Properties

Label 6003.2.a.m.1.3
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.24285\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24285 q^{2} +3.03039 q^{4} -3.33222 q^{5} +0.336371 q^{7} -2.31101 q^{8} +O(q^{10})\) \(q-2.24285 q^{2} +3.03039 q^{4} -3.33222 q^{5} +0.336371 q^{7} -2.31101 q^{8} +7.47368 q^{10} -5.35570 q^{11} -2.46960 q^{13} -0.754431 q^{14} -0.877521 q^{16} -3.61233 q^{17} -5.53686 q^{19} -10.0979 q^{20} +12.0120 q^{22} -1.00000 q^{23} +6.10369 q^{25} +5.53895 q^{26} +1.01934 q^{28} +1.00000 q^{29} +8.47832 q^{31} +6.59017 q^{32} +8.10192 q^{34} -1.12086 q^{35} +9.55887 q^{37} +12.4184 q^{38} +7.70079 q^{40} +11.0317 q^{41} +3.41828 q^{43} -16.2299 q^{44} +2.24285 q^{46} +9.57079 q^{47} -6.88685 q^{49} -13.6897 q^{50} -7.48385 q^{52} +6.66459 q^{53} +17.8464 q^{55} -0.777358 q^{56} -2.24285 q^{58} +1.21308 q^{59} +7.12445 q^{61} -19.0156 q^{62} -13.0257 q^{64} +8.22926 q^{65} +5.16723 q^{67} -10.9468 q^{68} +2.51393 q^{70} -2.09303 q^{71} -10.2973 q^{73} -21.4391 q^{74} -16.7788 q^{76} -1.80150 q^{77} -3.62841 q^{79} +2.92409 q^{80} -24.7426 q^{82} -12.6742 q^{83} +12.0371 q^{85} -7.66669 q^{86} +12.3771 q^{88} -11.8040 q^{89} -0.830703 q^{91} -3.03039 q^{92} -21.4659 q^{94} +18.4500 q^{95} -3.01739 q^{97} +15.4462 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24285 −1.58594 −0.792968 0.609263i \(-0.791465\pi\)
−0.792968 + 0.609263i \(0.791465\pi\)
\(3\) 0 0
\(4\) 3.03039 1.51519
\(5\) −3.33222 −1.49021 −0.745107 0.666945i \(-0.767602\pi\)
−0.745107 + 0.666945i \(0.767602\pi\)
\(6\) 0 0
\(7\) 0.336371 0.127136 0.0635682 0.997977i \(-0.479752\pi\)
0.0635682 + 0.997977i \(0.479752\pi\)
\(8\) −2.31101 −0.817066
\(9\) 0 0
\(10\) 7.47368 2.36338
\(11\) −5.35570 −1.61480 −0.807402 0.590001i \(-0.799127\pi\)
−0.807402 + 0.590001i \(0.799127\pi\)
\(12\) 0 0
\(13\) −2.46960 −0.684944 −0.342472 0.939528i \(-0.611264\pi\)
−0.342472 + 0.939528i \(0.611264\pi\)
\(14\) −0.754431 −0.201630
\(15\) 0 0
\(16\) −0.877521 −0.219380
\(17\) −3.61233 −0.876118 −0.438059 0.898946i \(-0.644334\pi\)
−0.438059 + 0.898946i \(0.644334\pi\)
\(18\) 0 0
\(19\) −5.53686 −1.27024 −0.635121 0.772413i \(-0.719050\pi\)
−0.635121 + 0.772413i \(0.719050\pi\)
\(20\) −10.0979 −2.25796
\(21\) 0 0
\(22\) 12.0120 2.56098
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 6.10369 1.22074
\(26\) 5.53895 1.08628
\(27\) 0 0
\(28\) 1.01934 0.192636
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 8.47832 1.52275 0.761376 0.648311i \(-0.224524\pi\)
0.761376 + 0.648311i \(0.224524\pi\)
\(32\) 6.59017 1.16499
\(33\) 0 0
\(34\) 8.10192 1.38947
\(35\) −1.12086 −0.189460
\(36\) 0 0
\(37\) 9.55887 1.57147 0.785734 0.618565i \(-0.212285\pi\)
0.785734 + 0.618565i \(0.212285\pi\)
\(38\) 12.4184 2.01452
\(39\) 0 0
\(40\) 7.70079 1.21760
\(41\) 11.0317 1.72287 0.861434 0.507870i \(-0.169567\pi\)
0.861434 + 0.507870i \(0.169567\pi\)
\(42\) 0 0
\(43\) 3.41828 0.521282 0.260641 0.965436i \(-0.416066\pi\)
0.260641 + 0.965436i \(0.416066\pi\)
\(44\) −16.2299 −2.44674
\(45\) 0 0
\(46\) 2.24285 0.330691
\(47\) 9.57079 1.39604 0.698022 0.716077i \(-0.254064\pi\)
0.698022 + 0.716077i \(0.254064\pi\)
\(48\) 0 0
\(49\) −6.88685 −0.983836
\(50\) −13.6897 −1.93601
\(51\) 0 0
\(52\) −7.48385 −1.03782
\(53\) 6.66459 0.915452 0.457726 0.889093i \(-0.348664\pi\)
0.457726 + 0.889093i \(0.348664\pi\)
\(54\) 0 0
\(55\) 17.8464 2.40640
\(56\) −0.777358 −0.103879
\(57\) 0 0
\(58\) −2.24285 −0.294501
\(59\) 1.21308 0.157930 0.0789650 0.996877i \(-0.474838\pi\)
0.0789650 + 0.996877i \(0.474838\pi\)
\(60\) 0 0
\(61\) 7.12445 0.912193 0.456096 0.889930i \(-0.349247\pi\)
0.456096 + 0.889930i \(0.349247\pi\)
\(62\) −19.0156 −2.41499
\(63\) 0 0
\(64\) −13.0257 −1.62822
\(65\) 8.22926 1.02071
\(66\) 0 0
\(67\) 5.16723 0.631278 0.315639 0.948879i \(-0.397781\pi\)
0.315639 + 0.948879i \(0.397781\pi\)
\(68\) −10.9468 −1.32749
\(69\) 0 0
\(70\) 2.51393 0.300472
\(71\) −2.09303 −0.248397 −0.124199 0.992257i \(-0.539636\pi\)
−0.124199 + 0.992257i \(0.539636\pi\)
\(72\) 0 0
\(73\) −10.2973 −1.20520 −0.602602 0.798042i \(-0.705869\pi\)
−0.602602 + 0.798042i \(0.705869\pi\)
\(74\) −21.4391 −2.49225
\(75\) 0 0
\(76\) −16.7788 −1.92466
\(77\) −1.80150 −0.205300
\(78\) 0 0
\(79\) −3.62841 −0.408229 −0.204114 0.978947i \(-0.565431\pi\)
−0.204114 + 0.978947i \(0.565431\pi\)
\(80\) 2.92409 0.326924
\(81\) 0 0
\(82\) −24.7426 −2.73236
