Properties

Label 289.10.a.g.1.4
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 1.4
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-37.5513 q^{2} -70.9462 q^{3} +898.103 q^{4} +98.5382 q^{5} +2664.12 q^{6} +4159.85 q^{7} -14498.7 q^{8} -14649.6 q^{9} +O(q^{10})\) \(q-37.5513 q^{2} -70.9462 q^{3} +898.103 q^{4} +98.5382 q^{5} +2664.12 q^{6} +4159.85 q^{7} -14498.7 q^{8} -14649.6 q^{9} -3700.24 q^{10} +17666.5 q^{11} -63717.0 q^{12} +125323. q^{13} -156208. q^{14} -6990.91 q^{15} +84616.0 q^{16} +550113. q^{18} +186769. q^{19} +88497.5 q^{20} -295126. q^{21} -663401. q^{22} +880420. q^{23} +1.02863e6 q^{24} -1.94342e6 q^{25} -4.70603e6 q^{26} +2.43577e6 q^{27} +3.73598e6 q^{28} +472555. q^{29} +262518. q^{30} +5.47929e6 q^{31} +4.24588e6 q^{32} -1.25337e6 q^{33} +409905. q^{35} -1.31569e7 q^{36} -1.99919e7 q^{37} -7.01344e6 q^{38} -8.89116e6 q^{39} -1.42867e6 q^{40} -1.70530e7 q^{41} +1.10824e7 q^{42} -2.41245e7 q^{43} +1.58663e7 q^{44} -1.44355e6 q^{45} -3.30609e7 q^{46} -3.99422e7 q^{47} -6.00318e6 q^{48} -2.30492e7 q^{49} +7.29778e7 q^{50} +1.12553e8 q^{52} -3.20031e7 q^{53} -9.14664e7 q^{54} +1.74083e6 q^{55} -6.03124e7 q^{56} -1.32506e7 q^{57} -1.77451e7 q^{58} +1.43681e8 q^{59} -6.27856e6 q^{60} +9.63074e7 q^{61} -2.05755e8 q^{62} -6.09404e7 q^{63} -2.02762e8 q^{64} +1.23491e7 q^{65} +4.70658e7 q^{66} +1.54095e8 q^{67} -6.24624e7 q^{69} -1.53925e7 q^{70} -3.43693e8 q^{71} +2.12400e8 q^{72} -1.81429e8 q^{73} +7.50721e8 q^{74} +1.37878e8 q^{75} +1.67738e8 q^{76} +7.34901e7 q^{77} +3.33875e8 q^{78} +4.31537e8 q^{79} +8.33791e6 q^{80} +1.15540e8 q^{81} +6.40364e8 q^{82} -3.37832e8 q^{83} -2.65053e8 q^{84} +9.05906e8 q^{86} -3.35260e7 q^{87} -2.56141e8 q^{88} -2.13172e8 q^{89} +5.42072e7 q^{90} +5.21324e8 q^{91} +7.90707e8 q^{92} -3.88735e8 q^{93} +1.49988e9 q^{94} +1.84039e7 q^{95} -3.01229e8 q^{96} +5.74705e8 q^{97} +8.65529e8 q^{98} -2.58808e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −37.5513 −1.65955 −0.829775 0.558098i \(-0.811531\pi\)
−0.829775 + 0.558098i \(0.811531\pi\)
\(3\) −70.9462 −0.505689 −0.252845 0.967507i \(-0.581366\pi\)
−0.252845 + 0.967507i \(0.581366\pi\)
\(4\) 898.103 1.75411
\(5\) 98.5382 0.0705082 0.0352541 0.999378i \(-0.488776\pi\)
0.0352541 + 0.999378i \(0.488776\pi\)
\(6\) 2664.12 0.839216
\(7\) 4159.85 0.654843 0.327421 0.944878i \(-0.393820\pi\)
0.327421 + 0.944878i \(0.393820\pi\)
\(8\) −14498.7 −1.25148
\(9\) −14649.6 −0.744279
\(10\) −3700.24 −0.117012
\(11\) 17666.5 0.363817 0.181909 0.983315i \(-0.441772\pi\)
0.181909 + 0.983315i \(0.441772\pi\)
\(12\) −63717.0 −0.887033
\(13\) 125323. 1.21698 0.608491 0.793561i \(-0.291775\pi\)
0.608491 + 0.793561i \(0.291775\pi\)
\(14\) −156208. −1.08674
\(15\) −6990.91 −0.0356552
\(16\) 84616.0 0.322784
\(17\) 0 0
\(18\) 550113. 1.23517
\(19\) 186769. 0.328787 0.164393 0.986395i \(-0.447433\pi\)
0.164393 + 0.986395i \(0.447433\pi\)
\(20\) 88497.5 0.123679
\(21\) −295126. −0.331147
\(22\) −663401. −0.603773
\(23\) 880420. 0.656016 0.328008 0.944675i \(-0.393623\pi\)
0.328008 + 0.944675i \(0.393623\pi\)
\(24\) 1.02863e6 0.632859
\(25\) −1.94342e6 −0.995029
\(26\) −4.70603e6 −2.01964
\(27\) 2.43577e6 0.882063
\(28\) 3.73598e6 1.14866
\(29\) 472555. 0.124069 0.0620343 0.998074i \(-0.480241\pi\)
0.0620343 + 0.998074i \(0.480241\pi\)
\(30\) 262518. 0.0591717
\(31\) 5.47929e6 1.06561 0.532803 0.846240i \(-0.321139\pi\)
0.532803 + 0.846240i \(0.321139\pi\)
\(32\) 4.24588e6 0.715802
\(33\) −1.25337e6 −0.183978
\(34\) 0 0
\(35\) 409905. 0.0461718
\(36\) −1.31569e7 −1.30554
\(37\) −1.99919e7 −1.75366 −0.876830 0.480801i \(-0.840346\pi\)
−0.876830 + 0.480801i \(0.840346\pi\)
\(38\) −7.01344e6 −0.545638
\(39\) −8.89116e6 −0.615415
\(40\) −1.42867e6 −0.0882395
\(41\) −1.70530e7 −0.942484 −0.471242 0.882004i \(-0.656194\pi\)
−0.471242 + 0.882004i \(0.656194\pi\)
\(42\) 1.10824e7 0.549555
\(43\) −2.41245e7 −1.07609 −0.538046 0.842915i \(-0.680837\pi\)
−0.538046 + 0.842915i \(0.680837\pi\)
\(44\) 1.58663e7 0.638175
\(45\) −1.44355e6 −0.0524778
\(46\) −3.30609e7 −1.08869
\(47\) −3.99422e7 −1.19397 −0.596983 0.802254i \(-0.703634\pi\)
−0.596983 + 0.802254i \(0.703634\pi\)
\(48\) −6.00318e6 −0.163228
\(49\) −2.30492e7 −0.571181
\(50\) 7.29778e7 1.65130
\(51\) 0 0
\(52\) 1.12553e8 2.13472
\(53\) −3.20031e7 −0.557123 −0.278561 0.960418i \(-0.589858\pi\)
−0.278561 + 0.960418i \(0.589858\pi\)
\(54\) −9.14664e7 −1.46383
\(55\) 1.74083e6 0.0256521
\(56\) −6.03124e7 −0.819522
\(57\) −1.32506e7 −0.166264
\(58\) −1.77451e7 −0.205898
\(59\) 1.43681e8 1.54371 0.771856 0.635797i \(-0.219328\pi\)
0.771856 + 0.635797i \(0.219328\pi\)
\(60\) −6.27856e6 −0.0625431
\(61\) 9.63074e7 0.890585 0.445293 0.895385i \(-0.353100\pi\)
0.445293 + 0.895385i \(0.353100\pi\)
\(62\) −2.05755e8 −1.76843
\(63\) −6.09404e7 −0.487385
\(64\) −2.02762e8 −1.51069
\(65\) 1.23491e7 0.0858073
\(66\) 4.70658e7 0.305321
\(67\) 1.54095e8 0.934224 0.467112 0.884198i \(-0.345294\pi\)
0.467112 + 0.884198i \(0.345294\pi\)
\(68\) 0 0
\(69\) −6.24624e7 −0.331740
\(70\) −1.53925e7 −0.0766244
\(71\) −3.43693e8 −1.60512 −0.802562 0.596568i \(-0.796530\pi\)
−0.802562 + 0.596568i \(0.796530\pi\)
\(72\) 2.12400e8 0.931449
\(73\) −1.81429e8 −0.747748 −0.373874 0.927480i \(-0.621971\pi\)
−0.373874 + 0.927480i \(0.621971\pi\)
\(74\) 7.50721e8 2.91029
