Properties

Label 177.10.a.c.1.12
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 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.33644 q^{2} -81.0000 q^{3} -510.214 q^{4} +2090.38 q^{5} -108.251 q^{6} +107.167 q^{7} -1366.13 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+1.33644 q^{2} -81.0000 q^{3} -510.214 q^{4} +2090.38 q^{5} -108.251 q^{6} +107.167 q^{7} -1366.13 q^{8} +6561.00 q^{9} +2793.66 q^{10} -839.126 q^{11} +41327.3 q^{12} +34005.3 q^{13} +143.222 q^{14} -169321. q^{15} +259404. q^{16} -84723.3 q^{17} +8768.37 q^{18} +928571. q^{19} -1.06654e6 q^{20} -8680.50 q^{21} -1121.44 q^{22} -971930. q^{23} +110656. q^{24} +2.41656e6 q^{25} +45445.9 q^{26} -531441. q^{27} -54677.9 q^{28} +534314. q^{29} -226287. q^{30} -1.99772e6 q^{31} +1.04613e6 q^{32} +67969.2 q^{33} -113227. q^{34} +224019. q^{35} -3.34751e6 q^{36} -9.60421e6 q^{37} +1.24098e6 q^{38} -2.75443e6 q^{39} -2.85572e6 q^{40} +1.18062e7 q^{41} -11600.9 q^{42} -1.85229e7 q^{43} +428134. q^{44} +1.37150e7 q^{45} -1.29892e6 q^{46} -1.01847e7 q^{47} -2.10117e7 q^{48} -4.03421e7 q^{49} +3.22958e6 q^{50} +6.86258e6 q^{51} -1.73500e7 q^{52} -3.57403e7 q^{53} -710238. q^{54} -1.75409e6 q^{55} -146403. q^{56} -7.52143e7 q^{57} +714077. q^{58} +1.21174e7 q^{59} +8.63898e7 q^{60} -6.03548e7 q^{61} -2.66983e6 q^{62} +703120. q^{63} -1.31417e8 q^{64} +7.10839e7 q^{65} +90836.6 q^{66} +2.83501e8 q^{67} +4.32270e7 q^{68} +7.87263e7 q^{69} +299387. q^{70} +3.57688e8 q^{71} -8.96315e6 q^{72} +3.74577e8 q^{73} -1.28354e7 q^{74} -1.95741e8 q^{75} -4.73770e8 q^{76} -89926.3 q^{77} -3.68112e6 q^{78} +6.00766e7 q^{79} +5.42252e8 q^{80} +4.30467e7 q^{81} +1.57783e7 q^{82} +6.16047e8 q^{83} +4.42891e6 q^{84} -1.77104e8 q^{85} -2.47547e7 q^{86} -4.32794e7 q^{87} +1.14635e6 q^{88} +1.58856e8 q^{89} +1.83292e7 q^{90} +3.64423e6 q^{91} +4.95892e8 q^{92} +1.61815e8 q^{93} -1.36113e7 q^{94} +1.94107e9 q^{95} -8.47368e7 q^{96} +1.10346e9 q^{97} -5.39147e7 q^{98} -5.50551e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33644 0.0590628 0.0295314 0.999564i \(-0.490599\pi\)
0.0295314 + 0.999564i \(0.490599\pi\)
\(3\) −81.0000 −0.577350
\(4\) −510.214 −0.996512
\(5\) 2090.38 1.49575 0.747877 0.663838i \(-0.231073\pi\)
0.747877 + 0.663838i \(0.231073\pi\)
\(6\) −108.251 −0.0340999
\(7\) 107.167 0.0168701 0.00843506 0.999964i \(-0.497315\pi\)
0.00843506 + 0.999964i \(0.497315\pi\)
\(8\) −1366.13 −0.117919
\(9\) 6561.00 0.333333
\(10\) 2793.66 0.0883433
\(11\) −839.126 −0.0172807 −0.00864033 0.999963i \(-0.502750\pi\)
−0.00864033 + 0.999963i \(0.502750\pi\)
\(12\) 41327.3 0.575336
\(13\) 34005.3 0.330218 0.165109 0.986275i \(-0.447202\pi\)
0.165109 + 0.986275i \(0.447202\pi\)
\(14\) 143.222 0.000996396 0
\(15\) −169321. −0.863574
\(16\) 259404. 0.989547
\(17\) −84723.3 −0.246027 −0.123013 0.992405i \(-0.539256\pi\)
−0.123013 + 0.992405i \(0.539256\pi\)
\(18\) 8768.37 0.0196876
\(19\) 928571. 1.63465 0.817323 0.576179i \(-0.195457\pi\)
0.817323 + 0.576179i \(0.195457\pi\)
\(20\) −1.06654e6 −1.49054
\(21\) −8680.50 −0.00973997
\(22\) −1121.44 −0.00102064
\(23\) −971930. −0.724202 −0.362101 0.932139i \(-0.617940\pi\)
−0.362101 + 0.932139i \(0.617940\pi\)
\(24\) 110656. 0.0680808
\(25\) 2.41656e6 1.23728
\(26\) 45445.9 0.0195036
\(27\) −531441. −0.192450
\(28\) −54677.9 −0.0168113
\(29\) 534314. 0.140283 0.0701415 0.997537i \(-0.477655\pi\)
0.0701415 + 0.997537i \(0.477655\pi\)
\(30\) −226287. −0.0510050
\(31\) −1.99772e6 −0.388514 −0.194257 0.980951i \(-0.562230\pi\)
−0.194257 + 0.980951i \(0.562230\pi\)
\(32\) 1.04613e6 0.176365
\(33\) 67969.2 0.00997699
\(34\) −113227. −0.0145310
\(35\) 224019. 0.0252335
\(36\) −3.34751e6 −0.332171
\(37\) −9.60421e6 −0.842469 −0.421235 0.906952i \(-0.638403\pi\)
−0.421235 + 0.906952i \(0.638403\pi\)
\(38\) 1.24098e6 0.0965468
\(39\) −2.75443e6 −0.190652
\(40\) −2.85572e6 −0.176378
\(41\) 1.18062e7 0.652506 0.326253 0.945283i \(-0.394214\pi\)
0.326253 + 0.945283i \(0.394214\pi\)
\(42\) −11600.9 −0.000575270 0
\(43\) −1.85229e7 −0.826230 −0.413115 0.910679i \(-0.635559\pi\)
−0.413115 + 0.910679i \(0.635559\pi\)
\(44\) 428134. 0.0172204
\(45\) 1.37150e7 0.498584
\(46\) −1.29892e6 −0.0427734
\(47\) −1.01847e7 −0.304445 −0.152223 0.988346i \(-0.548643\pi\)
−0.152223 + 0.988346i \(0.548643\pi\)
\(48\) −2.10117e7 −0.571315
\(49\) −4.03421e7 −0.999715
\(50\) 3.22958e6 0.0730771
\(51\) 6.86258e6 0.142044
\(52\) −1.73500e7 −0.329066
\(53\) −3.57403e7 −0.622181 −0.311090 0.950380i \(-0.600694\pi\)
−0.311090 + 0.950380i \(0.600694\pi\)
\(54\) −710238. −0.0113666
\(55\) −1.75409e6 −0.0258476
\(56\) −146403. −0.00198932
\(57\) −7.52143e7 −0.943764
\(58\) 714077. 0.00828551
\(59\) 1.21174e7 0.130189
\(60\) 8.63898e7 0.860561
\(61\) −6.03548e7 −0.558120 −0.279060 0.960274i \(-0.590023\pi\)
−0.279060 + 0.960274i \(0.590023\pi\)
\(62\) −2.66983e6 −0.0229467
\(63\) 703120. 0.00562338
\(64\) −1.31417e8 −0.979130
\(65\) 7.10839e7 0.493925
\(66\) 90836.6 0.000589268 0
\(67\) 2.83501e8 1.71877 0.859386 0.511327i \(-0.170846\pi\)
0.859386 + 0.511327i \(0.170846\pi\)
\(68\) 4.32270e7 0.245169
\(69\) 7.87263e7 0.418118
\(70\) 299387. 0.00149036
\(71\) 3.57688e8 1.67048 0.835241 0.549884i \(-0.185328\pi\)
0.835241 + 0.549884i \(0.185328\pi\)
\(72\) −8.96315e6 −0.0393065
\(73\) 3.74577e8 1.54379 0.771895 0.635750i \(-0.219309\pi\)
0.771895 + 0.635750i \(0.219309\pi\)
\(74\) −1.28354e7 −0.0497585
\(75\) −1.95741e8 −0.714343
\(76\) −4.73770e8 −1.62894
\(77\) −89926.3 −0.000291527 0
