Properties

Label 177.12.a.c.1.15
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.32183 q^{2} -243.000 q^{3} -2036.97 q^{4} +10388.6 q^{5} +807.204 q^{6} +36007.4 q^{7} +13569.5 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-3.32183 q^{2} -243.000 q^{3} -2036.97 q^{4} +10388.6 q^{5} +807.204 q^{6} +36007.4 q^{7} +13569.5 q^{8} +59049.0 q^{9} -34509.2 q^{10} +210488. q^{11} +494983. q^{12} -165388. q^{13} -119610. q^{14} -2.52444e6 q^{15} +4.12663e6 q^{16} +1.10693e7 q^{17} -196151. q^{18} +6.36628e6 q^{19} -2.11613e7 q^{20} -8.74979e6 q^{21} -699203. q^{22} +3.65341e7 q^{23} -3.29740e6 q^{24} +5.90953e7 q^{25} +549389. q^{26} -1.43489e7 q^{27} -7.33458e7 q^{28} +4.69684e7 q^{29} +8.38574e6 q^{30} +2.92595e8 q^{31} -4.14984e7 q^{32} -5.11485e7 q^{33} -3.67704e7 q^{34} +3.74067e8 q^{35} -1.20281e8 q^{36} -8.53685e7 q^{37} -2.11477e7 q^{38} +4.01892e7 q^{39} +1.40969e8 q^{40} -1.98363e8 q^{41} +2.90653e7 q^{42} -1.07429e9 q^{43} -4.28756e8 q^{44} +6.13438e8 q^{45} -1.21360e8 q^{46} +4.33042e8 q^{47} -1.00277e9 q^{48} -6.80797e8 q^{49} -1.96305e8 q^{50} -2.68984e9 q^{51} +3.36889e8 q^{52} +5.70841e7 q^{53} +4.76646e7 q^{54} +2.18668e9 q^{55} +4.88604e8 q^{56} -1.54701e9 q^{57} -1.56021e8 q^{58} -7.14924e8 q^{59} +5.14219e9 q^{60} -7.10908e9 q^{61} -9.71951e8 q^{62} +2.12620e9 q^{63} -8.31349e9 q^{64} -1.71815e9 q^{65} +1.69906e8 q^{66} -1.47067e10 q^{67} -2.25478e10 q^{68} -8.87779e9 q^{69} -1.24259e9 q^{70} -4.78497e8 q^{71} +8.01268e8 q^{72} +1.94031e10 q^{73} +2.83579e8 q^{74} -1.43602e10 q^{75} -1.29679e10 q^{76} +7.57910e9 q^{77} -1.33501e8 q^{78} -1.66351e10 q^{79} +4.28700e10 q^{80} +3.48678e9 q^{81} +6.58929e8 q^{82} +1.27453e10 q^{83} +1.78230e10 q^{84} +1.14995e11 q^{85} +3.56860e9 q^{86} -1.14133e10 q^{87} +2.85622e9 q^{88} +2.31158e10 q^{89} -2.03773e9 q^{90} -5.95517e9 q^{91} -7.44188e10 q^{92} -7.11007e10 q^{93} -1.43849e9 q^{94} +6.61369e10 q^{95} +1.00841e10 q^{96} -7.93508e10 q^{97} +2.26149e9 q^{98} +1.24291e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.32183 −0.0734027 −0.0367013 0.999326i \(-0.511685\pi\)
−0.0367013 + 0.999326i \(0.511685\pi\)
\(3\) −243.000 −0.577350
\(4\) −2036.97 −0.994612
\(5\) 10388.6 1.48670 0.743349 0.668903i \(-0.233236\pi\)
0.743349 + 0.668903i \(0.233236\pi\)
\(6\) 807.204 0.0423791
\(7\) 36007.4 0.809752 0.404876 0.914372i \(-0.367315\pi\)
0.404876 + 0.914372i \(0.367315\pi\)
\(8\) 13569.5 0.146410
\(9\) 59049.0 0.333333
\(10\) −34509.2 −0.109128
\(11\) 210488. 0.394064 0.197032 0.980397i \(-0.436870\pi\)
0.197032 + 0.980397i \(0.436870\pi\)
\(12\) 494983. 0.574240
\(13\) −165388. −0.123542 −0.0617710 0.998090i \(-0.519675\pi\)
−0.0617710 + 0.998090i \(0.519675\pi\)
\(14\) −119610. −0.0594380
\(15\) −2.52444e6 −0.858346
\(16\) 4.12663e6 0.983865
\(17\) 1.10693e7 1.89083 0.945413 0.325873i \(-0.105658\pi\)
0.945413 + 0.325873i \(0.105658\pi\)
\(18\) −196151. −0.0244676
\(19\) 6.36628e6 0.589849 0.294925 0.955521i \(-0.404705\pi\)
0.294925 + 0.955521i \(0.404705\pi\)
\(20\) −2.11613e7 −1.47869
\(21\) −8.74979e6 −0.467511
\(22\) −699203. −0.0289254
\(23\) 3.65341e7 1.18357 0.591787 0.806094i \(-0.298423\pi\)
0.591787 + 0.806094i \(0.298423\pi\)
\(24\) −3.29740e6 −0.0845298
\(25\) 5.90953e7 1.21027
\(26\) 549389. 0.00906831
\(27\) −1.43489e7 −0.192450
\(28\) −7.33458e7 −0.805389
\(29\) 4.69684e7 0.425223 0.212612 0.977137i \(-0.431803\pi\)
0.212612 + 0.977137i \(0.431803\pi\)
\(30\) 8.38574e6 0.0630049
\(31\) 2.92595e8 1.83560 0.917800 0.397043i \(-0.129964\pi\)
0.917800 + 0.397043i \(0.129964\pi\)
\(32\) −4.14984e7 −0.218628
\(33\) −5.11485e7 −0.227513
\(34\) −3.67704e7 −0.138792
\(35\) 3.74067e8 1.20386
\(36\) −1.20281e8 −0.331537
\(37\) −8.53685e7 −0.202390 −0.101195 0.994867i \(-0.532267\pi\)
−0.101195 + 0.994867i \(0.532267\pi\)
\(38\) −2.11477e7 −0.0432965
\(39\) 4.01892e7 0.0713270
\(40\) 1.40969e8 0.217667
\(41\) −1.98363e8 −0.267393 −0.133697 0.991022i \(-0.542685\pi\)
−0.133697 + 0.991022i \(0.542685\pi\)
\(42\) 2.90653e7 0.0343165
\(43\) −1.07429e9 −1.11441 −0.557203 0.830376i \(-0.688126\pi\)
−0.557203 + 0.830376i \(0.688126\pi\)
\(44\) −4.28756e8 −0.391941
\(45\) 6.13438e8 0.495566
\(46\) −1.21360e8 −0.0868776
\(47\) 4.33042e8 0.275418 0.137709 0.990473i \(-0.456026\pi\)
0.137709 + 0.990473i \(0.456026\pi\)
\(48\) −1.00277e9 −0.568035
\(49\) −6.80797e8 −0.344302
\(50\) −1.96305e8 −0.0888373
\(51\) −2.68984e9 −1.09167
\(52\) 3.36889e8 0.122876
\(53\) 5.70841e7 0.0187498 0.00937492 0.999956i \(-0.497016\pi\)
0.00937492 + 0.999956i \(0.497016\pi\)
\(54\) 4.76646e7 0.0141264
\(55\) 2.18668e9 0.585854
\(56\) 4.88604e8 0.118556
\(57\) −1.54701e9 −0.340550
\(58\) −1.56021e8 −0.0312125
\(59\) −7.14924e8 −0.130189
\(60\) 5.14219e9 0.853721
\(61\) −7.10908e9 −1.07770 −0.538852 0.842401i \(-0.681142\pi\)
−0.538852 + 0.842401i \(0.681142\pi\)
\(62\) −9.71951e8 −0.134738
\(63\) 2.12620e9 0.269917
\(64\) −8.31349e9 −0.967817
\(65\) −1.71815e9 −0.183670
\(66\) 1.69906e8 0.0167001
\(67\) −1.47067e10 −1.33077 −0.665385 0.746500i \(-0.731733\pi\)
−0.665385 + 0.746500i \(0.731733\pi\)
\(68\) −2.25478e10 −1.88064
\(69\) −8.87779e9 −0.683337
\(70\) −1.24259e9 −0.0883664
\(71\) −4.78497e8 −0.0314745 −0.0157372 0.999876i \(-0.505010\pi\)
−0.0157372 + 0.999876i \(0.505010\pi\)
\(72\) 8.01268e8 0.0488033
\(73\) 1.94031e10 1.09546 0.547730 0.836655i \(-0.315492\pi\)
0.547730 + 0.836655i \(0.315492\pi\)
\(74\) 2.83579e8 0.0148559
\(75\) −1.43602e10 −0.698751
\(76\) −1.29679e10 −0.586671
