Properties

Label 289.10.a.h.1.10
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 1.10
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-22.4936 q^{2} +161.121 q^{3} -6.03889 q^{4} +1284.66 q^{5} -3624.20 q^{6} +9354.17 q^{7} +11652.5 q^{8} +6277.10 q^{9} +O(q^{10})\) \(q-22.4936 q^{2} +161.121 q^{3} -6.03889 q^{4} +1284.66 q^{5} -3624.20 q^{6} +9354.17 q^{7} +11652.5 q^{8} +6277.10 q^{9} -28896.7 q^{10} +57101.0 q^{11} -972.994 q^{12} -147205. q^{13} -210409. q^{14} +206987. q^{15} -259016. q^{16} -141194. q^{18} -495550. q^{19} -7757.93 q^{20} +1.50716e6 q^{21} -1.28441e6 q^{22} +2.06028e6 q^{23} +1.87747e6 q^{24} -302768. q^{25} +3.31117e6 q^{26} -2.15998e6 q^{27} -56488.8 q^{28} +1.09429e6 q^{29} -4.65587e6 q^{30} +8.20471e6 q^{31} -139917. q^{32} +9.20020e6 q^{33} +1.20169e7 q^{35} -37906.7 q^{36} +1.78074e7 q^{37} +1.11467e7 q^{38} -2.37179e7 q^{39} +1.49696e7 q^{40} -1.40060e7 q^{41} -3.39013e7 q^{42} -2.12860e6 q^{43} -344827. q^{44} +8.06395e6 q^{45} -4.63431e7 q^{46} +1.57971e7 q^{47} -4.17330e7 q^{48} +4.71468e7 q^{49} +6.81033e6 q^{50} +888955. q^{52} -3.85001e7 q^{53} +4.85856e7 q^{54} +7.33555e7 q^{55} +1.09000e8 q^{56} -7.98436e7 q^{57} -2.46146e7 q^{58} +6.56446e7 q^{59} -1.24997e6 q^{60} +4.06936e7 q^{61} -1.84553e8 q^{62} +5.87170e7 q^{63} +1.35763e8 q^{64} -1.89109e8 q^{65} -2.06945e8 q^{66} +1.29000e8 q^{67} +3.31955e8 q^{69} -2.70304e8 q^{70} -1.56798e8 q^{71} +7.31442e7 q^{72} +2.48477e8 q^{73} -4.00551e8 q^{74} -4.87823e7 q^{75} +2.99257e6 q^{76} +5.34133e8 q^{77} +5.33500e8 q^{78} +5.41804e8 q^{79} -3.32748e8 q^{80} -4.71571e8 q^{81} +3.15045e8 q^{82} +7.51897e7 q^{83} -9.10155e6 q^{84} +4.78798e7 q^{86} +1.76314e8 q^{87} +6.65373e8 q^{88} +4.56857e8 q^{89} -1.81387e8 q^{90} -1.37698e9 q^{91} -1.24418e7 q^{92} +1.32195e9 q^{93} -3.55333e8 q^{94} -6.36614e8 q^{95} -2.25436e7 q^{96} -1.00520e9 q^{97} -1.06050e9 q^{98} +3.58429e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.4936 −0.994085 −0.497043 0.867726i \(-0.665581\pi\)
−0.497043 + 0.867726i \(0.665581\pi\)
\(3\) 161.121 1.14844 0.574219 0.818702i \(-0.305306\pi\)
0.574219 + 0.818702i \(0.305306\pi\)
\(4\) −6.03889 −0.0117947
\(5\) 1284.66 0.919230 0.459615 0.888118i \(-0.347987\pi\)
0.459615 + 0.888118i \(0.347987\pi\)
\(6\) −3624.20 −1.14165
\(7\) 9354.17 1.47253 0.736265 0.676694i \(-0.236588\pi\)
0.736265 + 0.676694i \(0.236588\pi\)
\(8\) 11652.5 1.00581
\(9\) 6277.10 0.318910
\(10\) −28896.7 −0.913792
\(11\) 57101.0 1.17592 0.587959 0.808891i \(-0.299932\pi\)
0.587959 + 0.808891i \(0.299932\pi\)
\(12\) −972.994 −0.0135455
\(13\) −147205. −1.42948 −0.714739 0.699391i \(-0.753455\pi\)
−0.714739 + 0.699391i \(0.753455\pi\)
\(14\) −210409. −1.46382
\(15\) 206987. 1.05568
\(16\) −259016. −0.988066
\(17\) 0 0
\(18\) −141194. −0.317023
\(19\) −495550. −0.872360 −0.436180 0.899859i \(-0.643669\pi\)
−0.436180 + 0.899859i \(0.643669\pi\)
\(20\) −7757.93 −0.0108420
\(21\) 1.50716e6 1.69111
\(22\) −1.28441e6 −1.16896
\(23\) 2.06028e6 1.53515 0.767576 0.640958i \(-0.221463\pi\)
0.767576 + 0.640958i \(0.221463\pi\)
\(24\) 1.87747e6 1.15511
\(25\) −302768. −0.155017
\(26\) 3.31117e6 1.42102
\(27\) −2.15998e6 −0.782190
\(28\) −56488.8 −0.0173680
\(29\) 1.09429e6 0.287305 0.143652 0.989628i \(-0.454115\pi\)
0.143652 + 0.989628i \(0.454115\pi\)
\(30\) −4.65587e6 −1.04943
\(31\) 8.20471e6 1.59564 0.797822 0.602894i \(-0.205986\pi\)
0.797822 + 0.602894i \(0.205986\pi\)
\(32\) −139917. −0.0235882
\(33\) 9.20020e6 1.35047
\(34\) 0 0
\(35\) 1.20169e7 1.35359
\(36\) −37906.7 −0.00376144
\(37\) 1.78074e7 1.56204 0.781019 0.624507i \(-0.214700\pi\)
0.781019 + 0.624507i \(0.214700\pi\)
\(38\) 1.11467e7 0.867201
\(39\) −2.37179e7 −1.64167
\(40\) 1.49696e7 0.924570
\(41\) −1.40060e7 −0.774082 −0.387041 0.922062i \(-0.626503\pi\)
−0.387041 + 0.922062i \(0.626503\pi\)
\(42\) −3.39013e7 −1.68111
\(43\) −2.12860e6 −0.0949479 −0.0474740 0.998872i \(-0.515117\pi\)
−0.0474740 + 0.998872i \(0.515117\pi\)
\(44\) −344827. −0.0138696
\(45\) 8.06395e6 0.293151
\(46\) −4.63431e7 −1.52607
\(47\) 1.57971e7 0.472212 0.236106 0.971727i \(-0.424129\pi\)
0.236106 + 0.971727i \(0.424129\pi\)
\(48\) −4.17330e7 −1.13473
\(49\) 4.71468e7 1.16834
\(50\) 6.81033e6 0.154100
\(51\) 0 0
\(52\) 888955. 0.0168603
\(53\) −3.85001e7 −0.670225 −0.335113 0.942178i \(-0.608774\pi\)
−0.335113 + 0.942178i \(0.608774\pi\)
\(54\) 4.85856e7 0.777564
\(55\) 7.33555e7 1.08094
\(56\) 1.09000e8 1.48108
\(57\) −7.98436e7 −1.00185
\(58\) −2.46146e7 −0.285605
\(59\) 6.56446e7 0.705285 0.352643 0.935758i \(-0.385283\pi\)
0.352643 + 0.935758i \(0.385283\pi\)
\(60\) −1.24997e6 −0.0124514
\(61\) 4.06936e7 0.376307 0.188153 0.982140i \(-0.439750\pi\)
0.188153 + 0.982140i \(0.439750\pi\)
\(62\) −1.84553e8 −1.58621
\(63\) 5.87170e7 0.469604
\(64\) 1.35763e8 1.01151
\(65\) −1.89109e8 −1.31402
\(66\) −2.06945e8 −1.34248
\(67\) 1.29000e8 0.782083 0.391041 0.920373i \(-0.372115\pi\)
0.391041 + 0.920373i \(0.372115\pi\)
\(68\) 0 0
\(69\) 3.31955e8 1.76303
\(70\) −2.70304e8 −1.34559
\(71\) −1.56798e8 −0.732280 −0.366140 0.930560i \(-0.619321\pi\)
−0.366140 + 0.930560i \(0.619321\pi\)
\(72\) 7.31442e7 0.320762
\(73\) 2.48477e8 1.02408 0.512039 0.858962i \(-0.328890\pi\)
0.512039 + 0.858962i \(0.328890\pi\)
\(74\) −4.00551e8 −1.55280
\(75\) −4.87823e7 −0.178027
