Properties

Label 177.10.a.c.1.9
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.19311 q^{2} -81.0000 q^{3} -427.487 q^{4} -1961.85 q^{5} +744.642 q^{6} +11918.6 q^{7} +8636.80 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-9.19311 q^{2} -81.0000 q^{3} -427.487 q^{4} -1961.85 q^{5} +744.642 q^{6} +11918.6 q^{7} +8636.80 q^{8} +6561.00 q^{9} +18035.5 q^{10} -13131.0 q^{11} +34626.4 q^{12} -42343.4 q^{13} -109569. q^{14} +158910. q^{15} +139474. q^{16} +430458. q^{17} -60316.0 q^{18} -224648. q^{19} +838665. q^{20} -965407. q^{21} +120714. q^{22} -33946.2 q^{23} -699581. q^{24} +1.89573e6 q^{25} +389267. q^{26} -531441. q^{27} -5.09505e6 q^{28} -3.34218e6 q^{29} -1.46087e6 q^{30} +419744. q^{31} -5.70424e6 q^{32} +1.06361e6 q^{33} -3.95725e6 q^{34} -2.33825e7 q^{35} -2.80474e6 q^{36} -1.22263e7 q^{37} +2.06521e6 q^{38} +3.42982e6 q^{39} -1.69441e7 q^{40} -2.21659e7 q^{41} +8.87509e6 q^{42} +2.53123e7 q^{43} +5.61332e6 q^{44} -1.28717e7 q^{45} +312071. q^{46} -2.03404e7 q^{47} -1.12974e7 q^{48} +1.01700e8 q^{49} -1.74276e7 q^{50} -3.48671e7 q^{51} +1.81012e7 q^{52} -6.12300e6 q^{53} +4.88559e6 q^{54} +2.57610e7 q^{55} +1.02939e8 q^{56} +1.81965e7 q^{57} +3.07250e7 q^{58} +1.21174e7 q^{59} -6.79318e7 q^{60} -1.65926e8 q^{61} -3.85875e6 q^{62} +7.81980e7 q^{63} -1.89711e7 q^{64} +8.30714e7 q^{65} -9.77787e6 q^{66} +2.84272e8 q^{67} -1.84015e8 q^{68} +2.74964e6 q^{69} +2.14958e8 q^{70} +6.82960e7 q^{71} +5.66661e7 q^{72} +2.97684e7 q^{73} +1.12398e8 q^{74} -1.53554e8 q^{75} +9.60341e7 q^{76} -1.56503e8 q^{77} -3.15307e7 q^{78} -1.80907e8 q^{79} -2.73627e8 q^{80} +4.30467e7 q^{81} +2.03773e8 q^{82} -4.94682e8 q^{83} +4.12699e8 q^{84} -8.44494e8 q^{85} -2.32699e8 q^{86} +2.70717e8 q^{87} -1.13410e8 q^{88} -9.96619e7 q^{89} +1.18331e8 q^{90} -5.04674e8 q^{91} +1.45116e7 q^{92} -3.39993e7 q^{93} +1.86991e8 q^{94} +4.40726e8 q^{95} +4.62044e8 q^{96} +1.25595e9 q^{97} -9.34936e8 q^{98} -8.61523e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.19311 −0.406282 −0.203141 0.979150i \(-0.565115\pi\)
−0.203141 + 0.979150i \(0.565115\pi\)
\(3\) −81.0000 −0.577350
\(4\) −427.487 −0.834935
\(5\) −1961.85 −1.40378 −0.701892 0.712283i \(-0.747661\pi\)
−0.701892 + 0.712283i \(0.747661\pi\)
\(6\) 744.642 0.234567
\(7\) 11918.6 1.87622 0.938111 0.346334i \(-0.112573\pi\)
0.938111 + 0.346334i \(0.112573\pi\)
\(8\) 8636.80 0.745501
\(9\) 6561.00 0.333333
\(10\) 18035.5 0.570332
\(11\) −13131.0 −0.270414 −0.135207 0.990817i \(-0.543170\pi\)
−0.135207 + 0.990817i \(0.543170\pi\)
\(12\) 34626.4 0.482050
\(13\) −42343.4 −0.411188 −0.205594 0.978637i \(-0.565913\pi\)
−0.205594 + 0.978637i \(0.565913\pi\)
\(14\) −109569. −0.762275
\(15\) 158910. 0.810476
\(16\) 139474. 0.532052
\(17\) 430458. 1.25000 0.625001 0.780624i \(-0.285099\pi\)
0.625001 + 0.780624i \(0.285099\pi\)
\(18\) −60316.0 −0.135427
\(19\) −224648. −0.395468 −0.197734 0.980256i \(-0.563358\pi\)
−0.197734 + 0.980256i \(0.563358\pi\)
\(20\) 838665. 1.17207
\(21\) −965407. −1.08324
\(22\) 120714. 0.109864
\(23\) −33946.2 −0.0252939 −0.0126470 0.999920i \(-0.504026\pi\)
−0.0126470 + 0.999920i \(0.504026\pi\)
\(24\) −699581. −0.430415
\(25\) 1.89573e6 0.970612
\(26\) 389267. 0.167058
\(27\) −531441. −0.192450
\(28\) −5.09505e6 −1.56652
\(29\) −3.34218e6 −0.877483 −0.438742 0.898613i \(-0.644576\pi\)
−0.438742 + 0.898613i \(0.644576\pi\)
\(30\) −1.46087e6 −0.329281
\(31\) 419744. 0.0816313 0.0408157 0.999167i \(-0.487004\pi\)
0.0408157 + 0.999167i \(0.487004\pi\)
\(32\) −5.70424e6 −0.961664
\(33\) 1.06361e6 0.156124
\(34\) −3.95725e6 −0.507853
\(35\) −2.33825e7 −2.63381
\(36\) −2.80474e6 −0.278312
\(37\) −1.22263e7 −1.07248 −0.536240 0.844066i \(-0.680156\pi\)
−0.536240 + 0.844066i \(0.680156\pi\)
\(38\) 2.06521e6 0.160672
\(39\) 3.42982e6 0.237400
\(40\) −1.69441e7 −1.04652
\(41\) −2.21659e7 −1.22506 −0.612531 0.790447i \(-0.709848\pi\)
−0.612531 + 0.790447i \(0.709848\pi\)
\(42\) 8.87509e6 0.440100
\(43\) 2.53123e7 1.12908 0.564540 0.825406i \(-0.309054\pi\)
0.564540 + 0.825406i \(0.309054\pi\)
\(44\) 5.61332e6 0.225778
\(45\) −1.28717e7 −0.467928
\(46\) 312071. 0.0102765
\(47\) −2.03404e7 −0.608021 −0.304010 0.952669i \(-0.598326\pi\)
−0.304010 + 0.952669i \(0.598326\pi\)
\(48\) −1.12974e7 −0.307180
\(49\) 1.01700e8 2.52021
\(50\) −1.74276e7 −0.394342
\(51\) −3.48671e7 −0.721689
\(52\) 1.81012e7 0.343315
\(53\) −6.12300e6 −0.106591 −0.0532957 0.998579i \(-0.516973\pi\)
−0.0532957 + 0.998579i \(0.516973\pi\)
\(54\) 4.88559e6 0.0781890
\(55\) 2.57610e7 0.379604
\(56\) 1.02939e8 1.39873
\(57\) 1.81965e7 0.228324
\(58\) 3.07250e7 0.356505
\(59\) 1.21174e7 0.130189
\(60\) −6.79318e7 −0.676695
\(61\) −1.65926e8 −1.53437 −0.767184 0.641427i \(-0.778343\pi\)
−0.767184 + 0.641427i \(0.778343\pi\)
\(62\) −3.85875e6 −0.0331653
\(63\) 7.81980e7 0.625408
\(64\) −1.89711e7 −0.141345
\(65\) 8.30714e7 0.577220
\(66\) −9.77787e6 −0.0634303
\(67\) 2.84272e8 1.72344 0.861721 0.507382i \(-0.169387\pi\)
0.861721 + 0.507382i \(0.169387\pi\)
\(68\) −1.84015e8 −1.04367
\(69\) 2.74964e6 0.0146035
\(70\) 2.14958e8 1.07007
\(71\) 6.82960e7 0.318957 0.159479 0.987201i \(-0.449019\pi\)
0.159479 + 0.987201i \(0.449019\pi\)
\(72\) 5.66661e7 0.248500
\(73\) 2.97684e7 0.122688 0.0613440 0.998117i \(-0.480461\pi\)
0.0613440 + 0.998117i \(0.480461\pi\)
\(74\) 1.12398e8 0.435729
\(75\) −1.53554e8 −0.560383
\(76\) 9.60341e7 0.330190
\(77\) −1.56503e8 −0.507358
