Properties

Label 169.4.e.b.23.1
Level $169$
Weight $4$
Character 169.23
Analytic conductor $9.971$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.4.e.b.147.1

$q$-expansion

\(f(q)\) \(=\) \(q+(3.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +13.8564i q^{5} +(21.0000 + 12.1244i) q^{6} +(-19.5000 - 11.2583i) q^{7} +13.8564i q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})\) \(q+(3.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +13.8564i q^{5} +(21.0000 + 12.1244i) q^{6} +(-19.5000 - 11.2583i) q^{7} +13.8564i q^{8} +(-11.0000 + 19.0526i) q^{9} +(24.0000 + 41.5692i) q^{10} +(19.5000 - 11.2583i) q^{11} +28.0000 q^{12} -78.0000 q^{14} +(-84.0000 + 48.4974i) q^{15} +(40.0000 + 69.2820i) q^{16} +(-13.5000 + 23.3827i) q^{17} +76.2102i q^{18} +(76.5000 + 44.1673i) q^{19} +(48.0000 + 27.7128i) q^{20} -157.617i q^{21} +(39.0000 - 67.5500i) q^{22} +(-28.5000 - 49.3634i) q^{23} +(-84.0000 + 48.4974i) q^{24} -67.0000 q^{25} +35.0000 q^{27} +(-78.0000 + 45.0333i) q^{28} +(34.5000 + 59.7558i) q^{29} +(-168.000 + 290.985i) q^{30} -72.7461i q^{31} +(144.000 + 83.1384i) q^{32} +(136.500 + 78.8083i) q^{33} +93.5307i q^{34} +(156.000 - 270.200i) q^{35} +(44.0000 + 76.2102i) q^{36} +(34.5000 - 19.9186i) q^{37} +306.000 q^{38} -192.000 q^{40} +(340.500 - 196.588i) q^{41} +(-273.000 - 472.850i) q^{42} +(42.5000 - 73.6122i) q^{43} -90.0666i q^{44} +(-264.000 - 152.420i) q^{45} +(-171.000 - 98.7269i) q^{46} -342.946i q^{47} +(-280.000 + 484.974i) q^{48} +(82.0000 + 142.028i) q^{49} +(-201.000 + 116.047i) q^{50} -189.000 q^{51} +426.000 q^{53} +(105.000 - 60.6218i) q^{54} +(156.000 + 270.200i) q^{55} +(156.000 - 270.200i) q^{56} +618.342i q^{57} +(207.000 + 119.512i) q^{58} +(16.5000 + 9.52628i) q^{59} +387.979i q^{60} +(8.50000 - 14.7224i) q^{61} +(-126.000 - 218.238i) q^{62} +(429.000 - 247.683i) q^{63} -64.0000 q^{64} +546.000 q^{66} +(-142.500 + 82.2724i) q^{67} +(54.0000 + 93.5307i) q^{68} +(199.500 - 345.544i) q^{69} -1080.80i q^{70} +(-505.500 - 291.851i) q^{71} +(-264.000 - 152.420i) q^{72} +1004.59i q^{73} +(69.0000 - 119.512i) q^{74} +(-234.500 - 406.166i) q^{75} +(306.000 - 176.669i) q^{76} -507.000 q^{77} -1244.00 q^{79} +(-960.000 + 554.256i) q^{80} +(419.500 + 726.595i) q^{81} +(681.000 - 1179.53i) q^{82} -426.084i q^{83} +(-546.000 - 315.233i) q^{84} +(-324.000 - 187.061i) q^{85} -294.449i q^{86} +(-241.500 + 418.290i) q^{87} +(156.000 + 270.200i) q^{88} +(-265.500 + 153.286i) q^{89} -1056.00 q^{90} -228.000 q^{92} +(441.000 - 254.611i) q^{93} +(-594.000 - 1028.84i) q^{94} +(-612.000 + 1060.02i) q^{95} +1163.94i q^{96} +(-1069.50 - 617.476i) q^{97} +(492.000 + 284.056i) q^{98} +495.367i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{2} + 7 q^{3} + 4 q^{4} + 42 q^{6} - 39 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{2} + 7 q^{3} + 4 q^{4} + 42 q^{6} - 39 q^{7} - 22 q^{9} + 48 q^{10} + 39 q^{11} + 56 q^{12} - 156 q^{14} - 168 q^{15} + 80 q^{16} - 27 q^{17} + 153 q^{19} + 96 q^{20} + 78 q^{22} - 57 q^{23} - 168 q^{24} - 134 q^{25} + 70 q^{27} - 156 q^{28} + 69 q^{29} - 336 q^{30} + 288 q^{32} + 273 q^{33} + 312 q^{35} + 88 q^{36} + 69 q^{37} + 612 q^{38} - 384 q^{40} + 681 q^{41} - 546 q^{42} + 85 q^{43} - 528 q^{45} - 342 q^{46} - 560 q^{48} + 164 q^{49} - 402 q^{50} - 378 q^{51} + 852 q^{53} + 210 q^{54} + 312 q^{55} + 312 q^{56} + 414 q^{58} + 33 q^{59} + 17 q^{61} - 252 q^{62} + 858 q^{63} - 128 q^{64} + 1092 q^{66} - 285 q^{67} + 108 q^{68} + 399 q^{69} - 1011 q^{71} - 528 q^{72} + 138 q^{74} - 469 q^{75} + 612 q^{76} - 1014 q^{77} - 2488 q^{79} - 1920 q^{80} + 839 q^{81} + 1362 q^{82} - 1092 q^{84} - 648 q^{85} - 483 q^{87} + 312 q^{88} - 531 q^{89} - 2112 q^{90} - 456 q^{92} + 882 q^{93} - 1188 q^{94} - 1224 q^{95} - 2139 q^{97} + 984 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000 1.73205i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 3.50000 + 6.06218i 0.673575 + 1.16667i 0.976883 + 0.213774i \(0.0685756\pi\)
−0.303308 + 0.952893i \(0.598091\pi\)
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 13.8564i 1.23935i 0.784857 + 0.619677i \(0.212737\pi\)
−0.784857 + 0.619677i \(0.787263\pi\)
\(6\) 21.0000 + 12.1244i 1.42887 + 0.824958i
\(7\) −19.5000 11.2583i −1.05290 0.607893i −0.129441 0.991587i \(-0.541318\pi\)
−0.923460 + 0.383694i \(0.874652\pi\)
\(8\) 13.8564i 0.612372i
\(9\) −11.0000 + 19.0526i −0.407407 + 0.705650i
\(10\) 24.0000 + 41.5692i 0.758947 + 1.31453i
\(11\) 19.5000 11.2583i 0.534497 0.308592i −0.208349 0.978055i \(-0.566809\pi\)
0.742846 + 0.669462i \(0.233475\pi\)
\(12\) 28.0000 0.673575
\(13\) 0 0
\(14\) −78.0000 −1.48903
\(15\) −84.0000 + 48.4974i −1.44591 + 0.834799i
\(16\) 40.0000 + 69.2820i 0.625000 + 1.08253i
\(17\) −13.5000 + 23.3827i −0.192602 + 0.333596i −0.946112 0.323840i \(-0.895026\pi\)
0.753510 + 0.657437i \(0.228359\pi\)
\(18\) 76.2102i 0.997940i
\(19\) 76.5000 + 44.1673i 0.923700 + 0.533299i 0.884814 0.465945i \(-0.154286\pi\)
0.0388865 + 0.999244i \(0.487619\pi\)
\(20\) 48.0000 + 27.7128i 0.536656 + 0.309839i
\(21\) 157.617i 1.63785i
\(22\) 39.0000 67.5500i 0.377947 0.654623i
\(23\) −28.5000 49.3634i −0.258377 0.447521i 0.707431 0.706783i \(-0.249854\pi\)
−0.965807 + 0.259261i \(0.916521\pi\)
\(24\) −84.0000 + 48.4974i −0.714435 + 0.412479i
\(25\) −67.0000 −0.536000
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) −78.0000 + 45.0333i −0.526451 + 0.303946i
