Properties

Label 1045.6.a.h.1.10
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(167.601091705\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.34868 q^{2} -22.4542 q^{3} +8.30576 q^{4} +25.0000 q^{5} +142.555 q^{6} +214.893 q^{7} +150.427 q^{8} +261.192 q^{9} +O(q^{10})\) \(q-6.34868 q^{2} -22.4542 q^{3} +8.30576 q^{4} +25.0000 q^{5} +142.555 q^{6} +214.893 q^{7} +150.427 q^{8} +261.192 q^{9} -158.717 q^{10} +121.000 q^{11} -186.499 q^{12} -442.495 q^{13} -1364.29 q^{14} -561.355 q^{15} -1220.80 q^{16} -1314.46 q^{17} -1658.22 q^{18} +361.000 q^{19} +207.644 q^{20} -4825.25 q^{21} -768.191 q^{22} +2155.21 q^{23} -3377.72 q^{24} +625.000 q^{25} +2809.26 q^{26} -408.482 q^{27} +1784.85 q^{28} +5038.86 q^{29} +3563.87 q^{30} -436.198 q^{31} +2936.79 q^{32} -2716.96 q^{33} +8345.06 q^{34} +5372.33 q^{35} +2169.40 q^{36} +3960.63 q^{37} -2291.87 q^{38} +9935.87 q^{39} +3760.68 q^{40} +8185.36 q^{41} +30634.0 q^{42} +2467.24 q^{43} +1005.00 q^{44} +6529.79 q^{45} -13682.7 q^{46} +17130.2 q^{47} +27412.1 q^{48} +29372.0 q^{49} -3967.93 q^{50} +29515.1 q^{51} -3675.25 q^{52} -23996.2 q^{53} +2593.32 q^{54} +3025.00 q^{55} +32325.8 q^{56} -8105.97 q^{57} -31990.1 q^{58} -31353.1 q^{59} -4662.48 q^{60} +42578.9 q^{61} +2769.28 q^{62} +56128.3 q^{63} +20420.8 q^{64} -11062.4 q^{65} +17249.1 q^{66} +3535.51 q^{67} -10917.6 q^{68} -48393.5 q^{69} -34107.2 q^{70} -34547.2 q^{71} +39290.3 q^{72} +9028.46 q^{73} -25144.8 q^{74} -14033.9 q^{75} +2998.38 q^{76} +26002.1 q^{77} -63079.7 q^{78} +3140.13 q^{79} -30520.0 q^{80} -54297.5 q^{81} -51966.2 q^{82} -42776.4 q^{83} -40077.4 q^{84} -32861.4 q^{85} -15663.8 q^{86} -113144. q^{87} +18201.7 q^{88} +83224.0 q^{89} -41455.6 q^{90} -95089.0 q^{91} +17900.6 q^{92} +9794.47 q^{93} -108754. q^{94} +9025.00 q^{95} -65943.4 q^{96} -42553.9 q^{97} -186474. q^{98} +31604.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.34868 −1.12230 −0.561150 0.827714i \(-0.689641\pi\)
−0.561150 + 0.827714i \(0.689641\pi\)
\(3\) −22.4542 −1.44044 −0.720219 0.693746i \(-0.755959\pi\)
−0.720219 + 0.693746i \(0.755959\pi\)
\(4\) 8.30576 0.259555
\(5\) 25.0000 0.447214
\(6\) 142.555 1.61660
\(7\) 214.893 1.65759 0.828795 0.559552i \(-0.189027\pi\)
0.828795 + 0.559552i \(0.189027\pi\)
\(8\) 150.427 0.831001
\(9\) 261.192 1.07486
\(10\) −158.717 −0.501907
\(11\) 121.000 0.301511
\(12\) −186.499 −0.373873
\(13\) −442.495 −0.726189 −0.363094 0.931752i \(-0.618280\pi\)
−0.363094 + 0.931752i \(0.618280\pi\)
\(14\) −1364.29 −1.86031
\(15\) −561.355 −0.644184
\(16\) −1220.80 −1.19219
\(17\) −1314.46 −1.10312 −0.551561 0.834134i \(-0.685968\pi\)
−0.551561 + 0.834134i \(0.685968\pi\)
\(18\) −1658.22 −1.20632
\(19\) 361.000 0.229416
\(20\) 207.644 0.116077
\(21\) −4825.25 −2.38766
\(22\) −768.191 −0.338386
\(23\) 2155.21 0.849512 0.424756 0.905308i \(-0.360360\pi\)
0.424756 + 0.905308i \(0.360360\pi\)
\(24\) −3377.72 −1.19701
\(25\) 625.000 0.200000
\(26\) 2809.26 0.815001
\(27\) −408.482 −0.107836
\(28\) 1784.85 0.430236
\(29\) 5038.86 1.11260 0.556298 0.830983i \(-0.312221\pi\)
0.556298 + 0.830983i \(0.312221\pi\)
\(30\) 3563.87 0.722967
\(31\) −436.198 −0.0815228 −0.0407614 0.999169i \(-0.512978\pi\)
−0.0407614 + 0.999169i \(0.512978\pi\)
\(32\) 2936.79 0.506989
\(33\) −2716.96 −0.434309
\(34\) 8345.06 1.23803
\(35\) 5372.33 0.741297
\(36\) 2169.40 0.278986
\(37\) 3960.63 0.475620 0.237810 0.971312i \(-0.423570\pi\)
0.237810 + 0.971312i \(0.423570\pi\)
\(38\) −2291.87 −0.257473
\(39\) 9935.87 1.04603
\(40\) 3760.68 0.371635
\(41\) 8185.36 0.760463 0.380231 0.924891i \(-0.375844\pi\)
0.380231 + 0.924891i \(0.375844\pi\)
\(42\) 30634.0 2.67967
\(43\) 2467.24 0.203489 0.101745 0.994811i \(-0.467558\pi\)
0.101745 + 0.994811i \(0.467558\pi\)
\(44\) 1005.00 0.0782588
\(45\) 6529.79 0.480693
\(46\) −13682.7 −0.953407
\(47\) 17130.2 1.13114 0.565572 0.824699i \(-0.308656\pi\)
0.565572 + 0.824699i \(0.308656\pi\)
\(48\) 27412.1 1.71727
\(49\) 29372.0 1.74761
\(50\) −3967.93 −0.224460
\(51\) 29515.1 1.58898
\(52\) −3675.25 −0.188486
\(53\) −23996.2 −1.17342 −0.586709 0.809798i \(-0.699577\pi\)
−0.586709 + 0.809798i \(0.699577\pi\)
\(54\) 2593.32 0.121024
\(55\) 3025.00 0.134840
\(56\) 32325.8 1.37746
\(57\) −8105.97 −0.330459
\(58\) −31990.1 −1.24866
\(59\) −31353.1 −1.17260 −0.586301 0.810094i \(-0.699416\pi\)
−0.586301 + 0.810094i \(0.699416\pi\)
\(60\) −4662.48 −0.167201
\(61\) 42578.9 1.46511 0.732555 0.680708i \(-0.238328\pi\)
0.732555 + 0.680708i \(0.238328\pi\)
\(62\) 2769.28 0.0914929
\(63\) 56128.3 1.78168
\(64\) 20420.8 0.623193
\(65\) −11062.4 −0.324761
\(66\) 17249.1 0.487424
\(67\) 3535.51 0.0962199 0.0481100 0.998842i \(-0.484680\pi\)
0.0481100 + 0.998842i \(0.484680\pi\)
\(68\) −10917.6 −0.286321
\(69\) −48393.5 −1.22367
\(70\) −34107.2 −0.831957
\(71\) −34547.2 −0.813330 −0.406665 0.913577i \(-0.633308\pi\)
−0.406665 + 0.913577i \(0.633308\pi\)
\(72\) 39290.3 0.893212
\(73\) 9028.46 0.198293 0.0991464 0.995073i \(-0.468389\pi\)
0.0991464 + 0.995073i \(0.468389\pi\)
\(74\) −25144.8 −0.533788
\(75\) −14033.9 −0.288088
\(76\) 2998.38 0.0595460
\(77\) 26002.1 0.499782
\(78\) −63079.7 −1.17396
\(79\) 3140.13 0.0566083 0.0283042 0.999599i \(-0.490989\pi\)
