Properties

Label 2366.2.a.bd.1.3
Level 2366
Weight 2
Character 2366.1
Self dual yes
Analytic conductor 18.893
Analytic rank 0
Dimension 3
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(18.8926051182\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 2366.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.24698 q^{3} +1.00000 q^{4} +1.69202 q^{5} +2.24698 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.04892 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.24698 q^{3} +1.00000 q^{4} +1.69202 q^{5} +2.24698 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.04892 q^{9} +1.69202 q^{10} +0.445042 q^{11} +2.24698 q^{12} -1.00000 q^{14} +3.80194 q^{15} +1.00000 q^{16} -2.15883 q^{17} +2.04892 q^{18} +6.35690 q^{19} +1.69202 q^{20} -2.24698 q^{21} +0.445042 q^{22} -0.911854 q^{23} +2.24698 q^{24} -2.13706 q^{25} -2.13706 q^{27} -1.00000 q^{28} +3.58211 q^{29} +3.80194 q^{30} +8.89977 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.15883 q^{34} -1.69202 q^{35} +2.04892 q^{36} +10.8019 q^{37} +6.35690 q^{38} +1.69202 q^{40} +2.41789 q^{41} -2.24698 q^{42} +4.63102 q^{43} +0.445042 q^{44} +3.46681 q^{45} -0.911854 q^{46} -9.75063 q^{47} +2.24698 q^{48} +1.00000 q^{49} -2.13706 q^{50} -4.85086 q^{51} -8.74094 q^{53} -2.13706 q^{54} +0.753020 q^{55} -1.00000 q^{56} +14.2838 q^{57} +3.58211 q^{58} -10.1468 q^{59} +3.80194 q^{60} +1.37867 q^{61} +8.89977 q^{62} -2.04892 q^{63} +1.00000 q^{64} +1.00000 q^{66} +6.23490 q^{67} -2.15883 q^{68} -2.04892 q^{69} -1.69202 q^{70} -5.76271 q^{71} +2.04892 q^{72} -9.93661 q^{73} +10.8019 q^{74} -4.80194 q^{75} +6.35690 q^{76} -0.445042 q^{77} -6.30127 q^{79} +1.69202 q^{80} -10.9487 q^{81} +2.41789 q^{82} -2.91185 q^{83} -2.24698 q^{84} -3.65279 q^{85} +4.63102 q^{86} +8.04892 q^{87} +0.445042 q^{88} +18.1075 q^{89} +3.46681 q^{90} -0.911854 q^{92} +19.9976 q^{93} -9.75063 q^{94} +10.7560 q^{95} +2.24698 q^{96} -3.30798 q^{97} +1.00000 q^{98} +0.911854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} - 3q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} - 3q^{7} + 3q^{8} - 3q^{9} + q^{11} + 2q^{12} - 3q^{14} + 7q^{15} + 3q^{16} + 2q^{17} - 3q^{18} + 15q^{19} - 2q^{21} + q^{22} + q^{23} + 2q^{24} - q^{25} - q^{27} - 3q^{28} + 5q^{29} + 7q^{30} + 4q^{31} + 3q^{32} + 3q^{33} + 2q^{34} - 3q^{36} + 28q^{37} + 15q^{38} + 13q^{41} - 2q^{42} - q^{43} + q^{44} + 7q^{45} + q^{46} + 7q^{47} + 2q^{48} + 3q^{49} - q^{50} - q^{51} - 12q^{53} - q^{54} + 7q^{55} - 3q^{56} + 10q^{57} + 5q^{58} - 3q^{59} + 7q^{60} - 3q^{61} + 4q^{62} + 3q^{63} + 3q^{64} + 3q^{66} - 5q^{67} + 2q^{68} + 3q^{69} - 3q^{72} + 21q^{73} + 28q^{74} - 10q^{75} + 15q^{76} - q^{77} - 2q^{79} - q^{81} + 13q^{82} - 5q^{83} - 2q^{84} + 7q^{85} - q^{86} + 15q^{87} + q^{88} + 14q^{89} + 7q^{90} + q^{92} + 19q^{93} + 7q^{94} - 7q^{95} + 2q^{96} - 15q^{97} + 3q^{98} - q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.24698 1.29729 0.648647 0.761089i \(-0.275335\pi\)
0.648647 + 0.761089i \(0.275335\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.69202 0.756695 0.378348 0.925664i \(-0.376492\pi\)
0.378348 + 0.925664i \(0.376492\pi\)
\(6\) 2.24698 0.917326
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 2.04892 0.682972
\(10\) 1.69202 0.535064
\(11\) 0.445042 0.134185 0.0670926 0.997747i \(-0.478628\pi\)
0.0670926 + 0.997747i \(0.478628\pi\)
\(12\) 2.24698 0.648647
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 3.80194 0.981656
\(16\) 1.00000 0.250000
\(17\) −2.15883 −0.523594 −0.261797 0.965123i \(-0.584315\pi\)
−0.261797 + 0.965123i \(0.584315\pi\)
\(18\) 2.04892 0.482934
\(19\) 6.35690 1.45837 0.729186 0.684316i \(-0.239899\pi\)
0.729186 + 0.684316i \(0.239899\pi\)
\(20\) 1.69202 0.378348
\(21\) −2.24698 −0.490331
\(22\) 0.445042 0.0948832
\(23\) −0.911854 −0.190135 −0.0950674 0.995471i \(-0.530307\pi\)
−0.0950674 + 0.995471i \(0.530307\pi\)
\(24\) 2.24698 0.458663
\(25\) −2.13706 −0.427413
\(26\) 0 0
\(27\) −2.13706 −0.411278
\(28\) −1.00000 −0.188982
\(29\) 3.58211 0.665180 0.332590 0.943071i \(-0.392077\pi\)
0.332590 + 0.943071i \(0.392077\pi\)
\(30\) 3.80194 0.694136
\(31\) 8.89977 1.59845 0.799223 0.601034i \(-0.205245\pi\)
0.799223 + 0.601034i \(0.205245\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) −2.15883 −0.370237
\(35\) −1.69202 −0.286004
\(36\) 2.04892 0.341486
\(37\) 10.8019 1.77583 0.887914 0.460010i \(-0.152154\pi\)
0.887914 + 0.460010i \(0.152154\pi\)
\(38\) 6.35690 1.03122
\(39\) 0 0
\(40\) 1.69202 0.267532
\(41\) 2.41789 0.377612 0.188806 0.982014i \(-0.439538\pi\)
0.188806 + 0.982014i \(0.439538\pi\)
\(42\) −2.24698 −0.346716
\(43\) 4.63102 0.706224 0.353112 0.935581i \(-0.385123\pi\)
0.353112 + 0.935581i \(0.385123\pi\)
\(44\) 0.445042 0.0670926
\(45\) 3.46681 0.516802
\(46\) −0.911854 −0.134446
\(47\) −9.75063 −1.42228 −0.711138 0.703053i \(-0.751820\pi\)
−0.711138 + 0.703053i \(0.751820\pi\)
\(48\) 2.24698 0.324324
\(49\) 1.00000 0.142857
\(50\) −2.13706 −0.302226
\(51\) −4.85086 −0.679256
\(52\) 0 0
\(53\) −8.74094 −1.20066 −0.600330 0.799752i \(-0.704964\pi\)
