Properties

Label 1183.2.a.p.1.3
Level $1183$
Weight $2$
Character 1183.1
Self dual yes
Analytic conductor $9.446$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.7674048.1
Defining polynomial: \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.879640\) of defining polynomial
Character \(\chi\) \(=\) 1183.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.120360 q^{2} -0.582292 q^{3} -1.98551 q^{4} -1.68817 q^{5} -0.0700846 q^{6} -1.00000 q^{7} -0.479696 q^{8} -2.66094 q^{9} +O(q^{10})\) \(q+0.120360 q^{2} -0.582292 q^{3} -1.98551 q^{4} -1.68817 q^{5} -0.0700846 q^{6} -1.00000 q^{7} -0.479696 q^{8} -2.66094 q^{9} -0.203187 q^{10} -0.364618 q^{11} +1.15615 q^{12} -0.120360 q^{14} +0.983005 q^{15} +3.91329 q^{16} -3.18555 q^{17} -0.320270 q^{18} +1.44391 q^{19} +3.35188 q^{20} +0.582292 q^{21} -0.0438854 q^{22} -5.08321 q^{23} +0.279323 q^{24} -2.15010 q^{25} +3.29632 q^{27} +1.98551 q^{28} +8.19662 q^{29} +0.118314 q^{30} -4.69775 q^{31} +1.43040 q^{32} +0.212314 q^{33} -0.383412 q^{34} +1.68817 q^{35} +5.28332 q^{36} +6.31584 q^{37} +0.173789 q^{38} +0.809806 q^{40} +5.82732 q^{41} +0.0700846 q^{42} -0.773122 q^{43} +0.723954 q^{44} +4.49210 q^{45} -0.611815 q^{46} +12.7905 q^{47} -2.27868 q^{48} +1.00000 q^{49} -0.258786 q^{50} +1.85492 q^{51} +1.37110 q^{53} +0.396744 q^{54} +0.615536 q^{55} +0.479696 q^{56} -0.840776 q^{57} +0.986544 q^{58} +9.36197 q^{59} -1.95177 q^{60} -9.02484 q^{61} -0.565421 q^{62} +2.66094 q^{63} -7.65442 q^{64} +0.0255541 q^{66} +13.4759 q^{67} +6.32495 q^{68} +2.95991 q^{69} +0.203187 q^{70} -7.08115 q^{71} +1.27644 q^{72} -2.16083 q^{73} +0.760173 q^{74} +1.25198 q^{75} -2.86690 q^{76} +0.364618 q^{77} -6.88781 q^{79} -6.60628 q^{80} +6.06339 q^{81} +0.701376 q^{82} +0.567380 q^{83} -1.15615 q^{84} +5.37773 q^{85} -0.0930528 q^{86} -4.77282 q^{87} +0.174906 q^{88} -1.13893 q^{89} +0.540669 q^{90} +10.0928 q^{92} +2.73547 q^{93} +1.53947 q^{94} -2.43755 q^{95} -0.832908 q^{96} +7.92785 q^{97} +0.120360 q^{98} +0.970225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{14} + 20 q^{15} + 8 q^{16} - 4 q^{17} - 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} + 6 q^{27} - 4 q^{28} - 8 q^{29} + 8 q^{30} - 14 q^{31} + 8 q^{32} + 16 q^{33} - 2 q^{34} - 6 q^{35} - 10 q^{36} + 12 q^{37} - 2 q^{38} + 46 q^{40} + 28 q^{41} - 4 q^{42} + 2 q^{43} - 20 q^{44} + 16 q^{45} + 20 q^{46} + 14 q^{47} + 2 q^{48} + 6 q^{49} + 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} + 6 q^{55} - 12 q^{56} + 4 q^{58} - 2 q^{59} - 14 q^{61} - 4 q^{62} - 4 q^{63} + 26 q^{64} - 26 q^{66} + 24 q^{67} + 8 q^{68} + 4 q^{69} - 12 q^{70} + 4 q^{71} + 8 q^{72} + 36 q^{73} - 6 q^{74} + 46 q^{75} - 26 q^{76} - 4 q^{77} - 28 q^{79} + 36 q^{80} - 2 q^{81} + 14 q^{82} + 26 q^{83} - 2 q^{84} - 20 q^{85} - 24 q^{86} + 2 q^{87} - 14 q^{88} + 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.120360 0.0851073 0.0425536 0.999094i \(-0.486451\pi\)
0.0425536 + 0.999094i \(0.486451\pi\)
\(3\) −0.582292 −0.336186 −0.168093 0.985771i \(-0.553761\pi\)
−0.168093 + 0.985771i \(0.553761\pi\)
\(4\) −1.98551 −0.992757
\(5\) −1.68817 −0.754971 −0.377485 0.926016i \(-0.623211\pi\)
−0.377485 + 0.926016i \(0.623211\pi\)
\(6\) −0.0700846 −0.0286119
\(7\) −1.00000 −0.377964
\(8\) −0.479696 −0.169598
\(9\) −2.66094 −0.886979
\(10\) −0.203187 −0.0642535
\(11\) −0.364618 −0.109936 −0.0549682 0.998488i \(-0.517506\pi\)
−0.0549682 + 0.998488i \(0.517506\pi\)
\(12\) 1.15615 0.333751
\(13\) 0 0
\(14\) −0.120360 −0.0321675
\(15\) 0.983005 0.253811
\(16\) 3.91329 0.978323
\(17\) −3.18555 −0.772609 −0.386304 0.922371i \(-0.626249\pi\)
−0.386304 + 0.922371i \(0.626249\pi\)
\(18\) −0.320270 −0.0754884
\(19\) 1.44391 0.331255 0.165628 0.986188i \(-0.447035\pi\)
0.165628 + 0.986188i \(0.447035\pi\)
\(20\) 3.35188 0.749502
\(21\) 0.582292 0.127067
\(22\) −0.0438854 −0.00935640
\(23\) −5.08321 −1.05992 −0.529962 0.848022i \(-0.677794\pi\)
−0.529962 + 0.848022i \(0.677794\pi\)
\(24\) 0.279323 0.0570166
\(25\) −2.15010 −0.430020
\(26\) 0 0
\(27\) 3.29632 0.634377
\(28\) 1.98551 0.375227
\(29\) 8.19662 1.52207 0.761037 0.648709i \(-0.224691\pi\)
0.761037 + 0.648709i \(0.224691\pi\)
\(30\) 0.118314 0.0216012
\(31\) −4.69775 −0.843742 −0.421871 0.906656i \(-0.638626\pi\)
−0.421871 + 0.906656i \(0.638626\pi\)
\(32\) 1.43040 0.252861
\(33\) 0.212314 0.0369592
\(34\) −0.383412 −0.0657546
\(35\) 1.68817 0.285352
\(36\) 5.28332 0.880554
\(37\) 6.31584 1.03832 0.519159 0.854678i \(-0.326245\pi\)
0.519159 + 0.854678i \(0.326245\pi\)
\(38\) 0.173789 0.0281922
\(39\) 0 0
\(40\) 0.809806 0.128042
\(41\) 5.82732 0.910074 0.455037 0.890472i \(-0.349626\pi\)
0.455037 + 0.890472i \(0.349626\pi\)
\(42\) 0.0700846 0.0108143
\(43\) −0.773122 −0.117900 −0.0589500 0.998261i \(-0.518775\pi\)
−0.0589500 + 0.998261i \(0.518775\pi\)
\(44\) 0.723954 0.109140
\(45\) 4.49210 0.669643
\(46\) −0.611815 −0.0902072
\(47\) 12.7905 1.86569 0.932846 0.360275i \(-0.117317\pi\)
0.932846 + 0.360275i \(0.117317\pi\)
\(48\) −2.27868 −0.328899
\(49\) 1.00000 0.142857
\(50\) −0.258786 −0.0365978
\(51\) 1.85492 0.259741
\(52\) 0 0
\(53\) 1.37110 0.188334 0.0941672 0.995556i \(-0.469981\pi\)
0.0941672 + 0.995556i \(0.469981\pi\)
\(54\) 0.396744 0.0539901
\(55\) 0.615536 0.0829988
\(56\) 0.479696 0.0641021
