Properties

Label 950.6.a.d.1.2
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 1.2
Root \(-18.4803\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} +17.4803 q^{3} +16.0000 q^{4} +69.9210 q^{6} -132.921 q^{7} +64.0000 q^{8} +62.5592 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +17.4803 q^{3} +16.0000 q^{4} +69.9210 q^{6} -132.921 q^{7} +64.0000 q^{8} +62.5592 q^{9} +311.520 q^{11} +279.684 q^{12} -901.401 q^{13} -531.684 q^{14} +256.000 q^{16} +157.803 q^{17} +250.237 q^{18} +361.000 q^{19} -2323.49 q^{21} +1246.08 q^{22} +2522.53 q^{23} +1118.74 q^{24} -3605.61 q^{26} -3154.15 q^{27} -2126.74 q^{28} +4738.28 q^{29} -6587.76 q^{31} +1024.00 q^{32} +5445.44 q^{33} +631.210 q^{34} +1000.95 q^{36} -8508.60 q^{37} +1444.00 q^{38} -15756.7 q^{39} +19741.1 q^{41} -9293.97 q^{42} -10985.0 q^{43} +4984.32 q^{44} +10090.1 q^{46} -15085.5 q^{47} +4474.94 q^{48} +860.995 q^{49} +2758.43 q^{51} -14422.4 q^{52} -21699.6 q^{53} -12616.6 q^{54} -8506.94 q^{56} +6310.37 q^{57} +18953.1 q^{58} -40676.1 q^{59} +6151.79 q^{61} -26351.0 q^{62} -8315.44 q^{63} +4096.00 q^{64} +21781.8 q^{66} -62760.3 q^{67} +2524.84 q^{68} +44094.5 q^{69} -55311.0 q^{71} +4003.79 q^{72} +48528.1 q^{73} -34034.4 q^{74} +5776.00 q^{76} -41407.5 q^{77} -63026.9 q^{78} +31017.6 q^{79} -70337.2 q^{81} +78964.4 q^{82} -41068.7 q^{83} -37175.9 q^{84} -43939.8 q^{86} +82826.3 q^{87} +19937.3 q^{88} -17065.6 q^{89} +119815. q^{91} +40360.5 q^{92} -115156. q^{93} -60341.9 q^{94} +17899.8 q^{96} -139045. q^{97} +3443.98 q^{98} +19488.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 8q^{2} - 3q^{3} + 32q^{4} - 12q^{6} - 114q^{7} + 128q^{8} + 239q^{9} + O(q^{10}) \) \( 2q + 8q^{2} - 3q^{3} + 32q^{4} - 12q^{6} - 114q^{7} + 128q^{8} + 239q^{9} + 661q^{11} - 48q^{12} - 1613q^{13} - 456q^{14} + 512q^{16} - 64q^{17} + 956q^{18} + 722q^{19} - 2711q^{21} + 2644q^{22} + 3185q^{23} - 192q^{24} - 6452q^{26} - 1791q^{27} - 1824q^{28} - 2481q^{29} - 1180q^{31} + 2048q^{32} - 1712q^{33} - 256q^{34} + 3824q^{36} - 10488q^{37} + 2888q^{38} - 1183q^{39} + 16630q^{41} - 10844q^{42} - 11303q^{43} + 10576q^{44} + 12740q^{46} + 12155q^{47} - 768q^{48} - 15588q^{49} + 7301q^{51} - 25808q^{52} - 20585q^{53} - 7164q^{54} - 7296q^{56} - 1083q^{57} - 9924q^{58} - 78581q^{59} + 43621q^{61} - 4720q^{62} - 4977q^{63} + 8192q^{64} - 6848q^{66} - 7805q^{67} - 1024q^{68} + 30527q^{69} - 62488q^{71} + 15296q^{72} - 16218q^{73} - 41952q^{74} + 11552q^{76} - 34795q^{77} - 4732q^{78} + 67122q^{79} - 141130q^{81} + 66520q^{82} + 10714q^{83} - 43376q^{84} - 45212q^{86} + 230679q^{87} + 42304q^{88} + 128188q^{89} + 106351q^{91} + 50960q^{92} - 225908q^{93} + 48620q^{94} - 3072q^{96} - 178558q^{97} - 62352q^{98} + 81151q^{99} + O(q^{100}) \)

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
\(3\) 17.4803 1.12136 0.560679 0.828033i \(-0.310540\pi\)
0.560679 + 0.828033i \(0.310540\pi\)
\(4\) 16.0000 0.500000
\(5\) 0 0
\(6\) 69.9210 0.792920
\(7\) −132.921 −1.02529 −0.512647 0.858599i \(-0.671335\pi\)
−0.512647 + 0.858599i \(0.671335\pi\)
\(8\) 64.0000 0.353553
\(9\) 62.5592 0.257445
\(10\) 0 0
\(11\) 311.520 0.776254 0.388127 0.921606i \(-0.373122\pi\)
0.388127 + 0.921606i \(0.373122\pi\)
\(12\) 279.684 0.560679
\(13\) −901.401 −1.47931 −0.739656 0.672985i \(-0.765012\pi\)
−0.739656 + 0.672985i \(0.765012\pi\)
\(14\) −531.684 −0.724993
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) 157.803 0.132432 0.0662158 0.997805i \(-0.478907\pi\)
0.0662158 + 0.997805i \(0.478907\pi\)
\(18\) 250.237 0.182041
\(19\) 361.000 0.229416
\(20\) 0 0
\(21\) −2323.49 −1.14972
\(22\) 1246.08 0.548894
\(23\) 2522.53 0.994299 0.497150 0.867665i \(-0.334380\pi\)
0.497150 + 0.867665i \(0.334380\pi\)
\(24\) 1118.74 0.396460
\(25\) 0 0
\(26\) −3605.61 −1.04603
\(27\) −3154.15 −0.832670
\(28\) −2126.74 −0.512647
\(29\) 4738.28 1.04623 0.523113 0.852263i \(-0.324770\pi\)
0.523113 + 0.852263i \(0.324770\pi\)
\(30\) 0 0
\(31\) −6587.76 −1.23121 −0.615607 0.788053i \(-0.711089\pi\)
−0.615607 + 0.788053i \(0.711089\pi\)
\(32\) 1024.00 0.176777
\(33\) 5445.44 0.870459
\(34\) 631.210 0.0936433
\(35\) 0 0
\(36\) 1000.95 0.128723
\(37\) −8508.60 −1.02177 −0.510886 0.859648i \(-0.670683\pi\)
−0.510886 + 0.859648i \(0.670683\pi\)
\(38\) 1444.00 0.162221
\(39\) −15756.7 −1.65884
\(40\) 0 0
\(41\) 19741.1 1.83405 0.917027 0.398826i \(-0.130582\pi\)
0.917027 + 0.398826i \(0.130582\pi\)
\(42\) −9293.97 −0.812977
\(43\) −10985.0 −0.905997 −0.452999 0.891511i \(-0.649646\pi\)
−0.452999 + 0.891511i \(0.649646\pi\)
\(44\) 4984.32 0.388127
\(45\) 0 0
\(46\) 10090.1 0.703076
\(47\) −15085.5 −0.996127 −0.498063 0.867141i \(-0.665955\pi\)
−0.498063 + 0.867141i \(0.665955\pi\)
\(48\) 4474.94 0.280340
\(49\) 860.995 0.0512284
\(50\) 0 0
\(51\) 2758.43 0.148503
\(52\) −14422.4 −0.739656
\(53\) −21699.6 −1.06112 −0.530558 0.847649i \(-0.678018\pi\)
−0.530558 + 0.847649i \(0.678018\pi\)
\(54\) −12616.6 −0.588787
\(55\) 0 0
