Properties

Label 21.4.e.b.4.1
Level 21
Weight 4
Character 21.4
Analytic conductor 1.239
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 21 = 3 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 21.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.23904011012\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.1
Root \(2.65415 + 4.59712i\)
Character \(\chi\) = 21.4
Dual form 21.4.e.b.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.65415 - 4.59712i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -15.9249 q^{6} +(9.67799 - 15.7904i) q^{7} +64.6443 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-2.65415 - 4.59712i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-10.0890 + 17.4746i) q^{4} +(-2.78070 - 4.81631i) q^{5} -15.9249 q^{6} +(9.67799 - 15.7904i) q^{7} +64.6443 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-14.7608 + 25.5664i) q^{10} +(6.95869 - 12.0528i) q^{11} +(30.2670 + 52.4239i) q^{12} +38.6718 q^{13} +(-98.2771 - 2.58082i) q^{14} -16.6842 q^{15} +(-90.8636 - 157.380i) q^{16} +(-21.7394 + 37.6537i) q^{17} +(-23.8873 + 41.3741i) q^{18} +(54.5139 + 94.4208i) q^{19} +112.218 q^{20} +(-26.5077 - 48.8297i) q^{21} -73.8775 q^{22} +(37.4389 + 64.8461i) q^{23} +(96.9665 - 167.951i) q^{24} +(47.0354 - 81.4677i) q^{25} +(-102.641 - 177.779i) q^{26} -27.0000 q^{27} +(178.290 + 328.429i) q^{28} -72.3589 q^{29} +(44.2823 + 76.6992i) q^{30} +(-32.0215 + 55.4629i) q^{31} +(-223.754 + 387.553i) q^{32} +(-20.8761 - 36.1584i) q^{33} +230.798 q^{34} +(-102.963 - 2.70387i) q^{35} +181.602 q^{36} +(-94.3636 - 163.443i) q^{37} +(289.376 - 501.213i) q^{38} +(58.0077 - 100.472i) q^{39} +(-179.756 - 311.347i) q^{40} -24.7923 q^{41} +(-154.121 + 251.460i) q^{42} -243.881 q^{43} +(140.412 + 243.201i) q^{44} +(-25.0263 + 43.3468i) q^{45} +(198.737 - 344.222i) q^{46} +(310.274 + 537.411i) q^{47} -545.182 q^{48} +(-155.673 - 305.638i) q^{49} -499.356 q^{50} +(65.2182 + 112.961i) q^{51} +(-390.159 + 675.776i) q^{52} +(143.919 - 249.276i) q^{53} +(71.6620 + 124.122i) q^{54} -77.4001 q^{55} +(625.627 - 1020.76i) q^{56} +327.083 q^{57} +(192.051 + 332.642i) q^{58} +(-262.526 + 454.708i) q^{59} +(168.327 - 291.551i) q^{60} +(191.718 + 332.065i) q^{61} +339.960 q^{62} +(-166.625 - 4.37567i) q^{63} +921.681 q^{64} +(-107.535 - 186.255i) q^{65} +(-110.816 + 191.939i) q^{66} +(-99.0583 + 171.574i) q^{67} +(-438.657 - 759.776i) q^{68} +224.634 q^{69} +(260.849 + 480.510i) q^{70} +785.432 q^{71} +(-290.900 - 503.853i) q^{72} +(165.570 - 286.776i) q^{73} +(-500.910 + 867.602i) q^{74} +(-141.106 - 244.403i) q^{75} -2199.96 q^{76} +(-122.972 - 226.527i) q^{77} -615.844 q^{78} +(-218.823 - 379.013i) q^{79} +(-505.329 + 875.255i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(65.8024 + 113.973i) q^{82} +241.241 q^{83} +(1120.72 + 29.4308i) q^{84} +241.803 q^{85} +(647.297 + 1121.15i) q^{86} +(-108.538 + 187.994i) q^{87} +(449.840 - 779.145i) q^{88} +(-792.772 - 1373.12i) q^{89} +265.694 q^{90} +(374.265 - 610.643i) q^{91} -1510.88 q^{92} +(96.0646 + 166.389i) q^{93} +(1647.03 - 2852.73i) q^{94} +(303.173 - 525.112i) q^{95} +(671.261 + 1162.66i) q^{96} +79.2754 q^{97} +(-991.877 + 1526.86i) q^{98} -125.256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 9q^{3} - 25q^{4} - 11q^{5} - 6q^{6} - 13q^{7} + 78q^{8} - 27q^{9} + O(q^{10}) \) \( 6q - q^{2} + 9q^{3} - 25q^{4} - 11q^{5} - 6q^{6} - 13q^{7} + 78q^{8} - 27q^{9} + 55q^{10} - 35q^{11} + 75q^{12} + 124q^{13} - 326q^{14} - 66q^{15} - 241q^{16} - 48q^{17} - 9q^{18} + 202q^{19} + 878q^{20} + 3q^{21} - 14q^{22} - 216q^{23} + 117q^{24} - 130q^{25} - 274q^{26} - 162q^{27} - 201q^{28} + 106q^{29} - 165q^{30} + 95q^{31} - 683q^{32} + 105q^{33} - 48q^{34} + 56q^{35} + 450q^{36} - 262q^{37} + 398q^{38} + 186q^{39} - 21q^{40} + 488q^{41} - 219q^{42} + 720q^{43} + 905q^{44} - 99q^{45} + 1056q^{46} + 210q^{47} - 1446q^{48} - 303q^{49} - 2756q^{50} + 144q^{51} - 324q^{52} - 393q^{53} + 27q^{54} - 2062q^{55} + 1299q^{56} + 1212q^{57} + 1249q^{58} - 1143q^{59} + 1317q^{60} + 70q^{61} + 2118q^{62} + 126q^{63} - 798q^{64} + 472q^{65} - 21q^{66} + 628q^{67} - 1944q^{68} - 1296q^{69} + 3251q^{70} + 636q^{71} - 351q^{72} - 988q^{73} - 1002q^{74} + 390q^{75} - 4680q^{76} + 1073q^{77} - 1644q^{78} - 861q^{79} - 175q^{80} - 243q^{81} - 124q^{82} + 1038q^{83} + 1620q^{84} + 3600q^{85} + 3208q^{86} + 159q^{87} + 891q^{88} - 1766q^{89} - 990q^{90} - 654q^{91} - 1344q^{92} - 285q^{93} + 3294q^{94} + 736q^{95} + 2049q^{96} + 38q^{97} - 4267q^{98} + 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65415 4.59712i −0.938383 1.62533i −0.768488 0.639864i \(-0.778991\pi\)
−0.169895 0.985462i \(-0.554343\pi\)
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) −10.0890 + 17.4746i −1.26112 + 2.18433i
\(5\) −2.78070 4.81631i −0.248713 0.430784i 0.714456 0.699681i \(-0.246674\pi\)
−0.963169 + 0.268897i \(0.913341\pi\)
\(6\) −15.9249 −1.08355
\(7\) 9.67799 15.7904i 0.522562 0.852601i
\(8\) 64.6443 2.85690
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −14.7608 + 25.5664i −0.466777 + 0.808481i
\(11\) 6.95869 12.0528i 0.190738 0.330369i −0.754757 0.656005i \(-0.772245\pi\)
0.945495 + 0.325636i \(0.105578\pi\)
\(12\) 30.2670 + 52.4239i 0.728110 + 1.26112i
\(13\) 38.6718 0.825048 0.412524 0.910947i \(-0.364647\pi\)
0.412524 + 0.910947i \(0.364647\pi\)
\(14\) −98.2771 2.58082i −1.87612 0.0492680i
\(15\) −16.6842 −0.287189
\(16\) −90.8636 157.380i −1.41974 2.45907i
\(17\) −21.7394 + 37.6537i −0.310152 + 0.537198i −0.978395 0.206744i \(-0.933713\pi\)
0.668243 + 0.743943i \(0.267046\pi\)
\(18\) −23.8873 + 41.3741i −0.312794 + 0.541776i
\(19\) 54.5139 + 94.4208i 0.658228 + 1.14009i 0.981074 + 0.193633i \(0.0620273\pi\)
−0.322845 + 0.946452i \(0.604639\pi\)
\(20\) 112.218 1.25463
\(21\) −26.5077 48.8297i −0.275450 0.507406i
\(22\) −73.8775 −0.715943
