Properties

Label 1045.6.a.h.1.9
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 1.9
Character \(\chi\) \(=\) 1045.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.98489 q^{2} -3.88370 q^{3} +16.7886 q^{4} +25.0000 q^{5} +27.1272 q^{6} +123.805 q^{7} +106.250 q^{8} -227.917 q^{9} +O(q^{10})\) \(q-6.98489 q^{2} -3.88370 q^{3} +16.7886 q^{4} +25.0000 q^{5} +27.1272 q^{6} +123.805 q^{7} +106.250 q^{8} -227.917 q^{9} -174.622 q^{10} +121.000 q^{11} -65.2020 q^{12} +951.650 q^{13} -864.765 q^{14} -97.0925 q^{15} -1279.38 q^{16} -517.237 q^{17} +1591.97 q^{18} +361.000 q^{19} +419.716 q^{20} -480.822 q^{21} -845.171 q^{22} -3167.77 q^{23} -412.642 q^{24} +625.000 q^{25} -6647.16 q^{26} +1828.90 q^{27} +2078.52 q^{28} +5578.60 q^{29} +678.180 q^{30} +7694.65 q^{31} +5536.32 q^{32} -469.928 q^{33} +3612.84 q^{34} +3095.13 q^{35} -3826.41 q^{36} -8284.65 q^{37} -2521.54 q^{38} -3695.92 q^{39} +2656.24 q^{40} +3423.88 q^{41} +3358.49 q^{42} +1400.97 q^{43} +2031.42 q^{44} -5697.92 q^{45} +22126.5 q^{46} +4790.26 q^{47} +4968.72 q^{48} -1479.28 q^{49} -4365.55 q^{50} +2008.80 q^{51} +15976.9 q^{52} +28653.7 q^{53} -12774.7 q^{54} +3025.00 q^{55} +13154.3 q^{56} -1402.02 q^{57} -38965.8 q^{58} +5788.32 q^{59} -1630.05 q^{60} +19822.4 q^{61} -53746.2 q^{62} -28217.3 q^{63} +2269.54 q^{64} +23791.2 q^{65} +3282.39 q^{66} +59597.5 q^{67} -8683.70 q^{68} +12302.7 q^{69} -21619.1 q^{70} +36113.4 q^{71} -24216.1 q^{72} -73235.6 q^{73} +57867.4 q^{74} -2427.31 q^{75} +6060.69 q^{76} +14980.4 q^{77} +25815.6 q^{78} -109266. q^{79} -31984.5 q^{80} +48280.9 q^{81} -23915.4 q^{82} +12319.4 q^{83} -8072.35 q^{84} -12930.9 q^{85} -9785.64 q^{86} -21665.6 q^{87} +12856.2 q^{88} +85859.3 q^{89} +39799.3 q^{90} +117819. q^{91} -53182.5 q^{92} -29883.7 q^{93} -33459.4 q^{94} +9025.00 q^{95} -21501.4 q^{96} +17941.4 q^{97} +10332.6 q^{98} -27577.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + O(q^{10}) \) \( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.98489 −1.23477 −0.617383 0.786663i \(-0.711807\pi\)
−0.617383 + 0.786663i \(0.711807\pi\)
\(3\) −3.88370 −0.249140 −0.124570 0.992211i \(-0.539755\pi\)
−0.124570 + 0.992211i \(0.539755\pi\)
\(4\) 16.7886 0.524645
\(5\) 25.0000 0.447214
\(6\) 27.1272 0.307629
\(7\) 123.805 0.954979 0.477489 0.878638i \(-0.341547\pi\)
0.477489 + 0.878638i \(0.341547\pi\)
\(8\) 106.250 0.586952
\(9\) −227.917 −0.937929
\(10\) −174.622 −0.552204
\(11\) 121.000 0.301511
\(12\) −65.2020 −0.130710
\(13\) 951.650 1.56178 0.780888 0.624671i \(-0.214767\pi\)
0.780888 + 0.624671i \(0.214767\pi\)
\(14\) −864.765 −1.17917
\(15\) −97.0925 −0.111419
\(16\) −1279.38 −1.24939
\(17\) −517.237 −0.434078 −0.217039 0.976163i \(-0.569640\pi\)
−0.217039 + 0.976163i \(0.569640\pi\)
\(18\) 1591.97 1.15812
\(19\) 361.000 0.229416
\(20\) 419.716 0.234628
\(21\) −480.822 −0.237923
\(22\) −845.171 −0.372296
\(23\) −3167.77 −1.24863 −0.624315 0.781172i \(-0.714622\pi\)
−0.624315 + 0.781172i \(0.714622\pi\)
\(24\) −412.642 −0.146233
\(25\) 625.000 0.200000
\(26\) −6647.16 −1.92843
\(27\) 1828.90 0.482815
\(28\) 2078.52 0.501024
\(29\) 5578.60 1.23177 0.615885 0.787836i \(-0.288798\pi\)
0.615885 + 0.787836i \(0.288798\pi\)
\(30\) 678.180 0.137576
\(31\) 7694.65 1.43808 0.719042 0.694966i \(-0.244581\pi\)
0.719042 + 0.694966i \(0.244581\pi\)
\(32\) 5536.32 0.955754
\(33\) −469.928 −0.0751184
\(34\) 3612.84 0.535984
\(35\) 3095.13 0.427079
\(36\) −3826.41 −0.492080
\(37\) −8284.65 −0.994878 −0.497439 0.867499i \(-0.665726\pi\)
−0.497439 + 0.867499i \(0.665726\pi\)
\(38\) −2521.54 −0.283275
\(39\) −3695.92 −0.389100
\(40\) 2656.24 0.262493
\(41\) 3423.88 0.318096 0.159048 0.987271i \(-0.449157\pi\)
0.159048 + 0.987271i \(0.449157\pi\)
\(42\) 3358.49 0.293779
\(43\) 1400.97 0.115547 0.0577735 0.998330i \(-0.481600\pi\)
0.0577735 + 0.998330i \(0.481600\pi\)
\(44\) 2031.42 0.158186
\(45\) −5697.92 −0.419455
\(46\) 22126.5 1.54177
\(47\) 4790.26 0.316311 0.158156 0.987414i \(-0.449445\pi\)
0.158156 + 0.987414i \(0.449445\pi\)
\(48\) 4968.72 0.311273
\(49\) −1479.28 −0.0880159
\(50\) −4365.55 −0.246953
\(51\) 2008.80 0.108146
\(52\) 15976.9 0.819377
\(53\) 28653.7 1.40117 0.700585 0.713569i \(-0.252922\pi\)
0.700585 + 0.713569i \(0.252922\pi\)
\(54\) −12774.7 −0.596163
\(55\) 3025.00 0.134840
\(56\) 13154.3 0.560527
\(57\) −1402.02 −0.0571565
\(58\) −38965.8 −1.52095
\(59\) 5788.32 0.216482 0.108241 0.994125i \(-0.465478\pi\)
0.108241 + 0.994125i \(0.465478\pi\)
\(60\) −1630.05 −0.0584552
\(61\) 19822.4 0.682074 0.341037 0.940050i \(-0.389222\pi\)
0.341037 + 0.940050i \(0.389222\pi\)
\(62\) −53746.2 −1.77570
\(63\) −28217.3 −0.895703
\(64\) 2269.54 0.0692609
\(65\) 23791.2 0.698447
\(66\) 3282.39 0.0927536
\(67\) 59597.5 1.62196 0.810981 0.585072i \(-0.198934\pi\)
0.810981 + 0.585072i \(0.198934\pi\)
\(68\) −8683.70 −0.227737
\(69\) 12302.7 0.311083
\(70\) −21619.1 −0.527343
\(71\) 36113.4 0.850203 0.425101 0.905146i \(-0.360238\pi\)
0.425101 + 0.905146i \(0.360238\pi\)
\(72\) −24216.1 −0.550520
\(73\) −73235.6 −1.60848 −0.804239 0.594306i \(-0.797427\pi\)
−0.804239 + 0.594306i \(0.797427\pi\)
\(74\) 57867.4 1.22844
\(75\) −2427.31 −0.0498279
\(76\) 6060.69 0.120362
