Properties

Label 966.6.a.b.1.1
Level $966$
Weight $6$
Character 966.1
Self dual yes
Analytic conductor $154.931$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(154.930769939\)
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 \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +28.0000 q^{5} +36.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +28.0000 q^{5} +36.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +112.000 q^{10} -15.0000 q^{11} +144.000 q^{12} -1066.00 q^{13} +196.000 q^{14} +252.000 q^{15} +256.000 q^{16} -80.0000 q^{17} +324.000 q^{18} -1319.00 q^{19} +448.000 q^{20} +441.000 q^{21} -60.0000 q^{22} +529.000 q^{23} +576.000 q^{24} -2341.00 q^{25} -4264.00 q^{26} +729.000 q^{27} +784.000 q^{28} -3586.00 q^{29} +1008.00 q^{30} -7850.00 q^{31} +1024.00 q^{32} -135.000 q^{33} -320.000 q^{34} +1372.00 q^{35} +1296.00 q^{36} +5074.00 q^{37} -5276.00 q^{38} -9594.00 q^{39} +1792.00 q^{40} -17627.0 q^{41} +1764.00 q^{42} +10392.0 q^{43} -240.000 q^{44} +2268.00 q^{45} +2116.00 q^{46} -11805.0 q^{47} +2304.00 q^{48} +2401.00 q^{49} -9364.00 q^{50} -720.000 q^{51} -17056.0 q^{52} -345.000 q^{53} +2916.00 q^{54} -420.000 q^{55} +3136.00 q^{56} -11871.0 q^{57} -14344.0 q^{58} -31347.0 q^{59} +4032.00 q^{60} -5019.00 q^{61} -31400.0 q^{62} +3969.00 q^{63} +4096.00 q^{64} -29848.0 q^{65} -540.000 q^{66} -26552.0 q^{67} -1280.00 q^{68} +4761.00 q^{69} +5488.00 q^{70} -23492.0 q^{71} +5184.00 q^{72} -5356.00 q^{73} +20296.0 q^{74} -21069.0 q^{75} -21104.0 q^{76} -735.000 q^{77} -38376.0 q^{78} +99870.0 q^{79} +7168.00 q^{80} +6561.00 q^{81} -70508.0 q^{82} +47482.0 q^{83} +7056.00 q^{84} -2240.00 q^{85} +41568.0 q^{86} -32274.0 q^{87} -960.000 q^{88} -58182.0 q^{89} +9072.00 q^{90} -52234.0 q^{91} +8464.00 q^{92} -70650.0 q^{93} -47220.0 q^{94} -36932.0 q^{95} +9216.00 q^{96} +72722.0 q^{97} +9604.00 q^{98} -1215.00 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) 9.00000 0.577350
\(4\) 16.0000 0.500000
\(5\) 28.0000 0.500879 0.250440 0.968132i \(-0.419425\pi\)
0.250440 + 0.968132i \(0.419425\pi\)
\(6\) 36.0000 0.408248
\(7\) 49.0000 0.377964
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) 112.000 0.354175
\(11\) −15.0000 −0.0373774 −0.0186887 0.999825i \(-0.505949\pi\)
−0.0186887 + 0.999825i \(0.505949\pi\)
\(12\) 144.000 0.288675
\(13\) −1066.00 −1.74944 −0.874720 0.484629i \(-0.838954\pi\)
−0.874720 + 0.484629i \(0.838954\pi\)
\(14\) 196.000 0.267261
\(15\) 252.000 0.289183
\(16\) 256.000 0.250000
\(17\) −80.0000 −0.0671379 −0.0335689 0.999436i \(-0.510687\pi\)
−0.0335689 + 0.999436i \(0.510687\pi\)
\(18\) 324.000 0.235702
\(19\) −1319.00 −0.838225 −0.419113 0.907934i \(-0.637659\pi\)
−0.419113 + 0.907934i \(0.637659\pi\)
\(20\) 448.000 0.250440
\(21\) 441.000 0.218218
\(22\) −60.0000 −0.0264298
\(23\) 529.000 0.208514
\(24\) 576.000 0.204124
\(25\) −2341.00 −0.749120
\(26\) −4264.00 −1.23704
\(27\) 729.000 0.192450
\(28\) 784.000 0.188982
\(29\) −3586.00 −0.791800 −0.395900 0.918294i \(-0.629567\pi\)
−0.395900 + 0.918294i \(0.629567\pi\)
\(30\) 1008.00 0.204483
\(31\) −7850.00 −1.46712 −0.733560 0.679625i \(-0.762142\pi\)
−0.733560 + 0.679625i \(0.762142\pi\)
\(32\) 1024.00 0.176777
\(33\) −135.000 −0.0215799
\(34\) −320.000 −0.0474737
\(35\) 1372.00 0.189315
\(36\) 1296.00 0.166667
\(37\) 5074.00 0.609321 0.304661 0.952461i \(-0.401457\pi\)
0.304661 + 0.952461i \(0.401457\pi\)
\(38\) −5276.00 −0.592715
\(39\) −9594.00 −1.01004
\(40\) 1792.00 0.177088
\(41\) −17627.0 −1.63764 −0.818821 0.574049i \(-0.805372\pi\)
−0.818821 + 0.574049i \(0.805372\pi\)
\(42\) 1764.00 0.154303
\(43\) 10392.0 0.857093 0.428547 0.903520i \(-0.359026\pi\)
0.428547 + 0.903520i \(0.359026\pi\)
\(44\) −240.000 −0.0186887
\(45\) 2268.00 0.166960
\(46\) 2116.00 0.147442
\(47\) −11805.0 −0.779509 −0.389755 0.920919i \(-0.627440\pi\)
−0.389755 + 0.920919i \(0.627440\pi\)
\(48\) 2304.00 0.144338
\(49\) 2401.00 0.142857
\(50\) −9364.00 −0.529708
\(51\) −720.000 −0.0387621
\(52\) −17056.0 −0.874720
\(53\) −345.000 −0.0168706 −0.00843528 0.999964i \(-0.502685\pi\)
−0.00843528 + 0.999964i \(0.502685\pi\)
\(54\) 2916.00 0.136083
\(55\) −420.000 −0.0187216
\(56\) 3136.00 0.133631
\(57\) −11871.0 −0.483950
\(58\) −14344.0 −0.559887
\(59\) −31347.0 −1.17237 −0.586187 0.810176i \(-0.699371\pi\)
−0.586187 + 0.810176i \(0.699371\pi\)
\(60\) 4032.00 0.144591
\(61\) −5019.00 −0.172700 −0.0863501 0.996265i \(-0.527520\pi\)
−0.0863501 + 0.996265i \(0.527520\pi\)
\(62\) −31400.0 −1.03741
\(63\) 3969.00 0.125988
\(64\) 4096.00 0.125000
\(65\) −29848.0 −0.876258
\(66\) −540.000 −0.0152593
\(67\) −26552.0 −0.722620 −0.361310 0.932446i \(-0.617670\pi\)
−0.361310 + 0.932446i \(0.617670\pi\)
\(68\) −1280.00 −0.0335689
\(69\) 4761.00 0.120386
\(70\) 5488.00 0.133866
\(71\) −23492.0 −0.553062 −0.276531 0.961005i \(-0.589185\pi\)
−0.276531 + 0.961005i \(0.589185\pi\)
\(72\) 5184.00 0.117851
\(73\) −5356.00 −0.117634 −0.0588171 0.998269i \(-0.518733\pi\)
−0.0588171 + 0.998269i \(0.518733\pi\)
\(74\) 20296.0 0.430855
\(75\) −21069.0 −0.432505
\(76\) −21104.0 −0.419113
\(77\) −735.000 −0.0141273
\(78\) −38376.0 −0.714206
\(79\) 99870.0 1.80039 0.900197 0.435484i \(-0.143423\pi\)
