Properties

Label 570.6.a.j.1.2
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $1$
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: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 25872 x^{2} - 1407374 x - 6356280\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-121.221\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -171.600 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -171.600 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +409.367 q^{11} -144.000 q^{12} -730.649 q^{13} +686.401 q^{14} -225.000 q^{15} +256.000 q^{16} +248.437 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1544.40 q^{21} -1637.47 q^{22} +1713.53 q^{23} +576.000 q^{24} +625.000 q^{25} +2922.59 q^{26} -729.000 q^{27} -2745.60 q^{28} -935.716 q^{29} +900.000 q^{30} +396.792 q^{31} -1024.00 q^{32} -3684.30 q^{33} -993.748 q^{34} -4290.01 q^{35} +1296.00 q^{36} -495.885 q^{37} -1444.00 q^{38} +6575.84 q^{39} -1600.00 q^{40} +17125.9 q^{41} -6177.61 q^{42} -22082.9 q^{43} +6549.87 q^{44} +2025.00 q^{45} -6854.11 q^{46} +11811.6 q^{47} -2304.00 q^{48} +12639.6 q^{49} -2500.00 q^{50} -2235.93 q^{51} -11690.4 q^{52} +6642.10 q^{53} +2916.00 q^{54} +10234.2 q^{55} +10982.4 q^{56} -3249.00 q^{57} +3742.87 q^{58} +606.503 q^{59} -3600.00 q^{60} -33867.0 q^{61} -1587.17 q^{62} -13899.6 q^{63} +4096.00 q^{64} -18266.2 q^{65} +14737.2 q^{66} +4109.20 q^{67} +3974.99 q^{68} -15421.8 q^{69} +17160.0 q^{70} +39645.6 q^{71} -5184.00 q^{72} +40536.8 q^{73} +1983.54 q^{74} -5625.00 q^{75} +5776.00 q^{76} -70247.4 q^{77} -26303.4 q^{78} +62602.2 q^{79} +6400.00 q^{80} +6561.00 q^{81} -68503.6 q^{82} -31307.4 q^{83} +24710.4 q^{84} +6210.93 q^{85} +88331.5 q^{86} +8421.45 q^{87} -26199.5 q^{88} +84209.3 q^{89} -8100.00 q^{90} +125380. q^{91} +27416.4 q^{92} -3571.13 q^{93} -47246.3 q^{94} +9025.00 q^{95} +9216.00 q^{96} +17525.0 q^{97} -50558.6 q^{98} +33158.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} - 400q^{10} - 246q^{11} - 576q^{12} + 640q^{13} + 432q^{14} - 900q^{15} + 1024q^{16} - 612q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 972q^{21} + 984q^{22} - 1242q^{23} + 2304q^{24} + 2500q^{25} - 2560q^{26} - 2916q^{27} - 1728q^{28} - 6230q^{29} + 3600q^{30} - 11360q^{31} - 4096q^{32} + 2214q^{33} + 2448q^{34} - 2700q^{35} + 5184q^{36} - 4792q^{37} - 5776q^{38} - 5760q^{39} - 6400q^{40} + 9170q^{41} - 3888q^{42} - 11412q^{43} - 3936q^{44} + 8100q^{45} + 4968q^{46} - 29858q^{47} - 9216q^{48} + 31092q^{49} - 10000q^{50} + 5508q^{51} + 10240q^{52} + 27498q^{53} + 11664q^{54} - 6150q^{55} + 6912q^{56} - 12996q^{57} + 24920q^{58} + 54984q^{59} - 14400q^{60} + 20868q^{61} + 45440q^{62} - 8748q^{63} + 16384q^{64} + 16000q^{65} - 8856q^{66} - 20244q^{67} - 9792q^{68} + 11178q^{69} + 10800q^{70} + 86864q^{71} - 20736q^{72} - 3728q^{73} + 19168q^{74} - 22500q^{75} + 23104q^{76} + 18796q^{77} + 23040q^{78} + 164192q^{79} + 25600q^{80} + 26244q^{81} - 36680q^{82} - 60506q^{83} + 15552q^{84} - 15300q^{85} + 45648q^{86} + 56070q^{87} + 15744q^{88} + 113798q^{89} - 32400q^{90} + 159528q^{91} - 19872q^{92} + 102240q^{93} + 119432q^{94} + 36100q^{95} + 36864q^{96} + 79440q^{97} - 124368q^{98} - 19926q^{99} + O(q^{100}) \)

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
\(7\) −171.600 −1.32365 −0.661824 0.749659i \(-0.730218\pi\)
−0.661824 + 0.749659i \(0.730218\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) 409.367 1.02007 0.510036 0.860153i \(-0.329632\pi\)
0.510036 + 0.860153i \(0.329632\pi\)
\(12\) −144.000 −0.288675
\(13\) −730.649 −1.19909 −0.599543 0.800343i \(-0.704651\pi\)
−0.599543 + 0.800343i \(0.704651\pi\)
\(14\) 686.401 0.935961
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) 248.437 0.208494 0.104247 0.994551i \(-0.466757\pi\)
0.104247 + 0.994551i \(0.466757\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) 1544.40 0.764209
\(22\) −1637.47 −0.721300
\(23\) 1713.53 0.675416 0.337708 0.941251i \(-0.390348\pi\)
0.337708 + 0.941251i \(0.390348\pi\)
\(24\) 576.000 0.204124
\(25\) 625.000 0.200000
\(26\) 2922.59 0.847882
\(27\) −729.000 −0.192450
\(28\) −2745.60 −0.661824
\(29\) −935.716 −0.206609 −0.103305 0.994650i \(-0.532942\pi\)
−0.103305 + 0.994650i \(0.532942\pi\)
\(30\) 900.000 0.182574
\(31\) 396.792 0.0741582 0.0370791 0.999312i \(-0.488195\pi\)
0.0370791 + 0.999312i \(0.488195\pi\)
\(32\) −1024.00 −0.176777
\(33\) −3684.30 −0.588939
\(34\) −993.748 −0.147428
\(35\) −4290.01 −0.591954
\(36\) 1296.00 0.166667
\(37\) −495.885 −0.0595494 −0.0297747 0.999557i \(-0.509479\pi\)
−0.0297747 + 0.999557i \(0.509479\pi\)
\(38\) −1444.00 −0.162221
\(39\) 6575.84 0.692293
\(40\) −1600.00 −0.158114
\(41\) 17125.9 1.59109 0.795543 0.605897i \(-0.207186\pi\)
0.795543 + 0.605897i \(0.207186\pi\)
\(42\) −6177.61 −0.540377
\(43\) −22082.9 −1.82131 −0.910656 0.413165i \(-0.864423\pi\)
−0.910656 + 0.413165i \(0.864423\pi\)
\(44\) 6549.87 0.510036
\(45\) 2025.00 0.149071
\(46\) −6854.11 −0.477591
\(47\) 11811.6 0.779944 0.389972 0.920827i \(-0.372485\pi\)
0.389972 + 0.920827i \(0.372485\pi\)
\(48\) −2304.00 −0.144338
\(49\) 12639.6 0.752046
\(50\) −2500.00 −0.141421
\(51\) −2235.93 −0.120374
\(52\) −11690.4 −0.599543
\(53\) 6642.10 0.324800 0.162400 0.986725i \(-0.448077\pi\)
0.162400 + 0.986725i \(0.448077\pi\)
\(54\) 2916.00 0.136083
\(55\) 10234.2 0.456190
\(56\) 10982.4 0.467981