\(75\) 1.37878e8 0.503175
\(76\) 1.67738e8 0.576727
\(77\) 7.34901e7 0.238243
\(78\) 3.33875e8 1.02131
\(79\) 4.31537e8 1.24651 0.623255 0.782019i \(-0.285810\pi\)
0.623255 + 0.782019i \(0.285810\pi\)
\(80\) 8.33791e6 0.0227589
\(81\) 1.15540e8 0.298229
\(82\) 6.40364e8 1.56410
\(83\) −3.37832e8 −0.781357 −0.390678 0.920527i \(-0.627760\pi\)
−0.390678 + 0.920527i \(0.627760\pi\)
\(84\) −2.65053e8 −0.580867
\(85\) 0 0
\(86\) 9.05906e8 1.78583
\(87\) −3.35260e7 −0.0627401
\(88\) −2.56141e8 −0.455310
\(89\) −2.13172e8 −0.360144 −0.180072 0.983653i \(-0.557633\pi\)
−0.180072 + 0.983653i \(0.557633\pi\)
\(90\) 5.42072e7 0.0870895
\(91\) 5.21324e8 0.796932
\(92\) 7.90707e8 1.15072
\(93\) −3.88735e8 −0.538865
\(94\) 1.49988e9 1.98145
\(95\) 1.84039e7 0.0231822
\(96\) −3.01229e8 −0.361973
\(97\) 5.74705e8 0.659131 0.329566 0.944133i \(-0.393098\pi\)
0.329566 + 0.944133i \(0.393098\pi\)
\(98\) 8.65529e8 0.947904
\(99\) −2.58808e8 −0.270781
\(100\) −1.74539e9 −1.74539
\(101\) −1.61579e9 −1.54504 −0.772518 0.634993i \(-0.781003\pi\)
−0.772518 + 0.634993i \(0.781003\pi\)
\(102\) 0 0
\(103\) 1.58557e9 1.38809 0.694044 0.719932i \(-0.255827\pi\)
0.694044 + 0.719932i \(0.255827\pi\)
\(104\) −1.81701e9 −1.52303
\(105\) −2.90812e7 −0.0233486
\(106\) 1.20176e9 0.924573
\(107\) 1.83230e9 1.35135 0.675676 0.737199i \(-0.263852\pi\)
0.675676 + 0.737199i \(0.263852\pi\)
\(108\) 2.18757e9 1.54723
\(109\) 2.76044e9 1.87309 0.936546 0.350546i \(-0.114004\pi\)
0.936546 + 0.350546i \(0.114004\pi\)
\(110\) −6.53703e7 −0.0425710
\(111\) 1.41835e9 0.886807
\(112\) 3.51990e8 0.211373
\(113\) −1.15966e9 −0.669082 −0.334541 0.942381i \(-0.608581\pi\)
−0.334541 + 0.942381i \(0.608581\pi\)
\(114\) 4.97577e8 0.275923
\(115\) 8.67550e7 0.0462545
\(116\) 4.24403e8 0.217629
\(117\) −1.83593e9 −0.905774
\(118\) −5.39543e9 −2.56187
\(119\) 0 0
\(120\) 1.01359e8 0.0446218
\(121\) −2.04584e9 −0.867637
\(122\) −3.61647e9 −1.47797
\(123\) 1.20985e9 0.476604
\(124\) 4.92096e9 1.86919
\(125\) −3.83958e8 −0.140666
\(126\) 2.28839e9 0.808841
\(127\) 1.74470e9 0.595118 0.297559 0.954703i \(-0.403827\pi\)
0.297559 + 0.954703i \(0.403827\pi\)
\(128\) 5.44009e9 1.79127
\(129\) 1.71154e9 0.544168
\(130\) −4.63724e8 −0.142402
\(131\) 1.59935e9 0.474485 0.237242 0.971450i \(-0.423756\pi\)
0.237242 + 0.971450i \(0.423756\pi\)
\(132\) −1.12566e9 −0.322718
\(133\) 7.76934e8 0.215304
\(134\) −5.78646e9 −1.55039
\(135\) 2.40017e8 0.0621927
\(136\) 0 0
\(137\) 2.42729e9 0.588681 0.294340 0.955701i \(-0.404900\pi\)
0.294340 + 0.955701i \(0.404900\pi\)
\(138\) 2.34555e9 0.550539
\(139\) −1.63994e9 −0.372616 −0.186308 0.982491i \(-0.559652\pi\)
−0.186308 + 0.982491i \(0.559652\pi\)
\(140\) 3.68137e8 0.0809903
\(141\) 2.83375e9 0.603776
\(142\) 1.29061e10 2.66378
\(143\) 2.21401e9 0.442759
\(144\) −1.23959e9 −0.240241
\(145\) 4.65648e7 0.00874785
\(146\) 6.81292e9 1.24092
\(147\) 1.63525e9 0.288840
\(148\) −1.79547e10 −3.07611
\(149\) 2.74370e9 0.456036 0.228018 0.973657i \(-0.426776\pi\)
0.228018 + 0.973657i \(0.426776\pi\)
\(150\) −5.17750e9 −0.835044
\(151\) 8.07933e9 1.26467 0.632337 0.774693i \(-0.282096\pi\)
0.632337 + 0.774693i \(0.282096\pi\)
\(152\) −2.70791e9 −0.411470
\(153\) 0 0
\(154\) −2.75965e9 −0.395376
\(155\) 5.39919e8 0.0751339
\(156\) −7.98518e9 −1.07950
\(157\) −7.87840e9 −1.03488 −0.517440 0.855720i \(-0.673115\pi\)
−0.517440 + 0.855720i \(0.673115\pi\)
\(158\) −1.62048e10 −2.06865
\(159\) 2.27050e9 0.281731
\(160\) 4.18381e8 0.0504699
\(161\) 3.66242e9 0.429587
\(162\) −4.33869e9 −0.494927
\(163\) 7.99073e9 0.886630 0.443315 0.896366i \(-0.353802\pi\)
0.443315 + 0.896366i \(0.353802\pi\)
\(164\) −1.53154e10 −1.65322
\(165\) −1.23505e8 −0.0129720
\(166\) 1.26860e10 1.29670
\(167\) 3.09907e9 0.308324 0.154162 0.988046i \(-0.450732\pi\)
0.154162 + 0.988046i \(0.450732\pi\)
\(168\) 4.27893e9 0.414423
\(169\) 5.10126e9 0.481047
\(170\) 0 0
\(171\) −2.73610e9 −0.244709
\(172\) −2.16662e10 −1.88758
\(173\) −1.63993e10 −1.39193 −0.695967 0.718073i \(-0.745024\pi\)
−0.695967 + 0.718073i \(0.745024\pi\)
\(174\) 1.25895e9 0.104120
\(175\) −8.08433e9 −0.651587
\(176\) 1.49487e9 0.117435
\(177\) −1.01936e10 −0.780639
\(178\) 8.00490e9 0.597676
\(179\) −1.11112e10 −0.808950 −0.404475 0.914549i \(-0.632546\pi\)
−0.404475 + 0.914549i \(0.632546\pi\)
\(180\) −1.29646e9 −0.0920516
\(181\) −8.54950e9 −0.592090 −0.296045 0.955174i \(-0.595668\pi\)
−0.296045 + 0.955174i \(0.595668\pi\)
\(182\) −1.95764e10 −1.32255
\(183\) −6.83265e9 −0.450359
\(184\) −1.27649e10 −0.820990
\(185\) −1.96996e9 −0.123647
\(186\) 1.45975e10 0.894273
\(187\) 0 0
\(188\) −3.58722e10 −2.09434
\(189\) 1.01325e10 0.577612
\(190\) −6.91092e8 −0.0384720
\(191\) 8.58739e8 0.0466886 0.0233443 0.999727i \(-0.492569\pi\)
0.0233443 + 0.999727i \(0.492569\pi\)
\(192\) 1.43852e10 0.763941
\(193\) −1.58649e10 −0.823055 −0.411527 0.911397i \(-0.635005\pi\)
−0.411527 + 0.911397i \(0.635005\pi\)
\(194\) −2.15809e10 −1.09386
\(195\) −8.76120e8 −0.0433918
\(196\) −2.07006e10 −1.00191
\(197\) −3.61603e10 −1.71054 −0.855271 0.518180i \(-0.826610\pi\)
−0.855271 + 0.518180i \(0.826610\pi\)
\(198\) 9.71858e9 0.449375
\(199\) −1.67380e10 −0.756595 −0.378298 0.925684i \(-0.623490\pi\)
−0.378298 + 0.925684i \(0.623490\pi\)
\(200\) 2.81769e10 1.24526