\(77\) 7.57910e9 0.319094
\(78\) −1.33501e8 −0.00523559
\(79\) −1.66351e10 −0.608240 −0.304120 0.952634i \(-0.598362\pi\)
−0.304120 + 0.952634i \(0.598362\pi\)
\(80\) 4.28700e10 1.46271
\(81\) 3.48678e9 0.111111
\(82\) 6.58929e8 0.0196274
\(83\) 1.27453e10 0.355158 0.177579 0.984107i \(-0.443173\pi\)
0.177579 + 0.984107i \(0.443173\pi\)
\(84\) 1.78230e10 0.464992
\(85\) 1.14995e11 2.81109
\(86\) 3.56860e9 0.0818005
\(87\) −1.14133e10 −0.245503
\(88\) 2.85622e9 0.0576949
\(89\) 2.31158e10 0.438797 0.219399 0.975635i \(-0.429590\pi\)
0.219399 + 0.975635i \(0.429590\pi\)
\(90\) −2.03773e9 −0.0363759
\(91\) −5.95517e9 −0.100038
\(92\) −7.44188e10 −1.17720
\(93\) −7.11007e10 −1.05978
\(94\) −1.43849e9 −0.0202164
\(95\) 6.61369e10 0.876928
\(96\) 1.00841e10 0.126225
\(97\) −7.93508e10 −0.938224 −0.469112 0.883139i \(-0.655426\pi\)
−0.469112 + 0.883139i \(0.655426\pi\)
\(98\) 2.26149e9 0.0252727
\(99\) 1.24291e10 0.131355
\(100\) −1.20375e11 −1.20375
\(101\) 1.11992e11 1.06028 0.530138 0.847911i \(-0.322140\pi\)
0.530138 + 0.847911i \(0.322140\pi\)
\(102\) 8.93520e9 0.0801315
\(103\) −1.05658e10 −0.0898042 −0.0449021 0.998991i \(-0.514298\pi\)
−0.0449021 + 0.998991i \(0.514298\pi\)
\(104\) −2.24423e9 −0.0180878
\(105\) −9.08982e10 −0.695047
\(106\) −1.89623e8 −0.00137629
\(107\) 1.96255e11 1.35273 0.676363 0.736568i \(-0.263555\pi\)
0.676363 + 0.736568i \(0.263555\pi\)
\(108\) 2.92282e10 0.191413
\(109\) 1.50533e11 0.937103 0.468552 0.883436i \(-0.344776\pi\)
0.468552 + 0.883436i \(0.344776\pi\)
\(110\) −7.26376e9 −0.0430033
\(111\) 2.07446e10 0.116850
\(112\) 1.48589e11 0.796687
\(113\) 3.57354e11 1.82460 0.912299 0.409525i \(-0.134305\pi\)
0.912299 + 0.409525i \(0.134305\pi\)
\(114\) 5.13889e9 0.0249973
\(115\) 3.79539e11 1.75962
\(116\) −9.56731e10 −0.422932
\(117\) −9.76597e9 −0.0411806
\(118\) 2.37485e9 0.00955622
\(119\) 3.98577e11 1.53110
\(120\) −3.42554e10 −0.125670
\(121\) −2.41007e11 −0.844714
\(122\) 2.36151e10 0.0791063
\(123\) 4.82023e10 0.154379
\(124\) −5.96007e11 −1.82571
\(125\) 1.06662e11 0.312612
\(126\) −7.06286e9 −0.0198127
\(127\) −5.29513e11 −1.42219 −0.711093 0.703098i \(-0.751799\pi\)
−0.711093 + 0.703098i \(0.751799\pi\)
\(128\) 1.12605e11 0.289669
\(129\) 2.61052e11 0.643403
\(130\) 5.70739e9 0.0134818
\(131\) −1.60022e11 −0.362400 −0.181200 0.983446i \(-0.557998\pi\)
−0.181200 + 0.983446i \(0.557998\pi\)
\(132\) 1.04188e11 0.226287
\(133\) 2.29233e11 0.477631
\(134\) 4.88531e10 0.0976822
\(135\) −1.49065e11 −0.286115
\(136\) 1.50206e11 0.276836
\(137\) 4.42732e11 0.783750 0.391875 0.920019i \(-0.371827\pi\)
0.391875 + 0.920019i \(0.371827\pi\)
\(138\) 2.94905e10 0.0501588
\(139\) −9.70500e11 −1.58641 −0.793203 0.608958i \(-0.791588\pi\)
−0.793203 + 0.608958i \(0.791588\pi\)
\(140\) −7.61961e11 −1.19737
\(141\) −1.05229e11 −0.159013
\(142\) 1.58948e9 0.00231031
\(143\) −3.48120e10 −0.0486834
\(144\) 2.43673e11 0.327955
\(145\) 4.87937e11 0.632179
\(146\) −6.44539e10 −0.0804097
\(147\) 1.65434e11 0.198783
\(148\) 1.73893e11 0.201299
\(149\) −5.89226e11 −0.657290 −0.328645 0.944453i \(-0.606592\pi\)
−0.328645 + 0.944453i \(0.606592\pi\)
\(150\) 4.77020e10 0.0512902
\(151\) −6.30046e11 −0.653129 −0.326564 0.945175i \(-0.605891\pi\)
−0.326564 + 0.945175i \(0.605891\pi\)
\(152\) 8.63875e10 0.0863597
\(153\) 6.53632e11 0.630276
\(154\) −2.51765e10 −0.0234224
\(155\) 3.03966e12 2.72898
\(156\) −8.18640e10 −0.0709427
\(157\) −1.65494e12 −1.38463 −0.692315 0.721595i \(-0.743409\pi\)
−0.692315 + 0.721595i \(0.743409\pi\)
\(158\) 5.52588e10 0.0446465
\(159\) −1.38714e10 −0.0108252
\(160\) −4.31111e11 −0.325034
\(161\) 1.31550e12 0.958402
\(162\) −1.15825e10 −0.00815586
\(163\) 3.03764e11 0.206778 0.103389 0.994641i \(-0.467031\pi\)
0.103389 + 0.994641i \(0.467031\pi\)
\(164\) 4.04059e11 0.265952
\(165\) −5.31362e11 −0.338243
\(166\) −4.23378e10 −0.0260696
\(167\) 1.80369e12 1.07454 0.537269 0.843411i \(-0.319456\pi\)
0.537269 + 0.843411i \(0.319456\pi\)
\(168\) −1.18731e11 −0.0684482
\(169\) −1.76481e12 −0.984737
\(170\) −3.81993e11 −0.206342
\(171\) 3.75922e11 0.196616
\(172\) 2.18829e12 1.10840
\(173\) 1.00023e12 0.490735 0.245367 0.969430i \(-0.421091\pi\)
0.245367 + 0.969430i \(0.421091\pi\)
\(174\) 3.79131e10 0.0180206
\(175\) 2.12787e12 0.980021
\(176\) 8.68604e11 0.387706
\(177\) 1.73727e11 0.0751646
\(178\) −7.67867e10 −0.0322089
\(179\) 1.77601e12 0.722359 0.361180 0.932496i \(-0.382374\pi\)
0.361180 + 0.932496i \(0.382374\pi\)
\(180\) −1.24955e12 −0.492896
\(181\) 9.10888e11 0.348524 0.174262 0.984699i \(-0.444246\pi\)
0.174262 + 0.984699i \(0.444246\pi\)
\(182\) 1.97820e10 0.00734308
\(183\) 1.72751e12 0.622212
\(184\) 4.95752e11 0.173287
\(185\) −8.86861e11 −0.300892
\(186\) 2.36184e11 0.0777910
\(187\) 2.32995e12 0.745107
\(188\) −8.82092e11 −0.273934
\(189\) −5.16666e11 −0.155837
\(190\) −2.19695e11 −0.0643689
\(191\) 2.56867e12 0.731182 0.365591 0.930776i \(-0.380867\pi\)
0.365591 + 0.930776i \(0.380867\pi\)
\(192\) 2.02018e12 0.558770
\(193\) 2.96998e12 0.798341 0.399171 0.916877i \(-0.369298\pi\)
0.399171 + 0.916877i \(0.369298\pi\)
\(194\) 2.63590e11 0.0688682
\(195\) 4.17510e11 0.106042
\(196\) 1.38676e12 0.342446
\(197\) −3.59827e12 −0.864032 −0.432016 0.901866i \(-0.642198\pi\)
−0.432016 + 0.901866i \(0.642198\pi\)
\(198\) −4.12873e10 −0.00964179
\(199\) 7.64364e12 1.73623 0.868117 0.496360i \(-0.165330\pi\)
0.868117 + 0.496360i \(0.165330\pi\)
\(200\) 8.01897e11 0.177196
\(201\) 3.57372e12 0.768321
