Properties

Label 289.10.a.g.1.10
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 1.10
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 \(-0.694694\pi\)
−0.574219 + 0.818702i \(0.694694\pi\)
\(4\) −6.03889 −0.0117947
\(5\) −1284.66 −0.919230 −0.459615 0.888118i \(-0.652013\pi\)
−0.459615 + 0.888118i \(0.652013\pi\)
\(6\) 3624.20 1.14165
\(7\) −9354.17 −1.47253 −0.736265 0.676694i \(-0.763412\pi\)
−0.736265 + 0.676694i \(0.763412\pi\)
\(8\) 11652.5 1.00581
\(9\) 6277.10 0.318910
\(10\) 28896.7 0.913792
\(11\) −57101.0 −1.17592 −0.587959 0.808891i \(-0.700068\pi\)
−0.587959 + 0.808891i \(0.700068\pi\)
\(12\) 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 \(-0.778537\pi\)
−0.767576 + 0.640958i \(0.778537\pi\)
\(24\) −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 \(-0.545885\pi\)
−0.143652 + 0.989628i \(0.545885\pi\)
\(30\) −4.65587e6 −1.04943
\(31\) −8.20471e6 −1.59564 −0.797822 0.602894i \(-0.794014\pi\)
−0.797822 + 0.602894i \(0.794014\pi\)
\(32\) −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 \(-0.785300\pi\)
−0.781019 + 0.624507i \(0.785300\pi\)
\(38\) 1.11467e7 0.867201
\(39\) 2.37179e7 1.64167
\(40\) −1.49696e7 −0.924570
\(41\) 1.40060e7 0.774082 0.387041 0.922062i \(-0.373497\pi\)
0.387041 + 0.922062i \(0.373497\pi\)
\(42\) −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 \(-0.560250\pi\)
−0.188153 + 0.982140i \(0.560250\pi\)
\(62\) 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 \(-0.380679\pi\)
0.366140 + 0.930560i \(0.380679\pi\)
\(72\) 7.31442e7 0.320762
\(73\) −2.48477e8 −1.02408 −0.512039 0.858962i \(-0.671110\pi\)
−0.512039 + 0.858962i \(0.671110\pi\)
\(74\) 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 \(-0.786061\pi\)
−0.782511 + 0.622637i \(0.786061\pi\)
\(80\) 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 \(-0.304443\pi\)
0.576437 + 0.817142i \(0.304443\pi\)
\(98\) −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 \(-0.291728\pi\)
0.608609 + 0.793471i \(0.291728\pi\)
\(108\) −1.30439e7 −0.00922570
\(109\) 8.41832e8 0.571223 0.285612 0.958345i \(-0.407803\pi\)
0.285612 + 0.958345i \(0.407803\pi\)
\(110\) −1.65003e9 −1.07454
\(111\) 2.86915e9 1.79390
\(112\) 2.42288e9 1.45496
\(113\) 2.33505e9 1.34723 0.673617 0.739081i \(-0.264740\pi\)
0.673617 + 0.739081i \(0.264740\pi\)
\(114\) −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 \(-0.838929\pi\)
−0.874681 + 0.484698i \(0.838929\pi\)
\(132\) −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 \(-0.894957\pi\)
−0.946041 + 0.324046i \(0.894957\pi\)
\(140\) −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 \(-0.573743\pi\)
−0.229603 + 0.973284i \(0.573743\pi\)
\(164\) −8.45807e7 −0.00913007
\(165\) −1.18191e10 −1.24139
\(166\) −1.69129e9 −0.172874
\(167\) −1.30060e10 −1.29396 −0.646978 0.762508i \(-0.723968\pi\)
−0.646978 + 0.762508i \(0.723968\pi\)
\(168\) 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 \(-0.437038\pi\)
0.196514 + 0.980501i \(0.437038\pi\)
\(174\) −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 \(-0.586624\pi\)
−0.268791 + 0.963199i \(0.586624\pi\)
\(182\) −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 \(-0.591634\pi\)
−0.283917 + 0.958849i \(0.591634\pi\)
\(194\) −2.26106e10 −1.14605
\(195\) −3.04695e10 −1.50907
\(196\) −2.84714e8 −0.0137803
\(197\) −3.82220e9 −0.180807 −0.0904034 0.995905i \(-0.528816\pi\)
−0.0904034 + 0.995905i \(0.528816\pi\)
\(198\) 8.06234e9 0.372793
\(199\) 1.97634e10 0.893352 0.446676 0.894696i \(-0.352608\pi\)
0.446676 + 0.894696i \(0.352608\pi\)
\(200\) −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 \(-0.527595\pi\)
−0.0865840 + 0.996245i \(0.527595\pi\)
\(212\) 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 \(-0.617244\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(228\) −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 \(-0.755475\pi\)
−0.719165 + 0.694839i \(0.755475\pi\)
\(234\) 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 \(-0.732411\pi\)
