Properties

Label 289.10.a.g.1.19
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 1.19
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.561663 q^{2} +191.593 q^{3} -511.685 q^{4} +819.697 q^{5} -107.611 q^{6} +1085.21 q^{7} +574.966 q^{8} +17024.9 q^{9} +O(q^{10})\) \(q-0.561663 q^{2} +191.593 q^{3} -511.685 q^{4} +819.697 q^{5} -107.611 q^{6} +1085.21 q^{7} +574.966 q^{8} +17024.9 q^{9} -460.393 q^{10} -48291.1 q^{11} -98035.2 q^{12} -107794. q^{13} -609.525 q^{14} +157048. q^{15} +261660. q^{16} -9562.26 q^{18} +872306. q^{19} -419426. q^{20} +207920. q^{21} +27123.3 q^{22} +1.91838e6 q^{23} +110159. q^{24} -1.28122e6 q^{25} +60543.9 q^{26} -509272. q^{27} -555288. q^{28} +476986. q^{29} -88208.1 q^{30} -11704.8 q^{31} -441347. q^{32} -9.25225e6 q^{33} +889547. q^{35} -8.71138e6 q^{36} -3.41910e6 q^{37} -489942. q^{38} -2.06526e7 q^{39} +471297. q^{40} +6.67947e6 q^{41} -116781. q^{42} -2.97683e7 q^{43} +2.47098e7 q^{44} +1.39553e7 q^{45} -1.07748e6 q^{46} -4.42148e7 q^{47} +5.01322e7 q^{48} -3.91759e7 q^{49} +719615. q^{50} +5.51565e7 q^{52} +4.59898e7 q^{53} +286039. q^{54} -3.95841e7 q^{55} +623961. q^{56} +1.67128e8 q^{57} -267905. q^{58} +2.34565e6 q^{59} -8.03591e7 q^{60} +1.31038e8 q^{61} +6574.13 q^{62} +1.84757e7 q^{63} -1.33722e8 q^{64} -8.83584e7 q^{65} +5.19664e6 q^{66} -1.30959e8 q^{67} +3.67548e8 q^{69} -499625. q^{70} -1.91474e8 q^{71} +9.78873e6 q^{72} -3.50083e8 q^{73} +1.92038e6 q^{74} -2.45473e8 q^{75} -4.46346e8 q^{76} -5.24062e7 q^{77} +1.15998e7 q^{78} +4.60211e8 q^{79} +2.14481e8 q^{80} -4.32674e8 q^{81} -3.75161e6 q^{82} -8.12815e8 q^{83} -1.06389e8 q^{84} +1.67198e7 q^{86} +9.13873e7 q^{87} -2.77657e7 q^{88} -6.40777e8 q^{89} -7.83815e6 q^{90} -1.16980e8 q^{91} -9.81604e8 q^{92} -2.24255e6 q^{93} +2.48338e7 q^{94} +7.15027e8 q^{95} -8.45590e7 q^{96} +2.77833e8 q^{97} +2.20037e7 q^{98} -8.22152e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.561663 −0.0248222 −0.0124111 0.999923i \(-0.503951\pi\)
−0.0124111 + 0.999923i \(0.503951\pi\)
\(3\) 191.593 1.36563 0.682817 0.730590i \(-0.260755\pi\)
0.682817 + 0.730590i \(0.260755\pi\)
\(4\) −511.685 −0.999384
\(5\) 819.697 0.586527 0.293264 0.956032i \(-0.405259\pi\)
0.293264 + 0.956032i \(0.405259\pi\)
\(6\) −107.611 −0.0338981
\(7\) 1085.21 0.170834 0.0854170 0.996345i \(-0.472778\pi\)
0.0854170 + 0.996345i \(0.472778\pi\)
\(8\) 574.966 0.0496292
\(9\) 17024.9 0.864955
\(10\) −460.393 −0.0145589
\(11\) −48291.1 −0.994490 −0.497245 0.867610i \(-0.665655\pi\)
−0.497245 + 0.867610i \(0.665655\pi\)
\(12\) −98035.2 −1.36479
\(13\) −107794. −1.04677 −0.523383 0.852098i \(-0.675330\pi\)
−0.523383 + 0.852098i \(0.675330\pi\)
\(14\) −609.525 −0.00424048
\(15\) 157048. 0.800981
\(16\) 261660. 0.998152
\(17\) 0 0
\(18\) −9562.26 −0.0214701
\(19\) 872306. 1.53560 0.767799 0.640690i \(-0.221352\pi\)
0.767799 + 0.640690i \(0.221352\pi\)
\(20\) −419426. −0.586166
\(21\) 207920. 0.233297
\(22\) 27123.3 0.0246854
\(23\) 1.91838e6 1.42942 0.714708 0.699423i \(-0.246559\pi\)
0.714708 + 0.699423i \(0.246559\pi\)
\(24\) 110159. 0.0677752
\(25\) −1.28122e6 −0.655986
\(26\) 60543.9 0.0259831
\(27\) −509272. −0.184422
\(28\) −555288. −0.170729
\(29\) 476986. 0.125232 0.0626159 0.998038i \(-0.480056\pi\)
0.0626159 + 0.998038i \(0.480056\pi\)
\(30\) −88208.1 −0.0198821
\(31\) −11704.8 −0.00227633 −0.00113817 0.999999i \(-0.500362\pi\)
−0.00113817 + 0.999999i \(0.500362\pi\)
\(32\) −441347. −0.0744055
\(33\) −9.25225e6 −1.35811
\(34\) 0 0
\(35\) 889547. 0.100199
\(36\) −8.71138e6 −0.864422
\(37\) −3.41910e6 −0.299919 −0.149960 0.988692i \(-0.547914\pi\)
−0.149960 + 0.988692i \(0.547914\pi\)
\(38\) −489942. −0.0381170
\(39\) −2.06526e7 −1.42950
\(40\) 471297. 0.0291089
\(41\) 6.67947e6 0.369160 0.184580 0.982817i \(-0.440908\pi\)
0.184580 + 0.982817i \(0.440908\pi\)
\(42\) −116781. −0.00579094
\(43\) −2.97683e7 −1.32784 −0.663921 0.747803i \(-0.731109\pi\)
−0.663921 + 0.747803i \(0.731109\pi\)
\(44\) 2.47098e7 0.993877
\(45\) 1.39553e7 0.507320
\(46\) −1.07748e6 −0.0354813
\(47\) −4.42148e7 −1.32168 −0.660841 0.750526i \(-0.729800\pi\)
−0.660841 + 0.750526i \(0.729800\pi\)
\(48\) 5.01322e7 1.36311
\(49\) −3.91759e7 −0.970816
\(50\) 719615. 0.0162830
\(51\) 0 0
\(52\) 5.51565e7 1.04612
\(53\) 4.59898e7 0.800609 0.400304 0.916382i \(-0.368904\pi\)
0.400304 + 0.916382i \(0.368904\pi\)
\(54\) 286039. 0.00457777
\(55\) −3.95841e7 −0.583295
\(56\) 623961. 0.00847835
\(57\) 1.67128e8 2.09707
\(58\) −267905. −0.00310853
\(59\) 2.34565e6 0.0252017 0.0126008 0.999921i \(-0.495989\pi\)
0.0126008 + 0.999921i \(0.495989\pi\)
\(60\) −8.03591e7 −0.800488
\(61\) 1.31038e8 1.21175 0.605877 0.795559i \(-0.292823\pi\)
0.605877 + 0.795559i \(0.292823\pi\)
\(62\) 6574.13 5.65036e−5 0
\(63\) 1.84757e7 0.147764
\(64\) −1.33722e8 −0.996305
\(65\) −8.83584e7 −0.613957
\(66\) 5.19664e6 0.0337113
\(67\) −1.30959e8 −0.793962 −0.396981 0.917827i \(-0.629942\pi\)
−0.396981 + 0.917827i \(0.629942\pi\)
\(68\) 0 0
\(69\) 3.67548e8 1.95206
\(70\) −499625. −0.00248716
\(71\) −1.91474e8 −0.894227 −0.447114 0.894477i \(-0.647548\pi\)
−0.447114 + 0.894477i \(0.647548\pi\)
\(72\) 9.78873e6 0.0429270
\(73\) −3.50083e8 −1.44284 −0.721421 0.692497i \(-0.756511\pi\)
−0.721421 + 0.692497i \(0.756511\pi\)
\(74\) 1.92038e6 0.00744466
\(75\) −2.45473e8 −0.895836
\(76\) −4.46346e8 −1.53465
