Properties

Label 289.10.a.h.1.30
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 1.30
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+31.0070 q^{2} -53.8250 q^{3} +449.436 q^{4} -1141.73 q^{5} -1668.95 q^{6} -10049.6 q^{7} -1939.93 q^{8} -16785.9 q^{9} +O(q^{10})\) \(q+31.0070 q^{2} -53.8250 q^{3} +449.436 q^{4} -1141.73 q^{5} -1668.95 q^{6} -10049.6 q^{7} -1939.93 q^{8} -16785.9 q^{9} -35401.7 q^{10} +19297.2 q^{11} -24190.9 q^{12} -149324. q^{13} -311609. q^{14} +61453.7 q^{15} -290263. q^{16} -520480. q^{18} -789308. q^{19} -513135. q^{20} +540920. q^{21} +598350. q^{22} -649564. q^{23} +104417. q^{24} -649573. q^{25} -4.63009e6 q^{26} +1.96294e6 q^{27} -4.51666e6 q^{28} +5.71826e6 q^{29} +1.90550e6 q^{30} -139880. q^{31} -8.00694e6 q^{32} -1.03867e6 q^{33} +1.14740e7 q^{35} -7.54417e6 q^{36} +107316. q^{37} -2.44741e7 q^{38} +8.03736e6 q^{39} +2.21488e6 q^{40} -2.16829e6 q^{41} +1.67723e7 q^{42} -3.93320e7 q^{43} +8.67287e6 q^{44} +1.91650e7 q^{45} -2.01410e7 q^{46} -2.88624e7 q^{47} +1.56234e7 q^{48} +6.06411e7 q^{49} -2.01413e7 q^{50} -6.71116e7 q^{52} -1.39754e7 q^{53} +6.08648e7 q^{54} -2.20323e7 q^{55} +1.94955e7 q^{56} +4.24845e7 q^{57} +1.77306e8 q^{58} +7.21306e7 q^{59} +2.76195e7 q^{60} -1.66987e8 q^{61} -4.33725e6 q^{62} +1.68692e8 q^{63} -9.96569e7 q^{64} +1.70488e8 q^{65} -3.22062e7 q^{66} +2.47694e8 q^{67} +3.49628e7 q^{69} +3.55774e8 q^{70} -2.68803e8 q^{71} +3.25634e7 q^{72} -3.16534e7 q^{73} +3.32755e6 q^{74} +3.49633e7 q^{75} -3.54743e8 q^{76} -1.93930e8 q^{77} +2.49215e8 q^{78} +4.91473e7 q^{79} +3.31402e8 q^{80} +2.24741e8 q^{81} -6.72323e7 q^{82} +8.25474e8 q^{83} +2.43109e8 q^{84} -1.21957e9 q^{86} -3.07785e8 q^{87} -3.74352e7 q^{88} -1.30963e8 q^{89} +5.94249e8 q^{90} +1.50065e9 q^{91} -2.91937e8 q^{92} +7.52902e6 q^{93} -8.94939e8 q^{94} +9.01178e8 q^{95} +4.30973e8 q^{96} -8.84811e8 q^{97} +1.88030e9 q^{98} -3.23921e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.0070 1.37033 0.685165 0.728388i \(-0.259730\pi\)
0.685165 + 0.728388i \(0.259730\pi\)
\(3\) −53.8250 −0.383653 −0.191826 0.981429i \(-0.561441\pi\)
−0.191826 + 0.981429i \(0.561441\pi\)
\(4\) 449.436 0.877805
\(5\) −1141.73 −0.816957 −0.408478 0.912768i \(-0.633940\pi\)
−0.408478 + 0.912768i \(0.633940\pi\)
\(6\) −1668.95 −0.525731
\(7\) −10049.6 −1.58201 −0.791003 0.611812i \(-0.790441\pi\)
−0.791003 + 0.611812i \(0.790441\pi\)
\(8\) −1939.93 −0.167448
\(9\) −16785.9 −0.852811
\(10\) −35401.7 −1.11950
\(11\) 19297.2 0.397400 0.198700 0.980060i \(-0.436328\pi\)
0.198700 + 0.980060i \(0.436328\pi\)
\(12\) −24190.9 −0.336772
\(13\) −149324. −1.45006 −0.725028 0.688720i \(-0.758173\pi\)
−0.725028 + 0.688720i \(0.758173\pi\)
\(14\) −311609. −2.16787
\(15\) 61453.7 0.313428
\(16\) −290263. −1.10726
\(17\) 0 0
\(18\) −520480. −1.16863
\(19\) −789308. −1.38949 −0.694745 0.719257i \(-0.744483\pi\)
−0.694745 + 0.719257i \(0.744483\pi\)
\(20\) −513135. −0.717128
\(21\) 540920. 0.606941
\(22\) 598350. 0.544569
\(23\) −649564. −0.484001 −0.242001 0.970276i \(-0.577804\pi\)
−0.242001 + 0.970276i \(0.577804\pi\)
\(24\) 104417. 0.0642419
\(25\) −649573. −0.332581
\(26\) −4.63009e6 −1.98705
\(27\) 1.96294e6 0.710836
\(28\) −4.51666e6 −1.38869
\(29\) 5.71826e6 1.50132 0.750659 0.660690i \(-0.229736\pi\)
0.750659 + 0.660690i \(0.229736\pi\)
\(30\) 1.90550e6 0.429500
\(31\) −139880. −0.0272036 −0.0136018 0.999907i \(-0.504330\pi\)
−0.0136018 + 0.999907i \(0.504330\pi\)
\(32\) −8.00694e6 −1.34987
\(33\) −1.03867e6 −0.152464
\(34\) 0 0
\(35\) 1.14740e7 1.29243
\(36\) −7.54417e6 −0.748601
\(37\) 107316. 0.00941362 0.00470681 0.999989i \(-0.498502\pi\)
0.00470681 + 0.999989i \(0.498502\pi\)
\(38\) −2.44741e7 −1.90406
\(39\) 8.03736e6 0.556318
\(40\) 2.21488e6 0.136798
\(41\) −2.16829e6 −0.119837 −0.0599185 0.998203i \(-0.519084\pi\)
−0.0599185 + 0.998203i \(0.519084\pi\)
\(42\) 1.67723e7 0.831710
\(43\) −3.93320e7 −1.75444 −0.877220 0.480089i \(-0.840604\pi\)
−0.877220 + 0.480089i \(0.840604\pi\)
\(44\) 8.67287e6 0.348839
\(45\) 1.91650e7 0.696709
\(46\) −2.01410e7 −0.663242
\(47\) −2.88624e7 −0.862765 −0.431383 0.902169i \(-0.641974\pi\)
−0.431383 + 0.902169i \(0.641974\pi\)
\(48\) 1.56234e7 0.424805
\(49\) 6.06411e7 1.50274
\(50\) −2.01413e7 −0.455746
\(51\) 0 0
\(52\) −6.71116e7 −1.27287
\(53\) −1.39754e7 −0.243290 −0.121645 0.992574i \(-0.538817\pi\)
−0.121645 + 0.992574i \(0.538817\pi\)
\(54\) 6.08648e7 0.974080
\(55\) −2.20323e7 −0.324659
\(56\) 1.94955e7 0.264904
\(57\) 4.24845e7 0.533081
\(58\) 1.77306e8 2.05730
\(59\) 7.21306e7 0.774972 0.387486 0.921876i \(-0.373344\pi\)
0.387486 + 0.921876i \(0.373344\pi\)
\(60\) 2.76195e7 0.275128
\(61\) −1.66987e8 −1.54418 −0.772092 0.635511i \(-0.780789\pi\)
−0.772092 + 0.635511i \(0.780789\pi\)
\(62\) −4.33725e6 −0.0372780
\(63\) 1.68692e8 1.34915
\(64\) −9.96569e7 −0.742502
\(65\) 1.70488e8 1.18463
\(66\) −3.22062e7 −0.208925
\(67\) 2.47694e8 1.50169 0.750843 0.660480i \(-0.229647\pi\)
0.750843 + 0.660480i \(0.229647\pi\)
\(68\) 0 0
\(69\) 3.49628e7 0.185688
\(70\) 3.55774e8 1.77106
\(71\) −2.68803e8 −1.25537 −0.627684 0.778468i \(-0.715997\pi\)
−0.627684 + 0.778468i \(0.715997\pi\)
\(72\) 3.25634e7 0.142802
\(73\) −3.16534e7 −0.130457 −0.0652284 0.997870i \(-0.520778\pi\)
−0.0652284 + 0.997870i \(0.520778\pi\)
