Properties

Label 570.6.a.j.1.4
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 1.4
Root \(-57.4501\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +185.237 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +185.237 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +132.999 q^{11} -144.000 q^{12} +637.513 q^{13} -740.947 q^{14} -225.000 q^{15} +256.000 q^{16} -2266.20 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -1667.13 q^{21} -531.994 q^{22} -1230.65 q^{23} +576.000 q^{24} +625.000 q^{25} -2550.05 q^{26} -729.000 q^{27} +2963.79 q^{28} -6562.92 q^{29} +900.000 q^{30} -9179.09 q^{31} -1024.00 q^{32} -1196.99 q^{33} +9064.79 q^{34} +4630.92 q^{35} +1296.00 q^{36} +8686.63 q^{37} -1444.00 q^{38} -5737.62 q^{39} -1600.00 q^{40} -4870.80 q^{41} +6668.52 q^{42} -11536.3 q^{43} +2127.98 q^{44} +2025.00 q^{45} +4922.60 q^{46} -15404.7 q^{47} -2304.00 q^{48} +17505.6 q^{49} -2500.00 q^{50} +20395.8 q^{51} +10200.2 q^{52} -2495.54 q^{53} +2916.00 q^{54} +3324.96 q^{55} -11855.1 q^{56} -3249.00 q^{57} +26251.7 q^{58} +14154.2 q^{59} -3600.00 q^{60} -18805.9 q^{61} +36716.4 q^{62} +15004.2 q^{63} +4096.00 q^{64} +15937.8 q^{65} +4787.95 q^{66} +1965.60 q^{67} -36259.2 q^{68} +11075.9 q^{69} -18523.7 q^{70} +31989.3 q^{71} -5184.00 q^{72} -64181.4 q^{73} -34746.5 q^{74} -5625.00 q^{75} +5776.00 q^{76} +24636.2 q^{77} +22950.5 q^{78} +88164.8 q^{79} +6400.00 q^{80} +6561.00 q^{81} +19483.2 q^{82} -12857.4 q^{83} -26674.1 q^{84} -56654.9 q^{85} +46145.1 q^{86} +59066.2 q^{87} -8511.91 q^{88} -60163.6 q^{89} -8100.00 q^{90} +118091. q^{91} -19690.4 q^{92} +82611.8 q^{93} +61618.8 q^{94} +9025.00 q^{95} +9216.00 q^{96} -33842.2 q^{97} -70022.5 q^{98} +10772.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} - 400q^{10} - 246q^{11} - 576q^{12} + 640q^{13} + 432q^{14} - 900q^{15} + 1024q^{16} - 612q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 972q^{21} + 984q^{22} - 1242q^{23} + 2304q^{24} + 2500q^{25} - 2560q^{26} - 2916q^{27} - 1728q^{28} - 6230q^{29} + 3600q^{30} - 11360q^{31} - 4096q^{32} + 2214q^{33} + 2448q^{34} - 2700q^{35} + 5184q^{36} - 4792q^{37} - 5776q^{38} - 5760q^{39} - 6400q^{40} + 9170q^{41} - 3888q^{42} - 11412q^{43} - 3936q^{44} + 8100q^{45} + 4968q^{46} - 29858q^{47} - 9216q^{48} + 31092q^{49} - 10000q^{50} + 5508q^{51} + 10240q^{52} + 27498q^{53} + 11664q^{54} - 6150q^{55} + 6912q^{56} - 12996q^{57} + 24920q^{58} + 54984q^{59} - 14400q^{60} + 20868q^{61} + 45440q^{62} - 8748q^{63} + 16384q^{64} + 16000q^{65} - 8856q^{66} - 20244q^{67} - 9792q^{68} + 11178q^{69} + 10800q^{70} + 86864q^{71} - 20736q^{72} - 3728q^{73} + 19168q^{74} - 22500q^{75} + 23104q^{76} + 18796q^{77} + 23040q^{78} + 164192q^{79} + 25600q^{80} + 26244q^{81} - 36680q^{82} - 60506q^{83} + 15552q^{84} - 15300q^{85} + 45648q^{86} + 56070q^{87} + 15744q^{88} + 113798q^{89} - 32400q^{90} + 159528q^{91} - 19872q^{92} + 102240q^{93} + 119432q^{94} + 36100q^{95} + 36864q^{96} + 79440q^{97} - 124368q^{98} - 19926q^{99} + O(q^{100}) \)

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
\(7\) 185.237 1.42883 0.714417 0.699720i \(-0.246692\pi\)
0.714417 + 0.699720i \(0.246692\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) 132.999 0.331410 0.165705 0.986175i \(-0.447010\pi\)
0.165705 + 0.986175i \(0.447010\pi\)
\(12\) −144.000 −0.288675
\(13\) 637.513 1.04624 0.523119 0.852259i \(-0.324768\pi\)
0.523119 + 0.852259i \(0.324768\pi\)
\(14\) −740.947 −1.01034
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) −2266.20 −1.90185 −0.950923 0.309427i \(-0.899863\pi\)
−0.950923 + 0.309427i \(0.899863\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) −1667.13 −0.824938
\(22\) −531.994 −0.234342
\(23\) −1230.65 −0.485082 −0.242541 0.970141i \(-0.577981\pi\)
−0.242541 + 0.970141i \(0.577981\pi\)
\(24\) 576.000 0.204124
\(25\) 625.000 0.200000
\(26\) −2550.05 −0.739803
\(27\) −729.000 −0.192450
\(28\) 2963.79 0.714417
\(29\) −6562.92 −1.44911 −0.724556 0.689216i \(-0.757955\pi\)
−0.724556 + 0.689216i \(0.757955\pi\)
\(30\) 900.000 0.182574
\(31\) −9179.09 −1.71552 −0.857759 0.514052i \(-0.828144\pi\)
−0.857759 + 0.514052i \(0.828144\pi\)
\(32\) −1024.00 −0.176777
\(33\) −1196.99 −0.191340
\(34\) 9064.79 1.34481
\(35\) 4630.92 0.638994
\(36\) 1296.00 0.166667
\(37\) 8686.63 1.04315 0.521575 0.853205i \(-0.325345\pi\)
0.521575 + 0.853205i \(0.325345\pi\)
\(38\) −1444.00 −0.162221
\(39\) −5737.62 −0.604046
\(40\) −1600.00 −0.158114
\(41\) −4870.80 −0.452523 −0.226261 0.974067i \(-0.572650\pi\)
−0.226261 + 0.974067i \(0.572650\pi\)
\(42\) 6668.52 0.583319
\(43\) −11536.3 −0.951469 −0.475735 0.879589i \(-0.657818\pi\)
−0.475735 + 0.879589i \(0.657818\pi\)
\(44\) 2127.98 0.165705
\(45\) 2025.00 0.149071
\(46\) 4922.60 0.343005
\(47\) −15404.7 −1.01721 −0.508603 0.861001i \(-0.669838\pi\)
−0.508603 + 0.861001i \(0.669838\pi\)
\(48\) −2304.00 −0.144338
\(49\) 17505.6 1.04157
\(50\) −2500.00 −0.141421
\(51\) 20395.8 1.09803
\(52\) 10200.2 0.523119
\(53\) −2495.54 −0.122032 −0.0610161 0.998137i \(-0.519434\pi\)
−0.0610161 + 0.998137i \(0.519434\pi\)
\(54\) 2916.00 0.136083
\(55\) 3324.96 0.148211
\(56\) −11855.1 −0.505169
\(57\) −3249.00 −0.132453
\(58\) 26251.7 1.02468
\(59\) 14154.2 0.529366 0.264683 0.964335i \(-0.414733\pi\)
0.264683 + 0.964335i \(0.414733\pi\)
