Properties

Label 570.6.a.m.1.4
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 1.4
Root \(-13.3932\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +229.958 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +229.958 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -291.046 q^{11} +144.000 q^{12} +1157.69 q^{13} -919.833 q^{14} +225.000 q^{15} +256.000 q^{16} +1162.12 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +2069.62 q^{21} +1164.18 q^{22} -3807.41 q^{23} -576.000 q^{24} +625.000 q^{25} -4630.76 q^{26} +729.000 q^{27} +3679.33 q^{28} +7366.62 q^{29} -900.000 q^{30} +6149.97 q^{31} -1024.00 q^{32} -2619.41 q^{33} -4648.47 q^{34} +5748.95 q^{35} +1296.00 q^{36} -1728.76 q^{37} -1444.00 q^{38} +10419.2 q^{39} -1600.00 q^{40} -11006.7 q^{41} -8278.49 q^{42} +16853.6 q^{43} -4656.73 q^{44} +2025.00 q^{45} +15229.6 q^{46} -6749.24 q^{47} +2304.00 q^{48} +36073.7 q^{49} -2500.00 q^{50} +10459.1 q^{51} +18523.0 q^{52} -38538.0 q^{53} -2916.00 q^{54} -7276.15 q^{55} -14717.3 q^{56} +3249.00 q^{57} -29466.5 q^{58} +30949.2 q^{59} +3600.00 q^{60} -7283.72 q^{61} -24599.9 q^{62} +18626.6 q^{63} +4096.00 q^{64} +28942.3 q^{65} +10477.6 q^{66} -25655.9 q^{67} +18593.9 q^{68} -34266.7 q^{69} -22995.8 q^{70} -7321.98 q^{71} -5184.00 q^{72} -81106.7 q^{73} +6915.02 q^{74} +5625.00 q^{75} +5776.00 q^{76} -66928.4 q^{77} -41676.9 q^{78} -1786.83 q^{79} +6400.00 q^{80} +6561.00 q^{81} +44026.9 q^{82} +41472.9 q^{83} +33114.0 q^{84} +29052.9 q^{85} -67414.3 q^{86} +66299.6 q^{87} +18626.9 q^{88} +52047.0 q^{89} -8100.00 q^{90} +266220. q^{91} -60918.5 q^{92} +55349.8 q^{93} +26997.0 q^{94} +9025.00 q^{95} -9216.00 q^{96} -91522.8 q^{97} -144295. q^{98} -23574.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} - 400q^{10} + 338q^{11} + 576q^{12} + 1302q^{13} - 1072q^{14} + 900q^{15} + 1024q^{16} + 542q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 2412q^{21} - 1352q^{22} - 88q^{23} - 2304q^{24} + 2500q^{25} - 5208q^{26} + 2916q^{27} + 4288q^{28} + 5014q^{29} - 3600q^{30} + 4962q^{31} - 4096q^{32} + 3042q^{33} - 2168q^{34} + 6700q^{35} + 5184q^{36} + 8022q^{37} - 5776q^{38} + 11718q^{39} - 6400q^{40} + 2764q^{41} - 9648q^{42} + 25346q^{43} + 5408q^{44} + 8100q^{45} + 352q^{46} + 10008q^{47} + 9216q^{48} + 37248q^{49} - 10000q^{50} + 4878q^{51} + 20832q^{52} - 224q^{53} - 11664q^{54} + 8450q^{55} - 17152q^{56} + 12996q^{57} - 20056q^{58} + 29654q^{59} + 14400q^{60} + 27276q^{61} - 19848q^{62} + 21708q^{63} + 16384q^{64} + 32550q^{65} - 12168q^{66} + 26024q^{67} + 8672q^{68} - 792q^{69} - 26800q^{70} - 26940q^{71} - 20736q^{72} - 60916q^{73} - 32088q^{74} + 22500q^{75} + 23104q^{76} - 21228q^{77} - 46872q^{78} + 34902q^{79} + 25600q^{80} + 26244q^{81} - 11056q^{82} - 48430q^{83} + 38592q^{84} + 13550q^{85} - 101384q^{86} + 45126q^{87} - 21632q^{88} - 38348q^{89} - 32400q^{90} + 69280q^{91} - 1408q^{92} + 44658q^{93} - 40032q^{94} + 36100q^{95} - 36864q^{96} + 45942q^{97} - 148992q^{98} + 27378q^{99} + O(q^{100}) \)

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
\(7\) 229.958 1.77380 0.886898 0.461965i \(-0.152856\pi\)
0.886898 + 0.461965i \(0.152856\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) −291.046 −0.725236 −0.362618 0.931938i \(-0.618117\pi\)
−0.362618 + 0.931938i \(0.618117\pi\)
\(12\) 144.000 0.288675
\(13\) 1157.69 1.89991 0.949957 0.312380i \(-0.101126\pi\)
0.949957 + 0.312380i \(0.101126\pi\)
\(14\) −919.833 −1.25426
\(15\) 225.000 0.258199
\(16\) 256.000 0.250000
\(17\) 1162.12 0.975277 0.487638 0.873046i \(-0.337858\pi\)
0.487638 + 0.873046i \(0.337858\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) 2069.62 1.02410
\(22\) 1164.18 0.512820
\(23\) −3807.41 −1.50075 −0.750377 0.661010i \(-0.770128\pi\)
−0.750377 + 0.661010i \(0.770128\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) −4630.76 −1.34344
\(27\) 729.000 0.192450
\(28\) 3679.33 0.886898
\(29\) 7366.62 1.62657 0.813286 0.581864i \(-0.197677\pi\)
0.813286 + 0.581864i \(0.197677\pi\)
\(30\) −900.000 −0.182574
\(31\) 6149.97 1.14939 0.574697 0.818366i \(-0.305120\pi\)
0.574697 + 0.818366i \(0.305120\pi\)
\(32\) −1024.00 −0.176777
\(33\) −2619.41 −0.418715
\(34\) −4648.47 −0.689625
\(35\) 5748.95 0.793266
\(36\) 1296.00 0.166667
\(37\) −1728.76 −0.207601 −0.103800 0.994598i \(-0.533100\pi\)
−0.103800 + 0.994598i \(0.533100\pi\)
\(38\) −1444.00 −0.162221
\(39\) 10419.2 1.09692
\(40\) −1600.00 −0.158114
\(41\) −11006.7 −1.02258 −0.511291 0.859408i \(-0.670833\pi\)
−0.511291 + 0.859408i \(0.670833\pi\)
\(42\) −8278.49 −0.724149
\(43\) 16853.6 1.39002 0.695010 0.719000i \(-0.255400\pi\)
0.695010 + 0.719000i \(0.255400\pi\)
\(44\) −4656.73 −0.362618
\(45\) 2025.00 0.149071
\(46\) 15229.6 1.06119
\(47\) −6749.24 −0.445667 −0.222834 0.974857i \(-0.571531\pi\)
−0.222834 + 0.974857i \(0.571531\pi\)
\(48\) 2304.00 0.144338
\(49\) 36073.7 2.14635
\(50\) −2500.00 −0.141421
\(51\) 10459.1 0.563076
\(52\) 18523.0 0.949957
\(53\) −38538.0 −1.88451 −0.942257 0.334889i \(-0.891301\pi\)
−0.942257 + 0.334889i \(0.891301\pi\)
\(54\) −2916.00 −0.136083
\(55\) −7276.15 −0.324336
\(56\) −14717.3 −0.627132
\(57\) 3249.00 0.132453
\(58\) −29466.5 −1.15016
\(59\) 30949.2 1.15750 0.578748 0.815507i \(-0.303542\pi\)
0.578748 + 0.815507i \(0.303542\pi\)
\(60\) 3600.00 0.129099
