Properties

Label 177.10.a.b.1.7
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
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: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-22.9203 q^{2} -81.0000 q^{3} +13.3420 q^{4} +1892.34 q^{5} +1856.55 q^{6} -10585.6 q^{7} +11429.4 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-22.9203 q^{2} -81.0000 q^{3} +13.3420 q^{4} +1892.34 q^{5} +1856.55 q^{6} -10585.6 q^{7} +11429.4 q^{8} +6561.00 q^{9} -43373.0 q^{10} -11310.1 q^{11} -1080.70 q^{12} +75180.1 q^{13} +242625. q^{14} -153279. q^{15} -268797. q^{16} +10052.0 q^{17} -150380. q^{18} +190115. q^{19} +25247.5 q^{20} +857432. q^{21} +259232. q^{22} -1.70428e6 q^{23} -925782. q^{24} +1.62781e6 q^{25} -1.72315e6 q^{26} -531441. q^{27} -141233. q^{28} -4.88265e6 q^{29} +3.51321e6 q^{30} +1.15157e6 q^{31} +309062. q^{32} +916122. q^{33} -230394. q^{34} -2.00315e7 q^{35} +87536.8 q^{36} +1.23793e7 q^{37} -4.35750e6 q^{38} -6.08959e6 q^{39} +2.16283e7 q^{40} +2.65126e7 q^{41} -1.96526e7 q^{42} -3.02092e6 q^{43} -150900. q^{44} +1.24156e7 q^{45} +3.90626e7 q^{46} +1.63487e7 q^{47} +2.17726e7 q^{48} +7.17008e7 q^{49} -3.73101e7 q^{50} -814208. q^{51} +1.00305e6 q^{52} +8.99069e7 q^{53} +1.21808e7 q^{54} -2.14026e7 q^{55} -1.20987e8 q^{56} -1.53993e7 q^{57} +1.11912e8 q^{58} -1.21174e7 q^{59} -2.04505e6 q^{60} -7.84701e6 q^{61} -2.63943e7 q^{62} -6.94520e7 q^{63} +1.30540e8 q^{64} +1.42266e8 q^{65} -2.09978e7 q^{66} -1.02865e7 q^{67} +134113. q^{68} +1.38047e8 q^{69} +4.59128e8 q^{70} +7.77522e7 q^{71} +7.49884e7 q^{72} +9.47922e7 q^{73} -2.83738e8 q^{74} -1.31853e8 q^{75} +2.53651e6 q^{76} +1.19724e8 q^{77} +1.39575e8 q^{78} +2.02657e8 q^{79} -5.08655e8 q^{80} +4.30467e7 q^{81} -6.07678e8 q^{82} -5.81838e8 q^{83} +1.14398e7 q^{84} +1.90217e7 q^{85} +6.92405e7 q^{86} +3.95495e8 q^{87} -1.29268e8 q^{88} -1.16553e9 q^{89} -2.84570e8 q^{90} -7.95825e8 q^{91} -2.27385e7 q^{92} -9.32769e7 q^{93} -3.74717e8 q^{94} +3.59762e8 q^{95} -2.50340e7 q^{96} -1.43073e9 q^{97} -1.64341e9 q^{98} -7.42059e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.9203 −1.01295 −0.506473 0.862256i \(-0.669051\pi\)
−0.506473 + 0.862256i \(0.669051\pi\)
\(3\) −81.0000 −0.577350
\(4\) 13.3420 0.0260586
\(5\) 1892.34 1.35405 0.677023 0.735962i \(-0.263270\pi\)
0.677023 + 0.735962i \(0.263270\pi\)
\(6\) 1856.55 0.584824
\(7\) −10585.6 −1.66638 −0.833189 0.552989i \(-0.813487\pi\)
−0.833189 + 0.552989i \(0.813487\pi\)
\(8\) 11429.4 0.986550
\(9\) 6561.00 0.333333
\(10\) −43373.0 −1.37157
\(11\) −11310.1 −0.232917 −0.116458 0.993196i \(-0.537154\pi\)
−0.116458 + 0.993196i \(0.537154\pi\)
\(12\) −1080.70 −0.0150449
\(13\) 75180.1 0.730059 0.365030 0.930996i \(-0.381059\pi\)
0.365030 + 0.930996i \(0.381059\pi\)
\(14\) 242625. 1.68795
\(15\) −153279. −0.781759
\(16\) −268797. −1.02538
\(17\) 10052.0 0.0291897 0.0145949 0.999893i \(-0.495354\pi\)
0.0145949 + 0.999893i \(0.495354\pi\)
\(18\) −150380. −0.337648
\(19\) 190115. 0.334677 0.167338 0.985900i \(-0.446483\pi\)
0.167338 + 0.985900i \(0.446483\pi\)
\(20\) 25247.5 0.0352845
\(21\) 857432. 0.962083
\(22\) 259232. 0.235932
\(23\) −1.70428e6 −1.26989 −0.634944 0.772559i \(-0.718977\pi\)
−0.634944 + 0.772559i \(0.718977\pi\)
\(24\) −925782. −0.569585
\(25\) 1.62781e6 0.833441
\(26\) −1.72315e6 −0.739510
\(27\) −531441. −0.192450
\(28\) −141233. −0.0434234
\(29\) −4.88265e6 −1.28193 −0.640966 0.767570i \(-0.721466\pi\)
−0.640966 + 0.767570i \(0.721466\pi\)
\(30\) 3.51321e6 0.791879
\(31\) 1.15157e6 0.223955 0.111978 0.993711i \(-0.464281\pi\)
0.111978 + 0.993711i \(0.464281\pi\)
\(32\) 309062. 0.0521040
\(33\) 916122. 0.134475
\(34\) −230394. −0.0295676
\(35\) −2.00315e7 −2.25635
\(36\) 87536.8 0.00868619
\(37\) 1.23793e7 1.08590 0.542949 0.839766i \(-0.317308\pi\)
0.542949 + 0.839766i \(0.317308\pi\)
\(38\) −4.35750e6 −0.339009
\(39\) −6.08959e6 −0.421500
\(40\) 2.16283e7 1.33583
\(41\) 2.65126e7 1.46529 0.732647 0.680608i \(-0.238285\pi\)
0.732647 + 0.680608i \(0.238285\pi\)
\(42\) −1.96526e7 −0.974538
\(43\) −3.02092e6 −0.134751 −0.0673753 0.997728i \(-0.521462\pi\)
−0.0673753 + 0.997728i \(0.521462\pi\)
\(44\) −150900. −0.00606948
\(45\) 1.24156e7 0.451349
\(46\) 3.90626e7 1.28633
\(47\) 1.63487e7 0.488700 0.244350 0.969687i \(-0.421425\pi\)
0.244350 + 0.969687i \(0.421425\pi\)
\(48\) 2.17726e7 0.592003
\(49\) 7.17008e7 1.77681
\(50\) −3.73101e7 −0.844230
\(51\) −814208. −0.0168527
\(52\) 1.00305e6 0.0190243
\(53\) 8.99069e7 1.56513 0.782567 0.622567i \(-0.213910\pi\)
0.782567 + 0.622567i \(0.213910\pi\)
\(54\) 1.21808e7 0.194941
\(55\) −2.14026e7 −0.315380
\(56\) −1.20987e8 −1.64396
\(57\) −1.53993e7 −0.193226
\(58\) 1.11912e8 1.29853
\(59\) −1.21174e7 −0.130189
\(60\) −2.04505e6 −0.0203715
\(61\) −7.84701e6 −0.0725638 −0.0362819 0.999342i \(-0.511551\pi\)
−0.0362819 + 0.999342i \(0.511551\pi\)
\(62\) −2.63943e7 −0.226855
\(63\) −6.94520e7 −0.555459
\(64\) 1.30540e8 0.972601
\(65\) 1.42266e8 0.988534
\(66\) −2.09978e7 −0.136216
\(67\) −1.02865e7 −0.0623633 −0.0311816 0.999514i \(-0.509927\pi\)
−0.0311816 + 0.999514i \(0.509927\pi\)
\(68\) 134113. 0.000760643 0
\(69\) 1.38047e8 0.733170
\(70\) 4.59128e8 2.28556
\(71\) 7.77522e7 0.363120 0.181560 0.983380i \(-0.441885\pi\)
0.181560 + 0.983380i \(0.441885\pi\)
\(72\) 7.49884e7 0.328850
\(73\) 9.47922e7 0.390679 0.195339 0.980736i \(-0.437419\pi\)
0.195339 + 0.980736i \(0.437419\pi\)
\(74\) −2.83738e8 −1.09995
\(75\) −1.31853e8 −0.481187