\(23\) 37.4389 + 64.8461i 0.339415 + 0.587885i 0.984323 0.176376i \(-0.0564374\pi\)
−0.644907 + 0.764261i \(0.723104\pi\)
\(24\) 96.9665 167.951i 0.824717 1.42845i
\(25\) 47.0354 81.4677i 0.376283 0.651742i
\(26\) −102.641 177.779i −0.774211 1.34097i
\(27\) −27.0000 −0.192450
\(28\) 178.290 + 328.429i 1.20335 + 2.21668i
\(29\) −72.3589 −0.463335 −0.231667 0.972795i \(-0.574418\pi\)
−0.231667 + 0.972795i \(0.574418\pi\)
\(30\) 44.2823 + 76.6992i 0.269494 + 0.466777i
\(31\) −32.0215 + 55.4629i −0.185524 + 0.321337i −0.943753 0.330652i \(-0.892732\pi\)
0.758229 + 0.651988i \(0.226065\pi\)
\(32\) −223.754 + 387.553i −1.23608 + 2.14095i
\(33\) −20.8761 36.1584i −0.110123 0.190738i
\(34\) 230.798 1.16416
\(35\) −102.963 2.70387i −0.497255 0.0130582i
\(36\) 181.602 0.840749
\(37\) −94.3636 163.443i −0.419278 0.726211i 0.576589 0.817034i \(-0.304383\pi\)
−0.995867 + 0.0908235i \(0.971050\pi\)
\(38\) 289.376 501.213i 1.23534 2.13967i
\(39\) 58.0077 100.472i 0.238171 0.412524i
\(40\) −179.756 311.347i −0.710550 1.23071i
\(41\) −24.7923 −0.0944367 −0.0472184 0.998885i \(-0.515036\pi\)
−0.0472184 + 0.998885i \(0.515036\pi\)
\(42\) −154.121 + 251.460i −0.566223 + 0.923837i
\(43\) −243.881 −0.864920 −0.432460 0.901653i \(-0.642354\pi\)
−0.432460 + 0.901653i \(0.642354\pi\)
\(44\) 140.412 + 243.201i 0.481090 + 0.833272i
\(45\) −25.0263 + 43.3468i −0.0829044 + 0.143595i
\(46\) 198.737 344.222i 0.637003 1.10332i
\(47\) 310.274 + 537.411i 0.962940 + 1.66786i 0.715052 + 0.699071i \(0.246403\pi\)
0.247888 + 0.968789i \(0.420264\pi\)
\(48\) −545.182 −1.63938
\(49\) −155.673 305.638i −0.453857 0.891074i
\(50\) −499.356 −1.41239
\(51\) 65.2182 + 112.961i 0.179066 + 0.310152i
\(52\) −390.159 + 675.776i −1.04049 + 1.80218i
\(53\) 143.919 249.276i 0.372997 0.646050i −0.617028 0.786941i \(-0.711663\pi\)
0.990025 + 0.140891i \(0.0449967\pi\)
\(54\) 71.6620 + 124.122i 0.180592 + 0.312794i
\(55\) −77.4001 −0.189757
\(56\) 625.627 1020.76i 1.49291 2.43580i
\(57\) 327.083 0.760057
\(58\) 192.051 + 332.642i 0.434785 + 0.753070i
\(59\) −262.526 + 454.708i −0.579287 + 1.00335i 0.416275 + 0.909239i \(0.363336\pi\)
−0.995561 + 0.0941152i \(0.969998\pi\)
\(60\) 168.327 291.551i 0.362182 0.627317i
\(61\) 191.718 + 332.065i 0.402409 + 0.696993i 0.994016 0.109234i \(-0.0348397\pi\)
−0.591607 + 0.806226i \(0.701506\pi\)
\(62\) 339.960 0.696369
\(63\) −166.625 4.37567i −0.333218 0.00875052i
\(64\) 921.681 1.80016
\(65\) −107.535 186.255i −0.205200 0.355417i
\(66\) −110.816 + 191.939i −0.206675 + 0.357971i
\(67\) −99.0583 + 171.574i −0.180625 + 0.312852i −0.942094 0.335350i \(-0.891145\pi\)
0.761468 + 0.648202i \(0.224479\pi\)
\(68\) −438.657 759.776i −0.782279 1.35495i
\(69\) 224.634 0.391923
\(70\) 260.849 + 480.510i 0.445392 + 0.820456i
\(71\) 785.432 1.31287 0.656434 0.754384i \(-0.272064\pi\)
0.656434 + 0.754384i \(0.272064\pi\)
\(72\) −290.900 503.853i −0.476151 0.824717i
\(73\) 165.570 286.776i 0.265459 0.459789i −0.702224 0.711956i \(-0.747810\pi\)
0.967684 + 0.252166i \(0.0811430\pi\)
\(74\) −500.910 + 867.602i −0.786887 + 1.36293i
\(75\) −141.106 244.403i −0.217247 0.376283i
\(76\) −2199.96 −3.32043
\(77\) −122.972 226.527i −0.182000 0.335262i
\(78\) −615.844 −0.893981
\(79\) −218.823 379.013i −0.311640 0.539776i 0.667078 0.744988i \(-0.267545\pi\)
−0.978718 + 0.205212i \(0.934212\pi\)
\(80\) −505.329 + 875.255i −0.706219 + 1.22321i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 65.8024 + 113.973i 0.0886178 + 0.153491i
\(83\) 241.241 0.319032 0.159516 0.987195i \(-0.449007\pi\)
0.159516 + 0.987195i \(0.449007\pi\)
\(84\) 1120.72 + 29.4308i 1.45572 + 0.0382281i
\(85\) 241.803 0.308555
\(86\) 647.297 + 1121.15i 0.811626 + 1.40578i
\(87\) −108.538 + 187.994i −0.133753 + 0.231667i
\(88\) 449.840 779.145i 0.544921 0.943831i
\(89\) −792.772 1373.12i −0.944198 1.63540i −0.757349 0.653010i \(-0.773506\pi\)
−0.186849 0.982389i \(-0.559828\pi\)
\(90\) 265.694 0.311184
\(91\) 374.265 610.643i 0.431139 0.703437i
\(92\) −1510.88 −1.71218
\(93\) 96.0646 + 166.389i 0.107112 + 0.185524i
\(94\) 1647.03 2852.73i 1.80721 3.13018i
\(95\) 303.173 525.112i 0.327420 0.567109i
\(96\) 671.261 + 1162.66i 0.713649 + 1.23608i
\(97\) 79.2754 0.0829814 0.0414907 0.999139i \(-0.486789\pi\)
0.0414907 + 0.999139i \(0.486789\pi\)
\(98\) −991.877 + 1526.86i −1.02239 + 1.57384i
\(99\) −125.256 −0.127159
\(100\) 949.080 + 1643.85i 0.949080 + 1.64385i
\(101\) −577.487 + 1000.24i −0.568931 + 0.985418i 0.427741 + 0.903902i \(0.359310\pi\)
−0.996672 + 0.0815165i \(0.974024\pi\)
\(102\) 346.197 599.631i 0.336065 0.582082i
\(103\) 722.430 + 1251.28i 0.691098 + 1.19702i 0.971478 + 0.237128i \(0.0762061\pi\)
−0.280380 + 0.959889i \(0.590461\pi\)
\(104\) 2499.91 2.35708
\(105\) −161.469 + 263.450i −0.150074 + 0.244858i
\(106\) −1527.93 −1.40006
\(107\) −495.480 858.197i −0.447662 0.775374i 0.550571 0.834788i \(-0.314410\pi\)
−0.998233 + 0.0594143i \(0.981077\pi\)
\(108\) 272.403 471.816i 0.242703 0.420375i
\(109\) −976.585 + 1691.49i −0.858164 + 1.48638i 0.0155145 + 0.999880i \(0.495061\pi\)
−0.873678 + 0.486504i \(0.838272\pi\)
\(110\) 205.431 + 355.817i 0.178064 + 0.308417i
\(111\) −566.182 −0.484141
\(112\) −3364.48 88.3533i −2.83851 0.0745410i
\(113\) 672.882 0.560172 0.280086 0.959975i \(-0.409637\pi\)
0.280086 + 0.959975i \(0.409637\pi\)
\(114\) −868.127 1503.64i −0.713224 1.23534i
\(115\) 208.213 360.635i 0.168834 0.292430i
\(116\) 730.028 1264.45i 0.584323 1.01208i
\(117\) −174.023 301.417i −0.137508 0.238171i
\(118\) 2787.13 2.17437
\(119\) 384.174 + 707.686i 0.295942 + 0.545155i
\(120\) −1078.54 −0.820472
\(121\) 568.653 + 984.936i 0.427238 + 0.739997i
\(122\) 1017.69 1762.70i 0.755227 1.30809i
\(123\) −37.1884 + 64.4123i −0.0272615 + 0.0472184i
\(124\) −646.130 1119.13i −0.467937 0.810491i
\(125\) −1218.34 −0.871773