\(29\) 34.5000 + 59.7558i 0.220913 + 0.382633i 0.955086 0.296330i \(-0.0957628\pi\)
−0.734172 + 0.678963i \(0.762430\pi\)
\(30\) −168.000 + 290.985i −1.02242 + 1.77088i
\(31\) 72.7461i 0.421471i −0.977543 0.210735i \(-0.932414\pi\)
0.977543 0.210735i \(-0.0675858\pi\)
\(32\) 144.000 + 83.1384i 0.795495 + 0.459279i
\(33\) 136.500 + 78.8083i 0.720048 + 0.415720i
\(34\) 93.5307i 0.471776i
\(35\) 156.000 270.200i 0.753395 1.30492i
\(36\) 44.0000 + 76.2102i 0.203704 + 0.352825i
\(37\) 34.5000 19.9186i 0.153291 0.0885026i −0.421393 0.906878i \(-0.638459\pi\)
0.574683 + 0.818376i \(0.305125\pi\)
\(38\) 306.000 1.30631
\(39\) 0 0
\(40\) −192.000 −0.758947
\(41\) 340.500 196.588i 1.29700 0.748826i 0.317118 0.948386i \(-0.397285\pi\)
0.979886 + 0.199560i \(0.0639514\pi\)
\(42\) −273.000 472.850i −1.00297 1.73720i
\(43\) 42.5000 73.6122i 0.150725 0.261064i −0.780769 0.624820i \(-0.785172\pi\)
0.931494 + 0.363756i \(0.118506\pi\)
\(44\) 90.0666i 0.308592i
\(45\) −264.000 152.420i −0.874551 0.504922i
\(46\) −171.000 98.7269i −0.548099 0.316445i
\(47\) 342.946i 1.06434i −0.846639 0.532168i \(-0.821377\pi\)
0.846639 0.532168i \(-0.178623\pi\)
\(48\) −280.000 + 484.974i −0.841969 + 1.45833i
\(49\) 82.0000 + 142.028i 0.239067 + 0.414076i
\(50\) −201.000 + 116.047i −0.568514 + 0.328232i
\(51\) −189.000 −0.518927
\(52\) 0 0
\(53\) 426.000 1.10407 0.552034 0.833822i \(-0.313852\pi\)
0.552034 + 0.833822i \(0.313852\pi\)
\(54\) 105.000 60.6218i 0.264605 0.152770i
\(55\) 156.000 + 270.200i 0.382455 + 0.662432i
\(56\) 156.000 270.200i 0.372257 0.644768i
\(57\) 618.342i 1.43687i
\(58\) 207.000 + 119.512i 0.468628 + 0.270563i
\(59\) 16.5000 + 9.52628i 0.0364088 + 0.0210206i 0.518094 0.855324i \(-0.326642\pi\)
−0.481685 + 0.876344i \(0.659975\pi\)
\(60\) 387.979i 0.834799i
\(61\) 8.50000 14.7224i 0.0178412 0.0309019i −0.856967 0.515371i \(-0.827654\pi\)
0.874808 + 0.484469i \(0.160987\pi\)
\(62\) −126.000 218.238i −0.258097 0.447037i
\(63\) 429.000 247.683i 0.857919 0.495320i
\(64\) −64.0000 −0.125000
\(65\) 0 0
\(66\) 546.000 1.01830
\(67\) −142.500 + 82.2724i −0.259838 + 0.150018i −0.624261 0.781216i \(-0.714600\pi\)
0.364423 + 0.931234i \(0.381266\pi\)
\(68\) 54.0000 + 93.5307i 0.0963009 + 0.166798i
\(69\) 199.500 345.544i 0.348072 0.602879i
\(70\) 1080.80i 1.84543i
\(71\) −505.500 291.851i −0.844955 0.487835i 0.0139904 0.999902i \(-0.495547\pi\)
−0.858945 + 0.512067i \(0.828880\pi\)
\(72\) −264.000 152.420i −0.432121 0.249485i
\(73\) 1004.59i 1.61066i 0.592826 + 0.805331i \(0.298012\pi\)
−0.592826 + 0.805331i \(0.701988\pi\)
\(74\) 69.0000 119.512i 0.108393 0.187742i
\(75\) −234.500 406.166i −0.361036 0.625333i
\(76\) 306.000 176.669i 0.461850 0.266649i
\(77\) −507.000 −0.750364
\(78\) 0 0
\(79\) −1244.00 −1.77166 −0.885829 0.464012i \(-0.846409\pi\)
−0.885829 + 0.464012i \(0.846409\pi\)
\(80\) −960.000 + 554.256i −1.34164 + 0.774597i
\(81\) 419.500 + 726.595i 0.575446 + 0.996701i
\(82\) 681.000 1179.53i 0.917120 1.58850i
\(83\) 426.084i 0.563480i −0.959491 0.281740i \(-0.909088\pi\)
0.959491 0.281740i \(-0.0909116\pi\)
\(84\) −546.000 315.233i −0.709208 0.409462i
\(85\) −324.000 187.061i −0.413444 0.238702i
\(86\) 294.449i 0.369200i
\(87\) −241.500 + 418.290i −0.297604 + 0.515465i
\(88\) 156.000 + 270.200i 0.188973 + 0.327311i
\(89\) −265.500 + 153.286i −0.316213 + 0.182566i −0.649703 0.760188i \(-0.725107\pi\)
0.333490 + 0.942753i \(0.391774\pi\)
\(90\) −1056.00 −1.23680
\(91\) 0 0
\(92\) −228.000 −0.258377
\(93\) 441.000 254.611i 0.491716 0.283892i
\(94\) −594.000 1028.84i −0.651770 1.12890i
\(95\) −612.000 + 1060.02i −0.660946 + 1.14479i
\(96\) 1163.94i 1.23744i
\(97\) −1069.50 617.476i −1.11950 0.646342i −0.178225 0.983990i \(-0.557035\pi\)
−0.941273 + 0.337647i \(0.890369\pi\)
\(98\) 492.000 + 284.056i 0.507138 + 0.292796i
\(99\) 495.367i 0.502891i
\(100\) −134.000 + 232.095i −0.134000 + 0.232095i
\(101\) −979.500 1696.54i −0.964989 1.67141i −0.709645 0.704560i \(-0.751144\pi\)
−0.255345 0.966850i \(-0.582189\pi\)
\(102\) −567.000 + 327.358i −0.550406 + 0.317777i
\(103\) 1856.00 1.77551 0.887753 0.460320i \(-0.152265\pi\)
0.887753 + 0.460320i \(0.152265\pi\)
\(104\) 0 0
\(105\) 2184.00 2.02987
\(106\) 1278.00 737.854i 1.17104 0.676101i
\(107\) 127.500 + 220.836i 0.115195 + 0.199524i 0.917858 0.396909i \(-0.129917\pi\)
−0.802663 + 0.596433i \(0.796584\pi\)
\(108\) 70.0000 121.244i 0.0623681 0.108025i
\(109\) 609.682i 0.535752i −0.963453 0.267876i \(-0.913678\pi\)
0.963453 0.267876i \(-0.0863217\pi\)
\(110\) 936.000 + 540.400i 0.811310 + 0.468410i
\(111\) 241.500 + 139.430i 0.206506 + 0.119226i
\(112\) 1801.33i 1.51973i
\(113\) −205.500 + 355.936i −0.171078 + 0.296316i −0.938797 0.344471i \(-0.888058\pi\)
0.767719 + 0.640787i \(0.221392\pi\)
\(114\) 1071.00 + 1855.03i 0.879898 + 1.52403i
\(115\) 684.000 394.908i 0.554638 0.320220i
\(116\) 276.000 0.220913
\(117\) 0 0
\(118\) 66.0000 0.0514898
\(119\) 526.500 303.975i 0.405581 0.234162i
\(120\) −672.000 1163.94i −0.511208 0.885438i
\(121\) −412.000 + 713.605i −0.309542 + 0.536142i
\(122\) 58.8897i 0.0437018i
\(123\) 2383.50 + 1376.11i 1.74726 + 1.00878i
\(124\) −252.000 145.492i −0.182502 0.105368i
\(125\) 803.672i 0.575061i
\(126\) 858.000 1486.10i 0.606641 1.05073i
\(127\) 1121.50 + 1942.49i 0.783599 + 1.35723i 0.929833 + 0.367983i \(0.119951\pi\)
−0.146234 + 0.989250i \(0.546715\pi\)
\(128\) −1344.00 + 775.959i −0.928078 + 0.535826i
\(129\) 595.000 0.406099