\(61\) −7283.72 −0.250628 −0.125314 0.992117i \(-0.539994\pi\)
−0.125314 + 0.992117i \(0.539994\pi\)
\(62\) −24599.9 −0.812745
\(63\) 18626.6 0.591265
\(64\) 4096.00 0.125000
\(65\) 28942.3 0.849668
\(66\) 10477.6 0.296077
\(67\) −25655.9 −0.698233 −0.349117 0.937079i \(-0.613518\pi\)
−0.349117 + 0.937079i \(0.613518\pi\)
\(68\) 18593.9 0.487638
\(69\) −34266.7 −0.866461
\(70\) −22995.8 −0.560924
\(71\) −7321.98 −0.172378 −0.0861892 0.996279i \(-0.527469\pi\)
−0.0861892 + 0.996279i \(0.527469\pi\)
\(72\) −5184.00 −0.117851
\(73\) −81106.7 −1.78135 −0.890676 0.454638i \(-0.849769\pi\)
−0.890676 + 0.454638i \(0.849769\pi\)
\(74\) 6915.02 0.146796
\(75\) 5625.00 0.115470
\(76\) 5776.00 0.114708
\(77\) −66928.4 −1.28642
\(78\) −41676.9 −0.775637
\(79\) −1786.83 −0.0322119 −0.0161059 0.999870i \(-0.505127\pi\)
−0.0161059 + 0.999870i \(0.505127\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) 44026.9 0.723074
\(83\) 41472.9 0.660799 0.330399 0.943841i \(-0.392817\pi\)
0.330399 + 0.943841i \(0.392817\pi\)
\(84\) 33114.0 0.512051
\(85\) 29052.9 0.436157
\(86\) −67414.3 −0.982893
\(87\) 66299.6 0.939102
\(88\) 18626.9 0.256410
\(89\) 52047.0 0.696500 0.348250 0.937402i \(-0.386776\pi\)
0.348250 + 0.937402i \(0.386776\pi\)
\(90\) −8100.00 −0.105409
\(91\) 266220. 3.37006
\(92\) −60918.5 −0.750377
\(93\) 55349.8 0.663603
\(94\) 26997.0 0.315134
\(95\) 9025.00 0.102598
\(96\) −9216.00 −0.102062
\(97\) −91522.8 −0.987643 −0.493822 0.869563i \(-0.664400\pi\)
−0.493822 + 0.869563i \(0.664400\pi\)
\(98\) −144295. −1.51770
\(99\) −23574.7 −0.241745
\(100\) 10000.0 0.100000
\(101\) −93040.6 −0.907546 −0.453773 0.891117i \(-0.649922\pi\)
−0.453773 + 0.891117i \(0.649922\pi\)
\(102\) −41836.2 −0.398155
\(103\) −91771.6 −0.852345 −0.426173 0.904642i \(-0.640138\pi\)
−0.426173 + 0.904642i \(0.640138\pi\)
\(104\) −74092.2 −0.671721
\(105\) 51740.6 0.457992
\(106\) 154152. 1.33255
\(107\) 31356.1 0.264766 0.132383 0.991199i \(-0.457737\pi\)
0.132383 + 0.991199i \(0.457737\pi\)
\(108\) 11664.0 0.0962250
\(109\) −183541. −1.47968 −0.739838 0.672785i \(-0.765098\pi\)
−0.739838 + 0.672785i \(0.765098\pi\)
\(110\) 29104.6 0.229340
\(111\) −15558.8 −0.119858
\(112\) 58869.3 0.443449
\(113\) 65903.4 0.485525 0.242763 0.970086i \(-0.421946\pi\)
0.242763 + 0.970086i \(0.421946\pi\)
\(114\) −12996.0 −0.0936586
\(115\) −95185.2 −0.671158
\(116\) 117866. 0.813286
\(117\) 93772.9 0.633305
\(118\) −123797. −0.818473
\(119\) 267238. 1.72994
\(120\) −14400.0 −0.0912871
\(121\) −76343.3 −0.474032
\(122\) 29134.9 0.177220
\(123\) −99060.4 −0.590388
\(124\) 98399.6 0.574697
\(125\) 15625.0 0.0894427
\(126\) −74506.4 −0.418088
\(127\) 218617. 1.20275 0.601375 0.798967i \(-0.294620\pi\)
0.601375 + 0.798967i \(0.294620\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 151682. 0.802528
\(130\) −115769. −0.600806
\(131\) −83381.8 −0.424515 −0.212258 0.977214i \(-0.568082\pi\)
−0.212258 + 0.977214i \(0.568082\pi\)
\(132\) −41910.6 −0.209358
\(133\) 83014.9 0.406937
\(134\) 102624. 0.493725
\(135\) 18225.0 0.0860663
\(136\) −74375.5 −0.344812
\(137\) 121233. 0.551849 0.275925 0.961179i \(-0.411016\pi\)
0.275925 + 0.961179i \(0.411016\pi\)
\(138\) 137067. 0.612680
\(139\) −311739. −1.36853 −0.684266 0.729233i \(-0.739877\pi\)
−0.684266 + 0.729233i \(0.739877\pi\)
\(140\) 91983.3 0.396633
\(141\) −60743.2 −0.257306
\(142\) 29287.9 0.121890
\(143\) −336941. −1.37789
\(144\) 20736.0 0.0833333
\(145\) 184165. 0.727425
\(146\) 324427. 1.25961
\(147\) 324664. 1.23920
\(148\) −27660.1 −0.103800
\(149\) −1734.58 −0.00640070 −0.00320035 0.999995i \(-0.501019\pi\)
−0.00320035 + 0.999995i \(0.501019\pi\)
\(150\) −22500.0 −0.0816497
\(151\) −324438. −1.15795 −0.578974 0.815346i \(-0.696547\pi\)
−0.578974 + 0.815346i \(0.696547\pi\)
\(152\) −23104.0 −0.0811107
\(153\) 94131.5 0.325092
\(154\) 267713. 0.909637
\(155\) 153749. 0.514025
\(156\) 166707. 0.548458
\(157\) 367088. 1.18856 0.594279 0.804259i \(-0.297437\pi\)
0.594279 + 0.804259i \(0.297437\pi\)
\(158\) 7147.33 0.0227772
\(159\) −346842. −1.08803
\(160\) −25600.0 −0.0790569
\(161\) −875544. −2.66203
\(162\) −26244.0 −0.0785674
\(163\) −375507. −1.10700 −0.553502 0.832848i \(-0.686709\pi\)
−0.553502 + 0.832848i \(0.686709\pi\)
\(164\) −176107. −0.511291
\(165\) −65485.3 −0.187255
\(166\) −165892. −0.467255
\(167\) 571913. 1.58686 0.793430 0.608661i \(-0.208293\pi\)
0.793430 + 0.608661i \(0.208293\pi\)
\(168\) −132456. −0.362075
\(169\) 968954. 2.60968
\(170\) −116212. −0.308410
\(171\) 29241.0 0.0764719
\(172\) 269657. 0.695010
\(173\) 216729. 0.550557 0.275279 0.961364i \(-0.411230\pi\)
0.275279 + 0.961364i \(0.411230\pi\)
\(174\) −265198. −0.664045
\(175\) 143724. 0.354759
\(176\) −74507.7 −0.181309
\(177\) 278543. 0.668280
\(178\) −208188. −0.492500
\(179\) −665063. −1.55142 −0.775711 0.631088i \(-0.782609\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(180\) 32400.0 0.0745356
\(181\) 471472. 1.06969 0.534847 0.844949i \(-0.320369\pi\)
0.534847 + 0.844949i \(0.320369\pi\)
\(182\) −1.06488e6 −2.38299
\(183\) −65553.5 −0.144700
\(184\) 243674. 0.530597
\(185\) −43218.9 −0.0928420
\(186\) −221399. −0.469238
\(187\) −338230. −0.707306
\(188\) −107988. −0.222834
\(189\) 167639. 0.341367
\(190\) −36100.0 −0.0725476
\(191\) 569955. 1.13047 0.565233 0.824931i \(-0.308786\pi\)
