Properties

Label 289.10.a.g.1.14
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-15.8730 q^{2} -48.4836 q^{3} -260.047 q^{4} +2428.05 q^{5} +769.582 q^{6} -4466.03 q^{7} +12254.7 q^{8} -17332.3 q^{9} +O(q^{10})\) \(q-15.8730 q^{2} -48.4836 q^{3} -260.047 q^{4} +2428.05 q^{5} +769.582 q^{6} -4466.03 q^{7} +12254.7 q^{8} -17332.3 q^{9} -38540.5 q^{10} +21984.1 q^{11} +12608.0 q^{12} +143256. q^{13} +70889.3 q^{14} -117721. q^{15} -61375.5 q^{16} +275117. q^{18} -890052. q^{19} -631407. q^{20} +216529. q^{21} -348955. q^{22} +662306. q^{23} -594153. q^{24} +3.94231e6 q^{25} -2.27391e6 q^{26} +1.79464e6 q^{27} +1.16138e6 q^{28} -7.32340e6 q^{29} +1.86858e6 q^{30} +2.75885e6 q^{31} -5.30020e6 q^{32} -1.06587e6 q^{33} -1.08437e7 q^{35} +4.50722e6 q^{36} +7.46885e6 q^{37} +1.41278e7 q^{38} -6.94558e6 q^{39} +2.97551e7 q^{40} +2.16392e7 q^{41} -3.43697e6 q^{42} -3.56652e7 q^{43} -5.71691e6 q^{44} -4.20838e7 q^{45} -1.05128e7 q^{46} -2.23710e7 q^{47} +2.97570e6 q^{48} -2.04082e7 q^{49} -6.25763e7 q^{50} -3.72534e7 q^{52} -4.26210e7 q^{53} -2.84863e7 q^{54} +5.33786e7 q^{55} -5.47299e7 q^{56} +4.31529e7 q^{57} +1.16244e8 q^{58} -6.20388e7 q^{59} +3.06129e7 q^{60} -4.00168e7 q^{61} -4.37913e7 q^{62} +7.74067e7 q^{63} +1.15555e8 q^{64} +3.47834e8 q^{65} +1.69186e7 q^{66} +1.48549e8 q^{67} -3.21110e7 q^{69} +1.72123e8 q^{70} +6.12793e7 q^{71} -2.12403e8 q^{72} +7.82633e7 q^{73} -1.18553e8 q^{74} -1.91137e8 q^{75} +2.31455e8 q^{76} -9.81818e7 q^{77} +1.10247e8 q^{78} +6.49392e8 q^{79} -1.49023e8 q^{80} +2.54142e8 q^{81} -3.43480e8 q^{82} +4.35924e8 q^{83} -5.63077e7 q^{84} +5.66115e8 q^{86} +3.55065e8 q^{87} +2.69410e8 q^{88} -1.34302e8 q^{89} +6.67997e8 q^{90} -6.39786e8 q^{91} -1.72231e8 q^{92} -1.33759e8 q^{93} +3.55095e8 q^{94} -2.16109e9 q^{95} +2.56973e8 q^{96} +1.29796e9 q^{97} +3.23940e8 q^{98} -3.81037e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −15.8730 −0.701495 −0.350748 0.936470i \(-0.614073\pi\)
−0.350748 + 0.936470i \(0.614073\pi\)
\(3\) −48.4836 −0.345581 −0.172790 0.984959i \(-0.555278\pi\)
−0.172790 + 0.984959i \(0.555278\pi\)
\(4\) −260.047 −0.507904
\(5\) 2428.05 1.73737 0.868686 0.495363i \(-0.164965\pi\)
0.868686 + 0.495363i \(0.164965\pi\)
\(6\) 769.582 0.242423
\(7\) −4466.03 −0.703040 −0.351520 0.936180i \(-0.614335\pi\)
−0.351520 + 0.936180i \(0.614335\pi\)
\(8\) 12254.7 1.05779
\(9\) −17332.3 −0.880574
\(10\) −38540.5 −1.21876
\(11\) 21984.1 0.452733 0.226367 0.974042i \(-0.427315\pi\)
0.226367 + 0.974042i \(0.427315\pi\)
\(12\) 12608.0 0.175522
\(13\) 143256. 1.39113 0.695567 0.718462i \(-0.255153\pi\)
0.695567 + 0.718462i \(0.255153\pi\)
\(14\) 70889.3 0.493179
\(15\) −117721. −0.600402
\(16\) −61375.5 −0.234129
\(17\) 0 0
\(18\) 275117. 0.617719
\(19\) −890052. −1.56684 −0.783419 0.621494i \(-0.786526\pi\)
−0.783419 + 0.621494i \(0.786526\pi\)
\(20\) −631407. −0.882419
\(21\) 216529. 0.242957
\(22\) −348955. −0.317590
\(23\) 662306. 0.493495 0.246748 0.969080i \(-0.420638\pi\)
0.246748 + 0.969080i \(0.420638\pi\)
\(24\) −594153. −0.365551
\(25\) 3.94231e6 2.01846
\(26\) −2.27391e6 −0.975873
\(27\) 1.79464e6 0.649890
\(28\) 1.16138e6 0.357077
\(29\) −7.32340e6 −1.92274 −0.961372 0.275252i \(-0.911239\pi\)
−0.961372 + 0.275252i \(0.911239\pi\)
\(30\) 1.86858e6 0.421179
\(31\) 2.75885e6 0.536537 0.268269 0.963344i \(-0.413549\pi\)
0.268269 + 0.963344i \(0.413549\pi\)
\(32\) −5.30020e6 −0.893548
\(33\) −1.06587e6 −0.156456
\(34\) 0 0
\(35\) −1.08437e7 −1.22144
\(36\) 4.50722e6 0.447247
\(37\) 7.46885e6 0.655158 0.327579 0.944824i \(-0.393767\pi\)
0.327579 + 0.944824i \(0.393767\pi\)
\(38\) 1.41278e7 1.09913
\(39\) −6.94558e6 −0.480749
\(40\) 2.97551e7 1.83777
\(41\) 2.16392e7 1.19595 0.597977 0.801514i \(-0.295972\pi\)
0.597977 + 0.801514i \(0.295972\pi\)
\(42\) −3.43697e6 −0.170433
\(43\) −3.56652e7 −1.59088 −0.795439 0.606033i \(-0.792760\pi\)
−0.795439 + 0.606033i \(0.792760\pi\)
\(44\) −5.71691e6 −0.229945
\(45\) −4.20838e7 −1.52988
\(46\) −1.05128e7 −0.346185
\(47\) −2.23710e7 −0.668721 −0.334361 0.942445i \(-0.608520\pi\)
−0.334361 + 0.942445i \(0.608520\pi\)
\(48\) 2.97570e6 0.0809104
\(49\) −2.04082e7 −0.505735
\(50\) −6.25763e7 −1.41594
\(51\) 0 0
\(52\) −3.72534e7 −0.706563
\(53\) −4.26210e7 −0.741962 −0.370981 0.928640i \(-0.620979\pi\)
−0.370981 + 0.928640i \(0.620979\pi\)
\(54\) −2.84863e7 −0.455895
\(55\) 5.33786e7 0.786566
\(56\) −5.47299e7 −0.743667
\(57\) 4.31529e7 0.541469
\(58\) 1.16244e8 1.34880
\(59\) −6.20388e7 −0.666544 −0.333272 0.942831i \(-0.608153\pi\)
−0.333272 + 0.942831i \(0.608153\pi\)
\(60\) 3.06129e7 0.304947
\(61\) −4.00168e7 −0.370048 −0.185024 0.982734i \(-0.559236\pi\)
−0.185024 + 0.982734i \(0.559236\pi\)
\(62\) −4.37913e7 −0.376378
\(63\) 7.74067e7 0.619079
\(64\) 1.15555e8 0.860948
\(65\) 3.47834e8 2.41692
\(66\) 1.69186e7 0.109753
\(67\) 1.48549e8 0.900604 0.450302 0.892876i \(-0.351316\pi\)
0.450302 + 0.892876i \(0.351316\pi\)
\(68\) 0 0
\(69\) −3.21110e7 −0.170542
\(70\) 1.72123e8 0.856836
\(71\) 6.12793e7 0.286188 0.143094 0.989709i \(-0.454295\pi\)
0.143094 + 0.989709i \(0.454295\pi\)
\(72\) −2.12403e8 −0.931460
\(73\) 7.82633e7 0.322556 0.161278 0.986909i \(-0.448438\pi\)
0.161278 + 0.986909i \(0.448438\pi\)
\(74\) −1.18553e8 −0.459590
\(75\) −1.91137e8 −0.697541