\(57\) −3249.00 −0.132453
\(58\) 3742.87 0.146095
\(59\) 606.503 0.0226831 0.0113416 0.999936i \(-0.496390\pi\)
0.0113416 + 0.999936i \(0.496390\pi\)
\(60\) −3600.00 −0.129099
\(61\) −33867.0 −1.16534 −0.582669 0.812710i \(-0.697992\pi\)
−0.582669 + 0.812710i \(0.697992\pi\)
\(62\) −1587.17 −0.0524377
\(63\) −13899.6 −0.441216
\(64\) 4096.00 0.125000
\(65\) −18266.2 −0.536247
\(66\) 14737.2 0.416443
\(67\) 4109.20 0.111833 0.0559165 0.998435i \(-0.482192\pi\)
0.0559165 + 0.998435i \(0.482192\pi\)
\(68\) 3974.99 0.104247
\(69\) −15421.8 −0.389952
\(70\) 17160.0 0.418575
\(71\) 39645.6 0.933360 0.466680 0.884426i \(-0.345450\pi\)
0.466680 + 0.884426i \(0.345450\pi\)
\(72\) −5184.00 −0.117851
\(73\) 40536.8 0.890311 0.445156 0.895453i \(-0.353148\pi\)
0.445156 + 0.895453i \(0.353148\pi\)
\(74\) 1983.54 0.0421078
\(75\) −5625.00 −0.115470
\(76\) 5776.00 0.114708
\(77\) −70247.4 −1.35022
\(78\) −26303.4 −0.489525
\(79\) 62602.2 1.12855 0.564276 0.825586i \(-0.309155\pi\)
0.564276 + 0.825586i \(0.309155\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) −68503.6 −1.12507
\(83\) −31307.4 −0.498829 −0.249415 0.968397i \(-0.580238\pi\)
−0.249415 + 0.968397i \(0.580238\pi\)
\(84\) 24710.4 0.382105
\(85\) 6210.93 0.0932415
\(86\) 88331.5 1.28786
\(87\) 8421.45 0.119286
\(88\) −26199.5 −0.360650
\(89\) 84209.3 1.12690 0.563449 0.826151i \(-0.309474\pi\)
0.563449 + 0.826151i \(0.309474\pi\)
\(90\) −8100.00 −0.105409
\(91\) 125380. 1.58717
\(92\) 27416.4 0.337708
\(93\) −3571.13 −0.0428152
\(94\) −47246.3 −0.551504
\(95\) 9025.00 0.102598
\(96\) 9216.00 0.102062
\(97\) 17525.0 0.189117 0.0945583 0.995519i \(-0.469856\pi\)
0.0945583 + 0.995519i \(0.469856\pi\)
\(98\) −50558.6 −0.531777
\(99\) 33158.7 0.340024
\(100\) 10000.0 0.100000
\(101\) 4156.11 0.0405400 0.0202700 0.999795i \(-0.493547\pi\)
0.0202700 + 0.999795i \(0.493547\pi\)
\(102\) 8943.73 0.0851174
\(103\) 12638.4 0.117381 0.0586906 0.998276i \(-0.481307\pi\)
0.0586906 + 0.998276i \(0.481307\pi\)
\(104\) 46761.5 0.423941
\(105\) 38610.1 0.341765
\(106\) −26568.4 −0.229668
\(107\) −80915.4 −0.683238 −0.341619 0.939839i \(-0.610975\pi\)
−0.341619 + 0.939839i \(0.610975\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 31453.7 0.253574 0.126787 0.991930i \(-0.459533\pi\)
0.126787 + 0.991930i \(0.459533\pi\)
\(110\) −40936.7 −0.322575
\(111\) 4462.97 0.0343808
\(112\) −43929.7 −0.330912
\(113\) −73882.1 −0.544306 −0.272153 0.962254i \(-0.587736\pi\)
−0.272153 + 0.962254i \(0.587736\pi\)
\(114\) 12996.0 0.0936586
\(115\) 42838.2 0.302055
\(116\) −14971.5 −0.103305
\(117\) −59182.5 −0.399695
\(118\) −2426.01 −0.0160394
\(119\) −42631.9 −0.275973
\(120\) 14400.0 0.0912871
\(121\) 6530.00 0.0405462
\(122\) 135468. 0.824018
\(123\) −154133. −0.918614
\(124\) 6348.68 0.0370791
\(125\) 15625.0 0.0894427
\(126\) 55598.5 0.311987
\(127\) 197930. 1.08894 0.544469 0.838781i \(-0.316731\pi\)
0.544469 + 0.838781i \(0.316731\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 198746. 1.05154
\(130\) 73064.9 0.379184
\(131\) −296740. −1.51077 −0.755383 0.655283i \(-0.772549\pi\)
−0.755383 + 0.655283i \(0.772549\pi\)
\(132\) −58948.8 −0.294469
\(133\) −61947.7 −0.303666
\(134\) −16436.8 −0.0790779
\(135\) −18225.0 −0.0860663
\(136\) −15900.0 −0.0737138
\(137\) −103798. −0.472486 −0.236243 0.971694i \(-0.575916\pi\)
−0.236243 + 0.971694i \(0.575916\pi\)
\(138\) 61687.0 0.275738
\(139\) −208201. −0.914001 −0.457000 0.889466i \(-0.651076\pi\)
−0.457000 + 0.889466i \(0.651076\pi\)
\(140\) −68640.1 −0.295977
\(141\) −106304. −0.450301
\(142\) −158582. −0.659985
\(143\) −299103. −1.22315
\(144\) 20736.0 0.0833333
\(145\) −23392.9 −0.0923984
\(146\) −162147. −0.629545
\(147\) −113757. −0.434194
\(148\) −7934.17 −0.0297747
\(149\) −502065. −1.85265 −0.926327 0.376721i \(-0.877051\pi\)
−0.926327 + 0.376721i \(0.877051\pi\)
\(150\) 22500.0 0.0816497
\(151\) −367258. −1.31078 −0.655389 0.755292i \(-0.727495\pi\)
−0.655389 + 0.755292i \(0.727495\pi\)
\(152\) −23104.0 −0.0811107
\(153\) 20123.4 0.0694981
\(154\) 280990. 0.954747
\(155\) 9919.80 0.0331645
\(156\) 105213. 0.346146
\(157\) 154312. 0.499632 0.249816 0.968293i \(-0.419630\pi\)
0.249816 + 0.968293i \(0.419630\pi\)
\(158\) −250409. −0.798007
\(159\) −59778.9 −0.187523
\(160\) −25600.0 −0.0790569
\(161\) −294042. −0.894014
\(162\) −26244.0 −0.0785674
\(163\) −463772. −1.36721 −0.683606 0.729852i \(-0.739589\pi\)
−0.683606 + 0.729852i \(0.739589\pi\)
\(164\) 274014. 0.795543
\(165\) −92107.5 −0.263381
\(166\) 125230. 0.352726
\(167\) −540213. −1.49891 −0.749453 0.662058i \(-0.769683\pi\)
−0.749453 + 0.662058i \(0.769683\pi\)
\(168\) −98841.7 −0.270189
\(169\) 162555. 0.437807
\(170\) −24843.7 −0.0659317
\(171\) 29241.0 0.0764719
\(172\) −353326. −0.910656
\(173\) −381768. −0.969804 −0.484902 0.874569i \(-0.661145\pi\)
−0.484902 + 0.874569i \(0.661145\pi\)
\(174\) −33685.8 −0.0843478
\(175\) −107250. −0.264730
\(176\) 104798. 0.255018
\(177\) −5458.53 −0.0130961
\(178\) −336837. −0.796838
\(179\) 197548. 0.460828 0.230414 0.973093i \(-0.425992\pi\)
0.230414 + 0.973093i \(0.425992\pi\)
\(180\) 32400.0 0.0745356
\(181\) −641241. −1.45487 −0.727436 0.686176i \(-0.759288\pi\)
−0.727436 + 0.686176i \(0.759288\pi\)
\(182\) −501518. −1.12230
\(183\) 304803. 0.672808
\(184\) −109666. −0.238796
\(185\) −12397.1 −0.0266313
