Properties

Label 177.10.a.c.1.10
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-7.89550 q^{2} -81.0000 q^{3} -449.661 q^{4} +876.449 q^{5} +639.536 q^{6} -1202.42 q^{7} +7592.80 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-7.89550 q^{2} -81.0000 q^{3} -449.661 q^{4} +876.449 q^{5} +639.536 q^{6} -1202.42 q^{7} +7592.80 q^{8} +6561.00 q^{9} -6920.01 q^{10} +38810.0 q^{11} +36422.5 q^{12} +183461. q^{13} +9493.68 q^{14} -70992.4 q^{15} +170277. q^{16} +139737. q^{17} -51802.4 q^{18} -867454. q^{19} -394105. q^{20} +97395.7 q^{21} -306425. q^{22} +1.16660e6 q^{23} -615017. q^{24} -1.18496e6 q^{25} -1.44851e6 q^{26} -531441. q^{27} +540680. q^{28} +2.91181e6 q^{29} +560521. q^{30} +4.99286e6 q^{31} -5.23194e6 q^{32} -3.14361e6 q^{33} -1.10329e6 q^{34} -1.05386e6 q^{35} -2.95023e6 q^{36} -1.18814e6 q^{37} +6.84899e6 q^{38} -1.48603e7 q^{39} +6.65470e6 q^{40} -1.41883e7 q^{41} -768988. q^{42} -1.70225e7 q^{43} -1.74514e7 q^{44} +5.75038e6 q^{45} -9.21092e6 q^{46} +1.28461e7 q^{47} -1.37925e7 q^{48} -3.89078e7 q^{49} +9.35587e6 q^{50} -1.13187e7 q^{51} -8.24951e7 q^{52} +7.27522e7 q^{53} +4.19599e6 q^{54} +3.40150e7 q^{55} -9.12970e6 q^{56} +7.02638e7 q^{57} -2.29902e7 q^{58} +1.21174e7 q^{59} +3.19225e7 q^{60} -9.05578e7 q^{61} -3.94212e7 q^{62} -7.88905e6 q^{63} -4.58733e7 q^{64} +1.60794e8 q^{65} +2.48204e7 q^{66} -1.29418e7 q^{67} -6.28343e7 q^{68} -9.44949e7 q^{69} +8.32073e6 q^{70} +2.92250e8 q^{71} +4.98164e7 q^{72} -4.07144e8 q^{73} +9.38099e6 q^{74} +9.59819e7 q^{75} +3.90060e8 q^{76} -4.66658e7 q^{77} +1.17330e8 q^{78} +2.64575e8 q^{79} +1.49240e8 q^{80} +4.30467e7 q^{81} +1.12023e8 q^{82} -2.68636e8 q^{83} -4.37951e7 q^{84} +1.22472e8 q^{85} +1.34402e8 q^{86} -2.35857e8 q^{87} +2.94677e8 q^{88} +6.83062e8 q^{89} -4.54022e7 q^{90} -2.20596e8 q^{91} -5.24576e8 q^{92} -4.04422e8 q^{93} -1.01427e8 q^{94} -7.60280e8 q^{95} +4.23787e8 q^{96} +5.92565e8 q^{97} +3.07197e8 q^{98} +2.54633e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.89550 −0.348935 −0.174468 0.984663i \(-0.555820\pi\)
−0.174468 + 0.984663i \(0.555820\pi\)
\(3\) −81.0000 −0.577350
\(4\) −449.661 −0.878244
\(5\) 876.449 0.627136 0.313568 0.949566i \(-0.398476\pi\)
0.313568 + 0.949566i \(0.398476\pi\)
\(6\) 639.536 0.201458
\(7\) −1202.42 −0.189284 −0.0946419 0.995511i \(-0.530171\pi\)
−0.0946419 + 0.995511i \(0.530171\pi\)
\(8\) 7592.80 0.655386
\(9\) 6561.00 0.333333
\(10\) −6920.01 −0.218830
\(11\) 38810.0 0.799240 0.399620 0.916681i \(-0.369142\pi\)
0.399620 + 0.916681i \(0.369142\pi\)
\(12\) 36422.5 0.507055
\(13\) 183461. 1.78155 0.890774 0.454446i \(-0.150163\pi\)
0.890774 + 0.454446i \(0.150163\pi\)
\(14\) 9493.68 0.0660478
\(15\) −70992.4 −0.362077
\(16\) 170277. 0.649557
\(17\) 139737. 0.405781 0.202890 0.979201i \(-0.434967\pi\)
0.202890 + 0.979201i \(0.434967\pi\)
\(18\) −51802.4 −0.116312
\(19\) −867454. −1.52706 −0.763529 0.645774i \(-0.776535\pi\)
−0.763529 + 0.645774i \(0.776535\pi\)
\(20\) −394105. −0.550779
\(21\) 97395.7 0.109283
\(22\) −306425. −0.278883
\(23\) 1.16660e6 0.869256 0.434628 0.900610i \(-0.356880\pi\)
0.434628 + 0.900610i \(0.356880\pi\)
\(24\) −615017. −0.378387
\(25\) −1.18496e6 −0.606700
\(26\) −1.44851e6 −0.621645
\(27\) −531441. −0.192450
\(28\) 540680. 0.166237
\(29\) 2.91181e6 0.764492 0.382246 0.924061i \(-0.375151\pi\)
0.382246 + 0.924061i \(0.375151\pi\)
\(30\) 560521. 0.126342
\(31\) 4.99286e6 0.971006 0.485503 0.874235i \(-0.338636\pi\)
0.485503 + 0.874235i \(0.338636\pi\)
\(32\) −5.23194e6 −0.882039
\(33\) −3.14361e6 −0.461441
\(34\) −1.10329e6 −0.141591
\(35\) −1.05386e6 −0.118707
\(36\) −2.95023e6 −0.292748
\(37\) −1.18814e6 −0.104222 −0.0521112 0.998641i \(-0.516595\pi\)
−0.0521112 + 0.998641i \(0.516595\pi\)
\(38\) 6.84899e6 0.532844
\(39\) −1.48603e7 −1.02858
\(40\) 6.65470e6 0.411016
\(41\) −1.41883e7 −0.784155 −0.392077 0.919932i \(-0.628243\pi\)
−0.392077 + 0.919932i \(0.628243\pi\)
\(42\) −768988. −0.0381327
\(43\) −1.70225e7 −0.759305 −0.379653 0.925129i \(-0.623957\pi\)
−0.379653 + 0.925129i \(0.623957\pi\)
\(44\) −1.74514e7 −0.701928
\(45\) 5.75038e6 0.209045
\(46\) −9.21092e6 −0.303314
\(47\) 1.28461e7 0.384000 0.192000 0.981395i \(-0.438503\pi\)
0.192000 + 0.981395i \(0.438503\pi\)
\(48\) −1.37925e7 −0.375022
\(49\) −3.89078e7 −0.964172
\(50\) 9.35587e6 0.211699
\(51\) −1.13187e7 −0.234278
\(52\) −8.24951e7 −1.56463
\(53\) 7.27522e7 1.26650 0.633250 0.773948i \(-0.281721\pi\)
0.633250 + 0.773948i \(0.281721\pi\)
\(54\) 4.19599e6 0.0671526
\(55\) 3.40150e7 0.501232
\(56\) −9.12970e6 −0.124054
\(57\) 7.02638e7 0.881647
\(58\) −2.29902e7 −0.266758
\(59\) 1.21174e7 0.130189
\(60\) 3.19225e7 0.317992
\(61\) −9.05578e7 −0.837417 −0.418708 0.908121i \(-0.637517\pi\)
−0.418708 + 0.908121i \(0.637517\pi\)
\(62\) −3.94212e7 −0.338818
\(63\) −7.88905e6 −0.0630946
\(64\) −4.58733e7 −0.341782
\(65\) 1.60794e8 1.11727
\(66\) 2.48204e7 0.161013
\(67\) −1.29418e7 −0.0784616 −0.0392308 0.999230i \(-0.512491\pi\)
−0.0392308 + 0.999230i \(0.512491\pi\)
\(68\) −6.28343e7 −0.356374
\(69\) −9.44949e7 −0.501865
\(70\) 8.32073e6 0.0414210
\(71\) 2.92250e8 1.36487 0.682436 0.730945i \(-0.260921\pi\)
0.682436 + 0.730945i \(0.260921\pi\)
\(72\) 4.98164e7 0.218462
\(73\) −4.07144e8 −1.67801 −0.839007 0.544121i \(-0.816863\pi\)
−0.839007 + 0.544121i \(0.816863\pi\)
\(74\) 9.38099e6 0.0363669
\(75\) 9.59819e7 0.350279
\(76\) 3.90060e8 1.34113
\(77\) −4.66658e7 −0.151283
