Properties

Label 177.14.a.b.1.19
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+39.4833 q^{2} -729.000 q^{3} -6633.07 q^{4} +39747.6 q^{5} -28783.4 q^{6} -539057. q^{7} -585343. q^{8} +531441. q^{9} +O(q^{10})\) \(q+39.4833 q^{2} -729.000 q^{3} -6633.07 q^{4} +39747.6 q^{5} -28783.4 q^{6} -539057. q^{7} -585343. q^{8} +531441. q^{9} +1.56937e6 q^{10} -1.01761e7 q^{11} +4.83551e6 q^{12} +1.08564e6 q^{13} -2.12838e7 q^{14} -2.89760e7 q^{15} +3.12268e7 q^{16} +1.61734e8 q^{17} +2.09831e7 q^{18} +1.53748e8 q^{19} -2.63648e8 q^{20} +3.92972e8 q^{21} -4.01786e8 q^{22} +1.08113e8 q^{23} +4.26715e8 q^{24} +3.59167e8 q^{25} +4.28647e7 q^{26} -3.87420e8 q^{27} +3.57560e9 q^{28} +5.15790e9 q^{29} -1.14407e9 q^{30} -1.74651e8 q^{31} +6.02807e9 q^{32} +7.41838e9 q^{33} +6.38579e9 q^{34} -2.14262e10 q^{35} -3.52508e9 q^{36} -2.19273e10 q^{37} +6.07049e9 q^{38} -7.91431e8 q^{39} -2.32660e10 q^{40} +3.56936e10 q^{41} +1.55159e10 q^{42} +2.18836e10 q^{43} +6.74987e10 q^{44} +2.11235e10 q^{45} +4.26868e9 q^{46} -5.63281e10 q^{47} -2.27643e10 q^{48} +1.93693e11 q^{49} +1.41811e10 q^{50} -1.17904e11 q^{51} -7.20112e9 q^{52} -2.33624e10 q^{53} -1.52967e10 q^{54} -4.04475e11 q^{55} +3.15533e11 q^{56} -1.12082e11 q^{57} +2.03651e11 q^{58} -4.21805e10 q^{59} +1.92200e11 q^{60} -6.59589e11 q^{61} -6.89579e9 q^{62} -2.86477e11 q^{63} -1.78016e10 q^{64} +4.31515e10 q^{65} +2.92902e11 q^{66} +1.98586e10 q^{67} -1.07279e12 q^{68} -7.88147e10 q^{69} -8.45978e11 q^{70} +1.48511e12 q^{71} -3.11075e11 q^{72} -2.63525e11 q^{73} -8.65764e11 q^{74} -2.61833e11 q^{75} -1.01982e12 q^{76} +5.48550e12 q^{77} -3.12483e10 q^{78} +2.47859e12 q^{79} +1.24119e12 q^{80} +2.82430e11 q^{81} +1.40930e12 q^{82} -1.76625e12 q^{83} -2.60661e12 q^{84} +6.42852e12 q^{85} +8.64037e11 q^{86} -3.76011e12 q^{87} +5.95651e12 q^{88} +1.27082e12 q^{89} +8.34026e11 q^{90} -5.85221e11 q^{91} -7.17124e11 q^{92} +1.27320e11 q^{93} -2.22402e12 q^{94} +6.11112e12 q^{95} -4.39446e12 q^{96} +3.89183e12 q^{97} +7.64765e12 q^{98} -5.40800e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 39.4833 0.436233 0.218117 0.975923i \(-0.430009\pi\)
0.218117 + 0.975923i \(0.430009\pi\)
\(3\) −729.000 −0.577350
\(4\) −6633.07 −0.809700
\(5\) 39747.6 1.13764 0.568821 0.822461i \(-0.307400\pi\)
0.568821 + 0.822461i \(0.307400\pi\)
\(6\) −28783.4 −0.251859
\(7\) −539057. −1.73180 −0.865899 0.500219i \(-0.833253\pi\)
−0.865899 + 0.500219i \(0.833253\pi\)
\(8\) −585343. −0.789452
\(9\) 531441. 0.333333
\(10\) 1.56937e6 0.496277
\(11\) −1.01761e7 −1.73192 −0.865962 0.500109i \(-0.833293\pi\)
−0.865962 + 0.500109i \(0.833293\pi\)
\(12\) 4.83551e6 0.467481
\(13\) 1.08564e6 0.0623812 0.0311906 0.999513i \(-0.490070\pi\)
0.0311906 + 0.999513i \(0.490070\pi\)
\(14\) −2.12838e7 −0.755468
\(15\) −2.89760e7 −0.656818
\(16\) 3.12268e7 0.465315
\(17\) 1.61734e8 1.62511 0.812555 0.582885i \(-0.198076\pi\)
0.812555 + 0.582885i \(0.198076\pi\)
\(18\) 2.09831e7 0.145411
\(19\) 1.53748e8 0.749742 0.374871 0.927077i \(-0.377687\pi\)
0.374871 + 0.927077i \(0.377687\pi\)
\(20\) −2.63648e8 −0.921149
\(21\) 3.92972e8 0.999854
\(22\) −4.01786e8 −0.755523
\(23\) 1.08113e8 0.152282 0.0761411 0.997097i \(-0.475740\pi\)
0.0761411 + 0.997097i \(0.475740\pi\)
\(24\) 4.26715e8 0.455790
\(25\) 3.59167e8 0.294230
\(26\) 4.28647e7 0.0272128
\(27\) −3.87420e8 −0.192450
\(28\) 3.57560e9 1.40224
\(29\) 5.15790e9 1.61022 0.805111 0.593124i \(-0.202106\pi\)
0.805111 + 0.593124i \(0.202106\pi\)
\(30\) −1.14407e9 −0.286526
\(31\) −1.74651e8 −0.0353443 −0.0176721 0.999844i \(-0.505626\pi\)
−0.0176721 + 0.999844i \(0.505626\pi\)
\(32\) 6.02807e9 0.992438
\(33\) 7.41838e9 0.999927
\(34\) 6.38579e9 0.708927
\(35\) −2.14262e10 −1.97017
\(36\) −3.52508e9 −0.269900
\(37\) −2.19273e10 −1.40499 −0.702497 0.711687i \(-0.747931\pi\)
−0.702497 + 0.711687i \(0.747931\pi\)
\(38\) 6.07049e9 0.327062
\(39\) −7.91431e8 −0.0360158
\(40\) −2.32660e10 −0.898114
\(41\) 3.56936e10 1.17353 0.586766 0.809757i \(-0.300401\pi\)
0.586766 + 0.809757i \(0.300401\pi\)
\(42\) 1.55159e10 0.436170
\(43\) 2.18836e10 0.527927 0.263963 0.964533i \(-0.414970\pi\)
0.263963 + 0.964533i \(0.414970\pi\)
\(44\) 6.74987e10 1.40234
\(45\) 2.11235e10 0.379214
\(46\) 4.26868e9 0.0664305
\(47\) −5.63281e10 −0.762235 −0.381117 0.924527i \(-0.624461\pi\)
−0.381117 + 0.924527i \(0.624461\pi\)
\(48\) −2.27643e10 −0.268650
\(49\) 1.93693e11 1.99912
\(50\) 1.41811e10 0.128353
\(51\) −1.17904e11 −0.938257
\(52\) −7.20112e9 −0.0505101
\(53\) −2.33624e10 −0.144785 −0.0723925 0.997376i \(-0.523063\pi\)
−0.0723925 + 0.997376i \(0.523063\pi\)
\(54\) −1.52967e10 −0.0839531
\(55\) −4.04475e11 −1.97031
\(56\) 3.15533e11 1.36717
\(57\) −1.12082e11 −0.432864
\(58\) 2.03651e11 0.702433
\(59\) −4.21805e10 −0.130189
\(60\) 1.92200e11 0.531826
\(61\) −6.59589e11 −1.63919 −0.819596 0.572943i \(-0.805802\pi\)
−0.819596 + 0.572943i \(0.805802\pi\)
\(62\) −6.89579e9 −0.0154184
\(63\) −2.86477e11 −0.577266
\(64\) −1.78016e10 −0.0323809
\(65\) 4.31515e10 0.0709675
\(66\) 2.92902e11 0.436202
\(67\) 1.98586e10 0.0268203 0.0134101 0.999910i \(-0.495731\pi\)
0.0134101 + 0.999910i \(0.495731\pi\)
\(68\) −1.07279e12 −1.31585
\(69\) −7.88147e10 −0.0879201
\(70\) −8.45978e11 −0.859452
\(71\) 1.48511e12 1.37587 0.687937 0.725770i \(-0.258516\pi\)
0.687937 + 0.725770i \(0.258516\pi\)
\(72\) −3.11075e11 −0.263151
\(73\) −2.63525e11 −0.203809 −0.101905 0.994794i \(-0.532494\pi\)
−0.101905 + 0.994794i \(0.532494\pi\)
