Properties

Label 1815.4.a.r.1.2
Level $1815$
Weight $4$
Character 1815.1
Self dual yes
Analytic conductor $107.088$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(107.088466660\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.47528.1
Defining polynomial: \(x^{3} - x^{2} - 26 x - 22\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.906392\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.90639 q^{2} +3.00000 q^{3} -4.36567 q^{4} -5.00000 q^{5} +5.71918 q^{6} +22.9186 q^{7} -23.5738 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.90639 q^{2} +3.00000 q^{3} -4.36567 q^{4} -5.00000 q^{5} +5.71918 q^{6} +22.9186 q^{7} -23.5738 q^{8} +9.00000 q^{9} -9.53196 q^{10} -13.0970 q^{12} -66.7313 q^{13} +43.6917 q^{14} -15.0000 q^{15} -10.0156 q^{16} +3.45588 q^{17} +17.1575 q^{18} -78.2359 q^{19} +21.8283 q^{20} +68.7557 q^{21} +12.2907 q^{23} -70.7214 q^{24} +25.0000 q^{25} -127.216 q^{26} +27.0000 q^{27} -100.055 q^{28} +31.1827 q^{29} -28.5959 q^{30} +247.181 q^{31} +169.497 q^{32} +6.58825 q^{34} -114.593 q^{35} -39.2910 q^{36} +304.128 q^{37} -149.148 q^{38} -200.194 q^{39} +117.869 q^{40} +29.8219 q^{41} +131.075 q^{42} -269.060 q^{43} -45.0000 q^{45} +23.4309 q^{46} +225.463 q^{47} -30.0467 q^{48} +182.260 q^{49} +47.6598 q^{50} +10.3676 q^{51} +291.327 q^{52} -16.8371 q^{53} +51.4726 q^{54} -540.278 q^{56} -234.708 q^{57} +59.4464 q^{58} +28.0701 q^{59} +65.4850 q^{60} +853.742 q^{61} +471.224 q^{62} +206.267 q^{63} +403.252 q^{64} +333.657 q^{65} -36.7885 q^{67} -15.0872 q^{68} +36.8722 q^{69} -218.459 q^{70} +23.8552 q^{71} -212.164 q^{72} -707.265 q^{73} +579.787 q^{74} +75.0000 q^{75} +341.552 q^{76} -381.648 q^{78} +412.126 q^{79} +50.0778 q^{80} +81.0000 q^{81} +56.8522 q^{82} +552.596 q^{83} -300.165 q^{84} -17.2794 q^{85} -512.934 q^{86} +93.5480 q^{87} -1495.26 q^{89} -85.7876 q^{90} -1529.39 q^{91} -53.6573 q^{92} +741.543 q^{93} +429.820 q^{94} +391.179 q^{95} +508.491 q^{96} +1199.45 q^{97} +347.459 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90639 0.674011 0.337006 0.941503i \(-0.390586\pi\)
0.337006 + 0.941503i \(0.390586\pi\)
\(3\) 3.00000 0.577350
\(4\) −4.36567 −0.545709
\(5\) −5.00000 −0.447214
\(6\) 5.71918 0.389141
\(7\) 22.9186 1.23749 0.618743 0.785594i \(-0.287642\pi\)
0.618743 + 0.785594i \(0.287642\pi\)
\(8\) −23.5738 −1.04183
\(9\) 9.00000 0.333333
\(10\) −9.53196 −0.301427
\(11\) 0 0
\(12\) −13.0970 −0.315065
\(13\) −66.7313 −1.42369 −0.711844 0.702338i \(-0.752140\pi\)
−0.711844 + 0.702338i \(0.752140\pi\)
\(14\) 43.6917 0.834079
\(15\) −15.0000 −0.258199
\(16\) −10.0156 −0.156493
\(17\) 3.45588 0.0493043 0.0246522 0.999696i \(-0.492152\pi\)
0.0246522 + 0.999696i \(0.492152\pi\)
\(18\) 17.1575 0.224670
\(19\) −78.2359 −0.944660 −0.472330 0.881422i \(-0.656587\pi\)
−0.472330 + 0.881422i \(0.656587\pi\)
\(20\) 21.8283 0.244048
\(21\) 68.7557 0.714463
\(22\) 0 0
\(23\) 12.2907 0.111426 0.0557129 0.998447i \(-0.482257\pi\)
0.0557129 + 0.998447i \(0.482257\pi\)
\(24\) −70.7214 −0.601498
\(25\) 25.0000 0.200000
\(26\) −127.216 −0.959582
\(27\) 27.0000 0.192450
\(28\) −100.055 −0.675307
\(29\) 31.1827 0.199672 0.0998358 0.995004i \(-0.468168\pi\)
0.0998358 + 0.995004i \(0.468168\pi\)
\(30\) −28.5959 −0.174029
\(31\) 247.181 1.43210 0.716049 0.698050i \(-0.245949\pi\)
0.716049 + 0.698050i \(0.245949\pi\)
\(32\) 169.497 0.936347
\(33\) 0 0
\(34\) 6.58825 0.0332317
\(35\) −114.593 −0.553420
\(36\) −39.2910 −0.181903
\(37\) 304.128 1.35131 0.675653 0.737220i \(-0.263862\pi\)
0.675653 + 0.737220i \(0.263862\pi\)
\(38\) −149.148 −0.636712
\(39\) −200.194 −0.821967
\(40\) 117.869 0.465918
\(41\) 29.8219 0.113595 0.0567975 0.998386i \(-0.481911\pi\)
0.0567975 + 0.998386i \(0.481911\pi\)
\(42\) 131.075 0.481556
\(43\) −269.060 −0.954215 −0.477108 0.878845i \(-0.658315\pi\)
−0.477108 + 0.878845i \(0.658315\pi\)
\(44\) 0 0
\(45\) −45.0000 −0.149071
\(46\) 23.4309 0.0751023
\(47\) 225.463 0.699726 0.349863 0.936801i \(-0.386228\pi\)
0.349863 + 0.936801i \(0.386228\pi\)
\(48\) −30.0467 −0.0903514
\(49\) 182.260 0.531371
\(50\) 47.6598 0.134802
\(51\) 10.3676 0.0284659
\(52\) 291.327 0.776919
\(53\) −16.8371 −0.0436369 −0.0218184 0.999762i \(-0.506946\pi\)
−0.0218184 + 0.999762i \(0.506946\pi\)
\(54\) 51.4726 0.129714
\(55\) 0 0
\(56\) −540.278 −1.28924
\(57\) −234.708 −0.545400
\(58\) 59.4464 0.134581
\(59\) 28.0701 0.0619392 0.0309696 0.999520i \(-0.490140\pi\)
0.0309696 + 0.999520i \(0.490140\pi\)
\(60\) 65.4850 0.140901
\(61\) 853.742 1.79198 0.895988 0.444079i \(-0.146469\pi\)
0.895988 + 0.444079i \(0.146469\pi\)
\(62\) 471.224 0.965250
\(63\) 206.267 0.412495
\(64\) 403.252 0.787602
\(65\) 333.657 0.636693
\(66\) 0 0
\(67\) −36.7885 −0.0670810 −0.0335405 0.999437i \(-0.510678\pi\)
−0.0335405 + 0.999437i \(0.510678\pi\)
\(68\) −15.0872 −0.0269058
\(69\) 36.8722 0.0643317
\(70\) −218.459 −0.373012
\(71\) 23.8552 0.0398746 0.0199373 0.999801i \(-0.493653\pi\)
0.0199373 + 0.999801i \(0.493653\pi\)
