Properties

Label 546.6.a.h.1.1
Level $546$
Weight $6$
Character 546.1
Self dual yes
Analytic conductor $87.570$
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: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(87.5695656179\)
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

\(f(q)\) \(=\) \(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -16.0000 q^{5} +36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -16.0000 q^{5} +36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} -64.0000 q^{10} -114.000 q^{11} +144.000 q^{12} -169.000 q^{13} -196.000 q^{14} -144.000 q^{15} +256.000 q^{16} +538.000 q^{17} +324.000 q^{18} -536.000 q^{19} -256.000 q^{20} -441.000 q^{21} -456.000 q^{22} -4596.00 q^{23} +576.000 q^{24} -2869.00 q^{25} -676.000 q^{26} +729.000 q^{27} -784.000 q^{28} +1594.00 q^{29} -576.000 q^{30} +9364.00 q^{31} +1024.00 q^{32} -1026.00 q^{33} +2152.00 q^{34} +784.000 q^{35} +1296.00 q^{36} -12002.0 q^{37} -2144.00 q^{38} -1521.00 q^{39} -1024.00 q^{40} +4928.00 q^{41} -1764.00 q^{42} -14284.0 q^{43} -1824.00 q^{44} -1296.00 q^{45} -18384.0 q^{46} -22262.0 q^{47} +2304.00 q^{48} +2401.00 q^{49} -11476.0 q^{50} +4842.00 q^{51} -2704.00 q^{52} -474.000 q^{53} +2916.00 q^{54} +1824.00 q^{55} -3136.00 q^{56} -4824.00 q^{57} +6376.00 q^{58} -4182.00 q^{59} -2304.00 q^{60} -21830.0 q^{61} +37456.0 q^{62} -3969.00 q^{63} +4096.00 q^{64} +2704.00 q^{65} -4104.00 q^{66} +20780.0 q^{67} +8608.00 q^{68} -41364.0 q^{69} +3136.00 q^{70} +18682.0 q^{71} +5184.00 q^{72} -37866.0 q^{73} -48008.0 q^{74} -25821.0 q^{75} -8576.00 q^{76} +5586.00 q^{77} -6084.00 q^{78} -27840.0 q^{79} -4096.00 q^{80} +6561.00 q^{81} +19712.0 q^{82} -101914. q^{83} -7056.00 q^{84} -8608.00 q^{85} -57136.0 q^{86} +14346.0 q^{87} -7296.00 q^{88} -77644.0 q^{89} -5184.00 q^{90} +8281.00 q^{91} -73536.0 q^{92} +84276.0 q^{93} -89048.0 q^{94} +8576.00 q^{95} +9216.00 q^{96} -60050.0 q^{97} +9604.00 q^{98} -9234.00 q^{99} +O(q^{100})\)

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
\(5\) −16.0000 −0.286217 −0.143108 0.989707i \(-0.545710\pi\)
−0.143108 + 0.989707i \(0.545710\pi\)
\(6\) 36.0000 0.408248
\(7\) −49.0000 −0.377964
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) −64.0000 −0.202386
\(11\) −114.000 −0.284069 −0.142034 0.989862i \(-0.545364\pi\)
−0.142034 + 0.989862i \(0.545364\pi\)
\(12\) 144.000 0.288675
\(13\) −169.000 −0.277350
\(14\) −196.000 −0.267261
\(15\) −144.000 −0.165247
\(16\) 256.000 0.250000
\(17\) 538.000 0.451502 0.225751 0.974185i \(-0.427516\pi\)
0.225751 + 0.974185i \(0.427516\pi\)
\(18\) 324.000 0.235702
\(19\) −536.000 −0.340628 −0.170314 0.985390i \(-0.554478\pi\)
−0.170314 + 0.985390i \(0.554478\pi\)
\(20\) −256.000 −0.143108
\(21\) −441.000 −0.218218
\(22\) −456.000 −0.200867
\(23\) −4596.00 −1.81159 −0.905796 0.423714i \(-0.860726\pi\)
−0.905796 + 0.423714i \(0.860726\pi\)
\(24\) 576.000 0.204124
\(25\) −2869.00 −0.918080
\(26\) −676.000 −0.196116
\(27\) 729.000 0.192450
\(28\) −784.000 −0.188982
\(29\) 1594.00 0.351960 0.175980 0.984394i \(-0.443691\pi\)
0.175980 + 0.984394i \(0.443691\pi\)
\(30\) −576.000 −0.116847
\(31\) 9364.00 1.75008 0.875039 0.484053i \(-0.160836\pi\)
0.875039 + 0.484053i \(0.160836\pi\)
\(32\) 1024.00 0.176777
\(33\) −1026.00 −0.164007
\(34\) 2152.00 0.319260
\(35\) 784.000 0.108180
\(36\) 1296.00 0.166667
\(37\) −12002.0 −1.44128 −0.720642 0.693308i \(-0.756153\pi\)
−0.720642 + 0.693308i \(0.756153\pi\)
\(38\) −2144.00 −0.240861
\(39\) −1521.00 −0.160128
\(40\) −1024.00 −0.101193
\(41\) 4928.00 0.457837 0.228919 0.973446i \(-0.426481\pi\)
0.228919 + 0.973446i \(0.426481\pi\)
\(42\) −1764.00 −0.154303
\(43\) −14284.0 −1.17809 −0.589045 0.808100i \(-0.700496\pi\)
−0.589045 + 0.808100i \(0.700496\pi\)
\(44\) −1824.00 −0.142034
\(45\) −1296.00 −0.0954056
\(46\) −18384.0 −1.28099
\(47\) −22262.0 −1.47001 −0.735004 0.678063i \(-0.762820\pi\)
−0.735004 + 0.678063i \(0.762820\pi\)
\(48\) 2304.00 0.144338
\(49\) 2401.00 0.142857
\(50\) −11476.0 −0.649181
\(51\) 4842.00 0.260675
\(52\) −2704.00 −0.138675
\(53\) −474.000 −0.0231787 −0.0115893 0.999933i \(-0.503689\pi\)
−0.0115893 + 0.999933i \(0.503689\pi\)
\(54\) 2916.00 0.136083
\(55\) 1824.00 0.0813052
\(56\) −3136.00 −0.133631
\(57\) −4824.00 −0.196662
\(58\) 6376.00 0.248873
\(59\) −4182.00 −0.156406 −0.0782031 0.996937i \(-0.524918\pi\)
−0.0782031 + 0.996937i \(0.524918\pi\)
\(60\) −2304.00 −0.0826236
\(61\) −21830.0 −0.751154 −0.375577 0.926791i \(-0.622555\pi\)
−0.375577 + 0.926791i \(0.622555\pi\)
\(62\) 37456.0 1.23749
\(63\) −3969.00 −0.125988
\(64\) 4096.00 0.125000
\(65\) 2704.00 0.0793822
\(66\) −4104.00 −0.115970
\(67\) 20780.0 0.565534 0.282767 0.959189i \(-0.408748\pi\)
0.282767 + 0.959189i \(0.408748\pi\)
\(68\) 8608.00 0.225751
\(69\) −41364.0 −1.04592
\(70\) 3136.00 0.0764946
\(71\) 18682.0 0.439823 0.219911 0.975520i \(-0.429423\pi\)
0.219911 + 0.975520i \(0.429423\pi\)
\(72\) 5184.00 0.117851
\(73\) −37866.0 −0.831653 −0.415827 0.909444i \(-0.636508\pi\)
−0.415827 + 0.909444i \(0.636508\pi\)
\(74\) −48008.0 −1.01914
\(75\) −25821.0 −0.530054
\(76\) −8576.00 −0.170314
\(77\) 5586.00 0.107368
\(78\) −6084.00 −0.113228
