Properties

Label 289.4.b.b.288.4
Level $289$
Weight $4$
Character 289.288
Analytic conductor $17.052$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.0515519917\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.27793984.1
Defining polynomial: \( x^{6} - 2x^{3} + 49x^{2} - 14x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 17)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 288.4
Root \(-1.93854 + 1.93854i\) of defining polynomial
Character \(\chi\) \(=\) 289.288
Dual form 289.4.b.b.288.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.36122 q^{2} +3.15463i q^{3} -6.14708 q^{4} +3.03171i q^{5} -4.29415i q^{6} +7.94049i q^{7} +19.2573 q^{8} +17.0483 q^{9} +O(q^{10})\) \(q-1.36122 q^{2} +3.15463i q^{3} -6.14708 q^{4} +3.03171i q^{5} -4.29415i q^{6} +7.94049i q^{7} +19.2573 q^{8} +17.0483 q^{9} -4.12682i q^{10} -27.6161i q^{11} -19.3918i q^{12} +58.1117 q^{13} -10.8088i q^{14} -9.56391 q^{15} +22.9632 q^{16} -23.2065 q^{18} -89.1688 q^{19} -18.6361i q^{20} -25.0493 q^{21} +37.5916i q^{22} +115.269i q^{23} +60.7497i q^{24} +115.809 q^{25} -79.1029 q^{26} +138.956i q^{27} -48.8108i q^{28} -128.558i q^{29} +13.0186 q^{30} +273.460i q^{31} -185.316 q^{32} +87.1187 q^{33} -24.0732 q^{35} -104.797 q^{36} -132.351i q^{37} +121.379 q^{38} +183.321i q^{39} +58.3825i q^{40} +470.559i q^{41} +34.0977 q^{42} -352.642 q^{43} +169.758i q^{44} +51.6854i q^{45} -156.907i q^{46} +152.598 q^{47} +72.4403i q^{48} +279.949 q^{49} -157.641 q^{50} -357.217 q^{52} -527.614 q^{53} -189.150i q^{54} +83.7239 q^{55} +152.912i q^{56} -281.295i q^{57} +174.995i q^{58} +292.020 q^{59} +58.7901 q^{60} +53.8962i q^{61} -372.239i q^{62} +135.372i q^{63} +68.5514 q^{64} +176.178i q^{65} -118.588 q^{66} +52.9572 q^{67} -363.632 q^{69} +32.7690 q^{70} +788.400i q^{71} +328.304 q^{72} +295.780i q^{73} +180.159i q^{74} +365.334i q^{75} +548.127 q^{76} +219.285 q^{77} -249.541i q^{78} +720.325i q^{79} +69.6175i q^{80} +21.9487 q^{81} -640.535i q^{82} +116.051 q^{83} +153.980 q^{84} +480.024 q^{86} +405.552 q^{87} -531.812i q^{88} -813.329 q^{89} -70.3553i q^{90} +461.435i q^{91} -708.569i q^{92} -862.664 q^{93} -207.720 q^{94} -270.334i q^{95} -584.605i q^{96} +794.693i q^{97} -381.072 q^{98} -470.808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 50 q^{4} + 78 q^{8} - 118 q^{9} + 60 q^{13} - 216 q^{15} + 274 q^{16} - 206 q^{18} - 160 q^{19} - 384 q^{21} + 446 q^{25} - 52 q^{26} + 800 q^{30} + 142 q^{32} - 664 q^{33} - 664 q^{35} - 2626 q^{36} + 1448 q^{38} + 2256 q^{42} - 1112 q^{43} + 1280 q^{47} + 538 q^{49} + 1094 q^{50} - 1548 q^{52} - 604 q^{53} + 152 q^{55} - 1272 q^{59} - 2656 q^{60} - 1838 q^{64} - 4936 q^{66} + 2016 q^{67} + 1152 q^{69} + 3008 q^{70} - 1854 q^{72} + 1816 q^{76} + 1008 q^{77} - 1010 q^{81} + 4792 q^{83} - 4080 q^{84} - 2528 q^{86} - 2856 q^{87} - 340 q^{89} - 1264 q^{93} + 4032 q^{94} + 5714 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36122 −0.481264 −0.240632 0.970616i \(-0.577355\pi\)
−0.240632 + 0.970616i \(0.577355\pi\)
\(3\) 3.15463i 0.607109i 0.952814 + 0.303555i \(0.0981735\pi\)
−0.952814 + 0.303555i \(0.901827\pi\)
\(4\) −6.14708 −0.768385
\(5\) 3.03171i 0.271164i 0.990766 + 0.135582i \(0.0432904\pi\)
−0.990766 + 0.135582i \(0.956710\pi\)
\(6\) − 4.29415i − 0.292180i
\(7\) 7.94049i 0.428746i 0.976752 + 0.214373i \(0.0687708\pi\)
−0.976752 + 0.214373i \(0.931229\pi\)
\(8\) 19.2573 0.851061
\(9\) 17.0483 0.631419
\(10\) − 4.12682i − 0.130502i
\(11\) − 27.6161i − 0.756961i −0.925609 0.378481i \(-0.876447\pi\)
0.925609 0.378481i \(-0.123553\pi\)
\(12\) − 19.3918i − 0.466493i
\(13\) 58.1117 1.23979 0.619896 0.784684i \(-0.287175\pi\)
0.619896 + 0.784684i \(0.287175\pi\)
\(14\) − 10.8088i − 0.206340i
\(15\) −9.56391 −0.164626
\(16\) 22.9632 0.358799
\(17\) 0 0
\(18\) −23.2065 −0.303879
\(19\) −89.1688 −1.07667 −0.538335 0.842731i \(-0.680946\pi\)
−0.538335 + 0.842731i \(0.680946\pi\)
\(20\) − 18.6361i − 0.208358i
\(21\) −25.0493 −0.260296
\(22\) 37.5916i 0.364298i
\(23\) 115.269i 1.04501i 0.852635 + 0.522507i \(0.175003\pi\)
−0.852635 + 0.522507i \(0.824997\pi\)
\(24\) 60.7497i 0.516687i
\(25\) 115.809 0.926470
\(26\) −79.1029 −0.596668
\(27\) 138.956i 0.990449i
\(28\) − 48.8108i − 0.329442i
\(29\) − 128.558i − 0.823191i −0.911367 0.411596i \(-0.864972\pi\)
0.911367 0.411596i \(-0.135028\pi\)
\(30\) 13.0186 0.0792287
\(31\) 273.460i 1.58435i 0.610295 + 0.792174i \(0.291051\pi\)
−0.610295 + 0.792174i \(0.708949\pi\)
\(32\) −185.316 −1.02374
\(33\) 87.1187 0.459558
\(34\) 0 0
\(35\) −24.0732 −0.116260
\(36\) −104.797 −0.485172
\(37\) − 132.351i − 0.588063i −0.955796 0.294031i \(-0.905003\pi\)
0.955796 0.294031i \(-0.0949970\pi\)
\(38\) 121.379 0.518163
\(39\) 183.321i 0.752689i
\(40\) 58.3825i 0.230777i
\(41\) 470.559i 1.79241i 0.443636 + 0.896207i \(0.353688\pi\)
−0.443636 + 0.896207i \(0.646312\pi\)
\(42\) 34.0977 0.125271
\(43\) −352.642 −1.25064 −0.625318 0.780370i \(-0.715031\pi\)
−0.625318 + 0.780370i \(0.715031\pi\)
\(44\) 169.758i 0.581637i
\(45\) 51.6854i 0.171218i
\(46\) − 156.907i − 0.502928i
\(47\) 152.598 0.473589 0.236795 0.971560i \(-0.423903\pi\)
0.236795 + 0.971560i \(0.423903\pi\)
\(48\) 72.4403i 0.217830i
\(49\) 279.949 0.816177
\(50\) −157.641 −0.445877
\(51\) 0 0
\(52\) −357.217 −0.952637
\(53\) −527.614 −1.36742 −0.683711 0.729753i \(-0.739635\pi\)
−0.683711 + 0.729753i \(0.739635\pi\)