\(201\) −1.09324e10 −0.472427
\(202\) 6.06750e10 2.56406
\(203\) 1.96576e9 0.0812454
\(204\) 0 0
\(205\) −1.68038e9 −0.0664529
\(206\) −5.95402e10 −2.30360
\(207\) −1.28978e10 −0.488259
\(208\) 1.06043e10 0.392823
\(209\) 3.29956e9 0.119618
\(210\) 1.09204e9 0.0387481
\(211\) −7.73670e9 −0.268711 −0.134355 0.990933i \(-0.542896\pi\)
−0.134355 + 0.990933i \(0.542896\pi\)
\(212\) −2.87421e10 −0.977253
\(213\) 2.43837e10 0.811694
\(214\) −6.88052e10 −2.24264
\(215\) −2.37718e9 −0.0758734
\(216\) −3.53154e10 −1.10388
\(217\) 2.27930e10 0.697804
\(218\) −1.03658e11 −3.10849
\(219\) 1.28717e10 0.378128
\(220\) 1.56344e9 0.0449966
\(221\) 0 0
\(222\) −5.32608e10 −1.47170
\(223\) 3.19556e9 0.0865315 0.0432658 0.999064i \(-0.486224\pi\)
0.0432658 + 0.999064i \(0.486224\pi\)
\(224\) 1.76622e10 0.468738
\(225\) 2.84703e10 0.740579
\(226\) 4.35470e10 1.11038
\(227\) −4.05926e10 −1.01468 −0.507341 0.861745i \(-0.669372\pi\)
−0.507341 + 0.861745i \(0.669372\pi\)
\(228\) −1.19004e10 −0.291645
\(229\) −5.91362e10 −1.42100 −0.710500 0.703697i \(-0.751531\pi\)
−0.710500 + 0.703697i \(0.751531\pi\)
\(230\) −3.25777e9 −0.0767617
\(231\) −5.21384e9 −0.120477
\(232\) −6.85143e9 −0.155269
\(233\) 4.52505e10 1.00582 0.502912 0.864338i \(-0.332262\pi\)
0.502912 + 0.864338i \(0.332262\pi\)
\(234\) 6.89417e10 1.50318
\(235\) −3.93584e9 −0.0841844
\(236\) 1.29041e11 2.70784
\(237\) −3.06159e10 −0.630346
\(238\) 0 0
\(239\) −5.33414e10 −1.05748 −0.528742 0.848783i \(-0.677336\pi\)
−0.528742 + 0.848783i \(0.677336\pi\)
\(240\) −5.91543e8 −0.0115089
\(241\) 1.03808e11 1.98222 0.991111 0.133034i \(-0.0424720\pi\)
0.991111 + 0.133034i \(0.0424720\pi\)
\(242\) 7.68241e10 1.43989
\(243\) −5.61404e10 −1.03287
\(244\) 8.64940e10 1.56218
\(245\) −2.27123e9 −0.0402730
\(246\) −4.54314e10 −0.790948
\(247\) 2.34064e10 0.400128
\(248\) −7.94424e10 −1.33358
\(249\) 2.39679e10 0.395123
\(250\) 1.44181e10 0.233442
\(251\) 8.18530e10 1.30168 0.650838 0.759217i \(-0.274418\pi\)
0.650838 + 0.759217i \(0.274418\pi\)
\(252\) −5.47307e10 −0.854926
\(253\) 1.55539e10 0.238670
\(254\) −6.55157e10 −0.987629
\(255\) 0 0
\(256\) −1.00468e11 −1.46201
\(257\) −3.14222e10 −0.449301 −0.224650 0.974439i \(-0.572124\pi\)
−0.224650 + 0.974439i \(0.572124\pi\)
\(258\) −6.42706e10 −0.903074
\(259\) −8.31632e10 −1.14837
\(260\) 1.10907e10 0.150515
\(261\) −6.92276e9 −0.0923416
\(262\) −6.00577e10 −0.787432
\(263\) 5.82416e10 0.750641 0.375320 0.926895i \(-0.377533\pi\)
0.375320 + 0.926895i \(0.377533\pi\)
\(264\) 1.81722e10 0.230245
\(265\) −3.15353e9 −0.0392817
\(266\) −2.91749e10 −0.357307
\(267\) 1.51238e10 0.182121
\(268\) 1.38393e11 1.63873
\(269\) 6.48636e9 0.0755294 0.0377647 0.999287i \(-0.487976\pi\)
0.0377647 + 0.999287i \(0.487976\pi\)
\(270\) −9.01294e9 −0.103212
\(271\) 1.14924e11 1.29435 0.647173 0.762343i \(-0.275951\pi\)
0.647173 + 0.762343i \(0.275951\pi\)
\(272\) 0 0
\(273\) −3.69860e10 −0.403000
\(274\) −9.11481e10 −0.976945
\(275\) −3.43333e10 −0.362009
\(276\) −5.60977e10 −0.581908
\(277\) 4.72845e10 0.482570 0.241285 0.970454i \(-0.422431\pi\)
0.241285 + 0.970454i \(0.422431\pi\)
\(278\) 6.15819e10 0.618374
\(279\) −8.02696e10 −0.793107
\(280\) −5.94308e9 −0.0577830
\(281\) 6.88901e10 0.659141 0.329570 0.944131i \(-0.393096\pi\)
0.329570 + 0.944131i \(0.393096\pi\)
\(282\) −1.06411e11 −1.00200
\(283\) −1.62716e11 −1.50797 −0.753983 0.656894i \(-0.771870\pi\)
−0.753983 + 0.656894i \(0.771870\pi\)
\(284\) −3.08672e11 −2.81556
\(285\) −1.30569e9 −0.0117230
\(286\) −8.31391e10 −0.734781
\(287\) −7.09381e10 −0.617179
\(288\) −6.22006e10 −0.532756
\(289\) 0 0
\(290\) −1.74857e9 −0.0145175
\(291\) −4.07731e10 −0.333315
\(292\) −1.62942e11 −1.31163
\(293\) 1.10593e11 0.876646 0.438323 0.898818i \(-0.355573\pi\)
0.438323 + 0.898818i \(0.355573\pi\)
\(294\) −6.14060e10 −0.479344
\(295\) 1.41581e10 0.108844
\(296\) 2.89855e11 2.19467
\(297\) 4.30315e10 0.320910
\(298\) −1.03030e11 −0.756814
\(299\) 1.10336e11 0.798360
\(300\) 1.23829e11 0.882623
\(301\) −1.00354e11 −0.704671
\(302\) −3.03389e11 −2.09879
\(303\) 1.14634e11 0.781307
\(304\) 1.58037e10 0.106127
\(305\) 9.48996e9 0.0627936
\(306\) 0 0
\(307\) 2.01516e11 1.29476 0.647378 0.762169i \(-0.275866\pi\)
0.647378 + 0.762169i \(0.275866\pi\)
\(308\) 6.60016e10 0.417904
\(309\) −1.12490e11 −0.701941
\(310\) −2.02747e10 −0.124689
\(311\) −1.00156e11 −0.607091 −0.303545 0.952817i \(-0.598170\pi\)
−0.303545 + 0.952817i \(0.598170\pi\)
\(312\) 1.28910e11 0.770178
\(313\) 1.11324e10 0.0655602 0.0327801 0.999463i \(-0.489564\pi\)
0.0327801 + 0.999463i \(0.489564\pi\)
\(314\) 2.95844e11 1.71743
\(315\) −6.00496e9 −0.0343647
\(316\) 3.87564e11 2.18651
\(317\) −2.14276e11 −1.19181 −0.595906 0.803054i \(-0.703207\pi\)
−0.595906 + 0.803054i \(0.703207\pi\)
\(318\) −8.52603e10 −0.467546
\(319\) 8.34840e9 0.0451383
\(320\) −1.99798e10 −0.106516
\(321\) −1.29994e11 −0.683364
\(322\) −1.37529e11 −0.712922
\(323\) 0 0
\(324\) 1.03767e11 0.523126
\(325\) −2.43554e11 −1.21093
\(326\) −3.00063e11 −1.47141
\(327\) −1.95843e11 −0.947202
\(328\) 2.47246e11 1.17950
\(329\) −1.66154e11 −0.781860
\(330\) 4.63778e9 0.0215277
\(331\) −1.34835e11 −0.617413 −0.308707 0.951157i \(-0.599896\pi\)
−0.308707 + 0.951157i \(0.599896\pi\)
\(332\) −3.03408e11 −1.37058
\(333\) 2.92873e11 1.30521