0.900197 + 0.435484i \(0.143423\pi\)
\(80\) 7168.00 0.125220
\(81\) 6561.00 0.111111
\(82\) −70508.0 −1.15799
\(83\) 47482.0 0.756543 0.378272 0.925695i \(-0.376519\pi\)
0.378272 + 0.925695i \(0.376519\pi\)
\(84\) 7056.00 0.109109
\(85\) −2240.00 −0.0336280
\(86\) 41568.0 0.606056
\(87\) −32274.0 −0.457146
\(88\) −960.000 −0.0132149
\(89\) −58182.0 −0.778599 −0.389299 0.921111i \(-0.627283\pi\)
−0.389299 + 0.921111i \(0.627283\pi\)
\(90\) 9072.00 0.118058
\(91\) −52234.0 −0.661226
\(92\) 8464.00 0.104257
\(93\) −70650.0 −0.847042
\(94\) −47220.0 −0.551196
\(95\) −36932.0 −0.419850
\(96\) 9216.00 0.102062
\(97\) 72722.0 0.784759 0.392380 0.919803i \(-0.371652\pi\)
0.392380 + 0.919803i \(0.371652\pi\)
\(98\) 9604.00 0.101015
\(99\) −1215.00 −0.0124591
\(100\) −37456.0 −0.374560
\(101\) −7315.00 −0.0713528 −0.0356764 0.999363i \(-0.511359\pi\)
−0.0356764 + 0.999363i \(0.511359\pi\)
\(102\) −2880.00 −0.0274089
\(103\) 26791.0 0.248826 0.124413 0.992231i \(-0.460295\pi\)
0.124413 + 0.992231i \(0.460295\pi\)
\(104\) −68224.0 −0.618520
\(105\) 12348.0 0.109301
\(106\) −1380.00 −0.0119293
\(107\) 180228. 1.52182 0.760909 0.648858i \(-0.224753\pi\)
0.760909 + 0.648858i \(0.224753\pi\)
\(108\) 11664.0 0.0962250
\(109\) 170440. 1.37406 0.687029 0.726630i \(-0.258914\pi\)
0.687029 + 0.726630i \(0.258914\pi\)
\(110\) −1680.00 −0.0132382
\(111\) 45666.0 0.351792
\(112\) 12544.0 0.0944911
\(113\) 31666.0 0.233291 0.116645 0.993174i \(-0.462786\pi\)
0.116645 + 0.993174i \(0.462786\pi\)
\(114\) −47484.0 −0.342204
\(115\) 14812.0 0.104441
\(116\) −57376.0 −0.395900
\(117\) −86346.0 −0.583146
\(118\) −125388. −0.828993
\(119\) −3920.00 −0.0253757
\(120\) 16128.0 0.102242
\(121\) −160826. −0.998603
\(122\) −20076.0 −0.122117
\(123\) −158643. −0.945493
\(124\) −125600. −0.733560
\(125\) −153048. −0.876098
\(126\) 15876.0 0.0890871
\(127\) −58147.0 −0.319903 −0.159951 0.987125i \(-0.551134\pi\)
−0.159951 + 0.987125i \(0.551134\pi\)
\(128\) 16384.0 0.0883883
\(129\) 93528.0 0.494843
\(130\) −119392. −0.619608
\(131\) −95801.0 −0.487744 −0.243872 0.969807i \(-0.578418\pi\)
−0.243872 + 0.969807i \(0.578418\pi\)
\(132\) −2160.00 −0.0107899
\(133\) −64631.0 −0.316819
\(134\) −106208. −0.510970
\(135\) 20412.0 0.0963943
\(136\) −5120.00 −0.0237368
\(137\) 153687. 0.699577 0.349789 0.936829i \(-0.386253\pi\)
0.349789 + 0.936829i \(0.386253\pi\)
\(138\) 19044.0 0.0851257
\(139\) 316100. 1.38767 0.693837 0.720132i \(-0.255919\pi\)
0.693837 + 0.720132i \(0.255919\pi\)
\(140\) 21952.0 0.0946573
\(141\) −106245. −0.450050
\(142\) −93968.0 −0.391074
\(143\) 15990.0 0.0653896
\(144\) 20736.0 0.0833333
\(145\) −100408. −0.396596
\(146\) −21424.0 −0.0831799
\(147\) 21609.0 0.0824786
\(148\) 81184.0 0.304661
\(149\) −378667. −1.39731 −0.698653 0.715460i \(-0.746217\pi\)
−0.698653 + 0.715460i \(0.746217\pi\)
\(150\) −84276.0 −0.305827
\(151\) −97703.0 −0.348711 −0.174355 0.984683i \(-0.555784\pi\)
−0.174355 + 0.984683i \(0.555784\pi\)
\(152\) −84416.0 −0.296357
\(153\) −6480.00 −0.0223793
\(154\) −2940.00 −0.00998954
\(155\) −219800. −0.734850
\(156\) −153504. −0.505020
\(157\) −582567. −1.88624 −0.943120 0.332454i \(-0.892123\pi\)
−0.943120 + 0.332454i \(0.892123\pi\)
\(158\) 399480. 1.27307
\(159\) −3105.00 −0.00974022
\(160\) 28672.0 0.0885438
\(161\) 25921.0 0.0788110
\(162\) 26244.0 0.0785674
\(163\) −347407. −1.02416 −0.512082 0.858937i \(-0.671126\pi\)
−0.512082 + 0.858937i \(0.671126\pi\)
\(164\) −282032. −0.818821
\(165\) −3780.00 −0.0108089
\(166\) 189928. 0.534957
\(167\) 170559. 0.473242 0.236621 0.971602i \(-0.423960\pi\)
0.236621 + 0.971602i \(0.423960\pi\)
\(168\) 28224.0 0.0771517
\(169\) 765063. 2.06054
\(170\) −8960.00 −0.0237786
\(171\) −106839. −0.279408
\(172\) 166272. 0.428547
\(173\) 125346. 0.318416 0.159208 0.987245i \(-0.449106\pi\)
0.159208 + 0.987245i \(0.449106\pi\)
\(174\) −129096. −0.323251
\(175\) −114709. −0.283141
\(176\) −3840.00 −0.00934436
\(177\) −282123. −0.676870
\(178\) −232728. −0.550552
\(179\) 341736. 0.797183 0.398592 0.917129i \(-0.369499\pi\)
0.398592 + 0.917129i \(0.369499\pi\)
\(180\) 36288.0 0.0834799
\(181\) −26378.0 −0.0598474 −0.0299237 0.999552i \(-0.509526\pi\)
−0.0299237 + 0.999552i \(0.509526\pi\)
\(182\) −208936. −0.467557
\(183\) −45171.0 −0.0997085
\(184\) 33856.0 0.0737210
\(185\) 142072. 0.305196
\(186\) −282600. −0.598949
\(187\) 1200.00 0.00250944
\(188\) −188880. −0.389755
\(189\) 35721.0 0.0727393
\(190\) −147728. −0.296879
\(191\) 509995. 1.01154 0.505769 0.862669i \(-0.331209\pi\)
0.505769 + 0.862669i \(0.331209\pi\)
\(192\) 36864.0 0.0721688
\(193\) −265715. −0.513479 −0.256740 0.966481i \(-0.582648\pi\)
−0.256740 + 0.966481i \(0.582648\pi\)
\(194\) 290888. 0.554909
\(195\) −268632. −0.505908
\(196\) 38416.0 0.0714286
\(197\) −384814. −0.706456 −0.353228 0.935537i \(-0.614916\pi\)
−0.353228 + 0.935537i \(0.614916\pi\)
\(198\) −4860.00 −0.00880995
\(199\) −423655. −0.758367 −0.379184 0.925321i \(-0.623795\pi\)
−0.379184 + 0.925321i \(0.623795\pi\)
\(200\) −149824. −0.264854
\(201\) −238968. −0.417205
\(202\) −29260.0 −0.0504540
\(203\) −175714. −0.299272
\(204\) −11520.0 −0.0193810
\(205\) −493556. −0.820260
\(206\) 107164. 0.175947
\(207\) 42849.0 0.0695048
