Properties

Label 1045.6.a.h.1.5
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.5
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.55086 q^{2} +12.0717 q^{3} +41.1172 q^{4} +25.0000 q^{5} -103.224 q^{6} -150.646 q^{7} -77.9596 q^{8} -97.2734 q^{9} +O(q^{10})\) \(q-8.55086 q^{2} +12.0717 q^{3} +41.1172 q^{4} +25.0000 q^{5} -103.224 q^{6} -150.646 q^{7} -77.9596 q^{8} -97.2734 q^{9} -213.771 q^{10} +121.000 q^{11} +496.355 q^{12} -71.2149 q^{13} +1288.16 q^{14} +301.793 q^{15} -649.128 q^{16} +933.503 q^{17} +831.771 q^{18} +361.000 q^{19} +1027.93 q^{20} -1818.56 q^{21} -1034.65 q^{22} +2306.65 q^{23} -941.107 q^{24} +625.000 q^{25} +608.949 q^{26} -4107.69 q^{27} -6194.15 q^{28} +4095.48 q^{29} -2580.59 q^{30} +5443.15 q^{31} +8045.31 q^{32} +1460.68 q^{33} -7982.25 q^{34} -3766.16 q^{35} -3999.61 q^{36} +6724.50 q^{37} -3086.86 q^{38} -859.687 q^{39} -1948.99 q^{40} -11440.7 q^{41} +15550.3 q^{42} -13666.9 q^{43} +4975.18 q^{44} -2431.84 q^{45} -19723.9 q^{46} -20736.8 q^{47} -7836.09 q^{48} +5887.33 q^{49} -5344.29 q^{50} +11269.0 q^{51} -2928.16 q^{52} -19250.0 q^{53} +35124.3 q^{54} +3025.00 q^{55} +11744.3 q^{56} +4357.89 q^{57} -35019.8 q^{58} -46610.1 q^{59} +12408.9 q^{60} +16865.0 q^{61} -46543.6 q^{62} +14653.9 q^{63} -48022.2 q^{64} -1780.37 q^{65} -12490.1 q^{66} +45274.0 q^{67} +38383.0 q^{68} +27845.3 q^{69} +32203.9 q^{70} -16399.4 q^{71} +7583.40 q^{72} +9142.48 q^{73} -57500.3 q^{74} +7544.83 q^{75} +14843.3 q^{76} -18228.2 q^{77} +7351.06 q^{78} +92375.7 q^{79} -16228.2 q^{80} -25949.4 q^{81} +97827.9 q^{82} -16302.2 q^{83} -74774.1 q^{84} +23337.6 q^{85} +116863. q^{86} +49439.5 q^{87} -9433.11 q^{88} +56296.0 q^{89} +20794.3 q^{90} +10728.3 q^{91} +94843.0 q^{92} +65708.2 q^{93} +177318. q^{94} +9025.00 q^{95} +97120.7 q^{96} -90929.3 q^{97} -50341.7 q^{98} -11770.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + O(q^{10}) \) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.55086 −1.51159 −0.755796 0.654807i \(-0.772750\pi\)
−0.755796 + 0.654807i \(0.772750\pi\)
\(3\) 12.0717 0.774402 0.387201 0.921995i \(-0.373442\pi\)
0.387201 + 0.921995i \(0.373442\pi\)
\(4\) 41.1172 1.28491
\(5\) 25.0000 0.447214
\(6\) −103.224 −1.17058
\(7\) −150.646 −1.16202 −0.581010 0.813896i \(-0.697342\pi\)
−0.581010 + 0.813896i \(0.697342\pi\)
\(8\) −77.9596 −0.430670
\(9\) −97.2734 −0.400302
\(10\) −213.771 −0.676005
\(11\) 121.000 0.301511
\(12\) 496.355 0.995037
\(13\) −71.2149 −0.116873 −0.0584363 0.998291i \(-0.518611\pi\)
−0.0584363 + 0.998291i \(0.518611\pi\)
\(14\) 1288.16 1.75650
\(15\) 301.793 0.346323
\(16\) −649.128 −0.633914
\(17\) 933.503 0.783417 0.391709 0.920089i \(-0.371884\pi\)
0.391709 + 0.920089i \(0.371884\pi\)
\(18\) 831.771 0.605094
\(19\) 361.000 0.229416
\(20\) 1027.93 0.574630
\(21\) −1818.56 −0.899870
\(22\) −1034.65 −0.455762
\(23\) 2306.65 0.909207 0.454603 0.890694i \(-0.349781\pi\)
0.454603 + 0.890694i \(0.349781\pi\)
\(24\) −941.107 −0.333512
\(25\) 625.000 0.200000
\(26\) 608.949 0.176664
\(27\) −4107.69 −1.08440
\(28\) −6194.15 −1.49309
\(29\) 4095.48 0.904293 0.452147 0.891944i \(-0.350658\pi\)
0.452147 + 0.891944i \(0.350658\pi\)
\(30\) −2580.59 −0.523499
\(31\) 5443.15 1.01729 0.508647 0.860975i \(-0.330146\pi\)
0.508647 + 0.860975i \(0.330146\pi\)
\(32\) 8045.31 1.38889
\(33\) 1460.68 0.233491
\(34\) −7982.25 −1.18421
\(35\) −3766.16 −0.519671
\(36\) −3999.61 −0.514353
\(37\) 6724.50 0.807525 0.403762 0.914864i \(-0.367702\pi\)
0.403762 + 0.914864i \(0.367702\pi\)
\(38\) −3086.86 −0.346783
\(39\) −859.687 −0.0905063
\(40\) −1948.99 −0.192602
\(41\) −11440.7 −1.06290 −0.531451 0.847089i \(-0.678353\pi\)
−0.531451 + 0.847089i \(0.678353\pi\)
\(42\) 15550.3 1.36024
\(43\) −13666.9 −1.12719 −0.563596 0.826050i \(-0.690583\pi\)
−0.563596 + 0.826050i \(0.690583\pi\)
\(44\) 4975.18 0.387415
\(45\) −2431.84 −0.179021
\(46\) −19723.9 −1.37435
\(47\) −20736.8 −1.36930 −0.684648 0.728874i \(-0.740044\pi\)
−0.684648 + 0.728874i \(0.740044\pi\)
\(48\) −7836.09 −0.490904
\(49\) 5887.33 0.350290
\(50\) −5344.29 −0.302318
\(51\) 11269.0 0.606680
\(52\) −2928.16 −0.150171
\(53\) −19250.0 −0.941329 −0.470665 0.882312i \(-0.655986\pi\)
−0.470665 + 0.882312i \(0.655986\pi\)
\(54\) 35124.3 1.63917
\(55\) 3025.00 0.134840
\(56\) 11744.3 0.500447
\(57\) 4357.89 0.177660
\(58\) −35019.8 −1.36692
\(59\) −46610.1 −1.74321 −0.871605 0.490208i \(-0.836921\pi\)
−0.871605 + 0.490208i \(0.836921\pi\)
\(60\) 12408.9 0.444994
\(61\) 16865.0 0.580311 0.290155 0.956980i \(-0.406293\pi\)
0.290155 + 0.956980i \(0.406293\pi\)
\(62\) −46543.6 −1.53773
\(63\) 14653.9 0.465159
\(64\) −48022.2 −1.46552
\(65\) −1780.37 −0.0522670
\(66\) −12490.1 −0.352943
\(67\) 45274.0 1.23214 0.616072 0.787689i \(-0.288723\pi\)
0.616072 + 0.787689i \(0.288723\pi\)
\(68\) 38383.0 1.00662
\(69\) 27845.3 0.704091
\(70\) 32203.9 0.785531
\(71\) −16399.4 −0.386083 −0.193042 0.981191i \(-0.561835\pi\)
−0.193042 + 0.981191i \(0.561835\pi\)
\(72\) 7583.40 0.172398
\(73\) 9142.48 0.200797 0.100398 0.994947i \(-0.467988\pi\)
0.100398 + 0.994947i \(0.467988\pi\)
\(74\) −57500.3 −1.22065
\(75\) 7544.83 0.154880
\(76\) 14843.3 0.294779
\(77\) −18228.2 −0.350362
