Properties

Label 570.6.a.m.1.2
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.4187772934\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 39154 x^{2} - 3172892 x - 35506440\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-128.214\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -70.9208 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -70.9208 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -424.457 q^{11} +144.000 q^{12} +434.708 q^{13} +283.683 q^{14} +225.000 q^{15} +256.000 q^{16} -1586.72 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -638.287 q^{21} +1697.83 q^{22} -59.0837 q^{23} -576.000 q^{24} +625.000 q^{25} -1738.83 q^{26} +729.000 q^{27} -1134.73 q^{28} -3146.64 q^{29} -900.000 q^{30} +1192.82 q^{31} -1024.00 q^{32} -3820.11 q^{33} +6346.87 q^{34} -1773.02 q^{35} +1296.00 q^{36} +6112.20 q^{37} -1444.00 q^{38} +3912.37 q^{39} -1600.00 q^{40} +17325.3 q^{41} +2553.15 q^{42} +3183.12 q^{43} -6791.32 q^{44} +2025.00 q^{45} +236.335 q^{46} +13572.7 q^{47} +2304.00 q^{48} -11777.2 q^{49} -2500.00 q^{50} -14280.5 q^{51} +6955.33 q^{52} +16309.1 q^{53} -2916.00 q^{54} -10611.4 q^{55} +4538.93 q^{56} +3249.00 q^{57} +12586.6 q^{58} -3875.52 q^{59} +3600.00 q^{60} +37196.6 q^{61} -4771.27 q^{62} -5744.58 q^{63} +4096.00 q^{64} +10867.7 q^{65} +15280.5 q^{66} +10788.2 q^{67} -25387.5 q^{68} -531.753 q^{69} +7092.08 q^{70} +45527.6 q^{71} -5184.00 q^{72} -23326.8 q^{73} -24448.8 q^{74} +5625.00 q^{75} +5776.00 q^{76} +30102.8 q^{77} -15649.5 q^{78} +30489.0 q^{79} +6400.00 q^{80} +6561.00 q^{81} -69301.0 q^{82} -51553.1 q^{83} -10212.6 q^{84} -39667.9 q^{85} -12732.5 q^{86} -28319.7 q^{87} +27165.3 q^{88} -61870.8 q^{89} -8100.00 q^{90} -30829.9 q^{91} -945.339 q^{92} +10735.4 q^{93} -54291.0 q^{94} +9025.00 q^{95} -9216.00 q^{96} +33681.5 q^{97} +47109.0 q^{98} -34381.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} - 400q^{10} + 338q^{11} + 576q^{12} + 1302q^{13} - 1072q^{14} + 900q^{15} + 1024q^{16} + 542q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 2412q^{21} - 1352q^{22} - 88q^{23} - 2304q^{24} + 2500q^{25} - 5208q^{26} + 2916q^{27} + 4288q^{28} + 5014q^{29} - 3600q^{30} + 4962q^{31} - 4096q^{32} + 3042q^{33} - 2168q^{34} + 6700q^{35} + 5184q^{36} + 8022q^{37} - 5776q^{38} + 11718q^{39} - 6400q^{40} + 2764q^{41} - 9648q^{42} + 25346q^{43} + 5408q^{44} + 8100q^{45} + 352q^{46} + 10008q^{47} + 9216q^{48} + 37248q^{49} - 10000q^{50} + 4878q^{51} + 20832q^{52} - 224q^{53} - 11664q^{54} + 8450q^{55} - 17152q^{56} + 12996q^{57} - 20056q^{58} + 29654q^{59} + 14400q^{60} + 27276q^{61} - 19848q^{62} + 21708q^{63} + 16384q^{64} + 32550q^{65} - 12168q^{66} + 26024q^{67} + 8672q^{68} - 792q^{69} - 26800q^{70} - 26940q^{71} - 20736q^{72} - 60916q^{73} - 32088q^{74} + 22500q^{75} + 23104q^{76} - 21228q^{77} - 46872q^{78} + 34902q^{79} + 25600q^{80} + 26244q^{81} - 11056q^{82} - 48430q^{83} + 38592q^{84} + 13550q^{85} - 101384q^{86} + 45126q^{87} - 21632q^{88} - 38348q^{89} - 32400q^{90} + 69280q^{91} - 1408q^{92} + 44658q^{93} - 40032q^{94} + 36100q^{95} - 36864q^{96} + 45942q^{97} - 148992q^{98} + 27378q^{99} + O(q^{100}) \)

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
\(5\) 25.0000 0.447214
\(6\) −36.0000 −0.408248
\(7\) −70.9208 −0.547052 −0.273526 0.961865i \(-0.588190\pi\)
−0.273526 + 0.961865i \(0.588190\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) −424.457 −1.05767 −0.528837 0.848723i \(-0.677372\pi\)
−0.528837 + 0.848723i \(0.677372\pi\)
\(12\) 144.000 0.288675
\(13\) 434.708 0.713410 0.356705 0.934217i \(-0.383900\pi\)
0.356705 + 0.934217i \(0.383900\pi\)
\(14\) 283.683 0.386824
\(15\) 225.000 0.258199
\(16\) 256.000 0.250000
\(17\) −1586.72 −1.33161 −0.665805 0.746125i \(-0.731912\pi\)
−0.665805 + 0.746125i \(0.731912\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) −638.287 −0.315841
\(22\) 1697.83 0.747889
\(23\) −59.0837 −0.0232888 −0.0116444 0.999932i \(-0.503707\pi\)
−0.0116444 + 0.999932i \(0.503707\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) −1738.83 −0.504457
\(27\) 729.000 0.192450
\(28\) −1134.73 −0.273526
\(29\) −3146.64 −0.694787 −0.347394 0.937719i \(-0.612933\pi\)
−0.347394 + 0.937719i \(0.612933\pi\)
\(30\) −900.000 −0.182574
\(31\) 1192.82 0.222931 0.111465 0.993768i \(-0.464446\pi\)
0.111465 + 0.993768i \(0.464446\pi\)
\(32\) −1024.00 −0.176777
\(33\) −3820.11 −0.610649
\(34\) 6346.87 0.941591
\(35\) −1773.02 −0.244649
\(36\) 1296.00 0.166667
\(37\) 6112.20 0.733995 0.366998 0.930222i \(-0.380386\pi\)
0.366998 + 0.930222i \(0.380386\pi\)
\(38\) −1444.00 −0.162221
\(39\) 3912.37 0.411888
\(40\) −1600.00 −0.158114
\(41\) 17325.3 1.60961 0.804804 0.593541i \(-0.202271\pi\)
0.804804 + 0.593541i \(0.202271\pi\)
\(42\) 2553.15 0.223333
\(43\) 3183.12 0.262532 0.131266 0.991347i \(-0.458096\pi\)
0.131266 + 0.991347i \(0.458096\pi\)
\(44\) −6791.32 −0.528837
\(45\) 2025.00 0.149071
\(46\) 236.335 0.0164677
\(47\) 13572.7 0.896238 0.448119 0.893974i \(-0.352094\pi\)
0.448119 + 0.893974i \(0.352094\pi\)
\(48\) 2304.00 0.144338
\(49\) −11777.2 −0.700734
\(50\) −2500.00 −0.141421
\(51\) −14280.5 −0.768806
\(52\) 6955.33 0.356705
\(53\) 16309.1 0.797517 0.398758 0.917056i \(-0.369441\pi\)
0.398758 + 0.917056i \(0.369441\pi\)
\(54\) −2916.00 −0.136083
\(55\) −10611.4 −0.473007
\(56\) 4538.93 0.193412
