Properties

Label 289.10.a.g.1.15
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 1.15
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.3896 q^{2} +121.426 q^{3} -404.056 q^{4} -1455.35 q^{5} -1261.57 q^{6} +5787.38 q^{7} +9517.45 q^{8} -4938.65 q^{9} +O(q^{10})\) \(q-10.3896 q^{2} +121.426 q^{3} -404.056 q^{4} -1455.35 q^{5} -1261.57 q^{6} +5787.38 q^{7} +9517.45 q^{8} -4938.65 q^{9} +15120.5 q^{10} +2333.01 q^{11} -49063.1 q^{12} +34111.1 q^{13} -60128.5 q^{14} -176718. q^{15} +107995. q^{16} +51310.5 q^{18} -247026. q^{19} +588043. q^{20} +702741. q^{21} -24239.0 q^{22} -666606. q^{23} +1.15567e6 q^{24} +164913. q^{25} -354400. q^{26} -2.98972e6 q^{27} -2.33843e6 q^{28} -2.98746e6 q^{29} +1.83602e6 q^{30} +7.53740e6 q^{31} -5.99495e6 q^{32} +283288. q^{33} -8.42266e6 q^{35} +1.99549e6 q^{36} -981789. q^{37} +2.56650e6 q^{38} +4.14198e6 q^{39} -1.38512e7 q^{40} +2.32449e7 q^{41} -7.30119e6 q^{42} +2.36383e7 q^{43} -942666. q^{44} +7.18745e6 q^{45} +6.92576e6 q^{46} +5.99211e7 q^{47} +1.31134e7 q^{48} -6.85981e6 q^{49} -1.71337e6 q^{50} -1.37828e7 q^{52} +5.88160e7 q^{53} +3.10619e7 q^{54} -3.39534e6 q^{55} +5.50811e7 q^{56} -2.99955e7 q^{57} +3.10385e7 q^{58} -1.19067e8 q^{59} +7.14039e7 q^{60} +1.73852e8 q^{61} -7.83105e7 q^{62} -2.85819e7 q^{63} +6.99189e6 q^{64} -4.96435e7 q^{65} -2.94325e6 q^{66} -2.80991e8 q^{67} -8.09435e7 q^{69} +8.75079e7 q^{70} +1.98936e7 q^{71} -4.70033e7 q^{72} +3.38604e8 q^{73} +1.02004e7 q^{74} +2.00247e7 q^{75} +9.98126e7 q^{76} +1.35020e7 q^{77} -4.30335e7 q^{78} +1.90781e8 q^{79} -1.57170e8 q^{80} -2.65823e8 q^{81} -2.41505e8 q^{82} -5.33966e8 q^{83} -2.83947e8 q^{84} -2.45592e8 q^{86} -3.62756e8 q^{87} +2.22043e7 q^{88} -7.82829e8 q^{89} -7.46747e7 q^{90} +1.97414e8 q^{91} +2.69346e8 q^{92} +9.15239e8 q^{93} -6.22555e8 q^{94} +3.59509e8 q^{95} -7.27945e8 q^{96} -1.10279e9 q^{97} +7.12705e7 q^{98} -1.15219e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.3896 −0.459159 −0.229580 0.973290i \(-0.573735\pi\)
−0.229580 + 0.973290i \(0.573735\pi\)
\(3\) 121.426 0.865500 0.432750 0.901514i \(-0.357543\pi\)
0.432750 + 0.901514i \(0.357543\pi\)
\(4\) −404.056 −0.789173
\(5\) −1455.35 −1.04136 −0.520681 0.853751i \(-0.674322\pi\)
−0.520681 + 0.853751i \(0.674322\pi\)
\(6\) −1261.57 −0.397402
\(7\) 5787.38 0.911048 0.455524 0.890224i \(-0.349452\pi\)
0.455524 + 0.890224i \(0.349452\pi\)
\(8\) 9517.45 0.821515
\(9\) −4938.65 −0.250909
\(10\) 15120.5 0.478151
\(11\) 2333.01 0.0480451 0.0240225 0.999711i \(-0.492353\pi\)
0.0240225 + 0.999711i \(0.492353\pi\)
\(12\) −49063.1 −0.683029
\(13\) 34111.1 0.331246 0.165623 0.986189i \(-0.447037\pi\)
0.165623 + 0.986189i \(0.447037\pi\)
\(14\) −60128.5 −0.418316
\(15\) −176718. −0.901299
\(16\) 107995. 0.411966
\(17\) 0 0
\(18\) 51310.5 0.115207
\(19\) −247026. −0.434862 −0.217431 0.976076i \(-0.569768\pi\)
−0.217431 + 0.976076i \(0.569768\pi\)
\(20\) 588043. 0.821815
\(21\) 702741. 0.788512
\(22\) −24239.0 −0.0220603
\(23\) −666606. −0.496700 −0.248350 0.968670i \(-0.579888\pi\)
−0.248350 + 0.968670i \(0.579888\pi\)
\(24\) 1.15567e6 0.711022
\(25\) 164913. 0.0844352
\(26\) −354400. −0.152095
\(27\) −2.98972e6 −1.08266
\(28\) −2.33843e6 −0.718974
\(29\) −2.98746e6 −0.784352 −0.392176 0.919890i \(-0.628278\pi\)
−0.392176 + 0.919890i \(0.628278\pi\)
\(30\) 1.83602e6 0.413840
\(31\) 7.53740e6 1.46586 0.732932 0.680302i \(-0.238151\pi\)
0.732932 + 0.680302i \(0.238151\pi\)
\(32\) −5.99495e6 −1.01067
\(33\) 283288. 0.0415830
\(34\) 0 0
\(35\) −8.42266e6 −0.948730
\(36\) 1.99549e6 0.198011
\(37\) −981789. −0.0861213 −0.0430606 0.999072i \(-0.513711\pi\)
−0.0430606 + 0.999072i \(0.513711\pi\)
\(38\) 2.56650e6 0.199671
\(39\) 4.14198e6 0.286693
\(40\) −1.38512e7 −0.855495
\(41\) 2.32449e7 1.28470 0.642349 0.766412i \(-0.277960\pi\)
0.642349 + 0.766412i \(0.277960\pi\)
\(42\) −7.30119e6 −0.362053
\(43\) 2.36383e7 1.05441 0.527203 0.849739i \(-0.323241\pi\)
0.527203 + 0.849739i \(0.323241\pi\)
\(44\) −942666. −0.0379159
\(45\) 7.18745e6 0.261288
\(46\) 6.92576e6 0.228064
\(47\) 5.99211e7 1.79118 0.895590 0.444881i \(-0.146754\pi\)
0.895590 + 0.444881i \(0.146754\pi\)
\(48\) 1.31134e7 0.356557
\(49\) −6.85981e6 −0.169992
\(50\) −1.71337e6 −0.0387692
\(51\) 0 0
\(52\) −1.37828e7 −0.261410
\(53\) 5.88160e7 1.02389 0.511946 0.859017i \(-0.328925\pi\)
0.511946 + 0.859017i \(0.328925\pi\)
\(54\) 3.10619e7 0.497114
\(55\) −3.39534e6 −0.0500323
\(56\) 5.50811e7 0.748439
\(57\) −2.99955e7 −0.376374
\(58\) 3.10385e7 0.360142
\(59\) −1.19067e8 −1.27926 −0.639629 0.768684i \(-0.720912\pi\)
−0.639629 + 0.768684i \(0.720912\pi\)
\(60\) 7.14039e7 0.711281
\(61\) 1.73852e8 1.60766 0.803832 0.594857i \(-0.202791\pi\)
0.803832 + 0.594857i \(0.202791\pi\)
\(62\) −7.83105e7 −0.673065
\(63\) −2.85819e7 −0.228590
\(64\) 6.99189e6 0.0520936
\(65\) −4.96435e7 −0.344947
\(66\) −2.94325e6 −0.0190932
\(67\) −2.80991e8 −1.70355 −0.851776 0.523907i \(-0.824474\pi\)
−0.851776 + 0.523907i \(0.824474\pi\)
\(68\) 0 0
\(69\) −8.09435e7 −0.429894
\(70\) 8.75079e7 0.435618
\(71\) 1.98936e7 0.0929073 0.0464537 0.998920i \(-0.485208\pi\)
0.0464537 + 0.998920i \(0.485208\pi\)
\(72\) −4.70033e7 −0.206126
\(73\) 3.38604e8 1.39553 0.697764 0.716327i \(-0.254178\pi\)
0.697764 + 0.716327i \(0.254178\pi\)
\(74\) 1.02004e7 0.0395434
\(75\) 2.00247e7 0.0730787
