Properties

Label 950.6.a.d.1.1
Level $950$
Weight $6$
Character 950.1
Self dual yes
Analytic conductor $152.365$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(152.364628822\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{1441}) \)
Defining polynomial: \(x^{2} - x - 360\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(19.4803\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} -20.4803 q^{3} +16.0000 q^{4} -81.9210 q^{6} +18.9210 q^{7} +64.0000 q^{8} +176.441 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -20.4803 q^{3} +16.0000 q^{4} -81.9210 q^{6} +18.9210 q^{7} +64.0000 q^{8} +176.441 q^{9} +349.480 q^{11} -327.684 q^{12} -711.599 q^{13} +75.6840 q^{14} +256.000 q^{16} -221.803 q^{17} +705.763 q^{18} +361.000 q^{19} -387.507 q^{21} +1397.92 q^{22} +662.468 q^{23} -1310.74 q^{24} -2846.39 q^{26} +1363.15 q^{27} +302.736 q^{28} -7219.28 q^{29} +5407.76 q^{31} +1024.00 q^{32} -7157.44 q^{33} -887.210 q^{34} +2823.05 q^{36} -1979.40 q^{37} +1444.00 q^{38} +14573.7 q^{39} -3111.11 q^{41} -1550.03 q^{42} -318.049 q^{43} +5591.68 q^{44} +2649.87 q^{46} +27240.5 q^{47} -5242.94 q^{48} -16449.0 q^{49} +4542.57 q^{51} -11385.6 q^{52} +1114.63 q^{53} +5452.60 q^{54} +1210.94 q^{56} -7393.37 q^{57} -28877.1 q^{58} -37904.9 q^{59} +37469.2 q^{61} +21631.0 q^{62} +3338.44 q^{63} +4096.00 q^{64} -28629.8 q^{66} +54955.3 q^{67} -3548.84 q^{68} -13567.5 q^{69} -7177.04 q^{71} +11292.2 q^{72} -64746.1 q^{73} -7917.59 q^{74} +5776.00 q^{76} +6612.52 q^{77} +58294.9 q^{78} +36104.4 q^{79} -70792.8 q^{81} -12444.4 q^{82} +51782.7 q^{83} -6200.11 q^{84} -1272.20 q^{86} +147853. q^{87} +22366.7 q^{88} +145254. q^{89} -13464.2 q^{91} +10599.5 q^{92} -110752. q^{93} +108962. q^{94} -20971.8 q^{96} -39512.8 q^{97} -65796.0 q^{98} +61662.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 8q^{2} - 3q^{3} + 32q^{4} - 12q^{6} - 114q^{7} + 128q^{8} + 239q^{9} + O(q^{10}) \) \( 2q + 8q^{2} - 3q^{3} + 32q^{4} - 12q^{6} - 114q^{7} + 128q^{8} + 239q^{9} + 661q^{11} - 48q^{12} - 1613q^{13} - 456q^{14} + 512q^{16} - 64q^{17} + 956q^{18} + 722q^{19} - 2711q^{21} + 2644q^{22} + 3185q^{23} - 192q^{24} - 6452q^{26} - 1791q^{27} - 1824q^{28} - 2481q^{29} - 1180q^{31} + 2048q^{32} - 1712q^{33} - 256q^{34} + 3824q^{36} - 10488q^{37} + 2888q^{38} - 1183q^{39} + 16630q^{41} - 10844q^{42} - 11303q^{43} + 10576q^{44} + 12740q^{46} + 12155q^{47} - 768q^{48} - 15588q^{49} + 7301q^{51} - 25808q^{52} - 20585q^{53} - 7164q^{54} - 7296q^{56} - 1083q^{57} - 9924q^{58} - 78581q^{59} + 43621q^{61} - 4720q^{62} - 4977q^{63} + 8192q^{64} - 6848q^{66} - 7805q^{67} - 1024q^{68} + 30527q^{69} - 62488q^{71} + 15296q^{72} - 16218q^{73} - 41952q^{74} + 11552q^{76} - 34795q^{77} - 4732q^{78} + 67122q^{79} - 141130q^{81} + 66520q^{82} + 10714q^{83} - 43376q^{84} - 45212q^{86} + 230679q^{87} + 42304q^{88} + 128188q^{89} + 106351q^{91} + 50960q^{92} - 225908q^{93} + 48620q^{94} - 3072q^{96} - 178558q^{97} - 62352q^{98} + 81151q^{99} + O(q^{100}) \)

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
\(3\) −20.4803 −1.31381 −0.656904 0.753974i \(-0.728135\pi\)
−0.656904 + 0.753974i \(0.728135\pi\)
\(4\) 16.0000 0.500000
\(5\) 0 0
\(6\) −81.9210 −0.929003
\(7\) 18.9210 0.145948 0.0729742 0.997334i \(-0.476751\pi\)
0.0729742 + 0.997334i \(0.476751\pi\)
\(8\) 64.0000 0.353553
\(9\) 176.441 0.726094
\(10\) 0 0
\(11\) 349.480 0.870845 0.435423 0.900226i \(-0.356599\pi\)
0.435423 + 0.900226i \(0.356599\pi\)
\(12\) −327.684 −0.656904
\(13\) −711.599 −1.16782 −0.583911 0.811818i \(-0.698478\pi\)
−0.583911 + 0.811818i \(0.698478\pi\)
\(14\) 75.6840 0.103201
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) −221.803 −0.186142 −0.0930710 0.995659i \(-0.529668\pi\)
−0.0930710 + 0.995659i \(0.529668\pi\)
\(18\) 705.763 0.513426
\(19\) 361.000 0.229416
\(20\) 0 0
\(21\) −387.507 −0.191748
\(22\) 1397.92 0.615780
\(23\) 662.468 0.261123 0.130561 0.991440i \(-0.458322\pi\)
0.130561 + 0.991440i \(0.458322\pi\)
\(24\) −1310.74 −0.464502
\(25\) 0 0
\(26\) −2846.39 −0.825775
\(27\) 1363.15 0.359861
\(28\) 302.736 0.0729742
\(29\) −7219.28 −1.59404 −0.797019 0.603954i \(-0.793591\pi\)
−0.797019 + 0.603954i \(0.793591\pi\)
\(30\) 0 0
\(31\) 5407.76 1.01068 0.505339 0.862921i \(-0.331367\pi\)
0.505339 + 0.862921i \(0.331367\pi\)
\(32\) 1024.00 0.176777
\(33\) −7157.44 −1.14412
\(34\) −887.210 −0.131622
\(35\) 0 0
\(36\) 2823.05 0.363047
\(37\) −1979.40 −0.237700 −0.118850 0.992912i \(-0.537921\pi\)
−0.118850 + 0.992912i \(0.537921\pi\)
\(38\) 1444.00 0.162221
\(39\) 14573.7 1.53430
\(40\) 0 0
\(41\) −3111.11 −0.289039 −0.144519 0.989502i \(-0.546164\pi\)
−0.144519 + 0.989502i \(0.546164\pi\)
\(42\) −1550.03 −0.135586
\(43\) −318.049 −0.0262315 −0.0131157 0.999914i \(-0.504175\pi\)
−0.0131157 + 0.999914i \(0.504175\pi\)
\(44\) 5591.68 0.435423
\(45\) 0 0
\(46\) 2649.87 0.184642
\(47\) 27240.5 1.79875 0.899374 0.437181i \(-0.144023\pi\)
0.899374 + 0.437181i \(0.144023\pi\)
\(48\) −5242.94 −0.328452
