Properties

Label 162.4.c.f.109.1
Level 162
Weight 4
Character 162.109
Analytic conductor 9.558
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.55830942093\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 162.109
Dual form 162.4.c.f.55.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(8.00000 + 13.8564i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(8.00000 + 13.8564i) q^{7} -8.00000 q^{8} -12.0000 q^{10} +(-6.00000 - 10.3923i) q^{11} +(-19.0000 + 32.9090i) q^{13} +(-16.0000 + 27.7128i) q^{14} +(-8.00000 - 13.8564i) q^{16} -126.000 q^{17} +20.0000 q^{19} +(-12.0000 - 20.7846i) q^{20} +(12.0000 - 20.7846i) q^{22} +(-84.0000 + 145.492i) q^{23} +(44.5000 + 77.0763i) q^{25} -76.0000 q^{26} -64.0000 q^{28} +(-15.0000 - 25.9808i) q^{29} +(44.0000 - 76.2102i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-126.000 - 218.238i) q^{34} -96.0000 q^{35} +254.000 q^{37} +(20.0000 + 34.6410i) q^{38} +(24.0000 - 41.5692i) q^{40} +(-21.0000 + 36.3731i) q^{41} +(26.0000 + 45.0333i) q^{43} +48.0000 q^{44} -336.000 q^{46} +(48.0000 + 83.1384i) q^{47} +(43.5000 - 75.3442i) q^{49} +(-89.0000 + 154.153i) q^{50} +(-76.0000 - 131.636i) q^{52} +198.000 q^{53} +72.0000 q^{55} +(-64.0000 - 110.851i) q^{56} +(30.0000 - 51.9615i) q^{58} +(330.000 - 571.577i) q^{59} +(269.000 + 465.922i) q^{61} +176.000 q^{62} +64.0000 q^{64} +(-114.000 - 197.454i) q^{65} +(-442.000 + 765.566i) q^{67} +(252.000 - 436.477i) q^{68} +(-96.0000 - 166.277i) q^{70} +792.000 q^{71} +218.000 q^{73} +(254.000 + 439.941i) q^{74} +(-40.0000 + 69.2820i) q^{76} +(96.0000 - 166.277i) q^{77} +(260.000 + 450.333i) q^{79} +96.0000 q^{80} -84.0000 q^{82} +(246.000 + 426.084i) q^{83} +(378.000 - 654.715i) q^{85} +(-52.0000 + 90.0666i) q^{86} +(48.0000 + 83.1384i) q^{88} +810.000 q^{89} -608.000 q^{91} +(-336.000 - 581.969i) q^{92} +(-96.0000 + 166.277i) q^{94} +(-60.0000 + 103.923i) q^{95} +(-577.000 - 999.393i) q^{97} +174.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} - 6q^{5} + 16q^{7} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} - 6q^{5} + 16q^{7} - 16q^{8} - 24q^{10} - 12q^{11} - 38q^{13} - 32q^{14} - 16q^{16} - 252q^{17} + 40q^{19} - 24q^{20} + 24q^{22} - 168q^{23} + 89q^{25} - 152q^{26} - 128q^{28} - 30q^{29} + 88q^{31} + 32q^{32} - 252q^{34} - 192q^{35} + 508q^{37} + 40q^{38} + 48q^{40} - 42q^{41} + 52q^{43} + 96q^{44} - 672q^{46} + 96q^{47} + 87q^{49} - 178q^{50} - 152q^{52} + 396q^{53} + 144q^{55} - 128q^{56} + 60q^{58} + 660q^{59} + 538q^{61} + 352q^{62} + 128q^{64} - 228q^{65} - 884q^{67} + 504q^{68} - 192q^{70} + 1584q^{71} + 436q^{73} + 508q^{74} - 80q^{76} + 192q^{77} + 520q^{79} + 192q^{80} - 168q^{82} + 492q^{83} + 756q^{85} - 104q^{86} + 96q^{88} + 1620q^{89} - 1216q^{91} - 672q^{92} - 192q^{94} - 120q^{95} - 1154q^{97} + 348q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −3.00000 + 5.19615i −0.268328 + 0.464758i −0.968430 0.249285i \(-0.919804\pi\)
0.700102 + 0.714043i \(0.253138\pi\)
\(6\) 0 0
\(7\) 8.00000 + 13.8564i 0.431959 + 0.748176i 0.997042 0.0768587i \(-0.0244890\pi\)
−0.565083 + 0.825034i \(0.691156\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −12.0000 −0.379473
\(11\) −6.00000 10.3923i −0.164461 0.284854i 0.772003 0.635619i \(-0.219255\pi\)
−0.936464 + 0.350765i \(0.885922\pi\)
\(12\) 0 0
\(13\) −19.0000 + 32.9090i −0.405358 + 0.702100i −0.994363 0.106029i \(-0.966186\pi\)
0.589005 + 0.808129i \(0.299520\pi\)
\(14\) −16.0000 + 27.7128i −0.305441 + 0.529040i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −126.000 −1.79762 −0.898808 0.438342i \(-0.855566\pi\)
−0.898808 + 0.438342i \(0.855566\pi\)
\(18\) 0 0
\(19\) 20.0000 0.241490 0.120745 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(20\) −12.0000 20.7846i −0.134164 0.232379i
\(21\) 0 0
\(22\) 12.0000 20.7846i 0.116291 0.201422i
\(23\) −84.0000 + 145.492i −0.761531 + 1.31901i 0.180530 + 0.983569i \(0.442219\pi\)
−0.942061 + 0.335441i \(0.891115\pi\)
\(24\) 0 0
\(25\) 44.5000 + 77.0763i 0.356000 + 0.616610i
\(26\) −76.0000 −0.573263
\(27\) 0 0
\(28\) −64.0000 −0.431959
\(29\) −15.0000 25.9808i −0.0960493 0.166362i 0.813997 0.580869i \(-0.197287\pi\)
−0.910046 + 0.414507i \(0.863954\pi\)
\(30\) 0 0
\(31\) 44.0000 76.2102i 0.254924 0.441541i −0.709951 0.704251i \(-0.751283\pi\)
0.964875 + 0.262710i \(0.0846163\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −126.000 218.238i −0.635554 1.10081i
\(35\) −96.0000 −0.463627
\(36\) 0 0
\(37\) 254.000 1.12858 0.564288 0.825578i \(-0.309151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(38\) 20.0000 + 34.6410i 0.0853797 + 0.147882i
\(39\) 0 0
\(40\) 24.0000 41.5692i 0.0948683 0.164317i
\(41\) −21.0000 + 36.3731i −0.0799914 + 0.138549i −0.903246 0.429123i \(-0.858823\pi\)