\(60\) −3600.00 −0.129099
\(61\) −18805.9 −0.647096 −0.323548 0.946212i \(-0.604876\pi\)
−0.323548 + 0.946212i \(0.604876\pi\)
\(62\) 36716.4 1.21305
\(63\) 15004.2 0.476278
\(64\) 4096.00 0.125000
\(65\) 15937.8 0.467892
\(66\) 4787.95 0.135297
\(67\) 1965.60 0.0534944 0.0267472 0.999642i \(-0.491485\pi\)
0.0267472 + 0.999642i \(0.491485\pi\)
\(68\) −36259.2 −0.950923
\(69\) 11075.9 0.280062
\(70\) −18523.7 −0.451837
\(71\) 31989.3 0.753111 0.376556 0.926394i \(-0.377108\pi\)
0.376556 + 0.926394i \(0.377108\pi\)
\(72\) −5184.00 −0.117851
\(73\) −64181.4 −1.40962 −0.704810 0.709396i \(-0.748968\pi\)
−0.704810 + 0.709396i \(0.748968\pi\)
\(74\) −34746.5 −0.737619
\(75\) −5625.00 −0.115470
\(76\) 5776.00 0.114708
\(77\) 24636.2 0.473530
\(78\) 22950.5 0.427125
\(79\) 88164.8 1.58938 0.794690 0.607016i \(-0.207634\pi\)
0.794690 + 0.607016i \(0.207634\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) 19483.2 0.319982
\(83\) −12857.4 −0.204860 −0.102430 0.994740i \(-0.532662\pi\)
−0.102430 + 0.994740i \(0.532662\pi\)
\(84\) −26674.1 −0.412469
\(85\) −56654.9 −0.850532
\(86\) 46145.1 0.672790
\(87\) 59066.2 0.836645
\(88\) −8511.91 −0.117171
\(89\) −60163.6 −0.805117 −0.402558 0.915394i \(-0.631879\pi\)
−0.402558 + 0.915394i \(0.631879\pi\)
\(90\) −8100.00 −0.105409
\(91\) 118091. 1.49490
\(92\) −19690.4 −0.242541
\(93\) 82611.8 0.990455
\(94\) 61618.8 0.719273
\(95\) 9025.00 0.102598
\(96\) 9216.00 0.102062
\(97\) −33842.2 −0.365198 −0.182599 0.983187i \(-0.558451\pi\)
−0.182599 + 0.983187i \(0.558451\pi\)
\(98\) −70022.5 −0.736500
\(99\) 10772.9 0.110470
\(100\) 10000.0 0.100000
\(101\) 143321. 1.39800 0.698998 0.715124i \(-0.253630\pi\)
0.698998 + 0.715124i \(0.253630\pi\)
\(102\) −81583.1 −0.776426
\(103\) 92271.7 0.856990 0.428495 0.903544i \(-0.359044\pi\)
0.428495 + 0.903544i \(0.359044\pi\)
\(104\) −40800.8 −0.369901
\(105\) −41678.3 −0.368923
\(106\) 9982.14 0.0862897
\(107\) −114505. −0.966865 −0.483433 0.875382i \(-0.660610\pi\)
−0.483433 + 0.875382i \(0.660610\pi\)
\(108\) −11664.0 −0.0962250
\(109\) −239404. −1.93003 −0.965016 0.262190i \(-0.915555\pi\)
−0.965016 + 0.262190i \(0.915555\pi\)
\(110\) −13299.9 −0.104801
\(111\) −78179.7 −0.602263
\(112\) 47420.6 0.357209
\(113\) 204322. 1.50529 0.752644 0.658428i \(-0.228778\pi\)
0.752644 + 0.658428i \(0.228778\pi\)
\(114\) 12996.0 0.0936586
\(115\) −30766.3 −0.216935
\(116\) −105007. −0.724556
\(117\) 51638.6 0.348746
\(118\) −56616.9 −0.374318
\(119\) −419783. −2.71742
\(120\) 14400.0 0.0912871
\(121\) −143362. −0.890168
\(122\) 75223.4 0.457566
\(123\) 43837.2 0.261264
\(124\) −146865. −0.857759
\(125\) 15625.0 0.0894427
\(126\) −60016.7 −0.336779
\(127\) −60036.9 −0.330300 −0.165150 0.986268i \(-0.552811\pi\)
−0.165150 + 0.986268i \(0.552811\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 103827. 0.549331
\(130\) −63751.3 −0.330850
\(131\) −191437. −0.974648 −0.487324 0.873221i \(-0.662027\pi\)
−0.487324 + 0.873221i \(0.662027\pi\)
\(132\) −19151.8 −0.0956698
\(133\) 66870.4 0.327797
\(134\) −7862.40 −0.0378262
\(135\) −18225.0 −0.0860663
\(136\) 145037. 0.672404
\(137\) −334152. −1.52105 −0.760524 0.649310i \(-0.775058\pi\)
−0.760524 + 0.649310i \(0.775058\pi\)
\(138\) −44303.4 −0.198034
\(139\) 359419. 1.57784 0.788921 0.614494i \(-0.210640\pi\)
0.788921 + 0.614494i \(0.210640\pi\)
\(140\) 74094.7 0.319497
\(141\) 138642. 0.587284
\(142\) −127957. −0.532530
\(143\) 84788.4 0.346734
\(144\) 20736.0 0.0833333
\(145\) −164073. −0.648062
\(146\) 256726. 0.996752
\(147\) −157551. −0.601349
\(148\) 138986. 0.521575
\(149\) −331091. −1.22175 −0.610874 0.791728i \(-0.709182\pi\)
−0.610874 + 0.791728i \(0.709182\pi\)
\(150\) 22500.0 0.0816497
\(151\) 28606.3 0.102099 0.0510493 0.998696i \(-0.483743\pi\)
0.0510493 + 0.998696i \(0.483743\pi\)
\(152\) −23104.0 −0.0811107
\(153\) −183562. −0.633949
\(154\) −98544.9 −0.334836
\(155\) −229477. −0.767203
\(156\) −91801.9 −0.302023
\(157\) 96412.0 0.312163 0.156082 0.987744i \(-0.450114\pi\)
0.156082 + 0.987744i \(0.450114\pi\)
\(158\) −352659. −1.12386
\(159\) 22459.8 0.0704553
\(160\) −25600.0 −0.0790569
\(161\) −227962. −0.693102
\(162\) −26244.0 −0.0785674
\(163\) −330416. −0.974076 −0.487038 0.873381i \(-0.661923\pi\)
−0.487038 + 0.873381i \(0.661923\pi\)
\(164\) −77932.8 −0.226261
\(165\) −29924.7 −0.0855696
\(166\) 51429.5 0.144858
\(167\) −478346. −1.32725 −0.663623 0.748067i \(-0.730982\pi\)
−0.663623 + 0.748067i \(0.730982\pi\)
\(168\) 106696. 0.291660
\(169\) 35130.2 0.0946157
\(170\) 226620. 0.601417
\(171\) 29241.0 0.0764719
\(172\) −184581. −0.475735
\(173\) 466943. 1.18617 0.593087 0.805138i \(-0.297909\pi\)
0.593087 + 0.805138i \(0.297909\pi\)
\(174\) −236265. −0.591597
\(175\) 115773. 0.285767
\(176\) 34047.6 0.0828524
\(177\) −127388. −0.305630
\(178\) 240654. 0.569303
\(179\) −28144.5 −0.0656540 −0.0328270 0.999461i \(-0.510451\pi\)
−0.0328270 + 0.999461i \(0.510451\pi\)
\(180\) 32400.0 0.0745356
\(181\) 758889. 1.72180 0.860898 0.508777i \(-0.169902\pi\)
0.860898 + 0.508777i \(0.169902\pi\)
\(182\) −472363. −1.05706
\(183\) 169253. 0.373601
\(184\) 78761.6 0.171502
\(185\) 217166. 0.466511
\(186\) −330447. −0.700357
\(187\) −301401. −0.630290
\(188\) −246475. −0.508603
\(189\) −135038. −0.274979
\(190\) −36100.0 −0.0725476
