Properties

Label 289.10.a.h.1.14
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
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: \(0\)
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 \(-0.444722\pi\)
0.172790 + 0.984959i \(0.444722\pi\)
\(4\) −260.047 −0.507904
\(5\) −2428.05 −1.73737 −0.868686 0.495363i \(-0.835035\pi\)
−0.868686 + 0.495363i \(0.835035\pi\)
\(6\) −769.582 −0.242423
\(7\) 4466.03 0.703040 0.351520 0.936180i \(-0.385665\pi\)
0.351520 + 0.936180i \(0.385665\pi\)
\(8\) 12254.7 1.05779
\(9\) −17332.3 −0.880574
\(10\) 38540.5 1.21876
\(11\) −21984.1 −0.452733 −0.226367 0.974042i \(-0.572685\pi\)
−0.226367 + 0.974042i \(0.572685\pi\)
\(12\) −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 \(-0.579362\pi\)
−0.246748 + 0.969080i \(0.579362\pi\)
\(24\) 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 \(-0.0887612\pi\)
0.961372 + 0.275252i \(0.0887612\pi\)
\(30\) 1.86858e6 0.421179
\(31\) −2.75885e6 −0.536537 −0.268269 0.963344i \(-0.586451\pi\)
−0.268269 + 0.963344i \(0.586451\pi\)
\(32\) −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 \(-0.606233\pi\)
−0.327579 + 0.944824i \(0.606233\pi\)
\(38\) 1.41278e7 1.09913
\(39\) 6.94558e6 0.480749
\(40\) −2.97551e7 −1.83777
\(41\) −2.16392e7 −1.19595 −0.597977 0.801514i \(-0.704028\pi\)
−0.597977 + 0.801514i \(0.704028\pi\)
\(42\) −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 \(-0.440764\pi\)
0.185024 + 0.982734i \(0.440764\pi\)
\(62\) 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 \(-0.545705\pi\)
−0.143094 + 0.989709i \(0.545705\pi\)
\(72\) −2.12403e8 −0.931460
\(73\) −7.82633e7 −0.322556 −0.161278 0.986909i \(-0.551562\pi\)
−0.161278 + 0.986909i \(0.551562\pi\)
\(74\) 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 \(-0.887229\pi\)
−0.937897 + 0.346915i \(0.887229\pi\)
\(80\) 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 \(-0.767226\pi\)
−0.744319 + 0.667824i \(0.767226\pi\)
\(98\) 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 \(-0.424623\pi\)
0.234597 + 0.972093i \(0.424623\pi\)
\(108\) 4.66690e8 0.330082
\(109\) 5.87368e8 0.398557 0.199279 0.979943i \(-0.436140\pi\)
0.199279 + 0.979943i \(0.436140\pi\)
\(110\) −8.47280e8 −0.551772
\(111\) −3.62117e8 −0.226410
\(112\) −2.74104e8 −0.164602
\(113\) −8.71750e8 −0.502967 −0.251483 0.967862i \(-0.580918\pi\)
−0.251483 + 0.967862i \(0.580918\pi\)
\(114\) 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 \(-0.526506\pi\)
−0.0831752 + 0.996535i \(0.526506\pi\)
\(132\) 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 \(-0.410860\pi\)
0.276395 + 0.961044i \(0.410860\pi\)
\(140\) 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 \(-0.311294\pi\)
0.558716 + 0.829359i \(0.311294\pi\)
\(164\) 5.62721e9 0.607430
\(165\) 2.58799e9 0.271822
\(166\) −6.91943e9 −0.707268
\(167\) 1.49703e10 1.48938 0.744689 0.667412i \(-0.232598\pi\)
0.744689 + 0.667412i \(0.232598\pi\)
\(168\) 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 \(-0.655070\pi\)
−0.468125 + 0.883662i \(0.655070\pi\)
\(174\) −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 \(-0.497395\pi\)
0.00818406 + 0.999967i \(0.497395\pi\)
\(182\) −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 \(-0.436711\pi\)
0.197520 + 0.980299i \(0.436711\pi\)
\(194\) 2.06026e10 1.04427
\(195\) −1.68642e10 −0.835239
\(196\) 5.30710e9 0.256865
\(197\) 3.34785e10 1.58368 0.791841 0.610727i \(-0.209123\pi\)
0.791841 + 0.610727i \(0.209123\pi\)
\(198\) −6.04820e9 −0.279662
\(199\) 2.41289e10 1.09068 0.545341 0.838214i \(-0.316400\pi\)
0.545341 + 0.838214i \(0.316400\pi\)
\(200\) 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 \(-0.479593\pi\)
0.0640670 + 0.997946i \(0.479593\pi\)
\(212\) 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 \(-0.341858\pi\)
0.476632 + 0.879103i \(0.341858\pi\)
\(228\) 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 \(-0.285250\pi\)
0.624629 + 0.780922i \(0.285250\pi\)
