Properties

Label 17.10.a.a.1.1
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.75560921479\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 1596 x^{3} + 5754 x^{2} + 488987 x - 2711704\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-35.0613\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q-42.0613 q^{2} -256.773 q^{3} +1257.15 q^{4} +1407.25 q^{5} +10800.2 q^{6} -5138.64 q^{7} -31342.2 q^{8} +46249.6 q^{9} +O(q^{10})\) \(q-42.0613 q^{2} -256.773 q^{3} +1257.15 q^{4} +1407.25 q^{5} +10800.2 q^{6} -5138.64 q^{7} -31342.2 q^{8} +46249.6 q^{9} -59190.7 q^{10} +26560.4 q^{11} -322804. q^{12} +71402.0 q^{13} +216138. q^{14} -361344. q^{15} +674631. q^{16} -83521.0 q^{17} -1.94532e6 q^{18} -548715. q^{19} +1.76913e6 q^{20} +1.31947e6 q^{21} -1.11716e6 q^{22} +1.15988e6 q^{23} +8.04785e6 q^{24} +27218.8 q^{25} -3.00326e6 q^{26} -6.82160e6 q^{27} -6.46007e6 q^{28} +1.44199e6 q^{29} +1.51986e7 q^{30} -6.05781e6 q^{31} -1.23287e7 q^{32} -6.82000e6 q^{33} +3.51300e6 q^{34} -7.23134e6 q^{35} +5.81429e7 q^{36} -9.50334e6 q^{37} +2.30797e7 q^{38} -1.83341e7 q^{39} -4.41062e7 q^{40} +1.75776e7 q^{41} -5.54985e7 q^{42} -2.06503e7 q^{43} +3.33905e7 q^{44} +6.50846e7 q^{45} -4.87861e7 q^{46} +3.15997e7 q^{47} -1.73227e8 q^{48} -1.39480e7 q^{49} -1.14486e6 q^{50} +2.14460e7 q^{51} +8.97634e7 q^{52} -1.02011e8 q^{53} +2.86925e8 q^{54} +3.73770e7 q^{55} +1.61056e8 q^{56} +1.40895e8 q^{57} -6.06520e7 q^{58} -5.95270e7 q^{59} -4.54265e8 q^{60} +5.34058e7 q^{61} +2.54799e8 q^{62} -2.37660e8 q^{63} +1.73149e8 q^{64} +1.00480e8 q^{65} +2.86858e8 q^{66} -6.45107e7 q^{67} -1.04999e8 q^{68} -2.97827e8 q^{69} +3.04160e8 q^{70} -2.71132e8 q^{71} -1.44956e9 q^{72} +2.75443e8 q^{73} +3.99723e8 q^{74} -6.98908e6 q^{75} -6.89819e8 q^{76} -1.36484e8 q^{77} +7.71158e8 q^{78} -4.33372e8 q^{79} +9.49373e8 q^{80} +8.41275e8 q^{81} -7.39337e8 q^{82} +1.23703e8 q^{83} +1.65877e9 q^{84} -1.17535e8 q^{85} +8.68579e8 q^{86} -3.70264e8 q^{87} -8.32461e8 q^{88} -8.87168e8 q^{89} -2.73755e9 q^{90} -3.66909e8 q^{91} +1.45815e9 q^{92} +1.55548e9 q^{93} -1.32912e9 q^{94} -7.72177e8 q^{95} +3.16568e9 q^{96} -4.41697e8 q^{97} +5.86670e8 q^{98} +1.22841e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} - 42423q^{8} + 10981q^{9} + O(q^{10}) \) \( 5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} - 42423q^{8} + 10981q^{9} - 89328q^{10} - 68036q^{11} - 406010q^{12} - 158862q^{13} - 84700q^{14} - 687324q^{15} + 350225q^{16} - 417605q^{17} - 1911585q^{18} - 370992q^{19} + 1632640q^{20} + 1783880q^{21} + 122290q^{22} + 1645870q^{23} + 9678702q^{24} + 3270239q^{25} + 734846q^{26} - 2998268q^{27} + 183372q^{28} + 3668616q^{29} + 17048544q^{30} - 7262362q^{31} - 5605919q^{32} - 11334900q^{33} + 2756193q^{34} - 26503988q^{35} + 49782133q^{36} - 31420708q^{37} + 18513700q^{38} - 42449884q^{39} - 53930464q^{40} - 7996938q^{41} - 44519496q^{42} - 56908268q^{43} + 43323054q^{44} + 12799536q^{45} - 32063472q^{46} - 16903336q^{47} - 102794498q^{48} - 11784059q^{49} + 85921093q^{50} + 19710956q^{51} + 173619082q^{52} - 83362982q^{53} + 386329164q^{54} + 6363364q^{55} + 317409372q^{56} + 136615904q^{57} + 64577488q^{58} - 37946604q^{59} - 223158912q^{60} - 77685452q^{61} + 324855300q^{62} - 191945278q^{63} + 131623105q^{64} - 40321288q^{65} + 298037676q^{66} - 304503600q^{67} - 71243413q^{68} - 333409272q^{69} - 122787392q^{70} - 476602922q^{71} - 1301701911q^{72} - 289980486q^{73} + 262289012q^{74} - 153685772q^{75} - 1031276084q^{76} - 143385648q^{77} + 691646196q^{78} - 828240610q^{79} + 912750944q^{80} + 891328609q^{81} - 1109615654q^{82} + 194681148q^{83} + 1541719592q^{84} - 123611080q^{85} + 1164707144q^{86} + 158149884q^{87} - 1017979978q^{88} + 376848106q^{89} - 2240087472q^{90} + 194543664q^{91} + 2506713088q^{92} + 3494835920q^{93} - 2244811104q^{94} + 1498679864q^{95} + 2935047582q^{96} + 692035246q^{97} + 871744055q^{98} + 2027106408q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −42.0613 −1.85887 −0.929433 0.368992i \(-0.879703\pi\)
−0.929433 + 0.368992i \(0.879703\pi\)
\(3\) −256.773 −1.83022 −0.915112 0.403199i \(-0.867898\pi\)
−0.915112 + 0.403199i \(0.867898\pi\)
\(4\) 1257.15 2.45538
\(5\) 1407.25 1.00694 0.503472 0.864012i \(-0.332056\pi\)
0.503472 + 0.864012i \(0.332056\pi\)
\(6\) 10800.2 3.40214
\(7\) −5138.64 −0.808923 −0.404461 0.914555i \(-0.632541\pi\)
−0.404461 + 0.914555i \(0.632541\pi\)
\(8\) −31342.2 −2.70536
\(9\) 46249.6 2.34972
\(10\) −59190.7 −1.87177
\(11\) 26560.4 0.546975 0.273487 0.961876i \(-0.411823\pi\)
0.273487 + 0.961876i \(0.411823\pi\)
\(12\) −322804. −4.49390
\(13\) 71402.0 0.693371 0.346685 0.937981i \(-0.387307\pi\)
0.346685 + 0.937981i \(0.387307\pi\)
\(14\) 216138. 1.50368
\(15\) −361344. −1.84293
\(16\) 674631. 2.57351
\(17\) −83521.0 −0.242536
\(18\) −1.94532e6 −4.36782
\(19\) −548715. −0.965951 −0.482976 0.875634i \(-0.660444\pi\)
−0.482976 + 0.875634i \(0.660444\pi\)
\(20\) 1.76913e6 2.47243
\(21\) 1.31947e6 1.48051
\(22\) −1.11716e6 −1.01675
\(23\) 1.15988e6 0.864247 0.432124 0.901814i \(-0.357764\pi\)
0.432124 + 0.901814i \(0.357764\pi\)
\(24\) 8.04785e6 4.95141
\(25\) 27218.8 0.0139360
\(26\) −3.00326e6 −1.28888
\(27\) −6.82160e6 −2.47030
\(28\) −6.46007e6 −1.98621
\(29\) 1.44199e6 0.378592 0.189296 0.981920i \(-0.439380\pi\)
0.189296 + 0.981920i \(0.439380\pi\)
\(30\) 1.51986e7 3.42577
\(31\) −6.05781e6 −1.17812 −0.589058 0.808091i \(-0.700501\pi\)
−0.589058 + 0.808091i \(0.700501\pi\)
\(32\) −1.23287e7 −2.07846
\(33\) −6.82000e6 −1.00109
\(34\) 3.51300e6 0.450841
\(35\) −7.23134e6 −0.814540
\(36\) 5.81429e7 5.76947
\(37\) −9.50334e6 −0.833621 −0.416810 0.908993i \(-0.636852\pi\)