\(56\) −8506.94 −0.362496
\(57\) 6310.37 0.257257
\(58\) 18953.1 0.739794
\(59\) −40676.1 −1.52128 −0.760639 0.649175i \(-0.775114\pi\)
−0.760639 + 0.649175i \(0.775114\pi\)
\(60\) 0 0
\(61\) 6151.79 0.211679 0.105839 0.994383i \(-0.466247\pi\)
0.105839 + 0.994383i \(0.466247\pi\)
\(62\) −26351.0 −0.870600
\(63\) −8315.44 −0.263957
\(64\) 4096.00 0.125000
\(65\) 0 0
\(66\) 21781.8 0.615508
\(67\) −62760.3 −1.70804 −0.854019 0.520241i \(-0.825842\pi\)
−0.854019 + 0.520241i \(0.825842\pi\)
\(68\) 2524.84 0.0662158
\(69\) 44094.5 1.11497
\(70\) 0 0
\(71\) −55311.0 −1.30216 −0.651081 0.759008i \(-0.725684\pi\)
−0.651081 + 0.759008i \(0.725684\pi\)
\(72\) 4003.79 0.0910207
\(73\) 48528.1 1.06583 0.532913 0.846170i \(-0.321097\pi\)
0.532913 + 0.846170i \(0.321097\pi\)
\(74\) −34034.4 −0.722502
\(75\) 0 0
\(76\) 5776.00 0.114708
\(77\) −41407.5 −0.795889
\(78\) −63026.9 −1.17298
\(79\) 31017.6 0.559166 0.279583 0.960121i \(-0.409804\pi\)
0.279583 + 0.960121i \(0.409804\pi\)
\(80\) 0 0
\(81\) −70337.2 −1.19117
\(82\) 78964.4 1.29687
\(83\) −41068.7 −0.654358 −0.327179 0.944962i \(-0.606098\pi\)
−0.327179 + 0.944962i \(0.606098\pi\)
\(84\) −37175.9 −0.574861
\(85\) 0 0
\(86\) −43939.8 −0.640637
\(87\) 82826.3 1.17320
\(88\) 19937.3 0.274447
\(89\) −17065.6 −0.228373 −0.114187 0.993459i \(-0.536426\pi\)
−0.114187 + 0.993459i \(0.536426\pi\)
\(90\) 0 0
\(91\) 119815. 1.51673
\(92\) 40360.5 0.497150
\(93\) −115156. −1.38063
\(94\) −60341.9 −0.704368
\(95\) 0 0
\(96\) 17899.8 0.198230
\(97\) −139045. −1.50047 −0.750234 0.661172i \(-0.770059\pi\)
−0.750234 + 0.661172i \(0.770059\pi\)
\(98\) 3443.98 0.0362239
\(99\) 19488.4 0.199843
\(100\) 0 0
\(101\) −122253. −1.19249 −0.596247 0.802801i \(-0.703342\pi\)
−0.596247 + 0.802801i \(0.703342\pi\)
\(102\) 11033.7 0.105008
\(103\) 71932.4 0.668084 0.334042 0.942558i \(-0.391587\pi\)
0.334042 + 0.942558i \(0.391587\pi\)
\(104\) −57689.7 −0.523016
\(105\) 0 0
\(106\) −86798.5 −0.750322
\(107\) −14833.3 −0.125250 −0.0626249 0.998037i \(-0.519947\pi\)
−0.0626249 + 0.998037i \(0.519947\pi\)
\(108\) −50466.4 −0.416335
\(109\) 140025. 1.12886 0.564429 0.825482i \(-0.309096\pi\)
0.564429 + 0.825482i \(0.309096\pi\)
\(110\) 0 0
\(111\) −148733. −1.14577
\(112\) −34027.8 −0.256324
\(113\) −235172. −1.73256 −0.866282 0.499555i \(-0.833497\pi\)
−0.866282 + 0.499555i \(0.833497\pi\)
\(114\) 25241.5 0.181908
\(115\) 0 0
\(116\) 75812.5 0.523113
\(117\) −56391.0 −0.380842
\(118\) −162704. −1.07571
\(119\) −20975.3 −0.135781
\(120\) 0 0
\(121\) −64006.4 −0.397430
\(122\) 24607.2 0.149679
\(123\) 345080. 2.05663
\(124\) −105404. −0.615607
\(125\) 0 0
\(126\) −33261.8 −0.186646
\(127\) 24783.9 0.136351 0.0681757 0.997673i \(-0.478282\pi\)
0.0681757 + 0.997673i \(0.478282\pi\)
\(128\) 16384.0 0.0883883
\(129\) −192020. −1.01595
\(130\) 0 0
\(131\) −152549. −0.776661 −0.388331 0.921520i \(-0.626948\pi\)
−0.388331 + 0.921520i \(0.626948\pi\)
\(132\) 87127.1 0.435230
\(133\) −47984.5 −0.235219
\(134\) −251041. −1.20777
\(135\) 0 0
\(136\) 10099.4 0.0468216
\(137\) −192265. −0.875184 −0.437592 0.899174i \(-0.644169\pi\)
−0.437592 + 0.899174i \(0.644169\pi\)
\(138\) 176378. 0.788400
\(139\) −342833. −1.50503 −0.752515 0.658575i \(-0.771159\pi\)
−0.752515 + 0.658575i \(0.771159\pi\)
\(140\) 0 0
\(141\) −263698. −1.11702
\(142\) −221244. −0.920768
\(143\) −280804. −1.14832
\(144\) 16015.2 0.0643614
\(145\) 0 0
\(146\) 194112. 0.753652
\(147\) 15050.4 0.0574454
\(148\) −136138. −0.510886
\(149\) 335859. 1.23934 0.619671 0.784862i \(-0.287266\pi\)
0.619671 + 0.784862i \(0.287266\pi\)
\(150\) 0 0
\(151\) 266683. 0.951816 0.475908 0.879495i \(-0.342120\pi\)
0.475908 + 0.879495i \(0.342120\pi\)
\(152\) 23104.0 0.0811107
\(153\) 9872.01 0.0340939
\(154\) −165630. −0.562778
\(155\) 0 0
\(156\) −252108. −0.829420
\(157\) 173779. 0.562664 0.281332 0.959611i \(-0.409224\pi\)
0.281332 + 0.959611i \(0.409224\pi\)
\(158\) 124071. 0.395390
\(159\) −379315. −1.18989
\(160\) 0 0
\(161\) −335298. −1.01945
\(162\) −281349. −0.842282
\(163\) 406317. 1.19783 0.598917 0.800811i \(-0.295598\pi\)
0.598917 + 0.800811i \(0.295598\pi\)
\(164\) 315858. 0.917027
\(165\) 0 0
\(166\) −164275. −0.462701
\(167\) 319695. 0.887043 0.443522 0.896264i \(-0.353729\pi\)
0.443522 + 0.896264i \(0.353729\pi\)
\(168\) −148704. −0.406488
\(169\) 441231. 1.18836
\(170\) 0 0
\(171\) 22583.9 0.0590620
\(172\) −175759. −0.452999
\(173\) 427313. 1.08550 0.542752 0.839893i \(-0.317382\pi\)
0.542752 + 0.839893i \(0.317382\pi\)
\(174\) 331305. 0.829574
\(175\) 0 0
\(176\) 79749.1 0.194064
\(177\) −711028. −1.70590
\(178\) −68262.2 −0.161484
\(179\) 361946. 0.844329 0.422164 0.906519i \(-0.361271\pi\)
0.422164 + 0.906519i \(0.361271\pi\)
\(180\) 0 0
\(181\) −416686. −0.945393 −0.472697 0.881225i \(-0.656719\pi\)
−0.472697 + 0.881225i \(0.656719\pi\)
\(182\) 479261. 1.07249
\(183\) 107535. 0.237368
\(184\) 161442. 0.351538
\(185\) 0 0
\(186\) −460623. −0.976255
\(187\) 49158.6 0.102801