\(72\) −212.164 −0.347275
\(73\) −707.265 −1.13396 −0.566980 0.823731i \(-0.691889\pi\)
−0.566980 + 0.823731i \(0.691889\pi\)
\(74\) 579.787 0.910795
\(75\) 75.0000 0.115470
\(76\) 341.552 0.515509
\(77\) 0 0
\(78\) −381.648 −0.554015
\(79\) 412.126 0.586934 0.293467 0.955969i \(-0.405191\pi\)
0.293467 + 0.955969i \(0.405191\pi\)
\(80\) 50.0778 0.0699859
\(81\) 81.0000 0.111111
\(82\) 56.8522 0.0765643
\(83\) 552.596 0.730786 0.365393 0.930853i \(-0.380935\pi\)
0.365393 + 0.930853i \(0.380935\pi\)
\(84\) −300.165 −0.389889
\(85\) −17.2794 −0.0220496
\(86\) −512.934 −0.643152
\(87\) 93.5480 0.115280
\(88\) 0 0
\(89\) −1495.26 −1.78087 −0.890434 0.455113i \(-0.849599\pi\)
−0.890434 + 0.455113i \(0.849599\pi\)
\(90\) −85.7876 −0.100476
\(91\) −1529.39 −1.76179
\(92\) −53.6573 −0.0608060
\(93\) 741.543 0.826822
\(94\) 429.820 0.471623
\(95\) 391.179 0.422465
\(96\) 508.491 0.540600
\(97\) 1199.45 1.25552 0.627761 0.778406i \(-0.283971\pi\)
0.627761 + 0.778406i \(0.283971\pi\)
\(98\) 347.459 0.358150
\(99\) 0 0
\(100\) −109.142 −0.109142
\(101\) 1009.66 0.994701 0.497351 0.867550i \(-0.334306\pi\)
0.497351 + 0.867550i \(0.334306\pi\)
\(102\) 19.7648 0.0191863
\(103\) 1156.70 1.10653 0.553266 0.833004i \(-0.313381\pi\)
0.553266 + 0.833004i \(0.313381\pi\)
\(104\) 1573.11 1.48323
\(105\) −343.778 −0.319517
\(106\) −32.0981 −0.0294117
\(107\) −491.857 −0.444389 −0.222194 0.975002i \(-0.571322\pi\)
−0.222194 + 0.975002i \(0.571322\pi\)
\(108\) −117.873 −0.105022
\(109\) −1340.77 −1.17819 −0.589093 0.808066i \(-0.700515\pi\)
−0.589093 + 0.808066i \(0.700515\pi\)
\(110\) 0 0
\(111\) 912.384 0.780177
\(112\) −229.542 −0.193658
\(113\) 1849.21 1.53946 0.769729 0.638371i \(-0.220391\pi\)
0.769729 + 0.638371i \(0.220391\pi\)
\(114\) −447.445 −0.367606
\(115\) −61.4536 −0.0498311
\(116\) −136.133 −0.108963
\(117\) −600.582 −0.474563
\(118\) 53.5126 0.0417478
\(119\) 79.2037 0.0610134
\(120\) 353.607 0.268998
\(121\) 0 0
\(122\) 1627.57 1.20781
\(123\) 89.4656 0.0655841
\(124\) −1079.11 −0.781508
\(125\) −125.000 −0.0894427
\(126\) 393.226 0.278026
\(127\) 1020.24 0.712850 0.356425 0.934324i \(-0.383995\pi\)
0.356425 + 0.934324i \(0.383995\pi\)
\(128\) −587.219 −0.405495
\(129\) −807.180 −0.550917
\(130\) 636.080 0.429138
\(131\) −1003.30 −0.669147 −0.334574 0.942370i \(-0.608592\pi\)
−0.334574 + 0.942370i \(0.608592\pi\)
\(132\) 0 0
\(133\) −1793.05 −1.16900
\(134\) −70.1332 −0.0452134
\(135\) −135.000 −0.0860663
\(136\) −81.4682 −0.0513665
\(137\) 2665.14 1.66203 0.831016 0.556249i \(-0.187760\pi\)
0.831016 + 0.556249i \(0.187760\pi\)
\(138\) 70.2928 0.0433603
\(139\) −2557.64 −1.56069 −0.780347 0.625347i \(-0.784957\pi\)
−0.780347 + 0.625347i \(0.784957\pi\)
\(140\) 500.274 0.302006
\(141\) 676.388 0.403987
\(142\) 45.4774 0.0268759
\(143\) 0 0
\(144\) −90.1401 −0.0521644
\(145\) −155.913 −0.0892959
\(146\) −1348.32 −0.764303
\(147\) 546.781 0.306787
\(148\) −1327.72 −0.737419
\(149\) 2644.66 1.45409 0.727044 0.686591i \(-0.240894\pi\)
0.727044 + 0.686591i \(0.240894\pi\)
\(150\) 142.979 0.0778281
\(151\) 2871.44 1.54751 0.773757 0.633482i \(-0.218375\pi\)
0.773757 + 0.633482i \(0.218375\pi\)
\(152\) 1844.32 0.984171
\(153\) 31.1029 0.0164348
\(154\) 0 0
\(155\) −1235.91 −0.640454
\(156\) 873.981 0.448554
\(157\) 1048.51 0.532996 0.266498 0.963835i \(-0.414133\pi\)
0.266498 + 0.963835i \(0.414133\pi\)
\(158\) 785.674 0.395600
\(159\) −50.5113 −0.0251937
\(160\) −847.485 −0.418747
\(161\) 281.686 0.137888
\(162\) 154.418 0.0748901
\(163\) −1953.90 −0.938905 −0.469452 0.882958i \(-0.655549\pi\)
−0.469452 + 0.882958i \(0.655549\pi\)
\(164\) −130.192 −0.0619898
\(165\) 0 0
\(166\) 1053.46 0.492558
\(167\) −2085.79 −0.966488 −0.483244 0.875486i \(-0.660542\pi\)
−0.483244 + 0.875486i \(0.660542\pi\)
\(168\) −1620.83 −0.744345
\(169\) 2256.07 1.02689
\(170\) −32.9413 −0.0148616
\(171\) −704.123 −0.314887
\(172\) 1174.63 0.520724
\(173\) 3999.28 1.75757 0.878785 0.477218i \(-0.158355\pi\)
0.878785 + 0.477218i \(0.158355\pi\)
\(174\) 178.339 0.0777003
\(175\) 572.964 0.247497
\(176\) 0 0
\(177\) 84.2103 0.0357606
\(178\) −2850.55 −1.20032
\(179\) 2046.60 0.854580 0.427290 0.904115i \(-0.359468\pi\)
0.427290 + 0.904115i \(0.359468\pi\)
\(180\) 196.455 0.0813495
\(181\) 64.2973 0.0264043 0.0132022 0.999913i \(-0.495797\pi\)
0.0132022 + 0.999913i \(0.495797\pi\)
\(182\) −2915.61 −1.18747
\(183\) 2561.23 1.03460
\(184\) −289.739 −0.116086
\(185\) −1520.64 −0.604322
\(186\) 1413.67 0.557287
\(187\) 0 0
\(188\) −984.296 −0.381846
\(189\) 618.801 0.238154
\(190\) 745.741 0.284746
\(191\) 4816.60 1.82470 0.912348 0.409416i \(-0.134268\pi\)
0.912348 + 0.409416i \(0.134268\pi\)
\(192\) 1209.76 0.454722
\(193\) 295.804 0.110323 0.0551617 0.998477i \(-0.482433\pi\)
0.0551617 + 0.998477i \(0.482433\pi\)
\(194\) 2286.62 0.846237
\(195\) 1000.97 0.367595
\(196\) −795.688 −0.289974
\(197\) 2147.97 0.776835 0.388418 0.921483i \(-0.373022\pi\)
0.388418 + 0.921483i \(0.373022\pi\)