\(57\) 3249.00 0.132453
\(58\) 12586.6 0.491289
\(59\) −3875.52 −0.144944 −0.0724720 0.997370i \(-0.523089\pi\)
−0.0724720 + 0.997370i \(0.523089\pi\)
\(60\) 3600.00 0.129099
\(61\) 37196.6 1.27991 0.639955 0.768413i \(-0.278953\pi\)
0.639955 + 0.768413i \(0.278953\pi\)
\(62\) −4771.27 −0.157636
\(63\) −5744.58 −0.182351
\(64\) 4096.00 0.125000
\(65\) 10867.7 0.319047
\(66\) 15280.5 0.431794
\(67\) 10788.2 0.293604 0.146802 0.989166i \(-0.453102\pi\)
0.146802 + 0.989166i \(0.453102\pi\)
\(68\) −25387.5 −0.665805
\(69\) −531.753 −0.0134458
\(70\) 7092.08 0.172993
\(71\) 45527.6 1.07184 0.535919 0.844269i \(-0.319965\pi\)
0.535919 + 0.844269i \(0.319965\pi\)
\(72\) −5184.00 −0.117851
\(73\) −23326.8 −0.512329 −0.256164 0.966633i \(-0.582459\pi\)
−0.256164 + 0.966633i \(0.582459\pi\)
\(74\) −24448.8 −0.519013
\(75\) 5625.00 0.115470
\(76\) 5776.00 0.114708
\(77\) 30102.8 0.578603
\(78\) −15649.5 −0.291249
\(79\) 30489.0 0.549636 0.274818 0.961496i \(-0.411382\pi\)
0.274818 + 0.961496i \(0.411382\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) −69301.0 −1.13816
\(83\) −51553.1 −0.821410 −0.410705 0.911768i \(-0.634717\pi\)
−0.410705 + 0.911768i \(0.634717\pi\)
\(84\) −10212.6 −0.157920
\(85\) −39667.9 −0.595515
\(86\) −12732.5 −0.185638
\(87\) −28319.7 −0.401136
\(88\) 27165.3 0.373945
\(89\) −61870.8 −0.827962 −0.413981 0.910285i \(-0.635862\pi\)
−0.413981 + 0.910285i \(0.635862\pi\)
\(90\) −8100.00 −0.105409
\(91\) −30829.9 −0.390272
\(92\) −945.339 −0.0116444
\(93\) 10735.4 0.128709
\(94\) −54291.0 −0.633736
\(95\) 9025.00 0.102598
\(96\) −9216.00 −0.102062
\(97\) 33681.5 0.363465 0.181732 0.983348i \(-0.441830\pi\)
0.181732 + 0.983348i \(0.441830\pi\)
\(98\) 47109.0 0.495494
\(99\) −34381.0 −0.352558
\(100\) 10000.0 0.100000
\(101\) −8942.61 −0.0872290 −0.0436145 0.999048i \(-0.513887\pi\)
−0.0436145 + 0.999048i \(0.513887\pi\)
\(102\) 57121.8 0.543628
\(103\) −49830.9 −0.462813 −0.231407 0.972857i \(-0.574333\pi\)
−0.231407 + 0.972857i \(0.574333\pi\)
\(104\) −27821.3 −0.252229
\(105\) −15957.2 −0.141248
\(106\) −65236.3 −0.563929
\(107\) 190999. 1.61277 0.806383 0.591394i \(-0.201422\pi\)
0.806383 + 0.591394i \(0.201422\pi\)
\(108\) 11664.0 0.0962250
\(109\) −30577.0 −0.246507 −0.123253 0.992375i \(-0.539333\pi\)
−0.123253 + 0.992375i \(0.539333\pi\)
\(110\) 42445.7 0.334466
\(111\) 55009.8 0.423772
\(112\) −18155.7 −0.136763
\(113\) −117520. −0.865799 −0.432900 0.901442i \(-0.642510\pi\)
−0.432900 + 0.901442i \(0.642510\pi\)
\(114\) −12996.0 −0.0936586
\(115\) −1477.09 −0.0104151
\(116\) −50346.2 −0.347394
\(117\) 35211.4 0.237803
\(118\) 15502.1 0.102491
\(119\) 112531. 0.728460
\(120\) −14400.0 −0.0912871
\(121\) 19112.9 0.118676
\(122\) −148787. −0.905032
\(123\) 155927. 0.929307
\(124\) 19085.1 0.111465
\(125\) 15625.0 0.0894427
\(126\) 22978.3 0.128941
\(127\) 291458. 1.60349 0.801745 0.597666i \(-0.203905\pi\)
0.801745 + 0.597666i \(0.203905\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 28648.1 0.151573
\(130\) −43470.8 −0.225600
\(131\) −113849. −0.579632 −0.289816 0.957082i \(-0.593594\pi\)
−0.289816 + 0.957082i \(0.593594\pi\)
\(132\) −61121.8 −0.305324
\(133\) −25602.4 −0.125502
\(134\) −43152.9 −0.207610
\(135\) 18225.0 0.0860663
\(136\) 101550. 0.470796
\(137\) 30591.3 0.139250 0.0696252 0.997573i \(-0.477820\pi\)
0.0696252 + 0.997573i \(0.477820\pi\)
\(138\) 2127.01 0.00950763
\(139\) 217838. 0.956304 0.478152 0.878277i \(-0.341307\pi\)
0.478152 + 0.878277i \(0.341307\pi\)
\(140\) −28368.3 −0.122325
\(141\) 122155. 0.517443
\(142\) −182111. −0.757904
\(143\) −184515. −0.754556
\(144\) 20736.0 0.0833333
\(145\) −78666.0 −0.310718
\(146\) 93307.3 0.362271
\(147\) −105995. −0.404569
\(148\) 97795.2 0.366998
\(149\) −230640. −0.851079 −0.425539 0.904940i \(-0.639916\pi\)
−0.425539 + 0.904940i \(0.639916\pi\)
\(150\) −22500.0 −0.0816497
\(151\) 335694. 1.19812 0.599061 0.800703i \(-0.295541\pi\)
0.599061 + 0.800703i \(0.295541\pi\)
\(152\) −23104.0 −0.0811107
\(153\) −128524. −0.443870
\(154\) −120411. −0.409134
\(155\) 29820.4 0.0996976
\(156\) 62598.0 0.205944
\(157\) 103033. 0.333602 0.166801 0.985991i \(-0.446656\pi\)
0.166801 + 0.985991i \(0.446656\pi\)
\(158\) −121956. −0.388652
\(159\) 146782. 0.460446
\(160\) −25600.0 −0.0790569
\(161\) 4190.26 0.0127402
\(162\) −26244.0 −0.0785674
\(163\) 130792. 0.385577 0.192789 0.981240i \(-0.438247\pi\)
0.192789 + 0.981240i \(0.438247\pi\)
\(164\) 277204. 0.804804
\(165\) −95502.9 −0.273090
\(166\) 206212. 0.580824
\(167\) 235238. 0.652705 0.326352 0.945248i \(-0.394180\pi\)
0.326352 + 0.945248i \(0.394180\pi\)
\(168\) 40850.4 0.111666
\(169\) −182322. −0.491046
\(170\) 158672. 0.421092
\(171\) 29241.0 0.0764719
\(172\) 50929.9 0.131266
\(173\) 154896. 0.393483 0.196741 0.980455i \(-0.436964\pi\)
0.196741 + 0.980455i \(0.436964\pi\)
\(174\) 113279. 0.283646
\(175\) −44325.5 −0.109410
\(176\) −108661. −0.264419
\(177\) −34879.7 −0.0836835
\(178\) 247483. 0.585458
\(179\) 220690. 0.514814 0.257407 0.966303i \(-0.417132\pi\)
0.257407 + 0.966303i \(0.417132\pi\)
\(180\) 32400.0 0.0745356
\(181\) 460477. 1.04475 0.522373 0.852717i \(-0.325047\pi\)
0.522373 + 0.852717i \(0.325047\pi\)
\(182\) 123319. 0.275964
\(183\) 334770. 0.738956
\(184\) 3781.35 0.00823385
\(185\) 152805. 0.328253
\(186\) −42941.4 −0.0910111
\(187\) 673494. 1.40841
