Properties

Label 177.10.a.c.1.20
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 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+38.7622 q^{2} -81.0000 q^{3} +990.507 q^{4} -782.368 q^{5} -3139.74 q^{6} +8972.92 q^{7} +18548.0 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+38.7622 q^{2} -81.0000 q^{3} +990.507 q^{4} -782.368 q^{5} -3139.74 q^{6} +8972.92 q^{7} +18548.0 q^{8} +6561.00 q^{9} -30326.3 q^{10} +23175.9 q^{11} -80231.1 q^{12} +55195.9 q^{13} +347810. q^{14} +63371.8 q^{15} +211820. q^{16} -644241. q^{17} +254319. q^{18} +772218. q^{19} -774941. q^{20} -726807. q^{21} +898347. q^{22} +1.30489e6 q^{23} -1.50239e6 q^{24} -1.34103e6 q^{25} +2.13951e6 q^{26} -531441. q^{27} +8.88774e6 q^{28} +2.54967e6 q^{29} +2.45643e6 q^{30} +3.89754e6 q^{31} -1.28594e6 q^{32} -1.87725e6 q^{33} -2.49722e7 q^{34} -7.02013e6 q^{35} +6.49872e6 q^{36} -1.24288e7 q^{37} +2.99328e7 q^{38} -4.47087e6 q^{39} -1.45113e7 q^{40} +3.06543e7 q^{41} -2.81726e7 q^{42} +2.82292e7 q^{43} +2.29559e7 q^{44} -5.13312e6 q^{45} +5.05805e7 q^{46} -2.18793e7 q^{47} -1.71574e7 q^{48} +4.01597e7 q^{49} -5.19811e7 q^{50} +5.21835e7 q^{51} +5.46719e7 q^{52} +1.06767e8 q^{53} -2.05998e7 q^{54} -1.81321e7 q^{55} +1.66430e8 q^{56} -6.25496e7 q^{57} +9.88309e7 q^{58} +1.21174e7 q^{59} +6.27702e7 q^{60} +1.31642e8 q^{61} +1.51077e8 q^{62} +5.88714e7 q^{63} -1.58298e8 q^{64} -4.31835e7 q^{65} -7.27661e7 q^{66} +2.37913e8 q^{67} -6.38125e8 q^{68} -1.05696e8 q^{69} -2.72115e8 q^{70} -3.67874e8 q^{71} +1.21693e8 q^{72} +1.69715e8 q^{73} -4.81766e8 q^{74} +1.08623e8 q^{75} +7.64887e8 q^{76} +2.07955e8 q^{77} -1.73301e8 q^{78} -3.64180e7 q^{79} -1.65721e8 q^{80} +4.30467e7 q^{81} +1.18823e9 q^{82} -4.16778e8 q^{83} -7.19907e8 q^{84} +5.04033e8 q^{85} +1.09423e9 q^{86} -2.06524e8 q^{87} +4.29865e8 q^{88} +1.10229e9 q^{89} -1.98971e8 q^{90} +4.95269e8 q^{91} +1.29250e9 q^{92} -3.15701e8 q^{93} -8.48090e8 q^{94} -6.04158e8 q^{95} +1.04161e8 q^{96} +7.85297e8 q^{97} +1.55668e9 q^{98} +1.52057e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 38.7622 1.71306 0.856531 0.516095i \(-0.172615\pi\)
0.856531 + 0.516095i \(0.172615\pi\)
\(3\) −81.0000 −0.577350
\(4\) 990.507 1.93458
\(5\) −782.368 −0.559817 −0.279908 0.960027i \(-0.590304\pi\)
−0.279908 + 0.960027i \(0.590304\pi\)
\(6\) −3139.74 −0.989037
\(7\) 8972.92 1.41251 0.706257 0.707956i \(-0.250382\pi\)
0.706257 + 0.707956i \(0.250382\pi\)
\(8\) 18548.0 1.60100
\(9\) 6561.00 0.333333
\(10\) −30326.3 −0.959001
\(11\) 23175.9 0.477275 0.238638 0.971109i \(-0.423299\pi\)
0.238638 + 0.971109i \(0.423299\pi\)
\(12\) −80231.1 −1.11693
\(13\) 55195.9 0.535996 0.267998 0.963419i \(-0.413638\pi\)
0.267998 + 0.963419i \(0.413638\pi\)
\(14\) 347810. 2.41973
\(15\) 63371.8 0.323210
\(16\) 211820. 0.808030
\(17\) −644241. −1.87080 −0.935401 0.353588i \(-0.884961\pi\)
−0.935401 + 0.353588i \(0.884961\pi\)
\(18\) 254319. 0.571021
\(19\) 772218. 1.35940 0.679702 0.733489i \(-0.262109\pi\)
0.679702 + 0.733489i \(0.262109\pi\)
\(20\) −774941. −1.08301
\(21\) −726807. −0.815515
\(22\) 898347. 0.817602
\(23\) 1.30489e6 0.972298 0.486149 0.873876i \(-0.338401\pi\)
0.486149 + 0.873876i \(0.338401\pi\)
\(24\) −1.50239e6 −0.924338
\(25\) −1.34103e6 −0.686605
\(26\) 2.13951e6 0.918195
\(27\) −531441. −0.192450
\(28\) 8.88774e6 2.73263
\(29\) 2.54967e6 0.669412 0.334706 0.942323i \(-0.391363\pi\)
0.334706 + 0.942323i \(0.391363\pi\)
\(30\) 2.45643e6 0.553680
\(31\) 3.89754e6 0.757989 0.378994 0.925399i \(-0.376270\pi\)
0.378994 + 0.925399i \(0.376270\pi\)
\(32\) −1.28594e6 −0.216794
\(33\) −1.87725e6 −0.275555
\(34\) −2.49722e7 −3.20480
\(35\) −7.02013e6 −0.790749
\(36\) 6.49872e6 0.644861
\(37\) −1.24288e7 −1.09024 −0.545118 0.838360i \(-0.683515\pi\)
−0.545118 + 0.838360i \(0.683515\pi\)
\(38\) 2.99328e7 2.32874
\(39\) −4.47087e6 −0.309458
\(40\) −1.45113e7 −0.896267
\(41\) 3.06543e7 1.69420 0.847100 0.531433i \(-0.178346\pi\)
0.847100 + 0.531433i \(0.178346\pi\)
\(42\) −2.81726e7 −1.39703
\(43\) 2.82292e7 1.25919 0.629595 0.776924i \(-0.283221\pi\)
0.629595 + 0.776924i \(0.283221\pi\)
\(44\) 2.29559e7 0.923329
\(45\) −5.13312e6 −0.186606
\(46\) 5.05805e7 1.66561
\(47\) −2.18793e7 −0.654023 −0.327012 0.945020i \(-0.606042\pi\)
−0.327012 + 0.945020i \(0.606042\pi\)
\(48\) −1.71574e7 −0.466517
\(49\) 4.01597e7 0.995196
\(50\) −5.19811e7 −1.17620
\(51\) 5.21835e7 1.08011
\(52\) 5.46719e7 1.03693
\(53\) 1.06767e8 1.85864 0.929320 0.369275i \(-0.120394\pi\)
0.929320 + 0.369275i \(0.120394\pi\)
\(54\) −2.05998e7 −0.329679
\(55\) −1.81321e7 −0.267187
\(56\) 1.66430e8 2.26144
\(57\) −6.25496e7 −0.784852
\(58\) 9.88309e7 1.14675
\(59\) 1.21174e7 0.130189
\(60\) 6.27702e7 0.625278
\(61\) 1.31642e8 1.21734 0.608669 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(62\) 1.51077e8 1.29848
\(63\) 5.88714e7 0.470838
\(64\) −1.58298e8 −1.17941
\(65\) −4.31835e7 −0.300060
\(66\) −7.27661e7 −0.472043
\(67\) 2.37913e8 1.44238 0.721192 0.692735i \(-0.243594\pi\)
0.721192 + 0.692735i \(0.243594\pi\)
\(68\) −6.38125e8 −3.61922
\(69\) −1.05696e8 −0.561356
\(70\) −2.72115e8 −1.35460
\(71\) −3.67874e8 −1.71805 −0.859027 0.511930i \(-0.828931\pi\)
−0.859027 + 0.511930i \(0.828931\pi\)
\(72\) 1.21693e8 0.533667
\(73\) 1.69715e8 0.699469 0.349735 0.936849i \(-0.386272\pi\)
0.349735 + 0.936849i \(0.386272\pi\)
\(74\) −4.81766e8 −1.86764
\(75\) 1.08623e8 0.396412