−0.600330 + 0.799752i \(0.704964\pi\)
\(54\) −2.13706 −0.290817
\(55\) 0.753020 0.101537
\(56\) −1.00000 −0.133631
\(57\) 14.2838 1.89194
\(58\) 3.58211 0.470353
\(59\) −10.1468 −1.32099 −0.660497 0.750828i \(-0.729655\pi\)
−0.660497 + 0.750828i \(0.729655\pi\)
\(60\) 3.80194 0.490828
\(61\) 1.37867 0.176520 0.0882601 0.996097i \(-0.471869\pi\)
0.0882601 + 0.996097i \(0.471869\pi\)
\(62\) 8.89977 1.13027
\(63\) −2.04892 −0.258139
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.00000 0.123091
\(67\) 6.23490 0.761714 0.380857 0.924634i \(-0.375629\pi\)
0.380857 + 0.924634i \(0.375629\pi\)
\(68\) −2.15883 −0.261797
\(69\) −2.04892 −0.246661
\(70\) −1.69202 −0.202235
\(71\) −5.76271 −0.683908 −0.341954 0.939717i \(-0.611089\pi\)
−0.341954 + 0.939717i \(0.611089\pi\)
\(72\) 2.04892 0.241467
\(73\) −9.93661 −1.16299 −0.581496 0.813549i \(-0.697532\pi\)
−0.581496 + 0.813549i \(0.697532\pi\)
\(74\) 10.8019 1.25570
\(75\) −4.80194 −0.554480
\(76\) 6.35690 0.729186
\(77\) −0.445042 −0.0507172
\(78\) 0 0
\(79\) −6.30127 −0.708949 −0.354474 0.935066i \(-0.615340\pi\)
−0.354474 + 0.935066i \(0.615340\pi\)
\(80\) 1.69202 0.189174
\(81\) −10.9487 −1.21652
\(82\) 2.41789 0.267012
\(83\) −2.91185 −0.319617 −0.159809 0.987148i \(-0.551088\pi\)
−0.159809 + 0.987148i \(0.551088\pi\)
\(84\) −2.24698 −0.245166
\(85\) −3.65279 −0.396201
\(86\) 4.63102 0.499376
\(87\) 8.04892 0.862935
\(88\) 0.445042 0.0474416
\(89\) 18.1075 1.91939 0.959697 0.281037i \(-0.0906785\pi\)
0.959697 + 0.281037i \(0.0906785\pi\)
\(90\) 3.46681 0.365434
\(91\) 0 0
\(92\) −0.911854 −0.0950674
\(93\) 19.9976 2.07366
\(94\) −9.75063 −1.00570
\(95\) 10.7560 1.10354
\(96\) 2.24698 0.229331
\(97\) −3.30798 −0.335874 −0.167937 0.985798i \(-0.553711\pi\)
−0.167937 + 0.985798i \(0.553711\pi\)
\(98\) 1.00000 0.101015
\(99\) 0.911854 0.0916448
\(100\) −2.13706 −0.213706
\(101\) 2.08815 0.207778 0.103889 0.994589i \(-0.466871\pi\)
0.103889 + 0.994589i \(0.466871\pi\)
\(102\) −4.85086 −0.480306
\(103\) −11.3013 −1.11355 −0.556774 0.830664i \(-0.687961\pi\)
−0.556774 + 0.830664i \(0.687961\pi\)
\(104\) 0 0
\(105\) −3.80194 −0.371031
\(106\) −8.74094 −0.848995
\(107\) −7.13467 −0.689735 −0.344867 0.938651i \(-0.612076\pi\)
−0.344867 + 0.938651i \(0.612076\pi\)
\(108\) −2.13706 −0.205639
\(109\) −6.57002 −0.629294 −0.314647 0.949209i \(-0.601886\pi\)
−0.314647 + 0.949209i \(0.601886\pi\)
\(110\) 0.753020 0.0717977
\(111\) 24.2717 2.30377
\(112\) −1.00000 −0.0944911
\(113\) 10.6015 0.997304 0.498652 0.866802i \(-0.333829\pi\)
0.498652 + 0.866802i \(0.333829\pi\)
\(114\) 14.2838 1.33780
\(115\) −1.54288 −0.143874
\(116\) 3.58211 0.332590
\(117\) 0 0
\(118\) −10.1468 −0.934084
\(119\) 2.15883 0.197900
\(120\) 3.80194 0.347068
\(121\) −10.8019 −0.981994
\(122\) 1.37867 0.124819
\(123\) 5.43296 0.489874
\(124\) 8.89977 0.799223
\(125\) −12.0761 −1.08012
\(126\) −2.04892 −0.182532
\(127\) −21.5646 −1.91355 −0.956776 0.290824i \(-0.906070\pi\)
−0.956776 + 0.290824i \(0.906070\pi\)
\(128\) 1.00000 0.0883883
\(129\) 10.4058 0.916181
\(130\) 0 0
\(131\) 3.14675 0.274933 0.137467 0.990506i \(-0.456104\pi\)
0.137467 + 0.990506i \(0.456104\pi\)
\(132\) 1.00000 0.0870388
\(133\) −6.35690 −0.551213
\(134\) 6.23490 0.538613
\(135\) −3.61596 −0.311212
\(136\) −2.15883 −0.185118
\(137\) −3.93362 −0.336072 −0.168036 0.985781i \(-0.553743\pi\)
−0.168036 + 0.985781i \(0.553743\pi\)
\(138\) −2.04892 −0.174415
\(139\) −11.2078 −0.950629 −0.475315 0.879816i \(-0.657666\pi\)
−0.475315 + 0.879816i \(0.657666\pi\)
\(140\) −1.69202 −0.143002
\(141\) −21.9095 −1.84511
\(142\) −5.76271 −0.483596
\(143\) 0 0
\(144\) 2.04892 0.170743
\(145\) 6.06100 0.503339
\(146\) −9.93661 −0.822360
\(147\) 2.24698 0.185328
\(148\) 10.8019 0.887914
\(149\) −21.8726 −1.79188 −0.895938 0.444180i \(-0.853495\pi\)
−0.895938 + 0.444180i \(0.853495\pi\)
\(150\) −4.80194 −0.392077
\(151\) 18.3002 1.48925 0.744625 0.667483i \(-0.232628\pi\)
0.744625 + 0.667483i \(0.232628\pi\)
\(152\) 6.35690 0.515612
\(153\) −4.42327 −0.357600
\(154\) −0.445042 −0.0358625
\(155\) 15.0586 1.20954
\(156\) 0 0
\(157\) −10.8442 −0.865457 −0.432729 0.901524i \(-0.642449\pi\)
−0.432729 + 0.901524i \(0.642449\pi\)
\(158\) −6.30127 −0.501302
\(159\) −19.6407 −1.55761
\(160\) 1.69202 0.133766
\(161\) 0.911854 0.0718642
\(162\) −10.9487 −0.860210
\(163\) 14.4058 1.12835 0.564175 0.825655i \(-0.309194\pi\)
0.564175 + 0.825655i \(0.309194\pi\)
\(164\) 2.41789 0.188806
\(165\) 1.69202 0.131724
\(166\) −2.91185 −0.226004
\(167\) −13.6963 −1.05985 −0.529927 0.848043i \(-0.677781\pi\)
−0.529927 + 0.848043i \(0.677781\pi\)
\(168\) −2.24698 −0.173358
\(169\) 0 0
\(170\) −3.65279 −0.280156
\(171\) 13.0248 0.996028
\(172\) 4.63102 0.353112
\(173\) −4.47650 −0.340342 −0.170171 0.985415i \(-0.554432\pi\)
−0.170171 + 0.985415i \(0.554432\pi\)
\(174\) 8.04892 0.610187
\(175\) 2.13706 0.161547
\(176\) 0.445042 0.0335463
\(177\) −22.7995 −1.71372
\(178\) 18.1075 1.35722
\(179\) −23.0737 −1.72461 −0.862304 0.506392i \(-0.830979\pi\)
−0.862304 + 0.506392i \(0.830979\pi\)
\(180\) 3.46681 0.258401