\(76\) 2.99257e6 0.0102892
\(77\) 5.34133e8 1.73157
\(78\) 5.33500e8 1.63196
\(79\) 5.41804e8 1.56502 0.782511 0.622637i \(-0.213939\pi\)
0.782511 + 0.622637i \(0.213939\pi\)
\(80\) −3.32748e8 −0.908260
\(81\) −4.71571e8 −1.21721
\(82\) 3.15045e8 0.769504
\(83\) 7.51897e7 0.173903 0.0869515 0.996213i \(-0.472287\pi\)
0.0869515 + 0.996213i \(0.472287\pi\)
\(84\) −9.10155e6 −0.0199461
\(85\) 0 0
\(86\) 4.78798e7 0.0943863
\(87\) 1.76314e8 0.329952
\(88\) 6.65373e8 1.18275
\(89\) 4.56857e8 0.771836 0.385918 0.922533i \(-0.373885\pi\)
0.385918 + 0.922533i \(0.373885\pi\)
\(90\) −1.81387e8 −0.291417
\(91\) −1.37698e9 −2.10495
\(92\) −1.24418e7 −0.0181067
\(93\) 1.32195e9 1.83250
\(94\) −3.55333e8 −0.469419
\(95\) −6.36614e8 −0.801899
\(96\) −2.25436e7 −0.0270896
\(97\) −1.00520e9 −1.15287 −0.576437 0.817142i \(-0.695557\pi\)
−0.576437 + 0.817142i \(0.695557\pi\)
\(98\) −1.06050e9 −1.16143
\(99\) 3.58429e8 0.375011
\(100\) 1.82838e6 0.00182838
\(101\) −7.94017e8 −0.759248 −0.379624 0.925141i \(-0.623947\pi\)
−0.379624 + 0.925141i \(0.623947\pi\)
\(102\) 0 0
\(103\) 1.53373e9 1.34271 0.671353 0.741138i \(-0.265714\pi\)
0.671353 + 0.741138i \(0.265714\pi\)
\(104\) −1.71531e9 −1.43778
\(105\) 1.93619e9 1.55452
\(106\) 8.66006e8 0.666261
\(107\) −1.65042e9 −1.21722 −0.608609 0.793471i \(-0.708272\pi\)
−0.608609 + 0.793471i \(0.708272\pi\)
\(108\) 1.30439e7 0.00922570
\(109\) −8.41832e8 −0.571223 −0.285612 0.958345i \(-0.592197\pi\)
−0.285612 + 0.958345i \(0.592197\pi\)
\(110\) −1.65003e9 −1.07454
\(111\) 2.86915e9 1.79390
\(112\) −2.42288e9 −1.45496
\(113\) −2.33505e9 −1.34723 −0.673617 0.739081i \(-0.735260\pi\)
−0.673617 + 0.739081i \(0.735260\pi\)
\(114\) 1.79597e9 0.995926
\(115\) 2.64677e9 1.41116
\(116\) −6.60832e6 −0.00338867
\(117\) −9.24020e8 −0.455874
\(118\) −1.47658e9 −0.701114
\(119\) 0 0
\(120\) 2.41192e9 1.06181
\(121\) 9.02580e8 0.382782
\(122\) −9.15344e8 −0.374081
\(123\) −2.25667e9 −0.888985
\(124\) −4.95474e7 −0.0188201
\(125\) −2.89806e9 −1.06173
\(126\) −1.32076e9 −0.466826
\(127\) −1.32135e9 −0.450715 −0.225357 0.974276i \(-0.572355\pi\)
−0.225357 + 0.974276i \(0.572355\pi\)
\(128\) −2.98216e9 −0.981944
\(129\) −3.42963e8 −0.109042
\(130\) 4.25373e9 1.30625
\(131\) 5.89659e9 1.74936 0.874681 0.484698i \(-0.161071\pi\)
0.874681 + 0.484698i \(0.161071\pi\)
\(132\) −5.55590e7 −0.0159284
\(133\) −4.63545e9 −1.28458
\(134\) −2.90167e9 −0.777457
\(135\) −2.77484e9 −0.719012
\(136\) 0 0
\(137\) −4.07749e9 −0.988896 −0.494448 0.869207i \(-0.664630\pi\)
−0.494448 + 0.869207i \(0.664630\pi\)
\(138\) −7.46687e9 −1.75260
\(139\) 8.32735e9 1.89208 0.946041 0.324046i \(-0.105043\pi\)
0.946041 + 0.324046i \(0.105043\pi\)
\(140\) −7.25690e7 −0.0159652
\(141\) 2.54525e9 0.542306
\(142\) 3.52694e9 0.727949
\(143\) −8.40556e9 −1.68095
\(144\) −1.62587e9 −0.315104
\(145\) 1.40580e9 0.264099
\(146\) −5.58913e9 −1.01802
\(147\) 7.59636e9 1.34177
\(148\) −1.07537e8 −0.0184238
\(149\) 1.09294e10 1.81660 0.908301 0.418317i \(-0.137380\pi\)
0.908301 + 0.418317i \(0.137380\pi\)
\(150\) 1.09729e9 0.176974
\(151\) −1.08934e10 −1.70517 −0.852586 0.522586i \(-0.824967\pi\)
−0.852586 + 0.522586i \(0.824967\pi\)
\(152\) −5.77442e9 −0.877429
\(153\) 0 0
\(154\) −1.20146e10 −1.72133
\(155\) 1.05403e10 1.46676
\(156\) 1.43230e8 0.0193630
\(157\) 3.77707e7 0.00496143 0.00248072 0.999997i \(-0.499210\pi\)
0.00248072 + 0.999997i \(0.499210\pi\)
\(158\) −1.21871e10 −1.55576
\(159\) −6.20320e9 −0.769712
\(160\) −1.79746e8 −0.0216829
\(161\) 1.92722e10 2.26056
\(162\) 1.06073e10 1.21001
\(163\) 4.13858e9 0.459205 0.229603 0.973284i \(-0.426257\pi\)
0.229603 + 0.973284i \(0.426257\pi\)
\(164\) 8.45807e7 0.00913007
\(165\) 1.18191e10 1.24139
\(166\) −1.69129e9 −0.172874
\(167\) 1.30060e10 1.29396 0.646978 0.762508i \(-0.276032\pi\)
0.646978 + 0.762508i \(0.276032\pi\)
\(168\) 1.75622e10 1.70093
\(169\) 1.10648e10 1.04341
\(170\) 0 0
\(171\) −3.11061e9 −0.278204
\(172\) 1.28544e7 0.00111988
\(173\) −4.63053e9 −0.393028 −0.196514 0.980501i \(-0.562962\pi\)
−0.196514 + 0.980501i \(0.562962\pi\)
\(174\) −3.96593e9 −0.328000
\(175\) −2.83214e9 −0.228267
\(176\) −1.47901e10 −1.16188
\(177\) 1.05767e10 0.809976
\(178\) −1.02763e10 −0.767271
\(179\) −1.45886e9 −0.106212 −0.0531062 0.998589i \(-0.516912\pi\)
−0.0531062 + 0.998589i \(0.516912\pi\)
\(180\) −4.86973e7 −0.00345763
\(181\) 7.76243e9 0.537582 0.268791 0.963199i \(-0.413376\pi\)
0.268791 + 0.963199i \(0.413376\pi\)
\(182\) 3.09732e10 2.09250
\(183\) 6.55661e9 0.432165
\(184\) 2.40075e10 1.54407
\(185\) 2.28764e10 1.43587
\(186\) −2.97355e10 −1.82166
\(187\) 0 0
\(188\) −9.53969e7 −0.00556960
\(189\) −2.02048e10 −1.15180
\(190\) 1.43197e10 0.797156
\(191\) −3.61087e9 −0.196319 −0.0981595 0.995171i \(-0.531296\pi\)
−0.0981595 + 0.995171i \(0.531296\pi\)
\(192\) 2.18744e10 1.16166
\(193\) 1.09453e10 0.567833 0.283917 0.958849i \(-0.408366\pi\)
0.283917 + 0.958849i \(0.408366\pi\)
\(194\) 2.26106e10 1.14605
\(195\) −3.04695e10 −1.50907
\(196\) −2.84714e8 −0.0137803
\(197\) 3.82220e9 0.180807 0.0904034 0.995905i \(-0.471184\pi\)
0.0904034 + 0.995905i \(0.471184\pi\)
\(198\) −8.06234e9 −0.372793
\(199\) −1.97634e10 −0.893352 −0.446676 0.894696i \(-0.647392\pi\)
−0.446676 + 0.894696i \(0.647392\pi\)
\(200\) −3.52802e9 −0.155918