\(54\) − 189.150i − 0.476668i
\(55\) 83.7239 0.205261
\(56\) 152.912i 0.364889i
\(57\) − 281.295i − 0.653656i
\(58\) 174.995i 0.396173i
\(59\) 292.020 0.644368 0.322184 0.946677i \(-0.395583\pi\)
0.322184 + 0.946677i \(0.395583\pi\)
\(60\) 58.7901 0.126496
\(61\) 53.8962i 0.113126i 0.998399 + 0.0565632i \(0.0180142\pi\)
−0.998399 + 0.0565632i \(0.981986\pi\)
\(62\) − 372.239i − 0.762490i
\(63\) 135.372i 0.270718i
\(64\) 68.5514 0.133889
\(65\) 176.178i 0.336187i
\(66\) −118.588 −0.221169
\(67\) 52.9572 0.0965635 0.0482817 0.998834i \(-0.484625\pi\)
0.0482817 + 0.998834i \(0.484625\pi\)
\(68\) 0 0
\(69\) −363.632 −0.634437
\(70\) 32.7690 0.0559520
\(71\) 788.400i 1.31783i 0.752218 + 0.658915i \(0.228984\pi\)
−0.752218 + 0.658915i \(0.771016\pi\)
\(72\) 328.304 0.537375
\(73\) 295.780i 0.474224i 0.971482 + 0.237112i \(0.0762009\pi\)
−0.971482 + 0.237112i \(0.923799\pi\)
\(74\) 180.159i 0.283014i
\(75\) 365.334i 0.562468i
\(76\) 548.127 0.827296
\(77\) 219.285 0.324544
\(78\) − 249.541i − 0.362242i
\(79\) 720.325i 1.02586i 0.858430 + 0.512930i \(0.171440\pi\)
−0.858430 + 0.512930i \(0.828560\pi\)
\(80\) 69.6175i 0.0972934i
\(81\) 21.9487 0.0301079
\(82\) − 640.535i − 0.862625i
\(83\) 116.051 0.153473 0.0767363 0.997051i \(-0.475550\pi\)
0.0767363 + 0.997051i \(0.475550\pi\)
\(84\) 153.980 0.200007
\(85\) 0 0
\(86\) 480.024 0.601887
\(87\) 405.552 0.499767
\(88\) − 531.812i − 0.644220i
\(89\) −813.329 −0.968682 −0.484341 0.874879i \(-0.660941\pi\)
−0.484341 + 0.874879i \(0.660941\pi\)
\(90\) − 70.3553i − 0.0824011i
\(91\) 461.435i 0.531556i
\(92\) − 708.569i − 0.802972i
\(93\) −862.664 −0.961872
\(94\) −207.720 −0.227922
\(95\) − 270.334i − 0.291954i
\(96\) − 584.605i − 0.621521i
\(97\) 794.693i 0.831844i 0.909400 + 0.415922i \(0.136541\pi\)
−0.909400 + 0.415922i \(0.863459\pi\)
\(98\) −381.072 −0.392797
\(99\) − 470.808i − 0.477959i
\(100\) −711.885 −0.711885
\(101\) 265.513 0.261579 0.130790 0.991410i \(-0.458249\pi\)
0.130790 + 0.991410i \(0.458249\pi\)
\(102\) 0 0
\(103\) 523.107 0.500420 0.250210 0.968192i \(-0.419500\pi\)
0.250210 + 0.968192i \(0.419500\pi\)
\(104\) 1119.07 1.05514
\(105\) − 75.9421i − 0.0705828i
\(106\) 718.199 0.658091
\(107\) − 986.039i − 0.890878i −0.895312 0.445439i \(-0.853048\pi\)
0.895312 0.445439i \(-0.146952\pi\)
\(108\) − 854.174i − 0.761046i
\(109\) − 1814.39i − 1.59438i −0.603732 0.797188i \(-0.706320\pi\)
0.603732 0.797188i \(-0.293680\pi\)
\(110\) −113.967 −0.0987846
\(111\) 417.518 0.357018
\(112\) 182.339i 0.153834i
\(113\) 707.339i 0.588857i 0.955673 + 0.294429i \(0.0951293\pi\)
−0.955673 + 0.294429i \(0.904871\pi\)
\(114\) 382.904i 0.314581i
\(115\) −349.463 −0.283370
\(116\) 790.253i 0.632527i
\(117\) 990.706 0.782827
\(118\) −397.503 −0.310112
\(119\) 0 0
\(120\) −184.175 −0.140107
\(121\) 568.350 0.427010
\(122\) − 73.3647i − 0.0544437i
\(123\) −1484.44 −1.08819
\(124\) − 1680.98i − 1.21739i
\(125\) 730.061i 0.522389i
\(126\) − 184.271i − 0.130287i
\(127\) −2648.18 −1.85030 −0.925151 0.379600i \(-0.876062\pi\)
−0.925151 + 0.379600i \(0.876062\pi\)
\(128\) 1389.22 0.959302
\(129\) − 1112.46i − 0.759273i
\(130\) − 239.817i − 0.161795i
\(131\) − 1979.08i − 1.31995i −0.751289 0.659974i \(-0.770567\pi\)
0.751289 0.659974i \(-0.229433\pi\)
\(132\) −535.525 −0.353117
\(133\) − 708.044i − 0.461618i
\(134\) −72.0865 −0.0464726
\(135\) −421.274 −0.268574
\(136\) 0 0
\(137\) 3141.92 1.95936 0.979679 0.200570i \(-0.0642794\pi\)
0.979679 + 0.200570i \(0.0642794\pi\)
\(138\) 494.984 0.305332
\(139\) 1468.07i 0.895830i 0.894076 + 0.447915i \(0.147833\pi\)
−0.894076 + 0.447915i \(0.852167\pi\)
\(140\) 147.980 0.0893327
\(141\) 481.390i 0.287520i
\(142\) − 1073.19i − 0.634224i
\(143\) − 1604.82i − 0.938474i
\(144\) 391.483 0.226553
\(145\) 389.749 0.223220
\(146\) − 402.621i − 0.228227i
\(147\) 883.135i 0.495508i
\(148\) 813.570i 0.451858i
\(149\) −286.027 −0.157263 −0.0786316 0.996904i \(-0.525055\pi\)
−0.0786316 + 0.996904i \(0.525055\pi\)
\(150\) − 497.300i − 0.270696i
\(151\) 669.626 0.360883 0.180442 0.983586i \(-0.442247\pi\)
0.180442 + 0.983586i \(0.442247\pi\)
\(152\) −1717.15 −0.916311
\(153\) 0 0
\(154\) −298.496 −0.156191
\(155\) −829.049 −0.429618
\(156\) − 1126.89i − 0.578354i
\(157\) 720.809 0.366413 0.183206 0.983074i \(-0.441352\pi\)
0.183206 + 0.983074i \(0.441352\pi\)
\(158\) − 980.522i − 0.493710i
\(159\) − 1664.43i − 0.830174i
\(160\) − 561.825i − 0.277601i
\(161\) −915.294 −0.448045
\(162\) −29.8770 −0.0144899
\(163\) 676.599i 0.325125i 0.986698 + 0.162562i \(0.0519759\pi\)
−0.986698 + 0.162562i \(0.948024\pi\)
\(164\) − 2892.56i − 1.37726i
\(165\) 264.118i 0.124616i
\(166\) −157.971 −0.0738609
\(167\) − 2835.67i − 1.31396i −0.753909 0.656979i \(-0.771834\pi\)
0.753909 0.656979i \(-0.228166\pi\)
\(168\) −482.382 −0.221527
\(169\) 1179.97 0.537083
\(170\) 0 0
\(171\) −1520.18 −0.679829
\(172\) 2167.72 0.960970
\(173\) − 177.314i − 0.0779243i −0.999241 0.0389621i \(-0.987595\pi\)
0.999241 0.0389621i \(-0.0124052\pi\)
\(174\) −552.046 −0.240520
\(175\) 919.578i 0.397220i
\(176\) − 634.153i − 0.271597i
\(177\) 921.214i 0.391202i
\(178\) 1107.12 0.466192
\(179\) 1023.76 0.427483 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(180\) − 317.714i − 0.131561i
\(181\) 3450.21i 1.41686i 0.705779 + 0.708432i \(0.250597\pi\)
−0.705779 + 0.708432i \(0.749403\pi\)
\(182\) − 628.116i − 0.255819i
\(183\) −170.023 −0.0686800
