Properties

Label 177.10.a.d.1.18
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 1.18
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+35.4666 q^{2} +81.0000 q^{3} +745.883 q^{4} +1622.90 q^{5} +2872.80 q^{6} +5254.11 q^{7} +8295.05 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+35.4666 q^{2} +81.0000 q^{3} +745.883 q^{4} +1622.90 q^{5} +2872.80 q^{6} +5254.11 q^{7} +8295.05 q^{8} +6561.00 q^{9} +57558.7 q^{10} +63201.2 q^{11} +60416.5 q^{12} -93199.3 q^{13} +186346. q^{14} +131455. q^{15} -87694.6 q^{16} +312651. q^{17} +232697. q^{18} +295079. q^{19} +1.21049e6 q^{20} +425583. q^{21} +2.24154e6 q^{22} -660434. q^{23} +671899. q^{24} +680669. q^{25} -3.30547e6 q^{26} +531441. q^{27} +3.91895e6 q^{28} -1.79623e6 q^{29} +4.66226e6 q^{30} +900850. q^{31} -7.35730e6 q^{32} +5.11930e6 q^{33} +1.10887e7 q^{34} +8.52688e6 q^{35} +4.89374e6 q^{36} +4.38437e6 q^{37} +1.04655e7 q^{38} -7.54914e6 q^{39} +1.34620e7 q^{40} +1.15498e7 q^{41} +1.50940e7 q^{42} -6.76278e6 q^{43} +4.71407e7 q^{44} +1.06478e7 q^{45} -2.34234e7 q^{46} -3.09203e7 q^{47} -7.10326e6 q^{48} -1.27480e7 q^{49} +2.41411e7 q^{50} +2.53248e7 q^{51} -6.95158e7 q^{52} +1.17476e7 q^{53} +1.88484e7 q^{54} +1.02569e8 q^{55} +4.35831e7 q^{56} +2.39014e7 q^{57} -6.37062e7 q^{58} -1.21174e7 q^{59} +9.80498e7 q^{60} -3.57264e7 q^{61} +3.19501e7 q^{62} +3.44722e7 q^{63} -2.16039e8 q^{64} -1.51253e8 q^{65} +1.81564e8 q^{66} +2.25795e8 q^{67} +2.33201e8 q^{68} -5.34952e7 q^{69} +3.02420e8 q^{70} -1.64241e8 q^{71} +5.44238e7 q^{72} -2.45097e8 q^{73} +1.55499e8 q^{74} +5.51342e7 q^{75} +2.20095e8 q^{76} +3.32066e8 q^{77} -2.67743e8 q^{78} +2.30240e8 q^{79} -1.42319e8 q^{80} +4.30467e7 q^{81} +4.09632e8 q^{82} +3.71689e8 q^{83} +3.17435e8 q^{84} +5.07401e8 q^{85} -2.39853e8 q^{86} -1.45494e8 q^{87} +5.24257e8 q^{88} +2.06997e8 q^{89} +3.77643e8 q^{90} -4.89679e8 q^{91} -4.92607e8 q^{92} +7.29688e7 q^{93} -1.09664e9 q^{94} +4.78883e8 q^{95} -5.95941e8 q^{96} +8.17254e8 q^{97} -4.52127e8 q^{98} +4.14663e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 35.4666 1.56742 0.783710 0.621127i \(-0.213325\pi\)
0.783710 + 0.621127i \(0.213325\pi\)
\(3\) 81.0000 0.577350
\(4\) 745.883 1.45680
\(5\) 1622.90 1.16125 0.580625 0.814171i \(-0.302808\pi\)
0.580625 + 0.814171i \(0.302808\pi\)
\(6\) 2872.80 0.904950
\(7\) 5254.11 0.827100 0.413550 0.910481i \(-0.364289\pi\)
0.413550 + 0.910481i \(0.364289\pi\)
\(8\) 8295.05 0.716002
\(9\) 6561.00 0.333333
\(10\) 57558.7 1.82017
\(11\) 63201.2 1.30154 0.650772 0.759274i \(-0.274446\pi\)
0.650772 + 0.759274i \(0.274446\pi\)
\(12\) 60416.5 0.841086
\(13\) −93199.3 −0.905039 −0.452520 0.891754i \(-0.649475\pi\)
−0.452520 + 0.891754i \(0.649475\pi\)
\(14\) 186346. 1.29641
\(15\) 131455. 0.670448
\(16\) −87694.6 −0.334528
\(17\) 312651. 0.907905 0.453952 0.891026i \(-0.350014\pi\)
0.453952 + 0.891026i \(0.350014\pi\)
\(18\) 232697. 0.522473
\(19\) 295079. 0.519455 0.259727 0.965682i \(-0.416367\pi\)
0.259727 + 0.965682i \(0.416367\pi\)
\(20\) 1.21049e6 1.69171
\(21\) 425583. 0.477526
\(22\) 2.24154e6 2.04006
\(23\) −660434. −0.492101 −0.246050 0.969257i \(-0.579133\pi\)
−0.246050 + 0.969257i \(0.579133\pi\)
\(24\) 671899. 0.413384
\(25\) 680669. 0.348503
\(26\) −3.30547e6 −1.41858
\(27\) 531441. 0.192450
\(28\) 3.91895e6 1.20492
\(29\) −1.79623e6 −0.471596 −0.235798 0.971802i \(-0.575770\pi\)
−0.235798 + 0.971802i \(0.575770\pi\)
\(30\) 4.66226e6 1.05087
\(31\) 900850. 0.175196 0.0875981 0.996156i \(-0.472081\pi\)
0.0875981 + 0.996156i \(0.472081\pi\)
\(32\) −7.35730e6 −1.24035
\(33\) 5.11930e6 0.751446
\(34\) 1.10887e7 1.42307
\(35\) 8.52688e6 0.960470
\(36\) 4.89374e6 0.485601
\(37\) 4.38437e6 0.384591 0.192296 0.981337i \(-0.438407\pi\)
0.192296 + 0.981337i \(0.438407\pi\)
\(38\) 1.04655e7 0.814203
\(39\) −7.54914e6 −0.522525
\(40\) 1.34620e7 0.831457
\(41\) 1.15498e7 0.638331 0.319165 0.947699i \(-0.396597\pi\)
0.319165 + 0.947699i \(0.396597\pi\)
\(42\) 1.50940e7 0.748484
\(43\) −6.76278e6 −0.301660 −0.150830 0.988560i \(-0.548195\pi\)
−0.150830 + 0.988560i \(0.548195\pi\)
\(44\) 4.71407e7 1.89609
\(45\) 1.06478e7 0.387083
\(46\) −2.34234e7 −0.771328
\(47\) −3.09203e7 −0.924279 −0.462140 0.886807i \(-0.652918\pi\)
−0.462140 + 0.886807i \(0.652918\pi\)
\(48\) −7.10326e6 −0.193140
\(49\) −1.27480e7 −0.315906
\(50\) 2.41411e7 0.546250
\(51\) 2.53248e7 0.524179
\(52\) −6.95158e7 −1.31846
\(53\) 1.17476e7 0.204506 0.102253 0.994758i \(-0.467395\pi\)
0.102253 + 0.994758i \(0.467395\pi\)
\(54\) 1.88484e7 0.301650
\(55\) 1.02569e8 1.51142
\(56\) 4.35831e7 0.592205
\(57\) 2.39014e7 0.299907
\(58\) −6.37062e7 −0.739189
\(59\) −1.21174e7 −0.130189
\(60\) 9.80498e7 0.976711
\(61\) −3.57264e7 −0.330374 −0.165187 0.986262i \(-0.552823\pi\)
−0.165187 + 0.986262i \(0.552823\pi\)
\(62\) 3.19501e7 0.274606
\(63\) 3.44722e7 0.275700
\(64\) −2.16039e8 −1.60962
\(65\) −1.51253e8 −1.05098
\(66\) 1.81564e8 1.17783
\(67\) 2.25795e8 1.36892 0.684460 0.729051i \(-0.260038\pi\)
0.684460 + 0.729051i \(0.260038\pi\)
\(68\) 2.33201e8 1.32264
\(69\) −5.34952e7 −0.284115
\(70\) 3.02420e8 1.50546
\(71\) −1.64241e8 −0.767040 −0.383520 0.923533i \(-0.625288\pi\)
−0.383520 + 0.923533i \(0.625288\pi\)
\(72\) 5.44238e7 0.238667
\(73\) −2.45097e8 −1.01015 −0.505074 0.863076i \(-0.668535\pi\)
−0.505074 + 0.863076i \(0.668535\pi\)
\(74\) 1.55499e8 0.602815
\(75\) 5.51342e7 0.201208
\(76\) 2.20095e8 0.756743