\(188\) 217164. 0.448119
\(189\) −51701.3 −0.105280
\(190\) −36100.0 −0.0725476
\(191\) −519113. −1.02962 −0.514812 0.857303i \(-0.672138\pi\)
−0.514812 + 0.857303i \(0.672138\pi\)
\(192\) 36864.0 0.0721688
\(193\) 836538. 1.61656 0.808282 0.588796i \(-0.200398\pi\)
0.808282 + 0.588796i \(0.200398\pi\)
\(194\) −134726. −0.257008
\(195\) 97809.3 0.184202
\(196\) −188436. −0.350367
\(197\) 375924. 0.690136 0.345068 0.938578i \(-0.387856\pi\)
0.345068 + 0.938578i \(0.387856\pi\)
\(198\) 137524. 0.249296
\(199\) 931354. 1.66718 0.833589 0.552385i \(-0.186282\pi\)
0.833589 + 0.552385i \(0.186282\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 97093.9 0.169513
\(202\) 35770.4 0.0616802
\(203\) 223162. 0.380085
\(204\) −228487. −0.384403
\(205\) 433131. 0.719838
\(206\) 199324. 0.327258
\(207\) −4785.78 −0.00776295
\(208\) 111285. 0.178353
\(209\) −153229. −0.242647
\(210\) 63828.7 0.0998776
\(211\) 801186. 1.23887 0.619437 0.785046i \(-0.287361\pi\)
0.619437 + 0.785046i \(0.287361\pi\)
\(212\) 260945. 0.398758
\(213\) 409749. 0.618826
\(214\) −763995. −1.14040
\(215\) 79578.0 0.117408
\(216\) −46656.0 −0.0680414
\(217\) −84595.6 −0.121955
\(218\) 122308. 0.174307
\(219\) −209942. −0.295793
\(220\) −169783. −0.236503
\(221\) −689759. −0.949985
\(222\) −220039. −0.299652
\(223\) 721812. 0.971990 0.485995 0.873962i \(-0.338457\pi\)
0.485995 + 0.873962i \(0.338457\pi\)
\(224\) 72622.9 0.0967060
\(225\) 50625.0 0.0666667
\(226\) 470082. 0.612212
\(227\) −98999.5 −0.127517 −0.0637585 0.997965i \(-0.520309\pi\)
−0.0637585 + 0.997965i \(0.520309\pi\)
\(228\) 51984.0 0.0662266
\(229\) −1.20946e6 −1.52406 −0.762030 0.647542i \(-0.775797\pi\)
−0.762030 + 0.647542i \(0.775797\pi\)
\(230\) 5908.37 0.00736458
\(231\) 270926. 0.334057
\(232\) 201385. 0.245644
\(233\) 244144. 0.294616 0.147308 0.989091i \(-0.452939\pi\)
0.147308 + 0.989091i \(0.452939\pi\)
\(234\) −140845. −0.168152
\(235\) 339319. 0.400810
\(236\) −62008.4 −0.0724720
\(237\) 274401. 0.317333
\(238\) −450125. −0.515099
\(239\) −910052. −1.03056 −0.515278 0.857023i \(-0.672311\pi\)
−0.515278 + 0.857023i \(0.672311\pi\)
\(240\) 57600.0 0.0645497
\(241\) 1.13156e6 1.25497 0.627486 0.778627i \(-0.284084\pi\)
0.627486 + 0.778627i \(0.284084\pi\)
\(242\) −76451.7 −0.0839168
\(243\) 59049.0 0.0641500
\(244\) 595146. 0.639955
\(245\) −294431. −0.313378
\(246\) −623709. −0.657119
\(247\) 156930. 0.163668
\(248\) −76340.3 −0.0788179
\(249\) −463978. −0.474241
\(250\) −62500.0 −0.0632456
\(251\) 661454. 0.662698 0.331349 0.943508i \(-0.392496\pi\)
0.331349 + 0.943508i \(0.392496\pi\)
\(252\) −91913.4 −0.0911753
\(253\) 25078.5 0.0246320
\(254\) −1.16583e6 −1.13384
\(255\) −357011. −0.343820
\(256\) 65536.0 0.0625000
\(257\) −1.04229e6 −0.984364 −0.492182 0.870492i \(-0.663801\pi\)
−0.492182 + 0.870492i \(0.663801\pi\)
\(258\) −114592. −0.107178
\(259\) −433482. −0.401533
\(260\) 173883. 0.159523
\(261\) −254878. −0.231596
\(262\) 455398. 0.409862
\(263\) 827987. 0.738133 0.369066 0.929403i \(-0.379678\pi\)
0.369066 + 0.929403i \(0.379678\pi\)
\(264\) 244487. 0.215897
\(265\) 407727. 0.356660
\(266\) 102410. 0.0887435
\(267\) −556837. −0.478024
\(268\) 172611. 0.146802
\(269\) 1.20075e6 1.01175 0.505873 0.862608i \(-0.331170\pi\)
0.505873 + 0.862608i \(0.331170\pi\)
\(270\) −72900.0 −0.0608581
\(271\) 335669. 0.277644 0.138822 0.990317i \(-0.455668\pi\)
0.138822 + 0.990317i \(0.455668\pi\)
\(272\) −406200. −0.332903
\(273\) −277469. −0.225324
\(274\) −122365. −0.0984649
\(275\) −265286. −0.211535
\(276\) −8508.05 −0.00672291
\(277\) 1.89258e6 1.48202 0.741012 0.671492i \(-0.234346\pi\)
0.741012 + 0.671492i \(0.234346\pi\)
\(278\) −871350. −0.676209
\(279\) 96618.2 0.0743102
\(280\) 113473. 0.0864965
\(281\) 1.11184e6 0.839991 0.419996 0.907526i \(-0.362032\pi\)
0.419996 + 0.907526i \(0.362032\pi\)
\(282\) −488619. −0.365887
\(283\) −1.05166e6 −0.780567 −0.390284 0.920695i \(-0.627623\pi\)
−0.390284 + 0.920695i \(0.627623\pi\)
\(284\) 728442. 0.535919
\(285\) 81225.0 0.0592349
\(286\) 738060. 0.533552
\(287\) −1.22872e6 −0.880539
\(288\) −82944.0 −0.0589256
\(289\) 1.09782e6 0.773188
\(290\) 314664. 0.219711
\(291\) 303134. 0.209846
\(292\) −373229. −0.256164
\(293\) 1.11859e6 0.761202 0.380601 0.924739i \(-0.375717\pi\)
0.380601 + 0.924739i \(0.375717\pi\)
\(294\) 423981. 0.286074
\(295\) −96888.1 −0.0648209
\(296\) −391181. −0.259506
\(297\) −309429. −0.203550
\(298\) 922561. 0.601803
\(299\) −25684.2 −0.0166145
\(300\) 90000.0 0.0577350
\(301\) −225750. −0.143619
\(302\) −1.34278e6 −0.847201
\(303\) −80483.5 −0.0503617
\(304\) 92416.0 0.0573539
\(305\) 929916. 0.572393
\(306\) 514097. 0.313864
\(307\) 267560. 0.162022 0.0810112 0.996713i \(-0.474185\pi\)
0.0810112 + 0.996713i \(0.474185\pi\)
\(308\) 481646. 0.289302
\(309\) −448478. −0.267205
\(310\) −119282. −0.0704969
\(311\) 564281. 0.330822 0.165411 0.986225i \(-0.447105\pi\)
0.165411 + 0.986225i \(0.447105\pi\)
\(312\) −250392. −0.145624
\(313\) −401197. −0.231471 −0.115736 0.993280i \(-0.536923\pi\)
−0.115736 + 0.993280i \(0.536923\pi\)
\(314\) −412134. −0.235892
\(315\) −143615. −0.0815497
\(316\) 487824. 0.274818
\(317\) 16683.0 0.00932449 0.00466224 0.999989i \(-0.498516\pi\)
0.00466224 + 0.999989i \(0.498516\pi\)
\(318\) −587127. −0.325585
\(319\) 1.33561e6 0.734859
\(320\) 102400. 0.0559017