−0.666975 + 0.745080i \(0.732411\pi\)
\(242\) −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 \(-0.557831\pi\)
−0.180683 + 0.983541i \(0.557831\pi\)
\(270\) 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 \(-0.761617\pi\)
−0.732436 + 0.680835i \(0.761617\pi\)
\(278\) 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 \(-0.472583\pi\)
0.0860273 + 0.996293i \(0.472583\pi\)
\(284\) −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 \(-0.260778\pi\)
0.682763 + 0.730640i \(0.260778\pi\)
\(312\) 2.76374e11 1.65121
\(313\) 1.70381e11 1.00340 0.501699 0.865043i \(-0.332709\pi\)
0.501699 + 0.865043i \(0.332709\pi\)
\(314\) −8.49599e8 −0.00493209
\(315\) 7.54315e10 0.431674
\(316\) 3.27190e9 0.0184590
\(317\) −1.59870e11 −0.889203 −0.444602 0.895728i \(-0.646655\pi\)
−0.444602 + 0.895728i \(0.646655\pi\)
\(318\) −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 \(-0.418177\pi\)
0.254233 + 0.967143i \(0.418177\pi\)
\(338\) −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 \(-0.389155\pi\)
0.341236 + 0.939978i \(0.389155\pi\)
\(348\) −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 \(-0.382649\pi\)
0.360374 + 0.932808i \(0.382649\pi\)
\(368\) 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 \(-0.447512\pi\)
0.164149 + 0.986436i \(0.447512\pi\)
\(380\) −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 \(-0.250265\pi\)
0.706519 + 0.707694i \(0.250265\pi\)
\(398\) −4.44550e11 −0.888068
\(399\) −7.46871e11 −1.47526
\(400\) 7.84216e10 0.153167
\(401\) 2.39362e10 0.0462280 0.0231140 0.999733i \(-0.492642\pi\)
0.0231140 + 0.999733i \(0.492642\pi\)
\(402\) 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 \(-0.456689\pi\)
0.135646 + 0.990757i \(0.456689\pi\)
\(420\) 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 \(-0.817719\pi\)
−0.840466 + 0.541864i \(0.817719\pi\)
\(432\) −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 \(-0.646693\pi\)
−0.444709 + 0.895675i \(0.646693\pi\)
\(440\) 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 \(-0.476682\pi\)
0.0731907 + 0.997318i \(0.476682\pi\)
\(450\) 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 \(-0.316232\pi\)
0.545783 + 0.837927i \(0.316232\pi\)
\(480\) −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 \(-0.540535\pi\)
−0.127002 + 0.991903i \(0.540535\pi\)
\(488\) −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 \(-0.791508\pi\)
−0.793050 + 0.609157i \(0.791508\pi\)
\(500\) −1.75011e10 −0.0125227
\(501\) 2.09554e12 1.48603
\(502\) −2.13224e12 −1.49855
\(503\) 8.02912e10 0.0559258 0.0279629 0.999609i \(-0.491098\pi\)
0.0279629 + 0.999609i \(0.491098\pi\)
\(504\) −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 \(-0.459979\pi\)
0.125398 + 0.992107i \(0.459979\pi\)
\(522\) 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 \(-0.615691\pi\)
−0.355505 + 0.934674i \(0.615691\pi\)
\(542\) 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 \(-0.363418\pi\)
0.416038 + 0.909347i \(0.363418\pi\)
\(548\) 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 \(-0.412801\pi\)
0.270531 + 0.962711i \(0.412801\pi\)
\(572\) −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 \(-0.382757\pi\)
0.360057 + 0.932930i \(0.382757\pi\)
\(602\) −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 \(-0.775027\pi\)
−0.760461 + 0.649383i \(0.775027\pi\)
\(608\) 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 \(-0.374099\pi\)
0.385296 + 0.922793i \(0.374099\pi\)
\(618\) 5.55853e12 1.53289
\(619\) −1.51857e12 −0.415744 −0.207872 0.978156i \(-0.566654\pi\)
−0.207872 + 0.978156i \(0.566654\pi\)
\(620\) −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 \(-0.313372\pi\)
0.553291 + 0.832988i \(0.313372\pi\)
\(642\) 5.98145e12 1.38963
\(643\) −9.58308e11 −0.221083 −0.110542 0.993872i \(-0.535259\pi\)
−0.110542 + 0.993872i \(0.535259\pi\)
\(644\) −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 \(-0.318125\pi\)
