Properties

Label 43.6.a.b.1.10
Level 43
Weight 6
Character 43.1
Self dual yes
Analytic conductor 6.897
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-9.70631\) of \(x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.7063 q^{2} +18.3440 q^{3} +82.6251 q^{4} -72.1865 q^{5} +196.397 q^{6} -96.4803 q^{7} +542.008 q^{8} +93.5034 q^{9} +O(q^{10})\) \(q+10.7063 q^{2} +18.3440 q^{3} +82.6251 q^{4} -72.1865 q^{5} +196.397 q^{6} -96.4803 q^{7} +542.008 q^{8} +93.5034 q^{9} -772.851 q^{10} -684.136 q^{11} +1515.68 q^{12} +344.655 q^{13} -1032.95 q^{14} -1324.19 q^{15} +3158.90 q^{16} +1319.32 q^{17} +1001.08 q^{18} +739.016 q^{19} -5964.42 q^{20} -1769.84 q^{21} -7324.58 q^{22} +3165.85 q^{23} +9942.61 q^{24} +2085.89 q^{25} +3689.99 q^{26} -2742.37 q^{27} -7971.70 q^{28} +7073.21 q^{29} -14177.2 q^{30} -3791.93 q^{31} +16476.0 q^{32} -12549.8 q^{33} +14125.1 q^{34} +6964.58 q^{35} +7725.73 q^{36} -12682.3 q^{37} +7912.13 q^{38} +6322.37 q^{39} -39125.7 q^{40} -10882.5 q^{41} -18948.4 q^{42} +1849.00 q^{43} -56526.8 q^{44} -6749.68 q^{45} +33894.6 q^{46} +3873.59 q^{47} +57947.0 q^{48} -7498.54 q^{49} +22332.2 q^{50} +24201.7 q^{51} +28477.2 q^{52} +6479.38 q^{53} -29360.7 q^{54} +49385.4 q^{55} -52293.1 q^{56} +13556.5 q^{57} +75728.0 q^{58} +34750.3 q^{59} -109411. q^{60} +26452.9 q^{61} -40597.6 q^{62} -9021.24 q^{63} +75311.8 q^{64} -24879.4 q^{65} -134362. q^{66} -58007.3 q^{67} +109009. q^{68} +58074.5 q^{69} +74564.9 q^{70} -23477.7 q^{71} +50679.6 q^{72} +45184.4 q^{73} -135781. q^{74} +38263.6 q^{75} +61061.3 q^{76} +66005.7 q^{77} +67689.2 q^{78} +17895.9 q^{79} -228030. q^{80} -73027.4 q^{81} -116512. q^{82} +39799.2 q^{83} -146233. q^{84} -95237.3 q^{85} +19796.0 q^{86} +129751. q^{87} -370808. q^{88} -30802.0 q^{89} -72264.2 q^{90} -33252.5 q^{91} +261579. q^{92} -69559.2 q^{93} +41471.9 q^{94} -53346.9 q^{95} +302235. q^{96} +22524.5 q^{97} -80281.7 q^{98} -63969.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.7063 1.89263 0.946313 0.323251i \(-0.104776\pi\)
0.946313 + 0.323251i \(0.104776\pi\)
\(3\) 18.3440 1.17677 0.588385 0.808581i \(-0.299764\pi\)
0.588385 + 0.808581i \(0.299764\pi\)
\(4\) 82.6251 2.58203
\(5\) −72.1865 −1.29131 −0.645656 0.763629i \(-0.723416\pi\)
−0.645656 + 0.763629i \(0.723416\pi\)
\(6\) 196.397 2.22719
\(7\) −96.4803 −0.744207 −0.372103 0.928191i \(-0.621363\pi\)
−0.372103 + 0.928191i \(0.621363\pi\)
\(8\) 542.008 2.99420
\(9\) 93.5034 0.384788
\(10\) −772.851 −2.44397
\(11\) −684.136 −1.70475 −0.852376 0.522930i \(-0.824839\pi\)
−0.852376 + 0.522930i \(0.824839\pi\)
\(12\) 1515.68 3.03846
\(13\) 344.655 0.565622 0.282811 0.959176i \(-0.408733\pi\)
0.282811 + 0.959176i \(0.408733\pi\)
\(14\) −1032.95 −1.40851
\(15\) −1324.19 −1.51958
\(16\) 3158.90 3.08487
\(17\) 1319.32 1.10721 0.553604 0.832780i \(-0.313252\pi\)
0.553604 + 0.832780i \(0.313252\pi\)
\(18\) 1001.08 0.728260
\(19\) 739.016 0.469645 0.234823 0.972038i \(-0.424549\pi\)
0.234823 + 0.972038i \(0.424549\pi\)
\(20\) −5964.42 −3.33421
\(21\) −1769.84 −0.875760
\(22\) −7324.58 −3.22646
\(23\) 3165.85 1.24787 0.623937 0.781474i \(-0.285532\pi\)
0.623937 + 0.781474i \(0.285532\pi\)
\(24\) 9942.61 3.52349
\(25\) 2085.89 0.667484
\(26\) 3689.99 1.07051
\(27\) −2742.37 −0.723963
\(28\) −7971.70 −1.92157
\(29\) 7073.21 1.56179 0.780893 0.624665i \(-0.214765\pi\)
0.780893 + 0.624665i \(0.214765\pi\)
\(30\) −14177.2 −2.87599
\(31\) −3791.93 −0.708689 −0.354345 0.935115i \(-0.615296\pi\)
−0.354345 + 0.935115i \(0.615296\pi\)
\(32\) 16476.0 2.84430
\(33\) −12549.8 −2.00610
\(34\) 14125.1 2.09553
\(35\) 6964.58 0.961003
\(36\) 7725.73 0.993536
\(37\) −12682.3 −1.52298 −0.761489 0.648177i \(-0.775531\pi\)
−0.761489 + 0.648177i \(0.775531\pi\)
\(38\) 7912.13 0.888863
\(39\) 6322.37 0.665607
\(40\) −39125.7 −3.86644
\(41\) −10882.5 −1.01105 −0.505523 0.862813i \(-0.668700\pi\)
−0.505523 + 0.862813i \(0.668700\pi\)
\(42\) −18948.4 −1.65749
\(43\) 1849.00 0.152499
\(44\) −56526.8 −4.40173
\(45\) −6749.68 −0.496881
\(46\) 33894.6 2.36176
\(47\) 3873.59 0.255782 0.127891 0.991788i \(-0.459179\pi\)
0.127891 + 0.991788i \(0.459179\pi\)
\(48\) 57947.0 3.63018
\(49\) −7498.54 −0.446156
\(50\) 22332.2 1.26330
\(51\) 24201.7 1.30293
\(52\) 28477.2 1.46046
\(53\) 6479.38 0.316843 0.158421 0.987372i \(-0.449360\pi\)
0.158421 + 0.987372i \(0.449360\pi\)
\(54\) −29360.7 −1.37019
\(55\) 49385.4 2.20136
\(56\) −52293.1 −2.22830
\(57\) 13556.5 0.552664
\(58\) 75728.0 2.95588
\(59\) 34750.3 1.29966 0.649829 0.760081i \(-0.274841\pi\)
0.649829 + 0.760081i \(0.274841\pi\)
\(60\) −109411. −3.92360
\(61\) 26452.9 0.910224 0.455112 0.890434i \(-0.349599\pi\)
0.455112 + 0.890434i \(0.349599\pi\)
\(62\) −40597.6 −1.34128
\(63\) −9021.24 −0.286362
\(64\) 75311.8 2.29833
\(65\) −24879.4 −0.730394
\(66\) −134362. −3.79680
\(67\) −58007.3 −1.57868 −0.789342 0.613953i \(-0.789578\pi\)
−0.789342 + 0.613953i \(0.789578\pi\)
\(68\) 109009. 2.85885
\(69\) 58074.5 1.46846
\(70\) 74564.9 1.81882
\(71\) −23477.7 −0.552726 −0.276363 0.961053i \(-0.589129\pi\)
−0.276363 + 0.961053i \(0.589129\pi\)
\(72\) 50679.6 1.15213
\(73\) 45184.4 0.992388 0.496194 0.868212i \(-0.334731\pi\)
0.496194 + 0.868212i \(0.334731\pi\)
