Properties

Label 177.10.a.d.1.4
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-32.9800 q^{2} +81.0000 q^{3} +575.677 q^{4} -958.538 q^{5} -2671.38 q^{6} -5513.62 q^{7} -2100.07 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-32.9800 q^{2} +81.0000 q^{3} +575.677 q^{4} -958.538 q^{5} -2671.38 q^{6} -5513.62 q^{7} -2100.07 q^{8} +6561.00 q^{9} +31612.5 q^{10} +29319.9 q^{11} +46629.8 q^{12} +137970. q^{13} +181839. q^{14} -77641.6 q^{15} -225487. q^{16} -339574. q^{17} -216381. q^{18} +86213.0 q^{19} -551808. q^{20} -446603. q^{21} -966968. q^{22} +1.13467e6 q^{23} -170106. q^{24} -1.03433e6 q^{25} -4.55026e6 q^{26} +531441. q^{27} -3.17406e6 q^{28} -919965. q^{29} +2.56062e6 q^{30} +1.08392e6 q^{31} +8.51177e6 q^{32} +2.37491e6 q^{33} +1.11991e7 q^{34} +5.28501e6 q^{35} +3.77702e6 q^{36} -2.63442e6 q^{37} -2.84330e6 q^{38} +1.11756e7 q^{39} +2.01299e6 q^{40} +9.33124e6 q^{41} +1.47289e7 q^{42} +6.15092e6 q^{43} +1.68788e7 q^{44} -6.28897e6 q^{45} -3.74214e7 q^{46} -5.67705e7 q^{47} -1.82644e7 q^{48} -9.95366e6 q^{49} +3.41121e7 q^{50} -2.75055e7 q^{51} +7.94264e7 q^{52} +5.09861e7 q^{53} -1.75269e7 q^{54} -2.81042e7 q^{55} +1.15790e7 q^{56} +6.98325e6 q^{57} +3.03404e7 q^{58} -1.21174e7 q^{59} -4.46965e7 q^{60} -9.11400e7 q^{61} -3.57475e7 q^{62} -3.61748e7 q^{63} -1.65269e8 q^{64} -1.32250e8 q^{65} -7.83244e7 q^{66} -9.97942e7 q^{67} -1.95485e8 q^{68} +9.19083e7 q^{69} -1.74299e8 q^{70} +1.19704e8 q^{71} -1.37785e7 q^{72} -6.25750e6 q^{73} +8.68832e7 q^{74} -8.37807e7 q^{75} +4.96308e7 q^{76} -1.61658e8 q^{77} -3.68571e8 q^{78} -2.70096e8 q^{79} +2.16137e8 q^{80} +4.30467e7 q^{81} -3.07744e8 q^{82} -4.06610e8 q^{83} -2.57099e8 q^{84} +3.25494e8 q^{85} -2.02857e8 q^{86} -7.45172e7 q^{87} -6.15737e7 q^{88} +9.88909e8 q^{89} +2.07410e8 q^{90} -7.60716e8 q^{91} +6.53204e8 q^{92} +8.77972e7 q^{93} +1.87229e9 q^{94} -8.26384e7 q^{95} +6.89453e8 q^{96} -1.09717e9 q^{97} +3.28271e8 q^{98} +1.92368e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.9800 −1.45752 −0.728761 0.684768i \(-0.759903\pi\)
−0.728761 + 0.684768i \(0.759903\pi\)
\(3\) 81.0000 0.577350
\(4\) 575.677 1.12437
\(5\) −958.538 −0.685874 −0.342937 0.939358i \(-0.611422\pi\)
−0.342937 + 0.939358i \(0.611422\pi\)
\(6\) −2671.38 −0.841501
\(7\) −5513.62 −0.867951 −0.433976 0.900925i \(-0.642890\pi\)
−0.433976 + 0.900925i \(0.642890\pi\)
\(8\) −2100.07 −0.181271
\(9\) 6561.00 0.333333
\(10\) 31612.5 0.999676
\(11\) 29319.9 0.603803 0.301901 0.953339i \(-0.402379\pi\)
0.301901 + 0.953339i \(0.402379\pi\)
\(12\) 46629.8 0.649155
\(13\) 137970. 1.33980 0.669901 0.742450i \(-0.266336\pi\)
0.669901 + 0.742450i \(0.266336\pi\)
\(14\) 181839. 1.26506
\(15\) −77641.6 −0.395990
\(16\) −225487. −0.860163
\(17\) −339574. −0.986085 −0.493042 0.870005i \(-0.664115\pi\)
−0.493042 + 0.870005i \(0.664115\pi\)
\(18\) −216381. −0.485841
\(19\) 86213.0 0.151768 0.0758842 0.997117i \(-0.475822\pi\)
0.0758842 + 0.997117i \(0.475822\pi\)
\(20\) −551808. −0.771176
\(21\) −446603. −0.501112
\(22\) −966968. −0.880055
\(23\) 1.13467e6 0.845463 0.422731 0.906255i \(-0.361071\pi\)
0.422731 + 0.906255i \(0.361071\pi\)
\(24\) −170106. −0.104657
\(25\) −1.03433e6 −0.529577
\(26\) −4.55026e6 −1.95279
\(27\) 531441. 0.192450
\(28\) −3.17406e6 −0.975898
\(29\) −919965. −0.241535 −0.120768 0.992681i \(-0.538536\pi\)
−0.120768 + 0.992681i \(0.538536\pi\)
\(30\) 2.56062e6 0.577163
\(31\) 1.08392e6 0.210799 0.105399 0.994430i \(-0.466388\pi\)
0.105399 + 0.994430i \(0.466388\pi\)
\(32\) 8.51177e6 1.43498
\(33\) 2.37491e6 0.348606
\(34\) 1.11991e7 1.43724
\(35\) 5.28501e6 0.595305
\(36\) 3.77702e6 0.374790
\(37\) −2.63442e6 −0.231088 −0.115544 0.993302i \(-0.536861\pi\)
−0.115544 + 0.993302i \(0.536861\pi\)
\(38\) −2.84330e6 −0.221206
\(39\) 1.11756e7 0.773535
\(40\) 2.01299e6 0.124329
\(41\) 9.33124e6 0.515718 0.257859 0.966183i \(-0.416983\pi\)
0.257859 + 0.966183i \(0.416983\pi\)
\(42\) 1.47289e7 0.730381
\(43\) 6.15092e6 0.274367 0.137184 0.990546i \(-0.456195\pi\)
0.137184 + 0.990546i \(0.456195\pi\)
\(44\) 1.68788e7 0.678897
\(45\) −6.28897e6 −0.228625
\(46\) −3.74214e7 −1.23228
\(47\) −5.67705e7 −1.69700 −0.848501 0.529193i \(-0.822495\pi\)
−0.848501 + 0.529193i \(0.822495\pi\)
\(48\) −1.82644e7 −0.496615
\(49\) −9.95366e6 −0.246661
\(50\) 3.41121e7 0.771870
\(51\) −2.75055e7 −0.569316
\(52\) 7.94264e7 1.50643
\(53\) 5.09861e7 0.887587 0.443793 0.896129i \(-0.353632\pi\)
0.443793 + 0.896129i \(0.353632\pi\)
\(54\) −1.75269e7 −0.280500
\(55\) −2.81042e7 −0.414132
\(56\) 1.15790e7 0.157334
\(57\) 6.98325e6 0.0876235
\(58\) 3.03404e7 0.352043
\(59\) −1.21174e7 −0.130189
\(60\) −4.46965e7 −0.445238
\(61\) −9.11400e7 −0.842801 −0.421400 0.906875i \(-0.638461\pi\)
−0.421400 + 0.906875i \(0.638461\pi\)
\(62\) −3.57475e7 −0.307244
\(63\) −3.61748e7 −0.289317
\(64\) −1.65269e8 −1.23135
\(65\) −1.32250e8 −0.918936
\(66\) −7.83244e7 −0.508100
\(67\) −9.97942e7 −0.605018 −0.302509 0.953146i \(-0.597824\pi\)
−0.302509 + 0.953146i \(0.597824\pi\)
\(68\) −1.95485e8 −1.10872
\(69\) 9.19083e7 0.488128
\(70\) −1.74299e8 −0.867670
\(71\) 1.19704e8 0.559043 0.279521 0.960139i \(-0.409824\pi\)
0.279521 + 0.960139i \(0.409824\pi\)
\(72\) −1.37785e7 −0.0604237
\(73\) −6.25750e6 −0.0257898 −0.0128949 0.999917i \(-0.504105\pi\)
−0.0128949 + 0.999917i \(0.504105\pi\)
\(74\) 8.68832e7 0.336816
\(75\) −8.37807e7 −0.305751
\(76\) 4.96308e7 0.170644