\(57\) −0.840776 −0.111363
\(58\) 0.986544 0.129540
\(59\) 9.36197 1.21882 0.609412 0.792854i \(-0.291405\pi\)
0.609412 + 0.792854i \(0.291405\pi\)
\(60\) −1.95177 −0.251972
\(61\) −9.02484 −1.15551 −0.577756 0.816209i \(-0.696072\pi\)
−0.577756 + 0.816209i \(0.696072\pi\)
\(62\) −0.565421 −0.0718086
\(63\) 2.66094 0.335246
\(64\) −7.65442 −0.956802
\(65\) 0 0
\(66\) 0.0255541 0.00314549
\(67\) 13.4759 1.64635 0.823174 0.567789i \(-0.192201\pi\)
0.823174 + 0.567789i \(0.192201\pi\)
\(68\) 6.32495 0.767013
\(69\) 2.95991 0.356332
\(70\) 0.203187 0.0242855
\(71\) −7.08115 −0.840378 −0.420189 0.907437i \(-0.638036\pi\)
−0.420189 + 0.907437i \(0.638036\pi\)
\(72\) 1.27644 0.150430
\(73\) −2.16083 −0.252906 −0.126453 0.991973i \(-0.540359\pi\)
−0.126453 + 0.991973i \(0.540359\pi\)
\(74\) 0.760173 0.0883684
\(75\) 1.25198 0.144567
\(76\) −2.86690 −0.328856
\(77\) 0.364618 0.0415521
\(78\) 0 0
\(79\) −6.88781 −0.774940 −0.387470 0.921882i \(-0.626651\pi\)
−0.387470 + 0.921882i \(0.626651\pi\)
\(80\) −6.60628 −0.738605
\(81\) 6.06339 0.673710
\(82\) 0.701376 0.0774540
\(83\) 0.567380 0.0622780 0.0311390 0.999515i \(-0.490087\pi\)
0.0311390 + 0.999515i \(0.490087\pi\)
\(84\) −1.15615 −0.126146
\(85\) 5.37773 0.583297
\(86\) −0.0930528 −0.0100341
\(87\) −4.77282 −0.511700
\(88\) 0.174906 0.0186450
\(89\) −1.13893 −0.120727 −0.0603634 0.998176i \(-0.519226\pi\)
−0.0603634 + 0.998176i \(0.519226\pi\)
\(90\) 0.540669 0.0569915
\(91\) 0 0
\(92\) 10.0928 1.05225
\(93\) 2.73547 0.283655
\(94\) 1.53947 0.158784
\(95\) −2.43755 −0.250088
\(96\) −0.832908 −0.0850083
\(97\) 7.92785 0.804952 0.402476 0.915431i \(-0.368150\pi\)
0.402476 + 0.915431i \(0.368150\pi\)
\(98\) 0.120360 0.0121582
\(99\) 0.970225 0.0975113
\(100\) 4.26905 0.426905
\(101\) −15.5464 −1.54693 −0.773465 0.633839i \(-0.781478\pi\)
−0.773465 + 0.633839i \(0.781478\pi\)
\(102\) 0.223258 0.0221058
\(103\) 10.2982 1.01471 0.507354 0.861738i \(-0.330624\pi\)
0.507354 + 0.861738i \(0.330624\pi\)
\(104\) 0 0
\(105\) −0.983005 −0.0959315
\(106\) 0.165025 0.0160286
\(107\) −13.1244 −1.26878 −0.634391 0.773012i \(-0.718749\pi\)
−0.634391 + 0.773012i \(0.718749\pi\)
\(108\) −6.54488 −0.629782
\(109\) 10.4459 1.00054 0.500268 0.865871i \(-0.333235\pi\)
0.500268 + 0.865871i \(0.333235\pi\)
\(110\) 0.0740858 0.00706380
\(111\) −3.67766 −0.349068
\(112\) −3.91329 −0.369771
\(113\) 4.95262 0.465903 0.232952 0.972488i \(-0.425162\pi\)
0.232952 + 0.972488i \(0.425162\pi\)
\(114\) −0.101196 −0.00947784
\(115\) 8.58130 0.800211
\(116\) −16.2745 −1.51105
\(117\) 0 0
\(118\) 1.12681 0.103731
\(119\) 3.18555 0.292019
\(120\) −0.471544 −0.0430458
\(121\) −10.8671 −0.987914
\(122\) −1.08623 −0.0983425
\(123\) −3.39320 −0.305955
\(124\) 9.32746 0.837630
\(125\) 12.0705 1.07962
\(126\) 0.320270 0.0285319
\(127\) 8.06731 0.715858 0.357929 0.933749i \(-0.383483\pi\)
0.357929 + 0.933749i \(0.383483\pi\)
\(128\) −3.78208 −0.334291
\(129\) 0.450183 0.0396364
\(130\) 0 0
\(131\) 18.9039 1.65164 0.825820 0.563934i \(-0.190713\pi\)
0.825820 + 0.563934i \(0.190713\pi\)
\(132\) −0.421553 −0.0366915
\(133\) −1.44391 −0.125203
\(134\) 1.62196 0.140116
\(135\) −5.56473 −0.478936
\(136\) 1.52809 0.131033
\(137\) −18.2255 −1.55711 −0.778554 0.627577i \(-0.784047\pi\)
−0.778554 + 0.627577i \(0.784047\pi\)
\(138\) 0.356255 0.0303264
\(139\) 5.25085 0.445371 0.222686 0.974890i \(-0.428518\pi\)
0.222686 + 0.974890i \(0.428518\pi\)
\(140\) −3.35188 −0.283285
\(141\) −7.44783 −0.627220
\(142\) −0.852287 −0.0715223
\(143\) 0 0
\(144\) −10.4130 −0.867751
\(145\) −13.8372 −1.14912
\(146\) −0.260077 −0.0215241
\(147\) −0.582292 −0.0480266
\(148\) −12.5402 −1.03080
\(149\) 9.27309 0.759681 0.379841 0.925052i \(-0.375979\pi\)
0.379841 + 0.925052i \(0.375979\pi\)
\(150\) 0.150689 0.0123037
\(151\) −14.0132 −1.14038 −0.570189 0.821513i \(-0.693130\pi\)
−0.570189 + 0.821513i \(0.693130\pi\)
\(152\) −0.692636 −0.0561802
\(153\) 8.47654 0.685287
\(154\) 0.0438854 0.00353639
\(155\) 7.93059 0.637000
\(156\) 0 0
\(157\) −17.1825 −1.37131 −0.685656 0.727925i \(-0.740485\pi\)
−0.685656 + 0.727925i \(0.740485\pi\)
\(158\) −0.829017 −0.0659530
\(159\) −0.798378 −0.0633155
\(160\) −2.41474 −0.190902
\(161\) 5.08321 0.400613
\(162\) 0.729789 0.0573376
\(163\) −11.7927 −0.923679 −0.461840 0.886963i \(-0.652810\pi\)
−0.461840 + 0.886963i \(0.652810\pi\)
\(164\) −11.5702 −0.903482
\(165\) −0.358422 −0.0279031
\(166\) 0.0682898 0.00530031
\(167\) 4.31687 0.334049 0.167025 0.985953i \(-0.446584\pi\)
0.167025 + 0.985953i \(0.446584\pi\)
\(168\) −0.279323 −0.0215502
\(169\) 0 0
\(170\) 0.647263 0.0496428
\(171\) −3.84214 −0.293816
\(172\) 1.53504 0.117046
\(173\) 12.5197 0.951855 0.475928 0.879484i \(-0.342112\pi\)
0.475928 + 0.879484i \(0.342112\pi\)
\(174\) −0.574457 −0.0435494
\(175\) 2.15010 0.162532
\(176\) −1.42686 −0.107553
\(177\) −5.45140 −0.409752
\(178\) −0.137082 −0.0102747
\(179\) −6.59534 −0.492959 −0.246479 0.969148i \(-0.579274\pi\)
−0.246479 + 0.969148i \(0.579274\pi\)
\(180\) −8.91913 −0.664792
\(181\) 11.0157 0.818791 0.409395 0.912357i \(-0.365740\pi\)
0.409395 + 0.912357i \(0.365740\pi\)
\(182\) 0 0
\(183\) 5.25509 0.388468
\(184\) 2.43840 0.179761
\(185\) −10.6622 −0.783899
\(186\) 0.329240 0.0241411
\(187\) 1.16151 0.0849379
\(188\) −25.3958 −1.85218
