Properties

Label 570.6.a.m.1.1
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 1.1
Root \(231.807\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -88.0477 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -88.0477 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +673.384 q^{11} +144.000 q^{12} +382.024 q^{13} +352.191 q^{14} +225.000 q^{15} +256.000 q^{16} +1550.06 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -792.430 q^{21} -2693.54 q^{22} -893.502 q^{23} -576.000 q^{24} +625.000 q^{25} -1528.09 q^{26} +729.000 q^{27} -1408.76 q^{28} -474.899 q^{29} -900.000 q^{30} -2428.72 q^{31} -1024.00 q^{32} +6060.45 q^{33} -6200.22 q^{34} -2201.19 q^{35} +1296.00 q^{36} -4392.05 q^{37} -1444.00 q^{38} +3438.21 q^{39} -1600.00 q^{40} +249.364 q^{41} +3169.72 q^{42} -2051.37 q^{43} +10774.1 q^{44} +2025.00 q^{45} +3574.01 q^{46} +15777.3 q^{47} +2304.00 q^{48} -9054.60 q^{49} -2500.00 q^{50} +13950.5 q^{51} +6112.38 q^{52} +14192.2 q^{53} -2916.00 q^{54} +16834.6 q^{55} +5635.05 q^{56} +3249.00 q^{57} +1899.60 q^{58} +20269.0 q^{59} +3600.00 q^{60} -5375.18 q^{61} +9714.90 q^{62} -7131.87 q^{63} +4096.00 q^{64} +9550.59 q^{65} -24241.8 q^{66} +26312.4 q^{67} +24800.9 q^{68} -8041.52 q^{69} +8804.77 q^{70} -61569.4 q^{71} -5184.00 q^{72} +13678.7 q^{73} +17568.2 q^{74} +5625.00 q^{75} +5776.00 q^{76} -59289.9 q^{77} -13752.9 q^{78} -22542.0 q^{79} +6400.00 q^{80} +6561.00 q^{81} -997.457 q^{82} +60095.6 q^{83} -12678.9 q^{84} +38751.4 q^{85} +8205.50 q^{86} -4274.10 q^{87} -43096.6 q^{88} -58510.2 q^{89} -8100.00 q^{90} -33636.3 q^{91} -14296.0 q^{92} -21858.5 q^{93} -63109.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +100790. q^{97} +36218.4 q^{98} +54544.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} - 400q^{10} + 338q^{11} + 576q^{12} + 1302q^{13} - 1072q^{14} + 900q^{15} + 1024q^{16} + 542q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 2412q^{21} - 1352q^{22} - 88q^{23} - 2304q^{24} + 2500q^{25} - 5208q^{26} + 2916q^{27} + 4288q^{28} + 5014q^{29} - 3600q^{30} + 4962q^{31} - 4096q^{32} + 3042q^{33} - 2168q^{34} + 6700q^{35} + 5184q^{36} + 8022q^{37} - 5776q^{38} + 11718q^{39} - 6400q^{40} + 2764q^{41} - 9648q^{42} + 25346q^{43} + 5408q^{44} + 8100q^{45} + 352q^{46} + 10008q^{47} + 9216q^{48} + 37248q^{49} - 10000q^{50} + 4878q^{51} + 20832q^{52} - 224q^{53} - 11664q^{54} + 8450q^{55} - 17152q^{56} + 12996q^{57} - 20056q^{58} + 29654q^{59} + 14400q^{60} + 27276q^{61} - 19848q^{62} + 21708q^{63} + 16384q^{64} + 32550q^{65} - 12168q^{66} + 26024q^{67} + 8672q^{68} - 792q^{69} - 26800q^{70} - 26940q^{71} - 20736q^{72} - 60916q^{73} - 32088q^{74} + 22500q^{75} + 23104q^{76} - 21228q^{77} - 46872q^{78} + 34902q^{79} + 25600q^{80} + 26244q^{81} - 11056q^{82} - 48430q^{83} + 38592q^{84} + 13550q^{85} - 101384q^{86} + 45126q^{87} - 21632q^{88} - 38348q^{89} - 32400q^{90} + 69280q^{91} - 1408q^{92} + 44658q^{93} - 40032q^{94} + 36100q^{95} - 36864q^{96} + 45942q^{97} - 148992q^{98} + 27378q^{99} + O(q^{100}) \)

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
\(7\) −88.0477 −0.679161 −0.339581 0.940577i \(-0.610285\pi\)
−0.339581 + 0.940577i \(0.610285\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) 673.384 1.67796 0.838979 0.544164i \(-0.183153\pi\)
0.838979 + 0.544164i \(0.183153\pi\)
\(12\) 144.000 0.288675
\(13\) 382.024 0.626948 0.313474 0.949597i \(-0.398507\pi\)
0.313474 + 0.949597i \(0.398507\pi\)
\(14\) 352.191 0.480240
\(15\) 225.000 0.258199
\(16\) 256.000 0.250000
\(17\) 1550.06 1.30084 0.650422 0.759573i \(-0.274592\pi\)
0.650422 + 0.759573i \(0.274592\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) −792.430 −0.392114
\(22\) −2693.54 −1.18650
\(23\) −893.502 −0.352189 −0.176095 0.984373i \(-0.556346\pi\)
−0.176095 + 0.984373i \(0.556346\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) −1528.09 −0.443319
\(27\) 729.000 0.192450
\(28\) −1408.76 −0.339581
\(29\) −474.899 −0.104859 −0.0524296 0.998625i \(-0.516697\pi\)
−0.0524296 + 0.998625i \(0.516697\pi\)
\(30\) −900.000 −0.182574
\(31\) −2428.72 −0.453915 −0.226957 0.973905i \(-0.572878\pi\)
−0.226957 + 0.973905i \(0.572878\pi\)
\(32\) −1024.00 −0.176777
\(33\) 6060.45 0.968769
\(34\) −6200.22 −0.919835
\(35\) −2201.19 −0.303730
\(36\) 1296.00 0.166667
\(37\) −4392.05 −0.527428 −0.263714 0.964601i \(-0.584947\pi\)
−0.263714 + 0.964601i \(0.584947\pi\)
\(38\) −1444.00 −0.162221
\(39\) 3438.21 0.361969
\(40\) −1600.00 −0.158114
\(41\) 249.364 0.0231672 0.0115836 0.999933i \(-0.496313\pi\)
0.0115836 + 0.999933i \(0.496313\pi\)
\(42\) 3169.72 0.277267
\(43\) −2051.37 −0.169190 −0.0845948 0.996415i \(-0.526960\pi\)
−0.0845948 + 0.996415i \(0.526960\pi\)
\(44\) 10774.1 0.838979
\(45\) 2025.00 0.149071
\(46\) 3574.01 0.249035
\(47\) 15777.3 1.04181 0.520905 0.853615i \(-0.325595\pi\)
0.520905 + 0.853615i \(0.325595\pi\)
\(48\) 2304.00 0.144338
\(49\) −9054.60 −0.538740
\(50\) −2500.00 −0.141421
\(51\) 13950.5 0.751042
\(52\) 6112.38 0.313474
\(53\) 14192.2 0.694002 0.347001 0.937865i \(-0.387200\pi\)
0.347001 + 0.937865i \(0.387200\pi\)
\(54\) −2916.00 −0.136083
\(55\) 16834.6 0.750405
\(56\) 5635.05 0.240120
\(57\) 3249.00 0.132453
\(58\) 1899.60 0.0741467
\(59\) 20269.0 0.758059 0.379030 0.925385i \(-0.376258\pi\)
0.379030 + 0.925385i \(0.376258\pi\)