\(201\) 2.07846e10 0.898174
\(202\) 1.78603e10 0.754757
\(203\) 1.02362e10 0.423065
\(204\) 0 0
\(205\) −1.79930e10 −0.711559
\(206\) −3.44990e10 −1.33476
\(207\) 1.29326e10 0.489575
\(208\) 3.81284e10 1.41242
\(209\) −2.82964e10 −1.02582
\(210\) −4.35518e10 −1.54532
\(211\) 4.98585e9 0.173168 0.0865840 0.996245i \(-0.472405\pi\)
0.0865840 + 0.996245i \(0.472405\pi\)
\(212\) 2.32498e8 0.00790511
\(213\) −2.52635e10 −0.840978
\(214\) 3.71239e10 1.21002
\(215\) −2.73453e9 −0.0872790
\(216\) −2.51692e10 −0.786735
\(217\) 7.67483e10 2.34963
\(218\) 1.89358e10 0.567845
\(219\) 4.00349e10 1.17609
\(220\) −4.42986e8 −0.0127493
\(221\) 0 0
\(222\) −6.45374e10 −1.78329
\(223\) −6.96358e10 −1.88565 −0.942824 0.333291i \(-0.891841\pi\)
−0.942824 + 0.333291i \(0.891841\pi\)
\(224\) −1.30880e9 −0.0347343
\(225\) −1.90050e9 −0.0494364
\(226\) 5.25236e10 1.33927
\(227\) 2.88086e10 0.720122 0.360061 0.932929i \(-0.382756\pi\)
0.360061 + 0.932929i \(0.382756\pi\)
\(228\) 4.82167e8 0.0118165
\(229\) −7.61079e9 −0.182882 −0.0914408 0.995811i \(-0.529147\pi\)
−0.0914408 + 0.995811i \(0.529147\pi\)
\(230\) −5.95353e10 −1.40281
\(231\) 8.60602e10 1.98860
\(232\) 1.27513e10 0.288974
\(233\) 6.47083e10 1.43833 0.719165 0.694839i \(-0.244525\pi\)
0.719165 + 0.694839i \(0.244525\pi\)
\(234\) 2.07845e10 0.453178
\(235\) 2.02939e10 0.434071
\(236\) −3.96420e8 −0.00831863
\(237\) 8.72962e10 1.79733
\(238\) 0 0
\(239\) 3.98151e10 0.789328 0.394664 0.918825i \(-0.370861\pi\)
0.394664 + 0.918825i \(0.370861\pi\)
\(240\) −5.36128e10 −1.04308
\(241\) 6.98581e10 1.33395 0.666975 0.745080i \(-0.267589\pi\)
0.666975 + 0.745080i \(0.267589\pi\)
\(242\) −2.03023e10 −0.380518
\(243\) −3.34653e10 −0.615696
\(244\) −2.45744e8 −0.00443842
\(245\) 6.05678e10 1.07397
\(246\) 5.07605e10 0.883727
\(247\) 7.29474e10 1.24702
\(248\) 9.56058e10 1.60491
\(249\) 1.21147e10 0.199717
\(250\) 6.51878e10 1.05545
\(251\) 9.47934e10 1.50746 0.753731 0.657183i \(-0.228252\pi\)
0.753731 + 0.657183i \(0.228252\pi\)
\(252\) −3.54586e8 −0.00553884
\(253\) 1.17644e11 1.80521
\(254\) 2.97219e10 0.448049
\(255\) 0 0
\(256\) −2.43124e9 −0.0353792
\(257\) 3.19715e10 0.457156 0.228578 0.973526i \(-0.426592\pi\)
0.228578 + 0.973526i \(0.426592\pi\)
\(258\) 7.71446e9 0.108397
\(259\) 1.66573e11 2.30015
\(260\) 1.14201e9 0.0154985
\(261\) 6.86898e9 0.0916242
\(262\) −1.32635e11 −1.73902
\(263\) −1.28301e11 −1.65360 −0.826798 0.562498i \(-0.809840\pi\)
−0.826798 + 0.562498i \(0.809840\pi\)
\(264\) 1.07206e11 1.35831
\(265\) −4.94597e10 −0.616091
\(266\) 1.04268e11 1.27698
\(267\) 7.36094e10 0.886406
\(268\) −7.79016e8 −0.00922444
\(269\) 3.10336e10 0.361366 0.180683 0.983541i \(-0.442169\pi\)
0.180683 + 0.983541i \(0.442169\pi\)
\(270\) 6.24161e10 0.714759
\(271\) −1.15285e11 −1.29841 −0.649203 0.760615i \(-0.724897\pi\)
−0.649203 + 0.760615i \(0.724897\pi\)
\(272\) 0 0
\(273\) −2.21861e11 −2.41740
\(274\) 9.17174e10 0.983047
\(275\) −1.72883e10 −0.182287
\(276\) −2.00464e9 −0.0207944
\(277\) 1.43535e11 1.46487 0.732436 0.680835i \(-0.238383\pi\)
0.732436 + 0.680835i \(0.238383\pi\)
\(278\) −1.87312e11 −1.88089
\(279\) 5.15018e10 0.508866
\(280\) 1.40028e11 1.36146
\(281\) 9.65223e10 0.923526 0.461763 0.887003i \(-0.347217\pi\)
0.461763 + 0.887003i \(0.347217\pi\)
\(282\) −5.72517e10 −0.539098
\(283\) −1.85654e10 −0.172055 −0.0860273 0.996293i \(-0.527417\pi\)
−0.0860273 + 0.996293i \(0.527417\pi\)
\(284\) 9.46885e8 0.00863703
\(285\) −1.02572e11 −0.920932
\(286\) 1.89071e11 1.67101
\(287\) −1.31015e11 −1.13986
\(288\) −8.78270e8 −0.00752249
\(289\) 0 0
\(290\) −3.16214e10 −0.262537
\(291\) −1.61960e11 −1.32400
\(292\) −1.50052e9 −0.0120787
\(293\) −6.88004e10 −0.545364 −0.272682 0.962104i \(-0.587911\pi\)
−0.272682 + 0.962104i \(0.587911\pi\)
\(294\) −1.70869e11 −1.33383
\(295\) 8.43311e10 0.648319
\(296\) 2.07501e11 1.57111
\(297\) −1.23337e11 −0.919791
\(298\) −2.45842e11 −1.80586
\(299\) −3.03284e11 −2.19447
\(300\) 2.94591e8 0.00209978
\(301\) −1.99113e10 −0.139814
\(302\) 2.45032e11 1.69509
\(303\) −1.27933e11 −0.871949
\(304\) 1.28355e11 0.861950
\(305\) 5.22775e10 0.345912
\(306\) 0 0
\(307\) 9.12146e10 0.586059 0.293030 0.956103i \(-0.405337\pi\)
0.293030 + 0.956103i \(0.405337\pi\)
\(308\) −3.22557e9 −0.0204234
\(309\) 2.47116e11 1.54201
\(310\) −2.37089e11 −1.45809
\(311\) −2.25280e11 −1.36553 −0.682763 0.730640i \(-0.739222\pi\)
−0.682763 + 0.730640i \(0.739222\pi\)
\(312\) −2.76374e11 −1.65121
\(313\) −1.70381e11 −1.00340 −0.501699 0.865043i \(-0.667291\pi\)
−0.501699 + 0.865043i \(0.667291\pi\)
\(314\) −8.49599e8 −0.00493209
\(315\) 7.54315e10 0.431674
\(316\) −3.27190e9 −0.0184590
\(317\) 1.59870e11 0.889203 0.444602 0.895728i \(-0.353345\pi\)
0.444602 + 0.895728i \(0.353345\pi\)
\(318\) 1.39532e11 0.765160
\(319\) 6.24853e10 0.337847
\(320\) 1.74410e11 0.929814
\(321\) −2.65918e11 −1.39790
\(322\) −4.33501e11 −2.24719
\(323\) 0 0
\(324\) 2.84776e9 0.0143566
\(325\) 4.45689e10 0.221594
\(326\) −9.30914e10 −0.456489
\(327\) −1.35637e11 −0.656015
\(328\) −1.63206e11 −0.778580
\(329\) 1.47769e11 0.695345
\(330\) −2.65855e11 −1.23405
\(331\) 1.59564e11 0.730648 0.365324 0.930880i \(-0.380958\pi\)
0.365324 + 0.930880i \(0.380958\pi\)
\(332\) −4.54062e8 −0.00205113
\(333\) 1.11778e11 0.498149
\(334\) −2.92552e11 −1.28630