\(77\) 14980.4 0.287937
\(78\) 25815.6 0.480447
\(79\) −109266. −1.96978 −0.984888 0.173190i \(-0.944593\pi\)
−0.984888 + 0.173190i \(0.944593\pi\)
\(80\) −31984.5 −0.558745
\(81\) 48280.9 0.817641
\(82\) −23915.4 −0.392774
\(83\) 12319.4 0.196288 0.0981440 0.995172i \(-0.468709\pi\)
0.0981440 + 0.995172i \(0.468709\pi\)
\(84\) −8072.35 −0.124825
\(85\) −12930.9 −0.194125
\(86\) −9785.64 −0.142673
\(87\) −21665.6 −0.306883
\(88\) 12856.2 0.176973
\(89\) 85859.3 1.14898 0.574490 0.818512i \(-0.305201\pi\)
0.574490 + 0.818512i \(0.305201\pi\)
\(90\) 39799.3 0.517928
\(91\) 117819. 1.49146
\(92\) −53182.5 −0.655088
\(93\) −29883.7 −0.358284
\(94\) −33459.4 −0.390570
\(95\) 9025.00 0.102598
\(96\) −21501.4 −0.238116
\(97\) 17941.4 0.193610 0.0968050 0.995303i \(-0.469138\pi\)
0.0968050 + 0.995303i \(0.469138\pi\)
\(98\) 10332.6 0.108679
\(99\) −27577.9 −0.282796
\(100\) 10492.9 0.104929
\(101\) 70739.1 0.690011 0.345006 0.938601i \(-0.387877\pi\)
0.345006 + 0.938601i \(0.387877\pi\)
\(102\) −14031.2 −0.133535
\(103\) 71203.4 0.661314 0.330657 0.943751i \(-0.392730\pi\)
0.330657 + 0.943751i \(0.392730\pi\)
\(104\) 101112. 0.916688
\(105\) −12020.6 −0.106402
\(106\) −200143. −1.73012
\(107\) 69047.8 0.583029 0.291514 0.956566i \(-0.405841\pi\)
0.291514 + 0.956566i \(0.405841\pi\)
\(108\) 30704.7 0.253306
\(109\) −44429.0 −0.358179 −0.179090 0.983833i \(-0.557315\pi\)
−0.179090 + 0.983833i \(0.557315\pi\)
\(110\) −21129.3 −0.166496
\(111\) 32175.1 0.247864
\(112\) −158394. −1.19314
\(113\) −107473. −0.791777 −0.395888 0.918299i \(-0.629563\pi\)
−0.395888 + 0.918299i \(0.629563\pi\)
\(114\) 9792.92 0.0705749
\(115\) −79194.3 −0.558405
\(116\) 93657.0 0.646242
\(117\) −216897. −1.46484
\(118\) −40430.8 −0.267305
\(119\) −64036.6 −0.414535
\(120\) −10316.1 −0.0653974
\(121\) 14641.0 0.0909091
\(122\) −138457. −0.842201
\(123\) −13297.3 −0.0792504
\(124\) 129183. 0.754483
\(125\) 15625.0 0.0894427
\(126\) 197094. 1.10598
\(127\) −210725. −1.15933 −0.579663 0.814856i \(-0.696816\pi\)
−0.579663 + 0.814856i \(0.696816\pi\)
\(128\) −193015. −1.04128
\(129\) −5440.97 −0.0287874
\(130\) −166179. −0.862418
\(131\) −321047. −1.63452 −0.817261 0.576268i \(-0.804509\pi\)
−0.817261 + 0.576268i \(0.804509\pi\)
\(132\) −7889.45 −0.0394105
\(133\) 44693.7 0.219087
\(134\) −416282. −2.00274
\(135\) 45722.5 0.215921
\(136\) −54956.3 −0.254783
\(137\) −316103. −1.43889 −0.719445 0.694550i \(-0.755604\pi\)
−0.719445 + 0.694550i \(0.755604\pi\)
\(138\) −85932.8 −0.384115
\(139\) −235632. −1.03442 −0.517211 0.855858i \(-0.673030\pi\)
−0.517211 + 0.855858i \(0.673030\pi\)
\(140\) 51963.0 0.224065
\(141\) −18603.9 −0.0788056
\(142\) −252248. −1.04980
\(143\) 115150. 0.470893
\(144\) 291592. 1.17184
\(145\) 139465. 0.550865
\(146\) 511542. 1.98609
\(147\) 5745.09 0.0219282
\(148\) −139088. −0.521958
\(149\) 301573. 1.11283 0.556413 0.830906i \(-0.312177\pi\)
0.556413 + 0.830906i \(0.312177\pi\)
\(150\) 16954.5 0.0615258
\(151\) 364106. 1.29953 0.649763 0.760137i \(-0.274868\pi\)
0.649763 + 0.760137i \(0.274868\pi\)
\(152\) 38356.1 0.134656
\(153\) 117887. 0.407134
\(154\) −104637. −0.355534
\(155\) 192366. 0.643131
\(156\) −62049.5 −0.204139
\(157\) −381142. −1.23407 −0.617033 0.786937i \(-0.711665\pi\)
−0.617033 + 0.786937i \(0.711665\pi\)
\(158\) 763210. 2.43221
\(159\) −111282. −0.349087
\(160\) 138408. 0.427426
\(161\) −392186. −1.19242
\(162\) −337237. −1.00959
\(163\) −66067.6 −0.194769 −0.0973845 0.995247i \(-0.531048\pi\)
−0.0973845 + 0.995247i \(0.531048\pi\)
\(164\) 57482.2 0.166888
\(165\) −11748.2 −0.0335940
\(166\) −86049.5 −0.242370
\(167\) 176059. 0.488501 0.244251 0.969712i \(-0.421458\pi\)
0.244251 + 0.969712i \(0.421458\pi\)
\(168\) −51087.2 −0.139649
\(169\) 534344. 1.43914
\(170\) 90321.1 0.239699
\(171\) −82278.0 −0.215176
\(172\) 23520.4 0.0606212
\(173\) −119022. −0.302351 −0.151175 0.988507i \(-0.548306\pi\)
−0.151175 + 0.988507i \(0.548306\pi\)
\(174\) 151332. 0.378928
\(175\) 77378.2 0.190996
\(176\) −154805. −0.376706
\(177\) −22480.1 −0.0539343
\(178\) −599717. −1.41872
\(179\) −277375. −0.647044 −0.323522 0.946221i \(-0.604867\pi\)
−0.323522 + 0.946221i \(0.604867\pi\)
\(180\) −95660.3 −0.220065
\(181\) 448881. 1.01844 0.509219 0.860637i \(-0.329934\pi\)
0.509219 + 0.860637i \(0.329934\pi\)
\(182\) −822953. −1.84161
\(183\) −76984.2 −0.169932
\(184\) −336575. −0.732887
\(185\) −207116. −0.444923
\(186\) 208734. 0.442396
\(187\) −62585.7 −0.130879
\(188\) 80421.9 0.165951
\(189\) 226427. 0.461078
\(190\) −63038.6 −0.126684
\(191\) −681220. −1.35115 −0.675576 0.737291i \(-0.736105\pi\)
−0.675576 + 0.737291i \(0.736105\pi\)
\(192\) −8814.22 −0.0172556
\(193\) 797459. 1.54104 0.770522 0.637413i \(-0.219996\pi\)
0.770522 + 0.637413i \(0.219996\pi\)
\(194\) −125319. −0.239063
\(195\) −92398.1 −0.174011
\(196\) −24835.1 −0.0461770
\(197\) −183040. −0.336031 −0.168016 0.985784i \(-0.553736\pi\)
−0.168016 + 0.985784i \(0.553736\pi\)
\(198\) 192629. 0.349187
\(199\) −72289.3 −0.129402 −0.0647010 0.997905i \(-0.520609\pi\)
−0.0647010 + 0.997905i \(0.520609\pi\)
\(200\) 66406.1 0.117390
\(201\) −231459. −0.404095
\(202\) −494104. −0.852001
\(203\) 690659. 1.17631
\(204\) 33724.9 0.0567382