−0.416810 + 0.908993i \(0.636852\pi\)
\(38\) 2.30797e7 1.79557
\(39\) −1.83341e7 −1.26902
\(40\) −4.41062e7 −2.72414
\(41\) 1.75776e7 0.971476 0.485738 0.874104i \(-0.338551\pi\)
0.485738 + 0.874104i \(0.338551\pi\)
\(42\) −5.54985e7 −2.75207
\(43\) −2.06503e7 −0.921125 −0.460562 0.887627i \(-0.652352\pi\)
−0.460562 + 0.887627i \(0.652352\pi\)
\(44\) 3.33905e7 1.34303
\(45\) 6.50846e7 2.36604
\(46\) −4.87861e7 −1.60652
\(47\) 3.15997e7 0.944587 0.472294 0.881441i \(-0.343426\pi\)
0.472294 + 0.881441i \(0.343426\pi\)
\(48\) −1.73227e8 −4.71011
\(49\) −1.39480e7 −0.345644
\(50\) −1.14486e6 −0.0259052
\(51\) 2.14460e7 0.443895
\(52\) 8.97634e7 1.70249
\(53\) −1.02011e8 −1.77585 −0.887924 0.459990i \(-0.847853\pi\)
−0.887924 + 0.459990i \(0.847853\pi\)
\(54\) 2.86925e8 4.59195
\(55\) 3.73770e7 0.550773
\(56\) 1.61056e8 2.18842
\(57\) 1.40895e8 1.76791
\(58\) −6.06520e7 −0.703751
\(59\) −5.95270e7 −0.639558 −0.319779 0.947492i \(-0.603609\pi\)
−0.319779 + 0.947492i \(0.603609\pi\)
\(60\) −4.54265e8 −4.52510
\(61\) 5.34058e7 0.493860 0.246930 0.969033i \(-0.420578\pi\)
0.246930 + 0.969033i \(0.420578\pi\)
\(62\) 2.54799e8 2.18996
\(63\) −2.37660e8 −1.90074
\(64\) 1.73149e8 1.29006
\(65\) 1.00480e8 0.698185
\(66\) 2.86858e8 1.86089
\(67\) −6.45107e7 −0.391107 −0.195553 0.980693i \(-0.562650\pi\)
−0.195553 + 0.980693i \(0.562650\pi\)
\(68\) −1.04999e8 −0.595517
\(69\) −2.97827e8 −1.58177
\(70\) 3.04160e8 1.51412
\(71\) −2.71132e8 −1.26625 −0.633123 0.774051i \(-0.718227\pi\)
−0.633123 + 0.774051i \(0.718227\pi\)
\(72\) −1.44956e9 −6.35684
\(73\) 2.75443e8 1.13522 0.567609 0.823298i \(-0.307868\pi\)
0.567609 + 0.823298i \(0.307868\pi\)
\(74\) 3.99723e8 1.54959
\(75\) −6.98908e6 −0.0255061
\(76\) −6.89819e8 −2.37178
\(77\) −1.36484e8 −0.442460
\(78\) 7.71158e8 2.35895
\(79\) −4.33372e8 −1.25181 −0.625906 0.779898i \(-0.715271\pi\)
−0.625906 + 0.779898i \(0.715271\pi\)
\(80\) 9.49373e8 2.59138
\(81\) 8.41275e8 2.17148
\(82\) −7.39337e8 −1.80584
\(83\) 1.23703e8 0.286106 0.143053 0.989715i \(-0.454308\pi\)
0.143053 + 0.989715i \(0.454308\pi\)
\(84\) 1.65877e9 3.63522
\(85\) −1.17535e8 −0.244220
\(86\) 8.68579e8 1.71225
\(87\) −3.70264e8 −0.692908
\(88\) −8.32461e8 −1.47976
\(89\) −8.87168e8 −1.49882 −0.749412 0.662104i \(-0.769664\pi\)
−0.749412 + 0.662104i \(0.769664\pi\)
\(90\) −2.73755e9 −4.39815
\(91\) −3.66909e8 −0.560883
\(92\) 1.45815e9 2.12206
\(93\) 1.55548e9 2.15622
\(94\) −1.32912e9 −1.75586
\(95\) −7.72177e8 −0.972659
\(96\) 3.16568e9 3.80405
\(97\) −4.41697e8 −0.506585 −0.253292 0.967390i \(-0.581513\pi\)
−0.253292 + 0.967390i \(0.581513\pi\)
\(98\) 5.86670e8 0.642506
\(99\) 1.22841e9 1.28524
\(100\) 3.42183e7 0.0342183
\(101\) −1.14036e9 −1.09042 −0.545212 0.838298i \(-0.683551\pi\)
−0.545212 + 0.838298i \(0.683551\pi\)
\(102\) −9.02046e8 −0.825141
\(103\) 8.49153e8 0.743393 0.371696 0.928354i \(-0.378776\pi\)
0.371696 + 0.928354i \(0.378776\pi\)
\(104\) −2.23790e9 −1.87582
\(105\) 1.85682e9 1.49079
\(106\) 4.29072e9 3.30106
\(107\) 2.23234e9 1.64639 0.823196 0.567758i \(-0.192189\pi\)
0.823196 + 0.567758i \(0.192189\pi\)
\(108\) −8.57581e9 −6.06552
\(109\) 1.34014e9 0.909352 0.454676 0.890657i \(-0.349755\pi\)
0.454676 + 0.890657i \(0.349755\pi\)
\(110\) −1.57213e9 −1.02381
\(111\) 2.44021e9 1.52571
\(112\) −3.46669e9 −2.08177
\(113\) −2.00028e9 −1.15408 −0.577042 0.816715i \(-0.695793\pi\)
−0.577042 + 0.816715i \(0.695793\pi\)
\(114\) −5.92624e9 −3.28630
\(115\) 1.63224e9 0.870248
\(116\) 1.81280e9 0.929586
\(117\) 3.30232e9 1.62923
\(118\) 2.50379e9 1.18885
\(119\) 4.29184e8 0.196193
\(120\) 1.13253e10 4.98579
\(121\) −1.65249e9 −0.700819
\(122\) −2.24632e9 −0.918020
\(123\) −4.51346e9 −1.77802
\(124\) −7.61560e9 −2.89272
\(125\) −2.71023e9 −0.992911
\(126\) 9.99630e9 3.53323
\(127\) −3.35970e9 −1.14600 −0.572999 0.819556i \(-0.694220\pi\)
−0.572999 + 0.819556i \(0.694220\pi\)
\(128\) −9.70602e8 −0.319592
\(129\) 5.30245e9 1.68587
\(130\) −4.22633e9 −1.29783
\(131\) −2.27481e8 −0.0674876 −0.0337438 0.999431i \(-0.510743\pi\)
−0.0337438 + 0.999431i \(0.510743\pi\)
\(132\) −8.57380e9 −2.45805
\(133\) 2.81965e9 0.781380
\(134\) 2.71341e9 0.727014
\(135\) −9.59967e9 −2.48745
\(136\) 2.61773e9 0.656145
\(137\) −3.72862e9 −0.904285 −0.452142 0.891946i \(-0.649340\pi\)
−0.452142 + 0.891946i \(0.649340\pi\)
\(138\) 1.25270e10 2.94029
\(139\) −8.72554e8 −0.198256 −0.0991279 0.995075i \(-0.531605\pi\)
−0.0991279 + 0.995075i \(0.531605\pi\)
\(140\) −9.09091e9 −2.00001
\(141\) −8.11395e9 −1.72881
\(142\) 1.14042e10 2.35378
\(143\) 1.89647e9 0.379256
\(144\) 3.12014e10 6.04705
\(145\) 2.02923e9 0.381220
\(146\) −1.15855e10 −2.11022
\(147\) 3.58147e9 0.632606
\(148\) −1.19472e10 −2.04686
\(149\) 5.86193e9 0.974323 0.487161 0.873312i \(-0.338032\pi\)
0.487161 + 0.873312i \(0.338032\pi\)
\(150\) 2.93970e8 0.0474124
\(151\) 1.01489e10 1.58864 0.794318 0.607502i \(-0.207828\pi\)
0.794318 + 0.607502i \(0.207828\pi\)
\(152\) 1.71979e10 2.61324
\(153\) −3.86281e9 −0.569892
\(154\) 5.74071e9 0.822474
\(155\) −8.52483e9 −1.18630
\(156\) −2.30489e10 −3.11594
\(157\) −5.31929e9 −0.698723 −0.349362 0.936988i \(-0.613601\pi\)
−0.349362 + 0.936988i \(0.613601\pi\)
\(158\) 1.82282e10 2.32695
\(159\) 2.61937e10 3.25020
\(160\) −1.73495e10 −2.09289
\(161\) −5.96021e9 −0.699109
\(162\) −3.53851e10 −4.03648
\(163\) −1.08994e10 −1.20937 −0.604685 0.796465i \(-0.706701\pi\)
−0.604685 + 0.796465i \(0.706701\pi\)
\(164\) 2.20978e10 2.38534
\(165\) −9.59743e9 −1.00804
\(166\) −5.20309e9 −0.531833
\(167\) −5.90585e9 −0.587569 −0.293784 0.955872i \(-0.594915\pi\)
−0.293784 + 0.955872i \(0.594915\pi\)