\(202\) −3.72018e11 −0.0778271
\(203\) 1.69121e12 0.344326
\(204\) 5.47912e12 1.08579
\(205\) −2.06072e12 −0.397533
\(206\) 3.50977e10 0.00659187
\(207\) 2.15730e12 0.394525
\(208\) −6.82493e11 −0.121549
\(209\) 1.34002e12 0.232438
\(210\) 3.01948e11 0.0510183
\(211\) 6.08970e12 1.00240 0.501201 0.865331i \(-0.332892\pi\)
0.501201 + 0.865331i \(0.332892\pi\)
\(212\) −1.16278e11 −0.0186488
\(213\) 1.16275e11 0.0181718
\(214\) −6.51925e11 −0.0992938
\(215\) −1.11604e13 −1.65679
\(216\) −1.94708e11 −0.0281766
\(217\) 1.05356e13 1.48638
\(218\) −5.00046e11 −0.0687859
\(219\) −4.71496e12 −0.632464
\(220\) −4.45418e12 −0.582698
\(221\) −1.83073e12 −0.233596
\(222\) −6.89098e10 −0.00857708
\(223\) 6.69853e12 0.813397 0.406698 0.913562i \(-0.366680\pi\)
0.406698 + 0.913562i \(0.366680\pi\)
\(224\) −1.49425e12 −0.177035
\(225\) 3.48952e12 0.403424
\(226\) −1.18707e12 −0.133930
\(227\) −1.28260e13 −1.41237 −0.706184 0.708028i \(-0.749585\pi\)
−0.706184 + 0.708028i \(0.749585\pi\)
\(228\) 3.15120e12 0.338715
\(229\) −1.17983e13 −1.23801 −0.619007 0.785385i \(-0.712465\pi\)
−0.619007 + 0.785385i \(0.712465\pi\)
\(230\) −1.26076e12 −0.129161
\(231\) −1.84172e12 −0.184229
\(232\) 6.37341e11 0.0622569
\(233\) −4.42287e12 −0.421936 −0.210968 0.977493i \(-0.567662\pi\)
−0.210968 + 0.977493i \(0.567662\pi\)
\(234\) 3.24409e10 0.00302277
\(235\) 4.49871e12 0.409463
\(236\) 1.45628e12 0.129487
\(237\) 4.04232e12 0.351168
\(238\) −1.32400e12 −0.112387
\(239\) 2.33707e13 1.93858 0.969291 0.245917i \(-0.0790892\pi\)
0.969291 + 0.245917i \(0.0790892\pi\)
\(240\) −1.04174e13 −0.844497
\(241\) 8.46901e12 0.671026 0.335513 0.942036i \(-0.391090\pi\)
0.335513 + 0.942036i \(0.391090\pi\)
\(242\) 8.00582e11 0.0620043
\(243\) −8.47289e11 −0.0641500
\(244\) 1.44809e13 1.07190
\(245\) −7.07254e12 −0.511873
\(246\) −1.60120e11 −0.0113319
\(247\) −1.05290e12 −0.0728711
\(248\) 3.97039e12 0.268750
\(249\) −3.09712e12 −0.205051
\(250\) −3.54314e11 −0.0229466
\(251\) −1.99261e13 −1.26246 −0.631229 0.775597i \(-0.717449\pi\)
−0.631229 + 0.775597i \(0.717449\pi\)
\(252\) −4.33099e12 −0.268463
\(253\) 7.68998e12 0.466404
\(254\) 1.75895e12 0.104392
\(255\) −2.79438e13 −1.62298
\(256\) 1.66520e13 0.946555
\(257\) 2.25882e11 0.0125675 0.00628375 0.999980i \(-0.498000\pi\)
0.00628375 + 0.999980i \(0.498000\pi\)
\(258\) −8.67169e11 −0.0472275
\(259\) −3.07390e12 −0.163885
\(260\) 3.49981e12 0.182680
\(261\) 2.77344e12 0.141741
\(262\) 5.31566e11 0.0266011
\(263\) −1.12859e13 −0.553070 −0.276535 0.961004i \(-0.589186\pi\)
−0.276535 + 0.961004i \(0.589186\pi\)
\(264\) −6.94062e11 −0.0333101
\(265\) 5.93025e11 0.0278754
\(266\) −7.61472e11 −0.0350594
\(267\) −5.61714e12 −0.253340
\(268\) 2.99570e13 1.32360
\(269\) 2.12970e13 0.921894 0.460947 0.887428i \(-0.347510\pi\)
0.460947 + 0.887428i \(0.347510\pi\)
\(270\) 4.95169e11 0.0210016
\(271\) 5.21661e12 0.216799 0.108399 0.994107i \(-0.465427\pi\)
0.108399 + 0.994107i \(0.465427\pi\)
\(272\) 4.56790e13 1.86032
\(273\) 1.44711e12 0.0577572
\(274\) −1.47068e12 −0.0575293
\(275\) 1.24388e13 0.476925
\(276\) 1.80838e13 0.679655
\(277\) −3.60809e13 −1.32935 −0.664674 0.747134i \(-0.731430\pi\)
−0.664674 + 0.747134i \(0.731430\pi\)
\(278\) 3.22383e12 0.116446
\(279\) 1.72775e13 0.611867
\(280\) 5.07592e12 0.176257
\(281\) −9.47322e12 −0.322562 −0.161281 0.986909i \(-0.551563\pi\)
−0.161281 + 0.986909i \(0.551563\pi\)
\(282\) 3.49553e11 0.0116719
\(283\) 1.23634e12 0.0404867 0.0202434 0.999795i \(-0.493556\pi\)
0.0202434 + 0.999795i \(0.493556\pi\)
\(284\) 9.74682e11 0.0313049
\(285\) −1.60713e13 −0.506294
\(286\) 1.15640e11 0.00357349
\(287\) −7.14254e12 −0.216522
\(288\) −2.45044e12 −0.0728761
\(289\) 8.82579e13 2.57523
\(290\) −1.62084e12 −0.0464037
\(291\) 1.92822e13 0.541684
\(292\) −3.95235e13 −1.08956
\(293\) −1.31349e12 −0.0355348 −0.0177674 0.999842i \(-0.505656\pi\)
−0.0177674 + 0.999842i \(0.505656\pi\)
\(294\) −5.49542e11 −0.0145912
\(295\) −7.42708e12 −0.193552
\(296\) −1.15841e12 −0.0296318
\(297\) −3.02027e12 −0.0758376
\(298\) 1.95731e12 0.0482469
\(299\) −6.04229e12 −0.146221
\(300\) 2.92512e13 0.694986
\(301\) −3.86822e13 −0.902393
\(302\) 2.09290e12 0.0479414
\(303\) −2.72140e13 −0.612151
\(304\) 2.62713e13 0.580332
\(305\) −7.38535e13 −1.60222
\(306\) −2.17125e12 −0.0462639
\(307\) −1.49170e13 −0.312192 −0.156096 0.987742i \(-0.549891\pi\)
−0.156096 + 0.987742i \(0.549891\pi\)
\(308\) −1.54384e13 −0.317375
\(309\) 2.56748e12 0.0518485
\(310\) −1.00972e13 −0.200315
\(311\) 8.39872e13 1.63693 0.818466 0.574555i \(-0.194825\pi\)
0.818466 + 0.574555i \(0.194825\pi\)
\(312\) 5.45349e11 0.0104430
\(313\) 2.97502e13 0.559752 0.279876 0.960036i \(-0.409707\pi\)
0.279876 + 0.960036i \(0.409707\pi\)
\(314\) 5.49742e12 0.101636
\(315\) 2.20883e13 0.401286
\(316\) 3.38850e13 0.604963
\(317\) −9.01607e13 −1.58195 −0.790973 0.611852i \(-0.790425\pi\)
−0.790973 + 0.611852i \(0.790425\pi\)
\(318\) 4.60785e10 0.000794601 0
\(319\) 9.88628e12 0.167565
\(320\) −8.63657e13 −1.43885
\(321\) −4.76900e13 −0.780997
\(322\) −4.36986e12 −0.0703493
\(323\) 7.04704e13 1.11530
\(324\) −7.10246e12 −0.110512
\(325\) −9.77363e12 −0.149519
\(326\) −1.00905e12 −0.0151781
\(327\) −3.65796e13 −0.541037
\(328\) −2.69170e12 −0.0391490
\(329\) 1.55927e13 0.223020
\(330\) 1.76509e12 0.0248280
\(331\) −9.26480e13 −1.28169 −0.640844 0.767671i \(-0.721415\pi\)
−0.640844 + 0.767671i \(0.721415\pi\)
\(332\) −2.59618e13 −0.353245
\(333\) −5.04093e12 −0.0674632
