Properties

Label 177.10.a.c.1.14
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+17.2254 q^{2} -81.0000 q^{3} -215.286 q^{4} +27.4764 q^{5} -1395.26 q^{6} +8666.20 q^{7} -12527.8 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+17.2254 q^{2} -81.0000 q^{3} -215.286 q^{4} +27.4764 q^{5} -1395.26 q^{6} +8666.20 q^{7} -12527.8 q^{8} +6561.00 q^{9} +473.292 q^{10} +42328.6 q^{11} +17438.1 q^{12} -200715. q^{13} +149279. q^{14} -2225.59 q^{15} -105570. q^{16} +154813. q^{17} +113016. q^{18} -72431.9 q^{19} -5915.28 q^{20} -701962. q^{21} +729126. q^{22} +1.79253e6 q^{23} +1.01475e6 q^{24} -1.95237e6 q^{25} -3.45739e6 q^{26} -531441. q^{27} -1.86571e6 q^{28} +2.62285e6 q^{29} -38336.6 q^{30} -6.56272e6 q^{31} +4.59574e6 q^{32} -3.42861e6 q^{33} +2.66671e6 q^{34} +238116. q^{35} -1.41249e6 q^{36} +2.16272e6 q^{37} -1.24767e6 q^{38} +1.62579e7 q^{39} -344218. q^{40} -1.12147e7 q^{41} -1.20916e7 q^{42} -3.59092e7 q^{43} -9.11273e6 q^{44} +180273. q^{45} +3.08771e7 q^{46} +2.37517e7 q^{47} +8.55115e6 q^{48} +3.47495e7 q^{49} -3.36303e7 q^{50} -1.25398e7 q^{51} +4.32110e7 q^{52} +8.03425e6 q^{53} -9.15428e6 q^{54} +1.16304e6 q^{55} -1.08568e8 q^{56} +5.86699e6 q^{57} +4.51796e7 q^{58} +1.21174e7 q^{59} +479137. q^{60} +1.76705e8 q^{61} -1.13045e8 q^{62} +5.68590e7 q^{63} +1.33215e8 q^{64} -5.51492e6 q^{65} -5.90592e7 q^{66} +1.31033e8 q^{67} -3.33289e7 q^{68} -1.45195e8 q^{69} +4.10164e6 q^{70} +3.10987e8 q^{71} -8.21948e7 q^{72} +2.50223e8 q^{73} +3.72537e7 q^{74} +1.58142e8 q^{75} +1.55936e7 q^{76} +3.66828e8 q^{77} +2.80049e8 q^{78} +3.50930e8 q^{79} -2.90068e6 q^{80} +4.30467e7 q^{81} -1.93178e8 q^{82} +3.42539e8 q^{83} +1.51122e8 q^{84} +4.25369e6 q^{85} -6.18550e8 q^{86} -2.12451e8 q^{87} -5.30283e8 q^{88} +8.59131e8 q^{89} +3.10527e6 q^{90} -1.73943e9 q^{91} -3.85907e8 q^{92} +5.31580e8 q^{93} +4.09133e8 q^{94} -1.99017e6 q^{95} -3.72255e8 q^{96} +1.29447e9 q^{97} +5.98573e8 q^{98} +2.77718e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 17.2254 0.761262 0.380631 0.924727i \(-0.375707\pi\)
0.380631 + 0.924727i \(0.375707\pi\)
\(3\) −81.0000 −0.577350
\(4\) −215.286 −0.420480
\(5\) 27.4764 0.0196605 0.00983025 0.999952i \(-0.496871\pi\)
0.00983025 + 0.999952i \(0.496871\pi\)
\(6\) −1395.26 −0.439515
\(7\) 8666.20 1.36423 0.682115 0.731245i \(-0.261060\pi\)
0.682115 + 0.731245i \(0.261060\pi\)
\(8\) −12527.8 −1.08136
\(9\) 6561.00 0.333333
\(10\) 473.292 0.0149668
\(11\) 42328.6 0.871699 0.435849 0.900020i \(-0.356448\pi\)
0.435849 + 0.900020i \(0.356448\pi\)
\(12\) 17438.1 0.242764
\(13\) −200715. −1.94910 −0.974550 0.224169i \(-0.928033\pi\)
−0.974550 + 0.224169i \(0.928033\pi\)
\(14\) 149279. 1.03854
\(15\) −2225.59 −0.0113510
\(16\) −105570. −0.402717
\(17\) 154813. 0.449558 0.224779 0.974410i \(-0.427834\pi\)
0.224779 + 0.974410i \(0.427834\pi\)
\(18\) 113016. 0.253754
\(19\) −72431.9 −0.127508 −0.0637542 0.997966i \(-0.520307\pi\)
−0.0637542 + 0.997966i \(0.520307\pi\)
\(20\) −5915.28 −0.00826685
\(21\) −701962. −0.787639
\(22\) 729126. 0.663591
\(23\) 1.79253e6 1.33565 0.667824 0.744319i \(-0.267226\pi\)
0.667824 + 0.744319i \(0.267226\pi\)
\(24\) 1.01475e6 0.624322
\(25\) −1.95237e6 −0.999613
\(26\) −3.45739e6 −1.48378
\(27\) −531441. −0.192450
\(28\) −1.86571e6 −0.573631
\(29\) 2.62285e6 0.688624 0.344312 0.938855i \(-0.388112\pi\)
0.344312 + 0.938855i \(0.388112\pi\)
\(30\) −38336.6 −0.00864109
\(31\) −6.56272e6 −1.27631 −0.638155 0.769908i \(-0.720302\pi\)
−0.638155 + 0.769908i \(0.720302\pi\)
\(32\) 4.59574e6 0.774785
\(33\) −3.42861e6 −0.503275
\(34\) 2.66671e6 0.342232
\(35\) 238116. 0.0268215
\(36\) −1.41249e6 −0.140160
\(37\) 2.16272e6 0.189711 0.0948554 0.995491i \(-0.469761\pi\)
0.0948554 + 0.995491i \(0.469761\pi\)
\(38\) −1.24767e6 −0.0970673
\(39\) 1.62579e7 1.12531
\(40\) −344218. −0.0212600
\(41\) −1.12147e7 −0.619813 −0.309906 0.950767i \(-0.600298\pi\)
−0.309906 + 0.950767i \(0.600298\pi\)
\(42\) −1.20916e7 −0.599600
\(43\) −3.59092e7 −1.60176 −0.800880 0.598825i \(-0.795635\pi\)
−0.800880 + 0.598825i \(0.795635\pi\)
\(44\) −9.11273e6 −0.366532
\(45\) 180273. 0.00655350
\(46\) 3.08771e7 1.01678
\(47\) 2.37517e7 0.709994 0.354997 0.934868i \(-0.384482\pi\)
0.354997 + 0.934868i \(0.384482\pi\)
\(48\) 8.55115e6 0.232509
\(49\) 3.47495e7 0.861124
\(50\) −3.36303e7 −0.760968
\(51\) −1.25398e7 −0.259553
\(52\) 4.32110e7 0.819558
\(53\) 8.03425e6 0.139863 0.0699317 0.997552i \(-0.477722\pi\)
0.0699317 + 0.997552i \(0.477722\pi\)
\(54\) −9.15428e6 −0.146505
\(55\) 1.16304e6 0.0171380
\(56\) −1.08568e8 −1.47522
\(57\) 5.86699e6 0.0736170
\(58\) 4.51796e7 0.524224
\(59\) 1.21174e7 0.130189
\(60\) 479137. 0.00477287
\(61\) 1.76705e8 1.63405 0.817023 0.576605i \(-0.195623\pi\)
0.817023 + 0.576605i \(0.195623\pi\)
\(62\) −1.13045e8 −0.971606
\(63\) 5.68590e7 0.454743
\(64\) 1.33215e8 0.992531
\(65\) −5.51492e6 −0.0383203
\(66\) −5.90592e7 −0.383125
\(67\) 1.31033e8 0.794406 0.397203 0.917731i \(-0.369981\pi\)
0.397203 + 0.917731i \(0.369981\pi\)
\(68\) −3.33289e7 −0.189030
\(69\) −1.45195e8 −0.771137
\(70\) 4.10164e6 0.0204182
\(71\) 3.10987e8 1.45238 0.726189 0.687495i \(-0.241290\pi\)
0.726189 + 0.687495i \(0.241290\pi\)
\(72\) −8.21948e7 −0.360453
\(73\) 2.50223e8 1.03128 0.515638 0.856807i \(-0.327555\pi\)
0.515638 + 0.856807i \(0.327555\pi\)
\(74\) 3.72537e7 0.144420
\(75\) 1.58142e8 0.577127
\(76\) 1.55936e7 0.0536147
\(77\) 3.66828e8 1.18920
\(78\) 2.80049e8 0.856659