\(76\) 2.53651e6 0.00872120
\(77\) 1.19724e8 0.388128
\(78\) 1.39575e8 0.426956
\(79\) 2.02657e8 0.585382 0.292691 0.956207i \(-0.405449\pi\)
0.292691 + 0.956207i \(0.405449\pi\)
\(80\) −5.08655e8 −1.38841
\(81\) 4.30467e7 0.111111
\(82\) −6.07678e8 −1.48426
\(83\) −5.81838e8 −1.34571 −0.672854 0.739776i \(-0.734932\pi\)
−0.672854 + 0.739776i \(0.734932\pi\)
\(84\) 1.14398e7 0.0250705
\(85\) 1.90217e7 0.0395243
\(86\) 6.92405e7 0.136495
\(87\) 3.95495e8 0.740123
\(88\) −1.29268e8 −0.229784
\(89\) −1.16553e9 −1.96910 −0.984551 0.175100i \(-0.943975\pi\)
−0.984551 + 0.175100i \(0.943975\pi\)
\(90\) −2.84570e8 −0.457192
\(91\) −7.95825e8 −1.21655
\(92\) −2.27385e7 −0.0330914
\(93\) −9.32769e7 −0.129301
\(94\) −3.74717e8 −0.495026
\(95\) 3.59762e8 0.453168
\(96\) −2.50340e7 −0.0300823
\(97\) −1.43073e9 −1.64091 −0.820456 0.571709i \(-0.806281\pi\)
−0.820456 + 0.571709i \(0.806281\pi\)
\(98\) −1.64341e9 −1.79981
\(99\) −7.42059e7 −0.0776390
\(100\) 2.17183e7 0.0217183
\(101\) 1.67737e9 1.60392 0.801958 0.597381i \(-0.203792\pi\)
0.801958 + 0.597381i \(0.203792\pi\)
\(102\) 1.86619e7 0.0170709
\(103\) −2.83740e8 −0.248401 −0.124201 0.992257i \(-0.539637\pi\)
−0.124201 + 0.992257i \(0.539637\pi\)
\(104\) 8.59265e8 0.720239
\(105\) 1.62255e9 1.30271
\(106\) −2.06070e9 −1.58539
\(107\) 1.88662e9 1.39142 0.695710 0.718322i \(-0.255090\pi\)
0.695710 + 0.718322i \(0.255090\pi\)
\(108\) −7.09048e6 −0.00501497
\(109\) 2.26717e9 1.53838 0.769192 0.639017i \(-0.220659\pi\)
0.769192 + 0.639017i \(0.220659\pi\)
\(110\) 4.90555e8 0.319463
\(111\) −1.00272e9 −0.626943
\(112\) 2.84537e9 1.70867
\(113\) 3.82869e8 0.220901 0.110450 0.993882i \(-0.464771\pi\)
0.110450 + 0.993882i \(0.464771\pi\)
\(114\) 3.52958e8 0.195727
\(115\) −3.22507e9 −1.71949
\(116\) −6.51443e7 −0.0334053
\(117\) 4.93257e8 0.243353
\(118\) 2.77734e8 0.131874
\(119\) −1.06406e8 −0.0486411
\(120\) −1.75189e9 −0.771244
\(121\) −2.23003e9 −0.945750
\(122\) 1.79856e8 0.0735032
\(123\) −2.14752e9 −0.845988
\(124\) 1.53642e7 0.00583596
\(125\) −6.15598e8 −0.225529
\(126\) 1.59186e9 0.562650
\(127\) −1.91749e8 −0.0654057 −0.0327029 0.999465i \(-0.510412\pi\)
−0.0327029 + 0.999465i \(0.510412\pi\)
\(128\) −3.15027e9 −1.03730
\(129\) 2.44694e8 0.0777983
\(130\) −3.26079e9 −1.00133
\(131\) −1.24390e8 −0.0369034 −0.0184517 0.999830i \(-0.505874\pi\)
−0.0184517 + 0.999830i \(0.505874\pi\)
\(132\) 1.22229e7 0.00350422
\(133\) −2.01248e9 −0.557698
\(134\) 2.35769e8 0.0631706
\(135\) −1.00567e9 −0.260586
\(136\) 1.14888e8 0.0287971
\(137\) −2.59462e9 −0.629261 −0.314630 0.949214i \(-0.601881\pi\)
−0.314630 + 0.949214i \(0.601881\pi\)
\(138\) −3.16407e9 −0.742661
\(139\) −1.74072e9 −0.395514 −0.197757 0.980251i \(-0.563366\pi\)
−0.197757 + 0.980251i \(0.563366\pi\)
\(140\) −2.67260e8 −0.0587973
\(141\) −1.32424e9 −0.282151
\(142\) −1.78211e9 −0.367821
\(143\) −8.50298e8 −0.170043
\(144\) −1.76358e9 −0.341793
\(145\) −9.23962e9 −1.73579
\(146\) −2.17267e9 −0.395736
\(147\) −5.80776e9 −1.02584
\(148\) 1.65165e8 0.0282969
\(149\) −7.64215e9 −1.27021 −0.635107 0.772424i \(-0.719044\pi\)
−0.635107 + 0.772424i \(0.719044\pi\)
\(150\) 3.02211e9 0.487417
\(151\) −1.22281e10 −1.91410 −0.957048 0.289930i \(-0.906368\pi\)
−0.957048 + 0.289930i \(0.906368\pi\)
\(152\) 2.17290e9 0.330175
\(153\) 6.59509e7 0.00972991
\(154\) −2.74412e9 −0.393152
\(155\) 2.17915e9 0.303246
\(156\) −8.12472e7 −0.0109837
\(157\) 5.85575e9 0.769190 0.384595 0.923085i \(-0.374341\pi\)
0.384595 + 0.923085i \(0.374341\pi\)
\(158\) −4.64497e9 −0.592961
\(159\) −7.28246e9 −0.903630
\(160\) 5.84850e8 0.0705512
\(161\) 1.80408e10 2.11611
\(162\) −9.86645e8 −0.112549
\(163\) −1.43432e9 −0.159148 −0.0795742 0.996829i \(-0.525356\pi\)
−0.0795742 + 0.996829i \(0.525356\pi\)
\(164\) 3.53731e8 0.0381835
\(165\) 1.73361e9 0.182085
\(166\) 1.33359e10 1.36313
\(167\) −1.81042e10 −1.80117 −0.900584 0.434683i \(-0.856861\pi\)
−0.900584 + 0.434683i \(0.856861\pi\)
\(168\) 9.79994e9 0.949143
\(169\) −4.95245e9 −0.467014
\(170\) −4.35983e8 −0.0400359
\(171\) 1.24735e9 0.111559
\(172\) −4.03051e7 −0.00351141
\(173\) −1.89193e9 −0.160582 −0.0802910 0.996771i \(-0.525585\pi\)
−0.0802910 + 0.996771i \(0.525585\pi\)
\(174\) −9.06488e9 −0.749705
\(175\) −1.72313e10 −1.38883
\(176\) 3.04013e9 0.238828
\(177\) 9.81506e8 0.0751646
\(178\) 2.67143e10 1.99459
\(179\) −6.69832e9 −0.487671 −0.243836 0.969817i \(-0.578406\pi\)
−0.243836 + 0.969817i \(0.578406\pi\)
\(180\) 1.65649e8 0.0117615
\(181\) −4.76974e9 −0.330325 −0.165162 0.986266i \(-0.552815\pi\)
−0.165162 + 0.986266i \(0.552815\pi\)
\(182\) 1.82406e10 1.23230
\(183\) 6.35608e8 0.0418947
\(184\) −1.94789e10 −1.25281
\(185\) 2.34258e10 1.47036
\(186\) 2.13794e9 0.130975
\(187\) −1.13689e8 −0.00679879
\(188\) 2.18124e8 0.0127348
\(189\) 5.62561e9 0.320694
\(190\) −8.24587e9 −0.459034
\(191\) 6.63400e9 0.360683 0.180341 0.983604i \(-0.442280\pi\)
0.180341 + 0.983604i \(0.442280\pi\)
\(192\) −1.05738e10 −0.561531
\(193\) −1.51066e10 −0.783715 −0.391858 0.920026i \(-0.628167\pi\)
−0.391858 + 0.920026i \(0.628167\pi\)
\(194\) 3.27929e10 1.66216
\(195\) −1.15236e10 −0.570730
\(196\) 9.56631e8 0.0463012
\(197\) −1.63227e10 −0.772135 −0.386068 0.922470i \(-0.626167\pi\)
−0.386068 + 0.922470i \(0.626167\pi\)
\(198\) 1.70082e9 0.0786441
\(199\) −2.28537e9 −0.103304 −0.0516522 0.998665i \(-0.516449\pi\)
−0.0516522 + 0.998665i \(0.516449\pi\)
\(200\) 1.86050e10 0.822231
