 250.000 433.013i 0.222743 0.385802i
\(109\) 1551.92i 1.36373i −0.731477 0.681866i \(-0.761169\pi\)
0.731477 0.681866i \(-0.238831\pi\)
\(110\) 36.0000 + 20.7846i 0.0312042 + 0.0180158i
\(111\) 249.000 + 143.760i 0.212919 + 0.122929i
\(112\) 13.8564i 0.0116902i
\(113\) 343.500 594.959i 0.285962 0.495302i −0.686880 0.726771i \(-0.741020\pi\)
0.972842 + 0.231470i \(0.0743534\pi\)
\(114\) 198.000 + 342.946i 0.162670 + 0.281753i
\(115\) −117.000 + 67.5500i −0.0948722 + 0.0547745i
\(116\) −705.000 −0.564290
\(117\) 299.000 1035.77i 0.236261 0.818433i
\(118\) −492.000 −0.383833
\(119\) 1404.00 810.600i 1.08155 0.624433i
\(120\) 39.0000 + 67.5500i 0.0296683 + 0.0513870i
\(121\) −569.500 + 986.403i −0.427874 + 0.741099i
\(122\) 251.147i 0.186376i
\(123\) −471.000 271.932i −0.345273 0.199344i
\(124\) 675.000 + 389.711i 0.488845 + 0.282235i
\(125\) 427.817i 0.306121i
\(126\) −276.000 + 478.046i −0.195143 + 0.337998i
\(127\) −143.000 247.683i −0.0999149 0.173058i 0.811734 0.584027i \(-0.198524\pi\)
−0.911649 + 0.410969i \(0.865190\pi\)
\(128\) 799.500 461.592i 0.552082 0.318745i
\(129\) 208.000 0.141964
\(130\) 97.5000 + 101.325i 0.0657794 + 0.0683599i
\(131\) −1974.00 −1.31656 −0.658279 0.752774i \(-0.728715\pi\)
−0.658279 + 0.752774i \(0.728715\pi\)
\(132\) 120.000 69.2820i 0.0791262 0.0456835i
\(133\) 792.000 + 1371.78i 0.516354 + 0.894352i
\(134\) −681.000 + 1179.53i −0.439026 + 0.760415i
\(135\) 173.205i 0.110423i
\(136\) −2281.50 1317.22i −1.43851 0.830523i
\(137\) −733.500 423.486i −0.457424 0.264094i 0.253536 0.967326i \(-0.418406\pi\)
−0.710961 + 0.703232i \(0.751740\pi\)
\(138\) 270.200i 0.166674i
\(139\) −118.000 + 204.382i −0.0720045 + 0.124716i −0.899780 0.436344i \(-0.856273\pi\)
0.827775 + 0.561060i \(0.189606\pi\)
\(140\) 60.0000 + 103.923i 0.0362209 + 0.0627364i
\(141\) −522.000 + 301.377i −0.311775 + 0.180004i
\(142\) 1830.00 1.08148
\(143\) 468.000 450.333i 0.273679 0.263348i
\(144\) −23.0000 −0.0133102
\(145\) −211.500 + 122.110i −0.121132 + 0.0699355i
\(146\) −397.500 688.490i −0.225324 0.390273i
\(147\) −151.000 + 261.540i −0.0847229 + 0.146744i
\(148\) 718.801i 0.399224i
\(149\) −40.5000 23.3827i −0.0222677 0.0128563i 0.488825 0.872382i \(-0.337426\pi\)
−0.511093 + 0.859526i \(0.670759\pi\)
\(150\) −366.000 211.310i −0.199225 0.115023i
\(151\) 1770.16i 0.953995i 0.878905 + 0.476998i \(0.158275\pi\)
−0.878905 + 0.476998i \(0.841725\pi\)
\(152\) 1287.00 2229.15i 0.686773 1.18953i
\(153\) 1345.50 + 2330.47i 0.710962 + 1.23142i
\(154\) −288.000 + 166.277i −0.150699 + 0.0870063i
\(155\) 270.000 0.139916
\(156\) 455.000 112.583i 0.233520 0.0577813i
\(157\) 1211.00 0.615594 0.307797 0.951452i \(-0.400408\pi\)
0.307797 + 0.951452i \(0.400408\pi\)
\(158\) 1914.00 1105.05i 0.963732 0.556411i
\(159\) −93.0000 161.081i −0.0463860 0.0803430i
\(160\) 157.500 272.798i 0.0778217 0.134791i
\(161\) 1080.80i 0.529062i
\(162\) −631.500 364.597i −0.306267 0.176824i
\(163\) −870.000 502.295i −0.418059 0.241367i 0.276187 0.961104i \(-0.410929\pi\)
−0.694247 + 0.719737i \(0.744262\pi\)
\(164\) 1359.66i 0.647388i
\(165\) 24.0000 41.5692i 0.0113236 0.0196131i
\(166\) 684.000 + 1184.72i 0.319811 + 0.553930i
\(167\) 792.000 457.261i 0.366987 0.211880i −0.305154 0.952303i \(-0.598708\pi\)
0.672141 + 0.740423i \(0.265375\pi\)
\(168\) −624.000 −0.286563
\(169\) 1943.50 1024.51i 0.884615 0.466321i
\(170\) −351.000 −0.158356
\(171\) −2277.00 + 1314.63i −1.01828 + 0.587906i
\(172\) −260.000 450.333i −0.115261 0.199637i
\(173\) −1287.00 + 2229.15i −0.565600 + 0.979648i 0.431394 + 0.902164i \(0.358022\pi\)
−0.996994 + 0.0774841i \(0.975311\pi\)
\(174\) 488.438i 0.212807i
\(175\) −1464.00 845.241i −0.632389 0.365110i
\(176\) −12.0000 6.92820i −0.00513940 0.00296723i
\(177\) 568.113i 0.241254i
\(178\) −846.000 + 1465.31i −0.356238 + 0.617022i
\(179\) −1872.00 3242.40i −0.781675 1.35390i −0.930965 0.365108i \(-0.881032\pi\)
0.149290 0.988793i \(-0.452301\pi\)
\(180\) −172.500 + 99.5929i −0.0714299 + 0.0412401i
\(181\) −637.000 −0.261590 −0.130795 0.991409i \(-0.541753\pi\)
−0.130795 + 0.991409i \(0.541753\pi\)
\(182\) −1092.00 + 270.200i −0.444750 + 0.110047i
\(183\) 290.000 0.117144
\(184\) −1521.00 + 878.150i −0.609400 + 0.351837i
\(185\) −124.500 215.640i −0.0494780 0.0856983i
\(186\) −270.000 + 467.654i −0.106437 + 0.184355i
\(187\) 1621.20i 0.633978i
\(188\) 1305.00 + 753.442i 0.506260 + 0.292289i
\(189\) 1200.00 + 692.820i 0.461837 + 0.266642i
\(190\) 342.946i 0.130947i
\(191\) 1299.00 2249.93i 0.492106 0.852353i −0.507852 0.861444i \(-0.669560\pi\)