\(77\) −5.24062e7 −0.169893
\(78\) 1.15998e7 0.0354833
\(79\) 4.60211e8 1.32934 0.664669 0.747138i \(-0.268573\pi\)
0.664669 + 0.747138i \(0.268573\pi\)
\(80\) 2.14481e8 0.585443
\(81\) −4.32674e8 −1.11681
\(82\) −3.75161e6 −0.00916337
\(83\) −8.12815e8 −1.87992 −0.939962 0.341280i \(-0.889139\pi\)
−0.939962 + 0.341280i \(0.889139\pi\)
\(84\) −1.06389e8 −0.233153
\(85\) 0 0
\(86\) 1.67198e7 0.0329600
\(87\) 9.13873e7 0.171021
\(88\) −2.77657e7 −0.0493557
\(89\) −6.40777e8 −1.08256 −0.541280 0.840842i \(-0.682060\pi\)
−0.541280 + 0.840842i \(0.682060\pi\)
\(90\) −7.83815e6 −0.0125928
\(91\) −1.16980e8 −0.178823
\(92\) −9.81604e8 −1.42854
\(93\) −2.24255e6 −0.00310863
\(94\) 2.48338e7 0.0328071
\(95\) 7.15027e8 0.900671
\(96\) −8.45590e7 −0.101611
\(97\) 2.77833e8 0.318648 0.159324 0.987226i \(-0.449068\pi\)
0.159324 + 0.987226i \(0.449068\pi\)
\(98\) 2.20037e7 0.0240978
\(99\) −8.22152e8 −0.860189
\(100\) 6.55582e8 0.655582
\(101\) 1.68691e9 1.61304 0.806522 0.591204i \(-0.201347\pi\)
0.806522 + 0.591204i \(0.201347\pi\)
\(102\) 0 0
\(103\) 2.74439e8 0.240259 0.120129 0.992758i \(-0.461669\pi\)
0.120129 + 0.992758i \(0.461669\pi\)
\(104\) −6.19778e7 −0.0519501
\(105\) 1.70431e8 0.136835
\(106\) −2.58308e7 −0.0198729
\(107\) 1.26641e9 0.934002 0.467001 0.884257i \(-0.345334\pi\)
0.467001 + 0.884257i \(0.345334\pi\)
\(108\) 2.60587e8 0.184309
\(109\) −6.82388e8 −0.463033 −0.231517 0.972831i \(-0.574369\pi\)
−0.231517 + 0.972831i \(0.574369\pi\)
\(110\) 2.22329e7 0.0144787
\(111\) −6.55076e8 −0.409580
\(112\) 2.83957e8 0.170518
\(113\) −2.35663e9 −1.35968 −0.679842 0.733359i \(-0.737952\pi\)
−0.679842 + 0.733359i \(0.737952\pi\)
\(114\) −9.38695e7 −0.0520538
\(115\) 1.57249e9 0.838392
\(116\) −2.44067e8 −0.125155
\(117\) −1.83518e9 −0.905405
\(118\) −1.31747e6 −0.000625562 0
\(119\) 0 0
\(120\) 9.02973e7 0.0397520
\(121\) −2.59142e7 −0.0109902
\(122\) −7.35994e7 −0.0300784
\(123\) 1.27974e9 0.504137
\(124\) 5.98915e6 0.00227493
\(125\) −2.65118e9 −0.971281
\(126\) −1.03771e7 −0.00366782
\(127\) −1.95160e9 −0.665693 −0.332846 0.942981i \(-0.608009\pi\)
−0.332846 + 0.942981i \(0.608009\pi\)
\(128\) 3.01076e8 0.0991360
\(129\) −5.70340e9 −1.81334
\(130\) 4.96276e7 0.0152398
\(131\) −3.45384e9 −1.02466 −0.512331 0.858788i \(-0.671218\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(132\) 4.73423e9 1.35727
\(133\) 9.46639e8 0.262333
\(134\) 7.35550e7 0.0197079
\(135\) −4.17449e8 −0.108169
\(136\) 0 0
\(137\) −6.90720e9 −1.67517 −0.837586 0.546306i \(-0.816034\pi\)
−0.837586 + 0.546306i \(0.816034\pi\)
\(138\) −2.06438e8 −0.0484544
\(139\) 4.01418e9 0.912075 0.456038 0.889960i \(-0.349268\pi\)
0.456038 + 0.889960i \(0.349268\pi\)
\(140\) −4.55167e8 −0.100137
\(141\) −8.47124e9 −1.80493
\(142\) 1.07544e8 0.0221967
\(143\) 5.20549e9 1.04100
\(144\) 4.45473e9 0.863356
\(145\) 3.90984e8 0.0734519
\(146\) 1.96629e8 0.0358145
\(147\) −7.50583e9 −1.32578
\(148\) 1.74950e9 0.299734
\(149\) 6.40738e9 1.06498 0.532491 0.846436i \(-0.321256\pi\)
0.532491 + 0.846436i \(0.321256\pi\)
\(150\) 1.37873e8 0.0222366
\(151\) 1.00847e10 1.57858 0.789291 0.614019i \(-0.210448\pi\)
0.789291 + 0.614019i \(0.210448\pi\)
\(152\) 5.01546e8 0.0762105
\(153\) 0 0
\(154\) 2.94346e7 0.00421712
\(155\) −9.59436e6 −0.00133513
\(156\) 1.05676e10 1.42862
\(157\) −1.00244e10 −1.31677 −0.658384 0.752682i \(-0.728760\pi\)
−0.658384 + 0.752682i \(0.728760\pi\)
\(158\) −2.58483e8 −0.0329971
\(159\) 8.81133e9 1.09334
\(160\) −3.61771e8 −0.0436409
\(161\) 2.08185e9 0.244193
\(162\) 2.43017e8 0.0277217
\(163\) −1.21030e10 −1.34292 −0.671458 0.741042i \(-0.734332\pi\)
−0.671458 + 0.741042i \(0.734332\pi\)
\(164\) −3.41778e9 −0.368933
\(165\) −7.58404e9 −0.796568
\(166\) 4.56528e8 0.0466639
\(167\) 1.68715e10 1.67853 0.839265 0.543723i \(-0.182986\pi\)
0.839265 + 0.543723i \(0.182986\pi\)
\(168\) 1.19547e8 0.0115783
\(169\) 1.01505e9 0.0957185
\(170\) 0 0
\(171\) 1.48509e10 1.32822
\(172\) 1.52320e10 1.32702
\(173\) 5.48179e9 0.465280 0.232640 0.972563i \(-0.425264\pi\)
0.232640 + 0.972563i \(0.425264\pi\)
\(174\) −5.13288e7 −0.00424512
\(175\) −1.39040e9 −0.112065
\(176\) −1.26358e10 −0.992652
\(177\) 4.49411e8 0.0344163
\(178\) 3.59901e8 0.0268715
\(179\) −2.39604e10 −1.74443 −0.872217 0.489118i \(-0.837319\pi\)
−0.872217 + 0.489118i \(0.837319\pi\)
\(180\) −7.14069e9 −0.507007
\(181\) −1.12778e10 −0.781037 −0.390518 0.920595i \(-0.627704\pi\)
−0.390518 + 0.920595i \(0.627704\pi\)
\(182\) 6.57031e7 0.00443879
\(183\) 2.51060e10 1.65481
\(184\) 1.10300e9 0.0709407
\(185\) −2.80263e9 −0.175911
\(186\) 1.25956e6 7.71632e−5 0
\(187\) 0 0
\(188\) 2.26240e10 1.32087
\(189\) −5.52670e8 −0.0315056
\(190\) −4.01604e8 −0.0223566
\(191\) −2.75406e10 −1.49735 −0.748674 0.662939i \(-0.769309\pi\)
−0.748674 + 0.662939i \(0.769309\pi\)
\(192\) −2.56202e10 −1.36059
\(193\) −4.05941e9 −0.210598 −0.105299 0.994441i \(-0.533580\pi\)
−0.105299 + 0.994441i \(0.533580\pi\)
\(194\) −1.56049e8 −0.00790956
\(195\) −1.69289e10 −0.838440
\(196\) 2.00457e10 0.970218
\(197\) 1.28333e10 0.607071 0.303536 0.952820i \(-0.401833\pi\)
0.303536 + 0.952820i \(0.401833\pi\)
\(198\) 4.61772e8 0.0213518
\(199\) 3.32562e9 0.150326 0.0751629 0.997171i \(-0.476052\pi\)
0.0751629 + 0.997171i \(0.476052\pi\)
\(200\) −7.36659e8 −0.0325560
\(201\) −2.50909e10 −1.08426
\(202\) −9.47476e8 −0.0400393