\(334\) −5.99156e12 −0.0788741
\(335\) −1.52782e14 −1.97846
\(336\) −3.61071e13 −0.459967
\(337\) −3.89814e13 −0.488533 −0.244266 0.969708i \(-0.578547\pi\)
−0.244266 + 0.969708i \(0.578547\pi\)
\(338\) 5.86238e12 0.0722824
\(339\) −8.68370e13 −1.05343
\(340\) −2.34241e14 −2.79594
\(341\) 6.15877e13 0.723344
\(342\) −1.24875e12 −0.0144322
\(343\) −9.57120e13 −1.08855
\(344\) −1.45776e13 −0.163160
\(345\) −9.22280e13 −1.01592
\(346\) −3.32259e12 −0.0360212
\(347\) 6.88496e13 0.734665 0.367333 0.930090i \(-0.380271\pi\)
0.367333 + 0.930090i \(0.380271\pi\)
\(348\) 2.32486e13 0.244180
\(349\) 4.87913e12 0.0504431 0.0252216 0.999682i \(-0.491971\pi\)
0.0252216 + 0.999682i \(0.491971\pi\)
\(350\) −7.06841e12 −0.0719362
\(351\) 2.37313e12 0.0237757
\(352\) −8.73489e12 −0.0861535
\(353\) 1.21783e14 1.18257 0.591285 0.806463i \(-0.298621\pi\)
0.591285 + 0.806463i \(0.298621\pi\)
\(354\) −5.77090e11 −0.00551728
\(355\) −4.97092e12 −0.0467930
\(356\) −4.70861e13 −0.436433
\(357\) −9.68542e13 −0.883982
\(358\) −5.89959e12 −0.0530231
\(359\) −1.59489e14 −1.41160 −0.705799 0.708412i \(-0.749412\pi\)
−0.705799 + 0.708412i \(0.749412\pi\)
\(360\) 8.32407e12 0.0725558
\(361\) −7.59607e13 −0.652078
\(362\) −3.02581e12 −0.0255826
\(363\) 5.85646e13 0.487696
\(364\) 1.21305e13 0.0994993
\(365\) 2.01572e14 1.62862
\(366\) −5.73848e12 −0.0456721
\(367\) −1.62158e14 −1.27138 −0.635689 0.771945i \(-0.719284\pi\)
−0.635689 + 0.771945i \(0.719284\pi\)
\(368\) 1.50763e14 1.16448
\(369\) −1.17132e13 −0.0891310
\(370\) 2.94600e12 0.0220863
\(371\) 2.05545e12 0.0151827
\(372\) 1.44830e14 1.05407
\(373\) −6.90596e13 −0.495251 −0.247625 0.968856i \(-0.579650\pi\)
−0.247625 + 0.968856i \(0.579650\pi\)
\(374\) −7.73970e12 −0.0546928
\(375\) −2.59189e13 −0.180487
\(376\) 5.87619e12 0.0403239
\(377\) −7.76800e12 −0.0525329
\(378\) 1.71628e12 0.0114388
\(379\) 1.83874e14 1.20782 0.603912 0.797051i \(-0.293608\pi\)
0.603912 + 0.797051i \(0.293608\pi\)
\(380\) −1.34719e14 −0.872203
\(381\) 1.28672e14 0.821099
\(382\) −8.53269e12 −0.0536707
\(383\) 9.17114e13 0.568630 0.284315 0.958731i \(-0.408234\pi\)
0.284315 + 0.958731i \(0.408234\pi\)
\(384\) −2.73629e13 −0.167240
\(385\) 7.87364e13 0.474397
\(386\) −9.86577e12 −0.0586004
\(387\) −6.34356e13 −0.371469
\(388\) 1.61635e14 0.933169
\(389\) −2.04127e14 −1.16193 −0.580963 0.813930i \(-0.697324\pi\)
−0.580963 + 0.813930i \(0.697324\pi\)
\(390\) −1.38690e12 −0.00778375
\(391\) 4.04408e14 2.23793
\(392\) −9.23810e12 −0.0504092
\(393\) 3.88854e13 0.209232
\(394\) 1.19528e13 0.0634223
\(395\) −1.72815e14 −0.904270
\(396\) −2.53176e13 −0.130647
\(397\) 1.05923e14 0.539065 0.269533 0.962991i \(-0.413131\pi\)
0.269533 + 0.962991i \(0.413131\pi\)
\(398\) −2.53908e13 −0.127444
\(399\) −5.57036e13 −0.275761
\(400\) 2.43865e14 1.19075
\(401\) −3.46025e14 −1.66653 −0.833267 0.552871i \(-0.813532\pi\)
−0.833267 + 0.552871i \(0.813532\pi\)
\(402\) −1.18713e13 −0.0563968
\(403\) −4.83916e13 −0.226774
\(404\) −2.28124e14 −1.05456
\(405\) 3.62229e13 0.165189
\(406\) −5.61791e12 −0.0252744
\(407\) −1.79690e13 −0.0797545
\(408\) −3.65000e13 −0.159831
\(409\) 2.63269e14 1.13742 0.568710 0.822538i \(-0.307443\pi\)
0.568710 + 0.822538i \(0.307443\pi\)
\(410\) 6.84536e12 0.0291800
\(411\) −1.07584e14 −0.452498
\(412\) 2.15221e13 0.0893204
\(413\) −2.57425e13 −0.105421
\(414\) −7.16619e12 −0.0289592
\(415\) 1.32407e14 0.528013
\(416\) 6.86332e12 0.0270098
\(417\) 2.35832e14 0.915912
\(418\) −4.45132e12 −0.0170616
\(419\) −4.94698e14 −1.87138 −0.935692 0.352819i \(-0.885223\pi\)
−0.935692 + 0.352819i \(0.885223\pi\)
\(420\) 1.85157e14 0.691302
\(421\) −2.14561e14 −0.790679 −0.395339 0.918535i \(-0.629373\pi\)
−0.395339 + 0.918535i \(0.629373\pi\)
\(422\) −2.02289e13 −0.0735790
\(423\) 2.55707e13 0.0918059
\(424\) 7.74605e11 0.00274516
\(425\) 6.54145e14 2.28842
\(426\) −3.86245e11 −0.00133386
\(427\) −2.55979e14 −0.872672
\(428\) −3.99765e14 −1.34544
\(429\) 8.45932e12 0.0281074
\(430\) 3.70728e13 0.121613
\(431\) 6.20114e12 0.0200838 0.0100419 0.999950i \(-0.496804\pi\)
0.0100419 + 0.999950i \(0.496804\pi\)
\(432\) −5.92126e13 −0.189345
\(433\) 5.25433e13 0.165895 0.0829476 0.996554i \(-0.473567\pi\)
0.0829476 + 0.996554i \(0.473567\pi\)
\(434\) −3.49974e13 −0.109104
\(435\) −1.18569e14 −0.364989
\(436\) −3.06632e14 −0.932054
\(437\) 2.32586e14 0.698130
\(438\) 1.56623e13 0.0464246
\(439\) 4.16478e14 1.21909 0.609547 0.792750i \(-0.291351\pi\)
0.609547 + 0.792750i \(0.291351\pi\)
\(440\) 2.96722e13 0.0857749
\(441\) −4.02004e13 −0.114767
\(442\) 6.08136e12 0.0171466
\(443\) 3.80244e14 1.05887 0.529433 0.848352i \(-0.322405\pi\)
0.529433 + 0.848352i \(0.322405\pi\)
\(444\) −4.22559e13 −0.116220
\(445\) 2.40141e14 0.652359
\(446\) −2.22513e13 −0.0597055
\(447\) 1.43182e14 0.379487
\(448\) −2.99347e14 −0.783692
\(449\) 2.25663e14 0.583586 0.291793 0.956481i \(-0.405748\pi\)
0.291793 + 0.956481i \(0.405748\pi\)
\(450\) −1.15916e13 −0.0296124
\(451\) −4.17530e13 −0.105370
\(452\) −7.27918e14 −1.81477
\(453\) 1.53101e14 0.377084
\(454\) 4.26057e13 0.103672
\(455\) −6.18660e13 −0.148727
\(456\) −2.09922e13 −0.0498598
\(457\) −1.96353e14 −0.460786 −0.230393 0.973098i \(-0.574001\pi\)
−0.230393 + 0.973098i \(0.574001\pi\)
\(458\) 3.91920e13 0.0908736
\(459\) −1.58833e14 −0.363890
\(460\) −7.73108e14 −1.75014
\(461\) 8.18485e14 1.83086 0.915431 0.402475i \(-0.131850\pi\)
0.915431 + 0.402475i \(0.131850\pi\)
\(462\) 6.11788e12 0.0135229