\(78\) 7351.06 0.136809
\(79\) 92375.7 1.66529 0.832645 0.553807i \(-0.186825\pi\)
0.832645 + 0.553807i \(0.186825\pi\)
\(80\) −16228.2 −0.283495
\(81\) −25949.4 −0.439456
\(82\) 97827.9 1.60668
\(83\) −16302.2 −0.259747 −0.129873 0.991531i \(-0.541457\pi\)
−0.129873 + 0.991531i \(0.541457\pi\)
\(84\) −74774.1 −1.15625
\(85\) 23337.6 0.350355
\(86\) 116863. 1.70386
\(87\) 49439.5 0.700286
\(88\) −9433.11 −0.129852
\(89\) 56296.0 0.753360 0.376680 0.926343i \(-0.377066\pi\)
0.376680 + 0.926343i \(0.377066\pi\)
\(90\) 20794.3 0.270606
\(91\) 10728.3 0.135808
\(92\) 94843.0 1.16825
\(93\) 65708.2 0.787794
\(94\) 177318. 2.06982
\(95\) 9025.00 0.102598
\(96\) 97120.7 1.07556
\(97\) −90929.3 −0.981238 −0.490619 0.871374i \(-0.663229\pi\)
−0.490619 + 0.871374i \(0.663229\pi\)
\(98\) −50341.7 −0.529496
\(99\) −11770.1 −0.120696
\(100\) 25698.2 0.256982
\(101\) 8381.37 0.0817544 0.0408772 0.999164i \(-0.486985\pi\)
0.0408772 + 0.999164i \(0.486985\pi\)
\(102\) −96359.5 −0.917052
\(103\) 56329.3 0.523168 0.261584 0.965181i \(-0.415755\pi\)
0.261584 + 0.965181i \(0.415755\pi\)
\(104\) 5551.89 0.0503335
\(105\) −45464.0 −0.402434
\(106\) 164604. 1.42291
\(107\) 77738.1 0.656409 0.328204 0.944607i \(-0.393557\pi\)
0.328204 + 0.944607i \(0.393557\pi\)
\(108\) −168896. −1.39335
\(109\) −147584. −1.18979 −0.594897 0.803802i \(-0.702807\pi\)
−0.594897 + 0.803802i \(0.702807\pi\)
\(110\) −25866.3 −0.203823
\(111\) 81176.4 0.625348
\(112\) 97788.7 0.736621
\(113\) −104975. −0.773371 −0.386686 0.922212i \(-0.626380\pi\)
−0.386686 + 0.922212i \(0.626380\pi\)
\(114\) −37263.7 −0.268549
\(115\) 57666.3 0.406610
\(116\) 168394. 1.16194
\(117\) 6927.32 0.0467843
\(118\) 398556. 2.63502
\(119\) −140629. −0.910347
\(120\) −23527.7 −0.149151
\(121\) 14641.0 0.0909091
\(122\) −144210. −0.877194
\(123\) −138109. −0.823113
\(124\) 223807. 1.30713
\(125\) 15625.0 0.0894427
\(126\) −125303. −0.703131
\(127\) 209746. 1.15395 0.576973 0.816764i \(-0.304234\pi\)
0.576973 + 0.816764i \(0.304234\pi\)
\(128\) 153181. 0.826381
\(129\) −164983. −0.872899
\(130\) 15223.7 0.0790064
\(131\) −237616. −1.20976 −0.604878 0.796319i \(-0.706778\pi\)
−0.604878 + 0.796319i \(0.706778\pi\)
\(132\) 60059.0 0.300015
\(133\) −54383.3 −0.266586
\(134\) −387131. −1.86250
\(135\) −102692. −0.484957
\(136\) −72775.5 −0.337394
\(137\) 201445. 0.916971 0.458486 0.888702i \(-0.348392\pi\)
0.458486 + 0.888702i \(0.348392\pi\)
\(138\) −238101. −1.06430
\(139\) −8850.88 −0.0388552 −0.0194276 0.999811i \(-0.506184\pi\)
−0.0194276 + 0.999811i \(0.506184\pi\)
\(140\) −154854. −0.667731
\(141\) −250329. −1.06039
\(142\) 140229. 0.583600
\(143\) −8617.00 −0.0352384
\(144\) 63142.9 0.253757
\(145\) 102387. 0.404412
\(146\) −78176.1 −0.303523
\(147\) 71070.2 0.271265
\(148\) 276493. 1.03760
\(149\) 401386. 1.48114 0.740571 0.671978i \(-0.234555\pi\)
0.740571 + 0.671978i \(0.234555\pi\)
\(150\) −64514.8 −0.234116
\(151\) 199291. 0.711289 0.355644 0.934621i \(-0.384261\pi\)
0.355644 + 0.934621i \(0.384261\pi\)
\(152\) −28143.4 −0.0988025
\(153\) −90805.0 −0.313604
\(154\) 155867. 0.529605
\(155\) 136079. 0.454948
\(156\) −35347.9 −0.116293
\(157\) 59385.0 0.192277 0.0961385 0.995368i \(-0.469351\pi\)
0.0961385 + 0.995368i \(0.469351\pi\)
\(158\) −789891. −2.51724
\(159\) −232381. −0.728967
\(160\) 201133. 0.621130
\(161\) −347489. −1.05652
\(162\) 221890. 0.664278
\(163\) −291881. −0.860473 −0.430237 0.902716i \(-0.641570\pi\)
−0.430237 + 0.902716i \(0.641570\pi\)
\(164\) −470410. −1.36574
\(165\) 36517.0 0.104420
\(166\) 139398. 0.392631
\(167\) 472833. 1.31195 0.655974 0.754783i \(-0.272258\pi\)
0.655974 + 0.754783i \(0.272258\pi\)
\(168\) 141774. 0.387547
\(169\) −366221. −0.986341
\(170\) −199556. −0.529594
\(171\) −35115.7 −0.0918356
\(172\) −561943. −1.44834
\(173\) −428214. −1.08779 −0.543896 0.839153i \(-0.683051\pi\)
−0.543896 + 0.839153i \(0.683051\pi\)
\(174\) −422750. −1.05855
\(175\) −94154.0 −0.232404
\(176\) −78544.5 −0.191132
\(177\) −562664. −1.34995
\(178\) −481379. −1.13877
\(179\) 272677. 0.636085 0.318043 0.948076i \(-0.396974\pi\)
0.318043 + 0.948076i \(0.396974\pi\)
\(180\) −99990.2 −0.230026
\(181\) −116814. −0.265033 −0.132516 0.991181i \(-0.542306\pi\)
−0.132516 + 0.991181i \(0.542306\pi\)
\(182\) −91735.9 −0.205287
\(183\) 203589. 0.449394
\(184\) −179826. −0.391568
\(185\) 168113. 0.361136
\(186\) −561862. −1.19082
\(187\) 112954. 0.236209
\(188\) −852639. −1.75942
\(189\) 618808. 1.26009
\(190\) −77171.5 −0.155086
\(191\) −184952. −0.366840 −0.183420 0.983035i \(-0.558717\pi\)
−0.183420 + 0.983035i \(0.558717\pi\)
\(192\) −579711. −1.13490
\(193\) 55195.5 0.106662 0.0533311 0.998577i \(-0.483016\pi\)
0.0533311 + 0.998577i \(0.483016\pi\)
\(194\) 777524. 1.48323
\(195\) −21492.2 −0.0404756
\(196\) 242070. 0.450092
\(197\) 1.02034e6 1.87319 0.936593 0.350418i \(-0.113960\pi\)
0.936593 + 0.350418i \(0.113960\pi\)
\(198\) 100644. 0.182443
\(199\) −551326. −0.986906 −0.493453 0.869772i \(-0.664266\pi\)
−0.493453 + 0.869772i \(0.664266\pi\)
\(200\) −48724.8 −0.0861340
\(201\) 546535. 0.954175
\(202\) −71667.9 −0.123579
\(203\) −616968. −1.05081
\(204\) 463349. 0.779530
\(205\) −286018. −0.475344
\(206\) −481664. −0.790817