\(335\) 1.65721e11 0.718914
\(336\) −3.90377e11 −1.67093
\(337\) −1.20392e11 −0.508466 −0.254233 0.967143i \(-0.581823\pi\)
−0.254233 + 0.967143i \(0.581823\pi\)
\(338\) −2.48888e11 −1.03724
\(339\) −3.76226e11 −1.54721
\(340\) 0 0
\(341\) 4.68498e11 1.87634
\(342\) 6.99688e10 0.276559
\(343\) 6.35449e10 0.247889
\(344\) −2.48036e10 −0.0954996
\(345\) 4.26451e11 1.62063
\(346\) 1.04157e11 0.390703
\(347\) −1.84318e11 −0.682472 −0.341236 0.939978i \(-0.610845\pi\)
−0.341236 + 0.939978i \(0.610845\pi\)
\(348\) −1.06474e9 −0.00389168
\(349\) −3.67126e10 −0.132465 −0.0662325 0.997804i \(-0.521098\pi\)
−0.0662325 + 0.997804i \(0.521098\pi\)
\(350\) 6.37050e10 0.226917
\(351\) 3.17960e11 1.11812
\(352\) −7.98938e9 −0.0277378
\(353\) 2.10064e11 0.720055 0.360027 0.932942i \(-0.382767\pi\)
0.360027 + 0.932942i \(0.382767\pi\)
\(354\) −2.37909e11 −0.805185
\(355\) −2.01432e11 −0.673134
\(356\) −2.75891e9 −0.00910358
\(357\) 0 0
\(358\) 3.28150e10 0.105584
\(359\) −4.88942e11 −1.55358 −0.776788 0.629762i \(-0.783152\pi\)
−0.776788 + 0.629762i \(0.783152\pi\)
\(360\) 9.39656e10 0.294854
\(361\) −7.71182e10 −0.238987
\(362\) −1.74605e11 −0.534402
\(363\) 1.45425e11 0.439601
\(364\) 8.31544e9 0.0248273
\(365\) 3.19209e11 0.941362
\(366\) −1.47482e11 −0.429608
\(367\) −2.50484e11 −0.720748 −0.360374 0.932808i \(-0.617351\pi\)
−0.360374 + 0.932808i \(0.617351\pi\)
\(368\) −5.33645e11 −1.51683
\(369\) −8.79171e10 −0.246862
\(370\) −5.14573e11 −1.42738
\(371\) −3.60137e11 −0.986926
\(372\) −7.98314e9 −0.0216138
\(373\) 3.12819e11 0.836766 0.418383 0.908271i \(-0.362597\pi\)
0.418383 + 0.908271i \(0.362597\pi\)
\(374\) 0 0
\(375\) −4.66939e11 −1.21933
\(376\) 1.84076e11 0.474955
\(377\) −1.61086e11 −0.410696
\(378\) 4.54478e11 1.14499
\(379\) −1.31869e11 −0.328298 −0.164149 0.986436i \(-0.552488\pi\)
−0.164149 + 0.986436i \(0.552488\pi\)
\(380\) 3.84444e9 0.00945817
\(381\) −2.12898e11 −0.517618
\(382\) 8.12215e10 0.195158
\(383\) 4.82378e11 1.14549 0.572747 0.819732i \(-0.305878\pi\)
0.572747 + 0.819732i \(0.305878\pi\)
\(384\) −4.80490e11 −1.12770
\(385\) 6.86180e11 1.59171
\(386\) −2.46200e11 −0.564475
\(387\) −1.33614e10 −0.0302798
\(388\) 6.07032e9 0.0135978
\(389\) −5.41960e10 −0.120004 −0.0600018 0.998198i \(-0.519111\pi\)
−0.0600018 + 0.998198i \(0.519111\pi\)
\(390\) 6.85367e11 1.50014
\(391\) 0 0
\(392\) 5.49381e11 1.17513
\(393\) 9.50066e11 2.00903
\(394\) −8.59749e10 −0.179737
\(395\) 6.96035e11 1.43861
\(396\) −2.16451e9 −0.00442315
\(397\) −6.99376e11 −1.41304 −0.706519 0.707694i \(-0.749735\pi\)
−0.706519 + 0.707694i \(0.749735\pi\)
\(398\) 4.44550e11 0.888068
\(399\) −7.46871e11 −1.47526
\(400\) 7.84216e10 0.153167
\(401\) −2.39362e10 −0.0462280 −0.0231140 0.999733i \(-0.507358\pi\)
−0.0231140 + 0.999733i \(0.507358\pi\)
\(402\) −4.67521e11 −0.892861
\(403\) −1.20778e12 −2.28094
\(404\) 4.79498e9 0.00895510
\(405\) −6.05809e11 −1.11889
\(406\) −2.30249e11 −0.420562
\(407\) 1.01682e12 1.83683
\(408\) 0 0
\(409\) 3.57952e11 0.632514 0.316257 0.948674i \(-0.397574\pi\)
0.316257 + 0.948674i \(0.397574\pi\)
\(410\) 4.04727e11 0.707350
\(411\) −6.56971e11 −1.13569
\(412\) −9.26201e9 −0.0158368
\(413\) 6.14050e11 1.03855
\(414\) −2.90900e11 −0.486679
\(415\) 9.65934e10 0.159857
\(416\) 2.05964e10 0.0337188
\(417\) 1.34171e12 2.17294
\(418\) 6.36487e11 1.01976
\(419\) −1.71160e11 −0.271293 −0.135646 0.990757i \(-0.543311\pi\)
−0.135646 + 0.990757i \(0.543311\pi\)
\(420\) −1.16924e10 −0.0183351
\(421\) 1.13078e11 0.175432 0.0877159 0.996146i \(-0.472043\pi\)
0.0877159 + 0.996146i \(0.472043\pi\)
\(422\) −1.12150e11 −0.172144
\(423\) 9.91598e10 0.150593
\(424\) −4.48625e11 −0.674119
\(425\) 0 0
\(426\) 5.68266e11 0.836004
\(427\) 3.80655e11 0.554122
\(428\) 9.96672e9 0.0143567
\(429\) −1.35432e12 −1.93047
\(430\) 6.15094e10 0.0867627
\(431\) 1.20420e12 1.68093 0.840466 0.541864i \(-0.182281\pi\)
0.840466 + 0.541864i \(0.182281\pi\)
\(432\) 5.59468e11 0.772856
\(433\) 2.53234e11 0.346200 0.173100 0.984904i \(-0.444622\pi\)
0.173100 + 0.984904i \(0.444622\pi\)
\(434\) −1.72634e12 −2.33573
\(435\) 2.26504e11 0.303301
\(436\) 5.08373e9 0.00673741
\(437\) −1.02097e12 −1.33921
\(438\) −9.00528e11 −1.16913
\(439\) 6.92143e11 0.889417 0.444709 0.895675i \(-0.353307\pi\)
0.444709 + 0.895675i \(0.353307\pi\)
\(440\) 8.54779e11 1.08722
\(441\) 2.95945e11 0.372595
\(442\) 0 0
\(443\) 4.01866e11 0.495752 0.247876 0.968792i \(-0.420267\pi\)
0.247876 + 0.968792i \(0.420267\pi\)
\(444\) −1.73265e10 −0.0211586
\(445\) 5.86907e11 0.709495
\(446\) 1.56636e12 1.87449
\(447\) 1.76097e12 2.08625
\(448\) 1.26995e12 1.48949
\(449\) −1.26065e11 −0.146381 −0.0731907 0.997318i \(-0.523318\pi\)
−0.0731907 + 0.997318i \(0.523318\pi\)
\(450\) 4.27491e10 0.0491440
\(451\) −7.99758e11 −0.910257
\(452\) 1.41011e10 0.0158902
\(453\) −1.75516e12 −1.95828
\(454\) −6.48009e11 −0.715863
\(455\) −1.76896e12 −1.93493
\(456\) −9.30382e11 −1.00767
\(457\) 1.28002e12 1.37276 0.686380 0.727243i \(-0.259199\pi\)
0.686380 + 0.727243i \(0.259199\pi\)
\(458\) 1.71194e11 0.181800
\(459\) 0 0
\(460\) −1.59835e10 −0.0166442
\(461\) −2.46980e11 −0.254687 −0.127344 0.991859i \(-0.540645\pi\)
−0.127344 + 0.991859i \(0.540645\pi\)
\(462\) −1.93580e12 −1.97684
\(463\) −1.06166e12 −1.07367 −0.536833 0.843688i \(-0.680380\pi\)