\(74\) −8.65764e11 −0.612905
\(75\) −2.61833e11 −0.169874
\(76\) −1.01982e12 −0.607066
\(77\) 5.48550e12 2.99934
\(78\) −3.12483e10 −0.0157113
\(79\) 2.47859e12 1.14717 0.573585 0.819146i \(-0.305552\pi\)
0.573585 + 0.819146i \(0.305552\pi\)
\(80\) 1.24119e12 0.529362
\(81\) 2.82430e11 0.111111
\(82\) 1.40930e12 0.511934
\(83\) −1.76625e12 −0.592988 −0.296494 0.955035i \(-0.595817\pi\)
−0.296494 + 0.955035i \(0.595817\pi\)
\(84\) −2.60661e12 −0.809582
\(85\) 6.42852e12 1.84879
\(86\) 8.64037e11 0.230299
\(87\) −3.76011e12 −0.929662
\(88\) 5.95651e12 1.36727
\(89\) 1.27082e12 0.271050 0.135525 0.990774i \(-0.456728\pi\)
0.135525 + 0.990774i \(0.456728\pi\)
\(90\) 8.34026e11 0.165426
\(91\) −5.85221e11 −0.108032
\(92\) −7.17124e11 −0.123303
\(93\) 1.27320e11 0.0204060
\(94\) −2.22402e12 −0.332512
\(95\) 6.11112e12 0.852938
\(96\) −4.39446e12 −0.572984
\(97\) 3.89183e12 0.474392 0.237196 0.971462i \(-0.423772\pi\)
0.237196 + 0.971462i \(0.423772\pi\)
\(98\) 7.64765e12 0.872085
\(99\) −5.40800e12 −0.577308
\(100\) −2.38238e12 −0.238238
\(101\) 1.43375e13 1.34396 0.671978 0.740571i \(-0.265445\pi\)
0.671978 + 0.740571i \(0.265445\pi\)
\(102\) −4.65524e12 −0.409299
\(103\) 9.09071e11 0.0750163 0.0375082 0.999296i \(-0.488058\pi\)
0.0375082 + 0.999296i \(0.488058\pi\)
\(104\) −6.35471e11 −0.0492470
\(105\) 1.56197e13 1.13748
\(106\) −9.22424e11 −0.0631600
\(107\) −1.72384e13 −1.11046 −0.555230 0.831697i \(-0.687370\pi\)
−0.555230 + 0.831697i \(0.687370\pi\)
\(108\) 2.56979e12 0.155827
\(109\) 2.44984e13 1.39915 0.699577 0.714557i \(-0.253372\pi\)
0.699577 + 0.714557i \(0.253372\pi\)
\(110\) −1.59700e13 −0.859515
\(111\) 1.59850e13 0.811173
\(112\) −1.68330e13 −0.805832
\(113\) −3.44144e13 −1.55500 −0.777499 0.628884i \(-0.783512\pi\)
−0.777499 + 0.628884i \(0.783512\pi\)
\(114\) −4.42539e12 −0.188830
\(115\) 4.29725e12 0.173243
\(116\) −3.42127e13 −1.30380
\(117\) 5.76953e11 0.0207937
\(118\) −1.66543e12 −0.0567927
\(119\) −8.71837e13 −2.81436
\(120\) 1.69609e13 0.518526
\(121\) 6.90303e13 1.99956
\(122\) −2.60428e13 −0.715070
\(123\) −2.60206e13 −0.677539
\(124\) 1.15847e12 0.0286183
\(125\) −3.42440e13 −0.802914
\(126\) −1.13111e13 −0.251823
\(127\) −3.39799e13 −0.718619 −0.359309 0.933219i \(-0.616988\pi\)
−0.359309 + 0.933219i \(0.616988\pi\)
\(128\) −5.00848e13 −1.00656
\(129\) −1.59531e13 −0.304799
\(130\) 1.70377e12 0.0309584
\(131\) −1.62272e13 −0.280530 −0.140265 0.990114i \(-0.544796\pi\)
−0.140265 + 0.990114i \(0.544796\pi\)
\(132\) −4.92066e13 −0.809641
\(133\) −8.28790e13 −1.29840
\(134\) 7.84085e11 0.0116999
\(135\) −1.53990e13 −0.218939
\(136\) −9.46697e13 −1.28295
\(137\) −1.50222e14 −1.94111 −0.970557 0.240873i \(-0.922566\pi\)
−0.970557 + 0.240873i \(0.922566\pi\)
\(138\) −3.11187e12 −0.0383537
\(139\) −4.68636e12 −0.0551111 −0.0275556 0.999620i \(-0.508772\pi\)
−0.0275556 + 0.999620i \(0.508772\pi\)
\(140\) 1.42121e14 1.59524
\(141\) 4.10632e13 0.440076
\(142\) 5.86370e13 0.600202
\(143\) −1.10476e13 −0.108040
\(144\) 1.65952e13 0.155105
\(145\) 2.05014e14 1.83186
\(146\) −1.04049e13 −0.0889084
\(147\) −1.41202e14 −1.15420
\(148\) 1.45445e14 1.13762
\(149\) 4.80391e13 0.359654 0.179827 0.983698i \(-0.442446\pi\)
0.179827 + 0.983698i \(0.442446\pi\)
\(150\) −1.03380e13 −0.0741045
\(151\) 7.87849e13 0.540870 0.270435 0.962738i \(-0.412833\pi\)
0.270435 + 0.962738i \(0.412833\pi\)
\(152\) −8.99955e13 −0.591885
\(153\) 8.59519e13 0.541703
\(154\) 2.16586e14 1.30841
\(155\) −6.94194e12 −0.0402091
\(156\) 5.24962e12 0.0291620
\(157\) −3.02191e14 −1.61040 −0.805200 0.593003i \(-0.797942\pi\)
−0.805200 + 0.593003i \(0.797942\pi\)
\(158\) 9.78628e13 0.500434
\(159\) 1.70312e13 0.0835917
\(160\) 2.39601e14 1.12904
\(161\) −5.82793e13 −0.263722
\(162\) 1.11513e13 0.0484704
\(163\) 2.22757e14 0.930278 0.465139 0.885238i \(-0.346004\pi\)
0.465139 + 0.885238i \(0.346004\pi\)
\(164\) −2.36758e14 −0.950209
\(165\) 2.94863e14 1.13756
\(166\) −6.97376e13 −0.258681
\(167\) −3.81692e14 −1.36162 −0.680809 0.732461i \(-0.738372\pi\)
−0.680809 + 0.732461i \(0.738372\pi\)
\(168\) −2.30024e14 −0.789336
\(169\) −3.01696e14 −0.996109
\(170\) 2.53820e14 0.806505
\(171\) 8.17081e13 0.249914
\(172\) −1.45155e14 −0.427463
\(173\) 4.04749e13 0.114785 0.0573926 0.998352i \(-0.481721\pi\)
0.0573926 + 0.998352i \(0.481721\pi\)
\(174\) −1.48462e14 −0.405550
\(175\) −1.93611e14 −0.509546
\(176\) −3.17767e14 −0.805891
\(177\) 3.07496e13 0.0751646
\(178\) 5.01764e13 0.118241
\(179\) −8.88689e13 −0.201932 −0.100966 0.994890i \(-0.532193\pi\)
−0.100966 + 0.994890i \(0.532193\pi\)
\(180\) −1.40114e14 −0.307050
\(181\) 8.99177e13 0.190079 0.0950396 0.995473i \(-0.469702\pi\)
0.0950396 + 0.995473i \(0.469702\pi\)
\(182\) −2.31065e13 −0.0471270
\(183\) 4.80841e14 0.946387
\(184\) −6.32835e13 −0.120219
\(185\) −8.71558e14 −1.59838
\(186\) 5.02703e12 0.00890179
\(187\) −1.64582e15 −2.81457
\(188\) 3.73628e14 0.617182
\(189\) 2.08842e14 0.333285
\(190\) 2.41287e14 0.372080
\(191\) 9.77835e14 1.45730 0.728650 0.684887i \(-0.240148\pi\)
0.728650 + 0.684887i \(0.240148\pi\)
\(192\) 1.29774e13 0.0186951
\(193\) 1.24226e15 1.73017 0.865087 0.501622i \(-0.167263\pi\)
0.865087 + 0.501622i \(0.167263\pi\)
\(194\) 1.53662e14 0.206945
\(195\) −3.14575e13 −0.0409731
\(196\) −1.28478e15 −1.61869
\(197\) 7.37782e14 0.899286 0.449643 0.893208i \(-0.351551\pi\)
0.449643 + 0.893208i \(0.351551\pi\)
\(198\) −2.13526e14 −0.251841
\(199\) −6.49842e14 −0.741759 −0.370879 0.928681i \(-0.620944\pi\)
