Properties

Label 546.4.a.c.1.1
Level $546$
Weight $4$
Character 546.1
Self dual yes
Analytic conductor $32.215$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -14.0000 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -14.0000 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -28.0000 q^{10} +8.00000 q^{11} +12.0000 q^{12} +13.0000 q^{13} -14.0000 q^{14} -42.0000 q^{15} +16.0000 q^{16} -98.0000 q^{17} +18.0000 q^{18} -28.0000 q^{19} -56.0000 q^{20} -21.0000 q^{21} +16.0000 q^{22} -52.0000 q^{23} +24.0000 q^{24} +71.0000 q^{25} +26.0000 q^{26} +27.0000 q^{27} -28.0000 q^{28} -2.00000 q^{29} -84.0000 q^{30} -168.000 q^{31} +32.0000 q^{32} +24.0000 q^{33} -196.000 q^{34} +98.0000 q^{35} +36.0000 q^{36} -146.000 q^{37} -56.0000 q^{38} +39.0000 q^{39} -112.000 q^{40} -514.000 q^{41} -42.0000 q^{42} -236.000 q^{43} +32.0000 q^{44} -126.000 q^{45} -104.000 q^{46} -216.000 q^{47} +48.0000 q^{48} +49.0000 q^{49} +142.000 q^{50} -294.000 q^{51} +52.0000 q^{52} -66.0000 q^{53} +54.0000 q^{54} -112.000 q^{55} -56.0000 q^{56} -84.0000 q^{57} -4.00000 q^{58} -84.0000 q^{59} -168.000 q^{60} +446.000 q^{61} -336.000 q^{62} -63.0000 q^{63} +64.0000 q^{64} -182.000 q^{65} +48.0000 q^{66} +292.000 q^{67} -392.000 q^{68} -156.000 q^{69} +196.000 q^{70} +100.000 q^{71} +72.0000 q^{72} +450.000 q^{73} -292.000 q^{74} +213.000 q^{75} -112.000 q^{76} -56.0000 q^{77} +78.0000 q^{78} +392.000 q^{79} -224.000 q^{80} +81.0000 q^{81} -1028.00 q^{82} -292.000 q^{83} -84.0000 q^{84} +1372.00 q^{85} -472.000 q^{86} -6.00000 q^{87} +64.0000 q^{88} -402.000 q^{89} -252.000 q^{90} -91.0000 q^{91} -208.000 q^{92} -504.000 q^{93} -432.000 q^{94} +392.000 q^{95} +96.0000 q^{96} +314.000 q^{97} +98.0000 q^{98} +72.0000 q^{99} +O(q^{100})\)

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
\(5\) −14.0000 −1.25220 −0.626099 0.779744i \(-0.715349\pi\)
−0.626099 + 0.779744i \(0.715349\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −28.0000 −0.885438
\(11\) 8.00000 0.219281 0.109640 0.993971i \(-0.465030\pi\)
0.109640 + 0.993971i \(0.465030\pi\)
\(12\) 12.0000 0.288675
\(13\) 13.0000 0.277350
\(14\) −14.0000 −0.267261
\(15\) −42.0000 −0.722957
\(16\) 16.0000 0.250000
\(17\) −98.0000 −1.39815 −0.699073 0.715050i \(-0.746404\pi\)
−0.699073 + 0.715050i \(0.746404\pi\)
\(18\) 18.0000 0.235702
\(19\) −28.0000 −0.338086 −0.169043 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) −56.0000 −0.626099
\(21\) −21.0000 −0.218218
\(22\) 16.0000 0.155055
\(23\) −52.0000 −0.471424 −0.235712 0.971823i \(-0.575742\pi\)
−0.235712 + 0.971823i \(0.575742\pi\)
\(24\) 24.0000 0.204124
\(25\) 71.0000 0.568000
\(26\) 26.0000 0.196116
\(27\) 27.0000 0.192450
\(28\) −28.0000 −0.188982
\(29\) −2.00000 −0.0128066 −0.00640329 0.999979i \(-0.502038\pi\)
−0.00640329 + 0.999979i \(0.502038\pi\)
\(30\) −84.0000 −0.511208
\(31\) −168.000 −0.973345 −0.486672 0.873585i \(-0.661789\pi\)
−0.486672 + 0.873585i \(0.661789\pi\)
\(32\) 32.0000 0.176777
\(33\) 24.0000 0.126602
\(34\) −196.000 −0.988639
\(35\) 98.0000 0.473286
\(36\) 36.0000 0.166667
\(37\) −146.000 −0.648710 −0.324355 0.945936i \(-0.605147\pi\)
−0.324355 + 0.945936i \(0.605147\pi\)
\(38\) −56.0000 −0.239063
\(39\) 39.0000 0.160128
\(40\) −112.000 −0.442719
\(41\) −514.000 −1.95789 −0.978943 0.204135i \(-0.934562\pi\)
−0.978943 + 0.204135i \(0.934562\pi\)
\(42\) −42.0000 −0.154303
\(43\) −236.000 −0.836969 −0.418484 0.908224i \(-0.637439\pi\)
−0.418484 + 0.908224i \(0.637439\pi\)
\(44\) 32.0000 0.109640
\(45\) −126.000 −0.417399
\(46\) −104.000 −0.333347
\(47\) −216.000 −0.670358 −0.335179 0.942154i \(-0.608797\pi\)
−0.335179 + 0.942154i \(0.608797\pi\)
\(48\) 48.0000 0.144338
\(49\) 49.0000 0.142857
\(50\) 142.000 0.401637
\(51\) −294.000 −0.807220
\(52\) 52.0000 0.138675
\(53\) −66.0000 −0.171053 −0.0855264 0.996336i \(-0.527257\pi\)
−0.0855264 + 0.996336i \(0.527257\pi\)
\(54\) 54.0000 0.136083
\(55\) −112.000 −0.274583
\(56\) −56.0000 −0.133631
\(57\) −84.0000 −0.195194
\(58\) −4.00000 −0.00905562
\(59\) −84.0000 −0.185354 −0.0926769 0.995696i \(-0.529542\pi\)
−0.0926769 + 0.995696i \(0.529542\pi\)
\(60\) −168.000 −0.361478
\(61\) 446.000 0.936138 0.468069 0.883692i \(-0.344950\pi\)
0.468069 + 0.883692i \(0.344950\pi\)
\(62\) −336.000 −0.688259
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) −182.000 −0.347297
\(66\) 48.0000 0.0895211
\(67\) 292.000 0.532440 0.266220 0.963912i \(-0.414225\pi\)
0.266220 + 0.963912i \(0.414225\pi\)
\(68\) −392.000 −0.699073
\(69\) −156.000 −0.272177
\(70\) 196.000 0.334664
\(71\) 100.000 0.167152 0.0835762 0.996501i \(-0.473366\pi\)
0.0835762 + 0.996501i \(0.473366\pi\)
\(72\) 72.0000 0.117851
\(73\) 450.000 0.721487 0.360743 0.932665i \(-0.382523\pi\)
0.360743 + 0.932665i \(0.382523\pi\)
\(74\) −292.000 −0.458707
\(75\) 213.000 0.327935
\(76\) −112.000 −0.169043
\(77\) −56.0000 −0.0828804
\(78\) 78.0000 0.113228
\(79\) 392.000 0.558271 0.279136 0.960252i \(-0.409952\pi\)
0.279136 + 0.960252i \(0.409952\pi\)
\(80\) −224.000 −0.313050
\(81\) 81.0000 0.111111