\(49\) −16449.0 −0.978699
\(50\) 0 0
\(51\) 4542.57 0.244555
\(52\) −11385.6 −0.583911
\(53\) 1114.63 0.0545057 0.0272528 0.999629i \(-0.491324\pi\)
0.0272528 + 0.999629i \(0.491324\pi\)
\(54\) 5452.60 0.254460
\(55\) 0 0
\(56\) 1210.94 0.0516005
\(57\) −7393.37 −0.301408
\(58\) −28877.1 −1.12716
\(59\) −37904.9 −1.41764 −0.708820 0.705390i \(-0.750772\pi\)
−0.708820 + 0.705390i \(0.750772\pi\)
\(60\) 0 0
\(61\) 37469.2 1.28929 0.644644 0.764483i \(-0.277006\pi\)
0.644644 + 0.764483i \(0.277006\pi\)
\(62\) 21631.0 0.714658
\(63\) 3338.44 0.105972
\(64\) 4096.00 0.125000
\(65\) 0 0
\(66\) −28629.8 −0.809018
\(67\) 54955.3 1.49562 0.747812 0.663911i \(-0.231105\pi\)
0.747812 + 0.663911i \(0.231105\pi\)
\(68\) −3548.84 −0.0930710
\(69\) −13567.5 −0.343066
\(70\) 0 0
\(71\) −7177.04 −0.168966 −0.0844830 0.996425i \(-0.526924\pi\)
−0.0844830 + 0.996425i \(0.526924\pi\)
\(72\) 11292.2 0.256713
\(73\) −64746.1 −1.42202 −0.711011 0.703181i \(-0.751762\pi\)
−0.711011 + 0.703181i \(0.751762\pi\)
\(74\) −7917.59 −0.168079
\(75\) 0 0
\(76\) 5776.00 0.114708
\(77\) 6612.52 0.127098
\(78\) 58294.9 1.08491
\(79\) 36104.4 0.650866 0.325433 0.945565i \(-0.394490\pi\)
0.325433 + 0.945565i \(0.394490\pi\)
\(80\) 0 0
\(81\) −70792.8 −1.19888
\(82\) −12444.4 −0.204381
\(83\) 51782.7 0.825067 0.412534 0.910942i \(-0.364644\pi\)
0.412534 + 0.910942i \(0.364644\pi\)
\(84\) −6200.11 −0.0958741
\(85\) 0 0
\(86\) −1272.20 −0.0185485
\(87\) 147853. 2.09426
\(88\) 22366.7 0.307890
\(89\) 145254. 1.94380 0.971900 0.235392i \(-0.0756375\pi\)
0.971900 + 0.235392i \(0.0756375\pi\)
\(90\) 0 0
\(91\) −13464.2 −0.170442
\(92\) 10599.5 0.130561
\(93\) −110752. −1.32784
\(94\) 108962. 1.27191
\(95\) 0 0
\(96\) −20971.8 −0.232251
\(97\) −39512.8 −0.426391 −0.213196 0.977010i \(-0.568387\pi\)
−0.213196 + 0.977010i \(0.568387\pi\)
\(98\) −65796.0 −0.692045
\(99\) 61662.6 0.632315
\(100\) 0 0
\(101\) −16722.9 −0.163120 −0.0815602 0.996668i \(-0.525990\pi\)
−0.0815602 + 0.996668i \(0.525990\pi\)
\(102\) 18170.3 0.172926
\(103\) −92664.4 −0.860636 −0.430318 0.902677i \(-0.641599\pi\)
−0.430318 + 0.902677i \(0.641599\pi\)
\(104\) −45542.3 −0.412888
\(105\) 0 0
\(106\) 4458.53 0.0385413
\(107\) 47156.3 0.398180 0.199090 0.979981i \(-0.436201\pi\)
0.199090 + 0.979981i \(0.436201\pi\)
\(108\) 21810.4 0.179930
\(109\) 52450.1 0.422844 0.211422 0.977395i \(-0.432191\pi\)
0.211422 + 0.977395i \(0.432191\pi\)
\(110\) 0 0
\(111\) 40538.5 0.312292
\(112\) 4843.78 0.0364871
\(113\) −150596. −1.10947 −0.554737 0.832026i \(-0.687181\pi\)
−0.554737 + 0.832026i \(0.687181\pi\)
\(114\) −29573.5 −0.213128
\(115\) 0 0
\(116\) −115508. −0.797019
\(117\) −125555. −0.847948
\(118\) −151620. −1.00242
\(119\) −4196.73 −0.0271671
\(120\) 0 0
\(121\) −38914.6 −0.241629
\(122\) 149877. 0.911664
\(123\) 63716.4 0.379742
\(124\) 86524.2 0.505339
\(125\) 0 0
\(126\) 13353.8 0.0749337
\(127\) −352240. −1.93789 −0.968945 0.247276i \(-0.920465\pi\)
−0.968945 + 0.247276i \(0.920465\pi\)
\(128\) 16384.0 0.0883883
\(129\) 6513.72 0.0344632
\(130\) 0 0
\(131\) 19070.2 0.0970907 0.0485453 0.998821i \(-0.484541\pi\)
0.0485453 + 0.998821i \(0.484541\pi\)
\(132\) −114519. −0.572062
\(133\) 6830.49 0.0334829
\(134\) 219821. 1.05757
\(135\) 0 0
\(136\) −14195.4 −0.0658111
\(137\) 266677. 1.21390 0.606952 0.794738i \(-0.292392\pi\)
0.606952 + 0.794738i \(0.292392\pi\)
\(138\) −54270.0 −0.242584
\(139\) −294888. −1.29456 −0.647278 0.762254i \(-0.724093\pi\)
−0.647278 + 0.762254i \(0.724093\pi\)
\(140\) 0 0
\(141\) −557892. −2.36321
\(142\) −28708.2 −0.119477
\(143\) −248690. −1.01699
\(144\) 45168.8 0.181523
\(145\) 0 0
\(146\) −258984. −1.00552
\(147\) 336880. 1.28582
\(148\) −31670.3 −0.118850
\(149\) −103990. −0.383729 −0.191864 0.981421i \(-0.561453\pi\)
−0.191864 + 0.981421i \(0.561453\pi\)
\(150\) 0 0
\(151\) −477343. −1.70368 −0.851840 0.523802i \(-0.824513\pi\)
−0.851840 + 0.523802i \(0.824513\pi\)
\(152\) 23104.0 0.0811107
\(153\) −39135.0 −0.135156
\(154\) 26450.1 0.0898722
\(155\) 0 0
\(156\) 233180. 0.767148
\(157\) −434955. −1.40830 −0.704151 0.710051i \(-0.748672\pi\)
−0.704151 + 0.710051i \(0.748672\pi\)
\(158\) 144417. 0.460232
\(159\) −22827.9 −0.0716101
\(160\) 0 0
\(161\) 12534.6 0.0381105
\(162\) −283171. −0.847737
\(163\) 255083. 0.751990 0.375995 0.926622i \(-0.377301\pi\)
0.375995 + 0.926622i \(0.377301\pi\)
\(164\) −49777.8 −0.144519
\(165\) 0 0
\(166\) 207131. 0.583411
\(167\) −510501. −1.41646 −0.708232 0.705980i \(-0.750507\pi\)
−0.708232 + 0.705980i \(0.750507\pi\)
\(168\) −24800.5 −0.0677932
\(169\) 135080. 0.363809
\(170\) 0 0
\(171\) 63695.1 0.166577
\(172\) −5088.78 −0.0131157
\(173\) −773453. −1.96480 −0.982401 0.186783i \(-0.940194\pi\)
−0.982401 + 0.186783i \(0.940194\pi\)
\(174\) 591411. 1.48087
\(175\) 0 0
\(176\) 89466.9 0.217711
\(177\) 776303. 1.86251
\(178\) 581014. 1.37447
\(179\) −477664. −1.11427 −0.557135 0.830422i \(-0.688099\pi\)
−0.557135 + 0.830422i \(0.688099\pi\)
\(180\) 0 0
