Properties

Label 43.6.a.b.1.3
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 1.3
Root \(5.31531\) 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

\(f(q)\) \(=\) \(q-4.31531 q^{2} -23.8469 q^{3} -13.3781 q^{4} -52.5837 q^{5} +102.907 q^{6} -174.859 q^{7} +195.821 q^{8} +325.673 q^{9} +O(q^{10})\) \(q-4.31531 q^{2} -23.8469 q^{3} -13.3781 q^{4} -52.5837 q^{5} +102.907 q^{6} -174.859 q^{7} +195.821 q^{8} +325.673 q^{9} +226.915 q^{10} -447.981 q^{11} +319.027 q^{12} +669.141 q^{13} +754.569 q^{14} +1253.96 q^{15} -416.925 q^{16} -849.648 q^{17} -1405.38 q^{18} -1288.87 q^{19} +703.471 q^{20} +4169.83 q^{21} +1933.18 q^{22} -378.254 q^{23} -4669.71 q^{24} -359.956 q^{25} -2887.55 q^{26} -1971.50 q^{27} +2339.28 q^{28} +765.100 q^{29} -5411.21 q^{30} -7094.59 q^{31} -4467.10 q^{32} +10683.0 q^{33} +3666.49 q^{34} +9194.71 q^{35} -4356.90 q^{36} -7908.22 q^{37} +5561.87 q^{38} -15956.9 q^{39} -10297.0 q^{40} +12855.9 q^{41} -17994.1 q^{42} +1849.00 q^{43} +5993.15 q^{44} -17125.1 q^{45} +1632.28 q^{46} +26785.7 q^{47} +9942.37 q^{48} +13768.5 q^{49} +1553.32 q^{50} +20261.5 q^{51} -8951.86 q^{52} +30000.7 q^{53} +8507.60 q^{54} +23556.5 q^{55} -34240.9 q^{56} +30735.5 q^{57} -3301.64 q^{58} +1247.64 q^{59} -16775.6 q^{60} -48441.4 q^{61} +30615.3 q^{62} -56946.8 q^{63} +32618.5 q^{64} -35185.9 q^{65} -46100.2 q^{66} +67004.8 q^{67} +11366.7 q^{68} +9020.17 q^{69} -39678.0 q^{70} -74553.1 q^{71} +63773.5 q^{72} -18066.8 q^{73} +34126.4 q^{74} +8583.82 q^{75} +17242.7 q^{76} +78333.4 q^{77} +68859.0 q^{78} -63230.5 q^{79} +21923.5 q^{80} -32124.6 q^{81} -55477.3 q^{82} -88066.7 q^{83} -55784.5 q^{84} +44677.6 q^{85} -7979.00 q^{86} -18245.2 q^{87} -87724.0 q^{88} +50373.5 q^{89} +73900.0 q^{90} -117005. q^{91} +5060.33 q^{92} +169184. q^{93} -115588. q^{94} +67773.5 q^{95} +106526. q^{96} +17502.1 q^{97} -59415.5 q^{98} -145895. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.31531 −0.762846 −0.381423 0.924401i \(-0.624566\pi\)
−0.381423 + 0.924401i \(0.624566\pi\)
\(3\) −23.8469 −1.52978 −0.764889 0.644163i \(-0.777206\pi\)
−0.764889 + 0.644163i \(0.777206\pi\)
\(4\) −13.3781 −0.418067
\(5\) −52.5837 −0.940646 −0.470323 0.882494i \(-0.655863\pi\)
−0.470323 + 0.882494i \(0.655863\pi\)
\(6\) 102.907 1.16698
\(7\) −174.859 −1.34878 −0.674391 0.738374i \(-0.735594\pi\)
−0.674391 + 0.738374i \(0.735594\pi\)
\(8\) 195.821 1.08177
\(9\) 325.673 1.34022
\(10\) 226.915 0.717567
\(11\) −447.981 −1.11629 −0.558147 0.829742i \(-0.688487\pi\)
−0.558147 + 0.829742i \(0.688487\pi\)
\(12\) 319.027 0.639549
\(13\) 669.141 1.09814 0.549072 0.835775i \(-0.314981\pi\)
0.549072 + 0.835775i \(0.314981\pi\)
\(14\) 754.569 1.02891
\(15\) 1253.96 1.43898
\(16\) −416.925 −0.407154
\(17\) −849.648 −0.713045 −0.356522 0.934287i \(-0.616038\pi\)
−0.356522 + 0.934287i \(0.616038\pi\)
\(18\) −1405.38 −1.02238
\(19\) −1288.87 −0.819078 −0.409539 0.912293i \(-0.634310\pi\)
−0.409539 + 0.912293i \(0.634310\pi\)
\(20\) 703.471 0.393253
\(21\) 4169.83 2.06334
\(22\) 1933.18 0.851559
\(23\) −378.254 −0.149095 −0.0745476 0.997217i \(-0.523751\pi\)
−0.0745476 + 0.997217i \(0.523751\pi\)
\(24\) −4669.71 −1.65486
\(25\) −359.956 −0.115186
\(26\) −2887.55 −0.837715
\(27\) −1971.50 −0.520459
\(28\) 2339.28 0.563881
\(29\) 765.100 0.168936 0.0844682 0.996426i \(-0.473081\pi\)
0.0844682 + 0.996426i \(0.473081\pi\)
\(30\) −5411.21 −1.09772
\(31\) −7094.59 −1.32594 −0.662969 0.748647i \(-0.730704\pi\)
−0.662969 + 0.748647i \(0.730704\pi\)
\(32\) −4467.10 −0.771170
\(33\) 10683.0 1.70768
\(34\) 3666.49 0.543943
\(35\) 9194.71 1.26873
\(36\) −4356.90 −0.560301
\(37\) −7908.22 −0.949674 −0.474837 0.880074i \(-0.657493\pi\)
−0.474837 + 0.880074i \(0.657493\pi\)
\(38\) 5561.87 0.624830
\(39\) −15956.9 −1.67992
\(40\) −10297.0 −1.01756
\(41\) 12855.9 1.19438 0.597192 0.802098i \(-0.296283\pi\)
0.597192 + 0.802098i \(0.296283\pi\)
\(42\) −17994.1 −1.57401
\(43\) 1849.00 0.152499
\(44\) 5993.15 0.466685
\(45\) −17125.1 −1.26067
\(46\) 1632.28 0.113737
\(47\) 26785.7 1.76871 0.884357 0.466811i \(-0.154597\pi\)
0.884357 + 0.466811i \(0.154597\pi\)
\(48\) 9942.37 0.622855
\(49\) 13768.5 0.819215
\(50\) 1553.32 0.0878690
\(51\) 20261.5 1.09080
\(52\) −8951.86 −0.459098
\(53\) 30000.7 1.46704 0.733520 0.679668i \(-0.237876\pi\)
0.733520 + 0.679668i \(0.237876\pi\)
\(54\) 8507.60 0.397030
\(55\) 23556.5 1.05004
\(56\) −34240.9 −1.45907
\(57\) 30735.5 1.25301
\(58\) −3301.64 −0.128872
\(59\) 1247.64 0.0466614 0.0233307 0.999728i \(-0.492573\pi\)
0.0233307 + 0.999728i \(0.492573\pi\)
\(60\) −16775.6 −0.601589
\(61\) −48441.4 −1.66683 −0.833417 0.552644i \(-0.813619\pi\)
−0.833417 + 0.552644i \(0.813619\pi\)
\(62\) 30615.3 1.01149
\(63\) −56946.8 −1.80766
\(64\) 32618.5 0.995438
\(65\) −35185.9 −1.03296
\(66\) −46100.2 −1.30270
\(67\) 67004.8 1.82356 0.911778 0.410683i \(-0.134710\pi\)
0.911778 + 0.410683i \(0.134710\pi\)
\(68\) 11366.7 0.298100
\(69\) 9020.17 0.228082
\(70\) −39678.0 −0.967842
\(71\) −74553.1 −1.75517 −0.877587 0.479418i \(-0.840848\pi\)
−0.877587 + 0.479418i \(0.840848\pi\)
\(72\) 63773.5 1.44980
\(73\) −18066.8 −0.396802 −0.198401 0.980121i \(-0.563575\pi\)
−0.198401 + 0.980121i \(0.563575\pi\)
\(74\) 34126.4 0.724454