\(76\) 2.31455e8 0.795804
\(77\) −9.81818e7 −0.318290
\(78\) 1.10247e8 0.337243
\(79\) 6.49392e8 1.87579 0.937897 0.346915i \(-0.112771\pi\)
0.937897 + 0.346915i \(0.112771\pi\)
\(80\) −1.49023e8 −0.406769
\(81\) 2.54142e8 0.655985
\(82\) −3.43480e8 −0.838955
\(83\) 4.35924e8 1.00823 0.504114 0.863637i \(-0.331819\pi\)
0.504114 + 0.863637i \(0.331819\pi\)
\(84\) −5.63077e7 −0.123399
\(85\) 0 0
\(86\) 5.66115e8 1.11599
\(87\) 3.55065e8 0.664463
\(88\) 2.69410e8 0.478896
\(89\) −1.34302e8 −0.226896 −0.113448 0.993544i \(-0.536190\pi\)
−0.113448 + 0.993544i \(0.536190\pi\)
\(90\) 6.67997e8 1.07321
\(91\) −6.39786e8 −0.978022
\(92\) −1.72231e8 −0.250648
\(93\) −1.33759e8 −0.185417
\(94\) 3.55095e8 0.469105
\(95\) −2.16109e9 −2.72218
\(96\) 2.56973e8 0.308793
\(97\) 1.29796e9 1.48864 0.744319 0.667824i \(-0.232774\pi\)
0.744319 + 0.667824i \(0.232774\pi\)
\(98\) 3.23940e8 0.354771
\(99\) −3.81037e8 −0.398665
\(100\) −1.02519e9 −1.02519
\(101\) 4.94104e8 0.472468 0.236234 0.971696i \(-0.424087\pi\)
0.236234 + 0.971696i \(0.424087\pi\)
\(102\) 0 0
\(103\) −4.01668e8 −0.351641 −0.175820 0.984422i \(-0.556258\pi\)
−0.175820 + 0.984422i \(0.556258\pi\)
\(104\) 1.75557e9 1.47152
\(105\) 5.25744e8 0.422107
\(106\) 6.76524e8 0.520483
\(107\) −6.36178e8 −0.469193 −0.234597 0.972093i \(-0.575377\pi\)
−0.234597 + 0.972093i \(0.575377\pi\)
\(108\) −4.66690e8 −0.330082
\(109\) −5.87368e8 −0.398557 −0.199279 0.979943i \(-0.563860\pi\)
−0.199279 + 0.979943i \(0.563860\pi\)
\(110\) −8.47280e8 −0.551772
\(111\) −3.62117e8 −0.226410
\(112\) 2.74104e8 0.164602
\(113\) 8.71750e8 0.502967 0.251483 0.967862i \(-0.419082\pi\)
0.251483 + 0.967862i \(0.419082\pi\)
\(114\) −6.84968e8 −0.379838
\(115\) 1.60811e9 0.857385
\(116\) 1.90443e9 0.976570
\(117\) −2.48297e9 −1.22500
\(118\) 9.84743e8 0.467578
\(119\) 0 0
\(120\) −1.44263e9 −0.635098
\(121\) −1.87465e9 −0.795033
\(122\) 6.35188e8 0.259587
\(123\) −1.04915e9 −0.413298
\(124\) −7.17430e8 −0.272510
\(125\) 4.82983e9 1.76945
\(126\) −1.22868e9 −0.434281
\(127\) −3.22257e9 −1.09922 −0.549612 0.835420i \(-0.685224\pi\)
−0.549612 + 0.835420i \(0.685224\pi\)
\(128\) 8.79504e8 0.289596
\(129\) 1.72918e9 0.549777
\(130\) −5.52117e9 −1.69545
\(131\) 5.60718e8 0.166350 0.0831752 0.996535i \(-0.473494\pi\)
0.0831752 + 0.996535i \(0.473494\pi\)
\(132\) 2.77177e8 0.0794646
\(133\) 3.97500e9 1.10155
\(134\) −2.35793e9 −0.631770
\(135\) 4.35747e9 1.12910
\(136\) 0 0
\(137\) −1.78950e9 −0.434000 −0.217000 0.976172i \(-0.569627\pi\)
−0.217000 + 0.976172i \(0.569627\pi\)
\(138\) 5.09698e8 0.119635
\(139\) −2.43292e9 −0.552791 −0.276395 0.961044i \(-0.589140\pi\)
−0.276395 + 0.961044i \(0.589140\pi\)
\(140\) 2.81988e9 0.620376
\(141\) 1.08463e9 0.231097
\(142\) −9.72688e8 −0.200759
\(143\) 3.14937e9 0.629812
\(144\) 1.06378e9 0.206168
\(145\) −1.77816e10 −3.34052
\(146\) −1.24228e9 −0.226272
\(147\) 9.89464e8 0.174772
\(148\) −1.94225e9 −0.332758
\(149\) 9.51092e9 1.58083 0.790414 0.612573i \(-0.209866\pi\)
0.790414 + 0.612573i \(0.209866\pi\)
\(150\) 3.03393e9 0.489322
\(151\) −6.09642e9 −0.954286 −0.477143 0.878826i \(-0.658328\pi\)
−0.477143 + 0.878826i \(0.658328\pi\)
\(152\) −1.09073e10 −1.65738
\(153\) 0 0
\(154\) 1.55844e9 0.223279
\(155\) 6.69862e9 0.932165
\(156\) 1.80618e9 0.244174
\(157\) −8.40518e9 −1.10407 −0.552037 0.833819i \(-0.686149\pi\)
−0.552037 + 0.833819i \(0.686149\pi\)
\(158\) −1.03078e10 −1.31586
\(159\) 2.06642e9 0.256408
\(160\) −1.28692e10 −1.55242
\(161\) −2.95787e9 −0.346947
\(162\) −4.03400e9 −0.460170
\(163\) −1.00708e10 −1.11743 −0.558716 0.829359i \(-0.688706\pi\)
−0.558716 + 0.829359i \(0.688706\pi\)
\(164\) −5.62721e9 −0.607430
\(165\) −2.58799e9 −0.271822
\(166\) −6.91943e9 −0.707268
\(167\) −1.49703e10 −1.48938 −0.744689 0.667412i \(-0.767402\pi\)
−0.744689 + 0.667412i \(0.767402\pi\)
\(168\) 2.65350e9 0.256997
\(169\) 9.91787e9 0.935251
\(170\) 0 0
\(171\) 1.54267e10 1.37972
\(172\) 9.27464e9 0.808014
\(173\) 1.10306e10 0.936251 0.468125 0.883662i \(-0.344930\pi\)
0.468125 + 0.883662i \(0.344930\pi\)
\(174\) −5.63595e9 −0.466118
\(175\) −1.76064e10 −1.41906
\(176\) −1.34929e9 −0.105998
\(177\) 3.00786e9 0.230345
\(178\) 2.13178e9 0.159167
\(179\) 2.23877e10 1.62993 0.814967 0.579507i \(-0.196755\pi\)
0.814967 + 0.579507i \(0.196755\pi\)
\(180\) 1.09438e10 0.777035
\(181\) −2.36348e8 −0.0163681 −0.00818406 0.999967i \(-0.502605\pi\)
−0.00818406 + 0.999967i \(0.502605\pi\)
\(182\) 1.01553e10 0.686078
\(183\) 1.94016e9 0.127881
\(184\) 8.11637e9 0.522013
\(185\) 1.81348e10 1.13825
\(186\) 2.12316e9 0.130069
\(187\) 0 0
\(188\) 5.81751e9 0.339646
\(189\) −8.01490e9 −0.456899
\(190\) 3.43031e10 1.90960
\(191\) −3.52505e10 −1.91653 −0.958263 0.285888i \(-0.907712\pi\)
−0.958263 + 0.285888i \(0.907712\pi\)
\(192\) −5.60250e9 −0.297527
\(193\) −7.61462e9 −0.395039 −0.197520 0.980299i \(-0.563289\pi\)
−0.197520 + 0.980299i \(0.563289\pi\)
\(194\) −2.06026e10 −1.04427
\(195\) −1.68642e10 −0.835239
\(196\) 5.30710e9 0.256865
\(197\) −3.34785e10 −1.58368 −0.791841 0.610727i \(-0.790877\pi\)
−0.791841 + 0.610727i \(0.790877\pi\)
\(198\) 6.04820e9 0.279662
\(199\) −2.41289e10 −1.09068 −0.545341 0.838214i \(-0.683600\pi\)
−0.545341 + 0.838214i \(0.683600\pi\)
\(200\) 4.83119e10 2.13510
\(201\) −7.20221e9 −0.311231