\(184\) 2219.78i 0.889370i
\(185\) 401.248 0.159461
\(186\) 1174.28 0.462915
\(187\) 0 0
\(188\) −938.031 −0.363899
\(189\) −1103.38 −0.424651
\(190\) 367.984i 0.140507i
\(191\) −490.894 −0.185968 −0.0929839 0.995668i \(-0.529640\pi\)
−0.0929839 + 0.995668i \(0.529640\pi\)
\(192\) 216.254i 0.0812855i
\(193\) 3548.80i 1.32357i 0.749696 + 0.661783i \(0.230200\pi\)
−0.749696 + 0.661783i \(0.769800\pi\)
\(194\) − 1081.75i − 0.400337i
\(195\) −555.775 −0.204102
\(196\) −1720.87 −0.627138
\(197\) − 1363.15i − 0.492996i −0.969143 0.246498i \(-0.920720\pi\)
0.969143 0.246498i \(-0.0792799\pi\)
\(198\) 640.874i 0.230025i
\(199\) 3737.46i 1.33137i 0.746235 + 0.665683i \(0.231860\pi\)
−0.746235 + 0.665683i \(0.768140\pi\)
\(200\) 2230.16 0.788482
\(201\) 167.060i 0.0586246i
\(202\) −361.422 −0.125889
\(203\) 1020.81 0.352940
\(204\) 0 0
\(205\) −1426.60 −0.486038
\(206\) −712.064 −0.240834
\(207\) 1965.15i 0.659841i
\(208\) 1334.43 0.444836
\(209\) 2462.50i 0.814997i
\(210\) 103.374i 0.0339690i
\(211\) 5266.12i 1.71817i 0.511829 + 0.859087i \(0.328968\pi\)
−0.511829 + 0.859087i \(0.671032\pi\)
\(212\) 3243.28 1.05071
\(213\) −2487.11 −0.800066
\(214\) 1342.22i 0.428748i
\(215\) − 1069.11i − 0.339128i
\(216\) 2675.92i 0.842932i
\(217\) −2171.40 −0.679283
\(218\) 2469.78i 0.767316i
\(219\) −933.075 −0.287906
\(220\) −514.657 −0.157719
\(221\) 0 0
\(222\) −568.334 −0.171820
\(223\) −704.546 −0.211569 −0.105785 0.994389i \(-0.533735\pi\)
−0.105785 + 0.994389i \(0.533735\pi\)
\(224\) − 1471.50i − 0.438923i
\(225\) 1974.34 0.584990
\(226\) − 962.845i − 0.283396i
\(227\) 2151.26i 0.629006i 0.949256 + 0.314503i \(0.101838\pi\)
−0.949256 + 0.314503i \(0.898162\pi\)
\(228\) 1729.14i 0.502259i
\(229\) 3916.94 1.13030 0.565149 0.824989i \(-0.308819\pi\)
0.565149 + 0.824989i \(0.308819\pi\)
\(230\) 475.696 0.136376
\(231\) 691.764i 0.197034i
\(232\) − 2475.67i − 0.700586i
\(233\) − 5192.74i − 1.46003i −0.683429 0.730017i \(-0.739512\pi\)
0.683429 0.730017i \(-0.260488\pi\)
\(234\) −1348.57 −0.376747
\(235\) 462.632i 0.128420i
\(236\) −1795.07 −0.495123
\(237\) −2272.36 −0.622809
\(238\) 0 0
\(239\) 334.305 0.0904786 0.0452393 0.998976i \(-0.485595\pi\)
0.0452393 + 0.998976i \(0.485595\pi\)
\(240\) −219.618 −0.0590677
\(241\) − 1918.45i − 0.512773i −0.966574 0.256386i \(-0.917468\pi\)
0.966574 0.256386i \(-0.0825320\pi\)
\(242\) −773.651 −0.205505
\(243\) 3821.06i 1.00873i
\(244\) − 331.304i − 0.0869245i
\(245\) 848.722i 0.221318i
\(246\) 2020.65 0.523708
\(247\) −5181.75 −1.33485
\(248\) 5266.09i 1.34838i
\(249\) 366.097i 0.0931746i
\(250\) − 993.775i − 0.251407i
\(251\) 7695.71 1.93525 0.967627 0.252385i \(-0.0812148\pi\)
0.967627 + 0.252385i \(0.0812148\pi\)
\(252\) − 832.141i − 0.208016i
\(253\) 3183.29 0.791035
\(254\) 3604.76 0.890484
\(255\) 0 0
\(256\) −2439.44 −0.595567
\(257\) −5335.10 −1.29492 −0.647460 0.762099i \(-0.724169\pi\)
−0.647460 + 0.762099i \(0.724169\pi\)
\(258\) 1514.30i 0.365411i
\(259\) 1050.93 0.252130
\(260\) − 1082.98i − 0.258321i
\(261\) − 2191.69i − 0.519778i
\(262\) 2693.97i 0.635244i
\(263\) −3934.15 −0.922396 −0.461198 0.887297i \(-0.652580\pi\)
−0.461198 + 0.887297i \(0.652580\pi\)
\(264\) 1677.67 0.391112
\(265\) − 1599.57i − 0.370795i
\(266\) 963.804i 0.222160i
\(267\) − 2565.75i − 0.588095i
\(268\) −325.532 −0.0741979
\(269\) 3424.04i 0.776088i 0.921641 + 0.388044i \(0.126849\pi\)
−0.921641 + 0.388044i \(0.873151\pi\)
\(270\) 573.447 0.129255
\(271\) 549.034 0.123068 0.0615340 0.998105i \(-0.480401\pi\)
0.0615340 + 0.998105i \(0.480401\pi\)
\(272\) 0 0
\(273\) −1455.66 −0.322712
\(274\) −4276.85 −0.942970
\(275\) − 3198.19i − 0.701302i
\(276\) 2235.27 0.487492
\(277\) 5203.65i 1.12873i 0.825527 + 0.564363i \(0.190878\pi\)
−0.825527 + 0.564363i \(0.809122\pi\)
\(278\) − 1998.37i − 0.431131i
\(279\) 4662.02i 1.00039i
\(280\) −463.585 −0.0989447
\(281\) 1986.73 0.421774 0.210887 0.977510i \(-0.432365\pi\)
0.210887 + 0.977510i \(0.432365\pi\)
\(282\) − 655.279i − 0.138373i
\(283\) − 753.696i − 0.158313i −0.996862 0.0791565i \(-0.974777\pi\)
0.996862 0.0791565i \(-0.0252227\pi\)
\(284\) − 4846.36i − 1.01260i
\(285\) 852.803 0.177248
\(286\) 2184.51i 0.451654i
\(287\) −3736.47 −0.768490
\(288\) −3159.33 −0.646407
\(289\) 0 0
\(290\) −530.534 −0.107428
\(291\) −2506.96 −0.505020
\(292\) − 1818.18i − 0.364387i
\(293\) −7202.22 −1.43603 −0.718017 0.696025i \(-0.754950\pi\)
−0.718017 + 0.696025i \(0.754950\pi\)
\(294\) − 1202.14i − 0.238471i
\(295\) 885.318i 0.174729i
\(296\) − 2548.72i − 0.500477i
\(297\) 3837.43 0.749731
\(298\) 389.345 0.0756852
\(299\) 6698.50i 1.29560i
\(300\) − 2245.74i − 0.432192i
\(301\) − 2800.15i − 0.536205i
\(302\) −911.509 −0.173680
\(303\) 837.595i 0.158807i
\(304\) −2047.60 −0.386308
\(305\) −163.398 −0.0306758
\(306\) 0 0
\(307\) 2425.71 0.450953 0.225477 0.974249i \(-0.427606\pi\)
0.225477 + 0.974249i \(0.427606\pi\)
\(308\) −1347.96 −0.249375
\(309\) 1650.21i 0.303809i
\(310\) 1128.52 0.206760
\(311\) − 9544.94i − 1.74033i −0.492757 0.870167i \(-0.664011\pi\)
0.492757 0.870167i \(-0.335989\pi\)
\(312\) 3530.27i 0.640584i
\(313\) − 588.379i − 0.106253i −0.998588 0.0531264i \(-0.983081\pi\)
0.998588 0.0531264i \(-0.0169186\pi\)
\(314\) −981.180 −0.176341
\(315\) −410.407 −0.0734090
\(316\) − 4427.89i − 0.788255i
\(317\) − 7653.31i − 1.35600i −0.735061 0.678001i \(-0.762846\pi\)