\(76\) 9.98126e7 0.343182
\(77\) 1.35020e7 0.0437713
\(78\) −4.30335e7 −0.131638
\(79\) 1.90781e8 0.551078 0.275539 0.961290i \(-0.411144\pi\)
0.275539 + 0.961290i \(0.411144\pi\)
\(80\) −1.57170e8 −0.429006
\(81\) −2.65823e8 −0.686135
\(82\) −2.41505e8 −0.589881
\(83\) −5.33966e8 −1.23499 −0.617494 0.786576i \(-0.711852\pi\)
−0.617494 + 0.786576i \(0.711852\pi\)
\(84\) −2.83947e8 −0.622272
\(85\) 0 0
\(86\) −2.45592e8 −0.484141
\(87\) −3.62756e8 −0.678856
\(88\) 2.22043e7 0.0394697
\(89\) −7.82829e8 −1.32255 −0.661275 0.750144i \(-0.729984\pi\)
−0.661275 + 0.750144i \(0.729984\pi\)
\(90\) −7.46747e7 −0.119973
\(91\) 1.97414e8 0.301781
\(92\) 2.69346e8 0.391982
\(93\) 9.15239e8 1.26871
\(94\) −6.22555e8 −0.822437
\(95\) 3.59509e8 0.452849
\(96\) −7.27945e8 −0.874738
\(97\) −1.10279e9 −1.26479 −0.632397 0.774645i \(-0.717929\pi\)
−0.632397 + 0.774645i \(0.717929\pi\)
\(98\) 7.12705e7 0.0780536
\(99\) −1.15219e7 −0.0120550
\(100\) −6.66340e7 −0.0666340
\(101\) −8.85019e8 −0.846265 −0.423132 0.906068i \(-0.639069\pi\)
−0.423132 + 0.906068i \(0.639069\pi\)
\(102\) 0 0
\(103\) 1.22210e9 1.06989 0.534947 0.844886i \(-0.320332\pi\)
0.534947 + 0.844886i \(0.320332\pi\)
\(104\) 3.24651e8 0.272124
\(105\) −1.02273e9 −0.821126
\(106\) −6.11075e8 −0.470130
\(107\) −4.24642e8 −0.313181 −0.156591 0.987664i \(-0.550050\pi\)
−0.156591 + 0.987664i \(0.550050\pi\)
\(108\) 1.20801e9 0.854408
\(109\) 625767. 0.000424613 0 0.000212307 1.00000i \(-0.499932\pi\)
0.000212307 1.00000i \(0.499932\pi\)
\(110\) 3.52761e7 0.0229728
\(111\) −1.19215e8 −0.0745380
\(112\) 6.25006e8 0.375321
\(113\) −4.92103e8 −0.283925 −0.141962 0.989872i \(-0.545341\pi\)
−0.141962 + 0.989872i \(0.545341\pi\)
\(114\) 3.11641e8 0.172815
\(115\) 9.70143e8 0.517244
\(116\) 1.20710e9 0.618989
\(117\) −1.68463e8 −0.0831127
\(118\) 1.23706e9 0.587383
\(119\) 0 0
\(120\) −1.68190e9 −0.740431
\(121\) −2.35250e9 −0.997692
\(122\) −1.80625e9 −0.738173
\(123\) 2.82255e9 1.11191
\(124\) −3.04553e9 −1.15682
\(125\) 2.60247e9 0.953435
\(126\) 2.96954e8 0.104959
\(127\) −1.38264e9 −0.471620 −0.235810 0.971799i \(-0.575774\pi\)
−0.235810 + 0.971799i \(0.575774\pi\)
\(128\) 2.99677e9 0.986754
\(129\) 2.87031e9 0.912589
\(130\) 5.15776e8 0.158386
\(131\) −2.00175e9 −0.593867 −0.296934 0.954898i \(-0.595964\pi\)
−0.296934 + 0.954898i \(0.595964\pi\)
\(132\) −1.14464e8 −0.0328162
\(133\) −1.42964e9 −0.396180
\(134\) 2.91938e9 0.782201
\(135\) 4.35108e9 1.12744
\(136\) 0 0
\(137\) 2.67902e9 0.649731 0.324865 0.945760i \(-0.394681\pi\)
0.324865 + 0.945760i \(0.394681\pi\)
\(138\) 8.40969e8 0.197390
\(139\) −6.25930e9 −1.42219 −0.711097 0.703094i \(-0.751801\pi\)
−0.711097 + 0.703094i \(0.751801\pi\)
\(140\) 3.40323e9 0.748712
\(141\) 7.27599e9 1.55027
\(142\) −2.06686e8 −0.0426593
\(143\) 7.95814e7 0.0159147
\(144\) −5.33347e8 −0.103366
\(145\) 4.34779e9 0.816794
\(146\) −3.51795e9 −0.640770
\(147\) −8.32961e8 −0.147128
\(148\) 3.96698e8 0.0679645
\(149\) 4.42327e9 0.735200 0.367600 0.929984i \(-0.380180\pi\)
0.367600 + 0.929984i \(0.380180\pi\)
\(150\) −2.08049e8 −0.0335548
\(151\) 3.63327e8 0.0568724 0.0284362 0.999596i \(-0.490947\pi\)
0.0284362 + 0.999596i \(0.490947\pi\)
\(152\) −2.35106e9 −0.357246
\(153\) 0 0
\(154\) −1.40280e8 −0.0200980
\(155\) −1.09695e10 −1.52650
\(156\) −1.67360e9 −0.226251
\(157\) 7.98151e9 1.04842 0.524211 0.851588i \(-0.324360\pi\)
0.524211 + 0.851588i \(0.324360\pi\)
\(158\) −1.98213e9 −0.253032
\(159\) 7.14182e9 0.886179
\(160\) 8.72474e9 1.05248
\(161\) −3.85790e9 −0.452517
\(162\) 2.76179e9 0.315045
\(163\) −1.63762e10 −1.81705 −0.908527 0.417825i \(-0.862792\pi\)
−0.908527 + 0.417825i \(0.862792\pi\)
\(164\) −9.39227e9 −1.01385
\(165\) −4.12283e8 −0.0433030
\(166\) 5.54769e9 0.567056
\(167\) −1.04216e10 −1.03684 −0.518418 0.855127i \(-0.673479\pi\)
−0.518418 + 0.855127i \(0.673479\pi\)
\(168\) 6.68830e9 0.647774
\(169\) −9.44093e9 −0.890276
\(170\) 0 0
\(171\) 1.21998e9 0.109111
\(172\) −9.55121e9 −0.832109
\(173\) 7.86202e8 0.0667309 0.0333654 0.999443i \(-0.489377\pi\)
0.0333654 + 0.999443i \(0.489377\pi\)
\(174\) 3.76889e9 0.311703
\(175\) 9.54412e8 0.0769245
\(176\) 2.51952e8 0.0197930
\(177\) −1.44579e10 −1.10720
\(178\) 8.13327e9 0.607261
\(179\) −5.72805e9 −0.417031 −0.208515 0.978019i \(-0.566863\pi\)
−0.208515 + 0.978019i \(0.566863\pi\)
\(180\) −2.90414e9 −0.206201
\(181\) 9.74370e9 0.674793 0.337396 0.941363i \(-0.390454\pi\)
0.337396 + 0.941363i \(0.390454\pi\)
\(182\) −2.05105e9 −0.138565
\(183\) 2.11102e10 1.39143
\(184\) −6.34439e9 −0.408046
\(185\) 1.42884e9 0.0896834
\(186\) −9.50895e9 −0.582538
\(187\) 0 0
\(188\) −2.42115e10 −1.41355
\(189\) −1.73026e10 −0.986357
\(190\) −3.73515e9 −0.207930
\(191\) −2.52142e10 −1.37087 −0.685434 0.728135i \(-0.740387\pi\)
−0.685434 + 0.728135i \(0.740387\pi\)
\(192\) 8.48999e8 0.0450870
\(193\) 3.06794e10 1.59162 0.795810 0.605547i \(-0.207046\pi\)
0.795810 + 0.605547i \(0.207046\pi\)
\(194\) 1.14575e10 0.580742
\(195\) −6.02803e9 −0.298552
\(196\) 2.77175e9 0.134153
\(197\) −2.51918e9 −0.119169 −0.0595843 0.998223i \(-0.518978\pi\)
−0.0595843 + 0.998223i \(0.518978\pi\)
\(198\) 1.19708e8 0.00553514
\(199\) −3.31066e10 −1.49650 −0.748248 0.663419i \(-0.769105\pi\)
−0.748248 + 0.663419i \(0.769105\pi\)
\(200\) 1.56955e9 0.0693648
\(201\) −3.41197e10 −1.47442
