Properties

Label 1110.4.a.b.1.1
Level $1110$
Weight $4$
Character 1110.1
Self dual yes
Analytic conductor $65.492$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(65.4921201064\)
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 \(\chi\) \(=\) 1110.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +10.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +10.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +44.0000 q^{11} -12.0000 q^{12} +59.0000 q^{13} +20.0000 q^{14} +15.0000 q^{15} +16.0000 q^{16} -46.0000 q^{17} +18.0000 q^{18} -34.0000 q^{19} -20.0000 q^{20} -30.0000 q^{21} +88.0000 q^{22} +6.00000 q^{23} -24.0000 q^{24} +25.0000 q^{25} +118.000 q^{26} -27.0000 q^{27} +40.0000 q^{28} +7.00000 q^{29} +30.0000 q^{30} -182.000 q^{31} +32.0000 q^{32} -132.000 q^{33} -92.0000 q^{34} -50.0000 q^{35} +36.0000 q^{36} +37.0000 q^{37} -68.0000 q^{38} -177.000 q^{39} -40.0000 q^{40} +360.000 q^{41} -60.0000 q^{42} +101.000 q^{43} +176.000 q^{44} -45.0000 q^{45} +12.0000 q^{46} -35.0000 q^{47} -48.0000 q^{48} -243.000 q^{49} +50.0000 q^{50} +138.000 q^{51} +236.000 q^{52} -507.000 q^{53} -54.0000 q^{54} -220.000 q^{55} +80.0000 q^{56} +102.000 q^{57} +14.0000 q^{58} +821.000 q^{59} +60.0000 q^{60} +70.0000 q^{61} -364.000 q^{62} +90.0000 q^{63} +64.0000 q^{64} -295.000 q^{65} -264.000 q^{66} +612.000 q^{67} -184.000 q^{68} -18.0000 q^{69} -100.000 q^{70} +88.0000 q^{71} +72.0000 q^{72} +622.000 q^{73} +74.0000 q^{74} -75.0000 q^{75} -136.000 q^{76} +440.000 q^{77} -354.000 q^{78} +8.00000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +720.000 q^{82} +1223.00 q^{83} -120.000 q^{84} +230.000 q^{85} +202.000 q^{86} -21.0000 q^{87} +352.000 q^{88} +345.000 q^{89} -90.0000 q^{90} +590.000 q^{91} +24.0000 q^{92} +546.000 q^{93} -70.0000 q^{94} +170.000 q^{95} -96.0000 q^{96} +870.000 q^{97} -486.000 q^{98} +396.000 q^{99} +O(q^{100})\)

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
\(5\) −5.00000 −0.447214
\(6\) −6.00000 −0.408248
\(7\) 10.0000 0.539949 0.269975 0.962867i \(-0.412985\pi\)
0.269975 + 0.962867i \(0.412985\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −10.0000 −0.316228
\(11\) 44.0000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) −12.0000 −0.288675
\(13\) 59.0000 1.25874 0.629371 0.777105i \(-0.283312\pi\)
0.629371 + 0.777105i \(0.283312\pi\)
\(14\) 20.0000 0.381802
\(15\) 15.0000 0.258199
\(16\) 16.0000 0.250000
\(17\) −46.0000 −0.656273 −0.328136 0.944630i \(-0.606421\pi\)
−0.328136 + 0.944630i \(0.606421\pi\)
\(18\) 18.0000 0.235702
\(19\) −34.0000 −0.410533 −0.205267 0.978706i \(-0.565806\pi\)
−0.205267 + 0.978706i \(0.565806\pi\)
\(20\) −20.0000 −0.223607
\(21\) −30.0000 −0.311740
\(22\) 88.0000 0.852803
\(23\) 6.00000 0.0543951 0.0271975 0.999630i \(-0.491342\pi\)
0.0271975 + 0.999630i \(0.491342\pi\)
\(24\) −24.0000 −0.204124
\(25\) 25.0000 0.200000
\(26\) 118.000 0.890066
\(27\) −27.0000 −0.192450
\(28\) 40.0000 0.269975
\(29\) 7.00000 0.0448230 0.0224115 0.999749i \(-0.492866\pi\)
0.0224115 + 0.999749i \(0.492866\pi\)
\(30\) 30.0000 0.182574
\(31\) −182.000 −1.05446 −0.527228 0.849724i \(-0.676769\pi\)
−0.527228 + 0.849724i \(0.676769\pi\)
\(32\) 32.0000 0.176777
\(33\) −132.000 −0.696311
\(34\) −92.0000 −0.464055
\(35\) −50.0000 −0.241473
\(36\) 36.0000 0.166667
\(37\) 37.0000 0.164399
\(38\) −68.0000 −0.290291
\(39\) −177.000 −0.726735
\(40\) −40.0000 −0.158114
\(41\) 360.000 1.37128 0.685641 0.727940i \(-0.259522\pi\)
0.685641 + 0.727940i \(0.259522\pi\)
\(42\) −60.0000 −0.220433
\(43\) 101.000 0.358194 0.179097 0.983831i \(-0.442682\pi\)
0.179097 + 0.983831i \(0.442682\pi\)
\(44\) 176.000 0.603023
\(45\) −45.0000 −0.149071
\(46\) 12.0000 0.0384631
\(47\) −35.0000 −0.108623 −0.0543114 0.998524i \(-0.517296\pi\)
−0.0543114 + 0.998524i \(0.517296\pi\)
\(48\) −48.0000 −0.144338
\(49\) −243.000 −0.708455
\(50\) 50.0000 0.141421
\(51\) 138.000 0.378899
\(52\) 236.000 0.629371
\(53\) −507.000 −1.31400 −0.656998 0.753892i \(-0.728174\pi\)
−0.656998 + 0.753892i \(0.728174\pi\)
\(54\) −54.0000 −0.136083
\(55\) −220.000 −0.539360
\(56\) 80.0000 0.190901
\(57\) 102.000 0.237022
\(58\) 14.0000 0.0316947
\(59\) 821.000 1.81161 0.905806 0.423693i \(-0.139266\pi\)
0.905806 + 0.423693i \(0.139266\pi\)
\(60\) 60.0000 0.129099
\(61\) 70.0000 0.146928 0.0734638 0.997298i \(-0.476595\pi\)
0.0734638 + 0.997298i \(0.476595\pi\)
\(62\) −364.000 −0.745614
\(63\) 90.0000 0.179983
\(64\) 64.0000 0.125000
\(65\) −295.000 −0.562927
\(66\) −264.000 −0.492366
\(67\) 612.000 1.11594 0.557968 0.829863i \(-0.311581\pi\)
0.557968 + 0.829863i \(0.311581\pi\)
\(68\) −184.000 −0.328136
\(69\) −18.0000 −0.0314050
\(70\) −100.000 −0.170747
\(71\) 88.0000 0.147094 0.0735470 0.997292i \(-0.476568\pi\)
0.0735470 + 0.997292i \(0.476568\pi\)
\(72\) 72.0000 0.117851
\(73\) 622.000 0.997255 0.498627 0.866816i \(-0.333838\pi\)
0.498627 + 0.866816i \(0.333838\pi\)
\(74\) 74.0000 0.116248
\(75\) −75.0000 −0.115470
\(76\) −136.000 −0.205267
\(77\) 440.000 0.651203
\(78\) −354.000 −0.513880
\(79\) 8.00000 0.0113933 0.00569665 0.999984i \(-0.498187\pi\)