0.0283042 + 0.999599i \(0.490989\pi\)
\(80\) −30520.0 −0.533162
\(81\) −54297.5 −0.919532
\(82\) −51966.2 −0.853467
\(83\) −42776.4 −0.681568 −0.340784 0.940142i \(-0.610692\pi\)
−0.340784 + 0.940142i \(0.610692\pi\)
\(84\) −40077.4 −0.619729
\(85\) −32861.4 −0.493331
\(86\) −15663.8 −0.228376
\(87\) −113144. −1.60263
\(88\) 18201.7 0.250556
\(89\) 83224.0 1.11371 0.556857 0.830608i \(-0.312007\pi\)
0.556857 + 0.830608i \(0.312007\pi\)
\(90\) −41455.6 −0.539482
\(91\) −95089.0 −1.20372
\(92\) 17900.6 0.220495
\(93\) 9794.47 0.117429
\(94\) −108754. −1.26948
\(95\) 9025.00 0.102598
\(96\) −65943.4 −0.730286
\(97\) −42553.9 −0.459209 −0.229604 0.973284i \(-0.573743\pi\)
−0.229604 + 0.973284i \(0.573743\pi\)
\(98\) −186474. −1.96134
\(99\) 31604.2 0.324083
\(100\) 5191.10 0.0519110
\(101\) 107041. 1.04411 0.522054 0.852913i \(-0.325166\pi\)
0.522054 + 0.852913i \(0.325166\pi\)
\(102\) −187382. −1.78331
\(103\) −79882.8 −0.741925 −0.370963 0.928648i \(-0.620972\pi\)
−0.370963 + 0.928648i \(0.620972\pi\)
\(104\) −66563.2 −0.603463
\(105\) −120631. −1.06779
\(106\) 152344. 1.31693
\(107\) 83691.3 0.706677 0.353338 0.935496i \(-0.385046\pi\)
0.353338 + 0.935496i \(0.385046\pi\)
\(108\) −3392.76 −0.0279894
\(109\) 62991.4 0.507826 0.253913 0.967227i \(-0.418282\pi\)
0.253913 + 0.967227i \(0.418282\pi\)
\(110\) −19204.8 −0.151331
\(111\) −88932.9 −0.685102
\(112\) −262341. −1.97616
\(113\) 201880. 1.48730 0.743649 0.668570i \(-0.233093\pi\)
0.743649 + 0.668570i \(0.233093\pi\)
\(114\) 51462.2 0.370874
\(115\) 53880.2 0.379913
\(116\) 41851.6 0.288780
\(117\) −115576. −0.780554
\(118\) 199051. 1.31601
\(119\) −282467. −1.82853
\(120\) −84443.1 −0.535317
\(121\) 14641.0 0.0909091
\(122\) −270320. −1.64429
\(123\) −183796. −1.09540
\(124\) −3622.95 −0.0211597
\(125\) 15625.0 0.0894427
\(126\) −356341. −1.99958
\(127\) 250781. 1.37970 0.689851 0.723951i \(-0.257676\pi\)
0.689851 + 0.723951i \(0.257676\pi\)
\(128\) −223623. −1.20640
\(129\) −55400.0 −0.293114
\(130\) 70231.4 0.364480
\(131\) −156745. −0.798023 −0.399011 0.916946i \(-0.630647\pi\)
−0.399011 + 0.916946i \(0.630647\pi\)
\(132\) −22566.4 −0.112727
\(133\) 77576.4 0.380277
\(134\) −22445.8 −0.107988
\(135\) −10212.1 −0.0482257
\(136\) −197730. −0.916695
\(137\) 154367. 0.702672 0.351336 0.936249i \(-0.385727\pi\)
0.351336 + 0.936249i \(0.385727\pi\)
\(138\) 307235. 1.37332
\(139\) 303213. 1.33110 0.665550 0.746353i \(-0.268197\pi\)
0.665550 + 0.746353i \(0.268197\pi\)
\(140\) 44621.3 0.192407
\(141\) −384645. −1.62934
\(142\) 219329. 0.912799
\(143\) −53541.8 −0.218954
\(144\) −318863. −1.28144
\(145\) 125971. 0.497568
\(146\) −57318.8 −0.222544
\(147\) −659525. −2.51732
\(148\) 32896.1 0.123450
\(149\) −186944. −0.689837 −0.344918 0.938633i \(-0.612093\pi\)
−0.344918 + 0.938633i \(0.612093\pi\)
\(150\) 89096.7 0.323321
\(151\) −476803. −1.70175 −0.850877 0.525365i \(-0.823929\pi\)
−0.850877 + 0.525365i \(0.823929\pi\)
\(152\) 54304.2 0.190645
\(153\) −343325. −1.18571
\(154\) −165079. −0.560905
\(155\) −10904.9 −0.0364581
\(156\) 82525.0 0.271502
\(157\) 371660. 1.20336 0.601681 0.798737i \(-0.294498\pi\)
0.601681 + 0.798737i \(0.294498\pi\)
\(158\) −19935.7 −0.0635315
\(159\) 538816. 1.69024
\(160\) 73419.8 0.226732
\(161\) 463139. 1.40814
\(162\) 344717. 1.03199
\(163\) 451810. 1.33195 0.665974 0.745975i \(-0.268016\pi\)
0.665974 + 0.745975i \(0.268016\pi\)
\(164\) 67985.6 0.197382
\(165\) −67924.0 −0.194229
\(166\) 271574. 0.764923
\(167\) −350751. −0.973211 −0.486606 0.873622i \(-0.661765\pi\)
−0.486606 + 0.873622i \(0.661765\pi\)
\(168\) −725849. −1.98414
\(169\) −175492. −0.472650
\(170\) 208627. 0.553665
\(171\) 94290.2 0.246591
\(172\) 20492.3 0.0528166
\(173\) 704705. 1.79016 0.895080 0.445905i \(-0.147118\pi\)
0.895080 + 0.445905i \(0.147118\pi\)
\(174\) 718313. 1.79862
\(175\) 134308. 0.331518
\(176\) −147717. −0.359458
\(177\) 704009. 1.68906
\(178\) −528363. −1.24992
\(179\) −244688. −0.570794 −0.285397 0.958409i \(-0.592125\pi\)
−0.285397 + 0.958409i \(0.592125\pi\)
\(180\) 54234.9 0.124766
\(181\) −824064. −1.86967 −0.934834 0.355084i \(-0.884452\pi\)
−0.934834 + 0.355084i \(0.884452\pi\)
\(182\) 603690. 1.35094
\(183\) −956077. −2.11040
\(184\) 324202. 0.705945
\(185\) 99015.8 0.212704
\(186\) −62182.0 −0.131790
\(187\) −159049. −0.332604
\(188\) 142279. 0.293594
\(189\) −87780.0 −0.178748
\(190\) −57296.9 −0.115145
\(191\) −161668. −0.320657 −0.160329 0.987064i \(-0.551255\pi\)
−0.160329 + 0.987064i \(0.551255\pi\)
\(192\) −458533. −0.897672
\(193\) −532383. −1.02880 −0.514400 0.857550i \(-0.671985\pi\)
−0.514400 + 0.857550i \(0.671985\pi\)
\(194\) 270161. 0.515370
\(195\) 248397. 0.467799
\(196\) 243957. 0.453600
\(197\) 66466.1 0.122021 0.0610105 0.998137i \(-0.480568\pi\)
0.0610105 + 0.998137i \(0.480568\pi\)
\(198\) −200645. −0.363719
\(199\) 173073. 0.309810 0.154905 0.987929i \(-0.450493\pi\)
0.154905 + 0.987929i \(0.450493\pi\)
\(200\) 94017.0 0.166200
\(201\) −79387.1 −0.138599
\(202\) −679567. −1.17180
\(203\) 1.08282e6 1.84423
\(204\) 245145. 0.412428
\(205\) 204634. 0.340089
\(206\) 507150. 0.832662
\(207\) 562923. 0.913109
\(208\) 540197. 0.865752