\(205\) 85596.9 0.142257
\(206\) −497348. −0.816567
\(207\) 721988. 1.17113
\(208\) −1.21752e6 −1.95127
\(209\) 43681.0 0.0691714
\(210\) 83962.2 0.131382
\(211\) −1.09027e6 −1.68588 −0.842941 0.538005i \(-0.819178\pi\)
−0.842941 + 0.538005i \(0.819178\pi\)
\(212\) 481056. 0.735117
\(213\) −140254. −0.211819
\(214\) −482291. −0.719904
\(215\) 35024.4 0.0516742
\(216\) 194320. 0.283389
\(217\) 952637. 1.37334
\(218\) 310332. 0.442267
\(219\) 284425. 0.400736
\(220\) 50785.6 0.0707431
\(221\) −492229. −0.677932
\(222\) −224740. −0.306053
\(223\) −204245. −0.275036 −0.137518 0.990499i \(-0.543912\pi\)
−0.137518 + 0.990499i \(0.543912\pi\)
\(224\) 685425. 0.912725
\(225\) −142448. −0.187586
\(226\) 750686. 0.977658
\(227\) 1.44015e6 1.85499 0.927496 0.373833i \(-0.121957\pi\)
0.927496 + 0.373833i \(0.121957\pi\)
\(228\) −23537.9 −0.0299869
\(229\) −746076. −0.940144 −0.470072 0.882628i \(-0.655772\pi\)
−0.470072 + 0.882628i \(0.655772\pi\)
\(230\) 553163. 0.689499
\(231\) −58179.5 −0.0717365
\(232\) 592724. 0.722990
\(233\) −166863. −0.201358 −0.100679 0.994919i \(-0.532102\pi\)
−0.100679 + 0.994919i \(0.532102\pi\)
\(234\) 1.51500e6 1.80873
\(235\) 119756. 0.141459
\(236\) 97178.0 0.113576
\(237\) 424356. 0.490749
\(238\) 447289. 0.511853
\(239\) 194385. 0.220125 0.110062 0.993925i \(-0.464895\pi\)
0.110062 + 0.993925i \(0.464895\pi\)
\(240\) 124218. 0.139206
\(241\) 242121. 0.268528 0.134264 0.990946i \(-0.457133\pi\)
0.134264 + 0.990946i \(0.457133\pi\)
\(242\) −102266. −0.112251
\(243\) −631931. −0.686522
\(244\) 332791. 0.357846
\(245\) −36982.1 −0.0393619
\(246\) 92880.3 0.0978556
\(247\) 343546. 0.358296
\(248\) 817554. 0.844087
\(249\) −47844.8 −0.0489031
\(250\) −109139. −0.110441
\(251\) 285795. 0.286332 0.143166 0.989699i \(-0.454272\pi\)
0.143166 + 0.989699i \(0.454272\pi\)
\(252\) −473729. −0.469926
\(253\) −383300. −0.376476
\(254\) 1.47189e6 1.43150
\(255\) 50219.9 0.0483643
\(256\) 1.27556e6 1.21647
\(257\) 167621. 0.158305 0.0791525 0.996863i \(-0.474779\pi\)
0.0791525 + 0.996863i \(0.474779\pi\)
\(258\) 38004.5 0.0355456
\(259\) −1.02568e6 −0.950088
\(260\) 399422. 0.366437
\(261\) −1.27146e6 −1.15531
\(262\) 2.24248e6 2.01825
\(263\) 345126. 0.307673 0.153836 0.988096i \(-0.450837\pi\)
0.153836 + 0.988096i \(0.450837\pi\)
\(264\) −49929.7 −0.0440909
\(265\) 716342. 0.626623
\(266\) −312180. −0.270521
\(267\) −333452. −0.286256
\(268\) 1.00056e6 0.850954
\(269\) 1.26503e6 1.06591 0.532956 0.846143i \(-0.321081\pi\)
0.532956 + 0.846143i \(0.321081\pi\)
\(270\) −319367. −0.266612
\(271\) 1.02776e6 0.850096 0.425048 0.905171i \(-0.360257\pi\)
0.425048 + 0.905171i \(0.360257\pi\)
\(272\) 661742. 0.542333
\(273\) −457574. −0.371582
\(274\) 2.20794e6 1.77669
\(275\) 75625.0 0.0603023
\(276\) 206545. 0.163208
\(277\) −797584. −0.624564 −0.312282 0.949989i \(-0.601093\pi\)
−0.312282 + 0.949989i \(0.601093\pi\)
\(278\) 1.64586e6 1.27727
\(279\) −1.75374e6 −1.34882
\(280\) 328857. 0.250675
\(281\) −239823. −0.181186 −0.0905929 0.995888i \(-0.528876\pi\)
−0.0905929 + 0.995888i \(0.528876\pi\)
\(282\) 129946. 0.0973064
\(283\) 1.75755e6 1.30449 0.652247 0.758007i \(-0.273827\pi\)
0.652247 + 0.758007i \(0.273827\pi\)
\(284\) 606294. 0.446054
\(285\) −35050.4 −0.0255612
\(286\) −804307. −0.581442
\(287\) 423894. 0.303775
\(288\) −1.26182e6 −0.896430
\(289\) −1.15232e6 −0.811577
\(290\) −974146. −0.680188
\(291\) −69679.2 −0.0482359
\(292\) −1.22953e6 −0.843879
\(293\) −2.29399e6 −1.56107 −0.780537 0.625110i \(-0.785054\pi\)
−0.780537 + 0.625110i \(0.785054\pi\)
\(294\) −40128.8 −0.0270762
\(295\) 144708. 0.0968139
\(296\) −880242. −0.583946
\(297\) 221297. 0.145574
\(298\) −2.10646e6 −1.37408
\(299\) −3.01461e6 −1.95008
\(300\) −40751.3 −0.0261419
\(301\) 173448. 0.110345
\(302\) −2.54324e6 −1.60461
\(303\) −274730. −0.171909
\(304\) −461855. −0.286630
\(305\) 495560. 0.305033
\(306\) −823428. −0.502715
\(307\) 2.93267e6 1.77590 0.887948 0.459945i \(-0.152131\pi\)
0.887948 + 0.459945i \(0.152131\pi\)
\(308\) 251501. 0.151065
\(309\) −276533. −0.164759
\(310\) −1.34366e6 −0.794116
\(311\) −263120. −0.154260 −0.0771299 0.997021i \(-0.524576\pi\)
−0.0771299 + 0.997021i \(0.524576\pi\)
\(312\) −392691. −0.228383
\(313\) 3.04552e6 1.75712 0.878558 0.477635i \(-0.158506\pi\)
0.878558 + 0.477635i \(0.158506\pi\)
\(314\) 2.66224e6 1.52378
\(315\) −705432. −0.400570
\(316\) −1.83442e6 −1.03343
\(317\) −362904. −0.202835 −0.101418 0.994844i \(-0.532338\pi\)
−0.101418 + 0.994844i \(0.532338\pi\)
\(318\) 777295. 0.431040
\(319\) 675010. 0.371393
\(320\) 56738.5 0.0309744
\(321\) −268161. −0.145256
\(322\) 2.73938e6 1.47235
\(323\) −186723. −0.0995843
\(324\) 810570. 0.428971
\(325\) 594781. 0.312355
\(326\) 461475. 0.240494
\(327\) 172549. 0.0892366
\(328\) 363786. 0.186707
\(329\) 593059. 0.302070
\(330\) 82059.8 0.0414807
\(331\) −231296. −0.116037 −0.0580187 0.998315i \(-0.518478\pi\)
−0.0580187 + 0.998315i \(0.518478\pi\)
\(332\) 206826. 0.102981
\(333\) 1.88821e6 0.933126
\(334\) −1.22975e6 −0.603184
\(335\) 1.48994e6 0.725364
\(336\) 615154. 0.297259
\(337\) 876405. 0.420368 0.210184 0.977662i \(-0.432594\pi\)
0.210184 + 0.977662i \(0.432594\pi\)
\(338\) −3.73233e6 −1.77700
