Properties

Label 2366.2.a.bd.1.2
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 1.2
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 2366.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.554958 q^{3} +1.00000 q^{4} +1.35690 q^{5} +0.554958 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.69202 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.554958 q^{3} +1.00000 q^{4} +1.35690 q^{5} +0.554958 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.69202 q^{9} +1.35690 q^{10} +1.80194 q^{11} +0.554958 q^{12} -1.00000 q^{14} +0.753020 q^{15} +1.00000 q^{16} +5.29590 q^{17} -2.69202 q^{18} +1.95108 q^{19} +1.35690 q^{20} -0.554958 q^{21} +1.80194 q^{22} +4.85086 q^{23} +0.554958 q^{24} -3.15883 q^{25} -3.15883 q^{27} -1.00000 q^{28} +5.96077 q^{29} +0.753020 q^{30} -3.63102 q^{31} +1.00000 q^{32} +1.00000 q^{33} +5.29590 q^{34} -1.35690 q^{35} -2.69202 q^{36} +7.75302 q^{37} +1.95108 q^{38} +1.35690 q^{40} +0.0392287 q^{41} -0.554958 q^{42} +2.26875 q^{43} +1.80194 q^{44} -3.65279 q^{45} +4.85086 q^{46} +10.5700 q^{47} +0.554958 q^{48} +1.00000 q^{49} -3.15883 q^{50} +2.93900 q^{51} -3.66487 q^{53} -3.15883 q^{54} +2.44504 q^{55} -1.00000 q^{56} +1.08277 q^{57} +5.96077 q^{58} +4.07606 q^{59} +0.753020 q^{60} -11.5036 q^{61} -3.63102 q^{62} +2.69202 q^{63} +1.00000 q^{64} +1.00000 q^{66} -2.22521 q^{67} +5.29590 q^{68} +2.69202 q^{69} -1.35690 q^{70} +7.78986 q^{71} -2.69202 q^{72} +14.1032 q^{73} +7.75302 q^{74} -1.75302 q^{75} +1.95108 q^{76} -1.80194 q^{77} -12.0804 q^{79} +1.35690 q^{80} +6.32304 q^{81} +0.0392287 q^{82} +2.85086 q^{83} -0.554958 q^{84} +7.18598 q^{85} +2.26875 q^{86} +3.30798 q^{87} +1.80194 q^{88} -6.61894 q^{89} -3.65279 q^{90} +4.85086 q^{92} -2.01507 q^{93} +10.5700 q^{94} +2.64742 q^{95} +0.554958 q^{96} -3.64310 q^{97} +1.00000 q^{98} -4.85086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} - 3q^{7} + 3q^{8} - 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} - 3q^{7} + 3q^{8} - 3q^{9} + q^{11} + 2q^{12} - 3q^{14} + 7q^{15} + 3q^{16} + 2q^{17} - 3q^{18} + 15q^{19} - 2q^{21} + q^{22} + q^{23} + 2q^{24} - q^{25} - q^{27} - 3q^{28} + 5q^{29} + 7q^{30} + 4q^{31} + 3q^{32} + 3q^{33} + 2q^{34} - 3q^{36} + 28q^{37} + 15q^{38} + 13q^{41} - 2q^{42} - q^{43} + q^{44} + 7q^{45} + q^{46} + 7q^{47} + 2q^{48} + 3q^{49} - q^{50} - q^{51} - 12q^{53} - q^{54} + 7q^{55} - 3q^{56} + 10q^{57} + 5q^{58} - 3q^{59} + 7q^{60} - 3q^{61} + 4q^{62} + 3q^{63} + 3q^{64} + 3q^{66} - 5q^{67} + 2q^{68} + 3q^{69} - 3q^{72} + 21q^{73} + 28q^{74} - 10q^{75} + 15q^{76} - q^{77} - 2q^{79} - q^{81} + 13q^{82} - 5q^{83} - 2q^{84} + 7q^{85} - q^{86} + 15q^{87} + q^{88} + 14q^{89} + 7q^{90} + q^{92} + 19q^{93} + 7q^{94} - 7q^{95} + 2q^{96} - 15q^{97} + 3q^{98} - q^{99} + O(q^{100}) \)

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
\(3\) 0.554958 0.320405 0.160203 0.987084i \(-0.448785\pi\)
0.160203 + 0.987084i \(0.448785\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.35690 0.606822 0.303411 0.952860i \(-0.401874\pi\)
0.303411 + 0.952860i \(0.401874\pi\)
\(6\) 0.554958 0.226561
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) −2.69202 −0.897340
\(10\) 1.35690 0.429088
\(11\) 1.80194 0.543305 0.271652 0.962395i \(-0.412430\pi\)
0.271652 + 0.962395i \(0.412430\pi\)
\(12\) 0.554958 0.160203
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 0.753020 0.194429
\(16\) 1.00000 0.250000
\(17\) 5.29590 1.28444 0.642222 0.766519i \(-0.278013\pi\)
0.642222 + 0.766519i \(0.278013\pi\)
\(18\) −2.69202 −0.634516
\(19\) 1.95108 0.447609 0.223805 0.974634i \(-0.428152\pi\)
0.223805 + 0.974634i \(0.428152\pi\)
\(20\) 1.35690 0.303411
\(21\) −0.554958 −0.121102
\(22\) 1.80194 0.384174
\(23\) 4.85086 1.01147 0.505737 0.862688i \(-0.331221\pi\)
0.505737 + 0.862688i \(0.331221\pi\)
\(24\) 0.554958 0.113280
\(25\) −3.15883 −0.631767
\(26\) 0 0
\(27\) −3.15883 −0.607918
\(28\) −1.00000 −0.188982
\(29\) 5.96077 1.10689 0.553444 0.832887i \(-0.313313\pi\)
0.553444 + 0.832887i \(0.313313\pi\)
\(30\) 0.753020 0.137482
\(31\) −3.63102 −0.652151 −0.326075 0.945344i \(-0.605726\pi\)
−0.326075 + 0.945344i \(0.605726\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 5.29590 0.908239
\(35\) −1.35690 −0.229357
\(36\) −2.69202 −0.448670
\(37\) 7.75302 1.27459 0.637294 0.770620i \(-0.280054\pi\)
0.637294 + 0.770620i \(0.280054\pi\)
\(38\) 1.95108 0.316507
\(39\) 0 0
\(40\) 1.35690 0.214544
\(41\) 0.0392287 0.00612649 0.00306324 0.999995i \(-0.499025\pi\)
0.00306324 + 0.999995i \(0.499025\pi\)
\(42\) −0.554958 −0.0856319
\(43\) 2.26875 0.345981 0.172991 0.984923i \(-0.444657\pi\)
0.172991 + 0.984923i \(0.444657\pi\)
\(44\) 1.80194 0.271652
\(45\) −3.65279 −0.544526
\(46\) 4.85086 0.715220
\(47\) 10.5700 1.54180 0.770898 0.636958i \(-0.219808\pi\)
0.770898 + 0.636958i \(0.219808\pi\)
\(48\) 0.554958 0.0801013
\(49\) 1.00000 0.142857
\(50\) −3.15883 −0.446727
\(51\) 2.93900 0.411542
\(52\) 0 0
\(53\) −3.66487 −0.503409 −0.251705 0.967804i \(-0.580991\pi\)
−0.251705 + 0.967804i \(0.580991\pi\)
\(54\) −3.15883 −0.429863
\(55\) 2.44504 0.329689