\(201\) 8.33203e8 0.0360055
\(202\) −3.84458e10 −1.62468
\(203\) 5.16857e10 2.13618
\(204\) −1.08632e7 −0.000439157 0
\(205\) 5.01708e10 1.98408
\(206\) 6.50343e9 0.251617
\(207\) −1.11818e10 −0.423296
\(208\) −2.02082e10 −0.748588
\(209\) −2.15023e9 −0.0779519
\(210\) −3.71894e10 −1.31957
\(211\) 3.51058e10 1.21929 0.609647 0.792673i \(-0.291311\pi\)
0.609647 + 0.792673i \(0.291311\pi\)
\(212\) 1.19954e9 0.0407851
\(213\) −6.29793e9 −0.209648
\(214\) −4.32421e10 −1.40943
\(215\) −5.71660e9 −0.182459
\(216\) −6.07406e9 −0.189862
\(217\) −1.21900e10 −0.373194
\(218\) −5.19643e10 −1.55830
\(219\) −7.67817e9 −0.225559
\(220\) −2.85553e8 −0.00821836
\(221\) 7.55707e8 0.0213102
\(222\) 2.29828e10 0.635059
\(223\) 3.43402e10 0.929888 0.464944 0.885340i \(-0.346074\pi\)
0.464944 + 0.885340i \(0.346074\pi\)
\(224\) −3.27160e9 −0.0868249
\(225\) 1.06801e10 0.277814
\(226\) −8.77549e9 −0.223761
\(227\) −4.86859e10 −1.21699 −0.608495 0.793558i \(-0.708226\pi\)
−0.608495 + 0.793558i \(0.708226\pi\)
\(228\) −2.05458e8 −0.00503519
\(229\) 4.13835e10 0.994416 0.497208 0.867631i \(-0.334359\pi\)
0.497208 + 0.867631i \(0.334359\pi\)
\(230\) 7.39197e10 1.74175
\(231\) −9.69768e9 −0.224086
\(232\) −5.58058e10 −1.26469
\(233\) 1.43437e10 0.318831 0.159415 0.987212i \(-0.449039\pi\)
0.159415 + 0.987212i \(0.449039\pi\)
\(234\) −1.13056e10 −0.246503
\(235\) 3.09372e10 0.661722
\(236\) −1.61670e8 −0.00339254
\(237\) −1.64152e10 −0.337971
\(238\) 2.43885e9 0.0492708
\(239\) 6.98150e10 1.38407 0.692035 0.721864i \(-0.256714\pi\)
0.692035 + 0.721864i \(0.256714\pi\)
\(240\) 4.12010e10 0.801600
\(241\) 3.97202e10 0.758463 0.379232 0.925302i \(-0.376188\pi\)
0.379232 + 0.925302i \(0.376188\pi\)
\(242\) 5.11130e10 0.957993
\(243\) −3.48678e9 −0.0641500
\(244\) −1.04695e8 −0.00189091
\(245\) 1.35682e11 2.40589
\(246\) 4.92219e10 0.856940
\(247\) 1.42929e10 0.244334
\(248\) 1.31617e10 0.220943
\(249\) 4.71289e10 0.776944
\(250\) 1.41097e10 0.228448
\(251\) 1.98403e10 0.315512 0.157756 0.987478i \(-0.449574\pi\)
0.157756 + 0.987478i \(0.449574\pi\)
\(252\) −9.26627e8 −0.0144745
\(253\) 1.92756e10 0.295778
\(254\) 4.39495e9 0.0662525
\(255\) −1.54076e9 −0.0228193
\(256\) 5.36858e9 0.0781231
\(257\) −8.77270e10 −1.25440 −0.627198 0.778860i \(-0.715798\pi\)
−0.627198 + 0.778860i \(0.715798\pi\)
\(258\) −5.60848e9 −0.0788055
\(259\) −1.31042e11 −1.80951
\(260\) 1.89811e9 0.0257598
\(261\) −3.20351e10 −0.427310
\(262\) 2.85107e9 0.0373811
\(263\) −6.54118e10 −0.843054 −0.421527 0.906816i \(-0.638506\pi\)
−0.421527 + 0.906816i \(0.638506\pi\)
\(264\) 1.04707e10 0.132666
\(265\) 1.70134e11 2.11926
\(266\) 4.61267e10 0.564917
\(267\) 9.44078e10 1.13686
\(268\) −1.37242e8 −0.00162510
\(269\) −3.14568e10 −0.366293 −0.183147 0.983086i \(-0.558628\pi\)
−0.183147 + 0.983086i \(0.558628\pi\)
\(270\) 2.30502e10 0.263960
\(271\) −2.31709e10 −0.260964 −0.130482 0.991451i \(-0.541652\pi\)
−0.130482 + 0.991451i \(0.541652\pi\)
\(272\) −2.70194e9 −0.0299306
\(273\) 6.44618e10 0.702378
\(274\) 5.94695e10 0.637407
\(275\) −1.84108e10 −0.194123
\(276\) 1.84181e9 0.0191054
\(277\) −1.40346e11 −1.43233 −0.716163 0.697933i \(-0.754103\pi\)
−0.716163 + 0.697933i \(0.754103\pi\)
\(278\) 3.98979e10 0.400635
\(279\) 7.55543e9 0.0746518
\(280\) −2.28948e11 −2.22600
\(281\) −1.19944e11 −1.14762 −0.573812 0.818987i \(-0.694536\pi\)
−0.573812 + 0.818987i \(0.694536\pi\)
\(282\) 3.03521e10 0.285804
\(283\) −1.53845e11 −1.42575 −0.712875 0.701292i \(-0.752607\pi\)
−0.712875 + 0.701292i \(0.752607\pi\)
\(284\) 1.03737e9 0.00946239
\(285\) −2.91407e10 −0.261637
\(286\) 1.94891e10 0.172244
\(287\) −2.80651e11 −2.44173
\(288\) 2.02776e9 0.0173680
\(289\) −1.18487e11 −0.999148
\(290\) 2.11775e11 1.75826
\(291\) 1.15889e11 0.947381
\(292\) 1.26472e9 0.0101805
\(293\) 1.90706e11 1.51168 0.755840 0.654756i \(-0.227229\pi\)
0.755840 + 0.654756i \(0.227229\pi\)
\(294\) 1.33116e11 1.03912
\(295\) −2.29301e10 −0.176282
\(296\) 1.41488e11 1.07129
\(297\) 6.01068e9 0.0448249
\(298\) 1.75161e11 1.28666
\(299\) −1.28128e11 −0.927093
\(300\) −1.75918e9 −0.0125391
\(301\) 3.19782e10 0.224545
\(302\) 2.80273e11 1.93887
\(303\) −1.35867e11 −0.926021
\(304\) −5.11024e10 −0.343171
\(305\) −1.48492e10 −0.0982547
\(306\) −1.51162e9 −0.00985587
\(307\) −7.97764e10 −0.512568 −0.256284 0.966602i \(-0.582498\pi\)
−0.256284 + 0.966602i \(0.582498\pi\)
\(308\) 1.59736e9 0.0101140
\(309\) 2.29830e10 0.143415
\(310\) −4.99469e10 −0.307172
\(311\) −2.22045e9 −0.0134592 −0.00672961 0.999977i \(-0.502142\pi\)
−0.00672961 + 0.999977i \(0.502142\pi\)
\(312\) −6.96004e10 −0.415830
\(313\) 1.22486e11 0.721337 0.360668 0.932694i \(-0.382549\pi\)
0.360668 + 0.932694i \(0.382549\pi\)
\(314\) −1.34216e11 −0.779148
\(315\) −1.31427e11 −0.752117
\(316\) 2.70385e9 0.0152542
\(317\) 1.07146e11 0.595951 0.297975 0.954574i \(-0.403689\pi\)
0.297975 + 0.954574i \(0.403689\pi\)
\(318\) 1.66916e11 0.915328
\(319\) 5.52235e10 0.298584
\(320\) 2.47026e11 1.31695
\(321\) −1.52817e11 −0.803337
\(322\) −4.13500e11 −2.14350
\(323\) 1.91103e9 0.00976913
\(324\) 5.74329e8 0.00289540
\(325\) 1.22379e11 0.608461
\(326\) 3.28751e10 0.161209
\(327\) −1.83641e11 −0.888187
\(328\) 3.03023e11 1.44559
\(329\) −1.73060e11 −0.814358
\(330\) −3.97350e10 −0.184442
\(331\) −2.06304e11 −0.944676 −0.472338 0.881418i \(-0.656590\pi\)
−0.472338 + 0.881418i \(0.656590\pi\)
\(332\) −7.76288e9 −0.0350672
\(333\) 8.12207e10 0.361966
\(334\) 4.14953e11 1.82448
