Properties

Label 841.4.a.i.1.7
Level $841$
Weight $4$
Character 841.1
Self dual yes
Analytic conductor $49.621$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [841,4,Mod(1,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 841.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [21,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(49.6206063148\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 29)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 841.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.62919 q^{2} +5.65337 q^{3} -5.34573 q^{4} +13.9077 q^{5} -9.21044 q^{6} -14.2629 q^{7} +21.7428 q^{8} +4.96064 q^{9} -22.6583 q^{10} +54.7123 q^{11} -30.2214 q^{12} +14.8603 q^{13} +23.2371 q^{14} +78.6252 q^{15} +7.34260 q^{16} +118.208 q^{17} -8.08185 q^{18} -61.3862 q^{19} -74.3465 q^{20} -80.6338 q^{21} -89.1370 q^{22} -5.65413 q^{23} +122.920 q^{24} +68.4228 q^{25} -24.2102 q^{26} -124.597 q^{27} +76.2458 q^{28} -128.096 q^{30} -158.134 q^{31} -185.905 q^{32} +309.309 q^{33} -192.584 q^{34} -198.364 q^{35} -26.5182 q^{36} +415.980 q^{37} +100.010 q^{38} +84.0106 q^{39} +302.391 q^{40} +4.49844 q^{41} +131.368 q^{42} +200.555 q^{43} -292.477 q^{44} +68.9909 q^{45} +9.21168 q^{46} +151.533 q^{47} +41.5105 q^{48} -139.568 q^{49} -111.474 q^{50} +668.275 q^{51} -79.4389 q^{52} -89.7911 q^{53} +202.992 q^{54} +760.920 q^{55} -310.116 q^{56} -347.039 q^{57} +73.5684 q^{59} -420.309 q^{60} +51.0266 q^{61} +257.631 q^{62} -70.7534 q^{63} +244.134 q^{64} +206.671 q^{65} -503.925 q^{66} +848.107 q^{67} -631.909 q^{68} -31.9649 q^{69} +323.174 q^{70} +867.748 q^{71} +107.858 q^{72} -602.515 q^{73} -677.712 q^{74} +386.820 q^{75} +328.154 q^{76} -780.359 q^{77} -136.870 q^{78} -633.273 q^{79} +102.118 q^{80} -838.329 q^{81} -7.32883 q^{82} +851.856 q^{83} +431.046 q^{84} +1644.00 q^{85} -326.742 q^{86} +1189.60 q^{88} -1201.61 q^{89} -112.400 q^{90} -211.951 q^{91} +30.2254 q^{92} -893.991 q^{93} -246.877 q^{94} -853.739 q^{95} -1050.99 q^{96} +1716.07 q^{97} +227.384 q^{98} +271.408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{2} - q^{3} + 90 q^{4} + 35 q^{5} + 26 q^{6} + 37 q^{7} + 51 q^{8} + 188 q^{9} + 37 q^{10} - 7 q^{11} - 68 q^{12} + 97 q^{13} - 68 q^{14} - 330 q^{15} + 310 q^{16} + 70 q^{17} + 305 q^{18} - 73 q^{19}+ \cdots + 8702 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.62919 −0.576007 −0.288004 0.957629i \(-0.592991\pi\)
−0.288004 + 0.957629i \(0.592991\pi\)
\(3\) 5.65337 1.08799 0.543996 0.839088i \(-0.316911\pi\)
0.543996 + 0.839088i \(0.316911\pi\)
\(4\) −5.34573 −0.668216
\(5\) 13.9077 1.24394 0.621969 0.783042i \(-0.286333\pi\)
0.621969 + 0.783042i \(0.286333\pi\)
\(6\) −9.21044 −0.626691
\(7\) −14.2629 −0.770127 −0.385063 0.922890i \(-0.625820\pi\)
−0.385063 + 0.922890i \(0.625820\pi\)
\(8\) 21.7428 0.960904
\(9\) 4.96064 0.183727
\(10\) −22.6583 −0.716517
\(11\) 54.7123 1.49967 0.749835 0.661624i \(-0.230133\pi\)
0.749835 + 0.661624i \(0.230133\pi\)
\(12\) −30.2214 −0.727014
\(13\) 14.8603 0.317038 0.158519 0.987356i \(-0.449328\pi\)
0.158519 + 0.987356i \(0.449328\pi\)
\(14\) 23.2371 0.443598
\(15\) 78.6252 1.35340
\(16\) 7.34260 0.114728
\(17\) 118.208 1.68645 0.843226 0.537559i \(-0.180653\pi\)
0.843226 + 0.537559i \(0.180653\pi\)
\(18\) −8.08185 −0.105828
\(19\) −61.3862 −0.741209 −0.370604 0.928791i \(-0.620849\pi\)
−0.370604 + 0.928791i \(0.620849\pi\)
\(20\) −74.3465 −0.831219
\(21\) −80.6338 −0.837892
\(22\) −89.1370 −0.863821
\(23\) −5.65413 −0.0512595 −0.0256297 0.999672i \(-0.508159\pi\)
−0.0256297 + 0.999672i \(0.508159\pi\)
\(24\) 122.920 1.04546
\(25\) 68.4228 0.547383
\(26\) −24.2102 −0.182616
\(27\) −124.597 −0.888098
\(28\) 76.2458 0.514611
\(29\) 0 0
\(30\) −128.096 −0.779565
\(31\) −158.134 −0.916184 −0.458092 0.888905i \(-0.651467\pi\)
−0.458092 + 0.888905i \(0.651467\pi\)
\(32\) −185.905 −1.02699
\(33\) 309.309 1.63163
\(34\) −192.584 −0.971409
\(35\) −198.364 −0.957990
\(36\) −26.5182 −0.122770
\(37\) 415.980 1.84829 0.924144 0.382044i \(-0.124780\pi\)
0.924144 + 0.382044i \(0.124780\pi\)
\(38\) 100.010 0.426942
\(39\) 84.0106 0.344935
\(40\) 302.391 1.19531
\(41\) 4.49844 0.0171351 0.00856753 0.999963i \(-0.497273\pi\)
0.00856753 + 0.999963i \(0.497273\pi\)
\(42\) 131.368 0.482632
\(43\) 200.555 0.711263 0.355631 0.934626i \(-0.384266\pi\)
0.355631 + 0.934626i \(0.384266\pi\)
\(44\) −292.477 −1.00210
\(45\) 68.9909 0.228546
\(46\) 9.21168 0.0295258
\(47\) 151.533 0.470284 0.235142 0.971961i \(-0.424444\pi\)
0.235142 + 0.971961i \(0.424444\pi\)
\(48\) 41.5105 0.124823
\(49\) −139.568 −0.406905
\(50\) −111.474 −0.315296
\(51\) 668.275 1.83485
\(52\) −79.4389 −0.211850
\(53\) −89.7911 −0.232712 −0.116356 0.993208i \(-0.537121\pi\)
−0.116356 + 0.993208i \(0.537121\pi\)
\(54\) 202.992 0.511551
\(55\) 760.920 1.86550
\(56\) −310.116 −0.740018
\(57\) −347.039 −0.806430
\(58\) 0 0
\(59\) 73.5684 0.162335 0.0811677 0.996700i \(-0.474135\pi\)
0.0811677 + 0.996700i \(0.474135\pi\)
\(60\) −420.309 −0.904360
\(61\) 51.0266 0.107103 0.0535516 0.998565i \(-0.482946\pi\)
0.0535516 + 0.998565i \(0.482946\pi\)