\(321\) 1.71899e6 0.931130
\(322\) −16761.0 −0.00900868
\(323\) −572805. −0.305493
\(324\) 104976. 0.0555556
\(325\) 271693. 0.142682
\(326\) −523167. −0.272644
\(327\) −275193. −0.142321
\(328\) −1.10882e6 −0.569082
\(329\) −962590. −0.490288
\(330\) 382011. 0.193104
\(331\) −2.37141e6 −1.18970 −0.594849 0.803838i \(-0.702788\pi\)
−0.594849 + 0.803838i \(0.702788\pi\)
\(332\) −824850. −0.410705
\(333\) 495088. 0.244665
\(334\) −940953. −0.461532
\(335\) 269705. 0.131304
\(336\) −163402. −0.0789601
\(337\) −1.13740e6 −0.545555 −0.272778 0.962077i \(-0.587942\pi\)
−0.272778 + 0.962077i \(0.587942\pi\)
\(338\) 729287. 0.347222
\(339\) −1.05768e6 −0.499869
\(340\) −634687. −0.297757
\(341\) −506300. −0.235788
\(342\) −116964. −0.0540738
\(343\) 2.02722e6 0.930390
\(344\) −203720. −0.0928190
\(345\) −13293.8 −0.00601315
\(346\) −619585. −0.278234
\(347\) −1.38681e6 −0.618290 −0.309145 0.951015i \(-0.600043\pi\)
−0.309145 + 0.951015i \(0.600043\pi\)
\(348\) −453116. −0.200568
\(349\) −2.02768e6 −0.891121 −0.445560 0.895252i \(-0.646996\pi\)
−0.445560 + 0.895252i \(0.646996\pi\)
\(350\) 177302. 0.0773648
\(351\) 316902. 0.137296
\(352\) 434644. 0.186972
\(353\) −3.01402e6 −1.28739 −0.643693 0.765283i \(-0.722599\pi\)
−0.643693 + 0.765283i \(0.722599\pi\)
\(354\) 139519. 0.0591732
\(355\) 1.13819e6 0.479341
\(356\) −989933. −0.413981
\(357\) 1.01278e6 0.420577
\(358\) −882761. −0.364029
\(359\) −1.42115e6 −0.581974 −0.290987 0.956727i \(-0.593984\pi\)
−0.290987 + 0.956727i \(0.593984\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) −1.84191e6 −0.738748
\(363\) 172016. 0.0685178
\(364\) −493278. −0.195136
\(365\) −583171. −0.229120
\(366\) −1.33908e6 −0.522521
\(367\) 129477. 0.0501794 0.0250897 0.999685i \(-0.492013\pi\)
0.0250897 + 0.999685i \(0.492013\pi\)
\(368\) −15125.4 −0.00582221
\(369\) 1.40335e6 0.536536
\(370\) −611220. −0.232110
\(371\) −1.15665e6 −0.436283
\(372\) 171766. 0.0643545
\(373\) −1.88154e6 −0.700230 −0.350115 0.936707i \(-0.613858\pi\)
−0.350115 + 0.936707i \(0.613858\pi\)
\(374\) −2.69398e6 −0.995897
\(375\) 140625. 0.0516398
\(376\) −868656. −0.316868
\(377\) −1.36787e6 −0.495668
\(378\) 206805. 0.0744443
\(379\) −3.06386e6 −1.09565 −0.547824 0.836594i \(-0.684544\pi\)
−0.547824 + 0.836594i \(0.684544\pi\)
\(380\) 144400. 0.0512989
\(381\) 2.62312e6 0.925775
\(382\) 2.07645e6 0.728054
\(383\) −2.30188e6 −0.801837 −0.400919 0.916114i \(-0.631309\pi\)
−0.400919 + 0.916114i \(0.631309\pi\)
\(384\) −147456. −0.0510310
\(385\) 752571. 0.258759
\(386\) −3.34615e6 −1.14308
\(387\) 257833. 0.0875106
\(388\) 538904. 0.181732
\(389\) 4.00419e6 1.34165 0.670826 0.741614i \(-0.265940\pi\)
0.670826 + 0.741614i \(0.265940\pi\)
\(390\) −391237. −0.130250
\(391\) 93749.1 0.0310117
\(392\) 753743. 0.247747
\(393\) −1.02464e6 −0.334651
\(394\) −1.50370e6 −0.488000
\(395\) 762225. 0.245805
\(396\) −550097. −0.176279
\(397\) −946037. −0.301253 −0.150627 0.988591i \(-0.548129\pi\)
−0.150627 + 0.988591i \(0.548129\pi\)
\(398\) −3.72541e6 −1.17887
\(399\) −230422. −0.0724588
\(400\) 160000. 0.0500000
\(401\) −566175. −0.175829 −0.0879144 0.996128i \(-0.528020\pi\)
−0.0879144 + 0.996128i \(0.528020\pi\)
\(402\) −388376. −0.119863
\(403\) 518528. 0.159041
\(404\) −143082. −0.0436145
\(405\) 164025. 0.0496904
\(406\) −892648. −0.268760
\(407\) −2.59437e6 −0.776328
\(408\) 913949. 0.271814
\(409\) −1.77345e6 −0.524216 −0.262108 0.965038i \(-0.584418\pi\)
−0.262108 + 0.965038i \(0.584418\pi\)
\(410\) −1.73253e6 −0.509002
\(411\) 275322. 0.0803962
\(412\) −797295. −0.231407
\(413\) 274855. 0.0792919
\(414\) 19143.1 0.00548923
\(415\) −1.28883e6 −0.367346
\(416\) −445141. −0.126114
\(417\) 1.96054e6 0.552122
\(418\) 612916. 0.171578
\(419\) −3.72599e6 −1.03683 −0.518414 0.855130i \(-0.673477\pi\)
−0.518414 + 0.855130i \(0.673477\pi\)
\(420\) −255315. −0.0706241
\(421\) −186198. −0.0511999 −0.0256000 0.999672i \(-0.508150\pi\)
−0.0256000 + 0.999672i \(0.508150\pi\)
\(422\) −3.20475e6 −0.876017
\(423\) 1.09939e6 0.298746
\(424\) −1.04378e6 −0.281965
\(425\) −991699. −0.266322
\(426\) −1.63900e6 −0.437576
\(427\) −2.63802e6 −0.700177
\(428\) 3.05598e6 0.806383
\(429\) −1.66064e6 −0.435643
\(430\) −318312. −0.0830199
\(431\) 5.29721e6 1.37358 0.686790 0.726856i \(-0.259019\pi\)
0.686790 + 0.726856i \(0.259019\pi\)
\(432\) 186624. 0.0481125
\(433\) 6.39018e6 1.63792 0.818961 0.573849i \(-0.194550\pi\)
0.818961 + 0.573849i \(0.194550\pi\)
\(434\) 338382. 0.0862350
\(435\) −707994. −0.179393
\(436\) −489232. −0.123253
\(437\) −21329.2 −0.00534283
\(438\) 839766. 0.209157
\(439\) −1.57271e6 −0.389481 −0.194740 0.980855i \(-0.562386\pi\)
−0.194740 + 0.980855i \(0.562386\pi\)
\(440\) 679132. 0.167233
\(441\) −953956. −0.233578
\(442\) 2.75904e6 0.671741
\(443\) 1.60421e6 0.388375 0.194188 0.980964i \(-0.437793\pi\)
0.194188 + 0.980964i \(0.437793\pi\)
\(444\) 880157. 0.211886
\(445\) −1.54677e6 −0.370276
\(446\) −2.88725e6 −0.687301
\(447\) −2.07576e6 −0.491370
\(448\) −290492. −0.0683815
\(449\) −6.08434e6 −1.42429 −0.712144 0.702033i \(-0.752276\pi\)
−0.712144 + 0.702033i \(0.752276\pi\)
\(450\) −202500. −0.0471405
\(451\) −7.35383e6 −1.70244
\(452\) −1.88033e6 −0.432900
\(453\) 3.02125e6 0.691736
\(454\) 395998. 0.0901682
\(455\) −770746. −0.174535
\(456\) −207936. −0.0468293
\(457\) 5.27622e6 1.18177 0.590884 0.806757i \(-0.298779\pi\)