\(186\) 14284.5 0.0302749
\(187\) 101702. 0.212679
\(188\) 188985. 0.389972
\(189\) 125097. 0.254736
\(190\) −36100.0 −0.0725476
\(191\) −25116.2 −0.0498162 −0.0249081 0.999690i \(-0.507929\pi\)
−0.0249081 + 0.999690i \(0.507929\pi\)
\(192\) −36864.0 −0.0721688
\(193\) −53912.4 −0.104183 −0.0520913 0.998642i \(-0.516589\pi\)
−0.0520913 + 0.998642i \(0.516589\pi\)
\(194\) −70100.2 −0.133726
\(195\) 164396. 0.309603
\(196\) 202234. 0.376023
\(197\) 483800. 0.888179 0.444090 0.895982i \(-0.353527\pi\)
0.444090 + 0.895982i \(0.353527\pi\)
\(198\) −132635. −0.240433
\(199\) −808124. −1.44659 −0.723295 0.690540i \(-0.757373\pi\)
−0.723295 + 0.690540i \(0.757373\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −36982.8 −0.0645668
\(202\) −16624.4 −0.0286661
\(203\) 160569. 0.273478
\(204\) −35774.9 −0.0601871
\(205\) 428147. 0.711555
\(206\) −50553.6 −0.0830011
\(207\) 138796. 0.225139
\(208\) −187046. −0.299771
\(209\) 147781. 0.234020
\(210\) −154440. −0.241664
\(211\) −28301.7 −0.0437629 −0.0218814 0.999761i \(-0.506966\pi\)
−0.0218814 + 0.999761i \(0.506966\pi\)
\(212\) 106274. 0.162400
\(213\) −356811. −0.538876
\(214\) 323662. 0.483122
\(215\) −552072. −0.814516
\(216\) 46656.0 0.0680414
\(217\) −68089.6 −0.0981594
\(218\) −125815. −0.179304
\(219\) −364831. −0.514022
\(220\) 163747. 0.228095
\(221\) −181520. −0.250002
\(222\) −17851.9 −0.0243109
\(223\) 1.24055e6 1.67052 0.835260 0.549855i \(-0.185317\pi\)
0.835260 + 0.549855i \(0.185317\pi\)
\(224\) 175719. 0.233990
\(225\) 50625.0 0.0666667
\(226\) 295528. 0.384882
\(227\) −1.09798e6 −1.41427 −0.707134 0.707080i \(-0.750012\pi\)
−0.707134 + 0.707080i \(0.750012\pi\)
\(228\) −51984.0 −0.0662266
\(229\) 971661. 1.22441 0.612204 0.790700i \(-0.290283\pi\)
0.612204 + 0.790700i \(0.290283\pi\)
\(230\) −171353. −0.213585
\(231\) 632227. 0.779548
\(232\) 59885.9 0.0730473
\(233\) 84185.8 0.101590 0.0507948 0.998709i \(-0.483825\pi\)
0.0507948 + 0.998709i \(0.483825\pi\)
\(234\) 236730. 0.282627
\(235\) 295290. 0.348802
\(236\) 9704.05 0.0113416
\(237\) −563420. −0.651570
\(238\) 170527. 0.195143
\(239\) −1.37097e6 −1.55251 −0.776253 0.630422i \(-0.782882\pi\)
−0.776253 + 0.630422i \(0.782882\pi\)
\(240\) −57600.0 −0.0645497
\(241\) 936952. 1.03914 0.519571 0.854427i \(-0.326092\pi\)
0.519571 + 0.854427i \(0.326092\pi\)
\(242\) −26120.0 −0.0286705
\(243\) −59049.0 −0.0641500
\(244\) −541872. −0.582669
\(245\) 315991. 0.336325
\(246\) 616532. 0.649558
\(247\) −263764. −0.275089
\(248\) −25394.7 −0.0262189
\(249\) 281767. 0.287999
\(250\) −62500.0 −0.0632456
\(251\) −1.30701e6 −1.30946 −0.654732 0.755861i \(-0.727218\pi\)
−0.654732 + 0.755861i \(0.727218\pi\)
\(252\) −222394. −0.220608
\(253\) 701461. 0.688973
\(254\) −791722. −0.769996
\(255\) −55898.3 −0.0538330
\(256\) 65536.0 0.0625000
\(257\) −996635. −0.941246 −0.470623 0.882334i \(-0.655971\pi\)
−0.470623 + 0.882334i \(0.655971\pi\)
\(258\) −794983. −0.743548
\(259\) 85094.1 0.0788224
\(260\) −292259. −0.268124
\(261\) −75793.0 −0.0688697
\(262\) 1.18696e6 1.06827
\(263\) −380225. −0.338962 −0.169481 0.985533i \(-0.554209\pi\)
−0.169481 + 0.985533i \(0.554209\pi\)
\(264\) 235795. 0.208221
\(265\) 166053. 0.145255
\(266\) 247791. 0.214724
\(267\) −757884. −0.650615
\(268\) 65747.2 0.0559165
\(269\) 693730. 0.584534 0.292267 0.956337i \(-0.405590\pi\)
0.292267 + 0.956337i \(0.405590\pi\)
\(270\) 72900.0 0.0608581
\(271\) −2.05362e6 −1.69862 −0.849311 0.527892i \(-0.822983\pi\)
−0.849311 + 0.527892i \(0.822983\pi\)
\(272\) 63599.9 0.0521236
\(273\) −1.12842e6 −0.916352
\(274\) 415193. 0.334098
\(275\) 255854. 0.204014
\(276\) −246748. −0.194976
\(277\) −191006. −0.149571 −0.0747855 0.997200i \(-0.523827\pi\)
−0.0747855 + 0.997200i \(0.523827\pi\)
\(278\) 832806. 0.646296
\(279\) 32140.2 0.0247194
\(280\) 274560. 0.209287
\(281\) 771836. 0.583121 0.291561 0.956552i \(-0.405825\pi\)
0.291561 + 0.956552i \(0.405825\pi\)
\(282\) 425217. 0.318411
\(283\) −442073. −0.328117 −0.164058 0.986451i \(-0.552459\pi\)
−0.164058 + 0.986451i \(0.552459\pi\)
\(284\) 634330. 0.466680
\(285\) −81225.0 −0.0592349
\(286\) 1.19641e6 0.864900
\(287\) −2.93881e6 −2.10604
\(288\) −82944.0 −0.0589256
\(289\) −1.35814e6 −0.956530
\(290\) 93571.6 0.0653355
\(291\) −157725. −0.109187
\(292\) 648588. 0.445156
\(293\) 882501. 0.600546 0.300273 0.953853i \(-0.402922\pi\)
0.300273 + 0.953853i \(0.402922\pi\)
\(294\) 455027. 0.307022
\(295\) 15162.6 0.0101442
\(296\) 31736.7 0.0210539
\(297\) −298428. −0.196313
\(298\) 2.00826e6 1.31002
\(299\) −1.25199e6 −0.809882
\(300\) −90000.0 −0.0577350
\(301\) 3.78943e6 2.41078
\(302\) 1.46903e6 0.926860
\(303\) −37405.0 −0.0234058
\(304\) 92416.0 0.0573539
\(305\) −846674. −0.521155
\(306\) −80493.6 −0.0491426
\(307\) −2.40614e6 −1.45705 −0.728527 0.685017i \(-0.759795\pi\)
−0.728527 + 0.685017i \(0.759795\pi\)
\(308\) −1.12396e6 −0.675108
\(309\) −113746. −0.0677701
\(310\) −39679.2 −0.0234509
\(311\) 671897. 0.393914 0.196957 0.980412i \(-0.436894\pi\)
0.196957 + 0.980412i \(0.436894\pi\)
\(312\) −420854. −0.244762
\(313\) −2.60623e6 −1.50367 −0.751833 0.659353i \(-0.770830\pi\)
−0.751833 + 0.659353i \(0.770830\pi\)
\(314\) −617248. −0.353293
\(315\) −347491. −0.197318
\(316\) 1.00164e6 0.564276
\(317\) 1.80892e6 1.01104 0.505522 0.862814i \(-0.331300\pi\)
0.505522 + 0.862814i \(0.331300\pi\)