\(79\) 3.50930e8 1.01368 0.506838 0.862041i \(-0.330814\pi\)
0.506838 + 0.862041i \(0.330814\pi\)
\(80\) −2.90068e6 −0.00791762
\(81\) 4.30467e7 0.111111
\(82\) −1.93178e8 −0.471840
\(83\) 3.42539e8 0.792243 0.396121 0.918198i \(-0.370356\pi\)
0.396121 + 0.918198i \(0.370356\pi\)
\(84\) 1.51122e8 0.331186
\(85\) 4.25369e6 0.00883854
\(86\) −6.18550e8 −1.21936
\(87\) −2.12451e8 −0.397578
\(88\) −5.30283e8 −0.942618
\(89\) 8.59131e8 1.45146 0.725729 0.687981i \(-0.241503\pi\)
0.725729 + 0.687981i \(0.241503\pi\)
\(90\) 3.10527e6 0.00498893
\(91\) −1.73943e9 −2.65902
\(92\) −3.85907e8 −0.561613
\(93\) 5.31580e8 0.736878
\(94\) 4.09133e8 0.540491
\(95\) −1.99017e6 −0.00250688
\(96\) −3.72255e8 −0.447322
\(97\) 1.29447e9 1.48463 0.742317 0.670049i \(-0.233727\pi\)
0.742317 + 0.670049i \(0.233727\pi\)
\(98\) 5.98573e8 0.655541
\(99\) 2.77718e8 0.290566
\(100\) 4.20317e8 0.420317
\(101\) 7.34234e8 0.702082 0.351041 0.936360i \(-0.385828\pi\)
0.351041 + 0.936360i \(0.385828\pi\)
\(102\) −2.16003e8 −0.197588
\(103\) −1.48780e9 −1.30250 −0.651249 0.758864i \(-0.725755\pi\)
−0.651249 + 0.758864i \(0.725755\pi\)
\(104\) 2.51451e9 2.10767
\(105\) −1.92874e7 −0.0154854
\(106\) 1.38393e8 0.106473
\(107\) 1.83548e9 1.35370 0.676851 0.736120i \(-0.263344\pi\)
0.676851 + 0.736120i \(0.263344\pi\)
\(108\) 1.14412e8 0.0809214
\(109\) 9.99882e8 0.678468 0.339234 0.940702i \(-0.389832\pi\)
0.339234 + 0.940702i \(0.389832\pi\)
\(110\) 2.00338e7 0.0130465
\(111\) −1.75180e8 −0.109530
\(112\) −9.14889e8 −0.549398
\(113\) 1.86271e8 0.107471 0.0537355 0.998555i \(-0.482887\pi\)
0.0537355 + 0.998555i \(0.482887\pi\)
\(114\) 1.01061e8 0.0560419
\(115\) 4.92524e7 0.0262595
\(116\) −5.64662e8 −0.289553
\(117\) −1.31689e9 −0.649700
\(118\) 2.08726e8 0.0991079
\(119\) 1.34164e9 0.613301
\(120\) 2.78817e7 0.0122745
\(121\) −5.66241e8 −0.240141
\(122\) 3.04381e9 1.24394
\(123\) 9.08391e8 0.357849
\(124\) 1.41286e9 0.536662
\(125\) −1.07309e8 −0.0393134
\(126\) 9.79418e8 0.346179
\(127\) −3.39236e9 −1.15714 −0.578569 0.815634i \(-0.696389\pi\)
−0.578569 + 0.815634i \(0.696389\pi\)
\(128\) −5.83357e7 −0.0192083
\(129\) 2.90864e9 0.924777
\(130\) −9.49967e7 −0.0291718
\(131\) −3.75251e9 −1.11327 −0.556636 0.830756i \(-0.687908\pi\)
−0.556636 + 0.830756i \(0.687908\pi\)
\(132\) 7.38131e8 0.211617
\(133\) −6.27710e8 −0.173951
\(134\) 2.25709e9 0.604752
\(135\) −1.46021e7 −0.00378367
\(136\) −1.93946e9 −0.486133
\(137\) −2.12368e9 −0.515045 −0.257523 0.966272i \(-0.582906\pi\)
−0.257523 + 0.966272i \(0.582906\pi\)
\(138\) −2.50105e9 −0.587037
\(139\) 2.46199e9 0.559398 0.279699 0.960088i \(-0.409765\pi\)
0.279699 + 0.960088i \(0.409765\pi\)
\(140\) −5.12630e7 −0.0112779
\(141\) −1.92389e9 −0.409915
\(142\) 5.35687e9 1.10564
\(143\) −8.49597e9 −1.69903
\(144\) −6.92643e8 −0.134239
\(145\) 7.20665e7 0.0135387
\(146\) 4.31019e9 0.785071
\(147\) −2.81471e9 −0.497170
\(148\) −4.65602e8 −0.0797696
\(149\) −8.87541e9 −1.47520 −0.737598 0.675240i \(-0.764040\pi\)
−0.737598 + 0.675240i \(0.764040\pi\)
\(150\) 2.72406e9 0.439345
\(151\) −3.09187e8 −0.0483977 −0.0241989 0.999707i \(-0.507703\pi\)
−0.0241989 + 0.999707i \(0.507703\pi\)
\(152\) 9.07412e8 0.137882
\(153\) 1.01572e9 0.149853
\(154\) 6.31876e9 0.905291
\(155\) −1.80320e8 −0.0250929
\(156\) −3.50009e9 −0.473172
\(157\) −3.14639e9 −0.413299 −0.206649 0.978415i \(-0.566256\pi\)
−0.206649 + 0.978415i \(0.566256\pi\)
\(158\) 6.04491e9 0.771673
\(159\) −6.50774e8 −0.0807502
\(160\) 1.26275e8 0.0152327
\(161\) 1.55345e10 1.82213
\(162\) 7.41497e8 0.0845847
\(163\) −1.13192e10 −1.25595 −0.627976 0.778233i \(-0.716116\pi\)
−0.627976 + 0.778233i \(0.716116\pi\)
\(164\) 2.41437e9 0.260619
\(165\) −9.42059e7 −0.00989465
\(166\) 5.90037e9 0.603104
\(167\) 1.94041e10 1.93050 0.965248 0.261336i \(-0.0841630\pi\)
0.965248 + 0.261336i \(0.0841630\pi\)
\(168\) 8.79403e9 0.851719
\(169\) 2.96819e10 2.79899
\(170\) 7.32715e7 0.00672845
\(171\) −4.75226e8 −0.0425028
\(172\) 7.73073e9 0.673508
\(173\) 1.25396e10 1.06433 0.532165 0.846641i \(-0.321379\pi\)
0.532165 + 0.846641i \(0.321379\pi\)
\(174\) −3.65955e9 −0.302661
\(175\) −1.69196e10 −1.36370
\(176\) −4.46862e9 −0.351048
\(177\) −9.81506e8 −0.0751646
\(178\) 1.47989e10 1.10494
\(179\) 3.11531e8 0.0226810 0.0113405 0.999936i \(-0.496390\pi\)
0.0113405 + 0.999936i \(0.496390\pi\)
\(180\) −3.88101e7 −0.00275562
\(181\) 1.03952e10 0.719913 0.359956 0.932969i \(-0.382792\pi\)
0.359956 + 0.932969i \(0.382792\pi\)
\(182\) −2.99625e10 −2.02421
\(183\) −1.43131e10 −0.943417
\(184\) −2.24565e10 −1.44431
\(185\) 5.94237e7 0.00372981
\(186\) 9.15668e9 0.560957
\(187\) 6.55299e9 0.391879
\(188\) −5.11340e9 −0.298538
\(189\) −4.60558e9 −0.262546
\(190\) −3.42814e7 −0.00190839
\(191\) −3.78429e9 −0.205747 −0.102874 0.994694i \(-0.532804\pi\)
−0.102874 + 0.994694i \(0.532804\pi\)
\(192\) −1.07904e10 −0.573038
\(193\) 9.41435e9 0.488408 0.244204 0.969724i \(-0.421473\pi\)
0.244204 + 0.969724i \(0.421473\pi\)
\(194\) 2.22978e10 1.13020
\(195\) 4.46708e8 0.0221242
\(196\) −7.48106e9 −0.362085
\(197\) 7.75555e9 0.366872 0.183436 0.983032i \(-0.441278\pi\)
0.183436 + 0.983032i \(0.441278\pi\)
\(198\) 4.78380e9 0.221197
\(199\) 2.33479e10 1.05538 0.527690 0.849437i \(-0.323058\pi\)
0.527690 + 0.849437i \(0.323058\pi\)
\(200\) 2.44589e10 1.08094
\(201\) −1.06136e10 −0.458651
\(202\) 1.26475e10 0.534469
\(203\) 2.27302e10 0.939442
\(204\) 2.69964e9 0.109137