0.735061 0.678001i \(-0.237154\pi\)
\(318\) 2265.65i 0.399533i
\(319\) −3550.26 −0.623124
\(320\) 207.828i 0.0363060i
\(321\) 3110.59 0.540860
\(322\) 1245.92 0.215628
\(323\) 0 0
\(324\) −134.920 −0.0231345
\(325\) 6729.85 1.14863
\(326\) − 921.001i − 0.156471i
\(327\) 5723.73 0.967960
\(328\) 9061.70i 1.52545i
\(329\) 1211.70i 0.203050i
\(330\) − 359.523i − 0.0599730i
\(331\) −752.266 −0.124919 −0.0624597 0.998047i \(-0.519894\pi\)
−0.0624597 + 0.998047i \(0.519894\pi\)
\(332\) −713.373 −0.117926
\(333\) − 2256.36i − 0.371314i
\(334\) 3859.98i 0.632361i
\(335\) 160.551i 0.0261845i
\(336\) −575.211 −0.0933939
\(337\) − 1968.57i − 0.318204i −0.987262 0.159102i \(-0.949140\pi\)
0.987262 0.159102i \(-0.0508598\pi\)
\(338\) −1606.20 −0.258479
\(339\) −2231.39 −0.357501
\(340\) 0 0
\(341\) 7551.89 1.19929
\(342\) 2069.30 0.327178
\(343\) 4946.52i 0.778678i
\(344\) −6790.93 −1.06437
\(345\) − 1102.43i − 0.172037i
\(346\) 241.363i 0.0375022i
\(347\) − 3983.10i − 0.616207i −0.951353 0.308104i \(-0.900306\pi\)
0.951353 0.308104i \(-0.0996944\pi\)
\(348\) −2492.96 −0.384013
\(349\) −1495.61 −0.229393 −0.114697 0.993401i \(-0.536590\pi\)
−0.114697 + 0.993401i \(0.536590\pi\)
\(350\) − 1251.75i − 0.191168i
\(351\) 8074.98i 1.22795i
\(352\) 5117.72i 0.774930i
\(353\) 6482.49 0.977417 0.488708 0.872447i \(-0.337468\pi\)
0.488708 + 0.872447i \(0.337468\pi\)
\(354\) − 1253.98i − 0.188272i
\(355\) −2390.20 −0.357348
\(356\) 4999.59 0.744320
\(357\) 0 0
\(358\) −1393.56 −0.205732
\(359\) 4943.42 0.726751 0.363376 0.931643i \(-0.381624\pi\)
0.363376 + 0.931643i \(0.381624\pi\)
\(360\) 995.322i 0.145717i
\(361\) 1092.08 0.159218
\(362\) − 4696.50i − 0.681886i
\(363\) 1792.94i 0.259242i
\(364\) − 2836.48i − 0.408439i
\(365\) −896.717 −0.128593
\(366\) 231.439 0.0330533
\(367\) 14.8871i 0.00211743i 0.999999 + 0.00105872i \(0.000337000\pi\)
−0.999999 + 0.00105872i \(0.999663\pi\)
\(368\) 2646.95i 0.374950i
\(369\) 8022.23i 1.13176i
\(370\) −546.188 −0.0767431
\(371\) − 4189.51i − 0.586276i
\(372\) 5302.86 0.739088
\(373\) 1923.18 0.266966 0.133483 0.991051i \(-0.457384\pi\)
0.133483 + 0.991051i \(0.457384\pi\)
\(374\) 0 0
\(375\) −2303.07 −0.317147
\(376\) 2938.63 0.403053
\(377\) − 7470.70i − 1.02059i
\(378\) 1501.94 0.204369
\(379\) − 9592.87i − 1.30014i −0.759875 0.650069i \(-0.774740\pi\)
0.759875 0.650069i \(-0.225260\pi\)
\(380\) 1661.76i 0.224333i
\(381\) − 8354.04i − 1.12333i
\(382\) 668.215 0.0894996
\(383\) 9083.77 1.21190 0.605951 0.795502i \(-0.292793\pi\)
0.605951 + 0.795502i \(0.292793\pi\)
\(384\) 4382.47i 0.582401i
\(385\) 664.809i 0.0880046i
\(386\) − 4830.70i − 0.636985i
\(387\) −6011.95 −0.789675
\(388\) − 4885.04i − 0.639176i
\(389\) 1143.78 0.149079 0.0745396 0.997218i \(-0.476251\pi\)
0.0745396 + 0.997218i \(0.476251\pi\)
\(390\) 756.533 0.0982271
\(391\) 0 0
\(392\) 5391.06 0.694616
\(393\) 6243.27 0.801352
\(394\) 1855.55i 0.237262i
\(395\) −2183.81 −0.278176
\(396\) 2894.09i 0.367256i
\(397\) − 10604.5i − 1.34061i −0.742084 0.670307i \(-0.766162\pi\)
0.742084 0.670307i \(-0.233838\pi\)
\(398\) − 5087.51i − 0.640739i
\(399\) 2233.62 0.280252
\(400\) 2659.33 0.332417
\(401\) − 13785.4i − 1.71674i −0.513035 0.858368i \(-0.671479\pi\)
0.513035 0.858368i \(-0.328521\pi\)
\(402\) − 227.406i − 0.0282139i
\(403\) 15891.2i 1.96426i
\(404\) −1632.13 −0.200993
\(405\) 66.5420i 0.00816419i
\(406\) −1389.55 −0.169857
\(407\) −3655.01 −0.445141
\(408\) 0 0
\(409\) −9505.94 −1.14924 −0.574619 0.818421i \(-0.694850\pi\)
−0.574619 + 0.818421i \(0.694850\pi\)
\(410\) 1941.91 0.233913
\(411\) 9911.59i 1.18954i
\(412\) −3215.58 −0.384515
\(413\) 2318.78i 0.276270i
\(414\) − 2675.00i − 0.317558i
\(415\) 351.832i 0.0416162i
\(416\) −10769.1 −1.26922
\(417\) −4631.23 −0.543866
\(418\) − 3352.00i − 0.392229i
\(419\) − 9680.86i − 1.12874i −0.825523 0.564369i \(-0.809120\pi\)
0.825523 0.564369i \(-0.190880\pi\)
\(420\) 466.822i 0.0542347i
\(421\) −12360.3 −1.43089 −0.715444 0.698671i \(-0.753775\pi\)
−0.715444 + 0.698671i \(0.753775\pi\)
\(422\) − 7168.36i − 0.826897i
\(423\) 2601.54 0.299033
\(424\) −10160.4 −1.16376
\(425\) 0 0
\(426\) 3385.51 0.385043
\(427\) −427.962 −0.0485025
\(428\) 6061.25i 0.684537i
\(429\) 5062.61 0.569756
\(430\) 1455.29i 0.163210i
\(431\) − 2970.58i − 0.331990i −0.986127 0.165995i \(-0.946916\pi\)
0.986127 0.165995i \(-0.0530835\pi\)
\(432\) 3190.87i 0.355372i
\(433\) −6131.50 −0.680510 −0.340255 0.940333i \(-0.610513\pi\)
−0.340255 + 0.940333i \(0.610513\pi\)
\(434\) 2955.76 0.326915
\(435\) 1229.51i 0.135519i
\(436\) 11153.2i 1.22509i
\(437\) − 10278.4i − 1.12513i
\(438\) 1270.12 0.138559
\(439\) − 2544.91i − 0.276679i −0.990385 0.138339i \(-0.955824\pi\)
0.990385 0.138339i \(-0.0441765\pi\)
\(440\) 1612.30 0.174689
\(441\) 4772.65 0.515349
\(442\) 0 0
\(443\) 8529.82 0.914817 0.457408 0.889257i \(-0.348778\pi\)
0.457408 + 0.889257i \(0.348778\pi\)
\(444\) −2566.51 −0.274327
\(445\) − 2465.77i − 0.262672i
\(446\) 959.043 0.101821
\(447\) − 902.308i − 0.0954759i
\(448\) 544.331i 0.0574046i
\(449\) − 8855.74i − 0.930798i −0.885101 0.465399i \(-0.845911\pi\)
0.885101 0.465399i \(-0.154089\pi\)
\(450\) −2687.52 −0.281535
\(451\) 12995.0 1.35679
\(452\) − 4348.07i − 0.452469i
\(453\) 2112.42i 0.219095i
\(454\) − 2928.35i − 0.302718i
\(455\) −1398.94 −0.144139
\(456\) − 5416.98i − 0.556301i
\(457\) 7154.78 0.732356 0.366178 0.930545i \(-0.380666\pi\)