\(202\) −7.84293e9 −0.331434
\(203\) 3.27065e10 1.35177
\(204\) 0 0
\(205\) 5.25411e10 2.07782
\(206\) 6.37568e9 0.246674
\(207\) −1.14793e10 −0.434559
\(208\) −8.79242e9 −0.325704
\(209\) −1.95670e10 −0.709360
\(210\) −8.34514e9 −0.296106
\(211\) −3.68923e9 −0.128134 −0.0640670 0.997946i \(-0.520407\pi\)
−0.0640670 + 0.997946i \(0.520407\pi\)
\(212\) 1.10835e10 0.376846
\(213\) −2.97104e9 −0.0989009
\(214\) 1.00981e10 0.329137
\(215\) −8.65970e10 −2.76395
\(216\) 2.19928e10 0.687446
\(217\) −1.23211e10 −0.377207
\(218\) 9.32330e9 0.279586
\(219\) −3.79449e9 −0.111469
\(220\) −1.38810e10 −0.399500
\(221\) 0 0
\(222\) 5.74789e9 0.158826
\(223\) −2.42406e10 −0.656403 −0.328202 0.944608i \(-0.606443\pi\)
−0.328202 + 0.944608i \(0.606443\pi\)
\(224\) 2.36708e10 0.628200
\(225\) −6.83294e10 −1.77740
\(226\) −1.38373e10 −0.352829
\(227\) −3.81355e10 −0.953263 −0.476632 0.879103i \(-0.658142\pi\)
−0.476632 + 0.879103i \(0.658142\pi\)
\(228\) −1.12218e10 −0.275014
\(229\) −2.50865e10 −0.602811 −0.301405 0.953496i \(-0.597456\pi\)
−0.301405 + 0.953496i \(0.597456\pi\)
\(230\) −2.55256e10 −0.601452
\(231\) 4.76021e9 0.109995
\(232\) −8.97462e10 −2.03386
\(233\) −5.62023e10 −1.24926 −0.624629 0.780922i \(-0.714750\pi\)
−0.624629 + 0.780922i \(0.714750\pi\)
\(234\) 3.94122e10 0.859329
\(235\) −5.43179e10 −1.16182
\(236\) 1.61330e10 0.338541
\(237\) −3.14849e10 −0.648238
\(238\) 0 0
\(239\) −7.40488e10 −1.46800 −0.734002 0.679147i \(-0.762350\pi\)
−0.734002 + 0.679147i \(0.762350\pi\)
\(240\) 7.22516e9 0.140571
\(241\) 5.63579e10 1.07616 0.538081 0.842893i \(-0.319149\pi\)
0.538081 + 0.842893i \(0.319149\pi\)
\(242\) 2.97563e10 0.557712
\(243\) −4.76456e10 −0.876585
\(244\) 1.04063e10 0.187949
\(245\) −4.95522e10 −0.878649
\(246\) 1.66531e10 0.289927
\(247\) −1.27506e11 −2.17968
\(248\) 3.38089e10 0.567543
\(249\) −2.11352e10 −0.348424
\(250\) −7.66641e10 −1.24126
\(251\) 8.30760e10 1.32112 0.660562 0.750771i \(-0.270318\pi\)
0.660562 + 0.750771i \(0.270318\pi\)
\(252\) −2.01294e10 −0.314433
\(253\) 1.45602e10 0.223422
\(254\) 5.11520e10 0.771100
\(255\) 0 0
\(256\) −7.31243e10 −1.06410
\(257\) −9.70659e8 −0.0138793 −0.00693965 0.999976i \(-0.502209\pi\)
−0.00693965 + 0.999976i \(0.502209\pi\)
\(258\) −2.74473e10 −0.385666
\(259\) −3.33561e10 −0.460602
\(260\) −9.04531e10 −1.22756
\(261\) 1.26932e11 1.69312
\(262\) −8.90030e9 −0.116694
\(263\) 1.27231e10 0.163981 0.0819903 0.996633i \(-0.473872\pi\)
0.0819903 + 0.996633i \(0.473872\pi\)
\(264\) −1.30620e10 −0.165497
\(265\) −1.03486e11 −1.28906
\(266\) −6.30952e10 −0.772732
\(267\) 6.51145e9 0.0784110
\(268\) −3.86298e10 −0.457421
\(269\) 7.46392e10 0.869124 0.434562 0.900642i \(-0.356903\pi\)
0.434562 + 0.900642i \(0.356903\pi\)
\(270\) −6.91663e10 −0.792059
\(271\) 3.55669e10 0.400576 0.200288 0.979737i \(-0.435812\pi\)
0.200288 + 0.979737i \(0.435812\pi\)
\(272\) 0 0
\(273\) 3.10192e10 0.337986
\(274\) 2.84048e10 0.304449
\(275\) 8.66682e10 0.913825
\(276\) 8.35036e9 0.0866193
\(277\) −1.20820e11 −1.23305 −0.616523 0.787337i \(-0.711459\pi\)
−0.616523 + 0.787337i \(0.711459\pi\)
\(278\) 3.86178e10 0.387780
\(279\) −4.78173e10 −0.472461
\(280\) −1.32887e11 −1.29203
\(281\) 1.28296e11 1.22754 0.613770 0.789485i \(-0.289652\pi\)
0.613770 + 0.789485i \(0.289652\pi\)
\(282\) −1.72163e10 −0.162113
\(283\) −7.04261e10 −0.652672 −0.326336 0.945254i \(-0.605814\pi\)
−0.326336 + 0.945254i \(0.605814\pi\)
\(284\) −1.59355e10 −0.145356
\(285\) 1.04778e11 0.940733
\(286\) −4.99900e10 −0.441810
\(287\) −9.66413e10 −0.840803
\(288\) 9.18649e10 0.786835
\(289\) 0 0
\(290\) 2.82247e11 2.34336
\(291\) −6.29299e10 −0.514444
\(292\) −2.03521e10 −0.163828
\(293\) −7.69646e10 −0.610080 −0.305040 0.952340i \(-0.598670\pi\)
−0.305040 + 0.952340i \(0.598670\pi\)
\(294\) −1.57058e10 −0.122602
\(295\) −1.50633e11 −1.15804
\(296\) 9.15287e10 0.693018
\(297\) 3.94536e10 0.294227
\(298\) −1.50967e11 −1.10894
\(299\) 9.48795e10 0.686518
\(300\) 4.97047e10 0.354284
\(301\) 1.59282e11 1.11845
\(302\) 9.67686e10 0.669427
\(303\) −2.39559e10 −0.163276
\(304\) 5.46274e10 0.366842
\(305\) −9.71628e10 −0.642911
\(306\) 0 0
\(307\) 1.31136e11 0.842556 0.421278 0.906932i \(-0.361582\pi\)
0.421278 + 0.906932i \(0.361582\pi\)
\(308\) 2.55319e10 0.161661
\(309\) 1.94743e10 0.121520
\(310\) −1.06327e11 −0.653909
\(311\) 7.55464e10 0.457923 0.228961 0.973436i \(-0.426467\pi\)
0.228961 + 0.973436i \(0.426467\pi\)
\(312\) −8.51162e10 −0.508530
\(313\) −1.33488e11 −0.786124 −0.393062 0.919512i \(-0.628584\pi\)
−0.393062 + 0.919512i \(0.628584\pi\)
\(314\) 1.33416e11 0.774503
\(315\) 1.87947e11 1.07557
\(316\) −1.68872e11 −0.952724
\(317\) 1.70712e11 0.949504 0.474752 0.880120i \(-0.342538\pi\)
0.474752 + 0.880120i \(0.342538\pi\)
\(318\) −3.28003e10 −0.179869
\(319\) −1.60999e11 −0.870491
\(320\) 2.80572e11 1.49579
\(321\) 3.08442e10 0.162144
\(322\) 4.69504e10 0.243382
\(323\) 0 0
\(324\) −6.60889e10 −0.333177
\(325\) 5.64760e11 2.80795
\(326\) 1.59854e11 0.783873
\(327\) 2.84777e10 0.137734
\(328\) 2.65183e11 1.26506
\(329\) 9.99095e10 0.470138
\(330\) 4.10792e10 0.190682
\(331\) −3.45316e11 −1.58121 −0.790607 0.612324i \(-0.790235\pi\)
−0.790607 + 0.612324i \(0.790235\pi\)
\(332\) −1.13361e11 −0.512084
\(333\) −1.29453e11 −0.576915
\(334\) 2.37623e11 1.04479