\(130\) 0 0
\(131\) −372.000 −0.248105 −0.124053 0.992276i \(-0.539589\pi\)
−0.124053 + 0.992276i \(0.539589\pi\)
\(132\) 546.000 315.233i 0.360024 0.207860i
\(133\) −994.500 1722.52i −0.648377 1.12302i
\(134\) −285.000 + 493.634i −0.183733 + 0.318235i
\(135\) 484.974i 0.309185i
\(136\) −324.000 187.061i −0.204285 0.117944i
\(137\) 1030.50 + 594.959i 0.642639 + 0.371028i 0.785630 0.618696i \(-0.212339\pi\)
−0.142991 + 0.989724i \(0.545672\pi\)
\(138\) 1382.18i 0.852599i
\(139\) 1272.50 2204.03i 0.776490 1.34492i −0.157464 0.987525i \(-0.550332\pi\)
0.933953 0.357395i \(-0.116335\pi\)
\(140\) −624.000 1080.80i −0.376697 0.652459i
\(141\) 2079.00 1200.31i 1.24173 0.716911i
\(142\) −2022.00 −1.19495
\(143\) 0 0
\(144\) −1760.00 −1.01852
\(145\) −828.000 + 478.046i −0.474218 + 0.273790i
\(146\) 1740.00 + 3013.77i 0.986325 + 1.70836i
\(147\) −574.000 + 994.197i −0.322059 + 0.557823i
\(148\) 159.349i 0.0885026i
\(149\) −1129.50 652.117i −0.621022 0.358547i 0.156245 0.987718i \(-0.450061\pi\)
−0.777267 + 0.629171i \(0.783394\pi\)
\(150\) −1407.00 812.332i −0.765874 0.442177i
\(151\) 86.6025i 0.0466729i −0.999728 0.0233365i \(-0.992571\pi\)
0.999728 0.0233365i \(-0.00742890\pi\)
\(152\) −612.000 + 1060.02i −0.326577 + 0.565649i
\(153\) −297.000 514.419i −0.156935 0.271819i
\(154\) −1521.00 + 878.150i −0.795881 + 0.459502i
\(155\) 1008.00 0.522352
\(156\) 0 0
\(157\) −1534.00 −0.779787 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(158\) −3732.00 + 2154.67i −1.87913 + 1.08491i
\(159\) 1491.00 + 2582.49i 0.743673 + 1.28808i
\(160\) −1152.00 + 1995.32i −0.569210 + 0.985901i
\(161\) 1283.45i 0.628261i
\(162\) 2517.00 + 1453.19i 1.22070 + 0.704774i
\(163\) 1414.50 + 816.662i 0.679707 + 0.392429i 0.799745 0.600340i \(-0.204968\pi\)
−0.120038 + 0.992769i \(0.538302\pi\)
\(164\) 1572.70i 0.748826i
\(165\) −1092.00 + 1891.40i −0.515225 + 0.892395i
\(166\) −738.000 1278.25i −0.345060 0.597661i
\(167\) −1408.50 + 813.198i −0.652653 + 0.376809i −0.789472 0.613787i \(-0.789645\pi\)
0.136819 + 0.990596i \(0.456312\pi\)
\(168\) 2184.00 1.00297
\(169\) 0 0
\(170\) −1296.00 −0.584698
\(171\) −1683.00 + 971.681i −0.752645 + 0.434540i
\(172\) −170.000 294.449i −0.0753627 0.130532i
\(173\) 436.500 756.040i 0.191829 0.332258i −0.754027 0.656843i \(-0.771891\pi\)
0.945857 + 0.324585i \(0.105225\pi\)
\(174\) 1673.16i 0.728977i
\(175\) 1306.50 + 754.308i 0.564355 + 0.325830i
\(176\) 1560.00 + 900.666i 0.668122 + 0.385740i
\(177\) 133.368i 0.0566359i
\(178\) −531.000 + 919.719i −0.223596 + 0.387280i
\(179\) 643.500 + 1114.57i 0.268701 + 0.465403i 0.968527 0.248910i \(-0.0800724\pi\)
−0.699826 + 0.714314i \(0.746739\pi\)
\(180\) −1056.00 + 609.682i −0.437276 + 0.252461i
\(181\) 2.00000 0.000821319 0.000410660 1.00000i \(-0.499869\pi\)
0.000410660 1.00000i \(0.499869\pi\)
\(182\) 0 0
\(183\) 119.000 0.0480696
\(184\) 684.000 394.908i 0.274050 0.158223i
\(185\) 276.000 + 478.046i 0.109686 + 0.189982i
\(186\) 882.000 1527.67i 0.347696 0.602226i
\(187\) 607.950i 0.237742i
\(188\) −1188.00 685.892i −0.460871 0.266084i
\(189\) −682.500 394.042i −0.262670 0.151652i
\(190\) 4240.06i 1.61898i
\(191\) 1420.50 2460.38i 0.538135 0.932077i −0.460870 0.887468i \(-0.652462\pi\)
0.999005 0.0446092i \(-0.0142043\pi\)
\(192\) −224.000 387.979i −0.0841969 0.145833i
\(193\) 3676.50 2122.63i 1.37119 0.791659i 0.380115 0.924939i \(-0.375885\pi\)
0.991078 + 0.133281i \(0.0425512\pi\)
\(194\) −4278.00 −1.58321
\(195\) 0 0
\(196\) 656.000 0.239067
\(197\) −2383.50 + 1376.11i −0.862017 + 0.497686i −0.864687 0.502311i \(-0.832483\pi\)
0.00267023 + 0.999996i \(0.499150\pi\)
\(198\) 858.000 + 1486.10i 0.307957 + 0.533396i
\(199\) 842.500 1459.25i 0.300117 0.519818i −0.676045 0.736860i \(-0.736308\pi\)
0.976162 + 0.217042i \(0.0696410\pi\)
\(200\) 928.379i 0.328232i
\(201\) −997.500 575.907i −0.350041 0.202096i
\(202\) −5877.00 3393.09i −2.04705 1.18187i
\(203\) 1553.65i 0.537167i
\(204\) −378.000 + 654.715i −0.129732 + 0.224702i
\(205\) 2724.00 + 4718.11i 0.928061 + 1.60745i
\(206\) 5568.00 3214.69i 1.88321 1.08727i
\(207\) 1254.00 0.421058
\(208\) 0 0
\(209\) 1989.00 0.658287
\(210\) 6552.00 3782.80i 2.15300 1.24304i
\(211\) −840.500 1455.79i −0.274229 0.474979i 0.695711 0.718322i \(-0.255089\pi\)
−0.969940 + 0.243343i \(0.921756\pi\)
\(212\) 852.000 1475.71i 0.276017 0.478075i
\(213\) 4085.91i 1.31437i
\(214\) 765.000 + 441.673i 0.244366 + 0.141085i
\(215\) 1020.00 + 588.897i 0.323551 + 0.186802i
\(216\) 484.974i 0.152770i
\(217\) −819.000 + 1418.55i −0.256209 + 0.443767i
\(218\) −1056.00 1829.05i −0.328080 0.568250i
\(219\) −6090.00 + 3516.06i −1.87911 + 1.08490i
\(220\) 1248.00 0.382455
\(221\) 0 0
\(222\) 966.000 0.292044
\(223\) 3547.50 2048.15i 1.06528 0.615042i 0.138394 0.990377i \(-0.455806\pi\)
0.926889 + 0.375336i \(0.122473\pi\)
\(224\) −1872.00 3242.40i −0.558385 0.967151i
\(225\) 737.000 1276.52i 0.218370 0.378229i
\(226\) 1423.75i 0.419054i
\(227\) −379.500 219.104i −0.110962 0.0640638i 0.443492 0.896278i \(-0.353739\pi\)
−0.554454 + 0.832215i \(0.687073\pi\)
\(228\) 2142.00 + 1236.68i 0.622182 + 0.359217i
\(229\) 180.133i 0.0519805i 0.999662 + 0.0259903i \(0.00827389\pi\)
−0.999662 + 0.0259903i \(0.991726\pi\)
\(230\) 1368.00 2369.45i 0.392188 0.679290i
\(231\) −1774.50 3073.52i −0.505427 0.875424i
\(232\) −828.000 + 478.046i −0.234314 + 0.135281i
\(233\) −5778.00 −1.62459 −0.812295 0.583247i \(-0.801782\pi\)