\(208\) −272896. −0.437360
\(209\) 19785.0 0.0313307
\(210\) 49392.0 0.0772873
\(211\) 387057. 0.598506 0.299253 0.954174i \(-0.403262\pi\)
0.299253 + 0.954174i \(0.403262\pi\)
\(212\) −5520.00 −0.00843528
\(213\) −211428. −0.319311
\(214\) 720912. 1.07609
\(215\) 290976. 0.429300
\(216\) 46656.0 0.0680414
\(217\) −384650. −0.554519
\(218\) 681760. 0.971606
\(219\) −48204.0 −0.0679161
\(220\) −6720.00 −0.00936079
\(221\) 85280.0 0.117454
\(222\) 182664. 0.248754
\(223\) −299642. −0.403497 −0.201749 0.979437i \(-0.564662\pi\)
−0.201749 + 0.979437i \(0.564662\pi\)
\(224\) 50176.0 0.0668153
\(225\) −189621. −0.249707
\(226\) 126664. 0.164961
\(227\) −1.29649e6 −1.66995 −0.834974 0.550289i \(-0.814518\pi\)
−0.834974 + 0.550289i \(0.814518\pi\)
\(228\) −189936. −0.241975
\(229\) 449749. 0.566737 0.283368 0.959011i \(-0.408548\pi\)
0.283368 + 0.959011i \(0.408548\pi\)
\(230\) 59248.0 0.0738506
\(231\) −6615.00 −0.00815643
\(232\) −229504. −0.279943
\(233\) −529188. −0.638587 −0.319294 0.947656i \(-0.603446\pi\)
−0.319294 + 0.947656i \(0.603446\pi\)
\(234\) −345384. −0.412347
\(235\) −330540. −0.390440
\(236\) −501552. −0.586187
\(237\) 898830. 1.03946
\(238\) −15680.0 −0.0179434
\(239\) 413400. 0.468140 0.234070 0.972220i \(-0.424796\pi\)
0.234070 + 0.972220i \(0.424796\pi\)
\(240\) 64512.0 0.0722957
\(241\) 1.26352e6 1.40133 0.700663 0.713492i \(-0.252888\pi\)
0.700663 + 0.713492i \(0.252888\pi\)
\(242\) −643304. −0.706119
\(243\) 59049.0 0.0641500
\(244\) −80304.0 −0.0863501
\(245\) 67228.0 0.0715542
\(246\) −634572. −0.668564
\(247\) 1.40605e6 1.46642
\(248\) −502400. −0.518705
\(249\) 427338. 0.436790
\(250\) −612192. −0.619495
\(251\) 1.16018e6 1.16236 0.581180 0.813775i \(-0.302591\pi\)
0.581180 + 0.813775i \(0.302591\pi\)
\(252\) 63504.0 0.0629941
\(253\) −7935.00 −0.00779373
\(254\) −232588. −0.226205
\(255\) −20160.0 −0.0194151
\(256\) 65536.0 0.0625000
\(257\) −1.27815e6 −1.20712 −0.603558 0.797319i \(-0.706251\pi\)
−0.603558 + 0.797319i \(0.706251\pi\)
\(258\) 374112. 0.349907
\(259\) 248626. 0.230302
\(260\) −477568. −0.438129
\(261\) −290466. −0.263933
\(262\) −383204. −0.344887
\(263\) −622739. −0.555158 −0.277579 0.960703i \(-0.589532\pi\)
−0.277579 + 0.960703i \(0.589532\pi\)
\(264\) −8640.00 −0.00762964
\(265\) −9660.00 −0.00845011
\(266\) −258524. −0.224025
\(267\) −523638. −0.449524
\(268\) −424832. −0.361310
\(269\) −1.54439e6 −1.30130 −0.650650 0.759378i \(-0.725503\pi\)
−0.650650 + 0.759378i \(0.725503\pi\)
\(270\) 81648.0 0.0681610
\(271\) 1.02695e6 0.849425 0.424713 0.905328i \(-0.360375\pi\)
0.424713 + 0.905328i \(0.360375\pi\)
\(272\) −20480.0 −0.0167845
\(273\) −470106. −0.381759
\(274\) 614748. 0.494676
\(275\) 35115.0 0.0280002
\(276\) 76176.0 0.0601929
\(277\) −896465. −0.701995 −0.350997 0.936376i \(-0.614157\pi\)
−0.350997 + 0.936376i \(0.614157\pi\)
\(278\) 1.26440e6 0.981234
\(279\) −635850. −0.489040
\(280\) 87808.0 0.0669328
\(281\) 793958. 0.599835 0.299917 0.953965i \(-0.403041\pi\)
0.299917 + 0.953965i \(0.403041\pi\)
\(282\) −424980. −0.318233
\(283\) −220788. −0.163874 −0.0819369 0.996638i \(-0.526111\pi\)
−0.0819369 + 0.996638i \(0.526111\pi\)
\(284\) −375872. −0.276531
\(285\) −332388. −0.242400
\(286\) 63960.0 0.0462374
\(287\) −863723. −0.618970
\(288\) 82944.0 0.0589256
\(289\) −1.41346e6 −0.995493
\(290\) −401632. −0.280436
\(291\) 654498. 0.453081
\(292\) −85696.0 −0.0588171
\(293\) −541868. −0.368744 −0.184372 0.982857i \(-0.559025\pi\)
−0.184372 + 0.982857i \(0.559025\pi\)
\(294\) 86436.0 0.0583212
\(295\) −877716. −0.587217
\(296\) 324736. 0.215428
\(297\) −10935.0 −0.00719329
\(298\) −1.51467e6 −0.988045
\(299\) −563914. −0.364783
\(300\) −337104. −0.216252
\(301\) 509208. 0.323951
\(302\) −390812. −0.246576
\(303\) −65835.0 −0.0411955
\(304\) −337664. −0.209556
\(305\) −140532. −0.0865019
\(306\) −25920.0 −0.0158246
\(307\) −2.87122e6 −1.73869 −0.869343 0.494209i \(-0.835458\pi\)
−0.869343 + 0.494209i \(0.835458\pi\)
\(308\) −11760.0 −0.00706367
\(309\) 241119. 0.143660
\(310\) −879200. −0.519617
\(311\) 2.38904e6 1.40063 0.700315 0.713834i \(-0.253043\pi\)
0.700315 + 0.713834i \(0.253043\pi\)
\(312\) −614016. −0.357103
\(313\) 850937. 0.490949 0.245475 0.969403i \(-0.421056\pi\)
0.245475 + 0.969403i \(0.421056\pi\)
\(314\) −2.33027e6 −1.33377
\(315\) 111132. 0.0631049
\(316\) 1.59792e6 0.900197
\(317\) −24742.0 −0.0138289 −0.00691443 0.999976i \(-0.502201\pi\)
−0.00691443 + 0.999976i \(0.502201\pi\)
\(318\) −12420.0 −0.00688738
\(319\) 53790.0 0.0295954
\(320\) 114688. 0.0626099
\(321\) 1.62205e6 0.878622
\(322\) 103684. 0.0557278
\(323\) 105520. 0.0562767
\(324\) 104976. 0.0555556
\(325\) 2.49551e6 1.31054
\(326\) −1.38963e6 −0.724193
\(327\) 1.53396e6 0.793313
\(328\) −1.12813e6 −0.578994
\(329\) −578445. −0.294627
\(330\) −15120.0 −0.00764305
\(331\) −2.49814e6 −1.25327 −0.626637 0.779311i \(-0.715569\pi\)
−0.626637 + 0.779311i \(0.715569\pi\)
\(332\) 759712. 0.378272
\(333\) 410994. 0.203107
\(334\) 682236. 0.334633
\(335\) −743456. −0.361946
\(336\) 112896. 0.0545545
\(337\) −3.78265e6 −1.81435 −0.907175 0.420754i \(-0.861766\pi\)
−0.907175 + 0.420754i \(0.861766\pi\)
\(338\) 3.06025e6 1.45702
\(339\) 284994. 0.134690