\(82\) −1028.00 −1.38443
\(83\) −292.000 −0.386159 −0.193079 0.981183i \(-0.561847\pi\)
−0.193079 + 0.981183i \(0.561847\pi\)
\(84\) −84.0000 −0.109109
\(85\) 1372.00 1.75076
\(86\) −472.000 −0.591826
\(87\) −6.00000 −0.00739388
\(88\) 64.0000 0.0775275
\(89\) −402.000 −0.478786 −0.239393 0.970923i \(-0.576948\pi\)
−0.239393 + 0.970923i \(0.576948\pi\)
\(90\) −252.000 −0.295146
\(91\) −91.0000 −0.104828
\(92\) −208.000 −0.235712
\(93\) −504.000 −0.561961
\(94\) −432.000 −0.474015
\(95\) 392.000 0.423351
\(96\) 96.0000 0.102062
\(97\) 314.000 0.328679 0.164340 0.986404i \(-0.447451\pi\)
0.164340 + 0.986404i \(0.447451\pi\)
\(98\) 98.0000 0.101015
\(99\) 72.0000 0.0730937
\(100\) 284.000 0.284000
\(101\) 858.000 0.845289 0.422645 0.906296i \(-0.361102\pi\)
0.422645 + 0.906296i \(0.361102\pi\)
\(102\) −588.000 −0.570791
\(103\) −944.000 −0.903059 −0.451530 0.892256i \(-0.649121\pi\)
−0.451530 + 0.892256i \(0.649121\pi\)
\(104\) 104.000 0.0980581
\(105\) 294.000 0.273252
\(106\) −132.000 −0.120953
\(107\) 840.000 0.758933 0.379467 0.925205i \(-0.376107\pi\)
0.379467 + 0.925205i \(0.376107\pi\)
\(108\) 108.000 0.0962250
\(109\) 1334.00 1.17224 0.586119 0.810225i \(-0.300655\pi\)
0.586119 + 0.810225i \(0.300655\pi\)
\(110\) −224.000 −0.194160
\(111\) −438.000 −0.374533
\(112\) −112.000 −0.0944911
\(113\) 946.000 0.787542 0.393771 0.919209i \(-0.371170\pi\)
0.393771 + 0.919209i \(0.371170\pi\)
\(114\) −168.000 −0.138023
\(115\) 728.000 0.590316
\(116\) −8.00000 −0.00640329
\(117\) 117.000 0.0924500
\(118\) −168.000 −0.131065
\(119\) 686.000 0.528450
\(120\) −336.000 −0.255604
\(121\) −1267.00 −0.951916
\(122\) 892.000 0.661950
\(123\) −1542.00 −1.13039
\(124\) −672.000 −0.486672
\(125\) 756.000 0.540950
\(126\) −126.000 −0.0890871
\(127\) 904.000 0.631630 0.315815 0.948821i \(-0.397722\pi\)
0.315815 + 0.948821i \(0.397722\pi\)
\(128\) 128.000 0.0883883
\(129\) −708.000 −0.483224
\(130\) −364.000 −0.245576
\(131\) −1476.00 −0.984418 −0.492209 0.870477i \(-0.663810\pi\)
−0.492209 + 0.870477i \(0.663810\pi\)
\(132\) 96.0000 0.0633010
\(133\) 196.000 0.127785
\(134\) 584.000 0.376492
\(135\) −378.000 −0.240986
\(136\) −784.000 −0.494319
\(137\) −62.0000 −0.0386644 −0.0193322 0.999813i \(-0.506154\pi\)
−0.0193322 + 0.999813i \(0.506154\pi\)
\(138\) −312.000 −0.192458
\(139\) −908.000 −0.554069 −0.277034 0.960860i \(-0.589352\pi\)
−0.277034 + 0.960860i \(0.589352\pi\)
\(140\) 392.000 0.236643
\(141\) −648.000 −0.387032
\(142\) 200.000 0.118195
\(143\) 104.000 0.0608176
\(144\) 144.000 0.0833333
\(145\) 28.0000 0.0160364
\(146\) 900.000 0.510168
\(147\) 147.000 0.0824786
\(148\) −584.000 −0.324355
\(149\) −2514.00 −1.38225 −0.691124 0.722736i \(-0.742884\pi\)
−0.691124 + 0.722736i \(0.742884\pi\)
\(150\) 426.000 0.231885
\(151\) −1048.00 −0.564802 −0.282401 0.959297i \(-0.591131\pi\)
−0.282401 + 0.959297i \(0.591131\pi\)
\(152\) −224.000 −0.119532
\(153\) −882.000 −0.466049
\(154\) −112.000 −0.0586053
\(155\) 2352.00 1.21882
\(156\) 156.000 0.0800641
\(157\) 3166.00 1.60939 0.804695 0.593688i \(-0.202329\pi\)
0.804695 + 0.593688i \(0.202329\pi\)
\(158\) 784.000 0.394758
\(159\) −198.000 −0.0987574
\(160\) −448.000 −0.221359
\(161\) 364.000 0.178181
\(162\) 162.000 0.0785674
\(163\) −492.000 −0.236420 −0.118210 0.992989i \(-0.537716\pi\)
−0.118210 + 0.992989i \(0.537716\pi\)
\(164\) −2056.00 −0.978943
\(165\) −336.000 −0.158531
\(166\) −584.000 −0.273055
\(167\) −1104.00 −0.511557 −0.255779 0.966735i \(-0.582332\pi\)
−0.255779 + 0.966735i \(0.582332\pi\)
\(168\) −168.000 −0.0771517
\(169\) 169.000 0.0769231
\(170\) 2744.00 1.23797
\(171\) −252.000 −0.112695
\(172\) −944.000 −0.418484
\(173\) −2686.00 −1.18042 −0.590210 0.807249i \(-0.700955\pi\)
−0.590210 + 0.807249i \(0.700955\pi\)
\(174\) −12.0000 −0.00522826
\(175\) −497.000 −0.214684
\(176\) 128.000 0.0548202
\(177\) −252.000 −0.107014
\(178\) −804.000 −0.338553
\(179\) 2088.00 0.871868 0.435934 0.899979i \(-0.356418\pi\)
0.435934 + 0.899979i \(0.356418\pi\)
\(180\) −504.000 −0.208700
\(181\) −242.000 −0.0993797 −0.0496898 0.998765i \(-0.515823\pi\)
−0.0496898 + 0.998765i \(0.515823\pi\)
\(182\) −182.000 −0.0741249
\(183\) 1338.00 0.540480
\(184\) −416.000 −0.166674
\(185\) 2044.00 0.812313
\(186\) −1008.00 −0.397366
\(187\) −784.000 −0.306587
\(188\) −864.000 −0.335179
\(189\) −189.000 −0.0727393
\(190\) 784.000 0.299354
\(191\) −1284.00 −0.486424 −0.243212 0.969973i \(-0.578201\pi\)
−0.243212 + 0.969973i \(0.578201\pi\)
\(192\) 192.000 0.0721688
\(193\) −2734.00 −1.01968 −0.509838 0.860270i \(-0.670295\pi\)
−0.509838 + 0.860270i \(0.670295\pi\)
\(194\) 628.000 0.232411
\(195\) −546.000 −0.200512
\(196\) 196.000 0.0714286
\(197\) 5118.00 1.85098 0.925488 0.378776i \(-0.123655\pi\)
0.925488 + 0.378776i \(0.123655\pi\)
\(198\) 144.000 0.0516850
\(199\) 1528.00 0.544307 0.272153 0.962254i \(-0.412264\pi\)
0.272153 + 0.962254i \(0.412264\pi\)
\(200\) 568.000 0.200818
\(201\) 876.000 0.307404
\(202\) 1716.00 0.597710
\(203\) 14.0000 0.00484043
\(204\) −1176.00 −0.403610
\(205\) 7196.00 2.45166