\(205\) −3.08140e8 −0.0121858
\(206\) −2.56280e10 −0.991543
\(207\) 1.17608e10 0.445216
\(208\) 2.11894e10 0.784935
\(209\) −3.06594e9 −0.111149
\(210\) −3.32233e8 −0.0117884
\(211\) −1.25430e10 −0.435643 −0.217822 0.975989i \(-0.569895\pi\)
−0.217822 + 0.975989i \(0.569895\pi\)
\(212\) −1.72966e9 −0.0588097
\(213\) −2.51899e10 −0.838531
\(214\) 3.16169e10 1.03052
\(215\) −9.86655e8 −0.0314914
\(216\) 6.65778e9 0.208107
\(217\) −5.68738e10 −1.74118
\(218\) 1.72234e10 0.516492
\(219\) −2.02681e10 −0.595407
\(220\) −2.50385e8 −0.00720620
\(221\) −3.10732e10 −0.876234
\(222\) −3.01755e9 −0.0833807
\(223\) −4.79430e10 −1.29823 −0.649117 0.760688i \(-0.724862\pi\)
−0.649117 + 0.760688i \(0.724862\pi\)
\(224\) 3.98277e10 1.05698
\(225\) −1.28095e10 −0.333204
\(226\) 3.20859e9 0.0818137
\(227\) 4.75115e10 1.18763 0.593816 0.804601i \(-0.297621\pi\)
0.593816 + 0.804601i \(0.297621\pi\)
\(228\) −1.26308e9 −0.0309545
\(229\) 2.54035e10 0.610427 0.305214 0.952284i \(-0.401272\pi\)
0.305214 + 0.952284i \(0.401272\pi\)
\(230\) 8.48392e8 0.0199904
\(231\) −2.97131e10 −0.686584
\(232\) −3.28585e10 −0.744649
\(233\) 4.20530e10 0.934750 0.467375 0.884059i \(-0.345200\pi\)
0.467375 + 0.884059i \(0.345200\pi\)
\(234\) −2.26839e10 −0.494592
\(235\) 6.52611e8 0.0139588
\(236\) −2.60869e9 −0.0547418
\(237\) −2.84254e10 −0.585246
\(238\) 2.31102e10 0.466883
\(239\) −8.98700e10 −1.78166 −0.890829 0.454339i \(-0.849876\pi\)
−0.890829 + 0.454339i \(0.849876\pi\)
\(240\) 2.34955e8 0.00457124
\(241\) 2.72838e10 0.520989 0.260495 0.965475i \(-0.416114\pi\)
0.260495 + 0.965475i \(0.416114\pi\)
\(242\) −9.75372e9 −0.182811
\(243\) −3.48678e9 −0.0641500
\(244\) −3.80420e10 −0.687083
\(245\) 9.54790e8 0.0169301
\(246\) 1.56474e10 0.272417
\(247\) 1.45382e10 0.248527
\(248\) 8.22163e10 1.38015
\(249\) −2.77456e10 −0.457402
\(250\) −1.84844e9 −0.0299278
\(251\) −2.84422e10 −0.452305 −0.226153 0.974092i \(-0.572615\pi\)
−0.226153 + 0.974092i \(0.572615\pi\)
\(252\) −1.22409e10 −0.191210
\(253\) 7.58754e10 1.16428
\(254\) −5.84347e10 −0.880885
\(255\) −3.44549e8 −0.00510294
\(256\) −6.92111e10 −1.00715
\(257\) 1.08804e11 1.55578 0.777889 0.628402i \(-0.216291\pi\)
0.777889 + 0.628402i \(0.216291\pi\)
\(258\) 5.01025e10 0.703997
\(259\) 1.87425e10 0.258809
\(260\) 1.18728e9 0.0161129
\(261\) 1.72085e10 0.229541
\(262\) −6.46385e10 −0.847492
\(263\) −5.93819e10 −0.765338 −0.382669 0.923886i \(-0.624995\pi\)
−0.382669 + 0.923886i \(0.624995\pi\)
\(264\) 4.29529e10 0.544221
\(265\) 2.20752e8 0.00274979
\(266\) −1.08126e10 −0.132422
\(267\) −6.95896e10 −0.838000
\(268\) −2.82094e10 −0.334032
\(269\) −4.76655e10 −0.555033 −0.277516 0.960721i \(-0.589511\pi\)
−0.277516 + 0.960721i \(0.589511\pi\)
\(270\) −2.51527e8 −0.00288036
\(271\) −9.88434e9 −0.111323 −0.0556616 0.998450i \(-0.517727\pi\)
−0.0556616 + 0.998450i \(0.517727\pi\)
\(272\) −1.63435e10 −0.181045
\(273\) 1.40894e11 1.53519
\(274\) −3.65811e10 −0.392085
\(275\) −8.26410e10 −0.871362
\(276\) 3.12585e10 0.324248
\(277\) −1.03401e11 −1.05527 −0.527637 0.849470i \(-0.676922\pi\)
−0.527637 + 0.849470i \(0.676922\pi\)
\(278\) 4.24088e10 0.425848
\(279\) −4.30580e10 −0.425436
\(280\) −2.98307e9 −0.0290036
\(281\) −1.73580e11 −1.66082 −0.830408 0.557155i \(-0.811893\pi\)
−0.830408 + 0.557155i \(0.811893\pi\)
\(282\) −3.31397e10 −0.312053
\(283\) 1.94147e11 1.79925 0.899624 0.436665i \(-0.143840\pi\)
0.899624 + 0.436665i \(0.143840\pi\)
\(284\) −6.69510e10 −0.610696
\(285\) 1.61204e8 0.00144735
\(286\) −1.46346e11 −1.29341
\(287\) −9.71889e10 −0.845568
\(288\) 3.01527e10 0.258262
\(289\) −9.46210e10 −0.797897
\(290\) 1.24137e9 0.0103065
\(291\) −1.04852e11 −0.857154
\(292\) −5.38695e10 −0.433631
\(293\) 9.53710e10 0.755983 0.377992 0.925809i \(-0.376615\pi\)
0.377992 + 0.925809i \(0.376615\pi\)
\(294\) −4.84844e10 −0.378477
\(295\) 3.32941e8 0.00255958
\(296\) −2.70941e10 −0.205145
\(297\) −2.24951e10 −0.167758
\(298\) −1.52882e11 −1.12301
\(299\) −3.59788e11 −2.60331
\(300\) −3.40457e10 −0.242670
\(301\) −3.11196e11 −2.18517
\(302\) −5.32587e9 −0.0368433
\(303\) −5.94729e10 −0.405347
\(304\) 7.64662e9 0.0513498
\(305\) 4.85521e9 0.0321262
\(306\) 1.74963e10 0.114077
\(307\) −4.48666e10 −0.288270 −0.144135 0.989558i \(-0.546040\pi\)
−0.144135 + 0.989558i \(0.546040\pi\)
\(308\) −7.89728e10 −0.500034
\(309\) 1.20512e11 0.751998
\(310\) −3.10608e9 −0.0191023
\(311\) 1.91873e11 1.16303 0.581516 0.813535i \(-0.302460\pi\)
0.581516 + 0.813535i \(0.302460\pi\)
\(312\) −2.03675e11 −1.21687
\(313\) 2.55978e11 1.50748 0.753742 0.657170i \(-0.228247\pi\)
0.753742 + 0.657170i \(0.228247\pi\)
\(314\) −5.41978e10 −0.314629
\(315\) 1.56228e9 0.00894049
\(316\) −7.55503e10 −0.426230
\(317\) −1.27243e11 −0.707731 −0.353866 0.935296i \(-0.615133\pi\)
−0.353866 + 0.935296i \(0.615133\pi\)
\(318\) −1.12098e10 −0.0614720
\(319\) 1.11021e11 0.600273
\(320\) 3.66028e9 0.0195137
\(321\) −1.48674e11 −0.781561
\(322\) 2.67587e11 1.38712
\(323\) −1.12134e10 −0.0573225
\(324\) −9.26734e9 −0.0467200
\(325\) 3.91870e11 1.94835
\(326\) −1.94978e11 −0.956109
\(327\) −8.09904e10 −0.391714
\(328\) 1.40495e11 0.670239
\(329\) 2.05837e11 0.968595
\(330\) −1.62273e9 −0.00753242
\(331\) 1.12243e11 0.513963 0.256981 0.966416i \(-0.417272\pi\)
0.256981 + 0.966416i \(0.417272\pi\)
\(332\) −7.37437e10 −0.333122
\(333\) 1.41896e10 0.0632369
\(334\) 3.34243e11 1.46961
\(335\) 3.60030e9 0.0156184
\(336\) 7.41060e10 0.317195