\(191\) 657635. 1.30437 0.652186 0.758059i \(-0.273852\pi\)
0.652186 + 0.758059i \(0.273852\pi\)
\(192\) −36864.0 −0.0721688
\(193\) −983614. −1.90078 −0.950389 0.311063i \(-0.899315\pi\)
−0.950389 + 0.311063i \(0.899315\pi\)
\(194\) 135369. 0.258234
\(195\) −143440. −0.270138
\(196\) 280090. 0.520784
\(197\) 352468. 0.647074 0.323537 0.946216i \(-0.395128\pi\)
0.323537 + 0.946216i \(0.395128\pi\)
\(198\) −43091.5 −0.0781140
\(199\) −687176. −1.23009 −0.615043 0.788494i \(-0.710861\pi\)
−0.615043 + 0.788494i \(0.710861\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −17690.4 −0.0308850
\(202\) −573283. −0.988532
\(203\) −1.21569e6 −2.07054
\(204\) 326332. 0.549016
\(205\) −121770. −0.202374
\(206\) −369087. −0.605983
\(207\) −99682.7 −0.161694
\(208\) 163203. 0.261560
\(209\) 48012.5 0.0760306
\(210\) 166713. 0.260868
\(211\) 242486. 0.374957 0.187478 0.982269i \(-0.439969\pi\)
0.187478 + 0.982269i \(0.439969\pi\)
\(212\) −39928.6 −0.0610161
\(213\) −287904. −0.434809
\(214\) 458021. 0.683677
\(215\) −288407. −0.425510
\(216\) 46656.0 0.0680414
\(217\) −1.70030e6 −2.45119
\(218\) 957615. 1.36474
\(219\) 577632. 0.813844
\(220\) 53199.4 0.0741055
\(221\) −1.44473e6 −1.98979
\(222\) 312719. 0.425865
\(223\) −979581. −1.31910 −0.659551 0.751660i \(-0.729253\pi\)
−0.659551 + 0.751660i \(0.729253\pi\)
\(224\) −189682. −0.252585
\(225\) 50625.0 0.0666667
\(226\) −817289. −1.06440
\(227\) 364015. 0.468872 0.234436 0.972132i \(-0.424676\pi\)
0.234436 + 0.972132i \(0.424676\pi\)
\(228\) −51984.0 −0.0662266
\(229\) 352408. 0.444076 0.222038 0.975038i \(-0.428729\pi\)
0.222038 + 0.975038i \(0.428729\pi\)
\(230\) 123065. 0.153396
\(231\) −221726. −0.273392
\(232\) 420027. 0.512338
\(233\) −1.52721e6 −1.84293 −0.921465 0.388461i \(-0.873007\pi\)
−0.921465 + 0.388461i \(0.873007\pi\)
\(234\) −206554. −0.246601
\(235\) −385118. −0.454908
\(236\) 226468. 0.264683
\(237\) −793483. −0.917629
\(238\) 1.67913e6 1.92151
\(239\) −997411. −1.12948 −0.564741 0.825268i \(-0.691024\pi\)
−0.564741 + 0.825268i \(0.691024\pi\)
\(240\) −57600.0 −0.0645497
\(241\) 113719. 0.126122 0.0630610 0.998010i \(-0.479914\pi\)
0.0630610 + 0.998010i \(0.479914\pi\)
\(242\) 573450. 0.629444
\(243\) −59049.0 −0.0641500
\(244\) −300894. −0.323548
\(245\) 437641. 0.465803
\(246\) −175349. −0.184742
\(247\) 230142. 0.240024
\(248\) 587462. 0.606527
\(249\) 115716. 0.118276
\(250\) −62500.0 −0.0632456
\(251\) −303569. −0.304140 −0.152070 0.988370i \(-0.548594\pi\)
−0.152070 + 0.988370i \(0.548594\pi\)
\(252\) 240067. 0.238139
\(253\) −163675. −0.160761
\(254\) 240148. 0.233558
\(255\) 509894. 0.491055
\(256\) 65536.0 0.0625000
\(257\) 1.08192e6 1.02179 0.510896 0.859643i \(-0.329314\pi\)
0.510896 + 0.859643i \(0.329314\pi\)
\(258\) −415306. −0.388436
\(259\) 1.60908e6 1.49049
\(260\) 255005. 0.233946
\(261\) −531596. −0.483037
\(262\) 765748. 0.689180
\(263\) −702957. −0.626670 −0.313335 0.949643i \(-0.601446\pi\)
−0.313335 + 0.949643i \(0.601446\pi\)
\(264\) 76607.2 0.0676487
\(265\) −62388.4 −0.0545744
\(266\) −267482. −0.231788
\(267\) 541472. 0.464834
\(268\) 31449.6 0.0267472
\(269\) 505465. 0.425903 0.212951 0.977063i \(-0.431692\pi\)
0.212951 + 0.977063i \(0.431692\pi\)
\(270\) 72900.0 0.0608581
\(271\) 510720. 0.422434 0.211217 0.977439i \(-0.432257\pi\)
0.211217 + 0.977439i \(0.432257\pi\)
\(272\) −580147. −0.475462
\(273\) −1.06282e6 −0.863082
\(274\) 1.33661e6 1.07554
\(275\) 83124.1 0.0662820
\(276\) 177214. 0.140031
\(277\) 798121. 0.624984 0.312492 0.949920i \(-0.398836\pi\)
0.312492 + 0.949920i \(0.398836\pi\)
\(278\) −1.43767e6 −1.11570
\(279\) −743506. −0.571839
\(280\) −296379. −0.225919
\(281\) 422979. 0.319561 0.159780 0.987153i \(-0.448921\pi\)
0.159780 + 0.987153i \(0.448921\pi\)
\(282\) −554570. −0.415273
\(283\) −2.14117e6 −1.58923 −0.794613 0.607117i \(-0.792326\pi\)
−0.794613 + 0.607117i \(0.792326\pi\)
\(284\) 511829. 0.376556
\(285\) −81225.0 −0.0592349
\(286\) −339153. −0.245178
\(287\) −902251. −0.646580
\(288\) −82944.0 −0.0589256
\(289\) 3.71579e6 2.61702
\(290\) 656292. 0.458249
\(291\) 304580. 0.210847
\(292\) −1.02690e6 −0.704810
\(293\) −1.53788e6 −1.04653 −0.523267 0.852169i \(-0.675287\pi\)
−0.523267 + 0.852169i \(0.675287\pi\)
\(294\) 630203. 0.425218
\(295\) 353856. 0.236740
\(296\) −555944. −0.368810
\(297\) −96956.0 −0.0637798
\(298\) 1.32436e6 0.863906
\(299\) −784556. −0.507512
\(300\) −90000.0 −0.0577350
\(301\) −2.13694e6 −1.35949
\(302\) −114425. −0.0721946
\(303\) −1.28989e6 −0.807133
\(304\) 92416.0 0.0573539
\(305\) −470146. −0.289390
\(306\) 734248. 0.448270
\(307\) 2.79516e6 1.69263 0.846314 0.532684i \(-0.178817\pi\)
0.846314 + 0.532684i \(0.178817\pi\)
\(308\) 394179. 0.236765
\(309\) −830445. −0.494783
\(310\) 917909. 0.542495
\(311\) 212876. 0.124803 0.0624017 0.998051i \(-0.480124\pi\)
0.0624017 + 0.998051i \(0.480124\pi\)
\(312\) 367208. 0.213563
\(313\) 2.87678e6 1.65976 0.829882 0.557940i \(-0.188408\pi\)
0.829882 + 0.557940i \(0.188408\pi\)
\(314\) −385648. −0.220733
\(315\) 375104. 0.212998
\(316\) 1.41064e6 0.794690
\(317\) −1.92365e6 −1.07517 −0.537586 0.843209i \(-0.680664\pi\)
−0.537586 + 0.843209i \(0.680664\pi\)
\(318\) −89839.3 −0.0498194
\(319\) −872858. −0.480250
\(320\) 102400. 0.0559017
\(321\) 1.03055e6 0.558220
\(322\) 911847. 0.490097
\(323\) −818097. −0.436314