\(334\) −1.16374e11 −0.511679
\(335\) 1.51842e10 0.0658705
\(336\) −2.49724e10 −0.106889
\(337\) 3.74106e10 0.158001 0.0790005 0.996875i \(-0.474827\pi\)
0.0790005 + 0.996875i \(0.474827\pi\)
\(338\) −1.91559e11 −0.798321
\(339\) 8.22738e10 0.338348
\(340\) 0 0
\(341\) 9.67998e10 0.387686
\(342\) 1.02744e11 0.406107
\(343\) −2.63747e11 −1.02888
\(344\) 3.49773e11 1.34671
\(345\) −6.15494e9 −0.0233904
\(346\) 6.15817e11 2.30999
\(347\) −8.04529e10 −0.297892 −0.148946 0.988845i \(-0.547588\pi\)
−0.148946 + 0.988845i \(0.547588\pi\)
\(348\) −3.01098e10 −0.110053
\(349\) 4.32246e11 1.55961 0.779806 0.626021i \(-0.215318\pi\)
0.779806 + 0.626021i \(0.215318\pi\)
\(350\) 3.03577e11 1.08134
\(351\) 3.05257e11 1.07345
\(352\) 7.50098e10 0.260421
\(353\) −1.09770e11 −0.376269 −0.188135 0.982143i \(-0.560244\pi\)
−0.188135 + 0.982143i \(0.560244\pi\)
\(354\) 3.82785e11 1.29551
\(355\) −3.38670e10 −0.113174
\(356\) −1.91451e11 −0.631730
\(357\) 0 0
\(358\) 4.17240e11 1.34249
\(359\) −4.96246e10 −0.157678 −0.0788391 0.996887i \(-0.525121\pi\)
−0.0788391 + 0.996887i \(0.525121\pi\)
\(360\) 2.09296e10 0.0656748
\(361\) −2.87805e11 −0.891899
\(362\) 3.21045e11 0.982602
\(363\) 1.45145e11 0.438754
\(364\) 4.68202e11 1.39790
\(365\) −1.78777e10 −0.0527224
\(366\) 2.56575e11 0.747394
\(367\) 1.92703e11 0.554487 0.277243 0.960800i \(-0.410579\pi\)
0.277243 + 0.960800i \(0.410579\pi\)
\(368\) 7.44975e10 0.211752
\(369\) 2.49821e11 0.701471
\(370\) 7.39747e10 0.205199
\(371\) −1.33128e11 −0.364828
\(372\) −3.49124e11 −0.945227
\(373\) −2.91248e11 −0.779065 −0.389533 0.921013i \(-0.627363\pi\)
−0.389533 + 0.921013i \(0.627363\pi\)
\(374\) 0 0
\(375\) 2.72404e10 0.0711332
\(376\) 5.79110e11 1.49422
\(377\) 5.92219e10 0.150989
\(378\) −3.80487e11 −0.958577
\(379\) −4.17979e11 −1.04059 −0.520293 0.853988i \(-0.674177\pi\)
−0.520293 + 0.853988i \(0.674177\pi\)
\(380\) 1.65286e10 0.0406640
\(381\) −1.23780e11 −0.300945
\(382\) −3.22468e10 −0.0774821
\(383\) 6.50085e11 1.54374 0.771872 0.635778i \(-0.219321\pi\)
0.771872 + 0.635778i \(0.219321\pi\)
\(384\) −3.85953e11 −0.905825
\(385\) 7.24158e9 0.0167981
\(386\) 5.95747e11 1.36590
\(387\) 3.53415e11 0.800912
\(388\) 5.16144e11 1.15619
\(389\) −6.79183e11 −1.50388 −0.751941 0.659231i \(-0.770882\pi\)
−0.751941 + 0.659231i \(0.770882\pi\)
\(390\) 3.28995e10 0.0720109
\(391\) 0 0
\(392\) 3.34183e11 0.714821
\(393\) −1.13468e11 −0.239942
\(394\) 1.35787e12 2.83873
\(395\) 4.25228e10 0.0878892
\(396\) −2.32436e11 −0.474980
\(397\) −8.45189e11 −1.70764 −0.853820 0.520568i \(-0.825720\pi\)
−0.853820 + 0.520568i \(0.825720\pi\)
\(398\) 6.28533e11 1.25561
\(399\) −5.51205e10 −0.108877
\(400\) −1.64444e11 −0.321180
\(401\) −9.27527e11 −1.79134 −0.895668 0.444723i \(-0.853302\pi\)
−0.895668 + 0.444723i \(0.853302\pi\)
\(402\) 4.10527e11 0.784016
\(403\) 6.86679e11 1.29682
\(404\) −1.45114e12 −2.71016
\(405\) 1.13851e10 0.0210276
\(406\) −7.38170e10 −0.134831
\(407\) −3.53186e11 −0.638012
\(408\) 0 0
\(409\) 2.00626e11 0.354514 0.177257 0.984165i \(-0.443278\pi\)
0.177257 + 0.984165i \(0.443278\pi\)
\(410\) 6.31003e10 0.110282
\(411\) −1.72207e11 −0.297689
\(412\) 1.42400e12 2.43486
\(413\) 5.97694e11 1.01089
\(414\) 4.84331e11 0.810290
\(415\) −3.32894e10 −0.0550921
\(416\) 5.32105e11 0.871118
\(417\) 1.16347e11 0.188428
\(418\) −1.23903e11 −0.198513
\(419\) −1.21669e12 −1.92848 −0.964240 0.265031i \(-0.914618\pi\)
−0.964240 + 0.265031i \(0.914618\pi\)
\(420\) −2.61179e10 −0.0409559
\(421\) 8.68283e11 1.34708 0.673538 0.739153i \(-0.264774\pi\)
0.673538 + 0.739153i \(0.264774\pi\)
\(422\) 2.90524e11 0.445939
\(423\) 5.85139e11 0.888644
\(424\) 4.64003e11 0.697227
\(425\) 0 0
\(426\) −9.15642e11 −1.34705
\(427\) 4.00625e11 0.583193
\(428\) 1.64559e12 2.37042
\(429\) −1.57076e11 −0.223899
\(430\) 8.92663e10 0.125916
\(431\) −9.10662e11 −1.27119 −0.635594 0.772024i \(-0.719245\pi\)
−0.635594 + 0.772024i \(0.719245\pi\)
\(432\) 2.06105e11 0.284716
\(433\) 3.19740e10 0.0437121 0.0218560 0.999761i \(-0.493042\pi\)
0.0218560 + 0.999761i \(0.493042\pi\)
\(434\) −8.55909e11 −1.15804
\(435\) −3.30359e9 −0.00442369
\(436\) 2.47916e12 3.28560
\(437\) 1.64435e11 0.215690
\(438\) −4.83351e11 −0.627522
\(439\) 9.65386e10 0.124054 0.0620270 0.998074i \(-0.480244\pi\)
0.0620270 + 0.998074i \(0.480244\pi\)
\(440\) −2.52397e10 −0.0321031
\(441\) 3.37663e11 0.425118
\(442\) 0 0
\(443\) 4.55197e11 0.561542 0.280771 0.959775i \(-0.409410\pi\)
0.280771 + 0.959775i \(0.409410\pi\)
\(444\) 1.27382e12 1.55555
\(445\) −2.10056e10 −0.0253931
\(446\) −1.19997e11 −0.143603
\(447\) −1.94655e11 −0.230612
\(448\) −8.43460e11 −0.989266
\(449\) −1.54092e12 −1.78926 −0.894628 0.446812i \(-0.852559\pi\)
−0.894628 + 0.446812i \(0.852559\pi\)
\(450\) −1.06910e12 −1.22903
\(451\) −3.01267e11 −0.342892
\(452\) −1.04150e12 −1.17364
\(453\) −5.73197e11 −0.639532
\(454\) 1.52431e12 1.68392
\(455\) 5.13703e10 0.0561903
\(456\) 1.92116e11 0.208076
\(457\) −5.52148e10 −0.0592151 −0.0296076 0.999562i \(-0.509426\pi\)
−0.0296076 + 0.999562i \(0.509426\pi\)
\(458\) 2.22064e12 2.35822
\(459\) 0 0
\(460\) 7.79149e10 0.0811354
\(461\) −9.04347e11 −0.932568 −0.466284 0.884635i \(-0.654408\pi\)
−0.466284 + 0.884635i \(0.654408\pi\)
\(462\) 1.95787e11 0.199938
\(463\) −1.69193e12 −1.71107 −0.855535 0.517745i \(-0.826772\pi\)