\(203\) 5.17633e8 0.0213939
\(204\) 0 0
\(205\) 5.47514e9 0.216522
\(206\) −1.54142e8 −0.00596375
\(207\) 3.26602e10 1.23638
\(208\) −2.82053e10 −1.04483
\(209\) −4.21247e10 −1.52714
\(210\) −9.57248e7 −0.00339655
\(211\) −5.54278e10 −1.92511 −0.962557 0.271078i \(-0.912620\pi\)
−0.962557 + 0.271078i \(0.912620\pi\)
\(212\) −2.35323e10 −0.800116
\(213\) −3.66851e10 −1.22119
\(214\) −7.11296e8 −0.0231840
\(215\) −2.44010e10 −0.778815
\(216\) −2.92814e8 −0.00915272
\(217\) −1.27022e7 −0.000388875 0
\(218\) 3.83272e8 0.0114935
\(219\) −6.70736e10 −1.97039
\(220\) 2.02546e10 0.582936
\(221\) 0 0
\(222\) 3.67932e8 0.0101667
\(223\) 3.94370e9 0.106790 0.0533951 0.998573i \(-0.482996\pi\)
0.0533951 + 0.998573i \(0.482996\pi\)
\(224\) −4.78956e8 −0.0127110
\(225\) −2.18127e10 −0.567398
\(226\) 1.32363e9 0.0337504
\(227\) 7.53067e10 1.88242 0.941212 0.337817i \(-0.109689\pi\)
0.941212 + 0.337817i \(0.109689\pi\)
\(228\) −8.55167e10 −2.09577
\(229\) −4.18732e10 −1.00618 −0.503091 0.864234i \(-0.667804\pi\)
−0.503091 + 0.864234i \(0.667804\pi\)
\(230\) −8.83208e8 −0.0208107
\(231\) −1.00407e10 −0.232011
\(232\) 2.74251e8 0.00621515
\(233\) 7.83446e9 0.174144 0.0870718 0.996202i \(-0.472249\pi\)
0.0870718 + 0.996202i \(0.472249\pi\)
\(234\) 1.03075e9 0.0224742
\(235\) −3.62427e10 −0.775202
\(236\) −1.20023e9 −0.0251862
\(237\) 8.81733e10 1.81539
\(238\) 0 0
\(239\) 1.99505e10 0.395516 0.197758 0.980251i \(-0.436634\pi\)
0.197758 + 0.980251i \(0.436634\pi\)
\(240\) 4.10932e10 0.799501
\(241\) −9.79058e9 −0.186953 −0.0934763 0.995622i \(-0.529798\pi\)
−0.0934763 + 0.995622i \(0.529798\pi\)
\(242\) 1.45550e7 0.000272800 0
\(243\) −7.28734e10 −1.34073
\(244\) −6.70503e10 −1.21101
\(245\) −3.21124e10 −0.569410
\(246\) −7.18783e8 −0.0125138
\(247\) −9.40294e10 −1.60741
\(248\) −6.72984e6 −0.000112972 0
\(249\) −1.55730e11 −2.56729
\(250\) 1.48907e9 0.0241093
\(251\) 4.99029e10 0.793587 0.396793 0.917908i \(-0.370123\pi\)
0.396793 + 0.917908i \(0.370123\pi\)
\(252\) −9.45372e9 −0.147673
\(253\) −9.26406e10 −1.42154
\(254\) 1.09614e9 0.0165240
\(255\) 0 0
\(256\) 6.82965e10 0.993844
\(257\) −4.15019e10 −0.593429 −0.296715 0.954966i \(-0.595891\pi\)
−0.296715 + 0.954966i \(0.595891\pi\)
\(258\) 3.20339e9 0.0450112
\(259\) −3.71046e9 −0.0512364
\(260\) 4.52116e10 0.613578
\(261\) 8.12065e9 0.108320
\(262\) 1.93989e9 0.0254344
\(263\) −4.28114e10 −0.551770 −0.275885 0.961191i \(-0.588971\pi\)
−0.275885 + 0.961191i \(0.588971\pi\)
\(264\) −5.31972e9 −0.0674018
\(265\) 3.76977e10 0.469579
\(266\) −5.31692e8 −0.00651168
\(267\) −1.22768e11 −1.47838
\(268\) 6.70098e10 0.793473
\(269\) −9.09356e9 −0.105889 −0.0529443 0.998597i \(-0.516861\pi\)
−0.0529443 + 0.998597i \(0.516861\pi\)
\(270\) 2.34466e8 0.00268499
\(271\) −6.01033e10 −0.676919 −0.338459 0.940981i \(-0.609906\pi\)
−0.338459 + 0.940981i \(0.609906\pi\)
\(272\) 0 0
\(273\) −2.24125e10 −0.244207
\(274\) 3.87951e9 0.0415815
\(275\) 6.18717e10 0.652371
\(276\) −1.88069e11 −1.95086
\(277\) −1.16062e11 −1.18449 −0.592245 0.805758i \(-0.701758\pi\)
−0.592245 + 0.805758i \(0.701758\pi\)
\(278\) −2.25462e9 −0.0226397
\(279\) −1.99273e8 −0.00196892
\(280\) 5.11459e8 0.00497278
\(281\) −1.64638e10 −0.157526 −0.0787628 0.996893i \(-0.525097\pi\)
−0.0787628 + 0.996893i \(0.525097\pi\)
\(282\) 4.75798e9 0.0448024
\(283\) −2.94955e10 −0.273349 −0.136674 0.990616i \(-0.543641\pi\)
−0.136674 + 0.990616i \(0.543641\pi\)
\(284\) 9.79744e10 0.893676
\(285\) 1.36994e11 1.22999
\(286\) −2.92373e9 −0.0258399
\(287\) 7.24866e9 0.0630651
\(288\) −7.51389e9 −0.0643574
\(289\) 0 0
\(290\) −2.19601e8 −0.00182324
\(291\) 5.32310e10 0.435157
\(292\) 1.79132e11 1.44195
\(293\) 6.57753e10 0.521385 0.260693 0.965422i \(-0.416049\pi\)
0.260693 + 0.965422i \(0.416049\pi\)
\(294\) 4.21575e9 0.0329088
\(295\) 1.92272e9 0.0147815
\(296\) −1.96587e9 −0.0148847
\(297\) 2.45933e10 0.183406
\(298\) −3.59878e9 −0.0264352
\(299\) −2.06790e11 −1.49626
\(300\) 1.25605e11 0.895284
\(301\) −3.23050e10 −0.226841
\(302\) −5.66421e9 −0.0391839
\(303\) 3.23201e11 2.20283
\(304\) 2.28247e11 1.53276
\(305\) 1.07412e11 0.710726
\(306\) 0 0
\(307\) −1.32282e11 −0.849922 −0.424961 0.905212i \(-0.639712\pi\)
−0.424961 + 0.905212i \(0.639712\pi\)
\(308\) 2.68155e10 0.169788
\(309\) 5.25807e10 0.328105
\(310\) 5.38880e6 3.31409e−5 0
\(311\) −1.82289e11 −1.10494 −0.552469 0.833533i \(-0.686314\pi\)
−0.552469 + 0.833533i \(0.686314\pi\)
\(312\) −1.18745e10 −0.0709448
\(313\) 2.01875e11 1.18887 0.594433 0.804145i \(-0.297377\pi\)
0.594433 + 0.804145i \(0.297377\pi\)
\(314\) 5.63032e9 0.0326851
\(315\) 1.51445e10 0.0866675
\(316\) −2.35483e11 −1.32852
\(317\) −2.34059e11 −1.30184 −0.650922 0.759145i \(-0.725618\pi\)
−0.650922 + 0.759145i \(0.725618\pi\)
\(318\) −4.94900e9 −0.0271391
\(319\) −2.30342e10 −0.124542
\(320\) −1.09611e11 −0.584360
\(321\) 2.42636e11 1.27550
\(322\) −1.16930e9 −0.00606141
\(323\) 0 0
\(324\) 2.21393e11 1.11612
\(325\) 1.38108e11 0.686663
\(326\) 6.79781e9 0.0333342
\(327\) −1.30741e11 −0.632334
\(328\) 3.84047e9 0.0183211
\(329\) −4.79825e10 −0.225788
\(330\) 4.25967e9 0.0197726
\(331\) 3.53670e11 1.61947 0.809733 0.586799i \(-0.199612\pi\)
0.809733 + 0.586799i \(0.199612\pi\)
\(332\) 4.15905e11 1.87876
\(333\) −5.82099e10 −0.259417
\(334\) −9.47608e9 −0.0416648
\(335\) −1.07347e11 −0.465680