\(209\) 43681.0 0.0691714
\(210\) 765850. 1.19838
\(211\) −843188. −1.30382 −0.651911 0.758295i \(-0.726032\pi\)
−0.651911 + 0.758295i \(0.726032\pi\)
\(212\) −199307. −0.304567
\(213\) 775730. 1.17155
\(214\) −531330. −0.793103
\(215\) 61681.1 0.0910031
\(216\) −61446.8 −0.0896118
\(217\) −93735.8 −0.135131
\(218\) −399913. −0.569933
\(219\) −202727. −0.285628
\(220\) 25124.9 0.0349984
\(221\) 581640. 0.801075
\(222\) 564607. 0.768889
\(223\) 1.04352e6 1.40520 0.702599 0.711586i \(-0.252023\pi\)
0.702599 + 0.711586i \(0.252023\pi\)
\(224\) 631096. 0.840380
\(225\) 163245. 0.214973
\(226\) −1.28167e6 −1.66919
\(227\) −962243. −1.23942 −0.619712 0.784829i \(-0.712751\pi\)
−0.619712 + 0.784829i \(0.712751\pi\)
\(228\) −67326.3 −0.0857724
\(229\) −529304. −0.666986 −0.333493 0.942753i \(-0.608227\pi\)
−0.333493 + 0.942753i \(0.608227\pi\)
\(230\) −342068. −0.426376
\(231\) −583856. −0.719906
\(232\) 757981. 0.924567
\(233\) 66677.7 0.0804620 0.0402310 0.999190i \(-0.487191\pi\)
0.0402310 + 0.999190i \(0.487191\pi\)
\(234\) 733755. 0.876015
\(235\) 428255. 0.505863
\(236\) −260411. −0.304355
\(237\) −70509.2 −0.0815408
\(238\) 1.79330e6 2.05215
\(239\) −1.13029e6 −1.27996 −0.639980 0.768392i \(-0.721057\pi\)
−0.639980 + 0.768392i \(0.721057\pi\)
\(240\) 685302. 0.767987
\(241\) −1.39564e6 −1.54786 −0.773931 0.633271i \(-0.781712\pi\)
−0.773931 + 0.633271i \(0.781712\pi\)
\(242\) −92951.1 −0.102027
\(243\) 1.31847e6 1.43237
\(244\) 353651. 0.380277
\(245\) 734300. 0.781553
\(246\) 1.16686e6 1.22937
\(247\) −159741. −0.166599
\(248\) −65616.0 −0.0677455
\(249\) 960511. 0.981757
\(250\) −99198.2 −0.100381
\(251\) −226197. −0.226622 −0.113311 0.993560i \(-0.536146\pi\)
−0.113311 + 0.993560i \(0.536146\pi\)
\(252\) 466188. 0.462445
\(253\) 260780. 0.256138
\(254\) −1.59213e6 −1.54844
\(255\) 737877. 0.710614
\(256\) 766243. 0.730746
\(257\) −172685. −0.163088 −0.0815442 0.996670i \(-0.525985\pi\)
−0.0815442 + 0.996670i \(0.525985\pi\)
\(258\) 351717. 0.328961
\(259\) 851113. 0.788384
\(260\) −91881.4 −0.0842935
\(261\) 1.31611e6 1.19589
\(262\) 995124. 0.895620
\(263\) 717612. 0.639735 0.319867 0.947462i \(-0.396362\pi\)
0.319867 + 0.947462i \(0.396362\pi\)
\(264\) −408705. −0.360911
\(265\) −599905. −0.524769
\(266\) −492508. −0.426785
\(267\) −1.86873e6 −1.60424
\(268\) 29365.1 0.0249744
\(269\) 1.02921e6 0.867212 0.433606 0.901103i \(-0.357241\pi\)
0.433606 + 0.901103i \(0.357241\pi\)
\(270\) 64833.1 0.0541237
\(271\) −690396. −0.571051 −0.285525 0.958371i \(-0.592168\pi\)
−0.285525 + 0.958371i \(0.592168\pi\)
\(272\) 1.60469e6 1.31513
\(273\) 2.13515e6 1.73389
\(274\) −980026. −0.788608
\(275\) 75625.0 0.0603023
\(276\) −401945. −0.317610
\(277\) −1.51090e6 −1.18314 −0.591570 0.806254i \(-0.701492\pi\)
−0.591570 + 0.806254i \(0.701492\pi\)
\(278\) −1.92500e6 −1.49389
\(279\) −113931. −0.0876259
\(280\) 808144. 0.616018
\(281\) 463522. 0.350191 0.175095 0.984551i \(-0.443977\pi\)
0.175095 + 0.984551i \(0.443977\pi\)
\(282\) 2.44199e6 1.82861
\(283\) −260470. −0.193327 −0.0966633 0.995317i \(-0.530817\pi\)
−0.0966633 + 0.995317i \(0.530817\pi\)
\(284\) −286941. −0.211104
\(285\) −202649. −0.147786
\(286\) 339920. 0.245732
\(287\) 1.75898e6 1.26054
\(288\) 767066. 0.544944
\(289\) 307937. 0.216879
\(290\) −799753. −0.558420
\(291\) 955515. 0.661462
\(292\) 74988.3 0.0514679
\(293\) 3216.72 0.00218899 0.00109450 0.999999i \(-0.499652\pi\)
0.00109450 + 0.999999i \(0.499652\pi\)
\(294\) 4.18712e6 2.82518
\(295\) −783827. −0.524403
\(296\) 595787. 0.395241
\(297\) −49426.4 −0.0325138
\(298\) 1.18685e6 0.774203
\(299\) −953668. −0.616906
\(300\) −116562. −0.0747746
\(301\) 530194. 0.337302
\(302\) 3.02707e6 1.90988
\(303\) −2.40351e6 −1.50397
\(304\) −440708. −0.273506
\(305\) 1.06447e6 0.655217
\(306\) 2.17966e6 1.33072
\(307\) 1.38589e6 0.839234 0.419617 0.907701i \(-0.362164\pi\)
0.419617 + 0.907701i \(0.362164\pi\)
\(308\) 215967. 0.129721
\(309\) 1.79370e6 1.06870
\(310\) 69232.0 0.0409169
\(311\) −1.45086e6 −0.850600 −0.425300 0.905052i \(-0.639831\pi\)
−0.425300 + 0.905052i \(0.639831\pi\)
\(312\) 1.49462e6 0.869252
\(313\) −1.89622e6 −1.09403 −0.547014 0.837123i \(-0.684236\pi\)
−0.547014 + 0.837123i \(0.684236\pi\)
\(314\) −2.35955e6 −1.35053
\(315\) 1.40321e6 0.796793
\(316\) 26081.2 0.0146930
\(317\) −2.57214e6 −1.43763 −0.718814 0.695202i \(-0.755315\pi\)
−0.718814 + 0.695202i \(0.755315\pi\)
\(318\) −3.42077e6 −1.89695
\(319\) 609702. 0.335460
\(320\) 510520. 0.278700
\(321\) −1.87922e6 −1.01792
\(322\) −2.94032e6 −1.58036
\(323\) −474519. −0.253074
\(324\) −450982. −0.238669
\(325\) −276559. −0.145238
\(326\) −2.86840e6 −1.49484
\(327\) −1.41442e6 −0.731493
\(328\) 1.23130e6 0.631945
\(329\) 3.68116e6 1.87497
\(330\) 431228. 0.217983
\(331\) 909532. 0.456298 0.228149 0.973626i \(-0.426733\pi\)
0.228149 + 0.973626i \(0.426733\pi\)
\(332\) −355291. −0.176904
\(333\) 1.03449e6 0.511227
\(334\) 2.22680e6 1.09223
\(335\) 88387.8 0.0430309
\(336\) 5.89066e6 2.84653
\(337\) −2.37849e6 −1.14084 −0.570422 0.821352i \(-0.693220\pi\)
−0.570422 + 0.821352i \(0.693220\pi\)
\(338\) 1.11414e6 0.530454
\(339\) −4.53307e6 −2.14236
\(340\) −272939. −0.128047