\(207\) −224376. −0.363957
\(208\) 46227.6 0.0740871
\(209\) 43681.0 0.0691714
\(210\) 388757. 0.608316
\(211\) 275587. 0.426141 0.213071 0.977037i \(-0.431654\pi\)
0.213071 + 0.977037i \(0.431654\pi\)
\(212\) −791506. −1.20952
\(213\) −197968. −0.298983
\(214\) −664727. −0.992222
\(215\) −341672. −0.504096
\(216\) 320234. 0.467017
\(217\) −819991. −1.18212
\(218\) 1.26197e6 1.79848
\(219\) 110366. 0.155497
\(220\) 124379. 0.173257
\(221\) −66479.3 −0.0915600
\(222\) −694127. −0.945272
\(223\) 819552. 1.10361 0.551804 0.833974i \(-0.313940\pi\)
0.551804 + 0.833974i \(0.313940\pi\)
\(224\) −1.21200e6 −1.61392
\(225\) −60795.9 −0.0800604
\(226\) 897623. 1.16902
\(227\) −630266. −0.811819 −0.405909 0.913913i \(-0.633045\pi\)
−0.405909 + 0.913913i \(0.633045\pi\)
\(228\) 179184. 0.228277
\(229\) −247601. −0.312006 −0.156003 0.987757i \(-0.549861\pi\)
−0.156003 + 0.987757i \(0.549861\pi\)
\(230\) −493096. −0.614628
\(231\) −220046. −0.271321
\(232\) −319282. −0.389452
\(233\) 1.10045e6 1.32795 0.663976 0.747754i \(-0.268868\pi\)
0.663976 + 0.747754i \(0.268868\pi\)
\(234\) −59234.5 −0.0707189
\(235\) −518420. −0.612368
\(236\) −1.91647e6 −2.23987
\(237\) 1.11513e6 1.28960
\(238\) 1.20250e6 1.37607
\(239\) 110119. 0.124700 0.0623502 0.998054i \(-0.480140\pi\)
0.0623502 + 0.998054i \(0.480140\pi\)
\(240\) −195902. −0.219539
\(241\) −1.09463e6 −1.21402 −0.607008 0.794696i \(-0.707630\pi\)
−0.607008 + 0.794696i \(0.707630\pi\)
\(242\) −125193. −0.137417
\(243\) 684914. 0.744081
\(244\) 693439. 0.745648
\(245\) 147183. 0.156654
\(246\) 1.18095e6 1.24421
\(247\) −25708.6 −0.0268124
\(248\) −424346. −0.438118
\(249\) −196795. −0.201148
\(250\) −133607. −0.135201
\(251\) 389038. 0.389769 0.194885 0.980826i \(-0.437567\pi\)
0.194885 + 0.980826i \(0.437567\pi\)
\(252\) 602526. 0.597688
\(253\) 279105. 0.274136
\(254\) −1.79351e6 −1.74429
\(255\) 281725. 0.271315
\(256\) 226881. 0.216370
\(257\) 983830. 0.929153 0.464576 0.885533i \(-0.346207\pi\)
0.464576 + 0.885533i \(0.346207\pi\)
\(258\) 1.41074e6 1.31947
\(259\) −1.01302e6 −0.938360
\(260\) −73203.9 −0.0671585
\(261\) −398381. −0.361991
\(262\) 2.03182e6 1.82866
\(263\) −1.04245e6 −0.929321 −0.464660 0.885489i \(-0.653824\pi\)
−0.464660 + 0.885489i \(0.653824\pi\)
\(264\) −113874. −0.100558
\(265\) −481251. −0.420975
\(266\) 465024. 0.402969
\(267\) 679590. 0.583403
\(268\) 1.86154e6 1.58320
\(269\) 680363. 0.573271 0.286635 0.958040i \(-0.407463\pi\)
0.286635 + 0.958040i \(0.407463\pi\)
\(270\) 878106. 0.733057
\(271\) 736325. 0.609041 0.304520 0.952506i \(-0.401504\pi\)
0.304520 + 0.952506i \(0.401504\pi\)
\(272\) −605963. −0.496619
\(273\) 129509. 0.105170
\(274\) −1.72253e6 −1.38609
\(275\) 75625.0 0.0603023
\(276\) 1.14492e6 0.904695
\(277\) −836059. −0.654693 −0.327347 0.944904i \(-0.606154\pi\)
−0.327347 + 0.944904i \(0.606154\pi\)
\(278\) 75682.6 0.0587332
\(279\) −529474. −0.407225
\(280\) 293608. 0.223807
\(281\) 1.28526e6 0.971015 0.485508 0.874232i \(-0.338635\pi\)
0.485508 + 0.874232i \(0.338635\pi\)
\(282\) 2.14053e6 1.60287
\(283\) 706022. 0.524025 0.262013 0.965064i \(-0.415614\pi\)
0.262013 + 0.965064i \(0.415614\pi\)
\(284\) −674295. −0.496083
\(285\) 108947. 0.0794519
\(286\) 73682.8 0.0532661
\(287\) 1.72350e6 1.23511
\(288\) −782595. −0.555976
\(289\) −548430. −0.386257
\(290\) −875496. −0.611307
\(291\) −1.09767e6 −0.759873
\(292\) 375913. 0.258006
\(293\) 1.50033e6 1.02098 0.510491 0.859883i \(-0.329464\pi\)
0.510491 + 0.859883i \(0.329464\pi\)
\(294\) −607711. −0.410042
\(295\) −1.16525e6 −0.779588
\(296\) −524240. −0.347777
\(297\) −497030. −0.326958
\(298\) −3.43220e6 −2.23888
\(299\) −164268. −0.106261
\(300\) 310222. 0.199007
\(301\) 2.05886e6 1.30982
\(302\) −1.70411e6 −1.07518
\(303\) 101178. 0.0633108
\(304\) −234335. −0.145430
\(305\) 421624. 0.259523
\(306\) 776461. 0.474041
\(307\) 1.18027e6 0.714720 0.357360 0.933967i \(-0.383677\pi\)
0.357360 + 0.933967i \(0.383677\pi\)
\(308\) −749492. −0.450184
\(309\) 679992. 0.405142
\(310\) −1.16359e6 −0.687695
\(311\) 693645. 0.406664 0.203332 0.979110i \(-0.434823\pi\)
0.203332 + 0.979110i \(0.434823\pi\)
\(312\) 67020.9 0.0389784
\(313\) −292301. −0.168643 −0.0843217 0.996439i \(-0.526872\pi\)
−0.0843217 + 0.996439i \(0.526872\pi\)
\(314\) −507792. −0.290644
\(315\) 366347. 0.208025
\(316\) 3.79823e6 2.13975
\(317\) 2.66490e6 1.48948 0.744738 0.667357i \(-0.232574\pi\)
0.744738 + 0.667357i \(0.232574\pi\)
\(318\) 1.98706e6 1.10190
\(319\) 495553. 0.272655
\(320\) −1.20055e6 −0.655401
\(321\) 938433. 0.508324
\(322\) 2.97133e6 1.59702
\(323\) 336994. 0.179728
\(324\) −1.06697e6 −0.564662
\(325\) −44509.3 −0.0233745
\(326\) 2.49584e6 1.30068
\(327\) −1.78159e6 −0.921379
\(328\) 891913. 0.457760
\(329\) 3.12393e6 1.59115
\(330\) −312251. −0.157841
\(331\) 2.49691e6 1.25266 0.626331 0.779557i \(-0.284556\pi\)
0.626331 + 0.779557i \(0.284556\pi\)
\(332\) −670299. −0.333752
\(333\) −654116. −0.323254
\(334\) −4.04313e6 −1.98313
\(335\) 1.13185e6 0.551032
\(336\) 1.18048e6 0.570440
\(337\) 419810. 0.201362 0.100681 0.994919i \(-0.467898\pi\)
0.100681 + 0.994919i \(0.467898\pi\)
\(338\) 3.13151e6 1.49095
\(339\) −1.26722e6 −0.598900
