Properties

Label 177.14.a.b.1.2
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

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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 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-169.081 q^{2} -729.000 q^{3} +20396.4 q^{4} +15031.4 q^{5} +123260. q^{6} -257399. q^{7} -2.06354e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-169.081 q^{2} -729.000 q^{3} +20396.4 q^{4} +15031.4 q^{5} +123260. q^{6} -257399. q^{7} -2.06354e6 q^{8} +531441. q^{9} -2.54153e6 q^{10} -4.81287e6 q^{11} -1.48690e7 q^{12} -3.34772e7 q^{13} +4.35214e7 q^{14} -1.09579e7 q^{15} +1.81818e8 q^{16} -1.05741e8 q^{17} -8.98566e7 q^{18} +1.32508e8 q^{19} +3.06587e8 q^{20} +1.87644e8 q^{21} +8.13765e8 q^{22} +7.80853e8 q^{23} +1.50432e9 q^{24} -9.94759e8 q^{25} +5.66035e9 q^{26} -3.87420e8 q^{27} -5.25002e9 q^{28} -9.46595e8 q^{29} +1.85277e9 q^{30} +7.66826e9 q^{31} -1.38374e10 q^{32} +3.50858e9 q^{33} +1.78788e10 q^{34} -3.86908e9 q^{35} +1.08395e10 q^{36} +1.25449e10 q^{37} -2.24046e10 q^{38} +2.44048e10 q^{39} -3.10179e10 q^{40} -2.31196e10 q^{41} -3.17271e10 q^{42} +2.54394e10 q^{43} -9.81653e10 q^{44} +7.98831e9 q^{45} -1.32027e11 q^{46} +9.37427e9 q^{47} -1.32545e11 q^{48} -3.06346e10 q^{49} +1.68195e11 q^{50} +7.70852e10 q^{51} -6.82814e11 q^{52} +1.13282e11 q^{53} +6.55055e10 q^{54} -7.23442e10 q^{55} +5.31153e11 q^{56} -9.65985e10 q^{57} +1.60051e11 q^{58} -4.21805e10 q^{59} -2.23502e11 q^{60} -1.44401e11 q^{61} -1.29656e12 q^{62} -1.36793e11 q^{63} +8.50198e11 q^{64} -5.03209e11 q^{65} -5.93235e11 q^{66} -4.28988e11 q^{67} -2.15674e12 q^{68} -5.69242e11 q^{69} +6.54188e11 q^{70} +1.96469e12 q^{71} -1.09665e12 q^{72} -1.02505e12 q^{73} -2.12110e12 q^{74} +7.25180e11 q^{75} +2.70269e12 q^{76} +1.23883e12 q^{77} -4.12640e12 q^{78} +7.60306e11 q^{79} +2.73298e12 q^{80} +2.82430e11 q^{81} +3.90909e12 q^{82} +1.79334e12 q^{83} +3.82727e12 q^{84} -1.58944e12 q^{85} -4.30132e12 q^{86} +6.90068e11 q^{87} +9.93153e12 q^{88} +8.56658e12 q^{89} -1.35067e12 q^{90} +8.61700e12 q^{91} +1.59266e13 q^{92} -5.59016e12 q^{93} -1.58501e12 q^{94} +1.99179e12 q^{95} +1.00875e13 q^{96} +1.76137e12 q^{97} +5.17973e12 q^{98} -2.55775e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −169.081 −1.86810 −0.934050 0.357142i \(-0.883751\pi\)
−0.934050 + 0.357142i \(0.883751\pi\)
\(3\) −729.000 −0.577350
\(4\) 20396.4 2.48980
\(5\) 15031.4 0.430224 0.215112 0.976589i \(-0.430988\pi\)
0.215112 + 0.976589i \(0.430988\pi\)
\(6\) 123260. 1.07855
\(7\) −257399. −0.826933 −0.413466 0.910519i \(-0.635682\pi\)
−0.413466 + 0.910519i \(0.635682\pi\)
\(8\) −2.06354e6 −2.78309
\(9\) 531441. 0.333333
\(10\) −2.54153e6 −0.803702
\(11\) −4.81287e6 −0.819127 −0.409564 0.912282i \(-0.634319\pi\)
−0.409564 + 0.912282i \(0.634319\pi\)
\(12\) −1.48690e7 −1.43749
\(13\) −3.34772e7 −1.92361 −0.961804 0.273738i \(-0.911740\pi\)
−0.961804 + 0.273738i \(0.911740\pi\)
\(14\) 4.35214e7 1.54479
\(15\) −1.09579e7 −0.248390
\(16\) 1.81818e8 2.70929
\(17\) −1.05741e8 −1.06249 −0.531246 0.847218i \(-0.678276\pi\)
−0.531246 + 0.847218i \(0.678276\pi\)
\(18\) −8.98566e7 −0.622700
\(19\) 1.32508e8 0.646166 0.323083 0.946371i \(-0.395281\pi\)
0.323083 + 0.946371i \(0.395281\pi\)
\(20\) 3.06587e8 1.07117
\(21\) 1.87644e8 0.477430
\(22\) 8.13765e8 1.53021
\(23\) 7.80853e8 1.09986 0.549931 0.835210i \(-0.314654\pi\)
0.549931 + 0.835210i \(0.314654\pi\)
\(24\) 1.50432e9 1.60682
\(25\) −9.94759e8 −0.814907
\(26\) 5.66035e9 3.59349
\(27\) −3.87420e8 −0.192450
\(28\) −5.25002e9 −2.05889
\(29\) −9.46595e8 −0.295514 −0.147757 0.989024i \(-0.547205\pi\)
−0.147757 + 0.989024i \(0.547205\pi\)
\(30\) 1.85277e9 0.464018
\(31\) 7.66826e9 1.55184 0.775918 0.630834i \(-0.217287\pi\)
0.775918 + 0.630834i \(0.217287\pi\)
\(32\) −1.38374e10 −2.27814
\(33\) 3.50858e9 0.472923
\(34\) 1.78788e10 1.98484
\(35\) −3.86908e9 −0.355767
\(36\) 1.08395e10 0.829932
\(37\) 1.25449e10 0.803812 0.401906 0.915681i \(-0.368348\pi\)
0.401906 + 0.915681i \(0.368348\pi\)
\(38\) −2.24046e10 −1.20710
\(39\) 2.44048e10 1.11060
\(40\) −3.10179e10 −1.19735
\(41\) −2.31196e10 −0.760125 −0.380063 0.924961i \(-0.624098\pi\)
−0.380063 + 0.924961i \(0.624098\pi\)
\(42\) −3.17271e10 −0.891887
\(43\) 2.54394e10 0.613708 0.306854 0.951757i \(-0.400724\pi\)
0.306854 + 0.951757i \(0.400724\pi\)
\(44\) −9.81653e10 −2.03946
\(45\) 7.98831e9 0.143408
\(46\) −1.32027e11 −2.05465
\(47\) 9.37427e9 0.126853 0.0634266 0.997987i \(-0.479797\pi\)
0.0634266 + 0.997987i \(0.479797\pi\)
\(48\) −1.32545e11 −1.56421
\(49\) −3.06346e10 −0.316182
\(50\) 1.68195e11 1.52233
\(51\) 7.70852e10 0.613430
\(52\) −6.82814e11 −4.78940
\(53\) 1.13282e11 0.702050 0.351025 0.936366i \(-0.385833\pi\)
0.351025 + 0.936366i \(0.385833\pi\)
\(54\) 6.55055e10 0.359516
\(55\) −7.23442e10 −0.352409
\(56\) 5.31153e11 2.30143
\(57\) −9.65985e10 −0.373064
\(58\) 1.60051e11 0.552049
\(59\) −4.21805e10 −0.130189
\(60\) −2.23502e11 −0.618441
\(61\) −1.44401e11 −0.358860 −0.179430 0.983771i \(-0.557425\pi\)
−0.179430 + 0.983771i \(0.557425\pi\)
\(62\) −1.29656e12 −2.89898
\(63\) −1.36793e11 −0.275644
\(64\) 8.50198e11 1.54650
\(65\) −5.03209e11 −0.827583
\(66\) −5.93235e11 −0.883468
\(67\) −4.28988e11 −0.579374 −0.289687 0.957121i \(-0.593551\pi\)
−0.289687 + 0.957121i \(0.593551\pi\)
\(68\) −2.15674e12 −2.64539
\(69\) −5.69242e11 −0.635006
\(70\) 6.54188e11 0.664608
\(71\) 1.96469e12 1.82019 0.910093 0.414405i \(-0.136010\pi\)