\(78\) 1.17330e8 0.358907
\(79\) 2.64575e8 0.764234 0.382117 0.924114i \(-0.375195\pi\)
0.382117 + 0.924114i \(0.375195\pi\)
\(80\) 1.49240e8 0.407361
\(81\) 4.30467e7 0.111111
\(82\) 1.12023e8 0.273619
\(83\) −2.68636e8 −0.621317 −0.310658 0.950522i \(-0.600549\pi\)
−0.310658 + 0.950522i \(0.600549\pi\)
\(84\) −4.37951e7 −0.0959772
\(85\) 1.22472e8 0.254480
\(86\) 1.34402e8 0.264948
\(87\) −2.35857e8 −0.441379
\(88\) 2.94677e8 0.523810
\(89\) 6.83062e8 1.15400 0.576999 0.816745i \(-0.304224\pi\)
0.576999 + 0.816745i \(0.304224\pi\)
\(90\) −4.54022e7 −0.0729433
\(91\) −2.20596e8 −0.337218
\(92\) −5.24576e8 −0.763419
\(93\) −4.04422e8 −0.560611
\(94\) −1.01427e8 −0.133991
\(95\) −7.60280e8 −0.957673
\(96\) 4.23787e8 0.509245
\(97\) 5.92565e8 0.679615 0.339808 0.940495i \(-0.389638\pi\)
0.339808 + 0.940495i \(0.389638\pi\)
\(98\) 3.07197e8 0.336434
\(99\) 2.54633e8 0.266413
\(100\) 5.32831e8 0.532831
\(101\) 2.03064e9 1.94172 0.970862 0.239640i \(-0.0770295\pi\)
0.970862 + 0.239640i \(0.0770295\pi\)
\(102\) 8.93668e7 0.0817477
\(103\) 9.46965e8 0.829023 0.414511 0.910044i \(-0.363952\pi\)
0.414511 + 0.910044i \(0.363952\pi\)
\(104\) 1.39298e9 1.16760
\(105\) 8.53624e7 0.0685354
\(106\) −5.74416e8 −0.441926
\(107\) 1.03749e9 0.765165 0.382582 0.923921i \(-0.375035\pi\)
0.382582 + 0.923921i \(0.375035\pi\)
\(108\) 2.38968e8 0.169018
\(109\) −2.31698e9 −1.57219 −0.786093 0.618109i \(-0.787899\pi\)
−0.786093 + 0.618109i \(0.787899\pi\)
\(110\) −2.68566e8 −0.174898
\(111\) 9.62396e7 0.0601729
\(112\) −2.04744e8 −0.122951
\(113\) −2.73625e9 −1.57871 −0.789355 0.613937i \(-0.789585\pi\)
−0.789355 + 0.613937i \(0.789585\pi\)
\(114\) −5.54768e8 −0.307638
\(115\) 1.02247e9 0.545142
\(116\) −1.30933e9 −0.671410
\(117\) 1.20368e9 0.593849
\(118\) −9.56727e7 −0.0454275
\(119\) −1.68022e8 −0.0768077
\(120\) −5.39031e8 −0.237300
\(121\) −8.51728e8 −0.361216
\(122\) 7.15000e8 0.292204
\(123\) 1.14925e9 0.452732
\(124\) −2.24510e9 −0.852780
\(125\) −2.75037e9 −1.00762
\(126\) 6.22881e7 0.0220159
\(127\) 1.54966e9 0.528591 0.264295 0.964442i \(-0.414861\pi\)
0.264295 + 0.964442i \(0.414861\pi\)
\(128\) 3.04095e9 1.00130
\(129\) 1.37883e9 0.438385
\(130\) −1.26955e9 −0.389856
\(131\) 5.74257e9 1.70367 0.851835 0.523810i \(-0.175490\pi\)
0.851835 + 0.523810i \(0.175490\pi\)
\(132\) 1.41356e9 0.405258
\(133\) 1.04304e9 0.289047
\(134\) 1.02182e8 0.0273780
\(135\) −4.65781e8 −0.120692
\(136\) 1.06099e9 0.265943
\(137\) 6.92192e9 1.67874 0.839371 0.543559i \(-0.182923\pi\)
0.839371 + 0.543559i \(0.182923\pi\)
\(138\) 7.46085e8 0.175119
\(139\) 5.76134e9 1.30905 0.654526 0.756039i \(-0.272868\pi\)
0.654526 + 0.756039i \(0.272868\pi\)
\(140\) 4.73878e8 0.104254
\(141\) −1.04054e9 −0.221703
\(142\) −2.30746e9 −0.476252
\(143\) 7.12011e9 1.42388
\(144\) 1.11719e9 0.216519
\(145\) 2.55206e9 0.479440
\(146\) 3.21461e9 0.585518
\(147\) 3.15153e9 0.556665
\(148\) 5.34262e8 0.0915327
\(149\) −8.24091e9 −1.36974 −0.684868 0.728667i \(-0.740140\pi\)
−0.684868 + 0.728667i \(0.740140\pi\)
\(150\) −7.57825e8 −0.122225
\(151\) 1.12173e10 1.75587 0.877936 0.478779i \(-0.158920\pi\)
0.877936 + 0.478779i \(0.158920\pi\)
\(152\) −6.58641e9 −1.00081
\(153\) 9.16814e8 0.135260
\(154\) 3.68450e8 0.0527880
\(155\) 4.37599e9 0.608953
\(156\) 6.68210e9 0.903342
\(157\) 2.08610e8 0.0274023 0.0137011 0.999906i \(-0.495639\pi\)
0.0137011 + 0.999906i \(0.495639\pi\)
\(158\) −2.08895e9 −0.266668
\(159\) −5.89293e9 −0.731214
\(160\) −4.58553e9 −0.553159
\(161\) −1.40274e9 −0.164536
\(162\) −3.39876e8 −0.0387706
\(163\) 3.72795e9 0.413643 0.206821 0.978379i \(-0.433688\pi\)
0.206821 + 0.978379i \(0.433688\pi\)
\(164\) 6.37991e9 0.688679
\(165\) −2.75522e9 −0.289386
\(166\) 2.12102e9 0.216799
\(167\) −6.68944e9 −0.665527 −0.332763 0.943010i \(-0.607981\pi\)
−0.332763 + 0.943010i \(0.607981\pi\)
\(168\) 7.39506e8 0.0716226
\(169\) 2.30533e10 2.17391
\(170\) −9.66981e8 −0.0887969
\(171\) −5.69137e9 −0.509019
\(172\) 7.65438e9 0.666856
\(173\) −8.95552e9 −0.760122 −0.380061 0.924961i \(-0.624097\pi\)
−0.380061 + 0.924961i \(0.624097\pi\)
\(174\) 1.86221e9 0.154013
\(175\) 1.42482e9 0.114839
\(176\) 6.60848e9 0.519152
\(177\) −9.81506e8 −0.0751646
\(178\) −5.39312e9 −0.402671
\(179\) −1.53461e10 −1.11727 −0.558636 0.829413i \(-0.688675\pi\)
−0.558636 + 0.829413i \(0.688675\pi\)
\(180\) −2.58572e9 −0.183593
\(181\) 1.89956e9 0.131552 0.0657762 0.997834i \(-0.479048\pi\)
0.0657762 + 0.997834i \(0.479048\pi\)
\(182\) 1.74172e9 0.117667
\(183\) 7.33518e9 0.483483
\(184\) 8.85778e9 0.569698
\(185\) −1.04135e9 −0.0653617
\(186\) 3.19311e9 0.195617
\(187\) 5.42320e9 0.324316
\(188\) −5.77640e9 −0.337246
\(189\) 6.39013e8 0.0364277
\(190\) 6.00279e9 0.334166
\(191\) 1.47484e10 0.801853 0.400926 0.916110i \(-0.368688\pi\)
0.400926 + 0.916110i \(0.368688\pi\)
\(192\) 3.71573e9 0.197328
\(193\) −3.03486e10 −1.57446 −0.787229 0.616661i \(-0.788485\pi\)
−0.787229 + 0.616661i \(0.788485\pi\)
\(194\) −4.67860e9 −0.237142
\(195\) −1.30243e10 −0.645058
\(196\) 1.74953e10 0.846778
\(197\) 4.65026e9 0.219978 0.109989 0.993933i \(-0.464918\pi\)
0.109989 + 0.993933i \(0.464918\pi\)
\(198\) −2.01045e9 −0.0929610
\(199\) −1.09579e10 −0.495322 −0.247661 0.968847i \(-0.579662\pi\)
−0.247661 + 0.968847i \(0.579662\pi\)
\(200\) −8.99717e9 −0.397623
\(201\) 1.04828e9 0.0452998
\(202\) −1.60330e10 −0.677536
\(203\) −3.50121e9 −0.144706
\(204\) 5.08958e9 0.205753