\(76\) 7.64887e8 2.62988
\(77\) 2.07955e8 0.674158
\(78\) −1.73301e8 −0.530120
\(79\) −3.64180e7 −0.105195 −0.0525974 0.998616i \(-0.516750\pi\)
−0.0525974 + 0.998616i \(0.516750\pi\)
\(80\) −1.65721e8 −0.452349
\(81\) 4.30467e7 0.111111
\(82\) 1.18823e9 2.90227
\(83\) −4.16778e8 −0.963948 −0.481974 0.876186i \(-0.660080\pi\)
−0.481974 + 0.876186i \(0.660080\pi\)
\(84\) −7.19907e8 −1.57768
\(85\) 5.04033e8 1.04731
\(86\) 1.09423e9 2.15707
\(87\) −2.06524e8 −0.386485
\(88\) 4.29865e8 0.764118
\(89\) 1.10229e9 1.86227 0.931134 0.364677i \(-0.118821\pi\)
0.931134 + 0.364677i \(0.118821\pi\)
\(90\) −1.98971e8 −0.319667
\(91\) 4.95269e8 0.757102
\(92\) 1.29250e9 1.88099
\(93\) −3.15701e8 −0.437625
\(94\) −8.48090e8 −1.12038
\(95\) −6.04158e8 −0.761017
\(96\) 1.04161e8 0.125166
\(97\) 7.85297e8 0.900661 0.450330 0.892862i \(-0.351306\pi\)
0.450330 + 0.892862i \(0.351306\pi\)
\(98\) 1.55668e9 1.70483
\(99\) 1.52057e8 0.159092
\(100\) −1.32830e9 −1.32830
\(101\) 1.47978e9 1.41498 0.707491 0.706722i \(-0.249827\pi\)
0.707491 + 0.706722i \(0.249827\pi\)
\(102\) 2.02275e9 1.85029
\(103\) 1.56660e8 0.137148 0.0685741 0.997646i \(-0.478155\pi\)
0.0685741 + 0.997646i \(0.478155\pi\)
\(104\) 1.02377e9 0.858130
\(105\) 5.68630e8 0.456539
\(106\) 4.13852e9 3.18397
\(107\) −2.04239e9 −1.50630 −0.753149 0.657850i \(-0.771466\pi\)
−0.753149 + 0.657850i \(0.771466\pi\)
\(108\) −5.26396e8 −0.372311
\(109\) 6.43154e8 0.436411 0.218205 0.975903i \(-0.429980\pi\)
0.218205 + 0.975903i \(0.429980\pi\)
\(110\) −7.02838e8 −0.457708
\(111\) 1.00673e9 0.629448
\(112\) 1.90065e9 1.14135
\(113\) −2.17696e9 −1.25602 −0.628012 0.778204i \(-0.716131\pi\)
−0.628012 + 0.778204i \(0.716131\pi\)
\(114\) −2.42456e9 −1.34450
\(115\) −1.02091e9 −0.544309
\(116\) 2.52547e9 1.29503
\(117\) 3.62140e8 0.178665
\(118\) 4.69695e8 0.223022
\(119\) −5.78072e9 −2.64253
\(120\) 1.17542e9 0.517460
\(121\) −1.82083e9 −0.772208
\(122\) 5.10274e9 2.08538
\(123\) −2.48300e9 −0.978147
\(124\) 3.86054e9 1.46639
\(125\) 2.57724e9 0.944190
\(126\) 2.28198e9 0.806575
\(127\) 5.22667e8 0.178282 0.0891412 0.996019i \(-0.471588\pi\)
0.0891412 + 0.996019i \(0.471588\pi\)
\(128\) −5.47757e9 −1.80361
\(129\) −2.28657e9 −0.726994
\(130\) −1.67389e9 −0.514021
\(131\) −5.05312e9 −1.49913 −0.749563 0.661932i \(-0.769737\pi\)
−0.749563 + 0.661932i \(0.769737\pi\)
\(132\) −1.85942e9 −0.533084
\(133\) 6.92905e9 1.92018
\(134\) 9.22202e9 2.47090
\(135\) 4.15782e8 0.107737
\(136\) −1.19494e10 −2.99516
\(137\) −6.98295e9 −1.69354 −0.846771 0.531957i \(-0.821457\pi\)
−0.846771 + 0.531957i \(0.821457\pi\)
\(138\) −4.09702e9 −0.961639
\(139\) −1.15010e9 −0.261317 −0.130658 0.991427i \(-0.541709\pi\)
−0.130658 + 0.991427i \(0.541709\pi\)
\(140\) −6.95348e9 −1.52977
\(141\) 1.77222e9 0.377601
\(142\) −1.42596e10 −2.94314
\(143\) 1.27921e9 0.255818
\(144\) 1.38975e9 0.269343
\(145\) −1.99478e9 −0.374748
\(146\) 6.57854e9 1.19823
\(147\) −3.25294e9 −0.574577
\(148\) −1.23108e10 −2.10915
\(149\) −4.91077e9 −0.816228 −0.408114 0.912931i \(-0.633813\pi\)
−0.408114 + 0.912931i \(0.633813\pi\)
\(150\) 4.21047e9 0.679078
\(151\) 4.74005e9 0.741970 0.370985 0.928639i \(-0.379020\pi\)
0.370985 + 0.928639i \(0.379020\pi\)
\(152\) 1.43231e10 2.17641
\(153\) −4.22686e9 −0.623601
\(154\) 8.06080e9 1.15487
\(155\) −3.04931e9 −0.424335
\(156\) −4.42843e9 −0.598672
\(157\) −2.35916e9 −0.309891 −0.154946 0.987923i \(-0.549520\pi\)
−0.154946 + 0.987923i \(0.549520\pi\)
\(158\) −1.41164e9 −0.180205
\(159\) −8.64812e9 −1.07309
\(160\) 1.00608e9 0.121365
\(161\) 1.17087e10 1.37338
\(162\) 1.66858e9 0.190340
\(163\) 9.30511e9 1.03247 0.516235 0.856447i \(-0.327333\pi\)
0.516235 + 0.856447i \(0.327333\pi\)
\(164\) 3.03633e10 3.27757
\(165\) 1.46870e9 0.154260
\(166\) −1.61552e10 −1.65130
\(167\) 3.05481e9 0.303920 0.151960 0.988387i \(-0.451441\pi\)
0.151960 + 0.988387i \(0.451441\pi\)
\(168\) −1.34808e10 −1.30564
\(169\) −7.55791e9 −0.712708
\(170\) 1.95374e10 1.79410
\(171\) 5.06652e9 0.453135
\(172\) 2.79613e10 2.43601
\(173\) 1.61535e10 1.37107 0.685534 0.728041i \(-0.259569\pi\)
0.685534 + 0.728041i \(0.259569\pi\)
\(174\) −8.00530e9 −0.662074
\(175\) −1.20329e10 −0.969839
\(176\) 4.90912e9 0.385653
\(177\) −9.81506e8 −0.0751646
\(178\) 4.27273e10 3.19018
\(179\) −1.09942e10 −0.800436 −0.400218 0.916420i \(-0.631066\pi\)
−0.400218 + 0.916420i \(0.631066\pi\)
\(180\) −5.08439e9 −0.361004
\(181\) −1.47891e10 −1.02421 −0.512104 0.858924i \(-0.671134\pi\)
−0.512104 + 0.858924i \(0.671134\pi\)
\(182\) 1.91977e10 1.29696
\(183\) −1.06630e10 −0.702830
\(184\) 2.42031e10 1.55665
\(185\) 9.72387e9 0.610332
\(186\) −1.22372e10 −0.749679
\(187\) −1.49308e10 −0.892887
\(188\) −2.16716e10 −1.26526
\(189\) −4.76858e9 −0.271838
\(190\) −2.34185e10 −1.30367
\(191\) −7.33579e9 −0.398838 −0.199419 0.979914i \(-0.563906\pi\)
−0.199419 + 0.979914i \(0.563906\pi\)
\(192\) 1.28221e10 0.680934
\(193\) −2.32650e10 −1.20697 −0.603484 0.797375i \(-0.706221\pi\)
−0.603484 + 0.797375i \(0.706221\pi\)
\(194\) 3.04398e10 1.54289
\(195\) 3.49786e9 0.173240
\(196\) 3.97785e10 1.92529
\(197\) 1.54023e10 0.728598 0.364299 0.931282i \(-0.381309\pi\)
0.364299 + 0.931282i \(0.381309\pi\)
\(198\) 5.89406e9 0.272534
\(199\) −3.60701e9 −0.163045 −0.0815227 0.996671i \(-0.525978\pi\)
−0.0815227 + 0.996671i \(0.525978\pi\)
\(200\) −2.48733e10 −1.09926
\(201\) −1.92709e10 −0.832761