\(74\) 3.32755e6 0.0128998
\(75\) 3.49633e7 0.127596
\(76\) −3.54743e8 −1.21970
\(77\) −1.93930e8 −0.628689
\(78\) 2.49215e8 0.762339
\(79\) 4.91473e7 0.141964 0.0709819 0.997478i \(-0.477387\pi\)
0.0709819 + 0.997478i \(0.477387\pi\)
\(80\) 3.31402e8 0.904587
\(81\) 2.24741e8 0.580096
\(82\) −6.72323e7 −0.164216
\(83\) 8.25474e8 1.90920 0.954601 0.297888i \(-0.0962821\pi\)
0.954601 + 0.297888i \(0.0962821\pi\)
\(84\) 2.43109e8 0.532776
\(85\) 0 0
\(86\) −1.21957e9 −2.40416
\(87\) −3.07785e8 −0.575985
\(88\) −3.74352e7 −0.0665439
\(89\) −1.30963e8 −0.221256 −0.110628 0.993862i \(-0.535286\pi\)
−0.110628 + 0.993862i \(0.535286\pi\)
\(90\) 5.94249e8 0.954722
\(91\) 1.50065e9 2.29400
\(92\) −2.91937e8 −0.424859
\(93\) 7.52902e6 0.0104368
\(94\) −8.94939e8 −1.18227
\(95\) 9.01178e8 1.13515
\(96\) 4.30973e8 0.517881
\(97\) −8.84811e8 −1.01479 −0.507397 0.861713i \(-0.669392\pi\)
−0.507397 + 0.861713i \(0.669392\pi\)
\(98\) 1.88030e9 2.05925
\(99\) −3.23921e8 −0.338907
\(100\) −2.91941e8 −0.291941
\(101\) −6.77943e8 −0.648257 −0.324128 0.946013i \(-0.605071\pi\)
−0.324128 + 0.946013i \(0.605071\pi\)
\(102\) 0 0
\(103\) −1.16420e9 −1.01920 −0.509601 0.860411i \(-0.670207\pi\)
−0.509601 + 0.860411i \(0.670207\pi\)
\(104\) 2.89678e8 0.242809
\(105\) −6.17586e8 −0.495845
\(106\) −4.33336e8 −0.333387
\(107\) −1.13491e9 −0.837017 −0.418508 0.908213i \(-0.637447\pi\)
−0.418508 + 0.908213i \(0.637447\pi\)
\(108\) 8.82214e8 0.623975
\(109\) 1.50045e9 1.01812 0.509062 0.860730i \(-0.329992\pi\)
0.509062 + 0.860730i \(0.329992\pi\)
\(110\) −6.83155e8 −0.444889
\(111\) −5.77628e6 −0.00361156
\(112\) 2.91703e9 1.75170
\(113\) −3.11200e9 −1.79550 −0.897752 0.440501i \(-0.854801\pi\)
−0.897752 + 0.440501i \(0.854801\pi\)
\(114\) 1.31732e9 0.730497
\(115\) 7.41628e8 0.395408
\(116\) 2.56999e9 1.31786
\(117\) 2.50653e9 1.23662
\(118\) 2.23656e9 1.06197
\(119\) 0 0
\(120\) −1.19216e8 −0.0524829
\(121\) −1.98556e9 −0.842073
\(122\) −5.17778e9 −2.11604
\(123\) 1.16708e8 0.0459758
\(124\) −6.28670e7 −0.0238795
\(125\) 2.97158e9 1.08866
\(126\) 5.23062e9 1.84878
\(127\) −5.00555e9 −1.70740 −0.853699 0.520767i \(-0.825646\pi\)
−0.853699 + 0.520767i \(0.825646\pi\)
\(128\) 1.00949e9 0.332396
\(129\) 2.11705e9 0.673096
\(130\) 5.28633e9 1.62334
\(131\) 2.33318e8 0.0692194 0.0346097 0.999401i \(-0.488981\pi\)
0.0346097 + 0.999401i \(0.488981\pi\)
\(132\) −4.66817e8 −0.133833
\(133\) 7.93224e9 2.19818
\(134\) 7.68026e9 2.05781
\(135\) −2.24115e9 −0.580722
\(136\) 0 0
\(137\) −7.37764e9 −1.78927 −0.894633 0.446802i \(-0.852563\pi\)
−0.894633 + 0.446802i \(0.852563\pi\)
\(138\) 1.08409e9 0.254454
\(139\) 3.70573e9 0.841991 0.420995 0.907063i \(-0.361681\pi\)
0.420995 + 0.907063i \(0.361681\pi\)
\(140\) 5.15681e9 1.13450
\(141\) 1.55352e9 0.331002
\(142\) −8.33478e9 −1.72027
\(143\) −2.88154e9 −0.576252
\(144\) 4.87231e9 0.944286
\(145\) −6.52872e9 −1.22651
\(146\) −9.81477e8 −0.178769
\(147\) −3.26401e9 −0.576532
\(148\) 4.82317e7 0.00826332
\(149\) −5.60954e9 −0.932372 −0.466186 0.884687i \(-0.654372\pi\)
−0.466186 + 0.884687i \(0.654372\pi\)
\(150\) 1.08411e9 0.174848
\(151\) 4.72353e9 0.739385 0.369692 0.929154i \(-0.379463\pi\)
0.369692 + 0.929154i \(0.379463\pi\)
\(152\) 1.53120e9 0.232667
\(153\) 0 0
\(154\) −6.01318e9 −0.861512
\(155\) 1.59705e8 0.0222242
\(156\) 3.61228e9 0.488338
\(157\) −2.12404e9 −0.279007 −0.139503 0.990222i \(-0.544551\pi\)
−0.139503 + 0.990222i \(0.544551\pi\)
\(158\) 1.52391e9 0.194537
\(159\) 7.52227e8 0.0933387
\(160\) 9.14178e9 1.10278
\(161\) 6.52787e9 0.765693
\(162\) 6.96856e9 0.794924
\(163\) 6.96419e9 0.772728 0.386364 0.922346i \(-0.373731\pi\)
0.386364 + 0.922346i \(0.373731\pi\)
\(164\) −9.74509e8 −0.105193
\(165\) 1.18589e9 0.124556
\(166\) 2.55955e10 2.61624
\(167\) −1.47347e9 −0.146594 −0.0732971 0.997310i \(-0.523352\pi\)
−0.0732971 + 0.997310i \(0.523352\pi\)
\(168\) −1.04935e9 −0.101631
\(169\) 1.16932e10 1.10266
\(170\) 0 0
\(171\) 1.32492e10 1.18497
\(172\) −1.76772e10 −1.54005
\(173\) 1.29320e10 1.09764 0.548819 0.835941i \(-0.315078\pi\)
0.548819 + 0.835941i \(0.315078\pi\)
\(174\) −9.54351e9 −0.789289
\(175\) 6.52796e9 0.526146
\(176\) −5.60126e9 −0.440027
\(177\) −3.88243e9 −0.297320
\(178\) −4.06078e9 −0.303194
\(179\) −1.15426e10 −0.840358 −0.420179 0.907441i \(-0.638033\pi\)
−0.420179 + 0.907441i \(0.638033\pi\)
\(180\) 8.61342e9 0.611575
\(181\) 2.51937e10 1.74477 0.872384 0.488822i \(-0.162573\pi\)
0.872384 + 0.488822i \(0.162573\pi\)
\(182\) 4.65307e10 3.14353
\(183\) 8.98808e9 0.592430
\(184\) 1.26011e9 0.0810451
\(185\) −1.22526e8 −0.00769052
\(186\) 2.33453e8 0.0143018
\(187\) 0 0
\(188\) −1.29718e10 −0.757339
\(189\) −1.97268e10 −1.12455
\(190\) 2.79429e10 1.55553
\(191\) 7.47180e9 0.406233 0.203116 0.979155i \(-0.434893\pi\)
0.203116 + 0.979155i \(0.434893\pi\)
\(192\) 5.36403e9 0.284863
\(193\) −1.79297e10 −0.930177 −0.465089 0.885264i \(-0.653978\pi\)
−0.465089 + 0.885264i \(0.653978\pi\)
\(194\) −2.74354e10 −1.39060
\(195\) −9.17652e9 −0.454488
\(196\) 2.72543e10 1.31912
\(197\) −2.91218e10 −1.37759 −0.688795 0.724956i \(-0.741860\pi\)
−0.688795 + 0.724956i \(0.741860\pi\)
\(198\) −1.00438e10 −0.464414
\(199\) 1.83017e9 0.0827280 0.0413640 0.999144i \(-0.486830\pi\)
0.0413640 + 0.999144i \(0.486830\pi\)
\(200\) 1.26012e9 0.0556901