\(188\) −241368. −0.498063
\(189\) 419253. 0.853732
\(190\) 0 0
\(191\) 581586. 1.15353 0.576767 0.816909i \(-0.304314\pi\)
0.576767 + 0.816909i \(0.304314\pi\)
\(192\) 71599.1 0.140170
\(193\) 182832. 0.353312 0.176656 0.984273i \(-0.443472\pi\)
0.176656 + 0.984273i \(0.443472\pi\)
\(194\) −556181. −1.06099
\(195\) 0 0
\(196\) 13775.9 0.0256142
\(197\) 93344.9 0.171366 0.0856831 0.996322i \(-0.472693\pi\)
0.0856831 + 0.996322i \(0.472693\pi\)
\(198\) 77953.8 0.141310
\(199\) 723166. 1.29451 0.647255 0.762274i \(-0.275917\pi\)
0.647255 + 0.762274i \(0.275917\pi\)
\(200\) 0 0
\(201\) −1.09707e6 −1.91532
\(202\) −489012. −0.843221
\(203\) −629817. −1.07269
\(204\) 44134.8 0.0742517
\(205\) 0 0
\(206\) 287730. 0.472407
\(207\) 157808. 0.255978
\(208\) −230759. −0.369828
\(209\) 112459. 0.178085
\(210\) 0 0
\(211\) 85741.4 0.132582 0.0662910 0.997800i \(-0.478883\pi\)
0.0662910 + 0.997800i \(0.478883\pi\)
\(212\) −347194. −0.530558
\(213\) −966850. −1.46019
\(214\) −59333.0 −0.0885650
\(215\) 0 0
\(216\) −201866. −0.294393
\(217\) 875652. 1.26236
\(218\) 560100. 0.798223
\(219\) 848283. 1.19517
\(220\) 0 0
\(221\) −142243. −0.195908
\(222\) −594930. −0.810184
\(223\) −111106. −0.149615 −0.0748076 0.997198i \(-0.523834\pi\)
−0.0748076 + 0.997198i \(0.523834\pi\)
\(224\) −136111. −0.181248
\(225\) 0 0
\(226\) −940688. −1.22511
\(227\) 314299. 0.404835 0.202418 0.979299i \(-0.435120\pi\)
0.202418 + 0.979299i \(0.435120\pi\)
\(228\) 100966. 0.128629
\(229\) 1.45815e6 1.83744 0.918718 0.394913i \(-0.129225\pi\)
0.918718 + 0.394913i \(0.129225\pi\)
\(230\) 0 0
\(231\) −723814. −0.892477
\(232\) 303250. 0.369897
\(233\) −1.38626e6 −1.67284 −0.836418 0.548091i \(-0.815355\pi\)
−0.836418 + 0.548091i \(0.815355\pi\)
\(234\) −225564. −0.269296
\(235\) 0 0
\(236\) −650817. −0.760639
\(237\) 542196. 0.627026
\(238\) −83901.1 −0.0960119
\(239\) 365117. 0.413464 0.206732 0.978398i \(-0.433717\pi\)
0.206732 + 0.978398i \(0.433717\pi\)
\(240\) 0 0
\(241\) −312312. −0.346374 −0.173187 0.984889i \(-0.555407\pi\)
−0.173187 + 0.984889i \(0.555407\pi\)
\(242\) −256026. −0.281025
\(243\) −463054. −0.503056
\(244\) 98428.7 0.105839
\(245\) 0 0
\(246\) 1.38032e6 1.45426
\(247\) −325406. −0.339377
\(248\) −421617. −0.435300
\(249\) −717891. −0.733771
\(250\) 0 0
\(251\) −970095. −0.971919 −0.485959 0.873981i \(-0.661530\pi\)
−0.485959 + 0.873981i \(0.661530\pi\)
\(252\) −133047. −0.131979
\(253\) 785819. 0.771829
\(254\) 99135.5 0.0964151
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) −1.28988e6 −1.21819 −0.609096 0.793096i \(-0.708468\pi\)
−0.609096 + 0.793096i \(0.708468\pi\)
\(258\) −768079. −0.718384
\(259\) 1.13097e6 1.04762
\(260\) 0 0
\(261\) 296423. 0.269346
\(262\) −610197. −0.549183
\(263\) 501426. 0.447011 0.223505 0.974703i \(-0.428250\pi\)
0.223505 + 0.974703i \(0.428250\pi\)
\(264\) 348508. 0.307754
\(265\) 0 0
\(266\) −191938. −0.166325
\(267\) −298310. −0.256089
\(268\) −1.00416e6 −0.854019
\(269\) 1.42986e6 1.20479 0.602397 0.798197i \(-0.294213\pi\)
0.602397 + 0.798197i \(0.294213\pi\)
\(270\) 0 0
\(271\) −709506. −0.586857 −0.293429 0.955981i \(-0.594796\pi\)
−0.293429 + 0.955981i \(0.594796\pi\)
\(272\) 40397.4 0.0331079
\(273\) 2.09440e6 1.70080
\(274\) −769061. −0.618849
\(275\) 0 0
\(276\) 705512. 0.557483
\(277\) 766740. 0.600411 0.300205 0.953875i \(-0.402945\pi\)
0.300205 + 0.953875i \(0.402945\pi\)
\(278\) −1.37133e6 −1.06422
\(279\) −412125. −0.316970
\(280\) 0 0
\(281\) 5975.32 0.00451435 0.00225718 0.999997i \(-0.499282\pi\)
0.00225718 + 0.999997i \(0.499282\pi\)
\(282\) −1.05479e6 −0.789849
\(283\) 189246. 0.140463 0.0702314 0.997531i \(-0.477626\pi\)
0.0702314 + 0.997531i \(0.477626\pi\)
\(284\) −884975. −0.651081
\(285\) 0 0
\(286\) −1.12322e6 −0.811986
\(287\) −2.62401e6 −1.88044
\(288\) 64060.7 0.0455104
\(289\) −1.39496e6 −0.982462
\(290\) 0 0
\(291\) −2.43055e6 −1.68256
\(292\) 776449. 0.532913
\(293\) −986180. −0.671100 −0.335550 0.942022i \(-0.608922\pi\)
−0.335550 + 0.942022i \(0.608922\pi\)
\(294\) 60201.7 0.0406200
\(295\) 0 0
\(296\) −544551. −0.361251
\(297\) −982580. −0.646363
\(298\) 1.34343e6 0.876347
\(299\) −2.27381e6 −1.47088
\(300\) 0 0
\(301\) 1.46013e6 0.928914
\(302\) 1.06673e6 0.673035
\(303\) −2.13702e6 −1.33721
\(304\) 92416.0 0.0573539
\(305\) 0 0
\(306\) 39488.0 0.0241080
\(307\) 1.45722e6 0.882428 0.441214 0.897402i \(-0.354548\pi\)
0.441214 + 0.897402i \(0.354548\pi\)
\(308\) −662520. −0.397944
\(309\) 1.25740e6 0.749162
\(310\) 0 0
\(311\) 2.40526e6 1.41014 0.705069 0.709138i \(-0.250916\pi\)
0.705069 + 0.709138i \(0.250916\pi\)
\(312\) −1.00843e6 −0.586488
\(313\) 3.20380e6 1.84843 0.924217 0.381867i \(-0.124719\pi\)
0.924217 + 0.381867i \(0.124719\pi\)
\(314\) 695117. 0.397863
\(315\) 0 0
\(316\) 496282. 0.279583
\(317\) 603046. 0.337056 0.168528 0.985697i \(-0.446099\pi\)
0.168528 + 0.985697i \(0.446099\pi\)
\(318\) −1.51726e6 −0.841380
\(319\) 1.47607e6 0.812137
\(320\) 0 0