\(181\) 729114. 1.65424 0.827121 0.562024i \(-0.189977\pi\)
0.827121 + 0.562024i \(0.189977\pi\)
\(182\) −53856.7 −0.120521
\(183\) −767379. −1.69388
\(184\) 42397.9 0.0923209
\(185\) 0 0
\(186\) −443009. −0.938924
\(187\) −77515.6 −0.162101
\(188\) 435848. 0.899374
\(189\) 25792.2 0.0525211
\(190\) 0 0
\(191\) −285584. −0.566435 −0.283218 0.959056i \(-0.591402\pi\)
−0.283218 + 0.959056i \(0.591402\pi\)
\(192\) −83887.1 −0.164226
\(193\) 53690.2 0.103753 0.0518766 0.998654i \(-0.483480\pi\)
0.0518766 + 0.998654i \(0.483480\pi\)
\(194\) −158051. −0.301504
\(195\) 0 0
\(196\) −263184. −0.489350
\(197\) −14538.9 −0.0266910 −0.0133455 0.999911i \(-0.504248\pi\)
−0.0133455 + 0.999911i \(0.504248\pi\)
\(198\) 246650. 0.447114
\(199\) −143700. −0.257232 −0.128616 0.991695i \(-0.541053\pi\)
−0.128616 + 0.991695i \(0.541053\pi\)
\(200\) 0 0
\(201\) −1.12550e6 −1.96496
\(202\) −66891.6 −0.115343
\(203\) −136596. −0.232647
\(204\) 72681.2 0.122277
\(205\) 0 0
\(206\) −370658. −0.608562
\(207\) 116886. 0.189600
\(208\) −182169. −0.291956
\(209\) 126162. 0.199786
\(210\) 0 0
\(211\) 83653.6 0.129354 0.0646768 0.997906i \(-0.479398\pi\)
0.0646768 + 0.997906i \(0.479398\pi\)
\(212\) 17834.1 0.0272528
\(213\) 146988. 0.221989
\(214\) 188625. 0.281556
\(215\) 0 0
\(216\) 87241.6 0.127230
\(217\) 102320. 0.147507
\(218\) 209800. 0.298996
\(219\) 1.32602e6 1.86826
\(220\) 0 0
\(221\) 157834. 0.217381
\(222\) 162154. 0.220824
\(223\) 665414. 0.896045 0.448022 0.894022i \(-0.352128\pi\)
0.448022 + 0.894022i \(0.352128\pi\)
\(224\) 19375.1 0.0258003
\(225\) 0 0
\(226\) −602384. −0.784517
\(227\) −1.15382e6 −1.48619 −0.743096 0.669185i \(-0.766643\pi\)
−0.743096 + 0.669185i \(0.766643\pi\)
\(228\) −118294. −0.150704
\(229\) −433691. −0.546502 −0.273251 0.961943i \(-0.588099\pi\)
−0.273251 + 0.961943i \(0.588099\pi\)
\(230\) 0 0
\(231\) −135426. −0.166983
\(232\) −462034. −0.563578
\(233\) −387173. −0.467214 −0.233607 0.972331i \(-0.575053\pi\)
−0.233607 + 0.972331i \(0.575053\pi\)
\(234\) −502220. −0.599590
\(235\) 0 0
\(236\) −606479. −0.708820
\(237\) −739426. −0.855114
\(238\) −16786.9 −0.0192100
\(239\) −622463. −0.704886 −0.352443 0.935833i \(-0.614649\pi\)
−0.352443 + 0.935833i \(0.614649\pi\)
\(240\) 0 0
\(241\) −371454. −0.411967 −0.205984 0.978555i \(-0.566039\pi\)
−0.205984 + 0.978555i \(0.566039\pi\)
\(242\) −155658. −0.170857
\(243\) 1.11861e6 1.21524
\(244\) 599507. 0.644644
\(245\) 0 0
\(246\) 254865. 0.268518
\(247\) −256887. −0.267917
\(248\) 346097. 0.357329
\(249\) −1.06052e6 −1.08398
\(250\) 0 0
\(251\) 376098. 0.376805 0.188403 0.982092i \(-0.439669\pi\)
0.188403 + 0.982092i \(0.439669\pi\)
\(252\) 53415.0 0.0529861
\(253\) 231519. 0.227398
\(254\) −1.40896e6 −1.37030
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) −1.64382e6 −1.55247 −0.776233 0.630446i \(-0.782872\pi\)
−0.776233 + 0.630446i \(0.782872\pi\)
\(258\) 26054.9 0.0243691
\(259\) −37452.2 −0.0346919
\(260\) 0 0
\(261\) −1.27378e6 −1.15742
\(262\) 76280.9 0.0686535
\(263\) −775299. −0.691162 −0.345581 0.938389i \(-0.612318\pi\)
−0.345581 + 0.938389i \(0.612318\pi\)
\(264\) −458076. −0.404509
\(265\) 0 0
\(266\) 27321.9 0.0236760
\(267\) −2.97483e6 −2.55378
\(268\) 879284. 0.747812
\(269\) 334851. 0.282144 0.141072 0.989999i \(-0.454945\pi\)
0.141072 + 0.989999i \(0.454945\pi\)
\(270\) 0 0
\(271\) 893377. 0.738944 0.369472 0.929242i \(-0.379539\pi\)
0.369472 + 0.929242i \(0.379539\pi\)
\(272\) −56781.4 −0.0465355
\(273\) 275750. 0.223928
\(274\) 1.06671e6 0.858360
\(275\) 0 0
\(276\) −217080. −0.171533
\(277\) 1.13462e6 0.888483 0.444242 0.895907i \(-0.353473\pi\)
0.444242 + 0.895907i \(0.353473\pi\)
\(278\) −1.17955e6 −0.915389
\(279\) 954149. 0.733847
\(280\) 0 0
\(281\) −1.98111e6 −1.49672 −0.748362 0.663290i \(-0.769159\pi\)
−0.748362 + 0.663290i \(0.769159\pi\)
\(282\) −2.23157e6 −1.67104
\(283\) −1.32192e6 −0.981161 −0.490580 0.871396i \(-0.663215\pi\)
−0.490580 + 0.871396i \(0.663215\pi\)
\(284\) −114833. −0.0844830
\(285\) 0 0
\(286\) −994759. −0.719122
\(287\) −58865.4 −0.0421847
\(288\) 180675. 0.128356
\(289\) −1.37066e6 −0.965351
\(290\) 0 0
\(291\) 809232. 0.560197
\(292\) −1.03594e6 −0.711011
\(293\) −1.35808e6 −0.924179 −0.462089 0.886833i \(-0.652900\pi\)
−0.462089 + 0.886833i \(0.652900\pi\)
\(294\) 1.34752e6 0.909215
\(295\) 0 0
\(296\) −126681. −0.0840395
\(297\) 476394. 0.313383
\(298\) −415959. −0.271337
\(299\) −471411. −0.304945
\(300\) 0 0
\(301\) −6017.81 −0.00382844
\(302\) −1.90937e6 −1.20468
\(303\) 342489. 0.214309
\(304\) 92416.0 0.0573539
\(305\) 0 0
\(306\) −156540. −0.0955701
\(307\) 1.23842e6 0.749930 0.374965 0.927039i \(-0.377655\pi\)
0.374965 + 0.927039i \(0.377655\pi\)
\(308\) 105800. 0.0635492
\(309\) 1.89779e6 1.13071
\(310\) 0 0
\(311\) −1.78565e6 −1.04688 −0.523439 0.852063i \(-0.675351\pi\)
−0.523439 + 0.852063i \(0.675351\pi\)
\(312\) 932718. 0.542455
\(313\) 3.01608e6 1.74013 0.870066 0.492935i \(-0.164076\pi\)
0.870066 + 0.492935i \(0.164076\pi\)
\(314\) −1.73982e6 −0.995819