\(74\) −135781. −2.88243
\(75\) 38263.6 0.785475
\(76\) 61061.3 1.21264
\(77\) 66005.7 1.26869
\(78\) 67689.2 1.25975
\(79\) 17895.9 0.322617 0.161308 0.986904i \(-0.448429\pi\)
0.161308 + 0.986904i \(0.448429\pi\)
\(80\) −228030. −3.98352
\(81\) −73027.4 −1.23673
\(82\) −116512. −1.91353
\(83\) 39799.2 0.634132 0.317066 0.948403i \(-0.397302\pi\)
0.317066 + 0.948403i \(0.397302\pi\)
\(84\) −146233. −2.26124
\(85\) −95237.3 −1.42975
\(86\) 19796.0 0.288623
\(87\) 129751. 1.83786
\(88\) −370808. −5.10437
\(89\) −30802.0 −0.412197 −0.206098 0.978531i \(-0.566077\pi\)
−0.206098 + 0.978531i \(0.566077\pi\)
\(90\) −72264.2 −0.940410
\(91\) −33252.5 −0.420940
\(92\) 261579. 3.22206
\(93\) −69559.2 −0.833964
\(94\) 41471.9 0.484099
\(95\) −53346.9 −0.606458
\(96\) 302235. 3.34709
\(97\) 22524.5 0.243067 0.121533 0.992587i \(-0.461219\pi\)
0.121533 + 0.992587i \(0.461219\pi\)
\(98\) −80281.7 −0.844407
\(99\) −63969.1 −0.655968
\(100\) 172347. 1.72347
\(101\) 70592.5 0.688581 0.344290 0.938863i \(-0.388120\pi\)
0.344290 + 0.938863i \(0.388120\pi\)
\(102\) 259111. 2.46596
\(103\) −36628.5 −0.340193 −0.170097 0.985427i \(-0.554408\pi\)
−0.170097 + 0.985427i \(0.554408\pi\)
\(104\) 186806. 1.69359
\(105\) 127758. 1.13088
\(106\) 69370.2 0.599665
\(107\) −48388.9 −0.408588 −0.204294 0.978910i \(-0.565490\pi\)
−0.204294 + 0.978910i \(0.565490\pi\)
\(108\) −226589. −1.86930
\(109\) −75896.0 −0.611861 −0.305930 0.952054i \(-0.598967\pi\)
−0.305930 + 0.952054i \(0.598967\pi\)
\(110\) 528735. 4.16636
\(111\) −232645. −1.79220
\(112\) −304772. −2.29578
\(113\) −212156. −1.56300 −0.781500 0.623905i \(-0.785545\pi\)
−0.781500 + 0.623905i \(0.785545\pi\)
\(114\) 145140. 1.04599
\(115\) −228532. −1.61139
\(116\) 584424. 4.03258
\(117\) 32226.4 0.217645
\(118\) 372048. 2.45977
\(119\) −127289. −0.823992
\(120\) −717722. −4.54992
\(121\) 306992. 1.90618
\(122\) 283213. 1.72271
\(123\) −199630. −1.18977
\(124\) −313308. −1.82986
\(125\) 75009.8 0.429381
\(126\) −96584.3 −0.541976
\(127\) −74547.8 −0.410134 −0.205067 0.978748i \(-0.565741\pi\)
−0.205067 + 0.978748i \(0.565741\pi\)
\(128\) 279081. 1.50558
\(129\) 33918.1 0.179456
\(130\) −266367. −1.38236
\(131\) −57691.8 −0.293722 −0.146861 0.989157i \(-0.546917\pi\)
−0.146861 + 0.989157i \(0.546917\pi\)
\(132\) −1.03693e6 −5.17982
\(133\) −71300.5 −0.349513
\(134\) −621044. −2.98786
\(135\) 197962. 0.934862
\(136\) 715084. 3.31520
\(137\) −23674.0 −0.107763 −0.0538815 0.998547i \(-0.517159\pi\)
−0.0538815 + 0.998547i \(0.517159\pi\)
\(138\) 621763. 2.77925
\(139\) 234996. 1.03163 0.515815 0.856700i \(-0.327489\pi\)
0.515815 + 0.856700i \(0.327489\pi\)
\(140\) 575449. 2.48134
\(141\) 71057.3 0.300996
\(142\) −251360. −1.04610
\(143\) −235791. −0.964245
\(144\) 295368. 1.18702
\(145\) −510590. −2.01675
\(146\) 483758. 1.87822
\(147\) −137554. −0.525023
\(148\) −1.04788e6 −3.93238
\(149\) 236660. 0.873292 0.436646 0.899633i \(-0.356166\pi\)
0.436646 + 0.899633i \(0.356166\pi\)
\(150\) 409662. 1.48661
\(151\) −106852. −0.381363 −0.190681 0.981652i \(-0.561070\pi\)
−0.190681 + 0.981652i \(0.561070\pi\)
\(152\) 400553. 1.40621
\(153\) 123361. 0.426040
\(154\) 706678. 2.40115
\(155\) 273726. 0.915138
\(156\) 522386. 1.71862
\(157\) 316009. 1.02318 0.511588 0.859231i \(-0.329057\pi\)
0.511588 + 0.859231i \(0.329057\pi\)
\(158\) 191599. 0.610593
\(159\) 118858. 0.372851
\(160\) −1.18934e6 −3.67288
\(161\) −305442. −0.928677
\(162\) −781855. −2.34066
\(163\) −467943. −1.37951 −0.689753 0.724045i \(-0.742281\pi\)
−0.689753 + 0.724045i \(0.742281\pi\)
\(164\) −899172. −2.61056
\(165\) 905927. 2.59050
\(166\) 426103. 1.20017
\(167\) 329143. 0.913258 0.456629 0.889657i \(-0.349057\pi\)
0.456629 + 0.889657i \(0.349057\pi\)
\(168\) −959267. −2.62220
\(169\) −252506. −0.680072
\(170\) −1.01964e6 −2.70598
\(171\) 69100.5 0.180714
\(172\) 152774. 0.393757
\(173\) 197867. 0.502641 0.251321 0.967904i \(-0.419135\pi\)
0.251321 + 0.967904i \(0.419135\pi\)
\(174\) 1.38916e6 3.47839
\(175\) −201247. −0.496746
\(176\) −2.16112e6 −5.25893
\(177\) 637461. 1.52940
\(178\) −329776. −0.780134
\(179\) 71110.2 0.165882 0.0829410 0.996554i \(-0.473569\pi\)
0.0829410 + 0.996554i \(0.473569\pi\)
\(180\) −557693. −1.28296
\(181\) 111059. 0.251975 0.125987 0.992032i \(-0.459790\pi\)
0.125987 + 0.992032i \(0.459790\pi\)
\(182\) −356011. −0.796682
\(183\) 485252. 1.07112
\(184\) 1.71592e6 3.73639
\(185\) 915491. 1.96664
\(186\) −744723. −1.57838
\(187\) −902597. −1.88751
\(188\) 320056. 0.660437
\(189\) 264585. 0.538779
\(190\) −571149. −1.14780
\(191\) 620980. 1.23167 0.615835 0.787875i \(-0.288819\pi\)
0.615835 + 0.787875i \(0.288819\pi\)
\(192\) 1.38152e6 2.70461
\(193\) −725314. −1.40163 −0.700814 0.713344i \(-0.747180\pi\)
−0.700814 + 0.713344i \(0.747180\pi\)
\(194\) 241154. 0.460035
\(195\) −456389. −0.859506
\(196\) −619568. −1.15199
\(197\) 273782. 0.502619 0.251310 0.967907i \(-0.419139\pi\)
0.251310 + 0.967907i \(0.419139\pi\)
\(198\) −684873. −1.24150
\(199\) −314223. −0.562477 −0.281239 0.959638i \(-0.590745\pi\)
−0.281239 + 0.959638i \(0.590745\pi\)
\(200\) 1.13057e6 1.99858
\(201\) −1.06409e6 −1.85775
\(202\) 755785. 1.30323
\(203\) −682425. −1.16229
\(204\) 1.99967e6 3.36421