\(201\) −1.33321e10 −0.576126
\(202\) −2.10210e10 −0.888326
\(203\) −5.74663e10 −2.37509
\(204\) 0 0
\(205\) 2.47561e9 0.0979016
\(206\) −3.60984e10 −1.39664
\(207\) 1.09035e10 0.412762
\(208\) 4.33432e10 1.60559
\(209\) −1.52315e10 −0.552183
\(210\) −1.91495e10 −0.679471
\(211\) −2.37220e10 −0.823911 −0.411956 0.911204i \(-0.635154\pi\)
−0.411956 + 0.911204i \(0.635154\pi\)
\(212\) −6.28106e9 −0.213561
\(213\) 1.44683e10 0.481626
\(214\) −3.51902e10 −1.14699
\(215\) 4.49066e10 1.43330
\(216\) −3.80795e9 −0.119028
\(217\) 1.40574e9 0.0430363
\(218\) 4.65243e10 1.39517
\(219\) 1.70374e9 0.0500501
\(220\) −9.90209e9 −0.284987
\(221\) 0 0
\(222\) −1.79105e8 −0.00494903
\(223\) 1.54932e10 0.419537 0.209769 0.977751i \(-0.432729\pi\)
0.209769 + 0.977751i \(0.432729\pi\)
\(224\) 8.04666e10 2.13550
\(225\) 1.09036e10 0.283629
\(226\) −9.64939e10 −2.46043
\(227\) −7.62225e10 −1.90531 −0.952657 0.304047i \(-0.901662\pi\)
−0.952657 + 0.304047i \(0.901662\pi\)
\(228\) 1.90941e10 0.467941
\(229\) 2.17147e10 0.521789 0.260894 0.965367i \(-0.415983\pi\)
0.260894 + 0.965367i \(0.415983\pi\)
\(230\) 2.29957e10 0.541840
\(231\) 1.04383e10 0.241198
\(232\) −1.10930e10 −0.251393
\(233\) 3.10512e10 0.690202 0.345101 0.938566i \(-0.387845\pi\)
0.345101 + 0.938566i \(0.387845\pi\)
\(234\) 7.77202e10 1.69458
\(235\) 3.29532e10 0.704842
\(236\) 3.24181e10 0.680274
\(237\) −2.64535e9 −0.0544648
\(238\) 0 0
\(239\) −2.93690e10 −0.582236 −0.291118 0.956687i \(-0.594027\pi\)
−0.291118 + 0.956687i \(0.594027\pi\)
\(240\) −1.78377e10 −0.347047
\(241\) −1.95317e10 −0.372960 −0.186480 0.982459i \(-0.559708\pi\)
−0.186480 + 0.982459i \(0.559708\pi\)
\(242\) −6.15665e10 −1.15392
\(243\) −5.07332e10 −0.933391
\(244\) −7.50500e10 −1.35549
\(245\) −6.92359e10 −1.22768
\(246\) 3.61878e9 0.0630020
\(247\) 1.17863e11 2.01484
\(248\) 2.71356e8 0.00455520
\(249\) −4.44311e10 −0.732471
\(250\) 9.21400e10 1.49183
\(251\) −1.44535e10 −0.229848 −0.114924 0.993374i \(-0.536662\pi\)
−0.114924 + 0.993374i \(0.536662\pi\)
\(252\) 7.58160e10 1.18429
\(253\) −1.25348e10 −0.192342
\(254\) −1.55207e11 −2.33970
\(255\) 0 0
\(256\) 8.23255e10 1.19799
\(257\) −2.07523e10 −0.296734 −0.148367 0.988932i \(-0.547402\pi\)
−0.148367 + 0.988932i \(0.547402\pi\)
\(258\) 6.56433e10 0.922363
\(259\) −1.07848e9 −0.0148924
\(260\) 7.66234e10 1.03988
\(261\) −9.59859e10 −1.28034
\(262\) 7.23450e9 0.0948534
\(263\) 1.65098e10 0.212785 0.106392 0.994324i \(-0.466070\pi\)
0.106392 + 0.994324i \(0.466070\pi\)
\(264\) 2.01495e9 0.0255297
\(265\) 1.59562e10 0.198757
\(266\) 2.45955e11 3.01223
\(267\) 7.04910e9 0.0848854
\(268\) 1.11323e11 1.31819
\(269\) −1.13193e10 −0.131806 −0.0659028 0.997826i \(-0.520993\pi\)
−0.0659028 + 0.997826i \(0.520993\pi\)
\(270\) −6.94913e10 −0.795781
\(271\) −6.48755e10 −0.730666 −0.365333 0.930877i \(-0.619045\pi\)
−0.365333 + 0.930877i \(0.619045\pi\)
\(272\) 0 0
\(273\) −8.07724e10 −0.880098
\(274\) −2.28759e11 −2.45188
\(275\) −1.25350e10 −0.132168
\(276\) 1.57135e10 0.162998
\(277\) 1.78844e11 1.82522 0.912608 0.408835i \(-0.134065\pi\)
0.912608 + 0.408835i \(0.134065\pi\)
\(278\) 1.14904e11 1.15381
\(279\) 2.34800e9 0.0231996
\(280\) −2.22587e10 −0.216415
\(281\) −5.70196e10 −0.545564 −0.272782 0.962076i \(-0.587944\pi\)
−0.272782 + 0.962076i \(0.587944\pi\)
\(282\) 4.81701e10 0.453582
\(283\) −1.70549e11 −1.58055 −0.790276 0.612751i \(-0.790063\pi\)
−0.790276 + 0.612751i \(0.790063\pi\)
\(284\) −1.20810e11 −1.10197
\(285\) −4.85059e10 −0.435505
\(286\) −8.93480e10 −0.789655
\(287\) 2.17905e10 0.189583
\(288\) 1.34403e11 1.15118
\(289\) 0 0
\(290\) −2.02436e11 −1.68073
\(291\) 4.76249e10 0.389328
\(292\) −1.42262e10 −0.114516
\(293\) 1.07691e11 0.853639 0.426820 0.904337i \(-0.359634\pi\)
0.426820 + 0.904337i \(0.359634\pi\)
\(294\) −1.01207e11 −0.790039
\(295\) −8.23539e10 −0.633118
\(296\) −2.08185e8 −0.00157629
\(297\) 3.78792e10 0.282486
\(298\) −1.73935e11 −1.27766
\(299\) 9.69955e10 0.701829
\(300\) 1.57137e10 0.112004
\(301\) 3.95272e11 2.77553
\(302\) 1.46463e11 1.01320
\(303\) 3.64903e10 0.248705
\(304\) 2.29106e11 1.53853
\(305\) 1.90655e11 1.26153
\(306\) 0 0
\(307\) −6.36292e9 −0.0408822 −0.0204411 0.999791i \(-0.506507\pi\)
−0.0204411 + 0.999791i \(0.506507\pi\)
\(308\) −8.71590e10 −0.551866
\(309\) 6.26631e10 0.391020
\(310\) 4.95198e9 0.0304545
\(311\) −6.10770e10 −0.370217 −0.185108 0.982718i \(-0.559264\pi\)
−0.185108 + 0.982718i \(0.559264\pi\)
\(312\) −1.55919e10 −0.0931544
\(313\) 2.69912e11 1.58954 0.794772 0.606908i \(-0.207590\pi\)
0.794772 + 0.606908i \(0.207590\pi\)
\(314\) −6.58602e10 −0.382331
\(315\) −1.92600e11 −1.10220
\(316\) 2.20886e10 0.124616
\(317\) 7.17777e10 0.399230 0.199615 0.979874i \(-0.436031\pi\)
0.199615 + 0.979874i \(0.436031\pi\)
\(318\) 2.33243e10 0.127905
\(319\) 1.10347e11 0.596624
\(320\) 1.13781e11 0.606592
\(321\) 6.10865e10 0.321124
\(322\) 2.02410e11 1.04925
\(323\) 0 0
\(324\) 1.01007e11 0.509211
\(325\) 9.69969e10 0.482261
\(326\) 2.15939e11 1.05889
\(327\) −8.07614e10 −0.390606
\(328\) 4.20633e9 0.0200665
\(329\) 2.90056e11 1.36490
\(330\) 3.67708e10 0.170683
\(331\) −1.24902e11 −0.571929 −0.285965 0.958240i \(-0.592314\pi\)
−0.285965 + 0.958240i \(0.592314\pi\)
\(332\) 3.70998e11 1.67591
\(333\) −1.80139e9 −0.00802804
\(334\) −4.56879e10 −0.200882