−0.855535 + 0.517745i \(0.826772\pi\)
\(464\) 3.99857e10 0.0400474
\(465\) −3.83052e10 −0.0379944
\(466\) −1.69922e12 −1.66922
\(467\) 5.51847e11 0.536899 0.268450 0.963294i \(-0.413489\pi\)
0.268450 + 0.963294i \(0.413489\pi\)
\(468\) −1.64885e12 −1.58882
\(469\) 6.41012e11 0.611770
\(470\) 1.47796e11 0.139708
\(471\) 5.58943e11 0.523327
\(472\) −2.08319e12 −1.93192
\(473\) −4.26195e11 −0.391501
\(474\) 1.14967e12 1.04609
\(475\) −3.62971e11 −0.327152
\(476\) 0 0
\(477\) 4.68834e11 0.414655
\(478\) 2.00304e12 1.75495
\(479\) −2.30106e11 −0.199719 −0.0998594 0.995002i \(-0.531839\pi\)
−0.0998594 + 0.995002i \(0.531839\pi\)
\(480\) −2.96826e10 −0.0255221
\(481\) −2.50543e12 −2.13417
\(482\) −3.89811e12 −3.28960
\(483\) −2.59835e11 −0.217238
\(484\) −1.83738e12 −1.52193
\(485\) 5.66304e10 0.0464742
\(486\) 2.10815e12 1.71411
\(487\) 1.20979e12 0.974608 0.487304 0.873232i \(-0.337980\pi\)
0.487304 + 0.873232i \(0.337980\pi\)
\(488\) −1.39633e12 −1.11455
\(489\) −5.66912e11 −0.448359
\(490\) 8.52877e10 0.0668350
\(491\) 1.11945e12 0.869234 0.434617 0.900615i \(-0.356884\pi\)
0.434617 + 0.900615i \(0.356884\pi\)
\(492\) 1.08657e12 0.836014
\(493\) 0 0
\(494\) −8.78943e11 −0.664033
\(495\) −2.55025e10 −0.0190923
\(496\) 4.63635e11 0.343961
\(497\) −1.42972e12 −1.05110
\(498\) −9.00026e11 −0.655727
\(499\) −9.47198e11 −0.683893 −0.341947 0.939719i \(-0.611086\pi\)
−0.341947 + 0.939719i \(0.611086\pi\)
\(500\) −3.44834e11 −0.246743
\(501\) −2.19867e11 −0.155916
\(502\) −3.07369e12 −2.16020
\(503\) −8.69721e11 −0.605793 −0.302896 0.953023i \(-0.597954\pi\)
−0.302896 + 0.953023i \(0.597954\pi\)
\(504\) 8.83554e11 0.609952
\(505\) −1.59217e11 −0.108938
\(506\) −5.84071e11 −0.396085
\(507\) −3.61915e11 −0.243260
\(508\) 1.56692e12 1.04390
\(509\) 2.54306e12 1.67929 0.839646 0.543134i \(-0.182762\pi\)
0.839646 + 0.543134i \(0.182762\pi\)
\(510\) 0 0
\(511\) −7.54720e11 −0.489657
\(512\) 9.87401e11 0.635007
\(513\) 4.54927e11 0.290011
\(514\) 1.17994e12 0.745637
\(515\) 1.56239e11 0.0978717
\(516\) 1.53714e12 0.954529
\(517\) −7.05639e11 −0.434386
\(518\) 3.12289e12 1.90578
\(519\) 1.16347e12 0.703886
\(520\) −1.79045e11 −0.107386
\(521\) −3.03890e12 −1.80695 −0.903477 0.428638i \(-0.858994\pi\)
−0.903477 + 0.428638i \(0.858994\pi\)
\(522\) 2.59959e11 0.153245
\(523\) 2.02927e12 1.18599 0.592995 0.805206i \(-0.297945\pi\)
0.592995 + 0.805206i \(0.297945\pi\)
\(524\) 1.43638e12 0.832297
\(525\) 5.73552e11 0.329501
\(526\) −2.18705e12 −1.24573
\(527\) 0 0
\(528\) −1.06055e11 −0.0593853
\(529\) −1.02601e12 −0.569643
\(530\) 1.18419e11 0.0651900
\(531\) −2.10488e12 −1.14895
\(532\) 6.97766e11 0.377666
\(533\) −2.13713e12 −1.14699
\(534\) −5.67918e11 −0.302238
\(535\) 1.80551e11 0.0952815
\(536\) −2.23417e12 −1.16916
\(537\) 7.88296e11 0.409077
\(538\) −2.43572e11 −0.125345
\(539\) −4.07199e11 −0.207806
\(540\) 2.15559e11 0.109093
\(541\) −1.14736e12 −0.575855 −0.287927 0.957652i \(-0.592966\pi\)
−0.287927 + 0.957652i \(0.592966\pi\)
\(542\) −4.31557e12 −2.14803
\(543\) 6.06555e11 0.299413
\(544\) 0 0
\(545\) 2.72009e11 0.132068
\(546\) 1.38887e12 0.668799
\(547\) 1.20725e12 0.576573 0.288287 0.957544i \(-0.406914\pi\)
0.288287 + 0.957544i \(0.406914\pi\)
\(548\) 2.17996e12 1.03261
\(549\) −1.41087e12 −0.662844
\(550\) 1.28926e12 0.600772
\(551\) 8.82589e10 0.0407921
\(552\) 9.05622e11 0.415166
\(553\) 1.79513e12 0.816268
\(554\) −1.77560e12 −0.800849
\(555\) 1.39761e11 0.0625272
\(556\) −1.47283e12 −0.653608
\(557\) −3.91673e12 −1.72415 −0.862074 0.506782i \(-0.830835\pi\)
−0.862074 + 0.506782i \(0.830835\pi\)
\(558\) 3.01423e12 1.31620
\(559\) −3.02334e12 −1.30959
\(560\) 3.46845e10 0.0149035
\(561\) 0 0
\(562\) −2.58691e12 −1.09388
\(563\) 2.78380e11 0.116775 0.0583875 0.998294i \(-0.481404\pi\)
0.0583875 + 0.998294i \(0.481404\pi\)
\(564\) 2.54500e12 1.05909
\(565\) −1.14271e11 −0.0471758
\(566\) 6.11020e12 2.50254
\(567\) 4.80630e11 0.195293
\(568\) 4.98310e12 2.00878
\(569\) 1.05967e12 0.423804 0.211902 0.977291i \(-0.432034\pi\)
0.211902 + 0.977291i \(0.432034\pi\)
\(570\) 4.90304e10 0.0194549
\(571\) −2.19847e12 −0.865481 −0.432740 0.901519i \(-0.642453\pi\)
−0.432740 + 0.901519i \(0.642453\pi\)
\(572\) 1.98841e12 0.776647
\(573\) −6.09243e10 −0.0236099
\(574\) 2.66382e12 1.02424
\(575\) −1.71102e12 −0.652755
\(576\) 2.97039e12 1.12438
\(577\) −3.27165e12 −1.22878 −0.614392 0.789001i \(-0.710599\pi\)
−0.614392 + 0.789001i \(0.710599\pi\)
\(578\) 0 0
\(579\) 1.12555e12 0.416210
\(580\) 4.18199e10 0.0153447
\(581\) −1.40533e12 −0.511666
\(582\) 1.53108e12 0.553154
\(583\) −5.65383e11 −0.202691
\(584\) 2.63049e12 0.935790
\(585\) −1.80909e11 −0.0638645
\(586\) −4.15292e12 −1.45484
\(587\) 4.69052e12 1.63061 0.815304 0.579033i \(-0.196570\pi\)
0.815304 + 0.579033i \(0.196570\pi\)
\(588\) 1.46863e12 0.506656
\(589\) 1.02336e12 0.350357
\(590\) −5.31656e11 −0.180633
\(591\) 2.56544e12 0.865003
\(592\) −1.69163e12 −0.566054
\(593\) −3.23030e12 −1.07274 −0.536372 0.843982i \(-0.680206\pi\)
−0.536372 + 0.843982i \(0.680206\pi\)
\(594\) −1.61589e12 −0.532566
\(595\) 0 0
\(596\) 2.46413e12 0.799936
\(597\) 1.18749e12 0.382602
\(598\) −4.14328e12 −1.32492
\(599\) −7.65685e11 −0.243013 −0.121507 0.992591i \(-0.538773\pi\)
−0.121507 + 0.992591i \(0.538773\pi\)