\(62\) 257.631 0.527729
\(63\) −70.7534 −0.141493
\(64\) 244.134 0.476824
\(65\) 206.671 0.394376
\(66\) −503.925 −0.939831
\(67\) 848.107 1.54646 0.773229 0.634126i \(-0.218640\pi\)
0.773229 + 0.634126i \(0.218640\pi\)
\(68\) −631.909 −1.12691
\(69\) −31.9649 −0.0557699
\(70\) 323.174 0.551809
\(71\) 867.748 1.45046 0.725230 0.688506i \(-0.241733\pi\)
0.725230 + 0.688506i \(0.241733\pi\)
\(72\) 107.858 0.176545
\(73\) −602.515 −0.966014 −0.483007 0.875617i \(-0.660455\pi\)
−0.483007 + 0.875617i \(0.660455\pi\)
\(74\) −677.712 −1.06463
\(75\) 386.820 0.595548
\(76\) 328.154 0.495288
\(77\) −780.359 −1.15494
\(78\) −136.870 −0.198685
\(79\) −633.273 −0.901883 −0.450942 0.892553i \(-0.648912\pi\)
−0.450942 + 0.892553i \(0.648912\pi\)
\(80\) 102.118 0.142715
\(81\) −838.329 −1.14997
\(82\) −7.32883 −0.00986992
\(83\) 851.856 1.12655 0.563273 0.826271i \(-0.309542\pi\)
0.563273 + 0.826271i \(0.309542\pi\)
\(84\) 431.046 0.559893
\(85\) 1644.00 2.09784
\(86\) −326.742 −0.409692
\(87\) 0 0
\(88\) 1189.60 1.44104
\(89\) −1201.61 −1.43113 −0.715564 0.698547i \(-0.753830\pi\)
−0.715564 + 0.698547i \(0.753830\pi\)
\(90\) −112.400 −0.131644
\(91\) −211.951 −0.244159
\(92\) 30.2254 0.0342524
\(93\) −893.991 −0.996802
\(94\) −246.877 −0.270887
\(95\) −853.739 −0.922018
\(96\) −1050.99 −1.11736
\(97\) 1716.07 1.79629 0.898146 0.439698i \(-0.144915\pi\)
0.898146 + 0.439698i \(0.144915\pi\)
\(98\) 227.384 0.234380
\(99\) 271.408 0.275531
\(100\) −365.770 −0.365770
\(101\) −1623.25 −1.59920 −0.799600 0.600533i \(-0.794955\pi\)
−0.799600 + 0.600533i \(0.794955\pi\)
\(102\) −1088.75 −1.05689
\(103\) 1406.01 1.34503 0.672515 0.740084i \(-0.265214\pi\)
0.672515 + 0.740084i \(0.265214\pi\)
\(104\) 323.103 0.304643
\(105\) −1121.43 −1.04229
\(106\) 146.287 0.134044
\(107\) 520.276 0.470065 0.235033 0.971987i \(-0.424480\pi\)
0.235033 + 0.971987i \(0.424480\pi\)
\(108\) 666.060 0.593441
\(109\) 1055.28 0.927312 0.463656 0.886015i \(-0.346537\pi\)
0.463656 + 0.886015i \(0.346537\pi\)
\(110\) −1239.69 −1.07454
\(111\) 2351.69 2.01092
\(112\) −104.727 −0.0883552
\(113\) 294.227 0.244943 0.122471 0.992472i \(-0.460918\pi\)
0.122471 + 0.992472i \(0.460918\pi\)
\(114\) 565.395 0.464509
\(115\) −78.6357 −0.0637636
\(116\) 0 0
\(117\) 73.7164 0.0582486
\(118\) −119.857 −0.0935063
\(119\) −1686.00 −1.29878
\(120\) 1709.53 1.30048
\(121\) 1662.44 1.24901
\(122\) −83.1323 −0.0616921
\(123\) 25.4313 0.0186428
\(124\) 845.341 0.612209
\(125\) −786.856 −0.563028
\(126\) 115.271 0.0815012
\(127\) 955.074 0.667316 0.333658 0.942694i \(-0.391717\pi\)
0.333658 + 0.942694i \(0.391717\pi\)
\(128\) 1089.50 0.752334
\(129\) 1133.81 0.773848
\(130\) −336.708 −0.227163
\(131\) 2129.89 1.42053 0.710265 0.703934i \(-0.248575\pi\)
0.710265 + 0.703934i \(0.248575\pi\)
\(132\) −1653.48 −1.09028
\(133\) 875.549 0.570825
\(134\) −1381.73 −0.890771
\(135\) −1732.85 −1.10474
\(136\) 2570.17 1.62052
\(137\) −32.8073 −0.0204592 −0.0102296 0.999948i \(-0.503256\pi\)
−0.0102296 + 0.999948i \(0.503256\pi\)
\(138\) 52.0771 0.0321239
\(139\) −1888.16 −1.15217 −0.576085 0.817390i \(-0.695420\pi\)
−0.576085 + 0.817390i \(0.695420\pi\)
\(140\) 1060.40 0.640144
\(141\) 856.673 0.511666
\(142\) −1413.73 −0.835476
\(143\) 813.039 0.475453
\(144\) 36.4240 0.0210787
\(145\) 0 0
\(146\) 981.614 0.556431
\(147\) −789.033 −0.442710
\(148\) −2223.71 −1.23506
\(149\) 400.418 0.220158 0.110079 0.993923i \(-0.464890\pi\)
0.110079 + 0.993923i \(0.464890\pi\)
\(150\) −630.205 −0.343040
\(151\) 2464.12 1.32799 0.663996 0.747736i \(-0.268859\pi\)
0.663996 + 0.747736i \(0.268859\pi\)
\(152\) −1334.71 −0.712231
\(153\) 586.389 0.309848
\(154\) 1271.36 0.665252
\(155\) −2199.27 −1.13968
\(156\) −449.098 −0.230491
\(157\) −603.365 −0.306712 −0.153356 0.988171i \(-0.549008\pi\)
−0.153356 + 0.988171i \(0.549008\pi\)
\(158\) 1031.72 0.519491
\(159\) −507.623 −0.253189
\(160\) −2585.50 −1.27751
\(161\) 80.6446 0.0394763
\(162\) 1365.80 0.662392
\(163\) −518.585 −0.249195 −0.124597 0.992207i \(-0.539764\pi\)
−0.124597 + 0.992207i \(0.539764\pi\)
\(164\) −24.0474 −0.0114499
\(165\) 4301.76 2.02965
\(166\) −1387.84 −0.648899
\(167\) −1178.17 −0.545925 −0.272963 0.962025i \(-0.588004\pi\)
−0.272963 + 0.962025i \(0.588004\pi\)
\(168\) −1753.20 −0.805134
\(169\) −1976.17 −0.899487
\(170\) −2678.39 −1.20837
\(171\) −304.515 −0.136180
\(172\) −1072.11 −0.475277
\(173\) 116.569 0.0512288 0.0256144 0.999672i \(-0.491846\pi\)
0.0256144 + 0.999672i \(0.491846\pi\)
\(174\) 0 0
\(175\) −975.911 −0.421554
\(176\) 401.731 0.172054
\(177\) 415.910 0.176620
\(178\) 1957.66 0.824340
\(179\) 376.234 0.157101 0.0785504 0.996910i \(-0.474971\pi\)
0.0785504 + 0.996910i \(0.474971\pi\)
\(180\) −368.806 −0.152718
\(181\) −362.124 −0.148710 −0.0743549 0.997232i \(-0.523690\pi\)
−0.0743549 + 0.997232i \(0.523690\pi\)
\(182\) 345.309 0.140638
\(183\) 288.473 0.116527
\(184\) −122.937 −0.0492554
\(185\) 5785.30 2.29916
\(186\) 1456.48 0.574165
\(187\) 6467.44 2.52912
\(188\) −810.054 −0.314251
\(189\) 1777.12 0.683948
\(190\) 1390.91 0.531089