0.823255 + 0.567672i \(0.192156\pi\)
\(42\) 0 0
\(43\) 26.0000 + 45.0333i 0.0922084 + 0.159710i 0.908440 0.418015i \(-0.137274\pi\)
−0.816232 + 0.577725i \(0.803941\pi\)
\(44\) 48.0000 0.164461
\(45\) 0 0
\(46\) −336.000 −1.07697
\(47\) 48.0000 + 83.1384i 0.148969 + 0.258021i 0.930846 0.365410i \(-0.119071\pi\)
−0.781878 + 0.623431i \(0.785738\pi\)
\(48\) 0 0
\(49\) 43.5000 75.3442i 0.126822 0.219662i
\(50\) −89.0000 + 154.153i −0.251730 + 0.436009i
\(51\) 0 0
\(52\) −76.0000 131.636i −0.202679 0.351050i
\(53\) 198.000 0.513158 0.256579 0.966523i \(-0.417405\pi\)
0.256579 + 0.966523i \(0.417405\pi\)
\(54\) 0 0
\(55\) 72.0000 0.176518
\(56\) −64.0000 110.851i −0.152721 0.264520i
\(57\) 0 0
\(58\) 30.0000 51.9615i 0.0679171 0.117636i
\(59\) 330.000 571.577i 0.728175 1.26124i −0.229478 0.973314i \(-0.573702\pi\)
0.957654 0.287923i \(-0.0929647\pi\)
\(60\) 0 0
\(61\) 269.000 + 465.922i 0.564622 + 0.977953i 0.997085 + 0.0763018i \(0.0243112\pi\)
−0.432463 + 0.901652i \(0.642355\pi\)
\(62\) 176.000 0.360516
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −114.000 197.454i −0.217538 0.376787i
\(66\) 0 0
\(67\) −442.000 + 765.566i −0.805954 + 1.39595i 0.109692 + 0.993966i \(0.465014\pi\)
−0.915645 + 0.401987i \(0.868320\pi\)
\(68\) 252.000 436.477i 0.449404 0.778391i
\(69\) 0 0
\(70\) −96.0000 166.277i −0.163917 0.283913i
\(71\) 792.000 1.32385 0.661923 0.749572i \(-0.269740\pi\)
0.661923 + 0.749572i \(0.269740\pi\)
\(72\) 0 0
\(73\) 218.000 0.349520 0.174760 0.984611i \(-0.444085\pi\)
0.174760 + 0.984611i \(0.444085\pi\)
\(74\) 254.000 + 439.941i 0.399012 + 0.691109i
\(75\) 0 0
\(76\) −40.0000 + 69.2820i −0.0603726 + 0.104568i
\(77\) 96.0000 166.277i 0.142081 0.246091i
\(78\) 0 0
\(79\) 260.000 + 450.333i 0.370282 + 0.641347i 0.989609 0.143786i \(-0.0459277\pi\)
−0.619327 + 0.785133i \(0.712594\pi\)
\(80\) 96.0000 0.134164
\(81\) 0 0
\(82\) −84.0000 −0.113125
\(83\) 246.000 + 426.084i 0.325325 + 0.563480i 0.981578 0.191061i \(-0.0611928\pi\)
−0.656253 + 0.754541i \(0.727859\pi\)
\(84\) 0 0
\(85\) 378.000 654.715i 0.482351 0.835457i
\(86\) −52.0000 + 90.0666i −0.0652012 + 0.112932i
\(87\) 0 0
\(88\) 48.0000 + 83.1384i 0.0581456 + 0.100711i
\(89\) 810.000 0.964717 0.482359 0.875974i \(-0.339780\pi\)
0.482359 + 0.875974i \(0.339780\pi\)
\(90\) 0 0
\(91\) −608.000 −0.700393
\(92\) −336.000 581.969i −0.380765 0.659505i
\(93\) 0 0
\(94\) −96.0000 + 166.277i −0.105337 + 0.182448i
\(95\) −60.0000 + 103.923i −0.0647986 + 0.112235i
\(96\) 0 0
\(97\) −577.000 999.393i −0.603974 1.04611i −0.992213 0.124555i \(-0.960250\pi\)
0.388239 0.921559i \(-0.373084\pi\)
\(98\) 174.000 0.179354
\(99\) 0 0
\(100\) −356.000 −0.356000
\(101\) 309.000 + 535.204i 0.304422 + 0.527275i 0.977133 0.212631i \(-0.0682033\pi\)
−0.672710 + 0.739906i \(0.734870\pi\)
\(102\) 0 0
\(103\) −64.0000 + 110.851i −0.0612243 + 0.106044i −0.895013 0.446040i \(-0.852834\pi\)
0.833789 + 0.552084i \(0.186167\pi\)
\(104\) 152.000 263.272i 0.143316 0.248230i
\(105\) 0 0
\(106\) 198.000 + 342.946i 0.181429 + 0.314244i
\(107\) −1476.00 −1.33355 −0.666777 0.745257i \(-0.732327\pi\)
−0.666777 + 0.745257i \(0.732327\pi\)
\(108\) 0 0
\(109\) 1190.00 1.04570 0.522850 0.852425i \(-0.324869\pi\)
0.522850 + 0.852425i \(0.324869\pi\)
\(110\) 72.0000 + 124.708i 0.0624085 + 0.108095i
\(111\) 0 0
\(112\) 128.000 221.703i 0.107990 0.187044i
\(113\) 231.000 400.104i 0.192307 0.333085i −0.753708 0.657210i \(-0.771737\pi\)
0.946014 + 0.324125i \(0.105070\pi\)
\(114\) 0 0
\(115\) −504.000 872.954i −0.408680 0.707855i
\(116\) 120.000 0.0960493
\(117\) 0 0
\(118\) 1320.00 1.02980
\(119\) −1008.00 1745.91i −0.776498 1.34493i
\(120\) 0 0
\(121\) 593.500 1027.97i 0.445905 0.772331i
\(122\) −538.000 + 931.843i −0.399248 + 0.691517i
\(123\) 0 0
\(124\) 176.000 + 304.841i 0.127462 + 0.220770i
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) −2536.00 −1.77192 −0.885959 0.463763i \(-0.846499\pi\)
−0.885959 + 0.463763i \(0.846499\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 228.000 394.908i 0.153822 0.266428i
\(131\) −1146.00 + 1984.93i −0.764324 + 1.32385i 0.176279 + 0.984340i \(0.443594\pi\)
−0.940603 + 0.339508i \(0.889739\pi\)
\(132\) 0 0
\(133\) 160.000 + 277.128i 0.104314 + 0.180677i
\(134\) −1768.00 −1.13979
\(135\) 0 0
\(136\) 1008.00 0.635554
\(137\) 363.000 + 628.734i 0.226374 + 0.392091i 0.956731 0.290975i \(-0.0939796\pi\)
−0.730357 + 0.683066i \(0.760646\pi\)
\(138\) 0 0
\(139\) −190.000 + 329.090i −0.115939 + 0.200813i −0.918155 0.396222i \(-0.870321\pi\)
0.802215 + 0.597035i \(0.203655\pi\)
\(140\) 192.000 332.554i 0.115907 0.200757i
\(141\) 0 0
\(142\) 792.000 + 1371.78i 0.468050 + 0.810687i
\(143\) 456.000 0.266662
\(144\) 0 0
\(145\) 180.000 0.103091