\(337\) 2.62199e11 1.10738 0.553690 0.832723i \(-0.313219\pi\)
0.553690 + 0.832723i \(0.313219\pi\)
\(338\) 5.11283e11 2.13077
\(339\) −1.50879e10 −0.0620485
\(340\) −9.15759e8 −0.00371643
\(341\) −2.77790e11 −1.11256
\(342\) −8.18595e9 −0.0323558
\(343\) −4.85666e10 −0.189459
\(344\) 4.49862e11 1.73208
\(345\) −3.98944e9 −0.0151609
\(346\) 2.16000e11 0.810234
\(347\) 1.93522e11 0.716552 0.358276 0.933616i \(-0.383365\pi\)
0.358276 + 0.933616i \(0.383365\pi\)
\(348\) 4.57376e10 0.167173
\(349\) 2.92833e11 1.05659 0.528295 0.849061i \(-0.322832\pi\)
0.528295 + 0.849061i \(0.322832\pi\)
\(350\) −2.91447e11 −1.03814
\(351\) 1.06668e11 0.375105
\(352\) 1.94531e11 0.675379
\(353\) −2.02190e11 −0.693065 −0.346532 0.938038i \(-0.612641\pi\)
−0.346532 + 0.938038i \(0.612641\pi\)
\(354\) −1.69068e10 −0.0572200
\(355\) 8.54480e9 0.0285545
\(356\) −1.84959e11 −0.610309
\(357\) −1.08673e11 −0.354089
\(358\) 5.36625e9 0.0172662
\(359\) −4.49596e11 −1.42856 −0.714279 0.699861i \(-0.753245\pi\)
−0.714279 + 0.699861i \(0.753245\pi\)
\(360\) −2.25842e9 −0.00708668
\(361\) −3.17441e11 −0.983742
\(362\) 1.79062e11 0.548042
\(363\) 4.58655e10 0.138646
\(364\) 3.74475e11 1.11807
\(365\) 6.87523e9 0.0202754
\(366\) −2.46549e11 −0.718188
\(367\) 2.94702e11 0.847979 0.423990 0.905667i \(-0.360629\pi\)
0.423990 + 0.905667i \(0.360629\pi\)
\(368\) −1.89237e11 −0.537888
\(369\) −7.35797e10 −0.206604
\(370\) 1.02360e9 0.00283936
\(371\) 6.96265e10 0.190806
\(372\) −1.14442e11 −0.309842
\(373\) −2.80024e11 −0.749040 −0.374520 0.927219i \(-0.622193\pi\)
−0.374520 + 0.927219i \(0.622193\pi\)
\(374\) 1.12878e11 0.298323
\(375\) 8.69202e9 0.0226976
\(376\) −2.97556e11 −0.767757
\(377\) −5.26445e11 −1.34220
\(378\) −7.93329e10 −0.199867
\(379\) −6.78144e10 −0.168829 −0.0844143 0.996431i \(-0.526902\pi\)
−0.0844143 + 0.996431i \(0.526902\pi\)
\(380\) 4.28455e8 0.00105409
\(381\) 2.74781e11 0.668074
\(382\) −6.51858e10 −0.156627
\(383\) 7.06249e11 1.67712 0.838559 0.544811i \(-0.183399\pi\)
0.838559 + 0.544811i \(0.183399\pi\)
\(384\) 4.72519e9 0.0110899
\(385\) 1.00791e10 0.0233802
\(386\) 1.62166e11 0.371806
\(387\) −2.35600e11 −0.533920
\(388\) −2.78681e11 −0.624259
\(389\) 1.18632e11 0.262681 0.131340 0.991337i \(-0.458072\pi\)
0.131340 + 0.991337i \(0.458072\pi\)
\(390\) 7.69473e9 0.0168423
\(391\) 2.77507e11 0.600452
\(392\) −4.35334e11 −0.931183
\(393\) 3.03954e11 0.642748
\(394\) 1.33592e11 0.279286
\(395\) 9.64230e9 0.0199294
\(396\) −5.97886e10 −0.122177
\(397\) −7.04778e11 −1.42395 −0.711976 0.702204i \(-0.752199\pi\)
−0.711976 + 0.702204i \(0.752199\pi\)
\(398\) 4.02177e11 0.803421
\(399\) 5.08445e10 0.100431
\(400\) 2.06111e11 0.402561
\(401\) 6.83839e11 1.32070 0.660350 0.750958i \(-0.270408\pi\)
0.660350 + 0.750958i \(0.270408\pi\)
\(402\) −1.82824e11 −0.349153
\(403\) 1.31723e12 2.48766
\(404\) −1.58070e11 −0.295212
\(405\) 1.18277e9 0.00218450
\(406\) 3.91536e11 0.715162
\(407\) 9.15447e10 0.165371
\(408\) 1.57096e11 0.280669
\(409\) −3.58211e11 −0.632971 −0.316485 0.948597i \(-0.602503\pi\)
−0.316485 + 0.948597i \(0.602503\pi\)
\(410\) −5.30783e9 −0.00927662
\(411\) 1.72018e11 0.297362
\(412\) 3.20302e11 0.547674
\(413\) 1.05012e11 0.177608
\(414\) 2.02585e11 0.338926
\(415\) 9.41173e9 0.0155759
\(416\) −9.22434e11 −1.51013
\(417\) −1.99422e11 −0.322968
\(418\) −5.28120e10 −0.0846135
\(419\) 2.98661e11 0.473385 0.236693 0.971585i \(-0.423937\pi\)
0.236693 + 0.971585i \(0.423937\pi\)
\(420\) 4.15230e9 0.00651129
\(421\) 1.19703e12 1.85710 0.928549 0.371209i \(-0.121057\pi\)
0.928549 + 0.371209i \(0.121057\pi\)
\(422\) −2.16058e11 −0.331639
\(423\) 1.55835e11 0.236665
\(424\) −1.00651e11 −0.151242
\(425\) −3.02251e11 −0.449384
\(426\) −4.33907e11 −0.638342
\(427\) 1.53136e12 2.22921
\(428\) −3.95153e11 −0.569205
\(429\) 6.88173e11 0.980935
\(430\) −1.69955e10 −0.0239732
\(431\) 4.88311e11 0.681630 0.340815 0.940130i \(-0.389297\pi\)
0.340815 + 0.940130i \(0.389297\pi\)
\(432\) 5.61041e10 0.0775029
\(433\) 3.36258e11 0.459703 0.229851 0.973226i \(-0.426176\pi\)
0.229851 + 0.973226i \(0.426176\pi\)
\(434\) −9.79674e11 −1.32549
\(435\) −5.83738e9 −0.00781658
\(436\) −2.15260e11 −0.285282
\(437\) −1.29837e11 −0.170306
\(438\) −3.49126e11 −0.453261
\(439\) 1.51937e11 0.195243 0.0976213 0.995224i \(-0.468877\pi\)
0.0976213 + 0.995224i \(0.468877\pi\)
\(440\) −1.45703e10 −0.0185324
\(441\) 2.27991e11 0.287041
\(442\) −5.35247e11 −0.667044
\(443\) −1.98945e11 −0.245423 −0.122712 0.992442i \(-0.539159\pi\)
−0.122712 + 0.992442i \(0.539159\pi\)
\(444\) 3.77138e10 0.0460550
\(445\) 2.36058e10 0.0285364
\(446\) −8.25837e11 −0.988297
\(447\) 7.18908e11 0.851705
\(448\) 1.15447e12 1.35404
\(449\) 5.76477e11 0.669382 0.334691 0.942328i \(-0.391368\pi\)
0.334691 + 0.942328i \(0.391368\pi\)
\(450\) −2.20649e11 −0.253656
\(451\) −4.74702e11 −0.540290
\(452\) −4.01014e10 −0.0451894
\(453\) 2.50441e10 0.0279424
\(454\) 8.18404e11 0.904100
\(455\) −4.77934e10 −0.0522777
\(456\) −7.35003e10 −0.0796063
\(457\) −8.72269e10 −0.0935465 −0.0467732 0.998906i \(-0.514894\pi\)
−0.0467732 + 0.998906i \(0.514894\pi\)
\(458\) 4.37585e11 0.464695
\(459\) −8.22737e10 −0.0865175
\(460\) −1.06033e10 −0.0110416
\(461\) 5.48921e11 0.566052 0.283026 0.959112i \(-0.408662\pi\)
0.283026 + 0.959112i \(0.408662\pi\)
\(462\) −5.11819e11 −0.522670
\(463\) 1.79739e12 1.81773 0.908863 0.417095i \(-0.136952\pi\)
0.908863 + 0.417095i \(0.136952\pi\)