\(341\) −52779.9 −0.0245800
\(342\) −598619. −0.276748
\(343\) 2.70013e6 1.23922
\(344\) 371141. 0.169100
\(345\) −1.20984e6 −0.547242
\(346\) −4.47395e6 −2.00910
\(347\) 434960. 0.193921 0.0969606 0.995288i \(-0.469088\pi\)
0.0969606 + 0.995288i \(0.469088\pi\)
\(348\) −939744. −0.415969
\(349\) 2.16783e6 0.952712 0.476356 0.879252i \(-0.341957\pi\)
0.476356 + 0.879252i \(0.341957\pi\)
\(350\) −852680. −0.372062
\(351\) 180751. 0.0783093
\(352\) 355352. 0.152863
\(353\) 1.85492e6 0.792298 0.396149 0.918186i \(-0.370346\pi\)
0.396149 + 0.918186i \(0.370346\pi\)
\(354\) −4.46953e6 −1.89563
\(355\) −863679. −0.363732
\(356\) 691239. 0.289070
\(357\) 6.34258e6 2.63388
\(358\) 1.55344e6 0.640601
\(359\) 2.92377e6 1.19731 0.598656 0.801006i \(-0.295702\pi\)
0.598656 + 0.801006i \(0.295702\pi\)
\(360\) 982259. 0.399457
\(361\) 130321. 0.0526316
\(362\) 5.23172e6 2.09833
\(363\) −328752. −0.130949
\(364\) −789787. −0.312433
\(365\) 225712. 0.0886792
\(366\) 6.06983e6 2.36850
\(367\) −1.47511e6 −0.571687 −0.285843 0.958276i \(-0.592274\pi\)
−0.285843 + 0.958276i \(0.592274\pi\)
\(368\) −2.63107e6 −1.01278
\(369\) 2.13795e6 0.817393
\(370\) −628620. −0.238717
\(371\) −5.15662e6 −1.94505
\(372\) 81350.6 0.0304792
\(373\) 146573. 0.0545484 0.0272742 0.999628i \(-0.491317\pi\)
0.0272742 + 0.999628i \(0.491317\pi\)
\(374\) 1.00975e6 0.373281
\(375\) −350847. −0.128837
\(376\) 2.57685e6 0.939981
\(377\) −2.22967e6 −0.807954
\(378\) 557287. 0.200609
\(379\) 972954. 0.347932 0.173966 0.984752i \(-0.444342\pi\)
0.173966 + 0.984752i \(0.444342\pi\)
\(380\) 74959.5 0.0266298
\(381\) −5.63109e6 −1.98738
\(382\) 1.02638e6 0.359873
\(383\) −211037. −0.0735126 −0.0367563 0.999324i \(-0.511703\pi\)
−0.0367563 + 0.999324i \(0.511703\pi\)
\(384\) 5.02127e6 1.73774
\(385\) 650051. 0.223509
\(386\) 3.37993e6 1.15462
\(387\) 644424. 0.218723
\(388\) −353443. −0.119190
\(389\) 4.80689e6 1.61061 0.805305 0.592861i \(-0.202001\pi\)
0.805305 + 0.592861i \(0.202001\pi\)
\(390\) −1.57699e6 −0.525010
\(391\) −2.83293e6 −0.937116
\(392\) 4.41835e6 1.45226
\(393\) 3.51958e6 1.14950
\(394\) −421972. −0.136944
\(395\) 78503.3 0.0253160
\(396\) 262497. 0.0841175
\(397\) 4.71304e6 1.50081 0.750403 0.660980i \(-0.229859\pi\)
0.750403 + 0.660980i \(0.229859\pi\)
\(398\) −1.09878e6 −0.347700
\(399\) −1.74192e6 −0.547766
\(400\) −762999. −0.238437
\(401\) 2.26556e6 0.703583 0.351791 0.936078i \(-0.385573\pi\)
0.351791 + 0.936078i \(0.385573\pi\)
\(402\) 504004. 0.155549
\(403\) 193015. 0.0592009
\(404\) 889054. 0.271003
\(405\) −1.35744e6 −0.411227
\(406\) −6.87445e6 −2.06977
\(407\) 479237. 0.143405
\(408\) 4.43987e6 1.32044
\(409\) −373709. −0.110465 −0.0552325 0.998474i \(-0.517590\pi\)
−0.0552325 + 0.998474i \(0.517590\pi\)
\(410\) −1.29916e6 −0.381682
\(411\) −3.46619e6 −1.01216
\(412\) −663487. −0.192570
\(413\) −6.73756e6 −1.94369
\(414\) −3.57382e6 −1.02478
\(415\) −1.06941e6 −0.304807
\(416\) −1.29951e6 −0.368170
\(417\) −6.80841e6 −1.91737
\(418\) −277317. −0.0776310
\(419\) 1.38493e6 0.385383 0.192692 0.981259i \(-0.438278\pi\)
0.192692 + 0.981259i \(0.438278\pi\)
\(420\) −1.00194e6 −0.277151
\(421\) 2.63129e6 0.723542 0.361771 0.932267i \(-0.382172\pi\)
0.361771 + 0.932267i \(0.382172\pi\)
\(422\) 5.35313e6 1.46328
\(423\) 4.47427e6 1.21582
\(424\) −3.60968e6 −0.975112
\(425\) −821535. −0.220624
\(426\) −4.92486e6 −1.31483
\(427\) 9.14992e6 2.42855
\(428\) 695120. 0.183422
\(429\) 1.20224e6 0.315390
\(430\) −391594. −0.102133
\(431\) 4.19027e6 1.08655 0.543273 0.839556i \(-0.317185\pi\)
0.543273 + 0.839556i \(0.317185\pi\)
\(432\) 498675. 0.128561
\(433\) 6.50673e6 1.66780 0.833898 0.551918i \(-0.186104\pi\)
0.833898 + 0.551918i \(0.186104\pi\)
\(434\) 595099. 0.151658
\(435\) −2.82859e6 −0.716716
\(436\) 523192. 0.131809
\(437\) 778030. 0.194891
\(438\) 1.28705e6 0.320561
\(439\) −2.98302e6 −0.738744 −0.369372 0.929282i \(-0.620427\pi\)
−0.369372 + 0.929282i \(0.620427\pi\)
\(440\) 455042. 0.112052
\(441\) 7.67173e6 1.87844
\(442\) −3.69264e6 −0.899046
\(443\) 4.41180e6 1.06809 0.534044 0.845457i \(-0.320672\pi\)
0.534044 + 0.845457i \(0.320672\pi\)
\(444\) −738656. −0.177822
\(445\) 2.08060e6 0.498068
\(446\) −6.62496e6 −1.57705
\(447\) 4.19768e6 0.993667
\(448\) 4.38829e6 1.03300
\(449\) −6.39547e6 −1.49712 −0.748560 0.663068i \(-0.769254\pi\)
−0.748560 + 0.663068i \(0.769254\pi\)
\(450\) −1.03639e6 −0.241264
\(451\) 990428. 0.229288
\(452\) 1.67677e6 0.386036
\(453\) 1.07062e7 2.45127
\(454\) 6.10897e6 1.39100
\(455\) −2.37722e6 −0.538322
\(456\) −1.21936e6 −0.274612
\(457\) −1.32493e6 −0.296758 −0.148379 0.988931i \(-0.547406\pi\)
−0.148379 + 0.988931i \(0.547406\pi\)
\(458\) 3.36038e6 0.748557
\(459\) 536932. 0.118956
\(460\) 447516. 0.0986084
\(461\) −3.88934e6 −0.852361 −0.426181 0.904638i \(-0.640141\pi\)
−0.426181 + 0.904638i \(0.640141\pi\)
\(462\) 3.70671e6 0.807949
\(463\) 6.41968e6 1.39175 0.695875 0.718163i \(-0.255017\pi\)
0.695875 + 0.718163i \(0.255017\pi\)
\(464\) −6.15143e6 −1.32642
\(465\) 244862. 0.0525157
\(466\) −423316. −0.0903025
\(467\) 5.96749e6 1.26619 0.633096 0.774073i \(-0.281784\pi\)
0.633096 + 0.774073i \(0.281784\pi\)
\(468\) −959946. −0.202597
