Properties

Label 546.4.a.e.1.1
Level $546$
Weight $4$
Character 546.1
Self dual yes
Analytic conductor $32.215$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2150428631\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 546.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +9.00000 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +9.00000 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +18.0000 q^{10} +62.0000 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} +27.0000 q^{15} +16.0000 q^{16} -16.0000 q^{17} +18.0000 q^{18} +79.0000 q^{19} +36.0000 q^{20} -21.0000 q^{21} +124.000 q^{22} -155.000 q^{23} +24.0000 q^{24} -44.0000 q^{25} -26.0000 q^{26} +27.0000 q^{27} -28.0000 q^{28} +51.0000 q^{29} +54.0000 q^{30} +243.000 q^{31} +32.0000 q^{32} +186.000 q^{33} -32.0000 q^{34} -63.0000 q^{35} +36.0000 q^{36} +412.000 q^{37} +158.000 q^{38} -39.0000 q^{39} +72.0000 q^{40} -406.000 q^{41} -42.0000 q^{42} -103.000 q^{43} +248.000 q^{44} +81.0000 q^{45} -310.000 q^{46} +429.000 q^{47} +48.0000 q^{48} +49.0000 q^{49} -88.0000 q^{50} -48.0000 q^{51} -52.0000 q^{52} -169.000 q^{53} +54.0000 q^{54} +558.000 q^{55} -56.0000 q^{56} +237.000 q^{57} +102.000 q^{58} +320.000 q^{59} +108.000 q^{60} -614.000 q^{61} +486.000 q^{62} -63.0000 q^{63} +64.0000 q^{64} -117.000 q^{65} +372.000 q^{66} +258.000 q^{67} -64.0000 q^{68} -465.000 q^{69} -126.000 q^{70} -264.000 q^{71} +72.0000 q^{72} -121.000 q^{73} +824.000 q^{74} -132.000 q^{75} +316.000 q^{76} -434.000 q^{77} -78.0000 q^{78} -967.000 q^{79} +144.000 q^{80} +81.0000 q^{81} -812.000 q^{82} -679.000 q^{83} -84.0000 q^{84} -144.000 q^{85} -206.000 q^{86} +153.000 q^{87} +496.000 q^{88} +1059.00 q^{89} +162.000 q^{90} +91.0000 q^{91} -620.000 q^{92} +729.000 q^{93} +858.000 q^{94} +711.000 q^{95} +96.0000 q^{96} -21.0000 q^{97} +98.0000 q^{98} +558.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) 9.00000 0.804984 0.402492 0.915423i \(-0.368144\pi\)
0.402492 + 0.915423i \(0.368144\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 18.0000 0.569210
\(11\) 62.0000 1.69943 0.849714 0.527244i \(-0.176775\pi\)
0.849714 + 0.527244i \(0.176775\pi\)
\(12\) 12.0000 0.288675
\(13\) −13.0000 −0.277350
\(14\) −14.0000 −0.267261
\(15\) 27.0000 0.464758
\(16\) 16.0000 0.250000
\(17\) −16.0000 −0.228269 −0.114134 0.993465i \(-0.536409\pi\)
−0.114134 + 0.993465i \(0.536409\pi\)
\(18\) 18.0000 0.235702
\(19\) 79.0000 0.953886 0.476943 0.878934i \(-0.341745\pi\)
0.476943 + 0.878934i \(0.341745\pi\)
\(20\) 36.0000 0.402492
\(21\) −21.0000 −0.218218
\(22\) 124.000 1.20168
\(23\) −155.000 −1.40521 −0.702603 0.711582i \(-0.747979\pi\)
−0.702603 + 0.711582i \(0.747979\pi\)
\(24\) 24.0000 0.204124
\(25\) −44.0000 −0.352000
\(26\) −26.0000 −0.196116
\(27\) 27.0000 0.192450
\(28\) −28.0000 −0.188982
\(29\) 51.0000 0.326568 0.163284 0.986579i \(-0.447791\pi\)
0.163284 + 0.986579i \(0.447791\pi\)
\(30\) 54.0000 0.328634
\(31\) 243.000 1.40787 0.703937 0.710263i \(-0.251424\pi\)
0.703937 + 0.710263i \(0.251424\pi\)
\(32\) 32.0000 0.176777
\(33\) 186.000 0.981165
\(34\) −32.0000 −0.161410
\(35\) −63.0000 −0.304256
\(36\) 36.0000 0.166667
\(37\) 412.000 1.83060 0.915302 0.402767i \(-0.131952\pi\)
0.915302 + 0.402767i \(0.131952\pi\)
\(38\) 158.000 0.674500
\(39\) −39.0000 −0.160128
\(40\) 72.0000 0.284605
\(41\) −406.000 −1.54650 −0.773251 0.634101i \(-0.781371\pi\)
−0.773251 + 0.634101i \(0.781371\pi\)
\(42\) −42.0000 −0.154303
\(43\) −103.000 −0.365287 −0.182644 0.983179i \(-0.558465\pi\)
−0.182644 + 0.983179i \(0.558465\pi\)
\(44\) 248.000 0.849714
\(45\) 81.0000 0.268328
\(46\) −310.000 −0.993631
\(47\) 429.000 1.33141 0.665703 0.746217i \(-0.268132\pi\)
0.665703 + 0.746217i \(0.268132\pi\)
\(48\) 48.0000 0.144338
\(49\) 49.0000 0.142857
\(50\) −88.0000 −0.248902
\(51\) −48.0000 −0.131791
\(52\) −52.0000 −0.138675
\(53\) −169.000 −0.437999 −0.218999 0.975725i \(-0.570279\pi\)
−0.218999 + 0.975725i \(0.570279\pi\)
\(54\) 54.0000 0.136083
\(55\) 558.000 1.36801
\(56\) −56.0000 −0.133631
\(57\) 237.000 0.550727
\(58\) 102.000 0.230918
\(59\) 320.000 0.706109 0.353055 0.935603i \(-0.385143\pi\)
0.353055 + 0.935603i \(0.385143\pi\)
\(60\) 108.000 0.232379
\(61\) −614.000 −1.28876 −0.644382 0.764703i \(-0.722885\pi\)
−0.644382 + 0.764703i \(0.722885\pi\)
\(62\) 486.000 0.995517
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) −117.000 −0.223263
\(66\) 372.000 0.693788
\(67\) 258.000 0.470444 0.235222 0.971942i \(-0.424418\pi\)
0.235222 + 0.971942i \(0.424418\pi\)
\(68\) −64.0000 −0.114134
\(69\) −465.000 −0.811296
\(70\) −126.000 −0.215141
\(71\) −264.000 −0.441282 −0.220641 0.975355i \(-0.570815\pi\)
−0.220641 + 0.975355i \(0.570815\pi\)
\(72\) 72.0000 0.117851
\(73\) −121.000 −0.194000 −0.0969999 0.995284i \(-0.530925\pi\)
−0.0969999 + 0.995284i \(0.530925\pi\)
\(74\) 824.000 1.29443
\(75\) −132.000 −0.203227
\(76\) 316.000 0.476943
\(77\) −434.000 −0.642323
\(78\) −78.0000 −0.113228
\(79\) −967.000 −1.37716 −0.688582 0.725158i \(-0.741767\pi\)
−0.688582 + 0.725158i \(0.741767\pi\)