−0.812295 + 0.583247i \(0.801782\pi\)
\(234\) 0 0
\(235\) 4752.00 1.31909
\(236\) 66.0000 38.1051i 0.0182044 0.0105103i
\(237\) −4354.00 7541.35i −1.19334 2.06693i
\(238\) 1053.00 1823.85i 0.286789 0.496734i
\(239\) 1860.22i 0.503464i −0.967797 0.251732i \(-0.919000\pi\)
0.967797 0.251732i \(-0.0810001\pi\)
\(240\) −6720.00 3879.79i −1.80739 1.04350i
\(241\) −1783.50 1029.70i −0.476703 0.275224i 0.242339 0.970192i \(-0.422085\pi\)
−0.719041 + 0.694967i \(0.755419\pi\)
\(242\) 2854.42i 0.758219i
\(243\) −2464.00 + 4267.77i −0.650476 + 1.12666i
\(244\) −34.0000 58.8897i −0.00892060 0.0154509i
\(245\) −1968.00 + 1136.23i −0.513187 + 0.296289i
\(246\) 9534.00 2.47100
\(247\) 0 0
\(248\) 1008.00 0.258097
\(249\) 2583.00 1491.30i 0.657393 0.379546i
\(250\) 1392.00 + 2411.01i 0.352151 + 0.609944i
\(251\) −2245.50 + 3889.32i −0.564680 + 0.978055i 0.432399 + 0.901682i \(0.357667\pi\)
−0.997079 + 0.0763724i \(0.975666\pi\)
\(252\) 1981.47i 0.495320i
\(253\) −1111.50 641.725i −0.276203 0.159466i
\(254\) 6729.00 + 3884.99i 1.66226 + 0.959708i
\(255\) 2618.86i 0.643135i
\(256\) −2432.00 + 4212.35i −0.593750 + 1.02841i
\(257\) −2725.50 4720.70i −0.661525 1.14580i −0.980215 0.197936i \(-0.936576\pi\)
0.318690 0.947859i \(-0.396757\pi\)
\(258\) 1785.00 1030.57i 0.430734 0.248684i
\(259\) −897.000 −0.215200
\(260\) 0 0
\(261\) −1518.00 −0.360007
\(262\) −1116.00 + 644.323i −0.263155 + 0.151933i
\(263\) 391.500 + 678.098i 0.0917906 + 0.158986i 0.908265 0.418396i \(-0.137408\pi\)
−0.816474 + 0.577382i \(0.804074\pi\)
\(264\) −1092.00 + 1891.40i −0.254576 + 0.440938i
\(265\) 5902.83i 1.36833i
\(266\) −5967.00 3445.05i −1.37541 0.794096i
\(267\) −1858.50 1073.01i −0.425986 0.245943i
\(268\) 658.179i 0.150018i
\(269\) 2542.50 4403.74i 0.576279 0.998144i −0.419623 0.907699i \(-0.637838\pi\)
0.995901 0.0904453i \(-0.0288290\pi\)
\(270\) 840.000 + 1454.92i 0.189336 + 0.327940i
\(271\) 1147.50 662.509i 0.257216 0.148504i −0.365848 0.930675i \(-0.619221\pi\)
0.623064 + 0.782171i \(0.285888\pi\)
\(272\) −2160.00 −0.481505
\(273\) 0 0
\(274\) 4122.00 0.908829
\(275\) −1306.50 + 754.308i −0.286491 + 0.165405i
\(276\) −798.000 1382.18i −0.174036 0.301439i
\(277\) 1710.50 2962.67i 0.371025 0.642635i −0.618698 0.785629i \(-0.712340\pi\)
0.989724 + 0.142994i \(0.0456730\pi\)
\(278\) 8816.14i 1.90200i
\(279\) 1386.00 + 800.207i 0.297411 + 0.171710i
\(280\) 3744.00 + 2161.60i 0.799096 + 0.461358i
\(281\) 810.600i 0.172087i 0.996291 + 0.0860433i \(0.0274223\pi\)
−0.996291 + 0.0860433i \(0.972578\pi\)
\(282\) 4158.00 7201.87i 0.878033 1.52080i
\(283\) −3588.50 6215.46i −0.753760 1.30555i −0.945988 0.324201i \(-0.894905\pi\)
0.192228 0.981350i \(-0.438429\pi\)
\(284\) −2022.00 + 1167.40i −0.422478 + 0.243918i
\(285\) −8568.00 −1.78079
\(286\) 0 0
\(287\) −8853.00 −1.82082
\(288\) −3168.00 + 1829.05i −0.648181 + 0.374228i
\(289\) 2092.00 + 3623.45i 0.425809 + 0.737523i
\(290\) −1656.00 + 2868.28i −0.335323 + 0.580796i
\(291\) 8644.67i 1.74144i
\(292\) 3480.00 + 2009.18i 0.697437 + 0.402665i
\(293\) −8065.50 4656.62i −1.60816 0.928473i −0.989781 0.142595i \(-0.954456\pi\)
−0.618381 0.785878i \(-0.712211\pi\)
\(294\) 3976.79i 0.788881i
\(295\) −132.000 + 228.631i −0.0260520 + 0.0451234i
\(296\) 276.000 + 478.046i 0.0541965 + 0.0938712i
\(297\) 682.500 394.042i 0.133342 0.0769852i
\(298\) −4518.00 −0.878257
\(299\) 0 0
\(300\) −1876.00 −0.361036
\(301\) −1657.50 + 956.958i −0.317398 + 0.183250i
\(302\) −150.000 259.808i −0.0285812 0.0495041i
\(303\) 6856.50 11875.8i 1.29999 2.25164i
\(304\) 7066.77i 1.33325i
\(305\) 204.000 + 117.779i 0.0382984 + 0.0221116i
\(306\) −1782.00 1028.84i −0.332909 0.192205i
\(307\) 4777.00i 0.888070i −0.896009 0.444035i \(-0.853547\pi\)
0.896009 0.444035i \(-0.146453\pi\)
\(308\) −1014.00 + 1756.30i −0.187591 + 0.324917i
\(309\) 6496.00 + 11251.4i 1.19594 + 2.07142i
\(310\) 3024.00 1745.91i 0.554038 0.319874i
\(311\) 6192.00 1.12899 0.564495 0.825436i \(-0.309071\pi\)
0.564495 + 0.825436i \(0.309071\pi\)
\(312\) 0 0
\(313\) −770.000 −0.139051 −0.0695255 0.997580i \(-0.522149\pi\)
−0.0695255 + 0.997580i \(0.522149\pi\)
\(314\) −4602.00 + 2656.97i −0.827089 + 0.477520i
\(315\) 3432.00 + 5944.40i 0.613877 + 1.06327i
\(316\) −2488.00 + 4309.34i −0.442914 + 0.767150i
\(317\) 8057.50i 1.42762i 0.700341 + 0.713808i \(0.253031\pi\)
−0.700341 + 0.713808i \(0.746969\pi\)
\(318\) 8946.00 + 5164.98i 1.57757 + 0.910810i
\(319\) 1345.50 + 776.825i 0.236155 + 0.136344i
\(320\) 886.810i 0.154919i
\(321\) −892.500 + 1545.86i −0.155185 + 0.268789i
\(322\) 2223.00 + 3850.35i 0.384730 + 0.666371i
\(323\) −2065.50 + 1192.52i −0.355813 + 0.205429i
\(324\) 3356.00 0.575446
\(325\) 0 0
\(326\) 5658.00 0.961250
\(327\) 3696.00 2133.89i 0.625044 0.360869i
\(328\) 2724.00 + 4718.11i 0.458560 + 0.794250i
\(329\) −3861.00 + 6687.45i −0.647002 + 1.12064i
\(330\) 7565.60i 1.26204i
\(331\) 4570.50 + 2638.78i 0.758965 + 0.438189i 0.828924 0.559361i \(-0.188954\pi\)
−0.0699590 + 0.997550i \(0.522287\pi\)
\(332\) −1476.00 852.169i −0.243994 0.140870i
\(333\) 876.418i 0.144226i
\(334\) −2817.00 + 4879.19i −0.461495 + 0.799333i
\(335\) −1140.00 1974.54i −0.185925 0.322031i
\(336\) 10920.0 6304.66i 1.77302 1.02365i
\(337\) 8278.00 1.33808 0.669038 0.743228i \(-0.266706\pi\)
0.669038 + 0.743228i \(0.266706\pi\)
\(338\) 0 0
\(339\) −2877.00 −0.460936
\(340\) −1296.00 + 748.246i −0.206722 + 0.119351i