\(335\) −1.94654e10 −0.0844428
\(336\) −2.30475e11 −0.986500
\(337\) 1.93295e11 0.816368 0.408184 0.912900i \(-0.366162\pi\)
0.408184 + 0.912900i \(0.366162\pi\)
\(338\) 1.13512e11 0.473060
\(339\) −3.10124e10 −0.127537
\(340\) 2.53787e8 0.00102995
\(341\) −1.30244e10 −0.0521630
\(342\) −2.85896e10 −0.113003
\(343\) −3.31828e11 −1.29446
\(344\) −3.45273e10 −0.132938
\(345\) 2.61230e11 0.992746
\(346\) 4.33636e10 0.162661
\(347\) −4.00675e11 −1.48358 −0.741788 0.670634i \(-0.766022\pi\)
−0.741788 + 0.670634i \(0.766022\pi\)
\(348\) 5.27669e9 0.0192866
\(349\) −2.78406e11 −1.00453 −0.502266 0.864713i \(-0.667500\pi\)
−0.502266 + 0.864713i \(0.667500\pi\)
\(350\) 3.94948e11 1.40681
\(351\) −3.99538e10 −0.140500
\(352\) −3.49554e9 −0.0121359
\(353\) −2.58537e10 −0.0886209 −0.0443105 0.999018i \(-0.514109\pi\)
−0.0443105 + 0.999018i \(0.514109\pi\)
\(354\) −2.24965e10 −0.0761376
\(355\) 1.47133e11 0.491681
\(356\) −1.55505e10 −0.0513120
\(357\) 8.61886e9 0.0280830
\(358\) 1.53528e11 0.493984
\(359\) −2.86964e11 −0.911807 −0.455904 0.890029i \(-0.650684\pi\)
−0.455904 + 0.890029i \(0.650684\pi\)
\(360\) 1.41903e11 0.445278
\(361\) −2.86544e11 −0.887991
\(362\) 1.09324e11 0.334601
\(363\) 1.80632e11 0.546029
\(364\) −1.06179e10 −0.0317017
\(365\) 1.79379e11 0.528997
\(366\) −1.45684e10 −0.0424371
\(367\) −2.90965e11 −0.837227 −0.418614 0.908164i \(-0.637484\pi\)
−0.418614 + 0.908164i \(0.637484\pi\)
\(368\) 4.58105e11 1.30212
\(369\) 1.73949e11 0.488432
\(370\) −5.36928e11 −1.48939
\(371\) −9.51716e11 −2.60810
\(372\) −1.24450e9 −0.00336939
\(373\) 1.60534e11 0.429415 0.214708 0.976678i \(-0.431120\pi\)
0.214708 + 0.976678i \(0.431120\pi\)
\(374\) 2.60579e9 0.00688680
\(375\) 4.98634e10 0.130209
\(376\) 1.86856e11 0.482127
\(377\) −3.67078e11 −0.935886
\(378\) −1.28941e11 −0.324846
\(379\) −1.56835e10 −0.0390451 −0.0195226 0.999809i \(-0.506215\pi\)
−0.0195226 + 0.999809i \(0.506215\pi\)
\(380\) 4.79994e9 0.0118089
\(381\) 1.55317e10 0.0377620
\(382\) −1.52054e11 −0.365352
\(383\) 3.05782e11 0.726134 0.363067 0.931763i \(-0.381730\pi\)
0.363067 + 0.931763i \(0.381730\pi\)
\(384\) 2.55172e11 0.598883
\(385\) 2.26559e11 0.525543
\(386\) 3.46248e11 0.793861
\(387\) −1.98202e10 −0.0449169
\(388\) −1.90888e10 −0.0427598
\(389\) −5.78332e11 −1.28057 −0.640286 0.768136i \(-0.721184\pi\)
−0.640286 + 0.768136i \(0.721184\pi\)
\(390\) 2.64124e11 0.578119
\(391\) −1.71313e10 −0.0370677
\(392\) 8.19498e11 1.75291
\(393\) 1.00756e10 0.0213062
\(394\) 3.74121e11 0.782131
\(395\) 3.83495e11 0.792635
\(396\) −9.90054e8 −0.00202316
\(397\) −7.31453e11 −1.47785 −0.738923 0.673790i \(-0.764665\pi\)
−0.738923 + 0.673790i \(0.764665\pi\)
\(398\) 5.23816e10 0.104642
\(399\) 1.63011e11 0.321987
\(400\) −4.37552e11 −0.854593
\(401\) 9.78590e11 1.88995 0.944977 0.327137i \(-0.106084\pi\)
0.944977 + 0.327137i \(0.106084\pi\)
\(402\) −1.90973e10 −0.0364716
\(403\) 8.65750e10 0.163501
\(404\) 2.23794e10 0.0417958
\(405\) 8.14589e10 0.150450
\(406\) −1.18465e12 −2.16384
\(407\) −1.40012e11 −0.252924
\(408\) −9.30592e9 −0.0166260
\(409\) −3.33232e11 −0.588833 −0.294417 0.955677i \(-0.595125\pi\)
−0.294417 + 0.955677i \(0.595125\pi\)
\(410\) −1.14993e12 −2.00976
\(411\) 2.10164e11 0.363304
\(412\) −3.78566e9 −0.00647298
\(413\) 1.28269e11 0.216944
\(414\) 2.56290e11 0.428775
\(415\) −1.10103e12 −1.82215
\(416\) 2.32353e10 0.0380390
\(417\) 1.40998e11 0.228350
\(418\) 4.92840e10 0.0789610
\(419\) 6.63685e11 1.05196 0.525980 0.850497i \(-0.323699\pi\)
0.525980 + 0.850497i \(0.323699\pi\)
\(420\) 2.16480e10 0.0339466
\(421\) 2.83675e11 0.440100 0.220050 0.975489i \(-0.429378\pi\)
0.220050 + 0.975489i \(0.429378\pi\)
\(422\) −8.04638e11 −1.23508
\(423\) 1.07264e11 0.162900
\(424\) 1.02758e12 1.54408
\(425\) 1.63627e10 0.0243279
\(426\) 1.44351e11 0.212362
\(427\) 8.30651e10 0.120919
\(428\) 2.51713e10 0.0362584
\(429\) 6.88742e10 0.0981745
\(430\) 1.31026e11 0.184821
\(431\) 4.68713e11 0.654273 0.327137 0.944977i \(-0.393916\pi\)
0.327137 + 0.944977i \(0.393916\pi\)
\(432\) 1.42850e11 0.197334
\(433\) −5.38090e10 −0.0735630 −0.0367815 0.999323i \(-0.511711\pi\)
−0.0367815 + 0.999323i \(0.511711\pi\)
\(434\) 2.79399e11 0.378025
\(435\) 7.48409e11 1.00216
\(436\) 3.02486e10 0.0400881
\(437\) −3.24009e11 −0.425002
\(438\) 1.75986e11 0.228478
\(439\) 9.15078e11 1.17589 0.587947 0.808900i \(-0.299936\pi\)
0.587947 + 0.808900i \(0.299936\pi\)
\(440\) −2.44619e11 −0.311138
\(441\) 4.70429e11 0.592271
\(442\) −1.73211e10 −0.0215861
\(443\) −9.22618e11 −1.13816 −0.569082 0.822281i \(-0.692701\pi\)
−0.569082 + 0.822281i \(0.692701\pi\)
\(444\) −1.33783e10 −0.0163372
\(445\) −2.20557e12 −2.66625
\(446\) −7.87089e11 −0.941926
\(447\) 6.19014e11 0.733359
\(448\) −1.38184e12 −1.62072
\(449\) 1.57214e12 1.82551 0.912754 0.408510i \(-0.133952\pi\)
0.912754 + 0.408510i \(0.133952\pi\)
\(450\) −2.44791e11 −0.281410
\(451\) −2.99861e11 −0.341292
\(452\) 5.10824e9 0.00575636
\(453\) 9.90478e11 1.10510
\(454\) 1.11590e12 1.23274
\(455\) −1.50597e12 −1.64727
\(456\) −1.76005e11 −0.190627
\(457\) 5.15006e11 0.552318 0.276159 0.961112i \(-0.410938\pi\)
0.276159 + 0.961112i \(0.410938\pi\)
\(458\) −9.48525e11 −1.00729
\(459\) −5.34202e9 −0.00561757
\(460\) −4.30288e10 −0.0448073
\(461\) −1.01160e12 −1.04317 −0.521585 0.853199i \(-0.674659\pi\)
−0.521585 + 0.853199i \(0.674659\pi\)
\(462\) 2.22274e11 0.226986
\(463\) −7.03444e11 −0.711402 −0.355701 0.934600i \(-0.615758\pi\)