\(83\) −12.6742 −1.39117 −0.695587 0.718442i \(-0.744856\pi\)
−0.695587 + 0.718442i \(0.744856\pi\)
\(84\) 0 0
\(85\) 12.0371 1.30560
\(86\) −7.66669 −0.826721
\(87\) 0 0
\(88\) 12.3771 1.31940
\(89\) −11.8040 −1.25122 −0.625611 0.780135i \(-0.715150\pi\)
−0.625611 + 0.780135i \(0.715150\pi\)
\(90\) 0 0
\(91\) −0.830703 −0.0870814
\(92\) −3.03039 −0.315940
\(93\) 0 0
\(94\) −21.4659 −2.21404
\(95\) 18.4500 1.89293
\(96\) 0 0
\(97\) −3.01739 −0.306369 −0.153185 0.988198i \(-0.548953\pi\)
−0.153185 + 0.988198i \(0.548953\pi\)
\(98\) 15.4462 1.56030
\(99\) 0 0
\(100\) 18.4966 1.84966
\(101\) 16.5824 1.65001 0.825007 0.565122i \(-0.191171\pi\)
0.825007 + 0.565122i \(0.191171\pi\)
\(102\) 0 0
\(103\) 6.41290 0.631882 0.315941 0.948779i \(-0.397680\pi\)
0.315941 + 0.948779i \(0.397680\pi\)
\(104\) 5.70728 0.559644
\(105\) 0 0
\(106\) −14.9477 −1.45185
\(107\) −13.1923 −1.27535 −0.637673 0.770307i \(-0.720103\pi\)
−0.637673 + 0.770307i \(0.720103\pi\)
\(108\) 0 0
\(109\) −10.5087 −1.00655 −0.503274 0.864127i \(-0.667871\pi\)
−0.503274 + 0.864127i \(0.667871\pi\)
\(110\) −40.0268 −3.81640
\(111\) 0 0
\(112\) −0.295173 −0.0278912
\(113\) −3.10892 −0.292462 −0.146231 0.989250i \(-0.546714\pi\)
−0.146231 + 0.989250i \(0.546714\pi\)
\(114\) 0 0
\(115\) 3.33222 0.310731
\(116\) 3.03039 0.281365
\(117\) 0 0
\(118\) −2.72077 −0.250467
\(119\) −1.21508 −0.111387
\(120\) 0 0
\(121\) 17.6835 1.60759
\(122\) −15.9791 −1.44668
\(123\) 0 0
\(124\) 25.6926 2.30726
\(125\) −3.67774 −0.328947
\(126\) 0 0
\(127\) 14.8180 1.31489 0.657443 0.753504i \(-0.271638\pi\)
0.657443 + 0.753504i \(0.271638\pi\)
\(128\) 16.0345 1.41726
\(129\) 0 0
\(130\) −18.4570 −1.61879
\(131\) −2.63363 −0.230102 −0.115051 0.993360i \(-0.536703\pi\)
−0.115051 + 0.993360i \(0.536703\pi\)
\(132\) 0 0
\(133\) −1.86244 −0.161494
\(134\) −11.5893 −1.00117
\(135\) 0 0
\(136\) 8.34813 0.715846
\(137\) 11.2822 0.963901 0.481951 0.876198i \(-0.339928\pi\)
0.481951 + 0.876198i \(0.339928\pi\)
\(138\) 0 0
\(139\) 3.55731 0.301727 0.150863 0.988555i \(-0.451795\pi\)
0.150863 + 0.988555i \(0.451795\pi\)
\(140\) −3.39665 −0.287069
\(141\) 0 0
\(142\) 4.69437 0.393942
\(143\) 13.2264 1.10605
\(144\) 0 0
\(145\) −3.33222 −0.276726
\(146\) 23.0952 1.91138
\(147\) 0 0
\(148\) 28.9671 2.38108
\(149\) −14.5948 −1.19565 −0.597827 0.801625i \(-0.703969\pi\)
−0.597827 + 0.801625i \(0.703969\pi\)
\(150\) 0 0
\(151\) 18.5847 1.51240 0.756202 0.654338i \(-0.227053\pi\)
0.756202 + 0.654338i \(0.227053\pi\)
\(152\) 12.7957 1.03787
\(153\) 0 0
\(154\) 4.04051 0.325593
\(155\) −28.2516 −2.26923
\(156\) 0 0
\(157\) −9.26130 −0.739132 −0.369566 0.929204i \(-0.620494\pi\)
−0.369566 + 0.929204i \(0.620494\pi\)
\(158\) 8.13800 0.647425
\(159\) 0 0
\(160\) −21.9599 −1.73608
\(161\) −0.336371 −0.0265098
\(162\) 0 0
\(163\) −21.2102 −1.66131 −0.830655 0.556788i \(-0.812034\pi\)
−0.830655 + 0.556788i \(0.812034\pi\)
\(164\) 33.4304 2.61048
\(165\) 0 0
\(166\) 28.4264 2.20631
\(167\) 21.3627 1.65310 0.826549 0.562865i \(-0.190301\pi\)
0.826549 + 0.562865i \(0.190301\pi\)
\(168\) 0 0
\(169\) −6.90107 −0.530851
\(170\) −26.9974 −2.07060
\(171\) 0 0
\(172\) 10.3587 0.789844
\(173\) 10.6746 0.811578 0.405789 0.913967i \(-0.366997\pi\)
0.405789 + 0.913967i \(0.366997\pi\)
\(174\) 0 0
\(175\) 2.05311 0.155200
\(176\) 4.69974 0.354256
\(177\) 0 0
\(178\) 26.4746 1.98436
\(179\) 2.48471 0.185716 0.0928579 0.995679i \(-0.470400\pi\)
0.0928579 + 0.995679i \(0.470400\pi\)
\(180\) 0 0
\(181\) −10.3160 −0.766784 −0.383392 0.923586i \(-0.625244\pi\)
−0.383392 + 0.923586i \(0.625244\pi\)
\(182\) 1.86315 0.138106
\(183\) 0 0
\(184\) 2.31101 0.170370
\(185\) −31.8522 −2.34182
\(186\) 0 0
\(187\) 19.3466 1.41476
\(188\) 29.0032 2.11528
\(189\) 0 0
\(190\) −41.3807 −3.00207
\(191\) 21.4183 1.54977 0.774886 0.632101i \(-0.217807\pi\)
0.774886 + 0.632101i \(0.217807\pi\)
\(192\) 0 0
\(193\) −13.7870 −0.992409 −0.496204 0.868206i \(-0.665273\pi\)
−0.496204 + 0.868206i \(0.665273\pi\)
\(194\) 6.76756 0.485882
\(195\) 0 0
\(196\) −20.8698 −1.49070
\(197\) 15.4879 1.10347 0.551735 0.834019i \(-0.313966\pi\)
0.551735 + 0.834019i \(0.313966\pi\)
\(198\) 0 0
\(199\) 4.97074 0.352367 0.176183 0.984357i \(-0.443625\pi\)
0.176183 + 0.984357i \(0.443625\pi\)
\(200\) −14.1057 −0.997423
\(201\) 0 0
\(202\) −37.1920 −2.61682
\(203\) 0.336371 0.0236086
\(204\) 0 0
\(205\) −36.7602 −2.56744
