Properties

Label 177.6.a.a.1.2
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3879361069\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + 13849341 x^{3} - 23890558 x^{2} - 74443300 x - 14846072\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-8.44473\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.44473 q^{2} +9.00000 q^{3} +57.2030 q^{4} +13.7903 q^{5} -85.0026 q^{6} +67.4858 q^{7} -238.036 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-9.44473 q^{2} +9.00000 q^{3} +57.2030 q^{4} +13.7903 q^{5} -85.0026 q^{6} +67.4858 q^{7} -238.036 q^{8} +81.0000 q^{9} -130.245 q^{10} -138.804 q^{11} +514.827 q^{12} -485.356 q^{13} -637.385 q^{14} +124.112 q^{15} +417.688 q^{16} -2224.39 q^{17} -765.023 q^{18} +1850.55 q^{19} +788.844 q^{20} +607.372 q^{21} +1310.97 q^{22} -1008.66 q^{23} -2142.32 q^{24} -2934.83 q^{25} +4584.06 q^{26} +729.000 q^{27} +3860.39 q^{28} +1534.86 q^{29} -1172.21 q^{30} +5924.08 q^{31} +3672.19 q^{32} -1249.24 q^{33} +21008.8 q^{34} +930.646 q^{35} +4633.44 q^{36} +1074.65 q^{37} -17477.9 q^{38} -4368.21 q^{39} -3282.57 q^{40} -10573.5 q^{41} -5736.47 q^{42} +15070.3 q^{43} -7940.01 q^{44} +1117.01 q^{45} +9526.48 q^{46} -14991.6 q^{47} +3759.19 q^{48} -12252.7 q^{49} +27718.7 q^{50} -20019.6 q^{51} -27763.8 q^{52} -40821.3 q^{53} -6885.21 q^{54} -1914.14 q^{55} -16064.0 q^{56} +16654.9 q^{57} -14496.4 q^{58} +3481.00 q^{59} +7099.60 q^{60} -34218.1 q^{61} -55951.4 q^{62} +5466.35 q^{63} -48048.9 q^{64} -6693.19 q^{65} +11798.7 q^{66} +18426.3 q^{67} -127242. q^{68} -9077.90 q^{69} -8789.71 q^{70} +17658.3 q^{71} -19280.9 q^{72} -25695.8 q^{73} -10149.8 q^{74} -26413.5 q^{75} +105857. q^{76} -9367.30 q^{77} +41256.6 q^{78} -13512.5 q^{79} +5760.02 q^{80} +6561.00 q^{81} +99863.6 q^{82} -80373.4 q^{83} +34743.5 q^{84} -30675.0 q^{85} -142335. q^{86} +13813.8 q^{87} +33040.3 q^{88} +43704.2 q^{89} -10549.9 q^{90} -32754.7 q^{91} -57698.1 q^{92} +53316.7 q^{93} +141591. q^{94} +25519.5 q^{95} +33049.7 q^{96} +67602.6 q^{97} +115723. q^{98} -11243.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.44473 −1.66961 −0.834804 0.550547i \(-0.814419\pi\)
−0.834804 + 0.550547i \(0.814419\pi\)
\(3\) 9.00000 0.577350
\(4\) 57.2030 1.78759
\(5\) 13.7903 0.246688 0.123344 0.992364i \(-0.460638\pi\)
0.123344 + 0.992364i \(0.460638\pi\)
\(6\) −85.0026 −0.963949
\(7\) 67.4858 0.520556 0.260278 0.965534i \(-0.416186\pi\)
0.260278 + 0.965534i \(0.416186\pi\)
\(8\) −238.036 −1.31497
\(9\) 81.0000 0.333333
\(10\) −130.245 −0.411872
\(11\) −138.804 −0.345876 −0.172938 0.984933i \(-0.555326\pi\)
−0.172938 + 0.984933i \(0.555326\pi\)
\(12\) 514.827 1.03207
\(13\) −485.356 −0.796530 −0.398265 0.917270i \(-0.630388\pi\)
−0.398265 + 0.917270i \(0.630388\pi\)
\(14\) −637.385 −0.869125
\(15\) 124.112 0.142425
\(16\) 417.688 0.407898
\(17\) −2224.39 −1.86676 −0.933382 0.358884i \(-0.883157\pi\)
−0.933382 + 0.358884i \(0.883157\pi\)
\(18\) −765.023 −0.556536
\(19\) 1850.55 1.17602 0.588012 0.808852i \(-0.299911\pi\)
0.588012 + 0.808852i \(0.299911\pi\)
\(20\) 788.844 0.440977
\(21\) 607.372 0.300543
\(22\) 1310.97 0.577478
\(23\) −1008.66 −0.397579 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(24\) −2142.32 −0.759201
\(25\) −2934.83 −0.939145
\(26\) 4584.06 1.32989
\(27\) 729.000 0.192450
\(28\) 3860.39 0.930542
\(29\) 1534.86 0.338902 0.169451 0.985539i \(-0.445800\pi\)
0.169451 + 0.985539i \(0.445800\pi\)
\(30\) −1172.21 −0.237794
\(31\) 5924.08 1.10718 0.553588 0.832790i \(-0.313258\pi\)
0.553588 + 0.832790i \(0.313258\pi\)
\(32\) 3672.19 0.633943
\(33\) −1249.24 −0.199692
\(34\) 21008.8 3.11677
\(35\) 930.646 0.128415
\(36\) 4633.44 0.595865
\(37\) 1074.65 0.129051 0.0645257 0.997916i \(-0.479447\pi\)
0.0645257 + 0.997916i \(0.479447\pi\)
\(38\) −17477.9 −1.96350
\(39\) −4368.21 −0.459877
\(40\) −3282.57 −0.324388
\(41\) −10573.5 −0.982331 −0.491165 0.871066i \(-0.663429\pi\)
−0.491165 + 0.871066i \(0.663429\pi\)
\(42\) −5736.47 −0.501789
\(43\) 15070.3 1.24294 0.621470 0.783438i \(-0.286536\pi\)
0.621470 + 0.783438i \(0.286536\pi\)
\(44\) −7940.01 −0.618286
\(45\) 1117.01 0.0822292
\(46\) 9526.48 0.663801
\(47\) −14991.6 −0.989924 −0.494962 0.868915i \(-0.664818\pi\)
−0.494962 + 0.868915i \(0.664818\pi\)
\(48\) 3759.19 0.235500
\(49\) −12252.7 −0.729022
\(50\) 27718.7 1.56801
\(51\) −20019.6 −1.07778
\(52\) −27763.8 −1.42387
\(53\) −40821.3 −1.99617 −0.998084 0.0618654i \(-0.980295\pi\)
−0.998084 + 0.0618654i \(0.980295\pi\)
\(54\) −6885.21 −0.321316
\(55\) −1914.14 −0.0853233
\(56\) −16064.0 −0.684517
\(57\) 16654.9 0.678977
\(58\) −14496.4 −0.565835
\(59\) 3481.00 0.130189
\(60\) 7099.60 0.254598
\(61\) −34218.1 −1.17742 −0.588710 0.808345i \(-0.700364\pi\)
−0.588710 + 0.808345i \(0.700364\pi\)
\(62\) −55951.4 −1.84855
\(63\) 5466.35 0.173519
\(64\) −48048.9 −1.46634
\(65\) −6693.19 −0.196494
\(66\) 11798.7 0.333407
\(67\) 18426.3 0.501478 0.250739 0.968055i \(-0.419326\pi\)
0.250739 + 0.968055i \(0.419326\pi\)
\(68\) −127242. −3.33702
\(69\) −9077.90 −0.229542
\(70\) −8789.71 −0.214402
\(71\) 17658.3 0.415723 0.207861 0.978158i \(-0.433350\pi\)
0.207861 + 0.978158i \(0.433350\pi\)
\(72\) −19280.9 −0.438325
\(73\) −25695.8 −0.564357 −0.282179 0.959362i \(-0.591057\pi\)