\(234\) 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 \(-0.680851\pi\)
−0.538081 + 0.842893i \(0.680851\pi\)
\(242\) 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 \(-0.643097\pi\)
−0.434562 + 0.900642i \(0.643097\pi\)
\(270\) −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 \(-0.288541\pi\)
0.616523 + 0.787337i \(0.288541\pi\)
\(278\) −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 \(-0.394186\pi\)
0.326336 + 0.945254i \(0.394186\pi\)
\(284\) 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 \(-0.573533\pi\)
−0.228961 + 0.973436i \(0.573533\pi\)
\(312\) 8.51162e10 0.508530
\(313\) 1.33488e11 0.786124 0.393062 0.919512i \(-0.371416\pi\)
0.393062 + 0.919512i \(0.371416\pi\)
\(314\) 1.33416e11 0.774503
\(315\) 1.87947e11 1.07557
\(316\) 1.68872e11 0.952724
\(317\) −1.70712e11 −0.949504 −0.474752 0.880120i \(-0.657462\pi\)
−0.474752 + 0.880120i \(0.657462\pi\)
\(318\) 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 \(-0.473514\pi\)
0.0831124 + 0.996540i \(0.473514\pi\)
\(338\) −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 \(-0.310314\pi\)
0.561268 + 0.827634i \(0.310314\pi\)
\(348\) −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 \(-0.315585\pi\)
0.547485 + 0.836815i \(0.315585\pi\)
\(368\) 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 \(-0.552729\pi\)
−0.164895 + 0.986311i \(0.552729\pi\)
\(380\) −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 \(-0.477464\pi\)
0.0707400 + 0.997495i \(0.477464\pi\)
\(398\) −3.82998e11 −0.765108
\(399\) −1.92722e11 −0.380674
\(400\) −2.41961e11 −0.472580
\(401\) −5.37662e11 −1.03839 −0.519194 0.854656i \(-0.673768\pi\)
−0.519194 + 0.854656i \(0.673768\pi\)
\(402\) −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 \(-0.539027\pi\)
−0.122299 + 0.992493i \(0.539027\pi\)
\(420\) 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 \(-0.387358\pi\)
0.346536 + 0.938037i \(0.387358\pi\)
\(432\) 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 \(-0.0759398\pi\)
0.971676 + 0.236315i \(0.0759398\pi\)
\(440\) 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 \(-0.425409\pi\)
0.232196 + 0.972669i \(0.425409\pi\)
\(450\) 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 \(-0.122889\pi\)
0.926397 + 0.376548i \(0.122889\pi\)
\(480\) 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 \(-0.682198\pi\)
−0.541644 + 0.840608i \(0.682198\pi\)
\(488\) 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 \(-0.605514\pi\)
−0.325443 + 0.945562i \(0.605514\pi\)
\(500\) 1.25598e12 0.898709
\(501\) 7.25812e11 0.514700
\(502\) −1.31867e12 −0.926762
\(503\) 1.28195e12 0.892924 0.446462 0.894803i \(-0.352684\pi\)
0.446462 + 0.894803i \(0.352684\pi\)
\(504\) −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 \(-0.444314\pi\)
0.174052 + 0.984736i \(0.444314\pi\)
\(522\) 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 \(-0.381179\pi\)
0.364679 + 0.931133i \(0.381179\pi\)
\(542\) −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 \(-0.776063\pi\)
−0.762570 + 0.646906i \(0.776063\pi\)
\(548\) 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 \(-0.412383\pi\)
0.271794 + 0.962355i \(0.412383\pi\)
\(572\) 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 \(-0.747403\pi\)
−0.701314 + 0.712853i \(0.747403\pi\)
\(602\) 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 \(-0.228184\pi\)
0.753873 + 0.657021i \(0.228184\pi\)
\(608\) 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 \(-0.524632\pi\)
−0.0773066 + 0.997007i \(0.524632\pi\)
\(618\) 3.09116e11 0.0852459
\(619\) 2.87119e12 0.786058 0.393029 0.919526i \(-0.371427\pi\)
0.393029 + 0.919526i \(0.371427\pi\)
\(620\) −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 \(-0.475804\pi\)
0.0759410 + 0.997112i \(0.475804\pi\)
\(642\) −4.89591e11 −0.113743
\(643\) −2.06799e12 −0.477088 −0.238544 0.971132i \(-0.576670\pi\)
−0.238544 + 0.971132i \(0.576670\pi\)
\(644\) 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 \(-0.542428\pi\)