\(206\) −1888.00 −0.638559
\(207\) −468.000 −0.157141
\(208\) 208.000 0.0693375
\(209\) −224.000 −0.0741359
\(210\) 588.000 0.193218
\(211\) 268.000 0.0874402 0.0437201 0.999044i \(-0.486079\pi\)
0.0437201 + 0.999044i \(0.486079\pi\)
\(212\) −264.000 −0.0855264
\(213\) 300.000 0.0965055
\(214\) 1680.00 0.536647
\(215\) 3304.00 1.04805
\(216\) 216.000 0.0680414
\(217\) 1176.00 0.367890
\(218\) 2668.00 0.828898
\(219\) 1350.00 0.416550
\(220\) −448.000 −0.137292
\(221\) −1274.00 −0.387776
\(222\) −876.000 −0.264835
\(223\) 1392.00 0.418005 0.209003 0.977915i \(-0.432978\pi\)
0.209003 + 0.977915i \(0.432978\pi\)
\(224\) −224.000 −0.0668153
\(225\) 639.000 0.189333
\(226\) 1892.00 0.556876
\(227\) −6140.00 −1.79527 −0.897635 0.440740i \(-0.854716\pi\)
−0.897635 + 0.440740i \(0.854716\pi\)
\(228\) −336.000 −0.0975971
\(229\) 1870.00 0.539620 0.269810 0.962914i \(-0.413039\pi\)
0.269810 + 0.962914i \(0.413039\pi\)
\(230\) 1456.00 0.417417
\(231\) −168.000 −0.0478510
\(232\) −16.0000 −0.00452781
\(233\) 50.0000 0.0140584 0.00702920 0.999975i \(-0.497763\pi\)
0.00702920 + 0.999975i \(0.497763\pi\)
\(234\) 234.000 0.0653720
\(235\) 3024.00 0.839421
\(236\) −336.000 −0.0926769
\(237\) 1176.00 0.322318
\(238\) 1372.00 0.373670
\(239\) −3228.00 −0.873648 −0.436824 0.899547i \(-0.643897\pi\)
−0.436824 + 0.899547i \(0.643897\pi\)
\(240\) −672.000 −0.180739
\(241\) 5978.00 1.59783 0.798915 0.601444i \(-0.205408\pi\)
0.798915 + 0.601444i \(0.205408\pi\)
\(242\) −2534.00 −0.673106
\(243\) 243.000 0.0641500
\(244\) 1784.00 0.468069
\(245\) −686.000 −0.178885
\(246\) −3084.00 −0.799303
\(247\) −364.000 −0.0937683
\(248\) −1344.00 −0.344129
\(249\) −876.000 −0.222949
\(250\) 1512.00 0.382509
\(251\) −4084.00 −1.02701 −0.513506 0.858086i \(-0.671653\pi\)
−0.513506 + 0.858086i \(0.671653\pi\)
\(252\) −252.000 −0.0629941
\(253\) −416.000 −0.103374
\(254\) 1808.00 0.446630
\(255\) 4116.00 1.01080
\(256\) 256.000 0.0625000
\(257\) 2646.00 0.642229 0.321115 0.947040i \(-0.395943\pi\)
0.321115 + 0.947040i \(0.395943\pi\)
\(258\) −1416.00 −0.341691
\(259\) 1022.00 0.245189
\(260\) −728.000 −0.173649
\(261\) −18.0000 −0.00426886
\(262\) −2952.00 −0.696088
\(263\) 5164.00 1.21074 0.605372 0.795942i \(-0.293024\pi\)
0.605372 + 0.795942i \(0.293024\pi\)
\(264\) 192.000 0.0447605
\(265\) 924.000 0.214192
\(266\) 392.000 0.0903574
\(267\) −1206.00 −0.276427
\(268\) 1168.00 0.266220
\(269\) −4710.00 −1.06756 −0.533780 0.845623i \(-0.679229\pi\)
−0.533780 + 0.845623i \(0.679229\pi\)
\(270\) −756.000 −0.170403
\(271\) −3144.00 −0.704739 −0.352370 0.935861i \(-0.614624\pi\)
−0.352370 + 0.935861i \(0.614624\pi\)
\(272\) −1568.00 −0.349537
\(273\) −273.000 −0.0605228
\(274\) −124.000 −0.0273398
\(275\) 568.000 0.124552
\(276\) −624.000 −0.136088
\(277\) 3310.00 0.717973 0.358987 0.933343i \(-0.383122\pi\)
0.358987 + 0.933343i \(0.383122\pi\)
\(278\) −1816.00 −0.391786
\(279\) −1512.00 −0.324448
\(280\) 784.000 0.167332
\(281\) −4910.00 −1.04237 −0.521185 0.853444i \(-0.674510\pi\)
−0.521185 + 0.853444i \(0.674510\pi\)
\(282\) −1296.00 −0.273673
\(283\) 7436.00 1.56192 0.780962 0.624579i \(-0.214729\pi\)
0.780962 + 0.624579i \(0.214729\pi\)
\(284\) 400.000 0.0835762
\(285\) 1176.00 0.244422
\(286\) 208.000 0.0430045
\(287\) 3598.00 0.740011
\(288\) 288.000 0.0589256
\(289\) 4691.00 0.954814
\(290\) 56.0000 0.0113394
\(291\) 942.000 0.189763
\(292\) 1800.00 0.360743
\(293\) −310.000 −0.0618102 −0.0309051 0.999522i \(-0.509839\pi\)
−0.0309051 + 0.999522i \(0.509839\pi\)
\(294\) 294.000 0.0583212
\(295\) 1176.00 0.232100
\(296\) −1168.00 −0.229353
\(297\) 216.000 0.0422006
\(298\) −5028.00 −0.977397
\(299\) −676.000 −0.130749
\(300\) 852.000 0.163967
\(301\) 1652.00 0.316345
\(302\) −2096.00 −0.399375
\(303\) 2574.00 0.488028
\(304\) −448.000 −0.0845216
\(305\) −6244.00 −1.17223
\(306\) −1764.00 −0.329546
\(307\) −3516.00 −0.653644 −0.326822 0.945086i \(-0.605978\pi\)
−0.326822 + 0.945086i \(0.605978\pi\)
\(308\) −224.000 −0.0414402
\(309\) −2832.00 −0.521381
\(310\) 4704.00 0.861836
\(311\) 3216.00 0.586375 0.293188 0.956055i \(-0.405284\pi\)
0.293188 + 0.956055i \(0.405284\pi\)
\(312\) 312.000 0.0566139
\(313\) −1398.00 −0.252459 −0.126229 0.992001i \(-0.540288\pi\)
−0.126229 + 0.992001i \(0.540288\pi\)
\(314\) 6332.00 1.13801
\(315\) 882.000 0.157762
\(316\) 1568.00 0.279136
\(317\) −9034.00 −1.60063 −0.800315 0.599579i \(-0.795335\pi\)
−0.800315 + 0.599579i \(0.795335\pi\)
\(318\) −396.000 −0.0698320
\(319\) −16.0000 −0.00280824
\(320\) −896.000 −0.156525
\(321\) 2520.00 0.438170
\(322\) 728.000 0.125993
\(323\) 2744.00 0.472694
\(324\) 324.000 0.0555556
\(325\) 923.000 0.157535
\(326\) −984.000 −0.167174
\(327\) 4002.00 0.676792
\(328\) −4112.00 −0.692217
\(329\) 1512.00 0.253372
\(330\) −672.000 −0.112098
\(331\) 9108.00 1.51245 0.756225 0.654312i \(-0.227042\pi\)
0.756225 + 0.654312i \(0.227042\pi\)
\(332\) −1168.00 −0.193079
\(333\) −1314.00 −0.216237
\(334\) −2208.00 −0.361726
\(335\) −4088.00 −0.666720
\(336\) −336.000 −0.0545545