\(341\) −819.000 1418.55i −0.130063 0.225275i
\(342\) −3366.00 + 5830.08i −0.532200 + 0.921798i
\(343\) 4030.48i 0.634477i
\(344\) 1020.00 + 588.897i 0.159868 + 0.0923000i
\(345\) 4788.00 + 2764.35i 0.747180 + 0.431385i
\(346\) 3024.16i 0.469884i
\(347\) −3433.50 + 5947.00i −0.531181 + 0.920033i 0.468156 + 0.883646i \(0.344918\pi\)
−0.999338 + 0.0363875i \(0.988415\pi\)
\(348\) 966.000 + 1673.16i 0.148802 + 0.257732i
\(349\) −10525.5 + 6076.90i −1.61438 + 0.932060i −0.626036 + 0.779794i \(0.715324\pi\)
−0.988340 + 0.152266i \(0.951343\pi\)
\(350\) 5226.00 0.798118
\(351\) 0 0
\(352\) 3744.00 0.566920
\(353\) −5029.50 + 2903.78i −0.758338 + 0.437827i −0.828699 0.559695i \(-0.810918\pi\)
0.0703608 + 0.997522i \(0.477585\pi\)
\(354\) 231.000 + 400.104i 0.0346822 + 0.0600714i
\(355\) 4044.00 7004.41i 0.604601 1.04720i
\(356\) 1226.29i 0.182566i
\(357\) 3685.50 + 2127.82i 0.546379 + 0.315452i
\(358\) 3861.00 + 2229.15i 0.570001 + 0.329090i
\(359\) 1340.61i 0.197088i 0.995133 + 0.0985439i \(0.0314185\pi\)
−0.995133 + 0.0985439i \(0.968581\pi\)
\(360\) 2112.00 3658.09i 0.309200 0.535551i
\(361\) 472.000 + 817.528i 0.0688147 + 0.119191i
\(362\) 6.00000 3.46410i 0.000871141 0.000502953i
\(363\) −5768.00 −0.833999
\(364\) 0 0
\(365\) −13920.0 −1.99618
\(366\) 357.000 206.114i 0.0509855 0.0294365i
\(367\) −1832.50 3173.98i −0.260642 0.451446i 0.705770 0.708441i \(-0.250601\pi\)
−0.966413 + 0.256995i \(0.917268\pi\)
\(368\) 2280.00 3949.08i 0.322971 0.559402i
\(369\) 8649.86i 1.22031i
\(370\) 1656.00 + 956.092i 0.232679 + 0.134337i
\(371\) −8307.00 4796.05i −1.16247 0.671155i
\(372\) 2036.89i 0.283892i
\(373\) −2685.50 + 4651.42i −0.372788 + 0.645688i −0.989993 0.141114i \(-0.954931\pi\)
0.617205 + 0.786802i \(0.288265\pi\)
\(374\) 1053.00 + 1823.85i 0.145586 + 0.252163i
\(375\) −4872.00 + 2812.85i −0.670904 + 0.387347i
\(376\) 4752.00 0.651770
\(377\) 0 0
\(378\) −2730.00 −0.371471
\(379\) 9967.50 5754.74i 1.35091 0.779950i 0.362536 0.931970i \(-0.381911\pi\)
0.988377 + 0.152020i \(0.0485778\pi\)
\(380\) 2448.00 + 4240.06i 0.330473 + 0.572396i
\(381\) −7850.50 + 13597.5i −1.05563 + 1.82840i
\(382\) 9841.51i 1.31816i
\(383\) −2095.50 1209.84i −0.279569 0.161409i 0.353659 0.935374i \(-0.384937\pi\)
−0.633228 + 0.773965i \(0.718271\pi\)
\(384\) −9408.00 5431.71i −1.25026 0.721838i
\(385\) 7025.20i 0.929967i
\(386\) 7353.00 12735.8i 0.969580 1.67936i
\(387\) 935.000 + 1619.47i 0.122813 + 0.212719i
\(388\) −4278.00 + 2469.90i −0.559749 + 0.323171i
\(389\) −9858.00 −1.28489 −0.642443 0.766334i \(-0.722079\pi\)
−0.642443 + 0.766334i \(0.722079\pi\)
\(390\) 0 0
\(391\) 1539.00 0.199055
\(392\) −1968.00 + 1136.23i −0.253569 + 0.146398i
\(393\) −1302.00 2255.13i −0.167118 0.289456i
\(394\) −4767.00 + 8256.69i −0.609538 + 1.05575i
\(395\) 17237.4i 2.19571i
\(396\) 1716.00 + 990.733i 0.217758 + 0.125723i
\(397\) 7552.50 + 4360.44i 0.954784 + 0.551245i 0.894564 0.446941i \(-0.147486\pi\)
0.0602200 + 0.998185i \(0.480820\pi\)
\(398\) 5837.01i 0.735133i
\(399\) 6961.50 12057.7i 0.873461 1.51288i
\(400\) −2680.00 4641.90i −0.335000 0.580237i
\(401\) 6568.50 3792.33i 0.817993 0.472269i −0.0317308 0.999496i \(-0.510102\pi\)
0.849724 + 0.527228i \(0.176769\pi\)
\(402\) −3990.00 −0.495033
\(403\) 0 0
\(404\) −7836.00 −0.964989
\(405\) −10068.0 + 5812.76i −1.23527 + 0.713181i
\(406\) −2691.00 4660.95i −0.328946 0.569751i
\(407\) 448.500 776.825i 0.0546224 0.0946088i
\(408\) 2618.86i 0.317777i
\(409\) −3727.50 2152.07i −0.450643 0.260179i 0.257459 0.966289i \(-0.417115\pi\)
−0.708102 + 0.706110i \(0.750448\pi\)
\(410\) 16344.0 + 9436.21i 1.96871 + 1.13664i
\(411\) 8329.43i 0.999661i
\(412\) 3712.00 6429.37i 0.443876 0.768817i
\(413\) −214.500 371.525i −0.0255565 0.0442652i
\(414\) 3762.00 2171.99i 0.446600 0.257844i
\(415\) 5904.00 0.698352
\(416\) 0 0
\(417\) 17815.0 2.09210
\(418\) 5967.00 3445.05i 0.698219 0.403117i
\(419\) −2698.50 4673.94i −0.314631 0.544957i 0.664728 0.747085i \(-0.268547\pi\)
−0.979359 + 0.202129i \(0.935214\pi\)
\(420\) 4368.00 7565.60i 0.507468 0.878960i
\(421\) 7260.76i 0.840541i 0.907399 + 0.420270i \(0.138065\pi\)
−0.907399 + 0.420270i \(0.861935\pi\)
\(422\) −5043.00 2911.58i −0.581728 0.335861i
\(423\) 6534.00 + 3772.41i 0.751050 + 0.433619i
\(424\) 5902.83i 0.676101i
\(425\) 904.500 1566.64i 0.103235 0.178808i
\(426\) −7077.00 12257.7i −0.804887 1.39410i
\(427\) −331.500 + 191.392i −0.0375700 + 0.0216911i
\(428\) 1020.00 0.115195
\(429\) 0 0
\(430\) 4080.00 0.457570
\(431\) 421.500 243.353i 0.0471066 0.0271970i −0.476262 0.879304i \(-0.658009\pi\)
0.523368 + 0.852107i \(0.324675\pi\)
\(432\) 1400.00 + 2424.87i 0.155920 + 0.270062i
\(433\) −6069.50 + 10512.7i −0.673629 + 1.16676i 0.303238 + 0.952915i \(0.401932\pi\)
−0.976867 + 0.213846i \(0.931401\pi\)
\(434\) 5674.20i 0.627581i
\(435\) −5796.00 3346.32i −0.638844 0.368836i
\(436\) −2112.00 1219.36i −0.231987 0.133938i
\(437\) 5035.07i 0.551167i
\(438\) −12180.0 + 21096.4i −1.32873 + 2.30142i
\(439\) −230.500 399.238i −0.0250596 0.0434045i 0.853224 0.521545i \(-0.174644\pi\)
−0.878283 + 0.478141i \(0.841311\pi\)
\(440\) −3744.00 + 2161.60i −0.405655 + 0.234205i
\(441\) −3608.00 −0.389591
\(442\) 0 0
\(443\) 12156.0 1.30372 0.651861 0.758338i \(-0.273988\pi\)
0.651861 + 0.758338i \(0.273988\pi\)
\(444\) 966.000 557.720i 0.103253 0.0596131i
\(445\) −2124.00 3678.88i −0.226263 0.391900i
\(446\) 7095.00 12288.9i 0.753269 1.30470i