\(75\) 8583.82 0.176209
\(76\) 17242.7 0.342429
\(77\) 78333.4 1.50564
\(78\) 68859.0 1.28152
\(79\) −63230.5 −1.13988 −0.569939 0.821687i \(-0.693033\pi\)
−0.569939 + 0.821687i \(0.693033\pi\)
\(80\) 21923.5 0.382987
\(81\) −32124.6 −0.544033
\(82\) −55477.3 −0.911131
\(83\) −88066.7 −1.40319 −0.701595 0.712576i \(-0.747528\pi\)
−0.701595 + 0.712576i \(0.747528\pi\)
\(84\) −55784.5 −0.862612
\(85\) 44677.6 0.670723
\(86\) −7979.00 −0.116333
\(87\) −18245.2 −0.258435
\(88\) −87724.0 −1.20757
\(89\) 50373.5 0.674104 0.337052 0.941486i \(-0.390570\pi\)
0.337052 + 0.941486i \(0.390570\pi\)
\(90\) 73900.0 0.961697
\(91\) −117005. −1.48116
\(92\) 5060.33 0.0623317
\(93\) 169184. 2.02839
\(94\) −115588. −1.34926
\(95\) 67773.5 0.770462
\(96\) 106526. 1.17972
\(97\) 17502.1 0.188869 0.0944345 0.995531i \(-0.469896\pi\)
0.0944345 + 0.995531i \(0.469896\pi\)
\(98\) −59415.5 −0.624934
\(99\) −145895. −1.49608
\(100\) 4815.54 0.0481554
\(101\) 182669. 1.78181 0.890906 0.454188i \(-0.150071\pi\)
0.890906 + 0.454188i \(0.150071\pi\)
\(102\) −87434.4 −0.832112
\(103\) −110578. −1.02702 −0.513508 0.858085i \(-0.671654\pi\)
−0.513508 + 0.858085i \(0.671654\pi\)
\(104\) 131032. 1.18794
\(105\) −219265. −1.94087
\(106\) −129462. −1.11913
\(107\) −43935.4 −0.370984 −0.185492 0.982646i \(-0.559388\pi\)
−0.185492 + 0.982646i \(0.559388\pi\)
\(108\) 26374.9 0.217586
\(109\) −78170.4 −0.630197 −0.315098 0.949059i \(-0.602038\pi\)
−0.315098 + 0.949059i \(0.602038\pi\)
\(110\) −101654. −0.801015
\(111\) 188586. 1.45279
\(112\) 72903.0 0.549162
\(113\) 23097.5 0.170165 0.0850823 0.996374i \(-0.472885\pi\)
0.0850823 + 0.996374i \(0.472885\pi\)
\(114\) −132633. −0.955850
\(115\) 19890.0 0.140246
\(116\) −10235.6 −0.0706267
\(117\) 217921. 1.47175
\(118\) −5383.93 −0.0355955
\(119\) 148568. 0.961743
\(120\) 245550. 1.55664
\(121\) 39636.3 0.246110
\(122\) 209040. 1.27154
\(123\) −306574. −1.82714
\(124\) 94912.4 0.554330
\(125\) 183252. 1.04899
\(126\) 245743. 1.37897
\(127\) 218127. 1.20005 0.600027 0.799980i \(-0.295156\pi\)
0.600027 + 0.799980i \(0.295156\pi\)
\(128\) 2188.25 0.0118052
\(129\) −44092.9 −0.233289
\(130\) 151838. 0.787993
\(131\) 107160. 0.545575 0.272787 0.962074i \(-0.412054\pi\)
0.272787 + 0.962074i \(0.412054\pi\)
\(132\) −142918. −0.713924
\(133\) 225370. 1.10476
\(134\) −289146. −1.39109
\(135\) 103668. 0.489567
\(136\) −166379. −0.771348
\(137\) −168770. −0.768234 −0.384117 0.923284i \(-0.625494\pi\)
−0.384117 + 0.923284i \(0.625494\pi\)
\(138\) −38924.8 −0.173992
\(139\) 294636. 1.29345 0.646725 0.762723i \(-0.276138\pi\)
0.646725 + 0.762723i \(0.276138\pi\)
\(140\) −123008. −0.530412
\(141\) −638754. −2.70574
\(142\) 321720. 1.33893
\(143\) −299763. −1.22585
\(144\) −135781. −0.545675
\(145\) −40231.8 −0.158909
\(146\) 77963.8 0.302699
\(147\) −328337. −1.25322
\(148\) 105797. 0.397027
\(149\) 121995. 0.450169 0.225084 0.974339i \(-0.427734\pi\)
0.225084 + 0.974339i \(0.427734\pi\)
\(150\) −37041.8 −0.134420
\(151\) −515468. −1.83975 −0.919877 0.392208i \(-0.871711\pi\)
−0.919877 + 0.392208i \(0.871711\pi\)
\(152\) −252387. −0.886050
\(153\) −276708. −0.955636
\(154\) −338033. −1.14857
\(155\) 373060. 1.24724
\(156\) 213474. 0.702317
\(157\) 178197. 0.576969 0.288484 0.957485i \(-0.406849\pi\)
0.288484 + 0.957485i \(0.406849\pi\)
\(158\) 272859. 0.869552
\(159\) −715423. −2.24424
\(160\) 234896. 0.725398
\(161\) 66140.9 0.201097
\(162\) 138627. 0.415013
\(163\) −111853. −0.329747 −0.164873 0.986315i \(-0.552722\pi\)
−0.164873 + 0.986315i \(0.552722\pi\)
\(164\) −171988. −0.499332
\(165\) −561749. −1.60632
\(166\) 380035. 1.07042
\(167\) −128666. −0.357003 −0.178501 0.983940i \(-0.557125\pi\)
−0.178501 + 0.983940i \(0.557125\pi\)
\(168\) 816538. 2.23205
\(169\) 76457.2 0.205922
\(170\) −192798. −0.511658
\(171\) −419750. −1.09774
\(172\) −24736.2 −0.0637546
\(173\) 553314. 1.40558 0.702792 0.711396i \(-0.251937\pi\)
0.702792 + 0.711396i \(0.251937\pi\)
\(174\) 78733.8 0.197146
\(175\) 62941.4 0.155361
\(176\) 186775. 0.454503
\(177\) −29752.2 −0.0713816
\(178\) −217377. −0.514238
\(179\) −302733. −0.706200 −0.353100 0.935586i \(-0.614872\pi\)
−0.353100 + 0.935586i \(0.614872\pi\)
\(180\) 229102. 0.527044
\(181\) −702706. −1.59433 −0.797164 0.603763i \(-0.793667\pi\)
−0.797164 + 0.603763i \(0.793667\pi\)
\(182\) 504913. 1.12990
\(183\) 1.15518e6 2.54989
\(184\) −74069.9 −0.161286
\(185\) 415843. 0.893306
\(186\) −730080. −1.54735
\(187\) 380627. 0.795967
\(188\) −358342. −0.739440
\(189\) 344733. 0.701986
\(190\) −292464. −0.587743
\(191\) 105355. 0.208965 0.104482 0.994527i \(-0.466681\pi\)
0.104482 + 0.994527i \(0.466681\pi\)
\(192\) −777849. −1.52280
\(193\) 11272.6 0.0217836 0.0108918 0.999941i \(-0.496533\pi\)
0.0108918 + 0.999941i \(0.496533\pi\)
\(194\) −75526.9 −0.144078
\(195\) 839074. 1.58021
\(196\) −184197. −0.342486
\(197\) 44453.7 0.0816098 0.0408049 0.999167i \(-0.487008\pi\)
0.0408049 + 0.999167i \(0.487008\pi\)
\(198\) 629584. 1.14128
\(199\) 1.01040e6 1.80867 0.904333 0.426827i \(-0.140369\pi\)
0.904333 + 0.426827i \(0.140369\pi\)
\(200\) −70486.7 −0.124604
\(201\) −1.59786e6 −2.78963
\(202\) −788273. −1.35925
\(203\) −133784. −0.227858
\(204\) −271060. −0.456027