0.910093 + 0.414405i \(0.136010\pi\)
\(72\) −1.09665e12 −0.927697
\(73\) −1.02505e12 −0.792767 −0.396383 0.918085i \(-0.629735\pi\)
−0.396383 + 0.918085i \(0.629735\pi\)
\(74\) −2.12110e12 −1.50160
\(75\) 7.25180e11 0.470487
\(76\) 2.70269e12 1.60882
\(77\) 1.23883e12 0.677363
\(78\) −4.12640e12 −2.07470
\(79\) 7.60306e11 0.351894 0.175947 0.984400i \(-0.443701\pi\)
0.175947 + 0.984400i \(0.443701\pi\)
\(80\) 2.73298e12 1.16560
\(81\) 2.82430e11 0.111111
\(82\) 3.90909e12 1.41999
\(83\) 1.79334e12 0.602080 0.301040 0.953611i \(-0.402666\pi\)
0.301040 + 0.953611i \(0.402666\pi\)
\(84\) 3.82727e12 1.18870
\(85\) −1.58944e12 −0.457110
\(86\) −4.30132e12 −1.14647
\(87\) 6.90068e11 0.170615
\(88\) 9.93153e12 2.27971
\(89\) 8.56658e12 1.82714 0.913571 0.406680i \(-0.133313\pi\)
0.913571 + 0.406680i \(0.133313\pi\)
\(90\) −1.35067e12 −0.267901
\(91\) 8.61700e12 1.59069
\(92\) 1.59266e13 2.73843
\(93\) −5.59016e12 −0.895953
\(94\) −1.58501e12 −0.236974
\(95\) 1.99179e12 0.277997
\(96\) 1.00875e13 1.31528
\(97\) 1.76137e12 0.214701 0.107351 0.994221i \(-0.465763\pi\)
0.107351 + 0.994221i \(0.465763\pi\)
\(98\) 5.17973e12 0.590660
\(99\) −2.55775e12 −0.273042
\(100\) −2.02895e13 −2.02895
\(101\) 8.40147e12 0.787529 0.393765 0.919211i \(-0.371173\pi\)
0.393765 + 0.919211i \(0.371173\pi\)
\(102\) −1.30337e13 −1.14595
\(103\) −6.08513e12 −0.502143 −0.251072 0.967969i \(-0.580783\pi\)
−0.251072 + 0.967969i \(0.580783\pi\)
\(104\) 6.90813e13 5.35358
\(105\) 2.82056e12 0.205402
\(106\) −1.91539e13 −1.31150
\(107\) −1.19993e13 −0.772966 −0.386483 0.922297i \(-0.626310\pi\)
−0.386483 + 0.922297i \(0.626310\pi\)
\(108\) −7.90199e12 −0.479162
\(109\) 1.59918e12 0.0913323 0.0456661 0.998957i \(-0.485459\pi\)
0.0456661 + 0.998957i \(0.485459\pi\)
\(110\) 1.22320e13 0.658334
\(111\) −9.14520e12 −0.464081
\(112\) −4.67997e13 −2.24040
\(113\) 2.23014e13 1.00768 0.503838 0.863798i \(-0.331921\pi\)
0.503838 + 0.863798i \(0.331921\pi\)
\(114\) 1.63330e13 0.696921
\(115\) 1.17373e13 0.473187
\(116\) −1.93072e13 −0.735769
\(117\) −1.77911e13 −0.641203
\(118\) 7.13193e12 0.243206
\(119\) 2.72177e13 0.878609
\(120\) 2.26120e13 0.691292
\(121\) −1.13590e13 −0.329030
\(122\) 2.44154e13 0.670386
\(123\) 1.68542e13 0.438858
\(124\) 1.56405e14 3.86376
\(125\) −3.33016e13 −0.780817
\(126\) 2.31290e13 0.514931
\(127\) 1.38017e13 0.291883 0.145942 0.989293i \(-0.453379\pi\)
0.145942 + 0.989293i \(0.453379\pi\)
\(128\) −3.03962e13 −0.610877
\(129\) −1.85453e13 −0.354324
\(130\) 8.50832e13 1.54601
\(131\) 9.95920e13 1.72171 0.860857 0.508846i \(-0.169928\pi\)
0.860857 + 0.508846i \(0.169928\pi\)
\(132\) 7.15625e13 1.17748
\(133\) −3.41075e13 −0.534336
\(134\) 7.25338e13 1.08233
\(135\) −5.82348e12 −0.0827967
\(136\) 2.18200e14 2.95701
\(137\) −1.22658e14 −1.58493 −0.792466 0.609915i \(-0.791203\pi\)
−0.792466 + 0.609915i \(0.791203\pi\)
\(138\) 9.62480e13 1.18625
\(139\) −1.56326e13 −0.183837 −0.0919187 0.995767i \(-0.529300\pi\)
−0.0919187 + 0.995767i \(0.529300\pi\)
\(140\) −7.89153e13 −0.885787
\(141\) −6.83384e12 −0.0732387
\(142\) −3.32193e14 −3.40029
\(143\) 1.61121e14 1.57568
\(144\) 9.66253e13 0.903098
\(145\) −1.42287e13 −0.127137
\(146\) 1.73316e14 1.48097
\(147\) 2.23326e13 0.182548
\(148\) 2.55870e14 2.00133
\(149\) 1.74212e13 0.130427 0.0652135 0.997871i \(-0.479227\pi\)
0.0652135 + 0.997871i \(0.479227\pi\)
\(150\) −1.22614e14 −0.878916
\(151\) −2.42138e14 −1.66232 −0.831158 0.556037i \(-0.812321\pi\)
−0.831158 + 0.556037i \(0.812321\pi\)
\(152\) −2.73436e14 −1.79834
\(153\) −5.61951e13 −0.354164
\(154\) −2.09463e14 −1.26538
\(155\) 1.15265e14 0.667638
\(156\) 4.97771e14 2.76516
\(157\) 5.46292e13 0.291123 0.145562 0.989349i \(-0.453501\pi\)
0.145562 + 0.989349i \(0.453501\pi\)
\(158\) −1.28553e14 −0.657374
\(159\) −8.25826e13 −0.405329
\(160\) −2.07996e14 −0.980112
\(161\) −2.00991e14 −0.909512
\(162\) −4.77535e13 −0.207567
\(163\) −1.72738e13 −0.0721389 −0.0360694 0.999349i \(-0.511484\pi\)
−0.0360694 + 0.999349i \(0.511484\pi\)
\(164\) −4.71557e14 −1.89256
\(165\) 5.27389e13 0.203463
\(166\) −3.03219e14 −1.12475
\(167\) 1.44703e14 0.516203 0.258101 0.966118i \(-0.416903\pi\)
0.258101 + 0.966118i \(0.416903\pi\)
\(168\) −3.87211e14 −1.32873
\(169\) 8.17845e14 2.70027
\(170\) 2.68744e14 0.853927
\(171\) 7.04203e13 0.215389
\(172\) 5.18872e14 1.52801
\(173\) 2.42499e13 0.0687719 0.0343860 0.999409i \(-0.489052\pi\)
0.0343860 + 0.999409i \(0.489052\pi\)
\(174\) −1.16677e14 −0.318726
\(175\) 2.56050e14 0.673873
\(176\) −8.75064e14 −2.21926
\(177\) 3.07496e13 0.0751646
\(178\) −1.44845e15 −3.41328
\(179\) 1.43017e14 0.324970 0.162485 0.986711i \(-0.448049\pi\)
0.162485 + 0.986711i \(0.448049\pi\)
\(180\) 1.62933e14 0.357057
\(181\) −7.37868e14 −1.55980 −0.779898 0.625907i \(-0.784729\pi\)
−0.779898 + 0.625907i \(0.784729\pi\)
\(182\) −1.45697e15 −2.97158
\(183\) 1.05268e14 0.207188
\(184\) −1.61132e15 −3.06102
\(185\) 1.88567e14 0.345820
\(186\) 9.45191e14 1.67373
\(187\) 5.08918e14 0.870316
\(188\) 1.91201e14 0.315839
\(189\) 9.97218e13 0.159143
\(190\) −3.36773e14 −0.519325
\(191\) −1.08478e14 −0.161668 −0.0808339 0.996728i \(-0.525758\pi\)
−0.0808339 + 0.996728i \(0.525758\pi\)
\(192\) −6.19794e14 −0.892872
\(193\) −5.50034e14 −0.766067 −0.383034 0.923734i \(-0.625121\pi\)
−0.383034 + 0.923734i \(0.625121\pi\)
\(194\) −2.97814e14 −0.401083
\(195\) 3.66840e14 0.477806
\(196\) −6.24836e14 −0.787230