−0.282179 + 0.959362i \(0.591057\pi\)
\(74\) −10149.8 −0.215465
\(75\) −26413.5 −0.542216
\(76\) 105857. 2.10225
\(77\) −9367.30 −0.180048
\(78\) 41256.6 0.767815
\(79\) −13512.5 −0.243594 −0.121797 0.992555i \(-0.538866\pi\)
−0.121797 + 0.992555i \(0.538866\pi\)
\(80\) 5760.02 0.100623
\(81\) 6561.00 0.111111
\(82\) 99863.6 1.64011
\(83\) −80373.4 −1.28061 −0.640306 0.768120i \(-0.721192\pi\)
−0.640306 + 0.768120i \(0.721192\pi\)
\(84\) 34743.5 0.537249
\(85\) −30675.0 −0.460508
\(86\) −142335. −2.07522
\(87\) 13813.8 0.195665
\(88\) 33040.3 0.454818
\(89\) 43704.2 0.584855 0.292427 0.956288i \(-0.405537\pi\)
0.292427 + 0.956288i \(0.405537\pi\)
\(90\) −10549.9 −0.137291
\(91\) −32754.7 −0.414638
\(92\) −57698.1 −0.710710
\(93\) 53316.7 0.639229
\(94\) 141591. 1.65279
\(95\) 25519.5 0.290110
\(96\) 33049.7 0.366007
\(97\) 67602.6 0.729515 0.364757 0.931103i \(-0.381152\pi\)
0.364757 + 0.931103i \(0.381152\pi\)
\(98\) 115723. 1.21718
\(99\) −11243.1 −0.115292
\(100\) −167881. −1.67881
\(101\) 21691.1 0.211582 0.105791 0.994388i \(-0.466263\pi\)
0.105791 + 0.994388i \(0.466263\pi\)
\(102\) 189079. 1.79947
\(103\) 35953.6 0.333926 0.166963 0.985963i \(-0.446604\pi\)
0.166963 + 0.985963i \(0.446604\pi\)
\(104\) 115532. 1.04742
\(105\) 8375.82 0.0741402
\(106\) 385546. 3.33282
\(107\) −120880. −1.02069 −0.510347 0.859969i \(-0.670483\pi\)
−0.510347 + 0.859969i \(0.670483\pi\)
\(108\) 41701.0 0.344023
\(109\) −183993. −1.48332 −0.741661 0.670775i \(-0.765962\pi\)
−0.741661 + 0.670775i \(0.765962\pi\)
\(110\) 18078.6 0.142457
\(111\) 9671.85 0.0745079
\(112\) 28188.0 0.212334
\(113\) −68654.1 −0.505790 −0.252895 0.967494i \(-0.581383\pi\)
−0.252895 + 0.967494i \(0.581383\pi\)
\(114\) −157301. −1.13363
\(115\) −13909.6 −0.0980778
\(116\) 87798.8 0.605820
\(117\) −39313.9 −0.265510
\(118\) −32877.1 −0.217365
\(119\) −150115. −0.971755
\(120\) −29543.2 −0.187285
\(121\) −141784. −0.880370
\(122\) 323181. 1.96583
\(123\) −95161.2 −0.567149
\(124\) 338875. 1.97918
\(125\) −83566.6 −0.478363
\(126\) −51628.2 −0.289708
\(127\) 139438. 0.767136 0.383568 0.923513i \(-0.374695\pi\)
0.383568 + 0.923513i \(0.374695\pi\)
\(128\) 336299. 1.81426
\(129\) 135632. 0.717612
\(130\) 63215.4 0.328068
\(131\) −45314.3 −0.230705 −0.115353 0.993325i \(-0.536800\pi\)
−0.115353 + 0.993325i \(0.536800\pi\)
\(132\) −71460.1 −0.356968
\(133\) 124886. 0.612186
\(134\) −174032. −0.837272
\(135\) 10053.1 0.0474750
\(136\) 529485. 2.45475
\(137\) 72094.5 0.328171 0.164086 0.986446i \(-0.447533\pi\)
0.164086 + 0.986446i \(0.447533\pi\)
\(138\) 85738.3 0.383246
\(139\) −437395. −1.92016 −0.960078 0.279732i \(-0.909754\pi\)
−0.960078 + 0.279732i \(0.909754\pi\)
\(140\) 53235.8 0.229553
\(141\) −134924. −0.571533
\(142\) −166778. −0.694094
\(143\) 67369.4 0.275501
\(144\) 33832.7 0.135966
\(145\) 21166.2 0.0836030
\(146\) 242690. 0.942256
\(147\) −110274. −0.420901
\(148\) 61473.2 0.230692
\(149\) 236655. 0.873271 0.436636 0.899638i \(-0.356170\pi\)
0.436636 + 0.899638i \(0.356170\pi\)
\(150\) 249468. 0.905288
\(151\) 378542. 1.35105 0.675526 0.737336i \(-0.263917\pi\)
0.675526 + 0.737336i \(0.263917\pi\)
\(152\) −440496. −1.54644
\(153\) −180176. −0.622255
\(154\) 88471.7 0.300609
\(155\) 81694.6 0.273127
\(156\) −249875. −0.822073
\(157\) 103612. 0.335475 0.167738 0.985832i \(-0.446354\pi\)
0.167738 + 0.985832i \(0.446354\pi\)
\(158\) 127622. 0.406707
\(159\) −367392. −1.15249
\(160\) 50640.5 0.156386
\(161\) −68069.9 −0.206962
\(162\) −61966.9 −0.185512
\(163\) −318233. −0.938160 −0.469080 0.883156i \(-0.655414\pi\)
−0.469080 + 0.883156i \(0.655414\pi\)
\(164\) −604834. −1.75601
\(165\) −17227.3 −0.0492614
\(166\) 759106. 2.13812
\(167\) −24793.8 −0.0687942 −0.0343971 0.999408i \(-0.510951\pi\)
−0.0343971 + 0.999408i \(0.510951\pi\)
\(168\) −144576. −0.395206
\(169\) −135722. −0.365539
\(170\) 289717. 0.768868
\(171\) 149894. 0.392008
\(172\) 862065. 2.22187
\(173\) −313813. −0.797178 −0.398589 0.917130i \(-0.630500\pi\)
−0.398589 + 0.917130i \(0.630500\pi\)
\(174\) −130467. −0.326685
\(175\) −198059. −0.488877
\(176\) −57976.8 −0.141082
\(177\) 31329.0 0.0751646
\(178\) −412774. −0.976478
\(179\) −313044. −0.730253 −0.365126 0.930958i \(-0.618974\pi\)
−0.365126 + 0.930958i \(0.618974\pi\)
\(180\) 63896.4 0.146992
\(181\) −240755. −0.546235 −0.273117 0.961981i \(-0.588055\pi\)
−0.273117 + 0.961981i \(0.588055\pi\)
\(182\) 309359. 0.692284
\(183\) −307963. −0.679783
\(184\) 240096. 0.522806
\(185\) 14819.7 0.0318354
\(186\) −503563. −1.06726
\(187\) 308755. 0.645669
\(188\) −857562. −1.76958
\(189\) 49197.1 0.100181
\(190\) −241025. −0.484371
\(191\) 804807. 1.59628 0.798139 0.602474i \(-0.205818\pi\)
0.798139 + 0.602474i \(0.205818\pi\)
\(192\) −432440. −0.846589
\(193\) −724642. −1.40033 −0.700164 0.713982i \(-0.746890\pi\)
−0.700164 + 0.713982i \(0.746890\pi\)
\(194\) −638489. −1.21800
\(195\) −60238.7 −0.113446
\(196\) −700889. −1.30319
\(197\) −483578. −0.887771 −0.443886 0.896083i \(-0.646400\pi\)
−0.443886 + 0.896083i \(0.646400\pi\)
\(198\) 106188. 0.192493
\(199\) 356378. 0.637937 0.318968 0.947765i \(-0.396664\pi\)
0.318968 + 0.947765i \(0.396664\pi\)
\(200\) 698594. 1.23495
\(201\) 165837. 0.289528