\(202\) 5.73595e10 2.42395
\(203\) 2.28780e10 0.945554
\(204\) 5.16881e10 2.08956
\(205\) −2.39830e10 −0.948442
\(206\) 6.07247e9 0.234943
\(207\) 8.56140e9 0.324099
\(208\) 1.16916e10 0.433101
\(209\) 1.78968e10 0.648810
\(210\) 2.20414e10 0.782080
\(211\) 1.86756e10 0.648639 0.324320 0.945948i \(-0.394865\pi\)
0.324320 + 0.945948i \(0.394865\pi\)
\(212\) 1.05753e11 3.59570
\(213\) 2.97978e10 0.991919
\(214\) −7.91674e10 −2.58038
\(215\) −2.20857e10 −0.704916
\(216\) −9.85715e9 −0.308113
\(217\) 3.49723e10 1.07067
\(218\) 2.49300e10 0.747599
\(219\) −1.37470e10 −0.403839
\(220\) −1.79599e10 −0.516895
\(221\) −3.55594e10 −1.00274
\(222\) 3.90231e10 1.07828
\(223\) 4.34537e10 1.17667 0.588335 0.808617i \(-0.299784\pi\)
0.588335 + 0.808617i \(0.299784\pi\)
\(224\) −1.15387e10 −0.306224
\(225\) −8.79847e9 −0.228868
\(226\) −8.43838e10 −2.15165
\(227\) 5.10212e10 1.27536 0.637682 0.770300i \(-0.279893\pi\)
0.637682 + 0.770300i \(0.279893\pi\)
\(228\) −6.19558e10 −1.51836
\(229\) −7.68627e10 −1.84695 −0.923476 0.383655i \(-0.874665\pi\)
−0.923476 + 0.383655i \(0.874665\pi\)
\(230\) −3.95725e10 −0.932435
\(231\) −1.68444e10 −0.389225
\(232\) 4.72913e10 1.07173
\(233\) 8.12834e9 0.180676 0.0903380 0.995911i \(-0.471205\pi\)
0.0903380 + 0.995911i \(0.471205\pi\)
\(234\) 1.40373e10 0.306065
\(235\) 1.71177e10 0.366133
\(236\) 1.20023e10 0.251861
\(237\) 2.94986e9 0.0607343
\(238\) −2.24073e11 −4.52683
\(239\) 3.68954e8 0.00731445 0.00365722 0.999993i \(-0.498836\pi\)
0.00365722 + 0.999993i \(0.498836\pi\)
\(240\) 1.34234e10 0.261164
\(241\) −5.72365e10 −1.09294 −0.546470 0.837479i \(-0.684029\pi\)
−0.546470 + 0.837479i \(0.684029\pi\)
\(242\) −7.05792e10 −1.32284
\(243\) −3.48678e9 −0.0641500
\(244\) 1.30393e11 2.35504
\(245\) −3.14197e10 −0.557127
\(246\) −9.62466e10 −1.67563
\(247\) 4.26232e10 0.728635
\(248\) 7.22914e10 1.21354
\(249\) 3.37590e10 0.556535
\(250\) 9.98993e10 1.61746
\(251\) −5.86523e10 −0.932725 −0.466362 0.884594i \(-0.654436\pi\)
−0.466362 + 0.884594i \(0.654436\pi\)
\(252\) 5.83125e10 0.910876
\(253\) 3.02420e10 0.464054
\(254\) 2.02597e10 0.305409
\(255\) −4.08267e10 −0.604663
\(256\) −1.31274e11 −1.91029
\(257\) −2.92462e10 −0.418186 −0.209093 0.977896i \(-0.567051\pi\)
−0.209093 + 0.977896i \(0.567051\pi\)
\(258\) −8.86324e10 −1.24539
\(259\) −1.11522e11 −1.53997
\(260\) −4.27735e10 −0.580491
\(261\) 1.67284e10 0.223137
\(262\) −1.95870e11 −2.56810
\(263\) −3.94332e9 −0.0508232 −0.0254116 0.999677i \(-0.508090\pi\)
−0.0254116 + 0.999677i \(0.508090\pi\)
\(264\) −3.48191e10 −0.441164
\(265\) −8.35310e10 −1.04050
\(266\) 2.68585e11 3.28938
\(267\) −8.92858e10 −1.07518
\(268\) 2.35654e11 2.79041
\(269\) −3.59825e10 −0.418992 −0.209496 0.977809i \(-0.567182\pi\)
−0.209496 + 0.977809i \(0.567182\pi\)
\(270\) 1.61166e10 0.184560
\(271\) −2.98145e10 −0.335789 −0.167894 0.985805i \(-0.553697\pi\)
−0.167894 + 0.985805i \(0.553697\pi\)
\(272\) −1.36463e11 −1.51167
\(273\) −4.01168e10 −0.437113
\(274\) −2.70674e11 −2.90114
\(275\) −3.10794e10 −0.327700
\(276\) −1.04693e11 −1.08599
\(277\) 7.15684e9 0.0730403 0.0365201 0.999333i \(-0.488373\pi\)
0.0365201 + 0.999333i \(0.488373\pi\)
\(278\) −4.45802e10 −0.447652
\(279\) 2.55717e10 0.252663
\(280\) −1.30209e11 −1.26599
\(281\) 1.01358e11 0.969795 0.484898 0.874571i \(-0.338857\pi\)
0.484898 + 0.874571i \(0.338857\pi\)
\(282\) 6.86953e10 0.646854
\(283\) 6.48347e10 0.600853 0.300427 0.953805i \(-0.402871\pi\)
0.300427 + 0.953805i \(0.402871\pi\)
\(284\) −3.64382e11 −3.32372
\(285\) 4.89368e10 0.439373
\(286\) 4.95851e10 0.438232
\(287\) 2.75059e11 2.39308
\(288\) −8.43707e9 −0.0722646
\(289\) 2.96458e11 2.49990
\(290\) −7.73221e10 −0.641967
\(291\) −6.36091e10 −0.519997
\(292\) 1.68104e11 1.35318
\(293\) −1.83636e11 −1.45564 −0.727819 0.685769i \(-0.759466\pi\)
−0.727819 + 0.685769i \(0.759466\pi\)
\(294\) −1.26091e11 −0.984286
\(295\) −9.48023e9 −0.0728819
\(296\) −2.30528e11 −1.74547
\(297\) −1.23166e10 −0.0918517
\(298\) −1.90352e11 −1.39825
\(299\) 7.20247e10 0.521148
\(300\) 1.07592e11 0.766891
\(301\) 2.53299e11 1.77862
\(302\) 1.83735e11 1.27104
\(303\) −1.19862e11 −0.816941
\(304\) 1.63571e11 1.09844
\(305\) −1.02993e11 −0.681486
\(306\) −1.63842e11 −1.06827
\(307\) −3.31583e10 −0.213044 −0.106522 0.994310i \(-0.533971\pi\)
−0.106522 + 0.994310i \(0.533971\pi\)
\(308\) 2.05981e11 1.30421
\(309\) −1.26894e10 −0.0791825
\(310\) −1.18198e11 −0.726912
\(311\) −2.91372e11 −1.76614 −0.883071 0.469239i \(-0.844528\pi\)
−0.883071 + 0.469239i \(0.844528\pi\)
\(312\) −8.29255e10 −0.495442
\(313\) 1.72605e11 1.01649 0.508245 0.861212i \(-0.330294\pi\)
0.508245 + 0.861212i \(0.330294\pi\)
\(314\) −9.14463e10 −0.530863
\(315\) −4.60591e10 −0.263583
\(316\) −3.60723e10 −0.203508
\(317\) −1.11801e11 −0.621843 −0.310922 0.950436i \(-0.600638\pi\)
−0.310922 + 0.950436i \(0.600638\pi\)
\(318\) −3.35220e11 −1.83826
\(319\) 5.90909e10 0.319494
\(320\) 1.23847e11 0.660255
\(321\) 1.65433e11 0.869662
\(322\) 4.53855e11 2.35269
\(323\) −4.97494e11 −2.54318
\(324\) 4.26381e10 0.214954
\(325\) −7.40191e10 −0.368018
\(326\) 3.60686e11 1.76869
\(327\) −5.20954e10 −0.251962
\(328\) 5.68576e11 2.71242
\(329\) −1.96321e11 −0.923817
\(330\) 5.69299e10 0.264258
\(331\) −3.47020e11 −1.58902 −0.794509 0.607253i \(-0.792271\pi\)
−0.794509 + 0.607253i \(0.792271\pi\)
\(332\) −4.12822e11 −1.86484
\(333\) −8.15451e10 −0.363412