\(78\) −3.15307e7 −0.0964511
\(79\) −1.80907e8 −0.522557 −0.261279 0.965263i \(-0.584144\pi\)
−0.261279 + 0.965263i \(0.584144\pi\)
\(80\) −2.73627e8 −0.746886
\(81\) 4.30467e7 0.111111
\(82\) 2.03773e8 0.497720
\(83\) −4.94682e8 −1.14413 −0.572064 0.820209i \(-0.693857\pi\)
−0.572064 + 0.820209i \(0.693857\pi\)
\(84\) 4.12699e8 0.904433
\(85\) −8.44494e8 −1.75473
\(86\) −2.32699e8 −0.458724
\(87\) 2.70717e8 0.506615
\(88\) −1.13410e8 −0.201594
\(89\) −9.96619e7 −0.168374 −0.0841868 0.996450i \(-0.526829\pi\)
−0.0841868 + 0.996450i \(0.526829\pi\)
\(90\) 1.18331e8 0.190111
\(91\) −5.04674e8 −0.771481
\(92\) 1.45116e7 0.0211188
\(93\) −3.39993e7 −0.0471299
\(94\) 1.86991e8 0.247028
\(95\) 4.40726e8 0.555152
\(96\) 4.62044e8 0.555217
\(97\) 1.25595e9 1.44045 0.720225 0.693740i \(-0.244039\pi\)
0.720225 + 0.693740i \(0.244039\pi\)
\(98\) −9.34936e8 −1.02392
\(99\) −8.61523e7 −0.0901381
\(100\) −8.10398e8 −0.810398
\(101\) 1.70564e9 1.63095 0.815477 0.578789i \(-0.196475\pi\)
0.815477 + 0.578789i \(0.196475\pi\)
\(102\) 3.20537e8 0.293209
\(103\) 1.80769e9 1.58255 0.791274 0.611462i \(-0.209418\pi\)
0.791274 + 0.611462i \(0.209418\pi\)
\(104\) −3.65712e8 −0.306541
\(105\) 1.89398e9 1.52063
\(106\) 5.62893e7 0.0433062
\(107\) −2.41385e9 −1.78026 −0.890131 0.455706i \(-0.849387\pi\)
−0.890131 + 0.455706i \(0.849387\pi\)
\(108\) 2.27184e8 0.160683
\(109\) −5.49636e8 −0.372954 −0.186477 0.982459i \(-0.559707\pi\)
−0.186477 + 0.982459i \(0.559707\pi\)
\(110\) −2.36823e8 −0.154226
\(111\) 9.90334e8 0.619196
\(112\) 1.66234e9 0.998248
\(113\) 1.87303e9 1.08067 0.540334 0.841451i \(-0.318298\pi\)
0.540334 + 0.841451i \(0.318298\pi\)
\(114\) −1.67282e8 −0.0927638
\(115\) 6.65974e7 0.0355072
\(116\) 1.42874e9 0.732641
\(117\) −2.77815e8 −0.137063
\(118\) −1.11396e8 −0.0528934
\(119\) 5.13046e9 2.34528
\(120\) 1.37247e9 0.604210
\(121\) −2.18553e9 −0.926876
\(122\) 1.52537e9 0.623386
\(123\) 1.79544e9 0.707289
\(124\) −1.79435e8 −0.0681568
\(125\) 1.12606e8 0.0412540
\(126\) −7.18883e8 −0.254092
\(127\) −7.14197e8 −0.243613 −0.121807 0.992554i \(-0.538869\pi\)
−0.121807 + 0.992554i \(0.538869\pi\)
\(128\) 3.09498e9 1.01909
\(129\) −2.05030e9 −0.651874
\(130\) −7.63684e8 −0.234514
\(131\) 1.19291e9 0.353904 0.176952 0.984220i \(-0.443376\pi\)
0.176952 + 0.984220i \(0.443376\pi\)
\(132\) −4.54679e8 −0.130353
\(133\) −2.67749e9 −0.741987
\(134\) −2.61334e9 −0.700203
\(135\) 1.04261e9 0.270159
\(136\) 3.71778e9 0.931877
\(137\) −5.73531e9 −1.39096 −0.695479 0.718546i \(-0.744808\pi\)
−0.695479 + 0.718546i \(0.744808\pi\)
\(138\) −2.52778e7 −0.00593312
\(139\) −3.73823e9 −0.849375 −0.424688 0.905340i \(-0.639616\pi\)
−0.424688 + 0.905340i \(0.639616\pi\)
\(140\) 9.99572e9 2.19906
\(141\) 1.64757e9 0.351041
\(142\) −6.27852e8 −0.129587
\(143\) 5.56010e8 0.111191
\(144\) 9.15090e8 0.177351
\(145\) 6.55685e9 1.23180
\(146\) −2.73664e8 −0.0498459
\(147\) −8.23767e9 −1.45505
\(148\) 5.22660e9 0.895451
\(149\) 4.63492e9 0.770378 0.385189 0.922838i \(-0.374136\pi\)
0.385189 + 0.922838i \(0.374136\pi\)
\(150\) 1.41164e9 0.227674
\(151\) 6.79759e8 0.106404 0.0532021 0.998584i \(-0.483057\pi\)
0.0532021 + 0.998584i \(0.483057\pi\)
\(152\) −1.94024e9 −0.294822
\(153\) 2.82423e9 0.416667
\(154\) 1.43875e9 0.206130
\(155\) −8.23474e8 −0.114593
\(156\) −1.46620e9 −0.198213
\(157\) 3.46363e9 0.454970 0.227485 0.973782i \(-0.426950\pi\)
0.227485 + 0.973782i \(0.426950\pi\)
\(158\) 1.66310e9 0.212306
\(159\) 4.95963e8 0.0615406
\(160\) 1.11909e10 1.34997
\(161\) −4.04592e8 −0.0474570
\(162\) −3.95733e8 −0.0451424
\(163\) −4.98641e9 −0.553279 −0.276639 0.960974i \(-0.589221\pi\)
−0.276639 + 0.960974i \(0.589221\pi\)
\(164\) 9.47562e9 1.02285
\(165\) −2.08664e9 −0.219164
\(166\) 4.54766e9 0.464838
\(167\) −1.81973e10 −1.81044 −0.905218 0.424948i \(-0.860292\pi\)
−0.905218 + 0.424948i \(0.860292\pi\)
\(168\) −8.33803e9 −0.807554
\(169\) −8.81154e9 −0.830924
\(170\) 7.76352e9 0.712916
\(171\) −1.47392e9 −0.131823
\(172\) −1.08207e10 −0.942708
\(173\) −3.83288e8 −0.0325325 −0.0162662 0.999868i \(-0.505178\pi\)
−0.0162662 + 0.999868i \(0.505178\pi\)
\(174\) −2.48873e9 −0.205828
\(175\) 2.25944e10 1.82108
\(176\) −1.83143e9 −0.143874
\(177\) −9.81506e8 −0.0751646
\(178\) 9.16202e8 0.0684071
\(179\) 5.31802e9 0.387179 0.193589 0.981083i \(-0.437987\pi\)
0.193589 + 0.981083i \(0.437987\pi\)
\(180\) 5.50248e9 0.390690
\(181\) 2.49839e10 1.73024 0.865121 0.501564i \(-0.167242\pi\)
0.865121 + 0.501564i \(0.167242\pi\)
\(182\) 4.63953e9 0.313439
\(183\) 1.34400e10 0.885868
\(184\) −2.93187e8 −0.0188566
\(185\) 2.39863e10 1.50553
\(186\) 3.12559e8 0.0191480
\(187\) −5.65233e9 −0.338018
\(188\) 8.69524e9 0.507658
\(189\) −6.33404e9 −0.361079
\(190\) −4.05164e9 −0.225548
\(191\) 5.68179e9 0.308912 0.154456 0.988000i \(-0.450638\pi\)
0.154456 + 0.988000i \(0.450638\pi\)
\(192\) 1.53666e9 0.0816058
\(193\) 2.17897e10 1.13043 0.565214 0.824944i \(-0.308794\pi\)
0.565214 + 0.824944i \(0.308794\pi\)
\(194\) −1.15460e10 −0.585229
\(195\) −6.72878e9 −0.333258
\(196\) −4.34753e10 −2.10421
\(197\) −1.52598e10 −0.721855 −0.360928 0.932594i \(-0.617540\pi\)
−0.360928 + 0.932594i \(0.617540\pi\)
\(198\) 7.92007e8 0.0366215
\(199\) 2.69291e10 1.21726 0.608630 0.793454i \(-0.291720\pi\)
0.608630 + 0.793454i \(0.291720\pi\)
\(200\) 1.63730e10 0.723592
\(201\) −2.30260e10 −0.995030
\(202\) −1.56801e10 −0.662627
\(203\) −3.98341e10 −1.64635