\(77\) 3.32066e8 1.07651
\(78\) −2.67743e8 −0.819015
\(79\) 2.30240e8 0.665056 0.332528 0.943093i \(-0.392098\pi\)
0.332528 + 0.943093i \(0.392098\pi\)
\(80\) −1.42319e8 −0.388471
\(81\) 4.30467e7 0.111111
\(82\) 4.09632e8 1.00053
\(83\) 3.71689e8 0.859663 0.429831 0.902909i \(-0.358573\pi\)
0.429831 + 0.902909i \(0.358573\pi\)
\(84\) 3.17435e8 0.695662
\(85\) 5.07401e8 1.05430
\(86\) −2.39853e8 −0.472827
\(87\) −1.45494e8 −0.272276
\(88\) 5.24257e8 0.931907
\(89\) 2.06997e8 0.349711 0.174856 0.984594i \(-0.444054\pi\)
0.174856 + 0.984594i \(0.444054\pi\)
\(90\) 3.77643e8 0.606722
\(91\) −4.89679e8 −0.748558
\(92\) −4.92607e8 −0.716894
\(93\) 7.29688e7 0.101150
\(94\) −1.09664e9 −1.44873
\(95\) 4.78883e8 0.603217
\(96\) −5.95941e8 −0.716115
\(97\) 8.17254e8 0.937312 0.468656 0.883381i \(-0.344738\pi\)
0.468656 + 0.883381i \(0.344738\pi\)
\(98\) −4.52127e8 −0.495157
\(99\) 4.14663e8 0.433848
\(100\) 5.07700e8 0.507700
\(101\) −1.12280e8 −0.107363 −0.0536816 0.998558i \(-0.517096\pi\)
−0.0536816 + 0.998558i \(0.517096\pi\)
\(102\) 8.98185e8 0.821608
\(103\) −1.53844e9 −1.34683 −0.673417 0.739263i \(-0.735174\pi\)
−0.673417 + 0.739263i \(0.735174\pi\)
\(104\) −7.73092e8 −0.648010
\(105\) 6.90677e8 0.554528
\(106\) 4.16647e8 0.320547
\(107\) 6.12766e8 0.451927 0.225963 0.974136i \(-0.427447\pi\)
0.225963 + 0.974136i \(0.427447\pi\)
\(108\) 3.96393e8 0.280362
\(109\) 2.44993e9 1.66240 0.831199 0.555975i \(-0.187655\pi\)
0.831199 + 0.555975i \(0.187655\pi\)
\(110\) 3.63778e9 2.36902
\(111\) 3.55134e8 0.222044
\(112\) −4.60757e8 −0.276688
\(113\) −5.34351e8 −0.308300 −0.154150 0.988047i \(-0.549264\pi\)
−0.154150 + 0.988047i \(0.549264\pi\)
\(114\) 8.47703e8 0.470080
\(115\) −1.07182e9 −0.571452
\(116\) −1.33978e9 −0.687023
\(117\) −6.11480e8 −0.301680
\(118\) −4.29762e8 −0.204061
\(119\) 1.64270e9 0.750928
\(120\) 1.09042e9 0.480042
\(121\) 1.63645e9 0.694014
\(122\) −1.26710e9 −0.517834
\(123\) 9.35531e8 0.368541
\(124\) 6.71928e8 0.255226
\(125\) −2.06506e9 −0.756552
\(126\) 1.22261e9 0.432137
\(127\) −2.91038e9 −0.992734 −0.496367 0.868113i \(-0.665333\pi\)
−0.496367 + 0.868113i \(0.665333\pi\)
\(128\) −3.89524e9 −1.28260
\(129\) −5.47785e8 −0.174163
\(130\) −5.36443e9 −1.64732
\(131\) 2.39475e8 0.0710460 0.0355230 0.999369i \(-0.488690\pi\)
0.0355230 + 0.999369i \(0.488690\pi\)
\(132\) 3.81840e9 1.09471
\(133\) 1.55038e9 0.429641
\(134\) 8.00819e9 2.14567
\(135\) 8.62474e8 0.223483
\(136\) 2.59346e9 0.650061
\(137\) −3.30216e9 −0.800857 −0.400429 0.916328i \(-0.631139\pi\)
−0.400429 + 0.916328i \(0.631139\pi\)
\(138\) −1.89729e9 −0.445327
\(139\) −3.90848e9 −0.888057 −0.444029 0.896013i \(-0.646451\pi\)
−0.444029 + 0.896013i \(0.646451\pi\)
\(140\) 6.36005e9 1.39922
\(141\) −2.50454e9 −0.533633
\(142\) −5.82506e9 −1.20227
\(143\) −5.89031e9 −1.17795
\(144\) −5.75364e8 −0.111509
\(145\) −2.91509e9 −0.547642
\(146\) −8.69277e9 −1.58333
\(147\) −1.03258e9 −0.182388
\(148\) 3.27023e9 0.560273
\(149\) −8.32395e8 −0.138354 −0.0691770 0.997604i \(-0.522037\pi\)
−0.0691770 + 0.997604i \(0.522037\pi\)
\(150\) 1.95543e9 0.315377
\(151\) 2.24607e9 0.351582 0.175791 0.984427i \(-0.443752\pi\)
0.175791 + 0.984427i \(0.443752\pi\)
\(152\) 2.44770e9 0.371930
\(153\) 2.05131e9 0.302635
\(154\) 1.17773e10 1.68734
\(155\) 1.46199e9 0.203447
\(156\) −5.63078e9 −0.761216
\(157\) −5.86686e7 −0.00770650 −0.00385325 0.999993i \(-0.501227\pi\)
−0.00385325 + 0.999993i \(0.501227\pi\)
\(158\) 8.16583e9 1.04242
\(159\) 9.51553e8 0.118072
\(160\) −1.19401e10 −1.44035
\(161\) −3.46999e9 −0.407017
\(162\) 1.52672e9 0.174158
\(163\) 1.23008e10 1.36486 0.682432 0.730949i \(-0.260922\pi\)
0.682432 + 0.730949i \(0.260922\pi\)
\(164\) 8.61478e9 0.929922
\(165\) 8.30810e9 0.872617
\(166\) 1.31826e10 1.34745
\(167\) −1.62627e10 −1.61796 −0.808980 0.587836i \(-0.799980\pi\)
−0.808980 + 0.587836i \(0.799980\pi\)
\(168\) 3.53023e9 0.341910
\(169\) −1.91839e9 −0.180904
\(170\) 1.79958e10 1.65254
\(171\) 1.93602e9 0.173152
\(172\) −5.04424e9 −0.439459
\(173\) 6.36406e9 0.540166 0.270083 0.962837i \(-0.412949\pi\)
0.270083 + 0.962837i \(0.412949\pi\)
\(174\) −5.16020e9 −0.426771
\(175\) 3.57631e9 0.288246
\(176\) −5.54241e9 −0.435403
\(177\) −9.81506e8 −0.0751646
\(178\) 7.34150e9 0.548144
\(179\) −2.20122e10 −1.60260 −0.801299 0.598264i \(-0.795857\pi\)
−0.801299 + 0.598264i \(0.795857\pi\)
\(180\) 7.94203e9 0.563904
\(181\) 2.40644e10 1.66656 0.833280 0.552851i \(-0.186460\pi\)
0.833280 + 0.552851i \(0.186460\pi\)
\(182\) −1.73673e10 −1.17330
\(183\) −2.89384e9 −0.190741
\(184\) −5.47833e9 −0.352345
\(185\) 7.11538e9 0.446607
\(186\) 2.58796e9 0.158544
\(187\) 1.97600e10 1.18168
\(188\) −2.30629e10 −1.34649
\(189\) 2.79225e9 0.159175
\(190\) 1.69844e10 0.945494
\(191\) −7.26972e9 −0.395246 −0.197623 0.980278i \(-0.563322\pi\)
−0.197623 + 0.980278i \(0.563322\pi\)
\(192\) −1.74992e10 −0.929312
\(193\) −1.10884e9 −0.0575254 −0.0287627 0.999586i \(-0.509157\pi\)
−0.0287627 + 0.999586i \(0.509157\pi\)
\(194\) 2.89853e10 1.46916
\(195\) −1.22515e10 −0.606782
\(196\) −9.50848e9 −0.460213
\(197\) 4.82622e9 0.228302 0.114151 0.993463i \(-0.463585\pi\)
0.114151 + 0.993463i \(0.463585\pi\)
\(198\) 1.47067e10 0.680021
\(199\) 3.18609e10 1.44019 0.720094 0.693877i \(-0.244099\pi\)
0.720094 + 0.693877i \(0.244099\pi\)
\(200\) 5.64618e9 0.249528
\(201\) 1.82894e10 0.790346
\(202\) −3.98219e9 −0.168283
\(203\) −9.43758e9 −0.390057