−0.132897 + 0.991130i \(0.542428\pi\)
\(654\) −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 \(-0.206337\pi\)
0.797156 + 0.603774i \(0.206337\pi\)
\(674\) −6.24727e11 −0.116606
\(675\) −7.07501e12 −1.31178
\(676\) −2.57911e12 −0.475018
\(677\) −2.00433e12 −0.366707 −0.183354 0.983047i \(-0.558695\pi\)
−0.183354 + 0.983047i \(0.558695\pi\)
\(678\) 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 \(-0.784098\pi\)
−0.778656 + 0.627452i \(0.784098\pi\)
\(684\) −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 \(-0.641187\pi\)
−0.429151 + 0.903233i \(0.641187\pi\)
\(692\) 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 \(-0.751935\pi\)
−0.711392 + 0.702795i \(0.751935\pi\)
\(710\) −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 \(-0.252767\pi\)
0.700934 + 0.713226i \(0.252767\pi\)
\(720\) −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 \(-0.439992\pi\)
0.187407 + 0.982282i \(0.439992\pi\)
\(744\) −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 \(-0.308832\pi\)
0.565114 + 0.825013i \(0.308832\pi\)
\(752\) 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 \(-0.156479\pi\)
0.881582 + 0.472031i \(0.156479\pi\)
\(788\) −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 \(-0.730280\pi\)
−0.661971 + 0.749530i \(0.730280\pi\)
\(810\) 9.79476e12 0.799487
\(811\) 9.61956e12 0.780839 0.390420 0.920637i \(-0.372330\pi\)
0.390420 + 0.920637i \(0.372330\pi\)
\(812\) −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 \(-0.666503\pi\)
−0.499554 + 0.866283i \(0.666503\pi\)
\(822\) 1.37717e12 0.105212
\(823\) 1.73488e12 0.131817 0.0659083 0.997826i \(-0.479006\pi\)
0.0659083 + 0.997826i \(0.479006\pi\)
\(824\) −4.92233e12 −0.371962
\(825\) −4.20199e12 −0.315800
\(826\) 4.39789e12 0.328726
\(827\) 1.96073e13 1.45762 0.728809 0.684717i \(-0.240074\pi\)
0.728809 + 0.684717i \(0.240074\pi\)
\(828\) −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 \(-0.302623\pi\)
0.581100 + 0.813832i \(0.302623\pi\)
\(840\) −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 \(-0.660890\pi\)
−0.484201 + 0.874957i \(0.660890\pi\)
\(854\) −2.83677e12 −0.182500
\(855\) −3.74568e13 −2.39708
\(856\) 7.79619e12 0.496307
\(857\) 9.74340e12 0.617017 0.308508 0.951222i \(-0.400170\pi\)
0.308508 + 0.951222i \(0.400170\pi\)
\(858\) 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 \(-0.211294\pi\)
0.787657 + 0.616114i \(0.211294\pi\)
\(878\) −2.40050e13 −1.36325
\(879\) −3.73152e12 −0.210832
\(880\) −3.27614e12 −0.184158
\(881\) 9.63378e12 0.538772 0.269386 0.963032i \(-0.413179\pi\)
0.269386 + 0.963032i \(0.413179\pi\)
\(882\) −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 \(-0.437743\pi\)
0.194342 + 0.980934i \(0.437743\pi\)
\(888\) −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 \(-0.551733\pi\)
−0.161808 + 0.986822i \(0.551733\pi\)
\(908\) −9.91702e12 −0.484167
\(909\) −8.56398e12 −0.416043
\(910\) 2.46577e13 1.19197
\(911\) 8.62810e12 0.415033 0.207516 0.978232i \(-0.433462\pi\)
0.207516 + 0.978232i \(0.433462\pi\)
\(912\) 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 \(-0.547716\pi\)
−0.149343 + 0.988785i \(0.547716\pi\)
\(930\) −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 \(-0.684415\pi\)
−0.547486 + 0.836815i \(0.684415\pi\)
\(942\) 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 \(-0.346400\pi\)
0.464039 + 0.885815i \(0.346400\pi\)
\(948\) 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 \(-0.500496\pi\)
−0.00155723 + 0.999999i \(0.500496\pi\)
\(984\) −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 \(-0.615132\pi\)
−0.353864 + 0.935297i \(0.615132\pi\)
\(992\) 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 \(-0.444772\pi\)
0.172634 + 0.984986i \(0.444772\pi\)
\(998\) 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.h.1.14 yes 36
17.16 even 2 289.10.a.g.1.14 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.14 36 17.16 even 2
289.10.a.h.1.14 yes 36 1.1 even 1 trivial