\(77\) −1.61658e8 −0.524071
\(78\) −3.68571e8 −1.12744
\(79\) −2.70096e8 −0.780182 −0.390091 0.920776i \(-0.627557\pi\)
−0.390091 + 0.920776i \(0.627557\pi\)
\(80\) 2.16137e8 0.589963
\(81\) 4.30467e7 0.111111
\(82\) −3.07744e8 −0.751670
\(83\) −4.06610e8 −0.940431 −0.470215 0.882552i \(-0.655824\pi\)
−0.470215 + 0.882552i \(0.655824\pi\)
\(84\) −2.57099e8 −0.563435
\(85\) 3.25494e8 0.676330
\(86\) −2.02857e8 −0.399896
\(87\) −7.45172e7 −0.139450
\(88\) −6.15737e7 −0.109452
\(89\) 9.88909e8 1.67071 0.835355 0.549711i \(-0.185262\pi\)
0.835355 + 0.549711i \(0.185262\pi\)
\(90\) 2.07410e8 0.333225
\(91\) −7.60716e8 −1.16288
\(92\) 6.53204e8 0.950612
\(93\) 8.77972e7 0.121705
\(94\) 1.87229e9 2.47342
\(95\) −8.26384e7 −0.104094
\(96\) 6.89453e8 0.828484
\(97\) −1.09717e9 −1.25835 −0.629177 0.777262i \(-0.716608\pi\)
−0.629177 + 0.777262i \(0.716608\pi\)
\(98\) 3.28271e8 0.359514
\(99\) 1.92368e8 0.201268
\(100\) −5.95440e8 −0.595440
\(101\) −5.16631e8 −0.494008 −0.247004 0.969014i \(-0.579446\pi\)
−0.247004 + 0.969014i \(0.579446\pi\)
\(102\) 9.07130e8 0.829791
\(103\) −6.42155e8 −0.562176 −0.281088 0.959682i \(-0.590695\pi\)
−0.281088 + 0.959682i \(0.590695\pi\)
\(104\) −2.89747e8 −0.242867
\(105\) 4.28086e8 0.343700
\(106\) −1.68152e9 −1.29368
\(107\) 1.44354e9 1.06464 0.532319 0.846544i \(-0.321321\pi\)
0.532319 + 0.846544i \(0.321321\pi\)
\(108\) 3.05938e8 0.216385
\(109\) 1.04267e9 0.707501 0.353751 0.935340i \(-0.384906\pi\)
0.353751 + 0.935340i \(0.384906\pi\)
\(110\) 9.26875e8 0.603607
\(111\) −2.13388e8 −0.133419
\(112\) 1.24325e9 0.746579
\(113\) 2.39521e9 1.38194 0.690971 0.722882i \(-0.257183\pi\)
0.690971 + 0.722882i \(0.257183\pi\)
\(114\) −2.30307e8 −0.127713
\(115\) −1.08762e9 −0.579881
\(116\) −5.29603e8 −0.271575
\(117\) 9.05224e8 0.446601
\(118\) 3.99630e8 0.189753
\(119\) 1.87228e9 0.855873
\(120\) 1.63053e8 0.0717814
\(121\) −1.49829e9 −0.635423
\(122\) 3.00579e9 1.22840
\(123\) 7.55831e8 0.297750
\(124\) 6.23986e8 0.237016
\(125\) 2.86359e9 1.04910
\(126\) 1.19304e9 0.421686
\(127\) 7.45551e8 0.254308 0.127154 0.991883i \(-0.459416\pi\)
0.127154 + 0.991883i \(0.459416\pi\)
\(128\) 1.09253e9 0.359738
\(129\) 4.98225e8 0.158406
\(130\) 4.36159e9 1.33937
\(131\) 6.45907e9 1.91624 0.958118 0.286374i \(-0.0924500\pi\)
0.958118 + 0.286374i \(0.0924500\pi\)
\(132\) 1.36718e9 0.391961
\(133\) −4.75345e8 −0.131728
\(134\) 3.29121e9 0.881827
\(135\) −5.09406e8 −0.131997
\(136\) 7.13128e8 0.178749
\(137\) 3.91437e9 0.949336 0.474668 0.880165i \(-0.342568\pi\)
0.474668 + 0.880165i \(0.342568\pi\)
\(138\) −3.03113e9 −0.711457
\(139\) 1.24731e9 0.283405 0.141703 0.989909i \(-0.454742\pi\)
0.141703 + 0.989909i \(0.454742\pi\)
\(140\) 3.04246e9 0.669343
\(141\) −4.59841e9 −0.979765
\(142\) −3.94782e9 −0.814817
\(143\) 4.04527e9 0.808976
\(144\) −1.47942e9 −0.286721
\(145\) 8.81822e8 0.165663
\(146\) 2.06372e8 0.0375892
\(147\) −8.06246e8 −0.142410
\(148\) −1.51658e9 −0.259829
\(149\) −7.28493e9 −1.21084 −0.605421 0.795906i \(-0.706995\pi\)
−0.605421 + 0.795906i \(0.706995\pi\)
\(150\) 2.76308e9 0.445639
\(151\) 1.64429e9 0.257384 0.128692 0.991685i \(-0.458922\pi\)
0.128692 + 0.991685i \(0.458922\pi\)
\(152\) −1.81053e8 −0.0275112
\(153\) −2.22794e9 −0.328695
\(154\) 5.33149e9 0.763845
\(155\) −1.03897e9 −0.144581
\(156\) 6.43354e9 0.869740
\(157\) 6.59444e9 0.866222 0.433111 0.901341i \(-0.357416\pi\)
0.433111 + 0.901341i \(0.357416\pi\)
\(158\) 8.90775e9 1.13713
\(159\) 4.12988e9 0.512448
\(160\) −8.15885e9 −0.984213
\(161\) −6.25614e9 −0.733820
\(162\) −1.41968e9 −0.161947
\(163\) 7.39202e9 0.820199 0.410099 0.912041i \(-0.365494\pi\)
0.410099 + 0.912041i \(0.365494\pi\)
\(164\) 5.37178e9 0.579857
\(165\) −2.27644e9 −0.239099
\(166\) 1.34100e10 1.37070
\(167\) 2.40304e9 0.239076 0.119538 0.992830i \(-0.461859\pi\)
0.119538 + 0.992830i \(0.461859\pi\)
\(168\) 9.37896e8 0.0908371
\(169\) 8.43133e9 0.795071
\(170\) −1.07348e10 −0.985765
\(171\) 5.65643e8 0.0505895
\(172\) 3.54095e9 0.308490
\(173\) 7.67071e9 0.651071 0.325535 0.945530i \(-0.394455\pi\)
0.325535 + 0.945530i \(0.394455\pi\)
\(174\) 2.45757e9 0.203252
\(175\) 5.70290e9 0.459647
\(176\) −6.61124e9 −0.519369
\(177\) −9.81506e8 −0.0751646
\(178\) −3.26142e10 −2.43510
\(179\) 1.22387e10 0.891037 0.445519 0.895273i \(-0.353019\pi\)
0.445519 + 0.895273i \(0.353019\pi\)
\(180\) −3.62041e9 −0.257059
\(181\) 2.05532e10 1.42339 0.711697 0.702487i \(-0.247927\pi\)
0.711697 + 0.702487i \(0.247927\pi\)
\(182\) 2.50884e10 1.69493
\(183\) −7.38234e9 −0.486591
\(184\) −2.38289e9 −0.153258
\(185\) 2.52520e9 0.158497
\(186\) −2.89555e9 −0.177387
\(187\) −9.95626e9 −0.595400
\(188\) −3.26815e10 −1.90806
\(189\) −2.93016e9 −0.167037
\(190\) 2.72541e9 0.151719
\(191\) −8.98521e8 −0.0488515 −0.0244257 0.999702i \(-0.507776\pi\)
−0.0244257 + 0.999702i \(0.507776\pi\)
\(192\) −1.33868e10 −0.710919
\(193\) −1.81123e10 −0.939648 −0.469824 0.882760i \(-0.655683\pi\)
−0.469824 + 0.882760i \(0.655683\pi\)
\(194\) 3.61847e10 1.83408
\(195\) −1.07122e10 −0.530548
\(196\) −5.73009e9 −0.277338
\(197\) 6.57831e9 0.311183 0.155592 0.987821i \(-0.450272\pi\)
0.155592 + 0.987821i \(0.450272\pi\)
\(198\) −6.34428e9 −0.293352
\(199\) 4.97840e9 0.225035 0.112518 0.993650i \(-0.464109\pi\)
0.112518 + 0.993650i \(0.464109\pi\)
\(200\) 2.17216e9 0.0959970
\(201\) −8.08333e9 −0.349307
\(202\) 1.70385e10 0.720028
\(203\) 5.07233e9 0.209641