\(204\) 1.88893e10 0.763626
\(205\) 1.87441e10 0.741262
\(206\) −5.45634e10 −2.11105
\(207\) −4.33311e9 −0.164034
\(208\) 8.17307e9 0.302761
\(209\) 1.86494e10 0.676092
\(210\) 2.44960e10 0.869177
\(211\) −4.20930e10 −1.46197 −0.730986 0.682393i \(-0.760939\pi\)
−0.730986 + 0.682393i \(0.760939\pi\)
\(212\) 8.76232e9 0.297925
\(213\) −1.33035e10 −0.442851
\(214\) 2.17328e10 0.708358
\(215\) −1.09753e10 −0.350302
\(216\) 4.40833e9 0.137795
\(217\) 4.73316e9 0.144905
\(218\) 8.68909e10 2.60567
\(219\) −1.98528e10 −0.583209
\(220\) 7.65046e10 2.20184
\(221\) −2.91389e10 −0.821690
\(222\) 1.25954e10 0.348036
\(223\) −5.31108e9 −0.143817 −0.0719087 0.997411i \(-0.522909\pi\)
−0.0719087 + 0.997411i \(0.522909\pi\)
\(224\) −3.86560e10 −1.02589
\(225\) 4.46587e9 0.116168
\(226\) −1.89516e10 −0.483236
\(227\) −1.59250e10 −0.398073 −0.199037 0.979992i \(-0.563781\pi\)
−0.199037 + 0.979992i \(0.563781\pi\)
\(228\) 1.78277e10 0.436906
\(229\) 1.69346e10 0.406926 0.203463 0.979083i \(-0.434780\pi\)
0.203463 + 0.979083i \(0.434780\pi\)
\(230\) −3.80137e10 −0.895706
\(231\) 2.68974e10 0.621521
\(232\) −1.48998e10 −0.337664
\(233\) 1.13183e9 0.0251582 0.0125791 0.999921i \(-0.495996\pi\)
0.0125791 + 0.999921i \(0.495996\pi\)
\(234\) −2.16872e10 −0.472859
\(235\) −5.01805e10 −1.07332
\(236\) −9.03813e9 −0.189660
\(237\) 1.86494e10 0.383970
\(238\) 5.82612e10 1.17702
\(239\) −3.09052e10 −0.612691 −0.306346 0.951920i \(-0.599106\pi\)
−0.306346 + 0.951920i \(0.599106\pi\)
\(240\) −1.15279e10 −0.224284
\(241\) −2.09082e10 −0.399245 −0.199623 0.979873i \(-0.563972\pi\)
−0.199623 + 0.979873i \(0.563972\pi\)
\(242\) 5.80394e10 1.08781
\(243\) 3.48678e9 0.0641500
\(244\) −2.66477e10 −0.481289
\(245\) −2.06886e10 −0.366846
\(246\) 3.31802e10 0.577657
\(247\) −2.75012e10 −0.470127
\(248\) 7.47259e9 0.125441
\(249\) 3.01068e10 0.496327
\(250\) −7.32409e10 −1.18583
\(251\) −1.16586e11 −1.85402 −0.927008 0.375042i \(-0.877628\pi\)
−0.927008 + 0.375042i \(0.877628\pi\)
\(252\) 2.57122e10 0.401640
\(253\) −4.17403e10 −0.640491
\(254\) −1.03221e11 −1.55603
\(255\) 4.10995e10 0.608703
\(256\) −2.75393e10 −0.400749
\(257\) −1.22111e11 −1.74605 −0.873024 0.487677i \(-0.837844\pi\)
−0.873024 + 0.487677i \(0.837844\pi\)
\(258\) −1.94281e10 −0.272987
\(259\) 2.30359e10 0.318095
\(260\) −1.12817e11 −1.53107
\(261\) −1.17851e10 −0.157199
\(262\) 8.49339e9 0.111359
\(263\) 1.12528e10 0.145031 0.0725154 0.997367i \(-0.476897\pi\)
0.0725154 + 0.997367i \(0.476897\pi\)
\(264\) 4.24648e10 0.538037
\(265\) 1.90651e10 0.237483
\(266\) 5.49867e10 0.673427
\(267\) 1.67668e10 0.201906
\(268\) 1.68417e11 1.99425
\(269\) 8.53058e10 0.993330 0.496665 0.867942i \(-0.334558\pi\)
0.496665 + 0.867942i \(0.334558\pi\)
\(270\) 3.05891e10 0.350291
\(271\) 1.03784e10 0.116887 0.0584436 0.998291i \(-0.481386\pi\)
0.0584436 + 0.998291i \(0.481386\pi\)
\(272\) −2.74178e10 −0.303720
\(273\) −3.96640e10 −0.432180
\(274\) −1.17116e11 −1.25528
\(275\) 4.30191e10 0.453591
\(276\) −3.99011e10 −0.413899
\(277\) −6.80045e9 −0.0694030 −0.0347015 0.999398i \(-0.511048\pi\)
−0.0347015 + 0.999398i \(0.511048\pi\)
\(278\) −1.38621e11 −1.39196
\(279\) 5.91047e9 0.0583987
\(280\) 7.07308e10 0.687698
\(281\) −1.22009e11 −1.16738 −0.583690 0.811977i \(-0.698392\pi\)
−0.583690 + 0.811977i \(0.698392\pi\)
\(282\) −8.88278e10 −0.836427
\(283\) −6.75009e9 −0.0625562 −0.0312781 0.999511i \(-0.509958\pi\)
−0.0312781 + 0.999511i \(0.509958\pi\)
\(284\) −1.22504e11 −1.11743
\(285\) 3.87895e10 0.348267
\(286\) −2.08910e11 −1.84634
\(287\) 6.06837e10 0.527963
\(288\) −4.82712e10 −0.413449
\(289\) −2.08369e10 −0.175709
\(290\) −1.03389e11 −0.858384
\(291\) 6.61976e10 0.541157
\(292\) −1.82814e11 −1.47159
\(293\) −1.83585e9 −0.0145523 −0.00727616 0.999974i \(-0.502316\pi\)
−0.00727616 + 0.999974i \(0.502316\pi\)
\(294\) −3.66223e10 −0.285879
\(295\) −1.96652e10 −0.151182
\(296\) 3.63685e10 0.275368
\(297\) 3.35877e10 0.250482
\(298\) −2.95223e10 −0.216859
\(299\) 6.15520e10 0.445371
\(300\) 4.11237e10 0.293121
\(301\) −3.55324e10 −0.249503
\(302\) 7.96605e10 0.551077
\(303\) −9.09466e9 −0.0619862
\(304\) −2.58769e10 −0.173772
\(305\) −5.79803e10 −0.383647
\(306\) 7.27530e10 0.474356
\(307\) −2.58774e11 −1.66264 −0.831319 0.555796i \(-0.812414\pi\)
−0.831319 + 0.555796i \(0.812414\pi\)
\(308\) 2.47683e11 1.56826
\(309\) −1.24614e11 −0.777595
\(310\) 5.18517e10 0.318886
\(311\) −1.59772e11 −0.968453 −0.484227 0.874943i \(-0.660899\pi\)
−0.484227 + 0.874943i \(0.660899\pi\)
\(312\) −6.26205e10 −0.374129
\(313\) −2.57777e11 −1.51808 −0.759039 0.651046i \(-0.774331\pi\)
−0.759039 + 0.651046i \(0.774331\pi\)
\(314\) −2.08078e9 −0.0120793
\(315\) 5.59448e10 0.320157
\(316\) 1.71732e11 0.968856
\(317\) 6.14218e9 0.0341630 0.0170815 0.999854i \(-0.494563\pi\)
0.0170815 + 0.999854i \(0.494563\pi\)
\(318\) 3.37484e10 0.185068
\(319\) −1.13524e11 −0.613803
\(320\) −3.50609e11 −1.86917
\(321\) 4.96341e10 0.260920
\(322\) −1.23069e11 −0.637966
\(323\) 9.22570e10 0.471615
\(324\) 3.21078e10 0.161867
\(325\) −6.34379e10 −0.315409
\(326\) 4.36268e11 2.13931
\(327\) 1.98445e11 0.959786
\(328\) 9.58059e10 0.457046
\(329\) −1.62459e11 −0.764471
\(330\) 2.94660e11 1.36776
\(331\) −1.87466e11 −0.858415 −0.429207 0.903206i \(-0.641207\pi\)
−0.429207 + 0.903206i \(0.641207\pi\)
\(332\) 2.77236e11 1.25236
\(333\) 2.87658e10 0.128197
\(334\) −5.76783e11 −2.53602