\(198\) 0 0
\(199\) −876.260 −0.312143 −0.156071 0.987746i \(-0.549883\pi\)
−0.156071 + 0.987746i \(0.549883\pi\)
\(200\) −589.345 −0.208365
\(201\) −110.365 −0.0387292
\(202\) 1924.81 0.670440
\(203\) 714.662 0.247091
\(204\) −45.2616 −0.0155341
\(205\) −149.109 −0.0508012
\(206\) 2205.12 0.745815
\(207\) 110.617 0.0371419
\(208\) 668.352 0.222798
\(209\) 0 0
\(210\) −655.376 −0.215358
\(211\) −1413.99 −0.461341 −0.230670 0.973032i \(-0.574092\pi\)
−0.230670 + 0.973032i \(0.574092\pi\)
\(212\) 73.5052 0.0238130
\(213\) 71.5657 0.0230216
\(214\) −937.672 −0.299523
\(215\) 1345.30 0.426738
\(216\) −636.493 −0.200499
\(217\) 5665.03 1.77220
\(218\) −2556.03 −0.794110
\(219\) −2121.80 −0.654693
\(220\) 0 0
\(221\) −230.615 −0.0701939
\(222\) 1739.36 0.525848
\(223\) 3365.53 1.01064 0.505320 0.862932i \(-0.331374\pi\)
0.505320 + 0.862932i \(0.331374\pi\)
\(224\) 3884.62 1.15872
\(225\) 225.000 0.0666667
\(226\) 3525.31 1.03761
\(227\) 5724.31 1.67373 0.836864 0.547411i \(-0.184387\pi\)
0.836864 + 0.547411i \(0.184387\pi\)
\(228\) 1024.66 0.297629
\(229\) 2586.74 0.746447 0.373224 0.927741i \(-0.378252\pi\)
0.373224 + 0.927741i \(0.378252\pi\)
\(230\) −117.155 −0.0335867
\(231\) 0 0
\(232\) −735.095 −0.208023
\(233\) −5571.63 −1.56656 −0.783282 0.621666i \(-0.786456\pi\)
−0.783282 + 0.621666i \(0.786456\pi\)
\(234\) −1144.94 −0.319861
\(235\) −1127.31 −0.312927
\(236\) −122.545 −0.0338008
\(237\) 1236.38 0.338867
\(238\) 150.993 0.0411237
\(239\) 1822.92 0.493369 0.246685 0.969096i \(-0.420659\pi\)
0.246685 + 0.969096i \(0.420659\pi\)
\(240\) 150.233 0.0404064
\(241\) 2226.66 0.595152 0.297576 0.954698i \(-0.403822\pi\)
0.297576 + 0.954698i \(0.403822\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) −3727.16 −0.977897
\(245\) −911.301 −0.237636
\(246\) 170.556 0.0442044
\(247\) 5220.78 1.34490
\(248\) −5827.00 −1.49200
\(249\) 1657.79 0.421920
\(250\) −238.299 −0.0602854
\(251\) 7888.22 1.98367 0.991833 0.127543i \(-0.0407092\pi\)
0.991833 + 0.127543i \(0.0407092\pi\)
\(252\) −900.494 −0.225102
\(253\) 0 0
\(254\) 1944.98 0.480469
\(255\) −51.8381 −0.0127303
\(256\) −4345.49 −1.06091
\(257\) −4755.32 −1.15420 −0.577099 0.816674i \(-0.695815\pi\)
−0.577099 + 0.816674i \(0.695815\pi\)
\(258\) −1538.80 −0.371324
\(259\) 6970.17 1.67222
\(260\) −1456.64 −0.347449
\(261\) 280.644 0.0665572
\(262\) −1912.67 −0.451013
\(263\) 103.437 0.0242517 0.0121258 0.999926i \(-0.496140\pi\)
0.0121258 + 0.999926i \(0.496140\pi\)
\(264\) 0 0
\(265\) 84.1855 0.0195150
\(266\) −3418.26 −0.787921
\(267\) −4485.78 −1.02818
\(268\) 160.606 0.0366067
\(269\) −2179.50 −0.494002 −0.247001 0.969015i \(-0.579445\pi\)
−0.247001 + 0.969015i \(0.579445\pi\)
\(270\) −257.363 −0.0580097
\(271\) 3688.54 0.826800 0.413400 0.910550i \(-0.364341\pi\)
0.413400 + 0.910550i \(0.364341\pi\)
\(272\) −34.6126 −0.00771579
\(273\) −4588.16 −1.01717
\(274\) 5080.80 1.12023
\(275\) 0 0
\(276\) −160.972 −0.0351064
\(277\) 3087.18 0.669641 0.334821 0.942282i \(-0.391324\pi\)
0.334821 + 0.942282i \(0.391324\pi\)
\(278\) −4875.87 −1.05193
\(279\) 2224.63 0.477366
\(280\) 2701.39 0.576567
\(281\) −3338.91 −0.708836 −0.354418 0.935087i \(-0.615321\pi\)
−0.354418 + 0.935087i \(0.615321\pi\)
\(282\) 1289.46 0.272292
\(283\) −1483.75 −0.311661 −0.155830 0.987784i \(-0.549805\pi\)
−0.155830 + 0.987784i \(0.549805\pi\)
\(284\) −104.144 −0.0217599
\(285\) 1173.54 0.243910
\(286\) 0 0
\(287\) 683.474 0.140572
\(288\) 1525.47 0.312116
\(289\) −4901.06 −0.997569
\(290\) −297.232 −0.0601864
\(291\) 3598.35 0.724877
\(292\) 3087.69 0.618812
\(293\) 1590.55 0.317137 0.158569 0.987348i \(-0.449312\pi\)
0.158569 + 0.987348i \(0.449312\pi\)
\(294\) 1042.38 0.206778
\(295\) −140.350 −0.0277001
\(296\) −7169.45 −1.40782
\(297\) 0 0
\(298\) 5041.76 0.980071
\(299\) −820.177 −0.158636
\(300\) −327.425 −0.0630130
\(301\) −6166.47 −1.18083
\(302\) 5474.10 1.04304
\(303\) 3028.98 0.574291
\(304\) 783.577 0.147833
\(305\) −4268.71 −0.801396
\(306\) 59.2943 0.0110772
\(307\) −10175.3 −1.89164 −0.945818 0.324697i \(-0.894738\pi\)
−0.945818 + 0.324697i \(0.894738\pi\)
\(308\) 0 0
\(309\) 3470.09 0.638857
\(310\) −2356.12 −0.431673
\(311\) −6258.24 −1.14107 −0.570535 0.821274i \(-0.693264\pi\)
−0.570535 + 0.821274i \(0.693264\pi\)
\(312\) 4719.34 0.856346
\(313\) 9592.24 1.73222 0.866111 0.499852i \(-0.166612\pi\)
0.866111 + 0.499852i \(0.166612\pi\)
\(314\) 1998.88 0.359245
\(315\) −1031.34 −0.184473
\(316\) −1799.21 −0.320295
\(317\) −10632.3 −1.88381 −0.941907 0.335874i \(-0.890969\pi\)
−0.941907 + 0.335874i \(0.890969\pi\)
\(318\) −96.2943 −0.0169809
\(319\) 0 0
\(320\) −2016.26 −0.352226
\(321\) −1475.57 −0.256568
\(322\) 537.003 0.0929380
\(323\) −270.373 −0.0465758
\(324\) −353.619 −0.0606343
\(325\) −1668.28 −0.284738
\(326\) −3724.90 −0.632832
\(327\) −4022.30 −0.680226
\(328\) −703.015 −0.118346
\(329\) 5167.28 0.865901
\(330\) 0 0
\(331\) 8222.61 1.36542 0.682712 0.730687i \(-0.260800\pi\)
0.682712 + 0.730687i \(0.260800\pi\)