\(204\) −1.58343e10 −0.640122
\(205\) −8.94435e9 −0.353717
\(206\) 2.11783e10 0.819384
\(207\) 7.44457e9 0.281821
\(208\) −3.11105e10 −1.15245
\(209\) 2.52775e9 0.0916381
\(210\) −1.41182e10 −0.500950
\(211\) 6.78868e9 0.235784 0.117892 0.993026i \(-0.462386\pi\)
0.117892 + 0.993026i \(0.462386\pi\)
\(212\) 2.93516e10 0.997975
\(213\) 9.69600e9 0.322764
\(214\) −4.76079e10 −1.55173
\(215\) −5.89589e9 −0.188181
\(216\) −1.11606e9 −0.0348856
\(217\) −5.97630e9 −0.182963
\(218\) −3.43872e10 −1.03120
\(219\) −5.06858e8 −0.0148898
\(220\) −1.61789e10 −0.465638
\(221\) −4.68512e10 −1.32116
\(222\) 7.03754e9 0.194461
\(223\) 5.46776e10 1.48060 0.740299 0.672278i \(-0.234684\pi\)
0.740299 + 0.672278i \(0.234684\pi\)
\(224\) −4.69306e10 −1.24549
\(225\) −6.78624e9 −0.176526
\(226\) −7.89938e10 −2.01421
\(227\) 7.36629e8 0.0184133 0.00920666 0.999958i \(-0.497069\pi\)
0.00920666 + 0.999958i \(0.497069\pi\)
\(228\) 4.02010e9 0.0985212
\(229\) 1.70607e10 0.409955 0.204978 0.978767i \(-0.434288\pi\)
0.204978 + 0.978767i \(0.434288\pi\)
\(230\) 3.58698e10 0.845189
\(231\) −1.30943e10 −0.302573
\(232\) 1.93199e9 0.0437833
\(233\) −1.08113e10 −0.240311 −0.120156 0.992755i \(-0.538339\pi\)
−0.120156 + 0.992755i \(0.538339\pi\)
\(234\) −2.98542e10 −0.650931
\(235\) 5.44167e10 1.16393
\(236\) −6.97569e9 −0.146380
\(237\) −2.18778e10 −0.450438
\(238\) −6.17477e10 −1.24745
\(239\) 2.27031e10 0.450085 0.225043 0.974349i \(-0.427748\pi\)
0.225043 + 0.974349i \(0.427748\pi\)
\(240\) 1.75071e10 0.340615
\(241\) −4.42553e10 −0.845062 −0.422531 0.906348i \(-0.638858\pi\)
−0.422531 + 0.906348i \(0.638858\pi\)
\(242\) 4.94136e10 0.926142
\(243\) 3.48678e9 0.0641500
\(244\) −5.24672e10 −0.947619
\(245\) 9.54096e9 0.169178
\(246\) −2.49273e10 −0.433977
\(247\) 1.18948e10 0.203340
\(248\) −2.27630e9 −0.0382117
\(249\) −3.29354e10 −0.542958
\(250\) −9.44410e10 −1.52908
\(251\) −1.28595e10 −0.204499 −0.102250 0.994759i \(-0.532604\pi\)
−0.102250 + 0.994759i \(0.532604\pi\)
\(252\) −2.08250e10 −0.325299
\(253\) 3.32684e10 0.510493
\(254\) −2.45882e10 −0.370660
\(255\) 2.63651e10 0.390479
\(256\) 4.85861e10 0.707021
\(257\) 1.16625e11 1.66760 0.833800 0.552067i \(-0.186161\pi\)
0.833800 + 0.552067i \(0.186161\pi\)
\(258\) −1.64314e10 −0.230880
\(259\) 1.45252e10 0.200573
\(260\) −7.61332e10 −1.03322
\(261\) −6.03589e9 −0.0805117
\(262\) −2.13020e11 −2.79296
\(263\) 5.05137e10 0.651041 0.325520 0.945535i \(-0.394460\pi\)
0.325520 + 0.945535i \(0.394460\pi\)
\(264\) −4.98747e9 −0.0631921
\(265\) −4.88722e10 −0.608773
\(266\) 1.56769e10 0.191996
\(267\) 8.01016e10 0.964585
\(268\) −5.74492e10 −0.680264
\(269\) 9.77449e10 1.13817 0.569087 0.822277i \(-0.307297\pi\)
0.569087 + 0.822277i \(0.307297\pi\)
\(270\) 1.68002e10 0.192388
\(271\) −1.23145e10 −0.138693 −0.0693463 0.997593i \(-0.522091\pi\)
−0.0693463 + 0.997593i \(0.522091\pi\)
\(272\) 7.65693e10 0.848193
\(273\) −6.16180e10 −0.671391
\(274\) −1.29096e11 −1.38368
\(275\) −3.03264e10 −0.319760
\(276\) 5.29095e10 0.548836
\(277\) 3.89075e10 0.397077 0.198538 0.980093i \(-0.436381\pi\)
0.198538 + 0.980093i \(0.436381\pi\)
\(278\) −4.11362e10 −0.413069
\(279\) 7.11157e9 0.0702662
\(280\) −1.10989e10 −0.107912
\(281\) 1.86749e11 1.78682 0.893409 0.449244i \(-0.148307\pi\)
0.893409 + 0.449244i \(0.148307\pi\)
\(282\) 1.51655e11 1.42803
\(283\) −4.26909e9 −0.0395637 −0.0197818 0.999804i \(-0.506297\pi\)
−0.0197818 + 0.999804i \(0.506297\pi\)
\(284\) 6.89107e10 0.628571
\(285\) −6.69371e9 −0.0600987
\(286\) −1.33413e11 −1.17910
\(287\) −5.14489e10 −0.447618
\(288\) 5.58457e10 0.478326
\(289\) −3.27743e9 −0.0276372
\(290\) −2.90824e10 −0.241457
\(291\) −8.88711e10 −0.726511
\(292\) −3.60230e9 −0.0289973
\(293\) 2.26975e11 1.79918 0.899590 0.436735i \(-0.143865\pi\)
0.899590 + 0.436735i \(0.143865\pi\)
\(294\) 2.65900e10 0.207565
\(295\) 1.16150e10 0.0892932
\(296\) 5.53247e9 0.0418896
\(297\) 1.55818e10 0.116202
\(298\) 2.40257e11 1.76483
\(299\) 1.56551e11 1.13275
\(300\) −4.82306e10 −0.343777
\(301\) −3.39138e10 −0.238137
\(302\) −5.42285e10 −0.375143
\(303\) −4.18471e10 −0.285216
\(304\) −1.94399e10 −0.130546
\(305\) 8.73612e10 0.578055
\(306\) 7.34775e10 0.479080
\(307\) 3.32209e10 0.213446 0.106723 0.994289i \(-0.465964\pi\)
0.106723 + 0.994289i \(0.465964\pi\)
\(308\) −9.30631e10 −0.589249
\(309\) −5.20146e10 −0.324573
\(310\) 3.42653e10 0.210730
\(311\) −1.65167e10 −0.100115 −0.0500577 0.998746i \(-0.515941\pi\)
−0.0500577 + 0.998746i \(0.515941\pi\)
\(312\) −2.34695e10 −0.140220
\(313\) 8.71957e10 0.513506 0.256753 0.966477i \(-0.417347\pi\)
0.256753 + 0.966477i \(0.417347\pi\)
\(314\) −2.17484e11 −1.26254
\(315\) 3.46749e10 0.198435
\(316\) −1.55488e11 −0.877213
\(317\) −1.00209e11 −0.557368 −0.278684 0.960383i \(-0.589898\pi\)
−0.278684 + 0.960383i \(0.589898\pi\)
\(318\) −1.36203e11 −0.746905
\(319\) −2.69733e10 −0.145840
\(320\) 1.58416e11 0.844549
\(321\) 1.16927e11 0.614669
\(322\) 2.06327e11 1.06956
\(323\) −2.92757e10 −0.149656
\(324\) 2.47810e10 0.124930
\(325\) −1.42707e11 −0.709529
\(326\) −2.43789e11 −1.19546
\(327\) 8.44562e10 0.408476
\(328\) −1.95962e10 −0.0934847
\(329\) 3.13011e11 1.47292
\(330\) 7.50769e10 0.348493
\(331\) −2.47186e11 −1.13187 −0.565936 0.824449i \(-0.691485\pi\)
−0.565936 + 0.824449i \(0.691485\pi\)
\(332\) −2.34076e11 −1.05739
\(333\) −1.72845e10 −0.0770294
\(334\) −7.92520e10 −0.348459
\(335\) 9.56565e10 0.414966