\(202\) 9.19498e9 0.388570
\(203\) −1.72896e10 −0.714582
\(204\) 0 0
\(205\) −3.38295e10 −1.33784
\(206\) −1.26972e10 −0.491252
\(207\) 3.29213e9 0.124627
\(208\) 3.68381e9 0.136462
\(209\) −5.76314e8 −0.0208930
\(210\) 1.06258e10 0.377028
\(211\) −3.71348e10 −1.28976 −0.644882 0.764282i \(-0.723093\pi\)
−0.644882 + 0.764282i \(0.723093\pi\)
\(212\) −2.37650e10 −0.808028
\(213\) 2.41560e9 0.0804113
\(214\) 4.41185e9 0.143800
\(215\) −3.44019e10 −1.09802
\(216\) −2.84545e10 −0.889424
\(217\) 4.36218e10 1.33547
\(218\) −6.50146e6 −0.000194965 0
\(219\) 4.11154e10 1.20783
\(220\) 1.37191e9 0.0394841
\(221\) 0 0
\(222\) 1.23859e9 0.0342248
\(223\) 2.95004e10 0.798833 0.399416 0.916770i \(-0.369213\pi\)
0.399416 + 0.916770i \(0.369213\pi\)
\(224\) −3.46951e10 −0.920772
\(225\) −8.14445e8 −0.0211856
\(226\) 5.11275e9 0.130367
\(227\) 1.59933e9 0.0399781 0.0199890 0.999800i \(-0.493637\pi\)
0.0199890 + 0.999800i \(0.493637\pi\)
\(228\) 1.21199e10 0.297024
\(229\) 4.03603e10 0.969827 0.484914 0.874562i \(-0.338851\pi\)
0.484914 + 0.874562i \(0.338851\pi\)
\(230\) −1.00794e10 −0.237497
\(231\) 1.63950e9 0.0378841
\(232\) −2.84330e10 −0.644357
\(233\) −8.88023e10 −1.97389 −0.986944 0.161061i \(-0.948508\pi\)
−0.986944 + 0.161061i \(0.948508\pi\)
\(234\) 1.75026e9 0.0381620
\(235\) −8.72060e10 −1.86527
\(236\) 4.81099e10 1.00956
\(237\) 2.31658e10 0.476958
\(238\) 0 0
\(239\) −9.30238e10 −1.84418 −0.922090 0.386975i \(-0.873520\pi\)
−0.922090 + 0.386975i \(0.873520\pi\)
\(240\) −1.90845e10 −0.371305
\(241\) −7.97680e10 −1.52318 −0.761592 0.648057i \(-0.775582\pi\)
−0.761592 + 0.648057i \(0.775582\pi\)
\(242\) 2.44416e10 0.458099
\(243\) 2.65687e10 0.488812
\(244\) −7.02460e10 −1.26872
\(245\) 9.98340e9 0.177024
\(246\) −2.93251e10 −0.510542
\(247\) −8.42634e9 −0.144046
\(248\) 7.17368e10 1.20423
\(249\) −6.48376e10 −1.06888
\(250\) −2.70386e10 −0.437778
\(251\) 4.47092e10 0.710993 0.355497 0.934678i \(-0.384312\pi\)
0.355497 + 0.934678i \(0.384312\pi\)
\(252\) 1.15487e10 0.180397
\(253\) −1.55520e9 −0.0238640
\(254\) 1.43651e10 0.216549
\(255\) 0 0
\(256\) −3.47151e10 −0.505171
\(257\) −1.03452e11 −1.47925 −0.739624 0.673020i \(-0.764997\pi\)
−0.739624 + 0.673020i \(0.764997\pi\)
\(258\) −2.98213e10 −0.419024
\(259\) −5.68199e9 −0.0784606
\(260\) 2.00588e10 0.272223
\(261\) 1.47540e10 0.196801
\(262\) 2.07974e10 0.272680
\(263\) 8.72107e9 0.112401 0.0562003 0.998420i \(-0.482101\pi\)
0.0562003 + 0.998420i \(0.482101\pi\)
\(264\) 2.69618e9 0.0341611
\(265\) −8.55978e10 −1.06624
\(266\) 1.48533e10 0.181910
\(267\) −9.50561e10 −1.14467
\(268\) 1.13536e11 1.34440
\(269\) 1.46865e10 0.171014 0.0855071 0.996338i \(-0.472749\pi\)
0.0855071 + 0.996338i \(0.472749\pi\)
\(270\) −4.52059e10 −0.517676
\(271\) −2.26346e10 −0.254924 −0.127462 0.991843i \(-0.540683\pi\)
−0.127462 + 0.991843i \(0.540683\pi\)
\(272\) 0 0
\(273\) 2.39713e10 0.261191
\(274\) −2.78339e10 −0.298330
\(275\) 3.84742e8 0.00405670
\(276\) 3.27057e10 0.339260
\(277\) −2.04552e10 −0.208759 −0.104380 0.994538i \(-0.533286\pi\)
−0.104380 + 0.994538i \(0.533286\pi\)
\(278\) 6.50315e10 0.653014
\(279\) −3.72246e10 −0.367799
\(280\) −8.01622e10 −0.779397
\(281\) 5.58885e10 0.534741 0.267371 0.963594i \(-0.413845\pi\)
0.267371 + 0.963594i \(0.413845\pi\)
\(282\) −7.55946e10 −0.711819
\(283\) 3.87106e10 0.358749 0.179375 0.983781i \(-0.442593\pi\)
0.179375 + 0.983781i \(0.442593\pi\)
\(284\) −8.03812e9 −0.0733199
\(285\) 4.36539e10 0.391941
\(286\) −8.26818e8 −0.00730740
\(287\) 1.34527e11 1.17042
\(288\) 2.96070e10 0.253587
\(289\) 0 0
\(290\) −4.51718e10 −0.375039
\(291\) −1.33908e11 −1.09468
\(292\) −1.36815e11 −1.10131
\(293\) −2.87885e10 −0.228200 −0.114100 0.993469i \(-0.536398\pi\)
−0.114100 + 0.993469i \(0.536398\pi\)
\(294\) 8.65412e9 0.0675554
\(295\) 1.73284e11 1.33217
\(296\) −9.34413e9 −0.0707499
\(297\) −6.97503e9 −0.0520166
\(298\) −4.59560e10 −0.337574
\(299\) −2.27387e10 −0.164530
\(300\) −8.09112e9 −0.0576717
\(301\) 1.36804e11 0.960614
\(302\) −3.77482e9 −0.0261135
\(303\) −1.07465e11 −0.732442
\(304\) −2.66775e10 −0.179149
\(305\) −2.53015e11 −1.67416
\(306\) 0 0
\(307\) 8.97359e10 0.576558 0.288279 0.957546i \(-0.406917\pi\)
0.288279 + 0.957546i \(0.406917\pi\)
\(308\) −5.45557e9 −0.0345431
\(309\) 1.48396e11 0.925993
\(310\) 1.13969e11 0.700905
\(311\) −1.85255e11 −1.12292 −0.561458 0.827505i \(-0.689759\pi\)
−0.561458 + 0.827505i \(0.689759\pi\)
\(312\) 3.94211e10 0.235523
\(313\) 7.32601e10 0.431437 0.215719 0.976456i \(-0.430791\pi\)
0.215719 + 0.976456i \(0.430791\pi\)
\(314\) −8.29246e10 −0.481393
\(315\) 4.15965e10 0.238045
\(316\) −7.70862e10 −0.434896
\(317\) −6.70467e9 −0.0372916 −0.0186458 0.999826i \(-0.505935\pi\)
−0.0186458 + 0.999826i \(0.505935\pi\)
\(318\) −7.42005e10 −0.406897
\(319\) −6.96976e9 −0.0376842
\(320\) −1.01756e10 −0.0542483
\(321\) −5.15627e10 −0.271058
\(322\) 4.00820e10 0.207777
\(323\) 0 0
\(324\) 1.07407e11 0.541479
\(325\) 5.62535e9 0.0279688
\(326\) 1.70142e11 0.834318
\(327\) 7.59846e7 0.000367503 0
\(328\) 2.21233e11 1.05540
\(329\) 3.46786e11 1.63185
\(330\) 4.28345e9 0.0198830
\(331\) 3.70409e11 1.69612 0.848059 0.529902i \(-0.177771\pi\)
0.848059 + 0.529902i \(0.177771\pi\)
\(332\) 2.15753e11 0.974618
\(333\) 4.84871e9 0.0216086
\(334\) 1.08276e11 0.476073
\(335\) 4.08939e11 1.77401