\(332\) −2412.45 −0.398796
\(333\) 2737.15 0.450435
\(334\) −3976.34 −0.651424
\(335\) 183.942 0.0299995
\(336\) −688.627 −0.111809
\(337\) 2947.77 0.476484 0.238242 0.971206i \(-0.423429\pi\)
0.238242 + 0.971206i \(0.423429\pi\)
\(338\) 4300.96 0.692134
\(339\) 5547.62 0.888806
\(340\) 75.4361 0.0120326
\(341\) 0 0
\(342\) −1342.33 −0.212237
\(343\) −3683.92 −0.579922
\(344\) 6342.77 0.994126
\(345\) −184.361 −0.0287700
\(346\) 7624.20 1.18462
\(347\) −3322.43 −0.513999 −0.256999 0.966412i \(-0.582734\pi\)
−0.256999 + 0.966412i \(0.582734\pi\)
\(348\) −408.400 −0.0629096
\(349\) 9199.67 1.41102 0.705511 0.708699i \(-0.250717\pi\)
0.705511 + 0.708699i \(0.250717\pi\)
\(350\) 1092.29 0.166816
\(351\) −1801.75 −0.273989
\(352\) 0 0
\(353\) −10105.2 −1.52363 −0.761817 0.647792i \(-0.775693\pi\)
−0.761817 + 0.647792i \(0.775693\pi\)
\(354\) 160.538 0.0241031
\(355\) −119.276 −0.0178325
\(356\) 6527.81 0.971835
\(357\) 237.611 0.0352261
\(358\) 3901.62 0.575997
\(359\) 5236.42 0.769826 0.384913 0.922953i \(-0.374231\pi\)
0.384913 + 0.922953i \(0.374231\pi\)
\(360\) 1060.82 0.155306
\(361\) −738.148 −0.107617
\(362\) 122.576 0.0177968
\(363\) 0 0
\(364\) 6676.79 0.961426
\(365\) 3536.33 0.507123
\(366\) 4882.70 0.697330
\(367\) −9337.95 −1.32817 −0.664083 0.747659i \(-0.731178\pi\)
−0.664083 + 0.747659i \(0.731178\pi\)
\(368\) −123.099 −0.0174374
\(369\) 268.397 0.0378650
\(370\) −2898.93 −0.407320
\(371\) −385.882 −0.0540000
\(372\) −3237.33 −0.451204
\(373\) −14256.1 −1.97896 −0.989482 0.144659i \(-0.953791\pi\)
−0.989482 + 0.144659i \(0.953791\pi\)
\(374\) 0 0
\(375\) −375.000 −0.0516398
\(376\) −5315.02 −0.728992
\(377\) −2080.86 −0.284270
\(378\) 1179.68 0.160519
\(379\) 1911.19 0.259027 0.129514 0.991578i \(-0.458658\pi\)
0.129514 + 0.991578i \(0.458658\pi\)
\(380\) −1707.76 −0.230543
\(381\) 3060.73 0.411564
\(382\) 9182.32 1.22987
\(383\) 1743.91 0.232662 0.116331 0.993210i \(-0.462887\pi\)
0.116331 + 0.993210i \(0.462887\pi\)
\(384\) −1761.66 −0.234112
\(385\) 0 0
\(386\) 563.917 0.0743592
\(387\) −2421.54 −0.318072
\(388\) −5236.40 −0.685150
\(389\) −2734.88 −0.356462 −0.178231 0.983989i \(-0.557037\pi\)
−0.178231 + 0.983989i \(0.557037\pi\)
\(390\) 1908.24 0.247763
\(391\) 42.4752 0.00549377
\(392\) −4296.57 −0.553596
\(393\) −3009.89 −0.386332
\(394\) 4094.87 0.523596
\(395\) −2060.63 −0.262485
\(396\) 0 0
\(397\) −14879.5 −1.88106 −0.940530 0.339709i \(-0.889671\pi\)
−0.940530 + 0.339709i \(0.889671\pi\)
\(398\) −1670.50 −0.210388
\(399\) −5379.16 −0.674924
\(400\) −250.389 −0.0312986
\(401\) −11638.2 −1.44934 −0.724668 0.689098i \(-0.758007\pi\)
−0.724668 + 0.689098i \(0.758007\pi\)
\(402\) −210.400 −0.0261039
\(403\) −16494.7 −2.03886
\(404\) −4407.84 −0.542817
\(405\) −405.000 −0.0496904
\(406\) 1362.43 0.166542
\(407\) 0 0
\(408\) −244.405 −0.0296564
\(409\) −936.594 −0.113231 −0.0566157 0.998396i \(-0.518031\pi\)
−0.0566157 + 0.998396i \(0.518031\pi\)
\(410\) −284.261 −0.0342406
\(411\) 7995.42 0.959574
\(412\) −5049.76 −0.603845
\(413\) 643.326 0.0766489
\(414\) 210.878 0.0250341
\(415\) −2762.98 −0.326818
\(416\) −11310.8 −1.33307
\(417\) −7672.93 −0.901067
\(418\) 0 0
\(419\) 128.037 0.0149285 0.00746425 0.999972i \(-0.497624\pi\)
0.00746425 + 0.999972i \(0.497624\pi\)
\(420\) 1500.82 0.174363
\(421\) −6628.97 −0.767402 −0.383701 0.923457i \(-0.625351\pi\)
−0.383701 + 0.923457i \(0.625351\pi\)
\(422\) −2695.61 −0.310949
\(423\) 2029.16 0.233242
\(424\) 396.915 0.0454620
\(425\) 86.3969 0.00986086
\(426\) 136.432 0.0155168
\(427\) 19566.5 2.21754
\(428\) 2147.29 0.242507
\(429\) 0 0
\(430\) 2564.67 0.287626
\(431\) −14677.8 −1.64038 −0.820192 0.572089i \(-0.806133\pi\)
−0.820192 + 0.572089i \(0.806133\pi\)
\(432\) −270.420 −0.0301171
\(433\) −1150.36 −0.127674 −0.0638369 0.997960i \(-0.520334\pi\)
−0.0638369 + 0.997960i \(0.520334\pi\)
\(434\) 10799.8 1.19448
\(435\) −467.740 −0.0515550
\(436\) 5853.35 0.642946
\(437\) −961.576 −0.105259
\(438\) −4044.97 −0.441270
\(439\) 9308.30 1.01198 0.505992 0.862538i \(-0.331127\pi\)
0.505992 + 0.862538i \(0.331127\pi\)
\(440\) 0 0
\(441\) 1640.34 0.177124
\(442\) −439.643 −0.0473115
\(443\) −5689.21 −0.610164 −0.305082 0.952326i \(-0.598684\pi\)
−0.305082 + 0.952326i \(0.598684\pi\)
\(444\) −3983.17 −0.425749
\(445\) 7476.30 0.796428
\(446\) 6416.02 0.681183
\(447\) 7933.98 0.839518
\(448\) 9241.96 0.974646
\(449\) −6644.91 −0.698425 −0.349212 0.937044i \(-0.613551\pi\)
−0.349212 + 0.937044i \(0.613551\pi\)
\(450\) 428.938 0.0449341
\(451\) 0 0
\(452\) −8073.02 −0.840095
\(453\) 8614.33 0.893458
\(454\) 10912.8 1.12811
\(455\) 7646.93 0.787898
\(456\) 5532.95 0.568211
\(457\) 8355.11 0.855220 0.427610 0.903963i \(-0.359356\pi\)
0.427610 + 0.903963i \(0.359356\pi\)
\(458\) 4931.33 0.503114
\(459\) 93.3087 0.00948862
\(460\) 268.286 0.0271933
\(461\) 15580.5 1.57409 0.787044 0.616897i \(-0.211611\pi\)
0.787044 + 0.616897i \(0.211611\pi\)
\(462\) 0 0