\(335\) −2.82800e11 −1.22681
\(336\) −1.57009e11 −0.672044
\(337\) 3.00210e11 1.26792 0.633959 0.773367i \(-0.281429\pi\)
0.633959 + 0.773367i \(0.281429\pi\)
\(338\) 3.62570e11 1.51101
\(339\) 1.67503e11 0.688850
\(340\) 0 0
\(341\) −2.69929e9 −0.0108107
\(342\) 4.10819e11 1.62380
\(343\) −2.03882e11 −0.795343
\(344\) 7.63013e10 0.293778
\(345\) −3.99181e10 −0.151699
\(346\) 4.00984e11 1.50413
\(347\) −2.67538e11 −0.990610 −0.495305 0.868719i \(-0.664944\pi\)
−0.495305 + 0.868719i \(0.664944\pi\)
\(348\) −1.38330e11 −0.505602
\(349\) −4.04067e11 −1.45794 −0.728969 0.684546i \(-0.760000\pi\)
−0.728969 + 0.684546i \(0.760000\pi\)
\(350\) 2.02413e11 0.720993
\(351\) −2.93114e11 −1.03075
\(352\) −1.54512e11 −0.536438
\(353\) −3.87001e11 −1.32656 −0.663278 0.748373i \(-0.730835\pi\)
−0.663278 + 0.748373i \(0.730835\pi\)
\(354\) −1.20383e11 −0.407427
\(355\) 3.06901e11 1.02558
\(356\) −5.88596e10 −0.194219
\(357\) 0 0
\(358\) −3.57901e11 −1.15157
\(359\) −1.50661e11 −0.478714 −0.239357 0.970932i \(-0.576937\pi\)
−0.239357 + 0.970932i \(0.576937\pi\)
\(360\) −3.71786e10 −0.116663
\(361\) 3.00319e11 0.930680
\(362\) 7.81180e11 2.39091
\(363\) 1.06873e11 0.323064
\(364\) 6.74445e11 2.01368
\(365\) 3.61397e10 0.106578
\(366\) 2.78694e11 0.811825
\(367\) −1.26285e11 −0.363375 −0.181688 0.983356i \(-0.558156\pi\)
−0.181688 + 0.983356i \(0.558156\pi\)
\(368\) 1.88544e11 0.535917
\(369\) 3.63967e10 0.102198
\(370\) −3.79917e9 −0.0105386
\(371\) 1.40448e11 0.384886
\(372\) 3.38381e9 0.00916143
\(373\) 4.73905e9 0.0126766 0.00633828 0.999980i \(-0.497982\pi\)
0.00633828 + 0.999980i \(0.497982\pi\)
\(374\) 0 0
\(375\) −1.59945e11 −0.417668
\(376\) 5.59910e10 0.144468
\(377\) −8.53873e11 −2.17699
\(378\) −6.11668e11 −1.54100
\(379\) −5.25598e11 −1.30851 −0.654255 0.756274i \(-0.727018\pi\)
−0.654255 + 0.756274i \(0.727018\pi\)
\(380\) 4.05022e11 0.996442
\(381\) 2.69424e11 0.655048
\(382\) 2.31678e11 0.556673
\(383\) −5.38071e11 −1.27775 −0.638874 0.769311i \(-0.720600\pi\)
−0.638874 + 0.769311i \(0.720600\pi\)
\(384\) −5.43356e10 −0.127525
\(385\) 2.21416e11 0.513612
\(386\) −5.55947e11 −1.27465
\(387\) 6.60223e11 1.49620
\(388\) −3.97666e11 −0.890790
\(389\) −3.57957e11 −0.792607 −0.396303 0.918120i \(-0.629707\pi\)
−0.396303 + 0.918120i \(0.629707\pi\)
\(390\) −2.84537e11 −0.622798
\(391\) 0 0
\(392\) −1.17639e11 −0.251632
\(393\) −1.25583e10 −0.0265562
\(394\) −9.02981e11 −1.88775
\(395\) −5.61130e10 −0.115978
\(396\) −1.45582e11 −0.297494
\(397\) −8.11886e11 −1.64036 −0.820178 0.572109i \(-0.806125\pi\)
−0.820178 + 0.572109i \(0.806125\pi\)
\(398\) 5.67481e10 0.113365
\(399\) −4.26953e11 −0.843338
\(400\) 1.88547e11 0.368255
\(401\) 8.87187e11 1.71343 0.856713 0.515793i \(-0.172503\pi\)
0.856713 + 0.515793i \(0.172503\pi\)
\(402\) −4.13390e11 −0.789483
\(403\) 2.08874e10 0.0394468
\(404\) −3.04692e11 −0.569043
\(405\) −2.56594e11 −0.473914
\(406\) −1.78186e12 −3.25466
\(407\) 2.07090e9 0.00374097
\(408\) 0 0
\(409\) 6.58796e11 1.16412 0.582058 0.813147i \(-0.302248\pi\)
0.582058 + 0.813147i \(0.302248\pi\)
\(410\) 7.67613e10 0.134158
\(411\) 3.97101e11 0.686457
\(412\) −5.23234e11 −0.894660
\(413\) −7.24885e11 −1.22601
\(414\) 3.38085e11 0.565619
\(415\) −9.42470e11 −1.55974
\(416\) 1.19563e12 1.95738
\(417\) −1.99461e11 −0.323032
\(418\) −4.72282e11 −0.756673
\(419\) −1.19033e12 −1.88670 −0.943352 0.331794i \(-0.892346\pi\)
−0.943352 + 0.331794i \(0.892346\pi\)
\(420\) −2.77565e11 −0.435255
\(421\) −1.00113e12 −1.55317 −0.776587 0.630010i \(-0.783051\pi\)
−0.776587 + 0.630010i \(0.783051\pi\)
\(422\) −7.35549e11 −1.12903
\(423\) 4.84481e11 0.735775
\(424\) 2.71113e10 0.0407384
\(425\) 0 0
\(426\) 4.48619e11 0.659986
\(427\) 1.67816e12 2.44291
\(428\) −5.10069e11 −0.734737
\(429\) 1.55099e11 0.221081
\(430\) 1.39242e12 1.96410
\(431\) 1.16192e11 0.162192 0.0810962 0.996706i \(-0.474158\pi\)
0.0810962 + 0.996706i \(0.474158\pi\)
\(432\) −5.69767e11 −0.787083
\(433\) −1.16924e12 −1.59849 −0.799243 0.601007i \(-0.794766\pi\)
−0.799243 + 0.601007i \(0.794766\pi\)
\(434\) 4.35877e10 0.0589740
\(435\) 3.51408e11 0.470555
\(436\) 6.74354e11 0.893714
\(437\) 5.12706e11 0.672515
\(438\) 5.28280e10 0.0685852
\(439\) −1.03242e11 −0.132667 −0.0663337 0.997797i \(-0.521130\pi\)
−0.0663337 + 0.997797i \(0.521130\pi\)
\(440\) 4.27410e10 0.0543635
\(441\) −1.01791e12 −1.28156
\(442\) 0 0
\(443\) 7.45116e11 0.919194 0.459597 0.888128i \(-0.347994\pi\)
0.459597 + 0.888128i \(0.347994\pi\)
\(444\) −2.59607e9 −0.00317025
\(445\) 1.49525e11 0.180756
\(446\) 4.80400e11 0.574905
\(447\) 3.01934e11 0.357707
\(448\) 1.00151e12 1.17464
\(449\) −1.20015e12 −1.39357 −0.696784 0.717281i \(-0.745387\pi\)
−0.696784 + 0.717281i \(0.745387\pi\)
\(450\) 3.38090e11 0.388665
\(451\) −4.18420e10 −0.0476232
\(452\) −1.39864e12 −1.57610
\(453\) −2.54244e11 −0.283667
\(454\) −2.36343e12 −2.61091
\(455\) −1.71334e12 −1.87410
\(456\) −8.24168e10 −0.0892635
\(457\) −8.33431e11 −0.893814 −0.446907 0.894581i \(-0.647474\pi\)
−0.446907 + 0.894581i \(0.647474\pi\)
\(458\) 6.73309e11 0.715023
\(459\) 0 0
\(460\) 3.33314e11 0.347091
\(461\) 4.67123e11 0.481700 0.240850 0.970562i \(-0.422574\pi\)
0.240850 + 0.970562i \(0.422574\pi\)
\(462\) 3.23660e11 0.330521
\(463\) −5.85748e11 −0.592374 −0.296187 0.955130i \(-0.595715\pi\)