−0.355701 + 0.934600i \(0.615758\pi\)
\(464\) 1.31244e12 1.31447
\(465\) −1.76511e11 −0.175079
\(466\) −3.28763e11 −0.322958
\(467\) −1.33152e12 −1.29545 −0.647725 0.761874i \(-0.724279\pi\)
−0.647725 + 0.761874i \(0.724279\pi\)
\(468\) 6.58103e9 0.00634143
\(469\) 1.08888e11 0.103921
\(470\) −7.09091e11 −0.670288
\(471\) −4.74315e11 −0.444092
\(472\) −1.38494e11 −0.128438
\(473\) 3.41670e10 0.0313857
\(474\) 3.76242e11 0.342346
\(475\) 3.09472e11 0.278933
\(476\) −1.41966e9 −0.00126752
\(477\) 5.89879e11 0.521711
\(478\) −1.60018e12 −1.40199
\(479\) 1.70657e12 1.48120 0.740599 0.671947i \(-0.234542\pi\)
0.740599 + 0.671947i \(0.234542\pi\)
\(480\) −4.73728e10 −0.0407328
\(481\) 9.30678e11 0.792769
\(482\) −9.10400e11 −0.768282
\(483\) −1.46130e12 −1.22174
\(484\) −2.97530e10 −0.0246449
\(485\) −2.70743e12 −2.22187
\(486\) 7.99183e10 0.0649805
\(487\) −1.61398e12 −1.30022 −0.650112 0.759838i \(-0.725278\pi\)
−0.650112 + 0.759838i \(0.725278\pi\)
\(488\) −8.96867e10 −0.0715878
\(489\) 1.16180e11 0.0918843
\(490\) −3.10988e12 −2.43703
\(491\) −2.15992e12 −1.67714 −0.838572 0.544790i \(-0.816609\pi\)
−0.838572 + 0.544790i \(0.816609\pi\)
\(492\) −2.86522e10 −0.0220452
\(493\) −4.90802e10 −0.0374192
\(494\) −3.27598e11 −0.247497
\(495\) −1.40423e11 −0.105127
\(496\) −3.09538e11 −0.229639
\(497\) −8.23052e11 −0.605095
\(498\) −1.08021e12 −0.787002
\(499\) −2.03228e12 −1.46734 −0.733670 0.679506i \(-0.762194\pi\)
−0.733670 + 0.679506i \(0.762194\pi\)
\(500\) −8.21330e9 −0.00587696
\(501\) 1.46644e12 1.03990
\(502\) −4.54745e11 −0.319596
\(503\) 6.31371e11 0.439773 0.219886 0.975525i \(-0.429431\pi\)
0.219886 + 0.975525i \(0.429431\pi\)
\(504\) −7.93795e11 −0.547988
\(505\) 3.17414e12 2.17178
\(506\) −4.41804e11 −0.299607
\(507\) 4.01148e11 0.269631
\(508\) −2.55831e9 −0.00170438
\(509\) −2.03580e12 −1.34433 −0.672165 0.740401i \(-0.734635\pi\)
−0.672165 + 0.740401i \(0.734635\pi\)
\(510\) 3.53147e10 0.0231147
\(511\) −1.00343e12 −0.651018
\(512\) 1.48989e12 0.958161
\(513\) −1.01035e11 −0.0644086
\(514\) 2.01073e12 1.27063
\(515\) −5.36933e11 −0.336347
\(516\) 3.26471e9 0.00202731
\(517\) −1.84906e11 −0.113826
\(518\) 3.00353e12 1.83294
\(519\) 1.53246e11 0.0927120
\(520\) 1.62602e12 0.975237
\(521\) 1.62258e12 0.964796 0.482398 0.875952i \(-0.339766\pi\)
0.482398 + 0.875952i \(0.339766\pi\)
\(522\) 7.34255e11 0.432842
\(523\) 1.30110e12 0.760421 0.380210 0.924900i \(-0.375852\pi\)
0.380210 + 0.924900i \(0.375852\pi\)
\(524\) −1.65962e9 −0.000961649 0
\(525\) 1.39574e12 0.801840
\(526\) 1.49926e12 0.853968
\(527\) 1.15755e10 0.00653720
\(528\) −2.46251e11 −0.137888
\(529\) 1.10341e12 0.612613
\(530\) −3.89953e12 −2.14670
\(531\) −7.95020e10 −0.0433963
\(532\) −2.68505e10 −0.0145328
\(533\) 1.99322e12 1.06975
\(534\) −2.16386e12 −1.15158
\(535\) 3.57013e12 1.88405
\(536\) −1.17568e11 −0.0615245
\(537\) 5.42564e11 0.281557
\(538\) 7.21000e11 0.371035
\(539\) −8.10947e11 −0.413850
\(540\) −1.34176e10 −0.00679051
\(541\) −2.29207e12 −1.15038 −0.575189 0.818020i \(-0.695072\pi\)
−0.575189 + 0.818020i \(0.695072\pi\)
\(542\) 5.31084e11 0.264342
\(543\) 3.86349e11 0.190713
\(544\) 3.10668e9 0.00152090
\(545\) 4.29025e12 2.08304
\(546\) −1.47749e12 −0.711470
\(547\) −3.98480e12 −1.90311 −0.951553 0.307484i \(-0.900513\pi\)
−0.951553 + 0.307484i \(0.900513\pi\)
\(548\) −3.46174e10 −0.0163976
\(549\) −5.14842e10 −0.0241879
\(550\) 4.21982e11 0.196636
\(551\) −9.28266e11 −0.429033
\(552\) 1.57779e12 0.723308
\(553\) −2.14524e12 −0.975468
\(554\) 3.21678e12 1.45087
\(555\) −1.89749e12 −0.848910
\(556\) −2.32247e10 −0.0103065
\(557\) 2.70211e12 1.18947 0.594736 0.803921i \(-0.297257\pi\)
0.594736 + 0.803921i \(0.297257\pi\)
\(558\) −1.73173e11 −0.0756182
\(559\) −2.27113e11 −0.0983760
\(560\) 5.38440e12 2.31362
\(561\) 9.20881e9 0.00392528
\(562\) 2.74915e12 1.16248
\(563\) 2.46879e12 1.03561 0.517805 0.855498i \(-0.326749\pi\)
0.517805 + 0.855498i \(0.326749\pi\)
\(564\) −1.76680e10 −0.00735245
\(565\) 7.24517e11 0.299110
\(566\) 3.52617e12 1.44421
\(567\) −4.55674e11 −0.185153
\(568\) 8.88662e11 0.358236
\(569\) 2.28396e12 0.913446 0.456723 0.889609i \(-0.349023\pi\)
0.456723 + 0.889609i \(0.349023\pi\)
\(570\) 6.67915e11 0.265024
\(571\) 4.03714e11 0.158932 0.0794660 0.996838i \(-0.474678\pi\)
0.0794660 + 0.996838i \(0.474678\pi\)
\(572\) −1.13447e10 −0.00443108
\(573\) −5.37354e11 −0.208240
\(574\) 6.43262e12 2.47334
\(575\) −2.77425e12 −1.05838
\(576\) 8.56475e11 0.324200
\(577\) 7.02747e10 0.0263942 0.0131971 0.999913i \(-0.495799\pi\)
0.0131971 + 0.999913i \(0.495799\pi\)
\(578\) 2.71576e12 1.01208
\(579\) 1.22363e12 0.452478
\(580\) −1.23275e11 −0.0452323
\(581\) 6.15909e12 2.24246
\(582\) −2.65622e12 −0.959646
\(583\) −1.01686e12 −0.364546
\(584\) 1.08342e12 0.385424
\(585\) 9.33408e11 0.329511
\(586\) −4.37105e12 −1.53125
\(587\) −7.87103e11 −0.273628 −0.136814 0.990597i \(-0.543686\pi\)
−0.136814 + 0.990597i \(0.543686\pi\)
\(588\) −7.74871e10 −0.0267320
\(589\) 2.18930e11 0.0749527
\(590\) 5.25566e11 0.178564
\(591\) 1.32214e12 0.445793
\(592\) −3.32752e12 −1.11346
\(593\) −2.04023e12 −0.677536 −0.338768 0.940870i \(-0.610010\pi\)
−0.338768 + 0.940870i \(0.610010\pi\)
\(594\) −1.37767e11 −0.0454052
\(595\) −2.01355e11 −0.0658623
\(596\) −1.01961e11 −0.0331000
\(597\) 1.85115e11 0.0596428
\(598\) 2.93673e12 0.939094
\(599\) 5.37648e12 1.70638 0.853192 0.521596i \(-0.174663\pi\)