−0.536833 + 0.843688i \(0.680380\pi\)
\(464\) −2.83439e11 −0.283876
\(465\) 1.69827e12 1.68449
\(466\) −1.45552e12 −1.42982
\(467\) 2.02752e11 0.197260 0.0986302 0.995124i \(-0.468554\pi\)
0.0986302 + 0.995124i \(0.468554\pi\)
\(468\) 5.58006e9 0.00537690
\(469\) 1.20669e12 1.15164
\(470\) −4.56483e11 −0.431503
\(471\) 6.08567e9 0.00569790
\(472\) 7.64927e11 0.709383
\(473\) −1.21545e11 −0.111651
\(474\) −1.96360e12 −1.78670
\(475\) 1.50036e11 0.135231
\(476\) 0 0
\(477\) −2.41669e11 −0.213741
\(478\) −8.95585e11 −0.784659
\(479\) −1.25765e12 −1.09157 −0.545783 0.837927i \(-0.683768\pi\)
−0.545783 + 0.837927i \(0.683768\pi\)
\(480\) −2.89609e10 −0.0249015
\(481\) −2.62133e12 −2.23290
\(482\) −1.57136e12 −1.32606
\(483\) 3.10517e12 2.59611
\(484\) −5.45058e9 −0.00451480
\(485\) −1.29135e12 −1.05976
\(486\) 7.52754e11 0.612054
\(487\) 3.15297e11 0.254003 0.127002 0.991903i \(-0.459465\pi\)
0.127002 + 0.991903i \(0.459465\pi\)
\(488\) 4.74184e11 0.378493
\(489\) 6.66813e11 0.527369
\(490\) −1.36239e12 −1.06762
\(491\) −1.29498e12 −1.00553 −0.502765 0.864423i \(-0.667684\pi\)
−0.502765 + 0.864423i \(0.667684\pi\)
\(492\) 1.36278e10 0.0104853
\(493\) 0 0
\(494\) −1.64085e12 −1.23964
\(495\) 4.60460e11 0.344721
\(496\) −2.12515e12 −1.57660
\(497\) −1.46671e12 −1.07830
\(498\) −2.72502e11 −0.198535
\(499\) 2.19676e12 1.58610 0.793050 0.609157i \(-0.208492\pi\)
0.793050 + 0.609157i \(0.208492\pi\)
\(500\) 1.75011e10 0.0125227
\(501\) 2.09554e12 1.48603
\(502\) −2.13224e12 −1.49855
\(503\) −8.02912e10 −0.0559258 −0.0279629 0.999609i \(-0.508902\pi\)
−0.0279629 + 0.999609i \(0.508902\pi\)
\(504\) 6.84203e11 0.472332
\(505\) −1.02004e12 −0.697923
\(506\) −2.64624e12 −1.79453
\(507\) 1.78278e12 1.19829
\(508\) 7.97949e9 0.00531605
\(509\) −2.24252e12 −1.48083 −0.740417 0.672148i \(-0.765372\pi\)
−0.740417 + 0.672148i \(0.765372\pi\)
\(510\) 0 0
\(511\) 2.32429e12 1.50798
\(512\) 1.58155e12 1.01711
\(513\) 1.07038e12 0.682352
\(514\) −7.19154e11 −0.454452
\(515\) 1.97032e12 1.23425
\(516\) 2.07111e9 0.00128612
\(517\) 9.02030e11 0.555282
\(518\) −3.74682e12 −2.28654
\(519\) −7.46078e11 −0.451368
\(520\) −2.20360e12 −1.32165
\(521\) −4.21783e11 −0.250795 −0.125398 0.992107i \(-0.540021\pi\)
−0.125398 + 0.992107i \(0.540021\pi\)
\(522\) −1.54508e11 −0.0910823
\(523\) 6.85779e11 0.400799 0.200399 0.979714i \(-0.435776\pi\)
0.200399 + 0.979714i \(0.435776\pi\)
\(524\) −3.56088e10 −0.0206332
\(525\) −4.56318e11 −0.262151
\(526\) 2.88595e12 1.64382
\(527\) 0 0
\(528\) −2.38299e12 −1.33435
\(529\) 2.44361e12 1.35669
\(530\) 1.11253e12 0.612447
\(531\) 4.12057e11 0.224922
\(532\) 2.79930e10 0.0151512
\(533\) 2.06176e12 1.10653
\(534\) −1.65574e12 −0.881163
\(535\) −2.12024e12 −1.11890
\(536\) 1.50318e12 0.786627
\(537\) −2.35054e11 −0.121978
\(538\) −6.98057e11 −0.359228
\(539\) 2.69213e12 1.37387
\(540\) 1.67570e10 0.00848054
\(541\) 1.41665e12 0.711011 0.355505 0.934674i \(-0.384309\pi\)
0.355505 + 0.934674i \(0.384309\pi\)
\(542\) 2.59317e12 1.29073
\(543\) 1.25069e12 0.617379
\(544\) 0 0
\(545\) −1.08147e12 −0.525085
\(546\) 4.99045e12 2.40310
\(547\) −1.74223e12 −0.832076 −0.416038 0.909347i \(-0.636582\pi\)
−0.416038 + 0.909347i \(0.636582\pi\)
\(548\) 2.46235e10 0.0116637
\(549\) 2.55438e11 0.120008
\(550\) 3.88877e11 0.181209
\(551\) −5.42277e11 −0.250633
\(552\) 3.86813e12 1.77327
\(553\) 5.06813e12 2.30454
\(554\) −3.22862e12 −1.45621
\(555\) 3.68588e12 1.64901
\(556\) −5.02879e10 −0.0223166
\(557\) 9.15412e11 0.402966 0.201483 0.979492i \(-0.435424\pi\)
0.201483 + 0.979492i \(0.435424\pi\)
\(558\) −1.15846e12 −0.505856
\(559\) 3.13340e11 0.135726
\(560\) −3.11258e12 −1.33744
\(561\) 0 0
\(562\) −2.17113e12 −0.918064
\(563\) −3.05435e12 −1.28124 −0.640620 0.767858i \(-0.721323\pi\)
−0.640620 + 0.767858i \(0.721323\pi\)
\(564\) −1.53705e10 −0.00639634
\(565\) −2.99975e12 −1.23842
\(566\) 4.17603e11 0.171037
\(567\) −4.41115e12 −1.79237
\(568\) −1.82709e12 −0.736535
\(569\) −2.05865e11 −0.0823335 −0.0411668 0.999152i \(-0.513107\pi\)
−0.0411668 + 0.999152i \(0.513107\pi\)
\(570\) 2.30721e12 0.915485
\(571\) −1.37439e12 −0.541062 −0.270531 0.962711i \(-0.587199\pi\)
−0.270531 + 0.962711i \(0.587199\pi\)
\(572\) 5.07603e10 0.0198263
\(573\) −5.81789e11 −0.225460
\(574\) 2.94699e12 1.13312
\(575\) −6.23787e11 −0.237975
\(576\) 8.52199e11 0.322582
\(577\) −1.39056e12 −0.522275 −0.261138 0.965302i \(-0.584098\pi\)
−0.261138 + 0.965302i \(0.584098\pi\)
\(578\) 0 0
\(579\) 1.76353e12 0.652121
\(580\) −8.48946e9 −0.00311497
\(581\) 7.03337e11 0.256077
\(582\) 3.64306e12 1.31617
\(583\) −2.19840e12 −0.788130
\(584\) 2.89539e12 1.03003
\(585\) −1.18705e12 −0.419053
\(586\) 1.54757e12 0.542138
\(587\) −2.02089e12 −0.702539 −0.351269 0.936274i \(-0.614250\pi\)
−0.351269 + 0.936274i \(0.614250\pi\)
\(588\) −4.58736e10 −0.0158258
\(589\) −4.06584e12 −1.39198
\(590\) −1.89691e12 −0.644484
\(591\) 6.15837e11 0.207645
\(592\) −4.61238e12 −1.54340
\(593\) −2.56146e12 −0.850630 −0.425315 0.905045i \(-0.639837\pi\)
−0.425315 + 0.905045i \(0.639837\pi\)
\(594\) 2.77429e12 0.914351
\(595\) 0 0
\(596\) −6.60017e10 −0.0214263
\(597\) −3.18431e12 −1.02596
\(598\) 6.82194e12 2.18149
\(599\) −1.66546e12 −0.528583 −0.264291 0.964443i \(-0.585138\pi\)
−0.264291 + 0.964443i \(0.585138\pi\)
\(600\) −5.68439e11 −0.179062