\(78\) −3.68112e6 −0.0112604
\(79\) 6.00766e7 0.173534 0.0867668 0.996229i \(-0.472346\pi\)
0.0867668 + 0.996229i \(0.472346\pi\)
\(80\) 5.42252e8 1.48012
\(81\) 4.30467e7 0.111111
\(82\) 1.57783e7 0.0385388
\(83\) 6.16047e8 1.42483 0.712414 0.701759i \(-0.247602\pi\)
0.712414 + 0.701759i \(0.247602\pi\)
\(84\) 4.42891e6 0.00970599
\(85\) −1.77104e8 −0.367995
\(86\) −2.47547e7 −0.0487994
\(87\) −4.32794e7 −0.0809925
\(88\) 1.14635e6 0.00203773
\(89\) 1.58856e8 0.268379 0.134189 0.990956i \(-0.457157\pi\)
0.134189 + 0.990956i \(0.457157\pi\)
\(90\) 1.83292e7 0.0294478
\(91\) 3.64423e6 0.00557083
\(92\) 4.95892e8 0.721676
\(93\) 1.61815e8 0.224309
\(94\) −1.36113e7 −0.0179814
\(95\) 1.94107e9 2.44503
\(96\) −8.47368e7 −0.101824
\(97\) 1.10346e9 1.26557 0.632784 0.774328i \(-0.281912\pi\)
0.632784 + 0.774328i \(0.281912\pi\)
\(98\) −5.39147e7 −0.0590460
\(99\) −5.50551e6 −0.00576022
\(100\) −1.23296e9 −1.23296
\(101\) −2.92749e7 −0.0279930 −0.0139965 0.999902i \(-0.504455\pi\)
−0.0139965 + 0.999902i \(0.504455\pi\)
\(102\) 9.17142e6 0.00838949
\(103\) −5.30706e8 −0.464608 −0.232304 0.972643i \(-0.574626\pi\)
−0.232304 + 0.972643i \(0.574626\pi\)
\(104\) −4.64555e7 −0.0389392
\(105\) −1.81455e7 −0.0145686
\(106\) −4.77646e7 −0.0367477
\(107\) −1.46128e9 −1.07772 −0.538860 0.842395i \(-0.681145\pi\)
−0.538860 + 0.842395i \(0.681145\pi\)
\(108\) 2.71149e8 0.191779
\(109\) −6.89292e8 −0.467718 −0.233859 0.972271i \(-0.575135\pi\)
−0.233859 + 0.972271i \(0.575135\pi\)
\(110\) −2.34423e6 −0.00152663
\(111\) 7.77941e8 0.486400
\(112\) 2.77994e7 0.0166938
\(113\) 1.55105e9 0.894899 0.447450 0.894309i \(-0.352332\pi\)
0.447450 + 0.894309i \(0.352332\pi\)
\(114\) −1.00519e8 −0.0557413
\(115\) −2.03170e9 −1.08323
\(116\) −2.72614e8 −0.139794
\(117\) 2.23109e8 0.110073
\(118\) 1.61941e7 0.00768932
\(119\) −9.07950e6 −0.00415050
\(120\) 2.31313e8 0.101832
\(121\) −2.35724e9 −0.999701
\(122\) −8.06605e7 −0.0329641
\(123\) −9.56305e8 −0.376724
\(124\) 1.01926e9 0.387159
\(125\) 9.68752e8 0.354909
\(126\) 939676. 0.000332132 0
\(127\) 5.03627e9 1.71788 0.858939 0.512078i \(-0.171124\pi\)
0.858939 + 0.512078i \(0.171124\pi\)
\(128\) −7.11250e8 −0.234195
\(129\) 1.50035e9 0.477024
\(130\) 9.49992e7 0.0291726
\(131\) 1.31283e9 0.389482 0.194741 0.980855i \(-0.437613\pi\)
0.194741 + 0.980855i \(0.437613\pi\)
\(132\) −3.46788e7 −0.00994218
\(133\) 9.95118e7 0.0275767
\(134\) 3.78882e8 0.101515
\(135\) −1.11091e9 −0.287858
\(136\) 1.15743e8 0.0290114
\(137\) 1.89177e9 0.458803 0.229401 0.973332i \(-0.426323\pi\)
0.229401 + 0.973332i \(0.426323\pi\)
\(138\) 1.05213e8 0.0246952
\(139\) 4.40133e9 1.00004 0.500020 0.866014i \(-0.333326\pi\)
0.500020 + 0.866014i \(0.333326\pi\)
\(140\) −1.14298e8 −0.0251455
\(141\) 8.24963e8 0.175772
\(142\) 4.78028e8 0.0986632
\(143\) −2.85347e7 −0.00570639
\(144\) 1.70195e9 0.329849
\(145\) 1.11692e9 0.209829
\(146\) 5.00599e8 0.0911805
\(147\) 3.26771e9 0.577186
\(148\) 4.90020e9 0.839530
\(149\) 1.12491e10 1.86973 0.934865 0.355002i \(-0.115520\pi\)
0.934865 + 0.355002i \(0.115520\pi\)
\(150\) −2.61596e8 −0.0421911
\(151\) −1.01153e9 −0.158337 −0.0791685 0.996861i \(-0.525227\pi\)
−0.0791685 + 0.996861i \(0.525227\pi\)
\(152\) −1.26854e9 −0.192757
\(153\) −5.55869e8 −0.0820089
\(154\) −120181. −1.72184e−5 0
\(155\) −4.17599e9 −0.581121
\(156\) 1.40535e9 0.189987
\(157\) 5.95184e9 0.781813 0.390906 0.920430i \(-0.372162\pi\)
0.390906 + 0.920430i \(0.372162\pi\)
\(158\) 8.02887e7 0.0102494
\(159\) 2.89496e9 0.359216
\(160\) 2.18681e9 0.263798
\(161\) −1.04158e8 −0.0122174
\(162\) 5.75293e7 0.00656253
\(163\) 1.40093e10 1.55443 0.777216 0.629233i \(-0.216631\pi\)
0.777216 + 0.629233i \(0.216631\pi\)
\(164\) −6.02371e9 −0.650229
\(165\) 1.42081e8 0.0149231
\(166\) 8.23309e8 0.0841543
\(167\) 1.03853e9 0.103322 0.0516612 0.998665i \(-0.483548\pi\)
0.0516612 + 0.998665i \(0.483548\pi\)
\(168\) 1.18586e7 0.00114853
\(169\) −9.44814e9 −0.890956
\(170\) −2.36688e8 −0.0217348
\(171\) 6.09235e9 0.544882
\(172\) 9.45064e9 0.823347
\(173\) 1.27196e9 0.107961 0.0539804 0.998542i \(-0.482809\pi\)
0.0539804 + 0.998542i \(0.482809\pi\)
\(174\) −5.78402e7 −0.00478364
\(175\) 2.58974e8 0.0208730
\(176\) −2.17672e8 −0.0171000
\(177\) −9.81506e8 −0.0751646
\(178\) 2.12301e8 0.0158512
\(179\) 4.05826e9 0.295462 0.147731 0.989028i \(-0.452803\pi\)
0.147731 + 0.989028i \(0.452803\pi\)
\(180\) −6.99757e9 −0.496845
\(181\) 1.52164e8 0.0105380 0.00526900 0.999986i \(-0.498323\pi\)
0.00526900 + 0.999986i \(0.498323\pi\)
\(182\) 4.87029e6 0.000329028 0
\(183\) 4.88874e9 0.322231
\(184\) 1.32778e9 0.0853975
\(185\) −2.00764e10 −1.26013
\(186\) 2.16256e8 0.0132483
\(187\) 7.10935e7 0.00425150
\(188\) 5.19639e9 0.303383
\(189\) −5.69527e7 −0.00324666
\(190\) 2.59411e9 0.144410
\(191\) −1.40242e10 −0.762481 −0.381241 0.924476i \(-0.624503\pi\)
−0.381241 + 0.924476i \(0.624503\pi\)
\(192\) 1.06447e10 0.565301
\(193\) 8.79613e9 0.456335 0.228167 0.973622i \(-0.426727\pi\)
0.228167 + 0.973622i \(0.426727\pi\)
\(194\) 1.47471e9 0.0747480
\(195\) −5.75780e9 −0.285168
\(196\) 2.05831e10 0.996228
\(197\) −1.58607e10 −0.750281 −0.375140 0.926968i \(-0.622405\pi\)
−0.375140 + 0.926968i \(0.622405\pi\)
\(198\) −7.35777e6 −0.000340214 0
\(199\) 1.69260e8 0.00765094 0.00382547 0.999993i \(-0.498782\pi\)
0.00382547 + 0.999993i \(0.498782\pi\)
\(200\) −3.30132e9 −0.145899
\(201\) −2.29636e10 −0.992334
\(202\) −3.91241e7 −0.00165334
\(203\) 5.72606e7 0.00236659
\(204\) −3.50139e9 −0.141548