\(334\) 1.18411e11 0.520635
\(335\) −1.86135e11 −0.807471
\(336\) −1.53952e11 −0.658961
\(337\) −4.91604e10 −0.207625 −0.103813 0.994597i \(-0.533104\pi\)
−0.103813 + 0.994597i \(0.533104\pi\)
\(338\) −2.92961e11 −1.22091
\(339\) 1.76334e11 0.725166
\(340\) 4.99248e11 2.02610
\(341\) 9.03288e10 0.361769
\(342\) 1.96389e11 0.776248
\(343\) −1.73949e9 −0.00678574
\(344\) 5.23595e11 2.01596
\(345\) 8.26933e10 0.314257
\(346\) 6.26144e11 2.34872
\(347\) −3.01656e11 −1.11694 −0.558469 0.829526i \(-0.688611\pi\)
−0.558469 + 0.829526i \(0.688611\pi\)
\(348\) −2.04563e11 −0.747688
\(349\) −2.94274e11 −1.06179 −0.530894 0.847438i \(-0.678144\pi\)
−0.530894 + 0.847438i \(0.678144\pi\)
\(350\) −4.66422e11 −1.66140
\(351\) −2.93334e10 −0.103153
\(352\) −2.98028e10 −0.103470
\(353\) 8.08325e10 0.277077 0.138538 0.990357i \(-0.455760\pi\)
0.138538 + 0.990357i \(0.455760\pi\)
\(354\) −3.80453e10 −0.128762
\(355\) 2.87813e11 0.961796
\(356\) 1.09183e12 3.60271
\(357\) 4.68238e11 1.52567
\(358\) −4.26161e11 −1.37120
\(359\) 2.24898e11 0.714596 0.357298 0.933990i \(-0.383698\pi\)
0.357298 + 0.933990i \(0.383698\pi\)
\(360\) −9.52089e10 −0.298756
\(361\) 2.73632e11 0.847978
\(362\) −5.73257e11 −1.75453
\(363\) 1.47487e11 0.445835
\(364\) 4.90567e11 1.46468
\(365\) −1.32780e11 −0.391575
\(366\) −4.13322e11 −1.20399
\(367\) −3.79754e11 −1.09271 −0.546355 0.837554i \(-0.683985\pi\)
−0.546355 + 0.837554i \(0.683985\pi\)
\(368\) 2.76403e11 0.785646
\(369\) 2.01123e11 0.564733
\(370\) 3.76918e11 1.04554
\(371\) 9.58012e11 2.62536
\(372\) −3.12704e11 −0.846622
\(373\) 4.33543e11 1.15969 0.579845 0.814726i \(-0.303113\pi\)
0.579845 + 0.814726i \(0.303113\pi\)
\(374\) −5.78752e11 −1.52957
\(375\) −2.08756e11 −0.545128
\(376\) −4.05817e11 −1.04709
\(377\) 1.40732e11 0.358802
\(378\) −1.84841e11 −0.465676
\(379\) −6.05335e11 −1.50702 −0.753510 0.657436i \(-0.771641\pi\)
−0.753510 + 0.657436i \(0.771641\pi\)
\(380\) −5.98423e11 −1.47225
\(381\) −4.23360e10 −0.102931
\(382\) −2.84351e11 −0.683235
\(383\) −2.57434e11 −0.611324 −0.305662 0.952140i \(-0.598878\pi\)
−0.305662 + 0.952140i \(0.598878\pi\)
\(384\) 4.43683e11 1.04132
\(385\) −1.62698e11 −0.377405
\(386\) −9.01804e11 −2.06761
\(387\) 1.85212e11 0.419730
\(388\) 7.77842e11 1.74240
\(389\) −8.88676e11 −1.96775 −0.983875 0.178856i \(-0.942760\pi\)
−0.983875 + 0.178856i \(0.942760\pi\)
\(390\) 1.35585e11 0.296770
\(391\) −8.40664e11 −1.81898
\(392\) 7.44882e11 1.59331
\(393\) 4.09302e11 0.865521
\(394\) 5.97027e11 1.24813
\(395\) 2.84923e10 0.0588899
\(396\) 1.50613e11 0.307776
\(397\) 7.40056e11 1.49523 0.747614 0.664133i \(-0.231199\pi\)
0.747614 + 0.664133i \(0.231199\pi\)
\(398\) −1.39816e11 −0.279307
\(399\) −5.61253e11 −1.10861
\(400\) −2.84056e11 −0.554798
\(401\) −5.52820e11 −1.06766 −0.533831 0.845591i \(-0.679248\pi\)
−0.533831 + 0.845591i \(0.679248\pi\)
\(402\) −7.46984e11 −1.42657
\(403\) 2.15128e11 0.406279
\(404\) 1.46573e12 2.73740
\(405\) −3.36784e10 −0.0622019
\(406\) 8.86802e11 1.61979
\(407\) −2.88047e11 −0.520342
\(408\) 9.67898e11 1.72925
\(409\) 1.05922e11 0.187168 0.0935842 0.995611i \(-0.470168\pi\)
0.0935842 + 0.995611i \(0.470168\pi\)
\(410\) −9.29633e11 −1.62474
\(411\) 5.65619e11 0.977767
\(412\) 1.55173e11 0.265325
\(413\) 1.08728e11 0.183894
\(414\) 3.31858e11 0.555202
\(415\) 3.26074e11 0.539634
\(416\) −7.09788e10 −0.116201
\(417\) 9.31578e10 0.150871
\(418\) 6.93719e11 1.11145
\(419\) 5.41868e11 0.858876 0.429438 0.903096i \(-0.358712\pi\)
0.429438 + 0.903096i \(0.358712\pi\)
\(420\) 5.63232e11 0.883213
\(421\) 5.16303e11 0.801005 0.400502 0.916296i \(-0.368836\pi\)
0.400502 + 0.916296i \(0.368836\pi\)
\(422\) 7.23907e11 1.11116
\(423\) −1.43550e11 −0.218008
\(424\) 1.98031e12 2.97568
\(425\) 8.63943e11 1.28450
\(426\) 1.15503e12 1.69922
\(427\) 1.18122e12 1.71951
\(428\) −2.02300e12 −2.91406
\(429\) −1.03616e11 −0.147696
\(430\) −8.56088e11 −1.20756
\(431\) −5.12189e11 −0.714962 −0.357481 0.933920i \(-0.616364\pi\)
−0.357481 + 0.933920i \(0.616364\pi\)
\(432\) −1.12570e11 −0.155506
\(433\) 4.81703e11 0.658543 0.329272 0.944235i \(-0.393197\pi\)
0.329272 + 0.944235i \(0.393197\pi\)
\(434\) 1.35560e12 1.83412
\(435\) 1.61577e11 0.216361
\(436\) 6.37048e11 0.844273
\(437\) 1.00766e12 1.32175
\(438\) −5.32862e11 −0.691801
\(439\) −1.13484e12 −1.45830 −0.729148 0.684356i \(-0.760084\pi\)
−0.729148 + 0.684356i \(0.760084\pi\)
\(440\) −3.36313e11 −0.427766
\(441\) 2.63488e11 0.331732
\(442\) −1.37836e12 −1.71776
\(443\) 2.63450e11 0.324999 0.162499 0.986709i \(-0.448044\pi\)
0.162499 + 0.986709i \(0.448044\pi\)
\(444\) 9.97173e11 1.21772
\(445\) −8.62399e11 −1.04253
\(446\) 1.68436e12 2.01571
\(447\) 3.97772e11 0.471249
\(448\) −1.42040e12 −1.66594
\(449\) 3.92678e11 0.455961 0.227981 0.973666i \(-0.426788\pi\)
0.227981 + 0.973666i \(0.426788\pi\)
\(450\) −3.41048e11 −0.392066
\(451\) 7.10441e11 0.808600
\(452\) −2.15630e12 −2.42988
\(453\) −3.83944e11 −0.428377
\(454\) 1.97769e12 2.18478
\(455\) −3.87482e11 −0.423839
\(456\) −1.16017e12 −1.25655
\(457\) −2.03984e11 −0.218763 −0.109382 0.994000i \(-0.534887\pi\)
−0.109382 + 0.994000i \(0.534887\pi\)
\(458\) −2.97937e12 −3.16395
\(459\) 3.42376e11 0.360036
\(460\) −1.01121e12 −1.05301
\(461\) 4.72398e11 0.487140 0.243570 0.969883i \(-0.421681\pi\)
0.243570 + 0.969883i \(0.421681\pi\)
\(462\) −6.52925e11 −0.666767