\(79\) −27840.0 −0.501882 −0.250941 0.968002i \(-0.580740\pi\)
−0.250941 + 0.968002i \(0.580740\pi\)
\(80\) −4096.00 −0.0715542
\(81\) 6561.00 0.111111
\(82\) 19712.0 0.323740
\(83\) −101914. −1.62382 −0.811911 0.583781i \(-0.801573\pi\)
−0.811911 + 0.583781i \(0.801573\pi\)
\(84\) −7056.00 −0.109109
\(85\) −8608.00 −0.129228
\(86\) −57136.0 −0.833036
\(87\) 14346.0 0.203204
\(88\) −7296.00 −0.100433
\(89\) −77644.0 −1.03904 −0.519521 0.854458i \(-0.673889\pi\)
−0.519521 + 0.854458i \(0.673889\pi\)
\(90\) −5184.00 −0.0674619
\(91\) 8281.00 0.104828
\(92\) −73536.0 −0.905796
\(93\) 84276.0 1.01041
\(94\) −89048.0 −1.03945
\(95\) 8576.00 0.0974935
\(96\) 9216.00 0.102062
\(97\) −60050.0 −0.648013 −0.324006 0.946055i \(-0.605030\pi\)
−0.324006 + 0.946055i \(0.605030\pi\)
\(98\) 9604.00 0.101015
\(99\) −9234.00 −0.0946895
\(100\) −45904.0 −0.459040
\(101\) −28238.0 −0.275442 −0.137721 0.990471i \(-0.543978\pi\)
−0.137721 + 0.990471i \(0.543978\pi\)
\(102\) 19368.0 0.184325
\(103\) 192664. 1.78940 0.894700 0.446667i \(-0.147389\pi\)
0.894700 + 0.446667i \(0.147389\pi\)
\(104\) −10816.0 −0.0980581
\(105\) 7056.00 0.0624576
\(106\) −1896.00 −0.0163898
\(107\) 126192. 1.06555 0.532773 0.846258i \(-0.321150\pi\)
0.532773 + 0.846258i \(0.321150\pi\)
\(108\) 11664.0 0.0962250
\(109\) −161350. −1.30078 −0.650388 0.759602i \(-0.725394\pi\)
−0.650388 + 0.759602i \(0.725394\pi\)
\(110\) 7296.00 0.0574914
\(111\) −108018. −0.832125
\(112\) −12544.0 −0.0944911
\(113\) 162006. 1.19353 0.596767 0.802414i \(-0.296452\pi\)
0.596767 + 0.802414i \(0.296452\pi\)
\(114\) −19296.0 −0.139061
\(115\) 73536.0 0.518508
\(116\) 25504.0 0.175980
\(117\) −13689.0 −0.0924500
\(118\) −16728.0 −0.110596
\(119\) −26362.0 −0.170652
\(120\) −9216.00 −0.0584237
\(121\) −148055. −0.919305
\(122\) −87320.0 −0.531146
\(123\) 44352.0 0.264332
\(124\) 149824. 0.875039
\(125\) 95904.0 0.548987
\(126\) −15876.0 −0.0890871
\(127\) 22752.0 0.125173 0.0625864 0.998040i \(-0.480065\pi\)
0.0625864 + 0.998040i \(0.480065\pi\)
\(128\) 16384.0 0.0883883
\(129\) −128556. −0.680171
\(130\) 10816.0 0.0561317
\(131\) −282080. −1.43613 −0.718065 0.695976i \(-0.754972\pi\)
−0.718065 + 0.695976i \(0.754972\pi\)
\(132\) −16416.0 −0.0820035
\(133\) 26264.0 0.128745
\(134\) 83120.0 0.399893
\(135\) −11664.0 −0.0550824
\(136\) 34432.0 0.159630
\(137\) −83064.0 −0.378104 −0.189052 0.981967i \(-0.560541\pi\)
−0.189052 + 0.981967i \(0.560541\pi\)
\(138\) −165456. −0.739579
\(139\) −61420.0 −0.269633 −0.134816 0.990871i \(-0.543044\pi\)
−0.134816 + 0.990871i \(0.543044\pi\)
\(140\) 12544.0 0.0540899
\(141\) −200358. −0.848709
\(142\) 74728.0 0.311002
\(143\) 19266.0 0.0787864
\(144\) 20736.0 0.0833333
\(145\) −25504.0 −0.100737
\(146\) −151464. −0.588068
\(147\) 21609.0 0.0824786
\(148\) −192032. −0.720642
\(149\) −108932. −0.401966 −0.200983 0.979595i \(-0.564414\pi\)
−0.200983 + 0.979595i \(0.564414\pi\)
\(150\) −103284. −0.374805
\(151\) 345292. 1.23238 0.616189 0.787598i \(-0.288676\pi\)
0.616189 + 0.787598i \(0.288676\pi\)
\(152\) −34304.0 −0.120430
\(153\) 43578.0 0.150501
\(154\) 22344.0 0.0759205
\(155\) −149824. −0.500901
\(156\) −24336.0 −0.0800641
\(157\) 331998. 1.07495 0.537473 0.843281i \(-0.319379\pi\)
0.537473 + 0.843281i \(0.319379\pi\)
\(158\) −111360. −0.354884
\(159\) −4266.00 −0.0133822
\(160\) −16384.0 −0.0505964
\(161\) 225204. 0.684717
\(162\) 26244.0 0.0785674
\(163\) 144952. 0.427322 0.213661 0.976908i \(-0.431461\pi\)
0.213661 + 0.976908i \(0.431461\pi\)
\(164\) 78848.0 0.228919
\(165\) 16416.0 0.0469416
\(166\) −407656. −1.14822
\(167\) −28494.0 −0.0790610 −0.0395305 0.999218i \(-0.512586\pi\)
−0.0395305 + 0.999218i \(0.512586\pi\)
\(168\) −28224.0 −0.0771517
\(169\) 28561.0 0.0769231
\(170\) −34432.0 −0.0913776
\(171\) −43416.0 −0.113543
\(172\) −228544. −0.589045
\(173\) 217194. 0.551738 0.275869 0.961195i \(-0.411034\pi\)
0.275869 + 0.961195i \(0.411034\pi\)
\(174\) 57384.0 0.143687
\(175\) 140581. 0.347002
\(176\) −29184.0 −0.0710171
\(177\) −37638.0 −0.0903012
\(178\) −310576. −0.734713
\(179\) −594476. −1.38676 −0.693381 0.720571i \(-0.743880\pi\)
−0.693381 + 0.720571i \(0.743880\pi\)
\(180\) −20736.0 −0.0477028
\(181\) −127050. −0.288256 −0.144128 0.989559i \(-0.546038\pi\)
−0.144128 + 0.989559i \(0.546038\pi\)
\(182\) 33124.0 0.0741249
\(183\) −196470. −0.433679
\(184\) −294144. −0.640495
\(185\) 192032. 0.412519
\(186\) 337104. 0.714466
\(187\) −61332.0 −0.128258
\(188\) −356192. −0.735004
\(189\) −35721.0 −0.0727393
\(190\) 34304.0 0.0689383
\(191\) −415064. −0.823250 −0.411625 0.911353i \(-0.635039\pi\)
−0.411625 + 0.911353i \(0.635039\pi\)
\(192\) 36864.0 0.0721688
\(193\) 409546. 0.791424 0.395712 0.918375i \(-0.370498\pi\)
0.395712 + 0.918375i \(0.370498\pi\)
\(194\) −240200. −0.458214
\(195\) 24336.0 0.0458314
\(196\) 38416.0 0.0714286
\(197\) 757488. 1.39063 0.695313 0.718707i \(-0.255266\pi\)
0.695313 + 0.718707i \(0.255266\pi\)
\(198\) −36936.0 −0.0669556
\(199\) −722336. −1.29302 −0.646512 0.762904i \(-0.723773\pi\)
−0.646512 + 0.762904i \(0.723773\pi\)
\(200\) −183616. −0.324590
\(201\) 187020. 0.326511
\(202\) −112952. −0.194767
\(203\) −78106.0 −0.133028
\(204\) 77472.0 0.130337
\(205\) −78848.0 −0.131041
\(206\) 770656. 1.26530