\(205\) 2.46795e10 0.975987
\(206\) −7.09255e8 −0.0274410
\(207\) −6.37683e9 −0.241401
\(208\) 8.82110e9 0.326767
\(209\) −7.79188e8 −0.0282478
\(210\) −2.42504e7 −0.000860461 0
\(211\) −3.98459e10 −1.38393 −0.691963 0.721933i \(-0.743254\pi\)
−0.691963 + 0.721933i \(0.743254\pi\)
\(212\) 1.82352e10 0.620010
\(213\) −2.89727e10 −0.964453
\(214\) −1.95291e9 −0.0636531
\(215\) −3.87199e10 −1.23584
\(216\) 7.26015e8 0.0226936
\(217\) −2.14089e8 −0.00655428
\(218\) −9.21196e8 −0.0276247
\(219\) −3.03407e10 −0.891307
\(220\) 8.94962e8 0.0257574
\(221\) −2.88104e9 −0.0812426
\(222\) 1.03967e9 0.0287281
\(223\) 3.61870e10 0.979897 0.489949 0.871751i \(-0.337016\pi\)
0.489949 + 0.871751i \(0.337016\pi\)
\(224\) 1.12111e8 0.00297530
\(225\) 1.58550e10 0.412426
\(226\) 2.07289e9 0.0528552
\(227\) 3.37796e10 0.844381 0.422191 0.906507i \(-0.361261\pi\)
0.422191 + 0.906507i \(0.361261\pi\)
\(228\) 3.83754e10 0.940472
\(229\) −2.50877e10 −0.602838 −0.301419 0.953492i \(-0.597460\pi\)
−0.301419 + 0.953492i \(0.597460\pi\)
\(230\) −2.71524e9 −0.0639784
\(231\) 7.28403e6 0.000168313 0
\(232\) −7.29939e8 −0.0165421
\(233\) 3.91412e10 0.870027 0.435014 0.900424i \(-0.356744\pi\)
0.435014 + 0.900424i \(0.356744\pi\)
\(234\) 2.98171e8 0.00650120
\(235\) −2.12899e10 −0.455375
\(236\) −6.18245e9 −0.129735
\(237\) −4.86621e9 −0.100190
\(238\) −1.21342e7 −0.000245140 0
\(239\) 7.66958e10 1.52048 0.760241 0.649642i \(-0.225081\pi\)
0.760241 + 0.649642i \(0.225081\pi\)
\(240\) −4.39224e10 −0.854547
\(241\) −2.55250e10 −0.487405 −0.243702 0.969850i \(-0.578362\pi\)
−0.243702 + 0.969850i \(0.578362\pi\)
\(242\) −3.15031e9 −0.0590451
\(243\) −3.48678e9 −0.0641500
\(244\) 3.07939e10 0.556173
\(245\) −8.43303e10 −1.49533
\(246\) −1.27804e9 −0.0222504
\(247\) 3.15763e10 0.539790
\(248\) 2.72914e9 0.0458134
\(249\) −4.98998e10 −0.822625
\(250\) 1.29468e9 0.0209619
\(251\) 1.01377e11 1.61215 0.806076 0.591811i \(-0.201587\pi\)
0.806076 + 0.591811i \(0.201587\pi\)
\(252\) −3.58742e8 −0.00560376
\(253\) 8.15572e8 0.0125147
\(254\) 6.73066e9 0.101463
\(255\) 1.43454e10 0.212462
\(256\) 6.63348e10 0.965298
\(257\) −1.07253e10 −0.153360 −0.0766799 0.997056i \(-0.524432\pi\)
−0.0766799 + 0.997056i \(0.524432\pi\)
\(258\) 2.00513e9 0.0281744
\(259\) −1.02925e9 −0.0142126
\(260\) −3.62680e10 −0.492202
\(261\) 3.50563e9 0.0467610
\(262\) 1.75452e9 0.0230039
\(263\) −8.11509e10 −1.04591 −0.522953 0.852362i \(-0.675170\pi\)
−0.522953 + 0.852362i \(0.675170\pi\)
\(264\) −9.28545e7 −0.00117648
\(265\) −7.47107e10 −0.930629
\(266\) 1.32991e8 0.00162876
\(267\) −1.28673e10 −0.154948
\(268\) −1.44646e11 −1.71278
\(269\) −1.41843e10 −0.165166 −0.0825831 0.996584i \(-0.526317\pi\)
−0.0825831 + 0.996584i \(0.526317\pi\)
\(270\) −1.48467e9 −0.0170017
\(271\) 7.53268e10 0.848375 0.424188 0.905574i \(-0.360560\pi\)
0.424188 + 0.905574i \(0.360560\pi\)
\(272\) −2.19775e10 −0.243455
\(273\) −2.95183e8 −0.00321632
\(274\) 2.52824e9 0.0270982
\(275\) −2.02780e9 −0.0213810
\(276\) −4.01673e10 −0.416660
\(277\) −2.76122e10 −0.281801 −0.140900 0.990024i \(-0.545000\pi\)
−0.140900 + 0.990024i \(0.545000\pi\)
\(278\) 5.88210e9 0.0590651
\(279\) −1.31070e10 −0.129505
\(280\) −3.06038e8 −0.00297553
\(281\) −8.87886e10 −0.849531 −0.424765 0.905304i \(-0.639643\pi\)
−0.424765 + 0.905304i \(0.639643\pi\)
\(282\) 1.10251e9 0.0103816
\(283\) −1.21939e10 −0.113006 −0.0565032 0.998402i \(-0.517995\pi\)
−0.0565032 + 0.998402i \(0.517995\pi\)
\(284\) −1.82497e11 −1.66465
\(285\) −1.57226e11 −1.41164
\(286\) −3.81349e7 −0.000337035 0
\(287\) 1.26523e9 0.0110079
\(288\) 6.86368e9 0.0587883
\(289\) −1.11410e11 −0.939471
\(290\) 1.49269e9 0.0123931
\(291\) −8.93806e10 −0.730676
\(292\) −1.91114e11 −1.53840
\(293\) 6.57189e10 0.520938 0.260469 0.965482i \(-0.416123\pi\)
0.260469 + 0.965482i \(0.416123\pi\)
\(294\) 4.36709e9 0.0340902
\(295\) 2.53299e10 0.194730
\(296\) 1.31206e10 0.0993435
\(297\) 4.45946e8 0.00332566
\(298\) 1.50337e10 0.110431
\(299\) −3.30508e10 −0.239145
\(300\) 9.98699e10 0.711851
\(301\) −1.98504e9 −0.0139386
\(302\) −1.35185e9 −0.00935182
\(303\) 2.37127e9 0.0161618
\(304\) 2.40875e11 1.61756
\(305\) −1.26164e11 −0.834810
\(306\) −7.42885e8 −0.00484367
\(307\) −1.26973e11 −0.815808 −0.407904 0.913025i \(-0.633740\pi\)
−0.407904 + 0.913025i \(0.633740\pi\)
\(308\) 4.58816e7 0.000290510 0
\(309\) 4.29872e10 0.268241
\(310\) −5.58095e9 −0.0343226
\(311\) −1.42906e11 −0.866220 −0.433110 0.901341i \(-0.642584\pi\)
−0.433110 + 0.901341i \(0.642584\pi\)
\(312\) 3.76289e9 0.0224815
\(313\) −1.33349e11 −0.785308 −0.392654 0.919686i \(-0.628443\pi\)
−0.392654 + 0.919686i \(0.628443\pi\)
\(314\) 7.95426e9 0.0461760
\(315\) 1.46979e9 0.00841118
\(316\) −3.06519e10 −0.172928
\(317\) 2.43695e11 1.35544 0.677718 0.735322i \(-0.262969\pi\)
0.677718 + 0.735322i \(0.262969\pi\)
\(318\) 3.86894e9 0.0212163
\(319\) −4.48357e8 −0.00242418
\(320\) −2.74711e11 −1.46454
\(321\) 1.18364e11 0.622222
\(322\) −1.39201e8 −0.000721592 0
\(323\) −7.86716e10 −0.402167
\(324\) −2.19630e10 −0.110724
\(325\) 8.21757e10 0.408572
\(326\) 1.87225e10 0.0918091
\(327\) 5.58326e10 0.270037
\(328\) −1.61288e10 −0.0769431
\(329\) −1.09146e9 −0.00513603
\(330\) 1.89883e8 0.000881400 0
\(331\) 1.55235e11 0.710825 0.355413 0.934710i \(-0.384340\pi\)
0.355413 + 0.934710i \(0.384340\pi\)
\(332\) −3.14316e11 −1.41986
\(333\) −6.30132e10 −0.280823
\(334\) 1.38793e9 0.00610251
\(335\) 5.92625e11 2.57086
\(336\) −2.25175e9 −0.00963816