\(324\) 104976. 0.0555556
\(325\) 398446. 0.209248
\(326\) 1.32167e6 0.688775
\(327\) 2.15463e6 1.11430
\(328\) 311731. 0.159991
\(329\) −2.85352e6 −1.45342
\(330\) 119699. 0.0605069
\(331\) 3.01336e6 1.51175 0.755876 0.654714i \(-0.227211\pi\)
0.755876 + 0.654714i \(0.227211\pi\)
\(332\) −205718. −0.102430
\(333\) 703617. 0.347717
\(334\) 1.91339e6 0.938504
\(335\) 49140.0 0.0239234
\(336\) −426785. −0.206234
\(337\) 266837. 0.127988 0.0639942 0.997950i \(-0.479616\pi\)
0.0639942 + 0.997950i \(0.479616\pi\)
\(338\) −140521. −0.0669034
\(339\) −1.83890e6 −0.869078
\(340\) −906479. −0.425266
\(341\) −1.22081e6 −0.568540
\(342\) −116964. −0.0540738
\(343\) 129412. 0.0593934
\(344\) 738322. 0.336395
\(345\) 276896. 0.125248
\(346\) −1.86777e6 −0.838752
\(347\) 1.10566e6 0.492946 0.246473 0.969150i \(-0.420728\pi\)
0.246473 + 0.969150i \(0.420728\pi\)
\(348\) 945060. 0.418322
\(349\) 3.51702e6 1.54565 0.772825 0.634619i \(-0.218843\pi\)
0.772825 + 0.634619i \(0.218843\pi\)
\(350\) −463092. −0.202068
\(351\) −464747. −0.201349
\(352\) −136191. −0.0585855
\(353\) 1.50722e6 0.643783 0.321892 0.946776i \(-0.395681\pi\)
0.321892 + 0.946776i \(0.395681\pi\)
\(354\) 509552. 0.216113
\(355\) 799733. 0.336802
\(356\) −962618. −0.402558
\(357\) 3.77805e6 1.56891
\(358\) 112578. 0.0464244
\(359\) 524591. 0.214825 0.107413 0.994215i \(-0.465743\pi\)
0.107413 + 0.994215i \(0.465743\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) −3.03556e6 −1.21749
\(363\) 1.29026e6 0.513938
\(364\) 1.88945e6 0.747451
\(365\) −1.60453e6 −0.630401
\(366\) −677011. −0.264176
\(367\) −4.90971e6 −1.90279 −0.951394 0.307978i \(-0.900348\pi\)
−0.951394 + 0.307978i \(0.900348\pi\)
\(368\) −315047. −0.121271
\(369\) −394535. −0.150841
\(370\) −868663. −0.329873
\(371\) −462265. −0.174364
\(372\) 1.32179e6 0.495227
\(373\) −3.84049e6 −1.42927 −0.714636 0.699497i \(-0.753408\pi\)
−0.714636 + 0.699497i \(0.753408\pi\)
\(374\) 1.20560e6 0.445683
\(375\) −140625. −0.0516398
\(376\) 985901. 0.359637
\(377\) −4.18395e6 −1.51612
\(378\) 540150. 0.194440
\(379\) 2.26040e6 0.808328 0.404164 0.914687i \(-0.367563\pi\)
0.404164 + 0.914687i \(0.367563\pi\)
\(380\) 144400. 0.0512989
\(381\) 540332. 0.190699
\(382\) −2.63054e6 −0.922331
\(383\) −1.52801e6 −0.532267 −0.266133 0.963936i \(-0.585746\pi\)
−0.266133 + 0.963936i \(0.585746\pi\)
\(384\) 147456. 0.0510310
\(385\) 615905. 0.211769
\(386\) 3.93446e6 1.34405
\(387\) −934439. −0.317156
\(388\) −541475. −0.182599
\(389\) 3.23044e6 1.08240 0.541200 0.840894i \(-0.317970\pi\)
0.541200 + 0.840894i \(0.317970\pi\)
\(390\) 573762. 0.191016
\(391\) 2.78890e6 0.922552
\(392\) −1.12036e6 −0.368250
\(393\) 1.72293e6 0.562713
\(394\) −1.40987e6 −0.457550
\(395\) 2.20412e6 0.710792
\(396\) 172366. 0.0552350
\(397\) −492037. −0.156683 −0.0783414 0.996927i \(-0.524962\pi\)
−0.0783414 + 0.996927i \(0.524962\pi\)
\(398\) 2.74870e6 0.869802
\(399\) −601834. −0.189254
\(400\) 160000. 0.0500000
\(401\) 1.92955e6 0.599231 0.299615 0.954060i \(-0.403142\pi\)
0.299615 + 0.954060i \(0.403142\pi\)
\(402\) 70761.6 0.0218390
\(403\) −5.85179e6 −1.79484
\(404\) 2.29313e6 0.698998
\(405\) 164025. 0.0496904
\(406\) 4.86277e6 1.46409
\(407\) 1.15531e6 0.345710
\(408\) −1.30533e6 −0.388213
\(409\) 2.13887e6 0.632231 0.316115 0.948721i \(-0.397621\pi\)
0.316115 + 0.948721i \(0.397621\pi\)
\(410\) 487080. 0.143100
\(411\) 3.00737e6 0.878177
\(412\) 1.47635e6 0.428495
\(413\) 2.62188e6 0.756377
\(414\) 398731. 0.114335
\(415\) −321435. −0.0916162
\(416\) −652814. −0.184951
\(417\) −3.23477e6 −0.910968
\(418\) −192050. −0.0537618
\(419\) −5.76766e6 −1.60496 −0.802480 0.596678i \(-0.796487\pi\)
−0.802480 + 0.596678i \(0.796487\pi\)
\(420\) −666852. −0.184462
\(421\) −269913. −0.0742195 −0.0371098 0.999311i \(-0.511815\pi\)
−0.0371098 + 0.999311i \(0.511815\pi\)
\(422\) −969946. −0.265135
\(423\) −1.24778e6 −0.339069
\(424\) 159714. 0.0431449
\(425\) −1.41637e6 −0.380369
\(426\) 1.15162e6 0.307456
\(427\) −3.48353e6 −0.924592
\(428\) −1.83208e6 −0.483433
\(429\) −763095. −0.200187
\(430\) 1.15363e6 0.300881
\(431\) −6.23095e6 −1.61570 −0.807851 0.589386i \(-0.799370\pi\)
−0.807851 + 0.589386i \(0.799370\pi\)
\(432\) −186624. −0.0481125
\(433\) 311409. 0.0798198 0.0399099 0.999203i \(-0.487293\pi\)
0.0399099 + 0.999203i \(0.487293\pi\)
\(434\) 6.80122e6 1.73325
\(435\) 1.47666e6 0.374159
\(436\) −3.83046e6 −0.965016
\(437\) −444265. −0.111285
\(438\) −2.31053e6 −0.575475
\(439\) 3.18888e6 0.789727 0.394864 0.918740i \(-0.370792\pi\)
0.394864 + 0.918740i \(0.370792\pi\)
\(440\) −212798. −0.0524005
\(441\) 1.41796e6 0.347189
\(442\) 5.77892e6 1.40699
\(443\) −2.36934e6 −0.573611 −0.286805 0.957989i \(-0.592593\pi\)
−0.286805 + 0.957989i \(0.592593\pi\)
\(444\) −1.25088e6 −0.301132
\(445\) −1.50409e6 −0.360059
\(446\) 3.91832e6 0.932745
\(447\) 2.97982e6 0.705376
\(448\) 758729. 0.178604
\(449\) 6.92922e6 1.62207 0.811033 0.585001i \(-0.198906\pi\)
0.811033 + 0.585001i \(0.198906\pi\)
\(450\) −202500. −0.0471405
\(451\) −647809. −0.149971
\(452\) 3.26915e6 0.752644
\(453\) −257457. −0.0589467
\(454\) −1.45606e6 −0.331542
\(455\) 2.95227e6 0.668541
\(456\) 207936. 0.0468293
\(457\) 1.28266e6 0.287291 0.143645 0.989629i \(-0.454117\pi\)
0.143645 + 0.989629i \(0.454117\pi\)
\(458\) −1.40963e6 −0.314009