\(56\) −1.00000 −0.133631
\(57\) 1.08277 0.143416
\(58\) 5.96077 0.782688
\(59\) 4.07606 0.530658 0.265329 0.964158i \(-0.414519\pi\)
0.265329 + 0.964158i \(0.414519\pi\)
\(60\) 0.753020 0.0972145
\(61\) −11.5036 −1.47289 −0.736446 0.676497i \(-0.763497\pi\)
−0.736446 + 0.676497i \(0.763497\pi\)
\(62\) −3.63102 −0.461140
\(63\) 2.69202 0.339163
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.00000 0.123091
\(67\) −2.22521 −0.271853 −0.135926 0.990719i \(-0.543401\pi\)
−0.135926 + 0.990719i \(0.543401\pi\)
\(68\) 5.29590 0.642222
\(69\) 2.69202 0.324081
\(70\) −1.35690 −0.162180
\(71\) 7.78986 0.924486 0.462243 0.886753i \(-0.347045\pi\)
0.462243 + 0.886753i \(0.347045\pi\)
\(72\) −2.69202 −0.317258
\(73\) 14.1032 1.65066 0.825328 0.564654i \(-0.190990\pi\)
0.825328 + 0.564654i \(0.190990\pi\)
\(74\) 7.75302 0.901270
\(75\) −1.75302 −0.202421
\(76\) 1.95108 0.223805
\(77\) −1.80194 −0.205350
\(78\) 0 0
\(79\) −12.0804 −1.35915 −0.679574 0.733607i \(-0.737835\pi\)
−0.679574 + 0.733607i \(0.737835\pi\)
\(80\) 1.35690 0.151706
\(81\) 6.32304 0.702560
\(82\) 0.0392287 0.00433208
\(83\) 2.85086 0.312922 0.156461 0.987684i \(-0.449991\pi\)
0.156461 + 0.987684i \(0.449991\pi\)
\(84\) −0.554958 −0.0605509
\(85\) 7.18598 0.779429
\(86\) 2.26875 0.244646
\(87\) 3.30798 0.354653
\(88\) 1.80194 0.192087
\(89\) −6.61894 −0.701606 −0.350803 0.936449i \(-0.614091\pi\)
−0.350803 + 0.936449i \(0.614091\pi\)
\(90\) −3.65279 −0.385038
\(91\) 0 0
\(92\) 4.85086 0.505737
\(93\) −2.01507 −0.208953
\(94\) 10.5700 1.09021
\(95\) 2.64742 0.271619
\(96\) 0.554958 0.0566402
\(97\) −3.64310 −0.369901 −0.184951 0.982748i \(-0.559213\pi\)
−0.184951 + 0.982748i \(0.559213\pi\)
\(98\) 1.00000 0.101015
\(99\) −4.85086 −0.487529
\(100\) −3.15883 −0.315883
\(101\) 7.85086 0.781189 0.390595 0.920563i \(-0.372269\pi\)
0.390595 + 0.920563i \(0.372269\pi\)
\(102\) 2.93900 0.291004
\(103\) −17.0804 −1.68298 −0.841490 0.540273i \(-0.818321\pi\)
−0.841490 + 0.540273i \(0.818321\pi\)
\(104\) 0 0
\(105\) −0.753020 −0.0734873
\(106\) −3.66487 −0.355964
\(107\) 13.8562 1.33953 0.669766 0.742572i \(-0.266394\pi\)
0.669766 + 0.742572i \(0.266394\pi\)
\(108\) −3.15883 −0.303959
\(109\) −2.18060 −0.208864 −0.104432 0.994532i \(-0.533302\pi\)
−0.104432 + 0.994532i \(0.533302\pi\)
\(110\) 2.44504 0.233126
\(111\) 4.30260 0.408385
\(112\) −1.00000 −0.0944911
\(113\) −17.5090 −1.64711 −0.823555 0.567236i \(-0.808013\pi\)
−0.823555 + 0.567236i \(0.808013\pi\)
\(114\) 1.08277 0.101411
\(115\) 6.58211 0.613784
\(116\) 5.96077 0.553444
\(117\) 0 0
\(118\) 4.07606 0.375232
\(119\) −5.29590 −0.485474
\(120\) 0.753020 0.0687410
\(121\) −7.75302 −0.704820
\(122\) −11.5036 −1.04149
\(123\) 0.0217703 0.00196296
\(124\) −3.63102 −0.326075
\(125\) −11.0707 −0.990192
\(126\) 2.69202 0.239824
\(127\) −4.96316 −0.440410 −0.220205 0.975454i \(-0.570673\pi\)
−0.220205 + 0.975454i \(0.570673\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.25906 0.110854
\(130\) 0 0
\(131\) −11.0761 −0.967720 −0.483860 0.875145i \(-0.660766\pi\)
−0.483860 + 0.875145i \(0.660766\pi\)
\(132\) 1.00000 0.0870388
\(133\) −1.95108 −0.169180
\(134\) −2.22521 −0.192229
\(135\) −4.28621 −0.368898
\(136\) 5.29590 0.454119
\(137\) 10.3056 0.880466 0.440233 0.897884i \(-0.354896\pi\)
0.440233 + 0.897884i \(0.354896\pi\)
\(138\) 2.69202 0.229160
\(139\) 0.987918 0.0837941 0.0418971 0.999122i \(-0.486660\pi\)
0.0418971 + 0.999122i \(0.486660\pi\)
\(140\) −1.35690 −0.114679
\(141\) 5.86592 0.494000
\(142\) 7.78986 0.653710
\(143\) 0 0
\(144\) −2.69202 −0.224335
\(145\) 8.08815 0.671684
\(146\) 14.1032 1.16719
\(147\) 0.554958 0.0457722
\(148\) 7.75302 0.637294
\(149\) −5.60627 −0.459283 −0.229642 0.973275i \(-0.573755\pi\)
−0.229642 + 0.973275i \(0.573755\pi\)
\(150\) −1.75302 −0.143134
\(151\) −15.5894 −1.26865 −0.634324 0.773068i \(-0.718721\pi\)
−0.634324 + 0.773068i \(0.718721\pi\)
\(152\) 1.95108 0.158254
\(153\) −14.2567 −1.15258
\(154\) −1.80194 −0.145204
\(155\) −4.92692 −0.395740
\(156\) 0 0
\(157\) −8.49827 −0.678236 −0.339118 0.940744i \(-0.610129\pi\)
−0.339118 + 0.940744i \(0.610129\pi\)
\(158\) −12.0804 −0.961063
\(159\) −2.03385 −0.161295
\(160\) 1.35690 0.107272
\(161\) −4.85086 −0.382301
\(162\) 6.32304 0.496785
\(163\) 5.25906 0.411921 0.205961 0.978560i \(-0.433968\pi\)
0.205961 + 0.978560i \(0.433968\pi\)
\(164\) 0.0392287 0.00306324
\(165\) 1.35690 0.105634
\(166\) 2.85086 0.221269
\(167\) 14.0954 1.09074 0.545369 0.838196i \(-0.316390\pi\)
0.545369 + 0.838196i \(0.316390\pi\)
\(168\) −0.554958 −0.0428159
\(169\) 0 0
\(170\) 7.18598 0.551140
\(171\) −5.25236 −0.401658
\(172\) 2.26875 0.172991
\(173\) 17.8877 1.35998 0.679988 0.733223i \(-0.261985\pi\)
0.679988 + 0.733223i \(0.261985\pi\)
\(174\) 3.30798 0.250777
\(175\) 3.15883 0.238785
\(176\) 1.80194 0.135826
\(177\) 2.26205 0.170026
\(178\) −6.61894 −0.496111
\(179\) −0.0556221 −0.00415739 −0.00207870 0.999998i \(-0.500662\pi\)
−0.00207870 + 0.999998i \(0.500662\pi\)
\(180\) −3.65279 −0.272263
\(181\) −8.45042 −0.628115 −0.314057 0.949404i \(-0.601688\pi\)