−0.296187 + 0.955130i \(0.595715\pi\)
\(464\) −1.65980e12 −1.66236
\(465\) −8.59613e9 −0.00852638
\(466\) 9.62804e11 0.945804
\(467\) 1.36513e12 1.32815 0.664075 0.747666i \(-0.268825\pi\)
0.664075 + 0.747666i \(0.268825\pi\)
\(468\) 1.12653e12 1.08551
\(469\) −2.48923e12 −2.37568
\(470\) 1.02178e12 0.965866
\(471\) 1.14327e11 0.107042
\(472\) −1.39928e11 −0.129768
\(473\) −7.58999e11 −0.697214
\(474\) −8.20245e10 −0.0746348
\(475\) 5.12713e11 0.462118
\(476\) 0 0
\(477\) 2.34590e11 0.207480
\(478\) −9.10646e11 −0.797855
\(479\) 2.06482e12 1.79214 0.896071 0.443910i \(-0.146409\pi\)
0.896071 + 0.443910i \(0.146409\pi\)
\(480\) −4.92056e11 −0.423086
\(481\) −1.60249e10 −0.0136503
\(482\) −6.05619e11 −0.511079
\(483\) −3.51362e11 −0.293760
\(484\) −8.92384e11 −0.739176
\(485\) 1.01022e12 0.829043
\(486\) −1.57309e12 −1.27905
\(487\) −7.61982e11 −0.613853 −0.306926 0.951733i \(-0.599301\pi\)
−0.306926 + 0.951733i \(0.599301\pi\)
\(488\) 3.23943e11 0.258571
\(489\) −3.74848e11 −0.296459
\(490\) −2.14680e12 −1.68232
\(491\) −9.26040e11 −0.719057 −0.359528 0.933134i \(-0.617062\pi\)
−0.359528 + 0.933134i \(0.617062\pi\)
\(492\) 5.24529e10 0.0403577
\(493\) 0 0
\(494\) 3.65457e12 2.76099
\(495\) 3.69831e11 0.276872
\(496\) 4.06018e10 0.0301216
\(497\) 2.70136e12 1.98600
\(498\) −1.37768e12 −1.00373
\(499\) −1.46595e12 −1.05844 −0.529219 0.848485i \(-0.677515\pi\)
−0.529219 + 0.848485i \(0.677515\pi\)
\(500\) 1.33554e12 0.955632
\(501\) 7.93094e10 0.0562412
\(502\) −4.48160e11 −0.314968
\(503\) 3.47465e11 0.242022 0.121011 0.992651i \(-0.461386\pi\)
0.121011 + 0.992651i \(0.461386\pi\)
\(504\) −3.27249e11 −0.225913
\(505\) 7.74029e11 0.529598
\(506\) −3.88666e11 −0.263572
\(507\) −6.29385e11 −0.423039
\(508\) −2.24967e12 −1.49876
\(509\) 1.70164e12 1.12367 0.561834 0.827250i \(-0.310096\pi\)
0.561834 + 0.827250i \(0.310096\pi\)
\(510\) 0 0
\(511\) 3.18104e11 0.206384
\(512\) 2.03581e12 1.30925
\(513\) −1.54936e12 −0.987699
\(514\) −6.43468e11 −0.406624
\(515\) 1.32921e12 0.832644
\(516\) 9.51477e11 0.590846
\(517\) −5.56965e11 −0.342863
\(518\) −3.34406e10 −0.0204075
\(519\) −6.96066e11 −0.421112
\(520\) −3.30734e11 −0.198365
\(521\) 1.96790e11 0.117013 0.0585065 0.998287i \(-0.481366\pi\)
0.0585065 + 0.998287i \(0.481366\pi\)
\(522\) −2.97624e12 −1.75449
\(523\) −1.11906e12 −0.654027 −0.327013 0.945020i \(-0.606042\pi\)
−0.327013 + 0.945020i \(0.606042\pi\)
\(524\) 1.04862e11 0.0607611
\(525\) −3.51367e11 −0.201857
\(526\) 5.11919e11 0.291585
\(527\) 0 0
\(528\) 3.01488e11 0.168817
\(529\) −1.37922e12 −0.765743
\(530\) 4.94754e11 0.272363
\(531\) −1.21078e12 −0.660904
\(532\) 3.56503e12 1.92957
\(533\) 3.23778e11 0.173770
\(534\) 2.18572e11 0.116321
\(535\) 1.29576e12 0.683807
\(536\) −4.80509e11 −0.251455
\(537\) 6.21279e11 0.322406
\(538\) −3.50977e11 −0.180617
\(539\) 1.17021e12 0.597190
\(540\) −1.00725e12 −0.509761
\(541\) 7.15211e11 0.358960 0.179480 0.983762i \(-0.442558\pi\)
0.179480 + 0.983762i \(0.442558\pi\)
\(542\) −2.01160e12 −1.00125
\(543\) −1.35605e12 −0.669385
\(544\) 0 0
\(545\) −1.71311e12 −0.831764
\(546\) −2.50451e12 −1.20602
\(547\) 6.84615e11 0.326967 0.163483 0.986546i \(-0.447727\pi\)
0.163483 + 0.986546i \(0.447727\pi\)
\(548\) −3.31577e12 −1.57063
\(549\) 2.80303e12 1.31690
\(550\) −3.88672e11 −0.181114
\(551\) −4.51347e12 −2.08607
\(552\) −6.78252e10 −0.0310932
\(553\) −4.93911e11 −0.224588
\(554\) 5.54541e12 2.50115
\(555\) 6.59497e9 0.00295049
\(556\) 1.66549e12 0.739103
\(557\) 1.49708e12 0.659015 0.329508 0.944153i \(-0.393117\pi\)
0.329508 + 0.944153i \(0.393117\pi\)
\(558\) 7.28046e10 0.0317910
\(559\) 5.87322e12 2.54403
\(560\) −3.33046e12 −1.43106
\(561\) 0 0
\(562\) −1.76801e12 −0.747602
\(563\) 3.38224e12 1.41879 0.709393 0.704813i \(-0.248969\pi\)
0.709393 + 0.704813i \(0.248969\pi\)
\(564\) 6.98208e11 0.290555
\(565\) 3.55307e12 1.46685
\(566\) −5.28820e12 −2.16588
\(567\) −2.25856e12 −0.917716
\(568\) 5.21458e11 0.210209
\(569\) −1.27892e11 −0.0511490 −0.0255745 0.999673i \(-0.508142\pi\)
−0.0255745 + 0.999673i \(0.508142\pi\)
\(570\) −1.50402e12 −0.596785
\(571\) 1.00196e12 0.394444 0.197222 0.980359i \(-0.436808\pi\)
0.197222 + 0.980359i \(0.436808\pi\)
\(572\) −1.29507e12 −0.505837
\(573\) −4.02169e11 −0.155852
\(574\) 6.75659e11 0.259791
\(575\) 4.21939e11 0.160970
\(576\) 1.67283e12 0.633213
\(577\) −3.75406e11 −0.140997 −0.0704986 0.997512i \(-0.522459\pi\)
−0.0704986 + 0.997512i \(0.522459\pi\)
\(578\) 0 0
\(579\) 9.65067e11 0.356865
\(580\) −2.93424e12 −1.07664
\(581\) −8.29569e12 −3.02037
\(582\) 1.47671e12 0.533508
\(583\) −2.69687e11 −0.0966833
\(584\) 6.14052e10 0.0218448
\(585\) −2.86179e12 −1.01027
\(586\) 3.33917e12 1.16977
\(587\) 3.94381e11 0.137102 0.0685511 0.997648i \(-0.478162\pi\)
0.0685511 + 0.997648i \(0.478162\pi\)
\(588\) −1.46696e12 −0.506082
\(589\) 1.10408e11 0.0377992
\(590\) −2.55355e12 −0.867581
\(591\) 1.56748e12 0.528517
\(592\) −3.11498e10 −0.0104234
\(593\) −3.77125e12 −1.25239 −0.626195 0.779666i \(-0.715389\pi\)
−0.626195 + 0.779666i \(0.715389\pi\)
\(594\) 1.17452e12 0.387099
\(595\) 0 0
\(596\) −2.52113e12 −0.818441
\(597\) −9.85088e10 −0.0317388
\(598\) 3.00754e12 0.961737
\(599\) −2.55448e12 −0.810740 −0.405370 0.914153i \(-0.632857\pi\)
−0.405370 + 0.914153i \(0.632857\pi\)