\(181\) 8.46980 0.629555 0.314777 0.949165i \(-0.398070\pi\)
0.314777 + 0.949165i \(0.398070\pi\)
\(182\) 0 0
\(183\) 3.09783 0.228999
\(184\) −0.911854 −0.0672228
\(185\) 18.2771 1.34376
\(186\) 19.9976 1.46630
\(187\) −0.960771 −0.0702586
\(188\) −9.75063 −0.711138
\(189\) 2.13706 0.155448
\(190\) 10.7560 0.780323
\(191\) 19.7235 1.42714 0.713570 0.700583i \(-0.247077\pi\)
0.713570 + 0.700583i \(0.247077\pi\)
\(192\) 2.24698 0.162162
\(193\) −9.15883 −0.659267 −0.329634 0.944109i \(-0.606925\pi\)
−0.329634 + 0.944109i \(0.606925\pi\)
\(194\) −3.30798 −0.237499
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 3.73019 0.265765 0.132882 0.991132i \(-0.457577\pi\)
0.132882 + 0.991132i \(0.457577\pi\)
\(198\) 0.911854 0.0648026
\(199\) 19.5918 1.38883 0.694413 0.719577i \(-0.255664\pi\)
0.694413 + 0.719577i \(0.255664\pi\)
\(200\) −2.13706 −0.151113
\(201\) 14.0097 0.988167
\(202\) 2.08815 0.146921
\(203\) −3.58211 −0.251414
\(204\) −4.85086 −0.339628
\(205\) 4.09113 0.285737
\(206\) −11.3013 −0.787397
\(207\) −1.86831 −0.129857
\(208\) 0 0
\(209\) 2.82908 0.195692
\(210\) −3.80194 −0.262359
\(211\) 23.3860 1.60996 0.804978 0.593305i \(-0.202177\pi\)
0.804978 + 0.593305i \(0.202177\pi\)
\(212\) −8.74094 −0.600330
\(213\) −12.9487 −0.887230
\(214\) −7.13467 −0.487716
\(215\) 7.83579 0.534396
\(216\) −2.13706 −0.145409
\(217\) −8.89977 −0.604156
\(218\) −6.57002 −0.444978
\(219\) −22.3274 −1.50874
\(220\) 0.753020 0.0507686
\(221\) 0 0
\(222\) 24.2717 1.62901
\(223\) −21.7482 −1.45637 −0.728185 0.685381i \(-0.759636\pi\)
−0.728185 + 0.685381i \(0.759636\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −4.37867 −0.291911
\(226\) 10.6015 0.705200
\(227\) 6.55927 0.435354 0.217677 0.976021i \(-0.430152\pi\)
0.217677 + 0.976021i \(0.430152\pi\)
\(228\) 14.2838 0.945969
\(229\) −0.948690 −0.0626912 −0.0313456 0.999509i \(-0.509979\pi\)
−0.0313456 + 0.999509i \(0.509979\pi\)
\(230\) −1.54288 −0.101734
\(231\) −1.00000 −0.0657952
\(232\) 3.58211 0.235177
\(233\) −15.4765 −1.01390 −0.506950 0.861976i \(-0.669227\pi\)
−0.506950 + 0.861976i \(0.669227\pi\)
\(234\) 0 0
\(235\) −16.4983 −1.07623
\(236\) −10.1468 −0.660497
\(237\) −14.1588 −0.919715
\(238\) 2.15883 0.139936
\(239\) 25.3448 1.63942 0.819710 0.572779i \(-0.194135\pi\)
0.819710 + 0.572779i \(0.194135\pi\)
\(240\) 3.80194 0.245414
\(241\) −28.2664 −1.82080 −0.910398 0.413733i \(-0.864225\pi\)
−0.910398 + 0.413733i \(0.864225\pi\)
\(242\) −10.8019 −0.694375
\(243\) −18.1903 −1.16691
\(244\) 1.37867 0.0882601
\(245\) 1.69202 0.108099
\(246\) 5.43296 0.346393
\(247\) 0 0
\(248\) 8.89977 0.565136
\(249\) −6.54288 −0.414638
\(250\) −12.0761 −0.763757
\(251\) −13.7235 −0.866218 −0.433109 0.901341i \(-0.642584\pi\)
−0.433109 + 0.901341i \(0.642584\pi\)
\(252\) −2.04892 −0.129070
\(253\) −0.405813 −0.0255133
\(254\) −21.5646 −1.35309
\(255\) −8.20775 −0.513989
\(256\) 1.00000 0.0625000
\(257\) −13.3502 −0.832762 −0.416381 0.909190i \(-0.636702\pi\)
−0.416381 + 0.909190i \(0.636702\pi\)
\(258\) 10.4058 0.647838
\(259\) −10.8019 −0.671200
\(260\) 0 0
\(261\) 7.33944 0.454300
\(262\) 3.14675 0.194407
\(263\) 19.3153 1.19103 0.595515 0.803344i \(-0.296948\pi\)
0.595515 + 0.803344i \(0.296948\pi\)
\(264\) 1.00000 0.0615457
\(265\) −14.7899 −0.908534
\(266\) −6.35690 −0.389766
\(267\) 40.6872 2.49002
\(268\) 6.23490 0.380857
\(269\) 24.2935 1.48120 0.740601 0.671946i \(-0.234541\pi\)
0.740601 + 0.671946i \(0.234541\pi\)
\(270\) −3.61596 −0.220060
\(271\) 29.0368 1.76386 0.881931 0.471378i \(-0.156243\pi\)
0.881931 + 0.471378i \(0.156243\pi\)
\(272\) −2.15883 −0.130899
\(273\) 0 0
\(274\) −3.93362 −0.237639
\(275\) −0.951083 −0.0573524
\(276\) −2.04892 −0.123330
\(277\) 1.19029 0.0715177 0.0357589 0.999360i \(-0.488615\pi\)
0.0357589 + 0.999360i \(0.488615\pi\)
\(278\) −11.2078 −0.672196
\(279\) 18.2349 1.09169
\(280\) −1.69202 −0.101118
\(281\) 21.2325 1.26663 0.633313 0.773896i \(-0.281695\pi\)
0.633313 + 0.773896i \(0.281695\pi\)
\(282\) −21.9095 −1.30469
\(283\) 11.6756 0.694044 0.347022 0.937857i \(-0.387193\pi\)
0.347022 + 0.937857i \(0.387193\pi\)
\(284\) −5.76271 −0.341954
\(285\) 24.1685 1.43162
\(286\) 0 0
\(287\) −2.41789 −0.142724
\(288\) 2.04892 0.120734
\(289\) −12.3394 −0.725849
\(290\) 6.06100 0.355914
\(291\) −7.43296 −0.435728
\(292\) −9.93661 −0.581496
\(293\) 14.4101 0.841848 0.420924 0.907096i \(-0.361706\pi\)
0.420924 + 0.907096i \(0.361706\pi\)
\(294\) 2.24698 0.131047
\(295\) −17.1685 −0.999590
\(296\) 10.8019 0.627850
\(297\) −0.951083 −0.0551874
\(298\) −21.8726 −1.26705
\(299\) 0 0
\(300\) −4.80194 −0.277240
\(301\) −4.63102 −0.266928
\(302\) 18.3002 1.05306
\(303\) 4.69202 0.269550
\(304\) 6.35690 0.364593
\(305\) 2.33273 0.133572
\(306\) −4.42327 −0.252862
\(307\) 2.55257 0.145683 0.0728413 0.997344i \(-0.476793\pi\)
0.0728413 + 0.997344i \(0.476793\pi\)
\(308\) −0.445042 −0.0253586
\(309\) −25.3937 −1.44460
\(310\) 15.0586 0.855271
\(311\) −1.63533 −0.0927313 −0.0463657 0.998925i \(-0.514764\pi\)
−0.0463657 + 0.998925i \(0.514764\pi\)
\(312\) 0 0
\(313\) −12.7724 −0.721939 −0.360969 0.932578i \(-0.617554\pi\)