\(339\) 417393. 0.197263
\(340\) −217093. −0.101847
\(341\) 931052. 0.433599
\(342\) 574702. 0.265692
\(343\) −2.26394e6 −1.03903
\(344\) 148853. 0.0678206
\(345\) 307567. 0.139121
\(346\) 831353. 0.373332
\(347\) 3.59776e6 1.60402 0.802009 0.597313i \(-0.203765\pi\)
0.802009 + 0.597313i \(0.203765\pi\)
\(348\) −363736. −0.161004
\(349\) −3.45127e6 −1.51675 −0.758377 0.651817i \(-0.774007\pi\)
−0.758377 + 0.651817i \(0.774007\pi\)
\(350\) −540478. −0.235835
\(351\) 1.74047e6 0.754049
\(352\) 669895. 0.288171
\(353\) 2.57118e6 1.09823 0.549117 0.835745i \(-0.314964\pi\)
0.549117 + 0.835745i \(0.314964\pi\)
\(354\) 157021. 0.0665962
\(355\) 902835. 0.380222
\(356\) 1.44146e6 0.602806
\(357\) 248699. 0.103277
\(358\) 1.93743e6 0.798948
\(359\) 2.23456e6 0.915073 0.457536 0.889191i \(-0.348732\pi\)
0.457536 + 0.889191i \(0.348732\pi\)
\(360\) −605402. −0.246200
\(361\) 130321. 0.0526316
\(362\) −3.13538e6 −1.25753
\(363\) −56861.3 −0.0226491
\(364\) 1.97802e6 0.782488
\(365\) −1.83089e6 −0.719333
\(366\) 537726. 0.209826
\(367\) 2.79154e6 1.08188 0.540939 0.841062i \(-0.318069\pi\)
0.540939 + 0.841062i \(0.318069\pi\)
\(368\) 4.05278e6 1.56003
\(369\) −780359. −0.298352
\(370\) 1.44668e6 0.549376
\(371\) 3.54748e6 1.33809
\(372\) −501706. −0.187972
\(373\) 29973.8 0.0111550 0.00557750 0.999984i \(-0.498225\pi\)
0.00557750 + 0.999984i \(0.498225\pi\)
\(374\) 437154. 0.161605
\(375\) −60682.8 −0.0222837
\(376\) 508964. 0.185659
\(377\) 5.30887e6 1.92375
\(378\) −1.58157e6 −0.569323
\(379\) −4.38294e6 −1.56735 −0.783677 0.621168i \(-0.786658\pi\)
−0.783677 + 0.621168i \(0.786658\pi\)
\(380\) 151517. 0.0538274
\(381\) 818391. 0.288834
\(382\) 4.75824e6 1.66835
\(383\) 4.37696e6 1.52467 0.762334 0.647184i \(-0.224053\pi\)
0.762334 + 0.647184i \(0.224053\pi\)
\(384\) 749612. 0.259423
\(385\) 374511. 0.128769
\(386\) −5.57016e6 −1.90283
\(387\) −319306. −0.108375
\(388\) 301212. 0.101576
\(389\) 1.18185e6 0.395993 0.197997 0.980203i \(-0.436556\pi\)
0.197997 + 0.980203i \(0.436556\pi\)
\(390\) 645390. 0.214863
\(391\) 1.63849e6 0.542003
\(392\) −157173. −0.0516611
\(393\) 1.24685e6 0.407224
\(394\) 1.27851e6 0.414920
\(395\) −2.73165e6 −0.880911
\(396\) −462996. −0.148368
\(397\) 649750. 0.206904 0.103452 0.994634i \(-0.467011\pi\)
0.103452 + 0.994634i \(0.467011\pi\)
\(398\) 504932. 0.159781
\(399\) −173577. −0.0545833
\(400\) −799611. −0.249879
\(401\) 2.23774e6 0.694942 0.347471 0.937691i \(-0.387040\pi\)
0.347471 + 0.937691i \(0.387040\pi\)
\(402\) 1.61671e6 0.498963
\(403\) 7.32261e6 2.24597
\(404\) 1.18761e6 0.362011
\(405\) 1.20702e6 0.365660
\(406\) −4.82417e6 −1.45247
\(407\) −1.00244e6 −0.299967
\(408\) 213434. 0.0634765
\(409\) 1.65685e6 0.489751 0.244876 0.969554i \(-0.421253\pi\)
0.244876 + 0.969554i \(0.421253\pi\)
\(410\) −597885. −0.175654
\(411\) 1.22765e6 0.358484
\(412\) 1.19541e6 0.346955
\(413\) 716624. 0.206736
\(414\) −5.04301e6 −1.44607
\(415\) 307985. 0.0877827
\(416\) 5.26864e6 1.49267
\(417\) 915125. 0.257715
\(418\) −305107. −0.0854105
\(419\) 721624. 0.200806 0.100403 0.994947i \(-0.467987\pi\)
0.100403 + 0.994947i \(0.467987\pi\)
\(420\) −201809. −0.0558234
\(421\) 1.75150e6 0.481619 0.240810 0.970572i \(-0.422587\pi\)
0.240810 + 0.970572i \(0.422587\pi\)
\(422\) 7.61540e6 2.08167
\(423\) −1.09178e6 −0.296677
\(424\) 3.04445e6 0.822420
\(425\) −323273. −0.0868155
\(426\) 979656. 0.261547
\(427\) 2.45411e6 0.651366
\(428\) 1.15922e6 0.305883
\(429\) −447207. −0.117318
\(430\) −244641. −0.0638055
\(431\) 5.59085e6 1.44972 0.724861 0.688895i \(-0.241904\pi\)
0.724861 + 0.688895i \(0.241904\pi\)
\(432\) −2.33986e6 −0.603225
\(433\) 4.21253e6 1.07975 0.539875 0.841745i \(-0.318471\pi\)
0.539875 + 0.841745i \(0.318471\pi\)
\(434\) −6.65406e6 −1.69575
\(435\) −541640. −0.137242
\(436\) −745902. −0.187917
\(437\) −1.14357e6 −0.286456
\(438\) −1.98668e6 −0.494814
\(439\) 5.30842e6 1.31463 0.657315 0.753616i \(-0.271692\pi\)
0.657315 + 0.753616i \(0.271692\pi\)
\(440\) 321405. 0.0791446
\(441\) 337153. 0.0825527
\(442\) 3.43816e6 0.837087
\(443\) −2.94057e6 −0.711905 −0.355952 0.934504i \(-0.615843\pi\)
−0.355952 + 0.934504i \(0.615843\pi\)
\(444\) 540176. 0.130040
\(445\) 2.14648e6 0.513839
\(446\) 1.42663e6 0.339605
\(447\) −1.17122e6 −0.277249
\(448\) 280981. 0.0661427
\(449\) 1.58930e6 0.372041 0.186020 0.982546i \(-0.440441\pi\)
0.186020 + 0.982546i \(0.440441\pi\)
\(450\) 994983. 0.231624
\(451\) 414289. 0.0959096
\(452\) −1.80432e6 −0.415401
\(453\) −1.41408e6 −0.323764
\(454\) −1.00593e7 −2.29048
\(455\) 2.94548e6 0.667002
\(456\) −148964. −0.0335482
\(457\) −2.98769e6 −0.669184 −0.334592 0.942363i \(-0.608598\pi\)
−0.334592 + 0.942363i \(0.608598\pi\)
\(458\) 5.21126e6 1.16086
\(459\) −945976. −0.209579
\(460\) −1.32956e6 −0.292964
\(461\) 5.26844e6 1.15460 0.577298 0.816534i \(-0.304107\pi\)
0.577298 + 0.816534i \(0.304107\pi\)
\(462\) 406377. 0.0885777
\(463\) 5.41446e6 1.17382 0.586911 0.809651i \(-0.300344\pi\)
0.586911 + 0.809651i \(0.300344\pi\)
\(464\) −7.13713e6 −1.53897
\(465\) −747093. −0.160229
\(466\) 1.16552e6 0.248630
\(467\) −3.05243e6 −0.647670 −0.323835 0.946114i \(-0.604972\pi\)
−0.323835 + 0.946114i \(0.604972\pi\)