\(206\) −14.3832 −1.00212
\(207\) 0 0
\(208\) 2.16713 0.150263
\(209\) 29.6537 2.05119
\(210\) 0 0
\(211\) −26.1099 −1.79748 −0.898739 0.438484i \(-0.855516\pi\)
−0.898739 + 0.438484i \(0.855516\pi\)
\(212\) 20.1963 1.38709
\(213\) 0 0
\(214\) 29.5883 2.02262
\(215\) −11.3905 −0.776823
\(216\) 0 0
\(217\) 2.85186 0.193597
\(218\) 23.5694 1.59632
\(219\) 0 0
\(220\) 54.0814 3.64617
\(221\) 8.92101 0.600092
\(222\) 0 0
\(223\) −8.28206 −0.554608 −0.277304 0.960782i \(-0.589441\pi\)
−0.277304 + 0.960782i \(0.589441\pi\)
\(224\) 2.21675 0.148113
\(225\) 0 0
\(226\) 6.97284 0.463826
\(227\) 15.0362 0.997985 0.498992 0.866606i \(-0.333704\pi\)
0.498992 + 0.866606i \(0.333704\pi\)
\(228\) 0 0
\(229\) −9.35622 −0.618277 −0.309138 0.951017i \(-0.600041\pi\)
−0.309138 + 0.951017i \(0.600041\pi\)
\(230\) −7.47368 −0.492800
\(231\) 0 0
\(232\) −2.31101 −0.151725
\(233\) −1.51916 −0.0995233 −0.0497616 0.998761i \(-0.515846\pi\)
−0.0497616 + 0.998761i \(0.515846\pi\)
\(234\) 0 0
\(235\) −31.8920 −2.08040
\(236\) 3.67612 0.239295
\(237\) 0 0
\(238\) 2.72525 0.176652
\(239\) 13.1287 0.849225 0.424612 0.905375i \(-0.360410\pi\)
0.424612 + 0.905375i \(0.360410\pi\)
\(240\) 0 0
\(241\) 26.0253 1.67644 0.838218 0.545335i \(-0.183598\pi\)
0.838218 + 0.545335i \(0.183598\pi\)
\(242\) −39.6616 −2.54954
\(243\) 0 0
\(244\) 21.5899 1.38215
\(245\) 22.9485 1.46613
\(246\) 0 0
\(247\) 13.6738 0.870045
\(248\) −19.5935 −1.24419
\(249\) 0 0
\(250\) 8.24863 0.521689
\(251\) −24.1425 −1.52386 −0.761932 0.647657i \(-0.775749\pi\)
−0.761932 + 0.647657i \(0.775749\pi\)
\(252\) 0 0
\(253\) 5.35570 0.336710
\(254\) −33.2346 −2.08533
\(255\) 0 0
\(256\) −9.91149 −0.619468
\(257\) −23.1679 −1.44518 −0.722588 0.691279i \(-0.757048\pi\)
−0.722588 + 0.691279i \(0.757048\pi\)
\(258\) 0 0
\(259\) 3.21533 0.199791
\(260\) 24.9378 1.54658
\(261\) 0 0
\(262\) 5.90685 0.364927
\(263\) −11.8107 −0.728277 −0.364138 0.931345i \(-0.618636\pi\)
−0.364138 + 0.931345i \(0.618636\pi\)
\(264\) 0 0
\(265\) −22.2079 −1.36422
\(266\) 4.17718 0.256119
\(267\) 0 0
\(268\) 15.6587 0.956508
\(269\) 8.58123 0.523207 0.261603 0.965175i \(-0.415749\pi\)
0.261603 + 0.965175i \(0.415749\pi\)
\(270\) 0 0
\(271\) −11.0288 −0.669952 −0.334976 0.942227i \(-0.608728\pi\)
−0.334976 + 0.942227i \(0.608728\pi\)
\(272\) 3.16990 0.192203
\(273\) 0 0
\(274\) −25.3043 −1.52869
\(275\) −32.6895 −1.97125
\(276\) 0 0
\(277\) 9.78001 0.587624 0.293812 0.955863i \(-0.405076\pi\)
0.293812 + 0.955863i \(0.405076\pi\)
\(278\) −7.97851 −0.478520
\(279\) 0 0
\(280\) 2.59033 0.154802
\(281\) 2.79284 0.166607 0.0833034 0.996524i \(-0.473453\pi\)
0.0833034 + 0.996524i \(0.473453\pi\)
\(282\) 0 0
\(283\) −22.6337 −1.34544 −0.672718 0.739899i \(-0.734873\pi\)
−0.672718 + 0.739899i \(0.734873\pi\)
\(284\) −6.34270 −0.376370
\(285\) 0 0
\(286\) −29.6650 −1.75413
\(287\) 3.71076 0.219039
\(288\) 0 0
\(289\) −3.95108 −0.232417
\(290\) 7.47368 0.438870
\(291\) 0 0
\(292\) −31.2047 −1.82612
\(293\) −26.9534 −1.57463 −0.787316 0.616550i \(-0.788530\pi\)
−0.787316 + 0.616550i \(0.788530\pi\)
\(294\) 0 0
\(295\) −4.04226 −0.235350
\(296\) −22.0906 −1.28399
\(297\) 0 0
\(298\) 32.7340 1.89623
\(299\) 2.46960 0.142821
\(300\) 0 0
\(301\) 1.14981 0.0662740
\(302\) −41.6828 −2.39858
\(303\) 0 0
\(304\) 4.85871 0.278666
\(305\) −23.7402 −1.35936
\(306\) 0 0
\(307\) 10.5081 0.599727 0.299863 0.953982i \(-0.403059\pi\)
0.299863 + 0.953982i \(0.403059\pi\)
\(308\) −5.45926 −0.311070
\(309\) 0 0
\(310\) 63.3643 3.59885
\(311\) −31.8702 −1.80719 −0.903596 0.428385i \(-0.859083\pi\)
−0.903596 + 0.428385i \(0.859083\pi\)
\(312\) 0 0
\(313\) −21.3092 −1.20446 −0.602232 0.798321i \(-0.705722\pi\)
−0.602232 + 0.798321i \(0.705722\pi\)
\(314\) 20.7717 1.17222
\(315\) 0 0
\(316\) −10.9955 −0.618546
\(317\) −13.6193 −0.764935 −0.382467 0.923969i \(-0.624926\pi\)
−0.382467 + 0.923969i \(0.624926\pi\)
\(318\) 0 0
\(319\) −5.35570 −0.299862
\(320\) 43.4046 2.42639
\(321\) 0 0
\(322\) 0.754431 0.0420428
\(323\) 20.0009 1.11288
\(324\) 0 0
\(325\) −15.0737 −0.836138
\(326\) 47.5713 2.63473
\(327\) 0 0
\(328\) −25.4945 −1.40770
\(329\) 3.21934 0.177488
\(330\) 0 0
\(331\) −8.92149 −0.490370 −0.245185 0.969476i \(-0.578849\pi\)
−0.245185 + 0.969476i \(0.578849\pi\)
\(332\) −38.4078 −2.10790
\(333\) 0 0
\(334\) −47.9135 −2.62171
\(335\) −17.2183 −0.940739
\(336\) 0 0