−0.360969 + 0.932578i \(0.617554\pi\)
\(314\) −10.8442 −0.611971
\(315\) −3.46681 −0.195333
\(316\) −6.30127 −0.354474
\(317\) −10.9041 −0.612434 −0.306217 0.951962i \(-0.599063\pi\)
−0.306217 + 0.951962i \(0.599063\pi\)
\(318\) −19.6407 −1.10140
\(319\) 1.59419 0.0892573
\(320\) 1.69202 0.0945869
\(321\) −16.0315 −0.894789
\(322\) 0.911854 0.0508156
\(323\) −13.7235 −0.763595
\(324\) −10.9487 −0.608261
\(325\) 0 0
\(326\) 14.4058 0.797864
\(327\) −14.7627 −0.816380
\(328\) 2.41789 0.133506
\(329\) 9.75063 0.537569
\(330\) 1.69202 0.0931427
\(331\) 9.94869 0.546829 0.273415 0.961896i \(-0.411847\pi\)
0.273415 + 0.961896i \(0.411847\pi\)
\(332\) −2.91185 −0.159809
\(333\) 22.1323 1.21284
\(334\) −13.6963 −0.749430
\(335\) 10.5496 0.576385
\(336\) −2.24698 −0.122583
\(337\) 8.06829 0.439508 0.219754 0.975555i \(-0.429475\pi\)
0.219754 + 0.975555i \(0.429475\pi\)
\(338\) 0 0
\(339\) 23.8213 1.29380
\(340\) −3.65279 −0.198101
\(341\) 3.96077 0.214488
\(342\) 13.0248 0.704298
\(343\) −1.00000 −0.0539949
\(344\) 4.63102 0.249688
\(345\) −3.46681 −0.186647
\(346\) −4.47650 −0.240658
\(347\) −33.1769 −1.78103 −0.890514 0.454955i \(-0.849655\pi\)
−0.890514 + 0.454955i \(0.849655\pi\)
\(348\) 8.04892 0.431467
\(349\) 24.6872 1.32148 0.660739 0.750616i \(-0.270243\pi\)
0.660739 + 0.750616i \(0.270243\pi\)
\(350\) 2.13706 0.114231
\(351\) 0 0
\(352\) 0.445042 0.0237208
\(353\) 22.5754 1.20157 0.600784 0.799412i \(-0.294855\pi\)
0.600784 + 0.799412i \(0.294855\pi\)
\(354\) −22.7995 −1.21178
\(355\) −9.75063 −0.517510
\(356\) 18.1075 0.959697
\(357\) 4.85086 0.256734
\(358\) −23.0737 −1.21948
\(359\) 2.30798 0.121810 0.0609052 0.998144i \(-0.480601\pi\)
0.0609052 + 0.998144i \(0.480601\pi\)
\(360\) 3.46681 0.182717
\(361\) 21.4101 1.12685
\(362\) 8.46980 0.445163
\(363\) −24.2717 −1.27394
\(364\) 0 0
\(365\) −16.8130 −0.880030
\(366\) 3.09783 0.161926
\(367\) 25.1685 1.31379 0.656893 0.753984i \(-0.271870\pi\)
0.656893 + 0.753984i \(0.271870\pi\)
\(368\) −0.911854 −0.0475337
\(369\) 4.95407 0.257898
\(370\) 18.2771 0.950182
\(371\) 8.74094 0.453807
\(372\) 19.9976 1.03683
\(373\) 11.6407 0.602733 0.301367 0.953508i \(-0.402557\pi\)
0.301367 + 0.953508i \(0.402557\pi\)
\(374\) −0.960771 −0.0496803
\(375\) −27.1347 −1.40123
\(376\) −9.75063 −0.502850
\(377\) 0 0
\(378\) 2.13706 0.109919
\(379\) −16.5623 −0.850746 −0.425373 0.905018i \(-0.639857\pi\)
−0.425373 + 0.905018i \(0.639857\pi\)
\(380\) 10.7560 0.551771
\(381\) −48.4553 −2.48244
\(382\) 19.7235 1.00914
\(383\) −7.39506 −0.377870 −0.188935 0.981990i \(-0.560504\pi\)
−0.188935 + 0.981990i \(0.560504\pi\)
\(384\) 2.24698 0.114666
\(385\) −0.753020 −0.0383775
\(386\) −9.15883 −0.466172
\(387\) 9.48858 0.482332
\(388\) −3.30798 −0.167937
\(389\) 23.4674 1.18984 0.594922 0.803783i \(-0.297183\pi\)
0.594922 + 0.803783i \(0.297183\pi\)
\(390\) 0 0
\(391\) 1.96854 0.0995534
\(392\) 1.00000 0.0505076
\(393\) 7.07069 0.356669
\(394\) 3.73019 0.187924
\(395\) −10.6619 −0.536458
\(396\) 0.911854 0.0458224
\(397\) −0.0499823 −0.00250854 −0.00125427 0.999999i \(-0.500399\pi\)
−0.00125427 + 0.999999i \(0.500399\pi\)
\(398\) 19.5918 0.982048
\(399\) −14.2838 −0.715085
\(400\) −2.13706 −0.106853
\(401\) 4.84010 0.241703 0.120852 0.992671i \(-0.461437\pi\)
0.120852 + 0.992671i \(0.461437\pi\)
\(402\) 14.0097 0.698740
\(403\) 0 0
\(404\) 2.08815 0.103889
\(405\) −18.5254 −0.920535
\(406\) −3.58211 −0.177777
\(407\) 4.80731 0.238290
\(408\) −4.85086 −0.240153
\(409\) 29.8866 1.47780 0.738899 0.673816i \(-0.235346\pi\)
0.738899 + 0.673816i \(0.235346\pi\)
\(410\) 4.09113 0.202047
\(411\) −8.83877 −0.435985
\(412\) −11.3013 −0.556774
\(413\) 10.1468 0.499289
\(414\) −1.86831 −0.0918226
\(415\) −4.92692 −0.241853
\(416\) 0 0
\(417\) −25.1836 −1.23325
\(418\) 2.82908 0.138375
\(419\) 8.13898 0.397615 0.198808 0.980039i \(-0.436293\pi\)
0.198808 + 0.980039i \(0.436293\pi\)
\(420\) −3.80194 −0.185516
\(421\) −17.0398 −0.830470 −0.415235 0.909714i \(-0.636301\pi\)
−0.415235 + 0.909714i \(0.636301\pi\)
\(422\) 23.3860 1.13841
\(423\) −19.9782 −0.971375
\(424\) −8.74094 −0.424498
\(425\) 4.61356 0.223791
\(426\) −12.9487 −0.627366
\(427\) −1.37867 −0.0667183
\(428\) −7.13467 −0.344867
\(429\) 0 0
\(430\) 7.83579 0.377875
\(431\) −6.95779 −0.335145 −0.167572 0.985860i \(-0.553593\pi\)
−0.167572 + 0.985860i \(0.553593\pi\)
\(432\) −2.13706 −0.102820
\(433\) −6.80731 −0.327139 −0.163569 0.986532i \(-0.552301\pi\)
−0.163569 + 0.986532i \(0.552301\pi\)
\(434\) −8.89977 −0.427203
\(435\) 13.6189 0.652978
\(436\) −6.57002 −0.314647
\(437\) −5.79656 −0.277287
\(438\) −22.3274 −1.06684
\(439\) 26.3351 1.25691 0.628453 0.777847i \(-0.283688\pi\)
0.628453 + 0.777847i \(0.283688\pi\)
\(440\) 0.753020 0.0358988
\(441\) 2.04892 0.0975675
\(442\) 0 0
\(443\) 7.32437 0.347991 0.173996 0.984746i \(-0.444332\pi\)
0.173996 + 0.984746i \(0.444332\pi\)
\(444\) 24.2717 1.15189
\(445\) 30.6383 1.45240
\(446\) −21.7482 −1.02981
\(447\) −49.1473 −2.32459
\(448\) −1.00000 −0.0472456
\(449\) −41.4228 −1.95486 −0.977431 0.211253i \(-0.932245\pi\)