\(202\) −204866. −0.353258
\(203\) 103581. 0.176418
\(204\) −1.14518e6 −1.92663
\(205\) −145811. −0.242329
\(206\) −339573. −0.557525
\(207\) −81701.1 −0.132526
\(208\) −202727. −0.324903
\(209\) −256863. −0.406758
\(210\) −79107.4 −0.123785
\(211\) 64318.7 0.0994561 0.0497280 0.998763i \(-0.484165\pi\)
0.0497280 + 0.998763i \(0.484165\pi\)
\(212\) −2.33510e6 −3.56834
\(213\) 158925. 0.240018
\(214\) 1.14168e6 1.70416
\(215\) 207823. 0.306618
\(216\) −173528. −0.253067
\(217\) 399791. 0.576347
\(218\) 1.73777e6 2.47657
\(219\) −231262. −0.325832
\(220\) −109495. −0.152523
\(221\) 1.07962e6 1.48693
\(222\) −91348.1 −0.124399
\(223\) 359718. 0.484396 0.242198 0.970227i \(-0.422132\pi\)
0.242198 + 0.970227i \(0.422132\pi\)
\(224\) 247821. 0.330003
\(225\) −237721. −0.313048
\(226\) 648420. 0.844472
\(227\) 628492. 0.809533 0.404767 0.914420i \(-0.367353\pi\)
0.404767 + 0.914420i \(0.367353\pi\)
\(228\) 952711. 1.21374
\(229\) −712809. −0.898223 −0.449112 0.893476i \(-0.648259\pi\)
−0.449112 + 0.893476i \(0.648259\pi\)
\(230\) 131373. 0.163751
\(231\) −84305.7 −0.103951
\(232\) −365352. −0.445648
\(233\) 451301. 0.544598 0.272299 0.962213i \(-0.412216\pi\)
0.272299 + 0.962213i \(0.412216\pi\)
\(234\) 371309. 0.443298
\(235\) −206737. −0.244202
\(236\) 199124. 0.232725
\(237\) −121612. −0.140639
\(238\) 1.41780e6 1.62245
\(239\) 479799. 0.543331 0.271665 0.962392i \(-0.412426\pi\)
0.271665 + 0.962392i \(0.412426\pi\)
\(240\) 51840.2 0.0580950
\(241\) −165266. −0.183291 −0.0916456 0.995792i \(-0.529213\pi\)
−0.0916456 + 0.995792i \(0.529213\pi\)
\(242\) 1.33912e6 1.46987
\(243\) 59049.0 0.0641500
\(244\) −1.95738e6 −2.10475
\(245\) −168967. −0.179841
\(246\) 898772. 0.946917
\(247\) −898174. −0.936738
\(248\) −1.41014e6 −1.45591
\(249\) −723361. −0.739361
\(250\) 789264. 0.798679
\(251\) 1.49986e6 1.50268 0.751340 0.659915i \(-0.229408\pi\)
0.751340 + 0.659915i \(0.229408\pi\)
\(252\) 312692. 0.310181
\(253\) 140005. 0.137513
\(254\) −1.31696e6 −1.28082
\(255\) −276075. −0.265874
\(256\) −1.63869e6 −1.56278
\(257\) −602030. −0.568572 −0.284286 0.958739i \(-0.591757\pi\)
−0.284286 + 0.958739i \(0.591757\pi\)
\(258\) −1.28101e6 −1.19813
\(259\) 72523.6 0.0671785
\(260\) −382870. −0.351252
\(261\) 124324. 0.112967
\(262\) 427982. 0.385187
\(263\) −136455. −0.121647 −0.0608233 0.998149i \(-0.519373\pi\)
−0.0608233 + 0.998149i \(0.519373\pi\)
\(264\) 297363. 0.262589
\(265\) −562936. −0.492430
\(266\) −1.17951e6 −1.02211
\(267\) 393338. 0.337666
\(268\) 1.05404e6 0.896439
\(269\) 1.68628e6 1.42085 0.710425 0.703773i \(-0.248503\pi\)
0.710425 + 0.703773i \(0.248503\pi\)
\(270\) −94948.8 −0.0792648
\(271\) −459713. −0.380245 −0.190123 0.981760i \(-0.560889\pi\)
−0.190123 + 0.981760i \(0.560889\pi\)
\(272\) −929103. −0.761450
\(273\) −294792. −0.239392
\(274\) −680913. −0.547918
\(275\) 407366. 0.324828
\(276\) −519283. −0.410328
\(277\) −2.13458e6 −1.67152 −0.835761 0.549093i \(-0.814973\pi\)
−0.835761 + 0.549093i \(0.814973\pi\)
\(278\) 4.13108e6 3.20591
\(279\) 479851. 0.369059
\(280\) −221527. −0.168862
\(281\) 2.25092e6 1.70057 0.850284 0.526325i \(-0.176430\pi\)
0.850284 + 0.526325i \(0.176430\pi\)
\(282\) 1.27432e6 0.954237
\(283\) −5499.56 −0.00408189 −0.00204095 0.999998i \(-0.500650\pi\)
−0.00204095 + 0.999998i \(0.500650\pi\)
\(284\) 1.01011e6 0.743143
\(285\) 229676. 0.167495
\(286\) −636286. −0.459978
\(287\) −713559. −0.511358
\(288\) 297448. 0.211314
\(289\) 3.52808e6 2.48481
\(290\) −199909. −0.139584
\(291\) 608424. 0.421186
\(292\) −1.46987e6 −1.00884
\(293\) −902523. −0.614171 −0.307085 0.951682i \(-0.599354\pi\)
−0.307085 + 0.951682i \(0.599354\pi\)
\(294\) 1.04151e6 0.702740
\(295\) 48003.9 0.0321160
\(296\) −255805. −0.169699
\(297\) −101188. −0.0665639
\(298\) −2.23514e6 −1.45802
\(299\) 489557. 0.316684
\(300\) −1.51093e6 −0.969262
\(301\) 1.01703e6 0.647019
\(302\) −3.57523e6 −2.25573
\(303\) 195220. 0.122157
\(304\) 772951. 0.479698
\(305\) −471876. −0.290455
\(306\) 1.70171e6 1.03892
\(307\) 500034. 0.302798 0.151399 0.988473i \(-0.451622\pi\)
0.151399 + 0.988473i \(0.451622\pi\)
\(308\) −535838. −0.321852
\(309\) 323583. 0.192792
\(310\) −771584. −0.456015
\(311\) −1.44596e6 −0.847728 −0.423864 0.905726i \(-0.639327\pi\)
−0.423864 + 0.905726i \(0.639327\pi\)
\(312\) 1.03979e6 0.604726
\(313\) −1.78320e6 −1.02882 −0.514410 0.857544i \(-0.671989\pi\)
−0.514410 + 0.857544i \(0.671989\pi\)
\(314\) −978587. −0.560113
\(315\) 75382.3 0.0428049
\(316\) −772953. −0.435447
\(317\) −1.43302e6 −0.800948 −0.400474 0.916308i \(-0.631154\pi\)
−0.400474 + 0.916308i \(0.631154\pi\)
\(318\) 3.46992e6 1.92421
\(319\) −213045. −0.117218
\(320\) −662606. −0.361727
\(321\) −1.08792e6 −0.589298
\(322\) 642902. 0.345545
\(323\) −4.11634e6 −2.19536
\(324\) 375309. 0.198622
\(325\) 1.42444e6 0.748058
\(326\) 3.00563e6 1.56636
\(327\) −1.65594e6 −0.856396
\(328\) 2.51686e6 1.29174
\(329\) −1.01172e6 −0.515311
\(330\) 162707. 0.0822473
\(331\) 2.77285e6 1.39109 0.695547 0.718481i \(-0.255162\pi\)
0.695547 + 0.718481i \(0.255162\pi\)
\(332\) −4.59760e6 −2.28921
\(333\) 87046.7 0.0430171
\(334\) 234171. 0.114859
\(335\) 254104. 0.123708
\(336\) 253692. 0.122591
\(337\) −1.39166e6 −0.667509 −0.333754 0.942660i \(-0.608316\pi\)