\(468\) −3.64140e6 −0.768518
\(469\) 7.37848e6 1.54894
\(470\) −836485. −0.174668
\(471\) 1.48024e6 0.307455
\(472\) 615007. 0.127065
\(473\) 169518. 0.0348388
\(474\) −2.96408e6 −0.605960
\(475\) 225625. 0.0458831
\(476\) −1.07509e6 −0.217484
\(477\) −6.53066e6 −1.31420
\(478\) −1.35776e6 −0.271802
\(479\) −8.87454e6 −1.76729 −0.883644 0.468160i \(-0.844917\pi\)
−0.883644 + 0.468160i \(0.844917\pi\)
\(480\) −537535. −0.106489
\(481\) −7.88409e6 −1.55378
\(482\) −1.69119e6 −0.331570
\(483\) 1.52313e6 0.297078
\(484\) 245802. 0.0476950
\(485\) 448536. 0.0865851
\(486\) 4.41397e6 0.847693
\(487\) −6.19013e6 −1.18271 −0.591354 0.806412i \(-0.701406\pi\)
−0.591354 + 0.806412i \(0.701406\pi\)
\(488\) 2.10612e6 0.400345
\(489\) 256587. 0.0485246
\(490\) 258316. 0.0486027
\(491\) 3.30249e6 0.618212 0.309106 0.951028i \(-0.399970\pi\)
0.309106 + 0.951028i \(0.399970\pi\)
\(492\) −223244. −0.0415783
\(493\) −2.88546e6 −0.534684
\(494\) −2.39963e6 −0.442411
\(495\) −689448. −0.126470
\(496\) −9.84436e6 −1.79673
\(497\) 4.47102e6 0.811925
\(498\) 334191. 0.0603839
\(499\) −566277. −0.101807 −0.0509035 0.998704i \(-0.516210\pi\)
−0.0509035 + 0.998704i \(0.516210\pi\)
\(500\) 262322. 0.0469256
\(501\) −683759. −0.121705
\(502\) −1.99625e6 −0.353553
\(503\) −2.63666e6 −0.464660 −0.232330 0.972637i \(-0.574635\pi\)
−0.232330 + 0.972637i \(0.574635\pi\)
\(504\) −2.99808e6 −0.525735
\(505\) 1.76848e6 0.308582
\(506\) 2.67731e6 0.464860
\(507\) −2.07523e6 −0.358548
\(508\) −3.53778e6 −0.608235
\(509\) 7.45994e6 1.27627 0.638133 0.769926i \(-0.279707\pi\)
0.638133 + 0.769926i \(0.279707\pi\)
\(510\) −350780. −0.0597186
\(511\) −9.06695e6 −1.53606
\(512\) −2.73317e6 −0.460778
\(513\) 660233. 0.110765
\(514\) −1.17081e6 −0.195469
\(515\) 1.78008e6 0.295749
\(516\) −91346.3 −0.0151031
\(517\) 579621. 0.0953714
\(518\) 7.16428e6 1.17313
\(519\) 462245. 0.0753275
\(520\) 2.52781e6 0.409955
\(521\) 8.04703e6 1.29880 0.649399 0.760448i \(-0.275021\pi\)
0.649399 + 0.760448i \(0.275021\pi\)
\(522\) 8.88097e6 1.42654
\(523\) −1.12164e7 −1.79308 −0.896541 0.442961i \(-0.853928\pi\)
−0.896541 + 0.442961i \(0.853928\pi\)
\(524\) −5.38994e6 −0.857543
\(525\) −300514. −0.0475846
\(526\) −2.41067e6 −0.379903
\(527\) −3.97996e6 −0.624240
\(528\) 601216. 0.0938524
\(529\) 3.59843e6 0.559079
\(530\) −5.00357e6 −0.773732
\(531\) −1.31926e6 −0.203045
\(532\) 750345. 0.114943
\(533\) 3.25833e6 0.496795
\(534\) 2.32912e6 0.353459
\(535\) 1.72619e6 0.260738
\(536\) 6.33221e6 0.952015
\(537\) 1.07724e6 0.161204
\(538\) −8.83611e6 −1.31615
\(539\) −178993. −0.0265378
\(540\) 767618. 0.113282
\(541\) −4.08167e6 −0.599577 −0.299788 0.954006i \(-0.596916\pi\)
−0.299788 + 0.954006i \(0.596916\pi\)
\(542\) −7.17878e6 −1.04967
\(543\) −1.74332e6 −0.253733
\(544\) −2.86359e6 −0.414872
\(545\) −1.11073e6 −0.160183
\(546\) 3.19610e6 0.458817
\(547\) 4.38546e6 0.626681 0.313341 0.949641i \(-0.398552\pi\)
0.313341 + 0.949641i \(0.398552\pi\)
\(548\) −5.30694e6 −0.754906
\(549\) −4.51786e6 −0.639737
\(550\) −528232. −0.0744591
\(551\) 2.01387e6 0.282588
\(552\) 1.30716e6 0.182591
\(553\) −1.35277e7 −1.88109
\(554\) 5.57103e6 0.771190
\(555\) 804378. 0.110848
\(556\) −3.95594e6 −0.542704
\(557\) 6.05312e6 0.826687 0.413344 0.910575i \(-0.364361\pi\)
0.413344 + 0.910575i \(0.364361\pi\)
\(558\) 1.22497e7 1.66548
\(559\) 1.33324e6 0.180459
\(560\) −3.95984e6 −0.533590
\(561\) 243064. 0.0326072
\(562\) 1.67513e6 0.223722
\(563\) 3.87002e6 0.514567 0.257284 0.966336i \(-0.417173\pi\)
0.257284 + 0.966336i \(0.417173\pi\)
\(564\) −312335. −0.0413449
\(565\) −2.68682e6 −0.354093
\(566\) −1.22763e7 −1.61074
\(567\) 5.97742e6 0.780830
\(568\) 3.83704e6 0.499028
\(569\) −1.19092e7 −1.54207 −0.771033 0.636795i \(-0.780260\pi\)
−0.771033 + 0.636795i \(0.780260\pi\)
\(570\) 244823. 0.0315621
\(571\) −5.99201e6 −0.769099 −0.384550 0.923104i \(-0.625643\pi\)
−0.384550 + 0.923104i \(0.625643\pi\)
\(572\) 1.93320e6 0.247052
\(573\) 2.64566e6 0.336625
\(574\) −2.96085e6 −0.375091
\(575\) −1.97986e6 −0.249726
\(576\) −517267. −0.0649619
\(577\) −7.63283e6 −0.954434 −0.477217 0.878785i \(-0.658354\pi\)
−0.477217 + 0.878785i \(0.658354\pi\)
\(578\) 8.04884e6 1.00211
\(579\) −3.09709e6 −0.383935
\(580\) 2.34142e6 0.289008
\(581\) 1.52520e6 0.187451
\(582\) 486701. 0.0595601
\(583\) 3.46710e6 0.422469
\(584\) −7.78126e6 −0.944100
\(585\) −5.42242e6 −0.655094
\(586\) 1.60233e7 1.92756
\(587\) −1.17109e7 −1.40280 −0.701401 0.712767i \(-0.747442\pi\)
−0.701401 + 0.712767i \(0.747442\pi\)
\(588\) 96452.2 0.0115045
\(589\) 2.77777e6 0.329919
\(590\) −1.01077e6 −0.119542
\(591\) 710871. 0.0837187
\(592\) 1.05992e7 1.24299
\(593\) 1.07896e7 1.26000 0.629999 0.776596i \(-0.283055\pi\)
0.629999 + 0.776596i \(0.283055\pi\)
\(594\) −1.54573e6 −0.179750
\(595\) −1.60092e6 −0.185386
\(596\) 5.06300e6 0.583838
\(597\) 280750. 0.0322392
\(598\) 2.10567e7 2.40789
\(599\) −7.89443e6 −0.898988 −0.449494 0.893283i \(-0.648396\pi\)
−0.449494 + 0.893283i \(0.648396\pi\)
\(600\) −257901. −0.0292466
\(601\) −1.50210e7 −1.69634 −0.848170 0.529724i \(-0.822295\pi\)
−0.848170 + 0.529724i \(0.822295\pi\)
\(602\) −1.21151e6 −0.136250
\(603\) −1.35833e7 −1.52129