\(601\) −2.30323e12 −0.720114 −0.360057 0.932930i \(-0.617243\pi\)
−0.360057 + 0.932930i \(0.617243\pi\)
\(602\) 4.47875e11 0.138987
\(603\) 8.09745e11 0.249414
\(604\) 6.57842e10 0.0201120
\(605\) 1.15951e12 0.351865
\(606\) 2.87767e12 0.866791
\(607\) 5.08694e12 1.52092 0.760461 0.649383i \(-0.224973\pi\)
0.760461 + 0.649383i \(0.224973\pi\)
\(608\) 6.93356e10 0.0205774
\(609\) 1.64927e12 0.485863
\(610\) −1.17591e12 −0.343866
\(611\) −2.32541e12 −0.675016
\(612\) 0 0
\(613\) 5.87867e12 1.68154 0.840770 0.541393i \(-0.182103\pi\)
0.840770 + 0.541393i \(0.182103\pi\)
\(614\) −2.05174e12 −0.582593
\(615\) −2.89906e12 −0.817182
\(616\) 6.22401e12 1.74163
\(617\) −2.77401e12 −0.770592 −0.385296 0.922793i \(-0.625901\pi\)
−0.385296 + 0.922793i \(0.625901\pi\)
\(618\) −5.55853e12 −1.53289
\(619\) 1.51857e12 0.415744 0.207872 0.978156i \(-0.433346\pi\)
0.207872 + 0.978156i \(0.433346\pi\)
\(620\) −6.36516e10 −0.0173000
\(621\) −4.45016e12 −1.20078
\(622\) 5.06734e12 1.35745
\(623\) 4.27351e12 1.13655
\(624\) 6.14330e12 1.62208
\(625\) −3.13169e12 −0.820953
\(626\) 3.83249e12 0.997462
\(627\) −4.55915e12 −1.17810
\(628\) −2.28093e8 −5.85186e−5 0
\(629\) 0 0
\(630\) −1.69672e12 −0.429120
\(631\) −6.49509e12 −1.63100 −0.815499 0.578759i \(-0.803537\pi\)
−0.815499 + 0.578759i \(0.803537\pi\)
\(632\) 6.31340e12 1.57411
\(633\) 8.03326e11 0.198873
\(634\) −3.59605e12 −0.883944
\(635\) −1.69749e12 −0.414310
\(636\) 3.74604e10 0.00907853
\(637\) −6.94025e12 −1.67012
\(638\) −1.40552e12 −0.335848
\(639\) −9.84235e11 −0.233531
\(640\) −3.83107e12 −0.902632
\(641\) −4.72982e12 −1.10658 −0.553291 0.832988i \(-0.686628\pi\)
−0.553291 + 0.832988i \(0.686628\pi\)
\(642\) 5.98145e12 1.38963
\(643\) 9.58308e11 0.221083 0.110542 0.993872i \(-0.464741\pi\)
0.110542 + 0.993872i \(0.464741\pi\)
\(644\) −1.16383e11 −0.0266626
\(645\) −4.40591e11 −0.100234
\(646\) 0 0
\(647\) 1.17064e12 0.262635 0.131317 0.991340i \(-0.458079\pi\)
0.131317 + 0.991340i \(0.458079\pi\)
\(648\) −5.49500e12 −1.22428
\(649\) 3.74837e12 0.829357
\(650\) −1.00251e12 −0.220283
\(651\) 1.23658e13 2.69841
\(652\) −2.49924e10 −0.00541619
\(653\) −5.02539e12 −1.08158 −0.540792 0.841156i \(-0.681875\pi\)
−0.540792 + 0.841156i \(0.681875\pi\)
\(654\) 3.05096e12 0.652134
\(655\) 7.57512e12 1.60807
\(656\) 3.62778e12 0.764844
\(657\) 1.55971e12 0.326588
\(658\) −3.32384e12 −0.691232
\(659\) −3.15795e12 −0.652261 −0.326130 0.945325i \(-0.605745\pi\)
−0.326130 + 0.945325i \(0.605745\pi\)
\(660\) −7.13745e10 −0.0146418
\(661\) −1.46675e12 −0.298846 −0.149423 0.988773i \(-0.547742\pi\)
−0.149423 + 0.988773i \(0.547742\pi\)
\(662\) −3.58916e12 −0.726326
\(663\) 0 0
\(664\) 8.76152e11 0.174913
\(665\) −5.95499e12 −1.18082
\(666\) −2.51430e12 −0.495202
\(667\) 2.25455e12 0.441057
\(668\) −7.85418e10 −0.0152618
\(669\) −1.12198e13 −2.16555
\(670\) −3.72767e12 −0.714661
\(671\) 2.32365e12 0.442505
\(672\) −2.10876e11 −0.0398902
\(673\) 7.74648e12 1.45558 0.727791 0.685799i \(-0.240547\pi\)
0.727791 + 0.685799i \(0.240547\pi\)
\(674\) 2.70804e12 0.505459
\(675\) 6.53971e11 0.121253
\(676\) −6.68193e10 −0.0123067
\(677\) 7.62527e12 1.39510 0.697551 0.716535i \(-0.254273\pi\)
0.697551 + 0.716535i \(0.254273\pi\)
\(678\) 8.46268e12 1.53806
\(679\) −9.40285e12 −1.69764
\(680\) 0 0
\(681\) 4.64169e12 0.827016
\(682\) −1.05382e13 −1.86525
\(683\) 6.54245e12 1.15040 0.575198 0.818014i \(-0.304925\pi\)
0.575198 + 0.818014i \(0.304925\pi\)
\(684\) 1.87846e10 0.00328134
\(685\) −5.23820e12 −0.909023
\(686\) −1.42935e12 −0.246423
\(687\) −1.22626e12 −0.210028
\(688\) 5.51340e11 0.0938148
\(689\) 5.66742e12 0.958073
\(690\) −9.59240e12 −1.61104
\(691\) −4.12042e12 −0.687528 −0.343764 0.939056i \(-0.611702\pi\)
−0.343764 + 0.939056i \(0.611702\pi\)
\(692\) 2.79633e10 0.00463565
\(693\) 3.35280e12 0.552215
\(694\) 4.14597e12 0.678435
\(695\) 1.06978e13 1.73926
\(696\) 2.05451e12 0.331869
\(697\) 0 0
\(698\) 8.25798e11 0.131681
\(699\) 1.04259e13 1.65183
\(700\) 1.71030e10 0.00269234
\(701\) −8.29792e12 −1.29789 −0.648945 0.760835i \(-0.724789\pi\)
−0.648945 + 0.760835i \(0.724789\pi\)
\(702\) −7.15205e12 −1.11151
\(703\) −8.82443e12 −1.36266
\(704\) 7.75222e12 1.18946
\(705\) 3.26978e12 0.498503
\(706\) −4.72509e12 −0.715796
\(707\) −7.42736e12 −1.11801
\(708\) −6.38718e10 −0.00955343
\(709\) 9.99767e12 1.48590 0.742952 0.669345i \(-0.233425\pi\)
0.742952 + 0.669345i \(0.233425\pi\)
\(710\) 4.53093e12 0.669152
\(711\) 3.40096e12 0.499100
\(712\) 5.32355e12 0.776321
\(713\) 1.69040e13 2.44956
\(714\) 0 0
\(715\) −1.07983e13 −1.54518
\(716\) 8.80989e9 0.00125274
\(717\) 6.41507e12 0.906494
\(718\) 1.09981e13 1.54439
\(719\) 4.37408e12 0.610389 0.305194 0.952290i \(-0.401279\pi\)
0.305194 + 0.952290i \(0.401279\pi\)
\(720\) −2.08869e12 −0.289653
\(721\) 1.43467e13 1.97717
\(722\) 1.73467e12 0.237574
\(723\) 1.12556e13 1.53196
\(724\) −4.68765e10 −0.00634062
\(725\) −3.31317e11 −0.0445371
\(726\) −3.27113e12 −0.437001
\(727\) 3.97360e12 0.527568 0.263784 0.964582i \(-0.415029\pi\)
0.263784 + 0.964582i \(0.415029\pi\)
\(728\) −1.60453e13 −2.11718
\(729\) 3.88995e12 0.510118
\(730\) −7.18014e12 −0.935794
\(731\) 0 0
\(732\) −3.95946e10 −0.00509726
\(733\) 7.96904e12 1.01962 0.509810 0.860287i \(-0.329716\pi\)
0.509810 + 0.860287i \(0.329716\pi\)