\(321\) −259289. −0.140450
\(322\) −1.34119e6 −0.720860
\(323\) 56966.7 0.0303819
\(324\) −1.12540e6 −0.595584
\(325\) 0 0
\(326\) 1.62527e6 0.846996
\(327\) 2.44767e6 1.26585
\(328\) 1.26343e6 0.648436
\(329\) 2.00518e6 1.02132
\(330\) 0 0
\(331\) −3.77416e6 −1.89344 −0.946719 0.322062i \(-0.895624\pi\)
−0.946719 + 0.322062i \(0.895624\pi\)
\(332\) −657099. −0.327179
\(333\) −532292. −0.263051
\(334\) 1.27878e6 0.627234
\(335\) 0 0
\(336\) −594814. −0.287431
\(337\) 2.12850e6 1.02094 0.510470 0.859896i \(-0.329472\pi\)
0.510470 + 0.859896i \(0.329472\pi\)
\(338\) 1.76492e6 0.840300
\(339\) −4.11087e6 −1.94283
\(340\) 0 0
\(341\) −2.05222e6 −0.955735
\(342\) 90335.5 0.0417632
\(343\) 2.11956e6 0.972770
\(344\) −703037. −0.320318
\(345\) 0 0
\(346\) 1.70925e6 0.767567
\(347\) −2.40305e6 −1.07137 −0.535685 0.844418i \(-0.679947\pi\)
−0.535685 + 0.844418i \(0.679947\pi\)
\(348\) 1.32522e6 0.586598
\(349\) 3.71870e6 1.63428 0.817141 0.576438i \(-0.195558\pi\)
0.817141 + 0.576438i \(0.195558\pi\)
\(350\) 0 0
\(351\) 2.84315e6 1.23178
\(352\) 318996. 0.137224
\(353\) 2.04192e6 0.872174 0.436087 0.899905i \(-0.356364\pi\)
0.436087 + 0.899905i \(0.356364\pi\)
\(354\) −2.84411e6 −1.20625
\(355\) 0 0
\(356\) −273049. −0.114187
\(357\) −366653. −0.152260
\(358\) 1.44778e6 0.597030
\(359\) −949493. −0.388826 −0.194413 0.980920i \(-0.562280\pi\)
−0.194413 + 0.980920i \(0.562280\pi\)
\(360\) 0 0
\(361\) 130321. 0.0526316
\(362\) −1.66674e6 −0.668494
\(363\) −1.11885e6 −0.445661
\(364\) 1.91704e6 0.758365
\(365\) 0 0
\(366\) 430139. 0.167844
\(367\) −1.74418e6 −0.675967 −0.337984 0.941152i \(-0.609745\pi\)
−0.337984 + 0.941152i \(0.609745\pi\)
\(368\) 645768. 0.248575
\(369\) 1.23499e6 0.472169
\(370\) 0 0
\(371\) 2.88434e6 1.08796
\(372\) −1.84249e6 −0.690316
\(373\) −4.59987e6 −1.71188 −0.855940 0.517076i \(-0.827020\pi\)
−0.855940 + 0.517076i \(0.827020\pi\)
\(374\) 196634. 0.0726910
\(375\) 0 0
\(376\) −965471. −0.352184
\(377\) −4.27109e6 −1.54770
\(378\) 1.67701e6 0.603680
\(379\) −6993.69 −0.00250097 −0.00125048 0.999999i \(-0.500398\pi\)
−0.00125048 + 0.999999i \(0.500398\pi\)
\(380\) 0 0
\(381\) 433228. 0.152899
\(382\) 2.32634e6 0.815672
\(383\) −1.37680e6 −0.479594 −0.239797 0.970823i \(-0.577081\pi\)
−0.239797 + 0.970823i \(0.577081\pi\)
\(384\) 286396. 0.0991150
\(385\) 0 0
\(386\) 731327. 0.249829
\(387\) −687210. −0.233245
\(388\) −2.22472e6 −0.750234
\(389\) 1.40115e6 0.469473 0.234736 0.972059i \(-0.424577\pi\)
0.234736 + 0.972059i \(0.424577\pi\)
\(390\) 0 0
\(391\) 398062. 0.131677
\(392\) 55103.7 0.0181120
\(393\) −2.66660e6 −0.870916
\(394\) 373380. 0.121174
\(395\) 0 0
\(396\) 311815. 0.0999215
\(397\) −3.33402e6 −1.06168 −0.530839 0.847473i \(-0.678123\pi\)
−0.530839 + 0.847473i \(0.678123\pi\)
\(398\) 2.89266e6 0.915357
\(399\) −838781. −0.263764
\(400\) 0 0
\(401\) −5.32612e6 −1.65406 −0.827028 0.562161i \(-0.809970\pi\)
−0.827028 + 0.562161i \(0.809970\pi\)
\(402\) −4.38826e6 −1.35434
\(403\) 5.93822e6 1.82135
\(404\) −1.95605e6 −0.596247
\(405\) 0 0
\(406\) −2.51927e6 −0.758506
\(407\) −2.65060e6 −0.793155
\(408\) 176539. 0.0525039
\(409\) −3.00861e6 −0.889319 −0.444659 0.895700i \(-0.646675\pi\)
−0.444659 + 0.895700i \(0.646675\pi\)
\(410\) 0 0
\(411\) −3.36085e6 −0.981395
\(412\) 1.15092e6 0.334042
\(413\) 5.40670e6 1.55976
\(414\) 631231. 0.181004
\(415\) 0 0
\(416\) −923035. −0.261508
\(417\) −5.99280e6 −1.68768
\(418\) 449835. 0.125925
\(419\) 2.47470e6 0.688633 0.344317 0.938854i \(-0.388111\pi\)
0.344317 + 0.938854i \(0.388111\pi\)
\(420\) 0 0
\(421\) −3.25587e6 −0.895286 −0.447643 0.894212i \(-0.647737\pi\)
−0.447643 + 0.894212i \(0.647737\pi\)
\(422\) 342966. 0.0937496
\(423\) −943736. −0.256448
\(424\) −1.38878e6 −0.375161
\(425\) 0 0
\(426\) −3.86740e6 −1.03251
\(427\) −817702. −0.217033
\(428\) −237332. −0.0626249
\(429\) −4.90853e6 −1.28768
\(430\) 0 0
\(431\) −3.54756e6 −0.919891 −0.459945 0.887947i \(-0.652131\pi\)
−0.459945 + 0.887947i \(0.652131\pi\)
\(432\) −807462. −0.208168
\(433\) −2.58960e6 −0.663763 −0.331881 0.943321i \(-0.607683\pi\)
−0.331881 + 0.943321i \(0.607683\pi\)
\(434\) 3.50261e6 0.892621
\(435\) 0 0
\(436\) 2.24040e6 0.564429
\(437\) 910634. 0.228108
\(438\) 3.39313e6 0.845114
\(439\) −3.47682e6 −0.861036 −0.430518 0.902582i \(-0.641669\pi\)
−0.430518 + 0.902582i \(0.641669\pi\)
\(440\) 0 0
\(441\) 53863.2 0.0131885
\(442\) −568974. −0.138528
\(443\) 3.22496e6 0.780756 0.390378 0.920655i \(-0.372344\pi\)
0.390378 + 0.920655i \(0.372344\pi\)
\(444\) −2.37972e6 −0.572886
\(445\) 0 0
\(446\) −444424. −0.105794
\(447\) 5.87089e6 1.38975
\(448\) −544444. −0.128162
\(449\) −4.47721e6 −1.04807 −0.524036 0.851696i \(-0.675574\pi\)
−0.524036 + 0.851696i \(0.675574\pi\)
\(450\) 0 0
\(451\) 6.14975e6 1.42369
\(452\) −3.76275e6 −0.866282
\(453\) 4.66169e6 1.06733
\(454\) 1.25720e6 0.286262
\(455\) 0 0
\(456\) 403864. 0.0909542
\(457\) −563938. −0.126311 −0.0631555 0.998004i \(-0.520116\pi\)