\(80\) 144.000 0.201246
\(81\) 81.0000 0.111111
\(82\) −812.000 −1.09354
\(83\) −679.000 −0.897951 −0.448975 0.893544i \(-0.648211\pi\)
−0.448975 + 0.893544i \(0.648211\pi\)
\(84\) −84.0000 −0.109109
\(85\) −144.000 −0.183753
\(86\) −206.000 −0.258297
\(87\) 153.000 0.188544
\(88\) 496.000 0.600838
\(89\) 1059.00 1.26128 0.630639 0.776076i \(-0.282793\pi\)
0.630639 + 0.776076i \(0.282793\pi\)
\(90\) 162.000 0.189737
\(91\) 91.0000 0.104828
\(92\) −620.000 −0.702603
\(93\) 729.000 0.812836
\(94\) 858.000 0.941446
\(95\) 711.000 0.767864
\(96\) 96.0000 0.102062
\(97\) −21.0000 −0.0219817 −0.0109909 0.999940i \(-0.503499\pi\)
−0.0109909 + 0.999940i \(0.503499\pi\)
\(98\) 98.0000 0.101015
\(99\) 558.000 0.566476
\(100\) −176.000 −0.176000
\(101\) 894.000 0.880756 0.440378 0.897813i \(-0.354844\pi\)
0.440378 + 0.897813i \(0.354844\pi\)
\(102\) −96.0000 −0.0931904
\(103\) 128.000 0.122449 0.0612243 0.998124i \(-0.480499\pi\)
0.0612243 + 0.998124i \(0.480499\pi\)
\(104\) −104.000 −0.0980581
\(105\) −189.000 −0.175662
\(106\) −338.000 −0.309712
\(107\) −708.000 −0.639672 −0.319836 0.947473i \(-0.603628\pi\)
−0.319836 + 0.947473i \(0.603628\pi\)
\(108\) 108.000 0.0962250
\(109\) 1238.00 1.08788 0.543940 0.839124i \(-0.316932\pi\)
0.543940 + 0.839124i \(0.316932\pi\)
\(110\) 1116.00 0.967331
\(111\) 1236.00 1.05690
\(112\) −112.000 −0.0944911
\(113\) 1073.00 0.893269 0.446634 0.894717i \(-0.352623\pi\)
0.446634 + 0.894717i \(0.352623\pi\)
\(114\) 474.000 0.389423
\(115\) −1395.00 −1.13117
\(116\) 204.000 0.163284
\(117\) −117.000 −0.0924500
\(118\) 640.000 0.499295
\(119\) 112.000 0.0862775
\(120\) 216.000 0.164317
\(121\) 2513.00 1.88805
\(122\) −1228.00 −0.911294
\(123\) −1218.00 −0.892873
\(124\) 972.000 0.703937
\(125\) −1521.00 −1.08834
\(126\) −126.000 −0.0890871
\(127\) −1748.00 −1.22134 −0.610669 0.791886i \(-0.709099\pi\)
−0.610669 + 0.791886i \(0.709099\pi\)
\(128\) 128.000 0.0883883
\(129\) −309.000 −0.210899
\(130\) −234.000 −0.157870
\(131\) −936.000 −0.624265 −0.312132 0.950039i \(-0.601043\pi\)
−0.312132 + 0.950039i \(0.601043\pi\)
\(132\) 744.000 0.490582
\(133\) −553.000 −0.360535
\(134\) 516.000 0.332654
\(135\) 243.000 0.154919
\(136\) −128.000 −0.0807052
\(137\) −1128.00 −0.703442 −0.351721 0.936105i \(-0.614403\pi\)
−0.351721 + 0.936105i \(0.614403\pi\)
\(138\) −930.000 −0.573673
\(139\) −854.000 −0.521118 −0.260559 0.965458i \(-0.583907\pi\)
−0.260559 + 0.965458i \(0.583907\pi\)
\(140\) −252.000 −0.152128
\(141\) 1287.00 0.768688
\(142\) −528.000 −0.312034
\(143\) −806.000 −0.471336
\(144\) 144.000 0.0833333
\(145\) 459.000 0.262882
\(146\) −242.000 −0.137179
\(147\) 147.000 0.0824786
\(148\) 1648.00 0.915302
\(149\) −442.000 −0.243020 −0.121510 0.992590i \(-0.538774\pi\)
−0.121510 + 0.992590i \(0.538774\pi\)
\(150\) −264.000 −0.143703
\(151\) −1016.00 −0.547556 −0.273778 0.961793i \(-0.588273\pi\)
−0.273778 + 0.961793i \(0.588273\pi\)
\(152\) 632.000 0.337250
\(153\) −144.000 −0.0760896
\(154\) −868.000 −0.454191
\(155\) 2187.00 1.13332
\(156\) −156.000 −0.0800641
\(157\) −3880.00 −1.97234 −0.986171 0.165731i \(-0.947002\pi\)
−0.986171 + 0.165731i \(0.947002\pi\)
\(158\) −1934.00 −0.973802
\(159\) −507.000 −0.252879
\(160\) 288.000 0.142302
\(161\) 1085.00 0.531118
\(162\) 162.000 0.0785674
\(163\) −1604.00 −0.770767 −0.385383 0.922757i \(-0.625931\pi\)
−0.385383 + 0.922757i \(0.625931\pi\)
\(164\) −1624.00 −0.773251
\(165\) 1674.00 0.789823
\(166\) −1358.00 −0.634947
\(167\) 959.000 0.444369 0.222185 0.975005i \(-0.428681\pi\)
0.222185 + 0.975005i \(0.428681\pi\)
\(168\) −168.000 −0.0771517
\(169\) 169.000 0.0769231
\(170\) −288.000 −0.129933
\(171\) 711.000 0.317962
\(172\) −412.000 −0.182644
\(173\) −488.000 −0.214462 −0.107231 0.994234i \(-0.534198\pi\)
−0.107231 + 0.994234i \(0.534198\pi\)
\(174\) 306.000 0.133321
\(175\) 308.000 0.133043
\(176\) 992.000 0.424857
\(177\) 960.000 0.407672
\(178\) 2118.00 0.891858
\(179\) 2533.00 1.05768 0.528842 0.848721i \(-0.322627\pi\)
0.528842 + 0.848721i \(0.322627\pi\)
\(180\) 324.000 0.134164
\(181\) −3626.00 −1.48905 −0.744526 0.667593i \(-0.767325\pi\)
−0.744526 + 0.667593i \(0.767325\pi\)
\(182\) 182.000 0.0741249
\(183\) −1842.00 −0.744069
\(184\) −1240.00 −0.496815
\(185\) 3708.00 1.47361
\(186\) 1458.00 0.574762
\(187\) −992.000 −0.387926
\(188\) 1716.00 0.665703
\(189\) −189.000 −0.0727393
\(190\) 1422.00 0.542962
\(191\) −4992.00 −1.89114 −0.945572 0.325413i \(-0.894497\pi\)
−0.945572 + 0.325413i \(0.894497\pi\)
\(192\) 192.000 0.0721688
\(193\) −470.000 −0.175292 −0.0876460 0.996152i \(-0.527934\pi\)
−0.0876460 + 0.996152i \(0.527934\pi\)
\(194\) −42.0000 −0.0155434
\(195\) −351.000 −0.128901
\(196\) 196.000 0.0714286
\(197\) −3190.00 −1.15370 −0.576848 0.816852i \(-0.695717\pi\)
−0.576848 + 0.816852i \(0.695717\pi\)
\(198\) 1116.00 0.400559
\(199\) 1944.00 0.692495 0.346248 0.938143i \(-0.387456\pi\)
0.346248 + 0.938143i \(0.387456\pi\)
\(200\) −352.000 −0.124451
\(201\) 774.000 0.271611
\(202\) 1788.00 0.622788
\(203\) −357.000 −0.123431