−0.333754 + 0.942660i \(0.608316\pi\)
\(338\) 1.28186e6 0.610308
\(339\) −617887. −0.292018
\(340\) −1.75470e6 −0.823201
\(341\) −822287. −0.382946
\(342\) −1.41571e6 −0.654500
\(343\) −1.96111e6 −0.900052
\(344\) −3.58726e6 −1.63443
\(345\) −125187. −0.0566252
\(346\) 2.96388e6 1.33098
\(347\) −3.44484e6 −1.53584 −0.767918 0.640548i \(-0.778707\pi\)
−0.767918 + 0.640548i \(0.778707\pi\)
\(348\) 790189. 0.349770
\(349\) −1.33302e6 −0.585833 −0.292917 0.956138i \(-0.594626\pi\)
−0.292917 + 0.956138i \(0.594626\pi\)
\(350\) 1.87062e6 0.816234
\(351\) −353825. −0.153292
\(352\) −509715. −0.219266
\(353\) 3.77713e6 1.61334 0.806669 0.591003i \(-0.201268\pi\)
0.806669 + 0.591003i \(0.201268\pi\)
\(354\) −295894. −0.125495
\(355\) 243513. 0.102554
\(356\) 2.50001e6 1.04548
\(357\) −1.35104e6 −0.561043
\(358\) 2.95662e6 1.21924
\(359\) 331917. 0.135923 0.0679616 0.997688i \(-0.478350\pi\)
0.0679616 + 0.997688i \(0.478350\pi\)
\(360\) −265888. −0.108129
\(361\) 948422. 0.383031
\(362\) 2.27387e6 0.911998
\(363\) −1.27606e6 −0.508282
\(364\) −1.87366e6 −0.741205
\(365\) −354351. −0.139220
\(366\) 2.90863e6 1.13497
\(367\) −1.30195e6 −0.504578 −0.252289 0.967652i \(-0.581183\pi\)
−0.252289 + 0.967652i \(0.581183\pi\)
\(368\) −421303. −0.162172
\(369\) −856451. −0.327444
\(370\) −139968. −0.0531526
\(371\) −2.75486e6 −1.03912
\(372\) 3.04988e6 1.14268
\(373\) 5.01394e6 1.86598 0.932990 0.359903i \(-0.117190\pi\)
0.932990 + 0.359903i \(0.117190\pi\)
\(374\) −2.91611e6 −1.07801
\(375\) −752099. −0.276183
\(376\) 3.56852e6 1.30172
\(377\) −744956. −0.269946
\(378\) −464654. −0.167263
\(379\) 4.28983e6 1.53406 0.767030 0.641611i \(-0.221734\pi\)
0.767030 + 0.641611i \(0.221734\pi\)
\(380\) 1.45979e6 0.518599
\(381\) 1.25494e6 0.442906
\(382\) −7.60119e6 −2.66516
\(383\) 2.99051e6 1.04171 0.520856 0.853645i \(-0.325613\pi\)
0.520856 + 0.853645i \(0.325613\pi\)
\(384\) 3.02669e6 1.04747
\(385\) −129177. −0.0444155
\(386\) 6.84405e6 2.33800
\(387\) 1.22069e6 0.414313
\(388\) 3.86707e6 1.30408
\(389\) 5.18724e6 1.73805 0.869026 0.494767i \(-0.164746\pi\)
0.869026 + 0.494767i \(0.164746\pi\)
\(390\) 568938. 0.189410
\(391\) 2.24365e6 0.742186
\(392\) 2.91657e6 0.958645
\(393\) −407829. −0.133198
\(394\) 4.56727e6 1.48223
\(395\) −186340. −0.0600916
\(396\) −643141. −0.206095
\(397\) 2.45853e6 0.782887 0.391443 0.920202i \(-0.371976\pi\)
0.391443 + 0.920202i \(0.371976\pi\)
\(398\) −3.36589e6 −1.06511
\(399\) 1.12397e6 0.353446
\(400\) −1.22584e6 −0.383076
\(401\) −1.41766e6 −0.440261 −0.220130 0.975470i \(-0.570648\pi\)
−0.220130 + 0.975470i \(0.570648\pi\)
\(402\) −1.56629e6 −0.483399
\(403\) −2.87529e6 −0.881900
\(404\) 1.24079e6 0.378222
\(405\) 90477.9 0.0274097
\(406\) −978300. −0.294548
\(407\) −149166. −0.0446358
\(408\) 4.76537e6 1.41725
\(409\) −2.35592e6 −0.696391 −0.348195 0.937422i \(-0.613205\pi\)
−0.348195 + 0.937422i \(0.613205\pi\)
\(410\) 1.37714e6 0.404594
\(411\) 648850. 0.189470
\(412\) 2.05666e6 0.596924
\(413\) 234918. 0.0677706
\(414\) 771645. 0.221267
\(415\) −1.10837e6 −0.315911
\(416\) −1.78232e6 −0.504955
\(417\) −3.93655e6 −1.10860
\(418\) 2.42601e6 0.679127
\(419\) 4.25487e6 1.18400 0.592000 0.805938i \(-0.298339\pi\)
0.592000 + 0.805938i \(0.298339\pi\)
\(420\) 479122. 0.132533
\(421\) −1.91147e6 −0.525607 −0.262804 0.964849i \(-0.584647\pi\)
−0.262804 + 0.964849i \(0.584647\pi\)
\(422\) −607473. −0.166053
\(423\) −1.21432e6 −0.329975
\(424\) 9.71693e6 2.62491
\(425\) 6.52822e6 1.75316
\(426\) −1.50100e6 −0.400736
\(427\) −2.30923e6 −0.612912
\(428\) −6.91471e6 −1.82459
\(429\) 606325. 0.159060
\(430\) −1.96283e6 −0.511932
\(431\) −5.28060e6 −1.36927 −0.684637 0.728885i \(-0.740039\pi\)
−0.684637 + 0.728885i \(0.740039\pi\)
\(432\) 304494. 0.0785001
\(433\) −3.92135e6 −1.00512 −0.502558 0.864543i \(-0.667608\pi\)
−0.502558 + 0.864543i \(0.667608\pi\)
\(434\) −3.77592e6 −0.962274
\(435\) 190495. 0.0482682
\(436\) −1.05250e7 −2.65158
\(437\) −1.86656e6 −0.467562
\(438\) 2.18421e6 0.544012
\(439\) 3.26904e6 0.809578 0.404789 0.914410i \(-0.367345\pi\)
0.404789 + 0.914410i \(0.367345\pi\)
\(440\) 455634. 0.112198
\(441\) −992466. −0.243007
\(442\) −1.01968e7 −2.48260
\(443\) 6.03039e6 1.45994 0.729972 0.683477i \(-0.239533\pi\)
0.729972 + 0.683477i \(0.239533\pi\)
\(444\) 553259. 0.133190
\(445\) 602692. 0.144276
\(446\) −3.39745e6 −0.808752
\(447\) 2.12989e6 0.504183
\(448\) −3.24262e6 −0.763309
\(449\) 5.58738e6 1.30795 0.653976 0.756515i \(-0.273100\pi\)
0.653976 + 0.756515i \(0.273100\pi\)
\(450\) 2.24521e6 0.522668
\(451\) 1.46764e6 0.339765
\(452\) −3.92722e6 −0.904148
\(453\) 3.40688e6 0.780030
\(454\) −5.93594e6 −1.35160
\(455\) −451695. −0.102286
\(456\) −3.96446e6 −0.892838
\(457\) −2.59965e6 −0.582270 −0.291135 0.956682i \(-0.594033\pi\)
−0.291135 + 0.956682i \(0.594033\pi\)
\(458\) 6.73229e6 1.49968
\(459\) −1.62158e6 −0.359259
\(460\) −795672. −0.175323
\(461\) −4.29896e6 −0.942130 −0.471065 0.882099i \(-0.656130\pi\)
−0.471065 + 0.882099i \(0.656130\pi\)
\(462\) 796245. 0.173557
\(463\) −4.21015e6 −0.912735 −0.456367 0.889791i \(-0.650850\pi\)
−0.456367 + 0.889791i \(0.650850\pi\)
\(464\) 641094. 0.138238
\(465\) 735251. 0.157690
\(466\) −4.26242e6 −0.909266