\(336\) 7.58921e10 0.324840
\(337\) −2.14065e11 −0.904087 −0.452043 0.891996i \(-0.649305\pi\)
−0.452043 + 0.891996i \(0.649305\pi\)
\(338\) 9.80874e10 0.408779
\(339\) −5.97542e10 −0.245737
\(340\) 0 0
\(341\) 1.75848e10 0.0704276
\(342\) −1.26750e10 −0.0500994
\(343\) −2.73242e11 −1.06592
\(344\) 2.24976e11 0.866211
\(345\) 1.17801e11 0.447675
\(346\) −8.16832e9 −0.0306401
\(347\) 4.32305e10 0.160069 0.0800345 0.996792i \(-0.474497\pi\)
0.0800345 + 0.996792i \(0.474497\pi\)
\(348\) 1.46574e11 0.535735
\(349\) 2.70051e11 0.974387 0.487194 0.873294i \(-0.338021\pi\)
0.487194 + 0.873294i \(0.338021\pi\)
\(350\) −9.91595e9 −0.0353206
\(351\) −1.01982e11 −0.358628
\(352\) −1.39863e10 −0.0485579
\(353\) −5.33235e11 −1.82781 −0.913907 0.405923i \(-0.866950\pi\)
−0.913907 + 0.405923i \(0.866950\pi\)
\(354\) 1.50211e11 0.508380
\(355\) −2.89520e10 −0.0967502
\(356\) 3.16307e11 1.04372
\(357\) 0 0
\(358\) 5.95120e10 0.191483
\(359\) −5.40222e10 −0.171651 −0.0858257 0.996310i \(-0.527353\pi\)
−0.0858257 + 0.996310i \(0.527353\pi\)
\(360\) 6.84062e10 0.214652
\(361\) −2.61666e11 −0.810895
\(362\) −1.01233e11 −0.309837
\(363\) −2.85656e11 −0.863502
\(364\) −7.97664e10 −0.238157
\(365\) −4.92786e11 −1.45325
\(366\) −2.19326e11 −0.638889
\(367\) −1.80940e10 −0.0520640 −0.0260320 0.999661i \(-0.508287\pi\)
−0.0260320 + 0.999661i \(0.508287\pi\)
\(368\) −7.19898e10 −0.204624
\(369\) −1.14799e11 −0.322343
\(370\) −1.48451e10 −0.0411790
\(371\) 3.40391e11 0.932815
\(372\) −3.69808e11 −1.00123
\(373\) −2.44941e10 −0.0655196 −0.0327598 0.999463i \(-0.510430\pi\)
−0.0327598 + 0.999463i \(0.510430\pi\)
\(374\) 0 0
\(375\) 3.16008e11 0.825198
\(376\) 5.70296e11 1.47148
\(377\) −1.01905e11 −0.259813
\(378\) 1.79767e11 0.452895
\(379\) −6.10167e10 −0.151905 −0.0759526 0.997111i \(-0.524200\pi\)
−0.0759526 + 0.997111i \(0.524200\pi\)
\(380\) −1.45262e11 −0.357376
\(381\) −1.67889e11 −0.408188
\(382\) 2.61965e11 0.629446
\(383\) −2.92964e11 −0.695696 −0.347848 0.937551i \(-0.613087\pi\)
−0.347848 + 0.937551i \(0.613087\pi\)
\(384\) 3.63887e11 0.854036
\(385\) −1.96501e10 −0.0455818
\(386\) −3.18746e11 −0.730807
\(387\) −1.16741e11 −0.264561
\(388\) 4.45589e11 0.998141
\(389\) −4.44479e11 −0.984189 −0.492094 0.870542i \(-0.663769\pi\)
−0.492094 + 0.870542i \(0.663769\pi\)
\(390\) 6.26287e10 0.137083
\(391\) 0 0
\(392\) −6.52878e10 −0.139651
\(393\) −2.43065e11 −0.513992
\(394\) 2.61733e10 0.0547174
\(395\) −2.77652e11 −0.573871
\(396\) 4.65550e9 0.00951344
\(397\) −8.73577e11 −1.76500 −0.882498 0.470316i \(-0.844140\pi\)
−0.882498 + 0.470316i \(0.844140\pi\)
\(398\) 3.43964e11 0.687130
\(399\) −1.73595e11 −0.342894
\(400\) 1.78097e10 0.0347845
\(401\) 7.23977e11 1.39822 0.699109 0.715015i \(-0.253580\pi\)
0.699109 + 0.715015i \(0.253580\pi\)
\(402\) 3.54489e11 0.676995
\(403\) 2.57109e11 0.485562
\(404\) 3.57598e11 0.667849
\(405\) 3.86865e11 0.714515
\(406\) 1.79631e11 0.328107
\(407\) −2.29052e9 −0.00413770
\(408\) 0 0
\(409\) 5.85905e10 0.103531 0.0517657 0.998659i \(-0.483515\pi\)
0.0517657 + 0.998659i \(0.483515\pi\)
\(410\) 3.51474e11 0.614280
\(411\) 3.25304e11 0.562342
\(412\) −4.93799e11 −0.844331
\(413\) −6.89087e11 −1.16546
\(414\) −3.42039e10 −0.0572235
\(415\) 7.77107e11 1.28607
\(416\) −2.04494e11 −0.334781
\(417\) −7.60043e11 −1.23091
\(418\) 5.98766e9 0.00959321
\(419\) 2.55123e11 0.404378 0.202189 0.979347i \(-0.435195\pi\)
0.202189 + 0.979347i \(0.435195\pi\)
\(420\) 4.13242e11 0.648011
\(421\) −5.38001e11 −0.834668 −0.417334 0.908753i \(-0.637035\pi\)
−0.417334 + 0.908753i \(0.637035\pi\)
\(422\) 3.85815e11 0.592207
\(423\) −2.95929e11 −0.449424
\(424\) 5.59779e11 0.841143
\(425\) 0 0
\(426\) −2.50971e10 −0.0369216
\(427\) 1.00615e12 1.46466
\(428\) 1.71579e11 0.247154
\(429\) 9.66327e9 0.0137742
\(430\) 3.57422e11 0.504166
\(431\) −6.14842e11 −0.858253 −0.429127 0.903244i \(-0.641179\pi\)
−0.429127 + 0.903244i \(0.641179\pi\)
\(432\) −3.22873e11 −0.446021
\(433\) 4.79713e11 0.655822 0.327911 0.944709i \(-0.393655\pi\)
0.327911 + 0.944709i \(0.393655\pi\)
\(434\) −4.53213e11 −0.613195
\(435\) 5.27936e11 0.706935
\(436\) −2.52845e8 −0.000335093 0
\(437\) 1.64669e11 0.215996
\(438\) −4.27172e11 −0.554587
\(439\) 1.39973e11 0.179867 0.0899337 0.995948i \(-0.471334\pi\)
0.0899337 + 0.995948i \(0.471334\pi\)
\(440\) −3.23149e10 −0.0411023
\(441\) 3.38782e10 0.0426527
\(442\) 0 0
\(443\) 5.34602e11 0.659499 0.329749 0.944068i \(-0.393036\pi\)
0.329749 + 0.944068i \(0.393036\pi\)
\(444\) 4.81696e10 0.0588233
\(445\) 1.13929e12 1.37725
\(446\) −3.06497e11 −0.366791
\(447\) 5.37102e11 0.636316
\(448\) 4.04647e10 0.0474598
\(449\) −1.58754e12 −1.84339 −0.921695 0.387914i \(-0.873196\pi\)
−0.921695 + 0.387914i \(0.873196\pi\)
\(450\) 8.46175e9 0.00972756
\(451\) 5.42306e10 0.0617234
\(452\) 1.98837e11 0.224066
\(453\) 4.41175e10 0.0492231
\(454\) −1.66164e10 −0.0183563
\(455\) −2.87306e11 −0.314263
\(456\) −2.85481e11 −0.309197
\(457\) −1.56481e11 −0.167818 −0.0839092 0.996473i \(-0.526741\pi\)
−0.0839092 + 0.996473i \(0.526741\pi\)
\(458\) −4.19327e11 −0.445305
\(459\) 0 0
\(460\) −3.91993e11 −0.408195
\(461\) 1.32697e12 1.36838 0.684190 0.729304i \(-0.260156\pi\)
0.684190 + 0.729304i \(0.260156\pi\)
\(462\) −1.70337e10 −0.0173948
\(463\) −1.33241e12 −1.34748 −0.673739 0.738969i \(-0.735313\pi\)