\(204\) 1.49052e10 0.602563
\(205\) 4.34861e10 1.71972
\(206\) −1.66183e10 −0.642961
\(207\) −2.22721e8 −0.00843131
\(208\) −5.90581e9 −0.218773
\(209\) 2.94985e9 0.106940
\(210\) −1.74116e10 −0.617805
\(211\) 4.51984e10 1.56983 0.784914 0.619605i \(-0.212707\pi\)
0.784914 + 0.619605i \(0.212707\pi\)
\(212\) 2.61750e9 0.0889970
\(213\) −5.53197e9 −0.184150
\(214\) 2.21908e10 0.723288
\(215\) −4.96590e10 −1.58498
\(216\) −4.58995e9 −0.143472
\(217\) 5.00276e9 0.153159
\(218\) 5.05286e9 0.151525
\(219\) −2.41124e9 −0.0708340
\(220\) −1.10125e10 −0.316944
\(221\) −1.82271e10 −0.513986
\(222\) −9.10425e9 −0.251568
\(223\) −1.97431e10 −0.534619 −0.267309 0.963611i \(-0.586135\pi\)
−0.267309 + 0.963611i \(0.586135\pi\)
\(224\) −6.79867e10 −1.80430
\(225\) 1.24379e10 0.323537
\(226\) −1.72190e10 −0.439056
\(227\) −6.91707e10 −1.72904 −0.864521 0.502596i \(-0.832378\pi\)
−0.864521 + 0.502596i \(0.832378\pi\)
\(228\) −7.77876e9 −0.190635
\(229\) 3.20030e10 0.769009 0.384504 0.923123i \(-0.374372\pi\)
0.384504 + 0.923123i \(0.374372\pi\)
\(230\) −6.12237e8 −0.0144259
\(231\) 1.26767e10 0.292923
\(232\) −2.88657e10 −0.654164
\(233\) 5.89396e10 1.31010 0.655051 0.755584i \(-0.272647\pi\)
0.655051 + 0.755584i \(0.272647\pi\)
\(234\) 2.55398e9 0.0556861
\(235\) 3.99047e10 0.853530
\(236\) −5.18001e9 −0.108699
\(237\) 1.46535e10 0.301699
\(238\) −4.71649e10 −0.952845
\(239\) 6.52373e10 1.29332 0.646659 0.762779i \(-0.276166\pi\)
0.646659 + 0.762779i \(0.276166\pi\)
\(240\) 2.21638e10 0.431215
\(241\) −9.71508e9 −0.185511 −0.0927555 0.995689i \(-0.529568\pi\)
−0.0927555 + 0.995689i \(0.529568\pi\)
\(242\) 2.00918e10 0.376573
\(243\) −3.48678e9 −0.0641500
\(244\) 7.09311e10 1.28110
\(245\) −1.99519e11 −3.53784
\(246\) −1.65056e10 −0.287359
\(247\) 9.51237e9 0.162612
\(248\) 3.62525e9 0.0608562
\(249\) 4.00692e10 0.660563
\(250\) −1.03520e9 −0.0167607
\(251\) −7.77098e9 −0.123579 −0.0617894 0.998089i \(-0.519681\pi\)
−0.0617894 + 0.998089i \(0.519681\pi\)
\(252\) −3.34286e10 −0.522175
\(253\) 4.45747e8 0.00683984
\(254\) 6.56569e9 0.0989757
\(255\) 6.84040e10 1.01310
\(256\) −1.87393e10 −0.272692
\(257\) 1.14845e10 0.164215 0.0821077 0.996623i \(-0.473835\pi\)
0.0821077 + 0.996623i \(0.473835\pi\)
\(258\) 1.88486e10 0.264845
\(259\) −1.45721e11 −2.01221
\(260\) −3.55119e10 −0.481941
\(261\) −2.19280e10 −0.292494
\(262\) −1.09665e10 −0.143785
\(263\) −8.12519e10 −1.04721 −0.523604 0.851962i \(-0.675413\pi\)
−0.523604 + 0.851962i \(0.675413\pi\)
\(264\) 9.18618e9 0.116390
\(265\) 1.20124e10 0.149632
\(266\) 2.46145e10 0.301456
\(267\) 8.07261e9 0.0972106
\(268\) −1.21522e11 −1.43896
\(269\) −4.62770e10 −0.538865 −0.269433 0.963019i \(-0.586836\pi\)
−0.269433 + 0.963019i \(0.586836\pi\)
\(270\) −9.58480e9 −0.109760
\(271\) 1.22167e11 1.37591 0.687957 0.725752i \(-0.258508\pi\)
0.687957 + 0.725752i \(0.258508\pi\)
\(272\) 6.00378e10 0.665066
\(273\) 4.08786e10 0.445415
\(274\) 5.27253e10 0.565121
\(275\) −2.48927e10 −0.262468
\(276\) −1.17544e9 −0.0121929
\(277\) 1.63199e10 0.166556 0.0832778 0.996526i \(-0.473461\pi\)
0.0832778 + 0.996526i \(0.473461\pi\)
\(278\) 3.43660e10 0.345086
\(279\) 2.75394e9 0.0272104
\(280\) −2.01950e11 −1.96351
\(281\) 4.29565e10 0.411008 0.205504 0.978656i \(-0.434117\pi\)
0.205504 + 0.978656i \(0.434117\pi\)
\(282\) −1.51463e10 −0.142622
\(283\) 2.20393e10 0.204249 0.102124 0.994772i \(-0.467436\pi\)
0.102124 + 0.994772i \(0.467436\pi\)
\(284\) −2.91956e10 −0.266309
\(285\) −3.56988e10 −0.320517
\(286\) −5.11146e9 −0.0451750
\(287\) −2.64187e11 −2.29849
\(288\) −3.74255e10 −0.320555
\(289\) 6.67062e10 0.562504
\(290\) −6.02778e10 −0.500457
\(291\) −1.01732e11 −0.831644
\(292\) −1.27256e10 −0.102437
\(293\) 9.43449e10 0.747850 0.373925 0.927459i \(-0.378012\pi\)
0.373925 + 0.927459i \(0.378012\pi\)
\(294\) 7.57298e10 0.591158
\(295\) −2.37724e10 −0.182757
\(296\) −1.05597e11 −0.799534
\(297\) 6.97834e9 0.0520413
\(298\) −4.26093e10 −0.312991
\(299\) 1.43740e9 0.0104006
\(300\) 6.56423e10 0.467884
\(301\) 3.01688e11 2.11840
\(302\) −6.24910e9 −0.0432301
\(303\) −1.38157e11 −0.941632
\(304\) −3.13326e10 −0.210410
\(305\) 3.25521e11 2.15392
\(306\) −2.59635e10 −0.169284
\(307\) −2.75996e11 −1.77329 −0.886647 0.462447i \(-0.846971\pi\)
−0.886647 + 0.462447i \(0.846971\pi\)
\(308\) 6.69029e10 0.423611
\(309\) −1.46423e11 −0.913685
\(310\) 7.57029e9 0.0465570
\(311\) 1.57726e11 0.956050 0.478025 0.878346i \(-0.341353\pi\)
0.478025 + 0.878346i \(0.341353\pi\)
\(312\) 2.96226e10 0.176982
\(313\) 1.88819e11 1.11198 0.555990 0.831189i \(-0.312339\pi\)
0.555990 + 0.831189i \(0.312339\pi\)
\(314\) −3.18415e10 −0.184846
\(315\) −1.53413e11 −0.877938
\(316\) 7.73354e10 0.436301
\(317\) 1.75734e10 0.0977436 0.0488718 0.998805i \(-0.484437\pi\)
0.0488718 + 0.998805i \(0.484437\pi\)
\(318\) −4.55944e9 −0.0250028
\(319\) 4.38861e10 0.237284
\(320\) 3.72184e10 0.198419
\(321\) 1.95522e11 1.02783
\(322\) 3.71945e9 0.0192809
\(323\) −9.67016e10 −0.494336
\(324\) −1.84019e10 −0.0927706
\(325\) −8.02715e10 −0.399104
\(326\) 4.58406e10 0.224787
\(327\) 4.45205e10 0.215325
\(328\) −1.91442e11 −0.913284
\(329\) −2.42429e11 −1.14078
\(330\) 1.91827e10 0.0890424
\(331\) −8.64053e10 −0.395653 −0.197827 0.980237i \(-0.563388\pi\)
−0.197827 + 0.980237i \(0.563388\pi\)
\(332\) 2.11470e11 0.955273
\(333\) −8.02171e10 −0.357493
\(334\) 1.67290e11 0.735547
\(335\) −5.57698e11 −2.41934
\(336\) −1.34649e11 −0.576339