\(205\) −1.24353e10 −0.491772
\(206\) −7.47677e9 −0.289275
\(207\) 7.65408e9 0.289752
\(208\) 3.12392e10 1.15722
\(209\) −3.36659e10 −1.22048
\(210\) −6.73979e8 −0.0239144
\(211\) 5.11676e10 1.77715 0.888575 0.458731i \(-0.151696\pi\)
0.888575 + 0.458731i \(0.151696\pi\)
\(212\) −3.27138e10 −1.11230
\(213\) −2.36722e10 −0.788009
\(214\) −8.19147e9 −0.266993
\(215\) −1.49194e10 −0.476188
\(216\) −4.03512e9 −0.126129
\(217\) −6.00350e9 −0.183796
\(218\) 1.82938e10 0.548591
\(219\) 3.29787e10 0.968802
\(220\) −1.52952e10 −0.440204
\(221\) 2.56362e10 0.722918
\(222\) −7.59861e8 −0.0209964
\(223\) −4.46173e10 −1.20818 −0.604090 0.796916i \(-0.706463\pi\)
−0.604090 + 0.796916i \(0.706463\pi\)
\(224\) 6.29097e9 0.166956
\(225\) −7.77453e9 −0.202233
\(226\) 2.16041e10 0.550868
\(227\) 5.11536e10 1.27867 0.639336 0.768927i \(-0.279209\pi\)
0.639336 + 0.768927i \(0.279209\pi\)
\(228\) −3.15949e10 −0.774301
\(229\) 3.14014e10 0.754553 0.377277 0.926101i \(-0.376861\pi\)
0.377277 + 0.926101i \(0.376861\pi\)
\(230\) −8.07291e9 −0.190219
\(231\) 3.77993e9 0.0873434
\(232\) 2.21088e10 0.501037
\(233\) 2.10523e9 0.0467948 0.0233974 0.999726i \(-0.492552\pi\)
0.0233974 + 0.999726i \(0.492552\pi\)
\(234\) −9.50370e9 −0.207215
\(235\) 1.12590e10 0.240820
\(236\) −5.44870e9 −0.114338
\(237\) −2.14305e10 −0.441230
\(238\) 1.32662e9 0.0268009
\(239\) −6.19415e10 −1.22798 −0.613989 0.789314i \(-0.710436\pi\)
−0.613989 + 0.789314i \(0.710436\pi\)
\(240\) −1.20884e10 −0.235190
\(241\) 2.71277e10 0.518008 0.259004 0.965876i \(-0.416606\pi\)
0.259004 + 0.965876i \(0.416606\pi\)
\(242\) 6.72483e9 0.126041
\(243\) −3.48678e9 −0.0641500
\(244\) 4.07203e10 0.735456
\(245\) −3.41007e10 −0.604667
\(246\) −9.07390e9 −0.157974
\(247\) −1.59144e11 −2.72053
\(248\) 3.79098e10 0.636383
\(249\) 2.17595e10 0.358717
\(250\) 2.17156e10 0.351594
\(251\) −6.17270e10 −0.981620 −0.490810 0.871267i \(-0.663299\pi\)
−0.490810 + 0.871267i \(0.663299\pi\)
\(252\) 3.54740e9 0.0554125
\(253\) 4.52759e10 0.694744
\(254\) −1.22353e10 −0.184444
\(255\) −9.92027e9 −0.146924
\(256\) −5.22691e8 −0.00760615
\(257\) −8.11802e9 −0.116078 −0.0580392 0.998314i \(-0.518485\pi\)
−0.0580392 + 0.998314i \(0.518485\pi\)
\(258\) −1.08865e10 −0.152968
\(259\) 1.42864e9 0.0197276
\(260\) −7.23027e10 −0.981239
\(261\) 1.91044e10 0.254831
\(262\) −4.53405e10 −0.594471
\(263\) −1.79341e10 −0.231142 −0.115571 0.993299i \(-0.536870\pi\)
−0.115571 + 0.993299i \(0.536870\pi\)
\(264\) −2.38688e10 −0.302422
\(265\) 6.37636e10 0.794267
\(266\) −8.23534e9 −0.100859
\(267\) −5.53280e10 −0.666261
\(268\) 5.81941e9 0.0689085
\(269\) −8.51762e10 −0.991821 −0.495910 0.868374i \(-0.665166\pi\)
−0.495910 + 0.868374i \(0.665166\pi\)
\(270\) 3.67758e9 0.0421138
\(271\) −2.70972e10 −0.305185 −0.152592 0.988289i \(-0.548762\pi\)
−0.152592 + 0.988289i \(0.548762\pi\)
\(272\) 2.37941e10 0.263578
\(273\) 1.78683e10 0.194693
\(274\) −5.46521e10 −0.585772
\(275\) −4.59884e10 −0.484899
\(276\) 4.24907e10 0.440760
\(277\) −7.96559e10 −0.812941 −0.406470 0.913664i \(-0.633241\pi\)
−0.406470 + 0.913664i \(0.633241\pi\)
\(278\) −4.54887e10 −0.456775
\(279\) 3.27582e10 0.323669
\(280\) −8.00172e9 −0.0777987
\(281\) 1.84846e11 1.76861 0.884305 0.466909i \(-0.154633\pi\)
0.884305 + 0.466909i \(0.154633\pi\)
\(282\) 8.21555e9 0.0773599
\(283\) 1.40912e11 1.30590 0.652951 0.757400i \(-0.273531\pi\)
0.652951 + 0.757400i \(0.273531\pi\)
\(284\) −1.31413e11 −1.19869
\(285\) 6.15827e10 0.552913
\(286\) −5.62169e10 −0.496843
\(287\) 1.70602e10 0.148428
\(288\) −3.43268e10 −0.294013
\(289\) −9.90614e10 −0.835342
\(290\) −2.01498e10 −0.167294
\(291\) −4.79977e10 −0.392376
\(292\) 1.83077e11 1.47371
\(293\) −1.54732e11 −1.22652 −0.613260 0.789881i \(-0.710142\pi\)
−0.613260 + 0.789881i \(0.710142\pi\)
\(294\) −2.48829e10 −0.194240
\(295\) 1.06203e10 0.0816462
\(296\) −9.02134e9 −0.0683059
\(297\) −2.06252e10 −0.153814
\(298\) 6.50661e10 0.477949
\(299\) 2.14026e11 1.54862
\(300\) −4.31593e10 −0.307630
\(301\) 2.04682e10 0.143724
\(302\) −8.85664e10 −0.612685
\(303\) −1.64482e11 −1.12105
\(304\) −1.47708e11 −0.991911
\(305\) −7.93693e10 −0.525174
\(306\) −7.23871e9 −0.0471971
\(307\) −2.21886e10 −0.142563 −0.0712816 0.997456i \(-0.522709\pi\)
−0.0712816 + 0.997456i \(0.522709\pi\)
\(308\) 2.09838e10 0.132864
\(309\) −7.67042e10 −0.478637
\(310\) −3.45507e10 −0.212485
\(311\) 1.17393e11 0.711577 0.355789 0.934566i \(-0.384212\pi\)
0.355789 + 0.934566i \(0.384212\pi\)
\(312\) −1.12831e11 −0.674115
\(313\) 8.69675e10 0.512162 0.256081 0.966655i \(-0.417569\pi\)
0.256081 + 0.966655i \(0.417569\pi\)
\(314\) −1.64708e9 −0.00956161
\(315\) −6.91436e9 −0.0395689
\(316\) −1.18969e11 −0.671184
\(317\) 1.01021e11 0.561883 0.280941 0.959725i \(-0.409353\pi\)
0.280941 + 0.959725i \(0.409353\pi\)
\(318\) 4.65277e10 0.255146
\(319\) 1.13008e11 0.611012
\(320\) −4.02056e10 −0.214344
\(321\) −8.40363e10 −0.441768
\(322\) 1.10754e10 0.0574125
\(323\) −1.21215e11 −0.619650
\(324\) −1.93564e10 −0.0975827
\(325\) −2.17394e11 −1.08087
\(326\) −2.94340e10 −0.144335
\(327\) 1.87676e11 0.907702
\(328\) −1.07729e11 −0.513924
\(329\) −1.54464e10 −0.0726850
\(330\) 2.17538e10 0.100977
\(331\) −2.74015e11 −1.25472 −0.627362 0.778728i \(-0.715865\pi\)
−0.627362 + 0.778728i \(0.715865\pi\)
\(332\) 1.20795e11 0.545668
\(333\) −7.79541e9 −0.0347408
\(334\) 5.28165e10 0.232226
\(335\) −1.13428e10 −0.0492061
\(336\) 1.65843e10 0.0709856