−0.673739 + 0.738969i \(0.735313\pi\)
\(464\) −3.22629e11 −0.323127
\(465\) −1.33199e12 −1.32118
\(466\) 9.22620e11 0.906329
\(467\) 4.42532e10 0.0430545 0.0215273 0.999768i \(-0.493147\pi\)
0.0215273 + 0.999768i \(0.493147\pi\)
\(468\) 6.80685e10 0.0655903
\(469\) −1.62620e12 −1.55202
\(470\) 9.06034e11 0.856454
\(471\) 9.69165e11 0.907410
\(472\) −1.13322e12 −1.05093
\(473\) 5.51483e10 0.0506590
\(474\) −2.40683e11 −0.219000
\(475\) −4.07377e10 −0.0367177
\(476\) 0 0
\(477\) −2.90472e11 −0.256904
\(478\) 9.66479e11 0.846773
\(479\) 1.73977e12 1.51002 0.755010 0.655713i \(-0.227632\pi\)
0.755010 + 0.655713i \(0.227632\pi\)
\(480\) 1.05941e12 0.910919
\(481\) −3.34899e10 −0.0285273
\(482\) 8.28757e11 0.699384
\(483\) −4.68451e11 −0.391654
\(484\) 9.50545e11 0.787351
\(485\) 1.60494e12 1.31711
\(486\) −2.76038e11 −0.224443
\(487\) −5.20901e11 −0.419638 −0.209819 0.977740i \(-0.567287\pi\)
−0.209819 + 0.977740i \(0.567287\pi\)
\(488\) 1.65463e12 1.32072
\(489\) −1.98850e12 −1.57266
\(490\) −1.03723e11 −0.0812820
\(491\) −4.74925e11 −0.368772 −0.184386 0.982854i \(-0.559030\pi\)
−0.184386 + 0.982854i \(0.559030\pi\)
\(492\) −1.14047e12 −0.877486
\(493\) 0 0
\(494\) 8.75462e10 0.0661402
\(495\) 1.67684e10 0.0125536
\(496\) 8.13998e11 0.603887
\(497\) 1.15132e11 0.0846430
\(498\) 6.73636e11 0.490787
\(499\) −5.66987e10 −0.0409375 −0.0204687 0.999790i \(-0.506516\pi\)
−0.0204687 + 0.999790i \(0.506516\pi\)
\(500\) −1.05155e12 −0.752425
\(501\) −1.26546e12 −0.897382
\(502\) −4.64511e11 −0.326459
\(503\) 2.79705e10 0.0194825 0.00974125 0.999953i \(-0.496899\pi\)
0.00974125 + 0.999953i \(0.496899\pi\)
\(504\) −2.72026e11 −0.187790
\(505\) 1.28801e12 0.881268
\(506\) 1.61578e10 0.0109574
\(507\) −1.14638e12 −0.770534
\(508\) 5.58665e11 0.372190
\(509\) 2.28497e12 1.50887 0.754434 0.656376i \(-0.227911\pi\)
0.754434 + 0.656376i \(0.227911\pi\)
\(510\) 0 0
\(511\) 1.95963e12 1.27139
\(512\) −1.17367e12 −0.754800
\(513\) 7.38538e11 0.470809
\(514\) 1.07483e12 0.679211
\(515\) −1.77859e12 −1.11415
\(516\) −1.15977e12 −0.720190
\(517\) 1.39796e11 0.0860573
\(518\) 5.90335e10 0.0360259
\(519\) 9.54657e10 0.0577556
\(520\) −4.72480e11 −0.283379
\(521\) 2.38544e12 1.41840 0.709199 0.705008i \(-0.249057\pi\)
0.709199 + 0.705008i \(0.249057\pi\)
\(522\) −1.53288e11 −0.0903631
\(523\) 2.62970e12 1.53691 0.768454 0.639905i \(-0.221026\pi\)
0.768454 + 0.639905i \(0.221026\pi\)
\(524\) 8.08821e11 0.468664
\(525\) 1.15891e11 0.0665782
\(526\) −9.06083e10 −0.0516098
\(527\) 0 0
\(528\) 3.05936e10 0.0171308
\(529\) −1.35679e12 −0.753289
\(530\) 8.89326e11 0.489575
\(531\) 5.88031e11 0.320978
\(532\) 5.77653e11 0.312655
\(533\) 7.92910e11 0.425551
\(534\) 9.87594e11 0.525585
\(535\) 6.18002e11 0.326135
\(536\) −2.67431e12 −1.39949
\(537\) −6.95536e11 −0.360940
\(538\) −1.52586e11 −0.0785227
\(539\) −1.60040e10 −0.00816729
\(540\) −1.75808e12 −0.889748
\(541\) 3.24028e12 1.62628 0.813140 0.582069i \(-0.197756\pi\)
0.813140 + 0.582069i \(0.197756\pi\)
\(542\) 2.35164e11 0.117051
\(543\) 1.18314e12 0.584033
\(544\) 0 0
\(545\) −9.10709e8 −0.000442176 0
\(546\) −2.49051e11 −0.119928
\(547\) −1.35392e12 −0.646621 −0.323310 0.946293i \(-0.604796\pi\)
−0.323310 + 0.946293i \(0.604796\pi\)
\(548\) −1.08248e12 −0.512750
\(549\) −8.58593e11 −0.403378
\(550\) −3.99731e9 −0.00186267
\(551\) 7.37980e11 0.341085
\(552\) −7.70376e11 −0.353164
\(553\) 1.10412e12 0.502058
\(554\) 2.12521e11 0.0958537
\(555\) 1.73499e11 0.0776210
\(556\) 2.52911e12 1.12236
\(557\) 3.86259e12 1.70032 0.850159 0.526526i \(-0.176506\pi\)
0.850159 + 0.526526i \(0.176506\pi\)
\(558\) 3.86748e11 0.168878
\(559\) 8.06328e11 0.349268
\(560\) −9.09601e11 −0.390845
\(561\) 0 0
\(562\) −5.80658e11 −0.245531
\(563\) 3.23036e12 1.35507 0.677536 0.735489i \(-0.263048\pi\)
0.677536 + 0.735489i \(0.263048\pi\)
\(564\) −2.93991e12 −1.22343
\(565\) 7.16181e11 0.295668
\(566\) −4.02187e11 −0.164723
\(567\) −1.53842e12 −0.625102
\(568\) 1.89336e11 0.0763248
\(569\) −2.61773e12 −1.04693 −0.523467 0.852046i \(-0.675362\pi\)
−0.523467 + 0.852046i \(0.675362\pi\)
\(570\) −4.53546e11 −0.179963
\(571\) −7.43673e11 −0.292765 −0.146383 0.989228i \(-0.546763\pi\)
−0.146383 + 0.989228i \(0.546763\pi\)
\(572\) −3.21554e10 −0.0125595
\(573\) −3.06167e12 −1.18649
\(574\) −1.39768e12 −0.537410
\(575\) −1.09932e11 −0.0419389
\(576\) −3.45305e10 −0.0130708
\(577\) 1.94245e12 0.729556 0.364778 0.931094i \(-0.381145\pi\)
0.364778 + 0.931094i \(0.381145\pi\)
\(578\) 0 0
\(579\) 3.72529e12 1.37755
\(580\) −1.75675e12 −0.644592
\(581\) −3.09027e12 −1.12513
\(582\) 1.39125e12 0.502632
\(583\) 1.37218e11 0.0491930
\(584\) 3.22264e12 1.14645
\(585\) 2.45172e11 0.0865504
\(586\) 2.99101e11 0.104780
\(587\) 1.54986e12 0.538793 0.269396 0.963029i \(-0.413176\pi\)
0.269396 + 0.963029i \(0.413176\pi\)
\(588\) 3.36563e11 0.116110
\(589\) −1.86194e12 −0.637450
\(590\) −1.80035e12 −0.611678
\(591\) −3.05895e11 −0.103140
\(592\) −1.06028e11 −0.0354791
\(593\) −2.14021e12 −0.710738 −0.355369 0.934726i \(-0.615645\pi\)
−0.355369 + 0.934726i \(0.615645\pi\)
\(594\) 7.24676e10 0.0238839
\(595\) 0 0
\(596\) −1.78725e12 −0.580200
\(597\) −4.02001e12 −1.29522
\(598\) 2.36245e11 0.0755454
\(599\) 1.00259e12 0.318201 0.159100 0.987262i \(-0.449141\pi\)
0.159100 + 0.987262i \(0.449141\pi\)
\(600\) 1.90584e11 0.0600353