\(205\) 785573. 1.30557
\(206\) −392156. −0.643859
\(207\) 296018. 0.480167
\(208\) 1.08873e6 1.74487
\(209\) −505588. −0.800628
\(210\) 1.36782e6 2.14033
\(211\) −540561. −0.835869 −0.417935 0.908477i \(-0.637246\pi\)
−0.417935 + 0.908477i \(0.637246\pi\)
\(212\) 535359. 0.818099
\(213\) −430676. −0.650432
\(214\) −518066. −0.773305
\(215\) −133473. −0.196923
\(216\) −1.48639e6 −2.16769
\(217\) 365846. 0.527411
\(218\) −812566. −1.15802
\(219\) 828864. 1.16781
\(220\) 4.08047e6 5.68400
\(221\) 454712. 0.626261
\(222\) −2.49076e6 −3.39196
\(223\) −231856. −0.312216 −0.156108 0.987740i \(-0.549895\pi\)
−0.156108 + 0.987740i \(0.549895\pi\)
\(224\) −1.58961e6 −2.11675
\(225\) 195038. 0.256840
\(226\) −2.27141e6 −2.95818
\(227\) −1.39293e6 −1.79418 −0.897090 0.441848i \(-0.854323\pi\)
−0.897090 + 0.441848i \(0.854323\pi\)
\(228\) 1.12011e6 1.42700
\(229\) −565105. −0.712099 −0.356050 0.934467i \(-0.615877\pi\)
−0.356050 + 0.934467i \(0.615877\pi\)
\(230\) −2.44673e6 −3.04977
\(231\) 1.21081e6 1.49295
\(232\) 3.83374e6 4.67630
\(233\) 237550. 0.286658 0.143329 0.989675i \(-0.454219\pi\)
0.143329 + 0.989675i \(0.454219\pi\)
\(234\) 345026. 0.411920
\(235\) −279621. −0.330294
\(236\) 2.87125e6 3.35576
\(237\) 328284. 0.379645
\(238\) −1.36279e6 −1.55951
\(239\) 1.31472e6 1.48881 0.744403 0.667731i \(-0.232734\pi\)
0.744403 + 0.667731i \(0.232734\pi\)
\(240\) −4.18299e6 −4.68769
\(241\) 1.03644e6 1.14948 0.574739 0.818337i \(-0.305104\pi\)
0.574739 + 0.818337i \(0.305104\pi\)
\(242\) 3.28675e6 3.60768
\(243\) −673222. −0.731379
\(244\) 2.18567e6 2.35023
\(245\) 541293. 0.576126
\(246\) −2.13730e6 −2.25179
\(247\) 254706. 0.265642
\(248\) −2.05526e6 −2.12196
\(249\) 730079. 0.746227
\(250\) 803079. 0.812659
\(251\) −1.67030e6 −1.67344 −0.836720 0.547632i \(-0.815530\pi\)
−0.836720 + 0.547632i \(0.815530\pi\)
\(252\) −745381. −0.739396
\(253\) −2.16587e6 −2.12732
\(254\) −798132. −0.776230
\(255\) −1.74704e6 −1.68249
\(256\) 577949. 0.551175
\(257\) 311852. 0.294521 0.147261 0.989098i \(-0.452954\pi\)
0.147261 + 0.989098i \(0.452954\pi\)
\(258\) 363138. 0.339643
\(259\) 1.22359e6 1.13341
\(260\) −2.05567e6 −1.88590
\(261\) 661369. 0.600956
\(262\) −617666. −0.555905
\(263\) −341600. −0.304529 −0.152264 0.988340i \(-0.548657\pi\)
−0.152264 + 0.988340i \(0.548657\pi\)
\(264\) −6.80210e6 −6.00667
\(265\) −467723. −0.409142
\(266\) −763365. −0.661498
\(267\) −565034. −0.485061
\(268\) −4.79286e6 −4.07622
\(269\) 865544. 0.729304 0.364652 0.931144i \(-0.381188\pi\)
0.364652 + 0.931144i \(0.381188\pi\)
\(270\) 2.11944e6 1.76934
\(271\) 1.49244e6 1.23445 0.617226 0.786786i \(-0.288256\pi\)
0.617226 + 0.786786i \(0.288256\pi\)
\(272\) 4.16762e6 3.41559
\(273\) −609984. −0.495350
\(274\) −253461. −0.203955
\(275\) −1.42703e6 −1.13789
\(276\) 4.79841e6 3.79162
\(277\) −395961. −0.310065 −0.155033 0.987909i \(-0.549548\pi\)
−0.155033 + 0.987909i \(0.549548\pi\)
\(278\) 2.51595e6 1.95249
\(279\) −354558. −0.272695
\(280\) 3.77486e6 2.87743
\(281\) 2.19634e6 1.65934 0.829668 0.558257i \(-0.188530\pi\)
0.829668 + 0.558257i \(0.188530\pi\)
\(282\) 760761. 0.569673
\(283\) 562659. 0.417618 0.208809 0.977956i \(-0.433041\pi\)
0.208809 + 0.977956i \(0.433041\pi\)
\(284\) −1.93985e6 −1.42716
\(285\) −978598. −0.713661
\(286\) −2.52445e6 −1.82496
\(287\) 1.04995e6 0.752427
\(288\) 1.54056e6 1.09445
\(289\) 320758. 0.225909
\(290\) −5.46653e6 −3.81696
\(291\) 413190. 0.286034
\(292\) 3.73337e6 2.56238
\(293\) 2.24866e6 1.53022 0.765111 0.643898i \(-0.222684\pi\)
0.765111 + 0.643898i \(0.222684\pi\)
\(294\) −1.47269e6 −0.993672
\(295\) −2.50850e6 −1.67826
\(296\) −6.87391e6 −4.56010
\(297\) 1.87615e6 1.23418
\(298\) 2.53376e6 1.65282
\(299\) 1.09113e6 0.705826
\(300\) 3.16153e6 2.02812
\(301\) −178392. −0.113490
\(302\) −1.14399e6 −0.721778
\(303\) 1.29495e6 0.810301
\(304\) 2.33448e6 1.44879
\(305\) −1.90954e6 −1.17538
\(306\) 1.32074e6 0.806335
\(307\) 2.14795e6 1.30070 0.650352 0.759633i \(-0.274621\pi\)
0.650352 + 0.759633i \(0.274621\pi\)
\(308\) 5.45373e6 3.27580
\(309\) −671914. −0.400329
\(310\) 2.93059e6 1.73201
\(311\) −2.61384e6 −1.53242 −0.766210 0.642590i \(-0.777860\pi\)
−0.766210 + 0.642590i \(0.777860\pi\)
\(312\) 3.42677e6 1.99296
\(313\) 968697. 0.558891 0.279445 0.960162i \(-0.409849\pi\)
0.279445 + 0.960162i \(0.409849\pi\)
\(314\) 3.38329e6 1.93649
\(315\) 651212. 0.369782
\(316\) 1.47865e6 0.833007
\(317\) 289378. 0.161740 0.0808700 0.996725i \(-0.474230\pi\)
0.0808700 + 0.996725i \(0.474230\pi\)
\(318\) 1.27253e6 0.705667
\(319\) −4.83904e6 −2.66246
\(320\) −5.43649e6 −2.96786
\(321\) −887647. −0.480815
\(322\) −3.27016e6 −1.75764
\(323\) 975001. 0.519995
\(324\) −6.03390e6 −3.19327
\(325\) 718912. 0.377544
\(326\) −5.00994e6 −2.61089
\(327\) −1.39224e6 −0.720019
\(328\) −5.89843e6 −3.02727
\(329\) −373725. −0.190354
\(330\) 9.69914e6 4.90285
\(331\) 2.74453e6 1.37689 0.688443 0.725291i \(-0.258295\pi\)
0.688443 + 0.725291i \(0.258295\pi\)
\(332\) 3.28842e6 1.63735
\(333\) −1.18584e6 −0.586024
\(334\) 3.52391e6 1.72846
\(335\) 4.18734e6 2.03857
\(336\) −5.59075e6 −2.70161
\(337\) −1.03816e6 −0.497956 −0.248978 0.968509i \(-0.580095\pi\)
−0.248978 + 0.968509i \(0.580095\pi\)
\(338\) −2.70341e6 −1.28712