\(337\) 4.40943e11 1.86229 0.931146 0.364647i \(-0.118810\pi\)
0.931146 + 0.364647i \(0.118810\pi\)
\(338\) −1.82017e11 −0.758556
\(339\) 2.21636e11 0.911469
\(340\) −5.50711e10 −0.223495
\(341\) 1.93773e11 0.776066
\(342\) 4.49362e10 0.177615
\(343\) 9.53052e10 0.371786
\(344\) −1.29249e11 −0.497638
\(345\) −8.28200e10 −0.314738
\(346\) 7.07084e10 0.265234
\(347\) 3.61083e11 1.33698 0.668489 0.743722i \(-0.266941\pi\)
0.668489 + 0.743722i \(0.266941\pi\)
\(348\) 1.06056e11 0.387639
\(349\) 3.14559e11 1.13498 0.567490 0.823380i \(-0.307915\pi\)
0.567490 + 0.823380i \(0.307915\pi\)
\(350\) −1.12496e10 −0.0400712
\(351\) −9.74985e10 −0.342859
\(352\) −2.03052e11 −0.704961
\(353\) −2.70265e11 −0.926411 −0.463205 0.886251i \(-0.653301\pi\)
−0.463205 + 0.886251i \(0.653301\pi\)
\(354\) 7.74949e9 0.0262276
\(355\) 2.56142e11 0.855961
\(356\) −3.07146e11 −1.01349
\(357\) 1.36098e10 0.0443450
\(358\) 1.21165e11 0.389856
\(359\) 5.89942e10 0.187449 0.0937247 0.995598i \(-0.470123\pi\)
0.0937247 + 0.995598i \(0.470123\pi\)
\(360\) 4.36615e10 0.137005
\(361\) 4.29789e11 1.33190
\(362\) −1.49980e10 −0.0459032
\(363\) 6.89900e10 0.208548
\(364\) 9.91934e10 0.296160
\(365\) −3.56841e11 −1.05234
\(366\) −5.79150e10 −0.168704
\(367\) 2.24441e11 0.645810 0.322905 0.946431i \(-0.395341\pi\)
0.322905 + 0.946431i \(0.395341\pi\)
\(368\) 1.98646e11 0.564632
\(369\) −9.30892e10 −0.261385
\(370\) 8.22197e9 0.0228070
\(371\) −8.74785e10 −0.239728
\(372\) 1.81853e11 0.492353
\(373\) −1.80422e11 −0.482615 −0.241307 0.970449i \(-0.577576\pi\)
−0.241307 + 0.970449i \(0.577576\pi\)
\(374\) −4.28189e10 −0.113165
\(375\) 2.22780e11 0.581750
\(376\) 9.75379e10 0.251668
\(377\) 5.34203e11 1.36198
\(378\) −5.04533e9 −0.0127109
\(379\) 1.57364e11 0.391767 0.195884 0.980627i \(-0.437243\pi\)
0.195884 + 0.980627i \(0.437243\pi\)
\(380\) 3.41868e11 0.841071
\(381\) −1.25522e11 −0.305182
\(382\) −1.16446e11 −0.279795
\(383\) −1.42996e11 −0.339570 −0.169785 0.985481i \(-0.554307\pi\)
−0.169785 + 0.985481i \(0.554307\pi\)
\(384\) −2.46317e11 −0.578100
\(385\) −4.09002e10 −0.0948752
\(386\) 2.39618e11 0.549384
\(387\) −1.11685e11 −0.253102
\(388\) −2.66453e11 −0.596868
\(389\) −5.33550e11 −1.18141 −0.590706 0.806887i \(-0.701151\pi\)
−0.590706 + 0.806887i \(0.701151\pi\)
\(390\) 1.02833e11 0.225084
\(391\) 1.63018e11 0.352727
\(392\) −2.95419e11 −0.631904
\(393\) −4.65148e11 −0.983615
\(394\) −3.67161e10 −0.0767580
\(395\) 2.31886e11 0.479278
\(396\) −1.14498e11 −0.233976
\(397\) 7.64619e11 1.54486 0.772428 0.635102i \(-0.219042\pi\)
0.772428 + 0.635102i \(0.219042\pi\)
\(398\) 8.65179e10 0.172835
\(399\) −8.44863e10 −0.166882
\(400\) −2.01772e11 −0.394086
\(401\) 4.55767e11 0.880224 0.440112 0.897943i \(-0.354939\pi\)
0.440112 + 0.897943i \(0.354939\pi\)
\(402\) −8.27673e9 −0.0158067
\(403\) 9.15993e11 1.72989
\(404\) −9.13101e11 −1.70531
\(405\) 3.77283e10 0.0696818
\(406\) 2.76438e10 0.0504930
\(407\) −4.61119e10 −0.0832987
\(408\) −8.59406e10 −0.153542
\(409\) 5.90970e11 1.04426 0.522132 0.852864i \(-0.325137\pi\)
0.522132 + 0.852864i \(0.325137\pi\)
\(410\) 9.81829e10 0.171597
\(411\) −5.60676e11 −0.969222
\(412\) −4.25813e11 −0.728085
\(413\) −1.45701e10 −0.0246427
\(414\) −6.04328e10 −0.101105
\(415\) −2.35446e11 −0.389650
\(416\) −9.59855e11 −1.57140
\(417\) −4.66669e11 −0.755782
\(418\) 2.65810e11 0.425870
\(419\) 5.95379e11 0.943693 0.471846 0.881681i \(-0.343588\pi\)
0.471846 + 0.881681i \(0.343588\pi\)
\(420\) −3.83841e10 −0.0601908
\(421\) −1.75564e11 −0.272374 −0.136187 0.990683i \(-0.543485\pi\)
−0.136187 + 0.990683i \(0.543485\pi\)
\(422\) −4.03994e11 −0.620111
\(423\) 8.42833e10 0.128000
\(424\) 5.52393e11 0.830045
\(425\) −1.65583e11 −0.246187
\(426\) 1.86904e11 0.274964
\(427\) 1.08888e11 0.158510
\(428\) −4.66517e11 −0.672002
\(429\) −5.76729e11 −0.822080
\(430\) 1.17796e11 0.166159
\(431\) 9.36848e11 1.30774 0.653870 0.756607i \(-0.273144\pi\)
0.653870 + 0.756607i \(0.273144\pi\)
\(432\) −9.04924e10 −0.125007
\(433\) 1.26449e12 1.72871 0.864353 0.502886i \(-0.167728\pi\)
0.864353 + 0.502886i \(0.167728\pi\)
\(434\) 4.74006e10 0.0641328
\(435\) −2.06717e11 −0.276805
\(436\) 1.04186e12 1.38076
\(437\) −1.01197e12 −1.32740
\(438\) −2.60383e11 −0.338049
\(439\) 8.05824e11 1.03550 0.517749 0.855532i \(-0.326770\pi\)
0.517749 + 0.855532i \(0.326770\pi\)
\(440\) 2.58269e11 0.328500
\(441\) −2.55274e11 −0.321391
\(442\) −2.02411e11 −0.252252
\(443\) 5.61599e11 0.692802 0.346401 0.938086i \(-0.387404\pi\)
0.346401 + 0.938086i \(0.387404\pi\)
\(444\) −4.32752e10 −0.0528465
\(445\) 5.98669e11 0.723714
\(446\) 3.52276e11 0.421577
\(447\) 6.67514e11 0.790818
\(448\) 5.51587e10 0.0646939
\(449\) −2.97221e11 −0.345121 −0.172561 0.984999i \(-0.555204\pi\)
−0.172561 + 0.984999i \(0.555204\pi\)
\(450\) 6.13839e10 0.0705664
\(451\) −5.50647e11 −0.626728
\(452\) 1.23038e12 1.38649
\(453\) −9.08602e11 −1.01375
\(454\) −4.03883e11 −0.446174
\(455\) −1.93341e11 −0.211482
\(456\) 5.33499e11 0.577819
\(457\) 5.56886e11 0.597233 0.298616 0.954373i \(-0.403475\pi\)
0.298616 + 0.954373i \(0.403475\pi\)
\(458\) −2.47930e11 −0.263290
\(459\) −7.42620e10 −0.0780925
\(460\) −4.59764e11 −0.478768
\(461\) −5.80556e11 −0.598673 −0.299337 0.954148i \(-0.596765\pi\)
−0.299337 + 0.954148i \(0.596765\pi\)
\(462\) −2.98445e10 −0.0304772
\(463\) −3.71702e11 −0.375908 −0.187954 0.982178i \(-0.560186\pi\)
−0.187954 + 0.982178i \(0.560186\pi\)
