Properties

Label 546.4.a.d.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 $1$

Related objects

Downloads

Learn more

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

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0000 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0000 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -24.0000 q^{10} -50.0000 q^{11} +12.0000 q^{12} -13.0000 q^{13} +14.0000 q^{14} -36.0000 q^{15} +16.0000 q^{16} -58.0000 q^{17} +18.0000 q^{18} -40.0000 q^{19} -48.0000 q^{20} +21.0000 q^{21} -100.000 q^{22} -64.0000 q^{23} +24.0000 q^{24} +19.0000 q^{25} -26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} -110.000 q^{29} -72.0000 q^{30} +124.000 q^{31} +32.0000 q^{32} -150.000 q^{33} -116.000 q^{34} -84.0000 q^{35} +36.0000 q^{36} -50.0000 q^{37} -80.0000 q^{38} -39.0000 q^{39} -96.0000 q^{40} +84.0000 q^{41} +42.0000 q^{42} -12.0000 q^{43} -200.000 q^{44} -108.000 q^{45} -128.000 q^{46} -82.0000 q^{47} +48.0000 q^{48} +49.0000 q^{49} +38.0000 q^{50} -174.000 q^{51} -52.0000 q^{52} -442.000 q^{53} +54.0000 q^{54} +600.000 q^{55} +56.0000 q^{56} -120.000 q^{57} -220.000 q^{58} -618.000 q^{59} -144.000 q^{60} -278.000 q^{61} +248.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} +156.000 q^{65} -300.000 q^{66} +20.0000 q^{67} -232.000 q^{68} -192.000 q^{69} -168.000 q^{70} -390.000 q^{71} +72.0000 q^{72} -2.00000 q^{73} -100.000 q^{74} +57.0000 q^{75} -160.000 q^{76} -350.000 q^{77} -78.0000 q^{78} -680.000 q^{79} -192.000 q^{80} +81.0000 q^{81} +168.000 q^{82} +322.000 q^{83} +84.0000 q^{84} +696.000 q^{85} -24.0000 q^{86} -330.000 q^{87} -400.000 q^{88} +968.000 q^{89} -216.000 q^{90} -91.0000 q^{91} -256.000 q^{92} +372.000 q^{93} -164.000 q^{94} +480.000 q^{95} +96.0000 q^{96} +1022.00 q^{97} +98.0000 q^{98} -450.000 q^{99} +O(q^{100})\)

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
\(5\) −12.0000 −1.07331 −0.536656 0.843801i \(-0.680313\pi\)
−0.536656 + 0.843801i \(0.680313\pi\)
\(6\) 6.00000 0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −24.0000 −0.758947
\(11\) −50.0000 −1.37051 −0.685253 0.728305i \(-0.740308\pi\)
−0.685253 + 0.728305i \(0.740308\pi\)
\(12\) 12.0000 0.288675
\(13\) −13.0000 −0.277350
\(14\) 14.0000 0.267261
\(15\) −36.0000 −0.619677
\(16\) 16.0000 0.250000
\(17\) −58.0000 −0.827474 −0.413737 0.910396i \(-0.635777\pi\)
−0.413737 + 0.910396i \(0.635777\pi\)
\(18\) 18.0000 0.235702
\(19\) −40.0000 −0.482980 −0.241490 0.970403i \(-0.577636\pi\)
−0.241490 + 0.970403i \(0.577636\pi\)
\(20\) −48.0000 −0.536656
\(21\) 21.0000 0.218218
\(22\) −100.000 −0.969094
\(23\) −64.0000 −0.580214 −0.290107 0.956994i \(-0.593691\pi\)
−0.290107 + 0.956994i \(0.593691\pi\)
\(24\) 24.0000 0.204124
\(25\) 19.0000 0.152000
\(26\) −26.0000 −0.196116
\(27\) 27.0000 0.192450
\(28\) 28.0000 0.188982
\(29\) −110.000 −0.704362 −0.352181 0.935932i \(-0.614560\pi\)
−0.352181 + 0.935932i \(0.614560\pi\)
\(30\) −72.0000 −0.438178
\(31\) 124.000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 32.0000 0.176777
\(33\) −150.000 −0.791262
\(34\) −116.000 −0.585113
\(35\) −84.0000 −0.405674
\(36\) 36.0000 0.166667
\(37\) −50.0000 −0.222161 −0.111080 0.993811i \(-0.535431\pi\)
−0.111080 + 0.993811i \(0.535431\pi\)
\(38\) −80.0000 −0.341519
\(39\) −39.0000 −0.160128
\(40\) −96.0000 −0.379473
\(41\) 84.0000 0.319966 0.159983 0.987120i \(-0.448856\pi\)
0.159983 + 0.987120i \(0.448856\pi\)
\(42\) 42.0000 0.154303
\(43\) −12.0000 −0.0425577 −0.0212789 0.999774i \(-0.506774\pi\)
−0.0212789 + 0.999774i \(0.506774\pi\)
\(44\) −200.000 −0.685253
\(45\) −108.000 −0.357771
\(46\) −128.000 −0.410273
\(47\) −82.0000 −0.254488 −0.127244 0.991871i \(-0.540613\pi\)
−0.127244 + 0.991871i \(0.540613\pi\)
\(48\) 48.0000 0.144338
\(49\) 49.0000 0.142857
\(50\) 38.0000 0.107480
\(51\) −174.000 −0.477743
\(52\) −52.0000 −0.138675
\(53\) −442.000 −1.14554 −0.572768 0.819718i \(-0.694130\pi\)
−0.572768 + 0.819718i \(0.694130\pi\)
\(54\) 54.0000 0.136083
\(55\) 600.000 1.47098
\(56\) 56.0000 0.133631
\(57\) −120.000 −0.278849
\(58\) −220.000 −0.498059
\(59\) −618.000 −1.36367 −0.681837 0.731504i \(-0.738819\pi\)
−0.681837 + 0.731504i \(0.738819\pi\)
\(60\) −144.000 −0.309839
\(61\) −278.000 −0.583512 −0.291756 0.956493i \(-0.594240\pi\)
−0.291756 + 0.956493i \(0.594240\pi\)
\(62\) 248.000 0.508001
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) 156.000 0.297683
\(66\) −300.000 −0.559507
\(67\) 20.0000 0.0364685 0.0182342 0.999834i \(-0.494196\pi\)
0.0182342 + 0.999834i \(0.494196\pi\)
\(68\) −232.000 −0.413737
\(69\) −192.000 −0.334987
\(70\) −168.000 −0.286855
\(71\) −390.000 −0.651894 −0.325947 0.945388i \(-0.605683\pi\)
−0.325947 + 0.945388i \(0.605683\pi\)
\(72\) 72.0000 0.117851
\(73\) −2.00000 −0.00320661 −0.00160330 0.999999i \(-0.500510\pi\)
−0.00160330 + 0.999999i \(0.500510\pi\)
\(74\) −100.000 −0.157091
\(75\) 57.0000 0.0877572
\(76\) −160.000 −0.241490
\(77\) −350.000 −0.518003
\(78\) −78.0000 −0.113228
\(79\) −680.000 −0.968430 −0.484215 0.874949i \(-0.660895\pi\)