\(335\) 3.60685e11 1.56468
\(336\) −1.32896e10 −0.0568832
\(337\) −3.93578e10 −0.166225 −0.0831124 0.996540i \(-0.526486\pi\)
−0.0831124 + 0.996540i \(0.526486\pi\)
\(338\) −1.57427e11 −0.656075
\(339\) −4.22656e10 −0.173816
\(340\) 0 0
\(341\) 6.06509e10 0.242908
\(342\) −2.44868e11 −0.967865
\(343\) 2.71364e11 1.05859
\(344\) −4.37068e11 −1.68281
\(345\) −7.79671e10 −0.296296
\(346\) −1.75089e11 −0.656776
\(347\) −3.03167e11 −1.12254 −0.561268 0.827634i \(-0.689686\pi\)
−0.561268 + 0.827634i \(0.689686\pi\)
\(348\) −9.23335e10 −0.337484
\(349\) −2.17407e11 −0.784438 −0.392219 0.919872i \(-0.628292\pi\)
−0.392219 + 0.919872i \(0.628292\pi\)
\(350\) 2.79468e11 0.995463
\(351\) 2.57093e11 0.904083
\(352\) −1.16520e11 −0.404539
\(353\) 1.13984e10 0.0390713 0.0195357 0.999809i \(-0.493781\pi\)
0.0195357 + 0.999809i \(0.493781\pi\)
\(354\) −4.77439e10 −0.161586
\(355\) 1.48789e11 0.497215
\(356\) 3.49248e10 0.115242
\(357\) 0 0
\(358\) −3.55360e11 −1.14339
\(359\) 1.51806e11 0.482353 0.241177 0.970481i \(-0.422467\pi\)
0.241177 + 0.970481i \(0.422467\pi\)
\(360\) −5.15725e11 −1.61829
\(361\) 4.69505e11 1.45498
\(362\) 3.75156e9 0.0114822
\(363\) 9.08896e10 0.274748
\(364\) 1.66375e11 0.496742
\(365\) 1.90027e11 0.560400
\(366\) −3.07962e10 −0.0897082
\(367\) −3.80539e11 −1.09497 −0.547485 0.836815i \(-0.684415\pi\)
−0.547485 + 0.836815i \(0.684415\pi\)
\(368\) −4.06493e10 −0.115542
\(369\) −3.75058e11 −1.05313
\(370\) −2.87853e11 −0.798479
\(371\) 1.90346e11 0.521629
\(372\) 3.47836e10 0.0941741
\(373\) −3.16010e11 −0.845300 −0.422650 0.906293i \(-0.638900\pi\)
−0.422650 + 0.906293i \(0.638900\pi\)
\(374\) 0 0
\(375\) −2.34168e11 −0.611486
\(376\) −2.74150e11 −0.707365
\(377\) −1.04912e12 −2.67479
\(378\) 1.27221e11 0.320512
\(379\) 1.32469e11 0.329791 0.164895 0.986311i \(-0.447271\pi\)
0.164895 + 0.986311i \(0.447271\pi\)
\(380\) 5.61986e11 1.38261
\(381\) 1.56242e11 0.379870
\(382\) 5.59532e11 1.34443
\(383\) 4.90368e11 1.16447 0.582234 0.813021i \(-0.302179\pi\)
0.582234 + 0.813021i \(0.302179\pi\)
\(384\) −4.26416e10 −0.100079
\(385\) −2.38390e11 −0.552988
\(386\) 1.20867e11 0.277118
\(387\) 6.18162e11 1.40089
\(388\) −3.37531e11 −0.756086
\(389\) −3.90430e11 −0.864510 −0.432255 0.901751i \(-0.642282\pi\)
−0.432255 + 0.901751i \(0.642282\pi\)
\(390\) 2.67686e11 0.585916
\(391\) 0 0
\(392\) −2.50097e11 −0.534960
\(393\) −2.71857e10 −0.0574875
\(394\) 5.31405e11 1.11095
\(395\) 1.57676e12 3.25895
\(396\) 9.90874e10 0.202484
\(397\) −7.00249e10 −0.141480 −0.0707400 0.997495i \(-0.522536\pi\)
−0.0707400 + 0.997495i \(0.522536\pi\)
\(398\) 3.82998e11 0.765108
\(399\) −1.92722e11 −0.380674
\(400\) −2.41961e11 −0.472580
\(401\) 5.37662e11 1.03839 0.519194 0.854656i \(-0.326232\pi\)
0.519194 + 0.854656i \(0.326232\pi\)
\(402\) 1.14321e11 0.218327
\(403\) 3.95222e11 0.746395
\(404\) −1.28490e11 −0.239968
\(405\) 6.17070e11 1.13969
\(406\) −5.19151e11 −0.948258
\(407\) 1.64196e11 0.296612
\(408\) 0 0
\(409\) −5.21834e11 −0.922098 −0.461049 0.887375i \(-0.652527\pi\)
−0.461049 + 0.887375i \(0.652527\pi\)
\(410\) −8.33986e11 −1.45758
\(411\) 8.67615e10 0.149982
\(412\) 1.04453e11 0.178600
\(413\) 2.77067e11 0.468607
\(414\) 1.82211e11 0.304841
\(415\) 1.05844e12 1.75167
\(416\) −7.59288e11 −1.24304
\(417\) 1.17957e11 0.191034
\(418\) 3.10588e11 0.497613
\(419\) 1.54318e11 0.244598 0.122299 0.992493i \(-0.460973\pi\)
0.122299 + 0.992493i \(0.460973\pi\)
\(420\) −1.36718e11 −0.214390
\(421\) −1.13057e12 −1.75399 −0.876993 0.480503i \(-0.840454\pi\)
−0.876993 + 0.480503i \(0.840454\pi\)
\(422\) 5.85592e10 0.0898854
\(423\) 3.87742e11 0.588858
\(424\) −5.22308e11 −0.784839
\(425\) 0 0
\(426\) 4.71594e10 0.0693785
\(427\) 1.78716e11 0.260159
\(428\) 1.65436e11 0.238305
\(429\) −1.52693e11 −0.217651
\(430\) 1.37456e12 1.93890
\(431\) −4.96507e11 −0.693071 −0.346536 0.938037i \(-0.612642\pi\)
−0.346536 + 0.938037i \(0.612642\pi\)
\(432\) −1.10147e11 −0.152158
\(433\) 1.23842e12 1.69306 0.846528 0.532344i \(-0.178689\pi\)
0.846528 + 0.532344i \(0.178689\pi\)
\(434\) 1.95573e11 0.264609
\(435\) 8.62115e11 1.15442
\(436\) 1.52743e11 0.202429
\(437\) −5.89487e11 −0.773228
\(438\) 6.02300e10 0.0781951
\(439\) −1.51231e12 −1.94335 −0.971676 0.236315i \(-0.924060\pi\)
−0.971676 + 0.236315i \(0.924060\pi\)
\(440\) 6.54140e11 0.832020
\(441\) 3.53722e11 0.445337
\(442\) 0 0
\(443\) −2.39610e11 −0.295589 −0.147794 0.989018i \(-0.547217\pi\)
−0.147794 + 0.989018i \(0.547217\pi\)
\(444\) 9.41675e10 0.114995
\(445\) −3.26092e11 −0.394203
\(446\) 3.84771e11 0.460464
\(447\) −4.61124e11 −0.546303
\(448\) −5.16069e11 −0.605281
\(449\) −3.99939e11 −0.464393 −0.232196 0.972669i \(-0.574591\pi\)
−0.232196 + 0.972669i \(0.574591\pi\)
\(450\) 1.08459e12 1.24684
\(451\) 4.75720e11 0.541448
\(452\) −2.26696e11 −0.255459
\(453\) 2.95576e11 0.329783
\(454\) 6.05325e11 0.668710
\(455\) −1.55343e12 −1.69919
\(456\) 5.28827e11 0.572759
\(457\) 1.61345e12 1.73034 0.865171 0.501477i \(-0.167210\pi\)
0.865171 + 0.501477i \(0.167210\pi\)
\(458\) 3.98199e11 0.422869
\(459\) 0 0
\(460\) −4.18185e11 −0.435470
\(461\) −1.26730e12 −1.30685 −0.653425 0.756991i \(-0.726668\pi\)
−0.653425 + 0.756991i \(0.726668\pi\)
\(462\) −7.55589e10 −0.0771608
\(463\) −1.23047e12 −1.24439 −0.622196 0.782861i \(-0.713759\pi\)