\(600\) −1.99905e12 −0.629713
\(601\) 4.21877e12 1.31902 0.659510 0.751696i \(-0.270764\pi\)
0.659510 + 0.751696i \(0.270764\pi\)
\(602\) 3.76844e12 1.16944
\(603\) −2.25743e12 −0.695323
\(604\) 7.25606e12 2.21837
\(605\) −2.01594e11 −0.0611755
\(606\) −4.30466e12 −1.29662
\(607\) 6.53092e12 1.95265 0.976327 0.216301i \(-0.0693992\pi\)
0.976327 + 0.216301i \(0.0693992\pi\)
\(608\) 7.93000e11 0.235346
\(609\) −1.39463e11 −0.0410849
\(610\) −3.56361e11 −0.104209
\(611\) −5.00567e12 −1.45304
\(612\) 0 0
\(613\) 1.11938e12 0.320189 0.160095 0.987102i \(-0.448820\pi\)
0.160095 + 0.987102i \(0.448820\pi\)
\(614\) −7.56721e12 −2.14871
\(615\) 1.19216e11 0.0336045
\(616\) −1.06551e12 −0.298156
\(617\) 2.37749e11 0.0660442 0.0330221 0.999455i \(-0.489487\pi\)
0.0330221 + 0.999455i \(0.489487\pi\)
\(618\) 4.22415e12 1.16491
\(619\) 1.01284e12 0.277288 0.138644 0.990342i \(-0.455726\pi\)
0.138644 + 0.990342i \(0.455726\pi\)
\(620\) 4.84903e11 0.131793
\(621\) 2.14450e12 0.578647
\(622\) 3.76098e12 1.00750
\(623\) −8.86766e11 −0.235837
\(624\) −7.52334e11 −0.198646
\(625\) 3.75790e12 0.985110
\(626\) −4.18038e11 −0.108800
\(627\) −2.34091e11 −0.0604897
\(628\) −7.07561e12 −1.81529
\(629\) 0 0
\(630\) 2.25494e11 0.0570299
\(631\) −4.57844e12 −1.14970 −0.574851 0.818258i \(-0.694940\pi\)
−0.574851 + 0.818258i \(0.694940\pi\)
\(632\) −6.25671e12 −1.55998
\(633\) 5.48890e11 0.135884
\(634\) 8.04636e12 1.97787
\(635\) 1.71919e11 0.0419607
\(636\) 2.03914e12 0.494186
\(637\) −2.88859e12 −0.695117
\(638\) −3.13493e11 −0.0749092
\(639\) 5.03498e12 1.19466
\(640\) 5.36057e11 0.126299
\(641\) −6.84749e12 −1.60203 −0.801014 0.598645i \(-0.795706\pi\)
−0.801014 + 0.598645i \(0.795706\pi\)
\(642\) 4.88146e12 1.13408
\(643\) −2.56550e11 −0.0591864 −0.0295932 0.999562i \(-0.509421\pi\)
−0.0295932 + 0.999562i \(0.509421\pi\)
\(644\) 3.28923e12 0.753542
\(645\) 1.68652e11 0.0383683
\(646\) 0 0
\(647\) 4.79815e12 1.07648 0.538238 0.842793i \(-0.319090\pi\)
0.538238 + 0.842793i \(0.319090\pi\)
\(648\) −1.67518e12 −0.373228
\(649\) 2.53835e12 0.561629
\(650\) 9.14577e12 2.00960
\(651\) −1.61708e12 −0.352872
\(652\) 7.17650e12 1.55524
\(653\) −2.65352e12 −0.571101 −0.285550 0.958364i \(-0.592176\pi\)
−0.285550 + 0.958364i \(0.592176\pi\)
\(654\) 7.35415e12 1.57193
\(655\) 1.57597e11 0.0334551
\(656\) −1.44296e12 −0.304219
\(657\) 2.65788e12 0.556533
\(658\) 6.23930e12 1.29754
\(659\) −6.71596e12 −1.38715 −0.693575 0.720384i \(-0.743965\pi\)
−0.693575 + 0.720384i \(0.743965\pi\)
\(660\) −1.10920e11 −0.0227543
\(661\) −8.92190e11 −0.181782 −0.0908910 0.995861i \(-0.528971\pi\)
−0.0908910 + 0.995861i \(0.528971\pi\)
\(662\) 5.06322e12 1.02463
\(663\) 0 0
\(664\) 4.89811e12 0.977851
\(665\) 7.65577e10 0.0151807
\(666\) −1.09978e13 −2.16606
\(667\) 4.16047e11 0.0813909
\(668\) 2.78328e12 0.540833
\(669\) −2.26713e11 −0.0437580
\(670\) −5.70188e11 −0.109315
\(671\) 1.70141e12 0.324010
\(672\) −1.25307e12 −0.237035
\(673\) 1.94234e12 0.364970 0.182485 0.983209i \(-0.441586\pi\)
0.182485 + 0.983209i \(0.441586\pi\)
\(674\) −1.40482e12 −0.262211
\(675\) −4.73371e12 −0.877677
\(676\) 4.58146e12 0.843808
\(677\) −1.48181e12 −0.271109 −0.135555 0.990770i \(-0.543282\pi\)
−0.135555 + 0.990770i \(0.543282\pi\)
\(678\) −3.08949e12 −0.561505
\(679\) 2.39069e12 0.431627
\(680\) 0 0
\(681\) 2.87989e12 0.513114
\(682\) −3.63496e12 −0.643384
\(683\) −6.51135e12 −1.14493 −0.572464 0.819930i \(-0.694012\pi\)
−0.572464 + 0.819930i \(0.694012\pi\)
\(684\) −2.45730e12 −0.429246
\(685\) 2.39181e11 0.0415068
\(686\) 9.90403e12 1.70747
\(687\) 4.19549e12 0.718584
\(688\) −2.04131e12 −0.347346
\(689\) −4.01071e12 −0.678009
\(690\) 2.31126e11 0.0388176
\(691\) −5.42411e12 −0.905059 −0.452530 0.891749i \(-0.649478\pi\)
−0.452530 + 0.891749i \(0.649478\pi\)
\(692\) −1.47283e13 −2.44160
\(693\) −1.07660e12 −0.177319
\(694\) 3.02111e12 0.494367
\(695\) −1.61597e11 −0.0262725
\(696\) 4.86083e11 0.0785179
\(697\) 0 0
\(698\) −1.62314e13 −2.58825
\(699\) −3.21035e12 −0.508634
\(700\) −7.26056e12 −1.14295
\(701\) −1.83146e12 −0.286461 −0.143230 0.989689i \(-0.545749\pi\)
−0.143230 + 0.989689i \(0.545749\pi\)
\(702\) −1.14628e13 −1.78145
\(703\) −3.73387e12 −0.576581
\(704\) −3.58209e12 −0.549616
\(705\) 2.79233e11 0.0425711
\(706\) 4.12202e12 0.624438
\(707\) −6.72145e12 −1.01176
\(708\) −9.15494e12 −1.36932
\(709\) −4.41281e12 −0.655854 −0.327927 0.944703i \(-0.606350\pi\)
−0.327927 + 0.944703i \(0.606350\pi\)
\(710\) 1.27175e12 0.187819
\(711\) −6.32185e12 −0.927750
\(712\) 3.09072e12 0.450712
\(713\) 4.82407e12 0.699054
\(714\) 0 0
\(715\) 2.18165e11 0.0312182
\(716\) −9.97898e12 −1.41898
\(717\) 3.78437e12 0.534758
\(718\) 1.86347e12 0.261675
\(719\) −6.39579e12 −0.892513 −0.446256 0.894905i \(-0.647243\pi\)
−0.446256 + 0.894905i \(0.647243\pi\)
\(720\) −1.22147e11 −0.0169390
\(721\) 6.59573e12 0.908980
\(722\) 1.08075e13 1.48015
\(723\) −7.36476e12 −1.00239
\(724\) −7.67833e12 −1.03859
\(725\) −9.18371e11 −0.123452
\(726\) −5.45038e12 −0.728135
\(727\) −9.70659e12 −1.28873 −0.644365 0.764718i \(-0.722878\pi\)
−0.644365 + 0.764718i \(0.722878\pi\)
\(728\) −7.55851e12 −0.997343
\(729\) 1.70877e12 0.224084
\(730\) 6.71333e11 0.0874954
\(731\) 0 0
\(732\) −6.13642e12 −0.789978
\(733\) 1.27278e12 0.162849 0.0814246 0.996680i \(-0.474053\pi\)