\(335\) 3.66442e11 1.58966
\(336\) −3.73213e10 −0.159746
\(337\) −1.68990e11 −0.713717 −0.356858 0.934159i \(-0.616152\pi\)
−0.356858 + 0.934159i \(0.616152\pi\)
\(338\) −6.80390e10 −0.283552
\(339\) −4.32824e10 −0.177997
\(340\) 3.78462e11 1.53591
\(341\) 5.69348e10 0.228025
\(342\) 6.86640e10 0.271401
\(343\) −2.79001e11 −1.08839
\(344\) −5.60976e10 −0.215989
\(345\) −8.68171e10 −0.329928
\(346\) 2.25712e11 0.846666
\(347\) 1.40470e11 0.520116 0.260058 0.965593i \(-0.416258\pi\)
0.260058 + 0.965593i \(0.416258\pi\)
\(348\) −1.08522e11 −0.396653
\(349\) −1.59703e11 −0.576232 −0.288116 0.957596i \(-0.593029\pi\)
−0.288116 + 0.957596i \(0.593029\pi\)
\(350\) 1.26840e11 0.451803
\(351\) −4.95299e10 −0.174175
\(352\) −4.64990e11 −1.61437
\(353\) 1.13039e11 0.387474 0.193737 0.981054i \(-0.437939\pi\)
0.193737 + 0.981054i \(0.437939\pi\)
\(354\) −3.48107e10 −0.117814
\(355\) −2.66545e11 −0.890725
\(356\) 1.54396e11 0.509461
\(357\) 1.33059e11 0.433548
\(358\) −7.80698e11 −2.51194
\(359\) 2.28065e11 0.724658 0.362329 0.932050i \(-0.381982\pi\)
0.362329 + 0.932050i \(0.381982\pi\)
\(360\) 8.83242e10 0.277152
\(361\) −2.35616e11 −0.730167
\(362\) 8.53483e11 2.61220
\(363\) 1.32552e11 0.400689
\(364\) −3.65243e11 −1.09050
\(365\) −3.97767e11 −1.17303
\(366\) −1.02635e11 −0.298972
\(367\) 6.25844e11 1.80081 0.900407 0.435048i \(-0.143269\pi\)
0.900407 + 0.435048i \(0.143269\pi\)
\(368\) 5.79165e10 0.164622
\(369\) 7.57780e10 0.212777
\(370\) 2.52359e11 0.700020
\(371\) 6.17230e10 0.169147
\(372\) 5.44262e10 0.147355
\(373\) 6.76899e10 0.181065 0.0905324 0.995894i \(-0.471143\pi\)
0.0905324 + 0.995894i \(0.471143\pi\)
\(374\) 7.00820e11 1.85218
\(375\) −1.67270e11 −0.436795
\(376\) −2.56485e11 −0.661786
\(377\) 1.67407e11 0.426813
\(378\) 9.90317e10 0.249495
\(379\) 2.61371e11 0.650700 0.325350 0.945594i \(-0.394518\pi\)
0.325350 + 0.945594i \(0.394518\pi\)
\(380\) 3.57191e11 0.878768
\(381\) −2.35741e11 −0.573155
\(382\) −2.57833e11 −0.619517
\(383\) −1.12750e11 −0.267745 −0.133873 0.990999i \(-0.542741\pi\)
−0.133873 + 0.990999i \(0.542741\pi\)
\(384\) −3.15515e11 −0.740507
\(385\) 5.38909e11 1.25009
\(386\) −3.93267e10 −0.0901664
\(387\) −4.43706e10 −0.100553
\(388\) 6.09576e11 1.36548
\(389\) 5.33391e11 1.18106 0.590531 0.807015i \(-0.298918\pi\)
0.590531 + 0.807015i \(0.298918\pi\)
\(390\) −4.34519e11 −0.951082
\(391\) −2.06486e11 −0.446781
\(392\) −1.05745e11 −0.226189
\(393\) 1.93975e10 0.0410184
\(394\) 1.71170e11 0.357844
\(395\) 3.73655e11 0.772297
\(396\) 3.09290e11 0.632031
\(397\) 8.56941e11 1.73139 0.865693 0.500576i \(-0.166878\pi\)
0.865693 + 0.500576i \(0.166878\pi\)
\(398\) 1.13000e12 2.25738
\(399\) 1.25581e11 0.248053
\(400\) −5.96910e10 −0.116584
\(401\) 1.29537e11 0.250176 0.125088 0.992146i \(-0.460079\pi\)
0.125088 + 0.992146i \(0.460079\pi\)
\(402\) 6.48664e11 1.23880
\(403\) −8.39585e10 −0.158559
\(404\) −8.37476e10 −0.156407
\(405\) 6.98604e10 0.129028
\(406\) −3.34719e11 −0.611383
\(407\) 2.77097e11 0.500562
\(408\) 2.10070e11 0.375313
\(409\) −2.39667e11 −0.423501 −0.211750 0.977324i \(-0.567916\pi\)
−0.211750 + 0.977324i \(0.567916\pi\)
\(410\) 6.64790e11 1.16187
\(411\) −2.67475e11 −0.462375
\(412\) −1.14750e12 −1.96207
\(413\) −6.36659e10 −0.107679
\(414\) −1.53681e11 −0.257109
\(415\) 6.03213e11 0.998284
\(416\) 6.85695e11 1.12256
\(417\) −3.16587e11 −0.512720
\(418\) 6.61431e11 1.05972
\(419\) 7.69914e11 1.22033 0.610167 0.792272i \(-0.291102\pi\)
0.610167 + 0.792272i \(0.291102\pi\)
\(420\) 5.15164e11 0.807837
\(421\) 1.58818e11 0.246394 0.123197 0.992382i \(-0.460685\pi\)
0.123197 + 0.992382i \(0.460685\pi\)
\(422\) −1.49290e12 −2.29152
\(423\) −2.02868e11 −0.308093
\(424\) 9.74467e10 0.146427
\(425\) 2.12812e11 0.316407
\(426\) −4.71830e11 −0.694132
\(427\) −1.87711e11 −0.273252
\(428\) 4.57052e11 0.658368
\(429\) −4.77115e11 −0.680088
\(430\) −3.89257e11 −0.549071
\(431\) 6.16553e11 0.860642 0.430321 0.902676i \(-0.358400\pi\)
0.430321 + 0.902676i \(0.358400\pi\)
\(432\) −4.66045e10 −0.0643800
\(433\) 1.91051e11 0.261189 0.130594 0.991436i \(-0.458311\pi\)
0.130594 + 0.991436i \(0.458311\pi\)
\(434\) 1.67869e11 0.227126
\(435\) −2.36123e11 −0.316181
\(436\) 1.82736e12 2.42179
\(437\) −1.94880e11 −0.255624
\(438\) −7.04114e11 −0.914133
\(439\) 3.59506e11 0.461973 0.230986 0.972957i \(-0.425805\pi\)
0.230986 + 0.972957i \(0.425805\pi\)
\(440\) 8.50816e11 1.08218
\(441\) −8.36393e10 −0.105302
\(442\) −1.03346e12 −1.28793
\(443\) 2.77924e11 0.342854 0.171427 0.985197i \(-0.445162\pi\)
0.171427 + 0.985197i \(0.445162\pi\)
\(444\) 2.64888e11 0.323474
\(445\) 3.35935e11 0.406103
\(446\) −1.88366e11 −0.225422
\(447\) −6.74240e10 −0.0798787
\(448\) −1.13509e12 −1.33131
\(449\) −5.78433e11 −0.671653 −0.335826 0.941924i \(-0.609016\pi\)
−0.335826 + 0.941924i \(0.609016\pi\)
\(450\) 1.58389e11 0.182083
\(451\) 7.29960e11 0.830815
\(452\) −3.98564e11 −0.449133
\(453\) 1.81932e11 0.202986
\(454\) −5.64806e11 −0.623947
\(455\) −7.94699e11 −0.869263
\(456\) 1.98263e11 0.214734
\(457\) 1.39805e12 1.49933 0.749667 0.661815i \(-0.230214\pi\)
0.749667 + 0.661815i \(0.230214\pi\)
\(458\) 6.00613e11 0.637823
\(459\) 1.66156e11 0.174726
\(460\) −7.99450e11 −0.832494
\(461\) −1.30225e12 −1.34289 −0.671445 0.741054i \(-0.734326\pi\)
−0.671445 + 0.741054i \(0.734326\pi\)
\(462\) 9.53959e11 0.974184
\(463\) 1.77308e12 1.79313 0.896567 0.442908i \(-0.146053\pi\)