\(146\) 218.000 + 377.587i 0.123574 + 0.214036i
\(147\) 0 0
\(148\) −508.000 + 879.882i −0.282144 + 0.488688i
\(149\) −795.000 + 1376.98i −0.437107 + 0.757091i −0.997465 0.0711590i \(-0.977330\pi\)
0.560358 + 0.828251i \(0.310664\pi\)
\(150\) 0 0
\(151\) −1216.00 2106.17i −0.655342 1.13509i −0.981808 0.189877i \(-0.939191\pi\)
0.326466 0.945209i \(-0.394142\pi\)
\(152\) −160.000 −0.0853797
\(153\) 0 0
\(154\) 384.000 0.200932
\(155\) 264.000 + 457.261i 0.136806 + 0.236956i
\(156\) 0 0
\(157\) −307.000 + 531.740i −0.156059 + 0.270302i −0.933444 0.358723i \(-0.883212\pi\)
0.777385 + 0.629025i \(0.216546\pi\)
\(158\) −520.000 + 900.666i −0.261829 + 0.453501i
\(159\) 0 0
\(160\) 96.0000 + 166.277i 0.0474342 + 0.0821584i
\(161\) −2688.00 −1.31580
\(162\) 0 0
\(163\) −1852.00 −0.889938 −0.444969 0.895546i \(-0.646785\pi\)
−0.444969 + 0.895546i \(0.646785\pi\)
\(164\) −84.0000 145.492i −0.0399957 0.0692746i
\(165\) 0 0
\(166\) −492.000 + 852.169i −0.230040 + 0.398441i
\(167\) 1068.00 1849.83i 0.494876 0.857151i −0.505106 0.863057i \(-0.668547\pi\)
0.999983 + 0.00590641i \(0.00188008\pi\)
\(168\) 0 0
\(169\) 376.500 + 652.117i 0.171370 + 0.296822i
\(170\) 1512.00 0.682148
\(171\) 0 0
\(172\) −208.000 −0.0922084
\(173\) −879.000 1522.47i −0.386296 0.669084i 0.605652 0.795729i \(-0.292912\pi\)
−0.991948 + 0.126646i \(0.959579\pi\)
\(174\) 0 0
\(175\) −712.000 + 1233.22i −0.307555 + 0.532701i
\(176\) −96.0000 + 166.277i −0.0411152 + 0.0712136i
\(177\) 0 0
\(178\) 810.000 + 1402.96i 0.341079 + 0.590766i
\(179\) −540.000 −0.225483 −0.112742 0.993624i \(-0.535963\pi\)
−0.112742 + 0.993624i \(0.535963\pi\)
\(180\) 0 0
\(181\) 1982.00 0.813928 0.406964 0.913444i \(-0.366588\pi\)
0.406964 + 0.913444i \(0.366588\pi\)
\(182\) −608.000 1053.09i −0.247626 0.428901i
\(183\) 0 0
\(184\) 672.000 1163.94i 0.269242 0.466341i
\(185\) −762.000 + 1319.82i −0.302829 + 0.524515i
\(186\) 0 0
\(187\) 756.000 + 1309.43i 0.295637 + 0.512059i
\(188\) −384.000 −0.148969
\(189\) 0 0
\(190\) −240.000 −0.0916391
\(191\) 1344.00 + 2327.88i 0.509154 + 0.881881i 0.999944 + 0.0106027i \(0.00337499\pi\)
−0.490790 + 0.871278i \(0.663292\pi\)
\(192\) 0 0
\(193\) 1151.00 1993.59i 0.429279 0.743533i −0.567531 0.823352i \(-0.692101\pi\)
0.996809 + 0.0798198i \(0.0254345\pi\)
\(194\) 1154.00 1998.79i 0.427074 0.739714i
\(195\) 0 0
\(196\) 174.000 + 301.377i 0.0634111 + 0.109831i
\(197\) 4374.00 1.58190 0.790951 0.611880i \(-0.209586\pi\)
0.790951 + 0.611880i \(0.209586\pi\)
\(198\) 0 0
\(199\) −1600.00 −0.569955 −0.284977 0.958534i \(-0.591986\pi\)
−0.284977 + 0.958534i \(0.591986\pi\)
\(200\) −356.000 616.610i −0.125865 0.218005i
\(201\) 0 0
\(202\) −618.000 + 1070.41i −0.215259 + 0.372840i
\(203\) 240.000 415.692i 0.0829788 0.143724i
\(204\) 0 0
\(205\) −126.000 218.238i −0.0429279 0.0743533i
\(206\) −256.000 −0.0865843
\(207\) 0 0
\(208\) 608.000 0.202679
\(209\) −120.000 207.846i −0.0397157 0.0687895i
\(210\) 0 0
\(211\) −1666.00 + 2885.60i −0.543565 + 0.941482i 0.455131 + 0.890425i \(0.349592\pi\)
−0.998696 + 0.0510573i \(0.983741\pi\)
\(212\) −396.000 + 685.892i −0.128290 + 0.222204i
\(213\) 0 0
\(214\) −1476.00 2556.51i −0.471483 0.816632i
\(215\) −312.000 −0.0989685
\(216\) 0 0
\(217\) 1408.00 0.440467
\(218\) 1190.00 + 2061.14i 0.369711 + 0.640358i
\(219\) 0 0
\(220\) −144.000 + 249.415i −0.0441294 + 0.0764344i
\(221\) 2394.00 4146.53i 0.728678 1.26211i
\(222\) 0 0
\(223\) −1324.00 2293.24i −0.397586 0.688639i 0.595842 0.803102i \(-0.296819\pi\)
−0.993427 + 0.114463i \(0.963485\pi\)
\(224\) 512.000 0.152721
\(225\) 0 0
\(226\) 924.000 0.271963
\(227\) −1122.00 1943.36i −0.328061 0.568218i 0.654066 0.756437i \(-0.273062\pi\)
−0.982127 + 0.188220i \(0.939728\pi\)
\(228\) 0 0
\(229\) 2825.00 4893.04i 0.815202 1.41197i −0.0939808 0.995574i \(-0.529959\pi\)
0.909183 0.416397i \(-0.136707\pi\)
\(230\) 1008.00 1745.91i 0.288981 0.500529i
\(231\) 0 0
\(232\) 120.000 + 207.846i 0.0339586 + 0.0588180i
\(233\) 4698.00 1.32093 0.660464 0.750858i \(-0.270360\pi\)
0.660464 + 0.750858i \(0.270360\pi\)
\(234\) 0 0
\(235\) −576.000 −0.159890
\(236\) 1320.00 + 2286.31i 0.364088 + 0.630618i
\(237\) 0 0
\(238\) 2016.00 3491.81i 0.549067 0.951011i
\(239\) 600.000 1039.23i 0.162388 0.281265i −0.773337 0.633996i \(-0.781414\pi\)
0.935725 + 0.352731i \(0.114747\pi\)
\(240\) 0 0
\(241\) 359.000 + 621.806i 0.0959553 + 0.166199i 0.910007 0.414593i \(-0.136076\pi\)
−0.814052 + 0.580793i \(0.802743\pi\)
\(242\) 2374.00 0.630605
\(243\) 0 0
\(244\) −2152.00 −0.564622
\(245\) 261.000 + 452.065i 0.0680599 + 0.117883i
\(246\) 0 0
\(247\) −380.000 + 658.179i −0.0978900 + 0.169550i
\(248\) −352.000 + 609.682i −0.0901291 + 0.156108i
\(249\) 0 0
\(250\) −1284.00 2223.95i −0.324829 0.562621i
