Properties

Label 289.10.a.h.1.13
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 1.13
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.2320 q^{2} +276.194 q^{3} -248.524 q^{4} -1638.38 q^{5} -4483.17 q^{6} +8498.12 q^{7} +12344.8 q^{8} +56600.2 q^{9} +O(q^{10})\) \(q-16.2320 q^{2} +276.194 q^{3} -248.524 q^{4} -1638.38 q^{5} -4483.17 q^{6} +8498.12 q^{7} +12344.8 q^{8} +56600.2 q^{9} +26594.2 q^{10} +46186.5 q^{11} -68640.8 q^{12} +47090.3 q^{13} -137941. q^{14} -452512. q^{15} -73135.9 q^{16} -918732. q^{18} +192344. q^{19} +407177. q^{20} +2.34713e6 q^{21} -749697. q^{22} +1.30866e6 q^{23} +3.40956e6 q^{24} +731179. q^{25} -764368. q^{26} +1.01963e7 q^{27} -2.11198e6 q^{28} +3.14687e6 q^{29} +7.34516e6 q^{30} +3.13731e6 q^{31} -5.13339e6 q^{32} +1.27564e7 q^{33} -1.39232e7 q^{35} -1.40665e7 q^{36} -7.07531e6 q^{37} -3.12213e6 q^{38} +1.30061e7 q^{39} -2.02255e7 q^{40} +3.58972e6 q^{41} -3.80985e7 q^{42} +2.56336e7 q^{43} -1.14784e7 q^{44} -9.27329e7 q^{45} -2.12421e7 q^{46} -4.61978e7 q^{47} -2.01997e7 q^{48} +3.18645e7 q^{49} -1.18685e7 q^{50} -1.17031e7 q^{52} +7.23226e7 q^{53} -1.65506e8 q^{54} -7.56712e7 q^{55} +1.04907e8 q^{56} +5.31244e7 q^{57} -5.10799e7 q^{58} -6.44143e7 q^{59} +1.12460e8 q^{60} -1.13803e8 q^{61} -5.09247e7 q^{62} +4.80995e8 q^{63} +1.20771e8 q^{64} -7.71521e7 q^{65} -2.07062e8 q^{66} +3.92655e7 q^{67} +3.61444e8 q^{69} +2.26001e8 q^{70} -8.04952e7 q^{71} +6.98717e8 q^{72} -2.91761e8 q^{73} +1.14846e8 q^{74} +2.01947e8 q^{75} -4.78021e7 q^{76} +3.92498e8 q^{77} -2.11114e8 q^{78} -5.23679e8 q^{79} +1.19825e8 q^{80} +1.70210e9 q^{81} -5.82682e7 q^{82} -3.13638e8 q^{83} -5.83318e8 q^{84} -4.16084e8 q^{86} +8.69147e8 q^{87} +5.70162e8 q^{88} -6.56594e8 q^{89} +1.50524e9 q^{90} +4.00179e8 q^{91} -3.25232e8 q^{92} +8.66507e8 q^{93} +7.49881e8 q^{94} -3.15134e8 q^{95} -1.41781e9 q^{96} +1.11282e8 q^{97} -5.17223e8 q^{98} +2.61416e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.2320 −0.717358 −0.358679 0.933461i \(-0.616773\pi\)
−0.358679 + 0.933461i \(0.616773\pi\)
\(3\) 276.194 1.96865 0.984326 0.176360i \(-0.0564324\pi\)
0.984326 + 0.176360i \(0.0564324\pi\)
\(4\) −248.524 −0.485398
\(5\) −1638.38 −1.17233 −0.586166 0.810191i \(-0.699363\pi\)
−0.586166 + 0.810191i \(0.699363\pi\)
\(6\) −4483.17 −1.41223
\(7\) 8498.12 1.33777 0.668886 0.743365i \(-0.266772\pi\)
0.668886 + 0.743365i \(0.266772\pi\)
\(8\) 12344.8 1.06556
\(9\) 56600.2 2.87559
\(10\) 26594.2 0.840982
\(11\) 46186.5 0.951147 0.475573 0.879676i \(-0.342241\pi\)
0.475573 + 0.879676i \(0.342241\pi\)
\(12\) −68640.8 −0.955579
\(13\) 47090.3 0.457285 0.228642 0.973510i \(-0.426571\pi\)
0.228642 + 0.973510i \(0.426571\pi\)
\(14\) −137941. −0.959661
\(15\) −452512. −2.30791
\(16\) −73135.9 −0.278991
\(17\) 0 0
\(18\) −918732. −2.06283
\(19\) 192344. 0.338601 0.169301 0.985564i \(-0.445849\pi\)
0.169301 + 0.985564i \(0.445849\pi\)
\(20\) 407177. 0.569048
\(21\) 2.34713e6 2.63360
\(22\) −749697. −0.682313
\(23\) 1.30866e6 0.975104 0.487552 0.873094i \(-0.337890\pi\)
0.487552 + 0.873094i \(0.337890\pi\)
\(24\) 3.40956e6 2.09772
\(25\) 731179. 0.374364
\(26\) −764368. −0.328037
\(27\) 1.01963e7 3.69238
\(28\) −2.11198e6 −0.649351
\(29\) 3.14687e6 0.826205 0.413103 0.910684i \(-0.364445\pi\)
0.413103 + 0.910684i \(0.364445\pi\)
\(30\) 7.34516e6 1.65560
\(31\) 3.13731e6 0.610141 0.305070 0.952330i \(-0.401320\pi\)
0.305070 + 0.952330i \(0.401320\pi\)
\(32\) −5.13339e6 −0.865425
\(33\) 1.27564e7 1.87248
\(34\) 0 0
\(35\) −1.39232e7 −1.56831
\(36\) −1.40665e7 −1.39580
\(37\) −7.07531e6 −0.620637 −0.310318 0.950633i \(-0.600436\pi\)
−0.310318 + 0.950633i \(0.600436\pi\)
\(38\) −3.12213e6 −0.242898
\(39\) 1.30061e7 0.900234
\(40\) −2.02255e7 −1.24919
\(41\) 3.58972e6 0.198396 0.0991980 0.995068i \(-0.468372\pi\)
0.0991980 + 0.995068i \(0.468372\pi\)
\(42\) −3.80985e7 −1.88924
\(43\) 2.56336e7 1.14341 0.571705 0.820460i \(-0.306282\pi\)
0.571705 + 0.820460i \(0.306282\pi\)
\(44\) −1.14784e7 −0.461684
\(45\) −9.27329e7 −3.37115
\(46\) −2.12421e7 −0.699498
\(47\) −4.61978e7 −1.38096 −0.690480 0.723351i \(-0.742601\pi\)
−0.690480 + 0.723351i \(0.742601\pi\)
\(48\) −2.01997e7 −0.549237
\(49\) 3.18645e7 0.789631
\(50\) −1.18685e7 −0.268553
\(51\) 0 0
\(52\) −1.17031e7 −0.221965
\(53\) 7.23226e7 1.25902 0.629510 0.776993i \(-0.283256\pi\)
0.629510 + 0.776993i \(0.283256\pi\)
\(54\) −1.65506e8 −2.64876
\(55\) −7.56712e7 −1.11506
\(56\) 1.04907e8 1.42548
\(57\) 5.31244e7 0.666587
\(58\) −5.10799e7 −0.592685
\(59\) −6.44143e7 −0.692067 −0.346034 0.938222i \(-0.612472\pi\)
−0.346034 + 0.938222i \(0.612472\pi\)
\(60\) 1.12460e8 1.12026
\(61\) −1.13803e8 −1.05237 −0.526185 0.850370i \(-0.676378\pi\)
−0.526185 + 0.850370i \(0.676378\pi\)
\(62\) −5.09247e7 −0.437689
\(63\) 4.80995e8 3.84688
\(64\) 1.20771e8 0.899811
\(65\) −7.71521e7 −0.536090
\(66\) −2.07062e8 −1.34324
\(67\) 3.92655e7 0.238053 0.119027 0.992891i \(-0.462023\pi\)
0.119027 + 0.992891i \(0.462023\pi\)
\(68\) 0 0
\(69\) 3.61444e8 1.91964
\(70\) 2.26001e8 1.12504
\(71\) −8.04952e7 −0.375930 −0.187965 0.982176i \(-0.560189\pi\)
−0.187965 + 0.982176i \(0.560189\pi\)
\(72\) 6.98717e8 3.06412
\(73\) −2.91761e8 −1.20247 −0.601236 0.799071i \(-0.705325\pi\)
−0.601236 + 0.799071i \(0.705325\pi\)