\(469\) 759756. 0.159493
\(470\) −2.71885e6 −0.567729
\(471\) −8.34532e6 −1.73337
\(472\) −4.71636e6 −0.974432
\(473\) 298537. 0.0613543
\(474\) 447641. 0.0915132
\(475\) 225625. 0.0458831
\(476\) −2.34611e6 −0.474603
\(477\) −6.26761e6 −1.26126
\(478\) 7.17587e6 1.43650
\(479\) −3.09227e6 −0.615799 −0.307900 0.951419i \(-0.599626\pi\)
−0.307900 + 0.951419i \(0.599626\pi\)
\(480\) −1.64858e6 −0.326594
\(481\) −1.75256e6 −0.345390
\(482\) 8.86050e6 1.73716
\(483\) −1.03994e7 −2.02834
\(484\) 121605. 0.0235959
\(485\) −1.06385e6 −0.205364
\(486\) −8.37053e6 −1.60754
\(487\) −864592. −0.165192 −0.0825960 0.996583i \(-0.526321\pi\)
−0.0825960 + 0.996583i \(0.526321\pi\)
\(488\) 6.40503e6 1.21751
\(489\) −1.01450e7 −1.91859
\(490\) −4.66184e6 −0.877136
\(491\) 3.38763e6 0.634150 0.317075 0.948400i \(-0.397299\pi\)
0.317075 + 0.948400i \(0.397299\pi\)
\(492\) −1.52656e6 −0.284317
\(493\) −6.62336e6 −1.22733
\(494\) 1.01414e6 0.186974
\(495\) 790105. 0.144935
\(496\) 532509. 0.0971903
\(497\) −7.42395e6 −1.34817
\(498\) −6.09798e6 −1.10182
\(499\) 6.51412e6 1.17113 0.585564 0.810626i \(-0.300873\pi\)
0.585564 + 0.810626i \(0.300873\pi\)
\(500\) 129778. 0.0232153
\(501\) 7.87583e6 1.40185
\(502\) 1.43605e6 0.254338
\(503\) 2.21176e6 0.389779 0.194889 0.980825i \(-0.437565\pi\)
0.194889 + 0.980825i \(0.437565\pi\)
\(504\) 8.44322e6 1.48058
\(505\) 2.67602e6 0.466939
\(506\) −1.65561e6 −0.287463
\(507\) 3.94053e6 0.680823
\(508\) 2.08293e6 0.358109
\(509\) −4.25125e6 −0.727314 −0.363657 0.931533i \(-0.618472\pi\)
−0.363657 + 0.931533i \(0.618472\pi\)
\(510\) −4.68455e6 −0.797521
\(511\) 1.94015e6 0.328688
\(512\) 2.29129e6 0.386282
\(513\) −147462. −0.0247393
\(514\) 1.09632e6 0.183034
\(515\) −1.99707e6 −0.331799
\(516\) −460140. −0.0760791
\(517\) 2.07275e6 0.341053
\(518\) −5.40344e6 −0.884802
\(519\) −1.58236e7 −2.57862
\(520\) −1.66408e6 −0.269877
\(521\) 4.84292e6 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(522\) −8.35555e6 −1.34214
\(523\) 1.44653e6 0.231245 0.115623 0.993293i \(-0.463114\pi\)
0.115623 + 0.993293i \(0.463114\pi\)
\(524\) −1.30189e6 −0.207131
\(525\) −3.01578e6 −0.477531
\(526\) −4.55589e6 −0.717974
\(527\) 573363. 0.0899296
\(528\) 3.31686e6 0.517777
\(529\) −1.79142e6 −0.278329
\(530\) 3.80861e6 0.588947
\(531\) −8.18917e6 −1.26039
\(532\) 644331. 0.0987029
\(533\) −3.62198e6 −0.552239
\(534\) 1.18640e7 1.80043
\(535\) 2.09228e6 0.316036
\(536\) 531837. 0.0799588
\(537\) 5.49427e6 0.822193
\(538\) −6.53416e6 −0.973271
\(539\) 3.55401e6 0.526923
\(540\) −84818.9 −0.0125172
\(541\) −1.37576e6 −0.202093 −0.101046 0.994882i \(-0.532219\pi\)
−0.101046 + 0.994882i \(0.532219\pi\)
\(542\) 4.38310e6 0.640890
\(543\) 1.85037e7 2.69314
\(544\) −3.86028e6 −0.559271
\(545\) 1.57479e6 0.227107
\(546\) −1.35554e7 −1.94594
\(547\) 173572. 0.0248034 0.0124017 0.999923i \(-0.496052\pi\)
0.0124017 + 0.999923i \(0.496052\pi\)
\(548\) 1.28213e6 0.182382
\(549\) 1.11213e7 1.57479
\(550\) −480119. −0.0676772
\(551\) 1.81903e6 0.255247
\(552\) −7.27970e6 −1.01687
\(553\) 674793. 0.0938334
\(554\) 9.59222e6 1.32784
\(555\) −2.22332e6 −0.306387
\(556\) 2.51842e6 0.345494
\(557\) 3.70243e6 0.505649 0.252824 0.967512i \(-0.418641\pi\)
0.252824 + 0.967512i \(0.418641\pi\)
\(558\) 723313. 0.0983424
\(559\) −1.09174e6 −0.147771
\(560\) −6.55853e6 −0.883764
\(561\) 3.57132e6 0.479096
\(562\) −2.94276e6 −0.393019
\(563\) −1.15351e6 −0.153373 −0.0766866 0.997055i \(-0.524434\pi\)
−0.0766866 + 0.997055i \(0.524434\pi\)
\(564\) −3.19477e6 −0.422904
\(565\) 5.04701e6 0.665140
\(566\) 1.65364e6 0.216970
\(567\) −1.16681e7 −1.52421
\(568\) −5.19683e6 −0.675878
\(569\) −9.98168e6 −1.29248 −0.646238 0.763136i \(-0.723659\pi\)
−0.646238 + 0.763136i \(0.723659\pi\)
\(570\) 1.28656e6 0.165860
\(571\) 8.84063e6 1.13473 0.567365 0.823466i \(-0.307963\pi\)
0.567365 + 0.823466i \(0.307963\pi\)
\(572\) −444706. −0.0568307
\(573\) 3.63013e6 0.461887
\(574\) −1.11672e7 −1.41470
\(575\) 1.34700e6 0.169902
\(576\) 5.33374e6 0.669847
\(577\) −1.06489e7 −1.33158 −0.665788 0.746141i \(-0.731904\pi\)
−0.665788 + 0.746141i \(0.731904\pi\)
\(578\) −1.95500e6 −0.243403
\(579\) 1.19542e7 1.48192
\(580\) 1.04629e6 0.129146
\(581\) −9.19236e6 −1.12976
\(582\) −6.06626e6 −0.742358
\(583\) −2.90354e6 −0.353799
\(584\) 1.35813e6 0.164781
\(585\) −2.88940e6 −0.349074
\(586\) −20421.9 −0.00245670
\(587\) 7.69130e6 0.921307 0.460653 0.887580i \(-0.347615\pi\)
0.460653 + 0.887580i \(0.347615\pi\)
\(588\) −5.47786e6 −0.653383
\(589\) −157467. −0.0187026
\(590\) 4.97627e6 0.588537
\(591\) −1.49244e6 −0.175764
\(592\) −4.83514e6 −0.567028
\(593\) 4.06429e6 0.474622 0.237311 0.971434i \(-0.423734\pi\)
0.237311 + 0.971434i \(0.423734\pi\)
\(594\) 313792. 0.0364902
\(595\) −7.06169e6 −0.817741
\(596\) −1.55271e6 −0.179051
\(597\) −3.88621e6 −0.446263
\(598\) 6.05453e6 0.692353
\(599\) −5.33011e6 −0.606972 −0.303486 0.952836i \(-0.598151\pi\)
−0.303486 + 0.952836i \(0.598151\pi\)
\(600\) −2.11108e6 −0.239401
\(601\) 2.81513e6 0.317916 0.158958 0.987285i \(-0.449187\pi\)
0.158958 + 0.987285i \(0.449187\pi\)
\(602\) −3.36603e6 −0.378553
\(603\) 923446. 0.103423
\(604\) −3.96021e6 −0.441699