−0.622196 + 0.782861i \(0.713759\pi\)
\(464\) 4.49477e11 0.450170
\(465\) −3.24773e11 −0.322138
\(466\) 8.92100e11 0.876349
\(467\) −9.79986e11 −0.953441 −0.476721 0.879055i \(-0.658175\pi\)
−0.476721 + 0.879055i \(0.658175\pi\)
\(468\) 6.45688e11 0.622181
\(469\) −6.63425e11 −0.633161
\(470\) 8.62190e11 0.815009
\(471\) 4.07513e11 0.381547
\(472\) −7.60268e11 −0.705062
\(473\) −7.84070e11 −0.720244
\(474\) 4.99760e11 0.454736
\(475\) −3.50886e12 −3.16260
\(476\) 0 0
\(477\) 7.38721e11 0.653353
\(478\) 1.17538e12 1.02980
\(479\) −2.13470e12 −1.85279 −0.926397 0.376548i \(-0.877111\pi\)
−0.926397 + 0.376548i \(0.877111\pi\)
\(480\) 6.23944e11 0.536488
\(481\) 1.06996e12 0.911412
\(482\) −8.94570e11 −0.754923
\(483\) 1.43408e11 0.119898
\(484\) 4.87496e11 0.403800
\(485\) 3.15152e12 2.58632
\(486\) 7.56279e11 0.614921
\(487\) 1.34470e12 1.08329 0.541644 0.840608i \(-0.317802\pi\)
0.541644 + 0.840608i \(0.317802\pi\)
\(488\) −4.90395e11 −0.391432
\(489\) 4.88270e11 0.386163
\(490\) 7.86543e11 0.616368
\(491\) 1.75641e11 0.136383 0.0681913 0.997672i \(-0.478277\pi\)
0.0681913 + 0.997672i \(0.478277\pi\)
\(492\) 2.72828e11 0.209916
\(493\) 0 0
\(494\) 2.02390e12 1.52904
\(495\) −9.25176e11 −0.692630
\(496\) −1.69326e11 −0.125619
\(497\) −2.73675e11 −0.201201
\(498\) 3.35479e11 0.244418
\(499\) 9.01484e11 0.650887 0.325443 0.945562i \(-0.394486\pi\)
0.325443 + 0.945562i \(0.394486\pi\)
\(500\) −1.25598e12 −0.898709
\(501\) 7.25812e11 0.514700
\(502\) −1.31867e12 −0.926762
\(503\) −1.28195e12 −0.892924 −0.446462 0.894803i \(-0.647316\pi\)
−0.446462 + 0.894803i \(0.647316\pi\)
\(504\) 9.48597e11 0.654854
\(505\) 1.19971e12 0.820852
\(506\) −2.31115e11 −0.156729
\(507\) −4.80854e11 −0.323205
\(508\) 8.38020e11 0.558300
\(509\) 1.25166e12 0.826524 0.413262 0.910612i \(-0.364389\pi\)
0.413262 + 0.910612i \(0.364389\pi\)
\(510\) 0 0
\(511\) −3.49526e11 −0.226770
\(512\) 7.10398e11 0.456864
\(513\) −1.59732e12 −1.01827
\(514\) 1.54073e10 0.00973626
\(515\) −9.75270e11 −0.610931
\(516\) −4.49668e11 −0.279234
\(517\) −4.91807e11 −0.302752
\(518\) 5.29462e11 0.323110
\(519\) −5.34804e11 −0.323550
\(520\) 4.26260e12 2.55658
\(521\) −5.85435e11 −0.348104 −0.174052 0.984736i \(-0.555686\pi\)
−0.174052 + 0.984736i \(0.555686\pi\)
\(522\) −2.01479e12 −1.18771
\(523\) −1.16953e12 −0.683525 −0.341762 0.939786i \(-0.611024\pi\)
−0.341762 + 0.939786i \(0.611024\pi\)
\(524\) −1.45813e11 −0.0844901
\(525\) 8.53624e11 0.490399
\(526\) −2.01954e11 −0.115032
\(527\) 0 0
\(528\) 6.54183e10 0.0366308
\(529\) −1.36250e12 −0.756462
\(530\) 1.64263e12 0.904273
\(531\) 1.07528e12 0.586942
\(532\) −1.03369e12 −0.559482
\(533\) 3.09995e12 1.66373
\(534\) −1.03356e11 −0.0550049
\(535\) −1.54467e12 −0.815163
\(536\) 1.82043e12 0.952648
\(537\) −1.08543e12 −0.563274
\(538\) −1.18475e12 −0.609686
\(539\) −4.48657e11 −0.228963
\(540\) −1.13315e12 −0.573475
\(541\) −1.45321e12 −0.729357 −0.364679 0.931133i \(-0.618821\pi\)
−0.364679 + 0.931133i \(0.618821\pi\)
\(542\) −5.64555e11 −0.281002
\(543\) 1.14590e10 0.00565650
\(544\) 0 0
\(545\) −1.42616e12 −0.692442
\(546\) −4.92368e11 −0.237095
\(547\) 3.19340e12 1.52514 0.762570 0.646906i \(-0.223937\pi\)
0.762570 + 0.646906i \(0.223937\pi\)
\(548\) 4.65355e11 0.220430
\(549\) 6.93585e11 0.325855
\(550\) −1.37569e12 −0.641044
\(551\) 6.51821e12 3.01263
\(552\) −3.93511e11 −0.180398
\(553\) −2.90020e12 −1.31876
\(554\) 1.91778e12 0.864976
\(555\) −8.79239e11 −0.393358
\(556\) 6.32673e11 0.280765
\(557\) −1.04458e12 −0.459826 −0.229913 0.973211i \(-0.573844\pi\)
−0.229913 + 0.973211i \(0.573844\pi\)
\(558\) 7.59005e11 0.331429
\(559\) −5.10927e12 −2.21312
\(560\) 6.65539e11 0.285975
\(561\) 0 0
\(562\) −2.03645e12 −0.861113
\(563\) −2.66226e12 −1.11677 −0.558383 0.829583i \(-0.688578\pi\)
−0.558383 + 0.829583i \(0.688578\pi\)
\(564\) −2.82054e11 −0.117375
\(565\) 2.11665e12 0.873840
\(566\) 1.11788e12 0.457846
\(567\) −1.13500e12 −0.461184
\(568\) 7.50960e11 0.302726
\(569\) 9.20307e11 0.368067 0.184034 0.982920i \(-0.441084\pi\)
0.184034 + 0.982920i \(0.441084\pi\)
\(570\) −1.66314e12 −0.659920
\(571\) −1.38081e12 −0.543589 −0.271794 0.962355i \(-0.587617\pi\)
−0.271794 + 0.962355i \(0.587617\pi\)
\(572\) −8.18984e11 −0.319884
\(573\) 1.70907e12 0.662314
\(574\) 1.53399e12 0.589819
\(575\) 2.61101e12 0.996101
\(576\) −2.00283e12 −0.758129
\(577\) 1.98045e12 0.743828 0.371914 0.928267i \(-0.378702\pi\)
0.371914 + 0.928267i \(0.378702\pi\)
\(578\) 0 0
\(579\) 3.69184e11 0.136518
\(580\) 4.62405e12 1.69667
\(581\) −1.94685e12 −0.708825
\(582\) 9.98888e11 0.360880
\(583\) −9.36986e11 −0.335911
\(584\) 9.59095e11 0.341196
\(585\) −6.02877e12 −2.12827
\(586\) 1.22166e12 0.427968
\(587\) −5.11913e12 −1.77961 −0.889805 0.456341i \(-0.849160\pi\)
−0.889805 + 0.456341i \(0.849160\pi\)
\(588\) −2.57307e11 −0.0887675
\(589\) −2.45552e12 −0.840667
\(590\) 2.39101e12 0.812356
\(591\) 1.62316e12 0.547290
\(592\) −4.58404e11 −0.153391
\(593\) −8.08587e11 −0.268522 −0.134261 0.990946i \(-0.542866\pi\)
−0.134261 + 0.990946i \(0.542866\pi\)
\(594\) −6.26248e11 −0.206399
\(595\) 0 0
\(596\) −2.47329e12 −0.802909
\(597\) 1.16985e12 0.376918
\(598\) −1.50602e12 −0.481589
\(599\) −1.96284e12 −0.622967 −0.311484 0.950252i \(-0.600826\pi\)
−0.311484 + 0.950252i \(0.600826\pi\)