\(126\) 422.131 + 777.608i 0.298464 + 0.549800i
\(127\) 175.815 0.122843 0.0614216 0.998112i \(-0.480437\pi\)
0.0614216 + 0.998112i \(0.480437\pi\)
\(128\) −656.249 1136.66i −0.453163 0.784900i
\(129\) −365.822 + 633.622i −0.249681 + 0.432460i
\(130\) −570.825 + 988.698i −0.385113 + 0.667035i
\(131\) −562.965 975.085i −0.375470 0.650332i 0.614928 0.788584i \(-0.289185\pi\)
−0.990397 + 0.138251i \(0.955852\pi\)
\(132\) 842.474 0.555515
\(133\) 2018.53 + 53.0078i 1.31600 + 0.0345591i
\(134\) 1051.66 0.677983
\(135\) 75.0789 + 130.040i 0.0478649 + 0.0829044i
\(136\) −1405.33 + 2434.10i −0.886073 + 1.53472i
\(137\) −934.350 + 1618.34i −0.582678 + 1.00923i 0.412483 + 0.910966i \(0.364662\pi\)
−0.995161 + 0.0982624i \(0.968672\pi\)
\(138\) −596.210 1032.67i −0.367774 0.637003i
\(139\) −2817.19 −1.71907 −0.859537 0.511074i \(-0.829248\pi\)
−0.859537 + 0.511074i \(0.829248\pi\)
\(140\) 1086.04 1771.96i 0.655624 1.06970i
\(141\) 1861.65 1.11191
\(142\) −2084.65 3610.72i −1.23197 2.13384i
\(143\) 269.105 466.103i 0.157368 0.272570i
\(144\) −817.773 + 1416.42i −0.473248 + 0.819690i
\(145\) 201.208 + 348.503i 0.115238 + 0.199597i
\(146\) −1757.79 −0.996410
\(147\) −1027.58 54.0071i −0.576555 0.0303023i
\(148\) 3808.14 2.11505
\(149\) −900.163 1559.13i −0.494928 0.857240i 0.505055 0.863087i \(-0.331472\pi\)
−0.999983 + 0.00584714i \(0.998139\pi\)
\(150\) −749.034 + 1297.36i −0.407722 + 0.706196i
\(151\) 226.492 392.296i 0.122064 0.211421i −0.798517 0.601972i \(-0.794382\pi\)
0.920581 + 0.390551i \(0.127715\pi\)
\(152\) 3524.01 + 6103.77i 1.88050 + 3.25711i
\(153\) 391.309 0.206768
\(154\) −714.986 + 1166.56i −0.374125 + 0.610414i
\(155\) 356.169 0.184569
\(156\) 1170.48 + 2027.33i 0.600726 + 1.04049i
\(157\) 931.829 1613.98i 0.473682 0.820441i −0.525864 0.850569i \(-0.676258\pi\)
0.999546 + 0.0301273i \(0.00959128\pi\)
\(158\) −1161.58 + 2011.91i −0.584875 + 1.01303i
\(159\) −431.758 747.827i −0.215350 0.372997i
\(160\) 2488.77 1.22971
\(161\) 1386.28 + 36.4046i 0.678597 + 0.0178204i
\(162\) 429.972 0.208529
\(163\) −1160.57 2010.16i −0.557686 0.965940i −0.997689 0.0679437i \(-0.978356\pi\)
0.440004 0.897996i \(-0.354977\pi\)
\(164\) 250.129 433.237i 0.119096 0.206281i
\(165\) −116.100 + 201.091i −0.0547781 + 0.0948784i
\(166\) −640.290 1109.01i −0.299374 0.518531i
\(167\) 3211.62 1.48816 0.744079 0.668092i \(-0.232889\pi\)
0.744079 + 0.668092i \(0.232889\pi\)
\(168\) −1713.57 3156.57i −0.786934 1.44961i
\(169\) −701.494 −0.319296
\(170\) −641.780 1111.60i −0.289543 0.501503i
\(171\) 490.625 849.787i 0.219409 0.380028i
\(172\) 2460.52 4261.74i 1.09077 1.88927i
\(173\) −107.139 185.569i −0.0470844 0.0815525i 0.841523 0.540222i \(-0.181660\pi\)
−0.888607 + 0.458669i \(0.848326\pi\)
\(174\) 1152.31 0.502047
\(175\) −831.199 1531.15i −0.359044 0.661395i
\(176\) −2529.17 −1.08320
\(177\) 787.577 + 1364.12i 0.334451 + 0.579287i
\(178\) −4208.27 + 7288.93i −1.77204 + 3.06926i
\(179\) 1218.61 2110.70i 0.508845 0.881345i −0.491102 0.871102i \(-0.663406\pi\)
0.999948 0.0102437i \(-0.00326072\pi\)
\(180\) −504.980 874.652i −0.209106 0.362182i
\(181\) −248.631 −0.102103 −0.0510514 0.998696i \(-0.516257\pi\)
−0.0510514 + 0.998696i \(0.516257\pi\)
\(182\) −3800.55 99.8048i −1.54789 0.0406485i
\(183\) 1150.31 0.464662
\(184\) 2420.21 + 4191.93i 0.969677 + 1.67953i
\(185\) −524.794 + 908.970i −0.208560 + 0.361237i
\(186\) 509.939 883.241i 0.201025 0.348185i
\(187\) 302.555 + 524.041i 0.118316 + 0.204929i
\(188\) −12521.4 −4.85755
\(189\) −261.306 + 426.341i −0.100567 + 0.164083i
\(190\) −3218.67 −1.22898
\(191\) 2156.54 + 3735.24i 0.816972 + 1.41504i 0.907903 + 0.419180i \(0.137683\pi\)
−0.0909306 + 0.995857i \(0.528984\pi\)
\(192\) 1382.52 2394.60i 0.519661 0.900079i
\(193\) −1030.43 + 1784.75i −0.384309 + 0.665643i −0.991673 0.128781i \(-0.958894\pi\)
0.607364 + 0.794424i \(0.292227\pi\)
\(194\) −210.409 364.438i −0.0778683 0.134872i
\(195\) −645.208 −0.236945
\(196\) 6911.51 + 363.252i 2.51877 + 0.132380i
\(197\) −1666.09 −0.602557 −0.301279 0.953536i \(-0.597413\pi\)
−0.301279 + 0.953536i \(0.597413\pi\)
\(198\) 332.449 + 575.818i 0.119324 + 0.206675i
\(199\) 543.767 941.832i 0.193702 0.335501i −0.752773 0.658281i \(-0.771284\pi\)
0.946474 + 0.322780i \(0.104617\pi\)
\(200\) 3040.57 5266.43i 1.07501 1.86196i
\(201\) 297.175 + 514.722i 0.104284 + 0.180625i
\(202\) 6130.94 2.13550
\(203\) −700.288 + 1142.58i −0.242121 + 0.395040i
\(204\) −2631.94 −0.903298
\(205\) 68.9399 + 119.407i 0.0234877 + 0.0406818i
\(206\) 3834.87 6642.19i 1.29703 2.24652i
\(207\) 336.950 583.615i 0.113138 0.195962i
\(208\) −3513.86 6086.18i −1.17136 2.02885i
\(209\) 1517.38 0.502198
\(210\) 1639.67 + 43.0589i 0.538801 + 0.0141493i
\(211\) −4676.47 −1.52579 −0.762895 0.646522i \(-0.776223\pi\)
−0.762895 + 0.646522i \(0.776223\pi\)
\(212\) 2904.01 + 5029.88i 0.940792 + 1.62950i
\(213\) 1178.15 2040.61i 0.378992 0.656434i
\(214\) −2630.15 + 4555.56i −0.840157 + 1.45520i
\(215\) 678.161 + 1174.61i 0.215117 + 0.372594i
\(216\) −1745.40 −0.549811
\(217\) 565.878 + 1042.40i 0.177024 + 0.326096i
\(218\) 10368.0 3.22114
\(219\) −496.711 860.329i −0.153263 0.265459i
\(220\) 780.889 1352.54i 0.239307 0.414492i
\(221\) −840.701 + 1456.14i −0.255890 + 0.443214i
\(222\) 1502.73 + 2602.80i 0.454309 + 0.786887i
\(223\) 3246.03 0.974754 0.487377 0.873192i \(-0.337954\pi\)
0.487377 + 0.873192i \(0.337954\pi\)
\(224\) 3954.12 + 7283.89i 1.17945 + 2.17266i
\(225\) −846.638 −0.250856
\(226\) −1785.93 3093.32i −0.525656 0.910463i
\(227\) −2569.08 + 4449.77i −0.751171 + 1.30107i 0.196085 + 0.980587i \(0.437177\pi\)
−0.947256 + 0.320479i \(0.896156\pi\)
\(228\) −3299.94 + 5715.67i −0.958526 + 1.66022i
\(229\) −307.403 532.438i −0.0887064 0.153644i 0.818258 0.574851i \(-0.194940\pi\)
−0.906965 + 0.421207i \(0.861607\pi\)
\(230\) −2210.51 −0.633725