\(463\) 7139.16 0.716598 0.358299 0.933607i \(-0.383357\pi\)
0.358299 + 0.933607i \(0.383357\pi\)
\(464\) −312.312 −0.0312473
\(465\) −3707.72 −0.369766
\(466\) −10621.7 −1.05588
\(467\) −12415.1 −1.23019 −0.615097 0.788451i \(-0.710883\pi\)
−0.615097 + 0.788451i \(0.710883\pi\)
\(468\) 2621.94 0.258973
\(469\) −843.139 −0.0830118
\(470\) −2149.10 −0.210916
\(471\) 3145.54 0.307726
\(472\) −661.719 −0.0645299
\(473\) 0 0
\(474\) 2357.02 0.228400
\(475\) −1955.90 −0.188932
\(476\) −345.777 −0.0332955
\(477\) −151.534 −0.0145456
\(478\) 3475.21 0.332536
\(479\) 14151.0 1.34985 0.674925 0.737887i \(-0.264176\pi\)
0.674925 + 0.737887i \(0.264176\pi\)
\(480\) −2542.45 −0.241764
\(481\) −20294.9 −1.92384
\(482\) 4244.88 0.401139
\(483\) 845.057 0.0796096
\(484\) 0 0
\(485\) −5997.25 −0.561487
\(486\) 463.253 0.0432378
\(487\) −76.6358 −0.00713080 −0.00356540 0.999994i \(-0.501135\pi\)
−0.00356540 + 0.999994i \(0.501135\pi\)
\(488\) −20126.0 −1.86693
\(489\) −5861.71 −0.542077
\(490\) −1737.30 −0.160170
\(491\) 1707.54 0.156945 0.0784725 0.996916i \(-0.474996\pi\)
0.0784725 + 0.996916i \(0.474996\pi\)
\(492\) −390.577 −0.0357898
\(493\) 107.763 0.00984467
\(494\) 9952.86 0.906479
\(495\) 0 0
\(496\) −2475.66 −0.224114
\(497\) 546.728 0.0493443
\(498\) 3160.39 0.284379
\(499\) −13168.5 −1.18137 −0.590686 0.806902i \(-0.701143\pi\)
−0.590686 + 0.806902i \(0.701143\pi\)
\(500\) 545.709 0.0488097
\(501\) −6257.38 −0.558002
\(502\) 15038.0 1.33701
\(503\) 1525.32 0.135210 0.0676052 0.997712i \(-0.478464\pi\)
0.0676052 + 0.997712i \(0.478464\pi\)
\(504\) −4862.50 −0.429748
\(505\) −5048.29 −0.444844
\(506\) 0 0
\(507\) 6768.22 0.592874
\(508\) −4454.05 −0.389009
\(509\) 9006.01 0.784253 0.392126 0.919911i \(-0.371740\pi\)
0.392126 + 0.919911i \(0.371740\pi\)
\(510\) −98.8238 −0.00858038
\(511\) −16209.5 −1.40326
\(512\) −3586.45 −0.309571
\(513\) −2112.37 −0.181800
\(514\) −9065.51 −0.777942
\(515\) −5783.49 −0.494856
\(516\) 3523.88 0.300640
\(517\) 0 0
\(518\) 13287.9 1.12710
\(519\) 11997.8 1.01473
\(520\) −7865.56 −0.663322
\(521\) 21707.8 1.82541 0.912703 0.408623i \(-0.133991\pi\)
0.912703 + 0.408623i \(0.133991\pi\)
\(522\) 535.018 0.0448603
\(523\) 14015.0 1.17177 0.585883 0.810396i \(-0.300748\pi\)
0.585883 + 0.810396i \(0.300748\pi\)
\(524\) 4380.06 0.365160
\(525\) 1718.89 0.142893
\(526\) 197.191 0.0163459
\(527\) 854.227 0.0706086
\(528\) 0 0
\(529\) −12015.9 −0.987584
\(530\) 160.491 0.0131533
\(531\) 252.631 0.0206464
\(532\) 7827.88 0.637935
\(533\) −1990.05 −0.161724
\(534\) −8551.65 −0.693008
\(535\) 2459.29 0.198737
\(536\) 867.244 0.0698867
\(537\) 6139.79 0.493392
\(538\) −4154.98 −0.332963
\(539\) 0 0
\(540\) 589.365 0.0469671
\(541\) −14444.9 −1.14793 −0.573967 0.818878i \(-0.694596\pi\)
−0.573967 + 0.818878i \(0.694596\pi\)
\(542\) 7031.80 0.557273
\(543\) 192.892 0.0152445
\(544\) 585.760 0.0461659
\(545\) 6703.83 0.526900
\(546\) −8746.83 −0.685585
\(547\) −20286.4 −1.58571 −0.792854 0.609412i \(-0.791406\pi\)
−0.792854 + 0.609412i \(0.791406\pi\)
\(548\) −11635.1 −0.906985
\(549\) 7683.68 0.597325
\(550\) 0 0
\(551\) −2439.60 −0.188622
\(552\) −869.218 −0.0670224
\(553\) 9445.34 0.726323
\(554\) 5885.38 0.451346
\(555\) −4561.92 −0.348906
\(556\) 11165.8 0.851684
\(557\) 24482.4 1.86239 0.931196 0.364520i \(-0.118767\pi\)
0.931196 + 0.364520i \(0.118767\pi\)
\(558\) 4241.02 0.321750
\(559\) 17954.7 1.35851
\(560\) 1147.71 0.0866065
\(561\) 0 0
\(562\) −6365.27 −0.477763
\(563\) 20383.5 1.52587 0.762933 0.646478i \(-0.223759\pi\)
0.762933 + 0.646478i \(0.223759\pi\)
\(564\) −2952.89 −0.220459
\(565\) −9246.03 −0.688466
\(566\) −2828.62 −0.210063
\(567\) 1856.40 0.137498
\(568\) −562.359 −0.0415424
\(569\) −3297.74 −0.242967 −0.121484 0.992593i \(-0.538765\pi\)
−0.121484 + 0.992593i \(0.538765\pi\)
\(570\) 2237.22 0.164398
\(571\) 7213.03 0.528644 0.264322 0.964434i \(-0.414852\pi\)
0.264322 + 0.964434i \(0.414852\pi\)
\(572\) 0 0
\(573\) 14449.8 1.05349
\(574\) 1302.97 0.0947472
\(575\) 307.268 0.0222852
\(576\) 3629.27 0.262534
\(577\) −18080.4 −1.30450 −0.652251 0.758003i \(-0.726175\pi\)
−0.652251 + 0.758003i \(0.726175\pi\)
\(578\) −9343.34 −0.672373
\(579\) 887.411 0.0636952
\(580\) 680.666 0.0487295
\(581\) 12664.7 0.904337
\(582\) 6859.87 0.488575
\(583\) 0 0
\(584\) 16672.9 1.18139
\(585\) 3002.91 0.212231
\(586\) 3032.22 0.213754
\(587\) 13457.5 0.946250 0.473125 0.880995i \(-0.343126\pi\)
0.473125 + 0.880995i \(0.343126\pi\)
\(588\) −2387.06 −0.167416
\(589\) −19338.4 −1.35285
\(590\) −267.563 −0.0186702
\(591\) 6443.91 0.448506
\(592\) −3046.01 −0.211470
\(593\) 10262.3 0.710665 0.355332 0.934740i \(-0.384368\pi\)
0.355332 + 0.934740i \(0.384368\pi\)
\(594\) 0 0
\(595\) −396.018 −0.0272860
\(596\) −11545.7 −0.793508
\(597\) −2628.78 −0.180216
\(598\) −1563.58 −0.106922
\(599\) 23153.3 1.57933 0.789665 0.613538i \(-0.210254\pi\)
0.789665 + 0.613538i \(0.210254\pi\)
\(600\) −1768.04 −0.120300
\(601\) −14414.8 −0.978357 −0.489178 0.872184i \(-0.662703\pi\)