\(189\) −3.29632 −0.239772
\(190\) −0.293384 −0.0212843
\(191\) 5.93213 0.429234 0.214617 0.976698i \(-0.431150\pi\)
0.214617 + 0.976698i \(0.431150\pi\)
\(192\) 4.45711 0.321664
\(193\) 4.19595 0.302031 0.151016 0.988531i \(-0.451746\pi\)
0.151016 + 0.988531i \(0.451746\pi\)
\(194\) 0.954196 0.0685073
\(195\) 0 0
\(196\) −1.98551 −0.141822
\(197\) −5.78494 −0.412160 −0.206080 0.978535i \(-0.566071\pi\)
−0.206080 + 0.978535i \(0.566071\pi\)
\(198\) 0.116776 0.00829893
\(199\) 11.9598 0.847805 0.423903 0.905708i \(-0.360660\pi\)
0.423903 + 0.905708i \(0.360660\pi\)
\(200\) 1.03139 0.0729305
\(201\) −7.84693 −0.553480
\(202\) −1.87117 −0.131655
\(203\) −8.19662 −0.575290
\(204\) −3.68297 −0.257859
\(205\) −9.83748 −0.687079
\(206\) 1.23949 0.0863590
\(207\) 13.5261 0.940129
\(208\) 0 0
\(209\) −0.526475 −0.0364170
\(210\) −0.118314 −0.00816447
\(211\) −8.23591 −0.566983 −0.283492 0.958975i \(-0.591493\pi\)
−0.283492 + 0.958975i \(0.591493\pi\)
\(212\) −2.72233 −0.186970
\(213\) 4.12330 0.282524
\(214\) −1.57965 −0.107983
\(215\) 1.30516 0.0890110
\(216\) −1.58123 −0.107589
\(217\) 4.69775 0.318904
\(218\) 1.25727 0.0851528
\(219\) 1.25823 0.0850234
\(220\) −1.22215 −0.0823976
\(221\) 0 0
\(222\) −0.442643 −0.0297082
\(223\) −15.3015 −1.02466 −0.512331 0.858788i \(-0.671218\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(224\) −1.43040 −0.0955723
\(225\) 5.72127 0.381418
\(226\) 0.596097 0.0396518
\(227\) −6.95467 −0.461598 −0.230799 0.973002i \(-0.574134\pi\)
−0.230799 + 0.973002i \(0.574134\pi\)
\(228\) 1.66937 0.110557
\(229\) 27.4219 1.81209 0.906045 0.423180i \(-0.139086\pi\)
0.906045 + 0.423180i \(0.139086\pi\)
\(230\) 1.03284 0.0681038
\(231\) −0.212314 −0.0139693
\(232\) −3.93188 −0.258141
\(233\) −6.85333 −0.448976 −0.224488 0.974477i \(-0.572071\pi\)
−0.224488 + 0.974477i \(0.572071\pi\)
\(234\) 0 0
\(235\) −21.5926 −1.40854
\(236\) −18.5883 −1.21000
\(237\) 4.01072 0.260524
\(238\) 0.383412 0.0248529
\(239\) 22.0754 1.42794 0.713970 0.700177i \(-0.246895\pi\)
0.713970 + 0.700177i \(0.246895\pi\)
\(240\) 3.84679 0.248309
\(241\) −15.7971 −1.01758 −0.508790 0.860890i \(-0.669907\pi\)
−0.508790 + 0.860890i \(0.669907\pi\)
\(242\) −1.30796 −0.0840787
\(243\) −13.4196 −0.860869
\(244\) 17.9189 1.14714
\(245\) −1.68817 −0.107853
\(246\) −0.408405 −0.0260390
\(247\) 0 0
\(248\) 2.25349 0.143097
\(249\) −0.330381 −0.0209370
\(250\) 1.45281 0.0918838
\(251\) 22.5567 1.42376 0.711882 0.702299i \(-0.247843\pi\)
0.711882 + 0.702299i \(0.247843\pi\)
\(252\) −5.28332 −0.332818
\(253\) 1.85343 0.116524
\(254\) 0.970981 0.0609247
\(255\) −3.13141 −0.196097
\(256\) 14.8536 0.928352
\(257\) 20.4129 1.27332 0.636660 0.771145i \(-0.280315\pi\)
0.636660 + 0.771145i \(0.280315\pi\)
\(258\) 0.0541839 0.00337334
\(259\) −6.31584 −0.392447
\(260\) 0 0
\(261\) −21.8107 −1.35005
\(262\) 2.27527 0.140567
\(263\) −29.5402 −1.82153 −0.910764 0.412927i \(-0.864506\pi\)
−0.910764 + 0.412927i \(0.864506\pi\)
\(264\) −0.101846 −0.00626820
\(265\) −2.31464 −0.142187
\(266\) −0.173789 −0.0106557
\(267\) 0.663193 0.0405867
\(268\) −26.7567 −1.63442
\(269\) 27.9163 1.70209 0.851043 0.525096i \(-0.175971\pi\)
0.851043 + 0.525096i \(0.175971\pi\)
\(270\) −0.669770 −0.0407609
\(271\) −29.4491 −1.78890 −0.894451 0.447165i \(-0.852434\pi\)
−0.894451 + 0.447165i \(0.852434\pi\)
\(272\) −12.4660 −0.755861
\(273\) 0 0
\(274\) −2.19362 −0.132521
\(275\) 0.783965 0.0472748
\(276\) −5.87695 −0.353751
\(277\) 6.85854 0.412090 0.206045 0.978543i \(-0.433941\pi\)
0.206045 + 0.978543i \(0.433941\pi\)
\(278\) 0.631992 0.0379043
\(279\) 12.5004 0.748381
\(280\) −0.809806 −0.0483952
\(281\) 29.0940 1.73561 0.867803 0.496909i \(-0.165532\pi\)
0.867803 + 0.496909i \(0.165532\pi\)
\(282\) −0.896420 −0.0533810
\(283\) 11.6102 0.690156 0.345078 0.938574i \(-0.387853\pi\)
0.345078 + 0.938574i \(0.387853\pi\)
\(284\) 14.0597 0.834291
\(285\) 1.41937 0.0840761
\(286\) 0 0
\(287\) −5.82732 −0.343976
\(288\) −3.80619 −0.224282
\(289\) −6.85229 −0.403076
\(290\) −1.66545 −0.0977985
\(291\) −4.61633 −0.270614
\(292\) 4.29035 0.251074
\(293\) 17.7886 1.03922 0.519610 0.854403i \(-0.326077\pi\)
0.519610 + 0.854403i \(0.326077\pi\)
\(294\) −0.0700846 −0.00408742
\(295\) −15.8046 −0.920177
\(296\) −3.02968 −0.176097
\(297\) −1.20190 −0.0697412
\(298\) 1.11611 0.0646544
\(299\) 0 0
\(300\) −2.48583 −0.143520
\(301\) 0.773122 0.0445620
\(302\) −1.68663 −0.0970546
\(303\) 9.05257 0.520057
\(304\) 5.65043 0.324074
\(305\) 15.2354 0.872378
\(306\) 1.02024 0.0583230
\(307\) −9.07966 −0.518204 −0.259102 0.965850i \(-0.583427\pi\)
−0.259102 + 0.965850i \(0.583427\pi\)
\(308\) −0.723954 −0.0412511
\(309\) −5.99654 −0.341131
\(310\) 0.954525 0.0542134
\(311\) 1.57073 0.0890677 0.0445338 0.999008i \(-0.485820\pi\)
0.0445338 + 0.999008i \(0.485820\pi\)
\(312\) 0 0
\(313\) 20.6232 1.16569 0.582846 0.812582i \(-0.301939\pi\)
0.582846 + 0.812582i \(0.301939\pi\)
\(314\) −2.06808 −0.116709
\(315\) −4.49210 −0.253101
\(316\) 13.6758 0.769327
\(317\) 30.5435 1.71549 0.857747 0.514072i \(-0.171863\pi\)
0.857747 + 0.514072i \(0.171863\pi\)
\(318\) −0.0960927 −0.00538861
\(319\) −2.98863 −0.167331
\(320\) 12.9219 0.722358
\(321\) 7.64223 0.426548
\(322\) 0.611815 0.0340951
\(323\) −4.59964 −0.255931
\(324\) −12.0389 −0.668830