\(459\) 1.65206e6 0.366011
\(460\) −492260. −0.108468
\(461\) 3.50945e6 0.769107 0.384554 0.923103i \(-0.374355\pi\)
0.384554 + 0.923103i \(0.374355\pi\)
\(462\) 886904. 0.193318
\(463\) −2.63980e6 −0.572292 −0.286146 0.958186i \(-0.592374\pi\)
−0.286146 + 0.958186i \(0.592374\pi\)
\(464\) −1.68011e6 −0.362278
\(465\) 2.06530e6 0.442945
\(466\) 6.10884e6 1.30315
\(467\) 173235. 0.0367572 0.0183786 0.999831i \(-0.494150\pi\)
0.0183786 + 0.999831i \(0.494150\pi\)
\(468\) 826217. 0.174373
\(469\) 364101. 0.0764346
\(470\) 1.54047e6 0.321669
\(471\) −867708. −0.180228
\(472\) −905871. −0.187159
\(473\) −1.53431e6 −0.315326
\(474\) 3.17393e6 0.648862
\(475\) 225625. 0.0458831
\(476\) −6.71653e6 −1.35871
\(477\) −202138. −0.0406774
\(478\) 3.98964e6 0.798664
\(479\) −8.27582e6 −1.64806 −0.824029 0.566548i \(-0.808278\pi\)
−0.824029 + 0.566548i \(0.808278\pi\)
\(480\) 230400. 0.0456435
\(481\) 5.53784e6 1.09138
\(482\) −454876. −0.0891817
\(483\) 2.05165e6 0.400163
\(484\) −2.29380e6 −0.445084
\(485\) −846054. −0.163322
\(486\) 236196. 0.0453609
\(487\) 1.83772e6 0.351121 0.175560 0.984469i \(-0.443826\pi\)
0.175560 + 0.984469i \(0.443826\pi\)
\(488\) 1.20357e6 0.228783
\(489\) 2.97375e6 0.562383
\(490\) −1.75056e6 −0.329373
\(491\) −502846. −0.0941308 −0.0470654 0.998892i \(-0.514987\pi\)
−0.0470654 + 0.998892i \(0.514987\pi\)
\(492\) 701395. 0.130632
\(493\) 1.48729e7 2.75599
\(494\) −920569. −0.169722
\(495\) 269322. 0.0494036
\(496\) −2.34985e6 −0.428880
\(497\) 5.92560e6 1.07607
\(498\) −462866. −0.0836338
\(499\) 4.04170e6 0.726629 0.363314 0.931667i \(-0.381645\pi\)
0.363314 + 0.931667i \(0.381645\pi\)
\(500\) 250000. 0.0447214
\(501\) 4.30512e6 0.766286
\(502\) 1.21428e6 0.215059
\(503\) −9.14324e6 −1.61131 −0.805657 0.592382i \(-0.798188\pi\)
−0.805657 + 0.592382i \(0.798188\pi\)
\(504\) −960267. −0.168390
\(505\) 3.58302e6 0.625202
\(506\) 654699. 0.113675
\(507\) −316171. −0.0546264
\(508\) −960590. −0.165150
\(509\) 5.27340e6 0.902187 0.451093 0.892477i \(-0.351034\pi\)
0.451093 + 0.892477i \(0.351034\pi\)
\(510\) −2.03958e6 −0.347228
\(511\) −1.18887e7 −2.01411
\(512\) −262144. −0.0441942
\(513\) −263169. −0.0441511
\(514\) −4.32768e6 −0.722516
\(515\) 2.30679e6 0.383257
\(516\) 1.66123e6 0.274666
\(517\) −2.04880e6 −0.337112
\(518\) −6.43633e6 −1.05394
\(519\) −4.20249e6 −0.684838
\(520\) −1.02002e6 −0.165425
\(521\) 9.30638e6 1.50206 0.751029 0.660270i \(-0.229558\pi\)
0.751029 + 0.660270i \(0.229558\pi\)
\(522\) 2.12638e6 0.341559
\(523\) −8.13792e6 −1.30095 −0.650473 0.759529i \(-0.725429\pi\)
−0.650473 + 0.759529i \(0.725429\pi\)
\(524\) −3.06299e6 −0.487324
\(525\) −1.04196e6 −0.164988
\(526\) 2.81183e6 0.443123
\(527\) 2.08016e7 3.26265
\(528\) −306429. −0.0478349
\(529\) −4.92184e6 −0.764695
\(530\) 249554. 0.0385899
\(531\) 1.14649e6 0.176455
\(532\) 1.06993e6 0.163899
\(533\) −3.10520e6 −0.473447
\(534\) −2.16589e6 −0.328687
\(535\) −2.86263e6 −0.432395
\(536\) −125798. −0.0189131
\(537\) 253301. 0.0379054
\(538\) −2.02186e6 −0.301159
\(539\) 2.32822e6 0.345186
\(540\) −291600. −0.0430331
\(541\) −3.43794e6 −0.505015 −0.252508 0.967595i \(-0.581255\pi\)
−0.252508 + 0.967595i \(0.581255\pi\)
\(542\) −2.04288e6 −0.298706
\(543\) −6.83000e6 −0.994079
\(544\) 2.32059e6 0.336202
\(545\) −5.98509e6 −0.863137
\(546\) 4.25127e6 0.610291
\(547\) 8.85291e6 1.26508 0.632539 0.774528i \(-0.282013\pi\)
0.632539 + 0.774528i \(0.282013\pi\)
\(548\) −5.34643e6 −0.760524
\(549\) −1.52327e6 −0.215699
\(550\) −332496. −0.0468684
\(551\) −2.36921e6 −0.332449
\(552\) −708855. −0.0990170
\(553\) 1.63314e7 2.27096
\(554\) −3.19248e6 −0.441931
\(555\) −1.95449e6 −0.269340
\(556\) 5.75070e6 0.788921
\(557\) 202563. 0.0276644 0.0138322 0.999904i \(-0.495597\pi\)
0.0138322 + 0.999904i \(0.495597\pi\)
\(558\) 2.97403e6 0.404352
\(559\) −7.35453e6 −0.995464
\(560\) 1.18551e6 0.159749
\(561\) 2.71261e6 0.363898
\(562\) −1.69192e6 −0.225964
\(563\) 1.73026e6 0.230059 0.115030 0.993362i \(-0.463304\pi\)
0.115030 + 0.993362i \(0.463304\pi\)
\(564\) 2.21828e6 0.293642
\(565\) 5.10805e6 0.673185
\(566\) 8.56469e6 1.12375
\(567\) 1.21534e6 0.158759
\(568\) −2.04732e6 −0.266265
\(569\) −1.00719e7 −1.30416 −0.652081 0.758149i \(-0.726104\pi\)
−0.652081 + 0.758149i \(0.726104\pi\)
\(570\) 324900. 0.0418854
\(571\) 3.76172e6 0.482832 0.241416 0.970422i \(-0.422388\pi\)
0.241416 + 0.970422i \(0.422388\pi\)
\(572\) 1.35661e6 0.173367
\(573\) −5.91872e6 −0.753080
\(574\) 3.60900e6 0.457201
\(575\) −769157. −0.0970164
\(576\) 331776. 0.0416667
\(577\) −1.32750e7 −1.65995 −0.829973 0.557803i \(-0.811644\pi\)
−0.829973 + 0.557803i \(0.811644\pi\)
\(578\) −1.48632e7 −1.85051
\(579\) 8.85253e6 1.09742
\(580\) −2.62517e6 −0.324031
\(581\) −2.38166e6 −0.292711
\(582\) −1.21832e6 −0.149092
\(583\) −331903. −0.0404426
\(584\) 4.10761e6 0.498376
\(585\) 1.29096e6 0.155964
\(586\) 6.15151e6 0.740011
\(587\) −513155. −0.0614686 −0.0307343 0.999528i \(-0.509785\pi\)
−0.0307343 + 0.999528i \(0.509785\pi\)
\(588\) −2.52081e6 −0.300675
\(589\) −3.31365e6 −0.393567
\(590\) −1.41542e6 −0.167400
\(591\) −3.17221e6 −0.373588
\(592\) 2.22378e6 0.260788
\(593\) 6.75813e6 0.789204 0.394602 0.918852i \(-0.370882\pi\)
0.394602 + 0.918852i \(0.370882\pi\)
\(594\) 387824. 0.0450992
\(595\) −1.04946e7 −1.21527