0.00569665 + 0.999984i \(0.498187\pi\)
\(80\) −80.0000 −0.111803
\(81\) 81.0000 0.111111
\(82\) 720.000 0.969643
\(83\) 1223.00 1.61737 0.808685 0.588242i \(-0.200180\pi\)
0.808685 + 0.588242i \(0.200180\pi\)
\(84\) −120.000 −0.155870
\(85\) 230.000 0.293494
\(86\) 202.000 0.253282
\(87\) −21.0000 −0.0258786
\(88\) 352.000 0.426401
\(89\) 345.000 0.410898 0.205449 0.978668i \(-0.434135\pi\)
0.205449 + 0.978668i \(0.434135\pi\)
\(90\) −90.0000 −0.105409
\(91\) 590.000 0.679657
\(92\) 24.0000 0.0271975
\(93\) 546.000 0.608791
\(94\) −70.0000 −0.0768080
\(95\) 170.000 0.183596
\(96\) −96.0000 −0.102062
\(97\) 870.000 0.910671 0.455336 0.890320i \(-0.349519\pi\)
0.455336 + 0.890320i \(0.349519\pi\)
\(98\) −486.000 −0.500953
\(99\) 396.000 0.402015
\(100\) 100.000 0.100000
\(101\) 942.000 0.928045 0.464022 0.885824i \(-0.346406\pi\)
0.464022 + 0.885824i \(0.346406\pi\)
\(102\) 276.000 0.267922
\(103\) −453.000 −0.433354 −0.216677 0.976243i \(-0.569522\pi\)
−0.216677 + 0.976243i \(0.569522\pi\)
\(104\) 472.000 0.445033
\(105\) 150.000 0.139414
\(106\) −1014.00 −0.929136
\(107\) 65.0000 0.0587270 0.0293635 0.999569i \(-0.490652\pi\)
0.0293635 + 0.999569i \(0.490652\pi\)
\(108\) −108.000 −0.0962250
\(109\) 200.000 0.175748 0.0878740 0.996132i \(-0.471993\pi\)
0.0878740 + 0.996132i \(0.471993\pi\)
\(110\) −440.000 −0.381385
\(111\) −111.000 −0.0949158
\(112\) 160.000 0.134987
\(113\) 1938.00 1.61338 0.806689 0.590976i \(-0.201257\pi\)
0.806689 + 0.590976i \(0.201257\pi\)
\(114\) 204.000 0.167600
\(115\) −30.0000 −0.0243262
\(116\) 28.0000 0.0224115
\(117\) 531.000 0.419581
\(118\) 1642.00 1.28100
\(119\) −460.000 −0.354354
\(120\) 120.000 0.0912871
\(121\) 605.000 0.454545
\(122\) 140.000 0.103893
\(123\) −1080.00 −0.791710
\(124\) −728.000 −0.527228
\(125\) −125.000 −0.0894427
\(126\) 180.000 0.127267
\(127\) −2706.00 −1.89070 −0.945349 0.326060i \(-0.894279\pi\)
−0.945349 + 0.326060i \(0.894279\pi\)
\(128\) 128.000 0.0883883
\(129\) −303.000 −0.206804
\(130\) −590.000 −0.398049
\(131\) −988.000 −0.658946 −0.329473 0.944165i \(-0.606871\pi\)
−0.329473 + 0.944165i \(0.606871\pi\)
\(132\) −528.000 −0.348155
\(133\) −340.000 −0.221667
\(134\) 1224.00 0.789086
\(135\) 135.000 0.0860663
\(136\) −368.000 −0.232027
\(137\) −981.000 −0.611770 −0.305885 0.952068i \(-0.598952\pi\)
−0.305885 + 0.952068i \(0.598952\pi\)
\(138\) −36.0000 −0.0222067
\(139\) 553.000 0.337445 0.168722 0.985664i \(-0.446036\pi\)
0.168722 + 0.985664i \(0.446036\pi\)
\(140\) −200.000 −0.120736
\(141\) 105.000 0.0627134
\(142\) 176.000 0.104011
\(143\) 2596.00 1.51810
\(144\) 144.000 0.0833333
\(145\) −35.0000 −0.0200455
\(146\) 1244.00 0.705166
\(147\) 729.000 0.409027
\(148\) 148.000 0.0821995
\(149\) 848.000 0.466247 0.233124 0.972447i \(-0.425105\pi\)
0.233124 + 0.972447i \(0.425105\pi\)
\(150\) −150.000 −0.0816497
\(151\) −203.000 −0.109403 −0.0547017 0.998503i \(-0.517421\pi\)
−0.0547017 + 0.998503i \(0.517421\pi\)
\(152\) −272.000 −0.145145
\(153\) −414.000 −0.218758
\(154\) 880.000 0.460470
\(155\) 910.000 0.471567
\(156\) −708.000 −0.363368
\(157\) 2506.00 1.27389 0.636945 0.770910i \(-0.280198\pi\)
0.636945 + 0.770910i \(0.280198\pi\)
\(158\) 16.0000 0.00805628
\(159\) 1521.00 0.758636
\(160\) −160.000 −0.0790569
\(161\) 60.0000 0.0293706
\(162\) 162.000 0.0785674
\(163\) −916.000 −0.440164 −0.220082 0.975481i \(-0.570632\pi\)
−0.220082 + 0.975481i \(0.570632\pi\)
\(164\) 1440.00 0.685641
\(165\) 660.000 0.311400
\(166\) 2446.00 1.14365
\(167\) −394.000 −0.182567 −0.0912833 0.995825i \(-0.529097\pi\)
−0.0912833 + 0.995825i \(0.529097\pi\)
\(168\) −240.000 −0.110217
\(169\) 1284.00 0.584433
\(170\) 460.000 0.207532
\(171\) −306.000 −0.136844
\(172\) 404.000 0.179097
\(173\) 1639.00 0.720294 0.360147 0.932896i \(-0.382727\pi\)
0.360147 + 0.932896i \(0.382727\pi\)
\(174\) −42.0000 −0.0182989
\(175\) 250.000 0.107990
\(176\) 704.000 0.301511
\(177\) −2463.00 −1.04593
\(178\) 690.000 0.290549
\(179\) 1953.00 0.815498 0.407749 0.913094i \(-0.366314\pi\)
0.407749 + 0.913094i \(0.366314\pi\)
\(180\) −180.000 −0.0745356
\(181\) −4725.00 −1.94037 −0.970184 0.242371i \(-0.922075\pi\)
−0.970184 + 0.242371i \(0.922075\pi\)
\(182\) 1180.00 0.480590
\(183\) −210.000 −0.0848287
\(184\) 48.0000 0.0192316
\(185\) −185.000 −0.0735215
\(186\) 1092.00 0.430480
\(187\) −2024.00 −0.791495
\(188\) −140.000 −0.0543114
\(189\) −270.000 −0.103913
\(190\) 340.000 0.129822
\(191\) −132.000 −0.0500062 −0.0250031 0.999687i \(-0.507960\pi\)
−0.0250031 + 0.999687i \(0.507960\pi\)
\(192\) −192.000 −0.0721688
\(193\) 2919.00 1.08867 0.544337 0.838866i \(-0.316781\pi\)
0.544337 + 0.838866i \(0.316781\pi\)
\(194\) 1740.00 0.643942
\(195\) 885.000 0.325006
\(196\) −972.000 −0.354227
\(197\) −1602.00 −0.579380 −0.289690 0.957121i \(-0.593552\pi\)
−0.289690 + 0.957121i \(0.593552\pi\)
\(198\) 792.000 0.284268
\(199\) 1234.00 0.439578 0.219789 0.975547i \(-0.429463\pi\)
0.219789 + 0.975547i \(0.429463\pi\)
\(200\) 200.000 0.0707107
\(201\) −1836.00 −0.644286
\(202\) 1884.00 0.656227