\(604\) 6.11284e6 0.681790
\(605\) 366025. 0.0406558
\(606\) 1.91895e6 0.212267
\(607\) 5.98630e6 0.659457 0.329728 0.944076i \(-0.393043\pi\)
0.329728 + 0.944076i \(0.393043\pi\)
\(608\) 1.99861e6 0.219265
\(609\) −2.68231e6 −0.293067
\(610\) −3.46143e6 −0.376644
\(611\) 4.55865e6 0.494007
\(612\) 1.97916e6 0.213601
\(613\) 1.17656e7 1.26463 0.632314 0.774713i \(-0.282105\pi\)
0.632314 + 0.774713i \(0.282105\pi\)
\(614\) −2.04844e7 −2.19281
\(615\) −332433. −0.0354418
\(616\) 1.59167e6 0.169005
\(617\) 1.15013e7 1.21628 0.608139 0.793831i \(-0.291916\pi\)
0.608139 + 0.793831i \(0.291916\pi\)
\(618\) 1.93155e6 0.203439
\(619\) −1.92045e6 −0.201455 −0.100727 0.994914i \(-0.532117\pi\)
−0.100727 + 0.994914i \(0.532117\pi\)
\(620\) 3.22956e6 0.337415
\(621\) −5.79354e6 −0.602858
\(622\) 1.83786e6 0.190475
\(623\) 1.06298e7 1.09725
\(624\) 4.72848e6 0.486139
\(625\) 390625. 0.0400000
\(626\) −2.12726e7 −2.16963
\(627\) −169644. −0.0172333
\(628\) −6.39886e6 −0.647446
\(629\) 4.28513e6 0.431855
\(630\) 4.92736e6 0.494610
\(631\) 1.61846e7 1.61819 0.809095 0.587678i \(-0.199958\pi\)
0.809095 + 0.587678i \(0.199958\pi\)
\(632\) −1.16095e7 −1.15616
\(633\) 4.23428e6 0.420020
\(634\) 2.53484e6 0.250454
\(635\) −5.26811e6 −0.518467
\(636\) −1.86828e6 −0.183147
\(637\) −1.40776e6 −0.137461
\(638\) −4.71487e6 −0.458583
\(639\) −8.23085e6 −0.797430
\(640\) −4.82537e6 −0.465672
\(641\) −1.49719e6 −0.143923 −0.0719615 0.997407i \(-0.522926\pi\)
−0.0719615 + 0.997407i \(0.522926\pi\)
\(642\) 1.87307e6 0.179357
\(643\) 8.19022e6 0.781210 0.390605 0.920558i \(-0.372266\pi\)
0.390605 + 0.920558i \(0.372266\pi\)
\(644\) −6.58427e6 −0.625595
\(645\) −136024. −0.0128741
\(646\) 1.30424e6 0.122963
\(647\) −1.24419e7 −1.16849 −0.584247 0.811576i \(-0.698610\pi\)
−0.584247 + 0.811576i \(0.698610\pi\)
\(648\) 5.12983e6 0.479916
\(649\) 700387. 0.0652719
\(650\) −4.15448e6 −0.385685
\(651\) −3.69976e6 −0.342153
\(652\) −1.10918e6 −0.102184
\(653\) 7.28797e6 0.668842 0.334421 0.942424i \(-0.391459\pi\)
0.334421 + 0.942424i \(0.391459\pi\)
\(654\) −1.20524e6 −0.110186
\(655\) −8.02618e6 −0.730980
\(656\) −4.38043e6 −0.397427
\(657\) 1.66916e7 1.50864
\(658\) −4.14245e6 −0.372986
\(659\) −6.60381e6 −0.592354 −0.296177 0.955133i \(-0.595712\pi\)
−0.296177 + 0.955133i \(0.595712\pi\)
\(660\) −197236. −0.0176249
\(661\) −1.51636e7 −1.34989 −0.674944 0.737869i \(-0.735832\pi\)
−0.674944 + 0.737869i \(0.735832\pi\)
\(662\) 1.61558e6 0.143279
\(663\) 1.91167e6 0.168900
\(664\) 1.30893e6 0.115212
\(665\) 1.11734e6 0.0979787
\(666\) −1.31889e7 −1.15219
\(667\) −1.76717e7 −1.53803
\(668\) 2.95578e6 0.256290
\(669\) 793227. 0.0685223
\(670\) −1.04070e7 −0.895654
\(671\) 2.39851e6 0.205653
\(672\) −2.66199e6 −0.227396
\(673\) −1.25043e7 −1.06420 −0.532100 0.846681i \(-0.678597\pi\)
−0.532100 + 0.846681i \(0.678597\pi\)
\(674\) −6.12159e6 −0.519056
\(675\) 1.14306e6 0.0965630
\(676\) 8.97090e6 0.755039
\(677\) 3.79643e6 0.318349 0.159175 0.987250i \(-0.449117\pi\)
0.159175 + 0.987250i \(0.449117\pi\)
\(678\) −2.91544e6 −0.243573
\(679\) 2.22124e6 0.184893
\(680\) −1.37391e6 −0.113942
\(681\) −5.59310e6 −0.462152
\(682\) −6.50329e6 −0.535393
\(683\) 4.56570e6 0.374503 0.187252 0.982312i \(-0.440042\pi\)
0.187252 + 0.982312i \(0.440042\pi\)
\(684\) −1.38133e6 −0.112891
\(685\) −7.90258e6 −0.643491
\(686\) 1.58133e7 1.28296
\(687\) 2.89754e6 0.234227
\(688\) −1.79238e6 −0.144364
\(689\) 2.72683e7 2.18831
\(690\) −2.14832e6 −0.171781
\(691\) 5.23077e6 0.416745 0.208373 0.978050i \(-0.433183\pi\)
0.208373 + 0.978050i \(0.433183\pi\)
\(692\) −1.99821e6 −0.158627
\(693\) −3.41429e6 −0.270064
\(694\) −2.51300e7 −1.98058
\(695\) −5.89081e6 −0.462607
\(696\) −2.30196e6 −0.180126
\(697\) −1.77096e6 −0.138079
\(698\) 2.41067e7 1.87283
\(699\) 648045. 0.0501663
\(700\) 1.29907e6 0.100205
\(701\) 726058. 0.0558054 0.0279027 0.999611i \(-0.491117\pi\)
0.0279027 + 0.999611i \(0.491117\pi\)
\(702\) −1.21570e7 −0.931073
\(703\) −2.99076e6 −0.228241
\(704\) 274615. 0.0208830
\(705\) −465098. −0.0352429
\(706\) −1.79594e7 −1.35606
\(707\) 8.75786e6 0.658946
\(708\) −377410. −0.0282964
\(709\) 1.23991e7 0.926350 0.463175 0.886267i \(-0.346710\pi\)
0.463175 + 0.886267i \(0.346710\pi\)
\(710\) −6.30620e6 −0.469485
\(711\) 2.49035e7 1.84751
\(712\) 9.12252e6 0.674396
\(713\) −2.43749e7 −1.79564
\(714\) −1.73714e6 −0.127523
\(715\) 2.87874e6 0.210590
\(716\) −4.65674e6 −0.339468
\(717\) −754935. −0.0548418
\(718\) −1.56081e7 −1.12990
\(719\) −2.21865e7 −1.60054 −0.800270 0.599640i \(-0.795310\pi\)
−0.800270 + 0.599640i \(0.795310\pi\)
\(720\) 7.28980e6 0.524064
\(721\) 8.81535e6 0.631541
\(722\) −910277. −0.0649876
\(723\) −940327. −0.0669011
\(724\) 7.53609e6 0.534318
\(725\) 3.48662e6 0.246354
\(726\) 397170. 0.0279663
\(727\) −1.48634e7 −1.04299 −0.521496 0.853254i \(-0.674626\pi\)
−0.521496 + 0.853254i \(0.674626\pi\)
\(728\) 1.25182e7 0.875417
\(729\) −9.27802e6 −0.646601
\(730\) 1.27886e7 0.888208
\(731\) −724636. −0.0501564
\(732\) −1.29246e6 −0.0891537
\(733\) 1.62318e7 1.11585 0.557927 0.829890i \(-0.311597\pi\)
0.557927 + 0.829890i \(0.311597\pi\)
\(734\) −1.94986e7 −1.33587
\(735\) 143627. 0.00980661
\(736\) −1.75378e7 −1.19338