\(204\) −192.000 −0.0658955
\(205\) −3654.00 −1.24491
\(206\) 256.000 0.0865843
\(207\) −1395.00 −0.468402
\(208\) −208.000 −0.0693375
\(209\) 4898.00 1.62106
\(210\) −378.000 −0.124212
\(211\) −1139.00 −0.371621 −0.185810 0.982586i \(-0.559491\pi\)
−0.185810 + 0.982586i \(0.559491\pi\)
\(212\) −676.000 −0.218999
\(213\) −792.000 −0.254774
\(214\) −1416.00 −0.452317
\(215\) −927.000 −0.294051
\(216\) 216.000 0.0680414
\(217\) −1701.00 −0.532126
\(218\) 2476.00 0.769247
\(219\) −363.000 −0.112006
\(220\) 2232.00 0.684006
\(221\) 208.000 0.0633104
\(222\) 2472.00 0.747341
\(223\) 833.000 0.250143 0.125071 0.992148i \(-0.460084\pi\)
0.125071 + 0.992148i \(0.460084\pi\)
\(224\) −224.000 −0.0668153
\(225\) −396.000 −0.117333
\(226\) 2146.00 0.631636
\(227\) −3516.00 −1.02804 −0.514020 0.857778i \(-0.671844\pi\)
−0.514020 + 0.857778i \(0.671844\pi\)
\(228\) 948.000 0.275363
\(229\) 3222.00 0.929763 0.464882 0.885373i \(-0.346097\pi\)
0.464882 + 0.885373i \(0.346097\pi\)
\(230\) −2790.00 −0.799857
\(231\) −1302.00 −0.370846
\(232\) 408.000 0.115459
\(233\) −477.000 −0.134117 −0.0670586 0.997749i \(-0.521361\pi\)
−0.0670586 + 0.997749i \(0.521361\pi\)
\(234\) −234.000 −0.0653720
\(235\) 3861.00 1.07176
\(236\) 1280.00 0.353055
\(237\) −2901.00 −0.795106
\(238\) 224.000 0.0610074
\(239\) −6368.00 −1.72348 −0.861740 0.507350i \(-0.830625\pi\)
−0.861740 + 0.507350i \(0.830625\pi\)
\(240\) 432.000 0.116190
\(241\) 747.000 0.199662 0.0998309 0.995004i \(-0.468170\pi\)
0.0998309 + 0.995004i \(0.468170\pi\)
\(242\) 5026.00 1.33506
\(243\) 243.000 0.0641500
\(244\) −2456.00 −0.644382
\(245\) 441.000 0.114998
\(246\) −2436.00 −0.631356
\(247\) −1027.00 −0.264561
\(248\) 1944.00 0.497759
\(249\) −2037.00 −0.518432
\(250\) −3042.00 −0.769572
\(251\) 7518.00 1.89057 0.945283 0.326252i \(-0.105786\pi\)
0.945283 + 0.326252i \(0.105786\pi\)
\(252\) −252.000 −0.0629941
\(253\) −9610.00 −2.38805
\(254\) −3496.00 −0.863616
\(255\) −432.000 −0.106090
\(256\) 256.000 0.0625000
\(257\) 1094.00 0.265532 0.132766 0.991147i \(-0.457614\pi\)
0.132766 + 0.991147i \(0.457614\pi\)
\(258\) −618.000 −0.149128
\(259\) −2884.00 −0.691904
\(260\) −468.000 −0.111631
\(261\) 459.000 0.108856
\(262\) −1872.00 −0.441422
\(263\) −1289.00 −0.302217 −0.151109 0.988517i \(-0.548284\pi\)
−0.151109 + 0.988517i \(0.548284\pi\)
\(264\) 1488.00 0.346894
\(265\) −1521.00 −0.352582
\(266\) −1106.00 −0.254937
\(267\) 3177.00 0.728199
\(268\) 1032.00 0.235222
\(269\) −2060.00 −0.466916 −0.233458 0.972367i \(-0.575004\pi\)
−0.233458 + 0.972367i \(0.575004\pi\)
\(270\) 486.000 0.109545
\(271\) 576.000 0.129113 0.0645563 0.997914i \(-0.479437\pi\)
0.0645563 + 0.997914i \(0.479437\pi\)
\(272\) −256.000 −0.0570672
\(273\) 273.000 0.0605228
\(274\) −2256.00 −0.497409
\(275\) −2728.00 −0.598199
\(276\) −1860.00 −0.405648
\(277\) −5699.00 −1.23617 −0.618086 0.786110i \(-0.712092\pi\)
−0.618086 + 0.786110i \(0.712092\pi\)
\(278\) −1708.00 −0.368486
\(279\) 2187.00 0.469291
\(280\) −504.000 −0.107571
\(281\) 4062.00 0.862344 0.431172 0.902270i \(-0.358100\pi\)
0.431172 + 0.902270i \(0.358100\pi\)
\(282\) 2574.00 0.543544
\(283\) −772.000 −0.162158 −0.0810789 0.996708i \(-0.525837\pi\)
−0.0810789 + 0.996708i \(0.525837\pi\)
\(284\) −1056.00 −0.220641
\(285\) 2133.00 0.443326
\(286\) −1612.00 −0.333285
\(287\) 2842.00 0.584522
\(288\) 288.000 0.0589256
\(289\) −4657.00 −0.947893
\(290\) 918.000 0.185886
\(291\) −63.0000 −0.0126912
\(292\) −484.000 −0.0969999
\(293\) 7833.00 1.56180 0.780902 0.624653i \(-0.214760\pi\)
0.780902 + 0.624653i \(0.214760\pi\)
\(294\) 294.000 0.0583212
\(295\) 2880.00 0.568407
\(296\) 3296.00 0.647217
\(297\) 1674.00 0.327055
\(298\) −884.000 −0.171841
\(299\) 2015.00 0.389734
\(300\) −528.000 −0.101614
\(301\) 721.000 0.138066
\(302\) −2032.00 −0.387180
\(303\) 2682.00 0.508505
\(304\) 1264.00 0.238472
\(305\) −5526.00 −1.03744
\(306\) −288.000 −0.0538035
\(307\) −2891.00 −0.537453 −0.268727 0.963217i \(-0.586603\pi\)
−0.268727 + 0.963217i \(0.586603\pi\)
\(308\) −1736.00 −0.321162
\(309\) 384.000 0.0706958
\(310\) 4374.00 0.801376
\(311\) −3530.00 −0.643627 −0.321813 0.946803i \(-0.604292\pi\)
−0.321813 + 0.946803i \(0.604292\pi\)
\(312\) −312.000 −0.0566139
\(313\) 5490.00 0.991416 0.495708 0.868489i \(-0.334909\pi\)
0.495708 + 0.868489i \(0.334909\pi\)
\(314\) −7760.00 −1.39466
\(315\) −567.000 −0.101419
\(316\) −3868.00 −0.688582
\(317\) −5636.00 −0.998578 −0.499289 0.866435i \(-0.666405\pi\)
−0.499289 + 0.866435i \(0.666405\pi\)
\(318\) −1014.00 −0.178812
\(319\) 3162.00 0.554978
\(320\) 576.000 0.100623
\(321\) −2124.00 −0.369315
\(322\) 2170.00 0.375557
\(323\) −1264.00 −0.217743
\(324\) 324.000 0.0555556
\(325\) 572.000 0.0976272
\(326\) −3208.00 −0.545014
\(327\) 3714.00 0.628088
\(328\) −3248.00 −0.546771
\(329\) −3003.00 −0.503224
\(330\) 3348.00 0.558489
\(331\) −9962.00 −1.65426 −0.827131 0.562008i \(-0.810029\pi\)
−0.827131 + 0.562008i \(0.810029\pi\)
\(332\) −2716.00 −0.448975
\(333\) 3708.00 0.610202
\(334\) 1918.00 0.314216