0.999959 + 0.00909077i \(0.00289372\pi\)
\(192\) 307.000 + 531.740i 0.115395 + 0.199870i
\(193\) 967.500 558.586i 0.360840 0.208331i −0.308609 0.951189i \(-0.599863\pi\)
0.669449 + 0.742858i \(0.266530\pi\)
\(194\) 348.000 0.128788
\(195\) 117.000 112.583i 0.0429669 0.0413449i
\(196\) 755.000 0.275146
\(197\) 1776.00 1025.37i 0.642308 0.370837i −0.143195 0.989695i \(-0.545738\pi\)
0.785503 + 0.618858i \(0.212404\pi\)
\(198\) −276.000 478.046i −0.0990630 0.171582i
\(199\) 1261.00 2184.12i 0.449196 0.778030i −0.549138 0.835732i \(-0.685044\pi\)
0.998334 + 0.0577019i \(0.0183773\pi\)
\(200\) 2747.03i 0.971223i
\(201\) 1362.00 + 786.351i 0.477951 + 0.275945i
\(202\) −643.500 371.525i −0.224141 0.129408i
\(203\) 1953.75i 0.675500i
\(204\) −585.000 + 1013.25i −0.200775 + 0.347753i
\(205\) 235.500 + 407.898i 0.0802343 + 0.138970i
\(206\) 273.000 157.617i 0.0923340 0.0533091i
\(207\) 1794.00 0.602375
\(208\) −32.5000 33.7750i −0.0108340 0.0112590i
\(209\) −1584.00 −0.524247
\(210\) −72.0000 + 41.5692i −0.0236594 + 0.0136598i
\(211\) −521.000 902.398i −0.169986 0.294425i 0.768428 0.639936i \(-0.221039\pi\)
−0.938415 + 0.345511i \(0.887706\pi\)
\(212\) −232.500 + 402.702i −0.0753215 + 0.130461i
\(213\) 2113.10i 0.679753i
\(214\) 2259.00 + 1304.23i 0.721598 + 0.416615i
\(215\) −156.000 90.0666i −0.0494842 0.0285697i
\(216\) 2251.67i 0.709289i
\(217\) −1080.00 + 1870.61i −0.337858 + 0.585187i
\(218\) −1344.00 2327.88i −0.417556 0.723228i
\(219\) −795.000 + 458.993i −0.245302 + 0.141625i
\(220\) −120.000 −0.0367745
\(221\) −1521.00 + 5268.90i −0.462957 + 1.60373i
\(222\) 498.000 0.150557
\(223\) −2085.00 + 1203.78i −0.626107 + 0.361483i −0.779243 0.626722i \(-0.784396\pi\)
0.153136 + 0.988205i \(0.451063\pi\)
\(224\) 1260.00 + 2182.38i 0.375836 + 0.650967i
\(225\) 1403.00 2430.07i 0.415704 0.720020i
\(226\) 1189.92i 0.350231i
\(227\) 2085.00 + 1203.78i 0.609631 + 0.351971i 0.772821 0.634624i \(-0.218845\pi\)
−0.163190 + 0.986595i \(0.552178\pi\)
\(228\) −990.000 571.577i −0.287563 0.166025i
\(229\) 2508.01i 0.723729i −0.932231 0.361864i \(-0.882140\pi\)
0.932231 0.361864i \(-0.117860\pi\)
\(230\) −117.000 + 202.650i −0.0335424 + 0.0580971i
\(231\) 192.000 + 332.554i 0.0546869 + 0.0947205i
\(232\) −2749.50 + 1587.42i −0.778076 + 0.449222i
\(233\) −5850.00 −1.64483 −0.822417 0.568885i \(-0.807375\pi\)
−0.822417 + 0.568885i \(0.807375\pi\)
\(234\) −448.500 1812.59i −0.125296 0.506379i
\(235\) 522.000 0.144900
\(236\) 1230.00 710.141i 0.339263 0.195874i
\(237\) −1276.00 2210.10i −0.349726 0.605744i
\(238\) 1404.00 2431.80i 0.382386 0.662312i
\(239\) 5383.21i 1.45695i 0.685072 + 0.728475i \(0.259771\pi\)
−0.685072 + 0.728475i \(0.740229\pi\)
\(240\) −3.00000 1.73205i −0.000806872 0.000465847i
\(241\) 4258.50 + 2458.65i 1.13823 + 0.657159i 0.945992 0.324189i \(-0.105091\pi\)
0.192240 + 0.981348i \(0.438425\pi\)
\(242\) 1972.81i 0.524036i
\(243\) −1771.00 + 3067.46i −0.467530 + 0.809785i
\(244\) −362.500 627.868i −0.0951094 0.164734i
\(245\) 226.500 130.770i 0.0590635 0.0341003i
\(246\) −942.000 −0.244145
\(247\) −5148.00 1486.10i −1.32615 0.382827i
\(248\) 3510.00 0.898731
\(249\) 1368.00 789.815i 0.348167 0.201014i
\(250\) 370.500 + 641.725i 0.0937299 + 0.162345i
\(251\) 1989.00 3445.05i 0.500178 0.866333i −0.499822 0.866128i \(-0.666601\pi\)
1.00000 0.000205037i \(-6.52654e-5\pi\)
\(252\) 1593.49i 0.398334i
\(253\) 936.000 + 540.400i 0.232592 + 0.134287i
\(254\) −429.000 247.683i −0.105976 0.0611852i
\(255\) 405.300i 0.0995328i
\(256\) 2027.50 3511.73i 0.494995 0.857357i
\(257\) −1033.50 1790.07i −0.250848 0.434482i 0.712911 0.701254i \(-0.247376\pi\)
−0.963760 + 0.266772i \(0.914043\pi\)
\(258\) 312.000 180.133i 0.0752879 0.0434675i
\(259\) 1992.00 0.477903
\(260\) −390.000 112.583i −0.0930261 0.0268543i
\(261\) 3243.00 0.769106
\(262\) −2961.00 + 1709.53i −0.698211 + 0.403112i
\(263\) 1026.00 + 1777.08i 0.240555 + 0.416653i 0.960872 0.276991i \(-0.0893373\pi\)
−0.720318 + 0.693644i \(0.756004\pi\)
\(264\) 312.000 540.400i 0.0727359 0.125982i
\(265\) 161.081i 0.0373400i
\(266\) 2376.00 + 1371.78i 0.547676 + 0.316201i
\(267\) 1692.00 + 976.877i 0.387823 + 0.223910i
\(268\) 3931.76i 0.896157i
\(269\) −1665.00 + 2883.86i −0.377386 + 0.653652i −0.990681 0.136202i \(-0.956510\pi\)
0.613295 + 0.789854i \(0.289844\pi\)
\(270\) −150.000 259.808i −0.0338100 0.0585607i
\(271\) 2430.00 1402.96i 0.544694 0.314479i −0.202285 0.979327i \(-0.564837\pi\)
0.746979 + 0.664848i \(0.231504\pi\)
\(272\) 117.000 0.0260815
\(273\) 312.000 + 1260.93i 0.0691689 + 0.279543i