\(464\) 4.95816e11 0.496581
\(465\) −3.54455e11 −0.351579
\(466\) −1.66218e10 −0.0163284
\(467\) 1.02297e12 0.995264 0.497632 0.867388i \(-0.334203\pi\)
0.497632 + 0.867388i \(0.334203\pi\)
\(468\) −5.41250e11 −0.521545
\(469\) 1.55614e10 0.0148515
\(470\) −8.88952e10 −0.0840307
\(471\) −1.68974e10 −0.0158207
\(472\) 9.20047e10 0.0853239
\(473\) −6.60646e11 −0.606867
\(474\) 1.69205e11 0.153961
\(475\) 1.02790e12 0.926466
\(476\) 7.55530e10 0.0674559
\(477\) 4.77327e11 0.422166
\(478\) 4.89059e11 0.428485
\(479\) 7.36899e11 0.639584 0.319792 0.947488i \(-0.396387\pi\)
0.319792 + 0.947488i \(0.396387\pi\)
\(480\) 3.71428e11 0.319366
\(481\) −2.17978e11 −0.185677
\(482\) −2.14187e11 −0.180751
\(483\) 1.13622e11 0.0949950
\(484\) 3.82989e11 0.317236
\(485\) 5.19353e11 0.426211
\(486\) 2.75299e10 0.0223842
\(487\) −2.01369e12 −1.62223 −0.811114 0.584888i \(-0.801138\pi\)
−0.811114 + 0.584888i \(0.801138\pi\)
\(488\) −6.87587e11 −0.548831
\(489\) −3.01964e11 −0.238817
\(490\) 2.69242e11 0.210990
\(491\) 2.17028e12 1.68519 0.842595 0.538547i \(-0.181027\pi\)
0.842595 + 0.538547i \(0.181027\pi\)
\(492\) −5.16772e11 −0.397609
\(493\) 4.06888e11 0.310216
\(494\) 1.25652e12 0.949288
\(495\) 2.23173e11 0.167077
\(496\) 8.50172e11 0.630724
\(497\) −3.51406e11 −0.258348
\(498\) −1.71802e11 −0.125169
\(499\) −1.25122e12 −0.903405 −0.451702 0.892169i \(-0.649183\pi\)
−0.451702 + 0.892169i \(0.649183\pi\)
\(500\) 1.23674e12 0.884936
\(501\) 5.41845e11 0.384242
\(502\) 4.87366e11 0.342522
\(503\) 1.37573e12 0.958250 0.479125 0.877747i \(-0.340954\pi\)
0.479125 + 0.877747i \(0.340954\pi\)
\(504\) −5.99000e10 −0.0413513
\(505\) 1.77976e12 1.21772
\(506\) −3.57476e11 −0.242421
\(507\) −1.86732e12 −1.25511
\(508\) −6.96822e11 −0.464232
\(509\) 2.24355e12 1.48151 0.740756 0.671775i \(-0.234468\pi\)
0.740756 + 0.671775i \(0.234468\pi\)
\(510\) 7.83255e10 0.0512669
\(511\) 4.89557e11 0.317621
\(512\) −1.55284e12 −0.998645
\(513\) 4.61001e11 0.293882
\(514\) 6.40959e10 0.0405038
\(515\) 8.29967e11 0.519910
\(516\) −6.20004e11 −0.385009
\(517\) 4.98558e11 0.306908
\(518\) −1.12799e10 −0.00688367
\(519\) 7.25397e11 0.438857
\(520\) 1.22088e12 0.732245
\(521\) −1.16911e12 −0.695164 −0.347582 0.937650i \(-0.612997\pi\)
−0.347582 + 0.937650i \(0.612997\pi\)
\(522\) −1.50839e11 −0.0889194
\(523\) 1.78569e12 1.04363 0.521816 0.853058i \(-0.325255\pi\)
0.521816 + 0.853058i \(0.325255\pi\)
\(524\) −2.58221e12 −1.49624
\(525\) −1.15410e11 −0.0663021
\(526\) 1.41599e11 0.0806535
\(527\) 6.97687e11 0.394015
\(528\) −5.35286e11 −0.299732
\(529\) −4.40190e11 −0.244393
\(530\) −5.03446e11 −0.277148
\(531\) 7.95020e10 0.0433963
\(532\) −4.69015e11 −0.253854
\(533\) −2.60299e12 −1.39701
\(534\) 4.36843e11 0.232482
\(535\) 9.09303e11 0.479863
\(536\) −9.82643e10 −0.0514226
\(537\) 1.24303e12 0.645057
\(538\) 6.72509e11 0.346081
\(539\) −1.51001e12 −0.770604
\(540\) 2.09444e11 0.105997
\(541\) 1.16148e12 0.582941 0.291471 0.956580i \(-0.405855\pi\)
0.291471 + 0.956580i \(0.405855\pi\)
\(542\) 2.13946e11 0.106490
\(543\) −1.53864e11 −0.0759518
\(544\) −7.31096e11 −0.357914
\(545\) −2.03072e12 −0.985974
\(546\) −1.41079e11 −0.0679353
\(547\) −1.01125e12 −0.482965 −0.241482 0.970405i \(-0.577634\pi\)
−0.241482 + 0.970405i \(0.577634\pi\)
\(548\) −3.11252e12 −1.47435
\(549\) −5.94150e11 −0.279139
\(550\) 3.63102e11 0.169198
\(551\) −2.52587e12 −1.16742
\(552\) −7.17480e11 −0.328915
\(553\) −3.18129e11 −0.144657
\(554\) 6.28923e11 0.283664
\(555\) 8.43492e10 0.0377366
\(556\) −2.59065e12 −1.14967
\(557\) −8.34237e10 −0.0367232 −0.0183616 0.999831i \(-0.505845\pi\)
−0.0183616 + 0.999831i \(0.505845\pi\)
\(558\) −2.58642e11 −0.112939
\(559\) −3.12297e12 −1.35274
\(560\) −1.79448e11 −0.0771068
\(561\) −4.39279e11 −0.187244
\(562\) −1.45945e12 −0.617131
\(563\) −1.63117e12 −0.684243 −0.342121 0.939656i \(-0.611145\pi\)
−0.342121 + 0.939656i \(0.611145\pi\)
\(564\) 4.67888e11 0.194709
\(565\) −2.39818e12 −0.990067
\(566\) −1.11258e12 −0.455675
\(567\) −5.17601e10 −0.0210315
\(568\) 2.21900e12 0.894518
\(569\) −2.15020e12 −0.859951 −0.429976 0.902840i \(-0.641478\pi\)
−0.429976 + 0.902840i \(0.641478\pi\)
\(570\) −4.86226e11 −0.192931
\(571\) 1.46827e12 0.578021 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(572\) −3.20164e12 −1.25052
\(573\) −1.19462e12 −0.462950
\(574\) −1.34699e11 −0.0517917
\(575\) −1.38238e12 −0.527378
\(576\) −3.00974e11 −0.113927
\(577\) 4.55722e12 1.71162 0.855812 0.517286i \(-0.173058\pi\)
0.855812 + 0.517286i \(0.173058\pi\)
\(578\) 7.82140e11 0.291480
\(579\) 2.45824e12 0.909014
\(580\) −1.14756e12 −0.421066
\(581\) 3.23012e11 0.117605
\(582\) 3.78966e11 0.136914
\(583\) 2.82352e12 1.01224
\(584\) −3.09137e12 −1.09975
\(585\) 1.05497e12 0.372424
\(586\) 1.22168e12 0.427976
\(587\) −1.84926e12 −0.642875 −0.321437 0.946931i \(-0.604166\pi\)
−0.321437 + 0.946931i \(0.604166\pi\)
\(588\) −1.41712e12 −0.488888
\(589\) −4.33108e12 −1.48278
\(590\) −8.38523e10 −0.0284892
\(591\) −3.76671e11 −0.127004
\(592\) −2.02314e11 −0.0676984
\(593\) 1.67093e12 0.554897 0.277449 0.960740i \(-0.410511\pi\)
0.277449 + 0.960740i \(0.410511\pi\)
\(594\) 1.62847e11 0.0536710
\(595\) −1.47263e11 −0.0481689
\(596\) 3.70562e12 1.20296
\(597\) 8.87587e11 0.285974
\(598\) −1.68984e12 −0.540369
\(599\) −1.82405e12 −0.578915 −0.289458 0.957191i \(-0.593475\pi\)
−0.289458 + 0.957191i \(0.593475\pi\)
\(600\) 7.28771e11 0.229568