\(325\) 0 0
\(326\) −1.41937 −0.0786118
\(327\) −6.08256 −0.336366
\(328\) −2.79534 −0.154347
\(329\) −12.7905 −0.705165
\(330\) −0.0431396 −0.00237476
\(331\) −25.8531 −1.42101 −0.710507 0.703690i \(-0.751534\pi\)
−0.710507 + 0.703690i \(0.751534\pi\)
\(332\) −1.12654 −0.0618269
\(333\) −16.8060 −0.920965
\(334\) 0.519578 0.0284300
\(335\) −22.7496 −1.24294
\(336\) 2.27868 0.124312
\(337\) 21.3954 1.16548 0.582742 0.812657i \(-0.301980\pi\)
0.582742 + 0.812657i \(0.301980\pi\)
\(338\) 0 0
\(339\) −2.88387 −0.156630
\(340\) −10.6776 −0.579072
\(341\) 1.71289 0.0927580
\(342\) −0.462440 −0.0250059
\(343\) −1.00000 −0.0539949
\(344\) 0.370863 0.0199956
\(345\) −4.99682 −0.269020
\(346\) 1.50687 0.0810098
\(347\) 2.20883 0.118576 0.0592882 0.998241i \(-0.481117\pi\)
0.0592882 + 0.998241i \(0.481117\pi\)
\(348\) 9.47651 0.507994
\(349\) −11.2912 −0.604402 −0.302201 0.953244i \(-0.597721\pi\)
−0.302201 + 0.953244i \(0.597721\pi\)
\(350\) 0.258786 0.0138327
\(351\) 0 0
\(352\) −0.521548 −0.0277986
\(353\) 35.6433 1.89710 0.948552 0.316623i \(-0.102549\pi\)
0.948552 + 0.316623i \(0.102549\pi\)
\(354\) −0.656130 −0.0348729
\(355\) 11.9542 0.634461
\(356\) 2.26137 0.119852
\(357\) −1.85492 −0.0981727
\(358\) −0.793815 −0.0419544
\(359\) −19.3218 −1.01976 −0.509882 0.860244i \(-0.670311\pi\)
−0.509882 + 0.860244i \(0.670311\pi\)
\(360\) −2.15484 −0.113570
\(361\) −16.9151 −0.890270
\(362\) 1.32585 0.0696851
\(363\) 6.32780 0.332123
\(364\) 0 0
\(365\) 3.64783 0.190936
\(366\) 0.632502 0.0330614
\(367\) −3.72065 −0.194216 −0.0971082 0.995274i \(-0.530959\pi\)
−0.0971082 + 0.995274i \(0.530959\pi\)
\(368\) −19.8921 −1.03695
\(369\) −15.5061 −0.807217
\(370\) −1.28330 −0.0667155
\(371\) −1.37110 −0.0711837
\(372\) −5.43130 −0.281600
\(373\) −3.51276 −0.181884 −0.0909420 0.995856i \(-0.528988\pi\)
−0.0909420 + 0.995856i \(0.528988\pi\)
\(374\) 0.139799 0.00722884
\(375\) −7.02858 −0.362954
\(376\) −6.13557 −0.316418
\(377\) 0 0
\(378\) −0.396744 −0.0204063
\(379\) −25.0163 −1.28500 −0.642500 0.766285i \(-0.722103\pi\)
−0.642500 + 0.766285i \(0.722103\pi\)
\(380\) 4.83980 0.248276
\(381\) −4.69753 −0.240662
\(382\) 0.713990 0.0365309
\(383\) −22.4654 −1.14793 −0.573964 0.818881i \(-0.694595\pi\)
−0.573964 + 0.818881i \(0.694595\pi\)
\(384\) 2.20227 0.112384
\(385\) −0.615536 −0.0313706
\(386\) 0.505024 0.0257051
\(387\) 2.05723 0.104575
\(388\) −15.7409 −0.799121
\(389\) −13.3364 −0.676184 −0.338092 0.941113i \(-0.609781\pi\)
−0.338092 + 0.941113i \(0.609781\pi\)
\(390\) 0 0
\(391\) 16.1928 0.818906
\(392\) −0.479696 −0.0242283
\(393\) −11.0076 −0.555259
\(394\) −0.696274 −0.0350778
\(395\) 11.6278 0.585057
\(396\) −1.92640 −0.0968050
\(397\) 25.8333 1.29654 0.648268 0.761412i \(-0.275494\pi\)
0.648268 + 0.761412i \(0.275494\pi\)
\(398\) 1.43948 0.0721544
\(399\) 0.840776 0.0420914
\(400\) −8.41396 −0.420698
\(401\) 17.5605 0.876930 0.438465 0.898748i \(-0.355522\pi\)
0.438465 + 0.898748i \(0.355522\pi\)
\(402\) −0.944456 −0.0471052
\(403\) 0 0
\(404\) 30.8677 1.53572
\(405\) −10.2360 −0.508631
\(406\) −0.986544 −0.0489613
\(407\) −2.30287 −0.114149
\(408\) −0.889797 −0.0440515
\(409\) 14.5282 0.718373 0.359186 0.933266i \(-0.383054\pi\)
0.359186 + 0.933266i \(0.383054\pi\)
\(410\) −1.18404 −0.0584755
\(411\) 10.6126 0.523479
\(412\) −20.4471 −1.00736
\(413\) −9.36197 −0.460672
\(414\) 1.62800 0.0800119
\(415\) −0.957831 −0.0470181
\(416\) 0 0
\(417\) −3.05753 −0.149728
\(418\) −0.0633664 −0.00309935
\(419\) −4.60192 −0.224819 −0.112409 0.993662i \(-0.535857\pi\)
−0.112409 + 0.993662i \(0.535857\pi\)
\(420\) 1.95177 0.0952366
\(421\) −19.2645 −0.938895 −0.469447 0.882960i \(-0.655547\pi\)
−0.469447 + 0.882960i \(0.655547\pi\)
\(422\) −0.991273 −0.0482544
\(423\) −34.0348 −1.65483
\(424\) −0.657709 −0.0319412
\(425\) 6.84924 0.332237
\(426\) 0.496280 0.0240448
\(427\) 9.02484 0.436743
\(428\) 26.0587 1.25959
\(429\) 0 0
\(430\) 0.157089 0.00757548
\(431\) 28.3651 1.36630 0.683149 0.730279i \(-0.260610\pi\)
0.683149 + 0.730279i \(0.260610\pi\)
\(432\) 12.8995 0.620625
\(433\) −12.5203 −0.601686 −0.300843 0.953674i \(-0.597268\pi\)
−0.300843 + 0.953674i \(0.597268\pi\)
\(434\) 0.565421 0.0271411
\(435\) 8.05732 0.386319
\(436\) −20.7405 −0.993288
\(437\) −7.33969 −0.351105
\(438\) 0.151441 0.00723611
\(439\) 31.7273 1.51426 0.757132 0.653262i \(-0.226600\pi\)
0.757132 + 0.653262i \(0.226600\pi\)
\(440\) −0.295270 −0.0140764
\(441\) −2.66094 −0.126711
\(442\) 0 0
\(443\) 1.73048 0.0822177 0.0411088 0.999155i \(-0.486911\pi\)
0.0411088 + 0.999155i \(0.486911\pi\)
\(444\) 7.30205 0.346540
\(445\) 1.92271 0.0911452
\(446\) −1.84168 −0.0872062
\(447\) −5.39965 −0.255394
\(448\) 7.65442 0.361637
\(449\) 10.5564 0.498186 0.249093 0.968480i \(-0.419868\pi\)
0.249093 + 0.968480i \(0.419868\pi\)
\(450\) 0.688612 0.0324615
\(451\) −2.12475 −0.100050
\(452\) −9.83349 −0.462528
\(453\) 8.15978 0.383380
\(454\) −0.837063 −0.0392853
\(455\) 0 0
\(456\) 0.403317 0.0188870
\(457\) 7.94894 0.371836 0.185918 0.982565i \(-0.440474\pi\)
0.185918 + 0.982565i \(0.440474\pi\)
\(458\) 3.30050 0.154222
\(459\) −10.5006 −0.490125
\(460\) −17.0383 −0.794415
\(461\) 10.8918 0.507284 0.253642 0.967298i \(-0.418371\pi\)
0.253642 + 0.967298i \(0.418371\pi\)
\(462\) −0.0255541 −0.00118889