\(339\) −3.89180e6 −1.83929
\(340\) −7.86900e6 −3.69166
\(341\) 2.59420e6 1.20814
\(342\) 739812. 0.342023
\(343\) 2.34501e6 1.07624
\(344\) 1.00217e6 0.456611
\(345\) −4.19219e6 −1.89624
\(346\) 2.11843e6 0.951312
\(347\) −1.87377e6 −0.835396 −0.417698 0.908586i \(-0.637163\pi\)
−0.417698 + 0.908586i \(0.637163\pi\)
\(348\) 1.07207e7 4.74542
\(349\) 46712.6 0.0205291 0.0102646 0.999947i \(-0.496733\pi\)
0.0102646 + 0.999947i \(0.496733\pi\)
\(350\) −2.15461e6 −0.940155
\(351\) −945172. −0.409490
\(352\) −1.12718e7 −4.84883
\(353\) 643022. 0.274656 0.137328 0.990526i \(-0.456149\pi\)
0.137328 + 0.990526i \(0.456149\pi\)
\(354\) 6.82486e6 2.89458
\(355\) 1.69477e6 0.713742
\(356\) −2.54502e6 −1.06431
\(357\) −2.33499e6 −0.969649
\(358\) 761328. 0.313953
\(359\) 361451. 0.148017 0.0740087 0.997258i \(-0.476421\pi\)
0.0740087 + 0.997258i \(0.476421\pi\)
\(360\) −3.65838e6 −1.48776
\(361\) −1.92995e6 −0.779434
\(362\) 1.18903e6 0.476894
\(363\) 5.63146e6 2.24313
\(364\) −2.74749e6 −1.08688
\(365\) −3.26170e6 −1.28148
\(366\) 5.19526e6 2.02724
\(367\) −1.12671e6 −0.436663 −0.218332 0.975875i \(-0.570061\pi\)
−0.218332 + 0.975875i \(0.570061\pi\)
\(368\) 1.00006e7 3.84953
\(369\) −1.01756e6 −0.389038
\(370\) 9.80153e6 3.72211
\(371\) −625132. −0.235796
\(372\) −5.74734e6 −2.15332
\(373\) −1.98041e6 −0.737027 −0.368514 0.929622i \(-0.620133\pi\)
−0.368514 + 0.929622i \(0.620133\pi\)
\(374\) −9.66349e6 −3.57236
\(375\) 1.37598e6 0.505283
\(376\) 2.09952e6 0.765861
\(377\) 2.43782e6 0.883380
\(378\) 2.83273e6 1.01971
\(379\) −870212. −0.311191 −0.155596 0.987821i \(-0.549730\pi\)
−0.155596 + 0.987821i \(0.549730\pi\)
\(380\) −4.40780e6 −1.56589
\(381\) −1.36751e6 −0.482633
\(382\) 6.64841e6 2.33109
\(383\) −2.78192e6 −0.969055 −0.484527 0.874776i \(-0.661008\pi\)
−0.484527 + 0.874776i \(0.661008\pi\)
\(384\) 5.11947e6 1.77173
\(385\) −4.76472e6 −1.63827
\(386\) −7.76544e6 −2.65276
\(387\) 172888. 0.0586796
\(388\) 1.86109e6 0.627607
\(389\) 5.01979e6 1.68195 0.840973 0.541077i \(-0.181983\pi\)
0.840973 + 0.541077i \(0.181983\pi\)
\(390\) −4.88625e6 −1.62672
\(391\) 4.17678e6 1.38166
\(392\) −4.06427e6 −1.33588
\(393\) −1.05830e6 −0.345643
\(394\) 2.93119e6 0.951270
\(395\) −1.29184e6 −0.416598
\(396\) −5.28545e6 −1.69373
\(397\) −3.26819e6 −1.04071 −0.520357 0.853949i \(-0.674201\pi\)
−0.520357 + 0.853949i \(0.674201\pi\)
\(398\) −3.36417e6 −1.06456
\(399\) −1.30794e6 −0.411297
\(400\) 6.58912e6 2.05910
\(401\) 3.63270e6 1.12815 0.564077 0.825722i \(-0.309232\pi\)
0.564077 + 0.825722i \(0.309232\pi\)
\(402\) −1.13924e7 −3.51603
\(403\) −1.30691e6 −0.400850
\(404\) 5.83271e6 1.77794
\(405\) 5.27159e6 1.59700
\(406\) −7.30626e6 −2.19978
\(407\) 8.67643e6 2.59630
\(408\) 1.31175e7 3.90123
\(409\) −4.93318e6 −1.45821 −0.729103 0.684404i \(-0.760063\pi\)
−0.729103 + 0.684404i \(0.760063\pi\)
\(410\) 8.41059e6 2.47097
\(411\) −434276. −0.126812
\(412\) −3.02643e6 −0.878391
\(413\) −3.35272e6 −0.967214
\(414\) 3.16926e6 0.908777
\(415\) −2.87297e6 −0.818861
\(416\) 5.67852e6 1.60880
\(417\) 4.31078e6 1.21399
\(418\) −5.41298e6 −1.51529
\(419\) 412864. 0.114887 0.0574437 0.998349i \(-0.481705\pi\)
0.0574437 + 0.998349i \(0.481705\pi\)
\(420\) 1.05561e7 2.91997
\(421\) −2.27168e6 −0.624656 −0.312328 0.949974i \(-0.601109\pi\)
−0.312328 + 0.949974i \(0.601109\pi\)
\(422\) −5.78741e6 −1.58199
\(423\) 362194. 0.0984216
\(424\) 3.51188e6 0.948690
\(425\) 2.75196e6 0.739044
\(426\) −4.61095e6 −1.23102
\(427\) −2.55218e6 −0.677395
\(428\) −3.99814e6 −1.05499
\(429\) −4.32536e6 −1.13469
\(430\) −1.42900e6 −0.372702
\(431\) −1.37855e6 −0.357461 −0.178731 0.983898i \(-0.557199\pi\)
−0.178731 + 0.983898i \(0.557199\pi\)
\(432\) −8.66288e6 −2.23333
\(433\) −4.50720e6 −1.15528 −0.577639 0.816292i \(-0.696026\pi\)
−0.577639 + 0.816292i \(0.696026\pi\)
\(434\) 3.91687e6 0.998193
\(435\) −9.36628e6 −2.37325
\(436\) −6.27091e6 −1.57985
\(437\) 2.33961e6 0.586058
\(438\) 8.87408e6 2.21023
\(439\) −1.97588e6 −0.489327 −0.244663 0.969608i \(-0.578677\pi\)
−0.244663 + 0.969608i \(0.578677\pi\)
\(440\) 2.67673e7 6.59132
\(441\) −701140. −0.171675
\(442\) 4.86829e6 1.18528
\(443\) −2.75707e6 −0.667481 −0.333740 0.942665i \(-0.608311\pi\)
−0.333740 + 0.942665i \(0.608311\pi\)
\(444\) −1.92223e7 −4.62751
\(445\) 2.22349e6 0.532274
\(446\) −2.48232e6 −0.590909
\(447\) 4.34130e6 1.02766
\(448\) −7.26611e6 −1.71044
\(449\) 5.19837e6 1.21689 0.608445 0.793596i \(-0.291794\pi\)
0.608445 + 0.793596i \(0.291794\pi\)
\(450\) 2.08813e6 0.486102
\(451\) 7.44515e6 1.72358
\(452\) −1.75294e7 −4.03572
\(453\) −1.96009e6 −0.448777
\(454\) −1.49132e7 −3.39571
\(455\) 2.40038e6 0.543564
\(456\) 7.34775e6 1.65479
\(457\) 7.85140e6 1.75856 0.879279 0.476307i \(-0.158025\pi\)
0.879279 + 0.476307i \(0.158025\pi\)
\(458\) −6.05019e6 −1.34774
\(459\) −3.61807e6 −0.801578
\(460\) −1.88825e7 −4.16068
\(461\) 528436. 0.115808 0.0579042 0.998322i \(-0.481558\pi\)
0.0579042 + 0.998322i \(0.481558\pi\)
\(462\) 1.29633e7 2.82560
\(463\) 825321. 0.178925 0.0894624 0.995990i \(-0.471485\pi\)
0.0894624 + 0.995990i \(0.471485\pi\)
\(464\) 2.23436e7 4.81790
\(465\) 5.02124e6 1.07691
\(466\) 2.54328e6 0.542537
\(467\) 4.03618e6 0.856404 0.428202 0.903683i \(-0.359147\pi\)