\(601\) 2.75646e11 0.0861819 0.0430909 0.999071i \(-0.486279\pi\)
0.0430909 + 0.999071i \(0.486279\pi\)
\(602\) −1.42134e12 −0.441075
\(603\) 1.38771e12 0.427437
\(604\) −1.46805e11 −0.0448821
\(605\) 3.42371e12 1.03896
\(606\) 1.11651e12 0.336308
\(607\) −3.23706e12 −0.967835 −0.483917 0.875114i \(-0.660786\pi\)
−0.483917 + 0.875114i \(0.660786\pi\)
\(608\) 1.48091e12 0.439504
\(609\) −2.09941e12 −0.618471
\(610\) 2.62872e12 0.768706
\(611\) 2.04397e12 0.593321
\(612\) 0 0
\(613\) −4.13642e12 −1.18318 −0.591592 0.806238i \(-0.701500\pi\)
−0.591592 + 0.806238i \(0.701500\pi\)
\(614\) −9.32319e11 −0.264732
\(615\) −4.10779e12 −1.15790
\(616\) 1.28505e11 0.0359588
\(617\) −2.35389e11 −0.0653887 −0.0326944 0.999465i \(-0.510409\pi\)
−0.0326944 + 0.999465i \(0.510409\pi\)
\(618\) −1.54177e12 −0.425178
\(619\) 3.08679e12 0.845081 0.422541 0.906344i \(-0.361138\pi\)
0.422541 + 0.906344i \(0.361138\pi\)
\(620\) 4.43231e12 1.20467
\(621\) 1.99296e12 0.537758
\(622\) 1.92472e12 0.515597
\(623\) −4.53053e12 −1.20491
\(624\) 4.47312e11 0.118108
\(625\) −4.10960e12 −1.07731
\(626\) −7.61142e11 −0.198098
\(627\) −6.99796e10 −0.0180829
\(628\) −3.22498e12 −0.827387
\(629\) 0 0
\(630\) −4.32171e11 −0.109301
\(631\) 1.50842e12 0.378783 0.189392 0.981902i \(-0.439348\pi\)
0.189392 + 0.981902i \(0.439348\pi\)
\(632\) 1.81575e12 0.452719
\(633\) −4.50914e12 −1.11629
\(634\) 6.96587e10 0.0171228
\(635\) 2.01222e12 0.491128
\(636\) −2.88570e12 −0.699349
\(637\) −2.33995e11 −0.0563093
\(638\) 7.24129e10 0.0173031
\(639\) −9.82473e10 −0.0233113
\(640\) −4.36135e12 −1.02757
\(641\) −6.22573e12 −1.45656 −0.728281 0.685279i \(-0.759680\pi\)
−0.728281 + 0.685279i \(0.759680\pi\)
\(642\) 5.35715e11 0.124459
\(643\) −7.75305e12 −1.78864 −0.894320 0.447428i \(-0.852340\pi\)
−0.894320 + 0.447428i \(0.852340\pi\)
\(644\) 1.55881e12 0.357114
\(645\) −4.17730e12 −0.950336
\(646\) 0 0
\(647\) 5.78109e11 0.129700 0.0648500 0.997895i \(-0.479343\pi\)
0.0648500 + 0.997895i \(0.479343\pi\)
\(648\) −2.52995e12 −0.563670
\(649\) −2.77784e11 −0.0614620
\(650\) −5.84450e10 −0.0128421
\(651\) 5.29684e12 1.15585
\(652\) 6.61690e12 1.43397
\(653\) 1.34041e12 0.288488 0.144244 0.989542i \(-0.453925\pi\)
0.144244 + 0.989542i \(0.453925\pi\)
\(654\) −7.89449e8 −0.000168742 0
\(655\) 2.91325e12 0.618431
\(656\) 2.51033e12 0.529253
\(657\) −1.67224e12 −0.350151
\(658\) −3.60297e12 −0.749279
\(659\) 7.95738e12 1.64356 0.821780 0.569805i \(-0.192981\pi\)
0.821780 + 0.569805i \(0.192981\pi\)
\(660\) 1.66586e11 0.0341735
\(661\) −4.99569e12 −1.01786 −0.508931 0.860807i \(-0.669959\pi\)
−0.508931 + 0.860807i \(0.669959\pi\)
\(662\) −3.84840e12 −0.778788
\(663\) 0 0
\(664\) −5.08200e12 −1.01456
\(665\) 2.08062e12 0.412567
\(666\) −5.03761e10 −0.00992180
\(667\) 1.99146e12 0.389587
\(668\) 4.21091e12 0.818243
\(669\) 3.58212e12 0.691390
\(670\) −4.24871e12 −0.814555
\(671\) 4.05597e11 0.0772403
\(672\) −4.21290e12 −0.796928
\(673\) −1.88855e12 −0.354863 −0.177431 0.984133i \(-0.556779\pi\)
−0.177431 + 0.984133i \(0.556779\pi\)
\(674\) 2.22404e12 0.415120
\(675\) −4.93042e11 −0.0914148
\(676\) 3.81467e12 0.702582
\(677\) −3.49370e12 −0.639200 −0.319600 0.947553i \(-0.603549\pi\)
−0.319600 + 0.947553i \(0.603549\pi\)
\(678\) 6.20822e11 0.112832
\(679\) −6.38226e12 −1.15229
\(680\) 0 0
\(681\) 1.94201e11 0.0346010
\(682\) −1.82699e11 −0.0323375
\(683\) −1.11112e12 −0.195375 −0.0976875 0.995217i \(-0.531145\pi\)
−0.0976875 + 0.995217i \(0.531145\pi\)
\(684\) −4.92939e11 −0.0861075
\(685\) −3.89891e12 −0.676605
\(686\) 2.83887e12 0.489426
\(687\) 4.90080e12 0.839386
\(688\) 2.55281e12 0.434380
\(689\) 2.00628e12 0.339160
\(690\) −1.22390e12 −0.205554
\(691\) −1.27071e12 −0.212030 −0.106015 0.994365i \(-0.533809\pi\)
−0.106015 + 0.994365i \(0.533809\pi\)
\(692\) −3.17670e11 −0.0526622
\(693\) −6.66816e10 −0.0109826
\(694\) −4.49147e11 −0.0734971
\(695\) 9.10946e12 1.48102
\(696\) −3.45251e12 −0.557691
\(697\) 0 0
\(698\) −2.80572e12 −0.447399
\(699\) −1.07829e13 −1.70840
\(700\) −3.85636e11 −0.0607067
\(701\) −7.14268e12 −1.11720 −0.558599 0.829438i \(-0.688661\pi\)
−0.558599 + 0.829438i \(0.688661\pi\)
\(702\) 1.05956e12 0.164667
\(703\) 2.42528e11 0.0374509
\(704\) 1.63121e10 0.00250284
\(705\) −1.05891e13 −1.61439
\(706\) 5.54009e12 0.839258
\(707\) −5.12194e12 −0.770987
\(708\) 5.84180e12 0.873770
\(709\) −4.09276e12 −0.608287 −0.304144 0.952626i \(-0.598370\pi\)
−0.304144 + 0.952626i \(0.598370\pi\)
\(710\) 3.00800e11 0.0444237
\(711\) −9.42200e11 −0.138271
\(712\) −7.45054e12 −1.08649
\(713\) −5.02447e12 −0.728094
\(714\) 0 0
\(715\) −1.15819e11 −0.0165730
\(716\) 2.31445e12 0.329109
\(717\) −1.12955e13 −1.59614
\(718\) 5.61269e11 0.0788154
\(719\) −3.19174e12 −0.445397 −0.222699 0.974887i \(-0.571487\pi\)
−0.222699 + 0.974887i \(0.571487\pi\)
\(720\) 7.76206e11 0.107642
\(721\) 7.07278e12 0.974724
\(722\) 2.71860e12 0.372330
\(723\) −9.68594e12 −1.31832
\(724\) −3.93701e12 −0.532528
\(725\) −4.92669e11 −0.0662269
\(726\) 2.96785e12 0.396485
\(727\) 1.43422e13 1.90419 0.952094 0.305806i \(-0.0989259\pi\)
0.952094 + 0.305806i \(0.0989259\pi\)
\(728\) 1.87888e12 0.247918
\(729\) 8.45833e12 1.10920
\(730\) 5.11985e12 0.667274
\(731\) 0 0
\(732\) −8.52971e12 −1.09808
\(733\) −6.30500e12 −0.806710 −0.403355 0.915044i \(-0.632156\pi\)
