Properties

Label 1.34.a.a.1.1
Level $1$
Weight $34$
Character 1.1
Self dual yes
Analytic conductor $6.898$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 34 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.89828288810\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Defining polynomial: \(x^{2} - x - 589050\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(767.996\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-171359. q^{2} +5.34420e7 q^{3} +2.07741e10 q^{4} -2.01492e11 q^{5} -9.15779e12 q^{6} +5.50153e13 q^{7} -2.08788e15 q^{8} -2.70301e15 q^{9} +O(q^{10})\) \(q-171359. q^{2} +5.34420e7 q^{3} +2.07741e10 q^{4} -2.01492e11 q^{5} -9.15779e12 q^{6} +5.50153e13 q^{7} -2.08788e15 q^{8} -2.70301e15 q^{9} +3.45276e16 q^{10} -8.18909e16 q^{11} +1.11021e18 q^{12} -1.90399e18 q^{13} -9.42739e18 q^{14} -1.07682e19 q^{15} +1.79329e20 q^{16} -3.33893e20 q^{17} +4.63187e20 q^{18} -1.40494e20 q^{19} -4.18583e21 q^{20} +2.94013e21 q^{21} +1.40328e22 q^{22} +3.12767e22 q^{23} -1.11580e23 q^{24} -7.58162e22 q^{25} +3.26267e23 q^{26} -4.41542e23 q^{27} +1.14289e24 q^{28} -1.50979e24 q^{29} +1.84522e24 q^{30} +5.18762e23 q^{31} -1.27950e25 q^{32} -4.37641e24 q^{33} +5.72158e25 q^{34} -1.10852e25 q^{35} -5.61527e25 q^{36} -3.01507e25 q^{37} +2.40749e25 q^{38} -1.01753e26 q^{39} +4.20691e26 q^{40} -2.18887e26 q^{41} -5.03818e26 q^{42} +1.76701e27 q^{43} -1.70121e27 q^{44} +5.44636e26 q^{45} -5.35955e27 q^{46} +3.25654e27 q^{47} +9.58369e27 q^{48} -4.70431e27 q^{49} +1.29918e28 q^{50} -1.78439e28 q^{51} -3.95538e28 q^{52} +9.17652e27 q^{53} +7.56623e28 q^{54} +1.65004e28 q^{55} -1.14865e29 q^{56} -7.50826e27 q^{57} +2.58716e29 q^{58} -1.18267e29 q^{59} -2.23699e29 q^{60} -9.92930e27 q^{61} -8.88948e28 q^{62} -1.48707e29 q^{63} +6.52116e29 q^{64} +3.83640e29 q^{65} +7.49940e29 q^{66} +1.11293e30 q^{67} -6.93634e30 q^{68} +1.67149e30 q^{69} +1.89955e30 q^{70} +7.58425e29 q^{71} +5.64355e30 q^{72} -6.06835e30 q^{73} +5.16661e30 q^{74} -4.05177e30 q^{75} -2.91863e30 q^{76} -4.50525e30 q^{77} +1.74364e31 q^{78} -5.57890e30 q^{79} -3.61334e31 q^{80} -8.57067e30 q^{81} +3.75083e31 q^{82} +4.13746e31 q^{83} +6.10785e31 q^{84} +6.72769e31 q^{85} -3.02793e32 q^{86} -8.06860e31 q^{87} +1.70978e32 q^{88} +6.21572e31 q^{89} -9.33286e31 q^{90} -1.04749e32 q^{91} +6.49745e32 q^{92} +2.77237e31 q^{93} -5.58039e32 q^{94} +2.83084e31 q^{95} -6.83789e32 q^{96} +4.04003e32 q^{97} +8.06129e32 q^{98} +2.21352e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 121680q^{2} + 37919880q^{3} + 14652233984q^{4} - 181061536500q^{5} - 9928922193216q^{6} - 67153080066800q^{7} - 2818750585098240q^{8} - 8021136954970854q^{9} + O(q^{10}) \) \( 2q - 121680q^{2} + 37919880q^{3} + 14652233984q^{4} - 181061536500q^{5} - 9928922193216q^{6} - 67153080066800q^{7} - 2818750585098240q^{8} - 8021136954970854q^{9} + 35542592216532000q^{10} + 133871815441914264q^{11} + 1205235433330467840q^{12} - 2981610478259443940q^{13} - 15496641262468340352q^{14} - 11085280069139874000q^{15} + \)\(19\!\cdots\!72\)\(q^{16} - 79361149261175525340q^{17} + \)\(19\!\cdots\!80\)\(q^{18} - \)\(13\!\cdots\!00\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(48\!\cdots\!24\)\(q^{21} + \)\(24\!\cdots\!40\)\(q^{22} + \)\(26\!\cdots\!40\)\(q^{23} - \)\(10\!\cdots\!00\)\(q^{24} - \)\(19\!\cdots\!50\)\(q^{25} + \)\(27\!\cdots\!04\)\(q^{26} - \)\(27\!\cdots\!40\)\(q^{27} + \)\(18\!\cdots\!60\)\(q^{28} - \)\(16\!\cdots\!00\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} - \)\(62\!\cdots\!16\)\(q^{31} - \)\(57\!\cdots\!80\)\(q^{32} - \)\(77\!\cdots\!40\)\(q^{33} + \)\(69\!\cdots\!08\)\(q^{34} - \)\(13\!\cdots\!00\)\(q^{35} - \)\(23\!\cdots\!68\)\(q^{36} - \)\(10\!\cdots\!20\)\(q^{37} - \)\(36\!\cdots\!60\)\(q^{38} - \)\(85\!\cdots\!48\)\(q^{39} + \)\(40\!\cdots\!00\)\(q^{40} + \)\(27\!\cdots\!44\)\(q^{41} - \)\(40\!\cdots\!40\)\(q^{42} + \)\(15\!\cdots\!00\)\(q^{43} - \)\(30\!\cdots\!12\)\(q^{44} + \)\(43\!\cdots\!00\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} + \)\(54\!\cdots\!40\)\(q^{47} + \)\(93\!\cdots\!40\)\(q^{48} + \)\(24\!\cdots\!14\)\(q^{49} + \)\(72\!\cdots\!00\)\(q^{50} - \)\(21\!\cdots\!96\)\(q^{51} - \)\(32\!\cdots\!00\)\(q^{52} - \)\(26\!\cdots\!20\)\(q^{53} + \)\(84\!\cdots\!00\)\(q^{54} + \)\(20\!\cdots\!00\)\(q^{55} - \)\(25\!\cdots\!00\)\(q^{56} + \)\(11\!\cdots\!20\)\(q^{57} + \)\(25\!\cdots\!60\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(22\!\cdots\!00\)\(q^{60} - \)\(57\!\cdots\!36\)\(q^{61} - \)\(42\!\cdots\!60\)\(q^{62} + \)\(50\!\cdots\!20\)\(q^{63} + \)\(86\!\cdots\!24\)\(q^{64} + \)\(36\!\cdots\!00\)\(q^{65} + \)\(58\!\cdots\!88\)\(q^{66} + \)\(15\!\cdots\!60\)\(q^{67} - \)\(84\!\cdots\!20\)\(q^{68} + \)\(17\!\cdots\!12\)\(q^{69} + \)\(17\!\cdots\!00\)\(q^{70} - \)\(26\!\cdots\!76\)\(q^{71} + \)\(95\!\cdots\!80\)\(q^{72} + \)\(94\!\cdots\!40\)\(q^{73} + \)\(14\!\cdots\!28\)\(q^{74} - \)\(22\!\cdots\!00\)\(q^{75} + \)\(45\!\cdots\!00\)\(q^{76} - \)\(30\!\cdots\!00\)\(q^{77} + \)\(18\!\cdots\!00\)\(q^{78} - \)\(85\!\cdots\!00\)\(q^{79} - \)\(35\!\cdots\!00\)\(q^{80} + \)\(18\!\cdots\!42\)\(q^{81} + \)\(62\!\cdots\!40\)\(q^{82} + \)\(29\!\cdots\!20\)\(q^{83} + \)\(49\!\cdots\!08\)\(q^{84} + \)\(72\!\cdots\!00\)\(q^{85} - \)\(31\!\cdots\!36\)\(q^{86} - \)\(78\!\cdots\!20\)\(q^{87} + \)\(13\!\cdots\!20\)\(q^{88} + \)\(13\!\cdots\!00\)\(q^{89} - \)\(98\!\cdots\!00\)\(q^{90} + \)\(26\!\cdots\!44\)\(q^{91} + \)\(68\!\cdots\!60\)\(q^{92} + \)\(13\!\cdots\!60\)\(q^{93} - \)\(45\!\cdots\!12\)\(q^{94} + \)\(33\!\cdots\!00\)\(q^{95} - \)\(79\!\cdots\!76\)\(q^{96} - \)\(36\!\cdots\!60\)\(q^{97} + \)\(11\!\cdots\!40\)\(q^{98} - \)\(92\!\cdots\!28\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −171359. −1.84890 −0.924449 0.381305i \(-0.875475\pi\)
−0.924449 + 0.381305i \(0.875475\pi\)
\(3\) 5.34420e7 0.716774 0.358387 0.933573i \(-0.383327\pi\)
0.358387 + 0.933573i \(0.383327\pi\)
\(4\) 2.07741e10 2.41843