\(337\) 6.68953 0.364402 0.182201 0.983261i \(-0.441678\pi\)
0.182201 + 0.983261i \(0.441678\pi\)
\(338\) 15.4781 0.841896
\(339\) 0 0
\(340\) 36.4770 1.97824
\(341\) −45.4074 −2.45895
\(342\) 0 0
\(343\) −4.67114 −0.252218
\(344\) −7.89968 −0.425922
\(345\) 0 0
\(346\) −23.9416 −1.28711
\(347\) 10.4807 0.562635 0.281317 0.959615i \(-0.409229\pi\)
0.281317 + 0.959615i \(0.409229\pi\)
\(348\) 0 0
\(349\) −21.7281 −1.16308 −0.581538 0.813519i \(-0.697549\pi\)
−0.581538 + 0.813519i \(0.697549\pi\)
\(350\) −4.60482 −0.246138
\(351\) 0 0
\(352\) −35.2950 −1.88123
\(353\) 24.6326 1.31106 0.655530 0.755169i \(-0.272445\pi\)
0.655530 + 0.755169i \(0.272445\pi\)
\(354\) 0 0
\(355\) 6.97445 0.370165
\(356\) −35.7707 −1.89584
\(357\) 0 0
\(358\) −5.57284 −0.294534
\(359\) 5.00818 0.264322 0.132161 0.991228i \(-0.457808\pi\)
0.132161 + 0.991228i \(0.457808\pi\)
\(360\) 0 0
\(361\) 11.6568 0.613515
\(362\) 23.1373 1.21607
\(363\) 0 0
\(364\) −2.51735 −0.131945
\(365\) 34.3127 1.79601
\(366\) 0 0
\(367\) −5.98074 −0.312192 −0.156096 0.987742i \(-0.549891\pi\)
−0.156096 + 0.987742i \(0.549891\pi\)
\(368\) 0.877521 0.0457440
\(369\) 0 0
\(370\) 71.4399 3.71398
\(371\) 2.24178 0.116387
\(372\) 0 0
\(373\) 25.9060 1.34136 0.670680 0.741747i \(-0.266002\pi\)
0.670680 + 0.741747i \(0.266002\pi\)
\(374\) −43.3915 −2.24372
\(375\) 0 0
\(376\) −22.1182 −1.14066
\(377\) −2.46960 −0.127191
\(378\) 0 0
\(379\) 34.7368 1.78431 0.892155 0.451729i \(-0.149193\pi\)
0.892155 + 0.451729i \(0.149193\pi\)
\(380\) 55.9107 2.86816
\(381\) 0 0
\(382\) −48.0380 −2.45784
\(383\) 22.0435 1.12637 0.563184 0.826331i \(-0.309576\pi\)
0.563184 + 0.826331i \(0.309576\pi\)
\(384\) 0 0
\(385\) 6.00301 0.305942
\(386\) 30.9222 1.57390
\(387\) 0 0
\(388\) −9.14386 −0.464209
\(389\) 10.7238 0.543716 0.271858 0.962337i \(-0.412362\pi\)
0.271858 + 0.962337i \(0.412362\pi\)
\(390\) 0 0
\(391\) 3.61233 0.182683
\(392\) 15.9156 0.803859
\(393\) 0 0
\(394\) −34.7372 −1.75003
\(395\) 12.0907 0.608348
\(396\) 0 0
\(397\) −7.85754 −0.394358 −0.197179 0.980367i \(-0.563178\pi\)
−0.197179 + 0.980367i \(0.563178\pi\)
\(398\) −11.1486 −0.558831
\(399\) 0 0
\(400\) −5.35612 −0.267806
\(401\) −15.0606 −0.752089 −0.376044 0.926602i \(-0.622716\pi\)
−0.376044 + 0.926602i \(0.622716\pi\)
\(402\) 0 0
\(403\) −20.9381 −1.04300
\(404\) 50.2512 2.50009
\(405\) 0 0
\(406\) −0.754431 −0.0374418
\(407\) −51.1944 −2.53761
\(408\) 0 0
\(409\) 29.3347 1.45051 0.725253 0.688483i \(-0.241723\pi\)
0.725253 + 0.688483i \(0.241723\pi\)
\(410\) 82.4476 4.07180
\(411\) 0 0
\(412\) 19.4336 0.957424
\(413\) 0.408047 0.0200787
\(414\) 0 0
\(415\) 42.2332 2.07315
\(416\) −16.2751 −0.797952
\(417\) 0 0
\(418\) −66.5090 −3.25306
\(419\) 28.4982 1.39223 0.696114 0.717931i \(-0.254911\pi\)
0.696114 + 0.717931i \(0.254911\pi\)
\(420\) 0 0
\(421\) 13.1838 0.642540 0.321270 0.946988i \(-0.395890\pi\)
0.321270 + 0.946988i \(0.395890\pi\)
\(422\) 58.5606 2.85069
\(423\) 0 0
\(424\) −15.4019 −0.747984
\(425\) −22.0485 −1.06951
\(426\) 0 0
\(427\) 2.39646 0.115973
\(428\) −39.9777 −1.93240
\(429\) 0 0
\(430\) 25.5471 1.23199
\(431\) −21.0595 −1.01440 −0.507200 0.861829i \(-0.669319\pi\)
−0.507200 + 0.861829i \(0.669319\pi\)
\(432\) 0 0
\(433\) −29.6426 −1.42453 −0.712267 0.701909i \(-0.752331\pi\)
−0.712267 + 0.701909i \(0.752331\pi\)
\(434\) −6.39631 −0.307033
\(435\) 0 0
\(436\) −31.8454 −1.52512
\(437\) 5.53686 0.264864
\(438\) 0 0
\(439\) 18.1064 0.864171 0.432086 0.901833i \(-0.357778\pi\)
0.432086 + 0.901833i \(0.357778\pi\)
\(440\) −41.2432 −1.96619
\(441\) 0 0
\(442\) −20.0085 −0.951708
\(443\) −20.7008 −0.983527 −0.491763 0.870729i \(-0.663647\pi\)
−0.491763 + 0.870729i \(0.663647\pi\)
\(444\) 0 0
\(445\) 39.3335 1.86459
\(446\) 18.5754 0.879573
\(447\) 0 0
\(448\) −4.38149 −0.207006
\(449\) 13.6101 0.642301 0.321150 0.947028i \(-0.395931\pi\)
0.321150 + 0.947028i \(0.395931\pi\)
\(450\) 0 0
\(451\) −59.0827 −2.78209
\(452\) −9.42122 −0.443137
\(453\) 0 0
\(454\) −33.7239 −1.58274
\(455\) 2.76809 0.129770
\(456\) 0 0
\(457\) 4.36067 0.203984 0.101992 0.994785i \(-0.467478\pi\)
0.101992 + 0.994785i \(0.467478\pi\)
\(458\) 20.9846 0.980548
\(459\) 0 0
\(460\) 10.0979 0.470818
\(461\) −1.61989 −0.0754459 −0.0377230 0.999288i \(-0.512010\pi\)
−0.0377230 + 0.999288i \(0.512010\pi\)
\(462\) 0 0
\(463\) −0.152373 −0.00708136 −0.00354068 0.999994i \(-0.501127\pi\)