\(463\) 35.8227 1.66482 0.832411 0.554158i \(-0.186960\pi\)
0.832411 + 0.554158i \(0.186960\pi\)
\(464\) 32.0757 1.48908
\(465\) −4.61792 −0.214151
\(466\) −0.824866 −0.0382112
\(467\) 19.8983 0.920785 0.460393 0.887715i \(-0.347709\pi\)
0.460393 + 0.887715i \(0.347709\pi\)
\(468\) 0 0
\(469\) −13.4759 −0.622261
\(470\) −2.59888 −0.119877
\(471\) 10.0052 0.461017
\(472\) −4.49090 −0.206710
\(473\) 0.281894 0.0129615
\(474\) 0.482730 0.0221725
\(475\) −3.10454 −0.142446
\(476\) −6.32495 −0.289904
\(477\) −3.64840 −0.167049
\(478\) 2.65699 0.121528
\(479\) 26.2902 1.20123 0.600615 0.799538i \(-0.294922\pi\)
0.600615 + 0.799538i \(0.294922\pi\)
\(480\) 1.40609 0.0641788
\(481\) 0 0
\(482\) −1.90134 −0.0866035
\(483\) −2.95991 −0.134681
\(484\) 21.5767 0.980758
\(485\) −13.3835 −0.607715
\(486\) −1.61518 −0.0732662
\(487\) 6.37962 0.289088 0.144544 0.989498i \(-0.453828\pi\)
0.144544 + 0.989498i \(0.453828\pi\)
\(488\) 4.32918 0.195973
\(489\) 6.86682 0.310528
\(490\) −0.203187 −0.00917907
\(491\) −2.96768 −0.133929 −0.0669647 0.997755i \(-0.521331\pi\)
−0.0669647 + 0.997755i \(0.521331\pi\)
\(492\) 6.73725 0.303739
\(493\) −26.1107 −1.17597
\(494\) 0 0
\(495\) −1.63790 −0.0736182
\(496\) −18.3837 −0.825452
\(497\) 7.08115 0.317633
\(498\) −0.0397646 −0.00178189
\(499\) −28.1331 −1.25941 −0.629704 0.776835i \(-0.716824\pi\)
−0.629704 + 0.776835i \(0.716824\pi\)
\(500\) −23.9662 −1.07180
\(501\) −2.51368 −0.112303
\(502\) 2.71492 0.121173
\(503\) −31.5376 −1.40619 −0.703097 0.711094i \(-0.748200\pi\)
−0.703097 + 0.711094i \(0.748200\pi\)
\(504\) −1.27644 −0.0568572
\(505\) 26.2450 1.16789
\(506\) 0.223079 0.00991706
\(507\) 0 0
\(508\) −16.0178 −0.710673
\(509\) −13.5944 −0.602560 −0.301280 0.953536i \(-0.597414\pi\)
−0.301280 + 0.953536i \(0.597414\pi\)
\(510\) −0.376896 −0.0166892
\(511\) 2.16083 0.0955893
\(512\) 9.35193 0.413301
\(513\) 4.75958 0.210140
\(514\) 2.45689 0.108369
\(515\) −17.3850 −0.766074
\(516\) −0.893844 −0.0393493
\(517\) −4.66366 −0.205108
\(518\) −0.760173 −0.0334001
\(519\) −7.29012 −0.320001
\(520\) 0 0
\(521\) 8.78344 0.384810 0.192405 0.981316i \(-0.438371\pi\)
0.192405 + 0.981316i \(0.438371\pi\)
\(522\) −2.62513 −0.114899
\(523\) 32.5698 1.42418 0.712088 0.702090i \(-0.247749\pi\)
0.712088 + 0.702090i \(0.247749\pi\)
\(524\) −37.5339 −1.63968
\(525\) −1.25198 −0.0546411
\(526\) −3.55546 −0.155025
\(527\) 14.9649 0.651882
\(528\) 0.830847 0.0361580
\(529\) 2.83905 0.123437
\(530\) −0.278589 −0.0121011
\(531\) −24.9116 −1.08107
\(532\) 2.86690 0.124296
\(533\) 0 0
\(534\) 0.0798218 0.00345423
\(535\) 22.1561 0.957894
\(536\) −6.46435 −0.279218
\(537\) 3.84041 0.165726
\(538\) 3.36000 0.144860
\(539\) −0.364618 −0.0157052
\(540\) 11.0488 0.475467
\(541\) 6.94870 0.298748 0.149374 0.988781i \(-0.452274\pi\)
0.149374 + 0.988781i \(0.452274\pi\)
\(542\) −3.54448 −0.152249
\(543\) −6.41436 −0.275266
\(544\) −4.55659 −0.195362
\(545\) −17.6344 −0.755375
\(546\) 0 0
\(547\) 10.9095 0.466457 0.233229 0.972422i \(-0.425071\pi\)
0.233229 + 0.972422i \(0.425071\pi\)
\(548\) 36.1870 1.54583
\(549\) 24.0145 1.02491
\(550\) 0.0943579 0.00402343
\(551\) 11.8352 0.504194
\(552\) −1.41986 −0.0604332
\(553\) 6.88781 0.292900
\(554\) 0.825493 0.0350718
\(555\) 6.20850 0.263536
\(556\) −10.4256 −0.442145
\(557\) 34.6295 1.46730 0.733650 0.679527i \(-0.237815\pi\)
0.733650 + 0.679527i \(0.237815\pi\)
\(558\) 1.50455 0.0636927
\(559\) 0 0
\(560\) 6.60628 0.279166
\(561\) −0.676337 −0.0285550
\(562\) 3.50176 0.147713
\(563\) 9.13679 0.385070 0.192535 0.981290i \(-0.438329\pi\)
0.192535 + 0.981290i \(0.438329\pi\)
\(564\) 14.7878 0.622677
\(565\) −8.36084 −0.351743
\(566\) 1.39740 0.0587373
\(567\) −6.06339 −0.254638
\(568\) 3.39680 0.142527
\(569\) 18.3000 0.767176 0.383588 0.923504i \(-0.374688\pi\)
0.383588 + 0.923504i \(0.374688\pi\)
\(570\) 0.170835 0.00715549
\(571\) 10.1791 0.425981 0.212990 0.977054i \(-0.431680\pi\)
0.212990 + 0.977054i \(0.431680\pi\)
\(572\) 0 0
\(573\) −3.45423 −0.144303
\(574\) −0.701376 −0.0292748
\(575\) 10.9294 0.455788
\(576\) 20.3679 0.848663
\(577\) 19.5165 0.812482 0.406241 0.913766i \(-0.366839\pi\)
0.406241 + 0.913766i \(0.366839\pi\)
\(578\) −0.824740 −0.0343047
\(579\) −2.44327 −0.101539
\(580\) 27.4740 1.14080
\(581\) −0.567380 −0.0235389
\(582\) −0.555621 −0.0230312
\(583\) −0.499926 −0.0207048
\(584\) 1.03654 0.0428923
\(585\) 0 0
\(586\) 2.14103 0.0884453
\(587\) 35.3900 1.46070 0.730351 0.683072i \(-0.239357\pi\)
0.730351 + 0.683072i \(0.239357\pi\)
\(588\) 1.15615 0.0476788
\(589\) −6.78312 −0.279494
\(590\) −1.90223 −0.0783137
\(591\) 3.36852 0.138562
\(592\) 24.7157 1.01581
\(593\) 18.0881 0.742790 0.371395 0.928475i \(-0.378880\pi\)
0.371395 + 0.928475i \(0.378880\pi\)
\(594\) −0.144660 −0.00593548
\(595\) −5.37773 −0.220465
\(596\) −18.4118 −0.754179
\(597\) −6.96407 −0.285021
\(598\) 0 0
\(599\) 9.05992 0.370178 0.185089 0.982722i \(-0.440743\pi\)
0.185089 + 0.982722i \(0.440743\pi\)
\(600\) −0.600572 −0.0245182
\(601\) 29.2881 1.19469 0.597343 0.801986i \(-0.296223\pi\)
0.597343 + 0.801986i \(0.296223\pi\)
\(602\) 0.0930528 0.00379255
\(603\) −35.8586 −1.46028
\(604\) 27.8234 1.13212
\(605\) 18.3454 0.745846
\(606\) 1.08957 0.0442606
\(607\) −39.3650 −1.59777 −0.798887 0.601481i \(-0.794578\pi\)