\(337\) −5.27486e10 −0.222780 −0.111390 0.993777i \(-0.535530\pi\)
−0.111390 + 0.993777i \(0.535530\pi\)
\(338\) 8.10054e10 0.337589
\(339\) −1.51716e11 −0.623924
\(340\) 3.61010e11 1.46509
\(341\) −5.51164e9 −0.0220743
\(342\) 1.35499e10 0.0535572
\(343\) 7.31159e11 2.85226
\(344\) 2.18618e11 0.841729
\(345\) −5.39439e9 −0.0205001
\(346\) 3.52360e9 0.0132174
\(347\) 5.27453e10 0.195300 0.0976498 0.995221i \(-0.468867\pi\)
0.0976498 + 0.995221i \(0.468867\pi\)
\(348\) −1.15728e11 −0.422991
\(349\) 1.59955e11 0.577143 0.288571 0.957458i \(-0.406820\pi\)
0.288571 + 0.957458i \(0.406820\pi\)
\(350\) −2.07713e11 −0.739874
\(351\) 2.25030e10 0.0791332
\(352\) 7.49023e10 0.260048
\(353\) 1.20699e11 0.413732 0.206866 0.978369i \(-0.433674\pi\)
0.206866 + 0.978369i \(0.433674\pi\)
\(354\) 9.02309e9 0.0305380
\(355\) −1.33986e11 −0.447748
\(356\) 4.26041e10 0.140581
\(357\) −4.15567e11 −1.35405
\(358\) −4.88891e10 −0.157304
\(359\) 3.65561e10 0.116154 0.0580771 0.998312i \(-0.481503\pi\)
0.0580771 + 0.998312i \(0.481503\pi\)
\(360\) −1.11170e11 −0.348841
\(361\) −2.72221e11 −0.843605
\(362\) −2.29680e11 −0.702966
\(363\) 1.77028e11 0.535132
\(364\) 2.15742e11 0.644136
\(365\) −5.84010e10 −0.172228
\(366\) −1.23555e11 −0.359912
\(367\) −1.22158e11 −0.351499 −0.175749 0.984435i \(-0.556235\pi\)
−0.175749 + 0.984435i \(0.556235\pi\)
\(368\) −4.73462e9 −0.0134577
\(369\) −1.45430e11 −0.408354
\(370\) −2.20508e11 −0.611670
\(371\) −7.29776e10 −0.199989
\(372\) 1.45342e10 0.0393504
\(373\) 4.46658e11 1.19477 0.597387 0.801953i \(-0.296206\pi\)
0.597387 + 0.801953i \(0.296206\pi\)
\(374\) 5.19625e10 0.137331
\(375\) −9.12107e9 −0.0238180
\(376\) −1.75676e11 −0.453280
\(377\) 1.41519e11 0.360811
\(378\) 5.82295e10 0.146700
\(379\) 3.06073e11 0.761988 0.380994 0.924577i \(-0.375582\pi\)
0.380994 + 0.924577i \(0.375582\pi\)
\(380\) −1.88404e11 −0.463516
\(381\) 5.78500e10 0.140650
\(382\) −5.22333e10 −0.125505
\(383\) 2.82653e11 0.671210 0.335605 0.942003i \(-0.391059\pi\)
0.335605 + 0.942003i \(0.391059\pi\)
\(384\) −2.50693e11 −0.588372
\(385\) 3.07035e11 0.712221
\(386\) −2.00315e11 −0.459272
\(387\) 1.66074e11 0.376360
\(388\) −5.36900e11 −1.20268
\(389\) 2.82569e11 0.625678 0.312839 0.949806i \(-0.398720\pi\)
0.312839 + 0.949806i \(0.398720\pi\)
\(390\) 6.18584e10 0.135397
\(391\) −1.46124e10 −0.0316174
\(392\) 8.78360e11 1.87882
\(393\) −9.66253e10 −0.204326
\(394\) 1.40285e11 0.293277
\(395\) 3.54913e11 0.733558
\(396\) 3.68290e10 0.0752595
\(397\) 8.96070e11 1.81044 0.905221 0.424941i \(-0.139705\pi\)
0.905221 + 0.424941i \(0.139705\pi\)
\(398\) −2.47562e11 −0.494550
\(399\) 2.16877e11 0.428386
\(400\) 2.64405e11 0.516416
\(401\) −2.06115e11 −0.398071 −0.199035 0.979992i \(-0.563781\pi\)
−0.199035 + 0.979992i \(0.563781\pi\)
\(402\) 2.11680e11 0.404263
\(403\) −1.77734e10 −0.0335658
\(404\) −7.29139e11 −1.36174
\(405\) −8.44512e10 −0.155976
\(406\) 3.66199e11 0.668883
\(407\) 1.60544e11 0.290014
\(408\) −3.01140e11 −0.538020
\(409\) 5.28783e11 0.934378 0.467189 0.884157i \(-0.345267\pi\)
0.467189 + 0.884157i \(0.345267\pi\)
\(410\) −3.99773e11 −0.698692
\(411\) 4.64560e11 0.803070
\(412\) −7.72765e11 −1.32133
\(413\) 1.44422e11 0.244263
\(414\) 2.04750e9 0.00342549
\(415\) 9.70491e11 1.60611
\(416\) 2.41537e11 0.395425
\(417\) 3.02797e11 0.490387
\(418\) −2.71183e10 −0.0434479
\(419\) −3.71368e11 −0.588629 −0.294314 0.955709i \(-0.595091\pi\)
−0.294314 + 0.955709i \(0.595091\pi\)
\(420\) −8.09653e11 −1.26963
\(421\) −3.20784e11 −0.497673 −0.248836 0.968546i \(-0.580048\pi\)
−0.248836 + 0.968546i \(0.580048\pi\)
\(422\) −4.15514e11 −0.637793
\(423\) −1.33453e11 −0.202674
\(424\) −5.28831e10 −0.0794640
\(425\) 8.16031e11 1.21327
\(426\) 5.08560e10 0.0748168
\(427\) −1.97760e12 −2.87882
\(428\) 1.03189e12 1.48640
\(429\) −4.50368e10 −0.0641963
\(430\) 4.56521e11 0.643950
\(431\) −2.10049e11 −0.293207 −0.146603 0.989195i \(-0.546834\pi\)
−0.146603 + 0.989195i \(0.546834\pi\)
\(432\) −7.41223e10 −0.102393
\(433\) 3.19478e11 0.436762 0.218381 0.975864i \(-0.429922\pi\)
0.218381 + 0.975864i \(0.429922\pi\)
\(434\) −4.59909e10 −0.0622255
\(435\) −5.31105e11 −0.711179
\(436\) 2.34962e11 0.311393
\(437\) 7.62595e9 0.0100029
\(438\) 2.21668e10 0.0287785
\(439\) −4.37962e10 −0.0562790 −0.0281395 0.999604i \(-0.508958\pi\)
−0.0281395 + 0.999604i \(0.508958\pi\)
\(440\) 2.22493e11 0.282995
\(441\) 6.67251e11 0.840071
\(442\) 1.67563e11 0.208823
\(443\) −3.83119e11 −0.472626 −0.236313 0.971677i \(-0.575939\pi\)
−0.236313 + 0.971677i \(0.575939\pi\)
\(444\) −4.23355e11 −0.516989
\(445\) 1.95522e11 0.236360
\(446\) 1.81501e11 0.217206
\(447\) −3.75429e11 −0.444778
\(448\) −2.26109e11 −0.265195
\(449\) 1.18786e12 1.37929 0.689644 0.724148i \(-0.257767\pi\)
0.689644 + 0.724148i \(0.257767\pi\)
\(450\) −1.14343e11 −0.131447
\(451\) 2.91060e11 0.331274
\(452\) −8.00697e11 −0.902288
\(453\) −5.50605e10 −0.0614325
\(454\) 6.35893e11 0.702478
\(455\) 9.90095e11 1.08299
\(456\) 1.57160e11 0.170215
\(457\) 1.61959e12 1.73693 0.868466 0.495749i \(-0.165106\pi\)
0.868466 + 0.495749i \(0.165106\pi\)
\(458\) −2.94207e11 −0.312434
\(459\) −2.28763e11 −0.240563
\(460\) −2.84695e10 −0.0296462
\(461\) 8.36570e11 0.862677 0.431338 0.902190i \(-0.358042\pi\)
0.431338 + 0.902190i \(0.358042\pi\)
\(462\) −1.16539e11 −0.119009
\(463\) 9.48718e11 0.959451 0.479725 0.877419i \(-0.340736\pi\)
0.479725 + 0.877419i \(0.340736\pi\)