\(463\) 5.09865e14 1.11368 0.556840 0.830620i \(-0.312014\pi\)
0.556840 + 0.830620i \(0.312014\pi\)
\(464\) 1.93821e14 0.418363
\(465\) −7.38638e14 −1.57558
\(466\) 1.46920e13 0.0309713
\(467\) −1.23439e14 −0.257164 −0.128582 0.991699i \(-0.541042\pi\)
−0.128582 + 0.991699i \(0.541042\pi\)
\(468\) 1.98929e13 0.0409588
\(469\) −5.29549e14 −1.07759
\(470\) −1.49439e13 −0.0300557
\(471\) 4.02150e14 0.799417
\(472\) −9.70120e12 −0.0190609
\(473\) −2.26124e14 −0.439148
\(474\) −1.34279e13 −0.0257767
\(475\) 3.76217e14 0.713878
\(476\) −8.11887e14 −1.52285
\(477\) 3.37076e12 0.00624995
\(478\) −7.76336e13 −0.142297
\(479\) −5.23224e14 −0.948073 −0.474037 0.880505i \(-0.657204\pi\)
−0.474037 + 0.880505i \(0.657204\pi\)
\(480\) 1.04760e14 0.187659
\(481\) 1.41189e13 0.0250036
\(482\) −2.81326e13 −0.0492551
\(483\) −3.19666e14 −0.553334
\(484\) 4.90922e14 0.840162
\(485\) −8.24345e14 −1.39486
\(486\) 2.81455e12 0.00470879
\(487\) −5.93984e14 −0.982574 −0.491287 0.870998i \(-0.663473\pi\)
−0.491287 + 0.870998i \(0.663473\pi\)
\(488\) −9.64670e13 −0.157786
\(489\) −7.38146e13 −0.119383
\(490\) 2.34938e13 0.0375728
\(491\) 3.03016e14 0.479200 0.239600 0.970872i \(-0.422984\pi\)
0.239600 + 0.970872i \(0.422984\pi\)
\(492\) −9.81864e13 −0.153548
\(493\) 5.19909e14 0.804024
\(494\) 3.49756e12 0.00534893
\(495\) 1.29121e14 0.195285
\(496\) 1.20743e15 1.80598
\(497\) −1.72294e13 −0.0254865
\(498\) 1.02881e13 0.0150513
\(499\) 7.21812e14 1.04441 0.522205 0.852820i \(-0.325110\pi\)
0.522205 + 0.852820i \(0.325110\pi\)
\(500\) −2.17267e14 −0.310928
\(501\) −4.38298e14 −0.620385
\(502\) 6.61911e13 0.0926678
\(503\) 1.05026e15 1.45436 0.727180 0.686446i \(-0.240830\pi\)
0.727180 + 0.686446i \(0.240830\pi\)
\(504\) 2.88516e13 0.0395186
\(505\) 1.16344e15 1.57631
\(506\) −2.55448e13 −0.0342353
\(507\) 4.28848e14 0.568538
\(508\) 1.07860e15 1.41452
\(509\) −1.00418e15 −1.30276 −0.651378 0.758753i \(-0.725809\pi\)
−0.651378 + 0.758753i \(0.725809\pi\)
\(510\) 9.28244e13 0.119131
\(511\) 6.98656e14 0.887051
\(512\) −2.85929e14 −0.359148
\(513\) −9.13491e13 −0.113517
\(514\) −7.50340e11 −0.000922488 0
\(515\) −1.09764e14 −0.133512
\(516\) −5.31753e14 −0.639936
\(517\) 9.11500e13 0.108532
\(518\) 1.02109e13 0.0120296
\(519\) −2.43056e14 −0.283326
\(520\) −2.33145e13 −0.0268910
\(521\) −6.69577e14 −0.764176 −0.382088 0.924126i \(-0.624795\pi\)
−0.382088 + 0.924126i \(0.624795\pi\)
\(522\) −9.21289e12 −0.0104042
\(523\) −7.80796e12 −0.00872525 −0.00436263 0.999990i \(-0.501389\pi\)
−0.00436263 + 0.999990i \(0.501389\pi\)
\(524\) 3.25960e14 0.360448
\(525\) −5.17072e14 −0.565815
\(526\) 3.74899e13 0.0405968
\(527\) 3.23883e15 3.47080
\(528\) −2.11071e14 −0.223842
\(529\) 3.81933e14 0.400849
\(530\) −1.96993e12 −0.00204613
\(531\) −4.22156e13 −0.0433963
\(532\) −4.66940e14 −0.475058
\(533\) 3.28068e13 0.0330343
\(534\) 1.86592e13 0.0185958
\(535\) 2.03882e15 2.01110
\(536\) −1.99563e14 −0.194838
\(537\) −4.31570e14 −0.417054
\(538\) −7.07450e13 −0.0676695
\(539\) −1.43299e14 −0.135677
\(540\) 3.03641e14 0.284574
\(541\) −1.78557e15 −1.65651 −0.828253 0.560354i \(-0.810665\pi\)
−0.828253 + 0.560354i \(0.810665\pi\)
\(542\) −1.73287e13 −0.0159136
\(543\) −2.21346e14 −0.201220
\(544\) −4.59359e14 −0.413388
\(545\) 1.56384e15 1.39319
\(546\) −4.80704e12 −0.00423953
\(547\) 1.41356e15 1.23420 0.617100 0.786885i \(-0.288307\pi\)
0.617100 + 0.786885i \(0.288307\pi\)
\(548\) −9.01829e14 −0.779527
\(549\) −4.19784e14 −0.359234
\(550\) −4.13197e13 −0.0350076
\(551\) 2.99014e14 0.250818
\(552\) −1.20468e14 −0.100047
\(553\) −5.98985e14 −0.492524
\(554\) 1.19855e14 0.0975777
\(555\) 2.15507e14 0.173720
\(556\) 1.97688e15 1.57786
\(557\) 1.23222e15 0.973832 0.486916 0.873449i \(-0.338122\pi\)
0.486916 + 0.873449i \(0.338122\pi\)
\(558\) −5.73927e13 −0.0449127
\(559\) 1.77674e14 0.137676
\(560\) 1.54364e15 1.18443
\(561\) −5.66179e14 −0.430188
\(562\) 3.14684e13 0.0236769
\(563\) −1.66422e15 −1.23998 −0.619991 0.784609i \(-0.712864\pi\)
−0.619991 + 0.784609i \(0.712864\pi\)
\(564\) 2.14348e14 0.158156
\(565\) 3.71242e15 2.71263
\(566\) −4.10691e12 −0.00297184
\(567\) 1.25550e14 0.0899725
\(568\) −6.49299e12 −0.00460817
\(569\) 1.26849e15 0.891598 0.445799 0.895133i \(-0.352920\pi\)
0.445799 + 0.895133i \(0.352920\pi\)
\(570\) 5.33859e13 0.0371634
\(571\) −3.62621e14 −0.250009 −0.125004 0.992156i \(-0.539894\pi\)
−0.125004 + 0.992156i \(0.539894\pi\)
\(572\) 7.09109e13 0.0484211
\(573\) −6.24188e14 −0.422148
\(574\) 2.37263e13 0.0158933
\(575\) 2.15900e15 1.43245
\(576\) −4.90903e14 −0.322606
\(577\) −2.06852e15 −1.34646 −0.673228 0.739435i \(-0.735093\pi\)
−0.673228 + 0.739435i \(0.735093\pi\)
\(578\) −2.93177e14 −0.189029
\(579\) −7.21706e14 −0.460923
\(580\) −9.93912e14 −0.628773
\(581\) 4.58926e14 0.287590
\(582\) −6.40523e13 −0.0397611
\(583\) 1.20155e13 0.00738864
\(584\) 2.63292e14 0.160386
\(585\) −1.01455e14 −0.0612232
\(586\) 4.36318e12 0.00260835
\(587\) −8.38675e14 −0.496688 −0.248344 0.968672i \(-0.579886\pi\)
−0.248344 + 0.968672i \(0.579886\pi\)
\(588\) −3.36983e14 −0.197712
\(589\) 1.86274e15 1.08273
\(590\) 2.46715e13 0.0142072
\(591\) 8.74380e14 0.498849
\(592\) −3.52284e14 −0.199124
\(593\) −1.65943e15 −0.929303 −0.464652 0.885494i \(-0.653820\pi\)
−0.464652 + 0.885494i \(0.653820\pi\)
\(594\) 1.00328e13 0.00556669
\(595\) 4.14067e15 2.27629
\(596\) 1.20023e15 0.653749
\(597\) −1.85740e15 −1.00242
\(598\) 2.00714e13 0.0107330
\(599\) 2.76061e15 1.46271 0.731354 0.681998i \(-0.238889\pi\)