\(205\) −676013. −1.12349
\(206\) 477180. 0.783455
\(207\) −123187. −0.199820
\(208\) −278982. −0.447114
\(209\) 577390. 0.914331
\(210\) 946196. 1.48058
\(211\) 758827. 1.17337 0.586687 0.809814i \(-0.300432\pi\)
0.586687 + 0.809814i \(0.300432\pi\)
\(212\) −401354. −0.613321
\(213\) 1.77786e6 2.68502
\(214\) 189595. 0.283003
\(215\) −97227.2 −0.143447
\(216\) −386059. −0.563014
\(217\) 1.24055e6 1.78840
\(218\) 337329. 0.480743
\(219\) 430837. 0.607019
\(220\) −315142. −0.438985
\(221\) −568535. −0.783026
\(222\) −813807. −1.10825
\(223\) −517178. −0.696431 −0.348215 0.937415i \(-0.613212\pi\)
−0.348215 + 0.937415i \(0.613212\pi\)
\(224\) 781110. 1.04014
\(225\) −117228. −0.154374
\(226\) −99672.9 −0.129809
\(227\) 627619. 0.808409 0.404205 0.914669i \(-0.367548\pi\)
0.404205 + 0.914669i \(0.367548\pi\)
\(228\) −411184. −0.523840
\(229\) 800425. 1.00863 0.504315 0.863520i \(-0.331745\pi\)
0.504315 + 0.863520i \(0.331745\pi\)
\(230\) −85831.3 −0.106986
\(231\) −1.86801e6 −2.30329
\(232\) 149822. 0.182750
\(233\) 102393. 0.123560 0.0617802 0.998090i \(-0.480322\pi\)
0.0617802 + 0.998090i \(0.480322\pi\)
\(234\) −940397. −1.12272
\(235\) −1.40849e6 −1.66373
\(236\) −16691.0 −0.0195076
\(237\) 1.50785e6 1.74376
\(238\) −641118. −0.733661
\(239\) −879306. −0.995739 −0.497869 0.867252i \(-0.665884\pi\)
−0.497869 + 0.867252i \(0.665884\pi\)
\(240\) −522806. −0.585885
\(241\) 196740. 0.218198 0.109099 0.994031i \(-0.465203\pi\)
0.109099 + 0.994031i \(0.465203\pi\)
\(242\) −171043. −0.187744
\(243\) 1.24514e6 1.35271
\(244\) 648056. 0.696848
\(245\) −724001. −0.770591
\(246\) 1.32296e6 1.39383
\(247\) −862436. −0.899466
\(248\) −1.38927e6 −1.43435
\(249\) 2.10011e6 2.14657
\(250\) −790788. −0.800221
\(251\) −798778. −0.800280 −0.400140 0.916454i \(-0.631038\pi\)
−0.400140 + 0.916454i \(0.631038\pi\)
\(252\) 761841. 0.755724
\(253\) 169451. 0.166434
\(254\) −941287. −0.915456
\(255\) −1.06542e6 −1.02606
\(256\) −1.05324e6 −1.00444
\(257\) −93933.3 −0.0887129 −0.0443565 0.999016i \(-0.514124\pi\)
−0.0443565 + 0.999016i \(0.514124\pi\)
\(258\) 190274. 0.177963
\(259\) 1.38282e6 1.28090
\(260\) 470722. 0.431848
\(261\) 249173. 0.226412
\(262\) −462428. −0.416189
\(263\) −898502. −0.800995 −0.400497 0.916298i \(-0.631163\pi\)
−0.400497 + 0.916298i \(0.631163\pi\)
\(264\) 2.09194e6 1.84731
\(265\) −1.57755e6 −1.37996
\(266\) −972541. −0.842760
\(267\) −1.20125e6 −1.03123
\(268\) −896400. −0.762368
\(269\) −921887. −0.776778 −0.388389 0.921495i \(-0.626968\pi\)
−0.388389 + 0.921495i \(0.626968\pi\)
\(270\) −447361. −0.373464
\(271\) −227722. −0.188357 −0.0941784 0.995555i \(-0.530022\pi\)
−0.0941784 + 0.995555i \(0.530022\pi\)
\(272\) 354240. 0.290319
\(273\) 2.79021e6 2.26584
\(274\) 728294. 0.586044
\(275\) 161253. 0.128581
\(276\) −120673. −0.0953537
\(277\) 1.76180e6 1.37961 0.689806 0.723994i \(-0.257696\pi\)
0.689806 + 0.723994i \(0.257696\pi\)
\(278\) −1.27145e6 −0.986702
\(279\) −2.31052e6 −1.77705
\(280\) 1.80051e6 1.37246
\(281\) −270410. −0.204295 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(282\) 2.75642e6 2.06406
\(283\) 2.04589e6 1.51851 0.759254 0.650795i \(-0.225564\pi\)
0.759254 + 0.650795i \(0.225564\pi\)
\(284\) 997381. 0.733779
\(285\) −1.61619e6 −1.17863
\(286\) 1.29357e6 0.935135
\(287\) −2.24797e6 −1.61096
\(288\) −1.45481e6 −1.03354
\(289\) −697955. −0.491567
\(290\) 173612. 0.121223
\(291\) −417370. −0.288927
\(292\) 241700. 0.165890
\(293\) 1.15172e6 0.783751 0.391875 0.920018i \(-0.371826\pi\)
0.391875 + 0.920018i \(0.371826\pi\)
\(294\) 1.41687e6 0.956010
\(295\) −65605.3 −0.0438919
\(296\) −1.54859e6 −1.02732
\(297\) 883193. 0.580984
\(298\) −526445. −0.343409
\(299\) −253105. −0.163728
\(300\) −114835. −0.0736670
\(301\) −323314. −0.205687
\(302\) 2.22440e6 1.40345
\(303\) −4.35609e6 −2.72578
\(304\) 537363. 0.333490
\(305\) 2.54723e6 1.56790
\(306\) 1.19408e6 0.729003
\(307\) −1.88053e6 −1.13877 −0.569384 0.822072i \(-0.692818\pi\)
−0.569384 + 0.822072i \(0.692818\pi\)
\(308\) −1.04795e6 −0.629456
\(309\) 2.63695e6 1.57111
\(310\) −1.60987e6 −0.951450
\(311\) 1.94805e6 1.14209 0.571043 0.820920i \(-0.306539\pi\)
0.571043 + 0.820920i \(0.306539\pi\)
\(312\) −3.12469e6 −1.81728
\(313\) −944428. −0.544889 −0.272445 0.962171i \(-0.587832\pi\)
−0.272445 + 0.962171i \(0.587832\pi\)
\(314\) −768977. −0.440138
\(315\) 2.99447e6 1.70037
\(316\) 845906. 0.476545
\(317\) 34149.2 0.0190868 0.00954339 0.999954i \(-0.496962\pi\)
0.00954339 + 0.999954i \(0.496962\pi\)
\(318\) 3.08727e6 1.71201
\(319\) −342751. −0.188583
\(320\) −1.71520e6 −0.936354
\(321\) 1.04772e6 0.567522
\(322\) −285418. −0.153406
\(323\) 1.09509e6 0.584039
\(324\) 429767. 0.227442
\(325\) −240861. −0.126491
\(326\) 482682. 0.251546
\(327\) 1.86412e6 0.964061
\(328\) 2.51746e6 1.29204
\(329\) −4.68370e6 −2.38561
\(330\) 2.42412e6 1.22538
\(331\) 1.73996e6 0.872908 0.436454 0.899727i \(-0.356234\pi\)
0.436454 + 0.899727i \(0.356234\pi\)
\(332\) 1.17817e6 0.586627
\(333\) −2.57549e6 −1.27277
\(334\) 555232. 0.272338
\(335\) −3.52336e6 −1.71532
\(336\) −1.73851e6 −0.840095
\(337\) −1.09453e6 −0.524990 −0.262495 0.964933i \(-0.584545\pi\)
−0.262495 + 0.964933i \(0.584545\pi\)
\(338\) −329936. −0.157086