0.428202 + 0.903683i \(0.359147\pi\)
\(468\) 2.66271e6 0.561966
\(469\) 5.59656e6 1.17487
\(470\) −2.99371e6 −0.625122
\(471\) 5.79688e6 1.20404
\(472\) 1.88350e7 3.89144
\(473\) −1.26497e6 −0.259972
\(474\) 3.51471e6 0.718527
\(475\) 1.54150e6 0.313481
\(476\) −1.05173e7 −2.12758
\(477\) 605844. 0.121917
\(478\) 1.40758e7 2.81775
\(479\) −6.39933e6 −1.27437 −0.637186 0.770710i \(-0.719902\pi\)
−0.637186 + 0.770710i \(0.719902\pi\)
\(480\) −2.18173e7 −4.32213
\(481\) −4.37102e6 −0.861431
\(482\) 1.10964e7 2.17553
\(483\) −5.60305e6 −1.09284
\(484\) 2.53652e7 4.92181
\(485\) −1.62596e6 −0.313875
\(486\) −7.20772e6 −1.38423
\(487\) 4.00561e6 0.765326 0.382663 0.923888i \(-0.375007\pi\)
0.382663 + 0.923888i \(0.375007\pi\)
\(488\) 1.43377e7 2.72539
\(489\) −8.58395e6 −1.62336
\(490\) 5.79526e6 1.09039
\(491\) −5.31835e6 −0.995573 −0.497786 0.867300i \(-0.665854\pi\)
−0.497786 + 0.867300i \(0.665854\pi\)
\(492\) −1.64944e7 −3.07202
\(493\) 9.33185e6 1.72922
\(494\) 2.72696e6 0.502760
\(495\) 4.61770e6 0.847058
\(496\) −1.19783e7 −2.18621
\(497\) 2.26514e6 0.411343
\(498\) 7.81645e6 1.41233
\(499\) 172551. 0.0310217 0.0155108 0.999880i \(-0.495063\pi\)
0.0155108 + 0.999880i \(0.495063\pi\)
\(500\) 6.19770e6 1.10868
\(501\) 6.03781e6 1.07470
\(502\) −1.78827e7 −3.16719
\(503\) 1.54456e6 0.272198 0.136099 0.990695i \(-0.456543\pi\)
0.136099 + 0.990695i \(0.456543\pi\)
\(504\) −4.88959e6 −0.857425
\(505\) −5.09582e6 −0.889172
\(506\) −2.31885e7 −4.02621
\(507\) −4.63197e6 −0.800288
\(508\) −6.15952e6 −1.05898
\(509\) 3.51269e6 0.600960 0.300480 0.953788i \(-0.402853\pi\)
0.300480 + 0.953788i \(0.402853\pi\)
\(510\) −1.87043e7 −3.18432
\(511\) −4.35941e6 −0.738542
\(512\) −2.74289e6 −0.462416
\(513\) −2.02665e6 −0.340006
\(514\) 3.33879e6 0.557418
\(515\) 2.64408e6 0.439295
\(516\) 2.80249e6 0.463361
\(517\) −2.65007e6 −0.436044
\(518\) 1.31002e7 2.14512
\(519\) 3.62968e6 0.591493
\(520\) −1.34849e7 −2.18695
\(521\) −1.33669e6 −0.215743 −0.107871 0.994165i \(-0.534403\pi\)
−0.107871 + 0.994165i \(0.534403\pi\)
\(522\) 7.08082e6 1.13739
\(523\) −1.35607e6 −0.216784 −0.108392 0.994108i \(-0.534570\pi\)
−0.108392 + 0.994108i \(0.534570\pi\)
\(524\) −4.76679e6 −0.758399
\(525\) −3.69168e6 −0.584556
\(526\) −3.65728e6 −0.576359
\(527\) −5.00278e6 −0.784666
\(528\) −3.96437e7 −6.18855
\(529\) 3.58627e6 0.557191
\(530\) −5.00759e6 −0.774354
\(531\) 3.24928e6 0.500092
\(532\) −5.89121e6 −0.902455
\(533\) −3.75073e6 −0.571870
\(534\) −6.04943e6 −0.918039
\(535\) 3.49302e6 0.527615
\(536\) −3.14404e7 −4.72690
\(537\) 1.30445e6 0.195205
\(538\) 9.26678e6 1.38030
\(539\) 5.13003e6 0.760585
\(540\) 1.63566e7 2.41385
\(541\) 1.28068e6 0.188125 0.0940625 0.995566i \(-0.470015\pi\)
0.0940625 + 0.995566i \(0.470015\pi\)
\(542\) 1.59785e7 2.33636
\(543\) 2.03727e6 0.296516
\(544\) 2.17371e7 3.14923
\(545\) 5.47866e6 0.790103
\(546\) −6.53068e6 −0.937512
\(547\) 1.13222e7 1.61793 0.808967 0.587854i \(-0.200027\pi\)
0.808967 + 0.587854i \(0.200027\pi\)
\(548\) −1.95606e6 −0.278248
\(549\) 2.47343e6 0.350243
\(550\) −1.52782e7 −2.15361
\(551\) 5.22721e6 0.733485
\(552\) 3.14768e7 4.39687
\(553\) −1.72661e6 −0.240093
\(554\) −4.23928e6 −0.586838
\(555\) 1.67938e7 2.31428
\(556\) 1.94166e7 2.66371
\(557\) −1.13494e7 −1.55002 −0.775008 0.631952i \(-0.782254\pi\)
−0.775008 + 0.631952i \(0.782254\pi\)
\(558\) −3.79601e6 −0.516110
\(559\) 637267. 0.0862566
\(560\) 2.20004e7 2.96457
\(561\) −1.65573e7 −2.22117
\(562\) 2.35147e7 3.14050
\(563\) −8.01199e6 −1.06529 −0.532647 0.846338i \(-0.678802\pi\)
−0.532647 + 0.846338i \(0.678802\pi\)
\(564\) 5.87112e6 0.777182
\(565\) 1.53148e7 2.01832
\(566\) 6.02401e6 0.790395
\(567\) 7.04571e6 0.920380
\(568\) −1.27251e7 −1.65497
\(569\) −6.18179e6 −0.800448 −0.400224 0.916417i \(-0.631068\pi\)
−0.400224 + 0.916417i \(0.631068\pi\)
\(570\) −1.04772e7 −1.35069
\(571\) 4.84960e6 0.622466 0.311233 0.950334i \(-0.399258\pi\)
0.311233 + 0.950334i \(0.399258\pi\)
\(572\) −1.94823e7 −2.48971
\(573\) 1.13913e7 1.44939
\(574\) 1.12411e7 1.42406
\(575\) 6.60361e6 0.832937
\(576\) 7.04191e6 0.884371
\(577\) −1.20012e6 −0.150067 −0.0750335 0.997181i \(-0.523906\pi\)
−0.0750335 + 0.997181i \(0.523906\pi\)
\(578\) 3.43414e6 0.427561
\(579\) −1.33052e7 −1.64939
\(580\) −4.21875e7 −5.20732
\(581\) −3.83984e6 −0.471925
\(582\) 4.42374e6 0.541355
\(583\) −4.43278e6 −0.540138
\(584\) 2.44903e7 2.97141
\(585\) −2.32631e6 −0.281047
\(586\) 2.40748e7 2.89614
\(587\) 2.03492e6 0.243754 0.121877 0.992545i \(-0.461109\pi\)
0.121877 + 0.992545i \(0.461109\pi\)
\(588\) −1.13654e7 −1.35563
\(589\) −2.80229e6 −0.332832
\(590\) −2.68568e7 −3.17632
\(591\) 5.02226e6 0.591467
\(592\) −4.00622e7 −4.69819
\(593\) −1.38521e7 −1.61762 −0.808812 0.588067i \(-0.799889\pi\)
−0.808812 + 0.588067i \(0.799889\pi\)
\(594\) 2.00867e7 2.33584
\(595\) 9.18853e6 1.06403
\(596\) 1.95541e7 2.25487
\(597\) −5.76411e6 −0.661906
\(598\) 1.16819e7 1.33586
\(599\) −1.64523e7 −1.87352 −0.936760 0.349972i \(-0.886191\pi\)
−0.936760 + 0.349972i \(0.886191\pi\)
\(600\) 2.07392e7 2.35187
\(601\) 1.48314e7 1.67493 0.837465 0.546491i \(-0.184037\pi\)
0.837465 + 0.546491i \(0.184037\pi\)
\(602\) −1.90992e6 −0.214795