\(336\) 1.00703e11 0.431038
\(337\) −7.13003e10 −0.301132 −0.150566 0.988600i \(-0.548110\pi\)
−0.150566 + 0.988600i \(0.548110\pi\)
\(338\) −2.78065e11 −1.15883
\(339\) 1.94012e11 0.797865
\(340\) 1.87380e11 0.760444
\(341\) 3.17803e10 0.127281
\(342\) −1.86549e10 −0.0737352
\(343\) 2.77375e11 1.08204
\(344\) −1.29174e10 −0.0497348
\(345\) −8.80976e10 −0.334794
\(346\) −2.52980e11 −0.948950
\(347\) −3.59303e11 −1.33039 −0.665194 0.746670i \(-0.731651\pi\)
−0.665194 + 0.746670i \(0.731651\pi\)
\(348\) −4.28978e10 −0.156794
\(349\) −1.90779e11 −0.688360 −0.344180 0.938904i \(-0.611843\pi\)
−0.344180 + 0.938904i \(0.611843\pi\)
\(350\) −1.88081e11 −0.669945
\(351\) 7.33231e10 0.257845
\(352\) 2.49564e11 0.866443
\(353\) 1.88170e11 0.645005 0.322503 0.946569i \(-0.395476\pi\)
0.322503 + 0.946569i \(0.395476\pi\)
\(354\) 3.23700e10 0.109554
\(355\) −1.14741e11 −0.383433
\(356\) 5.69292e11 1.87850
\(357\) 1.51655e11 0.494139
\(358\) −4.03631e11 −1.29871
\(359\) −4.34117e10 −0.137937 −0.0689686 0.997619i \(-0.521971\pi\)
−0.0689686 + 0.997619i \(0.521971\pi\)
\(360\) 1.32073e10 0.0414430
\(361\) −3.15255e11 −0.976966
\(362\) −6.77842e11 −2.07463
\(363\) −1.21362e11 −0.366861
\(364\) −4.37927e11 −1.30751
\(365\) 5.99805e9 0.0176886
\(366\) 2.43469e11 0.709217
\(367\) −3.73765e11 −1.07548 −0.537739 0.843112i \(-0.680721\pi\)
−0.537739 + 0.843112i \(0.680721\pi\)
\(368\) −2.55853e11 −0.727236
\(369\) 6.12223e10 0.171906
\(370\) −8.32808e10 −0.231013
\(371\) −2.81118e11 −0.770382
\(372\) 5.05428e10 0.136841
\(373\) 2.34265e11 0.626640 0.313320 0.949648i \(-0.398559\pi\)
0.313320 + 0.949648i \(0.398559\pi\)
\(374\) 3.28357e11 0.867809
\(375\) 2.31951e11 0.605696
\(376\) 1.19222e11 0.307617
\(377\) −1.26928e11 −0.323609
\(378\) 9.66366e10 0.243460
\(379\) 5.95023e11 1.48135 0.740675 0.671864i \(-0.234506\pi\)
0.740675 + 0.671864i \(0.234506\pi\)
\(380\) −4.75730e10 −0.117040
\(381\) 6.03897e10 0.146825
\(382\) 2.96332e10 0.0712021
\(383\) −4.69626e11 −1.11521 −0.557606 0.830105i \(-0.688280\pi\)
−0.557606 + 0.830105i \(0.688280\pi\)
\(384\) 8.84945e10 0.207695
\(385\) 1.54956e11 0.359447
\(386\) 5.97342e11 1.36956
\(387\) 4.03562e10 0.0914557
\(388\) −6.31618e11 −1.41485
\(389\) −3.91024e11 −0.865826 −0.432913 0.901436i \(-0.642514\pi\)
−0.432913 + 0.901436i \(0.642514\pi\)
\(390\) 3.53289e11 0.773285
\(391\) −3.85305e11 −0.833698
\(392\) 2.09034e10 0.0447125
\(393\) 5.23184e11 1.10634
\(394\) −2.16952e11 −0.453556
\(395\) 2.58897e11 0.535107
\(396\) 1.10742e11 0.226299
\(397\) 1.93489e11 0.390929 0.195465 0.980711i \(-0.437379\pi\)
0.195465 + 0.980711i \(0.437379\pi\)
\(398\) −1.64187e11 −0.327994
\(399\) −3.85029e10 −0.0760529
\(400\) 2.33227e11 0.455522
\(401\) −7.18517e11 −1.38767 −0.693837 0.720132i \(-0.744081\pi\)
−0.693837 + 0.720132i \(0.744081\pi\)
\(402\) 2.66588e11 0.509123
\(403\) 1.49548e11 0.282429
\(404\) −2.97413e11 −0.555448
\(405\) −4.12619e10 −0.0762082
\(406\) −1.67285e11 −0.305556
\(407\) −7.72410e10 −0.139532
\(408\) 5.77634e10 0.103201
\(409\) 3.48286e11 0.615433 0.307716 0.951478i \(-0.400435\pi\)
0.307716 + 0.951478i \(0.400435\pi\)
\(410\) 2.94984e11 0.515551
\(411\) 3.17064e11 0.548099
\(412\) −3.69674e11 −0.632094
\(413\) 6.68105e10 0.112998
\(414\) −2.45522e11 −0.410760
\(415\) 3.89751e11 0.645017
\(416\) 1.17437e12 1.92259
\(417\) 1.01032e11 0.163624
\(418\) −8.33651e10 −0.133565
\(419\) 7.27209e11 1.15265 0.576323 0.817222i \(-0.304487\pi\)
0.576323 + 0.817222i \(0.304487\pi\)
\(420\) 2.46439e11 0.386445
\(421\) −3.29826e11 −0.511700 −0.255850 0.966716i \(-0.582355\pi\)
−0.255850 + 0.966716i \(0.582355\pi\)
\(422\) −2.23890e11 −0.343660
\(423\) −3.72471e11 −0.565668
\(424\) −1.07074e11 −0.160894
\(425\) 3.51231e11 0.522208
\(426\) −3.19774e11 −0.470435
\(427\) 5.02511e11 0.731510
\(428\) 8.31013e11 1.19705
\(429\) 3.27667e11 0.467063
\(430\) 1.94446e11 0.274278
\(431\) −3.37955e11 −0.471749 −0.235874 0.971784i \(-0.575795\pi\)
−0.235874 + 0.971784i \(0.575795\pi\)
\(432\) −1.19833e11 −0.165538
\(433\) −2.67392e11 −0.365554 −0.182777 0.983154i \(-0.558509\pi\)
−0.182777 + 0.983154i \(0.558509\pi\)
\(434\) 1.97098e11 0.266673
\(435\) 7.14275e10 0.0956454
\(436\) 6.00241e11 0.795493
\(437\) 9.78233e10 0.128315
\(438\) 1.67161e10 0.0217021
\(439\) 2.73505e11 0.351460 0.175730 0.984438i \(-0.443771\pi\)
0.175730 + 0.984438i \(0.443771\pi\)
\(440\) 5.90207e10 0.0750702
\(441\) −6.53059e10 −0.0822203
\(442\) 1.54515e12 1.92562
\(443\) 9.56113e11 1.17949 0.589743 0.807591i \(-0.299229\pi\)
0.589743 + 0.807591i \(0.299229\pi\)
\(444\) −1.22843e11 −0.150012
\(445\) −9.47906e11 −1.14590
\(446\) −1.80326e12 −2.15800
\(447\) −5.90080e11 −0.699080
\(448\) 9.11228e11 1.06875
\(449\) −5.34222e11 −0.620317 −0.310158 0.950685i \(-0.600382\pi\)
−0.310158 + 0.950685i \(0.600382\pi\)
\(450\) 2.23810e11 0.257290
\(451\) 2.73591e11 0.311392
\(452\) 1.37887e12 1.55381
\(453\) 1.33187e11 0.148601
\(454\) −2.42940e10 −0.0268378
\(455\) 7.29175e11 0.797591
\(456\) −1.46653e10 −0.0158836
\(457\) 1.04929e12 1.12531 0.562655 0.826692i \(-0.309780\pi\)
0.562655 + 0.826692i \(0.309780\pi\)
\(458\) −5.62660e11 −0.597518
\(459\) −1.80464e11 −0.189772
\(460\) −6.26121e11 −0.652000
\(461\) 1.19364e12 1.23089 0.615446 0.788179i \(-0.288976\pi\)
0.615446 + 0.788179i \(0.288976\pi\)
\(462\) 4.31851e11 0.441006
\(463\) −1.18352e12 −1.19691 −0.598453 0.801158i \(-0.704218\pi\)