0.565233 + 0.824931i \(0.308786\pi\)
\(192\) 36864.0 0.0721688
\(193\) 980863. 1.89546 0.947731 0.319071i \(-0.103371\pi\)
0.947731 + 0.319071i \(0.103371\pi\)
\(194\) 366091. 0.698369
\(195\) 260480. 0.490556
\(196\) 577180. 1.07318
\(197\) 903143. 1.65802 0.829012 0.559230i \(-0.188903\pi\)
0.829012 + 0.559230i \(0.188903\pi\)
\(198\) 94298.8 0.170940
\(199\) 1.01374e6 1.81465 0.907324 0.420433i \(-0.138122\pi\)
0.907324 + 0.420433i \(0.138122\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −230903. −0.403125
\(202\) 372162. 0.641732
\(203\) 1.69401e6 2.88521
\(204\) 167345. 0.281538
\(205\) −275168. −0.457312
\(206\) 367087. 0.602699
\(207\) −308400. −0.500251
\(208\) 296369. 0.474979
\(209\) −105068. −0.166381
\(210\) −206962. −0.323849
\(211\) 115673. 0.178866 0.0894329 0.995993i \(-0.471495\pi\)
0.0894329 + 0.995993i \(0.471495\pi\)
\(212\) −616608. −0.942257
\(213\) −65897.8 −0.0995227
\(214\) −125424. −0.187218
\(215\) 421339. 0.621636
\(216\) −46656.0 −0.0680414
\(217\) 1.41424e6 2.03879
\(218\) 734164. 1.04629
\(219\) −729961. −1.02846
\(220\) −116418. −0.162168
\(221\) 1.34537e6 1.85294
\(222\) 62235.2 0.0847527
\(223\) 1.14304e6 1.53921 0.769605 0.638520i \(-0.220453\pi\)
0.769605 + 0.638520i \(0.220453\pi\)
\(224\) −235477. −0.313566
\(225\) 50625.0 0.0666667
\(226\) −263614. −0.343318
\(227\) −953897. −1.22867 −0.614337 0.789043i \(-0.710577\pi\)
−0.614337 + 0.789043i \(0.710577\pi\)
\(228\) 51984.0 0.0662266
\(229\) −197852. −0.249317 −0.124658 0.992200i \(-0.539783\pi\)
−0.124658 + 0.992200i \(0.539783\pi\)
\(230\) 380741. 0.474580
\(231\) −602355. −0.742716
\(232\) −471464. −0.575080
\(233\) −1.27481e6 −1.53835 −0.769174 0.639040i \(-0.779332\pi\)
−0.769174 + 0.639040i \(0.779332\pi\)
\(234\) −375092. −0.447814
\(235\) −168731. −0.199308
\(236\) 495187. 0.578748
\(237\) −16081.5 −0.0185975
\(238\) −1.06895e6 −1.22325
\(239\) 1.28302e6 1.45290 0.726452 0.687217i \(-0.241168\pi\)
0.726452 + 0.687217i \(0.241168\pi\)
\(240\) 57600.0 0.0645497
\(241\) 510281. 0.565936 0.282968 0.959129i \(-0.408681\pi\)
0.282968 + 0.959129i \(0.408681\pi\)
\(242\) 305373. 0.335191
\(243\) 59049.0 0.0641500
\(244\) −116540. −0.125314
\(245\) 901844. 0.959878
\(246\) 396242. 0.417467
\(247\) 417926. 0.435870
\(248\) −393598. −0.406372
\(249\) 373256. 0.381512
\(250\) −62500.0 −0.0632456
\(251\) −675369. −0.676639 −0.338320 0.941031i \(-0.609858\pi\)
−0.338320 + 0.941031i \(0.609858\pi\)
\(252\) 298026. 0.295633
\(253\) 1.10813e6 1.08840
\(254\) −874470. −0.850473
\(255\) 261477. 0.251815
\(256\) 65536.0 0.0625000
\(257\) −1.18632e6 −1.12039 −0.560197 0.828360i \(-0.689274\pi\)
−0.560197 + 0.828360i \(0.689274\pi\)
\(258\) −606729. −0.567473
\(259\) −397541. −0.368242
\(260\) 463076. 0.424834
\(261\) 596696. 0.542191
\(262\) 333527. 0.300178
\(263\) 1.35875e6 1.21129 0.605646 0.795734i \(-0.292915\pi\)
0.605646 + 0.795734i \(0.292915\pi\)
\(264\) 167642. 0.148038
\(265\) −963450. −0.842781
\(266\) −332060. −0.287748
\(267\) 468423. 0.402124
\(268\) −410495. −0.349117
\(269\) −1.47868e6 −1.24593 −0.622966 0.782249i \(-0.714073\pi\)
−0.622966 + 0.782249i \(0.714073\pi\)
\(270\) −72900.0 −0.0608581
\(271\) 726992. 0.601321 0.300661 0.953731i \(-0.402793\pi\)
0.300661 + 0.953731i \(0.402793\pi\)
\(272\) 297502. 0.243819
\(273\) 2.39598e6 1.94571
\(274\) −484933. −0.390216
\(275\) −181904. −0.145047
\(276\) −548267. −0.433230
\(277\) −2.45996e6 −1.92632 −0.963159 0.268934i \(-0.913329\pi\)
−0.963159 + 0.268934i \(0.913329\pi\)
\(278\) 1.24696e6 0.967698
\(279\) 498148. 0.383131
\(280\) −367933. −0.280462
\(281\) 1.96509e6 1.48463 0.742313 0.670054i \(-0.233729\pi\)
0.742313 + 0.670054i \(0.233729\pi\)
\(282\) 242973. 0.181943
\(283\) 903195. 0.670371 0.335186 0.942152i \(-0.391201\pi\)
0.335186 + 0.942152i \(0.391201\pi\)
\(284\) −117152. −0.0861892
\(285\) 81225.0 0.0592349
\(286\) 1.34776e6 0.974313
\(287\) −2.53108e6 −1.81385
\(288\) −82944.0 −0.0589256
\(289\) −69339.2 −0.0488353
\(290\) −736662. −0.514367
\(291\) −823705. −0.570216
\(292\) −1.29771e6 −0.890676
\(293\) −2.30809e6 −1.57066 −0.785331 0.619076i \(-0.787507\pi\)
−0.785331 + 0.619076i \(0.787507\pi\)
\(294\) −1.29865e6 −0.876245
\(295\) 773730. 0.517648
\(296\) 110640. 0.0733980
\(297\) −212172. −0.139572
\(298\) 6938.30 0.00452598
\(299\) −4.40780e6 −2.85131
\(300\) 90000.0 0.0577350
\(301\) 3.87562e6 2.46561
\(302\) 1.29775e6 0.818793
\(303\) −837365. −0.523972
\(304\) 92416.0 0.0573539
\(305\) −182093. −0.112084
\(306\) −376526. −0.229875
\(307\) −2.00588e6 −1.21467 −0.607335 0.794446i \(-0.707761\pi\)
−0.607335 + 0.794446i \(0.707761\pi\)
\(308\) −1.07085e6 −0.643211
\(309\) −825945. −0.492102
\(310\) −614997. −0.363470
\(311\) 589437. 0.345570 0.172785 0.984960i \(-0.444723\pi\)
0.172785 + 0.984960i \(0.444723\pi\)
\(312\) −666830. −0.387818
\(313\) 266249. 0.153612 0.0768062 0.997046i \(-0.475528\pi\)
0.0768062 + 0.997046i \(0.475528\pi\)
\(314\) −1.46835e6 −0.840438
\(315\) 465665. 0.264422
\(316\) −28589.3 −0.0161059
\(317\) 585368. 0.327175 0.163588 0.986529i \(-0.447693\pi\)
0.163588 + 0.986529i \(0.447693\pi\)
\(318\) 1.38737e6 0.769350
\(319\) −2.14402e6 −1.17965
\(320\) 102400. 0.0559017
\(321\) 282205. 0.152863
\(322\) 3.50218e6 1.88234
\(323\) 419525. 0.223744
\(324\) 104976. 0.0555556