\(74\) 1.14846e8 0.445219
\(75\) 2.01947e8 0.736992
\(76\) −4.78021e7 −0.164356
\(77\) 3.92498e8 1.27242
\(78\) −2.11114e8 −0.645790
\(79\) −5.23679e8 −1.51267 −0.756333 0.654187i \(-0.773011\pi\)
−0.756333 + 0.654187i \(0.773011\pi\)
\(80\) 1.19825e8 0.327071
\(81\) 1.70210e9 4.39342
\(82\) −5.82682e7 −0.142321
\(83\) −3.13638e8 −0.725398 −0.362699 0.931906i \(-0.618145\pi\)
−0.362699 + 0.931906i \(0.618145\pi\)
\(84\) −5.83318e8 −1.27835
\(85\) 0 0
\(86\) −4.16084e8 −0.820234
\(87\) 8.69147e8 1.62651
\(88\) 5.70162e8 1.01351
\(89\) −6.56594e8 −1.10928 −0.554641 0.832090i \(-0.687144\pi\)
−0.554641 + 0.832090i \(0.687144\pi\)
\(90\) 1.50524e9 2.41832
\(91\) 4.00179e8 0.611742
\(92\) −3.25232e8 −0.473313
\(93\) 8.66507e8 1.20115
\(94\) 7.49881e8 0.990643
\(95\) −3.15134e8 −0.396953
\(96\) −1.41781e9 −1.70372
\(97\) 1.11282e8 0.127630 0.0638151 0.997962i \(-0.479673\pi\)
0.0638151 + 0.997962i \(0.479673\pi\)
\(98\) −5.17223e8 −0.566448
\(99\) 2.61416e9 2.73511
\(100\) −1.81715e8 −0.181715
\(101\) 8.39306e8 0.802554 0.401277 0.915957i \(-0.368566\pi\)
0.401277 + 0.915957i \(0.368566\pi\)
\(102\) 0 0
\(103\) 1.31010e9 1.14693 0.573467 0.819229i \(-0.305598\pi\)
0.573467 + 0.819229i \(0.305598\pi\)
\(104\) 5.81320e8 0.487265
\(105\) −3.84550e9 −3.08746
\(106\) −1.17394e9 −0.903167
\(107\) −8.31146e8 −0.612986 −0.306493 0.951873i \(-0.599156\pi\)
−0.306493 + 0.951873i \(0.599156\pi\)
\(108\) −2.53402e9 −1.79227
\(109\) 1.16494e9 0.790470 0.395235 0.918580i \(-0.370663\pi\)
0.395235 + 0.918580i \(0.370663\pi\)
\(110\) 1.22829e9 0.799897
\(111\) −1.95416e9 −1.22182
\(112\) −6.21518e8 −0.373227
\(113\) −1.30540e9 −0.753164 −0.376582 0.926383i \(-0.622901\pi\)
−0.376582 + 0.926383i \(0.622901\pi\)
\(114\) −8.62313e8 −0.478182
\(115\) −2.14408e9 −1.14315
\(116\) −7.82072e8 −0.401038
\(117\) 2.66532e9 1.31496
\(118\) 1.04557e9 0.496460
\(119\) 0 0
\(120\) −5.58617e9 −2.45923
\(121\) −2.24759e8 −0.0953197
\(122\) 1.84724e9 0.754925
\(123\) 9.91459e8 0.390573
\(124\) −7.79696e8 −0.296161
\(125\) 2.00202e9 0.733454
\(126\) −7.80750e9 −2.75959
\(127\) 1.36724e9 0.466367 0.233184 0.972433i \(-0.425086\pi\)
0.233184 + 0.972433i \(0.425086\pi\)
\(128\) 6.67953e8 0.219939
\(129\) 7.07985e9 2.25097
\(130\) 1.25233e9 0.384568
\(131\) 3.65407e9 1.08407 0.542034 0.840357i \(-0.317654\pi\)
0.542034 + 0.840357i \(0.317654\pi\)
\(132\) −3.17027e9 −0.908896
\(133\) 1.63457e9 0.452971
\(134\) −6.37355e8 −0.170769
\(135\) −1.67055e10 −4.32870
\(136\) 0 0
\(137\) −1.90939e9 −0.463077 −0.231538 0.972826i \(-0.574376\pi\)
−0.231538 + 0.972826i \(0.574376\pi\)
\(138\) −5.86694e9 −1.37707
\(139\) 8.29279e9 1.88423 0.942115 0.335289i \(-0.108834\pi\)
0.942115 + 0.335289i \(0.108834\pi\)
\(140\) 3.46024e9 0.761255
\(141\) −1.27596e10 −2.71863
\(142\) 1.30659e9 0.269677
\(143\) 2.17494e9 0.434945
\(144\) −4.13951e9 −0.802265
\(145\) −5.15579e9 −0.968587
\(146\) 4.73586e9 0.862603
\(147\) 8.80078e9 1.55451
\(148\) 1.75838e9 0.301256
\(149\) 1.38793e9 0.230690 0.115345 0.993326i \(-0.463203\pi\)
0.115345 + 0.993326i \(0.463203\pi\)
\(150\) −3.27800e9 −0.528687
\(151\) 7.05930e9 1.10501 0.552504 0.833510i \(-0.313672\pi\)
0.552504 + 0.833510i \(0.313672\pi\)
\(152\) 2.37445e9 0.360800
\(153\) 0 0
\(154\) −6.37101e9 −0.912778
\(155\) −5.14012e9 −0.715288
\(156\) −3.23232e9 −0.436972
\(157\) −3.82538e9 −0.502489 −0.251244 0.967924i \(-0.580840\pi\)
−0.251244 + 0.967924i \(0.580840\pi\)
\(158\) 8.50033e9 1.08512
\(159\) 1.99751e10 2.47857
\(160\) 8.41047e9 1.01457
\(161\) 1.11211e10 1.30447
\(162\) −2.76284e10 −3.15165
\(163\) −1.16179e10 −1.28909 −0.644545 0.764567i \(-0.722953\pi\)
−0.644545 + 0.764567i \(0.722953\pi\)
\(164\) −8.92130e8 −0.0963010
\(165\) −2.08999e10 −2.19517
\(166\) 5.09095e9 0.520370
\(167\) −3.47032e9 −0.345259 −0.172630 0.984987i \(-0.555226\pi\)
−0.172630 + 0.984987i \(0.555226\pi\)
\(168\) 2.89748e10 2.80627
\(169\) −8.38700e9 −0.790891
\(170\) 0 0
\(171\) 1.08867e10 0.973677
\(172\) −6.37056e9 −0.555008
\(173\) 1.36446e8 0.0115812 0.00579061 0.999983i \(-0.498157\pi\)
0.00579061 + 0.999983i \(0.498157\pi\)
\(174\) −1.41080e10 −1.16679
\(175\) 6.21365e9 0.500813
\(176\) −3.37789e9 −0.265362
\(177\) −1.77909e10 −1.36244
\(178\) 1.06578e10 0.795752
\(179\) 1.66738e10 1.21394 0.606969 0.794726i \(-0.292385\pi\)
0.606969 + 0.794726i \(0.292385\pi\)
\(180\) 2.30463e10 1.63635
\(181\) −5.19059e9 −0.359471 −0.179735 0.983715i \(-0.557524\pi\)
−0.179735 + 0.983715i \(0.557524\pi\)
\(182\) −6.49570e9 −0.438838
\(183\) −3.14316e10 −2.07175
\(184\) 1.61551e10 1.03903
\(185\) 1.15921e10 0.727593
\(186\) −1.40651e10 −0.861657
\(187\) 0 0
\(188\) 1.14813e10 0.670315
\(189\) 8.66495e10 4.93956
\(190\) 5.11524e9 0.284757
\(191\) 2.87746e10 1.56444 0.782220 0.623003i \(-0.214087\pi\)
0.782220 + 0.623003i \(0.214087\pi\)
\(192\) 3.33561e10 1.77141
\(193\) −1.92651e10 −0.999455 −0.499727 0.866183i \(-0.666566\pi\)
−0.499727 + 0.866183i \(0.666566\pi\)
\(194\) −1.80633e9 −0.0915565
\(195\) −2.13090e10 −1.05537
\(196\) −7.91907e9 −0.383285
\(197\) 7.46589e9 0.353170 0.176585 0.984285i \(-0.443495\pi\)
0.176585 + 0.984285i \(0.443495\pi\)
\(198\) −4.24330e10 −1.96205
\(199\) −2.74384e10 −1.24028 −0.620140 0.784491i \(-0.712924\pi\)
−0.620140 + 0.784491i \(0.712924\pi\)