\(191\) 87.3223 0.0330807 0.0165404 0.999863i \(-0.494735\pi\)
0.0165404 + 0.999863i \(0.494735\pi\)
\(192\) 1380.18 0.518781
\(193\) 4135.28 1.54230 0.771150 0.636654i \(-0.219682\pi\)
0.771150 + 0.636654i \(0.219682\pi\)
\(194\) −2795.81 −1.03468
\(195\) 1168.39 0.429078
\(196\) 746.095 0.271900
\(197\) 3849.76 1.39231 0.696153 0.717893i \(-0.254894\pi\)
0.696153 + 0.717893i \(0.254894\pi\)
\(198\) −442.177 −0.158708
\(199\) 3008.75 1.07178 0.535891 0.844287i \(-0.319976\pi\)
0.535891 + 0.844287i \(0.319976\pi\)
\(200\) 1487.70 0.525982
\(201\) 4794.67 1.68254
\(202\) 2644.59 0.921150
\(203\) 0 0
\(204\) −3572.42 −1.22607
\(205\) 62.5627 0.0213150
\(206\) −2290.66 −0.774747
\(207\) −28.0481 −0.00941778
\(208\) 109.113 0.0363732
\(209\) −3358.58 −1.11157
\(210\) 1827.02 0.600364
\(211\) −829.766 −0.270727 −0.135364 0.990796i \(-0.543220\pi\)
−0.135364 + 0.990796i \(0.543220\pi\)
\(212\) 479.999 0.155502
\(213\) 4905.70 1.57809
\(214\) −847.630 −0.270761
\(215\) 2789.24 0.884767
\(216\) −2709.08 −0.853377
\(217\) 2255.46 0.705578
\(218\) −1719.25 −0.534138
\(219\) −3406.24 −1.05102
\(220\) −4067.67 −1.24656
\(221\) 1756.60 0.534670
\(222\) −3831.36 −1.15831
\(223\) −5325.02 −1.59906 −0.799529 0.600628i \(-0.794917\pi\)
−0.799529 + 0.600628i \(0.794917\pi\)
\(224\) 2651.55 0.790911
\(225\) 339.421 0.100569
\(226\) −479.353 −0.141089
\(227\) 1411.72 0.412771 0.206385 0.978471i \(-0.433830\pi\)
0.206385 + 0.978471i \(0.433830\pi\)
\(228\) 1855.18 0.538869
\(229\) 960.471 0.277160 0.138580 0.990351i \(-0.455746\pi\)
0.138580 + 0.990351i \(0.455746\pi\)
\(230\) 128.113 0.0367283
\(231\) −4411.66 −1.25656
\(232\) 0 0
\(233\) −1798.72 −0.505744 −0.252872 0.967500i \(-0.581375\pi\)
−0.252872 + 0.967500i \(0.581375\pi\)
\(234\) −120.098 −0.0335516
\(235\) 2107.47 0.585005
\(236\) −393.276 −0.108475
\(237\) −3580.13 −0.981242
\(238\) 2746.82 0.748108
\(239\) 3313.26 0.896723 0.448361 0.893852i \(-0.352008\pi\)
0.448361 + 0.893852i \(0.352008\pi\)
\(240\) 577.313 0.155273
\(241\) −372.620 −0.0995956 −0.0497978 0.998759i \(-0.515858\pi\)
−0.0497978 + 0.998759i \(0.515858\pi\)
\(242\) −2708.43 −0.719440
\(243\) −1375.28 −0.363062
\(244\) −272.774 −0.0715680
\(245\) −1941.07 −0.506165
\(246\) −41.4326 −0.0107384
\(247\) −912.215 −0.234991
\(248\) −3438.27 −0.880365
\(249\) 4815.86 1.22567
\(250\) 1281.94 0.324308
\(251\) −113.182 −0.0284620 −0.0142310 0.999899i \(-0.504530\pi\)
−0.0142310 + 0.999899i \(0.504530\pi\)
\(252\) 378.228 0.0945481
\(253\) −309.351 −0.0768724
\(254\) −1556.00 −0.384379
\(255\) 9294.14 2.28244
\(256\) −3728.07 −0.910174
\(257\) −1696.91 −0.411869 −0.205934 0.978566i \(-0.566023\pi\)
−0.205934 + 0.978566i \(0.566023\pi\)
\(258\) −1847.20 −0.445742
\(259\) −5933.10 −1.42342
\(260\) −1104.81 −0.263528
\(261\) 0 0
\(262\) −3470.01 −0.818236
\(263\) −134.322 −0.0314929 −0.0157464 0.999876i \(-0.505012\pi\)
−0.0157464 + 0.999876i \(0.505012\pi\)
\(264\) 6725.24 1.56784
\(265\) −1248.78 −0.289480
\(266\) −1426.44 −0.328799
\(267\) −6793.15 −1.55706
\(268\) −4533.75 −1.03337
\(269\) −3099.06 −0.702427 −0.351214 0.936295i \(-0.614231\pi\)
−0.351214 + 0.936295i \(0.614231\pi\)
\(270\) 2823.15 0.636338
\(271\) 2281.66 0.511442 0.255721 0.966751i \(-0.417687\pi\)
0.255721 + 0.966751i \(0.417687\pi\)
\(272\) 867.956 0.193484
\(273\) −1198.24 −0.265644
\(274\) 53.4494 0.0117847
\(275\) 3743.57 0.820894
\(276\) 170.876 0.0372663
\(277\) 289.918 0.0628862 0.0314431 0.999506i \(-0.489990\pi\)
0.0314431 + 0.999506i \(0.489990\pi\)
\(278\) 3076.18 0.663658
\(279\) −784.446 −0.168328
\(280\) −4312.99 −0.920537
\(281\) −5428.45 −1.15243 −0.576217 0.817297i \(-0.695472\pi\)
−0.576217 + 0.817297i \(0.695472\pi\)
\(282\) −1395.69 −0.294723
\(283\) 3063.67 0.643521 0.321761 0.946821i \(-0.395725\pi\)
0.321761 + 0.946821i \(0.395725\pi\)
\(284\) −4638.74 −0.969221
\(285\) −4826.50 −1.00315
\(286\) −1324.60 −0.273864
\(287\) −64.1609 −0.0131962
\(288\) −922.207 −0.188686
\(289\) 9060.18 1.84412
\(290\) 0 0
\(291\) 9701.57 1.95435
\(292\) 3220.88 0.645506
\(293\) 1436.15 0.286351 0.143176 0.989697i \(-0.454269\pi\)
0.143176 + 0.989697i \(0.454269\pi\)
\(294\) 1285.49 0.255004
\(295\) 1023.16 0.201935
\(296\) 9044.56 1.77603
\(297\) −6816.97 −1.33186
\(298\) −652.359 −0.126813
\(299\) −84.0219 −0.0162512
\(300\) −2067.83 −0.397955
\(301\) −2860.50 −0.547762
\(302\) −4014.52 −0.764933
\(303\) −9176.83 −1.73992
\(304\) −450.735 −0.0850375
\(305\) 709.661 0.133230
\(306\) −955.341 −0.178475
\(307\) −6595.85 −1.22621 −0.613103 0.790003i \(-0.710079\pi\)
−0.613103 + 0.790003i \(0.710079\pi\)
\(308\) 4171.58 0.771747
\(309\) 7948.69 1.46338
\(310\) 3583.04 0.656462
\(311\) 6486.49 1.18269 0.591343 0.806421i \(-0.298598\pi\)
0.591343 + 0.806421i \(0.298598\pi\)
\(312\) 1826.62 0.331449
\(313\) −115.663 −0.0208871 −0.0104436 0.999945i \(-0.503324\pi\)
−0.0104436 + 0.999945i \(0.503324\pi\)
\(314\) 982.999 0.176668
\(315\) −984.013 −0.176009
\(316\) 3385.30 0.602653
\(317\) −9397.64 −1.66506 −0.832530 0.553979i \(-0.813109\pi\)
−0.832530 + 0.553979i \(0.813109\pi\)
\(318\) 827.016 0.145839
\(319\) 0 0