\(464\) −2.76894e11 −0.277321
\(465\) 1.46059e10 0.0144874
\(466\) 7.24380e11 0.711590
\(467\) −1.58907e12 −1.54603 −0.773013 0.634391i \(-0.781251\pi\)
−0.773013 + 0.634391i \(0.781251\pi\)
\(468\) 2.83508e11 0.273186
\(469\) 1.13555e12 1.08375
\(470\) 1.12415e10 0.0106263
\(471\) 2.54858e11 0.238618
\(472\) −1.51804e11 −0.140781
\(473\) −1.51998e12 −1.39625
\(474\) −4.89638e11 −0.445526
\(475\) 1.41414e11 0.127459
\(476\) −2.88835e11 −0.257881
\(477\) 5.27127e10 0.0466211
\(478\) −1.54805e12 −1.35631
\(479\) 4.96331e11 0.430786 0.215393 0.976527i \(-0.430897\pi\)
0.215393 + 0.976527i \(0.430897\pi\)
\(480\) −1.02282e10 −0.00879458
\(481\) −4.34089e11 −0.369765
\(482\) 4.69975e11 0.396609
\(483\) −1.25829e12 −1.05201
\(484\) 1.21904e11 0.100975
\(485\) 3.55674e10 0.0291887
\(486\) −6.00612e10 −0.0488350
\(487\) −3.90751e10 −0.0314789 −0.0157394 0.999876i \(-0.505010\pi\)
−0.0157394 + 0.999876i \(0.505010\pi\)
\(488\) −2.21372e12 −1.76699
\(489\) 9.16859e11 0.725124
\(490\) 1.64466e10 0.0128883
\(491\) 8.90650e11 0.691576 0.345788 0.938313i \(-0.387612\pi\)
0.345788 + 0.938313i \(0.387612\pi\)
\(492\) −1.95564e11 −0.150468
\(493\) 4.06050e11 0.309577
\(494\) 2.50426e11 0.189194
\(495\) 7.63068e9 0.00571268
\(496\) 6.92824e11 0.513991
\(497\) 2.69508e12 1.98138
\(498\) −4.77930e11 −0.348203
\(499\) −1.41461e12 −1.02137 −0.510687 0.859767i \(-0.670609\pi\)
−0.510687 + 0.859767i \(0.670609\pi\)
\(500\) 2.31021e10 0.0165305
\(501\) −1.57173e12 −1.11457
\(502\) −4.89928e11 −0.344323
\(503\) −1.87741e12 −1.30768 −0.653842 0.756631i \(-0.726844\pi\)
−0.653842 + 0.756631i \(0.726844\pi\)
\(504\) −7.12317e11 −0.491740
\(505\) 2.01741e10 0.0138033
\(506\) 1.30698e12 0.886324
\(507\) −2.40424e12 −1.61600
\(508\) 7.30326e11 0.486553
\(509\) −2.71545e12 −1.79313 −0.896564 0.442914i \(-0.853945\pi\)
−0.896564 + 0.442914i \(0.853945\pi\)
\(510\) −5.93499e9 −0.00388467
\(511\) 2.16848e12 1.40690
\(512\) −1.16232e12 −0.747500
\(513\) 3.84933e10 0.0245390
\(514\) 1.87420e12 1.18435
\(515\) −4.08794e10 −0.0256078
\(516\) −6.26189e11 −0.388850
\(517\) 1.00538e12 0.618900
\(518\) 3.22848e11 0.197022
\(519\) −1.01571e12 −0.614491
\(520\) 6.90897e10 0.0414380
\(521\) 8.14744e11 0.484453 0.242226 0.970220i \(-0.422122\pi\)
0.242226 + 0.970220i \(0.422122\pi\)
\(522\) 2.96424e11 0.174741
\(523\) −1.99159e12 −1.16397 −0.581987 0.813198i \(-0.697724\pi\)
−0.581987 + 0.813198i \(0.697724\pi\)
\(524\) 8.07862e11 0.468109
\(525\) 1.37049e12 0.787334
\(526\) −1.02288e12 −0.582623
\(527\) −1.01599e12 −0.573775
\(528\) 3.61958e11 0.202677
\(529\) 1.41202e12 0.783956
\(530\) 3.80255e9 0.00209331
\(531\) 7.95020e10 0.0433963
\(532\) 1.35137e11 0.0731428
\(533\) 2.25096e12 1.20808
\(534\) −1.19871e12 −0.637937
\(535\) 5.04324e10 0.0266145
\(536\) −1.64155e12 −0.859037
\(537\) −2.52340e10 −0.0130949
\(538\) −8.21056e11 −0.422525
\(539\) 1.47089e12 0.750641
\(540\) 3.14362e9 0.00159096
\(541\) −2.12747e12 −1.06776 −0.533882 0.845559i \(-0.679267\pi\)
−0.533882 + 0.845559i \(0.679267\pi\)
\(542\) −1.70262e11 −0.0847462
\(543\) −8.42013e11 −0.415642
\(544\) 7.11479e11 0.348311
\(545\) 2.74731e10 0.0133390
\(546\) 2.42696e12 1.16868
\(547\) −2.87537e12 −1.37325 −0.686627 0.727010i \(-0.740910\pi\)
−0.686627 + 0.727010i \(0.740910\pi\)
\(548\) 4.57197e11 0.216566
\(549\) 1.15936e12 0.544682
\(550\) −1.42352e12 −0.663335
\(551\) −1.89978e11 −0.0878054
\(552\) 1.81897e12 0.833875
\(553\) 3.04123e12 1.38289
\(554\) −1.78112e12 −0.803341
\(555\) −4.81332e9 −0.00215341
\(556\) −5.30032e11 −0.235215
\(557\) −2.82464e12 −1.24341 −0.621706 0.783251i \(-0.713560\pi\)
−0.621706 + 0.783251i \(0.713560\pi\)
\(558\) −7.41691e11 −0.323869
\(559\) 7.20750e12 3.12199
\(560\) −2.51379e10 −0.0108015
\(561\) −5.30792e11 −0.226252
\(562\) −2.98999e12 −1.26432
\(563\) 4.36111e11 0.182940 0.0914702 0.995808i \(-0.470843\pi\)
0.0914702 + 0.995808i \(0.470843\pi\)
\(564\) 4.14186e11 0.172361
\(565\) 5.11805e9 0.00211294
\(566\) 3.34426e12 1.36970
\(567\) 3.73052e11 0.151581
\(568\) −3.89598e12 −1.57054
\(569\) 1.82046e12 0.728074 0.364037 0.931385i \(-0.381398\pi\)
0.364037 + 0.931385i \(0.381398\pi\)
\(570\) 2.77680e9 0.00110181
\(571\) −1.82132e12 −0.717009 −0.358505 0.933528i \(-0.616713\pi\)
−0.358505 + 0.933528i \(0.616713\pi\)
\(572\) 1.82906e12 0.714407
\(573\) 3.06527e11 0.118788
\(574\) −1.67412e12 −0.643699
\(575\) −3.49969e12 −1.33513
\(576\) 8.74025e11 0.330844
\(577\) −1.30800e12 −0.491266 −0.245633 0.969363i \(-0.578996\pi\)
−0.245633 + 0.969363i \(0.578996\pi\)
\(578\) −1.62988e12 −0.607409
\(579\) −7.62562e11 −0.281982
\(580\) −1.55149e10 −0.00569275
\(581\) 2.96851e12 1.08080
\(582\) −1.80612e12 −0.652519
\(583\) 3.40078e11 0.121919
\(584\) −3.13474e12 −1.11518
\(585\) −3.61834e10 −0.0127734
\(586\) 1.64280e12 0.575501
\(587\) −3.56619e12 −1.23975 −0.619873 0.784702i \(-0.712816\pi\)
−0.619873 + 0.784702i \(0.712816\pi\)
\(588\) 6.05966e11 0.209050
\(589\) 4.75350e11 0.162740
\(590\) 5.73505e9 0.00194851
\(591\) −6.28199e11 −0.211814
\(592\) −2.28318e11 −0.0763997
\(593\) −1.29385e12 −0.429673 −0.214837 0.976650i \(-0.568922\pi\)
−0.214837 + 0.976650i \(0.568922\pi\)
\(594\) −3.87488e11 −0.127708
\(595\) 3.68633e10 0.0120578
\(596\) 1.91075e12 0.620291
\(597\) −1.89118e12 −0.609324
\(598\) −6.19749e12 −1.98180
\(599\) 5.93442e12 1.88347 0.941733 0.336361i \(-0.109196\pi\)
0.941733 + 0.336361i \(0.109196\pi\)
\(600\) −1.98117e12 −0.624081