\(337\) −1566.00 −0.253132 −0.126566 0.991958i \(-0.540396\pi\)
−0.126566 + 0.991958i \(0.540396\pi\)
\(338\) 338.000 0.0543928
\(339\) 2838.00 0.454687
\(340\) 5488.00 0.875378
\(341\) −1344.00 −0.213436
\(342\) −504.000 −0.0796877
\(343\) −343.000 −0.0539949
\(344\) −1888.00 −0.295913
\(345\) 2184.00 0.340819
\(346\) −5372.00 −0.834684
\(347\) 4528.00 0.700507 0.350253 0.936655i \(-0.386096\pi\)
0.350253 + 0.936655i \(0.386096\pi\)
\(348\) −24.0000 −0.00369694
\(349\) −1090.00 −0.167182 −0.0835908 0.996500i \(-0.526639\pi\)
−0.0835908 + 0.996500i \(0.526639\pi\)
\(350\) −994.000 −0.151804
\(351\) 351.000 0.0533761
\(352\) 256.000 0.0387638
\(353\) −11234.0 −1.69384 −0.846920 0.531720i \(-0.821546\pi\)
−0.846920 + 0.531720i \(0.821546\pi\)
\(354\) −504.000 −0.0756703
\(355\) −1400.00 −0.209308
\(356\) −1608.00 −0.239393
\(357\) 2058.00 0.305101
\(358\) 4176.00 0.616504
\(359\) 3444.00 0.506316 0.253158 0.967425i \(-0.418531\pi\)
0.253158 + 0.967425i \(0.418531\pi\)
\(360\) −1008.00 −0.147573
\(361\) −6075.00 −0.885698
\(362\) −484.000 −0.0702720
\(363\) −3801.00 −0.549589
\(364\) −364.000 −0.0524142
\(365\) −6300.00 −0.903444
\(366\) 2676.00 0.382177
\(367\) 11712.0 1.66583 0.832917 0.553397i \(-0.186669\pi\)
0.832917 + 0.553397i \(0.186669\pi\)
\(368\) −832.000 −0.117856
\(369\) −4626.00 −0.652629
\(370\) 4088.00 0.574392
\(371\) 462.000 0.0646519
\(372\) −2016.00 −0.280980
\(373\) 10990.0 1.52558 0.762789 0.646647i \(-0.223829\pi\)
0.762789 + 0.646647i \(0.223829\pi\)
\(374\) −1568.00 −0.216790
\(375\) 2268.00 0.312317
\(376\) −1728.00 −0.237007
\(377\) −26.0000 −0.00355190
\(378\) −378.000 −0.0514344
\(379\) −7004.00 −0.949265 −0.474632 0.880184i \(-0.657419\pi\)
−0.474632 + 0.880184i \(0.657419\pi\)
\(380\) 1568.00 0.211676
\(381\) 2712.00 0.364672
\(382\) −2568.00 −0.343954
\(383\) −5472.00 −0.730042 −0.365021 0.930999i \(-0.618938\pi\)
−0.365021 + 0.930999i \(0.618938\pi\)
\(384\) 384.000 0.0510310
\(385\) 784.000 0.103783
\(386\) −5468.00 −0.721020
\(387\) −2124.00 −0.278990
\(388\) 1256.00 0.164340
\(389\) 1910.00 0.248948 0.124474 0.992223i \(-0.460276\pi\)
0.124474 + 0.992223i \(0.460276\pi\)
\(390\) −1092.00 −0.141784
\(391\) 5096.00 0.659120
\(392\) 392.000 0.0505076
\(393\) −4428.00 −0.568354
\(394\) 10236.0 1.30884
\(395\) −5488.00 −0.699066
\(396\) 288.000 0.0365468
\(397\) −13234.0 −1.67304 −0.836518 0.547939i \(-0.815413\pi\)
−0.836518 + 0.547939i \(0.815413\pi\)
\(398\) 3056.00 0.384883
\(399\) 588.000 0.0737765
\(400\) 1136.00 0.142000
\(401\) 4586.00 0.571107 0.285554 0.958363i \(-0.407823\pi\)
0.285554 + 0.958363i \(0.407823\pi\)
\(402\) 1752.00 0.217368
\(403\) −2184.00 −0.269957
\(404\) 3432.00 0.422645
\(405\) −1134.00 −0.139133
\(406\) 28.0000 0.00342270
\(407\) −1168.00 −0.142250
\(408\) −2352.00 −0.285395
\(409\) −4174.00 −0.504624 −0.252312 0.967646i \(-0.581191\pi\)
−0.252312 + 0.967646i \(0.581191\pi\)
\(410\) 14392.0 1.73359
\(411\) −186.000 −0.0223229
\(412\) −3776.00 −0.451530
\(413\) 588.000 0.0700571
\(414\) −936.000 −0.111116
\(415\) 4088.00 0.483547
\(416\) 416.000 0.0490290
\(417\) −2724.00 −0.319892
\(418\) −448.000 −0.0524220
\(419\) −10012.0 −1.16735 −0.583673 0.811989i \(-0.698385\pi\)
−0.583673 + 0.811989i \(0.698385\pi\)
\(420\) 1176.00 0.136626
\(421\) −1250.00 −0.144706 −0.0723531 0.997379i \(-0.523051\pi\)
−0.0723531 + 0.997379i \(0.523051\pi\)
\(422\) 536.000 0.0618296
\(423\) −1944.00 −0.223453
\(424\) −528.000 −0.0604763
\(425\) −6958.00 −0.794147
\(426\) 600.000 0.0682397
\(427\) −3122.00 −0.353827
\(428\) 3360.00 0.379467
\(429\) 312.000 0.0351131
\(430\) 6608.00 0.741084
\(431\) 6236.00 0.696932 0.348466 0.937321i \(-0.386703\pi\)
0.348466 + 0.937321i \(0.386703\pi\)
\(432\) 432.000 0.0481125
\(433\) −3966.00 −0.440170 −0.220085 0.975481i \(-0.570634\pi\)
−0.220085 + 0.975481i \(0.570634\pi\)
\(434\) 2352.00 0.260137
\(435\) 84.0000 0.00925860
\(436\) 5336.00 0.586119
\(437\) 1456.00 0.159382
\(438\) 2700.00 0.294546
\(439\) 8776.00 0.954113 0.477057 0.878873i \(-0.341704\pi\)
0.477057 + 0.878873i \(0.341704\pi\)
\(440\) −896.000 −0.0970798
\(441\) 441.000 0.0476190
\(442\) −2548.00 −0.274199
\(443\) 6096.00 0.653792 0.326896 0.945060i \(-0.393997\pi\)
0.326896 + 0.945060i \(0.393997\pi\)
\(444\) −1752.00 −0.187266
\(445\) 5628.00 0.599534
\(446\) 2784.00 0.295574
\(447\) −7542.00 −0.798041
\(448\) −448.000 −0.0472456
\(449\) −9390.00 −0.986952 −0.493476 0.869759i \(-0.664274\pi\)
−0.493476 + 0.869759i \(0.664274\pi\)
\(450\) 1278.00 0.133879
\(451\) −4112.00 −0.429327
\(452\) 3784.00 0.393771
\(453\) −3144.00 −0.326088
\(454\) −12280.0 −1.26945
\(455\) 1274.00 0.131266
\(456\) −672.000 −0.0690116
\(457\) −6.00000 −0.000614154 0 −0.000307077 1.00000i \(-0.500098\pi\)
−0.000307077 1.00000i \(0.500098\pi\)
\(458\) 3740.00 0.381569
\(459\) −2646.00 −0.269073
\(460\) 2912.00 0.295158
\(461\) −9374.00 −0.947051 −0.473526 0.880780i \(-0.657019\pi\)
−0.473526 + 0.880780i \(0.657019\pi\)
\(462\) −336.000 −0.0338358
\(463\) 4008.00 0.402306 0.201153 0.979560i \(-0.435531\pi\)