\(60\) 3600.00 0.129099
\(61\) −5375.18 −0.184956 −0.0924780 0.995715i \(-0.529479\pi\)
−0.0924780 + 0.995715i \(0.529479\pi\)
\(62\) 9714.90 0.320966
\(63\) −7131.87 −0.226387
\(64\) 4096.00 0.125000
\(65\) 9550.59 0.280380
\(66\) −24241.8 −0.685023
\(67\) 26312.4 0.716100 0.358050 0.933702i \(-0.383442\pi\)
0.358050 + 0.933702i \(0.383442\pi\)
\(68\) 24800.9 0.650422
\(69\) −8041.52 −0.203336
\(70\) 8804.77 0.214770
\(71\) −61569.4 −1.44950 −0.724751 0.689011i \(-0.758045\pi\)
−0.724751 + 0.689011i \(0.758045\pi\)
\(72\) −5184.00 −0.117851
\(73\) 13678.7 0.300426 0.150213 0.988654i \(-0.452004\pi\)
0.150213 + 0.988654i \(0.452004\pi\)
\(74\) 17568.2 0.372948
\(75\) 5625.00 0.115470
\(76\) 5776.00 0.114708
\(77\) −59289.9 −1.13960
\(78\) −13752.9 −0.255951
\(79\) −22542.0 −0.406372 −0.203186 0.979140i \(-0.565130\pi\)
−0.203186 + 0.979140i \(0.565130\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) −997.457 −0.0163817
\(83\) 60095.6 0.957519 0.478760 0.877946i \(-0.341086\pi\)
0.478760 + 0.877946i \(0.341086\pi\)
\(84\) −12678.9 −0.196057
\(85\) 38751.4 0.581755
\(86\) 8205.50 0.119635
\(87\) −4274.10 −0.0605405
\(88\) −43096.6 −0.593248
\(89\) −58510.2 −0.782990 −0.391495 0.920180i \(-0.628042\pi\)
−0.391495 + 0.920180i \(0.628042\pi\)
\(90\) −8100.00 −0.105409
\(91\) −33636.3 −0.425799
\(92\) −14296.0 −0.176095
\(93\) −21858.5 −0.262068
\(94\) −63109.3 −0.736671
\(95\) 9025.00 0.102598
\(96\) −9216.00 −0.102062
\(97\) 100790. 1.08765 0.543825 0.839199i \(-0.316975\pi\)
0.543825 + 0.839199i \(0.316975\pi\)
\(98\) 36218.4 0.380946
\(99\) 54544.1 0.559319
\(100\) 10000.0 0.100000
\(101\) 589.088 0.00574615 0.00287308 0.999996i \(-0.499085\pi\)
0.00287308 + 0.999996i \(0.499085\pi\)
\(102\) −55802.0 −0.531067
\(103\) 84424.7 0.784109 0.392054 0.919942i \(-0.371765\pi\)
0.392054 + 0.919942i \(0.371765\pi\)
\(104\) −24449.5 −0.221660
\(105\) −19810.7 −0.175359
\(106\) −56768.9 −0.490733
\(107\) −120490. −1.01740 −0.508700 0.860944i \(-0.669874\pi\)
−0.508700 + 0.860944i \(0.669874\pi\)
\(108\) 11664.0 0.0962250
\(109\) −90184.8 −0.727055 −0.363528 0.931583i \(-0.618428\pi\)
−0.363528 + 0.931583i \(0.618428\pi\)
\(110\) −67338.4 −0.530617
\(111\) −39528.5 −0.304511
\(112\) −22540.2 −0.169790
\(113\) −1770.32 −0.0130423 −0.00652116 0.999979i \(-0.502076\pi\)
−0.00652116 + 0.999979i \(0.502076\pi\)
\(114\) −12996.0 −0.0936586
\(115\) −22337.5 −0.157504
\(116\) −7598.39 −0.0524296
\(117\) 30943.9 0.208983
\(118\) −81076.1 −0.536029
\(119\) −136479. −0.883483
\(120\) −14400.0 −0.0912871
\(121\) 292395. 1.81554
\(122\) 21500.7 0.130784
\(123\) 2244.28 0.0133756
\(124\) −38859.6 −0.226957
\(125\) 15625.0 0.0894427
\(126\) 28527.5 0.160080
\(127\) 14293.0 0.0786349 0.0393174 0.999227i \(-0.487482\pi\)
0.0393174 + 0.999227i \(0.487482\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −18462.4 −0.0976817
\(130\) −38202.4 −0.198259
\(131\) 133554. 0.679954 0.339977 0.940434i \(-0.389581\pi\)
0.339977 + 0.940434i \(0.389581\pi\)
\(132\) 96967.3 0.484385
\(133\) −31785.2 −0.155810
\(134\) −105250. −0.506359
\(135\) 18225.0 0.0860663
\(136\) −99203.6 −0.459918
\(137\) 38155.0 0.173680 0.0868400 0.996222i \(-0.472323\pi\)
0.0868400 + 0.996222i \(0.472323\pi\)
\(138\) 32166.1 0.143781
\(139\) 85303.6 0.374482 0.187241 0.982314i \(-0.440046\pi\)
0.187241 + 0.982314i \(0.440046\pi\)
\(140\) −35219.1 −0.151865
\(141\) 141996. 0.601489
\(142\) 246277. 1.02495
\(143\) 257249. 1.05199
\(144\) 20736.0 0.0833333
\(145\) −11872.5 −0.0468945
\(146\) −54714.7 −0.212433
\(147\) −81491.4 −0.311041
\(148\) −70272.8 −0.263714
\(149\) 82177.9 0.303242 0.151621 0.988439i \(-0.451551\pi\)
0.151621 + 0.988439i \(0.451551\pi\)
\(150\) −22500.0 −0.0816497
\(151\) 273374. 0.975696 0.487848 0.872929i \(-0.337782\pi\)
0.487848 + 0.872929i \(0.337782\pi\)
\(152\) −23104.0 −0.0811107
\(153\) 125555. 0.433614
\(154\) 237160. 0.805822
\(155\) −60718.1 −0.202997
\(156\) 55011.4 0.180984
\(157\) 477563. 1.54626 0.773128 0.634250i \(-0.218691\pi\)
0.773128 + 0.634250i \(0.218691\pi\)
\(158\) 90167.9 0.287349
\(159\) 127730. 0.400682
\(160\) −25600.0 −0.0790569
\(161\) 78670.8 0.239193
\(162\) −26244.0 −0.0785674
\(163\) 400404. 1.18040 0.590200 0.807257i \(-0.299049\pi\)
0.590200 + 0.807257i \(0.299049\pi\)
\(164\) 3989.83 0.0115836
\(165\) 151511. 0.433247
\(166\) −240382. −0.677069
\(167\) 13669.4 0.0379280 0.0189640 0.999820i \(-0.493963\pi\)
0.0189640 + 0.999820i \(0.493963\pi\)
\(168\) 50715.5 0.138633
\(169\) −225351. −0.606936
\(170\) −155006. −0.411363
\(171\) 29241.0 0.0764719
\(172\) −32822.0 −0.0845948
\(173\) −227151. −0.577031 −0.288515 0.957475i \(-0.593162\pi\)
−0.288515 + 0.957475i \(0.593162\pi\)
\(174\) 17096.4 0.0428086
\(175\) −55029.8 −0.135832
\(176\) 172386. 0.419489
\(177\) 182421. 0.437666
\(178\) 234041. 0.553658
\(179\) −81231.2 −0.189492 −0.0947459 0.995501i \(-0.530204\pi\)
−0.0947459 + 0.995501i \(0.530204\pi\)
\(180\) 32400.0 0.0745356
\(181\) 673705. 1.52853 0.764264 0.644903i \(-0.223102\pi\)
0.764264 + 0.644903i \(0.223102\pi\)
\(182\) 134545. 0.301086
\(183\) −48376.6 −0.106784
\(184\) 57184.1 0.124518
\(185\) −109801. −0.235873
\(186\) 87434.1 0.185310
\(187\) 1.04378e6 2.18276
\(188\) 252437. 0.520905
\(189\) −64186.8 −0.130705
\(190\) −36100.0 −0.0725476