−0.977431 + 0.211253i \(0.932245\pi\)
\(450\) −4.37867 −0.206412
\(451\) 1.07606 0.0506699
\(452\) 10.6015 0.498652
\(453\) 41.1202 1.93200
\(454\) 6.55927 0.307842
\(455\) 0 0
\(456\) 14.2838 0.668901
\(457\) 11.7125 0.547886 0.273943 0.961746i \(-0.411672\pi\)
0.273943 + 0.961746i \(0.411672\pi\)
\(458\) −0.948690 −0.0443294
\(459\) 4.61356 0.215343
\(460\) −1.54288 −0.0719370
\(461\) −20.6461 −0.961584 −0.480792 0.876835i \(-0.659651\pi\)
−0.480792 + 0.876835i \(0.659651\pi\)
\(462\) −1.00000 −0.0465242
\(463\) 10.9312 0.508017 0.254009 0.967202i \(-0.418251\pi\)
0.254009 + 0.967202i \(0.418251\pi\)
\(464\) 3.58211 0.166295
\(465\) 33.8364 1.56912
\(466\) −15.4765 −0.716935
\(467\) 15.4450 0.714711 0.357356 0.933968i \(-0.383678\pi\)
0.357356 + 0.933968i \(0.383678\pi\)
\(468\) 0 0
\(469\) −6.23490 −0.287901
\(470\) −16.4983 −0.761008
\(471\) −24.3666 −1.12275
\(472\) −10.1468 −0.467042
\(473\) 2.06100 0.0947648
\(474\) −14.1588 −0.650337
\(475\) −13.5851 −0.623327
\(476\) 2.15883 0.0989500
\(477\) −17.9095 −0.820018
\(478\) 25.3448 1.15924
\(479\) 25.2828 1.15520 0.577599 0.816321i \(-0.303990\pi\)
0.577599 + 0.816321i \(0.303990\pi\)
\(480\) 3.80194 0.173534
\(481\) 0 0
\(482\) −28.2664 −1.28750
\(483\) 2.04892 0.0932290
\(484\) −10.8019 −0.490997
\(485\) −5.59717 −0.254154
\(486\) −18.1903 −0.825128
\(487\) 1.01938 0.0461924 0.0230962 0.999733i \(-0.492648\pi\)
0.0230962 + 0.999733i \(0.492648\pi\)
\(488\) 1.37867 0.0624093
\(489\) 32.3696 1.46380
\(490\) 1.69202 0.0764377
\(491\) −36.7198 −1.65714 −0.828570 0.559886i \(-0.810845\pi\)
−0.828570 + 0.559886i \(0.810845\pi\)
\(492\) 5.43296 0.244937
\(493\) −7.73317 −0.348284
\(494\) 0 0
\(495\) 1.54288 0.0693471
\(496\) 8.89977 0.399612
\(497\) 5.76271 0.258493
\(498\) −6.54288 −0.293193
\(499\) −41.4685 −1.85638 −0.928192 0.372102i \(-0.878637\pi\)
−0.928192 + 0.372102i \(0.878637\pi\)
\(500\) −12.0761 −0.540058
\(501\) −30.7754 −1.37494
\(502\) −13.7235 −0.612509
\(503\) −2.15346 −0.0960179 −0.0480089 0.998847i \(-0.515288\pi\)
−0.0480089 + 0.998847i \(0.515288\pi\)
\(504\) −2.04892 −0.0912660
\(505\) 3.53319 0.157225
\(506\) −0.405813 −0.0180406
\(507\) 0 0
\(508\) −21.5646 −0.956776
\(509\) −7.62565 −0.338001 −0.169000 0.985616i \(-0.554054\pi\)
−0.169000 + 0.985616i \(0.554054\pi\)
\(510\) −8.20775 −0.363445
\(511\) 9.93661 0.439570
\(512\) 1.00000 0.0441942
\(513\) −13.5851 −0.599796
\(514\) −13.3502 −0.588852
\(515\) −19.1220 −0.842616
\(516\) 10.4058 0.458090
\(517\) −4.33944 −0.190848
\(518\) −10.8019 −0.474610
\(519\) −10.0586 −0.441524
\(520\) 0 0
\(521\) 20.8377 0.912917 0.456458 0.889745i \(-0.349118\pi\)
0.456458 + 0.889745i \(0.349118\pi\)
\(522\) 7.33944 0.321238
\(523\) 38.3491 1.67689 0.838445 0.544986i \(-0.183465\pi\)
0.838445 + 0.544986i \(0.183465\pi\)
\(524\) 3.14675 0.137467
\(525\) 4.80194 0.209574
\(526\) 19.3153 0.842186
\(527\) −19.2131 −0.836937
\(528\) 1.00000 0.0435194
\(529\) −22.1685 −0.963849
\(530\) −14.7899 −0.642430
\(531\) −20.7899 −0.902203
\(532\) −6.35690 −0.275606
\(533\) 0 0
\(534\) 40.6872 1.76071
\(535\) −12.0720 −0.521919
\(536\) 6.23490 0.269307
\(537\) −51.8461 −2.23732
\(538\) 24.2935 1.04737
\(539\) 0.445042 0.0191693
\(540\) −3.61596 −0.155606
\(541\) −5.46740 −0.235062 −0.117531 0.993069i \(-0.537498\pi\)
−0.117531 + 0.993069i \(0.537498\pi\)
\(542\) 29.0368 1.24724
\(543\) 19.0315 0.816718
\(544\) −2.15883 −0.0925592
\(545\) −11.1166 −0.476184
\(546\) 0 0
\(547\) −6.26636 −0.267930 −0.133965 0.990986i \(-0.542771\pi\)
−0.133965 + 0.990986i \(0.542771\pi\)
\(548\) −3.93362 −0.168036
\(549\) 2.82477 0.120558
\(550\) −0.951083 −0.0405543
\(551\) 22.7711 0.970080
\(552\) −2.04892 −0.0872077
\(553\) 6.30127 0.267957
\(554\) 1.19029 0.0505707
\(555\) 41.0683 1.74325
\(556\) −11.2078 −0.475315
\(557\) −23.1371 −0.980349 −0.490174 0.871624i \(-0.663067\pi\)
−0.490174 + 0.871624i \(0.663067\pi\)
\(558\) 18.2349 0.771945
\(559\) 0 0
\(560\) −1.69202 −0.0715010
\(561\) −2.15883 −0.0911460
\(562\) 21.2325 0.895639
\(563\) 1.21685 0.0512841 0.0256420 0.999671i \(-0.491837\pi\)
0.0256420 + 0.999671i \(0.491837\pi\)
\(564\) −21.9095 −0.922555
\(565\) 17.9379 0.754655
\(566\) 11.6756 0.490763
\(567\) 10.9487 0.459802
\(568\) −5.76271 −0.241798
\(569\) −28.5816 −1.19820 −0.599102 0.800673i \(-0.704476\pi\)
−0.599102 + 0.800673i \(0.704476\pi\)
\(570\) 24.1685 1.01231
\(571\) −32.1825 −1.34680 −0.673398 0.739280i \(-0.735166\pi\)
−0.673398 + 0.739280i \(0.735166\pi\)
\(572\) 0 0
\(573\) 44.3183 1.85142
\(574\) −2.41789 −0.100921
\(575\) 1.94869 0.0812660
\(576\) 2.04892 0.0853716
\(577\) −2.94810 −0.122731 −0.0613655 0.998115i \(-0.519546\pi\)
−0.0613655 + 0.998115i \(0.519546\pi\)
\(578\) −12.3394 −0.513253
\(579\) −20.5797 −0.855264
\(580\) 6.06100 0.251669
\(581\) 2.91185 0.120804
\(582\) −7.43296 −0.308106
\(583\) −3.89008 −0.161111
\(584\) −9.93661 −0.411180
\(585\) 0 0
\(586\) 14.4101 0.595277
\(587\) 2.77538 0.114552 0.0572761 0.998358i \(-0.481758\pi\)
0.0572761 + 0.998358i \(0.481758\pi\)
\(588\) 2.24698 0.0926639
\(589\) 56.5749 2.33113