0.201153 + 0.979560i \(0.435531\pi\)
\(464\) −32.0000 −0.00320164
\(465\) 7056.00 0.703686
\(466\) 100.000 0.00994080
\(467\) −3260.00 −0.323030 −0.161515 0.986870i \(-0.551638\pi\)
−0.161515 + 0.986870i \(0.551638\pi\)
\(468\) 468.000 0.0462250
\(469\) −2044.00 −0.201243
\(470\) 6048.00 0.593561
\(471\) 9498.00 0.929182
\(472\) −672.000 −0.0655324
\(473\) −1888.00 −0.183531
\(474\) 2352.00 0.227913
\(475\) −1988.00 −0.192033
\(476\) 2744.00 0.264225
\(477\) −594.000 −0.0570176
\(478\) −6456.00 −0.617763
\(479\) 12696.0 1.21105 0.605527 0.795825i \(-0.292962\pi\)
0.605527 + 0.795825i \(0.292962\pi\)
\(480\) −1344.00 −0.127802
\(481\) −1898.00 −0.179920
\(482\) 11956.0 1.12984
\(483\) 1092.00 0.102873
\(484\) −5068.00 −0.475958
\(485\) −4396.00 −0.411571
\(486\) 486.000 0.0453609
\(487\) 10760.0 1.00120 0.500598 0.865680i \(-0.333114\pi\)
0.500598 + 0.865680i \(0.333114\pi\)
\(488\) 3568.00 0.330975
\(489\) −1476.00 −0.136497
\(490\) −1372.00 −0.126491
\(491\) −11600.0 −1.06619 −0.533096 0.846055i \(-0.678972\pi\)
−0.533096 + 0.846055i \(0.678972\pi\)
\(492\) −6168.00 −0.565193
\(493\) 196.000 0.0179055
\(494\) −728.000 −0.0663042
\(495\) −1008.00 −0.0915277
\(496\) −2688.00 −0.243336
\(497\) −700.000 −0.0631776
\(498\) −1752.00 −0.157649
\(499\) −15908.0 −1.42713 −0.713567 0.700587i \(-0.752922\pi\)
−0.713567 + 0.700587i \(0.752922\pi\)
\(500\) 3024.00 0.270475
\(501\) −3312.00 −0.295348
\(502\) −8168.00 −0.726207
\(503\) −12232.0 −1.08429 −0.542145 0.840285i \(-0.682388\pi\)
−0.542145 + 0.840285i \(0.682388\pi\)
\(504\) −504.000 −0.0445435
\(505\) −12012.0 −1.05847
\(506\) −832.000 −0.0730967
\(507\) 507.000 0.0444116
\(508\) 3616.00 0.315815
\(509\) −13350.0 −1.16253 −0.581266 0.813714i \(-0.697442\pi\)
−0.581266 + 0.813714i \(0.697442\pi\)
\(510\) 8232.00 0.714743
\(511\) −3150.00 −0.272696
\(512\) 512.000 0.0441942
\(513\) −756.000 −0.0650647
\(514\) 5292.00 0.454125
\(515\) 13216.0 1.13081
\(516\) −2832.00 −0.241612
\(517\) −1728.00 −0.146997
\(518\) 2044.00 0.173375
\(519\) −8058.00 −0.681516
\(520\) −1456.00 −0.122788
\(521\) −18282.0 −1.53733 −0.768665 0.639652i \(-0.779079\pi\)
−0.768665 + 0.639652i \(0.779079\pi\)
\(522\) −36.0000 −0.00301854
\(523\) −6108.00 −0.510677 −0.255339 0.966852i \(-0.582187\pi\)
−0.255339 + 0.966852i \(0.582187\pi\)
\(524\) −5904.00 −0.492209
\(525\) −1491.00 −0.123948
\(526\) 10328.0 0.856126
\(527\) 16464.0 1.36088
\(528\) 384.000 0.0316505
\(529\) −9463.00 −0.777760
\(530\) 1848.00 0.151457
\(531\) −756.000 −0.0617846
\(532\) 784.000 0.0638923
\(533\) −6682.00 −0.543020
\(534\) −2412.00 −0.195463
\(535\) −11760.0 −0.950335
\(536\) 2336.00 0.188246
\(537\) 6264.00 0.503373
\(538\) −9420.00 −0.754879
\(539\) 392.000 0.0313259
\(540\) −1512.00 −0.120493
\(541\) −14906.0 −1.18458 −0.592291 0.805724i \(-0.701776\pi\)
−0.592291 + 0.805724i \(0.701776\pi\)
\(542\) −6288.00 −0.498326
\(543\) −726.000 −0.0573769
\(544\) −3136.00 −0.247160
\(545\) −18676.0 −1.46788
\(546\) −546.000 −0.0427960
\(547\) 5492.00 0.429289 0.214644 0.976692i \(-0.431141\pi\)
0.214644 + 0.976692i \(0.431141\pi\)
\(548\) −248.000 −0.0193322
\(549\) 4014.00 0.312046
\(550\) 1136.00 0.0880713
\(551\) 56.0000 0.00432973
\(552\) −1248.00 −0.0962290
\(553\) −2744.00 −0.211007
\(554\) 6620.00 0.507684
\(555\) 6132.00 0.468989
\(556\) −3632.00 −0.277034
\(557\) −6746.00 −0.513173 −0.256586 0.966521i \(-0.582598\pi\)
−0.256586 + 0.966521i \(0.582598\pi\)
\(558\) −3024.00 −0.229420
\(559\) −3068.00 −0.232133
\(560\) 1568.00 0.118322
\(561\) −2352.00 −0.177008
\(562\) −9820.00 −0.737067
\(563\) 596.000 0.0446153 0.0223076 0.999751i \(-0.492899\pi\)
0.0223076 + 0.999751i \(0.492899\pi\)
\(564\) −2592.00 −0.193516
\(565\) −13244.0 −0.986158
\(566\) 14872.0 1.10445
\(567\) −567.000 −0.0419961
\(568\) 800.000 0.0590973
\(569\) −2638.00 −0.194360 −0.0971799 0.995267i \(-0.530982\pi\)
−0.0971799 + 0.995267i \(0.530982\pi\)
\(570\) 2352.00 0.172832
\(571\) −22612.0 −1.65724 −0.828619 0.559813i \(-0.810873\pi\)
−0.828619 + 0.559813i \(0.810873\pi\)
\(572\) 416.000 0.0304088
\(573\) −3852.00 −0.280837
\(574\) 7196.00 0.523267
\(575\) −3692.00 −0.267769
\(576\) 576.000 0.0416667
\(577\) −1806.00 −0.130303 −0.0651514 0.997875i \(-0.520753\pi\)
−0.0651514 + 0.997875i \(0.520753\pi\)
\(578\) 9382.00 0.675155
\(579\) −8202.00 −0.588711
\(580\) 112.000 0.00801818
\(581\) 2044.00 0.145954
\(582\) 1884.00 0.134183
\(583\) −528.000 −0.0375086
\(584\) 3600.00 0.255084
\(585\) −1638.00 −0.115766
\(586\) −620.000 −0.0437064
\(587\) −27156.0 −1.90945 −0.954726 0.297487i \(-0.903851\pi\)
−0.954726 + 0.297487i \(0.903851\pi\)
\(588\) 588.000 0.0412393
\(589\) 4704.00 0.329075
\(590\) 2352.00 0.164119
\(591\) 15354.0 1.06866
\(592\) −2336.00 −0.162177
\(593\) −6034.00 −0.417853 −0.208926 0.977931i \(-0.566997\pi\)
−0.208926 + 0.977931i \(0.566997\pi\)
\(594\) 432.000 0.0298404
\(595\) −9604.00 −0.661724
\(596\) −10056.0 −0.691124
\(597\) 4584.00 0.314256
\(598\) −1352.00 −0.0924538
\(599\) 19284.0 1.31540 0.657699 0.753281i \(-0.271530\pi\)
0.657699 + 0.753281i \(0.271530\pi\)