\(603\) −5.42388e6 −0.607459
\(604\) −8.82862e6 −0.984692
\(605\) −2.21606e7 −2.46147
\(606\) 1.38641e7 1.53360
\(607\) −1.64197e7 −1.80881 −0.904404 0.426677i \(-0.859684\pi\)
−0.904404 + 0.426677i \(0.859684\pi\)
\(608\) 1.21760e7 1.33581
\(609\) −1.25184e7 −1.36775
\(610\) −2.04441e7 −2.22456
\(611\) 1.33505e6 0.144676
\(612\) 1.01927e7 1.10005
\(613\) 8.77423e6 0.943100 0.471550 0.881839i \(-0.343695\pi\)
0.471550 + 0.881839i \(0.343695\pi\)
\(614\) 2.29966e7 2.46175
\(615\) 1.44106e7 1.53636
\(616\) 3.57756e7 3.79871
\(617\) 1.23910e7 1.31037 0.655183 0.755470i \(-0.272591\pi\)
0.655183 + 0.755470i \(0.272591\pi\)
\(618\) −7.19372e6 −0.757674
\(619\) −1.58048e6 −0.165791 −0.0828957 0.996558i \(-0.526417\pi\)
−0.0828957 + 0.996558i \(0.526417\pi\)
\(620\) 2.26166e7 2.36292
\(621\) −8.68193e6 −0.903415
\(622\) −2.79846e7 −2.90030
\(623\) 2.97179e6 0.306760
\(624\) 1.99718e7 2.05331
\(625\) −1.19331e7 −1.22195
\(626\) 1.03712e7 1.05777
\(627\) −9.27451e6 −0.942155
\(628\) 2.61103e7 2.64188
\(629\) −1.67321e7 −1.68625
\(630\) 6.97208e6 0.699859
\(631\) −3.95881e6 −0.395814 −0.197907 0.980221i \(-0.563414\pi\)
−0.197907 + 0.980221i \(0.563414\pi\)
\(632\) 9.69974e6 0.965979
\(633\) −9.91606e6 −0.983626
\(634\) 3.09817e6 0.306113
\(635\) 5.38135e6 0.529611
\(636\) 9.82065e6 0.962714
\(637\) −2.58441e6 −0.252356
\(638\) −5.18082e7 −5.03903
\(639\) −2.19525e6 −0.212682
\(640\) −2.01459e7 −1.94418
\(641\) 8.19225e6 0.787514 0.393757 0.919215i \(-0.371175\pi\)
0.393757 + 0.919215i \(0.371175\pi\)
\(642\) −9.50343e6 −0.910003
\(643\) −9.53703e6 −0.909674 −0.454837 0.890575i \(-0.650303\pi\)
−0.454837 + 0.890575i \(0.650303\pi\)
\(644\) −2.52372e7 −2.39788
\(645\) −2.44843e6 −0.231733
\(646\) 1.04387e7 0.984155
\(647\) −1.17034e7 −1.09913 −0.549566 0.835450i \(-0.685207\pi\)
−0.549566 + 0.835450i \(0.685207\pi\)
\(648\) −3.95815e7 −3.70301
\(649\) −2.37740e7 −2.21559
\(650\) 7.69690e6 0.714549
\(651\) 6.71110e6 0.620642
\(652\) −3.86638e7 −3.56193
\(653\) 9.87401e6 0.906172 0.453086 0.891467i \(-0.350323\pi\)
0.453086 + 0.891467i \(0.350323\pi\)
\(654\) −1.49057e7 −1.36273
\(655\) 4.16457e6 0.379286
\(656\) −3.43769e7 −3.11894
\(657\) 4.22490e6 0.381859
\(658\) −4.00122e6 −0.360270
\(659\) 1.87688e7 1.68354 0.841770 0.539836i \(-0.181514\pi\)
0.841770 + 0.539836i \(0.181514\pi\)
\(660\) 7.48523e7 6.68876
\(661\) 1.84811e6 0.164522 0.0822612 0.996611i \(-0.473786\pi\)
0.0822612 + 0.996611i \(0.473786\pi\)
\(662\) 2.93838e7 2.60593
\(663\) 8.34125e6 0.736966
\(664\) 2.15715e7 1.89872
\(665\) 5.14693e6 0.451330
\(666\) −1.26960e7 −1.10912
\(667\) 2.23927e7 1.94891
\(668\) 2.71955e7 2.35806
\(669\) −4.25317e6 −0.367407
\(670\) 4.48310e7 3.85826
\(671\) −1.80974e7 −1.55171
\(672\) −2.91598e7 −2.49093
\(673\) −3.40289e6 −0.289608 −0.144804 0.989460i \(-0.546255\pi\)
−0.144804 + 0.989460i \(0.546255\pi\)
\(674\) −1.11149e7 −0.942445
\(675\) −5.72028e6 −0.483234
\(676\) −2.08633e7 −1.75597
\(677\) 2.23309e7 1.87255 0.936276 0.351266i \(-0.114249\pi\)
0.936276 + 0.351266i \(0.114249\pi\)
\(678\) −4.16668e7 −3.48109
\(679\) −2.17317e6 −0.180892
\(680\) −5.16194e7 −4.28096
\(681\) −2.55520e7 −2.11134
\(682\) 2.77743e7 2.28655
\(683\) 7.78181e6 0.638306 0.319153 0.947703i \(-0.396602\pi\)
0.319153 + 0.947703i \(0.396602\pi\)
\(684\) 5.70944e6 0.466609
\(685\) 1.70894e6 0.139155
\(686\) 2.51064e7 2.03692
\(687\) −1.03663e7 −0.837977
\(688\) 5.84082e6 0.470438
\(689\) 2.23315e6 0.179213
\(690\) −4.48829e7 −3.58888
\(691\) 2.39450e7 1.90775 0.953873 0.300211i \(-0.0970570\pi\)
0.953873 + 0.300211i \(0.0970570\pi\)
\(692\) 1.63488e7 1.29784
\(693\) 6.17176e6 0.488176
\(694\) −2.00612e7 −1.58109
\(695\) −1.69636e7 −1.33216
\(696\) 7.03262e7 5.50293
\(697\) −1.43576e7 −1.11944
\(698\) 500120. 0.0388540
\(699\) 4.35762e6 0.337331
\(700\) −1.66281e7 −1.28262
\(701\) −6.24393e6 −0.479914 −0.239957 0.970784i \(-0.577133\pi\)
−0.239957 + 0.970784i \(0.577133\pi\)
\(702\) −1.01193e7 −0.775011
\(703\) −9.37242e6 −0.715259
\(704\) −5.15235e7 −3.91809
\(705\) −5.12938e6 −0.388680
\(706\) 6.88439e6 0.519821
\(707\) −6.81079e6 −0.512447
\(708\) 5.26703e7 3.94896
\(709\) −9.29599e6 −0.694513 −0.347256 0.937770i \(-0.612887\pi\)
−0.347256 + 0.937770i \(0.612887\pi\)
\(710\) 1.81448e7 1.35085
\(711\) 1.67333e6 0.124139
\(712\) −1.66950e7 −1.23420
\(713\) −1.20047e7 −0.884355
\(714\) −2.49991e7 −1.83518
\(715\) 1.70209e7 1.24514
\(716\) 5.87549e6 0.428313
\(717\) 2.41172e7 1.75198
\(718\) 3.86980e6 0.280142
\(719\) 1.77934e7 1.28362 0.641811 0.766863i \(-0.278184\pi\)
0.641811 + 0.766863i \(0.278184\pi\)
\(720\) −2.13216e7 −1.53281
\(721\) 3.53393e6 0.253174
\(722\) −2.06627e7 −1.47518
\(723\) 1.90124e7 1.35267
\(724\) 9.17626e6 0.650608
\(725\) 1.47539e7 1.04247
\(726\) 6.02922e7 4.24541
\(727\) −1.60920e7 −1.12921 −0.564604 0.825362i \(-0.690971\pi\)
−0.564604 + 0.825362i \(0.690971\pi\)
\(728\) −1.80231e7 −1.26038
\(729\) 5.39607e6 0.376061
\(730\) −3.49208e7 −2.42536
\(731\) 2.43943e6 0.168848
\(732\) 4.00940e7 2.76568
\(733\) 2.32899e7 1.60106 0.800529 0.599295i \(-0.204552\pi\)
0.800529 + 0.599295i \(0.204552\pi\)
\(734\) −1.20629e7 −0.826441
\(735\) 9.92950e6 0.677968
\(736\) 5.21604e7 3.54933