−0.798887 + 0.601481i \(0.794578\pi\)
\(608\) 2.06536 0.0837613
\(609\) 4.77282 0.193405
\(610\) 1.83373 0.0742457
\(611\) 0 0
\(612\) −16.8303 −0.680324
\(613\) −5.53316 −0.223482 −0.111741 0.993737i \(-0.535643\pi\)
−0.111741 + 0.993737i \(0.535643\pi\)
\(614\) −1.09283 −0.0441029
\(615\) 5.72829 0.230987
\(616\) −0.174906 −0.00704716
\(617\) 12.5815 0.506514 0.253257 0.967399i \(-0.418498\pi\)
0.253257 + 0.967399i \(0.418498\pi\)
\(618\) −0.721742 −0.0290327
\(619\) −22.3955 −0.900149 −0.450075 0.892991i \(-0.648603\pi\)
−0.450075 + 0.892991i \(0.648603\pi\)
\(620\) −15.7463 −0.632386
\(621\) −16.7559 −0.672390
\(622\) 0.189052 0.00758031
\(623\) 1.13893 0.0456305
\(624\) 0 0
\(625\) −9.62659 −0.385064
\(626\) 2.48221 0.0992090
\(627\) 0.306562 0.0122429
\(628\) 34.1161 1.36138
\(629\) −20.1194 −0.802213
\(630\) −0.540669 −0.0215408
\(631\) −1.94888 −0.0775836 −0.0387918 0.999247i \(-0.512351\pi\)
−0.0387918 + 0.999247i \(0.512351\pi\)
\(632\) 3.30406 0.131428
\(633\) 4.79570 0.190612
\(634\) 3.67621 0.146001
\(635\) −13.6190 −0.540452
\(636\) 1.58519 0.0628569
\(637\) 0 0
\(638\) −0.359712 −0.0142411
\(639\) 18.8425 0.745397
\(640\) 6.38477 0.252380
\(641\) 10.4210 0.411605 0.205803 0.978594i \(-0.434019\pi\)
0.205803 + 0.978594i \(0.434019\pi\)
\(642\) 0.919818 0.0363023
\(643\) 15.2706 0.602214 0.301107 0.953590i \(-0.402644\pi\)
0.301107 + 0.953590i \(0.402644\pi\)
\(644\) −10.0928 −0.397712
\(645\) −0.759983 −0.0299243
\(646\) −0.553612 −0.0217816
\(647\) 17.5066 0.688254 0.344127 0.938923i \(-0.388175\pi\)
0.344127 + 0.938923i \(0.388175\pi\)
\(648\) −2.90858 −0.114260
\(649\) −3.41354 −0.133993
\(650\) 0 0
\(651\) −2.73547 −0.107211
\(652\) 23.4147 0.916989
\(653\) −10.1834 −0.398506 −0.199253 0.979948i \(-0.563852\pi\)
−0.199253 + 0.979948i \(0.563852\pi\)
\(654\) −0.732096 −0.0286272
\(655\) −31.9129 −1.24694
\(656\) 22.8040 0.890346
\(657\) 5.74982 0.224322
\(658\) −1.53947 −0.0600147
\(659\) −43.8587 −1.70849 −0.854247 0.519867i \(-0.825981\pi\)
−0.854247 + 0.519867i \(0.825981\pi\)
\(660\) 0.711651 0.0277010
\(661\) −32.9270 −1.28071 −0.640356 0.768078i \(-0.721213\pi\)
−0.640356 + 0.768078i \(0.721213\pi\)
\(662\) −3.11167 −0.120939
\(663\) 0 0
\(664\) −0.272170 −0.0105622
\(665\) 2.43755 0.0945243
\(666\) −2.02277 −0.0783808
\(667\) −41.6651 −1.61328
\(668\) −8.57120 −0.331630
\(669\) 8.90992 0.344478
\(670\) −2.73814 −0.105784
\(671\) 3.29062 0.127033
\(672\) 0.832908 0.0321301
\(673\) 26.6845 1.02861 0.514307 0.857606i \(-0.328049\pi\)
0.514307 + 0.857606i \(0.328049\pi\)
\(674\) 2.57515 0.0991912
\(675\) −7.08740 −0.272794
\(676\) 0 0
\(677\) 29.5328 1.13504 0.567519 0.823361i \(-0.307904\pi\)
0.567519 + 0.823361i \(0.307904\pi\)
\(678\) −0.347102 −0.0133304
\(679\) −7.92785 −0.304243
\(680\) −2.57968 −0.0989261
\(681\) 4.04965 0.155183
\(682\) 0.206163 0.00789438
\(683\) 18.2880 0.699771 0.349885 0.936793i \(-0.386221\pi\)
0.349885 + 0.936793i \(0.386221\pi\)
\(684\) 7.62863 0.291688
\(685\) 30.7676 1.17557
\(686\) −0.120360 −0.00459536
\(687\) −15.9676 −0.609200
\(688\) −3.02545 −0.115344
\(689\) 0 0
\(690\) −0.601417 −0.0228956
\(691\) 10.3406 0.393376 0.196688 0.980466i \(-0.436981\pi\)
0.196688 + 0.980466i \(0.436981\pi\)
\(692\) −24.8580 −0.944961
\(693\) −0.970225 −0.0368558
\(694\) 0.265855 0.0100917
\(695\) −8.86430 −0.336242
\(696\) 2.28950 0.0867834
\(697\) −18.5632 −0.703131
\(698\) −1.35900 −0.0514390
\(699\) 3.99064 0.150940
\(700\) −4.26905 −0.161355
\(701\) −41.6959 −1.57483 −0.787415 0.616423i \(-0.788581\pi\)
−0.787415 + 0.616423i \(0.788581\pi\)
\(702\) 0 0
\(703\) 9.11948 0.343948
\(704\) 2.79094 0.105188
\(705\) 12.5732 0.473533
\(706\) 4.29003 0.161457
\(707\) 15.5464 0.584684
\(708\) 10.8238 0.406784
\(709\) −0.0109463 −0.000411095 0 −0.000205548 1.00000i \(-0.500065\pi\)
−0.000205548 1.00000i \(0.500065\pi\)
\(710\) 1.43880 0.0539972
\(711\) 18.3280 0.687355
\(712\) 0.546342 0.0204750
\(713\) 23.8797 0.894301
\(714\) −0.223258 −0.00835521
\(715\) 0 0
\(716\) 13.0951 0.489388
\(717\) −12.8543 −0.480054
\(718\) −2.32557 −0.0867894
\(719\) −25.4660 −0.949722 −0.474861 0.880061i \(-0.657502\pi\)
−0.474861 + 0.880061i \(0.657502\pi\)
\(720\) 17.5789 0.655127
\(721\) −10.2982 −0.383523
\(722\) −2.03590 −0.0757685
\(723\) 9.19853 0.342097
\(724\) −21.8718 −0.812860
\(725\) −17.6235 −0.654521
\(726\) 0.761613 0.0282661
\(727\) 23.5565 0.873663 0.436831 0.899543i \(-0.356101\pi\)
0.436831 + 0.899543i \(0.356101\pi\)
\(728\) 0 0
\(729\) −10.3760 −0.384297
\(730\) 0.439053 0.0162501
\(731\) 2.46282 0.0910905
\(732\) −10.4341 −0.385654
\(733\) 6.23249 0.230202 0.115101 0.993354i \(-0.463281\pi\)
0.115101 + 0.993354i \(0.463281\pi\)
\(734\) −0.447817 −0.0165292
\(735\) 0.983005 0.0362587
\(736\) −7.27100 −0.268013
\(737\) −4.91357 −0.180994
\(738\) −1.86632 −0.0687000
\(739\) 1.29718 0.0477174 0.0238587 0.999715i \(-0.492405\pi\)
0.0238587 + 0.999715i \(0.492405\pi\)
\(740\) 21.1699 0.778221
\(741\) 0 0
\(742\) −0.165025 −0.00605825
\(743\) −6.06942 −0.222665 −0.111333 0.993783i \(-0.535512\pi\)
−0.111333 + 0.993783i \(0.535512\pi\)
\(744\) −1.31219 −0.0481073
\(745\) −15.6545 −0.573537
\(746\) −0.422796 −0.0154797
\(747\) −1.50976 −0.0552393
\(748\) −2.30619 −0.0843227
\(749\) 13.1244 0.479555
\(750\) −0.845960 −0.0308901