0.853192 + 0.521596i \(0.174663\pi\)
\(600\) −1.50700e12 −0.474715
\(601\) −1.55803e12 −0.487125 −0.243562 0.969885i \(-0.578316\pi\)
−0.243562 + 0.969885i \(0.578316\pi\)
\(602\) −7.32950e11 −0.227452
\(603\) −6.74894e10 −0.0207878
\(604\) −1.63148e11 −0.0498786
\(605\) −4.21996e12 −1.28059
\(606\) 3.11411e12 0.938009
\(607\) −4.79310e12 −1.43307 −0.716535 0.697552i \(-0.754273\pi\)
−0.716535 + 0.697552i \(0.754273\pi\)
\(608\) 5.87574e10 0.0174380
\(609\) −4.18654e12 −1.23332
\(610\) 3.40349e11 0.0995267
\(611\) 1.22910e12 0.356780
\(612\) 8.79916e8 0.000253548 0
\(613\) −5.79540e12 −1.65772 −0.828861 0.559455i \(-0.811010\pi\)
−0.828861 + 0.559455i \(0.811010\pi\)
\(614\) 1.82850e12 0.519203
\(615\) −4.06383e12 −1.14551
\(616\) 1.36838e12 0.382907
\(617\) −2.65602e12 −0.737815 −0.368908 0.929466i \(-0.620268\pi\)
−0.368908 + 0.929466i \(0.620268\pi\)
\(618\) −5.26778e11 −0.145271
\(619\) −2.06524e12 −0.565410 −0.282705 0.959207i \(-0.591232\pi\)
−0.282705 + 0.959207i \(0.591232\pi\)
\(620\) 2.90742e10 0.00790216
\(621\) 9.05723e11 0.244390
\(622\) 5.08936e10 0.0136335
\(623\) 1.23378e13 3.28127
\(624\) 1.63686e12 0.432197
\(625\) −4.34424e12 −1.13882
\(626\) −2.80743e12 −0.730675
\(627\) 1.74169e11 0.0450055
\(628\) 7.81273e10 0.0200440
\(629\) 1.24436e11 0.0316971
\(630\) 3.01234e12 0.761854
\(631\) 1.41149e12 0.354443 0.177222 0.984171i \(-0.443289\pi\)
0.177222 + 0.984171i \(0.443289\pi\)
\(632\) 2.31625e12 0.577509
\(633\) −2.84357e12 −0.703959
\(634\) −2.45583e12 −0.603666
\(635\) −3.62853e11 −0.0885624
\(636\) −9.71624e10 −0.0235473
\(637\) 5.39048e12 1.29718
\(638\) −1.26574e12 −0.302449
\(639\) 5.10132e11 0.121040
\(640\) −5.96137e12 −1.40455
\(641\) 2.33049e12 0.545238 0.272619 0.962122i \(-0.412110\pi\)
0.272619 + 0.962122i \(0.412110\pi\)
\(642\) 3.50261e12 0.813737
\(643\) 4.60509e12 1.06240 0.531201 0.847246i \(-0.321741\pi\)
0.531201 + 0.847246i \(0.321741\pi\)
\(644\) 2.40700e11 0.0551428
\(645\) 4.63044e11 0.105343
\(646\) −4.38014e10 −0.00989560
\(647\) 1.96037e11 0.0439815 0.0219907 0.999758i \(-0.493000\pi\)
0.0219907 + 0.999758i \(0.493000\pi\)
\(648\) 4.91999e11 0.109617
\(649\) 1.37049e11 0.0303232
\(650\) −2.80497e12 −0.616338
\(651\) 9.87390e11 0.215464
\(652\) −1.91367e10 −0.00414718
\(653\) −2.50898e12 −0.539993 −0.269997 0.962861i \(-0.587023\pi\)
−0.269997 + 0.962861i \(0.587023\pi\)
\(654\) 4.20911e12 0.899685
\(655\) −2.35389e11 −0.0499689
\(656\) −7.12651e12 −1.50248
\(657\) 6.21932e11 0.130226
\(658\) 3.96660e12 0.824900
\(659\) 3.10145e12 0.640591 0.320296 0.947318i \(-0.396218\pi\)
0.320296 + 0.947318i \(0.396218\pi\)
\(660\) 2.31298e10 0.00474487
\(661\) 2.50610e12 0.510612 0.255306 0.966860i \(-0.417824\pi\)
0.255306 + 0.966860i \(0.417824\pi\)
\(662\) 4.72857e12 0.956905
\(663\) −6.12123e10 −0.0123035
\(664\) −6.65006e12 −1.32761
\(665\) −3.80829e12 −0.755148
\(666\) −1.86161e12 −0.366652
\(667\) 8.32140e12 1.62791
\(668\) −2.41545e11 −0.0469359
\(669\) −2.78156e12 −0.536871
\(670\) 4.46154e11 0.0855359
\(671\) 8.87509e10 0.0169013
\(672\) 2.65000e11 0.0501284
\(673\) −3.21035e12 −0.603232 −0.301616 0.953430i \(-0.597526\pi\)
−0.301616 + 0.953430i \(0.597526\pi\)
\(674\) −4.43039e12 −0.826936
\(675\) −8.65087e11 −0.160396
\(676\) −6.60755e10 −0.0121697
\(677\) −4.53361e12 −0.829460 −0.414730 0.909945i \(-0.636124\pi\)
−0.414730 + 0.909945i \(0.636124\pi\)
\(678\) 7.10815e11 0.129188
\(679\) 1.51451e13 2.73438
\(680\) 2.17407e11 0.0389926
\(681\) 3.94356e12 0.702629
\(682\) 2.98523e11 0.0528383
\(683\) 2.98484e12 0.524841 0.262421 0.964954i \(-0.415479\pi\)
0.262421 + 0.964954i \(0.415479\pi\)
\(684\) 1.66421e10 0.00290707
\(685\) −4.90989e12 −0.852048
\(686\) 7.60561e12 1.31122
\(687\) −3.35207e12 −0.574126
\(688\) 8.12014e11 0.138171
\(689\) 6.75921e12 1.14264
\(690\) −5.98749e12 −1.00560
\(691\) 3.29209e12 0.549314 0.274657 0.961542i \(-0.411436\pi\)
0.274657 + 0.961542i \(0.411436\pi\)
\(692\) −2.52421e10 −0.00418454
\(693\) 7.85512e11 0.129376
\(694\) 9.18361e12 1.50278
\(695\) −3.29403e12 −0.535545
\(696\) 4.52027e12 0.730168
\(697\) 2.66503e11 0.0427716
\(698\) 6.38116e12 1.01754
\(699\) −1.16184e12 −0.184077
\(700\) −2.29900e11 −0.0361908
\(701\) 3.95680e11 0.0618889 0.0309445 0.999521i \(-0.490148\pi\)
0.0309445 + 0.999521i \(0.490148\pi\)
\(702\) 9.15755e11 0.142319
\(703\) 2.35350e12 0.363425
\(704\) −1.47643e12 −0.226535
\(705\) −2.50591e12 −0.382045
\(706\) 5.92575e11 0.0897682
\(707\) −1.77559e13 −2.67273
\(708\) 1.30952e10 0.00195868
\(709\) −2.61919e12 −0.389278 −0.194639 0.980875i \(-0.562353\pi\)
−0.194639 + 0.980875i \(0.562353\pi\)
\(710\) −3.37235e12 −0.498047
\(711\) 1.32963e12 0.195127
\(712\) −1.33213e13 −1.94262
\(713\) −1.96259e12 −0.284398
\(714\) −1.97547e11 −0.0284465
\(715\) −1.60905e12 −0.230246
\(716\) −8.93689e10 −0.0127080
\(717\) −5.65501e12 −0.799093
\(718\) 6.57732e12 0.923611
\(719\) −1.29488e13 −1.80697 −0.903484 0.428621i \(-0.859000\pi\)
−0.903484 + 0.428621i \(0.859000\pi\)
\(720\) −3.33728e12 −0.462804
\(721\) 3.00356e12 0.413930
\(722\) 6.56768e12 0.899487
\(723\) −3.21733e12 −0.437899
\(724\) −6.36379e10 −0.00860780
\(725\) −7.94805e12 −1.06841
\(726\) −4.14015e12 −0.553097
\(727\) −9.17093e12 −1.21761 −0.608806 0.793319i \(-0.708351\pi\)
−0.608806 + 0.793319i \(0.708351\pi\)
\(728\) −9.09581e12 −1.20019
\(729\) 2.82430e11 0.0370370
\(730\) −4.11142e12 −0.535845
\(731\) −3.03661e10 −0.00393334
\(732\) 8.48027e9 0.00109172