\(274\) −1467.00 −0.323448
\(275\) 1464.00 845.241i 0.321027 0.185345i
\(276\) 390.000 + 675.500i 0.0850552 + 0.147320i
\(277\) −188.500 + 326.492i −0.0408876 + 0.0708194i −0.885745 0.464172i \(-0.846352\pi\)
0.844857 + 0.534992i \(0.179685\pi\)
\(278\) 408.764i 0.0881872i
\(279\) −3105.00 1792.67i −0.666278 0.384676i
\(280\) 468.000 + 270.200i 0.0998870 + 0.0576698i
\(281\) 36.3731i 0.00772183i 0.999993 + 0.00386092i \(0.00122897\pi\)
−0.999993 + 0.00386092i \(0.998771\pi\)
\(282\) −522.000 + 904.131i −0.110229 + 0.190923i
\(283\) 3562.00 + 6169.56i 0.748194 + 1.29591i 0.948688 + 0.316215i \(0.102412\pi\)
−0.200493 + 0.979695i \(0.564255\pi\)
\(284\) −4575.00 + 2641.38i −0.955902 + 0.551891i
\(285\) −396.000 −0.0823053
\(286\) 312.000 1080.80i 0.0645068 0.223458i
\(287\) −3768.00 −0.774976
\(288\) −3622.50 + 2091.45i −0.741173 + 0.427917i
\(289\) −4388.00 7600.24i −0.893141 1.54696i
\(290\) −211.500 + 366.329i −0.0428266 + 0.0741778i
\(291\) 401.836i 0.0809486i
\(292\) 1987.50 + 1147.48i 0.398321 + 0.229971i
\(293\) −7207.50 4161.25i −1.43709 0.829703i −0.439441 0.898271i \(-0.644823\pi\)
−0.997646 + 0.0685685i \(0.978157\pi\)
\(294\) 523.079i 0.103764i
\(295\) 246.000 426.084i 0.0485514 0.0840936i
\(296\) −1618.50 2803.32i −0.317816 0.550473i
\(297\) −1200.00 + 692.820i −0.234448 + 0.135359i
\(298\) −81.0000 −0.0157457
\(299\) 2535.00 + 2634.45i 0.490310 + 0.509546i
\(300\) 1220.00 0.234789
\(301\) 1248.00 720.533i 0.238982 0.137976i
\(302\) 1533.00 + 2655.23i 0.292100 + 0.505932i
\(303\) −429.000 + 743.050i −0.0813380 + 0.140882i
\(304\) 114.315i 0.0215672i
\(305\) −217.500 125.574i −0.0408328 0.0235748i
\(306\) 4036.50 + 2330.47i 0.754089 + 0.435374i
\(307\) 2220.49i 0.412801i 0.978468 + 0.206401i \(0.0661750\pi\)
−0.978468 + 0.206401i \(0.933825\pi\)
\(308\) 480.000 831.384i 0.0888004 0.153807i
\(309\) −182.000 315.233i −0.0335069 0.0580356i
\(310\) 405.000 233.827i 0.0742015 0.0428402i
\(311\) 4914.00 0.895972 0.447986 0.894041i \(-0.352141\pi\)
0.447986 + 0.894041i \(0.352141\pi\)
\(312\) 1521.00 1463.58i 0.275993 0.265574i
\(313\) −518.000 −0.0935434 −0.0467717 0.998906i \(-0.514893\pi\)
−0.0467717 + 0.998906i \(0.514893\pi\)
\(314\) 1816.50 1048.76i 0.326468 0.188487i
\(315\) −276.000 478.046i −0.0493677 0.0855074i
\(316\) −3190.00 + 5525.24i −0.567885 + 0.983605i
\(317\) 3916.17i 0.693861i −0.937891 0.346930i \(-0.887224\pi\)
0.937891 0.346930i \(-0.112776\pi\)
\(318\) −279.000 161.081i −0.0491998 0.0284055i
\(319\) 1692.00 + 976.877i 0.296971 + 0.171456i
\(320\) 531.740i 0.0928911i
\(321\) 1506.00 2608.47i 0.261859 0.453553i
\(322\) −936.000 1621.20i −0.161991 0.280577i
\(323\) 11583.0 6687.45i 1.99534 1.15201i
\(324\) 2105.00 0.360940
\(325\) 5551.00 1373.52i 0.947428 0.234428i
\(326\) −1740.00 −0.295613
\(327\) −2688.00 + 1551.92i −0.454577 + 0.262450i
\(328\) 3061.50 + 5302.67i 0.515375 + 0.892656i
\(329\) −2088.00 + 3616.52i −0.349894 + 0.606034i
\(330\) 83.1384i 0.0138685i
\(331\) −6456.00 3727.37i −1.07207 0.618958i −0.143321 0.989676i \(-0.545778\pi\)
−0.928745 + 0.370719i \(0.879111\pi\)
\(332\) −3420.00 1974.54i −0.565352 0.326406i
\(333\) 3306.48i 0.544127i
\(334\) 792.000 1371.78i 0.129749 0.224733i
\(335\) −681.000 1179.53i −0.111066 0.192371i
\(336\) 24.0000 13.8564i 0.00389675 0.00224979i
\(337\) −3575.00 −0.577871 −0.288936 0.957349i \(-0.593301\pi\)
−0.288936 + 0.957349i \(0.593301\pi\)
\(338\) 2028.00 3219.88i 0.326357 0.518161i
\(339\) −1374.00 −0.220134
\(340\) 877.500 506.625i 0.139968 0.0808106i
\(341\) −1080.00 1870.61i −0.171511 0.297066i
\(342\) −2277.00 + 3943.88i −0.360018 + 0.623569i
\(343\) 6845.06i 1.07755i
\(344\) −2028.00 1170.87i −0.317856 0.183514i
\(345\) 234.000 + 135.100i 0.0365163 + 0.0210827i
\(346\) 4458.30i 0.692716i
\(347\) 3483.00 6032.73i 0.538839 0.933297i −0.460128 0.887853i \(-0.652196\pi\)
0.998967 0.0454442i \(-0.0144703\pi\)
\(348\) 705.000 + 1221.10i 0.108598 + 0.188097i
\(349\) −5760.00 + 3325.54i −0.883455 + 0.510063i −0.871796 0.489869i \(-0.837045\pi\)
−0.0116588 + 0.999932i \(0.503711\pi\)
\(350\) −2928.00 −0.447166
\(351\) −4550.00 + 1125.83i −0.691912 + 0.171204i
\(352\) −2520.00 −0.381581
\(353\) 4876.50 2815.45i 0.735269 0.424508i −0.0850777 0.996374i \(-0.527114\pi\)
0.820347 + 0.571867i \(0.193781\pi\)
\(354\) 492.000 + 852.169i 0.0738687 + 0.127944i
\(355\) −915.000 + 1584.83i −0.136798 + 0.236940i
\(356\) 4884.38i 0.727168i
\(357\) −2808.00 1621.20i −0.416289 0.240344i
\(358\) −5616.00 3242.40i −0.829092 0.478676i