\(337\) −1.06540e11 −0.449963 −0.224981 0.974363i \(-0.572232\pi\)
−0.224981 + 0.974363i \(0.572232\pi\)
\(338\) −1.26269e10 −0.0526223
\(339\) −1.25635e11 −0.516670
\(340\) 9.03608e10 0.366712
\(341\) 1.67634e9 0.00671378
\(342\) 8.14205e9 0.0321823
\(343\) −8.64789e9 −0.0337355
\(344\) 2.53046e10 0.0974286
\(345\) 1.64568e11 0.625402
\(346\) 1.69989e9 0.00637646
\(347\) −3.12994e11 −1.15892 −0.579460 0.815001i \(-0.696736\pi\)
−0.579460 + 0.815001i \(0.696736\pi\)
\(348\) 2.20818e10 0.0807099
\(349\) 4.73312e11 1.70779 0.853893 0.520448i \(-0.174235\pi\)
0.853893 + 0.520448i \(0.174235\pi\)
\(350\) 3.46103e8 0.00123282
\(351\) −1.80718e10 −0.0635506
\(352\) −8.77838e8 −0.00304770
\(353\) −6.70290e10 −0.229761 −0.114881 0.993379i \(-0.536649\pi\)
−0.114881 + 0.993379i \(0.536649\pi\)
\(354\) −1.31172e9 −0.00443943
\(355\) 7.47703e11 2.49863
\(356\) −8.10504e10 −0.267442
\(357\) 7.35440e8 0.00239629
\(358\) 5.42361e9 0.0174508
\(359\) 4.49086e10 0.142694 0.0713468 0.997452i \(-0.477270\pi\)
0.0713468 + 0.997452i \(0.477270\pi\)
\(360\) −1.87364e10 −0.0587928
\(361\) 5.39557e11 1.67207
\(362\) 2.03358e8 0.000622403 0
\(363\) 1.90937e11 0.577178
\(364\) −1.85934e9 −0.00555139
\(365\) 7.83008e11 2.30913
\(366\) 6.53350e9 0.0190318
\(367\) 4.86775e11 1.40065 0.700327 0.713822i \(-0.253037\pi\)
0.700327 + 0.713822i \(0.253037\pi\)
\(368\) −2.52122e11 −0.716632
\(369\) 7.74607e10 0.217502
\(370\) −2.68309e10 −0.0744265
\(371\) −3.83016e9 −0.0104963
\(372\) −8.25604e10 −0.223526
\(373\) 4.49243e11 1.20169 0.600844 0.799367i \(-0.294831\pi\)
0.600844 + 0.799367i \(0.294831\pi\)
\(374\) 9.50120e7 0.000251106 0
\(375\) −7.84689e10 −0.204907
\(376\) 1.39136e10 0.0359000
\(377\) 1.81695e10 0.0463241
\(378\) −7.61138e7 −0.000191757 0
\(379\) −2.57491e11 −0.641041 −0.320520 0.947242i \(-0.603858\pi\)
−0.320520 + 0.947242i \(0.603858\pi\)
\(380\) −9.90359e11 −2.43650
\(381\) −4.07938e11 −0.991817
\(382\) −1.87425e10 −0.0450342
\(383\) −2.56704e11 −0.609591 −0.304796 0.952418i \(-0.598588\pi\)
−0.304796 + 0.952418i \(0.598588\pi\)
\(384\) 5.76113e10 0.135213
\(385\) −1.87980e8 −0.000436052 0
\(386\) 1.17555e10 0.0269524
\(387\) −1.21529e11 −0.275410
\(388\) −5.63003e11 −1.26115
\(389\) −2.78839e10 −0.0617418 −0.0308709 0.999523i \(-0.509828\pi\)
−0.0308709 + 0.999523i \(0.509828\pi\)
\(390\) −7.69494e9 −0.0168428
\(391\) 8.23451e10 0.178173
\(392\) 5.51124e10 0.117886
\(393\) −1.06339e11 −0.224868
\(394\) −2.11968e10 −0.0443136
\(395\) 1.25583e11 0.259563
\(396\) 2.80899e9 0.00574012
\(397\) 5.56039e10 0.112344 0.0561718 0.998421i \(-0.482111\pi\)
0.0561718 + 0.998421i \(0.482111\pi\)
\(398\) 2.26205e8 0.000451886 0
\(399\) −8.06046e9 −0.0159214
\(400\) 6.26864e11 1.22434
\(401\) −3.14865e11 −0.608100 −0.304050 0.952656i \(-0.598339\pi\)
−0.304050 + 0.952656i \(0.598339\pi\)
\(402\) −3.06894e10 −0.0586100
\(403\) −6.79330e10 −0.128295
\(404\) 1.49365e10 0.0278954
\(405\) 8.99840e10 0.166195
\(406\) 7.65252e7 0.000139778 0
\(407\) 8.05914e9 0.0145584
\(408\) −9.37515e9 −0.0167497
\(409\) −7.50752e11 −1.32660 −0.663302 0.748352i \(-0.730846\pi\)
−0.663302 + 0.748352i \(0.730846\pi\)
\(410\) 3.29826e10 0.0576445
\(411\) −1.53234e11 −0.264890
\(412\) 2.70773e11 0.462987
\(413\) 1.29858e9 0.00219630
\(414\) −8.52224e9 −0.0142578
\(415\) 1.28777e12 2.13119
\(416\) 3.55741e10 0.0582389
\(417\) −3.56508e11 −0.577373
\(418\) −1.04134e9 −0.00166839
\(419\) 7.08699e11 1.12331 0.561653 0.827373i \(-0.310165\pi\)
0.561653 + 0.827373i \(0.310165\pi\)
\(420\) 9.25810e9 0.0145178
\(421\) 5.65648e11 0.877560 0.438780 0.898594i \(-0.355411\pi\)
0.438780 + 0.898594i \(0.355411\pi\)
\(422\) −5.32516e10 −0.0817385
\(423\) −6.68220e10 −0.101482
\(424\) 4.88257e10 0.0733672
\(425\) −2.04739e11 −0.304404
\(426\) −3.87202e10 −0.0569633
\(427\) −6.46802e9 −0.00941556
\(428\) 7.45565e11 1.07396
\(429\) 2.31131e9 0.00329459
\(430\) −5.17467e10 −0.0729919
\(431\) −3.52572e11 −0.492153 −0.246076 0.969250i \(-0.579141\pi\)
−0.246076 + 0.969250i \(0.579141\pi\)
\(432\) −1.37858e11 −0.190438
\(433\) 8.77496e10 0.119964 0.0599818 0.998199i \(-0.480896\pi\)
0.0599818 + 0.998199i \(0.480896\pi\)
\(434\) −2.86116e8 −0.000387114 0
\(435\) −9.04704e10 −0.121145
\(436\) 3.51686e11 0.466086
\(437\) −9.02506e11 −1.18381
\(438\) −4.05485e10 −0.0526431
\(439\) 3.23555e11 0.415775 0.207887 0.978153i \(-0.433341\pi\)
0.207887 + 0.978153i \(0.433341\pi\)
\(440\) 2.39631e9 0.00304793
\(441\) −2.64685e11 −0.333238
\(442\) −3.85033e9 −0.00479841
\(443\) 1.05919e12 1.30664 0.653319 0.757083i \(-0.273376\pi\)
0.653319 + 0.757083i \(0.273376\pi\)
\(444\) −3.96916e11 −0.484703
\(445\) 3.32069e11 0.401428
\(446\) 4.83616e10 0.0578754
\(447\) −9.11176e11 −1.07949
\(448\) −1.40835e10 −0.0165181
\(449\) −4.93194e11 −0.572676 −0.286338 0.958129i \(-0.592438\pi\)
−0.286338 + 0.958129i \(0.592438\pi\)
\(450\) 2.11893e10 0.0243590
\(451\) −9.90692e9 −0.0112757
\(452\) −7.91370e11 −0.891777
\(453\) 8.19339e10 0.0914159
\(454\) 4.51444e10 0.0498715
\(455\) 7.61782e9 0.00833258
\(456\) 1.02752e11 0.111288
\(457\) −7.63784e11 −0.819121 −0.409560 0.912283i \(-0.634318\pi\)
−0.409560 + 0.912283i \(0.634318\pi\)
\(458\) −3.35281e10 −0.0356053
\(459\) 4.50254e10 0.0473479
\(460\) 1.03660e12 1.07945
\(461\) −8.27441e11 −0.853263 −0.426631 0.904426i \(-0.640300\pi\)
−0.426631 + 0.904426i \(0.640300\pi\)
\(462\) 9.73465e6 9.94103e−6 0
\(463\) 1.49878e12 1.51574 0.757869 0.652407i \(-0.226241\pi\)
0.757869 + 0.652407i \(0.226241\pi\)
\(464\) 1.38603e11 0.138817