\(447\) 9129.64i 0.966034i
\(448\) 1248.00 + 720.533i 0.131613 + 0.0759866i
\(449\) 256.500 + 148.090i 0.0269599 + 0.0155653i 0.513419 0.858138i \(-0.328379\pi\)
−0.486459 + 0.873703i \(0.661712\pi\)
\(450\) 5106.09i 0.534896i
\(451\) 4426.50 7666.92i 0.462164 0.800491i
\(452\) 822.000 + 1423.75i 0.0855390 + 0.148158i
\(453\) 525.000 303.109i 0.0544518 0.0314377i
\(454\) −1518.00 −0.156924
\(455\) 0 0
\(456\) −8568.00 −0.879898
\(457\) −529.500 + 305.707i −0.0541990 + 0.0312918i −0.526855 0.849955i \(-0.676629\pi\)
0.472656 + 0.881247i \(0.343295\pi\)
\(458\) 312.000 + 540.400i 0.0318314 + 0.0551337i
\(459\) −472.500 + 818.394i −0.0480488 + 0.0832230i
\(460\) 3159.26i 0.320220i
\(461\) 11368.5 + 6563.61i 1.14855 + 0.663119i 0.948535 0.316673i \(-0.102566\pi\)
0.200020 + 0.979792i \(0.435899\pi\)
\(462\) −10647.0 6147.05i −1.07217 0.619019i
\(463\) 834.848i 0.0837985i −0.999122 0.0418992i \(-0.986659\pi\)
0.999122 0.0418992i \(-0.0133408\pi\)
\(464\) −2760.00 + 4780.46i −0.276142 + 0.478292i
\(465\) 3528.00 + 6110.68i 0.351843 + 0.609410i
\(466\) −17334.0 + 10007.8i −1.72314 + 0.994854i
\(467\) 14496.0 1.43639 0.718196 0.695841i \(-0.244968\pi\)
0.718196 + 0.695841i \(0.244968\pi\)
\(468\) 0 0
\(469\) 3705.00 0.364778
\(470\) 14256.0 8230.71i 1.39911 0.807775i
\(471\) −5369.00 9299.38i −0.525245 0.909751i
\(472\) −132.000 + 228.631i −0.0128724 + 0.0222957i
\(473\) 1913.92i 0.186051i
\(474\) −26124.0 15082.7i −2.53147 1.46154i
\(475\) −5125.50 2959.21i −0.495103 0.285848i
\(476\) 2431.80i 0.234162i
\(477\) −4686.00 + 8116.39i −0.449805 + 0.779086i
\(478\) −3222.00 5580.67i −0.308307 0.534004i
\(479\) 7705.50 4448.77i 0.735017 0.424362i −0.0852376 0.996361i \(-0.527165\pi\)
0.820255 + 0.571998i \(0.193832\pi\)
\(480\) −16128.0 −1.53362
\(481\) 0 0
\(482\) −7134.00 −0.674159
\(483\) −7780.50 + 4492.07i −0.732971 + 0.423181i
\(484\) 1648.00 + 2854.42i 0.154771 + 0.268071i
\(485\) 8556.00 14819.4i 0.801047 1.38745i
\(486\) 17071.1i 1.59333i
\(487\) −4117.50 2377.24i −0.383125 0.221197i 0.296052 0.955172i \(-0.404330\pi\)
−0.679177 + 0.733975i \(0.737663\pi\)
\(488\) 204.000 + 117.779i 0.0189235 + 0.0109255i
\(489\) 11433.3i 1.05732i
\(490\) −3936.00 + 6817.35i −0.362878 + 0.628524i
\(491\) 817.500 + 1415.95i 0.0751390 + 0.130145i 0.901147 0.433514i \(-0.142727\pi\)
−0.826008 + 0.563659i \(0.809393\pi\)
\(492\) 9534.00 5504.46i 0.873630 0.504390i
\(493\) −1863.00 −0.170193
\(494\) 0 0
\(495\) −6864.00 −0.623260
\(496\) 5040.00 2909.85i 0.456255 0.263419i
\(497\) 6571.50 + 11382.2i 0.593103 + 1.02728i
\(498\) 5166.00 8947.77i 0.464847 0.805139i
\(499\) 14434.9i 1.29498i −0.762074 0.647490i \(-0.775819\pi\)
0.762074 0.647490i \(-0.224181\pi\)
\(500\) 2784.00 + 1607.34i 0.249009 + 0.143765i
\(501\) −9859.50 5692.38i −0.879222 0.507619i
\(502\) 15557.3i 1.38318i
\(503\) −6343.50 + 10987.3i −0.562312 + 0.973952i 0.434983 + 0.900439i \(0.356754\pi\)
−0.997294 + 0.0735133i \(0.976579\pi\)
\(504\) 3432.00 + 5944.40i 0.303320 + 0.525366i
\(505\) 23508.0 13572.4i 2.07147 1.19596i
\(506\) −4446.00 −0.390610
\(507\) 0 0
\(508\) 8972.00 0.783599
\(509\) 4978.50 2874.34i 0.433533 0.250300i −0.267318 0.963608i \(-0.586137\pi\)
0.700850 + 0.713308i \(0.252804\pi\)
\(510\) −4536.00 7856.58i −0.393838 0.682148i
\(511\) 11310.0 19589.5i 0.979109 1.69587i
\(512\) 4434.05i 0.382733i
\(513\) 2677.50 + 1545.86i 0.230438 + 0.133043i
\(514\) −16353.0 9441.41i −1.40331 0.810200i
\(515\) 25717.5i 2.20048i
\(516\) 1190.00 2061.14i 0.101525 0.175846i
\(517\) −3861.00 6687.45i −0.328446 0.568885i
\(518\) −2691.00 + 1553.65i −0.228254 + 0.131783i
\(519\) 6111.00 0.516846
\(520\) 0 0
\(521\) 6054.00 0.509080 0.254540 0.967062i \(-0.418076\pi\)
0.254540 + 0.967062i \(0.418076\pi\)
\(522\) −4554.00 + 2629.25i −0.381845 + 0.220458i
\(523\) 7401.50 + 12819.8i 0.618824 + 1.07183i 0.989701 + 0.143153i \(0.0457240\pi\)
−0.370877 + 0.928682i \(0.620943\pi\)
\(524\) −744.000 + 1288.65i −0.0620263 + 0.107433i
\(525\) 10560.3i 0.877885i
\(526\) 2349.00 + 1356.20i 0.194717 + 0.112420i
\(527\) 1701.00 + 982.073i 0.140601 + 0.0811760i
\(528\) 12609.3i 1.03930i
\(529\) 4459.00 7723.21i 0.366483 0.634767i
\(530\) 10224.0 + 17708.5i 0.837929 + 1.45133i
\(531\) −363.000 + 209.578i −0.0296664 + 0.0171279i
\(532\) −7956.00 −0.648377
\(533\) 0 0
\(534\) −7434.00 −0.602436
\(535\) −3060.00 + 1766.69i −0.247281 + 0.142768i
\(536\) −1140.00 1974.54i −0.0918666 0.159118i
\(537\) −4504.50 + 7802.02i −0.361980 + 0.626969i
\(538\) 17615.0i 1.41159i
\(539\) 3198.00 + 1846.37i 0.255561 + 0.147548i
\(540\) 1680.00 + 969.948i 0.133881 + 0.0772962i
\(541\) 21470.5i 1.70626i −0.521695 0.853132i \(-0.674700\pi\)
0.521695 0.853132i \(-0.325300\pi\)
\(542\) 2295.00 3975.06i 0.181880 0.315025i
\(543\) 7.00000 + 12.1244i 0.000553221 + 0.000958206i
\(544\) −3888.00 + 2244.74i −0.306428 + 0.176916i
\(545\) 8448.00 0.663986
\(546\) 0 0
\(547\) −13516.0 −1.05649 −0.528247 0.849091i \(-0.677151\pi\)
−0.528247 + 0.849091i \(0.677151\pi\)
\(548\) 4122.00 2379.84i 0.321320 0.185514i
\(549\) 187.000 + 323.894i 0.0145373 + 0.0251793i
\(550\) −2613.00 + 4525.85i −0.202579 + 0.350878i
\(551\) 6095.09i 0.471251i
\(552\) 4788.00 + 2764.35i 0.369186 + 0.213150i
\(553\) 24258.0 + 14005.4i 1.86538 + 1.07698i
\(554\) 11850.7i 0.908822i
\(555\) −1932.00 + 3346.32i −0.147764 + 0.255934i
\(556\) −5090.00 8816.14i −0.388245 0.672460i