\(315\) 0 0
\(316\) 577670. 0.325433
\(317\) −515839. −0.288314 −0.144157 0.989555i \(-0.546047\pi\)
−0.144157 + 0.989555i \(0.546047\pi\)
\(318\) −91311.8 −0.0506360
\(319\) −2.52300e6 −1.38816
\(320\) 0 0
\(321\) −965772. −0.523133
\(322\) 50138.2 0.0269482
\(323\) −80070.7 −0.0427039
\(324\) −1.13268e6 −0.599441
\(325\) 0 0
\(326\) 1.02033e6 0.531737
\(327\) −1.07419e6 −0.555536
\(328\) −199111. −0.102191
\(329\) 515417. 0.262524
\(330\) 0 0
\(331\) −2.25449e6 −1.13104 −0.565521 0.824734i \(-0.691325\pi\)
−0.565521 + 0.824734i \(0.691325\pi\)
\(332\) 828523. 0.412534
\(333\) −349246. −0.172592
\(334\) −2.04200e6 −1.00159
\(335\) 0 0
\(336\) −99201.8 −0.0479371
\(337\) −2.40261e6 −1.15242 −0.576208 0.817303i \(-0.695468\pi\)
−0.576208 + 0.817303i \(0.695468\pi\)
\(338\) 540319. 0.257252
\(339\) 3.08424e6 1.45764
\(340\) 0 0
\(341\) 1.88991e6 0.880145
\(342\) 254780. 0.117788
\(343\) −629237. −0.288788
\(344\) −20355.1 −0.00927423
\(345\) 0 0
\(346\) −3.09381e6 −1.38933
\(347\) 684693. 0.305262 0.152631 0.988283i \(-0.451225\pi\)
0.152631 + 0.988283i \(0.451225\pi\)
\(348\) 2.36564e6 1.04713
\(349\) 2.19857e6 0.966220 0.483110 0.875560i \(-0.339507\pi\)
0.483110 + 0.875560i \(0.339507\pi\)
\(350\) 0 0
\(351\) −970016. −0.420253
\(352\) 357868. 0.153945
\(353\) −2.03446e6 −0.868987 −0.434493 0.900675i \(-0.643073\pi\)
−0.434493 + 0.900675i \(0.643073\pi\)
\(354\) 3.10521e6 1.31699
\(355\) 0 0
\(356\) 2.32406e6 0.971900
\(357\) 85950.1 0.0356924
\(358\) −1.91066e6 −0.787907
\(359\) 2.30592e6 0.944298 0.472149 0.881519i \(-0.343478\pi\)
0.472149 + 0.881519i \(0.343478\pi\)
\(360\) 0 0
\(361\) 130321. 0.0526316
\(362\) 2.91646e6 1.16973
\(363\) 796980. 0.317454
\(364\) −215427. −0.0852209
\(365\) 0 0
\(366\) −3.06952e6 −1.19775
\(367\) −2.64475e6 −1.02499 −0.512495 0.858690i \(-0.671279\pi\)
−0.512495 + 0.858690i \(0.671279\pi\)
\(368\) 169592. 0.0652807
\(369\) −548927. −0.209869
\(370\) 0 0
\(371\) 21090.0 0.00795502
\(372\) −1.77204e6 −0.663919
\(373\) −173405. −0.0645342 −0.0322671 0.999479i \(-0.510273\pi\)
−0.0322671 + 0.999479i \(0.510273\pi\)
\(374\) −310062. −0.114623
\(375\) 0 0
\(376\) 1.74339e6 0.635953
\(377\) 5.13723e6 1.86155
\(378\) 103169. 0.0371380
\(379\) 2.23408e6 0.798915 0.399458 0.916752i \(-0.369198\pi\)
0.399458 + 0.916752i \(0.369198\pi\)
\(380\) 0 0
\(381\) 7.21396e6 2.54602
\(382\) −1.14234e6 −0.400530
\(383\) 4.44976e6 1.55003 0.775014 0.631944i \(-0.217743\pi\)
0.775014 + 0.631944i \(0.217743\pi\)
\(384\) −335548. −0.116125
\(385\) 0 0
\(386\) 214761. 0.0733646
\(387\) −56116.8 −0.0190465
\(388\) −632204. −0.213196
\(389\) 2.43083e6 0.814480 0.407240 0.913321i \(-0.366491\pi\)
0.407240 + 0.913321i \(0.366491\pi\)
\(390\) 0 0
\(391\) −146937. −0.0486059
\(392\) −1.05274e6 −0.346022
\(393\) −390563. −0.127559
\(394\) −58155.5 −0.0188734
\(395\) 0 0
\(396\) 986601. 0.316158
\(397\) −2.61205e6 −0.831775 −0.415887 0.909416i \(-0.636529\pi\)
−0.415887 + 0.909416i \(0.636529\pi\)
\(398\) −574800. −0.181890
\(399\) −139890. −0.0439901
\(400\) 0 0
\(401\) 1.42660e6 0.443038 0.221519 0.975156i \(-0.428899\pi\)
0.221519 + 0.975156i \(0.428899\pi\)
\(402\) −4.50199e6 −1.38944
\(403\) −3.84816e6 −1.18029
\(404\) −267566. −0.0815602
\(405\) 0 0
\(406\) −546384. −0.164507
\(407\) −691760. −0.207000
\(408\) 290725. 0.0864632
\(409\) 4.73321e6 1.39910 0.699548 0.714586i \(-0.253385\pi\)
0.699548 + 0.714586i \(0.253385\pi\)
\(410\) 0 0
\(411\) −5.46162e6 −1.59484
\(412\) −1.48263e6 −0.430318
\(413\) −717200. −0.206902
\(414\) 467545. 0.134067
\(415\) 0 0
\(416\) −728677. −0.206444
\(417\) 6.03939e6 1.70080
\(418\) 504649. 0.141270
\(419\) −357759. −0.0995531 −0.0497766 0.998760i \(-0.515851\pi\)
−0.0497766 + 0.998760i \(0.515851\pi\)
\(420\) 0 0
\(421\) 652504. 0.179423 0.0897115 0.995968i \(-0.471405\pi\)
0.0897115 + 0.995968i \(0.471405\pi\)
\(422\) 334614. 0.0914668
\(423\) 4.80633e6 1.30606
\(424\) 71336.4 0.0192707
\(425\) 0 0
\(426\) 587950. 0.156970
\(427\) 708955. 0.188169
\(428\) 754500. 0.199090
\(429\) 5.09323e6 1.33613
\(430\) 0 0
\(431\) −6.25148e6 −1.62103 −0.810513 0.585721i \(-0.800812\pi\)
−0.810513 + 0.585721i \(0.800812\pi\)
\(432\) 348966. 0.0899651
\(433\) −4.45832e6 −1.14275 −0.571375 0.820689i \(-0.693590\pi\)
−0.571375 + 0.820689i \(0.693590\pi\)
\(434\) 409281. 0.104303
\(435\) 0 0
\(436\) 839201. 0.211422
\(437\) 239151. 0.0599057
\(438\) 5.30406e6 1.32106
\(439\) 5.00652e6 1.23986 0.619932 0.784655i \(-0.287160\pi\)
0.619932 + 0.784655i \(0.287160\pi\)
\(440\) 0 0
\(441\) −2.90227e6 −0.710627
\(442\) 631338. 0.153711
\(443\) −715908. −0.173320 −0.0866599 0.996238i \(-0.527619\pi\)
−0.0866599 + 0.996238i \(0.527619\pi\)
\(444\) 648617. 0.156146
\(445\) 0 0
\(446\) 2.66166e6 0.633599
\(447\) 2.12974e6 0.504147
\(448\) 77500.5 0.0182435
\(449\) −4.83183e6 −1.13109 −0.565544 0.824718i \(-0.691334\pi\)
−0.565544 + 0.824718i \(0.691334\pi\)
\(450\) 0 0
\(451\) −1.08727e6 −0.251708
\(452\) −2.40954e6 −0.554737
\(453\) 9.77610e6 2.23831