\(463\) 1.40807e12 1.42399 0.711997 0.702182i \(-0.247791\pi\)
0.711997 + 0.702182i \(0.247791\pi\)
\(464\) 5.40073e11 0.540905
\(465\) 2.46994e11 0.244990
\(466\) 3.15072e11 0.309509
\(467\) 1.98958e12 1.93569 0.967845 0.251549i \(-0.0809398\pi\)
0.967845 + 0.251549i \(0.0809398\pi\)
\(468\) 3.58702e11 0.345643
\(469\) 2.13477e12 2.03739
\(470\) 6.63518e11 0.627209
\(471\) 1.91092e11 0.178916
\(472\) 2.24752e11 0.208433
\(473\) 6.54237e11 0.600980
\(474\) 1.14343e11 0.104042
\(475\) −1.03556e12 −0.933373
\(476\) −5.72584e12 −5.11220
\(477\) 7.00498e11 0.619547
\(478\) 1.43015e10 0.0125301
\(479\) 9.67025e11 0.839320 0.419660 0.907681i \(-0.362149\pi\)
0.419660 + 0.907681i \(0.362149\pi\)
\(480\) −8.14925e10 −0.0700700
\(481\) −6.86017e11 −0.584362
\(482\) −2.21861e12 −1.87228
\(483\) −9.48404e11 −0.792924
\(484\) −1.80354e12 −1.49390
\(485\) −6.14391e11 −0.504205
\(486\) −1.35155e11 −0.109893
\(487\) 1.03101e11 0.0830585 0.0415292 0.999137i \(-0.486777\pi\)
0.0415292 + 0.999137i \(0.486777\pi\)
\(488\) 2.44170e12 1.94896
\(489\) −7.53714e11 −0.596097
\(490\) −1.21790e12 −0.954394
\(491\) 9.83800e11 0.763906 0.381953 0.924182i \(-0.375252\pi\)
0.381953 + 0.924182i \(0.375252\pi\)
\(492\) −2.45943e12 −1.89231
\(493\) −1.64260e12 −1.25234
\(494\) 1.65217e12 1.24820
\(495\) −1.18964e11 −0.0890622
\(496\) 8.25578e11 0.612478
\(497\) −3.30091e12 −2.42678
\(498\) 1.30857e12 0.953380
\(499\) 3.95589e11 0.285622 0.142811 0.989750i \(-0.454386\pi\)
0.142811 + 0.989750i \(0.454386\pi\)
\(500\) 2.55277e12 1.82661
\(501\) −2.47440e11 −0.175469
\(502\) −2.27349e12 −1.59782
\(503\) 6.12598e9 0.00426697 0.00213348 0.999998i \(-0.499321\pi\)
0.00213348 + 0.999998i \(0.499321\pi\)
\(504\) 1.09194e12 0.753812
\(505\) −1.15773e12 −0.792131
\(506\) 1.17225e12 0.794953
\(507\) 6.12191e11 0.411482
\(508\) 5.17705e11 0.344902
\(509\) 6.88882e11 0.454899 0.227449 0.973790i \(-0.426961\pi\)
0.227449 + 0.973790i \(0.426961\pi\)
\(510\) −1.58253e12 −1.03583
\(511\) 1.52284e12 0.988010
\(512\) −2.28395e12 −1.46883
\(513\) −4.10388e11 −0.261617
\(514\) −1.13365e12 −0.716379
\(515\) −1.22566e11 −0.0767778
\(516\) −2.26486e12 −1.40643
\(517\) −5.07072e11 −0.312149
\(518\) −4.32285e12 −2.63807
\(519\) −1.30843e12 −0.791586
\(520\) −8.00966e11 −0.480396
\(521\) 2.58272e12 1.53570 0.767852 0.640627i \(-0.221325\pi\)
0.767852 + 0.640627i \(0.221325\pi\)
\(522\) 6.48430e11 0.382248
\(523\) 1.15585e12 0.675531 0.337765 0.941230i \(-0.390329\pi\)
0.337765 + 0.941230i \(0.390329\pi\)
\(524\) −5.00515e12 −2.90019
\(525\) 9.74667e11 0.559937
\(526\) −1.52852e11 −0.0870633
\(527\) −2.51095e12 −1.41805
\(528\) −3.97639e11 −0.222657
\(529\) −9.84099e10 −0.0546372
\(530\) −3.23785e12 −1.78244
\(531\) 7.95020e10 0.0433963
\(532\) 6.86327e12 3.71474
\(533\) 1.69199e12 0.908085
\(534\) −3.46091e12 −1.84185
\(535\) 1.59790e12 0.843251
\(536\) 4.41280e12 2.30926
\(537\) 8.90534e11 0.462132
\(538\) −1.39476e12 −0.717760
\(539\) 9.30737e11 0.474982
\(540\) 4.11835e11 0.208426
\(541\) 6.25431e11 0.313900 0.156950 0.987607i \(-0.449834\pi\)
0.156950 + 0.987607i \(0.449834\pi\)
\(542\) −1.15568e12 −0.575227
\(543\) 1.19792e12 0.591326
\(544\) 8.28456e11 0.405578
\(545\) −5.03183e11 −0.244310
\(546\) −1.55501e12 −0.748802
\(547\) −1.04302e12 −0.498139 −0.249069 0.968486i \(-0.580125\pi\)
−0.249069 + 0.968486i \(0.580125\pi\)
\(548\) −6.91666e12 −3.27630
\(549\) 8.63705e11 0.405779
\(550\) −1.20471e12 −0.561370
\(551\) 1.96890e12 0.910001
\(552\) −1.96045e12 −0.898732
\(553\) −3.26776e11 −0.148589
\(554\) 2.77415e11 0.125123
\(555\) −7.87633e11 −0.352375
\(556\) −1.13918e12 −0.505539
\(557\) −2.65888e12 −1.17044 −0.585221 0.810874i \(-0.698992\pi\)
−0.585221 + 0.810874i \(0.698992\pi\)
\(558\) 9.91217e11 0.432827
\(559\) 1.55814e12 0.674921
\(560\) −1.48701e12 −0.638949
\(561\) 1.20940e12 0.515509
\(562\) 3.92886e12 1.66132
\(563\) −3.94005e11 −0.165277 −0.0826387 0.996580i \(-0.526335\pi\)
−0.0826387 + 0.996580i \(0.526335\pi\)
\(564\) 1.75540e12 0.730500
\(565\) 1.70319e12 0.703143
\(566\) 2.51313e12 1.02930
\(567\) 3.86255e11 0.156946
\(568\) −6.82332e12 −2.75061
\(569\) −8.48239e11 −0.339245 −0.169622 0.985509i \(-0.554255\pi\)
−0.169622 + 0.985509i \(0.554255\pi\)
\(570\) 1.89690e12 0.752674
\(571\) 9.38062e11 0.369291 0.184646 0.982805i \(-0.440886\pi\)
0.184646 + 0.982805i \(0.440886\pi\)
\(572\) 1.26707e12 0.494901
\(573\) 5.94199e11 0.230269
\(574\) 1.06619e13 4.09950
\(575\) −1.74989e12 −0.667585
\(576\) −1.03859e12 −0.393137
\(577\) 2.77817e12 1.04344 0.521721 0.853116i \(-0.325290\pi\)
0.521721 + 0.853116i \(0.325290\pi\)
\(578\) 1.14914e13 4.28249
\(579\) 1.88447e12 0.696843
\(580\) −1.97585e12 −0.724982
\(581\) −3.73972e12 −1.36159
\(582\) −2.46563e12 −0.890787
\(583\) 2.47442e12 0.887083
\(584\) 3.14788e12 1.11985
\(585\) −2.83327e11 −0.100020
\(586\) −7.11813e12 −2.49360
\(587\) 3.10109e12 1.07806 0.539030 0.842286i \(-0.318791\pi\)
0.539030 + 0.842286i \(0.318791\pi\)
\(588\) −3.22206e12 −1.11157
\(589\) 3.00975e12 1.03041
\(590\) −3.67475e11 −0.124851
\(591\) −1.24759e12 −0.420656
\(592\) −2.63266e12 −0.880943
\(593\) −2.44676e12 −0.812540 −0.406270 0.913753i \(-0.633171\pi\)
−0.406270 + 0.913753i \(0.633171\pi\)
\(594\) −4.77418e11 −0.157348
\(595\) 4.52265e12 1.47934
\(596\) −4.86415e12 −1.57906
\(597\) 2.92168e11 0.0941343
\(598\) 2.79183e12 0.892759
\(599\) −3.55102e12 −1.12702 −0.563511 0.826108i \(-0.690550\pi\)