\(318\) 239116. 0.132599
\(319\) −383051. −0.210756
\(320\) 102400. 0.0559017
\(321\) 728239. 0.394468
\(322\) 1.17617e6 0.632163
\(323\) 89685.8 0.0478319
\(324\) 104976. 0.0555556
\(325\) −456655. −0.239817
\(326\) 1.85509e6 0.966764
\(327\) −283083. −0.146401
\(328\) −1.09606e6 −0.562534
\(329\) −2.02687e6 −1.03237
\(330\) 368430. 0.186239
\(331\) −1.77150e6 −0.888735 −0.444367 0.895845i \(-0.646571\pi\)
−0.444367 + 0.895845i \(0.646571\pi\)
\(332\) −500919. −0.249415
\(333\) −40166.7 −0.0198498
\(334\) 2.16085e6 1.05989
\(335\) 102730. 0.0500132
\(336\) 395367. 0.191052
\(337\) 1.77477e6 0.851271 0.425636 0.904895i \(-0.360051\pi\)
0.425636 + 0.904895i \(0.360051\pi\)
\(338\) −650218. −0.309576
\(339\) 664939. 0.314255
\(340\) 99374.8 0.0466207
\(341\) 162433. 0.0756466
\(342\) −116964. −0.0540738
\(343\) 715119. 0.328203
\(344\) 1.41330e6 0.643931
\(345\) −385544. −0.174392
\(346\) 1.52707e6 0.685755
\(347\) −2.21658e6 −0.988235 −0.494117 0.869395i \(-0.664509\pi\)
−0.494117 + 0.869395i \(0.664509\pi\)
\(348\) 134743. 0.0596429
\(349\) 2.44678e6 1.07531 0.537653 0.843166i \(-0.319311\pi\)
0.537653 + 0.843166i \(0.319311\pi\)
\(350\) 429001. 0.187192
\(351\) 532643. 0.230764
\(352\) −419191. −0.180325
\(353\) 637853. 0.272448 0.136224 0.990678i \(-0.456503\pi\)
0.136224 + 0.990678i \(0.456503\pi\)
\(354\) 21834.1 0.00926035
\(355\) 991141. 0.417411
\(356\) 1.34735e6 0.563449
\(357\) 383687. 0.159333
\(358\) −790191. −0.325855
\(359\) 3.99786e6 1.63716 0.818580 0.574392i \(-0.194761\pi\)
0.818580 + 0.574392i \(0.194761\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) 2.56496e6 1.02875
\(363\) −58770.0 −0.0234093
\(364\) 2.00607e6 0.793584
\(365\) 1.01342e6 0.398159
\(366\) −1.21921e6 −0.475747
\(367\) 2.49330e6 0.966294 0.483147 0.875539i \(-0.339494\pi\)
0.483147 + 0.875539i \(0.339494\pi\)
\(368\) 438663. 0.168854
\(369\) 1.38720e6 0.530362
\(370\) 49588.5 0.0188312
\(371\) −1.13979e6 −0.429921
\(372\) −57138.1 −0.0214076
\(373\) −3.44698e6 −1.28282 −0.641411 0.767197i \(-0.721651\pi\)
−0.641411 + 0.767197i \(0.721651\pi\)
\(374\) −406807. −0.150387
\(375\) −140625. −0.0516398
\(376\) −755941. −0.275752
\(377\) 683680. 0.247742
\(378\) −500386. −0.180126
\(379\) 1.53562e6 0.549143 0.274572 0.961567i \(-0.411464\pi\)
0.274572 + 0.961567i \(0.411464\pi\)
\(380\) 144400. 0.0512989
\(381\) −1.78137e6 −0.628699
\(382\) 100465. 0.0352254
\(383\) −3.26271e6 −1.13653 −0.568267 0.822844i \(-0.692386\pi\)
−0.568267 + 0.822844i \(0.692386\pi\)
\(384\) 147456. 0.0510310
\(385\) −1.75619e6 −0.603835
\(386\) 215650. 0.0736683
\(387\) −1.78871e6 −0.607104
\(388\) 280401. 0.0945583
\(389\) −2.17490e6 −0.728728 −0.364364 0.931257i \(-0.618714\pi\)
−0.364364 + 0.931257i \(0.618714\pi\)
\(390\) −657584. −0.218922
\(391\) 425704. 0.140820
\(392\) −808937. −0.265889
\(393\) 2.67066e6 0.872242
\(394\) −1.93520e6 −0.628038
\(395\) 1.56506e6 0.504704
\(396\) 530539. 0.170012
\(397\) 4.42115e6 1.40786 0.703930 0.710270i \(-0.251427\pi\)
0.703930 + 0.710270i \(0.251427\pi\)
\(398\) 3.23250e6 1.02289
\(399\) 557529. 0.175322
\(400\) 160000. 0.0500000
\(401\) −761947. −0.236627 −0.118313 0.992976i \(-0.537749\pi\)
−0.118313 + 0.992976i \(0.537749\pi\)
\(402\) 147931. 0.0456556
\(403\) −289916. −0.0889220
\(404\) 66497.7 0.0202700
\(405\) 164025. 0.0496904
\(406\) −642277. −0.193378
\(407\) −202999. −0.0607446
\(408\) 143100. 0.0425587
\(409\) −2.47581e6 −0.731829 −0.365915 0.930648i \(-0.619244\pi\)
−0.365915 + 0.930648i \(0.619244\pi\)
\(410\) −1.71259e6 −0.503146
\(411\) 934185. 0.272790
\(412\) 202214. 0.0586906
\(413\) −104076. −0.0300245
\(414\) −555183. −0.159197
\(415\) −782685. −0.223083
\(416\) 748184. 0.211970
\(417\) 1.87381e6 0.527699
\(418\) −591125. −0.165477
\(419\) 3.00254e6 0.835514 0.417757 0.908559i \(-0.362816\pi\)
0.417757 + 0.908559i \(0.362816\pi\)
\(420\) 617761. 0.170882
\(421\) −999018. −0.274706 −0.137353 0.990522i \(-0.543859\pi\)
−0.137353 + 0.990522i \(0.543859\pi\)
\(422\) 113207. 0.0309450
\(423\) 956738. 0.259981
\(424\) −425094. −0.114834
\(425\) 155273. 0.0416989
\(426\) 1.42724e6 0.381043
\(427\) 5.81158e6 1.54250
\(428\) −1.29465e6 −0.341619
\(429\) 2.69193e6 0.706188
\(430\) 2.20829e6 0.575950
\(431\) 2.42741e6 0.629433 0.314717 0.949186i \(-0.398091\pi\)
0.314717 + 0.949186i \(0.398091\pi\)
\(432\) −186624. −0.0481125
\(433\) −1.03044e6 −0.264120 −0.132060 0.991242i \(-0.542159\pi\)
−0.132060 + 0.991242i \(0.542159\pi\)
\(434\) 272359. 0.0694091
\(435\) 210536. 0.0533462
\(436\) 503259. 0.126787
\(437\) 618584. 0.154951
\(438\) 1.45932e6 0.363468
\(439\) −1.35893e6 −0.336540 −0.168270 0.985741i \(-0.553818\pi\)
−0.168270 + 0.985741i \(0.553818\pi\)
\(440\) −654987. −0.161287
\(441\) 1.02381e6 0.250682
\(442\) 726081. 0.176778
\(443\) 1.54725e6 0.374586 0.187293 0.982304i \(-0.440029\pi\)
0.187293 + 0.982304i \(0.440029\pi\)
\(444\) 71407.5 0.0171904
\(445\) 2.10523e6 0.503965
\(446\) −4.96220e6 −1.18124
\(447\) 4.51858e6 1.06963
\(448\) −702875. −0.165456
\(449\) −1.84939e6 −0.432924 −0.216462 0.976291i \(-0.569452\pi\)
−0.216462 + 0.976291i \(0.569452\pi\)
\(450\) −202500. −0.0471405
\(451\) 7.01077e6 1.62302
\(452\) −1.18211e6 −0.272153
\(453\) 3.30532e6 0.756778
\(454\) 4.39194e6 1.00004
\(455\) 3.13449e6 0.709803
\(456\) 207936. 0.0468293