\(197\) 1.39304e15 1.69799 0.848993 0.528404i \(-0.177209\pi\)
0.848993 + 0.528404i \(0.177209\pi\)
\(198\) 4.32468e14 0.510071
\(199\) 8.63797e14 0.985977 0.492989 0.870036i \(-0.335904\pi\)
0.492989 + 0.870036i \(0.335904\pi\)
\(200\) 2.05272e15 2.26796
\(201\) 3.12733e14 0.334502
\(202\) −1.42053e15 −1.47118
\(203\) 2.43653e14 0.244370
\(204\) 1.57226e15 1.52732
\(205\) −3.47520e14 −0.327024
\(206\) 1.02888e15 0.938054
\(207\) 4.14977e14 0.366621
\(208\) −6.08674e15 −5.21162
\(209\) −6.37744e14 −0.529292
\(210\) −4.76903e14 −0.383711
\(211\) 4.70340e14 0.366924 0.183462 0.983027i \(-0.441270\pi\)
0.183462 + 0.983027i \(0.441270\pi\)
\(212\) 2.31055e15 1.74796
\(213\) −1.43226e15 −1.05088
\(214\) 2.02885e15 1.44398
\(215\) 3.82390e14 0.264032
\(216\) 7.99456e14 0.535606
\(217\) −1.97380e15 −1.28326
\(218\) −2.70391e14 −0.170618
\(219\) 7.47260e14 0.457704
\(220\) −1.47556e15 −0.877426
\(221\) 3.53991e15 2.04382
\(222\) 1.54628e15 0.866950
\(223\) 1.64133e15 0.893744 0.446872 0.894598i \(-0.352538\pi\)
0.446872 + 0.894598i \(0.352538\pi\)
\(224\) 3.56174e15 1.88387
\(225\) −5.28656e14 −0.271636
\(226\) −3.77074e15 −1.88244
\(227\) −2.58555e15 −1.25425 −0.627125 0.778918i \(-0.715769\pi\)
−0.627125 + 0.778918i \(0.715769\pi\)
\(228\) −1.97026e15 −0.928854
\(229\) −2.74237e15 −1.25659 −0.628297 0.777974i \(-0.716248\pi\)
−0.628297 + 0.777974i \(0.716248\pi\)
\(230\) −1.98456e15 −0.883961
\(231\) −9.03106e14 −0.391076
\(232\) 1.95333e15 0.822441
\(233\) −1.40319e15 −0.574516 −0.287258 0.957853i \(-0.592744\pi\)
−0.287258 + 0.957853i \(0.592744\pi\)
\(234\) 3.00814e15 1.19783
\(235\) 1.40909e14 0.0545753
\(236\) −8.60332e14 −0.324144
\(237\) −5.54263e14 −0.203166
\(238\) −4.60199e15 −1.64133
\(239\) −9.69016e14 −0.336314 −0.168157 0.985760i \(-0.553782\pi\)
−0.168157 + 0.985760i \(0.553782\pi\)
\(240\) −1.99234e15 −0.672962
\(241\) 3.93767e15 1.29458 0.647289 0.762245i \(-0.275903\pi\)
0.647289 + 0.762245i \(0.275903\pi\)
\(242\) 1.92060e15 0.614662
\(243\) −2.05891e14 −0.0641500
\(244\) −2.94525e15 −0.893488
\(245\) −4.60482e14 −0.136029
\(246\) −2.84972e15 −0.819831
\(247\) −4.43600e15 −1.24297
\(248\) −1.58237e16 −4.31890
\(249\) −1.30734e15 −0.347611
\(250\) 5.63066e15 1.45864
\(251\) 7.77142e15 1.96165 0.980825 0.194892i \(-0.0624357\pi\)
0.980825 + 0.194892i \(0.0624357\pi\)
\(252\) −2.79008e15 −0.686298
\(253\) −3.75814e15 −0.900927
\(254\) −2.33361e15 −0.545267
\(255\) 1.15870e15 0.263912
\(256\) −1.82540e15 −0.405321
\(257\) −8.48906e15 −1.83778 −0.918892 0.394510i \(-0.870914\pi\)
−0.918892 + 0.394510i \(0.870914\pi\)
\(258\) 3.13566e15 0.661913
\(259\) −3.22904e15 −0.664698
\(260\) −1.02637e16 −2.06051
\(261\) −5.03060e14 −0.0985045
\(262\) −1.68391e16 −3.21633
\(263\) 4.59142e15 0.855528 0.427764 0.903890i \(-0.359301\pi\)
0.427764 + 0.903890i \(0.359301\pi\)
\(264\) −7.24008e15 −1.31619
\(265\) 1.70279e15 0.302039
\(266\) 5.76694e15 0.998193
\(267\) −6.24503e15 −1.05490
\(268\) −8.74983e15 −1.44252
\(269\) 1.05501e16 1.69773 0.848865 0.528609i \(-0.177286\pi\)
0.848865 + 0.528609i \(0.177286\pi\)
\(270\) 9.84641e14 0.154673
\(271\) 2.76727e15 0.424376 0.212188 0.977229i \(-0.431941\pi\)
0.212188 + 0.977229i \(0.431941\pi\)
\(272\) −1.92256e16 −2.87860
\(273\) −6.28179e15 −0.918388
\(274\) 2.07391e16 2.96081
\(275\) 4.78765e15 0.667513
\(276\) −1.16105e16 −1.58104
\(277\) −8.05495e15 −1.07138 −0.535691 0.844414i \(-0.679949\pi\)
−0.535691 + 0.844414i \(0.679949\pi\)
\(278\) 2.64317e15 0.343426
\(279\) 4.07523e15 0.517279
\(280\) 7.98398e15 0.990131
\(281\) 9.17393e14 0.111164 0.0555820 0.998454i \(-0.482299\pi\)
0.0555820 + 0.998454i \(0.482299\pi\)
\(282\) 1.15547e15 0.136817
\(283\) −1.16050e16 −1.34287 −0.671433 0.741065i \(-0.734321\pi\)
−0.671433 + 0.741065i \(0.734321\pi\)
\(284\) 4.00727e16 4.53189
\(285\) −1.45201e15 −0.160501
\(286\) −2.72425e16 −2.94353
\(287\) 5.95097e15 0.628572
\(288\) −7.35378e15 −0.759380
\(289\) 1.27659e15 0.128889
\(290\) 2.40580e15 0.237505
\(291\) −1.28404e15 −0.123958
\(292\) −2.09073e16 −1.97383
\(293\) −1.53153e16 −1.41411 −0.707057 0.707156i \(-0.749978\pi\)
−0.707057 + 0.707156i \(0.749978\pi\)
\(294\) −3.77602e15 −0.341018
\(295\) −6.34033e14 −0.0560104
\(296\) −2.58868e16 −2.23708
\(297\) 1.86460e15 0.157641
\(298\) −2.94560e15 −0.243651
\(299\) −2.61407e16 −2.11570
\(300\) 1.47911e16 1.17142
\(301\) −6.54808e15 −0.507495
\(302\) 4.09410e16 3.10537
\(303\) −6.12468e15 −0.454680
\(304\) 2.40923e16 1.75065
\(305\) −2.17055e15 −0.154390
\(306\) 9.50153e15 0.661614
\(307\) −1.73057e15 −0.117975 −0.0589874 0.998259i \(-0.518787\pi\)
−0.0589874 + 0.998259i \(0.518787\pi\)
\(308\) 2.52677e16 1.68650
\(309\) 4.43606e15 0.289913
\(310\) −1.94891e16 −1.24721
\(311\) 2.75558e16 1.72691 0.863456 0.504423i \(-0.168295\pi\)
0.863456 + 0.504423i \(0.168295\pi\)
\(312\) −5.03603e16 −3.09089
\(313\) 7.57965e15 0.455628 0.227814 0.973705i \(-0.426842\pi\)
0.227814 + 0.973705i \(0.426842\pi\)
\(314\) −9.23676e15 −0.543847
\(315\) −2.05619e15 −0.118589
\(316\) 1.55075e16 0.876146
\(317\) 2.65849e16 1.47146 0.735732 0.677273i \(-0.236838\pi\)
0.735732 + 0.677273i \(0.236838\pi\)
\(318\) 1.39632e16 0.757195
\(319\) 4.55584e15 0.242063
\(320\) 1.27797e16 0.665342
\(321\) 8.74747e15 0.446272
\(322\) 3.39838e16 1.69906
\(323\) −1.40116e16 −0.686546
\(324\) 5.76055e15 0.276644
\(325\) 3.33017e16 1.56756
\(326\) 2.92068e15 0.134763
\(327\) −1.16580e15 −0.0527307
\(328\) 4.77081e16 2.11550