−0.563511 + 0.826108i \(0.690550\pi\)
\(600\) 2.01474e12 0.634655
\(601\) 4.12990e11 0.129123 0.0645616 0.997914i \(-0.479435\pi\)
0.0645616 + 0.997914i \(0.479435\pi\)
\(602\) 9.81842e12 3.04689
\(603\) 1.56095e12 0.480795
\(604\) 4.69505e12 1.43540
\(605\) 1.42456e12 0.432295
\(606\) −4.64612e12 −1.39947
\(607\) −3.64443e12 −1.08963 −0.544817 0.838555i \(-0.683401\pi\)
−0.544817 + 0.838555i \(0.683401\pi\)
\(608\) −9.93027e11 −0.294710
\(609\) −1.85312e12 −0.545916
\(610\) −3.99222e12 −1.16743
\(611\) −1.20765e12 −0.350554
\(612\) −4.18674e12 −1.20641
\(613\) −3.75688e11 −0.107462 −0.0537310 0.998555i \(-0.517111\pi\)
−0.0537310 + 0.998555i \(0.517111\pi\)
\(614\) −1.28529e12 −0.364958
\(615\) 1.94262e12 0.547583
\(616\) 3.85715e12 1.07933
\(617\) −3.87030e12 −1.07513 −0.537565 0.843222i \(-0.680656\pi\)
−0.537565 + 0.843222i \(0.680656\pi\)
\(618\) −4.91870e11 −0.135645
\(619\) 1.65184e12 0.452231 0.226116 0.974100i \(-0.427397\pi\)
0.226116 + 0.974100i \(0.427397\pi\)
\(620\) −3.02036e12 −0.820911
\(621\) −6.93473e11 −0.187119
\(622\) −1.12942e13 −3.02551
\(623\) 9.89079e12 2.63048
\(624\) −9.47021e11 −0.250051
\(625\) 6.02843e11 0.158032
\(626\) 6.69054e12 1.74131
\(627\) −1.44964e12 −0.374590
\(628\) −2.33677e12 −0.599511
\(629\) 8.00711e12 2.03961
\(630\) −1.78535e12 −0.451534
\(631\) −1.53939e12 −0.386560 −0.193280 0.981144i \(-0.561913\pi\)
−0.193280 + 0.981144i \(0.561913\pi\)
\(632\) −6.75481e11 −0.168417
\(633\) −1.51272e12 −0.374492
\(634\) −4.33367e12 −1.06526
\(635\) −4.08918e11 −0.0998055
\(636\) −8.56603e12 −2.07598
\(637\) 2.21665e12 0.533421
\(638\) 2.29049e12 0.547313
\(639\) −2.41362e12 −0.572685
\(640\) 4.28548e12 1.00969
\(641\) 5.68465e12 1.32997 0.664986 0.746856i \(-0.268438\pi\)
0.664986 + 0.746856i \(0.268438\pi\)
\(642\) 6.41256e12 1.48979
\(643\) −2.55828e12 −0.590198 −0.295099 0.955467i \(-0.595353\pi\)
−0.295099 + 0.955467i \(0.595353\pi\)
\(644\) 1.15975e13 2.65693
\(645\) 1.78894e12 0.406983
\(646\) −1.92839e13 −4.35662
\(647\) 2.20782e12 0.495331 0.247665 0.968846i \(-0.420337\pi\)
0.247665 + 0.968846i \(0.420337\pi\)
\(648\) 7.98429e11 0.177889
\(649\) 2.80830e11 0.0621359
\(650\) −2.86914e12 −0.630437
\(651\) −2.83276e12 −0.618151
\(652\) 9.21678e12 1.99740
\(653\) 3.11675e12 0.670800 0.335400 0.942076i \(-0.391129\pi\)
0.335400 + 0.942076i \(0.391129\pi\)
\(654\) −2.01933e12 −0.431626
\(655\) 3.95340e12 0.839237
\(656\) 6.49321e12 1.36897
\(657\) 1.11350e12 0.233156
\(658\) −7.60985e12 −1.58256
\(659\) −1.69500e12 −0.350095 −0.175047 0.984560i \(-0.556008\pi\)
−0.175047 + 0.984560i \(0.556008\pi\)
\(660\) 1.45475e12 0.298429
\(661\) −3.82564e12 −0.779468 −0.389734 0.920928i \(-0.627433\pi\)
−0.389734 + 0.920928i \(0.627433\pi\)
\(662\) −1.34513e13 −2.72209
\(663\) 2.88031e12 0.578934
\(664\) −7.73039e12 −1.54328
\(665\) −5.42106e12 −1.07495
\(666\) −3.16087e12 −0.622547
\(667\) 3.32705e12 0.650868
\(668\) 3.02581e12 0.587960
\(669\) −3.51975e12 −0.679351
\(670\) −7.21501e12 −1.38325
\(671\) 3.05092e12 0.581005
\(672\) 9.34632e11 0.176799
\(673\) −3.10596e12 −0.583618 −0.291809 0.956477i \(-0.594257\pi\)
−0.291809 + 0.956477i \(0.594257\pi\)
\(674\) −1.90556e12 −0.355675
\(675\) 7.12676e11 0.132137
\(676\) −7.48616e12 −1.37879
\(677\) −5.54110e12 −1.01379 −0.506893 0.862009i \(-0.669206\pi\)
−0.506893 + 0.862009i \(0.669206\pi\)
\(678\) 6.83509e12 1.24225
\(679\) 7.04641e12 1.27220
\(680\) 9.34879e12 1.67674
\(681\) −4.13272e12 −0.736332
\(682\) 3.50134e12 0.619733
\(683\) −8.19430e12 −1.44085 −0.720425 0.693533i \(-0.756053\pi\)
−0.720425 + 0.693533i \(0.756053\pi\)
\(684\) 5.01842e12 0.876627
\(685\) 5.46323e12 0.948074
\(686\) −6.74262e10 −0.0116244
\(687\) 6.22588e12 1.06634
\(688\) 5.97953e12 1.01746
\(689\) 5.89310e12 0.996224
\(690\) 3.20537e12 0.538341
\(691\) −7.97079e12 −1.32999 −0.664997 0.746846i \(-0.731567\pi\)
−0.664997 + 0.746846i \(0.731567\pi\)
\(692\) 1.60001e13 2.65244
\(693\) 1.36439e12 0.224719
\(694\) −1.16928e13 −1.91338
\(695\) 8.99798e11 0.146290
\(696\) −3.83059e12 −0.618763
\(697\) −1.97488e13 −3.16951
\(698\) −1.14067e13 −1.81891
\(699\) −6.58396e11 −0.104313
\(700\) −1.19187e13 −1.87624
\(701\) −6.03771e12 −0.944368 −0.472184 0.881500i \(-0.656534\pi\)
−0.472184 + 0.881500i \(0.656534\pi\)
\(702\) −1.13703e12 −0.176707
\(703\) −9.59771e12 −1.48207
\(704\) −3.66869e12 −0.562904
\(705\) −1.38653e12 −0.211387
\(706\) 3.13324e12 0.474650
\(707\) 1.32780e13 1.99868
\(708\) −9.72189e11 −0.145412
\(709\) 7.31879e12 1.08775 0.543877 0.839165i \(-0.316956\pi\)
0.543877 + 0.839165i \(0.316956\pi\)
\(710\) 1.11563e13 1.64762
\(711\) −2.38939e11 −0.0350650
\(712\) 2.04453e13 2.98149
\(713\) 5.08586e12 0.736991
\(714\) 1.81499e13 2.61356
\(715\) −1.00081e12 −0.143211
\(716\) −1.08899e13 −1.54851
\(717\) −2.98853e10 −0.00422300
\(718\) 8.71754e12 1.22415
\(719\) −8.32682e12 −1.16198 −0.580991 0.813910i \(-0.697335\pi\)
−0.580991 + 0.813910i \(0.697335\pi\)
\(720\) −1.08730e12 −0.150783
\(721\) 1.40570e12 0.193724
\(722\) 1.06066e13 1.45264
\(723\) 4.63616e12 0.631009
\(724\) −1.46487e13 −1.98141
\(725\) −3.41918e12 −0.459622
\(726\) 5.71692e12 0.763743
\(727\) 1.05665e13 1.40290 0.701450 0.712719i \(-0.252537\pi\)
0.701450 + 0.712719i \(0.252537\pi\)
\(728\) 9.18623e12 1.21212
\(729\) 2.82430e11 0.0370370
\(730\) −5.14684e12 −0.670792
\(731\) −1.81864e13 −2.35569