\(191\) 336104. 0.666638 0.333319 0.942814i \(-0.391831\pi\)
0.333319 + 0.942814i \(0.391831\pi\)
\(192\) 36864.0 0.0721688
\(193\) −819885. −1.58438 −0.792191 0.610274i \(-0.791059\pi\)
−0.792191 + 0.610274i \(0.791059\pi\)
\(194\) −403161. −0.769085
\(195\) 85955.3 0.161877
\(196\) −144874. −0.269370
\(197\) −211127. −0.387595 −0.193797 0.981042i \(-0.562080\pi\)
−0.193797 + 0.981042i \(0.562080\pi\)
\(198\) −218176. −0.395498
\(199\) −355298. −0.636004 −0.318002 0.948090i \(-0.603012\pi\)
−0.318002 + 0.948090i \(0.603012\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 236812. 0.413441
\(202\) −2356.35 −0.00406314
\(203\) 41813.8 0.0712164
\(204\) 223208. 0.375521
\(205\) 6234.10 0.0103607
\(206\) −337699. −0.554449
\(207\) −72373.7 −0.117396
\(208\) 97798.0 0.156737
\(209\) 243092. 0.384950
\(210\) 79243.0 0.123997
\(211\) 1.06615e6 1.64859 0.824293 0.566163i \(-0.191573\pi\)
0.824293 + 0.566163i \(0.191573\pi\)
\(212\) 227075. 0.347001
\(213\) −554124. −0.836870
\(214\) 481961. 0.719411
\(215\) −51284.3 −0.0756639
\(216\) −46656.0 −0.0680414
\(217\) 213844. 0.308281
\(218\) 360739. 0.514106
\(219\) 123108. 0.173451
\(220\) 269354. 0.375203
\(221\) 592158. 0.815562
\(222\) 158114. 0.215322
\(223\) −241120. −0.324691 −0.162346 0.986734i \(-0.551906\pi\)
−0.162346 + 0.986734i \(0.551906\pi\)
\(224\) 90160.9 0.120060
\(225\) 50625.0 0.0666667
\(226\) 7081.26 0.00922231
\(227\) 300231. 0.386715 0.193358 0.981128i \(-0.438062\pi\)
0.193358 + 0.981128i \(0.438062\pi\)
\(228\) 51984.0 0.0662266
\(229\) 845991. 1.06605 0.533024 0.846100i \(-0.321055\pi\)
0.533024 + 0.846100i \(0.321055\pi\)
\(230\) 89350.2 0.111372
\(231\) −533609. −0.657951
\(232\) 30393.6 0.0370733
\(233\) 1.02473e6 1.23658 0.618289 0.785951i \(-0.287826\pi\)
0.618289 + 0.785951i \(0.287826\pi\)
\(234\) −123776. −0.147773
\(235\) 394433. 0.465912
\(236\) 324305. 0.379030
\(237\) −202878. −0.234619
\(238\) 545916. 0.624717
\(239\) −664838. −0.752872 −0.376436 0.926443i \(-0.622851\pi\)
−0.376436 + 0.926443i \(0.622851\pi\)
\(240\) 57600.0 0.0645497
\(241\) 881395. 0.977526 0.488763 0.872417i \(-0.337448\pi\)
0.488763 + 0.872417i \(0.337448\pi\)
\(242\) −1.16958e6 −1.28378
\(243\) 59049.0 0.0641500
\(244\) −86002.8 −0.0924780
\(245\) −226365. −0.240932
\(246\) −8977.11 −0.00945799
\(247\) 137911. 0.143832
\(248\) 155438. 0.160483
\(249\) 540861. 0.552824
\(250\) −62500.0 −0.0632456
\(251\) −185133. −0.185481 −0.0927407 0.995690i \(-0.529563\pi\)
−0.0927407 + 0.995690i \(0.529563\pi\)
\(252\) −114110. −0.113194
\(253\) −601670. −0.590958
\(254\) −57172.2 −0.0556033
\(255\) 348763. 0.335876
\(256\) 65536.0 0.0625000
\(257\) −25696.6 −0.0242685 −0.0121343 0.999926i \(-0.503863\pi\)
−0.0121343 + 0.999926i \(0.503863\pi\)
\(258\) 73849.5 0.0690714
\(259\) 386710. 0.358209
\(260\) 152809. 0.140190
\(261\) −38466.9 −0.0349531
\(262\) −534217. −0.480800
\(263\) 881127. 0.785505 0.392752 0.919644i \(-0.371523\pi\)
0.392752 + 0.919644i \(0.371523\pi\)
\(264\) −387869. −0.342512
\(265\) 354805. 0.310367
\(266\) 127141. 0.110175
\(267\) −526592. −0.452060
\(268\) 420999. 0.358050
\(269\) −811974. −0.684166 −0.342083 0.939670i \(-0.611132\pi\)
−0.342083 + 0.939670i \(0.611132\pi\)
\(270\) −72900.0 −0.0608581
\(271\) 1.15348e6 0.954083 0.477042 0.878881i \(-0.341709\pi\)
0.477042 + 0.878881i \(0.341709\pi\)
\(272\) 396814. 0.325211
\(273\) −302727. −0.245835
\(274\) −152620. −0.122810
\(275\) 420865. 0.335592
\(276\) −128664. −0.101668
\(277\) −1.17659e6 −0.921351 −0.460676 0.887569i \(-0.652393\pi\)
−0.460676 + 0.887569i \(0.652393\pi\)
\(278\) −341215. −0.264799
\(279\) −196727. −0.151305
\(280\) 140876. 0.107385
\(281\) 29392.4 0.0222059 0.0111030 0.999938i \(-0.496466\pi\)
0.0111030 + 0.999938i \(0.496466\pi\)
\(282\) −567984. −0.425317
\(283\) −303660. −0.225383 −0.112692 0.993630i \(-0.535947\pi\)
−0.112692 + 0.993630i \(0.535947\pi\)
\(284\) −985110. −0.724751
\(285\) 81225.0 0.0592349
\(286\) −1.02899e6 −0.743871
\(287\) −21955.9 −0.0157343
\(288\) −82944.0 −0.0589256
\(289\) 982815. 0.692193
\(290\) 47489.9 0.0331594
\(291\) 907112. 0.627955
\(292\) 218859. 0.150213
\(293\) −482439. −0.328302 −0.164151 0.986435i \(-0.552488\pi\)
−0.164151 + 0.986435i \(0.552488\pi\)
\(294\) 325966. 0.219940
\(295\) 506726. 0.339014
\(296\) 281091. 0.186474
\(297\) 490897. 0.322923
\(298\) −328712. −0.214424
\(299\) −341339. −0.220804
\(300\) 90000.0 0.0577350
\(301\) 180619. 0.114907
\(302\) −1.09350e6 −0.689921
\(303\) 5301.79 0.00331754
\(304\) 92416.0 0.0573539
\(305\) −134379. −0.0827148
\(306\) −502218. −0.306612
\(307\) 2.32875e6 1.41019 0.705094 0.709114i \(-0.250905\pi\)
0.705094 + 0.709114i \(0.250905\pi\)
\(308\) −948639. −0.569802
\(309\) 759822. 0.452705
\(310\) 242872. 0.143540
\(311\) −613376. −0.359605 −0.179802 0.983703i \(-0.557546\pi\)
−0.179802 + 0.983703i \(0.557546\pi\)
\(312\) −220046. −0.127975
\(313\) 3.21218e6 1.85327 0.926636 0.375959i \(-0.122687\pi\)
0.926636 + 0.375959i \(0.122687\pi\)
\(314\) −1.91025e6 −1.09337
\(315\) −178297. −0.101243
\(316\) −360672. −0.203186
\(317\) −821969. −0.459417 −0.229709 0.973259i \(-0.573777\pi\)
−0.229709 + 0.973259i \(0.573777\pi\)
\(318\) −510920. −0.283325
\(319\) −319790. −0.175949
\(320\) 102400. 0.0559017
\(321\) −1.08441e6 −0.587397
\(322\) −314683. −0.169135