\(737\) 3.96849e7 2.69126
\(738\) −1.08943e7 −0.736304
\(739\) −1.68335e7 −1.13387 −0.566934 0.823763i \(-0.691871\pi\)
−0.566934 + 0.823763i \(0.691871\pi\)
\(740\) 7.56425e7 5.07793
\(741\) 4.67233e6 0.312599
\(742\) −6.69286e6 −0.446275
\(743\) 5.88483e6 0.391077 0.195538 0.980696i \(-0.437355\pi\)
0.195538 + 0.980696i \(0.437355\pi\)
\(744\) −3.77017e7 −2.49706
\(745\) −1.70837e7 −1.12769
\(746\) −2.12029e7 −1.39492
\(747\) 3.72137e6 0.244006
\(748\) −7.45772e7 −4.87363
\(749\) 4.66858e6 0.304074
\(750\) 1.47317e7 0.956312
\(751\) −2.45954e7 −1.59131 −0.795655 0.605750i \(-0.792873\pi\)
−0.795655 + 0.605750i \(0.792873\pi\)
\(752\) 1.22363e7 0.789052
\(753\) −3.06400e7 −1.96925
\(754\) 2.61000e7 1.67191
\(755\) 7.71324e6 0.492458
\(756\) 2.18613e7 1.39114
\(757\) 1.55533e7 0.986467 0.493233 0.869897i \(-0.335815\pi\)
0.493233 + 0.869897i \(0.335815\pi\)
\(758\) −9.31676e6 −0.588969
\(759\) −3.97309e7 −2.50336
\(760\) −2.89145e7 −1.81586
\(761\) −1.20979e7 −0.757264 −0.378632 0.925547i \(-0.623605\pi\)
−0.378632 + 0.925547i \(0.623605\pi\)
\(762\) −1.46410e7 −0.913445
\(763\) 7.32247e6 0.455351
\(764\) 5.13086e7 3.18022
\(765\) −8.90502e6 −0.550150
\(766\) −2.97841e7 −1.83406
\(767\) 1.19769e7 0.735115
\(768\) 1.06019e7 0.648606
\(769\) 6.89705e6 0.420579 0.210289 0.977639i \(-0.432559\pi\)
0.210289 + 0.977639i \(0.432559\pi\)
\(770\) −5.10126e7 −3.10063
\(771\) 5.72063e6 0.346584
\(772\) −5.99291e7 −3.61905
\(773\) 2.76899e7 1.66676 0.833380 0.552701i \(-0.186403\pi\)
0.833380 + 0.552701i \(0.186403\pi\)
\(774\) 1.85099e6 0.111059
\(775\) −7.90953e6 −0.473039
\(776\) 1.22085e7 0.727791
\(777\) 2.24456e7 1.33376
\(778\) 5.37435e7 3.18329
\(779\) −8.04237e6 −0.474833
\(780\) −3.77092e7 −2.21927
\(781\) 1.60620e7 0.942261
\(782\) 4.47179e7 2.61496
\(783\) −1.93973e7 −1.13068
\(784\) −2.36872e7 −1.37633
\(785\) −2.28116e7 −1.32124
\(786\) −1.13305e7 −0.654173
\(787\) 2.46071e6 0.141620 0.0708098 0.997490i \(-0.477442\pi\)
0.0708098 + 0.997490i \(0.477442\pi\)
\(788\) 2.26213e7 1.29778
\(789\) −6.26632e6 −0.358360
\(790\) −1.38309e7 −0.788465
\(791\) 2.04689e7 1.16320
\(792\) −3.46718e7 −1.96410
\(793\) 9.11712e6 0.514843
\(794\) −3.49903e7 −1.96968
\(795\) −8.57993e6 −0.481466
\(796\) −2.59627e7 −1.45234
\(797\) 1.86050e7 1.03749 0.518746 0.854928i \(-0.326399\pi\)
0.518746 + 0.854928i \(0.326399\pi\)
\(798\) −1.40032e7 −0.778431
\(799\) 5.11052e6 0.283203
\(800\) 3.43670e7 1.89853
\(801\) −2.88010e6 −0.158608
\(802\) 3.88928e7 2.13517
\(803\) −3.09123e7 −1.69177
\(804\) −8.79203e7 −4.79677
\(805\) 2.20488e7 1.19921
\(806\) −1.39922e7 −0.758660
\(807\) 1.58776e7 0.858223
\(808\) 3.82617e7 2.06175
\(809\) −2.26776e7 −1.21822 −0.609110 0.793085i \(-0.708473\pi\)
−0.609110 + 0.793085i \(0.708473\pi\)
\(810\) 5.64393e7 3.02252
\(811\) −1.84184e7 −0.983329 −0.491665 0.870785i \(-0.663611\pi\)
−0.491665 + 0.870785i \(0.663611\pi\)
\(812\) −5.63855e7 −3.00108
\(813\) 2.73774e7 1.45267
\(814\) 9.28925e7 4.91382
\(815\) 3.37791e7 1.78137
\(816\) 7.64509e7 4.01936
\(817\) 1.36644e6 0.0716202
\(818\) −5.28162e7 −2.75984
\(819\) −3.10922e6 −0.161973
\(820\) 6.49080e7 3.37104
\(821\) 1.39401e7 0.721783 0.360891 0.932608i \(-0.382472\pi\)
0.360891 + 0.932608i \(0.382472\pi\)
\(822\) −4.64949e6 −0.240008
\(823\) 1.86303e6 0.0958781 0.0479391 0.998850i \(-0.484735\pi\)
0.0479391 + 0.998850i \(0.484735\pi\)
\(824\) −1.98529e7 −1.01861
\(825\) −2.61775e7 −1.33904
\(826\) −3.58953e7 −1.83058
\(827\) 1.84625e7 0.938698 0.469349 0.883013i \(-0.344489\pi\)
0.469349 + 0.883013i \(0.344489\pi\)
\(828\) 2.44585e7 1.23981
\(829\) 6.01093e6 0.303777 0.151889 0.988398i \(-0.451464\pi\)
0.151889 + 0.988398i \(0.451464\pi\)
\(830\) −3.07589e7 −1.54980
\(831\) −7.26353e6 −0.364876
\(832\) 2.59566e7 1.29999
\(833\) −9.89301e6 −0.493987
\(834\) 4.61526e7 2.29763
\(835\) −2.37597e7 −1.17930
\(836\) −4.17742e7 −2.06725
\(837\) 1.03989e7 0.513065
\(838\) 4.42025e6 0.217439
\(839\) −2.60373e7 −1.27700 −0.638500 0.769622i \(-0.720445\pi\)
−0.638500 + 0.769622i \(0.720445\pi\)
\(840\) 6.92461e7 3.38608
\(841\) 2.95191e7 1.43917
\(842\) −2.43213e7 −1.18224
\(843\) 4.02898e7 1.95266
\(844\) −4.46639e7 −2.15824
\(845\) 1.82275e7 0.878184
\(846\) 3.87776e6 0.186275
\(847\) −2.96187e7 −1.41859
\(848\) 2.04677e7 0.977418
\(849\) 1.03214e7 0.491441
\(850\) 2.94634e7 1.39873
\(851\) −4.01503e7 −1.90049
\(852\) −3.55847e7 −1.67944
\(853\) 1.81066e7 0.852050 0.426025 0.904711i \(-0.359914\pi\)
0.426025 + 0.904711i \(0.359914\pi\)
\(854\) −2.73245e7 −1.28206
\(855\) −4.98812e6 −0.233358
\(856\) −2.62272e7 −1.22340
\(857\) 2.48924e7 1.15775 0.578874 0.815417i \(-0.303492\pi\)
0.578874 + 0.815417i \(0.303492\pi\)
\(858\) −4.63087e7 −2.14755
\(859\) −8.53406e6 −0.394614 −0.197307 0.980342i \(-0.563220\pi\)
−0.197307 + 0.980342i \(0.563220\pi\)
\(860\) −1.10282e7 −0.508462
\(861\) 1.92603e7 0.885434
\(862\) −1.47592e7 −0.676541
\(863\) −2.14592e7 −0.980815 −0.490407 0.871493i \(-0.663152\pi\)
−0.490407 + 0.871493i \(0.663152\pi\)
\(864\) −4.51832e7 −2.05917
\(865\) −1.42833e7 −0.649066
\(866\) −4.82555e7 −2.18651
\(867\) 5.88400e6 0.265843
\(868\) 3.02281e7 1.36179
\(869\) −1.22433e7 −0.549981
\(870\) −1.00278e8 −4.49168