\(251\) 6012.00 1.51185 0.755924 0.654659i \(-0.227188\pi\)
0.755924 + 0.654659i \(0.227188\pi\)
\(252\) 0 0
\(253\) 2016.00 0.500968
\(254\) −2536.00 4392.48i −0.626468 1.08507i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1023.00 1771.89i 0.248300 0.430067i −0.714755 0.699375i \(-0.753462\pi\)
0.963054 + 0.269308i \(0.0867949\pi\)
\(258\) 0 0
\(259\) 2032.00 + 3519.53i 0.487499 + 0.844374i
\(260\) 912.000 0.217538
\(261\) 0 0
\(262\) −4584.00 −1.08092
\(263\) 3036.00 + 5258.51i 0.711817 + 1.23290i 0.964175 + 0.265269i \(0.0854606\pi\)
−0.252358 + 0.967634i \(0.581206\pi\)
\(264\) 0 0
\(265\) −594.000 + 1028.84i −0.137695 + 0.238494i
\(266\) −320.000 + 554.256i −0.0737611 + 0.127758i
\(267\) 0 0
\(268\) −1768.00 3062.27i −0.402977 0.697976i
\(269\) −6930.00 −1.57074 −0.785371 0.619025i \(-0.787528\pi\)
−0.785371 + 0.619025i \(0.787528\pi\)
\(270\) 0 0
\(271\) 1352.00 0.303056 0.151528 0.988453i \(-0.451581\pi\)
0.151528 + 0.988453i \(0.451581\pi\)
\(272\) 1008.00 + 1745.91i 0.224702 + 0.389195i
\(273\) 0 0
\(274\) −726.000 + 1257.47i −0.160070 + 0.277250i
\(275\) 534.000 924.915i 0.117096 0.202816i
\(276\) 0 0
\(277\) 593.000 + 1027.11i 0.128628 + 0.222790i 0.923145 0.384451i \(-0.125609\pi\)
−0.794517 + 0.607241i \(0.792276\pi\)
\(278\) −760.000 −0.163963
\(279\) 0 0
\(280\) 768.000 0.163917
\(281\) −1221.00 2114.83i −0.259213 0.448969i 0.706819 0.707395i \(-0.250130\pi\)
−0.966031 + 0.258425i \(0.916796\pi\)
\(282\) 0 0
\(283\) −1414.00 + 2449.12i −0.297009 + 0.514435i −0.975450 0.220220i \(-0.929323\pi\)
0.678441 + 0.734655i \(0.262656\pi\)
\(284\) −1584.00 + 2743.57i −0.330962 + 0.573242i
\(285\) 0 0
\(286\) 456.000 + 789.815i 0.0942792 + 0.163296i
\(287\) −672.000 −0.138212
\(288\) 0 0
\(289\) 10963.0 2.23143
\(290\) 180.000 + 311.769i 0.0364482 + 0.0631301i
\(291\) 0 0
\(292\) −436.000 + 755.174i −0.0873800 + 0.151347i
\(293\) −2379.00 + 4120.55i −0.474344 + 0.821587i −0.999568 0.0293763i \(-0.990648\pi\)
0.525225 + 0.850963i \(0.323981\pi\)
\(294\) 0 0
\(295\) 1980.00 + 3429.46i 0.390780 + 0.676851i
\(296\) −2032.00 −0.399012
\(297\) 0 0
\(298\) −3180.00 −0.618163
\(299\) −3192.00 5528.71i −0.617385 1.06934i
\(300\) 0 0
\(301\) −416.000 + 720.533i −0.0796606 + 0.137976i
\(302\) 2432.00 4212.35i 0.463397 0.802627i
\(303\) 0 0
\(304\) −160.000 277.128i −0.0301863 0.0522842i
\(305\) −3228.00 −0.606016
\(306\) 0 0
\(307\) −8476.00 −1.57574 −0.787868 0.615844i \(-0.788815\pi\)
−0.787868 + 0.615844i \(0.788815\pi\)
\(308\) 384.000 + 665.108i 0.0710404 + 0.123046i
\(309\) 0 0
\(310\) −528.000 + 914.523i −0.0967367 + 0.167553i
\(311\) −2316.00 + 4011.43i −0.422278 + 0.731406i −0.996162 0.0875302i \(-0.972103\pi\)
0.573884 + 0.818936i \(0.305436\pi\)
\(312\) 0 0
\(313\) 2411.00 + 4175.97i 0.435392 + 0.754122i 0.997328 0.0730597i \(-0.0232764\pi\)
−0.561935 + 0.827181i \(0.689943\pi\)
\(314\) −1228.00 −0.220701
\(315\) 0 0
\(316\) −2080.00 −0.370282
\(317\) 1713.00 + 2967.00i 0.303507 + 0.525689i 0.976928 0.213570i \(-0.0685091\pi\)
−0.673421 + 0.739259i \(0.735176\pi\)
\(318\) 0 0
\(319\) −180.000 + 311.769i −0.0315927 + 0.0547201i
\(320\) −192.000 + 332.554i −0.0335410 + 0.0580948i
\(321\) 0 0
\(322\) −2688.00 4655.75i −0.465206 0.805761i
\(323\) −2520.00 −0.434107
\(324\) 0 0
\(325\) −3382.00 −0.577230
\(326\) −1852.00 3207.76i −0.314640 0.544973i
\(327\) 0 0
\(328\) 168.000 290.985i 0.0282812 0.0489846i
\(329\) −768.000 + 1330.22i −0.128697 + 0.222909i
\(330\) 0 0
\(331\) 1394.00 + 2414.48i 0.231484 + 0.400942i 0.958245 0.285948i \(-0.0923086\pi\)
−0.726761 + 0.686890i \(0.758975\pi\)
\(332\) −1968.00 −0.325325
\(333\) 0 0
\(334\) 4272.00 0.699861
\(335\) −2652.00 4593.40i −0.432520 0.749147i
\(336\) 0 0
\(337\) −217.000 + 375.855i −0.0350764 + 0.0607541i −0.883031 0.469315i \(-0.844501\pi\)
0.847954 + 0.530069i \(0.177834\pi\)
\(338\) −753.000 + 1304.23i −0.121177 + 0.209885i
\(339\) 0 0
\(340\) 1512.00 + 2618.86i 0.241176 + 0.417728i
\(341\) −1056.00 −0.167700
\(342\) 0 0
\(343\) 6880.00 1.08305
\(344\) −208.000 360.267i −0.0326006 0.0564659i
\(345\) 0 0
\(346\) 1758.00 3044.95i 0.273152 0.473114i
\(347\) −3342.00 + 5788.51i −0.517026 + 0.895515i 0.482779 + 0.875742i \(0.339628\pi\)
−0.999805 + 0.0197726i \(0.993706\pi\)
\(348\) 0 0
\(349\) −1315.00 2277.65i −0.201692 0.349340i 0.747382 0.664395i \(-0.231311\pi\)
−0.949074 + 0.315055i \(0.897977\pi\)
\(350\) −2848.00 −0.434949
\(351\) 0 0
\(352\) −384.000 −0.0581456
\(353\) 3711.00 + 6427.64i 0.559537 + 0.969147i 0.997535 + 0.0701707i \(0.0223544\pi\)
−0.437998 + 0.898976i \(0.644312\pi\)
\(354\) 0 0
\(355\) −2376.00 + 4115.35i −0.355225 + 0.615268i
\(356\) −1620.00 + 2805.92i −0.241179 + 0.417735i
\(357\) 0 0