\(320\) 3395.33 0.593140
\(321\) 2941.31 0.511427
\(322\) −131.386 −0.0227386
\(323\) −7256.36 −1.25001
\(324\) 4481.48 0.768429
\(325\) 1016.78 0.173541
\(326\) 844.876 0.143538
\(327\) 5965.87 1.00891
\(328\) 97.8085 0.0164652
\(329\) −2161.31 −0.362178
\(330\) −7008.41 −1.16909
\(331\) −9526.26 −1.58191 −0.790953 0.611877i \(-0.790415\pi\)
−0.790953 + 0.611877i \(0.790415\pi\)
\(332\) −4553.79 −0.752776
\(333\) 2063.53 0.339581
\(334\) 1919.47 0.314457
\(335\) 11795.2 1.92370
\(336\) −592.062 −0.0961298
\(337\) −3596.56 −0.581357 −0.290678 0.956821i \(-0.593881\pi\)
−0.290678 + 0.956821i \(0.593881\pi\)
\(338\) 3219.57 0.518111
\(339\) 1663.38 0.266496
\(340\) −8788.37 −1.40181
\(341\) −8651.88 −1.37397
\(342\) 496.114 0.0784409
\(343\) 6882.85 1.08349
\(344\) 4360.61 0.683455
\(345\) −444.557 −0.0693744
\(346\) −189.913 −0.0295081
\(347\) −3544.68 −0.548381 −0.274190 0.961675i \(-0.588410\pi\)
−0.274190 + 0.961675i \(0.588410\pi\)
\(348\) 0 0
\(349\) −8579.96 −1.31597 −0.657987 0.753029i \(-0.728592\pi\)
−0.657987 + 0.753029i \(0.728592\pi\)
\(350\) 1589.95 0.242818
\(351\) −1851.54 −0.281561
\(352\) −10171.3 −1.54014
\(353\) −1804.92 −0.272142 −0.136071 0.990699i \(-0.543448\pi\)
−0.136071 + 0.990699i \(0.543448\pi\)
\(354\) −677.597 −0.101734
\(355\) 12068.3 1.80428
\(356\) 6423.48 0.956303
\(357\) −9531.57 −1.41307
\(358\) −612.958 −0.0904912
\(359\) −3681.07 −0.541169 −0.270584 0.962696i \(-0.587217\pi\)
−0.270584 + 0.962696i \(0.587217\pi\)
\(360\) 1500.05 0.219610
\(361\) −3090.73 −0.450609
\(362\) 589.970 0.0856579
\(363\) 9398.37 1.35892
\(364\) 1133.03 0.163151
\(365\) −8379.57 −1.20166
\(366\) −469.978 −0.0671206
\(367\) 1468.37 0.208851 0.104426 0.994533i \(-0.466700\pi\)
0.104426 + 0.994533i \(0.466700\pi\)
\(368\) −41.5160 −0.00588091
\(369\) 22.3151 0.00314818
\(370\) −9425.38 −1.32433
\(371\) 1280.69 0.179218
\(372\) 4779.03 0.666079
\(373\) −5580.95 −0.774720 −0.387360 0.921928i \(-0.626613\pi\)
−0.387360 + 0.921928i \(0.626613\pi\)
\(374\) −10536.7 −1.45679
\(375\) −4448.39 −0.612570
\(376\) 3294.75 0.451898
\(377\) 0 0
\(378\) −2895.27 −0.393959
\(379\) −6117.61 −0.829130 −0.414565 0.910020i \(-0.636066\pi\)
−0.414565 + 0.910020i \(0.636066\pi\)
\(380\) 4563.85 0.616107
\(381\) 5399.39 0.726035
\(382\) −142.265 −0.0190547
\(383\) 2667.05 0.355822 0.177911 0.984047i \(-0.443066\pi\)
0.177911 + 0.984047i \(0.443066\pi\)
\(384\) 6159.33 0.818534
\(385\) −10853.0 −1.43667
\(386\) −6737.17 −0.888376
\(387\) 994.880 0.130678
\(388\) −9173.63 −1.20031
\(389\) −7781.12 −1.01419 −0.507093 0.861891i \(-0.669280\pi\)
−0.507093 + 0.861891i \(0.669280\pi\)
\(390\) −1903.53 −0.247152
\(391\) −668.365 −0.0864467
\(392\) −3034.61 −0.390997
\(393\) 12041.1 1.54553
\(394\) −6272.01 −0.801978
\(395\) −8807.34 −1.12189
\(396\) −1450.87 −0.184114
\(397\) 2454.12 0.310249 0.155125 0.987895i \(-0.450422\pi\)
0.155125 + 0.987895i \(0.450422\pi\)
\(398\) −4901.84 −0.617354
\(399\) 4949.80 0.621053
\(400\) 502.402 0.0628002
\(401\) −5487.12 −0.683326 −0.341663 0.939823i \(-0.610990\pi\)
−0.341663 + 0.939823i \(0.610990\pi\)
\(402\) −7811.44 −0.969152
\(403\) −2349.91 −0.290465
\(404\) 8677.44 1.06861
\(405\) −11659.2 −1.43049
\(406\) 0 0
\(407\) 22759.2 2.77182
\(408\) 14530.2 1.76311
\(409\) 256.848 0.0310521 0.0155261 0.999879i \(-0.495058\pi\)
0.0155261 + 0.999879i \(0.495058\pi\)
\(410\) −101.927 −0.0122776
\(411\) −185.472 −0.0222595
\(412\) −7516.13 −0.898770
\(413\) −1049.30 −0.125019
\(414\) 45.6958 0.00542471
\(415\) 11847.3 1.40135
\(416\) −2762.59 −0.325594
\(417\) −10674.5 −1.25355
\(418\) 5471.78 0.640272
\(419\) −5193.75 −0.605564 −0.302782 0.953060i \(-0.597915\pi\)
−0.302782 + 0.953060i \(0.597915\pi\)
\(420\) 5994.84 0.696472
\(421\) 10429.9 1.20742 0.603710 0.797204i \(-0.293688\pi\)
0.603710 + 0.797204i \(0.293688\pi\)
\(422\) 1351.85 0.155941
\(423\) 751.701 0.0864041
\(424\) −1952.31 −0.223614
\(425\) 8088.14 0.923135
\(426\) −7992.34 −0.908991
\(427\) −727.790 −0.0824829
\(428\) −2781.25 −0.314105
\(429\) 4596.41 0.517289
\(430\) −4544.22 −0.509632
\(431\) −12985.3 −1.45123 −0.725616 0.688100i \(-0.758445\pi\)
−0.725616 + 0.688100i \(0.758445\pi\)
\(432\) −914.864 −0.101890
\(433\) 3663.82 0.406632 0.203316 0.979113i \(-0.434828\pi\)
0.203316 + 0.979113i \(0.434828\pi\)
\(434\) −3674.58 −0.406418
\(435\) 0 0
\(436\) −5641.21 −0.619645
\(437\) 347.086 0.0379940
\(438\) 5549.43 0.605393
\(439\) −12233.9 −1.33005 −0.665025 0.746821i \(-0.731579\pi\)
−0.665025 + 0.746821i \(0.731579\pi\)
\(440\) 16544.5 1.79256
\(441\) −692.349 −0.0747596
\(442\) −2861.85 −0.307974
\(443\) −1596.82 −0.171258 −0.0856291 0.996327i \(-0.527290\pi\)
−0.0856291 + 0.996327i \(0.527290\pi\)
\(444\) −12571.5 −1.34373
\(445\) −16711.6 −1.78024
\(446\) 8675.49 0.921068
\(447\) 2263.71 0.239530
\(448\) −3482.07 −0.367215
\(449\) −13784.2 −1.44882 −0.724408 0.689372i \(-0.757887\pi\)
−0.724408 + 0.689372i \(0.757887\pi\)
\(450\) −552.983 −0.0579286
\(451\) 246.120 0.0256970
\(452\) −1572.86 −0.163675
\(453\) 13930.6 1.44485
\(454\) −2299.96 −0.237759
\(455\) −2947.74 −0.303719