\(200\) 9.02625e9 0.398908
\(201\) 1.08449e10 0.468644
\(202\) −1.36236e10 −0.575719
\(203\) 2.67425e10 1.10527
\(204\) 0 0
\(205\) −5.88134e9 −0.232586
\(206\) −2.12655e10 −0.822762
\(207\) 7.40703e10 2.80400
\(208\) −3.44400e9 −0.127579
\(209\) 8.88371e9 0.322059
\(210\) 6.24201e10 2.21481
\(211\) 1.26357e10 0.438863 0.219432 0.975628i \(-0.429580\pi\)
0.219432 + 0.975628i \(0.429580\pi\)
\(212\) −1.79739e10 −0.611125
\(213\) −2.22323e10 −0.740076
\(214\) 1.34911e10 0.439730
\(215\) −4.19977e10 −1.34046
\(216\) 1.25871e11 3.93446
\(217\) 2.66613e10 0.816228
\(218\) −1.89093e10 −0.567050
\(219\) −8.05828e10 −2.36725
\(220\) 1.88061e10 0.541248
\(221\) 0 0
\(222\) 3.17198e10 0.876480
\(223\) 5.64536e10 1.52869 0.764346 0.644806i \(-0.223062\pi\)
0.764346 + 0.644806i \(0.223062\pi\)
\(224\) −4.36242e10 −1.15774
\(225\) 4.13849e10 1.07652
\(226\) 2.11892e10 0.540288
\(227\) −4.94426e9 −0.123591 −0.0617953 0.998089i \(-0.519683\pi\)
−0.0617953 + 0.998089i \(0.519683\pi\)
\(228\) −1.32027e10 −0.323560
\(229\) −5.68904e10 −1.36703 −0.683516 0.729935i \(-0.739550\pi\)
−0.683516 + 0.729935i \(0.739550\pi\)
\(230\) 3.48027e10 0.820045
\(231\) 1.08406e11 2.50494
\(232\) 3.88474e10 0.880373
\(233\) 7.42331e10 1.65005 0.825023 0.565099i \(-0.191162\pi\)
0.825023 + 0.565099i \(0.191162\pi\)
\(234\) −4.32634e10 −0.943299
\(235\) 7.56898e10 1.61895
\(236\) 1.60085e10 0.335928
\(237\) −1.44637e11 −2.97791
\(238\) 0 0
\(239\) 4.47275e10 0.886715 0.443357 0.896345i \(-0.353787\pi\)
0.443357 + 0.896345i \(0.353787\pi\)
\(240\) 3.30949e10 0.643888
\(241\) 2.80613e10 0.535835 0.267918 0.963442i \(-0.413665\pi\)
0.267918 + 0.963442i \(0.413665\pi\)
\(242\) 3.64827e9 0.0683783
\(243\) 2.69416e11 4.95673
\(244\) 2.82826e10 0.510817
\(245\) −5.22063e10 −0.925711
\(246\) −1.60933e10 −0.280180
\(247\) 9.05756e9 0.154837
\(248\) 3.87294e10 0.650143
\(249\) −8.66248e10 −1.42806
\(250\) −3.24967e10 −0.526149
\(251\) 6.53333e10 1.03897 0.519485 0.854480i \(-0.326124\pi\)
0.519485 + 0.854480i \(0.326124\pi\)
\(252\) −1.19539e11 −1.86727
\(253\) 6.04423e10 0.927467
\(254\) −2.21930e10 −0.334552
\(255\) 0 0
\(256\) −7.26767e10 −1.05759
\(257\) 4.29846e10 0.614630 0.307315 0.951608i \(-0.400569\pi\)
0.307315 + 0.951608i \(0.400569\pi\)
\(258\) −1.14920e11 −1.61475
\(259\) −6.01268e10 −0.830270
\(260\) 1.91741e10 0.260217
\(261\) 1.78114e11 2.37583
\(262\) −5.93127e10 −0.777664
\(263\) 2.22590e10 0.286882 0.143441 0.989659i \(-0.454183\pi\)
0.143441 + 0.989659i \(0.454183\pi\)
\(264\) 1.57475e11 1.99524
\(265\) −1.18492e11 −1.47599
\(266\) −2.65322e10 −0.324942
\(267\) −1.81347e11 −2.18379
\(268\) −9.75840e9 −0.115551
\(269\) 2.70459e10 0.314931 0.157466 0.987524i \(-0.449668\pi\)
0.157466 + 0.987524i \(0.449668\pi\)
\(270\) 2.71163e11 3.10522
\(271\) 1.20580e11 1.35805 0.679023 0.734117i \(-0.262404\pi\)
0.679023 + 0.734117i \(0.262404\pi\)
\(272\) 0 0
\(273\) 1.10527e11 1.20431
\(274\) 3.09932e10 0.332192
\(275\) 3.37706e10 0.356075
\(276\) −8.98273e10 −0.931788
\(277\) −1.46871e11 −1.49891 −0.749456 0.662055i \(-0.769685\pi\)
−0.749456 + 0.662055i \(0.769685\pi\)
\(278\) −1.34608e11 −1.35167
\(279\) 1.77572e11 1.75451
\(280\) −1.71879e11 −1.67113
\(281\) −1.74963e11 −1.67404 −0.837022 0.547169i \(-0.815705\pi\)
−0.837022 + 0.547169i \(0.815705\pi\)
\(282\) 2.07113e11 1.95023
\(283\) 8.22402e10 0.762159 0.381079 0.924542i \(-0.375552\pi\)
0.381079 + 0.924542i \(0.375552\pi\)
\(284\) 2.00050e10 0.182476
\(285\) −8.70382e10 −0.781462
\(286\) −3.53035e10 −0.312011
\(287\) 3.05059e10 0.265408
\(288\) −2.90551e11 −2.48861
\(289\) 0 0
\(290\) 8.36885e10 0.694824
\(291\) 3.07355e10 0.251259
\(292\) 7.25096e10 0.583677
\(293\) −1.72364e10 −0.136629 −0.0683144 0.997664i \(-0.521762\pi\)
−0.0683144 + 0.997664i \(0.521762\pi\)
\(294\) −1.42854e11 −1.11514
\(295\) 1.05535e11 0.811333
\(296\) −8.73432e10 −0.661327
\(297\) 4.70932e11 3.51199
\(298\) −2.25287e10 −0.165487
\(299\) 6.16251e10 0.445900
\(300\) −5.01887e10 −0.357734
\(301\) 2.17838e11 1.52962
\(302\) −1.14586e11 −0.792687
\(303\) 2.31811e11 1.57995
\(304\) −1.40673e10 −0.0944668
\(305\) 1.86453e11 1.23373
\(306\) 0 0
\(307\) −2.56161e11 −1.64585 −0.822925 0.568150i \(-0.807659\pi\)
−0.822925 + 0.568150i \(0.807659\pi\)
\(308\) −9.75451e10 −0.617628
\(309\) 3.61843e11 2.25791
\(310\) 8.34342e10 0.513117
\(311\) −9.76715e10 −0.592033 −0.296017 0.955183i \(-0.595658\pi\)
−0.296017 + 0.955183i \(0.595658\pi\)
\(312\) 1.60557e11 0.959255
\(313\) −2.36302e11 −1.39161 −0.695805 0.718230i \(-0.744952\pi\)
−0.695805 + 0.718230i \(0.744952\pi\)
\(314\) 6.20935e10 0.360464
\(315\) −7.88055e11 −4.50982
\(316\) 1.30147e11 0.734245
\(317\) −4.50722e10 −0.250693 −0.125346 0.992113i \(-0.540004\pi\)
−0.125346 + 0.992113i \(0.540004\pi\)
\(318\) −3.24234e11 −1.77802
\(319\) 1.45343e11 0.785843
\(320\) −1.97869e11 −1.05488
\(321\) −2.29558e11 −1.20676
\(322\) −1.80518e11 −0.935769
\(323\) 0 0
\(324\) −4.23012e11 −2.13255
\(325\) 3.44315e10 0.171191
\(326\) 1.88581e11 0.924738
\(327\) 3.21750e11 1.55616
\(328\) 4.43143e10 0.211403
\(329\) −3.92595e11 −1.84741
\(330\) 3.39247e11 1.57472
\(331\) −5.28894e10 −0.242183 −0.121091 0.992641i \(-0.538639\pi\)
−0.121091 + 0.992641i \(0.538639\pi\)
\(332\) 7.79463e10 0.352107
\(333\) −4.00464e11 −1.78470