\(732\) −1.05618e13 −1.35968
\(733\) 8.59093e11 0.109919 0.0549595 0.998489i \(-0.482497\pi\)
0.0549595 + 0.998489i \(0.482497\pi\)
\(734\) −1.47201e13 −1.87188
\(735\) 2.54500e12 0.321658
\(736\) −1.67802e12 −0.210788
\(737\) 5.51383e12 0.688415
\(738\) 7.79597e12 0.967424
\(739\) 1.46767e13 1.81021 0.905105 0.425189i \(-0.139792\pi\)
0.905105 + 0.425189i \(0.139792\pi\)
\(740\) 9.63156e12 1.18074
\(741\) −3.45248e12 −0.420678
\(742\) 3.71346e13 4.49740
\(743\) 7.23429e12 0.870856 0.435428 0.900224i \(-0.356597\pi\)
0.435428 + 0.900224i \(0.356597\pi\)
\(744\) −5.85560e12 −0.700638
\(745\) 3.84203e12 0.456938
\(746\) 1.68051e13 1.98662
\(747\) −2.73448e12 −0.321316
\(748\) −1.47891e13 −1.72737
\(749\) −1.83262e13 −2.12767
\(750\) −8.09185e12 −0.933839
\(751\) 2.69122e12 0.308723 0.154361 0.988014i \(-0.450668\pi\)
0.154361 + 0.988014i \(0.450668\pi\)
\(752\) −4.63448e12 −0.528471
\(753\) 4.75084e12 0.538509
\(754\) 5.45506e12 0.614651
\(755\) −3.70846e12 −0.415367
\(756\) −4.72331e12 −0.525894
\(757\) 1.82924e12 0.202460 0.101230 0.994863i \(-0.467722\pi\)
0.101230 + 0.994863i \(0.467722\pi\)
\(758\) −2.34641e13 −2.58162
\(759\) −2.44960e12 −0.267921
\(760\) −1.12059e13 −1.21839
\(761\) −1.71665e12 −0.185545 −0.0927727 0.995687i \(-0.529573\pi\)
−0.0927727 + 0.995687i \(0.529573\pi\)
\(762\) −1.64104e12 −0.176328
\(763\) 5.77097e12 0.616436
\(764\) −7.26615e12 −0.771586
\(765\) 3.30696e12 0.349102
\(766\) −9.97870e12 −1.04724
\(767\) 6.68829e11 0.0697808
\(768\) 1.06332e13 1.10291
\(769\) 3.03361e12 0.312817 0.156409 0.987692i \(-0.450008\pi\)
0.156409 + 0.987692i \(0.450008\pi\)
\(770\) −6.30651e12 −0.646518
\(771\) 2.36894e12 0.241440
\(772\) −2.30442e13 −2.33498
\(773\) −4.55357e12 −0.458717 −0.229358 0.973342i \(-0.573663\pi\)
−0.229358 + 0.973342i \(0.573663\pi\)
\(774\) 7.17922e12 0.719024
\(775\) −5.22670e12 −0.520439
\(776\) 1.45657e13 1.44196
\(777\) 9.03331e12 0.889104
\(778\) −3.44470e13 −3.37088
\(779\) 2.36718e13 2.30310
\(780\) 3.46466e12 0.335146
\(781\) −8.52581e12 −0.819985
\(782\) −3.25860e13 −3.11602
\(783\) −1.35500e12 −0.128828
\(784\) 8.50665e12 0.804149
\(785\) 1.84573e12 0.173482
\(786\) 1.58655e13 1.48269
\(787\) −1.85363e13 −1.72241 −0.861205 0.508258i \(-0.830289\pi\)
−0.861205 + 0.508258i \(0.830289\pi\)
\(788\) 1.52561e13 1.40953
\(789\) 3.19409e11 0.0293428
\(790\) 1.10442e12 0.100882
\(791\) −1.95337e13 −1.77415
\(792\) 2.82035e12 0.254706
\(793\) 7.26611e12 0.652488
\(794\) 2.86862e13 2.56142
\(795\) 6.76601e12 0.600732
\(796\) −3.57277e12 −0.315425
\(797\) 4.37734e12 0.384280 0.192140 0.981368i \(-0.438457\pi\)
0.192140 + 0.981368i \(0.438457\pi\)
\(798\) −2.17554e13 −1.89913
\(799\) 1.40955e13 1.22355
\(800\) 1.72448e12 0.148852
\(801\) 7.23215e12 0.620756
\(802\) −2.14285e13 −1.82897
\(803\) 3.93330e12 0.333839
\(804\) −1.90880e13 −1.61105
\(805\) −9.16051e12 −0.768844
\(806\) 8.33883e12 0.695981
\(807\) 2.91458e12 0.241905
\(808\) 2.74469e13 2.26539
\(809\) −9.22845e12 −0.757461 −0.378730 0.925507i \(-0.623639\pi\)
−0.378730 + 0.925507i \(0.623639\pi\)
\(810\) −1.30545e12 −0.106556
\(811\) 1.34091e13 1.08844 0.544222 0.838941i \(-0.316825\pi\)
0.544222 + 0.838941i \(0.316825\pi\)
\(812\) 2.26608e13 1.82925
\(813\) 2.41498e12 0.193868
\(814\) −1.11653e13 −0.891379
\(815\) −7.28002e12 −0.577994
\(816\) 1.10535e13 0.872760
\(817\) 2.17991e13 1.71175
\(818\) 4.10578e12 0.320631
\(819\) 3.24946e12 0.252367
\(820\) −2.37553e13 −1.83484
\(821\) −4.11930e11 −0.0316431 −0.0158216 0.999875i \(-0.505036\pi\)
−0.0158216 + 0.999875i \(0.505036\pi\)
\(822\) 2.19246e13 1.67498
\(823\) 1.90727e13 1.44915 0.724573 0.689198i \(-0.242037\pi\)
0.724573 + 0.689198i \(0.242037\pi\)
\(824\) 2.90572e12 0.219574
\(825\) 2.51743e12 0.189197
\(826\) 4.21454e12 0.315021
\(827\) −5.32819e12 −0.396100 −0.198050 0.980192i \(-0.563461\pi\)
−0.198050 + 0.980192i \(0.563461\pi\)
\(828\) 8.48012e12 0.626997
\(829\) −7.10890e12 −0.522766 −0.261383 0.965235i \(-0.584178\pi\)
−0.261383 + 0.965235i \(0.584178\pi\)
\(830\) 1.26393e13 0.924427
\(831\) −5.79704e11 −0.0421698
\(832\) −8.73740e12 −0.632160
\(833\) −2.58725e13 −1.86181
\(834\) 3.61100e12 0.258452
\(835\) −2.38998e12 −0.170140
\(836\) 1.77269e13 1.25518
\(837\) −2.07131e12 −0.145875
\(838\) 2.10040e13 1.47131
\(839\) −2.40461e13 −1.67539 −0.837694 0.546141i \(-0.816096\pi\)
−0.837694 + 0.546141i \(0.816096\pi\)
\(840\) 1.05469e13 0.730920
\(841\) −8.00631e12 −0.551887
\(842\) 2.00130e13 1.37217
\(843\) −8.21001e12 −0.559912
\(844\) 1.84983e13 1.25485
\(845\) 5.91307e12 0.398986
\(846\) −5.56432e12 −0.373461
\(847\) −1.63381e13 −1.09076
\(848\) 2.26154e13 1.50184
\(849\) −5.25161e12 −0.346903
\(850\) 3.34883e13 2.20043
\(851\) −1.62182e13 −1.06003
\(852\) 2.95149e13 1.91895
\(853\) 1.82317e13 1.17911 0.589557 0.807727i \(-0.299302\pi\)
0.589557 + 0.807727i \(0.299302\pi\)
\(854\) 4.57865e13 2.94562
\(855\) −3.96388e12 −0.253672
\(856\) −3.78821e13 −2.41158
\(857\) 1.43832e13 0.910838 0.455419 0.890277i \(-0.349489\pi\)
0.455419 + 0.890277i \(0.349489\pi\)
\(858\) −4.01639e12 −0.253013
\(859\) 2.27585e13 1.42618 0.713089 0.701074i \(-0.247296\pi\)
0.713089 + 0.701074i \(0.247296\pi\)
\(860\) −2.18760e13 −1.36372
\(861\) −2.22798e13 −1.38165
\(862\) −1.98536e13 −1.22477
\(863\) 5.25755e12 0.322652 0.161326 0.986901i \(-0.448423\pi\)
0.161326 + 0.986901i \(0.448423\pi\)
\(864\) 6.83403e11 0.0417220