\(325\) 723557. 0.379983
\(326\) 1.50203e6 0.782769
\(327\) −1.65187e6 −0.854291
\(328\) 704430. 0.361537
\(329\) −1.55204e6 −0.790522
\(330\) 261941. 0.132409
\(331\) 3.05508e6 1.53268 0.766341 0.642434i \(-0.222075\pi\)
0.766341 + 0.642434i \(0.222075\pi\)
\(332\) 663566. 0.330399
\(333\) −140029. −0.0692003
\(334\) −2.28765e6 −1.12208
\(335\) −641398. −0.312259
\(336\) 529824. 0.256025
\(337\) −2.95410e6 −1.41694 −0.708468 0.705743i \(-0.750613\pi\)
−0.708468 + 0.705743i \(0.750613\pi\)
\(338\) −3.87582e6 −1.84532
\(339\) 593131. 0.280318
\(340\) 464847. 0.218079
\(341\) −1.78992e6 −0.833583
\(342\) −116964. −0.0540738
\(343\) 4.43054e6 2.03340
\(344\) −1.07863e6 −0.491446
\(345\) −856666. −0.387493
\(346\) −866918. −0.389303
\(347\) −1.13529e6 −0.506156 −0.253078 0.967446i \(-0.581443\pi\)
−0.253078 + 0.967446i \(0.581443\pi\)
\(348\) 1.06079e6 0.469551
\(349\) 3.82641e6 1.68162 0.840811 0.541328i \(-0.182078\pi\)
0.840811 + 0.541328i \(0.182078\pi\)
\(350\) −574895. −0.250853
\(351\) 843956. 0.365639
\(352\) 298031. 0.128205
\(353\) 108668. 0.0464156 0.0232078 0.999731i \(-0.492612\pi\)
0.0232078 + 0.999731i \(0.492612\pi\)
\(354\) −1.11417e6 −0.472545
\(355\) −183050. −0.0770899
\(356\) 832752. 0.348250
\(357\) 2.40515e6 0.998782
\(358\) 2.66025e6 1.09702
\(359\) −1.93771e6 −0.793512 −0.396756 0.917924i \(-0.629864\pi\)
−0.396756 + 0.917924i \(0.629864\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) −1.88589e6 −0.756387
\(363\) −687090. −0.273683
\(364\) 4.25953e6 1.68503
\(365\) −2.02767e6 −0.796645
\(366\) 262214. 0.102318
\(367\) −2.43925e6 −0.945346 −0.472673 0.881238i \(-0.656711\pi\)
−0.472673 + 0.881238i \(0.656711\pi\)
\(368\) −974696. −0.375189
\(369\) −891544. −0.340861
\(370\) 172876. 0.0656492
\(371\) −8.86213e6 −3.34275
\(372\) 885596. 0.331802
\(373\) −1.17165e6 −0.436038 −0.218019 0.975945i \(-0.569959\pi\)
−0.218019 + 0.975945i \(0.569959\pi\)
\(374\) 1.35292e6 0.500141
\(375\) 140625. 0.0516398
\(376\) 431952. 0.157567
\(377\) 8.52826e6 3.09035
\(378\) −670558. −0.241383
\(379\) −61153.7 −0.0218688 −0.0109344 0.999940i \(-0.503481\pi\)
−0.0109344 + 0.999940i \(0.503481\pi\)
\(380\) 144400. 0.0512989
\(381\) 1.96756e6 0.694408
\(382\) −2.27982e6 −0.799360
\(383\) 1.24915e6 0.435130 0.217565 0.976046i \(-0.430189\pi\)
0.217565 + 0.976046i \(0.430189\pi\)
\(384\) −147456. −0.0510310
\(385\) −1.67321e6 −0.575305
\(386\) −3.92345e6 −1.34029
\(387\) 1.36514e6 0.463340
\(388\) −1.46437e6 −0.493822
\(389\) −3.81154e6 −1.27710 −0.638552 0.769578i \(-0.720466\pi\)
−0.638552 + 0.769578i \(0.720466\pi\)
\(390\) −1.04192e6 −0.346875
\(391\) −4.42465e6 −1.46365
\(392\) −2.30872e6 −0.758850
\(393\) −750437. −0.245094
\(394\) −3.61257e6 −1.17240
\(395\) −44670.8 −0.0144056
\(396\) −377195. −0.120873
\(397\) 3.59979e6 1.14631 0.573153 0.819449i \(-0.305720\pi\)
0.573153 + 0.819449i \(0.305720\pi\)
\(398\) −4.05494e6 −1.28315
\(399\) 747134. 0.234945
\(400\) 160000. 0.0500000
\(401\) −5.52249e6 −1.71504 −0.857520 0.514451i \(-0.827996\pi\)
−0.857520 + 0.514451i \(0.827996\pi\)
\(402\) 923613. 0.285052
\(403\) 7.11977e6 2.18375
\(404\) −1.48865e6 −0.453773
\(405\) 164025. 0.0496904
\(406\) −6.77606e6 −2.04015
\(407\) 503147. 0.150560
\(408\) −669380. −0.199078
\(409\) −6.58383e6 −1.94612 −0.973061 0.230548i \(-0.925948\pi\)
−0.973061 + 0.230548i \(0.925948\pi\)
\(410\) 1.10067e6 0.323369
\(411\) 1.09110e6 0.318610
\(412\) −1.46835e6 −0.426173
\(413\) 7.11702e6 2.05316
\(414\) 1.23360e6 0.353731
\(415\) 1.03682e6 0.295518
\(416\) −1.18547e6 −0.335861
\(417\) −2.80565e6 −0.790122
\(418\) 420270. 0.117649
\(419\) 3.61585e6 1.00618 0.503089 0.864235i \(-0.332197\pi\)
0.503089 + 0.864235i \(0.332197\pi\)
\(420\) 827849. 0.228996
\(421\) −416769. −0.114602 −0.0573008 0.998357i \(-0.518249\pi\)
−0.0573008 + 0.998357i \(0.518249\pi\)
\(422\) −462694. −0.126477
\(423\) −546689. −0.148556
\(424\) 2.46643e6 0.666277
\(425\) 726324. 0.195055
\(426\) 263591. 0.0703732
\(427\) −1.67495e6 −0.444562
\(428\) 501698. 0.132383
\(429\) −3.03247e6 −0.795524
\(430\) −1.68536e6 −0.439563
\(431\) −3.47346e6 −0.900677 −0.450338 0.892858i \(-0.648697\pi\)
−0.450338 + 0.892858i \(0.648697\pi\)
\(432\) 186624. 0.0481125
\(433\) 1.69137e6 0.433530 0.216765 0.976224i \(-0.430450\pi\)
0.216765 + 0.976224i \(0.430450\pi\)
\(434\) −5.65695e6 −1.44164
\(435\) 1.65749e6 0.419979
\(436\) −2.93665e6 −0.739838
\(437\) −1.37447e6 −0.344297
\(438\) 2.91984e6 0.727234
\(439\) 275786. 0.0682985 0.0341493 0.999417i \(-0.489128\pi\)
0.0341493 + 0.999417i \(0.489128\pi\)
\(440\) 465673. 0.114670
\(441\) 2.92197e6 0.715451
\(442\) −5.38149e6 −1.31023
\(443\) 5.60621e6 1.35725 0.678625 0.734485i \(-0.262576\pi\)
0.678625 + 0.734485i \(0.262576\pi\)
\(444\) −248941. −0.0599292
\(445\) 1.30118e6 0.311484
\(446\) −4.57215e6 −1.08839
\(447\) −15611.2 −0.00369545
\(448\) 941909. 0.221725
\(449\) −3.45046e6 −0.807719 −0.403860 0.914821i \(-0.632332\pi\)
−0.403860 + 0.914821i \(0.632332\pi\)
\(450\) −202500. −0.0471405
\(451\) 3.20346e6 0.741614
\(452\) 1.05445e6 0.242763
\(453\) −2.91994e6 −0.668542
\(454\) 3.81559e6 0.868804
\(455\) 6.65551e6 1.50714
\(456\) −207936. −0.0468293
\(457\) −5.99883e6 −1.34362 −0.671809 0.740724i \(-0.734482\pi\)
−0.671809 + 0.740724i \(0.734482\pi\)
\(458\) 791407. 0.176294
\(459\) 847184. 0.187692