−0.370879 + 0.928681i \(0.620944\pi\)
\(200\) −2.10236e14 −0.232280
\(201\) −1.44769e13 −0.0154847
\(202\) 5.66093e14 0.586278
\(203\) −2.78040e15 −2.78858
\(204\) 7.82064e14 0.759707
\(205\) 1.41873e15 1.33506
\(206\) 3.58932e13 0.0327246
\(207\) 5.74559e13 0.0507607
\(208\) 3.39010e13 0.0290269
\(209\) −1.56456e15 −1.29850
\(210\) 6.16718e14 0.496205
\(211\) −3.09358e13 −0.0241337 −0.0120669 0.999927i \(-0.503841\pi\)
−0.0120669 + 0.999927i \(0.503841\pi\)
\(212\) 1.54964e14 0.117232
\(213\) −1.08264e15 −0.794361
\(214\) −6.80630e14 −0.484419
\(215\) 8.69820e14 0.600592
\(216\) 2.26774e14 0.151930
\(217\) 9.41466e13 0.0612092
\(218\) 9.67279e14 0.610358
\(219\) 1.92110e14 0.117669
\(220\) 2.68291e15 1.59536
\(221\) 1.75585e14 0.101376
\(222\) 6.31142e14 0.353861
\(223\) −6.13798e14 −0.334229 −0.167114 0.985938i \(-0.553445\pi\)
−0.167114 + 0.985938i \(0.553445\pi\)
\(224\) −3.24947e15 −1.71870
\(225\) 1.90876e14 0.0980765
\(226\) −1.35879e15 −0.678342
\(227\) −2.02574e15 −0.982686 −0.491343 0.870966i \(-0.663494\pi\)
−0.491343 + 0.870966i \(0.663494\pi\)
\(228\) 7.43451e14 0.350490
\(229\) 2.82538e14 0.129463 0.0647315 0.997903i \(-0.479381\pi\)
0.0647315 + 0.997903i \(0.479381\pi\)
\(230\) 1.69670e14 0.0755742
\(231\) −3.99893e15 −1.73167
\(232\) −3.01914e15 −1.27119
\(233\) −2.28292e15 −0.934709 −0.467354 0.884070i \(-0.654793\pi\)
−0.467354 + 0.884070i \(0.654793\pi\)
\(234\) 2.27800e13 0.00907092
\(235\) −2.23890e15 −0.867150
\(236\) 2.79786e14 0.105414
\(237\) −1.80689e15 −0.662319
\(238\) −3.44230e15 −1.22772
\(239\) −2.57641e15 −0.894187 −0.447094 0.894487i \(-0.647541\pi\)
−0.447094 + 0.894487i \(0.647541\pi\)
\(240\) −9.04827e14 −0.305627
\(241\) −7.04715e14 −0.231688 −0.115844 0.993267i \(-0.536957\pi\)
−0.115844 + 0.993267i \(0.536957\pi\)
\(242\) 2.72555e15 0.872276
\(243\) −2.05891e14 −0.0641500
\(244\) 4.37510e15 1.32725
\(245\) 7.69884e15 2.27429
\(246\) −1.02738e15 −0.295565
\(247\) 1.66915e14 0.0467698
\(248\) 1.02231e14 0.0279026
\(249\) 1.28760e15 0.342362
\(250\) −1.35207e15 −0.350258
\(251\) 2.49900e15 0.630793 0.315397 0.948960i \(-0.397862\pi\)
0.315397 + 0.948960i \(0.397862\pi\)
\(252\) 1.90022e15 0.467413
\(253\) −1.10017e15 −0.263741
\(254\) −1.34164e15 −0.313485
\(255\) −4.68639e15 −1.06740
\(256\) −1.83168e15 −0.406716
\(257\) −9.37515e14 −0.202961 −0.101481 0.994838i \(-0.532358\pi\)
−0.101481 + 0.994838i \(0.532358\pi\)
\(258\) −6.29883e14 −0.132963
\(259\) 1.18201e16 2.43316
\(260\) −2.86227e14 −0.0574624
\(261\) 2.74112e15 0.536741
\(262\) −6.40704e14 −0.122377
\(263\) 8.60213e15 1.60285 0.801427 0.598093i \(-0.204075\pi\)
0.801427 + 0.598093i \(0.204075\pi\)
\(264\) −4.34230e15 −0.789394
\(265\) −9.28597e14 −0.164714
\(266\) −3.27234e15 −0.566406
\(267\) −9.26430e14 −0.156491
\(268\) −1.31724e14 −0.0217164
\(269\) −1.09969e16 −1.76962 −0.884809 0.465955i \(-0.845711\pi\)
−0.884809 + 0.465955i \(0.845711\pi\)
\(270\) −6.08005e14 −0.0955086
\(271\) −1.98040e15 −0.303705 −0.151852 0.988403i \(-0.548524\pi\)
−0.151852 + 0.988403i \(0.548524\pi\)
\(272\) 5.05042e15 0.756188
\(273\) 4.26626e14 0.0623721
\(274\) −5.93128e15 −0.846778
\(275\) −3.65492e15 −0.509583
\(276\) 5.22783e14 0.0711890
\(277\) −1.29200e16 −1.71848 −0.859238 0.511577i \(-0.829062\pi\)
−0.859238 + 0.511577i \(0.829062\pi\)
\(278\) −1.85033e14 −0.0240413
\(279\) −9.28165e13 −0.0117814
\(280\) 1.25417e16 1.55535
\(281\) −1.58154e15 −0.191641 −0.0958207 0.995399i \(-0.530548\pi\)
−0.0958207 + 0.995399i \(0.530548\pi\)
\(282\) 1.62131e15 0.191976
\(283\) −7.97822e14 −0.0923197 −0.0461598 0.998934i \(-0.514698\pi\)
−0.0461598 + 0.998934i \(0.514698\pi\)
\(284\) −9.85082e15 −1.11405
\(285\) −4.45501e15 −0.492444
\(286\) −4.36195e14 −0.0471305
\(287\) −1.92409e16 −2.03232
\(288\) 3.20356e15 0.330813
\(289\) 1.62532e16 1.64098
\(290\) 8.09464e15 0.799117
\(291\) −2.83714e15 −0.273890
\(292\) 1.74798e15 0.165024
\(293\) 2.88481e15 0.266365 0.133182 0.991092i \(-0.457480\pi\)
0.133182 + 0.991092i \(0.457480\pi\)
\(294\) −5.57514e15 −0.503498
\(295\) −1.67657e15 −0.148108
\(296\) 1.28350e16 1.10917
\(297\) 3.94243e15 0.333309
\(298\) 1.89675e15 0.156893
\(299\) 1.17372e14 0.00949954
\(300\) 1.73675e15 0.137547
\(301\) −1.17965e16 −0.914262
\(302\) 3.11069e15 0.235945
\(303\) −1.04520e16 −0.775933
\(304\) 4.80106e15 0.348866
\(305\) −2.62171e16 −1.86481
\(306\) 3.39367e15 0.236309
\(307\) −2.70735e16 −1.84563 −0.922815 0.385242i \(-0.874118\pi\)
−0.922815 + 0.385242i \(0.874118\pi\)
\(308\) −3.63857e16 −2.42857
\(309\) −6.62713e14 −0.0433107
\(310\) −2.74091e14 −0.0175406
\(311\) −1.50598e16 −0.943790 −0.471895 0.881655i \(-0.656430\pi\)
−0.471895 + 0.881655i \(0.656430\pi\)
\(312\) 4.63259e14 0.0284327
\(313\) 2.92034e16 1.75548 0.877739 0.479139i \(-0.159051\pi\)
0.877739 + 0.479139i \(0.159051\pi\)
\(314\) −1.19315e16 −0.702510
\(315\) −1.13868e16 −0.656722
\(316\) −1.64406e16 −0.928864
\(317\) 1.21142e16 0.670516 0.335258 0.942126i \(-0.391177\pi\)
0.335258 + 0.942126i \(0.391177\pi\)
\(318\) 6.72447e14 0.0364655
\(319\) −5.24873e16 −2.78878
\(320\) −7.07570e14 −0.0368379
\(321\) 1.25668e16 0.641124
\(322\) −2.30106e15 −0.115044
\(323\) 2.48663e16 1.21841
\(324\) −1.87337e15 −0.0899667
\(325\) 3.89926e14 0.0183544
\(326\) 8.79521e15 0.405818
\(327\) −1.78593e16 −0.807802
\(328\) −2.08930e16 −0.926446
\(329\) 3.03640e16 1.32004
\(330\) 1.16422e16 0.496241
\(331\) −1.29603e16 −0.541667 −0.270833 0.962626i \(-0.587299\pi\)