0.896567 + 0.442908i \(0.146053\pi\)
\(464\) 1.57519e11 0.157762
\(465\) 1.18421e11 0.117460
\(466\) 4.01422e10 0.0394334
\(467\) −5.78947e11 −0.563265 −0.281632 0.959522i \(-0.590876\pi\)
−0.281632 + 0.959522i \(0.590876\pi\)
\(468\) −4.56093e11 −0.439488
\(469\) 1.18635e12 1.13223
\(470\) −1.77973e12 −1.68234
\(471\) −4.75216e9 −0.00444935
\(472\) −1.00514e11 −0.0932155
\(473\) −4.27416e11 −0.392623
\(474\) 6.61432e11 0.601842
\(475\) 2.00851e11 0.181031
\(476\) 1.22527e12 1.09395
\(477\) 7.70758e10 0.0681688
\(478\) −1.09611e12 −0.960344
\(479\) 2.87330e10 0.0249385 0.0124693 0.999922i \(-0.496031\pi\)
0.0124693 + 0.999922i \(0.496031\pi\)
\(480\) −9.67151e11 −0.831589
\(481\) −4.08620e11 −0.348070
\(482\) −7.41543e11 −0.625785
\(483\) −2.81069e11 −0.234991
\(484\) 1.22060e12 1.01104
\(485\) 1.32632e12 1.08845
\(486\) 1.23665e11 0.100550
\(487\) −4.24889e11 −0.342291 −0.171145 0.985246i \(-0.554747\pi\)
−0.171145 + 0.985246i \(0.554747\pi\)
\(488\) −2.96352e11 −0.236548
\(489\) 9.96366e11 0.788005
\(490\) −7.33756e11 −0.575002
\(491\) 2.40381e12 1.86652 0.933261 0.359199i \(-0.116950\pi\)
0.933261 + 0.359199i \(0.116950\pi\)
\(492\) 6.97797e11 0.536891
\(493\) −5.61593e11 −0.428165
\(494\) −9.75375e11 −0.736886
\(495\) 6.72956e11 0.503806
\(496\) −7.89996e10 −0.0586081
\(497\) −8.62938e11 −0.634418
\(498\) 1.06779e12 0.777952
\(499\) −2.16393e12 −1.56240 −0.781199 0.624283i \(-0.785391\pi\)
−0.781199 + 0.624283i \(0.785391\pi\)
\(500\) −1.54030e12 −1.10215
\(501\) −1.31728e12 −0.934130
\(502\) −4.13490e12 −2.90602
\(503\) −4.78087e10 −0.0333005 −0.0166503 0.999861i \(-0.505300\pi\)
−0.0166503 + 0.999861i \(0.505300\pi\)
\(504\) 2.85949e11 0.197402
\(505\) −1.82219e11 −0.124676
\(506\) −1.48039e12 −1.00392
\(507\) −1.55390e11 −0.104445
\(508\) −2.17080e12 −1.44622
\(509\) 6.59076e11 0.435216 0.217608 0.976036i \(-0.430175\pi\)
0.217608 + 0.976036i \(0.430175\pi\)
\(510\) 1.45766e12 0.954093
\(511\) −1.28777e12 −0.835493
\(512\) 1.01764e12 0.654454
\(513\) 1.56817e11 0.0999691
\(514\) −4.33087e12 −2.73679
\(515\) −2.49673e12 −1.56401
\(516\) −4.08584e11 −0.253722
\(517\) −1.95420e12 −1.20299
\(518\) 8.17008e11 0.498588
\(519\) 5.15489e11 0.311865
\(520\) −1.25465e12 −0.752501
\(521\) −9.54421e11 −0.567505 −0.283753 0.958897i \(-0.591579\pi\)
−0.283753 + 0.958897i \(0.591579\pi\)
\(522\) −4.17976e11 −0.246396
\(523\) −3.29305e12 −1.92460 −0.962300 0.271992i \(-0.912318\pi\)
−0.962300 + 0.271992i \(0.912318\pi\)
\(524\) 1.78621e11 0.103500
\(525\) 2.89681e11 0.166419
\(526\) 3.99100e11 0.227324
\(527\) 2.81652e11 0.159061
\(528\) −4.48935e11 −0.251380
\(529\) −1.36498e12 −0.757837
\(530\) 6.76175e11 0.372236
\(531\) −7.95020e10 −0.0433963
\(532\) 1.15640e12 0.625902
\(533\) −1.07643e12 −0.577715
\(534\) 5.94662e11 0.316471
\(535\) 9.94457e11 0.524800
\(536\) 1.87298e12 0.980148
\(537\) −1.78299e12 −0.925260
\(538\) 3.02551e12 1.55696
\(539\) −8.05686e11 −0.411165
\(540\) 6.43305e11 0.325570
\(541\) 8.28435e11 0.415787 0.207893 0.978151i \(-0.433339\pi\)
0.207893 + 0.978151i \(0.433339\pi\)
\(542\) 3.68086e11 0.183211
\(543\) 1.94921e12 0.962189
\(544\) −2.30027e12 −1.12612
\(545\) 3.97599e12 1.93046
\(546\) −1.40675e12 −0.677407
\(547\) 2.61365e12 1.24826 0.624130 0.781320i \(-0.285453\pi\)
0.624130 + 0.781320i \(0.285453\pi\)
\(548\) −2.46302e12 −1.16669
\(549\) −2.34401e11 −0.110125
\(550\) 1.52574e12 0.710967
\(551\) −5.30030e11 −0.244973
\(552\) −4.43745e11 −0.203427
\(553\) 1.20970e12 0.550068
\(554\) −2.41189e11 −0.108784
\(555\) 5.76345e11 0.257848
\(556\) −2.91527e12 −1.29372
\(557\) 3.51699e12 1.54819 0.774093 0.633072i \(-0.218206\pi\)
0.774093 + 0.633072i \(0.218206\pi\)
\(558\) 2.09625e11 0.0915353
\(559\) 6.30286e11 0.273014
\(560\) −7.47761e11 −0.321304
\(561\) 1.60056e12 0.682242
\(562\) −4.32724e12 −1.82977
\(563\) 2.45632e12 1.03038 0.515190 0.857076i \(-0.327721\pi\)
0.515190 + 0.857076i \(0.327721\pi\)
\(564\) −1.86810e12 −0.777398
\(565\) −8.67197e11 −0.358014
\(566\) −2.39403e11 −0.0980518
\(567\) 2.26172e11 0.0919000
\(568\) −1.36238e12 −0.549202
\(569\) 1.66431e12 0.665624 0.332812 0.942993i \(-0.392003\pi\)
0.332812 + 0.942993i \(0.392003\pi\)
\(570\) 1.37574e12 0.545881
\(571\) −2.28653e12 −0.900150 −0.450075 0.892991i \(-0.648603\pi\)
−0.450075 + 0.892991i \(0.648603\pi\)
\(572\) −4.39348e12 −1.71604
\(573\) −5.88848e11 −0.228196
\(574\) 2.15225e12 0.827540
\(575\) −4.49537e11 −0.171498
\(576\) −1.41743e12 −0.536539
\(577\) 4.56676e12 1.71521 0.857604 0.514310i \(-0.171952\pi\)
0.857604 + 0.514310i \(0.171952\pi\)
\(578\) −7.39016e11 −0.275409
\(579\) −8.98157e10 −0.0332123
\(580\) −2.17432e12 −0.797806
\(581\) 1.95289e12 0.711027
\(582\) 2.34781e12 0.848221
\(583\) 7.42461e11 0.266174
\(584\) −2.03309e12 −0.723267
\(585\) −9.92370e11 −0.350326
\(586\) −6.51113e10 −0.0228096
\(587\) 4.67076e12 1.62374 0.811870 0.583838i \(-0.198450\pi\)
0.811870 + 0.583838i \(0.198450\pi\)
\(588\) −7.70187e11 −0.265704
\(589\) 2.65822e11 0.0910065
\(590\) −6.97460e11 −0.236965
\(591\) 3.90924e11 0.131810
\(592\) −3.84485e11 −0.128657
\(593\) 1.37887e12 0.457907 0.228954 0.973437i \(-0.426470\pi\)
0.228954 + 0.973437i \(0.426470\pi\)
\(594\) 1.19124e12 0.392610
\(595\) 2.66594e12 0.872015
\(596\) −6.20870e11 −0.201554
\(597\) 2.58073e12 0.831493
\(598\) 2.18304e12 0.698083
\(599\) 3.94924e12 1.25341 0.626705 0.779257i \(-0.284403\pi\)
0.626705 + 0.779257i \(0.284403\pi\)