\(358\) −540.000 935.307i −0.0797204 0.138080i
\(359\) −10440.0 −1.53482 −0.767412 0.641154i \(-0.778456\pi\)
−0.767412 + 0.641154i \(0.778456\pi\)
\(360\) 0 0
\(361\) −6459.00 −0.941682
\(362\) 1982.00 + 3432.92i 0.287767 + 0.498427i
\(363\) 0 0
\(364\) 1216.00 2106.17i 0.175098 0.303279i
\(365\) −654.000 + 1132.76i −0.0937861 + 0.162442i
\(366\) 0 0
\(367\) −5212.00 9027.45i −0.741319 1.28400i −0.951895 0.306425i \(-0.900867\pi\)
0.210575 0.977578i \(-0.432466\pi\)
\(368\) 2688.00 0.380765
\(369\) 0 0
\(370\) −3048.00 −0.428265
\(371\) 1584.00 + 2743.57i 0.221664 + 0.383933i
\(372\) 0 0
\(373\) −1639.00 + 2838.83i −0.227518 + 0.394073i −0.957072 0.289851i \(-0.906394\pi\)
0.729554 + 0.683923i \(0.239728\pi\)
\(374\) −1512.00 + 2618.86i −0.209047 + 0.362080i
\(375\) 0 0
\(376\) −384.000 665.108i −0.0526683 0.0912242i
\(377\) 1140.00 0.155737
\(378\) 0 0
\(379\) 6140.00 0.832165 0.416083 0.909327i \(-0.363403\pi\)
0.416083 + 0.909327i \(0.363403\pi\)
\(380\) −240.000 415.692i −0.0323993 0.0561173i
\(381\) 0 0
\(382\) −2688.00 + 4655.75i −0.360026 + 0.623584i
\(383\) 1536.00 2660.43i 0.204924 0.354939i −0.745184 0.666858i \(-0.767639\pi\)
0.950109 + 0.311919i \(0.100972\pi\)
\(384\) 0 0
\(385\) 576.000 + 997.661i 0.0762485 + 0.132066i
\(386\) 4604.00 0.607092
\(387\) 0 0
\(388\) 4616.00 0.603974
\(389\) −3075.00 5326.06i −0.400794 0.694195i 0.593028 0.805182i \(-0.297932\pi\)
−0.993822 + 0.110987i \(0.964599\pi\)
\(390\) 0 0
\(391\) 10584.0 18332.0i 1.36894 2.37108i
\(392\) −348.000 + 602.754i −0.0448384 + 0.0776624i
\(393\) 0 0
\(394\) 4374.00 + 7575.99i 0.559287 + 0.968713i
\(395\) −3120.00 −0.397428
\(396\) 0 0
\(397\) −106.000 −0.0134005 −0.00670024 0.999978i \(-0.502133\pi\)
−0.00670024 + 0.999978i \(0.502133\pi\)
\(398\) −1600.00 2771.28i −0.201509 0.349025i
\(399\) 0 0
\(400\) 712.000 1233.22i 0.0890000 0.154153i
\(401\) 879.000 1522.47i 0.109464 0.189598i −0.806089 0.591794i \(-0.798420\pi\)
0.915553 + 0.402197i \(0.131753\pi\)
\(402\) 0 0
\(403\) 1672.00 + 2895.99i 0.206671 + 0.357964i
\(404\) −2472.00 −0.304422
\(405\) 0 0
\(406\) 960.000 0.117350
\(407\) −1524.00 2639.65i −0.185607 0.321480i
\(408\) 0 0
\(409\) 1835.00 3178.31i 0.221846 0.384248i −0.733523 0.679665i \(-0.762125\pi\)
0.955368 + 0.295417i \(0.0954585\pi\)
\(410\) 252.000 436.477i 0.0303546 0.0525757i
\(411\) 0 0
\(412\) −256.000 443.405i −0.0306122 0.0530218i
\(413\) 10560.0 1.25817
\(414\) 0 0
\(415\) −2952.00 −0.349176
\(416\) 608.000 + 1053.09i 0.0716578 + 0.124115i
\(417\) 0 0
\(418\) 240.000 415.692i 0.0280832 0.0486416i
\(419\) 4830.00 8365.81i 0.563153 0.975409i −0.434066 0.900881i \(-0.642922\pi\)
0.997219 0.0745280i \(-0.0237450\pi\)
\(420\) 0 0
\(421\) −4231.00 7328.31i −0.489801 0.848361i 0.510130 0.860097i \(-0.329597\pi\)
−0.999931 + 0.0117367i \(0.996264\pi\)
\(422\) −6664.00 −0.768717
\(423\) 0 0
\(424\) −1584.00 −0.181429
\(425\) −5607.00 9711.61i −0.639952 1.10843i
\(426\) 0 0
\(427\) −4304.00 + 7454.75i −0.487787 + 0.844872i
\(428\) 2952.00 5113.01i 0.333389 0.577446i
\(429\) 0 0
\(430\) −312.000 540.400i −0.0349906 0.0606056i
\(431\) 9792.00 1.09435 0.547174 0.837019i \(-0.315704\pi\)
0.547174 + 0.837019i \(0.315704\pi\)
\(432\) 0 0
\(433\) −7342.00 −0.814859 −0.407430 0.913237i \(-0.633575\pi\)
−0.407430 + 0.913237i \(0.633575\pi\)
\(434\) 1408.00 + 2438.73i 0.155728 + 0.269730i
\(435\) 0 0
\(436\) −2380.00 + 4122.28i −0.261425 + 0.452801i
\(437\) −1680.00 + 2909.85i −0.183902 + 0.318528i
\(438\) 0 0
\(439\) −5320.00 9214.51i −0.578382 1.00179i −0.995665 0.0930106i \(-0.970351\pi\)
0.417283 0.908777i \(-0.362982\pi\)
\(440\) −576.000 −0.0624085
\(441\) 0 0
\(442\) 9576.00 1.03051
\(443\) 8706.00 + 15079.2i 0.933712 + 1.61724i 0.776914 + 0.629606i \(0.216784\pi\)
0.156798 + 0.987631i \(0.449883\pi\)
\(444\) 0 0
\(445\) −2430.00 + 4208.88i −0.258861 + 0.448360i
\(446\) 2648.00 4586.47i 0.281136 0.486941i
\(447\) 0 0
\(448\) 512.000 + 886.810i 0.0539949 + 0.0935220i
\(449\) −1710.00 −0.179732 −0.0898662 0.995954i \(-0.528644\pi\)
−0.0898662 + 0.995954i \(0.528644\pi\)
\(450\) 0 0
\(451\) 504.000 0.0526218
\(452\) 924.000 + 1600.41i 0.0961533 + 0.166542i
\(453\) 0 0
\(454\) 2244.00 3886.72i 0.231974 0.401791i
\(455\) 1824.00 3159.26i 0.187935 0.325513i
\(456\) 0 0
\(457\) 323.000 + 559.452i 0.0330619 + 0.0572649i 0.882083 0.471094i \(-0.156141\pi\)
−0.849021 + 0.528359i \(0.822807\pi\)
\(458\) 11300.0 1.15287
\(459\) 0 0
\(460\) 4032.00 0.408680
\(461\) 3009.00 + 5211.74i 0.303998 + 0.526540i 0.977038 0.213066i \(-0.0683450\pi\)
−0.673040 + 0.739606i \(0.735012\pi\)
\(462\) 0 0
\(463\) 3356.00 5812.76i 0.336861 0.583460i −0.646980 0.762507i \(-0.723968\pi\)
0.983840 + 0.179047i \(0.0573015\pi\)
\(464\) −240.000 + 415.692i −0.0240123 + 0.0415906i