\(168\) −4.13550e10 −4.00531
\(169\) −5.50625e9 −0.519237
\(170\) 4.94366e9 0.453972
\(171\) −2.53778e10 −2.26972
\(172\) −2.59606e10 −2.26171
\(173\) 1.33412e10 1.13237 0.566183 0.824280i \(-0.308420\pi\)
0.566183 + 0.824280i \(0.308420\pi\)
\(174\) 1.55738e10 1.28802
\(175\) −1.39868e8 −0.0112732
\(176\) 1.79185e10 1.40765
\(177\) 1.52850e10 1.17054
\(178\) 3.73154e10 2.78611
\(179\) 1.62530e10 1.18330 0.591651 0.806194i \(-0.298476\pi\)
0.591651 + 0.806194i \(0.298476\pi\)
\(180\) 8.18214e10 5.80953
\(181\) −4.03320e9 −0.279316 −0.139658 0.990200i \(-0.544600\pi\)
−0.139658 + 0.990200i \(0.544600\pi\)
\(182\) 1.54327e10 1.04261
\(183\) −1.37132e10 −0.903875
\(184\) −3.63532e10 −2.33810
\(185\) −1.33735e10 −0.839409
\(186\) −6.54257e10 −4.00812
\(187\) −2.21835e9 −0.132661
\(188\) 3.97257e10 2.31932
\(189\) 3.50537e10 1.99828
\(190\) 3.24788e10 1.80804
\(191\) −1.09015e10 −0.592700 −0.296350 0.955079i \(-0.595769\pi\)
−0.296350 + 0.955079i \(0.595769\pi\)
\(192\) −4.44601e10 −2.36110
\(193\) 1.29615e10 0.672428 0.336214 0.941786i \(-0.390853\pi\)
0.336214 + 0.941786i \(0.390853\pi\)
\(194\) 1.85784e10 0.941673
\(195\) −2.58007e10 −1.27784
\(196\) −1.75348e10 −0.848687
\(197\) 7.15882e9 0.338644 0.169322 0.985561i \(-0.445842\pi\)
0.169322 + 0.985561i \(0.445842\pi\)
\(198\) −5.16684e10 −2.38909
\(199\) 3.03762e9 0.137307 0.0686537 0.997641i \(-0.478130\pi\)
0.0686537 + 0.997641i \(0.478130\pi\)
\(200\) −8.53098e8 −0.0377020
\(201\) 1.65646e10 0.715813
\(202\) 4.79650e10 2.02695
\(203\) −7.40986e9 −0.306251
\(204\) 2.69609e10 1.08993
\(205\) 2.47360e10 0.978222
\(206\) −3.57165e10 −1.38187
\(207\) 5.36440e10 2.03074
\(208\) 4.81700e10 1.78440
\(209\) −1.45741e10 −0.528351
\(210\) −7.81001e10 −2.77118
\(211\) −3.30011e10 −1.14619 −0.573097 0.819488i \(-0.694258\pi\)
−0.573097 + 0.819488i \(0.694258\pi\)
\(212\) −1.28244e11 −4.36038
\(213\) 6.96195e10 2.31752
\(214\) −9.38951e10 −3.06042
\(215\) −2.90601e10 −0.927521
\(216\) 2.13804e11 6.68304
\(217\) 3.11289e10 0.953004
\(218\) −5.63682e10 −1.69036
\(219\) −7.07266e10 −2.07771
\(220\) 4.69887e10 1.35236
\(221\) −5.96357e9 −0.168167
\(222\) −1.02638e11 −2.83610
\(223\) −3.03057e10 −0.820640 −0.410320 0.911942i \(-0.634583\pi\)
−0.410320 + 0.911942i \(0.634583\pi\)
\(224\) 6.33526e10 1.68131
\(225\) 1.25886e9 0.0327459
\(226\) 8.41343e10 2.14529
\(227\) −4.49193e10 −1.12284 −0.561418 0.827532i \(-0.689744\pi\)
−0.561418 + 0.827532i \(0.689744\pi\)
\(228\) 1.77127e11 4.34089
\(229\) 4.68022e10 1.12462 0.562311 0.826926i \(-0.309913\pi\)
0.562311 + 0.826926i \(0.309913\pi\)
\(230\) −6.86541e10 −1.61767
\(231\) 3.50455e10 0.809802
\(232\) −4.51951e10 −1.02423
\(233\) −2.08143e10 −0.462658 −0.231329 0.972876i \(-0.574307\pi\)
−0.231329 + 0.972876i \(0.574307\pi\)
\(234\) −1.38900e11 −3.02852
\(235\) 4.44685e10 0.951146
\(236\) −7.48347e10 −1.57036
\(237\) 1.11279e11 2.29110
\(238\) −1.80521e10 −0.364696
\(239\) 1.23779e9 0.0245390 0.0122695 0.999925i \(-0.496094\pi\)
0.0122695 + 0.999925i \(0.496094\pi\)
\(240\) −2.43774e11 −4.74282
\(241\) −3.29491e10 −0.629167 −0.314584 0.949230i \(-0.601865\pi\)
−0.314584 + 0.949230i \(0.601865\pi\)
\(242\) 6.95061e10 1.30273
\(243\) −8.17474e10 −1.50399
\(244\) 6.71394e10 1.21262
\(245\) −1.96283e10 −0.348044
\(246\) 1.89842e11 3.30510
\(247\) −3.91793e10 −0.669762
\(248\) 1.89865e11 3.18722
\(249\) −3.17635e10 −0.523638
\(250\) 1.13996e11 1.84569
\(251\) −3.15140e10 −0.501154 −0.250577 0.968097i \(-0.580620\pi\)
−0.250577 + 0.968097i \(0.580620\pi\)
\(252\) −2.98776e11 −4.66705
\(253\) 3.08069e10 0.472721
\(254\) 1.41313e11 2.13026
\(255\) 3.01798e10 0.446977
\(256\) −4.78276e10 −0.695983
\(257\) −7.36840e10 −1.05360 −0.526798 0.849991i \(-0.676607\pi\)
−0.526798 + 0.849991i \(0.676607\pi\)
\(258\) −2.23028e11 −3.13380
\(259\) 4.88342e10 0.674335
\(260\) 1.26319e11 1.71431
\(261\) 6.66914e10 0.889585
\(262\) 9.56814e9 0.125450
\(263\) −5.81832e10 −0.749888 −0.374944 0.927047i \(-0.622338\pi\)
−0.374944 + 0.927047i \(0.622338\pi\)
\(264\) 2.13754e11 2.70830
\(265\) −1.43555e11 −1.78818
\(266\) −1.18598e11 −1.45248
\(267\) 2.27801e11 2.74318
\(268\) −8.10999e10 −0.960315
\(269\) 1.32703e11 1.54523 0.772617 0.634872i \(-0.218947\pi\)
0.772617 + 0.634872i \(0.218947\pi\)
\(270\) 4.03775e11 4.62384
\(271\) −1.25505e11 −1.41351 −0.706757 0.707456i \(-0.749843\pi\)
−0.706757 + 0.707456i \(0.749843\pi\)
\(272\) −5.63459e10 −0.624169
\(273\) 9.42126e10 1.02654
\(274\) 1.56831e11 1.68094
\(275\) 7.22943e8 0.00762267
\(276\) −3.74414e11 −3.88384
\(277\) −1.08560e11 −1.10792 −0.553961 0.832542i \(-0.686884\pi\)
−0.553961 + 0.832542i \(0.686884\pi\)
\(278\) 3.67008e10 0.368531
\(279\) −2.80171e11 −2.76825
\(280\) 2.26646e11 2.20362
\(281\) −1.21647e11 −1.16392 −0.581961 0.813216i \(-0.697714\pi\)
−0.581961 + 0.813216i \(0.697714\pi\)
\(282\) 3.41284e11 3.21362
\(283\) 1.97694e11 1.83212 0.916060 0.401041i \(-0.131352\pi\)
0.916060 + 0.401041i \(0.131352\pi\)
\(284\) −3.40855e11 −3.10912
\(285\) 1.98275e11 1.78018
\(286\) −7.97678e10 −0.704986
\(287\) −9.03249e10 −0.785849
\(288\) −5.70196e11 −4.88380
\(289\) 6.97576e9 0.0588235
\(290\) −8.53523e10 −0.708637
\(291\) 1.13416e11 0.927164
\(292\) 3.46275e11 2.78739
\(293\) −5.29206e10 −0.419489 −0.209745 0.977756i \(-0.567263\pi\)
−0.209745 + 0.977756i \(0.567263\pi\)
\(294\) −1.50641e11 −1.17593
\(295\) −8.37692e10 −0.643999
\(296\) 2.97856e11 2.25524
\(297\) −1.81184e11 −1.35119
\(298\) −2.46561e11 −1.81113
\(299\) 8.28178e10 0.599244
\(300\) −8.78635e9 −0.0626272
\(301\) 1.06115e11 0.745119
\(302\) −4.26878e11 −2.95306
\(303\) 2.92814e11 1.99572
\(304\) −3.70180e11 −2.48589