\(456\) −7545.60 −0.774902
\(457\) −657.534 −0.0673045 −0.0336523 0.999434i \(-0.510714\pi\)
−0.0336523 + 0.999434i \(0.510714\pi\)
\(458\) −1564.79 −0.159646
\(459\) −14728.4 −1.49774
\(460\) 420.365 0.0426079
\(461\) 2230.20 0.225316 0.112658 0.993634i \(-0.464064\pi\)
0.112658 + 0.993634i \(0.464064\pi\)
\(462\) 7187.45 0.723789
\(463\) −4959.02 −0.497765 −0.248883 0.968534i \(-0.580063\pi\)
−0.248883 + 0.968534i \(0.580063\pi\)
\(464\) 0 0
\(465\) −12433.3 −1.23996
\(466\) 2930.47 0.291312
\(467\) 8429.37 0.835256 0.417628 0.908618i \(-0.362862\pi\)
0.417628 + 0.908618i \(0.362862\pi\)
\(468\) −394.068 −0.0389226
\(469\) −12096.5 −1.19097
\(470\) −3433.47 −0.336967
\(471\) −3411.05 −0.333700
\(472\) 1599.58 0.155989
\(473\) 10972.8 1.06666
\(474\) 5832.73 0.565202
\(475\) −4200.22 −0.405725
\(476\) 9012.88 0.867867
\(477\) −445.422 −0.0427557
\(478\) −5397.94 −0.516519
\(479\) 26.7718 0.00255373 0.00127686 0.999999i \(-0.499594\pi\)
0.00127686 + 0.999999i \(0.499594\pi\)
\(480\) −14616.8 −1.38992
\(481\) 6181.57 0.585978
\(482\) 607.070 0.0573678
\(483\) 455.914 0.0429499
\(484\) −8886.93 −0.834610
\(485\) 23866.5 2.23448
\(486\) 2240.59 0.209126
\(487\) 3924.73 0.365188 0.182594 0.983188i \(-0.441551\pi\)
0.182594 + 0.983188i \(0.441551\pi\)
\(488\) 1109.46 0.102916
\(489\) −2931.76 −0.271122
\(490\) 3162.38 0.291555
\(491\) −20977.8 −1.92814 −0.964070 0.265650i \(-0.914413\pi\)
−0.964070 + 0.265650i \(0.914413\pi\)
\(492\) −135.949 −0.0124574
\(493\) 0 0
\(494\) 1486.18 0.135357
\(495\) 3774.65 0.342743
\(496\) −1161.12 −0.105112
\(497\) −12376.6 −1.11704
\(498\) −7845.97 −0.705997
\(499\) −1063.31 −0.0953914 −0.0476957 0.998862i \(-0.515188\pi\)
−0.0476957 + 0.998862i \(0.515188\pi\)
\(500\) 4206.32 0.376224
\(501\) −6660.64 −0.593963
\(502\) 184.395 0.0163943
\(503\) −1339.19 −0.118711 −0.0593556 0.998237i \(-0.518905\pi\)
−0.0593556 + 0.998237i \(0.518905\pi\)
\(504\) −1538.37 −0.135962
\(505\) −22575.6 −1.98931
\(506\) 503.992 0.0442790
\(507\) −11172.0 −0.978635
\(508\) −5105.57 −0.445911
\(509\) −14925.8 −1.29975 −0.649876 0.760040i \(-0.725179\pi\)
−0.649876 + 0.760040i \(0.725179\pi\)
\(510\) −15142.0 −1.31470
\(511\) 8593.63 0.743953
\(512\) −2642.21 −0.228067
\(513\) 7648.53 0.658266
\(514\) 2764.59 0.237239
\(515\) 19554.3 1.67313
\(516\) −6061.04 −0.517098
\(517\) 8290.72 0.705272
\(518\) 9666.17 0.819898
\(519\) 659.008 0.0557365
\(520\) 4493.61 0.378957
\(521\) 16074.0 1.35166 0.675829 0.737058i \(-0.263786\pi\)
0.675829 + 0.737058i \(0.263786\pi\)
\(522\) 0 0
\(523\) −4739.93 −0.396295 −0.198148 0.980172i \(-0.563493\pi\)
−0.198148 + 0.980172i \(0.563493\pi\)
\(524\) −11385.8 −0.949221
\(525\) −5517.19 −0.458647
\(526\) 218.836 0.0181401
\(527\) −18692.7 −1.54510
\(528\) 2271.13 0.187194
\(529\) −12135.0 −0.997372
\(530\) 2034.51 0.166743
\(531\) 364.946 0.0298255
\(532\) −4680.44 −0.381434
\(533\) 66.8479 0.00543247
\(534\) 11067.4 0.896876
\(535\) 7235.82 0.584732
\(536\) 18440.2 1.48600
\(537\) 2126.99 0.170925
\(538\) 5048.97 0.404603
\(539\) −7636.11 −0.610224
\(540\) 9263.33 0.738204
\(541\) −818.479 −0.0650446 −0.0325223 0.999471i \(-0.510354\pi\)
−0.0325223 + 0.999471i \(0.510354\pi\)
\(542\) −3717.27 −0.294594
\(543\) −2047.22 −0.161795
\(544\) −21975.5 −1.73197
\(545\) 14676.4 1.15352
\(546\) 1952.16 0.153013
\(547\) −369.700 −0.0288980 −0.0144490 0.999896i \(-0.504599\pi\)
−0.0144490 + 0.999896i \(0.504599\pi\)
\(548\) 175.379 0.0136712
\(549\) 253.125 0.0196778
\(550\) −6099.00 −0.472841
\(551\) 0 0
\(552\) −695.006 −0.0535896
\(553\) 9032.34 0.694564
\(554\) −472.333 −0.0362229
\(555\) 32706.5 2.50147
\(556\) 10093.6 0.769898
\(557\) 19844.9 1.50961 0.754806 0.655948i \(-0.227731\pi\)
0.754806 + 0.655948i \(0.227731\pi\)
\(558\) 1278.02 0.0969583
\(559\) 2980.29 0.225497
\(560\) −1456.51 −0.109908
\(561\) 36562.9 2.75167
\(562\) 8844.00 0.663810
\(563\) 14158.5 1.05988 0.529938 0.848036i \(-0.322215\pi\)
0.529938 + 0.848036i \(0.322215\pi\)
\(564\) −4579.54 −0.341903
\(565\) 4092.01 0.304694
\(566\) −4991.32 −0.370673
\(567\) 11957.0 0.885624
\(568\) 18867.2 1.39375
\(569\) −15174.2 −1.11799 −0.558993 0.829173i \(-0.688812\pi\)
−0.558993 + 0.829173i \(0.688812\pi\)
\(570\) 7863.31 0.577821
\(571\) −20125.3 −1.47499 −0.737493 0.675355i \(-0.763990\pi\)
−0.737493 + 0.675355i \(0.763990\pi\)
\(572\) −4346.28 −0.317705
\(573\) 493.665 0.0359916
\(574\) 104.531 0.00760109
\(575\) −386.872 −0.0280585
\(576\) 1211.06 0.0876058
\(577\) −24675.7 −1.78035 −0.890177 0.455614i \(-0.849420\pi\)
−0.890177 + 0.455614i \(0.849420\pi\)
\(578\) −14760.8 −1.06223
\(579\) 23378.3 1.67801
\(580\) 0 0
\(581\) −12150.0 −0.867583
\(582\) −15805.7 −1.12572
\(583\) −4912.68 −0.348992
\(584\) −13100.3 −0.928247
\(585\) 1025.22 0.0724577
\(586\) −2339.77 −0.164940
\(587\) 5450.22 0.383228 0.191614 0.981470i \(-0.438628\pi\)
0.191614 + 0.981470i \(0.438628\pi\)
\(588\) 4217.95 0.295826
\(589\) 9707.26 0.679084
\(590\) −1666.93 −0.116316
\(591\) 21764.2 1.51482
\(592\) 3054.38 0.212051
\(593\) 17788.4 1.23184 0.615922 0.787807i \(-0.288784\pi\)