−0.484215 + 0.874949i \(0.660895\pi\)
\(80\) −192.000 −0.268328
\(81\) 81.0000 0.111111
\(82\) 168.000 0.226250
\(83\) 322.000 0.425832 0.212916 0.977070i \(-0.431704\pi\)
0.212916 + 0.977070i \(0.431704\pi\)
\(84\) 84.0000 0.109109
\(85\) 696.000 0.888139
\(86\) −24.0000 −0.0300929
\(87\) −330.000 −0.406663
\(88\) −400.000 −0.484547
\(89\) 968.000 1.15290 0.576448 0.817134i \(-0.304438\pi\)
0.576448 + 0.817134i \(0.304438\pi\)
\(90\) −216.000 −0.252982
\(91\) −91.0000 −0.104828
\(92\) −256.000 −0.290107
\(93\) 372.000 0.414781
\(94\) −164.000 −0.179950
\(95\) 480.000 0.518389
\(96\) 96.0000 0.102062
\(97\) 1022.00 1.06978 0.534889 0.844923i \(-0.320354\pi\)
0.534889 + 0.844923i \(0.320354\pi\)
\(98\) 98.0000 0.101015
\(99\) −450.000 −0.456835
\(100\) 76.0000 0.0760000
\(101\) 54.0000 0.0532000 0.0266000 0.999646i \(-0.491532\pi\)
0.0266000 + 0.999646i \(0.491532\pi\)
\(102\) −348.000 −0.337815
\(103\) 1416.00 1.35459 0.677294 0.735712i \(-0.263152\pi\)
0.677294 + 0.735712i \(0.263152\pi\)
\(104\) −104.000 −0.0980581
\(105\) −252.000 −0.234216
\(106\) −884.000 −0.810016
\(107\) 1252.00 1.13117 0.565586 0.824689i \(-0.308650\pi\)
0.565586 + 0.824689i \(0.308650\pi\)
\(108\) 108.000 0.0962250
\(109\) 930.000 0.817228 0.408614 0.912707i \(-0.366012\pi\)
0.408614 + 0.912707i \(0.366012\pi\)
\(110\) 1200.00 1.04014
\(111\) −150.000 −0.128265
\(112\) 112.000 0.0944911
\(113\) −1034.00 −0.860801 −0.430401 0.902638i \(-0.641628\pi\)
−0.430401 + 0.902638i \(0.641628\pi\)
\(114\) −240.000 −0.197176
\(115\) 768.000 0.622751
\(116\) −440.000 −0.352181
\(117\) −117.000 −0.0924500
\(118\) −1236.00 −0.964263
\(119\) −406.000 −0.312756
\(120\) −288.000 −0.219089
\(121\) 1169.00 0.878287
\(122\) −556.000 −0.412606
\(123\) 252.000 0.184732
\(124\) 496.000 0.359211
\(125\) 1272.00 0.910169
\(126\) 126.000 0.0890871
\(127\) −2280.00 −1.59305 −0.796525 0.604606i \(-0.793331\pi\)
−0.796525 + 0.604606i \(0.793331\pi\)
\(128\) 128.000 0.0883883
\(129\) −36.0000 −0.0245707
\(130\) 312.000 0.210494
\(131\) −1552.00 −1.03511 −0.517553 0.855651i \(-0.673157\pi\)
−0.517553 + 0.855651i \(0.673157\pi\)
\(132\) −600.000 −0.395631
\(133\) −280.000 −0.182549
\(134\) 40.0000 0.0257871
\(135\) −324.000 −0.206559
\(136\) −464.000 −0.292556
\(137\) 48.0000 0.0299337 0.0149668 0.999888i \(-0.495236\pi\)
0.0149668 + 0.999888i \(0.495236\pi\)
\(138\) −384.000 −0.236871
\(139\) 28.0000 0.0170858 0.00854291 0.999964i \(-0.497281\pi\)
0.00854291 + 0.999964i \(0.497281\pi\)
\(140\) −336.000 −0.202837
\(141\) −246.000 −0.146929
\(142\) −780.000 −0.460959
\(143\) 650.000 0.380110
\(144\) 144.000 0.0833333
\(145\) 1320.00 0.756000
\(146\) −4.00000 −0.00226741
\(147\) 147.000 0.0824786
\(148\) −200.000 −0.111080
\(149\) 2596.00 1.42733 0.713666 0.700486i \(-0.247033\pi\)
0.713666 + 0.700486i \(0.247033\pi\)
\(150\) 114.000 0.0620537
\(151\) −2052.00 −1.10589 −0.552945 0.833218i \(-0.686496\pi\)
−0.552945 + 0.833218i \(0.686496\pi\)
\(152\) −320.000 −0.170759
\(153\) −522.000 −0.275825
\(154\) −700.000 −0.366283
\(155\) −1488.00 −0.771091
\(156\) −156.000 −0.0800641
\(157\) −2522.00 −1.28202 −0.641011 0.767532i \(-0.721485\pi\)
−0.641011 + 0.767532i \(0.721485\pi\)
\(158\) −1360.00 −0.684783
\(159\) −1326.00 −0.661375
\(160\) −384.000 −0.189737
\(161\) −448.000 −0.219300
\(162\) 162.000 0.0785674
\(163\) −848.000 −0.407488 −0.203744 0.979024i \(-0.565311\pi\)
−0.203744 + 0.979024i \(0.565311\pi\)
\(164\) 336.000 0.159983
\(165\) 1800.00 0.849272
\(166\) 644.000 0.301109
\(167\) 854.000 0.395716 0.197858 0.980231i \(-0.436602\pi\)
0.197858 + 0.980231i \(0.436602\pi\)
\(168\) 168.000 0.0771517
\(169\) 169.000 0.0769231
\(170\) 1392.00 0.628009
\(171\) −360.000 −0.160993
\(172\) −48.0000 −0.0212789
\(173\) 2046.00 0.899159 0.449579 0.893240i \(-0.351574\pi\)
0.449579 + 0.893240i \(0.351574\pi\)
\(174\) −660.000 −0.287554
\(175\) 133.000 0.0574506
\(176\) −800.000 −0.342627
\(177\) −1854.00 −0.787317
\(178\) 1936.00 0.815221
\(179\) −1688.00 −0.704844 −0.352422 0.935841i \(-0.614642\pi\)
−0.352422 + 0.935841i \(0.614642\pi\)
\(180\) −432.000 −0.178885
\(181\) −266.000 −0.109235 −0.0546177 0.998507i \(-0.517394\pi\)
−0.0546177 + 0.998507i \(0.517394\pi\)
\(182\) −182.000 −0.0741249
\(183\) −834.000 −0.336891
\(184\) −512.000 −0.205137
\(185\) 600.000 0.238448
\(186\) 744.000 0.293294
\(187\) 2900.00 1.13406
\(188\) −328.000 −0.127244
\(189\) 189.000 0.0727393
\(190\) 960.000 0.366556
\(191\) 2876.00 1.08953 0.544765 0.838589i \(-0.316619\pi\)
0.544765 + 0.838589i \(0.316619\pi\)
\(192\) 192.000 0.0721688
\(193\) 3058.00 1.14052 0.570258 0.821466i \(-0.306843\pi\)
0.570258 + 0.821466i \(0.306843\pi\)
\(194\) 2044.00 0.756447
\(195\) 468.000 0.171868
\(196\) 196.000 0.0714286
\(197\) −2952.00 −1.06762 −0.533810 0.845604i \(-0.679240\pi\)
−0.533810 + 0.845604i \(0.679240\pi\)
\(198\) −900.000 −0.323031
\(199\) 3064.00 1.09146 0.545732 0.837960i \(-0.316252\pi\)
0.545732 + 0.837960i \(0.316252\pi\)
\(200\) 152.000 0.0537401
\(201\) 60.0000 0.0210551
\(202\) 108.000 0.0376181