\(203\) 70.0000 0.0242022
\(204\) 552.000 0.189450
\(205\) −1800.00 −0.613256
\(206\) −906.000 −0.306427
\(207\) 54.0000 0.0181317
\(208\) 944.000 0.314686
\(209\) −1496.00 −0.495122
\(210\) 300.000 0.0985808
\(211\) −3773.00 −1.23101 −0.615507 0.788131i \(-0.711049\pi\)
−0.615507 + 0.788131i \(0.711049\pi\)
\(212\) −2028.00 −0.656998
\(213\) −264.000 −0.0849248
\(214\) 130.000 0.0415262
\(215\) −505.000 −0.160189
\(216\) −216.000 −0.0680414
\(217\) −1820.00 −0.569353
\(218\) 400.000 0.124273
\(219\) −1866.00 −0.575765
\(220\) −880.000 −0.269680
\(221\) −2714.00 −0.826079
\(222\) −222.000 −0.0671156
\(223\) 4688.00 1.40777 0.703883 0.710316i \(-0.251448\pi\)
0.703883 + 0.710316i \(0.251448\pi\)
\(224\) 320.000 0.0954504
\(225\) 225.000 0.0666667
\(226\) 3876.00 1.14083
\(227\) 24.0000 0.00701734 0.00350867 0.999994i \(-0.498883\pi\)
0.00350867 + 0.999994i \(0.498883\pi\)
\(228\) 408.000 0.118511
\(229\) 3935.00 1.13551 0.567756 0.823197i \(-0.307812\pi\)
0.567756 + 0.823197i \(0.307812\pi\)
\(230\) −60.0000 −0.0172012
\(231\) −1320.00 −0.375972
\(232\) 56.0000 0.0158473
\(233\) 1018.00 0.286229 0.143115 0.989706i \(-0.454288\pi\)
0.143115 + 0.989706i \(0.454288\pi\)
\(234\) 1062.00 0.296689
\(235\) 175.000 0.0485776
\(236\) 3284.00 0.905806
\(237\) −24.0000 −0.00657792
\(238\) −920.000 −0.250566
\(239\) 707.000 0.191347 0.0956737 0.995413i \(-0.469499\pi\)
0.0956737 + 0.995413i \(0.469499\pi\)
\(240\) 240.000 0.0645497
\(241\) −314.000 −0.0839275 −0.0419637 0.999119i \(-0.513361\pi\)
−0.0419637 + 0.999119i \(0.513361\pi\)
\(242\) 1210.00 0.321412
\(243\) −243.000 −0.0641500
\(244\) 280.000 0.0734638
\(245\) 1215.00 0.316831
\(246\) −2160.00 −0.559823
\(247\) −2006.00 −0.516756
\(248\) −1456.00 −0.372807
\(249\) −3669.00 −0.933789
\(250\) −250.000 −0.0632456
\(251\) 2943.00 0.740082 0.370041 0.929015i \(-0.379344\pi\)
0.370041 + 0.929015i \(0.379344\pi\)
\(252\) 360.000 0.0899915
\(253\) 264.000 0.0656029
\(254\) −5412.00 −1.33693
\(255\) −690.000 −0.169449
\(256\) 256.000 0.0625000
\(257\) −2616.00 −0.634948 −0.317474 0.948267i \(-0.602835\pi\)
−0.317474 + 0.948267i \(0.602835\pi\)
\(258\) −606.000 −0.146232
\(259\) 370.000 0.0887671
\(260\) −1180.00 −0.281463
\(261\) 63.0000 0.0149410
\(262\) −1976.00 −0.465945
\(263\) −1151.00 −0.269862 −0.134931 0.990855i \(-0.543081\pi\)
−0.134931 + 0.990855i \(0.543081\pi\)
\(264\) −1056.00 −0.246183
\(265\) 2535.00 0.587637
\(266\) −680.000 −0.156742
\(267\) −1035.00 −0.237232
\(268\) 2448.00 0.557968
\(269\) 3018.00 0.684055 0.342027 0.939690i \(-0.388886\pi\)
0.342027 + 0.939690i \(0.388886\pi\)
\(270\) 270.000 0.0608581
\(271\) 4657.00 1.04388 0.521942 0.852981i \(-0.325208\pi\)
0.521942 + 0.852981i \(0.325208\pi\)
\(272\) −736.000 −0.164068
\(273\) −1770.00 −0.392400
\(274\) −1962.00 −0.432587
\(275\) 1100.00 0.241209
\(276\) −72.0000 −0.0157025
\(277\) 4474.00 0.970457 0.485229 0.874387i \(-0.338736\pi\)
0.485229 + 0.874387i \(0.338736\pi\)
\(278\) 1106.00 0.238610
\(279\) −1638.00 −0.351486
\(280\) −400.000 −0.0853735
\(281\) −4035.00 −0.856612 −0.428306 0.903634i \(-0.640889\pi\)
−0.428306 + 0.903634i \(0.640889\pi\)
\(282\) 210.000 0.0443451
\(283\) 2876.00 0.604101 0.302050 0.953292i \(-0.402329\pi\)
0.302050 + 0.953292i \(0.402329\pi\)
\(284\) 352.000 0.0735470
\(285\) −510.000 −0.105999
\(286\) 5192.00 1.07346
\(287\) 3600.00 0.740423
\(288\) 288.000 0.0589256
\(289\) −2797.00 −0.569306
\(290\) −70.0000 −0.0141743
\(291\) −2610.00 −0.525776
\(292\) 2488.00 0.498627
\(293\) −142.000 −0.0283131 −0.0141565 0.999900i \(-0.504506\pi\)
−0.0141565 + 0.999900i \(0.504506\pi\)
\(294\) 1458.00 0.289225
\(295\) −4105.00 −0.810177
\(296\) 296.000 0.0581238
\(297\) −1188.00 −0.232104
\(298\) 1696.00 0.329687
\(299\) 354.000 0.0684694
\(300\) −300.000 −0.0577350
\(301\) 1010.00 0.193407
\(302\) −406.000 −0.0773599
\(303\) −2826.00 −0.535807
\(304\) −544.000 −0.102633
\(305\) −350.000 −0.0657080
\(306\) −828.000 −0.154685
\(307\) −4356.00 −0.809805 −0.404902 0.914360i \(-0.632694\pi\)
−0.404902 + 0.914360i \(0.632694\pi\)
\(308\) 1760.00 0.325602
\(309\) 1359.00 0.250197
\(310\) 1820.00 0.333449
\(311\) 4405.00 0.803166 0.401583 0.915823i \(-0.368460\pi\)
0.401583 + 0.915823i \(0.368460\pi\)
\(312\) −1416.00 −0.256940
\(313\) −169.000 −0.0305190 −0.0152595 0.999884i \(-0.504857\pi\)
−0.0152595 + 0.999884i \(0.504857\pi\)
\(314\) 5012.00 0.900776
\(315\) −450.000 −0.0804909
\(316\) 32.0000 0.00569665
\(317\) −7071.00 −1.25283 −0.626415 0.779490i \(-0.715478\pi\)
−0.626415 + 0.779490i \(0.715478\pi\)
\(318\) 3042.00 0.536437
\(319\) 308.000 0.0540586
\(320\) −320.000 −0.0559017
\(321\) −195.000 −0.0339060
\(322\) 120.000 0.0207681
\(323\) 1564.00 0.269422
\(324\) 324.000 0.0555556
\(325\) 1475.00 0.251749
\(326\) −1832.00 −0.311243
\(327\) −600.000 −0.101468
\(328\) 2880.00 0.484821
\(329\) −350.000 −0.0586508
\(330\) 1320.00 0.220193
\(331\) −6136.00 −1.01893 −0.509464 0.860492i \(-0.670156\pi\)
−0.509464 + 0.860492i \(0.670156\pi\)
\(332\) 4892.00 0.808685
\(333\) 333.000 0.0547997
\(334\) −788.000 −0.129094