\(5\) −2.01492e11 −0.590545 −0.295273 0.955413i \(-0.595411\pi\)
−0.295273 + 0.955413i \(0.595411\pi\)
\(6\) −9.15779e12 −1.32524
\(7\) 5.50153e13 0.625699 0.312850 0.949803i \(-0.398716\pi\)
0.312850 + 0.949803i \(0.398716\pi\)
\(8\) −2.08788e15 −2.62253
\(9\) −2.70301e15 −0.486236
\(10\) 3.45276e16 1.09186
\(11\) −8.18909e16 −0.537349 −0.268674 0.963231i \(-0.586586\pi\)
−0.268674 + 0.963231i \(0.586586\pi\)
\(12\) 1.11021e18 1.73346
\(13\) −1.90399e18 −0.793597 −0.396798 0.917906i \(-0.629879\pi\)
−0.396798 + 0.917906i \(0.629879\pi\)
\(14\) −9.42739e18 −1.15685
\(15\) −1.07682e19 −0.423287
\(16\) 1.79329e20 2.43036
\(17\) −3.33893e20 −1.66418 −0.832090 0.554640i \(-0.812856\pi\)
−0.832090 + 0.554640i \(0.812856\pi\)
\(18\) 4.63187e20 0.899000
\(19\) −1.40494e20 −0.111743 −0.0558717 0.998438i \(-0.517794\pi\)
−0.0558717 + 0.998438i \(0.517794\pi\)
\(20\) −4.18583e21 −1.42819
\(21\) 2.94013e21 0.448485
\(22\) 1.40328e22 0.993503
\(23\) 3.12767e22 1.06344 0.531718 0.846922i \(-0.321547\pi\)
0.531718 + 0.846922i \(0.321547\pi\)
\(24\) −1.11580e23 −1.87976
\(25\) −7.58162e22 −0.651256
\(26\) 3.26267e23 1.46728
\(27\) −4.41542e23 −1.06529
\(28\) 1.14289e24 1.51321
\(29\) −1.50979e24 −1.12034 −0.560168 0.828379i \(-0.689264\pi\)
−0.560168 + 0.828379i \(0.689264\pi\)
\(30\) 1.84522e24 0.782616
\(31\) 5.18762e23 0.128086 0.0640428 0.997947i \(-0.479601\pi\)
0.0640428 + 0.997947i \(0.479601\pi\)
\(32\) −1.27950e25 −1.87096
\(33\) −4.37641e24 −0.385157
\(34\) 5.72158e25 3.07690
\(35\) −1.10852e25 −0.369504
\(36\) −5.61527e25 −1.17592
\(37\) −3.01507e25 −0.401762 −0.200881 0.979616i \(-0.564380\pi\)
−0.200881 + 0.979616i \(0.564380\pi\)
\(38\) 2.40749e25 0.206602
\(39\) −1.01753e26 −0.568829
\(40\) 4.20691e26 1.54872
\(41\) −2.18887e26 −0.536149 −0.268075 0.963398i \(-0.586387\pi\)
−0.268075 + 0.963398i \(0.586387\pi\)
\(42\) −5.03818e26 −0.829203
\(43\) 1.76701e27 1.97246 0.986232 0.165369i \(-0.0528817\pi\)
0.986232 + 0.165369i \(0.0528817\pi\)
\(44\) −1.70121e27 −1.29954
\(45\) 5.44636e26 0.287144
\(46\) −5.35955e27 −1.96618
\(47\) 3.25654e27 0.837802 0.418901 0.908032i \(-0.362415\pi\)
0.418901 + 0.908032i \(0.362415\pi\)
\(48\) 9.58369e27 1.74202
\(49\) −4.70431e27 −0.608500
\(50\) 1.29918e28 1.20411
\(51\) −1.78439e28 −1.19284
\(52\) −3.95538e28 −1.91926
\(53\) 9.17652e27 0.325182 0.162591 0.986694i \(-0.448015\pi\)
0.162591 + 0.986694i \(0.448015\pi\)
\(54\) 7.56623e28 1.96962
\(55\) 1.65004e28 0.317329
\(56\) −1.14865e29 −1.64091
\(57\) −7.50826e27 −0.0800948
\(58\) 2.58716e29 2.07139
\(59\) −1.18267e29 −0.714174 −0.357087 0.934071i \(-0.616230\pi\)
−0.357087 + 0.934071i \(0.616230\pi\)
\(60\) −2.23699e29 −1.02369
\(61\) −9.92930e27 −0.0345920 −0.0172960 0.999850i \(-0.505506\pi\)
−0.0172960 + 0.999850i \(0.505506\pi\)
\(62\) −8.88948e28 −0.236817
\(63\) −1.48707e29 −0.304237
\(64\) 6.52116e29 1.02886
\(65\) 3.83640e29 0.468655
\(66\) 7.49940e29 0.712117
\(67\) 1.11293e30 0.824583 0.412291 0.911052i \(-0.364729\pi\)
0.412291 + 0.911052i \(0.364729\pi\)
\(68\) −6.93634e30 −4.02470
\(69\) 1.67149e30 0.762242
\(70\) 1.89955e30 0.683175
\(71\) 7.58425e29 0.215849 0.107924 0.994159i \(-0.465580\pi\)
0.107924 + 0.994159i \(0.465580\pi\)
\(72\) 5.64355e30 1.27517
\(73\) −6.06835e30 −1.09205 −0.546026 0.837768i \(-0.683860\pi\)
−0.546026 + 0.837768i \(0.683860\pi\)
\(74\) 5.16661e30 0.742818
\(75\) −4.05177e30 −0.466803
\(76\) −2.91863e30 −0.270243
\(77\) −4.50525e30 −0.336219
\(78\) 1.74364e31 1.05171
\(79\) −5.57890e30 −0.272711 −0.136355 0.990660i \(-0.543539\pi\)
−0.136355 + 0.990660i \(0.543539\pi\)
\(80\) −3.61334e31 −1.43524
\(81\) −8.57067e30 −0.277339
\(82\) 3.75083e31 0.991286
\(83\) 4.13746e31 0.895252 0.447626 0.894221i \(-0.352270\pi\)
0.447626 + 0.894221i \(0.352270\pi\)
\(84\) 6.10785e31 1.08463
\(85\) 6.72769e31 0.982775
\(86\) −3.02793e32 −3.64688
\(87\) −8.06860e31 −0.803028
\(88\) 1.70978e32 1.40921
\(89\) 6.21572e31 0.425164 0.212582 0.977143i \(-0.431813\pi\)
0.212582 + 0.977143i \(0.431813\pi\)
\(90\) −9.33286e31 −0.530900
\(91\) −1.04749e32 −0.496553
\(92\) 6.49745e32 2.57184
\(93\) 2.77237e31 0.0918084
\(94\) −5.58039e32 −1.54901
\(95\) 2.83084e31 0.0659896
\(96\) −6.83789e32 −1.34106
\(97\) 4.04003e32 0.667808 0.333904 0.942607i \(-0.391634\pi\)
0.333904 + 0.942607i \(0.391634\pi\)
\(98\) 8.06129e32 1.12506
\(99\) 2.21352e32 0.261278
\(100\) −1.57501e33 −1.57501
\(101\) −1.20576e33 −1.02319 −0.511596 0.859226i \(-0.670946\pi\)
−0.511596 + 0.859226i \(0.670946\pi\)
\(102\) 3.05773e33 2.20544
\(103\) −1.69378e33 −1.04002 −0.520011 0.854159i \(-0.674072\pi\)
−0.520011 + 0.854159i \(0.674072\pi\)
\(104\) 3.97530e33 2.08123
\(105\) −5.92413e32 −0.264851
\(106\) −1.57248e33 −0.601228
\(107\) 7.07121e32 0.231559 0.115780 0.993275i \(-0.463063\pi\)
0.115780 + 0.993275i \(0.463063\pi\)
\(108\) −9.17264e33 −2.57634
\(109\) 4.42814e33 1.06828 0.534139 0.845397i \(-0.320636\pi\)
0.534139 + 0.845397i \(0.320636\pi\)
\(110\) −2.82750e33 −0.586709
\(111\) −1.61131e33 −0.287973
\(112\) 9.86582e33 1.52067
\(113\) 1.36496e34 1.81687 0.908437 0.418023i \(-0.137277\pi\)
0.908437 + 0.418023i \(0.137277\pi\)
\(114\) 1.28661e33 0.148087
\(115\) −6.30200e33 −0.628007
\(116\) −3.13645e34 −2.70945
\(117\) 5.14652e33 0.385875
\(118\) 2.02661e34 1.32043
\(119\) −1.83692e34 −1.04128
\(120\) 2.24826e34 1.11008
\(121\) −1.65190e34 −0.711256
\(122\) 1.70148e33 0.0639572
\(123\) −1.16977e34 −0.384298
\(124\) 1.07768e34 0.309766
\(125\) 3.87332e34 0.975142
\(126\) 2.54823e34 0.562504
\(127\) −7.12185e34 −1.37985 −0.689925 0.723881i \(-0.742356\pi\)
−0.689925 + 0.723881i \(0.742356\pi\)
\(128\) −1.83832e33 −0.0312936
\(129\) 9.44324e34 1.41381
\(130\) −6.57403e34 −0.866496
\(131\) −2.95217e34 −0.342898 −0.171449 0.985193i \(-0.554845\pi\)
−0.171449 + 0.985193i \(0.554845\pi\)
\(132\) −9.09161e34 −0.931475
\(133\) −7.72929e33 −0.0699178
\(134\) −1.90711e35 −1.52457
\(135\) 8.89673e34 0.629105