\(359\) 7129.12i 1.04808i 0.851694 + 0.524040i \(0.175576\pi\)
−0.851694 + 0.524040i \(0.824424\pi\)
\(360\) −448.500 + 776.825i −0.0656612 + 0.113729i
\(361\) 3104.50 + 5377.15i 0.452617 + 0.783956i
\(362\) −955.500 + 551.658i −0.138729 + 0.0800953i
\(363\) 2278.00 0.329377
\(364\) 2340.00 2251.67i 0.336949 0.324229i
\(365\) 795.000 0.114006
\(366\) 435.000 251.147i 0.0621252 0.0358680i
\(367\) −1.00000 1.73205i −0.000142233 0.000246355i 0.865954 0.500123i \(-0.166712\pi\)
−0.866097 + 0.499877i \(0.833379\pi\)
\(368\) 39.0000 67.5500i 0.00552450 0.00956871i
\(369\) 6254.44i 0.882366i
\(370\) −373.500 215.640i −0.0524793 0.0302989i
\(371\) −1116.00 644.323i −0.156172 0.0901660i
\(372\) 1558.85i 0.217264i
\(373\) −1749.50 + 3030.22i −0.242857 + 0.420641i −0.961527 0.274711i \(-0.911418\pi\)
0.718670 + 0.695351i \(0.244751\pi\)
\(374\) 1404.00 + 2431.80i 0.194115 + 0.336218i
\(375\) 741.000 427.817i 0.102040 0.0589129i
\(376\) 6786.00 0.930748
\(377\) 4582.50 + 4762.27i 0.626023 + 0.650582i
\(378\) 2400.00 0.326568
\(379\) 4779.00 2759.16i 0.647706 0.373953i −0.139871 0.990170i \(-0.544669\pi\)
0.787577 + 0.616216i \(0.211335\pi\)
\(380\) 495.000 + 857.365i 0.0668236 + 0.115742i
\(381\) −286.000 + 495.367i −0.0384573 + 0.0666100i
\(382\) 4499.87i 0.602705i
\(383\) −6378.00 3682.34i −0.850915 0.491276i 0.0100443 0.999950i \(-0.496803\pi\)
−0.860960 + 0.508673i \(0.830136\pi\)
\(384\) −1599.00 923.183i −0.212496 0.122685i
\(385\) 332.554i 0.0440221i
\(386\) 967.500 1675.76i 0.127576 0.220969i
\(387\) 1196.00 + 2071.53i 0.157096 + 0.272098i
\(388\) −870.000 + 502.295i −0.113834 + 0.0657220i
\(389\) −1209.00 −0.157580 −0.0787901 0.996891i \(-0.525106\pi\)
−0.0787901 + 0.996891i \(0.525106\pi\)
\(390\) 78.0000 270.200i 0.0101274 0.0350823i
\(391\) −9126.00 −1.18036
\(392\) 2944.50 1700.01i 0.379387 0.219039i
\(393\) 1974.00 + 3419.07i 0.253372 + 0.438853i
\(394\) 1776.00 3076.12i 0.227090 0.393332i
\(395\) 2210.10i 0.281524i
\(396\) 1380.00 + 796.743i 0.175120 + 0.101106i
\(397\) 10128.0 + 5847.40i 1.28038 + 0.739226i 0.976917 0.213618i \(-0.0685248\pi\)
0.303460 + 0.952844i \(0.401858\pi\)
\(398\) 4368.23i 0.550150i
\(399\) 1584.00 2743.57i 0.198745 0.344236i
\(400\) −61.0000 105.655i −0.00762500 0.0132069i
\(401\) −2581.50 + 1490.43i −0.321481 + 0.185607i −0.652053 0.758174i \(-0.726092\pi\)
0.330571 + 0.943781i \(0.392759\pi\)
\(402\) 2724.00 0.337962
\(403\) −1755.00 7092.75i −0.216930 0.876712i
\(404\) 2145.00 0.264153
\(405\) 631.500 364.597i 0.0774802 0.0447332i
\(406\) −1692.00 2930.63i −0.206829 0.358238i
\(407\) −996.000 + 1725.12i −0.121302 + 0.210101i
\(408\) 5268.90i 0.639337i
\(409\) 37.5000 + 21.6506i 0.00453363 + 0.00261749i 0.502265 0.864714i \(-0.332500\pi\)
−0.497731 + 0.867331i \(0.665833\pi\)
\(410\) 706.500 + 407.898i 0.0851013 + 0.0491333i
\(411\) 1693.95i 0.203300i
\(412\) −455.000 + 788.083i −0.0544084 + 0.0942380i
\(413\) 1968.00 + 3408.68i 0.234477 + 0.406126i
\(414\) 2691.00 1553.65i 0.319458 0.184439i
\(415\) −1368.00 −0.161813
\(416\) −8190.00 2364.25i −0.965259 0.278646i
\(417\) 472.000 0.0554291
\(418\) −2376.00 + 1371.78i −0.278024 + 0.160517i
\(419\) 4731.00 + 8194.33i 0.551610 + 0.955416i 0.998159 + 0.0606569i \(0.0193195\pi\)
−0.446549 + 0.894759i \(0.647347\pi\)
\(420\) 120.000 207.846i 0.0139414 0.0241473i
\(421\) 7068.50i 0.818284i −0.912471 0.409142i \(-0.865828\pi\)
0.912471 0.409142i \(-0.134172\pi\)
\(422\) −1563.00 902.398i −0.180298 0.104095i
\(423\) −6003.00 3465.83i −0.690014 0.398380i
\(424\) 2094.05i 0.239849i
\(425\) −7137.00 + 12361.6i −0.814577 + 1.41089i
\(426\) −1830.00 3169.65i −0.208131 0.360493i
\(427\) 1740.00 1004.59i 0.197200 0.113854i
\(428\) −7530.00 −0.850412
\(429\) −1248.00 360.267i −0.140452 0.0405451i
\(430\) −312.000 −0.0349906
\(431\) −8598.00 + 4964.06i −0.960907 + 0.554780i −0.896452 0.443140i \(-0.853864\pi\)
−0.0644552 + 0.997921i \(0.520531\pi\)
\(432\) 50.0000 + 86.6025i 0.00556858 + 0.00964506i
\(433\) 3308.50 5730.49i 0.367197 0.636004i −0.621929 0.783074i \(-0.713651\pi\)
0.989126 + 0.147070i \(0.0469841\pi\)
\(434\) 3741.23i 0.413790i
\(435\) 423.000 + 244.219i 0.0466237 + 0.0269182i
\(436\) 6720.00 + 3879.79i 0.738141 + 0.426166i
\(437\) 8916.60i 0.976061i
\(438\) −795.000 + 1376.98i −0.0867273 + 0.150216i
\(439\) −6994.00 12114.0i −0.760377 1.31701i −0.942656 0.333765i \(-0.891681\pi\)
0.182280 0.983247i \(-0.441652\pi\)
\(440\) −468.000 + 270.200i −0.0507069 + 0.0292756i
\(441\) −3473.00 −0.375013
\(442\) 2281.50 + 9220.57i 0.245520 + 0.992258i
\(443\) 2004.00 0.214928 0.107464 0.994209i \(-0.465727\pi\)