\(454\) −4.61530e6 −1.05090
\(455\) 0 0
\(456\) −473176. −0.106564
\(457\) 6.44410e6 1.44335 0.721675 0.692232i \(-0.243372\pi\)
0.721675 + 0.692232i \(0.243372\pi\)
\(458\) −1.73477e6 −0.386436
\(459\) −302350. −0.0669851
\(460\) 0 0
\(461\) −4.10108e6 −0.898764 −0.449382 0.893340i \(-0.648356\pi\)
−0.449382 + 0.893340i \(0.648356\pi\)
\(462\) −541704. −0.118075
\(463\) −8.98683e6 −1.94829 −0.974146 0.225919i \(-0.927461\pi\)
−0.974146 + 0.225919i \(0.927461\pi\)
\(464\) −1.84814e6 −0.398510
\(465\) 0 0
\(466\) −1.54869e6 −0.330370
\(467\) 8.84409e6 1.87655 0.938276 0.345886i \(-0.112422\pi\)
0.938276 + 0.345886i \(0.112422\pi\)
\(468\) −2.00888e6 −0.423974
\(469\) 1.03981e6 0.218284
\(470\) 0 0
\(471\) 8.90800e6 1.85024
\(472\) −2.42592e6 −0.501211
\(473\) −111152. −0.0228436
\(474\) −2.95771e6 −0.604657
\(475\) 0 0
\(476\) −67147.7 −0.0135836
\(477\) 196667. 0.0395762
\(478\) −2.48985e6 −0.498430
\(479\) 2.89320e6 0.576155 0.288077 0.957607i \(-0.406984\pi\)
0.288077 + 0.957607i \(0.406984\pi\)
\(480\) 0 0
\(481\) 1.40854e6 0.277591
\(482\) −1.48582e6 −0.291305
\(483\) −256711. −0.0500699
\(484\) −622633. −0.120814
\(485\) 0 0
\(486\) 4.47443e6 0.859305
\(487\) 3.18166e6 0.607900 0.303950 0.952688i \(-0.401694\pi\)
0.303950 + 0.952688i \(0.401694\pi\)
\(488\) 2.39803e6 0.455832
\(489\) −5.22416e6 −0.987971
\(490\) 0 0
\(491\) −4.45509e6 −0.833975 −0.416987 0.908912i \(-0.636914\pi\)
−0.416987 + 0.908912i \(0.636914\pi\)
\(492\) 1.01946e6 0.189871
\(493\) 1.60125e6 0.296717
\(494\) −1.02755e6 −0.189446
\(495\) 0 0
\(496\) 1.38439e6 0.252670
\(497\) −135797. −0.0246603
\(498\) −4.24209e6 −0.766490
\(499\) 9.31472e6 1.67463 0.837315 0.546721i \(-0.184124\pi\)
0.837315 + 0.546721i \(0.184124\pi\)
\(500\) 0 0
\(501\) 1.04552e7 1.86096
\(502\) 1.50439e6 0.266442
\(503\) 2.04835e6 0.360980 0.180490 0.983577i \(-0.442232\pi\)
0.180490 + 0.983577i \(0.442232\pi\)
\(504\) 213660. 0.0374668
\(505\) 0 0
\(506\) 926077. 0.160794
\(507\) −2.76647e6 −0.477976
\(508\) −5.63584e6 −0.968945
\(509\) −166211. −0.0284358 −0.0142179 0.999899i \(-0.504526\pi\)
−0.0142179 + 0.999899i \(0.504526\pi\)
\(510\) 0 0
\(511\) −1.22506e6 −0.207542
\(512\) 262144. 0.0441942
\(513\) 492097. 0.0825577
\(514\) −6.57529e6 −1.09776
\(515\) 0 0
\(516\) 104220. 0.0172316
\(517\) 9.52001e6 1.56643
\(518\) −149809. −0.0245309
\(519\) 1.58405e7 2.58137
\(520\) 0 0
\(521\) 2.64602e6 0.427069 0.213535 0.976935i \(-0.431502\pi\)
0.213535 + 0.976935i \(0.431502\pi\)
\(522\) −5.09510e6 −0.818421
\(523\) 7.02287e6 1.12269 0.561346 0.827581i \(-0.310284\pi\)
0.561346 + 0.827581i \(0.310284\pi\)
\(524\) 305124. 0.0485453
\(525\) 0 0
\(526\) −3.10120e6 −0.488726
\(527\) −1.19945e6 −0.188130
\(528\) −1.83231e6 −0.286031
\(529\) −5.99748e6 −0.931815
\(530\) 0 0
\(531\) −6.68798e6 −1.02934
\(532\) 109288. 0.0167414
\(533\) 2.21386e6 0.337546
\(534\) −1.18993e7 −1.80580
\(535\) 0 0
\(536\) 3.51714e6 0.528783
\(537\) 9.78268e6 1.46394
\(538\) 1.33940e6 0.199506
\(539\) −5.74860e6 −0.852295
\(540\) 0 0
\(541\) 4.35066e6 0.639090 0.319545 0.947571i \(-0.396470\pi\)
0.319545 + 0.947571i \(0.396470\pi\)
\(542\) 3.57351e6 0.522512
\(543\) −1.49324e7 −2.17336
\(544\) −227126. −0.0329056
\(545\) 0 0
\(546\) 1.10300e6 0.158341
\(547\) −9.77794e6 −1.39727 −0.698633 0.715480i \(-0.746208\pi\)
−0.698633 + 0.715480i \(0.746208\pi\)
\(548\) 4.26684e6 0.606952
\(549\) 6.61110e6 0.936144
\(550\) 0 0
\(551\) −2.60616e6 −0.365698
\(552\) −868320. −0.121292
\(553\) 683131. 0.0949929
\(554\) 4.53846e6 0.628252
\(555\) 0 0
\(556\) −4.71822e6 −0.647278
\(557\) −6.69323e6 −0.914108 −0.457054 0.889439i \(-0.651095\pi\)
−0.457054 + 0.889439i \(0.651095\pi\)
\(558\) 3.81660e6 0.518909
\(559\) 226323. 0.0306337
\(560\) 0 0
\(561\) 1.58754e6 0.212969
\(562\) −7.92442e6 −1.05834
\(563\) −7.54034e6 −1.00258 −0.501291 0.865279i \(-0.667141\pi\)
−0.501291 + 0.865279i \(0.667141\pi\)
\(564\) −8.92627e6 −1.18161
\(565\) 0 0
\(566\) −5.28769e6 −0.693785
\(567\) −1.33947e6 −0.174975
\(568\) −459331. −0.0597385
\(569\) 1.34726e6 0.174450 0.0872252 0.996189i \(-0.472200\pi\)
0.0872252 + 0.996189i \(0.472200\pi\)
\(570\) 0 0
\(571\) 2.05762e6 0.264104 0.132052 0.991243i \(-0.457843\pi\)
0.132052 + 0.991243i \(0.457843\pi\)
\(572\) −3.97904e6 −0.508496
\(573\) 5.84883e6 0.744188
\(574\) −235462. −0.0298291
\(575\) 0 0
\(576\) 722701. 0.0907617
\(577\) −7.88561e6 −0.986043 −0.493021 0.870017i \(-0.664108\pi\)
−0.493021 + 0.870017i \(0.664108\pi\)
\(578\) −5.48264e6 −0.682606
\(579\) −1.09959e6 −0.136312
\(580\) 0 0
\(581\) 979781. 0.120417
\(582\) 3.23693e6 0.396119
\(583\) 389542. 0.0474660
\(584\) −4.14375e6 −0.502761
\(585\) 0 0
\(586\) −5.43232e6 −0.653493
\(587\) −1.90439e6 −0.228119 −0.114059 0.993474i \(-0.536385\pi\)
−0.114059 + 0.993474i \(0.536385\pi\)
\(588\) 5.39007e6 0.642912
\(589\) 1.95220e6 0.231866
\(590\) 0 0
\(591\) 297760. 0.0350669
\(592\) −506726. −0.0594249
\(593\) 1.35835e7 1.58626 0.793132 0.609050i \(-0.208449\pi\)