\(600\) 1704.00 0.115943
\(601\) 10490.0 0.711973 0.355987 0.934491i \(-0.384145\pi\)
0.355987 + 0.934491i \(0.384145\pi\)
\(602\) 3304.00 0.223689
\(603\) 2628.00 0.177480
\(604\) −4192.00 −0.282401
\(605\) 17738.0 1.19199
\(606\) 5148.00 0.345088
\(607\) −13216.0 −0.883725 −0.441862 0.897083i \(-0.645682\pi\)
−0.441862 + 0.897083i \(0.645682\pi\)
\(608\) −896.000 −0.0597658
\(609\) 42.0000 0.00279462
\(610\) −12488.0 −0.828892
\(611\) −2808.00 −0.185924
\(612\) −3528.00 −0.233024
\(613\) −8242.00 −0.543053 −0.271526 0.962431i \(-0.587528\pi\)
−0.271526 + 0.962431i \(0.587528\pi\)
\(614\) −7032.00 −0.462196
\(615\) 21588.0 1.41547
\(616\) −448.000 −0.0293027
\(617\) −18206.0 −1.18792 −0.593959 0.804495i \(-0.702436\pi\)
−0.593959 + 0.804495i \(0.702436\pi\)
\(618\) −5664.00 −0.368672
\(619\) 16580.0 1.07659 0.538293 0.842758i \(-0.319069\pi\)
0.538293 + 0.842758i \(0.319069\pi\)
\(620\) 9408.00 0.609410
\(621\) −1404.00 −0.0907256
\(622\) 6432.00 0.414630
\(623\) 2814.00 0.180964
\(624\) 624.000 0.0400320
\(625\) −19459.0 −1.24538
\(626\) −2796.00 −0.178515
\(627\) −672.000 −0.0428024
\(628\) 12664.0 0.804695
\(629\) 14308.0 0.906991
\(630\) 1764.00 0.111555
\(631\) 21040.0 1.32740 0.663700 0.747999i \(-0.268985\pi\)
0.663700 + 0.747999i \(0.268985\pi\)
\(632\) 3136.00 0.197379
\(633\) 804.000 0.0504836
\(634\) −18068.0 −1.13182
\(635\) −12656.0 −0.790926
\(636\) −792.000 −0.0493787
\(637\) 637.000 0.0396214
\(638\) −32.0000 −0.00198572
\(639\) 900.000 0.0557174
\(640\) −1792.00 −0.110680
\(641\) 170.000 0.0104752 0.00523759 0.999986i \(-0.498333\pi\)
0.00523759 + 0.999986i \(0.498333\pi\)
\(642\) 5040.00 0.309833
\(643\) 23924.0 1.46729 0.733647 0.679530i \(-0.237816\pi\)
0.733647 + 0.679530i \(0.237816\pi\)
\(644\) 1456.00 0.0890907
\(645\) 9912.00 0.605092
\(646\) 5488.00 0.334245
\(647\) 22992.0 1.39708 0.698538 0.715572i \(-0.253834\pi\)
0.698538 + 0.715572i \(0.253834\pi\)
\(648\) 648.000 0.0392837
\(649\) −672.000 −0.0406445
\(650\) 1846.00 0.111394
\(651\) 3528.00 0.212401
\(652\) −1968.00 −0.118210
\(653\) 12990.0 0.778466 0.389233 0.921139i \(-0.372740\pi\)
0.389233 + 0.921139i \(0.372740\pi\)
\(654\) 8004.00 0.478564
\(655\) 20664.0 1.23269
\(656\) −8224.00 −0.489471
\(657\) 4050.00 0.240496
\(658\) 3024.00 0.179161
\(659\) 11088.0 0.655428 0.327714 0.944777i \(-0.393722\pi\)
0.327714 + 0.944777i \(0.393722\pi\)
\(660\) −1344.00 −0.0792653
\(661\) 6886.00 0.405196 0.202598 0.979262i \(-0.435062\pi\)
0.202598 + 0.979262i \(0.435062\pi\)
\(662\) 18216.0 1.06946
\(663\) −3822.00 −0.223883
\(664\) −2336.00 −0.136528
\(665\) −2744.00 −0.160012
\(666\) −2628.00 −0.152902
\(667\) 104.000 0.00603733
\(668\) −4416.00 −0.255779
\(669\) 4176.00 0.241336
\(670\) −8176.00 −0.471442
\(671\) 3568.00 0.205277
\(672\) −672.000 −0.0385758
\(673\) −8238.00 −0.471845 −0.235922 0.971772i \(-0.575811\pi\)
−0.235922 + 0.971772i \(0.575811\pi\)
\(674\) −3132.00 −0.178991
\(675\) 1917.00 0.109312
\(676\) 676.000 0.0384615
\(677\) 778.000 0.0441669 0.0220834 0.999756i \(-0.492970\pi\)
0.0220834 + 0.999756i \(0.492970\pi\)
\(678\) 5676.00 0.321512
\(679\) −2198.00 −0.124229
\(680\) 10976.0 0.618986
\(681\) −18420.0 −1.03650
\(682\) −2688.00 −0.150922
\(683\) 19552.0 1.09537 0.547684 0.836685i \(-0.315510\pi\)
0.547684 + 0.836685i \(0.315510\pi\)
\(684\) −1008.00 −0.0563477
\(685\) 868.000 0.0484154
\(686\) −686.000 −0.0381802
\(687\) 5610.00 0.311550
\(688\) −3776.00 −0.209242
\(689\) −858.000 −0.0474415
\(690\) 4368.00 0.240996
\(691\) −31700.0 −1.74519 −0.872594 0.488446i \(-0.837564\pi\)
−0.872594 + 0.488446i \(0.837564\pi\)
\(692\) −10744.0 −0.590210
\(693\) −504.000 −0.0276268
\(694\) 9056.00 0.495333
\(695\) 12712.0 0.693804
\(696\) −48.0000 −0.00261413
\(697\) 50372.0 2.73741
\(698\) −2180.00 −0.118215
\(699\) 150.000 0.00811663
\(700\) −1988.00 −0.107342
\(701\) 1470.00 0.0792028 0.0396014 0.999216i \(-0.487391\pi\)
0.0396014 + 0.999216i \(0.487391\pi\)
\(702\) 702.000 0.0377426
\(703\) 4088.00 0.219320
\(704\) 512.000 0.0274101
\(705\) 9072.00 0.484640
\(706\) −22468.0 −1.19773
\(707\) −6006.00 −0.319489
\(708\) −1008.00 −0.0535070
\(709\) 26718.0 1.41525 0.707627 0.706586i \(-0.249766\pi\)
0.707627 + 0.706586i \(0.249766\pi\)
\(710\) −2800.00 −0.148003
\(711\) 3528.00 0.186090
\(712\) −3216.00 −0.169276
\(713\) 8736.00 0.458858
\(714\) 4116.00 0.215739
\(715\) −1456.00 −0.0761557
\(716\) 8352.00 0.435934
\(717\) −9684.00 −0.504401
\(718\) 6888.00 0.358019
\(719\) −7408.00 −0.384244 −0.192122 0.981371i \(-0.561537\pi\)
−0.192122 + 0.981371i \(0.561537\pi\)
\(720\) −2016.00 −0.104350
\(721\) 6608.00 0.341324
\(722\) −12150.0 −0.626283
\(723\) 17934.0 0.922507
\(724\) −968.000 −0.0496898
\(725\) −142.000 −0.00727413
\(726\) −7602.00 −0.388618
\(727\) −21120.0 −1.07744 −0.538719 0.842486i \(-0.681092\pi\)
−0.538719 + 0.842486i \(0.681092\pi\)
\(728\) −728.000 −0.0370625
\(729\) 729.000 0.0370370
\(730\) −12600.0 −0.638831
\(731\) 23128.0 1.17021
\(732\) 5352.00 0.270240
\(733\) −39354.0 −1.98305 −0.991523 0.129929i \(-0.958525\pi\)