\(339\) −550804. −0.260314
\(340\) −597703. −0.280407
\(341\) 3.17825e6 1.48014
\(342\) 1.81135e6 0.837408
\(343\) 531301. 0.243840
\(344\) 362072. 0.164968
\(345\) −474314. −0.214545
\(346\) −2.38772e6 −1.07224
\(347\) −561799. −0.250471 −0.125236 0.992127i \(-0.539969\pi\)
−0.125236 + 0.992127i \(0.539969\pi\)
\(348\) 244087. 0.108043
\(349\) 2.06827e6 0.908957 0.454478 0.890758i \(-0.349826\pi\)
0.454478 + 0.890758i \(0.349826\pi\)
\(350\) −271611. −0.118516
\(351\) −1.31921e6 −0.571539
\(352\) 2.00118e6 0.860852
\(353\) 568169. 0.242684 0.121342 0.992611i \(-0.461280\pi\)
0.121342 + 0.992611i \(0.461280\pi\)
\(354\) 128390. 0.0544531
\(355\) 3.92028e6 1.65100
\(356\) −673903. −0.281821
\(357\) −3.54289e6 −1.47125
\(358\) 1.30639e6 0.538722
\(359\) 2.57455e6 1.05430 0.527151 0.849771i \(-0.323260\pi\)
0.527151 + 0.849771i \(0.323260\pi\)
\(360\) −3.35345e6 −1.36375
\(361\) −814914. −0.329112
\(362\) 3.03239e6 1.21623
\(363\) −945202. −0.376494
\(364\) 1.56531e6 0.619223
\(365\) 950019. 0.373250
\(366\) −4.98494e6 −1.94517
\(367\) 272102. 0.105455 0.0527274 0.998609i \(-0.483209\pi\)
0.0527274 + 0.998609i \(0.483209\pi\)
\(368\) 157704. 0.0607047
\(369\) 4.18683e6 1.60074
\(370\) −1.79449e6 −0.681455
\(371\) −5.24589e6 −1.97872
\(372\) −2.26336e6 −0.848002
\(373\) −268967. −0.100098 −0.0500491 0.998747i \(-0.515938\pi\)
−0.0500491 + 0.998747i \(0.515938\pi\)
\(374\) −1.64252e6 −0.607200
\(375\) −4.36998e6 −1.60473
\(376\) 5.24518e6 1.91333
\(377\) 511960. 0.185517
\(378\) −1.48763e6 −0.535507
\(379\) −522052. −0.186688 −0.0933438 0.995634i \(-0.529756\pi\)
−0.0933438 + 0.995634i \(0.529756\pi\)
\(380\) −906683. −0.322104
\(381\) −5.20166e6 −1.83582
\(382\) −454640. −0.159408
\(383\) 2.00529e6 0.698523 0.349262 0.937025i \(-0.386432\pi\)
0.349262 + 0.937025i \(0.386432\pi\)
\(384\) −52183.0 −0.0180593
\(385\) −4.11906e6 −1.41627
\(386\) −48644.5 −0.0166175
\(387\) 602170. 0.204381
\(388\) −234145. −0.0789598
\(389\) −1.10827e6 −0.371340 −0.185670 0.982612i \(-0.559446\pi\)
−0.185670 + 0.982612i \(0.559446\pi\)
\(390\) −3.62086e6 −1.20545
\(391\) 321383. 0.106312
\(392\) 2.69616e6 0.886198
\(393\) −2.55543e6 −0.834608
\(394\) −191831. −0.0622557
\(395\) 3.32489e6 1.07222
\(396\) 1.95181e6 0.625460
\(397\) −3.77816e6 −1.20311 −0.601554 0.798832i \(-0.705452\pi\)
−0.601554 + 0.798832i \(0.705452\pi\)
\(398\) −4.36016e6 −1.37973
\(399\) −5.37437e6 −1.69003
\(400\) 150075. 0.0468983
\(401\) 1.64922e6 0.512173 0.256086 0.966654i \(-0.417567\pi\)
0.256086 + 0.966654i \(0.417567\pi\)
\(402\) 6.89524e6 2.12806
\(403\) −4.74729e6 −1.45607
\(404\) −2.44377e6 −0.744916
\(405\) 1.68923e6 0.511742
\(406\) 577320. 0.173821
\(407\) 3.54273e6 1.06011
\(408\) 3.96761e6 1.17999
\(409\) −2.14199e6 −0.633153 −0.316577 0.948567i \(-0.602533\pi\)
−0.316577 + 0.948567i \(0.602533\pi\)
\(410\) 2.91720e6 0.857051
\(411\) 4.02463e6 1.17523
\(412\) 1.47933e6 0.429361
\(413\) −218160. −0.0629361
\(414\) 531590. 0.152432
\(415\) 4.63087e6 1.31990
\(416\) −2.98912e6 −0.846857
\(417\) −7.02616e6 −1.97869
\(418\) −2.49161e6 −0.697493
\(419\) 6.49479e6 1.80730 0.903650 0.428272i \(-0.140877\pi\)
0.903650 + 0.428272i \(0.140877\pi\)
\(420\) 2.93336e6 0.811413
\(421\) 3.30359e6 0.908408 0.454204 0.890898i \(-0.349924\pi\)
0.454204 + 0.890898i \(0.349924\pi\)
\(422\) −3.27457e6 −0.895103
\(423\) 8.72337e6 2.37046
\(424\) 5.87476e6 1.58699
\(425\) 305836. 0.0821327
\(426\) −7.67200e6 −2.04826
\(427\) 8.47040e6 2.24820
\(428\) 587773. 0.155096
\(429\) 7.14841e6 1.87528
\(430\) 419565. 0.109428
\(431\) −2.23343e6 −0.579133 −0.289567 0.957158i \(-0.593511\pi\)
−0.289567 + 0.957158i \(0.593511\pi\)
\(432\) 821966. 0.211907
\(433\) −3.81775e6 −0.978561 −0.489280 0.872127i \(-0.662741\pi\)
−0.489280 + 0.872127i \(0.662741\pi\)
\(434\) −5.35336e6 −1.36427
\(435\) 959402. 0.243096
\(436\) 1.04577e6 0.263464
\(437\) 487520. 0.122121
\(438\) −1.85919e6 −0.463062
\(439\) 4.94254e6 1.22402 0.612011 0.790850i \(-0.290361\pi\)
0.612011 + 0.790850i \(0.290361\pi\)
\(440\) 4.61285e6 1.13589
\(441\) 4.48404e6 1.09793
\(442\) 2.45340e6 0.597328
\(443\) −740033. −0.179160 −0.0895802 0.995980i \(-0.528553\pi\)
−0.0895802 + 0.995980i \(0.528553\pi\)
\(444\) −2.52293e6 −0.607363
\(445\) −2.64882e6 −0.634093
\(446\) 2.23178e6 0.531269
\(447\) −2.90919e6 −0.688658
\(448\) −5.70363e6 −1.34263
\(449\) −1.75356e6 −0.410492 −0.205246 0.978710i \(-0.565799\pi\)
−0.205246 + 0.978710i \(0.565799\pi\)
\(450\) 505874. 0.117764
\(451\) −5.75922e6 −1.33328
\(452\) −309002. −0.0711402
\(453\) 1.22923e7 2.81441
\(454\) −2.70837e6 −0.616692
\(455\) 6.15256e6 1.39325
\(456\) 6.01864e6 1.35546
\(457\) 1.43140e6 0.320605 0.160302 0.987068i \(-0.448753\pi\)
0.160302 + 0.987068i \(0.448753\pi\)
\(458\) −3.45408e6 −0.769429
\(459\) 1.67508e6 0.371110
\(460\) −266091. −0.0586321
\(461\) −8.02421e6 −1.75853 −0.879265 0.476332i \(-0.841966\pi\)
−0.879265 + 0.476332i \(0.841966\pi\)
\(462\) 8.06102e6 1.75705
\(463\) −5.42639e6 −1.17641 −0.588205 0.808712i \(-0.700165\pi\)
−0.588205 + 0.808712i \(0.700165\pi\)
\(464\) −318990. −0.0687831
\(465\) −8.89631e6 −1.90800
\(466\) −441856. −0.0942575
\(467\) −4.68842e6 −0.994796 −0.497398 0.867522i \(-0.665711\pi\)