0.590884 + 0.806757i \(0.298779\pi\)
\(458\) 4.83783e6 1.07767
\(459\) −1.15672e6 −0.256269
\(460\) −23633.5 −0.00520754
\(461\) −5.02650e6 −1.10157 −0.550787 0.834646i \(-0.685672\pi\)
−0.550787 + 0.834646i \(0.685672\pi\)
\(462\) −1.08370e6 −0.236214
\(463\) 5.23215e6 1.13430 0.567150 0.823615i \(-0.308046\pi\)
0.567150 + 0.823615i \(0.308046\pi\)
\(464\) −805539. −0.173697
\(465\) 268384. 0.0575605
\(466\) −976576. −0.208325
\(467\) 1.53407e6 0.325501 0.162750 0.986667i \(-0.447963\pi\)
0.162750 + 0.986667i \(0.447963\pi\)
\(468\) 563382. 0.118902
\(469\) −765109. −0.160617
\(470\) −1.35727e6 −0.283415
\(471\) 927301. 0.192605
\(472\) 248034. 0.0512455
\(473\) −1.35110e6 −0.277673
\(474\) −1.09760e6 −0.224388
\(475\) 225625. 0.0458831
\(476\) 1.80050e6 0.364230
\(477\) 1.32104e6 0.265839
\(478\) 3.64021e6 0.728713
\(479\) 479006. 0.0953898 0.0476949 0.998862i \(-0.484812\pi\)
0.0476949 + 0.998862i \(0.484812\pi\)
\(480\) −230400. −0.0456435
\(481\) 2.65702e6 0.523640
\(482\) −4.52623e6 −0.887400
\(483\) 37712.3 0.00735556
\(484\) 305807. 0.0593381
\(485\) 842038. 0.162546
\(486\) −236196. −0.0453609
\(487\) −2.75400e6 −0.526190 −0.263095 0.964770i \(-0.584743\pi\)
−0.263095 + 0.964770i \(0.584743\pi\)
\(488\) −2.38058e6 −0.452516
\(489\) 1.17713e6 0.222613
\(490\) 1.17772e6 0.221592
\(491\) −3.42335e6 −0.640837 −0.320419 0.947276i \(-0.603824\pi\)
−0.320419 + 0.947276i \(0.603824\pi\)
\(492\) 2.49484e6 0.464654
\(493\) 4.99283e6 0.925186
\(494\) −627719. −0.115730
\(495\) −859526. −0.157669
\(496\) 305361. 0.0557327
\(497\) −3.22886e6 −0.586351
\(498\) 1.85591e6 0.335339
\(499\) −1.85318e6 −0.333170 −0.166585 0.986027i \(-0.553274\pi\)
−0.166585 + 0.986027i \(0.553274\pi\)
\(500\) 250000. 0.0447214
\(501\) 2.11714e6 0.376839
\(502\) −2.64582e6 −0.468598
\(503\) 6.45275e6 1.13717 0.568584 0.822625i \(-0.307491\pi\)
0.568584 + 0.822625i \(0.307491\pi\)
\(504\) 367653. 0.0644707
\(505\) −223565. −0.0390100
\(506\) −100314. −0.0174175
\(507\) −1.64090e6 −0.283505
\(508\) 4.66332e6 0.801745
\(509\) −1.13203e7 −1.93671 −0.968355 0.249576i \(-0.919709\pi\)
−0.968355 + 0.249576i \(0.919709\pi\)
\(510\) 1.42805e6 0.243118
\(511\) 1.65436e6 0.280270
\(512\) −262144. −0.0441942
\(513\) 263169. 0.0441511
\(514\) 4.16916e6 0.696051
\(515\) −1.24577e6 −0.206976
\(516\) 458369. 0.0757864
\(517\) −5.76105e6 −0.947928
\(518\) 1.73393e6 0.283927
\(519\) 1.39407e6 0.227177
\(520\) −695533. −0.112800
\(521\) −5.48806e6 −0.885777 −0.442888 0.896577i \(-0.646046\pi\)
−0.442888 + 0.896577i \(0.646046\pi\)
\(522\) 1.01951e6 0.163763
\(523\) 6.89470e6 1.10220 0.551101 0.834439i \(-0.314208\pi\)
0.551101 + 0.834439i \(0.314208\pi\)
\(524\) −1.82159e6 −0.289816
\(525\) −398929. −0.0631681
\(526\) −3.31195e6 −0.521939
\(527\) −1.89266e6 −0.296857
\(528\) −977949. −0.152662
\(529\) −6.43285e6 −0.999458
\(530\) −1.63091e6 −0.252197
\(531\) −313917. −0.0483147
\(532\) −409639. −0.0627512
\(533\) 7.53143e6 1.14831
\(534\) 2.22735e6 0.338014
\(535\) 4.77497e6 0.721250
\(536\) −690446. −0.103805
\(537\) 1.98621e6 0.297228
\(538\) −4.80300e6 −0.715413
\(539\) 4.99893e6 0.741149
\(540\) 291600. 0.0430331
\(541\) −2.80191e6 −0.411587 −0.205793 0.978595i \(-0.565977\pi\)
−0.205793 + 0.978595i \(0.565977\pi\)
\(542\) −1.34268e6 −0.196324
\(543\) 4.14429e6 0.603185
\(544\) 1.62480e6 0.235398
\(545\) −764426. −0.110241
\(546\) 1.10987e6 0.159328
\(547\) 6.37022e6 0.910304 0.455152 0.890414i \(-0.349585\pi\)
0.455152 + 0.890414i \(0.349585\pi\)
\(548\) 489461. 0.0696252
\(549\) 3.01293e6 0.426636
\(550\) 1.06114e6 0.149578
\(551\) −1.13594e6 −0.159395
\(552\) 34032.2 0.00475381
\(553\) −2.16230e6 −0.300680
\(554\) −7.57033e6 −1.04795
\(555\) 1.37524e6 0.189517
\(556\) 3.48540e6 0.478152
\(557\) 8.20081e6 1.12000 0.560001 0.828492i \(-0.310801\pi\)
0.560001 + 0.828492i \(0.310801\pi\)
\(558\) −386473. −0.0525453
\(559\) 1.38373e6 0.187293
\(560\) −453893. −0.0611623
\(561\) 6.06144e6 0.813147
\(562\) −4.44734e6 −0.593964
\(563\) 9.42484e6 1.25315 0.626575 0.779361i \(-0.284456\pi\)
0.626575 + 0.779361i \(0.284456\pi\)
\(564\) 1.95448e6 0.258721
\(565\) −2.93801e6 −0.387197
\(566\) 4.20665e6 0.551945
\(567\) −465311. −0.0607835
\(568\) −2.91377e6 −0.378952
\(569\) −9.94455e6 −1.28767 −0.643835 0.765164i \(-0.722658\pi\)
−0.643835 + 0.765164i \(0.722658\pi\)
\(570\) −324900. −0.0418854
\(571\) −2.04818e6 −0.262892 −0.131446 0.991323i \(-0.541962\pi\)
−0.131446 + 0.991323i \(0.541962\pi\)
\(572\) −2.95224e6 −0.377278
\(573\) −4.67202e6 −0.594454
\(574\) 4.91488e6 0.622635
\(575\) −36927.3 −0.00465777
\(576\) 331776. 0.0416667
\(577\) −1.18520e6 −0.148202 −0.0741008 0.997251i \(-0.523609\pi\)
−0.0741008 + 0.997251i \(0.523609\pi\)
\(578\) −4.39126e6 −0.546726
\(579\) 7.52885e6 0.933323
\(580\) −1.25866e6 −0.155359
\(581\) 3.65619e6 0.449354
\(582\) −1.21253e6 −0.148384
\(583\) −6.92251e6 −0.843513
\(584\) 1.49292e6 0.181136
\(585\) 880284. 0.106349
\(586\) −4.47434e6 −0.538251
\(587\) −9.38735e6 −1.12447 −0.562235 0.826978i \(-0.690058\pi\)
−0.562235 + 0.826978i \(0.690058\pi\)
\(588\) −1.69592e6 −0.202285
\(589\) 430607. 0.0511438
\(590\) 387552. 0.0458353
\(591\) 3.38332e6 0.398450
\(592\) 1.56472e6 0.183499
\(593\) 522811. 0.0610531 0.0305266 0.999534i \(-0.490282\pi\)
0.0305266 + 0.999534i \(0.490282\pi\)