\(207\) −372276. −0.603864
\(208\) −43264.0 −0.0693375
\(209\) 61104.0 0.0967618
\(210\) 28224.0 0.0441642
\(211\) 255476. 0.395043 0.197521 0.980299i \(-0.436711\pi\)
0.197521 + 0.980299i \(0.436711\pi\)
\(212\) −7584.00 −0.0115893
\(213\) 168138. 0.253932
\(214\) 504768. 0.753455
\(215\) 228544. 0.337189
\(216\) 46656.0 0.0680414
\(217\) −458836. −0.661467
\(218\) −645400. −0.919788
\(219\) −340794. −0.480155
\(220\) 29184.0 0.0406526
\(221\) −90922.0 −0.125224
\(222\) −432072. −0.588401
\(223\) −203212. −0.273645 −0.136822 0.990596i \(-0.543689\pi\)
−0.136822 + 0.990596i \(0.543689\pi\)
\(224\) −50176.0 −0.0668153
\(225\) −232389. −0.306027
\(226\) 648024. 0.843956
\(227\) 116722. 0.150345 0.0751723 0.997171i \(-0.476049\pi\)
0.0751723 + 0.997171i \(0.476049\pi\)
\(228\) −77184.0 −0.0983309
\(229\) −866934. −1.09244 −0.546220 0.837642i \(-0.683934\pi\)
−0.546220 + 0.837642i \(0.683934\pi\)
\(230\) 294144. 0.366640
\(231\) 50274.0 0.0619888
\(232\) 102016. 0.124437
\(233\) −1.32089e6 −1.59396 −0.796979 0.604007i \(-0.793570\pi\)
−0.796979 + 0.604007i \(0.793570\pi\)
\(234\) −54756.0 −0.0653720
\(235\) 356192. 0.420741
\(236\) −66912.0 −0.0782031
\(237\) −250560. −0.289762
\(238\) −105448. −0.120669
\(239\) 311802. 0.353089 0.176544 0.984293i \(-0.443508\pi\)
0.176544 + 0.984293i \(0.443508\pi\)
\(240\) −36864.0 −0.0413118
\(241\) 116326. 0.129013 0.0645066 0.997917i \(-0.479453\pi\)
0.0645066 + 0.997917i \(0.479453\pi\)
\(242\) −592220. −0.650047
\(243\) 59049.0 0.0641500
\(244\) −349280. −0.375577
\(245\) −38416.0 −0.0408881
\(246\) 177408. 0.186911
\(247\) 90584.0 0.0944733
\(248\) 599296. 0.618746
\(249\) −917226. −0.937514
\(250\) 383616. 0.388192
\(251\) 1.03090e6 1.03283 0.516417 0.856337i \(-0.327265\pi\)
0.516417 + 0.856337i \(0.327265\pi\)
\(252\) −63504.0 −0.0629941
\(253\) 523944. 0.514616
\(254\) 91008.0 0.0885106
\(255\) −77472.0 −0.0746095
\(256\) 65536.0 0.0625000
\(257\) 525774. 0.496554 0.248277 0.968689i \(-0.420136\pi\)
0.248277 + 0.968689i \(0.420136\pi\)
\(258\) −514224. −0.480953
\(259\) 588098. 0.544754
\(260\) 43264.0 0.0396911
\(261\) 129114. 0.117320
\(262\) −1.12832e6 −1.01550
\(263\) 1.96271e6 1.74971 0.874855 0.484384i \(-0.160956\pi\)
0.874855 + 0.484384i \(0.160956\pi\)
\(264\) −65664.0 −0.0579852
\(265\) 7584.00 0.00663412
\(266\) 105056. 0.0910368
\(267\) −698796. −0.599891
\(268\) 332480. 0.282767
\(269\) −870174. −0.733205 −0.366602 0.930378i \(-0.619479\pi\)
−0.366602 + 0.930378i \(0.619479\pi\)
\(270\) −46656.0 −0.0389492
\(271\) −492496. −0.407361 −0.203681 0.979037i \(-0.565290\pi\)
−0.203681 + 0.979037i \(0.565290\pi\)
\(272\) 137728. 0.112876
\(273\) 74529.0 0.0605228
\(274\) −332256. −0.267360
\(275\) 327066. 0.260798
\(276\) −661824. −0.522962
\(277\) −201378. −0.157693 −0.0788465 0.996887i \(-0.525124\pi\)
−0.0788465 + 0.996887i \(0.525124\pi\)
\(278\) −245680. −0.190659
\(279\) 758484. 0.583359
\(280\) 50176.0 0.0382473
\(281\) 1.79382e6 1.35523 0.677614 0.735418i \(-0.263014\pi\)
0.677614 + 0.735418i \(0.263014\pi\)
\(282\) −801432. −0.600128
\(283\) 1.13907e6 0.845442 0.422721 0.906260i \(-0.361075\pi\)
0.422721 + 0.906260i \(0.361075\pi\)
\(284\) 298912. 0.219911
\(285\) 77184.0 0.0562879
\(286\) 77064.0 0.0557104
\(287\) −241472. −0.173046
\(288\) 82944.0 0.0589256
\(289\) −1.13041e6 −0.796146
\(290\) −102016. −0.0712317
\(291\) −540450. −0.374130
\(292\) −605856. −0.415827
\(293\) −545244. −0.371041 −0.185520 0.982640i \(-0.559397\pi\)
−0.185520 + 0.982640i \(0.559397\pi\)
\(294\) 86436.0 0.0583212
\(295\) 66912.0 0.0447661
\(296\) −768128. −0.509571
\(297\) −83106.0 −0.0546690
\(298\) −435728. −0.284233
\(299\) 776724. 0.502445
\(300\) −413136. −0.265027
\(301\) 699916. 0.445276
\(302\) 1.38117e6 0.871423
\(303\) −254142. −0.159027
\(304\) −137216. −0.0851571
\(305\) 349280. 0.214993
\(306\) 174312. 0.106420
\(307\) −1.67382e6 −1.01359 −0.506796 0.862066i \(-0.669170\pi\)
−0.506796 + 0.862066i \(0.669170\pi\)
\(308\) 89376.0 0.0536839
\(309\) 1.73398e6 1.03311
\(310\) −599296. −0.354191
\(311\) −1.17590e6 −0.689397 −0.344699 0.938713i \(-0.612019\pi\)
−0.344699 + 0.938713i \(0.612019\pi\)
\(312\) −97344.0 −0.0566139
\(313\) −513002. −0.295977 −0.147989 0.988989i \(-0.547280\pi\)
−0.147989 + 0.988989i \(0.547280\pi\)
\(314\) 1.32799e6 0.760101
\(315\) 63504.0 0.0360599
\(316\) −445440. −0.250941
\(317\) −217416. −0.121519 −0.0607594 0.998152i \(-0.519352\pi\)
−0.0607594 + 0.998152i \(0.519352\pi\)
\(318\) −17064.0 −0.00946266
\(319\) −181716. −0.0999808
\(320\) −65536.0 −0.0357771
\(321\) 1.13573e6 0.615194
\(322\) 900816. 0.484168
\(323\) −288368. −0.153794
\(324\) 104976. 0.0555556
\(325\) 484861. 0.254630
\(326\) 579808. 0.302162
\(327\) −1.45215e6 −0.751004
\(328\) 315392. 0.161870
\(329\) 1.09084e6 0.555611
\(330\) 65664.0 0.0331927
\(331\) 1.79477e6 0.900408 0.450204 0.892926i \(-0.351351\pi\)
0.450204 + 0.892926i \(0.351351\pi\)
\(332\) −1.63062e6 −0.811911
\(333\) −972162. −0.480428
\(334\) −113976. −0.0559046
\(335\) −332480. −0.161865
\(336\) −112896. −0.0545545
\(337\) 4.05965e6 1.94721 0.973606 0.228234i \(-0.0732950\pi\)
0.973606 + 0.228234i \(0.0732950\pi\)
\(338\) 114244. 0.0543928