\(203\) −770.000 −0.266224
\(204\) −696.000 −0.238871
\(205\) −1008.00 −0.343423
\(206\) 2832.00 0.957839
\(207\) −576.000 −0.193405
\(208\) −208.000 −0.0693375
\(209\) 2000.00 0.661928
\(210\) −504.000 −0.165616
\(211\) 604.000 0.197067 0.0985334 0.995134i \(-0.468585\pi\)
0.0985334 + 0.995134i \(0.468585\pi\)
\(212\) −1768.00 −0.572768
\(213\) −1170.00 −0.376371
\(214\) 2504.00 0.799859
\(215\) 144.000 0.0456778
\(216\) 216.000 0.0680414
\(217\) 868.000 0.271538
\(218\) 1860.00 0.577867
\(219\) −6.00000 −0.00185134
\(220\) 2400.00 0.735491
\(221\) 754.000 0.229500
\(222\) −300.000 −0.0906968
\(223\) 5628.00 1.69004 0.845020 0.534735i \(-0.179589\pi\)
0.845020 + 0.534735i \(0.179589\pi\)
\(224\) 224.000 0.0668153
\(225\) 171.000 0.0506667
\(226\) −2068.00 −0.608678
\(227\) −1122.00 −0.328061 −0.164030 0.986455i \(-0.552449\pi\)
−0.164030 + 0.986455i \(0.552449\pi\)
\(228\) −480.000 −0.139424
\(229\) 4426.00 1.27720 0.638599 0.769540i \(-0.279514\pi\)
0.638599 + 0.769540i \(0.279514\pi\)
\(230\) 1536.00 0.440351
\(231\) −1050.00 −0.299069
\(232\) −880.000 −0.249029
\(233\) 2190.00 0.615758 0.307879 0.951425i \(-0.400381\pi\)
0.307879 + 0.951425i \(0.400381\pi\)
\(234\) −234.000 −0.0653720
\(235\) 984.000 0.273145
\(236\) −2472.00 −0.681837
\(237\) −2040.00 −0.559123
\(238\) −812.000 −0.221152
\(239\) −1230.00 −0.332896 −0.166448 0.986050i \(-0.553230\pi\)
−0.166448 + 0.986050i \(0.553230\pi\)
\(240\) −576.000 −0.154919
\(241\) −786.000 −0.210086 −0.105043 0.994468i \(-0.533498\pi\)
−0.105043 + 0.994468i \(0.533498\pi\)
\(242\) 2338.00 0.621043
\(243\) 243.000 0.0641500
\(244\) −1112.00 −0.291756
\(245\) −588.000 −0.153330
\(246\) 504.000 0.130625
\(247\) 520.000 0.133955
\(248\) 992.000 0.254000
\(249\) 966.000 0.245854
\(250\) 2544.00 0.643587
\(251\) −280.000 −0.0704121 −0.0352061 0.999380i \(-0.511209\pi\)
−0.0352061 + 0.999380i \(0.511209\pi\)
\(252\) 252.000 0.0629941
\(253\) 3200.00 0.795187
\(254\) −4560.00 −1.12646
\(255\) 2088.00 0.512767
\(256\) 256.000 0.0625000
\(257\) −3806.00 −0.923781 −0.461891 0.886937i \(-0.652829\pi\)
−0.461891 + 0.886937i \(0.652829\pi\)
\(258\) −72.0000 −0.0173741
\(259\) −350.000 −0.0839689
\(260\) 624.000 0.148842
\(261\) −990.000 −0.234787
\(262\) −3104.00 −0.731930
\(263\) −3816.00 −0.894694 −0.447347 0.894360i \(-0.647631\pi\)
−0.447347 + 0.894360i \(0.647631\pi\)
\(264\) −1200.00 −0.279753
\(265\) 5304.00 1.22952
\(266\) −560.000 −0.129082
\(267\) 2904.00 0.665625
\(268\) 80.0000 0.0182342
\(269\) −3026.00 −0.685868 −0.342934 0.939360i \(-0.611421\pi\)
−0.342934 + 0.939360i \(0.611421\pi\)
\(270\) −648.000 −0.146059
\(271\) 2480.00 0.555901 0.277951 0.960595i \(-0.410345\pi\)
0.277951 + 0.960595i \(0.410345\pi\)
\(272\) −928.000 −0.206869
\(273\) −273.000 −0.0605228
\(274\) 96.0000 0.0211663
\(275\) −950.000 −0.208317
\(276\) −768.000 −0.167493
\(277\) 3590.00 0.778708 0.389354 0.921088i \(-0.372698\pi\)
0.389354 + 0.921088i \(0.372698\pi\)
\(278\) 56.0000 0.0120815
\(279\) 1116.00 0.239474
\(280\) −672.000 −0.143427
\(281\) 4832.00 1.02581 0.512906 0.858445i \(-0.328569\pi\)
0.512906 + 0.858445i \(0.328569\pi\)
\(282\) −492.000 −0.103894
\(283\) −5700.00 −1.19728 −0.598639 0.801019i \(-0.704292\pi\)
−0.598639 + 0.801019i \(0.704292\pi\)
\(284\) −1560.00 −0.325947
\(285\) 1440.00 0.299292
\(286\) 1300.00 0.268778
\(287\) 588.000 0.120936
\(288\) 288.000 0.0589256
\(289\) −1549.00 −0.315286
\(290\) 2640.00 0.534573
\(291\) 3066.00 0.617636
\(292\) −8.00000 −0.00160330
\(293\) −6384.00 −1.27289 −0.636446 0.771321i \(-0.719596\pi\)
−0.636446 + 0.771321i \(0.719596\pi\)
\(294\) 294.000 0.0583212
\(295\) 7416.00 1.46365
\(296\) −400.000 −0.0785457
\(297\) −1350.00 −0.263754
\(298\) 5192.00 1.00928
\(299\) 832.000 0.160922
\(300\) 228.000 0.0438786
\(301\) −84.0000 −0.0160853
\(302\) −4104.00 −0.781982
\(303\) 162.000 0.0307150
\(304\) −640.000 −0.120745
\(305\) 3336.00 0.626291
\(306\) −1044.00 −0.195038
\(307\) 3836.00 0.713134 0.356567 0.934270i \(-0.383947\pi\)
0.356567 + 0.934270i \(0.383947\pi\)
\(308\) −1400.00 −0.259001
\(309\) 4248.00 0.782072
\(310\) −2976.00 −0.545243
\(311\) 6116.00 1.11513 0.557567 0.830132i \(-0.311735\pi\)
0.557567 + 0.830132i \(0.311735\pi\)
\(312\) −312.000 −0.0566139
\(313\) −642.000 −0.115936 −0.0579680 0.998318i \(-0.518462\pi\)
−0.0579680 + 0.998318i \(0.518462\pi\)
\(314\) −5044.00 −0.906527
\(315\) −756.000 −0.135225
\(316\) −2720.00 −0.484215
\(317\) −9136.00 −1.61870 −0.809352 0.587325i \(-0.800181\pi\)
−0.809352 + 0.587325i \(0.800181\pi\)
\(318\) −2652.00 −0.467663
\(319\) 5500.00 0.965332
\(320\) −768.000 −0.134164
\(321\) 3756.00 0.653082
\(322\) −896.000 −0.155069
\(323\) 2320.00 0.399654
\(324\) 324.000 0.0555556
\(325\) −247.000 −0.0421572
\(326\) −1696.00 −0.288137
\(327\) 2790.00 0.471827
\(328\) 672.000 0.113125
\(329\) −574.000 −0.0961874
\(330\) 3600.00 0.600526
\(331\) −3060.00 −0.508135 −0.254068 0.967186i \(-0.581769\pi\)
−0.254068 + 0.967186i \(0.581769\pi\)
\(332\) 1288.00 0.212916
\(333\) −450.000 −0.0740536
\(334\) 1708.00 0.279813