−0.314057 + 0.949404i \(0.601688\pi\)
\(182\) 0 0
\(183\) −6.38404 −0.471922
\(184\) 4.85086 0.357610
\(185\) 10.5200 0.773449
\(186\) −2.01507 −0.147752
\(187\) 9.54288 0.697844
\(188\) 10.5700 0.770898
\(189\) 3.15883 0.229771
\(190\) 2.64742 0.192064
\(191\) −4.33273 −0.313506 −0.156753 0.987638i \(-0.550103\pi\)
−0.156753 + 0.987638i \(0.550103\pi\)
\(192\) 0.554958 0.0400507
\(193\) −1.70410 −0.122664 −0.0613320 0.998117i \(-0.519535\pi\)
−0.0613320 + 0.998117i \(0.519535\pi\)
\(194\) −3.64310 −0.261560
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −25.7700 −1.83604 −0.918018 0.396538i \(-0.870212\pi\)
−0.918018 + 0.396538i \(0.870212\pi\)
\(198\) −4.85086 −0.344735
\(199\) 6.72587 0.476785 0.238392 0.971169i \(-0.423380\pi\)
0.238392 + 0.971169i \(0.423380\pi\)
\(200\) −3.15883 −0.223363
\(201\) −1.23490 −0.0871030
\(202\) 7.85086 0.552384
\(203\) −5.96077 −0.418364
\(204\) 2.93900 0.205771
\(205\) 0.0532292 0.00371769
\(206\) −17.0804 −1.19005
\(207\) −13.0586 −0.907636
\(208\) 0 0
\(209\) 3.51573 0.243188
\(210\) −0.753020 −0.0519633
\(211\) −26.7536 −1.84179 −0.920897 0.389805i \(-0.872542\pi\)
−0.920897 + 0.389805i \(0.872542\pi\)
\(212\) −3.66487 −0.251705
\(213\) 4.32304 0.296210
\(214\) 13.8562 0.947193
\(215\) 3.07846 0.209949
\(216\) −3.15883 −0.214931
\(217\) 3.63102 0.246490
\(218\) −2.18060 −0.147689
\(219\) 7.82669 0.528879
\(220\) 2.44504 0.164845
\(221\) 0 0
\(222\) 4.30260 0.288772
\(223\) 20.5851 1.37848 0.689240 0.724533i \(-0.257945\pi\)
0.689240 + 0.724533i \(0.257945\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 8.50365 0.566910
\(226\) −17.5090 −1.16468
\(227\) −22.2543 −1.47707 −0.738534 0.674216i \(-0.764482\pi\)
−0.738534 + 0.674216i \(0.764482\pi\)
\(228\) 1.08277 0.0717081
\(229\) 16.3230 1.07866 0.539329 0.842095i \(-0.318678\pi\)
0.539329 + 0.842095i \(0.318678\pi\)
\(230\) 6.58211 0.434011
\(231\) −1.00000 −0.0657952
\(232\) 5.96077 0.391344
\(233\) 6.88769 0.451228 0.225614 0.974217i \(-0.427561\pi\)
0.225614 + 0.974217i \(0.427561\pi\)
\(234\) 0 0
\(235\) 14.3424 0.935596
\(236\) 4.07606 0.265329
\(237\) −6.70410 −0.435478
\(238\) −5.29590 −0.343282
\(239\) 14.1709 0.916640 0.458320 0.888787i \(-0.348451\pi\)
0.458320 + 0.888787i \(0.348451\pi\)
\(240\) 0.753020 0.0486073
\(241\) 3.91484 0.252177 0.126088 0.992019i \(-0.459758\pi\)
0.126088 + 0.992019i \(0.459758\pi\)
\(242\) −7.75302 −0.498383
\(243\) 12.9855 0.833022
\(244\) −11.5036 −0.736446
\(245\) 1.35690 0.0866889
\(246\) 0.0217703 0.00138802
\(247\) 0 0
\(248\) −3.63102 −0.230570
\(249\) 1.58211 0.100262
\(250\) −11.0707 −0.700172
\(251\) 10.3327 0.652196 0.326098 0.945336i \(-0.394266\pi\)
0.326098 + 0.945336i \(0.394266\pi\)
\(252\) 2.69202 0.169581
\(253\) 8.74094 0.549538
\(254\) −4.96316 −0.311417
\(255\) 3.98792 0.249733
\(256\) 1.00000 0.0625000
\(257\) −14.3884 −0.897521 −0.448760 0.893652i \(-0.648134\pi\)
−0.448760 + 0.893652i \(0.648134\pi\)
\(258\) 1.25906 0.0783857
\(259\) −7.75302 −0.481749
\(260\) 0 0
\(261\) −16.0465 −0.993255
\(262\) −11.0761 −0.684282
\(263\) −17.6069 −1.08569 −0.542843 0.839834i \(-0.682652\pi\)
−0.542843 + 0.839834i \(0.682652\pi\)
\(264\) 1.00000 0.0615457
\(265\) −4.97285 −0.305480
\(266\) −1.95108 −0.119629
\(267\) −3.67324 −0.224798
\(268\) −2.22521 −0.135926
\(269\) −4.15213 −0.253160 −0.126580 0.991956i \(-0.540400\pi\)
−0.126580 + 0.991956i \(0.540400\pi\)
\(270\) −4.28621 −0.260850
\(271\) 17.5278 1.06474 0.532369 0.846512i \(-0.321302\pi\)
0.532369 + 0.846512i \(0.321302\pi\)
\(272\) 5.29590 0.321111
\(273\) 0 0
\(274\) 10.3056 0.622583
\(275\) −5.69202 −0.343242
\(276\) 2.69202 0.162041
\(277\) −29.9855 −1.80166 −0.900828 0.434177i \(-0.857039\pi\)
−0.900828 + 0.434177i \(0.857039\pi\)
\(278\) 0.987918 0.0592514
\(279\) 9.77479 0.585201
\(280\) −1.35690 −0.0810900
\(281\) −9.24027 −0.551229 −0.275614 0.961268i \(-0.588881\pi\)
−0.275614 + 0.961268i \(0.588881\pi\)
\(282\) 5.86592 0.349310
\(283\) 32.0291 1.90393 0.951965 0.306206i \(-0.0990597\pi\)
0.951965 + 0.306206i \(0.0990597\pi\)
\(284\) 7.78986 0.462243
\(285\) 1.46921 0.0870282
\(286\) 0 0
\(287\) −0.0392287 −0.00231559
\(288\) −2.69202 −0.158629
\(289\) 11.0465 0.649796
\(290\) 8.08815 0.474952
\(291\) −2.02177 −0.118518
\(292\) 14.1032 0.825328
\(293\) −22.1933 −1.29655 −0.648273 0.761408i \(-0.724508\pi\)
−0.648273 + 0.761408i \(0.724508\pi\)
\(294\) 0.554958 0.0323658
\(295\) 5.53079 0.322015
\(296\) 7.75302 0.450635
\(297\) −5.69202 −0.330285
\(298\) −5.60627 −0.324762
\(299\) 0 0
\(300\) −1.75302 −0.101211
\(301\) −2.26875 −0.130769
\(302\) −15.5894 −0.897069
\(303\) 4.35690 0.250297
\(304\) 1.95108 0.111902
\(305\) −15.6093 −0.893783
\(306\) −14.2567 −0.814999
\(307\) −20.8170 −1.18809 −0.594045 0.804432i \(-0.702470\pi\)
−0.594045 + 0.804432i \(0.702470\pi\)
\(308\) −1.80194 −0.102675
\(309\) −9.47889 −0.539235
\(310\) −4.92692 −0.279830
\(311\) 28.1836 1.59814 0.799072 0.601235i \(-0.205324\pi\)
0.799072 + 0.601235i \(0.205324\pi\)
\(312\) 0 0
\(313\) 16.0248 0.905773 0.452886 0.891568i \(-0.350394\pi\)
0.452886 + 0.891568i \(0.350394\pi\)