0.731354 + 0.681998i \(0.238889\pi\)
\(600\) −1.94861e14 −0.102304
\(601\) 8.93942e14 0.465050 0.232525 0.972590i \(-0.425301\pi\)
0.232525 + 0.972590i \(0.425301\pi\)
\(602\) 1.28496e14 0.0662381
\(603\) −8.68415e14 −0.443590
\(604\) 1.28338e15 0.649610
\(605\) −2.50373e15 −1.25583
\(606\) 9.04003e13 0.0449335
\(607\) 9.27961e14 0.457080 0.228540 0.973535i \(-0.426605\pi\)
0.228540 + 0.973535i \(0.426605\pi\)
\(608\) −2.64190e14 −0.128958
\(609\) −4.10964e14 −0.198796
\(610\) 2.45329e14 0.117607
\(611\) −7.16198e13 −0.0340256
\(612\) −1.33143e15 −0.626880
\(613\) −2.04765e15 −0.955485 −0.477743 0.878500i \(-0.658545\pi\)
−0.477743 + 0.878500i \(0.658545\pi\)
\(614\) 4.95518e13 0.0229157
\(615\) 5.00755e14 0.229516
\(616\) 1.02845e14 0.0467185
\(617\) 1.00220e15 0.451217 0.225609 0.974218i \(-0.427563\pi\)
0.225609 + 0.974218i \(0.427563\pi\)
\(618\) −8.52874e12 −0.00380582
\(619\) 2.85171e15 1.26126 0.630632 0.776082i \(-0.282796\pi\)
0.630632 + 0.776082i \(0.282796\pi\)
\(620\) −6.19169e15 −2.71428
\(621\) −5.24225e14 −0.227779
\(622\) −2.78991e14 −0.120155
\(623\) 8.32339e14 0.355317
\(624\) 1.65846e14 0.0701761
\(625\) −1.77744e15 −0.745513
\(626\) −9.88249e13 −0.0410873
\(627\) −3.25626e14 −0.134198
\(628\) 3.37105e15 1.37717
\(629\) −9.44971e14 −0.382684
\(630\) −7.33734e13 −0.0294555
\(631\) 7.28646e14 0.289971 0.144986 0.989434i \(-0.453686\pi\)
0.144986 + 0.989434i \(0.453686\pi\)
\(632\) −2.25730e14 −0.0890524
\(633\) −1.47980e15 −0.578737
\(634\) 2.99498e14 0.116119
\(635\) −5.50091e15 −2.11436
\(636\) 2.82556e13 0.0107669
\(637\) 1.12595e14 0.0425357
\(638\) −3.28405e13 −0.0122997
\(639\) −2.82548e13 −0.0104915
\(640\) 1.16981e15 0.430650
\(641\) −2.42963e15 −0.886790 −0.443395 0.896326i \(-0.646226\pi\)
−0.443395 + 0.896326i \(0.646226\pi\)
\(642\) 1.58418e14 0.0573273
\(643\) −5.36655e15 −1.92546 −0.962730 0.270464i \(-0.912823\pi\)
−0.962730 + 0.270464i \(0.912823\pi\)
\(644\) −2.67962e15 −0.953238
\(645\) 2.71197e15 0.956547
\(646\) −2.34090e14 −0.0818662
\(647\) 2.30015e14 0.0797595 0.0398797 0.999204i \(-0.487303\pi\)
0.0398797 + 0.999204i \(0.487303\pi\)
\(648\) 4.73141e13 0.0162678
\(649\) −1.50483e14 −0.0513028
\(650\) 3.24663e13 0.0109751
\(651\) −2.56015e15 −0.858163
\(652\) −6.18756e14 −0.205664
\(653\) −2.22055e14 −0.0731876 −0.0365938 0.999330i \(-0.511651\pi\)
−0.0365938 + 0.999330i \(0.511651\pi\)
\(654\) 1.21511e14 0.0397136
\(655\) −1.66241e15 −0.538780
\(656\) −8.18572e14 −0.263079
\(657\) 1.14574e15 0.365153
\(658\) −5.17963e13 −0.0163703
\(659\) 1.70683e15 0.534958 0.267479 0.963564i \(-0.413809\pi\)
0.267479 + 0.963564i \(0.413809\pi\)
\(660\) 1.08237e15 0.336421
\(661\) 3.88940e14 0.119888 0.0599438 0.998202i \(-0.480908\pi\)
0.0599438 + 0.998202i \(0.480908\pi\)
\(662\) 3.07761e14 0.0940793
\(663\) 4.44867e14 0.134867
\(664\) 1.72948e14 0.0519987
\(665\) 2.38141e15 0.710094
\(666\) 1.67451e13 0.00495198
\(667\) 1.71595e15 0.503284
\(668\) −3.67406e15 −1.06875
\(669\) −1.62774e15 −0.469615
\(670\) 5.07516e14 0.145224
\(671\) −1.49637e15 −0.424684
\(672\) 3.63102e14 0.102211
\(673\) 2.57391e14 0.0718639 0.0359320 0.999354i \(-0.488560\pi\)
0.0359320 + 0.999354i \(0.488560\pi\)
\(674\) 1.29490e14 0.0358596
\(675\) −8.47954e14 −0.232917
\(676\) 3.59485e15 0.979432
\(677\) −6.09512e15 −1.64719 −0.823596 0.567177i \(-0.808036\pi\)
−0.823596 + 0.567177i \(0.808036\pi\)
\(678\) 2.88458e14 0.0773248
\(679\) −2.85721e15 −0.759729
\(680\) 1.56043e15 0.411571
\(681\) 3.11671e15 0.815432
\(682\) −2.04584e14 −0.0530954
\(683\) 8.80864e14 0.226775 0.113388 0.993551i \(-0.463830\pi\)
0.113388 + 0.993551i \(0.463830\pi\)
\(684\) −7.65741e14 −0.195557
\(685\) 4.59937e15 1.16520
\(686\) 3.17939e14 0.0799026
\(687\) 2.86700e15 0.714768
\(688\) −4.43318e15 −1.09643
\(689\) −9.44099e12 −0.00231639
\(690\) 3.06366e14 0.0745710
\(691\) 9.96161e14 0.240547 0.120274 0.992741i \(-0.461623\pi\)
0.120274 + 0.992741i \(0.461623\pi\)
\(692\) −2.03744e15 −0.488091
\(693\) 4.47538e14 0.106365
\(694\) −2.28707e14 −0.0539264
\(695\) −1.00822e16 −2.35851
\(696\) −1.54874e14 −0.0359441
\(697\) −2.19575e15 −0.505594
\(698\) −1.62076e13 −0.00370266
\(699\) 1.07476e15 0.243605
\(700\) −4.33439e15 −0.974741
\(701\) 1.99748e15 0.445691 0.222846 0.974854i \(-0.428465\pi\)
0.222846 + 0.974854i \(0.428465\pi\)
\(702\) −7.88313e12 −0.00174520
\(703\) −5.43480e14 −0.119379
\(704\) −1.74989e15 −0.381382
\(705\) −1.09319e15 −0.236404
\(706\) −4.04543e14 −0.0868038
\(707\) 4.03253e15 0.858561
\(708\) −3.53875e14 −0.0747596
\(709\) 1.18551e15 0.248513 0.124257 0.992250i \(-0.460345\pi\)
0.124257 + 0.992250i \(0.460345\pi\)
\(710\) 1.65126e13 0.00343474
\(711\) −9.82284e14 −0.202747
\(712\) 3.13671e14 0.0642443
\(713\) 1.06897e16 2.17257
\(714\) 3.21733e14 0.0648866
\(715\) −3.61649e14 −0.0723776
\(716\) −3.61767e15 −0.718467
\(717\) −5.67909e15 −1.11924
\(718\) 5.29795e14 0.103615
\(719\) −3.16369e15 −0.614023 −0.307011 0.951706i \(-0.599329\pi\)
−0.307011 + 0.951706i \(0.599329\pi\)
\(720\) 2.53143e15 0.487570
\(721\) −3.80446e14 −0.0727192
\(722\) 2.52328e14 0.0478643
\(723\) −2.05797e15 −0.387417
\(724\) −1.85545e15 −0.346646
\(725\) 2.77562e15 0.514636
\(726\) −1.94542e14 −0.0357982
\(727\) −1.22235e15 −0.223231 −0.111616 0.993751i \(-0.535603\pi\)
−0.111616 + 0.993751i \(0.535603\pi\)
\(728\) −8.08089e13 −0.0146466
\(729\) 2.05891e14 0.0370370
\(730\) −6.69587e14 −0.119545
\(731\) −1.18916e16 −2.10715