\(457\) −2.80271e6 −0.627751 −0.313876 0.949464i \(-0.601628\pi\)
−0.313876 + 0.949464i \(0.601628\pi\)
\(458\) −3.88665e6 −0.865787
\(459\) −181111. −0.0401247
\(460\) 685411. 0.151028
\(461\) 7.18545e6 1.57471 0.787357 0.616497i \(-0.211449\pi\)
0.787357 + 0.616497i \(0.211449\pi\)
\(462\) −2.52891e6 −0.551224
\(463\) −2.63573e6 −0.571411 −0.285706 0.958317i \(-0.592228\pi\)
−0.285706 + 0.958317i \(0.592228\pi\)
\(464\) −239543. −0.0516523
\(465\) −89278.2 −0.0191476
\(466\) −336743. −0.0718346
\(467\) −8.54094e6 −1.81223 −0.906115 0.423031i \(-0.860966\pi\)
−0.906115 + 0.423031i \(0.860966\pi\)
\(468\) −946921. −0.199848
\(469\) −705139. −0.148028
\(470\) −1.18116e6 −0.246640
\(471\) −1.38881e6 −0.288463
\(472\) −38816.2 −0.00801970
\(473\) −9.03999e6 −1.85787
\(474\) 2.25368e6 0.460730
\(475\) 225625. 0.0458831
\(476\) −682110. −0.137987
\(477\) 538010. 0.108267
\(478\) 5.48388e6 1.09779
\(479\) 2.83289e6 0.564145 0.282072 0.959393i \(-0.408978\pi\)
0.282072 + 0.959393i \(0.408978\pi\)
\(480\) 230400. 0.0456435
\(481\) 362318. 0.0714048
\(482\) −3.74781e6 −0.734784
\(483\) 2.64638e6 0.516159
\(484\) 104480. 0.0202731
\(485\) 438126. 0.0845755
\(486\) 236196. 0.0453609
\(487\) 8.31365e6 1.58843 0.794217 0.607634i \(-0.207881\pi\)
0.794217 + 0.607634i \(0.207881\pi\)
\(488\) 2.16749e6 0.412009
\(489\) 4.17395e6 0.789360
\(490\) −1.26396e6 −0.237818
\(491\) −5.74720e6 −1.07585 −0.537926 0.842992i \(-0.680792\pi\)
−0.537926 + 0.842992i \(0.680792\pi\)
\(492\) −2.46613e6 −0.459307
\(493\) −232467. −0.0430768
\(494\) 1.05506e6 0.194517
\(495\) 828967. 0.152063
\(496\) 101579. 0.0185395
\(497\) −6.80320e6 −1.23544
\(498\) −1.12707e6 −0.203646
\(499\) −1.91364e6 −0.344040 −0.172020 0.985093i \(-0.555029\pi\)
−0.172020 + 0.985093i \(0.555029\pi\)
\(500\) 250000. 0.0447214
\(501\) 4.86192e6 0.865393
\(502\) 5.22802e6 0.925930
\(503\) −5.35043e6 −0.942906 −0.471453 0.881891i \(-0.656270\pi\)
−0.471453 + 0.881891i \(0.656270\pi\)
\(504\) 889576. 0.155994
\(505\) 103903. 0.0181300
\(506\) −2.80584e6 −0.487178
\(507\) −1.46299e6 −0.252768
\(508\) 3.16689e6 0.544469
\(509\) −1.51272e6 −0.258801 −0.129400 0.991592i \(-0.541305\pi\)
−0.129400 + 0.991592i \(0.541305\pi\)
\(510\) 223593. 0.0380657
\(511\) −6.95612e6 −1.17846
\(512\) −262144. −0.0441942
\(513\) −263169. −0.0441511
\(514\) 3.98654e6 0.665562
\(515\) 315960. 0.0524945
\(516\) 3.17993e6 0.525768
\(517\) 4.83527e6 0.795599
\(518\) −340376. −0.0557359
\(519\) 3.43591e6 0.559916
\(520\) 1.16904e6 0.189592
\(521\) 3.46529e6 0.559300 0.279650 0.960102i \(-0.409782\pi\)
0.279650 + 0.960102i \(0.409782\pi\)
\(522\) 303172. 0.0486982
\(523\) −1.12493e7 −1.79833 −0.899165 0.437609i \(-0.855825\pi\)
−0.899165 + 0.437609i \(0.855825\pi\)
\(524\) −4.74784e6 −0.755383
\(525\) 965251. 0.152842
\(526\) 1.52090e6 0.239683
\(527\) 98577.9 0.0154615
\(528\) −943181. −0.147235
\(529\) −3.50017e6 −0.543813
\(530\) −664210. −0.102711
\(531\) 49126.8 0.00756105
\(532\) −991163. −0.151833
\(533\) −1.25130e7 −1.90785
\(534\) 3.03153e6 0.460055
\(535\) −2.02289e6 −0.305553
\(536\) −262989. −0.0395389
\(537\) −1.77793e6 −0.266059
\(538\) −2.77492e6 −0.413328
\(539\) 5.17425e6 0.767141
\(540\) −291600. −0.0430331
\(541\) −2.89954e6 −0.425928 −0.212964 0.977060i \(-0.568312\pi\)
−0.212964 + 0.977060i \(0.568312\pi\)
\(542\) 8.21448e6 1.20111
\(543\) 5.77116e6 0.839970
\(544\) −254400. −0.0368569
\(545\) 786342. 0.113402
\(546\) 4.51366e6 0.647959
\(547\) 5.58514e6 0.798116 0.399058 0.916926i \(-0.369337\pi\)
0.399058 + 0.916926i \(0.369337\pi\)
\(548\) −1.66077e6 −0.236243
\(549\) −2.74322e6 −0.388446
\(550\) −1.02342e6 −0.144260
\(551\) −337794. −0.0473994
\(552\) 986992. 0.137869
\(553\) −1.07426e7 −1.49381
\(554\) 764024. 0.105763
\(555\) 111574. 0.0153756
\(556\) −3.33122e6 −0.457000
\(557\) 8.64348e6 1.18046 0.590229 0.807236i \(-0.299037\pi\)
0.590229 + 0.807236i \(0.299037\pi\)
\(558\) −128561. −0.0174792
\(559\) 1.61348e7 2.18391
\(560\) −1.09824e6 −0.147988
\(561\) −915317. −0.122790
\(562\) −3.08734e6 −0.412329
\(563\) −6.25367e6 −0.831503 −0.415751 0.909478i \(-0.636481\pi\)
−0.415751 + 0.909478i \(0.636481\pi\)
\(564\) −1.70087e6 −0.225150
\(565\) −1.84705e6 −0.243421
\(566\) 1.76829e6 0.232014
\(567\) −1.12587e6 −0.147072
\(568\) −2.53732e6 −0.329993
\(569\) 4.27118e6 0.553054 0.276527 0.961006i \(-0.410816\pi\)
0.276527 + 0.961006i \(0.410816\pi\)
\(570\) 324900. 0.0418854
\(571\) 5.52096e6 0.708638 0.354319 0.935125i \(-0.384713\pi\)
0.354319 + 0.935125i \(0.384713\pi\)
\(572\) −4.78565e6 −0.611577
\(573\) 226046. 0.0287614
\(574\) 1.17552e7 1.48919
\(575\) 1.07095e6 0.135083
\(576\) 331776. 0.0416667
\(577\) 9.36372e6 1.17087 0.585435 0.810719i \(-0.300924\pi\)
0.585435 + 0.810719i \(0.300924\pi\)
\(578\) 5.43254e6 0.676369
\(579\) 485212. 0.0601499
\(580\) −374287. −0.0461992
\(581\) 5.37236e6 0.660275
\(582\) 630901. 0.0772065
\(583\) 2.71905e6 0.331319
\(584\) −2.59435e6 −0.314773
\(585\) −1.47956e6 −0.178749
\(586\) −3.53000e6 −0.424650
\(587\) −884221. −0.105917 −0.0529585 0.998597i \(-0.516865\pi\)
−0.0529585 + 0.998597i \(0.516865\pi\)
\(588\) −1.82011e6 −0.217097
\(589\) 143242. 0.0170130
\(590\) −60650.3 −0.00717304
\(591\) −4.35420e6 −0.512791
\(592\) −126947. −0.0148873
\(593\) 511432. 0.0597243 0.0298621 0.999554i \(-0.490493\pi\)
0.0298621 + 0.999554i \(0.490493\pi\)