\(467\) 5.46044e6 1.15860 0.579302 0.815113i \(-0.303325\pi\)
0.579302 + 0.815113i \(0.303325\pi\)
\(468\) −2.24887e6 −0.474624
\(469\) 1.24352e6 0.261047
\(470\) 1.95258e6 0.407722
\(471\) 932508. 0.193687
\(472\) −828602. −0.171195
\(473\) −2.09182e6 −0.429903
\(474\) 1.14859e6 0.234812
\(475\) −5.43104e6 −1.10446
\(476\) −8.58703e6 −1.73710
\(477\) −3.30653e6 −0.665390
\(478\) −4.53157e6 −0.907150
\(479\) −692304. −0.137866 −0.0689331 0.997621i \(-0.521960\pi\)
−0.0689331 + 0.997621i \(0.521960\pi\)
\(480\) 455764. 0.0902895
\(481\) −521588. −0.102793
\(482\) 1.56090e6 0.306025
\(483\) −612629. −0.119490
\(484\) −8.11050e6 −1.57374
\(485\) 932257. 0.179962
\(486\) −557702. −0.107105
\(487\) 9.19622e6 1.75706 0.878530 0.477686i \(-0.158524\pi\)
0.878530 + 0.477686i \(0.158524\pi\)
\(488\) 8.14513e6 1.54828
\(489\) −2.86410e6 −0.541647
\(490\) 1.59585e6 0.300263
\(491\) 454736. 0.0851247 0.0425623 0.999094i \(-0.486448\pi\)
0.0425623 + 0.999094i \(0.486448\pi\)
\(492\) −5.44351e6 −1.01383
\(493\) −3.41414e6 −0.632651
\(494\) 8.48302e6 1.56399
\(495\) −155046. −0.0284411
\(496\) 2.47442e6 0.451615
\(497\) 1.19169e6 0.216407
\(498\) 6.83195e6 1.23444
\(499\) −4.56440e6 −0.820601 −0.410301 0.911950i \(-0.634576\pi\)
−0.410301 + 0.911950i \(0.634576\pi\)
\(500\) −4.78026e6 −0.855119
\(501\) −223144. −0.0397184
\(502\) −1.41658e7 −2.50889
\(503\) −1.87618e6 −0.330639 −0.165320 0.986240i \(-0.552866\pi\)
−0.165320 + 0.986240i \(0.552866\pi\)
\(504\) −1.30119e6 −0.228172
\(505\) 299125. 0.0521945
\(506\) −1.32231e6 −0.229593
\(507\) −1.22150e6 −0.211044
\(508\) 7.97629e6 1.37133
\(509\) 2.91027e6 0.497897 0.248948 0.968517i \(-0.419915\pi\)
0.248948 + 0.968517i \(0.419915\pi\)
\(510\) 2.60745e6 0.443906
\(511\) −1.73410e6 −0.293779
\(512\) 4.71542e6 0.794960
\(513\) 1.34905e6 0.226326
\(514\) 5.68602e6 0.949293
\(515\) 495810. 0.0823753
\(516\) 7.75859e6 1.28280
\(517\) 2.08089e6 0.342391
\(518\) −684966. −0.112162
\(519\) −2.82431e6 −0.460251
\(520\) 1.59322e6 0.258385
\(521\) −6.05299e6 −0.976958 −0.488479 0.872576i \(-0.662448\pi\)
−0.488479 + 0.872576i \(0.662448\pi\)
\(522\) −1.17421e6 −0.188612
\(523\) 4.76464e6 0.761685 0.380843 0.924640i \(-0.375634\pi\)
0.380843 + 0.924640i \(0.375634\pi\)
\(524\) −2.59212e6 −0.412407
\(525\) −1.78253e6 −0.282254
\(526\) 1.28878e6 0.203102
\(527\) −1.31775e7 −2.06684
\(528\) −521791. −0.0814539
\(529\) −5.41896e6 −0.841931
\(530\) 5.31678e6 0.822166
\(531\) 281961. 0.0433963
\(532\) 7.14383e6 1.09434
\(533\) 5.13190e6 0.782456
\(534\) −3.71497e6 −0.563770
\(535\) −1.66697e6 −0.251792
\(536\) −4.38613e6 −0.659431
\(537\) −2.81740e6 −0.421612
\(538\) −1.59264e7 −2.37226
\(539\) 1.70072e6 0.252151
\(540\) 575067. 0.0848661
\(541\) 1.03136e7 1.51502 0.757511 0.652822i \(-0.226415\pi\)
0.757511 + 0.652822i \(0.226415\pi\)
\(542\) 4.34187e6 0.634861
\(543\) −2.16680e6 −0.315369
\(544\) −8.16840e6 −1.18342
\(545\) −2.53731e6 −0.365917
\(546\) 2.78423e6 0.399690
\(547\) 9.32864e6 1.33306 0.666530 0.745478i \(-0.267779\pi\)
0.666530 + 0.745478i \(0.267779\pi\)
\(548\) 4.12402e6 0.586637
\(549\) −2.77166e6 −0.392473
\(550\) −3.84746e6 −0.542335
\(551\) 2.84034e6 0.398557
\(552\) 2.16086e6 0.301842
\(553\) −911899. −0.126804
\(554\) 2.01605e7 2.79079
\(555\) 133377. 0.0183802
\(556\) −2.50203e7 −3.43246
\(557\) 1.72698e6 0.235857 0.117929 0.993022i \(-0.462375\pi\)
0.117929 + 0.993022i \(0.462375\pi\)
\(558\) −4.53206e6 −0.616184
\(559\) −7.31445e6 −0.990039
\(560\) 388720. 0.0523801
\(561\) 2.77879e6 0.372777
\(562\) −2.12593e7 −2.83928
\(563\) −2.82325e6 −0.375386 −0.187693 0.982228i \(-0.560101\pi\)
−0.187693 + 0.982228i \(0.560101\pi\)
\(564\) −7.71806e6 −1.02167
\(565\) −946758. −0.124772
\(566\) 51941.9 0.00681517
\(567\) 442774. 0.0578395
\(568\) −4.20331e6 −0.546664
\(569\) 1.12737e7 1.45978 0.729888 0.683567i \(-0.239572\pi\)
0.729888 + 0.683567i \(0.239572\pi\)
\(570\) −2.16922e6 −0.279652
\(571\) 7.15556e6 0.918445 0.459223 0.888321i \(-0.348128\pi\)
0.459223 + 0.888321i \(0.348128\pi\)
\(572\) 3.85373e6 0.492483
\(573\) 7.24326e6 0.921611
\(574\) 6.73937e6 0.853768
\(575\) 2.96023e6 0.373384
\(576\) −3.89196e6 −0.488779
\(577\) 6.00795e6 0.751254 0.375627 0.926771i \(-0.377427\pi\)
0.375627 + 0.926771i \(0.377427\pi\)
\(578\) −3.33217e7 −4.14866
\(579\) −6.52178e6 −0.808480
\(580\) 1.21077e6 0.149448
\(581\) −5.42406e6 −0.666629
\(582\) −5.74640e6 −0.703215
\(583\) 5.66616e6 0.690427
\(584\) 6.11651e6 0.742115
\(585\) −542148. −0.0654980
\(586\) 8.52409e6 1.02542
\(587\) −6.67034e6 −0.799011 −0.399505 0.916731i \(-0.630818\pi\)
−0.399505 + 0.916731i \(0.630818\pi\)
\(588\) −6.30801e6 −0.752400
\(589\) 1.09628e7 1.30207
\(590\) −453384. −0.0536211
\(591\) −4.35220e6 −0.512555
\(592\) 448868. 0.0526399
\(593\) 1.86332e6 0.217596 0.108798 0.994064i \(-0.465300\pi\)
0.108798 + 0.994064i \(0.465300\pi\)
\(594\) 955695. 0.111136
\(595\) −2.07012e6 −0.239720
\(596\) 1.35374e7 1.56105
\(597\) 3.20740e6 0.368313
\(598\) −4.62374e6 −0.528738
\(599\) 1.74289e6 0.198474 0.0992369 0.995064i \(-0.468360\pi\)
0.0992369 + 0.995064i \(0.468360\pi\)
\(600\) 6.28735e6 0.713000
\(601\) 4.23218e6 0.477945 0.238972 0.971026i \(-0.423189\pi\)
0.238972 + 0.971026i \(0.423189\pi\)