−0.497398 + 0.867522i \(0.665711\pi\)
\(468\) −2.91538e6 −0.615291
\(469\) −1.17164e7 −2.45958
\(470\) 6.07806e6 1.26917
\(471\) −4.24945e6 −0.882634
\(472\) 244313. 0.0504768
\(473\) −828318. −0.170233
\(474\) −6.50683e6 −1.33022
\(475\) 463936. 0.0943461
\(476\) −1.98757e6 −0.402072
\(477\) 9.77043e6 1.96615
\(478\) 3.79448e6 0.759595
\(479\) 2.64873e6 0.527471 0.263735 0.964595i \(-0.415045\pi\)
0.263735 + 0.964595i \(0.415045\pi\)
\(480\) −5.60154e6 −1.10970
\(481\) −5.29172e6 −1.04288
\(482\) −848994. −0.166451
\(483\) −1.57725e6 −0.307634
\(484\) −530260. −0.102890
\(485\) −920324. −0.177659
\(486\) −5.37318e6 −1.03191
\(487\) 2.23774e6 0.427550 0.213775 0.976883i \(-0.431424\pi\)
0.213775 + 0.976883i \(0.431424\pi\)
\(488\) −9.48583e6 −1.80312
\(489\) 2.66736e6 0.504439
\(490\) 3.12428e6 0.587842
\(491\) 3.10094e6 0.580484 0.290242 0.956953i \(-0.406264\pi\)
0.290242 + 0.956953i \(0.406264\pi\)
\(492\) 4.10138e6 0.763867
\(493\) −650066. −0.120459
\(494\) 3.72168e6 0.686153
\(495\) 7.67172e6 1.40728
\(496\) 2.95792e6 0.539861
\(497\) 1.30363e7 2.36735
\(498\) −9.06264e6 −1.63750
\(499\) 5.58008e6 1.00320 0.501601 0.865099i \(-0.332744\pi\)
0.501601 + 0.865099i \(0.332744\pi\)
\(500\) −2.45157e6 −0.438550
\(501\) 3.06827e6 0.546135
\(502\) 3.44697e6 0.610490
\(503\) 5.10876e6 0.900317 0.450158 0.892949i \(-0.351368\pi\)
0.450158 + 0.892949i \(0.351368\pi\)
\(504\) −1.11513e7 −1.95547
\(505\) −9.60542e6 −1.67605
\(506\) −731231. −0.126963
\(507\) −1.82327e6 −0.315014
\(508\) −2.91814e6 −0.501703
\(509\) 2.93415e6 0.501982 0.250991 0.967989i \(-0.419244\pi\)
0.250991 + 0.967989i \(0.419244\pi\)
\(510\) 4.59762e6 0.782722
\(511\) 3.15914e6 0.535200
\(512\) 4.47501e6 0.754430
\(513\) 2.54100e6 0.426296
\(514\) 405351. 0.0676743
\(515\) 5.81462e6 0.966058
\(516\) 589880. 0.0975303
\(517\) −1.19995e7 −1.97440
\(518\) −5.96729e6 −0.977131
\(519\) −1.31948e7 −2.15023
\(520\) −6.89013e6 −1.11743
\(521\) −9.22452e6 −1.48885 −0.744423 0.667709i \(-0.767275\pi\)
−0.744423 + 0.667709i \(0.767275\pi\)
\(522\) −1.07526e6 −0.172717
\(523\) −4.64359e6 −0.742335 −0.371168 0.928566i \(-0.621042\pi\)
−0.371168 + 0.928566i \(0.621042\pi\)
\(524\) −1.43360e6 −0.228087
\(525\) −1.50095e6 −0.237667
\(526\) 3.87731e6 0.611035
\(527\) 6.02791e6 0.945453
\(528\) −4.45399e6 −0.695288
\(529\) −6.29327e6 −0.977771
\(530\) 6.80761e6 1.05270
\(531\) 406322. 0.0625365
\(532\) −3.01503e6 −0.461862
\(533\) 8.60244e6 1.31161
\(534\) 5.18376e6 0.786669
\(535\) 2.31028e6 0.348964
\(536\) 1.31209e7 1.97266
\(537\) 7.21924e6 1.08033
\(538\) 3.97823e6 0.592562
\(539\) −6.16805e6 −0.914484
\(540\) −1.38689e6 −0.204672
\(541\) 3.62594e6 0.532632 0.266316 0.963886i \(-0.414193\pi\)
0.266316 + 0.963886i \(0.414193\pi\)
\(542\) 982690. 0.143687
\(543\) 1.67573e7 2.43897
\(544\) 3.79546e6 0.549879
\(545\) 4.11049e6 0.592792
\(546\) −1.20406e7 −1.72849
\(547\) −5.56425e6 −0.795131 −0.397565 0.917574i \(-0.630145\pi\)
−0.397565 + 0.917574i \(0.630145\pi\)
\(548\) 2.25782e6 0.321173
\(549\) −1.57761e7 −2.23392
\(550\) −695858. −0.0980876
\(551\) −986114. −0.138372
\(552\) 1.76633e6 0.246732
\(553\) 1.10564e7 1.53745
\(554\) −7.60271e6 −1.05243
\(555\) −9.91656e6 −1.36656
\(556\) −3.94169e6 −0.540748
\(557\) 6.83963e6 0.934103 0.467052 0.884230i \(-0.345316\pi\)
0.467052 + 0.884230i \(0.345316\pi\)
\(558\) 9.97059e6 1.35561
\(559\) 1.23724e6 0.167465
\(560\) −3.83351e6 −0.516567
\(561\) −9.07675e6 −1.21765
\(562\) 1.16690e6 0.155845
\(563\) −5.62439e6 −0.747833 −0.373916 0.927462i \(-0.621985\pi\)
−0.373916 + 0.927462i \(0.621985\pi\)
\(564\) 8.54534e6 1.13118
\(565\) −1.21455e6 −0.160065
\(566\) −8.82866e6 −1.15839
\(567\) 5.61726e6 0.733782
\(568\) −1.45990e7 −1.89869
\(569\) −4.17021e6 −0.539979 −0.269990 0.962863i \(-0.587020\pi\)
−0.269990 + 0.962863i \(0.587020\pi\)
\(570\) 6.97434e6 0.899116
\(571\) −8.60607e6 −1.10462 −0.552312 0.833637i \(-0.686254\pi\)
−0.552312 + 0.833637i \(0.686254\pi\)
\(572\) 4.01027e6 0.512487
\(573\) −2.51239e6 −0.319669
\(574\) 9.70069e6 1.22892
\(575\) 136155. 0.0171737
\(576\) 1.06230e7 1.33410
\(577\) −3.23538e6 −0.404563 −0.202282 0.979327i \(-0.564836\pi\)
−0.202282 + 0.979327i \(0.564836\pi\)
\(578\) 3.01189e6 0.374990
\(579\) −268815. −0.0333240
\(580\) 538226. 0.0664347
\(581\) 1.53992e7 1.89260
\(582\) 1.80108e6 0.220407
\(583\) −1.34398e7 −1.63765
\(584\) −3.53785e6 −0.429247
\(585\) −1.14591e7 −1.38440
\(586\) −4.97003e6 −0.597881
\(587\) −1.12970e7 −1.35322 −0.676609 0.736342i \(-0.736551\pi\)
−0.676609 + 0.736342i \(0.736551\pi\)
\(588\) 4.39253e6 0.523928
\(589\) 9.14401e6 1.08605
\(590\) 283107. 0.0334827
\(591\) −1.06008e6 −0.124845
\(592\) 3.29714e6 0.386663
\(593\) 1.61368e7 1.88444 0.942218 0.335000i \(-0.108736\pi\)
0.942218 + 0.335000i \(0.108736\pi\)
\(594\) −3.81125e6 −0.443201
\(595\) −7.81227e6 −0.904659
\(596\) −1.63206e6 −0.188201
\(597\) −2.40948e7 −2.76686
\(598\) 1.09223e6 0.124899
\(599\) 1.14121e7 1.29957 0.649785 0.760118i \(-0.274859\pi\)
0.649785 + 0.760118i \(0.274859\pi\)
\(600\) 1.68089e6 0.190617
\(601\) 1.15192e7 1.30088 0.650438 0.759559i \(-0.274585\pi\)
0.650438 + 0.759559i \(0.274585\pi\)
\(602\) 1.39520e6 0.156908
\(603\) 2.18217e7 2.44396
\(604\) 6.89600e6 0.769139