\(339\) 1.45805e6 0.689087
\(340\) −137728. −0.0646138
\(341\) −1.06750e6 −0.497142
\(342\) −173664. −0.0802869
\(343\) −117649. −0.0539949
\(344\) −914176. −0.416518
\(345\) 661824. 0.299361
\(346\) 868776. 0.390137
\(347\) −3.06307e6 −1.36563 −0.682815 0.730591i \(-0.739244\pi\)
−0.682815 + 0.730591i \(0.739244\pi\)
\(348\) 229536. 0.101602
\(349\) 3.31390e6 1.45638 0.728192 0.685373i \(-0.240361\pi\)
0.728192 + 0.685373i \(0.240361\pi\)
\(350\) 562324. 0.245367
\(351\) −123201. −0.0533761
\(352\) −116736. −0.0502167
\(353\) −160208. −0.0684301 −0.0342151 0.999414i \(-0.510893\pi\)
−0.0342151 + 0.999414i \(0.510893\pi\)
\(354\) −150552. −0.0638526
\(355\) −298912. −0.125885
\(356\) −1.24230e6 −0.519521
\(357\) −237258. −0.0985259
\(358\) −2.37790e6 −0.980588
\(359\) 2.23895e6 0.916873 0.458436 0.888727i \(-0.348410\pi\)
0.458436 + 0.888727i \(0.348410\pi\)
\(360\) −82944.0 −0.0337310
\(361\) −2.18880e6 −0.883972
\(362\) −508200. −0.203828
\(363\) −1.33250e6 −0.530761
\(364\) 132496. 0.0524142
\(365\) 605856. 0.238033
\(366\) −785880. −0.306657
\(367\) 1.13122e6 0.438413 0.219207 0.975678i \(-0.429653\pi\)
0.219207 + 0.975678i \(0.429653\pi\)
\(368\) −1.17658e6 −0.452898
\(369\) 399168. 0.152612
\(370\) 768128. 0.291695
\(371\) 23226.0 0.00876072
\(372\) 1.34842e6 0.505204
\(373\) 5.03396e6 1.87343 0.936716 0.350091i \(-0.113849\pi\)
0.936716 + 0.350091i \(0.113849\pi\)
\(374\) −245328. −0.0906918
\(375\) 863136. 0.316958
\(376\) −1.42477e6 −0.519726
\(377\) −269386. −0.0976161
\(378\) −142884. −0.0514344
\(379\) 3.69438e6 1.32113 0.660563 0.750771i \(-0.270318\pi\)
0.660563 + 0.750771i \(0.270318\pi\)
\(380\) 137216. 0.0487468
\(381\) 204768. 0.0722686
\(382\) −1.66026e6 −0.582126
\(383\) 3.63011e6 1.26451 0.632256 0.774760i \(-0.282129\pi\)
0.632256 + 0.774760i \(0.282129\pi\)
\(384\) 147456. 0.0510310
\(385\) −89376.0 −0.0307305
\(386\) 1.63818e6 0.559622
\(387\) −1.15700e6 −0.392697
\(388\) −960800. −0.324006
\(389\) 3.04213e6 1.01930 0.509651 0.860381i \(-0.329774\pi\)
0.509651 + 0.860381i \(0.329774\pi\)
\(390\) 97344.0 0.0324077
\(391\) −2.47265e6 −0.817938
\(392\) 153664. 0.0505076
\(393\) −2.53872e6 −0.829151
\(394\) 3.02995e6 0.983321
\(395\) 445440. 0.143647
\(396\) −147744. −0.0473448
\(397\) 4.87184e6 1.55137 0.775687 0.631118i \(-0.217403\pi\)
0.775687 + 0.631118i \(0.217403\pi\)
\(398\) −2.88934e6 −0.914306
\(399\) 236376. 0.0743312
\(400\) −734464. −0.229520
\(401\) −1.27962e6 −0.397393 −0.198696 0.980061i \(-0.563671\pi\)
−0.198696 + 0.980061i \(0.563671\pi\)
\(402\) 748080. 0.230878
\(403\) −1.58252e6 −0.485384
\(404\) −451808. −0.137721
\(405\) −104976. −0.0318019
\(406\) −312424. −0.0940653
\(407\) 1.36823e6 0.409423
\(408\) 309888. 0.0921625
\(409\) 3.48286e6 1.02950 0.514752 0.857339i \(-0.327884\pi\)
0.514752 + 0.857339i \(0.327884\pi\)
\(410\) −315392. −0.0926597
\(411\) −747576. −0.218299
\(412\) 3.08262e6 0.894700
\(413\) 204918. 0.0591160
\(414\) −1.48910e6 −0.426996
\(415\) 1.63062e6 0.464765
\(416\) −173056. −0.0490290
\(417\) −552780. −0.155673
\(418\) 244416. 0.0684209
\(419\) −4.32376e6 −1.20317 −0.601584 0.798809i \(-0.705464\pi\)
−0.601584 + 0.798809i \(0.705464\pi\)
\(420\) 112896. 0.0312288
\(421\) −924310. −0.254163 −0.127082 0.991892i \(-0.540561\pi\)
−0.127082 + 0.991892i \(0.540561\pi\)
\(422\) 1.02190e6 0.279337
\(423\) −1.80322e6 −0.490002
\(424\) −30336.0 −0.00819490
\(425\) −1.54352e6 −0.414515
\(426\) 672552. 0.179557
\(427\) 1.06967e6 0.283910
\(428\) 2.01907e6 0.532773
\(429\) 173394. 0.0454874
\(430\) 914176. 0.238429
\(431\) 3.98154e6 1.03242 0.516212 0.856461i \(-0.327342\pi\)
0.516212 + 0.856461i \(0.327342\pi\)
\(432\) 186624. 0.0481125
\(433\) 6.37749e6 1.63467 0.817334 0.576164i \(-0.195451\pi\)
0.817334 + 0.576164i \(0.195451\pi\)
\(434\) −1.83534e6 −0.467728
\(435\) −229536. −0.0581604
\(436\) −2.58160e6 −0.650388
\(437\) 2.46346e6 0.617080
\(438\) −1.36318e6 −0.339521
\(439\) −4.36784e6 −1.08170 −0.540848 0.841120i \(-0.681897\pi\)
−0.540848 + 0.841120i \(0.681897\pi\)
\(440\) 116736. 0.0287457
\(441\) 194481. 0.0476190
\(442\) −363688. −0.0885469
\(443\) −2.50270e6 −0.605897 −0.302948 0.953007i \(-0.597971\pi\)
−0.302948 + 0.953007i \(0.597971\pi\)
\(444\) −1.72829e6 −0.416063
\(445\) 1.24230e6 0.297391
\(446\) −812848. −0.193496
\(447\) −980388. −0.232075
\(448\) −200704. −0.0472456
\(449\) −6.84852e6 −1.60318 −0.801588 0.597877i \(-0.796011\pi\)
−0.801588 + 0.597877i \(0.796011\pi\)
\(450\) −929556. −0.216394
\(451\) −561792. −0.130057
\(452\) 2.59210e6 0.596767
\(453\) 3.10763e6 0.711514
\(454\) 466888. 0.106310
\(455\) −132496. −0.0300037
\(456\) −308736. −0.0695305
\(457\) −897250. −0.200966 −0.100483 0.994939i \(-0.532039\pi\)
−0.100483 + 0.994939i \(0.532039\pi\)
\(458\) −3.46774e6 −0.772471
\(459\) 392202. 0.0868917
\(460\) 1.17658e6 0.259254
\(461\) −448184. −0.0982209 −0.0491105 0.998793i \(-0.515639\pi\)
−0.0491105 + 0.998793i \(0.515639\pi\)
\(462\) 201096. 0.0438327
\(463\) 6.98583e6 1.51449 0.757244 0.653132i \(-0.226546\pi\)
0.757244 + 0.653132i \(0.226546\pi\)
\(464\) 408064. 0.0879900
\(465\) −1.34842e6 −0.289195
\(466\) −5.28356e6 −1.12710
\(467\) −175272. −0.0371895 −0.0185948 0.999827i \(-0.505919\pi\)