\(340\) −35840.0 −0.0168140
\(341\) 117750. 0.0548372
\(342\) −427356. −0.197572
\(343\) 117649. 0.0539949
\(344\) 665088. 0.303028
\(345\) 133308. 0.0602988
\(346\) 501384. 0.225154
\(347\) −1.25095e6 −0.557718 −0.278859 0.960332i \(-0.589956\pi\)
−0.278859 + 0.960332i \(0.589956\pi\)
\(348\) −516384. −0.228573
\(349\) 4.06863e6 1.78807 0.894036 0.447995i \(-0.147862\pi\)
0.894036 + 0.447995i \(0.147862\pi\)
\(350\) −458836. −0.200211
\(351\) −777114. −0.336680
\(352\) −15360.0 −0.00660746
\(353\) 2.47899e6 1.05886 0.529430 0.848353i \(-0.322406\pi\)
0.529430 + 0.848353i \(0.322406\pi\)
\(354\) −1.12849e6 −0.478619
\(355\) −657776. −0.277017
\(356\) −930912. −0.389299
\(357\) −35280.0 −0.0146507
\(358\) 1.36694e6 0.563694
\(359\) 4.14936e6 1.69920 0.849601 0.527426i \(-0.176843\pi\)
0.849601 + 0.527426i \(0.176843\pi\)
\(360\) 145152. 0.0590292
\(361\) −736338. −0.297378
\(362\) −105512. −0.0423185
\(363\) −1.44743e6 −0.576544
\(364\) −835744. −0.330613
\(365\) −149968. −0.0589205
\(366\) −180684. −0.0705045
\(367\) 3.70454e6 1.43572 0.717860 0.696188i \(-0.245122\pi\)
0.717860 + 0.696188i \(0.245122\pi\)
\(368\) 135424. 0.0521286
\(369\) −1.42779e6 −0.545880
\(370\) 568288. 0.215806
\(371\) −16905.0 −0.00637647
\(372\) −1.13040e6 −0.423521
\(373\) −57154.0 −0.0212703 −0.0106352 0.999943i \(-0.503385\pi\)
−0.0106352 + 0.999943i \(0.503385\pi\)
\(374\) 4800.00 0.00177444
\(375\) −1.37743e6 −0.505815
\(376\) −755520. −0.275598
\(377\) 3.82268e6 1.38521
\(378\) 142884. 0.0514344
\(379\) −3.85427e6 −1.37830 −0.689150 0.724619i \(-0.742016\pi\)
−0.689150 + 0.724619i \(0.742016\pi\)
\(380\) −590912. −0.209925
\(381\) −523323. −0.184696
\(382\) 2.03998e6 0.715266
\(383\) −4.72959e6 −1.64751 −0.823753 0.566949i \(-0.808124\pi\)
−0.823753 + 0.566949i \(0.808124\pi\)
\(384\) 147456. 0.0510310
\(385\) −20580.0 −0.00707609
\(386\) −1.06286e6 −0.363085
\(387\) 841752. 0.285698
\(388\) 1.16355e6 0.392380
\(389\) −3.23052e6 −1.08243 −0.541213 0.840886i \(-0.682035\pi\)
−0.541213 + 0.840886i \(0.682035\pi\)
\(390\) −1.07453e6 −0.357731
\(391\) −42320.0 −0.0139992
\(392\) 153664. 0.0505076
\(393\) −862209. −0.281599
\(394\) −1.53926e6 −0.499540
\(395\) 2.79636e6 0.901779
\(396\) −19440.0 −0.00622957
\(397\) 414238. 0.131909 0.0659544 0.997823i \(-0.478991\pi\)
0.0659544 + 0.997823i \(0.478991\pi\)
\(398\) −1.69462e6 −0.536247
\(399\) −581679. −0.182916
\(400\) −599296. −0.187280
\(401\) 1.52752e6 0.474379 0.237189 0.971463i \(-0.423774\pi\)
0.237189 + 0.971463i \(0.423774\pi\)
\(402\) −955872. −0.295009
\(403\) 8.36810e6 2.56664
\(404\) −117040. −0.0356764
\(405\) 183708. 0.0556532
\(406\) −702856. −0.211617
\(407\) −76110.0 −0.0227749
\(408\) −46080.0 −0.0137045
\(409\) −2.83674e6 −0.838516 −0.419258 0.907867i \(-0.637710\pi\)
−0.419258 + 0.907867i \(0.637710\pi\)
\(410\) −1.97422e6 −0.580012
\(411\) 1.38318e6 0.403901
\(412\) 428656. 0.124413
\(413\) −1.53600e6 −0.443115
\(414\) 171396. 0.0491473
\(415\) 1.32950e6 0.378937
\(416\) −1.09158e6 −0.309260
\(417\) 2.84490e6 0.801174
\(418\) 79140.0 0.0221542
\(419\) −78114.0 −0.0217367 −0.0108684 0.999941i \(-0.503460\pi\)
−0.0108684 + 0.999941i \(0.503460\pi\)
\(420\) 197568. 0.0546504
\(421\) −1.58554e6 −0.435984 −0.217992 0.975951i \(-0.569951\pi\)
−0.217992 + 0.975951i \(0.569951\pi\)
\(422\) 1.54823e6 0.423208
\(423\) −956205. −0.259836
\(424\) −22080.0 −0.00596464
\(425\) 187280. 0.0502943
\(426\) −845712. −0.225787
\(427\) −245931. −0.0652745
\(428\) 2.88365e6 0.760909
\(429\) 143910. 0.0377527
\(430\) 1.16390e6 0.303561
\(431\) −1.02160e6 −0.264903 −0.132452 0.991189i \(-0.542285\pi\)
−0.132452 + 0.991189i \(0.542285\pi\)
\(432\) 186624. 0.0481125
\(433\) 246539. 0.0631926 0.0315963 0.999501i \(-0.489941\pi\)
0.0315963 + 0.999501i \(0.489941\pi\)
\(434\) −1.53860e6 −0.392104
\(435\) −903672. −0.228975
\(436\) 2.72704e6 0.687029
\(437\) −697751. −0.174782
\(438\) −192816. −0.0480239
\(439\) −619792. −0.153492 −0.0767458 0.997051i \(-0.524453\pi\)
−0.0767458 + 0.997051i \(0.524453\pi\)
\(440\) −26880.0 −0.00661908
\(441\) 194481. 0.0476190
\(442\) 341120. 0.0830523
\(443\) −5.74450e6 −1.39073 −0.695366 0.718656i \(-0.744758\pi\)
−0.695366 + 0.718656i \(0.744758\pi\)
\(444\) 730656. 0.175896
\(445\) −1.62910e6 −0.389984
\(446\) −1.19857e6 −0.285316
\(447\) −3.40800e6 −0.806735
\(448\) 200704. 0.0472456
\(449\) 4.80635e6 1.12512 0.562561 0.826756i \(-0.309816\pi\)
0.562561 + 0.826756i \(0.309816\pi\)
\(450\) −758484. −0.176569
\(451\) 264405. 0.0612108
\(452\) 506656. 0.116645
\(453\) −879327. −0.201328
\(454\) −5.18594e6 −1.18083
\(455\) −1.46255e6 −0.331194
\(456\) −759744. −0.171102
\(457\) −2.65447e6 −0.594549 −0.297275 0.954792i \(-0.596078\pi\)
−0.297275 + 0.954792i \(0.596078\pi\)
\(458\) 1.79900e6 0.400744
\(459\) −58320.0 −0.0129207
\(460\) 236992. 0.0522203
\(461\) 6.45797e6 1.41528 0.707642 0.706571i \(-0.249759\pi\)
0.707642 + 0.706571i \(0.249759\pi\)
\(462\) −26460.0 −0.00576746
\(463\) −3.39535e6 −0.736092 −0.368046 0.929808i \(-0.619973\pi\)
−0.368046 + 0.929808i \(0.619973\pi\)
\(464\) −918016. −0.197950
\(465\) −1.97820e6 −0.424266
\(466\) −2.11675e6 −0.451549
\(467\) −3.62989e6 −0.770197 −0.385098 0.922876i \(-0.625833\pi\)