\(732\) −3.51887e15 −0.618860
\(733\) 1.08174e15 0.188822 0.0944108 0.995533i \(-0.469903\pi\)
0.0944108 + 0.995533i \(0.469903\pi\)
\(734\) 5.38660e14 0.0933225
\(735\) 1.71863e15 0.295530
\(736\) −1.51611e15 −0.258763
\(737\) −3.09557e15 −0.524409
\(738\) 3.89091e13 0.00654246
\(739\) 9.51167e15 1.58749 0.793747 0.608248i \(-0.208127\pi\)
0.793747 + 0.608248i \(0.208127\pi\)
\(740\) 1.80651e15 0.299271
\(741\) 2.55855e14 0.0420721
\(742\) −6.82784e12 −0.00111445
\(743\) 8.40092e15 1.36110 0.680548 0.732704i \(-0.261742\pi\)
0.680548 + 0.732704i \(0.261742\pi\)
\(744\) −9.64804e14 −0.155163
\(745\) −6.12124e15 −0.977192
\(746\) 2.29404e14 0.0363528
\(747\) 7.52600e14 0.118386
\(748\) −4.74604e15 −0.741092
\(749\) 7.06662e15 1.09537
\(750\) 8.60982e13 0.0132482
\(751\) 5.38899e15 0.823167 0.411583 0.911372i \(-0.364976\pi\)
0.411583 + 0.911372i \(0.364976\pi\)
\(752\) 1.78700e15 0.270974
\(753\) 4.84204e15 0.728880
\(754\) 2.58039e13 0.00385606
\(755\) −6.54531e15 −0.971006
\(756\) 1.05243e15 0.154997
\(757\) −7.91662e15 −1.15748 −0.578739 0.815513i \(-0.696455\pi\)
−0.578739 + 0.815513i \(0.696455\pi\)
\(758\) −6.10796e14 −0.0886575
\(759\) −1.86867e15 −0.269279
\(760\) 8.97447e14 0.128391
\(761\) −4.02627e15 −0.571857 −0.285928 0.958251i \(-0.592302\pi\)
−0.285928 + 0.958251i \(0.592302\pi\)
\(762\) −4.27425e14 −0.0602709
\(763\) 5.42031e15 0.758821
\(764\) −5.23230e15 −0.727242
\(765\) 6.79034e15 0.937030
\(766\) −3.04649e14 −0.0417390
\(767\) 1.18240e14 0.0160838
\(768\) −4.04643e15 −0.546494
\(769\) −1.17462e16 −1.57508 −0.787541 0.616263i \(-0.788646\pi\)
−0.787541 + 0.616263i \(0.788646\pi\)
\(770\) −2.61549e14 −0.0348220
\(771\) −5.48892e13 −0.00725585
\(772\) −6.04975e15 −0.794040
\(773\) 5.51156e15 0.718270 0.359135 0.933286i \(-0.383072\pi\)
0.359135 + 0.933286i \(0.383072\pi\)
\(774\) 2.10722e14 0.0272668
\(775\) 1.72910e16 2.22158
\(776\) −1.07675e15 −0.137365
\(777\) 7.46957e14 0.0946193
\(778\) 6.78076e14 0.0852885
\(779\) −1.26284e15 −0.157722
\(780\) −8.50454e14 −0.105470
\(781\) −1.00718e14 −0.0124030
\(782\) −1.34337e15 −0.164270
\(783\) −6.73946e14 −0.0818343
\(784\) −2.80940e15 −0.338746
\(785\) −1.71925e16 −2.05853
\(786\) −1.29171e14 −0.0153582
\(787\) −7.24348e15 −0.855237 −0.427618 0.903959i \(-0.640647\pi\)
−0.427618 + 0.903959i \(0.640647\pi\)
\(788\) 7.32955e15 0.859376
\(789\) 2.74248e15 0.319315
\(790\) 5.74063e14 0.0663759
\(791\) 1.28674e16 1.47747
\(792\) 1.68657e14 0.0192316
\(793\) 1.17575e15 0.133142
\(794\) −3.51857e14 −0.0395689
\(795\) −1.44105e14 −0.0160938
\(796\) −1.55698e16 −1.72688
\(797\) −9.01023e15 −0.992465 −0.496233 0.868190i \(-0.665284\pi\)
−0.496233 + 0.868190i \(0.665284\pi\)
\(798\) 1.85038e14 0.0202416
\(799\) 4.79348e15 0.520767
\(800\) −2.45236e15 −0.264600
\(801\) 1.36496e15 0.146266
\(802\) 1.14944e15 0.122328
\(803\) 4.08412e15 0.431681
\(804\) −7.27955e15 −0.764181
\(805\) 1.36662e16 1.42485
\(806\) 1.60749e14 0.0166458
\(807\) −5.17517e15 −0.532256
\(808\) 1.51968e15 0.155235
\(809\) −6.21630e15 −0.630689 −0.315345 0.948977i \(-0.602120\pi\)
−0.315345 + 0.948977i \(0.602120\pi\)
\(810\) −1.20326e14 −0.0121253
\(811\) 9.36711e15 0.937542 0.468771 0.883320i \(-0.344697\pi\)
0.468771 + 0.883320i \(0.344697\pi\)
\(812\) −3.44494e15 −0.342470
\(813\) −1.26764e15 −0.125169
\(814\) 5.96900e13 0.00585419
\(815\) 3.15569e15 0.307416
\(816\) −1.11000e16 −1.07406
\(817\) −6.83921e15 −0.657332
\(818\) −8.74533e14 −0.0834897
\(819\) −3.51647e14 −0.0333461
\(820\) 4.19762e15 0.395391
\(821\) 1.82498e16 1.70754 0.853768 0.520654i \(-0.174312\pi\)
0.853768 + 0.520654i \(0.174312\pi\)
\(822\) 3.57375e14 0.0332146
\(823\) 1.96146e16 1.81084 0.905422 0.424513i \(-0.139555\pi\)
0.905422 + 0.424513i \(0.139555\pi\)
\(824\) −1.43373e14 −0.0131482
\(825\) −3.02264e15 −0.275353
\(826\) 8.55123e13 0.00773817
\(827\) −1.78609e15 −0.160555 −0.0802773 0.996773i \(-0.525581\pi\)
−0.0802773 + 0.996773i \(0.525581\pi\)
\(828\) −4.39435e15 −0.392399
\(829\) 1.19781e16 1.06252 0.531261 0.847208i \(-0.321718\pi\)
0.531261 + 0.847208i \(0.321718\pi\)
\(830\) −4.39832e14 −0.0387576
\(831\) 8.76766e15 0.767499
\(832\) 1.37495e15 0.119566
\(833\) −7.53595e15 −0.651015
\(834\) −7.83392e14 −0.0672304
\(835\) 1.87379e16 1.59752
\(836\) −2.72958e15 −0.231186
\(837\) −4.19842e15 −0.353261
\(838\) 1.64330e15 0.137365
\(839\) 1.03328e15 0.0858076 0.0429038 0.999079i \(-0.486339\pi\)
0.0429038 + 0.999079i \(0.486339\pi\)
\(840\) −1.23345e15 −0.101762
\(841\) −9.99447e15 −0.819185
\(842\) 7.12736e14 0.0580380
\(843\) 2.30199e15 0.186231
\(844\) −1.24045e16 −0.997001
\(845\) −1.83339e16 −1.46401
\(846\) −8.49415e13 −0.00673880
\(847\) −8.67801e15 −0.684009
\(848\) 2.35565e14 0.0184473
\(849\) −3.00431e14 −0.0233750
\(850\) −2.17296e15 −0.167976
\(851\) −3.11886e15 −0.239543
\(852\) −2.36848e14 −0.0180739
\(853\) −4.84684e15 −0.367484 −0.183742 0.982974i \(-0.558821\pi\)
−0.183742 + 0.982974i \(0.558821\pi\)
\(854\) 8.50318e14 0.0640565
\(855\) 3.90532e15 0.292309
\(856\) 2.66309e15 0.198053
\(857\) 2.05524e16 1.51868 0.759342 0.650692i \(-0.225521\pi\)
0.759342 + 0.650692i \(0.225521\pi\)
\(858\) −2.81004e13 −0.00206316
\(859\) 7.33281e15 0.534944 0.267472 0.963566i \(-0.413812\pi\)
0.267472 + 0.963566i \(0.413812\pi\)
\(860\) 2.27333e16 1.64786
\(861\) 1.73564e15 0.125009
\(862\) −2.05991e13 −0.00147421
\(863\) 1.33948e16 0.952526 0.476263 0.879303i \(-0.341991\pi\)
0.476263 + 0.879303i \(0.341991\pi\)
\(864\) 5.95456e14 0.0420750