−0.403355 + 0.915044i \(0.632156\pi\)
\(734\) 1.87989e11 0.0239057
\(735\) 1.21225e12 0.153214
\(736\) 3.99627e12 0.502001
\(737\) −6.55553e11 −0.0818472
\(738\) 1.19271e12 0.148007
\(739\) −8.54398e12 −1.05381 −0.526903 0.849926i \(-0.676647\pi\)
−0.526903 + 0.849926i \(0.676647\pi\)
\(740\) −5.77334e11 −0.0707757
\(741\) −1.02318e12 −0.124672
\(742\) −3.53652e12 −0.428311
\(743\) −8.28397e12 −0.997215 −0.498607 0.866828i \(-0.666155\pi\)
−0.498607 + 0.866828i \(0.666155\pi\)
\(744\) 8.71074e12 1.04226
\(745\) −6.43740e12 −0.765610
\(746\) 2.54483e11 0.0300839
\(747\) 2.63707e12 0.309870
\(748\) 0 0
\(749\) −2.45757e12 −0.285323
\(750\) −3.28320e12 −0.378897
\(751\) 1.48068e13 1.69857 0.849284 0.527937i \(-0.177034\pi\)
0.849284 + 0.527937i \(0.177034\pi\)
\(752\) 6.47115e12 0.737906
\(753\) 5.42888e12 0.615365
\(754\) 1.05876e12 0.119296
\(755\) −5.28767e11 −0.0592247
\(756\) 6.99124e12 0.778406
\(757\) 1.52757e13 1.69072 0.845359 0.534199i \(-0.179387\pi\)
0.845359 + 0.534199i \(0.179387\pi\)
\(758\) 6.33939e11 0.0697487
\(759\) −1.88842e11 −0.0206543
\(760\) 3.42161e12 0.372023
\(761\) −8.91048e12 −0.963098 −0.481549 0.876419i \(-0.659926\pi\)
−0.481549 + 0.876419i \(0.659926\pi\)
\(762\) 1.74430e12 0.187423
\(763\) 3.62155e9 0.000386843 0
\(764\) 1.01880e13 1.08185
\(765\) 0 0
\(766\) 3.04377e12 0.319435
\(767\) −4.06151e12 −0.423749
\(768\) −4.21532e12 −0.437226
\(769\) 1.69319e13 1.74597 0.872986 0.487745i \(-0.162181\pi\)
0.872986 + 0.487745i \(0.162181\pi\)
\(770\) 2.04156e11 0.0209293
\(771\) −1.25618e13 −1.28029
\(772\) −1.23962e13 −1.25606
\(773\) −8.71332e12 −0.877760 −0.438880 0.898546i \(-0.644625\pi\)
−0.438880 + 0.898546i \(0.644625\pi\)
\(774\) 1.21289e12 0.121475
\(775\) 1.24301e12 0.123771
\(776\) −1.04957e13 −1.03905
\(777\) −6.89943e11 −0.0679076
\(778\) 4.61796e12 0.451899
\(779\) −5.74211e12 −0.558667
\(780\) 2.43566e12 0.235609
\(781\) 4.64118e10 0.00446374
\(782\) 0 0
\(783\) 8.93165e12 0.849188
\(784\) −7.40821e11 −0.0700312
\(785\) −1.16159e13 −1.09179
\(786\) 2.52535e12 0.236004
\(787\) −1.28811e13 −1.19692 −0.598460 0.801153i \(-0.704220\pi\)
−0.598460 + 0.801153i \(0.704220\pi\)
\(788\) 1.01789e12 0.0940446
\(789\) 1.05897e12 0.0972828
\(790\) 2.88469e12 0.263498
\(791\) −2.84799e12 −0.258669
\(792\) −1.09659e11 −0.00990333
\(793\) 5.93028e12 0.532532
\(794\) 9.07610e12 0.810414
\(795\) −1.03938e13 −0.922834
\(796\) 1.33769e13 1.18099
\(797\) 1.35922e13 1.19324 0.596620 0.802524i \(-0.296510\pi\)
0.596620 + 0.802524i \(0.296510\pi\)
\(798\) 1.80358e12 0.157443
\(799\) 0 0
\(800\) −9.88643e11 −0.0853364
\(801\) 3.86612e12 0.331840
\(802\) −7.52182e12 −0.642005
\(803\) 7.89964e11 0.0670483
\(804\) 1.37863e13 1.16358
\(805\) 5.61459e12 0.471234
\(806\) −2.67126e12 −0.222950
\(807\) 1.78332e12 0.148013
\(808\) −8.42312e12 −0.695219
\(809\) −2.22215e13 −1.82391 −0.911957 0.410287i \(-0.865429\pi\)
−0.911957 + 0.410287i \(0.865429\pi\)
\(810\) −4.01936e12 −0.328076
\(811\) −8.95583e12 −0.726962 −0.363481 0.931602i \(-0.618412\pi\)
−0.363481 + 0.931602i \(0.618412\pi\)
\(812\) 6.98596e12 0.563928
\(813\) −2.74843e12 −0.220637
\(814\) 2.37975e10 0.00189986
\(815\) 2.38330e13 1.89221
\(816\) 0 0
\(817\) −5.83928e12 −0.458522
\(818\) −6.08731e11 −0.0475374
\(819\) −9.74958e11 −0.0757196
\(820\) 1.36690e13 1.05578
\(821\) −2.26555e13 −1.74032 −0.870160 0.492768i \(-0.835985\pi\)
−0.870160 + 0.492768i \(0.835985\pi\)
\(822\) −3.37977e12 −0.258205
\(823\) −8.51338e12 −0.646849 −0.323424 0.946254i \(-0.604834\pi\)
−0.323424 + 0.946254i \(0.604834\pi\)
\(824\) 1.16313e13 0.878934
\(825\) 4.67178e10 0.00351107
\(826\) 7.15933e12 0.535134
\(827\) −6.30754e12 −0.468905 −0.234453 0.972128i \(-0.575330\pi\)
−0.234453 + 0.972128i \(0.575330\pi\)
\(828\) −1.33021e12 −0.0983519
\(829\) −1.64758e13 −1.21158 −0.605790 0.795625i \(-0.707143\pi\)
−0.605790 + 0.795625i \(0.707143\pi\)
\(830\) −8.07382e12 −0.590511
\(831\) −2.48380e12 −0.180681
\(832\) 2.38501e11 0.0172558
\(833\) 0 0
\(834\) 7.89654e12 0.565184
\(835\) 1.51671e13 1.07972
\(836\) 2.32863e11 0.0164882
\(837\) −2.25347e13 −1.58704
\(838\) −2.65063e12 −0.185674
\(839\) 7.27086e12 0.506591 0.253295 0.967389i \(-0.418486\pi\)
0.253295 + 0.967389i \(0.418486\pi\)
\(840\) −9.73380e12 −0.674568
\(841\) −5.58224e12 −0.384793
\(842\) 5.58961e12 0.383245
\(843\) 6.78633e12 0.462819
\(844\) 1.50046e13 1.01785
\(845\) 1.37398e13 0.927100
\(846\) 3.07458e12 0.206357
\(847\) −1.36148e13 −0.908945
\(848\) 6.35181e12 0.421809
\(849\) 4.70049e12 0.310497
\(850\) 0 0
\(851\) 6.54466e11 0.0427764
\(852\) −9.76039e11 −0.0634584
\(853\) 2.51770e13 1.62830 0.814148 0.580658i \(-0.197204\pi\)
0.814148 + 0.580658i \(0.197204\pi\)
\(854\) −1.04535e13 −0.672511
\(855\) −1.77549e12 −0.113624
\(856\) −4.04151e12 −0.257283
\(857\) 1.61645e13 1.02364 0.511821 0.859092i \(-0.328971\pi\)
0.511821 + 0.859092i \(0.328971\pi\)
\(858\) −1.00397e11 −0.00632455
\(859\) −6.12904e12 −0.384081 −0.192041 0.981387i \(-0.561511\pi\)
−0.192041 + 0.981387i \(0.561511\pi\)
\(860\) 1.39003e13 0.866527
\(861\) 1.63352e13 1.01300
\(862\) 6.38795e12 0.394075
\(863\) −2.11554e13 −1.29829 −0.649147 0.760663i \(-0.724874\pi\)
−0.649147 + 0.760663i \(0.724874\pi\)
\(864\) 1.79232e13 1.09422
\(865\) −1.14420e12 −0.0694910
\(866\) −4.98402e12 −0.301127
\(867\) 0 0