0.615922 + 0.787807i \(0.288784\pi\)
\(594\) 11106.2 0.767158
\(595\) −23448.3 −1.61560
\(596\) −2140.53 −0.147113
\(597\) 17009.6 1.16609
\(598\) 136.888 0.00936081
\(599\) −17037.8 −1.16218 −0.581089 0.813840i \(-0.697373\pi\)
−0.581089 + 0.813840i \(0.697373\pi\)
\(600\) 8410.54 0.572265
\(601\) 2105.40 0.142897 0.0714484 0.997444i \(-0.477238\pi\)
0.0714484 + 0.997444i \(0.477238\pi\)
\(602\) 4660.31 0.315515
\(603\) 4207.15 0.284127
\(604\) −13172.5 −0.887386
\(605\) 23120.6 1.55370
\(606\) 14950.8 1.00220
\(607\) 14072.9 0.941025 0.470513 0.882393i \(-0.344069\pi\)
0.470513 + 0.882393i \(0.344069\pi\)
\(608\) 11412.0 0.761213
\(609\) 0 0
\(610\) −1156.17 −0.0767412
\(611\) 2251.82 0.149098
\(612\) −3134.67 −0.207045
\(613\) 26905.0 1.77273 0.886364 0.462989i \(-0.153223\pi\)
0.886364 + 0.462989i \(0.153223\pi\)
\(614\) 10745.9 0.706303
\(615\) 353.690 0.0231905
\(616\) −16967.2 −1.10978
\(617\) 3978.90 0.259618 0.129809 0.991539i \(-0.458564\pi\)
0.129809 + 0.991539i \(0.458564\pi\)
\(618\) −12950.0 −0.842919
\(619\) 14188.1 0.921274 0.460637 0.887589i \(-0.347621\pi\)
0.460637 + 0.887589i \(0.347621\pi\)
\(620\) 11756.7 0.761550
\(621\) 704.486 0.0455235
\(622\) −10567.7 −0.681235
\(623\) 17138.5 1.10215
\(624\) 616.857 0.0395738
\(625\) −19496.2 −1.24775
\(626\) 188.438 0.0120311
\(627\) −18987.3 −1.20938
\(628\) 3225.43 0.204950
\(629\) 49172.2 3.11705
\(630\) 1603.15 0.101382
\(631\) 13764.1 0.868368 0.434184 0.900824i \(-0.357037\pi\)
0.434184 + 0.900824i \(0.357037\pi\)
\(632\) −13769.1 −0.866623
\(633\) −4690.98 −0.294549
\(634\) 15310.6 0.959087
\(635\) 13282.8 0.830100
\(636\) 2713.61 0.169185
\(637\) −2074.02 −0.129004
\(638\) 0 0
\(639\) 4304.59 0.266490
\(640\) 15152.3 0.935857
\(641\) 6823.67 0.420466 0.210233 0.977651i \(-0.432578\pi\)
0.210233 + 0.977651i \(0.432578\pi\)
\(642\) −4791.97 −0.294586
\(643\) 7965.35 0.488527 0.244264 0.969709i \(-0.421454\pi\)
0.244264 + 0.969709i \(0.421454\pi\)
\(644\) −431.104 −0.0263787
\(645\) 15768.6 0.962620
\(646\) 11822.0 0.720017
\(647\) 3344.19 0.203205 0.101602 0.994825i \(-0.467603\pi\)
0.101602 + 0.994825i \(0.467603\pi\)
\(648\) −18227.6 −1.10501
\(649\) 4025.09 0.243450
\(650\) −1656.53 −0.0999609
\(651\) 12750.9 0.767663
\(652\) 2772.21 0.166516
\(653\) 18155.4 1.08802 0.544009 0.839079i \(-0.316906\pi\)
0.544009 + 0.839079i \(0.316906\pi\)
\(654\) −9719.55 −0.581139
\(655\) 29621.8 1.76705
\(656\) 33.0302 0.00196587
\(657\) −2988.86 −0.177483
\(658\) 3521.19 0.208617
\(659\) −10927.7 −0.645954 −0.322977 0.946407i \(-0.604684\pi\)
−0.322977 + 0.946407i \(0.604684\pi\)
\(660\) −22996.1 −1.35624
\(661\) 12431.0 0.731483 0.365741 0.930716i \(-0.380815\pi\)
0.365741 + 0.930716i \(0.380815\pi\)
\(662\) 15520.1 0.911189
\(663\) 9930.74 0.581717
\(664\) 18521.7 1.08250
\(665\) 12176.8 0.710071
\(666\) −3361.89 −0.195601
\(667\) 0 0
\(668\) 6298.17 0.364796
\(669\) −30104.3 −1.73976
\(670\) −19216.6 −1.10806
\(671\) 2791.78 0.160619
\(672\) 14990.2 0.860505
\(673\) −24349.2 −1.39464 −0.697319 0.716761i \(-0.745624\pi\)
−0.697319 + 0.716761i \(0.745624\pi\)
\(674\) 5859.50 0.334866
\(675\) −8525.26 −0.486130
\(676\) 10564.1 0.601051
\(677\) −2495.14 −0.141649 −0.0708244 0.997489i \(-0.522563\pi\)
−0.0708244 + 0.997489i \(0.522563\pi\)
\(678\) −2709.96 −0.153504
\(679\) −24476.2 −1.38337
\(680\) 35745.1 2.01583
\(681\) 7980.96 0.449091
\(682\) 14095.6 0.791419
\(683\) 24024.9 1.34596 0.672978 0.739662i \(-0.265015\pi\)
0.672978 + 0.739662i \(0.265015\pi\)
\(684\) 1627.85 0.0909979
\(685\) −456.272 −0.0254500
\(686\) −11213.5 −0.624101
\(687\) 5429.90 0.301548
\(688\) 1472.59 0.0816019
\(689\) −1334.32 −0.0737787
\(690\) 724.270 0.0399601
\(691\) 35630.3 1.96156 0.980781 0.195111i \(-0.0625067\pi\)
0.980781 + 0.195111i \(0.0625067\pi\)
\(692\) −623.146 −0.0342319
\(693\) −3871.08 −0.212194
\(694\) 5774.97 0.315871
\(695\) −26259.9 −1.43323
\(696\) 0 0
\(697\) 531.752 0.0288975
\(698\) 13978.4 0.758010
\(699\) −10168.9 −0.550245
\(700\) 5216.95 0.281689
\(701\) −19555.8 −1.05365 −0.526827 0.849973i \(-0.676618\pi\)
−0.526827 + 0.849973i \(0.676618\pi\)
\(702\) 3016.52 0.162181
\(703\) −25535.4 −1.36997
\(704\) 13357.1 0.715080
\(705\) 11914.3 0.636481
\(706\) 2940.56 0.156756
\(707\) 23152.3 1.23159
\(708\) −2223.34 −0.118020
\(709\) 4929.02 0.261090 0.130545 0.991442i \(-0.458327\pi\)
0.130545 + 0.991442i \(0.458327\pi\)
\(710\) −19661.7 −1.03928
\(711\) −3141.44 −0.165701
\(712\) −26126.3 −1.37518
\(713\) 894.111 0.0469631
\(714\) 15528.8 0.813936
\(715\) 11307.5 0.591434
\(716\) −2011.24 −0.104977
\(717\) 18731.1 0.975627
\(718\) 5997.18 0.311717
\(719\) −18112.0 −0.939447 −0.469723 0.882814i \(-0.655646\pi\)
−0.469723 + 0.882814i \(0.655646\pi\)
\(720\) 506.573 0.0262206
\(721\) −20053.8 −1.03584
\(722\) 5035.40 0.259554
\(723\) −2106.56 −0.108359
\(724\) 1935.82 0.0993702
\(725\) 0 0
\(726\) −15311.8 −0.782746
\(727\) −4624.52 −0.235920 −0.117960 0.993018i \(-0.537636\pi\)
−0.117960 + 0.993018i \(0.537636\pi\)
\(728\) −4608.40 −0.234614
\(729\) 14859.9 0.754963
\(730\) 13651.9 0.692166
\(731\) 23707.2 1.19951