\(557\) −2503.50 + 1445.40i −0.190443 + 0.109952i −0.592190 0.805798i \(-0.701736\pi\)
0.401747 + 0.915751i \(0.368403\pi\)
\(558\) 5544.00 0.420603
\(559\) 0 0
\(560\) 24960.0 1.88349
\(561\) −3685.50 + 2127.82i −0.277365 + 0.160137i
\(562\) 1404.00 + 2431.80i 0.105381 + 0.182525i
\(563\) −5791.50 + 10031.2i −0.433539 + 0.750912i −0.997175 0.0751113i \(-0.976069\pi\)
0.563636 + 0.826023i \(0.309402\pi\)
\(564\) 9602.49i 0.716911i
\(565\) −4932.00 2847.49i −0.367240 0.212026i
\(566\) −21531.0 12430.9i −1.59897 0.923164i
\(567\) 18891.5i 1.39924i
\(568\) 4044.00 7004.41i 0.298737 0.517427i
\(569\) −6439.50 11153.5i −0.474443 0.821759i 0.525129 0.851023i \(-0.324017\pi\)
−0.999572 + 0.0292638i \(0.990684\pi\)
\(570\) −25704.0 + 14840.2i −1.88881 + 1.09051i
\(571\) −11636.0 −0.852805 −0.426402 0.904534i \(-0.640219\pi\)
−0.426402 + 0.904534i \(0.640219\pi\)
\(572\) 0 0
\(573\) 19887.0 1.44990
\(574\) −26559.0 + 15333.8i −1.93127 + 1.11502i
\(575\) 1909.50 + 3307.35i 0.138490 + 0.239871i
\(576\) 704.000 1219.36i 0.0509259 0.0882063i
\(577\) 12311.4i 0.888269i 0.895960 + 0.444134i \(0.146489\pi\)
−0.895960 + 0.444134i \(0.853511\pi\)
\(578\) 12552.0 + 7246.90i 0.903277 + 0.521507i
\(579\) 25735.5 + 14858.4i 1.84720 + 1.06648i
\(580\) 3824.37i 0.273790i
\(581\) −4797.00 + 8308.65i −0.342535 + 0.593289i
\(582\) −14973.0 25934.0i −1.06641 1.84708i
\(583\) 8307.00 4796.05i 0.590121 0.340707i
\(584\) −13920.0 −0.986325
\(585\) 0 0
\(586\) −32262.0 −2.27428
\(587\) 13549.5 7822.81i 0.952722 0.550054i 0.0587964 0.998270i \(-0.481274\pi\)
0.893925 + 0.448216i \(0.147940\pi\)
\(588\) 2296.00 + 3976.79i 0.161030 + 0.278912i
\(589\) 3213.00 5565.08i 0.224770 0.389313i
\(590\) 914.523i 0.0638141i
\(591\) −16684.5 9632.80i −1.16127 0.670458i
\(592\) 2760.00 + 1593.49i 0.191614 + 0.110628i
\(593\) 25821.4i 1.78813i 0.447942 + 0.894063i \(0.352157\pi\)
−0.447942 + 0.894063i \(0.647843\pi\)
\(594\) 1365.00 2364.25i 0.0942873 0.163310i
\(595\) 4212.00 + 7295.40i 0.290210 + 0.502659i
\(596\) −4518.00 + 2608.47i −0.310511 + 0.179274i
\(597\) 11795.0 0.808605
\(598\) 0 0
\(599\) 1668.00 0.113777 0.0568887 0.998381i \(-0.481882\pi\)
0.0568887 + 0.998381i \(0.481882\pi\)
\(600\) 5628.00 3249.33i 0.382937 0.221089i
\(601\) −6849.50 11863.7i −0.464887 0.805207i 0.534310 0.845289i \(-0.320572\pi\)
−0.999196 + 0.0400813i \(0.987238\pi\)
\(602\) −3315.00 + 5741.75i −0.224434 + 0.388731i
\(603\) 3619.99i 0.244473i
\(604\) −300.000 173.205i −0.0202100 0.0116682i
\(605\) −9888.00 5708.84i −0.664470 0.383632i
\(606\) 47503.2i 3.18430i
\(607\) 11586.5 20068.4i 0.774764 1.34193i −0.160164 0.987090i \(-0.551202\pi\)
0.934927 0.354839i \(-0.115464\pi\)
\(608\) 7344.00 + 12720.2i 0.489866 + 0.848473i
\(609\) 9418.50 5437.77i 0.626694 0.361822i
\(610\) 816.000 0.0541621
\(611\) 0 0
\(612\) −2376.00 −0.156935
\(613\) −14389.5 + 8307.78i −0.948102 + 0.547387i −0.892491 0.451066i \(-0.851044\pi\)
−0.0556111 + 0.998453i \(0.517711\pi\)
\(614\) −8274.00 14331.0i −0.543830 0.941941i
\(615\) −19068.0 + 33026.7i −1.25024 + 2.16547i
\(616\) 7025.20i 0.459502i
\(617\) −24589.5 14196.8i −1.60443 0.926321i −0.990585 0.136897i \(-0.956287\pi\)
−0.613849 0.789423i \(-0.710380\pi\)
\(618\) 38976.0 + 22502.8i 2.53697 + 1.46472i
\(619\) 6245.78i 0.405556i −0.979225 0.202778i \(-0.935003\pi\)
0.979225 0.202778i \(-0.0649969\pi\)
\(620\) 2016.00 3491.81i 0.130588 0.226185i
\(621\) −997.500 1727.72i −0.0644578 0.111644i
\(622\) 18576.0 10724.9i 1.19748 0.691363i
\(623\) 6903.00 0.443921
\(624\) 0 0
\(625\) −19511.0 −1.24870
\(626\) −2310.00 + 1333.68i −0.147486 + 0.0851510i
\(627\) 6961.50 + 12057.7i 0.443406 + 0.768002i
\(628\) −3068.00 + 5313.93i −0.194947 + 0.337658i
\(629\) 1075.60i 0.0681830i
\(630\) 20592.0 + 11888.8i 1.30223 + 0.751843i
\(631\) −19381.5 11189.9i −1.22277 0.705964i −0.257259 0.966342i \(-0.582819\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(632\) 17237.4i 1.08491i
\(633\) 5883.50 10190.5i 0.369428 0.639869i
\(634\) 13956.0 + 24172.5i 0.874233 + 1.51422i
\(635\) −26916.0 + 15540.0i −1.68209 + 0.971157i
\(636\) 11928.0 0.743673
\(637\) 0 0
\(638\) 5382.00 0.333974
\(639\) 11121.0 6420.71i 0.688482 0.397495i
\(640\) −10752.0 18623.0i −0.664078 1.15022i
\(641\) −9913.50 + 17170.7i −0.610858 + 1.05804i 0.380239 + 0.924888i \(0.375842\pi\)
−0.991096 + 0.133148i \(0.957491\pi\)
\(642\) 6183.42i 0.380125i
\(643\) 7318.50 + 4225.34i 0.448855 + 0.259146i 0.707346 0.706867i \(-0.249892\pi\)
−0.258492 + 0.966013i \(0.583225\pi\)
\(644\) 4446.00 + 2566.90i 0.272045 + 0.157065i
\(645\) 8244.56i 0.503301i
\(646\) −4131.00 + 7155.10i −0.251598 + 0.435780i
\(647\) −1474.50 2553.91i −0.0895959 0.155185i 0.817744 0.575581i \(-0.195224\pi\)
−0.907340 + 0.420397i \(0.861891\pi\)
\(648\) −10068.0 + 5812.76i −0.610352 + 0.352387i
\(649\) 429.000 0.0259472
\(650\) 0 0
\(651\) −11466.0 −0.690304
\(652\) 5658.00 3266.65i 0.339853 0.196214i
\(653\) −6019.50 10426.1i −0.360737 0.624815i 0.627345 0.778741i \(-0.284141\pi\)
−0.988082 + 0.153926i \(0.950808\pi\)
\(654\) 7392.00 12803.3i 0.441973 0.765519i
\(655\) 5154.58i 0.307490i
\(656\) 27240.0 + 15727.0i 1.62126 + 0.936032i
\(657\) −19140.0 11050.5i −1.13656 0.656196i
\(658\) 26749.8i 1.58483i
\(659\) −1681.50 + 2912.44i −0.0993960 + 0.172159i −0.911435 0.411445i \(-0.865024\pi\)
0.812039 + 0.583603i \(0.198358\pi\)
\(660\) 4368.00 + 7565.60i 0.257612 + 0.446198i
\(661\) −8797.50 + 5079.24i −0.517675 + 0.298880i −0.735983 0.677000i \(-0.763280\pi\)