\(605\) −2.08422e6 −0.231503
\(606\) 1.87979e7 2.07935
\(607\) 1.48986e7 1.64125 0.820625 0.571466i \(-0.193625\pi\)
0.820625 + 0.571466i \(0.193625\pi\)
\(608\) 5.75751e6 0.631648
\(609\) 3.19034e6 0.348573
\(610\) −1.09921e7 −1.19607
\(611\) 1.79234e7 1.94230
\(612\) 3.70183e6 0.399520
\(613\) −5.39999e6 −0.580419 −0.290210 0.956963i \(-0.593725\pi\)
−0.290210 + 0.956963i \(0.593725\pi\)
\(614\) 8.11508e6 0.868704
\(615\) 1.61208e7 1.71869
\(616\) 1.53393e7 1.62875
\(617\) −1.26228e7 −1.33489 −0.667443 0.744660i \(-0.732611\pi\)
−0.667443 + 0.744660i \(0.732611\pi\)
\(618\) −1.13792e7 −1.19851
\(619\) 1.43557e7 1.50591 0.752953 0.658074i \(-0.228629\pi\)
0.752953 + 0.658074i \(0.228629\pi\)
\(620\) −4.99084e6 −0.521428
\(621\) 745725. 0.0775979
\(622\) −8.40642e6 −0.871235
\(623\) −8.80824e6 −0.909220
\(624\) 6.65285e6 0.683984
\(625\) −8.51120e6 −0.871546
\(626\) 4.07550e6 0.415666
\(627\) −1.37689e7 −1.39872
\(628\) −2.38395e6 −0.241211
\(629\) 6.71920e6 0.677160
\(630\) −1.29221e7 −1.29712
\(631\) −6.76873e6 −0.676759 −0.338379 0.941010i \(-0.609879\pi\)
−0.338379 + 0.941010i \(0.609879\pi\)
\(632\) −1.23818e7 −1.23308
\(633\) −1.80956e7 −1.79500
\(634\) −147364. −0.0145603
\(635\) −1.14699e7 −1.12883
\(636\) 9.57103e6 0.938244
\(637\) 9.21310e6 0.899616
\(638\) 1.47907e6 0.143859
\(639\) −2.42799e7 −2.35232
\(640\) −115066. −0.0111045
\(641\) −1.51643e6 −0.145773 −0.0728867 0.997340i \(-0.523221\pi\)
−0.0728867 + 0.997340i \(0.523221\pi\)
\(642\) −4.52124e6 −0.432932
\(643\) 6.58876e6 0.628458 0.314229 0.949347i \(-0.398254\pi\)
0.314229 + 0.949347i \(0.398254\pi\)
\(644\) −884842. −0.0840719
\(645\) 2.31857e6 0.219442
\(646\) −4.72563e6 −0.445532
\(647\) 9.99129e6 0.938341 0.469171 0.883108i \(-0.344553\pi\)
0.469171 + 0.883108i \(0.344553\pi\)
\(648\) −6.29065e6 −0.588516
\(649\) −558918. −0.0520878
\(650\) 1.03939e6 0.0964929
\(651\) −2.95833e7 −2.73586
\(652\) 1.49639e6 0.137856
\(653\) −1.32714e7 −1.21796 −0.608980 0.793186i \(-0.708421\pi\)
−0.608980 + 0.793186i \(0.708421\pi\)
\(654\) −8.04425e6 −0.735430
\(655\) −5.63486e6 −0.513192
\(656\) −5.35997e6 −0.486298
\(657\) −5.88387e6 −0.531802
\(658\) 2.02116e7 1.81985
\(659\) 3.69381e6 0.331330 0.165665 0.986182i \(-0.447023\pi\)
0.165665 + 0.986182i \(0.447023\pi\)
\(660\) 7.51515e6 0.671549
\(661\) 8.97800e6 0.799238 0.399619 0.916681i \(-0.369142\pi\)
0.399619 + 0.916681i \(0.369142\pi\)
\(662\) −7.50845e6 −0.665894
\(663\) 1.35578e7 1.19786
\(664\) −1.72453e7 −1.51792
\(665\) −1.18508e7 −1.03919
\(666\) 1.11140e7 0.970927
\(667\) −289402. −0.0251876
\(668\) 1.72131e6 0.149251
\(669\) 1.23331e7 1.06538
\(670\) 1.52044e7 1.30852
\(671\) 2.17009e7 1.86068
\(672\) −1.86270e7 −1.59118
\(673\) 8.59992e6 0.731909 0.365954 0.930633i \(-0.380743\pi\)
0.365954 + 0.930633i \(0.380743\pi\)
\(674\) 4.72322e6 0.400487
\(675\) 709651. 0.0599495
\(676\) −1.02285e6 −0.0860889
\(677\) −8.01663e6 −0.672233 −0.336117 0.941820i \(-0.609114\pi\)
−0.336117 + 0.941820i \(0.609114\pi\)
\(678\) 2.37689e6 0.198579
\(679\) −3.06039e6 −0.254743
\(680\) 8.74880e6 0.725565
\(681\) −1.49667e7 −1.23669
\(682\) −1.37151e7 −1.12911
\(683\) 2.81320e6 0.230754 0.115377 0.993322i \(-0.463192\pi\)
0.115377 + 0.993322i \(0.463192\pi\)
\(684\) 5.61547e6 0.458930
\(685\) 8.87454e6 0.722636
\(686\) −2.29273e6 −0.186012
\(687\) −1.90876e7 −1.54298
\(688\) −770895. −0.0620904
\(689\) 2.00747e7 1.61102
\(690\) 2.04681e6 0.163665
\(691\) 1.04922e7 0.835935 0.417967 0.908462i \(-0.362743\pi\)
0.417967 + 0.908462i \(0.362743\pi\)
\(692\) −7.40231e6 −0.587628
\(693\) 2.55111e7 2.01788
\(694\) 2.42434e6 0.191071
\(695\) −1.54931e7 −1.21668
\(696\) −3.57279e6 −0.279566
\(697\) −1.09230e7 −0.851650
\(698\) −8.92521e6 −0.693394
\(699\) −2.44175e6 −0.189020
\(700\) −842038. −0.0649511
\(701\) −2.37537e7 −1.82573 −0.912865 0.408263i \(-0.866135\pi\)
−0.912865 + 0.408263i \(0.866135\pi\)
\(702\) 5.69279e6 0.435996
\(703\) 1.01927e7 0.777856
\(704\) −1.46125e7 −1.11120
\(705\) 3.35880e7 2.54514
\(706\) −2.45182e6 −0.185130
\(707\) −3.19413e7 −2.40328
\(708\) 398029. 0.0298423
\(709\) −1.72000e7 −1.28503 −0.642516 0.766273i \(-0.722109\pi\)
−0.642516 + 0.766273i \(0.722109\pi\)
\(710\) −1.69172e7 −1.25945
\(711\) −2.05925e7 −1.52769
\(712\) 9.86417e6 0.729223
\(713\) 2.68356e6 0.197691
\(714\) 1.52887e7 1.12234
\(715\) 1.57626e7 1.15309
\(716\) 4.05001e6 0.295239
\(717\) 2.09687e7 1.52326
\(718\) −1.11100e7 −0.804270
\(719\) 2.22034e7 1.60176 0.800878 0.598827i \(-0.204366\pi\)
0.800878 + 0.598827i \(0.204366\pi\)
\(720\) 7.13989e6 0.513287
\(721\) 1.93356e7 1.38522
\(722\) 3.51660e6 0.251062
\(723\) −4.69164e6 −0.333794
\(724\) 9.40090e6 0.666535
\(725\) −275402. −0.0194591
\(726\) 4.07884e6 0.287207
\(727\) −1.95017e7 −1.36847 −0.684236 0.729261i \(-0.739864\pi\)
−0.684236 + 0.729261i \(0.739864\pi\)
\(728\) −2.29120e7 −1.60227
\(729\) −2.18865e7 −1.52531
\(730\) −4.09962e6 −0.284732
\(731\) −1.57100e6 −0.108738
\(732\) −1.54541e7 −1.06602
\(733\) 1.07906e7 0.741798 0.370899 0.928673i \(-0.379050\pi\)
0.370899 + 0.928673i \(0.379050\pi\)
\(734\) −1.17420e6 −0.0804457
\(735\) 1.72651e7 1.17883
\(736\) 1.68970e6 0.114978
\(737\) −3.00169e7 −2.03562
\(738\) −1.80675e7 −1.22111