\(231\) −772.994 20.2993i −0.220170 0.00578180i
\(232\) −4677.59 −1.32370
\(233\) −1413.71 2448.61i −0.397490 0.688472i 0.595926 0.803039i \(-0.296785\pi\)
−0.993415 + 0.114567i \(0.963452\pi\)
\(234\) −923.765 + 1600.01i −0.258070 + 0.446991i
\(235\) 1725.56 2988.76i 0.478992 0.829638i
\(236\) −5297.24 9175.09i −1.46111 2.53071i
\(237\) −1312.94 −0.359851
\(238\) 2233.66 3644.39i 0.608348 0.992567i
\(239\) −3432.45 −0.928983 −0.464491 0.885578i \(-0.653763\pi\)
−0.464491 + 0.885578i \(0.653763\pi\)
\(240\) 1515.99 + 2625.77i 0.407736 + 0.706219i
\(241\) 1318.06 2282.94i 0.352296 0.610195i −0.634355 0.773042i \(-0.718734\pi\)
0.986651 + 0.162847i \(0.0520675\pi\)
\(242\) 3018.58 5228.33i 0.801825 1.38880i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) −7736.96 −2.02995
\(245\) −1039.17 + 1599.66i −0.270980 + 0.417137i
\(246\) 394.814 0.102327
\(247\) 2108.15 + 3651.42i 0.543070 + 0.940625i
\(248\) −2070.01 + 3585.37i −0.530024 + 0.918028i
\(249\) 361.862 626.763i 0.0920967 0.159516i
\(250\) 3233.65 + 5600.85i 0.818057 + 1.41692i
\(251\) 2057.57 0.517422 0.258711 0.965955i \(-0.416702\pi\)
0.258711 + 0.965955i \(0.416702\pi\)
\(252\) 1757.54 2867.57i 0.439344 0.716824i
\(253\) 1042.10 0.258958
\(254\) −466.639 808.243i −0.115274 0.199660i
\(255\) 362.704 628.222i 0.0890722 0.154278i
\(256\) 203.161 351.885i 0.0495998 0.0859093i
\(257\) −1075.10 1862.13i −0.260946 0.451972i 0.705548 0.708663i \(-0.250701\pi\)
−0.966494 + 0.256691i \(0.917368\pi\)
\(258\) 3883.78 0.937185
\(259\) −3494.07 91.7566i −0.838267 0.0220134i
\(260\) 4339.66 1.03513
\(261\) 325.615 + 563.982i 0.0772225 + 0.133753i
\(262\) −2988.39 + 5176.04i −0.704668 + 1.22052i
\(263\) 2295.08 3975.19i 0.538100 0.932017i −0.460906 0.887449i \(-0.652475\pi\)
0.999006 0.0445683i \(-0.0141912\pi\)
\(264\) −1349.52 2337.44i −0.314610 0.544921i
\(265\) −1600.79 −0.371078
\(266\) −5113.78 9420.09i −1.17874 2.17136i
\(267\) −4756.63 −1.09027
\(268\) −1998.80 3462.02i −0.455582 0.789091i
\(269\) 189.689 328.551i 0.0429945 0.0744687i −0.843727 0.536772i \(-0.819644\pi\)
0.886722 + 0.462303i \(0.152977\pi\)
\(270\) 398.541 690.293i 0.0898312 0.155592i
\(271\) 2684.42 + 4649.55i 0.601723 + 1.04221i 0.992560 + 0.121755i \(0.0388521\pi\)
−0.390837 + 0.920460i \(0.627815\pi\)
\(272\) 7901.28 1.76134
\(273\) −1025.10 1888.33i −0.227259 0.418634i
\(274\) 9919.61 2.18710
\(275\) −654.610 1133.82i −0.143543 0.248624i
\(276\) −2266.33 + 3925.39i −0.494264 + 0.856090i
\(277\) 2390.80 4140.99i 0.518590 0.898224i −0.481177 0.876624i \(-0.659791\pi\)
0.999767 0.0216003i \(-0.00687613\pi\)
\(278\) 7477.25 + 12951.0i 1.61315 + 2.79406i
\(279\) 576.388 0.123683
\(280\) −6655.98 174.790i −1.42061 0.0373061i
\(281\) −2076.57 −0.440845 −0.220423 0.975404i \(-0.570744\pi\)
−0.220423 + 0.975404i \(0.570744\pi\)
\(282\) −4941.08 8558.20i −1.04339 1.80721i
\(283\) −1278.81 + 2214.96i −0.268612 + 0.465250i −0.968504 0.248999i \(-0.919898\pi\)
0.699892 + 0.714249i \(0.253232\pi\)
\(284\) −7924.21 + 13725.1i −1.65569 + 2.86774i
\(285\) −909.520 1575.34i −0.189036 0.327420i
\(286\) −2856.97 −0.590687
\(287\) −239.940 + 391.480i −0.0493491 + 0.0805169i
\(288\) 4027.56 0.824050
\(289\) 1511.30 + 2617.65i 0.307612 + 0.532800i
\(290\) 1068.07 1849.96i 0.216274 0.374597i
\(291\) 118.913 205.963i 0.0239547 0.0414907i
\(292\) 3340.88 + 5786.57i 0.669555 + 1.15970i
\(293\) 560.049 0.111667 0.0558335 0.998440i \(-0.482218\pi\)
0.0558335 + 0.998440i \(0.482218\pi\)
\(294\) 2479.08 + 4867.26i 0.491778 + 0.965524i
\(295\) 2920.02 0.576305
\(296\) −6100.08 10565.6i −1.19784 2.07471i
\(297\) −187.885 + 325.426i −0.0367076 + 0.0635795i
\(298\) −4778.33 + 8276.31i −0.928863 + 1.60884i
\(299\) 1447.83 + 2507.71i 0.280034 + 0.485033i
\(300\) 5694.48 1.09590
\(301\) −2360.28 + 3850.98i −0.451975 + 0.737432i
\(302\) −2404.57 −0.458171
\(303\) 1732.46 + 3000.71i 0.328473 + 0.568931i
\(304\) 9906.66 17158.8i 1.86903 3.23726i
\(305\) 1066.22 1846.75i 0.200169 0.346703i
\(306\) −1038.59 1798.89i −0.194027 0.336065i
\(307\) 3653.02 0.679117 0.339558 0.940585i \(-0.389722\pi\)
0.339558 + 0.940585i \(0.389722\pi\)
\(308\) 5199.15 + 136.533i 0.961848 + 0.0252587i
\(309\) 4334.58 0.798011
\(310\) −945.325 1637.35i −0.173196 0.299985i
\(311\) −1746.13 + 3024.39i −0.318374 + 0.551439i −0.980149 0.198263i \(-0.936470\pi\)
0.661775 + 0.749702i \(0.269803\pi\)
\(312\) 3749.87 6494.96i 0.680431 1.17854i
\(313\) −4356.05 7544.90i −0.786640 1.36250i −0.928014 0.372544i \(-0.878485\pi\)
0.141374 0.989956i \(-0.454848\pi\)
\(314\) −9892.85 −1.77798
\(315\) 442.259 + 814.685i 0.0791063 + 0.145722i
\(316\) 8830.83 1.57207
\(317\) −970.165 1680.37i −0.171892 0.297726i 0.767189 0.641421i \(-0.221655\pi\)
−0.939081 + 0.343695i \(0.888321\pi\)
\(318\) −2291.90 + 3969.69i −0.404162 + 0.700029i
\(319\) −503.523 + 872.127i −0.0883758 + 0.153071i
\(320\) −2562.92 4439.11i −0.447724 0.775480i
\(321\) −2972.88 −0.516916
\(322\) −3512.03 6469.51i −0.607820 1.11966i
\(323\) −4740.39 −0.816602
\(324\) −817.208 1415.45i −0.140125 0.242703i
\(325\) 1818.94 3150.50i 0.310452 0.537718i
\(326\) −6160.64 + 10670.5i −1.04665 + 1.81284i
\(327\) 2929.75 + 5074.48i 0.495461 + 0.858164i
\(328\) −1602.68 −0.269797
\(329\) 11488.8 + 301.702i 1.92522 + 0.0505574i
\(330\) 1232.59 0.205611
\(331\) 2865.75 + 4963.63i 0.475879 + 0.824247i 0.999618 0.0276315i \(-0.00879650\pi\)
−0.523739 + 0.851879i \(0.675463\pi\)
\(332\) −2433.88 + 4215.61i −0.402339 + 0.696872i
\(333\) −849.273 + 1470.98i −0.139759 + 0.242070i
\(334\) −8524.10 14764.2i −1.39646 2.41874i
\(335\) 1101.81 0.179696
\(336\) −5276.26 + 8608.64i −0.856678 + 1.39774i
\(337\) 2403.74 0.388547 0.194273 0.980947i \(-0.437765\pi\)
0.194273 + 0.980947i \(0.437765\pi\)
\(338\) 1861.87 + 3224.85i 0.299622 + 0.518960i
\(339\) 1009.32 1748.20i 0.161708 0.280086i