\(871\) −1.99925e7 −0.892939
\(872\) −4.11363e7 −1.83203
\(873\) 2.10612e6 0.0935292
\(874\) 2.50486e7 1.10919
\(875\) −7.23698e6 −0.319549
\(876\) 6.84850e7 3.01533
\(877\) 3.45569e7 1.51717 0.758587 0.651572i \(-0.225890\pi\)
0.758587 + 0.651572i \(0.225890\pi\)
\(878\) −2.11544e7 −0.926112
\(879\) 4.12495e7 1.80072
\(880\) 1.56004e8 6.79092
\(881\) 780223. 0.0338672 0.0169336 0.999857i \(-0.494610\pi\)
0.0169336 + 0.999857i \(0.494610\pi\)
\(882\) −7.50662e6 −0.324917
\(883\) −1.51541e7 −0.654077 −0.327039 0.945011i \(-0.606051\pi\)
−0.327039 + 0.945011i \(0.606051\pi\)
\(884\) 3.75706e7 1.61703
\(885\) −4.60161e7 −1.97493
\(886\) −2.95181e7 −1.26329
\(887\) −2.42062e7 −1.03304 −0.516520 0.856275i \(-0.672773\pi\)
−0.516520 + 0.856275i \(0.672773\pi\)
\(888\) −1.26095e8 −5.36619
\(889\) 7.19240e6 0.305225
\(890\) 2.38054e7 1.00740
\(891\) 4.99607e7 2.10831
\(892\) −1.91571e7 −0.806153
\(893\) 2.86265e6 0.120127
\(894\) 4.64793e7 1.94498
\(895\) −5.13320e6 −0.214205
\(896\) −2.69258e7 −1.12047
\(897\) 2.00157e7 0.830594
\(898\) 5.56554e7 2.30312
\(899\) −2.68211e7 −1.10682
\(900\) 1.61150e7 0.663169
\(901\) 8.54840e6 0.350811
\(902\) 7.97101e7 3.26210
\(903\) −3.27243e6 −0.133552
\(904\) −1.14990e8 −4.67994
\(905\) −8.01696e6 −0.325378
\(906\) −2.09853e7 −0.849366
\(907\) −3.38285e7 −1.36541 −0.682706 0.730693i \(-0.739197\pi\)
−0.682706 + 0.730693i \(0.739197\pi\)
\(908\) −1.15091e8 −4.63264
\(909\) 6.60064e6 0.264958
\(910\) 2.56992e7 1.02876
\(911\) −3.51743e7 −1.40420 −0.702101 0.712077i \(-0.747755\pi\)
−0.702101 + 0.712077i \(0.747755\pi\)
\(912\) 4.28238e7 1.70490
\(913\) −2.72281e7 −1.08104
\(914\) 8.40595e7 3.32829
\(915\) −3.50287e7 −1.38315
\(916\) −4.66919e7 −1.83866
\(917\) 5.56612e6 0.218590
\(918\) −3.87362e7 −1.51709
\(919\) 7.15839e6 0.279593 0.139797 0.990180i \(-0.455355\pi\)
0.139797 + 0.990180i \(0.455355\pi\)
\(920\) −1.23866e8 −4.82484
\(921\) 3.94021e7 1.53063
\(922\) 5.65760e6 0.219182
\(923\) −8.09172e6 −0.312634
\(924\) 1.00043e8 3.85486
\(925\) −2.64539e7 −1.01656
\(926\) 8.83615e6 0.338638
\(927\) −3.42489e6 −0.130902
\(928\) 1.16538e8 4.44219
\(929\) −4.60865e7 −1.75200 −0.876000 0.482311i \(-0.839798\pi\)
−0.876000 + 0.482311i \(0.839798\pi\)
\(930\) 5.37589e7 2.03818
\(931\) −5.54154e6 −0.209535
\(932\) 1.96276e7 0.740162
\(933\) −4.79484e7 −1.80331
\(934\) 4.32126e7 1.62085
\(935\) 6.51553e7 2.43737
\(936\) 1.74670e7 0.651671
\(937\) 2.18537e7 0.813160 0.406580 0.913615i \(-0.366721\pi\)
0.406580 + 0.913615i \(0.366721\pi\)
\(938\) 5.99185e7 2.22359
\(939\) 1.77698e7 0.657686
\(940\) −2.31037e7 −0.852829
\(941\) −1.41230e7 −0.519941 −0.259970 0.965617i \(-0.583713\pi\)
−0.259970 + 0.965617i \(0.583713\pi\)
\(942\) 6.20632e7 2.27880
\(943\) −3.44525e7 −1.26166
\(944\) 1.09773e8 4.00927
\(945\) −1.90994e7 −0.695731
\(946\) −1.35431e7 −0.492030
\(947\) −1.31237e6 −0.0475535 −0.0237768 0.999717i \(-0.507569\pi\)
−0.0237768 + 0.999717i \(0.507569\pi\)
\(948\) 2.71245e7 0.980258
\(949\) 1.55730e7 0.561316
\(950\) 1.65038e7 0.593302
\(951\) 5.30836e6 0.190331
\(952\) −6.89916e7 −2.46720
\(953\) 2.64202e7 0.942333 0.471167 0.882044i \(-0.343833\pi\)
0.471167 + 0.882044i \(0.343833\pi\)
\(954\) 6.48636e6 0.230744
\(955\) −4.48264e7 −1.59047
\(956\) 1.08629e8 3.84415
\(957\) −8.87675e7 −3.13310
\(958\) −6.85133e7 −2.41191
\(959\) 2.28407e6 0.0801979
\(960\) −9.97272e7 −3.49249
\(961\) −1.42504e7 −0.497760
\(962\) −4.67975e7 −1.63037
\(963\) −4.52453e6 −0.157220
\(964\) 8.56358e7 2.96799
\(965\) 5.23579e7 1.80994
\(966\) −5.99880e7 −2.06834
\(967\) 1.50682e7 0.518199 0.259099 0.965851i \(-0.416574\pi\)
0.259099 + 0.965851i \(0.416574\pi\)
\(968\) 1.66392e8 5.70747
\(969\) 1.78855e7 0.611914
\(970\) −1.74081e7 −0.594048
\(971\) −5.19475e7 −1.76814 −0.884070 0.467354i \(-0.845207\pi\)
−0.884070 + 0.467354i \(0.845207\pi\)
\(972\) −5.56250e7 −1.88845
\(973\) −2.26725e7 −0.767747
\(974\) 4.28853e7 1.44848
\(975\) 1.31877e7 0.444282
\(976\) 8.35621e7 2.80792
\(977\) −3.80206e7 −1.27433 −0.637166 0.770727i \(-0.719893\pi\)
−0.637166 + 0.770727i \(0.719893\pi\)
\(978\) −9.19025e7 −3.07242
\(979\) 2.10728e7 0.702693
\(980\) 4.47244e7 1.48758
\(981\) −7.09654e6 −0.235437
\(982\) −5.69399e7 −1.88425
\(983\) 4.43240e7 1.46304 0.731518 0.681822i \(-0.238812\pi\)
0.731518 + 0.681822i \(0.238812\pi\)
\(984\) −1.08201e8 −3.56241
\(985\) −1.97633e7 −0.649038
\(986\) 9.99097e7 3.27277
\(987\) −6.85563e6 −0.224003
\(988\) 2.10451e7 0.685896
\(989\) 5.85366e6 0.190299
\(990\) 4.94386e7 1.60316
\(991\) 1.06776e7 0.345373 0.172687 0.984977i \(-0.444755\pi\)
0.172687 + 0.984977i \(0.444755\pi\)
\(992\) −6.24756e7 −2.01573
\(993\) 5.03457e7 1.62028
\(994\) 2.42513e7 0.778518
\(995\) 2.26826e7 0.726333
\(996\) 6.03228e7 1.92679
\(997\) −2.28612e7 −0.728386 −0.364193 0.931324i \(-0.618655\pi\)
−0.364193 + 0.931324i \(0.618655\pi\)
\(998\) 1.84738e6 0.0587124
\(999\) 3.47796e7 1.10258
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 43.6.a.b.1.10 10
3.2 odd 2 387.6.a.e.1.1 10
4.3 odd 2 688.6.a.h.1.3 10
5.4 even 2 1075.6.a.b.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.10 10 1.1 even 1 trivial
387.6.a.e.1.1 10 3.2 odd 2
688.6.a.h.1.3 10 4.3 odd 2
1075.6.a.b.1.1 10 5.4 even 2