\(329\) −2.41293e15 −0.104899
\(330\) −8.91716e15 −0.380090
\(331\) 8.69548e15 0.363422 0.181711 0.983352i \(-0.441836\pi\)
0.181711 + 0.983352i \(0.441836\pi\)
\(332\) 3.65777e16 1.49906
\(333\) 6.66685e15 0.267937
\(334\) −2.44665e16 −0.964319
\(335\) −6.44831e15 −0.249261
\(336\) 3.41170e16 1.29350
\(337\) 6.16978e15 0.229443 0.114722 0.993398i \(-0.463402\pi\)
0.114722 + 0.993398i \(0.463402\pi\)
\(338\) −1.38282e17 −5.04438
\(339\) −1.62577e16 −0.581783
\(340\) −3.24188e16 −1.13811
\(341\) −3.69063e16 −1.27115
\(342\) −1.19067e16 −0.402368
\(343\) 3.28245e16 1.08839
\(344\) −5.24951e16 −1.70800
\(345\) −8.55651e15 −0.273195
\(346\) −4.10021e15 −0.128473
\(347\) 2.83759e15 0.0872585 0.0436292 0.999048i \(-0.486108\pi\)
0.0436292 + 0.999048i \(0.486108\pi\)
\(348\) 1.40749e16 0.424796
\(349\) 6.03272e16 1.78710 0.893548 0.448968i \(-0.148208\pi\)
0.893548 + 0.448968i \(0.148208\pi\)
\(350\) −4.32933e16 −1.25886
\(351\) 1.29697e16 0.370199
\(352\) 6.65977e16 1.86609
\(353\) −7.92367e15 −0.217967 −0.108983 0.994044i \(-0.534760\pi\)
−0.108983 + 0.994044i \(0.534760\pi\)
\(354\) −5.19918e15 −0.140415
\(355\) 2.95321e16 0.783088
\(356\) 1.74727e17 4.54921
\(357\) −1.98417e16 −0.507265
\(358\) −2.41815e16 −0.607076
\(359\) 1.88282e16 0.464190 0.232095 0.972693i \(-0.425442\pi\)
0.232095 + 0.972693i \(0.425442\pi\)
\(360\) −1.64842e16 −0.399118
\(361\) −2.44946e16 −0.582469
\(362\) 1.24759e17 2.91385
\(363\) 8.28073e15 0.189966
\(364\) 1.75756e17 3.96051
\(365\) −1.54079e16 −0.341068
\(366\) −1.77988e16 −0.387048
\(367\) −2.52607e16 −0.539655 −0.269827 0.962909i \(-0.586967\pi\)
−0.269827 + 0.962909i \(0.586967\pi\)
\(368\) 1.41973e17 2.97985
\(369\) −1.22867e16 −0.253375
\(370\) −3.18831e16 −0.646026
\(371\) −2.91587e16 −0.580548
\(372\) −1.14019e17 −2.23074
\(373\) 8.77358e16 1.68682 0.843412 0.537268i \(-0.180544\pi\)
0.843412 + 0.537268i \(0.180544\pi\)
\(374\) −8.60483e16 −1.62584
\(375\) 2.42768e16 0.450805
\(376\) −1.93441e16 −0.353044
\(377\) 3.16893e16 0.568452
\(378\) −1.68611e16 −0.297296
\(379\) 8.32382e16 1.44267 0.721336 0.692585i \(-0.243528\pi\)
0.721336 + 0.692585i \(0.243528\pi\)
\(380\) 4.06253e16 0.692155
\(381\) −1.00614e16 −0.168519
\(382\) 1.83415e16 0.302011
\(383\) 4.84608e15 0.0784509 0.0392255 0.999230i \(-0.487511\pi\)
0.0392255 + 0.999230i \(0.487511\pi\)
\(384\) 2.21588e16 0.352690
\(385\) 1.86214e16 0.291418
\(386\) 9.30003e16 1.43109
\(387\) 1.35195e16 0.204569
\(388\) 3.59256e16 0.534562
\(389\) −2.86897e16 −0.419811 −0.209905 0.977722i \(-0.567316\pi\)
−0.209905 + 0.977722i \(0.567316\pi\)
\(390\) −6.20256e16 −0.892588
\(391\) −8.25682e16 −1.16859
\(392\) 6.32156e16 0.879964
\(393\) −7.26026e16 −0.994032
\(394\) −2.35537e17 −3.17201
\(395\) 1.14285e16 0.151394
\(396\) −5.21690e16 −0.679820
\(397\) −1.12294e17 −1.43953 −0.719763 0.694220i \(-0.755750\pi\)
−0.719763 + 0.694220i \(0.755750\pi\)
\(398\) −1.46052e17 −1.84190
\(399\) 2.48644e16 0.308499
\(400\) −1.80865e17 −2.20782
\(401\) −6.86571e16 −0.824607 −0.412304 0.911047i \(-0.635276\pi\)
−0.412304 + 0.911047i \(0.635276\pi\)
\(402\) −5.28772e16 −0.624883
\(403\) −2.56712e17 −2.98513
\(404\) 1.71360e17 1.96079
\(405\) 4.24532e15 0.0478027
\(406\) −4.11971e16 −0.456507
\(407\) −6.03767e16 −0.658424
\(408\) −1.59068e17 −1.70723
\(409\) −1.01572e17 −1.07294 −0.536469 0.843920i \(-0.680242\pi\)
−0.536469 + 0.843920i \(0.680242\pi\)
\(410\) 5.87591e16 0.610914
\(411\) 8.94174e16 0.915061
\(412\) −1.24115e17 −1.25023
\(413\) 1.08572e16 0.107657
\(414\) −7.01648e16 −0.684884
\(415\) 2.69564e16 0.259030
\(416\) 4.63238e17 4.38225
\(417\) 1.13961e16 0.106139
\(418\) 1.07831e17 0.988771
\(419\) −8.75813e16 −0.790715 −0.395358 0.918527i \(-0.629379\pi\)
−0.395358 + 0.918527i \(0.629379\pi\)
\(420\) 5.75293e16 0.511409
\(421\) −1.51127e17 −1.32284 −0.661420 0.750016i \(-0.730046\pi\)
−0.661420 + 0.750016i \(0.730046\pi\)
\(422\) −7.95256e16 −0.685450
\(423\) 4.98187e15 0.0422844
\(424\) −2.33762e17 −1.95387
\(425\) 1.05187e17 0.865832
\(426\) 2.42168e17 1.96316
\(427\) 3.71686e16 0.296753
\(428\) −2.44742e17 −1.92453
\(429\) −1.17457e17 −0.909720
\(430\) −6.46549e16 −0.493238
\(431\) −2.09940e16 −0.157758 −0.0788791 0.996884i \(-0.525134\pi\)
−0.0788791 + 0.996884i \(0.525134\pi\)
\(432\) −7.04399e16 −0.521404
\(433\) 2.00541e17 1.46228 0.731142 0.682225i \(-0.238988\pi\)
0.731142 + 0.682225i \(0.238988\pi\)
\(434\) 3.33733e17 2.39727
\(435\) 1.03727e16 0.0734027
\(436\) 3.26175e16 0.227399
\(437\) 1.03469e17 0.710694
\(438\) −1.26348e17 −0.855037
\(439\) −2.34587e17 −1.56417 −0.782085 0.623172i \(-0.785844\pi\)
−0.782085 + 0.623172i \(0.785844\pi\)
\(440\) 1.49285e17 0.980785
\(441\) −1.62805e16 −0.105394
\(442\) −5.98532e17 −3.81806
\(443\) −1.56695e17 −0.984989 −0.492494 0.870316i \(-0.663915\pi\)
−0.492494 + 0.870316i \(0.663915\pi\)
\(444\) −1.86529e17 −1.15547
\(445\) 1.28768e17 0.786081
\(446\) −2.77517e17 −1.66960
\(447\) −1.27001e16 −0.0753020
\(448\) −2.18840e17 −1.27885
\(449\) 2.39276e17 1.37815 0.689076 0.724689i \(-0.258017\pi\)
0.689076 + 0.724689i \(0.258017\pi\)
\(450\) 8.93857e16 0.507443
\(451\) 1.11272e17 0.622639
\(452\) 4.54868e17 2.50891
\(453\) 1.76519e17 0.959738
\(454\) 4.37167e17 2.34307
\(455\) 1.29526e17 0.684356
\(456\) 1.99334e17 1.03827
\(457\) −1.14996e17 −0.590509 −0.295254 0.955419i \(-0.595404\pi\)
−0.295254 + 0.955419i \(0.595404\pi\)
\(458\) 4.63683e17 2.34744
\(459\) 4.09662e16 0.204477