\(336\) 5.44042e10 0.232866
\(337\) −1.79455e10 −0.0757918 −0.0378959 0.999282i \(-0.512066\pi\)
−0.0378959 + 0.999282i \(0.512066\pi\)
\(338\) −5.70114e8 −0.00237595
\(339\) −4.51513e11 −1.85683
\(340\) 0 0
\(341\) 5.65237e8 0.00226379
\(342\) −8.34122e9 −0.0329695
\(343\) −8.63066e10 −0.336682
\(344\) −1.71158e10 −0.0658996
\(345\) 3.01278e11 1.14494
\(346\) −3.07892e9 −0.0115493
\(347\) 2.92641e11 1.08356 0.541780 0.840520i \(-0.317751\pi\)
0.541780 + 0.840520i \(0.317751\pi\)
\(348\) −4.67615e10 −0.170915
\(349\) −3.69601e11 −1.33358 −0.666790 0.745245i \(-0.732332\pi\)
−0.666790 + 0.745245i \(0.732332\pi\)
\(350\) 7.80937e8 0.00278170
\(351\) 5.48965e10 0.193047
\(352\) 2.13131e10 0.0739955
\(353\) 2.48893e11 0.853151 0.426575 0.904452i \(-0.359720\pi\)
0.426575 + 0.904452i \(0.359720\pi\)
\(354\) −2.52417e8 −0.000854289 0
\(355\) −1.56951e11 −0.524489
\(356\) 3.27876e11 1.08189
\(357\) 0 0
\(358\) 1.34576e10 0.0433007
\(359\) −1.11262e11 −0.353525 −0.176763 0.984254i \(-0.556562\pi\)
−0.176763 + 0.984254i \(0.556562\pi\)
\(360\) 8.02379e9 0.0251778
\(361\) 4.38230e11 1.35806
\(362\) 6.33433e9 0.0193871
\(363\) −4.96498e9 −0.0150085
\(364\) 5.98567e10 0.178713
\(365\) −2.86962e11 −0.846266
\(366\) −1.41011e10 −0.0410761
\(367\) 4.78209e11 1.37601 0.688004 0.725707i \(-0.258487\pi\)
0.688004 + 0.725707i \(0.258487\pi\)
\(368\) 5.01962e11 1.42677
\(369\) 1.13717e11 0.319307
\(370\) 1.57413e9 0.00436650
\(371\) 4.99088e10 0.136771
\(372\) 1.14748e9 0.00310672
\(373\) −2.01183e9 −0.00538147 −0.00269073 0.999996i \(-0.500856\pi\)
−0.00269073 + 0.999996i \(0.500856\pi\)
\(374\) 0 0
\(375\) −5.07948e11 −1.32641
\(376\) −2.54220e10 −0.0655939
\(377\) −5.14163e10 −0.131088
\(378\) 3.10414e8 0.000782039 0
\(379\) 2.36032e11 0.587617 0.293809 0.955864i \(-0.405077\pi\)
0.293809 + 0.955864i \(0.405077\pi\)
\(380\) −3.65868e11 −0.900116
\(381\) −3.73913e11 −0.909092
\(382\) 1.54685e10 0.0371675
\(383\) 2.18959e11 0.519959 0.259979 0.965614i \(-0.416284\pi\)
0.259979 + 0.965614i \(0.416284\pi\)
\(384\) 5.76841e10 0.135383
\(385\) −4.29572e10 −0.0996467
\(386\) 2.28002e9 0.00522752
\(387\) −5.06803e11 −1.14852
\(388\) −1.42163e11 −0.318452
\(389\) −3.26424e11 −0.722785 −0.361393 0.932414i \(-0.617699\pi\)
−0.361393 + 0.932414i \(0.617699\pi\)
\(390\) 9.50831e9 0.0208119
\(391\) 0 0
\(392\) −2.25248e10 −0.0481808
\(393\) −6.61731e11 −1.39931
\(394\) −7.20797e9 −0.0150689
\(395\) 3.77234e11 0.779693
\(396\) 4.20682e11 0.859659
\(397\) 5.53429e11 1.11816 0.559081 0.829113i \(-0.311154\pi\)
0.559081 + 0.829113i \(0.311154\pi\)
\(398\) −1.86788e9 −0.00373142
\(399\) 1.81370e11 0.358250
\(400\) −3.35244e11 −0.654773
\(401\) 6.02853e11 1.16429 0.582146 0.813084i \(-0.302213\pi\)
0.582146 + 0.813084i \(0.302213\pi\)
\(402\) 1.40926e10 0.0269138
\(403\) 1.26170e9 0.00238278
\(404\) −8.63167e11 −1.61205
\(405\) −3.54662e11 −0.655038
\(406\) −2.90735e8 −0.000531044 0
\(407\) 1.65112e11 0.298267
\(408\) 0 0
\(409\) −4.44389e11 −0.785251 −0.392626 0.919698i \(-0.628433\pi\)
−0.392626 + 0.919698i \(0.628433\pi\)
\(410\) −3.07518e9 −0.00537457
\(411\) −1.32337e12 −2.28767
\(412\) −1.40426e11 −0.240110
\(413\) 2.54554e9 0.00430531
\(414\) −1.83440e10 −0.0306897
\(415\) −6.66262e11 −1.10263
\(416\) 4.75745e10 0.0778851
\(417\) 7.69090e11 1.24556
\(418\) 2.36599e10 0.0379069
\(419\) 4.80215e10 0.0761154 0.0380577 0.999276i \(-0.487883\pi\)
0.0380577 + 0.999276i \(0.487883\pi\)
\(420\) −8.72069e10 −0.136751
\(421\) −1.06241e12 −1.64825 −0.824125 0.566408i \(-0.808333\pi\)
−0.824125 + 0.566408i \(0.808333\pi\)
\(422\) 3.11317e10 0.0477856
\(423\) −7.52752e11 −1.14320
\(424\) 2.64426e10 0.0397335
\(425\) 0 0
\(426\) 2.06047e10 0.0303126
\(427\) 1.42205e11 0.207009
\(428\) −6.48003e11 −0.933426
\(429\) 9.97337e11 1.42162
\(430\) 1.37051e10 0.0193319
\(431\) 4.85426e11 0.677603 0.338802 0.940858i \(-0.389978\pi\)
0.338802 + 0.940858i \(0.389978\pi\)
\(432\) −1.33256e11 −0.184081
\(433\) −4.47519e11 −0.611809 −0.305905 0.952062i \(-0.598959\pi\)
−0.305905 + 0.952062i \(0.598959\pi\)
\(434\) 7.13435e6 9.65274e−6 0
\(435\) 7.49099e10 0.100308
\(436\) 3.49167e11 0.462748
\(437\) 1.67341e12 2.19501
\(438\) 3.76727e10 0.0489095
\(439\) −1.06264e12 −1.36551 −0.682756 0.730646i \(-0.739219\pi\)
−0.682756 + 0.730646i \(0.739219\pi\)
\(440\) −2.27595e10 −0.0289485
\(441\) −6.66966e11 −0.839712
\(442\) 0 0
\(443\) 9.71271e11 1.19818 0.599092 0.800680i \(-0.295528\pi\)
0.599092 + 0.800680i \(0.295528\pi\)
\(444\) 3.35192e11 0.409327
\(445\) −5.25243e11 −0.634951
\(446\) −2.21503e9 −0.00265077
\(447\) 1.22761e12 1.45437
\(448\) −1.45117e11 −0.170203
\(449\) 1.32225e12 1.53535 0.767673 0.640842i \(-0.221415\pi\)
0.767673 + 0.640842i \(0.221415\pi\)
\(450\) 1.22514e10 0.0140841
\(451\) −3.22559e11 −0.367126
\(452\) 1.20585e12 1.35885
\(453\) 1.93216e12 2.15576
\(454\) −4.22970e10 −0.0467259
\(455\) −9.58878e10 −0.104885
\(456\) 9.60927e10 0.104076
\(457\) 6.63489e11 0.711559 0.355780 0.934570i \(-0.384215\pi\)
0.355780 + 0.934570i \(0.384215\pi\)
\(458\) 2.35186e10 0.0249756
\(459\) 0 0
\(460\) −8.04618e11 −0.837875
\(461\) −5.21820e11 −0.538105 −0.269052 0.963126i \(-0.586710\pi\)
−0.269052 + 0.963126i \(0.586710\pi\)
\(462\) 5.63947e9 0.00575903
\(463\) 7.05702e11 0.713686 0.356843 0.934164i \(-0.383853\pi\)
0.356843 + 0.934164i \(0.383853\pi\)