\(465\) 3.38255e11 0.335511
\(466\) 5.23098e10 0.0513862
\(467\) 4.33053e11 0.421323 0.210661 0.977559i \(-0.432438\pi\)
0.210661 + 0.977559i \(0.432438\pi\)
\(468\) −1.13833e11 −0.109689
\(469\) 3.03819e10 0.0289959
\(470\) −2.84527e10 −0.0268957
\(471\) −4.82099e11 −0.451380
\(472\) −1.65538e10 −0.0153518
\(473\) 1.55430e10 0.0142778
\(474\) −6.50338e9 −0.00591748
\(475\) 2.24395e12 2.02251
\(476\) 4.63249e9 0.00413603
\(477\) −2.34492e11 −0.207394
\(478\) 1.02499e11 0.0898038
\(479\) 1.89550e12 1.64518 0.822592 0.568631i \(-0.192527\pi\)
0.822592 + 0.568631i \(0.192527\pi\)
\(480\) −1.77132e11 −0.152304
\(481\) −3.26594e11 −0.278199
\(482\) −3.41126e10 −0.0287875
\(483\) 8.43684e9 0.00705371
\(484\) 1.20270e12 0.996214
\(485\) 2.30666e12 1.89298
\(486\) −4.65987e9 −0.00378888
\(487\) 2.33531e12 1.88133 0.940663 0.339343i \(-0.110205\pi\)
0.940663 + 0.339343i \(0.110205\pi\)
\(488\) 8.24522e10 0.0658132
\(489\) −1.13475e12 −0.897452
\(490\) −1.12702e11 −0.0883182
\(491\) 1.57618e12 1.22388 0.611942 0.790903i \(-0.290389\pi\)
0.611942 + 0.790903i \(0.290389\pi\)
\(492\) 4.87920e11 0.375410
\(493\) −4.52688e10 −0.0345134
\(494\) 4.21998e10 0.0318815
\(495\) −1.15086e10 −0.00861586
\(496\) −5.18216e11 −0.384453
\(497\) 3.83322e10 0.0281812
\(498\) −6.66880e10 −0.0485865
\(499\) 1.54552e11 0.111589 0.0557947 0.998442i \(-0.482231\pi\)
0.0557947 + 0.998442i \(0.482231\pi\)
\(500\) −4.94271e11 −0.353671
\(501\) −8.41208e10 −0.0596532
\(502\) 1.35484e11 0.0952182
\(503\) −1.11366e12 −0.775708 −0.387854 0.921721i \(-0.626784\pi\)
−0.387854 + 0.921721i \(0.626784\pi\)
\(504\) −9.60550e8 −0.000663106 0
\(505\) −6.11957e10 −0.0418706
\(506\) 1.08996e9 0.000739152 0
\(507\) 7.65299e11 0.514394
\(508\) −2.56958e12 −1.71189
\(509\) −1.16983e12 −0.772490 −0.386245 0.922396i \(-0.626228\pi\)
−0.386245 + 0.922396i \(0.626228\pi\)
\(510\) 1.91717e10 0.0125486
\(511\) 4.01421e10 0.0260439
\(512\) 4.52812e11 0.291208
\(513\) −4.93481e11 −0.314588
\(514\) −1.43337e10 −0.00905785
\(515\) −1.10938e12 −0.694938
\(516\) −7.65502e11 −0.475360
\(517\) 8.54627e9 0.00526101
\(518\) −1.37553e9 −0.000839433 0
\(519\) −1.03029e11 −0.0623312
\(520\) −9.71095e10 −0.0582434
\(521\) −1.13256e12 −0.673428 −0.336714 0.941607i \(-0.609315\pi\)
−0.336714 + 0.941607i \(0.609315\pi\)
\(522\) 4.68506e9 0.00276184
\(523\) 1.29127e12 0.754674 0.377337 0.926076i \(-0.376840\pi\)
0.377337 + 0.926076i \(0.376840\pi\)
\(524\) −6.69825e11 −0.388124
\(525\) −2.09769e10 −0.0120511
\(526\) −1.08453e11 −0.0617741
\(527\) 1.69253e11 0.0955849
\(528\) 1.76315e10 0.00987270
\(529\) −8.56504e11 −0.475531
\(530\) −9.98462e10 −0.0549655
\(531\) 7.95020e10 0.0433963
\(532\) −5.07723e10 −0.0274805
\(533\) 4.01475e11 0.215469
\(534\) −1.71964e10 −0.00915168
\(535\) −3.05463e12 −1.61200
\(536\) −3.87298e11 −0.202677
\(537\) −3.28719e11 −0.170585
\(538\) −1.89564e10 −0.00975518
\(539\) 3.38521e10 0.0172757
\(540\) 5.66803e11 0.286854
\(541\) −1.73934e12 −0.872964 −0.436482 0.899713i \(-0.643776\pi\)
−0.436482 + 0.899713i \(0.643776\pi\)
\(542\) 1.00670e11 0.0501074
\(543\) −1.23253e10 −0.00608412
\(544\) −8.86318e10 −0.0433905
\(545\) −1.44088e12 −0.699590
\(546\) −3.94493e8 −0.000189965 0
\(547\) 1.01841e12 0.486385 0.243193 0.969978i \(-0.421805\pi\)
0.243193 + 0.969978i \(0.421805\pi\)
\(548\) −9.65208e11 −0.457202
\(549\) −3.95988e11 −0.186040
\(550\) −2.71002e9 −0.00126282
\(551\) 4.96148e11 0.229313
\(552\) −1.07550e11 −0.0493043
\(553\) 6.43821e9 0.00292753
\(554\) −3.69020e10 −0.0166439
\(555\) 1.62619e12 0.727534
\(556\) −2.24562e12 −0.996551
\(557\) 2.18895e12 0.963578 0.481789 0.876287i \(-0.339987\pi\)
0.481789 + 0.876287i \(0.339987\pi\)
\(558\) −1.75167e10 −0.00764891
\(559\) −6.29876e11 −0.272836
\(560\) 5.81113e10 0.0249698
\(561\) −5.75857e9 −0.00245461
\(562\) −1.18660e11 −0.0501756
\(563\) −3.42758e12 −1.43780 −0.718901 0.695112i \(-0.755355\pi\)
−0.718901 + 0.695112i \(0.755355\pi\)
\(564\) −4.20908e11 −0.175158
\(565\) 3.24229e12 1.33855
\(566\) −1.62964e10 −0.00667447
\(567\) 4.61317e9 0.00187446
\(568\) −4.88646e11 −0.196982
\(569\) −4.02290e12 −1.60892 −0.804460 0.594007i \(-0.797545\pi\)
−0.804460 + 0.594007i \(0.797545\pi\)
\(570\) −2.10123e11 −0.0833752
\(571\) 9.47651e11 0.373066 0.186533 0.982449i \(-0.440275\pi\)
0.186533 + 0.982449i \(0.440275\pi\)
\(572\) 1.45588e10 0.00568648
\(573\) 1.13596e12 0.440219
\(574\) 1.69091e9 0.000650154 0
\(575\) −2.34873e12 −0.896039
\(576\) −8.62225e11 −0.326377
\(577\) −1.11164e12 −0.417517 −0.208759 0.977967i \(-0.566942\pi\)
−0.208759 + 0.977967i \(0.566942\pi\)
\(578\) −1.48892e11 −0.0554877
\(579\) −7.12486e11 −0.263465
\(580\) −5.69867e11 −0.209097
\(581\) 6.60197e10 0.0240370
\(582\) −1.19452e11 −0.0431558
\(583\) 2.99906e10 0.0107517
\(584\) −5.11719e11 −0.182043
\(585\) 4.66382e11 0.164642
\(586\) 8.78292e10 0.0307680
\(587\) −1.50367e12 −0.522735 −0.261368 0.965239i \(-0.584174\pi\)
−0.261368 + 0.965239i \(0.584174\pi\)
\(588\) −1.66723e12 −0.575172
\(589\) −1.85502e12 −0.635084
\(590\) 3.38518e10 0.0115013
\(591\) 1.28471e12 0.433175
\(592\) −2.49137e12 −0.833663
\(593\) −2.18166e12 −0.724504 −0.362252 0.932080i \(-0.617992\pi\)
−0.362252 + 0.932080i \(0.617992\pi\)
\(594\) 5.95979e8 0.000196423 0
\(595\) −1.89796e10 −0.00620813
\(596\) −5.73944e12 −1.86321
\(597\) −1.37100e10 −0.00441727
\(598\) −4.41703e10 −0.0141246
\(599\) 1.70673e12 0.541681 0.270841 0.962624i \(-0.412698\pi\)
0.270841 + 0.962624i \(0.412698\pi\)
\(600\) 2.67407e11 0.0842349