−0.0631555 + 0.998004i \(0.520116\pi\)
\(458\) 5.83259e6 1.29926
\(459\) −497733. −0.110272
\(460\) 0 0
\(461\) −3.05325e6 −0.669130 −0.334565 0.942373i \(-0.608589\pi\)
−0.334565 + 0.942373i \(0.608589\pi\)
\(462\) −2.89526e6 −0.631076
\(463\) −7.31911e6 −1.58674 −0.793370 0.608740i \(-0.791675\pi\)
−0.793370 + 0.608740i \(0.791675\pi\)
\(464\) 1.21300e6 0.261557
\(465\) 0 0
\(466\) −5.54502e6 −1.18287
\(467\) 3.83007e6 0.812671 0.406336 0.913724i \(-0.366806\pi\)
0.406336 + 0.913724i \(0.366806\pi\)
\(468\) −902256. −0.190421
\(469\) 8.34216e6 1.75124
\(470\) 0 0
\(471\) 3.03771e6 0.630948
\(472\) −2.60327e6 −0.537853
\(473\) −3.42203e6 −0.703284
\(474\) 2.16879e6 0.443374
\(475\) 0 0
\(476\) −335604. −0.0678907
\(477\) −1.35751e6 −0.273179
\(478\) 1.46047e6 0.292363
\(479\) −852140. −0.169696 −0.0848481 0.996394i \(-0.527040\pi\)
−0.0848481 + 0.996394i \(0.527040\pi\)
\(480\) 0 0
\(481\) 7.66967e6 1.51152
\(482\) −1.24925e6 −0.244924
\(483\) −5.86109e6 −1.14317
\(484\) −1.02410e6 −0.198715
\(485\) 0 0
\(486\) −1.85222e6 −0.355714
\(487\) 1.76953e6 0.338093 0.169046 0.985608i \(-0.445931\pi\)
0.169046 + 0.985608i \(0.445931\pi\)
\(488\) 393715. 0.0748397
\(489\) 7.10253e6 1.34320
\(490\) 0 0
\(491\) −1.12702e6 −0.210973 −0.105487 0.994421i \(-0.533640\pi\)
−0.105487 + 0.994421i \(0.533640\pi\)
\(492\) 5.52127e6 1.02832
\(493\) 747713. 0.138553
\(494\) −1.30162e6 −0.239976
\(495\) 0 0
\(496\) −1.68647e6 −0.307803
\(497\) 7.35199e6 1.33510
\(498\) −2.87156e6 −0.518854
\(499\) −5.96123e6 −1.07173 −0.535864 0.844304i \(-0.680014\pi\)
−0.535864 + 0.844304i \(0.680014\pi\)
\(500\) 0 0
\(501\) 5.58835e6 0.994694
\(502\) −3.88038e6 −0.687250
\(503\) 5.66845e6 0.998951 0.499476 0.866328i \(-0.333526\pi\)
0.499476 + 0.866328i \(0.333526\pi\)
\(504\) −532188. −0.0933230
\(505\) 0 0
\(506\) 3.14327e6 0.545765
\(507\) 7.71283e6 1.33258
\(508\) 396542. 0.0681757
\(509\) 8.42220e6 1.44089 0.720446 0.693512i \(-0.243937\pi\)
0.720446 + 0.693512i \(0.243937\pi\)
\(510\) 0 0
\(511\) −6.45040e6 −1.09278
\(512\) 262144. 0.0441942
\(513\) −1.13865e6 −0.191028
\(514\) −5.15951e6 −0.861392
\(515\) 0 0
\(516\) −3.07232e6 −0.507974
\(517\) −4.69943e6 −0.773247
\(518\) 4.52389e6 0.740777
\(519\) 7.46955e6 1.21724
\(520\) 0 0
\(521\) 5.81861e6 0.939128 0.469564 0.882899i \(-0.344411\pi\)
0.469564 + 0.882899i \(0.344411\pi\)
\(522\) 1.18569e6 0.190457
\(523\) −4.81037e6 −0.768996 −0.384498 0.923126i \(-0.625625\pi\)
−0.384498 + 0.923126i \(0.625625\pi\)
\(524\) −2.44079e6 −0.388331
\(525\) 0 0
\(526\) 2.00571e6 0.316084
\(527\) −1.03957e6 −0.163052
\(528\) 1.39403e6 0.217615
\(529\) −73173.3 −0.0113688
\(530\) 0 0
\(531\) −2.54466e6 −0.391646
\(532\) −767752. −0.117609
\(533\) −1.77947e7 −2.71314
\(534\) −1.19324e6 −0.181082
\(535\) 0 0
\(536\) −4.01666e6 −0.603883
\(537\) 6.32691e6 0.946795
\(538\) 5.71944e6 0.851918
\(539\) 268217. 0.0397662
\(540\) 0 0
\(541\) 3.11994e6 0.458304 0.229152 0.973391i \(-0.426405\pi\)
0.229152 + 0.973391i \(0.426405\pi\)
\(542\) −2.83802e6 −0.414971
\(543\) −7.28378e6 −1.06012
\(544\) 161590. 0.0234108
\(545\) 0 0
\(546\) 8.37760e6 1.20265
\(547\) −2.61616e6 −0.373848 −0.186924 0.982374i \(-0.559852\pi\)
−0.186924 + 0.982374i \(0.559852\pi\)
\(548\) −3.07624e6 −0.437592
\(549\) 384851. 0.0544957
\(550\) 0 0
\(551\) 1.71052e6 0.240021
\(552\) 2.82205e6 0.394200
\(553\) −4.12290e6 −0.573310
\(554\) 3.06696e6 0.424555
\(555\) 0 0
\(556\) −5.48532e6 −0.752515
\(557\) −1.91062e6 −0.260937 −0.130469 0.991452i \(-0.541648\pi\)
−0.130469 + 0.991452i \(0.541648\pi\)
\(558\) −1.64850e6 −0.224132
\(559\) 9.90185e6 1.34025
\(560\) 0 0
\(561\) 859305. 0.115276
\(562\) 23901.3 0.00319213
\(563\) −84059.8 −0.0111768 −0.00558840 0.999984i \(-0.501779\pi\)
−0.00558840 + 0.999984i \(0.501779\pi\)
\(564\) −4.21917e6 −0.558508
\(565\) 0 0
\(566\) 756986. 0.0993222
\(567\) 9.34930e6 1.22130
\(568\) −3.53990e6 −0.460384
\(569\) −2.22862e6 −0.288572 −0.144286 0.989536i \(-0.546089\pi\)
−0.144286 + 0.989536i \(0.546089\pi\)
\(570\) 0 0
\(571\) 8.28284e6 1.06314 0.531568 0.847015i \(-0.321603\pi\)
0.531568 + 0.847015i \(0.321603\pi\)
\(572\) −4.49287e6 −0.574161
\(573\) 1.01663e7 1.29353
\(574\) −1.04960e7 −1.32968
\(575\) 0 0
\(576\) 256243. 0.0321807
\(577\) 1.50122e7 1.87717 0.938585 0.345047i \(-0.112137\pi\)
0.938585 + 0.345047i \(0.112137\pi\)
\(578\) −5.57982e6 −0.694705
\(579\) 3.19595e6 0.396190
\(580\) 0 0
\(581\) 5.45889e6 0.670910
\(582\) −9.72218e6 −1.18975
\(583\) −6.75986e6 −0.823695
\(584\) 3.10580e6 0.376826
\(585\) 0 0
\(586\) −3.94472e6 −0.474539
\(587\) 4.07944e6 0.488658 0.244329 0.969692i \(-0.421432\pi\)
0.244329 + 0.969692i \(0.421432\pi\)
\(588\) 240807. 0.0287227
\(589\) −2.37818e6 −0.282460
\(590\) 0 0
\(591\) 1.63169e6 0.192163
\(592\) −2.17820e6 −0.255443
\(593\) 545602. 0.0637147 0.0318573 0.999492i \(-0.489858\pi\)
0.0318573 + 0.999492i \(0.489858\pi\)
\(594\) −3.93032e6 −0.457048
\(595\) 0 0
\(596\) 5.37374e6 0.619671