\(460\) −1.52296e6 −0.335579
\(461\) −282491. −0.0619088 −0.0309544 0.999521i \(-0.509855\pi\)
−0.0309544 + 0.999521i \(0.509855\pi\)
\(462\) 2.40942e6 0.525179
\(463\) −4.64797e6 −1.00765 −0.503826 0.863805i \(-0.668075\pi\)
−0.503826 + 0.863805i \(0.668075\pi\)
\(464\) 1.88585e6 0.406643
\(465\) 1.38374e6 0.296772
\(466\) 5.09923e6 1.08778
\(467\) 6.16529e6 1.30816 0.654080 0.756425i \(-0.273056\pi\)
0.654080 + 0.756425i \(0.273056\pi\)
\(468\) 1.50037e6 0.316652
\(469\) −5.89979e6 −1.23852
\(470\) 674924. 0.140932
\(471\) 3.30379e6 0.686215
\(472\) −1.98075e6 −0.409236
\(473\) −4.90516e6 −1.00809
\(474\) 64326.0 0.0131504
\(475\) 225625. 0.0458831
\(476\) 4.27582e6 0.864971
\(477\) −3.12158e6 −0.628172
\(478\) −5.13206e6 −1.02736
\(479\) 2.53771e6 0.505364 0.252682 0.967549i \(-0.418687\pi\)
0.252682 + 0.967549i \(0.418687\pi\)
\(480\) −230400. −0.0456435
\(481\) −2.00136e6 −0.394424
\(482\) −2.04113e6 −0.400177
\(483\) −7.87990e6 −1.53693
\(484\) −1.22149e6 −0.237016
\(485\) −2.28807e6 −0.441687
\(486\) −236196. −0.0453609
\(487\) −2.28659e6 −0.436885 −0.218442 0.975850i \(-0.570098\pi\)
−0.218442 + 0.975850i \(0.570098\pi\)
\(488\) 466158. 0.0886102
\(489\) −3.37956e6 −0.639129
\(490\) −3.60737e6 −0.678736
\(491\) 3.43905e6 0.643776 0.321888 0.946778i \(-0.395683\pi\)
0.321888 + 0.946778i \(0.395683\pi\)
\(492\) −1.58497e6 −0.295194
\(493\) 8.56088e6 1.58636
\(494\) −1.67170e6 −0.308207
\(495\) −589368. −0.108112
\(496\) 1.57439e6 0.287349
\(497\) −1.68375e6 −0.305764
\(498\) −1.49302e6 −0.269770
\(499\) 5.40289e6 0.971347 0.485674 0.874140i \(-0.338574\pi\)
0.485674 + 0.874140i \(0.338574\pi\)
\(500\) 250000. 0.0447214
\(501\) 5.14722e6 0.916174
\(502\) 2.70148e6 0.478456
\(503\) 399731. 0.0704446 0.0352223 0.999380i \(-0.488786\pi\)
0.0352223 + 0.999380i \(0.488786\pi\)
\(504\) −1.19210e6 −0.209044
\(505\) −2.32601e6 −0.405867
\(506\) −4.43252e6 −0.769616
\(507\) 8.72059e6 1.50670
\(508\) 3.49788e6 0.601375
\(509\) −102806. −0.0175883 −0.00879413 0.999961i \(-0.502799\pi\)
−0.00879413 + 0.999961i \(0.502799\pi\)
\(510\) −1.04591e6 −0.178060
\(511\) −1.86512e7 −3.15976
\(512\) −262144. −0.0441942
\(513\) 263169. 0.0441511
\(514\) 4.74529e6 0.792237
\(515\) −2.29429e6 −0.381180
\(516\) 2.42692e6 0.401264
\(517\) 1.96434e6 0.323214
\(518\) 1.59017e6 0.260386
\(519\) 1.95056e6 0.317864
\(520\) −1.85230e6 −0.300403
\(521\) 2.74729e6 0.443415 0.221708 0.975113i \(-0.428837\pi\)
0.221708 + 0.975113i \(0.428837\pi\)
\(522\) −2.38678e6 −0.383387
\(523\) −5.20431e6 −0.831972 −0.415986 0.909371i \(-0.636563\pi\)
−0.415986 + 0.909371i \(0.636563\pi\)
\(524\) −1.33411e6 −0.212258
\(525\) 1.29351e6 0.204820
\(526\) −5.43499e6 −0.856513
\(527\) 7.14699e6 1.12098
\(528\) −670570. −0.104679
\(529\) 8.06000e6 1.25226
\(530\) 3.85380e6 0.595936
\(531\) 2.50688e6 0.385832
\(532\) 1.32824e6 0.203468
\(533\) −1.27424e7 −1.94282
\(534\) −1.87369e6 −0.284345
\(535\) 783903. 0.118407
\(536\) 1.64198e6 0.246863
\(537\) −5.98556e6 −0.895714
\(538\) 5.91473e6 0.881007
\(539\) −1.04991e7 −1.55661
\(540\) 291600. 0.0430331
\(541\) −3.01712e6 −0.443199 −0.221600 0.975138i \(-0.571128\pi\)
−0.221600 + 0.975138i \(0.571128\pi\)
\(542\) −2.90797e6 −0.425198
\(543\) 4.24325e6 0.617588
\(544\) −1.19001e6 −0.172406
\(545\) −4.58852e6 −0.661731
\(546\) −9.58393e6 −1.37582
\(547\) −4.91651e6 −0.702568 −0.351284 0.936269i \(-0.614255\pi\)
−0.351284 + 0.936269i \(0.614255\pi\)
\(548\) 1.93973e6 0.275925
\(549\) −589982. −0.0835425
\(550\) 727615. 0.102564
\(551\) 2.65935e6 0.373161
\(552\) 2.19307e6 0.306340
\(553\) −410897. −0.0571373
\(554\) 9.83982e6 1.36211
\(555\) −388970. −0.0536023
\(556\) −4.98783e6 −0.684266
\(557\) −8.90547e6 −1.21624 −0.608119 0.793846i \(-0.708076\pi\)
−0.608119 + 0.793846i \(0.708076\pi\)
\(558\) −1.99259e6 −0.270915
\(559\) 1.95112e7 2.64092
\(560\) 1.47173e6 0.198316
\(561\) −3.04407e6 −0.408363
\(562\) −7.86037e6 −1.04979
\(563\) −324608. −0.0431607 −0.0215804 0.999767i \(-0.506870\pi\)
−0.0215804 + 0.999767i \(0.506870\pi\)
\(564\) −971891. −0.128653
\(565\) 1.64759e6 0.217133
\(566\) −3.61278e6 −0.474024
\(567\) 1.50876e6 0.197088
\(568\) 468607. 0.0609449
\(569\) −2.63526e6 −0.341227 −0.170613 0.985338i \(-0.554575\pi\)
−0.170613 + 0.985338i \(0.554575\pi\)
\(570\) −324900. −0.0418854
\(571\) −1.71414e6 −0.220016 −0.110008 0.993931i \(-0.535088\pi\)
−0.110008 + 0.993931i \(0.535088\pi\)
\(572\) −5.39106e6 −0.688944
\(573\) 5.12960e6 0.652675
\(574\) 1.01243e7 1.28259
\(575\) −2.37963e6 −0.300151
\(576\) 331776. 0.0416667
\(577\) 2.34313e6 0.292993 0.146496 0.989211i \(-0.453200\pi\)
0.146496 + 0.989211i \(0.453200\pi\)
\(578\) 277357. 0.0345318
\(579\) 8.82776e6 1.09435
\(580\) 2.94665e6 0.363713
\(581\) 9.53703e6 1.17212
\(582\) 3.29482e6 0.403204
\(583\) 1.12163e7 1.36672
\(584\) 5.19083e6 0.629803
\(585\) 2.34432e6 0.283223
\(586\) 9.23234e6 1.11063
\(587\) −3.07807e6 −0.368709 −0.184354 0.982860i \(-0.559019\pi\)
−0.184354 + 0.982860i \(0.559019\pi\)
\(588\) 5.19462e6 0.619599
\(589\) 2.22014e6 0.263689
\(590\) −3.09492e6 −0.366032
\(591\) 8.12829e6 0.957261
\(592\) −442561. −0.0519002
\(593\) 9.59641e6 1.12066 0.560328 0.828271i \(-0.310675\pi\)
0.560328 + 0.828271i \(0.310675\pi\)
\(594\) 848690. 0.0986922
\(595\) 6.68096e6 0.773654
\(596\) −27753.2 −0.00320035