−0.270833 + 0.962626i \(0.587299\pi\)
\(332\) 1.17157e16 0.480142
\(333\) −1.16531e16 −0.468331
\(334\) −1.50705e16 −0.593984
\(335\) 7.89333e14 0.0305119
\(336\) 1.22713e16 0.465247
\(337\) 2.54197e16 0.945315 0.472658 0.881246i \(-0.343295\pi\)
0.472658 + 0.881246i \(0.343295\pi\)
\(338\) −1.19120e16 −0.434536
\(339\) 2.50881e16 0.897779
\(340\) −4.26408e16 −1.49697
\(341\) 1.77726e15 0.0612136
\(342\) 3.22611e15 0.109021
\(343\) −5.21829e16 −1.73028
\(344\) −1.28094e16 −0.416773
\(345\) −3.13269e15 −0.100022
\(346\) 1.59808e15 0.0500731
\(347\) 5.45411e16 1.67719 0.838595 0.544756i \(-0.183378\pi\)
0.838595 + 0.544756i \(0.183378\pi\)
\(348\) 2.49410e16 0.752748
\(349\) 6.05705e16 1.79430 0.897151 0.441724i \(-0.145633\pi\)
0.897151 + 0.441724i \(0.145633\pi\)
\(350\) −7.64442e15 −0.222281
\(351\) −4.20599e14 −0.0120053
\(352\) −6.13422e16 −1.71883
\(353\) −4.09890e16 −1.12754 −0.563770 0.825932i \(-0.690649\pi\)
−0.563770 + 0.825932i \(0.690649\pi\)
\(354\) 1.21410e15 0.0327893
\(355\) 5.90294e16 1.56525
\(356\) −8.42946e15 −0.219470
\(357\) 6.35569e16 1.62487
\(358\) −3.50884e15 −0.0880895
\(359\) −6.30612e16 −1.55471 −0.777353 0.629065i \(-0.783438\pi\)
−0.777353 + 0.629065i \(0.783438\pi\)
\(360\) −1.23645e16 −0.299371
\(361\) −1.84145e16 −0.437887
\(362\) 3.55025e15 0.0829189
\(363\) −5.03231e16 −1.15445
\(364\) 3.88181e15 0.0874733
\(365\) −1.04745e16 −0.231862
\(366\) 1.89852e16 0.412846
\(367\) −1.03944e16 −0.222060 −0.111030 0.993817i \(-0.535415\pi\)
−0.111030 + 0.993817i \(0.535415\pi\)
\(368\) 3.37604e15 0.0708592
\(369\) 1.89690e16 0.391177
\(370\) −3.44120e16 −0.697267
\(371\) 1.25936e16 0.250738
\(372\) −8.44524e14 −0.0165228
\(373\) 8.47541e15 0.162950 0.0814748 0.996675i \(-0.474037\pi\)
0.0814748 + 0.996675i \(0.474037\pi\)
\(374\) −6.49824e16 −1.22781
\(375\) 2.49639e16 0.463563
\(376\) 3.29712e16 0.601748
\(377\) 5.59962e15 0.100448
\(378\) 8.24576e15 0.145390
\(379\) −5.81147e16 −1.00724 −0.503618 0.863926i \(-0.667998\pi\)
−0.503618 + 0.863926i \(0.667998\pi\)
\(380\) −4.05355e16 −0.690624
\(381\) 2.47714e16 0.414895
\(382\) 3.86082e16 0.635723
\(383\) −3.72322e16 −0.602735 −0.301368 0.953508i \(-0.597443\pi\)
−0.301368 + 0.953508i \(0.597443\pi\)
\(384\) 3.65118e16 0.581140
\(385\) 2.18035e17 3.41218
\(386\) 4.90486e16 0.754760
\(387\) 1.16298e16 0.175976
\(388\) −2.58147e16 −0.384115
\(389\) 8.98330e16 1.31451 0.657254 0.753669i \(-0.271718\pi\)
0.657254 + 0.753669i \(0.271718\pi\)
\(390\) −1.24205e15 −0.0178738
\(391\) 1.74856e16 0.247475
\(392\) −1.13377e17 −1.57821
\(393\) 1.18296e16 0.161964
\(394\) 2.91301e16 0.392298
\(395\) 9.85178e16 1.30507
\(396\) 3.58716e16 0.467447
\(397\) −4.90872e16 −0.629259 −0.314630 0.949215i \(-0.601880\pi\)
−0.314630 + 0.949215i \(0.601880\pi\)
\(398\) −2.56579e16 −0.323580
\(399\) 6.04188e16 0.749633
\(400\) 1.12156e16 0.136910
\(401\) −7.31157e16 −0.878157 −0.439078 0.898449i \(-0.644695\pi\)
−0.439078 + 0.898449i \(0.644695\pi\)
\(402\) −5.71598e14 −0.00675494
\(403\) −1.89608e14 −0.00220482
\(404\) −9.51017e16 −1.08820
\(405\) 1.12259e16 0.126405
\(406\) −1.09779e17 −1.21647
\(407\) 2.23135e17 2.43334
\(408\) 6.90142e16 0.740709
\(409\) 8.27643e16 0.874262 0.437131 0.899398i \(-0.355995\pi\)
0.437131 + 0.899398i \(0.355995\pi\)
\(410\) 5.60163e16 0.582397
\(411\) 1.09512e17 1.12070
\(412\) −6.02993e15 −0.0607408
\(413\) 2.27377e16 0.225461
\(414\) 2.26855e15 0.0221435
\(415\) −7.02043e16 −0.674608
\(416\) 6.54431e15 0.0619095
\(417\) 3.41636e15 0.0318184
\(418\) −6.17740e16 −0.566447
\(419\) 7.63073e16 0.688929 0.344465 0.938799i \(-0.388060\pi\)
0.344465 + 0.938799i \(0.388060\pi\)
\(420\) −1.03607e17 −0.921015
\(421\) 1.51693e17 1.32780 0.663901 0.747821i \(-0.268900\pi\)
0.663901 + 0.747821i \(0.268900\pi\)
\(422\) −1.22145e15 −0.0105279
\(423\) −2.99350e16 −0.254078
\(424\) 1.36750e16 0.114301
\(425\) 5.80894e16 0.478155
\(426\) −4.27464e16 −0.346527
\(427\) 3.55556e17 2.83875
\(428\) 1.14344e17 0.899140
\(429\) 8.05368e15 0.0623767
\(430\) 3.43434e16 0.261998
\(431\) −1.95964e17 −1.47256 −0.736281 0.676676i \(-0.763420\pi\)
−0.736281 + 0.676676i \(0.763420\pi\)
\(432\) −1.20979e16 −0.0895500
\(433\) 1.94301e17 1.41678 0.708392 0.705819i \(-0.249421\pi\)
0.708392 + 0.705819i \(0.249421\pi\)
\(434\) 3.71722e15 0.0267015
\(435\) −1.49455e17 −1.05762
\(436\) −1.62500e17 −1.13290
\(437\) 1.66223e16 0.114172
\(438\) 7.58514e15 0.0513313
\(439\) 1.99015e17 1.32699 0.663494 0.748182i \(-0.269073\pi\)
0.663494 + 0.748182i \(0.269073\pi\)
\(440\) 2.36757e17 1.55546
\(441\) 1.02937e17 0.666375
\(442\) 6.93266e15 0.0442237
\(443\) −7.49549e15 −0.0471168 −0.0235584 0.999722i \(-0.507500\pi\)
−0.0235584 + 0.999722i \(0.507500\pi\)
\(444\) −1.06030e17 −0.656807
\(445\) 5.05122e16 0.308358
\(446\) −2.42348e16 −0.145802
\(447\) −3.50205e16 −0.207646
\(448\) 9.59606e15 0.0560772
\(449\) −2.82724e17 −1.62840 −0.814201 0.580583i \(-0.802825\pi\)
−0.814201 + 0.580583i \(0.802825\pi\)
\(450\) 7.53642e15 0.0427843
\(451\) −3.63221e17 −2.03247
\(452\) 2.28273e17 1.25908
\(453\) −5.74342e16 −0.312271
\(454\) −7.99828e16 −0.428680
\(455\) −2.32611e16 −0.122901
\(456\) 6.56067e16 0.341725
\(457\) 1.30903e17 0.672196 0.336098 0.941827i \(-0.390893\pi\)
0.336098 + 0.941827i \(0.390893\pi\)
\(458\) 1.11555e16 0.0564761
\(459\) −6.26590e16 −0.312752
\(460\) −2.85039e16 −0.140275
\(461\) −2.79235e17 −1.35492 −0.677459 0.735560i \(-0.736919\pi\)