\(335\) 2322.00 0.378700
\(336\) −336.000 −0.0545545
\(337\) −11415.0 −1.84515 −0.922574 0.385821i \(-0.873918\pi\)
−0.922574 + 0.385821i \(0.873918\pi\)
\(338\) 338.000 0.0543928
\(339\) 3219.00 0.515729
\(340\) −576.000 −0.0918764
\(341\) 15066.0 2.39258
\(342\) 1422.00 0.224833
\(343\) −343.000 −0.0539949
\(344\) −824.000 −0.129149
\(345\) −4185.00 −0.653081
\(346\) −976.000 −0.151648
\(347\) 4864.00 0.752488 0.376244 0.926521i \(-0.377216\pi\)
0.376244 + 0.926521i \(0.377216\pi\)
\(348\) 612.000 0.0942720
\(349\) −469.000 −0.0719341 −0.0359670 0.999353i \(-0.511451\pi\)
−0.0359670 + 0.999353i \(0.511451\pi\)
\(350\) 616.000 0.0940760
\(351\) −351.000 −0.0533761
\(352\) 1984.00 0.300419
\(353\) 4198.00 0.632966 0.316483 0.948598i \(-0.397498\pi\)
0.316483 + 0.948598i \(0.397498\pi\)
\(354\) 1920.00 0.288268
\(355\) −2376.00 −0.355225
\(356\) 4236.00 0.630639
\(357\) 336.000 0.0498123
\(358\) 5066.00 0.747895
\(359\) 3408.00 0.501023 0.250512 0.968114i \(-0.419401\pi\)
0.250512 + 0.968114i \(0.419401\pi\)
\(360\) 648.000 0.0948683
\(361\) −618.000 −0.0901006
\(362\) −7252.00 −1.05292
\(363\) 7539.00 1.09007
\(364\) 364.000 0.0524142
\(365\) −1089.00 −0.156167
\(366\) −3684.00 −0.526136
\(367\) −8290.00 −1.17911 −0.589557 0.807727i \(-0.700697\pi\)
−0.589557 + 0.807727i \(0.700697\pi\)
\(368\) −2480.00 −0.351301
\(369\) −3654.00 −0.515500
\(370\) 7416.00 1.04200
\(371\) 1183.00 0.165548
\(372\) 2916.00 0.406418
\(373\) −9906.00 −1.37510 −0.687551 0.726136i \(-0.741314\pi\)
−0.687551 + 0.726136i \(0.741314\pi\)
\(374\) −1984.00 −0.274305
\(375\) −4563.00 −0.628353
\(376\) 3432.00 0.470723
\(377\) −663.000 −0.0905736
\(378\) −378.000 −0.0514344
\(379\) −9238.00 −1.25204 −0.626021 0.779806i \(-0.715318\pi\)
−0.626021 + 0.779806i \(0.715318\pi\)
\(380\) 2844.00 0.383932
\(381\) −5244.00 −0.705140
\(382\) −9984.00 −1.33724
\(383\) 4972.00 0.663335 0.331668 0.943396i \(-0.392389\pi\)
0.331668 + 0.943396i \(0.392389\pi\)
\(384\) 384.000 0.0510310
\(385\) −3906.00 −0.517060
\(386\) −940.000 −0.123950
\(387\) −927.000 −0.121762
\(388\) −84.0000 −0.0109909
\(389\) 7454.00 0.971550 0.485775 0.874084i \(-0.338538\pi\)
0.485775 + 0.874084i \(0.338538\pi\)
\(390\) −702.000 −0.0911465
\(391\) 2480.00 0.320765
\(392\) 392.000 0.0505076
\(393\) −2808.00 −0.360419
\(394\) −6380.00 −0.815786
\(395\) −8703.00 −1.10860
\(396\) 2232.00 0.283238
\(397\) 7219.00 0.912623 0.456311 0.889820i \(-0.349170\pi\)
0.456311 + 0.889820i \(0.349170\pi\)
\(398\) 3888.00 0.489668
\(399\) −1659.00 −0.208155
\(400\) −704.000 −0.0880000
\(401\) 10772.0 1.34147 0.670733 0.741699i \(-0.265980\pi\)
0.670733 + 0.741699i \(0.265980\pi\)
\(402\) 1548.00 0.192058
\(403\) −3159.00 −0.390474
\(404\) 3576.00 0.440378
\(405\) 729.000 0.0894427
\(406\) −714.000 −0.0872789
\(407\) 25544.0 3.11098
\(408\) −384.000 −0.0465952
\(409\) 13151.0 1.58991 0.794957 0.606665i \(-0.207493\pi\)
0.794957 + 0.606665i \(0.207493\pi\)
\(410\) −7308.00 −0.880284
\(411\) −3384.00 −0.406132
\(412\) 512.000 0.0612243
\(413\) −2240.00 −0.266884
\(414\) −2790.00 −0.331210
\(415\) −6111.00 −0.722837
\(416\) −416.000 −0.0490290
\(417\) −2562.00 −0.300867
\(418\) 9796.00 1.14626
\(419\) 6034.00 0.703533 0.351766 0.936088i \(-0.385581\pi\)
0.351766 + 0.936088i \(0.385581\pi\)
\(420\) −756.000 −0.0878310
\(421\) 8864.00 1.02614 0.513070 0.858347i \(-0.328508\pi\)
0.513070 + 0.858347i \(0.328508\pi\)
\(422\) −2278.00 −0.262776
\(423\) 3861.00 0.443802
\(424\) −1352.00 −0.154856
\(425\) 704.000 0.0803506
\(426\) −1584.00 −0.180153
\(427\) 4298.00 0.487107
\(428\) −2832.00 −0.319836
\(429\) −2418.00 −0.272126
\(430\) −1854.00 −0.207925
\(431\) −134.000 −0.0149758 −0.00748788 0.999972i \(-0.502383\pi\)
−0.00748788 + 0.999972i \(0.502383\pi\)
\(432\) 432.000 0.0481125
\(433\) 12376.0 1.37356 0.686781 0.726864i \(-0.259023\pi\)
0.686781 + 0.726864i \(0.259023\pi\)
\(434\) −3402.00 −0.376270
\(435\) 1377.00 0.151775
\(436\) 4952.00 0.543940
\(437\) −12245.0 −1.34041
\(438\) −726.000 −0.0792000
\(439\) 14198.0 1.54358 0.771792 0.635875i \(-0.219361\pi\)
0.771792 + 0.635875i \(0.219361\pi\)
\(440\) 4464.00 0.483666
\(441\) 441.000 0.0476190
\(442\) 416.000 0.0447672
\(443\) 7657.00 0.821208 0.410604 0.911814i \(-0.365318\pi\)
0.410604 + 0.911814i \(0.365318\pi\)
\(444\) 4944.00 0.528450
\(445\) 9531.00 1.01531
\(446\) 1666.00 0.176878
\(447\) −1326.00 −0.140308
\(448\) −448.000 −0.0472456
\(449\) 15500.0 1.62915 0.814577 0.580055i \(-0.196969\pi\)
0.814577 + 0.580055i \(0.196969\pi\)
\(450\) −792.000 −0.0829672
\(451\) −25172.0 −2.62817
\(452\) 4292.00 0.446634
\(453\) −3048.00 −0.316131
\(454\) −7032.00 −0.726934
\(455\) 819.000 0.0843853
\(456\) 1896.00 0.194711
\(457\) 10184.0 1.04242 0.521212 0.853427i \(-0.325480\pi\)
0.521212 + 0.853427i \(0.325480\pi\)
\(458\) 6444.00 0.657442
\(459\) −432.000 −0.0439304
\(460\) −5580.00 −0.565584
\(461\) 19250.0 1.94482 0.972410 0.233279i \(-0.0749455\pi\)
0.972410 + 0.233279i \(0.0749455\pi\)
\(462\) −2604.00 −0.262227
\(463\) −15622.0 −1.56807 −0.784034 0.620717i \(-0.786841\pi\)