\(305\) 7.51551e10 0.497290
\(306\) 1.62475e11 1.05935
\(307\) 6.66906e10 0.428491 0.214246 0.976780i \(-0.431271\pi\)
0.214246 + 0.976780i \(0.431271\pi\)
\(308\) −1.71582e11 −1.08641
\(309\) −2.18040e11 −1.36058
\(310\) 3.58566e11 2.20516
\(311\) 2.16895e11 1.31470 0.657352 0.753584i \(-0.271676\pi\)
0.657352 + 0.753584i \(0.271676\pi\)
\(312\) 5.74633e11 3.43316
\(313\) 2.03438e11 1.19807 0.599034 0.800723i \(-0.295551\pi\)
0.599034 + 0.800723i \(0.295551\pi\)
\(314\) 2.23736e11 1.29883
\(315\) −3.34446e11 −1.91394
\(316\) −5.44816e11 −3.07368
\(317\) 2.27635e11 1.26611 0.633056 0.774106i \(-0.281800\pi\)
0.633056 + 0.774106i \(0.281800\pi\)
\(318\) −1.10174e12 −6.04169
\(319\) 3.82998e10 0.207080
\(320\) 2.43664e11 1.29902
\(321\) −5.73205e11 −3.01327
\(322\) 2.50694e11 1.29955
\(323\) 4.58292e10 0.234278
\(324\) 1.05761e12 5.33180
\(325\) 1.94348e9 0.00966285
\(326\) 4.58444e11 2.24806
\(327\) −3.44113e11 −1.66432
\(328\) −5.50921e11 −2.62819
\(329\) −1.62379e11 −0.764098
\(330\) 4.03680e11 1.87381
\(331\) 1.97602e11 0.904828 0.452414 0.891808i \(-0.350563\pi\)
0.452414 + 0.891808i \(0.350563\pi\)
\(332\) 1.55513e11 0.702499
\(333\) −4.39526e11 −1.95878
\(334\) 2.48408e11 1.09221
\(335\) −9.07825e10 −0.393822
\(336\) 8.90153e11 3.81011
\(337\) 4.61396e9 0.0194867 0.00974337 0.999953i \(-0.496899\pi\)
0.00974337 + 0.999953i \(0.496899\pi\)
\(338\) 2.31600e11 0.965192
\(339\) 5.13618e11 2.11223
\(340\) −1.47759e11 −0.599653
\(341\) −1.60898e11 −0.644399
\(342\) 1.06743e12 4.21910
\(343\) 2.79036e11 1.08852
\(344\) 6.47226e11 2.49197
\(345\) −4.19115e11 −1.59275
\(346\) −5.61148e11 −2.10492
\(347\) −3.34855e11 −1.23987 −0.619933 0.784655i \(-0.712840\pi\)
−0.619933 + 0.784655i \(0.712840\pi\)
\(348\) −4.65480e11 −1.70135
\(349\) −1.38047e11 −0.498095 −0.249048 0.968491i \(-0.580118\pi\)
−0.249048 + 0.968491i \(0.580118\pi\)
\(350\) 5.88303e9 0.0209553
\(351\) −4.87076e11 −1.71283
\(352\) −3.27454e11 −1.13686
\(353\) 3.22524e11 1.10554 0.552771 0.833333i \(-0.313570\pi\)
0.552771 + 0.833333i \(0.313570\pi\)
\(354\) −6.42906e11 −2.17587
\(355\) −3.81550e11 −1.27504
\(356\) −1.11531e12 −3.68018
\(357\) −1.10203e11 −0.359077
\(358\) −6.83624e11 −2.19960
\(359\) 1.09669e11 0.348465 0.174232 0.984705i \(-0.444256\pi\)
0.174232 + 0.984705i \(0.444256\pi\)
\(360\) −2.03990e12 −6.40098
\(361\) −2.16000e10 −0.0669378
\(362\) 1.69642e11 0.519212
\(363\) 4.24316e11 1.28266
\(364\) −4.61262e11 −1.37718
\(365\) 3.87617e11 1.14310
\(366\) 5.76795e11 1.68018
\(367\) 1.91239e11 0.550273 0.275137 0.961405i \(-0.411277\pi\)
0.275137 + 0.961405i \(0.411277\pi\)
\(368\) 7.82492e11 2.22415
\(369\) 8.12957e11 2.28270
\(370\) 5.62509e11 1.56035
\(371\) 5.24198e11 1.43652
\(372\) 1.95548e12 5.29433
\(373\) 1.18077e11 0.315846 0.157923 0.987451i \(-0.449520\pi\)
0.157923 + 0.987451i \(0.449520\pi\)
\(374\) 9.33067e10 0.246599
\(375\) 6.95914e11 1.81725
\(376\) −9.90403e11 −2.55545
\(377\) 1.02961e11 0.262504
\(378\) −1.47441e12 −3.71453
\(379\) −1.76959e11 −0.440551 −0.220276 0.975438i \(-0.570696\pi\)
−0.220276 + 0.975438i \(0.570696\pi\)
\(380\) −9.70746e11 −2.38825
\(381\) 8.62682e11 2.09743
\(382\) 4.58530e11 1.10175
\(383\) 1.29043e11 0.306436 0.153218 0.988192i \(-0.451036\pi\)
0.153218 + 0.988192i \(0.451036\pi\)
\(384\) 2.49225e11 0.584926
\(385\) −1.92067e11 −0.445533
\(386\) −5.45176e11 −1.24995
\(387\) −9.55069e11 −2.16439
\(388\) −5.55282e11 −1.24386
\(389\) 6.86269e10 0.151957 0.0759785 0.997109i \(-0.475792\pi\)
0.0759785 + 0.997109i \(0.475792\pi\)
\(390\) 1.08521e12 2.37533
\(391\) −9.68744e10 −0.209611
\(392\) 4.37160e11 0.935090
\(393\) 5.84110e10 0.123517
\(394\) −3.01110e11 −0.629494
\(395\) −6.09862e11 −1.26051
\(396\) 1.54430e12 3.15575
\(397\) 7.83412e11 1.58283 0.791413 0.611282i \(-0.209346\pi\)
0.791413 + 0.611282i \(0.209346\pi\)
\(398\) −1.27766e11 −0.255236
\(399\) −7.24011e11 −1.43010
\(400\) 1.83627e10 0.0358646
\(401\) 1.06747e11 0.206161 0.103080 0.994673i \(-0.467130\pi\)
0.103080 + 0.994673i \(0.467130\pi\)
\(402\) −6.96730e11 −1.33060
\(403\) −4.32540e11 −0.816871
\(404\) −1.43361e12 −2.67741
\(405\) 1.18388e12 2.18656
\(406\) 3.11669e11 0.569280
\(407\) −2.52412e11 −0.455969
\(408\) −6.72164e11 −1.20089
\(409\) −1.08641e12 −1.91973 −0.959863 0.280469i \(-0.909510\pi\)
−0.959863 + 0.280469i \(0.909510\pi\)
\(410\) −1.04043e12 −1.81838
\(411\) 9.57410e11 1.65504
\(412\) 1.06752e12 1.82531
\(413\) 3.05888e11 0.517353
\(414\) −2.25634e12 −3.77488
\(415\) 1.74080e11 0.288093
\(416\) −8.80292e11 −1.44114
\(417\) 2.24049e11 0.362853
\(418\) 6.13005e11 0.982134
\(419\) 6.48628e11 1.02809 0.514047 0.857762i \(-0.328146\pi\)
0.514047 + 0.857762i \(0.328146\pi\)
\(420\) 2.33430e12 3.66046
\(421\) −8.74376e11 −1.35653 −0.678264 0.734818i \(-0.737267\pi\)
−0.678264 + 0.734818i \(0.737267\pi\)
\(422\) 1.38807e12 2.13062
\(423\) 1.46147e12 2.21952
\(424\) 3.19725e12 4.80430
\(425\) −2.27334e9 −0.00337999
\(426\) −2.92829e12 −4.30795
\(427\) −2.74433e11 −0.399495
\(428\) 2.80640e12 4.04252
\(429\) −4.86962e11 −0.694124
\(430\) 1.22231e12 1.72414
\(431\) 2.93756e10 0.0410052 0.0205026 0.999790i \(-0.493473\pi\)
0.0205026 + 0.999790i \(0.493473\pi\)
\(432\) −4.60206e12 −6.35734
\(433\) −1.33717e12 −1.82806 −0.914029 0.405648i \(-0.867046\pi\)
−0.914029 + 0.405648i \(0.867046\pi\)
\(434\) −1.30932e12 −1.77151
\(435\) −5.21053e11 −0.697719
\(436\) 1.68477e12 2.23280
\(437\) −6.36443e11 −0.834821
\(438\) 2.97485e12 3.86218
\(439\) 7.90604e11 1.01594 0.507971 0.861374i \(-0.330396\pi\)
0.507971 + 0.861374i \(0.330396\pi\)
\(440\) −1.17148e12 −1.49004
\(441\) −6.45089e11 −0.812168
\(442\) 2.50836e11 0.312600