\(600\) 4.57341e11 0.144065
\(601\) 3.41758e12 1.06852 0.534261 0.845319i \(-0.320590\pi\)
0.534261 + 0.845319i \(0.320590\pi\)
\(602\) −1.26021e12 −0.391075
\(603\) 1.48144e12 0.456306
\(604\) 1.67530e12 0.512186
\(605\) 2.65579e12 0.805925
\(606\) −3.22557e11 −0.0971583
\(607\) 3.04748e12 0.911154 0.455577 0.890196i \(-0.349433\pi\)
0.455577 + 0.890196i \(0.349433\pi\)
\(608\) −2.17099e12 −0.644304
\(609\) −7.64444e11 −0.225200
\(610\) −2.05637e12 −0.601335
\(611\) 2.88175e12 0.836509
\(612\) 1.53003e12 0.440879
\(613\) 2.00612e12 0.573833 0.286916 0.957956i \(-0.407370\pi\)
0.286916 + 0.957956i \(0.407370\pi\)
\(614\) −9.17784e12 −2.60605
\(615\) 1.51827e12 0.427968
\(616\) 2.75450e12 0.770780
\(617\) 5.13085e12 1.42530 0.712650 0.701520i \(-0.247495\pi\)
0.712650 + 0.701520i \(0.247495\pi\)
\(618\) −4.41964e12 −1.21882
\(619\) 5.80716e12 1.58985 0.794924 0.606709i \(-0.207511\pi\)
0.794924 + 0.606709i \(0.207511\pi\)
\(620\) 1.09047e12 0.296382
\(621\) −3.50982e11 −0.0947049
\(622\) −5.66657e12 −1.51797
\(623\) 1.08759e12 0.289246
\(624\) 6.62019e11 0.174799
\(625\) −4.68082e12 −1.22705
\(626\) −9.14247e12 −2.37946
\(627\) 1.51060e12 0.390342
\(628\) −4.37599e10 −0.0112269
\(629\) 1.37078e12 0.349172
\(630\) 1.98418e12 0.501820
\(631\) 5.78092e11 0.145166 0.0725830 0.997362i \(-0.476876\pi\)
0.0725830 + 0.997362i \(0.476876\pi\)
\(632\) 1.90985e12 0.476181
\(633\) −3.40953e12 −0.844070
\(634\) 2.17842e11 0.0535477
\(635\) −4.72325e12 −1.15281
\(636\) 7.09748e11 0.172007
\(637\) 1.18810e12 0.285907
\(638\) −4.02631e12 −0.962087
\(639\) −1.07758e12 −0.255680
\(640\) −6.32158e12 −1.48942
\(641\) 1.17584e12 0.275097 0.137548 0.990495i \(-0.456078\pi\)
0.137548 + 0.990495i \(0.456078\pi\)
\(642\) 1.76035e12 0.408971
\(643\) −4.79162e12 −1.10543 −0.552717 0.833369i \(-0.686409\pi\)
−0.552717 + 0.833369i \(0.686409\pi\)
\(644\) −2.58821e12 −0.592943
\(645\) −8.88999e11 −0.202247
\(646\) 3.27205e12 0.739219
\(647\) −6.93263e11 −0.155535 −0.0777676 0.996972i \(-0.524779\pi\)
−0.0777676 + 0.996972i \(0.524779\pi\)
\(648\) 3.57075e11 0.0795557
\(649\) −7.65832e11 −0.169446
\(650\) −2.24993e12 −0.494377
\(651\) 3.83386e11 0.0836608
\(652\) 9.17497e12 1.98834
\(653\) 6.48149e12 1.39497 0.697486 0.716598i \(-0.254302\pi\)
0.697486 + 0.716598i \(0.254302\pi\)
\(654\) 7.03816e12 1.50439
\(655\) 3.88644e11 0.0825022
\(656\) −1.01285e12 −0.213540
\(657\) −1.60808e12 −0.336716
\(658\) −5.76186e12 −1.19825
\(659\) −2.34935e12 −0.485248 −0.242624 0.970120i \(-0.578008\pi\)
−0.242624 + 0.970120i \(0.578008\pi\)
\(660\) 6.19687e12 1.27123
\(661\) 7.15134e12 1.45707 0.728536 0.685007i \(-0.240201\pi\)
0.728536 + 0.685007i \(0.240201\pi\)
\(662\) −6.64880e12 −1.34550
\(663\) −2.36025e12 −0.474403
\(664\) 3.08318e12 0.615520
\(665\) 2.51610e12 0.498920
\(666\) 1.02023e12 0.200938
\(667\) 1.18629e12 0.232073
\(668\) −1.21301e13 −2.35705
\(669\) −4.30198e11 −0.0830330
\(670\) 1.29965e13 2.49166
\(671\) −2.25795e12 −0.429995
\(672\) −3.13114e12 −0.592299
\(673\) −1.03521e13 −1.94518 −0.972592 0.232519i \(-0.925303\pi\)
−0.972592 + 0.232519i \(0.925303\pi\)
\(674\) −5.99350e12 −1.11869
\(675\) 3.61736e11 0.0670694
\(676\) −1.43090e12 −0.263541
\(677\) −4.12518e12 −0.754733 −0.377367 0.926064i \(-0.623170\pi\)
−0.377367 + 0.926064i \(0.623170\pi\)
\(678\) −1.53508e12 −0.278996
\(679\) 4.29394e12 0.775251
\(680\) 4.20892e12 0.754884
\(681\) −1.28992e12 −0.229828
\(682\) 2.01929e12 0.357411
\(683\) 7.10900e12 1.25002 0.625008 0.780618i \(-0.285096\pi\)
0.625008 + 0.780618i \(0.285096\pi\)
\(684\) 1.44404e12 0.252248
\(685\) −5.35906e12 −0.929996
\(686\) −9.89524e12 −1.70596
\(687\) 1.37170e12 0.234939
\(688\) 5.93059e11 0.100914
\(689\) −1.09487e12 −0.185086
\(690\) −3.07911e12 −0.517136
\(691\) −5.47912e12 −0.914239 −0.457119 0.889405i \(-0.651119\pi\)
−0.457119 + 0.889405i \(0.651119\pi\)
\(692\) 4.74685e12 0.786915
\(693\) 2.17869e12 0.358835
\(694\) 4.98199e12 0.815239
\(695\) −6.34306e12 −1.03126
\(696\) −1.20688e12 −0.194950
\(697\) 3.61105e12 0.579544
\(698\) −5.66411e12 −0.903197
\(699\) 9.16781e10 0.0145251
\(700\) 2.66751e12 0.419918
\(701\) −3.79491e12 −0.593568 −0.296784 0.954945i \(-0.595914\pi\)
−0.296784 + 0.954945i \(0.595914\pi\)
\(702\) −1.75666e12 −0.273005
\(703\) 1.29374e12 0.199778
\(704\) −1.36539e13 −2.09498
\(705\) −4.06462e12 −0.619682
\(706\) 4.00912e12 0.607334
\(707\) −5.89930e11 −0.0888001
\(708\) −7.32089e11 −0.109500
\(709\) −3.93622e12 −0.585021 −0.292510 0.956262i \(-0.594491\pi\)
−0.292510 + 0.956262i \(0.594491\pi\)
\(710\) −9.45347e12 −1.39614
\(711\) 1.51060e12 0.221685
\(712\) 1.71705e12 0.250394
\(713\) −5.94952e11 −0.0862142
\(714\) 4.71916e12 0.679552
\(715\) −9.55937e12 −1.36789
\(716\) −1.64185e13 −2.33467
\(717\) −2.50332e12 −0.353737
\(718\) 8.08869e12 1.13584
\(719\) 3.83409e12 0.535036 0.267518 0.963553i \(-0.413797\pi\)
0.267518 + 0.963553i \(0.413797\pi\)
\(720\) −9.33757e11 −0.129490
\(721\) −8.08315e12 −1.11397
\(722\) −8.35651e12 −1.14448
\(723\) −1.69356e12 −0.230504
\(724\) 1.79492e13 2.42785
\(725\) −1.22264e12 −0.164353
\(726\) 4.70119e12 0.628048
\(727\) −1.18819e13 −1.57754 −0.788769 0.614689i \(-0.789281\pi\)
−0.788769 + 0.614689i \(0.789281\pi\)
\(728\) −4.06191e12 −0.535969
\(729\) 2.82430e11 0.0370370
\(730\) −1.41075e13 −1.83864
\(731\) −2.11439e12 −0.273878
\(732\) −2.15847e12 −0.277872