\(464\) 1.24808e11 0.125000
\(465\) −1.83821e9 −0.00182330
\(466\) −4.40033e9 −0.00432263
\(467\) −4.78900e10 −0.0465928 −0.0232964 0.999729i \(-0.507416\pi\)
−0.0232964 + 0.999729i \(0.507416\pi\)
\(468\) 9.39035e11 0.904847
\(469\) −1.42119e11 −0.135636
\(470\) 2.03562e10 0.0192422
\(471\) −1.92060e12 −1.79822
\(472\) 1.34867e9 0.00125074
\(473\) 1.43755e12 1.32052
\(474\) −4.95236e10 −0.0450620
\(475\) −1.11762e12 −1.00733
\(476\) 0 0
\(477\) 7.82973e11 0.692490
\(478\) −1.12055e10 −0.00981758
\(479\) 1.02694e12 0.891325 0.445662 0.895201i \(-0.352968\pi\)
0.445662 + 0.895201i \(0.352968\pi\)
\(480\) −6.93127e10 −0.0595974
\(481\) 3.68559e11 0.313945
\(482\) 5.49900e9 0.00464058
\(483\) 3.98868e11 0.333478
\(484\) 1.32599e10 0.0109834
\(485\) 2.27739e11 0.186896
\(486\) 4.09303e10 0.0332799
\(487\) 1.58420e12 1.27623 0.638117 0.769939i \(-0.279713\pi\)
0.638117 + 0.769939i \(0.279713\pi\)
\(488\) 7.53425e10 0.0601383
\(489\) −2.31885e12 −1.83393
\(490\) 1.80363e10 0.0141340
\(491\) 1.84598e12 1.43338 0.716689 0.697393i \(-0.245657\pi\)
0.716689 + 0.697393i \(0.245657\pi\)
\(492\) −6.54823e11 −0.503827
\(493\) 0 0
\(494\) 5.28128e10 0.0398995
\(495\) −6.73915e11 −0.504524
\(496\) −3.06267e9 −0.00227212
\(497\) −2.07791e11 −0.152764
\(498\) 8.74675e10 0.0637257
\(499\) −2.56834e12 −1.85438 −0.927192 0.374587i \(-0.877784\pi\)
−0.927192 + 0.374587i \(0.877784\pi\)
\(500\) 1.35657e12 0.970682
\(501\) 3.23246e12 2.29226
\(502\) −2.80286e10 −0.0196986
\(503\) 2.19698e11 0.153028 0.0765139 0.997069i \(-0.475621\pi\)
0.0765139 + 0.997069i \(0.475621\pi\)
\(504\) 1.06229e10 0.00733339
\(505\) 1.38276e12 0.946094
\(506\) 5.20328e10 0.0352858
\(507\) 1.94476e11 0.130716
\(508\) 9.98603e11 0.665282
\(509\) 1.18957e12 0.785523 0.392762 0.919640i \(-0.371520\pi\)
0.392762 + 0.919640i \(0.371520\pi\)
\(510\) 0 0
\(511\) −3.79916e11 −0.246486
\(512\) −1.92511e11 −0.123805
\(513\) −4.44241e11 −0.283198
\(514\) 2.33101e10 0.0147302
\(515\) 2.24957e11 0.140918
\(516\) 2.91834e12 1.81223
\(517\) 2.13518e12 1.31440
\(518\) 2.08403e9 0.00127180
\(519\) 1.05027e12 0.635403
\(520\) −5.08030e10 −0.0304701
\(521\) −1.42213e12 −0.845611 −0.422805 0.906221i \(-0.638955\pi\)
−0.422805 + 0.906221i \(0.638955\pi\)
\(522\) −4.56107e9 −0.00268874
\(523\) 1.87654e12 1.09673 0.548365 0.836239i \(-0.315250\pi\)
0.548365 + 0.836239i \(0.315250\pi\)
\(524\) 1.76727e12 1.02403
\(525\) −2.66391e11 −0.153039
\(526\) 2.40456e10 0.0136962
\(527\) 0 0
\(528\) −2.42094e12 −1.35560
\(529\) 1.87902e12 1.04323
\(530\) −2.11734e10 −0.0116560
\(531\) 3.99345e10 0.0217983
\(532\) −4.84381e11 −0.262171
\(533\) −7.20007e11 −0.386424
\(534\) 6.89545e10 0.0366967
\(535\) 1.03807e12 0.547818
\(536\) −7.52971e10 −0.0394037
\(537\) −4.59064e12 −2.38226
\(538\) 5.10752e9 0.00262839
\(539\) 1.89185e12 0.965466
\(540\) 2.13602e11 0.108102
\(541\) −1.39571e11 −0.0700501 −0.0350251 0.999386i \(-0.511151\pi\)
−0.0350251 + 0.999386i \(0.511151\pi\)
\(542\) 3.37578e10 0.0168026
\(543\) −2.16075e12 −1.06661
\(544\) 0 0
\(545\) −5.59351e11 −0.271582
\(546\) 1.25883e10 0.00606176
\(547\) −2.15413e12 −1.02879 −0.514396 0.857552i \(-0.671984\pi\)
−0.514396 + 0.857552i \(0.671984\pi\)
\(548\) 3.53431e12 1.67414
\(549\) 2.23092e12 1.04811
\(550\) −3.47510e10 −0.0161933
\(551\) 4.16078e11 0.192306
\(552\) 2.11327e11 0.0968790
\(553\) 4.99428e11 0.227096
\(554\) 6.51877e10 0.0294017
\(555\) −5.36964e11 −0.240230
\(556\) −2.05400e12 −0.911513
\(557\) 2.19665e12 0.966967 0.483484 0.875353i \(-0.339371\pi\)
0.483484 + 0.875353i \(0.339371\pi\)
\(558\) 1.11924e8 4.88731e−5 0
\(559\) 3.20885e12 1.38994
\(560\) 2.32758e11 0.100014
\(561\) 0 0
\(562\) 9.24709e9 0.00391013
\(563\) −2.37997e12 −0.998351 −0.499176 0.866501i \(-0.666364\pi\)
−0.499176 + 0.866501i \(0.666364\pi\)
\(564\) 4.33460e12 1.80382
\(565\) −1.93172e12 −0.797492
\(566\) 1.65665e10 0.00678512
\(567\) −4.69544e11 −0.190789
\(568\) −1.10091e11 −0.0443797
\(569\) −3.68803e12 −1.47499 −0.737496 0.675351i \(-0.763992\pi\)
−0.737496 + 0.675351i \(0.763992\pi\)
\(570\) −7.69445e10 −0.0305310
\(571\) −1.37282e11 −0.0540446 −0.0270223 0.999635i \(-0.508603\pi\)
−0.0270223 + 0.999635i \(0.508603\pi\)
\(572\) −2.66357e12 −1.04036
\(573\) −5.27658e12 −2.04483
\(574\) −4.07130e9 −0.00156542
\(575\) −2.45787e12 −0.937677
\(576\) −2.27660e12 −0.861759
\(577\) 1.13535e12 0.426421 0.213211 0.977006i \(-0.431608\pi\)
0.213211 + 0.977006i \(0.431608\pi\)
\(578\) 0 0
\(579\) −7.77755e11 −0.287600
\(580\) −2.00061e11 −0.0734067
\(581\) −8.82078e11 −0.321155
\(582\) −2.98978e10 −0.0108016
\(583\) −2.22090e12 −0.796197
\(584\) −2.01286e11 −0.0716070
\(585\) −1.50429e12 −0.531045
\(586\) −3.69436e10 −0.0129419
\(587\) 1.87198e12 0.650775 0.325387 0.945581i \(-0.394505\pi\)
0.325387 + 0.945581i \(0.394505\pi\)
\(588\) 3.84062e12 1.32496
\(589\) −1.02101e10 −0.00349553
\(590\) −1.07992e9 −0.000366909 0
\(591\) 2.45877e12 0.829037
\(592\) −8.94641e11 −0.299365
\(593\) −1.38472e12 −0.459849 −0.229924 0.973208i \(-0.573848\pi\)
−0.229924 + 0.973208i \(0.573848\pi\)
\(594\) −1.38132e10 −0.00455254
\(595\) 0 0
\(596\) −3.27855e12 −1.06433
\(597\) 6.37165e11 0.205290
\(598\) 1.16146e11 0.0371406
\(599\) 1.12797e12 0.357994 0.178997 0.983850i \(-0.442715\pi\)
0.178997 + 0.983850i \(0.442715\pi\)
\(600\) −1.41139e11 −0.0444596