\(460\) 2.39399e17 1.17814
\(461\) 2.49498e17 1.21063 0.605314 0.795987i \(-0.293048\pi\)
0.605314 + 0.795987i \(0.293048\pi\)
\(462\) 1.52698e17 0.730569
\(463\) −3.34372e17 −1.57744 −0.788722 0.614750i \(-0.789257\pi\)
−0.788722 + 0.614750i \(0.789257\pi\)
\(464\) −1.72108e17 −0.800633
\(465\) −8.40281e16 −0.385461
\(466\) 2.37252e17 1.07325
\(467\) −5.83675e16 −0.260382 −0.130191 0.991489i \(-0.541559\pi\)
−0.130191 + 0.991489i \(0.541559\pi\)
\(468\) −3.62875e17 −1.59647
\(469\) 1.10421e17 0.479104
\(470\) −2.38250e16 −0.101952
\(471\) −3.98247e16 −0.168080
\(472\) 8.70411e16 0.362327
\(473\) −1.22436e17 −0.502705
\(474\) 9.37154e16 0.379535
\(475\) −1.31814e17 −0.526565
\(476\) 5.55143e17 2.18756
\(477\) 6.02027e16 0.234017
\(478\) 1.63842e17 0.628268
\(479\) −7.63797e16 −0.288933 −0.144466 0.989510i \(-0.546147\pi\)
−0.144466 + 0.989510i \(0.546147\pi\)
\(480\) 1.51629e17 0.565868
\(481\) −4.19966e17 −1.54622
\(482\) −6.65785e17 −2.41840
\(483\) 1.46522e17 0.525107
\(484\) −2.31683e17 −0.819219
\(485\) 2.64759e16 0.0923697
\(486\) 3.48123e16 0.119839
\(487\) −1.51731e16 −0.0515390 −0.0257695 0.999668i \(-0.508204\pi\)
−0.0257695 + 0.999668i \(0.508204\pi\)
\(488\) 2.97976e17 0.998739
\(489\) 1.25926e16 0.0416494
\(490\) 7.78587e16 0.254116
\(491\) −5.62266e17 −1.81097 −0.905486 0.424376i \(-0.860493\pi\)
−0.905486 + 0.424376i \(0.860493\pi\)
\(492\) 3.43765e17 1.09267
\(493\) 1.00094e17 0.313981
\(494\) 7.50043e17 2.32199
\(495\) −3.84467e16 −0.117470
\(496\) 1.39422e18 4.20438
\(497\) −5.05711e17 −1.50517
\(498\) 2.21047e17 0.649372
\(499\) −3.04338e17 −0.882476 −0.441238 0.897390i \(-0.645460\pi\)
−0.441238 + 0.897390i \(0.645460\pi\)
\(500\) −6.79232e17 −1.94408
\(501\) −1.05488e17 −0.298030
\(502\) −1.31400e18 −3.66456
\(503\) 1.36107e17 0.374705 0.187353 0.982293i \(-0.440009\pi\)
0.187353 + 0.982293i \(0.440009\pi\)
\(504\) 2.82276e17 0.767143
\(505\) 1.26286e17 0.338814
\(506\) 6.35430e17 1.68302
\(507\) −5.96209e17 −1.55900
\(508\) 2.81506e17 0.726730
\(509\) −4.90782e17 −1.25090 −0.625450 0.780264i \(-0.715085\pi\)
−0.625450 + 0.780264i \(0.715085\pi\)
\(510\) −1.95914e17 −0.493015
\(511\) 2.63847e17 0.655565
\(512\) 5.57647e17 1.36806
\(513\) −5.13364e16 −0.124355
\(514\) 1.43534e18 3.43316
\(515\) −9.14681e16 −0.216034
\(516\) −3.78258e17 −0.882196
\(517\) −4.51171e16 −0.103909
\(518\) 5.45969e17 1.24172
\(519\) −1.76782e16 −0.0397055
\(520\) 1.03839e18 2.30324
\(521\) 2.22597e17 0.487611 0.243806 0.969824i \(-0.421604\pi\)
0.243806 + 0.969824i \(0.421604\pi\)
\(522\) 8.50579e16 0.184016
\(523\) −6.36879e17 −1.36081 −0.680403 0.732838i \(-0.738195\pi\)
−0.680403 + 0.732838i \(0.738195\pi\)
\(524\) 2.03132e18 4.28672
\(525\) −1.86661e17 −0.389061
\(526\) −7.76322e17 −1.59821
\(527\) −8.10850e17 −1.64881
\(528\) 6.37922e17 1.28129
\(529\) 1.05695e17 0.209696
\(530\) −2.87910e17 −0.564239
\(531\) −2.24165e16 −0.0433963
\(532\) −6.95671e17 −1.33039
\(533\) 7.73978e17 1.46218
\(534\) 1.05592e18 1.97066
\(535\) −1.80366e17 −0.332549
\(536\) 8.85233e17 1.61245
\(537\) −1.04259e17 −0.187621
\(538\) −1.78383e18 −3.17153
\(539\) 1.47440e17 0.258994
\(540\) −1.18778e17 −0.206147
\(541\) 7.84768e17 1.34573 0.672867 0.739763i \(-0.265063\pi\)
0.672867 + 0.739763i \(0.265063\pi\)
\(542\) −4.67893e17 −0.792777
\(543\) 5.37905e17 0.900548
\(544\) 1.46318e18 2.42051
\(545\) 2.40379e16 0.0392934
\(546\) 1.06213e18 1.71564
\(547\) 8.71489e16 0.139105 0.0695527 0.997578i \(-0.477843\pi\)
0.0695527 + 0.997578i \(0.477843\pi\)
\(548\) −2.50178e18 −3.94616
\(549\) −7.67404e16 −0.119620
\(550\) −8.09500e17 −1.24698
\(551\) −1.25432e17 −0.190951
\(552\) 1.17465e18 1.76728
\(553\) −1.95702e17 −0.290993
\(554\) 1.36194e18 2.00145
\(555\) −1.37465e17 −0.199659
\(556\) −3.18848e17 −0.457718
\(557\) 3.40843e17 0.483610 0.241805 0.970325i \(-0.422260\pi\)
0.241805 + 0.970325i \(0.422260\pi\)
\(558\) −6.89044e17 −0.966328
\(559\) −8.51638e17 −1.18053
\(560\) −7.03466e17 −0.963876
\(561\) −3.71001e17 −0.502477
\(562\) −1.55114e17 −0.207666
\(563\) −7.11918e17 −0.942162 −0.471081 0.882090i \(-0.656136\pi\)
−0.471081 + 0.882090i \(0.656136\pi\)
\(564\) −1.39386e17 −0.182349
\(565\) 3.35221e17 0.433527
\(566\) 1.96218e18 2.50861
\(567\) −7.26972e16 −0.0918814
\(568\) −4.05422e18 −5.06574
\(569\) −1.09261e18 −1.34969 −0.674845 0.737959i \(-0.735790\pi\)
−0.674845 + 0.737959i \(0.735790\pi\)
\(570\) 2.45508e17 0.299833
\(571\) 4.69203e17 0.566534 0.283267 0.959041i \(-0.408582\pi\)
0.283267 + 0.959041i \(0.408582\pi\)
\(572\) 3.28629e18 3.92312
\(573\) 7.90802e16 0.0933389
\(574\) −1.00620e18 −1.17424
\(575\) −7.76761e17 −0.896285
\(576\) 4.51830e17 0.515500
\(577\) 6.98382e17 0.787863 0.393931 0.919140i \(-0.371115\pi\)
0.393931 + 0.919140i \(0.371115\pi\)
\(578\) −2.15847e17 −0.240777
\(579\) 4.00975e17 0.442289
\(580\) −2.90214e17 −0.316546
\(581\) −4.61604e17 −0.497880
\(582\) 2.17107e17 0.231565
\(583\) −5.45212e17 −0.575068
\(584\) 2.11522e18 2.20634
\(585\) −2.67426e17 −0.275861
\(586\) 2.58952e18 2.64171
\(587\) −1.12669e18 −1.13673 −0.568364 0.822777i \(-0.692424\pi\)
−0.568364 + 0.822777i \(0.692424\pi\)
\(588\) 4.55506e17 0.454507
\(589\) 1.01611e18 1.00274
\(590\) 1.07203e17 0.104633
\(591\) −1.01553e18 −0.980333
\(592\) 2.28088e18 2.17776
\(593\) −1.00836e18 −0.952269 −0.476135 0.879372i \(-0.657963\pi\)
−0.476135 + 0.879372i \(0.657963\pi\)
\(594\) −3.15269e17 −0.294489
\(595\) 4.09120e17 0.377999