\(601\) −5.10011e12 −1.59457 −0.797286 0.603602i \(-0.793732\pi\)
−0.797286 + 0.603602i \(0.793732\pi\)
\(602\) −1.61607e11 −0.0501505
\(603\) −8.49110e10 −0.0261539
\(604\) −5.04399e12 −1.54208
\(605\) −7.46497e11 −0.226532
\(606\) 1.29867e12 0.391176
\(607\) −5.91080e12 −1.76725 −0.883624 0.468198i \(-0.844904\pi\)
−0.883624 + 0.468198i \(0.844904\pi\)
\(608\) 4.53847e12 1.34692
\(609\) 2.83598e11 0.0835460
\(610\) 6.26661e11 0.183252
\(611\) 2.35676e12 0.684115
\(612\) −4.12256e11 −0.118791
\(613\) 5.98563e12 1.71213 0.856066 0.516866i \(-0.172901\pi\)
0.856066 + 0.516866i \(0.172901\pi\)
\(614\) 1.75190e11 0.0497453
\(615\) 1.00726e12 0.283925
\(616\) −3.54324e11 −0.0991488
\(617\) 2.07156e12 0.575459 0.287729 0.957712i \(-0.407100\pi\)
0.287729 + 0.957712i \(0.407100\pi\)
\(618\) 6.05618e11 0.167013
\(619\) −2.82773e12 −0.774157 −0.387079 0.922047i \(-0.626516\pi\)
−0.387079 + 0.922047i \(0.626516\pi\)
\(620\) −1.96771e12 −0.534809
\(621\) −6.19981e11 −0.167288
\(622\) −9.26880e11 −0.248294
\(623\) −8.21325e11 −0.218433
\(624\) −2.53038e12 −0.668120
\(625\) −9.61858e10 −0.0252145
\(626\) −6.86652e11 −0.178711
\(627\) 2.72694e12 0.704647
\(628\) −9.38037e10 −0.0240659
\(629\) −1.66028e11 −0.0422914
\(630\) 5.45923e10 0.0138070
\(631\) −1.01693e12 −0.255364 −0.127682 0.991815i \(-0.540754\pi\)
−0.127682 + 0.991815i \(0.540754\pi\)
\(632\) 2.00886e12 0.500868
\(633\) −4.14458e12 −1.02604
\(634\) −7.97613e11 −0.196061
\(635\) 1.35820e12 0.331498
\(636\) 2.64982e12 0.642184
\(637\) −7.13805e12 −1.71772
\(638\) −8.92252e11 −0.213204
\(639\) 1.91745e12 0.454957
\(640\) 2.66523e12 0.627951
\(641\) −5.29037e12 −1.23773 −0.618864 0.785498i \(-0.712407\pi\)
−0.618864 + 0.785498i \(0.712407\pi\)
\(642\) 6.63509e11 0.154148
\(643\) 3.07318e12 0.708987 0.354494 0.935058i \(-0.384653\pi\)
0.354494 + 0.935058i \(0.384653\pi\)
\(644\) 6.30759e11 0.144503
\(645\) 1.20847e12 0.274927
\(646\) 9.57057e11 0.216218
\(647\) −6.32449e11 −0.141891 −0.0709457 0.997480i \(-0.522602\pi\)
−0.0709457 + 0.997480i \(0.522602\pi\)
\(648\) 3.26845e11 0.0728206
\(649\) 4.70275e11 0.104052
\(650\) 1.71643e12 0.377152
\(651\) 4.86283e11 0.106115
\(652\) −1.67631e12 −0.363279
\(653\) 4.83475e12 1.04055 0.520277 0.853998i \(-0.325829\pi\)
0.520277 + 0.853998i \(0.325829\pi\)
\(654\) −1.48179e12 −0.316729
\(655\) 5.03307e12 1.06843
\(656\) −2.41594e12 −0.509353
\(657\) −2.67127e12 −0.559338
\(658\) 1.21957e11 0.0253624
\(659\) −1.05700e12 −0.218319 −0.109159 0.994024i \(-0.534816\pi\)
−0.109159 + 0.994024i \(0.534816\pi\)
\(660\) 1.23891e12 0.254152
\(661\) 7.55120e12 1.53854 0.769271 0.638922i \(-0.220619\pi\)
0.769271 + 0.638922i \(0.220619\pi\)
\(662\) 2.16349e12 0.437818
\(663\) −2.07653e12 −0.417377
\(664\) −2.03970e12 −0.407202
\(665\) 9.14173e11 0.181272
\(666\) 6.15487e10 0.0121223
\(667\) 3.39693e12 0.664539
\(668\) 3.00798e12 0.584495
\(669\) 3.61400e12 0.697543
\(670\) 8.95572e10 0.0171697
\(671\) −3.51455e12 −0.669297
\(672\) −5.09568e11 −0.0963920
\(673\) −5.73880e12 −1.07833 −0.539167 0.842199i \(-0.681261\pi\)
−0.539167 + 0.842199i \(0.681261\pi\)
\(674\) −3.48147e12 −0.649819
\(675\) 6.29737e11 0.116760
\(676\) −1.03662e13 −1.90923
\(677\) −4.34589e12 −0.795115 −0.397558 0.917577i \(-0.630142\pi\)
−0.397558 + 0.917577i \(0.630142\pi\)
\(678\) −1.74993e12 −0.318044
\(679\) −7.12509e11 −0.128640
\(680\) 9.29908e11 0.166782
\(681\) −4.14344e12 −0.738242
\(682\) −1.52994e12 −0.270797
\(683\) 3.76552e10 0.00662112 0.00331056 0.999995i \(-0.498946\pi\)
0.00331056 + 0.999995i \(0.498946\pi\)
\(684\) 2.55919e12 0.447043
\(685\) 6.06671e12 1.05280
\(686\) −7.52483e11 −0.129729
\(687\) −2.54352e12 −0.435641
\(688\) −2.89856e12 −0.493212
\(689\) 1.33472e13 2.25633
\(690\) 6.53905e11 0.109823
\(691\) 1.07494e13 1.79364 0.896819 0.442397i \(-0.145872\pi\)
0.896819 + 0.442397i \(0.145872\pi\)
\(692\) 4.02695e12 0.667573
\(693\) −3.06174e11 −0.0504277
\(694\) −2.85093e12 −0.466519
\(695\) 5.04952e12 0.820954
\(696\) −1.79081e12 −0.289274
\(697\) −1.98262e12 −0.318195
\(698\) −2.48361e12 −0.396035
\(699\) −1.70524e11 −0.0270170
\(700\) −6.40685e11 −0.100856
\(701\) −5.69152e12 −0.890220 −0.445110 0.895476i \(-0.646835\pi\)
−0.445110 + 0.895476i \(0.646835\pi\)
\(702\) 7.69800e11 0.119636
\(703\) 1.03066e12 0.159154
\(704\) −1.78034e12 −0.273166
\(705\) −9.11976e11 −0.139038
\(706\) 2.13388e12 0.323257
\(707\) −2.44168e12 −0.367537
\(708\) 4.41345e11 0.0660129
\(709\) 1.00026e13 1.48663 0.743315 0.668942i \(-0.233252\pi\)
0.743315 + 0.668942i \(0.233252\pi\)
\(710\) −2.02237e12 −0.298675
\(711\) 1.73587e12 0.254745
\(712\) 5.18635e12 0.756314
\(713\) 5.82469e12 0.844053
\(714\) −1.07456e11 −0.0154735
\(715\) 6.24042e12 0.892969
\(716\) 6.90053e12 0.981237
\(717\) 5.01726e12 0.708974
\(718\) −4.65789e11 −0.0654077
\(719\) 1.17214e13 1.63569 0.817845 0.575439i \(-0.195169\pi\)
0.817845 + 0.575439i \(0.195169\pi\)
\(720\) 9.79161e11 0.135787
\(721\) −1.13865e12 −0.156921
\(722\) −3.39340e12 −0.464749
\(723\) −2.19734e12 −0.299072
\(724\) −8.54156e11 −0.115535
\(725\) −3.45039e12 −0.463817
\(726\) −5.44711e11 −0.0727698
\(727\) 6.94405e11 0.0921951 0.0460976 0.998937i \(-0.485321\pi\)
0.0460976 + 0.998937i \(0.485321\pi\)
\(728\) −1.67494e12 −0.221008
\(729\) 2.82430e11 0.0370370
\(730\) 2.81744e12 0.367200
\(731\) −2.37868e12 −0.308111
\(732\) −3.29835e12 −0.424616
\(733\) 1.79471e12 0.229628 0.114814 0.993387i \(-0.463373\pi\)