−0.991523 + 0.129929i \(0.958525\pi\)
\(734\) 23424.0 1.17792
\(735\) −2058.00 −0.103280
\(736\) −1664.00 −0.0833368
\(737\) 2336.00 0.116754
\(738\) −9252.00 −0.461478
\(739\) −15596.0 −0.776330 −0.388165 0.921590i \(-0.626891\pi\)
−0.388165 + 0.921590i \(0.626891\pi\)
\(740\) 8176.00 0.406156
\(741\) −1092.00 −0.0541371
\(742\) 924.000 0.0457158
\(743\) 4468.00 0.220612 0.110306 0.993898i \(-0.464817\pi\)
0.110306 + 0.993898i \(0.464817\pi\)
\(744\) −4032.00 −0.198683
\(745\) 35196.0 1.73085
\(746\) 21980.0 1.07875
\(747\) −2628.00 −0.128720
\(748\) −3136.00 −0.153293
\(749\) −5880.00 −0.286850
\(750\) 4536.00 0.220842
\(751\) 5440.00 0.264325 0.132163 0.991228i \(-0.457808\pi\)
0.132163 + 0.991228i \(0.457808\pi\)
\(752\) −3456.00 −0.167590
\(753\) −12252.0 −0.592945
\(754\) −52.0000 −0.00251158
\(755\) 14672.0 0.707243
\(756\) −756.000 −0.0363696
\(757\) 14638.0 0.702810 0.351405 0.936224i \(-0.385704\pi\)
0.351405 + 0.936224i \(0.385704\pi\)
\(758\) −14008.0 −0.671231
\(759\) −1248.00 −0.0596832
\(760\) 3136.00 0.149677
\(761\) 35950.0 1.71247 0.856233 0.516590i \(-0.172799\pi\)
0.856233 + 0.516590i \(0.172799\pi\)
\(762\) 5424.00 0.257862
\(763\) −9338.00 −0.443065
\(764\) −5136.00 −0.243212
\(765\) 12348.0 0.583585
\(766\) −10944.0 −0.516218
\(767\) −1092.00 −0.0514079
\(768\) 768.000 0.0360844
\(769\) −24974.0 −1.17111 −0.585556 0.810632i \(-0.699124\pi\)
−0.585556 + 0.810632i \(0.699124\pi\)
\(770\) 1568.00 0.0733855
\(771\) 7938.00 0.370791
\(772\) −10936.0 −0.509838
\(773\) −41254.0 −1.91954 −0.959769 0.280790i \(-0.909404\pi\)
−0.959769 + 0.280790i \(0.909404\pi\)
\(774\) −4248.00 −0.197275
\(775\) −11928.0 −0.552860
\(776\) 2512.00 0.116206
\(777\) 3066.00 0.141560
\(778\) 3820.00 0.176033
\(779\) 14392.0 0.661934
\(780\) −2184.00 −0.100256
\(781\) 800.000 0.0366533
\(782\) 10192.0 0.466068
\(783\) −54.0000 −0.00246463
\(784\) 784.000 0.0357143
\(785\) −44324.0 −2.01528
\(786\) −8856.00 −0.401887
\(787\) 26780.0 1.21297 0.606483 0.795097i \(-0.292580\pi\)
0.606483 + 0.795097i \(0.292580\pi\)
\(788\) 20472.0 0.925488
\(789\) 15492.0 0.699024
\(790\) −10976.0 −0.494315
\(791\) −6622.00 −0.297663
\(792\) 576.000 0.0258425
\(793\) 5798.00 0.259638
\(794\) −26468.0 −1.18302
\(795\) 2772.00 0.123664
\(796\) 6112.00 0.272153
\(797\) −18222.0 −0.809857 −0.404929 0.914348i \(-0.632704\pi\)
−0.404929 + 0.914348i \(0.632704\pi\)
\(798\) 1176.00 0.0521679
\(799\) 21168.0 0.937259
\(800\) 2272.00 0.100409
\(801\) −3618.00 −0.159595
\(802\) 9172.00 0.403834
\(803\) 3600.00 0.158208
\(804\) 3504.00 0.153702
\(805\) −5096.00 −0.223119
\(806\) −4368.00 −0.190889
\(807\) −14130.0 −0.616356
\(808\) 6864.00 0.298855
\(809\) 7338.00 0.318900 0.159450 0.987206i \(-0.449028\pi\)
0.159450 + 0.987206i \(0.449028\pi\)
\(810\) −2268.00 −0.0983820
\(811\) 12500.0 0.541226 0.270613 0.962688i \(-0.412774\pi\)
0.270613 + 0.962688i \(0.412774\pi\)
\(812\) 56.0000 0.00242022
\(813\) −9432.00 −0.406882
\(814\) −2336.00 −0.100586
\(815\) 6888.00 0.296044
\(816\) −4704.00 −0.201805
\(817\) 6608.00 0.282968
\(818\) −8348.00 −0.356823
\(819\) −819.000 −0.0349428
\(820\) 28784.0 1.22583
\(821\) 44830.0 1.90570 0.952849 0.303445i \(-0.0981370\pi\)
0.952849 + 0.303445i \(0.0981370\pi\)
\(822\) −372.000 −0.0157847
\(823\) 11152.0 0.472338 0.236169 0.971712i \(-0.424108\pi\)
0.236169 + 0.971712i \(0.424108\pi\)
\(824\) −7552.00 −0.319280
\(825\) 1704.00 0.0719099
\(826\) 1176.00 0.0495379
\(827\) −2408.00 −0.101251 −0.0506254 0.998718i \(-0.516121\pi\)
−0.0506254 + 0.998718i \(0.516121\pi\)
\(828\) −1872.00 −0.0785706
\(829\) −44922.0 −1.88203 −0.941017 0.338360i \(-0.890128\pi\)
−0.941017 + 0.338360i \(0.890128\pi\)
\(830\) 8176.00 0.341919
\(831\) 9930.00 0.414522
\(832\) 832.000 0.0346688
\(833\) −4802.00 −0.199735
\(834\) −5448.00 −0.226198
\(835\) 15456.0 0.640571
\(836\) −896.000 −0.0370680
\(837\) −4536.00 −0.187320
\(838\) −20024.0 −0.825439
\(839\) 36720.0 1.51098 0.755492 0.655158i \(-0.227398\pi\)
0.755492 + 0.655158i \(0.227398\pi\)
\(840\) 2352.00 0.0966092
\(841\) −24385.0 −0.999836
\(842\) −2500.00 −0.102323
\(843\) −14730.0 −0.601813
\(844\) 1072.00 0.0437201
\(845\) −2366.00 −0.0963229
\(846\) −3888.00 −0.158005
\(847\) 8869.00 0.359790
\(848\) −1056.00 −0.0427632
\(849\) 22308.0 0.901777
\(850\) −13916.0 −0.561547
\(851\) 7592.00 0.305817
\(852\) 1200.00 0.0482527
\(853\) 16006.0 0.642479 0.321240 0.946998i \(-0.395900\pi\)
0.321240 + 0.946998i \(0.395900\pi\)
\(854\) −6244.00 −0.250194
\(855\) 3528.00 0.141117
\(856\) 6720.00 0.268323
\(857\) 37278.0 1.48587 0.742936 0.669363i \(-0.233433\pi\)
0.742936 + 0.669363i \(0.233433\pi\)
\(858\) 624.000 0.0248287
\(859\) −45236.0 −1.79678 −0.898389 0.439201i \(-0.855262\pi\)
−0.898389 + 0.439201i \(0.855262\pi\)
\(860\) 13216.0 0.524025
\(861\) 10794.0 0.427246
\(862\) 12472.0 0.492805
\(863\) −23916.0 −0.943349 −0.471674 0.881773i \(-0.656350\pi\)
−0.471674 + 0.881773i \(0.656350\pi\)
\(864\) 864.000 0.0340207
\(865\) 37604.0 1.47812
\(866\) −7932.00 −0.311247