0.366178 + 0.930545i \(0.380666\pi\)
\(458\) −5331.82 −0.543973
\(459\) 0 0
\(460\) 2148.17 0.217737
\(461\) 7263.06 0.733784 0.366892 0.930264i \(-0.380422\pi\)
0.366892 + 0.930264i \(0.380422\pi\)
\(462\) − 941.645i − 0.0948253i
\(463\) 352.898 0.0354224 0.0177112 0.999843i \(-0.494362\pi\)
0.0177112 + 0.999843i \(0.494362\pi\)
\(464\) − 2952.09i − 0.295360i
\(465\) − 2615.34i − 0.260825i
\(466\) 7068.47i 0.702662i
\(467\) −1483.02 −0.146951 −0.0734753 0.997297i \(-0.523409\pi\)
−0.0734753 + 0.997297i \(0.523409\pi\)
\(468\) −6089.94 −0.601512
\(469\) 420.506i 0.0414012i
\(470\) − 629.745i − 0.0618042i
\(471\) 2273.89i 0.222452i
\(472\) 5623.51 0.548396
\(473\) 9738.60i 0.946683i
\(474\) 3093.19 0.299736
\(475\) −10326.5 −0.997502
\(476\) 0 0
\(477\) −8994.92 −0.863415
\(478\) −455.063 −0.0435441
\(479\) − 9990.10i − 0.952942i −0.879190 0.476471i \(-0.841916\pi\)
0.879190 0.476471i \(-0.158084\pi\)
\(480\) 1772.35 0.168534
\(481\) − 7691.13i − 0.729075i
\(482\) 2611.44i 0.246779i
\(483\) − 2887.42i − 0.272012i
\(484\) −3493.69 −0.328108
\(485\) −2409.27 −0.225566
\(486\) − 5201.30i − 0.485465i
\(487\) 1129.88i 0.105133i 0.998617 + 0.0525663i \(0.0167401\pi\)
−0.998617 + 0.0525663i \(0.983260\pi\)
\(488\) 1037.90i 0.0962774i
\(489\) −2134.42 −0.197386
\(490\) − 1155.30i − 0.106512i
\(491\) −18774.9 −1.72566 −0.862832 0.505491i \(-0.831311\pi\)
−0.862832 + 0.505491i \(0.831311\pi\)
\(492\) 9124.97 0.836149
\(493\) 0 0
\(494\) 7053.51 0.642414
\(495\) 1427.35 0.129605
\(496\) 6279.49i 0.568463i
\(497\) −6260.28 −0.565014
\(498\) − 498.339i − 0.0448416i
\(499\) − 17329.1i − 1.55462i −0.629118 0.777310i \(-0.716584\pi\)
0.629118 0.777310i \(-0.283416\pi\)
\(500\) − 4487.74i − 0.401396i
\(501\) 8945.50 0.797716
\(502\) −10475.6 −0.931369
\(503\) 20837.0i 1.84707i 0.383518 + 0.923533i \(0.374712\pi\)
−0.383518 + 0.923533i \(0.625288\pi\)
\(504\) 2606.90i 0.230398i
\(505\) 804.957i 0.0709309i
\(506\) −4333.16 −0.380697
\(507\) 3722.37i 0.326068i
\(508\) 16278.6 1.42174
\(509\) 11835.0 1.03060 0.515301 0.857009i \(-0.327680\pi\)
0.515301 + 0.857009i \(0.327680\pi\)
\(510\) 0 0
\(511\) −2348.63 −0.203322
\(512\) −7793.12 −0.672676
\(513\) − 12390.6i − 1.06639i
\(514\) 7262.26 0.623199
\(515\) 1585.91i 0.135696i
\(516\) 6838.35i 0.583414i
\(517\) − 4214.16i − 0.358489i
\(518\) −1430.55 −0.121341
\(519\) 559.359 0.0473086
\(520\) 3392.71i 0.286115i
\(521\) − 7686.37i − 0.646346i −0.946340 0.323173i \(-0.895250\pi\)
0.946340 0.323173i \(-0.104750\pi\)
\(522\) 2983.37i 0.250151i
\(523\) 11476.4 0.959518 0.479759 0.877400i \(-0.340724\pi\)
0.479759 + 0.877400i \(0.340724\pi\)
\(524\) 12165.6i 1.01423i
\(525\) −2900.93 −0.241156
\(526\) 5355.25 0.443916
\(527\) 0 0
\(528\) 2000.52 0.164889
\(529\) −1120.01 −0.0920535
\(530\) 2177.37i 0.178451i
\(531\) 4978.44 0.406866
\(532\) 4352.40i 0.354700i
\(533\) 27345.0i 2.22222i
\(534\) 3492.56i 0.283029i
\(535\) 2989.38 0.241574
\(536\) 1019.81 0.0821814
\(537\) 3229.59i 0.259529i
\(538\) − 4660.88i − 0.373504i
\(539\) − 7731.09i − 0.617814i
\(540\) 2589.60 0.206368
\(541\) − 546.481i − 0.0434289i −0.999764 0.0217145i \(-0.993088\pi\)
0.999764 0.0217145i \(-0.00691247\pi\)
\(542\) −747.357 −0.0592283
\(543\) −10884.1 −0.860191
\(544\) 0 0
\(545\) 5500.69 0.432337
\(546\) 1981.47 0.155310
\(547\) 8397.33i 0.656388i 0.944610 + 0.328194i \(0.106440\pi\)
−0.944610 + 0.328194i \(0.893560\pi\)
\(548\) −19313.6 −1.50554
\(549\) 918.839i 0.0714301i
\(550\) 4353.44i 0.337512i
\(551\) 11463.3i 0.886305i
\(552\) −7002.58 −0.539945
\(553\) −5719.73 −0.439833
\(554\) − 7083.32i − 0.543215i
\(555\) 1265.79i 0.0968105i
\(556\) − 9024.36i − 0.688342i
\(557\) −4881.65 −0.371350 −0.185675 0.982611i \(-0.559447\pi\)
−0.185675 + 0.982611i \(0.559447\pi\)
\(558\) − 6346.04i − 0.481451i
\(559\) −20492.6 −1.55053
\(560\) −552.797 −0.0417142
\(561\) 0 0
\(562\) −2704.38 −0.202985
\(563\) −7198.57 −0.538870 −0.269435 0.963019i \(-0.586837\pi\)
−0.269435 + 0.963019i \(0.586837\pi\)
\(564\) − 2959.14i − 0.220926i
\(565\) −2144.44 −0.159677
\(566\) 1025.95i 0.0761904i
\(567\) 174.283i 0.0129087i
\(568\) 15182.5i 1.12155i
\(569\) 23946.9 1.76433 0.882167 0.470937i \(-0.156084\pi\)
0.882167 + 0.470937i \(0.156084\pi\)
\(570\) −1160.85 −0.0853032
\(571\) − 1593.15i − 0.116763i −0.998294 0.0583813i \(-0.981406\pi\)
0.998294 0.0583813i \(-0.0185939\pi\)
\(572\) 9864.95i 0.721109i
\(573\) − 1548.59i − 0.112903i
\(574\) 5086.16 0.369847
\(575\) 13349.2i 0.968174i
\(576\) 1168.69 0.0845403
\(577\) 12937.4 0.933435 0.466717 0.884406i \(-0.345436\pi\)
0.466717 + 0.884406i \(0.345436\pi\)
\(578\) 0 0
\(579\) −11195.2 −0.803549
\(580\) −2395.82 −0.171519
\(581\) 921.499i 0.0658007i
\(582\) 3412.53 0.243048
\(583\) 14570.6i 1.03508i
\(584\) 5695.92i 0.403594i
\(585\) 3003.53i 0.212275i
\(586\) 9803.82 0.691112
\(587\) 12899.2 0.906998 0.453499 0.891257i \(-0.350176\pi\)
0.453499 + 0.891257i \(0.350176\pi\)
\(588\) − 5428.70i − 0.380741i
\(589\) − 24384.1i − 1.70582i
\(590\) − 1205.11i − 0.0840911i
\(591\) 4300.23 0.299302
\(592\) − 3039.19i − 0.210997i
\(593\) −4357.13 −0.301730 −0.150865 0.988554i \(-0.548206\pi\)
−0.150865 + 0.988554i \(0.548206\pi\)
\(594\) −5223.59 −0.360819
\(595\) 0 0
\(596\) 1758.23 0.120839
\(597\) −11790.3 −0.808284
\(598\) − 9118.14i − 0.623526i
\(599\) 13726.8 0.936328 0.468164 0.883642i \(-0.344916\pi\)
0.468164 + 0.883642i \(0.344916\pi\)