−0.598453 + 0.801158i \(0.704218\pi\)
\(464\) 2.07440e11 0.207760
\(465\) −8.41569e10 −0.0834741
\(466\) 3.56555e11 0.350259
\(467\) −2.71301e11 −0.263952 −0.131976 0.991253i \(-0.542132\pi\)
−0.131976 + 0.991253i \(0.542132\pi\)
\(468\) 5.21117e11 0.502144
\(469\) 5.50227e11 0.525126
\(470\) −1.79466e12 −1.69645
\(471\) 5.34149e11 0.500113
\(472\) 2.54473e10 0.0235995
\(473\) 1.80344e11 0.165664
\(474\) 7.21528e11 0.656524
\(475\) −8.91726e10 −0.0803730
\(476\) 1.07783e12 0.962318
\(477\) 3.34520e11 0.295862
\(478\) −7.48747e11 −0.656009
\(479\) −1.66233e12 −1.44280 −0.721400 0.692519i \(-0.756501\pi\)
−0.721400 + 0.692519i \(0.756501\pi\)
\(480\) −6.60867e11 −0.568236
\(481\) −3.63473e11 −0.309613
\(482\) 1.45954e12 1.23170
\(483\) −5.06747e11 −0.423671
\(484\) −8.62533e11 −0.714450
\(485\) 1.05168e12 0.863072
\(486\) −1.14994e11 −0.0935001
\(487\) 1.70962e12 1.37727 0.688635 0.725108i \(-0.258210\pi\)
0.688635 + 0.725108i \(0.258210\pi\)
\(488\) 1.91400e11 0.152775
\(489\) 5.98754e11 0.473542
\(490\) −3.14660e11 −0.246581
\(491\) −1.66144e12 −1.29008 −0.645041 0.764148i \(-0.723160\pi\)
−0.645041 + 0.764148i \(0.723160\pi\)
\(492\) 4.35115e11 0.334781
\(493\) 3.12396e11 0.238174
\(494\) −3.92291e11 −0.296372
\(495\) −1.84392e11 −0.138044
\(496\) −2.44408e11 −0.181321
\(497\) −6.60000e11 −0.485222
\(498\) 1.08621e12 0.791373
\(499\) 2.04870e12 1.47920 0.739598 0.673049i \(-0.235016\pi\)
0.739598 + 0.673049i \(0.235016\pi\)
\(500\) 1.64850e12 1.17957
\(501\) 1.94646e11 0.138031
\(502\) 4.24105e11 0.298062
\(503\) −2.20450e12 −1.53552 −0.767759 0.640739i \(-0.778628\pi\)
−0.767759 + 0.640739i \(0.778628\pi\)
\(504\) 7.59696e10 0.0524448
\(505\) 4.95210e11 0.338827
\(506\) −1.09719e12 −0.744054
\(507\) 6.82938e11 0.459035
\(508\) 4.29197e11 0.285937
\(509\) 1.04417e12 0.689511 0.344756 0.938692i \(-0.387962\pi\)
0.344756 + 0.938692i \(0.387962\pi\)
\(510\) −8.69518e11 −0.569132
\(511\) 3.45015e10 0.0223843
\(512\) −2.16174e12 −1.39024
\(513\) 4.58171e10 0.0292078
\(514\) −3.84628e12 −2.43056
\(515\) 6.15530e11 0.385582
\(516\) 2.86817e11 0.178107
\(517\) −1.66450e12 −1.02465
\(518\) −4.79040e11 −0.292340
\(519\) 6.21328e11 0.375896
\(520\) 2.77734e11 0.166576
\(521\) −1.07856e12 −0.641318 −0.320659 0.947195i \(-0.603904\pi\)
−0.320659 + 0.947195i \(0.603904\pi\)
\(522\) 1.99063e11 0.117348
\(523\) −1.13837e12 −0.665315 −0.332657 0.943048i \(-0.607945\pi\)
−0.332657 + 0.943048i \(0.607945\pi\)
\(524\) 3.71834e12 2.15456
\(525\) 4.61935e11 0.265377
\(526\) −1.66594e12 −0.948906
\(527\) −3.68070e11 −0.207865
\(528\) −5.35510e11 −0.299858
\(529\) −5.13676e11 −0.285193
\(530\) 1.61180e12 0.887299
\(531\) −7.95020e10 −0.0433963
\(532\) −2.73645e11 −0.148110
\(533\) 1.28744e12 0.690960
\(534\) −2.64175e12 −1.40590
\(535\) −1.38369e12 −0.730207
\(536\) 2.09575e11 0.109672
\(537\) 9.91333e11 0.514441
\(538\) −3.22362e12 −1.65891
\(539\) −2.91840e11 −0.148934
\(540\) −2.93254e11 −0.148413
\(541\) 7.84035e11 0.393503 0.196751 0.980453i \(-0.436961\pi\)
0.196751 + 0.980453i \(0.436961\pi\)
\(542\) 4.06130e11 0.202148
\(543\) 1.66481e12 0.821797
\(544\) −2.89037e12 −1.41501
\(545\) −9.99438e11 −0.485257
\(546\) 2.03216e12 0.978567
\(547\) 2.01623e12 0.962934 0.481467 0.876464i \(-0.340104\pi\)
0.481467 + 0.876464i \(0.340104\pi\)
\(548\) 2.25342e12 1.06740
\(549\) −5.97970e11 −0.280934
\(550\) 1.00016e12 0.466057
\(551\) −7.93129e10 −0.0366574
\(552\) −1.93014e11 −0.0884835
\(553\) 1.48920e12 0.677160
\(554\) −1.28317e12 −0.578748
\(555\) 2.04541e11 0.0915086
\(556\) 7.18048e11 0.318652
\(557\) 1.98586e12 0.874180 0.437090 0.899418i \(-0.356009\pi\)
0.437090 + 0.899418i \(0.356009\pi\)
\(558\) −2.34539e11 −0.102415
\(559\) 8.48645e11 0.367598
\(560\) −1.19170e12 −0.512059
\(561\) −8.06457e11 −0.343755
\(562\) −6.15898e12 −2.60433
\(563\) −6.20064e11 −0.260105 −0.130053 0.991507i \(-0.541515\pi\)
−0.130053 + 0.991507i \(0.541515\pi\)
\(564\) −2.64720e12 −1.10162
\(565\) −2.29590e12 −0.947838
\(566\) 1.40794e11 0.0576649
\(567\) −2.37343e11 −0.0964390
\(568\) −2.51386e11 −0.101338
\(569\) 4.37693e12 1.75051 0.875255 0.483662i \(-0.160693\pi\)
0.875255 + 0.483662i \(0.160693\pi\)
\(570\) 2.20758e11 0.0875951
\(571\) 2.44447e12 0.962325 0.481162 0.876631i \(-0.340215\pi\)
0.481162 + 0.876631i \(0.340215\pi\)
\(572\) 2.32877e12 0.909588
\(573\) −7.27802e10 −0.0282044
\(574\) 1.69678e12 0.652413
\(575\) −1.17362e12 −0.447738
\(576\) −1.08433e12 −0.410449
\(577\) −2.44903e12 −0.919819 −0.459910 0.887966i \(-0.652118\pi\)
−0.459910 + 0.887966i \(0.652118\pi\)
\(578\) 1.08090e11 0.0402818
\(579\) −1.46710e12 −0.542506
\(580\) 5.07644e11 0.186266
\(581\) 2.24189e12 0.816248
\(582\) 2.93096e12 1.05890
\(583\) 1.49491e12 0.535927
\(584\) 1.31412e10 0.00467494
\(585\) −8.67691e11 −0.306312
\(586\) −7.48564e12 −2.62234
\(587\) 4.47127e12 1.55439 0.777195 0.629260i \(-0.216642\pi\)
0.777195 + 0.629260i \(0.216642\pi\)
\(588\) −4.64137e11 −0.160121
\(589\) 9.34476e10 0.0319926
\(590\) −3.83060e11 −0.130147
\(591\) 5.32843e11 0.179662
\(592\) 5.94027e11 0.198774
\(593\) −6.41097e11 −0.212901 −0.106450 0.994318i \(-0.533949\pi\)
−0.106450 + 0.994318i \(0.533949\pi\)
\(594\) −5.13886e11 −0.169367
\(595\) −1.79465e12 −0.587021
\(596\) −4.19377e12 −1.36143
\(597\) 4.03250e11 0.129924
\(598\) −5.16304e12 −1.65101
\(599\) −2.76079e12 −0.876221 −0.438110 0.898921i \(-0.644352\pi\)
−0.438110 + 0.898921i \(0.644352\pi\)