−0.0185948 + 0.999827i \(0.505919\pi\)
\(468\) −219024. −0.0462250
\(469\) −1.01822e6 −0.213752
\(470\) 1.42477e6 0.297509
\(471\) 2.98798e6 0.620620
\(472\) −267648. −0.0552979
\(473\) 1.62838e6 0.334658
\(474\) −1.00224e6 −0.204892
\(475\) 1.53778e6 0.312724
\(476\) −421792. −0.0853259
\(477\) −38394.0 −0.00772623
\(478\) 1.24721e6 0.249672
\(479\) 4.63880e6 0.923776 0.461888 0.886938i \(-0.347172\pi\)
0.461888 + 0.886938i \(0.347172\pi\)
\(480\) −147456. −0.0292119
\(481\) 2.02834e6 0.399740
\(482\) 465304. 0.0912261
\(483\) 2.02684e6 0.395322
\(484\) −2.36888e6 −0.459653
\(485\) 960800. 0.185472
\(486\) 236196. 0.0453609
\(487\) 648212. 0.123850 0.0619248 0.998081i \(-0.480276\pi\)
0.0619248 + 0.998081i \(0.480276\pi\)
\(488\) −1.39712e6 −0.265573
\(489\) 1.30457e6 0.246714
\(490\) −153664. −0.0289123
\(491\) −9.81755e6 −1.83781 −0.918903 0.394484i \(-0.870923\pi\)
−0.918903 + 0.394484i \(0.870923\pi\)
\(492\) 709632. 0.132166
\(493\) 857572. 0.158911
\(494\) 362336. 0.0668027
\(495\) 147744. 0.0271017
\(496\) 2.39718e6 0.437519
\(497\) −915418. −0.166237
\(498\) −3.66890e6 −0.662923
\(499\) 1.09873e7 1.97533 0.987666 0.156573i \(-0.0500447\pi\)
0.987666 + 0.156573i \(0.0500447\pi\)
\(500\) 1.53446e6 0.274493
\(501\) −256446. −0.0456459
\(502\) 4.12358e6 0.730324
\(503\) −690876. −0.121753 −0.0608766 0.998145i \(-0.519390\pi\)
−0.0608766 + 0.998145i \(0.519390\pi\)
\(504\) −254016. −0.0445435
\(505\) 451808. 0.0788362
\(506\) 2.09578e6 0.363889
\(507\) 257049. 0.0444116
\(508\) 364032. 0.0625864
\(509\) −8.58750e6 −1.46917 −0.734585 0.678517i \(-0.762623\pi\)
−0.734585 + 0.678517i \(0.762623\pi\)
\(510\) −309888. −0.0527569
\(511\) 1.85543e6 0.314335
\(512\) 262144. 0.0441942
\(513\) −390744. −0.0655540
\(514\) 2.10310e6 0.351117
\(515\) −3.08262e6 −0.512156
\(516\) −2.05690e6 −0.340085
\(517\) 2.53787e6 0.417583
\(518\) 2.35239e6 0.385199
\(519\) 1.95475e6 0.318546
\(520\) 173056. 0.0280659
\(521\) 3.13186e6 0.505485 0.252743 0.967534i \(-0.418667\pi\)
0.252743 + 0.967534i \(0.418667\pi\)
\(522\) 516456. 0.0829578
\(523\) 7.72288e6 1.23460 0.617298 0.786729i \(-0.288227\pi\)
0.617298 + 0.786729i \(0.288227\pi\)
\(524\) −4.51328e6 −0.718065
\(525\) 1.26523e6 0.200341
\(526\) 7.85083e6 1.23723
\(527\) 5.03783e6 0.790164
\(528\) −262656. −0.0410018
\(529\) 1.46869e7 2.28187
\(530\) 30336.0 0.00469103
\(531\) −338742. −0.0521354
\(532\) 420224. 0.0643727
\(533\) −832832. −0.126981
\(534\) −2.79518e6 −0.424187
\(535\) −2.01907e6 −0.304977
\(536\) 1.32992e6 0.199946
\(537\) −5.35028e6 −0.800647
\(538\) −3.48070e6 −0.518454
\(539\) −273714. −0.0405812
\(540\) −186624. −0.0275412
\(541\) 660842. 0.0970743 0.0485372 0.998821i \(-0.484544\pi\)
0.0485372 + 0.998821i \(0.484544\pi\)
\(542\) −1.96998e6 −0.288048
\(543\) −1.14345e6 −0.166425
\(544\) 550912. 0.0798151
\(545\) 2.58160e6 0.372304
\(546\) 298116. 0.0427960
\(547\) 9.39795e6 1.34297 0.671483 0.741020i \(-0.265658\pi\)
0.671483 + 0.741020i \(0.265658\pi\)
\(548\) −1.32902e6 −0.189052
\(549\) −1.76823e6 −0.250385
\(550\) 1.30826e6 0.184412
\(551\) −854384. −0.119888
\(552\) −2.64730e6 −0.369790
\(553\) 1.36416e6 0.189694
\(554\) −805512. −0.111506
\(555\) 1.72829e6 0.238168
\(556\) −982720. −0.134816
\(557\) −21324.0 −0.00291226 −0.00145613 0.999999i \(-0.500464\pi\)
−0.00145613 + 0.999999i \(0.500464\pi\)
\(558\) 3.03394e6 0.412497
\(559\) 2.41400e6 0.326744
\(560\) 200704. 0.0270449
\(561\) −551988. −0.0740496
\(562\) 7.17526e6 0.958290
\(563\) −8.72447e6 −1.16003 −0.580013 0.814607i \(-0.696953\pi\)
−0.580013 + 0.814607i \(0.696953\pi\)
\(564\) −3.20573e6 −0.424355
\(565\) −2.59210e6 −0.341610
\(566\) 4.55627e6 0.597817
\(567\) −321489. −0.0419961
\(568\) 1.19565e6 0.155501
\(569\) 2.97609e6 0.385358 0.192679 0.981262i \(-0.438282\pi\)
0.192679 + 0.981262i \(0.438282\pi\)
\(570\) 308736. 0.0398016
\(571\) −6.80377e6 −0.873292 −0.436646 0.899633i \(-0.643834\pi\)
−0.436646 + 0.899633i \(0.643834\pi\)
\(572\) 308256. 0.0393932
\(573\) −3.73558e6 −0.475304
\(574\) −965888. −0.122362
\(575\) 1.31859e7 1.66319
\(576\) 331776. 0.0416667
\(577\) 4.45680e6 0.557293 0.278647 0.960394i \(-0.410114\pi\)
0.278647 + 0.960394i \(0.410114\pi\)
\(578\) −4.52165e6 −0.562960
\(579\) 3.68591e6 0.456929
\(580\) −408064. −0.0503684
\(581\) 4.99379e6 0.613747
\(582\) −2.16180e6 −0.264550
\(583\) 54036.0 0.00658433
\(584\) −2.42342e6 −0.294034
\(585\) 219024. 0.0264607
\(586\) −2.18098e6 −0.262366
\(587\) −1.24077e7 −1.48626 −0.743132 0.669145i \(-0.766661\pi\)
−0.743132 + 0.669145i \(0.766661\pi\)
\(588\) 345744. 0.0412393
\(589\) −5.01910e6 −0.596126
\(590\) 267648. 0.0316544
\(591\) 6.81739e6 0.802878
\(592\) −3.07251e6 −0.360321
\(593\) −7.15682e6 −0.835763 −0.417882 0.908501i \(-0.637227\pi\)
−0.417882 + 0.908501i \(0.637227\pi\)
\(594\) −332424. −0.0386568
\(595\) 421792. 0.0488434
\(596\) −1.74291e6 −0.200983
\(597\) −6.50102e6 −0.746528
\(598\) 3.10690e6 0.355282
\(599\) −1.40339e7 −1.59812 −0.799061 0.601250i \(-0.794670\pi\)
−0.799061 + 0.601250i \(0.794670\pi\)
\(600\) −1.65254e6 −0.187402
\(601\) −1.39661e7 −1.57721 −0.788606 0.614899i \(-0.789197\pi\)
−0.788606 + 0.614899i \(0.789197\pi\)
\(602\) 2.79966e6 0.314858
\(603\) 1.68318e6 0.188511