\(340\) −2439.55 + 4225.42i −0.389127 + 0.673987i
\(341\) 445.656 + 771.898i 0.0707731 + 0.122583i
\(342\) −5208.76 −0.823560
\(343\) −6332.75 499.826i −0.996900 0.0786824i
\(344\) −15765.6 −2.47099
\(345\) −624.638 1081.91i −0.0974765 0.168834i
\(346\) −568.723 + 985.057i −0.0883663 + 0.153055i
\(347\) 1668.22 2889.45i 0.258083 0.447013i −0.707645 0.706568i \(-0.750242\pi\)
0.965728 + 0.259555i \(0.0835758\pi\)
\(348\) −2190.09 3793.34i −0.337359 0.584323i
\(349\) −2424.54 −0.371870 −0.185935 0.982562i \(-0.559531\pi\)
−0.185935 + 0.982562i \(0.559531\pi\)
\(350\) −4832.76 + 7885.02i −0.738062 + 1.20421i
\(351\) −1044.14 −0.158781
\(352\) 3114.06 + 5393.71i 0.471534 + 0.816721i
\(353\) 6201.56 10741.4i 0.935059 1.61957i 0.160531 0.987031i \(-0.448679\pi\)
0.774528 0.632540i \(-0.217987\pi\)
\(354\) 4180.69 7241.17i 0.627687 1.08719i
\(355\) −2184.05 3782.88i −0.326528 0.565562i
\(356\) 31993.1 4.76300
\(357\) 2414.88 + 63.4163i 0.358009 + 0.00940153i
\(358\) −12937.5 −1.90997
\(359\) −676.921 1172.46i −0.0995168 0.172368i 0.811968 0.583702i \(-0.198396\pi\)
−0.911485 + 0.411334i \(0.865063\pi\)
\(360\) −1617.81 + 2802.13i −0.236850 + 0.410236i
\(361\) −2514.03 + 4354.42i −0.366529 + 0.634848i
\(362\) 659.903 + 1142.99i 0.0958114 + 0.165950i
\(363\) 3411.92 0.493332
\(364\) 6894.81 + 12700.9i 0.992819 + 1.82887i
\(365\) −1841.61 −0.264093
\(366\) −3053.08 5288.10i −0.436031 0.755227i
\(367\) 689.031 1193.44i 0.0980031 0.169746i −0.812855 0.582466i \(-0.802088\pi\)
0.910858 + 0.412720i \(0.135421\pi\)
\(368\) 6803.67 11784.3i 0.963766 1.66929i
\(369\) 111.565 + 193.237i 0.0157395 + 0.0272615i
\(370\) 5571.52 0.782837
\(371\) −2543.31 4685.03i −0.355909 0.655619i
\(372\) −3876.78 −0.540327
\(373\) −2728.46 4725.83i −0.378752 0.656017i 0.612129 0.790758i \(-0.290313\pi\)
−0.990881 + 0.134741i \(0.956980\pi\)
\(374\) 1606.05 2781.76i 0.222051 0.384603i
\(375\) −1827.51 + 3165.34i −0.251659 + 0.435887i
\(376\) 20057.5 + 34740.6i 2.75103 + 4.76492i
\(377\) −2798.25 −0.382273
\(378\) 2653.48 + 69.6821i 0.361059 + 0.00948164i
\(379\) 554.675 0.0751761 0.0375881 0.999293i \(-0.488033\pi\)
0.0375881 + 0.999293i \(0.488033\pi\)
\(380\) 6117.43 + 10595.7i 0.825836 + 1.43039i
\(381\) 263.723 456.781i 0.0354618 0.0614216i
\(382\) 11447.5 19827.7i 1.53327 2.65569i
\(383\) −2930.33 5075.48i −0.390948 0.677141i 0.601627 0.798777i \(-0.294519\pi\)
−0.992575 + 0.121636i \(0.961186\pi\)
\(384\) −3937.50 −0.523267
\(385\) −749.077 + 1222.18i −0.0991597 + 0.161787i
\(386\) 10939.6 1.44252
\(387\) 1097.47 + 1900.87i 0.144153 + 0.249681i
\(388\) −799.809 + 1385.31i −0.104650 + 0.181259i
\(389\) −3889.43 + 6736.69i −0.506946 + 0.878056i 0.493022 + 0.870017i \(0.335892\pi\)
−0.999968 + 0.00803932i \(0.997441\pi\)
\(390\) 1712.48 + 2966.10i 0.222345 + 0.385113i
\(391\) −3255.60 −0.421081
\(392\) −10063.4 19757.8i −1.29663 2.54571i
\(393\) −3377.79 −0.433555
\(394\) 4422.04 + 7659.20i 0.565429 + 0.979352i
\(395\) −1216.96 + 2107.84i −0.155018 + 0.268499i
\(396\) 1263.71 2188.81i 0.160363 0.277757i
\(397\) −4013.94 6952.35i −0.507440 0.878912i −0.999963 0.00861270i \(-0.997258\pi\)
0.492523 0.870300i \(-0.336075\pi\)
\(398\) −5772.95 −0.727065
\(399\) 3165.51 5164.77i 0.397177 0.648025i
\(400\) −17095.2 −2.13690
\(401\) −389.990 675.482i −0.0485665 0.0841196i 0.840720 0.541470i \(-0.182132\pi\)
−0.889287 + 0.457350i \(0.848799\pi\)
\(402\) 1577.49 2732.30i 0.195717 0.338991i
\(403\) −1238.33 + 2144.85i −0.153066 + 0.265118i
\(404\) −11652.5 20182.8i −1.43499 2.48547i
\(405\) 450.473 0.0552696
\(406\) 7111.22 + 186.745i 0.869271 + 0.0228276i
\(407\) −2626.59 −0.319890
\(408\) 4215.99 + 7302.30i 0.511574 + 0.886073i
\(409\) −7346.25 + 12724.1i −0.888139 + 1.53830i −0.0460654 + 0.998938i \(0.514668\pi\)
−0.842073 + 0.539363i \(0.818665\pi\)
\(410\) 365.953 633.850i 0.0440809 0.0763503i
\(411\) 2803.05 + 4855.02i 0.336409 + 0.582678i
\(412\) −29154.4 −3.48624
\(413\) 4639.29 + 8546.04i 0.552748 + 1.01822i
\(414\) −3577.26 −0.424669
\(415\) −670.820 1161.89i −0.0793476 0.137434i
\(416\) −8652.95 + 14987.3i −1.01982 + 1.76638i
\(417\) −4225.79 + 7319.28i −0.496254 + 0.859537i
\(418\) −4027.35 6975.57i −0.471254 0.816236i
\(419\) 3370.31 0.392960 0.196480 0.980508i \(-0.437049\pi\)
0.196480 + 0.980508i \(0.437049\pi\)
\(420\) −2974.63 5479.57i −0.345589 0.636608i
\(421\) 15651.0 1.81184 0.905919 0.423450i \(-0.139181\pi\)
0.905919 + 0.423450i \(0.139181\pi\)
\(422\) 12412.0 + 21498.3i 1.43178 + 2.47991i
\(423\) 2792.47 4836.70i 0.320980 0.555953i
\(424\) 9303.58 16114.3i 1.06562 1.84570i
\(425\) 2045.04 + 3542.12i 0.233410 + 0.404277i
\(426\) −12507.9 −1.42256
\(427\) 7098.88 + 186.421i 0.804541 + 0.0211277i
\(428\) 19995.6 2.25823
\(429\) −807.314 1398.31i −0.0908567 0.157368i
\(430\) 3599.88 6235.17i 0.403724 0.699271i
\(431\) −2444.06 + 4233.24i −0.273147 + 0.473104i −0.969666 0.244434i \(-0.921398\pi\)
0.696519 + 0.717538i \(0.254731\pi\)
\(432\) 2453.32 + 4249.27i 0.273230 + 0.473248i
\(433\) −5255.73 −0.583313 −0.291656 0.956523i \(-0.594206\pi\)
−0.291656 + 0.956523i \(0.594206\pi\)
\(434\) 3290.12 5368.10i 0.363896 0.593725i
\(435\) 1207.25 0.133065
\(436\) −19705.5 34131.0i −2.16450 3.74903i
\(437\) −4081.88 + 7070.03i −0.446826 + 0.773925i
\(438\) −2636.69 + 4566.88i −0.287639 + 0.498205i
\(439\) 412.488 + 714.451i 0.0448451 + 0.0776740i 0.887577 0.460660i \(-0.152387\pi\)
−0.842732 + 0.538334i \(0.819054\pi\)
\(440\) −5003.48 −0.542117
\(441\) −1681.69 + 2588.72i −0.181588 + 0.279530i
\(442\) 8925.37 0.960490
\(443\) −6513.64 11281.9i −0.698583 1.20998i −0.968958 0.247226i \(-0.920481\pi\)
0.270375 0.962755i \(-0.412852\pi\)
\(444\) 5712.21 9893.83i 0.610561 1.05752i
\(445\) −4408.92 + 7636.47i −0.469669 + 0.813491i
\(446\) −8615.44 14922.4i −0.914693 1.58429i
\(447\) −5400.98 −0.571493