\(323\) 559570. 0.298434
\(324\) 104976. 0.0555556
\(325\) 238765. 0.125390
\(326\) −1.60161e6 −0.834668
\(327\) −811664. −0.419765
\(328\) −15959.3 −0.00819086
\(329\) −1.38916e6 −0.707557
\(330\) −606045. −0.306352
\(331\) 14113.6 0.00708055 0.00354027 0.999994i \(-0.498873\pi\)
0.00354027 + 0.999994i \(0.498873\pi\)
\(332\) 961530. 0.478760
\(333\) −355756. −0.175809
\(334\) −54677.8 −0.0268191
\(335\) 657811. 0.320250
\(336\) −202862. −0.0980285
\(337\) −497082. −0.238426 −0.119213 0.992869i \(-0.538037\pi\)
−0.119213 + 0.992869i \(0.538037\pi\)
\(338\) 901404. 0.429168
\(339\) −15932.8 −0.00752998
\(340\) 620022. 0.290877
\(341\) −1.63546e6 −0.761649
\(342\) −116964. −0.0540738
\(343\) 2.27705e6 1.04505
\(344\) 131288. 0.0598176
\(345\) −201038. −0.0909348
\(346\) 908603. 0.408022
\(347\) 512930. 0.228683 0.114342 0.993441i \(-0.463524\pi\)
0.114342 + 0.993441i \(0.463524\pi\)
\(348\) −68385.5 −0.0302703
\(349\) −2.63907e6 −1.15981 −0.579905 0.814684i \(-0.696910\pi\)
−0.579905 + 0.814684i \(0.696910\pi\)
\(350\) 220119. 0.0960479
\(351\) 278495. 0.120656
\(352\) −689545. −0.296624
\(353\) 2.09325e6 0.894096 0.447048 0.894510i \(-0.352475\pi\)
0.447048 + 0.894510i \(0.352475\pi\)
\(354\) −729685. −0.309476
\(355\) −1.53923e6 −0.648237
\(356\) −936163. −0.391495
\(357\) −1.22831e6 −0.510079
\(358\) 324925. 0.133991
\(359\) −4.24105e6 −1.73675 −0.868375 0.495908i \(-0.834835\pi\)
−0.868375 + 0.495908i \(0.834835\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) −2.69482e6 −1.08083
\(363\) 2.63155e6 1.04820
\(364\) −538181. −0.212900
\(365\) 341967. 0.134354
\(366\) 193506. 0.0755079
\(367\) 566845. 0.219685 0.109842 0.993949i \(-0.464965\pi\)
0.109842 + 0.993949i \(0.464965\pi\)
\(368\) −228736. −0.0880473
\(369\) 20198.5 0.00772241
\(370\) 439205. 0.166787
\(371\) −1.24959e6 −0.471339
\(372\) −349736. −0.131034
\(373\) −997949. −0.371395 −0.185698 0.982607i \(-0.559454\pi\)
−0.185698 + 0.982607i \(0.559454\pi\)
\(374\) −4.17513e6 −1.54344
\(375\) 140625. 0.0516398
\(376\) −1.00975e6 −0.368336
\(377\) −181423. −0.0657413
\(378\) 256747. 0.0924222
\(379\) −2.15610e6 −0.771030 −0.385515 0.922702i \(-0.625976\pi\)
−0.385515 + 0.922702i \(0.625976\pi\)
\(380\) 144400. 0.0512989
\(381\) 128637. 0.0453999
\(382\) −1.34441e6 −0.471384
\(383\) 2.00565e6 0.698647 0.349323 0.937002i \(-0.386411\pi\)
0.349323 + 0.937002i \(0.386411\pi\)
\(384\) −147456. −0.0510310
\(385\) −1.48225e6 −0.509647
\(386\) 3.27954e6 1.12033
\(387\) −166161. −0.0563965
\(388\) 1.61264e6 0.543825
\(389\) −695097. −0.232901 −0.116450 0.993197i \(-0.537152\pi\)
−0.116450 + 0.993197i \(0.537152\pi\)
\(390\) −343821. −0.114465
\(391\) −1.38498e6 −0.458143
\(392\) 579494. 0.190473
\(393\) 1.20199e6 0.392572
\(394\) 844508. 0.274071
\(395\) −563549. −0.181735
\(396\) 872705. 0.279660
\(397\) −5.52435e6 −1.75916 −0.879579 0.475752i \(-0.842176\pi\)
−0.879579 + 0.475752i \(0.842176\pi\)
\(398\) 1.42119e6 0.449723
\(399\) −286067. −0.0899571
\(400\) 160000. 0.0500000
\(401\) −1.97770e6 −0.614187 −0.307093 0.951679i \(-0.599356\pi\)
−0.307093 + 0.951679i \(0.599356\pi\)
\(402\) −947247. −0.292347
\(403\) −927830. −0.284581
\(404\) 9425.41 0.00287308
\(405\) 164025. 0.0496904
\(406\) −167255. −0.0503576
\(407\) −2.95754e6 −0.885002
\(408\) −892832. −0.265534
\(409\) 2.16796e6 0.640831 0.320416 0.947277i \(-0.396177\pi\)
0.320416 + 0.947277i \(0.396177\pi\)
\(410\) −24936.4 −0.00732613
\(411\) 343395. 0.100274
\(412\) 1.35079e6 0.392054
\(413\) −1.78464e6 −0.514845
\(414\) 289495. 0.0830118
\(415\) 1.50239e6 0.428216
\(416\) −391192. −0.110830
\(417\) 767733. 0.216207
\(418\) −972366. −0.272201
\(419\) −1.59744e6 −0.444518 −0.222259 0.974988i \(-0.571343\pi\)
−0.222259 + 0.974988i \(0.571343\pi\)
\(420\) −316972. −0.0876794
\(421\) −6.57659e6 −1.80840 −0.904202 0.427104i \(-0.859534\pi\)
−0.904202 + 0.427104i \(0.859534\pi\)
\(422\) −4.26460e6 −1.16573
\(423\) 1.27796e6 0.347270
\(424\) −908302. −0.245367
\(425\) 968785. 0.260169
\(426\) 2.21650e6 0.591757
\(427\) 473272. 0.125615
\(428\) −1.92784e6 −0.508700
\(429\) 2.31524e6 0.607368
\(430\) 205137. 0.0535024
\(431\) −6.32694e6 −1.64059 −0.820295 0.571940i \(-0.806191\pi\)
−0.820295 + 0.571940i \(0.806191\pi\)
\(432\) 186624. 0.0481125
\(433\) 1.47846e6 0.378957 0.189478 0.981885i \(-0.439320\pi\)
0.189478 + 0.981885i \(0.439320\pi\)
\(434\) −855375. −0.217988
\(435\) −106852. −0.0270745
\(436\) −1.44296e6 −0.363528
\(437\) −322554. −0.0807977
\(438\) −492432. −0.122648
\(439\) −1.57942e6 −0.391145 −0.195572 0.980689i \(-0.562656\pi\)
−0.195572 + 0.980689i \(0.562656\pi\)
\(440\) −1.07741e6 −0.265308
\(441\) −733422. −0.179580
\(442\) −2.36863e6 −0.576689
\(443\) −4.32168e6 −1.04627 −0.523134 0.852250i \(-0.675237\pi\)
−0.523134 + 0.852250i \(0.675237\pi\)
\(444\) −632455. −0.152255
\(445\) −1.46275e6 −0.350164
\(446\) 964479. 0.229591
\(447\) 739601. 0.175077
\(448\) −360643. −0.0848952
\(449\) 2.77014e6 0.648464 0.324232 0.945978i \(-0.394894\pi\)
0.324232 + 0.945978i \(0.394894\pi\)
\(450\) −202500. −0.0471405
\(451\) 167918. 0.0388737
\(452\) −28325.1 −0.00652116
\(453\) 2.46036e6 0.563318
\(454\) −1.20093e6 −0.273449
\(455\) −840908. −0.190423
\(456\) −207936. −0.0468293
\(457\) 1.11804e6 0.250420 0.125210 0.992130i \(-0.460040\pi\)
0.125210 + 0.992130i \(0.460040\pi\)