\(136\) 6.97128e35 4.36436
\(137\) 8.90834e34 0.494205 0.247103 0.968989i \(-0.420521\pi\)
0.247103 + 0.968989i \(0.420521\pi\)
\(138\) −2.86425e35 −1.40931
\(139\) −3.61707e35 −1.57984 −0.789920 0.613210i \(-0.789878\pi\)
−0.789920 + 0.613210i \(0.789878\pi\)
\(140\) −2.30284e35 −0.893618
\(141\) 1.74036e35 0.600515
\(142\) −1.29963e35 −0.399083
\(143\) 1.55920e35 0.426438
\(144\) −4.84728e35 −1.18173
\(145\) 3.04210e35 0.661610
\(146\) 1.03987e36 2.01909
\(147\) −2.51408e35 −0.436157
\(148\) −6.26354e35 −0.971632
\(149\) 1.73500e35 0.240839 0.120419 0.992723i \(-0.461576\pi\)
0.120419 + 0.992723i \(0.461576\pi\)
\(150\) 6.94309e35 0.863072
\(151\) −1.35744e36 −1.51217 −0.756085 0.654473i \(-0.772891\pi\)
−0.756085 + 0.654473i \(0.772891\pi\)
\(152\) 2.93333e35 0.293050
\(153\) 9.02518e35 0.809184
\(154\) 7.72017e35 0.621634
\(155\) −1.04527e35 −0.0756404
\(156\) −2.11383e36 −1.37567
\(157\) −2.78049e36 −1.62846 −0.814229 0.580543i \(-0.802840\pi\)
−0.814229 + 0.580543i \(0.802840\pi\)
\(158\) 9.55998e35 0.504214
\(159\) 4.90411e35 0.233082
\(160\) 2.57809e36 1.10489
\(161\) 1.72069e36 0.665390
\(162\) 1.46866e36 0.512773
\(163\) 2.81381e36 0.887565 0.443782 0.896135i \(-0.353636\pi\)
0.443782 + 0.896135i \(0.353636\pi\)
\(164\) −4.54718e36 −1.29664
\(165\) 8.81813e35 0.227453
\(166\) −7.08993e36 −1.65523
\(167\) 6.77893e36 1.43331 0.716653 0.697430i \(-0.245673\pi\)
0.716653 + 0.697430i \(0.245673\pi\)
\(168\) −6.13862e36 −1.17616
\(169\) −2.13094e36 −0.370204
\(170\) −1.15285e37 −1.81705
\(171\) 3.79756e35 0.0543336
\(172\) 3.67080e37 4.77026
\(173\) −1.42570e37 −1.68370 −0.841852 0.539708i \(-0.818535\pi\)
−0.841852 + 0.539708i \(0.818535\pi\)
\(174\) 1.38263e37 1.48472
\(175\) −4.17105e36 −0.407490
\(176\) −1.46854e37 −1.30595
\(177\) −6.32040e36 −0.511901
\(178\) −1.06512e37 −0.786085
\(179\) 7.37934e36 0.496527 0.248263 0.968693i \(-0.420140\pi\)
0.248263 + 0.968693i \(0.420140\pi\)
\(180\) 1.13143e37 0.694437
\(181\) 2.39313e36 0.134051 0.0670254 0.997751i \(-0.478649\pi\)
0.0670254 + 0.997751i \(0.478649\pi\)
\(182\) 1.79497e37 0.918076
\(183\) −5.30642e35 −0.0247947
\(184\) −6.53018e37 −2.78889
\(185\) 6.07513e36 0.237259
\(186\) −4.75072e36 −0.169744
\(187\) 2.73428e37 0.894245
\(188\) 6.76517e37 2.02616
\(189\) −2.42915e37 −0.666554
\(190\) −4.85091e36 −0.122008
\(191\) −6.98026e35 −0.0160998 −0.00804991 0.999968i \(-0.502562\pi\)
−0.00804991 + 0.999968i \(0.502562\pi\)
\(192\) 3.48504e37 0.737458
\(193\) 6.67098e36 0.129567 0.0647835 0.997899i \(-0.479364\pi\)
0.0647835 + 0.997899i \(0.479364\pi\)
\(194\) −6.92298e37 −1.23471
\(195\) 2.05025e37 0.335920
\(196\) −9.77280e37 −1.47161
\(197\) −8.89563e37 −1.23164 −0.615821 0.787886i \(-0.711175\pi\)
−0.615821 + 0.787886i \(0.711175\pi\)
\(198\) −3.79308e37 −0.483077
\(199\) 1.05106e38 1.23183 0.615916 0.787812i \(-0.288786\pi\)
0.615916 + 0.787812i \(0.288786\pi\)
\(200\) 1.58295e38 1.70794
\(201\) 5.94773e37 0.591039
\(202\) 2.06618e38 1.89178
\(203\) −8.30613e37 −0.700994
\(204\) −3.70692e38 −2.88480
\(205\) 4.41040e37 0.316621
\(206\) 2.90245e38 1.92290
\(207\) −8.45412e37 −0.517080
\(208\) −3.41441e38 −1.92873
\(209\) 1.15051e37 0.0600452
\(210\) 1.01516e38 0.489682
\(211\) −5.59870e37 −0.249705 −0.124852 0.992175i \(-0.539846\pi\)
−0.124852 + 0.992175i \(0.539846\pi\)
\(212\) 1.90634e38 0.786428
\(213\) 4.05318e37 0.154715
\(214\) −1.21172e38 −0.428129
\(215\) −3.56038e38 −1.16483
\(216\) 9.21884e38 2.79376
\(217\) 2.85398e37 0.0801431
\(218\) −7.58804e38 −1.97514
\(219\) −3.24305e38 −0.782755
\(220\) 3.42781e38 0.767436
\(221\) 6.35730e38 1.32069
\(222\) 2.76114e38 0.532432
\(223\) 4.65676e38 0.833784 0.416892 0.908956i \(-0.363119\pi\)
0.416892 + 0.908956i \(0.363119\pi\)
\(224\) −7.03919e38 −1.17066
\(225\) 2.04932e38 0.316664
\(226\) −2.33898e39 −3.35921
\(227\) −2.61802e38 −0.349580 −0.174790 0.984606i \(-0.555925\pi\)
−0.174790 + 0.984606i \(0.555925\pi\)
\(228\) −1.55977e38 −0.193703
\(229\) 9.20963e38 1.06404 0.532018 0.846733i \(-0.321434\pi\)
0.532018 + 0.846733i \(0.321434\pi\)
\(230\) 1.07991e39 1.16112
\(231\) −2.40770e38 −0.240993
\(232\) 3.15225e39 2.93811
\(233\) 7.13755e37 0.0619693 0.0309847 0.999520i \(-0.490136\pi\)
0.0309847 + 0.999520i \(0.490136\pi\)
\(234\) −8.81904e38 −0.713444
\(235\) −6.56167e38 −0.494760
\(236\) −2.45688e39 −1.72718
\(237\) −2.98148e38 −0.195472
\(238\) 3.14774e39 1.92522
\(239\) −1.83178e39 −1.04546 −0.522731 0.852498i \(-0.675087\pi\)
−0.522731 + 0.852498i \(0.675087\pi\)
\(240\) −1.93104e39 −1.02874
\(241\) −3.05313e39 −1.51867 −0.759336 0.650698i \(-0.774476\pi\)
−0.759336 + 0.650698i \(0.774476\pi\)
\(242\) 2.83069e39 1.31504
\(243\) 1.99652e39 0.866505
\(244\) −2.06272e38 −0.0836583
\(245\) 9.47883e38 0.359347
\(246\) 2.00452e39 0.710527
\(247\) 2.67499e38 0.0886793
\(248\) −1.08311e39 −0.335908
\(249\) 2.21114e39 0.641693
\(250\) −6.63729e39 −1.80294
\(251\) 3.03407e39 0.771631 0.385815 0.922576i \(-0.373920\pi\)
0.385815 + 0.922576i \(0.373920\pi\)
\(252\) −3.08926e39 −0.735775
\(253\) −2.56127e39 −0.571435
\(254\) 1.22040e40 2.55120
\(255\) 3.59541e39 0.704427
\(256\) −5.28662e39 −0.970999
\(257\) −2.91186e39 −0.501503 −0.250752 0.968051i \(-0.580678\pi\)
−0.250752 + 0.968051i \(0.580678\pi\)
\(258\) −1.61819e40 −2.61399
\(259\) −1.65875e39 −0.251382
\(260\) 7.96978e39 1.13341
\(261\) 4.08097e39 0.544748
\(262\) 5.05883e39 0.633984
\(263\) −5.62907e39 −0.662471 −0.331236 0.943548i \(-0.607466\pi\)
−0.331236 + 0.943548i \(0.607466\pi\)
\(264\) 9.13740e39 1.01009
\(265\) −1.84900e39 −0.192035
\(266\) 1.32449e39 0.129271
\(267\) 3.32180e39 0.304746
\(268\) 2.31202e40 1.99419
\(269\) −9.77080e39 −0.792533 −0.396266 0.918136i \(-0.629694\pi\)
−0.396266 + 0.918136i \(0.629694\pi\)
\(270\) −1.52454e40 −1.16315
\(271\) 2.38779e40 1.71397 0.856985 0.515342i \(-0.172335\pi\)
0.856985 + 0.515342i \(0.172335\pi\)
\(272\) −5.98767e40 −4.04456
\(273\) −5.59798e39 −0.355916