\(596\) −5.29745e6 −0.610874
\(597\) 6.18459e6 0.710190
\(598\) 3.13822e6 0.358865
\(599\) −2.71104e6 −0.308723 −0.154361 0.988014i \(-0.549332\pi\)
−0.154361 + 0.988014i \(0.549332\pi\)
\(600\) 360000. 0.0408248
\(601\) 5.20578e6 0.587895 0.293948 0.955822i \(-0.405031\pi\)
0.293948 + 0.955822i \(0.405031\pi\)
\(602\) 8.54777e6 0.961306
\(603\) 159214. 0.0178315
\(604\) 457701. 0.0510493
\(605\) −3.58406e6 −0.398095
\(606\) 5.15955e6 0.570729
\(607\) −1.50241e6 −0.165507 −0.0827535 0.996570i \(-0.526371\pi\)
−0.0827535 + 0.996570i \(0.526371\pi\)
\(608\) −369664. −0.0405554
\(609\) 1.09412e7 1.19543
\(610\) 1.88059e6 0.204630
\(611\) −9.82071e6 −1.06424
\(612\) −2.93699e6 −0.316974
\(613\) −1.09306e7 −1.17488 −0.587439 0.809268i \(-0.699864\pi\)
−0.587439 + 0.809268i \(0.699864\pi\)
\(614\) −1.11807e7 −1.19687
\(615\) 1.09593e6 0.116841
\(616\) −1.57672e6 −0.167418
\(617\) 1.59629e6 0.168810 0.0844049 0.996432i \(-0.473101\pi\)
0.0844049 + 0.996432i \(0.473101\pi\)
\(618\) 3.32178e6 0.349865
\(619\) 2.26197e6 0.237279 0.118640 0.992937i \(-0.462147\pi\)
0.118640 + 0.992937i \(0.462147\pi\)
\(620\) −3.67164e6 −0.383602
\(621\) 897144. 0.0933541
\(622\) −851506. −0.0882494
\(623\) −1.11445e7 −1.15038
\(624\) −1.46883e6 −0.151012
\(625\) 390625. 0.0400000
\(626\) −1.15071e7 −1.17363
\(627\) −432112. −0.0438963
\(628\) 1.54259e6 0.156082
\(629\) −1.96856e7 −1.98391
\(630\) −1.50042e6 −0.150612
\(631\) −1.16013e7 −1.15993 −0.579967 0.814640i \(-0.696934\pi\)
−0.579967 + 0.814640i \(0.696934\pi\)
\(632\) −5.64255e6 −0.561931
\(633\) −2.18238e6 −0.216481
\(634\) 7.69460e6 0.760261
\(635\) −1.50092e6 −0.147715
\(636\) 359357. 0.0352276
\(637\) 1.11601e7 1.08973
\(638\) 3.49143e6 0.339588
\(639\) 2.59113e6 0.251037
\(640\) −409600. −0.0395285
\(641\) −1.44428e7 −1.38838 −0.694189 0.719793i \(-0.744237\pi\)
−0.694189 + 0.719793i \(0.744237\pi\)
\(642\) −4.12219e6 −0.394721
\(643\) −1.24720e7 −1.18962 −0.594809 0.803867i \(-0.702772\pi\)
−0.594809 + 0.803867i \(0.702772\pi\)
\(644\) −3.64739e6 −0.346551
\(645\) 2.59566e6 0.245668
\(646\) 3.27239e6 0.308520
\(647\) −3.00553e6 −0.282267 −0.141134 0.989991i \(-0.545075\pi\)
−0.141134 + 0.989991i \(0.545075\pi\)
\(648\) −419904. −0.0392837
\(649\) 1.88249e6 0.175437
\(650\) −1.59378e6 −0.147961
\(651\) 1.53027e7 1.41520
\(652\) −5.28666e6 −0.487038
\(653\) −7.77905e6 −0.713910 −0.356955 0.934122i \(-0.616185\pi\)
−0.356955 + 0.934122i \(0.616185\pi\)
\(654\) −8.61853e6 −0.787932
\(655\) −4.78593e6 −0.435876
\(656\) −1.24692e6 −0.113131
\(657\) −5.19869e6 −0.469873
\(658\) 1.14141e7 1.02772
\(659\) 4.55109e6 0.408227 0.204113 0.978947i \(-0.434569\pi\)
0.204113 + 0.978947i \(0.434569\pi\)
\(660\) −478795. −0.0427848
\(661\) −1.47211e7 −1.31050 −0.655252 0.755411i \(-0.727437\pi\)
−0.655252 + 0.755411i \(0.727437\pi\)
\(662\) −1.20534e7 −1.06897
\(663\) 1.30026e7 1.14880
\(664\) 822873. 0.0724290
\(665\) 1.67176e6 0.146595
\(666\) −2.81447e6 −0.245873
\(667\) 8.07666e6 0.702938
\(668\) −7.65354e6 −0.663623
\(669\) 8.81623e6 0.761584
\(670\) −196560. −0.0169164
\(671\) −2.50115e6 −0.214454
\(672\) 1.70714e6 0.145830
\(673\) −5.53394e6 −0.470974 −0.235487 0.971877i \(-0.575669\pi\)
−0.235487 + 0.971877i \(0.575669\pi\)
\(674\) −1.06735e6 −0.0905015
\(675\) −455625. −0.0384900
\(676\) 562082. 0.0473079
\(677\) −8.48504e6 −0.711512 −0.355756 0.934579i \(-0.615777\pi\)
−0.355756 + 0.934579i \(0.615777\pi\)
\(678\) 7.35560e6 0.614531
\(679\) −6.26881e6 −0.521808
\(680\) 3.62592e6 0.300708
\(681\) −3.27613e6 −0.270703
\(682\) 4.88322e6 0.402018
\(683\) −2.24787e7 −1.84382 −0.921910 0.387404i \(-0.873372\pi\)
−0.921910 + 0.387404i \(0.873372\pi\)
\(684\) 467856. 0.0382360
\(685\) −8.35380e6 −0.680233
\(686\) −517647. −0.0419975
\(687\) −3.17167e6 −0.256387
\(688\) −2.95329e6 −0.237867
\(689\) −1.59094e6 −0.127675
\(690\) −1.10759e6 −0.0885635
\(691\) −6.37709e6 −0.508075 −0.254037 0.967194i \(-0.581759\pi\)
−0.254037 + 0.967194i \(0.581759\pi\)
\(692\) 7.47109e6 0.593087
\(693\) 1.99553e6 0.157843
\(694\) −4.42265e6 −0.348565
\(695\) 8.98547e6 0.705633
\(696\) −3.78024e6 −0.295799
\(697\) 1.10382e7 0.860629
\(698\) −1.40681e7 −1.09294
\(699\) 1.37449e7 1.06402
\(700\) 1.85237e6 0.142883
\(701\) 3.20106e6 0.246036 0.123018 0.992404i \(-0.460743\pi\)
0.123018 + 0.992404i \(0.460743\pi\)
\(702\) 1.85899e6 0.142375
\(703\) 3.13587e6 0.239315
\(704\) 544762. 0.0414262
\(705\) 3.46606e6 0.262641
\(706\) −6.02888e6 −0.455224
\(707\) 2.65483e7 1.99750
\(708\) −2.03821e6 −0.152815
\(709\) 1.47460e7 1.10168 0.550842 0.834609i \(-0.314307\pi\)
0.550842 + 0.834609i \(0.314307\pi\)
\(710\) −3.19893e6 −0.238155
\(711\) 7.14135e6 0.529793
\(712\) 3.85047e6 0.284652
\(713\) 1.12963e7 0.832167
\(714\) −1.51122e7 −1.10938
\(715\) 2.11971e6 0.155064
\(716\) −450313. −0.0328270
\(717\) 8.97670e6 0.652107
\(718\) −2.09837e6 −0.151904
\(719\) −5.76458e6 −0.415858 −0.207929 0.978144i \(-0.566672\pi\)
−0.207929 + 0.978144i \(0.566672\pi\)
\(720\) 518400. 0.0372678
\(721\) 1.70921e7 1.22450
\(722\) −521284. −0.0372161
\(723\) −1.02347e6 −0.0728165
\(724\) 1.21422e7 0.860898
\(725\) −4.10182e6 −0.289822
\(726\) −5.16105e6 −0.363409
\(727\) 2.04059e7 1.43192 0.715960 0.698141i \(-0.245989\pi\)
0.715960 + 0.698141i \(0.245989\pi\)
\(728\) −7.55781e6 −0.528528
\(729\) 531441. 0.0370370