\(868\) −1.76257e13 −1.05392
\(869\) 4.45093e11 0.0264766
\(870\) −5.48504e12 −0.324596
\(871\) −9.58490e12 −0.564294
\(872\) 5.95571e9 0.000348826 0
\(873\) 5.44629e12 0.317349
\(874\) −1.71084e12 −0.0991766
\(875\) 1.50615e13 0.868624
\(876\) −1.66129e13 −0.953187
\(877\) −6.02432e12 −0.343882 −0.171941 0.985107i \(-0.555004\pi\)
−0.171941 + 0.985107i \(0.555004\pi\)
\(878\) −1.45426e12 −0.0825878
\(879\) −3.49568e12 −0.197507
\(880\) −3.66678e11 −0.0206116
\(881\) 1.40880e13 0.787877 0.393939 0.919137i \(-0.371112\pi\)
0.393939 + 0.919137i \(0.371112\pi\)
\(882\) −3.51980e11 −0.0195844
\(883\) −2.17863e13 −1.20604 −0.603019 0.797727i \(-0.706036\pi\)
−0.603019 + 0.797727i \(0.706036\pi\)
\(884\) 0 0
\(885\) 2.10413e13 1.15299
\(886\) −5.55430e12 −0.302815
\(887\) 2.02400e13 1.09788 0.548939 0.835862i \(-0.315032\pi\)
0.548939 + 0.835862i \(0.315032\pi\)
\(888\) −1.13462e12 −0.0612341
\(889\) −8.00187e12 −0.429669
\(890\) −1.18367e13 −0.632379
\(891\) −6.20166e11 −0.0329654
\(892\) −1.19198e13 −0.630417
\(893\) −1.48021e13 −0.778917
\(894\) −5.58027e12 −0.292170
\(895\) 8.33630e12 0.434280
\(896\) 1.73435e13 0.898980
\(897\) −2.76107e12 −0.142401
\(898\) 1.64939e13 0.846410
\(899\) −2.25177e13 −1.14975
\(900\) 3.29082e11 0.0167191
\(901\) 0 0
\(902\) −5.63433e11 −0.0283409
\(903\) 1.66116e13 0.831412
\(904\) −4.68356e12 −0.233248
\(905\) −1.41805e13 −0.702704
\(906\) −4.58362e11 −0.0226012
\(907\) 5.58311e12 0.273932 0.136966 0.990576i \(-0.456265\pi\)
0.136966 + 0.990576i \(0.456265\pi\)
\(908\) −6.46220e11 −0.0315496
\(909\) 4.37080e12 0.212336
\(910\) 2.98499e12 0.144297
\(911\) −5.00192e12 −0.240605 −0.120302 0.992737i \(-0.538386\pi\)
−0.120302 + 0.992737i \(0.538386\pi\)
\(912\) −3.23935e12 −0.155053
\(913\) −1.24575e12 −0.0593350
\(914\) 1.62578e12 0.0770554
\(915\) −3.07227e13 −1.44899
\(916\) −1.63078e13 −0.765361
\(917\) −1.15849e13 −0.541041
\(918\) 0 0
\(919\) 4.12676e13 1.90849 0.954245 0.299027i \(-0.0966620\pi\)
0.954245 + 0.299027i \(0.0966620\pi\)
\(920\) 9.23329e12 0.424924
\(921\) 1.08963e13 0.499011
\(922\) −1.37867e13 −0.628304
\(923\) 6.78591e11 0.0307752
\(924\) −6.62450e11 −0.0298971
\(925\) −1.61909e11 −0.00727167
\(926\) 1.38431e13 0.618707
\(927\) −6.03554e12 −0.268446
\(928\) 1.79097e13 0.792723
\(929\) −3.84635e11 −0.0169425 −0.00847127 0.999964i \(-0.502697\pi\)
−0.00847127 + 0.999964i \(0.502697\pi\)
\(930\) 1.38388e13 0.606633
\(931\) 1.69455e12 0.0739233
\(932\) 3.58812e13 1.55774
\(933\) −2.24948e13 −0.971884
\(934\) −4.59772e11 −0.0197689
\(935\) 0 0
\(936\) −1.60334e12 −0.0682784
\(937\) 1.61950e13 0.686360 0.343180 0.939270i \(-0.388496\pi\)
0.343180 + 0.939270i \(0.388496\pi\)
\(938\) 1.68955e13 0.712623
\(939\) 8.89570e12 0.373409
\(940\) 3.52361e13 1.47202
\(941\) −4.47189e13 −1.85925 −0.929625 0.368507i \(-0.879869\pi\)
−0.929625 + 0.368507i \(0.879869\pi\)
\(942\) −1.00692e13 −0.416646
\(943\) −1.54952e13 −0.638109
\(944\) −1.28586e13 −0.527011
\(945\) 2.51814e13 1.02715
\(946\) −5.72968e11 −0.0232606
\(947\) −1.54921e13 −0.625945 −0.312972 0.949762i \(-0.601325\pi\)
−0.312972 + 0.949762i \(0.601325\pi\)
\(948\) −9.36030e12 −0.376402
\(949\) 1.15501e13 0.462263
\(950\) 4.23248e11 0.0168593
\(951\) −8.14123e11 −0.0322759
\(952\) 0 0
\(953\) −2.48096e13 −0.974321 −0.487160 0.873313i \(-0.661967\pi\)
−0.487160 + 0.873313i \(0.661967\pi\)
\(954\) 3.01788e12 0.117960
\(955\) 3.66955e13 1.42757
\(956\) 3.75869e13 1.45538
\(957\) −8.46312e11 −0.0326157
\(958\) −1.80755e13 −0.693340
\(959\) 1.55045e13 0.591936
\(960\) −1.23559e12 −0.0469519
\(961\) 3.03728e13 1.14876
\(962\) 3.47946e11 0.0130986
\(963\) 2.09716e12 0.0785801
\(964\) 3.22308e13 1.20205
\(965\) −4.46492e13 −1.65745
\(966\) 4.86701e12 0.179831
\(967\) −4.72891e13 −1.73917 −0.869585 0.493784i \(-0.835613\pi\)
−0.869585 + 0.493784i \(0.835613\pi\)
\(968\) −2.23898e13 −0.819619
\(969\) 0 0
\(970\) −1.66747e13 −0.604763
\(971\) 2.61695e13 0.944733 0.472367 0.881402i \(-0.343400\pi\)
0.472367 + 0.881402i \(0.343400\pi\)
\(972\) −1.07353e13 −0.385757
\(973\) −3.62250e13 −1.29569
\(974\) 5.41194e12 0.192681
\(975\) 6.83065e11 0.0242070
\(976\) 1.87751e13 0.662303
\(977\) −6.84591e12 −0.240384 −0.120192 0.992751i \(-0.538351\pi\)
−0.120192 + 0.992751i \(0.538351\pi\)
\(978\) 2.06597e13 0.722102
\(979\) −1.82635e12 −0.0635420
\(980\) −4.03386e12 −0.139702
\(981\) −3.09044e9 −0.000106539 0
\(982\) 4.93428e12 0.169325
\(983\) −7.40291e11 −0.0252878 −0.0126439 0.999920i \(-0.504025\pi\)
−0.0126439 + 0.999920i \(0.504025\pi\)
\(984\) 2.68635e13 0.913448
\(985\) 3.66629e12 0.124098
\(986\) 0 0
\(987\) 4.21090e13 1.41237
\(988\) 3.40472e12 0.113678
\(989\) −1.57574e13 −0.523723
\(990\) −1.74216e11 −0.00576409
\(991\) 3.36050e13 1.10681 0.553404 0.832913i \(-0.313329\pi\)
0.553404 + 0.832913i \(0.313329\pi\)
\(992\) −4.51864e13 −1.48151
\(993\) 4.49774e13 1.46799
\(994\) −1.19617e12 −0.0388646
\(995\) 4.81816e13 1.55839
\(996\) 2.61980e13 0.843532
\(997\) 1.42102e12 0.0455482 0.0227741 0.999741i \(-0.492750\pi\)
0.0227741 + 0.999741i \(0.492750\pi\)
\(998\) 5.89076e11 0.0187968
\(999\) 2.93527e12 0.0932402
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.1.15 36
17.16 even 2 289.10.a.h.1.15 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.15 36 1.1 even 1 trivial
289.10.a.h.1.15 yes 36 17.16 even 2