\(335\) −3060.00 −0.499062
\(336\) −480.000 −0.0779350
\(337\) 2564.00 0.414451 0.207225 0.978293i \(-0.433557\pi\)
0.207225 + 0.978293i \(0.433557\pi\)
\(338\) 2568.00 0.413257
\(339\) −5814.00 −0.931484
\(340\) 920.000 0.146747
\(341\) −8008.00 −1.27172
\(342\) −612.000 −0.0967637
\(343\) −5860.00 −0.922479
\(344\) 808.000 0.126641
\(345\) 90.0000 0.0140447
\(346\) 3278.00 0.509325
\(347\) 9084.00 1.40534 0.702672 0.711513i \(-0.251990\pi\)
0.702672 + 0.711513i \(0.251990\pi\)
\(348\) −84.0000 −0.0129393
\(349\) −2149.00 −0.329608 −0.164804 0.986326i \(-0.552699\pi\)
−0.164804 + 0.986326i \(0.552699\pi\)
\(350\) 500.000 0.0763604
\(351\) −1593.00 −0.242245
\(352\) 1408.00 0.213201
\(353\) −204.000 −0.0307587 −0.0153794 0.999882i \(-0.504896\pi\)
−0.0153794 + 0.999882i \(0.504896\pi\)
\(354\) −4926.00 −0.739587
\(355\) −440.000 −0.0657825
\(356\) 1380.00 0.205449
\(357\) 1380.00 0.204586
\(358\) 3906.00 0.576644
\(359\) −6792.00 −0.998518 −0.499259 0.866453i \(-0.666394\pi\)
−0.499259 + 0.866453i \(0.666394\pi\)
\(360\) −360.000 −0.0527046
\(361\) −5703.00 −0.831462
\(362\) −9450.00 −1.37205
\(363\) −1815.00 −0.262432
\(364\) 2360.00 0.339829
\(365\) −3110.00 −0.445986
\(366\) −420.000 −0.0599829
\(367\) 3076.00 0.437509 0.218755 0.975780i \(-0.429801\pi\)
0.218755 + 0.975780i \(0.429801\pi\)
\(368\) 96.0000 0.0135988
\(369\) 3240.00 0.457094
\(370\) −370.000 −0.0519875
\(371\) −5070.00 −0.709491
\(372\) 2184.00 0.304395
\(373\) −1394.00 −0.193508 −0.0967541 0.995308i \(-0.530846\pi\)
−0.0967541 + 0.995308i \(0.530846\pi\)
\(374\) −4048.00 −0.559671
\(375\) 375.000 0.0516398
\(376\) −280.000 −0.0384040
\(377\) 413.000 0.0564206
\(378\) −540.000 −0.0734778
\(379\) −11735.0 −1.59047 −0.795233 0.606304i \(-0.792651\pi\)
−0.795233 + 0.606304i \(0.792651\pi\)
\(380\) 680.000 0.0917981
\(381\) 8118.00 1.09160
\(382\) −264.000 −0.0353597
\(383\) 6028.00 0.804220 0.402110 0.915591i \(-0.368277\pi\)
0.402110 + 0.915591i \(0.368277\pi\)
\(384\) −384.000 −0.0510310
\(385\) −2200.00 −0.291227
\(386\) 5838.00 0.769809
\(387\) 909.000 0.119398
\(388\) 3480.00 0.455336
\(389\) −2985.00 −0.389063 −0.194532 0.980896i \(-0.562319\pi\)
−0.194532 + 0.980896i \(0.562319\pi\)
\(390\) 1770.00 0.229814
\(391\) −276.000 −0.0356980
\(392\) −1944.00 −0.250477
\(393\) 2964.00 0.380443
\(394\) −3204.00 −0.409683
\(395\) −40.0000 −0.00509524
\(396\) 1584.00 0.201008
\(397\) −5562.00 −0.703146 −0.351573 0.936161i \(-0.614353\pi\)
−0.351573 + 0.936161i \(0.614353\pi\)
\(398\) 2468.00 0.310828
\(399\) 1020.00 0.127980
\(400\) 400.000 0.0500000
\(401\) −11631.0 −1.44844 −0.724220 0.689569i \(-0.757800\pi\)
−0.724220 + 0.689569i \(0.757800\pi\)
\(402\) −3672.00 −0.455579
\(403\) −10738.0 −1.32729
\(404\) 3768.00 0.464022
\(405\) −405.000 −0.0496904
\(406\) 140.000 0.0171135
\(407\) 1628.00 0.198273
\(408\) 1104.00 0.133961
\(409\) 4490.00 0.542827 0.271413 0.962463i \(-0.412509\pi\)
0.271413 + 0.962463i \(0.412509\pi\)
\(410\) −3600.00 −0.433637
\(411\) 2943.00 0.353206
\(412\) −1812.00 −0.216677
\(413\) 8210.00 0.978178
\(414\) 108.000 0.0128210
\(415\) −6115.00 −0.723310
\(416\) 1888.00 0.222516
\(417\) −1659.00 −0.194824
\(418\) −2992.00 −0.350104
\(419\) −5196.00 −0.605826 −0.302913 0.953018i \(-0.597959\pi\)
−0.302913 + 0.953018i \(0.597959\pi\)
\(420\) 600.000 0.0697071
\(421\) −5582.00 −0.646200 −0.323100 0.946365i \(-0.604725\pi\)
−0.323100 + 0.946365i \(0.604725\pi\)
\(422\) −7546.00 −0.870459
\(423\) −315.000 −0.0362076
\(424\) −4056.00 −0.464568
\(425\) −1150.00 −0.131255
\(426\) −528.000 −0.0600509
\(427\) 700.000 0.0793334
\(428\) 260.000 0.0293635
\(429\) −7788.00 −0.876476
\(430\) −1010.00 −0.113271
\(431\) 7204.00 0.805115 0.402557 0.915395i \(-0.368121\pi\)
0.402557 + 0.915395i \(0.368121\pi\)
\(432\) −432.000 −0.0481125
\(433\) −16524.0 −1.83393 −0.916966 0.398965i \(-0.869370\pi\)
−0.916966 + 0.398965i \(0.869370\pi\)
\(434\) −3640.00 −0.402594
\(435\) 105.000 0.0115733
\(436\) 800.000 0.0878740
\(437\) −204.000 −0.0223310
\(438\) −3732.00 −0.407128
\(439\) −6230.00 −0.677316 −0.338658 0.940910i \(-0.609973\pi\)
−0.338658 + 0.940910i \(0.609973\pi\)
\(440\) −1760.00 −0.190693
\(441\) −2187.00 −0.236152
\(442\) −5428.00 −0.584126
\(443\) 13809.0 1.48101 0.740503 0.672053i \(-0.234587\pi\)
0.740503 + 0.672053i \(0.234587\pi\)
\(444\) −444.000 −0.0474579
\(445\) −1725.00 −0.183759
\(446\) 9376.00 0.995441
\(447\) −2544.00 −0.269188
\(448\) 640.000 0.0674937
\(449\) 402.000 0.0422529 0.0211265 0.999777i \(-0.493275\pi\)
0.0211265 + 0.999777i \(0.493275\pi\)
\(450\) 450.000 0.0471405
\(451\) 15840.0 1.65383
\(452\) 7752.00 0.806689
\(453\) 609.000 0.0631641
\(454\) 48.0000 0.00496201
\(455\) −2950.00 −0.303952
\(456\) 816.000 0.0837998
\(457\) −15569.0 −1.59363 −0.796813 0.604226i \(-0.793482\pi\)
−0.796813 + 0.604226i \(0.793482\pi\)
\(458\) 7870.00 0.802928
\(459\) 1242.00 0.126300
\(460\) −120.000 −0.0121631
\(461\) −14285.0 −1.44321 −0.721604 0.692306i \(-0.756595\pi\)
−0.721604 + 0.692306i \(0.756595\pi\)
\(462\) −2640.00 −0.265853