\(274\) −1.52653e40 −0.913736
\(275\) 6.20865e39 0.349952
\(276\) 3.47237e40 1.84343
\(277\) −1.39835e40 −0.699358 −0.349679 0.936870i \(-0.613709\pi\)
−0.349679 + 0.936870i \(0.613709\pi\)
\(278\) 6.19820e40 2.92096
\(279\) −1.40222e39 −0.0622798
\(280\) 2.31444e40 0.969033
\(281\) −2.89927e40 −1.14455 −0.572274 0.820062i \(-0.693939\pi\)
−0.572274 + 0.820062i \(0.693939\pi\)
\(282\) −2.98227e40 −1.11029
\(283\) −1.50945e40 −0.530081 −0.265040 0.964237i \(-0.585385\pi\)
−0.265040 + 0.964237i \(0.585385\pi\)
\(284\) 1.57556e40 0.522015
\(285\) 1.51286e39 0.0472996
\(286\) −2.67183e40 −0.788441
\(287\) −1.20421e40 −0.335468
\(288\) 3.45850e40 0.909728
\(289\) 7.12303e40 1.76950
\(290\) −5.21293e40 −1.22325
\(291\) 2.15907e40 0.478667
\(292\) −1.26065e41 −2.64105
\(293\) −1.40305e40 −0.277816 −0.138908 0.990305i \(-0.544359\pi\)
−0.138908 + 0.990305i \(0.544359\pi\)
\(294\) 4.30811e40 0.806410
\(295\) 2.38298e40 0.421752
\(296\) 6.29509e40 1.05363
\(297\) 3.61582e40 0.572435
\(298\) −2.97309e40 −0.445286
\(299\) −5.95505e40 −0.843939
\(300\) −8.41719e40 −1.12893
\(301\) 9.72124e40 1.23417
\(302\) 2.32610e41 2.79585
\(303\) −6.44381e40 −0.733398
\(304\) −2.51945e40 −0.271577
\(305\) 2.00068e39 0.0204282
\(306\) −1.54655e41 −1.49610
\(307\) −2.92194e40 −0.267848 −0.133924 0.990992i \(-0.542758\pi\)
−0.133924 + 0.990992i \(0.542758\pi\)
\(308\) −9.35926e40 −0.813120
\(309\) −9.05190e40 −0.745461
\(310\) 1.79116e40 0.139851
\(311\) −2.24927e41 −1.66531 −0.832653 0.553794i \(-0.813179\pi\)
−0.832653 + 0.553794i \(0.813179\pi\)
\(312\) 2.12448e41 1.49177
\(313\) 1.17836e41 0.784868 0.392434 0.919780i \(-0.371633\pi\)
0.392434 + 0.919780i \(0.371633\pi\)
\(314\) 4.76463e41 3.01086
\(315\) 2.99633e40 0.179666
\(316\) −1.15897e41 −0.659530
\(317\) −9.02704e40 −0.487604 −0.243802 0.969825i \(-0.578395\pi\)
−0.243802 + 0.969825i \(0.578395\pi\)
\(318\) −8.40366e40 −0.430944
\(319\) 1.23638e41 0.602012
\(320\) −1.31396e41 −0.607588
\(321\) 3.77900e40 0.165975
\(322\) −2.94857e41 −1.23024
\(323\) 4.69099e40 0.185961
\(324\) −1.78048e41 −0.670725
\(325\) 1.44353e41 0.516835
\(326\) −4.82174e41 −1.64102
\(327\) 2.36649e41 0.765714
\(328\) 4.57008e41 1.40607
\(329\) 1.79159e41 0.524212
\(330\) −1.51107e41 −0.420537
\(331\) −2.91394e41 −0.771469 −0.385734 0.922610i \(-0.626052\pi\)
−0.385734 + 0.922610i \(0.626052\pi\)
\(332\) 8.59521e41 2.16510
\(333\) 8.14977e40 0.195351
\(334\) −1.16163e42 −2.65004
\(335\) −2.24247e41 −0.486954
\(336\) 5.27249e41 1.08998
\(337\) −5.69474e41 −1.12094 −0.560468 0.828176i \(-0.689379\pi\)
−0.560468 + 0.828176i \(0.689379\pi\)
\(338\) 3.65157e41 0.684470
\(339\) 7.29460e41 1.30229
\(340\) 1.39762e42 2.37677
\(341\) −4.24819e40 −0.0688266
\(342\) −6.50748e40 −0.100457
\(343\) −6.84132e41 −1.00644
\(344\) −3.68929e42 −5.17284
\(345\) −3.36792e41 −0.450139
\(346\) 2.44306e42 3.11300
\(347\) 4.85020e41 0.589283 0.294641 0.955608i \(-0.404800\pi\)
0.294641 + 0.955608i \(0.404800\pi\)
\(348\) −1.67618e42 −1.94206
\(349\) 5.38533e41 0.595104 0.297552 0.954706i \(-0.403830\pi\)
0.297552 + 0.954706i \(0.403830\pi\)
\(350\) 7.14748e41 0.753408
\(351\) 8.40692e41 0.845414
\(352\) 1.04779e42 1.00536
\(353\) −9.77578e41 −0.895094 −0.447547 0.894260i \(-0.647702\pi\)
−0.447547 + 0.894260i \(0.647702\pi\)
\(354\) 1.08306e42 0.946453
\(355\) −1.52817e41 −0.127469
\(356\) 1.29126e42 1.02823
\(357\) −9.81689e41 −0.746360
\(358\) −1.26452e42 −0.918027
\(359\) 1.18143e42 0.819124 0.409562 0.912282i \(-0.365682\pi\)
0.409562 + 0.912282i \(0.365682\pi\)
\(360\) −1.13713e42 −0.753043
\(361\) −1.56103e42 −0.987513
\(362\) −4.10085e41 −0.247846
\(363\) −8.82811e41 −0.509810
\(364\) −2.17606e42 −1.20088
\(365\) 1.22273e42 0.644907
\(366\) 9.09304e40 0.0458428
\(367\) 7.16875e41 0.345504 0.172752 0.984965i \(-0.444734\pi\)
0.172752 + 0.984965i \(0.444734\pi\)
\(368\) 5.60881e42 2.58453
\(369\) 5.91654e41 0.260695
\(370\) −1.04103e42 −0.438668
\(371\) 5.04849e41 0.203466
\(372\) 5.75935e41 0.222032
\(373\) −6.80691e41 −0.251047 −0.125523 0.992091i \(-0.540061\pi\)
−0.125523 + 0.992091i \(0.540061\pi\)
\(374\) −4.68545e42 −1.65337
\(375\) 2.06998e42 0.698956
\(376\) −6.79925e42 −2.19716
\(377\) 2.87462e42 0.889096
\(378\) 4.16258e42 1.23239
\(379\) 5.14200e42 1.45742 0.728711 0.684821i \(-0.240120\pi\)
0.728711 + 0.684821i \(0.240120\pi\)
\(380\) 5.88082e41 0.159591
\(381\) −3.80606e42 −0.989040
\(382\) 1.19613e41 0.0297669
\(383\) −6.82496e42 −1.62675 −0.813375 0.581740i \(-0.802372\pi\)
−0.813375 + 0.581740i \(0.802372\pi\)
\(384\) −9.82434e40 −0.0224305
\(385\) 9.07773e41 0.198552
\(386\) −1.14314e42 −0.239556
\(387\) −4.77624e42 −0.959082
\(388\) 8.39281e42 1.61504
\(389\) 3.03602e42 0.559933 0.279966 0.960010i \(-0.409677\pi\)
0.279966 + 0.960010i \(0.409677\pi\)
\(390\) −3.51329e42 −0.621081
\(391\) −1.04431e43 −1.76975
\(392\) 9.82202e42 1.59581
\(393\) −1.57770e42 −0.245781
\(394\) 1.52435e43 2.27718
\(395\) 1.12411e42 0.161048
\(396\) 4.59839e42 0.631882
\(397\) 8.54761e42 1.12668 0.563341 0.826225i \(-0.309516\pi\)
0.563341 + 0.826225i \(0.309516\pi\)
\(398\) −1.80109e43 −2.27753
\(399\) −4.13069e41 −0.0501152
\(400\) −1.35960e43 −1.58279
\(401\) 4.64638e42 0.519078 0.259539 0.965733i \(-0.416429\pi\)
0.259539 + 0.965733i \(0.416429\pi\)
\(402\) −1.01920e43 −1.09277
\(403\) −9.87719e41 −0.101648
\(404\) −2.50486e43 −2.47452
\(405\) 1.72692e42 0.163782
\(406\) 1.42333e43 1.29607
\(407\) 2.46907e42 0.215886
\(408\) 3.72559e43 3.12826
\(409\) 1.73477e43 1.39897 0.699483 0.714649i \(-0.253414\pi\)
0.699483 + 0.714649i \(0.253414\pi\)
\(410\) −7.55763e42 −0.585399
\(411\) 4.76080e42 0.354233
\(412\) −3.51868e43 −2.51522
\(413\) −6.50647e42 −0.446858
\(414\) 1.44869e43 0.956028
\(415\) −8.33667e42 −0.528687
\(416\) 2.43615e43 1.48479
\(417\) −1.93304e43 −1.13239
\(418\) −1.97151e42 −0.111017
\(419\) 1.59552e43 0.863717 0.431858 0.901941i \(-0.357858\pi\)
0.431858 + 0.901941i \(0.357858\pi\)