\(600\) −6.78262e10 −0.0213657
\(601\) 6.12364e11 0.191458 0.0957292 0.995407i \(-0.469482\pi\)
0.0957292 + 0.995407i \(0.469482\pi\)
\(602\) 1.22562e13 3.80340
\(603\) −4.15776e12 −1.28065
\(604\) 2.12292e12 0.649035
\(605\) 2.26698e12 0.687938
\(606\) 1.13146e12 0.340809
\(607\) 1.75946e12 0.526053 0.263027 0.964789i \(-0.415279\pi\)
0.263027 + 0.964789i \(0.415279\pi\)
\(608\) 6.31994e12 1.87563
\(609\) 3.09312e12 0.911212
\(610\) 5.91163e12 1.72871
\(611\) 4.30986e12 1.25106
\(612\) 0 0
\(613\) −1.24362e12 −0.355725 −0.177863 0.984055i \(-0.556918\pi\)
−0.177863 + 0.984055i \(0.556918\pi\)
\(614\) −1.97295e11 −0.0560221
\(615\) −1.33250e11 −0.0375602
\(616\) 3.76209e11 0.105273
\(617\) −3.95577e12 −1.09887 −0.549437 0.835535i \(-0.685158\pi\)
−0.549437 + 0.835535i \(0.685158\pi\)
\(618\) 1.94300e12 0.535826
\(619\) 4.31640e12 1.18172 0.590859 0.806774i \(-0.298789\pi\)
0.590859 + 0.806774i \(0.298789\pi\)
\(620\) 7.17772e10 0.0195085
\(621\) −1.27505e12 −0.344046
\(622\) −1.89382e12 −0.507319
\(623\) 1.31613e12 0.350028
\(624\) −2.33295e12 −0.615991
\(625\) −2.12405e12 −0.556808
\(626\) 8.36917e12 2.17820
\(627\) 8.19833e11 0.211847
\(628\) −9.54621e11 −0.244913
\(629\) 0 0
\(630\) −5.97197e12 −1.51038
\(631\) 2.88522e12 0.724513 0.362257 0.932078i \(-0.382006\pi\)
0.362257 + 0.932078i \(0.382006\pi\)
\(632\) −9.53421e10 −0.0237716
\(633\) 1.27684e12 0.316096
\(634\) 2.22561e12 0.547077
\(635\) 5.71499e12 1.39487
\(636\) 3.38078e11 0.0819332
\(637\) −9.05518e12 −2.17906
\(638\) 3.42152e12 0.817572
\(639\) 4.51209e12 1.07059
\(640\) −1.15256e12 −0.271553
\(641\) 5.39283e12 1.26170 0.630850 0.775905i \(-0.282706\pi\)
0.630850 + 0.775905i \(0.282706\pi\)
\(642\) 1.89411e12 0.440046
\(643\) 2.99884e12 0.691836 0.345918 0.938265i \(-0.387567\pi\)
0.345918 + 0.938265i \(0.387567\pi\)
\(644\) 2.93386e12 0.672129
\(645\) −2.41710e12 −0.549890
\(646\) 0 0
\(647\) −6.57141e12 −1.47431 −0.737156 0.675722i \(-0.763832\pi\)
−0.737156 + 0.675722i \(0.763832\pi\)
\(648\) −4.35982e11 −0.0971361
\(649\) 1.39192e12 0.307974
\(650\) 3.00758e12 0.660857
\(651\) −7.56638e10 −0.0165110
\(652\) 3.12996e12 0.678304
\(653\) −1.00670e12 −0.216666 −0.108333 0.994115i \(-0.534551\pi\)
−0.108333 + 0.994115i \(0.534551\pi\)
\(654\) −2.50417e12 −0.535260
\(655\) −2.66387e11 −0.0565493
\(656\) 6.29374e11 0.132691
\(657\) 5.31329e11 0.111255
\(658\) 8.99379e12 1.87036
\(659\) −3.16289e11 −0.0653282 −0.0326641 0.999466i \(-0.510399\pi\)
−0.0326641 + 0.999466i \(0.510399\pi\)
\(660\) 5.32980e11 0.109336
\(661\) 7.77865e12 1.58488 0.792442 0.609947i \(-0.208809\pi\)
0.792442 + 0.609947i \(0.208809\pi\)
\(662\) −3.87283e12 −0.783732
\(663\) 0 0
\(664\) −1.60136e12 −0.319692
\(665\) −9.05649e12 −1.79582
\(666\) −5.58558e10 −0.0110011
\(667\) −3.71437e12 −0.726640
\(668\) −6.62229e11 −0.128681
\(669\) −8.33924e11 −0.160957
\(670\) −8.76880e12 −1.68114
\(671\) −3.22239e12 −0.613658
\(672\) −4.33112e12 −0.819291
\(673\) −3.79653e12 −0.713377 −0.356688 0.934223i \(-0.616094\pi\)
−0.356688 + 0.934223i \(0.616094\pi\)
\(674\) 9.30863e12 1.73747
\(675\) −1.27507e12 −0.236411
\(676\) 5.25533e12 0.967921
\(677\) 4.11221e12 0.752362 0.376181 0.926546i \(-0.377237\pi\)
0.376181 + 0.926546i \(0.377237\pi\)
\(678\) 5.19378e12 0.943952
\(679\) 8.89201e12 1.60541
\(680\) 0 0
\(681\) 4.10267e12 0.730979
\(682\) −8.36970e10 −0.0148143
\(683\) 9.35979e12 1.64578 0.822892 0.568197i \(-0.192359\pi\)
0.822892 + 0.568197i \(0.192359\pi\)
\(684\) 5.95467e12 1.04017
\(685\) 8.42328e12 1.46175
\(686\) −6.32177e12 −1.08988
\(687\) −1.16880e12 −0.200186
\(688\) 1.14166e13 1.94263
\(689\) 2.08687e12 0.352783
\(690\) −1.23774e12 −0.207878
\(691\) −1.29891e12 −0.216734 −0.108367 0.994111i \(-0.534562\pi\)
−0.108367 + 0.994111i \(0.534562\pi\)
\(692\) 5.81212e12 0.963511
\(693\) 3.25528e12 0.536153
\(694\) −8.29555e12 −1.35746
\(695\) −4.23095e12 −0.687870
\(696\) 5.97081e11 0.0964476
\(697\) 0 0
\(698\) −1.25289e13 −1.99786
\(699\) −1.67133e12 −0.264798
\(700\) 2.93390e12 0.461853
\(701\) −5.92387e12 −0.926562 −0.463281 0.886211i \(-0.653328\pi\)
−0.463281 + 0.886211i \(0.653328\pi\)
\(702\) −9.08858e12 −1.41247
\(703\) −8.47054e10 −0.0130801
\(704\) −1.92310e12 −0.295070
\(705\) −1.77370e12 −0.270415
\(706\) −1.19997e13 −1.81782
\(707\) 6.81307e12 1.02555
\(708\) −1.74490e12 −0.260989
\(709\) 3.45867e12 0.514045 0.257022 0.966405i \(-0.417259\pi\)
0.257022 + 0.966405i \(0.417259\pi\)
\(710\) 9.51608e12 1.40539
\(711\) −8.24980e11 −0.121068
\(712\) 2.54059e11 0.0370489
\(713\) 9.08608e10 0.0131666
\(714\) 0 0
\(715\) 3.28995e12 0.470773
\(716\) −5.18765e12 −0.737670
\(717\) 1.58079e12 0.223376
\(718\) −4.67155e12 −0.655996
\(719\) 4.97594e10 0.00694377 0.00347188 0.999994i \(-0.498895\pi\)
0.00347188 + 0.999994i \(0.498895\pi\)
\(720\) −5.56287e12 −0.771441
\(721\) 1.16998e13 1.61238
\(722\) 9.31200e12 1.27534
\(723\) 1.05129e12 0.143087
\(724\) 1.13229e13 1.53156
\(725\) −3.71443e12 −0.499311
\(726\) 3.31381e12 0.442704
\(727\) −9.82294e11 −0.130418 −0.0652089 0.997872i \(-0.520771\pi\)
−0.0652089 + 0.997872i \(0.520771\pi\)
\(728\) −2.91115e12 −0.384126
\(729\) −1.69287e12 −0.221998
\(730\) 1.12058e12 0.146047
\(731\) 0 0
\(732\) 4.03957e12 0.520038
\(733\) 7.22406e12 0.924301 0.462151 0.886802i \(-0.347078\pi\)