\(601\) −2.75644e12 −0.861812 −0.430906 0.902397i \(-0.641806\pi\)
−0.430906 + 0.902397i \(0.641806\pi\)
\(602\) −5.36048e12 −1.66349
\(603\) 8.59705e11 0.264802
\(604\) 6.65635e10 0.0203503
\(605\) −1.55583e10 −0.00472130
\(606\) −1.02444e12 −0.308576
\(607\) −1.28829e12 −0.385180 −0.192590 0.981279i \(-0.561689\pi\)
−0.192590 + 0.981279i \(0.561689\pi\)
\(608\) −3.32879e11 −0.0987916
\(609\) −1.84114e12 −0.542387
\(610\) 8.36330e10 0.0244564
\(611\) −4.76732e12 −1.38385
\(612\) −2.18671e11 −0.0630101
\(613\) −4.32866e12 −1.23817 −0.619086 0.785323i \(-0.712497\pi\)
−0.619086 + 0.785323i \(0.712497\pi\)
\(614\) −7.72844e11 −0.219449
\(615\) 2.49593e10 0.00703550
\(616\) −4.59554e12 −1.28595
\(617\) 1.32521e12 0.368131 0.184066 0.982914i \(-0.441074\pi\)
0.184066 + 0.982914i \(0.441074\pi\)
\(618\) 2.07586e12 0.572467
\(619\) 3.57099e12 0.977645 0.488823 0.872383i \(-0.337427\pi\)
0.488823 + 0.872383i \(0.337427\pi\)
\(620\) 3.88203e10 0.0105511
\(621\) −9.52626e11 −0.257046
\(622\) 3.30509e12 0.885372
\(623\) 7.44540e12 1.98012
\(624\) −1.71634e12 −0.453183
\(625\) 3.81027e12 0.998841
\(626\) 4.40932e12 1.14759
\(627\) 2.48341e11 0.0641719
\(628\) 6.77373e11 0.173784
\(629\) 3.34816e11 0.0852860
\(630\) 2.69109e10 0.00680605
\(631\) 4.33954e12 1.08971 0.544856 0.838530i \(-0.316584\pi\)
0.544856 + 0.838530i \(0.316584\pi\)
\(632\) −4.39638e12 −1.09615
\(633\) 1.01598e12 0.251519
\(634\) −2.19182e12 −0.538769
\(635\) −9.32098e10 −0.0227499
\(636\) 1.40102e11 0.0339538
\(637\) −6.97473e12 −1.67842
\(638\) 1.91239e12 0.456965
\(639\) 2.04039e12 0.484126
\(640\) −1.60285e9 −0.000377645 0
\(641\) −3.93432e11 −0.0920467 −0.0460233 0.998940i \(-0.514655\pi\)
−0.0460233 + 0.998940i \(0.514655\pi\)
\(642\) −2.56097e12 −0.594972
\(643\) 2.11944e12 0.488958 0.244479 0.969655i \(-0.421383\pi\)
0.244479 + 0.969655i \(0.421383\pi\)
\(644\) −3.34435e12 −0.766170
\(645\) 7.99190e10 0.0181816
\(646\) −1.93155e11 −0.0436374
\(647\) 3.53345e12 0.792739 0.396370 0.918091i \(-0.370270\pi\)
0.396370 + 0.918091i \(0.370270\pi\)
\(648\) −5.39280e11 −0.120151
\(649\) 5.12910e11 0.113486
\(650\) 6.75011e12 1.48320
\(651\) 4.60678e12 1.00527
\(652\) 2.43687e12 0.528103
\(653\) −4.17496e12 −0.898551 −0.449275 0.893393i \(-0.648318\pi\)
−0.449275 + 0.893393i \(0.648318\pi\)
\(654\) −1.39509e12 −0.298197
\(655\) −1.03106e11 −0.0218875
\(656\) 1.18393e12 0.249609
\(657\) 1.64171e12 0.343758
\(658\) 3.54563e12 0.737355
\(659\) 7.07218e11 0.146073 0.0730363 0.997329i \(-0.476731\pi\)
0.0730363 + 0.997329i \(0.476731\pi\)
\(660\) 2.02812e10 0.00416050
\(661\) −4.72588e12 −0.962889 −0.481444 0.876477i \(-0.659888\pi\)
−0.481444 + 0.876477i \(0.659888\pi\)
\(662\) 1.93342e12 0.391260
\(663\) 2.51693e12 0.505894
\(664\) −4.29125e12 −0.856698
\(665\) −1.72472e10 −0.00341996
\(666\) 2.44421e11 0.0481399
\(667\) 4.70155e12 0.919760
\(668\) −4.17742e12 −0.811735
\(669\) 3.88338e12 0.749536
\(670\) 6.20167e10 0.0118897
\(671\) 7.47966e12 1.42440
\(672\) −3.22604e12 −0.610250
\(673\) 3.81623e11 0.0717078 0.0358539 0.999357i \(-0.488585\pi\)
0.0358539 + 0.999357i \(0.488585\pi\)
\(674\) 4.51648e12 0.843007
\(675\) 1.03757e12 0.192376
\(676\) −6.39009e12 −1.17692
\(677\) 6.27405e12 1.14789 0.573943 0.818895i \(-0.305413\pi\)
0.573943 + 0.818895i \(0.305413\pi\)
\(678\) −2.59896e11 −0.0472351
\(679\) 1.12181e13 2.02538
\(680\) −5.32893e10 −0.00955763
\(681\) −3.84843e12 −0.685680
\(682\) −4.78505e12 −0.846948
\(683\) 4.49896e11 0.0791078 0.0395539 0.999217i \(-0.487406\pi\)
0.0395539 + 0.999217i \(0.487406\pi\)
\(684\) 1.02309e11 0.0178716
\(685\) −5.83509e10 −0.0101261
\(686\) −8.36580e11 −0.144228
\(687\) −2.05768e12 −0.352430
\(688\) 3.79092e12 0.645056
\(689\) −1.61259e12 −0.272608
\(690\) −6.87197e10 −0.0115415
\(691\) −4.47844e12 −0.747266 −0.373633 0.927577i \(-0.621888\pi\)
−0.373633 + 0.927577i \(0.621888\pi\)
\(692\) −2.69960e12 −0.447529
\(693\) 2.40676e12 0.396399
\(694\) 3.33349e12 0.545484
\(695\) 6.76467e10 0.0109980
\(696\) 2.66154e12 0.429923
\(697\) −1.73618e12 −0.278642
\(698\) 5.04417e12 0.804342
\(699\) −3.40630e12 −0.539678
\(700\) 3.64256e12 0.573410
\(701\) −8.09287e12 −1.26582 −0.632909 0.774226i \(-0.718139\pi\)
−0.632909 + 0.774226i \(0.718139\pi\)
\(702\) 1.83740e12 0.285553
\(703\) −1.56650e11 −0.0241897
\(704\) 5.63881e12 0.865188
\(705\) −5.28615e10 −0.00805914
\(706\) −3.48281e12 −0.527604
\(707\) 6.36302e12 0.957802
\(708\) 2.11304e11 0.0316052
\(709\) −4.40528e12 −0.654735 −0.327368 0.944897i \(-0.606162\pi\)
−0.327368 + 0.944897i \(0.606162\pi\)
\(710\) 1.47188e11 0.0217375
\(711\) 2.30245e12 0.337892
\(712\) −1.07630e13 −1.56955
\(713\) −1.17639e13 −1.70470
\(714\) −1.87193e12 −0.269555
\(715\) −2.33439e11 −0.0334038
\(716\) −6.70682e10 −0.00953691
\(717\) 7.27947e12 1.02864
\(718\) −7.74447e12 −1.08751
\(719\) −8.91334e12 −1.24383 −0.621914 0.783085i \(-0.713645\pi\)
−0.621914 + 0.783085i \(0.713645\pi\)
\(720\) −1.90313e10 −0.00263921
\(721\) −1.28936e13 −1.77691
\(722\) −5.46805e12 −0.748885
\(723\) −2.20999e12 −0.300793
\(724\) −2.23794e12 −0.302709
\(725\) −5.12077e12 −0.688358
\(726\) 7.90052e11 0.105546
\(727\) 1.39275e13 1.84913 0.924565 0.381023i \(-0.124428\pi\)
0.924565 + 0.381023i \(0.124428\pi\)
\(728\) 2.17913e13 2.87535
\(729\) 2.82430e11 0.0370370
\(730\) 1.18429e11 0.0154349
\(731\) −5.55919e12 −0.720084
\(732\) 3.08140e12 0.396688
\(733\) 1.08129e12 0.138349 0.0691744 0.997605i \(-0.477964\pi\)