−0.784034 + 0.620717i \(0.786841\pi\)
\(464\) 816.000 0.0816419
\(465\) 6561.00 0.654321
\(466\) −954.000 −0.0948352
\(467\) −15594.0 −1.54519 −0.772596 0.634898i \(-0.781042\pi\)
−0.772596 + 0.634898i \(0.781042\pi\)
\(468\) −468.000 −0.0462250
\(469\) −1806.00 −0.177811
\(470\) 7722.00 0.757850
\(471\) −11640.0 −1.13873
\(472\) 2560.00 0.249647
\(473\) −6386.00 −0.620779
\(474\) −5802.00 −0.562225
\(475\) −3476.00 −0.335768
\(476\) 448.000 0.0431388
\(477\) −1521.00 −0.146000
\(478\) −12736.0 −1.21868
\(479\) 3239.00 0.308964 0.154482 0.987996i \(-0.450629\pi\)
0.154482 + 0.987996i \(0.450629\pi\)
\(480\) 864.000 0.0821584
\(481\) −5356.00 −0.507718
\(482\) 1494.00 0.141182
\(483\) 3255.00 0.306641
\(484\) 10052.0 0.944027
\(485\) −189.000 −0.0176949
\(486\) 486.000 0.0453609
\(487\) 1798.00 0.167300 0.0836501 0.996495i \(-0.473342\pi\)
0.0836501 + 0.996495i \(0.473342\pi\)
\(488\) −4912.00 −0.455647
\(489\) −4812.00 −0.445002
\(490\) 882.000 0.0813157
\(491\) 13708.0 1.25995 0.629973 0.776617i \(-0.283066\pi\)
0.629973 + 0.776617i \(0.283066\pi\)
\(492\) −4872.00 −0.446436
\(493\) −816.000 −0.0745452
\(494\) −2054.00 −0.187073
\(495\) 5022.00 0.456004
\(496\) 3888.00 0.351968
\(497\) 1848.00 0.166789
\(498\) −4074.00 −0.366587
\(499\) −11936.0 −1.07080 −0.535400 0.844599i \(-0.679839\pi\)
−0.535400 + 0.844599i \(0.679839\pi\)
\(500\) −6084.00 −0.544170
\(501\) 2877.00 0.256557
\(502\) 15036.0 1.33683
\(503\) 2562.00 0.227105 0.113553 0.993532i \(-0.463777\pi\)
0.113553 + 0.993532i \(0.463777\pi\)
\(504\) −504.000 −0.0445435
\(505\) 8046.00 0.708995
\(506\) −19220.0 −1.68860
\(507\) 507.000 0.0444116
\(508\) −6992.00 −0.610669
\(509\) −8055.00 −0.701437 −0.350719 0.936481i \(-0.614063\pi\)
−0.350719 + 0.936481i \(0.614063\pi\)
\(510\) −864.000 −0.0750168
\(511\) 847.000 0.0733250
\(512\) 512.000 0.0441942
\(513\) 2133.00 0.183576
\(514\) 2188.00 0.187760
\(515\) 1152.00 0.0985693
\(516\) −1236.00 −0.105449
\(517\) 26598.0 2.26263
\(518\) −5768.00 −0.489250
\(519\) −1464.00 −0.123820
\(520\) −936.000 −0.0789352
\(521\) −5980.00 −0.502857 −0.251429 0.967876i \(-0.580900\pi\)
−0.251429 + 0.967876i \(0.580900\pi\)
\(522\) 918.000 0.0769727
\(523\) 19238.0 1.60845 0.804225 0.594325i \(-0.202581\pi\)
0.804225 + 0.594325i \(0.202581\pi\)
\(524\) −3744.00 −0.312132
\(525\) 924.000 0.0768127
\(526\) −2578.00 −0.213700
\(527\) −3888.00 −0.321374
\(528\) 2976.00 0.245291
\(529\) 11858.0 0.974603
\(530\) −3042.00 −0.249313
\(531\) 2880.00 0.235370
\(532\) −2212.00 −0.180268
\(533\) 5278.00 0.428922
\(534\) 6354.00 0.514915
\(535\) −6372.00 −0.514926
\(536\) 2064.00 0.166327
\(537\) 7599.00 0.610654
\(538\) −4120.00 −0.330160
\(539\) 3038.00 0.242775
\(540\) 972.000 0.0774597
\(541\) 13012.0 1.03407 0.517033 0.855966i \(-0.327036\pi\)
0.517033 + 0.855966i \(0.327036\pi\)
\(542\) 1152.00 0.0912964
\(543\) −10878.0 −0.859705
\(544\) −512.000 −0.0403526
\(545\) 11142.0 0.875726
\(546\) 546.000 0.0427960
\(547\) 18055.0 1.41129 0.705645 0.708565i \(-0.250657\pi\)
0.705645 + 0.708565i \(0.250657\pi\)
\(548\) −4512.00 −0.351721
\(549\) −5526.00 −0.429588
\(550\) −5456.00 −0.422990
\(551\) 4029.00 0.311508
\(552\) −3720.00 −0.286836
\(553\) 6769.00 0.520519
\(554\) −11398.0 −0.874106
\(555\) 11124.0 0.850788
\(556\) −3416.00 −0.260559
\(557\) −19608.0 −1.49159 −0.745797 0.666174i \(-0.767931\pi\)
−0.745797 + 0.666174i \(0.767931\pi\)
\(558\) 4374.00 0.331839
\(559\) 1339.00 0.101312
\(560\) −1008.00 −0.0760639
\(561\) −2976.00 −0.223969
\(562\) 8124.00 0.609769
\(563\) −13512.0 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 5148.00 0.384344
\(565\) 9657.00 0.719067
\(566\) −1544.00 −0.114663
\(567\) −567.000 −0.0419961
\(568\) −2112.00 −0.156017
\(569\) −4061.00 −0.299202 −0.149601 0.988746i \(-0.547799\pi\)
−0.149601 + 0.988746i \(0.547799\pi\)
\(570\) 4266.00 0.313479
\(571\) −2255.00 −0.165269 −0.0826347 0.996580i \(-0.526333\pi\)
−0.0826347 + 0.996580i \(0.526333\pi\)
\(572\) −3224.00 −0.235668
\(573\) −14976.0 −1.09185
\(574\) 5684.00 0.413320
\(575\) 6820.00 0.494632
\(576\) 576.000 0.0416667
\(577\) −254.000 −0.0183261 −0.00916305 0.999958i \(-0.502917\pi\)
−0.00916305 + 0.999958i \(0.502917\pi\)
\(578\) −9314.00 −0.670262
\(579\) −1410.00 −0.101205
\(580\) 1836.00 0.131441
\(581\) 4753.00 0.339394
\(582\) −126.000 −0.00897400
\(583\) −10478.0 −0.744347
\(584\) −968.000 −0.0685893
\(585\) −1053.00 −0.0744208
\(586\) 15666.0 1.10436
\(587\) 15057.0 1.05872 0.529360 0.848397i \(-0.322432\pi\)
0.529360 + 0.848397i \(0.322432\pi\)
\(588\) 588.000 0.0412393
\(589\) 19197.0 1.34295
\(590\) 5760.00 0.401924
\(591\) −9570.00 −0.666087
\(592\) 6592.00 0.457651
\(593\) 19917.0 1.37925 0.689623 0.724168i \(-0.257776\pi\)
0.689623 + 0.724168i \(0.257776\pi\)
\(594\) 3348.00 0.231263
\(595\) 1008.00 0.0694521
\(596\) −1768.00 −0.121510
\(597\) 5832.00 0.399812
\(598\) 4030.00 0.275584
\(599\) −15107.0 −1.03048 −0.515238 0.857047i \(-0.672297\pi\)
−0.515238 + 0.857047i \(0.672297\pi\)
\(600\) −1056.00 −0.0718517