\(340\) 959575. 0.450175
\(341\) 658622. 0.306726
\(342\) 300269. 0.138818
\(343\) 1.64501e6 0.754976
\(344\) 1.06546e6 0.485448
\(345\) 696132. 0.314879
\(346\) 3.66160e6 1.64430
\(347\) 961596. 0.428715 0.214358 0.976755i \(-0.431234\pi\)
0.214358 + 0.976755i \(0.431234\pi\)
\(348\) 2.03281e6 0.899806
\(349\) 94162.7 0.0413824 0.0206912 0.999786i \(-0.493413\pi\)
0.0206912 + 0.999786i \(0.493413\pi\)
\(350\) 805097. 0.351300
\(351\) 292529. 0.126736
\(352\) 973482. 0.418766
\(353\) −767720. −0.327918 −0.163959 0.986467i \(-0.552427\pi\)
−0.163959 + 0.986467i \(0.552427\pi\)
\(354\) 4.81126e6 2.04057
\(355\) −409984. −0.172662
\(356\) 2.31473e6 0.968001
\(357\) −1.69763e6 −0.704974
\(358\) −2.33162e6 −0.961502
\(359\) 1.78125e6 0.729439 0.364719 0.931118i \(-0.381165\pi\)
0.364719 + 0.931118i \(0.381165\pi\)
\(360\) 189585. 0.0770988
\(361\) 130321. 0.0526316
\(362\) 998863. 0.400622
\(363\) 176742. 0.0704001
\(364\) 441116. 0.174502
\(365\) 228562. 0.0897991
\(366\) −1.74086e6 −0.679300
\(367\) 3.54586e6 1.37422 0.687111 0.726553i \(-0.258879\pi\)
0.687111 + 0.726553i \(0.258879\pi\)
\(368\) −1.49731e6 −0.576359
\(369\) 1.11288e6 0.425482
\(370\) −1.43751e6 −0.545891
\(371\) 2.89995e6 1.09384
\(372\) 2.70174e6 1.01225
\(373\) 1.45653e6 0.542061 0.271030 0.962571i \(-0.412636\pi\)
0.271030 + 0.962571i \(0.412636\pi\)
\(374\) −965852. −0.357052
\(375\) 188621. 0.0692646
\(376\) 1.61663e6 0.589715
\(377\) −291659. −0.105687
\(378\) −5.29134e6 −1.90474
\(379\) 134543. 0.0481132 0.0240566 0.999711i \(-0.492342\pi\)
0.0240566 + 0.999711i \(0.492342\pi\)
\(380\) 371082. 0.131829
\(381\) 2.53200e6 0.893617
\(382\) 1.58150e6 0.554512
\(383\) −1.48481e6 −0.517217 −0.258608 0.965982i \(-0.583264\pi\)
−0.258608 + 0.965982i \(0.583264\pi\)
\(384\) 1.84916e6 0.639950
\(385\) −455705. −0.156687
\(386\) −471969. −0.161230
\(387\) 1.32942e6 0.451218
\(388\) −3.73876e6 −1.26080
\(389\) −2.64085e6 −0.884851 −0.442425 0.896805i \(-0.645882\pi\)
−0.442425 + 0.896805i \(0.645882\pi\)
\(390\) 183777. 0.0611827
\(391\) 2.15327e6 0.712288
\(392\) −458974. −0.150859
\(393\) −2.86844e6 −0.936836
\(394\) −8.72482e6 −2.83149
\(395\) 2.30939e6 0.744741
\(396\) −483953. −0.155083
\(397\) −704306. −0.224277 −0.112139 0.993693i \(-0.535770\pi\)
−0.112139 + 0.993693i \(0.535770\pi\)
\(398\) 4.71431e6 1.49180
\(399\) −656501. −0.206444
\(400\) −405705. −0.126783
\(401\) 1.61703e6 0.502179 0.251089 0.967964i \(-0.419211\pi\)
0.251089 + 0.967964i \(0.419211\pi\)
\(402\) −4.67334e6 −1.44232
\(403\) −387634. −0.118894
\(404\) 344618. 0.105047
\(405\) −648736. −0.196531
\(406\) 5.27561e6 1.58839
\(407\) 813665. 0.243478
\(408\) −878526. −0.261279
\(409\) 3.28128e6 0.969919 0.484959 0.874537i \(-0.338834\pi\)
0.484959 + 0.874537i \(0.338834\pi\)
\(410\) 2.44570e6 0.718527
\(411\) 2.43179e6 0.710104
\(412\) 2.31610e6 0.672225
\(413\) 7.02164e6 2.02565
\(414\) 1.91861e6 0.550155
\(415\) −407554. −0.116162
\(416\) −572946. −0.162323
\(417\) −106845. −0.0300895
\(418\) −373510. −0.104559
\(419\) −128186. −0.0356701 −0.0178351 0.999841i \(-0.505677\pi\)
−0.0178351 + 0.999841i \(0.505677\pi\)
\(420\) −1.86935e6 −0.517092
\(421\) 2.48599e6 0.683587 0.341794 0.939775i \(-0.388966\pi\)
0.341794 + 0.939775i \(0.388966\pi\)
\(422\) −2.35651e6 −0.644152
\(423\) 2.01714e6 0.548132
\(424\) 1.50072e6 0.405402
\(425\) 583439. 0.156683
\(426\) 1.69280e6 0.451941
\(427\) −2.54065e6 −0.674333
\(428\) 3.19637e6 0.843427
\(429\) −104022. −0.0272887
\(430\) 2.92159e6 0.761987
\(431\) 172232. 0.0446603 0.0223301 0.999751i \(-0.492892\pi\)
0.0223301 + 0.999751i \(0.492892\pi\)
\(432\) 2.66641e6 0.687414
\(433\) 1.96024e6 0.502446 0.251223 0.967929i \(-0.419167\pi\)
0.251223 + 0.967929i \(0.419167\pi\)
\(434\) 7.01163e6 1.78688
\(435\) 1.23599e6 0.313177
\(436\) −6.06822e6 −1.52878
\(437\) 832702. 0.208586
\(438\) −943720. −0.235049
\(439\) 1.99952e6 0.495180 0.247590 0.968865i \(-0.420361\pi\)
0.247590 + 0.968865i \(0.420361\pi\)
\(440\) −235828. −0.0580715
\(441\) −572680. −0.140222
\(442\) 568455. 0.138401
\(443\) −3.10911e6 −0.752708 −0.376354 0.926476i \(-0.622822\pi\)
−0.376354 + 0.926476i \(0.622822\pi\)
\(444\) 3.33774e6 0.803517
\(445\) 1.40740e6 0.336913
\(446\) −7.00788e6 −1.66820
\(447\) 4.84542e6 1.14700
\(448\) 7.23437e6 1.70296
\(449\) −8.32331e6 −1.94841 −0.974205 0.225666i \(-0.927544\pi\)
−0.974205 + 0.225666i \(0.927544\pi\)
\(450\) 519857. 0.121019
\(451\) −1.38433e6 −0.320477
\(452\) −4.31626e6 −0.993713
\(453\) 2.40579e6 0.550823
\(454\) 5.38931e6 1.22714
\(455\) 268207. 0.0607353
\(456\) −339740. −0.0765128
\(457\) 5.83535e6 1.30700 0.653501 0.756926i \(-0.273300\pi\)
0.653501 + 0.756926i \(0.273300\pi\)
\(458\) 2.11720e6 0.471626
\(459\) −3.83454e6 −0.849535
\(460\) 2.37108e6 0.522457
\(461\) 4.38829e6 0.961709 0.480854 0.876801i \(-0.340327\pi\)
0.480854 + 0.876801i \(0.340327\pi\)
\(462\) 1.88158e6 0.410127
\(463\) −8.33830e6 −1.80769 −0.903847 0.427855i \(-0.859269\pi\)
−0.903847 + 0.427855i \(0.859269\pi\)
\(464\) −2.65849e6 −0.573244
\(465\) 1.64271e6 0.352312
\(466\) −9.40983e6 −2.00732
\(467\) 1.15648e6 0.245384 0.122692 0.992445i \(-0.460847\pi\)
0.122692 + 0.992445i \(0.460847\pi\)