\(465\) 0 0
\(466\) 4698.00 + 8137.17i 0.467019 + 0.808900i
\(467\) 5364.00 0.531512 0.265756 0.964040i \(-0.414378\pi\)
0.265756 + 0.964040i \(0.414378\pi\)
\(468\) 0 0
\(469\) −14144.0 −1.39256
\(470\) −576.000 997.661i −0.0565296 0.0979121i
\(471\) 0 0
\(472\) −2640.00 + 4572.61i −0.257449 + 0.445914i
\(473\) 312.000 540.400i 0.0303293 0.0525319i
\(474\) 0 0
\(475\) 890.000 + 1541.53i 0.0859705 + 0.148905i
\(476\) 8064.00 0.776498
\(477\) 0 0
\(478\) 2400.00 0.229652
\(479\) −4920.00 8521.69i −0.469312 0.812873i 0.530072 0.847952i \(-0.322165\pi\)
−0.999385 + 0.0350799i \(0.988831\pi\)
\(480\) 0 0
\(481\) −4826.00 + 8358.88i −0.457477 + 0.792374i
\(482\) −718.000 + 1243.61i −0.0678506 + 0.117521i
\(483\) 0 0
\(484\) 2374.00 + 4111.89i 0.222953 + 0.386165i
\(485\) 6924.00 0.648253
\(486\) 0 0
\(487\) 1424.00 0.132500 0.0662501 0.997803i \(-0.478896\pi\)
0.0662501 + 0.997803i \(0.478896\pi\)
\(488\) −2152.00 3727.37i −0.199624 0.345759i
\(489\) 0 0
\(490\) −522.000 + 904.131i −0.0481256 + 0.0833560i
\(491\) 2274.00 3938.68i 0.209011 0.362017i −0.742393 0.669965i \(-0.766309\pi\)
0.951403 + 0.307948i \(0.0996424\pi\)
\(492\) 0 0
\(493\) 1890.00 + 3273.58i 0.172660 + 0.299056i
\(494\) −1520.00 −0.138437
\(495\) 0 0
\(496\) −1408.00 −0.127462
\(497\) 6336.00 + 10974.3i 0.571848 + 0.990470i
\(498\) 0 0
\(499\) −3250.00 + 5629.17i −0.291563 + 0.505002i −0.974180 0.225775i \(-0.927509\pi\)
0.682616 + 0.730777i \(0.260842\pi\)
\(500\) 2568.00 4447.91i 0.229689 0.397833i
\(501\) 0 0
\(502\) 6012.00 + 10413.1i 0.534519 + 0.925815i
\(503\) 12168.0 1.07862 0.539308 0.842108i \(-0.318686\pi\)
0.539308 + 0.842108i \(0.318686\pi\)
\(504\) 0 0
\(505\) −3708.00 −0.326740
\(506\) 2016.00 + 3491.81i 0.177119 + 0.306779i
\(507\) 0 0
\(508\) 5072.00 8784.96i 0.442980 0.767263i
\(509\) 10545.0 18264.5i 0.918269 1.59049i 0.116226 0.993223i \(-0.462920\pi\)
0.802043 0.597266i \(-0.203746\pi\)
\(510\) 0 0
\(511\) 1744.00 + 3020.70i 0.150979 + 0.261502i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 4092.00 0.351149
\(515\) −384.000 665.108i −0.0328564 0.0569090i
\(516\) 0 0
\(517\) 576.000 997.661i 0.0489989 0.0848687i
\(518\) −4064.00 + 7039.05i −0.344714 + 0.597062i
\(519\) 0 0
\(520\) 912.000 + 1579.63i 0.0769112 + 0.133214i
\(521\) −5238.00 −0.440462 −0.220231 0.975448i \(-0.570681\pi\)
−0.220231 + 0.975448i \(0.570681\pi\)
\(522\) 0 0
\(523\) 8588.00 0.718025 0.359012 0.933333i \(-0.383114\pi\)
0.359012 + 0.933333i \(0.383114\pi\)
\(524\) −4584.00 7939.72i −0.382162 0.661924i
\(525\) 0 0
\(526\) −6072.00 + 10517.0i −0.503330 + 0.871794i
\(527\) −5544.00 + 9602.49i −0.458255 + 0.793721i
\(528\) 0 0
\(529\) −8028.50 13905.8i −0.659859 1.14291i
\(530\) −2376.00 −0.194730
\(531\) 0 0
\(532\) −1280.00 −0.104314
\(533\) −798.000 1382.18i −0.0648503 0.112324i
\(534\) 0 0
\(535\) 4428.00 7669.52i 0.357830 0.619780i
\(536\) 3536.00 6124.53i 0.284948 0.493544i
\(537\) 0 0
\(538\) −6930.00 12003.1i −0.555341 0.961879i
\(539\) −1044.00 −0.0834291
\(540\) 0 0
\(541\) 3062.00 0.243338 0.121669 0.992571i \(-0.461175\pi\)
0.121669 + 0.992571i \(0.461175\pi\)
\(542\) 1352.00 + 2341.73i 0.107146 + 0.185583i
\(543\) 0 0
\(544\) −2016.00 + 3491.81i −0.158888 + 0.275203i
\(545\) −3570.00 + 6183.42i −0.280591 + 0.485998i
\(546\) 0 0
\(547\) 4238.00 + 7340.43i 0.331268 + 0.573774i 0.982761 0.184881i \(-0.0591901\pi\)
−0.651492 + 0.758655i \(0.725857\pi\)
\(548\) −2904.00 −0.226374
\(549\) 0 0
\(550\) 2136.00 0.165599
\(551\) −300.000 519.615i −0.0231950 0.0401749i
\(552\) 0 0
\(553\) −4160.00 + 7205.33i −0.319894 + 0.554072i
\(554\) −1186.00 + 2054.21i −0.0909536 + 0.157536i
\(555\) 0 0
\(556\) −760.000 1316.36i −0.0579697 0.100407i
\(557\) −12546.0 −0.954383 −0.477191 0.878799i \(-0.658345\pi\)
−0.477191 + 0.878799i \(0.658345\pi\)
\(558\) 0 0
\(559\) −1976.00 −0.149510
\(560\) 768.000 + 1330.22i 0.0579534 + 0.100378i
\(561\) 0 0
\(562\) 2442.00 4229.67i 0.183291 0.317469i
\(563\) 6.00000 10.3923i 0.000449147 0.000777946i −0.865801 0.500389i \(-0.833190\pi\)
0.866250 + 0.499611i \(0.166524\pi\)
\(564\) 0 0
\(565\) 1386.00 + 2400.62i 0.103203 + 0.178752i
\(566\) −5656.00 −0.420034
\(567\) 0 0
\(568\) −6336.00 −0.468050
\(569\) −9645.00 16705.6i −0.710614 1.23082i −0.964627 0.263619i \(-0.915084\pi\)
0.254013 0.967201i \(-0.418249\pi\)
\(570\) 0 0
\(571\) 6074.00 10520.5i 0.445165 0.771048i −0.552899 0.833248i \(-0.686478\pi\)
0.998064 + 0.0622005i \(0.0198118\pi\)
\(572\) −912.000 + 1579.63i −0.0666654 + 0.115468i
\(573\) 0 0
\(574\) −672.000 1163.94i −0.0488654 0.0846374i
\(575\) −14952.0 −1.08442
\(576\) 0 0
\(577\) −10366.0 −0.747907 −0.373953 0.927447i \(-0.621998\pi\)
−0.373953 + 0.927447i \(0.621998\pi\)