\(734\) 5.63429e12 0.716485
\(735\) 9.75876e12 1.23339
\(736\) −2.88268e11 −0.0362114
\(737\) 7.36603e12 0.919665
\(738\) 1.97757e12 0.245402
\(739\) −3.39911e12 −0.419243 −0.209621 0.977783i \(-0.567223\pi\)
−0.209621 + 0.977783i \(0.567223\pi\)
\(740\) −1.38148e11 −0.0169357
\(741\) 1.17534e13 1.43213
\(742\) 8.10076e12 0.981089
\(743\) 7.05502e12 0.849276 0.424638 0.905363i \(-0.360401\pi\)
0.424638 + 0.905363i \(0.360401\pi\)
\(744\) 1.54041e13 1.84314
\(745\) 1.40406e13 1.66987
\(746\) −7.03643e12 −0.831816
\(747\) 4.71973e11 0.0554593
\(748\) 0 0
\(749\) −1.54383e13 −1.79239
\(750\) 1.05031e13 1.21211
\(751\) −1.65358e13 −1.89690 −0.948452 0.316920i \(-0.897351\pi\)
−0.948452 + 0.316920i \(0.897351\pi\)
\(752\) −4.09169e12 −0.466576
\(753\) 1.52732e13 1.73123
\(754\) 3.62339e12 0.408267
\(755\) −1.39944e13 −1.56745
\(756\) 1.22015e11 0.0135851
\(757\) −5.91466e11 −0.0654634 −0.0327317 0.999464i \(-0.510421\pi\)
−0.0327317 + 0.999464i \(0.510421\pi\)
\(758\) 2.96622e12 0.326356
\(759\) 1.89550e13 2.07317
\(760\) −7.41818e12 −0.806559
\(761\) −4.42291e12 −0.478054 −0.239027 0.971013i \(-0.576829\pi\)
−0.239027 + 0.971013i \(0.576829\pi\)
\(762\) 4.78884e12 0.514556
\(763\) −7.87463e12 −0.841143
\(764\) 2.18057e10 0.00231552
\(765\) 0 0
\(766\) −1.08504e13 −1.13872
\(767\) −9.66321e12 −1.00819
\(768\) −3.91724e11 −0.0406308
\(769\) −3.54128e12 −0.365167 −0.182583 0.983190i \(-0.558446\pi\)
−0.182583 + 0.983190i \(0.558446\pi\)
\(770\) −1.54346e13 −1.58230
\(771\) 5.15130e12 0.525015
\(772\) −6.60976e10 −0.00669743
\(773\) −1.02567e13 −1.03323 −0.516617 0.856217i \(-0.672809\pi\)
−0.516617 + 0.856217i \(0.672809\pi\)
\(774\) 3.00546e11 0.0301007
\(775\) −2.48412e12 −0.247352
\(776\) −1.17132e13 −1.15957
\(777\) 2.68385e13 2.64158
\(778\) 1.21906e12 0.119294
\(779\) 6.94067e12 0.675279
\(780\) 1.84002e11 0.0177990
\(781\) −8.95332e12 −0.861101
\(782\) 0 0
\(783\) −2.36365e12 −0.224727
\(784\) −1.22118e13 −1.15440
\(785\) 4.85227e10 0.00456070
\(786\) −2.13704e13 −1.99715
\(787\) −9.34742e11 −0.0868571 −0.0434285 0.999057i \(-0.513828\pi\)
−0.0434285 + 0.999057i \(0.513828\pi\)
\(788\) −2.30818e10 −0.00213256
\(789\) −2.06721e13 −1.89905
\(790\) −1.56563e13 −1.43011
\(791\) −2.18424e13 −1.98384
\(792\) 4.17661e12 0.377190
\(793\) −5.99030e12 −0.537922
\(794\) 1.57315e13 1.40468
\(795\) −7.96901e12 −0.707542
\(796\) 1.19349e11 0.0105368
\(797\) 1.26917e13 1.11418 0.557091 0.830452i \(-0.311918\pi\)
0.557091 + 0.830452i \(0.311918\pi\)
\(798\) 1.67998e13 1.46653
\(799\) 0 0
\(800\) 4.23622e10 0.00365657
\(801\) 2.86773e12 0.246146
\(802\) 5.38411e11 0.0459546
\(803\) 1.41883e13 1.20423
\(804\) −1.25516e11 −0.0105937
\(805\) 2.47583e13 2.07797
\(806\) 2.71672e13 2.26745
\(807\) 5.00018e12 0.415006
\(808\) −9.25232e12 −0.763659
\(809\) 6.05218e11 0.0496757 0.0248378 0.999691i \(-0.492093\pi\)
0.0248378 + 0.999691i \(0.492093\pi\)
\(810\) 1.36268e13 1.11227
\(811\) −2.19232e13 −1.77955 −0.889774 0.456402i \(-0.849138\pi\)
−0.889774 + 0.456402i \(0.849138\pi\)
\(812\) −6.18153e10 −0.00498992
\(813\) −1.85749e13 −1.49114
\(814\) −2.28719e13 −1.82596
\(815\) 5.31668e12 0.422115
\(816\) 0 0
\(817\) 1.05483e12 0.0828288
\(818\) −8.05163e12 −0.628773
\(819\) −8.64344e12 −0.671288
\(820\) 1.08658e11 0.00839263
\(821\) −3.11270e12 −0.239107 −0.119554 0.992828i \(-0.538146\pi\)
−0.119554 + 0.992828i \(0.538146\pi\)
\(822\) 1.47776e13 1.12897
\(823\) −2.30422e13 −1.75075 −0.875375 0.483444i \(-0.839386\pi\)
−0.875375 + 0.483444i \(0.839386\pi\)
\(824\) 1.78718e13 1.35051
\(825\) −2.78552e12 −0.209346
\(826\) −1.38122e13 −1.03241
\(827\) −1.32673e13 −0.986297 −0.493148 0.869945i \(-0.664154\pi\)
−0.493148 + 0.869945i \(0.664154\pi\)
\(828\) −7.80985e10 −0.00577439
\(829\) 7.58786e12 0.557987 0.278994 0.960293i \(-0.409999\pi\)
0.278994 + 0.960293i \(0.409999\pi\)
\(830\) −2.17273e12 −0.158911
\(831\) 2.31266e13 1.68232
\(832\) −1.99850e13 −1.44594
\(833\) 0 0
\(834\) −3.01799e13 −2.16009
\(835\) 1.67083e13 1.18944
\(836\) 1.70879e11 0.0120993
\(837\) −1.77220e13 −1.24810
\(838\) 3.84999e12 0.269688
\(839\) 2.06984e13 1.44214 0.721070 0.692862i \(-0.243651\pi\)
0.721070 + 0.692862i \(0.243651\pi\)
\(840\) 2.25615e13 1.56355
\(841\) −1.33097e13 −0.917456
\(842\) −2.54353e12 −0.174394
\(843\) 1.55518e13 1.06061
\(844\) −3.01090e10 −0.00204247
\(845\) 1.42146e13 0.959133
\(846\) −2.23046e12 −0.149702
\(847\) 8.44289e12 0.563658
\(848\) 9.97214e12 0.662227
\(849\) −2.99129e12 −0.197594
\(850\) 0 0
\(851\) 3.66882e13 2.39797
\(852\) 1.52563e11 0.00991909
\(853\) −7.03835e12 −0.455198 −0.227599 0.973755i \(-0.573087\pi\)
−0.227599 + 0.973755i \(0.573087\pi\)
\(854\) −8.56228e12 −0.550845
\(855\) −3.99609e12 −0.255733
\(856\) −1.92316e13 −1.22429
\(857\) 1.87674e13 1.18848 0.594239 0.804289i \(-0.297453\pi\)
0.594239 + 0.804289i \(0.297453\pi\)
\(858\) 3.04634e13 1.91905
\(859\) −4.63544e12 −0.290484 −0.145242 0.989396i \(-0.546396\pi\)
−0.145242 + 0.989396i \(0.546396\pi\)
\(860\) 1.65135e10 0.00102943
\(861\) −2.11092e13 −1.30906
\(862\) −2.70867e13 −1.67099
\(863\) 2.59525e13 1.59269 0.796343 0.604845i \(-0.206765\pi\)
0.796343 + 0.604845i \(0.206765\pi\)
\(864\) 3.02217e11 0.0184504
\(865\) −5.94867e12 −0.361283
\(866\) −5.69614e12 −0.344152
\(867\) 0 0
\(868\) −4.63474e11 −0.0277132