\(443\) 1.18811e12 1.46569 0.732843 0.680398i \(-0.238193\pi\)
0.732843 + 0.680398i \(0.238193\pi\)
\(444\) 3.06772e12 3.74621
\(445\) −1.24846e12 −1.50923
\(446\) 1.27470e12 1.52546
\(447\) −1.50519e12 −1.78323
\(448\) −8.89751e11 −1.04356
\(449\) 6.04411e11 0.701817 0.350909 0.936410i \(-0.385873\pi\)
0.350909 + 0.936410i \(0.385873\pi\)
\(450\) −5.29493e10 −0.0608701
\(451\) 4.66868e11 0.531373
\(452\) −2.51466e12 −2.83371
\(453\) −2.60598e12 −2.90756
\(454\) 1.88936e12 2.08720
\(455\) −5.16332e11 −0.564778
\(456\) −4.41597e12 −4.78282
\(457\) −9.65513e11 −1.03546 −0.517732 0.855543i \(-0.673224\pi\)
−0.517732 + 0.855543i \(0.673224\pi\)
\(458\) −1.96856e12 −2.09052
\(459\) 5.69747e11 0.599135
\(460\) 2.05198e12 2.13679
\(461\) 5.15082e10 0.0531156 0.0265578 0.999647i \(-0.491545\pi\)
0.0265578 + 0.999647i \(0.491545\pi\)
\(462\) −1.47406e12 −1.50531
\(463\) −7.66043e11 −0.774709 −0.387355 0.921931i \(-0.626611\pi\)
−0.387355 + 0.921931i \(0.626611\pi\)
\(464\) 9.72811e11 0.974310
\(465\) 2.18895e12 2.17119
\(466\) 8.75477e11 0.860019
\(467\) −1.55842e12 −1.51621 −0.758104 0.652133i \(-0.773874\pi\)
−0.758104 + 0.652133i \(0.773874\pi\)
\(468\) 4.15152e12 4.00038
\(469\) 3.31497e11 0.316375
\(470\) −1.87041e12 −1.76805
\(471\) 1.36585e12 1.27882
\(472\) 1.86571e12 1.73023
\(473\) −5.48480e11 −0.503832
\(474\) −4.68052e12 −4.25885
\(475\) −1.49354e10 −0.0134615
\(476\) 5.39551e11 0.481728
\(477\) −4.71797e12 −4.17275
\(478\) −5.20632e10 −0.0456147
\(479\) 1.36399e12 1.18386 0.591931 0.805989i \(-0.298366\pi\)
0.591931 + 0.805989i \(0.298366\pi\)
\(480\) 4.45489e12 3.83046
\(481\) −6.78558e11 −0.578008
\(482\) 1.38588e12 1.16954
\(483\) 1.53042e12 1.27953
\(484\) −2.07744e12 −1.72078
\(485\) −6.21577e11 −0.510102
\(486\) 3.43841e12 2.79572
\(487\) −9.00584e11 −0.725511 −0.362755 0.931884i \(-0.618164\pi\)
−0.362755 + 0.931884i \(0.618164\pi\)
\(488\) −1.67386e12 −1.33607
\(489\) 2.79868e12 2.21342
\(490\) 8.25590e11 0.646967
\(491\) 2.39477e12 1.85950 0.929751 0.368189i \(-0.120022\pi\)
0.929751 + 0.368189i \(0.120022\pi\)
\(492\) −5.67412e12 −4.36572
\(493\) −1.20436e11 −0.0918219
\(494\) 1.64793e12 1.24500
\(495\) 1.72867e12 1.29416
\(496\) −4.08679e12 −3.03190
\(497\) 1.39325e12 1.02430
\(498\) 1.33602e12 0.973373
\(499\) −1.19891e12 −0.865637 −0.432819 0.901481i \(-0.642481\pi\)
−0.432819 + 0.901481i \(0.642481\pi\)
\(500\) −3.40717e12 −2.43797
\(501\) 1.51647e12 1.07538
\(502\) 1.32552e12 0.931579
\(503\) −3.61742e11 −0.251967 −0.125983 0.992032i \(-0.540209\pi\)
−0.125983 + 0.992032i \(0.540209\pi\)
\(504\) 7.44879e12 5.14219
\(505\) −1.60477e12 −1.09800
\(506\) −1.29578e12 −0.878725
\(507\) 1.41386e12 0.950321
\(508\) −4.22366e12 −2.81386
\(509\) 1.61404e12 1.06582 0.532910 0.846172i \(-0.321098\pi\)
0.532910 + 0.846172i \(0.321098\pi\)
\(510\) −1.26940e12 −0.830870
\(511\) −1.41541e12 −0.918304
\(512\) 2.50864e12 1.61333
\(513\) 3.74311e12 2.38619
\(514\) 3.09924e12 1.95849
\(515\) 1.19497e12 0.748555
\(516\) 6.66600e12 4.13944
\(517\) 8.39299e11 0.516665
\(518\) −2.05403e12 −1.25350
\(519\) −3.42566e12 −2.07248
\(520\) −3.14927e12 −1.88884
\(521\) −2.86199e12 −1.70176 −0.850881 0.525358i \(-0.823931\pi\)
−0.850881 + 0.525358i \(0.823931\pi\)
\(522\) −2.80513e12 −1.65362
\(523\) 1.01799e12 0.594957 0.297479 0.954728i \(-0.403854\pi\)
0.297479 + 0.954728i \(0.403854\pi\)
\(524\) −2.85979e11 −0.165708
\(525\) 3.59143e10 0.0206325
\(526\) 2.44726e12 1.39394
\(527\) 5.05954e11 0.285735
\(528\) −4.60099e12 −2.57631
\(529\) −4.55830e11 −0.253077
\(530\) 6.03810e12 3.32399
\(531\) −2.75310e12 −1.50278
\(532\) 3.54473e12 1.91859
\(533\) 1.25508e12 0.673593
\(534\) −9.58161e12 −5.09921
\(535\) 3.14145e12 1.65782
\(536\) 2.02191e12 1.05808
\(537\) −4.17335e12 −2.16571
\(538\) −5.58165e12 −2.87238
\(539\) −3.70464e11 −0.189058
\(540\) −1.20683e13 −6.10764
\(541\) −1.10637e12 −0.555283 −0.277642 0.960685i \(-0.589553\pi\)
−0.277642 + 0.960685i \(0.589553\pi\)
\(542\) 5.27892e12 2.62753
\(543\) 1.03562e12 0.511212
\(544\) 1.02970e12 0.504100
\(545\) 1.88591e12 0.915666
\(546\) −3.96271e12 −1.90820
\(547\) −1.37273e12 −0.655605 −0.327803 0.944746i \(-0.606308\pi\)
−0.327803 + 0.944746i \(0.606308\pi\)
\(548\) −4.68745e12 −2.22036
\(549\) 2.47000e12 1.16044
\(550\) −3.04079e10 −0.0141695
\(551\) −7.91240e11 −0.365701
\(552\) 9.33454e12 4.27924
\(553\) 2.22695e12 1.01262
\(554\) 4.56616e12 2.05948
\(555\) 3.43397e12 1.53631
\(556\) −1.09694e12 −0.486793
\(557\) −2.29710e12 −1.01119 −0.505594 0.862771i \(-0.668727\pi\)
−0.505594 + 0.862771i \(0.668727\pi\)
\(558\) 1.17844e13 5.14580
\(559\) −1.47447e12 −0.638681
\(560\) −4.87849e12 −2.09623
\(561\) 5.69613e11 0.242799
\(562\) 5.11665e12 2.16358
\(563\) −1.84812e11 −0.0775250 −0.0387625 0.999248i \(-0.512342\pi\)
−0.0387625 + 0.999248i \(0.512342\pi\)
\(564\) −1.02005e13 −4.24488
\(565\) −2.81488e12 −1.16210
\(566\) −8.31526e12 −3.40566
\(567\) −4.32301e12 −1.75656
\(568\) 8.49788e12 3.42565
\(569\) −2.10912e11 −0.0843523 −0.0421761 0.999110i \(-0.513429\pi\)
−0.0421761 + 0.999110i \(0.513429\pi\)
\(570\) −8.33969e12 −3.30912
\(571\) 2.37391e12 0.934548 0.467274 0.884112i \(-0.345236\pi\)
0.467274 + 0.884112i \(0.345236\pi\)
\(572\) 2.38415e12 0.931219
\(573\) 2.79921e12 1.08477
\(574\) 3.79919e12 1.46079
\(575\) 3.15706e10 0.0120442
\(576\) 8.00808e12 3.03129
\(577\) 1.71792e12 0.645225 0.322613 0.946531i \(-0.395439\pi\)
0.322613 + 0.946531i \(0.395439\pi\)
\(578\) −2.93410e11 −0.109345
\(579\) −3.32816e12 −1.23070
\(580\) 2.55106e12 0.936041
\(581\) −6.35663e11 −0.231438
\(582\) −4.77043e12 −1.72347
\(583\) −2.70945e12 −0.971344