\(314\) −8.49827 −0.479585
\(315\) 3.65279 0.205812
\(316\) −12.0804 −0.679574
\(317\) 29.0834 1.63348 0.816742 0.577003i \(-0.195778\pi\)
0.816742 + 0.577003i \(0.195778\pi\)
\(318\) −2.03385 −0.114053
\(319\) 10.7409 0.601377
\(320\) 1.35690 0.0758528
\(321\) 7.68963 0.429193
\(322\) −4.85086 −0.270328
\(323\) 10.3327 0.574929
\(324\) 6.32304 0.351280
\(325\) 0 0
\(326\) 5.25906 0.291272
\(327\) −1.21014 −0.0669211
\(328\) 0.0392287 0.00216604
\(329\) −10.5700 −0.582744
\(330\) 1.35690 0.0746947
\(331\) −7.32304 −0.402511 −0.201255 0.979539i \(-0.564502\pi\)
−0.201255 + 0.979539i \(0.564502\pi\)
\(332\) 2.85086 0.156461
\(333\) −20.8713 −1.14374
\(334\) 14.0954 0.771268
\(335\) −3.01938 −0.164966
\(336\) −0.554958 −0.0302754
\(337\) −27.1618 −1.47960 −0.739799 0.672828i \(-0.765080\pi\)
−0.739799 + 0.672828i \(0.765080\pi\)
\(338\) 0 0
\(339\) −9.71678 −0.527743
\(340\) 7.18598 0.389715
\(341\) −6.54288 −0.354317
\(342\) −5.25236 −0.284015
\(343\) −1.00000 −0.0539949
\(344\) 2.26875 0.122323
\(345\) 3.65279 0.196660
\(346\) 17.8877 0.961648
\(347\) −12.8890 −0.691919 −0.345959 0.938249i \(-0.612447\pi\)
−0.345959 + 0.938249i \(0.612447\pi\)
\(348\) 3.30798 0.177326
\(349\) −19.6732 −1.05308 −0.526542 0.850149i \(-0.676512\pi\)
−0.526542 + 0.850149i \(0.676512\pi\)
\(350\) 3.15883 0.168847
\(351\) 0 0
\(352\) 1.80194 0.0960436
\(353\) 30.3980 1.61792 0.808962 0.587861i \(-0.200030\pi\)
0.808962 + 0.587861i \(0.200030\pi\)
\(354\) 2.26205 0.120226
\(355\) 10.5700 0.560999
\(356\) −6.61894 −0.350803
\(357\) −2.93900 −0.155548
\(358\) −0.0556221 −0.00293972
\(359\) 2.64310 0.139498 0.0697489 0.997565i \(-0.477780\pi\)
0.0697489 + 0.997565i \(0.477780\pi\)
\(360\) −3.65279 −0.192519
\(361\) −15.1933 −0.799646
\(362\) −8.45042 −0.444144
\(363\) −4.30260 −0.225828
\(364\) 0 0
\(365\) 19.1366 1.00165
\(366\) −6.38404 −0.333699
\(367\) 2.46921 0.128891 0.0644457 0.997921i \(-0.479472\pi\)
0.0644457 + 0.997921i \(0.479472\pi\)
\(368\) 4.85086 0.252868
\(369\) −0.105604 −0.00549755
\(370\) 10.5200 0.546911
\(371\) 3.66487 0.190271
\(372\) −2.01507 −0.104476
\(373\) −5.96615 −0.308915 −0.154458 0.987999i \(-0.549363\pi\)
−0.154458 + 0.987999i \(0.549363\pi\)
\(374\) 9.54288 0.493450
\(375\) −6.14377 −0.317263
\(376\) 10.5700 0.545107
\(377\) 0 0
\(378\) 3.15883 0.162473
\(379\) 22.0519 1.13273 0.566365 0.824155i \(-0.308349\pi\)
0.566365 + 0.824155i \(0.308349\pi\)
\(380\) 2.64742 0.135810
\(381\) −2.75435 −0.141110
\(382\) −4.33273 −0.221682
\(383\) 26.1758 1.33752 0.668761 0.743478i \(-0.266825\pi\)
0.668761 + 0.743478i \(0.266825\pi\)
\(384\) 0.554958 0.0283201
\(385\) −2.44504 −0.124611
\(386\) −1.70410 −0.0867366
\(387\) −6.10752 −0.310463
\(388\) −3.64310 −0.184951
\(389\) −15.4655 −0.784131 −0.392066 0.919937i \(-0.628239\pi\)
−0.392066 + 0.919937i \(0.628239\pi\)
\(390\) 0 0
\(391\) 25.6896 1.29918
\(392\) 1.00000 0.0505076
\(393\) −6.14675 −0.310063
\(394\) −25.7700 −1.29827
\(395\) −16.3918 −0.824762
\(396\) −4.85086 −0.243765
\(397\) −34.9778 −1.75548 −0.877742 0.479134i \(-0.840951\pi\)
−0.877742 + 0.479134i \(0.840951\pi\)
\(398\) 6.72587 0.337138
\(399\) −1.08277 −0.0542063
\(400\) −3.15883 −0.157942
\(401\) −27.3739 −1.36699 −0.683493 0.729957i \(-0.739540\pi\)
−0.683493 + 0.729957i \(0.739540\pi\)
\(402\) −1.23490 −0.0615911
\(403\) 0 0
\(404\) 7.85086 0.390595
\(405\) 8.57971 0.426329
\(406\) −5.96077 −0.295828
\(407\) 13.9705 0.692490
\(408\) 2.93900 0.145502
\(409\) −29.0810 −1.43796 −0.718981 0.695030i \(-0.755391\pi\)
−0.718981 + 0.695030i \(0.755391\pi\)
\(410\) 0.0532292 0.00262880
\(411\) 5.71917 0.282106
\(412\) −17.0804 −0.841490
\(413\) −4.07606 −0.200570
\(414\) −13.0586 −0.641795
\(415\) 3.86831 0.189888
\(416\) 0 0
\(417\) 0.548253 0.0268481
\(418\) 3.51573 0.171960
\(419\) −40.3086 −1.96920 −0.984601 0.174815i \(-0.944067\pi\)
−0.984601 + 0.174815i \(0.944067\pi\)
\(420\) −0.753020 −0.0367436
\(421\) 4.26981 0.208098 0.104049 0.994572i \(-0.466820\pi\)
0.104049 + 0.994572i \(0.466820\pi\)
\(422\) −26.7536 −1.30235
\(423\) −28.4547 −1.38352
\(424\) −3.66487 −0.177982
\(425\) −16.7289 −0.811469
\(426\) 4.32304 0.209452
\(427\) 11.5036 0.556701
\(428\) 13.8562 0.669766
\(429\) 0 0
\(430\) 3.07846 0.148456
\(431\) −6.25475 −0.301281 −0.150640 0.988589i \(-0.548134\pi\)
−0.150640 + 0.988589i \(0.548134\pi\)
\(432\) −3.15883 −0.151979
\(433\) −15.9705 −0.767491 −0.383746 0.923439i \(-0.625366\pi\)
−0.383746 + 0.923439i \(0.625366\pi\)
\(434\) 3.63102 0.174295
\(435\) 4.48858 0.215211
\(436\) −2.18060 −0.104432
\(437\) 9.46442 0.452745
\(438\) 7.82669 0.373974
\(439\) 30.4058 1.45119 0.725595 0.688122i \(-0.241565\pi\)
0.725595 + 0.688122i \(0.241565\pi\)
\(440\) 2.44504 0.116563
\(441\) −2.69202 −0.128191
\(442\) 0 0
\(443\) −13.0291 −0.619030 −0.309515 0.950895i \(-0.600167\pi\)
−0.309515 + 0.950895i \(0.600167\pi\)
\(444\) 4.30260 0.204192
\(445\) −8.98121 −0.425750
\(446\) 20.5851 0.974732
\(447\) −3.11124 −0.147157
\(448\) −1.00000 −0.0472456
\(449\) 20.2258 0.954515 0.477257 0.878764i \(-0.341631\pi\)
0.477257 + 0.878764i \(0.341631\pi\)