\(335\) −240.000 −0.0391421
\(336\) 336.000 0.0545545
\(337\) 4734.00 0.765215 0.382607 0.923911i \(-0.375026\pi\)
0.382607 + 0.923911i \(0.375026\pi\)
\(338\) 338.000 0.0543928
\(339\) −3102.00 −0.496984
\(340\) 2784.00 0.444069
\(341\) −6200.00 −0.984601
\(342\) −720.000 −0.113840
\(343\) 343.000 0.0539949
\(344\) −96.0000 −0.0150464
\(345\) 2304.00 0.359545
\(346\) 4092.00 0.635801
\(347\) −11096.0 −1.71661 −0.858306 0.513138i \(-0.828483\pi\)
−0.858306 + 0.513138i \(0.828483\pi\)
\(348\) −1320.00 −0.203332
\(349\) 2366.00 0.362891 0.181446 0.983401i \(-0.441922\pi\)
0.181446 + 0.983401i \(0.441922\pi\)
\(350\) 266.000 0.0406237
\(351\) −351.000 −0.0533761
\(352\) −1600.00 −0.242274
\(353\) −11076.0 −1.67002 −0.835008 0.550237i \(-0.814537\pi\)
−0.835008 + 0.550237i \(0.814537\pi\)
\(354\) −3708.00 −0.556717
\(355\) 4680.00 0.699686
\(356\) 3872.00 0.576448
\(357\) −1218.00 −0.180570
\(358\) −3376.00 −0.498400
\(359\) −6406.00 −0.941771 −0.470885 0.882194i \(-0.656065\pi\)
−0.470885 + 0.882194i \(0.656065\pi\)
\(360\) −864.000 −0.126491
\(361\) −5259.00 −0.766730
\(362\) −532.000 −0.0772412
\(363\) 3507.00 0.507079
\(364\) −364.000 −0.0524142
\(365\) 24.0000 0.00344169
\(366\) −1668.00 −0.238218
\(367\) 2000.00 0.284466 0.142233 0.989833i \(-0.454572\pi\)
0.142233 + 0.989833i \(0.454572\pi\)
\(368\) −1024.00 −0.145054
\(369\) 756.000 0.106655
\(370\) 1200.00 0.168608
\(371\) −3094.00 −0.432972
\(372\) 1488.00 0.207390
\(373\) −3662.00 −0.508341 −0.254170 0.967159i \(-0.581802\pi\)
−0.254170 + 0.967159i \(0.581802\pi\)
\(374\) 5800.00 0.801901
\(375\) 3816.00 0.525486
\(376\) −656.000 −0.0899750
\(377\) 1430.00 0.195355
\(378\) 378.000 0.0514344
\(379\) 6008.00 0.814275 0.407138 0.913367i \(-0.366527\pi\)
0.407138 + 0.913367i \(0.366527\pi\)
\(380\) 1920.00 0.259195
\(381\) −6840.00 −0.919748
\(382\) 5752.00 0.770413
\(383\) 11202.0 1.49451 0.747253 0.664540i \(-0.231373\pi\)
0.747253 + 0.664540i \(0.231373\pi\)
\(384\) 384.000 0.0510310
\(385\) 4200.00 0.555979
\(386\) 6116.00 0.806467
\(387\) −108.000 −0.0141859
\(388\) 4088.00 0.534889
\(389\) −10858.0 −1.41522 −0.707612 0.706601i \(-0.750228\pi\)
−0.707612 + 0.706601i \(0.750228\pi\)
\(390\) 936.000 0.121529
\(391\) 3712.00 0.480112
\(392\) 392.000 0.0505076
\(393\) −4656.00 −0.597619
\(394\) −5904.00 −0.754922
\(395\) 8160.00 1.03943
\(396\) −1800.00 −0.228418
\(397\) −5850.00 −0.739554 −0.369777 0.929120i \(-0.620566\pi\)
−0.369777 + 0.929120i \(0.620566\pi\)
\(398\) 6128.00 0.771781
\(399\) −840.000 −0.105395
\(400\) 304.000 0.0380000
\(401\) −11404.0 −1.42017 −0.710086 0.704115i \(-0.751344\pi\)
−0.710086 + 0.704115i \(0.751344\pi\)
\(402\) 120.000 0.0148882
\(403\) −1612.00 −0.199254
\(404\) 216.000 0.0266000
\(405\) −972.000 −0.119257
\(406\) −1540.00 −0.188249
\(407\) 2500.00 0.304473
\(408\) −1392.00 −0.168908
\(409\) −10194.0 −1.23242 −0.616211 0.787581i \(-0.711333\pi\)
−0.616211 + 0.787581i \(0.711333\pi\)
\(410\) −2016.00 −0.242837
\(411\) 144.000 0.0172822
\(412\) 5664.00 0.677294
\(413\) −4326.00 −0.515420
\(414\) −1152.00 −0.136758
\(415\) −3864.00 −0.457051
\(416\) −416.000 −0.0490290
\(417\) 84.0000 0.00986450
\(418\) 4000.00 0.468054
\(419\) 3192.00 0.372170 0.186085 0.982534i \(-0.440420\pi\)
0.186085 + 0.982534i \(0.440420\pi\)
\(420\) −1008.00 −0.117108
\(421\) 10474.0 1.21252 0.606261 0.795266i \(-0.292669\pi\)
0.606261 + 0.795266i \(0.292669\pi\)
\(422\) 1208.00 0.139347
\(423\) −738.000 −0.0848293
\(424\) −3536.00 −0.405008
\(425\) −1102.00 −0.125776
\(426\) −2340.00 −0.266135
\(427\) −1946.00 −0.220547
\(428\) 5008.00 0.565586
\(429\) 1950.00 0.219457
\(430\) 288.000 0.0322991
\(431\) 7902.00 0.883123 0.441561 0.897231i \(-0.354425\pi\)
0.441561 + 0.897231i \(0.354425\pi\)
\(432\) 432.000 0.0481125
\(433\) −16954.0 −1.88166 −0.940828 0.338884i \(-0.889951\pi\)
−0.940828 + 0.338884i \(0.889951\pi\)
\(434\) 1736.00 0.192006
\(435\) 3960.00 0.436477
\(436\) 3720.00 0.408614
\(437\) 2560.00 0.280232
\(438\) −12.0000 −0.00130909
\(439\) 13960.0 1.51771 0.758855 0.651260i \(-0.225759\pi\)
0.758855 + 0.651260i \(0.225759\pi\)
\(440\) 4800.00 0.520071
\(441\) 441.000 0.0476190
\(442\) 1508.00 0.162281
\(443\) −1884.00 −0.202058 −0.101029 0.994883i \(-0.532213\pi\)
−0.101029 + 0.994883i \(0.532213\pi\)
\(444\) −600.000 −0.0641323
\(445\) −11616.0 −1.23742
\(446\) 11256.0 1.19504
\(447\) 7788.00 0.824071
\(448\) 448.000 0.0472456
\(449\) −11436.0 −1.20200 −0.601000 0.799249i \(-0.705231\pi\)
−0.601000 + 0.799249i \(0.705231\pi\)
\(450\) 342.000 0.0358267
\(451\) −4200.00 −0.438515
\(452\) −4136.00 −0.430401
\(453\) −6156.00 −0.638486
\(454\) −2244.00 −0.231974
\(455\) 1092.00 0.112514
\(456\) −960.000 −0.0985880
\(457\) 11486.0 1.17569 0.587847 0.808972i \(-0.299976\pi\)
0.587847 + 0.808972i \(0.299976\pi\)
\(458\) 8852.00 0.903115
\(459\) −1566.00 −0.159248
\(460\) 3072.00 0.311376
\(461\) 11172.0 1.12870 0.564351 0.825535i \(-0.309126\pi\)
0.564351 + 0.825535i \(0.309126\pi\)
\(462\) −2100.00 −0.211474
\(463\) −11688.0 −1.17319 −0.586595 0.809880i \(-0.699532\pi\)