0.540792 + 0.841156i \(0.318125\pi\)
\(654\) 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 \(-0.759453\pi\)
−0.727791 + 0.685799i \(0.759453\pi\)
\(674\) −2.70804e12 −0.505459
\(675\) −6.53971e11 −0.121253
\(676\) −6.68193e10 −0.0123067
\(677\) −7.62527e12 −1.39510 −0.697551 0.716535i \(-0.745727\pi\)
−0.697551 + 0.716535i \(0.745727\pi\)
\(678\) 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 \(-0.695075\pi\)
−0.575198 + 0.818014i \(0.695075\pi\)
\(684\) 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 \(-0.388298\pi\)
0.343764 + 0.939056i \(0.388298\pi\)
\(692\) −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 \(-0.766575\pi\)
−0.742952 + 0.669345i \(0.766575\pi\)
\(710\) 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 \(-0.598721\pi\)
−0.305194 + 0.952290i \(0.598721\pi\)
\(720\) 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 \(-0.639599\pi\)
−0.424638 + 0.905363i \(0.639599\pi\)
\(744\) 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 \(-0.102649\pi\)
0.948452 + 0.316920i \(0.102649\pi\)
\(752\) −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 \(-0.486172\pi\)
0.0434285 + 0.999057i \(0.486172\pi\)
\(788\) 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 \(-0.507907\pi\)
−0.0248378 + 0.999691i \(0.507907\pi\)
\(810\) −1.36268e13 −1.11227
\(811\) 2.19232e13 1.77955 0.889774 0.456402i \(-0.150862\pi\)
0.889774 + 0.456402i \(0.150862\pi\)
\(812\) −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 \(-0.461854\pi\)
0.119554 + 0.992828i \(0.461854\pi\)
\(822\) −1.47776e13 −1.12897
\(823\) 2.30422e13 1.75075 0.875375 0.483444i \(-0.160614\pi\)
0.875375 + 0.483444i \(0.160614\pi\)
\(824\) 1.78718e13 1.35051
\(825\) −2.78552e12 −0.209346
\(826\) 1.38122e13 1.03241
\(827\) 1.32673e13 0.986297 0.493148 0.869945i \(-0.335846\pi\)
0.493148 + 0.869945i \(0.335846\pi\)
\(828\) 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 \(-0.756349\pi\)
−0.721070 + 0.692862i \(0.756349\pi\)
\(840\) −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 \(-0.426913\pi\)
0.227599 + 0.973755i \(0.426913\pi\)
\(854\) −8.56228e12 −0.550845
\(855\) 3.99609e12 0.255733
\(856\) 1.92316e13 1.22429
\(857\) −1.87674e13 −1.18848 −0.594239 0.804289i \(-0.702547\pi\)
−0.594239 + 0.804289i \(0.702547\pi\)
\(858\) 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 \(-0.593936\pi\)
−0.290844 + 0.956771i \(0.593936\pi\)
\(878\) 1.55688e13 0.884157
\(879\) 1.10852e13 0.626317
\(880\) −1.90002e13 −1.06804
\(881\) −2.42334e12 −0.135526 −0.0677630 0.997701i \(-0.521586\pi\)
−0.0677630 + 0.997701i \(0.521586\pi\)
\(882\) −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 \(-0.574401\pi\)
−0.231616 + 0.972807i \(0.574401\pi\)
\(888\) 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 \(-0.494218\pi\)
0.0181642 + 0.999835i \(0.494218\pi\)
\(908\) 1.73972e11 0.00849363
\(909\) −4.98412e12 −0.242131
\(910\) 3.97901e13 1.92349
\(911\) −3.49415e12 −0.168077 −0.0840385 0.996463i \(-0.526782\pi\)
−0.0840385 + 0.996463i \(0.526782\pi\)
\(912\) −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 \(-0.586078\pi\)
−0.267138 + 0.963658i \(0.586078\pi\)
\(930\) 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 \(-0.189053\pi\)
0.828748 + 0.559621i \(0.189053\pi\)
\(942\) 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 \(-0.533320\pi\)
−0.104486 + 0.994526i \(0.533320\pi\)
\(948\) −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 \(-0.498203\pi\)
0.00564568 + 0.999984i \(0.498203\pi\)
\(984\) −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 \(-0.369559\pi\)
0.398420 + 0.917203i \(0.369559\pi\)
\(992\) 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 \(-0.193685\pi\)
0.820519 + 0.571619i \(0.193685\pi\)
\(998\) 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.g.1.10 36
17.16 even 2 289.10.a.h.1.10 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.10 36 1.1 even 1 trivial
289.10.a.h.1.10 yes 36 17.16 even 2