\(448\) 8920.02 14553.7i 0.940695 1.53482i
\(449\) 16526.1 1.73700 0.868500 0.495689i \(-0.165084\pi\)
0.868500 + 0.495689i \(0.165084\pi\)
\(450\) 2247.10 + 3892.09i 0.235399 + 0.407722i
\(451\) −172.522 + 298.817i −0.0180127 + 0.0311989i
\(452\) −6788.71 + 11758.4i −0.706447 + 1.22360i
\(453\) −679.476 1176.89i −0.0704737 0.122064i
\(454\) 27274.9 2.81954
\(455\) −3981.76 104.564i −0.410259 0.0107737i
\(456\) 21144.1 2.17141
\(457\) 1855.41 + 3213.67i 0.189918 + 0.328947i 0.945223 0.326426i \(-0.105844\pi\)
−0.755305 + 0.655374i \(0.772511\pi\)
\(458\) −1631.79 + 2826.34i −0.166481 + 0.288354i
\(459\) 586.963 1016.65i 0.0596887 0.103384i
\(460\) 4201.31 + 7276.89i 0.425842 + 0.737580i
\(461\) −9714.00 −0.981401 −0.490701 0.871328i \(-0.663259\pi\)
−0.490701 + 0.871328i \(0.663259\pi\)
\(462\) 1958.32 + 3607.42i 0.197206 + 0.363274i
\(463\) −43.2780 −0.00434406 −0.00217203 0.999998i \(-0.500691\pi\)
−0.00217203 + 0.999998i \(0.500691\pi\)
\(464\) 6574.79 + 11387.9i 0.657817 + 1.13937i
\(465\) 534.254 925.355i 0.0532805 0.0922845i
\(466\) −7504.38 + 12998.0i −0.745995 + 1.29210i
\(467\) 766.618 + 1327.82i 0.0759633 + 0.131572i 0.901505 0.432769i \(-0.142463\pi\)
−0.825541 + 0.564341i \(0.809130\pi\)
\(468\) 7022.87 0.693659
\(469\) 1750.54 + 3224.66i 0.172350 + 0.317486i
\(470\) −18319.6 −1.79791
\(471\) −2795.49 4841.93i −0.273480 0.473682i
\(472\) −16970.8 + 29394.3i −1.65497 + 2.86649i
\(473\) −1697.09 + 2939.45i −0.164974 + 0.285743i
\(474\) 3484.74 + 6035.74i 0.337678 + 0.584875i
\(475\) 10256.3 0.990722
\(476\) −16242.5 426.538i −1.56402 0.0410721i
\(477\) −2590.55 −0.248665
\(478\) 9110.23 + 15779.4i 0.871741 + 1.50990i
\(479\) 3517.69 6092.81i 0.335547 0.581185i −0.648042 0.761604i \(-0.724412\pi\)
0.983590 + 0.180419i \(0.0577454\pi\)
\(480\) 3733.15 6466.00i 0.354988 0.614857i
\(481\) −3649.21 6320.62i −0.345924 0.599159i
\(482\) −13993.3 −1.32236
\(483\) 2174.00 3547.05i 0.204804 0.334154i
\(484\) −22948.6 −2.15520
\(485\) −220.441 381.815i −0.0206386 0.0357471i
\(486\) 644.958 1117.10i 0.0601973 0.104265i
\(487\) 7685.64 13311.9i 0.715132 1.23865i −0.247776 0.968817i \(-0.579700\pi\)
0.962908 0.269828i \(-0.0869669\pi\)
\(488\) 12393.5 + 21466.1i 1.14964 + 1.99124i
\(489\) −6963.41 −0.643960
\(490\) 10111.9 + 531.458i 0.932266 + 0.0489976i
\(491\) −2393.35 −0.219980 −0.109990 0.993933i \(-0.535082\pi\)
−0.109990 + 0.993933i \(0.535082\pi\)
\(492\) −750.388 1299.71i −0.0687604 0.119096i
\(493\) 1573.04 2724.58i 0.143704 0.248903i
\(494\) 11190.7 19382.8i 1.01921 1.76533i
\(495\) 348.300 + 603.274i 0.0316261 + 0.0547781i
\(496\) 11638.4 1.05359
\(497\) 7601.40 12402.3i 0.686055 1.11935i
\(498\) −3841.74 −0.345688
\(499\) −346.760 600.606i −0.0311084 0.0538814i 0.850052 0.526699i \(-0.176570\pi\)
−0.881160 + 0.472817i \(0.843237\pi\)
\(500\) 12291.8 21290.1i 1.09941 1.90424i
\(501\) 4817.43 8344.03i 0.429594 0.744079i
\(502\) −5461.10 9458.91i −0.485540 0.840979i
\(503\) −8646.95 −0.766498 −0.383249 0.923645i \(-0.625195\pi\)
−0.383249 + 0.923645i \(0.625195\pi\)
\(504\) −10771.4 282.863i −0.951973 0.0249994i
\(505\) 6423.27 0.566003
\(506\) −2765.89 4790.67i −0.243002 0.420892i
\(507\) −1052.24 + 1822.53i −0.0921729 + 0.159648i
\(508\) −1773.80 + 3072.31i −0.154920 + 0.268330i
\(509\) 7750.44 + 13424.1i 0.674916 + 1.16899i 0.976494 + 0.215546i \(0.0691533\pi\)
−0.301578 + 0.953441i \(0.597513\pi\)
\(510\) −3850.68 −0.334335
\(511\) −2925.92 5389.84i −0.253298 0.466600i
\(512\) −12656.9 −1.09250
\(513\) −1471.87 2549.36i −0.126676 0.219409i
\(514\) −5706.96 + 9884.75i −0.489734 + 0.848245i
\(515\) 4017.72 6958.89i 0.343771 0.595428i
\(516\) −7381.55 12785.2i −0.629757 1.09077i
\(517\) 8636.41 0.734678
\(518\) 8851.97 + 16306.2i 0.750836 + 1.38311i
\(519\) −642.831 −0.0543683
\(520\) −6951.50 12040.4i −0.586238 1.01539i
\(521\) −432.354 + 748.858i −0.0363565 + 0.0629714i −0.883631 0.468184i \(-0.844909\pi\)
0.847275 + 0.531155i \(0.178242\pi\)
\(522\) 1728.46 2993.78i 0.144928 0.251023i
\(523\) 3127.81 + 5417.52i 0.261509 + 0.452947i 0.966643 0.256127i \(-0.0824465\pi\)
−0.705134 + 0.709074i \(0.749113\pi\)
\(524\) 22719.0 1.89406
\(525\) −5224.85 137.208i −0.434345 0.0114062i
\(526\) −24365.9 −2.01978
\(527\) −1392.26 2411.46i −0.115081 0.199326i
\(528\) −3793.75 + 6570.97i −0.312693 + 0.541600i
\(529\) 3280.15 5681.39i 0.269594 0.466951i
\(530\) 4248.72 + 7359.01i 0.348213 + 0.603122i
\(531\) 4725.46 0.386191
\(532\) −21291.2 + 34738.2i −1.73513 + 2.83100i
\(533\) −958.762 −0.0779148
\(534\) 12624.8 + 21866.8i 1.02309 + 1.77204i
\(535\) −2755.56 + 4772.78i −0.222679 + 0.385692i
\(536\) −6403.56 + 11091.3i −0.516029 + 0.893789i
\(537\) −3655.83 6332.09i −0.293782 0.508845i
\(538\) −2013.85 −0.161381
\(539\) −4767.08 250.546i −0.380951 0.0200218i
\(540\) −3029.88 −0.241454
\(541\) −71.9353 124.596i −0.00571671 0.00990164i 0.863153 0.504943i \(-0.168486\pi\)
−0.868870 + 0.495041i \(0.835153\pi\)
\(542\) 14249.7 24681.2i 1.12929 1.95599i
\(543\) −372.946 + 645.962i −0.0294745 + 0.0510514i
\(544\) −9728.53 16850.3i −0.766741 1.32804i
\(545\) 10862.4 0.853747
\(546\) −5960.13 + 9724.41i −0.467161 + 0.762210i
\(547\) 5455.65 0.426448 0.213224 0.977003i \(-0.431604\pi\)
0.213224 + 0.977003i \(0.431604\pi\)
\(548\) −18853.3 32654.9i −1.46966 2.54552i
\(549\) 1725.46 2988.58i 0.134136 0.232331i
\(550\) −3474.86 + 6018.63i −0.269397 + 0.466610i
\(551\) −3944.56 6832.18i −0.304980 0.528241i
\(552\) 14521.3 1.11969
\(553\) −8102.54 212.778i −0.623065 0.0163621i
\(554\) −25382.2 −1.94654
\(555\) 1574.38 + 2726.91i 0.120412 + 0.208560i
\(556\) 28422.7 49229.5i 2.16797 3.75503i
\(557\) −12404.9 + 21486.0i −0.943652 + 1.63445i −0.185223 + 0.982696i \(0.559301\pi\)
−0.758428 + 0.651756i \(0.774032\pi\)
\(558\) −1529.82 2649.72i −0.116062 0.201025i
\(559\) −9431.33 −0.713600