\(597\) 9.12363e6 1.04769
\(598\) 1.76312e7 2.01618
\(599\) −4.33148e6 −0.493253 −0.246626 0.969111i \(-0.579322\pi\)
−0.246626 + 0.969111i \(0.579322\pi\)
\(600\) −360000. −0.0408248
\(601\) 9.61995e6 1.08639 0.543196 0.839606i \(-0.317214\pi\)
0.543196 + 0.839606i \(0.317214\pi\)
\(602\) −1.55025e7 −1.74345
\(603\) −2.07813e6 −0.232744
\(604\) −5.19100e6 −0.578974
\(605\) −1.90858e6 −0.211994
\(606\) 3.34946e6 0.370504
\(607\) 721982. 0.0795343 0.0397672 0.999209i \(-0.487338\pi\)
0.0397672 + 0.999209i \(0.487338\pi\)
\(608\) −369664. −0.0405554
\(609\) 1.52461e7 1.66577
\(610\) 728372. 0.0792554
\(611\) −7.81354e6 −0.846729
\(612\) 1.50610e6 0.162546
\(613\) 182994. 0.0196691 0.00983455 0.999952i \(-0.496870\pi\)
0.00983455 + 0.999952i \(0.496870\pi\)
\(614\) 8.02350e6 0.858901
\(615\) −2.47651e6 −0.264029
\(616\) 4.28341e6 0.454819
\(617\) −9.48979e6 −1.00356 −0.501781 0.864995i \(-0.667322\pi\)
−0.501781 + 0.864995i \(0.667322\pi\)
\(618\) 3.30378e6 0.347968
\(619\) −2.44121e6 −0.256082 −0.128041 0.991769i \(-0.540869\pi\)
−0.128041 + 0.991769i \(0.540869\pi\)
\(620\) 2.45999e6 0.257012
\(621\) −2.77560e6 −0.288820
\(622\) −2.35775e6 −0.244355
\(623\) 1.19686e7 1.23545
\(624\) 2.66732e6 0.274229
\(625\) 390625. 0.0400000
\(626\) −1.06499e6 −0.108620
\(627\) −945608. −0.0960599
\(628\) 5.87340e6 0.594279
\(629\) −2.00902e6 −0.202468
\(630\) −1.86266e6 −0.186975
\(631\) −9.44666e6 −0.944506 −0.472253 0.881463i \(-0.656559\pi\)
−0.472253 + 0.881463i \(0.656559\pi\)
\(632\) 114357. 0.0113886
\(633\) 1.04106e6 0.103268
\(634\) −2.34147e6 −0.231348
\(635\) 5.46544e6 0.537886
\(636\) −5.54947e6 −0.544013
\(637\) 4.17622e7 4.07789
\(638\) 8.57609e6 0.834138
\(639\) −593080. −0.0574594
\(640\) −409600. −0.0395285
\(641\) 3.66728e6 0.352532 0.176266 0.984343i \(-0.443598\pi\)
0.176266 + 0.984343i \(0.443598\pi\)
\(642\) −1.12882e6 −0.108090
\(643\) 3.06676e6 0.292518 0.146259 0.989246i \(-0.453277\pi\)
0.146259 + 0.989246i \(0.453277\pi\)
\(644\) −1.40087e7 −1.33102
\(645\) 3.79206e6 0.358902
\(646\) −1.67810e6 −0.158211
\(647\) 5.09003e6 0.478035 0.239018 0.971015i \(-0.423175\pi\)
0.239018 + 0.971015i \(0.423175\pi\)
\(648\) −419904. −0.0392837
\(649\) −9.00763e6 −0.839458
\(650\) −2.89423e6 −0.268688
\(651\) 1.27281e7 1.17710
\(652\) −6.00811e6 −0.553502
\(653\) −5.68522e6 −0.521752 −0.260876 0.965372i \(-0.584011\pi\)
−0.260876 + 0.965372i \(0.584011\pi\)
\(654\) 6.60747e6 0.604075
\(655\) −2.08455e6 −0.189849
\(656\) −2.81772e6 −0.255645
\(657\) −6.56965e6 −0.593784
\(658\) 6.20817e6 0.558984
\(659\) −1.92464e6 −0.172638 −0.0863188 0.996268i \(-0.527510\pi\)
−0.0863188 + 0.996268i \(0.527510\pi\)
\(660\) −1.04776e6 −0.0936276
\(661\) −1.97116e7 −1.75476 −0.877380 0.479796i \(-0.840711\pi\)
−0.877380 + 0.479796i \(0.840711\pi\)
\(662\) −1.22203e7 −1.08377
\(663\) 1.21084e7 1.06980
\(664\) −2.65427e6 −0.233628
\(665\) 2.07537e6 0.181988
\(666\) 560117. 0.0489320
\(667\) −2.80477e7 −2.44108
\(668\) 9.15061e6 0.793430
\(669\) 1.02873e7 0.888663
\(670\) 2.56559e6 0.220801
\(671\) 2.11990e6 0.181764
\(672\) −2.11929e6 −0.181037
\(673\) −8.94473e6 −0.761254 −0.380627 0.924729i \(-0.624292\pi\)
−0.380627 + 0.924729i \(0.624292\pi\)
\(674\) 1.18164e7 1.00192
\(675\) 455625. 0.0384900
\(676\) 1.55033e7 1.30484
\(677\) 1.15197e7 0.965982 0.482991 0.875625i \(-0.339550\pi\)
0.482991 + 0.875625i \(0.339550\pi\)
\(678\) −2.37252e6 −0.198215
\(679\) −2.10464e7 −1.75188
\(680\) −1.85939e6 −0.154205
\(681\) −8.58508e6 −0.709376
\(682\) 7.15970e6 0.589432
\(683\) 9.96639e6 0.817497 0.408748 0.912647i \(-0.365965\pi\)
0.408748 + 0.912647i \(0.365965\pi\)
\(684\) 467856. 0.0382360
\(685\) 3.03083e6 0.246794
\(686\) −1.77222e7 −1.43783
\(687\) −1.78067e6 −0.143943
\(688\) 4.31452e6 0.347505
\(689\) −4.46151e7 −3.58042
\(690\) 3.42667e6 0.273999
\(691\) 4.75473e6 0.378818 0.189409 0.981898i \(-0.439343\pi\)
0.189409 + 0.981898i \(0.439343\pi\)
\(692\) 3.46767e6 0.275279
\(693\) −5.42120e6 −0.428807
\(694\) 4.54117e6 0.357906
\(695\) −7.79348e6 −0.612026
\(696\) −4.24317e6 −0.332023
\(697\) −1.27911e7 −0.997300
\(698\) −1.53057e7 −1.18909
\(699\) −1.14733e7 −0.888165
\(700\) 2.29958e6 0.177380
\(701\) 658865. 0.0506409 0.0253204 0.999679i \(-0.491939\pi\)
0.0253204 + 0.999679i \(0.491939\pi\)
\(702\) −3.37583e6 −0.258546
\(703\) −624081. −0.0476269
\(704\) −1.19212e6 −0.0906546
\(705\) −1.51858e6 −0.115071
\(706\) −434671. −0.0328208
\(707\) −2.13954e7 −1.60980
\(708\) 4.45668e6 0.334140
\(709\) 7.34317e6 0.548615 0.274308 0.961642i \(-0.411551\pi\)
0.274308 + 0.961642i \(0.411551\pi\)
\(710\) 732198. 0.0545108
\(711\) −144733. −0.0107373
\(712\) −3.33101e6 −0.246250
\(713\) −2.34154e7 −1.72496
\(714\) −9.62058e6 −0.706246
\(715\) −8.42352e6 −0.616210
\(716\) −1.06410e7 −0.775711
\(717\) 1.15471e7 0.838835
\(718\) 7.75085e6 0.561097
\(719\) 2.73781e6 0.197507 0.0987533 0.995112i \(-0.468515\pi\)
0.0987533 + 0.995112i \(0.468515\pi\)
\(720\) 518400. 0.0372678
\(721\) −2.11036e7 −1.51189
\(722\) −521284. −0.0372161
\(723\) 4.59253e6 0.326743
\(724\) 7.54355e6 0.534847
\(725\) 4.60414e6 0.325314
\(726\) 2.74836e6 0.193523
\(727\) −223032. −0.0156506 −0.00782532 0.999969i \(-0.502491\pi\)
−0.00782532 + 0.999969i \(0.502491\pi\)
\(728\) −1.70381e7 −1.19150
\(729\) 531441. 0.0370370