\(594\) 1.19371e6 0.138814
\(595\) −1.06580e6 −0.123419
\(596\) −8.03304e6 −0.926327
\(597\) 7.27311e6 0.835189
\(598\) 5.00795e6 0.572673
\(599\) −703758. −0.0801412 −0.0400706 0.999197i \(-0.512758\pi\)
−0.0400706 + 0.999197i \(0.512758\pi\)
\(600\) 360000. 0.0408248
\(601\) 709095. 0.0800790 0.0400395 0.999198i \(-0.487252\pi\)
0.0400395 + 0.999198i \(0.487252\pi\)
\(602\) −1.51577e7 −1.70468
\(603\) 332845. 0.0372777
\(604\) −5.87613e6 −0.655389
\(605\) 163250. 0.0181328
\(606\) 149620. 0.0165504
\(607\) 2.68774e6 0.296084 0.148042 0.988981i \(-0.452703\pi\)
0.148042 + 0.988981i \(0.452703\pi\)
\(608\) −369664. −0.0405554
\(609\) −1.44512e6 −0.157892
\(610\) 3.38670e6 0.368512
\(611\) −8.63012e6 −0.935220
\(612\) 321974. 0.0347490
\(613\) −411753. −0.0442574 −0.0221287 0.999755i \(-0.507044\pi\)
−0.0221287 + 0.999755i \(0.507044\pi\)
\(614\) 9.62458e6 1.03029
\(615\) −3.85333e6 −0.410817
\(616\) 4.49583e6 0.477374
\(617\) 1.67449e6 0.177080 0.0885402 0.996073i \(-0.471780\pi\)
0.0885402 + 0.996073i \(0.471780\pi\)
\(618\) 454982. 0.0479207
\(619\) −5.59624e6 −0.587043 −0.293521 0.955953i \(-0.594827\pi\)
−0.293521 + 0.955953i \(0.594827\pi\)
\(620\) 158717. 0.0165823
\(621\) −1.24916e6 −0.129984
\(622\) −2.68759e6 −0.278539
\(623\) −1.44503e7 −1.49162
\(624\) 1.68341e6 0.173073
\(625\) 390625. 0.0400000
\(626\) 1.04249e7 1.06325
\(627\) −1.33003e6 −0.135112
\(628\) 2.46899e6 0.249816
\(629\) −123196. −0.0124157
\(630\) 1.38996e6 0.139525
\(631\) 8.26101e6 0.825961 0.412980 0.910740i \(-0.364488\pi\)
0.412980 + 0.910740i \(0.364488\pi\)
\(632\) −4.00654e6 −0.399004
\(633\) 254715. 0.0252665
\(634\) −7.23566e6 −0.714916
\(635\) 4.94826e6 0.486988
\(636\) −956463. −0.0937616
\(637\) −9.23514e6 −0.901768
\(638\) 1.53220e6 0.149027
\(639\) 3.21130e6 0.311120
\(640\) −409600. −0.0395285
\(641\) −9.91722e6 −0.953333 −0.476667 0.879084i \(-0.658155\pi\)
−0.476667 + 0.879084i \(0.658155\pi\)
\(642\) −2.91296e6 −0.278931
\(643\) −1.85918e7 −1.77334 −0.886672 0.462398i \(-0.846989\pi\)
−0.886672 + 0.462398i \(0.846989\pi\)
\(644\) −4.70467e6 −0.447007
\(645\) 4.96865e6 0.470261
\(646\) −358743. −0.0338222
\(647\) 1.58431e7 1.48792 0.743961 0.668223i \(-0.232945\pi\)
0.743961 + 0.668223i \(0.232945\pi\)
\(648\) −419904. −0.0392837
\(649\) 248282. 0.0231384
\(650\) 1.82662e6 0.169576
\(651\) 612807. 0.0566723
\(652\) −7.42035e6 −0.683606
\(653\) −1.30198e7 −1.19487 −0.597435 0.801918i \(-0.703813\pi\)
−0.597435 + 0.801918i \(0.703813\pi\)
\(654\) 1.13233e6 0.103521
\(655\) −7.41849e6 −0.675635
\(656\) 4.38423e6 0.397771
\(657\) 3.28348e6 0.296770
\(658\) 8.10748e6 0.729997
\(659\) 4.47538e6 0.401436 0.200718 0.979649i \(-0.435672\pi\)
0.200718 + 0.979649i \(0.435672\pi\)
\(660\) −1.47372e6 −0.131691
\(661\) 406289. 0.0361686 0.0180843 0.999836i \(-0.494243\pi\)
0.0180843 + 0.999836i \(0.494243\pi\)
\(662\) 7.08601e6 0.628430
\(663\) 1.63368e6 0.144339
\(664\) 2.00367e6 0.176363
\(665\) −1.54869e6 −0.135804
\(666\) 160667. 0.0140359
\(667\) −1.60338e6 −0.139547
\(668\) −8.64342e6 −0.749453
\(669\) −1.11649e7 −0.964476
\(670\) −410920. −0.0353647
\(671\) −1.38640e7 −1.18873
\(672\) −1.58147e6 −0.135094
\(673\) −1.64638e7 −1.40118 −0.700588 0.713566i \(-0.747079\pi\)
−0.700588 + 0.713566i \(0.747079\pi\)
\(674\) −7.09909e6 −0.601940
\(675\) −455625. −0.0384900
\(676\) 2.60087e6 0.218903
\(677\) 1.62449e7 1.36222 0.681108 0.732183i \(-0.261498\pi\)
0.681108 + 0.732183i \(0.261498\pi\)
\(678\) −2.65976e6 −0.222212
\(679\) −3.00730e6 −0.250324
\(680\) −397499. −0.0329658
\(681\) 9.88186e6 0.816528
\(682\) −649734. −0.0534902
\(683\) −1.69563e7 −1.39084 −0.695422 0.718601i \(-0.744783\pi\)
−0.695422 + 0.718601i \(0.744783\pi\)
\(684\) 467856. 0.0382360
\(685\) −2.59496e6 −0.211302
\(686\) −2.86048e6 −0.232075
\(687\) −8.74495e6 −0.706912
\(688\) −5.65322e6 −0.455328
\(689\) −4.85304e6 −0.389463
\(690\) 1.54218e6 0.123314
\(691\) 4.86180e6 0.387348 0.193674 0.981066i \(-0.437960\pi\)
0.193674 + 0.981066i \(0.437960\pi\)
\(692\) −6.10828e6 −0.484902
\(693\) −5.69004e6 −0.450072
\(694\) 8.86633e6 0.698787
\(695\) −5.20503e6 −0.408754
\(696\) −538973. −0.0421739
\(697\) 4.25471e6 0.331732
\(698\) −9.78714e6 −0.760356
\(699\) −757672. −0.0586527
\(700\) −1.71600e6 −0.132365
\(701\) 3.68475e6 0.283213 0.141606 0.989923i \(-0.454773\pi\)
0.141606 + 0.989923i \(0.454773\pi\)
\(702\) −2.13057e6 −0.163175
\(703\) −179015. −0.0136616
\(704\) 1.67677e6 0.127509
\(705\) −2.65761e6 −0.201381
\(706\) −2.55141e6 −0.192650
\(707\) −713189. −0.0536607
\(708\) −87336.5 −0.00654806
\(709\) −1.23146e7 −0.920036 −0.460018 0.887910i \(-0.652157\pi\)
−0.460018 + 0.887910i \(0.652157\pi\)
\(710\) −3.96456e6 −0.295154
\(711\) 5.07078e6 0.376184
\(712\) −5.38939e6 −0.398419
\(713\) 679914. 0.0500876
\(714\) −1.53475e6 −0.112666
\(715\) −7.47758e6 −0.547011
\(716\) 3.16076e6 0.230414
\(717\) 1.23387e7 0.896340
\(718\) −1.59914e7 −1.15765
\(719\) −3.56575e6 −0.257234 −0.128617 0.991694i \(-0.541054\pi\)
−0.128617 + 0.991694i \(0.541054\pi\)
\(720\) 518400. 0.0372678
\(721\) −2.16875e6 −0.155372
\(722\) −521284. −0.0372161
\(723\) −8.43257e6 −0.599949
\(724\) −1.02598e7 −0.727436
\(725\) −584823. −0.0413218
\(726\) 235080. 0.0165529
\(727\) −3.60456e6 −0.252939 −0.126469 0.991970i \(-0.540365\pi\)
−0.126469 + 0.991970i \(0.540365\pi\)