\(732\) −1542.10 −0.0778654
\(733\) −27052.1 −1.36316 −0.681578 0.731745i \(-0.738706\pi\)
−0.681578 + 0.731745i \(0.738706\pi\)
\(734\) −2392.27 −0.120300
\(735\) −10973.6 −0.550703
\(736\) 1051.13 0.0526429
\(737\) 46401.9 2.31918
\(738\) −36.3557 −0.00181338
\(739\) −35147.3 −1.74954 −0.874772 0.484534i \(-0.838989\pi\)
−0.874772 + 0.484534i \(0.838989\pi\)
\(740\) −30926.7 −1.53633
\(741\) −5157.10 −0.255669
\(742\) −2086.49 −0.103231
\(743\) 1467.33 0.0724510 0.0362255 0.999344i \(-0.488467\pi\)
0.0362255 + 0.999344i \(0.488467\pi\)
\(744\) −19437.8 −0.957831
\(745\) 5568.88 0.273863
\(746\) 9092.45 0.446245
\(747\) 4225.75 0.206978
\(748\) −34573.2 −1.69000
\(749\) −7420.67 −0.362010
\(750\) 7247.29 0.352845
\(751\) 7477.83 0.363342 0.181671 0.983359i \(-0.441849\pi\)
0.181671 + 0.983359i \(0.441849\pi\)
\(752\) 1112.65 0.0539548
\(753\) −639.859 −0.0309665
\(754\) 0 0
\(755\) 34270.1 1.65194
\(756\) −9499.98 −0.457025
\(757\) −9561.20 −0.459059 −0.229530 0.973302i \(-0.573719\pi\)
−0.229530 + 0.973302i \(0.573719\pi\)
\(758\) 9966.77 0.477585
\(759\) −1748.87 −0.0836365
\(760\) −18562.7 −0.885971
\(761\) 9454.04 0.450340 0.225170 0.974319i \(-0.427706\pi\)
0.225170 + 0.974319i \(0.427706\pi\)
\(762\) −8796.66 −0.418201
\(763\) −15051.3 −0.714148
\(764\) −466.801 −0.0221051
\(765\) 8155.29 0.385432
\(766\) −4345.14 −0.204956
\(767\) 1093.24 0.0514665
\(768\) −21076.2 −0.990263
\(769\) −35952.4 −1.68592 −0.842962 0.537973i \(-0.819190\pi\)
−0.842962 + 0.537973i \(0.819190\pi\)
\(770\) 17681.6 0.827532
\(771\) −9593.26 −0.448110
\(772\) −22106.1 −1.03059
\(773\) −4101.58 −0.190845 −0.0954226 0.995437i \(-0.530420\pi\)
−0.0954226 + 0.995437i \(0.530420\pi\)
\(774\) −1620.85 −0.0752717
\(775\) −10820.0 −0.501503
\(776\) 37312.1 1.72606
\(777\) −33542.0 −1.54867
\(778\) 12677.0 0.584178
\(779\) −276.142 −0.0127007
\(780\) −6245.90 −0.286717
\(781\) 47476.5 2.17521
\(782\) 1088.90 0.0497939
\(783\) 0 0
\(784\) −1024.80 −0.0466835
\(785\) −8391.40 −0.381531
\(786\) −19617.2 −0.890234
\(787\) 10136.2 0.459106 0.229553 0.973296i \(-0.426274\pi\)
0.229553 + 0.973296i \(0.426274\pi\)
\(788\) −20579.8 −0.930361
\(789\) −759.370 −0.0342640
\(790\) 14348.9 0.646215
\(791\) −4196.54 −0.188637
\(792\) 5901.17 0.264759
\(793\) 758.269 0.0339558
\(794\) −3998.24 −0.178706
\(795\) −7059.84 −0.314952
\(796\) −16084.0 −0.716182
\(797\) −26581.1 −1.18137 −0.590685 0.806903i \(-0.701142\pi\)
−0.590685 + 0.806903i \(0.701142\pi\)
\(798\) −8064.19 −0.357731
\(799\) 17912.4 0.793112
\(800\) −12720.1 −0.562156
\(801\) −5960.76 −0.262938
\(802\) 8939.59 0.393601
\(803\) −32965.0 −1.44870
\(804\) −25631.0 −1.12430
\(805\) 1121.58 0.0491061
\(806\) 3828.46 0.167310
\(807\) −17520.1 −0.764236
\(808\) −35293.9 −1.53668
\(809\) −44869.4 −1.94997 −0.974985 0.222273i \(-0.928652\pi\)
−0.974985 + 0.222273i \(0.928652\pi\)
\(810\) 18995.1 0.823975
\(811\) −10490.1 −0.454199 −0.227100 0.973872i \(-0.572924\pi\)
−0.227100 + 0.973872i \(0.572924\pi\)
\(812\) 0 0
\(813\) 12899.1 0.556446
\(814\) −37079.2 −1.59659
\(815\) −7212.30 −0.309983
\(816\) 4906.88 0.210509
\(817\) −12311.3 −0.527194
\(818\) −418.455 −0.0178862
\(819\) −1051.41 −0.0448588
\(820\) −334.443 −0.0142430
\(821\) 1522.68 0.0647281 0.0323640 0.999476i \(-0.489696\pi\)
0.0323640 + 0.999476i \(0.489696\pi\)
\(822\) 302.170 0.0128216
\(823\) −9450.65 −0.400278 −0.200139 0.979767i \(-0.564139\pi\)
−0.200139 + 0.979767i \(0.564139\pi\)
\(824\) 30570.5 1.29244
\(825\) 21163.8 0.893126
\(826\) 1709.52 0.0720117
\(827\) 30862.6 1.29770 0.648850 0.760916i \(-0.275250\pi\)
0.648850 + 0.760916i \(0.275250\pi\)
\(828\) 149.938 0.00629311
\(829\) −12584.4 −0.527229 −0.263614 0.964628i \(-0.584915\pi\)
−0.263614 + 0.964628i \(0.584915\pi\)
\(830\) −19301.6 −0.807190
\(831\) 1639.01 0.0684197
\(832\) 3627.90 0.151171
\(833\) −16498.1 −0.686226
\(834\) 17390.8 0.722055
\(835\) −16385.6 −0.679097
\(836\) 17954.1 0.742768
\(837\) 19703.0 0.813662
\(838\) 8461.63 0.348809
\(839\) −18688.9 −0.769026 −0.384513 0.923120i \(-0.625631\pi\)
−0.384513 + 0.923120i \(0.625631\pi\)
\(840\) −24382.9 −1.00154
\(841\) 0 0
\(842\) −16992.4 −0.695483
\(843\) −30689.0 −1.25384
\(844\) 4435.70 0.180904
\(845\) −27483.9 −1.11891
\(846\) −1224.67 −0.0497694
\(847\) −23711.2 −0.961898
\(848\) −659.301 −0.0266987
\(849\) 17320.1 0.700146
\(850\) −13177.1 −0.531732
\(851\) −2352.01 −0.0947423
\(852\) −26224.5 −1.05450
\(853\) 34110.3 1.36919 0.684593 0.728926i \(-0.259980\pi\)
0.684593 + 0.728926i \(0.259980\pi\)
\(854\) 1185.71 0.0475108
\(855\) −4235.09 −0.169400
\(856\) 11312.2 0.451688
\(857\) −14542.6 −0.579656 −0.289828 0.957079i \(-0.593598\pi\)
−0.289828 + 0.957079i \(0.593598\pi\)
\(858\) −7488.45 −0.297962
\(859\) 26425.8 1.04964 0.524818 0.851214i \(-0.324133\pi\)
0.524818 + 0.851214i \(0.324133\pi\)
\(860\) −14910.5 −0.591215
\(861\) −362.726 −0.0143573
\(862\) 21155.6 0.835920
\(863\) 14687.6 0.579342 0.289671 0.957126i \(-0.406454\pi\)
0.289671 + 0.957126i \(0.406454\pi\)
\(864\) 23163.1 0.912067
\(865\) 1621.20 0.0637254
\(866\) −5969.07 −0.234223