\(594\) 1.23772e6 0.143931
\(595\) 2.81328e6 0.325777
\(596\) −3.69025e6 −0.425539
\(597\) 8.38218e6 0.962546
\(598\) 102737. 0.0117482
\(599\) 2.07339e6 0.236110 0.118055 0.993007i \(-0.462334\pi\)
0.118055 + 0.993007i \(0.462334\pi\)
\(600\) −360000. −0.0408248
\(601\) −1.48680e7 −1.67906 −0.839531 0.543311i \(-0.817170\pi\)
−0.839531 + 0.543311i \(0.817170\pi\)
\(602\) 902998. 0.101554
\(603\) 873845. 0.0978681
\(604\) 5.37111e6 0.599061
\(605\) 477823. 0.0530736
\(606\) 321934. 0.0356111
\(607\) 6.42430e6 0.707707 0.353854 0.935301i \(-0.384871\pi\)
0.353854 + 0.935301i \(0.384871\pi\)
\(608\) −369664. −0.0405554
\(609\) 2.00846e6 0.219442
\(610\) −3.71966e6 −0.404743
\(611\) 5.90018e6 0.639385
\(612\) −2.05639e6 −0.221935
\(613\) 1.34202e7 1.44247 0.721235 0.692690i \(-0.243575\pi\)
0.721235 + 0.692690i \(0.243575\pi\)
\(614\) −1.07024e6 −0.114567
\(615\) 3.89818e6 0.415599
\(616\) −1.92658e6 −0.204567
\(617\) 1.44685e7 1.53007 0.765033 0.643991i \(-0.222723\pi\)
0.765033 + 0.643991i \(0.222723\pi\)
\(618\) 1.79391e6 0.188943
\(619\) 1.51094e7 1.58497 0.792483 0.609894i \(-0.208788\pi\)
0.792483 + 0.609894i \(0.208788\pi\)
\(620\) 477127. 0.0498488
\(621\) −43072.0 −0.00448194
\(622\) −2.25713e6 −0.233927
\(623\) 4.38793e6 0.452938
\(624\) 1.00157e6 0.102972
\(625\) 390625. 0.0400000
\(626\) 1.60479e6 0.163675
\(627\) −1.37906e6 −0.140092
\(628\) 1.64854e6 0.166801
\(629\) −9.69833e6 −0.977396
\(630\) 574458. 0.0576643
\(631\) 827007. 0.0826868 0.0413434 0.999145i \(-0.486836\pi\)
0.0413434 + 0.999145i \(0.486836\pi\)
\(632\) −1.95130e6 −0.194326
\(633\) 7.21068e6 0.715265
\(634\) −66731.8 −0.00659341
\(635\) 7.28644e6 0.717102
\(636\) 2.34851e6 0.230223
\(637\) −5.11966e6 −0.499911
\(638\) −5.34245e6 −0.519624
\(639\) 3.68774e6 0.357279
\(640\) −409600. −0.0395285
\(641\) 2.10060e6 0.201929 0.100964 0.994890i \(-0.467807\pi\)
0.100964 + 0.994890i \(0.467807\pi\)
\(642\) −6.87596e6 −0.658409
\(643\) 2.96705e6 0.283008 0.141504 0.989938i \(-0.454806\pi\)
0.141504 + 0.989938i \(0.454806\pi\)
\(644\) 67044.2 0.00637010
\(645\) 716202. 0.0677854
\(646\) 2.29122e6 0.216016
\(647\) −2.57086e6 −0.241445 −0.120723 0.992686i \(-0.538521\pi\)
−0.120723 + 0.992686i \(0.538521\pi\)
\(648\) −419904. −0.0392837
\(649\) 1.64499e6 0.153304
\(650\) −1.08677e6 −0.100891
\(651\) −761360. −0.0704105
\(652\) 2.09267e6 0.192789
\(653\) −700959. −0.0643294 −0.0321647 0.999483i \(-0.510240\pi\)
−0.0321647 + 0.999483i \(0.510240\pi\)
\(654\) 1.10077e6 0.100636
\(655\) −2.84623e6 −0.259219
\(656\) 4.43526e6 0.402402
\(657\) −1.88947e6 −0.170776
\(658\) 3.85036e6 0.346686
\(659\) −1.71014e7 −1.53398 −0.766989 0.641660i \(-0.778246\pi\)
−0.766989 + 0.641660i \(0.778246\pi\)
\(660\) −1.52805e6 −0.136545
\(661\) 1.85258e7 1.64920 0.824601 0.565715i \(-0.191400\pi\)
0.824601 + 0.565715i \(0.191400\pi\)
\(662\) 9.48564e6 0.841243
\(663\) −6.20783e6 −0.548474
\(664\) 3.29940e6 0.290412
\(665\) −640060. −0.0561263
\(666\) −1.98035e6 −0.173004
\(667\) 185915. 0.0161808
\(668\) 3.76381e6 0.326352
\(669\) 6.49631e6 0.561179
\(670\) −1.07882e6 −0.0928458
\(671\) −1.57884e7 −1.35373
\(672\) 653606. 0.0558332
\(673\) 1.62516e7 1.38311 0.691557 0.722322i \(-0.256925\pi\)
0.691557 + 0.722322i \(0.256925\pi\)
\(674\) 4.54960e6 0.385766
\(675\) 455625. 0.0384900
\(676\) −2.91715e6 −0.245523
\(677\) 8.11531e6 0.680508 0.340254 0.940334i \(-0.389487\pi\)
0.340254 + 0.940334i \(0.389487\pi\)
\(678\) 4.23073e6 0.353461
\(679\) −2.38872e6 −0.198834
\(680\) 2.53875e6 0.210546
\(681\) −890995. −0.0736220
\(682\) 2.02520e6 0.166727
\(683\) −1.47875e7 −1.21295 −0.606475 0.795103i \(-0.707417\pi\)
−0.606475 + 0.795103i \(0.707417\pi\)
\(684\) 467856. 0.0382360
\(685\) 764782. 0.0622747
\(686\) −8.10887e6 −0.657885
\(687\) −1.08851e7 −0.879916
\(688\) 814879. 0.0656330
\(689\) 7.08969e6 0.568957
\(690\) 53175.3 0.00425194
\(691\) −1.57667e7 −1.25616 −0.628081 0.778148i \(-0.716159\pi\)
−0.628081 + 0.778148i \(0.716159\pi\)
\(692\) 2.47834e6 0.196741
\(693\) 2.43833e6 0.192868
\(694\) 5.54723e6 0.437197
\(695\) 5.44594e6 0.427672
\(696\) 1.81246e6 0.141823
\(697\) −2.74903e7 −2.14337
\(698\) 8.11073e6 0.630118
\(699\) 2.19730e6 0.170097
\(700\) −709208. −0.0547052
\(701\) −1.51464e7 −1.16416 −0.582082 0.813130i \(-0.697762\pi\)
−0.582082 + 0.813130i \(0.697762\pi\)
\(702\) −1.26761e6 −0.0970829
\(703\) 2.20650e6 0.168390
\(704\) −1.73858e6 −0.132209
\(705\) 3.05387e6 0.231408
\(706\) 1.20561e7 0.910320
\(707\) 634217. 0.0477188
\(708\) −558075. −0.0418417
\(709\) 8.26009e6 0.617119 0.308560 0.951205i \(-0.400153\pi\)
0.308560 + 0.951205i \(0.400153\pi\)
\(710\) −4.55276e6 −0.338945
\(711\) 2.46961e6 0.183212
\(712\) 3.95973e6 0.292729
\(713\) −70476.0 −0.00519180
\(714\) −4.05113e6 −0.297393
\(715\) −4.61288e6 −0.337448
\(716\) 3.53104e6 0.257407
\(717\) −8.19046e6 −0.594991
\(718\) 5.68460e6 0.411518
\(719\) 6.81658e6 0.491750 0.245875 0.969302i \(-0.420925\pi\)
0.245875 + 0.969302i \(0.420925\pi\)
\(720\) 518400. 0.0372678
\(721\) 3.53405e6 0.253183
\(722\) −521284. −0.0372161
\(723\) 1.01840e7 0.724559
\(724\) 7.36763e6 0.522373
\(725\) −1.96665e6 −0.138957
\(726\) −688066. −0.0484494
\(727\) 5.61211e6 0.393813 0.196907 0.980422i \(-0.436910\pi\)
0.196907 + 0.980422i \(0.436910\pi\)
\(728\) 1.97311e6 0.137982
\(729\) 531441. 0.0370370