\(468\) 284832. 0.0601137
\(469\) −6.82036e6 −1.43178
\(470\) 4.43294e6 0.925651
\(471\) 716879. 0.148900
\(472\) 3.63370e6 0.750749
\(473\) −1.65369e6 −0.339861
\(474\) −9.53535e6 −1.94935
\(475\) 225625. 0.0458831
\(476\) −5.78226e6 −1.16971
\(477\) 1.87252e6 0.376816
\(478\) −941612. −0.188496
\(479\) 1.28731e6 0.256356 0.128178 0.991751i \(-0.459087\pi\)
0.128178 + 0.991751i \(0.459087\pi\)
\(480\) 2.42802e6 0.481004
\(481\) −478885. −0.0943775
\(482\) 9.36001e6 1.83510
\(483\) −4.19479e6 −0.818168
\(484\) 601996. 0.116810
\(485\) −2.27323e6 −0.438823
\(486\) −5.85660e6 −1.12475
\(487\) 7.64647e6 1.46096 0.730480 0.682934i \(-0.239296\pi\)
0.730480 + 0.682934i \(0.239296\pi\)
\(488\) −1.31479e6 −0.249923
\(489\) −3.52351e6 −0.666352
\(490\) −1.25854e6 −0.236798
\(491\) 5.66387e6 1.06025 0.530127 0.847918i \(-0.322144\pi\)
0.530127 + 0.847918i \(0.322144\pi\)
\(492\) −5.67866e6 −1.05763
\(493\) 3.82314e6 0.708439
\(494\) 219830. 0.0405294
\(495\) −294252. −0.0539767
\(496\) −3.53330e6 −0.644877
\(497\) 2.47050e6 0.448636
\(498\) 1.68277e6 0.304054
\(499\) −3.51678e6 −0.632257 −0.316129 0.948716i \(-0.602383\pi\)
−0.316129 + 0.948716i \(0.602383\pi\)
\(500\) 642456. 0.114926
\(501\) 5.70791e6 1.01597
\(502\) −3.32661e6 −0.589172
\(503\) −9.49940e6 −1.67408 −0.837040 0.547141i \(-0.815716\pi\)
−0.837040 + 0.547141i \(0.815716\pi\)
\(504\) −1.14241e6 −0.200330
\(505\) 209534. 0.0365617
\(506\) −2.38659e6 −0.414382
\(507\) −4.42092e6 −0.763824
\(508\) 8.62418e6 1.48272
\(509\) −3.27119e6 −0.559643 −0.279822 0.960052i \(-0.590275\pi\)
−0.279822 + 0.960052i \(0.590275\pi\)
\(510\) −2.40899e6 −0.410118
\(511\) −1.37728e6 −0.233330
\(512\) −6.84182e6 −1.15344
\(513\) −1.48288e6 −0.248778
\(514\) −8.41259e6 −1.40450
\(515\) 1.40823e6 0.233968
\(516\) −6.78362e6 −1.12160
\(517\) −2.50915e6 −0.412858
\(518\) 8.66221e6 1.41842
\(519\) −5.16928e6 −0.842388
\(520\) 138797. 0.0225098
\(521\) 3.61278e6 0.583105 0.291553 0.956555i \(-0.405828\pi\)
0.291553 + 0.956555i \(0.405828\pi\)
\(522\) 3.40650e6 0.547182
\(523\) 5.79421e6 0.926275 0.463137 0.886287i \(-0.346724\pi\)
0.463137 + 0.886287i \(0.346724\pi\)
\(524\) −9.77010e6 −1.55443
\(525\) −1.13660e6 −0.179974
\(526\) 8.91384e6 1.40475
\(527\) 5.08120e6 0.796966
\(528\) −948167. −0.148013
\(529\) −1.11570e6 −0.173343
\(530\) 4.11510e6 0.636343
\(531\) 4.53392e6 0.697811
\(532\) −2.23609e6 −0.342539
\(533\) 814749. 0.124224
\(534\) −5.81108e6 −0.881868
\(535\) 1.94345e6 0.293555
\(536\) −3.52954e6 −0.530648
\(537\) 3.29168e6 0.492586
\(538\) −5.81768e6 −0.866552
\(539\) 712366. 0.105616
\(540\) −4.22241e6 −0.623126
\(541\) −8.73015e6 −1.28241 −0.641207 0.767368i \(-0.721566\pi\)
−0.641207 + 0.767368i \(0.721566\pi\)
\(542\) −6.29621e6 −0.920621
\(543\) −1.41015e6 −0.205242
\(544\) 7.51032e6 1.08808
\(545\) −3.68959e6 −0.532092
\(546\) −1.10741e6 −0.158974
\(547\) 4.64429e6 0.663668 0.331834 0.943338i \(-0.392333\pi\)
0.331834 + 0.943338i \(0.392333\pi\)
\(548\) 8.28286e6 1.17823
\(549\) −1.64051e6 −0.232300
\(550\) −646659. −0.0911524
\(551\) 1.47847e6 0.207459
\(552\) −2.17081e6 −0.303231
\(553\) −1.39161e7 −1.93510
\(554\) 7.14903e6 0.989629
\(555\) 2.02941e6 0.279664
\(556\) −363923. −0.0499255
\(557\) 1.09819e7 1.49982 0.749911 0.661539i \(-0.230096\pi\)
0.749911 + 0.661539i \(0.230096\pi\)
\(558\) 4.52746e6 0.615558
\(559\) 973285. 0.131738
\(560\) 2.44472e6 0.329427
\(561\) 1.36355e6 0.182921
\(562\) −1.09901e7 −1.46778
\(563\) 130130. 0.0173024 0.00865119 0.999963i \(-0.497246\pi\)
0.00865119 + 0.999963i \(0.497246\pi\)
\(564\) −1.02928e7 −1.36250
\(565\) −2.62436e6 −0.345862
\(566\) −6.03709e6 −0.792113
\(567\) 3.90919e6 0.510656
\(568\) 1.27849e6 0.166274
\(569\) −2.55163e6 −0.330398 −0.165199 0.986260i \(-0.552827\pi\)
−0.165199 + 0.986260i \(0.552827\pi\)
\(570\) −931593. −0.120099
\(571\) 6.91946e6 0.888141 0.444070 0.895992i \(-0.353534\pi\)
0.444070 + 0.895992i \(0.353534\pi\)
\(572\) −354307. −0.0452782
\(573\) −2.23269e6 −0.284081
\(574\) −1.47374e7 −1.86699
\(575\) 1.44166e6 0.181841
\(576\) 4.67128e6 0.586651
\(577\) 2.32530e6 0.290764 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(578\) 4.68955e6 0.583863
\(579\) 666305. 0.0825993
\(580\) 4.20986e6 0.519634
\(581\) 2.45586e6 0.301831
\(582\) 9.38605e6 1.14862
\(583\) −2.32925e6 −0.283821
\(584\) −712745. −0.0864772
\(585\) 173183. 0.0209226
\(586\) −1.28291e7 −1.54331
\(587\) 8.24919e6 0.988134 0.494067 0.869424i \(-0.335510\pi\)
0.494067 + 0.869424i \(0.335510\pi\)
\(588\) 2.92220e6 0.348552
\(589\) 1.96498e6 0.233383
\(590\) 9.96391e6 1.17842
\(591\) 1.23173e7 1.45060
\(592\) −4.36506e6 −0.511901
\(593\) 1.53834e7 1.79646 0.898228 0.439530i \(-0.144855\pi\)
0.898228 + 0.439530i \(0.144855\pi\)
\(594\) 4.25003e6 0.494227
\(595\) −3.51572e6 −0.407119
\(596\) 1.65039e7 1.90314
\(597\) −6.65546e6 −0.764262
\(598\) 1.40463e6 0.160624
\(599\) 1.47994e7 1.68530 0.842652 0.538459i \(-0.180993\pi\)
0.842652 + 0.538459i \(0.180993\pi\)
\(600\) −588192. −0.0667023
\(601\) 3.39646e6 0.383566 0.191783 0.981437i \(-0.438573\pi\)
0.191783 + 0.981437i \(0.438573\pi\)
\(602\) −1.76051e7 −1.97991
\(603\) −4.40396e6 −0.493230
\(604\) 8.19429e6 0.913943