0.462151 + 0.886802i \(0.347078\pi\)
\(734\) −3.91573e12 −0.497944
\(735\) 3.72662e12 0.471002
\(736\) 5.20102e12 0.653338
\(737\) 4.77981e12 0.596770
\(738\) 1.12855e12 0.140045
\(739\) 9.71249e12 1.19793 0.598964 0.800776i \(-0.295579\pi\)
0.598964 + 0.800776i \(0.295579\pi\)
\(740\) −5.50676e10 −0.00675078
\(741\) −6.34395e12 −0.772998
\(742\) 4.35486e12 0.527420
\(743\) 1.04007e13 1.25202 0.626012 0.779813i \(-0.284686\pi\)
0.626012 + 0.779813i \(0.284686\pi\)
\(744\) −1.46058e10 −0.00174762
\(745\) 6.40460e12 0.761708
\(746\) 1.46944e11 0.0173711
\(747\) −1.38563e13 −1.62819
\(748\) 0 0
\(749\) 1.14054e13 1.32417
\(750\) −4.95943e12 −0.572343
\(751\) 1.32487e13 1.51982 0.759911 0.650027i \(-0.225243\pi\)
0.759911 + 0.650027i \(0.225243\pi\)
\(752\) 8.37769e12 0.955309
\(753\) 7.77959e11 0.0881819
\(754\) −2.64761e13 −2.98320
\(755\) −5.39301e12 −0.604045
\(756\) −8.86591e12 −0.987132
\(757\) −4.44291e12 −0.491740 −0.245870 0.969303i \(-0.579074\pi\)
−0.245870 + 0.969303i \(0.579074\pi\)
\(758\) −1.62972e13 −1.79309
\(759\) 6.74684e11 0.0737926
\(760\) −1.74822e12 −0.190079
\(761\) 2.09223e12 0.226141 0.113070 0.993587i \(-0.463931\pi\)
0.113070 + 0.993587i \(0.463931\pi\)
\(762\) 8.35402e12 0.897632
\(763\) −1.50789e13 −1.61068
\(764\) 3.35809e12 0.356593
\(765\) 0 0
\(766\) −1.66840e13 −1.75094
\(767\) −1.07708e13 −1.12375
\(768\) −4.43117e12 −0.459614
\(769\) −4.94365e12 −0.509776 −0.254888 0.966971i \(-0.582039\pi\)
−0.254888 + 0.966971i \(0.582039\pi\)
\(770\) 6.86544e12 0.703818
\(771\) 1.11699e12 0.113843
\(772\) −8.05826e12 −0.816514
\(773\) −9.50527e12 −0.957540 −0.478770 0.877940i \(-0.658917\pi\)
−0.478770 + 0.877940i \(0.658917\pi\)
\(774\) 2.04715e13 2.05029
\(775\) 9.08621e10 0.00904743
\(776\) 1.71647e12 0.169925
\(777\) 5.80494e10 0.00571351
\(778\) −1.10992e13 −1.08613
\(779\) 1.71145e12 0.166512
\(780\) −4.12426e12 −0.398951
\(781\) −5.18715e12 −0.498883
\(782\) 0 0
\(783\) 1.12246e13 1.06719
\(784\) −1.76018e13 −1.66393
\(785\) 2.42509e12 0.227936
\(786\) −3.89397e11 −0.0363908
\(787\) −5.91450e12 −0.549581 −0.274790 0.961504i \(-0.588608\pi\)
−0.274790 + 0.961504i \(0.588608\pi\)
\(788\) −1.30884e13 −1.20926
\(789\) −8.88638e11 −0.0816354
\(790\) −1.73990e12 −0.158929
\(791\) 3.12744e13 2.84050
\(792\) 6.28382e11 0.0567493
\(793\) 2.49352e13 2.23915
\(794\) −2.51742e13 −2.24783
\(795\) −8.58842e11 −0.0762537
\(796\) 8.22544e11 0.0726190
\(797\) 1.23941e13 1.08806 0.544029 0.839067i \(-0.316898\pi\)
0.544029 + 0.839067i \(0.316898\pi\)
\(798\) −1.32385e13 −1.15565
\(799\) 0 0
\(800\) 5.20109e12 0.448941
\(801\) 2.19833e12 0.188689
\(802\) 2.75090e13 2.34796
\(803\) −6.10822e11 −0.0518436
\(804\) −5.99194e12 −0.505726
\(805\) −7.45307e12 −0.625538
\(806\) 6.47656e11 0.0540551
\(807\) 6.09260e11 0.0505675
\(808\) 1.31516e12 0.108549
\(809\) −3.25319e11 −0.0267019 −0.0133509 0.999911i \(-0.504250\pi\)
−0.0133509 + 0.999911i \(0.504250\pi\)
\(810\) −7.95623e12 −0.649418
\(811\) −1.73188e12 −0.140580 −0.0702899 0.997527i \(-0.522392\pi\)
−0.0702899 + 0.997527i \(0.522392\pi\)
\(812\) −2.58274e13 −2.08487
\(813\) 3.49192e12 0.280322
\(814\) 6.42125e10 0.00512637
\(815\) −7.95124e12 −0.631285
\(816\) 0 0
\(817\) 3.10451e13 2.43777
\(818\) 2.04273e13 1.59522
\(819\) −2.51897e13 −1.95634
\(820\) 1.11263e12 0.0859385
\(821\) 6.79797e12 0.522198 0.261099 0.965312i \(-0.415915\pi\)
0.261099 + 0.965312i \(0.415915\pi\)
\(822\) 1.23129e13 0.940672
\(823\) −7.36235e12 −0.559393 −0.279697 0.960088i \(-0.590234\pi\)
−0.279697 + 0.960088i \(0.590234\pi\)
\(824\) 2.25846e12 0.170664
\(825\) 6.74694e11 0.0507065
\(826\) −2.24765e13 −1.68004
\(827\) −2.22177e13 −1.65167 −0.825836 0.563911i \(-0.809296\pi\)
−0.825836 + 0.563911i \(0.809296\pi\)
\(828\) 4.90042e12 0.362324
\(829\) 8.11644e12 0.596857 0.298428 0.954432i \(-0.403538\pi\)
0.298428 + 0.954432i \(0.403538\pi\)
\(830\) −2.92232e13 −2.13735
\(831\) −9.62626e12 −0.700249
\(832\) 1.48812e13 1.07667
\(833\) 0 0
\(834\) −6.18469e12 −0.442661
\(835\) 1.68231e12 0.119761
\(836\) −6.84556e12 −0.484709
\(837\) −2.74575e11 −0.0193373
\(838\) −3.69085e13 −2.58541
\(839\) −7.13705e12 −0.497267 −0.248634 0.968598i \(-0.579981\pi\)
−0.248634 + 0.968598i \(0.579981\pi\)
\(840\) 1.19807e12 0.0830283
\(841\) 1.81913e13 1.25396
\(842\) −3.10420e13 −2.12836
\(843\) 3.06908e12 0.209307
\(844\) −1.06615e13 −0.723233
\(845\) −1.33505e13 −0.900826
\(846\) 1.50223e13 1.00826
\(847\) 1.99542e13 1.33217
\(848\) 4.05654e12 0.269386
\(849\) 9.17977e12 0.606383
\(850\) 0 0
\(851\) −6.97086e10 −0.00455621
\(852\) 6.50258e12 0.422773
\(853\) 7.08729e12 0.458363 0.229182 0.973384i \(-0.426395\pi\)
0.229182 + 0.973384i \(0.426395\pi\)
\(854\) 5.20347e13 3.34759
\(855\) −1.51271e13 −0.968070
\(856\) 2.20164e12 0.140157
\(857\) −2.66839e13 −1.68980 −0.844900 0.534925i \(-0.820340\pi\)
−0.844900 + 0.534925i \(0.820340\pi\)
\(858\) 4.80915e12 0.302953
\(859\) 1.11623e13 0.699496 0.349748 0.936844i \(-0.386267\pi\)
0.349748 + 0.936844i \(0.386267\pi\)
\(860\) 2.01827e13 1.25816
\(861\) −1.17287e12 −0.0727339
\(862\) 3.60278e12 0.222257
\(863\) 1.18982e13 0.730183 0.365091 0.930972i \(-0.381038\pi\)
0.365091 + 0.930972i \(0.381038\pi\)
\(864\) −1.57171e13 −0.959535
\(865\) −1.47649e13 −0.896723
\(866\) −3.62547e13 −2.19045