\(600\) 7035.35i 0.478695i
\(601\) − 2531.41i − 0.171811i −0.996303 0.0859056i \(-0.972622\pi\)
0.996303 0.0859056i \(-0.0273783\pi\)
\(602\) 3811.62i 0.258057i
\(603\) 902.830 0.0609720
\(604\) −4116.24 −0.277297
\(605\) 1723.07i 0.115790i
\(606\) − 1140.15i − 0.0764283i
\(607\) 185.004i 0.0123708i 0.999981 + 0.00618540i \(0.00196889\pi\)
−0.999981 + 0.00618540i \(0.998031\pi\)
\(608\) 16524.4 1.10223
\(609\) 3220.28i 0.214273i
\(610\) 222.420 0.0147632
\(611\) 8867.73 0.587152
\(612\) 0 0
\(613\) −17706.9 −1.16668 −0.583339 0.812228i \(-0.698254\pi\)
−0.583339 + 0.812228i \(0.698254\pi\)
\(614\) −3301.93 −0.217028
\(615\) − 4500.39i − 0.295078i
\(616\) 4222.84 0.276207
\(617\) − 6183.89i − 0.403491i −0.979438 0.201746i \(-0.935339\pi\)
0.979438 0.201746i \(-0.0646614\pi\)
\(618\) − 2246.30i − 0.146213i
\(619\) 1247.51i 0.0810046i 0.999179 + 0.0405023i \(0.0128958\pi\)
−0.999179 + 0.0405023i \(0.987104\pi\)
\(620\) 5096.23 0.330112
\(621\) −16017.4 −1.03503
\(622\) 12992.8i 0.837561i
\(623\) − 6458.23i − 0.415318i
\(624\) 4209.63i 0.270064i
\(625\) 12262.8 0.784817
\(626\) 800.914i 0.0511357i
\(627\) −7768.27 −0.494792
\(628\) −4430.87 −0.281546
\(629\) 0 0
\(630\) 558.655 0.0353292
\(631\) −24053.3 −1.51750 −0.758752 0.651379i \(-0.774191\pi\)
−0.758752 + 0.651379i \(0.774191\pi\)
\(632\) 13871.5i 0.873069i
\(633\) −16612.7 −1.04312
\(634\) 10417.8i 0.652596i
\(635\) − 8028.51i − 0.501735i
\(636\) 10231.4i 0.637893i
\(637\) 16268.3 1.01189
\(638\) 4832.69 0.299887
\(639\) 13440.9i 0.832102i
\(640\) 4211.70i 0.260128i
\(641\) − 21286.8i − 1.31167i −0.754905 0.655834i \(-0.772317\pi\)
0.754905 0.655834i \(-0.227683\pi\)
\(642\) −4234.20 −0.260297
\(643\) − 1789.41i − 0.109747i −0.998493 0.0548736i \(-0.982524\pi\)
0.998493 0.0548736i \(-0.0174756\pi\)
\(644\) 5626.38 0.344271
\(645\) 3372.64 0.205888
\(646\) 0 0
\(647\) −4378.61 −0.266060 −0.133030 0.991112i \(-0.542471\pi\)
−0.133030 + 0.991112i \(0.542471\pi\)
\(648\) 422.672 0.0256237
\(649\) − 8064.45i − 0.487762i
\(650\) −9160.81 −0.552795
\(651\) − 6849.97i − 0.412399i
\(652\) − 4159.11i − 0.249821i
\(653\) 7665.15i 0.459358i 0.973266 + 0.229679i \(0.0737676\pi\)
−0.973266 + 0.229679i \(0.926232\pi\)
\(654\) −7791.26 −0.465845
\(655\) 5999.99 0.357922
\(656\) 10805.5i 0.643117i
\(657\) 5042.54i 0.299434i
\(658\) − 1649.39i − 0.0977205i
\(659\) −4710.22 −0.278428 −0.139214 0.990262i \(-0.544458\pi\)
−0.139214 + 0.990262i \(0.544458\pi\)
\(660\) − 1623.55i − 0.0957527i
\(661\) 31266.6 1.83983 0.919916 0.392116i \(-0.128257\pi\)
0.919916 + 0.392116i \(0.128257\pi\)
\(662\) 1024.00 0.0601192
\(663\) 0 0
\(664\) 2234.82 0.130614
\(665\) 2146.58 0.125174
\(666\) 3071.40i 0.178700i
\(667\) 14818.7 0.860246
\(668\) 17431.1i 1.00962i
\(669\) − 2222.58i − 0.128446i
\(670\) − 218.545i − 0.0126017i
\(671\) 1488.40 0.0856322
\(672\) 4642.05 0.266474
\(673\) − 11723.0i − 0.671454i −0.941959 0.335727i \(-0.891018\pi\)
0.941959 0.335727i \(-0.108982\pi\)
\(674\) 2679.65i 0.153140i
\(675\) 16092.3i 0.917621i
\(676\) −7253.37 −0.412686
\(677\) − 289.531i − 0.0164366i −0.999966 0.00821829i \(-0.997384\pi\)
0.999966 0.00821829i \(-0.00261599\pi\)
\(678\) 3037.42 0.172052
\(679\) −6310.25 −0.356650
\(680\) 0 0
\(681\) −6786.45 −0.381875
\(682\) −10279.8 −0.577175
\(683\) 1720.10i 0.0963660i 0.998839 + 0.0481830i \(0.0153431\pi\)
−0.998839 + 0.0481830i \(0.984657\pi\)
\(684\) 9344.64 0.522370
\(685\) 9525.37i 0.531308i
\(686\) − 6733.30i − 0.374750i
\(687\) 12356.5i 0.686215i
\(688\) −8097.77 −0.448728
\(689\) −30660.5 −1.69532
\(690\) 1500.65i 0.0827951i
\(691\) 16777.7i 0.923665i 0.886967 + 0.461832i \(0.152808\pi\)
−0.886967 + 0.461832i \(0.847192\pi\)
\(692\) 1089.96i 0.0598758i
\(693\) 3738.44 0.204923
\(694\) 5421.88i 0.296559i
\(695\) −4450.77 −0.242917
\(696\) 7809.84 0.425332
\(697\) 0 0
\(698\) 2035.86 0.110399
\(699\) 16381.2 0.886400
\(700\) − 5652.71i − 0.305218i
\(701\) 23981.1 1.29209 0.646043 0.763301i \(-0.276423\pi\)
0.646043 + 0.763301i \(0.276423\pi\)
\(702\) − 10991.8i − 0.590969i
\(703\) 11801.6i 0.633150i
\(704\) − 1893.12i − 0.101349i
\(705\) −1459.43 −0.0779652
\(706\) −8824.10 −0.470396
\(707\) 2108.30i 0.112151i
\(708\) − 5662.78i − 0.300593i
\(709\) − 7709.28i − 0.408361i −0.978933 0.204181i \(-0.934547\pi\)
0.978933 0.204181i \(-0.0654530\pi\)
\(710\) 3253.59 0.171979
\(711\) 12280.3i 0.647747i
\(712\) −15662.5 −0.824407
\(713\) −31521.5 −1.65567
\(714\) 0 0
\(715\) 4865.34 0.254480
\(716\) −6293.13 −0.328471
\(717\) 1054.61i 0.0549304i
\(718\) −6729.09 −0.349760
\(719\) − 11976.5i − 0.621209i −0.950539 0.310605i \(-0.899468\pi\)
0.950539 0.310605i \(-0.100532\pi\)
\(720\) 1186.86i 0.0614329i
\(721\) 4153.72i 0.214553i
\(722\) −1486.56 −0.0766260
\(723\) 6052.00 0.311309
\(724\) − 21208.7i − 1.08870i
\(725\) − 14888.1i − 0.762662i
\(726\) − 2440.58i − 0.124764i
\(727\) −18597.3 −0.948745 −0.474372 0.880324i \(-0.657325\pi\)
−0.474372 + 0.880324i \(0.657325\pi\)
\(728\) 8886.00i 0.452386i
\(729\) −11461.4 −0.582300
\(730\) 1220.63 0.0618870
\(731\) 0 0
\(732\) 1045.14 0.0527727
\(733\) 23569.5 1.18767 0.593833 0.804588i \(-0.297614\pi\)
0.593833 + 0.804588i \(0.297614\pi\)
\(734\) − 20.2646i − 0.00101905i
\(735\) −2677.41 −0.134364
\(736\) − 21361.3i − 1.06982i
\(737\) − 1462.47i − 0.0730948i
\(738\) − 10920.0i − 0.544678i
\(739\) −10149.1 −0.505199 −0.252599 0.967571i \(-0.581285\pi\)