−0.385098 + 0.922876i \(0.625833\pi\)
\(468\) −1.38154e6 −0.291573
\(469\) −1.30105e6 −0.273125
\(470\) −1.32216e6 −0.276083
\(471\) −5.24310e6 −1.08902
\(472\) −2.00621e6 −0.414497
\(473\) −155880. −0.0320359
\(474\) 3.59532e6 0.735007
\(475\) 3.08778e6 0.627931
\(476\) −62720.0 −0.0126879
\(477\) −27945.0 −0.00562352
\(478\) 1.65360e6 0.331025
\(479\) −600524. −0.119589 −0.0597945 0.998211i \(-0.519045\pi\)
−0.0597945 + 0.998211i \(0.519045\pi\)
\(480\) 258048. 0.0511208
\(481\) −5.40888e6 −1.06597
\(482\) 5.05408e6 0.990887
\(483\) 233289. 0.0455016
\(484\) −2.57322e6 −0.499301
\(485\) 2.03622e6 0.393070
\(486\) 236196. 0.0453609
\(487\) −2.40688e6 −0.459866 −0.229933 0.973206i \(-0.573851\pi\)
−0.229933 + 0.973206i \(0.573851\pi\)
\(488\) −321216. −0.0610587
\(489\) −3.12666e6 −0.591301
\(490\) 268912. 0.0505964
\(491\) −2.77493e6 −0.519455 −0.259728 0.965682i \(-0.583633\pi\)
−0.259728 + 0.965682i \(0.583633\pi\)
\(492\) −2.53829e6 −0.472746
\(493\) 286880. 0.0531598
\(494\) 5.62422e6 1.03692
\(495\) −34020.0 −0.00624053
\(496\) −2.00960e6 −0.366780
\(497\) −1.15111e6 −0.209038
\(498\) 1.70935e6 0.308857
\(499\) 3.68872e6 0.663168 0.331584 0.943426i \(-0.392417\pi\)
0.331584 + 0.943426i \(0.392417\pi\)
\(500\) −2.44877e6 −0.438049
\(501\) 1.53503e6 0.273227
\(502\) 4.64071e6 0.821912
\(503\) 6.32946e6 1.11544 0.557720 0.830029i \(-0.311676\pi\)
0.557720 + 0.830029i \(0.311676\pi\)
\(504\) 254016. 0.0445435
\(505\) −204820. −0.0357391
\(506\) −31740.0 −0.00551100
\(507\) 6.88557e6 1.18965
\(508\) −930352. −0.159951
\(509\) 2.86719e6 0.490526 0.245263 0.969457i \(-0.421126\pi\)
0.245263 + 0.969457i \(0.421126\pi\)
\(510\) −80640.0 −0.0137286
\(511\) −262444. −0.0444615
\(512\) 262144. 0.0441942
\(513\) −961551. −0.161317
\(514\) −5.11260e6 −0.853561
\(515\) 750148. 0.124632
\(516\) 1.49645e6 0.247421
\(517\) 177075. 0.0291361
\(518\) 994504. 0.162848
\(519\) 1.12811e6 0.183838
\(520\) −1.91027e6 −0.309804
\(521\) −7.27474e6 −1.17415 −0.587075 0.809533i \(-0.699720\pi\)
−0.587075 + 0.809533i \(0.699720\pi\)
\(522\) −1.16186e6 −0.186629
\(523\) 1.17334e7 1.87573 0.937863 0.347006i \(-0.112802\pi\)
0.937863 + 0.347006i \(0.112802\pi\)
\(524\) −1.53282e6 −0.243872
\(525\) −1.03238e6 −0.163471
\(526\) −2.49096e6 −0.392556
\(527\) 628000. 0.0984993
\(528\) −34560.0 −0.00539497
\(529\) 279841. 0.0434783
\(530\) −38640.0 −0.00597513
\(531\) −2.53911e6 −0.390791
\(532\) −1.03410e6 −0.158410
\(533\) 1.87904e7 2.86495
\(534\) −2.09455e6 −0.317862
\(535\) 5.04638e6 0.762247
\(536\) −1.69933e6 −0.255485
\(537\) 3.07562e6 0.460254
\(538\) −6.17758e6 −0.920158
\(539\) −36015.0 −0.00533963
\(540\) 326592. 0.0481971
\(541\) 3.98664e6 0.585617 0.292808 0.956171i \(-0.405410\pi\)
0.292808 + 0.956171i \(0.405410\pi\)
\(542\) 4.10779e6 0.600634
\(543\) −237402. −0.0345529
\(544\) −81920.0 −0.0118684
\(545\) 4.77232e6 0.688237
\(546\) −1.88042e6 −0.269944
\(547\) 8.47845e6 1.21157 0.605784 0.795629i \(-0.292859\pi\)
0.605784 + 0.795629i \(0.292859\pi\)
\(548\) 2.45899e6 0.349789
\(549\) −406539. −0.0575667
\(550\) 140460. 0.0197991
\(551\) 4.72993e6 0.663707
\(552\) 304704. 0.0425628
\(553\) 4.89363e6 0.680485
\(554\) −3.58586e6 −0.496385
\(555\) 1.27865e6 0.176205
\(556\) 5.05760e6 0.693837
\(557\) 1.11666e7 1.52505 0.762524 0.646960i \(-0.223960\pi\)
0.762524 + 0.646960i \(0.223960\pi\)
\(558\) −2.54340e6 −0.345803
\(559\) −1.10779e7 −1.49943
\(560\) 351232. 0.0473286
\(561\) 10800.0 0.00144883
\(562\) 3.17583e6 0.424147
\(563\) −3.61705e6 −0.480932 −0.240466 0.970658i \(-0.577300\pi\)
−0.240466 + 0.970658i \(0.577300\pi\)
\(564\) −1.69992e6 −0.225025
\(565\) 886648. 0.116850
\(566\) −883152. −0.115876
\(567\) 321489. 0.0419961
\(568\) −1.50349e6 −0.195537
\(569\) −5.53948e6 −0.717279 −0.358640 0.933476i \(-0.616759\pi\)
−0.358640 + 0.933476i \(0.616759\pi\)
\(570\) −1.32955e6 −0.171403
\(571\) 5.99194e6 0.769091 0.384545 0.923106i \(-0.374358\pi\)
0.384545 + 0.923106i \(0.374358\pi\)
\(572\) 255840. 0.0326948
\(573\) 4.58996e6 0.584012
\(574\) −3.45489e6 −0.437678
\(575\) −1.23839e6 −0.156202
\(576\) 331776. 0.0416667
\(577\) −2.12121e6 −0.265243 −0.132622 0.991167i \(-0.542339\pi\)
−0.132622 + 0.991167i \(0.542339\pi\)
\(578\) −5.65383e6 −0.703920
\(579\) −2.39144e6 −0.296457
\(580\) −1.60653e6 −0.198298
\(581\) 2.32662e6 0.285946
\(582\) 2.61799e6 0.320377
\(583\) 5175.00 0.000630578 0
\(584\) −342784. −0.0415900
\(585\) −2.41769e6 −0.292086
\(586\) −2.16747e6 −0.260741
\(587\) −5.73403e6 −0.686854 −0.343427 0.939179i \(-0.611588\pi\)
−0.343427 + 0.939179i \(0.611588\pi\)
\(588\) 345744. 0.0412393
\(589\) 1.03542e7 1.22978
\(590\) −3.51086e6 −0.415225
\(591\) −3.46333e6 −0.407873
\(592\) 1.29894e6 0.152330
\(593\) −1.19277e7 −1.39290 −0.696448 0.717608i \(-0.745237\pi\)
−0.696448 + 0.717608i \(0.745237\pi\)
\(594\) −43740.0 −0.00508643
\(595\) −109760. −0.0127102
\(596\) −6.05867e6 −0.698653
\(597\) −3.81290e6 −0.437844
\(598\) −2.25566e6 −0.257941
\(599\) −1.08379e7 −1.23418 −0.617090 0.786892i \(-0.711689\pi\)
−0.617090 + 0.786892i \(0.711689\pi\)
\(600\) −1.34842e6 −0.152913
\(601\) 6.61816e6 0.747397 0.373698 0.927550i \(-0.378089\pi\)
0.373698 + 0.927550i \(0.378089\pi\)