−0.00354068 + 0.999994i \(0.501127\pi\)
\(464\) −0.877521 −0.0407379
\(465\) 0 0
\(466\) 3.40725 0.157838
\(467\) −25.7057 −1.18952 −0.594758 0.803904i \(-0.702752\pi\)
−0.594758 + 0.803904i \(0.702752\pi\)
\(468\) 0 0
\(469\) 1.73811 0.0802584
\(470\) 71.5290 3.29939
\(471\) 0 0
\(472\) −2.80345 −0.129039
\(473\) −18.3073 −0.841769
\(474\) 0 0
\(475\) −33.7953 −1.55063
\(476\) −3.68218 −0.168772
\(477\) 0 0
\(478\) −29.4457 −1.34682
\(479\) −5.89195 −0.269210 −0.134605 0.990899i \(-0.542977\pi\)
−0.134605 + 0.990899i \(0.542977\pi\)
\(480\) 0 0
\(481\) −23.6066 −1.07637
\(482\) −58.3709 −2.65872
\(483\) 0 0
\(484\) 53.5880 2.43582
\(485\) 10.0546 0.456556
\(486\) 0 0
\(487\) −31.3733 −1.42166 −0.710831 0.703363i \(-0.751681\pi\)
−0.710831 + 0.703363i \(0.751681\pi\)
\(488\) −16.4647 −0.745321
\(489\) 0 0
\(490\) −51.4701 −2.32518
\(491\) −2.87963 −0.129956 −0.0649778 0.997887i \(-0.520698\pi\)
−0.0649778 + 0.997887i \(0.520698\pi\)
\(492\) 0 0
\(493\) −3.61233 −0.162691
\(494\) −30.6684 −1.37984
\(495\) 0 0
\(496\) −7.43991 −0.334062
\(497\) −0.704036 −0.0315804
\(498\) 0 0
\(499\) 43.8494 1.96297 0.981484 0.191542i \(-0.0613489\pi\)
0.981484 + 0.191542i \(0.0613489\pi\)
\(500\) −11.1450 −0.498419
\(501\) 0 0
\(502\) 54.1482 2.41675
\(503\) 41.9172 1.86900 0.934498 0.355969i \(-0.115849\pi\)
0.934498 + 0.355969i \(0.115849\pi\)
\(504\) 0 0
\(505\) −55.2563 −2.45887
\(506\) −12.0120 −0.534001
\(507\) 0 0
\(508\) 44.9044 1.99231
\(509\) 15.4761 0.685966 0.342983 0.939342i \(-0.388563\pi\)
0.342983 + 0.939342i \(0.388563\pi\)
\(510\) 0 0
\(511\) −3.46370 −0.153225
\(512\) −9.83894 −0.434824
\(513\) 0 0
\(514\) 51.9623 2.29196
\(515\) −21.3692 −0.941640
\(516\) 0 0
\(517\) −51.2583 −2.25434
\(518\) −7.21151 −0.316856
\(519\) 0 0
\(520\) −19.0179 −0.833990
\(521\) −1.20679 −0.0528705 −0.0264352 0.999651i \(-0.508416\pi\)
−0.0264352 + 0.999651i \(0.508416\pi\)
\(522\) 0 0
\(523\) −8.84819 −0.386905 −0.193452 0.981110i \(-0.561968\pi\)
−0.193452 + 0.981110i \(0.561968\pi\)
\(524\) −7.98094 −0.348649
\(525\) 0 0
\(526\) 26.4896 1.15500
\(527\) −30.6265 −1.33411
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 49.8090 2.16357
\(531\) 0 0
\(532\) −5.64392 −0.244695
\(533\) −27.2440 −1.18007
\(534\) 0 0
\(535\) 43.9596 1.90054
\(536\) −11.9415 −0.515795
\(537\) 0 0
\(538\) −19.2464 −0.829772
\(539\) 36.8839 1.58870
\(540\) 0 0
\(541\) 22.1794 0.953567 0.476783 0.879021i \(-0.341803\pi\)
0.476783 + 0.879021i \(0.341803\pi\)
\(542\) 24.7360 1.06250
\(543\) 0 0
\(544\) −23.8059 −1.02067
\(545\) 35.0172 1.49997
\(546\) 0 0
\(547\) 22.7728 0.973697 0.486848 0.873486i \(-0.338146\pi\)
0.486848 + 0.873486i \(0.338146\pi\)
\(548\) 34.1894 1.46050
\(549\) 0 0
\(550\) 73.3178 3.12628
\(551\) −5.53686 −0.235878
\(552\) 0 0
\(553\) −1.22049 −0.0519007
\(554\) −21.9351 −0.931934
\(555\) 0 0
\(556\) 10.7800 0.457175
\(557\) −0.846399 −0.0358631 −0.0179315 0.999839i \(-0.505708\pi\)
−0.0179315 + 0.999839i \(0.505708\pi\)
\(558\) 0 0
\(559\) −8.44179 −0.357049
\(560\) 0.983582 0.0415639
\(561\) 0 0
\(562\) −6.26393 −0.264228
\(563\) 40.0831 1.68930 0.844650 0.535318i \(-0.179808\pi\)
0.844650 + 0.535318i \(0.179808\pi\)
\(564\) 0 0
\(565\) 10.3596 0.435831
\(566\) 50.7641 2.13378
\(567\) 0 0
\(568\) 4.83702 0.202957
\(569\) −23.3038 −0.976945 −0.488472 0.872579i \(-0.662446\pi\)
−0.488472 + 0.872579i \(0.662446\pi\)
\(570\) 0 0
\(571\) −0.411433 −0.0172179 −0.00860896 0.999963i \(-0.502740\pi\)
−0.00860896 + 0.999963i \(0.502740\pi\)
\(572\) 40.0813 1.67588
\(573\) 0 0
\(574\) −8.32269 −0.347382
\(575\) −6.10369 −0.254541
\(576\) 0 0
\(577\) −13.5456 −0.563910 −0.281955 0.959428i \(-0.590983\pi\)
−0.281955 + 0.959428i \(0.590983\pi\)
\(578\) 8.86169 0.368598
\(579\) 0 0
\(580\) −10.0979 −0.419293
\(581\) −4.26324 −0.176869
\(582\) 0 0
\(583\) −35.6936 −1.47828
\(584\) 23.7971 0.984730
\(585\) 0 0
\(586\) 60.4524 2.49727
\(587\) −33.9417 −1.40092 −0.700461 0.713690i \(-0.747022\pi\)
−0.700461 + 0.713690i \(0.747022\pi\)
\(588\) 0 0
\(589\) −46.9433 −1.93426
\(590\) 9.06620 0.373250
\(591\) 0 0
\(592\) −8.38811 −0.344749
\(593\) 35.4814 1.45705 0.728524 0.685021i \(-0.240207\pi\)
0.728524 + 0.685021i \(0.240207\pi\)
\(594\) 0 0
\(595\) 4.04893 0.165990
\(596\) −44.2280 −1.81165
\(597\) 0 0
\(598\) −5.53895 −0.226505
\(599\) −39.5554 −1.61619 −0.808094 0.589054i \(-0.799501\pi\)
−0.808094 + 0.589054i \(0.799501\pi\)