\(458\) −3.38396e6 −0.753810
\(459\) 1.12999e6 0.250347
\(460\) −357401. −0.0787519
\(461\) 6.12279e6 1.34183 0.670914 0.741535i \(-0.265902\pi\)
0.670914 + 0.741535i \(0.265902\pi\)
\(462\) 2.13444e6 0.465241
\(463\) −31678.1 −0.00686763 −0.00343381 0.999994i \(-0.501093\pi\)
−0.00343381 + 0.999994i \(0.501093\pi\)
\(464\) −121574. −0.0262148
\(465\) −546463. −0.117200
\(466\) −4.09894e6 −0.874393
\(467\) −1.07954e6 −0.229058 −0.114529 0.993420i \(-0.536536\pi\)
−0.114529 + 0.993420i \(0.536536\pi\)
\(468\) 495103. 0.104491
\(469\) −2.31675e6 −0.486348
\(470\) −1.57773e6 −0.329449
\(471\) 4.29806e6 0.892731
\(472\) −1.29722e6 −0.268014
\(473\) −1.38136e6 −0.283893
\(474\) 811511. 0.165901
\(475\) 225625. 0.0458831
\(476\) −2.18366e6 −0.441741
\(477\) 1.14957e6 0.231334
\(478\) 2.65935e6 0.532361
\(479\) −5.41987e6 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(480\) −230400. −0.0456435
\(481\) −1.67787e6 −0.330670
\(482\) −3.52558e6 −0.691215
\(483\) 708037. 0.138098
\(484\) 4.67832e6 0.907771
\(485\) 2.51976e6 0.486412
\(486\) −236196. −0.0453609
\(487\) 9.27460e6 1.77204 0.886018 0.463650i \(-0.153461\pi\)
0.886018 + 0.463650i \(0.153461\pi\)
\(488\) 344011. 0.0653918
\(489\) 3.60363e6 0.681504
\(490\) 905460. 0.170364
\(491\) −4.15914e6 −0.778573 −0.389287 0.921117i \(-0.627278\pi\)
−0.389287 + 0.921117i \(0.627278\pi\)
\(492\) 35908.4 0.00668781
\(493\) −736121. −0.136405
\(494\) −551642. −0.101704
\(495\) 1.36360e6 0.250135
\(496\) −621754. −0.113479
\(497\) 5.42104e6 0.984446
\(498\) −2.16344e6 −0.390906
\(499\) −9.27819e6 −1.66806 −0.834031 0.551718i \(-0.813972\pi\)
−0.834031 + 0.551718i \(0.813972\pi\)
\(500\) 250000. 0.0447214
\(501\) 123025. 0.0218977
\(502\) 740534. 0.131155
\(503\) 6.17971e6 1.08905 0.544525 0.838745i \(-0.316710\pi\)
0.544525 + 0.838745i \(0.316710\pi\)
\(504\) 456439. 0.0800400
\(505\) 14727.2 0.00256976
\(506\) 2.40668e6 0.417871
\(507\) −2.02816e6 −0.350414
\(508\) 228689. 0.0393174
\(509\) 5.51603e6 0.943697 0.471848 0.881680i \(-0.343587\pi\)
0.471848 + 0.881680i \(0.343587\pi\)
\(510\) −1.39505e6 −0.237500
\(511\) −1.20438e6 −0.204038
\(512\) −262144. −0.0441942
\(513\) 263169. 0.0441511
\(514\) 102786. 0.0171604
\(515\) 2.11062e6 0.350664
\(516\) −295398. −0.0488408
\(517\) 1.06242e7 1.74811
\(518\) −1.54684e6 −0.253292
\(519\) −2.04436e6 −0.333149
\(520\) −611238. −0.0991293
\(521\) −5.98446e6 −0.965896 −0.482948 0.875649i \(-0.660434\pi\)
−0.482948 + 0.875649i \(0.660434\pi\)
\(522\) 153867. 0.0247156
\(523\) 8.69622e6 1.39020 0.695099 0.718915i \(-0.255361\pi\)
0.695099 + 0.718915i \(0.255361\pi\)
\(524\) 2.13687e6 0.339977
\(525\) −495268. −0.0784228
\(526\) −3.52451e6 −0.555436
\(527\) −3.76466e6 −0.590472
\(528\) 1.55148e6 0.242192
\(529\) −5.63800e6 −0.875963
\(530\) −1.41922e6 −0.219463
\(531\) 1.64179e6 0.252686
\(532\) −508564. −0.0779052
\(533\) 95263.0 0.0145247
\(534\) 2.10637e6 0.319654
\(535\) −3.01225e6 −0.454995
\(536\) −1.68400e6 −0.253180
\(537\) −731081. −0.109403
\(538\) 3.24790e6 0.483779
\(539\) −6.09722e6 −0.903982
\(540\) 291600. 0.0430331
\(541\) 1.26428e7 1.85716 0.928581 0.371129i \(-0.121029\pi\)
0.928581 + 0.371129i \(0.121029\pi\)
\(542\) −4.61391e6 −0.674639
\(543\) 6.06335e6 0.882496
\(544\) −1.58726e6 −0.229959
\(545\) −2.25462e6 −0.325149
\(546\) 1.21091e6 0.173832
\(547\) 1.69788e6 0.242626 0.121313 0.992614i \(-0.461289\pi\)
0.121313 + 0.992614i \(0.461289\pi\)
\(548\) 610480. 0.0868400
\(549\) −435389. −0.0616520
\(550\) −1.68346e6 −0.237299
\(551\) −171439. −0.0240564
\(552\) 514657. 0.0718903
\(553\) 1.98477e6 0.275992
\(554\) 4.70635e6 0.651494
\(555\) −988212. −0.136181
\(556\) 1.36486e6 0.187241
\(557\) −1.06395e7 −1.45306 −0.726532 0.687133i \(-0.758869\pi\)
−0.726532 + 0.687133i \(0.758869\pi\)
\(558\) 786907. 0.106989
\(559\) −783673. −0.106073
\(560\) −563505. −0.0759326
\(561\) 9.39404e6 1.26022
\(562\) −117570. −0.0157020
\(563\) −1.00325e7 −1.33395 −0.666976 0.745079i \(-0.732412\pi\)
−0.666976 + 0.745079i \(0.732412\pi\)
\(564\) 2.27193e6 0.300745
\(565\) −44257.9 −0.00583270
\(566\) 1.21464e6 0.159370
\(567\) −577681. −0.0754624
\(568\) 3.94044e6 0.512476
\(569\) 1.29186e7 1.67277 0.836385 0.548143i \(-0.184665\pi\)
0.836385 + 0.548143i \(0.184665\pi\)
\(570\) −324900. −0.0418854
\(571\) 2.25861e6 0.289902 0.144951 0.989439i \(-0.453698\pi\)
0.144951 + 0.989439i \(0.453698\pi\)
\(572\) 4.11598e6 0.525996
\(573\) 3.02493e6 0.384883
\(574\) 87823.8 0.0111258
\(575\) −558439. −0.0704378
\(576\) 331776. 0.0416667
\(577\) 4.76183e6 0.595436 0.297718 0.954654i \(-0.403775\pi\)
0.297718 + 0.954654i \(0.403775\pi\)
\(578\) −3.93126e6 −0.489455
\(579\) −7.37897e6 −0.914743
\(580\) −189960. −0.0234472
\(581\) −5.29128e6 −0.650310
\(582\) −3.62845e6 −0.444031
\(583\) 9.55681e6 1.16451
\(584\) −875435. −0.106217
\(585\) 773598. 0.0934600
\(586\) 1.92976e6 0.232145
\(587\) 898103. 0.107580 0.0537899 0.998552i \(-0.482870\pi\)
0.0537899 + 0.998552i \(0.482870\pi\)
\(588\) −1.30386e6 −0.155521
\(589\) −876770. −0.104135
\(590\) −2.02690e6 −0.239719
\(591\) −1.90014e6 −0.223778
\(592\) −1.12437e6 −0.131857
\(593\) 1.20329e7 1.40518 0.702591 0.711594i \(-0.252026\pi\)
0.702591 + 0.711594i \(0.252026\pi\)
\(594\) −1.96359e6 −0.228341
\(595\) −3.41197e6 −0.395105
\(596\) 1.31485e6 0.151621