−0.677459 + 0.735560i \(0.736919\pi\)
\(462\) −1.57891e17 −0.755413
\(463\) −2.05969e17 −0.971685 −0.485843 0.874046i \(-0.661487\pi\)
−0.485843 + 0.874046i \(0.661487\pi\)
\(464\) 1.61065e17 0.749261
\(465\) 5.06068e15 0.0232148
\(466\) −9.01371e16 −0.407751
\(467\) 1.82294e17 0.813230 0.406615 0.913600i \(-0.366709\pi\)
0.406615 + 0.913600i \(0.366709\pi\)
\(468\) −3.82697e15 −0.0168367
\(469\) −1.07049e16 −0.0464473
\(470\) −8.83994e16 −0.378280
\(471\) 2.20297e17 0.929765
\(472\) 2.46901e16 0.102778
\(473\) −2.22690e17 −0.914329
\(474\) −7.13420e16 −0.288926
\(475\) 5.52213e16 0.220596
\(476\) 5.78295e17 2.27879
\(477\) −1.24157e16 −0.0482617
\(478\) −1.01725e17 −0.390074
\(479\) −1.74764e17 −0.661108 −0.330554 0.943787i \(-0.607236\pi\)
−0.330554 + 0.943787i \(0.607236\pi\)
\(480\) −1.74669e17 −0.651851
\(481\) −2.38052e16 −0.0876452
\(482\) −2.78245e16 −0.101070
\(483\) 4.24856e16 0.152260
\(484\) −4.57883e17 −1.61905
\(485\) 1.54691e17 0.539688
\(486\) −8.12927e15 −0.0279844
\(487\) −3.30318e16 −0.112200 −0.0561002 0.998425i \(-0.517867\pi\)
−0.0561002 + 0.998425i \(0.517867\pi\)
\(488\) 3.86086e17 1.29406
\(489\) −1.62390e17 −0.537096
\(490\) 3.03976e17 0.992120
\(491\) −5.07135e17 −1.63341 −0.816703 0.577058i \(-0.804201\pi\)
−0.816703 + 0.577058i \(0.804201\pi\)
\(492\) 1.72596e17 0.548603
\(493\) 8.34206e17 2.61679
\(494\) 6.59037e15 0.0204026
\(495\) −2.14955e17 −0.656770
\(496\) −5.45378e15 −0.0164462
\(497\) −8.00558e17 −2.38274
\(498\) 5.08387e16 0.149350
\(499\) −2.64604e17 −0.767261 −0.383630 0.923487i \(-0.625326\pi\)
−0.383630 + 0.923487i \(0.625326\pi\)
\(500\) 2.27143e17 0.650120
\(501\) 2.78253e17 0.786131
\(502\) 9.86688e16 0.275173
\(503\) −2.50951e17 −0.690870 −0.345435 0.938443i \(-0.612269\pi\)
−0.345435 + 0.938443i \(0.612269\pi\)
\(504\) 1.67687e17 0.455724
\(505\) 5.69881e17 1.52894
\(506\) −4.34385e16 −0.115053
\(507\) 2.19937e17 0.575104
\(508\) 2.25391e17 0.581866
\(509\) 4.29578e17 1.09491 0.547453 0.836836i \(-0.315597\pi\)
0.547453 + 0.836836i \(0.315597\pi\)
\(510\) −1.85034e17 −0.465636
\(511\) 1.42055e17 0.352956
\(512\) 3.37974e17 0.829140
\(513\) −5.95652e16 −0.144288
\(514\) −3.70162e16 −0.0885384
\(515\) 3.61334e16 0.0853417
\(516\) 1.05818e17 0.246796
\(517\) 5.73200e17 1.32013
\(518\) 4.66696e17 1.06143
\(519\) −2.95062e16 −0.0662712
\(520\) −2.52585e16 −0.0560254
\(521\) −2.44624e17 −0.535862 −0.267931 0.963438i \(-0.586340\pi\)
−0.267931 + 0.963438i \(0.586340\pi\)
\(522\) 1.08229e17 0.234144
\(523\) 5.77350e17 1.23361 0.616805 0.787116i \(-0.288427\pi\)
0.616805 + 0.787116i \(0.288427\pi\)
\(524\) 1.07636e17 0.227146
\(525\) 1.41143e17 0.294187
\(526\) 3.39641e17 0.699218
\(527\) −2.82469e16 −0.0574383
\(528\) 2.31652e17 0.465281
\(529\) −4.92348e17 −0.976810
\(530\) −3.66641e16 −0.0718535
\(531\) −2.24165e16 −0.0433963
\(532\) 5.49742e17 1.05132
\(533\) 3.87503e16 0.0732063
\(534\) −3.65786e16 −0.0682666
\(535\) −6.85185e17 −1.26331
\(536\) −1.16241e16 −0.0211733
\(537\) 6.47854e16 0.116586
\(538\) −4.34193e17 −0.771966
\(539\) −1.97104e18 −3.46233
\(540\) 1.02143e17 0.177275
\(541\) −2.66477e16 −0.0456959 −0.0228480 0.999739i \(-0.507273\pi\)
−0.0228480 + 0.999739i \(0.507273\pi\)
\(542\) −7.81927e16 −0.132486
\(543\) −6.55500e16 −0.109742
\(544\) 9.74942e17 1.61282
\(545\) 9.73752e17 1.59174
\(546\) 1.68446e16 0.0272088
\(547\) −4.19740e17 −0.669981 −0.334991 0.942221i \(-0.608733\pi\)
−0.334991 + 0.942221i \(0.608733\pi\)
\(548\) 9.96435e17 1.57172
\(549\) −3.50533e17 −0.546397
\(550\) −1.44308e17 −0.222297
\(551\) 7.93018e17 1.20725
\(552\) 4.61337e16 0.0694087
\(553\) −1.33610e18 −1.98667
\(554\) −5.10124e17 −0.749656
\(555\) 6.35366e17 0.922825
\(556\) 3.10849e16 0.0446235
\(557\) 1.02642e18 1.45635 0.728173 0.685393i \(-0.240370\pi\)
0.728173 + 0.685393i \(0.240370\pi\)
\(558\) −3.66471e15 −0.00513945
\(559\) 2.37577e16 0.0329327
\(560\) −6.69071e17 −0.916749
\(561\) 1.19980e18 1.62499
\(562\) −6.24445e16 −0.0836003
\(563\) −3.37558e17 −0.446729 −0.223364 0.974735i \(-0.571704\pi\)
−0.223364 + 0.974735i \(0.571704\pi\)
\(564\) −2.72375e17 −0.356330
\(565\) −1.36789e18 −1.76903
\(566\) −3.15007e16 −0.0402729
\(567\) −1.52246e17 −0.192422
\(568\) −8.69298e17 −1.08619
\(569\) 2.22383e17 0.274708 0.137354 0.990522i \(-0.456140\pi\)
0.137354 + 0.990522i \(0.456140\pi\)
\(570\) −1.75899e17 −0.214821
\(571\) 9.51406e17 1.14877 0.574383 0.818587i \(-0.305242\pi\)
0.574383 + 0.818587i \(0.305242\pi\)
\(572\) 7.32793e16 0.0874797
\(573\) −7.12842e17 −0.841372
\(574\) −7.59693e17 −0.886565
\(575\) 3.88308e16 0.0448059
\(576\) −9.46049e15 −0.0107936
\(577\) 8.05161e15 0.00908322 0.00454161 0.999990i \(-0.498554\pi\)
0.00454161 + 0.999990i \(0.498554\pi\)
\(578\) 6.41731e17 0.715850
\(579\) −9.05607e17 −0.998917
\(580\) −1.35987e18 −1.48326
\(581\) 9.52111e17 1.02693
\(582\) −1.12020e17 −0.119480
\(583\) 2.37738e17 0.250757
\(584\) 1.54253e17 0.160898
\(585\) 2.29325e16 0.0236558
\(586\) 1.13902e17 0.116197
\(587\) −7.16555e17 −0.722939 −0.361469 0.932384i \(-0.617725\pi\)
−0.361469 + 0.932384i \(0.617725\pi\)
\(588\) 9.36604e17 0.934552
\(589\) −2.68522e16 −0.0264991
\(590\) −6.61967e16 −0.0646098
\(591\) −5.37843e17 −0.519203
\(592\) −6.84720e17 −0.653765
\(593\) 1.49489e18 1.41173 0.705866 0.708345i \(-0.250558\pi\)
0.705866 + 0.708345i \(0.250558\pi\)
\(594\) 1.55660e17 0.145401
\(595\) −3.46534e18 −3.20174
\(596\) −3.18647e17 −0.291212
\(597\) 4.73735e17 0.428255
\(598\) 4.63425e15 0.00414402