−0.252599 + 0.967571i \(0.581285\pi\)
\(740\) −2466.50 −0.122528
\(741\) − 16346.5i − 0.810397i
\(742\) 5702.85i 0.282154i
\(743\) 27758.0i 1.37058i 0.728269 + 0.685291i \(0.240325\pi\)
−0.728269 + 0.685291i \(0.759675\pi\)
\(744\) −16612.6 −0.818611
\(745\) − 867.148i − 0.0426441i
\(746\) −2617.87 −0.128481
\(747\) 1978.47 0.0969054
\(748\) 0 0
\(749\) 7829.63 0.381960
\(750\) 3134.99 0.152632
\(751\) − 815.225i − 0.0396112i −0.999804 0.0198056i \(-0.993695\pi\)
0.999804 0.0198056i \(-0.00630473\pi\)
\(752\) 3504.13 0.169924
\(753\) 24277.1i 1.17491i
\(754\) 10169.3i 0.491172i
\(755\) 2030.11i 0.0978585i
\(756\) 6782.56 0.326295
\(757\) 13239.4 0.635659 0.317829 0.948148i \(-0.397046\pi\)
0.317829 + 0.948148i \(0.397046\pi\)
\(758\) 13058.0i 0.625710i
\(759\) 10042.1i 0.480244i
\(760\) − 5205.90i − 0.248471i
\(761\) −11028.2 −0.525324 −0.262662 0.964888i \(-0.584600\pi\)
−0.262662 + 0.964888i \(0.584600\pi\)
\(762\) 11371.7i 0.540621i
\(763\) 14407.1 0.683582
\(764\) 3017.56 0.142895
\(765\) 0 0
\(766\) −12365.0 −0.583246
\(767\) 16969.8 0.798882
\(768\) − 7695.55i − 0.361574i
\(769\) −18921.2 −0.887277 −0.443639 0.896206i \(-0.646313\pi\)
−0.443639 + 0.896206i \(0.646313\pi\)
\(770\) − 904.952i − 0.0423535i
\(771\) − 16830.3i − 0.786158i
\(772\) − 21814.7i − 1.01701i
\(773\) −38728.6 −1.80203 −0.901016 0.433786i \(-0.857177\pi\)
−0.901016 + 0.433786i \(0.857177\pi\)
\(774\) 8183.59 0.380043
\(775\) 31669.0i 1.46785i
\(776\) 15303.6i 0.707949i
\(777\) 3315.29i 0.153070i
\(778\) −1556.93 −0.0717465
\(779\) − 41959.2i − 1.92984i
\(780\) 3416.39 0.156829
\(781\) 21772.5 0.997545
\(782\) 0 0
\(783\) 17863.9 0.815329
\(784\) 6428.50 0.292844
\(785\) 2185.28i 0.0993579i
\(786\) −8498.47 −0.385662
\(787\) − 20587.3i − 0.932477i −0.884659 0.466239i \(-0.845609\pi\)
0.884659 0.466239i \(-0.154391\pi\)
\(788\) 8379.37i 0.378811i
\(789\) − 12410.8i − 0.559995i
\(790\) 2972.66 0.133876
\(791\) −5616.62 −0.252470
\(792\) − 9066.49i − 0.406772i
\(793\) 3132.00i 0.140253i
\(794\) 14435.0i 0.645190i
\(795\) 5046.05 0.225113
\(796\) − 22974.5i − 1.02300i
\(797\) 15871.4 0.705385 0.352693 0.935739i \(-0.385266\pi\)
0.352693 + 0.935739i \(0.385266\pi\)
\(798\) −3040.45 −0.134876
\(799\) 0 0
\(800\) −21461.3 −0.948463
\(801\) −13865.9 −0.611644
\(802\) 18765.0i 0.826204i
\(803\) 8168.28 0.358969
\(804\) − 1026.93i − 0.0450462i
\(805\) − 2774.90i − 0.121494i
\(806\) − 21631.4i − 0.945329i
\(807\) −10801.6 −0.471170
\(808\) 5113.06 0.222620
\(809\) − 39667.1i − 1.72388i −0.507007 0.861942i \(-0.669248\pi\)
0.507007 0.861942i \(-0.330752\pi\)
\(810\) − 90.5783i − 0.00392913i
\(811\) 8003.87i 0.346552i 0.984873 + 0.173276i \(0.0554353\pi\)
−0.984873 + 0.173276i \(0.944565\pi\)
\(812\) −6275.00 −0.271194
\(813\) 1732.00i 0.0747157i
\(814\) 4975.28 0.214230
\(815\) −2051.25 −0.0881621
\(816\) 0 0
\(817\) 31444.7 1.34652
\(818\) 12939.7 0.553088
\(819\) 7866.69i 0.335634i
\(820\) 8769.40 0.373464
\(821\) − 13279.1i − 0.564489i −0.959343 0.282244i \(-0.908921\pi\)
0.959343 0.282244i \(-0.0910789\pi\)
\(822\) − 13491.9i − 0.572486i
\(823\) − 28934.0i − 1.22549i −0.790281 0.612745i \(-0.790065\pi\)
0.790281 0.612745i \(-0.209935\pi\)
\(824\) 10073.6 0.425887
\(825\) 10089.1 0.425767
\(826\) − 3156.37i − 0.132959i
\(827\) 13679.6i 0.575193i 0.957752 + 0.287597i \(0.0928563\pi\)
−0.957752 + 0.287597i \(0.907144\pi\)
\(828\) − 12079.9i − 0.507012i
\(829\) 16514.5 0.691886 0.345943 0.938256i \(-0.387559\pi\)
0.345943 + 0.938256i \(0.387559\pi\)
\(830\) − 478.921i − 0.0200284i
\(831\) −16415.6 −0.685260
\(832\) 3983.64 0.165995
\(833\) 0 0
\(834\) 6304.13 0.261744
\(835\) 8596.93 0.356298
\(836\) − 15137.1i − 0.626231i
\(837\) −37998.9 −1.56922
\(838\) 13177.8i 0.543221i
\(839\) 87.9839i 0.00362043i 0.999998 + 0.00181022i \(0.000576210\pi\)
−0.999998 + 0.00181022i \(0.999424\pi\)
\(840\) − 1462.44i − 0.0600702i
\(841\) 7861.94 0.322356
\(842\) 16825.1 0.688635
\(843\) 6267.41i 0.256063i
\(844\) − 32371.3i − 1.32022i
\(845\) 3577.33i 0.145638i
\(846\) −3541.27 −0.143914
\(847\) 4512.98i 0.183079i
\(848\) −12115.7 −0.490630
\(849\) 2377.63 0.0961133
\(850\) 0 0
\(851\) 15256.0 0.614534
\(852\) 15288.5 0.614758
\(853\) 8162.96i 0.327660i 0.986489 + 0.163830i \(0.0523849\pi\)
−0.986489 + 0.163830i \(0.947615\pi\)
\(854\) 582.551 0.0233425
\(855\) − 4608.73i − 0.184345i
\(856\) − 18988.4i − 0.758191i
\(857\) − 18724.9i − 0.746361i −0.927759 0.373181i \(-0.878267\pi\)
0.927759 0.373181i \(-0.121733\pi\)
\(858\) −6891.34 −0.274203
\(859\) 46422.5 1.84391 0.921953 0.387301i \(-0.126593\pi\)
0.921953 + 0.387301i \(0.126593\pi\)
\(860\) 6571.88i 0.260580i
\(861\) − 11787.2i − 0.466557i
\(862\) 4043.61i 0.159775i
\(863\) 29112.3 1.14831 0.574157 0.818746i \(-0.305330\pi\)
0.574157 + 0.818746i \(0.305330\pi\)
\(864\) − 25750.8i − 1.01396i
\(865\) 537.563 0.0211303
\(866\) 8346.33 0.327505
\(867\) 0 0
\(868\) 13347.8 0.521950
\(869\) 19892.6 0.776536
\(870\) − 1673.64i − 0.0652204i
\(871\) 3077.43 0.119719
\(872\) − 34940.2i − 1.35691i
\(873\) 13548.2i 0.525241i
\(874\) 13991.2i 0.541487i
\(875\) −5797.04 −0.223972
\(876\) 5735.69 0.221222
\(877\) − 39163.0i − 1.50791i −0.656924 0.753957i \(-0.728143\pi\)
0.656924 0.753957i \(-0.271857\pi\)
\(878\) 3464.19i 0.133156i
\(879\) − 22720.3i − 0.871830i
\(880\) 1922.57 0.0736473
\(881\) − 35073.2i − 1.34125i −0.741795 0.670627i \(-0.766025\pi\)