\(463\) 14673.0 1.47281 0.736406 0.676540i \(-0.236521\pi\)
0.736406 + 0.676540i \(0.236521\pi\)
\(464\) 112.000 0.0112058
\(465\) −2730.00 −0.272260
\(466\) 2036.00 0.202395
\(467\) 8126.00 0.805196 0.402598 0.915377i \(-0.368107\pi\)
0.402598 + 0.915377i \(0.368107\pi\)
\(468\) 2124.00 0.209790
\(469\) 6120.00 0.602549
\(470\) 350.000 0.0343496
\(471\) −7518.00 −0.735480
\(472\) 6568.00 0.640501
\(473\) 4444.00 0.431999
\(474\) −48.0000 −0.00465129
\(475\) −850.000 −0.0821067
\(476\) −1840.00 −0.177177
\(477\) −4563.00 −0.437999
\(478\) 1414.00 0.135303
\(479\) −6019.00 −0.574144 −0.287072 0.957909i \(-0.592682\pi\)
−0.287072 + 0.957909i \(0.592682\pi\)
\(480\) 480.000 0.0456435
\(481\) 2183.00 0.206936
\(482\) −628.000 −0.0593457
\(483\) −180.000 −0.0169571
\(484\) 2420.00 0.227273
\(485\) −4350.00 −0.407265
\(486\) −486.000 −0.0453609
\(487\) 1425.00 0.132593 0.0662966 0.997800i \(-0.478882\pi\)
0.0662966 + 0.997800i \(0.478882\pi\)
\(488\) 560.000 0.0519467
\(489\) 2748.00 0.254129
\(490\) 2430.00 0.224033
\(491\) 16654.0 1.53072 0.765361 0.643601i \(-0.222560\pi\)
0.765361 + 0.643601i \(0.222560\pi\)
\(492\) −4320.00 −0.395855
\(493\) −322.000 −0.0294161
\(494\) −4012.00 −0.365402
\(495\) −1980.00 −0.179787
\(496\) −2912.00 −0.263614
\(497\) 880.000 0.0794233
\(498\) −7338.00 −0.660288
\(499\) −14954.0 −1.34155 −0.670775 0.741661i \(-0.734038\pi\)
−0.670775 + 0.741661i \(0.734038\pi\)
\(500\) −500.000 −0.0447214
\(501\) 1182.00 0.105405
\(502\) 5886.00 0.523317
\(503\) 7422.00 0.657914 0.328957 0.944345i \(-0.393303\pi\)
0.328957 + 0.944345i \(0.393303\pi\)
\(504\) 720.000 0.0636336
\(505\) −4710.00 −0.415034
\(506\) 528.000 0.0463883
\(507\) −3852.00 −0.337423
\(508\) −10824.0 −0.945349
\(509\) 5916.00 0.515171 0.257586 0.966255i \(-0.417073\pi\)
0.257586 + 0.966255i \(0.417073\pi\)
\(510\) −1380.00 −0.119818
\(511\) 6220.00 0.538467
\(512\) 512.000 0.0441942
\(513\) 918.000 0.0790072
\(514\) −5232.00 −0.448976
\(515\) 2265.00 0.193802
\(516\) −1212.00 −0.103402
\(517\) −1540.00 −0.131004
\(518\) 740.000 0.0627678
\(519\) −4917.00 −0.415862
\(520\) −2360.00 −0.199025
\(521\) −1266.00 −0.106458 −0.0532289 0.998582i \(-0.516951\pi\)
−0.0532289 + 0.998582i \(0.516951\pi\)
\(522\) 126.000 0.0105649
\(523\) 14900.0 1.24576 0.622879 0.782318i \(-0.285963\pi\)
0.622879 + 0.782318i \(0.285963\pi\)
\(524\) −3952.00 −0.329473
\(525\) −750.000 −0.0623480
\(526\) −2302.00 −0.190821
\(527\) 8372.00 0.692011
\(528\) −2112.00 −0.174078
\(529\) −12131.0 −0.997041
\(530\) 5070.00 0.415522
\(531\) 7389.00 0.603871
\(532\) −1360.00 −0.110834
\(533\) 21240.0 1.72609
\(534\) −2070.00 −0.167748
\(535\) −325.000 −0.0262635
\(536\) 4896.00 0.394543
\(537\) −5859.00 −0.470828
\(538\) 6036.00 0.483700
\(539\) −10692.0 −0.854429
\(540\) 540.000 0.0430331
\(541\) 1958.00 0.155603 0.0778013 0.996969i \(-0.475210\pi\)
0.0778013 + 0.996969i \(0.475210\pi\)
\(542\) 9314.00 0.738138
\(543\) 14175.0 1.12027
\(544\) −1472.00 −0.116014
\(545\) −1000.00 −0.0785969
\(546\) −3540.00 −0.277469
\(547\) −8225.00 −0.642917 −0.321459 0.946924i \(-0.604173\pi\)
−0.321459 + 0.946924i \(0.604173\pi\)
\(548\) −3924.00 −0.305885
\(549\) 630.000 0.0489759
\(550\) 2200.00 0.170561
\(551\) −238.000 −0.0184013
\(552\) −144.000 −0.0111033
\(553\) 80.0000 0.00615180
\(554\) 8948.00 0.686217
\(555\) 555.000 0.0424476
\(556\) 2212.00 0.168722
\(557\) −1196.00 −0.0909805 −0.0454903 0.998965i \(-0.514485\pi\)
−0.0454903 + 0.998965i \(0.514485\pi\)
\(558\) −3276.00 −0.248538
\(559\) 5959.00 0.450874
\(560\) −800.000 −0.0603682
\(561\) 6072.00 0.456970
\(562\) −8070.00 −0.605716
\(563\) 5084.00 0.380577 0.190289 0.981728i \(-0.439058\pi\)
0.190289 + 0.981728i \(0.439058\pi\)
\(564\) 420.000 0.0313567
\(565\) −9690.00 −0.721525
\(566\) 5752.00 0.427164
\(567\) 810.000 0.0599944
\(568\) 704.000 0.0520056
\(569\) 13622.0 1.00363 0.501814 0.864976i \(-0.332666\pi\)
0.501814 + 0.864976i \(0.332666\pi\)
\(570\) −1020.00 −0.0749528
\(571\) −2428.00 −0.177949 −0.0889743 0.996034i \(-0.528359\pi\)
−0.0889743 + 0.996034i \(0.528359\pi\)
\(572\) 10384.0 0.759050
\(573\) 396.000 0.0288711
\(574\) 7200.00 0.523558
\(575\) 150.000 0.0108790
\(576\) 576.000 0.0416667
\(577\) −23746.0 −1.71327 −0.856637 0.515920i \(-0.827450\pi\)
−0.856637 + 0.515920i \(0.827450\pi\)
\(578\) −5594.00 −0.402560
\(579\) −8757.00 −0.628547
\(580\) −140.000 −0.0100227
\(581\) 12230.0 0.873298
\(582\) −5220.00 −0.371780
\(583\) −22308.0 −1.58474
\(584\) 4976.00 0.352583
\(585\) −2655.00 −0.187642
\(586\) −284.000 −0.0200204
\(587\) −8146.00 −0.572779 −0.286390 0.958113i \(-0.592455\pi\)
−0.286390 + 0.958113i \(0.592455\pi\)
\(588\) 2916.00 0.204513
\(589\) 6188.00 0.432890
\(590\) −8210.00 −0.572882
\(591\) 4806.00 0.334505
\(592\) 592.000 0.0410997
\(593\) 23365.0 1.61802 0.809010 0.587795i \(-0.200004\pi\)
0.809010 + 0.587795i \(0.200004\pi\)
\(594\) −2376.00 −0.164122
\(595\) 2300.00 0.158472
\(596\) 3392.00 0.233124
\(597\) −3702.00 −0.253790
\(598\) 708.000 0.0484152
\(599\) 7996.00 0.545422 0.272711 0.962096i \(-0.412080\pi\)