−0.586595 + 0.809880i \(0.699532\pi\)
\(464\) −1760.00 −0.176090
\(465\) −4464.00 −0.445189
\(466\) 4380.00 0.435407
\(467\) −2448.00 −0.242569 −0.121285 0.992618i \(-0.538701\pi\)
−0.121285 + 0.992618i \(0.538701\pi\)
\(468\) −468.000 −0.0462250
\(469\) 140.000 0.0137838
\(470\) 1968.00 0.193143
\(471\) −7566.00 −0.740176
\(472\) −4944.00 −0.482131
\(473\) 600.000 0.0583256
\(474\) −4080.00 −0.395360
\(475\) −760.000 −0.0734130
\(476\) −1624.00 −0.156378
\(477\) −3978.00 −0.381845
\(478\) −2460.00 −0.235393
\(479\) 698.000 0.0665813 0.0332906 0.999446i \(-0.489401\pi\)
0.0332906 + 0.999446i \(0.489401\pi\)
\(480\) −1152.00 −0.109545
\(481\) 650.000 0.0616163
\(482\) −1572.00 −0.148553
\(483\) −1344.00 −0.126613
\(484\) 4676.00 0.439144
\(485\) −12264.0 −1.14821
\(486\) 486.000 0.0453609
\(487\) −8156.00 −0.758899 −0.379449 0.925213i \(-0.623887\pi\)
−0.379449 + 0.925213i \(0.623887\pi\)
\(488\) −2224.00 −0.206303
\(489\) −2544.00 −0.235263
\(490\) −1176.00 −0.108421
\(491\) −10484.0 −0.963618 −0.481809 0.876276i \(-0.660020\pi\)
−0.481809 + 0.876276i \(0.660020\pi\)
\(492\) 1008.00 0.0923662
\(493\) 6380.00 0.582841
\(494\) 1040.00 0.0947203
\(495\) 5400.00 0.490327
\(496\) 1984.00 0.179605
\(497\) −2730.00 −0.246393
\(498\) 1932.00 0.173845
\(499\) −6980.00 −0.626188 −0.313094 0.949722i \(-0.601365\pi\)
−0.313094 + 0.949722i \(0.601365\pi\)
\(500\) 5088.00 0.455085
\(501\) 2562.00 0.228467
\(502\) −560.000 −0.0497889
\(503\) 5180.00 0.459175 0.229587 0.973288i \(-0.426262\pi\)
0.229587 + 0.973288i \(0.426262\pi\)
\(504\) 504.000 0.0445435
\(505\) −648.000 −0.0571002
\(506\) 6400.00 0.562282
\(507\) 507.000 0.0444116
\(508\) −9120.00 −0.796525
\(509\) 4860.00 0.423214 0.211607 0.977355i \(-0.432130\pi\)
0.211607 + 0.977355i \(0.432130\pi\)
\(510\) 4176.00 0.362581
\(511\) −14.0000 −0.00121198
\(512\) 512.000 0.0441942
\(513\) −1080.00 −0.0929496
\(514\) −7612.00 −0.653212
\(515\) −16992.0 −1.45390
\(516\) −144.000 −0.0122854
\(517\) 4100.00 0.348777
\(518\) −700.000 −0.0593750
\(519\) 6138.00 0.519130
\(520\) 1248.00 0.105247
\(521\) −17390.0 −1.46232 −0.731161 0.682205i \(-0.761021\pi\)
−0.731161 + 0.682205i \(0.761021\pi\)
\(522\) −1980.00 −0.166020
\(523\) −12556.0 −1.04978 −0.524891 0.851170i \(-0.675894\pi\)
−0.524891 + 0.851170i \(0.675894\pi\)
\(524\) −6208.00 −0.517553
\(525\) 399.000 0.0331691
\(526\) −7632.00 −0.632645
\(527\) −7192.00 −0.594475
\(528\) −2400.00 −0.197816
\(529\) −8071.00 −0.663352
\(530\) 10608.0 0.869400
\(531\) −5562.00 −0.454558
\(532\) −1120.00 −0.0912747
\(533\) −1092.00 −0.0887425
\(534\) 5808.00 0.470668
\(535\) −15024.0 −1.21410
\(536\) 160.000 0.0128936
\(537\) −5064.00 −0.406942
\(538\) −6052.00 −0.484982
\(539\) −2450.00 −0.195787
\(540\) −1296.00 −0.103280
\(541\) −19398.0 −1.54156 −0.770781 0.637100i \(-0.780134\pi\)
−0.770781 + 0.637100i \(0.780134\pi\)
\(542\) 4960.00 0.393082
\(543\) −798.000 −0.0630671
\(544\) −1856.00 −0.146278
\(545\) −11160.0 −0.877141
\(546\) −546.000 −0.0427960
\(547\) −9308.00 −0.727571 −0.363786 0.931483i \(-0.618516\pi\)
−0.363786 + 0.931483i \(0.618516\pi\)
\(548\) 192.000 0.0149668
\(549\) −2502.00 −0.194504
\(550\) −1900.00 −0.147302
\(551\) 4400.00 0.340193
\(552\) −1536.00 −0.118436
\(553\) −4760.00 −0.366032
\(554\) 7180.00 0.550630
\(555\) 1800.00 0.137668
\(556\) 112.000 0.00854291
\(557\) −19524.0 −1.48520 −0.742602 0.669733i \(-0.766408\pi\)
−0.742602 + 0.669733i \(0.766408\pi\)
\(558\) 2232.00 0.169334
\(559\) 156.000 0.0118034
\(560\) −1344.00 −0.101419
\(561\) 8700.00 0.654749
\(562\) 9664.00 0.725358
\(563\) −772.000 −0.0577903 −0.0288951 0.999582i \(-0.509199\pi\)
−0.0288951 + 0.999582i \(0.509199\pi\)
\(564\) −984.000 −0.0734643
\(565\) 12408.0 0.923909
\(566\) −11400.0 −0.846604
\(567\) 567.000 0.0419961
\(568\) −3120.00 −0.230479
\(569\) −8226.00 −0.606067 −0.303033 0.952980i \(-0.597999\pi\)
−0.303033 + 0.952980i \(0.597999\pi\)
\(570\) 2880.00 0.211631
\(571\) −11852.0 −0.868635 −0.434318 0.900760i \(-0.643010\pi\)
−0.434318 + 0.900760i \(0.643010\pi\)
\(572\) 2600.00 0.190055
\(573\) 8628.00 0.629040
\(574\) 1176.00 0.0855144
\(575\) −1216.00 −0.0881925
\(576\) 576.000 0.0416667
\(577\) 11282.0 0.813996 0.406998 0.913429i \(-0.366576\pi\)
0.406998 + 0.913429i \(0.366576\pi\)
\(578\) −3098.00 −0.222941
\(579\) 9174.00 0.658477
\(580\) 5280.00 0.378000
\(581\) 2254.00 0.160950
\(582\) 6132.00 0.436735
\(583\) 22100.0 1.56996
\(584\) −16.0000 −0.00113371
\(585\) 1404.00 0.0992278
\(586\) −12768.0 −0.900070
\(587\) 14994.0 1.05429 0.527145 0.849775i \(-0.323262\pi\)
0.527145 + 0.849775i \(0.323262\pi\)
\(588\) 588.000 0.0412393
\(589\) −4960.00 −0.346983
\(590\) 14832.0 1.03496
\(591\) −8856.00 −0.616391
\(592\) −800.000 −0.0555402
\(593\) −21544.0 −1.49192 −0.745958 0.665993i \(-0.768008\pi\)
−0.745958 + 0.665993i \(0.768008\pi\)
\(594\) −2700.00 −0.186502
\(595\) 4872.00 0.335685
\(596\) 10384.0 0.713666
\(597\) 9192.00 0.630157
\(598\) 1664.00 0.113789
\(599\) −4824.00 −0.329054 −0.164527 0.986373i \(-0.552610\pi\)