\(450\) 8.50365 0.400866
\(451\) 0.0706876 0.00332855
\(452\) −17.5090 −0.823555
\(453\) −8.65146 −0.406481
\(454\) −22.2543 −1.04444
\(455\) 0 0
\(456\) 1.08277 0.0507053
\(457\) 20.5569 0.961610 0.480805 0.876828i \(-0.340344\pi\)
0.480805 + 0.876828i \(0.340344\pi\)
\(458\) 16.3230 0.762726
\(459\) −16.7289 −0.780836
\(460\) 6.58211 0.306892
\(461\) −15.2513 −0.710323 −0.355162 0.934805i \(-0.615574\pi\)
−0.355162 + 0.934805i \(0.615574\pi\)
\(462\) −1.00000 −0.0465242
\(463\) −25.3207 −1.17675 −0.588375 0.808588i \(-0.700232\pi\)
−0.588375 + 0.808588i \(0.700232\pi\)
\(464\) 5.96077 0.276722
\(465\) −2.73423 −0.126797
\(466\) 6.88769 0.319066
\(467\) 16.8019 0.777501 0.388750 0.921343i \(-0.372907\pi\)
0.388750 + 0.921343i \(0.372907\pi\)
\(468\) 0 0
\(469\) 2.22521 0.102751
\(470\) 14.3424 0.661567
\(471\) −4.71618 −0.217310
\(472\) 4.07606 0.187616
\(473\) 4.08815 0.187973
\(474\) −6.70410 −0.307930
\(475\) −6.16315 −0.282785
\(476\) −5.29590 −0.242737
\(477\) 9.86592 0.451729
\(478\) 14.1709 0.648163
\(479\) −27.5870 −1.26048 −0.630241 0.776399i \(-0.717044\pi\)
−0.630241 + 0.776399i \(0.717044\pi\)
\(480\) 0.753020 0.0343705
\(481\) 0 0
\(482\) 3.91484 0.178316
\(483\) −2.69202 −0.122491
\(484\) −7.75302 −0.352410
\(485\) −4.94331 −0.224464
\(486\) 12.9855 0.589035
\(487\) −29.4698 −1.33540 −0.667702 0.744429i \(-0.732722\pi\)
−0.667702 + 0.744429i \(0.732722\pi\)
\(488\) −11.5036 −0.520746
\(489\) 2.91856 0.131982
\(490\) 1.35690 0.0612983
\(491\) −8.30691 −0.374886 −0.187443 0.982276i \(-0.560020\pi\)
−0.187443 + 0.982276i \(0.560020\pi\)
\(492\) 0.0217703 0.000981479 0
\(493\) 31.5676 1.42173
\(494\) 0 0
\(495\) −6.58211 −0.295844
\(496\) −3.63102 −0.163038
\(497\) −7.78986 −0.349423
\(498\) 1.58211 0.0708958
\(499\) −42.2043 −1.88932 −0.944662 0.328046i \(-0.893610\pi\)
−0.944662 + 0.328046i \(0.893610\pi\)
\(500\) −11.0707 −0.495096
\(501\) 7.82238 0.349478
\(502\) 10.3327 0.461172
\(503\) 17.5133 0.780881 0.390441 0.920628i \(-0.372323\pi\)
0.390441 + 0.920628i \(0.372323\pi\)
\(504\) 2.69202 0.119912
\(505\) 10.6528 0.474043
\(506\) 8.74094 0.388582
\(507\) 0 0
\(508\) −4.96316 −0.220205
\(509\) 6.94869 0.307995 0.153998 0.988071i \(-0.450785\pi\)
0.153998 + 0.988071i \(0.450785\pi\)
\(510\) 3.98792 0.176588
\(511\) −14.1032 −0.623889
\(512\) 1.00000 0.0441942
\(513\) −6.16315 −0.272110
\(514\) −14.3884 −0.634643
\(515\) −23.1763 −1.02127
\(516\) 1.25906 0.0554271
\(517\) 19.0465 0.837665
\(518\) −7.75302 −0.340648
\(519\) 9.92692 0.435743
\(520\) 0 0
\(521\) −33.3889 −1.46280 −0.731398 0.681951i \(-0.761132\pi\)
−0.731398 + 0.681951i \(0.761132\pi\)
\(522\) −16.0465 −0.702337
\(523\) −0.281422 −0.0123057 −0.00615287 0.999981i \(-0.501959\pi\)
−0.00615287 + 0.999981i \(0.501959\pi\)
\(524\) −11.0761 −0.483860
\(525\) 1.75302 0.0765081
\(526\) −17.6069 −0.767696
\(527\) −19.2295 −0.837651
\(528\) 1.00000 0.0435194
\(529\) 0.530795 0.0230780
\(530\) −4.97285 −0.216007
\(531\) −10.9729 −0.476181
\(532\) −1.95108 −0.0845902
\(533\) 0 0
\(534\) −3.67324 −0.158956
\(535\) 18.8015 0.812858
\(536\) −2.22521 −0.0961144
\(537\) −0.0308679 −0.00133205
\(538\) −4.15213 −0.179011
\(539\) 1.80194 0.0776150
\(540\) −4.28621 −0.184449
\(541\) 33.4655 1.43879 0.719397 0.694599i \(-0.244418\pi\)
0.719397 + 0.694599i \(0.244418\pi\)
\(542\) 17.5278 0.752884
\(543\) −4.68963 −0.201251
\(544\) 5.29590 0.227060
\(545\) −2.95885 −0.126743
\(546\) 0 0
\(547\) 25.9148 1.10804 0.554019 0.832504i \(-0.313093\pi\)
0.554019 + 0.832504i \(0.313093\pi\)
\(548\) 10.3056 0.440233
\(549\) 30.9681 1.32168
\(550\) −5.69202 −0.242709
\(551\) 11.6300 0.495453
\(552\) 2.69202 0.114580
\(553\) 12.0804 0.513710
\(554\) −29.9855 −1.27396
\(555\) 5.83818 0.247817
\(556\) 0.987918 0.0418971
\(557\) −24.1588 −1.02364 −0.511821 0.859092i \(-0.671029\pi\)
−0.511821 + 0.859092i \(0.671029\pi\)
\(558\) 9.77479 0.413800
\(559\) 0 0
\(560\) −1.35690 −0.0573393
\(561\) 5.29590 0.223593
\(562\) −9.24027 −0.389777
\(563\) 5.58987 0.235585 0.117793 0.993038i \(-0.462418\pi\)
0.117793 + 0.993038i \(0.462418\pi\)
\(564\) 5.86592 0.247000
\(565\) −23.7579 −0.999503
\(566\) 32.0291 1.34628
\(567\) −6.32304 −0.265543
\(568\) 7.78986 0.326855
\(569\) 40.5217 1.69876 0.849379 0.527783i \(-0.176977\pi\)
0.849379 + 0.527783i \(0.176977\pi\)
\(570\) 1.46921 0.0615382
\(571\) 33.2180 1.39013 0.695066 0.718946i \(-0.255375\pi\)
0.695066 + 0.718946i \(0.255375\pi\)
\(572\) 0 0
\(573\) −2.40449 −0.100449
\(574\) −0.0392287 −0.00163737
\(575\) −15.3230 −0.639015
\(576\) −2.69202 −0.112168
\(577\) −17.4896 −0.728104 −0.364052 0.931379i \(-0.618607\pi\)
−0.364052 + 0.931379i \(0.618607\pi\)
\(578\) 11.0465 0.459475
\(579\) −0.945706 −0.0393022
\(580\) 8.08815 0.335842
\(581\) −2.85086 −0.118273
\(582\) −2.02177 −0.0838051
\(583\) −6.60388 −0.273505
\(584\) 14.1032 0.583595
\(585\) 0 0
\(586\) −22.1933 −0.916796
\(587\) −35.8224 −1.47855 −0.739274 0.673405i \(-0.764831\pi\)
−0.739274 + 0.673405i \(0.764831\pi\)
\(588\) 0.554958 0.0228861
\(589\) −7.08443 −0.291909
\(590\) 5.53079 0.227699