\(600\) −2.34233e12 −0.737850
\(601\) 4.48619e12 1.40263 0.701314 0.712853i \(-0.252597\pi\)
0.701314 + 0.712853i \(0.252597\pi\)
\(602\) −2.52829e12 −0.784589
\(603\) −2.57471e12 −0.793049
\(604\) 1.58536e12 0.484686
\(605\) −4.55173e12 −1.38127
\(606\) 3.80253e11 0.114537
\(607\) −5.04286e12 −1.50775 −0.753873 0.657021i \(-0.771816\pi\)
−0.753873 + 0.657021i \(0.771816\pi\)
\(608\) 4.71746e12 1.40004
\(609\) −1.58573e12 −0.467144
\(610\) 1.54227e12 0.450999
\(611\) −3.20479e12 −0.930280
\(612\) 0 0
\(613\) 3.39549e12 0.971249 0.485625 0.874168i \(-0.338592\pi\)
0.485625 + 0.874168i \(0.338592\pi\)
\(614\) −2.08152e12 −0.591049
\(615\) −2.54738e12 −0.718053
\(616\) −1.20319e12 −0.336683
\(617\) 5.56583e11 0.154613 0.0773066 0.997007i \(-0.475368\pi\)
0.0773066 + 0.997007i \(0.475368\pi\)
\(618\) −3.09116e11 −0.0852459
\(619\) −2.87119e12 −0.786058 −0.393029 0.919526i \(-0.628573\pi\)
−0.393029 + 0.919526i \(0.628573\pi\)
\(620\) −1.74196e12 −0.473451
\(621\) 1.18860e12 0.320718
\(622\) −1.19915e12 −0.321231
\(623\) 5.99796e11 0.159517
\(624\) 4.26288e11 0.112557
\(625\) 4.02726e12 1.05572
\(626\) 2.11885e12 0.551463
\(627\) 9.48681e11 0.245141
\(628\) 2.18574e12 0.560764
\(629\) 0 0
\(630\) −2.98329e12 −0.754507
\(631\) 1.47246e12 0.369754 0.184877 0.982762i \(-0.440811\pi\)
0.184877 + 0.982762i \(0.440811\pi\)
\(632\) 7.95812e12 1.98419
\(633\) 1.78867e11 0.0442806
\(634\) −2.70971e12 −0.666073
\(635\) −7.82457e12 −1.90976
\(636\) −5.37366e11 −0.130231
\(637\) −2.92361e12 −0.703544
\(638\) 2.55554e12 0.610645
\(639\) −1.06211e12 −0.252009
\(640\) 2.13548e12 0.503137
\(641\) −6.49183e11 −0.151882 −0.0759410 0.997112i \(-0.524196\pi\)
−0.0759410 + 0.997112i \(0.524196\pi\)
\(642\) −4.89591e11 −0.113743
\(643\) 2.06799e12 0.477088 0.238544 0.971132i \(-0.423330\pi\)
0.238544 + 0.971132i \(0.423330\pi\)
\(644\) 7.69186e11 0.176216
\(645\) 4.19854e12 0.955167
\(646\) 0 0
\(647\) 2.01350e12 0.451733 0.225866 0.974158i \(-0.427479\pi\)
0.225866 + 0.974158i \(0.427479\pi\)
\(648\) 3.11444e12 0.693893
\(649\) −1.36387e12 −0.301767
\(650\) −8.96445e12 −1.96976
\(651\) 5.97371e11 0.130356
\(652\) 2.61889e12 0.567548
\(653\) 1.23496e12 0.265793 0.132897 0.991130i \(-0.457572\pi\)
0.132897 + 0.991130i \(0.457572\pi\)
\(654\) −4.52027e11 −0.0966195
\(655\) 1.36145e12 0.289013
\(656\) −1.32812e12 −0.280007
\(657\) −1.35649e12 −0.284035
\(658\) −1.58587e12 −0.329799
\(659\) 7.92786e12 1.63746 0.818732 0.574176i \(-0.194678\pi\)
0.818732 + 0.574176i \(0.194678\pi\)
\(660\) 6.72999e11 0.138060
\(661\) 7.17711e11 0.146232 0.0731161 0.997323i \(-0.476706\pi\)
0.0731161 + 0.997323i \(0.476706\pi\)
\(662\) 5.48121e12 1.10921
\(663\) 0 0
\(664\) 5.34212e12 1.06649
\(665\) 9.65149e12 1.91380
\(666\) 2.05481e12 0.404703
\(667\) −4.85033e12 −0.948866
\(668\) 3.89297e12 0.756462
\(669\) 1.17527e12 0.226840
\(670\) −5.72517e12 −1.09762
\(671\) −8.79735e11 −0.167533
\(672\) −1.14765e12 −0.217094
\(673\) −8.48479e12 −1.59431 −0.797156 0.603774i \(-0.793663\pi\)
−0.797156 + 0.603774i \(0.793663\pi\)
\(674\) 6.24727e11 0.116606
\(675\) 7.07501e12 1.31178
\(676\) −2.57911e12 −0.475018
\(677\) 2.00433e12 0.366707 0.183354 0.983047i \(-0.441305\pi\)
0.183354 + 0.983047i \(0.441305\pi\)
\(678\) 6.70883e11 0.121931
\(679\) −5.79673e12 −1.04657
\(680\) 0 0
\(681\) 1.84895e12 0.329429
\(682\) −9.62713e11 −0.170399
\(683\) 8.85663e12 1.55731 0.778656 0.627452i \(-0.215902\pi\)
0.778656 + 0.627452i \(0.215902\pi\)
\(684\) −4.01166e12 −0.700764
\(685\) −4.34500e12 −0.754019
\(686\) −4.30737e12 −0.742597
\(687\) 1.21629e12 0.208320
\(688\) 2.18897e12 0.372471
\(689\) −6.10572e12 −1.03217
\(690\) 1.23757e12 0.207850
\(691\) 5.14389e12 0.858303 0.429151 0.903233i \(-0.358813\pi\)
0.429151 + 0.903233i \(0.358813\pi\)
\(692\) −2.86848e12 −0.475526
\(693\) 1.70172e12 0.280278
\(694\) 4.81219e12 0.787453
\(695\) −5.90725e12 −0.960403
\(696\) 4.35122e12 0.702861
\(697\) 0 0
\(698\) 3.45090e12 0.550279
\(699\) 2.72489e12 0.431719
\(700\) 4.57850e12 0.720746
\(701\) 3.26944e12 0.511378 0.255689 0.966759i \(-0.417698\pi\)
0.255689 + 0.966759i \(0.417698\pi\)
\(702\) −4.08085e12 −0.634210
\(703\) −6.64767e12 −1.02653
\(704\) 2.54037e12 0.389780
\(705\) 2.63353e12 0.401501
\(706\) −1.80927e11 −0.0274084
\(707\) −2.20668e12 −0.332164
\(708\) −7.82186e11 −0.116993
\(709\) 9.57298e12 1.42278 0.711392 0.702795i \(-0.248065\pi\)
0.711392 + 0.702795i \(0.248065\pi\)
\(710\) −2.36173e12 −0.348794
\(711\) −1.12555e13 −1.65177
\(712\) −1.64583e12 −0.240008
\(713\) 1.82720e12 0.264779
\(714\) 0 0
\(715\) 7.64682e12 1.09422
\(716\) −5.82184e12 −0.827851
\(717\) 3.59015e12 0.507314
\(718\) −2.40963e12 −0.338369
\(719\) −1.00459e13 −1.40187 −0.700934 0.713226i \(-0.747233\pi\)
−0.700934 + 0.713226i \(0.747233\pi\)
\(720\) 2.58291e12 0.358190
\(721\) 1.79386e12 0.247218
\(722\) −7.45247e12 −1.02066
\(723\) −2.73243e12 −0.371901
\(724\) 6.14617e10 0.00831344
\(725\) −2.88711e13 −3.88098
\(726\) −1.44269e12 −0.192734
\(727\) 9.98108e12 1.32517 0.662587 0.748985i \(-0.269459\pi\)
0.662587 + 0.748985i \(0.269459\pi\)
\(728\) −7.84041e12 −1.03454
\(729\) −2.69225e12 −0.353054
\(730\) −3.01631e12 −0.393118
\(731\) 0 0
\(732\) −5.04533e11 −0.0649515
\(733\) −4.32594e12 −0.553494 −0.276747 0.960943i \(-0.589256\pi\)