\(867\) 14073.0 0.551262
\(868\) 4704.00 0.183945
\(869\) 3136.00 0.122418
\(870\) 168.000 0.00654682
\(871\) 3796.00 0.147672
\(872\) 10672.0 0.414449
\(873\) 2826.00 0.109560
\(874\) 2912.00 0.112700
\(875\) −5292.00 −0.204460
\(876\) 5400.00 0.208275
\(877\) −24538.0 −0.944800 −0.472400 0.881384i \(-0.656612\pi\)
−0.472400 + 0.881384i \(0.656612\pi\)
\(878\) 17552.0 0.674660
\(879\) −930.000 −0.0356861
\(880\) −1792.00 −0.0686458
\(881\) 910.000 0.0347999 0.0173999 0.999849i \(-0.494461\pi\)
0.0173999 + 0.999849i \(0.494461\pi\)
\(882\) 882.000 0.0336718
\(883\) 10460.0 0.398649 0.199324 0.979934i \(-0.436125\pi\)
0.199324 + 0.979934i \(0.436125\pi\)
\(884\) −5096.00 −0.193888
\(885\) 3528.00 0.134003
\(886\) 12192.0 0.462301
\(887\) 20048.0 0.758902 0.379451 0.925212i \(-0.376113\pi\)
0.379451 + 0.925212i \(0.376113\pi\)
\(888\) −3504.00 −0.132417
\(889\) −6328.00 −0.238734
\(890\) 11256.0 0.423935
\(891\) 648.000 0.0243646
\(892\) 5568.00 0.209003
\(893\) 6048.00 0.226639
\(894\) −15084.0 −0.564300
\(895\) −29232.0 −1.09175
\(896\) −896.000 −0.0334077
\(897\) −2028.00 −0.0754882
\(898\) −18780.0 −0.697881
\(899\) 336.000 0.0124652
\(900\) 2556.00 0.0946667
\(901\) 6468.00 0.239157
\(902\) −8224.00 −0.303580
\(903\) 4956.00 0.182642
\(904\) 7568.00 0.278438
\(905\) 3388.00 0.124443
\(906\) −6288.00 −0.230579
\(907\) −876.000 −0.0320696 −0.0160348 0.999871i \(-0.505104\pi\)
−0.0160348 + 0.999871i \(0.505104\pi\)
\(908\) −24560.0 −0.897635
\(909\) 7722.00 0.281763
\(910\) 2548.00 0.0928191
\(911\) 14796.0 0.538105 0.269052 0.963126i \(-0.413290\pi\)
0.269052 + 0.963126i \(0.413290\pi\)
\(912\) −1344.00 −0.0487986
\(913\) −2336.00 −0.0846772
\(914\) −12.0000 −0.000434272 0
\(915\) −18732.0 −0.676788
\(916\) 7480.00 0.269810
\(917\) 10332.0 0.372075
\(918\) −5292.00 −0.190264
\(919\) 728.000 0.0261311 0.0130656 0.999915i \(-0.495841\pi\)
0.0130656 + 0.999915i \(0.495841\pi\)
\(920\) 5824.00 0.208708
\(921\) −10548.0 −0.377382
\(922\) −18748.0 −0.669666
\(923\) 1300.00 0.0463597
\(924\) −672.000 −0.0239255
\(925\) −10366.0 −0.368467
\(926\) 8016.00 0.284473
\(927\) −8496.00 −0.301020
\(928\) −64.0000 −0.00226390
\(929\) 39894.0 1.40891 0.704456 0.709747i \(-0.251191\pi\)
0.704456 + 0.709747i \(0.251191\pi\)
\(930\) 14112.0 0.497581
\(931\) −1372.00 −0.0482980
\(932\) 200.000 0.00702920
\(933\) 9648.00 0.338544
\(934\) −6520.00 −0.228416
\(935\) 10976.0 0.383908
\(936\) 936.000 0.0326860
\(937\) 18906.0 0.659159 0.329580 0.944128i \(-0.393093\pi\)
0.329580 + 0.944128i \(0.393093\pi\)
\(938\) −4088.00 −0.142301
\(939\) −4194.00 −0.145757
\(940\) 12096.0 0.419711
\(941\) 49514.0 1.71531 0.857657 0.514222i \(-0.171919\pi\)
0.857657 + 0.514222i \(0.171919\pi\)
\(942\) 18996.0 0.657031
\(943\) 26728.0 0.922994
\(944\) −1344.00 −0.0463384
\(945\) 2646.00 0.0910840
\(946\) −3776.00 −0.129776
\(947\) 16384.0 0.562205 0.281103 0.959678i \(-0.409300\pi\)
0.281103 + 0.959678i \(0.409300\pi\)
\(948\) 4704.00 0.161159
\(949\) 5850.00 0.200104
\(950\) −3976.00 −0.135788
\(951\) −27102.0 −0.924125
\(952\) 5488.00 0.186835
\(953\) −30742.0 −1.04494 −0.522472 0.852657i \(-0.674990\pi\)
−0.522472 + 0.852657i \(0.674990\pi\)
\(954\) −1188.00 −0.0403175
\(955\) 17976.0 0.609099
\(956\) −12912.0 −0.436824
\(957\) −48.0000 −0.00162134
\(958\) 25392.0 0.856345
\(959\) 434.000 0.0146138
\(960\) −2688.00 −0.0903696
\(961\) −1567.00 −0.0525998
\(962\) −3796.00 −0.127222
\(963\) 7560.00 0.252978
\(964\) 23912.0 0.798915
\(965\) 38276.0 1.27684
\(966\) 2184.00 0.0727423
\(967\) −41376.0 −1.37597 −0.687985 0.725725i \(-0.741504\pi\)
−0.687985 + 0.725725i \(0.741504\pi\)
\(968\) −10136.0 −0.336553
\(969\) 8232.00 0.272910
\(970\) −8792.00 −0.291025
\(971\) 57300.0 1.89376 0.946882 0.321582i \(-0.104214\pi\)
0.946882 + 0.321582i \(0.104214\pi\)
\(972\) 972.000 0.0320750
\(973\) 6356.00 0.209418
\(974\) 21520.0 0.707952
\(975\) 2769.00 0.0909528
\(976\) 7136.00 0.234035
\(977\) −7734.00 −0.253258 −0.126629 0.991950i \(-0.540416\pi\)
−0.126629 + 0.991950i \(0.540416\pi\)
\(978\) −2952.00 −0.0965179
\(979\) −3216.00 −0.104989
\(980\) −2744.00 −0.0894427
\(981\) 12006.0 0.390746
\(982\) −23200.0 −0.753912
\(983\) −31432.0 −1.01986 −0.509931 0.860215i \(-0.670329\pi\)
−0.509931 + 0.860215i \(0.670329\pi\)
\(984\) −12336.0 −0.399652
\(985\) −71652.0 −2.31779
\(986\) 392.000 0.0126611
\(987\) 4536.00 0.146284
\(988\) −1456.00 −0.0468841
\(989\) 12272.0 0.394567
\(990\) −2016.00 −0.0647199
\(991\) −24432.0 −0.783156 −0.391578 0.920145i \(-0.628071\pi\)
−0.391578 + 0.920145i \(0.628071\pi\)
\(992\) −5376.00 −0.172065
\(993\) 27324.0 0.873213
\(994\) −1400.00 −0.0446733
\(995\) −21392.0 −0.681580
\(996\) −3504.00 −0.111474
\(997\) 3094.00 0.0982828 0.0491414 0.998792i \(-0.484352\pi\)
0.0491414 + 0.998792i \(0.484352\pi\)
\(998\) −31816.0 −1.00914
\(999\) −3942.00 −0.124844
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.c.1.1 1
3.2 odd 2 1638.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.4.a.c.1.1 1 1.1 even 1 trivial
1638.4.a.h.1.1 1 3.2 odd 2