\(560\) 8930.06 + 16450.1i 0.673864 + 1.24132i
\(561\) 1815.33 0.136619
\(562\) 5511.51 + 9546.22i 0.413682 + 0.716517i
\(563\) −8184.91 + 14176.7i −0.612705 + 1.06124i 0.378077 + 0.925774i \(0.376585\pi\)
−0.990782 + 0.135462i \(0.956748\pi\)
\(564\) −18782.1 + 32531.6i −1.40225 + 2.42877i
\(565\) −1871.08 3240.81i −0.139322 0.241313i
\(566\) 13576.6 1.00824
\(567\) 715.707 + 1318.40i 0.0530104 + 0.0976503i
\(568\) 50773.7 3.75074
\(569\) 9225.29 + 15978.7i 0.679691 + 1.17726i 0.975074 + 0.221881i \(0.0712195\pi\)
−0.295383 + 0.955379i \(0.595447\pi\)
\(570\) −4828.00 + 8362.34i −0.354777 + 0.614491i
\(571\) 3554.34 6156.30i 0.260499 0.451197i −0.705876 0.708335i \(-0.749446\pi\)
0.966374 + 0.257139i \(0.0827797\pi\)
\(572\) 5429.99 + 9405.02i 0.396922 + 0.687489i
\(573\) 12939.2 0.943358
\(574\) 2436.52 + 63.9844i 0.177175 + 0.00465271i
\(575\) 7043.82 0.510865
\(576\) −4147.57 7183.80i −0.300026 0.519661i
\(577\) −3797.09 + 6576.75i −0.273960 + 0.474512i −0.969872 0.243615i \(-0.921667\pi\)
0.695912 + 0.718127i \(0.255000\pi\)
\(578\) 8022.42 13895.2i 0.577316 0.999940i
\(579\) 3091.28 + 5354.25i 0.221881 + 0.384309i
\(580\) −8119.96 −0.581315
\(581\) 2334.73 3809.30i 0.166714 0.272007i
\(582\) −1262.45 −0.0899146
\(583\) −2002.98 3469.26i −0.142290 0.246453i
\(584\) 10703.2 18538.5i 0.758392 1.31357i
\(585\) −967.811 + 1676.30i −0.0684001 + 0.118472i
\(586\) −1486.45 2574.61i −0.104786 0.181495i
\(587\) −1763.34 −0.123988 −0.0619939 0.998077i \(-0.519746\pi\)
−0.0619939 + 0.998077i \(0.519746\pi\)
\(588\) 11311.0 17411.8i 0.793297 1.22117i
\(589\) −6982.47 −0.488468
\(590\) −7750.16 13423.7i −0.540795 0.936684i
\(591\) −2499.13 + 4328.62i −0.173943 + 0.301279i
\(592\) −17148.4 + 29702.0i −1.19054 + 2.06207i
\(593\) 6158.07 + 10666.1i 0.426445 + 0.738624i 0.996554 0.0829448i \(-0.0264325\pi\)
−0.570109 + 0.821569i \(0.693099\pi\)
\(594\) 1994.69 0.137783
\(595\) 2340.16 3818.16i 0.161239 0.263075i
\(596\) 36327.0 2.49666
\(597\) −1631.30 2825.49i −0.111834 0.193702i
\(598\) 7685.50 13311.7i 0.525558 0.910293i
\(599\) 4451.70 7710.57i 0.303659 0.525952i −0.673303 0.739367i \(-0.735125\pi\)
0.976962 + 0.213414i \(0.0684584\pi\)
\(600\) −9121.72 15799.3i −0.620655 1.07501i
\(601\) −19157.1 −1.30022 −0.650112 0.759838i \(-0.725278\pi\)
−0.650112 + 0.759838i \(0.725278\pi\)
\(602\) 23968.0 + 629.413i 1.62269 + 0.0426129i
\(603\) 1783.05 0.120417
\(604\) 4570.15 + 7915.74i 0.307876 + 0.533256i
\(605\) 3162.51 5477.62i 0.212519 0.368094i
\(606\) 9196.41 15928.6i 0.616466 1.06775i
\(607\) 3784.96 + 6555.75i 0.253092 + 0.438369i 0.964376 0.264537i \(-0.0852191\pi\)
−0.711283 + 0.702905i \(0.751886\pi\)
\(608\) −48790.7 −3.25448
\(609\) 1918.07 + 3533.27i 0.127625 + 0.235099i
\(610\) −11319.6 −0.751340
\(611\) 11998.9 + 20782.6i 0.794471 + 1.37606i
\(612\) −3947.91 + 6837.99i −0.260760 + 0.451649i
\(613\) −1453.56 + 2517.65i −0.0957730 + 0.165884i −0.909931 0.414760i \(-0.863866\pi\)
0.814158 + 0.580643i \(0.197199\pi\)
\(614\) −9695.65 16793.4i −0.637272 1.10379i
\(615\) 413.640 0.0271212
\(616\) −7949.47 14643.7i −0.519956 0.957811i
\(617\) −12510.9 −0.816320 −0.408160 0.912910i \(-0.633829\pi\)
−0.408160 + 0.912910i \(0.633829\pi\)
\(618\) −11504.6 19926.6i −0.748840 1.29703i
\(619\) −5032.78 + 8717.03i −0.326792 + 0.566021i −0.981873 0.189538i \(-0.939301\pi\)
0.655081 + 0.755558i \(0.272634\pi\)
\(620\) −3593.39 + 6223.93i −0.232764 + 0.403160i
\(621\) −1010.85 1750.84i −0.0653205 0.113138i
\(622\) 18538.0 1.19503
\(623\) −29354.6 770.869i −1.88775 0.0495734i
\(624\) −21083.2 −1.35257
\(625\) −2491.59 4315.56i −0.159462 0.276196i
\(626\) −23123.2 + 40050.5i −1.47634 + 2.55709i
\(627\) 2276.07 3942.27i 0.144972 0.251099i
\(628\) 18802.4 + 32566.8i 1.19474 + 2.06936i
\(629\) 8205.63 0.520159
\(630\) 2571.38 4195.41i 0.162613 0.265316i
\(631\) −25146.6 −1.58648 −0.793242 0.608907i \(-0.791608\pi\)
−0.793242 + 0.608907i \(0.791608\pi\)
\(632\) −14145.7 24501.1i −0.890325 1.54209i
\(633\) −7014.71 + 12149.8i −0.440458 + 0.762895i
\(634\) −5149.92 + 8919.92i −0.322602 + 0.558762i
\(635\) −488.889 846.781i −0.0305527 0.0529189i
\(636\) 17424.0 1.08633
\(637\) −6020.16 11819.6i −0.374454 0.735179i
\(638\) 5345.70 0.331721
\(639\) −3534.44 6121.83i −0.218811 0.378992i
\(640\) −3649.66 + 6321.41i −0.225415 + 0.390430i
\(641\) 14479.5 25079.1i 0.892206 1.54535i 0.0549809 0.998487i \(-0.482490\pi\)
0.837225 0.546859i \(-0.184176\pi\)
\(642\) 7890.46 + 13666.7i 0.485065 + 0.840157i
\(643\) 7341.90 0.450290 0.225145 0.974325i \(-0.427714\pi\)
0.225145 + 0.974325i \(0.427714\pi\)
\(644\) −14622.3 + 23857.5i −0.894721 + 1.45981i
\(645\) 4068.97 0.248396
\(646\) 12581.7 + 21792.1i 0.766285 + 1.32725i
\(647\) −3035.99 + 5258.49i −0.184478 + 0.319525i −0.943400 0.331656i \(-0.892393\pi\)
0.758923 + 0.651181i \(0.225726\pi\)
\(648\) −2618.10 + 4534.67i −0.158717 + 0.274906i
\(649\) 3653.67 + 6328.34i 0.220985 + 0.382756i
\(650\) −19311.0 −1.16529
\(651\) 3557.06 + 93.4105i 0.214151 + 0.00562373i
\(652\) 46835.9 2.81324
\(653\) −13131.1 22743.7i −0.786920 1.36298i −0.927846 0.372965i \(-0.878341\pi\)
0.140926 0.990020i \(-0.454992\pi\)
\(654\) 15552.0 26936.9i 0.929864 1.61057i
\(655\) −3130.88 + 5422.84i −0.186769 + 0.323493i
\(656\) 2252.72 + 3901.82i 0.134076 + 0.232226i
\(657\) −2980.27 −0.176973
\(658\) −29105.9 53615.9i −1.72442 3.17655i
\(659\) 26130.1 1.54459 0.772296 0.635263i \(-0.219108\pi\)
0.772296 + 0.635263i \(0.219108\pi\)
\(660\) −2342.67 4057.62i −0.138164 0.239307i
\(661\) 5962.75 10327.8i 0.350868 0.607722i −0.635533 0.772073i \(-0.719220\pi\)
0.986402 + 0.164351i \(0.0525531\pi\)
\(662\) 15212.3 26348.4i 0.893114 1.54692i
\(663\) 2522.10 + 4368.41i 0.147738 + 0.255890i
\(664\) 15594.9 0.911444
\(665\) −5357.61 9869.25i −0.312420 0.575509i
\(666\) 9016.38 0.524591
\(667\) −2709.04 4692.19i −0.157263 0.272387i