−0.164527 + 0.986373i \(0.552610\pi\)
\(600\) 456.000 0.0310269
\(601\) 4718.00 0.320218 0.160109 0.987099i \(-0.448815\pi\)
0.160109 + 0.987099i \(0.448815\pi\)
\(602\) −168.000 −0.0113740
\(603\) 180.000 0.0121562
\(604\) −8208.00 −0.552945
\(605\) −14028.0 −0.942677
\(606\) 324.000 0.0217188
\(607\) 4720.00 0.315616 0.157808 0.987470i \(-0.449557\pi\)
0.157808 + 0.987470i \(0.449557\pi\)
\(608\) −1280.00 −0.0853797
\(609\) −2310.00 −0.153704
\(610\) 6672.00 0.442855
\(611\) 1066.00 0.0705822
\(612\) −2088.00 −0.137912
\(613\) 16078.0 1.05935 0.529677 0.848199i \(-0.322313\pi\)
0.529677 + 0.848199i \(0.322313\pi\)
\(614\) 7672.00 0.504262
\(615\) −3024.00 −0.198276
\(616\) −2800.00 −0.183142
\(617\) 12840.0 0.837794 0.418897 0.908034i \(-0.362417\pi\)
0.418897 + 0.908034i \(0.362417\pi\)
\(618\) 8496.00 0.553008
\(619\) −22332.0 −1.45008 −0.725039 0.688707i \(-0.758179\pi\)
−0.725039 + 0.688707i \(0.758179\pi\)
\(620\) −5952.00 −0.385545
\(621\) −1728.00 −0.111662
\(622\) 12232.0 0.788519
\(623\) 6776.00 0.435754
\(624\) −624.000 −0.0400320
\(625\) −17639.0 −1.12890
\(626\) −1284.00 −0.0819792
\(627\) 6000.00 0.382164
\(628\) −10088.0 −0.641011
\(629\) 2900.00 0.183832
\(630\) −1512.00 −0.0956183
\(631\) −23756.0 −1.49875 −0.749375 0.662146i \(-0.769646\pi\)
−0.749375 + 0.662146i \(0.769646\pi\)
\(632\) −5440.00 −0.342392
\(633\) 1812.00 0.113777
\(634\) −18272.0 −1.14460
\(635\) 27360.0 1.70984
\(636\) −5304.00 −0.330688
\(637\) −637.000 −0.0396214
\(638\) 11000.0 0.682593
\(639\) −3510.00 −0.217298
\(640\) −1536.00 −0.0948683
\(641\) 10170.0 0.626663 0.313331 0.949644i \(-0.398555\pi\)
0.313331 + 0.949644i \(0.398555\pi\)
\(642\) 7512.00 0.461799
\(643\) −19404.0 −1.19008 −0.595038 0.803697i \(-0.702863\pi\)
−0.595038 + 0.803697i \(0.702863\pi\)
\(644\) −1792.00 −0.109650
\(645\) 432.000 0.0263721
\(646\) 4640.00 0.282598
\(647\) 13704.0 0.832705 0.416352 0.909203i \(-0.363308\pi\)
0.416352 + 0.909203i \(0.363308\pi\)
\(648\) 648.000 0.0392837
\(649\) 30900.0 1.86892
\(650\) −494.000 −0.0298097
\(651\) 2604.00 0.156772
\(652\) −3392.00 −0.203744
\(653\) −19230.0 −1.15242 −0.576208 0.817303i \(-0.695468\pi\)
−0.576208 + 0.817303i \(0.695468\pi\)
\(654\) 5580.00 0.333632
\(655\) 18624.0 1.11099
\(656\) 1344.00 0.0799914
\(657\) −18.0000 −0.00106887
\(658\) −1148.00 −0.0680147
\(659\) 18608.0 1.09995 0.549973 0.835182i \(-0.314638\pi\)
0.549973 + 0.835182i \(0.314638\pi\)
\(660\) 7200.00 0.424636
\(661\) −7394.00 −0.435088 −0.217544 0.976050i \(-0.569805\pi\)
−0.217544 + 0.976050i \(0.569805\pi\)
\(662\) −6120.00 −0.359306
\(663\) 2262.00 0.132502
\(664\) 2576.00 0.150554
\(665\) 3360.00 0.195933
\(666\) −900.000 −0.0523638
\(667\) 7040.00 0.408680
\(668\) 3416.00 0.197858
\(669\) 16884.0 0.975745
\(670\) −480.000 −0.0276776
\(671\) 13900.0 0.799707
\(672\) 672.000 0.0385758
\(673\) 450.000 0.0257745 0.0128872 0.999917i \(-0.495898\pi\)
0.0128872 + 0.999917i \(0.495898\pi\)
\(674\) 9468.00 0.541089
\(675\) 513.000 0.0292524
\(676\) 676.000 0.0384615
\(677\) 6666.00 0.378427 0.189214 0.981936i \(-0.439406\pi\)
0.189214 + 0.981936i \(0.439406\pi\)
\(678\) −6204.00 −0.351421
\(679\) 7154.00 0.404338
\(680\) 5568.00 0.314004
\(681\) −3366.00 −0.189406
\(682\) −12400.0 −0.696218
\(683\) −11082.0 −0.620851 −0.310425 0.950598i \(-0.600471\pi\)
−0.310425 + 0.950598i \(0.600471\pi\)
\(684\) −1440.00 −0.0804967
\(685\) −576.000 −0.0321282
\(686\) 686.000 0.0381802
\(687\) 13278.0 0.737391
\(688\) −192.000 −0.0106394
\(689\) 5746.00 0.317714
\(690\) 4608.00 0.254237
\(691\) 19308.0 1.06297 0.531484 0.847068i \(-0.321635\pi\)
0.531484 + 0.847068i \(0.321635\pi\)
\(692\) 8184.00 0.449579
\(693\) −3150.00 −0.172668
\(694\) −22192.0 −1.21383
\(695\) −336.000 −0.0183384
\(696\) −2640.00 −0.143777
\(697\) −4872.00 −0.264763
\(698\) 4732.00 0.256603
\(699\) 6570.00 0.355508
\(700\) 532.000 0.0287253
\(701\) 15318.0 0.825325 0.412663 0.910884i \(-0.364599\pi\)
0.412663 + 0.910884i \(0.364599\pi\)
\(702\) −702.000 −0.0377426
\(703\) 2000.00 0.107299
\(704\) −3200.00 −0.171313
\(705\) 2952.00 0.157700
\(706\) −22152.0 −1.18088
\(707\) 378.000 0.0201077
\(708\) −7416.00 −0.393659
\(709\) −16486.0 −0.873265 −0.436632 0.899640i \(-0.643829\pi\)
−0.436632 + 0.899640i \(0.643829\pi\)
\(710\) 9360.00 0.494753
\(711\) −6120.00 −0.322810
\(712\) 7744.00 0.407610
\(713\) −7936.00 −0.416838
\(714\) −2436.00 −0.127682
\(715\) −7800.00 −0.407977
\(716\) −6752.00 −0.352422
\(717\) −3690.00 −0.192197
\(718\) −12812.0 −0.665933
\(719\) 10740.0 0.557072 0.278536 0.960426i \(-0.410151\pi\)
0.278536 + 0.960426i \(0.410151\pi\)
\(720\) −1728.00 −0.0894427
\(721\) 9912.00 0.511986
\(722\) −10518.0 −0.542160
\(723\) −2358.00 −0.121293
\(724\) −1064.00 −0.0546177
\(725\) −2090.00 −0.107063
\(726\) 7014.00 0.358559
\(727\) 22736.0 1.15988 0.579939 0.814660i \(-0.303076\pi\)
0.579939 + 0.814660i \(0.303076\pi\)
\(728\) −728.000 −0.0370625
\(729\) 729.000 0.0370370
\(730\) 48.0000 0.00243364
\(731\) 696.000 0.0352154
\(732\) −3336.00 −0.168446