\(601\) 23674.0 1.60679 0.803397 0.595444i \(-0.203024\pi\)
0.803397 + 0.595444i \(0.203024\pi\)
\(602\) 1442.00 0.0976271
\(603\) 2322.00 0.156815
\(604\) −4064.00 −0.273778
\(605\) 22617.0 1.51985
\(606\) 5364.00 0.359567
\(607\) 23746.0 1.58784 0.793921 0.608021i \(-0.208036\pi\)
0.793921 + 0.608021i \(0.208036\pi\)
\(608\) 2528.00 0.168625
\(609\) −1071.00 −0.0712629
\(610\) −11052.0 −0.733578
\(611\) −5577.00 −0.369266
\(612\) −576.000 −0.0380448
\(613\) −19216.0 −1.26611 −0.633056 0.774106i \(-0.718200\pi\)
−0.633056 + 0.774106i \(0.718200\pi\)
\(614\) −5782.00 −0.380037
\(615\) −10962.0 −0.718749
\(616\) −3472.00 −0.227096
\(617\) 20862.0 1.36122 0.680610 0.732646i \(-0.261715\pi\)
0.680610 + 0.732646i \(0.261715\pi\)
\(618\) 768.000 0.0499895
\(619\) 124.000 0.00805167 0.00402583 0.999992i \(-0.498719\pi\)
0.00402583 + 0.999992i \(0.498719\pi\)
\(620\) 8748.00 0.566658
\(621\) −4185.00 −0.270432
\(622\) −7060.00 −0.455113
\(623\) −7413.00 −0.476718
\(624\) −624.000 −0.0400320
\(625\) −8189.00 −0.524096
\(626\) 10980.0 0.701037
\(627\) 14694.0 0.935920
\(628\) −15520.0 −0.986171
\(629\) −6592.00 −0.417870
\(630\) −1134.00 −0.0717137
\(631\) 23942.0 1.51048 0.755242 0.655446i \(-0.227519\pi\)
0.755242 + 0.655446i \(0.227519\pi\)
\(632\) −7736.00 −0.486901
\(633\) −3417.00 −0.214555
\(634\) −11272.0 −0.706101
\(635\) −15732.0 −0.983158
\(636\) −2028.00 −0.126439
\(637\) −637.000 −0.0396214
\(638\) 6324.00 0.392429
\(639\) −2376.00 −0.147094
\(640\) 1152.00 0.0711512
\(641\) −15723.0 −0.968832 −0.484416 0.874838i \(-0.660968\pi\)
−0.484416 + 0.874838i \(0.660968\pi\)
\(642\) −4248.00 −0.261145
\(643\) −5544.00 −0.340022 −0.170011 0.985442i \(-0.554380\pi\)
−0.170011 + 0.985442i \(0.554380\pi\)
\(644\) 4340.00 0.265559
\(645\) −2781.00 −0.169770
\(646\) −2528.00 −0.153967
\(647\) −6078.00 −0.369321 −0.184661 0.982802i \(-0.559119\pi\)
−0.184661 + 0.982802i \(0.559119\pi\)
\(648\) 648.000 0.0392837
\(649\) 19840.0 1.19998
\(650\) 1144.00 0.0690329
\(651\) −5103.00 −0.307223
\(652\) −6416.00 −0.385383
\(653\) 30778.0 1.84447 0.922233 0.386635i \(-0.126363\pi\)
0.922233 + 0.386635i \(0.126363\pi\)
\(654\) 7428.00 0.444125
\(655\) −8424.00 −0.502524
\(656\) −6496.00 −0.386625
\(657\) −1089.00 −0.0646666
\(658\) −6006.00 −0.355833
\(659\) −11205.0 −0.662344 −0.331172 0.943570i \(-0.607444\pi\)
−0.331172 + 0.943570i \(0.607444\pi\)
\(660\) 6696.00 0.394911
\(661\) −20785.0 −1.22306 −0.611530 0.791221i \(-0.709446\pi\)
−0.611530 + 0.791221i \(0.709446\pi\)
\(662\) −19924.0 −1.16974
\(663\) 624.000 0.0365523
\(664\) −5432.00 −0.317474
\(665\) −4977.00 −0.290225
\(666\) 7416.00 0.431478
\(667\) −7905.00 −0.458895
\(668\) 3836.00 0.222185
\(669\) 2499.00 0.144420
\(670\) 4644.00 0.267781
\(671\) −38068.0 −2.19016
\(672\) −672.000 −0.0385758
\(673\) 1297.00 0.0742878 0.0371439 0.999310i \(-0.488174\pi\)
0.0371439 + 0.999310i \(0.488174\pi\)
\(674\) −22830.0 −1.30472
\(675\) −1188.00 −0.0677424
\(676\) 676.000 0.0384615
\(677\) 7310.00 0.414987 0.207493 0.978236i \(-0.433469\pi\)
0.207493 + 0.978236i \(0.433469\pi\)
\(678\) 6438.00 0.364675
\(679\) 147.000 0.00830831
\(680\) −1152.00 −0.0649664
\(681\) −10548.0 −0.593539
\(682\) 30132.0 1.69181
\(683\) −26384.0 −1.47812 −0.739060 0.673640i \(-0.764730\pi\)
−0.739060 + 0.673640i \(0.764730\pi\)
\(684\) 2844.00 0.158981
\(685\) −10152.0 −0.566260
\(686\) −686.000 −0.0381802
\(687\) 9666.00 0.536799
\(688\) −1648.00 −0.0913218
\(689\) 2197.00 0.121479
\(690\) −8370.00 −0.461798
\(691\) −27823.0 −1.53175 −0.765873 0.642992i \(-0.777693\pi\)
−0.765873 + 0.642992i \(0.777693\pi\)
\(692\) −1952.00 −0.107231
\(693\) −3906.00 −0.214108
\(694\) 9728.00 0.532089
\(695\) −7686.00 −0.419492
\(696\) 1224.00 0.0666603
\(697\) 6496.00 0.353018
\(698\) −938.000 −0.0508651
\(699\) −1431.00 −0.0774326
\(700\) 1232.00 0.0665217
\(701\) 24117.0 1.29941 0.649705 0.760186i \(-0.274892\pi\)
0.649705 + 0.760186i \(0.274892\pi\)
\(702\) −702.000 −0.0377426
\(703\) 32548.0 1.74619
\(704\) 3968.00 0.212428
\(705\) 11583.0 0.618782
\(706\) 8396.00 0.447575
\(707\) −6258.00 −0.332894
\(708\) 3840.00 0.203836
\(709\) 28286.0 1.49831 0.749156 0.662394i \(-0.230459\pi\)
0.749156 + 0.662394i \(0.230459\pi\)
\(710\) −4752.00 −0.251182
\(711\) −8703.00 −0.459055
\(712\) 8472.00 0.445929
\(713\) −37665.0 −1.97835
\(714\) 672.000 0.0352226
\(715\) −7254.00 −0.379418
\(716\) 10132.0 0.528842
\(717\) −19104.0 −0.995052
\(718\) 6816.00 0.354277
\(719\) −26346.0 −1.36654 −0.683268 0.730167i \(-0.739442\pi\)
−0.683268 + 0.730167i \(0.739442\pi\)
\(720\) 1296.00 0.0670820
\(721\) −896.000 −0.0462813
\(722\) −1236.00 −0.0637107
\(723\) 2241.00 0.115275
\(724\) −14504.0 −0.744526
\(725\) −2244.00 −0.114952
\(726\) 15078.0 0.770795
\(727\) −22862.0 −1.16631 −0.583153 0.812362i \(-0.698181\pi\)
−0.583153 + 0.812362i \(0.698181\pi\)
\(728\) 728.000 0.0370625
\(729\) 729.000 0.0370370
\(730\) −2178.00 −0.110427
\(731\) 1648.00 0.0833837
\(732\) −7368.00 −0.372034
\(733\) 18587.0 0.936598 0.468299 0.883570i \(-0.344867\pi\)