0.218308 + 0.975880i \(0.429946\pi\)
\(662\) 18282.0 1.07334
\(663\) 0 0
\(664\) 5904.00 0.345060
\(665\) 23868.0 13780.2i 1.39182 0.803569i
\(666\) 1518.00 + 2629.25i 0.0883203 + 0.152975i
\(667\) 1966.50 3406.08i 0.114158 0.197727i
\(668\) 6505.58i 0.376809i
\(669\) 24832.5 + 14337.1i 1.43510 + 0.828554i
\(670\) −6840.00 3949.08i −0.394406 0.227711i
\(671\) 382.783i 0.0220226i
\(672\) 13104.0 22696.8i 0.752229 1.30290i
\(673\) 9084.50 + 15734.8i 0.520329 + 0.901237i 0.999721 + 0.0236358i \(0.00752419\pi\)
−0.479391 + 0.877601i \(0.659142\pi\)
\(674\) 24834.0 14337.9i 1.41924 0.819400i
\(675\) −2345.00 −0.133717
\(676\) 0 0
\(677\) 9042.00 0.513312 0.256656 0.966503i \(-0.417379\pi\)
0.256656 + 0.966503i \(0.417379\pi\)
\(678\) −8631.00 + 4983.11i −0.488896 + 0.282264i
\(679\) 13903.5 + 24081.6i 0.785813 + 1.36107i
\(680\) 2592.00 4489.48i 0.146175 0.253182i
\(681\) 3067.46i 0.172607i
\(682\) −4914.00 2837.10i −0.275904 0.159293i
\(683\) 10792.5 + 6231.05i 0.604632 + 0.349084i 0.770862 0.637003i \(-0.219826\pi\)
−0.166230 + 0.986087i \(0.553159\pi\)
\(684\) 7773.44i 0.434540i
\(685\) −8244.00 + 14279.0i −0.459835 + 0.796458i
\(686\) 6981.00 + 12091.4i 0.388536 + 0.672964i
\(687\) −1092.00 + 630.466i −0.0606440 + 0.0350128i
\(688\) 6800.00 0.376813
\(689\) 0 0
\(690\) 19152.0 1.05667
\(691\) 3739.50 2159.00i 0.205872 0.118860i −0.393520 0.919316i \(-0.628743\pi\)
0.599391 + 0.800456i \(0.295409\pi\)
\(692\) −1746.00 3024.16i −0.0959147 0.166129i
\(693\) 5577.00 9659.65i 0.305704 0.529494i
\(694\) 23788.0i 1.30112i
\(695\) 30540.0 + 17632.3i 1.66683 + 0.962346i
\(696\) −5796.00 3346.32i −0.315656 0.182244i
\(697\) 10615.7i 0.576901i
\(698\) −21051.0 + 36461.4i −1.14154 + 1.97720i
\(699\) −20223.0 35027.3i −1.09428 1.89535i
\(700\) 5226.00 3017.23i 0.282177 0.162915i
\(701\) −18270.0 −0.984377 −0.492189 0.870489i \(-0.663803\pi\)
−0.492189 + 0.870489i \(0.663803\pi\)
\(702\) 0 0
\(703\) 3519.00 0.188793
\(704\) −1248.00 + 720.533i −0.0668122 + 0.0385740i
\(705\) 16632.0 + 28807.5i 0.888507 + 1.53894i
\(706\) −10059.0 + 17422.7i −0.536226 + 0.928770i
\(707\) 44110.1i 2.34644i
\(708\) 462.000 + 266.736i 0.0245240 + 0.0141590i
\(709\) −1411.50 814.930i −0.0747673 0.0431669i 0.462150 0.886802i \(-0.347078\pi\)
−0.536918 + 0.843635i \(0.680411\pi\)
\(710\) 28017.7i 1.48096i
\(711\) 13684.0 23701.4i 0.721786 1.25017i
\(712\) −2124.00 3678.88i −0.111798 0.193640i
\(713\) −3591.00 + 2073.26i −0.188617 + 0.108898i
\(714\) 14742.0 0.772697
\(715\) 0 0
\(716\) 5148.00 0.268701
\(717\) 11277.0 6510.78i 0.587374 0.339121i
\(718\) 2322.00 + 4021.82i 0.120691 + 0.209043i
\(719\) −4915.50 + 8513.90i −0.254961 + 0.441606i −0.964885 0.262673i \(-0.915396\pi\)
0.709924 + 0.704279i \(0.248729\pi\)
\(720\) 24387.3i 1.26231i
\(721\) −36192.0 20895.5i −1.86943 1.07932i
\(722\) 2832.00 + 1635.06i 0.145978 + 0.0842804i
\(723\) 14415.9i 0.741537i
\(724\) 4.00000 6.92820i 0.000205330 0.000355642i
\(725\) −2311.50 4003.64i −0.118410 0.205091i
\(726\) −17304.0 + 9990.47i −0.884589 + 0.510718i
\(727\) −15464.0 −0.788897 −0.394448 0.918918i \(-0.629064\pi\)
−0.394448 + 0.918918i \(0.629064\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) −41760.0 + 24110.1i −2.11727 + 1.22241i
\(731\) 1147.50 + 1987.53i 0.0580599 + 0.100563i
\(732\) 238.000 412.228i 0.0120174 0.0208147i
\(733\) 12616.3i 0.635733i −0.948136 0.317866i \(-0.897034\pi\)
0.948136 0.317866i \(-0.102966\pi\)
\(734\) −10995.0 6347.97i −0.552906 0.319220i
\(735\) −13776.0 7953.58i −0.691341 0.399146i
\(736\) 9477.78i 0.474668i
\(737\) −1852.50 + 3208.62i −0.0925885 + 0.160368i
\(738\) 14982.0 + 25949.6i 0.747283 + 1.29433i
\(739\) 14101.5 8141.50i 0.701938 0.405264i −0.106131 0.994352i \(-0.533846\pi\)
0.808069 + 0.589088i \(0.200513\pi\)
\(740\) 2208.00 0.109686
\(741\) 0 0
\(742\) −33228.0 −1.64399
\(743\) −9358.50 + 5403.13i −0.462086 + 0.266786i −0.712921 0.701244i \(-0.752628\pi\)
0.250835 + 0.968030i \(0.419295\pi\)
\(744\) 3528.00 + 6110.68i 0.173848 + 0.301113i
\(745\) 9036.00 15650.8i 0.444367 0.769666i
\(746\) 18605.7i 0.913140i
\(747\) 8118.00 + 4686.93i 0.397620 + 0.229566i
\(748\) 2106.00 + 1215.90i 0.102945 + 0.0594354i
\(749\) 5741.75i 0.280105i
\(750\) −9744.00 + 16877.1i −0.474401 + 0.821686i
\(751\) 6807.50 + 11790.9i 0.330771 + 0.572913i 0.982663 0.185399i \(-0.0593578\pi\)
−0.651892 + 0.758312i \(0.726024\pi\)
\(752\) 23760.0 13717.8i 1.15218 0.665210i
\(753\) −31437.0 −1.52142
\(754\) 0 0
\(755\) 1200.00 0.0578443
\(756\) −2730.00 + 1576.17i −0.131335 + 0.0758262i
\(757\) −2775.50 4807.31i −0.133259 0.230812i 0.791672 0.610947i \(-0.209211\pi\)
−0.924931 + 0.380135i \(0.875878\pi\)
\(758\) 19935.0 34528.4i 0.955240 1.65452i
\(759\) 8984.15i 0.429649i
\(760\) −14688.0 8480.12i −0.701039 0.404745i
\(761\) −8731.50 5041.13i −0.415922 0.240133i 0.277409 0.960752i \(-0.410524\pi\)
−0.693331 + 0.720619i \(0.743858\pi\)
\(762\) 54389.9i 2.58574i
\(763\) −6864.00 + 11888.8i −0.325680 + 0.564093i
\(764\) −5682.00 9841.51i −0.269067 0.466039i
\(765\) 7128.00 4115.35i 0.336880 0.194498i
\(766\) −8382.00 −0.395371
\(767\) 0 0
\(768\) −34048.0 −1.59974
\(769\) −25771.5 + 14879.2i −1.20851 + 0.697733i −0.962434 0.271517i \(-0.912475\pi\)
−0.246076 + 0.969250i \(0.579141\pi\)
\(770\) −12168.0 21075.6i −0.569486 0.986379i
\(771\) 19078.5 33044.9i 0.891174 1.54356i
\(772\) 16981.0i 0.791659i