\(590\) −17.1685 −0.706817
\(591\) 8.38165 0.344775
\(592\) 10.8019 0.443957
\(593\) 21.5241 0.883888 0.441944 0.897043i \(-0.354289\pi\)
0.441944 + 0.897043i \(0.354289\pi\)
\(594\) −0.951083 −0.0390234
\(595\) 3.65279 0.149750
\(596\) −21.8726 −0.895938
\(597\) 44.0224 1.80172
\(598\) 0 0
\(599\) 23.3230 0.952954 0.476477 0.879187i \(-0.341914\pi\)
0.476477 + 0.879187i \(0.341914\pi\)
\(600\) −4.80194 −0.196038
\(601\) 15.7429 0.642165 0.321082 0.947051i \(-0.395953\pi\)
0.321082 + 0.947051i \(0.395953\pi\)
\(602\) −4.63102 −0.188746
\(603\) 12.7748 0.520230
\(604\) 18.3002 0.744625
\(605\) −18.2771 −0.743070
\(606\) 4.69202 0.190600
\(607\) −19.7845 −0.803027 −0.401514 0.915853i \(-0.631516\pi\)
−0.401514 + 0.915853i \(0.631516\pi\)
\(608\) 6.35690 0.257806
\(609\) −8.04892 −0.326159
\(610\) 2.33273 0.0944496
\(611\) 0 0
\(612\) −4.42327 −0.178800
\(613\) −7.24996 −0.292823 −0.146412 0.989224i \(-0.546772\pi\)
−0.146412 + 0.989224i \(0.546772\pi\)
\(614\) 2.55257 0.103013
\(615\) 9.19269 0.370685
\(616\) −0.445042 −0.0179312
\(617\) −36.7415 −1.47916 −0.739579 0.673070i \(-0.764975\pi\)
−0.739579 + 0.673070i \(0.764975\pi\)
\(618\) −25.3937 −1.02149
\(619\) −17.4959 −0.703219 −0.351609 0.936147i \(-0.614365\pi\)
−0.351609 + 0.936147i \(0.614365\pi\)
\(620\) 15.0586 0.604768
\(621\) 1.94869 0.0781982
\(622\) −1.63533 −0.0655709
\(623\) −18.1075 −0.725463
\(624\) 0 0
\(625\) −9.74764 −0.389906
\(626\) −12.7724 −0.510488
\(627\) 6.35690 0.253870
\(628\) −10.8442 −0.432729
\(629\) −23.3196 −0.929813
\(630\) −3.46681 −0.138121
\(631\) 31.4644 1.25258 0.626289 0.779591i \(-0.284573\pi\)
0.626289 + 0.779591i \(0.284573\pi\)
\(632\) −6.30127 −0.250651
\(633\) 52.5478 2.08859
\(634\) −10.9041 −0.433057
\(635\) −36.4878 −1.44798
\(636\) −19.6407 −0.778805
\(637\) 0 0
\(638\) 1.59419 0.0631145
\(639\) −11.8073 −0.467090
\(640\) 1.69202 0.0668830
\(641\) −24.6799 −0.974799 −0.487400 0.873179i \(-0.662054\pi\)
−0.487400 + 0.873179i \(0.662054\pi\)
\(642\) −16.0315 −0.632711
\(643\) −11.1588 −0.440061 −0.220031 0.975493i \(-0.570616\pi\)
−0.220031 + 0.975493i \(0.570616\pi\)
\(644\) 0.911854 0.0359321
\(645\) 17.6069 0.693269
\(646\) −13.7235 −0.539943
\(647\) 14.8791 0.584956 0.292478 0.956272i \(-0.405520\pi\)
0.292478 + 0.956272i \(0.405520\pi\)
\(648\) −10.9487 −0.430105
\(649\) −4.51573 −0.177258
\(650\) 0 0
\(651\) −19.9976 −0.783768
\(652\) 14.4058 0.564175
\(653\) −5.13600 −0.200987 −0.100494 0.994938i \(-0.532042\pi\)
−0.100494 + 0.994938i \(0.532042\pi\)
\(654\) −14.7627 −0.577268
\(655\) 5.32437 0.208040
\(656\) 2.41789 0.0944029
\(657\) −20.3593 −0.794292
\(658\) 9.75063 0.380119
\(659\) 8.42998 0.328385 0.164193 0.986428i \(-0.447498\pi\)
0.164193 + 0.986428i \(0.447498\pi\)
\(660\) 1.69202 0.0658618
\(661\) 20.3793 0.792661 0.396331 0.918108i \(-0.370283\pi\)
0.396331 + 0.918108i \(0.370283\pi\)
\(662\) 9.94869 0.386667
\(663\) 0 0
\(664\) −2.91185 −0.113002
\(665\) −10.7560 −0.417100
\(666\) 22.1323 0.857608
\(667\) −3.26636 −0.126474
\(668\) −13.6963 −0.529927
\(669\) −48.8678 −1.88934
\(670\) 10.5496 0.407566
\(671\) 0.613564 0.0236864
\(672\) −2.24698 −0.0866791
\(673\) 21.6383 0.834096 0.417048 0.908884i \(-0.363065\pi\)
0.417048 + 0.908884i \(0.363065\pi\)
\(674\) 8.06829 0.310779
\(675\) 4.56704 0.175785
\(676\) 0 0
\(677\) 40.5351 1.55789 0.778945 0.627092i \(-0.215755\pi\)
0.778945 + 0.627092i \(0.215755\pi\)
\(678\) 23.8213 0.914852
\(679\) 3.30798 0.126949
\(680\) −3.65279 −0.140078
\(681\) 14.7385 0.564782
\(682\) 3.96077 0.151666
\(683\) 21.6969 0.830210 0.415105 0.909774i \(-0.363745\pi\)
0.415105 + 0.909774i \(0.363745\pi\)
\(684\) 13.0248 0.498014
\(685\) −6.65578 −0.254304
\(686\) −1.00000 −0.0381802
\(687\) −2.13169 −0.0813289
\(688\) 4.63102 0.176556
\(689\) 0 0
\(690\) −3.46681 −0.131979
\(691\) 28.0610 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(692\) −4.47650 −0.170171
\(693\) −0.911854 −0.0346385
\(694\) −33.1769 −1.25938
\(695\) −18.9638 −0.719336
\(696\) 8.04892 0.305093
\(697\) −5.21983 −0.197715
\(698\) 24.6872 0.934426
\(699\) −34.7754 −1.31533
\(700\) 2.13706 0.0807734
\(701\) −13.7380 −0.518875 −0.259438 0.965760i \(-0.583537\pi\)
−0.259438 + 0.965760i \(0.583537\pi\)
\(702\) 0 0
\(703\) 68.6668 2.58982
\(704\) 0.445042 0.0167731
\(705\) −37.0713 −1.39619
\(706\) 22.5754 0.849636
\(707\) −2.08815 −0.0785328
\(708\) −22.7995 −0.856859
\(709\) −23.0586 −0.865984 −0.432992 0.901398i \(-0.642542\pi\)
−0.432992 + 0.901398i \(0.642542\pi\)
\(710\) −9.75063 −0.365935
\(711\) −12.9108 −0.484192
\(712\) 18.1075 0.678608
\(713\) −8.11529 −0.303920
\(714\) 4.85086 0.181539
\(715\) 0 0
\(716\) −23.0737 −0.862304
\(717\) 56.9493 2.12681
\(718\) 2.30798 0.0861330
\(719\) 22.8750 0.853094 0.426547 0.904465i \(-0.359730\pi\)
0.426547 + 0.904465i \(0.359730\pi\)
\(720\) 3.46681 0.129200
\(721\) 11.3013 0.420881
\(722\) 21.4101 0.796802
\(723\) −63.5139 −2.36211
\(724\) 8.46980 0.314777
\(725\) −7.65519 −0.284306
\(726\) −24.2717 −0.900809
\(727\) 9.76377 0.362118 0.181059 0.983472i \(-0.442047\pi\)