\(730\) 8.11067e6 0.563313
\(731\) 1.95858e7 1.35565
\(732\) −1.04886e6 −0.0723499
\(733\) 2.39223e7 1.64453 0.822266 0.569103i \(-0.192710\pi\)
0.822266 + 0.569103i \(0.192710\pi\)
\(734\) 9.75699e6 0.668460
\(735\) 8.11659e6 0.554186
\(736\) 3.89878e6 0.265298
\(737\) 7.46705e6 0.506384
\(738\) 3.56618e6 0.241025
\(739\) −3.91073e6 −0.263419 −0.131709 0.991288i \(-0.542047\pi\)
−0.131709 + 0.991288i \(0.542047\pi\)
\(740\) −691502. −0.0464210
\(741\) 3.76134e6 0.251650
\(742\) 3.54485e7 2.36368
\(743\) −1.88216e7 −1.25079 −0.625394 0.780309i \(-0.715062\pi\)
−0.625394 + 0.780309i \(0.715062\pi\)
\(744\) −3.54239e6 −0.234619
\(745\) −43364.4 −0.00286248
\(746\) 4.68658e6 0.308325
\(747\) 3.35930e6 0.220266
\(748\) −5.41167e6 −0.353653
\(749\) 7.21059e6 0.469642
\(750\) −562500. −0.0365148
\(751\) −1.84421e6 −0.119320 −0.0596598 0.998219i \(-0.519002\pi\)
−0.0596598 + 0.998219i \(0.519002\pi\)
\(752\) −1.72781e6 −0.111417
\(753\) −6.07832e6 −0.390658
\(754\) −3.41131e7 −2.18521
\(755\) −8.11094e6 −0.517850
\(756\) 2.68223e6 0.170684
\(757\) 5.64442e6 0.357997 0.178999 0.983849i \(-0.442714\pi\)
0.178999 + 0.983849i \(0.442714\pi\)
\(758\) 244615. 0.0154636
\(759\) 9.97317e6 0.628389
\(760\) −577600. −0.0362738
\(761\) −3.50019e6 −0.219094 −0.109547 0.993982i \(-0.534940\pi\)
−0.109547 + 0.993982i \(0.534940\pi\)
\(762\) −7.87023e6 −0.491021
\(763\) −4.22067e7 −2.62464
\(764\) 9.11929e6 0.565233
\(765\) 2.35329e6 0.145386
\(766\) −4.99662e6 −0.307683
\(767\) 3.58296e7 2.19914
\(768\) 589824. 0.0360844
\(769\) 9.75513e6 0.594864 0.297432 0.954743i \(-0.403870\pi\)
0.297432 + 0.954743i \(0.403870\pi\)
\(770\) 6.69284e6 0.406802
\(771\) −1.06769e7 −0.646859
\(772\) 1.56938e7 0.947731
\(773\) 2.85516e7 1.71863 0.859315 0.511447i \(-0.170890\pi\)
0.859315 + 0.511447i \(0.170890\pi\)
\(774\) −5.46056e6 −0.327631
\(775\) 3.84373e6 0.229879
\(776\) 5.85746e6 0.349185
\(777\) −3.57787e6 −0.212604
\(778\) 1.52462e7 0.903049
\(779\) −3.97342e6 −0.234596
\(780\) 4.16769e6 0.245278
\(781\) 2.13103e6 0.125015
\(782\) 1.76986e7 1.03496
\(783\) 5.37027e6 0.313034
\(784\) 9.23488e6 0.536588
\(785\) 9.17719e6 0.531540
\(786\) 3.00175e6 0.173308
\(787\) −5.65502e6 −0.325460 −0.162730 0.986671i \(-0.552030\pi\)
−0.162730 + 0.986671i \(0.552030\pi\)
\(788\) 1.44503e7 0.829012
\(789\) 1.22287e7 0.699340
\(790\) 178683. 0.0101863
\(791\) 1.51550e7 0.861223
\(792\) 1.50878e6 0.0854699
\(793\) −8.43230e6 −0.476171
\(794\) −1.43991e7 −0.810560
\(795\) −8.67105e6 −0.486580
\(796\) 1.62198e7 0.907324
\(797\) 1.33543e7 0.744688 0.372344 0.928095i \(-0.378554\pi\)
0.372344 + 0.928095i \(0.378554\pi\)
\(798\) −2.98854e6 −0.166131
\(799\) −7.84342e6 −0.434649
\(800\) −640000. −0.0353553
\(801\) 4.21581e6 0.232167
\(802\) 2.20900e7 1.21272
\(803\) 2.36058e7 1.29190
\(804\) −3.69445e6 −0.201563
\(805\) −2.18886e7 −1.19050
\(806\) −2.84791e7 −1.54415
\(807\) −1.33081e7 −0.719339
\(808\) 5.95460e6 0.320866
\(809\) −2.75572e7 −1.48035 −0.740174 0.672416i \(-0.765257\pi\)
−0.740174 + 0.672416i \(0.765257\pi\)
\(810\) −656100. −0.0351364
\(811\) −1.53702e7 −0.820595 −0.410297 0.911952i \(-0.634575\pi\)
−0.410297 + 0.911952i \(0.634575\pi\)
\(812\) 2.71042e7 1.44260
\(813\) 6.54293e6 0.347173
\(814\) −2.01259e6 −0.106462
\(815\) −9.38767e6 −0.495067
\(816\) 2.67752e6 0.140769
\(817\) 6.08414e6 0.318892
\(818\) 2.63353e7 1.37612
\(819\) 2.15638e7 1.12335
\(820\) −4.40269e6 −0.228656
\(821\) 12638.7 0.000654401 0 0.000327201 1.00000i \(-0.499896\pi\)
0.000327201 1.00000i \(0.499896\pi\)
\(822\) −4.36440e6 −0.225291
\(823\) 4.24914e6 0.218676 0.109338 0.994005i \(-0.465127\pi\)
0.109338 + 0.994005i \(0.465127\pi\)
\(824\) 5.87339e6 0.301349
\(825\) −1.63713e6 −0.0837431
\(826\) −2.84681e7 −1.45180
\(827\) −3.83907e7 −1.95192 −0.975961 0.217945i \(-0.930065\pi\)
−0.975961 + 0.217945i \(0.930065\pi\)
\(828\) −4.93440e6 −0.250126
\(829\) −3.82855e7 −1.93485 −0.967427 0.253152i \(-0.918533\pi\)
−0.967427 + 0.253152i \(0.918533\pi\)
\(830\) −4.14729e6 −0.208963
\(831\) −2.21396e7 −1.11216
\(832\) 4.74190e6 0.237489
\(833\) 4.19219e7 2.09329
\(834\) 1.12226e7 0.558700
\(835\) 1.42978e7 0.709666
\(836\) −1.68108e6 −0.0831903
\(837\) 4.48333e6 0.221201
\(838\) −1.44634e7 −0.711475
\(839\) 2.01150e7 0.986543 0.493272 0.869875i \(-0.335801\pi\)
0.493272 + 0.869875i \(0.335801\pi\)
\(840\) −3.31140e6 −0.161925
\(841\) 3.37559e7 1.64574
\(842\) 1.66708e6 0.0810355
\(843\) 1.76858e7 0.857149
\(844\) 1.85077e6 0.0894329
\(845\) 2.42239e7 1.16708
\(846\) 2.18676e6 0.105045
\(847\) −1.75558e7 −0.840836
\(848\) −9.86573e6 −0.471129
\(849\) 8.12876e6 0.387039
\(850\) −2.90529e6 −0.137925
\(851\) 6.58208e6 0.311558
\(852\) −1.05437e6 −0.0497613
\(853\) 2.66932e7 1.25611 0.628054 0.778169i \(-0.283852\pi\)
0.628054 + 0.778169i \(0.283852\pi\)
\(854\) 6.69981e6 0.314353
\(855\) 731025. 0.0341993
\(856\) −2.00679e6 −0.0936090
\(857\) −4.71902e6 −0.219482 −0.109741 0.993960i \(-0.535002\pi\)
−0.109741 + 0.993960i \(0.535002\pi\)
\(858\) 1.21299e7 0.562520
\(859\) −7.71598e6 −0.356786 −0.178393 0.983959i \(-0.557090\pi\)
−0.178393 + 0.983959i \(0.557090\pi\)
\(860\) 6.74143e6 0.310818
\(861\) −2.27797e7 −1.04723
\(862\) 1.38938e7 0.636875
\(863\) −1.13038e6 −0.0516651 −0.0258325 0.999666i \(-0.508224\pi\)
−0.0258325 + 0.999666i \(0.508224\pi\)