\(605\) 366025. 0.0406558
\(606\) 1.52591e7 1.68791
\(607\) 7.34287e6 0.808899 0.404449 0.914560i \(-0.367463\pi\)
0.404449 + 0.914560i \(0.367463\pi\)
\(608\) 1.06018e6 0.116311
\(609\) −2.43138e7 −2.65650
\(610\) −6.75800e6 −0.735350
\(611\) −7.58002e6 −0.821424
\(612\) −2.85158e6 −0.307756
\(613\) 7.56546e6 0.813176 0.406588 0.913612i \(-0.366719\pi\)
0.406588 + 0.913612i \(0.366719\pi\)
\(614\) −8.79858e6 −0.941871
\(615\) −4.59489e6 −0.489878
\(616\) 3.91142e6 0.415319
\(617\) 4.37973e6 0.463163 0.231582 0.972815i \(-0.425610\pi\)
0.231582 + 0.972815i \(0.425610\pi\)
\(618\) −1.13877e7 −1.19940
\(619\) 1.23890e7 1.29960 0.649802 0.760104i \(-0.274852\pi\)
0.649802 + 0.760104i \(0.274852\pi\)
\(620\) −90573.8 −0.00946288
\(621\) −880364. −0.0916080
\(622\) 9.21107e6 0.954628
\(623\) 1.78843e7 1.84608
\(624\) −1.21297e7 −1.24706
\(625\) 390625. 0.0400000
\(626\) 1.20385e7 1.22783
\(627\) −980823. −0.0996372
\(628\) 3.08692e6 0.312339
\(629\) −5.20608e6 −0.524667
\(630\) −8.90852e6 −0.894240
\(631\) −8.71435e6 −0.871287 −0.435644 0.900119i \(-0.643479\pi\)
−0.435644 + 0.900119i \(0.643479\pi\)
\(632\) 472361. 0.0470415
\(633\) 1.89331e7 1.87808
\(634\) 1.63297e7 1.61345
\(635\) 6.26953e6 0.617022
\(636\) 4.47528e6 0.438710
\(637\) −1.29970e7 −1.26909
\(638\) −3.87080e6 −0.376487
\(639\) −9.02344e6 −0.874218
\(640\) −5.59056e6 −0.539518
\(641\) −1.03994e7 −0.999689 −0.499844 0.866115i \(-0.666610\pi\)
−0.499844 + 0.866115i \(0.666610\pi\)
\(642\) 1.19306e7 1.14242
\(643\) −8.89559e6 −0.848491 −0.424245 0.905547i \(-0.639461\pi\)
−0.424245 + 0.905547i \(0.639461\pi\)
\(644\) 3.84672e6 0.365491
\(645\) −1.38500e6 −0.131084
\(646\) 3.01257e6 0.284024
\(647\) 7.13614e6 0.670197 0.335099 0.942183i \(-0.391230\pi\)
0.335099 + 0.942183i \(0.391230\pi\)
\(648\) −8.16781e6 −0.764132
\(649\) −3.79372e6 −0.353553
\(650\) 1.75579e6 0.163000
\(651\) 2.10476e6 0.194648
\(652\) 3.75263e6 0.345714
\(653\) 8.51933e6 0.781849 0.390924 0.920423i \(-0.372155\pi\)
0.390924 + 0.920423i \(0.372155\pi\)
\(654\) 8.97972e6 0.820953
\(655\) −3.91862e6 −0.356887
\(656\) −9.99267e6 −0.906613
\(657\) 2.35816e6 0.213138
\(658\) −2.33705e7 −2.10428
\(659\) −7.43040e6 −0.666498 −0.333249 0.942839i \(-0.608145\pi\)
−0.333249 + 0.942839i \(0.608145\pi\)
\(660\) −564161. −0.0504130
\(661\) −1.74159e7 −1.55039 −0.775195 0.631722i \(-0.782349\pi\)
−0.775195 + 0.631722i \(0.782349\pi\)
\(662\) −5.77433e6 −0.512102
\(663\) −1.30603e7 −1.15390
\(664\) −6.43474e6 −0.566383
\(665\) 1.93941e6 0.170065
\(666\) −6.56762e6 −0.573749
\(667\) 1.08598e7 0.945163
\(668\) −2.91325e6 −0.252602
\(669\) −2.34314e7 −2.02410
\(670\) −561146. −0.0482935
\(671\) 5.15205e6 0.441747
\(672\) −1.41708e7 −1.21052
\(673\) 1.83440e7 1.56120 0.780598 0.625034i \(-0.214915\pi\)
0.780598 + 0.625034i \(0.214915\pi\)
\(674\) 1.51003e7 1.28037
\(675\) −255301. −0.0215672
\(676\) −1.45759e6 −0.122679
\(677\) 7.17551e6 0.601701 0.300851 0.953671i \(-0.402729\pi\)
0.300851 + 0.953671i \(0.402729\pi\)
\(678\) 2.87790e7 2.40437
\(679\) −9.14454e6 −0.761180
\(680\) −4.94325e6 −0.409959
\(681\) 2.16064e7 1.78531
\(682\) 335083. 0.0275862
\(683\) 4.40234e6 0.361104 0.180552 0.983565i \(-0.442212\pi\)
0.180552 + 0.983565i \(0.442212\pi\)
\(684\) 783152. 0.0640038
\(685\) 3.85917e6 0.314245
\(686\) −1.71423e7 −1.39078
\(687\) 1.18851e7 0.960752
\(688\) −3.01201e6 −0.242597
\(689\) 1.06182e7 0.852123
\(690\) 7.68087e6 0.614169
\(691\) 8.79245e6 0.700511 0.350256 0.936654i \(-0.386095\pi\)
0.350256 + 0.936654i \(0.386095\pi\)
\(692\) 5.85311e6 0.464645
\(693\) 6.79152e6 0.537198
\(694\) −2.76142e6 −0.217638
\(695\) 7.58032e6 0.595286
\(696\) −1.70199e7 −1.33178
\(697\) −1.07593e7 −0.838883
\(698\) −1.37629e7 −1.06923
\(699\) −1.49720e6 −0.115901
\(700\) 1.11553e6 0.0860472
\(701\) −1.56298e6 −0.120132 −0.0600660 0.998194i \(-0.519131\pi\)
−0.0600660 + 0.998194i \(0.519131\pi\)
\(702\) −1.14753e6 −0.0878865
\(703\) 1.42979e6 0.109115
\(704\) 2.47092e6 0.187900
\(705\) −9.61613e6 −0.728664
\(706\) −1.17763e7 −0.889196
\(707\) 2.30023e7 1.73070
\(708\) 5.84733e6 0.438404
\(709\) −2.47555e7 −1.84950 −0.924752 0.380570i \(-0.875728\pi\)
−0.924752 + 0.380570i \(0.875728\pi\)
\(710\) 5.48323e6 0.408216
\(711\) 820177. 0.0608462
\(712\) 1.25192e7 0.925497
\(713\) −940097. −0.0692546
\(714\) −4.02670e7 −2.95600
\(715\) −1.33855e6 −0.0979193
\(716\) −2.03232e6 −0.148152
\(717\) 2.53798e7 1.84370
\(718\) −1.85621e7 −1.34374
\(719\) 2.11341e7 1.52462 0.762311 0.647211i \(-0.224065\pi\)
0.762311 + 0.647211i \(0.224065\pi\)
\(720\) −7.97156e6 −0.573076
\(721\) −1.71662e7 −1.22981
\(722\) −827367. −0.0590684
\(723\) 3.13381e7 2.22960
\(724\) −6.84448e6 −0.485282
\(725\) 3.14929e6 0.222519
\(726\) 2.08714e6 0.146964
\(727\) 1.83094e7 1.28481 0.642405 0.766366i \(-0.277937\pi\)
0.642405 + 0.766366i \(0.277937\pi\)
\(728\) −1.43040e7 −1.00029
\(729\) −1.64109e7 −1.14370
\(730\) −1.43297e6 −0.0995246
\(731\) −3.24308e6 −0.224473
\(732\) −7.94095e6 −0.547765
\(733\) 2.29199e6 0.157563 0.0787813 0.996892i \(-0.474897\pi\)
0.0787813 + 0.996892i \(0.474897\pi\)
\(734\) 9.36498e6 0.641603
\(735\) −1.64881e7 −1.12578
\(736\) 6.32940e6 0.430693