\(733\) 10082.0 0.508032 0.254016 0.967200i \(-0.418248\pi\)
0.254016 + 0.967200i \(0.418248\pi\)
\(734\) 4000.00 0.201148
\(735\) −1764.00 −0.0885253
\(736\) −2048.00 −0.102568
\(737\) −1000.00 −0.0499803
\(738\) 1512.00 0.0754167
\(739\) −24676.0 −1.22831 −0.614155 0.789185i \(-0.710503\pi\)
−0.614155 + 0.789185i \(0.710503\pi\)
\(740\) 2400.00 0.119224
\(741\) 1560.00 0.0773388
\(742\) −6188.00 −0.306157
\(743\) 29178.0 1.44070 0.720348 0.693613i \(-0.243982\pi\)
0.720348 + 0.693613i \(0.243982\pi\)
\(744\) 2976.00 0.146647
\(745\) −31152.0 −1.53197
\(746\) −7324.00 −0.359451
\(747\) 2898.00 0.141944
\(748\) 11600.0 0.567029
\(749\) 8764.00 0.427543
\(750\) 7632.00 0.371575
\(751\) 13432.0 0.652651 0.326325 0.945258i \(-0.394190\pi\)
0.326325 + 0.945258i \(0.394190\pi\)
\(752\) −1312.00 −0.0636220
\(753\) −840.000 −0.0406525
\(754\) 2860.00 0.138137
\(755\) 24624.0 1.18697
\(756\) 756.000 0.0363696
\(757\) 114.000 0.00547345 0.00273672 0.999996i \(-0.499129\pi\)
0.00273672 + 0.999996i \(0.499129\pi\)
\(758\) 12016.0 0.575779
\(759\) 9600.00 0.459101
\(760\) 3840.00 0.183278
\(761\) −5052.00 −0.240650 −0.120325 0.992735i \(-0.538394\pi\)
−0.120325 + 0.992735i \(0.538394\pi\)
\(762\) −13680.0 −0.650360
\(763\) 6510.00 0.308883
\(764\) 11504.0 0.544765
\(765\) 6264.00 0.296046
\(766\) 22404.0 1.05677
\(767\) 8034.00 0.378215
\(768\) 768.000 0.0360844
\(769\) −36862.0 −1.72858 −0.864290 0.502994i \(-0.832232\pi\)
−0.864290 + 0.502994i \(0.832232\pi\)
\(770\) 8400.00 0.393136
\(771\) −11418.0 −0.533345
\(772\) 12232.0 0.570258
\(773\) −1472.00 −0.0684918 −0.0342459 0.999413i \(-0.510903\pi\)
−0.0342459 + 0.999413i \(0.510903\pi\)
\(774\) −216.000 −0.0100310
\(775\) 2356.00 0.109200
\(776\) 8176.00 0.378223
\(777\) −1050.00 −0.0484795
\(778\) −21716.0 −1.00072
\(779\) −3360.00 −0.154537
\(780\) 1872.00 0.0859338
\(781\) 19500.0 0.893425
\(782\) 7424.00 0.339491
\(783\) −2970.00 −0.135554
\(784\) 784.000 0.0357143
\(785\) 30264.0 1.37601
\(786\) −9312.00 −0.422580
\(787\) −23620.0 −1.06984 −0.534919 0.844904i \(-0.679658\pi\)
−0.534919 + 0.844904i \(0.679658\pi\)
\(788\) −11808.0 −0.533810
\(789\) −11448.0 −0.516552
\(790\) 16320.0 0.734987
\(791\) −7238.00 −0.325352
\(792\) −3600.00 −0.161516
\(793\) 3614.00 0.161837
\(794\) −11700.0 −0.522944
\(795\) 15912.0 0.709862
\(796\) 12256.0 0.545732
\(797\) 13986.0 0.621593 0.310796 0.950476i \(-0.399404\pi\)
0.310796 + 0.950476i \(0.399404\pi\)
\(798\) −1680.00 −0.0745255
\(799\) 4756.00 0.210582
\(800\) 608.000 0.0268701
\(801\) 8712.00 0.384299
\(802\) −22808.0 −1.00421
\(803\) 100.000 0.00439467
\(804\) 240.000 0.0105275
\(805\) 5376.00 0.235378
\(806\) −3224.00 −0.140894
\(807\) −9078.00 −0.395986
\(808\) 432.000 0.0188090
\(809\) −30738.0 −1.33584 −0.667918 0.744235i \(-0.732814\pi\)
−0.667918 + 0.744235i \(0.732814\pi\)
\(810\) −1944.00 −0.0843274
\(811\) 25480.0 1.10324 0.551618 0.834097i \(-0.314011\pi\)
0.551618 + 0.834097i \(0.314011\pi\)
\(812\) −3080.00 −0.133112
\(813\) 7440.00 0.320950
\(814\) 5000.00 0.215295
\(815\) 10176.0 0.437362
\(816\) −2784.00 −0.119436
\(817\) 480.000 0.0205546
\(818\) −20388.0 −0.871454
\(819\) −819.000 −0.0349428
\(820\) −4032.00 −0.171712
\(821\) 23484.0 0.998291 0.499146 0.866518i \(-0.333647\pi\)
0.499146 + 0.866518i \(0.333647\pi\)
\(822\) 288.000 0.0122204
\(823\) −1632.00 −0.0691227 −0.0345613 0.999403i \(-0.511003\pi\)
−0.0345613 + 0.999403i \(0.511003\pi\)
\(824\) 11328.0 0.478919
\(825\) −2850.00 −0.120272
\(826\) −8652.00 −0.364457
\(827\) 25734.0 1.08205 0.541027 0.841005i \(-0.318036\pi\)
0.541027 + 0.841005i \(0.318036\pi\)
\(828\) −2304.00 −0.0967023
\(829\) 22314.0 0.934858 0.467429 0.884031i \(-0.345180\pi\)
0.467429 + 0.884031i \(0.345180\pi\)
\(830\) −7728.00 −0.323184
\(831\) 10770.0 0.449587
\(832\) −832.000 −0.0346688
\(833\) −2842.00 −0.118211
\(834\) 168.000 0.00697526
\(835\) −10248.0 −0.424727
\(836\) 8000.00 0.330964
\(837\) 3348.00 0.138260
\(838\) 6384.00 0.263164
\(839\) 8330.00 0.342769 0.171385 0.985204i \(-0.445176\pi\)
0.171385 + 0.985204i \(0.445176\pi\)
\(840\) −2016.00 −0.0828079
\(841\) −12289.0 −0.503875
\(842\) 20948.0 0.857382
\(843\) 14496.0 0.592252
\(844\) 2416.00 0.0985334
\(845\) −2028.00 −0.0825625
\(846\) −1476.00 −0.0599834
\(847\) 8183.00 0.331961
\(848\) −7072.00 −0.286384
\(849\) −17100.0 −0.691249
\(850\) −2204.00 −0.0889371
\(851\) 3200.00 0.128901
\(852\) −4680.00 −0.188186
\(853\) −4522.00 −0.181513 −0.0907563 0.995873i \(-0.528928\pi\)
−0.0907563 + 0.995873i \(0.528928\pi\)
\(854\) −3892.00 −0.155950
\(855\) 4320.00 0.172796
\(856\) 10016.0 0.399930
\(857\) −40126.0 −1.59939 −0.799695 0.600406i \(-0.795006\pi\)
−0.799695 + 0.600406i \(0.795006\pi\)
\(858\) 3900.00 0.155179
\(859\) 34484.0 1.36971 0.684854 0.728680i \(-0.259866\pi\)
0.684854 + 0.728680i \(0.259866\pi\)
\(860\) 576.000 0.0228389
\(861\) 1764.00 0.0698223
\(862\) 15804.0 0.624462
\(863\) −6714.00 −0.264829 −0.132414 0.991194i \(-0.542273\pi\)
−0.132414 + 0.991194i \(0.542273\pi\)
\(864\) 864.000 0.0340207
\(865\) −24552.0 −0.965079
\(866\) −33908.0 −1.33053