\(591\) −14.3013 −0.588276
\(592\) 7.75302 0.318647
\(593\) 12.0750 0.495861 0.247930 0.968778i \(-0.420250\pi\)
0.247930 + 0.968778i \(0.420250\pi\)
\(594\) −5.69202 −0.233546
\(595\) −7.18598 −0.294596
\(596\) −5.60627 −0.229642
\(597\) 3.73258 0.152764
\(598\) 0 0
\(599\) 20.6256 0.842741 0.421371 0.906889i \(-0.361549\pi\)
0.421371 + 0.906889i \(0.361549\pi\)
\(600\) −1.75302 −0.0715668
\(601\) −38.8025 −1.58279 −0.791394 0.611306i \(-0.790644\pi\)
−0.791394 + 0.611306i \(0.790644\pi\)
\(602\) −2.26875 −0.0924673
\(603\) 5.99031 0.243944
\(604\) −15.5894 −0.634324
\(605\) −10.5200 −0.427701
\(606\) 4.35690 0.176987
\(607\) 2.24459 0.0911050 0.0455525 0.998962i \(-0.485495\pi\)
0.0455525 + 0.998962i \(0.485495\pi\)
\(608\) 1.95108 0.0791269
\(609\) −3.30798 −0.134046
\(610\) −15.6093 −0.632000
\(611\) 0 0
\(612\) −14.2567 −0.576292
\(613\) 4.24267 0.171360 0.0856799 0.996323i \(-0.472694\pi\)
0.0856799 + 0.996323i \(0.472694\pi\)
\(614\) −20.8170 −0.840106
\(615\) 0.0295400 0.00119117
\(616\) −1.80194 −0.0726021
\(617\) 0.147817 0.00595089 0.00297544 0.999996i \(-0.499053\pi\)
0.00297544 + 0.999996i \(0.499053\pi\)
\(618\) −9.47889 −0.381297
\(619\) 35.3575 1.42114 0.710569 0.703628i \(-0.248438\pi\)
0.710569 + 0.703628i \(0.248438\pi\)
\(620\) −4.92692 −0.197870
\(621\) −15.3230 −0.614893
\(622\) 28.1836 1.13006
\(623\) 6.61894 0.265182
\(624\) 0 0
\(625\) 0.772398 0.0308959
\(626\) 16.0248 0.640478
\(627\) 1.95108 0.0779187
\(628\) −8.49827 −0.339118
\(629\) 41.0592 1.63714
\(630\) 3.65279 0.145531
\(631\) 2.33214 0.0928411 0.0464205 0.998922i \(-0.485219\pi\)
0.0464205 + 0.998922i \(0.485219\pi\)
\(632\) −12.0804 −0.480532
\(633\) −14.8471 −0.590121
\(634\) 29.0834 1.15505
\(635\) −6.73450 −0.267250
\(636\) −2.03385 −0.0806475
\(637\) 0 0
\(638\) 10.7409 0.425238
\(639\) −20.9705 −0.829579
\(640\) 1.35690 0.0536360
\(641\) −17.5767 −0.694239 −0.347120 0.937821i \(-0.612840\pi\)
−0.347120 + 0.937821i \(0.612840\pi\)
\(642\) 7.68963 0.303485
\(643\) −3.70410 −0.146076 −0.0730378 0.997329i \(-0.523269\pi\)
−0.0730378 + 0.997329i \(0.523269\pi\)
\(644\) −4.85086 −0.191150
\(645\) 1.70841 0.0672688
\(646\) 10.3327 0.406536
\(647\) 50.4935 1.98510 0.992552 0.121823i \(-0.0388739\pi\)
0.992552 + 0.121823i \(0.0388739\pi\)
\(648\) 6.32304 0.248393
\(649\) 7.34481 0.288309
\(650\) 0 0
\(651\) 2.01507 0.0789766
\(652\) 5.25906 0.205961
\(653\) 33.5109 1.31138 0.655692 0.755028i \(-0.272377\pi\)
0.655692 + 0.755028i \(0.272377\pi\)
\(654\) −1.21014 −0.0473204
\(655\) −15.0291 −0.587234
\(656\) 0.0392287 0.00153162
\(657\) −37.9661 −1.48120
\(658\) −10.5700 −0.412062
\(659\) 12.8194 0.499373 0.249686 0.968327i \(-0.419672\pi\)
0.249686 + 0.968327i \(0.419672\pi\)
\(660\) 1.35690 0.0528171
\(661\) −24.3163 −0.945796 −0.472898 0.881117i \(-0.656792\pi\)
−0.472898 + 0.881117i \(0.656792\pi\)
\(662\) −7.32304 −0.284618
\(663\) 0 0
\(664\) 2.85086 0.110635
\(665\) −2.64742 −0.102662
\(666\) −20.8713 −0.808746
\(667\) 28.9148 1.11959
\(668\) 14.0954 0.545369
\(669\) 11.4239 0.441672
\(670\) −3.01938 −0.116649
\(671\) −20.7289 −0.800229
\(672\) −0.554958 −0.0214080
\(673\) −17.9812 −0.693125 −0.346562 0.938027i \(-0.612651\pi\)
−0.346562 + 0.938027i \(0.612651\pi\)
\(674\) −27.1618 −1.04623
\(675\) 9.97823 0.384062
\(676\) 0 0
\(677\) −1.81461 −0.0697411 −0.0348706 0.999392i \(-0.511102\pi\)
−0.0348706 + 0.999392i \(0.511102\pi\)
\(678\) −9.71678 −0.373171
\(679\) 3.64310 0.139810
\(680\) 7.18598 0.275570
\(681\) −12.3502 −0.473260
\(682\) −6.54288 −0.250540
\(683\) −37.9081 −1.45051 −0.725257 0.688478i \(-0.758279\pi\)
−0.725257 + 0.688478i \(0.758279\pi\)
\(684\) −5.25236 −0.200829
\(685\) 13.9836 0.534286
\(686\) −1.00000 −0.0381802
\(687\) 9.05861 0.345607
\(688\) 2.26875 0.0864953
\(689\) 0 0
\(690\) 3.65279 0.139059
\(691\) 30.0881 1.14461 0.572304 0.820042i \(-0.306050\pi\)
0.572304 + 0.820042i \(0.306050\pi\)
\(692\) 17.8877 0.679988
\(693\) 4.85086 0.184269
\(694\) −12.8890 −0.489260
\(695\) 1.34050 0.0508482
\(696\) 3.30798 0.125389
\(697\) 0.207751 0.00786913
\(698\) −19.6732 −0.744643
\(699\) 3.82238 0.144576
\(700\) 3.15883 0.119393
\(701\) −18.4625 −0.697319 −0.348660 0.937249i \(-0.613363\pi\)
−0.348660 + 0.937249i \(0.613363\pi\)
\(702\) 0 0
\(703\) 15.1268 0.570517
\(704\) 1.80194 0.0679131
\(705\) 7.95944 0.299770
\(706\) 30.3980 1.14405
\(707\) −7.85086 −0.295262
\(708\) 2.26205 0.0850129
\(709\) −3.07308 −0.115412 −0.0577060 0.998334i \(-0.518379\pi\)
−0.0577060 + 0.998334i \(0.518379\pi\)
\(710\) 10.5700 0.396686
\(711\) 32.5206 1.21962
\(712\) −6.61894 −0.248055
\(713\) −17.6136 −0.659633
\(714\) −2.93900 −0.109989
\(715\) 0 0
\(716\) −0.0556221 −0.00207870
\(717\) 7.86426 0.293696
\(718\) 2.64310 0.0986398
\(719\) 28.6213 1.06740 0.533698 0.845675i \(-0.320802\pi\)
0.533698 + 0.845675i \(0.320802\pi\)
\(720\) −3.65279 −0.136132
\(721\) 17.0804 0.636106
\(722\) −15.1933 −0.565435
\(723\) 2.17257 0.0807988
\(724\) −8.45042 −0.314057
\(725\) −18.8291 −0.699295
\(726\) −4.30260 −0.159685
\(727\) 35.8799 1.33071 0.665356 0.746526i \(-0.268280\pi\)