\(596\) 3.55330e17 0.324737
\(597\) −6.29708e17 −0.569254
\(598\) 4.41990e18 3.95235
\(599\) 7.20482e17 0.637307 0.318654 0.947871i \(-0.396769\pi\)
0.318654 + 0.947871i \(0.396769\pi\)
\(600\) −1.49643e18 −1.30941
\(601\) −1.82789e18 −1.58222 −0.791108 0.611676i \(-0.790496\pi\)
−0.791108 + 0.611676i \(0.790496\pi\)
\(602\) 1.10716e18 0.948051
\(603\) −2.27982e17 −0.193125
\(604\) −4.93875e18 −4.13883
\(605\) −1.70742e17 −0.141557
\(606\) 1.03557e18 0.849388
\(607\) −1.46250e16 −0.0118678 −0.00593390 0.999982i \(-0.501889\pi\)
−0.00593390 + 0.999982i \(0.501889\pi\)
\(608\) −1.83357e18 −1.47206
\(609\) −1.77623e17 −0.141087
\(610\) 3.66998e17 0.288416
\(611\) −3.13824e17 −0.244016
\(612\) −1.14618e18 −0.881796
\(613\) 2.16294e18 1.64646 0.823231 0.567706i \(-0.192169\pi\)
0.823231 + 0.567706i \(0.192169\pi\)
\(614\) 2.92606e17 0.220389
\(615\) 2.53342e17 0.188808
\(616\) −2.55637e18 −1.88516
\(617\) −6.90608e17 −0.503939 −0.251970 0.967735i \(-0.581078\pi\)
−0.251970 + 0.967735i \(0.581078\pi\)
\(618\) −7.50053e17 −0.541586
\(619\) −1.72650e18 −1.23361 −0.616805 0.787116i \(-0.711573\pi\)
−0.616805 + 0.787116i \(0.711573\pi\)
\(620\) 2.35099e18 1.66228
\(621\) −3.02518e17 −0.211669
\(622\) −4.65916e18 −3.22605
\(623\) −2.20503e18 −1.51092
\(624\) 4.43723e18 3.00893
\(625\) 7.13736e17 0.478980
\(626\) −1.28157e18 −0.851159
\(627\) 4.64916e17 0.305587
\(628\) 1.11424e18 0.724838
\(629\) −1.32651e18 −0.854044
\(630\) 3.47662e17 0.221536
\(631\) −7.24337e17 −0.456825 −0.228413 0.973564i \(-0.573354\pi\)
−0.228413 + 0.973564i \(0.573354\pi\)
\(632\) −1.56892e18 −0.979354
\(633\) −3.42878e17 −0.211844
\(634\) −4.49500e18 −2.74884
\(635\) 2.07459e17 0.125575
\(636\) −1.68439e18 −1.00919
\(637\) 1.02556e18 0.608211
\(638\) −7.70306e17 −0.452198
\(639\) 1.04412e18 0.606728
\(640\) −4.56897e17 −0.262814
\(641\) −3.82643e17 −0.217880 −0.108940 0.994048i \(-0.534746\pi\)
−0.108940 + 0.994048i \(0.534746\pi\)
\(642\) −1.47903e18 −0.833681
\(643\) 1.78480e18 0.995908 0.497954 0.867203i \(-0.334085\pi\)
0.497954 + 0.867203i \(0.334085\pi\)
\(644\) −4.09950e18 −2.26450
\(645\) −2.78762e17 −0.152439
\(646\) 2.36909e18 1.28254
\(647\) 2.66447e18 1.42802 0.714008 0.700137i \(-0.246878\pi\)
0.714008 + 0.700137i \(0.246878\pi\)
\(648\) −5.82804e17 −0.309232
\(649\) 2.03009e17 0.106641
\(650\) −5.63069e18 −2.92836
\(651\) 1.43890e18 0.740893
\(652\) −3.52324e17 −0.179611
\(653\) −8.25665e17 −0.416743 −0.208371 0.978050i \(-0.566816\pi\)
−0.208371 + 0.978050i \(0.566816\pi\)
\(654\) 1.97115e17 0.0985063
\(655\) 1.49701e18 0.740724
\(656\) −4.20355e18 −2.05940
\(657\) −5.44752e17 −0.264256
\(658\) 4.07981e17 0.195962
\(659\) −3.82149e18 −1.81752 −0.908758 0.417324i \(-0.862968\pi\)
−0.908758 + 0.417324i \(0.862968\pi\)
\(660\) 1.07569e18 0.506582
\(661\) 2.35646e18 1.09888 0.549440 0.835533i \(-0.314841\pi\)
0.549440 + 0.835533i \(0.314841\pi\)
\(662\) −1.47024e18 −0.678909
\(663\) −2.58059e18 −1.18000
\(664\) −3.70062e18 −1.67564
\(665\) −5.12684e17 −0.229884
\(666\) −1.12724e18 −0.500534
\(667\) −7.39152e17 −0.325024
\(668\) 2.95142e18 1.28524
\(669\) −1.19653e18 −0.516003
\(670\) 1.09029e18 0.465645
\(671\) 6.94980e17 0.293952
\(672\) −2.59651e18 −1.08765
\(673\) −4.43044e18 −1.83802 −0.919008 0.394238i \(-0.871008\pi\)
−0.919008 + 0.394238i \(0.871008\pi\)
\(674\) −1.04319e18 −0.428623
\(675\) 3.85390e17 0.156829
\(676\) 1.66811e19 6.72313
\(677\) 2.85814e18 1.14093 0.570463 0.821323i \(-0.306764\pi\)
0.570463 + 0.821323i \(0.306764\pi\)
\(678\) 2.74887e18 1.08683
\(679\) −4.53375e17 −0.177543
\(680\) 3.27986e18 1.27218
\(681\) 1.88486e18 0.724142
\(682\) 6.24016e18 2.37464
\(683\) 7.49096e17 0.282360 0.141180 0.989984i \(-0.454910\pi\)
0.141180 + 0.989984i \(0.454910\pi\)
\(684\) 1.43632e18 0.536274
\(685\) −1.84372e18 −0.681877
\(686\) −5.55000e18 −2.03323
\(687\) 1.99919e18 0.725495
\(688\) 4.62533e18 1.66271
\(689\) −3.79236e18 −1.35047
\(690\) 1.44674e18 0.510355
\(691\) −1.53441e18 −0.536210 −0.268105 0.963390i \(-0.586397\pi\)
−0.268105 + 0.963390i \(0.586397\pi\)
\(692\) 4.94612e17 0.171228
\(693\) 6.58364e17 0.225788
\(694\) −4.79782e17 −0.163008
\(695\) −2.34979e17 −0.0790913
\(696\) −1.42398e18 −0.474836
\(697\) 2.44469e18 0.807627
\(698\) −1.02002e19 −3.33847
\(699\) 1.02292e18 0.331697
\(700\) 5.22251e18 1.67781
\(701\) 1.98402e18 0.631508 0.315754 0.948841i \(-0.397743\pi\)
0.315754 + 0.948841i \(0.397743\pi\)
\(702\) −2.19294e18 −0.691568
\(703\) 1.66230e18 0.519396
\(704\) −4.09189e18 −1.26678
\(705\) −1.02722e17 −0.0315091
\(706\) 1.33974e18 0.407184
\(707\) −2.16253e18 −0.651234
\(708\) 6.27182e17 0.187145
\(709\) 1.60737e18 0.475243 0.237621 0.971358i \(-0.423632\pi\)
0.237621 + 0.971358i \(0.423632\pi\)
\(710\) −4.99333e18 −1.46289
\(711\) 4.04058e17 0.117298
\(712\) −1.76774e19 −5.08510
\(713\) 5.98778e18 1.70681
\(714\) 3.35485e18 0.947622
\(715\) 2.42188e18 0.677896
\(716\) 2.91703e18 0.809109
\(717\) 7.06413e17 0.194171
\(718\) −3.18350e18 −0.867154
\(719\) −5.71365e17 −0.154232 −0.0771162 0.997022i \(-0.524571\pi\)
−0.0771162 + 0.997022i \(0.524571\pi\)
\(720\) 1.45242e18 0.388535
\(721\) 1.56631e18 0.415239
\(722\) 4.14157e18 1.08811
\(723\) −2.87056e18 −0.747425
\(724\) −1.50499e19 −3.88357
\(725\) 9.41635e17 0.240816
\(726\) −1.40011e18 −0.354875
\(727\) −5.03265e18 −1.26422 −0.632110 0.774879i \(-0.717811\pi\)
−0.632110 + 0.774879i \(0.717811\pi\)
\(728\) −1.77815e19 −4.42705