\(602\) 2.03683e6 0.229068
\(603\) −2.15071e6 −0.240873
\(604\) −1.56325e6 −0.174355
\(605\) −4.50313e6 −0.500179
\(606\) −263340. −0.0291297
\(607\) −5.31644e6 −0.585665 −0.292833 0.956164i \(-0.594598\pi\)
−0.292833 + 0.956164i \(0.594598\pi\)
\(608\) −1.35066e6 −0.148179
\(609\) −1.58143e6 −0.172785
\(610\) −562128. −0.0611661
\(611\) 1.25841e7 1.36370
\(612\) −103680. −0.0111896
\(613\) −4.59787e6 −0.494203 −0.247101 0.968990i \(-0.579478\pi\)
−0.247101 + 0.968990i \(0.579478\pi\)
\(614\) −1.14849e7 −1.22944
\(615\) −4.44200e6 −0.473578
\(616\) −47040.0 −0.00499477
\(617\) 1.51913e7 1.60650 0.803250 0.595642i \(-0.203102\pi\)
0.803250 + 0.595642i \(0.203102\pi\)
\(618\) 964476. 0.101583
\(619\) 7.60144e6 0.797388 0.398694 0.917084i \(-0.369464\pi\)
0.398694 + 0.917084i \(0.369464\pi\)
\(620\) −3.51680e6 −0.367425
\(621\) 385641. 0.0401286
\(622\) 9.55618e6 0.990395
\(623\) −2.85092e6 −0.294283
\(624\) −2.45606e6 −0.252510
\(625\) 3.03028e6 0.310301
\(626\) 3.40375e6 0.347154
\(627\) 178065. 0.0180888
\(628\) −9.32107e6 −0.943120
\(629\) −405920. −0.0409085
\(630\) 444528. 0.0446219
\(631\) 4.70843e6 0.470763 0.235382 0.971903i \(-0.424366\pi\)
0.235382 + 0.971903i \(0.424366\pi\)
\(632\) 6.39168e6 0.636535
\(633\) 3.48351e6 0.345548
\(634\) −98968.0 −0.00977849
\(635\) −1.62812e6 −0.160233
\(636\) −49680.0 −0.00487011
\(637\) −2.55947e6 −0.249920
\(638\) 215160. 0.0209271
\(639\) −1.90285e6 −0.184354
\(640\) 458752. 0.0442719
\(641\) 345153. 0.0331793 0.0165896 0.999862i \(-0.494719\pi\)
0.0165896 + 0.999862i \(0.494719\pi\)
\(642\) 6.48821e6 0.621280
\(643\) 1.05491e7 1.00621 0.503104 0.864226i \(-0.332191\pi\)
0.503104 + 0.864226i \(0.332191\pi\)
\(644\) 414736. 0.0394055
\(645\) 2.61878e6 0.247857
\(646\) 422080. 0.0397936
\(647\) −1.49902e7 −1.40782 −0.703910 0.710289i \(-0.748564\pi\)
−0.703910 + 0.710289i \(0.748564\pi\)
\(648\) 419904. 0.0392837
\(649\) 470205. 0.0438203
\(650\) 9.98202e6 0.926692
\(651\) −3.46185e6 −0.320152
\(652\) −5.55851e6 −0.512082
\(653\) 658304. 0.0604148 0.0302074 0.999544i \(-0.490383\pi\)
0.0302074 + 0.999544i \(0.490383\pi\)
\(654\) 6.13584e6 0.560957
\(655\) −2.68243e6 −0.244301
\(656\) −4.51251e6 −0.409410
\(657\) −433836. −0.0392114
\(658\) −2.31378e6 −0.208333
\(659\) 2.09919e7 1.88295 0.941474 0.337086i \(-0.109441\pi\)
0.941474 + 0.337086i \(0.109441\pi\)
\(660\) −60480.0 −0.00540446
\(661\) 668861. 0.0595432 0.0297716 0.999557i \(-0.490522\pi\)
0.0297716 + 0.999557i \(0.490522\pi\)
\(662\) −9.99254e6 −0.886198
\(663\) 767520. 0.0678119
\(664\) 3.03885e6 0.267478
\(665\) −1.80967e6 −0.158688
\(666\) 1.64398e6 0.143618
\(667\) −1.89699e6 −0.165102
\(668\) 2.72894e6 0.236621
\(669\) −2.69678e6 −0.232959
\(670\) −2.97382e6 −0.255934
\(671\) 75285.0 0.00645509
\(672\) 451584. 0.0385758
\(673\) 2.60177e6 0.221427 0.110714 0.993852i \(-0.464686\pi\)
0.110714 + 0.993852i \(0.464686\pi\)
\(674\) −1.51306e7 −1.28294
\(675\) −1.70659e6 −0.144168
\(676\) 1.22410e7 1.03027
\(677\) 8.72440e6 0.731583 0.365792 0.930697i \(-0.380798\pi\)
0.365792 + 0.930697i \(0.380798\pi\)
\(678\) 1.13998e6 0.0952405
\(679\) 3.56338e6 0.296611
\(680\) −143360. −0.0118893
\(681\) −1.16684e7 −0.964145
\(682\) 471000. 0.0387757
\(683\) 2.08822e7 1.71287 0.856437 0.516251i \(-0.172673\pi\)
0.856437 + 0.516251i \(0.172673\pi\)
\(684\) −1.70942e6 −0.139704
\(685\) 4.30324e6 0.350404
\(686\) 470596. 0.0381802
\(687\) 4.04774e6 0.327206
\(688\) 2.66035e6 0.214273
\(689\) 367770. 0.0295140
\(690\) 533232. 0.0426377
\(691\) 8.86813e6 0.706540 0.353270 0.935521i \(-0.385070\pi\)
0.353270 + 0.935521i \(0.385070\pi\)
\(692\) 2.00554e6 0.159208
\(693\) −59535.0 −0.00470911
\(694\) −5.00378e6 −0.394366
\(695\) 8.85080e6 0.695057
\(696\) −2.06554e6 −0.161625
\(697\) 1.41016e6 0.109948
\(698\) 1.62745e7 1.26436
\(699\) −4.76269e6 −0.368688
\(700\) −1.83534e6 −0.141570
\(701\) −1.03054e7 −0.792084 −0.396042 0.918232i \(-0.629617\pi\)
−0.396042 + 0.918232i \(0.629617\pi\)
\(702\) −3.10846e6 −0.238069
\(703\) −6.69261e6 −0.510748
\(704\) −61440.0 −0.00467218
\(705\) −2.97486e6 −0.225421
\(706\) 9.91598e6 0.748727
\(707\) −358435. −0.0269688
\(708\) −4.51397e6 −0.338435
\(709\) −6.85327e6 −0.512014 −0.256007 0.966675i \(-0.582407\pi\)
−0.256007 + 0.966675i \(0.582407\pi\)
\(710\) −2.63110e6 −0.195881
\(711\) 8.08947e6 0.600131
\(712\) −3.72365e6 −0.275276
\(713\) −4.15265e6 −0.305916
\(714\) −141120. −0.0103596
\(715\) 447720. 0.0327523
\(716\) 5.46778e6 0.398592
\(717\) 3.72060e6 0.270281
\(718\) 1.65974e7 1.20152
\(719\) −1.25255e7 −0.903595 −0.451797 0.892121i \(-0.649217\pi\)
−0.451797 + 0.892121i \(0.649217\pi\)
\(720\) 580608. 0.0417399
\(721\) 1.31276e6 0.0940474
\(722\) −2.94535e6 −0.210278
\(723\) 1.13717e7 0.809056
\(724\) −422048. −0.0299237
\(725\) 8.39483e6 0.593153
\(726\) −5.78974e6 −0.407678
\(727\) 1.06505e7 0.747366 0.373683 0.927556i \(-0.378095\pi\)
0.373683 + 0.927556i \(0.378095\pi\)
\(728\) −3.34298e6 −0.233779
\(729\) 531441. 0.0370370
\(730\) −599872. −0.0416631
\(731\) −831360. −0.0575434
\(732\) −722736. −0.0498542
\(733\) −1.80782e7 −1.24278 −0.621390 0.783502i \(-0.713432\pi\)
−0.621390 + 0.783502i \(0.713432\pi\)
\(734\) 1.48182e7 1.01521
\(735\) 605052. 0.0413118