\(334\) 5.63301e10 0.247674
\(335\) −6.43319e10 −0.279078
\(336\) −1.71660e11 −0.734753
\(337\) 1.59919e11 0.675408 0.337704 0.941252i \(-0.390350\pi\)
0.337704 + 0.941252i \(0.390350\pi\)
\(338\) 1.36137e11 0.567352
\(339\) −3.60543e11 −1.48272
\(340\) 0 0
\(341\) 1.44901e11 0.580333
\(342\) −1.76713e11 −0.698475
\(343\) −7.21417e10 −0.281425
\(344\) 3.16441e11 1.21837
\(345\) −5.92184e11 −2.25046
\(346\) −2.21479e9 −0.00830789
\(347\) −4.45690e11 −1.65025 −0.825127 0.564948i \(-0.808896\pi\)
−0.825127 + 0.564948i \(0.808896\pi\)
\(348\) −2.16004e11 −0.789504
\(349\) −2.71132e10 −0.0978286 −0.0489143 0.998803i \(-0.515576\pi\)
−0.0489143 + 0.998803i \(0.515576\pi\)
\(350\) −1.00860e11 −0.359262
\(351\) 4.80148e11 1.68847
\(352\) −2.37093e11 −0.823146
\(353\) −3.52177e11 −1.20719 −0.603594 0.797292i \(-0.706265\pi\)
−0.603594 + 0.797292i \(0.706265\pi\)
\(354\) 2.88780e11 0.977357
\(355\) 1.31882e11 0.440715
\(356\) 1.63179e11 0.538442
\(357\) 0 0
\(358\) −2.70649e11 −0.870828
\(359\) −3.28144e11 −1.04265 −0.521326 0.853358i \(-0.674562\pi\)
−0.521326 + 0.853358i \(0.674562\pi\)
\(360\) −1.14477e12 −3.59216
\(361\) −2.85691e11 −0.885349
\(362\) 8.42535e10 0.257869
\(363\) −6.20771e10 −0.187651
\(364\) −9.94540e10 −0.296938
\(365\) 4.78018e11 1.40970
\(366\) 5.10197e11 1.48618
\(367\) −3.76306e11 −1.08279 −0.541394 0.840769i \(-0.682103\pi\)
−0.541394 + 0.840769i \(0.682103\pi\)
\(368\) −9.57099e10 −0.272046
\(369\) 2.03179e11 0.570505
\(370\) −1.88162e11 −0.521944
\(371\) 6.14606e11 1.68428
\(372\) −2.15347e11 −0.583037
\(373\) 2.49099e11 0.666319 0.333159 0.942871i \(-0.391885\pi\)
0.333159 + 0.942871i \(0.391885\pi\)
\(374\) 0 0
\(375\) 5.52945e11 1.44391
\(376\) −5.70302e11 −1.47150
\(377\) 1.48187e11 0.377811
\(378\) −1.40649e12 −3.54343
\(379\) 7.54823e11 1.87918 0.939590 0.342301i \(-0.111206\pi\)
0.939590 + 0.342301i \(0.111206\pi\)
\(380\) 7.83183e10 0.192680
\(381\) 3.77624e11 0.918114
\(382\) −4.67068e11 −1.12226
\(383\) 5.92227e11 1.40635 0.703176 0.711016i \(-0.251765\pi\)
0.703176 + 0.711016i \(0.251765\pi\)
\(384\) 1.84485e11 0.432982
\(385\) −6.43063e11 −1.49170
\(386\) 3.12710e11 0.716967
\(387\) 1.45087e12 3.28797
\(388\) −2.76563e10 −0.0619514
\(389\) 8.71873e11 1.93055 0.965273 0.261243i \(-0.0841322\pi\)
0.965273 + 0.261243i \(0.0841322\pi\)
\(390\) 3.45886e11 0.757081
\(391\) 0 0
\(392\) 3.93360e11 0.841401
\(393\) 1.00923e12 2.13415
\(394\) −1.21186e11 −0.253349
\(395\) 8.57987e11 1.77335
\(396\) −6.49681e11 −1.32761
\(397\) 1.93481e11 0.390913 0.195457 0.980712i \(-0.437381\pi\)
0.195457 + 0.980712i \(0.437381\pi\)
\(398\) 4.45379e11 0.889725
\(399\) 4.51458e11 0.891741
\(400\) −5.34755e10 −0.104444
\(401\) 2.79164e11 0.539150 0.269575 0.962979i \(-0.413117\pi\)
0.269575 + 0.962979i \(0.413117\pi\)
\(402\) −1.76034e11 −0.336185
\(403\) 1.47737e11 0.279008
\(404\) −2.08587e11 −0.389558
\(405\) −2.78869e12 −5.15055
\(406\) −4.34083e11 −0.792877
\(407\) −3.26783e11 −0.590317
\(408\) 0 0
\(409\) −4.08871e11 −0.722490 −0.361245 0.932471i \(-0.617648\pi\)
−0.361245 + 0.932471i \(0.617648\pi\)
\(410\) 9.54656e10 0.166848
\(411\) −5.27363e11 −0.911637
\(412\) −3.25592e11 −0.556719
\(413\) −5.47401e11 −0.925828
\(414\) −1.20231e12 −2.01147
\(415\) 5.13859e11 0.850408
\(416\) −2.41733e11 −0.395746
\(417\) 2.29042e12 3.70939
\(418\) −1.44200e11 −0.231032
\(419\) 4.92234e11 0.780205 0.390103 0.920771i \(-0.372440\pi\)
0.390103 + 0.920771i \(0.372440\pi\)
\(420\) 9.55699e11 1.49865
\(421\) 7.95456e11 1.23409 0.617045 0.786928i \(-0.288330\pi\)
0.617045 + 0.786928i \(0.288330\pi\)
\(422\) −2.05103e11 −0.314822
\(423\) −2.61481e12 −3.97107
\(424\) 8.92807e11 1.34156
\(425\) 0 0
\(426\) 3.60874e11 0.530899
\(427\) −9.67109e11 −1.40783
\(428\) 2.06559e11 0.297542
\(429\) 6.00705e11 0.856255
\(430\) 6.81705e11 0.961587
\(431\) −1.05149e11 −0.146777 −0.0733884 0.997303i \(-0.523381\pi\)
−0.0733884 + 0.997303i \(0.523381\pi\)
\(432\) −7.45717e11 −1.03014
\(433\) −2.40019e11 −0.328134 −0.164067 0.986449i \(-0.552461\pi\)
−0.164067 + 0.986449i \(0.552461\pi\)
\(434\) −4.32764e11 −0.585528
\(435\) −1.42400e12 −1.90681
\(436\) −2.89516e11 −0.383692
\(437\) 2.51713e11 0.330171
\(438\) 1.30802e12 1.69816
\(439\) 9.58953e11 1.23227 0.616137 0.787639i \(-0.288697\pi\)
0.616137 + 0.787639i \(0.288697\pi\)
\(440\) −9.34145e11 −1.18817
\(441\) 1.80354e12 2.27065
\(442\) 0 0
\(443\) −1.36741e12 −1.68688 −0.843439 0.537225i \(-0.819472\pi\)
−0.843439 + 0.537225i \(0.819472\pi\)
\(444\) 4.85654e11 0.593067
\(445\) 1.07575e12 1.30045
\(446\) −9.16353e11 −1.09662
\(447\) 3.83337e11 0.454147
\(448\) 1.02632e12 1.20374
\(449\) 7.35282e11 0.853779 0.426889 0.904304i \(-0.359609\pi\)
0.426889 + 0.904304i \(0.359609\pi\)
\(450\) −6.71758e11 −0.772247
\(451\) 1.65796e11 0.188704
\(452\) 3.24422e11 0.365584
\(453\) 1.94974e12 2.17538
\(454\) 8.02551e10 0.0886587
\(455\) −6.55648e11 −0.717165
\(456\) 6.55809e11 0.710290
\(457\) −1.16538e12 −1.24981 −0.624904 0.780702i \(-0.714862\pi\)
−0.624904 + 0.780702i \(0.714862\pi\)
\(458\) 9.23442e11 0.980652
\(459\) 0 0
\(460\) 5.32856e11 0.554880
\(461\) 1.00400e12 1.03533 0.517665 0.855583i \(-0.326801\pi\)
0.517665 + 0.855583i \(0.326801\pi\)
\(462\) −1.75964e12 −1.79694