\(597\) −3.19768e6 −0.367197
\(598\) 1.36536e6 0.156132
\(599\) −5.89455e6 −0.671249 −0.335625 0.941996i \(-0.608947\pi\)
−0.335625 + 0.941996i \(0.608947\pi\)
\(600\) −360000. −0.0408248
\(601\) −3.07149e6 −0.346867 −0.173433 0.984846i \(-0.555486\pi\)
−0.173433 + 0.984846i \(0.555486\pi\)
\(602\) −722475. −0.0812516
\(603\) 2.13131e6 0.238700
\(604\) 4.37398e6 0.487848
\(605\) 7.30987e6 0.811935
\(606\) −21207.2 −0.00234586
\(607\) −8.71551e6 −0.960110 −0.480055 0.877238i \(-0.659383\pi\)
−0.480055 + 0.877238i \(0.659383\pi\)
\(608\) −369664. −0.0405554
\(609\) 376324. 0.0411168
\(610\) 537518. 0.0584882
\(611\) 6.02731e6 0.653161
\(612\) 2.00887e6 0.216807
\(613\) 9.72932e6 1.04576 0.522879 0.852407i \(-0.324858\pi\)
0.522879 + 0.852407i \(0.324858\pi\)
\(614\) −9.31500e6 −0.997153
\(615\) 56106.9 0.00598176
\(616\) 3.79455e6 0.402911
\(617\) −1.67898e7 −1.77555 −0.887776 0.460276i \(-0.847750\pi\)
−0.887776 + 0.460276i \(0.847750\pi\)
\(618\) −3.03929e6 −0.320111
\(619\) −6.24714e6 −0.655322 −0.327661 0.944795i \(-0.606260\pi\)
−0.327661 + 0.944795i \(0.606260\pi\)
\(620\) −971490. −0.101498
\(621\) −651363. −0.0677788
\(622\) 2.45350e6 0.254279
\(623\) 5.15169e6 0.531777
\(624\) 880182. 0.0904922
\(625\) 390625. 0.0400000
\(626\) −1.28487e7 −1.31046
\(627\) 2.18782e6 0.222251
\(628\) 7.64100e6 0.773128
\(629\) −6.80792e6 −0.686101
\(630\) 713187. 0.0715899
\(631\) 4.34763e6 0.434690 0.217345 0.976095i \(-0.430260\pi\)
0.217345 + 0.976095i \(0.430260\pi\)
\(632\) 1.44269e6 0.143674
\(633\) 9.59534e6 0.951812
\(634\) 3.28788e6 0.324857
\(635\) 357326. 0.0351666
\(636\) 2.04368e6 0.200341
\(637\) −3.45907e6 −0.337762
\(638\) 1.27916e6 0.124415
\(639\) −4.98712e6 −0.483167
\(640\) −409600. −0.0395285
\(641\) 6.17267e6 0.593374 0.296687 0.954975i \(-0.404118\pi\)
0.296687 + 0.954975i \(0.404118\pi\)
\(642\) 4.33764e6 0.415352
\(643\) 8.28193e6 0.789958 0.394979 0.918690i \(-0.370752\pi\)
0.394979 + 0.918690i \(0.370752\pi\)
\(644\) 1.25873e6 0.119597
\(645\) −461559. −0.0436846
\(646\) −2.23828e6 −0.211025
\(647\) 1.20226e7 1.12912 0.564559 0.825393i \(-0.309046\pi\)
0.564559 + 0.825393i \(0.309046\pi\)
\(648\) −419904. −0.0392837
\(649\) 1.36488e7 1.27199
\(650\) −955059. −0.0886639
\(651\) 1.92459e6 0.177986
\(652\) 6.40646e6 0.590200
\(653\) −2.48403e6 −0.227968 −0.113984 0.993483i \(-0.536361\pi\)
−0.113984 + 0.993483i \(0.536361\pi\)
\(654\) 3.24665e6 0.296819
\(655\) 3.33886e6 0.304085
\(656\) 63837.2 0.00579181
\(657\) 1.10797e6 0.100142
\(658\) 5.55663e6 0.500319
\(659\) 345422. 0.0309839 0.0154920 0.999880i \(-0.495069\pi\)
0.0154920 + 0.999880i \(0.495069\pi\)
\(660\) 2.42418e6 0.216623
\(661\) −1.14796e7 −1.02194 −0.510968 0.859600i \(-0.670713\pi\)
−0.510968 + 0.859600i \(0.670713\pi\)
\(662\) −56454.3 −0.00500670
\(663\) 5.32942e6 0.470865
\(664\) −3.84612e6 −0.338534
\(665\) −794631. −0.0696805
\(666\) 1.42302e6 0.124316
\(667\) 424324. 0.0369303
\(668\) 218711. 0.0189640
\(669\) −2.17008e6 −0.187461
\(670\) −2.63124e6 −0.226451
\(671\) −3.61956e6 −0.310348
\(672\) 811448. 0.0693166
\(673\) −1.34462e7 −1.14436 −0.572181 0.820127i \(-0.693903\pi\)
−0.572181 + 0.820127i \(0.693903\pi\)
\(674\) 1.98833e6 0.168592
\(675\) 455625. 0.0384900
\(676\) −3.60562e6 −0.303468
\(677\) −1.16812e7 −0.979523 −0.489761 0.871857i \(-0.662916\pi\)
−0.489761 + 0.871857i \(0.662916\pi\)
\(678\) 63731.4 0.00532450
\(679\) −8.87435e6 −0.738690
\(680\) −2.48009e6 −0.205681
\(681\) 2.70208e6 0.223270
\(682\) 6.54186e6 0.538567
\(683\) 5.59312e6 0.458778 0.229389 0.973335i \(-0.426327\pi\)
0.229389 + 0.973335i \(0.426327\pi\)
\(684\) 467856. 0.0382360
\(685\) 953875. 0.0776721
\(686\) −9.10822e6 −0.738964
\(687\) 7.61392e6 0.615483
\(688\) −525152. −0.0422974
\(689\) 5.42176e6 0.435103
\(690\) 804152. 0.0643006
\(691\) −2.00642e6 −0.159855 −0.0799277 0.996801i \(-0.525469\pi\)
−0.0799277 + 0.996801i \(0.525469\pi\)
\(692\) −3.63441e6 −0.288515
\(693\) −4.80248e6 −0.379868
\(694\) −2.05172e6 −0.161703
\(695\) 2.13259e6 0.167473
\(696\) 273542. 0.0214043
\(697\) 386528. 0.0301370
\(698\) 1.05563e7 0.820110
\(699\) 9.22261e6 0.713939
\(700\) −880477. −0.0679161
\(701\) 1.93537e6 0.148754 0.0743769 0.997230i \(-0.476303\pi\)
0.0743769 + 0.997230i \(0.476303\pi\)
\(702\) −1.11398e6 −0.0853169
\(703\) −1.58553e6 −0.121000
\(704\) 2.75818e6 0.209745
\(705\) 3.54990e6 0.268994
\(706\) −8.37300e6 −0.632222
\(707\) −51867.9 −0.00390256
\(708\) 2.91874e6 0.218833
\(709\) −9.84386e6 −0.735445 −0.367722 0.929936i \(-0.619862\pi\)
−0.367722 + 0.929936i \(0.619862\pi\)
\(710\) 6.15694e6 0.458373
\(711\) −1.82590e6 −0.135457
\(712\) 3.74465e6 0.276829
\(713\) 2.17007e6 0.159864
\(714\) 4.91324e6 0.360680
\(715\) 6.43121e6 0.470466
\(716\) −1.29970e6 −0.0947459
\(717\) −5.98354e6 −0.434671
\(718\) 1.69642e7 1.22807
\(719\) −43867.3 −0.00316460 −0.00158230 0.999999i \(-0.500504\pi\)
−0.00158230 + 0.999999i \(0.500504\pi\)
\(720\) 518400. 0.0372678
\(721\) −7.43340e6 −0.532536
\(722\) −521284. −0.0372161
\(723\) 7.93256e6 0.564375
\(724\) 1.07793e7 0.764264
\(725\) −296812. −0.0209718
\(726\) −1.05262e7 −0.741192
\(727\) −8.54625e6 −0.599707 −0.299854 0.953985i \(-0.596938\pi\)
−0.299854 + 0.953985i \(0.596938\pi\)
\(728\) 2.15272e6 0.150543
\(729\) 531441. 0.0370370
\(730\) −1.36787e6 −0.0950029