\(605\) 366025. 0.0406558
\(606\) −865155. −0.0957001
\(607\) 1.28066e7 1.41079 0.705393 0.708816i \(-0.250770\pi\)
0.705393 + 0.708816i \(0.250770\pi\)
\(608\) 2.90436e6 0.318633
\(609\) −7.44787e6 −0.813746
\(610\) −3.60525e6 −0.392293
\(611\) 1.47677e6 0.160033
\(612\) −3.73365e6 −0.402953
\(613\) 9.28213e6 0.997692 0.498846 0.866691i \(-0.333757\pi\)
0.498846 + 0.866691i \(0.333757\pi\)
\(614\) −1.00923e7 −1.08036
\(615\) −3.45273e6 −0.368107
\(616\) 1.42106e6 0.150890
\(617\) −1.39823e7 −1.47865 −0.739323 0.673351i \(-0.764854\pi\)
−0.739323 + 0.673351i \(0.764854\pi\)
\(618\) −5.81451e6 −0.612410
\(619\) −544051. −0.0570706 −0.0285353 0.999593i \(-0.509084\pi\)
−0.0285353 + 0.999593i \(0.509084\pi\)
\(620\) 5.59518e6 0.584567
\(621\) −9.47501e6 −0.985940
\(622\) −5.93126e6 −0.614711
\(623\) −8.48079e6 −0.875419
\(624\) 558047. 0.0573732
\(625\) 390625. 0.0400000
\(626\) 2.49942e6 0.254920
\(627\) 527305. 0.0535665
\(628\) 2.44174e6 0.247059
\(629\) 6.27734e6 0.632629
\(630\) −3.13258e6 −0.314450
\(631\) −1.66107e7 −1.66079 −0.830394 0.557177i \(-0.811885\pi\)
−0.830394 + 0.557177i \(0.811885\pi\)
\(632\) −7.20157e6 −0.717191
\(633\) 3.32682e6 0.330004
\(634\) −2.27872e7 −2.25148
\(635\) 5.24366e6 0.516060
\(636\) −9.55485e6 −0.936658
\(637\) −419265. −0.0409393
\(638\) −4.23740e6 −0.412143
\(639\) 1.59522e6 0.154550
\(640\) 3.82953e6 0.369569
\(641\) −2.64658e6 −0.254414 −0.127207 0.991876i \(-0.540601\pi\)
−0.127207 + 0.991876i \(0.540601\pi\)
\(642\) −8.02440e6 −0.768379
\(643\) 1.28930e7 1.22978 0.614891 0.788612i \(-0.289200\pi\)
0.614891 + 0.788612i \(0.289200\pi\)
\(644\) −1.42878e7 −1.35753
\(645\) −4.12457e6 −0.390372
\(646\) −2.88159e6 −0.271676
\(647\) −477187. −0.0448155 −0.0224077 0.999749i \(-0.507133\pi\)
−0.0224077 + 0.999749i \(0.507133\pi\)
\(648\) 2.02301e6 0.189260
\(649\) −5.63982e6 −0.525598
\(650\) 380593. 0.0353327
\(651\) −9.89871e6 −0.915432
\(652\) −1.20013e7 −1.10563
\(653\) 1.91774e7 1.75997 0.879987 0.474998i \(-0.157551\pi\)
0.879987 + 0.474998i \(0.157551\pi\)
\(654\) 1.52341e7 1.39275
\(655\) −5.94040e6 −0.541019
\(656\) 7.42648e6 0.673789
\(657\) −889321. −0.0803795
\(658\) −2.67122e7 −2.40517
\(659\) −6.30280e6 −0.565354 −0.282677 0.959215i \(-0.591222\pi\)
−0.282677 + 0.959215i \(0.591222\pi\)
\(660\) 1.50147e6 0.134171
\(661\) −310525. −0.0276435 −0.0138218 0.999904i \(-0.504400\pi\)
−0.0138218 + 0.999904i \(0.504400\pi\)
\(662\) −2.13508e7 −1.89351
\(663\) −802520. −0.0709042
\(664\) 1.27091e6 0.111865
\(665\) −1.35958e6 −0.119221
\(666\) 5.59325e6 0.488628
\(667\) 9.44684e6 0.822190
\(668\) 1.94416e7 1.68574
\(669\) 9.89341e6 0.854635
\(670\) −9.67829e6 −0.832936
\(671\) 2.04066e6 0.174970
\(672\) −1.46309e7 −1.24982
\(673\) −2.36403e6 −0.201194 −0.100597 0.994927i \(-0.532075\pi\)
−0.100597 + 0.994927i \(0.532075\pi\)
\(674\) −3.58974e6 −0.304378
\(675\) −2.56730e6 −0.216879
\(676\) −1.50580e7 −1.26736
\(677\) −1.33591e7 −1.12023 −0.560114 0.828415i \(-0.689243\pi\)
−0.560114 + 0.828415i \(0.689243\pi\)
\(678\) 1.08359e7 0.905292
\(679\) 1.36982e7 1.14022
\(680\) −1.81939e6 −0.150887
\(681\) −7.60840e6 −0.628674
\(682\) −5.63178e6 −0.463644
\(683\) −1.06444e6 −0.0873109 −0.0436554 0.999047i \(-0.513900\pi\)
−0.0436554 + 0.999047i \(0.513900\pi\)
\(684\) −1.44386e6 −0.118001
\(685\) 5.03613e6 0.410082
\(686\) −1.40662e7 −1.14122
\(687\) −2.98897e6 −0.241618
\(688\) 8.87155e6 0.714543
\(689\) 1.37089e6 0.110016
\(690\) −5.95253e6 −0.475969
\(691\) −1.67272e6 −0.133269 −0.0666343 0.997777i \(-0.521226\pi\)
−0.0666343 + 0.997777i \(0.521226\pi\)
\(692\) −1.76070e7 −1.39772
\(693\) 1.77312e6 0.140251
\(694\) −8.22247e6 −0.648042
\(695\) −221272. −0.0173766
\(696\) −3.85428e6 −0.301592
\(697\) −1.06799e7 −0.832696
\(698\) −805172. −0.0625533
\(699\) 1.32844e7 1.02837
\(700\) −3.87134e6 −0.298619
\(701\) 1.53207e7 1.17756 0.588782 0.808292i \(-0.299608\pi\)
0.588782 + 0.808292i \(0.299608\pi\)
\(702\) −2.50137e6 −0.191573
\(703\) 2.42755e6 0.185259
\(704\) −5.81068e6 −0.441871
\(705\) −6.25823e6 −0.474219
\(706\) 6.56466e6 0.495679
\(707\) −1.26262e6 −0.0950003
\(708\) −2.31352e7 −1.73456
\(709\) −2.39436e7 −1.78885 −0.894426 0.447215i \(-0.852416\pi\)
−0.894426 + 0.447215i \(0.852416\pi\)
\(710\) 3.50571e6 0.260994
\(711\) −8.98570e6 −0.666620
\(712\) −4.38881e6 −0.324450
\(713\) 1.25555e7 0.924930
\(714\) 1.45162e7 1.06563
\(715\) −215425. −0.0157591
\(716\) 1.12117e7 0.817313
\(717\) 1.32933e6 0.0965682
\(718\) −1.52312e7 −1.10261
\(719\) −1.67724e7 −1.20996 −0.604982 0.796239i \(-0.706820\pi\)
−0.604982 + 0.796239i \(0.706820\pi\)
\(720\) 1.57857e6 0.113484
\(721\) −8.48580e6 −0.607932
\(722\) −1.11436e6 −0.0795575
\(723\) −1.32141e7 −0.940135
\(724\) −4.80307e6 −0.340544
\(725\) 2.55967e6 0.180859
\(726\) −1.51130e6 −0.106416
\(727\) 1.04512e7 0.733381 0.366690 0.930343i \(-0.380491\pi\)
0.366690 + 0.930343i \(0.380491\pi\)
\(728\) −836372. −0.0584885
\(729\) 1.45738e7 1.01567
\(730\) −1.95440e6 −0.135740
\(731\) −1.27581e7 −0.883062
\(732\) 8.37101e6 0.577431
\(733\) 2.43966e7 1.67714 0.838569 0.544796i \(-0.183393\pi\)
0.838569 + 0.544796i \(0.183393\pi\)
\(734\) −3.03202e7 −2.07726
\(735\) 1.77675e6 0.121313