\(867\) 51220.6 2.00639
\(868\) −12057.1 −0.471478
\(869\) −34647.8 −1.35253
\(870\) 0 0
\(871\) 12603.1 0.490286
\(872\) 22944.6 0.891058
\(873\) 8512.80 0.330028
\(874\) −565.470 −0.0218848
\(875\) 11222.9 0.433603
\(876\) 18208.8 0.702305
\(877\) −22840.6 −0.879444 −0.439722 0.898134i \(-0.644923\pi\)
−0.439722 + 0.898134i \(0.644923\pi\)
\(878\) 19931.4 0.766118
\(879\) 8119.11 0.311548
\(880\) 5587.13 0.214025
\(881\) −21209.1 −0.811072 −0.405536 0.914079i \(-0.632915\pi\)
−0.405536 + 0.914079i \(0.632915\pi\)
\(882\) 1127.97 0.0430621
\(883\) 15870.5 0.604854 0.302427 0.953173i \(-0.402203\pi\)
0.302427 + 0.953173i \(0.402203\pi\)
\(884\) −9390.33 −0.357275
\(885\) 5784.33 0.219704
\(886\) 2601.53 0.0986459
\(887\) 25122.6 0.950997 0.475498 0.879717i \(-0.342268\pi\)
0.475498 + 0.879717i \(0.342268\pi\)
\(888\) 51132.3 1.93231
\(889\) −13622.2 −0.513918
\(890\) 27226.4 1.02543
\(891\) −45866.9 −1.72458
\(892\) 28466.1 1.06852
\(893\) −9302.04 −0.348579
\(894\) −3688.03 −0.137971
\(895\) 5232.53 0.195424
\(896\) −15539.4 −0.579393
\(897\) −475.007 −0.0176812
\(898\) 22457.2 0.834528
\(899\) 0 0
\(900\) −1814.45 −0.0672020
\(901\) −10614.0 −0.392459
\(902\) −400.977 −0.0148016
\(903\) −16171.5 −0.595961
\(904\) 6397.31 0.235367
\(905\) −5036.29 −0.184986
\(906\) −22695.6 −0.832241
\(907\) −47430.9 −1.73640 −0.868201 0.496213i \(-0.834724\pi\)
−0.868201 + 0.496213i \(0.834724\pi\)
\(908\) −7546.65 −0.275820
\(909\) −8052.35 −0.293817
\(910\) 4802.44 0.174944
\(911\) −30167.2 −1.09713 −0.548565 0.836108i \(-0.684826\pi\)
−0.548565 + 0.836108i \(0.684826\pi\)
\(912\) −2548.17 −0.0925202
\(913\) 46607.0 1.68945
\(914\) 1071.25 0.0387679
\(915\) 4011.98 0.144953
\(916\) −5134.41 −0.185203
\(917\) −30378.5 −1.09399
\(918\) 23995.4 0.862707
\(919\) −13387.0 −0.480517 −0.240259 0.970709i \(-0.577232\pi\)
−0.240259 + 0.970709i \(0.577232\pi\)
\(920\) −1709.76 −0.0612707
\(921\) −37288.8 −1.33410
\(922\) −3633.43 −0.129784
\(923\) 12895.0 0.459851
\(924\) 23583.5 0.839655
\(925\) 28462.5 1.01172
\(926\) 8079.21 0.286716
\(927\) 6974.70 0.247119
\(928\) 0 0
\(929\) 40008.9 1.41297 0.706486 0.707727i \(-0.250280\pi\)
0.706486 + 0.707727i \(0.250280\pi\)
\(930\) 20256.3 0.714226
\(931\) 8567.58 0.301602
\(932\) 9615.48 0.337946
\(933\) 36670.6 1.28675
\(934\) −13733.1 −0.481113
\(935\) 89947.0 3.14607
\(936\) 1602.80 0.0559713
\(937\) −16407.0 −0.572032 −0.286016 0.958225i \(-0.592331\pi\)
−0.286016 + 0.958225i \(0.592331\pi\)
\(938\) 19707.5 0.686007
\(939\) −653.887 −0.0227250
\(940\) −11265.9 −0.390909
\(941\) 38360.3 1.32892 0.664458 0.747325i \(-0.268662\pi\)
0.664458 + 0.747325i \(0.268662\pi\)
\(942\) 5557.26 0.192214
\(943\) −25.4348 −0.000878335 0
\(944\) 540.183 0.0186244
\(945\) 24715.5 0.850789
\(946\) −17876.8 −0.614404
\(947\) −30441.9 −1.04459 −0.522296 0.852764i \(-0.674925\pi\)
−0.522296 + 0.852764i \(0.674925\pi\)
\(948\) 19138.4 0.655681
\(949\) −8953.53 −0.306263
\(950\) 6842.97 0.233700
\(951\) −53128.4 −1.81157
\(952\) −36658.3 −1.24801
\(953\) −21635.8 −0.735418 −0.367709 0.929941i \(-0.619858\pi\)
−0.367709 + 0.929941i \(0.619858\pi\)
\(954\) 725.678 0.0246276
\(955\) 1214.45 0.0411504
\(956\) −17711.8 −0.599204
\(957\) 0 0
\(958\) −43.6165 −0.00147097
\(959\) 467.928 0.0157562
\(960\) 19195.1 0.645332
\(961\) −4784.62 −0.160606
\(962\) −10071.0 −0.337527
\(963\) 2580.90 0.0863639
\(964\) 1991.92 0.0665514
\(965\) 57512.0 1.91853
\(966\) −742.772 −0.0247394
\(967\) 46.7093 0.00155333 0.000776665 1.00000i \(-0.499753\pi\)
0.000776665 1.00000i \(0.499753\pi\)
\(968\) 36146.0 1.20018
\(969\) −41022.9 −1.36001
\(970\) −38883.1 −1.28707
\(971\) 12150.1 0.401560 0.200780 0.979636i \(-0.435652\pi\)
0.200780 + 0.979636i \(0.435652\pi\)
\(972\) 7351.86 0.242604
\(973\) 26930.7 0.887316
\(974\) −6394.15 −0.210351
\(975\) 5748.24 0.188811
\(976\) 374.668 0.0122877
\(977\) −41772.5 −1.36788 −0.683942 0.729537i \(-0.739736\pi\)
−0.683942 + 0.729537i \(0.739736\pi\)
\(978\) 4776.40 0.156168
\(979\) −65742.9 −2.14622
\(980\) 10376.4 0.338227
\(981\) 5234.84 0.170373
\(982\) 34177.0 1.11062
\(983\) −4488.99 −0.145653 −0.0728264 0.997345i \(-0.523202\pi\)
−0.0728264 + 0.997345i \(0.523202\pi\)
\(984\) 552.948 0.0179140
\(985\) 53541.2 1.73194
\(986\) 0 0
\(987\) −12218.7 −0.394047
\(988\) 4876.45 0.157025
\(989\) −1133.96 −0.0364590
\(990\) −6149.64 −0.197423
\(991\) 17506.2 0.561152 0.280576 0.959832i \(-0.409475\pi\)
0.280576 + 0.959832i \(0.409475\pi\)
\(992\) 29397.9 0.940911
\(993\) −53855.5 −1.72110
\(994\) 20163.9 0.643422
\(995\) 41844.7 1.33323
\(996\) −25744.3 −0.819015
\(997\) 14604.7 0.463928 0.231964 0.972724i \(-0.425485\pi\)
0.231964 + 0.972724i \(0.425485\pi\)
\(998\) 1732.34 0.0549461
\(999\) −51829.7 −1.64146
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 841.4.a.i.1.7 21
29.4 even 14 29.4.d.a.16.3 42
29.22 even 14 29.4.d.a.20.3 yes 42
29.28 even 2 841.4.a.h.1.15 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.4.d.a.16.3 42 29.4 even 14
29.4.d.a.20.3 yes 42 29.22 even 14
841.4.a.h.1.15 21 29.28 even 2
841.4.a.i.1.7 21 1.1 even 1 trivial