−0.489178 + 0.872184i \(0.662703\pi\)
\(602\) −11755.7 −0.795891
\(603\) −331.096 −0.0223603
\(604\) −12535.8 −0.844492
\(605\) 0 0
\(606\) 5774.42 0.387079
\(607\) −10808.8 −0.722757 −0.361379 0.932419i \(-0.617694\pi\)
−0.361379 + 0.932419i \(0.617694\pi\)
\(608\) −13260.7 −0.884530
\(609\) 2143.99 0.142658
\(610\) −8137.84 −0.540150
\(611\) −15045.4 −0.996191
\(612\) −135.785 −0.00896860
\(613\) −12072.8 −0.795455 −0.397727 0.917504i \(-0.630201\pi\)
−0.397727 + 0.917504i \(0.630201\pi\)
\(614\) −19398.0 −1.27498
\(615\) −447.328 −0.0293301
\(616\) 0 0
\(617\) 11593.5 0.756462 0.378231 0.925711i \(-0.376532\pi\)
0.378231 + 0.925711i \(0.376532\pi\)
\(618\) 6615.36 0.430597
\(619\) 4037.96 0.262196 0.131098 0.991369i \(-0.458150\pi\)
0.131098 + 0.991369i \(0.458150\pi\)
\(620\) 5395.55 0.349501
\(621\) 331.850 0.0214439
\(622\) −11930.7 −0.769094
\(623\) −34269.2 −2.20380
\(624\) 2005.06 0.128632
\(625\) 625.000 0.0400000
\(626\) 18286.6 1.16754
\(627\) 0 0
\(628\) −4577.46 −0.290861
\(629\) 1051.03 0.0666252
\(630\) −1966.13 −0.124337
\(631\) 2896.22 0.182721 0.0913604 0.995818i \(-0.470878\pi\)
0.0913604 + 0.995818i \(0.470878\pi\)
\(632\) −9715.39 −0.611483
\(633\) −4241.96 −0.266355
\(634\) −20269.3 −1.26971
\(635\) −5101.22 −0.318796
\(636\) 220.516 0.0137484
\(637\) −12162.5 −0.756506
\(638\) 0 0
\(639\) 214.697 0.0132915
\(640\) 2936.09 0.181343
\(641\) 13371.2 0.823916 0.411958 0.911203i \(-0.364845\pi\)
0.411958 + 0.911203i \(0.364845\pi\)
\(642\) −2813.02 −0.172930
\(643\) 14063.6 0.862544 0.431272 0.902222i \(-0.358065\pi\)
0.431272 + 0.902222i \(0.358065\pi\)
\(644\) −1229.75 −0.0752466
\(645\) 4035.90 0.246377
\(646\) −515.438 −0.0313926
\(647\) 20899.7 1.26994 0.634971 0.772536i \(-0.281012\pi\)
0.634971 + 0.772536i \(0.281012\pi\)
\(648\) −1909.48 −0.115758
\(649\) 0 0
\(650\) −3180.40 −0.191916
\(651\) 16995.1 1.02318
\(652\) 8530.09 0.512368
\(653\) −1607.80 −0.0963523 −0.0481761 0.998839i \(-0.515341\pi\)
−0.0481761 + 0.998839i \(0.515341\pi\)
\(654\) −7668.08 −0.458480
\(655\) 5016.48 0.299252
\(656\) −298.683 −0.0177768
\(657\) −6365.39 −0.377987
\(658\) 9850.86 0.583627
\(659\) −14733.1 −0.870896 −0.435448 0.900214i \(-0.643410\pi\)
−0.435448 + 0.900214i \(0.643410\pi\)
\(660\) 0 0
\(661\) −16442.2 −0.967518 −0.483759 0.875201i \(-0.660729\pi\)
−0.483759 + 0.875201i \(0.660729\pi\)
\(662\) 15675.5 0.920312
\(663\) −691.846 −0.0405265
\(664\) −13026.8 −0.761351
\(665\) 8965.27 0.522794
\(666\) 5218.08 0.303598
\(667\) 383.258 0.0222486
\(668\) 9105.88 0.527421
\(669\) 10096.6 0.583493
\(670\) 350.666 0.0202200
\(671\) 0 0
\(672\) 11653.9 0.668985
\(673\) 25246.6 1.44604 0.723021 0.690826i \(-0.242753\pi\)
0.723021 + 0.690826i \(0.242753\pi\)
\(674\) 5619.60 0.321156
\(675\) 675.000 0.0384900
\(676\) −9849.26 −0.560381
\(677\) −24582.6 −1.39555 −0.697774 0.716318i \(-0.745826\pi\)
−0.697774 + 0.716318i \(0.745826\pi\)
\(678\) 10575.9 0.599065
\(679\) 27489.7 1.55369
\(680\) 407.341 0.0229718
\(681\) 17172.9 0.966327
\(682\) 0 0
\(683\) 11459.5 0.642000 0.321000 0.947079i \(-0.395981\pi\)
0.321000 + 0.947079i \(0.395981\pi\)
\(684\) 3073.97 0.171836
\(685\) −13325.7 −0.743283
\(686\) −7023.00 −0.390874
\(687\) 7760.21 0.430961
\(688\) 2694.79 0.149328
\(689\) 1123.56 0.0621253
\(690\) −351.464 −0.0193913
\(691\) −15683.8 −0.863445 −0.431723 0.902006i \(-0.642094\pi\)
−0.431723 + 0.902006i \(0.642094\pi\)
\(692\) −17459.5 −0.959121
\(693\) 0 0
\(694\) −6333.86 −0.346441
\(695\) 12788.2 0.697963
\(696\) −2205.28 −0.120102
\(697\) 103.061 0.00560072
\(698\) 17538.2 0.951045
\(699\) −16714.9 −0.904457
\(700\) −2501.37 −0.135061
\(701\) −6185.65 −0.333279 −0.166640 0.986018i \(-0.553292\pi\)
−0.166640 + 0.986018i \(0.553292\pi\)
\(702\) −3434.83 −0.184672
\(703\) −23793.7 −1.27652
\(704\) 0 0
\(705\) −3381.94 −0.180668
\(706\) −19264.4 −1.02695
\(707\) 23139.9 1.23093
\(708\) −367.634 −0.0195149
\(709\) −28031.2 −1.48481 −0.742407 0.669950i \(-0.766316\pi\)
−0.742407 + 0.669950i \(0.766316\pi\)
\(710\) −227.387 −0.0120193
\(711\) 3709.14 0.195645
\(712\) 35249.0 1.85535
\(713\) 3038.03 0.159573
\(714\) 452.980 0.0237428
\(715\) 0 0
\(716\) −8934.77 −0.466352
\(717\) 5468.77 0.284847
\(718\) 9982.67 0.518872
\(719\) 23313.0 1.20922 0.604610 0.796522i \(-0.293329\pi\)
0.604610 + 0.796522i \(0.293329\pi\)
\(720\) 450.700 0.0233286
\(721\) 26509.9 1.36932
\(722\) −1407.20 −0.0725354
\(723\) 6679.98 0.343611
\(724\) −280.701 −0.0144091
\(725\) 779.567 0.0399343
\(726\) 0 0
\(727\) −69.6810 −0.00355478 −0.00177739 0.999998i \(-0.500566\pi\)
−0.00177739 + 0.999998i \(0.500566\pi\)
\(728\) 36053.5 1.83548
\(729\) 729.000 0.0370370
\(730\) 6741.62 0.341806
\(731\) −929.838 −0.0470469
\(732\) −11181.5 −0.564589
\(733\) −15152.9 −0.763552 −0.381776 0.924255i \(-0.624687\pi\)
−0.381776 + 0.924255i \(0.624687\pi\)
\(734\) −17801.8 −0.895199
\(735\) −2733.90 −0.137199
\(736\) 2083.24 0.104333
\(737\) 0 0
\(738\) 511.669 0.0255214