\(597\) 1.26411e7 1.45161
\(598\) −9.09526e6 −1.04007
\(599\) −8.45396e6 −0.962704 −0.481352 0.876527i \(-0.659854\pi\)
−0.481352 + 0.876527i \(0.659854\pi\)
\(600\) 0 0
\(601\) −5.39862e6 −0.609673 −0.304836 0.952405i \(-0.598602\pi\)
−0.304836 + 0.952405i \(0.598602\pi\)
\(602\) 5.84052e6 0.656841
\(603\) −3.92623e6 −0.439727
\(604\) 4.26693e6 0.475908
\(605\) 0 0
\(606\) −8.54806e6 −0.945553
\(607\) 1.14275e7 1.25886 0.629432 0.777055i \(-0.283288\pi\)
0.629432 + 0.777055i \(0.283288\pi\)
\(608\) 369664. 0.0405554
\(609\) −1.10094e7 −1.20287
\(610\) 0 0
\(611\) 1.35981e7 1.47358
\(612\) 157952. 0.0170470
\(613\) 894639. 0.0961605 0.0480802 0.998843i \(-0.484690\pi\)
0.0480802 + 0.998843i \(0.484690\pi\)
\(614\) 5.82888e6 0.623971
\(615\) 0 0
\(616\) −2.65008e6 −0.281389
\(617\) −1.18925e7 −1.25765 −0.628826 0.777546i \(-0.716464\pi\)
−0.628826 + 0.777546i \(0.716464\pi\)
\(618\) 5.02958e6 0.529738
\(619\) 1.03513e7 1.08585 0.542924 0.839782i \(-0.317317\pi\)
0.542924 + 0.839782i \(0.317317\pi\)
\(620\) 0 0
\(621\) −7.95645e6 −0.827923
\(622\) 9.62106e6 0.997118
\(623\) 2.26837e6 0.234150
\(624\) −4.03372e6 −0.414710
\(625\) 0 0
\(626\) 1.28152e7 1.30704
\(627\) 1.96581e6 0.199697
\(628\) 2.78047e6 0.281332
\(629\) −1.34268e6 −0.135315
\(630\) 0 0
\(631\) −1.17088e6 −0.117068 −0.0585342 0.998285i \(-0.518643\pi\)
−0.0585342 + 0.998285i \(0.518643\pi\)
\(632\) 1.98513e6 0.197695
\(633\) 1.49878e6 0.148672
\(634\) 2.41219e6 0.238335
\(635\) 0 0
\(636\) −6.06904e6 −0.594946
\(637\) −776102. −0.0757828
\(638\) 5.90427e6 0.574268
\(639\) −3.46021e6 −0.335236
\(640\) 0 0
\(641\) −4.72990e6 −0.454681 −0.227341 0.973815i \(-0.573003\pi\)
−0.227341 + 0.973815i \(0.573003\pi\)
\(642\) −1.03716e6 −0.0993131
\(643\) 1.49075e7 1.42193 0.710963 0.703229i \(-0.248259\pi\)
0.710963 + 0.703229i \(0.248259\pi\)
\(644\) −5.36476e6 −0.509725
\(645\) 0 0
\(646\) 227867. 0.0214832
\(647\) 4.27732e6 0.401708 0.200854 0.979621i \(-0.435628\pi\)
0.200854 + 0.979621i \(0.435628\pi\)
\(648\) −4.50158e6 −0.421141
\(649\) −1.26714e7 −1.18090
\(650\) 0 0
\(651\) 1.53066e7 1.41555
\(652\) 6.50108e6 0.598917
\(653\) −2.25370e6 −0.206829 −0.103415 0.994638i \(-0.532977\pi\)
−0.103415 + 0.994638i \(0.532977\pi\)
\(654\) 9.79069e6 0.895094
\(655\) 0 0
\(656\) 5.05372e6 0.458513
\(657\) 3.03588e6 0.274392
\(658\) 8.02071e6 0.722184
\(659\) −2.93133e6 −0.262937 −0.131468 0.991320i \(-0.541969\pi\)
−0.131468 + 0.991320i \(0.541969\pi\)
\(660\) 0 0
\(661\) 6.56037e6 0.584016 0.292008 0.956416i \(-0.405677\pi\)
0.292008 + 0.956416i \(0.405677\pi\)
\(662\) −1.50967e7 −1.33886
\(663\) −2.48645e6 −0.219683
\(664\) −2.62840e6 −0.231351
\(665\) 0 0
\(666\) −2.12917e6 −0.186005
\(667\) 1.19525e7 1.04026
\(668\) 5.11512e6 0.443522
\(669\) −1.94216e6 −0.167772
\(670\) 0 0
\(671\) 1.91640e6 0.164316
\(672\) −2.37926e6 −0.203244
\(673\) 3.19596e6 0.271996 0.135998 0.990709i \(-0.456576\pi\)
0.135998 + 0.990709i \(0.456576\pi\)
\(674\) 8.51402e6 0.721913
\(675\) 0 0
\(676\) 7.05970e6 0.594182
\(677\) 2.06961e6 0.173547 0.0867734 0.996228i \(-0.472344\pi\)
0.0867734 + 0.996228i \(0.472344\pi\)
\(678\) −1.64435e7 −1.37379
\(679\) 1.84820e7 1.53842
\(680\) 0 0
\(681\) 5.49402e6 0.453965
\(682\) −8.20887e6 −0.675807
\(683\) 2.61594e6 0.214574 0.107287 0.994228i \(-0.465784\pi\)
0.107287 + 0.994228i \(0.465784\pi\)
\(684\) 361342. 0.0295310
\(685\) 0 0
\(686\) 8.47824e6 0.687852
\(687\) 2.54888e7 2.06043
\(688\) −2.81215e6 −0.226499
\(689\) 1.95601e7 1.56972
\(690\) 0 0
\(691\) −1.40203e7 −1.11703 −0.558513 0.829496i \(-0.688628\pi\)
−0.558513 + 0.829496i \(0.688628\pi\)
\(692\) 6.83701e6 0.542752
\(693\) −2.59042e6 −0.204898
\(694\) −9.61221e6 −0.757573
\(695\) 0 0
\(696\) 5.30088e6 0.414787
\(697\) 3.11520e6 0.242887
\(698\) 1.48748e7 1.15561
\(699\) −2.42321e7 −1.87585
\(700\) 0 0
\(701\) 3.42664e6 0.263375 0.131687 0.991291i \(-0.457961\pi\)
0.131687 + 0.991291i \(0.457961\pi\)
\(702\) 1.13726e7 0.870999
\(703\) −3.07161e6 −0.234411
\(704\) 1.27598e6 0.0970318
\(705\) 0 0
\(706\) 8.16770e6 0.616720
\(707\) 1.62500e7 1.22266
\(708\) −1.13764e7 −0.852950
\(709\) 8.04969e6 0.601400 0.300700 0.953719i \(-0.402780\pi\)
0.300700 + 0.953719i \(0.402780\pi\)
\(710\) 0 0
\(711\) 1.94044e6 0.143955
\(712\) −1.09220e6 −0.0807422
\(713\) −1.66178e7 −1.22420
\(714\) −1.46661e6 −0.107664
\(715\) 0 0
\(716\) 5.79114e6 0.422164
\(717\) 6.38234e6 0.463641
\(718\) −3.79797e6 −0.274942
\(719\) −2.66646e7 −1.92359 −0.961795 0.273771i \(-0.911729\pi\)
−0.961795 + 0.273771i \(0.911729\pi\)
\(720\) 0 0
\(721\) −9.56132e6 −0.684983
\(722\) 521284. 0.0372161
\(723\) −5.45929e6 −0.388410
\(724\) −6.66698e6 −0.472697
\(725\) 0 0
\(726\) −4.47540e6 −0.315130
\(727\) −1.25706e7 −0.882102 −0.441051 0.897482i \(-0.645394\pi\)
−0.441051 + 0.897482i \(0.645394\pi\)
\(728\) 7.66817e6 0.536245
\(729\) 8.99764e6 0.627061
\(730\) 0 0
\(731\) −1.73345e6 −0.119983
\(732\) 1.72056e6 0.118684