\(420\) −1.23069e43 −0.640522
\(421\) −2.07154e43 −1.03667 −0.518333 0.855179i \(-0.673447\pi\)
−0.518333 + 0.855179i \(0.673447\pi\)
\(422\) 9.59390e42 0.461679
\(423\) −8.80247e42 −0.407369
\(424\) −1.91594e43 −0.852797
\(425\) 2.53145e43 1.08381
\(426\) −6.94550e42 −0.286052
\(427\) −5.46263e41 −0.0216442
\(428\) 1.46898e43 0.560008
\(429\) 8.33266e42 0.305660
\(430\) 6.10105e43 2.15365
\(431\) −2.15255e43 −0.731272 −0.365636 0.930758i \(-0.619149\pi\)
−0.365636 + 0.930758i \(0.619149\pi\)
\(432\) −7.91812e43 −2.58905
\(433\) −2.62411e43 −0.825908 −0.412954 0.910752i \(-0.635503\pi\)
−0.412954 + 0.910752i \(0.635503\pi\)
\(434\) −4.89057e42 −0.148176
\(435\) 1.62576e43 0.474225
\(436\) 9.19908e43 2.58355
\(437\) −4.39417e42 −0.118832
\(438\) 5.55727e43 1.44723
\(439\) 1.50091e43 0.376434 0.188217 0.982127i \(-0.439729\pi\)
0.188217 + 0.982127i \(0.439729\pi\)
\(440\) −3.44507e43 −0.832203
\(441\) 1.27158e43 0.295875
\(442\) −1.08938e44 −2.44182
\(443\) 1.03686e43 0.223902 0.111951 0.993714i \(-0.464290\pi\)
0.111951 + 0.993714i \(0.464290\pi\)
\(444\) −3.34736e43 −0.696440
\(445\) −1.25242e43 −0.251079
\(446\) −7.97979e43 −1.54158
\(447\) 9.27219e42 0.172627
\(448\) 3.58764e43 0.643756
\(449\) −3.05007e42 −0.0527528 −0.0263764 0.999652i \(-0.508397\pi\)
−0.0263764 + 0.999652i \(0.508397\pi\)
\(450\) −3.51171e43 −0.585479
\(451\) 1.79248e43 0.288099
\(452\) 2.83558e44 4.39397
\(453\) −7.25443e43 −1.08388
\(454\) 4.48623e43 0.646338
\(455\) 2.11061e43 0.293237
\(456\) 1.56763e43 0.210051
\(457\) −8.15124e43 −1.05343 −0.526716 0.850042i \(-0.676577\pi\)
−0.526716 + 0.850042i \(0.676577\pi\)
\(458\) −1.57816e44 −1.96730
\(459\) 1.47428e44 1.77284
\(460\) −1.30919e44 −1.51879
\(461\) 9.49311e43 1.06253 0.531267 0.847204i \(-0.321716\pi\)
0.531267 + 0.847204i \(0.321716\pi\)
\(462\) 4.12581e43 0.445571
\(463\) −6.84730e43 −0.713564 −0.356782 0.934188i \(-0.616126\pi\)
−0.356782 + 0.934188i \(0.616126\pi\)
\(464\) −2.70748e44 −2.72282
\(465\) −5.58611e42 −0.0542170
\(466\) −1.22309e43 −0.114575
\(467\) 1.13867e44 1.02961 0.514803 0.857308i \(-0.327865\pi\)
0.514803 + 0.857308i \(0.327865\pi\)
\(468\) 1.06914e44 0.933210
\(469\) 6.12282e43 0.515941
\(470\) 1.12440e44 0.914762
\(471\) −1.48595e44 −1.16724
\(472\) 2.46926e44 1.87294
\(473\) −1.44702e44 −1.05990
\(474\) 5.10904e43 0.361407
\(475\) 1.06517e43 0.0727736
\(476\) −3.81605e44 −2.51825
\(477\) −2.48042e43 −0.158115
\(478\) 3.13893e44 1.93295
\(479\) −2.43710e44 −1.44990 −0.724948 0.688804i \(-0.758136\pi\)
−0.724948 + 0.688804i \(0.758136\pi\)
\(480\) 1.37778e44 0.791954
\(481\) 5.74067e43 0.318837
\(482\) 5.23183e44 2.80787
\(483\) 9.19573e43 0.476934
\(484\) −3.43169e44 −1.72012
\(485\) −8.14036e43 −0.394371
\(486\) −3.42123e44 −1.60208
\(487\) −1.55812e44 −0.705300 −0.352650 0.935755i \(-0.614719\pi\)
−0.352650 + 0.935755i \(0.614719\pi\)
\(488\) 2.07311e43 0.0907185
\(489\) 1.50376e44 0.636183
\(490\) −1.62429e44 −0.664397
\(491\) −2.64492e43 −0.104609 −0.0523044 0.998631i \(-0.516657\pi\)
−0.0523044 + 0.998631i \(0.516657\pi\)
\(492\) −2.43010e44 −0.929396
\(493\) 5.04108e44 1.86444
\(494\) −4.58384e43 −0.163959
\(495\) −4.46007e43 −0.154297
\(496\) 9.30290e43 0.311294
\(497\) 4.17250e43 0.135057
\(498\) −3.78900e44 −1.18643
\(499\) 3.31565e44 1.00441 0.502203 0.864750i \(-0.332523\pi\)
0.502203 + 0.864750i \(0.332523\pi\)
\(500\) 8.04647e44 2.35831
\(501\) 3.62279e44 1.02736
\(502\) −5.19917e44 −1.42667
\(503\) −4.39485e44 −1.16700 −0.583502 0.812112i \(-0.698318\pi\)
−0.583502 + 0.812112i \(0.698318\pi\)
\(504\) 3.10482e44 0.797870
\(505\) 2.42951e44 0.604242
\(506\) 4.38898e44 1.05653
\(507\) −1.13882e44 −0.265352
\(508\) −1.47950e45 −3.33706
\(509\) −7.37330e44 −1.60997 −0.804986 0.593294i \(-0.797827\pi\)
−0.804986 + 0.593294i \(0.797827\pi\)
\(510\) −6.16108e44 −1.30241
\(511\) −3.33852e44 −0.683296
\(512\) 9.21704e44 1.82657
\(513\) 6.20338e43 0.119040
\(514\) 4.98975e44 0.927229
\(515\) 3.41284e44 0.614181
\(516\) 1.96175e45 3.41919
\(517\) −2.66681e44 −0.450192
\(518\) 2.84242e44 0.464780
\(519\) −7.61920e44 −1.20684
\(520\) −8.00992e44 −1.22906
\(521\) 1.67201e43 0.0248552 0.0124276 0.999923i \(-0.496044\pi\)
0.0124276 + 0.999923i \(0.496044\pi\)
\(522\) −6.99313e44 −1.00718
\(523\) 1.06261e45 1.48284 0.741420 0.671041i \(-0.234153\pi\)
0.741420 + 0.671041i \(0.234153\pi\)
\(524\) −6.13288e44 −0.829275
\(525\) −2.22909e44 −0.292078
\(526\) 9.64595e44 1.22484
\(527\) −1.73211e44 −0.213158
\(528\) −7.84817e44 −0.936071
\(529\) 1.13224e44 0.130894
\(530\) 3.16843e44 0.355052
\(531\) 3.19676e44 0.347257
\(532\) −1.60569e44 −0.169091
\(533\) 4.16759e44 0.425486
\(534\) −5.69223e44 −0.563445
\(535\) −1.42480e44 −0.136746
\(536\) −2.32366e45 −2.16249
\(537\) 3.94367e44 0.355897
\(538\) 1.67432e45 1.46531
\(539\) 3.85240e44 0.326977
\(540\) 1.84822e45 1.52144
\(541\) −1.73107e45 −1.38217 −0.691084 0.722774i \(-0.742867\pi\)
−0.691084 + 0.722774i \(0.742867\pi\)
\(542\) −4.09171e45 −3.16896
\(543\) 1.27894e44 0.0960841
\(544\) 4.27216e45 3.11362
\(545\) −8.92237e44 −0.630867
\(546\) 9.59267e44 0.658053
\(547\) 1.88809e45 1.25670 0.628350 0.777931i \(-0.283731\pi\)
0.628350 + 0.777931i \(0.283731\pi\)
\(548\) 1.85063e45 1.19520
\(549\) 2.68390e43 0.0168199
\(550\) −1.06391e45 −0.647025
\(551\) 2.12115e44 0.125190
\(552\) −3.48986e45 −1.99900
\(553\) −3.06925e44 −0.170635
\(554\) 2.39620e45 1.29304
\(555\) 3.24667e44 0.170061
\(556\) −7.51415e45 −3.82073
\(557\) 1.82254e45 0.899636 0.449818 0.893120i \(-0.351489\pi\)
0.449818 + 0.893120i \(0.351489\pi\)
\(558\) 2.40284e44 0.115149
\(559\) −3.36437e45 −1.56534
\(560\) −1.98789e45 −0.898027
\(561\) 1.46125e45 0.640972
\(562\) 4.96817e45 2.11615
\(563\) 3.54966e45 1.46824 0.734122 0.679018i \(-0.237594\pi\)
0.734122 + 0.679018i \(0.237594\pi\)
\(564\) 3.61544e45 1.45230
\(565\) −2.75028e45 −1.07295
\(566\) 2.58658e45 0.980066
\(567\) −4.71517e44 −0.173531