\(751\) −36.6046 −1.33572 −0.667860 0.744287i \(-0.732790\pi\)
−0.667860 + 0.744287i \(0.732790\pi\)
\(752\) 50.0531 1.82525
\(753\) −13.1346 −0.478650
\(754\) 0 0
\(755\) 23.6566 0.860952
\(756\) 6.54488 0.238035
\(757\) 11.6798 0.424510 0.212255 0.977214i \(-0.431919\pi\)
0.212255 + 0.977214i \(0.431919\pi\)
\(758\) −3.01096 −0.109363
\(759\) −1.07924 −0.0391739
\(760\) 1.16928 0.0424144
\(761\) 39.7688 1.44162 0.720810 0.693133i \(-0.243770\pi\)
0.720810 + 0.693133i \(0.243770\pi\)
\(762\) −0.565394 −0.0204821
\(763\) −10.4459 −0.378167
\(764\) −11.7783 −0.426125
\(765\) −14.3098 −0.517372
\(766\) −2.70393 −0.0976970
\(767\) 0 0
\(768\) −8.64915 −0.312099
\(769\) 9.95937 0.359144 0.179572 0.983745i \(-0.442529\pi\)
0.179572 + 0.983745i \(0.442529\pi\)
\(770\) −0.0740858 −0.00266987
\(771\) −11.8863 −0.428073
\(772\) −8.33112 −0.299843
\(773\) 12.7518 0.458649 0.229324 0.973350i \(-0.426348\pi\)
0.229324 + 0.973350i \(0.426348\pi\)
\(774\) 0.247608 0.00890007
\(775\) 10.1006 0.362825
\(776\) −3.80296 −0.136518
\(777\) 3.67766 0.131935
\(778\) −1.60517 −0.0575482
\(779\) 8.41411 0.301467
\(780\) 0 0
\(781\) 2.58192 0.0923882
\(782\) 1.94897 0.0696949
\(783\) 27.0186 0.965568
\(784\) 3.91329 0.139760
\(785\) 29.0069 1.03530
\(786\) −1.32487 −0.0472566
\(787\) −8.68773 −0.309684 −0.154842 0.987939i \(-0.549487\pi\)
−0.154842 + 0.987939i \(0.549487\pi\)
\(788\) 11.4861 0.409174
\(789\) 17.2010 0.612373
\(790\) 1.39952 0.0497926
\(791\) −4.95262 −0.176095
\(792\) −0.465413 −0.0165377
\(793\) 0 0
\(794\) 3.10929 0.110345
\(795\) 1.34779 0.0478013
\(796\) −23.7463 −0.841664
\(797\) 38.7438 1.37237 0.686187 0.727425i \(-0.259283\pi\)
0.686187 + 0.727425i \(0.259283\pi\)
\(798\) 0.101196 0.00358229
\(799\) −40.7449 −1.44145
\(800\) −3.07549 −0.108735
\(801\) 3.03063 0.107082
\(802\) 2.11358 0.0746331
\(803\) 0.787876 0.0278036
\(804\) 15.5802 0.549471
\(805\) −8.58130 −0.302451
\(806\) 0 0
\(807\) −16.2554 −0.572218
\(808\) 7.45757 0.262356
\(809\) 28.8550 1.01449 0.507244 0.861802i \(-0.330664\pi\)
0.507244 + 0.861802i \(0.330664\pi\)
\(810\) −1.23200 −0.0432882
\(811\) −12.3917 −0.435131 −0.217566 0.976046i \(-0.569812\pi\)
−0.217566 + 0.976046i \(0.569812\pi\)
\(812\) 16.2745 0.571123
\(813\) 17.1479 0.601405
\(814\) −0.277173 −0.00971491
\(815\) 19.9081 0.697351
\(816\) 7.25884 0.254110
\(817\) −1.11632 −0.0390549
\(818\) 1.74861 0.0611388
\(819\) 0 0
\(820\) 19.5324 0.682103
\(821\) −41.0238 −1.43174 −0.715870 0.698233i \(-0.753970\pi\)
−0.715870 + 0.698233i \(0.753970\pi\)
\(822\) 1.27733 0.0445519
\(823\) −2.13613 −0.0744608 −0.0372304 0.999307i \(-0.511854\pi\)
−0.0372304 + 0.999307i \(0.511854\pi\)
\(824\) −4.93999 −0.172093
\(825\) −0.456496 −0.0158932
\(826\) −1.12681 −0.0392066
\(827\) −8.54938 −0.297291 −0.148645 0.988891i \(-0.547491\pi\)
−0.148645 + 0.988891i \(0.547491\pi\)
\(828\) −26.8563 −0.933320
\(829\) −14.7569 −0.512528 −0.256264 0.966607i \(-0.582492\pi\)
−0.256264 + 0.966607i \(0.582492\pi\)
\(830\) −0.115284 −0.00400158
\(831\) −3.99367 −0.138539
\(832\) 0 0
\(833\) −3.18555 −0.110373
\(834\) −0.368004 −0.0127429
\(835\) −7.28758 −0.252197
\(836\) 1.04532 0.0361532
\(837\) −15.4853 −0.535250
\(838\) −0.553887 −0.0191337
\(839\) −26.9716 −0.931164 −0.465582 0.885005i \(-0.654155\pi\)
−0.465582 + 0.885005i \(0.654155\pi\)
\(840\) 0.471544 0.0162698
\(841\) 38.1845 1.31671
\(842\) −2.31867 −0.0799068
\(843\) −16.9412 −0.583487
\(844\) 16.3525 0.562877
\(845\) 0 0
\(846\) −4.09643 −0.140838
\(847\) 10.8671 0.373396
\(848\) 5.36549 0.184252
\(849\) −6.76053 −0.232021
\(850\) 0.824374 0.0282758
\(851\) −32.1047 −1.10054
\(852\) −8.18686 −0.280477
\(853\) −25.6332 −0.877665 −0.438832 0.898569i \(-0.644608\pi\)
−0.438832 + 0.898569i \(0.644608\pi\)
\(854\) 1.08623 0.0371700
\(855\) 6.48618 0.221823
\(856\) 6.29572 0.215183
\(857\) 11.7653 0.401894 0.200947 0.979602i \(-0.435598\pi\)
0.200947 + 0.979602i \(0.435598\pi\)
\(858\) 0 0
\(859\) −21.7761 −0.742992 −0.371496 0.928435i \(-0.621155\pi\)
−0.371496 + 0.928435i \(0.621155\pi\)
\(860\) −2.59141 −0.0883663
\(861\) 3.39320 0.115640
\(862\) 3.41402 0.116282
\(863\) 41.0575 1.39761 0.698807 0.715310i \(-0.253715\pi\)
0.698807 + 0.715310i \(0.253715\pi\)
\(864\) 4.71504 0.160409
\(865\) −21.1353 −0.718623
\(866\) −1.50694 −0.0512079
\(867\) 3.99003 0.135509
\(868\) −9.32746 −0.316594
\(869\) 2.51142 0.0851942
\(870\) 0.969778 0.0328785
\(871\) 0 0
\(872\) −5.01085 −0.169689
\(873\) −21.0955 −0.713975
\(874\) −0.883404 −0.0298816
\(875\) −12.0705 −0.408059
\(876\) −2.49824 −0.0844076
\(877\) 6.89112 0.232696 0.116348 0.993208i \(-0.462881\pi\)
0.116348 + 0.993208i \(0.462881\pi\)
\(878\) 3.81870 0.128875
\(879\) −10.3582 −0.349372
\(880\) 2.40877 0.0811996
\(881\) −10.6458 −0.358665 −0.179332 0.983789i \(-0.557394\pi\)
−0.179332 + 0.983789i \(0.557394\pi\)
\(882\) −0.320270 −0.0107841
\(883\) −21.3844 −0.719641 −0.359821 0.933022i \(-0.617162\pi\)
−0.359821 + 0.933022i \(0.617162\pi\)
\(884\) 0 0
\(885\) 9.20286 0.309351
\(886\) 0.208281 0.00699732
\(887\) −34.1150 −1.14547 −0.572735 0.819740i \(-0.694118\pi\)
−0.572735 + 0.819740i \(0.694118\pi\)
\(888\) 1.76416 0.0592013
\(889\) −8.06731 −0.270569
\(890\) 0.231417 0.00775712
\(891\) −2.21082 −0.0740653
\(892\) 30.3813 1.01724