\(464\) −4.66148e11 −0.466866
\(465\) 6.67014e10 0.0661602
\(466\) −5.41838e11 −0.532271
\(467\) −1.41899e12 −1.38055 −0.690277 0.723546i \(-0.742511\pi\)
−0.690277 + 0.723546i \(0.742511\pi\)
\(468\) 1.18762e11 0.114438
\(469\) 3.38812e12 3.23356
\(470\) −3.66848e11 −0.346774
\(471\) −2.80554e11 −0.262677
\(472\) 1.04655e11 0.0970559
\(473\) −3.32376e11 −0.305319
\(474\) −1.34711e11 −0.122575
\(475\) −4.25872e11 −0.383846
\(476\) −2.19320e12 −1.95816
\(477\) −4.01730e10 −0.0355305
\(478\) −5.99734e11 −0.525452
\(479\) 2.15506e12 1.87046 0.935232 0.354037i \(-0.115191\pi\)
0.935232 + 0.354037i \(0.115191\pi\)
\(480\) −9.06460e11 −0.779405
\(481\) 5.17705e11 0.440991
\(482\) 8.93118e10 0.0753698
\(483\) 3.27719e10 0.0273993
\(484\) 9.34283e11 0.773881
\(485\) −2.46398e12 −2.02208
\(486\) 3.20544e10 0.0260630
\(487\) 5.94194e11 0.478683 0.239341 0.970935i \(-0.423069\pi\)
0.239341 + 0.970935i \(0.423069\pi\)
\(488\) −1.43307e12 −1.14387
\(489\) 4.03899e11 0.319436
\(490\) 1.83420e12 1.43736
\(491\) −8.19610e11 −0.636415 −0.318208 0.948021i \(-0.603081\pi\)
−0.318208 + 0.948021i \(0.603081\pi\)
\(492\) −7.67526e11 −0.590541
\(493\) −1.43867e12 −1.09686
\(494\) −8.74482e10 −0.0660662
\(495\) 1.69018e11 0.126535
\(496\) 5.85434e10 0.0434321
\(497\) 8.13993e11 0.598435
\(498\) −3.68361e11 −0.268375
\(499\) 2.10419e12 1.51926 0.759629 0.650356i \(-0.225380\pi\)
0.759629 + 0.650356i \(0.225380\pi\)
\(500\) −4.81375e10 −0.0344444
\(501\) 1.47398e12 1.04526
\(502\) 7.14395e10 0.0502078
\(503\) −2.45097e12 −1.70719 −0.853596 0.520936i \(-0.825583\pi\)
−0.853596 + 0.520936i \(0.825583\pi\)
\(504\) 6.75381e11 0.466242
\(505\) −3.34621e12 −2.28951
\(506\) −4.09780e9 −0.00277890
\(507\) 7.13734e11 0.479734
\(508\) 3.05310e11 0.203401
\(509\) 2.92569e12 1.93196 0.965979 0.258619i \(-0.0832675\pi\)
0.965979 + 0.258619i \(0.0832675\pi\)
\(510\) −6.28845e11 −0.411602
\(511\) 3.54798e11 0.230190
\(512\) −1.41236e12 −0.908300
\(513\) 1.19387e11 0.0761079
\(514\) −1.05579e11 −0.0667178
\(515\) −3.54642e12 −2.22156
\(516\) 8.76476e11 0.544273
\(517\) 2.67089e11 0.164418
\(518\) 1.33963e12 0.817524
\(519\) 3.10463e10 0.0187826
\(520\) 7.17471e11 0.430318
\(521\) 3.35536e12 1.99512 0.997561 0.0698015i \(-0.0222366\pi\)
0.997561 + 0.0698015i \(0.0222366\pi\)
\(522\) 2.01587e11 0.118835
\(523\) 1.51898e12 0.887758 0.443879 0.896087i \(-0.353602\pi\)
0.443879 + 0.896087i \(0.353602\pi\)
\(524\) −5.09951e11 −0.295487
\(525\) −1.83015e12 −1.05140
\(526\) 7.46958e11 0.425461
\(527\) 1.80682e11 0.102039
\(528\) 1.48346e11 0.0830659
\(529\) −1.80000e12 −0.999360
\(530\) −1.10431e11 −0.0607926
\(531\) 7.95020e10 0.0433963
\(532\) 1.14459e12 0.619511
\(533\) 9.38579e11 0.503731
\(534\) −7.42124e10 −0.0394949
\(535\) 4.73561e12 2.49910
\(536\) 2.45520e12 1.28483
\(537\) −4.30760e11 −0.223538
\(538\) 4.25430e11 0.218931
\(539\) −1.33542e12 −0.681501
\(540\) −4.45701e11 −0.225565
\(541\) 3.04854e11 0.153004 0.0765022 0.997069i \(-0.475625\pi\)
0.0765022 + 0.997069i \(0.475625\pi\)
\(542\) −1.12309e12 −0.559009
\(543\) −2.02370e12 −0.998955
\(544\) −2.45544e12 −1.20208
\(545\) 1.07830e12 0.523548
\(546\) −3.75802e11 −0.180964
\(547\) 2.30181e12 1.09932 0.549662 0.835387i \(-0.314757\pi\)
0.549662 + 0.835387i \(0.314757\pi\)
\(548\) 2.45177e12 1.16136
\(549\) −1.08864e12 −0.511456
\(550\) 2.28842e11 0.106636
\(551\) 7.50814e11 0.347017
\(552\) 2.37481e10 0.0108869
\(553\) −2.15616e12 −0.980434
\(554\) −1.50031e11 −0.0676685
\(555\) −1.94289e12 −0.869219
\(556\) 1.59804e12 0.709173
\(557\) −1.50422e12 −0.662162 −0.331081 0.943602i \(-0.607413\pi\)
−0.331081 + 0.943602i \(0.607413\pi\)
\(558\) −2.53173e10 −0.0110551
\(559\) −1.07181e12 −0.464264
\(560\) −3.26126e12 −1.40133
\(561\) 4.57839e11 0.195155
\(562\) −3.94904e11 −0.166985
\(563\) 2.07661e12 0.871100 0.435550 0.900164i \(-0.356554\pi\)
0.435550 + 0.900164i \(0.356554\pi\)
\(564\) −7.04314e11 −0.293096
\(565\) −3.67461e12 −1.51703
\(566\) −2.02610e11 −0.0829825
\(567\) 5.13057e11 0.208469
\(568\) 5.89859e11 0.237783
\(569\) −2.25353e12 −0.901277 −0.450639 0.892707i \(-0.648804\pi\)
−0.450639 + 0.892707i \(0.648804\pi\)
\(570\) 3.28183e11 0.130220
\(571\) 1.00192e12 0.394429 0.197214 0.980360i \(-0.436810\pi\)
0.197214 + 0.980360i \(0.436810\pi\)
\(572\) −2.37687e11 −0.0928374
\(573\) −4.60225e11 −0.178350
\(574\) 2.42870e12 0.933834
\(575\) −6.43528e10 −0.0245506
\(576\) −1.24469e11 −0.0471151
\(577\) −3.34207e12 −1.25523 −0.627616 0.778523i \(-0.715969\pi\)
−0.627616 + 0.778523i \(0.715969\pi\)
\(578\) −6.13237e11 −0.228535
\(579\) −1.76496e12 −0.652653
\(580\) −2.80297e12 −1.02847
\(581\) −5.89592e12 −2.14664
\(582\) 9.35230e11 0.337882
\(583\) 8.04009e10 0.0288239
\(584\) 2.57103e11 0.0914640
\(585\) 5.45031e11 0.192407
\(586\) −8.67323e11 −0.303838
\(587\) −3.25354e11 −0.113106 −0.0565528 0.998400i \(-0.518011\pi\)
−0.0565528 + 0.998400i \(0.518011\pi\)
\(588\) 3.52150e12 1.21487
\(589\) −9.42947e10 −0.0322826
\(590\) 2.18543e11 0.0742509
\(591\) 1.23604e12 0.416763
\(592\) −1.70526e12 −0.570615
\(593\) 5.66345e11 0.188077 0.0940383 0.995569i \(-0.470022\pi\)
0.0940383 + 0.995569i \(0.470022\pi\)
\(594\) −6.41526e10 −0.0211434
\(595\) −1.00652e13 −3.29227
\(596\) −1.98137e12 −0.643216
\(597\) −2.18126e12 −0.702785
\(598\) −1.32142e10 −0.00422556
\(599\) −5.94324e11 −0.188626 −0.0943132 0.995543i \(-0.530066\pi\)
−0.0943132 + 0.995543i \(0.530066\pi\)