\(601\) 4.09698e12 1.28094 0.640470 0.767983i \(-0.278740\pi\)
0.640470 + 0.767983i \(0.278740\pi\)
\(602\) −2.65288e9 −0.000823252 0
\(603\) 1.86005e12 0.572924
\(604\) 5.16096e11 0.157785
\(605\) −4.92753e12 −1.49531
\(606\) 3.16905e9 0.000954559 0
\(607\) −4.05392e12 −1.21206 −0.606032 0.795440i \(-0.707240\pi\)
−0.606032 + 0.795440i \(0.707240\pi\)
\(608\) 9.71409e11 0.288294
\(609\) −4.63811e9 −0.00136635
\(610\) −1.68611e11 −0.0493062
\(611\) −3.46335e11 −0.100533
\(612\) 2.83612e11 0.0817229
\(613\) 2.62140e12 0.749828 0.374914 0.927060i \(-0.377672\pi\)
0.374914 + 0.927060i \(0.377672\pi\)
\(614\) −1.69691e11 −0.0481839
\(615\) −1.99904e12 −0.563487
\(616\) 1.22851e8 3.43767e−5 0
\(617\) −1.92608e11 −0.0535046 −0.0267523 0.999642i \(-0.508517\pi\)
−0.0267523 + 0.999642i \(0.508517\pi\)
\(618\) 5.74497e10 0.0158431
\(619\) 2.14110e12 0.586178 0.293089 0.956085i \(-0.405317\pi\)
0.293089 + 0.956085i \(0.405317\pi\)
\(620\) 2.13065e12 0.579094
\(621\) 5.16524e11 0.139373
\(622\) −1.90985e11 −0.0511614
\(623\) 1.70240e10 0.00452758
\(624\) −7.14509e11 −0.188659
\(625\) −2.69478e12 −0.706421
\(626\) −1.78213e11 −0.0463825
\(627\) 6.31142e10 0.0163089
\(628\) −3.03671e12 −0.779085
\(629\) 8.13700e11 0.207270
\(630\) 1.96428e9 0.000496788 0
\(631\) 1.85087e12 0.464776 0.232388 0.972623i \(-0.425346\pi\)
0.232388 + 0.972623i \(0.425346\pi\)
\(632\) −8.20722e10 −0.0204630
\(633\) 3.22752e12 0.799010
\(634\) 3.25683e11 0.0800558
\(635\) 1.05277e13 2.56952
\(636\) −1.47705e12 −0.357963
\(637\) −1.37185e12 −0.330124
\(638\) −5.99201e8 −0.000143179 0
\(639\) 2.34679e12 0.556827
\(640\) −1.48678e12 −0.350298
\(641\) 2.62055e12 0.613099 0.306550 0.951855i \(-0.400825\pi\)
0.306550 + 0.951855i \(0.400825\pi\)
\(642\) 1.58186e11 0.0367501
\(643\) −2.10252e12 −0.485054 −0.242527 0.970145i \(-0.577976\pi\)
−0.242527 + 0.970145i \(0.577976\pi\)
\(644\) 5.31431e10 0.0121748
\(645\) 3.13631e12 0.713510
\(646\) −1.05140e11 −0.0237531
\(647\) 8.42611e11 0.189042 0.0945209 0.995523i \(-0.469868\pi\)
0.0945209 + 0.995523i \(0.469868\pi\)
\(648\) −5.88072e10 −0.0131022
\(649\) −1.01680e10 −0.00224975
\(650\) 1.09823e11 0.0241314
\(651\) 1.73412e10 0.00378412
\(652\) −7.14774e12 −1.54901
\(653\) 6.38379e12 1.37395 0.686973 0.726683i \(-0.258939\pi\)
0.686973 + 0.726683i \(0.258939\pi\)
\(654\) 7.46168e10 0.0159491
\(655\) 2.74431e12 0.582570
\(656\) 3.06258e12 0.645685
\(657\) 2.45760e12 0.514597
\(658\) −1.45867e9 −0.000303348 0
\(659\) −7.01173e12 −1.44824 −0.724120 0.689674i \(-0.757754\pi\)
−0.724120 + 0.689674i \(0.757754\pi\)
\(660\) −7.24919e10 −0.0148711
\(661\) −4.26630e12 −0.869250 −0.434625 0.900611i \(-0.643119\pi\)
−0.434625 + 0.900611i \(0.643119\pi\)
\(662\) 2.07461e11 0.0419833
\(663\) 2.33364e11 0.0469054
\(664\) −8.41598e11 −0.168015
\(665\) 2.08017e11 0.0412479
\(666\) −8.42133e10 −0.0165862
\(667\) −5.19316e11 −0.101593
\(668\) −5.29872e11 −0.102962
\(669\) −2.93115e12 −0.565744
\(670\) 7.92007e11 0.151842
\(671\) 5.06453e10 0.00964468
\(672\) −9.08095e9 −0.00171779
\(673\) 4.19265e12 0.787809 0.393905 0.919151i \(-0.371124\pi\)
0.393905 + 0.919151i \(0.371124\pi\)
\(674\) −1.42384e11 −0.0265760
\(675\) −1.28426e12 −0.238114
\(676\) 4.82057e12 0.887848
\(677\) −4.51587e12 −0.826214 −0.413107 0.910682i \(-0.635557\pi\)
−0.413107 + 0.910682i \(0.635557\pi\)
\(678\) −1.67904e11 −0.0305160
\(679\) 1.18255e11 0.0213503
\(680\) 2.41946e11 0.0433938
\(681\) −2.73615e12 −0.487504
\(682\) 2.24032e9 0.000396534 0
\(683\) −1.90757e12 −0.335419 −0.167709 0.985836i \(-0.553637\pi\)
−0.167709 + 0.985836i \(0.553637\pi\)
\(684\) −3.10840e12 −0.542982
\(685\) 3.95452e12 0.686256
\(686\) −1.15574e10 −0.00199251
\(687\) 2.03210e12 0.348048
\(688\) −4.80491e12 −0.817593
\(689\) −1.21536e12 −0.205455
\(690\) 2.19935e11 0.0369380
\(691\) 9.17365e12 1.53070 0.765352 0.643612i \(-0.222565\pi\)
0.765352 + 0.643612i \(0.222565\pi\)
\(692\) −6.48971e11 −0.107584
\(693\) −5.90006e8 −9.71756e−5 0
\(694\) −4.18297e11 −0.0684490
\(695\) 9.20044e12 1.49581
\(696\) 5.91251e10 0.00955059
\(697\) −1.00026e12 −0.160534
\(698\) 6.32553e11 0.100867
\(699\) −3.17044e12 −0.502310
\(700\) −1.32132e11 −0.0208002
\(701\) 7.00511e12 1.09568 0.547840 0.836583i \(-0.315450\pi\)
0.547840 + 0.836583i \(0.315450\pi\)
\(702\) −2.41518e10 −0.00375347
\(703\) −8.91819e12 −1.37714
\(704\) 1.10275e11 0.0169200
\(705\) 1.72449e12 0.262911
\(706\) −8.95801e10 −0.0135703
\(707\) −3.13729e9 −0.000472246 0
\(708\) 5.00778e11 0.0749024
\(709\) 2.04764e12 0.304331 0.152166 0.988355i \(-0.451375\pi\)
0.152166 + 0.988355i \(0.451375\pi\)
\(710\) 9.99259e11 0.147576
\(711\) 3.94163e11 0.0578445
\(712\) −2.17017e11 −0.0316471
\(713\) 1.94164e12 0.281363
\(714\) 9.82870e8 0.000141532 0
\(715\) −5.96484e10 −0.00853535
\(716\) −2.07058e12 −0.294431
\(717\) −6.21236e12 −0.877850
\(718\) 6.00175e10 0.00842788
\(719\) −8.05377e12 −1.12388 −0.561939 0.827178i \(-0.689945\pi\)
−0.561939 + 0.827178i \(0.689945\pi\)
\(720\) 3.55772e12 0.493373
\(721\) −5.68739e10 −0.00783799
\(722\) 7.21084e11 0.0987571
\(723\) 2.06753e12 0.281403
\(724\) −7.76362e10 −0.0105012
\(725\) 1.29120e12 0.173569
\(726\) 2.55175e11 0.0340897
\(727\) −4.54514e12 −0.603451 −0.301726 0.953395i \(-0.597563\pi\)
−0.301726 + 0.953395i \(0.597563\pi\)
\(728\) −4.97848e9 −0.000656909 0
\(729\) 2.82430e11 0.0370370
\(730\) 1.04644e12 0.136384
\(731\) 1.56932e12 0.203275
\(732\) −2.49430e12 −0.321107
\(733\) 2.35412e12 0.301204 0.150602 0.988594i \(-0.451879\pi\)