\(730\) 2.33268e6 0.162013
\(731\) −5.05072e6 −0.349590
\(732\) 5.35632e6 0.369478
\(733\) −6.12350e6 −0.420959 −0.210479 0.977598i \(-0.567503\pi\)
−0.210479 + 0.977598i \(0.567503\pi\)
\(734\) −517906. −0.0354822
\(735\) −2.64988e6 −0.180929
\(736\) 60501.7 0.00411692
\(737\) −4.57913e6 −0.310538
\(738\) −5.61338e6 −0.379388
\(739\) −1.87069e7 −1.26006 −0.630031 0.776570i \(-0.716958\pi\)
−0.630031 + 0.776570i \(0.716958\pi\)
\(740\) 2.44488e6 0.164126
\(741\) 1.41237e6 0.0944935
\(742\) 4.62661e6 0.308499
\(743\) −1.63435e7 −1.08611 −0.543055 0.839697i \(-0.682733\pi\)
−0.543055 + 0.839697i \(0.682733\pi\)
\(744\) −687063. −0.0455055
\(745\) −5.76601e6 −0.380614
\(746\) 7.52615e6 0.495137
\(747\) −4.17580e6 −0.273803
\(748\) 1.07759e7 0.704206
\(749\) −1.35458e7 −0.882266
\(750\) −562500. −0.0365148
\(751\) −3.02253e7 −1.95556 −0.977779 0.209640i \(-0.932771\pi\)
−0.977779 + 0.209640i \(0.932771\pi\)
\(752\) 3.47462e6 0.224059
\(753\) 5.95309e6 0.382609
\(754\) 5.47148e6 0.350490
\(755\) 8.39235e6 0.535817
\(756\) −827220. −0.0526401
\(757\) 6.42262e6 0.407354 0.203677 0.979038i \(-0.434711\pi\)
0.203677 + 0.979038i \(0.434711\pi\)
\(758\) 1.22554e7 0.774740
\(759\) 225706. 0.0142213
\(760\) −577600. −0.0362738
\(761\) 205823. 0.0128835 0.00644173 0.999979i \(-0.497950\pi\)
0.00644173 + 0.999979i \(0.497950\pi\)
\(762\) −1.04925e7 −0.654622
\(763\) 2.16855e6 0.134852
\(764\) −8.30581e6 −0.514812
\(765\) −3.21310e6 −0.198505
\(766\) 9.20753e6 0.566984
\(767\) −1.68472e6 −0.103405
\(768\) 589824. 0.0360844
\(769\) −2.52857e6 −0.154191 −0.0770955 0.997024i \(-0.524565\pi\)
−0.0770955 + 0.997024i \(0.524565\pi\)
\(770\) −3.01028e6 −0.182970
\(771\) −9.38061e6 −0.568323
\(772\) 1.33846e7 0.808282
\(773\) −1.30603e7 −0.786148 −0.393074 0.919507i \(-0.628588\pi\)
−0.393074 + 0.919507i \(0.628588\pi\)
\(774\) −1.03133e6 −0.0618794
\(775\) 745511. 0.0445861
\(776\) −2.15562e6 −0.128504
\(777\) −3.90134e6 −0.231825
\(778\) −1.60167e7 −0.948692
\(779\) 6.25442e6 0.369269
\(780\) 1.56495e6 0.0921009
\(781\) −1.93245e7 −1.13366
\(782\) −374996. −0.0219286
\(783\) −2.29390e6 −0.133712
\(784\) −3.01497e6 −0.175184
\(785\) 2.57584e6 0.149192
\(786\) 4.09858e6 0.236634
\(787\) 2.45143e7 1.41086 0.705429 0.708781i \(-0.250755\pi\)
0.705429 + 0.708781i \(0.250755\pi\)
\(788\) 6.01478e6 0.345068
\(789\) 7.45189e6 0.426161
\(790\) −3.04890e6 −0.173810
\(791\) 8.33464e6 0.473637
\(792\) 2.20039e6 0.124648
\(793\) 1.61697e7 0.913100
\(794\) 3.78415e6 0.213018
\(795\) 3.66954e6 0.205918
\(796\) 1.49017e7 0.833589
\(797\) 286670. 0.0159859 0.00799294 0.999968i \(-0.497456\pi\)
0.00799294 + 0.999968i \(0.497456\pi\)
\(798\) 921687. 0.0512361
\(799\) −2.15361e7 −1.19344
\(800\) −640000. −0.0353553
\(801\) −5.01153e6 −0.275987
\(802\) 2.26470e6 0.124330
\(803\) 9.90124e6 0.541877
\(804\) 1.55350e6 0.0847563
\(805\) 104757. 0.00569759
\(806\) −2.07411e6 −0.112459
\(807\) 1.08067e7 0.584132
\(808\) 572327. 0.0308401
\(809\) 1.78669e7 0.959791 0.479896 0.877326i \(-0.340675\pi\)
0.479896 + 0.877326i \(0.340675\pi\)
\(810\) −656100. −0.0351364
\(811\) −1.20577e7 −0.643745 −0.321873 0.946783i \(-0.604312\pi\)
−0.321873 + 0.946783i \(0.604312\pi\)
\(812\) 3.57059e6 0.190042
\(813\) 3.02102e6 0.160298
\(814\) 1.03775e7 0.548947
\(815\) 3.26979e6 0.172435
\(816\) −3.65580e6 −0.192201
\(817\) 1.14911e6 0.0602289
\(818\) 7.09380e6 0.370677
\(819\) −2.49722e6 −0.130091
\(820\) 6.93010e6 0.359919
\(821\) −1.17493e7 −0.608352 −0.304176 0.952616i \(-0.598381\pi\)
−0.304176 + 0.952616i \(0.598381\pi\)
\(822\) −1.10129e6 −0.0568487
\(823\) 1.10676e7 0.569577 0.284789 0.958590i \(-0.408077\pi\)
0.284789 + 0.958590i \(0.408077\pi\)
\(824\) 3.18918e6 0.163629
\(825\) −2.38757e6 −0.122130
\(826\) −1.09942e6 −0.0560678
\(827\) 2.51507e7 1.27875 0.639376 0.768895i \(-0.279193\pi\)
0.639376 + 0.768895i \(0.279193\pi\)
\(828\) −76572.4 −0.00388147
\(829\) −463735. −0.0234360 −0.0117180 0.999931i \(-0.503730\pi\)
−0.0117180 + 0.999931i \(0.503730\pi\)
\(830\) 5.15531e6 0.259752
\(831\) 1.70332e7 0.855647
\(832\) 1.78056e6 0.0891763
\(833\) 1.86872e7 0.933105
\(834\) −7.84215e6 −0.390409
\(835\) 5.88096e6 0.291898
\(836\) −2.45166e6 −0.121324
\(837\) 869564. 0.0429030
\(838\) 1.49040e7 0.733148
\(839\) 3.53079e7 1.73168 0.865840 0.500321i \(-0.166785\pi\)
0.865840 + 0.500321i \(0.166785\pi\)
\(840\) 1.02126e6 0.0499388
\(841\) −1.06098e7 −0.517271
\(842\) 744791. 0.0362038
\(843\) 1.00065e7 0.484969
\(844\) 1.28190e7 0.619437
\(845\) −4.55805e6 −0.219602
\(846\) −4.39757e6 −0.211245
\(847\) −1.35550e6 −0.0649221
\(848\) 4.17512e6 0.199379
\(849\) −9.46497e6 −0.450661
\(850\) 3.96679e6 0.188318
\(851\) −361131. −0.0170939
\(852\) 6.55598e6 0.309413
\(853\) −2.30045e6 −0.108253 −0.0541266 0.998534i \(-0.517237\pi\)
−0.0541266 + 0.998534i \(0.517237\pi\)
\(854\) 1.05521e7 0.495100
\(855\) 731025. 0.0341993
\(856\) −1.22239e7 −0.570199
\(857\) −1.10358e7 −0.513275 −0.256637 0.966508i \(-0.582615\pi\)
−0.256637 + 0.966508i \(0.582615\pi\)
\(858\) 6.64254e6 0.308046
\(859\) −1.14946e7 −0.531509 −0.265754 0.964041i \(-0.585621\pi\)
−0.265754 + 0.964041i \(0.585621\pi\)
\(860\) 1.27325e6 0.0587039
\(861\) −1.10585e7 −0.508379
\(862\) −2.11888e7 −0.971268
\(863\) −2.89632e7 −1.32379 −0.661896 0.749596i \(-0.730248\pi\)
−0.661896 + 0.749596i \(0.730248\pi\)