\(865\) 1.03910e16 0.729574
\(866\) −1.74540e14 −0.0121772
\(867\) −2.14467e16 −1.48681
\(868\) −2.14606e16 −1.47837
\(869\) −3.50147e15 −0.239686
\(870\) 3.93865e14 0.0267912
\(871\) 2.43230e15 0.164406
\(872\) 2.04267e15 0.137201
\(873\) −4.68559e15 −0.312741
\(874\) −7.72612e14 −0.0512447
\(875\) 3.84063e15 0.253138
\(876\) 9.60422e15 0.629056
\(877\) 7.59948e15 0.494636 0.247318 0.968934i \(-0.420451\pi\)
0.247318 + 0.968934i \(0.420451\pi\)
\(878\) −1.38347e15 −0.0894848
\(879\) 3.19177e14 0.0205160
\(880\) 9.02360e15 0.576402
\(881\) −2.82049e16 −1.79043 −0.895213 0.445638i \(-0.852977\pi\)
−0.895213 + 0.445638i \(0.852977\pi\)
\(882\) 1.33539e14 0.00842422
\(883\) −7.08941e15 −0.444453 −0.222227 0.974995i \(-0.571332\pi\)
−0.222227 + 0.974995i \(0.571332\pi\)
\(884\) 3.72913e15 0.232338
\(885\) 1.80478e15 0.111747
\(886\) −1.26310e15 −0.0777237
\(887\) −2.49307e15 −0.152459 −0.0762296 0.997090i \(-0.524288\pi\)
−0.0762296 + 0.997090i \(0.524288\pi\)
\(888\) 2.81494e14 0.0171080
\(889\) −1.90664e16 −1.15162
\(890\) −7.97708e14 −0.0478849
\(891\) 7.33925e14 0.0437849
\(892\) −1.36447e16 −0.809014
\(893\) 2.75687e15 0.162455
\(894\) −4.75625e14 −0.0278553
\(895\) 1.84503e16 1.07393
\(896\) 4.05460e15 0.234560
\(897\) 1.46828e15 0.0844208
\(898\) −7.49613e14 −0.0428368
\(899\) 1.37428e16 0.780540
\(900\) −7.10803e15 −0.401251
\(901\) 6.31882e14 0.0354527
\(902\) 1.38696e14 0.00773444
\(903\) 9.39978e15 0.520997
\(904\) 4.84913e15 0.267139
\(905\) 9.46287e15 0.518150
\(906\) −5.08575e14 −0.0276790
\(907\) 5.93175e15 0.320880 0.160440 0.987046i \(-0.448709\pi\)
0.160440 + 0.987046i \(0.448709\pi\)
\(908\) 2.61261e16 1.40476
\(909\) 6.61301e15 0.353425
\(910\) 2.05508e14 0.0109170
\(911\) 1.05821e16 0.558754 0.279377 0.960182i \(-0.409872\pi\)
0.279377 + 0.960182i \(0.409872\pi\)
\(912\) −6.38392e15 −0.335055
\(913\) 2.68274e15 0.139955
\(914\) 6.52252e14 0.0338230
\(915\) 1.79464e16 0.925042
\(916\) 2.40328e16 1.23134
\(917\) −5.76198e15 −0.293454
\(918\) 5.27614e14 0.0267105
\(919\) 6.28506e15 0.316282 0.158141 0.987417i \(-0.449450\pi\)
0.158141 + 0.987417i \(0.449450\pi\)
\(920\) 5.15018e15 0.257626
\(921\) 3.62484e15 0.180244
\(922\) −2.71887e15 −0.134390
\(923\) 7.91374e13 0.00388842
\(924\) 3.75152e15 0.183236
\(925\) −5.04488e15 −0.244947
\(926\) −1.69368e15 −0.0817471
\(927\) −6.23899e14 −0.0299347
\(928\) −1.94911e15 −0.0929659
\(929\) 1.25567e13 0.000595374 0 0.000297687 1.00000i \(-0.499905\pi\)
0.000297687 1.00000i \(0.499905\pi\)
\(930\) 2.45363e15 0.115652
\(931\) −4.33414e15 −0.203086
\(932\) 9.00924e15 0.419663
\(933\) −2.04089e16 −0.945083
\(934\) 4.10043e14 0.0188765
\(935\) 2.42050e16 1.10775
\(936\) −1.32520e14 −0.00602925
\(937\) −1.43024e16 −0.646907 −0.323453 0.946244i \(-0.604844\pi\)
−0.323453 + 0.946244i \(0.604844\pi\)
\(938\) 1.75907e15 0.0790983
\(939\) −7.22929e15 −0.323173
\(940\) −9.16372e15 −0.407257
\(941\) 8.90168e15 0.393304 0.196652 0.980473i \(-0.436993\pi\)
0.196652 + 0.980473i \(0.436993\pi\)
\(942\) −1.33587e15 −0.0586793
\(943\) −7.24703e15 −0.316480
\(944\) −2.95023e15 −0.128088
\(945\) −5.36745e15 −0.231682
\(946\) 7.51145e14 0.0322346
\(947\) −7.97878e15 −0.340417 −0.170209 0.985408i \(-0.554444\pi\)
−0.170209 + 0.985408i \(0.554444\pi\)
\(948\) −8.23406e15 −0.349276
\(949\) −3.20904e15 −0.135335
\(950\) −1.24973e15 −0.0524006
\(951\) 2.19091e16 0.913336
\(952\) 5.40851e15 0.224168
\(953\) −3.43098e16 −1.41386 −0.706932 0.707282i \(-0.749921\pi\)
−0.706932 + 0.707282i \(0.749921\pi\)
\(954\) −1.11971e13 −0.000458763 0
\(955\) 2.66850e16 1.08705
\(956\) −4.76054e16 −1.92814
\(957\) −2.40236e15 −0.0967438
\(958\) 1.73806e15 0.0695911
\(959\) 1.59416e16 0.634643
\(960\) 2.09869e16 0.830722
\(961\) 6.02036e16 2.36943
\(962\) −4.69005e13 −0.00183533
\(963\) 1.15887e16 0.450909
\(964\) −1.72511e16 −0.667410
\(965\) 3.08540e16 1.18689
\(966\) 1.06187e15 0.0406162
\(967\) −3.86522e16 −1.47004 −0.735019 0.678047i \(-0.762827\pi\)
−0.735019 + 0.678047i \(0.762827\pi\)
\(968\) −3.27035e15 −0.123674
\(969\) −1.71243e16 −0.643920
\(970\) 2.73833e15 0.102386
\(971\) −1.63748e16 −0.608794 −0.304397 0.952545i \(-0.598455\pi\)
−0.304397 + 0.952545i \(0.598455\pi\)
\(972\) 1.72590e15 0.0638044
\(973\) −3.49452e16 −1.28460
\(974\) 1.97311e15 0.0721236
\(975\) 2.37499e15 0.0863251
\(976\) −2.93365e16 −1.06031
\(977\) 3.71306e16 1.33448 0.667239 0.744844i \(-0.267476\pi\)
0.667239 + 0.744844i \(0.267476\pi\)
\(978\) 2.45199e14 0.00876305
\(979\) 4.86559e15 0.172914
\(980\) 1.44065e16 0.509115
\(981\) 8.88885e15 0.312368
\(982\) −1.00657e15 −0.0351746
\(983\) −4.04066e16 −1.40413 −0.702066 0.712112i \(-0.747739\pi\)
−0.702066 + 0.712112i \(0.747739\pi\)
\(984\) 6.54083e14 0.0226027
\(985\) −3.73811e16 −1.28455
\(986\) −1.72705e15 −0.0590175
\(987\) −3.78903e15 −0.128761
\(988\) 2.14473e15 0.0724785
\(989\) −3.92481e16 −1.31898
\(990\) −4.28918e14 −0.0143344
\(991\) 2.25060e16 0.747987 0.373993 0.927431i \(-0.377988\pi\)
0.373993 + 0.927431i \(0.377988\pi\)
\(992\) −1.21422e16 −0.401314
\(993\) 2.25135e16 0.739983
\(994\) 5.72331e13 0.00187078
\(995\) 7.94069e16 2.58126
\(996\) 6.30872e15 0.203946
\(997\) 3.07794e16 0.989548 0.494774 0.869022i \(-0.335251\pi\)
0.494774 + 0.869022i \(0.335251\pi\)
\(998\) −2.39773e15 −0.0766625
\(999\) 1.22494e15 0.0389499
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 177.12.a.c.1.15 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.15 27 1.1 even 1 trivial