\(733\) 1.12272e7 0.771814 0.385907 0.922538i \(-0.373889\pi\)
0.385907 + 0.922538i \(0.373889\pi\)
\(734\) −6.97671e6 −0.477981
\(735\) 0 0
\(736\) 2.58307e6 0.175769
\(737\) −1.95511e7 −1.32587
\(738\) 4.93996e6 0.333874
\(739\) 1.05677e7 0.711820 0.355910 0.934520i \(-0.384171\pi\)
0.355910 + 0.934520i \(0.384171\pi\)
\(740\) 0 0
\(741\) −5.68818e6 −0.380564
\(742\) 1.15373e7 0.769301
\(743\) 5.83579e6 0.387817 0.193909 0.981020i \(-0.437883\pi\)
0.193909 + 0.981020i \(0.437883\pi\)
\(744\) −7.36997e6 −0.488127
\(745\) 0 0
\(746\) −1.83995e7 −1.21048
\(747\) −2.56923e6 −0.168462
\(748\) 786538. 0.0514003
\(749\) 1.97165e6 0.128418
\(750\) 0 0
\(751\) 4.48767e6 0.290349 0.145175 0.989406i \(-0.453626\pi\)
0.145175 + 0.989406i \(0.453626\pi\)
\(752\) −3.86188e6 −0.249032
\(753\) −1.69575e7 −1.08987
\(754\) −1.70844e7 −1.09439
\(755\) 0 0
\(756\) 6.70805e6 0.426866
\(757\) −7.81327e6 −0.495557 −0.247778 0.968817i \(-0.579700\pi\)
−0.247778 + 0.968817i \(0.579700\pi\)
\(758\) −27974.8 −0.00176845
\(759\) 1.37363e7 0.865497
\(760\) 0 0
\(761\) 1.81639e7 1.13697 0.568483 0.822695i \(-0.307531\pi\)
0.568483 + 0.822695i \(0.307531\pi\)
\(762\) 1.73291e6 0.108116
\(763\) −1.86123e7 −1.15741
\(764\) 9.30537e6 0.576767
\(765\) 0 0
\(766\) −5.50720e6 −0.339124
\(767\) 3.66655e7 2.25045
\(768\) 1.14559e6 0.0700849
\(769\) −4.47189e6 −0.272694 −0.136347 0.990661i \(-0.543536\pi\)
−0.136347 + 0.990661i \(0.543536\pi\)
\(770\) 0 0
\(771\) −2.25474e7 −1.36603
\(772\) 2.92531e6 0.176656
\(773\) 2.53207e7 1.52415 0.762075 0.647489i \(-0.224181\pi\)
0.762075 + 0.647489i \(0.224181\pi\)
\(774\) −2.74884e6 −0.164929
\(775\) 0 0
\(776\) −8.89889e6 −0.530496
\(777\) 1.97697e7 1.17475
\(778\) 5.60460e6 0.331967
\(779\) 7.12654e6 0.420761
\(780\) 0 0
\(781\) −1.72305e7 −1.01081
\(782\) 1.59225e6 0.0931095
\(783\) −1.49452e7 −0.871161
\(784\) 220415. 0.0128071
\(785\) 0 0
\(786\) −1.06664e7 −0.615831
\(787\) −4.73524e6 −0.272524 −0.136262 0.990673i \(-0.543509\pi\)
−0.136262 + 0.990673i \(0.543509\pi\)
\(788\) 1.49352e6 0.0856831
\(789\) 8.76506e6 0.501259
\(790\) 0 0
\(791\) 3.12593e7 1.77639
\(792\) 1.24726e6 0.0706552
\(793\) −5.54523e6 −0.313139
\(794\) −1.33361e7 −0.750719
\(795\) 0 0
\(796\) 1.15707e7 0.647255
\(797\) −1.54780e7 −0.863116 −0.431558 0.902085i \(-0.642036\pi\)
−0.431558 + 0.902085i \(0.642036\pi\)
\(798\) −3.35512e6 −0.186510
\(799\) −2.38053e6 −0.131919
\(800\) 0 0
\(801\) −1.06761e6 −0.0587937
\(802\) −2.13045e7 −1.16959
\(803\) 1.51175e7 0.827351
\(804\) −1.75530e7 −0.957662
\(805\) 0 0
\(806\) 2.37529e7 1.28789
\(807\) 2.49943e7 1.35101
\(808\) −7.82420e6 −0.421611
\(809\) 5.54794e6 0.298031 0.149015 0.988835i \(-0.452390\pi\)
0.149015 + 0.988835i \(0.452390\pi\)
\(810\) 0 0
\(811\) 9.82955e6 0.524785 0.262392 0.964961i \(-0.415489\pi\)
0.262392 + 0.964961i \(0.415489\pi\)
\(812\) −1.00771e7 −0.536345
\(813\) −1.24023e7 −0.658078
\(814\) −1.06024e7 −0.560845
\(815\) 0 0
\(816\) 706158. 0.0371258
\(817\) −3.96557e6 −0.207850
\(818\) −1.20344e7 −0.628843
\(819\) 7.49555e6 0.390475
\(820\) 0 0
\(821\) 1.78229e7 0.922830 0.461415 0.887185i \(-0.347342\pi\)
0.461415 + 0.887185i \(0.347342\pi\)
\(822\) −1.34434e7 −0.693951
\(823\) 1.29509e7 0.666502 0.333251 0.942838i \(-0.391854\pi\)
0.333251 + 0.942838i \(0.391854\pi\)
\(824\) 4.60367e6 0.236204
\(825\) 0 0
\(826\) 2.16268e7 1.10292
\(827\) 2.57276e7 1.30808 0.654042 0.756458i \(-0.273072\pi\)
0.654042 + 0.756458i \(0.273072\pi\)
\(828\) 2.52492e6 0.127989
\(829\) 2.26984e7 1.14712 0.573559 0.819164i \(-0.305562\pi\)
0.573559 + 0.819164i \(0.305562\pi\)
\(830\) 0 0
\(831\) 1.34028e7 0.673276
\(832\) −3.69214e6 −0.184914
\(833\) 135867. 0.00678426
\(834\) −2.39712e7 −1.19337
\(835\) 0 0
\(836\) 1.79934e6 0.0890424
\(837\) 2.07788e7 1.02519
\(838\) 9.89881e6 0.486937
\(839\) −9.22885e6 −0.452629 −0.226315 0.974054i \(-0.572668\pi\)
−0.226315 + 0.974054i \(0.572668\pi\)
\(840\) 0 0
\(841\) 1.94015e6 0.0945898
\(842\) −1.30235e7 −0.633063
\(843\) 104450. 0.00506221
\(844\) 1.37186e6 0.0662910
\(845\) 0 0
\(846\) −3.77495e6 −0.181336
\(847\) 8.50780e6 0.407482
\(848\) −5.55511e6 −0.265279
\(849\) 3.30807e6 0.157509
\(850\) 0 0
\(851\) −2.14632e7 −1.01595
\(852\) −1.54696e7 −0.730096
\(853\) 3.17055e7 1.49198 0.745989 0.665959i \(-0.231977\pi\)
0.745989 + 0.665959i \(0.231977\pi\)
\(854\) −3.27081e6 −0.153465
\(855\) 0 0
\(856\) −949328. −0.0442825
\(857\) −3.01353e7 −1.40160 −0.700799 0.713359i \(-0.747173\pi\)
−0.700799 + 0.713359i \(0.747173\pi\)
\(858\) −1.96341e7 −0.910528
\(859\) −1.58417e7 −0.732520 −0.366260 0.930513i \(-0.619362\pi\)
−0.366260 + 0.930513i \(0.619362\pi\)
\(860\) 0 0
\(861\) −4.58683e7 −2.10865
\(862\) −1.41902e7 −0.650461
\(863\) 2.32831e7 1.06418 0.532089 0.846689i \(-0.321407\pi\)
0.532089 + 0.846689i \(0.321407\pi\)
\(864\) −3.22985e6 −0.147197
\(865\) 0 0
\(866\) −1.03584e7 −0.469351
\(867\) −2.43842e7 −1.10169
\(868\) 1.40104e7 0.631178
\(869\) 9.66261e6 0.434055