\(736\) 541696. 0.0368605
\(737\) 398280. 0.0270097
\(738\) −5.71115e6 −0.385996
\(739\) −6.39122e6 −0.430500 −0.215250 0.976559i \(-0.569057\pi\)
−0.215250 + 0.976559i \(0.569057\pi\)
\(740\) 2.27315e6 0.152598
\(741\) 1.26545e7 0.846640
\(742\) −67620.0 −0.00450885
\(743\) 7.48524e6 0.497432 0.248716 0.968576i \(-0.419991\pi\)
0.248716 + 0.968576i \(0.419991\pi\)
\(744\) −4.52160e6 −0.299474
\(745\) −1.06027e7 −0.699882
\(746\) −228616. −0.0150404
\(747\) 3.84604e6 0.252181
\(748\) 19200.0 0.00125472
\(749\) 8.83117e6 0.575193
\(750\) −5.50973e6 −0.357665
\(751\) −9.45033e6 −0.611430 −0.305715 0.952123i \(-0.598896\pi\)
−0.305715 + 0.952123i \(0.598896\pi\)
\(752\) −3.02208e6 −0.194877
\(753\) 1.04416e7 0.671088
\(754\) 1.52907e7 0.979488
\(755\) −2.73568e6 −0.174662
\(756\) 571536. 0.0363696
\(757\) −1.32568e7 −0.840813 −0.420406 0.907336i \(-0.638113\pi\)
−0.420406 + 0.907336i \(0.638113\pi\)
\(758\) −1.54171e7 −0.974605
\(759\) −71415.0 −0.00449971
\(760\) −2.36365e6 −0.148439
\(761\) 1.45780e7 0.912509 0.456255 0.889849i \(-0.349191\pi\)
0.456255 + 0.889849i \(0.349191\pi\)
\(762\) −2.09329e6 −0.130600
\(763\) 8.35156e6 0.519345
\(764\) 8.15992e6 0.505769
\(765\) −181440. −0.0112093
\(766\) −1.89184e7 −1.16496
\(767\) 3.34159e7 2.05100
\(768\) 589824. 0.0360844
\(769\) −3.47693e6 −0.212022 −0.106011 0.994365i \(-0.533808\pi\)
−0.106011 + 0.994365i \(0.533808\pi\)
\(770\) −82320.0 −0.00500355
\(771\) −1.15034e7 −0.696929
\(772\) −4.25144e6 −0.256740
\(773\) 1.20953e7 0.728064 0.364032 0.931386i \(-0.381400\pi\)
0.364032 + 0.931386i \(0.381400\pi\)
\(774\) 3.36701e6 0.202019
\(775\) 1.83768e7 1.09905
\(776\) 4.65421e6 0.277454
\(777\) 2.23763e6 0.132965
\(778\) −1.29221e7 −0.765391
\(779\) 2.32500e7 1.37271
\(780\) −4.29811e6 −0.252954
\(781\) 352380. 0.0206721
\(782\) −169280. −0.00989894
\(783\) −2.61419e6 −0.152382
\(784\) 614656. 0.0357143
\(785\) −1.63119e7 −0.944778
\(786\) −3.44884e6 −0.199121
\(787\) −5.54933e6 −0.319377 −0.159689 0.987167i \(-0.551049\pi\)
−0.159689 + 0.987167i \(0.551049\pi\)
\(788\) −6.15702e6 −0.353228
\(789\) −5.60465e6 −0.320521
\(790\) 1.11854e7 0.637654
\(791\) 1.55163e6 0.0881755
\(792\) −77760.0 −0.00440497
\(793\) 5.35025e6 0.302128
\(794\) 1.65695e6 0.0932736
\(795\) −86940.0 −0.00487867
\(796\) −6.77848e6 −0.379184
\(797\) 3.29305e7 1.83634 0.918168 0.396191i \(-0.129668\pi\)
0.918168 + 0.396191i \(0.129668\pi\)
\(798\) −2.32672e6 −0.129341
\(799\) 944400. 0.0523346
\(800\) −2.39718e6 −0.132427
\(801\) −4.71274e6 −0.259533
\(802\) 6.11007e6 0.335436
\(803\) 80340.0 0.00439686
\(804\) −3.82349e6 −0.208603
\(805\) 725788. 0.0394748
\(806\) 3.34724e7 1.81489
\(807\) −1.38995e7 −0.751306
\(808\) −468160. −0.0252270
\(809\) 7.09564e6 0.381171 0.190586 0.981671i \(-0.438961\pi\)
0.190586 + 0.981671i \(0.438961\pi\)
\(810\) 734832. 0.0393528
\(811\) 1.56211e7 0.833988 0.416994 0.908909i \(-0.363084\pi\)
0.416994 + 0.908909i \(0.363084\pi\)
\(812\) −2.81142e6 −0.149636
\(813\) 9.24253e6 0.490416
\(814\) −304440. −0.0161043
\(815\) −9.72740e6 −0.512983
\(816\) −184320. −0.00969052
\(817\) −1.37070e7 −0.718437
\(818\) −1.13470e7 −0.592921
\(819\) −4.23095e6 −0.220409
\(820\) −7.89690e6 −0.410130
\(821\) 2.26882e7 1.17474 0.587371 0.809318i \(-0.300163\pi\)
0.587371 + 0.809318i \(0.300163\pi\)
\(822\) 5.53273e6 0.285601
\(823\) 1.61712e7 0.832230 0.416115 0.909312i \(-0.363391\pi\)
0.416115 + 0.909312i \(0.363391\pi\)
\(824\) 1.71462e6 0.0879733
\(825\) 316035. 0.0161659
\(826\) −6.14401e6 −0.313330
\(827\) 2.97150e6 0.151082 0.0755410 0.997143i \(-0.475932\pi\)
0.0755410 + 0.997143i \(0.475932\pi\)
\(828\) 685584. 0.0347524
\(829\) −3.42265e7 −1.72972 −0.864861 0.502011i \(-0.832594\pi\)
−0.864861 + 0.502011i \(0.832594\pi\)
\(830\) 5.31798e6 0.267949
\(831\) −8.06819e6 −0.405297
\(832\) −4.36634e6 −0.218680
\(833\) −192080. −0.00959113
\(834\) 1.13796e7 0.566516
\(835\) 4.77565e6 0.237037
\(836\) 316560. 0.0156654
\(837\) −5.72265e6 −0.282347
\(838\) −312456. −0.0153702
\(839\) 3.58526e7 1.75839 0.879197 0.476458i \(-0.158080\pi\)
0.879197 + 0.476458i \(0.158080\pi\)
\(840\) 790272. 0.0386437
\(841\) −7.65175e6 −0.373053
\(842\) −6.34214e6 −0.308287
\(843\) 7.14562e6 0.346315
\(844\) 6.19291e6 0.299253
\(845\) 2.14218e7 1.03208
\(846\) −3.82482e6 −0.183732
\(847\) −7.88047e6 −0.377436
\(848\) −88320.0 −0.00421764
\(849\) −1.98709e6 −0.0946126
\(850\) 749120. 0.0355635
\(851\) 2.68415e6 0.127052
\(852\) −3.38285e6 −0.159655
\(853\) −2.14702e7 −1.01033 −0.505165 0.863023i \(-0.668568\pi\)
−0.505165 + 0.863023i \(0.668568\pi\)
\(854\) −983724. −0.0461560
\(855\) −2.99149e6 −0.139950
\(856\) 1.15346e7 0.538044
\(857\) −1.90679e7 −0.886853 −0.443426 0.896311i \(-0.646237\pi\)
−0.443426 + 0.896311i \(0.646237\pi\)
\(858\) 575640. 0.0266952
\(859\) −3.81485e7 −1.76398 −0.881991 0.471266i \(-0.843797\pi\)
−0.881991 + 0.471266i \(0.843797\pi\)
\(860\) 4.65562e6 0.214650
\(861\) −7.77351e6 −0.357363
\(862\) −4.08640e6 −0.187315
\(863\) 3.78204e7 1.72862 0.864309 0.502961i \(-0.167756\pi\)
0.864309 + 0.502961i \(0.167756\pi\)
\(864\) 746496. 0.0340207
\(865\) 3.50969e6 0.159488
\(866\) 986156. 0.0446839
\(867\) −1.27211e7 −0.574748