0.114814 + 0.993387i \(0.463373\pi\)
\(734\) −1.77207e12 −0.225346
\(735\) 2.76216e12 0.349105
\(736\) −6.10360e12 −0.766718
\(737\) −5.02271e11 −0.0627096
\(738\) 7.34986e11 0.0912064
\(739\) 1.20936e13 1.49161 0.745803 0.666167i \(-0.232066\pi\)
0.745803 + 0.666167i \(0.232066\pi\)
\(740\) 4.68254e11 0.0574035
\(741\) 1.28906e13 1.57070
\(742\) 6.90687e11 0.0836495
\(743\) 5.82688e11 0.0701434 0.0350717 0.999385i \(-0.488834\pi\)
0.0350717 + 0.999385i \(0.488834\pi\)
\(744\) −3.07069e12 −0.367416
\(745\) −7.22274e12 −0.859011
\(746\) 1.42453e12 0.168401
\(747\) −1.76252e12 −0.207106
\(748\) −2.43860e12 −0.284829
\(749\) −1.24749e12 −0.144833
\(750\) −1.75896e12 −0.202993
\(751\) 9.19635e10 0.0105496 0.00527480 0.999986i \(-0.498321\pi\)
0.00527480 + 0.999986i \(0.498321\pi\)
\(752\) 2.18740e12 0.249430
\(753\) 4.99989e12 0.566739
\(754\) −4.21780e12 −0.475242
\(755\) 9.83141e12 1.10117
\(756\) −2.87339e11 −0.0319924
\(757\) −1.08916e13 −1.20548 −0.602741 0.797937i \(-0.705925\pi\)
−0.602741 + 0.797937i \(0.705925\pi\)
\(758\) −1.24247e12 −0.136701
\(759\) −3.66735e12 −0.401111
\(760\) −5.77265e12 −0.627645
\(761\) −6.35015e11 −0.0686362 −0.0343181 0.999411i \(-0.510926\pi\)
−0.0343181 + 0.999411i \(0.510926\pi\)
\(762\) 9.91063e11 0.106489
\(763\) 2.78598e12 0.297589
\(764\) −6.63178e12 −0.704222
\(765\) 8.03541e11 0.0848266
\(766\) 1.12903e12 0.118488
\(767\) 2.22306e12 0.231938
\(768\) 4.23380e10 0.00439141
\(769\) −1.04080e13 −1.07324 −0.536620 0.843824i \(-0.680299\pi\)
−0.536620 + 0.843824i \(0.680299\pi\)
\(770\) 3.22928e11 0.0331053
\(771\) 6.57560e11 0.0670179
\(772\) 1.36466e13 1.38276
\(773\) −7.08749e11 −0.0713978 −0.0356989 0.999363i \(-0.511366\pi\)
−0.0356989 + 0.999363i \(0.511366\pi\)
\(774\) 8.81809e11 0.0883161
\(775\) −5.91635e12 −0.589110
\(776\) 4.49922e12 0.445410
\(777\) −1.15720e11 −0.0113898
\(778\) 4.21264e12 0.412237
\(779\) 1.23077e13 1.19745
\(780\) 5.85652e12 0.566519
\(781\) 1.13422e13 1.09086
\(782\) −1.28711e12 −0.123079
\(783\) −1.54746e12 −0.147126
\(784\) −6.62512e12 −0.626284
\(785\) 1.82836e11 0.0171849
\(786\) 3.67258e12 0.343218
\(787\) −1.88880e13 −1.75509 −0.877546 0.479492i \(-0.840821\pi\)
−0.877546 + 0.479492i \(0.840821\pi\)
\(788\) −2.09104e12 −0.193194
\(789\) 1.45266e12 0.133450
\(790\) −1.83086e12 −0.167237
\(791\) 3.29011e12 0.298825
\(792\) 1.93337e12 0.174603
\(793\) −1.66138e13 −1.49190
\(794\) −6.03705e12 −0.539055
\(795\) −5.16486e12 −0.458570
\(796\) 4.92733e12 0.435013
\(797\) 2.99654e11 0.0263062 0.0131531 0.999913i \(-0.495813\pi\)
0.0131531 + 0.999913i \(0.495813\pi\)
\(798\) 6.67062e11 0.0582309
\(799\) 1.79508e12 0.155820
\(800\) 6.19965e12 0.535133
\(801\) 4.48157e12 0.384666
\(802\) −3.59851e12 −0.307141
\(803\) −1.58013e13 −1.34114
\(804\) −4.71372e11 −0.0397843
\(805\) −1.22943e12 −0.103187
\(806\) −7.23223e12 −0.603621
\(807\) 6.89927e12 0.572628
\(808\) 1.54183e13 1.27258
\(809\) 1.98124e13 1.62618 0.813091 0.582136i \(-0.197783\pi\)
0.813091 + 0.582136i \(0.197783\pi\)
\(810\) −2.97884e11 −0.0243144
\(811\) −7.08065e12 −0.574751 −0.287375 0.957818i \(-0.592783\pi\)
−0.287375 + 0.957818i \(0.592783\pi\)
\(812\) 1.57436e12 0.127087
\(813\) 2.19487e12 0.176198
\(814\) 3.64077e11 0.0290659
\(815\) 3.26736e12 0.259410
\(816\) −1.92732e12 −0.152177
\(817\) 1.47663e13 1.15950
\(818\) −4.66601e12 −0.364381
\(819\) −1.44733e12 −0.112406
\(820\) 5.59167e12 0.431896
\(821\) 2.37038e13 1.82085 0.910423 0.413677i \(-0.135756\pi\)
0.910423 + 0.413677i \(0.135756\pi\)
\(822\) 4.42682e12 0.338196
\(823\) −1.32450e13 −1.00636 −0.503179 0.864182i \(-0.667836\pi\)
−0.503179 + 0.864182i \(0.667836\pi\)
\(824\) 7.19012e12 0.543330
\(825\) 3.72506e12 0.279957
\(826\) 1.15038e11 0.00859869
\(827\) 4.25854e12 0.316582 0.158291 0.987392i \(-0.449402\pi\)
0.158291 + 0.987392i \(0.449402\pi\)
\(828\) −3.44174e12 −0.254473
\(829\) −7.94186e12 −0.584019 −0.292009 0.956415i \(-0.594324\pi\)
−0.292009 + 0.956415i \(0.594324\pi\)
\(830\) 1.85896e12 0.135963
\(831\) 6.45212e12 0.469351
\(832\) −8.41593e12 −0.608902
\(833\) −5.43686e12 −0.391242
\(834\) 3.68458e12 0.263719
\(835\) −5.86295e12 −0.417376
\(836\) 1.51383e13 1.07188
\(837\) −2.65341e12 −0.186870
\(838\) −4.70082e12 −0.329288
\(839\) −6.48406e12 −0.451771 −0.225885 0.974154i \(-0.572528\pi\)
−0.225885 + 0.974154i \(0.572528\pi\)
\(840\) 6.48140e11 0.0449171
\(841\) −6.02848e12 −0.415553
\(842\) 1.38616e12 0.0950408
\(843\) −1.49725e13 −1.02111
\(844\) −2.30081e13 −1.56077
\(845\) 2.02050e13 1.36334
\(846\) −6.65460e11 −0.0446637
\(847\) 1.02413e12 0.0683724
\(848\) 1.23881e13 0.822663
\(849\) −1.14139e13 −0.753963
\(850\) 1.30736e12 0.0859034
\(851\) −1.38609e12 −0.0905960
\(852\) 1.06445e13 0.692064
\(853\) 1.67071e13 1.08052 0.540258 0.841500i \(-0.318327\pi\)
0.540258 + 0.841500i \(0.318327\pi\)
\(854\) −8.59727e11 −0.0553096
\(855\) −4.98820e12 −0.319224
\(856\) 7.87742e12 0.501478
\(857\) −1.85113e13 −1.17226 −0.586129 0.810218i \(-0.699349\pi\)
−0.586129 + 0.810218i \(0.699349\pi\)
\(858\) 4.55357e12 0.286853
\(859\) 2.23892e12 0.140304 0.0701518 0.997536i \(-0.477652\pi\)
0.0701518 + 0.997536i \(0.477652\pi\)
\(860\) 6.70867e12 0.418209
\(861\) −1.38188e12 −0.0856949
\(862\) −7.39689e12 −0.456317
\(863\) 1.52935e13 0.938553 0.469277 0.883051i \(-0.344515\pi\)
0.469277 + 0.883051i \(0.344515\pi\)
\(864\) 2.78047e12 0.169748
\(865\) −7.84906e12 −0.476700