\(867\) −4647.00 −0.182030
\(868\) 3472.00 0.135769
\(869\) 34000.0 1.32724
\(870\) 7920.00 0.308636
\(871\) −260.000 −0.0101145
\(872\) 7440.00 0.288934
\(873\) 9198.00 0.356592
\(874\) 5120.00 0.198154
\(875\) 8904.00 0.344012
\(876\) −24.0000 −0.000925668 0
\(877\) −18362.0 −0.707002 −0.353501 0.935434i \(-0.615009\pi\)
−0.353501 + 0.935434i \(0.615009\pi\)
\(878\) 27920.0 1.07318
\(879\) −19152.0 −0.734904
\(880\) 9600.00 0.367745
\(881\) 18018.0 0.689037 0.344519 0.938779i \(-0.388042\pi\)
0.344519 + 0.938779i \(0.388042\pi\)
\(882\) 882.000 0.0336718
\(883\) −5892.00 −0.224554 −0.112277 0.993677i \(-0.535814\pi\)
−0.112277 + 0.993677i \(0.535814\pi\)
\(884\) 3016.00 0.114750
\(885\) 22248.0 0.845038
\(886\) −3768.00 −0.142876
\(887\) −35544.0 −1.34549 −0.672746 0.739874i \(-0.734885\pi\)
−0.672746 + 0.739874i \(0.734885\pi\)
\(888\) −1200.00 −0.0453484
\(889\) −15960.0 −0.602116
\(890\) −23232.0 −0.874987
\(891\) −4050.00 −0.152278
\(892\) 22512.0 0.845020
\(893\) 3280.00 0.122913
\(894\) 15576.0 0.582706
\(895\) 20256.0 0.756518
\(896\) 896.000 0.0334077
\(897\) 2496.00 0.0929086
\(898\) −22872.0 −0.849943
\(899\) −13640.0 −0.506028
\(900\) 684.000 0.0253333
\(901\) 25636.0 0.947901
\(902\) −8400.00 −0.310077
\(903\) −252.000 −0.00928686
\(904\) −8272.00 −0.304339
\(905\) 3192.00 0.117244
\(906\) −12312.0 −0.451478
\(907\) 21020.0 0.769523 0.384762 0.923016i \(-0.374284\pi\)
0.384762 + 0.923016i \(0.374284\pi\)
\(908\) −4488.00 −0.164030
\(909\) 486.000 0.0177333
\(910\) 2184.00 0.0795592
\(911\) 30172.0 1.09730 0.548651 0.836051i \(-0.315141\pi\)
0.548651 + 0.836051i \(0.315141\pi\)
\(912\) −1920.00 −0.0697122
\(913\) −16100.0 −0.583606
\(914\) 22972.0 0.831342
\(915\) 10008.0 0.361589
\(916\) 17704.0 0.638599
\(917\) −10864.0 −0.391233
\(918\) −3132.00 −0.112605
\(919\) 25528.0 0.916312 0.458156 0.888872i \(-0.348510\pi\)
0.458156 + 0.888872i \(0.348510\pi\)
\(920\) 6144.00 0.220176
\(921\) 11508.0 0.411728
\(922\) 22344.0 0.798113
\(923\) 5070.00 0.180803
\(924\) −4200.00 −0.149534
\(925\) −950.000 −0.0337684
\(926\) −23376.0 −0.829571
\(927\) 12744.0 0.451530
\(928\) −3520.00 −0.124515
\(929\) −28460.0 −1.00510 −0.502552 0.864547i \(-0.667606\pi\)
−0.502552 + 0.864547i \(0.667606\pi\)
\(930\) −8928.00 −0.314796
\(931\) −1960.00 −0.0689972
\(932\) 8760.00 0.307879
\(933\) 18348.0 0.643823
\(934\) −4896.00 −0.171522
\(935\) −34800.0 −1.21720
\(936\) −936.000 −0.0326860
\(937\) −10682.0 −0.372429 −0.186214 0.982509i \(-0.559622\pi\)
−0.186214 + 0.982509i \(0.559622\pi\)
\(938\) 280.000 0.00974661
\(939\) −1926.00 −0.0669357
\(940\) 3936.00 0.136573
\(941\) 49992.0 1.73187 0.865937 0.500154i \(-0.166723\pi\)
0.865937 + 0.500154i \(0.166723\pi\)
\(942\) −15132.0 −0.523383
\(943\) −5376.00 −0.185649
\(944\) −9888.00 −0.340918
\(945\) −2268.00 −0.0780720
\(946\) 1200.00 0.0412425
\(947\) 24338.0 0.835141 0.417571 0.908644i \(-0.362882\pi\)
0.417571 + 0.908644i \(0.362882\pi\)
\(948\) −8160.00 −0.279562
\(949\) 26.0000 0.000889353 0
\(950\) −1520.00 −0.0519109
\(951\) −27408.0 −0.934559
\(952\) −3248.00 −0.110576
\(953\) 24558.0 0.834745 0.417372 0.908736i \(-0.362951\pi\)
0.417372 + 0.908736i \(0.362951\pi\)
\(954\) −7956.00 −0.270005
\(955\) −34512.0 −1.16941
\(956\) −4920.00 −0.166448
\(957\) 16500.0 0.557335
\(958\) 1396.00 0.0470801
\(959\) 336.000 0.0113139
\(960\) −2304.00 −0.0774597
\(961\) −14415.0 −0.483871
\(962\) 1300.00 0.0435693
\(963\) 11268.0 0.377057
\(964\) −3144.00 −0.105043
\(965\) −36696.0 −1.22413
\(966\) −2688.00 −0.0895290
\(967\) −17764.0 −0.590746 −0.295373 0.955382i \(-0.595444\pi\)
−0.295373 + 0.955382i \(0.595444\pi\)
\(968\) 9352.00 0.310521
\(969\) 6960.00 0.230740
\(970\) −24528.0 −0.811904
\(971\) 39300.0 1.29886 0.649432 0.760420i \(-0.275007\pi\)
0.649432 + 0.760420i \(0.275007\pi\)
\(972\) 972.000 0.0320750
\(973\) 196.000 0.00645783
\(974\) −16312.0 −0.536622
\(975\) −741.000 −0.0243395
\(976\) −4448.00 −0.145878
\(977\) 3940.00 0.129019 0.0645096 0.997917i \(-0.479452\pi\)
0.0645096 + 0.997917i \(0.479452\pi\)
\(978\) −5088.00 −0.166356
\(979\) −48400.0 −1.58005
\(980\) −2352.00 −0.0766652
\(981\) 8370.00 0.272409
\(982\) −20968.0 −0.681381
\(983\) 33682.0 1.09287 0.546434 0.837502i \(-0.315985\pi\)
0.546434 + 0.837502i \(0.315985\pi\)
\(984\) 2016.00 0.0653127
\(985\) 35424.0 1.14589
\(986\) 12760.0 0.412131
\(987\) −1722.00 −0.0555338
\(988\) 2080.00 0.0669773
\(989\) 768.000 0.0246926
\(990\) 10800.0 0.346714
\(991\) −15352.0 −0.492101 −0.246051 0.969257i \(-0.579133\pi\)
−0.246051 + 0.969257i \(0.579133\pi\)
\(992\) 3968.00 0.127000
\(993\) −9180.00 −0.293372
\(994\) −5460.00 −0.174226
\(995\) −36768.0 −1.17148
\(996\) 3864.00 0.122927
\(997\) 6942.00 0.220517 0.110258 0.993903i \(-0.464832\pi\)
0.110258 + 0.993903i \(0.464832\pi\)
\(998\) −13960.0 −0.442782
\(999\) −1350.00 −0.0427549
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.d.1.1 1
3.2 odd 2 1638.4.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.4.a.d.1.1 1 1.1 even 1 trivial
1638.4.a.g.1.1 1 3.2 odd 2