\(600\) 1.75945e11 0.0554239
\(601\) −8.81619e11 −0.275642 −0.137821 0.990457i \(-0.544010\pi\)
−0.137821 + 0.990457i \(0.544010\pi\)
\(602\) 1.11848e12 0.347090
\(603\) −6.54750e11 −0.201673
\(604\) 9.46579e11 0.289395
\(605\) 1.43617e12 0.435820
\(606\) 1.38011e12 0.415708
\(607\) −1.37826e12 −0.412080 −0.206040 0.978544i \(-0.566058\pi\)
−0.206040 + 0.978544i \(0.566058\pi\)
\(608\) 7.33825e11 0.217784
\(609\) 4.10859e11 0.121036
\(610\) −2.88117e12 −0.842528
\(611\) −7.83265e12 −2.27365
\(612\) −1.28258e12 −0.369574
\(613\) 4.20522e12 1.20287 0.601433 0.798924i \(-0.294597\pi\)
0.601433 + 0.798924i \(0.294597\pi\)
\(614\) −1.09562e12 −0.311102
\(615\) −7.24493e11 −0.204219
\(616\) 3.39494e11 0.0949989
\(617\) 1.72073e12 0.478002 0.239001 0.971019i \(-0.423180\pi\)
0.239001 + 0.971019i \(0.423180\pi\)
\(618\) 1.71544e12 0.473072
\(619\) 2.41835e12 0.662081 0.331040 0.943617i \(-0.392600\pi\)
0.331040 + 0.943617i \(0.392600\pi\)
\(620\) −5.98114e11 −0.162563
\(621\) 6.03010e11 0.162709
\(622\) 5.44719e11 0.145920
\(623\) −5.45246e12 −1.45009
\(624\) −2.51995e12 −0.665367
\(625\) −7.24683e11 −0.189971
\(626\) −2.87571e12 −0.748446
\(627\) 2.04748e11 0.0529073
\(628\) 3.79627e12 0.973953
\(629\) 8.94582e11 0.227873
\(630\) −1.14358e12 −0.289223
\(631\) −5.20973e12 −1.30823 −0.654113 0.756397i \(-0.726958\pi\)
−0.654113 + 0.756397i \(0.726958\pi\)
\(632\) 5.67220e11 0.141424
\(633\) 5.49883e11 0.136130
\(634\) 3.30490e12 0.812376
\(635\) −7.14639e11 −0.174424
\(636\) 2.37748e12 0.576181
\(637\) −1.37331e12 −0.330477
\(638\) 8.89577e11 0.212564
\(639\) 7.85376e11 0.186348
\(640\) −1.04723e12 −0.246735
\(641\) −6.57069e12 −1.53727 −0.768635 0.639688i \(-0.779063\pi\)
−0.768635 + 0.639688i \(0.779063\pi\)
\(642\) −3.85624e12 −0.895893
\(643\) −5.46128e12 −1.25993 −0.629963 0.776625i \(-0.716930\pi\)
−0.629963 + 0.776625i \(0.716930\pi\)
\(644\) −3.60151e12 −0.825085
\(645\) −4.77567e11 −0.108647
\(646\) 9.65510e11 0.218128
\(647\) 1.58624e12 0.355876 0.177938 0.984042i \(-0.443057\pi\)
0.177938 + 0.984042i \(0.443057\pi\)
\(648\) −9.04010e10 −0.0201412
\(649\) −3.55279e11 −0.0786084
\(650\) 4.70647e12 1.03415
\(651\) −4.84080e11 −0.105634
\(652\) 4.25542e12 0.922207
\(653\) 2.41513e11 0.0519793 0.0259897 0.999662i \(-0.491726\pi\)
0.0259897 + 0.999662i \(0.491726\pi\)
\(654\) −2.78536e12 −0.595363
\(655\) −6.19126e12 −1.31430
\(656\) −2.10407e12 −0.443601
\(657\) −4.10555e10 −0.00859660
\(658\) −1.03231e13 −2.14681
\(659\) 2.47059e12 0.510290 0.255145 0.966903i \(-0.417877\pi\)
0.255145 + 0.966903i \(0.417877\pi\)
\(660\) −1.31049e12 −0.268836
\(661\) 2.40593e12 0.490204 0.245102 0.969497i \(-0.421179\pi\)
0.245102 + 0.969497i \(0.421179\pi\)
\(662\) 8.15217e12 1.64973
\(663\) −3.79494e12 −0.762771
\(664\) 8.53909e11 0.170473
\(665\) 4.55636e11 0.0903485
\(666\) 5.70041e11 0.112272
\(667\) −1.04386e12 −0.204209
\(668\) 1.38337e12 0.268810
\(669\) 4.42888e12 0.854824
\(670\) −3.15475e12 −0.604822
\(671\) −2.67221e12 −0.508885
\(672\) −3.80138e12 −0.719084
\(673\) −4.41273e12 −0.829163 −0.414581 0.910012i \(-0.636072\pi\)
−0.414581 + 0.910012i \(0.636072\pi\)
\(674\) 2.35148e12 0.438906
\(675\) −5.49685e11 −0.101917
\(676\) 4.85373e12 0.893954
\(677\) −1.62377e12 −0.297081 −0.148541 0.988906i \(-0.547458\pi\)
−0.148541 + 0.988906i \(0.547458\pi\)
\(678\) −6.39850e12 −1.16291
\(679\) 6.04939e12 1.09219
\(680\) −6.83561e11 −0.122599
\(681\) 5.96669e10 0.0106309
\(682\) −1.04811e12 −0.185515
\(683\) 9.25217e12 1.62686 0.813431 0.581662i \(-0.197597\pi\)
0.813431 + 0.581662i \(0.197597\pi\)
\(684\) 3.25628e11 0.0568812
\(685\) −3.75208e12 −0.651125
\(686\) −9.14781e12 −1.57710
\(687\) 1.38191e12 0.236688
\(688\) −1.38695e12 −0.236001
\(689\) 7.03458e12 1.18919
\(690\) 2.90545e12 0.487970
\(691\) 5.15435e11 0.0860048 0.0430024 0.999075i \(-0.486308\pi\)
0.0430024 + 0.999075i \(0.486308\pi\)
\(692\) 4.41585e12 0.732044
\(693\) −1.06064e12 −0.174690
\(694\) 1.18498e13 1.93907
\(695\) −1.19559e12 −0.194380
\(696\) 1.56491e11 0.0252783
\(697\) −3.16865e12 −0.508541
\(698\) 6.29188e12 1.00330
\(699\) −8.75712e11 −0.138744
\(700\) 3.28303e12 0.516813
\(701\) 3.50104e12 0.547603 0.273802 0.961786i \(-0.411719\pi\)
0.273802 + 0.961786i \(0.411719\pi\)
\(702\) −2.41819e12 −0.375815
\(703\) −2.27122e11 −0.0350719
\(704\) −4.84565e12 −0.743491
\(705\) 4.40775e12 0.671995
\(706\) −6.20582e12 −0.940109
\(707\) 2.84850e12 0.428775
\(708\) −5.65031e11 −0.0845128
\(709\) 1.99580e12 0.296625 0.148313 0.988941i \(-0.452616\pi\)
0.148313 + 0.988941i \(0.452616\pi\)
\(710\) 3.78414e12 0.558862
\(711\) −1.77210e12 −0.260061
\(712\) −2.07678e12 −0.302851
\(713\) 1.22989e12 0.178222
\(714\) −5.00156e12 −0.720218
\(715\) −3.87755e12 −0.554856
\(716\) 7.04553e12 1.00186
\(717\) 1.83895e12 0.259857
\(718\) 1.43171e12 0.201046
\(719\) −1.16662e13 −1.62798 −0.813989 0.580880i \(-0.802709\pi\)
−0.813989 + 0.580880i \(0.802709\pi\)
\(720\) 1.41808e12 0.196654
\(721\) 3.54060e12 0.487942
\(722\) 1.03971e13 1.42395
\(723\) −3.58468e12 −0.487897
\(724\) 1.18320e13 1.60042
\(725\) 9.51547e11 0.127911
\(726\) 4.00250e12 0.534708
\(727\) 1.24565e13 1.65383 0.826917 0.562324i \(-0.190093\pi\)
0.826917 + 0.562324i \(0.190093\pi\)
\(728\) 1.59755e12 0.210797
\(729\) 2.82430e11 0.0370370
\(730\) −1.97815e11 −0.0257815
\(731\) −2.08869e12 −0.270549
\(732\) −4.24984e12 −0.547108