\(737\) 427797. 0.0290114
\(738\) −1.35732e7 −0.917360
\(739\) −1.99162e7 −1.34151 −0.670756 0.741678i \(-0.734030\pi\)
−0.670756 + 0.741678i \(0.734030\pi\)
\(740\) 822402. 0.0552084
\(741\) 3.58685e6 0.239976
\(742\) 3.27377e7 2.18292
\(743\) −2.76901e7 −1.84015 −0.920074 0.391745i \(-0.871872\pi\)
−0.920074 + 0.391745i \(0.871872\pi\)
\(744\) 1.47336e6 0.0975832
\(745\) −4.67360e6 −0.308504
\(746\) −930545. −0.0612196
\(747\) −1.11729e7 −0.732593
\(748\) −1.32102e6 −0.0863290
\(749\) 1.79847e7 1.17138
\(750\) 2.22742e6 0.144593
\(751\) −8.97875e6 −0.580920 −0.290460 0.956887i \(-0.593808\pi\)
−0.290460 + 0.956887i \(0.593808\pi\)
\(752\) −2.09125e7 −1.34853
\(753\) 5.07907e6 0.326435
\(754\) 1.41555e7 0.906766
\(755\) −1.19201e7 −0.761048
\(756\) −729080. −0.0463949
\(757\) 3.20582e6 0.203329 0.101664 0.994819i \(-0.467583\pi\)
0.101664 + 0.994819i \(0.467583\pi\)
\(758\) −6.17697e6 −0.390484
\(759\) −5.85561e6 −0.368950
\(760\) 1.35761e6 0.0852589
\(761\) 2.39816e7 1.50113 0.750563 0.660798i \(-0.229782\pi\)
0.750563 + 0.660798i \(0.229782\pi\)
\(762\) 3.57500e7 2.23043
\(763\) 1.35364e7 0.841768
\(764\) −1.34278e6 −0.0832282
\(765\) −8.58313e6 −0.530264
\(766\) 1.33981e6 0.0825031
\(767\) 1.38736e7 0.851530
\(768\) −1.72054e7 −1.05259
\(769\) 1.43654e7 0.875993 0.437996 0.898977i \(-0.355688\pi\)
0.437996 + 0.898977i \(0.355688\pi\)
\(770\) −4.12697e6 −0.250844
\(771\) 3.87752e6 0.234919
\(772\) −4.42185e6 −0.267030
\(773\) −6.44514e6 −0.387957 −0.193978 0.981006i \(-0.562139\pi\)
−0.193978 + 0.981006i \(0.562139\pi\)
\(774\) −4.09124e6 −0.245473
\(775\) −272623. −0.0163046
\(776\) −6.40127e6 −0.381603
\(777\) −1.91111e7 −1.13562
\(778\) −3.05174e7 −1.80759
\(779\) 2.95491e6 0.174462
\(780\) 2.06312e6 0.121420
\(781\) −4.18021e6 −0.245228
\(782\) 1.79853e7 1.05172
\(783\) −2.05828e6 −0.119978
\(784\) −3.58573e7 −2.08347
\(785\) 9.29149e6 0.538160
\(786\) −2.23447e7 −1.29009
\(787\) −2.51823e7 −1.44930 −0.724651 0.689116i \(-0.757999\pi\)
−0.724651 + 0.689116i \(0.757999\pi\)
\(788\) 552052. 0.0316712
\(789\) −1.61134e7 −0.921499
\(790\) −498393. −0.0284121
\(791\) 4.33827e7 2.46533
\(792\) 4.75413e6 0.269314
\(793\) −1.88409e7 −1.06395
\(794\) −2.99216e7 −1.68435
\(795\) 1.34704e7 0.755897
\(796\) 1.43750e6 0.0804128
\(797\) −9.18132e6 −0.511988 −0.255994 0.966678i \(-0.582403\pi\)
−0.255994 + 0.966678i \(0.582403\pi\)
\(798\) 1.10589e7 0.614757
\(799\) −2.25169e7 −1.24779
\(800\) 1.83550e6 0.101398
\(801\) 2.17374e7 1.19709
\(802\) −1.43833e7 −0.789630
\(803\) 1.09244e6 0.0597875
\(804\) −659370. −0.0359741
\(805\) 1.15785e7 0.629741
\(806\) −1.22539e6 −0.0664412
\(807\) −2.31102e7 −1.24917
\(808\) 1.61018e7 0.867654
\(809\) −3.43308e6 −0.184422 −0.0922110 0.995739i \(-0.529393\pi\)
−0.0922110 + 0.995739i \(0.529393\pi\)
\(810\) 8.61793e6 0.461520
\(811\) 2.88260e7 1.53898 0.769490 0.638659i \(-0.220511\pi\)
0.769490 + 0.638659i \(0.220511\pi\)
\(812\) 8.99361e6 0.478679
\(813\) 1.55023e7 0.822564
\(814\) −3.04252e6 −0.160943
\(815\) 1.12953e7 0.595665
\(816\) −3.60320e7 −1.89436
\(817\) 890675. 0.0466836
\(818\) 2.37256e6 0.123975
\(819\) −2.48365e7 −1.29384
\(820\) 1.69964e6 0.0882719
\(821\) 2.39942e7 1.24236 0.621181 0.783667i \(-0.286653\pi\)
0.621181 + 0.783667i \(0.286653\pi\)
\(822\) 2.20057e7 1.13594
\(823\) −1.59498e6 −0.0820835 −0.0410417 0.999157i \(-0.513068\pi\)
−0.0410417 + 0.999157i \(0.513068\pi\)
\(824\) −1.20165e7 −0.616540
\(825\) −1.69810e6 −0.0868617
\(826\) 4.27746e7 2.18140
\(827\) 3.38957e7 1.72338 0.861690 0.507435i \(-0.169406\pi\)
0.861690 + 0.507435i \(0.169406\pi\)
\(828\) 4.67550e6 0.237002
\(829\) −1.65958e7 −0.838710 −0.419355 0.907822i \(-0.637744\pi\)
−0.419355 + 0.907822i \(0.637744\pi\)
\(830\) 6.78935e6 0.342084
\(831\) 3.39261e7 1.70424
\(832\) −9.03609e6 −0.452556
\(833\) −3.86082e7 −1.92782
\(834\) 4.32244e7 2.15186
\(835\) −8.76876e6 −0.435233
\(836\) 362804. 0.0179538
\(837\) 178179. 0.00879109
\(838\) −8.79249e6 −0.432515
\(839\) 1.90010e7 0.931906 0.465953 0.884809i \(-0.345712\pi\)
0.465953 + 0.884809i \(0.345712\pi\)
\(840\) −1.81462e7 −0.887336
\(841\) 4.87895e6 0.237868
\(842\) −1.67052e7 −0.812030
\(843\) −1.04080e7 −0.504429
\(844\) −7.00332e6 −0.338414
\(845\) −4.38729e6 −0.211375
\(846\) −2.84057e7 −1.36452
\(847\) 3.14625e6 0.150690
\(848\) 2.92945e7 1.39893
\(849\) 5.84865e6 0.278475
\(850\) 5.21566e6 0.247607
\(851\) 8.53599e6 0.404045
\(852\) 6.44303e6 0.304082
\(853\) 176459. 0.00830372 0.00415186 0.999991i \(-0.498678\pi\)
0.00415186 + 0.999991i \(0.498678\pi\)
\(854\) −5.80899e7 −2.72556
\(855\) 2.35726e6 0.110279
\(856\) 1.25894e7 0.587249
\(857\) 1.16255e7 0.540703 0.270351 0.962762i \(-0.412860\pi\)
0.270351 + 0.962762i \(0.412860\pi\)
\(858\) −7.63264e6 −0.353962
\(859\) −2.09751e7 −0.969888 −0.484944 0.874545i \(-0.661160\pi\)
−0.484944 + 0.874545i \(0.661160\pi\)
\(860\) 512309. 0.0236203
\(861\) −3.94964e7 −1.81572
\(862\) −2.66027e7 −1.21943
\(863\) 2.75794e7 1.26054 0.630272 0.776375i \(-0.282944\pi\)
0.630272 + 0.776375i \(0.282944\pi\)
\(864\) −1.19963e6 −0.0546717
\(865\) 1.76176e7 0.800584
\(866\) −4.13092e7 −1.87177
\(867\) −6.91449e6 −0.312401
\(868\) −778547. −0.0350740