\(600\) −1.32621e12 −0.417766
\(601\) −2.90192e12 −0.907297 −0.453649 0.891181i \(-0.649878\pi\)
−0.453649 + 0.891181i \(0.649878\pi\)
\(602\) −2.77345e12 −0.860669
\(603\) 1.86511e12 0.574481
\(604\) −2.90588e11 −0.0888407
\(605\) 4.28767e12 1.30113
\(606\) 1.27009e12 0.382568
\(607\) 3.51179e11 0.104998 0.0524988 0.998621i \(-0.483281\pi\)
0.0524988 + 0.998621i \(0.483281\pi\)
\(608\) 1.28145e12 0.380307
\(609\) 3.22656e12 0.950523
\(610\) −2.99255e12 −0.875100
\(611\) 8.61280e11 0.250011
\(612\) −1.20732e12 −0.347890
\(613\) −5.12212e12 −1.46513 −0.732567 0.680695i \(-0.761678\pi\)
−0.732567 + 0.680695i \(0.761678\pi\)
\(614\) 2.53726e12 0.720457
\(615\) −3.52238e12 −0.992882
\(616\) −1.35168e12 −0.378235
\(617\) 9.01901e11 0.250539 0.125270 0.992123i \(-0.460020\pi\)
0.125270 + 0.992123i \(0.460020\pi\)
\(618\) 1.34608e12 0.371213
\(619\) −3.28812e12 −0.900200 −0.450100 0.892978i \(-0.648612\pi\)
−0.450100 + 0.892978i \(0.648612\pi\)
\(620\) 3.52024e11 0.0956776
\(621\) 1.80404e10 0.00486782
\(622\) −1.44999e12 −0.388426
\(623\) −1.18783e12 −0.315906
\(624\) 4.78371e11 0.126309
\(625\) −3.92351e12 −1.02852
\(626\) −1.73584e12 −0.451777
\(627\) −2.38938e11 −0.0617420
\(628\) −1.48065e12 −0.379870
\(629\) −5.26293e12 −1.34060
\(630\) 1.41034e12 0.356690
\(631\) 4.50112e12 1.13029 0.565144 0.824993i \(-0.308821\pi\)
0.565144 + 0.824993i \(0.308821\pi\)
\(632\) −1.56246e12 −0.389567
\(633\) −3.66107e12 −0.906341
\(634\) −1.61554e11 −0.0397115
\(635\) 1.40115e12 0.341981
\(636\) −2.12017e11 −0.0513824
\(637\) −4.30631e12 −1.03628
\(638\) −4.03449e11 −0.0964042
\(639\) 4.48090e11 0.106319
\(640\) −6.07188e12 −1.43058
\(641\) −8.70282e11 −0.203610 −0.101805 0.994804i \(-0.532462\pi\)
−0.101805 + 0.994804i \(0.532462\pi\)
\(642\) −1.79745e12 −0.417590
\(643\) 6.00697e12 1.38582 0.692909 0.721025i \(-0.256329\pi\)
0.692909 + 0.721025i \(0.256329\pi\)
\(644\) 1.72958e11 0.0396235
\(645\) 4.02238e12 0.915091
\(646\) 8.88988e11 0.200840
\(647\) −7.90490e12 −1.77348 −0.886742 0.462265i \(-0.847037\pi\)
−0.886742 + 0.462265i \(0.847037\pi\)
\(648\) 3.71786e11 0.0828334
\(649\) −1.59113e11 −0.0352049
\(650\) 7.37945e11 0.162149
\(651\) −4.05224e11 −0.0884261
\(652\) 2.13163e12 0.461952
\(653\) 4.71501e12 1.01478 0.507391 0.861716i \(-0.330610\pi\)
0.507391 + 0.861716i \(0.330610\pi\)
\(654\) −4.09282e11 −0.0874827
\(655\) −2.34030e12 −0.496805
\(656\) −3.09157e12 −0.651796
\(657\) 1.95310e11 0.0408960
\(658\) 2.22867e12 0.463479
\(659\) 8.35700e12 1.72610 0.863050 0.505118i \(-0.168551\pi\)
0.863050 + 0.505118i \(0.168551\pi\)
\(660\) 8.92011e11 0.182988
\(661\) 3.92695e12 0.800109 0.400054 0.916491i \(-0.368991\pi\)
0.400054 + 0.916491i \(0.368991\pi\)
\(662\) 7.94333e11 0.160747
\(663\) 1.47639e12 0.296750
\(664\) −4.27247e12 −0.852948
\(665\) 5.25284e12 1.04159
\(666\) 7.37444e11 0.145243
\(667\) 1.13454e11 0.0221950
\(668\) 7.77911e12 1.51160
\(669\) 1.59919e12 0.308662
\(670\) 5.12698e12 0.982935
\(671\) 2.17877e12 0.414915
\(672\) 5.50692e12 1.04171
\(673\) 5.66048e12 1.06362 0.531808 0.846865i \(-0.321513\pi\)
0.531808 + 0.846865i \(0.321513\pi\)
\(674\) 4.84923e11 0.0905115
\(675\) −1.00747e12 −0.186794
\(676\) 3.76682e12 0.693768
\(677\) 2.99150e12 0.547319 0.273659 0.961827i \(-0.411766\pi\)
0.273659 + 0.961827i \(0.411766\pi\)
\(678\) 1.39474e12 0.253489
\(679\) 1.49691e13 2.70261
\(680\) −7.29372e12 −1.30816
\(681\) 5.60282e12 0.998263
\(682\) 5.06691e10 0.00896838
\(683\) 1.36018e10 0.00239169 0.00119584 0.999999i \(-0.499619\pi\)
0.00119584 + 0.999999i \(0.499619\pi\)
\(684\) 6.30080e11 0.110063
\(685\) 1.12518e13 1.95261
\(686\) −6.72163e12 −1.15882
\(687\) −2.59224e12 −0.443987
\(688\) 3.53042e12 0.600729
\(689\) 2.59268e11 0.0438292
\(690\) 4.95912e10 0.00832882
\(691\) 4.14572e12 0.691749 0.345875 0.938281i \(-0.387582\pi\)
0.345875 + 0.938281i \(0.387582\pi\)
\(692\) 1.63850e11 0.0271625
\(693\) −1.02682e12 −0.169119
\(694\) −4.84894e11 −0.0793467
\(695\) 7.33385e12 1.19234
\(696\) 2.33813e12 0.377682
\(697\) −9.54148e12 −1.53133
\(698\) −1.47048e12 −0.234483
\(699\) −4.77411e12 −0.756388
\(700\) −9.65882e12 −1.52049
\(701\) −9.78363e11 −0.153027 −0.0765137 0.997069i \(-0.524379\pi\)
−0.0765137 + 0.997069i \(0.524379\pi\)
\(702\) −2.06873e11 −0.0321504
\(703\) 2.74663e12 0.424132
\(704\) 2.49108e11 0.0382218
\(705\) −3.23228e12 −0.492786
\(706\) −1.10960e12 −0.168092
\(707\) 2.03289e13 3.06003
\(708\) 4.19581e11 0.0627576
\(709\) −5.55448e12 −0.825535 −0.412767 0.910837i \(-0.635438\pi\)
−0.412767 + 0.910837i \(0.635438\pi\)
\(710\) 1.23175e12 0.181912
\(711\) −1.18693e12 −0.174186
\(712\) −8.60760e11 −0.125523
\(713\) −1.42487e10 −0.00206478
\(714\) 3.82035e12 0.550125
\(715\) −1.09081e12 −0.156089
\(716\) −2.27338e12 −0.323269
\(717\) −5.28422e12 −0.746698
\(718\) −3.36064e11 −0.0471913
\(719\) −7.47950e12 −1.04374 −0.521870 0.853025i \(-0.674766\pi\)
−0.521870 + 0.853025i \(0.674766\pi\)
\(720\) −1.79527e12 −0.248962
\(721\) 2.15452e13 2.96921
\(722\) 2.50256e12 0.342741
\(723\) 7.86922e11 0.107105
\(724\) −1.06803e13 −1.44464
\(725\) −6.33586e12 −0.851696
\(726\) −1.62743e12 −0.217414
\(727\) −3.23304e12 −0.429246 −0.214623 0.976697i \(-0.568852\pi\)
−0.214623 + 0.976697i \(0.568852\pi\)
\(728\) −4.35877e12 −0.575139
\(729\) 2.82430e11 0.0370370
\(730\) 5.36887e11 0.0699729
\(731\) 1.08959e13 1.41135
\(732\) −5.74542e12 −0.739642