\(668\) −32402.0 + 56121.9i −1.87675 + 3.25063i
\(669\) 4869.04 8433.43i 0.281387 0.487377i
\(670\) −2924.35 5065.13i −0.168623 0.292064i
\(671\) 5336.42 0.307019
\(672\) 24855.3 + 652.715i 1.42681 + 0.0374688i
\(673\) −6359.85 −0.364271 −0.182135 0.983273i \(-0.558301\pi\)
−0.182135 + 0.983273i \(0.558301\pi\)
\(674\) −6379.89 11050.3i −0.364606 0.631516i
\(675\) −1269.96 + 2199.63i −0.0724158 + 0.125428i
\(676\) 7077.36 12258.4i 0.402672 0.697449i
\(677\) −4280.81 7414.57i −0.243020 0.420924i 0.718553 0.695472i \(-0.244805\pi\)
−0.961573 + 0.274549i \(0.911472\pi\)
\(678\) −10715.6 −0.606975
\(679\) 767.226 1251.79i 0.0433629 0.0707500i
\(680\) 15631.2 0.881513
\(681\) 7707.24 + 13349.3i 0.433689 + 0.751171i
\(682\) 2365.67 4097.46i 0.132824 0.230059i
\(683\) 3352.94 5807.47i 0.187843 0.325354i −0.756688 0.653776i \(-0.773184\pi\)
0.944531 + 0.328423i \(0.106517\pi\)
\(684\) 9899.82 + 17147.0i 0.553405 + 0.958526i
\(685\) 10392.6 0.579679
\(686\) 14510.3 + 30439.0i 0.807589 + 1.69412i
\(687\) −1844.42 −0.102429
\(688\) 22160.0 + 38382.2i 1.22797 + 2.12690i
\(689\) 5565.62 9639.94i 0.307741 0.533022i
\(690\) −3315.76 + 5743.07i −0.182941 + 0.316862i
\(691\) 12665.3 + 21937.0i 0.697267 + 1.20770i 0.969410 + 0.245445i \(0.0789342\pi\)
−0.272143 + 0.962257i \(0.587732\pi\)
\(692\) 4323.68 0.237517
\(693\) −1212.23 + 1977.85i −0.0664485 + 0.108416i
\(694\) −17710.8 −0.968723
\(695\) 7833.77 + 13568.5i 0.427557 + 0.740550i
\(696\) −7016.39 + 12152.7i −0.382120 + 0.661851i
\(697\) 538.969 933.522i 0.0292897 0.0507312i
\(698\) 6435.08 + 11145.9i 0.348956 + 0.604410i
\(699\) −8482.25 −0.458981
\(700\) 35142.3 + 922.859i 1.89751 + 0.0498297i
\(701\) −27184.1 −1.46467 −0.732333 0.680947i \(-0.761568\pi\)
−0.732333 + 0.680947i \(0.761568\pi\)
\(702\) 2771.30 + 4800.03i 0.148997 + 0.258070i
\(703\) 10288.3 17819.8i 0.551961 0.956025i
\(704\) 6413.69 11108.8i 0.343360 0.594716i
\(705\) −5176.68 8966.27i −0.276546 0.478992i
\(706\) −65839.5 −3.50977
\(707\) 10205.2 + 18799.0i 0.542867 + 1.00001i
\(708\) −31783.4 −1.68714
\(709\) −8072.75 13982.4i −0.427614 0.740649i 0.569047 0.822305i \(-0.307312\pi\)
−0.996661 + 0.0816561i \(0.973979\pi\)
\(710\) −11593.6 + 20080.7i −0.612816 + 1.06143i
\(711\) −1969.41 + 3411.12i −0.103880 + 0.179925i
\(712\) −51248.2 88764.5i −2.69748 4.67218i
\(713\) −4795.41 −0.251879
\(714\) −6117.92 11269.8i −0.320669 0.590703i
\(715\) −2993.20 −0.156558
\(716\) 24589.1 + 42589.6i 1.28343 + 2.22297i
\(717\) −5148.68 + 8917.77i −0.268174 + 0.464491i
\(718\) −3593.30 + 6223.77i −0.186770 + 0.323494i
\(719\) −8648.74 14980.0i −0.448600 0.776998i 0.549695 0.835365i \(-0.314744\pi\)
−0.998295 + 0.0583673i \(0.981411\pi\)
\(720\) 9095.92 0.470812
\(721\) 26749.9 + 702.470i 1.38172 + 0.0362848i
\(722\) 26690.4 1.37578
\(723\) −3954.17 6848.82i −0.203398 0.352296i
\(724\) 2508.44 4344.74i 0.128764 0.223026i
\(725\) −3403.43 + 5894.91i −0.174345 + 0.301975i
\(726\) −9055.74 15685.0i −0.462934 0.801825i
\(727\) 3514.71 0.179303 0.0896516 0.995973i \(-0.471425\pi\)
0.0896516 + 0.995973i \(0.471425\pi\)
\(728\) 24194.1 39474.6i 1.23172 2.00965i
\(729\) 729.000 0.0370370
\(730\) 4887.89 + 8466.08i 0.247821 + 0.429238i
\(731\) 5301.83 9183.04i 0.268256 0.464633i
\(732\) −11605.4 + 20101.2i −0.585996 + 1.01498i
\(733\) 13755.6 + 23825.4i 0.693144 + 1.20056i 0.970802 + 0.239881i \(0.0771083\pi\)
−0.277658 + 0.960680i \(0.589558\pi\)
\(734\) −7315.16 −0.367858
\(735\) 2597.28 + 5099.33i 0.130343 + 0.255907i
\(736\) −33508.4 −1.67817
\(737\) 1378.63 + 2387.86i 0.0689044 + 0.119346i
\(738\) 592.222 1025.76i 0.0295393 0.0511635i
\(739\) −8050.80 + 13944.4i −0.400749 + 0.694117i −0.993816 0.111035i \(-0.964583\pi\)
0.593068 + 0.805153i \(0.297917\pi\)
\(740\) −10589.3 18341.2i −0.526040 0.911129i
\(741\) 12648.9 0.627083
\(742\) −14787.3 + 24126.7i −0.731617 + 1.19369i
\(743\) 14682.4 0.724961 0.362480 0.931991i \(-0.381930\pi\)
0.362480 + 0.931991i \(0.381930\pi\)
\(744\) 6210.03 + 10756.1i 0.306009 + 0.530024i
\(745\) −5006.17 + 8670.93i −0.246190 + 0.426414i
\(746\) −14483.5 + 25086.1i −0.710828 + 1.23119i
\(747\) −1085.59 1880.29i −0.0531720 0.0920967i
\(748\) −12209.9 −0.596843
\(749\) −18346.5 481.791i −0.895016 0.0235037i
\(750\) 19401.9 0.944611
\(751\) 3636.53 + 6298.66i 0.176696 + 0.306047i 0.940747 0.339109i \(-0.110126\pi\)
−0.764051 + 0.645156i \(0.776792\pi\)
\(752\) 56385.3 97662.2i 2.73426 4.73587i
\(753\) 3086.36 5345.73i 0.149367 0.258711i
\(754\) 7426.96 + 12863.9i 0.358719 + 0.621319i
\(755\) −2519.23 −0.121436
\(756\) −4813.84 8867.57i −0.231584 0.426601i
\(757\) 8505.93 0.408393 0.204196 0.978930i \(-0.434542\pi\)
0.204196 + 0.978930i \(0.434542\pi\)
\(758\) −1472.19 2549.91i −0.0705440 0.122186i
\(759\) 1563.15 2707.46i 0.0747548 0.129479i
\(760\) 19598.4 33945.5i 0.935408 1.62017i
\(761\) −7108.86 12312.9i −0.338628 0.586521i 0.645547 0.763721i \(-0.276630\pi\)
−0.984175 + 0.177200i \(0.943296\pi\)
\(762\) −2799.84 −0.133107
\(763\) 17258.0 + 31790.9i 0.818848 + 1.50840i
\(764\) −87029.3 −4.12121
\(765\) −1088.11 1884.67i −0.0514259 0.0890722i
\(766\) −15555.1 + 26942.2i −0.733717 + 1.27084i
\(767\) −10152.3 + 17584.4i −0.477939 + 0.827815i
\(768\) −609.482 1055.65i −0.0286364 0.0495998i
\(769\) 16379.1 0.768068 0.384034 0.923319i \(-0.374534\pi\)
0.384034 + 0.923319i \(0.374534\pi\)
\(770\) 7606.66 + 199.756i 0.356006 + 0.00934895i
\(771\) −6450.62 −0.301314
\(772\) −20791.9 36012.6i −0.969323 1.67892i
\(773\) 19948.3 34551.6i 0.928192 1.60768i 0.141846 0.989889i \(-0.454696\pi\)
0.786346 0.617787i \(-0.211970\pi\)
\(774\) 5825.67 10090.4i 0.270542 0.468593i
\(775\) 3012.29 + 5217.45i 0.139619 + 0.241827i
\(776\) 5124.70 0.237070
\(777\) −5479.50 + 8940.23i −0.252994 + 0.412779i
\(778\) 41292.5 1.90284
\(779\) −1351.52 2340.91i −0.0621609