\(578\) 10963.0 + 18988.5i 0.788929 + 1.36646i
\(579\) 0 0
\(580\) −360.000 + 623.538i −0.0257727 + 0.0446397i
\(581\) −3936.00 + 6817.35i −0.281055 + 0.486801i
\(582\) 0 0
\(583\) −1188.00 2057.68i −0.0843944 0.146175i
\(584\) −1744.00 −0.123574
\(585\) 0 0
\(586\) −9516.00 −0.670823
\(587\) −3822.00 6619.90i −0.268741 0.465473i 0.699796 0.714343i \(-0.253274\pi\)
−0.968537 + 0.248870i \(0.919941\pi\)
\(588\) 0 0
\(589\) 880.000 1524.20i 0.0615616 0.106628i
\(590\) −3960.00 + 6858.92i −0.276323 + 0.478606i
\(591\) 0 0
\(592\) −2032.00 3519.53i −0.141072 0.244344i
\(593\) 8658.00 0.599564 0.299782 0.954008i \(-0.403086\pi\)
0.299782 + 0.954008i \(0.403086\pi\)
\(594\) 0 0
\(595\) 12096.0 0.833425
\(596\) −3180.00 5507.92i −0.218553 0.378546i
\(597\) 0 0
\(598\) 6384.00 11057.4i 0.436557 0.756139i
\(599\) −12900.0 + 22343.5i −0.879933 + 1.52409i −0.0285192 + 0.999593i \(0.509079\pi\)
−0.851414 + 0.524495i \(0.824254\pi\)
\(600\) 0 0
\(601\) −8101.00 14031.3i −0.549828 0.952330i −0.998286 0.0585262i \(-0.981360\pi\)
0.448458 0.893804i \(-0.351973\pi\)
\(602\) −1664.00 −0.112657
\(603\) 0 0
\(604\) 9728.00 0.655342
\(605\) 3561.00 + 6167.83i 0.239298 + 0.414476i
\(606\) 0 0
\(607\) 12068.0 20902.4i 0.806960 1.39770i −0.107999 0.994151i \(-0.534444\pi\)
0.914960 0.403546i \(-0.132222\pi\)
\(608\) 320.000 554.256i 0.0213449 0.0369705i
\(609\) 0 0
\(610\) −3228.00 5591.06i −0.214259 0.371107i
\(611\) −3648.00 −0.241542
\(612\) 0 0
\(613\) −4642.00 −0.305854 −0.152927 0.988237i \(-0.548870\pi\)
−0.152927 + 0.988237i \(0.548870\pi\)
\(614\) −8476.00 14680.9i −0.557107 0.964937i
\(615\) 0 0
\(616\) −768.000 + 1330.22i −0.0502331 + 0.0870063i
\(617\) 3363.00 5824.89i 0.219432 0.380067i −0.735203 0.677847i \(-0.762913\pi\)
0.954634 + 0.297781i \(0.0962464\pi\)
\(618\) 0 0
\(619\) 10610.0 + 18377.1i 0.688937 + 1.19327i 0.972182 + 0.234226i \(0.0752556\pi\)
−0.283245 + 0.959047i \(0.591411\pi\)
\(620\) −2112.00 −0.136806
\(621\) 0 0
\(622\) −9264.00 −0.597191
\(623\) 6480.00 + 11223.7i 0.416719 + 0.721778i
\(624\) 0 0
\(625\) −1710.50 + 2962.67i −0.109472 + 0.189611i
\(626\) −4822.00 + 8351.95i −0.307869 + 0.533244i
\(627\) 0 0
\(628\) −1228.00 2126.96i −0.0780295 0.135151i
\(629\) −32004.0 −2.02875
\(630\) 0 0
\(631\) 29792.0 1.87956 0.939779 0.341783i \(-0.111031\pi\)
0.939779 + 0.341783i \(0.111031\pi\)
\(632\) −2080.00 3602.67i −0.130914 0.226751i
\(633\) 0 0
\(634\) −3426.00 + 5934.01i −0.214612 + 0.371718i
\(635\) 7608.00 13177.4i 0.475456 0.823513i
\(636\) 0 0
\(637\) 1653.00 + 2863.08i 0.102817 + 0.178084i
\(638\) −720.000 −0.0446788
\(639\) 0 0
\(640\) −768.000 −0.0474342
\(641\) 5079.00 + 8797.09i 0.312962 + 0.542066i 0.979002 0.203850i \(-0.0653455\pi\)
−0.666040 + 0.745916i \(0.732012\pi\)
\(642\) 0 0
\(643\) −14914.0 + 25831.8i −0.914698 + 1.58430i −0.107355 + 0.994221i \(0.534238\pi\)
−0.807343 + 0.590082i \(0.799095\pi\)
\(644\) 5376.00 9311.51i 0.328950 0.569759i
\(645\) 0 0
\(646\) −2520.00 4364.77i −0.153480 0.265835i
\(647\) 1944.00 0.118124 0.0590622 0.998254i \(-0.481189\pi\)
0.0590622 + 0.998254i \(0.481189\pi\)
\(648\) 0 0
\(649\) −7920.00 −0.479025
\(650\) −3382.00 5857.80i −0.204081 0.353479i
\(651\) 0 0
\(652\) 3704.00 6415.52i 0.222484 0.385354i
\(653\) −13359.0 + 23138.5i −0.800579 + 1.38664i 0.118657 + 0.992935i \(0.462141\pi\)
−0.919236 + 0.393708i \(0.871192\pi\)
\(654\) 0 0
\(655\) −6876.00 11909.6i −0.410179 0.710452i
\(656\) 672.000 0.0399957
\(657\) 0 0
\(658\) −3072.00 −0.182005
\(659\) −2130.00 3689.27i −0.125907 0.218078i 0.796180 0.605060i \(-0.206851\pi\)
−0.922087 + 0.386982i \(0.873518\pi\)
\(660\) 0 0
\(661\) −11431.0 + 19799.1i −0.672639 + 1.16504i 0.304514 + 0.952508i \(0.401506\pi\)
−0.977153 + 0.212537i \(0.931827\pi\)
\(662\) −2788.00 + 4828.96i −0.163684 + 0.283509i
\(663\) 0 0
\(664\) −1968.00 3408.68i −0.115020 0.199220i
\(665\) −1920.00 −0.111962
\(666\) 0 0
\(667\) 5040.00 0.292578
\(668\) 4272.00 + 7399.32i 0.247438 + 0.428575i
\(669\) 0 0
\(670\) 5304.00 9186.80i 0.305838 0.529727i
\(671\) 3228.00 5591.06i 0.185716 0.321670i
\(672\) 0 0
\(673\) 16271.0 + 28182.2i 0.931948 + 1.61418i 0.779988 + 0.625795i \(0.215225\pi\)
0.151960 + 0.988387i \(0.451442\pi\)
\(674\) −868.000 −0.0496055
\(675\) 0 0
\(676\) −3012.00 −0.171370
\(677\) −7107.00 12309.7i −0.403463 0.698818i 0.590679 0.806907i \(-0.298860\pi\)
−0.994141 + 0.108089i \(0.965527\pi\)
\(678\) 0 0
\(679\) 9232.00 15990.3i 0.521784 0.903757i
\(680\) −3024.00 + 5237.72i −0.170537 + 0.295379i
\(681\) 0 0
\(682\) −1056.00 1829.05i −0.0592908 0.102695i
\(683\) −7092.00 −0.397317 −0.198659 0.980069i \(-0.563659\pi\)
−0.198659 + 0.980069i \(0.563659\pi\)
\(684\) 0 0
\(685\) −4356.00 −0.242970
\(686\) 6880.00 + 11916.5i 0.382915 + 0.663228i