\(868\) −6.15440e6 −0.277259
\(869\) −1.49805e6 −0.0672941
\(870\) −3.61469e6 −0.161910
\(871\) 2.83044e7 1.26418
\(872\) 1.09082e7 0.485803
\(873\) 5.89048e6 0.261586
\(874\) −2.79100e6 −0.123590
\(875\) −7.49935e6 −0.331134
\(876\) −771264. −0.0339581
\(877\) 1.39887e7 0.614157 0.307079 0.951684i \(-0.400649\pi\)
0.307079 + 0.951684i \(0.400649\pi\)
\(878\) −2.47917e6 −0.108535
\(879\) −4.87681e6 −0.212894
\(880\) −107520. −0.00468040
\(881\) 1.28587e7 0.558160 0.279080 0.960268i \(-0.409971\pi\)
0.279080 + 0.960268i \(0.409971\pi\)
\(882\) 777924. 0.0336718
\(883\) 2.84134e7 1.22637 0.613184 0.789940i \(-0.289888\pi\)
0.613184 + 0.789940i \(0.289888\pi\)
\(884\) 1.36448e6 0.0587268
\(885\) −7.89944e6 −0.339030
\(886\) −2.29780e7 −0.983396
\(887\) −1.59646e7 −0.681315 −0.340657 0.940187i \(-0.610650\pi\)
−0.340657 + 0.940187i \(0.610650\pi\)
\(888\) 2.92262e6 0.124377
\(889\) −2.84920e6 −0.120912
\(890\) −6.51638e6 −0.275760
\(891\) −98415.0 −0.00415305
\(892\) −4.79427e6 −0.201749
\(893\) 1.55708e7 0.653405
\(894\) −1.36320e7 −0.570448
\(895\) 9.56861e6 0.399293
\(896\) 802816. 0.0334077
\(897\) −5.07523e6 −0.210608
\(898\) 1.92254e7 0.795582
\(899\) 2.81501e7 1.16166
\(900\) −3.03394e6 −0.124853
\(901\) 27600.0 0.00113265
\(902\) 1.05762e6 0.0432826
\(903\) 4.58287e6 0.187033
\(904\) 2.02662e6 0.0824807
\(905\) −738584. −0.0299763
\(906\) −3.51731e6 −0.142361
\(907\) −1.77405e7 −0.716056 −0.358028 0.933711i \(-0.616551\pi\)
−0.358028 + 0.933711i \(0.616551\pi\)
\(908\) −2.07438e7 −0.834974
\(909\) −592515. −0.0237843
\(910\) −5.85021e6 −0.234190
\(911\) 771952. 0.0308173 0.0154086 0.999881i \(-0.495095\pi\)
0.0154086 + 0.999881i \(0.495095\pi\)
\(912\) −3.03898e6 −0.120987
\(913\) −712230. −0.0282777
\(914\) −1.06179e7 −0.420410
\(915\) −1.26479e6 −0.0499419
\(916\) 7.19598e6 0.283368
\(917\) −4.69425e6 −0.184350
\(918\) −233280. −0.00913631
\(919\) −5.43187e6 −0.212159 −0.106079 0.994358i \(-0.533830\pi\)
−0.106079 + 0.994358i \(0.533830\pi\)
\(920\) 947968. 0.0369253
\(921\) −2.58410e7 −1.00383
\(922\) 2.58319e7 1.00076
\(923\) 2.50425e7 0.967549
\(924\) −105840. −0.00407821
\(925\) −1.18782e7 −0.456455
\(926\) −1.35814e7 −0.520496
\(927\) 2.17007e6 0.0829420
\(928\) −3.67206e6 −0.139972
\(929\) 8.30088e6 0.315562 0.157781 0.987474i \(-0.449566\pi\)
0.157781 + 0.987474i \(0.449566\pi\)
\(930\) −7.91280e6 −0.300001
\(931\) −3.16692e6 −0.119746
\(932\) −8.46701e6 −0.319294
\(933\) 2.15014e7 0.808654
\(934\) −1.45196e7 −0.544611
\(935\) 33600.0 0.00125693
\(936\) −5.52614e6 −0.206173
\(937\) −8.19947e6 −0.305096 −0.152548 0.988296i \(-0.548748\pi\)
−0.152548 + 0.988296i \(0.548748\pi\)
\(938\) −5.20419e6 −0.193128
\(939\) 7.65843e6 0.283450
\(940\) −5.28864e6 −0.195220
\(941\) −1.01275e7 −0.372847 −0.186423 0.982470i \(-0.559690\pi\)
−0.186423 + 0.982470i \(0.559690\pi\)
\(942\) −2.09724e7 −0.770054
\(943\) −9.32468e6 −0.341472
\(944\) −8.02483e6 −0.293093
\(945\) 1.00019e6 0.0364336
\(946\) −623520. −0.0226528
\(947\) 1.46006e7 0.529050 0.264525 0.964379i \(-0.414785\pi\)
0.264525 + 0.964379i \(0.414785\pi\)
\(948\) 1.43813e7 0.519729
\(949\) 5.70950e6 0.205794
\(950\) 1.23511e7 0.444015
\(951\) −222678. −0.00798410
\(952\) −250880. −0.00897168
\(953\) −2.15955e7 −0.770249 −0.385124 0.922865i \(-0.625841\pi\)
−0.385124 + 0.922865i \(0.625841\pi\)
\(954\) −111780. −0.00397643
\(955\) 1.42799e7 0.506659
\(956\) 6.61440e6 0.234070
\(957\) 484110. 0.0170869
\(958\) −2.40210e6 −0.0845623
\(959\) 7.53066e6 0.264415
\(960\) 1.03219e6 0.0361478
\(961\) 3.29933e7 1.15244
\(962\) −2.16355e7 −0.753755
\(963\) 1.45985e7 0.507273
\(964\) 2.02163e7 0.700663
\(965\) −7.44002e6 −0.257191
\(966\) 933156. 0.0321745
\(967\) −1.45924e7 −0.501835 −0.250917 0.968008i \(-0.580732\pi\)
−0.250917 + 0.968008i \(0.580732\pi\)
\(968\) −1.02929e7 −0.353059
\(969\) 949680. 0.0324914
\(970\) 8.14486e6 0.277942
\(971\) 4.07609e7 1.38738 0.693690 0.720274i \(-0.255984\pi\)
0.693690 + 0.720274i \(0.255984\pi\)
\(972\) 944784. 0.0320750
\(973\) 1.54889e7 0.524492
\(974\) −9.62750e6 −0.325174
\(975\) 2.24596e7 0.756641
\(976\) −1.28486e6 −0.0431750
\(977\) 3.40986e7 1.14288 0.571439 0.820645i \(-0.306386\pi\)
0.571439 + 0.820645i \(0.306386\pi\)
\(978\) −1.25067e7 −0.418113
\(979\) 872730. 0.0291020
\(980\) 1.07565e6 0.0357771
\(981\) 1.38056e7 0.458020
\(982\) −1.10997e7 −0.367310
\(983\) 4.01373e7 1.32484 0.662421 0.749131i \(-0.269529\pi\)
0.662421 + 0.749131i \(0.269529\pi\)
\(984\) −1.01532e7 −0.334282
\(985\) −1.07748e7 −0.353849
\(986\) 1.14752e6 0.0375896
\(987\) −5.20600e6 −0.170103
\(988\) 2.24969e7 0.733212
\(989\) 5.49737e6 0.178716
\(990\) −136080. −0.00441272
\(991\) −2.97245e7 −0.961458 −0.480729 0.876869i \(-0.659628\pi\)
−0.480729 + 0.876869i \(0.659628\pi\)
\(992\) −8.03840e6 −0.259352
\(993\) −2.24832e7 −0.723578
\(994\) −4.60443e6 −0.147812
\(995\) −1.18623e7 −0.379850
\(996\) 6.83741e6 0.218395
\(997\) 486768. 0.0155090 0.00775451 0.999970i \(-0.497532\pi\)
0.00775451 + 0.999970i \(0.497532\pi\)
\(998\) 1.47549e7 0.468931
\(999\) 3.69895e6 0.117264
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 966.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.6.a.b.1.1 1 1.1 even 1 trivial