\(601\) −1.59905e12 −0.499950 −0.249975 0.968252i \(-0.580422\pi\)
−0.249975 + 0.968252i \(0.580422\pi\)
\(602\) 1.81445e10 0.00563069
\(603\) −2.22957e12 −0.686741
\(604\) −5.16019e12 −1.57761
\(605\) −2.12418e10 −0.00644603
\(606\) −1.81530e11 −0.0546791
\(607\) 6.28574e12 1.87935 0.939675 0.342070i \(-0.111128\pi\)
0.939675 + 0.342070i \(0.111128\pi\)
\(608\) −3.84990e11 −0.114257
\(609\) 9.91748e10 0.0292162
\(610\) −6.03292e10 −0.0176418
\(611\) 4.76609e12 1.38349
\(612\) 0 0
\(613\) 4.11174e12 1.17612 0.588062 0.808816i \(-0.299891\pi\)
0.588062 + 0.808816i \(0.299891\pi\)
\(614\) 7.42980e10 0.0210969
\(615\) 1.04900e12 0.295690
\(616\) −3.01318e10 −0.00843163
\(617\) −1.45708e12 −0.404763 −0.202382 0.979307i \(-0.564868\pi\)
−0.202382 + 0.979307i \(0.564868\pi\)
\(618\) −2.95326e10 −0.00814430
\(619\) −5.12989e12 −1.40443 −0.702215 0.711965i \(-0.747805\pi\)
−0.702215 + 0.711965i \(0.747805\pi\)
\(620\) 4.90929e9 0.00133431
\(621\) −9.76977e11 −0.263616
\(622\) 1.02385e11 0.0274270
\(623\) −6.95381e11 −0.184938
\(624\) −5.40395e12 −1.42686
\(625\) 3.29220e11 0.0863031
\(626\) −1.13386e11 −0.0295103
\(627\) −8.07079e12 −2.08551
\(628\) 5.12932e12 1.31596
\(629\) 0 0
\(630\) −8.50608e9 −0.00215128
\(631\) 2.41230e12 0.605758 0.302879 0.953029i \(-0.402052\pi\)
0.302879 + 0.953029i \(0.402052\pi\)
\(632\) 2.64606e11 0.0659739
\(633\) −1.06196e13 −2.62900
\(634\) 1.31462e11 0.0323147
\(635\) −1.59972e12 −0.390447
\(636\) −4.50862e12 −1.09266
\(637\) 4.22293e12 1.01622
\(638\) 1.29375e10 0.00309141
\(639\) −3.25983e12 −0.773466
\(640\) 2.46791e11 0.0581460
\(641\) 7.11788e12 1.66529 0.832644 0.553808i \(-0.186826\pi\)
0.832644 + 0.553808i \(0.186826\pi\)
\(642\) −1.36279e11 −0.0316608
\(643\) −1.35629e12 −0.312898 −0.156449 0.987686i \(-0.550005\pi\)
−0.156449 + 0.987686i \(0.550005\pi\)
\(644\) −1.06525e12 −0.244043
\(645\) −4.67506e12 −1.06358
\(646\) 0 0
\(647\) 6.77234e12 1.51939 0.759696 0.650279i \(-0.225348\pi\)
0.759696 + 0.650279i \(0.225348\pi\)
\(648\) −2.48773e11 −0.0554262
\(649\) −1.13274e11 −0.0250628
\(650\) −7.75702e10 −0.0170445
\(651\) −2.43365e9 −0.000531060 0
\(652\) 6.19292e12 1.34209
\(653\) −3.75856e12 −0.808932 −0.404466 0.914553i \(-0.632543\pi\)
−0.404466 + 0.914553i \(0.632543\pi\)
\(654\) 7.34323e10 0.0156959
\(655\) −2.83110e12 −0.600993
\(656\) 1.74775e12 0.368478
\(657\) −5.96014e12 −1.24799
\(658\) 2.69500e10 0.00560457
\(659\) −5.81223e11 −0.120049 −0.0600245 0.998197i \(-0.519118\pi\)
−0.0600245 + 0.998197i \(0.519118\pi\)
\(660\) 3.88063e12 0.796077
\(661\) 2.62625e11 0.0535093 0.0267547 0.999642i \(-0.491483\pi\)
0.0267547 + 0.999642i \(0.491483\pi\)
\(662\) −1.98643e11 −0.0401987
\(663\) 0 0
\(664\) −4.67340e11 −0.0932990
\(665\) 7.75957e11 0.153865
\(666\) 3.26943e10 0.00643930
\(667\) 9.15040e11 0.179009
\(668\) −8.63287e12 −1.67750
\(669\) 7.55585e11 0.145836
\(670\) 6.02928e10 0.0115592
\(671\) −6.32799e12 −1.20508
\(672\) −9.17647e10 −0.0173586
\(673\) −1.29413e11 −0.0243171 −0.0121585 0.999926i \(-0.503870\pi\)
−0.0121585 + 0.999926i \(0.503870\pi\)
\(674\) 1.00793e10 0.00188132
\(675\) 6.52491e11 0.120978
\(676\) −5.19384e11 −0.0956595
\(677\) −7.30256e12 −1.33606 −0.668030 0.744134i \(-0.732862\pi\)
−0.668030 + 0.744134i \(0.732862\pi\)
\(678\) 2.53598e11 0.0460906
\(679\) 3.01509e11 0.0544360
\(680\) 0 0
\(681\) 1.44282e13 2.57070
\(682\) −3.17472e8 −5.61922e−5 0
\(683\) 4.16386e12 0.732155 0.366077 0.930584i \(-0.380701\pi\)
0.366077 + 0.930584i \(0.380701\pi\)
\(684\) −7.59899e12 −1.32741
\(685\) −5.66181e12 −0.982534
\(686\) 4.84752e10 0.00835721
\(687\) −8.02261e12 −1.37407
\(688\) −7.78916e12 −1.32539
\(689\) −4.95743e12 −0.838050
\(690\) −1.69217e11 −0.0284199
\(691\) 2.56802e12 0.428497 0.214249 0.976779i \(-0.431270\pi\)
0.214249 + 0.976779i \(0.431270\pi\)
\(692\) −2.80495e12 −0.464994
\(693\) −8.92211e11 −0.146950
\(694\) −1.64366e11 −0.0268964
\(695\) 3.29041e12 0.534957
\(696\) 5.25445e10 0.00848762
\(697\) 0 0
\(698\) 2.07591e11 0.0331024
\(699\) 1.50103e12 0.237816
\(700\) 7.11447e11 0.111996
\(701\) −7.09539e11 −0.110980 −0.0554901 0.998459i \(-0.517672\pi\)
−0.0554901 + 0.998459i \(0.517672\pi\)
\(702\) −3.08333e10 −0.00479185
\(703\) −2.98250e12 −0.460556
\(704\) 6.45758e12 0.990815
\(705\) −6.94385e12 −1.05864
\(706\) −1.39794e11 −0.0211771
\(707\) 1.83066e12 0.275563
\(708\) −2.29957e11 −0.0343951
\(709\) −7.62898e12 −1.13386 −0.566929 0.823767i \(-0.691869\pi\)
−0.566929 + 0.823767i \(0.691869\pi\)
\(710\) 8.81534e10 0.0130190
\(711\) 7.83505e12 1.14982
\(712\) −3.68425e11 −0.0537265
\(713\) −2.24542e10 −0.00325382
\(714\) 0 0
\(715\) 4.26693e12 0.610574
\(716\) 1.22601e13 1.74336
\(717\) 3.82238e12 0.540129
\(718\) 6.24915e10 0.00877528
\(719\) −1.27543e13 −1.77982 −0.889912 0.456132i \(-0.849235\pi\)
−0.889912 + 0.456132i \(0.849235\pi\)
\(720\) 3.65153e12 0.506382
\(721\) 2.97826e11 0.0410443
\(722\) −2.46138e11 −0.0337102
\(723\) −1.87581e12 −0.255309
\(724\) 5.77068e12 0.780555
\(725\) −6.11125e11 −0.0821503
\(726\) 2.78865e9 0.000372545 0
\(727\) 1.32065e13 1.75341 0.876706 0.481027i \(-0.159736\pi\)
0.876706 + 0.481027i \(0.159736\pi\)
\(728\) −6.72593e10 −0.00887485
\(729\) −5.44571e12 −0.714135
\(730\) 1.61176e11 0.0210062
\(731\) 0 0
\(732\) −1.28464e13 −1.65379
\(733\) −3.68770e12 −0.471832 −0.235916 0.971773i \(-0.575809\pi\)