\(733\) 8.21832e12 1.05151 0.525757 0.850635i \(-0.323782\pi\)
0.525757 + 0.850635i \(0.323782\pi\)
\(734\) 1.12301e12 0.142808
\(735\) 1.61611e13 2.04257
\(736\) 1.93638e11 0.0243242
\(737\) −3.73276e12 −0.466044
\(738\) 1.33696e12 0.165907
\(739\) 1.56769e13 1.93358 0.966788 0.255581i \(-0.0822669\pi\)
0.966788 + 0.255581i \(0.0822669\pi\)
\(740\) −1.02538e13 −1.25702
\(741\) −7.70502e11 −0.0938840
\(742\) 6.70891e11 0.0812520
\(743\) 7.40850e12 0.891827 0.445913 0.895076i \(-0.352879\pi\)
0.445913 + 0.895076i \(0.352879\pi\)
\(744\) −2.93645e11 −0.0351353
\(745\) −9.09302e12 −1.08145
\(746\) −4.10618e12 −0.485415
\(747\) −3.24561e12 −0.381376
\(748\) 2.41630e12 0.282223
\(749\) −2.87698e13 −3.34017
\(750\) 8.38510e10 0.00967682
\(751\) 6.22107e12 0.713650 0.356825 0.934171i \(-0.383859\pi\)
0.356825 + 0.934171i \(0.383859\pi\)
\(752\) −2.83696e12 −0.323499
\(753\) 6.29450e11 0.0713483
\(754\) −1.30100e12 −0.146591
\(755\) −1.33359e12 −0.149369
\(756\) 2.70772e12 0.301478
\(757\) −1.66700e13 −1.84503 −0.922517 0.385957i \(-0.873871\pi\)
−0.922517 + 0.385957i \(0.873871\pi\)
\(758\) −2.81376e12 −0.309582
\(759\) −3.61055e10 −0.00394898
\(760\) 3.80646e12 0.413866
\(761\) 4.24003e12 0.458288 0.229144 0.973393i \(-0.426407\pi\)
0.229144 + 0.973393i \(0.426407\pi\)
\(762\) −5.31821e11 −0.0571437
\(763\) −6.55089e12 −0.699745
\(764\) −2.42889e12 −0.257921
\(765\) −5.54072e12 −0.584911
\(766\) −2.59846e12 −0.272700
\(767\) −5.13090e11 −0.0535321
\(768\) 1.51788e12 0.157439
\(769\) 3.56728e12 0.367848 0.183924 0.982940i \(-0.441120\pi\)
0.183924 + 0.982940i \(0.441120\pi\)
\(770\) −2.82261e12 −0.289362
\(771\) −9.30247e11 −0.0948099
\(772\) −9.31480e12 −0.943834
\(773\) −8.49494e12 −0.855761 −0.427881 0.903835i \(-0.640740\pi\)
−0.427881 + 0.903835i \(0.640740\pi\)
\(774\) −1.52674e12 −0.152908
\(775\) 7.95720e11 0.0792324
\(776\) 1.08474e13 1.07386
\(777\) 1.18034e13 1.16175
\(778\) −2.59768e12 −0.254201
\(779\) 4.97953e12 0.484473
\(780\) 2.87646e12 0.278249
\(781\) −8.96793e11 −0.0862506
\(782\) 1.34334e11 0.0128456
\(783\) 1.77617e12 0.168872
\(784\) 1.41845e13 1.34088
\(785\) −6.79511e12 −0.638680
\(786\) 8.88287e11 0.0830141
\(787\) 2.03085e13 1.88708 0.943541 0.331256i \(-0.107472\pi\)
0.943541 + 0.331256i \(0.107472\pi\)
\(788\) 6.52335e12 0.602702
\(789\) 6.58141e12 0.604606
\(790\) −3.26275e12 −0.298031
\(791\) 2.23239e13 2.02757
\(792\) −7.44080e11 −0.0671980
\(793\) 7.02586e12 0.630914
\(794\) −8.23767e12 −0.735550
\(795\) −9.73004e11 −0.0863898
\(796\) −1.15118e13 −1.01633
\(797\) −5.43593e12 −0.477212 −0.238606 0.971116i \(-0.576690\pi\)
−0.238606 + 0.971116i \(0.576690\pi\)
\(798\) −1.99377e12 −0.174045
\(799\) −8.75567e12 −0.760027
\(800\) −1.08137e13 −0.933403
\(801\) −6.53882e11 −0.0561245
\(802\) 1.89484e12 0.161729
\(803\) −3.90888e11 −0.0331766
\(804\) 9.84331e12 0.830785
\(805\) 7.93748e11 0.0666195
\(806\) 1.63393e11 0.0136372
\(807\) 3.74844e12 0.311114
\(808\) 1.47313e13 1.21588
\(809\) −1.03468e13 −0.849252 −0.424626 0.905369i \(-0.639594\pi\)
−0.424626 + 0.905369i \(0.639594\pi\)
\(810\) 7.76369e11 0.0633702
\(811\) −1.89503e13 −1.53824 −0.769118 0.639107i \(-0.779304\pi\)
−0.769118 + 0.639107i \(0.779304\pi\)
\(812\) 1.70286e13 1.37460
\(813\) −9.89551e12 −0.794384
\(814\) −1.47590e12 −0.117827
\(815\) 9.78259e12 0.776685
\(816\) −4.86306e12 −0.383976
\(817\) −5.68637e12 −0.446515
\(818\) −4.86116e12 −0.379621
\(819\) −3.31117e12 −0.257160
\(820\) −1.85897e13 −1.43586
\(821\) −3.52666e12 −0.270906 −0.135453 0.990784i \(-0.543249\pi\)
−0.135453 + 0.990784i \(0.543249\pi\)
\(822\) −4.27075e12 −0.326273
\(823\) 2.14238e13 1.62778 0.813892 0.581016i \(-0.197345\pi\)
0.813892 + 0.581016i \(0.197345\pi\)
\(824\) 1.56127e13 1.17979
\(825\) 2.01631e12 0.151536
\(826\) −1.32769e12 −0.0992398
\(827\) 2.09765e13 1.55940 0.779701 0.626152i \(-0.215371\pi\)
0.779701 + 0.626152i \(0.215371\pi\)
\(828\) 9.52103e10 0.00703959
\(829\) −1.03818e13 −0.763443 −0.381722 0.924277i \(-0.624669\pi\)
−0.381722 + 0.924277i \(0.624669\pi\)
\(830\) −8.92183e12 −0.652533
\(831\) −1.32191e12 −0.0961609
\(832\) 8.03299e11 0.0581196
\(833\) 4.37774e13 3.15027
\(834\) −2.78364e12 −0.199235
\(835\) 3.57004e13 2.54146
\(836\) −1.26102e12 −0.0892882
\(837\) −2.23069e11 −0.0157100
\(838\) 3.41403e12 0.239149
\(839\) 1.61587e13 1.12584 0.562920 0.826511i \(-0.309678\pi\)
0.562920 + 0.826511i \(0.309678\pi\)
\(840\) 1.63580e13 1.13363
\(841\) −3.33698e12 −0.230023
\(842\) 2.94900e12 0.202195
\(843\) −3.47948e12 −0.237296
\(844\) −1.93217e13 −1.31070
\(845\) 1.72869e13 1.16644
\(846\) 1.22685e12 0.0823426
\(847\) −2.60484e13 −1.73903
\(848\) −8.54000e11 −0.0567122
\(849\) −1.78518e12 −0.117923
\(850\) −7.50186e12 −0.492928
\(851\) 4.15038e11 0.0271272
\(852\) 2.36485e12 0.153753
\(853\) −2.50358e13 −1.61916 −0.809582 0.587007i \(-0.800306\pi\)
−0.809582 + 0.587007i \(0.800306\pi\)
\(854\) 1.81803e13 1.16961
\(855\) 2.89160e12 0.185051
\(856\) −2.08480e13 −1.32719
\(857\) 1.15136e13 0.729120 0.364560 0.931180i \(-0.381219\pi\)
0.364560 + 0.931180i \(0.381219\pi\)
\(858\) 4.14028e11 0.0260818
\(859\) −2.58247e13 −1.61832 −0.809162 0.587585i \(-0.800079\pi\)
−0.809162 + 0.587585i \(0.800079\pi\)
\(860\) 2.12286e13 1.32336
\(861\) 2.13991e13 1.32703
\(862\) 1.93101e12 0.119125
\(863\) −1.68218e13 −1.03234 −0.516172 0.856485i \(-0.672643\pi\)
−0.516172 + 0.856485i \(0.672643\pi\)
\(864\) 3.03147e12 0.185072
\(865\) 7.51953e11 0.0456686