0.107464 + 0.994209i \(0.465727\pi\)
\(444\) −1245.00 + 718.801i −0.133075 + 0.0768306i
\(445\) −846.000 1465.31i −0.0901219 0.156096i
\(446\) −2085.00 + 3611.33i −0.221362 + 0.383411i
\(447\) 93.5307i 0.00989676i
\(448\) 3684.00 + 2126.96i 0.388510 + 0.224307i
\(449\) 7866.00 + 4541.44i 0.826769 + 0.477336i 0.852745 0.522327i \(-0.174936\pi\)
−0.0259758 + 0.999663i \(0.508269\pi\)
\(450\) 4860.13i 0.509131i
\(451\) 1884.00 3263.18i 0.196705 0.340704i
\(452\) 1717.50 + 2974.80i 0.178727 + 0.309563i
\(453\) 3066.00 1770.16i 0.317998 0.183596i
\(454\) 4170.00 0.431074
\(455\) 312.000 1080.80i 0.0321468 0.111360i
\(456\) −5148.00 −0.528678
\(457\) 2185.50 1261.80i 0.223705 0.129156i −0.383959 0.923350i \(-0.625440\pi\)
0.607665 + 0.794194i \(0.292106\pi\)
\(458\) −2172.00 3762.01i −0.221596 0.383815i
\(459\) 5850.00 10132.5i 0.594890 1.03038i
\(460\) 675.500i 0.0684681i
\(461\) 16963.5 + 9793.88i 1.71382 + 0.989472i 0.929270 + 0.369400i \(0.120437\pi\)
0.784545 + 0.620072i \(0.212897\pi\)
\(462\) 576.000 + 332.554i 0.0580042 + 0.0334887i
\(463\) 8632.54i 0.866497i −0.901274 0.433249i \(-0.857367\pi\)
0.901274 0.433249i \(-0.142633\pi\)
\(464\) 70.5000 122.110i 0.00705362 0.0122172i
\(465\) −270.000 467.654i −0.0269268 0.0466385i
\(466\) −8775.00 + 5066.25i −0.872305 + 0.503625i
\(467\) 5460.00 0.541025 0.270512 0.962716i \(-0.412807\pi\)
0.270512 + 0.962716i \(0.412807\pi\)
\(468\) 3737.50 + 3884.12i 0.369158 + 0.383640i
\(469\) 10896.0 1.07277
\(470\) 783.000 452.065i 0.0768449 0.0443664i
\(471\) −1211.00 2097.51i −0.118471 0.205198i
\(472\) 3198.00 5539.10i 0.311864 0.540165i
\(473\) 1441.07i 0.140085i
\(474\) −3828.00 2210.10i −0.370941 0.214163i
\(475\) −12078.0 6973.24i −1.16669 0.673587i
\(476\) 8106.00i 0.780542i
\(477\) 1069.50 1852.43i 0.102660 0.177813i
\(478\) 4662.00 + 8074.82i 0.446098 + 0.772665i
\(479\) −2211.00 + 1276.52i −0.210904 + 0.121766i −0.601732 0.798698i \(-0.705522\pi\)
0.390827 + 0.920464i \(0.372189\pi\)
\(480\) −630.000 −0.0599072
\(481\) −4855.50 + 4672.21i −0.460274 + 0.442899i
\(482\) 8517.00 0.804852
\(483\) −1872.00 + 1080.80i −0.176354 + 0.101818i
\(484\) −2847.50 4932.01i −0.267421 0.463187i
\(485\) −174.000 + 301.377i −0.0162906 + 0.0282161i
\(486\) 6134.92i 0.572605i
\(487\) 9378.00 + 5414.39i 0.872603 + 0.503798i 0.868212 0.496193i \(-0.165269\pi\)
0.00439074 + 0.999990i \(0.498602\pi\)
\(488\) −2827.50 1632.46i −0.262285 0.151430i
\(489\) 2009.18i 0.185804i
\(490\) 226.500 392.310i 0.0208821 0.0361689i
\(491\) −5694.00 9862.30i −0.523354 0.906475i −0.999631 0.0271797i \(-0.991347\pi\)
0.476277 0.879295i \(-0.341986\pi\)
\(492\) 2355.00 1359.66i 0.215796 0.124590i
\(493\) −16497.0 −1.50707
\(494\) −9009.00 + 2229.15i −0.820514 + 0.203025i
\(495\) 552.000 0.0501223
\(496\) −135.000 + 77.9423i −0.0122211 + 0.00705587i
\(497\) −7320.00 12678.6i −0.660658 1.14429i
\(498\) 1368.00 2369.45i 0.123095 0.213208i
\(499\) 17677.3i 1.58586i 0.609311 + 0.792931i \(0.291446\pi\)
−0.609311 + 0.792931i \(0.708554\pi\)
\(500\) −1852.50 1069.54i −0.165693 0.0956627i
\(501\) −1584.00 914.523i −0.141253 0.0815526i
\(502\) 6890.10i 0.612590i
\(503\) −1938.00 + 3356.71i −0.171792 + 0.297552i −0.939046 0.343791i \(-0.888289\pi\)
0.767255 + 0.641343i \(0.221622\pi\)
\(504\) −3588.00 6214.60i −0.317108 0.549246i
\(505\) 643.500 371.525i 0.0567037 0.0327379i
\(506\) 1872.00 0.164467
\(507\) −3718.00 2341.73i −0.325685 0.205128i
\(508\) 1430.00 0.124894
\(509\) −14779.5 + 8532.95i −1.28701 + 0.743058i −0.978120 0.208039i \(-0.933292\pi\)
−0.308893 + 0.951097i \(0.599958\pi\)
\(510\) 351.000 + 607.950i 0.0304756 + 0.0527852i
\(511\) −3180.00 + 5507.92i −0.275293 + 0.476822i
\(512\) 361.999i 0.0312465i
\(513\) 9900.00 + 5715.77i 0.852038 + 0.491925i
\(514\) −3100.50 1790.07i −0.266065 0.153612i
\(515\) 315.233i 0.0269725i
\(516\) −520.000 + 900.666i −0.0443638 + 0.0768404i
\(517\) −2088.00 3616.52i −0.177621 0.307649i
\(518\) 2988.00 1725.12i 0.253446 0.146327i
\(519\) 5148.00 0.435399
\(520\) −1774.50 + 439.075i −0.149648 + 0.0370283i
\(521\) 2121.00 0.178355 0.0891773 0.996016i \(-0.471576\pi\)
0.0891773 + 0.996016i \(0.471576\pi\)
\(522\) 4864.50 2808.52i 0.407880 0.235490i
\(523\) 5732.00 + 9928.12i 0.479241 + 0.830069i 0.999717 0.0238072i \(-0.00757878\pi\)
−0.520476 + 0.853876i \(0.674245\pi\)
\(524\) 4935.00 8547.67i 0.411425 0.712608i
\(525\) 3380.96i 0.281062i
\(526\) 3078.00 + 1777.08i 0.255147 + 0.147309i
\(527\) 15795.0 + 9119.25i 1.30558 + 0.753777i
\(528\) 27.7128i 0.00228418i