0.468299 + 0.883570i \(0.344867\pi\)
\(734\) −16580.0 −0.833759
\(735\) 1323.00 0.0663940
\(736\) −4960.00 −0.248408
\(737\) 15996.0 0.799485
\(738\) −7308.00 −0.364514
\(739\) 5102.00 0.253965 0.126982 0.991905i \(-0.459471\pi\)
0.126982 + 0.991905i \(0.459471\pi\)
\(740\) 14832.0 0.736804
\(741\) −3081.00 −0.152744
\(742\) 2366.00 0.117060
\(743\) 27428.0 1.35429 0.677144 0.735851i \(-0.263217\pi\)
0.677144 + 0.735851i \(0.263217\pi\)
\(744\) 5832.00 0.287381
\(745\) −3978.00 −0.195628
\(746\) −19812.0 −0.972344
\(747\) −6111.00 −0.299317
\(748\) −3968.00 −0.193963
\(749\) 4956.00 0.241773
\(750\) −9126.00 −0.444313
\(751\) 125.000 0.00607365 0.00303683 0.999995i \(-0.499033\pi\)
0.00303683 + 0.999995i \(0.499033\pi\)
\(752\) 6864.00 0.332851
\(753\) 22554.0 1.09152
\(754\) −1326.00 −0.0640452
\(755\) −9144.00 −0.440774
\(756\) −756.000 −0.0363696
\(757\) −27907.0 −1.33989 −0.669945 0.742410i \(-0.733682\pi\)
−0.669945 + 0.742410i \(0.733682\pi\)
\(758\) −18476.0 −0.885328
\(759\) −28830.0 −1.37874
\(760\) 5688.00 0.271481
\(761\) 7793.00 0.371217 0.185608 0.982624i \(-0.440574\pi\)
0.185608 + 0.982624i \(0.440574\pi\)
\(762\) −10488.0 −0.498609
\(763\) −8666.00 −0.411180
\(764\) −19968.0 −0.945572
\(765\) −1296.00 −0.0612510
\(766\) 9944.00 0.469049
\(767\) −4160.00 −0.195839
\(768\) 768.000 0.0360844
\(769\) 29393.0 1.37833 0.689167 0.724603i \(-0.257977\pi\)
0.689167 + 0.724603i \(0.257977\pi\)
\(770\) −7812.00 −0.365617
\(771\) 3282.00 0.153305
\(772\) −1880.00 −0.0876460
\(773\) 20326.0 0.945764 0.472882 0.881126i \(-0.343214\pi\)
0.472882 + 0.881126i \(0.343214\pi\)
\(774\) −1854.00 −0.0860990
\(775\) −10692.0 −0.495572
\(776\) −168.000 −0.00777171
\(777\) −8652.00 −0.399471
\(778\) 14908.0 0.686989
\(779\) −32074.0 −1.47519
\(780\) −1404.00 −0.0644503
\(781\) −16368.0 −0.749927
\(782\) 4960.00 0.226815
\(783\) 1377.00 0.0628480
\(784\) 784.000 0.0357143
\(785\) −34920.0 −1.58770
\(786\) −5616.00 −0.254855
\(787\) 16679.0 0.755454 0.377727 0.925917i \(-0.376706\pi\)
0.377727 + 0.925917i \(0.376706\pi\)
\(788\) −12760.0 −0.576848
\(789\) −3867.00 −0.174485
\(790\) −17406.0 −0.783896
\(791\) −7511.00 −0.337624
\(792\) 4464.00 0.200279
\(793\) 7982.00 0.357439
\(794\) 14438.0 0.645322
\(795\) −4563.00 −0.203563
\(796\) 7776.00 0.346248
\(797\) −9282.00 −0.412529 −0.206264 0.978496i \(-0.566131\pi\)
−0.206264 + 0.978496i \(0.566131\pi\)
\(798\) −3318.00 −0.147188
\(799\) −6864.00 −0.303918
\(800\) −1408.00 −0.0622254
\(801\) 9531.00 0.420426
\(802\) 21544.0 0.948560
\(803\) −7502.00 −0.329688
\(804\) 3096.00 0.135805
\(805\) 9765.00 0.427542
\(806\) −6318.00 −0.276107
\(807\) −6180.00 −0.269574
\(808\) 7152.00 0.311394
\(809\) −883.000 −0.0383741 −0.0191870 0.999816i \(-0.506108\pi\)
−0.0191870 + 0.999816i \(0.506108\pi\)
\(810\) 1458.00 0.0632456
\(811\) −12684.0 −0.549193 −0.274596 0.961560i \(-0.588544\pi\)
−0.274596 + 0.961560i \(0.588544\pi\)
\(812\) −1428.00 −0.0617155
\(813\) 1728.00 0.0745432
\(814\) 51088.0 2.19980
\(815\) −14436.0 −0.620455
\(816\) −768.000 −0.0329478
\(817\) −8137.00 −0.348443
\(818\) 26302.0 1.12424
\(819\) 819.000 0.0349428
\(820\) −14616.0 −0.622455
\(821\) −34126.0 −1.45068 −0.725338 0.688393i \(-0.758317\pi\)
−0.725338 + 0.688393i \(0.758317\pi\)
\(822\) −6768.00 −0.287179
\(823\) −7568.00 −0.320539 −0.160270 0.987073i \(-0.551236\pi\)
−0.160270 + 0.987073i \(0.551236\pi\)
\(824\) 1024.00 0.0432921
\(825\) −8184.00 −0.345370
\(826\) −4480.00 −0.188716
\(827\) 32076.0 1.34872 0.674360 0.738403i \(-0.264420\pi\)
0.674360 + 0.738403i \(0.264420\pi\)
\(828\) −5580.00 −0.234201
\(829\) −22598.0 −0.946756 −0.473378 0.880859i \(-0.656966\pi\)
−0.473378 + 0.880859i \(0.656966\pi\)
\(830\) −12222.0 −0.511123
\(831\) −17097.0 −0.713704
\(832\) −832.000 −0.0346688
\(833\) −784.000 −0.0326098
\(834\) −5124.00 −0.212745
\(835\) 8631.00 0.357710
\(836\) 19592.0 0.810530
\(837\) 6561.00 0.270945
\(838\) 12068.0 0.497473
\(839\) 25480.0 1.04847 0.524236 0.851573i \(-0.324351\pi\)
0.524236 + 0.851573i \(0.324351\pi\)
\(840\) −1512.00 −0.0621059
\(841\) −21788.0 −0.893354
\(842\) 17728.0 0.725591
\(843\) 12186.0 0.497874
\(844\) −4556.00 −0.185810
\(845\) 1521.00 0.0619219
\(846\) 7722.00 0.313815
\(847\) −17591.0 −0.713617
\(848\) −2704.00 −0.109500
\(849\) −2316.00 −0.0936218
\(850\) 1408.00 0.0568165
\(851\) −63860.0 −2.57238
\(852\) −3168.00 −0.127387
\(853\) −22939.0 −0.920770 −0.460385 0.887719i \(-0.652289\pi\)
−0.460385 + 0.887719i \(0.652289\pi\)
\(854\) 8596.00 0.344437
\(855\) 6399.00 0.255955
\(856\) −5664.00 −0.226158
\(857\) −38782.0 −1.54582 −0.772910 0.634516i \(-0.781200\pi\)
−0.772910 + 0.634516i \(0.781200\pi\)
\(858\) −4836.00 −0.192422
\(859\) −13970.0 −0.554890 −0.277445 0.960742i \(-0.589488\pi\)
−0.277445 + 0.960742i \(0.589488\pi\)
\(860\) −3708.00 −0.147025
\(861\) 8526.00 0.337474
\(862\) −268.000 −0.0105895
\(863\) −22212.0 −0.876136 −0.438068 0.898942i \(-0.644337\pi\)
−0.438068 + 0.898942i \(0.644337\pi\)
\(864\) 864.000 0.0340207
\(865\) −4392.00 −0.172639