−0.276747 + 0.960943i \(0.589256\pi\)
\(734\) 6.04031e12 0.768116
\(735\) 2.40247e12 0.303644
\(736\) −3.51035e12 −0.440962
\(737\) 3.26573e12 0.407734
\(738\) 5.95331e12 0.738762
\(739\) 1.24858e12 0.153999 0.0769994 0.997031i \(-0.475466\pi\)
0.0769994 + 0.997031i \(0.475466\pi\)
\(740\) −4.71589e12 −0.578124
\(741\) 6.18193e12 0.753256
\(742\) −3.02137e12 −0.365920
\(743\) −3.11363e12 −0.374815 −0.187407 0.982282i \(-0.560008\pi\)
−0.187407 + 0.982282i \(0.560008\pi\)
\(744\) −1.63918e12 −0.196132
\(745\) 2.30930e13 2.74649
\(746\) 5.01603e12 0.592974
\(747\) −7.55558e12 −0.887820
\(748\) 0 0
\(749\) 2.84119e12 0.329862
\(750\) 3.71695e12 0.428954
\(751\) −9.85249e12 −1.13023 −0.565114 0.825013i \(-0.691168\pi\)
−0.565114 + 0.825013i \(0.691168\pi\)
\(752\) 1.37303e12 0.156567
\(753\) −4.02782e12 −0.456555
\(754\) 1.66528e13 1.87636
\(755\) −1.48024e13 −1.65795
\(756\) 2.08425e12 0.232061
\(757\) 4.15725e12 0.460124 0.230062 0.973176i \(-0.426107\pi\)
0.230062 + 0.973176i \(0.426107\pi\)
\(758\) −2.10269e12 −0.231347
\(759\) −7.05932e11 −0.0772103
\(760\) −2.64836e13 −2.87949
\(761\) −4.49422e12 −0.485762 −0.242881 0.970056i \(-0.578093\pi\)
−0.242881 + 0.970056i \(0.578093\pi\)
\(762\) −2.48003e12 −0.266477
\(763\) 2.62320e12 0.280202
\(764\) 9.16678e12 0.973412
\(765\) 0 0
\(766\) −7.78362e12 −0.816869
\(767\) −8.88744e12 −0.927252
\(768\) 3.54533e12 0.367732
\(769\) −4.28087e12 −0.441432 −0.220716 0.975338i \(-0.570839\pi\)
−0.220716 + 0.975338i \(0.570839\pi\)
\(770\) 3.78398e12 0.387918
\(771\) 4.70610e10 0.00479642
\(772\) 1.98016e12 0.200642
\(773\) 1.39605e13 1.40634 0.703172 0.711020i \(-0.251766\pi\)
0.703172 + 0.711020i \(0.251766\pi\)
\(774\) −9.81210e12 −0.982715
\(775\) 1.08762e13 1.08298
\(776\) 1.59062e13 1.57466
\(777\) 1.61722e12 0.159175
\(778\) 6.19730e12 0.606450
\(779\) −1.92600e13 −1.87387
\(780\) 4.38549e12 0.424222
\(781\) 1.34717e12 0.129567
\(782\) 0 0
\(783\) −1.31428e13 −1.24957
\(784\) 1.25256e12 0.118407
\(785\) −2.04082e13 −1.91819
\(786\) 4.31519e11 0.0403272
\(787\) −1.89749e13 −1.76316 −0.881582 0.472031i \(-0.843521\pi\)
−0.881582 + 0.472031i \(0.843521\pi\)
\(788\) 8.70599e12 0.804359
\(789\) −6.16862e11 −0.0566685
\(790\) −2.50279e13 −2.28614
\(791\) −3.89326e12 −0.353606
\(792\) −4.66950e12 −0.421703
\(793\) −5.73266e12 −0.514786
\(794\) 1.11151e12 0.0992475
\(795\) 5.01737e12 0.445476
\(796\) 6.27464e12 0.553962
\(797\) −1.03483e13 −0.908464 −0.454232 0.890884i \(-0.650086\pi\)
−0.454232 + 0.890884i \(0.650086\pi\)
\(798\) 3.05908e12 0.267041
\(799\) 0 0
\(800\) −2.08950e13 −1.80359
\(801\) 2.32777e12 0.199799
\(802\) −8.53432e12 −0.728424
\(803\) 1.72055e12 0.146032
\(804\) 1.87291e12 0.158076
\(805\) −7.18187e12 −0.602776
\(806\) −6.27337e12 −0.523593
\(807\) −3.61878e12 −0.300352
\(808\) 6.05511e12 0.499771
\(809\) 1.61301e13 1.32394 0.661971 0.749530i \(-0.269720\pi\)
0.661971 + 0.749530i \(0.269720\pi\)
\(810\) −9.79476e12 −0.799487
\(811\) −9.61956e12 −0.780839 −0.390420 0.920637i \(-0.627670\pi\)
−0.390420 + 0.920637i \(0.627670\pi\)
\(812\) −8.50522e12 −0.686568
\(813\) −1.72441e12 −0.138431
\(814\) −2.60629e12 −0.208072
\(815\) −2.44525e13 −1.94139
\(816\) 0 0
\(817\) 3.17439e13 2.49265
\(818\) 8.28308e12 0.646848
\(819\) 1.10890e13 0.861221
\(820\) −1.36632e13 −1.05533
\(821\) 1.30064e13 0.999107 0.499554 0.866283i \(-0.333497\pi\)
0.499554 + 0.866283i \(0.333497\pi\)
\(822\) −1.37717e12 −0.105212
\(823\) −1.73488e12 −0.131817 −0.0659083 0.997826i \(-0.520994\pi\)
−0.0659083 + 0.997826i \(0.520994\pi\)
\(824\) −4.92233e12 −0.371962
\(825\) −4.20199e12 −0.315800
\(826\) −4.39789e12 −0.328726
\(827\) −1.96073e13 −1.45762 −0.728809 0.684717i \(-0.759926\pi\)
−0.728809 + 0.684717i \(0.759926\pi\)
\(828\) 2.98516e12 0.220715
\(829\) −1.71286e13 −1.25958 −0.629791 0.776765i \(-0.716859\pi\)
−0.629791 + 0.776765i \(0.716859\pi\)
\(830\) −1.68007e13 −1.22879
\(831\) 5.85778e12 0.426117
\(832\) 1.65539e13 1.19769
\(833\) 0 0
\(834\) −1.87233e12 −0.134009
\(835\) −3.63485e13 −2.58760
\(836\) 5.08835e12 0.360287
\(837\) 4.95113e12 0.348690
\(838\) −2.44950e12 −0.171585
\(839\) −1.66805e13 −1.16220 −0.581100 0.813832i \(-0.697377\pi\)
−0.581100 + 0.813832i \(0.697377\pi\)
\(840\) 6.44284e12 0.446499
\(841\) 3.91250e13 2.69695
\(842\) 1.79455e13 1.23041
\(843\) −6.22026e12 −0.424214
\(844\) 9.59373e11 0.0650798
\(845\) 2.40811e13 1.62488
\(846\) −6.15463e12 −0.413081
\(847\) 8.37221e12 0.558940
\(848\) 2.61588e12 0.173715
\(849\) 3.41451e12 0.225551
\(850\) 0 0
\(851\) 4.94666e12 0.323318
\(852\) 7.72610e11 0.0502322
\(853\) 1.49736e13 0.968402 0.484201 0.874957i \(-0.339110\pi\)
0.484201 + 0.874957i \(0.339110\pi\)
\(854\) −2.83677e12 −0.182500
\(855\) 3.74568e13 2.39708
\(856\) −7.79619e12 −0.496307
\(857\) −9.74340e12 −0.617017 −0.308508 0.951222i \(-0.599830\pi\)
−0.308508 + 0.951222i \(0.599830\pi\)
\(858\) 2.42370e12 0.152681
\(859\) 5.47136e12 0.342867 0.171434 0.985196i \(-0.445160\pi\)
0.171434 + 0.985196i \(0.445160\pi\)
\(860\) 2.25193e13 1.40382
\(861\) 4.68552e12 0.290565
\(862\) 7.88107e12 0.486186
\(863\) 1.55255e12 0.0952788 0.0476394 0.998865i \(-0.484830\pi\)
0.0476394 + 0.998865i \(0.484830\pi\)
\(864\) −9.51194e12 −0.580708
\(865\) 2.67829e13 1.62662
\(866\) −1.96574e13 −1.18767