\(599\) 1.51378e18 1.33902 0.669512 0.742801i \(-0.266503\pi\)
0.669512 + 0.742801i \(0.266503\pi\)
\(600\) 1.53262e17 0.134107
\(601\) −2.90568e17 −0.251515 −0.125758 0.992061i \(-0.540136\pi\)
−0.125758 + 0.992061i \(0.540136\pi\)
\(602\) −4.65765e17 −0.398832
\(603\) 1.05537e16 0.00894009
\(604\) −5.22585e17 −0.437942
\(605\) 2.74379e18 2.27479
\(606\) −4.12682e17 −0.338488
\(607\) 3.89647e17 0.316188 0.158094 0.987424i \(-0.449465\pi\)
0.158094 + 0.987424i \(0.449465\pi\)
\(608\) 9.26805e17 0.744072
\(609\) 2.02691e18 1.60999
\(610\) −1.03514e18 −0.813494
\(611\) −6.11520e16 −0.0475491
\(612\) −5.70125e17 −0.438617
\(613\) 3.31013e17 0.251972 0.125986 0.992032i \(-0.459791\pi\)
0.125986 + 0.992032i \(0.459791\pi\)
\(614\) −1.06895e18 −0.805126
\(615\) −1.03426e18 −0.770797
\(616\) −3.21090e18 −2.36784
\(617\) −2.30491e18 −1.68190 −0.840952 0.541109i \(-0.818004\pi\)
−0.840952 + 0.541109i \(0.818004\pi\)
\(618\) −2.61661e16 −0.0188936
\(619\) 1.02217e17 0.0730352 0.0365176 0.999333i \(-0.488373\pi\)
0.0365176 + 0.999333i \(0.488373\pi\)
\(620\) 4.60464e16 0.0325574
\(621\) −4.18854e16 −0.0293067
\(622\) −5.94609e17 −0.411713
\(623\) −6.85046e17 −0.469405
\(624\) −2.47138e16 −0.0167587
\(625\) −1.79955e18 −1.20766
\(626\) 1.15305e18 0.765798
\(627\) 1.14056e18 0.749687
\(628\) 2.00445e18 1.30394
\(629\) −3.54639e18 −2.28327
\(630\) −4.49587e17 −0.286484
\(631\) −2.06481e18 −1.30224 −0.651119 0.758976i \(-0.725700\pi\)
−0.651119 + 0.758976i \(0.725700\pi\)
\(632\) −1.45082e18 −0.905635
\(633\) 2.25522e16 0.0139336
\(634\) 4.78309e17 0.292501
\(635\) −1.35062e18 −0.817531
\(636\) −1.12969e17 −0.0676842
\(637\) 2.10281e17 0.124708
\(638\) −2.07237e18 −1.21656
\(639\) 7.89247e17 0.458625
\(640\) −1.99075e18 −1.14511
\(641\) 2.74428e18 1.56261 0.781306 0.624149i \(-0.214554\pi\)
0.781306 + 0.624149i \(0.214554\pi\)
\(642\) 4.96179e17 0.279680
\(643\) 5.66233e17 0.315954 0.157977 0.987443i \(-0.449503\pi\)
0.157977 + 0.987443i \(0.449503\pi\)
\(644\) 3.86571e17 0.213536
\(645\) −6.34099e17 −0.346752
\(646\) 9.81804e17 0.531512
\(647\) −1.70444e18 −0.913491 −0.456745 0.889597i \(-0.650985\pi\)
−0.456745 + 0.889597i \(0.650985\pi\)
\(648\) −1.65318e17 −0.0877169
\(649\) 4.29233e17 0.225477
\(650\) 1.53956e16 0.00800680
\(651\) −6.86329e16 −0.0353391
\(652\) −1.47757e18 −0.753247
\(653\) 1.24185e18 0.626804 0.313402 0.949620i \(-0.398531\pi\)
0.313402 + 0.949620i \(0.398531\pi\)
\(654\) −7.05146e17 −0.352390
\(655\) −6.44991e17 −0.319143
\(656\) 1.11459e18 0.546062
\(657\) −1.40048e17 −0.0679364
\(658\) 1.19887e18 0.575844
\(659\) 2.19988e18 1.04627 0.523134 0.852250i \(-0.324763\pi\)
0.523134 + 0.852250i \(0.324763\pi\)
\(660\) −1.95584e18 −0.921082
\(661\) 1.41911e18 0.661770 0.330885 0.943671i \(-0.392653\pi\)
0.330885 + 0.943671i \(0.392653\pi\)
\(662\) −5.11715e17 −0.236293
\(663\) −1.28001e17 −0.0585296
\(664\) 1.03386e18 0.468135
\(665\) −3.29424e18 −1.47712
\(666\) −4.60102e17 −0.204302
\(667\) 5.57638e17 0.245208
\(668\) 2.53179e18 1.10250
\(669\) 4.47459e17 0.192967
\(670\) 3.11655e16 0.0133103
\(671\) 6.71205e18 2.83896
\(672\) 2.36886e18 0.992293
\(673\) −3.61377e18 −1.49921 −0.749605 0.661885i \(-0.769756\pi\)
−0.749605 + 0.661885i \(0.769756\pi\)
\(674\) 1.00366e18 0.412378
\(675\) −1.39149e17 −0.0566245
\(676\) 2.00117e18 0.806550
\(677\) −1.28727e18 −0.513858 −0.256929 0.966430i \(-0.582711\pi\)
−0.256929 + 0.966430i \(0.582711\pi\)
\(678\) 9.90561e17 0.391641
\(679\) −2.09792e18 −0.821551
\(680\) −3.76289e18 −1.45953
\(681\) 1.47676e18 0.567354
\(682\) 7.01723e16 0.0267034
\(683\) −1.78382e17 −0.0672384 −0.0336192 0.999435i \(-0.510703\pi\)
−0.0336192 + 0.999435i \(0.510703\pi\)
\(684\) −5.41975e17 −0.202355
\(685\) −5.97097e18 −2.20829
\(686\) −2.06036e18 −0.754807
\(687\) −2.05970e17 −0.0747455
\(688\) 6.83354e17 0.245652
\(689\) −2.53631e16 −0.00903186
\(690\) −1.23689e17 −0.0436328
\(691\) −3.98126e18 −1.39127 −0.695637 0.718393i \(-0.744878\pi\)
−0.695637 + 0.718393i \(0.744878\pi\)
\(692\) −2.68472e17 −0.0929416
\(693\) 2.91522e18 0.999781
\(694\) 2.15346e18 0.731646
\(695\) −1.86271e17 −0.0626967
\(696\) 2.20095e18 0.733924
\(697\) 5.77285e18 1.90712
\(698\) 2.39152e18 0.782735
\(699\) 1.66425e18 0.539654
\(700\) 1.28424e18 0.412580
\(701\) −2.72040e18 −0.865895 −0.432947 0.901419i \(-0.642526\pi\)
−0.432947 + 0.901419i \(0.642526\pi\)
\(702\) −1.66066e16 −0.00523710
\(703\) −3.37129e18 −1.05338
\(704\) 1.81151e17 0.0560813
\(705\) 1.63216e18 0.500650
\(706\) −1.61838e18 −0.491870
\(707\) −7.72873e18 −2.32746
\(708\) −2.03964e17 −0.0608608
\(709\) 3.78329e18 1.11859 0.559293 0.828970i \(-0.311073\pi\)
0.559293 + 0.828970i \(0.311073\pi\)
\(710\) 2.33068e18 0.682815
\(711\) 1.31722e18 0.382390
\(712\) −7.43868e17 −0.213981
\(713\) −1.88821e16 −0.00538230
\(714\) 2.50944e18 0.708823
\(715\) −4.39114e17 −0.122910
\(716\) 5.89473e17 0.163504
\(717\) 1.87820e18 0.516259
\(718\) −2.48987e18 −0.678215
\(719\) −5.92790e18 −1.60016 −0.800079 0.599895i \(-0.795209\pi\)
−0.800079 + 0.599895i \(0.795209\pi\)
\(720\) 6.59619e17 0.176454
\(721\) −4.90041e17 −0.129913
\(722\) −7.27064e17 −0.191021
\(723\) 5.13737e17 0.133765
\(724\) −5.96430e17 −0.153907
\(725\) 1.85255e18 0.473775
\(726\) −1.98692e18 −0.503609
\(727\) −1.64674e18 −0.413669 −0.206834 0.978376i \(-0.566316\pi\)
−0.206834 + 0.978376i \(0.566316\pi\)
\(728\) 3.42555e17 0.0852858
\(729\) 1.50095e17 0.0370370
\(730\) −4.13568e17 −0.101146