0.181059 + 0.983472i \(0.442047\pi\)
\(728\) 0 0
\(729\) −8.02715 −0.297302
\(730\) −16.8130 −0.622275
\(731\) −9.99761 −0.369775
\(732\) 3.09783 0.114499
\(733\) 2.65519 0.0980715 0.0490358 0.998797i \(-0.484385\pi\)
0.0490358 + 0.998797i \(0.484385\pi\)
\(734\) 25.1685 0.928987
\(735\) 3.80194 0.140237
\(736\) −0.911854 −0.0336114
\(737\) 2.77479 0.102211
\(738\) 4.95407 0.182362
\(739\) 0.135144 0.00497137 0.00248568 0.999997i \(-0.499209\pi\)
0.00248568 + 0.999997i \(0.499209\pi\)
\(740\) 18.2771 0.671880
\(741\) 0 0
\(742\) 8.74094 0.320890
\(743\) −38.1943 −1.40121 −0.700607 0.713547i \(-0.747087\pi\)
−0.700607 + 0.713547i \(0.747087\pi\)
\(744\) 19.9976 0.733148
\(745\) −37.0090 −1.35590
\(746\) 11.6407 0.426197
\(747\) −5.96615 −0.218290
\(748\) −0.960771 −0.0351293
\(749\) 7.13467 0.260695
\(750\) −27.1347 −0.990818
\(751\) 31.9614 1.16629 0.583143 0.812369i \(-0.301823\pi\)
0.583143 + 0.812369i \(0.301823\pi\)
\(752\) −9.75063 −0.355569
\(753\) −30.8364 −1.12374
\(754\) 0 0
\(755\) 30.9643 1.12691
\(756\) 2.13706 0.0777242
\(757\) −51.4258 −1.86910 −0.934551 0.355829i \(-0.884198\pi\)
−0.934551 + 0.355829i \(0.884198\pi\)
\(758\) −16.5623 −0.601568
\(759\) −0.911854 −0.0330982
\(760\) 10.7560 0.390161
\(761\) 29.4782 1.06858 0.534291 0.845301i \(-0.320579\pi\)
0.534291 + 0.845301i \(0.320579\pi\)
\(762\) −48.4553 −1.75535
\(763\) 6.57002 0.237851
\(764\) 19.7235 0.713570
\(765\) −7.48427 −0.270594
\(766\) −7.39506 −0.267194
\(767\) 0 0
\(768\) 2.24698 0.0810809
\(769\) −24.7114 −0.891116 −0.445558 0.895253i \(-0.646995\pi\)
−0.445558 + 0.895253i \(0.646995\pi\)
\(770\) −0.753020 −0.0271370
\(771\) −29.9976 −1.08034
\(772\) −9.15883 −0.329634
\(773\) −22.3032 −0.802190 −0.401095 0.916036i \(-0.631370\pi\)
−0.401095 + 0.916036i \(0.631370\pi\)
\(774\) 9.48858 0.341060
\(775\) −19.0194 −0.683196
\(776\) −3.30798 −0.118750
\(777\) −24.2717 −0.870744
\(778\) 23.4674 0.841347
\(779\) 15.3703 0.550698
\(780\) 0 0
\(781\) −2.56465 −0.0917703
\(782\) 1.96854 0.0703949
\(783\) −7.65519 −0.273574
\(784\) 1.00000 0.0357143
\(785\) −18.3485 −0.654887
\(786\) 7.07069 0.252203
\(787\) −16.4896 −0.587792 −0.293896 0.955837i \(-0.594952\pi\)
−0.293896 + 0.955837i \(0.594952\pi\)
\(788\) 3.73019 0.132882
\(789\) 43.4010 1.54512
\(790\) −10.6619 −0.379333
\(791\) −10.6015 −0.376945
\(792\) 0.911854 0.0324013
\(793\) 0 0
\(794\) −0.0499823 −0.00177380
\(795\) −33.2325 −1.17864
\(796\) 19.5918 0.694413
\(797\) −1.00106 −0.0354595 −0.0177298 0.999843i \(-0.505644\pi\)
−0.0177298 + 0.999843i \(0.505644\pi\)
\(798\) −14.2838 −0.505642
\(799\) 21.0500 0.744695
\(800\) −2.13706 −0.0755566
\(801\) 37.1008 1.31089
\(802\) 4.84010 0.170910
\(803\) −4.42221 −0.156056
\(804\) 14.0097 0.494084
\(805\) 1.54288 0.0543793
\(806\) 0 0
\(807\) 54.5870 1.92155
\(808\) 2.08815 0.0734607
\(809\) −49.9172 −1.75500 −0.877498 0.479580i \(-0.840789\pi\)
−0.877498 + 0.479580i \(0.840789\pi\)
\(810\) −18.5254 −0.650917
\(811\) 32.9554 1.15722 0.578610 0.815604i \(-0.303595\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(812\) −3.58211 −0.125707
\(813\) 65.2452 2.28825
\(814\) 4.80731 0.168496
\(815\) 24.3749 0.853817
\(816\) −4.85086 −0.169814
\(817\) 29.4389 1.02994
\(818\) 29.8866 1.04496
\(819\) 0 0
\(820\) 4.09113 0.142868
\(821\) 29.3129 1.02303 0.511513 0.859275i \(-0.329085\pi\)
0.511513 + 0.859275i \(0.329085\pi\)
\(822\) −8.83877 −0.308288
\(823\) −11.3013 −0.393938 −0.196969 0.980410i \(-0.563110\pi\)
−0.196969 + 0.980410i \(0.563110\pi\)
\(824\) −11.3013 −0.393699
\(825\) −2.13706 −0.0744030
\(826\) 10.1468 0.353051
\(827\) −32.8568 −1.14254 −0.571272 0.820761i \(-0.693550\pi\)
−0.571272 + 0.820761i \(0.693550\pi\)
\(828\) −1.86831 −0.0649284
\(829\) 36.6853 1.27413 0.637067 0.770809i \(-0.280148\pi\)
0.637067 + 0.770809i \(0.280148\pi\)
\(830\) −4.92692 −0.171016
\(831\) 2.67456 0.0927796
\(832\) 0 0
\(833\) −2.15883 −0.0747992
\(834\) −25.1836 −0.872036
\(835\) −23.1745 −0.801986
\(836\) 2.82908 0.0978459
\(837\) −19.0194 −0.657406
\(838\) 8.13898 0.281156
\(839\) −23.7687 −0.820586 −0.410293 0.911954i \(-0.634574\pi\)
−0.410293 + 0.911954i \(0.634574\pi\)
\(840\) −3.80194 −0.131179
\(841\) −16.1685 −0.557535
\(842\) −17.0398 −0.587231
\(843\) 47.7090 1.64319
\(844\) 23.3860 0.804978
\(845\) 0 0
\(846\) −19.9782 −0.686866
\(847\) 10.8019 0.371159
\(848\) −8.74094 −0.300165
\(849\) 26.2349 0.900379
\(850\) 4.61356 0.158244
\(851\) −9.84979 −0.337646
\(852\) −12.9487 −0.443615
\(853\) 33.6437 1.15194 0.575969 0.817471i \(-0.304625\pi\)
0.575969 + 0.817471i \(0.304625\pi\)
\(854\) −1.37867 −0.0471770
\(855\) 22.0382 0.753689
\(856\) −7.13467 −0.243858
\(857\) −35.2646 −1.20461 −0.602307 0.798264i \(-0.705752\pi\)
−0.602307 + 0.798264i \(0.705752\pi\)
\(858\) 0 0
\(859\) 9.80433 0.334519 0.167260 0.985913i \(-0.446508\pi\)
0.167260 + 0.985913i \(0.446508\pi\)
\(860\) 7.83579 0.267198
\(861\) −5.43296 −0.185155
\(862\) −6.95779 −0.236983
\(863\) 34.2586 1.16618 0.583088 0.812409i \(-0.301844\pi\)
0.583088 + 0.812409i \(0.301844\pi\)
\(864\) −2.13706 −0.0727044
\(865\) −7.57434 −0.257535