\(731\) −3.17974e6 −0.220089
\(732\) −774026. −0.0533922
\(733\) −8.13177e6 −0.559017 −0.279509 0.960143i \(-0.590172\pi\)
−0.279509 + 0.960143i \(0.590172\pi\)
\(734\) −2.26738e6 −0.155340
\(735\) −2.03728e6 −0.139102
\(736\) 914946. 0.0622588
\(737\) 1.77184e7 1.20159
\(738\) −80794.0 −0.00546057
\(739\) 1.73946e6 0.117167 0.0585833 0.998283i \(-0.481342\pi\)
0.0585833 + 0.998283i \(0.481342\pi\)
\(740\) −1.75682e6 −0.117936
\(741\) 1.24119e6 0.0830413
\(742\) 4.99837e6 0.333287
\(743\) −7.54362e6 −0.501312 −0.250656 0.968076i \(-0.580646\pi\)
−0.250656 + 0.968076i \(0.580646\pi\)
\(744\) 1.39895e6 0.0926549
\(745\) 2.05445e6 0.135614
\(746\) 3.99180e6 0.262616
\(747\) 4.86775e6 0.319173
\(748\) 1.67005e7 1.09138
\(749\) 1.06089e7 0.690979
\(750\) −562500. −0.0365148
\(751\) 2.78689e6 0.180310 0.0901552 0.995928i \(-0.471264\pi\)
0.0901552 + 0.995928i \(0.471264\pi\)
\(752\) 4.03899e6 0.260453
\(753\) −1.66620e6 −0.107088
\(754\) 725691. 0.0464861
\(755\) 6.83435e6 0.436345
\(756\) −1.02699e6 −0.0653523
\(757\) −2.75404e7 −1.74675 −0.873375 0.487048i \(-0.838074\pi\)
−0.873375 + 0.487048i \(0.838074\pi\)
\(758\) 8.62441e6 0.545201
\(759\) −5.41503e6 −0.341190
\(760\) −577600. −0.0362738
\(761\) −1.77762e7 −1.11270 −0.556350 0.830948i \(-0.687799\pi\)
−0.556350 + 0.830948i \(0.687799\pi\)
\(762\) −514549. −0.0321026
\(763\) 7.94057e6 0.493788
\(764\) 5.37766e6 0.333319
\(765\) 3.13886e6 0.193918
\(766\) −8.02259e6 −0.494018
\(767\) 7.74325e6 0.475264
\(768\) 589824. 0.0360844
\(769\) 1.99569e7 1.21696 0.608481 0.793568i \(-0.291779\pi\)
0.608481 + 0.793568i \(0.291779\pi\)
\(770\) 5.92899e6 0.360374
\(771\) −231270. −0.0140114
\(772\) −1.31182e7 −0.792191
\(773\) −5.97752e6 −0.359809 −0.179905 0.983684i \(-0.557579\pi\)
−0.179905 + 0.983684i \(0.557579\pi\)
\(774\) 664645. 0.0398784
\(775\) −1.51795e6 −0.0907829
\(776\) −6.45058e6 −0.384542
\(777\) 3.48039e6 0.206812
\(778\) 2.78039e6 0.164686
\(779\) 90020.5 0.00531493
\(780\) 1.37529e6 0.0809387
\(781\) −4.14598e7 −2.43220
\(782\) 5.53991e6 0.323956
\(783\) −346202. −0.0201802
\(784\) −2.31798e6 −0.134685
\(785\) 1.19391e7 0.691506
\(786\) −4.80796e6 −0.277590
\(787\) −2.75647e7 −1.58641 −0.793206 0.608954i \(-0.791590\pi\)
−0.793206 + 0.608954i \(0.791590\pi\)
\(788\) −3.37803e6 −0.193797
\(789\) 7.93014e6 0.453511
\(790\) 2.25420e6 0.128506
\(791\) 155872. 0.00885784
\(792\) −3.49082e6 −0.197749
\(793\) −2.05344e6 −0.115958
\(794\) 2.20974e7 1.24391
\(795\) 3.19325e6 0.179190
\(796\) −5.68476e6 −0.318002
\(797\) 1.31021e7 0.730626 0.365313 0.930885i \(-0.380962\pi\)
0.365313 + 0.930885i \(0.380962\pi\)
\(798\) 1.14427e6 0.0636093
\(799\) 2.44557e7 1.35523
\(800\) −640000. −0.0353553
\(801\) −4.73932e6 −0.260997
\(802\) 7.91082e6 0.434296
\(803\) 9.21100e6 0.504101
\(804\) 3.78899e6 0.206720
\(805\) 1.96677e6 0.106970
\(806\) 3.71132e6 0.201229
\(807\) −7.30777e6 −0.395004
\(808\) −37701.7 −0.00203157
\(809\) −1.40566e7 −0.755105 −0.377553 0.925988i \(-0.623234\pi\)
−0.377553 + 0.925988i \(0.623234\pi\)
\(810\) −656100. −0.0351364
\(811\) −1.55976e7 −0.832732 −0.416366 0.909197i \(-0.636697\pi\)
−0.416366 + 0.909197i \(0.636697\pi\)
\(812\) 669021. 0.0356082
\(813\) 1.03813e7 0.550840
\(814\) 1.18301e7 0.625791
\(815\) 1.00101e7 0.527891
\(816\) 3.57133e6 0.187761
\(817\) −740546. −0.0388148
\(818\) −8.67185e6 −0.453136
\(819\) −2.72454e6 −0.141933
\(820\) 99745.7 0.00518035
\(821\) −3.55150e7 −1.83888 −0.919442 0.393227i \(-0.871359\pi\)
−0.919442 + 0.393227i \(0.871359\pi\)
\(822\) −1.37358e6 −0.0709046
\(823\) 5.20836e6 0.268041 0.134021 0.990979i \(-0.457211\pi\)
0.134021 + 0.990979i \(0.457211\pi\)
\(824\) −5.40318e6 −0.277224
\(825\) 3.78778e6 0.193754
\(826\) 7.13857e6 0.364050
\(827\) 3.89931e6 0.198255 0.0991273 0.995075i \(-0.468395\pi\)
0.0991273 + 0.995075i \(0.468395\pi\)
\(828\) −1.15798e6 −0.0586982
\(829\) −3.70442e7 −1.87212 −0.936060 0.351841i \(-0.885556\pi\)
−0.936060 + 0.351841i \(0.885556\pi\)
\(830\) −6.00956e6 −0.302794
\(831\) −1.05893e7 −0.531942
\(832\) 1.56477e6 0.0783686
\(833\) −1.40351e7 −0.700816
\(834\) −3.07093e6 −0.152881
\(835\) 341736. 0.0169619
\(836\) 3.88947e6 0.192475
\(837\) −1.77054e6 −0.0873559
\(838\) 6.38976e6 0.314322
\(839\) 3.20457e6 0.157168 0.0785841 0.996907i \(-0.474960\pi\)
0.0785841 + 0.996907i \(0.474960\pi\)
\(840\) 1.26789e6 0.0619987
\(841\) −2.02856e7 −0.989005
\(842\) 2.63064e7 1.27874
\(843\) 264532. 0.0128206
\(844\) 1.70584e7 0.824293
\(845\) −5.63377e6 −0.271430
\(846\) −5.11185e6 −0.245557
\(847\) −2.57447e7 −1.23305
\(848\) 3.63321e6 0.173500
\(849\) −2.73294e6 −0.130125
\(850\) −3.87514e6 −0.183967
\(851\) 3.92431e6 0.185754
\(852\) −8.86599e6 −0.418435
\(853\) −1.28143e7 −0.603007 −0.301503 0.953465i \(-0.597488\pi\)
−0.301503 + 0.953465i \(0.597488\pi\)
\(854\) −1.89309e6 −0.0888232
\(855\) 731025. 0.0341993
\(856\) 7.71137e6 0.359705
\(857\) −2.87527e7 −1.33729 −0.668646 0.743581i \(-0.733126\pi\)
−0.668646 + 0.743581i \(0.733126\pi\)
\(858\) −9.26095e6 −0.429474
\(859\) 2.15002e7 0.994169 0.497085 0.867702i \(-0.334404\pi\)
0.497085 + 0.867702i \(0.334404\pi\)
\(860\) −820550. −0.0378319
\(861\) −197604. −0.00908420
\(862\) 2.53077e7 1.16007
\(863\) 2.37713e7 1.08649 0.543246 0.839574i \(-0.317195\pi\)
0.543246 + 0.839574i \(0.317195\pi\)