\(604\) 5.52467e6 0.616189
\(605\) 2.36888e6 0.263120
\(606\) −1.01657e6 −0.112449
\(607\) −1.29378e7 −1.42525 −0.712624 0.701546i \(-0.752493\pi\)
−0.712624 + 0.701546i \(0.752493\pi\)
\(608\) −548864. −0.0602152
\(609\) −702954. −0.0768040
\(610\) 1.39712e6 0.152023
\(611\) 3.76228e6 0.407707
\(612\) 697248. 0.0752504
\(613\) 2.87327e6 0.308834 0.154417 0.988006i \(-0.450650\pi\)
0.154417 + 0.988006i \(0.450650\pi\)
\(614\) −6.69528e6 −0.716717
\(615\) −709632. −0.0756564
\(616\) 357504. 0.0379603
\(617\) 1.47111e7 1.55572 0.777860 0.628438i \(-0.216305\pi\)
0.777860 + 0.628438i \(0.216305\pi\)
\(618\) 6.93590e6 0.730520
\(619\) 1.36624e7 1.43318 0.716591 0.697494i \(-0.245702\pi\)
0.716591 + 0.697494i \(0.245702\pi\)
\(620\) −2.39718e6 −0.250451
\(621\) −3.35048e6 −0.348641
\(622\) −4.70360e6 −0.487477
\(623\) 3.80456e6 0.392721
\(624\) −389376. −0.0400320
\(625\) 7.43116e6 0.760951
\(626\) −2.05201e6 −0.209287
\(627\) 549936. 0.0558654
\(628\) 5.31197e6 0.537473
\(629\) −6.45708e6 −0.650743
\(630\) 254016. 0.0254982
\(631\) −8.58332e6 −0.858187 −0.429094 0.903260i \(-0.641167\pi\)
−0.429094 + 0.903260i \(0.641167\pi\)
\(632\) −1.78176e6 −0.177442
\(633\) 2.29928e6 0.228078
\(634\) −869664. −0.0859267
\(635\) −364032. −0.0358266
\(636\) −68256.0 −0.00669111
\(637\) −405769. −0.0396214
\(638\) −726864. −0.0706971
\(639\) 1.51324e6 0.146608
\(640\) −262144. −0.0252982
\(641\) −1.05127e7 −1.01058 −0.505288 0.862951i \(-0.668614\pi\)
−0.505288 + 0.862951i \(0.668614\pi\)
\(642\) 4.54291e6 0.435008
\(643\) −1.48608e7 −1.41747 −0.708737 0.705473i \(-0.750735\pi\)
−0.708737 + 0.705473i \(0.750735\pi\)
\(644\) 3.60326e6 0.342359
\(645\) 2.05690e6 0.194676
\(646\) −1.15347e6 −0.108749
\(647\) −4.88877e6 −0.459133 −0.229567 0.973293i \(-0.573731\pi\)
−0.229567 + 0.973293i \(0.573731\pi\)
\(648\) 419904. 0.0392837
\(649\) 476748. 0.0444301
\(650\) 1.93944e6 0.180050
\(651\) −4.12952e6 −0.381898
\(652\) 2.31923e6 0.213661
\(653\) −1.54853e7 −1.42114 −0.710571 0.703625i \(-0.751563\pi\)
−0.710571 + 0.703625i \(0.751563\pi\)
\(654\) −5.80860e6 −0.531040
\(655\) 4.51328e6 0.411045
\(656\) 1.26157e6 0.114459
\(657\) −3.06715e6 −0.277218
\(658\) 4.36335e6 0.392876
\(659\) −3.75198e6 −0.336548 −0.168274 0.985740i \(-0.553819\pi\)
−0.168274 + 0.985740i \(0.553819\pi\)
\(660\) 262656. 0.0234708
\(661\) −7.20379e6 −0.641295 −0.320647 0.947199i \(-0.603900\pi\)
−0.320647 + 0.947199i \(0.603900\pi\)
\(662\) 7.17909e6 0.636685
\(663\) −818298. −0.0722982
\(664\) −6.52250e6 −0.574108
\(665\) −420224. −0.0368491
\(666\) −3.88865e6 −0.339714
\(667\) −7.32602e6 −0.637608
\(668\) −455904. −0.0395305
\(669\) −1.82891e6 −0.157989
\(670\) −1.32992e6 −0.114456
\(671\) 2.48862e6 0.213379
\(672\) −451584. −0.0385758
\(673\) −9.03912e6 −0.769287 −0.384644 0.923065i \(-0.625676\pi\)
−0.384644 + 0.923065i \(0.625676\pi\)
\(674\) 1.62386e7 1.37689
\(675\) −2.09150e6 −0.176685
\(676\) 456976. 0.0384615
\(677\) −1.22830e7 −1.02999 −0.514997 0.857192i \(-0.672207\pi\)
−0.514997 + 0.857192i \(0.672207\pi\)
\(678\) 5.83222e6 0.487258
\(679\) 2.94245e6 0.244926
\(680\) −550912. −0.0456888
\(681\) 1.05050e6 0.0868015
\(682\) −4.26998e6 −0.351532
\(683\) −9.12026e6 −0.748093 −0.374046 0.927410i \(-0.622030\pi\)
−0.374046 + 0.927410i \(0.622030\pi\)
\(684\) −694656. −0.0567714
\(685\) 1.32902e6 0.108220
\(686\) −470596. −0.0381802
\(687\) −7.80241e6 −0.630720
\(688\) −3.65670e6 −0.294523
\(689\) 80106.0 0.00642861
\(690\) 2.64730e6 0.211680
\(691\) 8.20200e6 0.653469 0.326734 0.945116i \(-0.394052\pi\)
0.326734 + 0.945116i \(0.394052\pi\)
\(692\) 3.47510e6 0.275869
\(693\) 452466. 0.0357893
\(694\) −1.22523e7 −0.965646
\(695\) 982720. 0.0771734
\(696\) 918144. 0.0718435
\(697\) 2.65126e6 0.206715
\(698\) 1.32556e7 1.02982
\(699\) −1.18880e7 −0.920272
\(700\) 2.24930e6 0.173501
\(701\) −1.90496e7 −1.46416 −0.732082 0.681216i \(-0.761451\pi\)
−0.732082 + 0.681216i \(0.761451\pi\)
\(702\) −492804. −0.0377426
\(703\) 6.43307e6 0.490942
\(704\) −466944. −0.0355086
\(705\) 3.20573e6 0.242915
\(706\) −640832. −0.0483874
\(707\) 1.38366e6 0.104107
\(708\) −602208. −0.0451506
\(709\) 8.84088e6 0.660511 0.330255 0.943892i \(-0.392865\pi\)
0.330255 + 0.943892i \(0.392865\pi\)
\(710\) −1.19565e6 −0.0890138
\(711\) −2.25504e6 −0.167294
\(712\) −4.96922e6 −0.367357
\(713\) −4.30369e7 −3.17043
\(714\) −949032. −0.0696683
\(715\) −308256. −0.0225500
\(716\) −9.51162e6 −0.693381
\(717\) 2.80622e6 0.203856
\(718\) 8.95582e6 0.648327
\(719\) −8.91757e6 −0.643316 −0.321658 0.946856i \(-0.604240\pi\)
−0.321658 + 0.946856i \(0.604240\pi\)
\(720\) −331776. −0.0238514
\(721\) −9.44054e6 −0.676330
\(722\) −8.75521e6 −0.625063
\(723\) 1.04693e6 0.0744858
\(724\) −2.03280e6 −0.144128
\(725\) −4.57319e6 −0.323127
\(726\) −5.32998e6 −0.375305
\(727\) 2.27113e7 1.59370 0.796849 0.604179i \(-0.206499\pi\)
0.796849 + 0.604179i \(0.206499\pi\)
\(728\) 529984. 0.0370625
\(729\) 531441. 0.0370370
\(730\) 2.42342e6 0.168315
\(731\) −7.68479e6 −0.531911
\(732\) −3.14352e6 −0.216840
\(733\) 192242. 0.0132156 0.00660782 0.999978i \(-0.497897\pi\)
0.00660782 + 0.999978i \(0.497897\pi\)
\(734\) 4.52490e6 0.310005
\(735\) −345744. −0.0236068