0.741795 0.670627i \(-0.233975\pi\)
\(882\) −6496.63 −0.248019
\(883\) −48775.7 −1.85893 −0.929463 0.368915i \(-0.879729\pi\)
−0.929463 + 0.368915i \(0.879729\pi\)
\(884\) 0 0
\(885\) −2792.85 −0.106080
\(886\) −11611.0 −0.440269
\(887\) 13296.0i 0.503309i 0.967817 + 0.251654i \(0.0809746\pi\)
−0.967817 + 0.251654i \(0.919025\pi\)
\(888\) 8040.27 0.303844
\(889\) − 21027.9i − 0.793309i
\(890\) 3356.46i 0.126415i
\(891\) − 606.137i − 0.0227905i
\(892\) 4330.90 0.162566
\(893\) −13607.0 −0.509899
\(894\) 1228.24i 0.0459492i
\(895\) 3103.74i 0.115918i
\(896\) 11031.1i 0.411297i
\(897\) −21131.3 −0.786570
\(898\) 12054.6i 0.447960i
\(899\) 35155.3 1.30422
\(900\) −12136.4 −0.449498
\(901\) 0 0
\(902\) −17689.1 −0.652974
\(903\) 8833.44 0.325535
\(904\) 13621.4i 0.501153i
\(905\) −10460.0 −0.384202
\(906\) − 2875.47i − 0.105443i
\(907\) 11675.0i 0.427410i 0.976898 + 0.213705i \(0.0685532\pi\)
−0.976898 + 0.213705i \(0.931447\pi\)
\(908\) − 13224.0i − 0.483319i
\(909\) 4526.54 0.165166
\(910\) 1904.26 0.0693689
\(911\) − 18552.9i − 0.674738i −0.941372 0.337369i \(-0.890463\pi\)
0.941372 0.337369i \(-0.109537\pi\)
\(912\) − 6459.41i − 0.234531i
\(913\) − 3204.87i − 0.116173i
\(914\) −9739.24 −0.352457
\(915\) − 515.459i − 0.0186235i
\(916\) −24077.7 −0.868504
\(917\) 15714.9 0.565922
\(918\) 0 0
\(919\) 33956.8 1.21886 0.609429 0.792841i \(-0.291399\pi\)
0.609429 + 0.792841i \(0.291399\pi\)
\(920\) −6729.71 −0.241165
\(921\) 7652.23i 0.273778i
\(922\) −9886.63 −0.353144
\(923\) 45815.3i 1.63383i
\(924\) − 4252.33i − 0.151398i
\(925\) − 15327.4i − 0.544823i
\(926\) −480.372 −0.0170475
\(927\) 8918.08 0.315974
\(928\) 23823.8i 0.842732i
\(929\) 23695.3i 0.836832i 0.908256 + 0.418416i \(0.137415\pi\)
−0.908256 + 0.418416i \(0.862585\pi\)
\(930\) 3560.06i 0.125526i
\(931\) −24962.7 −0.878753
\(932\) 31920.2i 1.12187i
\(933\) 30110.8 1.05657
\(934\) 2018.72 0.0707221
\(935\) 0 0
\(936\) 19078.3 0.666234
\(937\) −7990.62 −0.278593 −0.139297 0.990251i \(-0.544484\pi\)
−0.139297 + 0.990251i \(0.544484\pi\)
\(938\) − 572.402i − 0.0199249i
\(939\) 1856.12 0.0645071
\(940\) − 2843.83i − 0.0986762i
\(941\) − 24385.9i − 0.844799i −0.906410 0.422400i \(-0.861188\pi\)
0.906410 0.422400i \(-0.138812\pi\)
\(942\) − 3095.26i − 0.107058i
\(943\) −54241.0 −1.87310
\(944\) 6705.69 0.231199
\(945\) − 3345.12i − 0.115150i
\(946\) − 13256.4i − 0.455605i
\(947\) − 1174.62i − 0.0403064i −0.999797 0.0201532i \(-0.993585\pi\)
0.999797 0.0201532i \(-0.00641539\pi\)
\(948\) 13968.4 0.478557
\(949\) 17188.3i 0.587939i
\(950\) 14056.7 0.480063
\(951\) 24143.4 0.823241
\(952\) 0 0
\(953\) −33546.9 −1.14029 −0.570143 0.821546i \(-0.693112\pi\)
−0.570143 + 0.821546i \(0.693112\pi\)
\(954\) 12244.1 0.415531
\(955\) − 1488.25i − 0.0504277i
\(956\) −2055.00 −0.0695224
\(957\) − 11199.8i − 0.378304i
\(958\) 13598.7i 0.458617i
\(959\) 24948.4i 0.840067i
\(960\) −655.620 −0.0220417
\(961\) −44989.1 −1.51016
\(962\) 10469.3i 0.350878i
\(963\) − 16810.3i − 0.562517i
\(964\) 11792.9i 0.394007i
\(965\) −10758.9 −0.358903
\(966\) 3930.41i 0.130910i
\(967\) −24766.8 −0.823625 −0.411813 0.911269i \(-0.635104\pi\)
−0.411813 + 0.911269i \(0.635104\pi\)
\(968\) 10944.9 0.363411
\(969\) 0 0
\(970\) 3279.56 0.108557
\(971\) −42324.3 −1.39882 −0.699409 0.714721i \(-0.746553\pi\)
−0.699409 + 0.714721i \(0.746553\pi\)
\(972\) − 23488.3i − 0.775091i
\(973\) −11657.2 −0.384083
\(974\) − 1538.01i − 0.0505966i
\(975\) 21230.2i 0.697344i
\(976\) 1237.63i 0.0405896i
\(977\) 11320.4 0.370698 0.185349 0.982673i \(-0.440658\pi\)
0.185349 + 0.982673i \(0.440658\pi\)
\(978\) 2905.42 0.0949949
\(979\) 22461.0i 0.733254i
\(980\) − 5217.16i − 0.170057i
\(981\) − 30932.2i − 1.00672i
\(982\) 25556.8 0.830500
\(983\) − 11311.9i − 0.367032i −0.983017 0.183516i \(-0.941252\pi\)
0.983017 0.183516i \(-0.0587478\pi\)
\(984\) −28586.3 −0.926116
\(985\) 4132.66 0.133683
\(986\) 0 0
\(987\) −3822.47 −0.123273
\(988\) 31852.6 1.02568
\(989\) − 40648.8i − 1.30693i
\(990\) −1942.94 −0.0623744
\(991\) − 29405.5i − 0.942580i −0.881978 0.471290i \(-0.843788\pi\)
0.881978 0.471290i \(-0.156212\pi\)
\(992\) − 50676.5i − 1.62196i
\(993\) − 2373.12i − 0.0758397i
\(994\) 8521.63 0.271921
\(995\) −11330.9 −0.361018
\(996\) − 2250.43i − 0.0715939i
\(997\) 54905.9i 1.74412i 0.489398 + 0.872060i \(0.337216\pi\)
−0.489398 + 0.872060i \(0.662784\pi\)
\(998\) 23588.7i 0.748183i
\(999\) 18390.9 0.582446
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 289.4.b.b.288.4 6
17.4 even 4 17.4.a.b.1.2 3
17.13 even 4 289.4.a.b.1.2 3
17.16 even 2 inner 289.4.b.b.288.3 6
51.38 odd 4 153.4.a.g.1.2 3
68.55 odd 4 272.4.a.h.1.2 3
85.4 even 4 425.4.a.g.1.2 3
85.38 odd 4 425.4.b.f.324.3 6
85.72 odd 4 425.4.b.f.324.4 6
119.55 odd 4 833.4.a.d.1.2 3
136.21 even 4 1088.4.a.v.1.2 3
136.123 odd 4 1088.4.a.x.1.2 3
187.21 odd 4 2057.4.a.e.1.2 3
204.191 even 4 2448.4.a.bi.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.b.1.2 3 17.4 even 4
153.4.a.g.1.2 3 51.38 odd 4
272.4.a.h.1.2 3 68.55 odd 4
289.4.a.b.1.2 3 17.13 even 4
289.4.b.b.288.3 6 17.16 even 2 inner
289.4.b.b.288.4 6 1.1 even 1 trivial
425.4.a.g.1.2 3 85.4 even 4
425.4.b.f.324.3 6 85.38 odd 4
425.4.b.f.324.4 6 85.72 odd 4
833.4.a.d.1.2 3 119.55 odd 4
1088.4.a.v.1.2 3 136.21 even 4
1088.4.a.x.1.2 3 136.123 odd 4
2057.4.a.e.1.2 3 187.21 odd 4
2448.4.a.bi.1.1 3 204.191 even 4