\(600\) 0 0
\(601\) 15.7875 0.643984 0.321992 0.946742i \(-0.395648\pi\)
0.321992 + 0.946742i \(0.395648\pi\)
\(602\) −2.57886 −0.105106
\(603\) 0 0
\(604\) 56.3190 2.29159
\(605\) −58.9254 −2.39566
\(606\) 0 0
\(607\) 23.3376 0.947244 0.473622 0.880728i \(-0.342946\pi\)
0.473622 + 0.880728i \(0.342946\pi\)
\(608\) −36.4888 −1.47982
\(609\) 0 0
\(610\) 53.2459 2.15586
\(611\) −23.6360 −0.956212
\(612\) 0 0
\(613\) −37.7636 −1.52526 −0.762628 0.646837i \(-0.776091\pi\)
−0.762628 + 0.646837i \(0.776091\pi\)
\(614\) −23.5680 −0.951129
\(615\) 0 0
\(616\) 4.16329 0.167744
\(617\) 19.3263 0.778046 0.389023 0.921228i \(-0.372813\pi\)
0.389023 + 0.921228i \(0.372813\pi\)
\(618\) 0 0
\(619\) 40.2999 1.61979 0.809894 0.586576i \(-0.199524\pi\)
0.809894 + 0.586576i \(0.199524\pi\)
\(620\) −85.6134 −3.43832
\(621\) 0 0
\(622\) 71.4801 2.86609
\(623\) −3.97053 −0.159076
\(624\) 0 0
\(625\) −18.2634 −0.730537
\(626\) 47.7933 1.91020
\(627\) 0 0
\(628\) −28.0653 −1.11993
\(629\) −34.5298 −1.37679
\(630\) 0 0
\(631\) −4.24160 −0.168855 −0.0844276 0.996430i \(-0.526906\pi\)
−0.0844276 + 0.996430i \(0.526906\pi\)
\(632\) 8.38530 0.333549
\(633\) 0 0
\(634\) 30.5460 1.21314
\(635\) −49.3769 −1.95946
\(636\) 0 0
\(637\) 17.0078 0.673873
\(638\) 12.0120 0.475562
\(639\) 0 0
\(640\) −53.4304 −2.11202
\(641\) −14.6358 −0.578080 −0.289040 0.957317i \(-0.593336\pi\)
−0.289040 + 0.957317i \(0.593336\pi\)
\(642\) 0 0
\(643\) −7.97033 −0.314319 −0.157159 0.987573i \(-0.550234\pi\)
−0.157159 + 0.987573i \(0.550234\pi\)
\(644\) −1.01934 −0.0401675
\(645\) 0 0
\(646\) −44.8592 −1.76496
\(647\) 0.258751 0.0101726 0.00508628 0.999987i \(-0.498381\pi\)
0.00508628 + 0.999987i \(0.498381\pi\)
\(648\) 0 0
\(649\) −6.49691 −0.255026
\(650\) 33.8081 1.32606
\(651\) 0 0
\(652\) −64.2751 −2.51721
\(653\) −25.8829 −1.01288 −0.506438 0.862276i \(-0.669038\pi\)
−0.506438 + 0.862276i \(0.669038\pi\)
\(654\) 0 0
\(655\) 8.77585 0.342901
\(656\) −9.68058 −0.377963
\(657\) 0 0
\(658\) −7.22051 −0.281485
\(659\) 2.80499 0.109267 0.0546335 0.998506i \(-0.482601\pi\)
0.0546335 + 0.998506i \(0.482601\pi\)
\(660\) 0 0
\(661\) 33.3102 1.29562 0.647809 0.761803i \(-0.275685\pi\)
0.647809 + 0.761803i \(0.275685\pi\)
\(662\) 20.0096 0.777695
\(663\) 0 0
\(664\) 29.2902 1.13668
\(665\) 6.20606 0.240661
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 64.7374 2.50476
\(669\) 0 0
\(670\) 38.6182 1.49195
\(671\) −38.1564 −1.47301
\(672\) 0 0
\(673\) −0.265368 −0.0102292 −0.00511459 0.999987i \(-0.501628\pi\)
−0.00511459 + 0.999987i \(0.501628\pi\)
\(674\) −15.0036 −0.577918
\(675\) 0 0
\(676\) −20.9129 −0.804343
\(677\) −16.0535 −0.616987 −0.308494 0.951226i \(-0.599825\pi\)
−0.308494 + 0.951226i \(0.599825\pi\)
\(678\) 0 0
\(679\) −1.01496 −0.0389507
\(680\) −27.8178 −1.06676
\(681\) 0 0
\(682\) 101.842 3.89973
\(683\) −32.7737 −1.25405 −0.627025 0.778999i \(-0.715728\pi\)
−0.627025 + 0.778999i \(0.715728\pi\)
\(684\) 0 0
\(685\) −37.5947 −1.43642
\(686\) 10.4767 0.400001
\(687\) 0 0
\(688\) −2.99961 −0.114359
\(689\) −16.4589 −0.627034
\(690\) 0 0
\(691\) 45.9477 1.74793 0.873966 0.485986i \(-0.161540\pi\)
0.873966 + 0.485986i \(0.161540\pi\)
\(692\) 32.3483 1.22970
\(693\) 0 0
\(694\) −23.5067 −0.892303
\(695\) −11.8537 −0.449638
\(696\) 0 0
\(697\) −39.8503 −1.50944
\(698\) 48.7328 1.84457
\(699\) 0 0
\(700\) 6.22171 0.235159
\(701\) 11.1726 0.421984 0.210992 0.977488i \(-0.432331\pi\)
0.210992 + 0.977488i \(0.432331\pi\)
\(702\) 0 0
\(703\) −52.9261 −1.99614
\(704\) 69.7620 2.62925
\(705\) 0 0
\(706\) −55.2473 −2.07926
\(707\) 5.57786 0.209777
\(708\) 0 0
\(709\) −0.376876 −0.0141539 −0.00707693 0.999975i \(-0.502253\pi\)
−0.00707693 + 0.999975i \(0.502253\pi\)
\(710\) −15.6427 −0.587059
\(711\) 0 0
\(712\) 27.2792 1.02233
\(713\) −8.47832 −0.317516
\(714\) 0 0
\(715\) −44.0734 −1.64825
\(716\) 7.52963 0.281396
\(717\) 0 0
\(718\) −11.2326 −0.419198
\(719\) −33.2548 −1.24020 −0.620098 0.784525i \(-0.712907\pi\)
−0.620098 + 0.784525i \(0.712907\pi\)
\(720\) 0 0
\(721\) 2.15712 0.0803352
\(722\) −26.1444 −0.972995
\(723\) 0 0
\(724\) −31.2616 −1.16183
\(725\) 6.10369 0.226685
\(726\) 0 0
\(727\) −10.5234 −0.390293 −0.195146 0.980774i \(-0.562518\pi\)
−0.195146 + 0.980774i \(0.562518\pi\)
\(728\) 1.91976 0.0711512
\(729\) 0 0
\(730\) −76.9584 −2.84836
\(731\) −12.3479 −0.456705
\(732\) 0 0