\(728\) −8.02429e6 −0.561149
\(729\) 531441. 0.0370370
\(730\) −4.05368e6 −0.281541
\(731\) −5.48620e6 −0.379733
\(732\) 4.87684e6 0.336404
\(733\) 4.02534e6 0.276721 0.138361 0.990382i \(-0.455817\pi\)
0.138361 + 0.990382i \(0.455817\pi\)
\(734\) −9.97320e6 −0.683273
\(735\) −2.84392e6 −0.194178
\(736\) −1.75465e6 −0.119398
\(737\) 1.68217e6 0.114078
\(738\) −5.54879e6 −0.375023
\(739\) −1.64929e7 −1.11093 −0.555463 0.831542i \(-0.687459\pi\)
−0.555463 + 0.831542i \(0.687459\pi\)
\(740\) −198354. −0.0133156
\(741\) 2.37388e6 0.158823
\(742\) 4.55914e6 0.304000
\(743\) −1.78193e7 −1.18419 −0.592093 0.805870i \(-0.701698\pi\)
−0.592093 + 0.805870i \(0.701698\pi\)
\(744\) 228552. 0.0151375
\(745\) −1.25516e7 −0.828532
\(746\) 1.37879e7 0.907092
\(747\) −2.53590e6 −0.166276
\(748\) 1.62723e6 0.106340
\(749\) 1.38851e7 0.904367
\(750\) 562500. 0.0365148
\(751\) −1.50688e7 −0.974941 −0.487471 0.873139i \(-0.662080\pi\)
−0.487471 + 0.873139i \(0.662080\pi\)
\(752\) 3.02377e6 0.194986
\(753\) 1.17631e7 0.756019
\(754\) −2.73472e6 −0.175180
\(755\) −9.18145e6 −0.586197
\(756\) 2.00155e6 0.127368
\(757\) 1.62784e7 1.03246 0.516228 0.856451i \(-0.327336\pi\)
0.516228 + 0.856451i \(0.327336\pi\)
\(758\) −6.14248e6 −0.388303
\(759\) −6.31315e6 −0.397779
\(760\) −577600. −0.0362738
\(761\) 4.51093e6 0.282361 0.141180 0.989984i \(-0.454910\pi\)
0.141180 + 0.989984i \(0.454910\pi\)
\(762\) 7.12550e6 0.444557
\(763\) −5.39746e6 −0.335644
\(764\) −401859. −0.0249081
\(765\) 503085. 0.0310805
\(766\) 1.30509e7 0.803650
\(767\) −443141. −0.0271990
\(768\) −589824. −0.0360844
\(769\) 9.47467e6 0.577761 0.288881 0.957365i \(-0.406717\pi\)
0.288881 + 0.957365i \(0.406717\pi\)
\(770\) 7.02474e6 0.426976
\(771\) 8.96971e6 0.543429
\(772\) −862598. −0.0520913
\(773\) −2.83231e6 −0.170487 −0.0852436 0.996360i \(-0.527167\pi\)
−0.0852436 + 0.996360i \(0.527167\pi\)
\(774\) 7.15485e6 0.429287
\(775\) 247995. 0.0148316
\(776\) −1.12160e6 −0.0668628
\(777\) −765847. −0.0455082
\(778\) 8.69961e6 0.515289
\(779\) 6.18245e6 0.365020
\(780\) 2.63034e6 0.154801
\(781\) 1.62296e7 0.952094
\(782\) −1.70282e6 −0.0995751
\(783\) 682137. 0.0397619
\(784\) 3.23575e6 0.188012
\(785\) 3.85780e6 0.223442
\(786\) −1.06826e7 −0.616768
\(787\) 7.88470e6 0.453783 0.226892 0.973920i \(-0.427144\pi\)
0.226892 + 0.973920i \(0.427144\pi\)
\(788\) 7.74081e6 0.444090
\(789\) 3.42203e6 0.195700
\(790\) −6.26022e6 −0.356880
\(791\) 1.26782e7 0.720470
\(792\) −2.12216e6 −0.120217
\(793\) 2.47449e7 1.39734
\(794\) −1.76846e7 −0.995507
\(795\) −1.49447e6 −0.0838630
\(796\) −1.29300e7 −0.723295
\(797\) 2.80785e7 1.56577 0.782884 0.622168i \(-0.213748\pi\)
0.782884 + 0.622168i \(0.213748\pi\)
\(798\) −2.23012e6 −0.123971
\(799\) 2.93444e6 0.162614
\(800\) −640000. −0.0353553
\(801\) 6.82095e6 0.375633
\(802\) 3.04779e6 0.167320
\(803\) 1.65944e7 0.908181
\(804\) −591724. −0.0322834
\(805\) −7.35105e6 −0.399815
\(806\) 1.15966e6 0.0628773
\(807\) −6.24357e6 −0.337481
\(808\) −265991. −0.0143330
\(809\) −6.92130e6 −0.371806 −0.185903 0.982568i \(-0.559521\pi\)
−0.185903 + 0.982568i \(0.559521\pi\)
\(810\) −656100. −0.0351364
\(811\) 1.34048e6 0.0715661 0.0357831 0.999360i \(-0.488607\pi\)
0.0357831 + 0.999360i \(0.488607\pi\)
\(812\) 2.56911e6 0.136739
\(813\) 1.84826e7 0.980700
\(814\) 811996. 0.0429529
\(815\) −1.15943e7 −0.611435
\(816\) −572399. −0.0300936
\(817\) −7.97192e6 −0.417838
\(818\) 9.90326e6 0.517481
\(819\) 1.01557e7 0.529056
\(820\) 6.85036e6 0.355778
\(821\) −1.10064e7 −0.569883 −0.284942 0.958545i \(-0.591974\pi\)
−0.284942 + 0.958545i \(0.591974\pi\)
\(822\) −3.73674e6 −0.192892
\(823\) 2.42966e7 1.25039 0.625195 0.780468i \(-0.285019\pi\)
0.625195 + 0.780468i \(0.285019\pi\)
\(824\) −808857. −0.0415006
\(825\) −2.30269e6 −0.117788
\(826\) 416304. 0.0212305
\(827\) 2.55224e7 1.29765 0.648826 0.760937i \(-0.275260\pi\)
0.648826 + 0.760937i \(0.275260\pi\)
\(828\) 2.22073e6 0.112569
\(829\) 1.78840e7 0.903814 0.451907 0.892065i \(-0.350744\pi\)
0.451907 + 0.892065i \(0.350744\pi\)
\(830\) 3.13074e6 0.157744
\(831\) 1.71905e6 0.0863549
\(832\) −2.99274e6 −0.149886
\(833\) 3.14016e6 0.156797
\(834\) −7.49525e6 −0.373139
\(835\) −1.35053e7 −0.670331
\(836\) 2.36450e6 0.117010
\(837\) −289262. −0.0142717
\(838\) −1.20102e7 −0.590798
\(839\) −3.35619e7 −1.64605 −0.823023 0.568008i \(-0.807714\pi\)
−0.823023 + 0.568008i \(0.807714\pi\)
\(840\) −2.47104e6 −0.120832
\(841\) −1.96356e7 −0.957313
\(842\) 3.99607e6 0.194246
\(843\) −6.94652e6 −0.336665
\(844\) −452826. −0.0218814
\(845\) 4.06386e6 0.195793
\(846\) −3.82695e6 −0.183835
\(847\) −1.12055e6 −0.0536689
\(848\) 1.70038e6 0.0812000
\(849\) 3.97866e6 0.189438
\(850\) −621093. −0.0294855
\(851\) −849714. −0.0402206
\(852\) −5.70897e6 −0.269438
\(853\) 1.75136e7 0.824142 0.412071 0.911152i \(-0.364805\pi\)
0.412071 + 0.911152i \(0.364805\pi\)
\(854\) −2.32463e7 −1.09071
\(855\) 731025. 0.0341993
\(856\) 5.17859e6 0.241561
\(857\) 1.91536e7 0.890840 0.445420 0.895322i \(-0.353054\pi\)
0.445420 + 0.895322i \(0.353054\pi\)
\(858\) −1.07677e7 −0.499350
\(859\) 3.02413e7 1.39836 0.699178 0.714948i \(-0.253549\pi\)
0.699178 + 0.714948i \(0.253549\pi\)
\(860\) −8.83315e6 −0.407258
\(861\) 2.64493e7 1.21592
\(862\) −9.70963e6 −0.445076
\(863\) −1.44389e7 −0.659946 −0.329973 0.943990i \(-0.607040\pi\)