\(602\) −9.60557e6 −1.08027
\(603\) 1.49253e6 0.167159
\(604\) 2.16538e7 2.41513
\(605\) −1.95524e6 −0.217176
\(606\) −1.84380e6 −0.203954
\(607\) −1.13339e7 −1.24856 −0.624279 0.781201i \(-0.714607\pi\)
−0.624279 + 0.781201i \(0.714607\pi\)
\(608\) 6.79556e6 0.745532
\(609\) 932233. 0.101855
\(610\) 4.45674e6 0.484946
\(611\) 7.27624e6 0.788505
\(612\) −1.03066e7 −1.11234
\(613\) 1.16293e7 1.24997 0.624987 0.780635i \(-0.285104\pi\)
0.624987 + 0.780635i \(0.285104\pi\)
\(614\) −4.72269e6 −0.505555
\(615\) −1.31230e6 −0.139909
\(616\) 2.22975e6 0.236758
\(617\) −1.03462e7 −1.09413 −0.547066 0.837090i \(-0.684255\pi\)
−0.547066 + 0.837090i \(0.684255\pi\)
\(618\) −3.05615e6 −0.321887
\(619\) −1.09852e7 −1.15234 −0.576169 0.817331i \(-0.695453\pi\)
−0.576169 + 0.817331i \(0.695453\pi\)
\(620\) 4.67318e6 0.488240
\(621\) −735310. −0.0765141
\(622\) 1.36568e7 1.41537
\(623\) 2.94941e6 0.304449
\(624\) −1.82455e6 −0.187583
\(625\) 8.01894e6 0.821139
\(626\) 1.68419e7 1.71773
\(627\) −2.31177e6 −0.234842
\(628\) 5.92692e6 0.599694
\(629\) −2.39045e6 −0.240909
\(630\) −711966. −0.0714674
\(631\) 1.54733e7 1.54707 0.773535 0.633753i \(-0.218487\pi\)
0.773535 + 0.633753i \(0.218487\pi\)
\(632\) 3.21645e6 0.320320
\(633\) 578868. 0.0574210
\(634\) 1.35345e7 1.33727
\(635\) 1.92289e6 0.189243
\(636\) −2.10159e7 −2.06018
\(637\) 5.94691e6 0.580688
\(638\) 2.01216e6 0.195709
\(639\) 1.43032e6 0.138574
\(640\) 4.63765e6 0.447556
\(641\) 1.22578e7 1.17833 0.589166 0.808012i \(-0.299456\pi\)
0.589166 + 0.808012i \(0.299456\pi\)
\(642\) 1.02751e7 0.983897
\(643\) −1.32338e7 −1.26228 −0.631141 0.775668i \(-0.717413\pi\)
−0.631141 + 0.775668i \(0.717413\pi\)
\(644\) −3.89380e6 −0.369964
\(645\) 1.87041e6 0.177026
\(646\) 3.88778e7 3.66539
\(647\) −1.49533e7 −1.40436 −0.702178 0.712002i \(-0.747789\pi\)
−0.702178 + 0.712002i \(0.747789\pi\)
\(648\) −1.56175e6 −0.146108
\(649\) −483177. −0.0450292
\(650\) −1.34534e7 −1.24896
\(651\) 3.59812e6 0.332754
\(652\) −1.82039e7 −1.67705
\(653\) −1.46185e7 −1.34159 −0.670794 0.741643i \(-0.734047\pi\)
−0.670794 + 0.741643i \(0.734047\pi\)
\(654\) 1.56399e7 1.42985
\(655\) −624896. −0.0569121
\(656\) −4.41641e6 −0.400691
\(657\) −2.08136e6 −0.188119
\(658\) 9.55539e6 0.860367
\(659\) −7.89681e6 −0.708334 −0.354167 0.935182i \(-0.615236\pi\)
−0.354167 + 0.935182i \(0.615236\pi\)
\(660\) −985453. −0.0880594
\(661\) 2.56132e6 0.228013 0.114007 0.993480i \(-0.463631\pi\)
0.114007 + 0.993480i \(0.463631\pi\)
\(662\) −2.61888e7 −2.32258
\(663\) 9.71662e6 0.858482
\(664\) 1.91317e7 1.68397
\(665\) 1.72220e6 0.151019
\(666\) −822133. −0.0718218
\(667\) −1.54815e6 −0.134740
\(668\) −1.41828e6 −0.122976
\(669\) 3.23747e6 0.279666
\(670\) −2.39994e6 −0.206545
\(671\) 4.74961e6 0.407241
\(672\) 2.23039e6 0.190527
\(673\) 1.96637e7 1.67351 0.836754 0.547578i \(-0.184450\pi\)
0.836754 + 0.547578i \(0.184450\pi\)
\(674\) 1.31438e7 1.11448
\(675\) −2.13949e6 −0.180739
\(676\) −7.76372e6 −0.653436
\(677\) 2.65672e6 0.222779 0.111389 0.993777i \(-0.464470\pi\)
0.111389 + 0.993777i \(0.464470\pi\)
\(678\) 5.83578e6 0.487556
\(679\) 4.56222e6 0.379753
\(680\) 7.30174e6 0.605556
\(681\) 5.65642e6 0.467384
\(682\) 7.76628e6 0.639370
\(683\) −360849. −0.0295988 −0.0147994 0.999890i \(-0.504711\pi\)
−0.0147994 + 0.999890i \(0.504711\pi\)
\(684\) 8.57440e6 0.700751
\(685\) 994201. 0.0809558
\(686\) 1.85222e7 1.50274
\(687\) −6.41528e6 −0.518589
\(688\) 6.29467e6 0.506993
\(689\) 1.98129e7 1.59001
\(690\) 1.18235e6 0.0945420
\(691\) 1.57193e7 1.25238 0.626191 0.779670i \(-0.284613\pi\)
0.626191 + 0.779670i \(0.284613\pi\)
\(692\) −1.79510e7 −1.42503
\(693\) −758751. −0.0600159
\(694\) 3.25356e7 2.56425
\(695\) −6.03179e6 −0.473679
\(696\) −3.28817e6 −0.257295
\(697\) 2.35196e7 1.83378
\(698\) 1.25901e7 0.978113
\(699\) 4.06171e6 0.314424
\(700\) −1.13296e7 −0.873914
\(701\) −2.32970e7 −1.79062 −0.895312 0.445440i \(-0.853047\pi\)
−0.895312 + 0.445440i \(0.853047\pi\)
\(702\) 3.34178e6 0.255938
\(703\) 1.98869e6 0.151767
\(704\) 6.66938e6 0.507170
\(705\) −1.86064e6 −0.140990
\(706\) −3.56740e7 −2.69364
\(707\) 1.46384e6 0.110140
\(708\) 1.79211e6 0.134364
\(709\) 5.36409e6 0.400756 0.200378 0.979719i \(-0.435783\pi\)
0.200378 + 0.979719i \(0.435783\pi\)
\(710\) −2.29991e6 −0.171224
\(711\) −1.09451e6 −0.0811980
\(712\) −1.04032e7 −0.769069
\(713\) −5.97536e6 −0.440190
\(714\) 1.27602e7 0.936722
\(715\) 929041. 0.0679626
\(716\) −1.79071e7 −1.30540
\(717\) 4.31819e6 0.313692
\(718\) −3.13487e6 −0.226939
\(719\) 2.10973e7 1.52196 0.760981 0.648774i \(-0.224718\pi\)
0.760981 + 0.648774i \(0.224718\pi\)
\(720\) 466562. 0.0335411
\(721\) 2.42636e6 0.173827
\(722\) −8.95759e6 −0.639511
\(723\) −1.48740e6 −0.105823
\(724\) −1.37719e7 −0.976446
\(725\) −4.50456e6 −0.318279
\(726\) 1.20520e7 0.848632
\(727\) 1.02219e7 0.717291 0.358646 0.933474i \(-0.383239\pi\)
0.358646 + 0.933474i \(0.383239\pi\)
\(728\) 7.79678e6 0.545239
\(729\) 531441. 0.0370370
\(730\) 3.34675e6 0.232443
\(731\) −3.35222e7 −2.32028
\(732\) −1.76164e7 −1.21518
\(733\) 1.18831e7 0.816900 0.408450 0.912781i \(-0.366069\pi\)
0.408450 + 0.912781i \(0.366069\pi\)
\(734\) 1.22965e7 0.842447
\(735\) −1.52071e6 −0.103831