\(737\) 7.21130e6 0.489040
\(738\) 5.45072e6 0.368394
\(739\) −2.51267e6 −0.169248 −0.0846242 0.996413i \(-0.526969\pi\)
−0.0846242 + 0.996413i \(0.526969\pi\)
\(740\) −3.47720e6 −0.233427
\(741\) −1.33423e6 −0.0892657
\(742\) −2.47787e7 −1.65222
\(743\) −8.00202e6 −0.531775 −0.265887 0.964004i \(-0.585665\pi\)
−0.265887 + 0.964004i \(0.585665\pi\)
\(744\) −3.17514e6 −0.210295
\(745\) 7.53933e6 0.497671
\(746\) −209364. −0.0137738
\(747\) −2.80780e6 −0.184104
\(748\) −1.05073e6 −0.0686651
\(749\) 8.54847e6 0.556780
\(750\) 423863. 0.0275152
\(751\) −1.10636e7 −0.715810 −0.357905 0.933758i \(-0.616509\pi\)
−0.357905 + 0.933758i \(0.616509\pi\)
\(752\) −6.12855e6 −0.395197
\(753\) −1.10994e6 −0.0713367
\(754\) −3.70818e7 −2.37538
\(755\) 9.10264e6 0.581166
\(756\) 3.80140e6 0.241902
\(757\) −1.42402e7 −0.903185 −0.451593 0.892224i \(-0.649144\pi\)
−0.451593 + 0.892224i \(0.649144\pi\)
\(758\) 3.06143e7 1.93531
\(759\) 1.48862e6 0.0937952
\(760\) 958904. 0.0602200
\(761\) 1.86828e6 0.116944 0.0584722 0.998289i \(-0.481377\pi\)
0.0584722 + 0.998289i \(0.481377\pi\)
\(762\) −5.71637e6 −0.356642
\(763\) −5.50054e6 −0.342054
\(764\) −1.14367e7 −0.708874
\(765\) 2.94718e6 0.182076
\(766\) −3.05725e7 −1.88261
\(767\) 5.50845e6 0.338097
\(768\) −4.95390e6 −0.303071
\(769\) 1.45878e6 0.0889558 0.0444779 0.999010i \(-0.485838\pi\)
0.0444779 + 0.999010i \(0.485838\pi\)
\(770\) −2.61591e6 −0.159000
\(771\) −650989. −0.0394400
\(772\) 1.33882e7 0.808500
\(773\) 3.14550e7 1.89340 0.946698 0.322123i \(-0.104397\pi\)
0.946698 + 0.322123i \(0.104397\pi\)
\(774\) 2.23031e6 0.133818
\(775\) 4.80915e6 0.287617
\(776\) 1.90627e6 0.113640
\(777\) 3.98345e6 0.236704
\(778\) −8.25508e6 −0.488959
\(779\) 1.23602e6 0.0729763
\(780\) −1.55124e6 −0.0912939
\(781\) 4.36972e6 0.256346
\(782\) −1.14447e7 −0.669246
\(783\) 1.02027e7 0.594717
\(784\) 1.89256e6 0.109966
\(785\) −9.52856e6 −0.551891
\(786\) −8.70912e6 −0.502826
\(787\) 1.58210e7 0.910534 0.455267 0.890355i \(-0.349544\pi\)
0.455267 + 0.890355i \(0.349544\pi\)
\(788\) −3.07298e6 −0.176297
\(789\) −1.34037e6 −0.0766534
\(790\) 1.90803e7 1.08772
\(791\) −1.33057e7 −0.756130
\(792\) −2.93015e6 −0.165988
\(793\) 1.88640e7 1.06525
\(794\) −4.53843e6 −0.255478
\(795\) −2.78206e6 −0.156116
\(796\) −1.21364e6 −0.0678901
\(797\) 2.10522e7 1.17395 0.586977 0.809604i \(-0.300318\pi\)
0.586977 + 0.809604i \(0.300318\pi\)
\(798\) 1.21241e6 0.0673975
\(799\) −2.47770e6 −0.137304
\(800\) 3.46020e6 0.191151
\(801\) −1.95688e7 −1.07766
\(802\) −1.56304e7 −0.858091
\(803\) −8.86151e6 −0.484974
\(804\) −3.88588e6 −0.212006
\(805\) −9.80466e6 −0.533265
\(806\) −5.11476e7 −2.77324
\(807\) −4.91301e6 −0.265561
\(808\) 7.51601e6 0.405003
\(809\) 2.24633e7 1.20671 0.603354 0.797474i \(-0.293831\pi\)
0.603354 + 0.797474i \(0.293831\pi\)
\(810\) −8.43091e6 −0.451504
\(811\) 5.10964e6 0.272796 0.136398 0.990654i \(-0.456447\pi\)
0.136398 + 0.990654i \(0.456447\pi\)
\(812\) 1.15952e7 0.617147
\(813\) −3.99151e6 −0.211793
\(814\) 7.00195e6 0.370389
\(815\) −1.65169e6 −0.0871033
\(816\) −2.57001e6 −0.135117
\(817\) 505752. 0.0265083
\(818\) −1.15729e7 −0.604728
\(819\) −2.68530e7 −1.39889
\(820\) 1.43706e6 0.0746344
\(821\) 2.14761e7 1.11198 0.555992 0.831188i \(-0.312339\pi\)
0.555992 + 0.831188i \(0.312339\pi\)
\(822\) −8.57500e6 −0.442644
\(823\) 1.82523e7 0.939329 0.469664 0.882845i \(-0.344375\pi\)
0.469664 + 0.882845i \(0.344375\pi\)
\(824\) 7.56534e6 0.388160
\(825\) −293705. −0.0150237
\(826\) −5.00554e6 −0.255270
\(827\) −3.71952e6 −0.189114 −0.0945568 0.995519i \(-0.530143\pi\)
−0.0945568 + 0.995519i \(0.530143\pi\)
\(828\) 1.21212e7 0.614426
\(829\) 1.00633e7 0.508576 0.254288 0.967128i \(-0.418159\pi\)
0.254288 + 0.967128i \(0.418159\pi\)
\(830\) −2.15124e6 −0.108391
\(831\) 3.09758e6 0.155604
\(832\) 2.15981e6 0.108170
\(833\) 765140. 0.0382057
\(834\) −6.39205e6 −0.318218
\(835\) 4.40146e6 0.218464
\(836\) 733344. 0.0362904
\(837\) 1.40727e7 0.694329
\(838\) −5.04046e6 −0.247948
\(839\) −2.09654e7 −1.02825 −0.514124 0.857716i \(-0.671883\pi\)
−0.514124 + 0.857716i \(0.671883\pi\)
\(840\) −1.27718e6 −0.0624531
\(841\) 1.06096e7 0.517259
\(842\) −1.22340e7 −0.594687
\(843\) 931400. 0.0451406
\(844\) −1.83041e7 −0.884489
\(845\) 1.33586e7 0.643605
\(846\) 7.62596e6 0.366327
\(847\) 1.81263e6 0.0868162
\(848\) −3.66589e7 −1.75061
\(849\) −6.82580e6 −0.325001
\(850\) 2.25803e6 0.107197
\(851\) 2.62439e7 1.24224
\(852\) −2.35467e6 −0.111130
\(853\) −1.69305e7 −0.796703 −0.398352 0.917233i \(-0.630418\pi\)
−0.398352 + 0.917233i \(0.630418\pi\)
\(854\) −1.71417e7 −0.804284
\(855\) −2.05695e6 −0.0962295
\(856\) 7.33630e6 0.342210
\(857\) −3.15364e7 −1.46676 −0.733381 0.679818i \(-0.762059\pi\)
−0.733381 + 0.679818i \(0.762059\pi\)
\(858\) 3.12369e6 0.144860
\(859\) −1.30486e7 −0.603364 −0.301682 0.953409i \(-0.597548\pi\)
−0.301682 + 0.953409i \(0.597548\pi\)
\(860\) 588011. 0.0271106
\(861\) −1.64628e6 −0.0756824
\(862\) −3.90514e7 −1.79007
\(863\) 1.90527e7 0.870823 0.435411 0.900232i \(-0.356603\pi\)
0.435411 + 0.900232i \(0.356603\pi\)
\(864\) 1.01254e7 0.461452
\(865\) −2.97554e6 −0.135215
\(866\) −2.94241e7 −1.33324
\(867\) 4.47528e6 0.202196