\(568\) −1.58350e45 −0.566070
\(569\) −3.23817e45 −1.12447 −0.562234 0.826978i \(-0.690058\pi\)
−0.562234 + 0.826978i \(0.690058\pi\)
\(570\) −2.59242e44 −0.0874522
\(571\) 1.75221e45 0.574237 0.287118 0.957895i \(-0.407303\pi\)
0.287118 + 0.957895i \(0.407303\pi\)
\(572\) 3.23909e45 1.03131
\(573\) −3.73039e43 −0.0115399
\(574\) 2.06353e45 0.620247
\(575\) −2.37128e45 −0.692569
\(576\) −1.76268e45 −0.500267
\(577\) −2.22828e45 −0.614566 −0.307283 0.951618i \(-0.599420\pi\)
−0.307283 + 0.951618i \(0.599420\pi\)
\(578\) −1.22060e46 −3.27162
\(579\) 3.56511e44 0.0928702
\(580\) 6.31970e45 1.60005
\(581\) 2.27624e45 0.560159
\(582\) −3.69978e45 −0.885006
\(583\) −7.51473e44 −0.174736
\(584\) 1.26700e46 2.86394
\(585\) −1.03698e45 −0.227877
\(586\) 2.40426e45 0.513654
\(587\) 1.91072e45 0.396889 0.198444 0.980112i \(-0.436411\pi\)
0.198444 + 0.980112i \(0.436411\pi\)
\(588\) −5.22278e45 −1.05481
\(589\) −7.28827e43 −0.0143127
\(590\) −4.08346e45 −0.779777
\(591\) −4.75400e45 −0.882808
\(592\) −5.40689e45 −0.976426
\(593\) 8.87275e45 1.55832 0.779158 0.626827i \(-0.215647\pi\)
0.779158 + 0.626827i \(0.215647\pi\)
\(594\) −6.19606e45 −1.05837
\(595\) 3.70126e45 0.614921
\(596\) 3.60431e45 0.582451
\(597\) 5.61707e45 0.882945
\(598\) 1.02045e46 1.56036
\(599\) −1.96939e45 −0.292947 −0.146474 0.989215i \(-0.546792\pi\)
−0.146474 + 0.989215i \(0.546792\pi\)
\(600\) 8.45959e45 1.22420
\(601\) 6.49113e45 0.913885 0.456942 0.889496i \(-0.348945\pi\)
0.456942 + 0.889496i \(0.348945\pi\)
\(602\) −1.66583e46 −2.28185
\(603\) −3.00827e45 −0.400941
\(604\) −2.81996e46 −3.65707
\(605\) 3.32846e45 0.420029
\(606\) 1.10421e46 1.35598
\(607\) −1.08656e46 −1.29849 −0.649247 0.760577i \(-0.724916\pi\)
−0.649247 + 0.760577i \(0.724916\pi\)
\(608\) 1.79761e45 0.209068
\(609\) −4.43896e45 −0.502454
\(610\) −3.42835e44 −0.0377696
\(611\) −6.20043e45 −0.664877
\(612\) 1.87490e46 1.95695
\(613\) 8.70542e45 0.884488 0.442244 0.896895i \(-0.354182\pi\)
0.442244 + 0.896895i \(0.354182\pi\)
\(614\) 5.00703e45 0.495224
\(615\) 2.35701e45 0.226945
\(616\) 9.40640e45 0.881742
\(617\) −1.12685e46 −1.02840 −0.514199 0.857671i \(-0.671911\pi\)
−0.514199 + 0.857671i \(0.671911\pi\)
\(618\) 1.55113e46 1.37828
\(619\) −1.07685e46 −0.931663 −0.465831 0.884874i \(-0.654245\pi\)
−0.465831 + 0.884874i \(0.654245\pi\)
\(620\) −2.17145e45 −0.182931
\(621\) −1.38099e46 −1.13287
\(622\) 3.85433e46 3.07898
\(623\) 3.41959e45 0.266025
\(624\) −1.82473e46 −1.38246
\(625\) 1.02173e45 0.0753905
\(626\) −2.01923e46 −1.45114
\(627\) 6.14858e44 0.0430388
\(628\) −5.77622e46 −3.93831
\(629\) 1.00671e46 0.668605
\(630\) −5.13450e45 −0.332184
\(631\) 2.47581e46 1.56039 0.780196 0.625535i \(-0.215119\pi\)
0.780196 + 0.625535i \(0.215119\pi\)
\(632\) 1.16481e46 0.715190
\(633\) −2.99206e45 −0.178982
\(634\) 1.54687e46 0.901531
\(635\) 1.43500e46 0.814864
\(636\) 1.01879e46 0.563691
\(637\) 8.95698e45 0.482904
\(638\) −2.11865e46 −1.11306
\(639\) −2.05003e45 −0.104953
\(640\) 3.70407e44 0.0184803
\(641\) −6.66844e45 −0.324240 −0.162120 0.986771i \(-0.551833\pi\)
−0.162120 + 0.986771i \(0.551833\pi\)
\(642\) −6.47567e45 −0.306872
\(643\) −8.88748e42 −0.000410485 0 −0.000205243 1.00000i \(-0.500065\pi\)
−0.000205243 1.00000i \(0.500065\pi\)
\(644\) 3.57459e46 1.60920
\(645\) −1.90274e46 −0.834919
\(646\) −8.03845e45 −0.343824
\(647\) −1.36920e46 −0.570884 −0.285442 0.958396i \(-0.592140\pi\)
−0.285442 + 0.958396i \(0.592140\pi\)
\(648\) 1.78945e46 0.727330
\(649\) 9.68495e45 0.383760
\(650\) −2.47363e46 −0.955575
\(651\) 1.52523e45 0.0574444
\(652\) 5.84545e46 2.14651
\(653\) −1.32140e46 −0.473115 −0.236557 0.971618i \(-0.576019\pi\)
−0.236557 + 0.971618i \(0.576019\pi\)
\(654\) −4.05520e46 −1.41573
\(655\) 5.94840e45 0.202497
\(656\) −3.92527e46 −1.30304
\(657\) 1.64028e46 0.530995
\(658\) −3.07007e46 −0.969215
\(659\) 3.14029e46 0.966852 0.483426 0.875385i \(-0.339392\pi\)
0.483426 + 0.875385i \(0.339392\pi\)
\(660\) 1.83189e46 0.550078
\(661\) −5.62366e46 −1.64701 −0.823503 0.567313i \(-0.807983\pi\)
−0.823503 + 0.567313i \(0.807983\pi\)
\(662\) 4.99331e46 1.42637
\(663\) 3.39747e46 0.946635
\(664\) −8.63851e46 −2.34782
\(665\) 1.55739e45 0.0412896
\(666\) −1.39654e46 −0.361184
\(667\) −4.72211e46 −1.19141
\(668\) 1.40826e47 3.46635
\(669\) 2.48866e46 0.597634
\(670\) 3.84269e46 0.900328
\(671\) 8.13119e44 0.0185880
\(672\) −3.76188e46 −0.839097
\(673\) 1.86687e45 0.0406317 0.0203159 0.999794i \(-0.493533\pi\)
0.0203159 + 0.999794i \(0.493533\pi\)
\(674\) 9.75848e46 2.07250
\(675\) 3.34760e46 0.693779
\(676\) −4.42685e46 −0.895311
\(677\) −3.19535e46 −0.630674 −0.315337 0.948980i \(-0.602118\pi\)
−0.315337 + 0.948980i \(0.602118\pi\)
\(678\) −1.25000e47 −2.40780
\(679\) 2.22264e46 0.417847
\(680\) −1.40466e47 −2.57735
\(681\) −1.39912e46 −0.250570
\(682\) 7.27967e45 0.127253
\(683\) −9.67204e46 −1.65035 −0.825176 0.564876i \(-0.808924\pi\)
−0.825176 + 0.564876i \(0.808924\pi\)
\(684\) 7.88910e45 0.131402
\(685\) −1.79496e46 −0.291851
\(686\) 1.17232e47 1.86080
\(687\) 4.92181e46 0.762673
\(688\) 3.16875e47 4.79379
\(689\) −1.74720e46 −0.258063
\(690\) 5.77124e46 0.832261
\(691\) −4.21417e46 −0.593368 −0.296684 0.954976i \(-0.595881\pi\)
−0.296684 + 0.954976i \(0.595881\pi\)
\(692\) −2.96176e47 −4.07192
\(693\) 1.21777e46 0.163481
\(694\) −8.31128e46 −1.08952
\(695\) 7.28813e46 0.932968
\(696\) 1.68462e47 2.10596
\(697\) 7.30848e46 0.892249
\(698\) −9.22827e46 −1.10029
\(699\) 3.81445e45 0.0444180
\(700\) −8.66499e46 −0.985485
\(701\) 1.07382e47 1.19284 0.596422 0.802671i \(-0.296589\pi\)
0.596422 + 0.802671i \(0.296589\pi\)
\(702\) −1.44061e47 −1.56309
\(703\) 4.23598e45 0.0448943
\(704\) −5.34024e46 −0.552856
\(705\) −3.50669e46 −0.354631
\(706\) 1.67517e47 1.65494
\(707\) −6.63351e46 −0.640211
\(708\) −1.31301e47 −1.23799
\(709\) 9.99645e46 0.920837 0.460419 0.887702i \(-0.347699\pi\)
0.460419 + 0.887702i \(0.347699\pi\)
\(710\) 2.61866e46 0.235677