\(463\) 7.44078e11 0.752496 0.376248 0.926519i \(-0.377214\pi\)
0.376248 + 0.926519i \(0.377214\pi\)
\(464\) −2.30149e11 −0.230504
\(465\) −1.41967e12 −1.40815
\(466\) −1.20495e12 −1.18367
\(467\) −8.92235e11 −0.868067 −0.434034 0.900897i \(-0.642910\pi\)
−0.434034 + 0.900897i \(0.642910\pi\)
\(468\) −6.62396e11 −0.638280
\(469\) 3.33683e11 0.318461
\(470\) −1.22859e12 −1.16136
\(471\) −1.05655e12 −0.989226
\(472\) −7.95181e11 −0.737441
\(473\) 1.18393e12 1.08755
\(474\) 2.34774e12 2.13623
\(475\) 1.40638e11 0.126760
\(476\) 0 0
\(477\) 4.09347e12 3.62042
\(478\) −7.26015e11 −0.636092
\(479\) 8.19136e8 0.000710962 0 0.000355481 1.00000i \(-0.499887\pi\)
0.000355481 1.00000i \(0.499887\pi\)
\(480\) 2.32292e12 1.99733
\(481\) −3.33179e11 −0.283808
\(482\) −4.55490e11 −0.384386
\(483\) 3.07159e12 2.56804
\(484\) 5.58579e10 0.0462679
\(485\) −1.82323e11 −0.149625
\(486\) −4.37315e12 −3.55575
\(487\) −2.03907e12 −1.64267 −0.821336 0.570444i \(-0.806771\pi\)
−0.821336 + 0.570444i \(0.806771\pi\)
\(488\) −1.40487e12 −1.12136
\(489\) −3.20879e12 −2.53777
\(490\) 8.47410e11 0.664066
\(491\) −6.01145e11 −0.466780 −0.233390 0.972383i \(-0.574982\pi\)
−0.233390 + 0.972383i \(0.574982\pi\)
\(492\) −2.46401e11 −0.189583
\(493\) 0 0
\(494\) −1.47022e11 −0.111074
\(495\) −4.28300e12 −3.20645
\(496\) −2.29450e11 −0.170224
\(497\) −6.84058e11 −0.502909
\(498\) 1.40609e12 1.02443
\(499\) −1.26416e12 −0.912742 −0.456371 0.889790i \(-0.650851\pi\)
−0.456371 + 0.889790i \(0.650851\pi\)
\(500\) −4.97548e11 −0.356017
\(501\) −9.58482e11 −0.679695
\(502\) −1.06049e12 −0.745313
\(503\) 4.72983e11 0.329450 0.164725 0.986340i \(-0.447326\pi\)
0.164725 + 0.986340i \(0.447326\pi\)
\(504\) 5.93779e12 4.09909
\(505\) −1.37511e12 −0.940860
\(506\) −9.81096e11 −0.665326
\(507\) −2.31644e12 −1.55699
\(508\) −3.39791e11 −0.226373
\(509\) 7.50257e11 0.495427 0.247714 0.968833i \(-0.420321\pi\)
0.247714 + 0.968833i \(0.420321\pi\)
\(510\) 0 0
\(511\) −2.47942e12 −1.60863
\(512\) 8.37693e11 0.538729
\(513\) 1.96120e12 1.25024
\(514\) −6.97724e11 −0.440910
\(515\) −2.14645e12 −1.34459
\(516\) −1.75951e12 −1.09262
\(517\) −2.13371e12 −1.31350
\(518\) 9.75976e11 0.595601
\(519\) 3.76857e10 0.0227994
\(520\) −9.52426e11 −0.571237
\(521\) 5.40736e11 0.321525 0.160763 0.986993i \(-0.448605\pi\)
0.160763 + 0.986993i \(0.448605\pi\)
\(522\) −2.89113e12 −1.70432
\(523\) 6.61335e11 0.386513 0.193256 0.981148i \(-0.438095\pi\)
0.193256 + 0.981148i \(0.438095\pi\)
\(524\) −9.08123e11 −0.526204
\(525\) 1.71617e12 0.985926
\(526\) −3.61306e11 −0.205797
\(527\) 0 0
\(528\) −9.32953e11 −0.522405
\(529\) −8.85673e10 −0.0491726
\(530\) 1.92336e12 1.05881
\(531\) −3.64586e12 −1.99010
\(532\) −4.06228e11 −0.219871
\(533\) 1.69041e11 0.0907235
\(534\) 2.94362e12 1.56656
\(535\) 1.36174e12 0.718623
\(536\) 4.84724e11 0.253660
\(537\) 4.60521e12 2.38982
\(538\) −4.39008e11 −0.225919
\(539\) 1.47171e12 0.751055
\(540\) 4.15171e12 2.10114
\(541\) −2.26946e12 −1.13903 −0.569514 0.821982i \(-0.692869\pi\)
−0.569514 + 0.821982i \(0.692869\pi\)
\(542\) −1.95725e12 −0.974205
\(543\) −1.43361e12 −0.707672
\(544\) 0 0
\(545\) −1.90862e12 −0.926694
\(546\) −1.79407e12 −0.863919
\(547\) −9.44132e11 −0.450910 −0.225455 0.974254i \(-0.572387\pi\)
−0.225455 + 0.974254i \(0.572387\pi\)
\(548\) 4.74530e11 0.224776
\(549\) −6.44125e12 −3.02618
\(550\) −5.48163e11 −0.255433
\(551\) 6.05283e11 0.279754
\(552\) 4.46194e12 2.04549
\(553\) −4.45029e12 −2.02360
\(554\) 2.38400e12 1.07526
\(555\) 3.20166e12 1.43238
\(556\) −2.06095e12 −0.914601
\(557\) −2.30243e12 −1.01354 −0.506768 0.862083i \(-0.669160\pi\)
−0.506768 + 0.862083i \(0.669160\pi\)
\(558\) −2.88235e12 −1.25861
\(559\) 1.20710e12 0.522864
\(560\) 1.01829e12 0.437546
\(561\) 0 0
\(562\) 2.83999e12 1.20089
\(563\) 1.68590e12 0.707201 0.353601 0.935396i \(-0.384957\pi\)
0.353601 + 0.935396i \(0.384957\pi\)
\(564\) 3.17106e12 1.31962
\(565\) 2.13874e12 0.882959
\(566\) −1.33492e12 −0.546740
\(567\) 1.44647e13 5.87739
\(568\) −9.93696e11 −0.400577
\(569\) −4.88221e12 −1.95259 −0.976295 0.216443i \(-0.930554\pi\)
−0.976295 + 0.216443i \(0.930554\pi\)
\(570\) 1.41280e12 0.560588
\(571\) 1.28951e12 0.507649 0.253824 0.967250i \(-0.418311\pi\)
0.253824 + 0.967250i \(0.418311\pi\)
\(572\) −5.40523e11 −0.211121
\(573\) 7.94737e12 3.07984
\(574\) −4.95170e11 −0.190393
\(575\) 9.56864e11 0.365044
\(576\) 6.83564e12 2.58749
\(577\) 3.35989e12 1.26193 0.630963 0.775813i \(-0.282660\pi\)
0.630963 + 0.775813i \(0.282660\pi\)
\(578\) 0 0
\(579\) −5.32090e12 −1.96758
\(580\) 1.28133e12 0.470150
\(581\) −2.66533e12 −0.970417
\(582\) −4.98898e11 −0.180243
\(583\) 3.34032e12 1.19751
\(584\) −3.60173e12 −1.28131
\(585\) −4.36682e12 −1.54157
\(586\) 2.79780e11 0.0980117
\(587\) 1.98787e11 0.0691059 0.0345530 0.999403i \(-0.488999\pi\)
0.0345530 + 0.999403i \(0.488999\pi\)
\(588\) −2.18720e12 −0.754555
\(589\) 6.03444e11 0.206594
\(590\) −1.71305e12 −0.582016
\(591\) 2.06204e12 0.695269
\(592\) 5.17459e11 0.173152
\(593\) −1.77542e12 −0.589598 −0.294799 0.955559i \(-0.595253\pi\)
−0.294799 + 0.955559i \(0.595253\pi\)
\(594\) −7.64414e12 −2.51936
\(595\) 0 0
\(596\) −3.44932e11 −0.111976
\(597\) −7.57832e12 −2.44168
\(598\) −1.00030e12 −0.319870
\(599\) −5.82261e12 −1.84798 −0.923990 0.382418i \(-0.875092\pi\)