\(529\) 3041.50 5268.03i 0.249979 0.432977i
\(530\) 139.500 + 241.621i 0.0114330 + 0.0198025i
\(531\) −5658.00 + 3266.65i −0.462404 + 0.266969i
\(532\) −7920.00 −0.645443
\(533\) 9184.50 8837.79i 0.746388 0.718212i
\(534\) 3384.00 0.274232
\(535\) −2259.00 + 1304.23i −0.182552 + 0.105396i
\(536\) −8853.00 15333.8i −0.713417 1.23567i
\(537\) −3744.00 + 6484.80i −0.300867 + 0.521117i
\(538\) 5767.73i 0.462202i
\(539\) −1812.00 1046.16i −0.144802 0.0836016i
\(540\) 750.000 + 433.013i 0.0597683 + 0.0345072i
\(541\) 4764.87i 0.378665i 0.981913 + 0.189333i \(0.0606324\pi\)
−0.981913 + 0.189333i \(0.939368\pi\)
\(542\) 2430.00 4208.88i 0.192578 0.333555i
\(543\) 637.000 + 1103.32i 0.0503431 + 0.0871968i
\(544\) 18427.5 10639.1i 1.45234 0.838508i
\(545\) 2688.00 0.211268
\(546\) 1560.00 + 1621.20i 0.122274 + 0.127071i
\(547\) 6554.00 0.512301 0.256151 0.966637i \(-0.417546\pi\)
0.256151 + 0.966637i \(0.417546\pi\)
\(548\) 3667.50 2117.43i 0.285890 0.165059i
\(549\) 1667.50 + 2888.19i 0.129631 + 0.224527i
\(550\) 1464.00 2535.72i 0.113500 0.196588i
\(551\) 16118.5i 1.24622i
\(552\) 3042.00 + 1756.30i 0.234558 + 0.135422i
\(553\) −15312.0 8840.39i −1.17745 0.679804i
\(554\) 652.983i 0.0500769i
\(555\) −249.000 + 431.281i −0.0190441 + 0.0329853i
\(556\) −590.000 1021.91i −0.0450028 0.0779472i
\(557\) −15685.5 + 9056.03i −1.19321 + 0.688898i −0.959032 0.283297i \(-0.908572\pi\)
−0.234174 + 0.972195i \(0.575239\pi\)
\(558\) −6210.00 −0.471130
\(559\) −1352.00 + 4683.47i −0.102296 + 0.354364i
\(560\) −24.0000 −0.00181104
\(561\) 2808.00 1621.20i 0.211326 0.122009i
\(562\) 31.5000 + 54.5596i 0.00236432 + 0.00409512i
\(563\) 6084.00 10537.8i 0.455435 0.788837i −0.543278 0.839553i \(-0.682817\pi\)
0.998713 + 0.0507160i \(0.0161503\pi\)
\(564\) 3013.77i 0.225005i
\(565\) 1030.50 + 594.959i 0.0767318 + 0.0443011i
\(566\) 10686.0 + 6169.56i 0.793580 + 0.458173i
\(567\) 5833.55i 0.432074i
\(568\) −11895.0 + 20602.7i −0.878703 + 1.52196i
\(569\) 3861.00 + 6687.45i 0.284467 + 0.492711i 0.972480 0.232988i \(-0.0748502\pi\)
−0.688013 + 0.725698i \(0.741517\pi\)
\(570\) −594.000 + 342.946i −0.0436490 + 0.0252008i
\(571\) 11440.0 0.838440 0.419220 0.907885i \(-0.362304\pi\)
0.419220 + 0.907885i \(0.362304\pi\)
\(572\) 780.000 + 3152.33i 0.0570165 + 0.230429i
\(573\) −5196.00 −0.378824
\(574\) −5652.00 + 3263.18i −0.410993 + 0.237287i
\(575\) 4758.00 + 8241.10i 0.345082 + 0.597700i
\(576\) −3530.50 + 6115.01i −0.255389 + 0.442347i
\(577\) 15444.7i 1.11433i −0.830400 0.557167i \(-0.811888\pi\)
0.830400 0.557167i \(-0.188112\pi\)
\(578\) −13164.0 7600.24i −0.947319 0.546935i
\(579\) −1935.00 1117.17i −0.138887 0.0801867i
\(580\) 1221.10i 0.0874194i
\(581\) 5472.00 9477.78i 0.390735 0.676772i
\(582\) −348.000 602.754i −0.0247853 0.0429295i
\(583\) 1116.00 644.323i 0.0792796 0.0457721i
\(584\) 10335.0 0.732304
\(585\) 1794.00 + 517.883i 0.126791 + 0.0366014i
\(586\) −14415.0 −1.01617
\(587\) −12186.0 + 7035.59i −0.856848 + 0.494702i −0.862956 0.505280i \(-0.831389\pi\)
0.00610719 + 0.999981i \(0.498056\pi\)
\(588\) −755.000 1307.70i −0.0529518 0.0917153i
\(589\) −8910.00 + 15432.6i −0.623311 + 1.07961i
\(590\) 852.169i 0.0594631i
\(591\) −3552.00 2050.75i −0.247225 0.142735i
\(592\) 124.500 + 71.8801i 0.00864344 + 0.00499029i
\(593\) 26938.6i 1.86549i −0.360538 0.932745i \(-0.617407\pi\)
0.360538 0.932745i \(-0.382593\pi\)
\(594\) −1200.00 + 2078.46i −0.0828899 + 0.143570i
\(595\) 1404.00 + 2431.80i 0.0967368 + 0.167553i
\(596\) 202.500 116.913i 0.0139173 0.00803517i
\(597\) −5044.00 −0.345791
\(598\) 6084.00 + 1756.30i 0.416042 + 0.120101i
\(599\) −10554.0 −0.719908 −0.359954 0.932970i \(-0.617208\pi\)
−0.359954 + 0.932970i \(0.617208\pi\)
\(600\) 4758.00 2747.03i 0.323741 0.186912i
\(601\) 7415.50 + 12844.0i 0.503302 + 0.871745i 0.999993 + 0.00381713i \(0.00121503\pi\)
−0.496691 + 0.867928i \(0.665452\pi\)
\(602\) 1248.00 2161.60i 0.0844928 0.146346i
\(603\) 18086.1i 1.22143i
\(604\) −7665.00 4425.39i −0.516365 0.298123i
\(605\) −1708.50 986.403i −0.114811 0.0662859i
\(606\) 1486.10i 0.0996183i
\(607\) 3977.00 6888.37i 0.265933 0.460610i −0.701874 0.712301i \(-0.747653\pi\)
0.967808 + 0.251691i \(0.0809866\pi\)
\(608\) 10395.0 + 18004.7i 0.693377 + 1.20096i
\(609\) −3384.00 + 1953.75i −0.225167 + 0.130000i
\(610\) −435.000 −0.0288732
\(611\) −3393.00 13712.6i −0.224658 0.907945i
\(612\) −13455.0 −0.888703
\(613\) 21841.5 12610.2i 1.43910 0.830866i 0.441315 0.897352i \(-0.354512\pi\)
0.997787 + 0.0664859i \(0.0211787\pi\)
\(614\) 1923.00 + 3330.73i 0.126394 + 0.218921i