0.272711 + 0.962096i \(0.412080\pi\)
\(600\) −600.000 −0.0408248
\(601\) −779.000 −0.0528720 −0.0264360 0.999651i \(-0.508416\pi\)
−0.0264360 + 0.999651i \(0.508416\pi\)
\(602\) 2020.00 0.136759
\(603\) 5508.00 0.371979
\(604\) −812.000 −0.0547017
\(605\) −3025.00 −0.203279
\(606\) −5652.00 −0.378873
\(607\) 5624.00 0.376064 0.188032 0.982163i \(-0.439789\pi\)
0.188032 + 0.982163i \(0.439789\pi\)
\(608\) −1088.00 −0.0725727
\(609\) −210.000 −0.0139731
\(610\) −700.000 −0.0464626
\(611\) −2065.00 −0.136728
\(612\) −1656.00 −0.109379
\(613\) −26718.0 −1.76041 −0.880204 0.474596i \(-0.842594\pi\)
−0.880204 + 0.474596i \(0.842594\pi\)
\(614\) −8712.00 −0.572618
\(615\) 5400.00 0.354063
\(616\) 3520.00 0.230235
\(617\) −6070.00 −0.396060 −0.198030 0.980196i \(-0.563454\pi\)
−0.198030 + 0.980196i \(0.563454\pi\)
\(618\) 2718.00 0.176916
\(619\) 5004.00 0.324924 0.162462 0.986715i \(-0.448057\pi\)
0.162462 + 0.986715i \(0.448057\pi\)
\(620\) 3640.00 0.235784
\(621\) −162.000 −0.0104683
\(622\) 8810.00 0.567924
\(623\) 3450.00 0.221864
\(624\) −2832.00 −0.181684
\(625\) 625.000 0.0400000
\(626\) −338.000 −0.0215802
\(627\) 4488.00 0.285859
\(628\) 10024.0 0.636945
\(629\) −1702.00 −0.107891
\(630\) −900.000 −0.0569156
\(631\) −6786.00 −0.428124 −0.214062 0.976820i \(-0.568669\pi\)
−0.214062 + 0.976820i \(0.568669\pi\)
\(632\) 64.0000 0.00402814
\(633\) 11319.0 0.710726
\(634\) −14142.0 −0.885884
\(635\) 13530.0 0.845546
\(636\) 6084.00 0.379318
\(637\) −14337.0 −0.891762
\(638\) 616.000 0.0382252
\(639\) 792.000 0.0490314
\(640\) −640.000 −0.0395285
\(641\) −6508.00 −0.401015 −0.200507 0.979692i \(-0.564259\pi\)
−0.200507 + 0.979692i \(0.564259\pi\)
\(642\) −390.000 −0.0239752
\(643\) 16751.0 1.02736 0.513682 0.857981i \(-0.328281\pi\)
0.513682 + 0.857981i \(0.328281\pi\)
\(644\) 240.000 0.0146853
\(645\) 1515.00 0.0924854
\(646\) 3128.00 0.190510
\(647\) −10250.0 −0.622827 −0.311414 0.950275i \(-0.600802\pi\)
−0.311414 + 0.950275i \(0.600802\pi\)
\(648\) 648.000 0.0392837
\(649\) 36124.0 2.18489
\(650\) 2950.00 0.178013
\(651\) 5460.00 0.328716
\(652\) −3664.00 −0.220082
\(653\) −28994.0 −1.73755 −0.868777 0.495203i \(-0.835094\pi\)
−0.868777 + 0.495203i \(0.835094\pi\)
\(654\) −1200.00 −0.0717488
\(655\) 4940.00 0.294690
\(656\) 5760.00 0.342820
\(657\) 5598.00 0.332418
\(658\) −700.000 −0.0414724
\(659\) −7314.00 −0.432341 −0.216171 0.976356i \(-0.569357\pi\)
−0.216171 + 0.976356i \(0.569357\pi\)
\(660\) 2640.00 0.155700
\(661\) −26192.0 −1.54123 −0.770613 0.637303i \(-0.780050\pi\)
−0.770613 + 0.637303i \(0.780050\pi\)
\(662\) −12272.0 −0.720491
\(663\) 8142.00 0.476937
\(664\) 9784.00 0.571827
\(665\) 1700.00 0.0991326
\(666\) 666.000 0.0387492
\(667\) 42.0000 0.00243815
\(668\) −1576.00 −0.0912833
\(669\) −14064.0 −0.812774
\(670\) −6120.00 −0.352890
\(671\) 3080.00 0.177201
\(672\) −960.000 −0.0551083
\(673\) 17552.0 1.00532 0.502660 0.864484i \(-0.332355\pi\)
0.502660 + 0.864484i \(0.332355\pi\)
\(674\) 5128.00 0.293061
\(675\) −675.000 −0.0384900
\(676\) 5136.00 0.292217
\(677\) 257.000 0.0145898 0.00729491 0.999973i \(-0.497678\pi\)
0.00729491 + 0.999973i \(0.497678\pi\)
\(678\) −11628.0 −0.658659
\(679\) 8700.00 0.491716
\(680\) 1840.00 0.103766
\(681\) −72.0000 −0.00405146
\(682\) −16016.0 −0.899244
\(683\) 11460.0 0.642027 0.321014 0.947075i \(-0.395976\pi\)
0.321014 + 0.947075i \(0.395976\pi\)
\(684\) −1224.00 −0.0684222
\(685\) 4905.00 0.273592
\(686\) −11720.0 −0.652291
\(687\) −11805.0 −0.655588
\(688\) 1616.00 0.0895486
\(689\) −29913.0 −1.65398
\(690\) 180.000 0.00993113
\(691\) −5953.00 −0.327732 −0.163866 0.986483i \(-0.552396\pi\)
−0.163866 + 0.986483i \(0.552396\pi\)
\(692\) 6556.00 0.360147
\(693\) 3960.00 0.217068
\(694\) 18168.0 0.993729
\(695\) −2765.00 −0.150910
\(696\) −168.000 −0.00914946
\(697\) −16560.0 −0.899935
\(698\) −4298.00 −0.233068
\(699\) −3054.00 −0.165254
\(700\) 1000.00 0.0539949
\(701\) 7509.00 0.404581 0.202290 0.979326i \(-0.435162\pi\)
0.202290 + 0.979326i \(0.435162\pi\)
\(702\) −3186.00 −0.171293
\(703\) −1258.00 −0.0674913
\(704\) 2816.00 0.150756
\(705\) −525.000 −0.0280463
\(706\) −408.000 −0.0217497
\(707\) 9420.00 0.501097
\(708\) −9852.00 −0.522967
\(709\) −22952.0 −1.21577 −0.607885 0.794025i \(-0.707982\pi\)
−0.607885 + 0.794025i \(0.707982\pi\)
\(710\) −880.000 −0.0465152
\(711\) 72.0000 0.00379777
\(712\) 2760.00 0.145274
\(713\) −1092.00 −0.0573573
\(714\) 2760.00 0.144664
\(715\) −12980.0 −0.678915
\(716\) 7812.00 0.407749
\(717\) −2121.00 −0.110474
\(718\) −13584.0 −0.706059
\(719\) −16666.0 −0.864446 −0.432223 0.901767i \(-0.642271\pi\)
−0.432223 + 0.901767i \(0.642271\pi\)
\(720\) −720.000 −0.0372678
\(721\) −4530.00 −0.233989
\(722\) −11406.0 −0.587933
\(723\) 942.000 0.0484555
\(724\) −18900.0 −0.970184
\(725\) 175.000 0.00896460
\(726\) −3630.00 −0.185567
\(727\) −11724.0 −0.598101 −0.299050 0.954237i \(-0.596670\pi\)
−0.299050 + 0.954237i \(0.596670\pi\)
\(728\) 4720.00 0.240295
\(729\) 729.000 0.0370370
\(730\) −6220.00 −0.315360
\(731\) −4646.00 −0.235073