\(733\) −9.05826e12 −1.15898 −0.579492 0.814978i \(-0.696749\pi\)
−0.579492 + 0.814978i \(0.696749\pi\)
\(734\) 6.66902e12 0.848066
\(735\) −1.09902e13 −1.38904
\(736\) −5.26728e11 −0.0661662
\(737\) 1.16341e11 0.0145255
\(738\) −3.98697e12 −0.494755
\(739\) 1.23920e13 1.52842 0.764208 0.644970i \(-0.223130\pi\)
0.764208 + 0.644970i \(0.223130\pi\)
\(740\) 3.12547e11 0.0383154
\(741\) −1.15772e12 −0.141066
\(742\) 2.18136e13 2.64187
\(743\) −5.77385e12 −0.695050 −0.347525 0.937671i \(-0.612978\pi\)
−0.347525 + 0.937671i \(0.612978\pi\)
\(744\) −1.06610e12 −0.127562
\(745\) −1.44615e13 −1.71993
\(746\) −3.67949e12 −0.434974
\(747\) −3.81744e12 −0.448569
\(748\) −1.51684e9 −0.000177167 0
\(749\) −1.99710e13 −2.31863
\(750\) −1.14289e12 −0.131895
\(751\) 1.09139e13 1.25198 0.625991 0.779830i \(-0.284695\pi\)
0.625991 + 0.779830i \(0.284695\pi\)
\(752\) −4.39448e12 −0.501103
\(753\) −1.60706e12 −0.182161
\(754\) 8.41356e12 0.948001
\(755\) −2.31397e13 −2.59177
\(756\) 7.50568e10 0.00835684
\(757\) 4.84513e12 0.536259 0.268129 0.963383i \(-0.413595\pi\)
0.268129 + 0.963383i \(0.413595\pi\)
\(758\) 3.59472e11 0.0395506
\(759\) −1.56133e12 −0.170768
\(760\) 4.11187e12 0.447072
\(761\) 4.06480e12 0.439348 0.219674 0.975573i \(-0.429501\pi\)
0.219674 + 0.975573i \(0.429501\pi\)
\(762\) −3.55991e11 −0.0382509
\(763\) −2.39993e13 −2.56353
\(764\) 8.85108e10 0.00939888
\(765\) 1.24801e11 0.0131748
\(766\) −7.00862e12 −0.735534
\(767\) −9.10985e11 −0.0950456
\(768\) −4.34855e11 −0.0451044
\(769\) −3.72731e12 −0.384351 −0.192175 0.981361i \(-0.561554\pi\)
−0.192175 + 0.981361i \(0.561554\pi\)
\(770\) −5.19281e12 −0.532346
\(771\) 7.10589e12 0.724225
\(772\) −2.01552e11 −0.0204225
\(773\) 9.34605e12 0.941500 0.470750 0.882267i \(-0.343983\pi\)
0.470750 + 0.882267i \(0.343983\pi\)
\(774\) 4.54287e11 0.0454984
\(775\) 1.87454e12 0.186654
\(776\) −1.63524e13 −1.61884
\(777\) 1.06144e13 1.04472
\(778\) 1.32556e13 1.29715
\(779\) 5.04045e12 0.490400
\(780\) −1.53747e11 −0.0148724
\(781\) −8.79389e11 −0.0845769
\(782\) 3.92656e11 0.0375475
\(783\) 2.59484e12 0.246708
\(784\) −1.92730e13 −1.82191
\(785\) 1.10810e13 1.04152
\(786\) −2.30937e11 −0.0215820
\(787\) 2.89984e12 0.269456 0.134728 0.990883i \(-0.456984\pi\)
0.134728 + 0.990883i \(0.456984\pi\)
\(788\) −2.17777e11 −0.0201207
\(789\) 5.29836e12 0.486738
\(790\) −8.78984e12 −0.802896
\(791\) −4.05289e12 −0.368104
\(792\) −8.48129e11 −0.0765947
\(793\) −5.89939e11 −0.0529759
\(794\) 1.67651e13 1.49698
\(795\) −1.37809e13 −1.22356
\(796\) −3.04914e10 −0.00269196
\(797\) 1.61987e13 1.42206 0.711032 0.703160i \(-0.248228\pi\)
0.711032 + 0.703160i \(0.248228\pi\)
\(798\) −3.73626e12 −0.326155
\(799\) 1.64336e11 0.0142650
\(800\) 5.03096e11 0.0434256
\(801\) −7.64704e12 −0.656367
\(802\) −2.24296e13 −1.91442
\(803\) −1.07211e12 −0.0909957
\(804\) 1.11166e10 0.000938251 0
\(805\) 3.41392e13 2.86531
\(806\) −1.98433e12 −0.165617
\(807\) 2.54800e12 0.211479
\(808\) 1.91713e13 1.58234
\(809\) −2.05504e13 −1.68676 −0.843379 0.537320i \(-0.819437\pi\)
−0.843379 + 0.537320i \(0.819437\pi\)
\(810\) −1.86707e12 −0.152397
\(811\) 1.71119e13 1.38901 0.694505 0.719488i \(-0.255624\pi\)
0.694505 + 0.719488i \(0.255624\pi\)
\(812\) 6.89590e11 0.0556658
\(813\) 1.87684e12 0.150668
\(814\) 3.20912e12 0.256198
\(815\) −2.71422e12 −0.215494
\(816\) 2.18857e11 0.0172804
\(817\) −5.74322e11 −0.0450979
\(818\) 7.63780e12 0.596456
\(819\) −5.22141e12 −0.405518
\(820\) 6.69378e11 0.0517022
\(821\) −1.29396e13 −0.993978 −0.496989 0.867757i \(-0.665561\pi\)
−0.496989 + 0.867757i \(0.665561\pi\)
\(822\) −4.81703e12 −0.368007
\(823\) 1.15453e13 0.877212 0.438606 0.898680i \(-0.355472\pi\)
0.438606 + 0.898680i \(0.355472\pi\)
\(824\) −3.24299e12 −0.245060
\(825\) 1.49128e12 0.112077
\(826\) −2.93997e12 −0.219752
\(827\) 1.58069e13 1.17509 0.587546 0.809190i \(-0.300094\pi\)
0.587546 + 0.809190i \(0.300094\pi\)
\(828\) −1.49187e11 −0.0110305
\(829\) 1.88409e12 0.138550 0.0692750 0.997598i \(-0.477931\pi\)
0.0692750 + 0.997598i \(0.477931\pi\)
\(830\) 2.52361e13 1.84574
\(831\) 1.13680e13 0.826954
\(832\) 9.81404e12 0.710056
\(833\) 7.20733e11 0.0518647
\(834\) −3.23173e12 −0.231306
\(835\) −3.42592e13 −2.43886
\(836\) −2.86884e10 −0.00203132
\(837\) −6.11990e11 −0.0431002
\(838\) −1.52119e13 −1.06558
\(839\) −1.77244e13 −1.23493 −0.617465 0.786598i \(-0.711840\pi\)
−0.617465 + 0.786598i \(0.711840\pi\)
\(840\) 1.85448e13 1.28518
\(841\) 9.33315e12 0.643348
\(842\) −6.50193e12 −0.445798
\(843\) 9.71545e12 0.662580
\(844\) 4.68382e11 0.0317730
\(845\) −9.37170e12 −0.632358
\(846\) −2.45852e12 −0.165009
\(847\) 2.36061e13 1.57598
\(848\) −2.41667e13 −1.60486
\(849\) 1.24614e13 0.823157
\(850\) −3.75039e11 −0.0246429
\(851\) −2.10978e13 −1.37897
\(852\) −8.40269e10 −0.00546312
\(853\) 4.32299e12 0.279585 0.139792 0.990181i \(-0.455356\pi\)
0.139792 + 0.990181i \(0.455356\pi\)
\(854\) −1.90388e12 −0.122484
\(855\) 2.36040e12 0.151056
\(856\) 2.15630e13 1.37271
\(857\) −1.08195e13 −0.685164 −0.342582 0.939488i \(-0.611301\pi\)
−0.342582 + 0.939488i \(0.611301\pi\)
\(858\) −1.57862e12 −0.0994454
\(859\) 1.50394e13 0.942453 0.471227 0.882012i \(-0.343811\pi\)
0.471227 + 0.882012i \(0.343811\pi\)
\(860\) −7.62708e10 −0.00475461
\(861\) 2.27327e13 1.40974
\(862\) −1.07431e13 −0.662743
\(863\) −6.00473e12 −0.368507 −0.184253 0.982879i \(-0.558987\pi\)
−0.184253 + 0.982879i \(0.558987\pi\)
\(864\) −1.64248e11 −0.0100274