0.793132 + 0.609050i \(0.208449\pi\)
\(594\) 1.90558e6 0.221595
\(595\) 0 0
\(596\) −1.66384e6 −0.191864
\(597\) 2.94301e6 0.337953
\(598\) −1.88564e6 −0.215629
\(599\) −1.04361e7 −1.18842 −0.594212 0.804309i \(-0.702536\pi\)
−0.594212 + 0.804309i \(0.702536\pi\)
\(600\) 0 0
\(601\) −1.17196e7 −1.32351 −0.661753 0.749722i \(-0.730187\pi\)
−0.661753 + 0.749722i \(0.730187\pi\)
\(602\) −24071.2 −0.00270712
\(603\) 9.69635e6 1.08596
\(604\) −7.63749e6 −0.851840
\(605\) 0 0
\(606\) 1.36996e6 0.151539
\(607\) 7.53524e6 0.830091 0.415045 0.909801i \(-0.363766\pi\)
0.415045 + 0.909801i \(0.363766\pi\)
\(608\) 369664. 0.0405554
\(609\) 2.79752e6 0.305654
\(610\) 0 0
\(611\) −1.93843e7 −2.10062
\(612\) −626160. −0.0675782
\(613\) 4.37292e6 0.470025 0.235012 0.971992i \(-0.424487\pi\)
0.235012 + 0.971992i \(0.424487\pi\)
\(614\) 4.95366e6 0.530280
\(615\) 0 0
\(616\) 423201. 0.0449361
\(617\) 7.50595e6 0.793767 0.396883 0.917869i \(-0.370092\pi\)
0.396883 + 0.917869i \(0.370092\pi\)
\(618\) 7.59116e6 0.799534
\(619\) −1.30877e7 −1.37289 −0.686447 0.727180i \(-0.740831\pi\)
−0.686447 + 0.727180i \(0.740831\pi\)
\(620\) 0 0
\(621\) 903043. 0.0939679
\(622\) −7.14261e6 −0.740254
\(623\) 2.74834e6 0.283695
\(624\) 3.73087e6 0.383574
\(625\) 0 0
\(626\) 1.20643e7 1.23046
\(627\) −2.58384e6 −0.262480
\(628\) −6.95929e6 −0.704151
\(629\) 439035. 0.0442459
\(630\) 0 0
\(631\) 8.92096e6 0.891945 0.445972 0.895047i \(-0.352858\pi\)
0.445972 + 0.895047i \(0.352858\pi\)
\(632\) 2.31068e6 0.230116
\(633\) −1.71325e6 −0.169946
\(634\) −2.06336e6 −0.203869
\(635\) 0 0
\(636\) −365247. −0.0358050
\(637\) 1.17051e7 1.14295
\(638\) −1.00920e7 −0.981578
\(639\) −1.26632e6 −0.122685
\(640\) 0 0
\(641\) 1.45438e7 1.39808 0.699041 0.715082i \(-0.253611\pi\)
0.699041 + 0.715082i \(0.253611\pi\)
\(642\) −3.86309e6 −0.369911
\(643\) −1.45757e7 −1.39028 −0.695140 0.718874i \(-0.744658\pi\)
−0.695140 + 0.718874i \(0.744658\pi\)
\(644\) 200553. 0.0190552
\(645\) 0 0
\(646\) −320283. −0.0301962
\(647\) 2.24522e6 0.210862 0.105431 0.994427i \(-0.466378\pi\)
0.105431 + 0.994427i \(0.466378\pi\)
\(648\) −4.53074e6 −0.423869
\(649\) −1.32470e7 −1.23454
\(650\) 0 0
\(651\) −2.09555e6 −0.193796
\(652\) 4.08132e6 0.375995
\(653\) −1.54461e7 −1.41754 −0.708770 0.705440i \(-0.750749\pi\)
−0.708770 + 0.705440i \(0.750749\pi\)
\(654\) −4.29676e6 −0.392823
\(655\) 0 0
\(656\) −796445. −0.0722597
\(657\) −1.14238e7 −1.03252
\(658\) 2.06167e6 0.185633
\(659\) 8.68940e6 0.779429 0.389714 0.920936i \(-0.372574\pi\)
0.389714 + 0.920936i \(0.372574\pi\)
\(660\) 0 0
\(661\) −2.03442e7 −1.81108 −0.905538 0.424266i \(-0.860532\pi\)
−0.905538 + 0.424266i \(0.860532\pi\)
\(662\) −9.01797e6 −0.799767
\(663\) −3.23249e6 −0.285597
\(664\) 3.31409e6 0.291705
\(665\) 0 0
\(666\) −1.39698e6 −0.122041
\(667\) −4.78254e6 −0.416240
\(668\) −8.16802e6 −0.708232
\(669\) −1.36278e7 −1.17723
\(670\) 0 0
\(671\) 1.30947e7 1.12277
\(672\) −396807. −0.0338966
\(673\) −1.71139e7 −1.45650 −0.728251 0.685310i \(-0.759667\pi\)
−0.728251 + 0.685310i \(0.759667\pi\)
\(674\) −9.61045e6 −0.814881
\(675\) 0 0
\(676\) 2.16128e6 0.181905
\(677\) −2.25299e6 −0.188924 −0.0944621 0.995528i \(-0.530113\pi\)
−0.0944621 + 0.995528i \(0.530113\pi\)
\(678\) 1.23370e7 1.03071
\(679\) −747622. −0.0622311
\(680\) 0 0
\(681\) 2.36306e7 1.95257
\(682\) 7.55962e6 0.622356
\(683\) −5.33481e6 −0.437590 −0.218795 0.975771i \(-0.570213\pi\)
−0.218795 + 0.975771i \(0.570213\pi\)
\(684\) 1.01912e6 0.0832887
\(685\) 0 0
\(686\) −2.51695e6 −0.204204
\(687\) 8.88211e6 0.718000
\(688\) −81420.5 −0.00655787
\(689\) −793171. −0.0636530
\(690\) 0 0
\(691\) 8.08495e6 0.644143 0.322071 0.946715i \(-0.395621\pi\)
0.322071 + 0.946715i \(0.395621\pi\)
\(692\) −1.23753e7 −0.982401
\(693\) 1.16672e6 0.0922854
\(694\) 2.73877e6 0.215853
\(695\) 0 0
\(696\) 9.46257e6 0.740433
\(697\) 690053. 0.0538022
\(698\) 8.79427e6 0.683221
\(699\) 7.92941e6 0.613829
\(700\) 0 0
\(701\) 7.88116e6 0.605752 0.302876 0.953030i \(-0.402053\pi\)
0.302876 + 0.953030i \(0.402053\pi\)
\(702\) −3.88006e6 −0.297164
\(703\) −714562. −0.0545320
\(704\) 1.43147e6 0.108856
\(705\) 0 0
\(706\) −8.13786e6 −0.614467
\(707\) −316414. −0.0238071
\(708\) 1.24208e7 0.931254
\(709\) −2.07701e7 −1.55175 −0.775876 0.630885i \(-0.782692\pi\)
−0.775876 + 0.630885i \(0.782692\pi\)
\(710\) 0 0
\(711\) 6.37028e6 0.472590
\(712\) 9.29623e6 0.687237
\(713\) 3.58247e6 0.263911
\(714\) 343800. 0.0252383
\(715\) 0 0
\(716\) −7.64263e6 −0.557135
\(717\) 1.27482e7 0.926086
\(718\) 9.22370e6 0.667719
\(719\) 1.03826e7 0.749004 0.374502 0.927226i \(-0.377814\pi\)
0.374502 + 0.927226i \(0.377814\pi\)
\(720\) 0 0
\(721\) −1.75330e6 −0.125608
\(722\) 521284. 0.0372161
\(723\) 7.60748e6 0.541246
\(724\) 1.16658e7 0.827121
\(725\) 0 0
\(726\) 3.18792e6 0.224474
\(727\) 6.52486e6 0.457863 0.228931 0.973443i \(-0.426477\pi\)
0.228931 + 0.973443i \(0.426477\pi\)
\(728\) −861707. −0.0602603
\(729\) −5.70674e6 −0.397712
\(730\) 0 0