\(732\) −840.000 −0.0424143
\(733\) −26992.0 −1.36013 −0.680063 0.733154i \(-0.738048\pi\)
−0.680063 + 0.733154i \(0.738048\pi\)
\(734\) 6152.00 0.309366
\(735\) −3645.00 −0.182922
\(736\) 192.000 0.00961578
\(737\) 26928.0 1.34587
\(738\) 6480.00 0.323214
\(739\) −8483.00 −0.422263 −0.211131 0.977458i \(-0.567715\pi\)
−0.211131 + 0.977458i \(0.567715\pi\)
\(740\) −740.000 −0.0367607
\(741\) 6018.00 0.298349
\(742\) −10140.0 −0.501686
\(743\) −21636.0 −1.06830 −0.534151 0.845389i \(-0.679368\pi\)
−0.534151 + 0.845389i \(0.679368\pi\)
\(744\) 4368.00 0.215240
\(745\) −4240.00 −0.208512
\(746\) −2788.00 −0.136831
\(747\) 11007.0 0.539123
\(748\) −8096.00 −0.395747
\(749\) 650.000 0.0317096
\(750\) 750.000 0.0365148
\(751\) 36564.0 1.77662 0.888308 0.459247i \(-0.151881\pi\)
0.888308 + 0.459247i \(0.151881\pi\)
\(752\) −560.000 −0.0271557
\(753\) −8829.00 −0.427286
\(754\) 826.000 0.0398954
\(755\) 1015.00 0.0489267
\(756\) −1080.00 −0.0519566
\(757\) 13539.0 0.650044 0.325022 0.945706i \(-0.394628\pi\)
0.325022 + 0.945706i \(0.394628\pi\)
\(758\) −23470.0 −1.12463
\(759\) −792.000 −0.0378759
\(760\) 1360.00 0.0649110
\(761\) −15460.0 −0.736432 −0.368216 0.929740i \(-0.620031\pi\)
−0.368216 + 0.929740i \(0.620031\pi\)
\(762\) 16236.0 0.771874
\(763\) 2000.00 0.0948950
\(764\) −528.000 −0.0250031
\(765\) 2070.00 0.0978314
\(766\) 12056.0 0.568670
\(767\) 48439.0 2.28035
\(768\) −768.000 −0.0360844
\(769\) −12532.0 −0.587666 −0.293833 0.955857i \(-0.594931\pi\)
−0.293833 + 0.955857i \(0.594931\pi\)
\(770\) −4400.00 −0.205929
\(771\) 7848.00 0.366587
\(772\) 11676.0 0.544337
\(773\) −6678.00 −0.310726 −0.155363 0.987857i \(-0.549655\pi\)
−0.155363 + 0.987857i \(0.549655\pi\)
\(774\) 1818.00 0.0844272
\(775\) −4550.00 −0.210891
\(776\) 6960.00 0.321971
\(777\) −1110.00 −0.0512497
\(778\) −5970.00 −0.275109
\(779\) −12240.0 −0.562957
\(780\) 3540.00 0.162503
\(781\) 3872.00 0.177402
\(782\) −552.000 −0.0252423
\(783\) −189.000 −0.00862619
\(784\) −3888.00 −0.177114
\(785\) −12530.0 −0.569700
\(786\) 5928.00 0.269014
\(787\) −18188.0 −0.823802 −0.411901 0.911229i \(-0.635135\pi\)
−0.411901 + 0.911229i \(0.635135\pi\)
\(788\) −6408.00 −0.289690
\(789\) 3453.00 0.155805
\(790\) −80.0000 −0.00360288
\(791\) 19380.0 0.871142
\(792\) 3168.00 0.142134
\(793\) 4130.00 0.184944
\(794\) −11124.0 −0.497199
\(795\) −7605.00 −0.339272
\(796\) 4936.00 0.219789
\(797\) 5322.00 0.236531 0.118265 0.992982i \(-0.462267\pi\)
0.118265 + 0.992982i \(0.462267\pi\)
\(798\) 2040.00 0.0904953
\(799\) 1610.00 0.0712862
\(800\) 800.000 0.0353553
\(801\) 3105.00 0.136966
\(802\) −23262.0 −1.02420
\(803\) 27368.0 1.20273
\(804\) −7344.00 −0.322143
\(805\) −300.000 −0.0131349
\(806\) −21476.0 −0.938536
\(807\) −9054.00 −0.394939
\(808\) 7536.00 0.328113
\(809\) 6239.00 0.271139 0.135570 0.990768i \(-0.456714\pi\)
0.135570 + 0.990768i \(0.456714\pi\)
\(810\) −810.000 −0.0351364
\(811\) −26476.0 −1.14636 −0.573180 0.819429i \(-0.694290\pi\)
−0.573180 + 0.819429i \(0.694290\pi\)
\(812\) 280.000 0.0121011
\(813\) −13971.0 −0.602687
\(814\) 3256.00 0.140200
\(815\) 4580.00 0.196847
\(816\) 2208.00 0.0947248
\(817\) −3434.00 −0.147051
\(818\) 8980.00 0.383837
\(819\) 5310.00 0.226552
\(820\) −7200.00 −0.306628
\(821\) 24980.0 1.06189 0.530943 0.847408i \(-0.321838\pi\)
0.530943 + 0.847408i \(0.321838\pi\)
\(822\) 5886.00 0.249754
\(823\) −26162.0 −1.10808 −0.554040 0.832490i \(-0.686915\pi\)
−0.554040 + 0.832490i \(0.686915\pi\)
\(824\) −3624.00 −0.153214
\(825\) −3300.00 −0.139262
\(826\) 16420.0 0.691677
\(827\) 32878.0 1.38244 0.691221 0.722643i \(-0.257073\pi\)
0.691221 + 0.722643i \(0.257073\pi\)
\(828\) 216.000 0.00906584
\(829\) −19038.0 −0.797608 −0.398804 0.917036i \(-0.630575\pi\)
−0.398804 + 0.917036i \(0.630575\pi\)
\(830\) −12230.0 −0.511457
\(831\) −13422.0 −0.560294
\(832\) 3776.00 0.157343
\(833\) 11178.0 0.464940
\(834\) −3318.00 −0.137761
\(835\) 1970.00 0.0816463
\(836\) −5984.00 −0.247561
\(837\) 4914.00 0.202930
\(838\) −10392.0 −0.428384
\(839\) −7836.00 −0.322442 −0.161221 0.986918i \(-0.551543\pi\)
−0.161221 + 0.986918i \(0.551543\pi\)
\(840\) 1200.00 0.0492904
\(841\) −24340.0 −0.997991
\(842\) −11164.0 −0.456932
\(843\) 12105.0 0.494565
\(844\) −15092.0 −0.615507
\(845\) −6420.00 −0.261367
\(846\) −630.000 −0.0256027
\(847\) 6050.00 0.245431
\(848\) −8112.00 −0.328499
\(849\) −8628.00 −0.348778
\(850\) −2300.00 −0.0928110
\(851\) 222.000 0.00894249
\(852\) −1056.00 −0.0424624
\(853\) 15517.0 0.622851 0.311426 0.950271i \(-0.399194\pi\)
0.311426 + 0.950271i \(0.399194\pi\)
\(854\) 1400.00 0.0560972
\(855\) 1530.00 0.0611987
\(856\) 520.000 0.0207631
\(857\) 36368.0 1.44960 0.724800 0.688959i \(-0.241932\pi\)
0.724800 + 0.688959i \(0.241932\pi\)
\(858\) −15576.0 −0.619762
\(859\) −8824.00 −0.350490 −0.175245 0.984525i \(-0.556072\pi\)
−0.175245 + 0.984525i \(0.556072\pi\)
\(860\) −2020.00 −0.0800947
\(861\) −10800.0 −0.427483
\(862\) 14408.0 0.569302
\(863\) 49655.0 1.95860 0.979302 0.202403i \(-0.0648750\pi\)
0.979302 + 0.202403i \(0.0648750\pi\)
\(864\) −864.000 −0.0340207