\(736\) −3.70398e6 −0.252042
\(737\) −2.55765e6 −0.173449
\(738\) 8.08895e6 0.546703
\(739\) −7.32133e6 −0.493150 −0.246575 0.969124i \(-0.579305\pi\)
−0.246575 + 0.969124i \(0.579305\pi\)
\(740\) 847731. 0.0569087
\(741\) −8.08357e6 −0.540826
\(742\) 2.60189e7 1.73492
\(743\) 1.09019e7 0.724484 0.362242 0.932084i \(-0.382011\pi\)
0.362242 + 0.932084i \(0.382011\pi\)
\(744\) −1.26913e7 −0.840569
\(745\) 3.26353e6 0.215425
\(746\) −4.73553e7 −3.11546
\(747\) −6.51025e6 −0.426870
\(748\) 1.76617e7 1.15419
\(749\) −8.15769e6 −0.531328
\(750\) 7.10338e6 0.461118
\(751\) −3.73740e6 −0.241808 −0.120904 0.992664i \(-0.538579\pi\)
−0.120904 + 0.992664i \(0.538579\pi\)
\(752\) −6.26179e6 −0.403788
\(753\) 1.34987e7 0.867573
\(754\) 7.03591e6 0.450704
\(755\) 5.22019e6 0.333288
\(756\) 2.81422e6 0.179083
\(757\) −1.93400e7 −1.22664 −0.613319 0.789835i \(-0.710166\pi\)
−0.613319 + 0.789835i \(0.710166\pi\)
\(758\) −4.05163e7 −2.56128
\(759\) 1.26005e6 0.0793931
\(760\) −6.07455e6 −0.381488
\(761\) 1.32949e7 0.832190 0.416095 0.909321i \(-0.363398\pi\)
0.416095 + 0.909321i \(0.363398\pi\)
\(762\) −1.18526e7 −0.739481
\(763\) −1.24169e7 −0.772152
\(764\) 4.60374e7 2.85350
\(765\) −2.48467e6 −0.153503
\(766\) −2.82445e7 −1.73925
\(767\) −1.68953e6 −0.103699
\(768\) −1.47482e7 −0.902269
\(769\) −1.41450e7 −0.862555 −0.431277 0.902219i \(-0.641937\pi\)
−0.431277 + 0.902219i \(0.641937\pi\)
\(770\) 1.22005e6 0.0741566
\(771\) −5.41827e6 −0.328265
\(772\) −4.14517e7 −2.50322
\(773\) 1.48281e7 0.892557 0.446278 0.894894i \(-0.352749\pi\)
0.446278 + 0.894894i \(0.352749\pi\)
\(774\) −1.15291e7 −0.691741
\(775\) −1.73862e7 −1.03980
\(776\) −1.60918e7 −0.959293
\(777\) 652713. 0.0387855
\(778\) −4.89921e7 −2.90187
\(779\) −1.95667e7 −1.15524
\(780\) −3.44583e6 −0.202795
\(781\) −2.45105e6 −0.143788
\(782\) −2.11907e7 −1.23916
\(783\) 1.11892e6 0.0652218
\(784\) −5.11779e6 −0.297367
\(785\) 1.42884e6 0.0827576
\(786\) 3.85184e6 0.222388
\(787\) −3.31567e7 −1.90825 −0.954123 0.299414i \(-0.903209\pi\)
−0.954123 + 0.299414i \(0.903209\pi\)
\(788\) −2.76621e7 −1.58697
\(789\) −1.22809e6 −0.0702326
\(790\) 1.75993e6 0.100330
\(791\) −4.63318e6 −0.263292
\(792\) 2.67627e6 0.151606
\(793\) 1.66080e7 0.937850
\(794\) −2.32202e7 −1.30712
\(795\) −5.06643e6 −0.284305
\(796\) 2.03859e7 1.14037
\(797\) 2.23535e7 1.24652 0.623261 0.782014i \(-0.285808\pi\)
0.623261 + 0.782014i \(0.285808\pi\)
\(798\) −1.06156e7 −0.590116
\(799\) 3.33471e7 1.84796
\(800\) −1.07773e7 −0.595365
\(801\) 3.54004e6 0.194952
\(802\) 1.33894e7 0.735063
\(803\) 3.56667e6 0.195198
\(804\) 9.48638e6 0.517559
\(805\) −938701. −0.0510549
\(806\) 2.71564e7 1.47243
\(807\) 1.51765e7 0.820328
\(808\) −5.16325e6 −0.278224
\(809\) −1.54732e6 −0.0831206 −0.0415603 0.999136i \(-0.513233\pi\)
−0.0415603 + 0.999136i \(0.513233\pi\)
\(810\) −854539. −0.0457635
\(811\) −2.84004e7 −1.51625 −0.758127 0.652107i \(-0.773885\pi\)
−0.758127 + 0.652107i \(0.773885\pi\)
\(812\) 5.92517e6 0.315363
\(813\) −4.13742e6 −0.219535
\(814\) 1.40883e6 0.0745243
\(815\) −4.38852e6 −0.231432
\(816\) −8.36192e6 −0.439623
\(817\) 2.78882e7 1.46173
\(818\) 2.22511e7 1.16270
\(819\) −2.65313e6 −0.138213
\(820\) −8.34082e6 −0.433186
\(821\) −3.12187e7 −1.61643 −0.808216 0.588886i \(-0.799567\pi\)
−0.808216 + 0.588886i \(0.799567\pi\)
\(822\) −6.12822e6 −0.316340
\(823\) 4.30753e6 0.221681 0.110841 0.993838i \(-0.464646\pi\)
0.110841 + 0.993838i \(0.464646\pi\)
\(824\) −8.55825e6 −0.439104
\(825\) 3.66630e6 0.187539
\(826\) −2.21874e6 −0.113150
\(827\) −3.37874e7 −1.71787 −0.858937 0.512081i \(-0.828875\pi\)
−0.858937 + 0.512081i \(0.828875\pi\)
\(828\) −4.67355e6 −0.236903
\(829\) 2.32056e7 1.17275 0.586377 0.810038i \(-0.300554\pi\)
0.586377 + 0.810038i \(0.300554\pi\)
\(830\) 1.04683e7 0.527448
\(831\) −1.92112e7 −0.965054
\(832\) 2.33208e7 1.16798
\(833\) 2.72548e7 1.36091
\(834\) 3.71797e7 1.85093
\(835\) −341913. −0.0169707
\(836\) −1.46934e7 −0.727119
\(837\) 4.31866e6 0.213076
\(838\) −4.01861e7 −1.97682
\(839\) −3.03381e7 −1.48794 −0.743968 0.668216i \(-0.767058\pi\)
−0.743968 + 0.668216i \(0.767058\pi\)
\(840\) −1.99374e6 −0.0974925
\(841\) −1.81553e7 −0.885145
\(842\) 1.80533e7 0.877559
\(843\) 2.02583e7 0.981823
\(844\) 3.67922e6 0.177787
\(845\) −1.87164e6 −0.0901740
\(846\) 1.14689e7 0.550929
\(847\) −9.56843e6 −0.458282
\(848\) −1.70506e7 −0.814234
\(849\) −49496.0 −0.00235668
\(850\) −6.16573e7 −2.92710
\(851\) −1.08395e6 −0.0513081
\(852\) 9.09098e6 0.429054
\(853\) −2.55496e7 −1.20230 −0.601149 0.799137i \(-0.705290\pi\)
−0.601149 + 0.799137i \(0.705290\pi\)
\(854\) 2.18101e7 1.02332
\(855\) 2.06708e6 0.0967034
\(856\) 2.87738e7 1.34219
\(857\) −3.85037e7 −1.79081 −0.895407 0.445250i \(-0.853115\pi\)
−0.895407 + 0.445250i \(0.853115\pi\)
\(858\) −5.72658e6 −0.265569
\(859\) 2.49038e7 1.15155 0.575774 0.817609i \(-0.304701\pi\)
0.575774 + 0.817609i \(0.304701\pi\)
\(860\) 1.18881e7 0.548108
\(861\) −6.42203e6 −0.295233
\(862\) 4.98739e7 2.28615
\(863\) −3.38580e7 −1.54751 −0.773756 0.633483i \(-0.781625\pi\)
−0.773756 + 0.633483i \(0.781625\pi\)
\(864\) 2.67703e6 0.122002
\(865\) −4.32756e6 −0.196654
\(866\) 3.70361e7 1.67815
\(867\) 3.17527e7 1.43461
\(868\) 2.28693e7 1.03027