0.665356 + 0.746526i \(0.268280\pi\)
\(728\) 0 0
\(729\) −11.7627 −0.435656
\(730\) 19.1366 0.708277
\(731\) 12.0151 0.444393
\(732\) −6.38404 −0.235961
\(733\) 13.8291 0.510789 0.255394 0.966837i \(-0.417795\pi\)
0.255394 + 0.966837i \(0.417795\pi\)
\(734\) 2.46921 0.0911400
\(735\) 0.753020 0.0277756
\(736\) 4.85086 0.178805
\(737\) −4.00969 −0.147699
\(738\) −0.105604 −0.00388735
\(739\) 50.6262 1.86232 0.931158 0.364616i \(-0.118800\pi\)
0.931158 + 0.364616i \(0.118800\pi\)
\(740\) 10.5200 0.386724
\(741\) 0 0
\(742\) 3.66487 0.134542
\(743\) −36.8866 −1.35324 −0.676620 0.736333i \(-0.736556\pi\)
−0.676620 + 0.736333i \(0.736556\pi\)
\(744\) −2.01507 −0.0738759
\(745\) −7.60712 −0.278703
\(746\) −5.96615 −0.218436
\(747\) −7.67456 −0.280798
\(748\) 9.54288 0.348922
\(749\) −13.8562 −0.506296
\(750\) −6.14377 −0.224339
\(751\) −10.3556 −0.377880 −0.188940 0.981989i \(-0.560505\pi\)
−0.188940 + 0.981989i \(0.560505\pi\)
\(752\) 10.5700 0.385449
\(753\) 5.73423 0.208967
\(754\) 0 0
\(755\) −21.1532 −0.769844
\(756\) 3.15883 0.114886
\(757\) 20.0234 0.727764 0.363882 0.931445i \(-0.381451\pi\)
0.363882 + 0.931445i \(0.381451\pi\)
\(758\) 22.0519 0.800961
\(759\) 4.85086 0.176075
\(760\) 2.64742 0.0960319
\(761\) 14.9694 0.542640 0.271320 0.962489i \(-0.412540\pi\)
0.271320 + 0.962489i \(0.412540\pi\)
\(762\) −2.75435 −0.0997795
\(763\) 2.18060 0.0789432
\(764\) −4.33273 −0.156753
\(765\) −19.3448 −0.699413
\(766\) 26.1758 0.945771
\(767\) 0 0
\(768\) 0.554958 0.0200253
\(769\) 6.11290 0.220437 0.110218 0.993907i \(-0.464845\pi\)
0.110218 + 0.993907i \(0.464845\pi\)
\(770\) −2.44504 −0.0881132
\(771\) −7.98493 −0.287570
\(772\) −1.70410 −0.0613320
\(773\) 21.3870 0.769238 0.384619 0.923075i \(-0.374333\pi\)
0.384619 + 0.923075i \(0.374333\pi\)
\(774\) −6.10752 −0.219530
\(775\) 11.4698 0.412007
\(776\) −3.64310 −0.130780
\(777\) −4.30260 −0.154355
\(778\) −15.4655 −0.554464
\(779\) 0.0765384 0.00274227
\(780\) 0 0
\(781\) 14.0368 0.502277
\(782\) 25.6896 0.918659
\(783\) −18.8291 −0.672897
\(784\) 1.00000 0.0357143
\(785\) −11.5313 −0.411569
\(786\) −6.14675 −0.219247
\(787\) −40.5623 −1.44589 −0.722944 0.690907i \(-0.757212\pi\)
−0.722944 + 0.690907i \(0.757212\pi\)
\(788\) −25.7700 −0.918018
\(789\) −9.77107 −0.347859
\(790\) −16.3918 −0.583195
\(791\) 17.5090 0.622549
\(792\) −4.85086 −0.172368
\(793\) 0 0
\(794\) −34.9778 −1.24131
\(795\) −2.75973 −0.0978774
\(796\) 6.72587 0.238392
\(797\) −40.6698 −1.44060 −0.720299 0.693664i \(-0.755995\pi\)
−0.720299 + 0.693664i \(0.755995\pi\)
\(798\) −1.08277 −0.0383296
\(799\) 55.9778 1.98035
\(800\) −3.15883 −0.111682
\(801\) 17.8183 0.629580
\(802\) −27.3739 −0.966605
\(803\) 25.4131 0.896809
\(804\) −1.23490 −0.0435515
\(805\) −6.58211 −0.231989
\(806\) 0 0
\(807\) −2.30426 −0.0811137
\(808\) 7.85086 0.276192
\(809\) −56.3666 −1.98174 −0.990872 0.134808i \(-0.956958\pi\)
−0.990872 + 0.134808i \(0.956958\pi\)
\(810\) 8.57971 0.301460
\(811\) 10.2397 0.359564 0.179782 0.983706i \(-0.442461\pi\)
0.179782 + 0.983706i \(0.442461\pi\)
\(812\) −5.96077 −0.209182
\(813\) 9.72720 0.341148
\(814\) 13.9705 0.489664
\(815\) 7.13600 0.249963
\(816\) 2.93900 0.102886
\(817\) 4.42652 0.154864
\(818\) −29.0810 −1.01679
\(819\) 0 0
\(820\) 0.0532292 0.00185884
\(821\) −29.6219 −1.03381 −0.516906 0.856042i \(-0.672916\pi\)
−0.516906 + 0.856042i \(0.672916\pi\)
\(822\) 5.71917 0.199479
\(823\) −17.0804 −0.595384 −0.297692 0.954662i \(-0.596217\pi\)
−0.297692 + 0.954662i \(0.596217\pi\)
\(824\) −17.0804 −0.595023
\(825\) −3.15883 −0.109976
\(826\) −4.07606 −0.141824
\(827\) −5.46575 −0.190063 −0.0950313 0.995474i \(-0.530295\pi\)
−0.0950313 + 0.995474i \(0.530295\pi\)
\(828\) −13.0586 −0.453818
\(829\) 41.7942 1.45157 0.725786 0.687921i \(-0.241476\pi\)
0.725786 + 0.687921i \(0.241476\pi\)
\(830\) 3.86831 0.134271
\(831\) −16.6407 −0.577260
\(832\) 0 0
\(833\) 5.29590 0.183492
\(834\) 0.548253 0.0189845
\(835\) 19.1260 0.661884
\(836\) 3.51573 0.121594
\(837\) 11.4698 0.396454
\(838\) −40.3086 −1.39244
\(839\) 9.38511 0.324010 0.162005 0.986790i \(-0.448204\pi\)
0.162005 + 0.986790i \(0.448204\pi\)
\(840\) −0.753020 −0.0259817
\(841\) 6.53079 0.225200
\(842\) 4.26981 0.147148
\(843\) −5.12797 −0.176617
\(844\) −26.7536 −0.920897
\(845\) 0 0
\(846\) −28.4547 −0.978294
\(847\) 7.75302 0.266397
\(848\) −3.66487 −0.125852
\(849\) 17.7748 0.610029
\(850\) −16.7289 −0.573795
\(851\) 37.6088 1.28921
\(852\) 4.32304 0.148105
\(853\) 6.23623 0.213524 0.106762 0.994285i \(-0.465952\pi\)
0.106762 + 0.994285i \(0.465952\pi\)
\(854\) 11.5036 0.393647
\(855\) −7.12690 −0.243735
\(856\) 13.8562 0.473596
\(857\) 50.7426 1.73333 0.866667 0.498887i \(-0.166258\pi\)
0.866667 + 0.498887i \(0.166258\pi\)
\(858\) 0 0
\(859\) 28.7681 0.981554 0.490777 0.871285i \(-0.336713\pi\)
0.490777 + 0.871285i \(0.336713\pi\)
\(860\) 3.07846 0.104975
\(861\) −0.0217703 −0.000741929 0
\(862\) −6.25475 −0.213038
\(863\) −32.1473 −1.09431 −0.547154 0.837032i \(-0.684289\pi\)
−0.547154 + 0.837032i \(0.684289\pi\)
\(864\) −3.15883 −0.107466
\(865\) 24.2717 0.825264