\(739\) 31557.9 1.57087 0.785437 0.618941i \(-0.212438\pi\)
0.785437 + 0.618941i \(0.212438\pi\)
\(740\) 6638.61 0.329784
\(741\) 15662.4 0.776479
\(742\) −735.642 −0.0363966
\(743\) −6925.00 −0.341929 −0.170965 0.985277i \(-0.554688\pi\)
−0.170965 + 0.985277i \(0.554688\pi\)
\(744\) −17481.0 −0.861404
\(745\) −13223.3 −0.650288
\(746\) −27177.7 −1.33384
\(747\) 4973.36 0.243595
\(748\) 0 0
\(749\) −11272.7 −0.549925
\(750\) −714.897 −0.0348058
\(751\) −22202.1 −1.07878 −0.539392 0.842055i \(-0.681346\pi\)
−0.539392 + 0.842055i \(0.681346\pi\)
\(752\) −2258.14 −0.109502
\(753\) 23664.7 1.14527
\(754\) −3966.94 −0.191601
\(755\) −14357.2 −0.692070
\(756\) −2701.48 −0.129963
\(757\) 18928.6 0.908813 0.454406 0.890795i \(-0.349851\pi\)
0.454406 + 0.890795i \(0.349851\pi\)
\(758\) 3643.48 0.174587
\(759\) 0 0
\(760\) −9221.59 −0.440134
\(761\) 22883.3 1.09004 0.545019 0.838423i \(-0.316522\pi\)
0.545019 + 0.838423i \(0.316522\pi\)
\(762\) 5834.95 0.277399
\(763\) −30728.4 −1.45799
\(764\) −21027.7 −0.995752
\(765\) −155.514 −0.00734985
\(766\) 3324.57 0.156817
\(767\) −1873.16 −0.0881822
\(768\) −13036.5 −0.612516
\(769\) −8903.82 −0.417529 −0.208765 0.977966i \(-0.566944\pi\)
−0.208765 + 0.977966i \(0.566944\pi\)
\(770\) 0 0
\(771\) −14266.0 −0.666376
\(772\) −1291.38 −0.0602044
\(773\) 24691.9 1.14891 0.574454 0.818537i \(-0.305214\pi\)
0.574454 + 0.818537i \(0.305214\pi\)
\(774\) −4616.40 −0.214384
\(775\) 6179.53 0.286420
\(776\) −28275.6 −1.30804
\(777\) 20910.5 0.965457
\(778\) −5213.75 −0.240259
\(779\) −2333.14 −0.107309
\(780\) −4369.91 −0.200600
\(781\) 0 0
\(782\) 80.9744 0.00370286
\(783\) 841.932 0.0384268
\(784\) −1825.44 −0.0831559
\(785\) −5242.56 −0.238363
\(786\) −5738.02 −0.260392
\(787\) 7418.83 0.336026 0.168013 0.985785i \(-0.446265\pi\)
0.168013 + 0.985785i \(0.446265\pi\)
\(788\) −9377.33 −0.423926
\(789\) 310.311 0.0140017
\(790\) −3928.37 −0.176918
\(791\) 42381.1 1.90506
\(792\) 0 0
\(793\) −56971.4 −2.55121
\(794\) −28366.2 −1.26786
\(795\) 252.556 0.0112670
\(796\) 3825.46 0.170339
\(797\) −27971.2 −1.24315 −0.621576 0.783354i \(-0.713507\pi\)
−0.621576 + 0.783354i \(0.713507\pi\)
\(798\) −10254.8 −0.454907
\(799\) 779.171 0.0344995
\(800\) 4237.42 0.187269
\(801\) −13457.3 −0.593622
\(802\) −22187.0 −0.976869
\(803\) 0 0
\(804\) 481.819 0.0211349
\(805\) −1408.43 −0.0616653
\(806\) −31445.4 −1.37421
\(807\) −6538.51 −0.285212
\(808\) −23801.5 −1.03630
\(809\) 10670.0 0.463704 0.231852 0.972751i \(-0.425521\pi\)
0.231852 + 0.972751i \(0.425521\pi\)
\(810\) −772.089 −0.0334919
\(811\) −40618.3 −1.75869 −0.879346 0.476182i \(-0.842020\pi\)
−0.879346 + 0.476182i \(0.842020\pi\)
\(812\) −3119.98 −0.134840
\(813\) 11065.6 0.477353
\(814\) 0 0
\(815\) 9769.51 0.419891
\(816\) −103.838 −0.00445471
\(817\) 21050.1 0.901409
\(818\) −1785.52 −0.0763192
\(819\) −13764.5 −0.587265
\(820\) 650.962 0.0277227
\(821\) −16710.5 −0.710355 −0.355178 0.934799i \(-0.615580\pi\)
−0.355178 + 0.934799i \(0.615580\pi\)
\(822\) 15242.4 0.646764
\(823\) −16920.5 −0.716661 −0.358331 0.933595i \(-0.616654\pi\)
−0.358331 + 0.933595i \(0.616654\pi\)
\(824\) −27267.8 −1.15281
\(825\) 0 0
\(826\) 1226.43 0.0516623
\(827\) 9478.39 0.398544 0.199272 0.979944i \(-0.436142\pi\)
0.199272 + 0.979944i \(0.436142\pi\)
\(828\) −482.915 −0.0202687
\(829\) −31908.1 −1.33681 −0.668405 0.743798i \(-0.733023\pi\)
−0.668405 + 0.743798i \(0.733023\pi\)
\(830\) −5267.32 −0.220279
\(831\) 9261.54 0.386618
\(832\) −26909.6 −1.12130
\(833\) 629.869 0.0261989
\(834\) −14627.6 −0.607329
\(835\) 10429.0 0.432226
\(836\) 0 0
\(837\) 6673.89 0.275607
\(838\) 244.090 0.0100620
\(839\) 25195.7 1.03677 0.518386 0.855147i \(-0.326533\pi\)
0.518386 + 0.855147i \(0.326533\pi\)
\(840\) 8104.17 0.332881
\(841\) −23416.6 −0.960131
\(842\) −12637.4 −0.517238
\(843\) −10016.7 −0.409246
\(844\) 6173.00 0.251758
\(845\) −11280.4 −0.459238
\(846\) 3868.38 0.157208
\(847\) 0 0
\(848\) 168.633 0.00682887
\(849\) −4451.26 −0.179938
\(850\) 164.706 0.00664633
\(851\) 3737.95 0.150570
\(852\) −312.432 −0.0125631
\(853\) −8239.19 −0.330720 −0.165360 0.986233i \(-0.552879\pi\)
−0.165360 + 0.986233i \(0.552879\pi\)
\(854\) 37301.5 1.49465
\(855\) 3520.61 0.140822
\(856\) 11594.9 0.462976
\(857\) −12912.8 −0.514694 −0.257347 0.966319i \(-0.582848\pi\)
−0.257347 + 0.966319i \(0.582848\pi\)
\(858\) 0 0
\(859\) 18534.6 0.736196 0.368098 0.929787i \(-0.380009\pi\)
0.368098 + 0.929787i \(0.380009\pi\)
\(860\) −5873.14 −0.232875
\(861\) 2050.42 0.0811594
\(862\) −27981.7 −1.10564
\(863\) −18743.4 −0.739318 −0.369659 0.929168i \(-0.620525\pi\)
−0.369659 + 0.929168i \(0.620525\pi\)
\(864\) 4576.42 0.180200
\(865\) −19996.4 −0.786009
\(866\) −2193.04 −0.0860536
\(867\) −14703.2 −0.575947
\(868\) −24731.7 −0.967105
\(869\) 0 0
\(870\) −891.696 −0.0347487
\(871\) 2454.94 0.0955024
\(872\) 31607.0 1.22746
\(873\) 10795.1 0.418508
\(874\) −1833.14 −0.0709461
\(875\) −2864.82 −0.110684
\(876\) 9263.06 0.357272