\(868\) 1.59935e7 0.720515
\(869\) −1.32212e7 −0.593910
\(870\) 3.78329e6 0.169462
\(871\) 5.67159e7 2.53314
\(872\) −4.72057e6 −0.210234
\(873\) −4.08916e6 −0.181593
\(874\) 7.98767e6 0.353705
\(875\) 1.93446e6 0.0854159
\(876\) 4.77511e6 0.210244
\(877\) −3.72328e7 −1.63466 −0.817328 0.576173i \(-0.804545\pi\)
−0.817328 + 0.576173i \(0.804545\pi\)
\(878\) −3.70787e7 −1.62326
\(879\) 8.90919e6 0.388925
\(880\) −3.87012e6 −0.168468
\(881\) 2.26816e7 0.984541 0.492271 0.870442i \(-0.336167\pi\)
0.492271 + 0.870442i \(0.336167\pi\)
\(882\) −2.35498e6 −0.101933
\(883\) −3.38426e7 −1.46070 −0.730352 0.683071i \(-0.760644\pi\)
−0.730352 + 0.683071i \(0.760644\pi\)
\(884\) −8.26384e6 −0.355673
\(885\) −562003. −0.0241202
\(886\) 2.05395e7 0.879035
\(887\) 2.29689e7 0.980237 0.490118 0.871656i \(-0.336954\pi\)
0.490118 + 0.871656i \(0.336954\pi\)
\(888\) 3.41860e6 0.145484
\(889\) −2.60888e7 −1.10713
\(890\) −1.49929e7 −0.634470
\(891\) 5.84199e6 0.246528
\(892\) −3.42899e6 −0.144296
\(893\) 1.72928e6 0.0725667
\(894\) 8.18084e6 0.342337
\(895\) −6.93436e6 −0.289367
\(896\) −2.38962e7 −0.994395
\(897\) 1.17078e7 0.485843
\(898\) −1.11011e7 −0.459383
\(899\) 4.29253e7 1.77139
\(900\) −2.39151e6 −0.0984159
\(901\) −1.48208e7 −0.608217
\(902\) −2.89376e6 −0.118426
\(903\) −673620. −0.0274913
\(904\) −1.14190e7 −0.464735
\(905\) 1.12220e7 0.455459
\(906\) 9.87717e6 0.399772
\(907\) 2.17023e7 0.875968 0.437984 0.898983i \(-0.355693\pi\)
0.437984 + 0.898983i \(0.355693\pi\)
\(908\) 2.41781e7 0.973212
\(909\) −1.61226e7 −0.647182
\(910\) −2.05738e7 −0.823591
\(911\) 2.37016e7 0.946197 0.473099 0.881010i \(-0.343135\pi\)
0.473099 + 0.881010i \(0.343135\pi\)
\(912\) 1.79371e6 0.0714110
\(913\) 1.49065e6 0.0591831
\(914\) 2.08687e7 0.826284
\(915\) −1.92461e6 −0.0759957
\(916\) −1.25256e7 −0.493241
\(917\) −3.97473e7 −1.56093
\(918\) 6.60753e6 0.258781
\(919\) 1.95881e7 0.765076 0.382538 0.923940i \(-0.375050\pi\)
0.382538 + 0.923940i \(0.375050\pi\)
\(920\) −8.41437e6 −0.327757
\(921\) −1.13896e7 −0.442446
\(922\) −3.67995e7 −1.42565
\(923\) 3.43673e7 1.32783
\(924\) −976754. −0.0376362
\(925\) −5.17791e6 −0.198976
\(926\) −3.78194e7 −1.44939
\(927\) −1.62285e7 −0.620266
\(928\) 3.08849e7 1.17727
\(929\) 1.85313e7 0.704478 0.352239 0.935910i \(-0.385420\pi\)
0.352239 + 0.935910i \(0.385420\pi\)
\(930\) 5.21836e6 0.197846
\(931\) −534021. −0.0201922
\(932\) −2.80139e6 −0.105641
\(933\) 1.02188e6 0.0384322
\(934\) 2.13209e7 0.799720
\(935\) −1.56464e6 −0.0585310
\(936\) −2.30452e7 −0.859788
\(937\) −4.36087e6 −0.162265 −0.0811324 0.996703i \(-0.525854\pi\)
−0.0811324 + 0.996703i \(0.525854\pi\)
\(938\) −5.15378e7 −1.91258
\(939\) −1.18279e7 −0.437767
\(940\) 2.01055e6 0.0742155
\(941\) −1.17176e7 −0.431383 −0.215692 0.976462i \(-0.569201\pi\)
−0.215692 + 0.976462i \(0.569201\pi\)
\(942\) −1.03393e7 −0.379634
\(943\) −1.08461e7 −0.397185
\(944\) −7.40545e6 −0.270471
\(945\) 5.66068e6 0.206200
\(946\) −1.18406e6 −0.0430177
\(947\) 5.25412e7 1.90382 0.951909 0.306382i \(-0.0991185\pi\)
0.951909 + 0.306382i \(0.0991185\pi\)
\(948\) 7.12436e6 0.257469
\(949\) −6.96946e7 −2.51208
\(950\) −1.57596e6 −0.0566549
\(951\) 1.40941e6 0.0505343
\(952\) −6.80387e6 −0.243312
\(953\) 4.26992e7 1.52296 0.761478 0.648191i \(-0.224474\pi\)
0.761478 + 0.648191i \(0.224474\pi\)
\(954\) 4.56159e7 1.62273
\(955\) −1.70305e7 −0.604253
\(956\) 3.26346e6 0.115487
\(957\) −2.62154e6 −0.0925287
\(958\) 6.19877e7 2.18218
\(959\) −3.91352e7 −1.37411
\(960\) −220356. −0.00771696
\(961\) 3.05784e7 1.06809
\(962\) 5.50694e7 1.91855
\(963\) −1.57371e7 −0.546840
\(964\) 4.06488e6 0.140882
\(965\) 1.99365e7 0.689176
\(966\) −1.06389e7 −0.366822
\(967\) −2.64143e7 −0.908391 −0.454196 0.890902i \(-0.650073\pi\)
−0.454196 + 0.890902i \(0.650073\pi\)
\(968\) 1.55560e6 0.0533593
\(969\) 725175. 0.0248104
\(970\) −3.13297e6 −0.106912
\(971\) 4.05408e7 1.37989 0.689945 0.723862i \(-0.257635\pi\)
0.689945 + 0.723862i \(0.257635\pi\)
\(972\) −1.06093e7 −0.360180
\(973\) −2.91725e7 −0.987851
\(974\) 4.32373e7 1.46037
\(975\) −2.30995e6 −0.0778200
\(976\) −2.53603e7 −0.852178
\(977\) 2.59650e7 0.870265 0.435133 0.900366i \(-0.356701\pi\)
0.435133 + 0.900366i \(0.356701\pi\)
\(978\) −1.79223e6 −0.0599165
\(979\) 1.03890e7 0.346430
\(980\) −620878. −0.0206510
\(981\) 1.01261e7 0.335947
\(982\) −2.30675e7 −0.763346
\(983\) 944035. 0.0311605 0.0155802 0.999879i \(-0.495040\pi\)
0.0155802 + 0.999879i \(0.495040\pi\)
\(984\) −1.41284e6 −0.0465162
\(985\) −4.57599e6 −0.150278
\(986\) 2.01546e7 0.660209
\(987\) −2.30326e6 −0.0752577
\(988\) 5.76766e6 0.187978
\(989\) −4.43796e6 −0.144276
\(990\) 4.81572e6 0.156161
\(991\) 1.25889e7 0.407197 0.203599 0.979054i \(-0.434736\pi\)
0.203599 + 0.979054i \(0.434736\pi\)
\(992\) 4.26000e7 1.37446
\(993\) 898285. 0.0289095
\(994\) −3.12296e7 −1.00254
\(995\) −1.80723e6 −0.0578704
\(996\) −803249. −0.0256568
\(997\) 1.11731e7 0.355989 0.177995 0.984031i \(-0.443039\pi\)
0.177995 + 0.984031i \(0.443039\pi\)
\(998\) 3.95538e6 0.125708
\(999\) −1.51518e7 −0.480342
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.1.9 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.h.1.9 40 1.1 even 1 trivial