\(584\) −8.63301e12 −3.07117
\(585\) 4.64717e12 1.64054
\(586\) 2.22591e12 0.779774
\(587\) 2.32455e12 0.808103 0.404052 0.914736i \(-0.367602\pi\)
0.404052 + 0.914736i \(0.367602\pi\)
\(588\) 4.50246e12 1.55329
\(589\) 3.32401e12 1.13800
\(590\) 3.52344e12 1.19711
\(591\) −1.83820e12 −0.619795
\(592\) −6.41125e12 −2.14533
\(593\) 2.36534e12 0.785503 0.392751 0.919645i \(-0.371523\pi\)
0.392751 + 0.919645i \(0.371523\pi\)
\(594\) 7.62085e12 2.51168
\(595\) 6.03968e11 0.197555
\(596\) 7.36936e12 2.39233
\(597\) −7.79979e11 −0.251303
\(598\) −3.48343e12 −1.11391
\(599\) 1.14807e12 0.364375 0.182188 0.983264i \(-0.441682\pi\)
0.182188 + 0.983264i \(0.441682\pi\)
\(600\) 2.19053e11 0.0690031
\(601\) −3.38041e12 −1.05690 −0.528451 0.848964i \(-0.677227\pi\)
−0.528451 + 0.848964i \(0.677227\pi\)
\(602\) −4.46332e12 −1.38508
\(603\) −2.98359e12 −0.918992
\(604\) 1.27588e13 3.90071
\(605\) −2.32547e12 −0.705685
\(606\) −1.23161e13 −3.70978
\(607\) 2.57549e12 0.770036 0.385018 0.922909i \(-0.374195\pi\)
0.385018 + 0.922909i \(0.374195\pi\)
\(608\) 6.76492e12 2.00769
\(609\) 1.90266e12 0.560509
\(610\) −3.16112e12 −0.924395
\(611\) 2.25628e12 0.654949
\(612\) −4.85615e12 −1.39930
\(613\) −1.91477e12 −0.547701 −0.273851 0.961772i \(-0.588297\pi\)
−0.273851 + 0.961772i \(0.588297\pi\)
\(614\) −2.80509e12 −0.796507
\(615\) −6.35155e12 −1.79037
\(616\) 4.27772e12 1.19701
\(617\) 5.24069e12 1.45581 0.727907 0.685676i \(-0.240493\pi\)
0.727907 + 0.685676i \(0.240493\pi\)
\(618\) 9.17105e12 2.52913
\(619\) −5.64576e10 −0.0154566 −0.00772831 0.999970i \(-0.502460\pi\)
−0.00772831 + 0.999970i \(0.502460\pi\)
\(620\) −1.07170e13 −2.91281
\(621\) −7.91224e12 −2.13495
\(622\) −9.12290e12 −2.44386
\(623\) 4.55884e12 1.21243
\(624\) −1.23688e13 −3.26585
\(625\) −3.86712e12 −1.01374
\(626\) −8.55685e12 −2.22705
\(627\) 3.74223e12 0.967001
\(628\) −6.68717e12 −1.71563
\(629\) 7.93728e11 0.202183
\(630\) 1.40673e13 3.55776
\(631\) 3.44629e12 0.865405 0.432703 0.901537i \(-0.357560\pi\)
0.432703 + 0.901537i \(0.357560\pi\)
\(632\) 1.35828e13 3.38660
\(633\) 8.47382e12 2.09779
\(634\) −9.57462e12 −2.35353
\(635\) −4.72793e12 −1.15396
\(636\) 3.29296e13 7.98048
\(637\) −9.95914e11 −0.239659
\(638\) −1.61094e12 −0.384934
\(639\) −1.25398e13 −2.97533
\(640\) −1.36588e12 −0.321811
\(641\) −5.50971e12 −1.28904 −0.644522 0.764586i \(-0.722943\pi\)
−0.644522 + 0.764586i \(0.722943\pi\)
\(642\) 2.41098e13 5.60126
\(643\) 5.98753e11 0.138133 0.0690667 0.997612i \(-0.477998\pi\)
0.0690667 + 0.997612i \(0.477998\pi\)
\(644\) −7.49291e12 −1.71658
\(645\) 7.46186e12 1.69757
\(646\) −1.92764e12 −0.435491
\(647\) −2.84687e12 −0.638701 −0.319351 0.947637i \(-0.603465\pi\)
−0.319351 + 0.947637i \(0.603465\pi\)
\(648\) −2.63674e13 −5.87462
\(649\) −1.58106e12 −0.349822
\(650\) −8.17454e10 −0.0179619
\(651\) −7.99307e12 −1.74421
\(652\) −1.37023e13 −2.96946
\(653\) −1.82215e12 −0.392170 −0.196085 0.980587i \(-0.562823\pi\)
−0.196085 + 0.980587i \(0.562823\pi\)
\(654\) 1.44739e13 3.09374
\(655\) −3.20122e11 −0.0679562
\(656\) 1.18584e13 2.50011
\(657\) 1.27392e13 2.66745
\(658\) 6.82989e12 1.42036
\(659\) −3.55378e12 −0.734017 −0.367008 0.930218i \(-0.619618\pi\)
−0.367008 + 0.930218i \(0.619618\pi\)
\(660\) −1.20655e13 −2.47512
\(661\) 4.80541e12 0.979093 0.489546 0.871977i \(-0.337162\pi\)
0.489546 + 0.871977i \(0.337162\pi\)
\(662\) −8.31141e12 −1.68195
\(663\) 1.53129e12 0.307784
\(664\) −3.87711e12 −0.774019
\(665\) 3.96794e12 0.786806
\(666\) 1.84870e13 3.64110
\(667\) 1.67253e12 0.327197
\(668\) −7.42457e12 −1.44270
\(669\) 7.78170e12 1.50196
\(670\) 3.81843e12 0.732063
\(671\) 1.41848e12 0.270129
\(672\) −1.62673e13 −3.07718
\(673\) 5.10315e12 0.958894 0.479447 0.877571i \(-0.340837\pi\)
0.479447 + 0.877571i \(0.340837\pi\)
\(674\) −1.94069e11 −0.0362232
\(675\) −1.85676e11 −0.0344262
\(676\) −6.92221e12 −1.27492
\(677\) 2.66255e12 0.487134 0.243567 0.969884i \(-0.421682\pi\)
0.243567 + 0.969884i \(0.421682\pi\)
\(678\) −2.16035e13 −3.92636
\(679\) 2.26972e12 0.409788
\(680\) 3.68380e12 0.660702
\(681\) 1.15341e13 2.05504
\(682\) 6.76757e12 1.19785
\(683\) −3.15981e12 −0.555607 −0.277804 0.960638i \(-0.589606\pi\)
−0.277804 + 0.960638i \(0.589606\pi\)
\(684\) −3.19039e13 −5.57302
\(685\) −5.24708e12 −0.910564
\(686\) −1.17366e13 −2.02342
\(687\) −1.20176e13 −2.05831
\(688\) −1.39313e13 −2.37053
\(689\) −7.28380e12 −1.23132
\(690\) 1.76286e13 2.96071
\(691\) −7.41599e12 −1.23742 −0.618711 0.785619i \(-0.712345\pi\)
−0.618711 + 0.785619i \(0.712345\pi\)
\(692\) 1.67719e13 2.78039
\(693\) −6.31234e12 −1.03966
\(694\) 1.40845e13 2.30474
\(695\) −1.22790e12 −0.199632
\(696\) 1.16049e13 1.87456
\(697\) −1.46810e12 −0.235618
\(698\) 5.80644e12 0.925892
\(699\) 5.34456e12 0.846768
\(700\) −1.75836e11 −0.0276800
\(701\) −9.39002e12 −1.46871 −0.734354 0.678767i \(-0.762515\pi\)
−0.734354 + 0.678767i \(0.762515\pi\)
\(702\) 2.04871e13 3.18392
\(703\) 5.21462e12 0.805237
\(704\) 4.59891e12 0.705631
\(705\) −1.14183e13 −1.74081
\(706\) −1.35658e13 −2.05505
\(707\) 5.85989e12 0.882069
\(708\) 1.92156e13 2.87411
\(709\) 4.58730e11 0.0681788 0.0340894 0.999419i \(-0.489147\pi\)
0.0340894 + 0.999419i \(0.489147\pi\)
\(710\) 1.60485e13 2.37013
\(711\) −2.00433e13 −2.94141
\(712\) 2.78058e13 4.05485
\(713\) −7.02633e12 −1.01818
\(714\) 4.63529e12 0.667475
\(715\) 2.66880e12 0.381890
\(716\) 2.04326e13 2.90546
\(717\) −3.17832e11 −0.0449119
\(718\) −4.61282e12 −0.647749
\(719\) 4.10035e12 0.572191 0.286096 0.958201i \(-0.407643\pi\)
0.286096 + 0.958201i \(0.407643\pi\)
\(720\) 4.39081e13 6.08904
\(721\) −4.36349e12 −0.601347
\(722\) 9.08525e11 0.124428