\(866\) −2.93699e12 −0.177449
\(867\) −5.40320e12 −0.324762
\(868\) −2.13862e12 −0.127877
\(869\) 2.37549e12 0.141307
\(870\) 4.88250e12 0.288939
\(871\) −1.20370e13 −0.708659
\(872\) −4.74709e12 −0.278038
\(873\) 8.24026e12 0.480150
\(874\) −7.01062e10 −0.00406401
\(875\) 1.34210e12 0.0774017
\(876\) 1.03077e12 0.0591418
\(877\) 7.86875e12 0.449167 0.224583 0.974455i \(-0.427898\pi\)
0.224583 + 0.974455i \(0.427898\pi\)
\(878\) 4.02623e11 0.0228651
\(879\) −7.64194e12 −0.431771
\(880\) 3.59299e12 0.201969
\(881\) 7.15687e12 0.400250 0.200125 0.979770i \(-0.435865\pi\)
0.200125 + 0.979770i \(0.435865\pi\)
\(882\) −6.13411e12 −0.341305
\(883\) −3.47556e13 −1.92399 −0.961993 0.273075i \(-0.911959\pi\)
−0.961993 + 0.273075i \(0.911959\pi\)
\(884\) 7.79183e12 0.429145
\(885\) 1.92557e12 0.105515
\(886\) 3.52206e12 0.192019
\(887\) 1.86780e13 1.01315 0.506576 0.862195i \(-0.330911\pi\)
0.506576 + 0.862195i \(0.330911\pi\)
\(888\) 8.55332e12 0.461611
\(889\) −8.51224e12 −0.457073
\(890\) −1.79745e12 −0.0960289
\(891\) −5.65245e11 −0.0300460
\(892\) 8.43993e12 0.446372
\(893\) 4.56943e12 0.240453
\(894\) 3.45135e12 0.180705
\(895\) −1.04332e13 −0.543515
\(896\) 3.68878e13 1.91204
\(897\) −1.16429e11 −0.00600477
\(898\) −1.09201e13 −0.560380
\(899\) −1.40286e12 −0.0716301
\(900\) −5.31702e12 −0.270133
\(901\) −2.63569e12 −0.133240
\(902\) −2.67574e12 −0.134591
\(903\) −2.44367e13 −1.22306
\(904\) 1.61770e13 0.805639
\(905\) −4.90147e13 −2.42889
\(906\) 5.06177e11 0.0249589
\(907\) 1.17757e13 0.577770 0.288885 0.957364i \(-0.406716\pi\)
0.288885 + 0.957364i \(0.406716\pi\)
\(908\) 2.95695e13 1.44364
\(909\) 1.11907e13 0.543651
\(910\) −9.10205e12 −0.440000
\(911\) −1.93498e13 −0.930774 −0.465387 0.885107i \(-0.654085\pi\)
−0.465387 + 0.885107i \(0.654085\pi\)
\(912\) 2.53794e12 0.121480
\(913\) 6.49565e12 0.309389
\(914\) −1.48891e13 −0.705684
\(915\) −2.63672e13 −1.24357
\(916\) −1.36809e13 −0.642072
\(917\) 1.42178e13 0.664002
\(918\) 2.10304e12 0.0977363
\(919\) −3.63385e13 −1.68053 −0.840266 0.542174i \(-0.817601\pi\)
−0.840266 + 0.542174i \(0.817601\pi\)
\(920\) 5.75188e11 0.0264707
\(921\) 2.23557e13 1.02381
\(922\) −7.69068e12 −0.350490
\(923\) −2.89188e12 −0.131152
\(924\) −5.41914e12 −0.244572
\(925\) −2.31778e13 −1.04096
\(926\) −8.72167e12 −0.389807
\(927\) 1.18603e13 0.527516
\(928\) 1.90646e13 0.843844
\(929\) 3.74342e13 1.64891 0.824456 0.565926i \(-0.191481\pi\)
0.824456 + 0.565926i \(0.191481\pi\)
\(930\) −6.13193e11 −0.0268797
\(931\) −2.28466e13 −0.996664
\(932\) −2.51959e13 −1.09385
\(933\) −1.27758e13 −0.551976
\(934\) 1.30449e13 0.560894
\(935\) 1.10890e13 0.474505
\(936\) −2.39943e12 −0.102180
\(937\) −2.49786e13 −1.05862 −0.529310 0.848428i \(-0.677549\pi\)
−0.529310 + 0.848428i \(0.677549\pi\)
\(938\) −3.11474e13 −1.31374
\(939\) −1.52944e13 −0.642002
\(940\) −1.70587e13 −0.712643
\(941\) 1.44515e13 0.600840 0.300420 0.953807i \(-0.402873\pi\)
0.300420 + 0.953807i \(0.402873\pi\)
\(942\) 2.57916e12 0.106721
\(943\) 7.52448e11 0.0309866
\(944\) 1.69006e12 0.0692672
\(945\) 1.24264e13 0.506878
\(946\) 3.05556e12 0.124046
\(947\) −1.75626e13 −0.709599 −0.354800 0.934942i \(-0.615451\pi\)
−0.354800 + 0.934942i \(0.615451\pi\)
\(948\) −6.26417e12 −0.251899
\(949\) −1.26049e12 −0.0504479
\(950\) 3.91508e12 0.155950
\(951\) −1.42344e12 −0.0564323
\(952\) 4.43108e13 1.74841
\(953\) 1.82144e13 0.715313 0.357657 0.933853i \(-0.383576\pi\)
0.357657 + 0.933853i \(0.383576\pi\)
\(954\) 3.69314e11 0.0144354
\(955\) −1.11468e13 −0.433646
\(956\) −2.78881e13 −1.07984
\(957\) −3.55477e12 −0.136996
\(958\) −1.98117e13 −0.759935
\(959\) −6.83569e13 −2.60975
\(960\) −3.01469e12 −0.114557
\(961\) −2.62634e13 −0.993336
\(962\) −4.75932e12 −0.179167
\(963\) −1.58373e13 −0.593420
\(964\) 4.15307e12 0.154890
\(965\) −4.27481e13 −1.58688
\(966\) −3.01276e11 −0.0111318
\(967\) 1.89427e13 0.696662 0.348331 0.937372i \(-0.386749\pi\)
0.348331 + 0.937372i \(0.386749\pi\)
\(968\) −1.88760e13 −0.690987
\(969\) 7.83283e12 0.285405
\(970\) 2.26516e13 0.821535
\(971\) 5.20045e12 0.187739 0.0938695 0.995585i \(-0.470076\pi\)
0.0938695 + 0.995585i \(0.470076\pi\)
\(972\) 1.49055e12 0.0535611
\(973\) −4.45545e13 −1.59362
\(974\) −5.46249e12 −0.194480
\(975\) 6.50199e12 0.230423
\(976\) −2.31424e13 −0.816363
\(977\) 1.58572e12 0.0556801 0.0278401 0.999612i \(-0.491137\pi\)
0.0278401 + 0.999612i \(0.491137\pi\)
\(978\) −3.71309e12 −0.129781
\(979\) 1.30866e12 0.0455306
\(980\) 8.52919e13 2.95386
\(981\) −3.60616e12 −0.124318
\(982\) 7.53476e12 0.258564
\(983\) 4.71124e13 1.60933 0.804663 0.593732i \(-0.202346\pi\)
0.804663 + 0.593732i \(0.202346\pi\)
\(984\) 1.55068e13 0.527285
\(985\) 2.99374e13 1.01333
\(986\) 1.32258e13 0.445632
\(987\) 1.96367e13 0.658631
\(988\) −4.06641e12 −0.135770
\(989\) −8.59258e11 −0.0285588
\(990\) −1.55380e12 −0.0514087
\(991\) 1.43146e13 0.471465 0.235732 0.971818i \(-0.424251\pi\)
0.235732 + 0.971818i \(0.424251\pi\)
\(992\) −2.39432e12 −0.0785019
\(993\) 6.99883e12 0.228430
\(994\) −7.48313e12 −0.243133
\(995\) −5.28308e13 −1.70877
\(996\) −1.71291e13 −0.551527
\(997\) −2.69941e12 −0.0865248 −0.0432624 0.999064i \(-0.513775\pi\)
−0.0432624 + 0.999064i \(0.513775\pi\)
\(998\) −1.93440e13 −0.617247
\(999\) 6.49758e12 0.206399
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.1.9 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.9 22 1.1 even 1 trivial