\(730\) 6.41814e6 0.445761
\(731\) 2.61435e7 1.80955
\(732\) 2.70804e6 0.186800
\(733\) −1.49257e7 −1.02607 −0.513034 0.858368i \(-0.671478\pi\)
−0.513034 + 0.858368i \(0.671478\pi\)
\(734\) 1.96388e7 1.34547
\(735\) −3.93877e6 −0.268932
\(736\) 1.26019e6 0.0857512
\(737\) 261422. 0.0177286
\(738\) 1.57814e6 0.106661
\(739\) −2.49017e7 −1.67732 −0.838662 0.544652i \(-0.816662\pi\)
−0.838662 + 0.544652i \(0.816662\pi\)
\(740\) 3.47465e6 0.233256
\(741\) −2.07128e6 −0.138578
\(742\) 1.84906e6 0.123294
\(743\) −9.85812e6 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(744\) −5.28716e6 −0.350179
\(745\) −8.27727e6 −0.546382
\(746\) 1.53620e7 1.01065
\(747\) −1.04145e6 −0.0682867
\(748\) −4.82242e6 −0.315145
\(749\) −2.12106e7 −1.38149
\(750\) 562500. 0.0365148
\(751\) −1.17506e7 −0.760254 −0.380127 0.924934i \(-0.624120\pi\)
−0.380127 + 0.924934i \(0.624120\pi\)
\(752\) −3.94361e6 −0.254301
\(753\) 2.73212e6 0.175595
\(754\) 1.67358e7 1.07206
\(755\) 715159. 0.0456599
\(756\) −2.16060e6 −0.137490
\(757\) −1.31194e7 −0.832100 −0.416050 0.909342i \(-0.636586\pi\)
−0.416050 + 0.909342i \(0.636586\pi\)
\(758\) −9.04160e6 −0.571574
\(759\) 1.47307e6 0.0928154
\(760\) −577600. −0.0362738
\(761\) −1.66140e7 −1.03995 −0.519974 0.854182i \(-0.674058\pi\)
−0.519974 + 0.854182i \(0.674058\pi\)
\(762\) −2.16133e6 −0.134844
\(763\) −4.43463e7 −2.75770
\(764\) 1.05222e7 0.652186
\(765\) −4.58905e6 −0.283511
\(766\) 6.11204e6 0.376369
\(767\) 9.02351e6 0.553843
\(768\) −589824. −0.0360844
\(769\) 1.24736e7 0.760636 0.380318 0.924856i \(-0.375815\pi\)
0.380318 + 0.924856i \(0.375815\pi\)
\(770\) −2.46362e6 −0.149743
\(771\) −9.73728e6 −0.589932
\(772\) −1.57378e7 −0.950389
\(773\) −424135. −0.0255303 −0.0127651 0.999919i \(-0.504063\pi\)
−0.0127651 + 0.999919i \(0.504063\pi\)
\(774\) 3.73776e6 0.224263
\(775\) −5.73693e6 −0.343104
\(776\) 2.16590e6 0.129117
\(777\) −1.44817e7 −0.860535
\(778\) −1.29218e7 −0.765372
\(779\) −1.75836e6 −0.103816
\(780\) −2.29505e6 −0.135069
\(781\) 4.25453e6 0.249588
\(782\) −1.11556e7 −0.652343
\(783\) 4.78437e6 0.278882
\(784\) 4.48144e6 0.260392
\(785\) 2.41030e6 0.139604
\(786\) −6.89173e6 −0.397898
\(787\) 2.22988e7 1.28335 0.641675 0.766977i \(-0.278240\pi\)
0.641675 + 0.766977i \(0.278240\pi\)
\(788\) 5.63949e6 0.323537
\(789\) 6.32661e6 0.361808
\(790\) −8.81648e6 −0.502606
\(791\) 3.78480e7 2.15081
\(792\) −689465. −0.0390570
\(793\) −1.19890e7 −0.677017
\(794\) 1.96815e6 0.110791
\(795\) 561496. 0.0315086
\(796\) −1.09948e7 −0.615043
\(797\) −6.36779e6 −0.355094 −0.177547 0.984112i \(-0.556816\pi\)
−0.177547 + 0.984112i \(0.556816\pi\)
\(798\) 2.40734e6 0.133823
\(799\) 3.49101e7 1.93457
\(800\) −640000. −0.0353553
\(801\) −4.87325e6 −0.268372
\(802\) −7.71818e6 −0.423720
\(803\) −8.53603e6 −0.467162
\(804\) −283046. −0.0154425
\(805\) −5.69904e6 −0.309965
\(806\) 2.34072e7 1.26914
\(807\) −4.54918e6 −0.245895
\(808\) −9.17253e6 −0.494266
\(809\) 1.21132e7 0.650709 0.325354 0.945592i \(-0.394516\pi\)
0.325354 + 0.945592i \(0.394516\pi\)
\(810\) −656100. −0.0351364
\(811\) −2.44812e7 −1.30701 −0.653507 0.756920i \(-0.726703\pi\)
−0.653507 + 0.756920i \(0.726703\pi\)
\(812\) −1.94511e7 −1.03527
\(813\) −4.59648e6 −0.243893
\(814\) −4.62124e6 −0.244454
\(815\) −8.26041e6 −0.435620
\(816\) 5.22132e6 0.274508
\(817\) −4.16460e6 −0.218282
\(818\) −8.55547e6 −0.447054
\(819\) 9.56536e6 0.498301
\(820\) −1.94832e6 −0.101187
\(821\) −2.53799e6 −0.131411 −0.0657056 0.997839i \(-0.520930\pi\)
−0.0657056 + 0.997839i \(0.520930\pi\)
\(822\) −1.20295e7 −0.620965
\(823\) 1.59503e7 0.820859 0.410430 0.911892i \(-0.365379\pi\)
0.410430 + 0.911892i \(0.365379\pi\)
\(824\) −5.90539e6 −0.302992
\(825\) −748117. −0.0382679
\(826\) −1.04875e7 −0.534839
\(827\) −1.34516e7 −0.683928 −0.341964 0.939713i \(-0.611092\pi\)
−0.341964 + 0.939713i \(0.611092\pi\)
\(828\) −1.59492e6 −0.0808470
\(829\) 1.99401e6 0.100772 0.0503862 0.998730i \(-0.483955\pi\)
0.0503862 + 0.998730i \(0.483955\pi\)
\(830\) 1.28574e6 0.0647825
\(831\) −7.18309e6 −0.360835
\(832\) 2.61125e6 0.130780
\(833\) −3.96712e7 −1.98090
\(834\) 1.29391e7 0.644151
\(835\) −1.19587e7 −0.593562
\(836\) 768200. 0.0380153
\(837\) 6.69156e6 0.330152
\(838\) 2.30706e7 1.13488
\(839\) −7.03249e6 −0.344909 −0.172454 0.985017i \(-0.555170\pi\)
−0.172454 + 0.985017i \(0.555170\pi\)
\(840\) 2.66741e6 0.130434
\(841\) 2.25607e7 1.09992
\(842\) 1.07965e6 0.0524811
\(843\) −3.80681e6 −0.184498
\(844\) 3.87978e6 0.187478
\(845\) 878254. 0.0423134
\(846\) 4.99113e6 0.239758
\(847\) −2.65560e7 −1.27190
\(848\) −638857. −0.0305080
\(849\) 1.92706e7 0.917540
\(850\) 5.66549e6 0.268962
\(851\) −1.06902e7 −0.506014
\(852\) −4.60646e6 −0.217404
\(853\) −1.14269e7 −0.537721 −0.268861 0.963179i \(-0.586647\pi\)
−0.268861 + 0.963179i \(0.586647\pi\)
\(854\) 1.39341e7 0.653786
\(855\) 731025. 0.0341993
\(856\) 7.32833e6 0.341838
\(857\) 2.16028e6 0.100475 0.0502374 0.998737i \(-0.484002\pi\)
0.0502374 + 0.998737i \(0.484002\pi\)
\(858\) 3.05238e6 0.141553
\(859\) −1.41213e7 −0.652968 −0.326484 0.945203i \(-0.605864\pi\)
−0.326484 + 0.945203i \(0.605864\pi\)
\(860\) −4.61451e6 −0.212755
\(861\) 8.12026e6 0.373303
\(862\) 2.49238e7 1.14247
\(863\) 3.85011e7 1.75973 0.879866 0.475221i \(-0.157632\pi\)
0.879866 + 0.475221i \(0.157632\pi\)