\(731\) 70544.1 0.00488278
\(732\) −1.22781e7 −0.846939
\(733\) 2.46101e6 0.169182 0.0845908 0.996416i \(-0.473042\pi\)
0.0845908 + 0.996416i \(0.473042\pi\)
\(734\) −1.05790e7 −0.724778
\(735\) 0 0
\(736\) 678367. 0.0461605
\(737\) 1.92058e7 1.30246
\(738\) −2.19571e6 −0.148400
\(739\) −7.33586e6 −0.494128 −0.247064 0.968999i \(-0.579466\pi\)
−0.247064 + 0.968999i \(0.579466\pi\)
\(740\) 0 0
\(741\) 5.26111e6 0.351991
\(742\) 84359.9 0.00562505
\(743\) −2.44394e7 −1.62412 −0.812060 0.583574i \(-0.801654\pi\)
−0.812060 + 0.583574i \(0.801654\pi\)
\(744\) −7.08815e6 −0.469462
\(745\) 0 0
\(746\) −693621. −0.0456326
\(747\) 9.13658e6 0.599076
\(748\) −1.24025e6 −0.0810504
\(749\) 892244. 0.0581138
\(750\) 0 0
\(751\) −2.11169e6 −0.136625 −0.0683126 0.997664i \(-0.521762\pi\)
−0.0683126 + 0.997664i \(0.521762\pi\)
\(752\) 6.97356e6 0.449687
\(753\) −7.70259e6 −0.495050
\(754\) 2.05489e7 1.31632
\(755\) 0 0
\(756\) 412675. 0.0262605
\(757\) 1.47627e7 0.936325 0.468162 0.883642i \(-0.344916\pi\)
0.468162 + 0.883642i \(0.344916\pi\)
\(758\) 8.93632e6 0.564919
\(759\) −4.74157e6 −0.298757
\(760\) 0 0
\(761\) 2.67074e7 1.67174 0.835871 0.548926i \(-0.184963\pi\)
0.835871 + 0.548926i \(0.184963\pi\)
\(762\) 2.88558e7 1.80031
\(763\) 992408. 0.0617133
\(764\) −4.56934e6 −0.283218
\(765\) 0 0
\(766\) 1.77990e7 1.09604
\(767\) 2.69731e7 1.65555
\(768\) −1.34219e6 −0.0821131
\(769\) 3.05104e6 0.186051 0.0930256 0.995664i \(-0.470346\pi\)
0.0930256 + 0.995664i \(0.470346\pi\)
\(770\) 0 0
\(771\) 3.36659e7 2.03964
\(772\) 859043. 0.0518766
\(773\) 2.18723e7 1.31657 0.658287 0.752767i \(-0.271281\pi\)
0.658287 + 0.752767i \(0.271281\pi\)
\(774\) −224467. −0.0134679
\(775\) 0 0
\(776\) −2.52882e6 −0.150752
\(777\) 767030. 0.0455785
\(778\) 9.72331e6 0.575924
\(779\) −1.12311e6 −0.0663100
\(780\) 0 0
\(781\) −2.50823e6 −0.147143
\(782\) −587748. −0.0343696
\(783\) −9.84096e6 −0.573632
\(784\) −4.21094e6 −0.244675
\(785\) 0 0
\(786\) −1.56225e6 −0.0901975
\(787\) 1.26837e7 0.729975 0.364987 0.931013i \(-0.381073\pi\)
0.364987 + 0.931013i \(0.381073\pi\)
\(788\) −232622. −0.0133455
\(789\) 1.58783e7 0.908055
\(790\) 0 0
\(791\) −2.84943e6 −0.161926
\(792\) 3.94640e6 0.223557
\(793\) −2.66630e7 −1.50566
\(794\) −1.04482e7 −0.588154
\(795\) 0 0
\(796\) −2.29920e6 −0.128616
\(797\) −7.28989e6 −0.406514 −0.203257 0.979125i \(-0.565153\pi\)
−0.203257 + 0.979125i \(0.565153\pi\)
\(798\) −559560. −0.0311057
\(799\) −6.04201e6 −0.334822
\(800\) 0 0
\(801\) 2.56286e7 1.41138
\(802\) 5.70640e6 0.313275
\(803\) −2.26275e7 −1.23836
\(804\) −1.80080e7 −0.982482
\(805\) 0 0
\(806\) −1.53926e7 −0.834593
\(807\) −6.85783e6 −0.370683
\(808\) −1.07027e6 −0.0576717
\(809\) −2.72506e7 −1.46388 −0.731939 0.681370i \(-0.761385\pi\)
−0.731939 + 0.681370i \(0.761385\pi\)
\(810\) 0 0
\(811\) 1.45954e7 0.779229 0.389615 0.920978i \(-0.372608\pi\)
0.389615 + 0.920978i \(0.372608\pi\)
\(812\) −2.18554e6 −0.116324
\(813\) −1.82966e7 −0.970831
\(814\) −2.76704e6 −0.146371
\(815\) 0 0
\(816\) 1.16290e6 0.0611387
\(817\) −114816. −0.00601791
\(818\) 1.89328e7 0.989310
\(819\) −2.37563e6 −0.123757
\(820\) 0 0
\(821\) 4.16570e6 0.215690 0.107845 0.994168i \(-0.465605\pi\)
0.107845 + 0.994168i \(0.465605\pi\)
\(822\) −2.18465e7 −1.12772
\(823\) 9.74487e6 0.501506 0.250753 0.968051i \(-0.419322\pi\)
0.250753 + 0.968051i \(0.419322\pi\)
\(824\) −5.93052e6 −0.304281
\(825\) 0 0
\(826\) −2.86880e6 −0.146302
\(827\) −1.04970e6 −0.0533707 −0.0266854 0.999644i \(-0.508495\pi\)
−0.0266854 + 0.999644i \(0.508495\pi\)
\(828\) 1.87018e6 0.0947999
\(829\) 1.87001e7 0.945056 0.472528 0.881316i \(-0.343342\pi\)
0.472528 + 0.881316i \(0.343342\pi\)
\(830\) 0 0
\(831\) −2.32372e7 −1.16730
\(832\) −2.91471e6 −0.145978
\(833\) 3.64843e6 0.182177
\(834\) 2.41576e7 1.20265
\(835\) 0 0
\(836\) 2.01860e6 0.0998928
\(837\) 7.37159e6 0.363703
\(838\) −1.43103e6 −0.0703947
\(839\) 1.96094e7 0.961742 0.480871 0.876791i \(-0.340320\pi\)
0.480871 + 0.876791i \(0.340320\pi\)
\(840\) 0 0
\(841\) 3.16068e7 1.54096
\(842\) 2.61002e6 0.126871
\(843\) 4.05735e7 1.96641
\(844\) 1.33846e6 0.0646768
\(845\) 0 0
\(846\) 1.92253e7 0.923523
\(847\) −736303. −0.0352653
\(848\) 285346. 0.0136264
\(849\) 2.70733e7 1.28906
\(850\) 0 0
\(851\) −1.31129e6 −0.0620688
\(852\) 2.35180e6 0.110995
\(853\) 5.00288e6 0.235422 0.117711 0.993048i \(-0.462444\pi\)
0.117711 + 0.993048i \(0.462444\pi\)
\(854\) 2.83582e6 0.133056
\(855\) 0 0
\(856\) 3.01800e6 0.140778
\(857\) −1.36218e7 −0.633553 −0.316776 0.948500i \(-0.602600\pi\)
−0.316776 + 0.948500i \(0.602600\pi\)
\(858\) 2.03729e7 0.944789
\(859\) 1.88600e7 0.872084 0.436042 0.899926i \(-0.356380\pi\)
0.436042 + 0.899926i \(0.356380\pi\)
\(860\) 0 0
\(861\) 1.20558e6 0.0554227
\(862\) −2.50059e7 −1.14624
\(863\) 3.62744e7 1.65796 0.828979 0.559280i \(-0.188922\pi\)
0.828979 + 0.559280i \(0.188922\pi\)
\(864\) 1.39587e6 0.0636150
\(865\) 0 0
\(866\) −1.78333e7 −0.808047
\(867\) 2.80715e7 1.26829
\(868\) 1.63712e6 0.0737535