\(736\) −4.70630e6 −0.320247
\(737\) −2.36892e6 −0.160650
\(738\) 1.59667e6 0.107913
\(739\) 5.59589e6 0.376928 0.188464 0.982080i \(-0.439649\pi\)
0.188464 + 0.982080i \(0.439649\pi\)
\(740\) 3.07251e6 0.206260
\(741\) 815256. 0.0545442
\(742\) 92904.0 0.00619476
\(743\) 1.26406e7 0.840032 0.420016 0.907517i \(-0.362024\pi\)
0.420016 + 0.907517i \(0.362024\pi\)
\(744\) 5.39366e6 0.357233
\(745\) 1.74291e6 0.115050
\(746\) 2.01358e7 1.32472
\(747\) −8.25503e6 −0.541274
\(748\) −981312. −0.0641288
\(749\) −6.18341e6 −0.402739
\(750\) 3.45254e6 0.224123
\(751\) 1.21630e7 0.786936 0.393468 0.919338i \(-0.371275\pi\)
0.393468 + 0.919338i \(0.371275\pi\)
\(752\) −5.69907e6 −0.367502
\(753\) 9.27806e6 0.596307
\(754\) −1.07754e6 −0.0690250
\(755\) −5.52467e6 −0.352727
\(756\) −571536. −0.0363696
\(757\) −1.67585e7 −1.06291 −0.531454 0.847087i \(-0.678354\pi\)
−0.531454 + 0.847087i \(0.678354\pi\)
\(758\) 1.47775e7 0.934177
\(759\) 4.71550e6 0.297114
\(760\) 548864. 0.0344692
\(761\) −1.65439e7 −1.03556 −0.517782 0.855513i \(-0.673242\pi\)
−0.517782 + 0.855513i \(0.673242\pi\)
\(762\) 819072. 0.0511016
\(763\) 7.90615e6 0.491647
\(764\) −6.64102e6 −0.411625
\(765\) −697248. −0.0430758
\(766\) 1.45204e7 0.894145
\(767\) 706758. 0.0433793
\(768\) 589824. 0.0360844
\(769\) −1.84752e7 −1.12661 −0.563304 0.826250i \(-0.690470\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(770\) −357504. −0.0217297
\(771\) 4.73197e6 0.286685
\(772\) 6.55274e6 0.395712
\(773\) −138524. −0.00833828 −0.00416914 0.999991i \(-0.501327\pi\)
−0.00416914 + 0.999991i \(0.501327\pi\)
\(774\) −4.62802e6 −0.277679
\(775\) −2.68653e7 −1.60671
\(776\) −3.84320e6 −0.229107
\(777\) 5.29288e6 0.314514
\(778\) 1.21685e7 0.720756
\(779\) −2.64141e6 −0.155952
\(780\) 389376. 0.0229157
\(781\) −2.12975e6 −0.124940
\(782\) −9.89059e6 −0.578370
\(783\) 1.16203e6 0.0677347
\(784\) 614656. 0.0357143
\(785\) −5.31197e6 −0.307667
\(786\) −1.01549e7 −0.586298
\(787\) −78668.0 −0.00452753 −0.00226376 0.999997i \(-0.500721\pi\)
−0.00226376 + 0.999997i \(0.500721\pi\)
\(788\) 1.21198e7 0.695313
\(789\) 1.76644e7 1.01020
\(790\) 1.78176e6 0.101574
\(791\) −7.93829e6 −0.451114
\(792\) −590976. −0.0334778
\(793\) 3.68927e6 0.208333
\(794\) 1.94874e7 1.09699
\(795\) 68256.0 0.00383021
\(796\) −1.15574e7 −0.646512
\(797\) 1.52352e7 0.849579 0.424789 0.905292i \(-0.360348\pi\)
0.424789 + 0.905292i \(0.360348\pi\)
\(798\) 945504. 0.0525601
\(799\) −1.19770e7 −0.663712
\(800\) −2.93786e6 −0.162295
\(801\) −6.28916e6 −0.346347
\(802\) −5.11848e6 −0.280999
\(803\) 4.31672e6 0.236247
\(804\) 2.99232e6 0.163256
\(805\) −3.60326e6 −0.195978
\(806\) −6.33006e6 −0.343218
\(807\) −7.83157e6 −0.423316
\(808\) −1.80723e6 −0.0973835
\(809\) −1.95478e7 −1.05009 −0.525046 0.851074i \(-0.675952\pi\)
−0.525046 + 0.851074i \(0.675952\pi\)
\(810\) −419904. −0.0224873
\(811\) 7.93340e6 0.423552 0.211776 0.977318i \(-0.432075\pi\)
0.211776 + 0.977318i \(0.432075\pi\)
\(812\) −1.24970e6 −0.0665142
\(813\) −4.43246e6 −0.235190
\(814\) 5.47291e6 0.289506
\(815\) −2.31923e6 −0.122307
\(816\) 1.23955e6 0.0651687
\(817\) 7.65622e6 0.401291
\(818\) 1.39314e7 0.727969
\(819\) 670761. 0.0349428
\(820\) −1.26157e6 −0.0655203
\(821\) −2.39886e7 −1.24207 −0.621036 0.783782i \(-0.713288\pi\)
−0.621036 + 0.783782i \(0.713288\pi\)
\(822\) −2.99030e6 −0.154360
\(823\) −9.36158e6 −0.481781 −0.240891 0.970552i \(-0.577439\pi\)
−0.240891 + 0.970552i \(0.577439\pi\)
\(824\) 1.23305e7 0.632649
\(825\) 2.94359e6 0.150572
\(826\) 819672. 0.0418013
\(827\) −2.69740e7 −1.37146 −0.685729 0.727857i \(-0.740516\pi\)
−0.685729 + 0.727857i \(0.740516\pi\)
\(828\) −5.95642e6 −0.301932
\(829\) −1.33436e7 −0.674350 −0.337175 0.941442i \(-0.609471\pi\)
−0.337175 + 0.941442i \(0.609471\pi\)
\(830\) 6.52250e6 0.328639
\(831\) −1.81240e6 −0.0910441
\(832\) −692224. −0.0346688
\(833\) 1.29174e6 0.0645003
\(834\) −2.21112e6 −0.110077
\(835\) 455904. 0.0226286
\(836\) 977664. 0.0483809
\(837\) 6.82636e6 0.336802
\(838\) −1.72950e7 −0.850769
\(839\) −1.24039e7 −0.608349 −0.304175 0.952616i \(-0.598381\pi\)
−0.304175 + 0.952616i \(0.598381\pi\)
\(840\) 451584. 0.0220821
\(841\) −1.79703e7 −0.876124
\(842\) −3.69724e6 −0.179720
\(843\) 1.61443e7 0.782441
\(844\) 4.08762e6 0.197521
\(845\) −456976. −0.0220167
\(846\) −7.21289e6 −0.346484
\(847\) 7.25470e6 0.347465
\(848\) −121344. −0.00579467
\(849\) 1.02516e7 0.488116
\(850\) −6.17409e6 −0.293107
\(851\) 5.51612e7 2.61102
\(852\) 2.69021e6 0.126966
\(853\) −1.12739e7 −0.530519 −0.265260 0.964177i \(-0.585458\pi\)
−0.265260 + 0.964177i \(0.585458\pi\)
\(854\) 4.27868e6 0.200754
\(855\) 694656. 0.0324978
\(856\) 8.07629e6 0.376728
\(857\) 1.79722e7 0.835892 0.417946 0.908472i \(-0.362750\pi\)
0.417946 + 0.908472i \(0.362750\pi\)
\(858\) 693576. 0.0321644
\(859\) −3.31079e7 −1.53091 −0.765454 0.643491i \(-0.777486\pi\)
−0.765454 + 0.643491i \(0.777486\pi\)
\(860\) 3.65670e6 0.168595
\(861\) −2.17325e6 −0.0999083
\(862\) 1.59262e7 0.730034
\(863\) 6.89937e6 0.315342 0.157671 0.987492i \(-0.449601\pi\)
0.157671 + 0.987492i \(0.449601\pi\)
\(864\) 746496. 0.0340207
\(865\) −3.47510e6 −0.157917
\(866\) 2.55099e7 1.15589
\(867\) −1.01737e7 −0.459655