\(864\) −746496. −0.0340207
\(865\) 5.41824e6 0.246217
\(866\) −6.76548e6 −0.306552
\(867\) −624052. −0.0281951
\(868\) 2.26278e7 1.01940
\(869\) 520050. 0.0233612
\(870\) −6.62996e6 −0.296970
\(871\) −2.97016e7 −1.32658
\(872\) 1.17466e7 0.523144
\(873\) −7.41335e6 −0.329214
\(874\) 5.49789e6 0.243455
\(875\) 3.59310e6 0.158653
\(876\) −1.16794e7 −0.514232
\(877\) 2.04712e7 0.898760 0.449380 0.893341i \(-0.351645\pi\)
0.449380 + 0.893341i \(0.351645\pi\)
\(878\) −1.10314e6 −0.0482943
\(879\) −2.07728e7 −0.906823
\(880\) −1.86269e6 −0.0810839
\(881\) 1.62109e6 0.0703668 0.0351834 0.999381i \(-0.488798\pi\)
0.0351834 + 0.999381i \(0.488798\pi\)
\(882\) −1.16879e7 −0.505900
\(883\) 1.30184e7 0.561895 0.280947 0.959723i \(-0.409351\pi\)
0.280947 + 0.959723i \(0.409351\pi\)
\(884\) 2.15260e7 0.926471
\(885\) 6.96357e6 0.298864
\(886\) −2.24248e7 −0.959721
\(887\) −1.11573e7 −0.476158 −0.238079 0.971246i \(-0.576518\pi\)
−0.238079 + 0.971246i \(0.576518\pi\)
\(888\) 995763. 0.0423764
\(889\) 5.02729e7 2.13343
\(890\) −5.20470e6 −0.220253
\(891\) −1.90955e6 −0.0805818
\(892\) 1.82886e7 0.769605
\(893\) −2.43648e6 −0.102243
\(894\) 62444.7 0.00261307
\(895\) −1.66266e7 −0.693817
\(896\) −3.76763e6 −0.156783
\(897\) −3.96702e7 −1.64620
\(898\) 1.38018e7 0.571144
\(899\) 4.53045e7 1.86957
\(900\) 810000. 0.0333333
\(901\) −4.47857e7 −1.83792
\(902\) −1.28138e7 −0.524400
\(903\) 3.48806e7 1.42352
\(904\) −4.21782e6 −0.171659
\(905\) 1.17868e7 0.478381
\(906\) 1.16798e7 0.472730
\(907\) 2.58907e7 1.04502 0.522510 0.852633i \(-0.324996\pi\)
0.522510 + 0.852633i \(0.324996\pi\)
\(908\) −1.52624e7 −0.614337
\(909\) −7.53628e6 −0.302515
\(910\) −2.66220e7 −1.06571
\(911\) −3.72906e7 −1.48869 −0.744344 0.667796i \(-0.767238\pi\)
−0.744344 + 0.667796i \(0.767238\pi\)
\(912\) 831744. 0.0331133
\(913\) −1.20705e7 −0.479235
\(914\) 2.39953e7 0.950081
\(915\) −1.63884e6 −0.0647118
\(916\) −3.16563e6 −0.124658
\(917\) −1.91743e7 −0.753003
\(918\) −3.38874e6 −0.132718
\(919\) 1.12907e7 0.440993 0.220496 0.975388i \(-0.429232\pi\)
0.220496 + 0.975388i \(0.429232\pi\)
\(920\) 6.09185e6 0.237290
\(921\) −1.80529e7 −0.701290
\(922\) 1.12996e6 0.0437761
\(923\) −8.47659e6 −0.327504
\(924\) −9.63768e6 −0.371358
\(925\) −1.08047e6 −0.0415202
\(926\) 1.85919e7 0.712518
\(927\) −7.43350e6 −0.284115
\(928\) −7.54342e6 −0.287540
\(929\) −3.11211e7 −1.18308 −0.591542 0.806274i \(-0.701481\pi\)
−0.591542 + 0.806274i \(0.701481\pi\)
\(930\) −5.53498e6 −0.209850
\(931\) 1.30226e7 0.492407
\(932\) −2.03969e7 −0.769174
\(933\) 5.30493e6 0.199515
\(934\) −2.46611e7 −0.925009
\(935\) −8.45574e6 −0.316317
\(936\) −6.00147e6 −0.223907
\(937\) 1.89467e7 0.704992 0.352496 0.935813i \(-0.385333\pi\)
0.352496 + 0.935813i \(0.385333\pi\)
\(938\) 2.35991e7 0.875768
\(939\) 2.39624e6 0.0886882
\(940\) −2.69970e6 −0.0996542
\(941\) −4.92849e7 −1.81443 −0.907214 0.420670i \(-0.861795\pi\)
−0.907214 + 0.420670i \(0.861795\pi\)
\(942\) −1.32152e7 −0.485227
\(943\) 4.19070e7 1.53464
\(944\) 7.92299e6 0.289374
\(945\) 4.19099e6 0.152664
\(946\) 1.96207e7 0.712829
\(947\) −5.25001e6 −0.190233 −0.0951164 0.995466i \(-0.530322\pi\)
−0.0951164 + 0.995466i \(0.530322\pi\)
\(948\) −257304. −0.00929877
\(949\) −9.38965e7 −3.38442
\(950\) −902500. −0.0324443
\(951\) 5.26831e6 0.188895
\(952\) −1.71033e7 −0.611627
\(953\) −2.16938e6 −0.0773755 −0.0386877 0.999251i \(-0.512318\pi\)
−0.0386877 + 0.999251i \(0.512318\pi\)
\(954\) 1.24863e7 0.444184
\(955\) 1.42489e7 0.505560
\(956\) 2.05282e7 0.726452
\(957\) −1.92962e7 −0.681071
\(958\) −1.01509e7 −0.357346
\(959\) 2.78786e7 0.978868
\(960\) 921600. 0.0322749
\(961\) 9.19303e6 0.321107
\(962\) 8.00546e6 0.278900
\(963\) 2.53985e6 0.0882555
\(964\) 8.16450e6 0.282968
\(965\) 2.45216e7 0.847676
\(966\) 3.15196e7 1.08677
\(967\) −3.26345e7 −1.12230 −0.561152 0.827713i \(-0.689642\pi\)
−0.561152 + 0.827713i \(0.689642\pi\)
\(968\) 4.88597e6 0.167596
\(969\) 3.77572e6 0.129179
\(970\) 9.15228e6 0.312320
\(971\) −7.38941e6 −0.251514 −0.125757 0.992061i \(-0.540136\pi\)
−0.125757 + 0.992061i \(0.540136\pi\)
\(972\) 944784. 0.0320750
\(973\) −7.16870e7 −2.42749
\(974\) 9.14638e6 0.308924
\(975\) 6.51201e6 0.219383
\(976\) −1.86463e6 −0.0626569
\(977\) −9.47674e6 −0.317631 −0.158815 0.987308i \(-0.550767\pi\)
−0.158815 + 0.987308i \(0.550767\pi\)
\(978\) 1.35182e7 0.451932
\(979\) −1.51481e7 −0.505127
\(980\) 1.44295e7 0.479939
\(981\) −1.48668e7 −0.493225
\(982\) −1.37562e7 −0.455218
\(983\) 2.98870e7 0.986504 0.493252 0.869886i \(-0.335808\pi\)
0.493252 + 0.869886i \(0.335808\pi\)
\(984\) 6.33987e6 0.208734
\(985\) 2.25786e7 0.741491
\(986\) −3.42435e7 −1.12172
\(987\) −1.39684e7 −0.456408
\(988\) 6.68682e6 0.217935
\(989\) −6.41684e7 −2.08608
\(990\) 2.35747e6 0.0764466
\(991\) −9.13509e6 −0.295481 −0.147740 0.989026i \(-0.547200\pi\)
−0.147740 + 0.989026i \(0.547200\pi\)
\(992\) −6.29757e6 −0.203186
\(993\) 2.74957e7 0.884895
\(994\) 6.73500e6 0.216208
\(995\) 2.53434e7 0.811535
\(996\) 5.97210e6 0.190756
\(997\) 1.77454e7 0.565389 0.282694 0.959210i \(-0.408772\pi\)
0.282694 + 0.959210i \(0.408772\pi\)
\(998\) −2.16115e7 −0.686846
\(999\) −1.26026e6 −0.0399528
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.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.m.1.4 4 1.1 even 1 trivial