\(733\) −17.1253 −0.632536 −0.316268 0.948670i \(-0.602430\pi\)
−0.316268 + 0.948670i \(0.602430\pi\)
\(734\) 13.4139 0.495117
\(735\) 0 0
\(736\) −6.59017 −0.242917
\(737\) −27.6741 −1.01939
\(738\) 0 0
\(739\) 20.9535 0.770788 0.385394 0.922752i \(-0.374065\pi\)
0.385394 + 0.922752i \(0.374065\pi\)
\(740\) −96.5247 −3.54832
\(741\) 0 0
\(742\) −5.02798 −0.184583
\(743\) −15.7655 −0.578381 −0.289190 0.957272i \(-0.593386\pi\)
−0.289190 + 0.957272i \(0.593386\pi\)
\(744\) 0 0
\(745\) 48.6332 1.78178
\(746\) −58.1033 −2.12731
\(747\) 0 0
\(748\) 58.6276 2.14364
\(749\) −4.43750 −0.162143
\(750\) 0 0
\(751\) 40.8709 1.49140 0.745700 0.666282i \(-0.232115\pi\)
0.745700 + 0.666282i \(0.232115\pi\)
\(752\) −8.39858 −0.306265
\(753\) 0 0
\(754\) 5.53895 0.201717
\(755\) −61.9284 −2.25381
\(756\) 0 0
\(757\) 37.3932 1.35908 0.679539 0.733639i \(-0.262180\pi\)
0.679539 + 0.733639i \(0.262180\pi\)
\(758\) −77.9096 −2.82980
\(759\) 0 0
\(760\) −42.6382 −1.54665
\(761\) 12.0596 0.437161 0.218581 0.975819i \(-0.429857\pi\)
0.218581 + 0.975819i \(0.429857\pi\)
\(762\) 0 0
\(763\) −3.53482 −0.127969
\(764\) 64.9057 2.34820
\(765\) 0 0
\(766\) −49.4402 −1.78635
\(767\) −2.99583 −0.108173
\(768\) 0 0
\(769\) 27.8157 1.00306 0.501531 0.865140i \(-0.332770\pi\)
0.501531 + 0.865140i \(0.332770\pi\)
\(770\) −13.4639 −0.485204
\(771\) 0 0
\(772\) −41.7799 −1.50369
\(773\) 12.1443 0.436801 0.218401 0.975859i \(-0.429916\pi\)
0.218401 + 0.975859i \(0.429916\pi\)
\(774\) 0 0
\(775\) 51.7491 1.85888
\(776\) 6.97321 0.250324
\(777\) 0 0
\(778\) −24.0518 −0.862299
\(779\) −61.0811 −2.18846
\(780\) 0 0
\(781\) 11.2097 0.401113
\(782\) −8.10192 −0.289724
\(783\) 0 0
\(784\) 6.04336 0.215834
\(785\) 30.8607 1.10147
\(786\) 0 0
\(787\) −18.7378 −0.667929 −0.333964 0.942586i \(-0.608387\pi\)
−0.333964 + 0.942586i \(0.608387\pi\)
\(788\) 46.9345 1.67197
\(789\) 0 0
\(790\) −27.1176 −0.964801
\(791\) −1.04575 −0.0371826
\(792\) 0 0
\(793\) −17.5946 −0.624801
\(794\) 17.6233 0.625427
\(795\) 0 0
\(796\) 15.0633 0.533904
\(797\) −26.9033 −0.952964 −0.476482 0.879184i \(-0.658088\pi\)
−0.476482 + 0.879184i \(0.658088\pi\)
\(798\) 0 0
\(799\) −34.5728 −1.22310
\(800\) 40.2244 1.42215
\(801\) 0 0
\(802\) 33.7786 1.19277
\(803\) 55.1490 1.94617
\(804\) 0 0
\(805\) 1.12086 0.0395052
\(806\) 46.9610 1.65413
\(807\) 0 0
\(808\) −38.3222 −1.34817
\(809\) 25.3753 0.892147 0.446073 0.894996i \(-0.352822\pi\)
0.446073 + 0.894996i \(0.352822\pi\)
\(810\) 0 0
\(811\) −26.9252 −0.945471 −0.472736 0.881204i \(-0.656733\pi\)
−0.472736 + 0.881204i \(0.656733\pi\)
\(812\) 1.01934 0.0357717
\(813\) 0 0
\(814\) 114.822 4.02449
\(815\) 70.6770 2.47571
\(816\) 0 0
\(817\) −18.9265 −0.662155
\(818\) −65.7933 −2.30041
\(819\) 0 0
\(820\) −111.398 −3.89017
\(821\) 24.9489 0.870722 0.435361 0.900256i \(-0.356621\pi\)
0.435361 + 0.900256i \(0.356621\pi\)
\(822\) 0 0
\(823\) 21.2224 0.739765 0.369882 0.929079i \(-0.379398\pi\)
0.369882 + 0.929079i \(0.379398\pi\)
\(824\) −14.8203 −0.516289
\(825\) 0 0
\(826\) −0.915189 −0.0318435
\(827\) −13.9717 −0.485844 −0.242922 0.970046i \(-0.578106\pi\)
−0.242922 + 0.970046i \(0.578106\pi\)
\(828\) 0 0
\(829\) 5.62458 0.195350 0.0976748 0.995218i \(-0.468859\pi\)
0.0976748 + 0.995218i \(0.468859\pi\)
\(830\) −94.7229 −3.28788
\(831\) 0 0
\(832\) 32.1684 1.11524
\(833\) 24.8776 0.861957
\(834\) 0 0
\(835\) −71.1853 −2.46347
\(836\) 89.8624 3.10796
\(837\) 0 0
\(838\) −63.9173 −2.20799
\(839\) −47.4932 −1.63965 −0.819824 0.572616i \(-0.805929\pi\)
−0.819824 + 0.572616i \(0.805929\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −29.5693 −1.01903
\(843\) 0 0
\(844\) −79.1231 −2.72353
\(845\) 22.9959 0.791082
\(846\) 0 0
\(847\) 5.94823 0.204384
\(848\) −5.84832 −0.200832
\(849\) 0 0
\(850\) 49.4516 1.69618
\(851\) −9.55887 −0.327674
\(852\) 0 0
\(853\) −10.5035 −0.359634 −0.179817 0.983700i \(-0.557550\pi\)
−0.179817 + 0.983700i \(0.557550\pi\)
\(854\) −5.37491 −0.183926
\(855\) 0 0
\(856\) 30.4875 1.04204
\(857\) 21.3106 0.727956 0.363978 0.931407i \(-0.381418\pi\)
0.363978 + 0.931407i \(0.381418\pi\)
\(858\) 0 0
\(859\) −21.9655 −0.749452 −0.374726 0.927136i \(-0.622263\pi\)
−0.374726 + 0.927136i \(0.622263\pi\)
\(860\) −34.5175 −1.17704
\(861\) 0 0
\(862\) 47.2333 1.60877
\(863\) −50.0442 −1.70353 −0.851763 0.523928i \(-0.824466\pi\)
−0.851763 + 0.523928i \(0.824466\pi\)
\(864\) 0 0
\(865\) −35.5702 −1.20942