0.0814246 + 0.996680i \(0.474053\pi\)
\(734\) −7.23625e12 −0.920198
\(735\) 1.61135e11 0.0203656
\(736\) 3.73815e12 0.469577
\(737\) 2.72231e12 0.339887
\(738\) −9.38110e12 −1.16413
\(739\) −8.07516e12 −0.995982 −0.497991 0.867182i \(-0.665929\pi\)
−0.497991 + 0.867182i \(0.665929\pi\)
\(740\) −1.76923e12 −0.216891
\(741\) −1.66060e12 −0.202340
\(742\) 4.99915e12 0.605450
\(743\) −9.55473e12 −1.15019 −0.575094 0.818088i \(-0.695034\pi\)
−0.575094 + 0.818088i \(0.695034\pi\)
\(744\) 5.63614e12 0.674378
\(745\) 2.70360e11 0.0321543
\(746\) 1.09368e13 1.29290
\(747\) 4.94911e12 0.581547
\(748\) 0 0
\(749\) 7.62209e12 0.884923
\(750\) −1.02291e12 −0.118049
\(751\) 6.20481e12 0.711785 0.355893 0.934527i \(-0.384177\pi\)
0.355893 + 0.934527i \(0.384177\pi\)
\(752\) −3.37975e12 −0.385394
\(753\) −5.80716e12 −0.658243
\(754\) −2.22386e12 −0.250574
\(755\) 7.96123e11 0.0891700
\(756\) 9.09998e12 1.01319
\(757\) 2.32006e12 0.256784 0.128392 0.991723i \(-0.459018\pi\)
0.128392 + 0.991723i \(0.459018\pi\)
\(758\) 1.56957e13 1.72690
\(759\) −1.10349e12 −0.120693
\(760\) −2.66833e11 −0.0290120
\(761\) 6.55124e12 0.708097 0.354048 0.935227i \(-0.384805\pi\)
0.354048 + 0.935227i \(0.384805\pi\)
\(762\) 4.64809e12 0.499433
\(763\) 1.14830e13 1.22658
\(764\) 7.71236e11 0.0818968
\(765\) 0 0
\(766\) −2.44115e13 −2.56192
\(767\) 1.80065e13 1.87867
\(768\) 7.12786e12 0.739322
\(769\) −8.34102e12 −0.860104 −0.430052 0.902804i \(-0.641505\pi\)
−0.430052 + 0.902804i \(0.641505\pi\)
\(770\) −2.71931e11 −0.0278773
\(771\) 2.22928e12 0.227206
\(772\) −1.42483e13 −1.44373
\(773\) −1.39783e13 −1.40815 −0.704073 0.710128i \(-0.748637\pi\)
−0.704073 + 0.710128i \(0.748637\pi\)
\(774\) −1.32712e13 −1.32915
\(775\) −1.06485e13 −1.06031
\(776\) −8.33245e12 −0.824888
\(777\) 5.90012e12 0.580719
\(778\) 2.55042e13 2.49577
\(779\) −3.18498e12 −0.309877
\(780\) −7.86846e11 −0.0761139
\(781\) −6.07186e12 −0.583972
\(782\) 0 0
\(783\) 1.15104e12 0.109436
\(784\) −1.95033e12 −0.184368
\(785\) −7.76324e11 −0.0729675
\(786\) 4.26087e12 0.398196
\(787\) 1.23909e13 1.15137 0.575686 0.817671i \(-0.304735\pi\)
0.575686 + 0.817671i \(0.304735\pi\)
\(788\) −3.24757e13 −3.00048
\(789\) −4.13202e12 −0.379591
\(790\) −1.59679e12 −0.145857
\(791\) −4.82404e12 −0.438144
\(792\) 3.75237e12 0.338877
\(793\) 1.20695e13 1.08383
\(794\) 3.17380e13 2.83391
\(795\) 2.23731e11 0.0198643
\(796\) −1.50324e13 −1.32715
\(797\) 5.26393e12 0.462112 0.231056 0.972940i \(-0.425782\pi\)
0.231056 + 0.972940i \(0.425782\pi\)
\(798\) 2.06985e12 0.180686
\(799\) 0 0
\(800\) −8.25151e12 −0.712243
\(801\) 3.12290e12 0.268047
\(802\) 3.48299e13 2.97281
\(803\) −3.20522e12 −0.272044
\(804\) −9.81845e12 −0.828687
\(805\) 3.60888e11 0.0302894
\(806\) −2.57857e13 −2.15214
\(807\) −4.60183e11 −0.0381944
\(808\) 2.34268e13 1.93358
\(809\) −7.01985e12 −0.576182 −0.288091 0.957603i \(-0.593021\pi\)
−0.288091 + 0.957603i \(0.593021\pi\)
\(810\) −4.27527e11 −0.0348964
\(811\) −1.35676e13 −1.10131 −0.550655 0.834733i \(-0.685622\pi\)
−0.550655 + 0.834733i \(0.685622\pi\)
\(812\) 1.76546e12 0.142513
\(813\) −8.15345e12 −0.654537
\(814\) 1.32626e13 1.05881
\(815\) 7.87393e11 0.0625147
\(816\) 0 0
\(817\) −4.50571e12 −0.353805
\(818\) −7.53379e12 −0.588333
\(819\) −7.63721e12 −0.593140
\(820\) −1.50915e12 −0.116565
\(821\) 1.09555e12 0.0841565 0.0420782 0.999114i \(-0.486602\pi\)
0.0420782 + 0.999114i \(0.486602\pi\)
\(822\) 6.46661e12 0.494030
\(823\) 2.21638e13 1.68401 0.842006 0.539469i \(-0.181375\pi\)
0.842006 + 0.539469i \(0.181375\pi\)
\(824\) −2.29886e13 −1.73716
\(825\) 2.43582e12 0.183064
\(826\) −2.24442e13 −1.67762
\(827\) 2.07994e13 1.54624 0.773119 0.634261i \(-0.218695\pi\)
0.773119 + 0.634261i \(0.218695\pi\)
\(828\) −1.15836e13 −0.856458
\(829\) 4.56048e12 0.335363 0.167682 0.985841i \(-0.446372\pi\)
0.167682 + 0.985841i \(0.446372\pi\)
\(830\) 1.25006e12 0.0914280
\(831\) −3.35466e12 −0.244030
\(832\) −2.54106e13 −1.83849
\(833\) 0 0
\(834\) −4.36900e12 −0.312705
\(835\) 3.05377e11 0.0217394
\(836\) 2.96335e12 0.209823
\(837\) 1.33463e13 0.939931
\(838\) 4.56881e13 3.20041
\(839\) −1.02208e13 −0.712125 −0.356063 0.934462i \(-0.615881\pi\)
−0.356063 + 0.934462i \(0.615881\pi\)
\(840\) 4.21639e11 0.0292202
\(841\) −1.42838e13 −0.984607
\(842\) −3.26052e13 −2.23554
\(843\) −4.88749e12 −0.333320
\(844\) −6.94836e12 −0.471347
\(845\) 5.02669e11 0.0339178
\(846\) −2.19728e13 −1.47475
\(847\) −8.51041e12 −0.568166
\(848\) −2.70797e12 −0.179830
\(849\) 1.15441e13 0.762562
\(850\) 0 0
\(851\) −1.76012e13 −1.15043
\(852\) 2.18991e13 1.42380
\(853\) 1.82858e13 1.18261 0.591306 0.806447i \(-0.298613\pi\)
0.591306 + 0.806447i \(0.298613\pi\)
\(854\) −1.50440e13 −0.967838
\(855\) −2.69611e11 −0.0172540
\(856\) −2.65659e13 −1.69119
\(857\) 2.38014e13 1.50726 0.753632 0.657297i \(-0.228300\pi\)
0.753632 + 0.657297i \(0.228300\pi\)
\(858\) 5.89840e12 0.371571
\(859\) 1.25917e13 0.789070 0.394535 0.918881i \(-0.370906\pi\)
0.394535 + 0.918881i \(0.370906\pi\)
\(860\) −2.13495e12 −0.133090
\(861\) 5.03279e12 0.312101
\(862\) 3.41966e13 2.10960
\(863\) −1.42262e13 −0.873052 −0.436526 0.899692i \(-0.643791\pi\)
−0.436526 + 0.899692i \(0.643791\pi\)
\(864\) 1.03420e13 0.631382
\(865\) −1.61596e12 −0.0981429