\(867\) 0 0
\(868\) 6.31789e11 0.0377775
\(869\) 9.48406e11 0.0564164
\(870\) 1.08961e13 0.644815
\(871\) −3.69867e13 −2.17753
\(872\) −2.91075e12 −0.170483
\(873\) 1.48523e13 0.865427
\(874\) 1.58975e13 0.921567
\(875\) −2.98633e13 −1.72227
\(876\) 7.65723e11 0.0439342
\(877\) −7.48241e12 −0.427113 −0.213557 0.976931i \(-0.568505\pi\)
−0.213557 + 0.976931i \(0.568505\pi\)
\(878\) −3.20121e12 −0.181798
\(879\) −5.79646e12 −0.327501
\(880\) 6.39514e12 0.359483
\(881\) −8.69387e12 −0.486208 −0.243104 0.970000i \(-0.578166\pi\)
−0.243104 + 0.970000i \(0.578166\pi\)
\(882\) −3.15625e13 −1.75615
\(883\) 2.71253e13 1.50159 0.750794 0.660536i \(-0.229671\pi\)
0.750794 + 0.660536i \(0.229671\pi\)
\(884\) 0 0
\(885\) 4.43270e12 0.242898
\(886\) 2.31038e13 1.25960
\(887\) −1.80206e13 −0.977494 −0.488747 0.872426i \(-0.662546\pi\)
−0.488747 + 0.872426i \(0.662546\pi\)
\(888\) 1.12056e10 0.000604749 0
\(889\) 5.03038e13 2.70111
\(890\) 4.63633e12 0.247696
\(891\) 4.33688e12 0.230530
\(892\) 6.96322e12 0.368272
\(893\) 2.27813e13 1.19880
\(894\) 9.36207e12 0.490177
\(895\) 1.31785e13 0.686536
\(896\) −1.01450e13 −0.525853
\(897\) −5.22078e12 −0.269259
\(898\) −3.72132e13 −1.90965
\(899\) −7.99868e11 −0.0408413
\(900\) 4.90049e12 0.248971
\(901\) 0 0
\(902\) −1.29740e12 −0.0652595
\(903\) −2.12755e13 −1.06484
\(904\) 6.03705e12 0.300654
\(905\) −2.87644e13 −1.42540
\(906\) −7.88335e12 −0.388717
\(907\) 2.15751e13 1.05857 0.529286 0.848443i \(-0.322460\pi\)
0.529286 + 0.848443i \(0.322460\pi\)
\(908\) −3.42571e13 −1.67249
\(909\) 1.13799e13 0.552840
\(910\) −5.31255e13 −2.56813
\(911\) 1.37712e13 0.662430 0.331215 0.943555i \(-0.392542\pi\)
0.331215 + 0.943555i \(0.392542\pi\)
\(912\) −1.23317e13 −0.590262
\(913\) 1.59294e13 0.758717
\(914\) −2.58422e13 −1.22482
\(915\) −1.02620e13 −0.483990
\(916\) 9.75938e12 0.458029
\(917\) −2.34476e12 −0.109505
\(918\) 0 0
\(919\) 7.38530e12 0.341546 0.170773 0.985310i \(-0.445374\pi\)
0.170773 + 0.985310i \(0.445374\pi\)
\(920\) −1.43870e12 −0.0662104
\(921\) 3.42484e11 0.0156846
\(922\) 1.44841e13 0.660088
\(923\) 4.01387e13 1.82035
\(924\) 4.69133e12 0.211725
\(925\) −6.97096e10 −0.00313080
\(926\) −1.81623e13 −0.811748
\(927\) 1.95421e13 0.869187
\(928\) −4.57857e13 −2.02658
\(929\) 2.18632e13 0.963038 0.481519 0.876436i \(-0.340085\pi\)
0.481519 + 0.876436i \(0.340085\pi\)
\(930\) −2.66540e11 −0.0116840
\(931\) −4.78645e13 −2.08805
\(932\) 1.39555e13 0.605862
\(933\) 3.28747e12 0.142035
\(934\) 4.23286e13 1.82000
\(935\) 0 0
\(936\) −4.86249e12 −0.207070
\(937\) 1.65419e13 0.701062 0.350531 0.936551i \(-0.386001\pi\)
0.350531 + 0.936551i \(0.386001\pi\)
\(938\) −7.71837e13 −3.25546
\(939\) −1.45280e13 −0.609833
\(940\) 1.48103e13 0.618714
\(941\) 1.02461e13 0.425995 0.212998 0.977053i \(-0.431677\pi\)
0.212998 + 0.977053i \(0.431677\pi\)
\(942\) 3.54493e12 0.146682
\(943\) 1.40844e12 0.0580012
\(944\) −2.09368e13 −0.858098
\(945\) 2.25227e13 0.918706
\(946\) −2.35343e13 −0.955414
\(947\) −1.33810e13 −0.540648 −0.270324 0.962769i \(-0.587131\pi\)
−0.270324 + 0.962769i \(0.587131\pi\)
\(948\) −1.18892e12 −0.0478095
\(949\) 4.72661e12 0.189170
\(950\) 1.58977e13 0.633255
\(951\) −3.86344e12 −0.153166
\(952\) 0 0
\(953\) −4.84663e13 −1.90336 −0.951682 0.307084i \(-0.900647\pi\)
−0.951682 + 0.307084i \(0.900647\pi\)
\(954\) 7.27393e12 0.284316
\(955\) −8.53079e12 −0.331875
\(956\) −1.31995e13 −0.511089
\(957\) −5.93940e12 −0.228896
\(958\) 6.40240e13 2.45583
\(959\) 7.41424e13 2.83063
\(960\) −6.12429e12 −0.232721
\(961\) −2.64201e13 −0.999260
\(962\) −4.96883e11 −0.0187054
\(963\) 1.90504e13 0.713817
\(964\) −8.77823e12 −0.327386
\(965\) 2.04709e13 0.759915
\(966\) −1.08947e13 −0.402549
\(967\) −9.25582e12 −0.340405 −0.170202 0.985409i \(-0.554442\pi\)
−0.170202 + 0.985409i \(0.554442\pi\)
\(968\) 3.85185e12 0.141004
\(969\) 0 0
\(970\) 3.13238e13 1.13606
\(971\) 4.19377e13 1.51397 0.756986 0.653431i \(-0.226671\pi\)
0.756986 + 0.653431i \(0.226671\pi\)
\(972\) −2.28013e13 −0.819335
\(973\) −3.72412e13 −1.33203
\(974\) −2.36268e13 −0.841181
\(975\) −5.22086e12 −0.185021
\(976\) 4.84701e13 1.70982
\(977\) −1.16863e13 −0.410346 −0.205173 0.978726i \(-0.565776\pi\)
−0.205173 + 0.978726i \(0.565776\pi\)
\(978\) −1.16229e13 −0.406247
\(979\) −2.52723e12 −0.0879271
\(980\) −3.11171e13 −1.07766
\(981\) −2.51863e13 −0.868267
\(982\) −2.87137e13 −0.985345
\(983\) 2.32178e13 0.793103 0.396551 0.918013i \(-0.370207\pi\)
0.396551 + 0.918013i \(0.370207\pi\)
\(984\) −2.26406e11 −0.00769856
\(985\) 3.32493e13 1.12543
\(986\) 0 0
\(987\) −1.56123e13 −0.523648
\(988\) 5.29717e13 1.76863
\(989\) 2.55487e13 0.849151
\(990\) 1.14674e13 0.379406
\(991\) 2.74583e13 0.904361 0.452181 0.891926i \(-0.350646\pi\)
0.452181 + 0.891926i \(0.350646\pi\)
\(992\) 1.12001e12 0.0367213
\(993\) 6.72283e12 0.219422
\(994\) 8.37613e13 2.72148
\(995\) −2.08956e12 −0.0675852
\(996\) −1.99689e13 −0.642966
\(997\) −6.82596e12 −0.218794 −0.109397 0.993998i \(-0.534892\pi\)
−0.109397 + 0.993998i \(0.534892\pi\)
\(998\) −4.54546e13 −1.45041
\(999\) 2.10655e11 0.00669154
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.1.30 yes 36
17.16 even 2 289.10.a.g.1.30 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.30 36 17.16 even 2
289.10.a.h.1.30 yes 36 1.1 even 1 trivial