\(723\) 8.46044e12 1.15152
\(724\) −5.07036e12 −0.685828
\(725\) 3.92493e10 0.00527607
\(726\) −1.78473e13 −2.38428
\(727\) 3.64967e12 0.484561 0.242280 0.970206i \(-0.422105\pi\)
0.242280 + 0.970206i \(0.422105\pi\)
\(728\) 1.14997e13 1.51739
\(729\) 4.43176e12 0.581169
\(730\) −1.63037e13 −2.12487
\(731\) 1.72473e12 0.223406
\(732\) −1.72396e13 −2.21936
\(733\) −2.77480e11 −0.0355029 −0.0177514 0.999842i \(-0.505651\pi\)
−0.0177514 + 0.999842i \(0.505651\pi\)
\(734\) −8.04375e12 −1.02288
\(735\) 5.04001e12 0.636999
\(736\) −1.42998e13 −1.79630
\(737\) −1.71343e12 −0.213925
\(738\) −3.41940e13 −4.24323
\(739\) 1.15877e13 1.42922 0.714608 0.699525i \(-0.246605\pi\)
0.714608 + 0.699525i \(0.246605\pi\)
\(740\) −1.68126e13 −2.06107
\(741\) 1.00602e13 1.22582
\(742\) −2.20485e13 −2.67031
\(743\) 4.79681e12 0.577434 0.288717 0.957414i \(-0.406771\pi\)
0.288717 + 0.957414i \(0.406771\pi\)
\(744\) −4.87523e13 −5.83333
\(745\) 8.24919e12 0.981088
\(746\) −4.96648e12 −0.587116
\(747\) 5.72119e12 0.672270
\(748\) −2.78881e12 −0.325733
\(749\) −1.14712e13 −1.33180
\(750\) −2.92711e13 −3.37802
\(751\) −2.32776e12 −0.267029 −0.133515 0.991047i \(-0.542626\pi\)
−0.133515 + 0.991047i \(0.542626\pi\)
\(752\) 2.13181e13 2.43091
\(753\) 8.09196e12 0.917225
\(754\) −4.33067e12 −0.487960
\(755\) 1.42821e13 1.59967
\(756\) 4.40680e13 4.90654
\(757\) −6.01494e12 −0.665732 −0.332866 0.942974i \(-0.608016\pi\)
−0.332866 + 0.942974i \(0.608016\pi\)
\(758\) 7.44314e12 0.818926
\(759\) −7.91039e12 −0.865187
\(760\) 2.42017e13 2.63139
\(761\) −1.12427e13 −1.21518 −0.607589 0.794252i \(-0.707863\pi\)
−0.607589 + 0.794252i \(0.707863\pi\)
\(762\) −3.62855e13 −3.89885
\(763\) −6.88651e12 −0.735595
\(764\) −1.37048e13 −1.45530
\(765\) −5.43593e12 −0.573849
\(766\) −5.42772e12 −0.569623
\(767\) −4.25035e12 −0.443451
\(768\) 1.22809e13 1.27381
\(769\) 1.35036e13 1.39246 0.696230 0.717819i \(-0.254860\pi\)
0.696230 + 0.717819i \(0.254860\pi\)
\(770\) 8.07860e12 0.828185
\(771\) 1.89201e13 1.92832
\(772\) 1.62946e13 1.65107
\(773\) 2.43055e12 0.244848 0.122424 0.992478i \(-0.460933\pi\)
0.122424 + 0.992478i \(0.460933\pi\)
\(774\) 4.01715e13 4.02331
\(775\) −1.64886e11 −0.0164183
\(776\) 1.38438e13 1.37049
\(777\) −1.25393e13 −1.23418
\(778\) −2.88654e12 −0.282468
\(779\) −9.64508e12 −0.938399
\(780\) −3.24354e13 −3.13757
\(781\) −7.20137e12 −0.692605
\(782\) 4.07466e12 0.389638
\(783\) −9.83667e12 −0.935234
\(784\) −9.40974e12 −0.889519
\(785\) −7.48555e12 −0.703575
\(786\) −2.45684e12 −0.229602
\(787\) −3.78714e12 −0.351905 −0.175953 0.984399i \(-0.556301\pi\)
−0.175953 + 0.984399i \(0.556301\pi\)
\(788\) 8.99975e12 0.831501
\(789\) 1.49399e13 1.37246
\(790\) 2.56516e13 2.34311
\(791\) 1.02787e13 0.933565
\(792\) −3.85010e13 −3.47703
\(793\) 3.81328e12 0.342428
\(794\) −3.29514e13 −2.94226
\(795\) 3.68611e13 3.27277
\(796\) 3.81875e12 0.337142
\(797\) 2.23878e12 0.196539 0.0982694 0.995160i \(-0.468669\pi\)
0.0982694 + 0.995160i \(0.468669\pi\)
\(798\) 3.04528e13 2.65837
\(799\) −2.63924e12 −0.229096
\(800\) −3.35572e11 −0.0289655
\(801\) −4.10311e13 −3.52182
\(802\) −4.48992e12 −0.383225
\(803\) 7.31588e12 0.620936
\(804\) 2.08243e13 1.75759
\(805\) −8.38749e12 −0.703964
\(806\) 1.81932e13 1.51845
\(807\) −3.40745e13 −2.82813
\(808\) 3.57414e13 2.94999
\(809\) −6.77107e12 −0.555762 −0.277881 0.960615i \(-0.589632\pi\)
−0.277881 + 0.960615i \(0.589632\pi\)
\(810\) −4.97956e13 −4.06451
\(811\) 1.26099e13 1.02357 0.511785 0.859113i \(-0.328984\pi\)
0.511785 + 0.859113i \(0.328984\pi\)
\(812\) −9.31534e12 −0.751964
\(813\) 3.22264e13 2.58705
\(814\) 1.06168e13 0.847586
\(815\) −1.53382e13 −1.21777
\(816\) 1.44681e13 1.14237
\(817\) 1.13311e13 0.889762
\(818\) 4.56959e13 3.56851
\(819\) −1.69694e13 −1.31792
\(820\) 3.10970e13 2.40191
\(821\) 1.40858e13 1.08203 0.541013 0.841014i \(-0.318041\pi\)
0.541013 + 0.841014i \(0.318041\pi\)
\(822\) −4.02699e13 −3.07650
\(823\) −1.62081e13 −1.23150 −0.615748 0.787943i \(-0.711146\pi\)
−0.615748 + 0.787943i \(0.711146\pi\)
\(824\) −2.66143e13 −2.01114
\(825\) −1.85633e11 −0.0139512
\(826\) −1.28661e13 −0.961690
\(827\) 8.84797e12 0.657762 0.328881 0.944371i \(-0.393329\pi\)
0.328881 + 0.944371i \(0.393329\pi\)
\(828\) 6.74388e13 4.98624
\(829\) 9.64554e12 0.709302 0.354651 0.934999i \(-0.384600\pi\)
0.354651 + 0.934999i \(0.384600\pi\)
\(830\) −7.32203e12 −0.535526
\(831\) 2.78752e13 2.02775
\(832\) 1.23632e13 0.894491
\(833\) 1.16495e12 0.0838310
\(834\) −9.42379e12 −0.674494
\(835\) −8.31099e12 −0.591649
\(836\) −1.83219e13 −1.29730
\(837\) 4.13239e13 2.91030
\(838\) −2.72822e13 −1.91109
\(839\) 1.77288e13 1.23524 0.617618 0.786478i \(-0.288098\pi\)
0.617618 + 0.786478i \(0.288098\pi\)
\(840\) −5.81967e13 −4.03312
\(841\) −1.24278e13 −0.856668
\(842\) 3.67774e13 2.52160
\(843\) 3.12358e13 2.13024
\(844\) −4.14876e13 −2.81434
\(845\) −7.74865e12 −0.522843
\(846\) −6.14714e13 −4.12579
\(847\) 8.49157e12 0.566908
\(848\) −6.88198e13 −4.57017
\(849\) −5.07625e13 −3.35319
\(850\) 9.56199e10 0.00628294
\(851\) −1.10227e13 −0.720454
\(852\) 8.75225e13 5.69039
\(853\) 1.82317e13 1.17911 0.589557 0.807727i \(-0.299303\pi\)
0.589557 + 0.807727i \(0.299303\pi\)
\(854\) 1.15430e13 0.742607
\(855\) −3.57129e13 −2.28548
\(856\) −6.99664e13 −4.45408
\(857\) −4.46174e12 −0.282547 −0.141273 0.989971i \(-0.545120\pi\)
−0.141273 + 0.989971i \(0.545120\pi\)
\(858\) 2.04823e13 1.29028
\(859\) 2.49571e13 1.56395 0.781977 0.623307i \(-0.214211\pi\)
0.781977 + 0.623307i \(0.214211\pi\)
\(860\) −3.65330e13 −2.27742
\(861\) 2.31930e13 1.43828
\(862\) −1.23558e12 −0.0762231
\(863\) −4.92247e12 −0.302089 −0.151044 0.988527i \(-0.548264\pi\)