\(866\) 66.4841 2.25922
\(867\) 0 0
\(868\) 8.64226 0.293337
\(869\) 19.4327 0.659209
\(870\) 0 0
\(871\) −12.7610 −0.432390
\(872\) 24.2857 0.822416
\(873\) 0 0
\(874\) −12.4184 −0.420057
\(875\) −1.23709 −0.0418211
\(876\) 0 0
\(877\) −26.3344 −0.889248 −0.444624 0.895717i \(-0.646663\pi\)
−0.444624 + 0.895717i \(0.646663\pi\)
\(878\) −40.6100 −1.37052
\(879\) 0 0
\(880\) −15.6606 −0.527918
\(881\) −53.3563 −1.79762 −0.898809 0.438340i \(-0.855567\pi\)
−0.898809 + 0.438340i \(0.855567\pi\)
\(882\) 0 0
\(883\) 2.46924 0.0830966 0.0415483 0.999136i \(-0.486771\pi\)
0.0415483 + 0.999136i \(0.486771\pi\)
\(884\) 27.0341 0.909256
\(885\) 0 0
\(886\) 46.4289 1.55981
\(887\) −53.9526 −1.81155 −0.905776 0.423757i \(-0.860711\pi\)
−0.905776 + 0.423757i \(0.860711\pi\)
\(888\) 0 0
\(889\) 4.98436 0.167170
\(890\) −88.2193 −2.95712
\(891\) 0 0
\(892\) −25.0979 −0.840339
\(893\) −52.9921 −1.77331
\(894\) 0 0
\(895\) −8.27960 −0.276756
\(896\) 5.39354 0.180186
\(897\) 0 0
\(898\) −30.5255 −1.01865
\(899\) 8.47832 0.282768
\(900\) 0 0
\(901\) −24.0747 −0.802044
\(902\) 132.514 4.41222
\(903\) 0 0
\(904\) 7.18474 0.238961
\(905\) 34.3753 1.14267
\(906\) 0 0
\(907\) 4.54378 0.150874 0.0754368 0.997151i \(-0.475965\pi\)
0.0754368 + 0.997151i \(0.475965\pi\)
\(908\) 45.5654 1.51214
\(909\) 0 0
\(910\) −6.20841 −0.205807
\(911\) 14.6485 0.485327 0.242664 0.970110i \(-0.421979\pi\)
0.242664 + 0.970110i \(0.421979\pi\)
\(912\) 0 0
\(913\) 67.8792 2.24647
\(914\) −9.78035 −0.323505
\(915\) 0 0
\(916\) −28.3530 −0.936809
\(917\) −0.885879 −0.0292543
\(918\) 0 0
\(919\) 14.7669 0.487114 0.243557 0.969887i \(-0.421686\pi\)
0.243557 + 0.969887i \(0.421686\pi\)
\(920\) −7.70079 −0.253888
\(921\) 0 0
\(922\) 3.63318 0.119652
\(923\) 5.16896 0.170138
\(924\) 0 0
\(925\) 58.3444 1.91835
\(926\) 0.341750 0.0112306
\(927\) 0 0
\(928\) 6.59017 0.216333
\(929\) 27.7957 0.911947 0.455973 0.889993i \(-0.349291\pi\)
0.455973 + 0.889993i \(0.349291\pi\)
\(930\) 0 0
\(931\) 38.1315 1.24971
\(932\) −4.60364 −0.150797
\(933\) 0 0
\(934\) 57.6541 1.88650
\(935\) −64.4670 −2.10830
\(936\) 0 0
\(937\) 7.42265 0.242487 0.121244 0.992623i \(-0.461312\pi\)
0.121244 + 0.992623i \(0.461312\pi\)
\(938\) −3.89832 −0.127285
\(939\) 0 0
\(940\) −96.6451 −3.15222
\(941\) −42.6205 −1.38939 −0.694695 0.719305i \(-0.744461\pi\)
−0.694695 + 0.719305i \(0.744461\pi\)
\(942\) 0 0
\(943\) −11.0317 −0.359243
\(944\) −1.06451 −0.0346468
\(945\) 0 0
\(946\) 41.0605 1.33499
\(947\) −18.8970 −0.614069 −0.307035 0.951698i \(-0.599337\pi\)
−0.307035 + 0.951698i \(0.599337\pi\)
\(948\) 0 0
\(949\) 25.4301 0.825497
\(950\) 75.7978 2.45920
\(951\) 0 0
\(952\) 2.80807 0.0910101
\(953\) 4.93984 0.160017 0.0800086 0.996794i \(-0.474505\pi\)
0.0800086 + 0.996794i \(0.474505\pi\)
\(954\) 0 0
\(955\) −71.3704 −2.30949
\(956\) 39.7851 1.28674
\(957\) 0 0
\(958\) 13.2148 0.426950
\(959\) 3.79500 0.122547
\(960\) 0 0
\(961\) 40.8820 1.31877
\(962\) 52.9461 1.70705
\(963\) 0 0
\(964\) 78.8667 2.54013
\(965\) 45.9413 1.47890
\(966\) 0 0
\(967\) 35.7015 1.14808 0.574041 0.818827i \(-0.305375\pi\)
0.574041 + 0.818827i \(0.305375\pi\)
\(968\) −40.8668 −1.31351
\(969\) 0 0
\(970\) −22.5510 −0.724069
\(971\) −57.8911 −1.85781 −0.928906 0.370315i \(-0.879250\pi\)
−0.928906 + 0.370315i \(0.879250\pi\)
\(972\) 0 0
\(973\) 1.19658 0.0383605
\(974\) 70.3658 2.25467
\(975\) 0 0
\(976\) −6.25186 −0.200117
\(977\) 24.1856 0.773766 0.386883 0.922129i \(-0.373552\pi\)
0.386883 + 0.922129i \(0.373552\pi\)
\(978\) 0 0
\(979\) 63.2187 2.02048
\(980\) 69.5429 2.22147
\(981\) 0 0
\(982\) 6.45858 0.206101
\(983\) 30.1771 0.962500 0.481250 0.876583i \(-0.340183\pi\)
0.481250 + 0.876583i \(0.340183\pi\)
\(984\) 0 0
\(985\) −51.6092 −1.64441
\(986\) 8.10192 0.258018
\(987\) 0 0
\(988\) 41.4370 1.31829
\(989\) −3.41828 −0.108695
\(990\) 0 0
\(991\) 24.1655 0.767642 0.383821 0.923407i \(-0.374608\pi\)
0.383821 + 0.923407i \(0.374608\pi\)
\(992\) 55.8736 1.77399
\(993\) 0 0
\(994\) 1.57905 0.0500844
\(995\) −16.5636 −0.525102
\(996\) 0 0
\(997\) −33.3183 −1.05520 −0.527600 0.849493i \(-0.676908\pi\)
−0.527600 + 0.849493i \(0.676908\pi\)
\(998\) −98.3478 −3.11314
\(999\) 0 0
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 6003.2.a.m.1.3 11
3.2 odd 2 2001.2.a.l.1.9 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.9 11 3.2 odd 2
6003.2.a.m.1.3 11 1.1 even 1 trivial