\(731\) 3.53931e18 0.857939
\(732\) −3.18945e18 −0.766290
\(733\) 3.18011e18 0.757296 0.378648 0.925541i \(-0.376389\pi\)
0.378648 + 0.925541i \(0.376389\pi\)
\(734\) −4.10406e17 −0.0968699
\(735\) −5.61245e18 −1.31306
\(736\) 6.51715e17 0.151131
\(737\) −2.02084e17 −0.0464507
\(738\) 7.48960e17 0.170645
\(739\) −4.55441e18 −1.02859 −0.514296 0.857613i \(-0.671947\pi\)
−0.514296 + 0.857613i \(0.671947\pi\)
\(740\) 5.78110e18 1.29421
\(741\) −1.21681e17 −0.0270026
\(742\) 4.97239e17 0.109380
\(743\) −4.15267e17 −0.0905525 −0.0452762 0.998975i \(-0.514417\pi\)
−0.0452762 + 0.998975i \(0.514417\pi\)
\(744\) −7.45261e16 −0.0161096
\(745\) 1.90944e18 0.409157
\(746\) 3.34638e17 0.0710841
\(747\) −9.38660e17 −0.197663
\(748\) 1.09168e19 2.27896
\(749\) 9.29248e18 1.92309
\(750\) 9.85656e17 0.202221
\(751\) −3.75814e18 −0.764386 −0.382193 0.924082i \(-0.624831\pi\)
−0.382193 + 0.924082i \(0.624831\pi\)
\(752\) −1.75894e18 −0.354680
\(753\) −1.82177e18 −0.364189
\(754\) 2.21092e17 0.0438186
\(755\) 3.13151e18 0.615316
\(756\) −1.38526e18 −0.269861
\(757\) −7.53010e18 −1.45438 −0.727190 0.686436i \(-0.759174\pi\)
−0.727190 + 0.686436i \(0.759174\pi\)
\(758\) −2.29456e18 −0.439390
\(759\) 8.02027e17 0.152271
\(760\) −3.57710e18 −0.673353
\(761\) 3.68111e17 0.0687035 0.0343518 0.999410i \(-0.489063\pi\)
0.0343518 + 0.999410i \(0.489063\pi\)
\(762\) 9.78057e17 0.180991
\(763\) −1.32060e19 −2.42305
\(764\) −6.48605e18 −1.17998
\(765\) 3.41638e18 0.616264
\(766\) −1.47005e18 −0.262933
\(767\) −4.57929e16 −0.00812134
\(768\) 1.33530e18 0.234817
\(769\) 9.13345e18 1.59263 0.796313 0.604885i \(-0.206781\pi\)
0.796313 + 0.604885i \(0.206781\pi\)
\(770\) 8.60876e18 1.48851
\(771\) 6.83448e17 0.117180
\(772\) −8.23999e18 −1.40092
\(773\) −3.94572e18 −0.665212 −0.332606 0.943066i \(-0.607928\pi\)
−0.332606 + 0.943066i \(0.607928\pi\)
\(774\) 4.59185e17 0.0767664
\(775\) −6.27288e16 −0.0103993
\(776\) −2.27805e18 −0.374509
\(777\) −8.61683e18 −1.40479
\(778\) 3.54690e18 0.573432
\(779\) 5.48782e18 0.879846
\(780\) 2.08660e17 0.0331759
\(781\) −1.51126e19 −2.38291
\(782\) 6.90390e17 0.107957
\(783\) −1.99828e18 −0.309887
\(784\) 6.04842e18 0.930223
\(785\) −1.20114e19 −1.83206
\(786\) 4.67073e17 0.0706542
\(787\) 4.37670e18 0.656615 0.328308 0.944571i \(-0.393522\pi\)
0.328308 + 0.944571i \(0.393522\pi\)
\(788\) −4.89376e18 −0.728152
\(789\) −6.27095e18 −0.925408
\(790\) 3.88981e18 0.569315
\(791\) 1.85513e19 2.69294
\(792\) 3.16553e18 0.455757
\(793\) −7.16076e17 −0.102255
\(794\) −1.93813e18 −0.274504
\(795\) 6.76947e17 0.0950974
\(796\) 4.31044e18 0.600602
\(797\) 1.39323e18 0.192550 0.0962751 0.995355i \(-0.469307\pi\)
0.0962751 + 0.995355i \(0.469307\pi\)
\(798\) 2.38554e18 0.327015
\(799\) −9.11015e18 −1.23871
\(800\) 2.16508e18 0.292005
\(801\) 6.75368e17 0.0903502
\(802\) −2.88685e18 −0.383081
\(803\) 2.68166e18 0.352982
\(804\) 9.60266e16 0.0125380
\(805\) −2.31646e18 −0.300021
\(806\) −7.48634e15 −0.000961816 0
\(807\) 8.01672e18 1.02169
\(808\) −8.39236e18 −1.06099
\(809\) 1.51208e19 1.89631 0.948154 0.317813i \(-0.102948\pi\)
0.948154 + 0.317813i \(0.102948\pi\)
\(810\) 4.43236e17 0.0551419
\(811\) 1.55860e19 1.92352 0.961762 0.273885i \(-0.0883089\pi\)
0.961762 + 0.273885i \(0.0883089\pi\)
\(812\) 1.84426e19 2.25791
\(813\) 1.44371e18 0.175344
\(814\) 8.81010e18 1.06151
\(815\) 8.85407e18 1.05832
\(816\) −3.68176e18 −0.436586
\(817\) 3.36456e18 0.395809
\(818\) 3.26781e18 0.381382
\(819\) −3.11011e17 −0.0360106
\(820\) −9.41055e18 −1.08100
\(821\) 2.41807e18 0.275574 0.137787 0.990462i \(-0.456001\pi\)
0.137787 + 0.990462i \(0.456001\pi\)
\(822\) 4.32390e18 0.488888
\(823\) −3.48773e18 −0.391241 −0.195621 0.980680i \(-0.562672\pi\)
−0.195621 + 0.980680i \(0.562672\pi\)
\(824\) −5.32118e17 −0.0592218
\(825\) 2.66444e18 0.294208
\(826\) 8.97760e17 0.0983536
\(827\) −1.15041e19 −1.25045 −0.625223 0.780446i \(-0.714992\pi\)
−0.625223 + 0.780446i \(0.714992\pi\)
\(828\) −3.81109e17 −0.0411010
\(829\) 2.18971e18 0.234305 0.117153 0.993114i \(-0.462623\pi\)
0.117153 + 0.993114i \(0.462623\pi\)
\(830\) −2.77190e18 −0.294286
\(831\) 9.41866e18 0.992162
\(832\) −1.93261e16 −0.00201996
\(833\) 3.13267e19 3.24880
\(834\) 1.34889e17 0.0138803
\(835\) −1.51713e19 −1.54904
\(836\) 1.03778e19 1.05139
\(837\) 6.76632e16 0.00680201
\(838\) 3.01286e18 0.300534
\(839\) 7.57490e18 0.749763 0.374882 0.927073i \(-0.377683\pi\)
0.374882 + 0.927073i \(0.377683\pi\)
\(840\) −9.14288e18 −0.897982
\(841\) 1.63433e19 1.59282
\(842\) 5.98936e18 0.579231
\(843\) 1.15294e18 0.110644
\(844\) 2.05199e17 0.0195411
\(845\) −1.19917e19 −1.13322
\(846\) −1.18194e18 −0.110837
\(847\) −3.72113e19 −3.46284
\(848\) −7.29531e17 −0.0673707
\(849\) 5.81612e17 0.0533008
\(850\) 2.29356e18 0.208587
\(851\) −2.37064e18 −0.213955
\(852\) 7.18125e18 0.643195
\(853\) −8.81050e18 −0.783127 −0.391563 0.920151i \(-0.628066\pi\)
−0.391563 + 0.920151i \(0.628066\pi\)
\(854\) 1.40385e19 1.23836
\(855\) 3.24770e18 0.284313
\(856\) 1.00904e19 0.876654
\(857\) −1.14302e19 −0.985547 −0.492773 0.870158i \(-0.664017\pi\)
−0.492773 + 0.870158i \(0.664017\pi\)
\(858\) 3.17986e17 0.0272108
\(859\) −2.00379e19 −1.70175 −0.850876 0.525366i \(-0.823928\pi\)
−0.850876 + 0.525366i \(0.823928\pi\)
\(860\) −5.76957e18 −0.486299
\(861\) 1.40266e19 1.17336
\(862\) −7.73730e18 −0.642380
\(863\) −9.43378e18 −0.777349 −0.388674 0.921375i \(-0.627067\pi\)
−0.388674 + 0.921375i \(0.627067\pi\)
\(864\) −2.33540e18 −0.190995