\(687\) 0 0
\(688\) 416.000 720.533i 0.0230521 0.0399274i
\(689\) −3762.00 + 6515.98i −0.208013 + 0.360289i
\(690\) 0 0
\(691\) 6614.00 + 11455.8i 0.364122 + 0.630678i 0.988635 0.150337i \(-0.0480357\pi\)
−0.624513 + 0.781015i \(0.714702\pi\)
\(692\) 7032.00 0.386296
\(693\) 0 0
\(694\) −13368.0 −0.731185
\(695\) −1140.00 1974.54i −0.0622197 0.107768i
\(696\) 0 0
\(697\) 2646.00 4583.01i 0.143794 0.249058i
\(698\) 2630.00 4555.29i 0.142617 0.247021i
\(699\) 0 0
\(700\) −2848.00 4932.88i −0.153778 0.266351i
\(701\) 28062.0 1.51196 0.755982 0.654592i \(-0.227160\pi\)
0.755982 + 0.654592i \(0.227160\pi\)
\(702\) 0 0
\(703\) 5080.00 0.272540
\(704\) −384.000 665.108i −0.0205576 0.0356068i
\(705\) 0 0
\(706\) −7422.00 + 12855.3i −0.395652 + 0.685290i
\(707\) −4944.00 + 8563.26i −0.262996 + 0.455523i
\(708\) 0 0
\(709\) 13625.0 + 23599.2i 0.721717 + 1.25005i 0.960311 + 0.278932i \(0.0899803\pi\)
−0.238594 + 0.971120i \(0.576686\pi\)
\(710\) −9504.00 −0.502364
\(711\) 0 0
\(712\) −6480.00 −0.341079
\(713\) 7392.00 + 12803.3i 0.388264 + 0.672494i
\(714\) 0 0
\(715\) −1368.00 + 2369.45i −0.0715529 + 0.123933i
\(716\) 1080.00 1870.61i 0.0563708 0.0976371i
\(717\) 0 0
\(718\) −10440.0 18082.6i −0.542643 0.939884i
\(719\) −14400.0 −0.746912 −0.373456 0.927648i \(-0.621827\pi\)
−0.373456 + 0.927648i \(0.621827\pi\)
\(720\) 0 0
\(721\) −2048.00 −0.105786
\(722\) −6459.00 11187.3i −0.332935 0.576660i
\(723\) 0 0
\(724\) −3964.00 + 6865.85i −0.203482 + 0.352441i
\(725\) 1335.00 2312.29i 0.0683871 0.118450i
\(726\) 0 0
\(727\) −8992.00 15574.6i −0.458727 0.794539i 0.540167 0.841558i \(-0.318361\pi\)
−0.998894 + 0.0470189i \(0.985028\pi\)
\(728\) 4864.00 0.247626
\(729\) 0 0
\(730\) −2616.00 −0.132634
\(731\) −3276.00 5674.20i −0.165755 0.287097i
\(732\) 0 0
\(733\) −8299.00 + 14374.3i −0.418186 + 0.724320i −0.995757 0.0920207i \(-0.970667\pi\)
0.577571 + 0.816341i \(0.304001\pi\)
\(734\) 10424.0 18054.9i 0.524192 0.907927i
\(735\) 0 0
\(736\) 2688.00 + 4655.75i 0.134621 + 0.233170i
\(737\) 10608.0 0.530191
\(738\) 0 0
\(739\) 1460.00 0.0726752 0.0363376 0.999340i \(-0.488431\pi\)
0.0363376 + 0.999340i \(0.488431\pi\)
\(740\) −3048.00 5279.29i −0.151414 0.262258i
\(741\) 0 0
\(742\) −3168.00 + 5487.14i −0.156740 + 0.271481i
\(743\) 15036.0 26043.1i 0.742419 1.28591i −0.208972 0.977922i \(-0.567012\pi\)
0.951391 0.307986i \(-0.0996549\pi\)
\(744\) 0 0
\(745\) −4770.00 8261.88i −0.234576 0.406298i
\(746\) −6556.00 −0.321759
\(747\) 0 0
\(748\) −6048.00 −0.295637
\(749\) −11808.0 20452.1i −0.576041 0.997733i
\(750\) 0 0
\(751\) 9044.00 15664.7i 0.439441 0.761134i −0.558205 0.829703i \(-0.688510\pi\)
0.997646 + 0.0685686i \(0.0218432\pi\)
\(752\) 768.000 1330.22i 0.0372421 0.0645053i
\(753\) 0 0
\(754\) 1140.00 + 1974.54i 0.0550615 + 0.0953693i
\(755\) 14592.0 0.703387
\(756\) 0 0
\(757\) 24734.0 1.18755 0.593773 0.804633i \(-0.297638\pi\)
0.593773 + 0.804633i \(0.297638\pi\)
\(758\) 6140.00 + 10634.8i 0.294215 + 0.509595i
\(759\) 0 0
\(760\) 480.000 831.384i 0.0229098 0.0396809i
\(761\) 11139.0 19293.3i 0.530602 0.919030i −0.468760 0.883326i \(-0.655299\pi\)
0.999362 0.0357047i \(-0.0113676\pi\)
\(762\) 0 0
\(763\) 9520.00 + 16489.1i 0.451700 + 0.782367i
\(764\) −10752.0 −0.509154
\(765\) 0 0
\(766\) 6144.00 0.289806
\(767\) 12540.0 + 21719.9i 0.590343 + 1.02250i
\(768\) 0 0
\(769\) −8065.00 + 13969.0i −0.378194 + 0.655052i −0.990800 0.135337i \(-0.956788\pi\)
0.612605 + 0.790389i \(0.290122\pi\)
\(770\) −1152.00 + 1995.32i −0.0539158 + 0.0933850i
\(771\) 0 0
\(772\) 4604.00 + 7974.36i 0.214639 + 0.371766i
\(773\) 29718.0 1.38277 0.691386 0.722486i \(-0.257001\pi\)
0.691386 + 0.722486i \(0.257001\pi\)
\(774\) 0 0
\(775\) 7832.00 0.363011
\(776\) 4616.00 + 7995.15i 0.213537 + 0.369857i
\(777\) 0 0
\(778\) 6150.00 10652.1i 0.283404 0.490870i
\(779\) −420.000 + 727.461i −0.0193172 + 0.0334583i
\(780\) 0 0
\(781\) −4752.00 8230.71i −0.217721 0.377103i
\(782\) 42336.0 1.93597
\(783\) 0 0
\(784\) −1392.00 −0.0634111
\(785\) −1842.00 3190.44i −0.0837501 0.145059i
\(786\) 0 0
\(787\) −4762.00 + 8248.03i −0.215689 + 0.373584i −0.953485 0.301439i \(-0.902533\pi\)
0.737797 + 0.675023i \(0.235866\pi\)
\(788\) −8748.00 + 15152.0i −0.395475 + 0.684983i
\(789\) 0 0
\(790\) −3120.00 5404.00i −0.140512 0.243374i
\(791\) 7392.00 0.332275
\(792\) 0 0
\(793\) −20444.0 −0.915495
\(794\) −106.000 183.597i −0.00473778 0.00820608i
\(795\) 0 0
\(796\) 3200.00 5542.56i 0.142489 0.246798i
\(797\) 16953.0 29363.5i 0.753458 1.30503i −0.192679 0.981262i \(-0.561718\pi\)
0.946137 0.323766i \(-0.104949\pi\)
\(798\) 0 0
\(799\) −6048.00 10475.4i −0.267788 0.463823i
\(800\) 2848.00 0.125865
\(801\) 0 0
\(802\) 3516.00 0.154806
\(803\)