−0.923990 + 0.382418i \(0.875092\pi\)
\(600\) 2.49300e12 0.785310
\(601\) −6.05010e12 −1.89159 −0.945796 0.324761i \(-0.894716\pi\)
−0.945796 + 0.324761i \(0.894716\pi\)
\(602\) −3.53593e12 −1.09728
\(603\) 2.22243e12 0.684543
\(604\) −1.75440e12 −0.536369
\(605\) 3.68241e11 0.111746
\(606\) −3.76275e12 −1.13339
\(607\) −2.29272e12 −0.685492 −0.342746 0.939428i \(-0.611357\pi\)
−0.342746 + 0.939428i \(0.611357\pi\)
\(608\) −9.87379e11 −0.293034
\(609\) 7.38612e12 2.17590
\(610\) −3.02649e12 −0.885024
\(611\) −2.17547e12 −0.631492
\(612\) 0 0
\(613\) −2.58028e12 −0.738064 −0.369032 0.929417i \(-0.620311\pi\)
−0.369032 + 0.929417i \(0.620311\pi\)
\(614\) 4.15799e12 1.18066
\(615\) −1.62439e12 −0.457881
\(616\) 4.84531e12 1.35584
\(617\) 4.99510e12 1.38759 0.693795 0.720172i \(-0.255937\pi\)
0.693795 + 0.720172i \(0.255937\pi\)
\(618\) −5.87342e12 −1.61973
\(619\) 6.13894e12 1.68068 0.840341 0.542058i \(-0.182355\pi\)
0.840341 + 0.542058i \(0.182355\pi\)
\(620\) 1.27744e12 0.347199
\(621\) 1.33435e13 3.60045
\(622\) 1.58540e12 0.424700
\(623\) −5.57981e12 −1.48396
\(624\) −9.51212e11 −0.251158
\(625\) −4.70816e12 −1.23422
\(626\) 3.83564e12 0.998283
\(627\) 2.45363e12 0.634022
\(628\) 9.50698e11 0.243907
\(629\) 0 0
\(630\) 1.27917e13 3.23516
\(631\) 1.08545e11 0.0272569 0.0136284 0.999907i \(-0.495662\pi\)
0.0136284 + 0.999907i \(0.495662\pi\)
\(632\) −6.46470e12 −1.61184
\(633\) 3.48991e12 0.863969
\(634\) 7.31610e11 0.179837
\(635\) −2.24006e12 −0.546737
\(636\) −4.96428e12 −1.20309
\(637\) 1.50051e12 0.361086
\(638\) −2.35920e12 −0.563730
\(639\) −4.55604e12 −1.08102
\(640\) −1.09436e12 −0.257841
\(641\) 3.07759e12 0.720029 0.360014 0.932947i \(-0.382772\pi\)
0.360014 + 0.932947i \(0.382772\pi\)
\(642\) 3.72617e12 0.865676
\(643\) 1.79981e12 0.415219 0.207609 0.978212i \(-0.433432\pi\)
0.207609 + 0.978212i \(0.433432\pi\)
\(644\) −2.76386e12 −0.633185
\(645\) −1.15995e13 −2.63889
\(646\) 0 0
\(647\) −1.16719e12 −0.261861 −0.130931 0.991392i \(-0.541797\pi\)
−0.130931 + 0.991392i \(0.541797\pi\)
\(648\) 2.10121e13 4.68146
\(649\) −2.97507e12 −0.658258
\(650\) −5.58890e11 −0.122805
\(651\) 7.36368e12 1.60687
\(652\) 2.88732e12 0.625721
\(653\) 4.28149e12 0.921480 0.460740 0.887535i \(-0.347584\pi\)
0.460740 + 0.887535i \(0.347584\pi\)
\(654\) −5.22264e12 −1.11632
\(655\) −5.98678e12 −1.27089
\(656\) −2.62537e11 −0.0553508
\(657\) −1.65138e13 −3.45781
\(658\) 6.37258e12 1.32525
\(659\) −2.61751e12 −0.540636 −0.270318 0.962771i \(-0.587129\pi\)
−0.270318 + 0.962771i \(0.587129\pi\)
\(660\) 5.19413e12 1.06553
\(661\) −6.71780e11 −0.136874 −0.0684369 0.997655i \(-0.521801\pi\)
−0.0684369 + 0.997655i \(0.521801\pi\)
\(662\) 8.58499e11 0.173732
\(663\) 0 0
\(664\) −3.87179e12 −0.772957
\(665\) −2.67805e12 −0.531032
\(666\) 6.50031e12 1.28027
\(667\) 4.11818e12 0.805636
\(668\) 8.62456e11 0.167588
\(669\) 1.55922e13 3.00946
\(670\) 1.04423e12 0.200199
\(671\) −5.25614e12 −1.00096
\(672\) −1.20487e13 −2.27919
\(673\) −5.97945e11 −0.112355 −0.0561776 0.998421i \(-0.517891\pi\)
−0.0561776 + 0.998421i \(0.517891\pi\)
\(674\) −2.59580e12 −0.484509
\(675\) 7.45533e12 1.38229
\(676\) 2.08437e12 0.383896
\(677\) 1.85086e12 0.338630 0.169315 0.985562i \(-0.445844\pi\)
0.169315 + 0.985562i \(0.445844\pi\)
\(678\) 5.85232e12 1.06364
\(679\) 9.45691e11 0.170740
\(680\) 0 0
\(681\) −1.36558e12 −0.243307
\(682\) −2.35203e12 −0.416307
\(683\) 3.09984e12 0.545062 0.272531 0.962147i \(-0.412139\pi\)
0.272531 + 0.962147i \(0.412139\pi\)
\(684\) −2.70561e12 −0.472621
\(685\) 3.12832e12 0.542880
\(686\) 1.17100e12 0.201883
\(687\) −1.57128e13 −2.69121
\(688\) −1.87474e12 −0.319001
\(689\) 3.40569e12 0.575730
\(690\) 9.61230e12 1.61438
\(691\) −2.04515e12 −0.341250 −0.170625 0.985336i \(-0.554579\pi\)
−0.170625 + 0.985336i \(0.554579\pi\)
\(692\) −3.39102e10 −0.00562150
\(693\) 2.22155e13 3.65895
\(694\) 7.23443e12 1.18382
\(695\) −1.35868e13 −2.20895
\(696\) 1.07294e13 1.73315
\(697\) 0 0
\(698\) 4.40100e11 0.0701781
\(699\) 2.05027e13 3.24836
\(700\) −1.54424e12 −0.243093
\(701\) 5.75738e12 0.900521 0.450261 0.892897i \(-0.351331\pi\)
0.450261 + 0.892897i \(0.351331\pi\)
\(702\) −7.79374e12 −1.21124
\(703\) −1.36090e12 −0.210148
\(704\) 5.57797e12 0.855852
\(705\) 2.09051e13 3.18714
\(706\) 5.71652e12 0.865986
\(707\) 7.13253e12 1.07363
\(708\) 4.42145e12 0.661325
\(709\) 2.30053e11 0.0341917 0.0170958 0.999854i \(-0.494558\pi\)
0.0170958 + 0.999854i \(0.494558\pi\)
\(710\) −2.14070e12 −0.316151
\(711\) −2.96403e13 −4.34980
\(712\) −8.10551e12 −1.18201
\(713\) 4.10567e12 0.594950
\(714\) 0 0
\(715\) −3.56338e12 −0.509900
\(716\) −4.14384e12 −0.589242
\(717\) 1.23535e13 1.74563
\(718\) 5.32642e12 0.747955
\(719\) 2.92429e12 0.408076 0.204038 0.978963i \(-0.434593\pi\)
0.204038 + 0.978963i \(0.434593\pi\)
\(720\) 6.78211e12 0.940521
\(721\) 1.11334e13 1.53433
\(722\) 4.63733e12 0.635112
\(723\) 7.75037e12 1.05487
\(724\) 1.28998e12 0.174486
\(725\) 2.30093e12 0.309301
\(726\) 1.00763e12 0.134613
\(727\) −1.35766e13 −1.80255 −0.901276 0.433246i \(-0.857368\pi\)
−0.901276 + 0.433246i \(0.857368\pi\)
\(728\) 4.94013e12 0.651849
\(729\) 4.09087e13 5.36465
\(730\) −7.75916e12 −1.01126
\(731\) 0 0
\(732\) 7.81150e12 1.00562
\(733\) 1.01336e12 0.129656 0.0648282 0.997896i \(-0.479350\pi\)