\(893\) 18.4684 0.618020
\(894\) −0.649901 −0.0217359
\(895\) 11.1340 0.372169
\(896\) 3.78208 0.126350
\(897\) 0 0
\(898\) 1.27056 0.0423992
\(899\) −38.5057 −1.28424
\(900\) −11.3597 −0.378655
\(901\) −4.36769 −0.145509
\(902\) −0.255734 −0.00851502
\(903\) −0.450183 −0.0149811
\(904\) −2.37575 −0.0790163
\(905\) −18.5963 −0.618163
\(906\) 0.982110 0.0326284
\(907\) 42.1515 1.39962 0.699810 0.714329i \(-0.253268\pi\)
0.699810 + 0.714329i \(0.253268\pi\)
\(908\) 13.8086 0.458254
\(909\) 41.3681 1.37209
\(910\) 0 0
\(911\) 20.9947 0.695584 0.347792 0.937572i \(-0.386932\pi\)
0.347792 + 0.937572i \(0.386932\pi\)
\(912\) −3.29020 −0.108949
\(913\) −0.206877 −0.00684663
\(914\) 0.956734 0.0316459
\(915\) −8.87147 −0.293282
\(916\) −54.4466 −1.79897
\(917\) −18.9039 −0.624261
\(918\) −1.26385 −0.0417132
\(919\) −14.2940 −0.471515 −0.235757 0.971812i \(-0.575757\pi\)
−0.235757 + 0.971812i \(0.575757\pi\)
\(920\) −4.11642 −0.135714
\(921\) 5.28701 0.174213
\(922\) 1.31094 0.0431736
\(923\) 0 0
\(924\) 0.421553 0.0138681
\(925\) −13.5797 −0.446497
\(926\) 4.31162 0.141689
\(927\) −27.4027 −0.900024
\(928\) 11.7244 0.384872
\(929\) 6.80723 0.223338 0.111669 0.993745i \(-0.464380\pi\)
0.111669 + 0.993745i \(0.464380\pi\)
\(930\) −0.555812 −0.0182258
\(931\) 1.44391 0.0473221
\(932\) 13.6074 0.445724
\(933\) −0.914621 −0.0299433
\(934\) 2.39496 0.0783655
\(935\) −1.96082 −0.0641256
\(936\) 0 0
\(937\) −5.22890 −0.170821 −0.0854104 0.996346i \(-0.527220\pi\)
−0.0854104 + 0.996346i \(0.527220\pi\)
\(938\) −1.62196 −0.0529590
\(939\) −12.0087 −0.391890
\(940\) 42.8723 1.39834
\(941\) −56.4403 −1.83990 −0.919951 0.392033i \(-0.871772\pi\)
−0.919951 + 0.392033i \(0.871772\pi\)
\(942\) 1.20423 0.0392359
\(943\) −29.6215 −0.964609
\(944\) 36.6361 1.19240
\(945\) 5.56473 0.181021
\(946\) 0.0339287 0.00110312
\(947\) −5.85027 −0.190108 −0.0950541 0.995472i \(-0.530302\pi\)
−0.0950541 + 0.995472i \(0.530302\pi\)
\(948\) −7.96334 −0.258637
\(949\) 0 0
\(950\) −0.373662 −0.0121232
\(951\) −17.7852 −0.576726
\(952\) −1.52809 −0.0495258
\(953\) −21.7484 −0.704499 −0.352249 0.935906i \(-0.614583\pi\)
−0.352249 + 0.935906i \(0.614583\pi\)
\(954\) −0.439121 −0.0142171
\(955\) −10.0144 −0.324059
\(956\) −43.8310 −1.41760
\(957\) 1.74026 0.0562546
\(958\) 3.16429 0.102233
\(959\) 18.2255 0.588532
\(960\) −7.52433 −0.242847
\(961\) −8.93110 −0.288100
\(962\) 0 0
\(963\) 34.9232 1.12538
\(964\) 31.3654 1.01021
\(965\) −7.08346 −0.228025
\(966\) −0.356255 −0.0114623
\(967\) 13.3251 0.428507 0.214253 0.976778i \(-0.431268\pi\)
0.214253 + 0.976778i \(0.431268\pi\)
\(968\) 5.21288 0.167548
\(969\) 2.67833 0.0860404
\(970\) −1.61084 −0.0517210
\(971\) 7.46185 0.239462 0.119731 0.992806i \(-0.461797\pi\)
0.119731 + 0.992806i \(0.461797\pi\)
\(972\) 26.6448 0.854633
\(973\) −5.25085 −0.168335
\(974\) 0.767850 0.0246035
\(975\) 0 0
\(976\) −35.3168 −1.13046
\(977\) 10.9605 0.350656 0.175328 0.984510i \(-0.443901\pi\)
0.175328 + 0.984510i \(0.443901\pi\)
\(978\) 0.826490 0.0264282
\(979\) 0.415276 0.0132723
\(980\) 3.35188 0.107072
\(981\) −27.7959 −0.887453
\(982\) −0.357189 −0.0113984
\(983\) −16.1441 −0.514918 −0.257459 0.966289i \(-0.582885\pi\)
−0.257459 + 0.966289i \(0.582885\pi\)
\(984\) 1.62771 0.0518893
\(985\) 9.76593 0.311168
\(986\) −3.14268 −0.100083
\(987\) 7.44783 0.237067
\(988\) 0 0
\(989\) 3.92994 0.124965
\(990\) −0.197138 −0.00626544
\(991\) 6.71496 0.213308 0.106654 0.994296i \(-0.465986\pi\)
0.106654 + 0.994296i \(0.465986\pi\)
\(992\) −6.71965 −0.213349
\(993\) 15.0540 0.477725
\(994\) 0.852287 0.0270329
\(995\) −20.1901 −0.640068
\(996\) 0.655975 0.0207854
\(997\) −18.4411 −0.584037 −0.292018 0.956413i \(-0.594327\pi\)
−0.292018 + 0.956413i \(0.594327\pi\)
\(998\) −3.38609 −0.107185
\(999\) 20.8190 0.658684
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 1183.2.a.p.1.3 6
7.6 odd 2 8281.2.a.ch.1.3 6
13.5 odd 4 1183.2.c.i.337.6 12
13.6 odd 12 91.2.q.a.36.3 12
13.8 odd 4 1183.2.c.i.337.7 12
13.11 odd 12 91.2.q.a.43.3 yes 12
13.12 even 2 1183.2.a.m.1.4 6
39.11 even 12 819.2.ct.a.316.4 12
39.32 even 12 819.2.ct.a.127.4 12
52.11 even 12 1456.2.cc.c.225.3 12
52.19 even 12 1456.2.cc.c.673.3 12
91.6 even 12 637.2.q.h.491.3 12
91.11 odd 12 637.2.u.h.30.4 12
91.19 even 12 637.2.u.i.361.4 12
91.24 even 12 637.2.u.i.30.4 12
91.32 odd 12 637.2.k.h.569.3 12
91.37 odd 12 637.2.k.h.459.4 12
91.45 even 12 637.2.k.g.569.3 12
91.58 odd 12 637.2.u.h.361.4 12
91.76 even 12 637.2.q.h.589.3 12
91.89 even 12 637.2.k.g.459.4 12
91.90 odd 2 8281.2.a.by.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.3 12 13.6 odd 12
91.2.q.a.43.3 yes 12 13.11 odd 12
637.2.k.g.459.4 12 91.89 even 12
637.2.k.g.569.3 12 91.45 even 12
637.2.k.h.459.4 12 91.37 odd 12
637.2.k.h.569.3 12 91.32 odd 12
637.2.q.h.491.3 12 91.6 even 12
637.2.q.h.589.3 12 91.76 even 12
637.2.u.h.30.4 12 91.11 odd 12
637.2.u.h.361.4 12 91.58 odd 12
637.2.u.i.30.4 12 91.24 even 12
637.2.u.i.361.4 12 91.19 even 12
819.2.ct.a.127.4 12 39.32 even 12
819.2.ct.a.316.4 12 39.11 even 12
1183.2.a.m.1.4 6 13.12 even 2
1183.2.a.p.1.3 6 1.1 even 1 trivial
1183.2.c.i.337.6 12 13.5 odd 4
1183.2.c.i.337.7 12 13.8 odd 4
1456.2.cc.c.225.3 12 52.11 even 12
1456.2.cc.c.673.3 12 52.19 even 12
8281.2.a.by.1.4 6 91.90 odd 2
8281.2.a.ch.1.3 6 7.6 odd 2