\(866\) −9.98381e12 −0.603206
\(867\) 8.02398e12 0.482285
\(868\) 2.69954e12 0.161418
\(869\) 1.02681e13 0.610806
\(870\) 1.63213e12 0.0965870
\(871\) −2.37431e12 −0.139783
\(872\) −1.75924e13 −1.03039
\(873\) 3.88782e12 0.226538
\(874\) 7.99005e12 0.463178
\(875\) 3.30709e12 0.190726
\(876\) −1.48292e13 −0.850845
\(877\) 3.67264e11 0.0209643 0.0104821 0.999945i \(-0.496663\pi\)
0.0104821 + 0.999945i \(0.496663\pi\)
\(878\) −6.36238e12 −0.361322
\(879\) 1.25333e13 0.708131
\(880\) 5.79199e12 0.325579
\(881\) −1.09629e13 −0.613104 −0.306552 0.951854i \(-0.599175\pi\)
−0.306552 + 0.951854i \(0.599175\pi\)
\(882\) 2.01552e12 0.112145
\(883\) 7.86390e12 0.435326 0.217663 0.976024i \(-0.430157\pi\)
0.217663 + 0.976024i \(0.430157\pi\)
\(884\) −1.15276e13 −0.634898
\(885\) −8.60241e11 −0.0471384
\(886\) −4.43411e12 −0.241743
\(887\) −6.50209e12 −0.352693 −0.176347 0.984328i \(-0.556428\pi\)
−0.176347 + 0.984328i \(0.556428\pi\)
\(888\) 7.30728e11 0.0394364
\(889\) −1.86334e12 −0.100054
\(890\) −4.72680e12 −0.252529
\(891\) 1.67065e12 0.0888044
\(892\) 2.00627e13 1.06108
\(893\) −1.11434e13 −0.586390
\(894\) −5.27036e12 −0.275944
\(895\) −1.34501e13 −0.700682
\(896\) −3.65648e12 −0.189530
\(897\) −1.73361e13 −0.894097
\(898\) 2.34671e12 0.120425
\(899\) 1.45383e13 0.742326
\(900\) 3.49590e12 0.177610
\(901\) 1.01662e13 0.513921
\(902\) 4.34764e12 0.218687
\(903\) −1.65792e12 −0.0829792
\(904\) −2.07758e13 −1.03466
\(905\) 1.66486e12 0.0825012
\(906\) 7.17387e12 0.353734
\(907\) −2.74257e13 −1.34563 −0.672813 0.739813i \(-0.734914\pi\)
−0.672813 + 0.739813i \(0.734914\pi\)
\(908\) −2.30018e13 −1.12299
\(909\) 1.33230e13 0.647241
\(910\) 1.52653e12 0.0737935
\(911\) 3.61196e13 1.73744 0.868720 0.495303i \(-0.164943\pi\)
0.868720 + 0.495303i \(0.164943\pi\)
\(912\) 1.19643e13 0.572680
\(913\) −1.04258e13 −0.496581
\(914\) −4.39690e12 −0.208396
\(915\) 6.42892e12 0.303210
\(916\) −1.41200e13 −0.662682
\(917\) −6.90496e12 −0.322477
\(918\) 5.86336e11 0.0272492
\(919\) −1.70082e13 −0.786572 −0.393286 0.919416i \(-0.628662\pi\)
−0.393286 + 0.919416i \(0.628662\pi\)
\(920\) 7.76340e12 0.357278
\(921\) 1.79728e12 0.0823089
\(922\) 4.58378e12 0.208898
\(923\) 5.36163e13 2.43159
\(924\) −1.69969e12 −0.0767088
\(925\) 1.40790e12 0.0632318
\(926\) 2.93478e12 0.131167
\(927\) 6.21304e12 0.276341
\(928\) −1.52344e13 −0.674311
\(929\) −3.02207e13 −1.33117 −0.665585 0.746322i \(-0.731818\pi\)
−0.665585 + 0.746322i \(0.731818\pi\)
\(930\) 2.79860e12 0.122678
\(931\) 3.37507e13 1.47235
\(932\) −9.46639e11 −0.0410973
\(933\) −9.50887e12 −0.410829
\(934\) −8.07689e12 −0.347283
\(935\) 4.75316e12 0.203390
\(936\) 9.13934e12 0.389200
\(937\) −2.32899e13 −0.987051 −0.493525 0.869731i \(-0.664292\pi\)
−0.493525 + 0.869731i \(0.664292\pi\)
\(938\) −1.22865e11 −0.00518222
\(939\) −7.04437e12 −0.295697
\(940\) −5.06272e12 −0.211499
\(941\) −1.92887e12 −0.0801955 −0.0400977 0.999196i \(-0.512767\pi\)
−0.0400977 + 0.999196i \(0.512767\pi\)
\(942\) 1.33413e11 0.00552040
\(943\) −1.65521e13 −0.681631
\(944\) 2.06331e12 0.0845651
\(945\) 5.60063e11 0.0228451
\(946\) 5.21613e12 0.211757
\(947\) −1.02453e13 −0.413954 −0.206977 0.978346i \(-0.566362\pi\)
−0.206977 + 0.978346i \(0.566362\pi\)
\(948\) 9.63648e12 0.387508
\(949\) −7.46949e13 −2.98946
\(950\) −8.11579e12 −0.323277
\(951\) −8.18272e12 −0.324403
\(952\) −1.27576e12 −0.0503387
\(953\) 2.00482e13 0.787332 0.393666 0.919253i \(-0.371207\pi\)
0.393666 + 0.919253i \(0.371207\pi\)
\(954\) −3.76874e12 −0.147309
\(955\) 1.29262e13 0.502871
\(956\) 2.78527e13 1.07847
\(957\) −9.15362e12 −0.352768
\(958\) −5.81819e12 −0.223174
\(959\) −8.32303e12 −0.317759
\(960\) 3.25665e12 0.123752
\(961\) −1.51096e12 −0.0571474
\(962\) 1.72104e12 0.0647894
\(963\) 6.80694e12 0.255055
\(964\) −1.21983e13 −0.454937
\(965\) −2.65990e13 −0.987399
\(966\) −8.97104e11 −0.0331471
\(967\) 5.25249e12 0.193173 0.0965865 0.995325i \(-0.469208\pi\)
0.0965865 + 0.995325i \(0.469208\pi\)
\(968\) −6.46700e12 −0.236736
\(969\) 9.81845e12 0.357755
\(970\) −4.10055e12 −0.148720
\(971\) −2.34931e13 −0.848114 −0.424057 0.905636i \(-0.639394\pi\)
−0.424057 + 0.905636i \(0.639394\pi\)
\(972\) 1.56787e12 0.0563394
\(973\) −6.92753e12 −0.247783
\(974\) 1.58991e13 0.566053
\(975\) 1.76089e13 0.624038
\(976\) −1.54200e13 −0.543950
\(977\) −2.81571e13 −0.988695 −0.494347 0.869264i \(-0.664593\pi\)
−0.494347 + 0.869264i \(0.664593\pi\)
\(978\) 2.38415e12 0.0833316
\(979\) 2.65097e13 0.922321
\(980\) 1.53338e13 0.531045
\(981\) −1.52017e13 −0.524062
\(982\) −1.71355e13 −0.588022
\(983\) −2.34417e13 −0.800754 −0.400377 0.916350i \(-0.631121\pi\)
−0.400377 + 0.916350i \(0.631121\pi\)
\(984\) 8.72602e12 0.296714
\(985\) 4.07572e12 0.137956
\(986\) −3.21259e12 −0.108245
\(987\) 1.25116e12 0.0419647
\(988\) 7.15607e13 2.38929
\(989\) −1.98586e13 −0.660031
\(990\) −1.76206e12 −0.0582992
\(991\) −5.51039e13 −1.81489 −0.907446 0.420169i \(-0.861971\pi\)
−0.907446 + 0.420169i \(0.861971\pi\)
\(992\) −2.61223e13 −0.856465
\(993\) 2.21952e13 0.724415
\(994\) 2.77453e12 0.0901468
\(995\) −9.60402e12 −0.310634
\(996\) −9.78441e12 −0.315041
\(997\) 7.08244e12 0.227015 0.113508 0.993537i \(-0.463791\pi\)
0.113508 + 0.993537i \(0.463791\pi\)
\(998\) 9.87904e12 0.315230
\(999\) 6.31428e11 0.0200576
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 177.10.a.c.1.10 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.10 22 1.1 even 1 trivial