0.0691744 + 0.997605i \(0.477964\pi\)
\(734\) 5.07635e12 0.645535
\(735\) −7.73380e10 −0.00977462
\(736\) 8.23803e12 1.03484
\(737\) 5.54642e12 0.692483
\(738\) −1.26744e12 −0.157280
\(739\) −3.69678e11 −0.0455956 −0.0227978 0.999740i \(-0.507257\pi\)
−0.0227978 + 0.999740i \(0.507257\pi\)
\(740\) −1.27931e10 −0.00156831
\(741\) −1.17759e12 −0.143487
\(742\) 1.19934e12 0.145253
\(743\) 1.56143e12 0.187963 0.0939816 0.995574i \(-0.470041\pi\)
0.0939816 + 0.995574i \(0.470041\pi\)
\(744\) −6.65952e12 −0.796828
\(745\) −2.43864e11 −0.0290031
\(746\) −4.82352e12 −0.570216
\(747\) 2.24740e12 0.264081
\(748\) −1.41077e12 −0.164777
\(749\) 1.59067e13 1.84676
\(750\) 1.49724e11 0.0172788
\(751\) −1.21763e12 −0.139680 −0.0698402 0.997558i \(-0.522249\pi\)
−0.0698402 + 0.997558i \(0.522249\pi\)
\(752\) −2.50746e12 −0.285926
\(753\) 2.30382e12 0.261139
\(754\) −9.06822e12 −1.02176
\(755\) −8.49534e9 −0.000951524 0
\(756\) 9.91515e11 0.110395
\(757\) −1.39602e12 −0.154511 −0.0772556 0.997011i \(-0.524616\pi\)
−0.0772556 + 0.997011i \(0.524616\pi\)
\(758\) −1.16813e12 −0.128523
\(759\) −6.14590e12 −0.672199
\(760\) 2.49324e10 0.00271083
\(761\) 2.93526e11 0.0317260 0.0158630 0.999874i \(-0.494950\pi\)
0.0158630 + 0.999874i \(0.494950\pi\)
\(762\) 4.73321e12 0.508579
\(763\) 8.66518e12 0.925587
\(764\) 8.14703e11 0.0865125
\(765\) 2.79085e10 0.00294618
\(766\) 1.21654e13 1.27673
\(767\) −2.43213e12 −0.253751
\(768\) 5.60610e12 0.581480
\(769\) 7.49150e12 0.772503 0.386251 0.922394i \(-0.373770\pi\)
0.386251 + 0.922394i \(0.373770\pi\)
\(770\) 1.73617e11 0.0177985
\(771\) −8.81316e12 −0.898229
\(772\) −2.02677e12 −0.205366
\(773\) −1.21725e12 −0.122623 −0.0613117 0.998119i \(-0.519528\pi\)
−0.0613117 + 0.998119i \(0.519528\pi\)
\(774\) −4.05831e12 −0.406453
\(775\) 1.28129e13 1.27582
\(776\) −1.62169e13 −1.60542
\(777\) −1.51815e12 −0.149424
\(778\) 2.04348e12 0.199969
\(779\) 8.12303e11 0.0790314
\(780\) −9.61699e10 −0.00930280
\(781\) 1.31636e13 1.26604
\(782\) 4.78016e12 0.457101
\(783\) −1.39389e12 −0.132526
\(784\) −3.66849e12 −0.346789
\(785\) −8.64514e10 −0.00812566
\(786\) 5.23572e12 0.489300
\(787\) −5.80375e12 −0.539290 −0.269645 0.962960i \(-0.586906\pi\)
−0.269645 + 0.962960i \(0.586906\pi\)
\(788\) −1.66966e12 −0.154262
\(789\) 4.80993e12 0.441868
\(790\) 1.66092e11 0.0151715
\(791\) 1.61426e12 0.146615
\(792\) −3.47919e12 −0.314206
\(793\) −3.54673e13 −3.18492
\(794\) −1.21401e13 −1.08400
\(795\) −1.78809e10 −0.00158759
\(796\) −5.02647e12 −0.443766
\(797\) −1.83092e13 −1.60734 −0.803669 0.595076i \(-0.797122\pi\)
−0.803669 + 0.595076i \(0.797122\pi\)
\(798\) 8.75817e11 0.0764540
\(799\) 3.67706e12 0.319183
\(800\) −8.97259e12 −0.774485
\(801\) 5.63676e12 0.483819
\(802\) 1.17794e13 1.00540
\(803\) 1.05916e13 0.898961
\(804\) 2.28496e12 0.192853
\(805\) 4.26831e11 0.0358240
\(806\) 2.26899e13 1.89376
\(807\) 3.86090e12 0.320448
\(808\) −9.19832e12 −0.759202
\(809\) 2.07773e12 0.170538 0.0852688 0.996358i \(-0.472825\pi\)
0.0852688 + 0.996358i \(0.472825\pi\)
\(810\) 2.03737e10 0.00166298
\(811\) 1.77755e13 1.44287 0.721437 0.692481i \(-0.243482\pi\)
0.721437 + 0.692481i \(0.243482\pi\)
\(812\) −4.89348e12 −0.395017
\(813\) 8.00632e11 0.0642725
\(814\) 1.57689e12 0.125890
\(815\) −3.11012e11 −0.0246927
\(816\) 1.32383e12 0.104526
\(817\) 2.60097e12 0.204238
\(818\) −6.17032e12 −0.481857
\(819\) −1.14124e13 −0.886341
\(820\) 6.63381e10 0.00512390
\(821\) −3.14471e12 −0.241566 −0.120783 0.992679i \(-0.538541\pi\)
−0.120783 + 0.992679i \(0.538541\pi\)
\(822\) 2.96307e12 0.226370
\(823\) −1.07039e13 −0.813286 −0.406643 0.913587i \(-0.633301\pi\)
−0.406643 + 0.913587i \(0.633301\pi\)
\(824\) 1.86388e13 1.40847
\(825\) 6.69392e12 0.503081
\(826\) 1.80886e12 0.135206
\(827\) 1.96147e13 1.45817 0.729083 0.684425i \(-0.239947\pi\)
0.729083 + 0.684425i \(0.239947\pi\)
\(828\) −2.53194e12 −0.187204
\(829\) 2.11168e13 1.55286 0.776431 0.630202i \(-0.217028\pi\)
0.776431 + 0.630202i \(0.217028\pi\)
\(830\) 1.62121e11 0.0118573
\(831\) 8.37548e12 0.609263
\(832\) −2.67383e13 −1.93454
\(833\) 5.37965e12 0.387125
\(834\) −3.43512e12 −0.245864
\(835\) 5.33154e11 0.0379545
\(836\) 6.60053e11 0.0467359
\(837\) 3.48770e12 0.245626
\(838\) 5.14455e12 0.360370
\(839\) 2.06022e13 1.43544 0.717718 0.696334i \(-0.245187\pi\)
0.717718 + 0.696334i \(0.245187\pi\)
\(840\) 2.41628e11 0.0167452
\(841\) −7.62780e12 −0.525796
\(842\) 2.06193e13 1.41374
\(843\) 1.40600e13 0.958873
\(844\) 2.70033e12 0.183179
\(845\) 8.15552e11 0.0550296
\(846\) 2.68432e12 0.180164
\(847\) −4.90716e12 −0.327608
\(848\) −8.48174e11 −0.0563253
\(849\) −1.57259e13 −1.03880
\(850\) −5.20640e12 −0.342099
\(851\) 3.87674e12 0.253387
\(852\) 5.42303e12 0.352585
\(853\) 1.13087e13 0.731375 0.365688 0.930738i \(-0.380834\pi\)
0.365688 + 0.930738i \(0.380834\pi\)
\(854\) 2.63783e13 1.69702
\(855\) −1.30575e10 −0.000835627 0
\(856\) −2.29945e13 −1.46384
\(857\) −1.77296e13 −1.12276 −0.561378 0.827560i \(-0.689729\pi\)
−0.561378 + 0.827560i \(0.689729\pi\)
\(858\) 1.18541e13 0.746748
\(859\) −2.03010e13 −1.27218 −0.636089 0.771616i \(-0.719449\pi\)
−0.636089 + 0.771616i \(0.719449\pi\)
\(860\) 2.12413e11 0.0132415
\(861\) 7.87230e12 0.488189
\(862\) 8.41135e12 0.518899
\(863\) 6.31451e12 0.387517 0.193759 0.981049i \(-0.437932\pi\)
0.193759 + 0.981049i \(0.437932\pi\)
\(864\) −2.44237e12 −0.149107
\(865\) 3.44543e11 0.0209253