\(865\) 1.60878e18 0.130584
\(866\) 7.67165e18 0.618049
\(867\) −1.18486e19 −0.947421
\(868\) −6.24481e17 −0.0495611
\(869\) −2.52223e19 −1.98681
\(870\) −5.90099e18 −0.461370
\(871\) 2.15593e16 0.00167308
\(872\) −1.43400e19 −1.10456
\(873\) 2.06828e18 0.158131
\(874\) 6.56302e17 0.0498058
\(875\) 1.84594e19 1.39049
\(876\) −1.27428e18 −0.0952769
\(877\) −9.99454e18 −0.741764 −0.370882 0.928680i \(-0.620944\pi\)
−0.370882 + 0.928680i \(0.620944\pi\)
\(878\) 7.85778e18 0.578876
\(879\) −2.10302e18 −0.153786
\(880\) −1.26305e19 −0.916816
\(881\) −1.65985e19 −1.19598 −0.597991 0.801503i \(-0.704034\pi\)
−0.597991 + 0.801503i \(0.704034\pi\)
\(882\) 4.06428e18 0.290695
\(883\) −2.07107e19 −1.47045 −0.735223 0.677825i \(-0.762923\pi\)
−0.735223 + 0.677825i \(0.762923\pi\)
\(884\) −1.16466e18 −0.0820844
\(885\) 1.22222e18 0.0855104
\(886\) −2.95947e17 −0.0205539
\(887\) −2.46265e18 −0.169785 −0.0848925 0.996390i \(-0.527055\pi\)
−0.0848925 + 0.996390i \(0.527055\pi\)
\(888\) −9.35672e18 −0.640382
\(889\) 1.83171e19 1.24450
\(890\) 1.99439e18 0.134516
\(891\) −2.87403e18 −0.192436
\(892\) 4.07136e18 0.270625
\(893\) −8.66034e18 −0.571479
\(894\) −1.38273e18 −0.0905822
\(895\) −3.53232e18 −0.229726
\(896\) 2.69985e19 1.74316
\(897\) −8.55644e16 −0.00548456
\(898\) −1.11629e19 −0.710363
\(899\) −9.00831e17 −0.0569122
\(900\) −1.26609e18 −0.0794126
\(901\) −3.77848e18 −0.235291
\(902\) −1.43412e19 −0.886630
\(903\) 8.59965e18 0.527850
\(904\) 2.01442e19 1.22760
\(905\) 3.57401e18 0.216242
\(906\) −2.26769e18 −0.136223
\(907\) 9.10587e18 0.543093 0.271546 0.962425i \(-0.412465\pi\)
0.271546 + 0.962425i \(0.412465\pi\)
\(908\) 1.34368e19 0.795681
\(909\) 7.61954e18 0.447985
\(910\) −9.18427e17 −0.0536137
\(911\) 1.08145e19 0.626813 0.313407 0.949619i \(-0.398530\pi\)
0.313407 + 0.949619i \(0.398530\pi\)
\(912\) −3.49998e18 −0.201418
\(913\) 1.79736e19 1.02701
\(914\) 5.16851e18 0.293234
\(915\) 1.91122e19 1.07665
\(916\) −1.87409e18 −0.104826
\(917\) 8.74738e18 0.485822
\(918\) −2.47398e18 −0.136433
\(919\) −6.28434e18 −0.344119 −0.172060 0.985087i \(-0.555042\pi\)
−0.172060 + 0.985087i \(0.555042\pi\)
\(920\) −2.51537e18 −0.136767
\(921\) 1.97366e19 1.06558
\(922\) −1.10251e19 −0.591060
\(923\) 1.61229e18 0.0858287
\(924\) 2.65251e19 1.40214
\(925\) −7.87557e18 −0.413391
\(926\) −8.13234e18 −0.423881
\(927\) 4.83118e17 0.0250054
\(928\) 3.10922e19 1.59805
\(929\) −2.70811e19 −1.38218 −0.691090 0.722769i \(-0.742869\pi\)
−0.691090 + 0.722769i \(0.742869\pi\)
\(930\) 1.99812e17 0.0101271
\(931\) 2.97800e19 1.49883
\(932\) 1.51427e19 0.756834
\(933\) 1.09786e19 0.544898
\(934\) 7.19759e18 0.354758
\(935\) −6.54173e19 −3.20197
\(936\) −3.37716e17 −0.0164157
\(937\) 2.81216e18 0.135748 0.0678738 0.997694i \(-0.478378\pi\)
0.0678738 + 0.997694i \(0.478378\pi\)
\(938\) −4.22667e17 −0.0202619
\(939\) −2.12893e19 −1.01353
\(940\) 1.48508e19 0.702132
\(941\) −5.77022e18 −0.270932 −0.135466 0.990782i \(-0.543253\pi\)
−0.135466 + 0.990782i \(0.543253\pi\)
\(942\) 8.69807e18 0.405595
\(943\) 3.85895e18 0.178708
\(944\) −1.31716e18 −0.0605789
\(945\) 8.30095e18 0.379159
\(946\) −8.79253e18 −0.398861
\(947\) 3.28036e19 1.47791 0.738953 0.673757i \(-0.235320\pi\)
0.738953 + 0.673757i \(0.235320\pi\)
\(948\) 1.19852e19 0.536280
\(949\) −2.86093e17 −0.0127139
\(950\) 2.18032e18 0.0962315
\(951\) −8.83124e18 −0.387123
\(952\) 5.10323e19 2.22180
\(953\) −2.07704e19 −0.898133 −0.449066 0.893498i \(-0.648243\pi\)
−0.449066 + 0.893498i \(0.648243\pi\)
\(954\) −4.90214e17 −0.0210533
\(955\) 3.88666e19 1.65789
\(956\) 1.70895e19 0.724024
\(957\) 3.82632e19 1.61010
\(958\) −6.90028e18 −0.288397
\(959\) 8.09784e19 3.36162
\(960\) 5.15818e17 0.0212684
\(961\) −2.43870e19 −0.998751
\(962\) −9.39907e17 −0.0382338
\(963\) −9.16120e18 −0.370153
\(964\) 4.67442e18 0.187598
\(965\) 4.93768e19 1.96832
\(966\) 1.67747e18 0.0664208
\(967\) 3.81385e19 1.50000 0.750000 0.661438i \(-0.230053\pi\)
0.750000 + 0.661438i \(0.230053\pi\)
\(968\) −4.04064e19 −1.57856
\(969\) −1.81275e19 −0.703451
\(970\) 6.10770e18 0.235430
\(971\) −4.46309e19 −1.70888 −0.854439 0.519553i \(-0.826099\pi\)
−0.854439 + 0.519553i \(0.826099\pi\)
\(972\) 1.36569e18 0.0519423
\(973\) 2.52621e18 0.0954414
\(974\) −1.30421e18 −0.0489455
\(975\) −2.84256e17 −0.0105969
\(976\) −2.05968e19 −0.762741
\(977\) −3.29520e19 −1.21218 −0.606089 0.795397i \(-0.707263\pi\)
−0.606089 + 0.795397i \(0.707263\pi\)
\(978\) −6.41171e18 −0.234299
\(979\) −1.29320e19 −0.469439
\(980\) −5.10669e19 −1.84149
\(981\) 1.30195e19 0.466385
\(982\) −2.00234e19 −0.712546
\(983\) −6.62960e18 −0.234363 −0.117182 0.993111i \(-0.537386\pi\)
−0.117182 + 0.993111i \(0.537386\pi\)
\(984\) 1.52310e19 0.534884
\(985\) 2.93251e19 1.02307
\(986\) 3.29372e19 1.14153
\(987\) −2.21354e19 −0.762124
\(988\) −1.10716e18 −0.0378695
\(989\) 2.36591e18 0.0803938
\(990\) −8.48713e18 −0.286505
\(991\) 1.82552e19 0.612221 0.306110 0.951996i \(-0.400972\pi\)
0.306110 + 0.951996i \(0.400972\pi\)
\(992\) −1.05281e18 −0.0350770
\(993\) 9.44804e18 0.312731
\(994\) −3.16087e19 −1.03943
\(995\) −2.58296e19 −0.843856
\(996\) −8.54073e18 −0.277210
\(997\) 2.75990e19 0.889968 0.444984 0.895538i \(-0.353209\pi\)
0.444984 + 0.895538i \(0.353209\pi\)
\(998\) −1.04474e19 −0.334705
\(999\) 8.49509e18 0.270391
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 177.14.a.b.1.19 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.19 31 1.1 even 1 trivial