−0.151044 + 0.988527i \(0.548264\pi\)
\(864\) 8.41013e13 5.13441
\(865\) 1.87743e13 1.14023
\(866\) 5.62430e13 3.39812
\(867\) −1.79119e12 −0.107660
\(868\) 3.91338e13 2.33999
\(869\) −1.15105e13 −0.684710
\(870\) 2.19162e13 1.29697
\(871\) −4.60619e12 −0.271182
\(872\) −4.20030e13 −2.46012
\(873\) −2.04283e13 −1.19033
\(874\) 2.67696e13 1.55182
\(875\) 1.39269e13 0.803188
\(876\) −8.89143e13 −5.10156
\(877\) −1.68831e13 −0.963725 −0.481863 0.876247i \(-0.660040\pi\)
−0.481863 + 0.876247i \(0.660040\pi\)
\(878\) −3.32539e13 −1.88850
\(879\) 1.35886e13 0.767760
\(880\) 2.52157e13 1.41742
\(881\) −1.26880e13 −0.709583 −0.354792 0.934945i \(-0.615448\pi\)
−0.354792 + 0.934945i \(0.615448\pi\)
\(882\) 2.71333e13 1.50971
\(883\) −2.65648e13 −1.47056 −0.735281 0.677762i \(-0.762950\pi\)
−0.735281 + 0.677762i \(0.762950\pi\)
\(884\) −7.49713e12 −0.412914
\(885\) 2.15097e13 1.17866
\(886\) −4.99736e13 −2.72451
\(887\) −5.71289e11 −0.0309885 −0.0154942 0.999880i \(-0.504932\pi\)
−0.0154942 + 0.999880i \(0.504932\pi\)
\(888\) −7.64814e13 −4.12760
\(889\) 1.72643e13 0.927023
\(890\) 5.25120e13 2.80546
\(891\) 2.23446e13 1.18774
\(892\) −3.80990e13 −2.01498
\(893\) −1.73392e13 −0.912425
\(894\) 6.33103e13 3.31478
\(895\) 2.28720e13 1.19152
\(896\) 4.98757e12 0.258525
\(897\) −2.12654e13 −1.09675
\(898\) −2.54223e13 −1.30458
\(899\) −8.73529e12 −0.446025
\(900\) 1.58258e12 0.0804035
\(901\) 8.52007e12 0.430706
\(902\) −1.96371e13 −0.987751
\(903\) −2.72474e13 −1.36374
\(904\) 6.26931e13 3.12221
\(905\) −5.67571e12 −0.281256
\(906\) 1.09611e14 5.40477
\(907\) 3.29210e12 0.161525 0.0807625 0.996733i \(-0.474264\pi\)
0.0807625 + 0.996733i \(0.474264\pi\)
\(908\) −5.64705e13 −2.75699
\(909\) −5.27411e13 −2.56219
\(910\) 2.17176e13 1.04985
\(911\) −1.27945e13 −0.615445 −0.307723 0.951476i \(-0.599567\pi\)
−0.307723 + 0.951476i \(0.599567\pi\)
\(912\) 9.50524e13 4.54974
\(913\) 3.28559e12 0.156493
\(914\) 4.06107e13 1.92479
\(915\) −1.92978e13 −0.910152
\(916\) 5.88376e13 2.76137
\(917\) 1.16894e12 0.0545922
\(918\) −2.39643e13 −1.11371
\(919\) −3.16626e13 −1.46429 −0.732146 0.681148i \(-0.761481\pi\)
−0.732146 + 0.681148i \(0.761481\pi\)
\(920\) −5.11579e13 −2.35433
\(921\) −1.71244e13 −0.784235
\(922\) −2.16650e12 −0.0987348
\(923\) −1.93594e13 −0.877979
\(924\) 4.40577e13 1.98837
\(925\) −2.58670e11 −0.0116174
\(926\) 3.22208e13 1.44008
\(927\) 3.92730e13 1.74677
\(928\) −1.77778e13 −0.786887
\(929\) −1.31826e13 −0.580673 −0.290336 0.956925i \(-0.593767\pi\)
−0.290336 + 0.956925i \(0.593767\pi\)
\(930\) −9.20701e13 −4.03595
\(931\) 7.65346e12 0.333875
\(932\) −2.61668e13 −1.13600
\(933\) −5.56929e13 −2.40620
\(934\) 6.55493e13 2.81843
\(935\) −3.12177e12 −0.133582
\(936\) −1.03502e14 −4.40765
\(937\) −2.06204e13 −0.873916 −0.436958 0.899482i \(-0.643944\pi\)
−0.436958 + 0.899482i \(0.643944\pi\)
\(938\) −1.39432e13 −0.588099
\(939\) −5.22374e13 −2.19273
\(940\) 5.59038e13 2.33543
\(941\) 2.43975e13 1.01436 0.507180 0.861840i \(-0.330688\pi\)
0.507180 + 0.861840i \(0.330688\pi\)
\(942\) −5.74495e13 −2.37715
\(943\) 2.03879e13 0.839596
\(944\) −4.01588e13 −1.64591
\(945\) 4.93293e13 2.01216
\(946\) 2.30698e13 0.936556
\(947\) −4.10278e13 −1.65769 −0.828845 0.559478i \(-0.811002\pi\)
−0.828845 + 0.559478i \(0.811002\pi\)
\(948\) 1.39894e14 5.62552
\(949\) 1.96672e13 0.787128
\(950\) 6.28202e11 0.0250232
\(951\) −5.84506e13 −2.31727
\(952\) −1.34516e13 −0.530771
\(953\) 4.09880e13 1.60968 0.804839 0.593494i \(-0.202252\pi\)
0.804839 + 0.593494i \(0.202252\pi\)
\(954\) 1.98444e14 7.75659
\(955\) −1.53410e13 −0.596815
\(956\) 1.55610e12 0.0602527
\(957\) −9.83437e12 −0.379003
\(958\) −5.73711e13 −2.20064
\(959\) 1.91600e13 0.731496
\(960\) −6.25663e13 −2.37750
\(961\) 1.02574e13 0.387956
\(962\) 2.85410e13 1.07444
\(963\) 1.03245e14 3.86856
\(964\) −4.14221e13 −1.54485
\(965\) 1.82400e13 0.677098
\(966\) −6.43716e13 −2.37847
\(967\) −4.45707e12 −0.163919 −0.0819597 0.996636i \(-0.526118\pi\)
−0.0819597 + 0.996636i \(0.526118\pi\)
\(968\) 5.17928e13 1.89596
\(969\) −1.17677e13 −0.428781
\(970\) 2.61444e13 0.948211
\(971\) 3.69975e13 1.33563 0.667815 0.744327i \(-0.267230\pi\)
0.667815 + 0.744327i \(0.267230\pi\)
\(972\) −1.02769e14 −3.69288
\(973\) 4.48374e12 0.160374
\(974\) 3.78797e13 1.34863
\(975\) −4.99034e11 −0.0176852
\(976\) 3.60292e13 1.27096
\(977\) 4.72608e13 1.65949 0.829746 0.558141i \(-0.188485\pi\)
0.829746 + 0.558141i \(0.188485\pi\)
\(978\) −1.17716e14 −4.11445
\(979\) −2.35635e13 −0.819819
\(980\) −2.46758e13 −0.854581
\(981\) 6.19811e13 2.13673
\(982\) −1.00727e14 −3.45656
\(983\) −1.37629e13 −0.470130 −0.235065 0.971980i \(-0.575530\pi\)
−0.235065 + 0.971980i \(0.575530\pi\)
\(984\) 1.41462e14 4.81018
\(985\) 1.00742e13 0.340996
\(986\) 5.06571e12 0.170685
\(987\) 4.16947e13 1.39847
\(988\) −4.92545e13 −1.64452
\(989\) −2.39519e13 −0.796080
\(990\) −7.27102e13 −2.40568
\(991\) −3.34745e13 −1.10251 −0.551255 0.834337i \(-0.685851\pi\)
−0.551255 + 0.834337i \(0.685851\pi\)
\(992\) 7.46847e13 2.44866
\(993\) −5.07390e13 −1.65604
\(994\) −5.86020e13 −1.90403
\(995\) 4.27468e12 0.138261
\(996\) −3.99317e13 −1.28573
\(997\) −4.78709e13 −1.53442 −0.767209 0.641398i \(-0.778355\pi\)
−0.767209 + 0.641398i \(0.778355\pi\)
\(998\) 5.04279e13 1.60910
\(999\) 6.48280e13 2.05929
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 17.10.a.a.1.1 5
3.2 odd 2 153.10.a.c.1.5 5
4.3 odd 2 272.10.a.f.1.5 5
17.16 even 2 289.10.a.a.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.a.1.1 5 1.1 even 1 trivial
153.10.a.c.1.5 5 3.2 odd 2
272.10.a.f.1.5 5 4.3 odd 2
289.10.a.a.1.1 5 17.16 even 2