\(866\) −1.20067e12 −0.0725424
\(867\) 0 0
\(868\) 2.04705e13 1.22402
\(869\) 7.62374e12 0.453502
\(870\) 1.24054e11 0.00734134
\(871\) 1.93116e13 1.13693
\(872\) −4.00227e13 −2.34413
\(873\) −8.41921e12 −0.490577
\(874\) −6.17477e12 −0.357948
\(875\) −1.59721e12 −0.0921141
\(876\) 1.15601e13 0.663276
\(877\) −1.86781e13 −1.06619 −0.533096 0.846055i \(-0.678972\pi\)
−0.533096 + 0.846055i \(0.678972\pi\)
\(878\) −3.62515e12 −0.205874
\(879\) −7.84617e12 −0.443310
\(880\) 1.47302e11 0.00828010
\(881\) −1.32102e13 −0.738783 −0.369392 0.929274i \(-0.620434\pi\)
−0.369392 + 0.929274i \(0.620434\pi\)
\(882\) −1.26797e13 −0.705504
\(883\) 5.54927e12 0.307194 0.153597 0.988134i \(-0.450914\pi\)
0.153597 + 0.988134i \(0.450914\pi\)
\(884\) 0 0
\(885\) −1.00446e12 −0.0550414
\(886\) −1.70932e13 −0.931907
\(887\) 1.26950e13 0.688613 0.344307 0.938857i \(-0.388114\pi\)
0.344307 + 0.938857i \(0.388114\pi\)
\(888\) −2.05641e13 −1.10982
\(889\) 7.25769e12 0.389709
\(890\) 7.88789e11 0.0421411
\(891\) 2.04119e12 0.108501
\(892\) 2.86994e12 0.151786
\(893\) −7.45999e12 −0.392561
\(894\) 7.30957e12 0.382713
\(895\) −1.09488e12 −0.0570376
\(896\) 2.26300e13 1.17300
\(897\) −7.82796e12 −0.403722
\(898\) 5.78637e13 2.96936
\(899\) 2.58927e12 0.132208
\(900\) 2.55693e13 1.29905
\(901\) 0 0
\(902\) 1.13130e13 0.569047
\(903\) 7.11975e12 0.356344
\(904\) 1.68136e13 0.837342
\(905\) −8.42453e11 −0.0417472
\(906\) 2.15243e13 1.06134
\(907\) 8.72745e12 0.428208 0.214104 0.976811i \(-0.431317\pi\)
0.214104 + 0.976811i \(0.431317\pi\)
\(908\) −3.64563e13 −1.77986
\(909\) 2.36707e13 1.14994
\(910\) −1.92903e12 −0.0932506
\(911\) 2.60110e13 1.25119 0.625596 0.780147i \(-0.284856\pi\)
0.625596 + 0.780147i \(0.284856\pi\)
\(912\) −1.12121e12 −0.0536674
\(913\) −5.96831e12 −0.284271
\(914\) 2.07339e12 0.0982704
\(915\) −6.73277e11 −0.0317540
\(916\) −5.31104e13 −2.49259
\(917\) 6.65306e12 0.310713
\(918\) 0 0
\(919\) 2.79205e13 1.29123 0.645615 0.763663i \(-0.276601\pi\)
0.645615 + 0.763663i \(0.276601\pi\)
\(920\) −1.25783e12 −0.0578865
\(921\) −1.42968e13 −0.654744
\(922\) 3.39594e13 1.54764
\(923\) −4.30726e13 −1.95341
\(924\) −4.68257e12 −0.211329
\(925\) 3.88525e13 1.74494
\(926\) 6.35342e13 2.83961
\(927\) −2.32280e13 −1.03312
\(928\) 2.00641e12 0.0888085
\(929\) 9.34734e12 0.411735 0.205867 0.978580i \(-0.433998\pi\)
0.205867 + 0.978580i \(0.433998\pi\)
\(930\) 1.43841e12 0.0630536
\(931\) −4.30489e12 −0.187797
\(932\) 4.06396e13 1.76432
\(933\) 7.10566e12 0.306999
\(934\) −2.07226e13 −0.891012
\(935\) 0 0
\(936\) 2.66186e13 1.13356
\(937\) 4.53001e13 1.91987 0.959933 0.280231i \(-0.0904112\pi\)
0.959933 + 0.280231i \(0.0904112\pi\)
\(938\) −2.40708e13 −1.01526
\(939\) −7.89804e11 −0.0331531
\(940\) −3.53479e12 −0.147669
\(941\) 3.85131e13 1.60124 0.800618 0.599176i \(-0.204505\pi\)
0.800618 + 0.599176i \(0.204505\pi\)
\(942\) −2.09890e13 −0.868487
\(943\) −1.50138e13 −0.618285
\(944\) 1.21577e13 0.498286
\(945\) 9.98434e11 0.0407264
\(946\) 1.60042e13 0.649716
\(947\) −3.56276e13 −1.43950 −0.719751 0.694233i \(-0.755744\pi\)
−0.719751 + 0.694233i \(0.755744\pi\)
\(948\) −2.74962e13 −1.10569
\(949\) −2.27372e13 −0.909996
\(950\) 1.36300e13 0.542926
\(951\) 1.52021e13 0.602686
\(952\) 0 0
\(953\) 3.24042e13 1.27257 0.636287 0.771452i \(-0.280469\pi\)
0.636287 + 0.771452i \(0.280469\pi\)
\(954\) −1.76053e13 −0.688140
\(955\) 8.46186e10 0.00329193
\(956\) −4.79061e13 −1.85494
\(957\) −5.92287e11 −0.0228259
\(958\) 8.64081e12 0.331443
\(959\) 1.00972e13 0.385493
\(960\) 1.41749e12 0.0538641
\(961\) 3.58296e12 0.135515
\(962\) 9.40823e13 3.54177
\(963\) −2.68425e13 −1.00578
\(964\) 9.32299e13 3.47703
\(965\) −1.56330e12 −0.0580321
\(966\) 9.75714e12 0.360517
\(967\) −1.85067e13 −0.680626 −0.340313 0.940312i \(-0.610533\pi\)
−0.340313 + 0.940312i \(0.610533\pi\)
\(968\) 2.96620e13 1.08583
\(969\) 0 0
\(970\) −2.12655e12 −0.0771262
\(971\) −9.11588e12 −0.329088 −0.164544 0.986370i \(-0.552615\pi\)
−0.164544 + 0.986370i \(0.552615\pi\)
\(972\) −5.04198e13 −1.81177
\(973\) −6.82191e12 −0.244005
\(974\) −4.54293e13 −1.61741
\(975\) 1.72792e13 0.612355
\(976\) 8.14914e12 0.287467
\(977\) −4.93720e13 −1.73363 −0.866813 0.498634i \(-0.833835\pi\)
−0.866813 + 0.498634i \(0.833835\pi\)
\(978\) 2.12883e13 0.744074
\(979\) −3.76601e12 −0.131026
\(980\) −2.03980e12 −0.0706431
\(981\) −4.04394e13 −1.39410
\(982\) −4.20367e13 −1.44254
\(983\) 4.75683e13 1.62490 0.812450 0.583030i \(-0.198133\pi\)
0.812450 + 0.583030i \(0.198133\pi\)
\(984\) −1.75412e13 −0.596460
\(985\) −3.56317e12 −0.120607
\(986\) 0 0
\(987\) 1.17880e13 0.395378
\(988\) 2.10214e13 0.701867
\(989\) −2.12396e13 −0.705934
\(990\) 9.57652e11 0.0316847
\(991\) −2.02242e13 −0.666101 −0.333050 0.942909i \(-0.608078\pi\)
−0.333050 + 0.942909i \(0.608078\pi\)
\(992\) 2.32644e13 0.762762
\(993\) 9.56601e12 0.312219
\(994\) 5.36877e13 1.74436
\(995\) −1.64933e12 −0.0533462
\(996\) 2.15256e13 0.693089
\(997\) 1.55512e13 0.498467 0.249233 0.968443i \(-0.419821\pi\)
0.249233 + 0.968443i \(0.419821\pi\)
\(998\) 3.55685e13 1.13495
\(999\) −4.86956e13 −1.54684
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.1.4 36
17.16 even 2 289.10.a.h.1.4 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.4 36 1.1 even 1 trivial
289.10.a.h.1.4 yes 36 17.16 even 2