\(868\) −7.34138e6 −0.330733
\(869\) 3.17376e6 0.142569
\(870\) −918144. −0.0411256
\(871\) −3.51182e6 −0.156851
\(872\) −1.03264e7 −0.459894
\(873\) −4.86405e6 −0.216004
\(874\) 9.85382e6 0.436341
\(875\) −4.69930e6 −0.207497
\(876\) −5.45270e6 −0.240078
\(877\) 7.26768e6 0.319078 0.159539 0.987192i \(-0.448999\pi\)
0.159539 + 0.987192i \(0.448999\pi\)
\(878\) −1.74714e7 −0.764875
\(879\) −4.90720e6 −0.214221
\(880\) 466944. 0.0203263
\(881\) −3.12139e7 −1.35490 −0.677451 0.735568i \(-0.736916\pi\)
−0.677451 + 0.735568i \(0.736916\pi\)
\(882\) 777924. 0.0336718
\(883\) 1.05434e7 0.455071 0.227535 0.973770i \(-0.426933\pi\)
0.227535 + 0.973770i \(0.426933\pi\)
\(884\) −1.45475e6 −0.0626121
\(885\) 602208. 0.0258457
\(886\) −1.00108e7 −0.428434
\(887\) −5.57824e6 −0.238061 −0.119030 0.992891i \(-0.537979\pi\)
−0.119030 + 0.992891i \(0.537979\pi\)
\(888\) −6.91315e6 −0.294201
\(889\) −1.11485e6 −0.0473109
\(890\) 4.96922e6 0.210287
\(891\) −747954. −0.0315632
\(892\) −3.25139e6 −0.136822
\(893\) 1.19324e7 0.500726
\(894\) −3.92155e6 −0.164102
\(895\) 9.51162e6 0.396914
\(896\) −802816. −0.0334077
\(897\) 6.99052e6 0.290087
\(898\) −2.73941e7 −1.13362
\(899\) 1.49262e7 0.615957
\(900\) −3.71822e6 −0.153013
\(901\) −255012. −0.0104652
\(902\) −2.24717e6 −0.0919643
\(903\) 6.29924e6 0.257080
\(904\) 1.03684e7 0.421978
\(905\) 2.03280e6 0.0825037
\(906\) 1.24305e7 0.503116
\(907\) −5.61475e6 −0.226627 −0.113314 0.993559i \(-0.536146\pi\)
−0.113314 + 0.993559i \(0.536146\pi\)
\(908\) 1.86755e6 0.0751723
\(909\) −2.28728e6 −0.0918141
\(910\) −529984. −0.0212158
\(911\) −4.20822e6 −0.167997 −0.0839986 0.996466i \(-0.526769\pi\)
−0.0839986 + 0.996466i \(0.526769\pi\)
\(912\) −1.23494e6 −0.0491655
\(913\) 1.16182e7 0.461277
\(914\) −3.58900e6 −0.142105
\(915\) 3.14352e6 0.124126
\(916\) −1.38709e7 −0.546220
\(917\) 1.38219e7 0.542806
\(918\) 1.56881e6 0.0614417
\(919\) 921112. 0.0359769 0.0179884 0.999838i \(-0.494274\pi\)
0.0179884 + 0.999838i \(0.494274\pi\)
\(920\) 4.70630e6 0.183320
\(921\) −1.50644e7 −0.585197
\(922\) −1.79274e6 −0.0694527
\(923\) −3.15726e6 −0.121985
\(924\) 804384. 0.0309944
\(925\) 3.44337e7 1.32321
\(926\) 2.79433e7 1.07090
\(927\) 1.56058e7 0.596467
\(928\) 1.63226e6 0.0622183
\(929\) −3.53309e7 −1.34312 −0.671560 0.740950i \(-0.734376\pi\)
−0.671560 + 0.740950i \(0.734376\pi\)
\(930\) −5.39366e6 −0.204492
\(931\) −1.28694e6 −0.0486612
\(932\) −2.11342e7 −0.796979
\(933\) −1.05831e7 −0.398024
\(934\) −701088. −0.0262969
\(935\) 981312. 0.0367095
\(936\) −876096. −0.0326860
\(937\) −4.50275e7 −1.67544 −0.837719 0.546101i \(-0.816111\pi\)
−0.837719 + 0.546101i \(0.816111\pi\)
\(938\) −4.07288e6 −0.151145
\(939\) −4.61702e6 −0.170882
\(940\) 5.69907e6 0.210370
\(941\) −1.92209e7 −0.707619 −0.353809 0.935318i \(-0.615114\pi\)
−0.353809 + 0.935318i \(0.615114\pi\)
\(942\) 1.19519e7 0.438845
\(943\) −2.26491e7 −0.829414
\(944\) −1.07059e6 −0.0391016
\(945\) 571536. 0.0208192
\(946\) 6.51350e6 0.236639
\(947\) 3.36408e7 1.21896 0.609482 0.792800i \(-0.291377\pi\)
0.609482 + 0.792800i \(0.291377\pi\)
\(948\) −4.00896e6 −0.144881
\(949\) 6.39935e6 0.230659
\(950\) 6.15114e6 0.221129
\(951\) −1.95674e6 −0.0701589
\(952\) −1.68717e6 −0.0603345
\(953\) −4.20151e7 −1.49856 −0.749278 0.662256i \(-0.769599\pi\)
−0.749278 + 0.662256i \(0.769599\pi\)
\(954\) −153576. −0.00546327
\(955\) 6.64102e6 0.235628
\(956\) 4.98883e6 0.176544
\(957\) −1.63544e6 −0.0577239
\(958\) 1.85552e7 0.653208
\(959\) 4.07014e6 0.142910
\(960\) −589824. −0.0206559
\(961\) 5.90553e7 2.06277
\(962\) 8.11335e6 0.282659
\(963\) 1.02216e7 0.355182
\(964\) 1.86122e6 0.0645066
\(965\) −6.55274e6 −0.226519
\(966\) 8.10734e6 0.279535
\(967\) 2.57052e7 0.884005 0.442003 0.897014i \(-0.354268\pi\)
0.442003 + 0.897014i \(0.354268\pi\)
\(968\) −9.47552e6 −0.325023
\(969\) −2.59531e6 −0.0887933
\(970\) 3.84320e6 0.131149
\(971\) 3.96757e7 1.35045 0.675223 0.737614i \(-0.264048\pi\)
0.675223 + 0.737614i \(0.264048\pi\)
\(972\) 944784. 0.0320750
\(973\) 3.00958e6 0.101912
\(974\) 2.59285e6 0.0875749
\(975\) 4.36375e6 0.147010
\(976\) −5.58848e6 −0.187789
\(977\) 1.85717e7 0.622464 0.311232 0.950334i \(-0.399258\pi\)
0.311232 + 0.950334i \(0.399258\pi\)
\(978\) 5.21827e6 0.174453
\(979\) 8.85142e6 0.295159
\(980\) −614656. −0.0204441
\(981\) −1.30694e7 −0.433592
\(982\) −3.92702e7 −1.29952
\(983\) −4.17572e7 −1.37831 −0.689157 0.724612i \(-0.742019\pi\)
−0.689157 + 0.724612i \(0.742019\pi\)
\(984\) 2.83853e6 0.0934556
\(985\) −1.21198e7 −0.398020
\(986\) 3.43029e6 0.112367
\(987\) 9.81754e6 0.320782
\(988\) 1.44934e6 0.0472367
\(989\) 6.56493e7 2.13422
\(990\) 590976. 0.0191638
\(991\) 3.03576e6 0.0981936 0.0490968 0.998794i \(-0.484366\pi\)
0.0490968 + 0.998794i \(0.484366\pi\)
\(992\) 9.58874e6 0.309373
\(993\) 1.61529e7 0.519851
\(994\) −3.66167e6 −0.117548
\(995\) 1.15574e7 0.370085
\(996\) −1.46756e7 −0.468757
\(997\) −2.73080e7 −0.870067 −0.435033 0.900414i \(-0.643263\pi\)
−0.435033 + 0.900414i \(0.643263\pi\)
\(998\) 4.39493e7 1.39677
\(999\) −8.74946e6 −0.277375
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 546.6.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.6.a.h.1.1 1 1.1 even 1 trivial