\(733\) 7.50616e12 0.960395 0.480198 0.877160i \(-0.340565\pi\)
0.480198 + 0.877160i \(0.340565\pi\)
\(734\) 2.21966e13 2.82263
\(735\) −1.67578e12 −0.211799
\(736\) 4.85901e12 0.610376
\(737\) 1.42705e13 1.78171
\(738\) 2.68759e12 0.333511
\(739\) −1.28013e13 −1.57890 −0.789452 0.613812i \(-0.789635\pi\)
−0.789452 + 0.613812i \(0.789635\pi\)
\(740\) 5.30724e12 0.650618
\(741\) −2.22760e12 −0.271428
\(742\) 2.18911e12 0.265124
\(743\) 1.22654e13 1.47649 0.738246 0.674531i \(-0.235654\pi\)
0.738246 + 0.674531i \(0.235654\pi\)
\(744\) 6.05280e11 0.0724233
\(745\) −1.35089e12 −0.160664
\(746\) 2.40073e12 0.283804
\(747\) 2.43865e12 0.286554
\(748\) 1.47386e13 1.72147
\(749\) 3.21954e12 0.373788
\(750\) −5.93251e12 −0.684641
\(751\) −3.60774e11 −0.0413862 −0.0206931 0.999786i \(-0.506587\pi\)
−0.0206931 + 0.999786i \(0.506587\pi\)
\(752\) 2.71154e12 0.309198
\(753\) −9.44344e12 −1.07042
\(754\) 5.93737e12 0.668995
\(755\) 3.64514e12 0.408275
\(756\) 2.08269e12 0.231887
\(757\) 1.08258e13 1.19820 0.599101 0.800674i \(-0.295525\pi\)
0.599101 + 0.800674i \(0.295525\pi\)
\(758\) 9.26995e12 1.01992
\(759\) −3.38096e12 −0.369787
\(760\) 3.97236e12 0.431904
\(761\) −4.20431e12 −0.454426 −0.227213 0.973845i \(-0.572961\pi\)
−0.227213 + 0.973845i \(0.572961\pi\)
\(762\) −8.36094e12 −0.898375
\(763\) 1.28722e13 1.37497
\(764\) −5.42236e12 −0.575796
\(765\) 3.32906e12 0.351435
\(766\) −3.99886e12 −0.419669
\(767\) 1.12933e12 0.117826
\(768\) −2.23068e12 −0.231373
\(769\) 1.45302e12 0.149831 0.0749155 0.997190i \(-0.476131\pi\)
0.0749155 + 0.997190i \(0.476131\pi\)
\(770\) 1.91133e13 1.95942
\(771\) −9.89100e12 −1.00808
\(772\) −8.27062e11 −0.0838031
\(773\) 7.94784e12 0.800648 0.400324 0.916374i \(-0.368898\pi\)
0.400324 + 0.916374i \(0.368898\pi\)
\(774\) −1.57368e12 −0.157609
\(775\) 6.13181e11 0.0610563
\(776\) 6.77916e12 0.671117
\(777\) 1.86591e12 0.183652
\(778\) 1.89176e13 1.85122
\(779\) 3.40810e12 0.331584
\(780\) −9.13817e12 −0.883962
\(781\) −1.03802e13 −0.998335
\(782\) −7.32336e12 −0.700293
\(783\) −9.54589e11 −0.0907588
\(784\) 1.11793e12 0.105680
\(785\) −9.52131e10 −0.00894918
\(786\) 6.87964e11 0.0642931
\(787\) −8.30103e12 −0.771340 −0.385670 0.922637i \(-0.626030\pi\)
−0.385670 + 0.922637i \(0.626030\pi\)
\(788\) 3.59979e12 0.332590
\(789\) 9.11478e11 0.0837336
\(790\) 1.32523e13 1.21051
\(791\) −2.80754e12 −0.254995
\(792\) 3.43965e12 0.310636
\(793\) 3.32968e12 0.299001
\(794\) 3.03928e13 2.71381
\(795\) 1.54427e12 0.137111
\(796\) 2.37645e13 2.09807
\(797\) −8.52949e12 −0.748791 −0.374396 0.927269i \(-0.622150\pi\)
−0.374396 + 0.927269i \(0.622150\pi\)
\(798\) 4.45393e12 0.388803
\(799\) −9.66728e12 −0.839158
\(800\) −5.00789e12 −0.432264
\(801\) 1.35811e12 0.116570
\(802\) 4.59425e12 0.392130
\(803\) −1.54904e13 −1.31475
\(804\) 1.36418e13 1.15138
\(805\) −5.63144e12 −0.472648
\(806\) −2.97773e12 −0.248529
\(807\) 6.90977e12 0.573499
\(808\) −9.31366e11 −0.0768722
\(809\) 5.02024e12 0.412056 0.206028 0.978546i \(-0.433946\pi\)
0.206028 + 0.978546i \(0.433946\pi\)
\(810\) 2.47771e12 0.202241
\(811\) −1.87975e11 −0.0152583 −0.00762917 0.999971i \(-0.502428\pi\)
−0.00762917 + 0.999971i \(0.502428\pi\)
\(812\) −7.03933e12 −0.568237
\(813\) 8.40647e11 0.0674849
\(814\) 9.82772e12 0.784590
\(815\) 1.99629e13 1.58495
\(816\) −2.22085e12 −0.175353
\(817\) −1.99556e12 −0.156698
\(818\) −8.50020e12 −0.663803
\(819\) −3.21278e12 −0.249519
\(820\) 1.39809e13 1.07987
\(821\) −2.48419e13 −1.90827 −0.954135 0.299375i \(-0.903222\pi\)
−0.954135 + 0.299375i \(0.903222\pi\)
\(822\) −9.48643e12 −0.724736
\(823\) 2.43389e13 1.84928 0.924638 0.380848i \(-0.124368\pi\)
0.924638 + 0.380848i \(0.124368\pi\)
\(824\) −1.27615e13 −0.964335
\(825\) 3.48455e12 0.261881
\(826\) −2.25802e12 −0.168778
\(827\) 1.01862e13 0.757248 0.378624 0.925551i \(-0.376397\pi\)
0.378624 + 0.925551i \(0.376397\pi\)
\(828\) −3.23199e12 −0.238965
\(829\) 1.02130e13 0.751029 0.375514 0.926817i \(-0.377466\pi\)
0.375514 + 0.926817i \(0.377466\pi\)
\(830\) 2.13939e13 1.56473
\(831\) −5.50836e11 −0.0400699
\(832\) 2.01347e13 1.45677
\(833\) −3.98567e12 −0.286813
\(834\) −1.12283e13 −0.803647
\(835\) −2.63926e13 −1.87886
\(836\) 1.39103e13 0.984933
\(837\) 4.78748e11 0.0337165
\(838\) 2.73063e13 1.91278
\(839\) −1.79221e13 −1.24870 −0.624352 0.781143i \(-0.714637\pi\)
−0.624352 + 0.781143i \(0.714637\pi\)
\(840\) 5.72920e12 0.397043
\(841\) −1.12807e13 −0.777597
\(842\) 5.63274e12 0.386203
\(843\) −9.88270e12 −0.673987
\(844\) −3.13965e13 −2.12980
\(845\) −3.11335e12 −0.210075
\(846\) −7.19505e12 −0.482911
\(847\) 8.59808e12 0.574019
\(848\) −1.03020e12 −0.0684132
\(849\) −5.46757e11 −0.0361169
\(850\) 7.54774e12 0.495943
\(851\) −2.89559e12 −0.189258
\(852\) −9.92284e12 −0.645146
\(853\) −1.03449e13 −0.669048 −0.334524 0.942387i \(-0.608575\pi\)
−0.334524 + 0.942387i \(0.608575\pi\)
\(854\) −6.65746e12 −0.428300
\(855\) 3.14195e12 0.201072
\(856\) 5.08293e12 0.323580
\(857\) 1.72812e12 0.109436 0.0547179 0.998502i \(-0.482574\pi\)
0.0547179 + 0.998502i \(0.482574\pi\)
\(858\) −1.69217e13 −1.06598
\(859\) 1.43047e13 0.896416 0.448208 0.893929i \(-0.352062\pi\)
0.448208 + 0.893929i \(0.352062\pi\)
\(860\) −8.18629e12 −0.510322
\(861\) 4.91538e12 0.304820
\(862\) 2.18671e13 1.34899
\(863\) −6.54341e12 −0.401565 −0.200782 0.979636i \(-0.564348\pi\)
−0.200782 + 0.979636i \(0.564348\pi\)
\(864\) −3.90997e12 −0.238705
\(865\) 1.03282e13 0.627267