−0.235916 + 0.971773i \(0.575809\pi\)
\(734\) −2.68592e11 −0.0341556
\(735\) −6.15251e12 −0.777605
\(736\) −8.46670e11 −0.106356
\(737\) 6.32417e12 0.789587
\(738\) −6.38708e10 −0.00792590
\(739\) 8.56654e12 1.05659 0.528294 0.849062i \(-0.322832\pi\)
0.528294 + 0.849062i \(0.322832\pi\)
\(740\) 1.43406e12 0.175802
\(741\) −1.80154e13 −2.19514
\(742\) −2.80319e10 −0.00339497
\(743\) 2.43702e12 0.293366 0.146683 0.989184i \(-0.453140\pi\)
0.146683 + 0.989184i \(0.453140\pi\)
\(744\) −1.28939e9 −0.000154279 0
\(745\) 5.25210e12 0.624641
\(746\) 1.12997e9 0.000133580 0
\(747\) −1.38381e13 −1.62605
\(748\) 0 0
\(749\) 1.37433e12 0.159559
\(750\) 2.85296e11 0.0329245
\(751\) 3.48665e12 0.399971 0.199986 0.979799i \(-0.435910\pi\)
0.199986 + 0.979799i \(0.435910\pi\)
\(752\) −1.15692e13 −1.31924
\(753\) 9.56106e12 1.08375
\(754\) 2.88786e10 0.00325391
\(755\) 8.26640e12 0.925881
\(756\) 2.82793e11 0.0314862
\(757\) −5.04037e12 −0.557868 −0.278934 0.960310i \(-0.589981\pi\)
−0.278934 + 0.960310i \(0.589981\pi\)
\(758\) −1.32570e11 −0.0145860
\(759\) −1.77493e13 −1.94130
\(760\) 4.11116e11 0.0446995
\(761\) 3.98658e12 0.430893 0.215447 0.976516i \(-0.430879\pi\)
0.215447 + 0.976516i \(0.430879\pi\)
\(762\) 2.10013e11 0.0225657
\(763\) −7.40538e11 −0.0791019
\(764\) 1.40921e13 1.49642
\(765\) 0 0
\(766\) −1.22981e11 −0.0129065
\(767\) −2.52847e11 −0.0263803
\(768\) 1.30851e13 1.35723
\(769\) 1.13185e13 1.16713 0.583567 0.812065i \(-0.301656\pi\)
0.583567 + 0.812065i \(0.301656\pi\)
\(770\) 2.41275e10 0.00247345
\(771\) −7.95148e12 −0.810407
\(772\) 2.07714e12 0.210469
\(773\) 1.89037e13 1.90431 0.952157 0.305610i \(-0.0988603\pi\)
0.952157 + 0.305610i \(0.0988603\pi\)
\(774\) 2.84652e11 0.0285089
\(775\) 1.49964e10 0.00149324
\(776\) 1.59745e11 0.0158142
\(777\) −7.10898e11 −0.0699702
\(778\) 1.83340e11 0.0179411
\(779\) 5.82654e12 0.566882
\(780\) 8.66223e12 0.837923
\(781\) 9.24651e12 0.889300
\(782\) 0 0
\(783\) −2.42916e11 −0.0230955
\(784\) −1.02508e13 −0.969022
\(785\) −8.21695e12 −0.772320
\(786\) 3.71670e11 0.0347341
\(787\) −1.40103e13 −1.30185 −0.650926 0.759141i \(-0.725619\pi\)
−0.650926 + 0.759141i \(0.725619\pi\)
\(788\) −6.56659e12 −0.606697
\(789\) −8.20236e12 −0.753516
\(790\) −2.11878e11 −0.0193537
\(791\) −2.55745e12 −0.232280
\(792\) −4.72709e11 −0.0426904
\(793\) −1.41251e13 −1.26842
\(794\) −3.10841e11 −0.0277553
\(795\) 7.22262e12 0.641273
\(796\) −1.70167e12 −0.150233
\(797\) 1.51222e13 1.32756 0.663779 0.747929i \(-0.268952\pi\)
0.663779 + 0.747929i \(0.268952\pi\)
\(798\) −1.01869e11 −0.00889257
\(799\) 0 0
\(800\) 5.65463e11 0.0488089
\(801\) −1.09092e13 −0.936366
\(802\) −3.38600e11 −0.0289003
\(803\) 1.69059e13 1.43489
\(804\) 1.28386e13 1.08359
\(805\) 1.70649e12 0.143226
\(806\) −7.08652e8 −5.91460e−5 0
\(807\) −1.74226e12 −0.144605
\(808\) 9.69916e11 0.0800540
\(809\) −1.21574e13 −0.997866 −0.498933 0.866640i \(-0.666275\pi\)
−0.498933 + 0.866640i \(0.666275\pi\)
\(810\) 1.99200e11 0.0162595
\(811\) 1.74499e12 0.141644 0.0708222 0.997489i \(-0.477438\pi\)
0.0708222 + 0.997489i \(0.477438\pi\)
\(812\) −2.64865e11 −0.0213807
\(813\) −1.15154e13 −0.924423
\(814\) −9.27374e10 −0.00740364
\(815\) −9.92079e12 −0.787657
\(816\) 0 0
\(817\) −2.59671e13 −2.03903
\(818\) 2.49597e11 0.0194917
\(819\) −1.99157e12 −0.154674
\(820\) −2.80154e12 −0.216389
\(821\) 1.53608e13 1.17997 0.589983 0.807416i \(-0.299135\pi\)
0.589983 + 0.807416i \(0.299135\pi\)
\(822\) 7.43288e11 0.0567851
\(823\) 9.62758e12 0.731506 0.365753 0.930712i \(-0.380811\pi\)
0.365753 + 0.930712i \(0.380811\pi\)
\(824\) 1.57793e11 0.0119238
\(825\) 1.18542e13 0.890900
\(826\) −1.42973e9 −0.000106867 0
\(827\) 2.95089e12 0.219370 0.109685 0.993966i \(-0.465016\pi\)
0.109685 + 0.993966i \(0.465016\pi\)
\(828\) −1.67117e13 −1.23562
\(829\) 1.75845e13 1.29311 0.646554 0.762868i \(-0.276209\pi\)
0.646554 + 0.762868i \(0.276209\pi\)
\(830\) 3.74214e11 0.0273696
\(831\) −2.22367e13 −1.61758
\(832\) 1.44144e13 1.04290
\(833\) 0 0
\(834\) −4.31969e11 −0.0309176
\(835\) 1.38295e13 0.984503
\(836\) 2.15545e13 1.52620
\(837\) 5.96092e9 0.000419806 0
\(838\) −2.69719e10 −0.00188935
\(839\) −1.82710e13 −1.27302 −0.636509 0.771269i \(-0.719622\pi\)
−0.636509 + 0.771269i \(0.719622\pi\)
\(840\) 9.79920e10 0.00679100
\(841\) −1.42796e13 −0.984317
\(842\) 5.96717e11 0.0409132
\(843\) −3.15435e12 −0.215122
\(844\) 2.83616e13 1.92393
\(845\) 8.32031e11 0.0561415
\(846\) 4.22793e11 0.0283766
\(847\) −2.81225e10 −0.00187749
\(848\) 1.20337e13 0.799129
\(849\) −5.65113e12 −0.373294
\(850\) 0 0
\(851\) −6.55913e12 −0.428709
\(852\) 1.87712e13 1.22043
\(853\) −2.21213e13 −1.43067 −0.715337 0.698780i \(-0.753727\pi\)
−0.715337 + 0.698780i \(0.753727\pi\)
\(854\) −7.98711e10 −0.00513842
\(855\) 1.21733e13 0.779039
\(856\) 7.28143e11 0.0463537
\(857\) 3.03667e12 0.192302 0.0961511 0.995367i \(-0.469347\pi\)
0.0961511 + 0.995367i \(0.469347\pi\)
\(858\) −5.60167e11 −0.0352878
\(859\) 1.80675e13 1.13221 0.566107 0.824332i \(-0.308449\pi\)
0.566107 + 0.824332i \(0.308449\pi\)
\(860\) 1.24856e13 0.778335
\(861\) 1.38879e12 0.0861238
\(862\) −2.72646e11 −0.0168196
\(863\) −4.21555e12 −0.258705 −0.129353 0.991599i \(-0.541290\pi\)
−0.129353 + 0.991599i \(0.541290\pi\)
\(864\) 2.24766e11 0.0137220
\(865\) 4.49340e12 0.272900
\(866\) 2.51355e11 0.0151865
\(867\) 0 0