−0.329973 + 0.943990i \(0.607040\pi\)
\(864\) 746496. 0.0340207
\(865\) −9.54419e6 −0.433709
\(866\) 4.12174e6 0.186761
\(867\) 1.22232e7 0.552253
\(868\) −1.08943e6 −0.0490797
\(869\) 2.56273e7 1.15120
\(870\) −842145. −0.0377215
\(871\) −3.00238e6 −0.134097
\(872\) −2.01304e6 −0.0896521
\(873\) 1.41953e6 0.0630389
\(874\) −2.47433e6 −0.109567
\(875\) −2.68125e6 −0.118391
\(876\) −5.83729e6 −0.257011
\(877\) −1.70799e7 −0.749870 −0.374935 0.927051i \(-0.622335\pi\)
−0.374935 + 0.927051i \(0.622335\pi\)
\(878\) 5.43574e6 0.237970
\(879\) −7.94251e6 −0.346725
\(880\) 2.61995e6 0.114047
\(881\) 2.02133e7 0.877400 0.438700 0.898634i \(-0.355439\pi\)
0.438700 + 0.898634i \(0.355439\pi\)
\(882\) −4.09525e6 −0.177259
\(883\) 2.66270e7 1.14926 0.574632 0.818412i \(-0.305145\pi\)
0.574632 + 0.818412i \(0.305145\pi\)
\(884\) −2.90432e6 −0.125001
\(885\) −136463. −0.00585676
\(886\) −6.18901e6 −0.264872
\(887\) 1.77998e7 0.759638 0.379819 0.925061i \(-0.375986\pi\)
0.379819 + 0.925061i \(0.375986\pi\)
\(888\) −285630. −0.0121555
\(889\) −3.39649e7 −1.44137
\(890\) −8.42093e6 −0.356357
\(891\) 2.68585e6 0.113341
\(892\) 1.98488e7 0.835260
\(893\) 4.26398e6 0.178931
\(894\) −1.80743e7 −0.756343
\(895\) 4.93869e6 0.206089
\(896\) 2.81150e6 0.116995
\(897\) 1.12679e7 0.467586
\(898\) 7.39754e6 0.306123
\(899\) −371285. −0.0153217
\(900\) 810000. 0.0333333
\(901\) 1.65014e6 0.0677189
\(902\) −2.80431e7 −1.14765
\(903\) −3.41048e7 −1.39186
\(904\) 4.72845e6 0.192441
\(905\) −1.60310e7 −0.650638
\(906\) −1.32213e7 −0.535123
\(907\) −4.04476e7 −1.63258 −0.816289 0.577643i \(-0.803973\pi\)
−0.816289 + 0.577643i \(0.803973\pi\)
\(908\) −1.75678e7 −0.707134
\(909\) 336645. 0.0135133
\(910\) −1.25380e7 −0.501907
\(911\) −8.24751e6 −0.329251 −0.164626 0.986356i \(-0.552642\pi\)
−0.164626 + 0.986356i \(0.552642\pi\)
\(912\) −831744. −0.0331133
\(913\) −1.28162e7 −0.508842
\(914\) 1.12108e7 0.443887
\(915\) 7.62007e6 0.300889
\(916\) 1.55466e7 0.612204
\(917\) 5.09206e7 1.99972
\(918\) 724442. 0.0283725
\(919\) −1.96298e7 −0.766704 −0.383352 0.923602i \(-0.625230\pi\)
−0.383352 + 0.923602i \(0.625230\pi\)
\(920\) −2.74164e6 −0.106793
\(921\) 2.16553e7 0.841231
\(922\) −2.87418e7 −1.11349
\(923\) −2.89670e7 −1.11918
\(924\) 1.01156e7 0.389774
\(925\) −309928. −0.0119099
\(926\) 1.05429e7 0.404049
\(927\) 1.02371e6 0.0391271
\(928\) 958174. 0.0365237
\(929\) −2.47430e6 −0.0940619 −0.0470310 0.998893i \(-0.514976\pi\)
−0.0470310 + 0.998893i \(0.514976\pi\)
\(930\) 357113. 0.0135394
\(931\) 4.56291e6 0.172531
\(932\) 1.34697e6 0.0507948
\(933\) −6.04707e6 −0.227426
\(934\) 3.41638e7 1.28144
\(935\) 2.54255e6 0.0951130
\(936\) 3.78768e6 0.141314
\(937\) −1.99378e7 −0.741872 −0.370936 0.928658i \(-0.620963\pi\)
−0.370936 + 0.928658i \(0.620963\pi\)
\(938\) 2.82056e6 0.104671
\(939\) 2.34561e7 0.868142
\(940\) 4.72463e6 0.174401
\(941\) −2.44027e6 −0.0898387 −0.0449193 0.998991i \(-0.514303\pi\)
−0.0449193 + 0.998991i \(0.514303\pi\)
\(942\) 5.55523e6 0.203974
\(943\) 2.93457e7 1.07465
\(944\) 155265. 0.00567078
\(945\) 3.12741e6 0.113922
\(946\) 3.61600e7 1.31371
\(947\) −2.17049e7 −0.786471 −0.393236 0.919438i \(-0.628644\pi\)
−0.393236 + 0.919438i \(0.628644\pi\)
\(948\) −9.01472e6 −0.325785
\(949\) −2.96181e7 −1.06756
\(950\) −902500. −0.0324443
\(951\) −1.62802e7 −0.583727
\(952\) 2.72844e6 0.0975713
\(953\) −1.92314e7 −0.685928 −0.342964 0.939349i \(-0.611431\pi\)
−0.342964 + 0.939349i \(0.611431\pi\)
\(954\) −2.15204e6 −0.0765561
\(955\) −627905. −0.0222785
\(956\) −2.19355e7 −0.776253
\(957\) 3.44746e6 0.121680
\(958\) −1.13316e7 −0.398911
\(959\) 1.78118e7 0.625405
\(960\) −921600. −0.0322749
\(961\) −2.84717e7 −0.994501
\(962\) −1.44927e6 −0.0504908
\(963\) −6.55415e6 −0.227746
\(964\) 1.49912e7 0.519571
\(965\) −1.34781e6 −0.0465919
\(966\) −1.05855e7 −0.364980
\(967\) −4.40745e7 −1.51573 −0.757865 0.652412i \(-0.773757\pi\)
−0.757865 + 0.652412i \(0.773757\pi\)
\(968\) −417920. −0.0143352
\(969\) −807172. −0.0276157
\(970\) −1.75250e6 −0.0598039
\(971\) 4.69411e7 1.59773 0.798867 0.601507i \(-0.205433\pi\)
0.798867 + 0.601507i \(0.205433\pi\)
\(972\) −944784. −0.0320750
\(973\) 3.57274e7 1.20982
\(974\) −3.32546e7 −1.12319
\(975\) 4.10990e6 0.138459
\(976\) −8.66995e6 −0.291334
\(977\) −2.26994e7 −0.760812 −0.380406 0.924820i \(-0.624216\pi\)
−0.380406 + 0.924820i \(0.624216\pi\)
\(978\) −1.66958e7 −0.558162
\(979\) 3.44725e7 1.14952
\(980\) 5.05586e6 0.168163
\(981\) 2.54775e6 0.0845248
\(982\) 2.29888e7 0.760743
\(983\) 8.94734e6 0.295332 0.147666 0.989037i \(-0.452824\pi\)
0.147666 + 0.989037i \(0.452824\pi\)
\(984\) 9.86452e6 0.324779
\(985\) 1.20950e7 0.397206
\(986\) 929867. 0.0304599
\(987\) 1.82418e7 0.596040
\(988\) −4.22023e6 −0.137545
\(989\) −3.78396e7 −1.23014
\(990\) −3.31587e6 −0.107525
\(991\) −4.83394e6 −0.156357 −0.0781785 0.996939i \(-0.524910\pi\)
−0.0781785 + 0.996939i \(0.524910\pi\)
\(992\) −406315. −0.0131094
\(993\) 1.59435e7 0.513111
\(994\) 2.72128e7 0.873589
\(995\) −2.02031e7 −0.646934
\(996\) 4.50827e6 0.144000
\(997\) 7.01989e6 0.223662 0.111831 0.993727i \(-0.464328\pi\)
0.111831 + 0.993727i \(0.464328\pi\)
\(998\) 7.65456e6 0.243273
\(999\) 361501. 0.0114603
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.j.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.j.1.2 4 1.1 even 1 trivial