0.0648282 + 0.997896i \(0.479350\pi\)
\(734\) 6.10818e12 0.776747
\(735\) −1.44191e13 −1.82240
\(736\) −6.71785e12 −0.843879
\(737\) 1.81353e12 0.226424
\(738\) −3.29799e12 −0.409256
\(739\) −7.79008e12 −0.960820 −0.480410 0.877044i \(-0.659512\pi\)
−0.480410 + 0.877044i \(0.659512\pi\)
\(740\) −2.88090e12 −0.353172
\(741\) 2.50165e12 0.304820
\(742\) −9.97626e12 −1.20823
\(743\) −8.73895e12 −1.05199 −0.525993 0.850489i \(-0.676306\pi\)
−0.525993 + 0.850489i \(0.676306\pi\)
\(744\) 1.06968e13 1.27990
\(745\) −2.27396e12 −0.270445
\(746\) −4.04336e12 −0.477989
\(747\) −1.77519e13 −2.08595
\(748\) 0 0
\(749\) −7.06318e12 −0.820035
\(750\) −8.97538e12 −1.03580
\(751\) −1.44210e12 −0.165430 −0.0827152 0.996573i \(-0.526359\pi\)
−0.0827152 + 0.996573i \(0.526359\pi\)
\(752\) 3.37872e12 0.385276
\(753\) 1.80447e13 2.04537
\(754\) −2.40537e12 −0.271026
\(755\) −1.15659e13 −1.29544
\(756\) −2.15344e13 −2.39765
\(757\) −2.38384e12 −0.263843 −0.131921 0.991260i \(-0.542115\pi\)
−0.131921 + 0.991260i \(0.542115\pi\)
\(758\) −1.22522e13 −1.34805
\(759\) 1.66938e13 1.82586
\(760\) −3.89026e12 −0.422978
\(761\) −1.06430e13 −1.15035 −0.575177 0.818029i \(-0.695067\pi\)
−0.575177 + 0.818029i \(0.695067\pi\)
\(762\) −6.12957e12 −0.658616
\(763\) 9.89983e12 1.05747
\(764\) −7.15116e12 −0.759375
\(765\) 0 0
\(766\) −9.61301e12 −1.00886
\(767\) −3.03329e12 −0.316472
\(768\) −2.00729e13 −2.08202
\(769\) 3.67087e12 0.378530 0.189265 0.981926i \(-0.439390\pi\)
0.189265 + 0.981926i \(0.439390\pi\)
\(770\) 1.04382e13 1.07008
\(771\) 1.18721e13 1.20999
\(772\) 4.78783e12 0.485133
\(773\) 3.56580e12 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(774\) −2.35504e13 −2.35865
\(775\) 2.29394e12 0.228415
\(776\) 1.37376e12 0.135998
\(777\) −1.66067e13 −1.63451
\(778\) −1.41522e13 −1.38489
\(779\) 6.90462e11 0.0671771
\(780\) 5.29578e12 0.512276
\(781\) −3.71779e12 −0.357565
\(782\) 0 0
\(783\) 3.20865e13 3.05066
\(784\) −2.33044e12 −0.220300
\(785\) 6.26745e12 0.589084
\(786\) −1.63818e13 −1.53095
\(787\) −1.73599e13 −1.61310 −0.806549 0.591167i \(-0.798667\pi\)
−0.806549 + 0.591167i \(0.798667\pi\)
\(788\) −1.85545e12 −0.171428
\(789\) 6.14779e12 0.564771
\(790\) −1.39268e13 −1.27213
\(791\) −1.10934e13 −1.00756
\(792\) 3.22713e13 2.91442
\(793\) −5.35900e12 −0.481232
\(794\) −3.14057e12 −0.280425
\(795\) −3.27268e13 −2.90571
\(796\) 6.81909e12 0.602029
\(797\) 3.92379e12 0.344464 0.172232 0.985056i \(-0.444902\pi\)
0.172232 + 0.985056i \(0.444902\pi\)
\(798\) −7.32804e12 −0.639698
\(799\) 0 0
\(800\) −3.75343e12 −0.323984
\(801\) −3.71633e13 −3.18984
\(802\) −4.53138e12 −0.386764
\(803\) −1.34754e13 −1.14373
\(804\) −2.69521e12 −0.227479
\(805\) −1.82207e13 −1.52927
\(806\) −2.39806e12 −0.200149
\(807\) 7.46992e12 0.619990
\(808\) 1.03611e13 0.855171
\(809\) 3.19512e12 0.262252 0.131126 0.991366i \(-0.458141\pi\)
0.131126 + 0.991366i \(0.458141\pi\)
\(810\) 4.52660e13 3.69479
\(811\) 1.04002e13 0.844204 0.422102 0.906548i \(-0.361292\pi\)
0.422102 + 0.906548i \(0.361292\pi\)
\(812\) −6.64614e12 −0.536497
\(813\) 3.33036e13 2.67352
\(814\) 5.30433e12 0.423468
\(815\) 1.90346e13 1.51124
\(816\) 0 0
\(817\) 4.93048e12 0.387160
\(818\) 6.63678e12 0.518284
\(819\) 2.26502e13 1.75912
\(820\) 1.46165e12 0.112897
\(821\) 5.23470e12 0.402112 0.201056 0.979580i \(-0.435563\pi\)
0.201056 + 0.979580i \(0.435563\pi\)
\(822\) 8.56014e12 0.653970
\(823\) 2.49083e13 1.89254 0.946271 0.323375i \(-0.104817\pi\)
0.946271 + 0.323375i \(0.104817\pi\)
\(824\) 1.61730e13 1.22213
\(825\) 9.32724e12 0.700987
\(826\) 8.88539e12 0.664150
\(827\) 5.31180e12 0.394882 0.197441 0.980315i \(-0.436737\pi\)
0.197441 + 0.980315i \(0.436737\pi\)
\(828\) −1.84082e13 −1.36105
\(829\) −1.03173e13 −0.758700 −0.379350 0.925253i \(-0.623852\pi\)
−0.379350 + 0.925253i \(0.623852\pi\)
\(830\) −8.34094e12 −0.610047
\(831\) −4.05648e13 −2.95083
\(832\) 5.68713e12 0.411470
\(833\) 0 0
\(834\) −3.71780e13 −2.66096
\(835\) 5.68572e12 0.404759
\(836\) −2.20781e12 −0.156327
\(837\) 3.19890e13 2.25287
\(838\) −7.98993e12 −0.559686
\(839\) −8.51253e12 −0.593103 −0.296551 0.955017i \(-0.595837\pi\)
−0.296551 + 0.955017i \(0.595837\pi\)
\(840\) −4.74719e13 −3.28988
\(841\) −4.60435e12 −0.317385
\(842\) −1.29118e13 −0.885285
\(843\) −4.83237e13 −3.29561
\(844\) −3.14028e12 −0.213023
\(845\) 1.37411e13 0.927187
\(846\) 4.24434e13 2.84868
\(847\) −1.91003e12 −0.127516
\(848\) −5.28938e12 −0.351256
\(849\) 2.27143e13 1.50042
\(850\) 0 0
\(851\) −9.25916e12 −0.605185
\(852\) 5.52525e12 0.359231
\(853\) 2.58704e13 1.67314 0.836571 0.547858i \(-0.184557\pi\)
0.836571 + 0.547858i \(0.184557\pi\)
\(854\) 1.56981e13 1.00992
\(855\) −1.78367e13 −1.14147
\(856\) −1.02603e13 −0.653174
\(857\) −1.63312e13 −1.03420 −0.517100 0.855925i \(-0.672988\pi\)
−0.517100 + 0.855925i \(0.672988\pi\)
\(858\) −9.75061e12 −0.614241
\(859\) −1.45571e13 −0.912235 −0.456118 0.889919i \(-0.650760\pi\)
−0.456118 + 0.889919i \(0.650760\pi\)
\(860\) 1.04374e13 0.650654
\(861\) 8.42554e12 0.522497
\(862\) 1.70677e12 0.105291
\(863\) −1.08493e13 −0.665817 −0.332909 0.942959i \(-0.608030\pi\)
−0.332909 + 0.942959i \(0.608030\pi\)
\(864\) −5.23417e13 −3.19548
\(865\) −2.23552e11 −0.0135771
\(866\) 3.89598e12 0.235389