\(866\) −6.80731 −0.231322
\(867\) −27.7265 −0.941640
\(868\) −8.89977 −0.302078
\(869\) −2.80433 −0.0951304
\(870\) 13.6189 0.461725
\(871\) 0 0
\(872\) −6.57002 −0.222489
\(873\) −6.77777 −0.229393
\(874\) −5.79656 −0.196072
\(875\) 12.0761 0.408245
\(876\) −22.3274 −0.754371
\(877\) −28.5174 −0.962964 −0.481482 0.876456i \(-0.659901\pi\)
−0.481482 + 0.876456i \(0.659901\pi\)
\(878\) 26.3351 0.888767
\(879\) 32.3793 1.09213
\(880\) 0.753020 0.0253843
\(881\) −55.3193 −1.86376 −0.931878 0.362773i \(-0.881830\pi\)
−0.931878 + 0.362773i \(0.881830\pi\)
\(882\) 2.04892 0.0689906
\(883\) 0.815938 0.0274585 0.0137293 0.999906i \(-0.495630\pi\)
0.0137293 + 0.999906i \(0.495630\pi\)
\(884\) 0 0
\(885\) −38.5773 −1.29676
\(886\) 7.32437 0.246067
\(887\) 39.8713 1.33875 0.669374 0.742926i \(-0.266563\pi\)
0.669374 + 0.742926i \(0.266563\pi\)
\(888\) 24.2717 0.814506
\(889\) 21.5646 0.723255
\(890\) 30.6383 1.02700
\(891\) −4.87263 −0.163239
\(892\) −21.7482 −0.728185
\(893\) −61.9837 −2.07421
\(894\) −49.1473 −1.64373
\(895\) −39.0411 −1.30500
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −41.4228 −1.38230
\(899\) 31.8799 1.06325
\(900\) −4.37867 −0.145956
\(901\) 18.8702 0.628659
\(902\) 1.07606 0.0358290
\(903\) −10.4058 −0.346284
\(904\) 10.6015 0.352600
\(905\) 14.3311 0.476381
\(906\) 41.1202 1.36613
\(907\) 5.54719 0.184191 0.0920957 0.995750i \(-0.470643\pi\)
0.0920957 + 0.995750i \(0.470643\pi\)
\(908\) 6.55927 0.217677
\(909\) 4.27844 0.141907
\(910\) 0 0
\(911\) 12.3357 0.408701 0.204350 0.978898i \(-0.434492\pi\)
0.204350 + 0.978898i \(0.434492\pi\)
\(912\) 14.2838 0.472984
\(913\) −1.29590 −0.0428879
\(914\) 11.7125 0.387414
\(915\) 5.24160 0.173282
\(916\) −0.948690 −0.0313456
\(917\) −3.14675 −0.103915
\(918\) 4.61356 0.152270
\(919\) 5.22223 0.172265 0.0861327 0.996284i \(-0.472549\pi\)
0.0861327 + 0.996284i \(0.472549\pi\)
\(920\) −1.54288 −0.0508671
\(921\) 5.73556 0.188993
\(922\) −20.6461 −0.679943
\(923\) 0 0
\(924\) −1.00000 −0.0328976
\(925\) −23.0844 −0.759011
\(926\) 10.9312 0.359223
\(927\) −23.1554 −0.760522
\(928\) 3.58211 0.117588
\(929\) 10.9957 0.360757 0.180378 0.983597i \(-0.442268\pi\)
0.180378 + 0.983597i \(0.442268\pi\)
\(930\) 33.8364 1.10954
\(931\) 6.35690 0.208339
\(932\) −15.4765 −0.506950
\(933\) −3.67456 −0.120300
\(934\) 15.4450 0.505377
\(935\) −1.62565 −0.0531643
\(936\) 0 0
\(937\) −21.5190 −0.702994 −0.351497 0.936189i \(-0.614327\pi\)
−0.351497 + 0.936189i \(0.614327\pi\)
\(938\) −6.23490 −0.203577
\(939\) −28.6993 −0.936567
\(940\) −16.4983 −0.538114
\(941\) −11.2784 −0.367667 −0.183833 0.982957i \(-0.558851\pi\)
−0.183833 + 0.982957i \(0.558851\pi\)
\(942\) −24.3666 −0.793906
\(943\) −2.20477 −0.0717971
\(944\) −10.1468 −0.330249
\(945\) 3.61596 0.117627
\(946\) 2.06100 0.0670089
\(947\) −1.92154 −0.0624417 −0.0312209 0.999513i \(-0.509940\pi\)
−0.0312209 + 0.999513i \(0.509940\pi\)
\(948\) −14.1588 −0.459858
\(949\) 0 0
\(950\) −13.5851 −0.440758
\(951\) −24.5013 −0.794508
\(952\) 2.15883 0.0699682
\(953\) 32.0538 1.03833 0.519163 0.854676i \(-0.326244\pi\)
0.519163 + 0.854676i \(0.326244\pi\)
\(954\) −17.9095 −0.579840
\(955\) 33.3726 1.07991
\(956\) 25.3448 0.819710
\(957\) 3.58211 0.115793
\(958\) 25.2828 0.816849
\(959\) 3.93362 0.127023
\(960\) 3.80194 0.122707
\(961\) 48.2059 1.55503
\(962\) 0 0
\(963\) −14.6183 −0.471070
\(964\) −28.2664 −0.910398
\(965\) −15.4969 −0.498864
\(966\) 2.04892 0.0659228
\(967\) 47.5080 1.52775 0.763876 0.645362i \(-0.223294\pi\)
0.763876 + 0.645362i \(0.223294\pi\)
\(968\) −10.8019 −0.347187
\(969\) −30.8364 −0.990607
\(970\) −5.59717 −0.179714
\(971\) 36.0224 1.15601 0.578006 0.816032i \(-0.303831\pi\)
0.578006 + 0.816032i \(0.303831\pi\)
\(972\) −18.1903 −0.583454
\(973\) 11.2078 0.359304
\(974\) 1.01938 0.0326630
\(975\) 0 0
\(976\) 1.37867 0.0441300
\(977\) −28.2620 −0.904183 −0.452091 0.891972i \(-0.649322\pi\)
−0.452091 + 0.891972i \(0.649322\pi\)
\(978\) 32.3696 1.03506
\(979\) 8.05861 0.257554
\(980\) 1.69202 0.0540496
\(981\) −13.4614 −0.429791
\(982\) −36.7198 −1.17177
\(983\) 8.60196 0.274360 0.137180 0.990546i \(-0.456196\pi\)
0.137180 + 0.990546i \(0.456196\pi\)
\(984\) 5.43296 0.173196
\(985\) 6.31155 0.201103
\(986\) −7.73317 −0.246274
\(987\) 21.9095 0.697386
\(988\) 0 0
\(989\) −4.22282 −0.134278
\(990\) 1.54288 0.0490358
\(991\) −17.8549 −0.567180 −0.283590 0.958946i \(-0.591525\pi\)
−0.283590 + 0.958946i \(0.591525\pi\)
\(992\) 8.89977 0.282568
\(993\) 22.3545 0.709399
\(994\) 5.76271 0.182782
\(995\) 33.1497 1.05092
\(996\) −6.54288 −0.207319
\(997\) −36.3247 −1.15041 −0.575207 0.818008i \(-0.695079\pi\)
−0.575207 + 0.818008i \(0.695079\pi\)
\(998\) −41.4685 −1.31266
\(999\) −23.0844 −0.730359
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 2366.2.a.bd.1.3 yes 3
13.5 odd 4 2366.2.d.p.337.3 6
13.8 odd 4 2366.2.d.p.337.6 6
13.12 even 2 2366.2.a.y.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2366.2.a.y.1.3 3 13.12 even 2
2366.2.a.bd.1.3 yes 3 1.1 even 1 trivial
2366.2.d.p.337.3 6 13.5 odd 4
2366.2.d.p.337.6 6 13.8 odd 4