\(733\) 9.57896e12 1.22560 0.612802 0.790236i \(-0.290042\pi\)
0.612802 + 0.790236i \(0.290042\pi\)
\(734\) 1.23267e13 1.56753
\(735\) 7.72817e11 0.0976751
\(736\) 9.65805e12 1.21322
\(737\) −2.92595e12 −0.365312
\(738\) −2.01911e12 −0.250557
\(739\) 1.19683e13 1.47616 0.738079 0.674714i \(-0.235733\pi\)
0.738079 + 0.674714i \(0.235733\pi\)
\(740\) 1.45370e12 0.178210
\(741\) 9.63482e11 0.117398
\(742\) 9.27126e12 1.12285
\(743\) 9.42113e12 1.13411 0.567053 0.823681i \(-0.308084\pi\)
0.567053 + 0.823681i \(0.308084\pi\)
\(744\) −1.84380e11 −0.0220615
\(745\) 6.98289e12 0.830485
\(746\) −7.72605e12 −0.913341
\(747\) −2.66777e12 −0.313477
\(748\) −5.73159e12 −0.669450
\(749\) −7.95912e12 −0.924054
\(750\) −7.64972e12 −0.882816
\(751\) 5.24381e12 0.601544 0.300772 0.953696i \(-0.402756\pi\)
0.300772 + 0.953696i \(0.402756\pi\)
\(752\) 1.28010e13 1.45970
\(753\) −1.04162e12 −0.118068
\(754\) 4.18608e12 0.471668
\(755\) −1.57611e12 −0.176533
\(756\) −1.68683e12 −0.187812
\(757\) 1.12096e13 1.24067 0.620337 0.784335i \(-0.286996\pi\)
0.620337 + 0.784335i \(0.286996\pi\)
\(758\) −1.96238e13 −2.15910
\(759\) 2.69474e12 0.294733
\(760\) 1.73546e11 0.0188692
\(761\) 9.44214e12 1.02056 0.510281 0.860008i \(-0.329541\pi\)
0.510281 + 0.860008i \(0.329541\pi\)
\(762\) −1.99165e12 −0.214001
\(763\) −5.74888e12 −0.614077
\(764\) −5.17258e11 −0.0549271
\(765\) 2.13557e12 0.225443
\(766\) 1.54882e13 1.62545
\(767\) −1.67184e12 −0.174427
\(768\) 3.93548e12 0.408199
\(769\) 1.11920e13 1.15409 0.577044 0.816713i \(-0.304206\pi\)
0.577044 + 0.816713i \(0.304206\pi\)
\(770\) −5.11043e12 −0.523901
\(771\) 9.44661e12 0.962789
\(772\) −1.04268e13 −1.05651
\(773\) 1.21128e13 1.22022 0.610109 0.792317i \(-0.291125\pi\)
0.610109 + 0.792317i \(0.291125\pi\)
\(774\) −1.33095e12 −0.133299
\(775\) −1.12113e12 −0.111634
\(776\) 2.30414e12 0.228103
\(777\) 1.17654e12 0.115801
\(778\) 1.28960e13 1.26196
\(779\) 8.04474e11 0.0782697
\(780\) −6.16679e12 −0.596532
\(781\) 3.50970e12 0.337551
\(782\) 1.27073e13 1.21513
\(783\) −4.88907e11 −0.0464835
\(784\) 2.24442e12 0.212169
\(785\) −6.32102e12 −0.594119
\(786\) −1.72546e13 −1.61251
\(787\) −6.46327e11 −0.0600573 −0.0300286 0.999549i \(-0.509560\pi\)
−0.0300286 + 0.999549i \(0.509560\pi\)
\(788\) 3.78698e12 0.349885
\(789\) 4.09161e12 0.375879
\(790\) −8.53842e12 −0.779930
\(791\) −1.32062e13 −1.19946
\(792\) −4.03985e11 −0.0364840
\(793\) −1.25746e13 −1.12919
\(794\) −6.38124e12 −0.569788
\(795\) −3.95864e12 −0.351475
\(796\) 2.86595e12 0.253023
\(797\) 5.88328e12 0.516484 0.258242 0.966080i \(-0.416857\pi\)
0.258242 + 0.966080i \(0.416857\pi\)
\(798\) 1.26983e12 0.110849
\(799\) 1.92778e13 1.67339
\(800\) −8.80398e12 −0.759931
\(801\) 6.48823e12 0.556903
\(802\) 2.36967e13 2.02256
\(803\) −1.83469e11 −0.0155719
\(804\) −4.65339e12 −0.392751
\(805\) 5.99674e12 0.503308
\(806\) −4.93210e12 −0.411646
\(807\) 7.91734e12 0.657125
\(808\) 1.08496e12 0.0895494
\(809\) −1.11236e13 −0.913012 −0.456506 0.889720i \(-0.650899\pi\)
−0.456506 + 0.889720i \(0.650899\pi\)
\(810\) 1.36082e12 0.111075
\(811\) 1.91451e13 1.55405 0.777023 0.629472i \(-0.216729\pi\)
0.777023 + 0.629472i \(0.216729\pi\)
\(812\) 2.92003e12 0.235714
\(813\) −9.97471e11 −0.0800743
\(814\) 2.54740e12 0.203371
\(815\) −7.08554e12 −0.562553
\(816\) 6.20212e12 0.489705
\(817\) 5.30289e11 0.0416403
\(818\) −1.14864e13 −0.897007
\(819\) −4.99106e12 −0.387628
\(820\) −5.14906e12 −0.397709
\(821\) −1.79095e13 −1.37575 −0.687876 0.725828i \(-0.741457\pi\)
−0.687876 + 0.725828i \(0.741457\pi\)
\(822\) −1.04568e13 −0.798867
\(823\) 6.67037e12 0.506816 0.253408 0.967359i \(-0.418448\pi\)
0.253408 + 0.967359i \(0.418448\pi\)
\(824\) 1.34857e12 0.101906
\(825\) −2.45644e12 −0.184613
\(826\) −2.20341e12 −0.164696
\(827\) 5.80949e11 0.0431880 0.0215940 0.999767i \(-0.493126\pi\)
0.0215940 + 0.999767i \(0.493126\pi\)
\(828\) 4.28567e12 0.316871
\(829\) 2.16695e13 1.59351 0.796754 0.604304i \(-0.206549\pi\)
0.796754 + 0.604304i \(0.206549\pi\)
\(830\) −1.28540e13 −0.940126
\(831\) 3.15151e12 0.229252
\(832\) −2.28022e13 −1.64976
\(833\) 3.38000e12 0.243228
\(834\) −3.33203e12 −0.238486
\(835\) −2.30340e12 −0.163976
\(836\) 1.45517e12 0.103035
\(837\) 5.76037e11 0.0405682
\(838\) −2.39833e13 −1.68001
\(839\) 1.21671e12 0.0847734 0.0423867 0.999101i \(-0.486504\pi\)
0.0423867 + 0.999101i \(0.486504\pi\)
\(840\) −8.99009e11 −0.0623028
\(841\) −1.36608e13 −0.941661
\(842\) 1.08776e13 0.745814
\(843\) 1.51267e13 1.03162
\(844\) 3.90809e12 0.265108
\(845\) −8.08175e12 −0.545319
\(846\) 1.22841e13 0.824473
\(847\) 8.26101e12 0.551516
\(848\) −1.14967e13 −0.763469
\(849\) −3.45797e11 −0.0228421
\(850\) −1.15836e13 −0.761129
\(851\) −2.98920e12 −0.195377
\(852\) 5.58177e12 0.362905
\(853\) −5.36001e12 −0.346653 −0.173326 0.984864i \(-0.555452\pi\)
−0.173326 + 0.984864i \(0.555452\pi\)
\(854\) −1.65728e13 −1.06619
\(855\) −5.42190e11 −0.0346980
\(856\) −3.03153e12 −0.192988
\(857\) −1.30221e13 −0.824644 −0.412322 0.911038i \(-0.635282\pi\)
−0.412322 + 0.911038i \(0.635282\pi\)
\(858\) −1.08064e13 −0.680754
\(859\) 2.19921e13 1.37816 0.689078 0.724688i \(-0.258016\pi\)
0.689078 + 0.724688i \(0.258016\pi\)
\(860\) −3.39413e12 −0.211585
\(861\) −4.16736e12 −0.258432
\(862\) 1.11457e13 0.687584
\(863\) −2.89089e13 −1.77412 −0.887060 0.461654i \(-0.847256\pi\)
−0.887060 + 0.461654i \(0.847256\pi\)
\(864\) 4.52350e12 0.276161
\(865\) −7.35267e12 −0.446552