\(711\) 1.50798e46 0.132602
\(712\) −1.29776e47 −1.11500
\(713\) 1.62251e46 0.136211
\(714\) 1.68222e47 1.37994
\(715\) −3.14166e46 −0.251831
\(716\) 1.53299e47 1.20081
\(717\) −9.78940e46 −0.749359
\(718\) −2.02449e47 −1.51448
\(719\) −7.93598e46 −0.580195 −0.290097 0.956997i \(-0.593688\pi\)
−0.290097 + 0.956997i \(0.593688\pi\)
\(720\) 9.76690e46 0.697863
\(721\) −9.31838e46 −0.650741
\(722\) 2.67498e47 1.82581
\(723\) −1.63165e47 −1.08854
\(724\) 4.97151e46 0.324192
\(725\) 1.14466e47 0.729626
\(726\) 1.51278e47 0.942587
\(727\) 1.33485e47 0.813046 0.406523 0.913641i \(-0.366741\pi\)
0.406523 + 0.913641i \(0.366741\pi\)
\(728\) 2.18702e47 1.30222
\(729\) 1.54343e47 0.898427
\(730\) −2.09526e47 −1.19237
\(731\) −5.89992e47 −3.28254
\(732\) −1.10236e46 −0.0599641
\(733\) 8.41792e46 0.447702 0.223851 0.974623i \(-0.428137\pi\)
0.223851 + 0.974623i \(0.428137\pi\)
\(734\) −1.22843e47 −0.638802
\(735\) 5.06568e46 0.257571
\(736\) −4.00184e47 −1.98965
\(737\) −9.11389e46 −0.443088
\(738\) −1.01385e47 −0.481998
\(739\) 2.39720e47 1.11448 0.557239 0.830352i \(-0.311861\pi\)
0.557239 + 0.830352i \(0.311861\pi\)
\(740\) 1.26206e47 0.573793
\(741\) 1.42957e46 0.0635630
\(742\) −8.65106e46 −0.376188
\(743\) 4.51636e47 1.92076 0.960380 0.278695i \(-0.0899020\pi\)
0.960380 + 0.278695i \(0.0899020\pi\)
\(744\) −5.78836e46 −0.240770
\(745\) −3.49589e46 −0.142226
\(746\) 1.16643e47 0.464160
\(747\) −1.11836e47 −0.435304
\(748\) 5.68023e47 2.16267
\(749\) 3.89025e46 0.144886
\(750\) −3.54710e47 −1.29230
\(751\) −2.31769e46 −0.0826030 −0.0413015 0.999147i \(-0.513150\pi\)
−0.0413015 + 0.999147i \(0.513150\pi\)
\(752\) 5.83991e47 2.03616
\(753\) 1.62147e47 0.553085
\(754\) −4.92594e47 −1.64385
\(755\) 2.73514e47 0.893006
\(756\) −5.04635e47 −1.61201
\(757\) −6.14297e46 −0.191998 −0.0959989 0.995381i \(-0.530605\pi\)
−0.0959989 + 0.995381i \(0.530605\pi\)
\(758\) −8.81131e47 −2.69463
\(759\) −1.36880e47 −0.409590
\(760\) −5.91044e46 −0.173059
\(761\) −4.18126e47 −1.19801 −0.599004 0.800746i \(-0.704437\pi\)
−0.599004 + 0.800746i \(0.704437\pi\)
\(762\) 6.52205e47 1.82863
\(763\) 2.43616e47 0.668421
\(764\) −1.45009e46 −0.0389362
\(765\) −1.81850e47 −0.477860
\(766\) 1.16952e48 3.00769
\(767\) 2.25179e47 0.566766
\(768\) −2.82528e47 −0.695987
\(769\) −2.07493e47 −0.500286 −0.250143 0.968209i \(-0.580478\pi\)
−0.250143 + 0.968209i \(0.580478\pi\)
\(770\) −1.55555e47 −0.367103
\(771\) −1.55616e47 −0.359464
\(772\) 1.38584e47 0.313348
\(773\) −3.82656e47 −0.846930 −0.423465 0.905912i \(-0.639186\pi\)
−0.423465 + 0.905912i \(0.639186\pi\)
\(774\) 8.18455e47 1.77324
\(775\) −3.93306e46 −0.0834165
\(776\) −8.43509e47 −1.75134
\(777\) −8.86469e46 −0.180184
\(778\) −5.20250e47 −1.03526
\(779\) 3.07522e46 0.0599112
\(780\) 4.25921e47 0.812397
\(781\) −6.21081e46 −0.115986
\(782\) 1.78952e48 3.27209
\(783\) 6.66634e47 1.19349
\(784\) −8.43619e47 −1.47887
\(785\) 5.60247e47 0.961679
\(786\) 2.70354e47 0.454423
\(787\) −6.26036e47 −1.03043 −0.515213 0.857062i \(-0.672287\pi\)
−0.515213 + 0.857062i \(0.672287\pi\)
\(788\) −1.84799e48 −2.97863
\(789\) −3.00829e47 −0.474842
\(790\) −1.92626e47 −0.297761
\(791\) 7.50935e47 1.13682
\(792\) −4.62156e47 −0.685208
\(793\) 1.89053e46 0.0274521
\(794\) −1.46471e48 −2.08312
\(795\) −9.88141e46 −0.137645
\(796\) 2.18348e48 2.97910
\(797\) 1.56391e47 0.209002 0.104501 0.994525i \(-0.466675\pi\)
0.104501 + 0.994525i \(0.466675\pi\)
\(798\) 7.07833e46 0.0926580
\(799\) −1.08734e48 −1.39425
\(800\) 9.70066e47 1.21847
\(801\) −1.68012e47 −0.206730
\(802\) −7.96201e47 −0.959722
\(803\) 4.96943e47 0.586813
\(804\) 1.23559e48 1.42938
\(805\) −3.46706e47 −0.392943
\(806\) 1.69255e47 0.187937
\(807\) −5.22171e47 −0.568067
\(808\) 2.51747e48 2.68335
\(809\) 4.01144e47 0.418938 0.209469 0.977815i \(-0.432826\pi\)
0.209469 + 0.977815i \(0.432826\pi\)
\(810\) −2.95925e47 −0.302816
\(811\) 2.34209e47 0.234833 0.117417 0.993083i \(-0.462539\pi\)
0.117417 + 0.993083i \(0.462539\pi\)
\(812\) −1.72553e48 −1.69530
\(813\) 1.27608e48 1.22853
\(814\) −4.23098e47 −0.399152
\(815\) −5.66962e47 −0.524147
\(816\) −3.19993e48 −2.89903
\(817\) −2.48253e47 −0.220410
\(818\) −2.97269e48 −2.58655
\(819\) 2.83137e47 0.241442
\(820\) 9.16221e47 0.765723
\(821\) 4.03504e47 0.330510 0.165255 0.986251i \(-0.447155\pi\)
0.165255 + 0.986251i \(0.447155\pi\)
\(822\) −8.15807e47 −0.654942
\(823\) 1.82505e48 1.43608 0.718039 0.696002i \(-0.245040\pi\)
0.718039 + 0.696002i \(0.245040\pi\)
\(824\) 3.53640e48 2.72749
\(825\) 3.31803e47 0.250836
\(826\) 1.11494e48 0.826195
\(827\) 7.52706e47 0.546744 0.273372 0.961908i \(-0.411861\pi\)
0.273372 + 0.961908i \(0.411861\pi\)
\(828\) −1.75627e48 −1.25052
\(829\) −2.19354e48 −1.53107 −0.765537 0.643392i \(-0.777526\pi\)
−0.765537 + 0.643392i \(0.777526\pi\)
\(830\) 1.42857e48 0.977489
\(831\) −7.47306e47 −0.501281
\(832\) −1.24162e48 −0.816499
\(833\) 1.57074e48 1.01265
\(834\) 3.31244e48 2.09367
\(835\) −1.36590e48 −0.846433
\(836\) 2.39009e47 0.145215
\(837\) −2.29055e47 −0.136449
\(838\) −2.73408e48 −1.59693
\(839\) −2.86394e48 −1.64018 −0.820091 0.572233i \(-0.806077\pi\)
−0.820091 + 0.572233i \(0.806077\pi\)
\(840\) 1.23688e48 0.694578
\(841\) 4.63381e47 0.255155
\(842\) 3.54978e48 1.91669
\(843\) −1.54943e48 −0.820382
\(844\) −1.16308e48 −0.603892
\(845\) 4.29368e47 0.218622
\(846\) 1.50839e48 0.753185
\(847\) −9.08800e47 −0.445033
\(848\) 1.64561e48 0.790308
\(849\) −8.06680e47 −0.379948
\(850\) −4.33788e48 −2.00385
\(851\) −9.43013e47 −0.427248
\(852\) 8.42012e47 0.374166
\(853\) 4.28657e48 1.86832 0.934158 0.356859i \(-0.116152\pi\)
0.934158 + 0.356859i \(0.116152\pi\)
\(854\) 9.36073e46 0.0400180
\(855\) −7.65179e46 −0.0320865
\(856\) −1.47638e48 −0.607270
\(857\) −8.64522e47 −0.348813 −0.174406 0.984674i \(-0.555801\pi\)
−0.174406 + 0.984674i \(0.555801\pi\)
\(858\) −1.42788e48 −0.565134
\(859\) 2.35883e48 0.915817 0.457909 0.888999i \(-0.348599\pi\)