\(864\) 746496. 0.0340207
\(865\) 1.16736e7 0.530473
\(866\) −1.24563e6 −0.0564411
\(867\) −3.34421e7 −1.51094
\(868\) −2.72049e7 −1.22560
\(869\) 1.17258e7 0.526736
\(870\) −5.90662e6 −0.264570
\(871\) 1.25310e6 0.0559679
\(872\) 1.53218e7 0.682370
\(873\) −2.74122e6 −0.121733
\(874\) 1.77706e6 0.0786907
\(875\) 2.89432e6 0.127799
\(876\) 9.24212e6 0.406922
\(877\) 3.66258e7 1.60801 0.804004 0.594624i \(-0.202699\pi\)
0.804004 + 0.594624i \(0.202699\pi\)
\(878\) −1.27555e7 −0.558421
\(879\) 1.38409e7 0.604216
\(880\) 851191. 0.0370527
\(881\) 2.85701e7 1.24014 0.620072 0.784545i \(-0.287103\pi\)
0.620072 + 0.784545i \(0.287103\pi\)
\(882\) −5.67182e6 −0.245500
\(883\) −4.70913e6 −0.203254 −0.101627 0.994823i \(-0.532405\pi\)
−0.101627 + 0.994823i \(0.532405\pi\)
\(884\) −2.31157e7 −0.994893
\(885\) −3.18470e6 −0.136682
\(886\) 9.47734e6 0.405604
\(887\) 3.52406e7 1.50395 0.751976 0.659191i \(-0.229101\pi\)
0.751976 + 0.659191i \(0.229101\pi\)
\(888\) 5.00350e6 0.212932
\(889\) −1.11210e7 −0.471944
\(890\) 6.01636e6 0.254600
\(891\) 872604. 0.0368233
\(892\) −1.56733e7 −0.659551
\(893\) −5.56110e6 −0.233363
\(894\) −1.19193e7 −0.498776
\(895\) −703613. −0.0293614
\(896\) −3.03492e6 −0.126292
\(897\) 7.06101e6 0.293012
\(898\) −2.77169e7 −1.14697
\(899\) 6.02416e7 2.48598
\(900\) 810000. 0.0333333
\(901\) 5.65538e6 0.232086
\(902\) 2.59124e6 0.106045
\(903\) 1.92325e7 0.784903
\(904\) −1.30766e7 −0.532199
\(905\) 1.89722e7 0.770011
\(906\) 1.02983e6 0.0416816
\(907\) −1.08073e7 −0.436215 −0.218108 0.975925i \(-0.569988\pi\)
−0.218108 + 0.975925i \(0.569988\pi\)
\(908\) 5.82423e6 0.234436
\(909\) 1.16090e7 0.465998
\(910\) −1.18091e7 −0.472730
\(911\) 3.58414e7 1.43083 0.715417 0.698698i \(-0.246237\pi\)
0.715417 + 0.698698i \(0.246237\pi\)
\(912\) −831744. −0.0331133
\(913\) −1.71001e6 −0.0678926
\(914\) −5.13065e6 −0.203145
\(915\) 4.23132e6 0.167079
\(916\) 5.63853e6 0.222038
\(917\) −3.54612e7 −1.39261
\(918\) −6.60823e6 −0.258809
\(919\) −4.80159e7 −1.87541 −0.937705 0.347432i \(-0.887054\pi\)
−0.937705 + 0.347432i \(0.887054\pi\)
\(920\) 1.96904e6 0.0766982
\(921\) −2.51565e7 −0.977239
\(922\) −1.40378e7 −0.543841
\(923\) 2.03936e7 0.787934
\(924\) −3.54762e6 −0.136696
\(925\) 5.42915e6 0.208630
\(926\) 1.05592e7 0.404672
\(927\) 7.47401e6 0.285663
\(928\) 6.72043e6 0.256169
\(929\) 4.20495e7 1.59853 0.799266 0.600978i \(-0.205222\pi\)
0.799266 + 0.600978i \(0.205222\pi\)
\(930\) −8.26118e6 −0.313209
\(931\) 6.31953e6 0.238952
\(932\) −2.44354e7 −0.921465
\(933\) −1.91589e6 −0.0720553
\(934\) −692938. −0.0259913
\(935\) −7.53503e6 −0.281874
\(936\) −3.30487e6 −0.123300
\(937\) 1.58814e7 0.590936 0.295468 0.955353i \(-0.404524\pi\)
0.295468 + 0.955353i \(0.404524\pi\)
\(938\) −1.45640e6 −0.0540474
\(939\) −2.58910e7 −0.958265
\(940\) −6.16188e6 −0.227454
\(941\) 1.60983e7 0.592659 0.296329 0.955086i \(-0.404237\pi\)
0.296329 + 0.955086i \(0.404237\pi\)
\(942\) 3.47083e6 0.127440
\(943\) 5.99425e6 0.219511
\(944\) 3.62348e6 0.132342
\(945\) −3.37594e6 −0.122974
\(946\) 6.13724e6 0.222969
\(947\) −1.47834e7 −0.535673 −0.267837 0.963464i \(-0.586309\pi\)
−0.267837 + 0.963464i \(0.586309\pi\)
\(948\) −1.26957e7 −0.458814
\(949\) −4.09165e7 −1.47480
\(950\) −902500. −0.0324443
\(951\) 1.73129e7 0.620751
\(952\) 2.68661e7 0.960754
\(953\) 3.55908e7 1.26942 0.634711 0.772750i \(-0.281119\pi\)
0.634711 + 0.772750i \(0.281119\pi\)
\(954\) 808554. 0.0287632
\(955\) 1.64409e7 0.583333
\(956\) −1.59586e7 −0.564741
\(957\) 7.85573e6 0.277272
\(958\) 3.31033e7 1.16535
\(959\) −6.18972e7 −2.17332
\(960\) −921600. −0.0322749
\(961\) 5.56265e7 1.94300
\(962\) −2.21514e7 −0.771726
\(963\) −9.27492e6 −0.322288
\(964\) 1.81951e6 0.0630610
\(965\) −2.45904e7 −0.850054
\(966\) −8.20662e6 −0.282958
\(967\) 2.33745e7 0.803852 0.401926 0.915672i \(-0.368341\pi\)
0.401926 + 0.915672i \(0.368341\pi\)
\(968\) 9.17519e6 0.314722
\(969\) 7.36288e6 0.251906
\(970\) 3.38422e6 0.115486
\(971\) −2.22140e7 −0.756100 −0.378050 0.925785i \(-0.623405\pi\)
−0.378050 + 0.925785i \(0.623405\pi\)
\(972\) −944784. −0.0320750
\(973\) 6.65775e7 2.25448
\(974\) −7.35087e6 −0.248280
\(975\) −3.58601e6 −0.120809
\(976\) −4.81430e6 −0.161774
\(977\) 2.45425e7 0.822590 0.411295 0.911502i \(-0.365077\pi\)
0.411295 + 0.911502i \(0.365077\pi\)
\(978\) −1.18950e7 −0.397665
\(979\) −8.00167e6 −0.266823
\(980\) 7.00225e6 0.232902
\(981\) −1.93917e7 −0.643344
\(982\) 2.01139e6 0.0665605
\(983\) 3.52199e7 1.16253 0.581265 0.813714i \(-0.302558\pi\)
0.581265 + 0.813714i \(0.302558\pi\)
\(984\) −2.80558e6 −0.0923709
\(985\) 8.81170e6 0.289380
\(986\) −5.94915e7 −1.94878
\(987\) 2.56817e7 0.839132
\(988\) 3.68228e6 0.120012
\(989\) 1.41971e7 0.461541
\(990\) −1.07729e6 −0.0349337
\(991\) −8.23228e6 −0.266278 −0.133139 0.991097i \(-0.542506\pi\)
−0.133139 + 0.991097i \(0.542506\pi\)
\(992\) 9.39939e6 0.303264
\(993\) −2.71202e7 −0.872811
\(994\) −2.37024e7 −0.760897
\(995\) −1.71794e7 −0.550111
\(996\) 1.85146e6 0.0591380
\(997\) 3.86043e7 1.22998 0.614989 0.788535i \(-0.289160\pi\)
0.614989 + 0.788535i \(0.289160\pi\)
\(998\) −1.61668e7 −0.513804
\(999\) −6.33255e6 −0.200754
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.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.j.1.4 4 1.1 even 1 trivial