0.150602 + 0.988594i \(0.451879\pi\)
\(734\) 6.50545e11 0.0827266
\(735\) 6.83076e12 0.863328
\(736\) −1.01677e12 −0.127724
\(737\) −2.37893e11 −0.0297015
\(738\) 1.03521e11 0.0128463
\(739\) −6.71592e12 −0.828335 −0.414167 0.910201i \(-0.635927\pi\)
−0.414167 + 0.910201i \(0.635927\pi\)
\(740\) 1.02433e13 1.25573
\(741\) −2.55768e12 −0.311648
\(742\) −5.11878e9 −0.000619938 0
\(743\) 4.74711e12 0.571452 0.285726 0.958311i \(-0.407765\pi\)
0.285726 + 0.958311i \(0.407765\pi\)
\(744\) −2.21060e11 −0.0264504
\(745\) 2.35149e13 2.79666
\(746\) 6.00385e11 0.0709750
\(747\) 4.04189e12 0.474943
\(748\) −3.62729e10 −0.00423667
\(749\) −1.56600e11 −0.0181813
\(750\) −1.04869e11 −0.0121024
\(751\) 3.17332e12 0.364028 0.182014 0.983296i \(-0.441738\pi\)
0.182014 + 0.983296i \(0.441738\pi\)
\(752\) −2.64196e12 −0.301263
\(753\) −8.21151e12 −0.930777
\(754\) 2.42824e10 0.00273603
\(755\) −2.11448e12 −0.236833
\(756\) 2.90581e10 0.00323533
\(757\) 4.08571e12 0.452206 0.226103 0.974103i \(-0.427401\pi\)
0.226103 + 0.974103i \(0.427401\pi\)
\(758\) −3.44121e11 −0.0378616
\(759\) −6.60613e10 −0.00722536
\(760\) −2.65174e12 −0.288317
\(761\) 7.13469e12 0.771159 0.385580 0.922675i \(-0.374002\pi\)
0.385580 + 0.922675i \(0.374002\pi\)
\(762\) −5.45184e11 −0.0585795
\(763\) −7.38691e10 −0.00789046
\(764\) 7.15536e12 0.759821
\(765\) −1.16198e12 −0.122665
\(766\) −3.43069e11 −0.0360041
\(767\) 4.12054e11 0.0429908
\(768\) −5.37312e12 −0.557315
\(769\) −1.06805e13 −1.10134 −0.550672 0.834722i \(-0.685628\pi\)
−0.550672 + 0.834722i \(0.685628\pi\)
\(770\) −2.51224e8 −2.57544e−5 0
\(771\) 8.68752e11 0.0885423
\(772\) −4.48791e12 −0.454743
\(773\) 6.56372e12 0.661214 0.330607 0.943768i \(-0.392747\pi\)
0.330607 + 0.943768i \(0.392747\pi\)
\(774\) −1.62416e11 −0.0162665
\(775\) −4.82761e12 −0.480700
\(776\) −1.50747e12 −0.149235
\(777\) 8.33693e10 0.00820563
\(778\) −3.72650e10 −0.00364664
\(779\) 1.09629e13 1.06662
\(780\) 2.93771e12 0.284173
\(781\) −3.00145e11 −0.0288670
\(782\) 1.10049e11 0.0105234
\(783\) −2.83956e11 −0.0269975
\(784\) −1.04649e13 −0.989265
\(785\) 1.24416e13 1.16940
\(786\) −1.42116e11 −0.0132813
\(787\) 1.61828e12 0.150372 0.0751860 0.997170i \(-0.476045\pi\)
0.0751860 + 0.997170i \(0.476045\pi\)
\(788\) 8.09234e12 0.747663
\(789\) 6.57322e12 0.603854
\(790\) 1.67834e11 0.0153305
\(791\) 1.66221e11 0.0150971
\(792\) 7.52121e9 0.000679242 0
\(793\) −2.05238e12 −0.184302
\(794\) 7.43112e10 0.00663532
\(795\) 6.05157e12 0.537299
\(796\) −8.63587e10 −0.00762425
\(797\) −1.19360e13 −1.04784 −0.523922 0.851766i \(-0.675532\pi\)
−0.523922 + 0.851766i \(0.675532\pi\)
\(798\) −1.07723e10 −0.000940363 0
\(799\) 8.62884e11 0.0749017
\(800\) 2.52804e12 0.218212
\(801\) 1.04225e12 0.0894595
\(802\) −4.20798e11 −0.0359161
\(803\) −3.14317e11 −0.0266777
\(804\) 1.17164e13 0.988872
\(805\) −2.17731e11 −0.0182742
\(806\) −9.07882e10 −0.00757743
\(807\) 1.14893e12 0.0953588
\(808\) 3.99932e10 0.00330092
\(809\) −1.73505e13 −1.42411 −0.712054 0.702124i \(-0.752235\pi\)
−0.712054 + 0.702124i \(0.752235\pi\)
\(810\) 1.20258e11 0.00981592
\(811\) 8.18568e12 0.664448 0.332224 0.943201i \(-0.392201\pi\)
0.332224 + 0.943201i \(0.392201\pi\)
\(812\) −2.92151e10 −0.00235834
\(813\) −6.10147e12 −0.489810
\(814\) 1.07705e10 0.000859860 0
\(815\) 2.92847e13 2.32505
\(816\) 1.78018e12 0.140559
\(817\) −1.71998e13 −1.35059
\(818\) −1.00333e12 −0.0783529
\(819\) 2.39098e10 0.00185694
\(820\) −1.25918e13 −0.972583
\(821\) 6.64204e12 0.510220 0.255110 0.966912i \(-0.417888\pi\)
0.255110 + 0.966912i \(0.417888\pi\)
\(822\) −2.04787e11 −0.0156451
\(823\) 5.51708e11 0.0419189 0.0209594 0.999780i \(-0.493328\pi\)
0.0209594 + 0.999780i \(0.493328\pi\)
\(824\) 7.25010e11 0.0547863
\(825\) 1.64252e11 0.0123443
\(826\) 1.73547e9 0.000129720 0
\(827\) −1.63550e13 −1.21584 −0.607919 0.793999i \(-0.707996\pi\)
−0.607919 + 0.793999i \(0.707996\pi\)
\(828\) 3.25355e12 0.240559
\(829\) 2.05391e12 0.151038 0.0755188 0.997144i \(-0.475939\pi\)
0.0755188 + 0.997144i \(0.475939\pi\)
\(830\) 1.72103e12 0.125874
\(831\) 2.23659e12 0.162698
\(832\) −4.46886e12 −0.323327
\(833\) 3.41792e12 0.245957
\(834\) −4.76450e11 −0.0341013
\(835\) 2.17092e12 0.154545
\(836\) 3.97553e11 0.0281492
\(837\) 1.06167e12 0.0747696
\(838\) 9.47131e11 0.0663456
\(839\) −9.49604e12 −0.661628 −0.330814 0.943696i \(-0.607323\pi\)
−0.330814 + 0.943696i \(0.607323\pi\)
\(840\) 2.47891e10 0.00171792
\(841\) −1.42217e13 −0.980321
\(842\) 7.55953e11 0.0518311
\(843\) 7.19188e12 0.490477
\(844\) 2.03300e13 1.37910
\(845\) −1.97502e13 −1.33265
\(846\) −8.93035e10 −0.00599379
\(847\) −2.52618e11 −0.0168651
\(848\) −9.27116e12 −0.615677
\(849\) 9.87705e11 0.0652443
\(850\) −2.73621e11 −0.0179789
\(851\) 9.33462e12 0.610118
\(852\) 1.47823e13 0.961089
\(853\) −3.90438e12 −0.252512 −0.126256 0.991998i \(-0.540296\pi\)
−0.126256 + 0.991998i \(0.540296\pi\)
\(854\) −8.64411e9 −0.000556109 0
\(855\) 1.27353e13 0.815010
\(856\) 1.99629e12 0.127084
\(857\) −3.20675e12 −0.203073 −0.101536 0.994832i \(-0.532376\pi\)
−0.101536 + 0.994832i \(0.532376\pi\)
\(858\) 3.08892e9 0.000194587 0
\(859\) −2.54347e13 −1.59389 −0.796944 0.604053i \(-0.793552\pi\)
−0.796944 + 0.604053i \(0.793552\pi\)
\(860\) 1.97554e13 1.23152
\(861\) −1.02484e11 −0.00635539
\(862\) −4.71190e11 −0.0290679
\(863\) −6.71265e12 −0.411951 −0.205975 0.978557i \(-0.566037\pi\)
−0.205975 + 0.978557i \(0.566037\pi\)
\(864\) −5.55958e11 −0.0339414
\(865\) 2.65888e12 0.161483