\(739\) −1.44802e7 −0.975358 −0.487679 0.873023i \(-0.662156\pi\)
−0.487679 + 0.873023i \(0.662156\pi\)
\(740\) −5.56321e6 −0.373462
\(741\) 2.05664e7 1.37598
\(742\) 2.26376e7 1.50946
\(743\) 5.44908e6 0.362119 0.181059 0.983472i \(-0.442047\pi\)
0.181059 + 0.983472i \(0.442047\pi\)
\(744\) 3.31297e7 2.19424
\(745\) −6.41493e6 −0.423449
\(746\) 1.16067e6 0.0763594
\(747\) −2.86809e7 −1.88058
\(748\) −5.09207e6 −0.332767
\(749\) 7.68248e6 0.500376
\(750\) 1.88578e7 1.22416
\(751\) −2.78004e6 −0.179867 −0.0899335 0.995948i \(-0.528665\pi\)
−0.0899335 + 0.995948i \(0.528665\pi\)
\(752\) −1.11676e7 −0.720139
\(753\) 1.90484e7 1.22425
\(754\) −2.20926e6 −0.141521
\(755\) 2.71052e7 1.73056
\(756\) −4.61188e6 −0.293477
\(757\) 2.46778e7 1.56519 0.782595 0.622531i \(-0.213895\pi\)
0.782595 + 0.622531i \(0.213895\pi\)
\(758\) 2.25281e6 0.142414
\(759\) −4.04087e6 −0.254607
\(760\) 1.32714e7 0.833459
\(761\) −8.63006e6 −0.540197 −0.270098 0.962833i \(-0.587056\pi\)
−0.270098 + 0.962833i \(0.587056\pi\)
\(762\) 2.24467e7 1.40044
\(763\) 1.36688e7 0.849999
\(764\) −1.40946e6 −0.0873611
\(765\) 1.45503e7 0.898915
\(766\) −8.65345e6 −0.532865
\(767\) 834845. 0.0512410
\(768\) 2.51164e7 1.53657
\(769\) −1.79104e6 −0.109217 −0.0546083 0.998508i \(-0.517391\pi\)
−0.0546083 + 0.998508i \(0.517391\pi\)
\(770\) 1.77750e7 1.08040
\(771\) 2.24002e6 0.135711
\(772\) −150806. −0.00910698
\(773\) −2.64220e7 −1.59044 −0.795219 0.606322i \(-0.792644\pi\)
−0.795219 + 0.606322i \(0.792644\pi\)
\(774\) −2.59855e6 −0.155911
\(775\) 2.55374e6 0.152729
\(776\) 3.42727e6 0.204312
\(777\) −3.29759e7 −1.95950
\(778\) 4.78253e6 0.283275
\(779\) −1.65696e7 −0.978293
\(780\) −1.12252e7 −0.660631
\(781\) 3.33984e7 1.95929
\(782\) −1.38686e6 −0.0810993
\(783\) −1.50839e6 −0.0879244
\(784\) −5.74045e6 −0.333546
\(785\) −9.37028e6 −0.542723
\(786\) 1.10275e7 0.636677
\(787\) 4.11413e6 0.236778 0.118389 0.992967i \(-0.462227\pi\)
0.118389 + 0.992967i \(0.462227\pi\)
\(788\) −594708. −0.0341184
\(789\) 2.14265e7 1.22534
\(790\) −1.43479e7 −0.817940
\(791\) −4.03880e6 −0.229515
\(792\) −2.85693e7 −1.61840
\(793\) −3.24142e7 −1.83043
\(794\) 1.63039e7 0.917786
\(795\) 3.76196e7 2.11104
\(796\) −1.35172e7 −0.756143
\(797\) 3.23381e6 0.180330 0.0901651 0.995927i \(-0.471261\pi\)
0.0901651 + 0.995927i \(0.471261\pi\)
\(798\) 2.31920e7 1.28923
\(799\) −2.27584e7 −1.26117
\(800\) 1.60796e6 0.0888279
\(801\) 1.64053e7 0.903447
\(802\) −7.11687e6 −0.390709
\(803\) 8.09359e6 0.442948
\(804\) 2.13763e7 1.16625
\(805\) −3.47793e6 −0.189161
\(806\) 2.04860e7 1.11076
\(807\) 2.19841e7 1.18830
\(808\) 3.57704e7 1.92750
\(809\) −1.52689e7 −0.820231 −0.410115 0.912034i \(-0.634512\pi\)
−0.410115 + 0.912034i \(0.634512\pi\)
\(810\) −7.28954e6 −0.390380
\(811\) −3.04480e7 −1.62558 −0.812788 0.582560i \(-0.802051\pi\)
−0.812788 + 0.582560i \(0.802051\pi\)
\(812\) 1.78978e6 0.0952600
\(813\) 5.43045e6 0.288144
\(814\) −1.52880e7 −0.808703
\(815\) 5.88167e6 0.310175
\(816\) −8.44751e6 −0.444123
\(817\) −2.38312e6 −0.124908
\(818\) 9.24334e6 0.482998
\(819\) −3.81054e7 −1.98508
\(820\) 9.04378e6 0.469695
\(821\) −2.25035e6 −0.116518 −0.0582590 0.998302i \(-0.518555\pi\)
−0.0582590 + 0.998302i \(0.518555\pi\)
\(822\) −1.73675e7 −0.896516
\(823\) −1.66620e7 −0.857485 −0.428743 0.903427i \(-0.641043\pi\)
−0.428743 + 0.903427i \(0.641043\pi\)
\(824\) −2.16535e7 −1.11099
\(825\) −3.84539e6 −0.196701
\(826\) 941428. 0.0480106
\(827\) 3.70905e7 1.88581 0.942907 0.333056i \(-0.108080\pi\)
0.942907 + 0.333056i \(0.108080\pi\)
\(828\) 1.64801e6 0.0835381
\(829\) 2.88276e7 1.45688 0.728438 0.685111i \(-0.240246\pi\)
0.728438 + 0.685111i \(0.240246\pi\)
\(830\) −1.99836e7 −1.00688
\(831\) −4.20134e7 −2.11050
\(832\) 2.18264e7 1.09313
\(833\) −1.16984e7 −0.584137
\(834\) 3.03200e7 1.50943
\(835\) 6.76572e6 0.335813
\(836\) −7.72439e6 −0.382251
\(837\) 1.39870e7 0.690096
\(838\) −2.80270e7 −1.37869
\(839\) −7.10869e6 −0.348646 −0.174323 0.984689i \(-0.555774\pi\)
−0.174323 + 0.984689i \(0.555774\pi\)
\(840\) −4.29366e7 −2.09957
\(841\) −1.99258e7 −0.971460
\(842\) −1.42560e7 −0.692975
\(843\) 6.44843e6 0.312525
\(844\) −1.01517e7 −0.490548
\(845\) −4.02040e6 −0.193699
\(846\) −3.76440e7 −1.80830
\(847\) −6.93075e6 −0.331949
\(848\) −1.25081e7 −0.597311
\(849\) −4.87882e7 −2.32298
\(850\) −1.31978e6 −0.0626546
\(851\) 2.99131e6 0.141592
\(852\) −2.37844e7 −1.12252
\(853\) 6.01755e6 0.283170 0.141585 0.989926i \(-0.454780\pi\)
0.141585 + 0.989926i \(0.454780\pi\)
\(854\) −3.65524e7 −1.71503
\(855\) 2.20720e7 1.03259
\(856\) −8.60345e6 −0.401317
\(857\) 1.40484e7 0.653392 0.326696 0.945129i \(-0.394065\pi\)
0.326696 + 0.945129i \(0.394065\pi\)
\(858\) −3.08476e7 −1.43055
\(859\) 2.38780e7 1.10412 0.552060 0.833805i \(-0.313842\pi\)
0.552060 + 0.833805i \(0.313842\pi\)
\(860\) 1.30072e6 0.0599704
\(861\) 5.36071e7 2.46442
\(862\) 9.63792e6 0.441789
\(863\) 3.12051e7 1.42626 0.713131 0.701031i \(-0.247277\pi\)
0.713131 + 0.701031i \(0.247277\pi\)
\(864\) 8.80686e6 0.401362
\(865\) −2.90953e7 −1.32216
\(866\) 1.64748e7 0.746491
\(867\) 1.66440e7 0.751988
\(868\) −1.65963e7 −0.747671
\(869\) 2.83261e7 1.27244
\(870\) −4.14011e6 −0.185445
\(871\) 4.48357e7 2.00253