\(864\) −746496. −0.0340207
\(865\) 3.87241e6 0.175971
\(866\) −2.55607e7 −1.15819
\(867\) 9.88034e6 0.446400
\(868\) −1.35353e6 −0.0609773
\(869\) −1.29413e7 −0.581337
\(870\) 2.83197e6 0.126850
\(871\) 4.68972e6 0.209460
\(872\) 1.95693e6 0.0871533
\(873\) 2.72820e6 0.121155
\(874\) 85316.8 0.00377795
\(875\) −1.10814e6 −0.0489298
\(876\) −3.35906e6 −0.147897
\(877\) −4.14794e7 −1.82110 −0.910550 0.413400i \(-0.864341\pi\)
−0.910550 + 0.413400i \(0.864341\pi\)
\(878\) 6.29082e6 0.275405
\(879\) 1.00673e7 0.439480
\(880\) −2.71653e6 −0.118252
\(881\) −1.07385e6 −0.0466125 −0.0233063 0.999728i \(-0.507419\pi\)
−0.0233063 + 0.999728i \(0.507419\pi\)
\(882\) 3.81583e6 0.165165
\(883\) −1.19542e7 −0.515963 −0.257981 0.966150i \(-0.583057\pi\)
−0.257981 + 0.966150i \(0.583057\pi\)
\(884\) −1.10361e7 −0.474993
\(885\) −871993. −0.0374244
\(886\) −6.41683e6 −0.274623
\(887\) −2.95563e7 −1.26137 −0.630683 0.776040i \(-0.717225\pi\)
−0.630683 + 0.776040i \(0.717225\pi\)
\(888\) −3.52063e6 −0.149826
\(889\) −2.06704e7 −0.877192
\(890\) 6.18708e6 0.261825
\(891\) −2.78486e6 −0.117519
\(892\) 1.15490e7 0.485995
\(893\) 4.89976e6 0.205611
\(894\) 8.30305e6 0.347451
\(895\) 5.51726e6 0.230232
\(896\) 1.16197e6 0.0483530
\(897\) −231157. −0.00959239
\(898\) 2.43374e7 1.00712
\(899\) −3.75337e6 −0.154889
\(900\) 810000. 0.0333333
\(901\) −2.58779e7 −1.06198
\(902\) 2.94153e7 1.20381
\(903\) −2.03175e6 −0.0829182
\(904\) 7.52130e6 0.306106
\(905\) 1.15119e7 0.467225
\(906\) −1.20850e7 −0.489132
\(907\) −2.22140e6 −0.0896620 −0.0448310 0.998995i \(-0.514275\pi\)
−0.0448310 + 0.998995i \(0.514275\pi\)
\(908\) −1.58399e6 −0.0637585
\(909\) −724351. −0.0290763
\(910\) 3.08299e6 0.123415
\(911\) 1.76872e7 0.706096 0.353048 0.935605i \(-0.385145\pi\)
0.353048 + 0.935605i \(0.385145\pi\)
\(912\) 831744. 0.0331133
\(913\) 2.18821e7 0.868784
\(914\) −2.11049e7 −0.835636
\(915\) 8.36924e6 0.330471
\(916\) −1.93513e7 −0.762030
\(917\) 8.07429e6 0.317089
\(918\) 4.62687e6 0.181209
\(919\) −1.05563e7 −0.412308 −0.206154 0.978520i \(-0.566095\pi\)
−0.206154 + 0.978520i \(0.566095\pi\)
\(920\) 94533.9 0.00368229
\(921\) 2.40804e6 0.0935437
\(922\) 2.01060e7 0.778930
\(923\) 1.97912e7 0.764661
\(924\) 4.33481e6 0.167028
\(925\) 3.82012e6 0.146799
\(926\) −2.09286e7 −0.802071
\(927\) −4.03630e6 −0.154271
\(928\) 3.22216e6 0.122822
\(929\) 1.03562e7 0.393698 0.196849 0.980434i \(-0.436929\pi\)
0.196849 + 0.980434i \(0.436929\pi\)
\(930\) −1.07354e6 −0.0407014
\(931\) −4.25158e6 −0.160759
\(932\) 3.90630e6 0.147308
\(933\) 5.07853e6 0.191000
\(934\) −6.13627e6 −0.230164
\(935\) 1.68373e7 0.629861
\(936\) −2.25353e6 −0.0840762
\(937\) −3.78726e7 −1.40921 −0.704606 0.709598i \(-0.748876\pi\)
−0.704606 + 0.709598i \(0.748876\pi\)
\(938\) 3.06043e6 0.113573
\(939\) −3.61077e6 −0.133640
\(940\) 5.42910e6 0.200405
\(941\) −3.06386e7 −1.12796 −0.563981 0.825788i \(-0.690731\pi\)
−0.563981 + 0.825788i \(0.690731\pi\)
\(942\) −3.70920e6 −0.136193
\(943\) −1.02364e6 −0.0374859
\(944\) −992134. −0.0362360
\(945\) −1.29253e6 −0.0470827
\(946\) 5.40440e6 0.196345
\(947\) 2.61377e7 0.947093 0.473546 0.880769i \(-0.342974\pi\)
0.473546 + 0.880769i \(0.342974\pi\)
\(948\) 4.39042e6 0.158666
\(949\) −1.01404e7 −0.365501
\(950\) −902500. −0.0324443
\(951\) 150147. 0.00538350
\(952\) −7.20200e6 −0.257550
\(953\) 2.26998e7 0.809635 0.404817 0.914398i \(-0.367335\pi\)
0.404817 + 0.914398i \(0.367335\pi\)
\(954\) −5.28414e6 −0.187976
\(955\) −1.29778e7 −0.460462
\(956\) −1.45608e7 −0.515278
\(957\) 1.20205e7 0.424271
\(958\) −1.91602e6 −0.0674508
\(959\) −2.16956e6 −0.0761772
\(960\) 921600. 0.0322749
\(961\) −2.72063e7 −0.950302
\(962\) −1.06281e7 −0.370269
\(963\) 1.54709e7 0.537588
\(964\) 1.81049e7 0.627486
\(965\) 2.09135e7 0.722949
\(966\) −150849. −0.00520117
\(967\) −7.85571e6 −0.270159 −0.135079 0.990835i \(-0.543129\pi\)
−0.135079 + 0.990835i \(0.543129\pi\)
\(968\) −1.22323e6 −0.0419584
\(969\) −5.15525e6 −0.176376
\(970\) −3.36815e6 −0.114938
\(971\) −1.04223e7 −0.354744 −0.177372 0.984144i \(-0.556760\pi\)
−0.177372 + 0.984144i \(0.556760\pi\)
\(972\) 944784. 0.0320750
\(973\) −1.54492e7 −0.523148
\(974\) 1.10160e7 0.372072
\(975\) 2.44523e6 0.0823775
\(976\) 9.52234e6 0.319977
\(977\) −1.15180e7 −0.386046 −0.193023 0.981194i \(-0.561829\pi\)
−0.193023 + 0.981194i \(0.561829\pi\)
\(978\) −4.70850e6 −0.157411
\(979\) 2.62615e7 0.875715
\(980\) −4.71090e6 −0.156689
\(981\) −2.47674e6 −0.0821689
\(982\) 1.36934e7 0.453140
\(983\) −9.96368e6 −0.328879 −0.164439 0.986387i \(-0.552582\pi\)
−0.164439 + 0.986387i \(0.552582\pi\)
\(984\) −9.97934e6 −0.328560
\(985\) 9.39810e6 0.308638
\(986\) −1.99713e7 −0.654205
\(987\) −8.66331e6 −0.283068
\(988\) 2.51087e6 0.0818338
\(989\) −188070. −0.00611406
\(990\) 3.43810e6 0.111489
\(991\) 5.86825e7 1.89812 0.949061 0.315091i \(-0.102035\pi\)
0.949061 + 0.315091i \(0.102035\pi\)
\(992\) −1.22145e6 −0.0394089
\(993\) −2.13427e7 −0.686872
\(994\) 1.29154e7 0.414613
\(995\) 2.32838e7 0.745585
\(996\) −7.42365e6 −0.237121
\(997\) −2.25368e7 −0.718049 −0.359025 0.933328i \(-0.616891\pi\)
−0.359025 + 0.933328i \(0.616891\pi\)
\(998\) 7.41270e6 0.235586
\(999\) 4.45579e6 0.141257
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 570.6.a.m.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.m.1.2 4 1.1 even 1 trivial