\(729\) 1.50095e17 0.0370370
\(730\) 2.60519e18 0.637149
\(731\) −2.68999e18 −0.652059
\(732\) 2.14709e18 0.515856
\(733\) −7.24584e18 −1.72549 −0.862746 0.505637i \(-0.831257\pi\)
−0.862746 + 0.505637i \(0.831257\pi\)
\(734\) 4.27111e18 1.00813
\(735\) 3.35691e17 0.0785366
\(736\) −1.08050e19 −2.50564
\(737\) 2.06466e18 0.474581
\(738\) 2.07745e18 0.473330
\(739\) −7.01404e18 −1.58409 −0.792044 0.610464i \(-0.790983\pi\)
−0.792044 + 0.610464i \(0.790983\pi\)
\(740\) 3.84609e18 0.861021
\(741\) 3.23384e18 0.717630
\(742\) 4.93019e18 1.08452
\(743\) 1.10490e18 0.240932 0.120466 0.992717i \(-0.461561\pi\)
0.120466 + 0.992717i \(0.461561\pi\)
\(744\) 1.15355e19 2.49352
\(745\) 2.61865e17 0.0561128
\(746\) −1.48345e19 −3.15115
\(747\) 9.53053e17 0.200693
\(748\) 1.03801e19 2.16691
\(749\) 3.08861e18 0.639191
\(750\) −4.10475e18 −0.842149
\(751\) 5.73835e18 1.16715 0.583576 0.812059i \(-0.301653\pi\)
0.583576 + 0.812059i \(0.301653\pi\)
\(752\) 1.70441e18 0.343682
\(753\) −5.66537e18 −1.13256
\(754\) −5.35807e18 −1.06193
\(755\) −3.63968e18 −0.715169
\(756\) 2.03397e18 0.396234
\(757\) −5.65708e18 −1.09262 −0.546310 0.837583i \(-0.683968\pi\)
−0.546310 + 0.837583i \(0.683968\pi\)
\(758\) −1.40740e19 −2.69506
\(759\) 2.73968e18 0.520150
\(760\) −4.11012e18 −0.773689
\(761\) −5.36784e18 −1.00184 −0.500921 0.865493i \(-0.667005\pi\)
−0.500921 + 0.865493i \(0.667005\pi\)
\(762\) 1.70120e18 0.314810
\(763\) −4.11627e17 −0.0755257
\(764\) −2.21256e18 −0.402520
\(765\) −8.44693e17 −0.152370
\(766\) −8.19380e17 −0.146554
\(767\) 1.41208e18 0.250433
\(768\) 1.33072e18 0.234012
\(769\) 1.14119e19 1.98993 0.994964 0.100234i \(-0.0319590\pi\)
0.994964 + 0.100234i \(0.0319590\pi\)
\(770\) −3.14852e18 −0.544398
\(771\) 6.18853e18 1.06104
\(772\) −1.12187e19 −1.90735
\(773\) −8.22705e18 −1.38700 −0.693502 0.720455i \(-0.743933\pi\)
−0.693502 + 0.720455i \(0.743933\pi\)
\(774\) −2.28590e18 −0.382156
\(775\) −7.62807e18 −1.26460
\(776\) −3.63465e18 −0.597533
\(777\) 2.35397e18 0.383764
\(778\) 4.85089e18 0.784248
\(779\) −3.06354e18 −0.491167
\(780\) 7.48221e18 1.18964
\(781\) −9.45581e18 −1.49096
\(782\) 1.39607e19 2.18305
\(783\) 3.66730e17 0.0568716
\(784\) −5.56991e18 −0.856631
\(785\) 8.21154e17 0.125248
\(786\) 1.22757e19 1.85695
\(787\) 3.97239e18 0.595958 0.297979 0.954572i \(-0.403687\pi\)
0.297979 + 0.954572i \(0.403687\pi\)
\(788\) 2.84131e19 4.22764
\(789\) −3.34714e18 −0.493939
\(790\) −1.93234e18 −0.282818
\(791\) −5.74035e18 −0.833281
\(792\) 5.27802e18 0.759902
\(793\) 4.83412e18 0.690306
\(794\) 1.89869e19 2.68918
\(795\) −1.24133e18 −0.174382
\(796\) 1.76184e19 2.45488
\(797\) 6.01437e18 0.831210 0.415605 0.909545i \(-0.363570\pi\)
0.415605 + 0.909545i \(0.363570\pi\)
\(798\) −4.20410e18 −0.576307
\(799\) −9.91245e17 −0.134780
\(800\) 1.37649e19 1.85647
\(801\) 4.55263e18 0.609047
\(802\) 1.16086e19 1.54045
\(803\) 4.93342e18 0.649377
\(804\) 6.37862e18 0.832842
\(805\) −3.02118e18 −0.391294
\(806\) 4.34051e19 5.57651
\(807\) −7.69106e18 −0.980185
\(808\) −1.73368e19 −2.19176
\(809\) −3.84204e18 −0.481833 −0.240916 0.970546i \(-0.577448\pi\)
−0.240916 + 0.970546i \(0.577448\pi\)
\(810\) −7.17803e17 −0.0893002
\(811\) 3.86489e18 0.476982 0.238491 0.971145i \(-0.423347\pi\)
0.238491 + 0.971145i \(0.423347\pi\)
\(812\) 4.96965e18 0.608431
\(813\) −2.01734e18 −0.245014
\(814\) 1.02086e19 1.23000
\(815\) −2.59650e17 −0.0310359
\(816\) 1.40154e19 1.66196
\(817\) 3.37093e18 0.396557
\(818\) 1.71740e19 2.00436
\(819\) 4.57943e18 0.530232
\(820\) −7.08817e18 −0.814224
\(821\) 3.29104e17 0.0375061 0.0187531 0.999824i \(-0.494030\pi\)
0.0187531 + 0.999824i \(0.494030\pi\)
\(822\) −1.51188e19 −1.70943
\(823\) −9.44893e17 −0.105995 −0.0529973 0.998595i \(-0.516877\pi\)
−0.0529973 + 0.998595i \(0.516877\pi\)
\(824\) 1.25569e19 1.39751
\(825\) −3.49019e18 −0.385389
\(826\) −1.83575e18 −0.201115
\(827\) 1.72578e19 1.87586 0.937929 0.346827i \(-0.112741\pi\)
0.937929 + 0.346827i \(0.112741\pi\)
\(828\) 8.46405e18 0.912811
\(829\) −2.53625e18 −0.271387 −0.135693 0.990751i \(-0.543326\pi\)
−0.135693 + 0.990751i \(0.543326\pi\)
\(830\) −4.55782e18 −0.483893
\(831\) 5.87206e18 0.618563
\(832\) −2.84622e19 −2.97486
\(833\) 3.23933e18 0.335941
\(834\) −1.92687e18 −0.198277
\(835\) 2.17509e18 0.222083
\(836\) −1.30077e19 −1.31783
\(837\) −2.97084e18 −0.298651
\(838\) 1.48083e19 1.47713
\(839\) −9.36061e18 −0.926513 −0.463256 0.886224i \(-0.653319\pi\)
−0.463256 + 0.886224i \(0.653319\pi\)
\(840\) −5.82032e18 −0.571652
\(841\) −9.36459e18 −0.912672
\(842\) 2.55526e19 2.47120
\(843\) −6.68780e17 −0.0641806
\(844\) 9.59325e18 0.913566
\(845\) 1.22934e19 1.16172
\(846\) −8.42340e17 −0.0789914
\(847\) 2.92380e18 0.272086
\(848\) 2.05967e19 1.90206
\(849\) 8.46004e18 0.775305
\(850\) −1.77851e19 −1.61746
\(851\) 9.79569e18 0.884082
\(852\) −2.92130e19 −2.61649
\(853\) 5.94715e18 0.528615 0.264308 0.964438i \(-0.414857\pi\)
0.264308 + 0.964438i \(0.414857\pi\)
\(854\) −6.28451e18 −0.554364
\(855\) 1.05852e18 0.0926655
\(856\) 2.47609e19 2.15123
\(857\) 9.17213e18 0.790852 0.395426 0.918498i \(-0.370597\pi\)
0.395426 + 0.918498i \(0.370597\pi\)
\(858\) 1.98598e19 1.69945
\(859\) −1.84411e19 −1.56614 −0.783072 0.621931i \(-0.786348\pi\)
−0.783072 + 0.621931i \(0.786348\pi\)
\(860\) 7.79939e18 0.657386
\(861\) −4.33826e18 −0.362906
\(862\) 3.54968e18 0.294708
\(863\) 4.45527e17 0.0367116 0.0183558 0.999832i \(-0.494157\pi\)
0.0183558 + 0.999832i \(0.494157\pi\)