\(870\) 0 0
\(871\) 5.65722e7 2.52672
\(872\) 8.96160e6 0.399111
\(873\) −8.69856e6 −0.386289
\(874\) 3.64254e6 0.161297
\(875\) 0 0
\(876\) 1.35725e7 0.597586
\(877\) −2.89258e7 −1.26995 −0.634975 0.772532i \(-0.718990\pi\)
−0.634975 + 0.772532i \(0.718990\pi\)
\(878\) −1.39073e7 −0.608844
\(879\) −1.72387e7 −0.752544
\(880\) 0 0
\(881\) −2.35636e7 −1.02283 −0.511413 0.859335i \(-0.670878\pi\)
−0.511413 + 0.859335i \(0.670878\pi\)
\(882\) 215453. 0.00932569
\(883\) 1.91319e6 0.0825764 0.0412882 0.999147i \(-0.486854\pi\)
0.0412882 + 0.999147i \(0.486854\pi\)
\(884\) −2.27589e6 −0.0979538
\(885\) 0 0
\(886\) 1.28998e7 0.552078
\(887\) −3.48791e7 −1.48852 −0.744262 0.667888i \(-0.767199\pi\)
−0.744262 + 0.667888i \(0.767199\pi\)
\(888\) −9.51888e6 −0.405092
\(889\) −3.29430e6 −0.139800
\(890\) 0 0
\(891\) −2.19114e7 −0.924648
\(892\) −1.77770e6 −0.0748076
\(893\) −5.44586e6 −0.228527
\(894\) 2.34836e7 0.982699
\(895\) 0 0
\(896\) −2.17778e6 −0.0906241
\(897\) −3.97468e7 −1.64938
\(898\) −1.79088e7 −0.741099
\(899\) −3.12146e7 −1.28813
\(900\) 0 0
\(901\) −3.42426e6 −0.140525
\(902\) 2.45990e7 1.00670
\(903\) 2.55235e7 1.04165
\(904\) −1.50510e7 −0.612554
\(905\) 0 0
\(906\) 1.86467e7 0.754714
\(907\) −1.34601e7 −0.543287 −0.271644 0.962398i \(-0.587567\pi\)
−0.271644 + 0.962398i \(0.587567\pi\)
\(908\) 5.02878e6 0.202418
\(909\) −7.64806e6 −0.307002
\(910\) 0 0
\(911\) −1.42316e7 −0.568144 −0.284072 0.958803i \(-0.591685\pi\)
−0.284072 + 0.958803i \(0.591685\pi\)
\(912\) 1.61546e6 0.0643143
\(913\) −1.27937e7 −0.507948
\(914\) −2.25575e6 −0.0893154
\(915\) 0 0
\(916\) 2.33303e7 0.918718
\(917\) 2.02770e7 0.796307
\(918\) −1.99093e6 −0.0779740
\(919\) 1.48289e7 0.579188 0.289594 0.957150i \(-0.406480\pi\)
0.289594 + 0.957150i \(0.406480\pi\)
\(920\) 0 0
\(921\) 2.54726e7 0.989518
\(922\) −1.22130e7 −0.473146
\(923\) 4.98574e7 1.92631
\(924\) −1.15810e7 −0.446238
\(925\) 0 0
\(926\) −2.92764e7 −1.12199
\(927\) 4.50003e6 0.171995
\(928\) 4.85200e6 0.184948
\(929\) 1.48557e7 0.564748 0.282374 0.959304i \(-0.408878\pi\)
0.282374 + 0.959304i \(0.408878\pi\)
\(930\) 0 0
\(931\) 310819. 0.0117526
\(932\) −2.21801e7 −0.836418
\(933\) 4.20446e7 1.58127
\(934\) 1.53203e7 0.574645
\(935\) 0 0
\(936\) −3.60902e6 −0.134648
\(937\) −9.74272e6 −0.362519 −0.181260 0.983435i \(-0.558017\pi\)
−0.181260 + 0.983435i \(0.558017\pi\)
\(938\) 3.33686e7 1.23832
\(939\) 5.60032e7 2.07276
\(940\) 0 0
\(941\) −2.16418e6 −0.0796745 −0.0398373 0.999206i \(-0.512684\pi\)
−0.0398373 + 0.999206i \(0.512684\pi\)
\(942\) 1.21508e7 0.446148
\(943\) 4.97976e7 1.82360
\(944\) −1.04131e7 −0.380320
\(945\) 0 0
\(946\) −1.36881e7 −0.497297
\(947\) −1.60138e7 −0.580254 −0.290127 0.956988i \(-0.593698\pi\)
−0.290127 + 0.956988i \(0.593698\pi\)
\(948\) 8.67514e6 0.313513
\(949\) −4.37433e7 −1.57669
\(950\) 0 0
\(951\) 1.05414e7 0.377961
\(952\) −1.34242e6 −0.0480060
\(953\) 2.67154e6 0.0952860 0.0476430 0.998864i \(-0.484829\pi\)
0.0476430 + 0.998864i \(0.484829\pi\)
\(954\) −5.43005e6 −0.193167
\(955\) 0 0
\(956\) 5.84188e6 0.206732
\(957\) 2.58020e7 0.910697
\(958\) −3.40856e6 −0.119993
\(959\) 2.55561e7 0.897321
\(960\) 0 0
\(961\) 1.47694e7 0.515888
\(962\) 3.06787e7 1.06881
\(963\) −927957. −0.0322450
\(964\) −4.99699e6 −0.173187
\(965\) 0 0
\(966\) −2.34443e7 −0.808342
\(967\) 7.08291e6 0.243582 0.121791 0.992556i \(-0.461136\pi\)
0.121791 + 0.992556i \(0.461136\pi\)
\(968\) −4.09641e6 −0.140513
\(969\) 995793. 0.0340690
\(970\) 0 0
\(971\) 2.85104e7 0.970411 0.485205 0.874400i \(-0.338745\pi\)
0.485205 + 0.874400i \(0.338745\pi\)
\(972\) −7.40887e6 −0.251528
\(973\) 4.55697e7 1.54310
\(974\) 7.07813e6 0.239068
\(975\) 0 0
\(976\) 1.57486e6 0.0529197
\(977\) 2.48752e7 0.833739 0.416869 0.908966i \(-0.363127\pi\)
0.416869 + 0.908966i \(0.363127\pi\)
\(978\) 2.84101e7 0.949786
\(979\) −5.31626e6 −0.177276
\(980\) 0 0
\(981\) 8.75985e6 0.290619
\(982\) −4.50808e6 −0.149181
\(983\) 2.66082e6 0.0878277 0.0439138 0.999035i \(-0.486017\pi\)
0.0439138 + 0.999035i \(0.486017\pi\)
\(984\) 2.20851e7 0.727129
\(985\) 0 0
\(986\) 2.99085e6 0.0979721
\(987\) 3.50510e7 1.14527
\(988\) −5.20649e6 −0.169689
\(989\) −2.77099e7 −0.900833
\(990\) 0 0
\(991\) 5.19709e7 1.68103 0.840516 0.541786i \(-0.182252\pi\)
0.840516 + 0.541786i \(0.182252\pi\)
\(992\) −6.74587e6 −0.217650
\(993\) −6.59734e7 −2.12322
\(994\) 2.94080e7 0.944058
\(995\) 0 0
\(996\) −1.14863e7 −0.366885
\(997\) 1.86644e7 0.594672 0.297336 0.954773i \(-0.403902\pi\)
0.297336 + 0.954773i \(0.403902\pi\)
\(998\) −2.38449e7 −0.757826
\(999\) 2.68374e7 0.850799
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.1.2 2
5.4 even 2 38.6.a.c.1.1 2
15.14 odd 2 342.6.a.i.1.2 2
20.19 odd 2 304.6.a.f.1.2 2
95.94 odd 2 722.6.a.c.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.6.a.c.1.1 2 5.4 even 2
304.6.a.f.1.2 2 20.19 odd 2
342.6.a.i.1.2 2 15.14 odd 2
722.6.a.c.1.2 2 95.94 odd 2
950.6.a.d.1.2 2 1.1 even 1 trivial