\(864\) −746496. −0.0340207
\(865\) −5.67877e6 −0.258056
\(866\) −5.91384e6 −0.267963
\(867\) 8.84534e6 0.399638
\(868\) 3.42150e6 0.154141
\(869\) −1.51794e7 −0.681876
\(870\) 427410. 0.0191446
\(871\) 1.00520e7 0.448958
\(872\) 5.77183e6 0.257053
\(873\) 8.16401e6 0.362550
\(874\) 1.29022e6 0.0571326
\(875\) −1.37575e6 −0.0607461
\(876\) 1.96973e6 0.0867254
\(877\) 3.15706e7 1.38607 0.693034 0.720905i \(-0.256274\pi\)
0.693034 + 0.720905i \(0.256274\pi\)
\(878\) 6.31770e6 0.276581
\(879\) −4.34195e6 −0.189545
\(880\) 4.30966e6 0.187601
\(881\) −2.85376e7 −1.23873 −0.619366 0.785103i \(-0.712610\pi\)
−0.619366 + 0.785103i \(0.712610\pi\)
\(882\) 2.93369e6 0.126982
\(883\) 9.21266e6 0.397634 0.198817 0.980037i \(-0.436290\pi\)
0.198817 + 0.980037i \(0.436290\pi\)
\(884\) 9.47453e6 0.407781
\(885\) 4.56053e6 0.195730
\(886\) 1.72867e7 0.739824
\(887\) 2.35055e7 1.00314 0.501569 0.865118i \(-0.332756\pi\)
0.501569 + 0.865118i \(0.332756\pi\)
\(888\) 2.52982e6 0.107661
\(889\) −1.25847e6 −0.0534058
\(890\) 5.85102e6 0.247603
\(891\) 4.41807e6 0.186440
\(892\) −3.85792e6 −0.162346
\(893\) 5.69561e6 0.239008
\(894\) −2.95840e6 −0.123798
\(895\) −2.03078e6 −0.0847433
\(896\) 1.44257e6 0.0600300
\(897\) −3.07205e6 −0.127481
\(898\) −1.10806e7 −0.458534
\(899\) 1.15340e6 0.0475971
\(900\) 810000. 0.0333333
\(901\) 2.19987e7 0.902788
\(902\) −671671. −0.0274878
\(903\) 1.62557e6 0.0663416
\(904\) 113300. 0.00461116
\(905\) 1.68426e7 0.683579
\(906\) −9.84146e6 −0.398326
\(907\) −2.79846e7 −1.12954 −0.564770 0.825249i \(-0.691035\pi\)
−0.564770 + 0.825249i \(0.691035\pi\)
\(908\) 4.80370e6 0.193358
\(909\) 47716.2 0.00191538
\(910\) 3.36363e6 0.134650
\(911\) 1.34431e7 0.536664 0.268332 0.963326i \(-0.413528\pi\)
0.268332 + 0.963326i \(0.413528\pi\)
\(912\) 831744. 0.0331133
\(913\) 4.04674e7 1.60668
\(914\) −4.47218e6 −0.177073
\(915\) −1.20942e6 −0.0477554
\(916\) 1.35359e7 0.533024
\(917\) −1.17592e7 −0.461799
\(918\) −4.51996e6 −0.177022
\(919\) 2.58583e7 1.00997 0.504987 0.863127i \(-0.331497\pi\)
0.504987 + 0.863127i \(0.331497\pi\)
\(920\) 1.42960e6 0.0556860
\(921\) 2.09587e7 0.814172
\(922\) −2.44912e7 −0.948816
\(923\) −2.35210e7 −0.908763
\(924\) −8.53775e6 −0.328975
\(925\) −2.74503e6 −0.105486
\(926\) 126712. 0.00485615
\(927\) 6.83840e6 0.261370
\(928\) 486297. 0.0185367
\(929\) −4.95947e7 −1.88537 −0.942683 0.333690i \(-0.891706\pi\)
−0.942683 + 0.333690i \(0.891706\pi\)
\(930\) 2.18585e6 0.0828731
\(931\) −3.26871e6 −0.123595
\(932\) 1.63957e7 0.618289
\(933\) −5.52038e6 −0.207618
\(934\) 4.31815e6 0.161969
\(935\) 2.60946e7 0.976160
\(936\) −1.98041e6 −0.0738866
\(937\) 4.19963e7 1.56265 0.781325 0.624124i \(-0.214544\pi\)
0.781325 + 0.624124i \(0.214544\pi\)
\(938\) 9.26700e6 0.343900
\(939\) 2.89096e7 1.06999
\(940\) 6.31093e6 0.232956
\(941\) 1.99145e7 0.733155 0.366578 0.930387i \(-0.380529\pi\)
0.366578 + 0.930387i \(0.380529\pi\)
\(942\) −1.71923e7 −0.631256
\(943\) −222807. −0.00815925
\(944\) 5.18887e6 0.189515
\(945\) −1.60467e6 −0.0584529
\(946\) 5.52545e6 0.200743
\(947\) 2.56341e7 0.928845 0.464422 0.885614i \(-0.346262\pi\)
0.464422 + 0.885614i \(0.346262\pi\)
\(948\) −3.24604e6 −0.117310
\(949\) 5.22558e6 0.188351
\(950\) −902500. −0.0324443
\(951\) −7.39772e6 −0.265245
\(952\) 8.73465e6 0.312358
\(953\) −1.32428e7 −0.472332 −0.236166 0.971713i \(-0.575891\pi\)
−0.236166 + 0.971713i \(0.575891\pi\)
\(954\) −4.59828e6 −0.163578
\(955\) 8.40259e6 0.298129
\(956\) −1.06374e7 −0.376436
\(957\) −2.87811e6 −0.101584
\(958\) 2.16795e7 0.763194
\(959\) −3.35946e6 −0.117957
\(960\) 921600. 0.0322749
\(961\) −2.27304e7 −0.793962
\(962\) 6.71147e6 0.233819
\(963\) −9.75970e6 −0.339134
\(964\) 1.41023e7 0.488763
\(965\) −2.04971e7 −0.708557
\(966\) −2.83215e6 −0.0976502
\(967\) 6.56406e6 0.225739 0.112869 0.993610i \(-0.463996\pi\)
0.112869 + 0.993610i \(0.463996\pi\)
\(968\) −1.87133e7 −0.641891
\(969\) 5.03613e6 0.172301
\(970\) −1.00790e7 −0.343945
\(971\) −1.63815e7 −0.557576 −0.278788 0.960353i \(-0.589933\pi\)
−0.278788 + 0.960353i \(0.589933\pi\)
\(972\) 944784. 0.0320750
\(973\) −7.51079e6 −0.254334
\(974\) −3.70984e7 −1.25302
\(975\) 2.14888e6 0.0723938
\(976\) −1.37605e6 −0.0462390
\(977\) −2.41670e7 −0.810004 −0.405002 0.914316i \(-0.632729\pi\)
−0.405002 + 0.914316i \(0.632729\pi\)
\(978\) −1.44145e7 −0.481896
\(979\) −3.93998e7 −1.31382
\(980\) −3.62184e6 −0.120466
\(981\) −7.30497e6 −0.242352
\(982\) 1.66365e7 0.550534
\(983\) 3.12684e7 1.03210 0.516050 0.856559i \(-0.327402\pi\)
0.516050 + 0.856559i \(0.327402\pi\)
\(984\) −143634. −0.00472899
\(985\) −5.27817e6 −0.173338
\(986\) 2.94448e6 0.0964532
\(987\) −1.25024e7 −0.408508
\(988\) 2.20657e6 0.0719159
\(989\) 1.83291e6 0.0595867
\(990\) −5.45441e6 −0.176872
\(991\) −1.95796e7 −0.633315 −0.316657 0.948540i \(-0.602561\pi\)
−0.316657 + 0.948540i \(0.602561\pi\)
\(992\) 2.48701e6 0.0802415
\(993\) 127022. 0.00408796
\(994\) −2.16842e7 −0.696108
\(995\) −8.88244e6 −0.284430
\(996\) 8.65377e6 0.276412
\(997\) −2.79862e7 −0.891675 −0.445838 0.895114i \(-0.647094\pi\)
−0.445838 + 0.895114i \(0.647094\pi\)
\(998\) 3.71128e7 1.17950
\(999\) −3.20181e6 −0.101504
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.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.m.1.1 4 1.1 even 1 trivial