\(866\) 1.17272e11 0.00708538
\(867\) 9.02420e12 0.542404
\(868\) 1.09231e11 0.00653142
\(869\) −5.04119e10 −0.00299877
\(870\) −1.20908e11 −0.00715514
\(871\) 9.64054e12 0.567570
\(872\) 9.41659e11 0.0551530
\(873\) 7.23983e12 0.421856
\(874\) −1.20614e12 −0.0699194
\(875\) 1.03818e11 0.00598736
\(876\) 1.54803e13 0.888198
\(877\) −4.93714e12 −0.281823 −0.140912 0.990022i \(-0.545003\pi\)
−0.140912 + 0.990022i \(0.545003\pi\)
\(878\) 4.32412e11 0.0245568
\(879\) −5.32323e12 −0.300764
\(880\) −4.55018e11 −0.0255774
\(881\) 2.75278e13 1.53950 0.769750 0.638345i \(-0.220381\pi\)
0.769750 + 0.638345i \(0.220381\pi\)
\(882\) −3.53735e11 −0.0196820
\(883\) 2.27999e13 1.26215 0.631073 0.775724i \(-0.282615\pi\)
0.631073 + 0.775724i \(0.282615\pi\)
\(884\) 1.46995e12 0.0809592
\(885\) −2.05172e12 −0.112428
\(886\) 1.41554e12 0.0771737
\(887\) −3.41001e13 −1.84969 −0.924847 0.380339i \(-0.875807\pi\)
−0.924847 + 0.380339i \(0.875807\pi\)
\(888\) −1.06277e12 −0.0573560
\(889\) 5.39720e11 0.0289808
\(890\) 4.43789e11 0.0237095
\(891\) −3.61216e10 −0.00192007
\(892\) −1.84631e13 −0.976479
\(893\) −9.45725e12 −0.497661
\(894\) −1.21773e12 −0.0637576
\(895\) 8.48330e12 0.441938
\(896\) −7.62223e10 −0.00395090
\(897\) 2.67711e12 0.138070
\(898\) −6.59123e11 −0.0338239
\(899\) −1.06741e12 −0.0545020
\(900\) −8.08946e12 −0.410987
\(901\) 3.02803e12 0.153073
\(902\) −1.32400e10 −0.000665975 0
\(903\) 1.60788e11 0.00804745
\(904\) −2.11893e12 −0.105526
\(905\) 3.18080e11 0.0157623
\(906\) 1.09500e11 0.00539927
\(907\) 2.77919e12 0.136359 0.0681797 0.997673i \(-0.478281\pi\)
0.0681797 + 0.997673i \(0.478281\pi\)
\(908\) −1.72348e13 −0.841436
\(909\) −1.92073e11 −0.00933100
\(910\) 1.01807e10 0.000492145 0
\(911\) −1.37455e13 −0.661193 −0.330596 0.943772i \(-0.607250\pi\)
−0.330596 + 0.943772i \(0.607250\pi\)
\(912\) −1.95109e13 −0.933899
\(913\) −5.16941e11 −0.0246220
\(914\) −1.02075e12 −0.0483795
\(915\) 1.02193e13 0.481978
\(916\) 1.28001e13 0.600735
\(917\) 1.40692e11 0.00657062
\(918\) 6.01737e10 0.00279650
\(919\) 1.00087e13 0.462869 0.231435 0.972850i \(-0.425658\pi\)
0.231435 + 0.972850i \(0.425658\pi\)
\(920\) 2.77556e12 0.127734
\(921\) 1.02848e13 0.471007
\(922\) −1.10582e12 −0.0503960
\(923\) 1.21633e13 0.551624
\(924\) −3.71641e9 −0.000167726 0
\(925\) −2.32091e13 −1.04237
\(926\) 2.00303e12 0.0895237
\(927\) −3.48196e12 −0.154869
\(928\) 5.58963e11 0.0247410
\(929\) 2.63958e13 1.16269 0.581345 0.813657i \(-0.302527\pi\)
0.581345 + 0.813657i \(0.302527\pi\)
\(930\) 4.52057e11 0.0198162
\(931\) −3.74605e13 −1.63418
\(932\) −1.99704e13 −0.866992
\(933\) 1.15754e13 0.500113
\(934\) 5.78748e11 0.0248845
\(935\) 1.48612e11 0.00635920
\(936\) −3.04794e11 −0.0129797
\(937\) −3.45669e13 −1.46498 −0.732492 0.680776i \(-0.761643\pi\)
−0.732492 + 0.680776i \(0.761643\pi\)
\(938\) 4.06035e10 0.00171258
\(939\) 1.08013e13 0.453398
\(940\) 1.08624e13 0.453787
\(941\) 7.72112e12 0.321016 0.160508 0.987035i \(-0.448687\pi\)
0.160508 + 0.987035i \(0.448687\pi\)
\(942\) −6.44295e11 −0.0266597
\(943\) −1.14748e13 −0.472546
\(944\) 3.14329e12 0.128828
\(945\) −1.19053e11 −0.00485620
\(946\) 2.07723e10 0.000843286 0
\(947\) 3.74173e13 1.51181 0.755906 0.654680i \(-0.227197\pi\)
0.755906 + 0.654680i \(0.227197\pi\)
\(948\) 2.48281e12 0.0998402
\(949\) 1.27376e13 0.509788
\(950\) 2.99889e12 0.119455
\(951\) −1.97393e13 −0.782562
\(952\) 1.24037e10 0.000489425 0
\(953\) 1.56325e13 0.613918 0.306959 0.951723i \(-0.400689\pi\)
0.306959 + 0.951723i \(0.400689\pi\)
\(954\) −3.13384e11 −0.0122492
\(955\) −2.93160e13 −1.14048
\(956\) −3.91313e13 −1.51518
\(957\) 3.63169e10 0.00139960
\(958\) 2.53322e12 0.0971692
\(959\) 2.02735e11 0.00774006
\(960\) 2.22516e13 0.845551
\(961\) −2.24487e13 −0.849057
\(962\) −4.36472e11 −0.0164312
\(963\) −9.58745e12 −0.359240
\(964\) 1.30232e13 0.485705
\(965\) 1.83872e13 0.682564
\(966\) 1.12753e10 0.000416612 0
\(967\) −1.73605e13 −0.638475 −0.319237 0.947675i \(-0.603427\pi\)
−0.319237 + 0.947675i \(0.603427\pi\)
\(968\) 3.22029e12 0.117884
\(969\) 6.37240e12 0.232191
\(970\) 3.08271e12 0.111805
\(971\) −3.63320e13 −1.31161 −0.655803 0.754932i \(-0.727670\pi\)
−0.655803 + 0.754932i \(0.727670\pi\)
\(972\) 1.77901e12 0.0639262
\(973\) 4.71676e11 0.0168708
\(974\) 3.12099e12 0.111116
\(975\) −6.65624e12 −0.235889
\(976\) −1.56563e13 −0.552286
\(977\) 1.69592e13 0.595498 0.297749 0.954644i \(-0.403764\pi\)
0.297749 + 0.954644i \(0.403764\pi\)
\(978\) −1.51653e12 −0.0530060
\(979\) −1.33300e11 −0.00463776
\(980\) 4.30265e13 1.49011
\(981\) −4.52244e12 −0.155906
\(982\) 2.10647e12 0.0722859
\(983\) −4.74799e13 −1.62188 −0.810941 0.585128i \(-0.801044\pi\)
−0.810941 + 0.585128i \(0.801044\pi\)
\(984\) 1.30643e12 0.0444231
\(985\) −3.31548e13 −1.12223
\(986\) −6.04989e10 −0.00203846
\(987\) 8.84085e10 0.00296529
\(988\) −1.61107e13 −0.537907
\(989\) 1.80030e13 0.598357
\(990\) −1.53805e10 −0.000508877 0
\(991\) −1.07567e13 −0.354281 −0.177141 0.984186i \(-0.556685\pi\)
−0.177141 + 0.984186i \(0.556685\pi\)
\(992\) −2.08988e12 −0.0685203
\(993\) −1.25740e13 −0.410395
\(994\) 5.12286e10 0.00166446
\(995\) 3.53817e11 0.0114439
\(996\) 2.54596e13 0.819755
\(997\) −4.06172e13 −1.30191 −0.650956 0.759115i \(-0.725632\pi\)
−0.650956 + 0.759115i \(0.725632\pi\)
\(998\) 2.06550e11 0.00659078
\(999\) 5.10407e12 0.162133
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.1.12 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.12 22 1.1 even 1 trivial