\(869\) 3.09376e13 1.84034
\(870\) −5.09489e12 −0.301507
\(871\) −1.89894e13 −1.11797
\(872\) −9.80948e12 −0.574542
\(873\) −6.30977e12 −0.367662
\(874\) 2.29653e13 1.33128
\(875\) −2.71089e13 −1.56342
\(876\) −2.41766e11 −0.0138716
\(877\) 1.01903e13 0.581688 0.290844 0.956771i \(-0.406064\pi\)
0.290844 + 0.956771i \(0.406064\pi\)
\(878\) −1.55688e13 −0.884157
\(879\) −1.10852e13 −0.626317
\(880\) −1.90002e13 −1.06804
\(881\) 2.42334e12 0.135526 0.0677630 0.997701i \(-0.478414\pi\)
0.0677630 + 0.997701i \(0.478414\pi\)
\(882\) −6.65687e12 −0.370392
\(883\) −7.32457e12 −0.405470 −0.202735 0.979234i \(-0.564983\pi\)
−0.202735 + 0.979234i \(0.564983\pi\)
\(884\) 0 0
\(885\) 1.35875e13 0.744554
\(886\) −9.03941e12 −0.492820
\(887\) 8.53993e12 0.463232 0.231616 0.972807i \(-0.425599\pi\)
0.231616 + 0.972807i \(0.425599\pi\)
\(888\) 3.34329e13 1.80433
\(889\) −1.23601e13 −0.663690
\(890\) −1.32016e13 −0.705298
\(891\) −2.69272e13 −1.43133
\(892\) 4.20523e11 0.0222407
\(893\) −7.82824e12 −0.411939
\(894\) −3.96104e13 −2.07391
\(895\) −1.87414e12 −0.0976335
\(896\) −2.78957e13 −1.44594
\(897\) −4.88655e13 −2.52021
\(898\) 2.83565e12 0.145516
\(899\) 8.97836e12 0.458436
\(900\) 1.14769e10 0.000583088 0
\(901\) 0 0
\(902\) 1.79894e13 0.904873
\(903\) −3.20813e12 −0.160567
\(904\) −2.72093e13 −1.35506
\(905\) 9.97211e12 0.494161
\(906\) 3.94799e13 1.94670
\(907\) −7.40422e11 −0.0363284 −0.0181642 0.999835i \(-0.505782\pi\)
−0.0181642 + 0.999835i \(0.505782\pi\)
\(908\) −1.73972e11 −0.00849363
\(909\) −4.98412e12 −0.242131
\(910\) 3.97901e13 1.92349
\(911\) 3.49415e12 0.168077 0.0840385 0.996463i \(-0.473218\pi\)
0.0840385 + 0.996463i \(0.473218\pi\)
\(912\) 2.06807e13 0.989896
\(913\) 4.29341e12 0.204495
\(914\) −2.87923e13 −1.36464
\(915\) 8.42303e12 0.397259
\(916\) 4.59607e10 0.00215704
\(917\) 5.51577e13 2.57599
\(918\) 0 0
\(919\) −7.01277e11 −0.0324317 −0.0162158 0.999869i \(-0.505162\pi\)
−0.0162158 + 0.999869i \(0.505162\pi\)
\(920\) 3.08416e13 1.41936
\(921\) 1.46966e13 0.673053
\(922\) 5.55546e12 0.253181
\(923\) 2.30814e13 1.04678
\(924\) −5.19708e11 −0.0234550
\(925\) −5.39149e12 −0.242143
\(926\) 2.38804e13 1.06732
\(927\) 9.62736e12 0.428202
\(928\) −1.53110e11 −0.00677700
\(929\) 1.21293e13 0.534276 0.267138 0.963658i \(-0.413922\pi\)
0.267138 + 0.963658i \(0.413922\pi\)
\(930\) −3.82001e13 −1.67452
\(931\) −2.33636e13 −1.01922
\(932\) −3.90766e11 −0.0169647
\(933\) −3.62974e13 −1.56822
\(934\) −4.56063e12 −0.196094
\(935\) 0 0
\(936\) −1.07672e13 −0.458523
\(937\) −2.23656e13 −0.947879 −0.473939 0.880558i \(-0.657168\pi\)
−0.473939 + 0.880558i \(0.657168\pi\)
\(938\) −2.71427e13 −1.14483
\(939\) −2.74521e13 −1.15234
\(940\) −1.22553e11 −0.00511974
\(941\) −3.98663e13 −1.65750 −0.828748 0.559621i \(-0.810947\pi\)
−0.828748 + 0.559621i \(0.810947\pi\)
\(942\) −1.36889e11 −0.00566420
\(943\) −2.88563e13 −1.18833
\(944\) −1.70030e13 −0.696868
\(945\) −2.59563e13 −1.05877
\(946\) 2.73399e12 0.110991
\(947\) 5.17204e12 0.208972 0.104486 0.994526i \(-0.466680\pi\)
0.104486 + 0.994526i \(0.466680\pi\)
\(948\) −5.27172e11 −0.0211990
\(949\) −3.65770e13 −1.46390
\(950\) −3.37486e12 −0.134431
\(951\) 2.57585e13 1.02119
\(952\) 0 0
\(953\) 3.55006e13 1.39417 0.697087 0.716986i \(-0.254479\pi\)
0.697087 + 0.716986i \(0.254479\pi\)
\(954\) 5.43600e12 0.212477
\(955\) −4.63875e12 −0.180462
\(956\) −2.40439e11 −0.00930990
\(957\) 1.00677e13 0.387996
\(958\) 2.82890e13 1.08511
\(959\) −3.81416e13 −1.45618
\(960\) 2.81012e13 1.06783
\(961\) 4.08777e13 1.54608
\(962\) 5.89632e13 2.21969
\(963\) −1.03599e13 −0.388182
\(964\) −4.21865e11 −0.0157336
\(965\) 1.40611e13 0.521969
\(966\) −6.98463e13 −2.58075
\(967\) −1.41239e13 −0.519440 −0.259720 0.965684i \(-0.583630\pi\)
−0.259720 + 0.965684i \(0.583630\pi\)
\(968\) 1.05174e13 0.385006
\(969\) 0 0
\(970\) 2.90470e13 1.05349
\(971\) 1.57589e13 0.568905 0.284452 0.958690i \(-0.408188\pi\)
0.284452 + 0.958690i \(0.408188\pi\)
\(972\) 2.02093e11 0.00726195
\(973\) 7.78954e13 2.78615
\(974\) −7.09215e12 −0.252501
\(975\) 7.18101e12 0.254486
\(976\) −1.05403e13 −0.371816
\(977\) 2.30148e13 0.808132 0.404066 0.914730i \(-0.367597\pi\)
0.404066 + 0.914730i \(0.367597\pi\)
\(978\) −1.49990e13 −0.524250
\(979\) 2.60870e13 0.907616
\(980\) −3.65762e11 −0.0126672
\(981\) −5.28426e12 −0.182169
\(982\) 2.91287e13 0.999583
\(983\) −3.30550e11 −0.0112914 −0.00564568 0.999984i \(-0.501797\pi\)
−0.00564568 + 0.999984i \(0.501797\pi\)
\(984\) −2.62959e13 −0.894150
\(985\) 4.91023e12 0.166203
\(986\) 0 0
\(987\) 2.38087e13 0.798561
\(988\) −4.40521e11 −0.0147082
\(989\) −4.38551e12 −0.145760
\(990\) −1.03574e13 −0.342683
\(991\) −2.41937e13 −0.796839 −0.398420 0.917203i \(-0.630441\pi\)
−0.398420 + 0.917203i \(0.630441\pi\)
\(992\) −1.14798e12 −0.0376383
\(993\) 2.57091e13 0.839104
\(994\) 3.29916e13 1.07193
\(995\) −2.53893e13 −0.821196
\(996\) −7.31591e10 −0.00235560
\(997\) −5.11973e13 −1.64104 −0.820519 0.571619i \(-0.806315\pi\)
−0.820519 + 0.571619i \(0.806315\pi\)
\(998\) −4.94130e13 −1.57672
\(999\) −3.84635e13 −1.22181
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.1.10 yes 36
17.16 even 2 289.10.a.g.1.10 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.10 36 17.16 even 2
289.10.a.h.1.10 yes 36 1.1 even 1 trivial