\(736\) 1.85577e7 1.26279
\(737\) 5.47815e6 0.371506
\(738\) −9.51606e6 −0.643156
\(739\) −7.71931e6 −0.519957 −0.259978 0.965614i \(-0.583715\pi\)
−0.259978 + 0.965614i \(0.583715\pi\)
\(740\) 6.91231e6 0.464028
\(741\) −310347. −0.0207636
\(742\) −2.47970e7 −1.65344
\(743\) 3.36291e6 0.223483 0.111741 0.993737i \(-0.464357\pi\)
0.111741 + 0.993737i \(0.464357\pi\)
\(744\) −5.12259e6 −0.339279
\(745\) 1.00347e7 0.662387
\(746\) −1.24546e7 −0.819375
\(747\) 1.58577e6 0.103977
\(748\) 4.64434e6 0.303508
\(749\) −1.17110e7 −0.762760
\(750\) −1.61287e6 −0.104700
\(751\) −598478. −0.0387211 −0.0193606 0.999813i \(-0.506163\pi\)
−0.0193606 + 0.999813i \(0.506163\pi\)
\(752\) 1.34608e7 0.868016
\(753\) 4.69636e6 0.301838
\(754\) 2.49393e6 0.159756
\(755\) 4.98228e6 0.318098
\(756\) 2.54436e7 1.61910
\(757\) −6.30804e6 −0.400087 −0.200044 0.979787i \(-0.564108\pi\)
−0.200044 + 0.979787i \(0.564108\pi\)
\(758\) −1.15046e6 −0.0727275
\(759\) 3.36928e6 0.212291
\(760\) −703585. −0.0441858
\(761\) −1.49217e7 −0.934020 −0.467010 0.884252i \(-0.654669\pi\)
−0.467010 + 0.884252i \(0.654669\pi\)
\(762\) −2.16508e7 −1.35078
\(763\) 2.22329e7 1.38257
\(764\) −7.60472e6 −0.471357
\(765\) −2.27013e6 −0.140248
\(766\) 1.26964e7 0.781821
\(767\) 3.31933e6 0.203734
\(768\) 2.73884e6 0.167557
\(769\) −2.22535e7 −1.35701 −0.678503 0.734597i \(-0.737371\pi\)
−0.678503 + 0.734597i \(0.737371\pi\)
\(770\) 3.89667e6 0.236846
\(771\) 1.18765e7 0.719537
\(772\) 2.26948e6 0.137051
\(773\) 1.29560e7 0.779871 0.389935 0.920842i \(-0.372497\pi\)
0.389935 + 0.920842i \(0.372497\pi\)
\(774\) −1.13677e7 −0.682057
\(775\) 3.40197e6 0.203459
\(776\) 7.08881e6 0.422590
\(777\) −1.22289e7 −0.726667
\(778\) 2.25815e7 1.33753
\(779\) −4.13010e6 −0.243847
\(780\) −883697. −0.0520076
\(781\) −1.98432e6 −0.116408
\(782\) −1.84123e7 −1.07669
\(783\) −1.68229e7 −0.980612
\(784\) −3.82163e6 −0.222054
\(785\) 1.48462e6 0.0859889
\(786\) 2.45276e7 1.41611
\(787\) −9.80748e6 −0.564443 −0.282222 0.959349i \(-0.591071\pi\)
−0.282222 + 0.959349i \(0.591071\pi\)
\(788\) 4.19537e7 2.40688
\(789\) −1.25842e7 −0.719667
\(790\) −1.97473e7 −1.12574
\(791\) 1.58140e7 0.898673
\(792\) 917591. 0.0519800
\(793\) −1.20104e6 −0.0678224
\(794\) 6.02242e6 0.339016
\(795\) −5.80952e6 −0.326004
\(796\) −2.26690e7 −1.26809
\(797\) 2.88620e7 1.60946 0.804730 0.593641i \(-0.202310\pi\)
0.804730 + 0.593641i \(0.202310\pi\)
\(798\) 5.61364e6 0.312060
\(799\) −1.93579e7 −1.07273
\(800\) 5.02832e6 0.277778
\(801\) −5.47611e6 −0.301572
\(802\) −1.38270e7 −0.759089
\(803\) 1.10624e6 0.0605426
\(804\) 2.24720e7 1.22603
\(805\) −8.68722e6 −0.472488
\(806\) 3.31460e6 0.179719
\(807\) 8.21315e6 0.443942
\(808\) −653408. −0.0352092
\(809\) −1.10942e7 −0.595969 −0.297984 0.954571i \(-0.596314\pi\)
−0.297984 + 0.954571i \(0.596314\pi\)
\(810\) 5.54725e6 0.297074
\(811\) −9.35372e6 −0.499381 −0.249691 0.968326i \(-0.580329\pi\)
−0.249691 + 0.968326i \(0.580329\pi\)
\(812\) −2.53680e7 −1.35019
\(813\) 8.88871e6 0.471642
\(814\) −6.95753e6 −0.368039
\(815\) −7.29703e6 −0.384815
\(816\) −7.31501e6 −0.384583
\(817\) −4.93374e6 −0.258596
\(818\) −2.80578e7 −1.46612
\(819\) −1.04358e6 −0.0543643
\(820\) −1.17602e7 −0.610775
\(821\) −6.81016e6 −0.352614 −0.176307 0.984335i \(-0.556415\pi\)
−0.176307 + 0.984335i \(0.556415\pi\)
\(822\) −2.07939e7 −1.07339
\(823\) −2.18259e7 −1.12324 −0.561620 0.827395i \(-0.689822\pi\)
−0.561620 + 0.827395i \(0.689822\pi\)
\(824\) −4.39141e6 −0.225313
\(825\) 912924. 0.0466982
\(826\) −6.00410e7 −3.06195
\(827\) −5.00263e6 −0.254352 −0.127176 0.991880i \(-0.540591\pi\)
−0.127176 + 0.991880i \(0.540591\pi\)
\(828\) −9.22571e6 −0.467653
\(829\) −1.56555e7 −0.791190 −0.395595 0.918425i \(-0.629462\pi\)
−0.395595 + 0.918425i \(0.629462\pi\)
\(830\) 3.48494e6 0.175590
\(831\) −1.00927e7 −0.506995
\(832\) 3.41990e6 0.171279
\(833\) 5.49583e6 0.274423
\(834\) 913619. 0.0454831
\(835\) 1.18208e7 0.586721
\(836\) 1.79604e6 0.0888792
\(837\) −2.23588e7 −1.10315
\(838\) 1.09610e6 0.0539187
\(839\) 2.18299e7 1.07065 0.535324 0.844647i \(-0.320189\pi\)
0.535324 + 0.844647i \(0.320189\pi\)
\(840\) 3.54436e6 0.173316
\(841\) −3.73823e6 −0.182254
\(842\) −2.12573e7 −1.03331
\(843\) 1.55153e7 0.751956
\(844\) 1.13314e7 0.547553
\(845\) −9.15554e6 −0.441105
\(846\) −1.72483e7 −0.828553
\(847\) −2.20561e6 −0.105638
\(848\) 1.24957e7 0.596722
\(849\) 8.52290e6 0.405806
\(850\) −4.98891e6 −0.236842
\(851\) 1.55111e7 0.734207
\(852\) −8.13990e6 −0.384167
\(853\) 3.83498e7 1.80464 0.902319 0.431069i \(-0.141863\pi\)
0.902319 + 0.431069i \(0.141863\pi\)
\(854\) 2.17247e7 1.01932
\(855\) −877893. −0.0410701
\(856\) −6.06043e6 −0.282696
\(857\) −7.58808e6 −0.352923 −0.176461 0.984308i \(-0.556465\pi\)
−0.176461 + 0.984308i \(0.556465\pi\)
\(858\) 889478. 0.0412494
\(859\) 2.05770e7 0.951477 0.475738 0.879587i \(-0.342181\pi\)
0.475738 + 0.879587i \(0.342181\pi\)
\(860\) −1.40486e7 −0.647718
\(861\) 2.08056e7 0.956474
\(862\) −1.47273e6 −0.0675082
\(863\) 2.01101e7 0.919153 0.459576 0.888138i \(-0.348001\pi\)
0.459576 + 0.888138i \(0.348001\pi\)
\(864\) −3.30476e7 −1.50611
\(865\) −1.07054e7 −0.486475
\(866\) −1.67617e7 −0.759493
\(867\) −6.62049e6 −0.299118