\(872\) −1.53074e7 −0.681725
\(873\) 5.69996e6 0.253126
\(874\) −2.10380e6 −0.0931591
\(875\) −3.20432e7 −1.41487
\(876\) −5.76379e6 −0.253775
\(877\) −2.97111e6 −0.130443 −0.0652213 0.997871i \(-0.520775\pi\)
−0.0652213 + 0.997871i \(0.520775\pi\)
\(878\) −2.13286e7 −0.933739
\(879\) −2.74649e7 −1.19896
\(880\) −9.82131e6 −0.427526
\(881\) 3.55211e7 1.54187 0.770934 0.636915i \(-0.219790\pi\)
0.770934 + 0.636915i \(0.219790\pi\)
\(882\) −1.93500e7 −0.837549
\(883\) 1.87105e7 0.807576 0.403788 0.914853i \(-0.367693\pi\)
0.403788 + 0.914853i \(0.367693\pi\)
\(884\) 7.60593e6 0.327357
\(885\) 1.56448e6 0.0671448
\(886\) 3.19347e6 0.136672
\(887\) 9.33897e6 0.398557 0.199278 0.979943i \(-0.436140\pi\)
0.199278 + 0.979943i \(0.436140\pi\)
\(888\) 3.69291e7 1.57158
\(889\) −3.81415e7 −1.61861
\(890\) 1.14305e7 0.483715
\(891\) 1.43912e7 0.607300
\(892\) 6.91887e6 0.291154
\(893\) −3.45232e7 −1.44871
\(894\) 1.25541e7 0.525340
\(895\) 1.59188e7 0.664284
\(896\) −382635. −0.0159226
\(897\) 6.03577e6 0.250468
\(898\) 7.56715e6 0.313142
\(899\) −5.42807e6 −0.223999
\(900\) 1.56829e6 0.0645387
\(901\) −2.54901e7 −1.04607
\(902\) 2.48528e7 1.01709
\(903\) 7.71002e6 0.314656
\(904\) 4.52297e6 0.184078
\(905\) 3.69509e7 1.49970
\(906\) −5.30451e7 −2.14696
\(907\) 3.89432e7 1.57186 0.785930 0.618315i \(-0.212184\pi\)
0.785930 + 0.618315i \(0.212184\pi\)
\(908\) −8.39637e6 −0.337969
\(909\) 5.94904e7 2.38802
\(910\) −2.65502e7 −1.06283
\(911\) 4.28351e7 1.71003 0.855015 0.518604i \(-0.173548\pi\)
0.855015 + 0.518604i \(0.173548\pi\)
\(912\) −1.28144e7 −0.510166
\(913\) 3.94522e7 1.56637
\(914\) −6.17692e6 −0.244572
\(915\) −6.07435e7 −2.39854
\(916\) −1.07082e7 −0.421675
\(917\) −1.87378e7 −0.735862
\(918\) −7.22847e6 −0.283100
\(919\) 881759. 0.0344398 0.0172199 0.999852i \(-0.494518\pi\)
0.0172199 + 0.999852i \(0.494518\pi\)
\(920\) 3.89487e6 0.151713
\(921\) 4.48448e7 1.74206
\(922\) 3.46269e7 1.34149
\(923\) −4.98866e7 −1.92743
\(924\) 2.49904e7 0.962928
\(925\) 2.84661e6 0.109389
\(926\) 2.34165e7 0.897419
\(927\) −3.60124e7 −1.37643
\(928\) −3.41778e6 −0.130279
\(929\) −1.81365e7 −0.689468 −0.344734 0.938700i \(-0.612031\pi\)
−0.344734 + 0.938700i \(0.612031\pi\)
\(930\) 3.83903e7 1.45551
\(931\) −1.77459e7 −0.671000
\(932\) −1.36982e6 −0.0516565
\(933\) −4.64548e7 −1.74714
\(934\) 2.02320e7 0.758876
\(935\) −2.00148e7 −0.748723
\(936\) 4.26735e7 1.59209
\(937\) −1.75363e7 −0.652512 −0.326256 0.945281i \(-0.605787\pi\)
−0.326256 + 0.945281i \(0.605787\pi\)
\(938\) 5.05597e7 1.87628
\(939\) 2.25217e7 0.833559
\(940\) 1.88429e7 0.695551
\(941\) 7.69478e6 0.283284 0.141642 0.989918i \(-0.454762\pi\)
0.141642 + 0.989918i \(0.454762\pi\)
\(942\) 1.83377e7 0.673313
\(943\) −4.86281e6 −0.178077
\(944\) −520171. −0.0189984
\(945\) −1.81273e7 −0.660320
\(946\) 3.57444e6 0.129862
\(947\) −3.00889e7 −1.09026 −0.545131 0.838351i \(-0.683520\pi\)
−0.545131 + 0.838351i \(0.683520\pi\)
\(948\) −2.01722e7 −0.729008
\(949\) −1.20892e7 −0.435746
\(950\) −2.00203e6 −0.0719715
\(951\) −814352. −0.0291985
\(952\) 2.90927e7 1.04038
\(953\) 2.31755e7 0.826601 0.413301 0.910595i \(-0.364376\pi\)
0.413301 + 0.910595i \(0.364376\pi\)
\(954\) −4.21624e7 −1.49987
\(955\) −5.53997e6 −0.196562
\(956\) 1.17635e7 0.416285
\(957\) 8.17353e6 0.288489
\(958\) −1.14301e7 −0.402379
\(959\) 2.95109e7 1.03618
\(960\) 4.09022e7 1.43241
\(961\) 2.17041e7 0.758112
\(962\) 2.28354e7 0.795556
\(963\) −1.43086e7 −0.497199
\(964\) −2.63202e6 −0.0912212
\(965\) −592752. −0.0204906
\(966\) 6.80633e6 0.234677
\(967\) −3.96944e7 −1.36510 −0.682548 0.730841i \(-0.739128\pi\)
−0.682548 + 0.730841i \(0.739128\pi\)
\(968\) 7.76160e6 0.266234
\(969\) −2.61144e7 −0.893450
\(970\) 3.97148e6 0.135526
\(971\) −6.90625e6 −0.235068 −0.117534 0.993069i \(-0.537499\pi\)
−0.117534 + 0.993069i \(0.537499\pi\)
\(972\) −1.66577e7 −0.565522
\(973\) −5.15197e7 −1.74458
\(974\) −9.65654e6 −0.326155
\(975\) 5.74379e6 0.193503
\(976\) 2.01965e7 0.678658
\(977\) −1.38767e7 −0.465104 −0.232552 0.972584i \(-0.574708\pi\)
−0.232552 + 0.972584i \(0.574708\pi\)
\(978\) −1.15105e7 −0.384809
\(979\) −2.25664e7 −0.752498
\(980\) 9.68578e6 0.322158
\(981\) −2.54580e7 −0.844602
\(982\) −1.33815e7 −0.442819
\(983\) 1.20330e7 0.397183 0.198591 0.980082i \(-0.436363\pi\)
0.198591 + 0.980082i \(0.436363\pi\)
\(984\) −6.00335e7 −1.97654
\(985\) −2.33754e6 −0.0767659
\(986\) 2.80523e6 0.0918918
\(987\) 1.11692e8 3.64945
\(988\) 1.15378e7 0.376037
\(989\) −699391. −0.0227368
\(990\) −3.31058e7 −1.07354
\(991\) 9.67955e6 0.313091 0.156546 0.987671i \(-0.449964\pi\)
0.156546 + 0.987671i \(0.449964\pi\)
\(992\) 3.16922e7 1.02252
\(993\) −4.14925e7 −1.33535
\(994\) −5.62554e7 −1.80592
\(995\) −5.31303e7 −1.70131
\(996\) −2.80956e7 −0.897408
\(997\) −273483. −0.00871351 −0.00435676 0.999991i \(-0.501387\pi\)
−0.00435676 + 0.999991i \(0.501387\pi\)
\(998\) −2.40797e7 −0.765289
\(999\) 1.55910e7 0.494266
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.1.3 10
3.2 odd 2 387.6.a.e.1.8 10
4.3 odd 2 688.6.a.h.1.9 10
5.4 even 2 1075.6.a.b.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.3 10 1.1 even 1 trivial
387.6.a.e.1.8 10 3.2 odd 2
688.6.a.h.1.9 10 4.3 odd 2
1075.6.a.b.1.8 10 5.4 even 2