\(866\) 24752.0 0.971255
\(867\) −13971.0 −0.547266
\(868\) −6804.00 −0.266063
\(869\) −59954.0 −2.34039
\(870\) 2754.00 0.107321
\(871\) −3354.00 −0.130478
\(872\) 9904.00 0.384624
\(873\) −189.000 −0.00732724
\(874\) −24490.0 −0.947811
\(875\) 10647.0 0.411353
\(876\) −1452.00 −0.0560029
\(877\) −24816.0 −0.955504 −0.477752 0.878495i \(-0.658548\pi\)
−0.477752 + 0.878495i \(0.658548\pi\)
\(878\) 28396.0 1.09148
\(879\) 23499.0 0.901708
\(880\) 8928.00 0.342003
\(881\) 7490.00 0.286430 0.143215 0.989692i \(-0.454256\pi\)
0.143215 + 0.989692i \(0.454256\pi\)
\(882\) 882.000 0.0336718
\(883\) 6092.00 0.232177 0.116088 0.993239i \(-0.462964\pi\)
0.116088 + 0.993239i \(0.462964\pi\)
\(884\) 832.000 0.0316552
\(885\) 8640.00 0.328170
\(886\) 15314.0 0.580682
\(887\) −6480.00 −0.245295 −0.122648 0.992450i \(-0.539139\pi\)
−0.122648 + 0.992450i \(0.539139\pi\)
\(888\) 9888.00 0.373671
\(889\) 12236.0 0.461622
\(890\) 19062.0 0.717932
\(891\) 5022.00 0.188825
\(892\) 3332.00 0.125071
\(893\) 33891.0 1.27001
\(894\) −2652.00 −0.0992127
\(895\) 22797.0 0.851419
\(896\) −896.000 −0.0334077
\(897\) 6045.00 0.225013
\(898\) 31000.0 1.15199
\(899\) 12393.0 0.459766
\(900\) −1584.00 −0.0586667
\(901\) 2704.00 0.0999815
\(902\) −50344.0 −1.85839
\(903\) 2163.00 0.0797122
\(904\) 8584.00 0.315818
\(905\) −32634.0 −1.19866
\(906\) −6096.00 −0.223539
\(907\) −12111.0 −0.443373 −0.221686 0.975118i \(-0.571156\pi\)
−0.221686 + 0.975118i \(0.571156\pi\)
\(908\) −14064.0 −0.514020
\(909\) 8046.00 0.293585
\(910\) 1638.00 0.0596694
\(911\) 7191.00 0.261524 0.130762 0.991414i \(-0.458258\pi\)
0.130762 + 0.991414i \(0.458258\pi\)
\(912\) 3792.00 0.137682
\(913\) −42098.0 −1.52600
\(914\) 20368.0 0.737105
\(915\) −16578.0 −0.598964
\(916\) 12888.0 0.464882
\(917\) 6552.00 0.235950
\(918\) −864.000 −0.0310635
\(919\) −12272.0 −0.440496 −0.220248 0.975444i \(-0.570687\pi\)
−0.220248 + 0.975444i \(0.570687\pi\)
\(920\) −11160.0 −0.399929
\(921\) −8673.00 −0.310299
\(922\) 38500.0 1.37520
\(923\) 3432.00 0.122390
\(924\) −5208.00 −0.185423
\(925\) −18128.0 −0.644373
\(926\) −31244.0 −1.10879
\(927\) 1152.00 0.0408162
\(928\) 1632.00 0.0577296
\(929\) 3285.00 0.116014 0.0580072 0.998316i \(-0.481525\pi\)
0.0580072 + 0.998316i \(0.481525\pi\)
\(930\) 13122.0 0.462675
\(931\) 3871.00 0.136269
\(932\) −1908.00 −0.0670586
\(933\) −10590.0 −0.371598
\(934\) −31188.0 −1.09262
\(935\) −8928.00 −0.312275
\(936\) −936.000 −0.0326860
\(937\) −5068.00 −0.176696 −0.0883481 0.996090i \(-0.528159\pi\)
−0.0883481 + 0.996090i \(0.528159\pi\)
\(938\) −3612.00 −0.125731
\(939\) 16470.0 0.572394
\(940\) 15444.0 0.535881
\(941\) 13571.0 0.470140 0.235070 0.971978i \(-0.424468\pi\)
0.235070 + 0.971978i \(0.424468\pi\)
\(942\) −23280.0 −0.805205
\(943\) 62930.0 2.17315
\(944\) 5120.00 0.176527
\(945\) −1701.00 −0.0585540
\(946\) −12772.0 −0.438957
\(947\) −17662.0 −0.606059 −0.303030 0.952981i \(-0.597998\pi\)
−0.303030 + 0.952981i \(0.597998\pi\)
\(948\) −11604.0 −0.397553
\(949\) 1573.00 0.0538058
\(950\) −6952.00 −0.237424
\(951\) −16908.0 −0.576529
\(952\) 896.000 0.0305037
\(953\) 37893.0 1.28801 0.644006 0.765021i \(-0.277271\pi\)
0.644006 + 0.765021i \(0.277271\pi\)
\(954\) −3042.00 −0.103237
\(955\) −44928.0 −1.52234
\(956\) −25472.0 −0.861740
\(957\) 9486.00 0.320417
\(958\) 6478.00 0.218470
\(959\) 7896.00 0.265876
\(960\) 1728.00 0.0580948
\(961\) 29258.0 0.982109
\(962\) −10712.0 −0.359011
\(963\) −6372.00 −0.213224
\(964\) 2988.00 0.0998309
\(965\) −4230.00 −0.141107
\(966\) 6510.00 0.216828
\(967\) −48914.0 −1.62665 −0.813324 0.581811i \(-0.802344\pi\)
−0.813324 + 0.581811i \(0.802344\pi\)
\(968\) 20104.0 0.667528
\(969\) −3792.00 −0.125714
\(970\) −378.000 −0.0125122
\(971\) 31110.0 1.02818 0.514092 0.857735i \(-0.328129\pi\)
0.514092 + 0.857735i \(0.328129\pi\)
\(972\) 972.000 0.0320750
\(973\) 5978.00 0.196964
\(974\) 3596.00 0.118299
\(975\) 1716.00 0.0563651
\(976\) −9824.00 −0.322191
\(977\) 22294.0 0.730039 0.365020 0.931000i \(-0.381062\pi\)
0.365020 + 0.931000i \(0.381062\pi\)
\(978\) −9624.00 −0.314664
\(979\) 65658.0 2.14345
\(980\) 1764.00 0.0574989
\(981\) 11142.0 0.362627
\(982\) 27416.0 0.890916
\(983\) −317.000 −0.0102856 −0.00514279 0.999987i \(-0.501637\pi\)
−0.00514279 + 0.999987i \(0.501637\pi\)
\(984\) −9744.00 −0.315678
\(985\) −28710.0 −0.928707
\(986\) −1632.00 −0.0527114
\(987\) −9009.00 −0.290537
\(988\) −4108.00 −0.132280
\(989\) 15965.0 0.513304
\(990\) 10044.0 0.322444
\(991\) 40564.0 1.30026 0.650130 0.759823i \(-0.274714\pi\)
0.650130 + 0.759823i \(0.274714\pi\)
\(992\) 7776.00 0.248879
\(993\) −29886.0 −0.955089
\(994\) 3696.00 0.117938
\(995\) 17496.0 0.557448
\(996\) −8148.00 −0.259216
\(997\) −57528.0 −1.82741 −0.913706 0.406376i \(-0.866792\pi\)
−0.913706 + 0.406376i \(0.866792\pi\)
\(998\) −23872.0 −0.757169
\(999\) 11124.0 0.352300
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 546.4.a.e.1.1 1
3.2 odd 2 1638.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.4.a.e.1.1 1 1.1 even 1 trivial
1638.4.a.b.1.1 1 3.2 odd 2