\(866\) 8.81856e12 0.532804
\(867\) −2.65472e11 −0.0159563
\(868\) −3.44042e12 −0.205718
\(869\) −7.91918e12 −0.471076
\(870\) −2.35568e12 −0.139405
\(871\) −1.37686e13 −0.810605
\(872\) −2.18968e12 −0.128250
\(873\) −7.19856e12 −0.419451
\(874\) −3.22621e12 −0.187021
\(875\) −1.57887e13 −0.910565
\(876\) −2.91786e11 −0.0167416
\(877\) 1.72809e13 0.986435 0.493217 0.869906i \(-0.335821\pi\)
0.493217 + 0.869906i \(0.335821\pi\)
\(878\) −9.02020e12 −0.512260
\(879\) 1.83850e13 1.03876
\(880\) 6.33712e12 0.356221
\(881\) 6.40170e12 0.358017 0.179009 0.983848i \(-0.442711\pi\)
0.179009 + 0.983848i \(0.442711\pi\)
\(882\) 2.15379e12 0.119838
\(883\) 5.02129e12 0.277966 0.138983 0.990295i \(-0.455617\pi\)
0.138983 + 0.990295i \(0.455617\pi\)
\(884\) −2.69711e13 −1.48547
\(885\) 9.40811e11 0.0515534
\(886\) −3.15326e13 −1.71912
\(887\) 2.62500e13 1.42388 0.711940 0.702240i \(-0.247817\pi\)
0.711940 + 0.702240i \(0.247817\pi\)
\(888\) 4.48130e11 0.0241850
\(889\) −4.11068e12 −0.220727
\(890\) 3.12619e13 1.67017
\(891\) 1.26212e12 0.0670892
\(892\) 3.14766e13 1.66474
\(893\) −4.89436e12 −0.257551
\(894\) 1.94608e13 1.01892
\(895\) −1.17312e13 −0.611139
\(896\) −6.02376e12 −0.312235
\(897\) 1.26806e13 0.653995
\(898\) 1.76186e13 0.904125
\(899\) −9.97165e11 −0.0509153
\(900\) −3.90668e12 −0.198480
\(901\) −1.73136e13 −0.875236
\(902\) −9.02301e12 −0.453860
\(903\) −2.74702e12 −0.137489
\(904\) −5.03010e12 −0.250506
\(905\) −1.97010e13 −0.976269
\(906\) −4.39251e12 −0.216589
\(907\) −1.31166e13 −0.643559 −0.321780 0.946815i \(-0.604281\pi\)
−0.321780 + 0.946815i \(0.604281\pi\)
\(908\) 4.24060e11 0.0207034
\(909\) −3.38961e12 −0.164669
\(910\) −2.40482e13 −1.16251
\(911\) 3.00427e13 1.44513 0.722565 0.691303i \(-0.242963\pi\)
0.722565 + 0.691303i \(0.242963\pi\)
\(912\) −1.57463e12 −0.0753705
\(913\) −1.19218e13 −0.567835
\(914\) −3.46055e13 −1.64016
\(915\) 7.07625e12 0.333740
\(916\) 9.82144e12 0.460941
\(917\) −3.56128e13 −1.66320
\(918\) 5.95168e12 0.276597
\(919\) −2.42329e13 −1.12069 −0.560345 0.828259i \(-0.689331\pi\)
−0.560345 + 0.828259i \(0.689331\pi\)
\(920\) 2.28409e12 0.105116
\(921\) 2.69089e12 0.123233
\(922\) −3.93662e13 −1.79405
\(923\) 1.65156e13 0.749007
\(924\) −7.53811e12 −0.340203
\(925\) 2.72486e12 0.122379
\(926\) 3.90323e13 1.74452
\(927\) −4.21318e12 −0.187392
\(928\) −7.83053e12 −0.346597
\(929\) −1.06966e13 −0.471167 −0.235583 0.971854i \(-0.575700\pi\)
−0.235583 + 0.971854i \(0.575700\pi\)
\(930\) 2.77549e12 0.121665
\(931\) −8.58134e11 −0.0374353
\(932\) −6.22379e12 −0.270199
\(933\) −1.33785e12 −0.0578016
\(934\) 8.94748e12 0.384716
\(935\) 9.54346e12 0.408370
\(936\) −1.90103e12 −0.0809558
\(937\) −2.83481e13 −1.20142 −0.600712 0.799465i \(-0.705116\pi\)
−0.600712 + 0.799465i \(0.705116\pi\)
\(938\) −1.81464e13 −0.765383
\(939\) 7.06285e12 0.296473
\(940\) 3.13265e13 1.30869
\(941\) −9.66030e12 −0.401641 −0.200820 0.979628i \(-0.564361\pi\)
−0.200820 + 0.979628i \(0.564361\pi\)
\(942\) −1.76162e13 −0.728926
\(943\) 1.05879e13 0.436020
\(944\) 2.73230e12 0.111984
\(945\) 2.80867e12 0.114567
\(946\) −5.94774e12 −0.241458
\(947\) −4.49566e13 −1.81643 −0.908214 0.418506i \(-0.862554\pi\)
−0.908214 + 0.418506i \(0.862554\pi\)
\(948\) −1.25945e13 −0.506459
\(949\) −8.63350e11 −0.0345532
\(950\) 2.94091e12 0.117145
\(951\) −8.11696e12 −0.321796
\(952\) −3.93192e12 −0.155145
\(953\) 1.78252e13 0.700030 0.350015 0.936744i \(-0.386176\pi\)
0.350015 + 0.936744i \(0.386176\pi\)
\(954\) −1.10325e13 −0.431226
\(955\) 8.61266e11 0.0335060
\(956\) 1.30697e13 0.506062
\(957\) −2.18483e12 −0.0842005
\(958\) 5.48234e13 2.10291
\(959\) −2.15824e13 −0.823977
\(960\) 1.28317e13 0.487601
\(961\) −2.52647e13 −0.955564
\(962\) 1.19873e13 0.451267
\(963\) 9.47107e12 0.354879
\(964\) −2.54768e13 −0.950162
\(965\) 1.73613e13 0.644480
\(966\) 1.67125e13 0.617510
\(967\) 3.12572e13 1.14956 0.574780 0.818308i \(-0.305088\pi\)
0.574780 + 0.818308i \(0.305088\pi\)
\(968\) 3.14652e12 0.115184
\(969\) −2.37133e12 −0.0864042
\(970\) −3.46844e13 −1.25795
\(971\) −9.61953e12 −0.347270 −0.173635 0.984810i \(-0.555551\pi\)
−0.173635 + 0.984810i \(0.555551\pi\)
\(972\) 2.00726e12 0.0721283
\(973\) −6.87719e12 −0.245982
\(974\) −5.63831e13 −2.00740
\(975\) −1.15593e13 −0.409647
\(976\) 2.05508e13 0.724946
\(977\) 1.16684e13 0.409719 0.204859 0.978791i \(-0.434326\pi\)
0.204859 + 0.978791i \(0.434326\pi\)
\(978\) −1.97469e13 −0.690198
\(979\) 2.89947e13 1.00878
\(980\) 5.49251e12 0.190219
\(981\) 6.84095e12 0.235834
\(982\) 5.47941e13 1.88032
\(983\) 4.38643e13 1.49837 0.749187 0.662358i \(-0.230444\pi\)
0.749187 + 0.662358i \(0.230444\pi\)
\(984\) −1.58730e12 −0.0539734
\(985\) −6.30556e12 −0.213432
\(986\) −1.03028e13 −0.347144
\(987\) 2.53539e13 0.850388
\(988\) 6.84759e12 0.228629
\(989\) 6.97927e12 0.231967
\(990\) 6.08123e12 0.201202
\(991\) −3.26972e13 −1.07691 −0.538454 0.842655i \(-0.680991\pi\)
−0.538454 + 0.842655i \(0.680991\pi\)
\(992\) 9.22604e12 0.302491
\(993\) −2.00220e13 −0.653487
\(994\) 2.17668e13 0.707221
\(995\) −4.77198e12 −0.154346
\(996\) −1.89602e13 −0.610485
\(997\) 3.11546e13 0.998606 0.499303 0.866428i \(-0.333589\pi\)
0.499303 + 0.866428i \(0.333589\pi\)
\(998\) −6.75660e13 −2.15596
\(999\) −1.40004e12 −0.0444730
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.1.4 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.4 22 1.1 even 1 trivial