\(866\) −15.9705 −0.542698
\(867\) 6.13036 0.208198
\(868\) 3.63102 0.123245
\(869\) −21.7681 −0.738432
\(870\) 4.48858 0.152177
\(871\) 0 0
\(872\) −2.18060 −0.0738446
\(873\) 9.80731 0.331927
\(874\) 9.46442 0.320139
\(875\) 11.0707 0.374258
\(876\) 7.82669 0.264439
\(877\) −24.5123 −0.827721 −0.413860 0.910340i \(-0.635820\pi\)
−0.413860 + 0.910340i \(0.635820\pi\)
\(878\) 30.4058 1.02615
\(879\) −12.3163 −0.415420
\(880\) 2.44504 0.0824223
\(881\) −48.2653 −1.62610 −0.813050 0.582195i \(-0.802194\pi\)
−0.813050 + 0.582195i \(0.802194\pi\)
\(882\) −2.69202 −0.0906451
\(883\) −44.9342 −1.51216 −0.756078 0.654481i \(-0.772887\pi\)
−0.756078 + 0.654481i \(0.772887\pi\)
\(884\) 0 0
\(885\) 3.06936 0.103175
\(886\) −13.0291 −0.437720
\(887\) 41.2610 1.38541 0.692704 0.721222i \(-0.256419\pi\)
0.692704 + 0.721222i \(0.256419\pi\)
\(888\) 4.30260 0.144386
\(889\) 4.96316 0.166459
\(890\) −8.98121 −0.301051
\(891\) 11.3937 0.381704
\(892\) 20.5851 0.689240
\(893\) 20.6230 0.690122
\(894\) −3.11124 −0.104056
\(895\) −0.0754734 −0.00252280
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 20.2258 0.674944
\(899\) −21.6437 −0.721858
\(900\) 8.50365 0.283455
\(901\) −19.4088 −0.646601
\(902\) 0.0706876 0.00235364
\(903\) −1.25906 −0.0418989
\(904\) −17.5090 −0.582341
\(905\) −11.4663 −0.381154
\(906\) −8.65146 −0.287426
\(907\) −30.0344 −0.997277 −0.498639 0.866810i \(-0.666167\pi\)
−0.498639 + 0.866810i \(0.666167\pi\)
\(908\) −22.2543 −0.738534
\(909\) −21.1347 −0.700993
\(910\) 0 0
\(911\) −15.4069 −0.510453 −0.255226 0.966881i \(-0.582150\pi\)
−0.255226 + 0.966881i \(0.582150\pi\)
\(912\) 1.08277 0.0358541
\(913\) 5.13706 0.170012
\(914\) 20.5569 0.679961
\(915\) −8.66248 −0.286373
\(916\) 16.3230 0.539329
\(917\) 11.0761 0.365764
\(918\) −16.7289 −0.552135
\(919\) 21.8073 0.719357 0.359678 0.933076i \(-0.382886\pi\)
0.359678 + 0.933076i \(0.382886\pi\)
\(920\) 6.58211 0.217006
\(921\) −11.5526 −0.380670
\(922\) −15.2513 −0.502275
\(923\) 0 0
\(924\) −1.00000 −0.0328976
\(925\) −24.4905 −0.805243
\(926\) −25.3207 −0.832088
\(927\) 45.9807 1.51021
\(928\) 5.96077 0.195672
\(929\) 38.4523 1.26158 0.630790 0.775953i \(-0.282731\pi\)
0.630790 + 0.775953i \(0.282731\pi\)
\(930\) −2.73423 −0.0896591
\(931\) 1.95108 0.0639442
\(932\) 6.88769 0.225614
\(933\) 15.6407 0.512054
\(934\) 16.8019 0.549776
\(935\) 12.9487 0.423467
\(936\) 0 0
\(937\) 57.4669 1.87736 0.938681 0.344786i \(-0.112048\pi\)
0.938681 + 0.344786i \(0.112048\pi\)
\(938\) 2.22521 0.0726557
\(939\) 8.89307 0.290214
\(940\) 14.3424 0.467798
\(941\) 14.1347 0.460777 0.230389 0.973099i \(-0.426000\pi\)
0.230389 + 0.973099i \(0.426000\pi\)
\(942\) −4.71618 −0.153662
\(943\) 0.190293 0.00619678
\(944\) 4.07606 0.132665
\(945\) 4.28621 0.139430
\(946\) 4.08815 0.132917
\(947\) 19.0858 0.620204 0.310102 0.950703i \(-0.399637\pi\)
0.310102 + 0.950703i \(0.399637\pi\)
\(948\) −6.70410 −0.217739
\(949\) 0 0
\(950\) −6.16315 −0.199959
\(951\) 16.1400 0.523377
\(952\) −5.29590 −0.171641
\(953\) −31.9571 −1.03519 −0.517595 0.855626i \(-0.673173\pi\)
−0.517595 + 0.855626i \(0.673173\pi\)
\(954\) 9.86592 0.319421
\(955\) −5.87907 −0.190242
\(956\) 14.1709 0.458320
\(957\) 5.96077 0.192684
\(958\) −27.5870 −0.891296
\(959\) −10.3056 −0.332785
\(960\) 0.753020 0.0243036
\(961\) −17.8157 −0.574699
\(962\) 0 0
\(963\) −37.3013 −1.20202
\(964\) 3.91484 0.126088
\(965\) −2.31229 −0.0744353
\(966\) −2.69202 −0.0866144
\(967\) 1.42268 0.0457503 0.0228752 0.999738i \(-0.492718\pi\)
0.0228752 + 0.999738i \(0.492718\pi\)
\(968\) −7.75302 −0.249192
\(969\) 5.73423 0.184210
\(970\) −4.94331 −0.158720
\(971\) −4.26742 −0.136948 −0.0684740 0.997653i \(-0.521813\pi\)
−0.0684740 + 0.997653i \(0.521813\pi\)
\(972\) 12.9855 0.416511
\(973\) −0.987918 −0.0316712
\(974\) −29.4698 −0.944273
\(975\) 0 0
\(976\) −11.5036 −0.368223
\(977\) −23.5375 −0.753031 −0.376516 0.926410i \(-0.622878\pi\)
−0.376516 + 0.926410i \(0.622878\pi\)
\(978\) 2.91856 0.0933252
\(979\) −11.9269 −0.381186
\(980\) 1.35690 0.0433444
\(981\) 5.87023 0.187422
\(982\) −8.30691 −0.265084
\(983\) 51.9734 1.65770 0.828848 0.559474i \(-0.188997\pi\)
0.828848 + 0.559474i \(0.188997\pi\)
\(984\) 0.0217703 0.000694011 0
\(985\) −34.9672 −1.11415
\(986\) 31.5676 1.00532
\(987\) −5.86592 −0.186714
\(988\) 0 0
\(989\) 11.0054 0.349951
\(990\) −6.58211 −0.209193
\(991\) −39.9332 −1.26852 −0.634259 0.773121i \(-0.718695\pi\)
−0.634259 + 0.773121i \(0.718695\pi\)
\(992\) −3.63102 −0.115285
\(993\) −4.06398 −0.128967
\(994\) −7.78986 −0.247079
\(995\) 9.12631 0.289323
\(996\) 1.58211 0.0501309
\(997\) −41.4827 −1.31377 −0.656886 0.753990i \(-0.728127\pi\)
−0.656886 + 0.753990i \(0.728127\pi\)
\(998\) −42.2043 −1.33595
\(999\) −24.4905 −0.774845
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.1.2 yes 3
13.5 odd 4 2366.2.d.p.337.2 6
13.8 odd 4 2366.2.d.p.337.5 6
13.12 even 2 2366.2.a.y.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2366.2.a.y.1.2 3 13.12 even 2
2366.2.a.bd.1.2 yes 3 1.1 even 1 trivial
2366.2.d.p.337.2 6 13.5 odd 4
2366.2.d.p.337.5 6 13.8 odd 4