\(866\) 6.77595e12 0.409392
\(867\) −1.68779e12 −0.101445
\(868\) 3.53039e12 0.211098
\(869\) 1.45514e13 0.865599
\(870\) −8.37447e12 −0.495588
\(871\) −2.10439e13 −1.23893
\(872\) 2.03223e13 1.19028
\(873\) 5.36200e12 0.312437
\(874\) −6.91176e12 −0.400670
\(875\) −1.08501e13 −0.625744
\(876\) −1.48079e13 −0.849621
\(877\) −1.57637e13 −0.899830 −0.449915 0.893071i \(-0.648546\pi\)
−0.449915 + 0.893071i \(0.648546\pi\)
\(878\) 1.27505e13 0.724105
\(879\) −1.48704e11 −0.00840178
\(880\) −8.99476e12 −0.505612
\(881\) −2.36603e13 −1.32321 −0.661606 0.749852i \(-0.730125\pi\)
−0.661606 + 0.749852i \(0.730125\pi\)
\(882\) −2.96641e12 −0.165052
\(883\) 7.82639e12 0.433250 0.216625 0.976255i \(-0.430495\pi\)
0.216625 + 0.976255i \(0.430495\pi\)
\(884\) −2.17342e13 −1.19704
\(885\) −1.59288e12 −0.0872849
\(886\) 9.85703e12 0.537396
\(887\) 1.92636e13 1.04492 0.522458 0.852665i \(-0.325015\pi\)
0.522458 + 0.852665i \(0.325015\pi\)
\(888\) 2.94585e12 0.158984
\(889\) −1.52915e13 −0.821090
\(890\) 1.19145e13 0.636533
\(891\) 2.72061e12 0.144616
\(892\) −3.96145e12 −0.209514
\(893\) −9.12394e12 −0.480121
\(894\) −2.39130e12 −0.125203
\(895\) −3.57235e13 −1.86102
\(896\) −2.04660e13 −1.06083
\(897\) 4.98571e12 0.257135
\(898\) −2.05151e13 −1.05276
\(899\) −1.61813e12 −0.0826219
\(900\) 3.33102e12 0.169233
\(901\) 3.67290e12 0.185672
\(902\) 2.58892e13 1.30224
\(903\) −2.87812e12 −0.144050
\(904\) −4.43247e12 −0.220743
\(905\) 3.90540e13 1.93529
\(906\) 6.45250e12 0.318164
\(907\) −3.54971e13 −1.74165 −0.870824 0.491595i \(-0.836414\pi\)
−0.870824 + 0.491595i \(0.836414\pi\)
\(908\) −1.18782e13 −0.579914
\(909\) −7.36668e11 −0.0357877
\(910\) −2.81853e13 −1.36250
\(911\) −2.79806e13 −1.34593 −0.672967 0.739672i \(-0.734981\pi\)
−0.672967 + 0.739672i \(0.734981\pi\)
\(912\) −2.09603e12 −0.100327
\(913\) 2.34912e13 1.11889
\(914\) 4.95840e13 2.35008
\(915\) −4.69641e12 −0.221498
\(916\) 1.26312e13 0.592811
\(917\) 1.25823e12 0.0587622
\(918\) 5.89299e12 0.273869
\(919\) 5.86841e12 0.271394 0.135697 0.990750i \(-0.456673\pi\)
0.135697 + 0.990750i \(0.456673\pi\)
\(920\) −8.89077e12 −0.409161
\(921\) −2.09607e13 −0.959925
\(922\) −4.61865e13 −2.10487
\(923\) 1.53071e13 0.694201
\(924\) 2.00623e13 0.905433
\(925\) 2.98430e12 0.134031
\(926\) 6.28850e13 2.81059
\(927\) −1.00937e13 −0.448945
\(928\) 1.32154e13 0.584944
\(929\) 3.20314e12 0.141093 0.0705464 0.997508i \(-0.477526\pi\)
0.0705464 + 0.997508i \(0.477526\pi\)
\(930\) 4.19999e12 0.184109
\(931\) −3.76166e12 −0.164099
\(932\) 8.44212e11 0.0366505
\(933\) −1.29415e13 −0.559137
\(934\) −2.05333e13 −0.882872
\(935\) 3.20684e13 1.37222
\(936\) −5.07226e12 −0.216003
\(937\) 2.84740e13 1.20676 0.603380 0.797454i \(-0.293820\pi\)
0.603380 + 0.797454i \(0.293820\pi\)
\(938\) 4.20759e13 1.77468
\(939\) −2.08799e13 −0.876462
\(940\) −3.74287e13 −1.56362
\(941\) 4.06774e13 1.69122 0.845609 0.533803i \(-0.179238\pi\)
0.845609 + 0.533803i \(0.179238\pi\)
\(942\) −1.68543e11 −0.00697400
\(943\) −7.62786e12 −0.314123
\(944\) 1.06263e12 0.0435519
\(945\) 4.53153e12 0.184843
\(946\) −1.51590e13 −0.615405
\(947\) −6.71090e11 −0.0271148 −0.0135574 0.999908i \(-0.504316\pi\)
−0.0135574 + 0.999908i \(0.504316\pi\)
\(948\) 1.39103e13 0.559369
\(949\) 2.28429e13 0.914224
\(950\) 7.12353e12 0.283752
\(951\) 4.97516e11 0.0197240
\(952\) 1.36263e13 0.537665
\(953\) 2.85607e13 1.12163 0.560816 0.827941i \(-0.310488\pi\)
0.560816 + 0.827941i \(0.310488\pi\)
\(954\) 2.73362e12 0.106849
\(955\) −1.17980e13 −0.458980
\(956\) −2.30517e13 −0.892570
\(957\) −9.19543e12 −0.354379
\(958\) 1.01906e12 0.0390892
\(959\) −1.73499e13 −0.662389
\(960\) −2.83993e13 −1.07916
\(961\) −2.56281e13 −0.969306
\(962\) −1.44924e13 −0.545572
\(963\) 4.02036e12 0.150642
\(964\) −1.55951e13 −0.581621
\(965\) −1.79953e12 −0.0668013
\(966\) −9.96859e12 −0.368330
\(967\) −1.66612e13 −0.612756 −0.306378 0.951910i \(-0.599117\pi\)
−0.306378 + 0.951910i \(0.599117\pi\)
\(968\) 1.35744e13 0.496915
\(969\) 7.47282e12 0.272287
\(970\) 4.70401e13 1.70606
\(971\) −4.12487e13 −1.48910 −0.744551 0.667566i \(-0.767336\pi\)
−0.744551 + 0.667566i \(0.767336\pi\)
\(972\) 2.60073e12 0.0934539
\(973\) −2.05356e13 −0.734512
\(974\) −1.50694e13 −0.536513
\(975\) −5.13847e12 −0.182101
\(976\) 3.13301e12 0.110519
\(977\) 3.51543e13 1.23439 0.617197 0.786809i \(-0.288268\pi\)
0.617197 + 0.786809i \(0.288268\pi\)
\(978\) 3.53377e13 1.23513
\(979\) 1.30825e13 0.455165
\(980\) −1.54313e13 −0.534422
\(981\) 1.60740e13 0.554132
\(982\) 8.52550e13 2.92562
\(983\) −6.62406e12 −0.226273 −0.113137 0.993579i \(-0.536090\pi\)
−0.113137 + 0.993579i \(0.536090\pi\)
\(984\) 7.76028e12 0.263876
\(985\) 7.83246e12 0.265115
\(986\) −1.99178e13 −0.671114
\(987\) −1.31591e13 −0.441368
\(988\) −2.05127e13 −0.684882
\(989\) 4.46637e12 0.148447
\(990\) 2.38675e13 0.789675
\(991\) −1.87240e12 −0.0616690 −0.0308345 0.999525i \(-0.509816\pi\)
−0.0308345 + 0.999525i \(0.509816\pi\)
\(992\) −6.62782e12 −0.217304
\(993\) −1.51848e13 −0.495606
\(994\) −3.06055e13 −0.994399
\(995\) 5.17069e13 1.67242
\(996\) 2.24562e13 0.723050
\(997\) 7.06126e12 0.226336 0.113168 0.993576i \(-0.463900\pi\)
0.113168 + 0.993576i \(0.463900\pi\)
\(998\) −7.67475e13 −2.44893
\(999\) 2.33003e12 0.0740146
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.d.1.18 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.18 22 1.1 even 1 trivial