\(615\) 471.000 815.796i 0.0308822 0.0534895i
\(616\) 4323.20i 0.282771i
\(617\) −15055.5 8692.30i −0.982353 0.567162i −0.0793731 0.996845i \(-0.525292\pi\)
−0.902980 + 0.429683i \(0.858625\pi\)
\(618\) −546.000 315.233i −0.0355394 0.0205187i
\(619\) 8209.92i 0.533093i 0.963822 + 0.266547i \(0.0858826\pi\)
−0.963822 + 0.266547i \(0.914117\pi\)
\(620\) −675.000 + 1169.13i −0.0437236 + 0.0757316i
\(621\) −3900.00 6755.00i −0.252015 0.436504i
\(622\) 7371.00 4255.65i 0.475161 0.274334i
\(623\) 13536.0 0.870479
\(624\) −26.0000 + 90.0666i −0.00166800 + 0.00577813i
\(625\) 14509.0 0.928576
\(626\) −777.000 + 448.601i −0.0496089 + 0.0286417i
\(627\) 1584.00 + 2743.57i 0.100891 + 0.174749i
\(628\) −3027.50 + 5243.78i −0.192373 + 0.333200i
\(629\) 16819.9i 1.06622i
\(630\) −828.000 478.046i −0.0523624 0.0302314i
\(631\) 11142.0 + 6432.84i 0.702941 + 0.405843i 0.808442 0.588576i \(-0.200311\pi\)
−0.105501 + 0.994419i \(0.533645\pi\)
\(632\) 28731.3i 1.80834i
\(633\) −1042.00 + 1804.80i −0.0654278 + 0.113324i
\(634\) −3391.50 5874.25i −0.212451 0.367975i
\(635\) 429.000 247.683i 0.0268100 0.0154788i
\(636\) 930.000 0.0579825
\(637\) −4907.50 5100.02i −0.305247 0.317222i
\(638\) 3384.00 0.209990
\(639\) 21045.0 12150.3i 1.30286 0.752206i
\(640\) 799.500 + 1384.77i 0.0493797 + 0.0855282i
\(641\) −3100.50 + 5370.22i −0.191049 + 0.330907i −0.945598 0.325337i \(-0.894522\pi\)
0.754549 + 0.656244i \(0.227856\pi\)
\(642\) 5216.94i 0.320710i
\(643\) −14568.0 8410.84i −0.893477 0.515849i −0.0183989 0.999831i \(-0.505857\pi\)
−0.875078 + 0.483981i \(0.839190\pi\)
\(644\) 4680.00 + 2702.00i 0.286363 + 0.165332i
\(645\) 360.267i 0.0219930i
\(646\) 11583.0 20062.3i 0.705460 1.22189i
\(647\) 6747.00 + 11686.1i 0.409972 + 0.710092i 0.994886 0.101003i \(-0.0322051\pi\)
−0.584914 + 0.811095i \(0.698872\pi\)
\(648\) 8209.50 4739.76i 0.497685 0.287338i
\(649\) −3936.00 −0.238061
\(650\) 7137.00 6867.58i 0.430671 0.414413i
\(651\) 4320.00 0.260083
\(652\) 4350.00 2511.47i 0.261287 0.150854i
\(653\) 5667.00 + 9815.53i 0.339612 + 0.588226i 0.984360 0.176170i \(-0.0563708\pi\)
−0.644747 + 0.764396i \(0.723037\pi\)
\(654\) −2688.00 + 4655.75i −0.160717 + 0.278371i
\(655\) 3419.07i 0.203960i
\(656\) −235.500 135.966i −0.0140164 0.00809235i
\(657\) −9142.50 5278.42i −0.542896 0.313441i
\(658\) 7233.04i 0.428531i
\(659\) −6618.00 + 11462.7i −0.391200 + 0.677578i −0.992608 0.121364i \(-0.961273\pi\)
0.601408 + 0.798942i \(0.294607\pi\)
\(660\) 120.000 + 207.846i 0.00707726 + 0.0122582i
\(661\) −10264.5 + 5926.21i −0.603998 + 0.348718i −0.770613 0.637304i \(-0.780050\pi\)
0.166615 + 0.986022i \(0.446716\pi\)
\(662\) −12912.0 −0.758065
\(663\) 10647.0 2634.45i 0.623673 0.154319i
\(664\) −17784.0 −1.03939
\(665\) −2376.00 + 1371.78i −0.138552 + 0.0799932i
\(666\) 2863.50 + 4959.73i 0.166604 + 0.288567i
\(667\) −5499.00 + 9524.55i −0.319224 + 0.552911i
\(668\) 4572.61i 0.264850i
\(669\) 4170.00 + 2407.55i 0.240989 + 0.139135i
\(670\) −2043.00 1179.53i −0.117803 0.0680136i
\(671\) 2009.18i 0.115594i
\(672\) 2520.00 4364.77i 0.144659 0.250557i
\(673\) −4010.50 6946.39i −0.229708 0.397866i 0.728014 0.685563i \(-0.240444\pi\)
−0.957722 + 0.287697i \(0.907110\pi\)
\(674\) −5362.50 + 3096.04i −0.306463 + 0.176936i
\(675\) −12200.0 −0.695671
\(676\) −422.500 + 10976.9i −0.0240385 + 0.624538i
\(677\) −21630.0 −1.22793 −0.613965 0.789333i \(-0.710426\pi\)
−0.613965 + 0.789333i \(0.710426\pi\)
\(678\) −2061.00 + 1189.92i −0.116744 + 0.0674020i
\(679\) −1392.00 2411.01i −0.0786746 0.136268i
\(680\) 2281.50 3951.67i 0.128664 0.222853i
\(681\) 4815.10i 0.270947i
\(682\) −3240.00 1870.61i −0.181915 0.105029i
\(683\) −22983.0 13269.2i −1.28758 0.743387i −0.309361 0.950945i \(-0.600115\pi\)
−0.978223 + 0.207557i \(0.933449\pi\)
\(684\) 13146.3i 0.734883i
\(685\) 733.500 1270.46i 0.0409133 0.0708639i
\(686\) 5928.00 + 10267.6i 0.329930 + 0.571456i
\(687\) −4344.00 + 2508.01i −0.241243 + 0.139282i
\(688\) 104.000 0.00576303
\(689\) 4231.50 1047.02i 0.233973 0.0578933i
\(690\) 468.000 0.0258210
\(691\) −720.000 + 415.692i −0.0396383 + 0.0228852i −0.519688 0.854356i \(-0.673952\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(692\) −6435.00 11145.7i −0.353500 0.612280i
\(693\) −2208.00 + 3824.37i −0.121032 + 0.209633i
\(694\) 12065.5i 0.659941i
\(695\) −354.000 204.382i −0.0193208 0.0111549i
\(696\) 5499.00 + 3174.85i 0.299481 + 0.172906i
\(697\) 31816.0i 1.72901i
\(698\) −5760.00 + 9976.61i −0.312348 + 0.541003i
\(699\) 5850.00 + 10132.5i 0.316548 + 0.548278i