\(869\) 1.87558e6 0.0842533
\(870\) −1.79918e6 −0.0805891
\(871\) −8.94334e6 −0.399442
\(872\) 4.37969e7 1.95053
\(873\) 5.47581e6 0.243172
\(874\) 1.76292e7 0.780646
\(875\) −5.63956e6 −0.249015
\(876\) −1.32289e7 −0.582455
\(877\) 4.91457e6 0.215768 0.107884 0.994163i \(-0.465593\pi\)
0.107884 + 0.994163i \(0.465593\pi\)
\(878\) −3.08752e7 −1.35168
\(879\) −8.12270e6 −0.354592
\(880\) −799514. −0.0348032
\(881\) 3.12482e7 1.35639 0.678196 0.734881i \(-0.262762\pi\)
0.678196 + 0.734881i \(0.262762\pi\)
\(882\) 9.37358e6 0.405727
\(883\) 2.31563e7 0.999466 0.499733 0.866179i \(-0.333431\pi\)
0.499733 + 0.866179i \(0.333431\pi\)
\(884\) 6.17577e7 2.65804
\(885\) 432035. 0.0185422
\(886\) −5.69555e7 −2.43754
\(887\) −1.87182e6 −0.0798832 −0.0399416 0.999202i \(-0.512717\pi\)
−0.0399416 + 0.999202i \(0.512717\pi\)
\(888\) −2.30225e6 −0.0979759
\(889\) 9.41010e6 0.399337
\(890\) −5.69226e6 −0.240885
\(891\) −910693. −0.0384307
\(892\) 2.05770e7 0.865903
\(893\) −2.77426e7 −1.16417
\(894\) −2.01163e7 −0.841789
\(895\) −4.31696e6 −0.180144
\(896\) 2.26954e7 0.944426
\(897\) 4.40602e6 0.182837
\(898\) −5.27713e7 −2.18377
\(899\) 9.09266e6 0.375225
\(900\) −1.35984e7 −0.559603
\(901\) 9.08027e7 3.72638
\(902\) −1.38615e7 −0.567274
\(903\) 9.15327e6 0.373557
\(904\) 1.63421e7 0.665101
\(905\) −3.32008e6 −0.134749
\(906\) −3.21771e7 −1.30235
\(907\) −1.61068e7 −0.650117 −0.325059 0.945694i \(-0.605384\pi\)
−0.325059 + 0.945694i \(0.605384\pi\)
\(908\) 3.59516e7 1.44712
\(909\) 1.75698e6 0.0705272
\(910\) 4.26614e6 0.170778
\(911\) −2.80661e7 −1.12043 −0.560217 0.828346i \(-0.689282\pi\)
−0.560217 + 0.828346i \(0.689282\pi\)
\(912\) 6.95656e6 0.276954
\(913\) 1.11562e7 0.442933
\(914\) 2.45530e7 0.972163
\(915\) −4.24688e6 −0.167694
\(916\) −4.07748e7 −1.60566
\(917\) −3.05807e6 −0.120095
\(918\) 1.53154e7 0.599822
\(919\) 1.01464e7 0.396301 0.198150 0.980172i \(-0.436507\pi\)
0.198150 + 0.980172i \(0.436507\pi\)
\(920\) 3.31099e6 0.128970
\(921\) 4.50031e6 0.174821
\(922\) 4.06025e7 1.57299
\(923\) −8.57058e6 −0.331136
\(924\) −4.82254e6 −0.185821
\(925\) −3.15391e6 −0.121198
\(926\) 3.97637e7 1.52391
\(927\) 2.91224e6 0.111309
\(928\) 5.63631e6 0.214845
\(929\) −1.17387e6 −0.0446254 −0.0223127 0.999751i \(-0.507103\pi\)
−0.0223127 + 0.999751i \(0.507103\pi\)
\(930\) −6.94425e6 −0.263280
\(931\) −2.26741e7 −0.857346
\(932\) 2.58158e7 0.973521
\(933\) −1.30137e7 −0.489436
\(934\) −5.15724e7 −1.93442
\(935\) 4.25781e6 0.159279
\(936\) 9.35810e6 0.349139
\(937\) −1.37307e7 −0.510908 −0.255454 0.966821i \(-0.582225\pi\)
−0.255454 + 0.966821i \(0.582225\pi\)
\(938\) −1.17447e7 −0.435847
\(939\) −1.60488e7 −0.593990
\(940\) −1.18260e7 −0.436534
\(941\) 8.16579e6 0.300624 0.150312 0.988639i \(-0.451972\pi\)
0.150312 + 0.988639i \(0.451972\pi\)
\(942\) −8.80729e6 −0.323381
\(943\) 1.06650e7 0.390554
\(944\) 1.45397e6 0.0531038
\(945\) 678441. 0.0247134
\(946\) 1.97566e7 0.717770
\(947\) −1.84586e6 −0.0668844 −0.0334422 0.999441i \(-0.510647\pi\)
−0.0334422 + 0.999441i \(0.510647\pi\)
\(948\) −6.95658e6 −0.251406
\(949\) 1.24716e7 0.449528
\(950\) 5.12947e7 1.84401
\(951\) −1.28972e7 −0.462427
\(952\) 3.57327e7 1.27783
\(953\) 2.06466e7 0.736403 0.368201 0.929746i \(-0.379974\pi\)
0.368201 + 0.929746i \(0.379974\pi\)
\(954\) 3.12293e7 1.11094
\(955\) 1.10985e7 0.393782
\(956\) 2.74459e7 0.971255
\(957\) −1.91741e6 −0.0676760
\(958\) 6.53862e6 0.230183
\(959\) 4.86535e6 0.170831
\(960\) −5.96346e6 −0.208843
\(961\) 6.46561e6 0.225840
\(962\) 4.92626e6 0.171625
\(963\) −9.79129e6 −0.340231
\(964\) −9.45373e6 −0.327650
\(965\) −9.99299e6 −0.345444
\(966\) 5.78612e6 0.199501
\(967\) 259971. 0.00894044 0.00447022 0.999990i \(-0.498577\pi\)
0.00447022 + 0.999990i \(0.498577\pi\)
\(968\) 3.37498e7 1.15766
\(969\) −3.70471e7 −1.26749
\(970\) −8.80492e6 −0.300467
\(971\) −4.97402e7 −1.69301 −0.846505 0.532380i \(-0.821298\pi\)
−0.846505 + 0.532380i \(0.821298\pi\)
\(972\) 3.37778e6 0.114674
\(973\) −2.95179e7 −0.999548
\(974\) −8.68558e7 −2.93360
\(975\) 1.28199e7 0.431891
\(976\) −1.42925e7 −0.480267
\(977\) −3.30137e6 −0.110652 −0.0553259 0.998468i \(-0.517620\pi\)
−0.0553259 + 0.998468i \(0.517620\pi\)
\(978\) 2.70507e7 0.904338
\(979\) −6.06632e6 −0.202287
\(980\) −9.66544e6 −0.321482
\(981\) −1.49034e7 −0.494441
\(982\) −4.29486e6 −0.142125
\(983\) 1.02213e7 0.337383 0.168692 0.985669i \(-0.446046\pi\)
0.168692 + 0.985669i \(0.446046\pi\)
\(984\) 2.26518e7 0.745786
\(985\) −6.66866e6 −0.219002
\(986\) 3.22457e7 1.05628
\(987\) −9.10545e6 −0.297515
\(988\) −5.13783e7 −1.67451
\(989\) −1.52007e7 −0.494167
\(990\) 1.46436e6 0.0474855
\(991\) −1.38660e7 −0.448506 −0.224253 0.974531i \(-0.571994\pi\)
−0.224253 + 0.974531i \(0.571994\pi\)
\(992\) 2.17544e7 0.701887
\(993\) 2.49556e7 0.803148
\(994\) −1.12552e7 −0.361315
\(995\) 4.91454e6 0.157371
\(996\) −4.13784e7 −1.32168
\(997\) −2.38978e7 −0.761412 −0.380706 0.924696i \(-0.624319\pi\)
−0.380706 + 0.924696i \(0.624319\pi\)
\(998\) 4.31095e7 1.37008
\(999\) 783420. 0.0248360
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 177.6.a.a.1.2 11
3.2 odd 2 531.6.a.b.1.10 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.2 11 1.1 even 1 trivial
531.6.a.b.1.10 11 3.2 odd 2