\(865\) −8195.00 −0.322125
\(866\) −33048.0 −1.29679
\(867\) 8391.00 0.328689
\(868\) −7280.00 −0.284677
\(869\) 352.000 0.0137408
\(870\) 210.000 0.00818353
\(871\) 36108.0 1.40468
\(872\) 1600.00 0.0621363
\(873\) 7830.00 0.303557
\(874\) −408.000 −0.0157904
\(875\) −1250.00 −0.0482945
\(876\) −7464.00 −0.287883
\(877\) −48566.0 −1.86996 −0.934981 0.354697i \(-0.884584\pi\)
−0.934981 + 0.354697i \(0.884584\pi\)
\(878\) −12460.0 −0.478935
\(879\) 426.000 0.0163466
\(880\) −3520.00 −0.134840
\(881\) −22100.0 −0.845140 −0.422570 0.906330i \(-0.638872\pi\)
−0.422570 + 0.906330i \(0.638872\pi\)
\(882\) −4374.00 −0.166984
\(883\) 47420.0 1.80726 0.903630 0.428315i \(-0.140892\pi\)
0.903630 + 0.428315i \(0.140892\pi\)
\(884\) −10856.0 −0.413039
\(885\) 12315.0 0.467756
\(886\) 27618.0 1.04723
\(887\) −29588.0 −1.12003 −0.560016 0.828482i \(-0.689205\pi\)
−0.560016 + 0.828482i \(0.689205\pi\)
\(888\) −888.000 −0.0335578
\(889\) −27060.0 −1.02088
\(890\) −3450.00 −0.129937
\(891\) 3564.00 0.134005
\(892\) 18752.0 0.703883
\(893\) 1190.00 0.0445933
\(894\) −5088.00 −0.190345
\(895\) −9765.00 −0.364702
\(896\) 1280.00 0.0477252
\(897\) −1062.00 −0.0395308
\(898\) 804.000 0.0298773
\(899\) −1274.00 −0.0472639
\(900\) 900.000 0.0333333
\(901\) 23322.0 0.862340
\(902\) 31680.0 1.16943
\(903\) −3030.00 −0.111663
\(904\) 15504.0 0.570415
\(905\) 23625.0 0.867759
\(906\) 1218.00 0.0446637
\(907\) −7607.00 −0.278485 −0.139243 0.990258i \(-0.544467\pi\)
−0.139243 + 0.990258i \(0.544467\pi\)
\(908\) 96.0000 0.00350867
\(909\) 8478.00 0.309348
\(910\) −5900.00 −0.214926
\(911\) 27085.0 0.985034 0.492517 0.870303i \(-0.336077\pi\)
0.492517 + 0.870303i \(0.336077\pi\)
\(912\) 1632.00 0.0592554
\(913\) 53812.0 1.95062
\(914\) −31138.0 −1.12686
\(915\) 1050.00 0.0379365
\(916\) 15740.0 0.567756
\(917\) −9880.00 −0.355798
\(918\) 2484.00 0.0893074
\(919\) −10830.0 −0.388736 −0.194368 0.980929i \(-0.562266\pi\)
−0.194368 + 0.980929i \(0.562266\pi\)
\(920\) −240.000 −0.00860061
\(921\) 13068.0 0.467541
\(922\) −28570.0 −1.02050
\(923\) 5192.00 0.185154
\(924\) −5280.00 −0.187986
\(925\) 925.000 0.0328798
\(926\) 29346.0 1.04144
\(927\) −4077.00 −0.144451
\(928\) 224.000 0.00792366
\(929\) 33994.0 1.20055 0.600273 0.799795i \(-0.295059\pi\)
0.600273 + 0.799795i \(0.295059\pi\)
\(930\) −5460.00 −0.192517
\(931\) 8262.00 0.290844
\(932\) 4072.00 0.143115
\(933\) −13215.0 −0.463708
\(934\) 16252.0 0.569359
\(935\) 10120.0 0.353967
\(936\) 4248.00 0.148344
\(937\) −8818.00 −0.307440 −0.153720 0.988114i \(-0.549125\pi\)
−0.153720 + 0.988114i \(0.549125\pi\)
\(938\) 12240.0 0.426066
\(939\) 507.000 0.0176201
\(940\) 700.000 0.0242888
\(941\) 33778.0 1.17017 0.585086 0.810971i \(-0.301061\pi\)
0.585086 + 0.810971i \(0.301061\pi\)
\(942\) −15036.0 −0.520063
\(943\) 2160.00 0.0745910
\(944\) 13136.0 0.452903
\(945\) 1350.00 0.0464714
\(946\) 8888.00 0.305469
\(947\) −14742.0 −0.505861 −0.252931 0.967484i \(-0.581394\pi\)
−0.252931 + 0.967484i \(0.581394\pi\)
\(948\) −96.0000 −0.00328896
\(949\) 36698.0 1.25529
\(950\) −1700.00 −0.0580582
\(951\) 21213.0 0.723321
\(952\) −3680.00 −0.125283
\(953\) −23850.0 −0.810679 −0.405340 0.914166i \(-0.632847\pi\)
−0.405340 + 0.914166i \(0.632847\pi\)
\(954\) −9126.00 −0.309712
\(955\) 660.000 0.0223635
\(956\) 2828.00 0.0956737
\(957\) −924.000 −0.0312107
\(958\) −12038.0 −0.405981
\(959\) −9810.00 −0.330325
\(960\) 960.000 0.0322749
\(961\) 3333.00 0.111879
\(962\) 4366.00 0.146326
\(963\) 585.000 0.0195757
\(964\) −1256.00 −0.0419637
\(965\) −14595.0 −0.486870
\(966\) −360.000 −0.0119905
\(967\) 42104.0 1.40018 0.700090 0.714055i \(-0.253143\pi\)
0.700090 + 0.714055i \(0.253143\pi\)
\(968\) 4840.00 0.160706
\(969\) −4692.00 −0.155551
\(970\) −8700.00 −0.287980
\(971\) −438.000 −0.0144759 −0.00723794 0.999974i \(-0.502304\pi\)
−0.00723794 + 0.999974i \(0.502304\pi\)
\(972\) −972.000 −0.0320750
\(973\) 5530.00 0.182203
\(974\) 2850.00 0.0937576
\(975\) −4425.00 −0.145347
\(976\) 1120.00 0.0367319
\(977\) 25564.0 0.837119 0.418559 0.908189i \(-0.362535\pi\)
0.418559 + 0.908189i \(0.362535\pi\)
\(978\) 5496.00 0.179696
\(979\) 15180.0 0.495562
\(980\) 4860.00 0.158415
\(981\) 1800.00 0.0585826
\(982\) 33308.0 1.08238
\(983\) 44312.0 1.43778 0.718888 0.695126i \(-0.244652\pi\)
0.718888 + 0.695126i \(0.244652\pi\)
\(984\) −8640.00 −0.279912
\(985\) 8010.00 0.259106
\(986\) −644.000 −0.0208003
\(987\) 1050.00 0.0338621
\(988\) −8024.00 −0.258378
\(989\) 606.000 0.0194840
\(990\) −3960.00 −0.127128
\(991\) −32690.0 −1.04786 −0.523931 0.851760i \(-0.675535\pi\)
−0.523931 + 0.851760i \(0.675535\pi\)
\(992\) −5824.00 −0.186403
\(993\) 18408.0 0.588278
\(994\) 1760.00 0.0561608
\(995\) −6170.00 −0.196585
\(996\) −14676.0 −0.466894
\(997\) −4014.00 −0.127507 −0.0637536 0.997966i \(-0.520307\pi\)
−0.0637536 + 0.997966i \(0.520307\pi\)
\(998\) −29908.0 −0.948618
\(999\) −999.000 −0.0316386
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 1110.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.4.a.b.1.1 1 1.1 even 1 trivial