\(868\) 6.49951e9 0.000388635 0
\(869\) −2.22241e13 −1.32201
\(870\) −4.20741e10 −0.00248988
\(871\) 1.41166e13 0.831092
\(872\) −3.92350e11 −0.0229800
\(873\) 4.73009e12 0.275616
\(874\) −9.39894e11 −0.0544850
\(875\) −2.87710e12 −0.165928
\(876\) 3.43205e13 1.96918
\(877\) 1.83513e12 0.104754 0.0523768 0.998627i \(-0.483320\pi\)
0.0523768 + 0.998627i \(0.483320\pi\)
\(878\) 5.96845e11 0.0338951
\(879\) 1.26021e13 0.712021
\(880\) −1.03576e13 −0.582217
\(881\) −2.66113e13 −1.48825 −0.744124 0.668042i \(-0.767133\pi\)
−0.744124 + 0.668042i \(0.767133\pi\)
\(882\) 3.74610e11 0.0208435
\(883\) −1.48033e13 −0.819472 −0.409736 0.912204i \(-0.634379\pi\)
−0.409736 + 0.912204i \(0.634379\pi\)
\(884\) 0 0
\(885\) 3.68381e11 0.0201861
\(886\) −5.45527e11 −0.0297416
\(887\) −2.12459e13 −1.15244 −0.576221 0.817294i \(-0.695473\pi\)
−0.576221 + 0.817294i \(0.695473\pi\)
\(888\) −3.76646e11 −0.0203271
\(889\) −2.11790e12 −0.113723
\(890\) 2.95009e11 0.0157609
\(891\) 2.08943e13 1.11065
\(892\) −2.01793e12 −0.106724
\(893\) −3.85688e13 −2.02957
\(894\) −6.89502e11 −0.0361008
\(895\) −1.96402e13 −1.02316
\(896\) 3.26732e11 0.0169358
\(897\) −3.96195e13 −2.04335
\(898\) −7.42660e11 −0.0381107
\(899\) −5.58302e9 −0.000285069 0
\(900\) 1.11612e13 0.567048
\(901\) 0 0
\(902\) 1.81169e11 0.00911288
\(903\) −6.18942e12 −0.309781
\(904\) −1.35498e12 −0.0674799
\(905\) −9.24439e12 −0.458099
\(906\) −1.08522e12 −0.0535109
\(907\) 6.95909e12 0.341444 0.170722 0.985319i \(-0.445390\pi\)
0.170722 + 0.985319i \(0.445390\pi\)
\(908\) −3.85333e13 −1.88126
\(909\) 2.87195e13 1.39521
\(910\) 5.38566e10 0.00260347
\(911\) 3.30588e13 1.59021 0.795105 0.606472i \(-0.207416\pi\)
0.795105 + 0.606472i \(0.207416\pi\)
\(912\) 4.37306e13 2.09319
\(913\) 3.92517e13 1.86956
\(914\) −3.72657e11 −0.0176625
\(915\) 2.05793e13 0.970592
\(916\) 2.14259e13 1.00556
\(917\) −3.74815e12 −0.175047
\(918\) 0 0
\(919\) 3.72968e13 1.72485 0.862425 0.506185i \(-0.168945\pi\)
0.862425 + 0.506185i \(0.168945\pi\)
\(920\) 9.04126e11 0.0416087
\(921\) −2.53444e13 −1.16068
\(922\) 2.93087e11 0.0133570
\(923\) 2.06398e13 0.936046
\(924\) 5.13766e12 0.231868
\(925\) 4.38063e12 0.196743
\(926\) −3.96367e11 −0.0177153
\(927\) 4.67230e12 0.207813
\(928\) −2.10516e11 −0.00931794
\(929\) 1.89331e13 0.833971 0.416986 0.908913i \(-0.363087\pi\)
0.416986 + 0.908913i \(0.363087\pi\)
\(930\) 1.03246e9 4.52583e−5 0
\(931\) −3.41734e13 −1.49078
\(932\) −4.00877e12 −0.174036
\(933\) −3.49252e13 −1.50894
\(934\) 2.68980e10 0.00115654
\(935\) 0 0
\(936\) −1.05517e12 −0.0449345
\(937\) −1.85059e13 −0.784300 −0.392150 0.919901i \(-0.628269\pi\)
−0.392150 + 0.919901i \(0.628269\pi\)
\(938\) 7.98229e10 0.00336678
\(939\) 3.86778e13 1.62355
\(940\) 1.85448e13 0.774725
\(941\) 9.74771e12 0.405274 0.202637 0.979254i \(-0.435049\pi\)
0.202637 + 0.979254i \(0.435049\pi\)
\(942\) 1.07873e12 0.0446359
\(943\) 1.28137e13 0.527683
\(944\) 6.13763e11 0.0251551
\(945\) −4.53022e11 −0.0184789
\(946\) −8.07416e11 −0.0327784
\(947\) −1.19050e13 −0.481009 −0.240504 0.970648i \(-0.577313\pi\)
−0.240504 + 0.970648i \(0.577313\pi\)
\(948\) −4.51169e13 −1.81427
\(949\) 3.77369e13 1.51032
\(950\) 6.27724e11 0.0250042
\(951\) −4.48441e13 −1.77784
\(952\) 0 0
\(953\) 5.94643e12 0.233527 0.116764 0.993160i \(-0.462748\pi\)
0.116764 + 0.993160i \(0.462748\pi\)
\(954\) −4.39767e11 −0.0171892
\(955\) −2.25749e13 −0.878235
\(956\) −1.02084e13 −0.395272
\(957\) −4.41320e12 −0.170079
\(958\) −5.76795e11 −0.0221247
\(959\) −7.49579e12 −0.286176
\(960\) −2.10008e13 −0.798022
\(961\) −2.64395e13 −0.999995
\(962\) −2.07006e11 −0.00779282
\(963\) 2.15605e13 0.807869
\(964\) 5.00969e12 0.186837
\(965\) −3.32749e12 −0.123522
\(966\) −2.24029e11 −0.00827767
\(967\) −1.78714e13 −0.657262 −0.328631 0.944458i \(-0.606587\pi\)
−0.328631 + 0.944458i \(0.606587\pi\)
\(968\) −1.48998e10 −0.000545432 0
\(969\) 0 0
\(970\) −1.27913e11 −0.00463917
\(971\) −7.79284e12 −0.281326 −0.140663 0.990058i \(-0.544923\pi\)
−0.140663 + 0.990058i \(0.544923\pi\)
\(972\) 3.72882e13 1.33990
\(973\) 4.35625e12 0.155814
\(974\) −8.89788e11 −0.0316790
\(975\) 2.64605e13 0.937731
\(976\) 3.42874e13 1.20951
\(977\) −3.49964e12 −0.122885 −0.0614424 0.998111i \(-0.519570\pi\)
−0.0614424 + 0.998111i \(0.519570\pi\)
\(978\) 1.30241e12 0.0455223
\(979\) 3.09439e13 1.07659
\(980\) 1.64314e13 0.569059
\(981\) −1.16176e13 −0.400503
\(982\) −1.03682e12 −0.0355796
\(983\) −1.22347e13 −0.417930 −0.208965 0.977923i \(-0.567009\pi\)
−0.208965 + 0.977923i \(0.567009\pi\)
\(984\) 7.35807e11 0.0250199
\(985\) 1.05194e13 0.356064
\(986\) 0 0
\(987\) −9.19312e12 −0.308344
\(988\) 4.81134e13 1.60642
\(989\) −5.71069e13 −1.89804
\(990\) 3.78513e11 0.0125234
\(991\) −4.06704e12 −0.133951 −0.0669756 0.997755i \(-0.521335\pi\)
−0.0669756 + 0.997755i \(0.521335\pi\)
\(992\) 5.16586e9 0.000169372 0
\(993\) 6.77607e13 2.21160
\(994\) 1.16708e11 0.00379195
\(995\) 2.72600e12 0.0881702
\(996\) 7.96845e13 2.56570
\(997\) 4.00990e13 1.28530 0.642650 0.766160i \(-0.277835\pi\)
0.642650 + 0.766160i \(0.277835\pi\)
\(998\) 1.44254e12 0.0460299
\(999\) 1.74125e12 0.0553118
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.1.19 36
17.16 even 2 289.10.a.h.1.19 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.19 36 1.1 even 1 trivial
289.10.a.h.1.19 yes 36 17.16 even 2