\(700\) 7320.00 4226.20i 0.395243 0.228194i
\(701\) 30186.0 1.62640 0.813202 0.581981i \(-0.197722\pi\)
0.813202 + 0.581981i \(0.197722\pi\)
\(702\) −5850.00 + 5629.17i −0.314521 + 0.302648i
\(703\) 16434.0 0.881679
\(704\) −3684.00 + 2126.96i −0.197224 + 0.113868i
\(705\) −522.000 904.131i −0.0278860 0.0483000i
\(706\) 4876.50 8446.35i 0.259957 0.450258i
\(707\) 5944.40i 0.316212i
\(708\) −2460.00 1420.28i −0.130583 0.0753919i
\(709\) −10288.5 5940.07i −0.544983 0.314646i 0.202113 0.979362i \(-0.435219\pi\)
−0.747096 + 0.664716i \(0.768552\pi\)
\(710\) 3169.65i 0.167542i
\(711\) 14674.0 25416.1i 0.774006 1.34062i
\(712\) −10998.0 19049.1i −0.578887 1.00266i
\(713\) 10530.0 6079.50i 0.553088 0.319325i
\(714\) −5616.00 −0.294361
\(715\) 780.000 + 810.600i 0.0407977 + 0.0423982i
\(716\) 18720.0 0.977094
\(717\) 9324.00 5383.21i 0.485650 0.280390i
\(718\) 6174.00 + 10693.7i 0.320908 + 0.555828i
\(719\) −9204.00 + 15941.8i −0.477401 + 0.826883i −0.999665 0.0259014i \(-0.991754\pi\)
0.522264 + 0.852784i \(0.325088\pi\)
\(720\) 39.8372i 0.00206201i
\(721\) −2184.00 1260.93i −0.112811 0.0651312i
\(722\) 9313.50 + 5377.15i 0.480073 + 0.277170i
\(723\) 9834.58i 0.505881i
\(724\) 1592.50 2758.29i 0.0817470 0.141590i
\(725\) 8601.00 + 14897.4i 0.440597 + 0.763137i
\(726\) 3417.00 1972.81i 0.174679 0.100851i
\(727\) 21112.0 1.07703 0.538515 0.842616i \(-0.318986\pi\)
0.538515 + 0.842616i \(0.318986\pi\)
\(728\) 4056.00 14050.4i 0.206491 0.715305i
\(729\) −4283.00 −0.217599
\(730\) 1192.50 688.490i 0.0604608 0.0349071i
\(731\) −6084.00 10537.8i −0.307832 0.533180i
\(732\) −725.000 + 1255.74i −0.0366076 + 0.0634062i
\(733\) 23959.5i 1.20732i 0.797243 + 0.603658i \(0.206291\pi\)
−0.797243 + 0.603658i \(0.793709\pi\)
\(734\) −3.00000 1.73205i −0.000150861 8.70997e-5i
\(735\) −453.000 261.540i −0.0227335 0.0131252i
\(736\) 14185.5i 0.710441i
\(737\) −5448.00 + 9436.21i −0.272293 + 0.471625i
\(738\) −5416.50 9381.65i −0.270168 0.467945i
\(739\) 2742.00 1583.09i 0.136490 0.0788025i −0.430200 0.902734i \(-0.641557\pi\)
0.566690 + 0.823931i \(0.308224\pi\)
\(740\) 1245.00 0.0618474
\(741\) 2574.00 + 10402.7i 0.127609 + 0.515726i
\(742\) −2232.00 −0.110430
\(743\) −26070.0 + 15051.5i −1.28723 + 0.743185i −0.978160 0.207852i \(-0.933353\pi\)
−0.309075 + 0.951038i \(0.600019\pi\)
\(744\) −3510.00 6079.50i −0.172961 0.299577i
\(745\) 40.5000 70.1481i 0.00199168 0.00344970i
\(746\) 6060.45i 0.297438i
\(747\) 15732.0 + 9082.87i 0.770554 + 0.444880i
\(748\) −7020.00 4053.00i −0.343151 0.198118i
\(749\) 20867.7i 1.01801i
\(750\) 741.000 1283.45i 0.0360767 0.0624866i
\(751\) −14248.0 24678.3i −0.692299 1.19910i −0.971083 0.238744i \(-0.923264\pi\)
0.278783 0.960354i \(-0.410069\pi\)
\(752\) −261.000 + 150.688i −0.0126565 + 0.00730724i
\(753\) −7956.00 −0.385037
\(754\) 10998.0 + 3174.85i 0.531198 + 0.153344i
\(755\) −3066.00 −0.147792
\(756\) −6000.00 + 3464.10i −0.288648 + 0.166651i
\(757\) −8711.00 15087.9i −0.418239 0.724411i 0.577524 0.816374i \(-0.304019\pi\)
−0.995762 + 0.0919633i \(0.970686\pi\)
\(758\) 4779.00 8277.47i 0.228999 0.396638i
\(759\) 2161.60i 0.103374i
\(760\) 3861.00 + 2229.15i 0.184281 + 0.106394i
\(761\) 35790.0 + 20663.4i 1.70484 + 0.984292i 0.940695 + 0.339252i \(0.110174\pi\)
0.764149 + 0.645040i \(0.223159\pi\)
\(762\) 990.733i 0.0471004i
\(763\) −10752.0 + 18623.0i −0.510155 + 0.883615i
\(764\) 6495.00 + 11249.7i 0.307567 + 0.532721i
\(765\) −4036.50 + 2330.47i −0.190771 + 0.110142i
\(766\) −12756.0 −0.601688
\(767\) −12792.0 3692.73i −0.602206 0.173842i
\(768\) −8110.00 −0.381047
\(769\) −12186.0 + 7035.59i −0.571441 + 0.329922i −0.757725 0.652574i \(-0.773689\pi\)
0.186283 + 0.982496i \(0.440356\pi\)
\(770\) −288.000 498.831i −0.0134790 0.0233462i
\(771\) −2067.00 + 3580.15i −0.0965515 + 0.167232i
\(772\) 5585.86i 0.260414i
\(773\) 174.000 + 100.459i 0.00809618 + 0.00467433i 0.504043 0.863679i \(-0.331845\pi\)
−0.495946 + 0.868353i \(0.665179\pi\)
\(774\) 3588.00 + 2071.53i 0.166625 + 0.0962012i
\(775\) 19017.9i 0.881476i
\(776\) −2262.00 + 3917.90i −0.104641 + 0.181243i
\(777\) −1992.00 3450.25i −0.0919725 0.159301i
\(778\) −1813.50 + 1047.02i −0.0835696 + 0.0482489i
\(779\) −31086.0 −1.42975
\(780\) 195.000 + 788.083i 0.00895144 + 0.0361768i
\(781\) 14640.0 0.670756
\(782\) −13689.0 + 7903.35i −0.625982 + 0.361411i
\(783\) −7050.00 12211.0i −0.321771 0.557323i
\(784\) −75.5000 + 130.770i −0.00343932 + 0.00595708i
\(785\) 2097.51i 0.0953675i
\(786\) 5922.00 + 3419.07i 0.268741 + 0.155158i
\(787\) −5979.00 3451.98i −0.270811 0.156353i 0.358445