\(864\) 5.36090e18 0.438428
\(865\) 3.64511e17 0.0295874
\(866\) −3.39077e19 −2.73169
\(867\) −9.30632e17 −0.0744139
\(868\) −4.02586e19 −3.19507
\(869\) −3.65925e18 −0.288246
\(870\) −1.75383e18 −0.137124
\(871\) 1.43613e19 1.11449
\(872\) −3.29996e18 −0.254186
\(873\) 9.36064e17 0.0715670
\(874\) −1.74947e19 −1.32765
\(875\) 8.57180e18 0.645683
\(876\) 1.52414e19 1.13959
\(877\) 2.22386e19 1.65048 0.825238 0.564785i \(-0.191041\pi\)
0.825238 + 0.564785i \(0.191041\pi\)
\(878\) 3.96642e19 2.92203
\(879\) 1.11648e19 0.816439
\(880\) −1.31535e19 −0.954778
\(881\) 2.93798e18 0.211693 0.105846 0.994382i \(-0.466245\pi\)
0.105846 + 0.994382i \(0.466245\pi\)
\(882\) 2.75272e18 0.196887
\(883\) 6.62315e18 0.470240 0.235120 0.971966i \(-0.424452\pi\)
0.235120 + 0.971966i \(0.424452\pi\)
\(884\) 7.22015e19 5.08869
\(885\) 4.62210e17 0.0323376
\(886\) 2.64942e19 1.84006
\(887\) 6.99765e18 0.482446 0.241223 0.970470i \(-0.422452\pi\)
0.241223 + 0.970470i \(0.422452\pi\)
\(888\) 1.88715e19 1.29158
\(889\) −3.55255e18 −0.241368
\(890\) −2.17722e19 −1.46848
\(891\) −1.35930e18 −0.0910141
\(892\) 3.34772e19 2.22524
\(893\) 1.24217e18 0.0819682
\(894\) 2.14734e18 0.140672
\(895\) 2.14975e18 0.139810
\(896\) 7.82395e18 0.505154
\(897\) 1.90566e19 1.22150
\(898\) −4.04570e19 −2.57453
\(899\) −7.25874e18 −0.458589
\(900\) −1.07827e19 −0.676318
\(901\) −1.19786e19 −0.745922
\(902\) −1.88139e19 −1.16315
\(903\) 4.77355e18 0.293002
\(904\) −4.60197e19 −2.80446
\(905\) −1.10912e19 −0.671062
\(906\) −2.98460e19 −1.79289
\(907\) −5.93077e18 −0.353723 −0.176862 0.984236i \(-0.556595\pi\)
−0.176862 + 0.984236i \(0.556595\pi\)
\(908\) −5.27359e19 −3.12283
\(909\) 4.46489e18 0.262510
\(910\) −2.19004e19 −1.27844
\(911\) 2.70660e19 1.56876 0.784378 0.620283i \(-0.212982\pi\)
0.784378 + 0.620283i \(0.212982\pi\)
\(912\) −1.75633e19 −1.01074
\(913\) −8.63109e18 −0.493180
\(914\) 1.94436e19 1.10313
\(915\) 1.58233e18 0.0891372
\(916\) −5.59345e19 −3.12866
\(917\) −2.56349e19 −1.42374
\(918\) −6.92662e18 −0.381983
\(919\) −1.30576e19 −0.715008 −0.357504 0.933912i \(-0.616372\pi\)
−0.357504 + 0.933912i \(0.616372\pi\)
\(920\) −2.42204e19 −1.31692
\(921\) 1.26158e18 0.0681128
\(922\) −4.21854e19 −2.26157
\(923\) −6.57724e19 −3.50132
\(924\) −1.84201e19 −0.973699
\(925\) −1.24791e19 −0.655032
\(926\) 5.65360e19 2.94682
\(927\) −3.23389e18 −0.167381
\(928\) 1.30984e19 0.673221
\(929\) −2.70921e19 −1.38274 −0.691371 0.722500i \(-0.742993\pi\)
−0.691371 + 0.722500i \(0.742993\pi\)
\(930\) 1.42076e19 0.720079
\(931\) −4.05933e18 −0.204306
\(932\) −2.86200e19 −1.43043
\(933\) −2.00882e19 −0.997034
\(934\) 9.86884e18 0.486420
\(935\) 7.64975e18 0.374431
\(936\) 3.67127e19 1.78453
\(937\) 3.25888e19 1.57312 0.786558 0.617516i \(-0.211861\pi\)
0.786558 + 0.617516i \(0.211861\pi\)
\(938\) −1.86702e19 −0.895014
\(939\) −5.52556e18 −0.263057
\(940\) 2.87403e18 0.135881
\(941\) −2.45508e19 −1.15274 −0.576372 0.817187i \(-0.695532\pi\)
−0.576372 + 0.817187i \(0.695532\pi\)
\(942\) 6.73360e18 0.313990
\(943\) −1.80530e19 −0.836033
\(944\) −7.66916e18 −0.352720
\(945\) 1.49896e18 0.0684673
\(946\) 2.07017e19 0.939103
\(947\) 8.54835e18 0.385130 0.192565 0.981284i \(-0.438319\pi\)
0.192565 + 0.981284i \(0.438319\pi\)
\(948\) −1.13050e19 −0.505843
\(949\) 3.43157e19 1.52497
\(950\) 2.22872e19 0.983677
\(951\) −1.93804e19 −0.849550
\(952\) −5.61647e19 −2.44525
\(953\) −1.91407e19 −0.827663 −0.413831 0.910354i \(-0.635810\pi\)
−0.413831 + 0.910354i \(0.635810\pi\)
\(954\) −1.01791e19 −0.437167
\(955\) −1.63057e18 −0.0695534
\(956\) −1.97645e19 −0.837353
\(957\) −3.32121e18 −0.139755
\(958\) 1.29144e19 0.539756
\(959\) 3.15720e19 1.31063
\(960\) −9.31639e18 −0.384136
\(961\) 3.43847e19 1.40819
\(962\) 7.10083e19 2.88849
\(963\) −6.37691e18 −0.257655
\(964\) 8.03143e19 3.22324
\(965\) −8.26779e18 −0.329581
\(966\) −2.47742e19 −0.980952
\(967\) 1.56848e19 0.616891 0.308445 0.951242i \(-0.400191\pi\)
0.308445 + 0.951242i \(0.400191\pi\)
\(968\) 2.34398e19 0.915721
\(969\) 1.02144e19 0.396378
\(970\) −4.47657e18 −0.172556
\(971\) −1.81360e19 −0.694409 −0.347205 0.937789i \(-0.612869\pi\)
−0.347205 + 0.937789i \(0.612869\pi\)
\(972\) −4.19944e18 −0.159721
\(973\) 4.02381e18 0.152021
\(974\) 2.56548e18 0.0962800
\(975\) −2.42770e19 −0.905032
\(976\) −2.62546e19 −0.972256
\(977\) 1.19351e18 0.0439047 0.0219523 0.999759i \(-0.493012\pi\)
0.0219523 + 0.999759i \(0.493012\pi\)
\(978\) −2.12918e18 −0.0778052
\(979\) −4.12298e19 −1.49666
\(980\) −9.39217e18 −0.338686
\(981\) 8.49868e17 0.0304441
\(982\) 9.50685e19 3.38308
\(983\) −2.48473e19 −0.878378 −0.439189 0.898395i \(-0.644734\pi\)
−0.439189 + 0.898395i \(0.644734\pi\)
\(984\) −3.47792e19 −1.22138
\(985\) 2.09394e19 0.730515
\(986\) −1.69240e19 −0.586547
\(987\) 1.75903e18 0.0605635
\(988\) −9.04785e19 −3.09475
\(989\) 1.98644e19 0.674994
\(990\) 6.50061e18 0.219445
\(991\) −4.39355e19 −1.47346 −0.736728 0.676189i \(-0.763630\pi\)
−0.736728 + 0.676189i \(0.763630\pi\)
\(992\) −1.06109e20 −3.53530
\(993\) −6.33900e18 −0.209822
\(994\) 8.55062e19 2.81181
\(995\) 1.29841e19 0.424191
\(996\) −2.66651e19 −0.865481
\(997\) 2.88935e19 0.931712 0.465856 0.884860i \(-0.345746\pi\)
0.465856 + 0.884860i \(0.345746\pi\)
\(998\) 5.14578e19 1.64855
\(999\) −4.86013e18 −0.154694
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.1.2 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.2 31 1.1 even 1 trivial