\(868\) −3.37157e7 −1.51891
\(869\) 1.11775e7 0.502104
\(870\) −1.05687e7 −0.473397
\(871\) −3.22418e6 −0.144004
\(872\) 1.15056e7 0.512409
\(873\) 8.84501e6 0.392792
\(874\) −7.12031e6 −0.315297
\(875\) −2.35385e6 −0.103934
\(876\) 4.53792e6 0.199800
\(877\) −7.34179e6 −0.322332 −0.161166 0.986927i \(-0.551525\pi\)
−0.161166 + 0.986927i \(0.551525\pi\)
\(878\) −1.70976e7 −0.748511
\(879\) 1.81116e7 0.790650
\(880\) −1.96361e6 −0.0854769
\(881\) −2.26545e7 −0.983364 −0.491682 0.870775i \(-0.663618\pi\)
−0.491682 + 0.870775i \(0.663618\pi\)
\(882\) 4.89691e6 0.211958
\(883\) 5.78873e6 0.249851 0.124926 0.992166i \(-0.460131\pi\)
0.124926 + 0.992166i \(0.460131\pi\)
\(884\) −2.73344e6 −0.117647
\(885\) −1.40666e7 −0.603714
\(886\) 2.65855e7 1.13779
\(887\) 2.24844e7 0.959558 0.479779 0.877389i \(-0.340717\pi\)
0.479779 + 0.877389i \(0.340717\pi\)
\(888\) −6.32848e6 −0.269319
\(889\) −3.15975e7 −1.34091
\(890\) −1.20345e7 −0.509275
\(891\) −3.13988e6 −0.132501
\(892\) 3.36977e7 1.41804
\(893\) −7.48599e6 −0.314138
\(894\) −4.14325e7 −1.73379
\(895\) 6.81692e6 0.284466
\(896\) −2.30762e7 −0.960271
\(897\) −1.98300e6 −0.0822889
\(898\) 7.11714e7 2.94520
\(899\) 2.22923e7 0.919932
\(900\) −2.49976e6 −0.102871
\(901\) −1.79699e7 −0.737454
\(902\) 1.18372e7 0.484431
\(903\) 2.48540e7 1.01433
\(904\) 8.18378e6 0.333068
\(905\) −2.92036e6 −0.118526
\(906\) −2.05716e7 −0.832620
\(907\) 1.32524e7 0.534903 0.267452 0.963571i \(-0.413818\pi\)
0.267452 + 0.963571i \(0.413818\pi\)
\(908\) −2.59147e7 −1.04312
\(909\) −815284. −0.0327265
\(910\) −2.29340e6 −0.0918070
\(911\) 1.78307e7 0.711826 0.355913 0.934519i \(-0.384170\pi\)
0.355913 + 0.934519i \(0.384170\pi\)
\(912\) −2.82883e6 −0.112621
\(913\) −1.97256e6 −0.0783166
\(914\) −4.98972e7 −1.97565
\(915\) 5.08973e6 0.200975
\(916\) −1.01806e7 −0.400900
\(917\) 3.57960e7 1.40576
\(918\) 3.27886e7 1.28415
\(919\) 1.08092e7 0.422186 0.211093 0.977466i \(-0.432298\pi\)
0.211093 + 0.977466i \(0.432298\pi\)
\(920\) −4.49564e6 −0.175115
\(921\) 1.42479e7 0.553480
\(922\) −3.75237e7 −1.45371
\(923\) 1.16788e6 0.0451225
\(924\) −9.04767e6 −0.348623
\(925\) 4.20281e6 0.161505
\(926\) 7.12996e7 2.73250
\(927\) −5.47934e6 −0.209425
\(928\) 3.29494e7 1.25596
\(929\) 1.75365e6 0.0666657 0.0333329 0.999444i \(-0.489388\pi\)
0.0333329 + 0.999444i \(0.489388\pi\)
\(930\) −1.40465e7 −0.532552
\(931\) 2.12532e6 0.0803621
\(932\) 4.52476e7 1.70630
\(933\) 8.37349e6 0.314921
\(934\) −9.88888e6 −0.370920
\(935\) 2.82385e6 0.105636
\(936\) −540051. −0.0201486
\(937\) 5.03273e7 1.87264 0.936321 0.351145i \(-0.114208\pi\)
0.936321 + 0.351145i \(0.114208\pi\)
\(938\) 5.83199e7 2.16426
\(939\) −3.52858e6 −0.130598
\(940\) −2.13160e7 −0.786839
\(941\) −3.20030e7 −1.17819 −0.589097 0.808063i \(-0.700516\pi\)
−0.589097 + 0.808063i \(0.700516\pi\)
\(942\) −6.12993e6 −0.225076
\(943\) −2.63897e7 −0.966398
\(944\) 3.02559e7 1.10505
\(945\) 1.54702e7 0.563529
\(946\) 1.41405e7 0.513732
\(947\) 1.41707e7 0.513473 0.256737 0.966481i \(-0.417353\pi\)
0.256737 + 0.966481i \(0.417353\pi\)
\(948\) 4.58512e7 1.65703
\(949\) −651081. −0.0234677
\(950\) −1.92929e6 −0.0693566
\(951\) 3.21700e7 1.15345
\(952\) 1.09634e7 0.392059
\(953\) −5.47820e6 −0.195392 −0.0976958 0.995216i \(-0.531147\pi\)
−0.0976958 + 0.995216i \(0.531147\pi\)
\(954\) −1.60116e7 −0.569592
\(955\) −4.62381e6 −0.164056
\(956\) 4.52778e6 0.160229
\(957\) 5.98217e6 0.211144
\(958\) −1.10076e7 −0.387505
\(959\) −3.03470e7 −1.06554
\(960\) −1.44928e7 −0.507543
\(961\) 998763. 0.0348862
\(962\) 4.09488e6 0.142660
\(963\) −7.56185e6 −0.262762
\(964\) −4.50080e7 −1.55990
\(965\) 1.37989e6 0.0477008
\(966\) 3.58690e7 1.23674
\(967\) −3.67623e7 −1.26426 −0.632130 0.774863i \(-0.717819\pi\)
−0.632130 + 0.774863i \(0.717819\pi\)
\(968\) −1.14141e6 −0.0391518
\(969\) 4.06810e6 0.139182
\(970\) 1.94381e7 0.663322
\(971\) −1.51254e7 −0.514823 −0.257412 0.966302i \(-0.582870\pi\)
−0.257412 + 0.966302i \(0.582870\pi\)
\(972\) 2.81617e7 0.956078
\(973\) 1.33335e6 0.0451505
\(974\) −6.53839e7 −2.20838
\(975\) −537304. −0.0181013
\(976\) −1.09475e7 −0.367867
\(977\) 1.01109e7 0.338887 0.169444 0.985540i \(-0.445803\pi\)
0.169444 + 0.985540i \(0.445803\pi\)
\(978\) 3.01290e7 1.00725
\(979\) 6.81182e6 0.227147
\(980\) 6.05175e6 0.201287
\(981\) 1.43560e7 0.476278
\(982\) −4.84310e7 −1.60267
\(983\) −1.46205e7 −0.482591 −0.241295 0.970452i \(-0.577572\pi\)
−0.241295 + 0.970452i \(0.577572\pi\)
\(984\) 1.07669e7 0.354490
\(985\) 2.55086e7 0.837715
\(986\) −3.26911e7 −1.07087
\(987\) 3.77112e7 1.23219
\(988\) −1.05706e6 −0.0344516
\(989\) −3.15247e7 −1.02485
\(990\) 2.51611e6 0.0815908
\(991\) −2.47379e7 −0.800163 −0.400082 0.916480i \(-0.631018\pi\)
−0.400082 + 0.916480i \(0.631018\pi\)
\(992\) 4.37918e7 1.41291
\(993\) 3.01421e7 0.970063
\(994\) −2.11249e7 −0.678155
\(995\) −1.37832e7 −0.441358
\(996\) −8.09167e6 −0.258458
\(997\) 1.98844e7 0.633540 0.316770 0.948502i \(-0.397402\pi\)
0.316770 + 0.948502i \(0.397402\pi\)
\(998\) 3.00715e7 0.955715
\(999\) −2.76222e7 −0.875677
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.1.5 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.5 40 1.1 even 1 trivial