\(869\) 379956. 0.0170681
\(870\) 1.79578e7 0.804369
\(871\) −1.56444e6 −0.0698738
\(872\) 9.47562e6 0.422004
\(873\) −1.11147e7 −0.493587
\(874\) −4.93947e6 −0.218726
\(875\) 3.35770e6 0.148259
\(876\) −1.68380e6 −0.0741363
\(877\) −2.64105e7 −1.15952 −0.579760 0.814787i \(-0.696854\pi\)
−0.579760 + 0.814787i \(0.696854\pi\)
\(878\) 1.89382e7 0.829092
\(879\) −72228.9 −0.00315311
\(880\) −3.69292e6 −0.160754
\(881\) 9.19881e6 0.399293 0.199647 0.979868i \(-0.436021\pi\)
0.199647 + 0.979868i \(0.436021\pi\)
\(882\) −4.87054e7 −2.10817
\(883\) −1.84109e7 −0.794645 −0.397323 0.917679i \(-0.630061\pi\)
−0.397323 + 0.917679i \(0.630061\pi\)
\(884\) 4.83096e6 0.207923
\(885\) 1.76002e7 0.755371
\(886\) −2.80091e7 −1.19871
\(887\) 1.18035e7 0.503734 0.251867 0.967762i \(-0.418956\pi\)
0.251867 + 0.967762i \(0.418956\pi\)
\(888\) −1.33779e7 −0.569320
\(889\) 5.38911e7 2.28698
\(890\) −1.32091e7 −0.558981
\(891\) −6.56999e6 −0.277249
\(892\) 8.66720e6 0.364726
\(893\) 6.18400e6 0.259502
\(894\) −2.66498e7 −1.11519
\(895\) −6.11719e6 −0.255267
\(896\) −4.80549e7 −1.99971
\(897\) 2.14139e7 0.888615
\(898\) 4.06028e7 1.68022
\(899\) −2.19794e6 −0.0907019
\(900\) 1.35587e6 0.0557972
\(901\) 3.15420e7 1.29442
\(902\) −6.28791e6 −0.257330
\(903\) −1.19051e7 −0.485862
\(904\) 3.03683e7 1.23595
\(905\) −2.06016e7 −0.836141
\(906\) −6.79705e7 −2.75106
\(907\) −3.85017e7 −1.55404 −0.777019 0.629478i \(-0.783269\pi\)
−0.777019 + 0.629478i \(0.783269\pi\)
\(908\) −7.99216e6 −0.321699
\(909\) 2.79581e7 1.12227
\(910\) 1.50922e7 0.604158
\(911\) −2.75916e7 −1.10149 −0.550746 0.834673i \(-0.685657\pi\)
−0.550746 + 0.834673i \(0.685657\pi\)
\(912\) 9.89576e6 0.393969
\(913\) −5.17595e6 −0.205501
\(914\) 8.41156e6 0.333051
\(915\) −2.39019e7 −0.943800
\(916\) −4.39627e6 −0.173120
\(917\) −3.36834e7 −1.32279
\(918\) −3.40881e6 −0.133505
\(919\) −4.44736e7 −1.73705 −0.868527 0.495641i \(-0.834933\pi\)
−0.868527 + 0.495641i \(0.834933\pi\)
\(920\) 8.10505e6 0.315708
\(921\) −3.11191e7 −1.20886
\(922\) 2.46922e7 0.956604
\(923\) 1.52869e7 0.590631
\(924\) −4.84937e6 −0.186855
\(925\) 2.47540e6 0.0951241
\(926\) −4.07565e7 −1.56196
\(927\) −2.08647e7 −0.797468
\(928\) 1.47981e7 0.564073
\(929\) 2.31988e7 0.881914 0.440957 0.897528i \(-0.354639\pi\)
0.440957 + 0.897528i \(0.354639\pi\)
\(930\) −1.55455e6 −0.0589383
\(931\) 1.06033e7 0.400928
\(932\) 553809. 0.0208843
\(933\) 3.25780e7 1.22524
\(934\) −3.78857e7 −1.42105
\(935\) −3.97623e6 −0.148745
\(936\) −1.73858e7 −0.648641
\(937\) −3.03590e7 −1.12964 −0.564818 0.825215i \(-0.691054\pi\)
−0.564818 + 0.825215i \(0.691054\pi\)
\(938\) −4.82345e6 −0.178999
\(939\) 4.25782e7 1.57588
\(940\) 3.55698e6 0.131299
\(941\) −3.40477e6 −0.125347 −0.0626734 0.998034i \(-0.519963\pi\)
−0.0626734 + 0.998034i \(0.519963\pi\)
\(942\) 5.29818e7 1.94536
\(943\) 1.76411e7 0.646022
\(944\) 3.82758e7 1.39796
\(945\) −2.19450e6 −0.0799385
\(946\) −1.89531e6 −0.0688578
\(947\) 1.89364e7 0.686155 0.343077 0.939307i \(-0.388531\pi\)
0.343077 + 0.939307i \(0.388531\pi\)
\(948\) −585633. −0.0211643
\(949\) −3.99505e6 −0.143998
\(950\) −1.43242e6 −0.0514946
\(951\) 5.77554e7 2.07082
\(952\) −4.24908e7 −1.51951
\(953\) −2.70929e6 −0.0966325 −0.0483162 0.998832i \(-0.515386\pi\)
−0.0483162 + 0.998832i \(0.515386\pi\)
\(954\) 3.97911e7 1.41552
\(955\) −4.04170e6 −0.143402
\(956\) −9.38794e6 −0.332220
\(957\) −1.36904e7 −0.483210
\(958\) 1.96319e7 0.691111
\(959\) 3.31724e7 1.16474
\(960\) −1.14633e7 −0.401451
\(961\) −2.84389e7 −0.993354
\(962\) 1.11264e7 0.387631
\(963\) 2.18595e7 0.759581
\(964\) −1.15919e7 −0.401755
\(965\) −1.33096e7 −0.460094
\(966\) 6.60226e7 2.27641
\(967\) −9.62962e6 −0.331164 −0.165582 0.986196i \(-0.552950\pi\)
−0.165582 + 0.986196i \(0.552950\pi\)
\(968\) 2.20240e6 0.0755455
\(969\) 1.06549e7 0.364537
\(970\) 6.75403e6 0.230480
\(971\) 1.14895e7 0.391068 0.195534 0.980697i \(-0.437356\pi\)
0.195534 + 0.980697i \(0.437356\pi\)
\(972\) 1.09509e7 0.371778
\(973\) 6.51584e7 2.20642
\(974\) 5.48902e6 0.185395
\(975\) 6.20992e6 0.209206
\(976\) −5.19803e7 −1.74668
\(977\) −6.23802e6 −0.209079 −0.104540 0.994521i \(-0.533337\pi\)
−0.104540 + 0.994521i \(0.533337\pi\)
\(978\) 6.44077e7 2.15323
\(979\) 1.00701e7 0.335797
\(980\) 6.09892e6 0.202856
\(981\) 1.64528e7 0.545844
\(982\) −2.15070e7 −0.711706
\(983\) 3.14604e7 1.03844 0.519218 0.854642i \(-0.326223\pi\)
0.519218 + 0.854642i \(0.326223\pi\)
\(984\) −2.76479e7 −0.910278
\(985\) 1.66165e6 0.0545694
\(986\) 4.20496e7 1.37743
\(987\) −8.26575e7 −2.70078
\(988\) −1.32677e6 −0.0432416
\(989\) 5.31743e6 0.172866
\(990\) −5.01613e6 −0.162660
\(991\) 9.19142e6 0.297302 0.148651 0.988890i \(-0.452507\pi\)
0.148651 + 0.988890i \(0.452507\pi\)
\(992\) −1.28102e6 −0.0413311
\(993\) −2.04228e7 −0.657269
\(994\) 4.71323e7 1.51305
\(995\) 4.32682e6 0.138551
\(996\) 7.97778e6 0.254820
\(997\) −4.36817e7 −1.39175 −0.695876 0.718162i \(-0.744984\pi\)
−0.695876 + 0.718162i \(0.744984\pi\)
\(998\) −4.13561e7 −1.31436
\(999\) −1.61785e6 −0.0512890
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 1045.6.a.h.1.10 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.10 40 1.1 even 1 trivial