\(877\) −25629.7 −0.986833 −0.493417 0.869793i \(-0.664252\pi\)
−0.493417 + 0.869793i \(0.664252\pi\)
\(878\) 17745.3 0.682088
\(879\) 4771.66 0.183099
\(880\) 0 0
\(881\) 14336.5 0.548250 0.274125 0.961694i \(-0.411612\pi\)
0.274125 + 0.961694i \(0.411612\pi\)
\(882\) 3127.13 0.119383
\(883\) 1012.36 0.0385827 0.0192914 0.999814i \(-0.493859\pi\)
0.0192914 + 0.999814i \(0.493859\pi\)
\(884\) 1006.79 0.0383054
\(885\) −421.051 −0.0159926
\(886\) −10845.9 −0.411258
\(887\) 2586.40 0.0979061 0.0489530 0.998801i \(-0.484412\pi\)
0.0489530 + 0.998801i \(0.484412\pi\)
\(888\) −21508.4 −0.812808
\(889\) 23382.5 0.882142
\(890\) 14252.8 0.536801
\(891\) 0 0
\(892\) −14692.8 −0.551515
\(893\) −17639.3 −0.661003
\(894\) 15125.3 0.565844
\(895\) −10233.0 −0.382180
\(896\) −13458.2 −0.501794
\(897\) −2460.53 −0.0915883
\(898\) −12667.8 −0.470746
\(899\) 7707.77 0.285949
\(900\) −982.276 −0.0363806
\(901\) −58.1869 −0.00215148
\(902\) 0 0
\(903\) −18499.4 −0.681751
\(904\) −43592.8 −1.60385
\(905\) −321.487 −0.0118084
\(906\) 16422.3 0.602201
\(907\) 43346.1 1.58686 0.793431 0.608660i \(-0.208293\pi\)
0.793431 + 0.608660i \(0.208293\pi\)
\(908\) −24990.5 −0.913368
\(909\) 9086.93 0.331567
\(910\) 14578.0 0.531052
\(911\) −5218.71 −0.189796 −0.0948978 0.995487i \(-0.530252\pi\)
−0.0948978 + 0.995487i \(0.530252\pi\)
\(912\) 2350.73 0.0853514
\(913\) 0 0
\(914\) 15928.1 0.576428
\(915\) −12806.1 −0.462686
\(916\) −11292.8 −0.407343
\(917\) −22994.1 −0.828060
\(918\) 177.883 0.00639544
\(919\) 29209.5 1.04846 0.524230 0.851577i \(-0.324353\pi\)
0.524230 + 0.851577i \(0.324353\pi\)
\(920\) 1448.70 0.0519153
\(921\) −30525.8 −1.09214
\(922\) 29702.5 1.06095
\(923\) −1591.89 −0.0567690
\(924\) 0 0
\(925\) 7603.20 0.270261
\(926\) 13610.0 0.482995
\(927\) 10410.3 0.368844
\(928\) 5285.37 0.186962
\(929\) −39401.0 −1.39150 −0.695751 0.718283i \(-0.744928\pi\)
−0.695751 + 0.718283i \(0.744928\pi\)
\(930\) −7068.36 −0.249226
\(931\) −14259.3 −0.501965
\(932\) 24323.9 0.854888
\(933\) −18774.7 −0.658797
\(934\) −23668.0 −0.829165
\(935\) 0 0
\(936\) 14158.0 0.494411
\(937\) −6099.66 −0.212665 −0.106332 0.994331i \(-0.533911\pi\)
−0.106332 + 0.994331i \(0.533911\pi\)
\(938\) −1607.35 −0.0559509
\(939\) 28776.7 1.00010
\(940\) 4921.48 0.170767
\(941\) −11534.4 −0.399587 −0.199793 0.979838i \(-0.564027\pi\)
−0.199793 + 0.979838i \(0.564027\pi\)
\(942\) 5996.63 0.207410
\(943\) 366.532 0.0126574
\(944\) −281.138 −0.00969307
\(945\) −3094.01 −0.106506
\(946\) 0 0
\(947\) −16680.4 −0.572376 −0.286188 0.958174i \(-0.592388\pi\)
−0.286188 + 0.958174i \(0.592388\pi\)
\(948\) −5397.62 −0.184923
\(949\) 47196.8 1.61441
\(950\) −3728.71 −0.127342
\(951\) −31896.9 −1.08762
\(952\) −1867.13 −0.0635653
\(953\) 17114.4 0.581733 0.290866 0.956764i \(-0.406057\pi\)
0.290866 + 0.956764i \(0.406057\pi\)
\(954\) −288.883 −0.00980391
\(955\) −24083.0 −0.816029
\(956\) −7958.29 −0.269236
\(957\) 0 0
\(958\) 26977.4 0.909814
\(959\) 61081.2 2.05674
\(960\) −6048.78 −0.203358
\(961\) 31307.5 1.05090
\(962\) −38690.0 −1.29669
\(963\) −4426.71 −0.148130
\(964\) −9720.86 −0.324780
\(965\) −1479.02 −0.0493381
\(966\) 1611.01 0.0536578
\(967\) 35200.4 1.17060 0.585299 0.810817i \(-0.300977\pi\)
0.585299 + 0.810817i \(0.300977\pi\)
\(968\) 0 0
\(969\) −811.120 −0.0268906
\(970\) −11433.1 −0.378449
\(971\) −43502.6 −1.43776 −0.718881 0.695134i \(-0.755345\pi\)
−0.718881 + 0.695134i \(0.755345\pi\)
\(972\) −1060.86 −0.0350072
\(973\) −58617.5 −1.93134
\(974\) −146.098 −0.00480624
\(975\) −5004.85 −0.164393
\(976\) −8550.71 −0.280432
\(977\) −5365.50 −0.175699 −0.0878494 0.996134i \(-0.527999\pi\)
−0.0878494 + 0.996134i \(0.527999\pi\)
\(978\) −11174.7 −0.365366
\(979\) 0 0
\(980\) 3978.44 0.129680
\(981\) −12066.9 −0.392728
\(982\) 3255.23 0.105783
\(983\) 42459.0 1.37765 0.688826 0.724926i \(-0.258126\pi\)
0.688826 + 0.724926i \(0.258126\pi\)
\(984\) −2109.05 −0.0683271
\(985\) −10739.8 −0.347411
\(986\) 205.439 0.00663542
\(987\) 15501.8 0.499928
\(988\) −22792.2 −0.733924
\(989\) −3306.94 −0.106324
\(990\) 0 0
\(991\) −6881.29 −0.220576 −0.110288 0.993900i \(-0.535177\pi\)
−0.110288 + 0.993900i \(0.535177\pi\)
\(992\) 41896.4 1.34094
\(993\) 24667.8 0.788328
\(994\) 1042.28 0.0332586
\(995\) 4381.30 0.139595
\(996\) −7237.35 −0.230245
\(997\) 3166.87 0.100597 0.0502987 0.998734i \(-0.483983\pi\)
0.0502987 + 0.998734i \(0.483983\pi\)
\(998\) −25104.4 −0.796258
\(999\) 8211.45 0.260059
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 1815.4.a.r.1.2 3
11.10 odd 2 165.4.a.e.1.2 3
33.32 even 2 495.4.a.k.1.2 3
55.32 even 4 825.4.c.k.199.3 6
55.43 even 4 825.4.c.k.199.4 6
55.54 odd 2 825.4.a.r.1.2 3
165.164 even 2 2475.4.a.t.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.4.a.e.1.2 3 11.10 odd 2
495.4.a.k.1.2 3 33.32 even 2
825.4.a.r.1.2 3 55.54 odd 2
825.4.c.k.199.3 6 55.32 even 4
825.4.c.k.199.4 6 55.43 even 4
1815.4.a.r.1.2 3 1.1 even 1 trivial
2475.4.a.t.1.2 3 165.164 even 2