\(867\) 0 0
\(868\) −6.62595e12 −0.396195
\(869\) −2.41869e13 −1.43877
\(870\) 2.31143e13 1.36787
\(871\) 1.84902e12 0.108858
\(872\) 1.43810e13 0.842294
\(873\) 6.29860e12 0.367012
\(874\) −4.08579e12 −0.236851
\(875\) 1.70134e13 0.981193
\(876\) 2.00267e13 1.14906
\(877\) 2.33213e12 0.133123 0.0665617 0.997782i \(-0.478797\pi\)
0.0665617 + 0.997782i \(0.478797\pi\)
\(878\) −1.55657e13 −0.883981
\(879\) −4.76059e12 −0.268974
\(880\) 5.53428e12 0.311092
\(881\) 1.99931e13 1.11812 0.559061 0.829127i \(-0.311162\pi\)
0.559061 + 0.829127i \(0.311162\pi\)
\(882\) −2.92749e13 −1.62887
\(883\) 1.20279e13 0.665834 0.332917 0.942956i \(-0.391967\pi\)
0.332917 + 0.942956i \(0.391967\pi\)
\(884\) 0 0
\(885\) 2.91483e13 1.59723
\(886\) 2.21958e13 1.21009
\(887\) 2.98647e11 0.0161995 0.00809975 0.999967i \(-0.497422\pi\)
0.00809975 + 0.999967i \(0.497422\pi\)
\(888\) −2.41237e13 −1.30192
\(889\) 1.16190e13 0.623892
\(890\) −1.74616e13 −0.932886
\(891\) 7.86140e13 4.17879
\(892\) −1.40301e13 −0.742023
\(893\) −8.88590e12 −0.467595
\(894\) −6.22231e12 −0.325786
\(895\) −2.73181e13 −1.42314
\(896\) 5.67635e12 0.294227
\(897\) 1.70205e13 0.877822
\(898\) −1.19351e13 −0.612465
\(899\) 9.87271e12 0.504101
\(900\) −1.02851e13 −0.522538
\(901\) 0 0
\(902\) −2.69120e12 −0.135368
\(903\) 6.01654e13 3.01129
\(904\) −1.61149e13 −0.802543
\(905\) 8.50419e12 0.421419
\(906\) −3.16481e13 −1.56052
\(907\) 1.85478e13 0.910041 0.455020 0.890481i \(-0.349632\pi\)
0.455020 + 0.890481i \(0.349632\pi\)
\(908\) 1.22877e12 0.0599906
\(909\) 4.75049e13 2.30781
\(910\) 1.06424e13 0.514464
\(911\) 2.65224e13 1.27580 0.637898 0.770121i \(-0.279804\pi\)
0.637898 + 0.770121i \(0.279804\pi\)
\(912\) −3.88530e12 −0.185972
\(913\) −1.44858e13 −0.689960
\(914\) 1.89163e13 0.896559
\(915\) 5.14971e13 2.42878
\(916\) 1.41386e13 0.663555
\(917\) 3.10528e13 1.45023
\(918\) 0 0
\(919\) 2.29442e13 1.06109 0.530546 0.847656i \(-0.321987\pi\)
0.530546 + 0.847656i \(0.321987\pi\)
\(920\) −2.64683e13 −1.21809
\(921\) −7.07502e13 −3.24010
\(922\) −1.62969e13 −0.742702
\(923\) −3.79055e12 −0.171907
\(924\) −2.69414e13 −1.21589
\(925\) −5.17332e12 −0.232344
\(926\) −1.20778e13 −0.539809
\(927\) 7.41521e13 3.29811
\(928\) −1.61541e13 −0.715019
\(929\) 3.61411e13 1.59195 0.795977 0.605326i \(-0.206957\pi\)
0.795977 + 0.605326i \(0.206957\pi\)
\(930\) 2.30440e13 1.01015
\(931\) 6.12895e12 0.267370
\(932\) −1.84487e13 −0.800928
\(933\) −2.69763e13 −1.16551
\(934\) 1.44827e13 0.622715
\(935\) 0 0
\(936\) 3.29028e13 1.40117
\(937\) 1.16635e13 0.494313 0.247156 0.968976i \(-0.420504\pi\)
0.247156 + 0.968976i \(0.420504\pi\)
\(938\) −5.41632e12 −0.228450
\(939\) −6.52652e13 −2.73960
\(940\) −1.88107e13 −0.785832
\(941\) −1.60493e13 −0.667273 −0.333636 0.942702i \(-0.608276\pi\)
−0.333636 + 0.942702i \(0.608276\pi\)
\(942\) 1.71498e13 0.709629
\(943\) 4.69771e12 0.193457
\(944\) 4.71100e12 0.193081
\(945\) −1.41965e14 −5.79080
\(946\) −1.92174e13 −0.780163
\(947\) −1.18470e13 −0.478667 −0.239334 0.970937i \(-0.576929\pi\)
−0.239334 + 0.970937i \(0.576929\pi\)
\(948\) 3.59457e13 1.44547
\(949\) −1.37391e13 −0.549872
\(950\) −2.28283e12 −0.0909323
\(951\) −1.24487e13 −0.493527
\(952\) 0 0
\(953\) 4.20395e13 1.65097 0.825485 0.564424i \(-0.190902\pi\)
0.825485 + 0.564424i \(0.190902\pi\)
\(954\) −6.64450e13 −2.59714
\(955\) −4.71438e13 −1.83404
\(956\) −1.11158e13 −0.430409
\(957\) 4.01428e13 1.54705
\(958\) −1.32962e10 −0.000510014 0
\(959\) −1.62263e13 −0.619491
\(960\) −5.46502e13 −2.07669
\(961\) −1.65969e13 −0.627728
\(962\) 5.40814e12 0.203592
\(963\) −4.70430e13 −1.76269
\(964\) −6.97390e12 −0.260093
\(965\) 3.15636e13 1.17169
\(966\) −4.98579e13 −1.84220
\(967\) −9.82534e12 −0.361350 −0.180675 0.983543i \(-0.557828\pi\)
−0.180675 + 0.983543i \(0.557828\pi\)
\(968\) −2.77460e12 −0.101569
\(969\) 0 0
\(970\) 2.95946e12 0.107335
\(971\) −1.13310e13 −0.409053 −0.204527 0.978861i \(-0.565566\pi\)
−0.204527 + 0.978861i \(0.565566\pi\)
\(972\) −6.69562e13 −2.40598
\(973\) 7.04732e13 2.52067
\(974\) 3.30980e13 1.17838
\(975\) 9.50977e12 0.337015
\(976\) 8.32306e12 0.293602
\(977\) −3.63787e13 −1.27738 −0.638692 0.769463i \(-0.720524\pi\)
−0.638692 + 0.769463i \(0.720524\pi\)
\(978\) 5.20850e13 1.82049
\(979\) −3.03257e13 −1.05509
\(980\) 1.29745e13 0.449338
\(981\) 6.59360e13 2.27307
\(982\) 9.75776e12 0.334848
\(983\) 3.68939e13 1.26027 0.630136 0.776485i \(-0.282999\pi\)
0.630136 + 0.776485i \(0.282999\pi\)
\(984\) 1.22394e13 0.416179
\(985\) −1.22320e13 −0.414033
\(986\) 0 0
\(987\) −1.08432e14 −3.63690
\(988\) −2.25102e12 −0.0751576
\(989\) 3.35456e13 1.11494
\(990\) 6.95215e13 2.30018
\(991\) −4.52933e13 −1.49177 −0.745885 0.666074i \(-0.767973\pi\)
−0.745885 + 0.666074i \(0.767973\pi\)
\(992\) −1.61050e13 −0.528031
\(993\) −1.46078e13 −0.476773
\(994\) 1.11036e13 0.360765
\(995\) 4.49546e13 1.45402
\(996\) 2.15283e13 0.693175
\(997\) −2.93423e13 −0.940515 −0.470257 0.882529i \(-0.655839\pi\)
−0.470257 + 0.882529i \(0.655839\pi\)
\(998\) 2.05197e13 0.654763
\(999\) −7.21421e13 −2.29163
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.1.13 yes 36
17.16 even 2 289.10.a.g.1.13 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.13 36 17.16 even 2
289.10.a.h.1.13 yes 36 1.1 even 1 trivial