0.457909 + 0.888999i \(0.348599\pi\)
\(860\) −7.39639e48 −2.81705
\(861\) −6.43555e47 −0.240455
\(862\) 3.68860e48 1.35205
\(863\) −6.27316e46 −0.0225584 −0.0112792 0.999936i \(-0.503590\pi\)
−0.0112792 + 0.999936i \(0.503590\pi\)
\(864\) 5.64951e48 1.99312
\(865\) 2.87267e48 0.994304
\(866\) 4.49666e48 1.52702
\(867\) 3.80669e48 1.26833
\(868\) 5.92890e47 0.193820
\(869\) 4.56861e47 0.146541
\(870\) −2.78590e48 −0.876793
\(871\) −2.11901e48 −0.654386
\(872\) −9.24541e48 −2.80159
\(873\) −1.09203e48 −0.324712
\(874\) 7.52982e47 0.219708
\(875\) 2.13092e48 0.610145
\(876\) −6.73715e48 −1.89303
\(877\) −2.00783e48 −0.553647 −0.276823 0.960921i \(-0.589282\pi\)
−0.276823 + 0.960921i \(0.589282\pi\)
\(878\) −2.57194e48 −0.695988
\(879\) −7.49818e47 −0.199131
\(880\) 2.95899e48 0.771223
\(881\) −4.20296e48 −1.07511 −0.537555 0.843229i \(-0.680652\pi\)
−0.537555 + 0.843229i \(0.680652\pi\)
\(882\) −2.17898e48 −0.547042
\(883\) 7.94997e48 1.95891 0.979453 0.201672i \(-0.0646376\pi\)
0.979453 + 0.201672i \(0.0646376\pi\)
\(884\) 1.32067e49 3.19399
\(885\) 1.27351e48 0.302301
\(886\) −1.77675e48 −0.413971
\(887\) −7.43922e48 −1.70133 −0.850664 0.525710i \(-0.823800\pi\)
−0.850664 + 0.525710i \(0.823800\pi\)
\(888\) 3.36422e48 0.755216
\(889\) −3.91811e48 −0.863371
\(890\) 2.14614e48 0.464219
\(891\) 7.01859e47 0.149028
\(892\) 9.67400e48 2.01644
\(893\) −4.57523e47 −0.0936189
\(894\) −1.58888e48 −0.319170
\(895\) −1.48688e48 −0.293222
\(896\) −1.01136e47 −0.0195804
\(897\) −3.18250e48 −0.604913
\(898\) 5.22659e47 0.0975345
\(899\) −7.83220e47 −0.143499
\(900\) 4.25728e48 0.765828
\(901\) −3.06398e48 −0.541161
\(902\) −3.07159e48 −0.532666
\(903\) 5.19523e48 0.884620
\(904\) −2.84986e49 −4.76480
\(905\) −4.82197e47 −0.0791631
\(906\) 1.24311e49 2.00399
\(907\) 8.96944e48 1.41986 0.709929 0.704273i \(-0.248727\pi\)
0.709929 + 0.704273i \(0.248727\pi\)
\(908\) −5.43871e48 −0.845433
\(909\) 3.25918e48 0.497513
\(910\) −3.61672e48 −0.542166
\(911\) 2.25421e48 0.331850 0.165925 0.986138i \(-0.446939\pi\)
0.165925 + 0.986138i \(0.446939\pi\)
\(912\) −1.34645e48 −0.194659
\(913\) −3.38820e48 −0.481063
\(914\) 1.39679e49 1.94769
\(915\) 1.06920e47 0.0146424
\(916\) 1.91322e49 2.57329
\(917\) −1.62415e48 −0.214551
\(918\) −2.52632e49 −3.27781
\(919\) −7.04277e48 −0.897507 −0.448754 0.893656i \(-0.648132\pi\)
−0.448754 + 0.893656i \(0.648132\pi\)
\(920\) 1.31578e49 1.64696
\(921\) −1.56155e48 −0.191987
\(922\) −1.62673e49 −1.96452
\(923\) −1.44404e48 −0.171297
\(924\) −5.00178e48 −0.582823
\(925\) 2.28591e48 0.261650
\(926\) 1.17335e49 1.31931
\(927\) 4.57831e48 0.505696
\(928\) 1.93177e49 2.09611
\(929\) 1.56732e49 1.67070 0.835348 0.549721i \(-0.185266\pi\)
0.835348 + 0.549721i \(0.185266\pi\)
\(930\) 9.57233e47 0.100242
\(931\) 6.60926e47 0.0679959
\(932\) 1.48276e48 0.149868
\(933\) −1.20205e49 −1.19365
\(934\) −1.95123e49 −1.90364
\(935\) −5.50937e48 −0.528093
\(936\) −1.07453e49 −1.01197
\(937\) 4.17295e48 0.386136 0.193068 0.981185i \(-0.438156\pi\)
0.193068 + 0.981185i \(0.438156\pi\)
\(938\) −1.04920e49 −0.953922
\(939\) 6.29740e48 0.562573
\(940\) −1.36313e49 −1.19654
\(941\) −5.21719e48 −0.449995 −0.224998 0.974359i \(-0.572237\pi\)
−0.224998 + 0.974359i \(0.572237\pi\)
\(942\) 2.54631e49 2.15810
\(943\) −6.84604e48 −0.570160
\(944\) −2.12086e49 −1.73570
\(945\) 4.89456e48 0.393630
\(946\) 2.47960e49 1.95965
\(947\) −1.05918e49 −0.822616 −0.411308 0.911496i \(-0.634928\pi\)
−0.411308 + 0.911496i \(0.634928\pi\)
\(948\) −6.19376e48 −0.472734
\(949\) 1.15541e49 0.866650
\(950\) −1.82527e48 −0.134551
\(951\) −4.82423e48 −0.349502
\(952\) 3.83527e49 2.73078
\(953\) 1.49599e49 1.04688 0.523438 0.852064i \(-0.324649\pi\)
0.523438 + 0.852064i \(0.324649\pi\)
\(954\) 4.25044e48 0.292338
\(955\) 1.40647e47 0.00950767
\(956\) −3.80536e49 −2.52837
\(957\) 6.60745e48 0.431506
\(958\) 4.17619e49 2.68071
\(959\) 4.90095e48 0.309224
\(960\) −7.02209e48 −0.435503
\(961\) −1.61344e49 −0.983594
\(962\) −9.83718e48 −0.589498
\(963\) −1.91136e48 −0.112592
\(964\) −6.34261e49 −3.67280
\(965\) −1.34415e48 −0.0765152
\(966\) −1.57578e49 −0.881803
\(967\) −2.39619e49 −1.31821 −0.659106 0.752050i \(-0.729065\pi\)
−0.659106 + 0.752050i \(0.729065\pi\)
\(968\) 3.44897e49 1.86529
\(969\) 2.50696e48 0.133292
\(970\) 1.39493e49 0.729151
\(971\) −1.35152e47 −0.00694552 −0.00347276 0.999994i \(-0.501105\pi\)
−0.00347276 + 0.999994i \(0.501105\pi\)
\(972\) 4.14760e49 2.09558
\(973\) −1.98994e49 −0.988505
\(974\) 2.66999e49 1.30403
\(975\) 7.71454e48 0.370454
\(976\) −1.78061e48 −0.0840711
\(977\) 1.84460e48 0.0856333 0.0428166 0.999083i \(-0.486367\pi\)
0.0428166 + 0.999083i \(0.486367\pi\)
\(978\) −2.57683e49 −1.17624
\(979\) −5.09011e48 −0.228461
\(980\) 1.96914e49 0.869055
\(981\) −1.19693e49 −0.519435
\(982\) 4.53233e48 0.193411
\(983\) −6.69809e48 −0.281072 −0.140536 0.990076i \(-0.544883\pi\)
−0.140536 + 0.990076i \(0.544883\pi\)
\(984\) 2.44234e49 1.00783
\(985\) 1.79240e49 0.727340
\(986\) −8.63836e49 −3.44717
\(987\) 9.57464e48 0.375742
\(988\) 5.55705e48 0.214464
\(989\) 5.52661e49 2.09759
\(990\) 7.64276e48 0.285279
\(991\) 1.17168e49 0.430123 0.215062 0.976600i \(-0.431005\pi\)
0.215062 + 0.976600i \(0.431005\pi\)
\(992\) −6.63755e48 −0.239643
\(993\) −1.55727e49 −0.552969
\(994\) −7.14997e48 −0.249706
\(995\) −2.11780e49 −0.727453
\(996\) 4.59345e49 1.55189
\(997\) 2.44007e49 0.810834 0.405417 0.914132i \(-0.367126\pi\)
0.405417 + 0.914132i \(0.367126\pi\)
\(998\) −5.68168e49 −1.85705
\(999\) 1.33128e49 0.427995
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 1.34.a.a.1.1 2
3.2 odd 2 9.34.a.b.1.2 2
4.3 odd 2 16.34.a.b.1.1 2
5.2 odd 4 25.34.b.a.24.1 4
5.3 odd 4 25.34.b.a.24.4 4
5.4 even 2 25.34.a.a.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.34.a.a.1.1 2 1.1 even 1 trivial
9.34.a.b.1.2 2 3.2 odd 2
16.34.a.b.1.1 2 4.3 odd 2
25.34.a.a.1.2 2 5.4 even 2
25.34.b.a.24.1 4 5.2 odd 4
25.34.b.a.24.4 4 5.3 odd 4