\(869\) 1.26178e7 0.566804
\(870\) 0 0
\(871\) −3.91061e7 −1.74662
\(872\) 3.35680e6 0.149498
\(873\) −6.97166e6 −0.309600
\(874\) 956603. 0.0423597
\(875\) 0 0
\(876\) 2.12163e7 0.934132
\(877\) 1.47531e7 0.647715 0.323857 0.946106i \(-0.395020\pi\)
0.323857 + 0.946106i \(0.395020\pi\)
\(878\) 2.00261e7 0.876717
\(879\) 2.78138e7 1.21419
\(880\) 0 0
\(881\) 1.41746e7 0.615277 0.307638 0.951503i \(-0.400461\pi\)
0.307638 + 0.951503i \(0.400461\pi\)
\(882\) −1.16091e7 −0.502489
\(883\) −2.05570e7 −0.887276 −0.443638 0.896206i \(-0.646312\pi\)
−0.443638 + 0.896206i \(0.646312\pi\)
\(884\) 2.52535e6 0.108690
\(885\) 0 0
\(886\) −2.86363e6 −0.122556
\(887\) 9.48962e6 0.404986 0.202493 0.979284i \(-0.435096\pi\)
0.202493 + 0.979284i \(0.435096\pi\)
\(888\) 2.59447e6 0.110412
\(889\) −6.66473e6 −0.282832
\(890\) 0 0
\(891\) −2.47407e7 −1.04404
\(892\) 1.06466e7 0.448022
\(893\) 9.83381e6 0.412661
\(894\) 8.51894e6 0.356485
\(895\) 0 0
\(896\) 310002. 0.0129001
\(897\) 9.65462e6 0.400640
\(898\) −1.93273e7 −0.799800
\(899\) −3.90401e7 −1.61106
\(900\) 0 0
\(901\) −247228. −0.0101458
\(902\) −4.34909e6 −0.177984
\(903\) 123246. 0.00502984
\(904\) −9.63814e6 −0.392258
\(905\) 0 0
\(906\) 3.91044e7 1.58272
\(907\) −1.30672e7 −0.527428 −0.263714 0.964601i \(-0.584947\pi\)
−0.263714 + 0.964601i \(0.584947\pi\)
\(908\) −1.84612e7 −0.743096
\(909\) −2.95060e6 −0.118441
\(910\) 0 0
\(911\) −4.60549e7 −1.83857 −0.919284 0.393594i \(-0.871232\pi\)
−0.919284 + 0.393594i \(0.871232\pi\)
\(912\) −1.89270e6 −0.0753521
\(913\) 1.80970e7 0.718506
\(914\) 2.57764e7 1.02060
\(915\) 0 0
\(916\) −6.93906e6 −0.273251
\(917\) 360828. 0.0141702
\(918\) −1.20940e6 −0.0473656
\(919\) −6.67836e6 −0.260844 −0.130422 0.991459i \(-0.541633\pi\)
−0.130422 + 0.991459i \(0.541633\pi\)
\(920\) 0 0
\(921\) −2.53631e7 −0.985264
\(922\) −1.64043e7 −0.635522
\(923\) 5.10717e6 0.197322
\(924\) −2.16682e6 −0.0834915
\(925\) 0 0
\(926\) −3.59473e7 −1.37765
\(927\) −1.63498e7 −0.624903
\(928\) −7.39254e6 −0.281789
\(929\) −84737.5 −0.00322134 −0.00161067 0.999999i \(-0.500513\pi\)
−0.00161067 + 0.999999i \(0.500513\pi\)
\(930\) 0 0
\(931\) −5.93809e6 −0.224529
\(932\) −6.19477e6 −0.233607
\(933\) 3.65706e7 1.37540
\(934\) 3.53763e7 1.32692
\(935\) 0 0
\(936\) −8.03552e6 −0.299795
\(937\) 3.12820e7 1.16398 0.581989 0.813196i \(-0.302275\pi\)
0.581989 + 0.813196i \(0.302275\pi\)
\(938\) 4.15924e6 0.154350
\(939\) −6.17701e7 −2.28620
\(940\) 0 0
\(941\) 2.88841e7 1.06337 0.531685 0.846942i \(-0.321559\pi\)
0.531685 + 0.846942i \(0.321559\pi\)
\(942\) 3.56320e7 1.30832
\(943\) −2.06101e6 −0.0754746
\(944\) −9.70367e6 −0.354410
\(945\) 0 0
\(946\) −444607. −0.0161528
\(947\) −1.99925e7 −0.724422 −0.362211 0.932096i \(-0.617978\pi\)
−0.362211 + 0.932096i \(0.617978\pi\)
\(948\) −1.18308e7 −0.427557
\(949\) 4.60732e7 1.66067
\(950\) 0 0
\(951\) 1.05645e7 0.378790
\(952\) −268591. −0.00960502
\(953\) −5.22187e7 −1.86249 −0.931244 0.364396i \(-0.881276\pi\)
−0.931244 + 0.364396i \(0.881276\pi\)
\(954\) 786666. 0.0279846
\(955\) 0 0
\(956\) −9.95941e6 −0.352443
\(957\) 5.16716e7 1.82378
\(958\) 1.15728e7 0.407403
\(959\) 5.04580e6 0.177167
\(960\) 0 0
\(961\) 614716. 0.0214717
\(962\) 5.63414e6 0.196286
\(963\) 8.32029e6 0.289116
\(964\) −5.94327e6 −0.205984
\(965\) 0 0
\(966\) −1.02684e6 −0.0354047
\(967\) −2.66303e7 −0.915818 −0.457909 0.888999i \(-0.651402\pi\)
−0.457909 + 0.888999i \(0.651402\pi\)
\(968\) −2.49053e6 −0.0854287
\(969\) 1.63987e6 0.0561047
\(970\) 0 0
\(971\) 1.04206e7 0.354686 0.177343 0.984149i \(-0.443250\pi\)
0.177343 + 0.984149i \(0.443250\pi\)
\(972\) 1.78977e7 0.607620
\(973\) −5.57959e6 −0.188938
\(974\) 1.27267e7 0.429850
\(975\) 0 0
\(976\) 9.59212e6 0.322322
\(977\) −1.82795e7 −0.612673 −0.306336 0.951923i \(-0.599103\pi\)
−0.306336 + 0.951923i \(0.599103\pi\)
\(978\) −2.08966e7 −0.698601
\(979\) 5.07633e7 1.69275
\(980\) 0 0
\(981\) 9.25433e6 0.307024
\(982\) −1.78204e7 −0.589709
\(983\) −2.25159e7 −0.743199 −0.371600 0.928393i \(-0.621191\pi\)
−0.371600 + 0.928393i \(0.621191\pi\)
\(984\) 4.07785e6 0.134259
\(985\) 0 0
\(986\) 6.40502e6 0.209811
\(987\) −1.05559e7 −0.344907
\(988\) −4.11019e6 −0.133958
\(989\) −210697. −0.00684964
\(990\) 0 0
\(991\) 3.42068e7 1.10644 0.553221 0.833034i \(-0.313398\pi\)
0.553221 + 0.833034i \(0.313398\pi\)
\(992\) 5.53755e6 0.178664
\(993\) 4.61726e7 1.48597
\(994\) −543187. −0.0174375
\(995\) 0 0
\(996\) −1.69684e7 −0.541990
\(997\) 1.12682e7 0.359018 0.179509 0.983756i \(-0.442549\pi\)
0.179509 + 0.983756i \(0.442549\pi\)
\(998\) 3.72589e7 1.18414
\(999\) −2.69821e6 −0.0855387
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 950.6.a.d.1.1 2
5.4 even 2 38.6.a.c.1.2 2
15.14 odd 2 342.6.a.i.1.1 2
20.19 odd 2 304.6.a.f.1.1 2
95.94 odd 2 722.6.a.c.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.6.a.c.1.2 2 5.4 even 2
304.6.a.f.1.1 2 20.19 odd 2
342.6.a.i.1.1 2 15.14 odd 2
722.6.a.c.1.1 2 95.94 odd 2
950.6.a.d.1.1 2 1.1 even 1 trivial