\(865\) −1.26380e13 −0.767547
\(866\) 1.86719e13 1.12813
\(867\) −2.40131e13 −1.44332
\(868\) 3.46403e13 2.07130
\(869\) −8.44020e11 −0.0502069
\(870\) 6.26309e12 0.370640
\(871\) 1.31318e13 0.773113
\(872\) 1.19292e13 0.698694
\(873\) 5.15234e12 0.300220
\(874\) 3.90591e13 2.26423
\(875\) 2.31254e13 1.33368
\(876\) −1.36164e13 −0.781260
\(877\) −2.87054e13 −1.63857 −0.819287 0.573384i \(-0.805630\pi\)
−0.819287 + 0.573384i \(0.805630\pi\)
\(878\) −4.39890e13 −2.49815
\(879\) 1.48745e13 0.840414
\(880\) −3.84074e12 −0.215895
\(881\) −1.61488e13 −0.903128 −0.451564 0.892239i \(-0.649134\pi\)
−0.451564 + 0.892239i \(0.649134\pi\)
\(882\) 1.02134e13 0.568278
\(883\) 1.27707e13 0.706957 0.353478 0.935443i \(-0.384999\pi\)
0.353478 + 0.935443i \(0.384999\pi\)
\(884\) −3.52219e13 −1.93989
\(885\) 7.67899e11 0.0420784
\(886\) 1.02119e13 0.556743
\(887\) −2.89772e13 −1.57181 −0.785905 0.618347i \(-0.787803\pi\)
−0.785905 + 0.618347i \(0.787803\pi\)
\(888\) 1.86728e13 1.00775
\(889\) 4.68985e12 0.251826
\(890\) −3.34285e13 −1.78592
\(891\) 9.97645e11 0.0530306
\(892\) 4.30412e13 2.27637
\(893\) −1.68956e13 −0.889082
\(894\) 1.54185e13 0.807280
\(895\) 8.60154e12 0.448098
\(896\) −4.91498e13 −2.54763
\(897\) −5.83400e12 −0.300885
\(898\) 1.52211e13 0.781090
\(899\) 9.93745e12 0.507407
\(900\) −8.71494e12 −0.442765
\(901\) −6.87836e13 −3.47715
\(902\) 2.75382e13 1.38518
\(903\) −2.05172e13 −1.02689
\(904\) −4.03782e13 −2.01090
\(905\) 1.15705e13 0.573368
\(906\) −1.48825e13 −0.733836
\(907\) −3.02300e13 −1.48322 −0.741609 0.670833i \(-0.765937\pi\)
−0.741609 + 0.670833i \(0.765937\pi\)
\(908\) 5.05369e13 2.46730
\(909\) 9.70884e12 0.471661
\(910\) −1.50197e13 −0.726062
\(911\) −1.91108e13 −0.919278 −0.459639 0.888106i \(-0.652021\pi\)
−0.459639 + 0.888106i \(0.652021\pi\)
\(912\) −1.32493e13 −0.634184
\(913\) −9.65919e12 −0.460068
\(914\) −7.90688e12 −0.374755
\(915\) 8.34241e12 0.393456
\(916\) −7.61330e13 −3.57309
\(917\) −4.53412e13 −2.11754
\(918\) 1.32712e13 0.616764
\(919\) −2.36415e13 −1.09334 −0.546670 0.837348i \(-0.684105\pi\)
−0.546670 + 0.837348i \(0.684105\pi\)
\(920\) −1.89357e13 −0.871438
\(921\) 2.68582e12 0.123001
\(922\) 1.83112e13 0.834501
\(923\) −2.03052e13 −0.920871
\(924\) −1.66845e13 −0.752989
\(925\) 1.66673e13 0.748561
\(926\) 5.45797e13 2.43939
\(927\) 1.02784e12 0.0457160
\(928\) −3.27873e12 −0.145124
\(929\) 2.93560e13 1.29308 0.646542 0.762878i \(-0.276215\pi\)
0.646542 + 0.762878i \(0.276215\pi\)
\(930\) 9.57402e12 0.419683
\(931\) 3.10121e13 1.35287
\(932\) 8.05118e12 0.349533
\(933\) 2.36011e13 1.01968
\(934\) 7.71205e13 3.31596
\(935\) 1.16814e13 0.499853
\(936\) 6.71697e12 0.286043
\(937\) 7.21413e12 0.305742 0.152871 0.988246i \(-0.451148\pi\)
0.152871 + 0.988246i \(0.451148\pi\)
\(938\) 8.27485e13 3.49017
\(939\) −1.39810e13 −0.586871
\(940\) 1.69552e13 0.708316
\(941\) −6.11502e12 −0.254240 −0.127120 0.991887i \(-0.540573\pi\)
−0.127120 + 0.991887i \(0.540573\pi\)
\(942\) 7.40715e12 0.306494
\(943\) 4.00006e13 1.64727
\(944\) 2.56670e12 0.105197
\(945\) 3.73078e12 0.152180
\(946\) 2.53597e13 1.02952
\(947\) 4.26509e13 1.72327 0.861635 0.507528i \(-0.169441\pi\)
0.861635 + 0.507528i \(0.169441\pi\)
\(948\) 2.92186e12 0.117496
\(949\) 9.36760e12 0.374913
\(950\) −4.01407e13 −1.59893
\(951\) 9.05592e12 0.359021
\(952\) −1.07221e14 −4.23070
\(953\) −1.29373e13 −0.508071 −0.254035 0.967195i \(-0.581758\pi\)
−0.254035 + 0.967195i \(0.581758\pi\)
\(954\) 2.71528e13 1.06132
\(955\) 5.73929e12 0.223276
\(956\) 3.65451e11 0.0141504
\(957\) −4.78636e12 −0.184460
\(958\) 3.74840e13 1.43781
\(959\) −6.26574e13 −2.39215
\(960\) −1.00316e13 −0.381198
\(961\) −1.12488e13 −0.425453
\(962\) −2.65915e13 −1.00105
\(963\) −1.34001e13 −0.502099
\(964\) −5.66931e13 −2.11438
\(965\) 1.82018e13 0.675681
\(966\) −3.67622e13 −1.35833
\(967\) 3.65748e13 1.34513 0.672563 0.740040i \(-0.265193\pi\)
0.672563 + 0.740040i \(0.265193\pi\)
\(968\) −3.37726e13 −1.23631
\(969\) 4.02970e13 1.46830
\(970\) −2.38152e13 −0.863735
\(971\) −2.65482e13 −0.958404 −0.479202 0.877705i \(-0.659074\pi\)
−0.479202 + 0.877705i \(0.659074\pi\)
\(972\) −3.45368e12 −0.124104
\(973\) −1.03197e13 −0.369114
\(974\) 3.99643e12 0.142284
\(975\) 5.99555e12 0.212475
\(976\) 2.78845e13 0.983646
\(977\) −4.69416e13 −1.64828 −0.824142 0.566383i \(-0.808342\pi\)
−0.824142 + 0.566383i \(0.808342\pi\)
\(978\) −2.92156e13 −1.02115
\(979\) 2.55466e13 0.888814
\(980\) −3.11214e13 −1.07781
\(981\) 4.21973e12 0.145470
\(982\) 3.81342e13 1.30862
\(983\) −2.90451e13 −0.992161 −0.496081 0.868276i \(-0.665228\pi\)
−0.496081 + 0.868276i \(0.665228\pi\)
\(984\) −4.60547e13 −1.56601
\(985\) −1.20503e13 −0.407881
\(986\) −6.36709e13 −2.14533
\(987\) 1.59020e13 0.533366
\(988\) 4.22186e13 1.40961
\(989\) 3.68361e13 1.22431
\(990\) −4.61132e12 −0.152569
\(991\) −1.03200e13 −0.339898 −0.169949 0.985453i \(-0.554360\pi\)
−0.169949 + 0.985453i \(0.554360\pi\)
\(992\) −5.01201e12 −0.164327
\(993\) 2.81086e13 0.917419
\(994\) −1.27950e14 −4.15722
\(995\) 2.82201e12 0.0912756
\(996\) 3.34385e13 1.07666
\(997\) 2.28352e13 0.731940 0.365970 0.930627i \(-0.380737\pi\)
0.365970 + 0.930627i \(0.380737\pi\)
\(998\) 1.53339e13 0.489289
\(999\) 6.60516e12 0.209816
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.1.20 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.20 22 1.1 even 1 trivial