\(865\) −3.58016e12 −0.217435
\(866\) 1.23332e12 0.0745154
\(867\) 9.59743e12 0.576858
\(868\) −1.62639e11 −0.00972491
\(869\) −2.29208e12 −0.136346
\(870\) −1.71538e13 −1.01513
\(871\) −7.73337e11 −0.0455289
\(872\) 2.59124e13 1.51769
\(873\) −9.38703e12 −0.546971
\(874\) 7.42640e12 0.430504
\(875\) 6.51646e12 0.375816
\(876\) −1.02442e11 −0.00587773
\(877\) −2.28028e13 −1.30164 −0.650820 0.759232i \(-0.725575\pi\)
−0.650820 + 0.759232i \(0.725575\pi\)
\(878\) −2.09739e13 −1.19112
\(879\) −1.54472e13 −0.872769
\(880\) 5.75296e12 0.323385
\(881\) 4.31310e12 0.241211 0.120606 0.992700i \(-0.461516\pi\)
0.120606 + 0.992700i \(0.461516\pi\)
\(882\) −1.07824e13 −0.599938
\(883\) −1.25619e13 −0.695397 −0.347699 0.937606i \(-0.613037\pi\)
−0.347699 + 0.937606i \(0.613037\pi\)
\(884\) 1.00826e10 0.000555314 0
\(885\) 1.85734e12 0.101776
\(886\) 2.11467e13 1.15290
\(887\) 4.26918e12 0.231573 0.115787 0.993274i \(-0.463061\pi\)
0.115787 + 0.993274i \(0.463061\pi\)
\(888\) −1.14605e13 −0.618511
\(889\) 2.02977e12 0.108991
\(890\) 5.05525e13 2.70077
\(891\) −4.86865e11 −0.0258797
\(892\) 4.58166e11 0.0242316
\(893\) 3.10813e12 0.163556
\(894\) −1.41880e13 −0.742853
\(895\) −1.26755e13 −0.660329
\(896\) 3.33474e13 1.72853
\(897\) 1.03784e13 0.535257
\(898\) −3.60341e13 −1.84914
\(899\) −5.62270e12 −0.287096
\(900\) 1.42494e11 0.00723943
\(901\) 9.03739e11 0.0456858
\(902\) 6.87292e12 0.345710
\(903\) −2.59023e12 −0.129641
\(904\) 4.37597e12 0.217930
\(905\) −9.02596e12 −0.447275
\(906\) −2.27021e13 −1.11941
\(907\) 2.50023e13 1.22672 0.613362 0.789802i \(-0.289817\pi\)
0.613362 + 0.789802i \(0.289817\pi\)
\(908\) −6.49567e11 −0.0317130
\(909\) 1.10052e13 0.534639
\(910\) 3.45173e13 1.66859
\(911\) 1.67793e13 0.807125 0.403563 0.914952i \(-0.367772\pi\)
0.403563 + 0.914952i \(0.367772\pi\)
\(912\) 4.13929e12 0.198130
\(913\) 6.58067e12 0.313438
\(914\) −1.18041e13 −0.559468
\(915\) 1.20278e12 0.0567274
\(916\) 5.52139e11 0.0259131
\(917\) 1.31674e12 0.0614949
\(918\) 1.22441e11 0.00569029
\(919\) −1.49972e13 −0.693568 −0.346784 0.937945i \(-0.612726\pi\)
−0.346784 + 0.937945i \(0.612726\pi\)
\(920\) −3.68606e13 −1.69636
\(921\) 6.46188e12 0.295931
\(922\) 2.31863e13 1.05667
\(923\) 5.84542e12 0.265099
\(924\) −1.29386e11 −0.00583935
\(925\) 2.01512e13 0.905031
\(926\) 1.61232e13 0.720612
\(927\) −1.86162e12 −0.0828004
\(928\) −1.50904e12 −0.0667937
\(929\) 2.27528e13 1.00222 0.501111 0.865383i \(-0.332925\pi\)
0.501111 + 0.865383i \(0.332925\pi\)
\(930\) 4.04570e12 0.177346
\(931\) 1.36314e13 0.594658
\(932\) 1.91374e11 0.00830827
\(933\) 1.79857e11 0.00777069
\(934\) 3.05188e13 1.31222
\(935\) −2.15138e11 −0.00920587
\(936\) 5.63764e12 0.240080
\(937\) 1.51844e13 0.643529 0.321765 0.946820i \(-0.395724\pi\)
0.321765 + 0.946820i \(0.395724\pi\)
\(938\) −2.49575e12 −0.105266
\(939\) −9.92139e12 −0.416464
\(940\) 4.12764e11 0.0172435
\(941\) −1.99509e13 −0.829487 −0.414744 0.909938i \(-0.636129\pi\)
−0.414744 + 0.909938i \(0.636129\pi\)
\(942\) 1.08715e13 0.449841
\(943\) −4.51848e13 −1.86076
\(944\) 3.25711e12 0.133493
\(945\) 1.06455e13 0.434235
\(946\) −7.83120e11 −0.0317920
\(947\) −3.60211e13 −1.45540 −0.727700 0.685895i \(-0.759411\pi\)
−0.727700 + 0.685895i \(0.759411\pi\)
\(948\) −2.19012e11 −0.00880703
\(949\) 7.12649e12 0.285219
\(950\) −7.09321e12 −0.282544
\(951\) −8.67885e12 −0.344072
\(952\) −1.21615e12 −0.0479869
\(953\) −2.12265e13 −0.833606 −0.416803 0.908997i \(-0.636849\pi\)
−0.416803 + 0.908997i \(0.636849\pi\)
\(954\) −1.35202e13 −0.528465
\(955\) 1.25538e13 0.488381
\(956\) 9.31471e11 0.0360669
\(957\) −4.47310e12 −0.172387
\(958\) −3.91151e13 −1.50037
\(959\) 2.74655e13 1.04859
\(960\) −2.00091e13 −0.760339
\(961\) −2.51135e13 −0.949844
\(962\) −2.13315e13 −0.803032
\(963\) 1.23781e13 0.463807
\(964\) 5.29946e11 0.0197645
\(965\) −2.85867e13 −1.06119
\(966\) 3.34935e13 1.23755
\(967\) −1.62338e12 −0.0597037 −0.0298519 0.999554i \(-0.509504\pi\)
−0.0298519 + 0.999554i \(0.509504\pi\)
\(968\) −2.54879e13 −0.933029
\(969\) −1.54793e11 −0.00564021
\(970\) 6.20551e13 2.25063
\(971\) −2.76845e13 −0.999425 −0.499712 0.866191i \(-0.666561\pi\)
−0.499712 + 0.866191i \(0.666561\pi\)
\(972\) −4.65206e10 −0.00167166
\(973\) 1.84265e13 0.659076
\(974\) 3.69930e13 1.31706
\(975\) −9.91272e12 −0.351295
\(976\) 2.10925e12 0.0744054
\(977\) −2.46215e13 −0.864547 −0.432273 0.901743i \(-0.642288\pi\)
−0.432273 + 0.901743i \(0.642288\pi\)
\(978\) −2.66288e12 −0.0930738
\(979\) 1.31823e13 0.458637
\(980\) 1.81027e12 0.0626940
\(981\) 1.48749e13 0.512795
\(982\) 4.95061e13 1.69886
\(983\) 1.50739e13 0.514913 0.257456 0.966290i \(-0.417116\pi\)
0.257456 + 0.966290i \(0.417116\pi\)
\(984\) −2.45449e13 −0.834609
\(985\) −3.08880e13 −1.04551
\(986\) 1.12493e12 0.0379037
\(987\) 1.40179e13 0.470170
\(988\) 1.90695e11 0.00636699
\(989\) 5.14848e12 0.171118
\(990\) 3.21853e12 0.106488
\(991\) −3.48630e13 −1.14824 −0.574120 0.818771i \(-0.694656\pi\)
−0.574120 + 0.818771i \(0.694656\pi\)
\(992\) 3.55906e11 0.0116690
\(993\) 1.67107e13 0.545409
\(994\) 1.88646e13 0.612928
\(995\) −4.32470e12 −0.139879
\(996\) 6.28793e11 0.0202461
\(997\) −3.56149e13 −1.14157 −0.570786 0.821099i \(-0.693361\pi\)
−0.570786 + 0.821099i \(0.693361\pi\)
\(998\) 4.65805e13 1.48634
\(999\) −6.57887e12 −0.208981
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.b.1.7 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.7 21 1.1 even 1 trivial