\(866\) 5.79218e12 0.349954
\(867\) 7.66430e12 0.460666
\(868\) 1.22441e13 0.732131
\(869\) 1.48544e13 0.883620
\(870\) −1.00551e11 −0.00595046
\(871\) −2.63002e13 −1.54838
\(872\) −1.25263e13 −0.733667
\(873\) 8.49303e12 0.494878
\(874\) −2.23649e12 −0.129648
\(875\) −9.29961e11 −0.0536326
\(876\) 4.36343e12 0.250357
\(877\) 8.63725e12 0.493035 0.246517 0.969138i \(-0.420714\pi\)
0.246517 + 0.969138i \(0.420714\pi\)
\(878\) 2.61718e12 0.148631
\(879\) −7.72505e12 −0.436467
\(880\) −1.22781e11 −0.00690178
\(881\) −5.05552e12 −0.282731 −0.141366 0.989957i \(-0.545149\pi\)
−0.141366 + 0.989957i \(0.545149\pi\)
\(882\) 3.92724e12 0.218514
\(883\) −1.22521e13 −0.678244 −0.339122 0.940742i \(-0.610130\pi\)
−0.339122 + 0.940742i \(0.610130\pi\)
\(884\) 6.68961e12 0.368439
\(885\) −2.69683e10 −0.00147777
\(886\) −3.42690e12 −0.186832
\(887\) −1.96690e13 −1.06691 −0.533454 0.845829i \(-0.679106\pi\)
−0.533454 + 0.845829i \(0.679106\pi\)
\(888\) 2.19462e12 0.118441
\(889\) −2.93989e13 −1.57860
\(890\) 4.06620e11 0.0217237
\(891\) 1.82211e12 0.0968554
\(892\) 1.03214e13 0.545882
\(893\) −1.72038e12 −0.0905302
\(894\) 1.23835e13 0.648371
\(895\) 8.55975e9 0.000445920 0
\(896\) −5.05549e11 −0.0262046
\(897\) 2.91428e13 1.50302
\(898\) 9.93005e12 0.509575
\(899\) −1.72130e13 −0.878898
\(900\) 2.75770e12 0.140106
\(901\) 1.24380e12 0.0628767
\(902\) −8.17694e12 −0.411302
\(903\) 2.52069e13 1.26161
\(904\) −2.33356e12 −0.116215
\(905\) 2.85623e11 0.0141539
\(906\) 4.31395e11 0.0212715
\(907\) −8.46134e11 −0.0415151 −0.0207576 0.999785i \(-0.506608\pi\)
−0.0207576 + 0.999785i \(0.506608\pi\)
\(908\) −1.02285e13 −0.499376
\(909\) 4.81731e12 0.234027
\(910\) −8.23260e11 −0.0397971
\(911\) 3.21048e12 0.154432 0.0772159 0.997014i \(-0.475397\pi\)
0.0772159 + 0.997014i \(0.475397\pi\)
\(912\) −6.19376e11 −0.0296468
\(913\) 1.44992e13 0.690597
\(914\) −1.50252e12 −0.0712134
\(915\) −3.93272e11 −0.0185481
\(916\) −5.46901e12 −0.256672
\(917\) −3.25200e13 −1.51876
\(918\) −1.41720e12 −0.0658625
\(919\) −1.14327e13 −0.528726 −0.264363 0.964423i \(-0.585162\pi\)
−0.264363 + 0.964423i \(0.585162\pi\)
\(920\) −6.17023e11 −0.0283959
\(921\) 3.63419e12 0.166433
\(922\) 9.45539e12 0.430914
\(923\) −6.24197e13 −2.83083
\(924\) 6.39680e12 0.288695
\(925\) −4.22242e12 −0.189637
\(926\) 3.09608e13 1.38377
\(927\) −9.76146e12 −0.434166
\(928\) 1.20539e13 0.533536
\(929\) −3.21191e13 −1.41479 −0.707396 0.706818i \(-0.750130\pi\)
−0.707396 + 0.706818i \(0.750130\pi\)
\(930\) 2.51592e11 0.0110287
\(931\) −2.51697e12 −0.109801
\(932\) −9.05342e12 −0.393044
\(933\) −1.55417e13 −0.671477
\(934\) −2.73723e13 −1.17693
\(935\) 1.80053e11 0.00770455
\(936\) 1.64977e13 0.702558
\(937\) 3.84448e13 1.62933 0.814665 0.579931i \(-0.196921\pi\)
0.814665 + 0.579931i \(0.196921\pi\)
\(938\) 1.95604e13 0.825020
\(939\) −2.07342e13 −0.870347
\(940\) −1.40498e11 −0.00586941
\(941\) 3.06768e13 1.27543 0.637715 0.770273i \(-0.279880\pi\)
0.637715 + 0.770273i \(0.279880\pi\)
\(942\) 4.39002e12 0.181651
\(943\) −2.01027e13 −0.827852
\(944\) −1.27923e12 −0.0524293
\(945\) −1.26545e11 −0.00516179
\(946\) −2.61823e13 −1.06291
\(947\) −2.27641e13 −0.919761 −0.459881 0.887981i \(-0.652108\pi\)
−0.459881 + 0.887981i \(0.652108\pi\)
\(948\) 6.11957e12 0.246084
\(949\) −5.02235e13 −2.01006
\(950\) 2.43591e12 0.0970298
\(951\) 1.03067e13 0.408609
\(952\) −1.68077e13 −0.663198
\(953\) 4.09179e13 1.60692 0.803462 0.595356i \(-0.202989\pi\)
0.803462 + 0.595356i \(0.202989\pi\)
\(954\) 9.07998e11 0.0354909
\(955\) −1.03979e11 −0.00404509
\(956\) 1.93477e13 0.749151
\(957\) −8.99274e12 −0.346568
\(958\) 8.54950e12 0.327941
\(959\) −1.84042e13 −0.702641
\(960\) −2.96482e11 −0.0112662
\(961\) 1.66296e13 0.628966
\(962\) −7.47736e12 −0.281488
\(963\) 1.20426e13 0.451234
\(964\) −5.87382e12 −0.219065
\(965\) 2.58672e11 0.00960234
\(966\) −2.16746e13 −0.800854
\(967\) 4.36312e13 1.60464 0.802320 0.596894i \(-0.203599\pi\)
0.802320 + 0.596894i \(0.203599\pi\)
\(968\) 7.09374e12 0.259679
\(969\) 9.08283e11 0.0330951
\(970\) 6.12663e11 0.0222202
\(971\) 3.13294e13 1.13101 0.565503 0.824746i \(-0.308682\pi\)
0.565503 + 0.824746i \(0.308682\pi\)
\(972\) 7.50655e11 0.0269738
\(973\) 2.13361e13 0.763147
\(974\) −6.73084e11 −0.0239637
\(975\) −3.17414e13 −1.12488
\(976\) −1.86547e13 −0.658058
\(977\) −1.36750e13 −0.480178 −0.240089 0.970751i \(-0.577177\pi\)
−0.240089 + 0.970751i \(0.577177\pi\)
\(978\) 1.57933e13 0.552010
\(979\) 3.63658e13 1.26523
\(980\) −2.05553e11 −0.00711878
\(981\) 6.56022e12 0.226156
\(982\) 1.53418e13 0.526471
\(983\) −3.93740e13 −1.34499 −0.672494 0.740103i \(-0.734777\pi\)
−0.672494 + 0.740103i \(0.734777\pi\)
\(984\) −1.13801e13 −0.386963
\(985\) 2.13095e11 0.00721289
\(986\) 6.99437e12 0.235669
\(987\) −1.66728e13 −0.559218
\(988\) −3.12986e12 −0.104500
\(989\) −6.43684e13 −2.13939
\(990\) 1.31442e11 0.00434885
\(991\) −2.46053e12 −0.0810397 −0.0405198 0.999179i \(-0.512901\pi\)
−0.0405198 + 0.999179i \(0.512901\pi\)
\(992\) −3.01606e13 −0.988865
\(993\) −9.09165e12 −0.296737
\(994\) 4.64238e13 1.50835
\(995\) 6.41516e11 0.0207493
\(996\) 5.97324e12 0.192328
\(997\) −4.74114e13 −1.51969 −0.759845 0.650104i \(-0.774725\pi\)
−0.759845 + 0.650104i \(0.774725\pi\)
\(998\) −2.43672e13 −0.777533
\(999\) −1.14936e12 −0.0365098
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.1.14 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.14 22 1.1 even 1 trivial