\(867\) 0 0
\(868\) 3.20406e12 0.191585
\(869\) 1.42763e13 0.849234
\(870\) −1.36844e13 −0.809820
\(871\) 2.12806e13 1.25286
\(872\) −7.19803e12 −0.421589
\(873\) −2.24967e13 −1.31086
\(874\) 9.35694e12 0.542416
\(875\) −2.15702e13 −1.24399
\(876\) 9.86745e11 0.0566157
\(877\) −2.75972e13 −1.57531 −0.787657 0.616114i \(-0.788706\pi\)
−0.787657 + 0.616114i \(0.788706\pi\)
\(878\) 2.40050e13 1.36325
\(879\) 3.73152e12 0.210832
\(880\) −3.27614e12 −0.184158
\(881\) −9.63378e12 −0.538772 −0.269386 0.963032i \(-0.586821\pi\)
−0.269386 + 0.963032i \(0.586821\pi\)
\(882\) −5.61464e12 −0.312402
\(883\) 5.06505e12 0.280389 0.140194 0.990124i \(-0.455227\pi\)
0.140194 + 0.990124i \(0.455227\pi\)
\(884\) 0 0
\(885\) 7.30324e12 0.400195
\(886\) 3.80333e12 0.207354
\(887\) −7.16561e12 −0.388684 −0.194342 0.980934i \(-0.562257\pi\)
−0.194342 + 0.980934i \(0.562257\pi\)
\(888\) −4.43764e12 −0.239494
\(889\) 1.43921e13 0.772798
\(890\) 5.17607e12 0.276532
\(891\) 5.58709e12 0.296986
\(892\) 6.30369e12 0.333390
\(893\) 1.99114e13 1.04778
\(894\) 7.31943e12 0.383229
\(895\) 5.43584e13 2.83180
\(896\) −3.92789e12 −0.203598
\(897\) −4.60010e12 −0.237247
\(898\) 6.34824e12 0.325769
\(899\) −2.02041e13 −1.03162
\(900\) 1.77689e13 0.902751
\(901\) 0 0
\(902\) −7.55111e12 −0.379823
\(903\) −7.72256e12 −0.386515
\(904\) 1.06831e13 0.532032
\(905\) −5.73866e11 −0.0284375
\(906\) −4.69169e12 −0.231341
\(907\) 6.59573e12 0.323616 0.161808 0.986822i \(-0.448267\pi\)
0.161808 + 0.986822i \(0.448267\pi\)
\(908\) 9.91702e12 0.484167
\(909\) −8.56398e12 −0.416043
\(910\) 2.46577e13 1.19197
\(911\) −8.62810e12 −0.415033 −0.207516 0.978232i \(-0.566538\pi\)
−0.207516 + 0.978232i \(0.566538\pi\)
\(912\) −2.64853e12 −0.126774
\(913\) 9.58341e12 0.456459
\(914\) −2.56103e13 −1.21383
\(915\) 4.71081e12 0.222178
\(916\) 6.52368e12 0.306170
\(917\) −2.50418e12 −0.116951
\(918\) 0 0
\(919\) 1.96750e13 0.909904 0.454952 0.890516i \(-0.349656\pi\)
0.454952 + 0.890516i \(0.349656\pi\)
\(920\) 1.97070e13 0.906932
\(921\) −6.35794e12 −0.291171
\(922\) 2.01159e13 0.916749
\(923\) 8.77864e12 0.398125
\(924\) −1.23788e12 −0.0558668
\(925\) 2.94445e13 1.32241
\(926\) 1.95313e13 0.872935
\(927\) 6.96184e12 0.309646
\(928\) 3.88155e13 1.71806
\(929\) 6.78089e12 0.298687 0.149343 0.988785i \(-0.452284\pi\)
0.149343 + 0.988785i \(0.452284\pi\)
\(930\) 5.15514e12 0.225978
\(931\) 1.81644e13 0.792405
\(932\) 1.46152e13 0.634504
\(933\) −3.66276e12 −0.158249
\(934\) 1.55553e13 0.668834
\(935\) 0 0
\(936\) −3.04281e13 −1.29579
\(937\) 3.12613e12 0.132489 0.0662444 0.997803i \(-0.478898\pi\)
0.0662444 + 0.997803i \(0.478898\pi\)
\(938\) 1.05306e13 0.444159
\(939\) 6.47196e12 0.271669
\(940\) 1.41252e13 0.590092
\(941\) 2.63364e13 1.09497 0.547486 0.836815i \(-0.315585\pi\)
0.547486 + 0.836815i \(0.315585\pi\)
\(942\) −6.46847e12 −0.267653
\(943\) 1.43318e13 0.590197
\(944\) 3.80766e12 0.156057
\(945\) −1.94606e13 −0.793803
\(946\) 1.24456e13 0.505248
\(947\) −2.29699e13 −0.928078 −0.464039 0.885815i \(-0.653600\pi\)
−0.464039 + 0.885815i \(0.653600\pi\)
\(948\) 8.18755e12 0.329243
\(949\) 1.12117e13 0.448719
\(950\) 5.56962e13 2.21855
\(951\) −8.27672e12 −0.328130
\(952\) 0 0
\(953\) −5.43234e12 −0.213338 −0.106669 0.994295i \(-0.534019\pi\)
−0.106669 + 0.994295i \(0.534019\pi\)
\(954\) −1.17257e13 −0.458324
\(955\) −8.55899e13 −3.32972
\(956\) 1.92562e13 0.745606
\(957\) 7.80579e12 0.300825
\(958\) 3.38842e13 1.29973
\(959\) 7.99196e12 0.305119
\(960\) −1.36032e13 −0.516915
\(961\) −1.88284e13 −0.712128
\(962\) −1.69835e13 −0.639351
\(963\) 1.10265e13 0.413159
\(964\) −1.46557e13 −0.546588
\(965\) −1.84887e13 −0.686330
\(966\) −2.27633e12 −0.0841080
\(967\) −1.59119e13 −0.585198 −0.292599 0.956235i \(-0.594520\pi\)
−0.292599 + 0.956235i \(0.594520\pi\)
\(968\) −2.29733e13 −0.840976
\(969\) 0 0
\(970\) −5.00241e13 −1.81429
\(971\) −2.24064e13 −0.808884 −0.404442 0.914564i \(-0.632534\pi\)
−0.404442 + 0.914564i \(0.632534\pi\)
\(972\) 1.23901e13 0.445222
\(973\) 1.08655e13 0.388634
\(974\) −2.13444e13 −0.759921
\(975\) −2.73816e13 −0.970372
\(976\) 2.45605e12 0.0866389
\(977\) 2.29831e13 0.807018 0.403509 0.914976i \(-0.367790\pi\)
0.403509 + 0.914976i \(0.367790\pi\)
\(978\) −7.75032e12 −0.270891
\(979\) −2.95251e12 −0.102724
\(980\) 1.28859e13 0.446270
\(981\) 1.01805e13 0.350959
\(982\) −2.78795e12 −0.0956718
\(983\) 9.11746e10 0.00311446 0.00155723 0.999999i \(-0.499504\pi\)
0.00155723 + 0.999999i \(0.499504\pi\)
\(984\) −1.28570e13 −0.437182
\(985\) −8.12876e13 −2.75145
\(986\) 0 0
\(987\) −4.84397e12 −0.162470
\(988\) 3.31575e13 1.10707
\(989\) −2.36213e13 −0.785092
\(990\) 1.46853e13 0.485877
\(991\) 2.14881e13 0.707728 0.353864 0.935297i \(-0.384868\pi\)
0.353864 + 0.935297i \(0.384868\pi\)
\(992\) −1.46225e13 −0.479422
\(993\) 1.67422e13 0.546437
\(994\) 4.34405e12 0.141142
\(995\) −5.85861e13 −1.89492
\(996\) 5.49613e12 0.176966
\(997\) −1.07717e13 −0.345267 −0.172634 0.984986i \(-0.555228\pi\)
−0.172634 + 0.984986i \(0.555228\pi\)
\(998\) −1.43093e13 −0.456594
\(999\) 1.34039e13 0.425781
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 289.10.a.g.1.14 36
17.16 even 2 289.10.a.h.1.14 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.14 36 1.1 even 1 trivial
289.10.a.h.1.14 yes 36 17.16 even 2